LMFDB - Embedded newform 22.12.c.a.5.5

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			5.5
Root			$-597.108 + 433.824i$ of defining polynomial
Character	$\chi$	$=$	22.5
Dual form			22.12.c.a.9.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(9.88854 + 30.4338i) q^{2} +(598.990 + 435.192i) q^{3} +(-828.433 + 601.892i) q^{4} +(2266.32 - 6975.01i) q^{5} +(-7321.40 + 22533.0i) q^{6} +(-58786.1 + 42710.6i) q^{7} +(-26509.9 - 19260.5i) q^{8} +(114656. + 352874. i) q^{9} +O(q^{10})$	\(q+(9.88854 + 30.4338i) q^{2} +(598.990 + 435.192i) q^{3} +(-828.433 + 601.892i) q^{4} +(2266.32 - 6975.01i) q^{5} +(-7321.40 + 22533.0i) q^{6} +(-58786.1 + 42710.6i) q^{7} +(-26509.9 - 19260.5i) q^{8} +(114656. + 352874. i) q^{9} +234687. q^{10} +(-445684. + 294410. i) q^{11} -758162. q^{12} +(292544. + 900357. i) q^{13} +(-1.88115e6 - 1.36674e6i) q^{14} +(4.39297e6 - 3.19168e6i) q^{15} +(324028. - 997255. i) q^{16} +(-243328. + 748886. i) q^{17} +(-9.60552e6 + 6.97882e6i) q^{18} +(1.25560e7 + 9.12246e6i) q^{19} +(2.32071e6 + 7.14241e6i) q^{20} -5.37996e7 q^{21} +(-1.33672e7 - 1.06526e7i) q^{22} -1.84856e7 q^{23} +(-7.49712e6 - 2.30737e7i) q^{24} +(-4.01181e6 - 2.91475e6i) q^{25} +(-2.45085e7 + 1.78064e7i) q^{26} +(-4.43601e7 + 1.36526e8i) q^{27} +(2.29932e7 - 7.07657e7i) q^{28} +(5.14980e7 - 3.74155e7i) q^{29} +(1.40575e8 + 1.02134e8i) q^{30} +(-5.44677e7 - 1.67634e8i) q^{31} +3.35544e7 q^{32} +(-3.95085e8 - 1.76097e7i) q^{33} -2.51976e7 q^{34} +(1.64679e8 + 5.06829e8i) q^{35} +(-3.07377e8 - 2.23322e8i) q^{36} +(6.79046e8 - 4.93356e8i) q^{37} +(-1.53471e8 + 4.72335e8i) q^{38} +(-2.16597e8 + 6.66618e8i) q^{39} +(-1.94422e8 + 1.41256e8i) q^{40} +(5.37640e8 + 3.90619e8i) q^{41} +(-5.31999e8 - 1.63733e9i) q^{42} +7.01588e8 q^{43} +(1.92017e8 - 5.12153e8i) q^{44} +2.72115e9 q^{45} +(-1.82795e8 - 5.62586e8i) q^{46} +(-1.25094e8 - 9.08860e7i) q^{47} +(6.28086e8 - 4.56332e8i) q^{48} +(1.02058e9 - 3.14103e9i) q^{49} +(4.90360e7 - 1.50917e8i) q^{50} +(-4.71660e8 + 3.42681e8i) q^{51} +(-7.84271e8 - 5.69806e8i) q^{52} +(-6.85755e8 - 2.11054e9i) q^{53} -4.59367e9 q^{54} +(1.04345e9 + 3.77588e9i) q^{55} +2.38104e9 q^{56} +(3.55089e9 + 1.09285e10i) q^{57} +(1.64794e9 + 1.19730e9i) q^{58} +(-3.20752e9 + 2.33040e9i) q^{59} +(-1.71824e9 + 5.28819e9i) q^{60} +(-2.84546e9 + 8.75743e9i) q^{61} +(4.56315e9 - 3.31532e9i) q^{62} +(-2.18116e10 - 1.58471e10i) q^{63} +(3.31804e8 + 1.02119e9i) q^{64} +6.94300e9 q^{65} +(-3.37089e9 - 1.21981e10i) q^{66} +6.35110e9 q^{67} +(-2.49168e8 - 7.66860e8i) q^{68} +(-1.10727e10 - 8.04476e9i) q^{69} +(-1.37963e10 + 1.00236e10i) q^{70} +(-7.48903e9 + 2.30489e10i) q^{71} +(3.75704e9 - 1.15630e10i) q^{72} +(2.61885e10 - 1.90270e10i) q^{73} +(2.17295e10 + 1.57874e10i) q^{74} +(-1.13456e9 - 3.49181e9i) q^{75} -1.58925e10 q^{76} +(1.36256e10 - 3.63426e10i) q^{77} -2.24295e10 q^{78} +(4.84995e9 + 1.49266e10i) q^{79} +(-6.22152e9 - 4.52020e9i) q^{80} +(-3.28117e10 + 2.38391e10i) q^{81} +(-6.57153e9 + 2.02251e10i) q^{82} +(-8.91033e9 + 2.74232e10i) q^{83} +(4.45694e10 - 3.23815e10i) q^{84} +(4.67203e9 + 3.39443e9i) q^{85} +(6.93768e9 + 2.13520e10i) q^{86} +4.71297e10 q^{87} +(1.74855e10 + 7.79364e8i) q^{88} +3.93384e9 q^{89} +(2.69082e10 + 8.28149e10i) q^{90} +(-5.56523e10 - 4.04338e10i) q^{91} +(1.53141e10 - 1.11263e10i) q^{92} +(4.03275e10 - 1.24115e11i) q^{93} +(1.52901e9 - 4.70581e9i) q^{94} +(9.20852e10 - 6.69038e10i) q^{95} +(2.00988e10 + 1.46026e10i) q^{96} +(2.82628e10 + 8.69839e10i) q^{97} +1.05685e11 q^{98} +(-1.54990e11 - 1.23515e11i) 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 $\left(\mathbb{Z}/22\mathbb{Z}\right)^\times$.

$n$	$13$
$\chi(n)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	9.88854	+	30.4338i	0.218508	+	0.672499i
$2$	9.88854	+	30.4338i	0.218508	+	0.672499i
$3$	598.990	+	435.192i	1.42316	+	1.03398i	0.991240	+	0.132070i	$0.0421623\pi$
$3$	598.990	+	435.192i	1.42316	+	1.03398i	0.431916	+	0.901914i	$0.357838\pi$
$4$	−828.433	+	601.892i	−0.404508	+	0.293893i
$5$	2266.32	−	6975.01i	0.324329	−	0.998182i	−0.647413	−	0.762139i	$-0.724149\pi$
$5$	2266.32	−	6975.01i	0.324329	−	0.998182i	0.971743	−	0.236043i	$-0.0758508\pi$
$6$	−7321.40	+	22533.0i	−0.384381	+	1.18300i
$7$	−58786.1	+	42710.6i	−1.32201	+	0.960498i	−0.322107	+	0.946703i	$0.604391\pi$
$7$	−58786.1	+	42710.6i	−1.32201	+	0.960498i	−0.999905	+	0.0137942i	$0.995609\pi$
$8$	−26509.9	−	19260.5i	−0.286031	−	0.207813i
$9$	114656.	+	352874.i	0.647235	+	1.99198i
$10$	234687.			0.742145
$11$	−445684.	+	294410.i	−0.834387	+	0.551179i
$11$	−445684.	+	294410.i	−0.834387	+	0.551179i
$12$	−758162.			−0.879559
$13$	292544.	+	900357.i	0.218526	+	0.672553i	0.998884	+	0.0472209i	$0.0150365\pi$
$13$	292544.	+	900357.i	0.218526	+	0.672553i	−0.780359	+	0.625332i	$0.784964\pi$
$14$	−1.88115e6	−	1.36674e6i	−0.934803	−	0.679174i
$15$	4.39297e6	−	3.19168e6i	1.49368	−	1.08522i
$16$	324028.	−	997255.i	0.0772542	−	0.237764i
$17$	−243328.	+	748886.i	−0.0415645	+	0.127922i	−0.969686	−	0.244356i	$-0.921423\pi$
$17$	−243328.	+	748886.i	−0.0415645	+	0.127922i	0.928121	+	0.372279i	$0.121423\pi$
$18$	−9.60552e6	+	6.97882e6i	−1.19818	+	0.870529i
$19$	1.25560e7	+	9.12246e6i	1.16334	+	0.845215i	0.990197	−	0.139681i	$-0.0446078\pi$
$19$	1.25560e7	+	9.12246e6i	1.16334	+	0.845215i	0.173143	+	0.984897i	$0.444608\pi$
$20$	2.32071e6	+	7.14241e6i	0.162165	+	0.499091i
$21$	−5.37996e7			−2.87457
$22$	−1.33672e7	−	1.06526e7i	−0.552987	−	0.440687i
$23$	−1.84856e7			−0.598866			−0.299433	−	0.954117i	$-0.596797\pi$
$23$	−1.84856e7			−0.598866			−0.299433	+	0.954117i	$0.596797\pi$
$24$	−7.49712e6	−	2.30737e7i	−0.192191	−	0.591502i
$25$	−4.01181e6	−	2.91475e6i	−0.0821619	−	0.0596941i
$26$	−2.45085e7	+	1.78064e7i	−0.404541	+	0.293916i
$27$	−4.43601e7	+	1.36526e8i	−0.594965	+	1.83112i
$28$	2.29932e7	−	7.07657e7i	0.252482	−	0.777059i
$29$	5.14980e7	−	3.74155e7i	0.466231	−	0.338737i	−0.329740	−	0.944072i	$-0.606961\pi$
$29$	5.14980e7	−	3.74155e7i	0.466231	−	0.338737i	0.795971	+	0.605335i	$0.206961\pi$
$30$	1.40575e8	+	1.02134e8i	1.05619	+	0.767366i
$31$	−5.44677e7	−	1.67634e8i	−0.341704	−	1.05166i	−0.963325	−	0.268338i	$-0.913526\pi$
$31$	−5.44677e7	−	1.67634e8i	−0.341704	−	1.05166i	0.621621	−	0.783318i	$-0.286474\pi$
$32$	3.35544e7			0.176777
$33$	−3.95085e8	−	1.76097e7i	−1.75737	−	0.0783296i
$34$	−2.51976e7			−0.0951099
$35$	1.64679e8	+	5.06829e8i	0.529985	+	1.63113i
$36$	−3.07377e8	−	2.23322e8i	−0.847242	−	0.615557i
$37$	6.79046e8	−	4.93356e8i	1.60987	−	1.16964i	0.745944	−	0.666008i	$-0.231999\pi$
$37$	6.79046e8	−	4.93356e8i	1.60987	−	1.16964i	0.863921	−	0.503627i	$-0.168001\pi$
$38$	−1.53471e8	+	4.72335e8i	−0.314207	+	0.967030i
$39$	−2.16597e8	+	6.66618e8i	−0.384413	+	1.18310i
$40$	−1.94422e8	+	1.41256e8i	−0.300204	+	0.218111i
$41$	5.37640e8	+	3.90619e8i	0.724737	+	0.526553i	0.887894	−	0.460048i	$-0.152168\pi$
$41$	5.37640e8	+	3.90619e8i	0.724737	+	0.526553i	−0.163157	+	0.986600i	$0.552168\pi$
$42$	−5.31999e8	−	1.63733e9i	−0.628116	−	1.93314i
$43$	7.01588e8			0.727789			0.363894	−	0.931440i	$-0.381447\pi$
$43$	7.01588e8			0.727789			0.363894	+	0.931440i	$0.381447\pi$
$44$	1.92017e8	−	5.12153e8i	0.175529	−	0.468177i
$45$	2.72115e9			2.19828
$46$	−1.82795e8	−	5.62586e8i	−0.130857	−	0.402736i
$47$	−1.25094e8	−	9.08860e7i	−0.0795606	−	0.0578041i	0.547294	−	0.836940i	$-0.315658\pi$
$47$	−1.25094e8	−	9.08860e7i	−0.0795606	−	0.0578041i	−0.626855	+	0.779136i	$0.715658\pi$
$48$	6.28086e8	−	4.56332e8i	0.355789	−	0.258496i
$49$	1.02058e9	−	3.14103e9i	0.516142	−	1.58852i
$50$	4.90360e7	−	1.50917e8i	0.0221912	−	0.0682974i
$51$	−4.71660e8	+	3.42681e8i	−0.191423	+	0.139077i
$52$	−7.84271e8	−	5.69806e8i	−0.286054	−	0.207830i
$53$	−6.85755e8	−	2.11054e9i	−0.225243	−	0.693227i	−0.998267	−	0.0588500i	$-0.981257\pi$
$53$	−6.85755e8	−	2.11054e9i	−0.225243	−	0.693227i	0.773024	−	0.634377i	$-0.218743\pi$
$54$	−4.59367e9			−1.36143
$55$	1.04345e9	+	3.77588e9i	0.279561	+	1.01163i
$56$	2.38104e9			0.577740
$57$	3.55089e9	+	1.09285e10i	0.781675	+	2.40575i
$58$	1.64794e9	+	1.19730e9i	0.329675	+	0.239523i
$59$	−3.20752e9	+	2.33040e9i	−0.584095	+	0.424370i	−0.840198	−	0.542280i	$-0.817561\pi$
$59$	−3.20752e9	+	2.33040e9i	−0.584095	+	0.424370i	0.256103	+	0.966649i	$0.417561\pi$
$60$	−1.71824e9	+	5.28819e9i	−0.285267	+	0.877960i
$61$	−2.84546e9	+	8.75743e9i	−0.431359	+	1.32759i	0.465414	+	0.885093i	$0.345906\pi$
$61$	−2.84546e9	+	8.75743e9i	−0.431359	+	1.32759i	−0.896772	+	0.442492i	$0.854094\pi$
$62$	4.56315e9	−	3.31532e9i	0.632572	−	0.459591i
$63$	−2.18116e10	−	1.58471e10i	−2.76895	−	2.01176i
$64$	3.31804e8	+	1.02119e9i	0.0386271	+	0.118882i
$65$	6.94300e9			0.742205
$66$	−3.37089e9	−	1.21981e10i	−0.331324	−	1.19895i
$67$	6.35110e9			0.574695			0.287348	−	0.957826i	$-0.407226\pi$
$67$	6.35110e9			0.574695			0.287348	+	0.957826i	$0.407226\pi$
$68$	−2.49168e8	−	7.66860e8i	−0.0207823	−	0.0639612i
$69$	−1.10727e10	−	8.04476e9i	−0.852280	−	0.619217i
$70$	−1.37963e10	+	1.00236e10i	−0.981124	+	0.712828i
$71$	−7.48903e9	+	2.30489e10i	−0.492612	+	1.51610i	0.328035	+	0.944666i	$0.393614\pi$
$71$	−7.48903e9	+	2.30489e10i	−0.492612	+	1.51610i	−0.820646	+	0.571437i	$0.806386\pi$
$72$	3.75704e9	−	1.15630e10i	0.228832	−	0.704273i
$73$	2.61885e10	−	1.90270e10i	1.47854	−	1.07423i	0.500523	−	0.865723i	$-0.333141\pi$
$73$	2.61885e10	−	1.90270e10i	1.47854	−	1.07423i	0.978022	−	0.208502i	$-0.0668588\pi$
$74$	2.17295e10	+	1.57874e10i	1.13835	+	0.827057i
$75$	−1.13456e9	−	3.49181e9i	−0.0552065	−	0.169908i
$76$	−1.58925e10			−0.718983
$77$	1.36256e10	−	3.63426e10i	0.573664	−	1.53009i
$78$	−2.24295e10			−0.879630
$79$	4.84995e9	+	1.49266e10i	0.177333	+	0.545774i	0.999732	−	0.0231365i	$-0.00736522\pi$
$79$	4.84995e9	+	1.49266e10i	0.177333	+	0.545774i	−0.822400	+	0.568910i	$0.807365\pi$
$80$	−6.22152e9	−	4.52020e9i	−0.212276	−	0.154228i
$81$	−3.28117e10	+	2.38391e10i	−1.04559	+	0.759665i
$82$	−6.57153e9	+	2.02251e10i	−0.195745	+	0.602441i
$83$	−8.91033e9	+	2.74232e10i	−0.248293	+	0.764167i	0.746784	+	0.665066i	$0.231597\pi$
$83$	−8.91033e9	+	2.74232e10i	−0.248293	+	0.764167i	−0.995077	+	0.0991010i	$0.968403\pi$
$84$	4.45694e10	−	3.23815e10i	1.16279	−	0.844814i
$85$	4.67203e9	+	3.39443e9i	0.114209	+	0.0829780i
$86$	6.93768e9	+	2.13520e10i	0.159028	+	0.489437i
$87$	4.71297e10			1.01377
$88$	1.74855e10	+	7.79364e8i	0.353203	+	0.0157429i
$89$	3.93384e9			0.0746744			0.0373372	−	0.999303i	$-0.488112\pi$
$89$	3.93384e9			0.0746744			0.0373372	+	0.999303i	$0.488112\pi$
$90$	2.69082e10	+	8.28149e10i	0.480342	+	1.47834i
$91$	−5.56523e10	−	4.04338e10i	−0.934879	−	0.679229i
$92$	1.53141e10	−	1.11263e10i	0.242246	−	0.176002i
$93$	4.03275e10	−	1.24115e11i	0.601097	−	1.84999i
$94$	1.52901e9	−	4.70581e9i	0.0214886	−	0.0661350i
$95$	9.20852e10	−	6.69038e10i	1.22098	−	0.887097i
$96$	2.00988e10	+	1.46026e10i	0.251581	+	0.182784i
$97$	2.82628e10	+	8.69839e10i	0.334172	+	1.02848i	0.967128	+	0.254289i	$0.0818414\pi$
$97$	2.82628e10	+	8.69839e10i	0.334172	+	1.02848i	−0.632956	+	0.774188i	$0.718159\pi$
$98$	1.05685e11			1.18106
$99$	−1.54990e11	−	1.23515e11i	−1.63798	−	1.30534i
$100$	5.07788e9			0.0507788
$101$	−4.15875e10	−	1.27993e11i	−0.393727	−	1.21177i	−0.929948	−	0.367690i	$-0.880149\pi$
$101$	−4.15875e10	−	1.27993e11i	−0.393727	−	1.21177i	0.536221	−	0.844077i	$-0.319851\pi$
$102$	−1.50931e10	−	1.09658e10i	−0.135356	−	0.0983420i
$103$	−7.04762e10	+	5.12039e10i	−0.599015	+	0.435210i	−0.845529	−	0.533930i	$-0.820715\pi$
$103$	−7.04762e10	+	5.12039e10i	−0.599015	+	0.435210i	0.246514	+	0.969139i	$0.420715\pi$
$104$	9.58608e9	−	2.95029e10i	0.0772605	−	0.237783i
$105$	−1.21927e11	+	3.75253e11i	−0.932306	+	2.86934i
$106$	5.74505e10	−	4.17403e10i	0.416977	−	0.302951i
$107$	−2.06029e10	−	1.49689e10i	−0.142009	−	0.103176i	0.514512	−	0.857483i	$-0.327973\pi$
$107$	−2.06029e10	−	1.49689e10i	−0.142009	−	0.103176i	−0.656522	+	0.754307i	$0.727973\pi$
$108$	−4.54247e10	−	1.39803e11i	−0.297483	−	0.915558i
$109$	−1.39114e11			−0.866016			−0.433008	−	0.901390i	$-0.642548\pi$
$109$	−1.39114e11			−0.866016			−0.433008	+	0.901390i	$0.642548\pi$
$110$	−1.04596e11	+	6.90941e10i	−0.619236	+	0.409054i
$111$	6.21446e11			3.50047
$112$	2.35450e10	+	7.24641e10i	0.126241	+	0.388529i
$113$	−2.25629e11	−	1.63929e11i	−1.15203	−	0.836998i	−0.163279	−	0.986580i	$-0.552207\pi$
$113$	−2.25629e11	−	1.63929e11i	−1.15203	−	0.836998i	−0.988749	+	0.149582i	$0.952207\pi$
$114$	−2.97484e11	+	2.16134e11i	−1.44706	+	1.05135i
$115$	−4.18942e10	+	1.28937e11i	−0.194230	+	0.597777i
$116$	−2.01426e10	+	6.19925e10i	−0.0890422	+	0.274044i
$117$	−2.84171e11	+	2.06462e11i	−1.19828	+	0.870600i
$118$	−1.02641e11	−	7.45728e10i	−0.413018	−	0.300075i
$119$	−1.76811e10	−	5.44168e10i	−0.0679204	−	0.209038i
$120$	−1.77931e11			−0.652760
$121$	1.11958e11	−	2.62428e11i	0.392404	−	0.919793i
$122$	−2.94659e11			−0.987055
$123$	1.52047e11	+	4.67953e11i	0.486968	+	1.49873i
$124$	1.46021e11	+	1.06090e11i	0.447296	+	0.324980i
$125$	2.60289e11	−	1.89111e11i	0.762872	−	0.554259i
$126$	2.66601e11	−	8.20515e11i	0.747867	−	2.30170i
$127$	5.91925e10	−	1.82176e11i	0.158981	−	0.489295i	−0.839561	−	0.543265i	$-0.817188\pi$
$127$	5.91925e10	−	1.82176e11i	0.158981	−	0.489295i	0.998543	+	0.0539707i	$0.0171878\pi$
$128$	−2.77976e10	+	2.01961e10i	−0.0715077	+	0.0519534i
$129$	4.20244e11	+	3.05325e11i	1.03576	+	0.752522i
$130$	6.86562e10	+	2.11302e11i	0.162178	+	0.499132i
$131$	−8.42331e10			−0.190762			−0.0953808	−	0.995441i	$-0.530407\pi$
$131$	−8.42331e10			−0.190762			−0.0953808	+	0.995441i	$0.530407\pi$
$132$	3.37901e11	−	2.23210e11i	0.733893	−	0.484794i
$133$	−1.12774e12			−2.34978
$134$	6.28032e10	+	1.93288e11i	0.125576	+	0.386482i
$135$	8.51739e11	+	6.18824e11i	1.63482	+	1.18777i
$136$	2.08746e10	−	1.51662e10i	0.0384727	−	0.0279521i
$137$	−9.34707e10	+	2.87673e11i	−0.165467	+	0.509256i	−0.999070	−	0.0431079i	$-0.986274\pi$
$137$	−9.34707e10	+	2.87673e11i	−0.165467	+	0.509256i	0.833603	+	0.552364i	$0.186274\pi$
$138$	1.35340e11	−	4.16534e11i	0.230193	−	0.708461i
$139$	−5.39462e10	+	3.91942e10i	−0.0881819	+	0.0640679i	−0.631003	−	0.775781i	$-0.717356\pi$
$139$	−5.39462e10	+	3.91942e10i	−0.0881819	+	0.0640679i	0.542821	+	0.839849i	$0.317356\pi$
$140$	−4.41482e11	−	3.20755e11i	−0.693759	−	0.504046i
$141$	−3.53771e10	−	1.08880e11i	−0.0534586	−	0.164529i
$142$	−7.75520e11			−1.12722
$143$	−3.95456e11	−	3.15148e11i	−0.553032	−	0.440723i
$144$	3.89057e11			0.523624
$145$	−1.44263e11	−	4.43995e11i	−0.186909	−	0.575246i
$146$	8.38031e11	+	6.08865e11i	1.04549	+	0.759592i
$147$	1.97827e12	−	1.43729e12i	2.37706	−	1.72703i
$148$	−2.65597e11	+	8.17425e11i	−0.307457	+	0.946255i
$149$	−5.78081e10	+	1.77915e11i	−0.0644859	+	0.198467i	−0.978108	−	0.208097i	$-0.933273\pi$
$149$	−5.78081e10	+	1.77915e11i	−0.0644859	+	0.198467i	0.913622	+	0.406564i	$0.133273\pi$
$150$	9.50500e10	−	6.90579e10i	0.102200	−	0.0742526i
$151$	5.23858e11	+	3.80605e11i	0.543051	+	0.394549i	0.825217	−	0.564816i	$-0.191053\pi$
$151$	5.23858e11	+	3.80605e11i	0.543051	+	0.394549i	−0.282166	+	0.959366i	$0.591053\pi$
$152$	−1.57154e11	−	4.83671e11i	−0.157104	−	0.483515i
$153$	−2.92162e11			−0.281722
$154$	1.24078e12	+	5.53041e10i	1.15433	+	0.0514510i
$155$	−1.29269e12			−1.16057
$156$	−2.21796e11	−	6.82617e11i	−0.192206	−	0.591550i
$157$	6.99849e11	+	5.08470e11i	0.585539	+	0.425419i	0.840717	−	0.541475i	$-0.182134\pi$
$157$	6.99849e11	+	5.08470e11i	0.585539	+	0.425419i	−0.255178	+	0.966894i	$0.582134\pi$
$158$	−4.06315e11	+	2.95205e11i	−0.328283	+	0.238512i
$159$	5.07728e11	−	1.56262e12i	0.396229	−	1.21947i
$160$	7.60450e10	−	2.34043e11i	0.0573338	−	0.176455i
$161$	1.08669e12	−	7.89529e11i	0.791707	−	0.575209i
$162$	−1.04997e12	−	7.62851e11i	−0.739343	−	0.537164i
$163$	9.41021e10	+	2.89616e11i	0.0640571	+	0.197147i	0.977963	−	0.208779i	$-0.0669489\pi$
$163$	9.41021e10	+	2.89616e11i	0.0640571	+	0.197147i	−0.913906	+	0.405926i	$0.866949\pi$
$164$	−6.80510e11			−0.447912
$165$	−1.01822e12	+	2.71581e12i	−0.648155	+	1.72877i
$166$	−9.22702e11			−0.568155
$167$	−4.02248e11	−	1.23799e12i	−0.239637	−	0.737526i	−0.996472	−	0.0839210i	$-0.973256\pi$
$167$	−4.02248e11	−	1.23799e12i	−0.239637	−	0.737526i	0.756836	−	0.653605i	$-0.226744\pi$
$168$	1.42622e12	+	1.03621e12i	0.822215	+	0.597374i
$169$	7.24827e11	−	5.26617e11i	0.404443	−	0.293845i
$170$	−5.71058e10	+	1.75754e11i	−0.0308469	+	0.0949370i
$171$	−1.77946e12	+	5.47663e12i	−0.930702	+	2.86441i
$172$	−5.81219e11	+	4.22280e11i	−0.294397	+	0.213892i
$173$	−5.79672e10	−	4.21156e10i	−0.0284399	−	0.0206628i	0.573474	−	0.819223i	$-0.305595\pi$
$173$	−5.79672e10	−	4.21156e10i	−0.0284399	−	0.0206628i	−0.601914	+	0.798561i	$0.705595\pi$
$174$	4.66044e11	+	1.43434e12i	0.221516	+	0.681758i
$175$	3.60329e11			0.165955
$176$	1.49187e11	+	5.39858e11i	0.0665905	+	0.240968i
$177$	−2.93544e12			−1.27005
$178$	3.89000e10	+	1.19722e11i	0.0163170	+	0.0502184i
$179$	−1.28033e12	−	9.30213e11i	−0.520751	−	0.378347i	0.296136	−	0.955146i	$-0.404302\pi$
$179$	−1.28033e12	−	9.30213e11i	−0.520751	−	0.378347i	−0.816887	+	0.576798i	$0.804302\pi$
$180$	−2.25429e12	+	1.63784e12i	−0.889223	+	0.646059i
$181$	7.61193e11	−	2.34271e12i	0.291248	−	0.896369i	−0.693208	−	0.720737i	$-0.743803\pi$
$181$	7.61193e11	−	2.34271e12i	0.291248	−	0.896369i	0.984456	−	0.175631i	$-0.0561966\pi$
$182$	6.80233e11	−	2.09354e12i	0.252502	−	0.777122i
$183$	−5.51556e12	+	4.00729e12i	−1.98659	+	1.44334i
$184$	4.90050e11	+	3.56042e11i	0.171294	+	0.124452i
$185$	−1.90223e12	−	5.85445e12i	−0.645384	−	1.98629i
$186$	4.17608e12			1.37546
$187$	−1.12032e11	−	4.05405e11i	−0.0358272	−	0.129646i
$188$	1.58336e11			0.0491711
$189$	−3.22336e12	−	9.92049e12i	−0.972231	−	2.99222i
$190$	2.94673e12	+	2.14092e12i	0.863366	+	0.627272i
$191$	3.60731e12	−	2.62086e12i	1.02683	−	0.746038i	0.0591611	−	0.998248i	$-0.481157\pi$
$191$	3.60731e12	−	2.62086e12i	1.02683	−	0.746038i	0.967672	+	0.252210i	$0.0811574\pi$
$192$	−2.45665e11	+	7.56081e11i	−0.0679497	+	0.209128i
$193$	−1.13652e12	+	3.49785e12i	−0.305500	+	0.940233i	0.673990	+	0.738741i	$0.264579\pi$
$193$	−1.13652e12	+	3.49785e12i	−0.305500	+	0.940233i	−0.979490	+	0.201492i	$0.935421\pi$
$194$	−2.36777e12	+	1.72029e12i	−0.618630	+	0.449461i
$195$	4.15879e12	+	3.02154e12i	1.05627	+	0.767428i
$196$	1.04507e12	+	3.21641e12i	0.258071	+	0.794261i
$197$	3.14082e11			0.0754186			0.0377093	−	0.999289i	$-0.487994\pi$
$197$	3.14082e11			0.0754186			0.0377093	+	0.999289i	$0.487994\pi$
$198$	2.22640e12	−	5.93831e12i	0.519930	−	1.38677i
$199$	7.52957e12			1.71032			0.855162	−	0.518361i	$-0.173458\pi$
$199$	7.52957e12			1.71032			0.855162	+	0.518361i	$0.173458\pi$
$200$	5.02129e10	+	1.54539e11i	0.0110956	+	0.0341487i
$201$	3.80425e12	+	2.76395e12i	0.817881	+	0.594226i
$202$	3.48408e12	−	2.53133e12i	0.728879	−	0.529562i
$203$	−1.42933e12	+	4.39902e12i	−0.291007	+	0.895628i
$204$	1.84482e11	−	5.67777e11i	0.0365585	−	0.112515i
$205$	3.94303e12	−	2.86478e12i	0.760649	−	0.552644i
$206$	−2.25524e12	−	1.63853e12i	−0.423567	−	0.307740i
$207$	−2.11948e12	−	6.52307e12i	−0.387607	−	1.19293i
$208$	9.92678e11			0.176791
$209$	−8.28175e12	−	3.69134e11i	−1.43654	−	0.0640294i
$210$	−1.26260e13			−2.13335
$211$	2.19830e12	+	6.76568e12i	0.361855	+	1.11367i	0.951927	+	0.306324i	$0.0990991\pi$
$211$	2.19830e12	+	6.76568e12i	0.361855	+	1.11367i	−0.590073	+	0.807350i	$0.700901\pi$
$212$	1.83842e12	+	1.33569e12i	0.294847	+	0.214219i
$213$	−1.45165e13	+	1.05469e13i	−2.26869	+	1.64830i
$214$	2.51827e11	−	7.75044e11i	0.0383554	−	0.118046i
$215$	1.59002e12	−	4.89358e12i	0.236043	−	0.726466i
$216$	3.80555e12	−	2.76490e12i	0.550709	−	0.400113i
$217$	1.03617e13	+	7.52822e12i	1.46185	+	1.06210i
$218$	−1.37564e12	−	4.23377e12i	−0.189231	−	0.582394i
$219$	2.39670e13			3.21493
$220$	−3.13710e12	−	2.50002e12i	−0.410396	−	0.327054i
$221$	−7.45449e11			−0.0951176
$222$	6.14519e12	+	1.89130e13i	0.764882	+	2.35406i
$223$	−3.01453e12	−	2.19019e12i	−0.366052	−	0.265953i	0.389520	−	0.921018i	$-0.372641\pi$
$223$	−3.01453e12	−	2.19019e12i	−0.366052	−	0.265953i	−0.755572	+	0.655066i	$0.772641\pi$
$224$	−1.97253e12	+	1.43313e12i	−0.233701	+	0.169794i
$225$	5.68563e11	−	1.74986e12i	0.0657317	−	0.202301i
$226$	2.75784e12	−	8.48776e12i	0.311152	−	0.957628i
$227$	−3.15929e12	+	2.29536e12i	−0.347895	+	0.252760i	−0.747985	−	0.663715i	$-0.768979\pi$
$227$	−3.15929e12	+	2.29536e12i	−0.347895	+	0.252760i	0.400091	+	0.916476i	$0.368979\pi$
$228$	−9.51948e12	−	6.91630e12i	−1.02323	−	0.743417i
$229$	−2.18482e12	−	6.72417e12i	−0.229255	−	0.705576i	−0.997832	−	0.0658174i	$-0.979035\pi$
$229$	−2.18482e12	−	6.72417e12i	−0.229255	−	0.705576i	0.768576	−	0.639758i	$-0.220965\pi$
$230$	−4.33832e12			−0.444445
$231$	2.39776e13	−	1.58391e13i	2.39850	−	1.58440i
$232$	−2.08585e12			−0.203750
$233$	3.60078e12	+	1.10821e13i	0.343509	+	1.05721i	0.962377	+	0.271718i	$0.0875918\pi$
$233$	3.60078e12	+	1.10821e13i	0.343509	+	1.05721i	−0.618868	+	0.785495i	$0.712408\pi$
$234$	−9.09347e12	−	6.60679e12i	−0.847310	−	0.615607i
$235$	−9.17434e11	+	6.66555e11i	−0.0835029	+	0.0606684i
$236$	1.25457e12	−	3.86116e12i	0.111552	−	0.343322i
$237$	−3.59087e12	+	1.10516e13i	−0.311949	+	0.960080i
$238$	1.48127e12	−	1.07621e12i	0.125736	−	0.0913528i
$239$	−9.12447e12	−	6.62931e12i	−0.756866	−	0.549895i	0.141081	−	0.989998i	$-0.454942\pi$
$239$	−9.12447e12	−	6.62931e12i	−0.756866	−	0.549895i	−0.897947	+	0.440103i	$0.854942\pi$
$240$	−1.75947e12	−	5.41510e12i	−0.142633	−	0.438980i
$241$	−1.01136e13			−0.801332			−0.400666	−	0.916224i	$-0.631221\pi$
$241$	−1.01136e13			−0.801332			−0.400666	+	0.916224i	$0.631221\pi$
$242$	9.09377e12	+	8.12268e11i	0.704303	+	0.0629093i
$243$	−4.59859e12			−0.348169
$244$	−2.91375e12	−	8.96761e12i	−0.215679	−	0.663793i
$245$	−1.95957e13	−	1.42371e13i	−1.41823	−	1.03041i
$246$	−1.27381e13	+	9.25475e12i	−0.901490	+	0.654971i
$247$	−4.54030e12	+	1.39736e13i	−0.314233	+	0.967109i
$248$	−1.78480e12	+	5.49304e12i	−0.120811	+	0.371817i
$249$	−1.72715e13	+	1.25485e13i	−1.14350	+	0.830799i
$250$	8.32926e12	+	6.05156e12i	0.539432	+	0.391920i
$251$	−5.65624e12	−	1.74081e13i	−0.358362	−	1.10293i	−0.954034	−	0.299698i	$-0.903114\pi$
$251$	−5.65624e12	−	1.74081e13i	−0.358362	−	1.10293i	0.595672	−	0.803228i	$-0.296886\pi$
$252$	2.76077e13			1.71130
$253$	8.23873e12	−	5.44233e12i	0.499686	−	0.330082i
$254$	6.12963e12			0.363789
$255$	1.32127e12	+	4.06646e12i	0.0767399	+	0.236181i
$256$	−8.89524e11	−	6.46277e11i	−0.0505636	−	0.0367366i
$257$	−1.58056e13	+	1.14834e13i	−0.879385	+	0.638911i	−0.933089	−	0.359646i	$-0.882897\pi$
$257$	−1.58056e13	+	1.14834e13i	−0.879385	+	0.638911i	0.0537037	+	0.998557i	$0.482897\pi$
$258$	−5.13660e12	+	1.58088e13i	−0.279748	+	0.860977i
$259$	−1.88469e13	+	5.80049e13i	−1.00483	+	3.09254i
$260$	−5.75181e12	+	4.17894e12i	−0.300228	+	0.218129i
$261$	1.91075e13	+	1.38824e13i	0.976520	+	0.709483i
$262$	−8.32943e11	−	2.56354e12i	−0.0416829	−	0.128287i
$263$	2.11354e13			1.03575			0.517873	−	0.855458i	$-0.326724\pi$
$263$	2.11354e13			1.03575			0.517873	+	0.855458i	$0.326724\pi$
$264$	1.01345e13	+	8.07639e12i	0.486385	+	0.387611i
$265$	−1.62752e13			−0.765020
$266$	−1.11517e13	−	3.43215e13i	−0.513445	−	1.58022i
$267$	2.35633e12	+	1.71198e12i	0.106273	+	0.0772122i
$268$	−5.26147e12	+	3.82268e12i	−0.232469	+	0.168899i
$269$	7.44331e12	−	2.29082e13i	0.322202	−	0.991637i	−0.650485	−	0.759519i	$-0.725434\pi$
$269$	7.44331e12	−	2.29082e13i	0.322202	−	0.991637i	0.972688	−	0.232118i	$-0.0745655\pi$
$270$	−1.04107e13	+	3.20409e13i	−0.441550	+	1.35895i
$271$	2.81650e13	−	2.04631e13i	1.17052	−	0.850433i	0.179450	−	0.983767i	$-0.442568\pi$
$271$	2.81650e13	−	2.04631e13i	1.17052	−	0.850433i	0.991071	+	0.133334i	$0.0425682\pi$
$272$	6.67986e11	+	4.85320e11i	0.0272043	+	0.0197651i
$273$	−1.57387e13	−	4.84388e13i	−0.628167	−	1.93330i
$274$	−9.67928e12			−0.378630
$275$	2.64613e12	+	1.17943e11i	0.101457	+	0.00452214i
$276$	1.40150e13			0.526738
$277$	4.06980e12	+	1.25256e13i	0.149946	+	0.461486i	0.997614	−	0.0690411i	$-0.0219940\pi$
$277$	4.06980e12	+	1.25256e13i	0.149946	+	0.461486i	−0.847668	+	0.530527i	$0.821994\pi$
$278$	−1.72628e12	−	1.25422e12i	−0.0623540	−	0.0453029i
$279$	5.29088e13	−	3.84405e13i	1.87372	−	1.36134i
$280$	5.39620e12	−	1.66078e13i	0.187378	−	0.576690i
$281$	9.22604e12	−	2.83948e13i	0.314145	−	0.966839i	−0.661960	−	0.749539i	$-0.730275\pi$
$281$	9.22604e12	−	2.83948e13i	0.314145	−	0.966839i	0.976105	−	0.217300i	$-0.0697250\pi$
$282$	2.96379e12	−	2.15332e12i	0.0989641	−	0.0719017i
$283$	−4.05152e13	−	2.94360e13i	−1.32676	−	0.963949i	−0.999821	−	0.0189040i	$-0.993982\pi$
$283$	−4.05152e13	−	2.94360e13i	−1.32676	−	0.963949i	−0.326941	−	0.945045i	$-0.606018\pi$
$284$	−7.66877e12	−	2.36020e13i	−0.246306	−	0.758051i
$285$	8.42741e13			2.65489
$286$	5.68065e12	−	1.51516e13i	0.175544	−	0.468215i
$287$	−4.82893e13			−1.46386
$288$	3.84721e12	+	1.18405e13i	0.114416	+	0.352136i
$289$	2.72249e13	+	1.97801e13i	0.794380	+	0.577151i
$290$	1.20859e13	−	8.78092e12i	0.346011	−	0.251392i
$291$	−2.09256e13	+	6.44022e13i	−0.587849	+	1.80921i
$292$	−1.02432e13	+	3.15253e13i	−0.282377	+	0.869067i
$293$	−1.54946e13	+	1.12575e13i	−0.419187	+	0.304557i	−0.777311	−	0.629117i	$-0.783417\pi$
$293$	−1.54946e13	+	1.12575e13i	−0.419187	+	0.304557i	0.358123	+	0.933674i	$0.383417\pi$
$294$	6.33045e13	+	4.59934e13i	1.68083	+	1.22120i
$295$	8.98531e12	+	2.76539e13i	0.234160	+	0.720669i
$296$	−2.75037e13			−0.703537
$297$	−2.04241e13	−	7.39077e13i	−0.512840	−	1.85579i
$298$	−5.98627e12			−0.147559
$299$	−5.40784e12	−	1.66436e13i	−0.130868	−	0.402769i
$300$	3.04160e12	+	2.20985e12i	0.0722662	+	0.0525045i
$301$	−4.12436e13	+	2.99652e13i	−0.962145	+	0.699039i
$302$	−6.40307e12	+	1.97066e13i	−0.146673	+	0.451413i
$303$	3.07911e13	−	9.47651e13i	0.692612	−	2.13164i
$304$	1.31659e13	−	9.56560e12i	0.290835	−	0.211304i
$305$	5.46345e13	+	3.96943e13i	1.18527	+	0.861149i
$306$	−2.88905e12	−	8.89159e12i	−0.0615584	−	0.189457i
$307$	−1.47470e13			−0.308633			−0.154317	−	0.988021i	$-0.549318\pi$
$307$	−1.47470e13			−0.308633			−0.154317	+	0.988021i	$0.549318\pi$
$308$	1.05864e13	+	3.83086e13i	0.217631	+	0.787531i
$309$	−6.44980e13			−1.30249
$310$	−1.27829e13	−	3.93416e13i	−0.253594	−	0.780481i
$311$	3.26254e13	+	2.37037e13i	0.635877	+	0.461992i	0.858431	−	0.512928i	$-0.171439\pi$
$311$	3.26254e13	+	2.37037e13i	0.635877	+	0.461992i	−0.222554	+	0.974920i	$0.571439\pi$
$312$	1.85814e13	−	1.35002e13i	0.355818	−	0.258517i
$313$	2.51029e13	−	7.72586e13i	0.472312	−	1.45363i	−0.377236	−	0.926117i	$-0.623125\pi$
$313$	2.51029e13	−	7.72586e13i	0.472312	−	1.45363i	0.849548	−	0.527511i	$-0.176875\pi$
$314$	−8.55419e12	+	2.63271e13i	−0.158149	+	0.486732i
$315$	−1.59966e14	+	1.16222e14i	−2.90615	+	2.11144i
$316$	−1.30021e13	−	9.44656e12i	−0.232131	−	0.168653i
$317$	9.09652e12	+	2.79962e13i	0.159606	+	0.491217i	0.998598	−	0.0529262i	$-0.0168548\pi$
$317$	9.09652e12	+	2.79962e13i	0.159606	+	0.491217i	−0.838992	+	0.544143i	$0.816855\pi$
$318$	5.25773e13			0.906670
$319$	−1.19364e13	+	3.18370e13i	−0.202313	+	0.539614i
$320$	7.87478e12			0.131194
$321$	−5.82658e12	−	1.79324e13i	−0.0954193	−	0.293671i
$322$	3.47742e13	+	2.52649e13i	0.559822	+	0.406734i
$323$	−9.88691e12	+	7.18326e12i	−0.156476	+	0.113686i
$324$	1.28337e13	−	3.94982e13i	0.199690	−	0.614582i
$325$	1.45069e12	−	4.46476e12i	0.0221930	−	0.0683029i
$326$	−7.88360e12	+	5.72777e12i	−0.118584	+	0.0861566i
$327$	−8.33280e13	−	6.05413e13i	−1.23248	−	0.895446i
$328$	−6.72925e12	−	2.07105e13i	−0.0978724	−	0.301220i
$329$	1.12356e13			0.160701
$330$	−9.27213e13	−	4.13277e12i	−1.30423	−	0.0581319i
$331$	−9.02057e13			−1.24790			−0.623951	−	0.781464i	$-0.714473\pi$
$331$	−9.02057e13			−1.24790			−0.623951	+	0.781464i	$0.714473\pi$
$332$	−9.12418e12	−	2.80813e13i	−0.124146	−	0.382084i
$333$	2.51949e14	+	1.83052e14i	3.37186	+	2.44980i
$334$	3.36992e13	−	2.44839e13i	0.443623	−	0.322311i
$335$	1.43936e13	−	4.42990e13i	0.186390	−	0.573651i
$336$	−1.74326e13	+	5.36519e13i	−0.222073	+	0.683469i
$337$	3.26039e13	−	2.36881e13i	0.408606	−	0.296870i	−0.364431	−	0.931230i	$-0.618737\pi$
$337$	3.26039e13	−	2.36881e13i	0.408606	−	0.296870i	0.773037	+	0.634361i	$0.218737\pi$
$338$	2.31945e13	+	1.68518e13i	0.285984	+	0.207780i
$339$	−6.38089e13	−	1.96384e14i	−0.774075	−	2.38236i
$340$	−5.91355e12			−0.0705853
$341$	7.36286e13	+	5.86762e13i	0.864764	+	0.689149i
$342$	−1.84271e14			−2.12968
$343$	2.97596e13	+	9.15907e13i	0.338462	+	1.04168i
$344$	−1.85990e13	−	1.35130e13i	−0.208170	−	0.151244i
$345$	−8.12065e13	+	5.90000e13i	−0.894511	+	0.649900i
$346$	7.08528e11	−	2.18062e12i	0.00768136	−	0.0236408i
$347$	−3.84636e12	+	1.18379e13i	−0.0410429	+	0.126317i	−0.969479	−	0.245176i	$-0.921154\pi$
$347$	−3.84636e12	+	1.18379e13i	−0.0410429	+	0.126317i	0.928436	+	0.371493i	$0.121154\pi$
$348$	−3.90438e13	+	2.83670e13i	−0.410078	+	0.297939i
$349$	−5.17739e13	−	3.76159e13i	−0.535268	−	0.388895i	0.287057	−	0.957914i	$-0.407323\pi$
$349$	−5.17739e13	−	3.76159e13i	−0.535268	−	0.388895i	−0.822325	+	0.569019i	$0.807323\pi$
$350$	3.56313e12	+	1.09662e13i	0.0362625	+	0.111604i
$351$	−1.35900e14			−1.36154
$352$	−1.49547e13	+	9.87875e12i	−0.147500	+	0.0974355i
$353$	1.49261e14			1.44939			0.724693	−	0.689072i	$-0.241982\pi$
$353$	1.49261e14			1.44939			0.724693	+	0.689072i	$0.241982\pi$
$354$	−2.90273e13	−	8.93368e13i	−0.277516	−	0.854107i
$355$	1.43794e14	+	1.04472e14i	1.35358	+	0.983432i
$356$	−3.25893e12	+	2.36775e12i	−0.0302064	+	0.0219463i
$357$	1.30909e13	−	4.02898e13i	0.119480	−	0.367722i
$358$	1.56493e13	−	4.81637e13i	0.140650	−	0.432876i
$359$	−3.77666e13	+	2.74390e13i	−0.334263	+	0.242856i	−0.742237	−	0.670137i	$-0.766235\pi$
$359$	−3.77666e13	+	2.74390e13i	−0.334263	+	0.242856i	0.407974	+	0.912993i	$0.366235\pi$
$360$	−7.21373e13	−	5.24108e13i	−0.628776	−	0.456832i
$361$	3.84362e13	+	1.18294e14i	0.329952	+	1.01549i
$362$	7.88247e13			0.666447
$363$	1.81268e14	−	1.08469e14i	1.50950	−	0.903269i
$364$	7.04410e13			0.577787
$365$	−7.33624e13	−	2.25786e14i	−0.592738	−	1.82426i
$366$	−1.76498e14	−	1.28233e14i	−1.40473	−	1.02060i
$367$	−7.93600e12	+	5.76584e12i	−0.0622212	+	0.0452063i	−0.618461	−	0.785815i	$-0.712244\pi$
$367$	−7.93600e12	+	5.76584e12i	−0.0622212	+	0.0452063i	0.556240	+	0.831022i	$0.312244\pi$
$368$	−5.98983e12	+	1.84348e13i	−0.0462649	+	0.142389i
$369$	−7.61956e13	+	2.34506e14i	−0.579809	+	1.78447i
$370$	1.59363e14	−	1.15784e14i	1.19475	−	0.868039i
$371$	1.30455e14	+	9.47812e13i	0.963617	+	0.700109i
$372$	4.12953e13	+	1.27094e14i	0.300549	+	0.924994i
$373$	−1.72936e14			−1.24019			−0.620094	−	0.784528i	$-0.712906\pi$
$373$	−1.72936e14			−1.24019			−0.620094	+	0.784528i	$0.712906\pi$
$374$	1.12302e13	−	7.41842e12i	0.0793585	−	0.0524225i
$375$	2.38210e14			1.65878
$376$	1.56571e12	+	4.81875e12i	0.0107443	+	0.0330675i
$377$	4.87527e13	+	3.54209e13i	0.329702	+	0.239542i
$378$	2.70044e14	−	1.96198e14i	1.79982	−	1.30765i
$379$	4.32239e13	−	1.33029e14i	0.283928	−	0.873841i	−0.702790	−	0.711397i	$-0.748063\pi$
$379$	4.32239e13	−	1.33029e14i	0.283928	−	0.873841i	0.986718	−	0.162443i	$-0.0519374\pi$
$380$	−3.60176e13	+	1.10851e14i	−0.233187	+	0.717676i
$381$	1.14737e14	−	8.33614e13i	0.732178	−	0.531959i
$382$	1.15434e14	+	8.38677e13i	0.726081	+	0.527529i
$383$	−3.35961e13	−	1.03398e14i	−0.208303	−	0.641091i	−0.999562	−	0.0296093i	$-0.990574\pi$
$383$	−3.35961e13	−	1.03398e14i	−0.208303	−	0.641091i	0.791258	−	0.611482i	$-0.209426\pi$
$384$	−2.54397e13			−0.155486
$385$	−2.22610e14	−	1.77403e14i	−1.34125	−	1.06887i
$386$	−1.17691e14			−0.699059
$387$	8.04410e13	+	2.47572e14i	0.471050	+	1.44974i
$388$	−7.57688e13	−	5.50492e13i	−0.437437	−	0.317817i
$389$	1.92241e14	−	1.39672e14i	1.09427	−	0.795033i	0.114154	−	0.993463i	$-0.463584\pi$
$389$	1.92241e14	−	1.39672e14i	1.09427	−	0.795033i	0.980115	+	0.198430i	$0.0635842\pi$
$390$	−5.08325e13	+	1.56446e14i	−0.285290	+	0.878032i
$391$	4.49805e12	−	1.38436e13i	0.0248916	−	0.0766084i
$392$	−8.75533e13	+	6.36112e13i	−0.477748	+	0.347105i
$393$	−5.04548e13	−	3.66576e13i	−0.271484	−	0.197244i
$394$	3.10581e12	+	9.55871e12i	0.0164796	+	0.0507189i
$395$	1.15105e14			0.602296
$396$	2.02741e14	+	9.03658e12i	1.04621	+	0.0466316i
$397$	−2.01690e14			−1.02645			−0.513225	−	0.858254i	$-0.671549\pi$
$397$	−2.01690e14			−1.02645			−0.513225	+	0.858254i	$0.671549\pi$
$398$	7.44565e13	+	2.29154e14i	0.373719	+	1.15019i
$399$	−6.75507e14	−	4.90785e14i	−3.34410	−	2.42963i
$400$	−4.20669e12	+	3.05634e12i	−0.0205405	+	0.0149235i
$401$	−4.39469e13	+	1.35255e14i	−0.211658	+	0.651416i	0.787716	+	0.616038i	$0.211263\pi$
$401$	−4.39469e13	+	1.35255e14i	−0.211658	+	0.651416i	−0.999374	+	0.0353774i	$0.988737\pi$
$402$	−4.64990e13	+	1.43109e14i	−0.220902	+	0.679867i
$403$	1.34997e14	−	9.80808e13i	0.632624	−	0.459628i
$404$	1.11491e14	+	8.10026e13i	0.515395	+	0.374457i
$405$	9.19162e13	+	2.82889e14i	0.419169	+	1.29007i
$406$	−1.48013e14			−0.665896
$407$	−1.57391e14	+	4.19799e14i	−0.698573	+	1.86325i
$408$	1.91039e13			0.0836547
$409$	8.86297e13	+	2.72774e14i	0.382914	+	1.17849i	0.937982	+	0.346683i	$0.112692\pi$
$409$	8.86297e13	+	2.72774e14i	0.382914	+	1.17849i	−0.555068	+	0.831805i	$0.687308\pi$
$410$	1.26177e14	+	9.16730e13i	0.537860	+	0.390778i
$411$	−1.81181e14	+	1.31636e14i	−0.762048	+	0.553660i
$412$	2.75656e13	−	8.48381e13i	0.114402	−	0.352092i
$413$	8.90248e13	−	2.73990e14i	0.364574	−	1.12204i
$414$	1.77563e14	−	1.29007e14i	0.717549	−	0.521330i
$415$	1.71083e14	+	1.24299e14i	0.682250	+	0.495683i
$416$	9.81614e12	+	3.02110e13i	0.0386303	+	0.118892i
$417$	−4.93702e13			−0.191742
$418$	−7.06603e13	−	2.55696e14i	−0.270836	−	0.980062i
$419$	−3.03480e14			−1.14803			−0.574015	−	0.818845i	$-0.694615\pi$
$419$	−3.03480e14			−1.14803			−0.574015	+	0.818845i	$0.694615\pi$
$420$	−1.24853e14	−	3.84259e14i	−0.466153	−	1.43467i
$421$	−7.48711e13	−	5.43971e13i	−0.275907	−	0.200458i	0.441223	−	0.897397i	$-0.354545\pi$
$421$	−7.48711e13	−	5.43971e13i	−0.275907	−	0.200458i	−0.717130	+	0.696939i	$0.754545\pi$
$422$	−1.84167e14	+	1.33805e14i	−0.669876	+	0.486693i
$423$	1.77286e13	−	5.45630e13i	0.0636506	−	0.195896i
$424$	−2.24708e13	+	6.91581e13i	−0.0796355	+	0.245093i
$425$	3.15900e12	−	2.29515e12i	0.0110512	−	0.00802919i
$426$	−4.64529e14	−	3.37500e14i	−1.60421	−	1.16552i
$427$	−2.06761e14	−	6.36346e14i	−0.704882	−	2.16940i
$428$	2.60777e13			0.0877665
$429$	−9.97247e13	−	3.60869e14i	−0.331350	−	1.19904i
$430$	1.64653e14			0.540125
$431$	1.28559e14	+	3.95663e14i	0.416367	+	1.28145i	0.911023	+	0.412356i	$0.135294\pi$
$431$	1.28559e14	+	3.95663e14i	0.416367	+	1.28145i	−0.494656	+	0.869089i	$0.664706\pi$
$432$	1.21778e14	+	8.84766e13i	0.389410	+	0.282923i
$433$	−1.35593e14	+	9.85140e13i	−0.428108	+	0.311039i	−0.780892	−	0.624666i	$-0.785235\pi$
$433$	−1.35593e14	+	9.85140e13i	−0.428108	+	0.311039i	0.352784	+	0.935705i	$0.385235\pi$
$434$	−1.26650e14	+	3.89789e14i	−0.394832	+	1.21517i
$435$	1.06811e14	−	3.28730e14i	0.328795	−	1.01193i
$436$	1.15247e14	−	8.37317e13i	0.350311	−	0.254516i
$437$	−2.32105e14	−	1.68634e14i	−0.696684	−	0.506170i
$438$	2.36999e14	+	7.29408e14i	0.702488	+	2.16204i
$439$	−5.77059e13			−0.168914			−0.0844570	−	0.996427i	$-0.526916\pi$
$439$	−5.77059e13			−0.168914			−0.0844570	+	0.996427i	$0.526916\pi$
$440$	4.50639e13	−	1.20195e14i	0.130268	−	0.347455i
$441$	1.22540e15			3.49837
$442$	−7.37141e12	−	2.26869e13i	−0.0207839	−	0.0639664i
$443$	1.94781e14	+	1.41517e14i	0.542408	+	0.394083i	0.824979	−	0.565164i	$-0.191187\pi$
$443$	1.94781e14	+	1.41517e14i	0.542408	+	0.394083i	−0.282570	+	0.959247i	$0.591187\pi$
$444$	−5.14826e14	+	3.74043e14i	−1.41597	+	1.02876i
$445$	8.91534e12	−	2.74386e13i	0.0242191	−	0.0745387i
$446$	3.68464e13	−	1.13401e14i	0.0988673	−	0.304282i
$447$	−1.12054e14	+	8.14118e13i	−0.296985	+	0.215772i
$448$	−6.31211e13	−	4.58601e13i	−0.165251	−	0.120062i
$449$	4.08404e13	+	1.25694e14i	0.105617	+	0.325056i	0.989875	−	0.141943i	$-0.0453350\pi$
$449$	4.08404e13	+	1.25694e14i	0.105617	+	0.325056i	−0.884258	+	0.466999i	$0.845335\pi$
$450$	5.88771e13			0.150410
$451$	−3.54620e14	−	1.58061e13i	−0.894936	−	0.0398891i
$452$	2.85586e14			0.711993
$453$	1.48149e14	+	4.55957e14i	0.364888	+	1.12301i
$454$	−1.01097e14	−	7.34516e13i	−0.245999	−	0.178729i
$455$	−4.08152e14	+	2.96540e14i	−0.981203	+	0.712886i
$456$	1.16356e14	−	3.58106e14i	0.276364	−	0.850560i
$457$	−5.51021e13	+	1.69587e14i	−0.129309	+	0.397972i	−0.994662	−	0.103191i	$-0.967095\pi$
$457$	−5.51021e13	+	1.69587e14i	−0.129309	+	0.397972i	0.865352	+	0.501164i	$0.167095\pi$
$458$	1.83037e14	−	1.32984e14i	0.424404	−	0.308348i
$459$	−9.14486e13	−	6.64413e13i	−0.209511	−	0.152219i
$460$	−4.28996e13	−	1.32031e14i	−0.0971148	−	0.298889i
$461$	−2.52722e14			−0.565312			−0.282656	−	0.959221i	$-0.591216\pi$
$461$	−2.52722e14			−0.565312			−0.282656	+	0.959221i	$0.591216\pi$
$462$	7.19148e14	+	5.73105e14i	1.58960	+	1.26679i
$463$	4.46426e14			0.975111			0.487555	−	0.873092i	$-0.337889\pi$
$463$	4.46426e14			0.975111			0.487555	+	0.873092i	$0.337889\pi$
$464$	−2.06260e13	−	6.34803e13i	−0.0445211	−	0.137022i
$465$	−7.74310e14	−	5.62569e14i	−1.65167	−	1.20001i
$466$	−3.01663e14	+	2.19171e14i	−0.635915	+	0.462019i
$467$	8.42401e13	−	2.59264e14i	0.175499	−	0.540132i	−0.824156	−	0.566362i	$-0.808350\pi$
$467$	8.42401e13	−	2.59264e14i	0.175499	−	0.540132i	0.999656	+	0.0262304i	$0.00835035\pi$
$468$	1.11149e14	−	3.42081e14i	0.228851	−	0.704330i
$469$	−3.73356e14	+	2.71259e14i	−0.759754	+	0.551993i
$470$	−2.93579e13	−	2.13297e13i	−0.0590455	−	0.0428990i
$471$	1.97921e14	+	6.09137e14i	0.393438	+	1.21088i
$472$	1.29916e14			0.255259
$473$	−3.12687e14	+	2.06554e14i	−0.607258	+	0.401142i
$474$	−3.71849e14			−0.713816
$475$	−2.37826e13	−	7.31952e13i	−0.0451278	−	0.138889i
$476$	4.74006e13	+	3.44386e13i	0.0889090	+	0.0645962i
$477$	6.66128e14	−	4.83970e14i	1.23511	−	0.897362i
$478$	1.11528e14	−	3.43246e14i	0.204423	−	0.629148i
$479$	2.67580e14	−	8.23525e14i	0.484850	−	1.49222i	−0.347347	−	0.937737i	$-0.612918\pi$
$479$	2.67580e14	−	8.23525e14i	0.484850	−	1.49222i	0.832198	−	0.554479i	$-0.187082\pi$
$480$	1.47404e14	−	1.07095e14i	0.264047	−	0.191841i
$481$	6.42847e14	+	4.67056e14i	1.13844	+	0.827124i
$482$	−1.00009e14	−	3.07796e14i	−0.175098	−	0.538895i
$483$	9.94515e14			1.72148
$484$	6.52037e13	+	2.84790e14i	0.111589	+	0.487389i
$485$	6.70767e14			1.13499
$486$	−4.54734e13	−	1.39953e14i	−0.0760777	−	0.234143i
$487$	1.56997e14	+	1.14065e14i	0.259706	+	0.188688i	0.710018	−	0.704184i	$-0.248687\pi$
$487$	1.56997e14	+	1.14065e14i	0.259706	+	0.188688i	−0.450311	+	0.892872i	$0.648687\pi$
$488$	2.44106e14	−	1.77353e14i	0.399272	−	0.290088i
$489$	−6.96724e13	+	2.14430e14i	−0.112684	+	0.346806i
$490$	2.39517e14	−	7.37157e14i	0.383052	−	1.17891i
$491$	5.71201e14	−	4.15002e14i	0.903319	−	0.656300i	−0.0359974	−	0.999352i	$-0.511461\pi$
$491$	5.71201e14	−	4.15002e14i	0.903319	−	0.656300i	0.939316	+	0.343052i	$0.111461\pi$
$492$	−4.07618e14	−	2.96152e14i	−0.637449	−	0.463134i
$493$	1.54890e13	+	4.76704e13i	0.0239534	+	0.0737209i
$494$	−4.70167e14			−0.719041
$495$	−1.21277e15	+	8.01132e14i	−1.83422	+	1.21165i
$496$	−1.84823e14			−0.276444
$497$	−5.44180e14	−	1.67481e15i	−0.804975	−	2.47746i
$498$	−5.52689e14	−	4.01552e14i	−0.808574	−	0.587463i
$499$	4.14438e14	−	3.01107e14i	0.599663	−	0.435680i	−0.246096	−	0.969245i	$-0.579148\pi$
$499$	4.14438e14	−	3.01107e14i	0.599663	−	0.435680i	0.845759	+	0.533565i	$0.179148\pi$
$500$	−1.01808e14	+	3.13332e14i	−0.145696	+	0.448405i
$501$	2.97821e14	−	9.16600e14i	0.421549	−	1.29740i
$502$	4.73863e14	−	3.44282e14i	0.663411	−	0.481996i
$503$	2.02496e14	+	1.47122e14i	0.280409	+	0.203729i	0.719096	−	0.694911i	$-0.244556\pi$
$503$	2.02496e14	+	1.47122e14i	0.280409	+	0.203729i	−0.438687	+	0.898640i	$0.644556\pi$
$504$	2.73000e14	+	8.40207e14i	0.373934	+	1.15085i
$505$	−9.87004e14			−1.33726
$506$	2.47100e14	+	1.96919e14i	0.331165	+	0.263913i
$507$	6.63343e14			0.879417
$508$	6.06132e13	+	1.86548e14i	0.0794907	+	0.244647i
$509$	1.02843e15	+	7.47199e14i	1.33422	+	0.969367i	0.999635	+	0.0270012i	$0.00859578\pi$
$509$	1.02843e15	+	7.47199e14i	1.33422	+	0.969367i	0.334584	+	0.942366i	$0.391404\pi$
$510$	−1.10692e14	+	8.04227e13i	−0.142063	+	0.103215i
$511$	−7.26862e14	+	2.23705e15i	−0.922862	+	2.84028i
$512$	1.08726e13	−	3.34623e13i	0.0136568	−	0.0420312i
$513$	−1.80244e15	+	1.30955e15i	−2.23983	+	1.62733i
$514$	−5.05779e14	−	3.67470e14i	−0.621819	−	0.451778i
$515$	1.97427e14	+	6.07616e14i	0.240141	+	0.739077i
$516$	−5.31917e14			−0.640133
$517$	8.25101e13	+	3.67764e12i	0.0982447	+	0.00437896i
$518$	−1.95168e15			−2.29929
$519$	−1.63934e13	−	5.04537e13i	−0.0191095	−	0.0588129i
$520$	−1.84058e14	−	1.33726e14i	−0.212293	−	0.154240i
$521$	1.27716e15	−	9.27910e14i	1.45760	−	1.05901i	0.473616	−	0.880732i	$-0.342949\pi$
$521$	1.27716e15	−	9.27910e14i	1.45760	−	1.05901i	0.983981	−	0.178274i	$-0.0570514\pi$
$522$	−2.33549e14	+	7.18791e14i	−0.263749	+	0.811736i
$523$	−2.11361e14	+	6.50502e14i	−0.236192	+	0.726924i	0.760769	+	0.649023i	$0.224822\pi$
$523$	−2.11361e14	+	6.50502e14i	−0.236192	+	0.726924i	−0.996961	+	0.0779017i	$0.975178\pi$
$524$	6.97816e13	−	5.06993e13i	0.0771647	−	0.0560634i
$525$	2.15834e14	+	1.56812e14i	0.236180	+	0.171595i
$526$	2.08998e14	+	6.43230e14i	0.226319	+	0.696538i
$527$	1.38793e14			0.148733
$528$	−1.45580e14	+	3.88295e14i	−0.154389	+	0.411789i
$529$	−6.11094e14			−0.641360
$530$	−1.60938e14	−	4.95315e14i	−0.167163	−	0.514475i
$531$	−1.19010e15	−	8.64657e14i	−1.22339	−	0.888841i
$532$	9.34260e14	−	6.78780e14i	0.950504	−	0.690582i
$533$	−1.94413e14	+	5.98342e14i	−0.195761	+	0.602490i
$534$	−2.88012e13	+	8.86411e13i	−0.0287035	+	0.0883402i
$535$	−1.51101e14	+	1.09781e14i	−0.149046	+	0.108288i
$536$	−1.68367e14	−	1.22326e14i	−0.164381	−	0.119429i
$537$	−3.62083e14	−	1.11438e15i	−0.349904	−	1.07690i
$538$	7.70786e14			0.737278
$539$	4.69891e14	+	1.70038e15i	0.444897	+	1.60993i
$540$	−1.07807e15			−1.01038
$541$	1.29823e14	+	3.99554e14i	0.120439	+	0.370673i	0.993043	−	0.117756i	$-0.0375701\pi$
$541$	1.29823e14	+	3.99554e14i	0.120439	+	0.370673i	−0.872604	+	0.488429i	$0.837570\pi$
$542$	9.01281e14	+	6.54819e14i	0.827684	+	0.601347i
$543$	1.47548e15	−	1.07200e15i	1.34132	−	0.974527i
$544$	−8.16473e12	+	2.51285e13i	−0.00734764	+	0.0226137i
$545$	−3.15277e14	+	9.70323e14i	−0.280874	+	0.864442i
$546$	1.31854e15	−	9.57979e14i	1.16288	−	0.844883i
$547$	−3.48177e14	−	2.52965e14i	−0.303997	−	0.220867i	0.425319	−	0.905043i	$-0.360162\pi$
$547$	−3.48177e14	−	2.52965e14i	−0.303997	−	0.220867i	−0.729317	+	0.684176i	$0.760162\pi$
$548$	−9.57140e13	−	2.94577e14i	−0.0827337	−	0.254628i
$549$	−3.41652e15			−2.92372
$550$	2.25769e13	+	8.16982e13i	0.0191280	+	0.0692178i
$551$	9.87930e14			0.828690
$552$	1.38588e14	+	4.26531e14i	0.115096	+	0.354230i
$553$	−9.22635e14	−	6.70333e14i	−0.758650	−	0.551192i
$554$	−3.40956e14	+	2.47719e14i	−0.277584	+	0.201677i
$555$	1.40839e15	−	4.33459e15i	1.13531	−	3.49411i
$556$	2.11002e13	−	6.49396e13i	0.0168413	−	0.0518320i
$557$	−7.59244e14	+	5.51623e14i	−0.600037	+	0.435952i	−0.845892	−	0.533354i	$-0.820931\pi$
$557$	−7.59244e14	+	5.51623e14i	−0.600037	+	0.435952i	0.245855	+	0.969307i	$0.420931\pi$
$558$	1.69308e15	+	1.23010e15i	1.32492	+	0.962611i
$559$	2.05245e14	+	6.31680e14i	0.159041	+	0.489477i
$560$	5.58799e14			0.428767
$561$	1.09323e14	−	2.91589e14i	0.0830645	−	0.221552i
$562$	9.55394e14			0.718841
$563$	−2.02853e14	−	6.24316e14i	−0.151142	−	0.465167i	0.846608	−	0.532217i	$-0.178641\pi$
$563$	−2.02853e14	−	6.24316e14i	−0.151142	−	0.465167i	−0.997750	+	0.0670507i	$0.978641\pi$
$564$	9.48414e13	+	6.89063e13i	0.0699782	+	0.0508421i
$565$	−1.65475e15	+	1.20225e15i	−1.20911	+	0.878472i
$566$	4.95214e14	−	1.52411e15i	0.358346	−	1.10288i
$567$	9.10689e14	−	2.80281e15i	0.652624	−	2.00857i
$568$	6.42467e14	−	4.66779e14i	0.455969	−	0.331281i
$569$	−1.92658e15	−	1.39975e15i	−1.35416	−	0.983856i	−0.998792	−	0.0491307i	$-0.984355\pi$
$569$	−1.92658e15	−	1.39975e15i	−1.35416	−	0.983856i	−0.355370	−	0.934726i	$-0.615645\pi$
$570$	8.33348e14	+	2.56478e15i	0.580116	+	1.78541i
$571$	2.25189e15			1.55256			0.776281	−	0.630387i	$-0.217104\pi$
$571$	2.25189e15			1.55256			0.776281	+	0.630387i	$0.217104\pi$
$572$	5.17294e14	+	2.30568e13i	0.353231	+	0.0157442i
$573$	3.30132e15			2.23274
$574$	−4.77511e14	−	1.46963e15i	−0.319866	−	0.984446i
$575$	7.41606e13	+	5.38808e13i	0.0492039	+	0.0357487i
$576$	−3.22308e14	+	2.34170e14i	−0.211810	+	0.153889i
$577$	−4.05840e14	+	1.24905e15i	−0.264173	+	0.813040i	0.727710	+	0.685885i	$0.240585\pi$
$577$	−4.05840e14	+	1.24905e15i	−0.264173	+	0.813040i	−0.991883	+	0.127155i	$0.959415\pi$
$578$	−3.32768e14	+	1.02415e15i	−0.214555	+	0.660332i
$579$	−2.20300e15	+	1.60057e15i	−1.40696	+	1.02222i
$580$	3.86749e14	+	2.80989e14i	0.244667	+	0.177761i
$581$	−6.47457e14	−	1.99267e15i	−0.405735	−	1.24872i
$582$	−2.16693e15			−1.34514
$583$	9.26993e14	+	7.38740e14i	0.570032	+	0.454271i
$584$	−1.06072e15			−0.646148
$585$	7.96055e14	+	2.45001e15i	0.480381	+	1.47846i
$586$	−4.95827e14	−	3.60239e14i	−0.296410	−	0.215355i
$587$	−3.93744e14	+	2.86071e14i	−0.233187	+	0.169420i	−0.698242	−	0.715861i	$-0.746034\pi$
$587$	−3.93744e14	+	2.86071e14i	−0.233187	+	0.169420i	0.465056	+	0.885281i	$0.346034\pi$
$588$	−7.73765e14	+	2.38141e15i	−0.453977	+	1.39720i
$589$	8.45342e14	−	2.60170e15i	0.491359	−	1.51225i
$590$	−7.52763e14	+	5.46914e14i	−0.433483	+	0.314944i
$591$	1.88132e14	+	1.36686e14i	0.107333	+	0.0779816i
$592$	−2.71972e14	−	8.37043e14i	−0.153728	−	0.473128i
$593$	−3.32983e15			−1.86475			−0.932375	−	0.361493i	$-0.882267\pi$
$593$	−3.32983e15			−1.86475			−0.932375	+	0.361493i	$0.882267\pi$
$594$	2.04733e15	−	1.35242e15i	1.13596	−	0.750389i
$595$	−4.19629e14			−0.230686
$596$	−5.91955e13	−	1.82185e14i	−0.0322429	−	0.0992335i
$597$	4.51014e15	+	3.27681e15i	2.43406	+	1.76845i
$598$	4.53053e14	−	3.29162e14i	0.242266	−	0.176016i
$599$	9.42894e14	−	2.90193e15i	0.499592	−	1.53759i	−0.310085	−	0.950709i	$-0.600357\pi$
$599$	9.42894e14	−	2.90193e15i	0.499592	−	1.53759i	0.809677	−	0.586876i	$-0.199643\pi$
$600$	−3.71772e13	+	1.14420e14i	−0.0195184	+	0.0600716i
$601$	2.90212e15	−	2.10852e15i	1.50975	−	1.09690i	0.543468	−	0.839430i	$-0.317111\pi$
$601$	2.90212e15	−	2.10852e15i	1.50975	−	1.09690i	0.966286	−	0.257471i	$-0.0828892\pi$
$602$	−1.31979e15	−	9.58887e14i	−0.680339	−	0.494295i
$603$	7.28190e14	+	2.24114e15i	0.371963	+	1.14478i
$604$	−6.63065e14			−0.335624
$605$	−1.57670e15	−	1.37565e15i	−0.790853	−	0.690007i
$606$	3.18854e15			1.58487
$607$	9.20178e14	+	2.83202e15i	0.453246	+	1.39495i	0.873182	+	0.487394i	$0.162053\pi$
$607$	9.20178e14	+	2.83202e15i	0.453246	+	1.39495i	−0.419936	+	0.907554i	$0.637947\pi$
$608$	4.21309e14	+	3.06099e14i	0.205651	+	0.149414i
$609$	−2.77057e15	+	2.01294e15i	−1.34021	+	0.973722i
$610$	−6.67792e14	+	2.05525e15i	−0.320131	+	0.985261i
$611$	4.52345e13	−	1.39217e14i	0.0214903	−	0.0661404i
$612$	2.42036e14	−	1.75850e14i	0.113959	−	0.0827959i
$613$	−1.57881e14	−	1.14707e14i	−0.0736711	−	0.0535252i	0.550340	−	0.834941i	$-0.314498\pi$
$613$	−1.57881e14	−	1.14707e14i	−0.0736711	−	0.0535252i	−0.624011	+	0.781415i	$0.714498\pi$
$614$	−1.45826e14	−	4.48807e14i	−0.0674388	−	0.207555i
$615$	3.60857e15			1.65395
$616$	−1.06119e15	+	7.01001e14i	−0.482059	+	0.318438i
$617$	6.07892e14			0.273689			0.136845	−	0.990593i	$-0.456304\pi$
$617$	6.07892e14			0.273689			0.136845	+	0.990593i	$0.456304\pi$
$618$	−6.37792e14	−	1.96292e15i	−0.284605	−	0.875923i
$619$	1.26863e15	+	9.21711e14i	0.561094	+	0.407658i	0.831859	−	0.554987i	$-0.187277\pi$
$619$	1.26863e15	+	9.21711e14i	0.561094	+	0.407658i	−0.270765	+	0.962645i	$0.587277\pi$
$620$	1.07091e15	−	7.78062e14i	0.469460	−	0.341083i
$621$	8.20021e14	−	2.52377e15i	0.356304	−	1.09659i
$622$	−3.98777e14	+	1.22731e15i	−0.171745	+	0.528576i
$623$	−2.31255e14	+	1.68017e14i	−0.0987205	+	0.0717246i
$624$	5.94604e14	+	4.32005e14i	0.251601	+	0.182799i
$625$	−8.03978e14	−	2.47439e15i	−0.337213	−	1.03783i
$626$	2.59951e15			1.08077
$627$	−4.80004e15	−	3.82526e15i	−1.97822	−	1.57648i
$628$	−8.85822e14			−0.361883
$629$	2.04236e14	+	6.28575e14i	0.0827094	+	0.254553i
$630$	−5.11890e15	−	3.71910e15i	−2.05496	−	1.49302i
$631$	−2.25410e15	+	1.63770e15i	−0.897042	+	0.651739i	−0.937704	−	0.347434i	$-0.887053\pi$
$631$	−2.25410e15	+	1.63770e15i	−0.897042	+	0.651739i	0.0406629	+	0.999173i	$0.487053\pi$
$632$	1.58923e14	−	4.89116e14i	0.0626965	−	0.192960i
$633$	−1.62761e15	+	5.00926e15i	−0.636545	+	1.95908i
$634$	−7.62080e14	+	5.53684e14i	−0.295468	+	0.214670i
$635$	−1.13653e15	−	8.25737e14i	−0.436843	−	0.317385i
$636$	5.19913e14	+	1.60013e15i	0.198115	+	0.609734i
$637$	3.12661e15			1.18115
$638$	−1.08695e15	−	4.84477e13i	−0.407097	−	0.0181451i
$639$	−8.99201e15			−3.33889
$640$	7.78701e13	+	2.39660e14i	0.0286669	+	0.0882277i
$641$	−3.38600e15	−	2.46007e15i	−1.23586	−	0.897902i	−0.238541	−	0.971132i	$-0.576669\pi$
$641$	−3.38600e15	−	2.46007e15i	−1.23586	−	0.897902i	−0.997315	+	0.0732305i	$0.976669\pi$
$642$	4.88134e14	−	3.54650e14i	0.176643	−	0.128339i
$643$	−1.22989e14	+	3.78521e14i	−0.0441272	+	0.135809i	−0.970693	−	0.240324i	$-0.922746\pi$
$643$	−1.22989e14	+	3.78521e14i	−0.0441272	+	0.135809i	0.926566	+	0.376133i	$0.122746\pi$
$644$	−4.25042e14	+	1.30814e15i	−0.151203	+	0.465354i
$645$	3.08205e15	−	2.23924e15i	1.08708	−	0.789810i
$646$	−3.16381e14	−	2.29864e14i	−0.110645	−	0.0803883i
$647$	−5.12144e13	−	1.57622e14i	−0.0177590	−	0.0546566i	0.941784	−	0.336218i	$-0.109148\pi$
$647$	−5.12144e13	−	1.57622e14i	−0.0177590	−	0.0546566i	−0.959543	+	0.281561i	$0.909148\pi$
$648$	1.32899e15			0.456939
$649$	7.43450e14	−	1.98295e15i	0.253458	−	0.676030i
$650$	1.50225e14			0.0507829
$651$	2.93034e15	+	9.01866e15i	0.982251	+	3.02306i
$652$	−2.52275e14	−	1.83289e14i	−0.0838518	−	0.0609219i
$653$	−8.20188e14	+	5.95902e14i	−0.270328	+	0.196405i	−0.714688	−	0.699444i	$-0.753431\pi$
$653$	−8.20188e14	+	5.95902e14i	−0.270328	+	0.196405i	0.444360	+	0.895848i	$0.353431\pi$
$654$	1.01851e15	−	3.13465e15i	0.332880	−	1.02450i
$655$	−1.90899e14	+	5.87527e14i	−0.0618695	+	0.190415i
$656$	5.63757e14	−	4.09593e14i	0.181184	−	0.131638i
$657$	9.71681e15	+	7.05967e15i	3.09681	+	2.24996i
$658$	1.11103e14	+	3.41941e14i	0.0351144	+	0.108071i
$659$	−4.92740e15			−1.54436			−0.772179	−	0.635405i	$-0.780833\pi$
$659$	−4.92740e15			−1.54436			−0.772179	+	0.635405i	$0.780833\pi$
$660$	−7.91102e14	−	2.86273e15i	−0.245890	−	0.889792i
$661$	2.41249e15			0.743632			0.371816	−	0.928306i	$-0.378735\pi$
$661$	2.41249e15			0.743632			0.371816	+	0.928306i	$0.378735\pi$
$662$	−8.92003e14	−	2.74530e15i	−0.272676	−	0.839212i
$663$	−4.46517e14	−	3.24413e14i	−0.135367	−	0.0983500i
$664$	7.64397e14	−	5.55367e14i	0.229824	−	0.166977i
$665$	−2.55583e15	+	7.86602e15i	−0.762101	+	2.34550i
$666$	−3.07955e15	+	9.47788e15i	−0.910707	+	2.80287i
$667$	−9.51969e14	+	6.91646e14i	−0.279210	+	0.202858i
$668$	1.07837e15	+	7.83484e14i	0.313689	+	0.227908i
$669$	−8.52524e14	−	2.62380e15i	−0.245959	−	0.756984i
$670$	1.49052e15			0.426507
$671$	−1.31009e15	−	4.74078e15i	−0.371816	−	1.34548i
$672$	−1.80521e15			−0.508157
$673$	−1.37426e15	−	4.22953e15i	−0.383694	−	1.18089i	−0.937423	−	0.348192i	$-0.886796\pi$
$673$	−1.37426e15	−	4.22953e15i	−0.383694	−	1.18089i	0.553729	−	0.832697i	$-0.313204\pi$
$674$	1.04332e15	+	7.58019e14i	0.288928	+	0.209919i
$675$	5.75905e14	−	4.18419e14i	0.158190	−	0.114932i
$676$	−2.83504e14	+	8.72535e14i	−0.0772417	+	0.237726i
$677$	1.48485e15	−	4.56989e15i	0.401277	−	1.23500i	−0.522687	−	0.852525i	$-0.675070\pi$
$677$	1.48485e15	−	4.56989e15i	0.401277	−	1.23500i	0.923964	−	0.382480i	$-0.124930\pi$
$678$	5.34572e15	−	3.88390e15i	1.43299	−	1.04113i
$679$	−5.37659e15	−	3.90632e15i	−1.42963	−	1.03869i
$680$	−5.84764e13	−	1.79972e14i	−0.0154234	−	0.0474685i
$681$	−2.89131e15			−0.756459
$682$	−1.05766e15	+	2.82102e15i	−0.274494	+	0.732137i
$683$	5.26233e15			1.35477			0.677383	−	0.735631i	$-0.263114\pi$
$683$	5.26233e15			1.35477			0.677383	+	0.735631i	$0.263114\pi$
$684$	−1.82217e15	−	5.60807e15i	−0.465351	−	1.43220i
$685$	1.79469e15	+	1.30392e15i	0.454665	+	0.330333i
$686$	−2.49317e15	+	1.81140e15i	−0.626571	+	0.455230i
$687$	1.61762e15	−	4.97852e15i	0.403287	−	1.24119i
$688$	2.27334e14	−	6.99662e14i	0.0562248	−	0.173042i
$689$	1.69962e15	−	1.23485e15i	0.417011	−	0.302976i
$690$	−2.59861e15	−	1.88800e15i	−0.632515	−	0.459549i
$691$	−6.64903e14	−	2.04636e15i	−0.160557	−	0.494143i	0.838125	−	0.545479i	$-0.183652\pi$
$691$	−6.64903e14	−	2.04636e15i	−0.160557	−	0.494143i	−0.998681	+	0.0513355i	$0.983652\pi$
$692$	7.33710e13			0.0175768
$693$	1.43866e16	+	6.41240e14i	3.41921	+	0.152401i
$694$	−3.98307e14			−0.0939162
$695$	1.51121e14	+	4.65102e14i	0.0353515	+	0.108801i
$696$	−1.24940e15	−	9.07744e14i	−0.289969	−	0.210675i
$697$	−4.23352e14	+	3.07583e14i	−0.0974813	+	0.0708243i
$698$	6.32828e14	−	1.94764e15i	0.144571	−	0.444943i
$699$	−2.66599e15	+	8.20507e15i	−0.604274	+	1.85976i
$700$	−2.98509e14	+	2.16879e14i	−0.0671302	+	0.0487729i
$701$	−1.38105e14	−	1.00339e14i	−0.0308149	−	0.0223883i	0.572271	−	0.820064i	$-0.306062\pi$
$701$	−1.38105e14	−	1.00339e14i	−0.0308149	−	0.0223883i	−0.603086	+	0.797676i	$0.706062\pi$
$702$	−1.34385e15	−	4.13595e15i	−0.297507	−	0.915632i
$703$	1.30267e16			2.86141
$704$	−4.48528e14	−	3.57442e14i	−0.0977552	−	0.0779032i
$705$	−8.39613e14			−0.181568
$706$	1.47597e15	+	4.54257e15i	0.316702	+	0.974710i
$707$	7.91143e15	+	5.74799e15i	1.68441	+	1.22380i
$708$	2.43182e15	−	1.76682e15i	0.513746	−	0.373258i
$709$	−1.77320e15	+	5.45734e15i	−0.371709	+	1.14400i	0.573964	+	0.818881i	$0.305405\pi$
$709$	−1.77320e15	+	5.45734e15i	−0.371709	+	1.14400i	−0.945672	+	0.325121i	$0.894595\pi$
$710$	−1.75758e15	+	5.40926e15i	−0.365589	+	1.12517i
$711$	−4.71114e15	+	3.42285e15i	−0.972397	+	0.706488i
$712$	−1.04286e14	−	7.57680e13i	−0.0213592	−	0.0155184i
$713$	1.00687e15	+	3.09882e15i	0.204635	+	0.629801i
$714$	1.35562e15			0.273400
$715$	−3.09439e15	+	2.04409e15i	−0.619286	+	0.409087i
$716$	1.62055e15			0.321842
$717$	−2.58044e15	−	7.94178e15i	−0.508556	−	1.56517i
$718$	−1.20853e15	−	8.78049e14i	−0.236360	−	0.171725i
$719$	1.19653e15	−	8.69333e14i	0.232229	−	0.168724i	−0.465585	−	0.885003i	$-0.654156\pi$
$719$	1.19653e15	−	8.69333e14i	0.232229	−	0.168724i	0.697814	+	0.716279i	$0.254156\pi$
$720$	8.81727e14	−	2.71368e15i	0.169827	−	0.522672i
$721$	1.95607e15	−	6.02016e15i	0.373886	−	1.15070i
$722$	−3.22007e15	+	2.33952e15i	−0.610817	+	0.443784i
$723$	−6.05795e15	−	4.40136e15i	−1.14042	−	0.828565i
$724$	7.79462e14	+	2.39894e15i	0.145624	+	0.448184i
$725$	−3.15657e14			−0.0585270
$726$	5.09358e15	+	4.44407e15i	0.937286	+	0.817767i
$727$	−6.96923e15			−1.27276			−0.636378	−	0.771377i	$-0.719568\pi$
$727$	−6.96923e15			−1.27276			−0.636378	+	0.771377i	$0.719568\pi$
$728$	6.96559e14	+	2.14379e15i	0.126251	+	0.388561i
$729$	3.05798e15	+	2.22175e15i	0.550090	+	0.399664i
$730$	6.14609e15	−	4.46539e15i	1.09729	−	0.797231i
$731$	−1.70716e14	+	5.25409e14i	−0.0302502	+	0.0931005i
$732$	2.15732e15	−	6.63955e15i	0.379405	−	1.16769i
$733$	−1.60511e15	+	1.16618e15i	−0.280177	+	0.203561i	−0.718995	−	0.695016i	$-0.755397\pi$
$733$	−1.60511e15	+	1.16618e15i	−0.280177	+	0.203561i	0.438817	+	0.898576i	$0.355397\pi$
$734$	−2.53952e14	−	1.84507e14i	−0.0439970	−	0.0319657i
$735$	−5.54176e15	−	1.70558e16i	−0.952945	−	2.93286i
$736$	−6.20272e14			−0.105865
$737$	−2.83059e15	+	1.86983e15i	−0.479519	+	0.316760i
$738$	−7.89038e15			−1.32675
$739$	−4.29101e13	−	1.32064e14i	−0.00716168	−	0.0220414i	0.947412	−	0.320017i	$-0.103689\pi$
$739$	−4.29101e13	−	1.32064e14i	−0.00716168	−	0.0220414i	−0.954574	+	0.297976i	$0.903689\pi$
$740$	5.09962e15	+	3.70509e15i	0.844818	+	0.613796i
$741$	−8.80079e15	+	6.39415e15i	−1.44718	+	1.05144i
$742$	−1.59454e15	+	4.90749e15i	−0.260264	+	0.801010i
$743$	−1.95841e14	+	6.02737e14i	−0.0317297	+	0.0976539i	−0.965667	−	0.259783i	$-0.916349\pi$
$743$	−1.95841e14	+	6.02737e14i	−0.0317297	+	0.0976539i	0.933937	+	0.357436i	$0.116349\pi$
$744$	−3.45960e15	+	2.51355e15i	−0.556385	+	0.404237i
$745$	1.10995e15	+	8.06425e14i	0.177192	+	0.128737i
$746$	−1.71009e15	−	5.26311e15i	−0.270991	−	0.834024i
$747$	−1.06986e16			−1.68291
$748$	3.36821e14	+	2.68420e14i	0.0525945	+	0.0419137i
$749$	1.85049e15			0.286838
$750$	2.35555e15	+	7.24965e15i	0.362457	+	1.11553i
$751$	6.47843e14	+	4.70685e14i	0.0989578	+	0.0718971i	0.636164	−	0.771554i	$-0.280520\pi$
$751$	6.47843e14	+	4.70685e14i	0.0989578	+	0.0718971i	−0.537206	+	0.843451i	$0.680520\pi$
$752$	−1.31170e14	+	9.53009e13i	−0.0198901	+	0.0144510i
$753$	4.18784e15	−	1.28888e16i	0.630402	−	1.94018i
$754$	−5.95900e14	+	1.83399e15i	−0.0890494	+	0.274066i
$755$	3.84195e15	−	2.79134e15i	0.569959	−	0.414100i
$756$	8.64141e15	+	6.27835e15i	1.27267	+	0.924646i
$757$	−1.29889e15	−	3.99757e15i	−0.189909	−	0.584479i	0.810090	−	0.586306i	$-0.199418\pi$
$757$	−1.29889e15	−	3.99757e15i	−0.189909	−	0.584479i	−0.999998	+	0.00182721i	$0.999418\pi$
$758$	4.47601e15			0.649697
$759$	7.30337e15	+	3.25526e14i	1.05243	+	0.0469089i
$760$	−3.72977e15			−0.533590
$761$	−8.57831e14	−	2.64013e15i	−0.121839	−	0.374982i	0.871473	−	0.490443i	$-0.163165\pi$
$761$	−8.57831e14	−	2.64013e15i	−0.121839	−	0.374982i	−0.993312	+	0.115462i	$0.963165\pi$
$762$	3.67159e15	+	2.66757e15i	0.517728	+	0.376152i
$763$	8.17798e15	−	5.94165e15i	1.14488	−	0.831806i
$764$	−1.41094e15	+	4.34242e15i	−0.196108	+	0.603558i
$765$	−6.62131e14	+	2.03783e15i	−0.0913705	+	0.281210i
$766$	2.81459e15	−	2.04492e15i	0.385617	−	0.280167i
$767$	−3.03653e15	−	2.20617e15i	−0.413051	−	0.300099i
$768$	−2.51561e14	−	7.74227e14i	−0.0339748	−	0.104564i
$769$	−1.50260e15			−0.201488			−0.100744	−	0.994912i	$-0.532122\pi$
$769$	−1.50260e15			−0.201488			−0.100744	+	0.994912i	$0.532122\pi$
$770$	3.19776e15	−	8.52913e15i	0.425742	−	1.13555i
$771$	−1.44649e16			−1.91213
$772$	−1.16380e15	−	3.58179e15i	−0.152750	−	0.470116i
$773$	5.31459e15	+	3.86128e15i	0.692600	+	0.503204i	0.877514	−	0.479551i	$-0.159201\pi$
$773$	5.31459e15	+	3.86128e15i	0.692600	+	0.503204i	−0.184914	+	0.982755i	$0.559201\pi$
$774$	−6.73912e15	+	4.89625e15i	−0.872022	+	0.633561i
$775$	−2.70098e14	+	8.31277e14i	−0.0347026	+	0.106804i
$776$	9.26115e14	−	2.85029e15i	0.118148	−	0.363621i
$777$	−3.65324e16	+	2.65423e16i	−4.62767	+	3.36220i
$778$	6.15173e15	+	4.46949e15i	0.773765	+	0.562173i
$779$	3.18721e15	+	9.80921e15i	0.398065	+	1.22512i
$780$	−5.26392e15			−0.652813
$781$	−3.44806e15	−	1.24774e16i	−0.424614	−	1.53653i
$782$	4.65792e14			0.0569580
$783$	2.82374e15	+	8.69059e15i	0.342875	+	1.05526i
$784$	−2.80171e15	−	2.03556e15i	−0.337819	−	0.245440i
$785$	5.13266e15	−	3.72910e15i	0.614554	−	0.446499i
$786$	6.16705e14	−	1.89802e15i	0.0733252	−	0.225672i
$787$	5.27087e14	−	1.62221e15i	0.0622330	−	0.191534i	−0.915106	−	0.403213i	$-0.867893\pi$
$787$	5.27087e14	−	1.62221e15i	0.0622330	−	0.191534i	0.977339	+	0.211680i	$0.0678933\pi$
$788$	−2.60196e14	+	1.89043e14i	−0.0305075	+	0.0221650i
$789$	1.26599e16	+	9.19794e15i	1.47403	+	1.07094i
$790$	1.13822e15	+	3.50308e15i	0.131606	+	0.405043i
$791$	2.02653e16			2.32693
$792$	1.72980e15	+	6.25955e15i	0.197245	+	0.713764i
$793$	−8.71724e15			−0.987135
$794$	−1.99442e15	−	6.13821e15i	−0.224287	−	0.690286i
$795$	−9.74866e15	−	7.08281e15i	−1.08874	−	0.791018i
$796$	−6.23775e15	+	4.53199e15i	−0.691841	+	0.502652i
$797$	−4.45819e15	+	1.37209e16i	−0.491064	+	1.51134i	0.331938	+	0.943301i	$0.392298\pi$
$797$	−4.45819e15	+	1.37209e16i	−0.491064	+	1.51134i	−0.823002	+	0.568038i	$0.807702\pi$
$798$	8.25666e15	−	2.54114e16i	0.903210	−	2.77979i
$799$	9.85021e13	−	7.15660e13i	0.0107013	−	0.00777498i
$800$	−1.34614e14	−	9.78028e13i	−0.0145243	−	0.0105525i
$801$	4.51038e14	+	1.38815e15i	0.0483319	+	0.148750i
$802$	−4.55089e15			−0.484325
$803$	−6.07005e15	+	1.61902e16i	−0.641589	+	1.71126i
$804$	−4.81516e15			−0.505478
$805$	−3.04418e15	−	9.36902e15i	−0.317390	−	0.976825i
$806$	4.31989e15	+	3.13859e15i	0.447332	+	0.325006i
$807$	1.44279e16	−	1.04825e16i	1.48388	−	1.07810i
$808$	−1.36274e15	+	4.19408e15i	−0.139204	+	0.428424i
$809$	−2.82591e15	+	8.69725e15i	−0.286709	+	0.882400i	0.699172	+	0.714953i	$0.253552\pi$
$809$	−2.82591e15	+	8.69725e15i	−0.286709	+	0.882400i	−0.985881	+	0.167446i	$0.946448\pi$
$810$	−7.70047e15	+	5.59472e15i	−0.775978	+	0.563781i
$811$	−6.55772e15	−	4.76446e15i	−0.656354	−	0.476869i	0.209076	−	0.977899i	$-0.432954\pi$
$811$	−6.55772e15	−	4.76446e15i	−0.656354	−	0.476869i	−0.865430	+	0.501030i	$0.832954\pi$
$812$	−1.46363e15	−	4.50459e15i	−0.145504	−	0.447814i
$813$	2.57759e16			2.54517
$814$	−1.43324e16	−	6.38825e14i	−1.40568	−	0.0626538i
$815$	2.23334e15			0.217565
$816$	1.88909e14	+	5.81404e14i	0.0182792	+	0.0562577i
$817$	8.80913e15	+	6.40021e15i	0.846665	+	0.615138i
$818$	−7.42514e15	+	5.39468e15i	−0.708862	+	0.515018i
$819$	7.88717e15	−	2.42742e16i	0.747928	−	2.30189i
$820$	−1.54225e15	+	4.74656e15i	−0.145271	+	0.447098i
$821$	9.90062e15	−	7.19322e15i	0.926350	−	0.673033i	−0.0187465	−	0.999824i	$-0.505968\pi$
$821$	9.90062e15	−	7.19322e15i	0.926350	−	0.673033i	0.945096	+	0.326792i	$0.105968\pi$
$822$	−5.79779e15	−	4.21234e15i	−0.538849	−	0.391497i
$823$	−2.02188e15	−	6.22270e15i	−0.186662	−	0.574486i	0.813311	−	0.581829i	$-0.197663\pi$
$823$	−2.02188e15	−	6.22270e15i	−0.186662	−	0.574486i	−0.999973	+	0.00734281i	$0.997663\pi$
$824$	2.85453e15			0.261779
$825$	1.53368e15	+	1.22222e15i	0.139713	+	0.111341i
$826$	9.21889e15			0.834235
$827$	−6.65208e14	−	2.04730e15i	−0.0597967	−	0.184035i	0.916696	−	0.399585i	$-0.130846\pi$
$827$	−6.65208e14	−	2.04730e15i	−0.0597967	−	0.184035i	−0.976493	+	0.215550i	$0.930846\pi$
$828$	5.68203e15	+	4.12824e15i	0.507384	+	0.368636i
$829$	1.13528e16	−	8.24828e15i	1.00705	−	0.731667i	0.0434645	−	0.999055i	$-0.486160\pi$
$829$	1.13528e16	−	8.24828e15i	1.00705	−	0.731667i	0.963589	+	0.267388i	$0.0861605\pi$
$830$	−2.09114e15	+	6.43586e15i	−0.184269	+	0.567123i
$831$	−3.01325e15	+	9.27383e15i	−0.263773	+	0.811809i
$832$	−8.22368e14	+	5.97485e14i	−0.0715135	+	0.0519576i
$833$	2.10394e15	+	1.52860e15i	0.181754	+	0.132052i
$834$	−4.88200e14	−	1.50252e15i	−0.0418971	−	0.128946i
$835$	−9.54664e15			−0.813907
$836$	7.08306e15	−	4.67892e15i	0.599910	−	0.396288i
$837$	2.53027e16			2.12901
$838$	−3.00098e15	−	9.23606e15i	−0.250854	−	0.772049i
$839$	−1.78110e16	−	1.29404e16i	−1.47910	−	1.07463i	−0.977846	−	0.209327i	$-0.932873\pi$
$839$	−1.78110e16	−	1.29404e16i	−1.47910	−	1.07463i	−0.501253	−	0.865301i	$-0.667127\pi$
$840$	1.04598e16	−	7.59952e15i	0.862956	−	0.626975i
$841$	−2.51804e15	+	7.74973e15i	−0.206388	+	0.635197i
$842$	9.15143e14	−	2.81652e15i	0.0745200	−	0.229349i
$843$	1.78835e16	−	1.29931e16i	1.44677	−	1.05114i
$844$	−5.89336e15	−	4.28178e15i	−0.473674	−	0.344144i
$845$	−2.03047e15	−	6.24916e15i	−0.162138	−	0.499010i
$846$	1.83587e15			0.145648
$847$	4.62689e15	+	2.02089e16i	0.364696	+	1.59288i
$848$	−2.32695e15			−0.182226
$849$	−1.14579e16	−	3.52638e16i	−0.891482	−	2.74370i
$850$	1.01088e14	+	7.34448e13i	0.00781440	+	0.00567750i
$851$	−1.25525e16	+	9.11995e15i	−0.964093	+	0.700455i
$852$	5.67790e15	−	1.74748e16i	0.433281	−	1.33350i
$853$	−9.33438e14	+	2.87283e15i	−0.0707727	+	0.217816i	−0.980187	−	0.198076i	$-0.936531\pi$
$853$	−9.33438e14	+	2.87283e15i	−0.0707727	+	0.217816i	0.909414	+	0.415892i	$0.136531\pi$
$854$	1.73219e16	−	1.25851e16i	1.30490	−	0.948064i
$855$	3.41667e16	+	2.48236e16i	2.55735	+	1.85802i
$856$	2.57871e14	+	7.93645e14i	0.0191777	+	0.0590229i
$857$	8.84423e15			0.653530			0.326765	−	0.945106i	$-0.394041\pi$
$857$	8.84423e15			0.653530			0.326765	+	0.945106i	$0.394041\pi$
$858$	9.99650e15	−	6.60348e15i	0.733952	−	0.484833i
$859$	−4.83822e15			−0.352958			−0.176479	−	0.984304i	$-0.556471\pi$
$859$	−4.83822e15			−0.352958			−0.176479	+	0.984304i	$0.556471\pi$
$860$	1.62818e15	+	5.01103e15i	0.118022	+	0.363233i
$861$	−2.89248e16	−	2.10151e16i	−2.08331	−	1.51361i
$862$	−1.07703e16	+	7.82505e15i	−0.770790	+	0.560012i
$863$	−7.01253e15	+	2.15824e16i	−0.498673	+	1.53476i	0.312481	+	0.949924i	$0.398840\pi$
$863$	−7.01253e15	+	2.15824e16i	−0.498673	+	1.53476i	−0.811154	+	0.584833i	$0.801160\pi$
$864$	−1.48848e15	+	4.58106e15i	−0.105176	+	0.323699i
$865$	−4.25129e14	+	3.08874e14i	−0.0298492	+	0.0216867i
$866$	−4.33897e15	−	3.15245e15i	−0.302718	−	0.219938i
$867$	7.69934e15	+	2.36961e16i	0.533763	+	1.64275i
$868$	−1.31152e16			−0.903473
$869$	−6.55609e15	−	5.22469e15i	−0.448783	−	0.357645i
$870$	1.10607e16			0.752363
$871$	1.85798e15	+	5.71826e15i	0.125586	+	0.386513i
$872$	3.68790e15	+	2.67942e15i	0.247707	+	0.179970i
$873$	−2.74539e16	+	1.99464e16i	−1.83242	+	1.33133i
$874$	2.83699e15	−	8.73137e15i	0.188168	−	0.579121i
$875$	−7.22434e15	+	2.22342e16i	−0.476161	+	1.46547i
$876$	−1.98551e16	+	1.44256e16i	−1.30047	+	0.944845i
$877$	−1.66291e16	−	1.20817e16i	−1.08236	−	0.786377i	−0.104263	−	0.994550i	$-0.533248\pi$
$877$	−1.66291e16	−	1.20817e16i	−1.08236	−	0.786377i	−0.978092	+	0.208173i	$0.933248\pi$
$878$	−5.70628e14	−	1.75621e15i	−0.0369091	−	0.113594i
$879$	−1.41803e16			−0.911477
$880$	4.10362e15	+	1.82907e14i	0.262128	+	0.0116835i
$881$	1.90747e16			1.21085			0.605426	−	0.795902i	$-0.293003\pi$
$881$	1.90747e16			1.21085			0.605426	+	0.795902i	$0.293003\pi$
$882$	1.21174e16	+	3.72936e16i	0.764423	+	2.35265i
$883$	1.60184e16	+	1.16380e16i	1.00423	+	0.729617i	0.962992	−	0.269532i	$-0.0868689\pi$
$883$	1.60184e16	+	1.16380e16i	1.00423	+	0.729617i	0.0412408	+	0.999149i	$0.486869\pi$
$884$	6.17555e14	−	4.48680e14i	0.0384759	−	0.0279543i
$885$	−6.65265e15	+	2.04748e16i	−0.411914	+	1.26774i
$886$	−2.38079e15	+	7.32732e15i	−0.146499	+	0.450879i
$887$	7.79159e15	−	5.66092e15i	0.476482	−	0.346184i	−0.323480	−	0.946235i	$-0.604853\pi$
$887$	7.79159e15	−	5.66092e15i	0.476482	−	0.346184i	0.799962	+	0.600051i	$0.204853\pi$
$888$	−1.64744e16	−	1.19694e16i	−1.00124	−	0.727446i
$889$	4.30114e15	+	1.32376e16i	0.259791	+	0.799554i
$890$	9.23221e14			0.0554192
$891$	7.60520e15	−	2.02848e16i	0.453715	−	1.21016i
$892$	3.81559e15			0.226233
$893$	−7.41574e14	−	2.28233e15i	−0.0436990	−	0.134492i
$894$	−3.58572e15	−	2.60518e15i	−0.210000	−	0.152574i
$895$	−9.38988e15	+	6.82215e15i	−0.546554	+	0.397095i
$896$	7.71523e14	−	2.37450e15i	0.0446329	−	0.137366i
$897$	4.00392e15	−	1.23228e16i	0.230211	−	0.708518i
$898$	−3.42149e15	+	2.48586e15i	−0.195522	+	0.142055i
$899$	−9.07710e15	−	6.59490e15i	−0.515548	−	0.374567i
$900$	5.82208e14	+	1.79185e15i	0.0328658	+	0.101151i
$901$	1.74742e15			0.0980415
$902$	−3.02563e15	−	1.09487e16i	−0.168725	−	0.610559i
$903$	−3.77451e16			−2.09208
$904$	2.82403e15	+	8.69147e15i	0.155576	+	0.478814i
$905$	−1.46153e16	−	1.06187e16i	−0.800279	−	0.581437i
$906$	−1.24115e16	+	9.01751e15i	−0.675492	+	0.490774i
$907$	9.82361e15	−	3.02340e16i	0.531412	−	1.63552i	−0.219866	−	0.975530i	$-0.570562\pi$
$907$	9.82361e15	−	3.02340e16i	0.531412	−	1.63552i	0.751277	−	0.659987i	$-0.229438\pi$
$908$	1.23571e15	−	3.80311e15i	0.0664420	−	0.204487i
$909$	4.03972e16	−	2.93503e16i	2.15899	−	1.56860i
$910$	−1.30609e16	−	9.48927e15i	−0.693816	−	0.504087i
$911$	−4.22776e15	−	1.30117e16i	−0.223234	−	0.687043i	−0.998466	−	0.0553665i	$-0.982367\pi$
$911$	−4.22776e15	−	1.30117e16i	−0.223234	−	0.687043i	0.775232	−	0.631676i	$-0.217633\pi$
$912$	1.20491e16			0.632388
$913$	−4.10245e15	−	1.48454e16i	−0.214020	−	0.774465i
$914$	−5.70605e15			−0.295891
$915$	1.54509e16	+	4.75529e16i	0.796411	+	2.45110i
$916$	5.85720e15	+	4.25550e15i	0.300099	+	0.218035i
$917$	4.95174e15	−	3.59765e15i	0.252189	−	0.183226i
$918$	1.11777e15	−	3.44014e15i	0.0565871	−	0.174157i
$919$	2.10452e15	−	6.47703e15i	0.105905	−	0.325942i	−0.884037	−	0.467417i	$-0.845185\pi$
$919$	2.10452e15	−	6.47703e15i	0.105905	−	0.325942i	0.989942	+	0.141475i	$0.0451845\pi$
$920$	3.59401e15	−	2.61120e15i	0.179782	−	0.130619i
$921$	−8.83330e15	−	6.41777e15i	−0.439233	−	0.319121i
$922$	−2.49905e15	−	7.69130e15i	−0.123525	−	0.380172i
$923$	−2.29431e16			−1.12731
$924$	−1.03304e16	+	2.75536e16i	−0.504571	+	1.34581i
$925$	−4.16221e15			−0.202090
$926$	4.41450e15	+	1.35864e16i	0.213070	+	0.655761i
$927$	−2.61490e16	−	1.89984e16i	−1.25463	−	0.911545i
$928$	1.72799e15	−	1.25546e15i	0.0824188	−	0.0598808i
$929$	−1.16633e16	+	3.58960e16i	−0.553014	+	1.70200i	0.148117	+	0.988970i	$0.452679\pi$
$929$	−1.16633e16	+	3.58960e16i	−0.553014	+	1.70200i	−0.701131	+	0.713032i	$0.747321\pi$
$930$	9.46433e15	−	2.91282e16i	0.446101	−	1.37296i
$931$	4.14683e16	−	3.01285e16i	1.94309	−	1.41174i
$932$	−9.65320e15	−	7.01346e15i	−0.449660	−	0.326697i
$933$	9.22661e15	+	2.83966e16i	0.427261	+	1.31497i
$934$	8.72341e15			0.401586
$935$	−3.08161e15	−	1.37353e14i	−0.141031	−	0.00628601i
$936$	1.15099e16			0.523667
$937$	9.03809e15	+	2.78164e16i	0.408798	+	1.25815i	0.917682	+	0.397316i	$0.130058\pi$
$937$	9.03809e15	+	2.78164e16i	0.408798	+	1.25815i	−0.508884	+	0.860835i	$0.669942\pi$
$938$	−1.19474e16	−	8.68030e15i	−0.537227	−	0.390318i
$939$	4.86587e16	−	3.53526e16i	2.17520	−	1.58038i
$940$	3.58839e14	−	1.10439e15i	0.0159476	−	0.0490818i
$941$	3.19994e15	−	9.84840e15i	0.141384	−	0.435134i	−0.855145	−	0.518389i	$-0.826532\pi$
$941$	3.19994e15	−	9.84840e15i	0.141384	−	0.435134i	0.996528	+	0.0832556i	$0.0265318\pi$
$942$	−1.65812e16	+	1.20469e16i	−0.728343	+	0.529172i
$943$	−9.93858e15	−	7.22080e15i	−0.434020	−	0.315334i
$944$	1.28468e15	+	3.95383e15i	0.0557761	+	0.171661i
$945$	−7.65007e16			−3.30210
$946$	−9.37825e15	−	7.47373e15i	−0.402458	−	0.320727i
$947$	3.71322e16			1.58426			0.792129	−	0.610354i	$-0.208973\pi$
$947$	3.71322e16			1.58426			0.792129	+	0.610354i	$0.208973\pi$
$948$	−3.67705e15	−	1.13168e16i	−0.155975	−	0.480040i
$949$	2.47924e16	+	1.80127e16i	1.04557	+	0.759654i
$950$	1.99243e15	−	1.44759e15i	0.0835418	−	0.0606967i
$951$	−6.73500e15	+	2.07282e16i	−0.280766	+	0.864109i
$952$	−5.79374e14	+	1.78313e15i	−0.0240135	+	0.0739060i
$953$	−1.59503e16	+	1.15886e16i	−0.657291	+	0.477550i	−0.865747	−	0.500482i	$-0.833156\pi$
$953$	−1.59503e16	+	1.15886e16i	−0.657291	+	0.477550i	0.208456	+	0.978032i	$0.433156\pi$
$954$	2.13161e16	+	1.54870e16i	0.873356	+	0.634531i
$955$	−1.01052e16	−	3.11008e16i	−0.411650	−	1.26693i
$956$	1.15491e16			0.467769
$957$	−2.10050e16	+	1.38754e16i	−0.845875	+	0.558767i
$958$	2.77090e16			1.10946
$959$	−6.79191e15	−	2.09034e16i	−0.270389	−	0.832173i
$960$	4.71692e15	+	3.42704e15i	0.186709	+	0.135652i
$961$	−4.57867e15	+	3.32660e15i	−0.180202	+	0.130925i
$962$	−7.85746e15	+	2.41828e16i	−0.307482	+	0.946332i
$963$	2.91988e15	−	8.98648e15i	0.113611	−	0.349659i
$964$	8.37846e15	−	6.08730e15i	0.324146	−	0.235506i
$965$	2.18218e16	+	1.58545e16i	0.839441	+	0.609890i
$966$	9.83430e15	+	3.02669e16i	0.376157	+	1.15769i
$967$	−4.01178e15			−0.152578			−0.0762890	−	0.997086i	$-0.524307\pi$
$967$	−4.01178e15			−0.152578			−0.0762890	+	0.997086i	$0.524307\pi$
$968$	−8.02248e15	+	4.80056e15i	−0.303385	+	0.181542i
$969$	−9.04826e15			−0.340239
$970$	6.63290e15	+	2.04140e16i	0.248004	+	0.763279i
$971$	1.54189e16	+	1.12025e16i	0.573255	+	0.416494i	0.836286	−	0.548293i	$-0.184722\pi$
$971$	1.54189e16	+	1.12025e16i	0.573255	+	0.416494i	−0.263031	+	0.964787i	$0.584722\pi$
$972$	3.80963e15	−	2.76786e15i	0.140837	−	0.102324i
$973$	1.49728e15	−	4.60815e15i	0.0550404	−	0.169397i
$974$	−1.91896e15	+	5.90596e15i	−0.0701443	+	0.215882i
$975$	2.81197e15	−	2.04302e15i	0.102208	−	0.0742586i
$976$	7.81138e15	+	5.67530e15i	0.282328	+	0.205123i
$977$	−1.62608e15	−	5.00457e15i	−0.0584417	−	0.179865i	0.917574	−	0.397565i	$-0.130145\pi$
$977$	−1.62608e15	−	5.00457e15i	−0.0584417	−	0.179865i	−0.976016	+	0.217700i	$0.930145\pi$
$978$	−7.21487e15			−0.257849
$979$	−1.75325e15	+	1.15816e15i	−0.0623074	+	0.0411589i
$980$	2.48030e16			0.876517
$981$	−1.59502e16	−	4.90898e16i	−0.560516	−	1.72509i
$982$	1.82784e16	+	1.32801e16i	0.638743	+	0.464074i
$983$	−3.56679e16	+	2.59143e16i	−1.23946	+	0.900522i	−0.997562	−	0.0697788i	$-0.977771\pi$
$983$	−3.56679e16	+	2.59143e16i	−1.23946	+	0.900522i	−0.241900	+	0.970301i	$0.577771\pi$
$984$	4.98228e15	−	1.53339e16i	0.172169	−	0.529882i
$985$	7.11810e14	−	2.19073e15i	0.0244605	−	0.0752816i
$986$	−1.29763e15	+	9.42781e14i	−0.0443432	+	0.0322172i
$987$	6.73000e15	+	4.88963e15i	0.228702	+	0.166162i
$988$	−4.64927e15	−	1.43090e16i	−0.157116	−	0.483554i
$989$	−1.29692e16			−0.435848
$990$	−3.63741e16	−	2.89873e16i	−1.21562	−	0.968755i
$991$	4.38473e16			1.45726			0.728631	−	0.684906i	$-0.240157\pi$
$991$	4.38473e16			1.45726			0.728631	+	0.684906i	$0.240157\pi$
$992$	−1.82763e15	−	5.62488e15i	−0.0604053	−	0.185908i
$993$	−5.40323e16	−	3.92568e16i	−1.77596	−	1.29031i
$994$	4.55898e16	−	3.31229e16i	1.49019	−	1.08269i
$995$	1.70644e16	−	5.25189e16i	0.554708	−	1.70722i
$996$	6.75547e15	−	2.07912e16i	0.218388	−	0.672130i
$997$	3.98760e14	−	2.89716e14i	0.0128200	−	0.00931429i	−0.581357	−	0.813649i	$-0.697478\pi$
$997$	3.98760e14	−	2.89716e14i	0.0128200	−	0.00931429i	0.594177	+	0.804334i	$0.297478\pi$
$998$	1.32620e16	+	9.63543e15i	0.424026	+	0.308073i
$999$	3.72335e16	+	1.14593e17i	1.18392	+	3.64374i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.12.c.a.5.5	✓	20
11.3	even	5		242.12.a.n.1.1		10
11.8	odd	10		242.12.a.m.1.1		10
11.9	even	5	inner	22.12.c.a.9.5	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.12.c.a.5.5	✓	20	1.1	even	1	trivial
22.12.c.a.9.5	yes	20	11.9	even	5	inner
242.12.a.m.1.1		10	11.8	odd	10
242.12.a.n.1.1		10	11.3	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)

\(f(q)\)	\(=\)	\(q+(9.88854 + 30.4338i) q^{2} +(598.990 + 435.192i) q^{3} +(-828.433 + 601.892i) q^{4} +(2266.32 - 6975.01i) q^{5} +(-7321.40 + 22533.0i) q^{6} +(-58786.1 + 42710.6i) q^{7} +(-26509.9 - 19260.5i) q^{8} +(114656. + 352874. i) q^{9} +O(q^{10})\)	\(q+(9.88854 + 30.4338i) q^{2} +(598.990 + 435.192i) q^{3} +(-828.433 + 601.892i) q^{4} +(2266.32 - 6975.01i) q^{5} +(-7321.40 + 22533.0i) q^{6} +(-58786.1 + 42710.6i) q^{7} +(-26509.9 - 19260.5i) q^{8} +(114656. + 352874. i) q^{9} +234687. q^{10} +(-445684. + 294410. i) q^{11} -758162. q^{12} +(292544. + 900357. i) q^{13} +(-1.88115e6 - 1.36674e6i) q^{14} +(4.39297e6 - 3.19168e6i) q^{15} +(324028. - 997255. i) q^{16} +(-243328. + 748886. i) q^{17} +(-9.60552e6 + 6.97882e6i) q^{18} +(1.25560e7 + 9.12246e6i) q^{19} +(2.32071e6 + 7.14241e6i) q^{20} -5.37996e7 q^{21} +(-1.33672e7 - 1.06526e7i) q^{22} -1.84856e7 q^{23} +(-7.49712e6 - 2.30737e7i) q^{24} +(-4.01181e6 - 2.91475e6i) q^{25} +(-2.45085e7 + 1.78064e7i) q^{26} +(-4.43601e7 + 1.36526e8i) q^{27} +(2.29932e7 - 7.07657e7i) q^{28} +(5.14980e7 - 3.74155e7i) q^{29} +(1.40575e8 + 1.02134e8i) q^{30} +(-5.44677e7 - 1.67634e8i) q^{31} +3.35544e7 q^{32} +(-3.95085e8 - 1.76097e7i) q^{33} -2.51976e7 q^{34} +(1.64679e8 + 5.06829e8i) q^{35} +(-3.07377e8 - 2.23322e8i) q^{36} +(6.79046e8 - 4.93356e8i) q^{37} +(-1.53471e8 + 4.72335e8i) q^{38} +(-2.16597e8 + 6.66618e8i) q^{39} +(-1.94422e8 + 1.41256e8i) q^{40} +(5.37640e8 + 3.90619e8i) q^{41} +(-5.31999e8 - 1.63733e9i) q^{42} +7.01588e8 q^{43} +(1.92017e8 - 5.12153e8i) q^{44} +2.72115e9 q^{45} +(-1.82795e8 - 5.62586e8i) q^{46} +(-1.25094e8 - 9.08860e7i) q^{47} +(6.28086e8 - 4.56332e8i) q^{48} +(1.02058e9 - 3.14103e9i) q^{49} +(4.90360e7 - 1.50917e8i) q^{50} +(-4.71660e8 + 3.42681e8i) q^{51} +(-7.84271e8 - 5.69806e8i) q^{52} +(-6.85755e8 - 2.11054e9i) q^{53} -4.59367e9 q^{54} +(1.04345e9 + 3.77588e9i) q^{55} +2.38104e9 q^{56} +(3.55089e9 + 1.09285e10i) q^{57} +(1.64794e9 + 1.19730e9i) q^{58} +(-3.20752e9 + 2.33040e9i) q^{59} +(-1.71824e9 + 5.28819e9i) q^{60} +(-2.84546e9 + 8.75743e9i) q^{61} +(4.56315e9 - 3.31532e9i) q^{62} +(-2.18116e10 - 1.58471e10i) q^{63} +(3.31804e8 + 1.02119e9i) q^{64} +6.94300e9 q^{65} +(-3.37089e9 - 1.21981e10i) q^{66} +6.35110e9 q^{67} +(-2.49168e8 - 7.66860e8i) q^{68} +(-1.10727e10 - 8.04476e9i) q^{69} +(-1.37963e10 + 1.00236e10i) q^{70} +(-7.48903e9 + 2.30489e10i) q^{71} +(3.75704e9 - 1.15630e10i) q^{72} +(2.61885e10 - 1.90270e10i) q^{73} +(2.17295e10 + 1.57874e10i) q^{74} +(-1.13456e9 - 3.49181e9i) q^{75} -1.58925e10 q^{76} +(1.36256e10 - 3.63426e10i) q^{77} -2.24295e10 q^{78} +(4.84995e9 + 1.49266e10i) q^{79} +(-6.22152e9 - 4.52020e9i) q^{80} +(-3.28117e10 + 2.38391e10i) q^{81} +(-6.57153e9 + 2.02251e10i) q^{82} +(-8.91033e9 + 2.74232e10i) q^{83} +(4.45694e10 - 3.23815e10i) q^{84} +(4.67203e9 + 3.39443e9i) q^{85} +(6.93768e9 + 2.13520e10i) q^{86} +4.71297e10 q^{87} +(1.74855e10 + 7.79364e8i) q^{88} +3.93384e9 q^{89} +(2.69082e10 + 8.28149e10i) q^{90} +(-5.56523e10 - 4.04338e10i) q^{91} +(1.53141e10 - 1.11263e10i) q^{92} +(4.03275e10 - 1.24115e11i) q^{93} +(1.52901e9 - 4.70581e9i) q^{94} +(9.20852e10 - 6.69038e10i) q^{95} +(2.00988e10 + 1.46026e10i) q^{96} +(2.82628e10 + 8.69839e10i) q^{97} +1.05685e11 q^{98} +(-1.54990e11 - 1.23515e11i) 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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