LMFDB - Embedded newform 22.12.c.a.3.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [22,12,Mod(3,22)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(22, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8]))

N = Newforms(chi, 12, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("22.3");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 22 = 2 \cdot 11 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	22.c (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$16.9035499723$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} + 339028 x^{18} - 38195378 x^{17} + 220926638311 x^{16} - 35915431412664 x^{15} + \cdots + 11\!\cdots\!00 $ x^20 - 4x^19 + 339028x^18 - 38195378x^17 + 220926638311x^16 - 35915431412664x^15 + 115759899998314350x^14 - 27226928185171403384x^13 + 41831014975562739810959x^12 - 3879797201571793549516048x^11 + 3316840467475291520075063190x^10 + 1067427514312498593848752050628x^9 + 750967910898548932251904101148531x^8 + 228128795234897755949671367783663114x^7 + 90326787979451743483651549716111634592x^6 + 21775725237124771428874092537573760059528x^5 + 5115171268695044278298633768429412143699481x^4 + 644893842489460735970879339730837145914702280x^3 + 40307167403308519805773510178453296556136973760x^2 - 118703222270772703791843925527006368174467110400*x + 1158220182319374358886221767374591631314546790400
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{24}\cdot 3^{4}\cdot 5\cdot 11^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			3.4
Root			$-76.6553 + 235.921i$ of defining polynomial
Character	$\chi$	$=$	22.3
Dual form			22.12.c.a.15.4

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-25.8885 + 18.8091i) q^{2} +(80.7733 + 248.595i) q^{3} +(316.433 - 973.882i) q^{4} +(7368.51 + 5353.53i) q^{5} +(-6766.95 - 4916.48i) q^{6} +(11301.1 - 34781.1i) q^{7} +(10125.9 + 31164.2i) q^{8} +(88039.9 - 63964.8i) q^{9} +O(q^{10})$	\(q+(-25.8885 + 18.8091i) q^{2} +(80.7733 + 248.595i) q^{3} +(316.433 - 973.882i) q^{4} +(7368.51 + 5353.53i) q^{5} +(-6766.95 - 4916.48i) q^{6} +(11301.1 - 34781.1i) q^{7} +(10125.9 + 31164.2i) q^{8} +(88039.9 - 63964.8i) q^{9} -291455. q^{10} +(-199698. - 495411. i) q^{11} +267661. q^{12} +(1.44566e6 - 1.05034e6i) q^{13} +(361635. + 1.11300e6i) q^{14} +(-735681. + 2.26419e6i) q^{15} +(-848316. - 616338. i) q^{16} +(-2.38666e6 - 1.73401e6i) q^{17} +(-1.07610e6 + 3.31191e6i) q^{18} +(4.96973e6 + 1.52953e7i) q^{19} +(7.54535e6 - 5.48202e6i) q^{20} +9.55923e6 q^{21} +(1.44881e7 + 9.06934e6i) q^{22} +5.59717e7 q^{23} +(-6.92936e6 + 5.03447e6i) q^{24} +(1.05458e7 + 3.24568e7i) q^{25} +(-1.76702e7 + 5.43833e7i) q^{26} +(6.04734e7 + 4.39365e7i) q^{27} +(-3.02967e7 - 2.20118e7i) q^{28} +(-1.03427e6 + 3.18315e6i) q^{29} +(-2.35418e7 - 7.24542e7i) q^{30} +(-1.47297e8 + 1.07018e8i) q^{31} +3.35544e7 q^{32} +(1.07026e8 - 8.96598e7i) q^{33} +9.44022e7 q^{34} +(2.69474e8 - 1.95784e8i) q^{35} +(-3.44353e7 - 1.05981e8i) q^{36} +(-6.08802e7 + 1.87370e8i) q^{37} +(-4.16350e8 - 3.02496e8i) q^{38} +(3.77879e8 + 2.74545e8i) q^{39} +(-9.22261e7 + 2.83843e8i) q^{40} +(-4.51796e8 - 1.39049e9i) q^{41} +(-2.47475e8 + 1.79801e8i) q^{42} -8.77136e8 q^{43} +(-5.45663e8 + 3.77171e7i) q^{44} +9.91160e8 q^{45} +(-1.44903e9 + 1.05278e9i) q^{46} +(3.14560e8 + 9.68117e8i) q^{47} +(8.46970e7 - 2.60670e8i) q^{48} +(5.17677e8 + 3.76114e8i) q^{49} +(-8.83500e8 - 6.41900e8i) q^{50} +(2.38287e8 - 7.33372e8i) q^{51} +(-5.65447e8 - 1.74027e9i) q^{52} +(1.78825e9 - 1.29924e9i) q^{53} -2.39197e9 q^{54} +(1.18073e9 - 4.71953e9i) q^{55} +1.19836e9 q^{56} +(-3.40090e9 + 2.47090e9i) q^{57} +(-3.30966e7 - 1.01861e8i) q^{58} +(-1.95231e9 + 6.00859e9i) q^{59} +(1.97226e9 + 1.43293e9i) q^{60} +(5.82978e9 + 4.23559e9i) q^{61} +(1.80040e9 - 5.54106e9i) q^{62} +(-1.22982e9 - 3.78500e9i) q^{63} +(-8.68675e8 + 6.31130e8i) q^{64} +1.62754e10 q^{65} +(-1.08434e9 + 4.33424e9i) q^{66} +4.22878e9 q^{67} +(-2.44394e9 + 1.77562e9i) q^{68} +(4.52102e9 + 1.39143e10i) q^{69} +(-3.29376e9 + 1.01371e10i) q^{70} +(-4.17052e9 - 3.03006e9i) q^{71} +(2.88489e9 + 2.09600e9i) q^{72} +(-1.87074e9 + 5.75756e9i) q^{73} +(-1.94817e9 - 5.99584e9i) q^{74} +(-7.21676e9 + 5.24328e9i) q^{75} +1.64684e10 q^{76} +(-1.94878e10 + 1.34703e9i) q^{77} -1.49467e10 q^{78} +(2.20221e10 - 1.60000e10i) q^{79} +(-2.95124e9 - 9.08297e9i) q^{80} +(-8.05953e7 + 2.48047e8i) q^{81} +(3.78502e10 + 2.74997e10i) q^{82} +(-3.40017e10 - 2.47037e10i) q^{83} +(3.02486e9 - 9.30957e9i) q^{84} +(-8.30302e9 - 2.55541e10i) q^{85} +(2.27078e10 - 1.64982e10i) q^{86} -8.74856e8 q^{87} +(1.34170e10 - 1.12399e10i) q^{88} -9.05901e10 q^{89} +(-2.56597e10 + 1.86429e10i) q^{90} +(-2.01943e10 - 6.21517e10i) q^{91} +(1.77113e10 - 5.45098e10i) q^{92} +(-3.85017e10 - 2.79731e10i) q^{93} +(-2.63530e10 - 1.91465e10i) q^{94} +(-4.52642e10 + 1.39309e11i) q^{95} +(2.71030e9 + 8.34145e9i) q^{96} +(2.51295e10 - 1.82577e10i) q^{97} -2.04763e10 q^{98} +(-4.92702e10 - 3.08424e10i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 160 q^{2} + 56 q^{3} - 5120 q^{4} - 362 q^{5} - 3488 q^{6} - 167178 q^{7} - 163840 q^{8} + 206411 q^{9}+O(q^{10}) $ 20 * q - 160 * q^2 + 56 * q^3 - 5120 * q^4 - 362 * q^5 - 3488 * q^6 - 167178 * q^7 - 163840 * q^8 + 206411 * q^9	\( 20 q - 160 q^{2} + 56 q^{3} - 5120 q^{4} - 362 q^{5} - 3488 q^{6} - 167178 q^{7} - 163840 q^{8} + 206411 q^{9} - 354944 q^{10} - 449801 q^{11} + 108544 q^{12} + 3369596 q^{13} - 5349696 q^{14} + 12264628 q^{15} - 5242880 q^{16} + 1661262 q^{17} - 19177088 q^{18} + 49176291 q^{19} - 370688 q^{20} - 74218796 q^{21} - 5153632 q^{22} - 127653292 q^{23} - 3571712 q^{24} + 33758041 q^{25} - 99025728 q^{26} - 135657199 q^{27} + 156930048 q^{28} + 555960754 q^{29} + 392468096 q^{30} - 13977916 q^{31} + 671088640 q^{32} - 1768265081 q^{33} - 357119936 q^{34} + 584997860 q^{35} - 613666816 q^{36} - 161000626 q^{37} - 1456805888 q^{38} + 1145816470 q^{39} + 193593344 q^{40} + 772614122 q^{41} - 545038272 q^{42} + 3749722062 q^{43} - 50755584 q^{44} - 1321716548 q^{45} - 1394938624 q^{46} + 1924889212 q^{47} + 58720256 q^{48} + 822161735 q^{49} - 805012448 q^{50} + 5262939047 q^{51} - 3168823296 q^{52} + 1531782992 q^{53} + 295824512 q^{54} + 3851857218 q^{55} + 912654336 q^{56} - 17257259731 q^{57} + 17790744128 q^{58} - 16014164779 q^{59} - 3503935488 q^{60} + 7822116636 q^{61} + 6939975808 q^{62} - 79975953122 q^{63} - 5368709120 q^{64} + 73754374272 q^{65} - 3094015232 q^{66} - 22092583538 q^{67} + 1701132288 q^{68} + 43044165458 q^{69} - 5227997760 q^{70} + 23107180542 q^{71} + 6763675648 q^{72} + 55731754682 q^{73} - 5152020032 q^{74} - 37848703409 q^{75} - 7477467136 q^{76} - 52140560296 q^{77} - 110695592320 q^{78} + 43369591752 q^{79} + 6194987008 q^{80} - 19607689666 q^{81} + 6103740704 q^{82} + 105219370951 q^{83} + 55441248256 q^{84} - 14375063614 q^{85} - 53785859936 q^{86} - 216242949124 q^{87} + 14186872832 q^{88} - 227930374154 q^{89} + 138289668864 q^{90} + 236440118278 q^{91} + 109996521472 q^{92} + 215529449050 q^{93} + 24423998144 q^{94} + 242007717988 q^{95} + 1879048192 q^{96} - 200605898215 q^{97} + 128896464000 q^{98} - 634415317547 q^{99}+O(q^{100}) \) 20 * q - 160 * q^2 + 56 * q^3 - 5120 * q^4 - 362 * q^5 - 3488 * q^6 - 167178 * q^7 - 163840 * q^8 + 206411 * q^9 - 354944 * q^10 - 449801 * q^11 + 108544 * q^12 + 3369596 * q^13 - 5349696 * q^14 + 12264628 * q^15 - 5242880 * q^16 + 1661262 * q^17 - 19177088 * q^18 + 49176291 * q^19 - 370688 * q^20 - 74218796 * q^21 - 5153632 * q^22 - 127653292 * q^23 - 3571712 * q^24 + 33758041 * q^25 - 99025728 * q^26 - 135657199 * q^27 + 156930048 * q^28 + 555960754 * q^29 + 392468096 * q^30 - 13977916 * q^31 + 671088640 * q^32 - 1768265081 * q^33 - 357119936 * q^34 + 584997860 * q^35 - 613666816 * q^36 - 161000626 * q^37 - 1456805888 * q^38 + 1145816470 * q^39 + 193593344 * q^40 + 772614122 * q^41 - 545038272 * q^42 + 3749722062 * q^43 - 50755584 * q^44 - 1321716548 * q^45 - 1394938624 * q^46 + 1924889212 * q^47 + 58720256 * q^48 + 822161735 * q^49 - 805012448 * q^50 + 5262939047 * q^51 - 3168823296 * q^52 + 1531782992 * q^53 + 295824512 * q^54 + 3851857218 * q^55 + 912654336 * q^56 - 17257259731 * q^57 + 17790744128 * q^58 - 16014164779 * q^59 - 3503935488 * q^60 + 7822116636 * q^61 + 6939975808 * q^62 - 79975953122 * q^63 - 5368709120 * q^64 + 73754374272 * q^65 - 3094015232 * q^66 - 22092583538 * q^67 + 1701132288 * q^68 + 43044165458 * q^69 - 5227997760 * q^70 + 23107180542 * q^71 + 6763675648 * q^72 + 55731754682 * q^73 - 5152020032 * q^74 - 37848703409 * q^75 - 7477467136 * q^76 - 52140560296 * q^77 - 110695592320 * q^78 + 43369591752 * q^79 + 6194987008 * q^80 - 19607689666 * q^81 + 6103740704 * q^82 + 105219370951 * q^83 + 55441248256 * q^84 - 14375063614 * q^85 - 53785859936 * q^86 - 216242949124 * q^87 + 14186872832 * q^88 - 227930374154 * q^89 + 138289668864 * q^90 + 236440118278 * q^91 + 109996521472 * q^92 + 215529449050 * q^93 + 24423998144 * q^94 + 242007717988 * q^95 + 1879048192 * q^96 - 200605898215 * q^97 + 128896464000 * q^98 - 634415317547 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/22\mathbb{Z}\right)^\times$.

$n$	$13$
$\chi(n)$	$e\left(\frac{4}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−25.8885	+	18.8091i	−0.572061	+	0.415627i
$2$	−25.8885	+	18.8091i	−0.572061	+	0.415627i
$3$	80.7733	+	248.595i	0.191912	+	0.590643i	0.999999	+	0.00158007i	$0.000502953\pi$
$3$	80.7733	+	248.595i	0.191912	+	0.590643i	−0.808087	+	0.589063i	$0.799497\pi$
$4$	316.433	−	973.882i	0.154508	−	0.475528i
$5$	7368.51	+	5353.53i	1.05449	+	0.766135i	0.973062	−	0.230544i	$-0.0740505\pi$
$5$	7368.51	+	5353.53i	1.05449	+	0.766135i	0.0814326	+	0.996679i	$0.474050\pi$
$6$	−6766.95	−	4916.48i	−0.355272	−	0.258120i
$7$	11301.1	−	34781.1i	0.254144	−	0.782176i	−0.739853	−	0.672769i	$-0.765105\pi$
$7$	11301.1	−	34781.1i	0.254144	−	0.782176i	0.993997	−	0.109407i	$-0.0348953\pi$
$8$	10125.9	+	31164.2i	0.109254	+	0.336249i
$9$	88039.9	−	63964.8i	0.496988	−	0.361083i
$10$	−291455.			−0.921662
$11$	−199698.	−	495411.i	−0.373863	−	0.927484i
$11$	−199698.	−	495411.i	−0.373863	−	0.927484i
$12$	267661.			0.310519
$13$	1.44566e6	−	1.05034e6i	1.07989	−	0.784584i	0.102224	−	0.994761i	$-0.467404\pi$
$13$	1.44566e6	−	1.05034e6i	1.07989	−	0.784584i	0.977663	+	0.210177i	$0.0674041\pi$
$14$	361635.	+	1.11300e6i	0.179707	+	0.553082i
$15$	−735681.	+	2.26419e6i	−0.250143	+	0.769860i
$16$	−848316.	−	616338.i	−0.202254	−	0.146946i
$17$	−2.38666e6	−	1.73401e6i	−0.407681	−	0.296198i	0.364981	−	0.931015i	$-0.381075\pi$
$17$	−2.38666e6	−	1.73401e6i	−0.407681	−	0.296198i	−0.772662	+	0.634817i	$0.781075\pi$
$18$	−1.07610e6	+	3.31191e6i	−0.134232	+	0.413123i
$19$	4.96973e6	+	1.52953e7i	0.460456	+	1.41714i	0.864608	+	0.502446i	$0.167567\pi$
$19$	4.96973e6	+	1.52953e7i	0.460456	+	1.41714i	−0.404152	+	0.914692i	$0.632433\pi$
$20$	7.54535e6	−	5.48202e6i	0.527247	−	0.383068i
$21$	9.55923e6			0.510760
$22$	1.44881e7	+	9.06934e6i	0.599360	+	0.375190i
$23$	5.59717e7			1.81328			0.906641	−	0.421902i	$-0.138637\pi$
$23$	5.59717e7			1.81328			0.906641	+	0.421902i	$0.138637\pi$
$24$	−6.92936e6	+	5.03447e6i	−0.177636	+	0.129060i
$25$	1.05458e7	+	3.24568e7i	0.215979	+	0.664714i
$26$	−1.76702e7	+	5.43833e7i	−0.291668	+	0.897661i
$27$	6.04734e7	+	4.39365e7i	0.811080	+	0.589284i
$28$	−3.02967e7	−	2.20118e7i	−0.332679	−	0.241706i
$29$	−1.03427e6	+	3.18315e6i	−0.00936363	+	0.0288183i	−0.955629	−	0.294572i	$-0.904823\pi$
$29$	−1.03427e6	+	3.18315e6i	−0.00936363	+	0.0288183i	0.946266	+	0.323391i	$0.104823\pi$
$30$	−2.35418e7	−	7.24542e7i	−0.176878	−	0.544373i
$31$	−1.47297e8	+	1.07018e8i	−0.924071	+	0.671377i	−0.944534	−	0.328414i	$-0.893486\pi$
$31$	−1.47297e8	+	1.07018e8i	−0.924071	+	0.671377i	0.0204632	+	0.999791i	$0.493486\pi$
$32$	3.35544e7			0.176777
$33$	1.07026e8	−	8.96598e7i	0.476063	−	0.398815i
$34$	9.44022e7			0.356327
$35$	2.69474e8	−	1.95784e8i	0.867247	−	0.630092i
$36$	−3.44353e7	−	1.05981e8i	−0.0949163	−	0.292122i
$37$	−6.08802e7	+	1.87370e8i	−0.144333	+	0.444212i	−0.996925	−	0.0783661i	$-0.975030\pi$
$37$	−6.08802e7	+	1.87370e8i	−0.144333	+	0.444212i	0.852591	+	0.522578i	$0.175030\pi$
$38$	−4.16350e8	−	3.02496e8i	−0.852410	−	0.619312i
$39$	3.77879e8	+	2.74545e8i	0.670652	+	0.487257i
$40$	−9.22261e7	+	2.83843e8i	−0.142405	+	0.438276i
$41$	−4.51796e8	−	1.39049e9i	−0.609020	−	1.87437i	−0.466353	−	0.884599i	$-0.654432\pi$
$41$	−4.51796e8	−	1.39049e9i	−0.609020	−	1.87437i	−0.142666	−	0.989771i	$-0.545568\pi$
$42$	−2.47475e8	+	1.79801e8i	−0.292186	+	0.212286i
$43$	−8.77136e8			−0.909893			−0.454947	−	0.890519i	$-0.650342\pi$
$43$	−8.77136e8			−0.909893			−0.454947	+	0.890519i	$0.650342\pi$
$44$	−5.45663e8	+	3.77171e7i	−0.498810	+	0.0344785i
$45$	9.91160e8			0.800709
$46$	−1.44903e9	+	1.05278e9i	−1.03731	+	0.753649i
$47$	3.14560e8	+	9.68117e8i	0.200063	+	0.615729i	0.999880	+	0.0154861i	$0.00492956\pi$
$47$	3.14560e8	+	9.68117e8i	0.200063	+	0.615729i	−0.799818	+	0.600243i	$0.795070\pi$
$48$	8.46970e7	−	2.60670e8i	0.0479779	−	0.147661i
$49$	5.17677e8	+	3.76114e8i	0.261807	+	0.190214i
$50$	−8.83500e8	−	6.41900e8i	−0.399826	−	0.290491i
$51$	2.38287e8	−	7.33372e8i	0.0967084	−	0.297638i
$52$	−5.65447e8	−	1.74027e9i	−0.206240	−	0.634742i
$53$	1.78825e9	−	1.29924e9i	0.587369	−	0.426749i	−0.254004	−	0.967203i	$-0.581748\pi$
$53$	1.78825e9	−	1.29924e9i	0.587369	−	0.426749i	0.841373	+	0.540455i	$0.181748\pi$
$54$	−2.39197e9			−0.708910
$55$	1.18073e9	−	4.71953e9i	0.316341	−	1.26446i
$56$	1.19836e9			0.290773
$57$	−3.40090e9	+	2.47090e9i	−0.748656	+	0.543930i
$58$	−3.30966e7	−	1.01861e8i	−0.00662109	−	0.0203776i
$59$	−1.95231e9	+	6.00859e9i	−0.355519	+	1.09417i	0.600190	+	0.799858i	$0.295092\pi$
$59$	−1.95231e9	+	6.00859e9i	−0.355519	+	1.09417i	−0.955708	+	0.294316i	$0.904908\pi$
$60$	1.97226e9	+	1.43293e9i	0.327441	+	0.237900i
$61$	5.82978e9	+	4.23559e9i	0.883768	+	0.642095i	0.934246	−	0.356630i	$-0.116074\pi$
$61$	5.82978e9	+	4.23559e9i	0.883768	+	0.642095i	−0.0504776	+	0.998725i	$0.516074\pi$
$62$	1.80040e9	−	5.54106e9i	0.249583	−	0.768137i
$63$	−1.22982e9	−	3.78500e9i	−0.156124	−	0.480499i
$64$	−8.68675e8	+	6.31130e8i	−0.101127	+	0.0734732i
$65$	1.62754e10			1.73983
$66$	−1.08434e9	+	4.33424e9i	−0.106579	+	0.426011i
$67$	4.22878e9			0.382652			0.191326	−	0.981527i	$-0.438721\pi$
$67$	4.22878e9			0.382652			0.191326	+	0.981527i	$0.438721\pi$
$68$	−2.44394e9	+	1.77562e9i	−0.203841	+	0.148099i
$69$	4.52102e9	+	1.39143e10i	0.347990	+	1.07100i
$70$	−3.29376e9	+	1.01371e10i	−0.234235	+	0.720902i
$71$	−4.17052e9	−	3.03006e9i	−0.274327	−	0.199310i	0.442112	−	0.896960i	$-0.354229\pi$
$71$	−4.17052e9	−	3.03006e9i	−0.274327	−	0.199310i	−0.716439	+	0.697649i	$0.754229\pi$
$72$	2.88489e9	+	2.09600e9i	0.175712	+	0.127662i
$73$	−1.87074e9	+	5.75756e9i	−0.105618	+	0.325059i	−0.989875	−	0.141942i	$-0.954665\pi$
$73$	−1.87074e9	+	5.75756e9i	−0.105618	+	0.325059i	0.884257	+	0.467001i	$0.154665\pi$
$74$	−1.94817e9	−	5.99584e9i	−0.102059	−	0.314105i
$75$	−7.21676e9	+	5.24328e9i	−0.351160	+	0.255133i
$76$	1.64684e10			0.745033
$77$	−1.94878e10	+	1.34703e9i	−0.820471	+	0.0567123i
$78$	−1.49467e10			−0.586171
$79$	2.20221e10	−	1.60000e10i	0.805212	−	0.585021i	−0.107226	−	0.994235i	$-0.534197\pi$
$79$	2.20221e10	−	1.60000e10i	0.805212	−	0.585021i	0.912439	+	0.409214i	$0.134197\pi$
$80$	−2.95124e9	−	9.08297e9i	−0.100695	−	0.309908i
$81$	−8.05953e7	+	2.48047e8i	−0.00256828	+	0.00790435i
$82$	3.78502e10	+	2.74997e10i	1.12743	+	0.819129i
$83$	−3.40017e10	−	2.47037e10i	−0.947482	−	0.688386i	0.00272773	−	0.999996i	$-0.499132\pi$
$83$	−3.40017e10	−	2.47037e10i	−0.947482	−	0.688386i	−0.950210	+	0.311610i	$0.899132\pi$
$84$	3.02486e9	−	9.30957e9i	0.0789168	−	0.242881i
$85$	−8.30302e9	−	2.55541e10i	−0.202970	−	0.624678i
$86$	2.27078e10	−	1.64982e10i	0.520515	−	0.378176i
$87$	−8.74856e8			−0.0188183
$88$	1.34170e10	−	1.12399e10i	0.271020	−	0.227043i
$89$	−9.05901e10			−1.71963			−0.859816	−	0.510604i	$-0.829422\pi$
$89$	−9.05901e10			−1.71963			−0.859816	+	0.510604i	$0.829422\pi$
$90$	−2.56597e10	+	1.86429e10i	−0.458055	+	0.332796i
$91$	−2.01943e10	−	6.21517e10i	−0.339236	−	1.04406i
$92$	1.77113e10	−	5.45098e10i	0.280168	−	0.862267i
$93$	−3.85017e10	−	2.79731e10i	−0.573884	−	0.416951i
$94$	−2.63530e10	−	1.91465e10i	−0.370362	−	0.269084i
$95$	−4.52642e10	+	1.39309e11i	−0.600171	+	1.84714i
$96$	2.71030e9	+	8.34145e9i	0.0339255	+	0.104412i
$97$	2.51295e10	−	1.82577e10i	0.297126	−	0.215874i	−0.429227	−	0.903197i	$-0.641214\pi$
$97$	2.51295e10	−	1.82577e10i	0.297126	−	0.215874i	0.726353	+	0.687322i	$0.241214\pi$
$98$	−2.04763e10			−0.228827
$99$	−4.92702e10	−	3.08424e10i	−0.520704	−	0.325953i
$100$	3.49461e10			0.349461
$101$	1.25251e11	−	9.10002e10i	1.18581	−	0.861539i	0.192992	−	0.981200i	$-0.438181\pi$
$101$	1.25251e11	−	9.10002e10i	1.18581	−	0.861539i	0.992815	+	0.119662i	$0.0381810\pi$
$102$	7.62518e9	+	2.34679e10i	0.0683832	+	0.210462i
$103$	−3.55694e10	+	1.09471e11i	−0.302324	+	0.930456i	0.678339	+	0.734749i	$0.262700\pi$
$103$	−3.55694e10	+	1.09471e11i	−0.302324	+	0.930456i	−0.980662	+	0.195707i	$0.937300\pi$
$104$	4.73715e10	+	3.44174e10i	0.381798	+	0.277392i
$105$	7.04373e10	+	5.11757e10i	0.538594	+	0.391311i
$106$	−2.18576e10	+	6.72709e10i	−0.158643	+	0.488253i
$107$	1.00761e10	+	3.10110e10i	0.0694514	+	0.213749i	0.979758	−	0.200185i	$-0.0641543\pi$
$107$	1.00761e10	+	3.10110e10i	0.0694514	+	0.213749i	−0.910307	+	0.413934i	$0.864154\pi$
$108$	6.19247e10	−	4.49910e10i	0.405540	−	0.294642i
$109$	8.67375e8			0.00539960			0.00269980	−	0.999996i	$-0.499141\pi$
$109$	8.67375e8			0.00539960			0.00269980	+	0.999996i	$0.499141\pi$
$110$	5.82029e10	+	1.44390e11i	0.344576	+	0.854827i
$111$	−5.14967e10			−0.290070
$112$	−3.10238e10	+	2.25401e10i	−0.166340	+	0.120853i
$113$	−1.94126e10	−	5.97458e10i	−0.0991179	−	0.305054i	0.889187	−	0.457544i	$-0.151271\pi$
$113$	−1.94126e10	−	5.97458e10i	−0.0991179	−	0.305054i	−0.988305	+	0.152490i	$0.951271\pi$
$114$	4.15689e10	−	1.27936e11i	0.202205	−	0.622323i
$115$	4.12428e11	+	2.99646e11i	1.91210	+	1.38922i
$116$	2.77274e9	+	2.01451e9i	0.0122572	+	0.00890534i
$117$	6.00916e10	−	1.84943e11i	0.253391	−	0.779858i
$118$	−6.24739e10	−	1.92275e11i	−0.251390	−	0.773698i
$119$	−8.72825e10	+	6.34145e10i	−0.335289	+	0.243602i
$120$	−7.80113e10			−0.286194
$121$	−2.05553e11	+	1.97865e11i	−0.720452	+	0.693505i
$122$	−2.30592e11			−0.772442
$123$	3.09174e11	−	2.24628e11i	0.990205	−	0.719426i
$124$	5.76128e10	+	1.77314e11i	0.176482	+	0.543155i
$125$	4.13764e10	−	1.27344e11i	0.121269	−	0.373226i
$126$	1.03031e11	+	7.48563e10i	0.289021	+	0.209986i
$127$	5.97216e10	+	4.33903e10i	0.160403	+	0.116539i	0.665091	−	0.746762i	$-0.268393\pi$
$127$	5.97216e10	+	4.33903e10i	0.160403	+	0.116539i	−0.504689	+	0.863301i	$0.668393\pi$
$128$	1.06177e10	−	3.26781e10i	0.0273135	−	0.0840623i
$129$	−7.08492e10	−	2.18051e11i	−0.174619	−	0.537422i
$130$	−4.21346e11	+	3.06126e11i	−0.995291	+	0.723121i
$131$	1.65096e10			0.0373891			0.0186946	−	0.999825i	$-0.494049\pi$
$131$	1.65096e10			0.0373891			0.0186946	+	0.999825i	$0.494049\pi$
$132$	−5.34513e10	−	1.32602e11i	−0.116092	−	0.288002i
$133$	5.88150e11			1.22547
$134$	−1.09477e11	+	7.95396e10i	−0.218900	+	0.159040i
$135$	2.10383e11	+	6.47492e11i	0.403808	+	1.24279i
$136$	2.98720e10	−	9.19366e10i	0.0550555	−	0.169443i
$137$	−4.84416e11	−	3.51949e11i	−0.857542	−	0.623041i	0.0696733	−	0.997570i	$-0.477804\pi$
$137$	−4.84416e11	−	3.51949e11i	−0.857542	−	0.623041i	−0.927215	+	0.374529i	$0.877804\pi$
$138$	−3.78758e11	−	2.75184e11i	−0.644209	−	0.468045i
$139$	1.19580e11	−	3.68028e11i	0.195468	−	0.601589i	−0.804503	−	0.593949i	$-0.797568\pi$
$139$	1.19580e11	−	3.68028e11i	0.195468	−	0.601589i	0.999971	−	0.00763990i	$-0.00243188\pi$
$140$	−1.05400e11	−	3.24389e11i	−0.165629	−	0.509755i
$141$	−2.15261e11	+	1.56396e11i	−0.325282	+	0.236331i
$142$	1.64961e11			0.239771
$143$	−8.09043e11	−	5.06448e11i	−1.13142	−	0.708251i
$144$	−1.14110e11			−0.153578
$145$	−2.46621e10	+	1.79181e10i	−0.0319526	+	0.0232149i
$146$	−5.98638e10	−	1.84242e11i	−0.0746833	−	0.229852i
$147$	−5.16856e10	+	1.59072e11i	−0.0621046	+	0.191138i
$148$	1.63212e11	+	1.18580e11i	0.188935	+	0.137269i
$149$	1.12409e12	+	8.16699e11i	1.25394	+	0.911040i	0.998444	−	0.0557697i	$-0.0177613\pi$
$149$	1.12409e12	+	8.16699e11i	1.25394	+	0.911040i	0.255496	+	0.966810i	$0.417761\pi$
$150$	8.82098e10	−	2.71482e11i	0.0948451	−	0.291903i
$151$	−3.17234e10	−	9.76346e10i	−0.0328857	−	0.101212i	0.933266	−	0.359185i	$-0.116945\pi$
$151$	−3.17234e10	−	9.76346e10i	−0.0328857	−	0.101212i	−0.966152	+	0.257973i	$0.916945\pi$
$152$	−4.26342e11	+	3.09756e11i	−0.426205	+	0.309656i
$153$	−3.21036e11			−0.309565
$154$	4.79174e11	−	4.01421e11i	0.445789	−	0.373453i
$155$	−1.65828e12			−1.48879
$156$	3.86948e11	−	2.81134e11i	0.335326	−	0.243629i
$157$	−1.96239e11	−	6.03963e11i	−0.164187	−	0.505315i	0.834789	−	0.550570i	$-0.185590\pi$
$157$	−1.96239e11	−	6.03963e11i	−0.164187	−	0.505315i	−0.998975	+	0.0452556i	$0.985590\pi$
$158$	−2.69175e11	+	8.28434e11i	−0.217480	+	0.669336i
$159$	4.67427e11	+	3.39606e11i	0.364779	+	0.265027i
$160$	2.47246e11	+	1.79635e11i	0.186410	+	0.135435i
$161$	6.32541e11	−	1.94676e12i	0.460836	−	1.41831i
$162$	−2.57905e9	−	7.93750e9i	−0.00181605	−	0.00558922i
$163$	−1.42643e12	+	1.03636e12i	−0.970999	+	0.705472i	−0.955679	−	0.294410i	$-0.904877\pi$
$163$	−1.42643e12	+	1.03636e12i	−0.970999	+	0.705472i	−0.0153203	+	0.999883i	$0.504877\pi$
$164$	−1.49713e12			−0.985414
$165$	1.26862e12	−	8.76891e10i	0.807552	−	0.0558193i
$166$	1.34491e12			0.828130
$167$	−8.00704e11	+	5.81746e11i	−0.477015	+	0.346571i	−0.800169	−	0.599775i	$-0.795257\pi$
$167$	−8.00704e11	+	5.81746e11i	−0.477015	+	0.346571i	0.323154	+	0.946346i	$0.395257\pi$
$168$	9.67956e10	+	2.97906e11i	0.0558026	+	0.171743i
$169$	4.32928e11	−	1.33241e12i	0.241568	−	0.743469i
$170$	6.95603e11	+	5.05385e11i	0.375744	+	0.272994i
$171$	1.41589e12	+	1.02871e12i	0.740545	+	0.538038i
$172$	−2.77555e11	+	8.54227e11i	−0.140586	+	0.432680i
$173$	−2.83219e11	−	8.71658e11i	−0.138953	−	0.427654i	0.857231	−	0.514933i	$-0.172183\pi$
$173$	−2.83219e11	−	8.71658e11i	−0.138953	−	0.427654i	−0.996184	+	0.0872784i	$0.972183\pi$
$174$	2.26487e10	−	1.64553e10i	0.0107652	−	0.00782140i
$175$	1.24806e12			0.574814
$176$	−1.35934e11	+	5.43347e11i	−0.0606748	+	0.242525i
$177$	−1.65140e12			−0.714494
$178$	2.34525e12	−	1.70392e12i	0.983735	−	0.714726i
$179$	−2.26883e11	−	6.98275e11i	−0.0922807	−	0.284011i	0.894255	−	0.447558i	$-0.147706\pi$
$179$	−2.26883e11	−	6.98275e11i	−0.0922807	−	0.284011i	−0.986535	+	0.163547i	$0.947706\pi$
$180$	3.13636e11	−	9.65273e11i	0.123716	−	0.380760i
$181$	3.71223e12	+	2.69709e12i	1.42037	+	1.03196i	0.991710	+	0.128496i	$0.0410149\pi$
$181$	3.71223e12	+	2.69709e12i	1.42037	+	1.03196i	0.428662	+	0.903465i	$0.358985\pi$
$182$	1.69182e12	+	1.22918e12i	0.628003	+	0.456271i
$183$	−5.82053e11	+	1.79138e12i	−0.209644	+	0.645217i
$184$	5.66762e11	+	1.74432e12i	0.198108	+	0.609715i
$185$	−1.45169e12	+	1.05471e12i	−0.492525	+	0.357840i
$186$	1.52290e12			0.501593
$187$	−3.82438e11	+	1.52865e12i	−0.122301	+	0.488855i
$188$	1.04237e12			0.323708
$189$	2.21158e12	−	1.60680e12i	0.667055	−	0.484644i
$190$	−1.44845e12	−	4.45788e12i	−0.424385	−	1.30612i
$191$	−1.52110e12	+	4.68148e12i	−0.432988	+	1.33260i	0.462147	+	0.886803i	$0.347079\pi$
$191$	−1.52110e12	+	4.68148e12i	−0.432988	+	1.33260i	−0.895135	+	0.445796i	$0.852921\pi$
$192$	−2.27061e11	−	1.64970e11i	−0.0628039	−	0.0456297i
$193$	−5.09883e12	−	3.70452e12i	−1.37058	−	0.995788i	−0.997691	−	0.0679134i	$-0.978366\pi$
$193$	−5.09883e12	−	3.70452e12i	−1.37058	−	0.995788i	−0.372893	−	0.927874i	$-0.621634\pi$
$194$	−3.07156e11	+	9.45330e11i	−0.0802509	+	0.246987i
$195$	1.31462e12	+	4.04597e12i	0.333894	+	1.02762i
$196$	5.30101e11	−	3.85141e11i	0.130903	−	0.0951068i
$197$	−5.64844e12			−1.35633			−0.678164	−	0.734911i	$-0.737224\pi$
$197$	−5.64844e12			−1.35633			−0.678164	+	0.734911i	$0.737224\pi$
$198$	1.85565e12	−	1.28266e11i	0.433349	−	0.0299538i
$199$	−6.93663e12			−1.57564			−0.787819	−	0.615907i	$-0.788790\pi$
$199$	−6.93663e12			−1.57564			−0.787819	+	0.615907i	$0.788790\pi$
$200$	−9.04704e11	+	6.57306e11i	−0.199913	+	0.145245i
$201$	3.41572e11	+	1.05125e12i	0.0734352	+	0.226010i
$202$	−1.53093e12	+	4.71173e12i	−0.320275	+	0.985706i
$203$	9.90253e10	+	7.19461e10i	0.0201613	+	0.0146480i
$204$	−6.38815e11	−	4.64127e11i	−0.126593	−	0.0919751i
$205$	4.11495e12	−	1.26645e13i	0.793813	−	2.44310i
$206$	−1.13822e12	−	3.50308e12i	−0.213775	−	0.657932i
$207$	4.92775e12	−	3.58022e12i	0.901180	−	0.654746i
$208$	−1.87374e12			−0.333704
$209$	6.58500e12	−	5.51649e12i	1.14222	−	0.956882i
$210$	−2.78609e12			−0.470748
$211$	1.23244e12	−	8.95420e11i	0.202867	−	0.147392i	−0.481713	−	0.876329i	$-0.659985\pi$
$211$	1.23244e12	−	8.95420e11i	0.202867	−	0.147392i	0.684581	+	0.728937i	$0.259985\pi$
$212$	−6.99444e11	−	2.15267e12i	−0.112178	−	0.345247i
$213$	4.16390e11	−	1.28152e12i	0.0650747	−	0.200279i
$214$	−8.44145e11	−	6.13307e11i	−0.128570	−	0.0934119i
$215$	−6.46318e12	−	4.69578e12i	−0.959478	−	0.697101i
$216$	−7.56901e11	+	2.32950e12i	−0.109533	+	0.337107i
$217$	2.05758e12	+	6.33258e12i	0.290287	+	0.893413i
$218$	−2.24551e10	+	1.63146e10i	−0.00308890	+	0.00224422i
$219$	−1.58240e12			−0.212263
$220$	−4.22264e12	−	2.64331e12i	−0.552407	−	0.345798i
$221$	−5.27159e12			−0.672642
$222$	1.33317e12	−	9.68607e11i	0.165938	−	0.120561i
$223$	1.97760e12	+	6.08643e12i	0.240139	+	0.739070i	0.996398	+	0.0847988i	$0.0270247\pi$
$223$	1.97760e12	+	6.08643e12i	0.240139	+	0.739070i	−0.756260	+	0.654272i	$0.772975\pi$
$224$	3.79201e11	−	1.16706e12i	0.0449268	−	0.138271i
$225$	3.00454e12	+	2.18293e12i	0.347356	+	0.252369i
$226$	1.62633e12	+	1.18160e12i	0.183490	+	0.133313i
$227$	−8.79693e10	+	2.70742e11i	−0.00968699	+	0.0298135i	−0.955783	−	0.294072i	$-0.904989\pi$
$227$	−8.79693e10	+	2.70742e11i	−0.00968699	+	0.0298135i	0.946096	+	0.323886i	$0.104989\pi$
$228$	1.33020e12	+	4.09395e12i	0.142980	+	0.440049i
$229$	1.99182e12	−	1.44714e12i	0.209004	−	0.151850i	−0.478359	−	0.878164i	$-0.658768\pi$
$229$	1.99182e12	−	1.44714e12i	0.209004	−	0.151850i	0.687363	+	0.726314i	$0.258768\pi$
$230$	−1.63132e13			−1.67123
$231$	−1.90896e12	−	4.73575e12i	−0.190955	−	0.473722i
$232$	−1.09673e11			−0.0107131
$233$	−1.10777e12	+	8.04842e11i	−0.105680	+	0.0767809i	−0.639370	−	0.768899i	$-0.720805\pi$
$233$	−1.10777e12	+	8.04842e11i	−0.105680	+	0.0767809i	0.533690	+	0.845680i	$0.320805\pi$
$234$	1.92293e12	+	5.91817e12i	0.179175	+	0.551443i
$235$	−2.86501e12	+	8.81759e12i	−0.260767	+	0.802558i
$236$	5.23388e12	+	3.80264e12i	0.465380	+	0.338118i
$237$	5.75632e12	+	4.18221e12i	0.500068	+	0.363321i
$238$	1.06685e12	−	3.28342e12i	0.0905584	−	0.278710i
$239$	3.15508e12	+	9.71033e12i	0.261711	+	0.805463i	0.992433	+	0.122788i	$0.0391835\pi$
$239$	3.15508e12	+	9.71033e12i	0.261711	+	0.805463i	−0.730722	+	0.682675i	$0.760817\pi$
$240$	2.01960e12	−	1.46732e12i	0.163720	−	0.118950i
$241$	1.06259e13			0.841922			0.420961	−	0.907079i	$-0.361693\pi$
$241$	1.06259e13			0.841922			0.420961	+	0.907079i	$0.361693\pi$
$242$	1.59981e12	−	8.98872e12i	0.123904	−	0.696167i
$243$	1.31734e13			0.997388
$244$	5.96970e12	−	4.33724e12i	0.441884	−	0.321048i
$245$	1.80097e12	+	5.54280e12i	0.130344	+	0.401159i
$246$	−3.77901e12	+	1.16306e13i	−0.267445	+	0.823112i
$247$	2.32497e13	+	1.68919e13i	1.60910	+	1.16908i
$248$	−4.82663e12	−	3.50676e12i	−0.326708	−	0.237367i
$249$	3.39477e12	−	1.04480e13i	0.224758	−	0.691733i
$250$	1.32405e12	+	4.07499e12i	0.0857498	+	0.263911i
$251$	−6.40008e12	+	4.64993e12i	−0.405490	+	0.294606i	−0.771773	−	0.635898i	$-0.780630\pi$
$251$	−6.40008e12	+	4.64993e12i	−0.405490	+	0.294606i	0.366284	+	0.930503i	$0.380630\pi$
$252$	−4.07530e12			−0.252614
$253$	−1.11774e13	−	2.77290e13i	−0.677920	−	1.68179i
$254$	−2.36224e12			−0.140197
$255$	5.68195e12	−	4.12818e12i	0.330009	−	0.239766i
$256$	3.39768e11	+	1.04570e12i	0.0193136	+	0.0594410i
$257$	−6.32468e12	+	1.94654e13i	−0.351890	+	1.08300i	0.605901	+	0.795540i	$0.292813\pi$
$257$	−6.32468e12	+	1.94654e13i	−0.351890	+	1.08300i	−0.957791	+	0.287465i	$0.907187\pi$
$258$	5.93554e12	+	4.31242e12i	0.323260	+	0.234862i
$259$	5.82893e12	+	4.23496e12i	0.310771	+	0.225788i
$260$	5.15007e12	−	1.58503e13i	0.268819	−	0.827340i
$261$	1.12553e11	+	3.46401e11i	0.00575218	+	0.0177034i
$262$	−4.27410e11	+	3.10532e11i	−0.0213889	+	0.0155399i
$263$	−3.96338e13			−1.94227			−0.971134	−	0.238537i	$-0.923332\pi$
$263$	−3.96338e13			−1.94227			−0.971134	+	0.238537i	$0.923332\pi$
$264$	3.87791e12	+	2.42751e12i	0.186113	+	0.116504i
$265$	2.01323e13			0.946325
$266$	−1.52263e13	+	1.10626e13i	−0.701046	+	0.509340i
$267$	−7.31726e12	−	2.25202e13i	−0.330017	−	1.01569i
$268$	1.33813e12	−	4.11833e12i	0.0591229	−	0.181962i
$269$	4.10032e12	+	2.97905e12i	0.177492	+	0.128956i	0.672984	−	0.739657i	$-0.265012\pi$
$269$	4.10032e12	+	2.97905e12i	0.177492	+	0.128956i	−0.495492	+	0.868613i	$0.665012\pi$
$270$	−1.76253e13	−	1.28055e13i	−0.747541	−	0.543121i
$271$	2.28945e12	−	7.04619e12i	0.0951479	−	0.292835i	−0.892144	−	0.451751i	$-0.850800\pi$
$271$	2.28945e12	−	7.04619e12i	0.0951479	−	0.292835i	0.987292	+	0.158915i	$0.0507997\pi$
$272$	9.55904e11	+	2.94197e12i	0.0389301	+	0.119815i
$273$	1.38194e13	−	1.00404e13i	0.551563	−	0.400734i
$274$	1.91607e13			0.749519
$275$	1.39735e13	−	1.17061e13i	0.535765	−	0.448829i
$276$	1.49815e13			0.563059
$277$	−2.37945e13	+	1.72877e13i	−0.876674	+	0.636941i	−0.932369	−	0.361507i	$-0.882262\pi$
$277$	−2.37945e13	+	1.72877e13i	−0.876674	+	0.636941i	0.0556956	+	0.998448i	$0.482262\pi$
$278$	3.82655e12	+	1.17769e13i	0.138217	+	0.425388i
$279$	−6.12268e12	+	1.88437e13i	−0.216829	+	0.667332i
$280$	8.83013e12	+	6.41546e12i	0.306618	+	0.222771i
$281$	−4.04550e13	−	2.93923e13i	−1.37749	−	1.00080i	−0.997110	−	0.0759716i	$-0.975794\pi$
$281$	−4.04550e13	−	2.93923e13i	−1.37749	−	1.00080i	−0.380377	−	0.924831i	$-0.624206\pi$
$282$	2.63111e12	−	8.09774e12i	0.0878556	−	0.270392i
$283$	3.94698e12	+	1.21476e13i	0.129253	+	0.397799i	0.994652	−	0.103284i	$-0.0329351\pi$
$283$	3.94698e12	+	1.21476e13i	0.129253	+	0.397799i	−0.865399	+	0.501083i	$0.832935\pi$
$284$	−4.27061e12	+	3.10278e12i	−0.137164	+	0.0996552i
$285$	−3.82876e13			−1.20618
$286$	3.04708e13	−	2.10619e12i	0.941609	−	0.0650856i
$287$	−5.34685e13			−1.62087
$288$	2.95413e12	−	2.14630e12i	0.0878559	−	0.0638310i
$289$	−7.90125e12	−	2.43176e13i	−0.230546	−	0.709548i
$290$	3.01443e11	−	9.27746e11i	0.00863010	−	0.0265607i
$291$	6.56856e12	+	4.77234e12i	0.184526	+	0.134066i
$292$	5.01521e12	+	3.64377e12i	0.138256	+	0.100449i
$293$	1.94261e12	−	5.97874e12i	0.0525549	−	0.161747i	−0.921334	−	0.388771i	$-0.872900\pi$
$293$	1.94261e12	−	5.97874e12i	0.0525549	−	0.161747i	0.973889	+	0.227024i	$0.0728996\pi$
$294$	−1.65394e12	−	5.09030e12i	−0.0439146	−	0.135155i
$295$	−4.65528e13	+	3.38226e13i	−1.21318	+	0.881425i
$296$	−6.45570e12			−0.165135
$297$	9.69025e12	−	3.87332e13i	0.243318	−	0.972575i
$298$	−4.44625e13			−1.09598
$299$	8.09162e13	−	5.87891e13i	1.95814	−	1.42267i
$300$	2.82271e12	+	8.68742e12i	0.0670656	+	0.206407i
$301$	−9.91258e12	+	3.05078e13i	−0.231244	+	0.711697i
$302$	2.65769e12	+	1.93093e12i	0.0608789	+	0.0442311i
$303$	3.27391e13	+	2.37864e13i	0.736432	+	0.535049i
$304$	5.21114e12	−	1.60382e13i	0.115114	−	0.354284i
$305$	2.02814e13	+	6.24199e13i	0.439997	+	1.35417i
$306$	8.31116e12	−	6.03841e12i	0.177090	−	0.128663i
$307$	−3.10523e13			−0.649880			−0.324940	−	0.945735i	$-0.605344\pi$
$307$	−3.10523e13			−0.649880			−0.324940	+	0.945735i	$0.605344\pi$
$308$	−4.85474e12	+	1.94050e13i	−0.0998015	+	0.398920i
$309$	−3.00871e13			−0.607587
$310$	4.29305e13	−	3.11909e13i	0.851681	−	0.618782i
$311$	−1.77738e13	−	5.47020e13i	−0.346416	−	1.06616i	−0.960822	−	0.277168i	$-0.910604\pi$
$311$	−1.77738e13	−	5.47020e13i	−0.346416	−	1.06616i	0.614406	−	0.788990i	$-0.289396\pi$
$312$	−4.72963e12	+	1.45563e13i	−0.0905684	+	0.278741i
$313$	6.04701e13	+	4.39341e13i	1.13775	+	0.826624i	0.986804	−	0.161918i	$-0.0517681\pi$
$313$	6.04701e13	+	4.39341e13i	1.13775	+	0.826624i	0.150946	+	0.988542i	$0.451768\pi$
$314$	1.64404e13	+	1.19446e13i	0.303947	+	0.220831i
$315$	1.12012e13	−	3.44737e13i	0.203496	−	0.626296i
$316$	−8.61359e12	−	2.65099e13i	−0.153782	−	0.473292i
$317$	−2.14647e13	+	1.55950e13i	−0.376616	+	0.273627i	−0.759949	−	0.649983i	$-0.774776\pi$
$317$	−2.14647e13	+	1.55950e13i	−0.376616	+	0.273627i	0.383333	+	0.923610i	$0.374776\pi$
$318$	−1.84887e13			−0.318828
$319$	1.78351e12	−	1.23279e11i	0.0302292	−	0.00208949i
$320$	−9.77961e12			−0.162928
$321$	−6.89529e12	+	5.00972e12i	−0.112921	+	0.0820419i
$322$	2.02413e13	+	6.22963e13i	0.325860	+	1.00289i
$323$	1.46611e13	−	4.51221e13i	0.232034	−	0.714127i
$324$	2.16065e11	+	1.56981e11i	0.00336192	+	0.00244258i
$325$	4.93362e13	+	3.58448e13i	0.754757	+	0.548363i
$326$	1.74351e13	−	5.36599e13i	0.262258	−	0.807147i
$327$	7.00608e10	+	2.15625e11i	0.00103624	+	0.00318923i
$328$	3.87586e13	−	2.81597e13i	0.563717	−	0.409565i
$329$	3.72271e13			0.532454
$330$	−3.11934e13	+	2.61318e13i	−0.438769	+	0.367572i
$331$	−1.19403e14			−1.65182			−0.825910	−	0.563802i	$-0.809338\pi$
$331$	−1.19403e14			−1.65182			−0.825910	+	0.563802i	$0.809338\pi$
$332$	−3.48177e13	+	2.52966e13i	−0.473741	+	0.344193i
$333$	6.62518e12	+	2.03902e13i	0.0886655	+	0.272884i
$334$	9.78694e12	−	3.01211e13i	0.128837	−	0.396520i
$335$	3.11598e13	+	2.26389e13i	0.403504	+	0.293163i
$336$	−8.10925e12	−	5.89171e12i	−0.103303	−	0.0750543i
$337$	−1.49978e13	+	4.61584e13i	−0.187959	+	0.578477i	−0.999987	−	0.00514102i	$-0.998364\pi$
$337$	−1.49978e13	+	4.61584e13i	−0.187959	+	0.578477i	0.812028	+	0.583618i	$0.198364\pi$
$338$	1.38537e13	+	4.26373e13i	0.170814	+	0.525712i
$339$	1.32845e13	−	9.65174e12i	0.161156	−	0.117087i
$340$	−2.75140e13			−0.328413
$341$	8.24327e13	+	5.16016e13i	0.968167	+	0.606057i
$342$	−5.60045e13			−0.647260
$343$	7.74344e13	−	5.62594e13i	0.880676	−	0.639849i
$344$	−8.88177e12	−	2.73353e13i	−0.0994095	−	0.305951i
$345$	−4.11773e13	+	1.26731e14i	−0.453579	+	1.39597i
$346$	2.37273e13	+	1.72389e13i	0.257234	+	0.186892i
$347$	4.39014e13	+	3.18962e13i	0.468453	+	0.340351i	0.796838	−	0.604193i	$-0.206504\pi$
$347$	4.39014e13	+	3.18962e13i	0.468453	+	0.340351i	−0.328385	+	0.944544i	$0.606504\pi$
$348$	−2.76834e11	+	8.52006e11i	−0.00290759	+	0.00894864i
$349$	−1.57840e13	−	4.85780e13i	−0.163183	−	0.502227i	0.835714	−	0.549164i	$-0.185054\pi$
$349$	−1.57840e13	−	4.85780e13i	−0.163183	−	0.502227i	−0.998898	+	0.0469373i	$0.985054\pi$
$350$	−3.23105e13	+	2.34750e13i	−0.328829	+	0.238908i
$351$	1.33572e14			1.33822
$352$	−6.70074e12	−	1.66233e13i	−0.0660904	−	0.163958i
$353$	1.71071e14			1.66117			0.830587	−	0.556889i	$-0.188005\pi$
$353$	1.71071e14			1.66117			0.830587	+	0.556889i	$0.188005\pi$
$354$	4.27523e13	−	3.10613e13i	0.408734	−	0.296963i
$355$	−1.45090e13	−	4.46540e13i	−0.136578	−	0.420344i
$356$	−2.86657e13	+	8.82240e13i	−0.265698	+	0.817734i
$357$	−2.28146e13	−	1.65758e13i	−0.208227	−	0.151286i
$358$	1.90076e13	+	1.38098e13i	0.170833	+	0.124117i
$359$	3.78988e13	−	1.16641e14i	0.335433	−	1.03236i	−0.631075	−	0.775722i	$-0.717386\pi$
$359$	3.78988e13	−	1.16641e14i	0.335433	−	1.03236i	0.966508	−	0.256636i	$-0.0826141\pi$
$360$	1.00364e13	+	3.08887e13i	0.0874807	+	0.269238i
$361$	−1.15004e14	+	8.35554e13i	−0.987243	+	0.717274i
$362$	−1.46834e14			−1.24145
$363$	−6.57914e13	−	3.51173e13i	−0.547877	−	0.292438i
$364$	−6.69186e13			−0.548895
$365$	−4.46078e13	+	3.24095e13i	−0.360413	+	0.261855i
$366$	−1.86257e13	−	5.73240e13i	−0.148240	−	0.456237i
$367$	5.27947e13	−	1.62485e14i	0.413930	−	1.27395i	−0.499275	−	0.866444i	$-0.666400\pi$
$367$	5.27947e13	−	1.62485e14i	0.413930	−	1.27395i	0.913205	−	0.407501i	$-0.133600\pi$
$368$	−4.74817e13	−	3.44975e13i	−0.366744	−	0.266455i
$369$	−1.28718e14	−	9.35192e13i	−0.979478	−	0.711633i
$370$	1.77438e13	−	5.46099e13i	0.133026	−	0.409413i
$371$	−2.49799e13	−	7.68802e13i	−0.184516	−	0.567882i
$372$	−3.94258e13	+	2.86445e13i	−0.286942	+	0.208475i
$373$	−1.59798e14			−1.14597			−0.572983	−	0.819567i	$-0.694214\pi$
$373$	−1.59798e14			−1.14597			−0.572983	+	0.819567i	$0.694214\pi$
$374$	−1.88519e13	−	4.67679e13i	−0.133217	−	0.330487i
$375$	3.49991e13			0.243716
$376$	−2.69854e13	+	1.96061e13i	−0.185181	+	0.134542i
$377$	1.84817e12	+	5.68809e12i	0.0124987	+	0.0384671i
$378$	−2.70319e13	+	8.31956e13i	−0.180165	+	0.554492i
$379$	1.93210e14	+	1.40376e14i	1.26916	+	0.922096i	0.999169	−	0.0407679i	$-0.0129804\pi$
$379$	1.93210e14	+	1.40376e14i	1.26916	+	0.922096i	0.269987	+	0.962864i	$0.412980\pi$
$380$	1.21347e14	+	8.81639e13i	0.785634	+	0.570796i
$381$	−5.96269e12	+	1.83513e13i	−0.0380500	+	0.117106i
$382$	−4.86754e13	−	1.49807e14i	−0.306169	−	0.942290i
$383$	−2.07659e14	+	1.50873e14i	−1.28753	+	0.935445i	−0.999752	−	0.0222527i	$-0.992916\pi$
$383$	−2.07659e14	+	1.50873e14i	−1.28753	+	0.935445i	−0.287777	+	0.957697i	$0.592916\pi$
$384$	8.98122e12			0.0548926
$385$	−1.50807e14	−	9.44029e13i	−0.908632	−	0.568789i
$386$	2.01680e14			1.19793
$387$	−7.72230e13	+	5.61058e13i	−0.452206	+	0.328547i
$388$	−9.82900e12	−	3.02505e13i	−0.0567459	−	0.174646i
$389$	8.30335e13	−	2.55551e14i	0.472640	−	1.45464i	−0.376474	−	0.926427i	$-0.622864\pi$
$389$	8.30335e13	−	2.55551e14i	0.472640	−	1.45464i	0.849114	−	0.528209i	$-0.177136\pi$
$390$	−1.10135e14	−	8.00175e13i	−0.618114	−	0.449086i
$391$	−1.33585e14	−	9.70554e13i	−0.739242	−	0.537090i
$392$	−6.47938e12	+	1.99415e13i	−0.0353558	+	0.108814i
$393$	1.33354e12	+	4.10420e12i	0.00717540	+	0.0220836i
$394$	1.46230e14	−	1.06242e14i	0.775902	−	0.563726i
$395$	2.47927e14			1.29730
$396$	−4.56276e13	+	3.82238e13i	−0.235453	+	0.197247i
$397$	−7.01572e13			−0.357046			−0.178523	−	0.983936i	$-0.557132\pi$
$397$	−7.01572e13			−0.357046			−0.178523	+	0.983936i	$0.557132\pi$
$398$	1.79579e14	−	1.30472e14i	0.901361	−	0.654877i
$399$	4.75068e13	+	1.46211e14i	0.235183	+	0.723818i
$400$	1.10581e13	−	3.40334e13i	0.0539947	−	0.166179i
$401$	7.71595e13	+	5.60596e13i	0.371617	+	0.269995i	0.757881	−	0.652393i	$-0.226235\pi$
$401$	7.71595e13	+	5.60596e13i	0.371617	+	0.269995i	−0.386264	+	0.922388i	$0.626235\pi$
$402$	−2.86159e13	−	2.07907e13i	−0.135945	−	0.0987702i
$403$	−1.00538e14	+	3.09423e14i	−0.471141	+	1.45002i
$404$	−4.89898e13	−	1.50775e14i	−0.226469	−	0.696999i
$405$	−1.92179e12	+	1.39626e12i	−0.00876404	+	0.00636744i
$406$	−3.91686e12			−0.0176216
$407$	1.04983e14	−	7.25658e12i	0.465960	−	0.0322079i
$408$	2.52678e13			0.110646
$409$	−2.32223e14	+	1.68720e14i	−1.00329	+	0.728934i	−0.962792	−	0.270245i	$-0.912895\pi$
$409$	−2.32223e14	+	1.68720e14i	−1.00329	+	0.728934i	−0.0405006	+	0.999180i	$0.512895\pi$
$410$	1.31678e14	+	4.05264e14i	0.561310	+	1.72754i
$411$	4.83647e13	−	1.48851e14i	0.203422	−	0.626070i
$412$	9.53568e13	+	6.92808e13i	0.395747	+	0.287527i
$413$	1.86922e14	+	1.35807e14i	0.765484	+	0.556156i
$414$	−6.02314e13	+	1.85373e14i	−0.243400	+	0.749109i
$415$	−1.18290e14	−	3.64058e14i	−0.471718	−	1.45180i
$416$	4.85084e13	−	3.52434e13i	0.190899	−	0.138696i
$417$	1.01149e14			0.392837
$418$	−6.67158e13	+	2.66672e14i	−0.255717	+	1.02213i
$419$	−6.73130e13			−0.254637			−0.127319	−	0.991862i	$-0.540637\pi$
$419$	−6.73130e13			−0.254637			−0.127319	+	0.991862i	$0.540637\pi$
$420$	7.21278e13	−	5.24039e13i	0.269297	−	0.195656i
$421$	2.40872e13	+	7.41326e13i	0.0887634	+	0.273186i	0.985578	−	0.169220i	$-0.0541250\pi$
$421$	2.40872e13	+	7.41326e13i	0.0887634	+	0.273186i	−0.896815	+	0.442406i	$0.854125\pi$
$422$	−1.50640e13	+	4.63622e13i	−0.0547926	+	0.168634i
$423$	8.96193e13	+	6.51122e13i	0.321758	+	0.233771i
$424$	5.85974e13	+	4.25735e13i	0.207666	+	0.150878i
$425$	3.11110e13	−	9.57497e13i	0.108836	−	0.334964i
$426$	1.33245e13	+	4.10085e13i	0.0460148	+	0.141619i
$427$	2.13201e14	−	1.54900e14i	0.726836	−	0.528078i
$428$	3.33894e13			0.112375
$429$	6.05513e13	−	2.42031e14i	0.201191	−	0.804186i
$430$	2.55646e14			0.838614
$431$	−1.70410e14	+	1.23810e14i	−0.551913	+	0.400988i	−0.828490	−	0.560004i	$-0.810800\pi$
$431$	−1.70410e14	+	1.23810e14i	−0.551913	+	0.400988i	0.276578	+	0.960992i	$0.410800\pi$
$432$	−2.42208e13	−	7.45440e13i	−0.0774512	−	0.238370i
$433$	−1.45459e14	+	4.47675e14i	−0.459257	+	1.41345i	0.406806	+	0.913514i	$0.366642\pi$
$433$	−1.45459e14	+	4.47675e14i	−0.459257	+	1.41345i	−0.866064	+	0.499934i	$0.833358\pi$
$434$	−1.72378e14	−	1.25240e14i	−0.537389	−	0.390436i
$435$	−6.44638e12	−	4.68357e12i	−0.0198438	−	0.0144174i
$436$	2.74467e11	−	8.44721e11i	0.000834284	−	0.00256766i
$437$	2.78164e14	+	8.56102e14i	0.834937	+	2.56967i
$438$	4.09661e13	−	2.97636e13i	0.121428	−	0.0882223i
$439$	1.99647e14			0.584396			0.292198	−	0.956358i	$-0.405613\pi$
$439$	1.99647e14			0.584396			0.292198	+	0.956358i	$0.405613\pi$
$440$	1.59036e14	−	1.09928e13i	0.459734	−	0.0317776i
$441$	6.96343e13			0.198798
$442$	1.36474e14	−	9.91540e13i	0.384793	−	0.279568i
$443$	−1.38189e14	−	4.25302e14i	−0.384816	−	1.18434i	−0.936613	−	0.350364i	$-0.886058\pi$
$443$	−1.38189e14	−	4.25302e14i	−0.384816	−	1.18434i	0.551797	−	0.833978i	$-0.313942\pi$
$444$	−1.62953e13	+	5.01517e13i	−0.0448183	+	0.137936i
$445$	−6.67514e14	−	4.84977e14i	−1.81334	−	1.31747i
$446$	−1.65678e14	−	1.20372e14i	−0.444552	−	0.322986i
$447$	−1.12231e14	+	3.45410e14i	−0.297454	+	0.915470i
$448$	1.21344e13	+	3.73460e13i	0.0317681	+	0.0977720i
$449$	3.67449e14	−	2.66967e14i	0.950259	−	0.690404i	−0.000608761	−	1.00000i	$-0.500194\pi$
$449$	3.67449e14	−	2.66967e14i	0.950259	−	0.690404i	0.950868	+	0.309596i	$0.100194\pi$
$450$	−1.18842e14			−0.303600
$451$	−5.98640e14	+	5.01502e14i	−1.51076	+	1.26561i
$452$	−6.43282e13			−0.160376
$453$	2.17090e13	−	1.57725e13i	0.0534688	−	0.0388474i
$454$	−2.81502e12	−	8.66373e12i	−0.00684974	−	0.0210813i
$455$	1.83929e14	−	5.66076e14i	0.442169	−	1.36086i
$456$	−1.11441e14	−	8.09664e13i	−0.264690	−	0.192308i
$457$	−3.68590e14	−	2.67796e14i	−0.864976	−	0.628442i	0.0642582	−	0.997933i	$-0.479532\pi$
$457$	−3.68590e14	−	2.67796e14i	−0.864976	−	0.628442i	−0.929234	+	0.369492i	$0.879532\pi$
$458$	−2.43458e13	+	7.49288e13i	−0.0564501	+	0.173736i
$459$	−6.81430e13	−	2.09723e14i	−0.156117	−	0.480480i
$460$	4.22326e14	−	3.06838e14i	0.956049	−	0.694610i
$461$	5.49644e14			1.22949			0.614747	−	0.788724i	$-0.289258\pi$
$461$	5.49644e14			1.22949			0.614747	+	0.788724i	$0.289258\pi$
$462$	1.38496e14	+	8.66960e13i	0.306129	+	0.191632i
$463$	−1.66297e14			−0.363236			−0.181618	−	0.983369i	$-0.558134\pi$
$463$	−1.66297e14			−0.363236			−0.181618	+	0.983369i	$0.558134\pi$
$464$	2.83928e12	−	2.06286e12i	0.00612858	−	0.00445267i
$465$	−1.33945e14	−	4.12240e14i	−0.285716	−	0.879345i
$466$	1.35402e13	−	4.16724e13i	0.0285431	−	0.0878467i
$467$	−3.37743e14	−	2.45385e14i	−0.703628	−	0.511216i	0.177484	−	0.984124i	$-0.443204\pi$
$467$	−3.37743e14	−	2.45385e14i	−0.703628	−	0.511216i	−0.881112	+	0.472908i	$0.843204\pi$
$468$	−1.61098e14	−	1.17044e14i	−0.331693	−	0.240989i
$469$	4.77898e13	−	1.47082e14i	0.0972488	−	0.299301i
$470$	−9.16803e13	−	2.82163e14i	−0.184390	−	0.567494i
$471$	1.34291e14	−	9.75681e13i	0.266951	−	0.193951i
$472$	−2.07022e14			−0.406757
$473$	1.75162e14	+	4.34543e14i	0.340176	+	0.843911i
$474$	−2.27687e14			−0.437076
$475$	−4.44025e14	+	3.22603e14i	−0.842543	+	0.612143i
$476$	3.41391e13	+	1.05069e14i	0.0640345	+	0.197078i
$477$	7.43319e13	−	2.28770e14i	0.137824	−	0.424178i
$478$	−2.64323e14	−	1.92042e14i	−0.484487	−	0.352000i
$479$	4.38718e14	+	3.18747e14i	0.794950	+	0.577565i	0.909428	−	0.415860i	$-0.136520\pi$
$479$	4.38718e14	+	3.18747e14i	0.794950	+	0.577565i	−0.114478	+	0.993426i	$0.536520\pi$
$480$	−2.46854e13	+	7.59737e13i	−0.0442194	+	0.136093i
$481$	1.08789e14	+	3.34818e14i	0.192658	+	0.592941i
$482$	−2.75089e14	+	1.99864e14i	−0.481631	+	0.349925i
$483$	5.35047e14			0.926153
$484$	1.27653e14	+	2.62796e14i	0.218465	+	0.449748i
$485$	2.82910e14			0.478706
$486$	−3.41041e14	+	2.47781e14i	−0.570567	+	0.414541i
$487$	6.49576e13	+	1.99919e14i	0.107453	+	0.330708i	0.990298	−	0.138957i	$-0.0443749\pi$
$487$	6.49576e13	+	1.99919e14i	0.107453	+	0.330708i	−0.882845	+	0.469665i	$0.844375\pi$
$488$	−7.29671e13	+	2.24570e14i	−0.119349	+	0.367318i
$489$	−3.72852e14	−	2.70893e14i	−0.603028	−	0.438126i
$490$	−1.50880e14	−	1.09621e14i	−0.241297	−	0.175313i
$491$	−1.69104e14	+	5.20447e14i	−0.267427	+	0.823054i	0.723698	+	0.690117i	$0.242441\pi$
$491$	−1.69104e14	+	5.20447e14i	−0.267427	+	0.823054i	−0.991124	+	0.132937i	$0.957559\pi$
$492$	−1.20928e14	−	3.72179e14i	−0.189112	−	0.582028i
$493$	7.98805e12	−	5.80366e12i	0.0123533	−	0.00897519i
$494$	−9.19623e14			−1.40641
$495$	−1.97932e14	−	4.91032e14i	−0.299356	−	0.742645i
$496$	1.90914e14			0.285554
$497$	−1.52520e14	+	1.10812e14i	−0.225615	+	0.163919i
$498$	1.08633e14	+	3.34337e14i	0.158928	+	0.489129i
$499$	1.89146e13	−	5.82130e13i	0.0273680	−	0.0842301i	−0.936440	−	0.350829i	$-0.885900\pi$
$499$	1.89146e13	−	5.82130e13i	0.0273680	−	0.0842301i	0.963808	+	0.266599i	$0.0858999\pi$
$500$	−1.10925e14	−	8.05915e13i	−0.158743	−	0.115333i
$501$	−2.09294e14	−	1.52061e14i	−0.296244	−	0.215234i
$502$	7.82276e13	−	2.40760e14i	0.109519	−	0.337065i
$503$	8.73547e13	+	2.68850e14i	0.120966	+	0.372294i	0.993145	−	0.116893i	$-0.0372935\pi$
$503$	8.73547e13	+	2.68850e14i	0.120966	+	0.372294i	−0.872179	+	0.489187i	$0.837293\pi$
$504$	1.05504e14	−	7.66528e13i	0.144510	−	0.104993i
$505$	1.41009e15			1.91048
$506$	8.10926e14	+	5.07627e14i	1.08681	+	0.680325i
$507$	3.66200e14			0.485484
$508$	6.11550e13	−	4.44317e13i	0.0802013	−	0.0582696i
$509$	−3.08973e14	−	9.50922e14i	−0.400842	−	1.23367i	−0.924318	−	0.381624i	$-0.875365\pi$
$509$	−3.08973e14	−	9.50922e14i	−0.400842	−	1.23367i	0.523475	−	0.852041i	$-0.324635\pi$
$510$	−6.94499e13	+	2.13745e14i	−0.0891325	+	0.274321i
$511$	1.79113e14	+	1.30133e14i	0.227411	+	0.165224i
$512$	−2.84648e13	−	2.06809e13i	−0.0357538	−	0.0259767i
$513$	−3.71483e14	+	1.14331e15i	−0.461630	+	1.42075i
$514$	−2.02390e14	−	6.22892e14i	−0.248824	−	0.765800i
$515$	−8.48152e14	+	6.16218e14i	−1.03165	+	0.749540i
$516$	−2.34775e14			−0.282539
$517$	4.16800e14	−	3.49168e14i	0.496283	−	0.415753i
$518$	−2.30558e14			−0.271623
$519$	1.93813e14	−	1.40813e14i	0.225924	−	0.164144i
$520$	1.64802e14	+	5.07209e14i	0.190084	+	0.585018i
$521$	4.20542e14	−	1.29430e15i	0.479957	−	1.47715i	−0.359198	−	0.933261i	$-0.616950\pi$
$521$	4.20542e14	−	1.29430e15i	0.479957	−	1.47715i	0.839155	−	0.543893i	$-0.183050\pi$
$522$	−9.42933e12	−	6.85081e12i	−0.0106486	−	0.00773667i
$523$	7.47100e14	+	5.42800e14i	0.834871	+	0.606569i	0.920933	−	0.389721i	$-0.127428\pi$
$523$	7.47100e14	+	5.42800e14i	0.834871	+	0.606569i	−0.0860625	+	0.996290i	$0.527428\pi$
$524$	5.22420e12	−	1.60784e13i	0.00577693	−	0.0177796i
$525$	1.00810e14	+	3.10262e14i	0.110313	+	0.339510i
$526$	1.02606e15	−	7.45477e14i	1.11110	−	0.807258i
$527$	5.37117e14			0.575587
$528$	−1.46053e14	+	1.00954e13i	−0.154890	+	0.0107063i
$529$	2.18002e15			2.28800
$530$	−5.21195e14	+	3.78670e14i	−0.541356	+	0.393318i
$531$	2.12457e14	+	6.53874e14i	0.218399	+	0.672163i
$532$	1.86110e14	−	5.72789e14i	0.189346	−	0.582748i
$533$	−2.11362e15	−	1.53564e15i	−2.12827	−	1.54628i
$534$	6.13019e14	+	4.45384e14i	0.610938	+	0.443872i
$535$	−9.17727e13	+	2.82447e14i	−0.0905248	+	0.278607i
$536$	4.28201e13	+	1.31787e14i	0.0418062	+	0.128666i
$537$	1.55261e14	−	1.12804e14i	0.150039	−	0.109010i
$538$	−1.62185e14			−0.155134
$539$	8.29526e13	−	3.31572e14i	0.0785401	−	0.313935i
$540$	6.97153e14			0.653375
$541$	−1.35848e15	+	9.86996e14i	−1.26029	+	0.915652i	−0.998772	−	0.0495478i	$-0.984222\pi$
$541$	−1.35848e15	+	9.86996e14i	−1.26029	+	0.915652i	−0.261515	+	0.965200i	$0.584222\pi$
$542$	7.32623e13	+	2.25478e14i	0.0672797	+	0.207066i
$543$	−3.70633e14	+	1.14069e15i	−0.336935	+	1.03698i
$544$	−8.00829e13	−	5.81836e13i	−0.0720686	−	0.0523609i
$545$	6.39126e12	+	4.64352e12i	0.00569385	+	0.00413682i
$546$	−1.68914e14	+	5.19863e14i	−0.148972	+	0.458489i
$547$	3.17670e14	+	9.77689e14i	0.277362	+	0.853632i	0.988585	+	0.150665i	$0.0481416\pi$
$547$	3.17670e14	+	9.77689e14i	0.277362	+	0.853632i	−0.711223	+	0.702966i	$0.751858\pi$
$548$	−4.96042e14	+	3.60396e14i	−0.428771	+	0.311520i
$549$	7.84182e14			0.671072
$550$	−1.41572e14	+	5.65882e14i	−0.119945	+	0.479436i
$551$	−5.38272e13			−0.0451510
$552$	−3.87848e14	+	2.81788e14i	−0.322105	+	0.234023i
$553$	−3.07625e14	−	9.46773e14i	−0.252949	−	0.778498i
$554$	2.90838e14	−	8.95108e14i	0.236781	−	0.728738i
$555$	−3.79453e14	−	2.75689e14i	−0.305877	−	0.222233i
$556$	−3.20577e14	−	2.32913e14i	−0.255871	−	0.185901i
$557$	4.03982e14	−	1.24333e15i	0.319270	−	0.982612i	−0.654691	−	0.755897i	$-0.727201\pi$
$557$	4.03982e14	−	1.24333e15i	0.319270	−	0.982612i	0.973961	−	0.226715i	$-0.0727987\pi$
$558$	−1.95926e14	−	6.02997e14i	−0.153322	−	0.471875i
$559$	−1.26804e15	+	9.21287e14i	−0.982582	+	0.713888i
$560$	−3.49268e14			−0.267994
$561$	−4.10906e14	+	2.84025e13i	−0.312210	+	0.0215805i
$562$	1.60016e15			1.20397
$563$	−1.14060e15	+	8.28692e14i	−0.849837	+	0.617443i	−0.925101	−	0.379721i	$-0.876020\pi$
$563$	−1.14060e15	+	8.28692e14i	−0.849837	+	0.617443i	0.0752639	+	0.997164i	$0.476020\pi$
$564$	8.41956e13	+	2.59128e14i	0.0621233	+	0.191196i
$565$	1.76809e14	−	5.44163e14i	0.129193	−	0.397615i
$566$	−3.30666e14	−	2.40243e14i	−0.239276	−	0.173844i
$567$	7.71654e12	+	5.60639e12i	0.00552988	+	0.00401769i
$568$	5.21993e13	−	1.60653e14i	0.0370466	−	0.114018i
$569$	−1.25580e14	−	3.86494e14i	−0.0882676	−	0.271660i	0.897173	−	0.441679i	$-0.145617\pi$
$569$	−1.25580e14	−	3.86494e14i	−0.0882676	−	0.271660i	−0.985441	+	0.170019i	$0.945617\pi$
$570$	9.91210e14	−	7.20156e14i	0.690007	−	0.501320i
$571$	−1.28684e15			−0.887207			−0.443604	−	0.896223i	$-0.646300\pi$
$571$	−1.28684e15			−0.887207			−0.443604	+	0.896223i	$0.646300\pi$
$572$	−7.49229e14	+	6.27656e14i	−0.511607	+	0.428591i
$573$	−1.28666e15			−0.870186
$574$	1.38422e15	−	1.00570e15i	0.927235	−	0.673676i
$575$	5.90269e14	+	1.81666e15i	0.391631	+	1.20532i
$576$	−3.61081e13	+	1.11129e14i	−0.0237291	+	0.0730306i
$577$	2.04930e15	+	1.48891e15i	1.33395	+	0.969171i	0.999643	+	0.0267069i	$0.00850209\pi$
$577$	2.04930e15	+	1.48891e15i	1.33395	+	0.969171i	0.334307	+	0.942464i	$0.391498\pi$
$578$	6.61944e14	+	4.80930e14i	0.426794	+	0.310084i
$579$	5.09074e14	−	1.56677e15i	0.325124	−	1.00063i
$580$	9.64617e12	+	2.96879e13i	0.00610241	+	0.0187813i
$581$	−1.24348e15	+	9.03440e14i	−0.779237	+	0.566149i
$582$	−2.59814e14			−0.161282
$583$	−1.00077e15	−	6.26465e14i	−0.615398	−	0.385230i
$584$	−1.98373e14			−0.120840
$585$	1.43288e15	−	1.04105e15i	0.864676	−	0.628224i
$586$	6.21635e13	+	1.91320e14i	0.0371620	+	0.114373i
$587$	7.20263e14	−	2.21674e15i	0.426561	−	1.31282i	−0.474930	−	0.880023i	$-0.657527\pi$
$587$	7.20263e14	−	2.21674e15i	0.426561	−	1.31282i	0.901491	−	0.432797i	$-0.142473\pi$
$588$	1.38562e14	+	1.00671e14i	0.0812960	+	0.0590650i
$589$	−2.36889e15	−	1.72110e15i	−1.37693	−	1.00040i
$590$	5.69010e14	−	1.75123e15i	0.327668	−	1.00846i
$591$	−4.56243e14	−	1.40417e15i	−0.260295	−	0.801105i
$592$	1.67129e14	−	1.21426e14i	0.0944673	−	0.0686345i
$593$	1.60143e13			0.00896824			0.00448412	−	0.999990i	$-0.498573\pi$
$593$	1.60143e13			0.00896824			0.00448412	+	0.999990i	$0.498573\pi$
$594$	4.77672e14	+	1.18501e15i	0.265035	+	0.657502i
$595$	−9.82633e14			−0.540192
$596$	1.15107e15	−	8.36300e14i	0.626970	−	0.455520i
$597$	−5.60294e14	−	1.72441e15i	−0.302383	−	0.930639i
$598$	−9.89032e14	+	3.04393e15i	−0.528876	+	1.62771i
$599$	−1.27818e15	−	9.28653e14i	−0.677243	−	0.492046i	0.195199	−	0.980764i	$-0.437465\pi$
$599$	−1.27818e15	−	9.28653e14i	−0.677243	−	0.492046i	−0.872442	+	0.488718i	$0.837465\pi$
$600$	−2.36479e14	−	1.71812e14i	−0.124154	−	0.0902030i
$601$	−1.06749e15	+	3.28539e15i	−0.555333	+	1.70914i	0.139729	+	0.990190i	$0.455377\pi$
$601$	−1.06749e15	+	3.28539e15i	−0.555333	+	1.70914i	−0.695062	+	0.718950i	$0.744623\pi$
$602$	−3.17203e14	−	9.76250e14i	−0.163514	−	0.503246i
$603$	3.72301e14	−	2.70493e14i	0.190173	−	0.138169i
$604$	−1.05123e14			−0.0532101
$605$	−2.57390e15	+	3.57532e14i	−1.29103	+	0.179333i
$606$	−1.29497e15			−0.643665
$607$	1.19666e14	−	8.69425e13i	0.0589431	−	0.0428247i	−0.557924	−	0.829892i	$-0.688402\pi$
$607$	1.19666e14	−	8.69425e13i	0.0589431	−	0.0428247i	0.616867	+	0.787068i	$0.288402\pi$
$608$	1.66757e14	+	5.13224e14i	0.0813979	+	0.250517i
$609$	−9.88682e12	+	3.04285e13i	−0.00478257	+	0.0147192i
$610$	−1.69912e15	−	1.23448e15i	−0.814536	−	0.591795i
$611$	1.47160e15	+	1.06918e15i	0.699136	+	0.507952i
$612$	−1.01587e14	+	3.12652e14i	−0.0478304	+	0.147207i
$613$	1.69345e14	+	5.21191e14i	0.0790207	+	0.243201i	0.982761	−	0.184880i	$-0.0591898\pi$
$613$	1.69345e14	+	5.21191e14i	0.0790207	+	0.243201i	−0.903740	+	0.428081i	$0.859190\pi$
$614$	8.03899e14	−	5.84067e14i	0.371771	−	0.270107i
$615$	3.48071e15			1.59534
$616$	−2.39310e14	−	5.93682e14i	−0.108709	−	0.269687i
$617$	−1.56720e15			−0.705594			−0.352797	−	0.935700i	$-0.614769\pi$
$617$	−1.56720e15			−0.705594			−0.352797	+	0.935700i	$0.614769\pi$
$618$	7.78910e14	−	5.65911e14i	0.347577	−	0.252529i
$619$	−1.14732e15	−	3.53107e15i	−0.507440	−	1.56174i	−0.796630	−	0.604467i	$-0.793386\pi$
$619$	−1.14732e15	−	3.53107e15i	−0.507440	−	1.56174i	0.289191	−	0.957271i	$-0.406614\pi$
$620$	−5.24736e14	+	1.61497e15i	−0.230031	+	0.707963i
$621$	3.38480e15	+	2.45920e15i	1.47072	+	1.06854i
$622$	1.48903e15	+	1.08185e15i	0.641295	+	0.465928i
$623$	−1.02377e15	+	3.15083e15i	−0.437035	+	1.34506i
$624$	−1.51348e14	−	4.65802e14i	−0.0640416	−	0.197100i
$625$	2.33473e15	−	1.69628e15i	0.979258	−	0.711473i
$626$	−2.39185e15			−0.994430
$627$	1.90326e15	+	1.19141e15i	0.784381	+	0.491010i
$628$	−6.50285e14			−0.265660
$629$	4.70201e14	−	3.41621e14i	0.190417	−	0.138346i
$630$	3.58438e14	+	1.10316e15i	0.143893	+	0.442858i
$631$	1.04828e15	−	3.22628e15i	0.417173	−	1.28393i	−0.493119	−	0.869962i	$-0.664143\pi$
$631$	1.04828e15	−	3.22628e15i	0.417173	−	1.28393i	0.910292	−	0.413966i	$-0.135857\pi$
$632$	7.21621e14	+	5.24289e14i	0.284686	+	0.206836i
$633$	3.22145e14	+	2.34052e14i	0.125988	+	0.0915360i
$634$	2.62361e14	−	8.07464e14i	0.101720	−	0.313063i
$635$	2.07768e14	+	6.39443e14i	0.0798588	+	0.245780i
$636$	4.78645e14	−	3.47756e14i	0.182389	−	0.132514i
$637$	1.14343e15			0.431960
$638$	−4.38537e13	+	3.67378e13i	−0.0164245	+	0.0137594i
$639$	−5.60989e14			−0.208305
$640$	2.53180e14	−	1.83946e14i	0.0932050	−	0.0677174i
$641$	1.35789e15	+	4.17917e15i	0.495618	+	1.52535i	0.815992	+	0.578063i	$0.196191\pi$
$641$	1.35789e15	+	4.17917e15i	0.495618	+	1.52535i	−0.320375	+	0.947291i	$0.603809\pi$
$642$	8.42805e13	−	2.59389e14i	0.0304989	−	0.0938660i
$643$	3.60811e15	+	2.62145e15i	1.29455	+	0.940547i	0.999887	−	0.0150532i	$-0.00479176\pi$
$643$	3.60811e15	+	2.62145e15i	1.29455	+	0.940547i	0.294666	+	0.955600i	$0.404792\pi$
$644$	−1.69576e15	−	1.23204e15i	−0.603242	−	0.438281i
$645$	6.45293e14	−	1.98601e15i	0.227603	−	0.700490i
$646$	4.69154e14	+	1.44391e15i	0.164073	+	0.504964i
$647$	−2.38889e15	+	1.73563e15i	−0.828366	+	0.601843i	−0.919097	−	0.394032i	$-0.871080\pi$
$647$	−2.38889e15	+	1.73563e15i	−0.828366	+	0.601843i	0.0907306	+	0.995875i	$0.471080\pi$
$648$	−8.54628e12			−0.00293843
$649$	3.36659e15	−	2.32704e14i	1.14774	−	0.0793339i
$650$	−1.95145e15			−0.659682
$651$	−1.40805e15	+	1.02301e15i	−0.471978	+	0.342912i
$652$	5.57925e14	+	1.71712e15i	0.185444	+	0.570739i
$653$	−4.96080e14	+	1.52678e15i	−0.163504	+	0.503214i	−0.998923	−	0.0463998i	$-0.985225\pi$
$653$	−4.96080e14	+	1.52678e15i	−0.163504	+	0.503214i	0.835419	+	0.549614i	$0.185225\pi$
$654$	−5.86949e12	−	4.26443e12i	−0.00191833	−	0.00139375i
$655$	1.21651e14	+	8.83848e13i	0.0394266	+	0.0286451i
$656$	−4.73743e14	+	1.45803e15i	−0.152255	+	0.468592i
$657$	2.03581e14	+	6.26556e14i	0.0648824	+	0.199687i
$658$	−9.63756e14	+	7.00209e14i	−0.304596	+	0.221302i
$659$	−1.22811e15			−0.384918			−0.192459	−	0.981305i	$-0.561646\pi$
$659$	−1.22811e15			−0.384918			−0.192459	+	0.981305i	$0.561646\pi$
$660$	3.16035e14	−	1.26324e15i	0.0982300	−	0.392638i
$661$	−1.72853e15			−0.532807			−0.266403	−	0.963862i	$-0.585835\pi$
$661$	−1.72853e15			−0.532807			−0.266403	+	0.963862i	$0.585835\pi$
$662$	3.09118e15	−	2.24587e15i	0.944942	−	0.686541i
$663$	−4.25804e14	−	1.31049e15i	−0.129088	−	0.397291i
$664$	4.25574e14	−	1.30978e15i	0.127953	−	0.393799i
$665$	4.33379e15	+	3.14868e15i	1.29226	+	0.938879i
$666$	−5.55039e14	−	4.03259e14i	−0.164140	−	0.119255i
$667$	−5.78898e13	+	1.78166e14i	−0.0169789	+	0.0522557i
$668$	3.13182e14	+	9.63875e14i	0.0911017	+	0.280382i
$669$	−1.35332e15	+	9.83242e14i	−0.390441	+	0.283672i
$670$	−1.23250e15			−0.352675
$671$	9.34164e14	−	3.73398e15i	0.265124	−	1.05974i
$672$	3.20755e14			0.0902905
$673$	−2.63717e14	+	1.91602e14i	−0.0736302	+	0.0534955i	−0.623991	−	0.781431i	$-0.714490\pi$
$673$	−2.63717e14	+	1.91602e14i	−0.0736302	+	0.0534955i	0.550361	+	0.834927i	$0.314490\pi$
$674$	−4.79929e14	−	1.47707e15i	−0.132907	−	0.409045i
$675$	−7.88293e14	+	2.42612e15i	−0.216529	+	0.666409i
$676$	−1.16062e15	−	8.43241e14i	−0.316216	−	0.229744i
$677$	−2.31187e15	−	1.67967e15i	−0.624777	−	0.453927i	0.229810	−	0.973236i	$-0.426190\pi$
$677$	−2.31187e15	−	1.67967e15i	−0.624777	−	0.453927i	−0.854587	+	0.519308i	$0.826190\pi$
$678$	−1.62375e14	+	4.99739e14i	−0.0435267	+	0.133961i
$679$	−3.51032e14	−	1.08037e15i	−0.0933390	−	0.287268i
$680$	7.12298e14	−	5.17515e14i	0.187872	−	0.136497i
$681$	−7.44105e13			−0.0194682
$682$	−3.10464e15	+	2.14598e14i	−0.805745	+	0.0556944i
$683$	2.11823e15			0.545330			0.272665	−	0.962109i	$-0.412095\pi$
$683$	2.11823e15			0.545330			0.272665	+	0.962109i	$0.412095\pi$
$684$	1.44987e15	−	1.05340e15i	0.370273	−	0.269019i
$685$	−1.68525e15	−	5.18667e15i	−0.426940	−	1.31399i
$686$	−9.46474e14	+	2.91295e15i	−0.237863	+	0.732066i
$687$	5.20638e14	+	3.78266e14i	0.129800	+	0.0943050i
$688$	7.44088e14	+	5.40612e14i	0.184030	+	0.133705i
$689$	1.22057e15	−	3.75652e15i	0.299472	−	0.921681i
$690$	−1.31768e15	−	4.05539e15i	−0.320729	−	0.987103i
$691$	2.53182e15	−	1.83947e15i	0.611368	−	0.444185i	−0.238528	−	0.971136i	$-0.576665\pi$
$691$	2.53182e15	−	1.83947e15i	0.611368	−	0.444185i	0.849896	+	0.526951i	$0.176665\pi$
$692$	−9.38512e14			−0.224831
$693$	−1.62954e15	+	1.36512e15i	−0.387286	+	0.324443i
$694$	−1.73648e15			−0.409443
$695$	2.85137e15	−	2.07164e15i	0.667018	−	0.484617i
$696$	−8.85868e12	−	2.72642e13i	−0.00205598	−	0.00632764i
$697$	−1.33283e15	+	4.10203e15i	−0.306898	+	0.944536i
$698$	1.32233e15	+	9.60732e14i	0.302090	+	0.219481i
$699$	−2.89558e14	−	2.10376e14i	−0.0656312	−	0.0476839i
$700$	3.94929e14	−	1.21547e15i	0.0888136	−	0.273340i
$701$	−1.73226e15	−	5.33135e15i	−0.386513	−	1.18956i	−0.935377	−	0.353652i	$-0.884940\pi$
$701$	−1.73226e15	−	5.33135e15i	−0.386513	−	1.18956i	0.548864	−	0.835911i	$-0.315060\pi$
$702$	−3.45799e15	+	2.51238e15i	−0.765543	+	0.556199i
$703$	−3.16843e15			−0.695969
$704$	4.86141e14	+	3.04317e14i	0.105953	+	0.0663248i
$705$	−2.42342e15			−0.524069
$706$	−4.42877e15	+	3.21769e15i	−0.950293	+	0.690428i
$707$	−1.74962e15	−	5.38477e15i	−0.372509	−	1.14646i
$708$	−5.22557e14	+	1.60827e15i	−0.110395	+	0.339762i
$709$	2.06089e15	+	1.49733e15i	0.432018	+	0.313879i	0.782455	−	0.622707i	$-0.213967\pi$
$709$	2.06089e15	+	1.49733e15i	0.432018	+	0.313879i	−0.350438	+	0.936586i	$0.613967\pi$
$710$	1.21552e15	+	8.83126e14i	0.252837	+	0.183697i
$711$	9.15390e14	−	2.81728e15i	0.188940	−	0.581497i
$712$	−9.17303e14	−	2.82317e15i	−0.187877	−	0.578225i
$713$	−8.24448e15	+	5.98996e15i	−1.67560	+	1.21740i
$714$	9.02413e14			0.181997
$715$	−3.25015e15	−	8.06301e15i	−0.650460	−	1.61367i
$716$	−7.51831e14			−0.149313
$717$	−2.15909e15	+	1.56867e15i	−0.425516	+	0.309155i
$718$	1.21276e15	+	3.73250e15i	0.237187	+	0.729987i
$719$	−3.46026e14	+	1.06496e15i	−0.0671583	+	0.206692i	−0.979004	−	0.203841i	$-0.934657\pi$
$719$	−3.46026e14	+	1.06496e15i	−0.0671583	+	0.206692i	0.911846	+	0.410533i	$0.134657\pi$
$720$	−8.40817e14	−	6.10889e14i	−0.161947	−	0.117661i
$721$	3.40557e15	+	2.47429e15i	0.650947	+	0.472941i
$722$	1.40569e15	−	4.32626e15i	0.266645	−	0.820650i
$723$	8.58289e14	+	2.64154e15i	0.161574	+	0.497275i
$724$	3.80132e15	−	2.76182e15i	0.710186	−	0.515980i
$725$	−1.14222e14			−0.0211783
$726$	2.36377e15	−	3.28344e14i	0.434964	−	0.0604195i
$727$	1.01882e14			0.0186062			0.00930310	−	0.999957i	$-0.497039\pi$
$727$	1.01882e14			0.0186062			0.00930310	+	0.999957i	$0.497039\pi$
$728$	1.73242e15	−	1.25868e15i	0.314002	−	0.228136i
$729$	1.07834e15	+	3.31878e15i	0.193979	+	0.597005i
$730$	5.45238e14	−	1.67807e15i	0.0973442	−	0.299595i
$731$	2.09342e15	+	1.52096e15i	0.370946	+	0.269508i
$732$	1.56041e15	+	1.13370e15i	0.274427	+	0.199383i
$733$	2.23075e15	−	6.86555e15i	0.389386	−	1.19841i	−0.543863	−	0.839174i	$-0.683039\pi$
$733$	2.23075e15	−	6.86555e15i	0.389386	−	1.19841i	0.933249	−	0.359231i	$-0.116961\pi$
$734$	1.68943e15	+	5.19953e15i	0.292693	+	0.900815i
$735$	−1.23244e15	+	8.95421e14i	−0.211927	+	0.153974i
$736$	1.87810e15			0.320546
$737$	−8.44477e14	−	2.09499e15i	−0.143059	−	0.354903i
$738$	5.09134e15			0.856095
$739$	1.40117e15	−	1.01801e15i	0.233854	−	0.169905i	−0.464687	−	0.885475i	$-0.653833\pi$
$739$	1.40117e15	−	1.01801e15i	0.233854	−	0.169905i	0.698541	+	0.715570i	$0.253833\pi$
$740$	5.67803e14	+	1.74752e15i	0.0940639	+	0.289499i
$741$	−2.32128e15	+	7.14417e15i	−0.381705	+	1.17477i
$742$	2.09274e15	+	1.52047e15i	0.341582	+	0.248174i
$743$	−1.21302e15	−	8.81313e14i	−0.196531	−	0.142788i	0.485168	−	0.874421i	$-0.338758\pi$
$743$	−1.21302e15	−	8.81313e14i	−0.196531	−	0.142788i	−0.681699	+	0.731633i	$0.738758\pi$
$744$	4.81898e14	−	1.48313e15i	0.0775003	−	0.238521i
$745$	3.91064e15	+	1.20357e16i	0.624292	+	1.92137i
$746$	4.13693e15	−	3.00565e15i	0.655563	−	0.476294i
$747$	−4.57367e15			−0.719452
$748$	1.36771e15	+	8.56166e14i	0.213568	+	0.133690i
$749$	1.19247e15			0.184840
$750$	−9.06075e14	+	6.58302e14i	−0.139421	+	0.101295i
$751$	1.37633e15	+	4.23590e15i	0.210234	+	0.647033i	0.999458	+	0.0329275i	$0.0104831\pi$
$751$	1.37633e15	+	4.23590e15i	0.210234	+	0.647033i	−0.789224	+	0.614105i	$0.789517\pi$
$752$	3.29841e14	−	1.01514e15i	0.0500156	−	0.153932i
$753$	−1.67290e15	−	1.21544e15i	−0.251825	−	0.182961i
$754$	−1.54835e14	−	1.12494e14i	−0.0231380	−	0.0168107i
$755$	2.88936e14	−	8.89253e14i	0.0428641	−	0.131922i
$756$	−8.65021e14	−	2.66226e15i	−0.127396	−	0.392085i
$757$	−7.84440e15	+	5.69929e15i	−1.14692	+	0.833285i	−0.988068	−	0.154018i	$-0.950779\pi$
$757$	−7.84440e15	+	5.69929e15i	−1.14692	+	0.833285i	−0.158850	+	0.987303i	$0.550779\pi$
$758$	−7.64228e15			−1.10928
$759$	5.99045e15	−	5.01841e15i	0.863237	−	0.723164i
$760$	−4.79979e15			−0.686669
$761$	3.72011e15	−	2.70282e15i	0.528372	−	0.383885i	−0.291376	−	0.956609i	$-0.594113\pi$
$761$	3.72011e15	−	2.70282e15i	0.528372	−	0.383885i	0.819749	+	0.572724i	$0.194113\pi$
$762$	−1.90806e14	−	5.87240e14i	−0.0269054	−	0.0828063i
$763$	9.80228e12	−	3.01683e13i	0.00137228	−	0.00422344i
$764$	4.07788e15	+	2.96275e15i	0.566788	+	0.411796i
$765$	−2.36556e15	−	1.71868e15i	−0.326434	−	0.237168i
$766$	2.53820e15	−	7.81176e15i	0.347750	−	1.07026i
$767$	3.48865e15	+	1.07370e16i	0.474551	+	1.46052i
$768$	−2.32511e14	+	1.68929e14i	−0.0314019	+	0.0228148i
$769$	−1.01837e16			−1.36556			−0.682782	−	0.730622i	$-0.739230\pi$
$769$	−1.01837e16			−1.36556			−0.682782	+	0.730622i	$0.739230\pi$
$770$	5.67981e15	−	3.92598e14i	0.756197	−	0.0522696i
$771$	−5.34985e15			−0.707201
$772$	−5.22121e15	+	3.79343e15i	−0.685292	+	0.497894i
$773$	2.00265e15	+	6.16351e15i	0.260986	+	0.803232i	0.992591	+	0.121503i	$0.0387715\pi$
$773$	2.00265e15	+	6.16351e15i	0.260986	+	0.803232i	−0.731605	+	0.681729i	$0.761228\pi$
$774$	9.43890e14	−	2.90499e15i	0.122137	−	0.375898i
$775$	−5.02682e15	−	3.65220e15i	−0.645853	−	0.469240i
$776$	8.23445e14	+	5.98268e14i	0.105050	+	0.0763231i
$777$	−5.81968e14	+	1.79111e15i	−0.0737197	+	0.226886i
$778$	2.65707e15	+	8.17762e15i	0.334207	+	1.02858i
$779$	1.90225e16	−	1.38207e16i	2.37581	−	1.72613i
$780$	4.35629e15			0.540252
$781$	−6.68283e14	+	2.67122e15i	−0.0822962	+	0.328949i
$782$	5.28385e15			0.646121
$783$	−2.02402e14	+	1.47054e14i	−0.0245768	+	0.0178561i
$784$	−2.07340e14	−	6.38128e14i	−0.0250003	−	0.0769430i
$785$	1.78734e15	−	5.50088e15i	0.214005	−	0.658641i
$786$	−1.11720e14	−	8.11692e13i	−0.0132833	−	0.00965089i
$787$	1.39817e15	+	1.01583e15i	0.165082	+	0.119939i	0.667259	−	0.744826i	$-0.267467\pi$
$787$	1.39817e15	+	1.01583e15i	0.165082	+	0.119939i	−0.502177	+	0.864765i	$0.667467\pi$
$788$	−1.78736e15	+	5.50092e15i	−0.209564	+	0.644972i
$789$	−3.20135e15	−	9.85275e15i	−0.372743	−	1.14719i
$790$	−6.41847e15	+	4.66329e15i	−0.742134	+	0.539192i
$791$	−2.29741e15			−0.263796
$792$	4.62275e14	−	1.84777e15i	0.0527123	−	0.210698i
$793$	1.28767e16			1.45815
$794$	1.81627e15	−	1.31960e15i	0.204252	−	0.148398i
$795$	1.62615e15	+	5.00477e15i	0.181611	+	0.558940i
$796$	−2.19498e15	+	6.75545e15i	−0.243449	+	0.749260i
$797$	−3.68688e15	−	2.67867e15i	−0.406104	−	0.295052i	0.365918	−	0.930647i	$-0.380755\pi$
$797$	−3.68688e15	−	2.67867e15i	−0.406104	−	0.295052i	−0.772023	+	0.635595i	$0.780755\pi$
$798$	−3.97998e15	−	2.89163e15i	−0.435377	−	0.316320i
$799$	9.27975e14	−	2.85601e15i	0.100816	−	0.310279i
$800$	3.53860e14	+	1.08907e15i	0.0381800	+	0.117506i
$801$	−7.97554e15	+	5.79457e15i	−0.854637	+	0.620930i
$802$	−3.05198e15			−0.324805
$803$	3.22594e15	−	2.22982e14i	0.340974	−	0.0235687i
$804$	1.13188e15			0.118821
$805$	1.50829e16	−	1.09584e16i	1.57256	−	1.14253i
$806$	−3.21720e15	−	9.90153e15i	−0.333147	−	1.02532i
$807$	−4.09381e14	+	1.25994e15i	−0.0421040	+	0.129583i
$808$	4.10423e15	+	2.98189e15i	0.419246	+	0.304600i
$809$	7.43128e15	+	5.39914e15i	0.753957	+	0.547782i	0.897051	−	0.441927i	$-0.145705\pi$
$809$	7.43128e15	+	5.39914e15i	0.753957	+	0.547782i	−0.143094	+	0.989709i	$0.545705\pi$
$810$	2.34899e13	−	7.22945e13i	0.00236708	−	0.00728514i
$811$	2.38455e15	+	7.33889e15i	0.238667	+	0.734541i	0.996614	+	0.0822247i	$0.0262025\pi$
$811$	2.38455e15	+	7.33889e15i	0.238667	+	0.734541i	−0.757947	+	0.652316i	$0.773797\pi$
$812$	1.01402e14	−	7.36728e13i	0.0100806	−	0.00732401i
$813$	1.93657e15			0.191221
$814$	−2.58136e15	+	2.16250e15i	−0.253171	+	0.212091i
$815$	−1.60589e16			−1.56440
$816$	−6.54147e14	+	4.75266e14i	−0.0632965	+	0.0459876i
$817$	−4.35913e15	−	1.34160e16i	−0.418966	−	1.28944i
$818$	2.83844e15	−	8.73583e15i	0.270980	−	0.833991i
$819$	−5.75343e15	−	4.18011e15i	−0.545588	−	0.396393i
$820$	−1.10316e16	−	8.01494e15i	−1.03911	−	0.754961i
$821$	−3.45453e15	+	1.06319e16i	−0.323222	+	0.994776i	0.649014	+	0.760776i	$0.275182\pi$
$821$	−3.45453e15	+	1.06319e16i	−0.323222	+	0.994776i	−0.972237	+	0.234000i	$0.924818\pi$
$822$	1.54767e15	+	4.76324e15i	0.143841	+	0.442698i
$823$	1.40981e15	−	1.02429e15i	0.130155	−	0.0945632i	−0.520803	−	0.853677i	$-0.674367\pi$
$823$	1.40981e15	−	1.02429e15i	0.130155	−	0.0945632i	0.650958	+	0.759114i	$0.274367\pi$
$824$	−3.77176e15			−0.345895
$825$	4.03875e15	+	2.52819e15i	0.367917	+	0.230310i
$826$	−7.39356e15			−0.669057
$827$	−7.30177e15	+	5.30505e15i	−0.656369	+	0.476880i	−0.865435	−	0.501022i	$-0.832958\pi$
$827$	−7.30177e15	+	5.30505e15i	−0.656369	+	0.476880i	0.209066	+	0.977902i	$0.432958\pi$
$828$	−1.92741e15	−	5.93194e15i	−0.172110	−	0.529700i
$829$	−7.41648e14	+	2.28256e15i	−0.0657881	+	0.202475i	−0.978547	−	0.206024i	$-0.933948\pi$
$829$	−7.41648e14	+	2.28256e15i	−0.0657881	+	0.202475i	0.912759	+	0.408499i	$0.133948\pi$
$830$	9.90997e15	+	7.20001e15i	0.873259	+	0.634459i
$831$	−6.21960e15	−	4.51880e15i	−0.544448	−	0.395565i
$832$	−5.92914e14	+	1.82480e15i	−0.0515600	+	0.158685i
$833$	−5.83332e14	−	1.79531e15i	−0.0503928	−	0.155093i
$834$	−2.61859e15	+	1.90252e15i	−0.224727	+	0.163274i
$835$	−9.01439e15			−0.768530
$836$	−3.28869e15	−	8.15862e15i	−0.278541	−	0.691006i
$837$	−1.36095e16			−1.14513
$838$	1.74264e15	−	1.26610e15i	0.145668	−	0.105834i
$839$	3.40026e13	+	1.04649e14i	0.00282372	+	0.00869052i	0.952458	−	0.304669i	$-0.0985457\pi$
$839$	3.40026e13	+	1.04649e14i	0.00282372	+	0.00869052i	−0.949635	+	0.313359i	$0.898546\pi$
$840$	−8.81611e14	+	2.71332e15i	−0.0727346	+	0.223854i
$841$	9.86136e15	+	7.16470e15i	0.808274	+	0.587246i
$842$	−2.01795e15	−	1.46613e15i	−0.164321	−	0.119387i
$843$	4.03908e15	−	1.24310e16i	0.326762	−	1.00567i
$844$	−4.82048e14	−	1.48359e15i	−0.0387442	−	0.119242i
$845$	1.03232e16	−	7.50021e15i	0.824329	−	0.598910i
$846$	−3.54482e15			−0.281227
$847$	4.55899e15	+	9.38547e15i	0.359344	+	0.739771i
$848$	−2.31777e15			−0.181507
$849$	−2.70101e15	+	1.96240e15i	−0.210152	+	0.152684i
$850$	9.95551e14	+	3.06399e15i	0.0769590	+	0.236855i
$851$	−3.40757e15	+	1.04874e16i	−0.261717	+	0.805482i
$852$	−1.11629e15	−	8.11029e14i	−0.0851839	−	0.0618897i
$853$	−1.12417e16	−	8.16761e15i	−0.852343	−	0.619263i	0.0734483	−	0.997299i	$-0.476600\pi$
$853$	−1.12417e16	−	8.16761e15i	−0.852343	−	0.619263i	−0.925791	+	0.378036i	$0.876600\pi$
$854$	−2.60594e15	+	8.02026e15i	−0.196312	+	0.604186i
$855$	4.92580e15	+	1.51601e16i	0.368691	+	1.13472i
$856$	−8.64404e14	+	6.28026e14i	−0.0642852	+	0.0467059i
$857$	1.65952e16			1.22627			0.613137	−	0.789977i	$-0.289908\pi$
$857$	1.65952e16			1.22627			0.613137	+	0.789977i	$0.289908\pi$
$858$	2.98482e15	+	7.40476e15i	0.219148	+	0.543664i
$859$	1.36118e16			0.993005			0.496503	−	0.868035i	$-0.334617\pi$
$859$	1.36118e16			0.993005			0.496503	+	0.868035i	$0.334617\pi$
$860$	−6.61830e15	+	4.80848e15i	−0.479739	+	0.348551i
$861$	−4.31882e15	−	1.32920e16i	−0.311063	−	0.957353i
$862$	2.08291e15	−	6.41053e15i	0.149066	−	0.458779i
$863$	6.32164e15	+	4.59294e15i	0.449542	+	0.326612i	0.789415	−	0.613860i	$-0.210384\pi$
$863$	6.32164e15	+	4.59294e15i	0.449542	+	0.326612i	−0.339873	+	0.940471i	$0.610384\pi$
$864$	2.02915e15	+	1.47426e15i	0.143380	+	0.104172i
$865$	2.57955e15	−	7.93904e15i	0.181115	−	0.557416i
$866$	−4.65467e15	−	1.43256e16i	−0.324744	−	0.999459i
$867$	5.40700e15	−	3.92842e15i	0.374845	−	0.272341i
$868$	6.81827e15			0.469695
$869$	−1.23244e16	−	7.71486e15i	−0.843637	−	0.528103i
$870$	2.54981e14			0.0173441
$871$	6.11339e15	−	4.44164e15i	0.413221	−	0.300222i
$872$	8.78293e12	+	2.70311e13i	0.000589928	+	0.00181561i
$873$	1.04456e15	−	3.21481e15i	0.0697193	−	0.214574i
$874$	−2.33038e16	−	1.69312e16i	−1.54566	−	1.12299i
$875$	−3.96156e15	−	2.87824e15i	−0.261109	−	0.189707i
$876$	−5.00725e14	+	1.54107e15i	−0.0327965	+	0.100937i
$877$	−4.60719e15	−	1.41795e16i	−0.299874	−	0.922916i	−0.981541	−	0.191253i	$-0.938745\pi$
$877$	−4.60719e15	−	1.41795e16i	−0.299874	−	0.922916i	0.681667	−	0.731662i	$-0.261255\pi$
$878$	−5.16856e15	+	3.75518e15i	−0.334310	+	0.242891i
$879$	1.64319e15			0.105621
$880$	−3.91045e15	+	3.27592e15i	−0.249789	+	0.209257i
$881$	2.46470e16			1.56458			0.782289	−	0.622915i	$-0.214052\pi$
$881$	2.46470e16			1.56458			0.782289	+	0.622915i	$0.214052\pi$
$882$	−1.80273e15	+	1.30976e15i	−0.113724	+	0.0826256i
$883$	3.18160e15	+	9.79197e15i	0.199463	+	0.613884i	0.999895	+	0.0144609i	$0.00460322\pi$
$883$	3.18160e15	+	9.79197e15i	0.199463	+	0.613884i	−0.800432	+	0.599423i	$0.795397\pi$
$884$	−1.66811e15	+	5.13390e15i	−0.103929	+	0.319860i
$885$	−1.21683e16	−	8.84081e15i	−0.753430	−	0.547399i
$886$	1.15771e16	+	8.41124e15i	0.712383	+	0.517577i
$887$	−5.68827e15	+	1.75067e16i	−0.347857	+	1.07059i	0.612180	+	0.790719i	$0.290293\pi$
$887$	−5.68827e15	+	1.75067e16i	−0.347857	+	1.07059i	−0.960037	+	0.279875i	$0.909707\pi$
$888$	−5.21448e14	−	1.60485e15i	−0.0316913	−	0.0975358i
$889$	2.18408e15	−	1.58683e15i	0.131920	−	0.0958452i
$890$	2.64029e16			1.58492
$891$	1.38980e14	−	9.60652e12i	0.00829134	−	0.000573111i
$892$	6.55324e15			0.388552
$893$	−1.32443e16	+	9.62257e15i	−0.780453	+	0.567033i
$894$	−3.59138e15	−	1.10531e16i	−0.210332	−	0.647335i
$895$	2.06645e15	−	6.35987e15i	0.120281	−	0.370187i
$896$	−1.01659e15	−	7.38595e14i	−0.0588100	−	0.0427279i
$897$	2.11505e16	+	1.53668e16i	1.21608	+	0.883535i
$898$	−4.49130e15	+	1.38228e16i	−0.256656	+	0.789907i
$899$	−1.88309e14	−	5.79554e14i	−0.0106953	−	0.0329167i
$900$	3.07665e15	−	2.23532e15i	0.173678	−	0.126184i
$901$	−6.52083e15			−0.365861
$902$	6.06511e15	−	2.42430e16i	0.338222	−	1.35192i
$903$	−8.38475e15			−0.464737
$904$	1.66536e15	−	1.20996e15i	0.0917450	−	0.0666567i
$905$	1.29146e16	+	3.97470e16i	0.707153	+	2.17639i
$906$	−2.65348e14	+	8.16656e14i	−0.0144414	+	0.0444462i
$907$	−4.68590e15	−	3.40450e15i	−0.253485	−	0.184168i	0.453785	−	0.891111i	$-0.350073\pi$
$907$	−4.68590e15	−	3.40450e15i	−0.253485	−	0.184168i	−0.707270	+	0.706944i	$0.750073\pi$
$908$	2.35834e14	+	1.71343e14i	0.0126804	+	0.00921288i
$909$	5.20629e15	−	1.60233e16i	0.278245	−	0.856349i
$910$	5.88574e15	+	1.81144e16i	0.312661	+	0.962271i
$911$	1.68359e16	−	1.22320e16i	0.888967	−	0.645872i	−0.0466417	−	0.998912i	$-0.514852\pi$
$911$	1.68359e16	−	1.22320e16i	0.888967	−	0.645872i	0.935608	+	0.353040i	$0.114852\pi$
$912$	4.40794e15			0.231347
$913$	−5.44843e15	+	2.17781e16i	−0.284238	+	1.13614i
$914$	1.45793e16			0.756017
$915$	−1.38790e16	+	1.00837e16i	−0.715391	+	0.519762i
$916$	−7.79067e14	−	2.39772e15i	−0.0399162	−	0.122850i
$917$	1.86577e14	−	5.74224e14i	0.00950223	−	0.0292449i
$918$	5.70882e15	+	4.14770e15i	0.289009	+	0.209977i
$919$	7.91005e15	+	5.74699e15i	0.398056	+	0.289204i	0.768749	−	0.639551i	$-0.220880\pi$
$919$	7.91005e15	+	5.74699e15i	0.398056	+	0.289204i	−0.370693	+	0.928756i	$0.620880\pi$
$920$	−5.16206e15	+	1.58872e16i	−0.258220	+	0.794719i
$921$	−2.50820e15	−	7.71944e15i	−0.124719	−	0.383847i
$922$	−1.42295e16	+	1.03383e16i	−0.703346	+	0.511011i
$923$	−9.21174e15			−0.452618
$924$	−5.21612e15	+	3.60547e14i	−0.254772	+	0.0176103i
$925$	−6.72345e15			−0.326447
$926$	4.30519e15	−	3.12791e15i	0.207794	−	0.150971i
$927$	3.87078e15	+	1.19130e16i	0.185721	+	0.571589i
$928$	−3.47043e13	+	1.06809e14i	−0.00165527	+	0.00509440i
$929$	3.24679e15	+	2.35893e15i	0.153946	+	0.111848i	0.662092	−	0.749423i	$-0.269669\pi$
$929$	3.24679e15	+	2.35893e15i	0.153946	+	0.111848i	−0.508146	+	0.861271i	$0.669669\pi$
$930$	1.12215e16	+	8.15291e15i	0.528927	+	0.384288i
$931$	−3.18005e15	+	9.78720e15i	−0.149009	+	0.458601i
$932$	4.33286e14	+	1.33352e15i	0.0201830	+	0.0621170i
$933$	1.21630e16	−	8.83693e15i	0.563237	−	0.409216i
$934$	1.33591e16			0.614994
$935$	−1.10017e16	+	9.21650e15i	−0.503496	+	0.421796i
$936$	6.37208e15			0.289911
$937$	5.47094e15	−	3.97487e15i	0.247454	−	0.179786i	−0.457144	−	0.889393i	$-0.651128\pi$
$937$	5.47094e15	−	3.97487e15i	0.247454	−	0.179786i	0.704598	+	0.709607i	$0.251128\pi$
$938$	1.52927e15	+	4.70662e15i	0.0687653	+	0.211638i
$939$	−6.03742e15	+	1.85813e16i	−0.269892	+	0.830643i
$940$	7.68070e15	+	5.58036e15i	0.341348	+	0.248004i
$941$	−6.45025e15	−	4.68638e15i	−0.284993	−	0.207059i	0.436100	−	0.899898i	$-0.356360\pi$
$941$	−6.45025e15	−	4.68638e15i	−0.284993	−	0.207059i	−0.721092	+	0.692839i	$0.756360\pi$
$942$	−1.64143e15	+	5.05179e15i	−0.0721011	+	0.221904i
$943$	−2.52878e16	−	7.78279e16i	−1.10432	−	3.39876i
$944$	5.35949e15	−	3.89390e15i	0.232690	−	0.169059i
$945$	2.48981e16			1.07471
$946$	−1.27081e16	−	7.95505e15i	−0.545354	−	0.341383i
$947$	−2.10078e16			−0.896305			−0.448152	−	0.893957i	$-0.647918\pi$
$947$	−2.10078e16			−0.896305			−0.448152	+	0.893957i	$0.647918\pi$
$948$	5.89447e15	−	4.28259e15i	0.250034	−	0.181660i
$949$	3.34290e15	+	1.02884e16i	0.140981	+	0.433894i
$950$	5.42727e15	−	1.67034e16i	0.227563	−	0.700367i
$951$	−5.61061e15	−	4.07635e15i	−0.233893	−	0.169933i
$952$	−2.86007e15	−	2.07797e15i	−0.118543	−	0.0861262i
$953$	4.96902e15	−	1.52931e16i	0.204767	−	0.630207i	−0.794956	−	0.606667i	$-0.792506\pi$
$953$	4.96902e15	−	1.52931e16i	0.204767	−	0.630207i	0.999723	−	0.0235403i	$-0.00749381\pi$
$954$	2.37862e15	+	7.32064e15i	0.0974561	+	0.299939i
$955$	−3.62707e16	+	2.63522e16i	−1.47753	+	1.07349i
$956$	1.04551e16			0.423457
$957$	1.74707e14	+	4.33414e14i	0.00703548	+	0.0174537i
$958$	−1.73531e16			−0.694812
$959$	−1.77156e16	+	1.28711e16i	−0.705267	+	0.512407i
$960$	−7.89932e14	−	2.43116e15i	−0.0312678	−	0.0962325i
$961$	2.39203e15	−	7.36191e15i	0.0941430	−	0.289742i
$962$	−9.11403e15	−	6.62173e15i	−0.356654	−	0.259125i
$963$	2.87071e15	+	2.08569e15i	0.111698	+	0.0811531i
$964$	3.36239e15	−	1.03484e16i	0.130084	−	0.400358i
$965$	−1.77385e16	−	5.45936e16i	−0.682366	−	2.10011i
$966$	−1.38516e16	+	1.00638e16i	−0.529816	+	0.384934i
$967$	2.39392e16			0.910465			0.455233	−	0.890373i	$-0.349556\pi$
$967$	2.39392e16			0.910465			0.455233	+	0.890373i	$0.349556\pi$
$968$	−8.24771e15	−	4.40236e15i	−0.311903	−	0.166483i
$969$	1.24013e16			0.466324
$970$	−7.32413e15	+	5.32130e15i	−0.273849	+	0.198963i
$971$	3.78322e15	+	1.16436e16i	0.140655	+	0.432893i	0.996427	−	0.0844614i	$-0.0269170\pi$
$971$	3.78322e15	+	1.16436e16i	0.140655	+	0.432893i	−0.855771	+	0.517354i	$0.826917\pi$
$972$	4.16851e15	−	1.28294e16i	0.154105	−	0.474286i
$973$	−1.14491e16	−	8.31823e15i	−0.420871	−	0.305781i
$974$	−5.44196e15	−	3.95381e15i	−0.198921	−	0.144525i
$975$	−4.92579e15	+	1.51600e16i	−0.179040	+	0.551029i
$976$	−2.33495e15	−	7.18623e15i	−0.0843923	−	0.259733i
$977$	1.58330e16	−	1.15033e16i	0.569040	−	0.413432i	−0.265716	−	0.964051i	$-0.585608\pi$
$977$	1.58330e16	−	1.15033e16i	0.569040	−	0.413432i	0.834756	+	0.550620i	$0.185608\pi$
$978$	1.47478e16			0.527066
$979$	1.80906e16	+	4.48794e16i	0.642908	+	1.59493i
$980$	5.96792e15			0.210902
$981$	7.63637e13	−	5.54815e13i	0.00268354	−	0.00194970i
$982$	−5.41131e15	−	1.66543e16i	−0.189099	−	0.581987i
$983$	1.51118e16	−	4.65092e16i	0.525135	−	1.61620i	−0.238915	−	0.971041i	$-0.576792\pi$
$983$	1.51118e16	−	4.65092e16i	0.525135	−	1.61620i	0.764049	−	0.645158i	$-0.223208\pi$
$984$	1.01310e16	+	7.36062e15i	0.350090	+	0.254356i
$985$	−4.16206e16	−	3.02391e16i	−1.43024	−	1.03913i
$986$	−9.76372e13	+	3.00497e14i	−0.00333651	+	0.0102687i
$987$	3.00696e15	+	9.25446e15i	0.102184	+	0.314490i
$988$	2.38077e16	−	1.72973e16i	0.804552	−	0.584541i
$989$	−4.90948e16			−1.64989
$990$	1.43601e16	+	8.98917e15i	0.479913	+	0.300418i
$991$	3.96995e16			1.31941			0.659705	−	0.751524i	$-0.270681\pi$
$991$	3.96995e16			1.31941			0.659705	+	0.751524i	$0.270681\pi$
$992$	−4.94247e15	+	3.59092e15i	−0.163354	+	0.118684i
$993$	−9.64460e15	−	2.96830e16i	−0.317003	−	0.975635i
$994$	1.86424e15	−	5.73755e15i	0.0609364	−	0.187543i
$995$	−5.11126e16	−	3.71354e16i	−1.66150	−	1.20715i
$996$	−9.10094e15	−	6.61222e15i	−0.294212	−	0.213757i
$997$	−1.28657e16	+	3.95966e16i	−0.413628	+	1.27302i	0.499844	+	0.866116i	$0.333391\pi$
$997$	−1.28657e16	+	3.95966e16i	−0.413628	+	1.27302i	−0.913472	+	0.406901i	$0.866609\pi$
$998$	6.05266e14	+	1.86282e15i	0.0193521	+	0.0595597i
$999$	−1.19140e16	+	8.65603e15i	−0.378833	+	0.275238i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.12.c.a.3.4	✓	20
11.2	odd	10		242.12.a.m.1.7		10
11.4	even	5	inner	22.12.c.a.15.4	yes	20
11.9	even	5		242.12.a.n.1.7		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.12.c.a.3.4	✓	20	1.1	even	1	trivial
22.12.c.a.15.4	yes	20	11.4	even	5	inner
242.12.a.m.1.7		10	11.2	odd	10
242.12.a.n.1.7		10	11.9	even	5

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 22 = 2 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	22.c (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-25.8885 + 18.8091i) q^{2} +(80.7733 + 248.595i) q^{3} +(316.433 - 973.882i) q^{4} +(7368.51 + 5353.53i) q^{5} +(-6766.95 - 4916.48i) q^{6} +(11301.1 - 34781.1i) q^{7} +(10125.9 + 31164.2i) q^{8} +(88039.9 - 63964.8i) q^{9} +O(q^{10})\)	\(q+(-25.8885 + 18.8091i) q^{2} +(80.7733 + 248.595i) q^{3} +(316.433 - 973.882i) q^{4} +(7368.51 + 5353.53i) q^{5} +(-6766.95 - 4916.48i) q^{6} +(11301.1 - 34781.1i) q^{7} +(10125.9 + 31164.2i) q^{8} +(88039.9 - 63964.8i) q^{9} -291455. q^{10} +(-199698. - 495411. i) q^{11} +267661. q^{12} +(1.44566e6 - 1.05034e6i) q^{13} +(361635. + 1.11300e6i) q^{14} +(-735681. + 2.26419e6i) q^{15} +(-848316. - 616338. i) q^{16} +(-2.38666e6 - 1.73401e6i) q^{17} +(-1.07610e6 + 3.31191e6i) q^{18} +(4.96973e6 + 1.52953e7i) q^{19} +(7.54535e6 - 5.48202e6i) q^{20} +9.55923e6 q^{21} +(1.44881e7 + 9.06934e6i) q^{22} +5.59717e7 q^{23} +(-6.92936e6 + 5.03447e6i) q^{24} +(1.05458e7 + 3.24568e7i) q^{25} +(-1.76702e7 + 5.43833e7i) q^{26} +(6.04734e7 + 4.39365e7i) q^{27} +(-3.02967e7 - 2.20118e7i) q^{28} +(-1.03427e6 + 3.18315e6i) q^{29} +(-2.35418e7 - 7.24542e7i) q^{30} +(-1.47297e8 + 1.07018e8i) q^{31} +3.35544e7 q^{32} +(1.07026e8 - 8.96598e7i) q^{33} +9.44022e7 q^{34} +(2.69474e8 - 1.95784e8i) q^{35} +(-3.44353e7 - 1.05981e8i) q^{36} +(-6.08802e7 + 1.87370e8i) q^{37} +(-4.16350e8 - 3.02496e8i) q^{38} +(3.77879e8 + 2.74545e8i) q^{39} +(-9.22261e7 + 2.83843e8i) q^{40} +(-4.51796e8 - 1.39049e9i) q^{41} +(-2.47475e8 + 1.79801e8i) q^{42} -8.77136e8 q^{43} +(-5.45663e8 + 3.77171e7i) q^{44} +9.91160e8 q^{45} +(-1.44903e9 + 1.05278e9i) q^{46} +(3.14560e8 + 9.68117e8i) q^{47} +(8.46970e7 - 2.60670e8i) q^{48} +(5.17677e8 + 3.76114e8i) q^{49} +(-8.83500e8 - 6.41900e8i) q^{50} +(2.38287e8 - 7.33372e8i) q^{51} +(-5.65447e8 - 1.74027e9i) q^{52} +(1.78825e9 - 1.29924e9i) q^{53} -2.39197e9 q^{54} +(1.18073e9 - 4.71953e9i) q^{55} +1.19836e9 q^{56} +(-3.40090e9 + 2.47090e9i) q^{57} +(-3.30966e7 - 1.01861e8i) q^{58} +(-1.95231e9 + 6.00859e9i) q^{59} +(1.97226e9 + 1.43293e9i) q^{60} +(5.82978e9 + 4.23559e9i) q^{61} +(1.80040e9 - 5.54106e9i) q^{62} +(-1.22982e9 - 3.78500e9i) q^{63} +(-8.68675e8 + 6.31130e8i) q^{64} +1.62754e10 q^{65} +(-1.08434e9 + 4.33424e9i) q^{66} +4.22878e9 q^{67} +(-2.44394e9 + 1.77562e9i) q^{68} +(4.52102e9 + 1.39143e10i) q^{69} +(-3.29376e9 + 1.01371e10i) q^{70} +(-4.17052e9 - 3.03006e9i) q^{71} +(2.88489e9 + 2.09600e9i) q^{72} +(-1.87074e9 + 5.75756e9i) q^{73} +(-1.94817e9 - 5.99584e9i) q^{74} +(-7.21676e9 + 5.24328e9i) q^{75} +1.64684e10 q^{76} +(-1.94878e10 + 1.34703e9i) q^{77} -1.49467e10 q^{78} +(2.20221e10 - 1.60000e10i) q^{79} +(-2.95124e9 - 9.08297e9i) q^{80} +(-8.05953e7 + 2.48047e8i) q^{81} +(3.78502e10 + 2.74997e10i) q^{82} +(-3.40017e10 - 2.47037e10i) q^{83} +(3.02486e9 - 9.30957e9i) q^{84} +(-8.30302e9 - 2.55541e10i) q^{85} +(2.27078e10 - 1.64982e10i) q^{86} -8.74856e8 q^{87} +(1.34170e10 - 1.12399e10i) q^{88} -9.05901e10 q^{89} +(-2.56597e10 + 1.86429e10i) q^{90} +(-2.01943e10 - 6.21517e10i) q^{91} +(1.77113e10 - 5.45098e10i) q^{92} +(-3.85017e10 - 2.79731e10i) q^{93} +(-2.63530e10 - 1.91465e10i) q^{94} +(-4.52642e10 + 1.39309e11i) q^{95} +(2.71030e9 + 8.34145e9i) q^{96} +(2.51295e10 - 1.82577e10i) q^{97} -2.04763e10 q^{98} +(-4.92702e10 - 3.08424e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 160 q^{2} + 56 q^{3} - 5120 q^{4} - 362 q^{5} - 3488 q^{6} - 167178 q^{7} - 163840 q^{8} + 206411 q^{9}+O(q^{10}) \) 20 * q - 160 * q^2 + 56 * q^3 - 5120 * q^4 - 362 * q^5 - 3488 * q^6 - 167178 * q^7 - 163840 * q^8 + 206411 * q^9	\( 20 q - 160 q^{2} + 56 q^{3} - 5120 q^{4} - 362 q^{5} - 3488 q^{6} - 167178 q^{7} - 163840 q^{8} + 206411 q^{9} - 354944 q^{10} - 449801 q^{11} + 108544 q^{12} + 3369596 q^{13} - 5349696 q^{14} + 12264628 q^{15} - 5242880 q^{16} + 1661262 q^{17} - 19177088 q^{18} + 49176291 q^{19} - 370688 q^{20} - 74218796 q^{21} - 5153632 q^{22} - 127653292 q^{23} - 3571712 q^{24} + 33758041 q^{25} - 99025728 q^{26} - 135657199 q^{27} + 156930048 q^{28} + 555960754 q^{29} + 392468096 q^{30} - 13977916 q^{31} + 671088640 q^{32} - 1768265081 q^{33} - 357119936 q^{34} + 584997860 q^{35} - 613666816 q^{36} - 161000626 q^{37} - 1456805888 q^{38} + 1145816470 q^{39} + 193593344 q^{40} + 772614122 q^{41} - 545038272 q^{42} + 3749722062 q^{43} - 50755584 q^{44} - 1321716548 q^{45} - 1394938624 q^{46} + 1924889212 q^{47} + 58720256 q^{48} + 822161735 q^{49} - 805012448 q^{50} + 5262939047 q^{51} - 3168823296 q^{52} + 1531782992 q^{53} + 295824512 q^{54} + 3851857218 q^{55} + 912654336 q^{56} - 17257259731 q^{57} + 17790744128 q^{58} - 16014164779 q^{59} - 3503935488 q^{60} + 7822116636 q^{61} + 6939975808 q^{62} - 79975953122 q^{63} - 5368709120 q^{64} + 73754374272 q^{65} - 3094015232 q^{66} - 22092583538 q^{67} + 1701132288 q^{68} + 43044165458 q^{69} - 5227997760 q^{70} + 23107180542 q^{71} + 6763675648 q^{72} + 55731754682 q^{73} - 5152020032 q^{74} - 37848703409 q^{75} - 7477467136 q^{76} - 52140560296 q^{77} - 110695592320 q^{78} + 43369591752 q^{79} + 6194987008 q^{80} - 19607689666 q^{81} + 6103740704 q^{82} + 105219370951 q^{83} + 55441248256 q^{84} - 14375063614 q^{85} - 53785859936 q^{86} - 216242949124 q^{87} + 14186872832 q^{88} - 227930374154 q^{89} + 138289668864 q^{90} + 236440118278 q^{91} + 109996521472 q^{92} + 215529449050 q^{93} + 24423998144 q^{94} + 242007717988 q^{95} + 1879048192 q^{96} - 200605898215 q^{97} + 128896464000 q^{98} - 634415317547 q^{99}+O(q^{100}) \) 20 * q - 160 * q^2 + 56 * q^3 - 5120 * q^4 - 362 * q^5 - 3488 * q^6 - 167178 * q^7 - 163840 * q^8 + 206411 * q^9 - 354944 * q^10 - 449801 * q^11 + 108544 * q^12 + 3369596 * q^13 - 5349696 * q^14 + 12264628 * q^15 - 5242880 * q^16 + 1661262 * q^17 - 19177088 * q^18 + 49176291 * q^19 - 370688 * q^20 - 74218796 * q^21 - 5153632 * q^22 - 127653292 * q^23 - 3571712 * q^24 + 33758041 * q^25 - 99025728 * q^26 - 135657199 * q^27 + 156930048 * q^28 + 555960754 * q^29 + 392468096 * q^30 - 13977916 * q^31 + 671088640 * q^32 - 1768265081 * q^33 - 357119936 * q^34 + 584997860 * q^35 - 613666816 * q^36 - 161000626 * q^37 - 1456805888 * q^38 + 1145816470 * q^39 + 193593344 * q^40 + 772614122 * q^41 - 545038272 * q^42 + 3749722062 * q^43 - 50755584 * q^44 - 1321716548 * q^45 - 1394938624 * q^46 + 1924889212 * q^47 + 58720256 * q^48 + 822161735 * q^49 - 805012448 * q^50 + 5262939047 * q^51 - 3168823296 * q^52 + 1531782992 * q^53 + 295824512 * q^54 + 3851857218 * q^55 + 912654336 * q^56 - 17257259731 * q^57 + 17790744128 * q^58 - 16014164779 * q^59 - 3503935488 * q^60 + 7822116636 * q^61 + 6939975808 * q^62 - 79975953122 * q^63 - 5368709120 * q^64 + 73754374272 * q^65 - 3094015232 * q^66 - 22092583538 * q^67 + 1701132288 * q^68 + 43044165458 * q^69 - 5227997760 * q^70 + 23107180542 * q^71 + 6763675648 * q^72 + 55731754682 * q^73 - 5152020032 * q^74 - 37848703409 * q^75 - 7477467136 * q^76 - 52140560296 * q^77 - 110695592320 * q^78 + 43369591752 * q^79 + 6194987008 * q^80 - 19607689666 * q^81 + 6103740704 * q^82 + 105219370951 * q^83 + 55441248256 * q^84 - 14375063614 * q^85 - 53785859936 * q^86 - 216242949124 * q^87 + 14186872832 * q^88 - 227930374154 * q^89 + 138289668864 * q^90 + 236440118278 * q^91 + 109996521472 * q^92 + 215529449050 * q^93 + 24423998144 * q^94 + 242007717988 * q^95 + 1879048192 * q^96 - 200605898215 * q^97 + 128896464000 * q^98 - 634415317547 * q^99

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