LMFDB - Embedded newform 42.9.g.b.31.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [42,9,Mod(19,42)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(42, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("42.19");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 42 = 2 \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	42.g (of order $6$, degree $2$, 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:	$17.1099016226$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 6683 x^{10} + 105006 x^{9} + 34690411 x^{8} + 548172728 x^{7} + \cdots + 30\!\cdots\!24 $ x^12 - 2x^11 + 6683x^10 + 105006x^9 + 34690411x^8 + 548172728x^7 + 69245553226x^6 + 2257669296800x^5 + 109555419264148x^4 + 2043640985398464x^3 + 35697604660076192x^2 + 112120335940899328*x + 305636965993402624
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{24}\cdot 3^{6}\cdot 7^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.6
Root			$-12.6321 - 21.8795i$ of defining polynomial
Character	$\chi$	$=$	42.31
Dual form			42.9.g.b.19.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.65685 + 9.79796i) q^{2} +(-40.5000 - 23.3827i) q^{3} +(-64.0000 + 110.851i) q^{4} +(607.249 - 350.595i) q^{5} -529.090i q^{6} +(-2120.49 + 1126.19i) q^{7} -1448.15 q^{8} +(1093.50 + 1894.00i) q^{9} +O(q^{10})$	\(q+(5.65685 + 9.79796i) q^{2} +(-40.5000 - 23.3827i) q^{3} +(-64.0000 + 110.851i) q^{4} +(607.249 - 350.595i) q^{5} -529.090i q^{6} +(-2120.49 + 1126.19i) q^{7} -1448.15 q^{8} +(1093.50 + 1894.00i) q^{9} +(6870.24 + 3966.53i) q^{10} +(25.6528 - 44.4320i) q^{11} +(5184.00 - 2992.98i) q^{12} +32507.4i q^{13} +(-23029.7 - 14405.8i) q^{14} -32791.4 q^{15} +(-8192.00 - 14189.0i) q^{16} +(-125645. - 72541.4i) q^{17} +(-12371.5 + 21428.1i) q^{18} +(-172719. + 99719.4i) q^{19} +89752.4i q^{20} +(112213. + 3972.17i) q^{21} +580.457 q^{22} +(-94405.8 - 163516. i) q^{23} +(58650.3 + 33861.7i) q^{24} +(50521.7 - 87506.1i) q^{25} +(-318506. + 183889. i) q^{26} -102276. i q^{27} +(10872.1 - 307136. i) q^{28} +45136.7 q^{29} +(-185496. - 321289. i) q^{30} +(-1.36356e6 - 787254. i) q^{31} +(92681.9 - 160530. i) q^{32} +(-2077.88 + 1199.66i) q^{33} -1.64142e6i q^{34} +(-892831. + 1.42731e6i) q^{35} -279936. q^{36} +(1.70067e6 + 2.94564e6i) q^{37} +(-1.95409e6 - 1.12820e6i) q^{38} +(760109. - 1.31655e6i) q^{39} +(-879390. + 507716. i) q^{40} +3.93773e6i q^{41} +(595856. + 1.12193e6i) q^{42} -1.55052e6 q^{43} +(3283.56 + 5687.29i) q^{44} +(1.32805e6 + 766752. i) q^{45} +(1.06808e6 - 1.84997e6i) q^{46} +(164462. - 94952.3i) q^{47} +766204. i q^{48} +(3.22819e6 - 4.77616e6i) q^{49} +1.14317e6 q^{50} +(3.39243e6 + 5.87585e6i) q^{51} +(-3.60348e6 - 2.08047e6i) q^{52} +(1.00262e6 - 1.73659e6i) q^{53} +(1.00209e6 - 578560. i) q^{54} -35975.0i q^{55} +(3.07080e6 - 1.63090e6i) q^{56} +9.32683e6 q^{57} +(255331. + 442247. i) q^{58} +(1.11644e7 + 6.44579e6i) q^{59} +(2.09865e6 - 3.63497e6i) q^{60} +(1.13103e7 - 6.53000e6i) q^{61} -1.78135e7i q^{62} +(-4.45176e6 - 2.78472e6i) q^{63} +2.09715e6 q^{64} +(1.13969e7 + 1.97401e7i) q^{65} +(-23508.5 - 13572.6i) q^{66} +(-8.75755e6 + 1.51685e7i) q^{67} +(1.60826e7 - 9.28530e6i) q^{68} +8.82984e6i q^{69} +(-1.90354e7 - 673822. i) q^{70} +8.61402e6 q^{71} +(-1.58356e6 - 2.74280e6i) q^{72} +(-3.32550e7 - 1.91998e7i) q^{73} +(-1.92409e7 + 3.33262e7i) q^{74} +(-4.09226e6 + 2.36266e6i) q^{75} -2.55282e7i q^{76} +(-4357.82 + 123108. i) q^{77} +1.71993e7 q^{78} +(-8.02831e6 - 1.39054e7i) q^{79} +(-9.94917e6 - 5.74415e6i) q^{80} +(-2.39148e6 + 4.14217e6i) q^{81} +(-3.85817e7 + 2.22751e7i) q^{82} +2.28342e7i q^{83} +(-7.62198e6 + 1.21848e7i) q^{84} -1.01731e8 q^{85} +(-8.77106e6 - 1.51919e7i) q^{86} +(-1.82803e6 - 1.05542e6i) q^{87} +(-37149.2 + 64344.4i) q^{88} +(9.09745e7 - 5.25241e7i) q^{89} +1.73496e7i q^{90} +(-3.66095e7 - 6.89317e7i) q^{91} +2.41679e7 q^{92} +(3.68162e7 + 6.37675e7i) q^{93} +(1.86068e6 + 1.07426e6i) q^{94} +(-6.99223e7 + 1.21109e8i) q^{95} +(-7.50723e6 + 4.33430e6i) q^{96} -6.95869e7i q^{97} +(6.50580e7 + 4.61168e6i) q^{98} +112205. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 486 q^{3} - 768 q^{4} - 1122 q^{5} - 4434 q^{7} + 13122 q^{9}+O(q^{10}) $ 12 * q - 486 * q^3 - 768 * q^4 - 1122 * q^5 - 4434 * q^7 + 13122 * q^9	\( 12 q - 486 q^{3} - 768 q^{4} - 1122 q^{5} - 4434 q^{7} + 13122 q^{9} + 4224 q^{10} + 9606 q^{11} + 62208 q^{12} - 19968 q^{14} + 60588 q^{15} - 98304 q^{16} - 227388 q^{17} + 315408 q^{19} + 155358 q^{21} + 557568 q^{22} - 663480 q^{23} + 601008 q^{25} - 585984 q^{26} + 398592 q^{28} + 5944884 q^{29} - 114048 q^{30} - 3214278 q^{31} - 778086 q^{33} - 1019784 q^{35} - 3359232 q^{36} + 1607760 q^{37} - 986880 q^{38} + 903636 q^{39} - 540672 q^{40} + 2788992 q^{42} + 12627648 q^{43} + 1229568 q^{44} - 2453814 q^{45} - 4608768 q^{46} - 7830240 q^{47} + 16477242 q^{49} - 16565760 q^{50} + 6139476 q^{51} - 4283904 q^{52} - 33200358 q^{53} - 8110080 q^{56} - 17032032 q^{57} + 5576064 q^{58} - 29657382 q^{59} - 3877632 q^{60} + 58344096 q^{61} - 2886840 q^{63} + 25165824 q^{64} + 30909216 q^{65} - 22581504 q^{66} + 7977444 q^{67} + 29105664 q^{68} - 59774976 q^{70} + 117213264 q^{71} - 170286636 q^{73} - 80311296 q^{74} - 48681648 q^{75} - 3340686 q^{77} + 31643136 q^{78} + 35420490 q^{79} + 18382848 q^{80} - 28697814 q^{81} + 154232832 q^{82} - 26085888 q^{84} + 416634600 q^{85} - 71958528 q^{86} - 240767802 q^{87} - 35684352 q^{88} + 78064092 q^{89} + 335513292 q^{91} + 169850880 q^{92} + 86785506 q^{93} - 18456576 q^{94} - 250727796 q^{95} - 150533376 q^{98} + 42016644 q^{99}+O(q^{100}) \) 12 * q - 486 * q^3 - 768 * q^4 - 1122 * q^5 - 4434 * q^7 + 13122 * q^9 + 4224 * q^10 + 9606 * q^11 + 62208 * q^12 - 19968 * q^14 + 60588 * q^15 - 98304 * q^16 - 227388 * q^17 + 315408 * q^19 + 155358 * q^21 + 557568 * q^22 - 663480 * q^23 + 601008 * q^25 - 585984 * q^26 + 398592 * q^28 + 5944884 * q^29 - 114048 * q^30 - 3214278 * q^31 - 778086 * q^33 - 1019784 * q^35 - 3359232 * q^36 + 1607760 * q^37 - 986880 * q^38 + 903636 * q^39 - 540672 * q^40 + 2788992 * q^42 + 12627648 * q^43 + 1229568 * q^44 - 2453814 * q^45 - 4608768 * q^46 - 7830240 * q^47 + 16477242 * q^49 - 16565760 * q^50 + 6139476 * q^51 - 4283904 * q^52 - 33200358 * q^53 - 8110080 * q^56 - 17032032 * q^57 + 5576064 * q^58 - 29657382 * q^59 - 3877632 * q^60 + 58344096 * q^61 - 2886840 * q^63 + 25165824 * q^64 + 30909216 * q^65 - 22581504 * q^66 + 7977444 * q^67 + 29105664 * q^68 - 59774976 * q^70 + 117213264 * q^71 - 170286636 * q^73 - 80311296 * q^74 - 48681648 * q^75 - 3340686 * q^77 + 31643136 * q^78 + 35420490 * q^79 + 18382848 * q^80 - 28697814 * q^81 + 154232832 * q^82 - 26085888 * q^84 + 416634600 * q^85 - 71958528 * q^86 - 240767802 * q^87 - 35684352 * q^88 + 78064092 * q^89 + 335513292 * q^91 + 169850880 * q^92 + 86785506 * q^93 - 18456576 * q^94 - 250727796 * q^95 - 150533376 * q^98 + 42016644 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/42\mathbb{Z}\right)^\times$.

$n$	$29$	$31$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	5.65685	+	9.79796i	0.353553	+	0.612372i
$2$	5.65685	+	9.79796i	0.353553	+	0.612372i
$3$	−40.5000	−	23.3827i	−0.500000	−	0.288675i
$3$	−40.5000	−	23.3827i	−0.500000	−	0.288675i
$4$	−64.0000	+	110.851i	−0.250000	+	0.433013i
$5$	607.249	−	350.595i	0.971598	−	0.560953i	0.0718752	−	0.997414i	$-0.477102\pi$
$5$	607.249	−	350.595i	0.971598	−	0.560953i	0.899723	+	0.436461i	$0.143768\pi$
$6$		−	529.090i		−	0.408248i
$7$	−2120.49	+	1126.19i	−0.883171	+	0.469050i
$7$	−2120.49	+	1126.19i	−0.883171	+	0.469050i
$8$	−1448.15			−0.353553
$9$	1093.50	+	1894.00i	0.166667	+	0.288675i
$10$	6870.24	+	3966.53i	0.687024	+	0.396653i
$11$	25.6528	−	44.4320i	0.00175212	−	0.00303476i	−0.865148	−	0.501517i	$-0.832776\pi$
$11$	25.6528	−	44.4320i	0.00175212	−	0.00303476i	0.866900	+	0.498482i	$0.166109\pi$
$12$	5184.00	−	2992.98i	0.250000	−	0.144338i
$13$			32507.4i			1.13817i	0.822278	+	0.569086i	$0.192703\pi$
$13$			32507.4i			1.13817i	−0.822278	+	0.569086i	$0.807297\pi$
$14$	−23029.7	−	14405.8i	−0.599482	−	0.374996i
$15$	−32791.4			−0.647732
$16$	−8192.00	−	14189.0i	−0.125000	−	0.216506i
$17$	−125645.	−	72541.4i	−1.50436	−	0.868541i	−0.999987	−	0.00505344i	$-0.998391\pi$
$17$	−125645.	−	72541.4i	−1.50436	−	0.868541i	−0.504370	−	0.863488i	$-0.668275\pi$
$18$	−12371.5	+	21428.1i	−0.117851	+	0.204124i
$19$	−172719.	+	99719.4i	−1.32534	+	0.765183i	−0.984574	−	0.174967i	$-0.944018\pi$
$19$	−172719.	+	99719.4i	−1.32534	+	0.765183i	−0.340762	+	0.940150i	$0.610685\pi$
$20$			89752.4i			0.560953i
$21$	112213.	+	3972.17i	0.576989	+	0.0204245i
$22$	580.457			0.00247787
$23$	−94405.8	−	163516.i	−0.337355	−	0.584316i	0.646579	−	0.762847i	$-0.276199\pi$
$23$	−94405.8	−	163516.i	−0.337355	−	0.584316i	−0.983934	+	0.178531i	$0.942866\pi$
$24$	58650.3	+	33861.7i	0.176777	+	0.102062i
$25$	50521.7	−	87506.1i	0.129335	−	0.224016i
$26$	−318506.	+	183889.i	−0.696986	+	0.402405i
$27$		−	102276.i		−	0.192450i
$28$	10872.1	−	307136.i	0.0176881	−	0.499687i
$29$	45136.7			0.0638171			0.0319086	−	0.999491i	$-0.489841\pi$
$29$	45136.7			0.0638171			0.0319086	+	0.999491i	$0.489841\pi$
$30$	−185496.	−	321289.i	−0.229008	−	0.396653i
$31$	−1.36356e6	−	787254.i	−1.47648	−	0.852448i	−0.476836	−	0.878992i	$-0.658216\pi$
$31$	−1.36356e6	−	787254.i	−1.47648	−	0.852448i	−0.999648	+	0.0265444i	$0.991550\pi$
$32$	92681.9	−	160530.i	0.0883883	−	0.153093i
$33$	−2077.88	+	1199.66i	−0.00175212	+	0.00101159i
$34$		−	1.64142e6i		−	1.22830i
$35$	−892831.	+	1.42731e6i	−0.594973	+	0.951146i
$36$	−279936.			−0.166667
$37$	1.70067e6	+	2.94564e6i	0.907429	+	1.57171i	0.817622	+	0.575755i	$0.195292\pi$
$37$	1.70067e6	+	2.94564e6i	0.907429	+	1.57171i	0.0898070	+	0.995959i	$0.471375\pi$
$38$	−1.95409e6	−	1.12820e6i	−0.937154	−	0.541066i
$39$	760109.	−	1.31655e6i	0.328562	−	0.569086i
$40$	−879390.	+	507716.i	−0.343512	+	0.198327i
$41$			3.93773e6i			1.39351i	0.717309	+	0.696755i	$0.245373\pi$
$41$			3.93773e6i			1.39351i	−0.717309	+	0.696755i	$0.754627\pi$
$42$	595856.	+	1.12193e6i	0.191489	+	0.360553i
$43$	−1.55052e6			−0.453527			−0.226764	−	0.973950i	$-0.572814\pi$
$43$	−1.55052e6			−0.453527			−0.226764	+	0.973950i	$0.572814\pi$
$44$	3283.56	+	5687.29i	0.000876061	+	0.00151738i
$45$	1.32805e6	+	766752.i	0.323866	+	0.186984i
$46$	1.06808e6	−	1.84997e6i	0.238546	−	0.413174i
$47$	164462.	−	94952.3i	0.0337035	−	0.0194587i	−0.483054	−	0.875591i	$-0.660472\pi$
$47$	164462.	−	94952.3i	0.0337035	−	0.0194587i	0.516757	+	0.856132i	$0.327139\pi$
$48$			766204.i			0.144338i
$49$	3.22819e6	−	4.77616e6i	0.559984	−	0.828504i
$50$	1.14317e6			0.182908
$51$	3.39243e6	+	5.87585e6i	0.501452	+	0.868541i
$52$	−3.60348e6	−	2.08047e6i	−0.492843	−	0.284543i
$53$	1.00262e6	−	1.73659e6i	0.127067	−	0.220087i	−0.795472	−	0.605991i	$-0.792777\pi$
$53$	1.00262e6	−	1.73659e6i	0.127067	−	0.220087i	0.922539	+	0.385904i	$0.126110\pi$
$54$	1.00209e6	−	578560.i	0.117851	−	0.0680414i
$55$		−	35975.0i		−	0.00393143i
$56$	3.07080e6	−	1.63090e6i	0.312248	−	0.165834i
$57$	9.32683e6			0.883557
$58$	255331.	+	442247.i	0.0225628	+	0.0390799i
$59$	1.11644e7	+	6.44579e6i	0.921359	+	0.531947i	0.884068	−	0.467357i	$-0.154794\pi$
$59$	1.11644e7	+	6.44579e6i	0.921359	+	0.531947i	0.0372907	+	0.999304i	$0.488127\pi$
$60$	2.09865e6	−	3.63497e6i	0.161933	−	0.280476i
$61$	1.13103e7	−	6.53000e6i	0.816873	−	0.471622i	−0.0324640	−	0.999473i	$-0.510335\pi$
$61$	1.13103e7	−	6.53000e6i	0.816873	−	0.471622i	0.849337	+	0.527851i	$0.177002\pi$
$62$		−	1.78135e7i		−	1.20554i
$63$	−4.45176e6	−	2.78472e6i	−0.282598	−	0.176775i
$64$	2.09715e6			0.125000
$65$	1.13969e7	+	1.97401e7i	0.638461	+	1.10585i
$66$	−23508.5	−	13572.6i	−0.00123894	−	0.000715301i
$67$	−8.75755e6	+	1.51685e7i	−0.434593	+	0.752738i	−0.997262	−	0.0739444i	$-0.976441\pi$
$67$	−8.75755e6	+	1.51685e7i	−0.434593	+	0.752738i	0.562669	+	0.826682i	$0.309775\pi$
$68$	1.60826e7	−	9.28530e6i	0.752179	−	0.434271i
$69$			8.82984e6i			0.389544i
$70$	−1.90354e7	−	673822.i	−0.792810	−	0.0280642i
$71$	8.61402e6			0.338979			0.169489	−	0.985532i	$-0.445788\pi$
$71$	8.61402e6			0.338979			0.169489	+	0.985532i	$0.445788\pi$
$72$	−1.58356e6	−	2.74280e6i	−0.0589256	−	0.102062i
$73$	−3.32550e7	−	1.91998e7i	−1.17102	−	0.676091i	−0.217102	−	0.976149i	$-0.569661\pi$
$73$	−3.32550e7	−	1.91998e7i	−1.17102	−	0.676091i	−0.953921	+	0.300058i	$0.902994\pi$
$74$	−1.92409e7	+	3.33262e7i	−0.641650	+	1.11137i
$75$	−4.09226e6	+	2.36266e6i	−0.129335	+	0.0746719i
$76$		−	2.55282e7i		−	0.765183i
$77$	−4357.82	+	123108.i	−0.000123967	+	0.00350205i
$78$	1.71993e7			0.464657
$79$	−8.02831e6	−	1.39054e7i	−0.206118	−	0.357007i	0.744370	−	0.667767i	$-0.232750\pi$
$79$	−8.02831e6	−	1.39054e7i	−0.206118	−	0.357007i	−0.950488	+	0.310760i	$0.899416\pi$
$80$	−9.94917e6	−	5.74415e6i	−0.242900	−	0.140238i
$81$	−2.39148e6	+	4.14217e6i	−0.0555556	+	0.0962250i
$82$	−3.85817e7	+	2.22751e7i	−0.853347	+	0.492680i
$83$			2.28342e7i			0.481141i	0.970632	+	0.240571i	$0.0773346\pi$
$83$			2.28342e7i			0.481141i	−0.970632	+	0.240571i	$0.922665\pi$
$84$	−7.62198e6	+	1.21848e7i	−0.153091	+	0.244737i
$85$	−1.01731e8			−1.94884
$86$	−8.77106e6	−	1.51919e7i	−0.160346	−	0.277727i
$87$	−1.82803e6	−	1.05542e6i	−0.0319086	−	0.0184224i
$88$	−37149.2	+	64344.4i	−0.000619469	+	0.00107295i
$89$	9.09745e7	−	5.25241e7i	1.44997	−	0.837142i	0.451493	−	0.892275i	$-0.350892\pi$
$89$	9.09745e7	−	5.25241e7i	1.44997	−	0.837142i	0.998479	+	0.0551329i	$0.0175583\pi$
$90$			1.73496e7i			0.264436i
$91$	−3.66095e7	−	6.89317e7i	−0.533860	−	1.00520i
$92$	2.41679e7			0.337355
$93$	3.68162e7	+	6.37675e7i	0.492161	+	0.852448i
$94$	1.86068e6	+	1.07426e6i	0.0238320	+	0.0137594i
$95$	−6.99223e7	+	1.21109e8i	−0.858463	+	1.48690i
$96$	−7.50723e6	+	4.33430e6i	−0.0883883	+	0.0510310i
$97$		−	6.95869e7i		−	0.786033i	−0.919531	−	0.393017i	$-0.871432\pi$
$97$		−	6.95869e7i		−	0.786033i	0.919531	−	0.393017i	$-0.128568\pi$
$98$	6.50580e7	+	4.61168e6i	0.705337	+	0.0499982i
$99$	112205.			0.00116808
$100$	6.46677e6	+	1.12008e7i	0.0646677	+	0.112008i
$101$	−7.51605e7	−	4.33939e7i	−0.722277	−	0.417007i	0.0933130	−	0.995637i	$-0.470254\pi$
$101$	−7.51605e7	−	4.33939e7i	−0.722277	−	0.417007i	−0.815590	+	0.578630i	$0.803588\pi$
$102$	−3.83809e7	+	6.64777e7i	−0.354580	+	0.614151i
$103$	−6.28284e7	+	3.62740e7i	−0.558222	+	0.322290i	−0.752432	−	0.658670i	$-0.771119\pi$
$103$	−6.28284e7	+	3.62740e7i	−0.558222	+	0.322290i	0.194209	+	0.980960i	$0.437786\pi$
$104$		−	4.70757e7i		−	0.402405i
$105$	6.95341e7	−	3.69294e7i	0.572059	−	0.303819i
$106$	2.26867e7			0.179700
$107$	−5.75474e7	−	9.96751e7i	−0.439027	−	0.760417i	0.558588	−	0.829445i	$-0.311343\pi$
$107$	−5.75474e7	−	9.96751e7i	−0.439027	−	0.760417i	−0.997615	+	0.0690288i	$0.978010\pi$
$108$	1.13374e7	+	6.54566e6i	0.0833333	+	0.0481125i
$109$	5.59443e7	−	9.68983e7i	0.396323	−	0.686452i	−0.596946	−	0.802282i	$-0.703619\pi$
$109$	5.59443e7	−	9.68983e7i	0.396323	−	0.686452i	0.993269	+	0.115830i	$0.0369526\pi$
$110$	352482.	−	203505.i	0.00240750	−	0.00138997i
$111$		−	1.59065e8i		−	1.04781i
$112$	3.33506e7	+	2.08619e7i	0.211949	+	0.132581i
$113$	1.68762e7			0.103505			0.0517523	−	0.998660i	$-0.483519\pi$
$113$	1.68762e7			0.103505			0.0517523	+	0.998660i	$0.483519\pi$
$114$	5.27605e7	+	9.13839e7i	0.312385	+	0.541066i
$115$	−1.14656e8	−	6.61965e7i	−0.655547	−	0.378480i
$116$	−2.88875e6	+	5.00345e6i	−0.0159543	+	0.0276336i
$117$	−6.15689e7	+	3.55468e7i	−0.328562	+	0.189695i
$118$			1.45852e8i			0.752287i
$119$	3.48126e8	+	1.23231e7i	1.73599	+	0.0614514i
$120$	4.74871e7			0.229008
$121$	1.07178e8	+	1.85638e8i	0.499994	+	0.866015i
$122$	1.27961e8	+	7.38785e7i	0.577616	+	0.333487i
$123$	9.20746e7	−	1.59478e8i	0.402272	−	0.696755i
$124$	1.74536e8	−	1.00768e8i	0.738242	−	0.426224i
$125$			2.03052e8i			0.831701i
$126$	2.10164e6	−	5.93710e7i	0.00833826	−	0.235555i
$127$	1.74028e8			0.668966			0.334483	−	0.942402i	$-0.391438\pi$
$127$	1.74028e8			0.668966			0.334483	+	0.942402i	$0.391438\pi$
$128$	1.18633e7	+	2.05478e7i	0.0441942	+	0.0765466i
$129$	6.27960e7	+	3.62553e7i	0.226764	+	0.130922i
$130$	−1.28942e8	+	2.23333e8i	−0.451460	+	0.781952i
$131$	−3.12000e8	+	1.80133e8i	−1.05942	+	0.611659i	−0.925273	−	0.379302i	$-0.876164\pi$
$131$	−3.12000e8	+	1.80133e8i	−1.05942	+	0.611659i	−0.134151	+	0.990961i	$0.542831\pi$
$132$		−	307114.i		−	0.00101159i
$133$	2.53947e8	−	4.05969e8i	0.811590	−	1.29744i
$134$	−1.98161e8			−0.614608
$135$	−3.58574e7	−	6.21069e7i	−0.107955	−	0.186984i
$136$	1.81954e8	+	1.05051e8i	0.531871	+	0.307076i
$137$	−1.00301e8	+	1.73727e8i	−0.284725	+	0.493157i	−0.972542	−	0.232726i	$-0.925235\pi$
$137$	−1.00301e8	+	1.73727e8i	−0.284725	+	0.493157i	0.687818	+	0.725883i	$0.258569\pi$
$138$	−8.65144e7	+	4.99491e7i	−0.238546	+	0.137725i
$139$			9.12135e6i			0.0244343i	0.999925	+	0.0122171i	$0.00388893\pi$
$139$			9.12135e6i			0.0244343i	−0.999925	+	0.0122171i	$0.996111\pi$
$140$	−1.01078e8	−	1.90319e8i	−0.263115	−	0.495417i
$141$	−8.88096e6			−0.0224690
$142$	4.87283e7	+	8.43998e7i	0.119847	+	0.207581i
$143$	1.44437e6	+	833905.i	0.00345409	+	0.00199422i
$144$	1.79159e7	−	3.10313e7i	0.0416667	−	0.0721688i
$145$	2.74092e7	−	1.58247e7i	0.0620046	−	0.0357984i
$146$		−	4.34441e8i		−	0.956136i
$147$	−2.42421e8	+	1.17951e8i	−0.519160	+	0.252598i
$148$	−4.35371e8			−0.907429
$149$	1.72687e8	+	2.99103e8i	0.350361	+	0.606843i	0.986313	−	0.164886i	$-0.0527256\pi$
$149$	1.72687e8	+	2.99103e8i	0.350361	+	0.606843i	−0.635952	+	0.771729i	$0.719392\pi$
$150$	−4.62986e7	−	2.67305e7i	−0.0914540	−	0.0528010i
$151$	3.09151e7	−	5.35465e7i	0.0594651	−	0.102997i	−0.834760	−	0.550613i	$-0.814394\pi$
$151$	3.09151e7	−	5.35465e7i	0.0594651	−	0.102997i	0.894225	+	0.447617i	$0.147727\pi$
$152$	2.50124e8	−	1.44409e8i	0.468577	−	0.270533i
$153$		−	3.17296e8i		−	0.579027i
$154$	−1.23086e6	+	653705.i	−0.00218839	+	0.00116225i
$155$	−1.10403e9			−1.91273
$156$	9.72940e7	+	1.68518e8i	0.164281	+	0.284543i
$157$	4.16486e8	+	2.40458e8i	0.685491	+	0.395769i	0.801921	−	0.597430i	$-0.203812\pi$
$157$	4.16486e8	+	2.40458e8i	0.685491	+	0.395769i	−0.116429	+	0.993199i	$0.537145\pi$
$158$	9.08299e7	−	1.57322e8i	0.145747	−	0.252442i
$159$	−8.12124e7	+	4.68880e7i	−0.127067	+	0.0733623i
$160$		−	1.29975e8i		−	0.198327i
$161$	3.84337e8	+	2.40415e8i	0.572016	+	0.357815i
$162$	−5.41131e7			−0.0785674
$163$	5.44041e8	+	9.42307e8i	0.770693	+	1.33488i	0.937184	+	0.348836i	$0.113423\pi$
$163$	5.44041e8	+	9.42307e8i	0.770693	+	1.33488i	−0.166491	+	0.986043i	$0.553244\pi$
$164$	−4.36502e8	−	2.52014e8i	−0.603407	−	0.348377i
$165$	−841193.	+	1.45699e6i	−0.00113491	+	0.00196571i
$166$	−2.23728e8	+	1.29170e8i	−0.294638	+	0.170109i
$167$		−	1.46053e9i		−	1.87778i	−0.344213	−	0.938892i	$-0.611854\pi$
$167$		−	1.46053e9i		−	1.87778i	0.344213	−	0.938892i	$-0.388146\pi$
$168$	−1.62502e8	−	5.75232e6i	−0.203996	−	0.00722114i
$169$	−2.40998e8			−0.295438
$170$	−5.75476e8	−	9.96754e8i	−0.689019	−	1.19342i
$171$	−3.77737e8	−	2.18086e8i	−0.441779	−	0.255061i
$172$	9.92332e7	−	1.71877e8i	0.113382	−	0.196383i
$173$	−1.11558e9	+	6.44083e8i	−1.24543	+	0.719047i	−0.970194	−	0.242330i	$-0.922088\pi$
$173$	−1.11558e9	+	6.44083e8i	−1.24543	+	0.719047i	−0.275233	+	0.961378i	$0.588755\pi$
$174$		−	2.38813e7i		−	0.0260532i
$175$	−8.58246e6	+	2.42453e8i	−0.00915081	+	0.258509i
$176$	−840591.			−0.000876061
$177$	−3.01440e8	−	5.22109e8i	−0.307120	−	0.531947i
$178$	1.02926e9	+	5.94243e8i	1.02529	+	0.591949i
$179$	−4.98256e8	+	8.63005e8i	−0.485334	+	0.840622i	−0.999858	−	0.0168533i	$-0.994635\pi$
$179$	−4.98256e8	+	8.63005e8i	−0.485334	+	0.840622i	0.514524	+	0.857476i	$0.327969\pi$
$180$	−1.69991e8	+	9.81443e7i	−0.161933	+	0.0934921i
$181$		−	1.19990e9i		−	1.11797i	−0.829177	−	0.558987i	$-0.811190\pi$
$181$		−	1.19990e9i		−	1.11797i	0.829177	−	0.558987i	$-0.188810\pi$
$182$	4.68295e8	−	7.48634e8i	0.426810	−	0.682314i
$183$	−6.10756e8			−0.544582
$184$	1.36714e8	+	2.36796e8i	0.119273	+	0.206587i
$185$	2.06546e9	+	1.19249e9i	1.76331	+	1.01805i
$186$	−4.16528e8	+	7.21447e8i	−0.348010	+	0.602772i
$187$	−6.44632e6	+	3.72178e6i	−0.00527163	+	0.00304358i
$188$			2.43078e7i			0.0194587i
$189$	1.15182e8	+	2.16875e8i	0.0902688	+	0.169966i
$190$	−1.58216e9			−1.21405
$191$	4.85771e8	+	8.41379e8i	0.365004	+	0.632206i	0.988777	−	0.149400i	$-0.0477343\pi$
$191$	4.85771e8	+	8.41379e8i	0.365004	+	0.632206i	−0.623773	+	0.781606i	$0.714401\pi$
$192$	−8.49347e7	−	4.90370e7i	−0.0625000	−	0.0360844i
$193$	−3.82023e8	+	6.61684e8i	−0.275335	+	0.476894i	−0.970219	−	0.242227i	$-0.922122\pi$
$193$	−3.82023e8	+	6.61684e8i	−0.275335	+	0.476894i	0.694885	+	0.719121i	$0.255455\pi$
$194$	6.81810e8	−	3.93643e8i	0.481345	−	0.277905i
$195$		−	1.06596e9i		−	0.737231i
$196$	3.22839e8	+	6.63524e8i	0.218757	+	0.449606i
$197$	3.44781e8			0.228917			0.114459	−	0.993428i	$-0.463487\pi$
$197$	3.44781e8			0.228917			0.114459	+	0.993428i	$0.463487\pi$
$198$	634730.	+	1.09938e6i	0.000412979	+	0.000715301i
$199$	3.73493e8	+	2.15637e8i	0.238161	+	0.137502i	0.614331	−	0.789048i	$-0.289426\pi$
$199$	3.73493e8	+	2.15637e8i	0.238161	+	0.137502i	−0.376170	+	0.926551i	$0.622759\pi$
$200$	−7.31632e7	+	1.26722e8i	−0.0457270	+	0.0792015i
$201$	7.09361e8	−	4.09550e8i	0.434593	−	0.250913i
$202$		−	9.81892e8i		−	0.589737i
$203$	−9.57120e7	+	5.08324e7i	−0.0563615	+	0.0299335i
$204$	−8.68461e8			−0.501452
$205$	1.38055e9	+	2.39118e9i	0.781693	+	1.35393i
$206$	−7.10822e8	−	4.10393e8i	−0.394723	−	0.227893i
$207$	2.06465e8	−	3.57609e8i	0.112452	−	0.194772i
$208$	4.61246e8	−	2.66300e8i	0.246422	−	0.142272i
$209$			1.02323e7i			0.00536278i
$210$	7.55177e8	+	4.72388e8i	0.388304	+	0.242897i
$211$	−3.27153e9			−1.65052			−0.825260	−	0.564753i	$-0.808971\pi$
$211$	−3.27153e9			−1.65052			−0.825260	+	0.564753i	$0.808971\pi$
$212$	1.28336e8	+	2.22284e8i	0.0635337	+	0.110044i
$213$	−3.48868e8	−	2.01419e8i	−0.169489	−	0.0978548i
$214$	6.51075e8	−	1.12769e9i	0.310439	−	0.537696i
$215$	−9.41551e8	+	5.43605e8i	−0.440646	+	0.254407i
$216$			1.48111e8i			0.0680414i
$217$	3.77803e9	+	1.33736e8i	1.70383	+	0.0603128i
$218$	1.26587e9			0.560486
$219$	8.97885e8	+	1.55518e9i	0.390341	+	0.676091i
$220$	3.98788e6	+	2.30240e6i	0.00170236	+	0.000982857i
$221$	2.35813e9	−	4.08440e9i	0.988550	−	1.71222i
$222$	1.55851e9	−	8.99807e8i	0.641650	−	0.370457i
$223$		−	1.21483e9i		−	0.491244i	−0.969366	−	0.245622i	$-0.921008\pi$
$223$		−	1.21483e9i		−	0.491244i	0.969366	−	0.245622i	$-0.0789922\pi$
$224$	−1.57445e7	+	4.44780e8i	−0.00625369	+	0.176666i
$225$	2.20982e8			0.0862237
$226$	9.54660e7	+	1.65352e8i	0.0365944	+	0.0633834i
$227$	1.72294e9	+	9.94740e8i	0.648884	+	0.374633i	0.788028	−	0.615639i	$-0.211102\pi$
$227$	1.72294e9	+	9.94740e8i	0.648884	+	0.374633i	−0.139145	+	0.990272i	$0.544435\pi$
$228$	−5.96917e8	+	1.03389e9i	−0.220889	+	0.382592i
$229$	3.20267e9	−	1.84906e9i	1.16458	−	0.672371i	0.212183	−	0.977230i	$-0.431943\pi$
$229$	3.20267e9	−	1.84906e9i	1.16458	−	0.672371i	0.952398	+	0.304859i	$0.0986092\pi$
$230$		−	1.49785e9i		−	0.535252i
$231$	3.05508e6	−	4.88396e6i	0.00107294	−	0.00171524i
$232$	−6.53649e7			−0.0225628
$233$	1.03108e9	+	1.78588e9i	0.349839	+	0.605939i	0.986221	−	0.165435i	$-0.0529029\pi$
$233$	1.03108e9	+	1.78588e9i	0.349839	+	0.605939i	−0.636381	+	0.771374i	$0.719570\pi$
$234$	−6.96572e8	−	4.02166e8i	−0.232329	−	0.134135i
$235$	6.65797e7	−	1.15319e8i	0.0218308	−	0.0378121i
$236$	−1.42905e9	+	8.25062e8i	−0.460680	+	0.265973i
$237$			7.50893e8i			0.238004i
$238$	1.84856e9	+	3.48063e9i	0.576136	+	1.08480i
$239$	−4.45572e9			−1.36561			−0.682804	−	0.730601i	$-0.739240\pi$
$239$	−4.45572e9			−1.36561			−0.682804	+	0.730601i	$0.739240\pi$
$240$	2.68627e8	+	4.65276e8i	0.0809665	+	0.140238i
$241$	−5.05448e9	−	2.91820e9i	−1.49833	−	0.865063i	−0.498334	−	0.866985i	$-0.666055\pi$
$241$	−5.05448e9	−	2.91820e9i	−1.49833	−	0.865063i	−0.999998	+	0.00192224i	$0.999388\pi$
$242$	−1.21258e9	+	2.10025e9i	−0.353549	+	0.612365i
$243$	1.93710e8	−	1.11839e8i	0.0555556	−	0.0320750i
$244$			1.67168e9i			0.471622i
$245$	2.85818e8	−	4.03211e9i	0.0793279	−	1.11910i
$246$	2.08341e9			0.568898
$247$	−3.24162e9	−	5.61464e9i	−0.870911	−	1.50846i
$248$	1.97465e9	+	1.14007e9i	0.522016	+	0.301386i
$249$	5.33924e8	−	9.24783e8i	0.138894	−	0.240571i
$250$	−1.98949e9	+	1.14864e9i	−0.509311	+	0.294051i
$251$		−	1.66381e9i		−	0.419189i	−0.977788	−	0.209594i	$-0.932786\pi$
$251$		−	1.66381e9i		−	0.419189i	0.977788	−	0.209594i	$-0.0672143\pi$
$252$	5.93603e8	−	3.15261e8i	0.147195	−	0.0781751i
$253$	−9.68710e6			−0.00236435
$254$	9.84451e8	+	1.70512e9i	0.236515	+	0.409657i
$255$	4.12009e9	+	2.37874e9i	0.974421	+	0.562582i
$256$	−1.34218e8	+	2.32472e8i	−0.0312500	+	0.0541266i
$257$	−7.47093e9	+	4.31334e9i	−1.71255	+	0.988738i	−0.781445	+	0.623974i	$0.785517\pi$
$257$	−7.47093e9	+	4.31334e9i	−1.71255	+	0.988738i	−0.931100	+	0.364764i	$0.881150\pi$
$258$			8.20364e8i			0.185152i
$259$	−6.92361e9	−	4.33095e9i	−1.53863	−	0.962463i
$260$	−2.91761e9			−0.638461
$261$	4.93569e7	+	8.54887e7i	0.0106362	+	0.0184224i
$262$	−3.52988e9	−	2.03798e9i	−0.749126	−	0.432508i
$263$	−3.91054e9	+	6.77325e9i	−0.817360	+	1.41571i	0.0902601	+	0.995918i	$0.471230\pi$
$263$	−3.91054e9	+	6.77325e9i	−0.817360	+	1.41571i	−0.907621	+	0.419792i	$0.862103\pi$
$264$	3.00909e6	−	1.73730e6i	0.000619469	−	0.000357650i
$265$		−	1.40606e9i		−	0.285115i
$266$	5.41421e9	+	1.91654e8i	1.08146	+	0.0382818i
$267$	−4.91262e9			−0.966648
$268$	−1.12097e9	−	1.94157e9i	−0.217297	−	0.376369i
$269$	4.64217e9	+	2.68016e9i	0.886567	+	0.511860i	0.872818	−	0.488046i	$-0.162290\pi$
$269$	4.64217e9	+	2.68016e9i	0.886567	+	0.511860i	0.0137489	+	0.999905i	$0.495623\pi$
$270$	4.05681e8	−	7.02659e8i	0.0763360	−	0.132218i
$271$	−4.60881e9	+	2.66090e9i	−0.854499	+	0.493345i	−0.862166	−	0.506626i	$-0.830893\pi$
$271$	−4.60881e9	+	2.66090e9i	−0.854499	+	0.493345i	0.00766747	+	0.999971i	$0.497559\pi$
$272$			2.37704e9i			0.434271i
$273$	−1.29125e8	+	3.64776e9i	−0.0232466	+	0.656713i
$274$	−2.26956e9			−0.402661
$275$	−2.59205e6	−	4.48956e6i	−0.000453223	−	0.000785005i
$276$	−9.78799e8	−	5.65110e8i	−0.168678	−	0.0973860i
$277$	−1.02775e8	+	1.78011e8i	−0.0174569	+	0.0302363i	−0.874622	−	0.484806i	$-0.838890\pi$
$277$	−1.02775e8	+	1.78011e8i	−0.0174569	+	0.0302363i	0.857165	+	0.515042i	$0.172224\pi$
$278$	−8.93706e7	+	5.15981e7i	−0.0149629	+	0.00863883i
$279$		−	3.44345e9i		−	0.568299i
$280$	1.29296e9	−	2.06697e9i	0.210355	−	0.336281i
$281$	5.51900e9			0.885188			0.442594	−	0.896722i	$-0.354058\pi$
$281$	5.51900e9			0.885188			0.442594	+	0.896722i	$0.354058\pi$
$282$	−5.02383e7	−	8.70153e7i	−0.00794399	−	0.0137594i
$283$	−6.16234e9	−	3.55783e9i	−0.960726	−	0.554675i	−0.0643297	−	0.997929i	$-0.520491\pi$
$283$	−6.16234e9	−	3.55783e9i	−0.960726	−	0.554675i	−0.896396	+	0.443253i	$0.853824\pi$
$284$	−5.51297e8	+	9.54875e8i	−0.0847447	+	0.146782i
$285$	5.66371e9	−	3.26994e9i	0.858463	−	0.495634i
$286$			1.88691e7i			0.00282025i
$287$	−4.43463e9	−	8.34993e9i	−0.653626	−	1.23071i
$288$	4.05391e8			0.0589256
$289$	7.03664e9	+	1.21878e10i	1.00873	+	1.74717i
$290$	3.10100e8	+	1.79036e8i	0.0438439	+	0.0253133i
$291$	−1.62713e9	+	2.81827e9i	−0.226908	+	0.393017i
$292$	4.25664e9	−	2.45757e9i	0.585512	−	0.338045i
$293$		−	1.66605e9i		−	0.226056i	−0.993592	−	0.113028i	$-0.963945\pi$
$293$		−	1.66605e9i		−	0.226056i	0.993592	−	0.113028i	$-0.0360550\pi$
$294$	−2.52702e9	−	1.70800e9i	−0.338235	−	0.228612i
$295$	9.03946e9			1.19359
$296$	−2.46283e9	−	4.26575e9i	−0.320825	−	0.555685i
$297$	−4.54432e6	−	2.62366e6i	−0.000584041	−	0.000337196i
$298$	−1.95374e9	+	3.38397e9i	−0.247743	+	0.429103i
$299$	5.31546e9	−	3.06888e9i	0.665053	−	0.383968i
$300$		−	6.04842e8i		−	0.0746719i
$301$	3.28787e9	−	1.74618e9i	0.400542	−	0.212727i
$302$	6.99528e8			0.0840964
$303$	2.02933e9	+	3.51491e9i	0.240759	+	0.417007i
$304$	2.82983e9	+	1.63380e9i	0.331334	+	0.191296i
$305$	4.57878e9	−	7.93067e9i	0.529115	−	0.916454i
$306$	3.10885e9	−	1.79490e9i	0.354580	−	0.204717i
$307$		−	3.39536e9i		−	0.382237i	−0.981567	−	0.191118i	$-0.938789\pi$
$307$		−	3.39536e9i		−	0.382237i	0.981567	−	0.191118i	$-0.0612115\pi$
$308$	−1.33677e7	−	8.36196e6i	−0.00148544	−	0.000929192i
$309$	3.39273e9			0.372148
$310$	−6.24534e9	−	1.08172e10i	−0.676253	−	1.17130i
$311$	5.73107e9	+	3.30884e9i	0.612625	+	0.353699i	0.773992	−	0.633195i	$-0.218257\pi$
$311$	5.73107e9	+	3.30884e9i	0.612625	+	0.353699i	−0.161367	+	0.986894i	$0.551590\pi$
$312$	−1.10076e9	+	1.90657e9i	−0.116164	+	0.201202i
$313$	−1.38453e10	+	7.99362e9i	−1.44254	+	0.832848i	−0.998018	−	0.0629220i	$-0.979958\pi$
$313$	−1.38453e10	+	7.99362e9i	−1.44254	+	0.832848i	−0.444517	+	0.895770i	$0.646625\pi$
$314$			5.44095e9i			0.559701i
$315$	−3.67964e9	−	1.30253e8i	−0.373734	−	0.0132296i
$316$	2.05525e9			0.206118
$317$	−6.95619e9	−	1.20485e10i	−0.688866	−	1.19315i	−0.972205	−	0.234131i	$-0.924776\pi$
$317$	−6.95619e9	−	1.20485e10i	−0.688866	−	1.19315i	0.283339	−	0.959020i	$-0.408558\pi$
$318$	−9.18813e8	−	5.30477e8i	−0.0898502	−	0.0518750i
$319$	1.15788e6	−	2.00551e6i	0.000111815	−	0.000193670i
$320$	1.27349e9	−	7.35252e8i	0.121450	−	0.0701191i
$321$			5.38246e9i			0.506944i
$322$	−1.81442e8	+	5.12571e9i	−0.0168777	+	0.476794i
$323$	2.89352e10			2.65837
$324$	−3.06110e8	−	5.30198e8i	−0.0277778	−	0.0481125i
$325$	2.84459e9	+	1.64233e9i	0.254969	+	0.147206i
$326$	−6.15512e9	+	1.06610e10i	−0.544962	+	0.943902i
$327$	−4.53149e9	+	2.61625e9i	−0.396323	+	0.228817i
$328$		−	5.70244e9i		−	0.492680i
$329$	−2.41807e8	+	3.86562e8i	−0.0206388	+	0.0329940i
$330$	−1.90340e7			−0.00160500
$331$	9.12792e9	+	1.58100e10i	0.760431	+	1.31710i	0.942629	+	0.333843i	$0.108346\pi$
$331$	9.12792e9	+	1.58100e10i	0.760431	+	1.31710i	−0.182198	+	0.983262i	$0.558321\pi$
$332$	−2.53120e9	−	1.46139e9i	−0.208340	−	0.120285i
$333$	−3.71936e9	+	6.44213e9i	−0.302476	+	0.523905i
$334$	1.43102e10	−	8.26202e9i	1.14990	−	0.663897i
$335$			1.22814e10i			0.975145i
$336$	−8.62891e8	−	1.62473e9i	−0.0677016	−	0.127475i
$337$	7.27644e9			0.564156			0.282078	−	0.959391i	$-0.408976\pi$
$337$	7.27644e9			0.564156			0.282078	+	0.959391i	$0.408976\pi$
$338$	−1.36329e9	−	2.36128e9i	−0.104453	−	0.180918i
$339$	−6.83485e8	−	3.94610e8i	−0.0517523	−	0.0298792i
$340$	6.51077e9	−	1.12770e10i	0.487210	−	0.843873i
$341$	−6.99585e7	+	4.03905e7i	−0.00517396	+	0.00298719i
$342$		−	4.93473e9i		−	0.360711i
$343$	−1.46651e9	+	1.37634e10i	−0.105952	+	0.994371i
$344$	2.24539e9			0.160346
$345$	3.09570e9	+	5.36191e9i	0.218516	+	0.378480i
$346$	−1.26214e10	−	7.28697e9i	−0.880650	−	0.508443i
$347$	5.18756e8	−	8.98512e8i	0.0357804	−	0.0619735i	−0.847581	−	0.530667i	$-0.821942\pi$
$347$	5.18756e8	−	8.98512e8i	0.0357804	−	0.0619735i	0.883361	+	0.468693i	$0.155275\pi$
$348$	2.33988e8	−	1.35093e8i	0.0159543	−	0.00921121i
$349$			1.93298e10i			1.30294i	0.758673	+	0.651471i	$0.225848\pi$
$349$			1.93298e10i			1.30294i	−0.758673	+	0.651471i	$0.774152\pi$
$350$	−2.42410e9	+	1.28743e9i	−0.161539	+	0.0857931i
$351$	3.32472e9			0.219041
$352$	−4.75510e6	−	8.23608e6i	−0.000309734	−	0.000536475i
$353$	−1.20662e10	−	6.96642e9i	−0.777090	−	0.448653i	0.0583081	−	0.998299i	$-0.481429\pi$
$353$	−1.20662e10	−	6.96642e9i	−0.777090	−	0.448653i	−0.835398	+	0.549646i	$0.814763\pi$
$354$	3.41040e9	−	5.90699e9i	0.217166	−	0.376143i
$355$	5.23086e9	−	3.02004e9i	0.329351	−	0.190151i
$356$			1.34462e10i			0.837142i
$357$	−1.38109e10	−	8.63920e9i	−0.850258	−	0.531864i
$358$	−1.12742e10			−0.686365
$359$	−8.46599e9	−	1.46635e10i	−0.509683	−	0.882796i	−0.999937	−	0.0112169i	$-0.996429\pi$
$359$	−8.46599e9	−	1.46635e10i	−0.509683	−	0.882796i	0.490254	−	0.871579i	$-0.336904\pi$
$360$	−1.92323e9	−	1.11038e9i	−0.114504	−	0.0661089i
$361$	1.13961e10	−	1.97387e10i	0.671010	−	1.16222i
$362$	1.17566e10	−	6.78767e9i	0.684616	−	0.395263i
$363$		−	1.00244e10i		−	0.577343i
$364$	9.98417e9	+	3.53424e8i	0.568730	+	0.0201321i
$365$	−2.69254e10			−1.51702
$366$	−3.45496e9	−	5.98416e9i	−0.192539	−	0.333487i
$367$	−6.87587e9	−	3.96979e9i	−0.379021	−	0.218828i	0.298371	−	0.954450i	$-0.403557\pi$
$367$	−6.87587e9	−	3.96979e9i	−0.379021	−	0.218828i	−0.677392	+	0.735622i	$0.736890\pi$
$368$	−1.54674e9	+	2.67904e9i	−0.0843388	+	0.146079i
$369$	−7.45804e9	+	4.30590e9i	−0.402272	+	0.232252i
$370$			2.69830e10i			1.43974i
$371$	−1.70322e8	+	4.81158e9i	−0.00899033	+	0.253976i
$372$	−9.42495e9			−0.492161
$373$	−8.14272e8	−	1.41036e9i	−0.0420663	−	0.0728610i	0.844226	−	0.535988i	$-0.180061\pi$
$373$	−8.14272e8	−	1.41036e9i	−0.0420663	−	0.0728610i	−0.886292	+	0.463127i	$0.846727\pi$
$374$	−7.29318e7	−	4.21072e7i	−0.00372761	−	0.00215214i
$375$	4.74790e9	−	8.22360e9i	0.240091	−	0.415850i
$376$	−2.38167e8	+	1.37506e8i	−0.0119160	+	0.00687969i
$377$			1.46727e9i			0.0726349i
$378$	−1.47337e9	+	2.35538e9i	−0.0721679	+	0.115370i
$379$	2.09430e10			1.01504			0.507518	−	0.861641i	$-0.330563\pi$
$379$	2.09430e10			1.01504			0.507518	+	0.861641i	$0.330563\pi$
$380$	−8.95006e9	−	1.55020e10i	−0.429231	−	0.743451i
$381$	−7.04814e9	−	4.06924e9i	−0.334483	−	0.193114i
$382$	−5.49587e9	+	9.51912e9i	−0.258097	+	0.447037i
$383$	−8.12348e9	+	4.69009e9i	−0.377526	+	0.217965i	−0.676741	−	0.736221i	$-0.736608\pi$
$383$	−8.12348e9	+	4.69009e9i	−0.377526	+	0.217965i	0.299215	+	0.954186i	$0.403275\pi$
$384$		−	1.10958e9i		−	0.0510310i
$385$	4.05147e7	+	7.62848e7i	0.00184404	+	0.00347213i
$386$	−8.64420e9			−0.389382
$387$	−1.69549e9	−	2.93668e9i	−0.0755878	−	0.130922i
$388$	7.71380e9	+	4.45356e9i	0.340362	+	0.196508i
$389$	7.05904e8	−	1.22266e9i	0.0308281	−	0.0533959i	−0.850200	−	0.526460i	$-0.823519\pi$
$389$	7.05904e8	−	1.22266e9i	0.0308281	−	0.0533959i	0.881028	+	0.473064i	$0.156852\pi$
$390$	1.04443e10	−	6.03000e9i	0.451460	−	0.260651i
$391$			2.73933e10i			1.17203i
$392$	−4.67492e9	+	6.91662e9i	−0.197984	+	0.292920i
$393$	1.68480e10			0.706282
$394$	1.95038e9	+	3.37815e9i	0.0809344	+	0.140183i
$395$	−9.75036e9	−	5.62937e9i	−0.400527	−	0.231245i
$396$	−7.18115e6	+	1.24381e7i	−0.000292020	+	0.000505794i
$397$	−1.27200e10	+	7.34391e9i	−0.512066	+	0.295641i	−0.733682	−	0.679493i	$-0.762200\pi$
$397$	−1.27200e10	+	7.34391e9i	−0.512066	+	0.295641i	0.221617	+	0.975134i	$0.428867\pi$
$398$			4.87930e9i			0.194458i
$399$	−1.97775e10	+	1.05038e10i	−0.780333	+	0.414433i
$400$	−1.65549e9			−0.0646677
$401$	−9.91295e9	−	1.71697e10i	−0.383376	−	0.664027i	0.608166	−	0.793810i	$-0.291905\pi$
$401$	−9.91295e9	−	1.71697e10i	−0.383376	−	0.664027i	−0.991542	+	0.129783i	$0.958572\pi$
$402$	8.02551e9	+	4.63353e9i	0.307304	+	0.177422i
$403$	2.55915e10	−	4.43258e10i	0.970233	−	1.68049i
$404$	9.62054e9	−	5.55442e9i	0.361139	−	0.208503i
$405$			3.35377e9i			0.124656i
$406$	−1.03948e9	−	6.50231e8i	−0.0382572	−	0.0239311i
$407$	1.74508e8			0.00635971
$408$	−4.91276e9	−	8.50915e9i	−0.177290	−	0.307076i
$409$	−2.31685e10	−	1.33763e10i	−0.827950	−	0.478017i	0.0252003	−	0.999682i	$-0.491978\pi$
$409$	−2.31685e10	−	1.33763e10i	−0.827950	−	0.478017i	−0.853150	+	0.521665i	$0.825311\pi$
$410$	−1.56191e10	+	2.70531e10i	−0.552740	+	0.957374i
$411$	8.12442e9	−	4.69064e9i	0.284725	−	0.164386i
$412$		−	9.28614e9i		−	0.322290i
$413$	−3.09333e10	−	1.09499e9i	−1.06323	−	0.0376366i
$414$	4.67178e9			0.159031
$415$	8.00555e9	+	1.38660e10i	0.269897	+	0.467476i
$416$	5.21840e9	+	3.01284e9i	0.174246	+	0.100601i
$417$	2.13282e8	−	3.69414e8i	0.00705357	−	0.0122171i
$418$	−1.00256e8	+	5.78828e7i	−0.00328402	+	0.00189603i
$419$		−	3.90074e10i		−	1.26558i	−0.774322	−	0.632792i	$-0.781909\pi$
$419$		−	3.90074e10i		−	1.26558i	0.774322	−	0.632792i	$-0.218091\pi$
$420$	−3.56512e8	+	1.00714e10i	−0.0114572	+	0.323663i
$421$	6.65431e9			0.211824			0.105912	−	0.994376i	$-0.466224\pi$
$421$	6.65431e9			0.211824			0.105912	+	0.994376i	$0.466224\pi$
$422$	−1.85066e10	−	3.20543e10i	−0.583547	−	1.01073i
$423$	3.59679e8	+	2.07661e8i	0.0112345	+	0.00648624i
$424$	−1.45195e9	+	2.51485e9i	−0.0449251	+	0.0778125i
$425$	−1.26956e10	+	7.32983e9i	−0.389134	+	0.224666i
$426$		−	4.55759e9i		−	0.138388i
$427$	−1.66294e10	+	2.65844e10i	−0.500225	+	0.799677i
$428$	1.47321e10			0.439027
$429$	−3.89979e7	−	6.75463e7i	−0.00115136	−	0.00199422i
$430$	−1.06524e10	−	6.15018e9i	−0.311584	−	0.179893i
$431$	7.33104e9	−	1.26977e10i	0.212450	−	0.367974i	−0.740031	−	0.672573i	$-0.765189\pi$
$431$	7.33104e9	−	1.26977e10i	0.212450	−	0.367974i	0.952481	+	0.304599i	$0.0985225\pi$
$432$	−1.45119e9	+	8.37844e8i	−0.0416667	+	0.0240563i
$433$			3.73328e10i			1.06204i	0.847361	+	0.531018i	$0.178190\pi$
$433$			3.73328e10i			1.06204i	−0.847361	+	0.531018i	$0.821810\pi$
$434$	2.00614e10	+	3.77735e10i	0.565461	+	1.06470i
$435$	−1.48010e9			−0.0413364
$436$	7.16087e9	+	1.24030e10i	0.198162	+	0.343226i
$437$	3.26114e10	+	1.88282e10i	0.894218	+	0.516277i
$438$	−1.01584e10	+	1.75949e10i	−0.276013	+	0.478068i
$439$	1.30334e10	−	7.52486e9i	0.350914	−	0.202600i	−0.314174	−	0.949366i	$-0.601727\pi$
$439$	1.30334e10	−	7.52486e9i	0.350914	−	0.202600i	0.665088	+	0.746765i	$0.268394\pi$
$440$			5.20974e7i			0.00138997i
$441$	1.25761e10	+	8.91462e8i	0.332499	+	0.0235694i
$442$	5.33584e10			1.39802
$443$	3.20575e10	+	5.55252e10i	0.832367	+	1.44170i	0.896157	+	0.443738i	$0.146348\pi$
$443$	3.20575e10	+	5.55252e10i	0.832367	+	1.44170i	−0.0637900	+	0.997963i	$0.520319\pi$
$444$	1.76325e10	+	1.01801e10i	0.453715	+	0.261952i
$445$	3.68294e10	−	6.37905e10i	0.939194	−	1.62673i
$446$	1.19029e10	−	6.87214e9i	0.300824	−	0.173681i
$447$		−	1.61516e10i		−	0.404562i
$448$	−4.44700e9	+	2.36179e9i	−0.110396	+	0.0586313i
$449$	3.80094e10			0.935203			0.467602	−	0.883939i	$-0.345118\pi$
$449$	3.80094e10			0.935203			0.467602	+	0.883939i	$0.345118\pi$
$450$	1.25006e9	+	2.16517e9i	0.0304847	+	0.0528010i
$451$	1.74961e8	+	1.01014e8i	0.00422897	+	0.00244160i
$452$	−1.08007e9	+	1.87074e9i	−0.0258762	+	0.0448188i
$453$	−2.50412e9	+	1.44575e9i	−0.0594651	+	0.0343322i
$454$			2.25084e10i			0.529811i
$455$	−4.63982e10	−	2.90236e10i	−1.08257	−	0.677182i
$456$	−1.35067e10			−0.312385
$457$	−2.07070e10	−	3.58656e10i	−0.474737	−	0.822268i	0.524845	−	0.851198i	$-0.324123\pi$
$457$	−2.07070e10	−	3.58656e10i	−0.474737	−	0.822268i	−0.999581	+	0.0289299i	$0.990790\pi$
$458$	3.62340e10	+	2.09197e10i	0.823483	+	0.475438i
$459$	−7.41924e9	+	1.28505e10i	−0.167151	+	0.289514i
$460$	1.46759e10	−	8.47315e9i	0.327774	−	0.189240i
$461$			2.71417e10i			0.600944i	0.953791	+	0.300472i	$0.0971442\pi$
$461$			2.71417e10i			0.600944i	−0.953791	+	0.300472i	$0.902856\pi$
$462$	6.51350e7	+	2.30568e6i	0.00142971	+	5.06093e-5i
$463$	−5.33868e10			−1.16174			−0.580871	−	0.813996i	$-0.697288\pi$
$463$	−5.33868e10			−1.16174			−0.580871	+	0.813996i	$0.697288\pi$
$464$	−3.69759e8	−	6.40442e8i	−0.00797714	−	0.0138168i
$465$	4.47132e10	+	2.58152e10i	0.956366	+	0.552158i
$466$	−1.16653e10	+	2.02049e10i	−0.247374	+	0.428464i
$467$	3.79032e10	−	2.18835e10i	0.796909	−	0.460096i	−0.0454800	−	0.998965i	$-0.514482\pi$
$467$	3.79032e10	−	2.18835e10i	0.796909	−	0.460096i	0.842389	+	0.538869i	$0.181148\pi$
$468$		−	9.09998e9i		−	0.189695i
$469$	1.48770e9	−	4.20274e10i	0.0307486	−	0.868643i
$470$	1.50653e9			0.0308735
$471$	−1.12451e10	−	1.94771e10i	−0.228497	−	0.395769i
$472$	−1.61678e10	−	9.33451e9i	−0.325750	−	0.188072i
$473$	−3.97752e7	+	6.88926e7i	−0.000794635	+	0.00137635i
$474$	−7.35722e9	+	4.24769e9i	−0.145747	+	0.0841472i
$475$			2.01520e10i			0.395861i
$476$	−2.36461e10	+	3.78015e10i	−0.460608	+	0.736345i
$477$	4.38547e9			0.0847115
$478$	−2.52054e10	−	4.36570e10i	−0.482816	−	0.836261i
$479$	8.72178e10	+	5.03552e10i	1.65677	+	0.956539i	0.974189	+	0.225732i	$0.0724775\pi$
$479$	8.72178e10	+	5.03552e10i	1.65677	+	0.956539i	0.682585	+	0.730806i	$0.260856\pi$
$480$	−3.03917e9	+	5.26400e9i	−0.0572520	+	0.0991633i
$481$	−9.57551e10	+	5.52843e10i	−1.78888	+	1.03281i
$482$		−	6.60314e10i		−	1.22338i
$483$	−9.94408e9	−	1.87236e10i	−0.182716	−	0.344034i
$484$	−2.74376e10			−0.499994
$485$	−2.43969e10	−	4.22566e10i	−0.440927	−	0.763708i
$486$	2.19158e9	+	1.26531e9i	0.0392837	+	0.0226805i
$487$	2.26332e10	−	3.92018e10i	0.402374	−	0.696932i	−0.591638	−	0.806204i	$-0.701519\pi$
$487$	2.26332e10	−	3.92018e10i	0.402374	−	0.696932i	0.994012	+	0.109272i	$0.0348519\pi$
$488$	−1.63791e10	+	9.45645e9i	−0.288808	+	0.166744i
$489$		−	5.08846e10i		−	0.889919i
$490$	4.11233e10	−	2.00086e10i	0.713351	−	0.347082i
$491$	1.02274e11			1.75969			0.879847	−	0.475256i	$-0.157645\pi$
$491$	1.02274e11			1.75969			0.879847	+	0.475256i	$0.157645\pi$
$492$	1.17855e10	+	2.04132e10i	0.201136	+	0.348377i
$493$	−5.67121e9	−	3.27428e9i	−0.0960038	−	0.0554278i
$494$	3.66747e10	−	6.35224e10i	0.615827	−	1.06664i
$495$	6.81366e7	−	3.93387e7i	0.00113491	−	0.000655238i
$496$			2.57967e10i			0.426224i
$497$	−1.82660e10	+	9.70102e9i	−0.299376	+	0.158998i
$498$	1.20813e10			0.196425
$499$	−2.36190e10	−	4.09093e10i	−0.380942	−	0.659811i	0.610255	−	0.792205i	$-0.291067\pi$
$499$	−2.36190e10	−	4.09093e10i	−0.380942	−	0.659811i	−0.991197	+	0.132394i	$0.957734\pi$
$500$	−2.25086e10	−	1.29953e10i	−0.360137	−	0.207925i
$501$	−3.41512e10	+	5.91516e10i	−0.542069	+	0.938892i
$502$	1.63020e10	−	9.41195e9i	0.256700	−	0.148206i
$503$			4.64077e10i			0.724966i	0.931990	+	0.362483i	$0.118071\pi$
$503$			4.64077e10i			0.724966i	−0.931990	+	0.362483i	$0.881929\pi$
$504$	6.44684e9	+	4.03271e9i	0.0999136	+	0.0624993i
$505$	−6.08548e10			−0.935684
$506$	−5.47985e7	−	9.49138e7i	−0.000835923	−	0.00144786i
$507$	9.76040e9	+	5.63517e9i	0.147719	+	0.0852855i
$508$	−1.11378e10	+	1.92912e10i	−0.167242	+	0.289671i
$509$	−4.70380e10	+	2.71574e10i	−0.700773	+	0.404591i	−0.807635	−	0.589682i	$-0.799253\pi$
$509$	−4.70380e10	+	2.71574e10i	−0.700773	+	0.404591i	0.106862	+	0.994274i	$0.465920\pi$
$510$			5.38247e10i			0.795611i
$511$	9.21396e10	+	3.26160e9i	1.35133	+	0.0478351i
$512$	−3.03700e9			−0.0441942
$513$	1.01989e10	+	1.76650e10i	0.147260	+	0.255061i
$514$	−8.45239e10	−	4.87999e10i	−1.21095	−	0.699144i
$515$	−2.54350e10	+	4.40547e10i	−0.361579	+	0.626272i
$516$	−8.03789e9	+	4.64068e9i	−0.113382	+	0.0654610i
$517$		−	9.74318e6i		−	0.000136376i
$518$	3.26858e9	−	9.23368e10i	0.0453983	−	1.28250i
$519$	6.02416e10			0.830284
$520$	−1.65045e10	−	2.85867e10i	−0.225730	−	0.390976i
$521$	−9.49506e10	−	5.48197e10i	−1.28868	−	0.744023i	−0.310265	−	0.950650i	$-0.600418\pi$
$521$	−9.49506e10	−	5.48197e10i	−1.28868	−	0.744023i	−0.978420	+	0.206628i	$0.933751\pi$
$522$	−5.58410e8	+	9.67194e8i	−0.00752092	+	0.0130266i
$523$	−2.93392e10	+	1.69390e10i	−0.392140	+	0.226402i	−0.683087	−	0.730337i	$-0.739363\pi$
$523$	−2.93392e10	+	1.69390e10i	−0.392140	+	0.226402i	0.290947	+	0.956739i	$0.406030\pi$
$524$		−	4.61141e10i		−	0.611659i
$525$	6.01680e9	−	9.61867e9i	0.0792005	−	0.126613i
$526$	−8.84854e10			−1.15592
$527$	1.14217e11	+	1.97830e11i	1.48077	+	2.56477i
$528$	3.40440e7	+	1.96553e7i	0.000438030	+	0.000252897i
$529$	2.13306e10	−	3.69457e10i	0.272383	−	0.471781i
$530$	1.37765e10	−	7.95387e9i	0.174597	−	0.100803i
$531$			2.81939e10i			0.354631i
$532$	2.87496e10	+	5.41324e10i	0.358909	+	0.675788i
$533$	−1.28005e11			−1.58605
$534$	−2.77900e10	−	4.81337e10i	−0.341762	−	0.591949i
$535$	−6.98912e10	−	4.03517e10i	−0.853115	−	0.492546i
$536$	1.26823e10	−	2.19664e10i	0.153652	−	0.266133i
$537$	4.03587e10	−	2.33011e10i	0.485334	−	0.280207i
$538$			6.06450e10i			0.723879i
$539$	−1.29402e8	−	2.65957e8i	−0.00153315	−	0.00315106i
$540$	9.17951e9			0.107955
$541$	5.67999e10	+	9.83803e10i	0.663068	+	1.14847i	0.979805	+	0.199955i	$0.0640794\pi$
$541$	5.67999e10	+	9.83803e10i	0.663068	+	1.14847i	−0.316737	+	0.948513i	$0.602587\pi$
$542$	−5.21427e10	−	3.01046e10i	−0.604222	−	0.348848i
$543$	−2.80569e10	+	4.85960e10i	−0.322731	+	0.558987i
$544$	−2.32901e10	+	1.34466e10i	−0.265935	+	0.153538i
$545$		−	7.84552e10i		−	0.889274i
$546$	−3.64710e10	+	1.93697e10i	−0.410372	+	0.217948i
$547$	−1.34000e11			−1.49678			−0.748388	−	0.663261i	$-0.769172\pi$
$547$	−1.34000e11			−1.49678			−0.748388	+	0.663261i	$0.769172\pi$
$548$	−1.28386e10	−	2.22371e10i	−0.142362	−	0.246579i
$549$	2.47356e10	+	1.42811e10i	0.272291	+	0.157207i
$550$	2.93257e7	−	5.07935e7i	0.000320477	−	0.000555083i
$551$	−7.79596e9	+	4.50100e9i	−0.0845792	+	0.0488318i
$552$		−	1.27870e10i		−	0.137725i
$553$	3.26841e10	+	2.04450e10i	0.349491	+	0.218618i
$554$	−2.32553e9			−0.0246878
$555$	−5.57674e10	−	9.65919e10i	−0.587771	−	1.01805i
$556$	−1.01111e9	−	5.83766e8i	−0.0105804	−	0.00610857i
$557$	−8.00384e10	+	1.38631e11i	−0.831530	+	1.44025i	0.0652955	+	0.997866i	$0.479201\pi$
$557$	−8.00384e10	+	1.38631e11i	−0.831530	+	1.44025i	−0.896825	+	0.442385i	$0.854132\pi$
$558$	3.37388e10	−	1.94791e10i	0.348010	−	0.200924i
$559$		−	5.04033e10i		−	0.516192i
$560$	2.75662e10	+	9.75798e8i	0.280301	+	0.00992220i
$561$	3.48101e8			0.00351442
$562$	3.12202e10	+	5.40750e10i	0.312961	+	0.542065i
$563$	1.99832e10	+	1.15373e10i	0.198899	+	0.114834i	0.596142	−	0.802879i	$-0.296700\pi$
$563$	1.99832e10	+	1.15373e10i	0.198899	+	0.114834i	−0.397243	+	0.917713i	$0.630033\pi$
$564$	5.68381e8	−	9.84466e8i	0.00561725	−	0.00972936i
$565$	1.02480e10	−	5.91671e9i	0.100565	−	0.0580612i
$566$		−	8.05044e10i		−	0.784430i
$567$	4.06258e8	−	1.14767e10i	0.00393069	−	0.111042i
$568$	−1.24744e10			−0.119847
$569$	2.13235e10	+	3.69333e10i	0.203427	+	0.352346i	0.949630	−	0.313372i	$-0.101459\pi$
$569$	2.13235e10	+	3.69333e10i	0.203427	+	0.352346i	−0.746203	+	0.665718i	$0.768125\pi$
$570$	6.40776e10	+	3.69952e10i	0.607025	+	0.350466i
$571$	4.78333e10	−	8.28497e10i	0.449972	−	0.779375i	−0.548411	−	0.836209i	$-0.684767\pi$
$571$	4.78333e10	−	8.28497e10i	0.449972	−	0.779375i	0.998384	+	0.0568339i	$0.0181006\pi$
$572$	−1.84879e8	+	1.06740e8i	−0.00172704	+	0.000997109i
$573$		−	4.54345e10i		−	0.421470i
$574$	5.67262e10	−	9.06846e10i	0.522560	−	0.835384i
$575$	−1.90782e10			−0.174528
$576$	2.29324e9	+	3.97200e9i	0.0208333	+	0.0360844i
$577$	−2.78602e10	−	1.60851e10i	−0.251351	−	0.145118i	0.369032	−	0.929417i	$-0.379689\pi$
$577$	−2.78602e10	−	1.60851e10i	−0.251351	−	0.145118i	−0.620383	+	0.784299i	$0.713023\pi$
$578$	−7.96104e10	+	1.37889e11i	−0.713278	+	1.23543i
$579$	3.09439e10	−	1.78655e10i	0.275335	−	0.158965i
$580$			4.05112e9i			0.0357984i
$581$	−2.57156e10	−	4.84197e10i	−0.225679	−	0.424930i
$582$	−3.68177e10			−0.320897
$583$	−5.14402e7	−	8.90970e7i	−0.000445275	−	0.000771238i
$584$	4.81584e10	+	2.78043e10i	0.414019	+	0.239034i
$585$	−2.49251e10	+	4.31715e10i	−0.212820	+	0.368616i
$586$	1.63238e10	−	9.42457e9i	0.138431	−	0.0799229i
$587$			4.64261e10i			0.391030i	0.980701	+	0.195515i	$0.0626378\pi$
$587$			4.64261e10i			0.391030i	−0.980701	+	0.195515i	$0.937362\pi$
$588$	2.43999e9	−	3.44215e10i	0.0204117	−	0.287953i
$589$	3.14018e11			2.60912
$590$	5.11349e10	+	8.85683e10i	0.421997	+	0.730920i
$591$	−1.39636e10	−	8.06190e9i	−0.114459	−	0.0660827i
$592$	2.78638e10	−	4.82614e10i	0.226857	−	0.392928i
$593$	1.44787e11	−	8.35927e10i	1.17087	−	0.676004i	0.216988	−	0.976174i	$-0.430377\pi$
$593$	1.44787e11	−	8.35927e10i	1.17087	−	0.676004i	0.953886	+	0.300170i	$0.0970433\pi$
$594$		−	5.93667e7i		−	0.000476867i
$595$	2.15719e11	−	1.14568e11i	1.72116	−	0.914105i
$596$	−4.42080e10			−0.350361
$597$	−1.00843e10	−	1.74666e10i	−0.0793870	−	0.137502i
$598$	6.01376e10	+	3.47204e10i	0.470263	+	0.271507i
$599$	5.41914e10	−	9.38622e10i	0.420943	−	0.729094i	−0.575089	−	0.818091i	$-0.695033\pi$
$599$	5.41914e10	−	9.38622e10i	0.420943	−	0.729094i	0.996032	+	0.0889966i	$0.0283660\pi$
$600$	5.92622e9	−	3.42150e9i	0.0457270	−	0.0264005i
$601$			3.09111e9i			0.0236928i	0.999930	+	0.0118464i	$0.00377092\pi$
$601$			3.09111e9i			0.0236928i	−0.999930	+	0.0118464i	$0.996229\pi$
$602$	3.57080e10	+	2.23365e10i	0.271881	+	0.170071i
$603$	−3.83055e10			−0.289729
$604$	3.95713e9	+	6.85395e9i	0.0297326	+	0.0514983i
$605$	1.30168e11	+	7.51523e10i	0.971586	+	0.560946i
$606$	−2.29593e10	+	3.97666e10i	−0.170242	+	0.294868i
$607$	−5.77092e10	+	3.33184e10i	−0.425100	+	0.245431i	−0.697257	−	0.716821i	$-0.745596\pi$
$607$	−5.77092e10	+	3.33184e10i	−0.425100	+	0.245431i	0.272157	+	0.962253i	$0.412263\pi$
$608$			3.69687e10i			0.270533i
$609$	5.06494e9	+	1.79291e8i	0.0368218	+	0.00130343i
$610$	1.03606e11			0.748282
$611$	3.08665e9	+	5.34623e9i	0.0221474	+	0.0383604i
$612$	3.51727e10	+	2.03070e10i	0.250726	+	0.144757i
$613$	−9.80316e10	+	1.69796e11i	−0.694263	+	1.20250i	0.276165	+	0.961110i	$0.410936\pi$
$613$	−9.80316e10	+	1.69796e11i	−0.694263	+	1.20250i	−0.970428	+	0.241389i	$0.922397\pi$
$614$	3.32676e10	−	1.92071e10i	0.234071	−	0.135141i
$615$		−	1.29124e11i		−	0.902621i
$616$	6.31079e6	−	1.78279e8i	4.38289e−5	−	0.00123816i
$617$	−9.94637e10			−0.686315			−0.343158	−	0.939278i	$-0.611497\pi$
$617$	−9.94637e10			−0.686315			−0.343158	+	0.939278i	$0.611497\pi$
$618$	1.91922e10	+	3.32419e10i	0.131574	+	0.227893i
$619$	−1.59483e11	−	9.20774e10i	−1.08630	−	0.627177i	−0.153713	−	0.988116i	$-0.549123\pi$
$619$	−1.59483e11	−	9.20774e10i	−1.08630	−	0.627177i	−0.932590	+	0.360938i	$0.882456\pi$
$620$	7.06579e10	−	1.22383e11i	0.478183	−	0.828237i
$621$	−1.67237e10	+	9.65543e9i	−0.112452	+	0.0649240i
$622$			7.48704e10i			0.500206i
$623$	−1.33759e11	+	2.13832e11i	−0.887912	+	1.41945i
$624$	−2.49073e10			−0.164281
$625$	9.09241e10	+	1.57485e11i	0.595880	+	1.03209i
$626$	−1.56642e11	−	9.04374e10i	−1.02003	−	0.588913i
$627$	2.39259e8	−	4.14410e8i	0.00154810	−	0.00268139i
$628$	−5.33102e10	+	3.07787e10i	−0.342746	+	0.197884i
$629$		−	4.93476e11i		−	3.15256i
$630$	−1.95390e10	−	3.67898e10i	−0.124034	−	0.233542i
$631$	−4.06646e10			−0.256507			−0.128253	−	0.991741i	$-0.540937\pi$
$631$	−4.06646e10			−0.256507			−0.128253	+	0.991741i	$0.540937\pi$
$632$	1.16262e10	+	2.01372e10i	0.0728737	+	0.126221i
$633$	1.32497e11	+	7.64971e10i	0.825260	+	0.476464i
$634$	7.87003e10	−	1.36313e11i	0.487102	−	0.843685i
$635$	1.05678e11	−	6.10134e10i	0.649967	−	0.375258i
$636$		−	1.20033e10i		−	0.0733623i
$637$	1.55260e11	+	1.04940e11i	0.942980	+	0.637358i
$638$	2.61999e7			0.000158131
$639$	9.41943e9	+	1.63149e10i	0.0564965	+	0.0978548i
$640$	1.44079e10	+	8.31842e9i	0.0858780	+	0.0495817i
$641$	−1.38149e11	+	2.39281e11i	−0.818304	+	1.41734i	0.0886267	+	0.996065i	$0.471752\pi$
$641$	−1.38149e11	+	2.39281e11i	−0.818304	+	1.41734i	−0.906931	+	0.421279i	$0.861581\pi$
$642$	−5.27371e10	+	3.04478e10i	−0.310439	+	0.179232i
$643$		−	7.00082e10i		−	0.409548i	−0.978809	−	0.204774i	$-0.934354\pi$
$643$		−	7.00082e10i		−	0.409548i	0.978809	−	0.204774i	$-0.0656460\pi$
$644$	−5.12479e10	+	2.72176e10i	−0.297942	+	0.158237i
$645$	5.08437e10			0.293764
$646$	1.63682e11	+	2.83505e11i	0.939876	+	1.62791i
$647$	−9.44301e10	−	5.45192e10i	−0.538882	−	0.311123i	0.205744	−	0.978606i	$-0.434039\pi$
$647$	−9.44301e10	−	5.45192e10i	−0.538882	−	0.311123i	−0.744626	+	0.667482i	$0.767372\pi$
$648$	3.46324e9	−	5.99851e9i	0.0196419	−	0.0340207i
$649$	5.72799e8	−	3.30705e8i	0.00322867	−	0.00186407i
$650$			3.71616e10i			0.208181i
$651$	−1.49883e11	−	9.37567e10i	−0.834504	−	0.522009i
$652$	−1.39274e11			−0.770693
$653$	−7.94409e10	−	1.37596e11i	−0.436910	−	0.756750i	0.560540	−	0.828128i	$-0.310594\pi$
$653$	−7.94409e10	−	1.37596e11i	−0.436910	−	0.756750i	−0.997449	+	0.0713779i	$0.977260\pi$
$654$	−5.12679e10	−	2.95995e10i	−0.280243	−	0.161798i
$655$	−1.26308e11	+	2.18772e11i	−0.686223	+	1.18857i
$656$	5.58722e10	−	3.22578e10i	0.301704	−	0.174189i
$657$		−	8.39798e10i		−	0.450727i
$658$	−5.15538e9	−	1.82492e8i	−0.0275015	−	0.000973511i
$659$	−1.48506e11			−0.787412			−0.393706	−	0.919236i	$-0.628807\pi$
$659$	−1.48506e11			−0.787412			−0.393706	+	0.919236i	$0.628807\pi$
$660$	−1.07673e8	−	1.86495e8i	−0.000567453	−	0.000982857i
$661$	1.98165e11	+	1.14411e11i	1.03806	+	0.599323i	0.919283	−	0.393598i	$-0.128770\pi$
$661$	1.98165e11	+	1.14411e11i	1.03806	+	0.599323i	0.118776	+	0.992921i	$0.462103\pi$
$662$	−1.03271e11	+	1.78870e11i	−0.537706	+	0.931334i
$663$	−1.91009e11	+	1.10279e11i	−0.988550	+	0.570740i
$664$		−	3.30674e10i		−	0.170109i
$665$	1.18782e10	−	3.35557e11i	0.0607384	−	1.71585i
$666$	−8.41596e10			−0.427766
$667$	−4.26116e9	−	7.38055e9i	−0.0215290	−	0.0372894i
$668$	1.61902e11	+	9.34741e10i	0.813104	+	0.469446i
$669$	−2.84061e10	+	4.92008e10i	−0.141810	+	0.245622i
$670$	−1.20333e11	+	6.94742e10i	−0.597152	+	0.344766i
$671$		−	6.70052e8i		−	0.00330536i
$672$	1.10378e10	−	1.76454e10i	0.0541259	−	0.0865277i
$673$	−1.83564e11			−0.894805			−0.447402	−	0.894333i	$-0.647651\pi$
$673$	−1.83564e11			−0.894805			−0.447402	+	0.894333i	$0.647651\pi$
$674$	4.11618e10	+	7.12943e10i	0.199459	+	0.345474i
$675$	−8.94976e9	−	5.16715e9i	−0.0431118	−	0.0248906i
$676$	1.54238e10	−	2.67149e10i	0.0738594	−	0.127928i
$677$	9.02613e10	−	5.21124e10i	0.429682	−	0.248077i	−0.269529	−	0.962992i	$-0.586868\pi$
$677$	9.02613e10	−	5.21124e10i	0.429682	−	0.248077i	0.699211	+	0.714915i	$0.253535\pi$
$678$		−	8.92901e9i		−	0.0422556i
$679$	7.83681e10	+	1.47559e11i	0.368689	+	0.694202i
$680$	1.47322e11			0.689019
$681$	−4.65194e10	−	8.05740e10i	−0.216295	−	0.374633i
$682$	−7.91490e8	−	4.56967e8i	−0.00365854	−	0.00211226i
$683$	5.73559e10	−	9.93434e10i	0.263570	−	0.456516i	−0.703618	−	0.710578i	$-0.748433\pi$
$683$	5.73559e10	−	9.93434e10i	0.263570	−	0.456516i	0.967188	+	0.254062i	$0.0817667\pi$
$684$	4.83503e10	−	2.79151e10i	0.220889	−	0.127531i
$685$			1.40661e11i			0.638868i
$686$	−1.43149e11	+	6.34887e10i	−0.646385	+	0.286681i
$687$	−1.72944e11			−0.776387
$688$	1.27018e10	+	2.20002e10i	0.0566909	+	0.0981915i
$689$	5.64520e10	+	3.25926e10i	0.250497	+	0.144625i
$690$	−3.50239e10	+	6.06631e10i	−0.154514	+	0.267626i
$691$	−3.02268e10	+	1.74514e10i	−0.132581	+	0.0765454i	−0.564823	−	0.825212i	$-0.691056\pi$
$691$	−3.02268e10	+	1.74514e10i	−0.132581	+	0.0765454i	0.432243	+	0.901757i	$0.357722\pi$
$692$		−	1.64885e11i		−	0.719047i
$693$	−2.37931e8	+	1.26365e8i	−0.00103162	+	0.000547889i
$694$	1.17381e10			0.0506012
$695$	3.19790e9	+	5.53893e9i	0.0137065	+	0.0237403i
$696$	2.64728e9	+	1.52841e9i	0.0112814	+	0.00651331i
$697$	2.85648e11	−	4.94757e11i	1.21032	−	2.09634i
$698$	−1.89392e11	+	1.09346e11i	−0.797886	+	0.460660i
$699$		−	9.64376e10i		−	0.403959i
$700$	−2.63270e10	−	1.64684e10i	−0.109650	−	0.0685897i
$701$	−4.04644e11			−1.67572			−0.837858	−	0.545888i	$-0.816192\pi$
$701$	−4.04644e11			−1.67572			−0.837858	+	0.545888i	$0.816192\pi$
$702$	1.88074e10	+	3.25755e10i	0.0774429	+	0.134135i
$703$	−5.87476e11	−	3.39179e11i	−2.40530	−	1.38870i
$704$	5.37978e7	−	9.31806e7i	0.000219015	−	0.000379345i
$705$	−5.39295e9	+	3.11362e9i	−0.0218308	+	0.0126040i
$706$		−	1.57632e11i		−	0.634491i
$707$	2.08247e11	+	7.37161e9i	0.833492	+	0.0295043i
$708$	7.71686e10			0.307120
$709$	−8.03552e10	−	1.39179e11i	−0.318001	−	0.550795i	0.662070	−	0.749442i	$-0.269678\pi$
$709$	−8.03552e10	−	1.39179e11i	−0.318001	−	0.550795i	−0.980071	+	0.198648i	$0.936345\pi$
$710$	5.91804e10	+	3.41678e10i	0.232887	+	0.134457i
$711$	1.75579e10	−	3.04112e10i	0.0687059	−	0.119002i
$712$	−1.31745e11	+	7.60631e10i	−0.512643	+	0.295974i
$713$			2.97285e11i			1.15031i
$714$	6.52002e9	−	1.84190e11i	0.0250874	−	0.708717i
$715$	1.16945e9			0.00447465
$716$	−6.37768e10	−	1.10465e11i	−0.242667	−	0.420311i
$717$	1.80457e11	+	1.04187e11i	0.682804	+	0.394217i
$718$	9.57817e10	−	1.65899e11i	0.360400	−	0.624231i
$719$	2.86258e11	−	1.65271e11i	1.07113	−	0.618416i	0.142639	−	0.989775i	$-0.454441\pi$
$719$	2.86258e11	−	1.65271e11i	1.07113	−	0.618416i	0.928489	+	0.371359i	$0.121108\pi$
$720$		−	2.51249e10i		−	0.0934921i
$721$	9.23759e10	−	1.47676e11i	0.341836	−	0.546471i
$722$	2.57865e11			0.948952
$723$	1.36471e11	+	2.36375e11i	0.499444	+	0.865063i
$724$	1.33011e11	+	7.67937e10i	0.484097	+	0.279493i
$725$	2.28038e9	−	3.94973e9i	0.00825382	−	0.0142960i
$726$	9.82191e10	−	5.67069e10i	0.353549	−	0.204122i
$727$			5.22460e11i			1.87032i	0.354230	+	0.935158i	$0.384743\pi$
$727$			5.22460e11i			1.87032i	−0.354230	+	0.935158i	$0.615257\pi$
$728$	5.30162e10	+	9.98237e10i	0.188748	+	0.355393i
$729$	−1.04604e10			−0.0370370
$730$	−1.52313e11	−	2.63814e11i	−0.536347	−	0.928981i
$731$	1.94816e11	+	1.12477e11i	0.682267	+	0.393907i
$732$	3.90884e10	−	6.77031e10i	0.136145	−	0.235811i
$733$	−2.59008e11	+	1.49539e11i	−0.897218	+	0.518009i	−0.876297	−	0.481772i	$-0.839993\pi$
$733$	−2.59008e11	+	1.49539e11i	−0.897218	+	0.518009i	−0.0209215	+	0.999781i	$0.506660\pi$
$734$		−	8.98260e10i		−	0.309470i
$735$	−1.05857e11	+	1.56617e11i	−0.362719	+	0.536649i
$736$	−3.49988e10			−0.119273
$737$	4.49311e8	+	7.78230e8i	0.00152292	+	0.00263778i
$738$	−8.43781e10	−	4.87157e10i	−0.284449	−	0.164227i
$739$	1.58713e11	−	2.74898e11i	0.532149	−	0.921710i	−0.467146	−	0.884180i	$-0.654718\pi$
$739$	1.58713e11	−	2.74898e11i	0.532149	−	0.921710i	0.999296	−	0.0375297i	$-0.0119489\pi$
$740$	−2.64379e11	+	1.52639e11i	−0.881657	+	0.509025i
$741$			3.03191e11i			1.00564i
$742$	−4.81071e10	+	2.55496e10i	−0.158706	+	0.0842885i
$743$	−2.55243e11			−0.837526			−0.418763	−	0.908096i	$-0.637536\pi$
$743$	−2.55243e11			−0.837526			−0.418763	+	0.908096i	$0.637536\pi$
$744$	−5.33156e10	−	9.23453e10i	−0.174005	−	0.301386i
$745$	2.09729e11	+	1.21087e11i	0.680820	+	0.393072i
$746$	9.21244e9	−	1.59564e10i	0.0297454	−	0.0515205i
$747$	−4.32478e10	+	2.49692e10i	−0.138894	+	0.0801902i
$748$		−	9.52776e8i		−	0.00304358i
$749$	2.34282e11	+	1.46551e11i	0.744409	+	0.465653i
$750$	1.07433e11			0.339540
$751$	−2.78274e10	−	4.81985e10i	−0.0874810	−	0.151521i	0.818965	−	0.573844i	$-0.194548\pi$
$751$	−2.78274e10	−	4.81985e10i	−0.0874810	−	0.151521i	−0.906446	+	0.422322i	$0.861215\pi$
$752$	−2.69455e9	−	1.55570e9i	−0.00842587	−	0.00486468i
$753$	−3.89044e10	+	6.73844e10i	−0.121009	+	0.209594i
$754$	−1.43763e10	+	8.30015e9i	−0.0444796	+	0.0256803i
$755$		−	4.33547e10i		−	0.133428i
$756$	−3.14126e10	−	1.11195e9i	−0.0961648	−	0.00340408i
$757$	1.51282e11			0.460684			0.230342	−	0.973110i	$-0.426015\pi$
$757$	1.51282e11			0.460684			0.230342	+	0.973110i	$0.426015\pi$
$758$	1.18471e11	+	2.05199e11i	0.358870	+	0.621581i
$759$	3.92327e8	+	2.26510e8i	0.00118217	+	0.000682529i
$760$	1.01258e11	−	1.75385e11i	0.303512	−	0.525699i
$761$	3.45291e11	−	1.99354e11i	1.02955	−	0.594411i	0.112694	−	0.993630i	$-0.464052\pi$
$761$	3.45291e11	−	1.99354e11i	1.02955	−	0.594411i	0.916856	+	0.399219i	$0.130719\pi$
$762$		−	9.20765e10i		−	0.273104i
$763$	−9.50363e9	+	2.68476e11i	−0.0280409	+	0.792150i
$764$	−1.24357e11			−0.365004
$765$	−1.11243e11	−	1.92678e11i	−0.324807	−	0.562582i
$766$	−9.19067e10	−	5.30623e10i	−0.266951	−	0.154124i
$767$	−2.09536e11	+	3.62926e11i	−0.605448	+	1.04867i
$768$	1.08716e10	−	6.27674e9i	0.0312500	−	0.0180422i
$769$		−	5.28713e10i		−	0.151187i	−0.997139	−	0.0755936i	$-0.975915\pi$
$769$		−	5.28713e10i		−	0.151187i	0.997139	−	0.0755936i	$-0.0240852\pi$
$770$	−5.18250e8	+	8.28494e8i	−0.00147427	+	0.00235682i
$771$	4.03430e11			1.14170
$772$	−4.88990e10	−	8.46956e10i	−0.137667	−	0.238447i
$773$	−2.30293e10	−	1.32960e10i	−0.0645005	−	0.0372394i	0.467403	−	0.884044i	$-0.345190\pi$
$773$	−2.30293e10	−	1.32960e10i	−0.0645005	−	0.0372394i	−0.531903	+	0.846805i	$0.678523\pi$
$774$	1.91823e10	−	3.32247e10i	0.0534487	−	0.0925758i
$775$	−1.37779e11	+	7.95467e10i	−0.381923	+	0.220504i
$776$			1.00773e11i			0.277905i
$777$	1.79137e11	+	3.37296e11i	0.491475	+	0.925395i
$778$	1.59728e10			0.0435976
$779$	−3.92668e11	−	6.80120e11i	−1.06629	−	1.84687i
$780$	1.18163e11	+	6.82216e10i	0.319230	+	0.184308i
$781$	2.20974e8	−	3.82738e8i	0.000593932	−	0.00102872i
$782$	−2.68399e11	+	1.54960e11i	−0.717717	+	0.414374i
$783$		−	4.61639e9i		−	0.0122816i
$784$	−9.42141e10	−	6.67842e9i	−0.249374	−	0.0176770i
$785$	3.37214e11			0.888030
$786$	9.53067e10	+	1.65076e11i	0.249709	+	0.432508i
$787$	1.39157e11	+	8.03422e10i	0.362748	+	0.209433i	0.670286	−	0.742103i	$-0.266172\pi$
$787$	1.39157e11	+	8.03422e10i	0.362748	+	0.209433i	−0.307537	+	0.951536i	$0.599505\pi$
$788$	−2.20660e10	+	3.82194e10i	−0.0572293	+	0.0991240i
$789$	3.16754e11	−	1.82878e11i	0.817360	−	0.471903i
$790$		−	1.27378e11i		−	0.327029i
$791$	−3.57858e10	+	1.90058e10i	−0.0914124	+	0.0485489i
$792$	−1.62491e8			−0.000412979
$793$	2.12273e11	+	3.67668e11i	0.536787	+	0.929743i
$794$	−1.43911e11	−	8.30868e10i	−0.362085	−	0.209050i
$795$	−3.28774e10	+	5.69454e10i	−0.0823056	+	0.142557i
$796$	−4.78072e10	+	2.76015e10i	−0.119081	+	0.0687512i
$797$			4.30829e11i			1.06776i	0.845562	+	0.533878i	$0.179266\pi$
$797$			4.30829e11i			1.06776i	−0.845562	+	0.533878i	$0.820734\pi$
$798$	−2.14794e11	−	1.34361e11i	−0.529677	−	0.331330i
$799$	−2.75519e10			−0.0676028
$800$	−9.36489e9	−	1.62205e10i	−0.0228635	−	0.0396007i
$801$	1.98961e11	+	1.14870e11i	0.483324	+	0.279047i
$802$	1.12152e11	−	1.94253e11i	0.271088	−	0.469538i
$803$	−1.70617e9	+	9.85057e8i	−0.00410355	+	0.00236919i
$804$			1.04845e11i			0.250913i
$805$	3.17676e11	+	1.12452e10i	0.756487	+	0.0267784i
$806$	5.79070e11			1.37212
$807$	−1.25338e11	−	2.17093e11i	−0.295522	−	0.511860i
$808$	1.08844e11	+	6.28411e10i	0.255364	+	0.147434i
$809$	2.79510e11	−	4.84126e11i	0.652535	−	1.13022i	−0.329971	−	0.943991i	$-0.607039\pi$
$809$	2.79510e11	−	4.84126e11i	0.652535	−	1.13022i	0.982506	−	0.186232i	$-0.0596276\pi$
$810$	−3.28601e10	+	1.89718e10i	−0.0763360	+	0.0440726i
$811$			1.62918e9i			0.00376605i	0.999998	+	0.00188303i	$0.000599387\pi$
$811$			1.62918e9i			0.00376605i	−0.999998	+	0.00188303i	$0.999401\pi$
$812$	4.90731e8	−	1.38631e10i	0.00112881	−	0.0318886i
$813$	2.48876e11			0.569666
$814$	9.87165e8	+	1.70982e9i	0.00224850	+	0.00389451i
$815$	6.60737e11	+	3.81476e11i	1.49761	+	0.864644i
$816$	5.55815e10	−	9.62700e10i	0.125363	−	0.217135i
$817$	2.67804e11	−	1.54617e11i	0.601076	−	0.347031i
$818$		−	3.02672e11i		−	0.676018i
$819$	9.05240e10	−	1.44715e11i	0.201200	−	0.321646i
$820$	−3.53420e11			−0.781693
$821$	−1.12094e11	−	1.94153e11i	−0.246723	−	0.427337i	0.715891	−	0.698212i	$-0.246021\pi$
$821$	−1.12094e11	−	1.94153e11i	−0.246723	−	0.427337i	−0.962615	+	0.270874i	$0.912687\pi$
$822$	9.19173e10	+	5.30685e10i	0.201331	+	0.116238i
$823$	−3.77547e11	+	6.53931e11i	−0.822947	+	1.42539i	0.0805307	+	0.996752i	$0.474339\pi$
$823$	−3.77547e11	+	6.53931e11i	−0.822947	+	1.42539i	−0.903478	+	0.428634i	$0.858995\pi$
$824$	9.09853e10	−	5.25304e10i	0.197361	−	0.113947i
$825$			2.42436e8i			0.000523337i
$826$	−1.64257e11	−	3.09278e11i	−0.352860	−	0.664398i
$827$	4.00032e11			0.855209			0.427605	−	0.903966i	$-0.359358\pi$
$827$	4.00032e11			0.855209			0.427605	+	0.903966i	$0.359358\pi$
$828$	2.64276e10	+	4.57739e10i	0.0562258	+	0.0973860i
$829$	−7.79461e11	−	4.50022e11i	−1.65035	−	0.952830i	−0.976927	−	0.213574i	$-0.931490\pi$
$829$	−7.79461e11	−	4.50022e11i	−1.65035	−	0.952830i	−0.673424	−	0.739257i	$-0.735177\pi$
$830$	−9.05725e10	+	1.56876e11i	−0.190846	+	0.330556i
$831$	8.32476e9	−	4.80630e9i	0.0174569	−	0.0100788i
$832$			6.81729e10i			0.142272i
$833$	−7.52077e11	+	3.65925e11i	−1.56200	+	0.759997i
$834$	4.82601e9			0.00997526
$835$	−5.12056e11	−	8.86907e11i	−1.05335	−	1.82445i
$836$	−1.13427e9	−	6.54869e8i	−0.00232215	−	0.00134069i
$837$	−8.05171e10	+	1.39460e11i	−0.164054	+	0.284149i
$838$	3.82193e11	−	2.20659e11i	0.775008	−	0.447451i
$839$			9.73366e11i			1.96439i	0.187855	+	0.982197i	$0.439847\pi$
$839$			9.73366e11i			1.96439i	−0.187855	+	0.982197i	$0.560153\pi$
$840$	−1.00696e11	+	5.34795e10i	−0.202253	+	0.107416i
$841$	−4.98209e11			−0.995927
$842$	3.76425e10	+	6.51987e10i	0.0748910	+	0.129715i
$843$	−2.23520e11	−	1.29049e11i	−0.442594	−	0.255532i
$844$	2.09378e11	−	3.62653e11i	0.412630	−	0.714696i
$845$	−1.46345e11	+	8.44926e10i	−0.287047	+	0.165726i
$846$			4.69883e9i			0.00917292i
$847$	−4.36334e11	−	2.72941e11i	−0.847785	−	0.530317i
$848$	−3.28539e10			−0.0635337
$849$	1.66383e11	+	2.88184e11i	0.320242	+	0.554675i
$850$	−1.43635e11	−	8.29275e10i	−0.275159	−	0.158863i
$851$	3.21106e11	−	5.56172e11i	0.612252	−	1.06045i
$852$	4.46551e10	−	2.57816e10i	0.0847447	−	0.0489274i
$853$		−	2.69191e11i		−	0.508469i	−0.967143	−	0.254235i	$-0.918176\pi$
$853$		−	2.69191e11i		−	0.508469i	0.967143	−	0.254235i	$-0.0818236\pi$
$854$	−3.54543e11	−	1.25502e10i	−0.666557	−	0.0235950i
$855$	−3.05840e11			−0.572309
$856$	8.33376e10	+	1.44345e11i	0.155219	+	0.268848i
$857$	−5.28096e11	−	3.04897e11i	−0.979016	−	0.565235i	−0.0770431	−	0.997028i	$-0.524548\pi$
$857$	−5.28096e11	−	3.04897e11i	−0.979016	−	0.565235i	−0.901973	+	0.431793i	$0.857881\pi$
$858$	4.41211e8	−	7.64199e8i	0.000814136	−	0.00141012i
$859$	9.14679e11	−	5.28090e11i	1.67995	−	0.969918i	0.718259	−	0.695776i	$-0.244939\pi$
$859$	9.14679e11	−	5.28090e11i	1.67995	−	0.969918i	0.961689	−	0.274142i	$-0.0883939\pi$
$860$		−	1.39163e11i		−	0.254407i
$861$	−1.56413e10	+	4.41865e11i	−0.0284617	+	0.804040i
$862$	1.65882e11			0.300449
$863$	1.32259e10	+	2.29080e10i	0.0238442	+	0.0412994i	0.877701	−	0.479208i	$-0.159076\pi$
$863$	1.32259e10	+	2.29080e10i	0.0238442	+	0.0412994i	−0.853857	+	0.520508i	$0.825743\pi$
$864$	−1.64183e10	−	9.47912e9i	−0.0294628	−	0.0170103i
$865$	−4.51625e11	+	7.82238e11i	−0.806703	+	1.39725i
$866$	−3.65785e11	+	2.11186e11i	−0.650361	+	0.375486i
$867$		−	6.58142e11i		−	1.16478i
$868$	−2.56618e11	+	4.10240e11i	−0.452073	+	0.722701i
$869$	−8.23795e8			−0.00144457
$870$	−8.37269e9	−	1.45019e10i	−0.0146146	−	0.0253133i
$871$	−4.93088e11	−	2.84685e11i	−0.856746	−	0.494643i
$872$	−8.10159e10	+	1.40324e11i	−0.140121	+	0.242697i
$873$	1.31798e11	−	7.60933e10i	0.226908	−	0.131006i
$874$			4.26033e11i			0.730126i
$875$	−2.28675e11	−	4.30571e11i	−0.390110	−	0.734534i
$876$	−2.29859e11			−0.390341
$877$	−6.42769e10	−	1.11331e11i	−0.108657	−	0.188199i	0.806570	−	0.591139i	$-0.201322\pi$
$877$	−6.42769e10	−	1.11331e11i	−0.108657	−	0.188199i	−0.915226	+	0.402940i	$0.867988\pi$
$878$	1.47456e11	+	8.51340e10i	0.248134	+	0.143260i
$879$	−3.89566e10	+	6.74748e10i	−0.0652568	+	0.113028i
$880$	−5.10448e8	+	2.94707e8i	−0.000851179	+	0.000491429i
$881$		−	1.98233e11i		−	0.329057i	−0.986372	−	0.164529i	$-0.947390\pi$
$881$		−	1.98233e11i		−	0.329057i	0.986372	−	0.164529i	$-0.0526103\pi$
$882$	6.24064e10	+	1.28263e11i	0.103123	+	0.211946i
$883$	9.19955e11			1.51330			0.756648	−	0.653823i	$-0.226836\pi$
$883$	9.19955e11			1.51330			0.756648	+	0.653823i	$0.226836\pi$
$884$	3.01841e11	+	5.22803e11i	0.494275	+	0.856109i
$885$	−3.66098e11	−	2.11367e11i	−0.596794	−	0.344559i
$886$	−3.62689e11	+	6.28196e11i	−0.588572	+	1.01944i
$887$	−5.12659e11	+	2.95984e11i	−0.828198	+	0.478161i	−0.853235	−	0.521526i	$-0.825363\pi$
$887$	−5.12659e11	+	2.95984e11i	−0.828198	+	0.478161i	0.0250371	+	0.999687i	$0.492030\pi$
$888$			2.30350e11i			0.370457i
$889$	−3.69026e11	+	1.95989e11i	−0.590812	+	0.313779i
$890$	8.33355e11			1.32822
$891$	1.22697e8	+	2.12517e8i	0.000194680	+	0.000337196i
$892$	1.34666e11	+	7.77494e10i	0.212715	+	0.122811i
$893$	−1.89372e10	+	3.28002e10i	−0.0297790	+	0.0515787i
$894$	1.58253e11	−	9.13672e10i	0.247743	−	0.143034i
$895$			6.98745e11i			1.08900i
$896$	−4.82968e10	−	3.02112e10i	−0.0749352	−	0.0468744i
$897$	−2.87035e11			−0.443369
$898$	2.15014e11	+	3.72415e11i	0.330644	+	0.572693i
$899$	−6.15467e10	−	3.55340e10i	−0.0942250	−	0.0544008i
$900$	−1.41428e10	+	2.44961e10i	−0.0215559	+	0.0373359i
$901$	−2.51950e11	+	1.45463e11i	−0.382309	+	0.220726i
$902$			2.28568e9i			0.00345294i
$903$	−1.73989e11	−	6.15893e9i	−0.261680	−	0.00926305i
$904$	−2.44393e10			−0.0365944
$905$	−4.20680e11	−	7.28639e11i	−0.627130	−	1.08622i
$906$	−2.83309e10	−	1.63568e10i	−0.0420482	−	0.0242765i
$907$	3.14821e11	−	5.45286e11i	0.465195	−	0.805741i	−0.534016	−	0.845475i	$-0.679318\pi$
$907$	3.14821e11	−	5.45286e11i	0.465195	−	0.805741i	0.999210	+	0.0397339i	$0.0126510\pi$
$908$	−2.20536e11	+	1.27327e11i	−0.324442	+	0.187317i
$909$		−	1.89805e11i		−	0.278005i
$910$	2.19042e10	−	6.18790e11i	0.0319419	−	0.902355i
$911$	6.13193e11			0.890274			0.445137	−	0.895462i	$-0.353155\pi$
$911$	6.13193e11			0.890274			0.445137	+	0.895462i	$0.353155\pi$
$912$	−7.64054e10	−	1.32338e11i	−0.110445	−	0.191296i
$913$	1.01457e9	+	5.85760e8i	0.00146015	+	0.000843018i
$914$	2.34273e11	−	4.05773e11i	0.335690	−	0.581431i
$915$	−3.70881e11	+	2.14128e11i	−0.529115	+	0.305485i
$916$			4.73359e11i			0.672371i
$917$	4.58730e11	−	7.33343e11i	0.648754	−	1.03712i
$918$	−1.67878e11			−0.236387
$919$	−2.17693e11	−	3.77056e11i	−0.305199	−	0.528620i	0.672107	−	0.740454i	$-0.265390\pi$
$919$	−2.17693e11	−	3.77056e11i	−0.305199	−	0.528620i	−0.977306	+	0.211834i	$0.932056\pi$
$920$	1.66039e11	+	9.58627e10i	0.231771	+	0.133813i
$921$	−7.93927e10	+	1.37512e11i	−0.110342	+	0.191118i
$922$	−2.65934e11	+	1.53537e11i	−0.368002	+	0.212466i
$923$			2.80019e11i			0.385817i
$924$	3.45868e8	+	6.51233e8i	0.000474486	+	0.000893406i
$925$	3.43683e11			0.469451
$926$	−3.02001e11	−	5.23081e11i	−0.410738	−	0.711419i
$927$	−1.37406e11	−	7.93312e10i	−0.186074	−	0.107430i
$928$	4.18335e9	−	7.24578e9i	0.00564069	−	0.00976997i
$929$	−1.98362e11	+	1.14524e11i	−0.266315	+	0.153757i	−0.627212	−	0.778849i	$-0.715804\pi$
$929$	−1.98362e11	+	1.14524e11i	−0.266315	+	0.153757i	0.360897	+	0.932606i	$0.382471\pi$
$930$			5.84131e11i			0.780869i
$931$	−8.12950e10	+	1.14685e12i	−0.108209	+	1.52654i
$932$	−2.63956e11			−0.349839
$933$	−1.54739e11	−	2.68016e11i	−0.204208	−	0.353699i
$934$	4.28826e11	+	2.47583e11i	0.563500	+	0.325337i
$935$	−2.60968e9	+	4.52010e9i	−0.00341461	+	0.00591427i
$936$	8.91612e10	−	5.14773e10i	0.116164	−	0.0670675i
$937$		−	5.11176e11i		−	0.663151i	−0.943429	−	0.331575i	$-0.892420\pi$
$937$		−	5.11176e11i		−	0.663151i	0.943429	−	0.331575i	$-0.107580\pi$
$938$	4.20199e11	−	2.23166e11i	0.542804	−	0.288282i
$939$	7.47649e11			0.961690
$940$	8.52220e9	+	1.47609e10i	0.0109154	+	0.0189061i
$941$	−5.15843e11	−	2.97822e11i	−0.657899	−	0.379838i	0.133577	−	0.991038i	$-0.457354\pi$
$941$	−5.15843e11	−	2.97822e11i	−0.657899	−	0.379838i	−0.791476	+	0.611200i	$0.790687\pi$
$942$	1.27224e11	−	2.20359e11i	0.161572	−	0.279851i
$943$	6.43880e11	−	3.71744e11i	0.814250	−	0.470108i
$944$		−	2.11216e11i		−	0.265973i
$945$	1.45980e11	+	9.13151e10i	0.183048	+	0.114503i
$946$	−9.00009e8			−0.00112378
$947$	6.38604e11	+	1.10609e12i	0.794020	+	1.37528i	0.923460	+	0.383696i	$0.125349\pi$
$947$	6.38604e11	+	1.10609e12i	0.794020	+	1.37528i	−0.129439	+	0.991587i	$0.541318\pi$
$948$	−8.32375e10	−	4.80572e10i	−0.103059	−	0.0595011i
$949$	6.24134e11	−	1.08103e12i	0.769508	−	1.33283i
$950$	−1.97448e11	+	1.13997e11i	−0.242415	+	0.139958i
$951$			6.50618e11i			0.795434i
$952$	−5.04140e11	−	1.78458e10i	−0.613767	−	0.0217264i
$953$	−5.58803e11			−0.677466			−0.338733	−	0.940883i	$-0.609998\pi$
$953$	−5.58803e11			−0.677466			−0.338733	+	0.940883i	$0.609998\pi$
$954$	2.48080e10	+	4.29686e10i	0.0299501	+	0.0518750i
$955$	5.89967e11	+	3.40618e11i	0.709275	+	0.409500i
$956$	2.85166e11	−	4.93922e11i	0.341402	−	0.591326i
$957$	−9.37885e7	+	5.41488e7i	−0.000111815	+	6.45567e-5i
$958$			1.13941e12i			1.35275i
$959$	1.70389e10	−	4.81346e11i	0.0201450	−	0.569093i
$960$	−6.87686e10			−0.0809665
$961$	8.13091e11	+	1.40832e12i	0.953335	+	1.65123i
$962$	−1.08335e12	−	6.25470e11i	−1.26493	−	0.730308i
$963$	1.25856e11	−	2.17989e11i	0.146342	−	0.253472i
$964$	6.46973e11	−	3.73530e11i	0.749166	−	0.432531i
$965$			5.35743e11i			0.617799i
$966$	1.27201e11	−	2.03349e11i	0.146077	−	0.233525i
$967$	6.89336e11			0.788361			0.394181	−	0.919033i	$-0.371028\pi$
$967$	6.89336e11			0.788361			0.394181	+	0.919033i	$0.371028\pi$
$968$	−1.55211e11	−	2.68832e11i	−0.176775	−	0.306182i
$969$	−1.17187e12	−	6.76582e11i	−1.32919	−	0.767406i
$970$	2.76019e11	−	4.78079e11i	0.311783	−	0.540023i
$971$	1.15517e12	−	6.66940e11i	1.29948	−	0.750257i	0.319168	−	0.947698i	$-0.396596\pi$
$971$	1.15517e12	−	6.66940e11i	1.29948	−	0.750257i	0.980315	+	0.197441i	$0.0632632\pi$
$972$			2.86307e10i			0.0320750i
$973$	−1.02724e10	−	1.93418e10i	−0.0114609	−	0.0215797i
$974$	5.12130e11			0.569042
$975$	−7.68040e10	−	1.33028e11i	−0.0849895	−	0.147206i
$976$	−1.85308e11	−	1.06988e11i	−0.204218	−	0.117905i
$977$	−5.40202e11	+	9.35657e11i	−0.592895	+	1.02692i	0.400945	+	0.916102i	$0.368682\pi$
$977$	−5.40202e11	+	9.35657e11i	−0.592895	+	1.02692i	−0.993840	+	0.110822i	$0.964652\pi$
$978$	4.98565e11	−	2.87847e11i	0.544962	−	0.314634i
$979$		−	5.38957e9i		−	0.00586710i
$980$	4.28672e11	+	2.89738e11i	0.464751	+	0.314124i
$981$	2.44700e11			0.264215
$982$	5.78547e11	+	1.00207e12i	0.622146	+	1.07759i
$983$	4.68508e11	+	2.70493e11i	0.501768	+	0.289696i	0.729443	−	0.684041i	$-0.239779\pi$
$983$	4.68508e11	+	2.70493e11i	0.501768	+	0.289696i	−0.227675	+	0.973737i	$0.573113\pi$
$984$	−1.33338e11	+	2.30949e11i	−0.142224	+	0.246340i
$985$	2.09368e11	−	1.20879e11i	0.222416	−	0.128412i
$986$		−	7.40884e10i		−	0.0783868i
$987$	1.88320e10	−	1.00016e10i	0.0198440	−	0.0105391i
$988$	8.29853e11			0.870911
$989$	1.46378e11	+	2.53534e11i	0.153000	+	0.265003i
$990$	7.70878e8	+	4.45066e8i	0.000802499	+	0.000463323i
$991$	−4.45266e11	+	7.71224e11i	−0.461663	+	0.799624i	−0.999044	−	0.0437158i	$-0.986080\pi$
$991$	−4.45266e11	+	7.71224e11i	−0.461663	+	0.799624i	0.537381	+	0.843340i	$0.319414\pi$
$992$	−2.52755e11	+	1.45928e11i	−0.261008	+	0.150693i
$993$		−	8.53741e11i		−	0.878070i
$994$	−1.98378e11	−	1.24092e11i	−0.203212	−	0.127116i
$995$	3.02405e11			0.308529
$996$	6.83423e10	+	1.18372e11i	0.0694468	+	0.120285i
$997$	8.12579e11	+	4.69143e11i	0.822403	+	0.474815i	0.851245	−	0.524769i	$-0.175848\pi$
$997$	8.12579e11	+	4.69143e11i	0.822403	+	0.474815i	−0.0288411	+	0.999584i	$0.509182\pi$
$998$	2.67218e11	−	4.62836e11i	0.269367	−	0.466557i
$999$	3.01268e11	−	1.73937e11i	0.302476	−	0.174635i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	42.9.g.b.31.6	yes	12
3.2	odd	2		126.9.n.c.73.1		12
7.3	odd	6		294.9.c.b.97.1		12
7.4	even	3		294.9.c.b.97.6		12
7.5	odd	6	inner	42.9.g.b.19.6	✓	12
21.5	even	6		126.9.n.c.19.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.9.g.b.19.6	✓	12	7.5	odd	6	inner
42.9.g.b.31.6	yes	12	1.1	even	1	trivial
126.9.n.c.19.1		12	21.5	even	6
126.9.n.c.73.1		12	3.2	odd	2
294.9.c.b.97.1		12	7.3	odd	6
294.9.c.b.97.6		12	7.4	even	3

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:	\( N \)	\(=\)	\( 42 = 2 \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	42.g (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(5.65685 + 9.79796i) q^{2} +(-40.5000 - 23.3827i) q^{3} +(-64.0000 + 110.851i) q^{4} +(607.249 - 350.595i) q^{5} -529.090i q^{6} +(-2120.49 + 1126.19i) q^{7} -1448.15 q^{8} +(1093.50 + 1894.00i) q^{9} +O(q^{10})\)	\(q+(5.65685 + 9.79796i) q^{2} +(-40.5000 - 23.3827i) q^{3} +(-64.0000 + 110.851i) q^{4} +(607.249 - 350.595i) q^{5} -529.090i q^{6} +(-2120.49 + 1126.19i) q^{7} -1448.15 q^{8} +(1093.50 + 1894.00i) q^{9} +(6870.24 + 3966.53i) q^{10} +(25.6528 - 44.4320i) q^{11} +(5184.00 - 2992.98i) q^{12} +32507.4i q^{13} +(-23029.7 - 14405.8i) q^{14} -32791.4 q^{15} +(-8192.00 - 14189.0i) q^{16} +(-125645. - 72541.4i) q^{17} +(-12371.5 + 21428.1i) q^{18} +(-172719. + 99719.4i) q^{19} +89752.4i q^{20} +(112213. + 3972.17i) q^{21} +580.457 q^{22} +(-94405.8 - 163516. i) q^{23} +(58650.3 + 33861.7i) q^{24} +(50521.7 - 87506.1i) q^{25} +(-318506. + 183889. i) q^{26} -102276. i q^{27} +(10872.1 - 307136. i) q^{28} +45136.7 q^{29} +(-185496. - 321289. i) q^{30} +(-1.36356e6 - 787254. i) q^{31} +(92681.9 - 160530. i) q^{32} +(-2077.88 + 1199.66i) q^{33} -1.64142e6i q^{34} +(-892831. + 1.42731e6i) q^{35} -279936. q^{36} +(1.70067e6 + 2.94564e6i) q^{37} +(-1.95409e6 - 1.12820e6i) q^{38} +(760109. - 1.31655e6i) q^{39} +(-879390. + 507716. i) q^{40} +3.93773e6i q^{41} +(595856. + 1.12193e6i) q^{42} -1.55052e6 q^{43} +(3283.56 + 5687.29i) q^{44} +(1.32805e6 + 766752. i) q^{45} +(1.06808e6 - 1.84997e6i) q^{46} +(164462. - 94952.3i) q^{47} +766204. i q^{48} +(3.22819e6 - 4.77616e6i) q^{49} +1.14317e6 q^{50} +(3.39243e6 + 5.87585e6i) q^{51} +(-3.60348e6 - 2.08047e6i) q^{52} +(1.00262e6 - 1.73659e6i) q^{53} +(1.00209e6 - 578560. i) q^{54} -35975.0i q^{55} +(3.07080e6 - 1.63090e6i) q^{56} +9.32683e6 q^{57} +(255331. + 442247. i) q^{58} +(1.11644e7 + 6.44579e6i) q^{59} +(2.09865e6 - 3.63497e6i) q^{60} +(1.13103e7 - 6.53000e6i) q^{61} -1.78135e7i q^{62} +(-4.45176e6 - 2.78472e6i) q^{63} +2.09715e6 q^{64} +(1.13969e7 + 1.97401e7i) q^{65} +(-23508.5 - 13572.6i) q^{66} +(-8.75755e6 + 1.51685e7i) q^{67} +(1.60826e7 - 9.28530e6i) q^{68} +8.82984e6i q^{69} +(-1.90354e7 - 673822. i) q^{70} +8.61402e6 q^{71} +(-1.58356e6 - 2.74280e6i) q^{72} +(-3.32550e7 - 1.91998e7i) q^{73} +(-1.92409e7 + 3.33262e7i) q^{74} +(-4.09226e6 + 2.36266e6i) q^{75} -2.55282e7i q^{76} +(-4357.82 + 123108. i) q^{77} +1.71993e7 q^{78} +(-8.02831e6 - 1.39054e7i) q^{79} +(-9.94917e6 - 5.74415e6i) q^{80} +(-2.39148e6 + 4.14217e6i) q^{81} +(-3.85817e7 + 2.22751e7i) q^{82} +2.28342e7i q^{83} +(-7.62198e6 + 1.21848e7i) q^{84} -1.01731e8 q^{85} +(-8.77106e6 - 1.51919e7i) q^{86} +(-1.82803e6 - 1.05542e6i) q^{87} +(-37149.2 + 64344.4i) q^{88} +(9.09745e7 - 5.25241e7i) q^{89} +1.73496e7i q^{90} +(-3.66095e7 - 6.89317e7i) q^{91} +2.41679e7 q^{92} +(3.68162e7 + 6.37675e7i) q^{93} +(1.86068e6 + 1.07426e6i) q^{94} +(-6.99223e7 + 1.21109e8i) q^{95} +(-7.50723e6 + 4.33430e6i) q^{96} -6.95869e7i q^{97} +(6.50580e7 + 4.61168e6i) q^{98} +112205. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 486 q^{3} - 768 q^{4} - 1122 q^{5} - 4434 q^{7} + 13122 q^{9}+O(q^{10}) \) 12 * q - 486 * q^3 - 768 * q^4 - 1122 * q^5 - 4434 * q^7 + 13122 * q^9	\( 12 q - 486 q^{3} - 768 q^{4} - 1122 q^{5} - 4434 q^{7} + 13122 q^{9} + 4224 q^{10} + 9606 q^{11} + 62208 q^{12} - 19968 q^{14} + 60588 q^{15} - 98304 q^{16} - 227388 q^{17} + 315408 q^{19} + 155358 q^{21} + 557568 q^{22} - 663480 q^{23} + 601008 q^{25} - 585984 q^{26} + 398592 q^{28} + 5944884 q^{29} - 114048 q^{30} - 3214278 q^{31} - 778086 q^{33} - 1019784 q^{35} - 3359232 q^{36} + 1607760 q^{37} - 986880 q^{38} + 903636 q^{39} - 540672 q^{40} + 2788992 q^{42} + 12627648 q^{43} + 1229568 q^{44} - 2453814 q^{45} - 4608768 q^{46} - 7830240 q^{47} + 16477242 q^{49} - 16565760 q^{50} + 6139476 q^{51} - 4283904 q^{52} - 33200358 q^{53} - 8110080 q^{56} - 17032032 q^{57} + 5576064 q^{58} - 29657382 q^{59} - 3877632 q^{60} + 58344096 q^{61} - 2886840 q^{63} + 25165824 q^{64} + 30909216 q^{65} - 22581504 q^{66} + 7977444 q^{67} + 29105664 q^{68} - 59774976 q^{70} + 117213264 q^{71} - 170286636 q^{73} - 80311296 q^{74} - 48681648 q^{75} - 3340686 q^{77} + 31643136 q^{78} + 35420490 q^{79} + 18382848 q^{80} - 28697814 q^{81} + 154232832 q^{82} - 26085888 q^{84} + 416634600 q^{85} - 71958528 q^{86} - 240767802 q^{87} - 35684352 q^{88} + 78064092 q^{89} + 335513292 q^{91} + 169850880 q^{92} + 86785506 q^{93} - 18456576 q^{94} - 250727796 q^{95} - 150533376 q^{98} + 42016644 q^{99}+O(q^{100}) \) 12 * q - 486 * q^3 - 768 * q^4 - 1122 * q^5 - 4434 * q^7 + 13122 * q^9 + 4224 * q^10 + 9606 * q^11 + 62208 * q^12 - 19968 * q^14 + 60588 * q^15 - 98304 * q^16 - 227388 * q^17 + 315408 * q^19 + 155358 * q^21 + 557568 * q^22 - 663480 * q^23 + 601008 * q^25 - 585984 * q^26 + 398592 * q^28 + 5944884 * q^29 - 114048 * q^30 - 3214278 * q^31 - 778086 * q^33 - 1019784 * q^35 - 3359232 * q^36 + 1607760 * q^37 - 986880 * q^38 + 903636 * q^39 - 540672 * q^40 + 2788992 * q^42 + 12627648 * q^43 + 1229568 * q^44 - 2453814 * q^45 - 4608768 * q^46 - 7830240 * q^47 + 16477242 * q^49 - 16565760 * q^50 + 6139476 * q^51 - 4283904 * q^52 - 33200358 * q^53 - 8110080 * q^56 - 17032032 * q^57 + 5576064 * q^58 - 29657382 * q^59 - 3877632 * q^60 + 58344096 * q^61 - 2886840 * q^63 + 25165824 * q^64 + 30909216 * q^65 - 22581504 * q^66 + 7977444 * q^67 + 29105664 * q^68 - 59774976 * q^70 + 117213264 * q^71 - 170286636 * q^73 - 80311296 * q^74 - 48681648 * q^75 - 3340686 * q^77 + 31643136 * q^78 + 35420490 * q^79 + 18382848 * q^80 - 28697814 * q^81 + 154232832 * q^82 - 26085888 * q^84 + 416634600 * q^85 - 71958528 * q^86 - 240767802 * q^87 - 35684352 * q^88 + 78064092 * q^89 + 335513292 * q^91 + 169850880 * q^92 + 86785506 * q^93 - 18456576 * q^94 - 250727796 * q^95 - 150533376 * q^98 + 42016644 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more