LMFDB - Embedded newform 42.12.f.a.5.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [42,12,Mod(5,42)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("42.5"); S:= CuspForms(chi, 12); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(42, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 5])) N = Newforms(chi, 12, names="a")

Level:	$ N $	$=$	$ 42 = 2 \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	42.f (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$32.2704135835$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$30$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.11
Character	$\chi$	$=$	42.5
Dual form			42.12.f.a.17.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-27.7128 - 16.0000i) q^{2} +(213.694 - 362.604i) q^{3} +(512.000 + 886.810i) q^{4} +(-1022.28 + 1770.64i) q^{5} +(-11723.7 + 6629.68i) q^{6} +(-41388.4 + 16258.2i) q^{7} -32768.0i q^{8} +(-85816.7 - 154973. i) q^{9} +(56660.5 - 32712.9i) q^{10} +(451873. - 260889. i) q^{11} +(430972. + 3852.72i) q^{12} +2.27340e6i q^{13} +(1.40712e6 + 211652. i) q^{14} +(423586. + 749058. i) q^{15} +(-524288. + 908093. i) q^{16} +(-2.12149e6 - 3.67453e6i) q^{17} +(-101344. + 5.66780e6i) q^{18} +(5.19355e6 + 2.99850e6i) q^{19} -2.09363e6 q^{20} +(-2.94915e6 + 1.84819e7i) q^{21} -1.66969e7 q^{22} +(-57216.3 - 33033.8i) q^{23} +(-1.18818e7 - 7.00233e6i) q^{24} +(2.23240e7 + 3.86662e7i) q^{25} +(3.63744e7 - 6.30023e7i) q^{26} +(-7.45323e7 - 1.99929e6i) q^{27} +(-3.56088e7 - 2.83794e7i) q^{28} +9.38324e7i q^{29} +(246160. - 2.75359e7i) q^{30} +(1.62569e8 - 9.38594e7i) q^{31} +(2.90590e7 - 1.67772e7i) q^{32} +(1.96315e6 - 2.19602e8i) q^{33} +1.35775e8i q^{34} +(1.35230e7 - 8.99043e7i) q^{35} +(9.34933e7 - 1.55449e8i) q^{36} +(-6.91103e7 + 1.19703e8i) q^{37} +(-9.59519e7 - 1.66194e8i) q^{38} +(8.24344e8 + 4.85812e8i) q^{39} +(5.80203e7 + 3.34980e7i) q^{40} +1.24884e9 q^{41} +(3.77439e8 - 4.64999e8i) q^{42} +6.01176e8 q^{43} +(4.62718e8 + 2.67150e8i) q^{44} +(3.62129e8 + 6.47510e6i) q^{45} +(1.05708e6 + 1.83092e6i) q^{46} +(5.77239e8 - 9.99807e8i) q^{47} +(2.17241e8 + 3.84163e8i) q^{48} +(1.44867e9 - 1.34580e9i) q^{49} -1.42873e9i q^{50} +(-1.78575e9 - 1.59639e7i) q^{51} +(-2.01607e9 + 1.16398e9i) q^{52} +(3.13675e9 - 1.81100e9i) q^{53} +(2.03351e9 + 1.24792e9i) q^{54} +1.06681e9i q^{55} +(5.32750e8 + 1.35621e9i) q^{56} +(2.19710e9 - 1.24244e9i) q^{57} +(1.50132e9 - 2.60036e9i) q^{58} +(-2.40795e9 - 4.17070e9i) q^{59} +(-4.47396e8 + 7.59158e8i) q^{60} +(-1.82926e9 - 1.05612e9i) q^{61} -6.00700e9 q^{62} +(6.07139e9 + 5.01884e9i) q^{63} -1.07374e9 q^{64} +(-4.02537e9 - 2.32405e9i) q^{65} +(-3.56803e9 + 6.05437e9i) q^{66} +(2.09762e8 + 3.63319e8i) q^{67} +(2.17240e9 - 3.76272e9i) q^{68} +(-2.42050e7 + 1.36877e7i) q^{69} +(-1.81323e9 + 2.27513e9i) q^{70} +2.77625e10i q^{71} +(-5.07815e9 + 2.81204e9i) q^{72} +(-3.55718e9 + 2.05374e9i) q^{73} +(3.83048e9 - 2.21153e9i) q^{74} +(1.87910e10 + 1.67984e8i) q^{75} +6.14092e9i q^{76} +(-1.44607e10 + 1.81444e10i) q^{77} +(-1.50719e10 - 2.66527e10i) q^{78} +(2.39071e10 - 4.14083e10i) q^{79} +(-1.07194e9 - 1.85665e9i) q^{80} +(-1.66521e10 + 2.65985e10i) q^{81} +(-3.46090e10 - 1.99815e10i) q^{82} +1.87924e10 q^{83} +(-1.78999e10 + 6.84739e9i) q^{84} +8.67502e9 q^{85} +(-1.66603e10 - 9.61881e9i) q^{86} +(3.40240e10 + 2.00514e10i) q^{87} +(-8.54881e9 - 1.48070e10i) q^{88} +(-5.08228e10 + 8.80276e10i) q^{89} +(-9.93202e9 - 5.97351e9i) q^{90} +(-3.69614e10 - 9.40922e10i) q^{91} -6.76533e7i q^{92} +(7.06277e8 - 7.90055e10i) q^{93} +(-3.19938e10 + 1.84716e10i) q^{94} +(-1.06185e10 + 6.13060e9i) q^{95} +(1.26246e8 - 1.41221e10i) q^{96} -9.98947e7i q^{97} +(-6.16795e10 + 1.41173e10i) q^{98} +(-7.92089e10 - 4.76394e10i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 30720 q^{4} - 95298 q^{7} - 91434 q^{9} + 245184 q^{10} - 8480820 q^{15} - 31457280 q^{16} + 12170496 q^{18} + 1649724 q^{19} + 43254216 q^{21} + 20705664 q^{22} + 4521984 q^{24} - 336132444 q^{25}+ \cdots + 288758042496 q^{99}+O(q^{100}) $ 60 * q + 30720 * q^4 - 95298 * q^7 - 91434 * q^9 + 245184 * q^10 - 8480820 * q^15 - 31457280 * q^16 + 12170496 * q^18 + 1649724 * q^19 + 43254216 * q^21 + 20705664 * q^22 + 4521984 * q^24 - 336132444 * q^25 + 28121088 * q^28 - 77109120 * q^30 - 275992974 * q^31 + 1056712914 * q^33 - 187256832 * q^36 + 555437556 * q^37 - 563926680 * q^39 + 251068416 * q^40 + 1167043776 * q^42 + 2546594304 * q^43 + 544480776 * q^45 - 452472192 * q^46 - 1309143414 * q^49 + 2007979044 * q^51 + 3219419136 * q^52 - 9840998592 * q^54 + 17053196256 * q^57 + 12235419456 * q^58 - 4342179840 * q^60 - 3056592000 * q^61 - 42499692960 * q^63 - 64424509440 * q^64 + 48796070400 * q^66 + 27979853436 * q^67 - 4966503360 * q^70 - 12462587904 * q^72 - 105678747168 * q^73 + 173211633504 * q^75 - 16600538880 * q^78 - 27787555926 * q^79 - 71399556486 * q^81 + 31231064832 * q^82 - 25272410112 * q^84 + 12868048152 * q^85 + 137017459998 * q^87 + 10601299968 * q^88 + 333571182180 * q^91 - 14607989424 * q^93 - 430917051648 * q^94 + 4630511616 * q^96 + 288758042496 * q^99

Character values

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

$n$	$29$	$31$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−27.7128	−	16.0000i	−0.612372	−	0.353553i
$2$	−27.7128	−	16.0000i	−0.612372	−	0.353553i
$3$	213.694	−	362.604i	0.507722	−	0.861521i
$3$	213.694	−	362.604i	0.507722	−	0.861521i
$4$	512.000	+	886.810i	0.250000	+	0.433013i
$5$	−1022.28	+	1770.64i	−0.146297	+	0.253393i	−0.929856	−	0.367924i	$-0.880069\pi$
$5$	−1022.28	+	1770.64i	−0.146297	+	0.253393i	0.783559	+	0.621317i	$0.213402\pi$
$6$	−11723.7	+	6629.68i	−0.615508	+	0.348065i
$7$	−41388.4	+	16258.2i	−0.930763	+	0.365624i
$7$	−41388.4	+	16258.2i	−0.930763	+	0.365624i
$8$		−	32768.0i		−	0.353553i
$9$	−85816.7	−	154973.i	−0.484438	−	0.874826i
$10$	56660.5	−	32712.9i	0.179176	−	0.103447i
$11$	451873.	−	260889.i	0.845973	−	0.488423i	−0.0133168	−	0.999911i	$-0.504239\pi$
$11$	451873.	−	260889.i	0.845973	−	0.488423i	0.859290	+	0.511488i	$0.170906\pi$
$12$	430972.	+	3852.72i	0.499980	+	0.00446962i
$13$			2.27340e6i			1.69819i	0.528237	+	0.849097i	$0.322853\pi$
$13$			2.27340e6i			1.69819i	−0.528237	+	0.849097i	$0.677147\pi$
$14$	1.40712e6	+	211652.i	0.699241	+	0.105177i
$15$	423586.	+	749058.i	0.144026	+	0.254691i
$16$	−524288.	+	908093.i	−0.125000	+	0.216506i
$17$	−2.12149e6	−	3.67453e6i	−0.362386	−	0.627671i	0.625967	−	0.779850i	$-0.284705\pi$
$17$	−2.12149e6	−	3.67453e6i	−0.362386	−	0.627671i	−0.988353	+	0.152178i	$0.951371\pi$
$18$	−101344.	+	5.66780e6i	−0.0126415	+	0.706994i
$19$	5.19355e6	+	2.99850e6i	0.481193	+	0.277817i	0.720914	−	0.693025i	$-0.243722\pi$
$19$	5.19355e6	+	2.99850e6i	0.481193	+	0.277817i	−0.239720	+	0.970842i	$0.577056\pi$
$20$	−2.09363e6			−0.146297
$21$	−2.94915e6	+	1.84819e7i	−0.157576	+	0.987507i
$22$	−1.66969e7			−0.690734
$23$	−57216.3	−	33033.8i	−0.00185360	−	0.00107018i	0.499073	−	0.866560i	$-0.333674\pi$
$23$	−57216.3	−	33033.8i	−0.00185360	−	0.00107018i	−0.500927	+	0.865490i	$0.667007\pi$
$24$	−1.18818e7	−	7.00233e6i	−0.304594	−	0.179507i
$25$	2.23240e7	+	3.86662e7i	0.457195	+	0.791884i
$26$	3.63744e7	−	6.30023e7i	0.600402	−	1.03993i
$27$	−7.45323e7	−	1.99929e6i	−0.999640	−	0.0268148i
$28$	−3.56088e7	−	2.83794e7i	−0.391010	−	0.311626i
$29$			9.38324e7i			0.849501i	0.905311	+	0.424750i	$0.139638\pi$
$29$			9.38324e7i			0.849501i	−0.905311	+	0.424750i	$0.860362\pi$
$30$	246160.	−	2.75359e7i	0.00184948	−	0.206886i
$31$	1.62569e8	−	9.38594e7i	1.01988	−	0.588828i	0.105811	−	0.994386i	$-0.466256\pi$
$31$	1.62569e8	−	9.38594e7i	1.01988	−	0.588828i	0.914069	+	0.405558i	$0.132923\pi$
$32$	2.90590e7	−	1.67772e7i	0.153093	−	0.0883883i
$33$	1.96315e6	−	2.19602e8i	0.00873225	−	0.976807i
$34$			1.35775e8i			0.512492i
$35$	1.35230e7	−	8.99043e7i	0.0435210	−	0.289339i
$36$	9.34933e7	−	1.55449e8i	0.257701	−	0.428474i
$37$	−6.91103e7	+	1.19703e8i	−0.163845	+	0.283788i	−0.936245	−	0.351349i	$-0.885723\pi$
$37$	−6.91103e7	+	1.19703e8i	−0.163845	+	0.283788i	0.772400	+	0.635137i	$0.219056\pi$
$38$	−9.59519e7	−	1.66194e8i	−0.196446	−	0.340255i
$39$	8.24344e8	+	4.85812e8i	1.46303	+	0.862210i
$40$	5.80203e7	+	3.34980e7i	0.0895881	+	0.0517237i
$41$	1.24884e9			1.68344			0.841719	−	0.539916i	$-0.181544\pi$
$41$	1.24884e9			1.68344			0.841719	+	0.539916i	$0.181544\pi$
$42$	3.77439e8	−	4.64999e8i	0.445632	−	0.549010i
$43$	6.01176e8			0.623627			0.311813	−	0.950143i	$-0.399064\pi$
$43$	6.01176e8			0.623627			0.311813	+	0.950143i	$0.399064\pi$
$44$	4.62718e8	+	2.67150e8i	0.422987	+	0.244211i
$45$	3.62129e8	+	6.47510e6i	0.292547	+	0.00523091i
$46$	1.05708e6	+	1.83092e6i	0.000756730	+	0.00131069i
$47$	5.77239e8	−	9.99807e8i	0.367128	−	0.635884i	−0.621987	−	0.783027i	$-0.713674\pi$
$47$	5.77239e8	−	9.99807e8i	0.367128	−	0.635884i	0.989115	+	0.147143i	$0.0470078\pi$
$48$	2.17241e8	+	3.84163e8i	0.123060	+	0.217615i
$49$	1.44867e9	−	1.34580e9i	0.732639	−	0.680618i
$50$		−	1.42873e9i		−	0.646571i
$51$	−1.78575e9	−	1.59639e7i	−0.724744	−	0.00647891i
$52$	−2.01607e9	+	1.16398e9i	−0.735339	+	0.424548i
$53$	3.13675e9	−	1.81100e9i	1.03030	−	0.594842i	0.113227	−	0.993569i	$-0.463881\pi$
$53$	3.13675e9	−	1.81100e9i	1.03030	−	0.594842i	0.917069	+	0.398727i	$0.130548\pi$
$54$	2.03351e9	+	1.24792e9i	0.602672	+	0.369847i
$55$			1.06681e9i			0.285819i
$56$	5.32750e8	+	1.35621e9i	0.129267	+	0.329074i
$57$	2.19710e9	−	1.24244e9i	0.483657	−	0.273504i
$58$	1.50132e9	−	2.60036e9i	0.300344	−	0.520211i
$59$	−2.40795e9	−	4.17070e9i	−0.438492	−	0.759491i	0.559081	−	0.829113i	$-0.311154\pi$
$59$	−2.40795e9	−	4.17070e9i	−0.438492	−	0.759491i	−0.997573	+	0.0696222i	$0.977821\pi$
$60$	−4.47396e8	+	7.59158e8i	−0.0742780	+	0.126038i
$61$	−1.82926e9	−	1.05612e9i	−0.277307	−	0.160104i	0.354896	−	0.934906i	$-0.384516\pi$
$61$	−1.82926e9	−	1.05612e9i	−0.277307	−	0.160104i	−0.632204	+	0.774802i	$0.717849\pi$
$62$	−6.00700e9			−0.832729
$63$	6.07139e9	+	5.01884e9i	0.770753	+	0.637134i
$64$	−1.07374e9			−0.125000
$65$	−4.02537e9	−	2.32405e9i	−0.430311	−	0.248440i
$66$	−3.56803e9	+	6.05437e9i	−0.350701	+	0.595082i
$67$	2.09762e8	+	3.63319e8i	0.0189808	+	0.0328758i	0.875360	−	0.483472i	$-0.160625\pi$
$67$	2.09762e8	+	3.63319e8i	0.0189808	+	0.0328758i	−0.856379	+	0.516348i	$0.827291\pi$
$68$	2.17240e9	−	3.76272e9i	0.181193	−	0.313836i
$69$	−2.42050e7	+	1.36877e7i	−0.00186309	+	0.00105357i
$70$	−1.81323e9	+	2.27513e9i	−0.128948	+	0.161796i
$71$			2.77625e10i			1.82616i	0.407784	+	0.913079i	$0.366302\pi$
$71$			2.77625e10i			1.82616i	−0.407784	+	0.913079i	$0.633698\pi$
$72$	−5.07815e9	+	2.81204e9i	−0.309298	+	0.171275i
$73$	−3.55718e9	+	2.05374e9i	−0.200831	+	0.115950i	−0.597043	−	0.802209i	$-0.703658\pi$
$73$	−3.55718e9	+	2.05374e9i	−0.200831	+	0.115950i	0.396212	+	0.918159i	$0.370325\pi$
$74$	3.83048e9	−	2.21153e9i	0.200668	−	0.115856i
$75$	1.87910e10	+	1.67984e8i	0.914353	+	0.00817394i
$76$			6.14092e9i			0.277817i
$77$	−1.44607e10	+	1.81444e10i	−0.608822	+	0.763914i
$78$	−1.50719e10	−	2.66527e10i	−0.591082	−	1.04525i
$79$	2.39071e10	−	4.14083e10i	0.874133	−	1.51404i	0.0164490	−	0.999865i	$-0.494764\pi$
$79$	2.39071e10	−	4.14083e10i	0.874133	−	1.51404i	0.857684	−	0.514178i	$-0.171903\pi$
$80$	−1.07194e9	−	1.85665e9i	−0.0365742	−	0.0633483i
$81$	−1.66521e10	+	2.65985e10i	−0.530641	+	0.847597i
$82$	−3.46090e10	−	1.99815e10i	−1.03089	−	0.595185i
$83$	1.87924e10			0.523664			0.261832	−	0.965113i	$-0.415673\pi$
$83$	1.87924e10			0.523664			0.261832	+	0.965113i	$0.415673\pi$
$84$	−1.78999e10	+	6.84739e9i	−0.466997	+	0.178644i
$85$	8.67502e9			0.212064
$86$	−1.66603e10	−	9.61881e9i	−0.381892	−	0.220485i
$87$	3.40240e10	+	2.00514e10i	0.731863	+	0.431310i
$88$	−8.54881e9	−	1.48070e10i	−0.172684	−	0.299097i
$89$	−5.08228e10	+	8.80276e10i	−0.964747	+	1.67099i	−0.254452	+	0.967085i	$0.581895\pi$
$89$	−5.08228e10	+	8.80276e10i	−0.964747	+	1.67099i	−0.710294	+	0.703905i	$0.751438\pi$
$90$	−9.93202e9	−	5.97351e9i	−0.177298	−	0.106634i
$91$	−3.69614e10	−	9.40922e10i	−0.620899	−	1.58062i
$92$		−	6.76533e7i		−	0.00107018i
$93$	7.06277e8	−	7.90055e10i	0.0105273	−	1.17761i
$94$	−3.19938e10	+	1.84716e10i	−0.449638	+	0.259599i
$95$	−1.06185e10	+	6.13060e9i	−0.140794	+	0.0812874i
$96$	1.26246e8	−	1.41221e10i	0.00158025	−	0.176770i
$97$		−	9.98947e7i		−	0.00118113i	−1.00000		0.000590565i	$-0.999812\pi$
$97$		−	9.98947e7i		−	0.00118113i	1.00000		0.000590565i	$-0.000187983\pi$
$98$	−6.16795e10	+	1.41173e10i	−0.689282	+	0.157764i
$99$	−7.92089e10	−	4.76394e10i	−0.837106	−	0.503469i
$100$	−2.28597e10	+	3.95942e10i	−0.228597	+	0.395942i
$101$	7.24624e10	+	1.25509e11i	0.686034	+	1.18824i	0.973111	+	0.230337i	$0.0739830\pi$
$101$	7.24624e10	+	1.25509e11i	0.686034	+	1.18824i	−0.287077	+	0.957907i	$0.592684\pi$
$102$	4.92327e10	+	2.90144e10i	0.441522	+	0.260203i
$103$	1.21920e11	+	7.03908e10i	1.03627	+	0.598289i	0.918774	−	0.394784i	$-0.129181\pi$
$103$	1.21920e11	+	7.03908e10i	1.03627	+	0.598289i	0.117494	+	0.993074i	$0.462514\pi$
$104$	7.44947e10			0.600402
$105$	−2.97099e10	−	2.41155e10i	−0.227175	−	0.184398i
$106$	−1.15904e11			−0.841233
$107$	−6.62819e10	−	3.82679e10i	−0.456861	−	0.263769i	0.253862	−	0.967240i	$-0.418299\pi$
$107$	−6.62819e10	−	3.82679e10i	−0.456861	−	0.263769i	−0.710724	+	0.703471i	$0.751632\pi$
$108$	−3.63875e10	−	6.71196e10i	−0.238299	−	0.439561i
$109$	1.22140e11	+	2.11553e11i	0.760350	+	1.31696i	0.942670	+	0.333725i	$0.108306\pi$
$109$	1.22140e11	+	2.11553e11i	0.760350	+	1.31696i	−0.182320	+	0.983239i	$0.558361\pi$
$110$	1.70689e10	−	2.95642e10i	0.101052	−	0.175027i
$111$	2.86362e10	+	5.06394e10i	0.161302	+	0.285241i
$112$	6.93543e9	−	4.61085e10i	0.0371855	−	0.247219i
$113$		−	1.33606e9i		−	0.00682172i	−0.999994	−	0.00341086i	$-0.998914\pi$
$113$		−	1.33606e9i		−	0.00682172i	0.999994	−	0.00341086i	$-0.00108571\pi$
$114$	−8.07668e10	−	7.22022e8i	−0.392877	−	0.00351216i
$115$	1.16982e8	−	6.75396e7i	0.000542352	−	0.000313127i
$116$	−8.32115e10	+	4.80422e10i	−0.367845	+	0.212375i
$117$	3.52315e11	−	1.95095e11i	1.48562	−	0.822669i
$118$			1.54109e11i			0.620122i
$119$	1.47546e11	+	1.17591e11i	0.566787	+	0.451716i
$120$	2.45451e10	−	1.38801e10i	0.0900468	−	0.0509208i
$121$	−6.52965e9	+	1.13097e10i	−0.0228860	+	0.0396398i
$122$	3.37960e10	+	5.85363e10i	0.113210	+	0.196086i
$123$	2.66871e11	−	4.52836e11i	0.854718	−	1.45032i
$124$	1.66471e11	+	9.61121e10i	0.509940	+	0.294414i
$125$	−1.91117e11			−0.560138
$126$	−8.79539e10	−	2.36229e11i	−0.246727	−	0.662666i
$127$	2.09224e11			0.561941			0.280970	−	0.959716i	$-0.409344\pi$
$127$	2.09224e11			0.561941			0.280970	+	0.959716i	$0.409344\pi$
$128$	2.97564e10	+	1.71799e10i	0.0765466	+	0.0441942i
$129$	1.28468e11	−	2.17989e11i	0.316629	−	0.537268i
$130$	7.43695e10	+	1.28812e11i	0.175674	+	0.304276i
$131$	1.68544e11	−	2.91927e11i	0.381699	−	0.661123i	−0.609606	−	0.792705i	$-0.708672\pi$
$131$	1.68544e11	−	2.91927e11i	0.381699	−	0.661123i	0.991305	+	0.131582i	$0.0420056\pi$
$132$	1.95750e11	−	1.10695e11i	0.425153	−	0.240421i
$133$	−2.63703e11	−	3.96649e10i	−0.549453	−	0.0826462i
$134$		−	1.34248e10i		−	0.0268430i
$135$	7.97328e10	−	1.29926e11i	0.153039	−	0.249379i
$136$	−1.20407e11	+	6.95170e10i	−0.221915	+	0.128123i
$137$	−4.31927e11	+	2.49373e11i	−0.764622	+	0.441455i	−0.830953	−	0.556343i	$-0.812204\pi$
$137$	−4.31927e11	+	2.49373e11i	−0.764622	+	0.441455i	0.0663305	+	0.997798i	$0.478871\pi$
$138$	8.89792e8	+	7.95438e6i	0.00151340	+	1.35292e-5i
$139$			2.22577e11i			0.363830i	0.983314	+	0.181915i	$0.0582295\pi$
$139$			2.22577e11i			0.363830i	−0.983314	+	0.181915i	$0.941770\pi$
$140$	8.66518e10	−	3.40387e10i	0.136168	−	0.0534895i
$141$	−2.39182e11	−	4.22962e11i	−0.361429	−	0.639141i
$142$	4.44201e11	−	7.69378e11i	0.645644	−	1.11829i
$143$	5.93105e11	+	1.02729e12i	0.829437	+	1.43663i
$144$	1.85722e11	+	3.32083e9i	0.249960	+	0.00446944i
$145$	−1.66143e11	−	9.59229e10i	−0.215258	−	0.124279i
$146$	1.31439e11			0.163978
$147$	−1.78423e11	−	8.12883e11i	−0.214390	−	0.976748i
$148$	−1.41538e11			−0.163845
$149$	2.95479e11	+	1.70595e11i	0.329612	+	0.190301i	0.655669	−	0.755049i	$-0.272387\pi$
$149$	2.95479e11	+	1.70595e11i	0.329612	+	0.190301i	−0.326057	+	0.945350i	$0.605720\pi$
$150$	−5.18065e11	−	3.05312e11i	−0.557034	−	0.328278i
$151$	3.35053e11	+	5.80329e11i	0.347329	+	0.601591i	0.985774	−	0.168076i	$-0.0537555\pi$
$151$	3.35053e11	+	5.80329e11i	0.347329	+	0.601591i	−0.638445	+	0.769667i	$0.720422\pi$
$152$	9.82547e10	−	1.70182e11i	0.0982231	−	0.170127i
$153$	−3.87393e11	+	6.44109e11i	−0.373550	+	0.621092i
$154$	6.91057e11	−	2.71462e11i	0.642910	−	0.252549i
$155$			3.83802e11i			0.344574i
$156$	−8.75876e9	+	9.79772e11i	−0.00759027	+	0.849063i
$157$	5.74000e11	−	3.31399e11i	0.480246	−	0.277270i	−0.240273	−	0.970705i	$-0.577237\pi$
$157$	5.74000e11	−	3.31399e11i	0.480246	−	0.277270i	0.720519	+	0.693435i	$0.243904\pi$
$158$	−1.32506e12	+	7.65026e11i	−1.07059	+	0.618105i
$159$	1.36275e10	−	1.52440e12i	0.0106349	−	1.18964i
$160$			6.86040e10i			0.0517237i
$161$	2.90516e9	+	4.36981e8i	0.00211655	+	0.000318361i
$162$	8.87051e11	−	4.70686e11i	0.624620	−	0.331435i
$163$	−1.23515e12	+	2.13934e12i	−0.840792	+	1.45629i	0.0484348	+	0.998826i	$0.484577\pi$
$163$	−1.23515e12	+	2.13934e12i	−0.840792	+	1.45629i	−0.889226	+	0.457467i	$0.848757\pi$
$164$	6.39408e11	+	1.10749e12i	0.420860	+	0.728950i
$165$	3.86828e11	+	2.27970e11i	0.246239	+	0.145116i
$166$	−5.20790e11	−	3.00678e11i	−0.320677	−	0.185143i
$167$	−2.65155e12			−1.57964			−0.789822	−	0.613337i	$-0.789827\pi$
$167$	−2.65155e12			−1.57964			−0.789822	+	0.613337i	$0.789827\pi$
$168$	6.05614e11	+	9.66376e10i	0.349136	+	0.0557115i
$169$	−3.37618e12			−1.88386
$170$	−2.40409e11	−	1.38800e11i	−0.129862	−	0.0749758i
$171$	1.89924e10	−	1.06218e12i	0.00993348	−	0.555545i
$172$	3.07802e11	+	5.33128e11i	0.155907	+	0.270038i
$173$	−1.82906e12	+	3.16802e12i	−0.897374	+	1.55430i	−0.0665348	+	0.997784i	$0.521194\pi$
$173$	−1.82906e12	+	3.16802e12i	−0.897374	+	1.55430i	−0.830839	+	0.556513i	$0.812139\pi$
$174$	−6.22078e11	−	1.10007e12i	−0.295682	−	0.522875i
$175$	−1.55260e12	−	1.23738e12i	−0.715071	−	0.569895i
$176$			5.47124e11i			0.244211i
$177$	−2.02688e12	−	1.81195e10i	−0.876949	−	0.00783957i
$178$	2.81688e12	−	1.62633e12i	1.18157	−	0.682179i
$179$	−3.38090e11	+	1.95196e11i	−0.137512	+	0.0793925i	−0.567178	−	0.823595i	$-0.691965\pi$
$179$	−3.38090e11	+	1.95196e11i	−0.137512	+	0.0793925i	0.429666	+	0.902988i	$0.358631\pi$
$180$	1.79668e11	+	3.24455e11i	0.0708716	+	0.127984i
$181$		−	3.49708e12i		−	1.33805i	−0.743238	−	0.669027i	$-0.766711\pi$
$181$		−	3.49708e12i		−	1.33805i	0.743238	−	0.669027i	$-0.233289\pi$
$182$	−4.81170e11	+	3.19894e12i	−0.178610	+	1.18745i
$183$	−7.73857e11	+	4.37610e11i	−0.278728	+	0.157618i
$184$	−1.08245e9	+	1.87486e9i	−0.000378365	+	0.000655347i
$185$	−1.41300e11	−	2.44739e11i	−0.0479400	−	0.0830344i
$186$	−1.28366e12	+	2.17817e12i	−0.422794	+	0.717414i
$187$	−1.91729e12	−	1.10695e12i	−0.613138	−	0.353996i
$188$	1.18219e12			0.367128
$189$	3.11727e12	−	1.12902e12i	0.940232	−	0.340534i
$190$	3.92358e11			0.114958
$191$	2.82790e12	+	1.63269e12i	0.804973	+	0.464751i	0.845207	−	0.534439i	$-0.179477\pi$
$191$	2.82790e12	+	1.63269e12i	0.804973	+	0.464751i	−0.0402342	+	0.999190i	$0.512810\pi$
$192$	−2.29452e11	+	3.89343e11i	−0.0634652	+	0.107690i
$193$	1.59517e11	+	2.76291e11i	0.0428786	+	0.0742679i	0.886668	−	0.462406i	$-0.153014\pi$
$193$	1.59517e11	+	2.76291e11i	0.0428786	+	0.0742679i	−0.843790	+	0.536674i	$0.819680\pi$
$194$	−1.59832e9	+	2.76836e9i	−0.000417593	+	0.000723292i
$195$	−1.70291e12	+	9.62980e11i	−0.432514	+	0.244583i
$196$	1.93519e12	+	5.95641e11i	0.477876	+	0.147088i
$197$		−	6.49177e12i		−	1.55883i	−0.626507	−	0.779415i	$-0.715516\pi$
$197$		−	6.49177e12i		−	1.55883i	0.626507	−	0.779415i	$-0.284484\pi$
$198$	1.43287e12	+	2.58756e12i	0.334618	+	0.604272i
$199$	1.17047e12	−	6.75769e11i	0.265869	−	0.153499i	−0.361140	−	0.932512i	$-0.617612\pi$
$199$	1.17047e12	−	6.75769e11i	0.265869	−	0.153499i	0.627009	+	0.779012i	$0.284279\pi$
$200$	1.26701e12	−	7.31511e11i	0.279973	−	0.161643i
$201$	1.76566e11	+	1.57843e9i	0.0379602	+	0.000339348i
$202$		−	4.63760e12i		−	0.970198i
$203$	−1.52555e12	−	3.88357e12i	−0.310597	−	0.790684i
$204$	−9.00146e11	−	1.59179e12i	−0.178380	−	0.315443i
$205$	−1.27667e12	+	2.21125e12i	−0.246281	+	0.426572i
$206$	−2.25251e12	−	3.90146e12i	−0.423054	−	0.732752i
$207$	−2.09236e8	+	1.17018e10i	−3.82647e−5	+	0.00214001i
$208$	−2.06446e12	−	1.19192e12i	−0.367670	−	0.212274i
$209$	3.12910e12			0.542769
$210$	4.37497e11	+	1.14367e12i	0.0739211	+	0.193238i
$211$	1.15344e13			1.89863			0.949315	−	0.314325i	$-0.101778\pi$
$211$	1.15344e13			1.89863			0.949315	+	0.314325i	$0.101778\pi$
$212$	3.21203e12	+	1.85447e12i	0.515148	+	0.297421i
$213$	1.00668e13	+	5.93269e12i	1.57327	+	0.927180i
$214$	1.22457e12	+	2.12102e12i	0.186513	+	0.323050i
$215$	−6.14569e11	+	1.06447e12i	−0.0912345	+	0.158023i
$216$	−6.55128e10	+	2.44227e12i	−0.00948048	+	0.353426i
$217$	−5.20249e12	+	6.52778e12i	−0.733977	+	0.920952i
$218$		−	7.81698e12i		−	1.07530i
$219$	−1.54541e10	+	1.72872e12i	−0.00207300	+	0.231890i
$220$	−9.46054e11	+	5.46205e11i	−0.123763	+	0.0714547i
$221$	8.35366e12	−	4.82299e12i	1.06591	−	0.615402i
$222$	1.66414e10	−	1.86154e12i	0.00207133	−	0.231703i
$223$			1.00462e13i			1.21990i	0.792440	+	0.609950i	$0.208811\pi$
$223$			1.00462e13i			1.21990i	−0.792440	+	0.609950i	$0.791189\pi$
$224$	−9.29936e11	+	1.16683e12i	−0.110177	+	0.138243i
$225$	4.07644e12	−	6.77781e12i	0.471279	−	0.783584i
$226$	−2.13769e10	+	3.70259e10i	−0.00241184	+	0.00417743i
$227$	5.22653e11	+	9.05262e11i	0.0575535	+	0.0996855i	0.893367	−	0.449328i	$-0.148337\pi$
$227$	5.22653e11	+	9.05262e11i	0.0575535	+	0.0996855i	−0.835813	+	0.549014i	$0.815003\pi$
$228$	2.22672e12	+	1.31228e12i	0.239345	+	0.141054i
$229$	−5.64955e12	−	3.26177e12i	−0.592815	−	0.342262i	0.173395	−	0.984852i	$-0.444526\pi$
$229$	−5.64955e12	−	3.26177e12i	−0.592815	−	0.342262i	−0.766210	+	0.642591i	$0.777860\pi$
$230$	−4.32253e9			−0.000442828
$231$	3.48908e12	+	9.12087e12i	0.349016	+	0.912368i
$232$	3.07470e12			0.300344
$233$	2.46805e12	+	1.42493e12i	0.235448	+	0.135936i	0.613083	−	0.790019i	$-0.289929\pi$
$233$	2.46805e12	+	1.42493e12i	0.235448	+	0.135936i	−0.377635	+	0.925955i	$0.623262\pi$
$234$	−1.28852e13	−	2.30395e11i	−1.20061	−	0.0214677i
$235$	1.18020e12	+	2.04416e12i	0.107419	+	0.186056i
$236$	2.46574e12	−	4.27079e12i	0.219246	−	0.379745i
$237$	−9.90601e12	−	1.75175e13i	−0.860563	−	1.52180i
$238$	−2.20747e12	−	5.61952e12i	−0.187379	−	0.477008i
$239$		−	8.21841e12i		−	0.681709i	−0.940116	−	0.340855i	$-0.889284\pi$
$239$		−	8.21841e12i		−	0.681709i	0.940116	−	0.340855i	$-0.110716\pi$
$240$	−9.02296e11	−	8.06616e9i	−0.0731454	−	0.000653890i
$241$	5.73184e12	−	3.30928e12i	0.454151	−	0.262204i	−0.255431	−	0.966827i	$-0.582217\pi$
$241$	5.73184e12	−	3.30928e12i	0.454151	−	0.262204i	0.709582	+	0.704623i	$0.248884\pi$
$242$	3.61910e11	−	2.08949e11i	0.0280295	−	0.0161829i
$243$	6.08628e12	+	1.17220e13i	0.460805	+	0.887501i
$244$		−	2.16294e12i		−	0.160104i
$245$	9.01991e11	+	3.94085e12i	0.0652813	+	0.285218i
$246$	−1.46411e13	+	8.27944e12i	−1.03617	+	0.585946i
$247$	−6.81678e12	+	1.18070e13i	−0.471787	+	0.817159i
$248$	−3.07559e12	−	5.32707e12i	−0.208182	−	0.360582i
$249$	4.01582e12	−	6.81420e12i	0.265876	−	0.451148i
$250$	5.29639e12	+	3.05788e12i	0.343013	+	0.198039i
$251$	−2.68213e13			−1.69932			−0.849659	−	0.527332i	$-0.823192\pi$
$251$	−2.68213e13			−1.69932			−0.849659	+	0.527332i	$0.823192\pi$
$252$	−1.34221e12	+	7.95382e12i	−0.0831986	+	0.493029i
$253$	−3.44727e10			−0.00209080
$254$	−5.79818e12	−	3.34758e12i	−0.344117	−	0.198676i
$255$	1.85380e12	−	3.14560e12i	0.107669	−	0.182697i
$256$	−5.49756e11	−	9.52205e11i	−0.0312500	−	0.0541266i
$257$	6.73713e12	−	1.16691e13i	0.374837	−	0.649237i	−0.615465	−	0.788164i	$-0.711032\pi$
$257$	6.73713e12	−	1.16691e13i	0.374837	−	0.649237i	0.990303	+	0.138927i	$0.0443652\pi$
$258$	−7.04802e12	+	3.98560e12i	−0.383848	+	0.217063i
$259$	9.14210e11	−	6.07790e12i	0.0487413	−	0.324045i
$260$		−	4.75965e12i		−	0.248440i
$261$	1.45415e13	−	8.05238e12i	0.743165	−	0.411530i
$262$	−9.34166e12	+	5.39341e12i	−0.467484	+	0.269902i
$263$	1.86471e13	−	1.07659e13i	0.913808	−	0.527588i	0.0321539	−	0.999483i	$-0.489763\pi$
$263$	1.86471e13	−	1.07659e13i	0.913808	−	0.527588i	0.881655	+	0.471895i	$0.156430\pi$
$264$	−7.19590e12	−	6.43284e10i	−0.345353	−	0.00308732i
$265$			7.40539e12i			0.348093i
$266$	6.67330e12	+	5.31847e12i	0.307250	+	0.244871i
$267$	2.10587e13	+	3.72395e13i	0.949771	+	1.67955i
$268$	−2.14796e11	+	3.72038e11i	−0.00949042	+	0.0164379i
$269$	1.42368e13	+	2.46589e13i	0.616276	+	1.06742i	0.990159	+	0.139946i	$0.0446928\pi$
$269$	1.42368e13	+	2.46589e13i	0.616276	+	1.06742i	−0.373883	+	0.927476i	$0.621974\pi$
$270$	−4.28844e12	+	2.32489e12i	−0.181886	+	0.0986056i
$271$	1.57172e13	+	9.07433e12i	0.653197	+	0.377124i	0.789680	−	0.613519i	$-0.210247\pi$
$271$	1.57172e13	+	9.07433e12i	0.653197	+	0.377124i	−0.136483	+	0.990642i	$0.543580\pi$
$272$	4.44909e12			0.181193
$273$	−4.20167e13	−	6.70458e12i	−1.67698	−	0.267595i
$274$	1.59599e13			0.624312
$275$	2.01752e13	+	1.16481e13i	0.773549	+	0.446609i
$276$	−2.45314e10	−	1.44571e10i	−0.000921981	−	0.000543352i
$277$	−8.89760e12	−	1.54111e13i	−0.327819	−	0.567799i	0.654260	−	0.756270i	$-0.272980\pi$
$277$	−8.89760e12	−	1.54111e13i	−0.327819	−	0.567799i	−0.982079	+	0.188471i	$0.939647\pi$
$278$	3.56123e12	−	6.16822e12i	0.128633	−	0.222799i
$279$	−2.84968e13	−	1.71391e13i	−1.00919	−	0.606967i
$280$	−2.94598e12	−	4.43121e11i	−0.102297	−	0.0153870i
$281$		−	4.80594e13i		−	1.63642i	−0.574922	−	0.818208i	$-0.694968\pi$
$281$		−	4.80594e13i		−	1.63642i	0.574922	−	0.818208i	$-0.305032\pi$
$282$	−1.38996e11	+	1.55484e13i	−0.00464123	+	0.519177i
$283$	−3.17682e13	+	1.83414e13i	−1.04032	+	0.600630i	−0.919924	−	0.392096i	$-0.871750\pi$
$283$	−3.17682e13	+	1.83414e13i	−1.04032	+	0.600630i	−0.120397	+	0.992726i	$0.538417\pi$
$284$	−2.46201e13	+	1.42144e13i	−0.790749	+	0.456539i
$285$	−4.61318e10	+	5.16039e12i	−0.00145329	+	0.162568i
$286$		−	3.79587e13i		−	1.17300i
$287$	−5.16876e13	+	2.03040e13i	−1.56688	+	0.615505i
$288$	−5.09376e12	−	3.06359e12i	−0.151488	−	0.0911112i
$289$	8.13452e12	−	1.40894e13i	0.237352	−	0.411106i
$290$	3.06953e12	+	5.31658e12i	0.0878786	+	0.152210i
$291$	−3.62222e10	−	2.13469e10i	−0.00101757	−	0.000599686i
$292$	−3.64256e12	−	2.10303e12i	−0.100415	−	0.0579749i
$293$	−1.38233e13			−0.373973			−0.186986	−	0.982362i	$-0.559872\pi$
$293$	−1.38233e13			−0.373973			−0.186986	+	0.982362i	$0.559872\pi$
$294$	−8.06154e12	+	2.53820e13i	−0.214046	+	0.673932i
$295$	9.84640e12			0.256600
$296$	3.92241e12	+	2.26461e12i	0.100334	+	0.0579279i
$297$	−3.42007e13	+	1.85412e13i	−0.858766	+	0.465563i
$298$	−5.45904e12	−	9.45534e12i	−0.134563	−	0.233071i
$299$	7.50991e10	−	1.30075e11i	0.00181737	−	0.00314778i
$300$	9.47204e12	+	1.67501e13i	0.225049	+	0.397970i
$301$	−2.48817e13	+	9.77405e12i	−0.580449	+	0.228013i
$302$		−	2.14434e13i		−	0.491197i
$303$	6.09947e13	+	5.45268e11i	1.37201	+	0.0122652i
$304$	−5.44583e12	+	3.14415e12i	−0.120298	+	0.0694542i
$305$	3.74003e12	−	2.15931e12i	0.0811383	−	0.0468452i
$306$	2.10415e13	−	1.16518e13i	0.448341	−	0.248270i
$307$		−	3.06718e13i		−	0.641916i	−0.947093	−	0.320958i	$-0.895995\pi$
$307$		−	3.06718e13i		−	0.641916i	0.947093	−	0.320958i	$-0.104005\pi$
$308$	−2.34945e13	−	3.53394e12i	−0.482990	−	0.0726491i
$309$	5.15777e13	−	2.91668e13i	1.04157	−	0.589002i
$310$	6.14084e12	−	1.06362e13i	0.121825	−	0.211008i
$311$	−4.46898e12	−	7.74050e12i	−0.0871017	−	0.150865i	0.819183	−	0.573532i	$-0.194427\pi$
$311$	−4.46898e12	−	7.74050e12i	−0.0871017	−	0.150865i	−0.906285	+	0.422667i	$0.861094\pi$
$312$	1.59191e13	−	2.70121e13i	0.304837	−	0.517259i
$313$	9.78688e12	+	5.65046e12i	0.184141	+	0.106314i	0.589237	−	0.807960i	$-0.299429\pi$
$313$	9.78688e12	+	5.65046e12i	0.184141	+	0.106314i	−0.405096	+	0.914274i	$0.632762\pi$
$314$	−2.12095e13			−0.392119
$315$	−1.50932e13	+	5.61959e12i	−0.274204	+	0.102093i
$316$	4.89617e13			0.874133
$317$	2.55691e12	+	1.47623e12i	0.0448632	+	0.0259018i	0.522264	−	0.852784i	$-0.325088\pi$
$317$	2.55691e12	+	1.47623e12i	0.0448632	+	0.0259018i	−0.477401	+	0.878686i	$0.658421\pi$
$318$	−2.47680e13	+	4.20273e13i	−0.427112	+	0.724740i
$319$	2.44798e13	+	4.24003e13i	0.414916	+	0.718655i
$320$	1.09766e12	−	1.90121e12i	0.0182871	−	0.0316742i
$321$	−2.80402e13	+	1.58565e13i	−0.459201	+	0.259674i
$322$	−7.35185e10	−	5.85925e10i	−0.00118356	−	0.000943268i
$323$		−	2.54451e13i		−	0.402708i
$324$	−3.21137e13	−	1.14879e12i	−0.499680	−	0.0178749i
$325$	−8.79037e13	+	5.07512e13i	−1.34477	+	0.776405i
$326$	6.84590e13	−	3.95248e13i	1.02976	−	0.594529i
$327$	1.02811e14	+	9.19087e11i	1.52064	+	0.0135939i
$328$		−	4.09221e13i		−	0.595185i
$329$	−7.63588e12	+	5.07653e13i	−0.109215	+	0.726088i
$330$	−7.07258e12	−	1.25069e13i	−0.0994835	−	0.175924i
$331$	−2.99821e13	+	5.19306e13i	−0.414771	+	0.718404i	−0.995404	−	0.0957607i	$-0.969472\pi$
$331$	−2.99821e13	+	5.19306e13i	−0.414771	+	0.718404i	0.580633	+	0.814165i	$0.302805\pi$
$332$	9.62171e12	+	1.66653e13i	0.130916	+	0.226753i
$333$	2.44814e13	+	4.37743e11i	0.327638	+	0.00585836i
$334$	7.34819e13	+	4.24248e13i	0.967330	+	0.558488i
$335$	−8.57742e11			−0.0111073
$336$	−1.52371e13	−	1.23679e13i	−0.194105	−	0.157555i
$337$	−1.61511e13			−0.202412			−0.101206	−	0.994865i	$-0.532270\pi$
$337$	−1.61511e13			−0.202412			−0.101206	+	0.994865i	$0.532270\pi$
$338$	9.35635e13	+	5.40189e13i	1.15362	+	0.666045i
$339$	−4.84460e11	−	2.85508e11i	−0.00587706	−	0.00346354i
$340$	4.44161e12	+	7.69309e12i	0.0530159	+	0.0918262i
$341$	4.89738e13	−	8.48251e13i	0.575194	−	0.996266i
$342$	−1.75212e13	+	2.91321e13i	−0.202498	+	0.336688i
$343$	−3.80775e13	+	7.92534e13i	−0.433063	+	0.901364i
$344$		−	1.96993e13i		−	0.220485i
$345$	5.08225e8	−	5.68510e10i	5.59823e−6	−	0.000626229i
$346$	1.01377e14	−	5.85298e13i	1.09905	−	0.634539i
$347$	8.44546e13	−	4.87599e13i	0.901179	−	0.520296i	0.0235966	−	0.999722i	$-0.492488\pi$
$347$	8.44546e13	−	4.87599e13i	0.901179	−	0.520296i	0.877583	+	0.479426i	$0.159155\pi$
$348$	−3.61510e11	+	4.04392e13i	−0.00379694	+	0.424733i
$349$		−	1.40421e14i		−	1.45175i	−0.687828	−	0.725874i	$-0.741436\pi$
$349$		−	1.40421e14i		−	1.45175i	0.687828	−	0.725874i	$-0.258564\pi$
$350$	2.32287e13	+	5.91329e13i	0.236401	+	0.601804i
$351$	4.54518e12	−	1.69442e14i	0.0455368	−	1.69758i
$352$	8.75398e12	−	1.51623e13i	0.0863418	−	0.149548i
$353$	−1.75721e13	−	3.04358e13i	−0.170633	−	0.295545i	0.768008	−	0.640440i	$-0.221248\pi$
$353$	−1.75721e13	−	3.04358e13i	−0.170633	−	0.295545i	−0.938641	+	0.344895i	$0.887915\pi$
$354$	5.58806e13	+	3.29322e13i	0.534248	+	0.314849i
$355$	−4.91574e13	−	2.83811e13i	−0.462736	−	0.267161i
$356$	−1.04085e14			−0.964747
$357$	7.41688e13	−	2.83724e13i	0.676933	−	0.258953i
$358$	1.24926e13			0.112278
$359$	1.09865e14	+	6.34304e13i	0.972385	+	0.561407i	0.899963	−	0.435967i	$-0.143594\pi$
$359$	1.09865e14	+	6.34304e13i	0.972385	+	0.561407i	0.0724226	+	0.997374i	$0.476927\pi$
$360$	2.12176e11	−	1.18663e13i	0.00184941	−	0.103431i
$361$	−4.02632e13	−	6.97379e13i	−0.345636	−	0.598658i
$362$	−5.59533e13	+	9.69140e13i	−0.473074	+	0.819388i
$363$	2.70559e12	+	4.78449e12i	0.0225308	+	0.0398428i
$364$	6.45177e13	−	8.09530e13i	0.529202	−	0.664011i
$365$		−	8.39799e12i		−	0.0678523i
$366$	2.84475e13	+	2.54309e11i	0.226412	+	0.00202403i
$367$	7.99222e13	−	4.61431e13i	0.626620	−	0.361779i	−0.152822	−	0.988254i	$-0.548836\pi$
$367$	7.99222e13	−	4.61431e13i	0.626620	−	0.361779i	0.779442	+	0.626475i	$0.215503\pi$
$368$	5.99956e10	−	3.46385e10i	0.000463401	−	0.000267544i
$369$	−1.07172e14	−	1.93537e14i	−0.815521	−	1.47272i
$370$			9.04320e12i			0.0677973i
$371$	−1.00381e14	+	1.25952e14i	−0.741473	+	0.930357i
$372$	7.04245e13	−	3.98245e13i	0.512552	−	0.289844i
$373$	−1.14942e14	+	1.99085e14i	−0.824288	+	1.42771i	0.0781743	+	0.996940i	$0.475091\pi$
$373$	−1.14942e14	+	1.99085e14i	−0.824288	+	1.42771i	−0.902462	+	0.430769i	$0.858242\pi$
$374$	3.54223e13	+	6.13532e13i	0.250313	+	0.433554i
$375$	−4.08406e13	+	6.92999e13i	−0.284394	+	0.482570i
$376$	−3.27617e13	−	1.89150e13i	−0.224819	−	0.129799i
$377$	−2.13318e14			−1.44262
$378$	−1.04453e14	−	1.85882e13i	−0.696169	−	0.123889i
$379$	1.71094e14			1.12388			0.561940	−	0.827178i	$-0.310055\pi$
$379$	1.71094e14			1.12388			0.561940	+	0.827178i	$0.310055\pi$
$380$	−1.08734e13	−	6.27773e12i	−0.0703969	−	0.0406437i
$381$	4.47099e13	−	7.58654e13i	0.285309	−	0.484124i
$382$	−5.22461e13	−	9.04929e13i	−0.328629	−	0.569202i
$383$	−1.14308e14	+	1.97988e14i	−0.708737	+	1.22757i	0.256589	+	0.966521i	$0.417401\pi$
$383$	−1.14308e14	+	1.97988e14i	−0.708737	+	1.22757i	−0.965326	+	0.261047i	$0.915932\pi$
$384$	1.25883e13	−	7.11856e12i	0.0769386	−	0.0435081i
$385$	−1.73444e13	−	4.41533e13i	−0.104502	−	0.266029i
$386$		−	1.02091e13i		−	0.0606395i
$387$	−5.15909e13	−	9.31658e13i	−0.302108	−	0.545565i
$388$	8.85876e10	−	5.11461e10i	0.000511445	−	0.000295283i
$389$	−9.00711e13	+	5.20026e13i	−0.512699	+	0.296007i	−0.733943	−	0.679212i	$-0.762322\pi$
$389$	−9.00711e13	+	5.20026e13i	−0.512699	+	0.296007i	0.221243	+	0.975219i	$0.428989\pi$
$390$	6.26000e13	+	5.59619e11i	0.351333	+	0.00314078i
$391$			2.80324e11i			0.00155127i
$392$	−4.40993e13	−	4.74699e13i	−0.240635	−	0.259027i
$393$	−6.98371e13	−	1.23498e14i	−0.375774	−	0.664508i
$394$	−1.03868e14	+	1.79905e14i	−0.551130	+	0.954585i
$395$	4.88794e13	+	8.46616e13i	0.255765	+	0.442999i
$396$	1.69213e12	−	9.46346e13i	0.00873190	−	0.488345i
$397$	−3.24991e14	−	1.87634e14i	−1.65395	−	0.954911i	−0.975423	−	0.220340i	$-0.929283\pi$
$397$	−3.24991e14	−	1.87634e14i	−1.65395	−	0.954911i	−0.678532	−	0.734571i	$-0.737383\pi$
$398$	−4.32492e13			−0.217081
$399$	−7.07344e13	+	8.71436e13i	−0.350171	+	0.431404i
$400$	−4.68167e13			−0.228597
$401$	1.86713e14	+	1.07799e14i	0.899250	+	0.519182i	0.876957	−	0.480569i	$-0.159570\pi$
$401$	1.86713e14	+	1.07799e14i	0.899250	+	0.519182i	0.0222930	+	0.999751i	$0.492903\pi$
$402$	−4.86788e12	−	2.86880e12i	−0.0231258	−	0.0136288i
$403$	2.13380e14	+	3.69585e14i	0.999944	+	1.73195i
$404$	−7.42015e13	+	1.28521e14i	−0.343017	+	0.594122i
$405$	−3.00733e13	−	5.66759e13i	−0.137144	−	0.258461i
$406$	−1.98598e13	+	1.32033e14i	−0.0893476	+	0.594006i
$407$			7.21205e13i			0.320103i
$408$	−5.23104e11	+	5.85154e13i	−0.00229064	+	0.256236i
$409$	4.97774e13	−	2.87390e13i	0.215057	−	0.124163i	−0.388602	−	0.921406i	$-0.627042\pi$
$409$	4.97774e13	−	2.87390e13i	0.215057	−	0.124163i	0.603659	+	0.797242i	$0.293709\pi$
$410$	7.07601e13	−	4.08534e13i	0.301632	−	0.174147i
$411$	−1.87649e12	+	2.09908e14i	−0.00789254	+	0.882875i
$412$			1.44160e14i			0.598289i
$413$	1.67469e14	+	1.33469e14i	0.685820	+	0.546583i
$414$	1.93028e11	−	3.20943e11i	0.000780041	−	0.00129696i
$415$	−1.92111e13	+	3.32746e13i	−0.0766103	+	0.132693i
$416$	3.81413e13	+	6.60627e13i	0.150101	+	0.259982i
$417$	8.07072e13	+	4.75633e13i	0.313447	+	0.184724i
$418$	−8.67161e13	−	5.00656e13i	−0.332377	−	0.191898i
$419$	−4.40050e14			−1.66466			−0.832328	−	0.554283i	$-0.812993\pi$
$419$	−4.40050e14			−1.66466			−0.832328	+	0.554283i	$0.812993\pi$
$420$	6.17441e12	−	3.86942e13i	0.0230528	−	0.144469i
$421$	2.81215e14			1.03630			0.518152	−	0.855289i	$-0.326620\pi$
$421$	2.81215e14			1.03630			0.518152	+	0.855289i	$0.326620\pi$
$422$	−3.19650e14	−	1.84550e14i	−1.16267	−	0.671267i
$423$	−2.04480e14	−	3.65622e12i	−0.734139	−	0.0131268i
$424$	−5.93429e13	−	1.02785e14i	−0.210308	−	0.364265i
$425$	9.47200e13	−	1.64060e14i	0.331362	−	0.573936i
$426$	−1.84057e14	−	3.25481e14i	−0.635622	−	1.12402i
$427$	9.28808e13	+	1.39707e13i	0.316645	+	0.0476283i
$428$		−	7.83726e13i		−	0.263769i
$429$	4.99242e14	+	4.46302e12i	1.65881	+	0.0148291i
$430$	3.40629e13	−	1.96662e13i	0.111739	−	0.0645126i
$431$	−2.93526e14	+	1.69467e14i	−0.950652	+	0.548859i	−0.893283	−	0.449494i	$-0.851604\pi$
$431$	−2.93526e14	+	1.69467e14i	−0.950652	+	0.548859i	−0.0573686	+	0.998353i	$0.518271\pi$
$432$	4.08919e13	−	6.66341e13i	0.130761	−	0.213077i
$433$		−	2.53309e14i		−	0.799775i	−0.916564	−	0.399888i	$-0.869049\pi$
$433$		−	2.53309e14i		−	0.799775i	0.916564	−	0.399888i	$-0.130951\pi$
$434$	2.48620e14	−	9.76633e13i	0.775073	−	0.304465i
$435$	−7.02859e13	+	3.97461e13i	−0.216360	+	0.122350i
$436$	−1.25072e14	+	2.16631e14i	−0.380175	+	0.658482i
$437$	−1.98104e11	−	3.43126e11i	−0.000594627	−	0.00102992i
$438$	2.80878e13	−	4.76605e13i	0.0832551	−	0.141270i
$439$	8.02552e13	+	4.63354e13i	0.234919	+	0.135631i	0.612839	−	0.790208i	$-0.290027\pi$
$439$	8.02552e13	+	4.63354e13i	0.234919	+	0.135631i	−0.377920	+	0.925838i	$0.623361\pi$
$440$	3.49571e13			0.101052
$441$	−3.32883e14	−	1.09012e14i	−0.950340	−	0.311215i
$442$	−3.08671e14			−0.870310
$443$	9.98220e13	+	5.76323e13i	0.277975	+	0.160489i	0.632506	−	0.774555i	$-0.282026\pi$
$443$	9.98220e13	+	5.76323e13i	0.277975	+	0.160489i	−0.354531	+	0.935044i	$0.615360\pi$
$444$	−3.02458e13	+	5.13222e13i	−0.0831876	+	0.141156i
$445$	−1.03910e14	−	1.79978e14i	−0.282278	−	0.488921i
$446$	1.60739e14	−	2.78408e14i	0.431300	−	0.747033i
$447$	1.25001e14	−	7.06869e13i	0.331300	−	0.187347i
$448$	4.44404e13	−	1.74571e13i	0.116345	−	0.0457029i
$449$		−	1.98884e14i		−	0.514334i	−0.966367	−	0.257167i	$-0.917211\pi$
$449$		−	1.98884e14i		−	0.514334i	0.966367	−	0.257167i	$-0.0827891\pi$
$450$	−2.21415e14	+	1.22609e14i	−0.565637	+	0.313223i
$451$	5.64319e14	−	3.25810e14i	1.42414	−	0.822230i
$452$	1.18483e12	−	6.84062e11i	0.00295389	−	0.00170543i
$453$	2.82029e14	+	2.52122e12i	0.694629	+	0.00620970i
$454$		−	3.34498e13i		−	0.0813929i
$455$	2.04388e14	+	3.07431e13i	0.491353	+	0.0739070i
$456$	−4.07123e13	−	7.19945e13i	−0.0966984	−	0.170999i
$457$	−1.92579e13	+	3.33557e13i	−0.0451929	+	0.0782763i	−0.887737	−	0.460351i	$-0.847724\pi$
$457$	−1.92579e13	+	3.33557e13i	−0.0451929	+	0.0782763i	0.842544	+	0.538627i	$0.181057\pi$
$458$	1.04377e14	+	1.80786e14i	0.242016	+	0.419183i
$459$	1.50773e14	+	2.78112e14i	0.345425	+	0.637163i
$460$	1.19790e11	+	6.91606e10i	0.000271176	+	0.000156563i
$461$	6.60166e14			1.47672			0.738360	−	0.674407i	$-0.235601\pi$
$461$	6.60166e14			1.47672			0.738360	+	0.674407i	$0.235601\pi$
$462$	4.92416e13	−	3.08590e14i	0.108843	−	0.682105i
$463$	4.97161e13			0.108593			0.0542964	−	0.998525i	$-0.482708\pi$
$463$	4.97161e13			0.108593			0.0542964	+	0.998525i	$0.482708\pi$
$464$	−8.52086e13	−	4.91952e13i	−0.183922	−	0.106188i
$465$	1.39168e14	+	8.20163e13i	0.296858	+	0.174948i
$466$	−4.55977e13	−	7.89775e13i	−0.0961214	−	0.166487i
$467$	1.69839e14	−	2.94170e14i	0.353830	−	0.612852i	−0.633087	−	0.774081i	$-0.718212\pi$
$467$	1.69839e14	−	2.94170e14i	0.353830	−	0.612852i	0.986917	+	0.161229i	$0.0515458\pi$
$468$	3.53398e14	+	2.12548e14i	0.727632	+	0.437627i
$469$	−1.45886e13	−	1.16268e13i	−0.0296868	−	0.0236597i
$470$		−	7.55327e13i		−	0.151914i
$471$	2.49372e12	−	2.78953e14i	0.00495716	−	0.554518i
$472$	−1.36665e14	+	7.89038e13i	−0.268521	+	0.155030i
$473$	2.71655e14	−	1.56840e14i	0.527572	−	0.304594i
$474$	−5.75670e12	+	6.43956e14i	−0.0110508	+	1.23616i
$475$			2.67753e14i			0.508066i
$476$	−2.87372e13	+	1.91052e14i	−0.0539021	+	0.358355i
$477$	−5.49841e14	−	3.30696e14i	−1.01950	−	0.613166i
$478$	−1.31494e14	+	2.27755e14i	−0.241021	+	0.417460i
$479$	8.68203e13	+	1.50377e14i	0.157317	+	0.272481i	0.933900	−	0.357533i	$-0.116382\pi$
$479$	8.68203e13	+	1.50377e14i	0.157317	+	0.272481i	−0.776583	+	0.630015i	$0.783049\pi$
$480$	2.48761e13	+	1.46603e13i	0.0445611	+	0.0262612i
$481$	−2.72132e14	−	1.57115e14i	−0.481927	−	0.278240i
$482$	−2.11794e14			−0.370813
$483$	7.79267e11	−	9.60043e11i	0.00134889	−	0.00166181i
$484$	−1.33727e13			−0.0228860
$485$	1.76878e11	+	1.02120e11i	0.000299291	+	0.000172795i
$486$	1.88850e13	−	4.22231e14i	0.0315949	−	0.706401i
$487$	4.13461e14	+	7.16136e14i	0.683952	+	1.18464i	0.973765	+	0.227556i	$0.0730736\pi$
$487$	4.13461e14	+	7.16136e14i	0.683952	+	1.18464i	−0.289813	+	0.957083i	$0.593593\pi$
$488$	−3.46071e13	+	5.99412e13i	−0.0566051	+	0.0980430i
$489$	5.11791e14	+	9.05037e14i	0.827740	+	1.46375i
$490$	3.80569e13	−	1.23644e14i	0.0608633	−	0.197740i
$491$		−	6.27447e14i		−	0.992267i	−0.868246	−	0.496134i	$-0.834753\pi$
$491$		−	6.27447e14i		−	0.992267i	0.868246	−	0.496134i	$-0.165247\pi$
$492$	5.38218e14	+	4.81145e12i	0.841685	+	0.00752432i
$493$	3.44790e14	−	1.99064e14i	0.533207	−	0.307847i
$494$	3.77824e14	−	2.18137e14i	0.577819	−	0.333604i
$495$	1.65326e14	−	9.15497e13i	0.250042	−	0.138461i
$496$			1.96838e14i			0.294414i
$497$	−4.51370e14	−	1.14905e15i	−0.667686	−	1.69972i
$498$	−2.20317e14	+	1.24588e14i	−0.322320	+	0.182269i
$499$	1.77819e14	−	3.07992e14i	0.257292	−	0.445642i	−0.708224	−	0.705988i	$-0.750503\pi$
$499$	1.77819e14	−	3.07992e14i	0.257292	−	0.445642i	0.965515	+	0.260346i	$0.0838365\pi$
$500$	−9.78520e13	−	1.69485e14i	−0.140034	−	0.242547i
$501$	−5.66620e14	+	9.61463e14i	−0.802019	+	1.36090i
$502$	7.43294e14	+	4.29141e14i	1.04062	+	0.600800i
$503$	2.48594e13			0.0344244			0.0172122	−	0.999852i	$-0.494521\pi$
$503$	2.48594e13			0.0344244			0.0172122	+	0.999852i	$0.494521\pi$
$504$	1.64457e14	−	1.98947e14i	0.225261	−	0.272502i
$505$	−2.96307e14			−0.401458
$506$	9.55334e11	+	5.51563e11i	0.00128035	+	0.000739209i
$507$	−7.21470e14	+	1.22422e15i	−0.956477	+	1.62299i
$508$	1.07123e14	+	1.85542e14i	0.140485	+	0.243327i
$509$	3.38386e14	−	5.86101e14i	0.439000	−	0.760369i	−0.558613	−	0.829428i	$-0.688666\pi$
$509$	3.38386e14	−	5.86101e14i	0.439000	−	0.760369i	0.997613	+	0.0690589i	$0.0219996\pi$
$510$	−1.01704e14	+	5.75126e13i	−0.130527	+	0.0738120i
$511$	1.13836e14	−	1.42835e14i	0.144532	−	0.181350i
$512$			3.51844e13i			0.0441942i
$513$	−3.81092e14	−	2.33868e14i	−0.473570	−	0.290620i
$514$	−3.73410e14	+	2.15588e14i	−0.459080	+	0.265050i
$515$	−2.49274e14	+	1.43918e14i	−0.303205	+	0.175055i
$516$	2.59090e14	+	2.31616e12i	0.311801	+	0.00278737i
$517$		−	6.02381e14i		−	0.717255i
$518$	−1.22582e14	+	1.53808e14i	−0.144415	+	0.181203i
$519$	7.57878e14	+	1.34021e15i	0.883444	+	1.56226i
$520$	−7.61544e13	+	1.31903e14i	−0.0878368	+	0.152138i
$521$	−2.32371e14	−	4.02478e14i	−0.265200	−	0.459340i	0.702416	−	0.711767i	$-0.252105\pi$
$521$	−2.32371e14	−	4.02478e14i	−0.265200	−	0.459340i	−0.967616	+	0.252427i	$0.918771\pi$
$522$	−5.31823e14	−	9.50932e12i	−0.600592	−	0.0107389i
$523$	−9.99205e14	−	5.76891e14i	−1.11659	−	0.644666i	−0.176065	−	0.984379i	$-0.556337\pi$
$523$	−9.99205e14	−	5.76891e14i	−1.11659	−	0.644666i	−0.940529	+	0.339713i	$0.889670\pi$
$524$	3.45178e14			0.381699
$525$	−7.80461e14	+	2.98556e14i	−0.854034	+	0.326701i
$526$	−6.89019e14			−0.746121
$527$	−6.89778e14	−	3.98244e14i	−0.739181	−	0.426767i
$528$	1.98389e14	+	1.16917e14i	0.210393	+	0.123991i
$529$	−4.76403e14	−	8.25154e14i	−0.499998	−	0.866021i
$530$	1.18486e14	−	2.05224e14i	0.123070	−	0.213163i
$531$	−4.39702e14	+	7.31082e14i	−0.452000	+	0.751530i
$532$	−9.98405e13	−	2.54163e14i	−0.101576	−	0.258582i
$533$			2.83912e15i			2.85880i
$534$	1.22379e13	−	1.36895e15i	0.0121963	−	1.36430i
$535$	1.35517e14	−	7.82409e13i	0.133675	−	0.0771770i
$536$	1.19052e13	−	6.87349e12i	0.0116233	−	0.00671074i
$537$	−1.46882e12	+	1.64305e14i	−0.00141942	+	0.158779i
$538$		−	9.11156e14i		−	0.871546i
$539$	3.03508e14	−	9.86073e14i	0.287364	−	0.933622i
$540$	1.56043e14	+	4.18577e12i	0.146244	+	0.00392292i
$541$	9.57455e14	−	1.65836e15i	0.888246	−	1.53849i	0.0462993	−	0.998928i	$-0.485257\pi$
$541$	9.57455e14	−	1.65836e15i	0.888246	−	1.53849i	0.841947	−	0.539560i	$-0.181409\pi$
$542$	−2.90379e14	−	5.02951e14i	−0.266667	−	0.461880i
$543$	−1.26806e15	−	7.47306e14i	−1.15276	−	0.679359i
$544$	−1.23297e14	−	7.11854e13i	−0.110958	−	0.0640614i
$545$	−4.99446e14			−0.444947
$546$	1.05713e15	+	8.58070e14i	0.932326	+	0.756769i
$547$	−3.55536e14			−0.310423			−0.155211	−	0.987881i	$-0.549606\pi$
$547$	−3.55536e14			−0.310423			−0.155211	+	0.987881i	$0.549606\pi$
$548$	−4.42293e14	−	2.55358e14i	−0.382311	−	0.220727i
$549$	−6.68947e12	+	3.74119e14i	−0.00572458	+	0.320156i
$550$	−3.72741e14	−	6.45606e14i	−0.315800	−	0.546982i
$551$	−2.81356e14	+	4.87323e14i	−0.236006	+	0.408774i
$552$	4.48520e11	+	7.93149e11i	0.000372492	+	0.000658703i
$553$	−3.16249e14	+	2.10251e15i	−0.260041	+	1.72882i
$554$			5.69447e14i			0.463606i
$555$	−1.18938e14	−	1.06326e12i	−0.0958761	−	0.000857093i
$556$	−1.97383e14	+	1.13959e14i	−0.157543	+	0.0909574i
$557$	1.17092e15	−	6.76028e14i	0.925384	−	0.534271i	0.0400354	−	0.999198i	$-0.487253\pi$
$557$	1.17092e15	−	6.76028e14i	0.925384	−	0.534271i	0.885349	+	0.464927i	$0.153920\pi$
$558$	5.15501e14	+	9.30922e14i	0.403405	+	0.728493i
$559$			1.36671e15i			1.05904i
$560$	7.45516e13	+	5.94159e13i	0.0572035	+	0.0455899i
$561$	−8.11097e14	+	4.58669e14i	−0.616278	+	0.348500i
$562$	−7.68951e14	+	1.33186e15i	−0.578561	+	1.00210i
$563$	−6.85084e13	−	1.18660e14i	−0.0510443	−	0.0884114i	0.839374	−	0.543554i	$-0.182922\pi$
$563$	−6.85084e13	−	1.18660e14i	−0.0510443	−	0.0884114i	−0.890419	+	0.455143i	$0.849588\pi$
$564$	2.52626e14	−	4.28665e14i	0.186399	−	0.316289i
$565$	2.36568e12	+	1.36582e12i	0.00172858	+	0.000997995i
$566$	1.17385e15			0.849418
$567$	2.56757e14	−	1.37160e15i	0.183999	−	0.982926i
$568$	9.09723e14			0.645644
$569$	−1.73985e15	−	1.00450e15i	−1.22291	−	0.706048i	−0.257373	−	0.966312i	$-0.582857\pi$
$569$	−1.73985e15	−	1.00450e15i	−1.22291	−	0.706048i	−0.965537	+	0.260265i	$0.916190\pi$
$570$	8.38447e13	−	1.42271e14i	0.0583665	−	0.0990385i
$571$	−6.17873e14	−	1.07019e15i	−0.425991	−	0.737838i	0.570521	−	0.821283i	$-0.306741\pi$
$571$	−6.17873e14	−	1.07019e15i	−0.425991	−	0.737838i	−0.996512	+	0.0834447i	$0.973408\pi$
$572$	−6.07339e14	+	1.05194e15i	−0.414718	+	0.718313i
$573$	1.19633e15	−	6.76514e14i	0.809095	−	0.457537i
$574$	1.75727e15	+	2.64321e14i	1.17713	+	0.177058i
$575$		−	2.94978e12i		−	0.00195712i
$576$	9.21449e13	+	1.66401e14i	0.0605547	+	0.109353i
$577$	−3.93595e14	+	2.27242e14i	−0.256202	+	0.147918i	−0.622601	−	0.782540i	$-0.713924\pi$
$577$	−3.93595e14	+	2.27242e14i	−0.256202	+	0.147918i	0.366399	+	0.930458i	$0.380591\pi$
$578$	−4.50861e14	+	2.60305e14i	−0.290696	+	0.167833i
$579$	1.34272e14	+	1.20034e12i	0.0857538	+	0.000766604i
$580$		−	1.96450e14i		−	0.124279i
$581$	−7.77787e14	+	3.05531e14i	−0.487407	+	0.191464i
$582$	6.62270e11	+	1.17114e12i	0.000411110	+	0.000726996i
$583$	9.44941e14	−	1.63669e15i	0.581069	−	1.00644i
$584$	6.72970e13	+	1.16562e14i	0.0409944	+	0.0710045i
$585$	−1.47205e13	+	8.23265e14i	−0.00888310	+	0.496801i
$586$	3.83083e14	+	2.21173e14i	0.229011	+	0.132219i
$587$	1.27232e15			0.753505			0.376752	−	0.926314i	$-0.377041\pi$
$587$	1.27232e15			0.753505			0.376752	+	0.926314i	$0.377041\pi$
$588$	6.29520e14	−	5.74423e14i	0.369347	−	0.337021i
$589$	1.12575e15			0.654346
$590$	−2.72871e14	−	1.57542e14i	−0.157135	−	0.0907217i
$591$	−2.35394e15	−	1.38725e15i	−1.34297	−	0.791452i
$592$	−7.24674e13	−	1.25517e14i	−0.0409612	−	0.0709470i
$593$	−5.52213e14	+	9.56460e14i	−0.309247	+	0.535631i	−0.978198	−	0.207675i	$-0.933410\pi$
$593$	−5.52213e14	+	9.56460e14i	−0.309247	+	0.535631i	0.668951	+	0.743307i	$0.266744\pi$
$594$	1.24446e15	+	3.33820e13i	0.690486	+	0.0185219i
$595$	−3.59045e14	+	1.41040e14i	−0.197381	+	0.0775355i
$596$			3.49379e14i			0.190301i
$597$	5.08505e12	−	5.68824e14i	0.00274433	−	0.306986i
$598$	−4.16241e12	+	2.40317e12i	−0.00222581	+	0.00128507i
$599$	1.24905e15	−	7.21141e14i	0.661810	−	0.382096i	−0.131157	−	0.991362i	$-0.541869\pi$
$599$	1.24905e15	−	7.21141e14i	0.661810	−	0.382096i	0.792966	+	0.609266i	$0.208536\pi$
$600$	5.50450e12	−	6.15745e14i	0.00288992	−	0.323272i
$601$			3.57240e15i			1.85845i	0.369515	+	0.929225i	$0.379524\pi$
$601$			3.57240e15i			1.85845i	−0.369515	+	0.929225i	$0.620476\pi$
$602$	8.45926e14	+	1.27240e14i	0.436065	+	0.0655909i
$603$	3.83034e13	−	6.36862e13i	0.0195656	−	0.0325312i
$604$	−3.43094e14	+	5.94257e14i	−0.173664	+	0.300795i
$605$	−1.33503e13	−	2.31233e13i	−0.00669630	−	0.0115983i
$606$	−1.68161e15	−	9.91027e14i	−0.835846	−	0.492590i
$607$	−2.20075e15	−	1.27061e15i	−1.08401	−	0.625854i	−0.152035	−	0.988375i	$-0.548583\pi$
$607$	−2.20075e15	−	1.27061e15i	−1.08401	−	0.625854i	−0.931976	+	0.362521i	$0.881916\pi$
$608$	2.01226e14			0.0982231
$609$	−1.73420e15	−	2.76725e14i	−0.838888	−	0.133861i
$610$	−1.38196e14			−0.0662492
$611$	2.27296e15	+	1.31229e15i	1.07985	+	0.623454i
$612$	−7.69547e14	−	1.37600e13i	−0.362328	−	0.00647865i
$613$	9.23648e14	+	1.59980e15i	0.430997	+	0.746508i	0.996959	−	0.0779229i	$-0.0248288\pi$
$613$	9.23648e14	+	1.59980e15i	0.430997	+	0.746508i	−0.565963	+	0.824431i	$0.691495\pi$
$614$	−4.90749e14	+	8.50002e14i	−0.226952	+	0.393092i
$615$	5.28993e14	+	9.35457e14i	0.242458	+	0.428756i
$616$	5.94557e14	+	4.73848e14i	0.270084	+	0.215251i
$617$			4.07817e14i			0.183610i	0.995777	+	0.0918052i	$0.0292637\pi$
$617$			4.07817e14i			0.183610i	−0.995777	+	0.0918052i	$0.970736\pi$
$618$	−1.89603e15	−	1.69497e13i	−0.846075	−	0.00756357i
$619$	2.06366e15	−	1.19145e15i	0.912724	−	0.526962i	0.0314176	−	0.999506i	$-0.489998\pi$
$619$	2.06366e15	−	1.19145e15i	0.912724	−	0.526962i	0.881307	+	0.472545i	$0.156665\pi$
$620$	−3.40360e14	+	1.96507e14i	−0.149205	+	0.0861436i
$621$	4.19842e12	+	2.57648e12i	0.00182424	+	0.00111950i
$622$			2.86015e14i			0.123180i
$623$	6.72298e14	−	4.46961e15i	0.286997	−	1.90803i
$624$	−8.73356e14	+	4.93876e14i	−0.369553	+	0.208979i
$625$	−8.94662e14	+	1.54960e15i	−0.375248	+	0.649949i
$626$	−1.80815e14	−	3.13180e14i	−0.0751752	−	0.130207i
$627$	6.68670e14	−	1.13462e15i	0.275575	−	0.467607i
$628$	5.87776e14	+	3.39352e14i	0.240123	+	0.138635i
$629$	5.86467e14			0.237501
$630$	5.08189e14	+	8.57568e13i	0.204010	+	0.0344267i
$631$	−1.28361e15			−0.510824			−0.255412	−	0.966832i	$-0.582211\pi$
$631$	−1.28361e15			−0.510824			−0.255412	+	0.966832i	$0.582211\pi$
$632$	−1.35687e15	−	7.83387e14i	−0.535295	−	0.309053i
$633$	2.46483e15	−	4.18241e15i	0.963976	−	1.63571i
$634$	−4.72395e13	−	8.18212e13i	−0.0183153	−	0.0317231i
$635$	−2.13885e14	+	3.70460e14i	−0.0822101	+	0.142392i
$636$	1.35883e15	−	7.68407e14i	0.517786	−	0.292804i
$637$	3.05955e15	+	3.29340e15i	1.15582	+	1.24416i
$638$		−	1.56671e15i		−	0.586779i
$639$	4.30244e15	−	2.38249e15i	1.59757	−	0.884659i
$640$	−6.08387e13	+	3.51252e13i	−0.0223970	+	0.0129309i
$641$	−2.51514e15	+	1.45211e15i	−0.917999	+	0.530007i	−0.882996	−	0.469380i	$-0.844477\pi$
$641$	−2.51514e15	+	1.45211e15i	−0.917999	+	0.530007i	−0.0350030	+	0.999387i	$0.511144\pi$
$642$	1.03078e15	+	9.21471e12i	0.373011	+	0.00333456i
$643$		−	2.82800e15i		−	1.01466i	−0.861753	−	0.507328i	$-0.830633\pi$
$643$		−	2.82800e15i		−	1.01466i	0.861753	−	0.507328i	$-0.169367\pi$
$644$	1.09992e12	+	2.80006e12i	0.000391282	+	0.000996082i
$645$	2.54650e14	+	4.50315e14i	0.0898183	+	0.158832i
$646$	−4.07122e14	+	7.05156e14i	−0.142379	+	0.246607i
$647$	1.75239e15	+	3.03522e15i	0.607654	+	1.05249i	0.991626	+	0.129143i	$0.0412226\pi$
$647$	1.75239e15	+	3.03522e15i	0.607654	+	1.05249i	−0.383972	+	0.923345i	$0.625444\pi$
$648$	8.71579e14	+	5.45655e14i	0.299671	+	0.187610i
$649$	−2.17618e15	−	1.25642e15i	−0.741905	−	0.428339i
$650$	3.24808e15			1.09800
$651$	1.25526e15	+	3.28139e15i	0.420763	+	1.09992i
$652$	−2.52959e15			−0.840792
$653$	−1.37576e15	−	7.94293e14i	−0.453439	−	0.261793i	0.255843	−	0.966718i	$-0.417647\pi$
$653$	−1.37576e15	−	7.94293e14i	−0.453439	−	0.261793i	−0.709282	+	0.704925i	$0.750980\pi$
$654$	−2.83447e15	−	1.67044e15i	−0.926391	−	0.545952i
$655$	3.44598e14	+	5.96862e14i	0.111683	+	0.193440i
$656$	−6.54754e14	+	1.13407e15i	−0.210430	+	0.364475i
$657$	6.23540e14	+	3.75021e14i	0.198726	+	0.119522i
$658$	1.02386e15	−	1.28467e15i	0.323591	−	0.406023i
$659$			4.33669e15i			1.35922i	0.733576	+	0.679608i	$0.237850\pi$
$659$			4.33669e15i			1.35922i	−0.733576	+	0.679608i	$0.762150\pi$
$660$	−4.11010e12	+	4.59764e14i	−0.00127750	+	0.142904i
$661$	9.09022e14	−	5.24824e14i	0.280199	−	0.161773i	−0.353315	−	0.935505i	$-0.614945\pi$
$661$	9.09022e14	−	5.24824e14i	0.280199	−	0.161773i	0.633514	+	0.773732i	$0.281612\pi$
$662$	1.66178e15	−	9.59428e14i	0.507989	−	0.293287i
$663$	3.62922e13	−	4.05972e15i	0.0110024	−	1.23075i
$664$		−	6.15789e14i		−	0.185143i
$665$	3.39810e14	−	4.26374e14i	0.101325	−	0.127137i
$666$	−6.71446e14	−	4.03834e14i	−0.198565	−	0.119425i
$667$	3.09964e12	−	5.36874e12i	0.000909117	−	0.00157464i
$668$	−1.35759e15	−	2.35142e15i	−0.394911	−	0.684006i
$669$	3.64279e15	+	2.14681e15i	1.05097	+	0.619370i
$670$	2.37704e13	+	1.37239e13i	0.00680183	+	0.00392704i
$671$	−1.10212e15			−0.312793
$672$	2.24375e14	+	5.86543e14i	0.0631603	+	0.165108i
$673$	6.92498e15			1.93346			0.966731	−	0.255796i	$-0.0823375\pi$
$673$	6.92498e15			1.93346			0.966731	+	0.255796i	$0.0823375\pi$
$674$	4.47592e14	+	2.58417e14i	0.123952	+	0.0715635i
$675$	−1.58655e15	−	2.92651e15i	−0.435796	−	0.803859i
$676$	−1.72860e15	−	2.99403e15i	−0.470965	−	0.815736i
$677$	−4.06523e14	+	7.04119e14i	−0.109862	+	0.190287i	−0.915714	−	0.401830i	$-0.868374\pi$
$677$	−4.06523e14	+	7.04119e14i	−0.109862	+	0.190287i	0.805852	+	0.592117i	$0.201708\pi$
$678$	8.85764e12	+	1.56636e13i	0.00237440	+	0.00419883i
$679$	1.62411e12	+	4.13448e12i	0.000431849	+	0.00109935i
$680$		−	2.84263e14i		−	0.0749758i
$681$	4.39940e14	+	3.93288e12i	0.115102	+	0.00102897i
$682$	−2.71440e15	+	1.56716e15i	−0.704466	+	0.406724i
$683$	−2.97862e15	+	1.71971e15i	−0.766834	+	0.442732i	−0.831744	−	0.555160i	$-0.812657\pi$
$683$	−2.97862e15	+	1.71971e15i	−0.766834	+	0.442732i	0.0649103	+	0.997891i	$0.479324\pi$
$684$	9.51676e14	−	5.26993e14i	0.243041	−	0.134585i
$685$		−	1.01972e15i		−	0.258334i
$686$	2.32329e15	−	1.58709e15i	0.583876	−	0.398859i
$687$	−2.39001e15	+	1.35153e15i	−0.595850	+	0.336949i
$688$	−3.15189e14	+	5.45924e14i	−0.0779534	+	0.135019i
$689$	4.11713e15	+	7.13107e15i	1.01016	+	1.74964i
$690$	−9.23700e11	+	1.56737e12i	−0.000224834	+	0.000381506i
$691$	9.48279e14	+	5.47489e14i	0.228985	+	0.132204i	0.610104	−	0.792322i	$-0.291128\pi$
$691$	9.48279e14	+	5.47489e14i	0.228985	+	0.132204i	−0.381119	+	0.924526i	$0.624461\pi$
$692$	−3.74591e15			−0.897374
$693$	4.05286e15	+	6.83920e14i	0.963228	+	0.162544i
$694$	−3.12063e15			−0.735810
$695$	−3.94103e14	−	2.27535e14i	−0.0921920	−	0.0532271i
$696$	6.57045e14	−	1.11490e15i	0.152491	−	0.258753i
$697$	−2.64941e15	−	4.58891e15i	−0.610055	−	1.05665i
$698$	−2.24673e15	+	3.89145e15i	−0.513270	+	0.889010i
$699$	1.04409e15	−	5.90425e14i	0.236654	−	0.133826i
$700$	3.02395e14	−	2.01040e15i	0.0680041	−	0.452109i
$701$			3.73696e15i			0.833814i	0.908949	+	0.416907i	$0.136886\pi$
$701$			3.73696e15i			0.833814i	−0.908949	+	0.416907i	$0.863114\pi$
$702$	−2.83703e15	+	4.62298e15i	−0.628072	+	1.02345i
$703$	−7.17855e14	+	4.14454e14i	−0.157682	+	0.0910378i
$704$	−4.85195e14	+	2.80127e14i	−0.105747	+	0.0610529i
$705$	9.93424e14	+	8.88081e12i	0.214830	+	0.00192049i
$706$			1.12462e15i			0.241312i
$707$	−5.03965e15	−	4.01648e15i	−1.07298	−	0.855144i
$708$	−1.02169e15	−	1.80673e15i	−0.215843	−	0.381690i
$709$	9.33088e14	−	1.61616e15i	0.195600	−	0.338789i	−0.751497	−	0.659736i	$-0.770668\pi$
$709$	9.33088e14	−	1.61616e15i	0.195600	−	0.338789i	0.947097	+	0.320948i	$0.104001\pi$
$710$	9.08194e14	+	1.57304e15i	0.188911	+	0.327204i
$711$	−8.46878e15	−	1.51427e14i	−1.74799	−	0.0312551i
$712$	2.88449e15	+	1.66536e15i	0.590784	+	0.341089i
$713$	−1.24021e13			−0.00252060
$714$	−2.50938e15	−	4.00421e14i	−0.506089	−	0.0807564i
$715$	−2.42527e15			−0.485375
$716$	−3.46204e14	−	1.99881e14i	−0.0687559	−	0.0396963i
$717$	−2.98003e15	−	1.75622e15i	−0.587307	−	0.346118i
$718$	−2.02977e15	−	3.51567e15i	−0.396975	−	0.687580i
$719$	−2.17434e15	+	3.76608e15i	−0.422007	+	0.730937i	−0.996136	−	0.0878277i	$-0.972008\pi$
$719$	−2.17434e15	+	3.76608e15i	−0.422007	+	0.730937i	0.574129	+	0.818765i	$0.305341\pi$
$720$	−1.95740e14	+	3.25453e14i	−0.0377009	+	0.0626843i
$721$	−6.19052e15	−	9.31149e14i	−1.18327	−	0.177982i
$722$			2.57684e15i			0.488802i
$723$	2.49018e13	−	2.78556e15i	0.00468781	−	0.524387i
$724$	3.10125e15	−	1.79051e15i	0.579395	−	0.334514i
$725$	−3.62814e15	+	2.09471e15i	−0.672706	+	0.388387i
$726$	1.57231e12	−	1.75881e14i	0.000289325	−	0.0323644i
$727$			1.47691e15i			0.269721i	0.990865	+	0.134860i	$0.0430586\pi$
$727$			1.47691e15i			0.269721i	−0.990865	+	0.134860i	$0.956941\pi$
$728$	−3.08321e15	+	1.21115e15i	−0.558832	+	0.219521i
$729$	5.55107e15	+	2.98023e14i	0.998562	+	0.0536104i
$730$	−1.34368e14	+	2.32732e14i	−0.0239894	+	0.0415509i
$731$	−1.27539e15	−	2.20904e15i	−0.225994	−	0.391433i
$732$	−7.84292e14	−	4.62208e14i	−0.137933	−	0.0812880i
$733$	−6.96346e15	−	4.02035e15i	−1.21549	−	0.701766i	−0.251544	−	0.967846i	$-0.580938\pi$
$733$	−6.96346e15	−	4.02035e15i	−1.21549	−	0.701766i	−0.963951	+	0.266080i	$0.914272\pi$
$734$	−2.95316e15			−0.511633
$735$	1.62172e15	+	5.15071e14i	0.278866	+	0.0885701i
$736$	−2.21686e12			−0.000378365
$737$	1.89572e14	+	1.09449e14i	0.0321146	+	0.0185414i
$738$	−1.26563e14	+	7.07820e15i	−0.0212812	+	1.19018i
$739$	4.63850e15	+	8.03412e15i	0.774165	+	1.34089i	0.935263	+	0.353954i	$0.115163\pi$
$739$	4.63850e15	+	8.03412e15i	0.774165	+	1.34089i	−0.161098	+	0.986938i	$0.551504\pi$
$740$	1.44691e14	−	2.50612e14i	0.0239700	−	0.0415172i
$741$	2.82456e15	+	4.99488e15i	0.464463	+	0.821344i
$742$	4.79708e15	−	1.88440e15i	0.782989	−	0.307575i
$743$		−	4.21178e15i		−	0.682382i	−0.939994	−	0.341191i	$-0.889170\pi$
$743$		−	4.21178e15i		−	0.682382i	0.939994	−	0.341191i	$-0.110830\pi$
$744$	−2.58885e15	−	2.31433e13i	−0.416348	−	0.00372198i
$745$	−6.04125e14	+	3.48791e14i	−0.0964422	+	0.0556809i
$746$	6.37071e15	−	3.67813e15i	1.00954	−	0.582860i
$747$	−1.61270e15	−	2.91231e15i	−0.253682	−	0.458115i
$748$		−	2.26703e15i		−	0.353996i
$749$	3.36547e15	+	5.06218e14i	0.521670	+	0.0784671i
$750$	2.24061e15	−	1.26705e15i	0.344769	−	0.194964i
$751$	3.06207e14	−	5.30366e14i	0.0467730	−	0.0810132i	−0.841691	−	0.539959i	$-0.818440\pi$
$751$	3.06207e14	−	5.30366e14i	0.0467730	−	0.0810132i	0.888464	+	0.458946i	$0.151773\pi$
$752$	6.05279e14	+	1.04837e15i	0.0917820	+	0.158971i
$753$	−5.73156e15	+	9.72552e15i	−0.862781	+	1.46400i
$754$	5.91165e15	+	3.41309e15i	0.883418	+	0.510042i
$755$	−1.37007e15			−0.203252
$756$	2.59727e15	+	2.18637e15i	0.382514	+	0.321999i
$757$	−8.80387e15			−1.28720			−0.643600	−	0.765362i	$-0.722560\pi$
$757$	−8.80387e15			−1.28720			−0.643600	+	0.765362i	$0.722560\pi$
$758$	−4.74151e15	−	2.73751e15i	−0.688233	−	0.397352i
$759$	−7.36661e12	+	1.24999e13i	−0.00106154	+	0.00180127i
$760$	2.00888e14	+	3.47947e14i	0.0287394	+	0.0497782i
$761$	6.67954e15	−	1.15693e16i	0.948704	−	1.64320i	0.200544	−	0.979685i	$-0.435729\pi$
$761$	6.67954e15	−	1.15693e16i	0.948704	−	1.64320i	0.748160	−	0.663519i	$-0.230938\pi$
$762$	−2.45288e15	+	1.38709e15i	−0.345879	+	0.195592i
$763$	−8.49467e15	−	6.77006e15i	−1.18922	−	0.947780i
$764$			3.34375e15i			0.464751i
$765$	−7.44461e14	−	1.34439e15i	−0.102732	−	0.185519i
$766$	6.33562e15	−	3.65787e15i	0.868022	−	0.501153i
$767$	9.48165e15	−	5.47424e15i	1.28976	−	0.744644i
$768$	−4.62753e14	−	4.13682e12i	−0.0624975	−	0.000558702i
$769$			6.40887e15i			0.859383i	0.902976	+	0.429692i	$0.141378\pi$
$769$			6.40887e15i			0.859383i	−0.902976	+	0.429692i	$0.858622\pi$
$770$	−2.25792e14	+	1.50112e15i	−0.0300614	+	0.199856i
$771$	−2.79156e15	−	4.93652e15i	−0.369019	−	0.652562i
$772$	−1.63345e14	+	2.82922e14i	−0.0214393	+	0.0371340i
$773$	1.38015e14	+	2.39049e14i	0.0179862	+	0.0311530i	0.874878	−	0.484343i	$-0.160941\pi$
$773$	1.38015e14	+	2.39049e14i	0.0179862	+	0.0311530i	−0.856892	+	0.515496i	$0.827608\pi$
$774$	−6.09253e13	+	3.40734e15i	−0.00788357	+	0.440900i
$775$	7.25838e15	+	4.19063e15i	0.932568	+	0.538418i
$776$	−3.27335e12			−0.000417593
$777$	−2.00851e15	−	1.63031e15i	−0.254424	−	0.206516i
$778$	3.32817e15			0.418617
$779$	6.48593e15	+	3.74466e15i	0.810059	+	0.467688i
$780$	−1.72587e15	−	1.01711e15i	−0.214036	−	0.126138i
$781$	7.24294e15	+	1.25451e16i	0.891937	+	1.54488i
$782$	4.48518e12	−	7.76856e12i	0.000548457	−	0.000949956i
$783$	1.87598e14	−	6.99354e15i	0.0227792	−	0.849195i
$784$	4.62597e14	+	2.02111e15i	0.0557782	+	0.243698i
$785$			1.35513e15i			0.162255i
$786$	−4.05845e13	+	4.53987e15i	−0.00482544	+	0.539783i
$787$	−3.23000e15	+	1.86484e15i	−0.381365	+	0.220181i	−0.678412	−	0.734682i	$-0.737332\pi$
$787$	−3.23000e15	+	1.86484e15i	−0.381365	+	0.220181i	0.297047	+	0.954863i	$0.403998\pi$
$788$	5.75697e15	−	3.32379e15i	0.674994	−	0.389708i
$789$	8.10118e13	−	9.06214e15i	0.00943246	−	1.05513i
$790$		−	3.12828e15i		−	0.361707i
$791$	2.17220e13	+	5.52973e13i	0.00249418	+	0.00634941i
$792$	−1.56105e15	+	2.59552e15i	−0.178003	+	0.295962i
$793$	2.40099e15	−	4.15864e15i	0.271887	−	0.470922i
$794$	6.00428e15	+	1.03997e16i	0.675224	+	1.16952i
$795$	2.68523e15	+	1.58249e15i	0.299890	+	0.176735i
$796$	1.19856e15	+	6.91988e14i	0.132934	+	0.0767497i
$797$	−1.35761e16			−1.49539			−0.747697	−	0.664040i	$-0.768840\pi$
$797$	−1.35761e16			−1.49539			−0.747697	+	0.664040i	$0.768840\pi$
$798$	3.35455e15	−	1.28324e15i	0.366959	−	0.140376i
$799$	−4.89843e15			−0.532169
$800$	1.29742e15	+	7.49068e14i	0.139987	+	0.0808213i
$801$	1.80033e16	+	3.21910e14i	1.92918	+	0.0344950i
$802$	−3.44956e15	−	5.97481e15i	−0.367117	−	0.635866i
$803$	−1.07160e15	+	1.85606e15i	−0.113265	+	0.196181i
$804$	8.90019e13	+	1.57388e14i	0.00934310	+	0.0165221i
$805$	−3.74362e12	+	4.69727e12i	−0.000390314	+	0.000489743i
$806$		−	1.36563e16i		−	1.41413i
$807$	1.19837e16	+	1.07130e14i	1.23250	+	0.0110181i
$808$	4.11267e15	−	2.37445e15i	0.420108	−	0.242549i
$809$	1.40898e16	−	8.13477e15i	1.42952	−	0.825331i	0.432434	−	0.901666i	$-0.357655\pi$
$809$	1.40898e16	−	8.13477e15i	1.42952	−	0.825331i	0.997082	+	0.0763343i	$0.0243216\pi$
$810$	−7.33991e13	+	2.05182e15i	−0.00739644	+	0.206762i
$811$			6.01908e15i			0.602443i	0.953554	+	0.301221i	$0.0973943\pi$
$811$			6.01908e15i			0.602443i	−0.953554	+	0.301221i	$0.902606\pi$
$812$	2.66291e15	−	3.34126e15i	0.264727	−	0.332164i
$813$	6.64907e15	−	3.75999e15i	0.656542	−	0.371269i
$814$	1.15393e15	−	1.99866e15i	0.113173	−	0.196022i
$815$	−2.52534e15	−	4.37402e15i	−0.246010	−	0.426102i
$816$	9.50743e14	−	1.61326e15i	0.0919957	−	0.156102i
$817$	3.12223e15	+	1.80262e15i	0.300085	+	0.173254i
$818$	−1.83929e15			−0.175593
$819$	−1.14098e16	+	1.38027e16i	−1.08198	+	1.30889i
$820$	−2.61462e15			−0.246281
$821$	−9.65524e15	−	5.57446e15i	−0.903391	−	0.521573i	−0.0250922	−	0.999685i	$-0.507988\pi$
$821$	−9.65524e15	−	5.57446e15i	−0.903391	−	0.521573i	−0.878299	+	0.478112i	$0.841321\pi$
$822$	3.41053e15	−	5.78712e15i	0.316977	−	0.537858i
$823$	3.92384e15	+	6.79630e15i	0.362254	+	0.627442i	0.988331	−	0.152319i	$-0.0486741\pi$
$823$	3.92384e15	+	6.79630e15i	0.362254	+	0.627442i	−0.626078	+	0.779761i	$0.715341\pi$
$824$	2.30657e15	−	3.99509e15i	0.211527	−	0.366376i
$825$	8.53499e15	−	4.82647e15i	0.777510	−	0.439676i
$826$	−2.50554e15	−	6.37832e15i	−0.226731	−	0.577186i
$827$		−	2.19110e16i		−	1.96961i	−0.173652	−	0.984807i	$-0.555557\pi$
$827$		−	2.19110e16i		−	1.96961i	0.173652	−	0.984807i	$-0.444443\pi$
$828$	−1.04844e13	+	5.80578e12i	−0.000936219	+	0.000518434i
$829$	−1.51773e16	+	8.76262e15i	−1.34631	+	0.777292i	−0.987725	−	0.156205i	$-0.950074\pi$
$829$	−1.51773e16	+	8.76262e15i	−1.34631	+	0.777292i	−0.358584	+	0.933497i	$0.616740\pi$
$830$	1.06479e15	−	6.14754e14i	0.0938281	−	0.0541717i
$831$	−7.48949e15	−	6.69530e13i	−0.655612	−	0.00586090i
$832$		−	2.44104e15i		−	0.212274i
$833$	−8.01852e15	−	2.46806e15i	−0.692703	−	0.213210i
$834$	−1.47561e15	−	2.60943e15i	−0.126636	−	0.223940i
$835$	2.71062e15	−	4.69494e15i	0.231097	−	0.400271i
$836$	1.60210e15	+	2.77492e15i	0.135692	+	0.235026i
$837$	−1.23043e16	+	6.67054e15i	−1.03530	+	0.561269i
$838$	1.21950e16	+	7.04080e15i	1.01939	+	0.588545i
$839$	5.07186e15			0.421188			0.210594	−	0.977574i	$-0.432460\pi$
$839$	5.07186e15			0.421188			0.210594	+	0.977574i	$0.432460\pi$
$840$	−7.90217e14	+	9.73534e14i	−0.0651944	+	0.0803184i
$841$	3.39600e15			0.278349
$842$	−7.79326e15	−	4.49944e15i	−0.634604	−	0.366389i
$843$	−1.74266e16	−	1.02700e16i	−1.40981	−	0.830844i
$844$	5.90560e15	+	1.02288e16i	0.474658	+	0.822131i
$845$	3.45140e15	−	5.97800e15i	0.275603	−	0.477358i
$846$	5.60821e15	+	3.37300e15i	0.444925	+	0.267596i
$847$	8.63760e13	−	5.74250e14i	0.00680823	−	0.0452629i
$848$			3.79794e15i			0.297421i
$849$	−1.38016e14	+	1.54387e16i	−0.0107383	+	1.20121i
$850$	−5.24992e15	+	3.03104e15i	−0.405834	+	0.234308i
$851$	7.90847e12	−	4.56596e12i	0.000607407	−	0.000350687i
$852$	−1.06961e14	+	1.19649e16i	−0.00816222	+	0.913042i
$853$		−	8.96188e15i		−	0.679484i	−0.940519	−	0.339742i	$-0.889660\pi$
$853$		−	8.96188e15i		−	0.679484i	0.940519	−	0.339742i	$-0.110340\pi$
$854$	−2.35046e15	−	1.87326e15i	−0.177066	−	0.141117i
$855$	1.86132e15	+	1.11947e15i	0.139318	+	0.0837915i
$856$	−1.25396e15	+	2.17193e15i	−0.0932564	+	0.161525i
$857$	1.07774e16	+	1.86670e16i	0.796378	+	1.37937i	0.921961	+	0.387284i	$0.126587\pi$
$857$	1.07774e16	+	1.86670e16i	0.796378	+	1.37937i	−0.125583	+	0.992083i	$0.540080\pi$
$858$	−1.37640e16	−	8.11155e15i	−1.01056	−	0.595558i
$859$	−2.73134e15	−	1.57694e15i	−0.199257	−	0.115041i	0.397052	−	0.917796i	$-0.370033\pi$
$859$	−2.73134e15	−	1.57694e15i	−0.199257	−	0.115041i	−0.596309	+	0.802755i	$0.703367\pi$
$860$	−1.25864e15			−0.0912345
$861$	−3.68302e15	+	2.30810e16i	−0.265269	+	1.66241i
$862$	1.08459e16			0.776204
$863$	6.98192e15	+	4.03101e15i	0.496496	+	0.286652i	0.727265	−	0.686357i	$-0.240791\pi$
$863$	6.98192e15	+	4.03101e15i	0.496496	+	0.286652i	−0.230770	+	0.973008i	$0.574124\pi$
$864$	−2.19938e15	+	1.19235e15i	−0.155408	+	0.0842514i
$865$	−3.73961e15	−	6.47720e15i	−0.262566	−	0.454777i
$866$	−4.05295e15	+	7.01992e15i	−0.282763	+	0.489760i
$867$	−3.37058e15	−	5.96043e15i	−0.233668	−	0.413212i
$868$	−8.45257e15	−	1.27140e15i	−0.582278	−	0.0875836i
$869$		−	2.49484e16i		−	1.70779i
$870$	2.58376e15	+	2.30977e13i	0.175750	+	0.00157113i
$871$	−8.25968e14	+	4.76873e14i	−0.0558295	+	0.0322332i
$872$	6.93218e15	−	4.00230e15i	0.465617	−	0.268824i
$873$	−1.54810e13	+	8.57263e12i	−0.00103328	+	0.000572184i
$874$			1.26786e13i			0.000840930i
$875$	7.91003e15	−	3.10723e15i	0.521355	−	0.204799i
$876$	−1.54096e15	+	8.71401e14i	−0.100930	+	0.0570749i
$877$	−1.07631e16	+	1.86422e16i	−0.700549	+	1.21339i	0.267726	+	0.963495i	$0.413728\pi$
$877$	−1.07631e16	+	1.86422e16i	−0.700549	+	1.21339i	−0.968274	+	0.249891i	$0.919605\pi$
$878$	−1.48273e15	−	2.56817e15i	−0.0959054	−	0.166113i
$879$	−2.95396e15	+	5.01239e15i	−0.189874	+	0.322186i
$880$	−9.68759e14	−	5.59313e14i	−0.0618815	−	0.0357273i
$881$	−2.57097e16			−1.63203			−0.816017	−	0.578028i	$-0.803822\pi$
$881$	−2.57097e16			−1.63203			−0.816017	+	0.578028i	$0.803822\pi$
$882$	7.48093e15	+	8.34714e15i	0.471931	+	0.526575i
$883$	2.69748e16			1.69112			0.845561	−	0.533879i	$-0.179266\pi$
$883$	2.69748e16			1.69112			0.845561	+	0.533879i	$0.179266\pi$
$884$	8.55415e15	+	4.93874e15i	0.532954	+	0.307701i
$885$	2.10412e15	−	3.57035e15i	0.130281	−	0.221066i
$886$	−1.84423e15	−	3.19430e15i	−0.113483	−	0.196558i
$887$	−5.17294e15	+	8.95980e15i	−0.316343	+	0.547921i	−0.979722	−	0.200362i	$-0.935788\pi$
$887$	−5.17294e15	+	8.95980e15i	−0.316343	+	0.547921i	0.663379	+	0.748283i	$0.269122\pi$
$888$	1.65935e15	−	9.38350e14i	0.100848	−	0.0570287i
$889$	−8.65943e15	+	3.40161e15i	−0.523034	+	0.205459i
$890$			6.65025e15i			0.399202i
$891$	−5.85365e14	+	1.63635e16i	−0.0349220	+	0.976221i
$892$	−8.90905e15	+	5.14364e15i	−0.528232	+	0.304975i
$893$	5.99584e15	−	3.46170e15i	0.353319	−	0.203989i
$894$	−4.59511e15	−	4.10784e13i	−0.269116	−	0.00240579i
$895$		−	7.98180e14i		−	0.0464594i
$896$	−1.51088e15	−	2.27260e14i	−0.0874051	−	0.0131471i
$897$	−3.11177e13	−	5.50276e13i	−0.00178916	−	0.00316390i
$898$	−3.18215e15	+	5.51164e15i	−0.181845	+	0.314964i
$899$	8.80705e15	+	1.52543e16i	0.500210	+	0.866389i
$900$	8.09777e15	+	1.44793e14i	0.457121	+	0.00817361i
$901$	−1.33091e16	−	7.68404e15i	−0.746730	−	0.431125i
$902$	−2.08518e16			−1.16281
$903$	−1.77295e15	+	1.11109e16i	−0.0982686	+	0.615836i
$904$	−4.37800e13			−0.00241184
$905$	6.19207e15	+	3.57500e15i	0.339054	+	0.195753i
$906$	−7.77547e15	−	4.58233e15i	−0.423176	−	0.249391i
$907$	−2.10914e15	−	3.65314e15i	−0.114095	−	0.197618i	0.803323	−	0.595544i	$-0.203063\pi$
$907$	−2.10914e15	−	3.65314e15i	−0.114095	−	0.197618i	−0.917418	+	0.397926i	$0.869730\pi$
$908$	−5.35197e14	+	9.26988e14i	−0.0287767	+	0.0498428i
$909$	1.32319e16	−	2.20004e16i	0.707167	−	1.17579i
$910$	−5.17229e15	−	4.12219e15i	−0.274761	−	0.218978i
$911$			1.74187e16i			0.919740i	0.887986	+	0.459870i	$0.152104\pi$
$911$			1.74187e16i			0.919740i	−0.887986	+	0.459870i	$0.847896\pi$
$912$	−2.36592e13	+	2.64657e15i	−0.00124174	+	0.138903i
$913$	8.49178e15	−	4.90273e15i	0.443006	−	0.255769i
$914$	1.06738e15	−	6.16253e14i	0.0553497	−	0.0319562i
$915$	1.62484e13	−	1.81758e15i	0.000837521	−	0.0936867i
$916$		−	6.68011e15i		−	0.342262i
$917$	−2.22955e15	+	1.48226e16i	−0.113550	+	0.754907i
$918$	2.71454e14	−	1.01196e16i	0.0137424	−	0.512307i
$919$	1.75643e16	−	3.04222e16i	0.883883	−	1.53093i	0.0368951	−	0.999319i	$-0.488253\pi$
$919$	1.75643e16	−	3.04222e16i	0.883883	−	1.53093i	0.846988	−	0.531612i	$-0.178413\pi$
$920$	−2.21314e12	−	3.83327e12i	−0.000110707	−	0.000191750i
$921$	−1.11217e16	−	6.55438e15i	−0.553024	−	0.325915i
$922$	−1.82951e16	−	1.05627e16i	−0.904303	−	0.522099i
$923$	−6.31153e16			−3.10117
$924$	−6.30207e15	+	7.76404e15i	−0.307813	+	0.379220i
$925$	−6.17126e15			−0.299636
$926$	−1.37777e15	−	7.95457e14i	−0.0664993	−	0.0383934i
$927$	4.45854e14	−	2.49351e16i	0.0213921	−	1.19639i
$928$	1.57425e15	+	2.72667e15i	0.0750860	+	0.130053i
$929$	3.66543e15	−	6.34871e15i	0.173795	−	0.301022i	−0.765948	−	0.642902i	$-0.777730\pi$
$929$	3.66543e15	−	6.34871e15i	0.173795	−	0.301022i	0.939744	+	0.341880i	$0.111064\pi$
$930$	−2.54448e15	−	4.49959e15i	−0.119934	−	0.212089i
$931$	1.15591e16	−	2.64567e15i	0.541628	−	0.123969i
$932$			2.91825e15i			0.135936i
$933$	−3.76173e15	−	3.36284e13i	−0.174196	−	0.00155724i
$934$	−9.41344e15	+	5.43485e15i	−0.433352	+	0.250196i
$935$	3.92001e15	−	2.26322e15i	0.179400	−	0.103577i
$936$	−6.39289e15	−	1.15447e16i	−0.290857	−	0.525247i
$937$		−	3.43547e16i		−	1.55388i	−0.629573	−	0.776941i	$-0.716770\pi$
$937$		−	3.43547e16i		−	1.55388i	0.629573	−	0.776941i	$-0.283230\pi$
$938$	2.18263e14	+	5.55629e14i	0.00981442	+	0.0249844i
$939$	4.14028e15	−	2.34129e15i	0.185084	−	0.104664i
$940$	−1.20852e15	+	2.09322e15i	−0.0537096	+	0.0930278i
$941$	−7.30397e14	−	1.26508e15i	−0.0322713	−	0.0558955i	0.849439	−	0.527687i	$-0.176941\pi$
$941$	−7.30397e14	−	1.26508e15i	−0.0322713	−	0.0558955i	−0.881710	+	0.471792i	$0.843607\pi$
$942$	−4.53235e15	+	7.69066e15i	−0.199087	+	0.337819i
$943$	−7.14542e13	−	4.12541e13i	−0.00312042	−	0.00180158i
$944$	5.04984e15			0.219246
$945$	−1.18764e15	+	6.67374e15i	−0.0512639	+	0.288068i
$946$	−1.00378e16			−0.430760
$947$	3.22967e16	+	1.86465e16i	1.37795	+	0.795560i	0.991913	−	0.126923i	$-0.0405102\pi$
$947$	3.22967e16	+	1.86465e16i	1.37795	+	0.795560i	0.386038	+	0.922483i	$0.373843\pi$
$948$	1.04628e16	−	1.77537e16i	0.443816	−	0.753084i
$949$	−4.66897e15	−	8.08690e15i	−0.196905	−	0.341050i
$950$	4.28405e15	−	7.42019e15i	0.179628	−	0.311125i
$951$	1.08169e15	−	6.11685e14i	0.0450929	−	0.0254997i
$952$	3.85322e15	−	4.83480e15i	0.159706	−	0.200390i
$953$			4.10723e16i			1.69254i	0.532756	+	0.846269i	$0.321157\pi$
$953$			4.10723e16i			1.69254i	−0.532756	+	0.846269i	$0.678843\pi$
$954$	9.94650e15	+	1.79620e16i	0.407525	+	0.735933i
$955$	−5.78182e15	+	3.33813e15i	−0.235530	+	0.135983i
$956$	7.28816e15	−	4.20782e15i	0.295189	−	0.170427i
$957$	2.06057e16	+	1.84207e14i	0.829798	+	0.00741805i
$958$		−	5.55650e15i		−	0.222480i
$959$	1.38224e16	−	1.73435e16i	0.550276	−	0.690454i
$960$	−4.54822e14	−	8.04295e14i	−0.0180032	−	0.0318364i
$961$	4.91495e15	−	8.51294e15i	0.193437	−	0.335043i
$962$	5.02769e15	+	8.70821e15i	0.196746	+	0.340774i
$963$	−2.42388e14	+	1.35559e16i	−0.00943119	+	0.527454i
$964$	5.86940e15	+	3.38870e15i	0.227076	+	0.131102i
$965$	−6.52282e14			−0.0250920
$966$	−3.69564e13	+	1.41372e13i	−0.00141356	+	0.000540742i
$967$	3.99889e16			1.52088			0.760438	−	0.649411i	$-0.224984\pi$
$967$	3.99889e16			1.52088			0.760438	+	0.649411i	$0.224984\pi$
$968$	3.70596e14	+	2.13964e14i	0.0140148	+	0.00809143i
$969$	−9.22650e15	−	5.43747e15i	−0.346942	−	0.204464i
$970$	−3.26785e12	−	5.66008e12i	−0.000122185	−	0.000211630i
$971$	−1.64395e16	+	2.84741e16i	−0.611200	+	1.05863i	0.379838	+	0.925053i	$0.375980\pi$
$971$	−1.64395e16	+	2.84741e16i	−0.611200	+	1.05863i	−0.991038	+	0.133577i	$0.957354\pi$
$972$	−7.27906e15	+	1.13991e16i	−0.269098	+	0.421410i
$973$	−3.61870e15	−	9.21208e15i	−0.133025	−	0.338639i
$974$		−	2.64615e16i		−	0.967254i
$975$	−3.81895e14	+	4.27195e16i	−0.0138809	+	1.55275i
$976$	1.91812e15	−	1.10743e15i	0.0693269	−	0.0400259i
$977$	4.13196e16	−	2.38559e16i	1.48503	−	0.857384i	0.485178	−	0.874415i	$-0.338755\pi$
$977$	4.13196e16	−	2.38559e16i	1.48503	−	0.857384i	0.999855	+	0.0170313i	$0.00542151\pi$
$978$	2.97418e14	−	3.32698e16i	0.0106293	−	1.18901i
$979$			5.30364e16i			1.88482i
$980$	−3.03297e15	+	2.81761e15i	−0.107183	+	0.0995721i
$981$	2.23033e16	−	3.70832e16i	0.783773	−	1.30316i
$982$	−1.00391e16	+	1.73883e16i	−0.350820	+	0.607637i
$983$	1.66197e15	+	2.87862e15i	0.0577537	+	0.100032i	0.893457	−	0.449149i	$-0.148273\pi$
$983$	1.66197e15	+	2.87862e15i	0.0577537	+	0.100032i	−0.835703	+	0.549182i	$0.814940\pi$
$984$	−1.48385e16	−	8.74482e15i	−0.512765	−	0.302188i
$985$	1.14946e16	+	6.63640e15i	0.394997	+	0.228052i
$986$	−1.27401e16			−0.435362
$987$	1.67760e16	+	1.36170e16i	0.570090	+	0.462742i
$988$	−1.39608e16			−0.471787
$989$	−3.43970e13	−	1.98591e13i	−0.00115596	−	0.000667392i
$990$	−6.04644e15	−	1.08114e14i	−0.202072	−	0.00361317i
$991$	−6.10674e15	−	1.05772e16i	−0.202957	−	0.351532i	0.746523	−	0.665360i	$-0.231722\pi$
$991$	−6.10674e15	−	1.05772e16i	−0.202957	−	0.351532i	−0.949480	+	0.313828i	$0.898389\pi$
$992$	3.14940e15	−	5.45492e15i	0.104091	−	0.180291i
$993$	1.24232e16	+	2.19689e16i	0.408332	+	0.722083i
$994$	−5.87601e15	+	3.90652e16i	−0.192069	+	1.27692i
$995$			2.76330e15i			0.0898258i
$996$	8.09901e15	+	7.24018e13i	0.261822	+	0.00234058i
$997$	1.56278e15	−	9.02270e14i	0.0502428	−	0.0290077i	−0.474668	−	0.880165i	$-0.657432\pi$
$997$	1.56278e15	−	9.02270e14i	0.0502428	−	0.0290077i	0.524911	+	0.851157i	$0.324099\pi$
$998$	−9.85574e15	+	5.69022e15i	−0.315117	+	0.181933i
$999$	5.39027e15	−	8.78353e15i	0.171396	−	0.279292i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	42.12.f.a.5.11	✓	60
3.2	odd	2	inner	42.12.f.a.5.30	yes	60
7.3	odd	6	inner	42.12.f.a.17.30	yes	60
21.17	even	6	inner	42.12.f.a.17.11	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.12.f.a.5.11	✓	60	1.1	even	1	trivial
42.12.f.a.5.30	yes	60	3.2	odd	2	inner
42.12.f.a.17.11	yes	60	21.17	even	6	inner
42.12.f.a.17.30	yes	60	7.3	odd	6	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 42 = 2 \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	42.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-27.7128 - 16.0000i) q^{2} +(213.694 - 362.604i) q^{3} +(512.000 + 886.810i) q^{4} +(-1022.28 + 1770.64i) q^{5} +(-11723.7 + 6629.68i) q^{6} +(-41388.4 + 16258.2i) q^{7} -32768.0i q^{8} +(-85816.7 - 154973. i) q^{9} +(56660.5 - 32712.9i) q^{10} +(451873. - 260889. i) q^{11} +(430972. + 3852.72i) q^{12} +2.27340e6i q^{13} +(1.40712e6 + 211652. i) q^{14} +(423586. + 749058. i) q^{15} +(-524288. + 908093. i) q^{16} +(-2.12149e6 - 3.67453e6i) q^{17} +(-101344. + 5.66780e6i) q^{18} +(5.19355e6 + 2.99850e6i) q^{19} -2.09363e6 q^{20} +(-2.94915e6 + 1.84819e7i) q^{21} -1.66969e7 q^{22} +(-57216.3 - 33033.8i) q^{23} +(-1.18818e7 - 7.00233e6i) q^{24} +(2.23240e7 + 3.86662e7i) q^{25} +(3.63744e7 - 6.30023e7i) q^{26} +(-7.45323e7 - 1.99929e6i) q^{27} +(-3.56088e7 - 2.83794e7i) q^{28} +9.38324e7i q^{29} +(246160. - 2.75359e7i) q^{30} +(1.62569e8 - 9.38594e7i) q^{31} +(2.90590e7 - 1.67772e7i) q^{32} +(1.96315e6 - 2.19602e8i) q^{33} +1.35775e8i q^{34} +(1.35230e7 - 8.99043e7i) q^{35} +(9.34933e7 - 1.55449e8i) q^{36} +(-6.91103e7 + 1.19703e8i) q^{37} +(-9.59519e7 - 1.66194e8i) q^{38} +(8.24344e8 + 4.85812e8i) q^{39} +(5.80203e7 + 3.34980e7i) q^{40} +1.24884e9 q^{41} +(3.77439e8 - 4.64999e8i) q^{42} +6.01176e8 q^{43} +(4.62718e8 + 2.67150e8i) q^{44} +(3.62129e8 + 6.47510e6i) q^{45} +(1.05708e6 + 1.83092e6i) q^{46} +(5.77239e8 - 9.99807e8i) q^{47} +(2.17241e8 + 3.84163e8i) q^{48} +(1.44867e9 - 1.34580e9i) q^{49} -1.42873e9i q^{50} +(-1.78575e9 - 1.59639e7i) q^{51} +(-2.01607e9 + 1.16398e9i) q^{52} +(3.13675e9 - 1.81100e9i) q^{53} +(2.03351e9 + 1.24792e9i) q^{54} +1.06681e9i q^{55} +(5.32750e8 + 1.35621e9i) q^{56} +(2.19710e9 - 1.24244e9i) q^{57} +(1.50132e9 - 2.60036e9i) q^{58} +(-2.40795e9 - 4.17070e9i) q^{59} +(-4.47396e8 + 7.59158e8i) q^{60} +(-1.82926e9 - 1.05612e9i) q^{61} -6.00700e9 q^{62} +(6.07139e9 + 5.01884e9i) q^{63} -1.07374e9 q^{64} +(-4.02537e9 - 2.32405e9i) q^{65} +(-3.56803e9 + 6.05437e9i) q^{66} +(2.09762e8 + 3.63319e8i) q^{67} +(2.17240e9 - 3.76272e9i) q^{68} +(-2.42050e7 + 1.36877e7i) q^{69} +(-1.81323e9 + 2.27513e9i) q^{70} +2.77625e10i q^{71} +(-5.07815e9 + 2.81204e9i) q^{72} +(-3.55718e9 + 2.05374e9i) q^{73} +(3.83048e9 - 2.21153e9i) q^{74} +(1.87910e10 + 1.67984e8i) q^{75} +6.14092e9i q^{76} +(-1.44607e10 + 1.81444e10i) q^{77} +(-1.50719e10 - 2.66527e10i) q^{78} +(2.39071e10 - 4.14083e10i) q^{79} +(-1.07194e9 - 1.85665e9i) q^{80} +(-1.66521e10 + 2.65985e10i) q^{81} +(-3.46090e10 - 1.99815e10i) q^{82} +1.87924e10 q^{83} +(-1.78999e10 + 6.84739e9i) q^{84} +8.67502e9 q^{85} +(-1.66603e10 - 9.61881e9i) q^{86} +(3.40240e10 + 2.00514e10i) q^{87} +(-8.54881e9 - 1.48070e10i) q^{88} +(-5.08228e10 + 8.80276e10i) q^{89} +(-9.93202e9 - 5.97351e9i) q^{90} +(-3.69614e10 - 9.40922e10i) q^{91} -6.76533e7i q^{92} +(7.06277e8 - 7.90055e10i) q^{93} +(-3.19938e10 + 1.84716e10i) q^{94} +(-1.06185e10 + 6.13060e9i) q^{95} +(1.26246e8 - 1.41221e10i) q^{96} -9.98947e7i q^{97} +(-6.16795e10 + 1.41173e10i) q^{98} +(-7.92089e10 - 4.76394e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 30720 q^{4} - 95298 q^{7} - 91434 q^{9} + 245184 q^{10} - 8480820 q^{15} - 31457280 q^{16} + 12170496 q^{18} + 1649724 q^{19} + 43254216 q^{21} + 20705664 q^{22} + 4521984 q^{24} - 336132444 q^{25}+ \cdots + 288758042496 q^{99}+O(q^{100}) \) 60 * q + 30720 * q^4 - 95298 * q^7 - 91434 * q^9 + 245184 * q^10 - 8480820 * q^15 - 31457280 * q^16 + 12170496 * q^18 + 1649724 * q^19 + 43254216 * q^21 + 20705664 * q^22 + 4521984 * q^24 - 336132444 * q^25 + 28121088 * q^28 - 77109120 * q^30 - 275992974 * q^31 + 1056712914 * q^33 - 187256832 * q^36 + 555437556 * q^37 - 563926680 * q^39 + 251068416 * q^40 + 1167043776 * q^42 + 2546594304 * q^43 + 544480776 * q^45 - 452472192 * q^46 - 1309143414 * q^49 + 2007979044 * q^51 + 3219419136 * q^52 - 9840998592 * q^54 + 17053196256 * q^57 + 12235419456 * q^58 - 4342179840 * q^60 - 3056592000 * q^61 - 42499692960 * q^63 - 64424509440 * q^64 + 48796070400 * q^66 + 27979853436 * q^67 - 4966503360 * q^70 - 12462587904 * q^72 - 105678747168 * q^73 + 173211633504 * q^75 - 16600538880 * q^78 - 27787555926 * q^79 - 71399556486 * q^81 + 31231064832 * q^82 - 25272410112 * q^84 + 12868048152 * q^85 + 137017459998 * q^87 + 10601299968 * q^88 + 333571182180 * q^91 - 14607989424 * q^93 - 430917051648 * q^94 + 4630511616 * q^96 + 288758042496 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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