LMFDB - Embedded newform 42.12.f.a.5.15

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			5.15
Character	$\chi$	$=$	42.5
Dual form			42.12.f.a.17.15

$q$-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} +(420.827 + 7.21258i) q^{3} +(512.000 + 886.810i) q^{4} +(1974.84 - 3420.52i) q^{5} +(-11546.9 - 6933.11i) q^{6} +(-23996.1 + 37436.8i) q^{7} -32768.0i q^{8} +(177043. + 6070.49i) q^{9} +(-109457. + 63194.8i) q^{10} +(236474. - 136529. i) q^{11} +(209067. + 376886. i) q^{12} -2.06091e6i q^{13} +(1.26399e6 - 653541. i) q^{14} +(855735. - 1.42520e6i) q^{15} +(-524288. + 908093. i) q^{16} +(3.47811e6 + 6.02427e6i) q^{17} +(-4.80923e6 - 3.00092e6i) q^{18} +(-6.21305e6 - 3.58711e6i) q^{19} +4.04447e6 q^{20} +(-1.03682e7 + 1.55813e7i) q^{21} -8.73783e6 q^{22} +(4.02714e7 + 2.32507e7i) q^{23} +(236342. - 1.37896e7i) q^{24} +(1.66141e7 + 2.87765e7i) q^{25} +(-3.29745e7 + 5.71135e7i) q^{26} +(7.44606e7 + 3.83156e6i) q^{27} +(-4.54853e7 - 2.11234e6i) q^{28} -1.78411e8i q^{29} +(-4.65180e7 + 2.58046e7i) q^{30} +(-2.04194e8 + 1.17891e8i) q^{31} +(2.90590e7 - 1.67772e7i) q^{32} +(1.00499e8 - 5.57493e7i) q^{33} -2.22599e8i q^{34} +(8.06649e7 + 1.56011e8i) q^{35} +(8.52626e7 + 1.60112e8i) q^{36} +(3.49094e8 - 6.04648e8i) q^{37} +(1.14787e8 + 1.98818e8i) q^{38} +(1.48644e7 - 8.67284e8i) q^{39} +(-1.12084e8 - 6.47115e7i) q^{40} +9.63754e8 q^{41} +(5.36634e8 - 2.65911e8i) q^{42} +1.37357e9 q^{43} +(2.42150e8 + 1.39805e8i) q^{44} +(3.70395e8 - 5.93591e8i) q^{45} +(-7.44022e8 - 1.28868e9i) q^{46} +(5.11807e8 - 8.86476e8i) q^{47} +(-2.27184e8 + 3.78368e8i) q^{48} +(-8.25701e8 - 1.79667e9i) q^{49} -1.06330e9i q^{50} +(1.42023e9 + 2.56026e9i) q^{51} +(1.82763e9 - 1.05518e9i) q^{52} +(1.19635e9 - 6.90713e8i) q^{53} +(-2.00221e9 - 1.29755e9i) q^{54} -1.07849e9i q^{55} +(1.22673e9 + 7.86304e8i) q^{56} +(-2.58875e9 - 1.55436e9i) q^{57} +(-2.85458e9 + 4.94427e9i) q^{58} +(1.99175e9 + 3.44981e9i) q^{59} +(1.70202e9 + 2.91710e7i) q^{60} +(1.86097e8 + 1.07443e8i) q^{61} +7.54505e9 q^{62} +(-4.47560e9 + 6.48225e9i) q^{63} -1.07374e9 q^{64} +(-7.04936e9 - 4.06995e9i) q^{65} +(-3.67711e9 - 6.30223e7i) q^{66} +(-2.29114e9 - 3.96837e9i) q^{67} +(-3.56159e9 + 6.16885e9i) q^{68} +(1.67796e10 + 1.00750e10i) q^{69} +(2.60721e8 - 5.61413e9i) q^{70} -1.53014e10i q^{71} +(1.98918e8 - 5.80134e9i) q^{72} +(2.05988e10 - 1.18927e10i) q^{73} +(-1.93487e10 + 1.11710e10i) q^{74} +(6.78410e9 + 1.22297e10i) q^{75} -7.34640e9i q^{76} +(-5.63271e8 + 1.21290e10i) q^{77} +(-1.42885e10 + 2.37970e10i) q^{78} +(-1.04391e10 + 1.80811e10i) q^{79} +(2.07077e9 + 3.58667e9i) q^{80} +(3.13074e10 + 2.14948e9i) q^{81} +(-2.67083e10 - 1.54201e10i) q^{82} -5.49793e10 q^{83} +(-1.91262e10 - 1.21700e9i) q^{84} +2.74748e10 q^{85} +(-3.80655e10 - 2.19772e10i) q^{86} +(1.28680e9 - 7.50801e10i) q^{87} +(-4.47377e9 - 7.74880e9i) q^{88} +(2.99939e9 - 5.19509e9i) q^{89} +(-1.97621e10 + 1.05237e10i) q^{90} +(7.71537e10 + 4.94537e10i) q^{91} +4.76174e10i q^{92} +(-8.67805e10 + 4.81391e10i) q^{93} +(-2.83672e10 + 1.63778e10i) q^{94} +(-2.45395e10 + 1.41679e10i) q^{95} +(1.23498e10 - 6.85071e9i) q^{96} +1.46160e10i q^{97} +(-5.86429e9 + 6.30021e10i) q^{98} +(4.26949e10 - 2.27359e10i) 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
$3$	420.827	+	7.21258i	0.999853	+	0.0171366i
$3$	420.827	+	7.21258i	0.999853	+	0.0171366i
$4$	512.000	+	886.810i	0.250000	+	0.433013i
$5$	1974.84	−	3420.52i	0.282616	−	0.489505i	−0.689412	−	0.724369i	$-0.742131\pi$
$5$	1974.84	−	3420.52i	0.282616	−	0.489505i	0.972028	+	0.234864i	$0.0754645\pi$
$6$	−11546.9	−	6933.11i	−0.606224	−	0.363995i
$7$	−23996.1	+	37436.8i	−0.539637	+	0.841898i
$7$	−23996.1	+	37436.8i	−0.539637	+	0.841898i
$8$		−	32768.0i		−	0.353553i
$9$	177043.	+	6070.49i	0.999413	+	0.0342681i
$10$	−109457.	+	63194.8i	−0.346132	+	0.199839i
$11$	236474.	−	136529.i	0.442715	−	0.255602i	−0.262033	−	0.965059i	$-0.584393\pi$
$11$	236474.	−	136529.i	0.442715	−	0.255602i	0.704749	+	0.709457i	$0.251060\pi$
$12$	209067.	+	376886.i	0.242543	+	0.437233i
$13$		−	2.06091e6i		−	1.53946i	−0.638367	−	0.769732i	$-0.720390\pi$
$13$		−	2.06091e6i		−	1.53946i	0.638367	−	0.769732i	$-0.279610\pi$
$14$	1.26399e6	−	653541.i	0.628115	−	0.324765i
$15$	855735.	−	1.42520e6i	0.290963	−	0.484590i
$16$	−524288.	+	908093.i	−0.125000	+	0.216506i
$17$	3.47811e6	+	6.02427e6i	0.594121	+	1.02905i	0.993670	+	0.112336i	$0.0358332\pi$
$17$	3.47811e6	+	6.02427e6i	0.594121	+	1.02905i	−0.399549	+	0.916712i	$0.630833\pi$
$18$	−4.80923e6	−	3.00092e6i	−0.599897	−	0.374331i
$19$	−6.21305e6	−	3.58711e6i	−0.575652	−	0.332353i	0.183751	−	0.982973i	$-0.441176\pi$
$19$	−6.21305e6	−	3.58711e6i	−0.575652	−	0.332353i	−0.759404	+	0.650620i	$0.774509\pi$
$20$	4.04447e6			0.282616
$21$	−1.03682e7	+	1.55813e7i	−0.553985	+	0.832527i
$22$	−8.73783e6			−0.361476
$23$	4.02714e7	+	2.32507e7i	1.30465	+	0.753239i	0.981197	−	0.193006i	$-0.0618238\pi$
$23$	4.02714e7	+	2.32507e7i	1.30465	+	0.753239i	0.323450	+	0.946245i	$0.395157\pi$
$24$	236342.	−	1.37896e7i	0.00605869	−	0.353501i
$25$	1.66141e7	+	2.87765e7i	0.340257	+	0.589342i
$26$	−3.29745e7	+	5.71135e7i	−0.544283	+	0.942725i
$27$	7.44606e7	+	3.83156e6i	0.998679	+	0.0513896i
$28$	−4.54853e7	−	2.11234e6i	−0.499462	−	0.0231950i
$29$		−	1.78411e8i		−	1.61522i	−0.589714	−	0.807612i	$-0.700759\pi$
$29$		−	1.78411e8i		−	1.61522i	0.589714	−	0.807612i	$-0.299241\pi$
$30$	−4.65180e7	+	2.58046e7i	−0.349506	+	0.193879i
$31$	−2.04194e8	+	1.17891e8i	−1.28101	+	0.739593i	−0.977034	−	0.213085i	$-0.931649\pi$
$31$	−2.04194e8	+	1.17891e8i	−1.28101	+	0.739593i	−0.303979	+	0.952679i	$0.598315\pi$
$32$	2.90590e7	−	1.67772e7i	0.153093	−	0.0883883i
$33$	1.00499e8	−	5.57493e7i	0.447030	−	0.247978i
$34$		−	2.22599e8i		−	0.840214i
$35$	8.06649e7	+	1.56011e8i	0.259603	+	0.502088i
$36$	8.52626e7	+	1.60112e8i	0.235015	+	0.441325i
$37$	3.49094e8	−	6.04648e8i	0.827623	−	1.43349i	−0.0722747	−	0.997385i	$-0.523026\pi$
$37$	3.49094e8	−	6.04648e8i	0.827623	−	1.43349i	0.899898	−	0.436101i	$-0.143641\pi$
$38$	1.14787e8	+	1.98818e8i	0.235009	+	0.407048i
$39$	1.48644e7	−	8.67284e8i	0.0263811	−	1.53924i
$40$	−1.12084e8	−	6.47115e7i	−0.173066	−	0.0999197i
$41$	9.63754e8			1.29914			0.649569	−	0.760303i	$-0.274950\pi$
$41$	9.63754e8			1.29914			0.649569	+	0.760303i	$0.274950\pi$
$42$	5.36634e8	−	2.65911e8i	0.633588	−	0.313953i
$43$	1.37357e9			1.42487			0.712434	−	0.701739i	$-0.247593\pi$
$43$	1.37357e9			1.42487			0.712434	+	0.701739i	$0.247593\pi$
$44$	2.42150e8	+	1.39805e8i	0.221358	+	0.127801i
$45$	3.70395e8	−	5.93591e8i	0.299224	−	0.479533i
$46$	−7.44022e8	−	1.28868e9i	−0.532620	−	0.922525i
$47$	5.11807e8	−	8.86476e8i	0.325513	−	0.563805i	−0.656103	−	0.754671i	$-0.727796\pi$
$47$	5.11807e8	−	8.86476e8i	0.325513	−	0.563805i	0.981616	+	0.190866i	$0.0611298\pi$
$48$	−2.27184e8	+	3.78368e8i	−0.128692	+	0.214332i
$49$	−8.25701e8	−	1.79667e9i	−0.417585	−	0.908638i
$50$		−	1.06330e9i		−	0.481196i
$51$	1.42023e9	+	2.56026e9i	0.576399	+	1.03908i
$52$	1.82763e9	−	1.05518e9i	0.666607	−	0.384866i
$53$	1.19635e9	−	6.90713e8i	0.392953	−	0.226872i	−0.290486	−	0.956879i	$-0.593817\pi$
$53$	1.19635e9	−	6.90713e8i	0.392953	−	0.226872i	0.683439	+	0.730008i	$0.260484\pi$
$54$	−2.00221e9	−	1.29755e9i	−0.593394	−	0.384556i
$55$		−	1.07849e9i		−	0.288948i
$56$	1.22673e9	+	7.86304e8i	0.297656	+	0.190790i
$57$	−2.58875e9	−	1.55436e9i	−0.569872	−	0.342169i
$58$	−2.85458e9	+	4.94427e9i	−0.571068	+	0.989119i
$59$	1.99175e9	+	3.44981e9i	0.362701	+	0.628216i	0.988404	−	0.151845i	$-0.0485215\pi$
$59$	1.99175e9	+	3.44981e9i	0.362701	+	0.628216i	−0.625704	+	0.780061i	$0.715188\pi$
$60$	1.70202e9	+	2.91710e7i	0.282574	+	0.00484306i
$61$	1.86097e8	+	1.07443e8i	0.0282114	+	0.0162879i	0.514039	−	0.857767i	$-0.328149\pi$
$61$	1.86097e8	+	1.07443e8i	0.0282114	+	0.0162879i	−0.485828	+	0.874054i	$0.661482\pi$
$62$	7.54505e9			1.04594
$63$	−4.47560e9	+	6.48225e9i	−0.568170	+	0.822911i
$64$	−1.07374e9			−0.125000
$65$	−7.04936e9	−	4.06995e9i	−0.753575	−	0.435077i
$66$	−3.67711e9	−	6.30223e7i	−0.361422	−	0.00619445i
$67$	−2.29114e9	−	3.96837e9i	−0.207319	−	0.359088i	0.743550	−	0.668680i	$-0.233141\pi$
$67$	−2.29114e9	−	3.96837e9i	−0.207319	−	0.359088i	−0.950869	+	0.309593i	$0.899807\pi$
$68$	−3.56159e9	+	6.16885e9i	−0.297060	+	0.514524i
$69$	1.67796e10	+	1.00750e10i	1.29155	+	0.775485i
$70$	2.60721e8	−	5.61413e9i	0.0185411	−	0.399249i
$71$		−	1.53014e10i		−	1.00649i	−0.864143	−	0.503247i	$-0.832139\pi$
$71$		−	1.53014e10i		−	1.00649i	0.864143	−	0.503247i	$-0.167861\pi$
$72$	1.98918e8	−	5.80134e9i	0.0121156	−	0.353346i
$73$	2.05988e10	−	1.18927e10i	1.16296	−	0.671438i	0.210952	−	0.977497i	$-0.432344\pi$
$73$	2.05988e10	−	1.18927e10i	1.16296	−	0.671438i	0.952013	+	0.306059i	$0.0990104\pi$
$74$	−1.93487e10	+	1.11710e10i	−1.01363	+	0.585218i
$75$	6.78410e9	+	1.22297e10i	0.330107	+	0.595086i
$76$		−	7.34640e9i		−	0.332353i
$77$	−5.63271e8	+	1.21290e10i	−0.0237148	+	0.510653i
$78$	−1.42885e10	+	2.37970e10i	−0.560358	+	0.933260i
$79$	−1.04391e10	+	1.80811e10i	−0.381694	+	0.661113i	−0.991305	−	0.131588i	$-0.957993\pi$
$79$	−1.04391e10	+	1.80811e10i	−0.381694	+	0.661113i	0.609611	+	0.792701i	$0.291326\pi$
$80$	2.07077e9	+	3.58667e9i	0.0706539	+	0.122376i
$81$	3.13074e10	+	2.14948e9i	0.997651	+	0.0684959i
$82$	−2.67083e10	−	1.54201e10i	−0.795556	−	0.459314i
$83$	−5.49793e10			−1.53204			−0.766019	−	0.642818i	$-0.777765\pi$
$83$	−5.49793e10			−1.53204			−0.766019	+	0.642818i	$0.777765\pi$
$84$	−1.91262e10	−	1.21700e9i	−0.498991	−	0.0317507i
$85$	2.74748e10			0.671632
$86$	−3.80655e10	−	2.19772e10i	−0.872550	−	0.503767i
$87$	1.28680e9	−	7.50801e10i	0.0276794	−	1.61499i
$88$	−4.47377e9	−	7.74880e9i	−0.0903689	−	0.156524i
$89$	2.99939e9	−	5.19509e9i	0.0569361	−	0.0986162i	−0.836153	−	0.548497i	$-0.815200\pi$
$89$	2.99939e9	−	5.19509e9i	0.0569361	−	0.0986162i	0.893089	+	0.449881i	$0.148534\pi$
$90$	−1.97621e10	+	1.05237e10i	−0.352777	+	0.187861i
$91$	7.71537e10	+	4.94537e10i	1.29607	+	0.830751i
$92$			4.76174e10i			0.753239i
$93$	−8.67805e10	+	4.81391e10i	−1.29350	+	0.717532i
$94$	−2.83672e10	+	1.63778e10i	−0.398670	+	0.230172i
$95$	−2.45395e10	+	1.41679e10i	−0.325377	+	0.187856i
$96$	1.23498e10	−	6.85071e9i	0.154585	−	0.0857519i
$97$			1.46160e10i			0.172816i	0.996260	+	0.0864078i	$0.0275388\pi$
$97$			1.46160e10i			0.172816i	−0.996260	+	0.0864078i	$0.972461\pi$
$98$	−5.86429e9	+	6.30021e10i	−0.0655348	+	0.704063i
$99$	4.26949e10	−	2.27359e10i	0.451214	−	0.240281i
$100$	−1.70128e10	+	2.94671e10i	−0.170128	+	0.294671i
$101$	3.28136e10	+	5.68348e10i	0.310660	+	0.538080i	0.978506	−	0.206221i	$-0.0661165\pi$
$101$	3.28136e10	+	5.68348e10i	0.310660	+	0.538080i	−0.667845	+	0.744300i	$0.732783\pi$
$102$	1.60552e9	−	9.36757e10i	0.0143984	−	0.840090i
$103$	−2.16714e10	−	1.25120e10i	−0.184197	−	0.106346i	0.405066	−	0.914287i	$-0.367249\pi$
$103$	−2.16714e10	−	1.25120e10i	−0.184197	−	0.106346i	−0.589263	+	0.807941i	$0.700582\pi$
$104$	−6.75317e10			−0.544283
$105$	3.28207e10	+	6.62352e10i	0.250961	+	0.506463i
$106$	−4.42056e10			−0.320845
$107$	−1.16079e9	−	6.70182e8i	−0.00800097	−	0.00461936i	0.495994	−	0.868326i	$-0.334804\pi$
$107$	−1.16079e9	−	6.70182e8i	−0.00800097	−	0.00461936i	−0.503995	+	0.863706i	$0.668137\pi$
$108$	3.47260e10	+	6.79942e10i	0.227417	+	0.445288i
$109$	3.13597e10	+	5.43166e10i	0.195221	+	0.338132i	0.946973	−	0.321314i	$-0.104124\pi$
$109$	3.13597e10	+	5.43166e10i	0.195221	+	0.338132i	−0.751752	+	0.659446i	$0.770791\pi$
$110$	−1.72558e10	+	2.98879e10i	−0.102159	+	0.176944i
$111$	1.51269e11	−	2.51934e11i	0.852067	−	1.41909i
$112$	−2.14152e10	−	4.14184e10i	−0.114822	−	0.222072i
$113$			8.00709e10i			0.408830i	0.978884	+	0.204415i	$0.0655292\pi$
$113$			8.00709e10i			0.408830i	−0.978884	+	0.204415i	$0.934471\pi$
$114$	4.68716e10	+	8.44957e10i	0.227999	+	0.411015i
$115$	1.59059e11	−	9.18326e10i	0.737428	−	0.425754i
$116$	1.58217e11	−	9.13465e10i	0.699413	−	0.403806i
$117$	1.25107e10	−	3.64869e11i	0.0527545	−	1.53856i
$118$		−	1.27472e11i		−	0.512936i
$119$	−3.08991e11	−	1.43495e10i	−1.18696	−	0.0551226i
$120$	−4.67010e10	−	2.80407e10i	−0.171328	−	0.102871i
$121$	−1.05376e11	+	1.82516e11i	−0.369335	+	0.639708i
$122$	−3.43818e9	−	5.95510e9i	−0.0115173	−	0.0199485i
$123$	4.05573e11	+	6.95115e9i	1.29895	+	0.0222628i
$124$	−2.09095e11	−	1.20721e11i	−0.640506	−	0.369797i
$125$	3.24096e11			0.949879
$126$	2.27748e11	−	1.08032e11i	0.638875	−	0.303050i
$127$	−4.77607e11			−1.28277			−0.641387	−	0.767218i	$-0.721641\pi$
$127$	−4.77607e11			−1.28277			−0.641387	+	0.767218i	$0.721641\pi$
$128$	2.97564e10	+	1.71799e10i	0.0765466	+	0.0441942i
$129$	5.78036e11	+	9.90700e9i	1.42466	+	0.0244174i
$130$	1.30238e11	+	2.25580e11i	0.307646	+	0.532858i
$131$	−1.09330e11	+	1.89365e11i	−0.247597	+	0.428851i	−0.962859	−	0.270006i	$-0.912974\pi$
$131$	−1.09330e11	+	1.89365e11i	−0.247597	+	0.428851i	0.715261	+	0.698857i	$0.246308\pi$
$132$	1.00895e11	+	6.05803e10i	0.219135	+	0.131575i
$133$	2.83379e11	−	1.46520e11i	0.590450	−	0.305291i
$134$			1.46633e11i			0.293194i
$135$	1.60153e11	−	2.47127e11i	0.307398	−	0.474335i
$136$	1.97403e11	−	1.13971e11i	0.363823	−	0.210053i
$137$	−1.93361e11	+	1.11637e11i	−0.342298	+	0.197626i	−0.661288	−	0.750132i	$-0.729990\pi$
$137$	−1.93361e11	+	1.11637e11i	−0.342298	+	0.197626i	0.318990	+	0.947758i	$0.396657\pi$
$138$	−3.03809e11	−	5.47679e11i	−0.516733	−	0.931517i
$139$			6.77238e10i			0.110703i	0.998467	+	0.0553516i	$0.0176280\pi$
$139$			6.77238e10i			0.110703i	−0.998467	+	0.0553516i	$0.982372\pi$
$140$	−9.70514e10	+	1.51412e11i	−0.152510	+	0.237934i
$141$	2.21776e11	−	3.69361e11i	0.335127	−	0.558144i
$142$	−2.44823e11	+	4.24046e11i	−0.355849	+	0.616349i
$143$	−2.81373e11	−	4.87351e11i	−0.393490	−	0.681544i
$144$	−9.83341e10	+	1.57589e11i	−0.132346	+	0.212096i
$145$	−6.10259e11	−	3.52333e11i	−0.790660	−	0.456488i
$146$	−7.61135e11			−0.949556
$147$	−3.34518e11	−	7.62044e11i	−0.401952	−	0.915661i
$148$	7.14944e11			0.827623
$149$	4.16717e11	+	2.40592e11i	0.464854	+	0.268384i	0.714083	−	0.700061i	$-0.246844\pi$
$149$	4.16717e11	+	2.40592e11i	0.464854	+	0.268384i	−0.249229	+	0.968445i	$0.580177\pi$
$150$	7.66915e9	−	4.47466e11i	0.00824604	−	0.481125i
$151$	1.49178e11	+	2.58385e11i	0.154644	+	0.267851i	0.932929	−	0.360060i	$-0.117244\pi$
$151$	1.49178e11	+	2.58385e11i	0.154644	+	0.267851i	−0.778285	+	0.627911i	$0.783910\pi$
$152$	−1.17542e11	+	2.03589e11i	−0.117505	+	0.203524i
$153$	5.79205e11	+	1.08767e12i	0.558508	+	1.04880i
$154$	2.09674e11	−	3.27116e11i	0.195065	−	0.304326i
$155$			9.31266e11i			0.836083i
$156$	7.76726e11	−	4.30867e11i	0.673105	−	0.373386i
$157$	4.53307e11	−	2.61717e11i	0.379267	−	0.218970i	−0.298233	−	0.954493i	$-0.596397\pi$
$157$	4.53307e11	−	2.61717e11i	0.379267	−	0.218970i	0.677499	+	0.735524i	$0.263064\pi$
$158$	5.78595e11	−	3.34052e11i	0.467478	−	0.269898i
$159$	5.08438e11	−	2.82042e11i	0.396783	−	0.220105i
$160$		−	1.32529e11i		−	0.0999197i
$161$	−1.83679e12	+	9.49705e11i	−1.33819	+	0.691905i
$162$	−8.33223e11	−	5.60486e11i	−0.586717	−	0.394668i
$163$	−2.63756e11	+	4.56839e11i	−0.179544	+	0.310979i	−0.941724	−	0.336386i	$-0.890795\pi$
$163$	−2.63756e11	+	4.56839e11i	−0.179544	+	0.310979i	0.762181	+	0.647364i	$0.224129\pi$
$164$	4.93442e11	+	8.54667e11i	0.324784	+	0.562543i
$165$	7.77868e9	−	4.53856e11i	0.00495158	−	0.288906i
$166$	1.52363e12	+	8.79668e11i	0.938178	+	0.541657i
$167$	−1.00327e12			−0.597690			−0.298845	−	0.954302i	$-0.596601\pi$
$167$	−1.00327e12			−0.597690			−0.298845	+	0.954302i	$0.596601\pi$
$168$	5.10569e11	+	3.39746e11i	0.294343	+	0.195863i
$169$	−2.45517e12			−1.36995
$170$	−7.61405e11	−	4.39597e11i	−0.411289	−	0.237458i
$171$	−1.07820e12	−	6.72788e11i	−0.563925	−	0.351884i
$172$	7.03269e11	+	1.21810e12i	0.356217	+	0.616986i
$173$	−1.40490e12	+	2.43336e12i	−0.689273	+	1.19386i	0.282800	+	0.959179i	$0.408737\pi$
$173$	−1.40490e12	+	2.43336e12i	−0.689273	+	1.19386i	−0.972073	+	0.234677i	$0.924597\pi$
$174$	−1.23694e12	+	2.06009e12i	−0.587934	+	0.979188i
$175$	−1.47597e12	−	6.85442e10i	−0.679781	−	0.0315690i
$176$			2.86321e11i			0.127801i
$177$	8.13298e11	+	1.46614e12i	0.351882	+	0.634339i
$178$	−1.66243e11	+	9.59804e10i	−0.0697322	+	0.0402599i
$179$	−3.85507e12	+	2.22572e12i	−1.56798	+	0.905273i	−0.571574	+	0.820551i	$0.693667\pi$
$179$	−3.85507e12	+	2.22572e12i	−1.56798	+	0.905273i	−0.996405	+	0.0847223i	$0.973000\pi$
$180$	7.16044e11	+	2.45519e10i	0.282450	+	0.00968470i
$181$			1.74543e12i			0.667838i	0.942602	+	0.333919i	$0.108371\pi$
$181$			1.74543e12i			0.667838i	−0.942602	+	0.333919i	$0.891629\pi$
$182$	−1.34689e12	−	2.60496e12i	−0.499964	−	0.966960i
$183$	7.75396e10	+	4.65571e10i	0.0279282	+	0.0167689i
$184$	7.61878e11	−	1.31961e12i	0.266310	−	0.461263i
$185$	−1.37881e12	−	2.38816e12i	−0.467799	−	0.810251i
$186$	3.17516e12	+	5.44193e10i	1.04579	+	0.0179239i
$187$	1.64497e12	+	9.49724e11i	0.526053	+	0.303717i
$188$	1.04818e12			0.325513
$189$	−1.93021e12	+	2.69562e12i	−0.582188	+	0.813054i
$190$	9.06746e11			0.265669
$191$	2.84809e12	+	1.64435e12i	0.810720	+	0.468069i	0.847206	−	0.531265i	$-0.178283\pi$
$191$	2.84809e12	+	1.64435e12i	0.810720	+	0.468069i	−0.0364861	+	0.999334i	$0.511616\pi$
$192$	−4.51859e11	−	7.74445e9i	−0.124982	−	0.00214207i
$193$	−1.75689e12	−	3.04303e12i	−0.472259	−	0.817977i	0.527237	−	0.849718i	$-0.323228\pi$
$193$	−1.75689e12	−	3.04303e12i	−0.472259	−	0.817977i	−0.999496	+	0.0317412i	$0.989895\pi$
$194$	2.33855e11	−	4.05049e11i	0.0610995	−	0.105827i
$195$	−2.93720e12	−	1.76359e12i	−0.746009	−	0.447927i
$196$	1.17055e12	−	1.65214e12i	0.289056	−	0.407979i
$197$		−	4.84901e12i		−	1.16436i	−0.813059	−	0.582182i	$-0.802199\pi$
$197$		−	4.84901e12i		−	1.16436i	0.813059	−	0.582182i	$-0.197801\pi$
$198$	−1.54697e12	−	5.30429e10i	−0.361263	−	0.0123871i
$199$	2.95956e12	−	1.70871e12i	0.672258	−	0.388128i	−0.124674	−	0.992198i	$-0.539788\pi$
$199$	2.95956e12	−	1.70871e12i	0.672258	−	0.388128i	0.796932	+	0.604070i	$0.206455\pi$
$200$	9.42947e11	−	5.44411e11i	0.208364	−	0.120299i
$201$	−9.35549e11	−	1.68652e12i	−0.201135	−	0.362588i
$202$		−	2.10007e12i		−	0.439340i
$203$	6.67914e12	+	4.28117e12i	1.35985	+	0.871635i
$204$	−1.54330e12	+	2.57033e12i	−0.305834	+	0.509358i
$205$	1.90326e12	−	3.29654e12i	0.367157	−	0.635934i
$206$	4.00384e11	+	6.93486e11i	0.0751982	+	0.130247i
$207$	6.98862e12	+	4.36084e12i	1.27807	+	0.797504i
$208$	1.87149e12	+	1.08051e12i	0.333304	+	0.192433i
$209$	−1.95897e12			−0.339800
$210$	1.50211e11	−	2.36070e12i	0.0253802	−	0.398872i
$211$	−9.78850e12			−1.61125			−0.805625	−	0.592426i	$-0.798170\pi$
$211$	−9.78850e12			−1.61125			−0.805625	+	0.592426i	$0.798170\pi$
$212$	1.22506e12	+	7.07290e11i	0.196477	+	0.113436i
$213$	1.10363e11	−	6.43925e12i	0.0172478	−	1.00635i
$214$	2.14458e10	+	3.71453e10i	0.00326638	+	0.00565754i
$215$	2.71258e12	−	4.69833e12i	0.402690	−	0.697480i
$216$	1.25553e11	−	2.43992e12i	0.0181690	−	0.353086i
$217$	4.86380e11	−	1.04733e13i	0.0686195	−	1.47759i
$218$		−	2.00702e12i		−	0.276084i
$219$	8.75430e12	−	4.85620e12i	1.17430	−	0.651410i
$220$	9.56413e11	−	5.52185e11i	0.125118	−	0.0722371i
$221$	1.24154e13	−	7.16806e12i	1.58418	−	0.914628i
$222$	−8.22304e12	+	4.56150e12i	−1.02351	+	0.567762i
$223$			1.08303e13i			1.31511i	0.753405	+	0.657557i	$0.228410\pi$
$223$			1.08303e13i			1.31511i	−0.753405	+	0.657557i	$0.771590\pi$
$224$	−6.92172e10	+	1.49046e12i	−0.00820068	+	0.176586i
$225$	2.76672e12	+	5.19553e12i	0.319861	+	0.600656i
$226$	1.28113e12	−	2.21899e12i	0.144543	−	0.250356i
$227$	2.98627e12	+	5.17236e12i	0.328841	+	0.569570i	0.982282	−	0.187408i	$-0.0600086\pi$
$227$	2.98627e12	+	5.17236e12i	0.328841	+	0.569570i	−0.653441	+	0.756977i	$0.726675\pi$
$228$	5.29865e10	−	3.09156e12i	0.00569539	−	0.332304i
$229$	2.99333e12	+	1.72820e12i	0.314094	+	0.181342i	0.648757	−	0.760996i	$-0.275289\pi$
$229$	2.99333e12	+	1.72820e12i	0.314094	+	0.181342i	−0.334663	+	0.942338i	$0.608622\pi$
$230$	−5.87729e12			−0.602107
$231$	−3.24521e11	+	5.10014e12i	−0.0324621	+	0.510172i
$232$	−5.84618e12			−0.571068
$233$	4.40106e12	+	2.54095e12i	0.419856	+	0.242404i	0.695016	−	0.718995i	$-0.255397\pi$
$233$	4.40106e12	+	2.54095e12i	0.419856	+	0.242404i	−0.275160	+	0.961398i	$0.588731\pi$
$234$	−6.18461e12	+	9.91137e12i	−0.576268	+	0.923520i
$235$	−2.02147e12	−	3.50129e12i	−0.183990	−	0.318680i
$236$	−2.03955e12	+	3.53260e12i	−0.181350	+	0.314108i
$237$	−4.52348e12	+	7.53372e12i	−0.392967	+	0.654475i
$238$	8.33341e12	+	5.34152e12i	0.707374	+	0.453410i
$239$		−	2.24883e13i		−	1.86539i	−0.360672	−	0.932693i	$-0.617453\pi$
$239$		−	2.24883e13i		−	1.86539i	0.360672	−	0.932693i	$-0.382547\pi$
$240$	8.45565e11	+	1.52430e12i	0.0685464	+	0.123569i
$241$	−1.07700e13	+	6.21804e12i	−0.853337	+	0.492674i	−0.861775	−	0.507290i	$-0.830647\pi$
$241$	−1.07700e13	+	6.21804e12i	−0.853337	+	0.492674i	0.00843852	+	0.999964i	$0.497314\pi$
$242$	5.84051e12	−	3.37202e12i	0.452342	−	0.261160i
$243$	1.31595e13	+	1.13036e12i	0.996331	+	0.0855822i
$244$			2.20043e11i			0.0162879i
$245$	−7.77618e12	−	7.23813e11i	−0.562799	−	0.0523858i
$246$	−1.11284e13	−	6.68181e12i	−0.787568	−	0.472880i
$247$	−7.39269e12	+	1.28045e13i	−0.511645	+	0.886196i
$248$	3.86307e12	+	6.69103e12i	0.261486	+	0.452906i
$249$	−2.31367e13	−	3.96542e11i	−1.53181	−	0.0262539i
$250$	−8.98161e12	−	5.18553e12i	−0.581680	−	0.335833i
$251$	1.59949e13			1.01339			0.506694	−	0.862126i	$-0.330867\pi$
$251$	1.59949e13			1.01339			0.506694	+	0.862126i	$0.330867\pi$
$252$	−8.04003e12	−	6.50093e11i	−0.498374	−	0.0402970i
$253$	1.26975e13			0.770117
$254$	1.32358e13	+	7.64171e12i	0.785535	+	0.453529i
$255$	1.15621e13	+	1.98164e11i	0.671533	+	0.0115095i
$256$	−5.49756e11	−	9.52205e11i	−0.0312500	−	0.0541266i
$257$	−3.05291e12	+	5.28780e12i	−0.169856	+	0.294200i	−0.938369	−	0.345634i	$-0.887664\pi$
$257$	−3.05291e12	+	5.28780e12i	−0.169856	+	0.294200i	0.768513	+	0.639834i	$0.220997\pi$
$258$	−1.58605e13	−	9.52312e12i	−0.863789	−	0.518646i
$259$	1.42592e13	+	2.75782e13i	0.760233	+	1.47034i
$260$		−	8.33526e12i		−	0.435077i
$261$	1.08304e12	−	3.15864e13i	0.0553507	−	1.61428i
$262$	6.05967e12	−	3.49855e12i	0.303244	−	0.175078i
$263$	−3.05337e12	+	1.76286e12i	−0.149631	+	0.0863897i	−0.572946	−	0.819593i	$-0.694200\pi$
$263$	−3.05337e12	+	1.76286e12i	−0.149631	+	0.0863897i	0.423315	+	0.905983i	$0.360866\pi$
$264$	−1.82679e12	−	3.29317e12i	−0.0876733	−	0.158049i
$265$		−	5.45618e12i		−	0.256470i
$266$	−1.01975e13	−	4.73574e11i	−0.469512	−	0.0218042i
$267$	1.29969e12	−	2.16460e12i	0.0586177	−	0.0976260i
$268$	2.34613e12	−	4.06361e12i	0.103660	−	0.179544i
$269$	−6.25069e12	−	1.08265e13i	−0.270577	−	0.468653i	0.698433	−	0.715676i	$-0.253881\pi$
$269$	−6.25069e12	−	1.08265e13i	−0.270577	−	0.468653i	−0.969010	+	0.247023i	$0.920548\pi$
$270$	−8.39234e12	+	4.28613e12i	−0.355944	+	0.181788i
$271$	−1.58081e13	−	9.12680e12i	−0.656974	−	0.379304i	0.134149	−	0.990961i	$-0.457170\pi$
$271$	−1.58081e13	−	9.12680e12i	−0.656974	−	0.379304i	−0.791123	+	0.611657i	$0.790503\pi$
$272$	−7.29413e12			−0.297060
$273$	3.21116e13	+	2.13679e13i	1.28165	+	0.852839i
$274$	7.14475e12			0.279485
$275$	7.85762e12	+	4.53660e12i	0.301274	+	0.173940i
$276$	−3.43444e11	+	2.00387e13i	−0.0129079	+	0.753128i
$277$	−6.77480e12	−	1.17343e13i	−0.249608	−	0.432333i	0.713809	−	0.700340i	$-0.246968\pi$
$277$	−6.77480e12	−	1.17343e13i	−0.249608	−	0.432333i	−0.963417	+	0.268007i	$0.913635\pi$
$278$	1.08358e12	−	1.87682e12i	0.0391395	−	0.0677916i
$279$	−3.68668e13	+	1.96323e13i	−1.30561	+	0.695261i
$280$	5.11216e12	−	2.64323e12i	0.177515	−	0.0917836i
$281$		−	3.50825e13i		−	1.19455i	−0.802035	−	0.597276i	$-0.796250\pi$
$281$		−	3.50825e13i		−	1.19455i	0.802035	−	0.597276i	$-0.203750\pi$
$282$	−1.20558e13	+	6.68762e12i	−0.402556	+	0.223307i
$283$	−1.83880e12	+	1.06163e12i	−0.0602155	+	0.0347654i	−0.529805	−	0.848119i	$-0.677735\pi$
$283$	−1.83880e12	+	1.06163e12i	−0.0602155	+	0.0347654i	0.469590	+	0.882885i	$0.344402\pi$
$284$	1.35695e13	−	7.83433e12i	0.435825	−	0.251623i
$285$	−1.04291e13	+	5.78524e12i	−0.328548	+	0.182253i
$286$			1.80078e13i			0.556479i
$287$	−2.31263e13	+	3.60799e13i	−0.701062	+	1.09374i
$288$	5.24654e12	−	2.79389e12i	0.156032	−	0.0830902i
$289$	−7.05861e12	+	1.22259e13i	−0.205959	+	0.356732i
$290$	1.12747e13	+	1.95283e13i	0.322786	+	0.559081i
$291$	−1.05419e11	+	6.15078e12i	−0.00296146	+	0.172790i
$292$	2.10932e13	+	1.21782e13i	0.581482	+	0.335719i
$293$	−6.06686e13			−1.64132			−0.820658	−	0.571419i	$-0.806393\pi$
$293$	−6.06686e13			−1.64132			−0.820658	+	0.571419i	$0.806393\pi$
$294$	−2.92226e12	+	2.64707e13i	−0.0775904	+	0.702837i
$295$	1.57335e13			0.410020
$296$	−1.98131e13	−	1.14391e13i	−0.506814	−	0.292609i
$297$	1.81311e13	−	9.25994e12i	0.455266	−	0.232513i
$298$	−7.69894e12	−	1.33349e13i	−0.189776	−	0.328702i
$299$	4.79175e13	−	8.29955e13i	1.15958	−	2.00846i
$300$	−7.37199e12	+	1.22778e13i	−0.175153	+	0.291712i
$301$	−3.29604e13	+	5.14221e13i	−0.768911	+	1.19959i
$302$		−	9.54742e12i		−	0.218699i
$303$	1.33989e13	+	2.41543e13i	0.301394	+	0.543324i
$304$	6.51486e12	−	3.76135e12i	0.143913	−	0.0830882i
$305$	7.35022e11	−	4.24365e11i	0.0159460	−	0.00920642i
$306$	1.35129e12	−	3.94096e13i	0.0287925	−	0.839720i
$307$			3.40325e13i			0.712250i	0.934438	+	0.356125i	$0.115902\pi$
$307$			3.40325e13i			0.712250i	−0.934438	+	0.356125i	$0.884098\pi$
$308$	−1.10445e13	+	5.71053e12i	−0.227048	+	0.117395i
$309$	−9.02968e12	−	5.42169e12i	−0.182348	−	0.109487i
$310$	1.49002e13	−	2.58080e13i	0.295600	−	0.511994i
$311$	3.28904e13	+	5.69678e13i	0.641042	+	1.11032i	0.985200	+	0.171406i	$0.0548310\pi$
$311$	3.28904e13	+	5.69678e13i	0.641042	+	1.11032i	−0.344158	+	0.938912i	$0.611836\pi$
$312$	−2.84191e13	−	4.87078e11i	−0.544203	−	0.00932714i
$313$	−7.38504e13	−	4.26375e13i	−1.38950	−	0.802229i	−0.396242	−	0.918146i	$-0.629686\pi$
$313$	−7.38504e13	−	4.26375e13i	−1.38950	−	0.802229i	−0.993259	+	0.115917i	$0.963019\pi$
$314$	−1.67499e13			−0.309670
$315$	1.33341e13	+	2.81103e13i	0.242245	+	0.510690i
$316$	−2.13793e13			−0.381694
$317$	7.21498e13	+	4.16557e13i	1.26593	+	0.730884i	0.974215	−	0.225621i	$-0.0724412\pi$
$317$	7.21498e13	+	4.16557e13i	1.26593	+	0.730884i	0.291714	+	0.956506i	$0.405775\pi$
$318$	−1.86029e13	−	3.18837e11i	−0.320798	−	0.00549818i
$319$	−2.43582e13	−	4.21897e13i	−0.412854	−	0.715085i
$320$	−2.12047e12	+	3.67275e12i	−0.0353270	+	0.0611881i
$321$	−4.83657e11	−	2.90403e11i	−0.00792063	−	0.00475579i
$322$	6.60978e13	+	3.06958e12i	1.06409	+	0.0494165i
$323$		−	4.99055e13i		−	0.789831i
$324$	1.41232e13	+	2.88642e13i	0.219753	+	0.449120i
$325$	5.93056e13	−	3.42401e13i	0.907271	−	0.523813i
$326$	1.46188e13	−	8.44019e12i	0.219895	−	0.126957i
$327$	1.28052e13	+	2.30840e13i	0.189398	+	0.341428i
$328$		−	3.15803e13i		−	0.459314i
$329$	2.09054e13	+	4.04324e13i	0.299007	+	0.578298i
$330$	−7.47727e12	+	1.24532e13i	−0.105176	+	0.175167i
$331$	3.54928e13	−	6.14754e13i	0.491006	−	0.850447i	−0.508940	−	0.860802i	$-0.669963\pi$
$331$	3.54928e13	−	6.14754e13i	0.491006	−	0.850447i	0.999946	+	0.0103543i	$0.00329595\pi$
$332$	−2.81494e13	−	4.87562e13i	−0.383009	−	0.663392i
$333$	6.54751e13	−	1.04930e14i	0.876260	−	1.40428i
$334$	2.78034e13	+	1.60523e13i	0.366009	+	0.211315i
$335$	−1.80985e13			−0.234367
$336$	−8.71337e12	−	1.75844e13i	−0.110999	−	0.224007i
$337$	−1.53662e14			−1.92576			−0.962879	−	0.269932i	$-0.912999\pi$
$337$	−1.53662e14			−1.92576			−0.962879	+	0.269932i	$0.912999\pi$
$338$	6.80396e13	+	3.92827e13i	0.838919	+	0.484350i
$339$	−5.77518e11	+	3.36959e13i	−0.00700595	+	0.408770i
$340$	1.40671e13	+	2.43650e13i	0.167908	+	0.290825i
$341$	−3.21911e13	+	5.57566e13i	−0.378083	+	0.654858i
$342$	1.91154e13	+	3.58961e13i	0.220922	+	0.414862i
$343$	8.70753e13	+	1.22016e13i	0.990325	+	0.138771i
$344$		−	4.50092e13i		−	0.503767i
$345$	6.75985e13	−	3.74984e13i	0.744616	−	0.413055i
$346$	7.78674e13	−	4.49567e13i	0.844184	−	0.487390i
$347$	−2.37042e13	+	1.36856e13i	−0.252938	+	0.146034i	−0.621109	−	0.783724i	$-0.713317\pi$
$347$	−2.37042e13	+	1.36856e13i	−0.252938	+	0.146034i	0.368171	+	0.929758i	$0.379984\pi$
$348$	6.72407e13	−	3.72999e13i	0.706230	−	0.391761i
$349$		−	8.13141e13i		−	0.840671i	−0.907369	−	0.420335i	$-0.861912\pi$
$349$		−	8.13141e13i		−	0.840671i	0.907369	−	0.420335i	$-0.138088\pi$
$350$	3.98066e13	+	2.55151e13i	0.405118	+	0.259671i
$351$	7.89648e12	−	1.53456e14i	0.0791124	−	1.53743i
$352$	4.58114e12	−	7.93477e12i	0.0451844	−	0.0782618i
$353$	7.68687e13	+	1.33140e14i	0.746429	+	1.29285i	0.949524	+	0.313694i	$0.101567\pi$
$353$	7.68687e13	+	1.33140e14i	0.746429	+	1.29285i	−0.203095	+	0.979159i	$0.565100\pi$
$354$	9.19401e11	−	5.36435e13i	0.00878996	−	0.512861i
$355$	−5.23388e13	−	3.02178e13i	−0.492684	−	0.284451i
$356$	6.14275e12			0.0569361
$357$	−1.29928e14	−	8.26728e12i	−1.18584	−	0.0754549i
$358$	1.42446e14			1.28025
$359$	−5.76791e13	−	3.33011e13i	−0.510504	−	0.294740i	0.222537	−	0.974924i	$-0.428566\pi$
$359$	−5.76791e13	−	3.33011e13i	−0.510504	−	0.294740i	−0.733041	+	0.680185i	$0.761900\pi$
$360$	−1.94508e13	−	1.21371e13i	−0.169540	−	0.105792i
$361$	−3.25105e13	−	5.63098e13i	−0.279083	−	0.483386i
$362$	2.79269e13	−	4.83709e13i	0.236116	−	0.408965i
$363$	−4.56613e13	+	7.60476e13i	−0.380244	+	0.633285i
$364$	−4.35333e12	+	9.37410e13i	−0.0357079	+	0.768903i
$365$		−	9.39448e13i		−	0.759035i
$366$	−1.40393e12	−	2.53086e12i	−0.0111737	−	0.0201429i
$367$	−1.92518e14	+	1.11151e14i	−1.50942	+	0.871461i	−0.509476	+	0.860485i	$0.670161\pi$
$367$	−1.92518e14	+	1.11151e14i	−1.50942	+	0.871461i	−0.999940	+	0.0109763i	$0.996506\pi$
$368$	−4.22276e13	+	2.43801e13i	−0.326162	+	0.188310i
$369$	1.70626e14	+	5.85046e12i	1.29837	+	0.0445190i
$370$			8.82437e13i			0.661567i
$371$	−2.84965e12	+	6.13619e13i	−0.0210492	+	0.453255i
$372$	−8.71218e13	−	5.23106e13i	−0.634075	−	0.380718i
$373$	8.23867e13	−	1.42698e14i	0.590825	−	1.02334i	−0.403297	−	0.915069i	$-0.632136\pi$
$373$	8.23867e13	−	1.42698e14i	0.590825	−	1.02334i	0.994122	−	0.108269i	$-0.0345308\pi$
$374$	−3.03912e13	−	5.26391e13i	−0.214760	−	0.371975i
$375$	1.36388e14	+	2.33757e12i	0.949740	+	0.0162777i
$376$	−2.90480e13	−	1.67709e13i	−0.199335	−	0.115086i
$377$	−3.67688e14			−2.48658
$378$	9.66214e13	−	4.38200e13i	0.643974	−	0.292057i
$379$	−7.00895e13			−0.460402			−0.230201	−	0.973143i	$-0.573938\pi$
$379$	−7.00895e13			−0.460402			−0.230201	+	0.973143i	$0.573938\pi$
$380$	−2.51285e13	−	1.45079e13i	−0.162688	−	0.0939282i
$381$	−2.00990e14	−	3.44478e12i	−1.28259	−	0.0219823i
$382$	−5.26191e13	−	9.11390e13i	−0.330975	−	0.573265i
$383$	−1.31064e14	+	2.27010e14i	−0.812626	+	1.40751i	0.0983947	+	0.995147i	$0.468629\pi$
$383$	−1.31064e14	+	2.27010e14i	−0.812626	+	1.40751i	−0.911020	+	0.412361i	$0.864704\pi$
$384$	1.23984e13	+	7.44437e12i	0.0757780	+	0.0454994i
$385$	4.03751e13	+	2.58795e13i	0.243265	+	0.155927i
$386$			1.12441e14i			0.667876i
$387$	2.43181e14	+	8.33826e12i	1.42403	+	0.0488275i
$388$	−1.29616e13	+	7.48337e12i	−0.0748313	+	0.0432039i
$389$	4.67712e13	−	2.70034e13i	0.266229	−	0.153708i	−0.360944	−	0.932588i	$-0.617545\pi$
$389$	4.67712e13	−	2.70034e13i	0.266229	−	0.153708i	0.627173	+	0.778880i	$0.284212\pi$
$390$	5.31808e13	+	9.58693e13i	0.298469	+	0.538052i
$391$			3.23474e14i			1.79006i
$392$	−5.88734e13	+	2.70566e13i	−0.321252	+	0.147638i
$393$	−4.73747e13	+	7.89011e13i	−0.254910	+	0.424545i
$394$	−7.75841e13	+	1.34380e14i	−0.411665	+	0.713024i
$395$	4.12312e13	+	7.14145e13i	0.215745	+	0.373682i
$396$	4.20222e13	+	2.62215e13i	0.216848	+	0.135311i
$397$	−1.05076e14	−	6.06657e13i	−0.534757	−	0.308742i	0.208194	−	0.978087i	$-0.433241\pi$
$397$	−1.05076e14	−	6.06657e13i	−0.534757	−	0.308742i	−0.742951	+	0.669345i	$0.766575\pi$
$398$	−1.09357e14			−0.548896
$399$	1.20310e14	−	5.96157e13i	0.595595	−	0.295128i
$400$	−3.48423e13			−0.170128
$401$	−7.18249e13	−	4.14681e13i	−0.345924	−	0.199720i	0.316964	−	0.948437i	$-0.397336\pi$
$401$	−7.18249e13	−	4.14681e13i	−0.345924	−	0.199720i	−0.662889	+	0.748718i	$0.730670\pi$
$402$	−1.05760e12	+	6.17070e13i	−0.00502433	+	0.293151i
$403$	2.42963e14	+	4.20824e14i	1.13858	+	1.97207i
$404$	−3.36011e13	+	5.81988e13i	−0.155330	+	0.269040i
$405$	6.91793e13	−	1.02843e14i	0.315481	−	0.468997i
$406$	−1.16599e14	−	2.25510e14i	−0.524568	−	1.01455i
$407$		−	1.90645e14i		−	0.846168i
$408$	8.38946e13	−	4.65382e13i	0.367369	−	0.203788i
$409$	3.04964e14	−	1.76071e14i	1.31756	−	0.760694i	0.334226	−	0.942493i	$-0.391525\pi$
$409$	3.04964e14	−	1.76071e14i	1.31756	−	0.760694i	0.983336	+	0.181799i	$0.0581920\pi$
$410$	−1.05489e14	+	6.09043e13i	−0.449673	+	0.259619i
$411$	−8.21764e13	+	4.55851e13i	−0.345635	+	0.191731i
$412$		−	2.56246e13i		−	0.106346i
$413$	−1.76944e14	−	8.21728e12i	−0.724620	−	0.0336514i
$414$	−1.23901e14	−	2.32669e14i	−0.500694	−	0.940235i
$415$	−1.08575e14	+	1.88058e14i	−0.432978	+	0.749940i
$416$	−3.45762e13	−	5.98878e13i	−0.136071	−	0.235681i
$417$	−4.88464e11	+	2.85000e13i	−0.00189707	+	0.110687i
$418$	5.42886e13	+	3.13435e13i	0.208084	+	0.120137i
$419$	5.58121e12			0.0211131			0.0105565	−	0.999944i	$-0.496640\pi$
$419$	5.58121e12			0.0211131			0.0105565	+	0.999944i	$0.496640\pi$
$420$	−4.19339e13	+	6.30182e13i	−0.156565	+	0.235285i
$421$	1.42028e13			0.0523386			0.0261693	−	0.999658i	$-0.491669\pi$
$421$	1.42028e13			0.0523386			0.0261693	+	0.999658i	$0.491669\pi$
$422$	2.71267e14	+	1.56616e14i	0.986685	+	0.569663i
$423$	9.59932e13	−	1.53837e14i	0.344642	−	0.552319i
$424$	−2.26333e13	−	3.92020e13i	−0.0802113	−	0.138930i
$425$	−1.15571e14	+	2.00176e14i	−0.404307	+	0.700281i
$426$	−1.06086e14	+	1.76684e14i	−0.366359	+	0.610161i
$427$	−8.48792e12	+	4.38866e12i	−0.0289366	+	0.0149616i
$428$		−	1.37253e12i		−	0.00461936i
$429$	−1.14894e14	−	2.07120e14i	−0.381753	−	0.688187i
$430$	−1.50347e14	+	8.68026e13i	−0.493193	+	0.284745i
$431$	4.39799e14	−	2.53918e14i	1.42439	−	0.822372i	0.427720	−	0.903911i	$-0.359317\pi$
$431$	4.39799e14	−	2.53918e14i	1.42439	−	0.822372i	0.996670	+	0.0815396i	$0.0259837\pi$
$432$	−4.25182e13	+	6.56083e13i	−0.135961	+	0.209797i
$433$			7.00433e13i			0.221148i	0.993868	+	0.110574i	$0.0352689\pi$
$433$			7.00433e13i			0.221148i	−0.993868	+	0.110574i	$0.964731\pi$
$434$	−1.81052e14	+	2.82463e14i	−0.564429	+	0.880577i
$435$	−2.54272e14	−	1.52673e14i	−0.782722	−	0.469970i
$436$	−3.21123e13	+	5.56202e13i	−0.0976104	+	0.169066i
$437$	−1.66805e14	−	2.88915e14i	−0.500682	−	0.867207i
$438$	−3.20306e14	−	5.48974e12i	−0.949417	−	0.0162721i
$439$	1.77394e14	+	1.02418e14i	0.519258	+	0.299794i	0.736631	−	0.676295i	$-0.236415\pi$
$439$	1.77394e14	+	1.02418e14i	0.519258	+	0.299794i	−0.217373	+	0.976089i	$0.569749\pi$
$440$	−3.53399e13			−0.102159
$441$	−1.35278e14	−	3.23101e14i	−0.386202	−	0.922414i
$442$	−4.58756e14			−1.29348
$443$	1.89086e14	+	1.09169e14i	0.526550	+	0.304004i	0.739610	−	0.673035i	$-0.235010\pi$
$443$	1.89086e14	+	1.09169e14i	0.526550	+	0.304004i	−0.213060	+	0.977039i	$0.568343\pi$
$444$	3.00867e14	+	5.15659e12i	0.827502	+	0.0141826i
$445$	−1.18466e13	−	2.05189e13i	−0.0321821	−	0.0557410i
$446$	1.73285e14	−	3.00138e14i	0.464963	−	0.805340i
$447$	1.73630e14	+	1.04253e14i	0.460187	+	0.276310i
$448$	2.57656e13	−	4.01975e13i	0.0674546	−	0.105237i
$449$			3.58847e14i			0.928013i	0.885832	+	0.464006i	$0.153589\pi$
$449$			3.58847e14i			0.928013i	−0.885832	+	0.464006i	$0.846411\pi$
$450$	6.45477e12	−	1.88250e14i	0.0164897	−	0.480913i
$451$	2.27903e14	−	1.31580e14i	0.575148	−	0.332062i
$452$	−7.10076e13	+	4.09963e13i	−0.177029	+	0.102208i
$453$	6.09146e13	+	1.09811e14i	0.150031	+	0.270462i
$454$		−	1.91121e14i		−	0.465052i
$455$	3.21523e14	−	1.66243e14i	0.772947	−	0.399650i
$456$	−5.09333e13	+	8.48280e13i	−0.120975	+	0.201480i
$457$	1.75912e14	−	3.04689e14i	0.412817	−	0.715020i	−0.582380	−	0.812917i	$-0.697878\pi$
$457$	1.75912e14	−	3.04689e14i	0.412817	−	0.715020i	0.995197	+	0.0978970i	$0.0312116\pi$
$458$	−5.53024e13	−	9.57866e13i	−0.128228	−	0.222098i
$459$	2.35900e14	+	4.61897e14i	0.540453	+	1.05822i
$460$	1.62876e14	+	9.40366e13i	0.368714	+	0.212877i
$461$	−3.85277e14			−0.861823			−0.430911	−	0.902394i	$-0.641808\pi$
$461$	−3.85277e14			−0.861823			−0.430911	+	0.902394i	$0.641808\pi$
$462$	9.05957e13	−	1.36147e14i	0.200252	−	0.300938i
$463$	4.47302e14			0.977024			0.488512	−	0.872557i	$-0.337540\pi$
$463$	4.47302e14			0.977024			0.488512	+	0.872557i	$0.337540\pi$
$464$	1.62014e14	+	9.35388e13i	0.349706	+	0.201903i
$465$	−6.71683e12	+	3.91901e14i	−0.0143276	+	0.835960i
$466$	−8.13105e13	−	1.40834e14i	−0.171405	−	0.296883i
$467$	3.85225e14	−	6.67229e14i	0.802549	−	1.39006i	−0.115384	−	0.993321i	$-0.536810\pi$
$467$	3.85225e14	−	6.67229e14i	0.802549	−	1.39006i	0.917933	−	0.396735i	$-0.129857\pi$
$468$	3.29975e14	−	1.75718e14i	0.679405	−	0.361797i
$469$	2.03541e14	+	9.45247e12i	0.414192	+	0.0192351i
$470$			1.29374e14i			0.260201i
$471$	1.92651e14	−	1.06868e14i	0.382963	−	0.212438i
$472$	1.13043e14	−	6.52656e13i	0.222108	−	0.128234i
$473$	3.24815e14	−	1.87532e14i	0.630811	−	0.364199i
$474$	2.45898e14	−	1.36405e14i	0.472034	−	0.261848i
$475$		−	2.38386e14i		−	0.452341i
$476$	−1.45478e14	−	2.81363e14i	−0.272872	−	0.527750i
$477$	2.15998e14	−	1.15023e14i	0.400497	−	0.213273i
$478$	−3.59813e14	+	6.23215e14i	−0.659513	+	1.14231i
$479$	−6.49862e13	−	1.12559e14i	−0.117754	−	0.203956i	0.801123	−	0.598499i	$-0.204236\pi$
$479$	−6.49862e13	−	1.12559e14i	−0.117754	−	0.203956i	−0.918877	+	0.394543i	$0.870903\pi$
$480$	9.55877e11	−	5.57718e13i	0.00171228	−	0.0999051i
$481$	−1.24612e15	−	7.19449e14i	−2.20680	−	1.27410i
$482$	3.97955e14			0.696747
$483$	−7.79818e14	+	3.86413e14i	−1.34985	+	0.668872i
$484$	−2.15809e14			−0.369335
$485$	4.99942e13	+	2.88641e13i	0.0845940	+	0.0488404i
$486$	−3.46600e14	−	2.41877e14i	−0.579868	−	0.404664i
$487$	−2.58558e14	−	4.47836e14i	−0.427709	−	0.740814i	0.568960	−	0.822365i	$-0.307346\pi$
$487$	−2.58558e14	−	4.47836e14i	−0.427709	−	0.740814i	−0.996669	+	0.0815510i	$0.974013\pi$
$488$	3.52069e12	−	6.09802e12i	0.00575863	−	0.00997424i
$489$	−1.14290e14	+	1.90347e14i	−0.184847	+	0.307857i
$490$	2.03919e14	+	1.44478e14i	0.326121	+	0.231059i
$491$			8.09817e14i			1.28067i	0.768094	+	0.640337i	$0.221205\pi$
$491$			8.09817e14i			1.28067i	−0.768094	+	0.640337i	$0.778795\pi$
$492$	2.01489e14	+	3.63225e14i	0.315097	+	0.568026i
$493$	1.07480e15	−	6.20534e14i	1.66214	−	0.959639i
$494$	4.09744e14	−	2.36566e14i	0.626635	−	0.361788i
$495$	6.54695e12	−	1.90939e14i	0.00990171	−	0.288779i
$496$		−	2.47236e14i		−	0.369797i
$497$	5.72837e14	+	3.67175e14i	0.847365	+	0.543141i
$498$	6.34839e14	+	3.81177e14i	0.928758	+	0.557655i
$499$	−1.51844e14	+	2.63001e14i	−0.219707	+	0.380543i	−0.954718	−	0.297511i	$-0.903843\pi$
$499$	−1.51844e14	+	2.63001e14i	−0.219707	+	0.380543i	0.735012	+	0.678055i	$0.237177\pi$
$500$	1.65937e14	+	2.87411e14i	0.237470	+	0.411310i
$501$	−4.22201e14	−	7.23614e12i	−0.597602	−	0.0102424i
$502$	−4.43263e14	−	2.55918e14i	−0.620571	−	0.358287i
$503$	1.09618e15			1.51795			0.758973	−	0.651122i	$-0.225701\pi$
$503$	1.09618e15			1.51795			0.758973	+	0.651122i	$0.225701\pi$
$504$	2.12410e14	+	1.46656e14i	0.290943	+	0.200878i
$505$	2.59206e14			0.351190
$506$	−3.51884e14	−	2.03161e14i	−0.471598	−	0.272277i
$507$	−1.03320e15	−	1.77081e13i	−1.36975	−	0.0234762i
$508$	−2.44535e14	−	4.23546e14i	−0.320693	−	0.555457i
$509$	2.40261e14	−	4.16144e14i	0.311699	−	0.539879i	−0.667031	−	0.745030i	$-0.732435\pi$
$509$	2.40261e14	−	4.16144e14i	0.311699	−	0.539879i	0.978730	+	0.205151i	$0.0657686\pi$
$510$	−3.17249e14	−	1.90486e14i	−0.407159	−	0.244471i
$511$	−4.90654e13	+	1.05653e15i	−0.0622960	+	1.34143i
$512$			3.51844e13i			0.0441942i
$513$	−4.48883e14	−	2.90904e14i	−0.557812	−	0.361496i
$514$	1.69210e14	−	9.76932e13i	0.208031	−	0.120107i
$515$	−8.55952e13	+	4.94184e13i	−0.104114	+	0.0601103i
$516$	2.87169e14	+	5.17680e14i	0.345592	+	0.623000i
$517$		−	2.79505e14i		−	0.332807i
$518$	4.60878e13	−	9.92415e14i	0.0542966	−	1.16918i
$519$	−6.08769e14	+	1.01389e15i	−0.709631	+	1.18187i
$520$	−1.33364e14	+	2.30994e14i	−0.153823	+	0.266429i
$521$	3.46986e14	+	6.00997e14i	0.396008	+	0.685906i	0.993229	−	0.116171i	$-0.0370619\pi$
$521$	3.46986e14	+	6.00997e14i	0.396008	+	0.685906i	−0.597221	+	0.802076i	$0.703729\pi$
$522$	−5.35397e14	+	8.58020e14i	−0.604628	+	0.968969i
$523$	2.75168e14	+	1.58868e14i	0.307495	+	0.177533i	0.645805	−	0.763502i	$-0.276522\pi$
$523$	2.75168e14	+	1.58868e14i	0.307495	+	0.177533i	−0.338310	+	0.941035i	$0.609855\pi$
$524$	−2.23907e14			−0.247597
$525$	−6.20634e14	−	3.94908e13i	−0.679140	−	0.0432135i
$526$	1.12823e14			0.122173
$527$	−1.42042e15	−	8.20080e14i	−1.52215	−	0.878815i
$528$	−2.06512e12	+	1.20492e14i	−0.00219007	+	0.127782i
$529$	6.04784e14	+	1.04752e15i	0.634737	+	1.09940i
$530$	−8.72989e13	+	1.51206e14i	−0.0906759	+	0.157055i
$531$	3.31683e14	+	6.22855e14i	0.340960	+	0.640276i
$532$	2.75026e14	+	1.76285e14i	0.279807	+	0.179350i
$533$		−	1.98621e15i		−	1.99998i
$534$	−7.06517e13	+	3.91921e13i	−0.0704118	+	0.0390590i
$535$	−4.58474e12	+	2.64700e12i	−0.00452240	+	0.00261101i
$536$	−1.30035e14	+	7.50760e13i	−0.126957	+	0.0732985i
$537$	−1.63837e15	+	9.08838e14i	−1.58326	+	0.878270i
$538$			4.00044e14i			0.382653i
$539$	−4.40555e14	−	3.12136e14i	−0.417121	−	0.295533i
$540$	3.01153e14	+	1.54966e13i	0.282242	+	0.0145235i
$541$	−7.55200e14	+	1.30805e15i	−0.700611	+	1.21349i	0.267641	+	0.963519i	$0.413756\pi$
$541$	−7.55200e14	+	1.30805e15i	−0.700611	+	1.21349i	−0.968252	+	0.249976i	$0.919577\pi$
$542$	2.92058e14	+	5.05859e14i	0.268208	+	0.464551i
$543$	−1.25891e13	+	7.34525e14i	−0.0114444	+	0.667740i
$544$	2.02141e14	+	1.16706e14i	0.181912	+	0.105027i
$545$	2.47721e14			0.220690
$546$	−5.48017e14	−	1.10595e15i	−0.483320	−	0.975385i
$547$	1.44141e15			1.25852			0.629258	−	0.777197i	$-0.283359\pi$
$547$	1.44141e15			1.25852			0.629258	+	0.777197i	$0.283359\pi$
$548$	−1.98001e14	−	1.14316e14i	−0.171149	−	0.0988130i
$549$	3.22949e13	+	2.01517e13i	0.0276367	+	0.0172451i
$550$	−1.45171e14	−	2.51444e14i	−0.122994	−	0.213033i
$551$	−6.39980e14	+	1.10848e15i	−0.536825	+	0.929808i
$552$	3.30136e14	−	5.49833e14i	0.274175	−	0.456631i
$553$	−4.26400e14	−	8.24684e14i	−0.350614	−	0.678108i
$554$			4.33587e14i			0.352998i
$555$	−5.63014e14	−	1.01495e15i	−0.453845	−	0.818149i
$556$	−6.00582e13	+	3.46746e13i	−0.0479359	+	0.0276758i
$557$	−1.02117e15	+	5.89573e14i	−0.807039	+	0.465944i	−0.845926	−	0.533300i	$-0.820952\pi$
$557$	−1.02117e15	+	5.89573e14i	−0.807039	+	0.465944i	0.0388877	+	0.999244i	$0.487619\pi$
$558$	1.33580e15	+	4.58022e13i	1.04533	+	0.0358425i
$559$		−	2.83080e15i		−	2.19353i
$560$	−1.83964e14	−	8.54329e12i	−0.141156	−	0.00655528i
$561$	6.85397e14	+	4.11534e14i	0.520771	+	0.312687i
$562$	−5.61319e14	+	9.72234e14i	−0.422338	+	0.731511i
$563$	−1.91317e14	−	3.31371e14i	−0.142547	−	0.246899i	0.785908	−	0.618343i	$-0.212196\pi$
$563$	−1.91317e14	−	3.31371e14i	−0.142547	−	0.246899i	−0.928455	+	0.371445i	$0.878863\pi$
$564$	4.41102e14	+	7.56009e12i	0.325465	+	0.00557817i
$565$	2.73884e14	+	1.58127e14i	0.200124	+	0.115542i
$566$	6.79443e13			0.0491657
$567$	−8.31724e14	+	1.12047e15i	−0.596036	+	0.802958i
$568$	−5.01397e14			−0.355849
$569$	−2.14303e14	−	1.23728e14i	−0.150630	−	0.0869660i	0.422791	−	0.906227i	$-0.361050\pi$
$569$	−2.14303e14	−	1.23728e14i	−0.150630	−	0.0869660i	−0.573420	+	0.819261i	$0.694384\pi$
$570$	3.81583e14	+	6.53998e12i	0.265630	+	0.00455265i
$571$	−1.02441e13	−	1.77433e13i	−0.00706278	−	0.0122331i	0.862472	−	0.506104i	$-0.168915\pi$
$571$	−1.02441e13	−	1.77433e13i	−0.00706278	−	0.0122331i	−0.869535	+	0.493871i	$0.835582\pi$
$572$	2.88125e14	−	4.99048e14i	0.196745	−	0.340772i
$573$	1.18669e15	+	7.12527e14i	0.802579	+	0.481893i
$574$	1.21817e15	−	6.29853e14i	0.816007	−	0.421914i
$575$			1.54516e15i			1.02518i
$576$	−1.90098e14	−	6.51814e12i	−0.124927	−	0.00428351i
$577$	−1.76932e15	+	1.02152e15i	−1.15170	+	0.664936i	−0.949302	−	0.314367i	$-0.898208\pi$
$577$	−1.76932e15	+	1.02152e15i	−1.15170	+	0.664936i	−0.202401	+	0.979303i	$0.564874\pi$
$578$	3.91228e14	−	2.25875e14i	0.252247	−	0.145635i
$579$	−7.17400e14	−	1.29326e15i	−0.458173	−	0.825950i
$580$		−	7.21578e14i		−	0.456488i
$581$	1.31929e15	−	2.05825e15i	0.826744	−	1.28982i
$582$	1.01334e14	−	1.68769e14i	0.0629041	−	0.104765i
$583$	1.88604e14	−	3.26672e14i	0.115978	−	0.200879i
$584$	−3.89701e14	−	6.74982e14i	−0.237389	−	0.411170i
$585$	−1.22333e15	−	7.63350e14i	−0.738223	−	0.460645i
$586$	1.68130e15	+	9.70698e14i	1.00510	+	0.580293i
$587$	7.61298e14			0.450864			0.225432	−	0.974259i	$-0.427621\pi$
$587$	7.61298e14			0.450864			0.225432	+	0.974259i	$0.427621\pi$
$588$	5.04515e14	−	6.86821e14i	0.296005	−	0.402966i
$589$	1.69156e15			0.983224
$590$	−4.36020e14	−	2.51736e14i	−0.251085	−	0.144964i
$591$	3.49739e13	−	2.04059e15i	0.0199532	−	1.16419i
$592$	3.66051e14	+	6.34020e14i	0.206906	+	0.358371i
$593$	−8.76328e14	+	1.51784e15i	−0.490756	+	0.850015i	−0.999943	−	0.0106410i	$-0.996613\pi$
$593$	−8.76328e14	+	1.51784e15i	−0.490756	+	0.850015i	0.509187	+	0.860656i	$0.329946\pi$
$594$	−6.50624e14	−	3.34795e13i	−0.360998	−	0.0185761i
$595$	−6.59289e14	+	1.02857e15i	−0.362437	+	0.565445i
$596$			4.92732e14i			0.268384i
$597$	1.25779e15	−	6.97722e14i	0.678810	−	0.376551i
$598$	−2.65585e15	+	1.53336e15i	−1.42019	+	0.819950i
$599$	−5.17440e14	+	2.98744e14i	−0.274165	+	0.158289i	−0.630779	−	0.775962i	$-0.717265\pi$
$599$	−5.17440e14	+	2.98744e14i	−0.274165	+	0.158289i	0.356614	+	0.934252i	$0.383931\pi$
$600$	4.00744e14	−	2.22301e14i	0.210395	−	0.116711i
$601$			1.36305e15i			0.709093i	0.935038	+	0.354547i	$0.115365\pi$
$601$			1.36305e15i			0.709093i	−0.935038	+	0.354547i	$0.884635\pi$
$602$	1.73618e15	−	8.97686e14i	0.894981	−	0.462747i
$603$	−3.81540e14	−	7.16480e14i	−0.194892	−	0.365981i
$604$	−1.52759e14	+	2.64586e14i	−0.0773219	+	0.133926i
$605$	4.16200e14	+	7.20879e14i	0.208760	+	0.361583i
$606$	1.51469e13	−	8.83765e14i	0.00752878	−	0.439276i
$607$	−2.24056e15	−	1.29359e15i	−1.10362	−	0.637174i	−0.166449	−	0.986050i	$-0.553230\pi$
$607$	−2.24056e15	−	1.29359e15i	−1.10362	−	0.637174i	−0.937169	+	0.348876i	$0.886563\pi$
$608$	−2.40727e14			−0.117505
$609$	2.77988e15	+	1.84980e15i	1.34472	+	0.894810i
$610$	−2.71594e13			−0.0130198
$611$	−1.82694e15	−	1.05479e15i	−0.867957	−	0.501115i
$612$	−6.68002e14	+	1.07053e15i	−0.314518	+	0.504042i
$613$	−3.24137e14	−	5.61421e14i	−0.151250	−	0.261973i	0.780437	−	0.625234i	$-0.214997\pi$
$613$	−3.24137e14	−	5.61421e14i	−0.151250	−	0.261973i	−0.931687	+	0.363261i	$0.881663\pi$
$614$	5.44520e14	−	9.43136e14i	0.251818	−	0.436162i
$615$	8.24718e14	−	1.37354e15i	0.378000	−	0.629549i
$616$	3.97443e14	+	1.84573e13i	0.180543	+	0.00838443i
$617$			3.48434e15i			1.56875i	0.620290	+	0.784373i	$0.287015\pi$
$617$			3.48434e15i			1.56875i	−0.620290	+	0.784373i	$0.712985\pi$
$618$	1.63491e14	+	2.94725e14i	0.0729552	+	0.131517i
$619$	−1.66237e14	+	9.59770e13i	−0.0735240	+	0.0424491i	−0.536311	−	0.844020i	$-0.680183\pi$
$619$	−1.66237e14	+	9.59770e13i	−0.0735240	+	0.0424491i	0.462787	+	0.886469i	$0.346849\pi$
$620$	−8.25856e14	+	4.76808e14i	−0.362034	+	0.209021i
$621$	2.90954e15	+	1.88556e15i	1.26422	+	0.819289i
$622$		−	2.10498e15i		−	0.906570i
$623$	1.22514e14	+	2.36949e14i	0.0523000	+	0.101151i
$624$	7.79781e14	+	4.68205e14i	0.329957	+	0.198116i
$625$	−1.71199e14	+	2.96525e14i	−0.0718059	+	0.124372i
$626$	1.36440e15	+	2.36321e15i	0.567262	+	0.982526i
$627$	−8.24387e14	−	1.41292e13i	−0.339750	−	0.00582301i
$628$	4.64187e14	+	2.67998e14i	0.189633	+	0.109485i
$629$	4.85675e15			1.96683
$630$	8.02393e13	−	9.92360e14i	0.0322117	−	0.398379i
$631$	1.48896e15			0.592544			0.296272	−	0.955104i	$-0.404256\pi$
$631$	1.48896e15			0.592544			0.296272	+	0.955104i	$0.404256\pi$
$632$	5.92482e14	+	3.42069e14i	0.233739	+	0.134949i
$633$	−4.11926e15	−	7.06004e13i	−1.61101	−	0.0276113i
$634$	−1.33298e15	−	2.30879e15i	−0.516813	−	0.895147i
$635$	−9.43196e14	+	1.63366e15i	−0.362532	+	0.627924i
$636$	5.10437e14	+	3.06482e14i	0.194504	+	0.116786i
$637$	−3.70278e15	+	1.70169e15i	−1.39882	+	0.642856i
$638$			1.55893e15i			0.583864i
$639$	9.28872e13	−	2.70901e15i	0.0344906	−	1.00590i
$640$	1.17528e14	−	6.78549e13i	0.0432665	−	0.0249799i
$641$	3.12488e15	−	1.80415e15i	1.14055	−	0.658497i	0.193983	−	0.981005i	$-0.437859\pi$
$641$	3.12488e15	−	1.80415e15i	1.14055	−	0.658497i	0.946567	+	0.322508i	$0.104526\pi$
$642$	8.75706e12	+	1.57864e13i	0.00316895	+	0.00571268i
$643$			6.68440e14i			0.239829i	0.992784	+	0.119915i	$0.0382621\pi$
$643$			6.68440e14i			0.239829i	−0.992784	+	0.119915i	$0.961738\pi$
$644$	−1.78264e15	−	1.14263e15i	−0.634150	−	0.406475i
$645$	1.17541e15	−	1.95762e15i	0.414584	−	0.690477i
$646$	−7.98488e14	+	1.38302e15i	−0.279248	+	0.483671i
$647$	−7.88033e14	−	1.36491e15i	−0.273257	−	0.473295i	0.696437	−	0.717618i	$-0.254768\pi$
$647$	−7.88033e14	−	1.36491e15i	−0.273257	−	0.473295i	−0.969694	+	0.244323i	$0.921434\pi$
$648$	7.04340e13	−	1.02588e15i	0.0242170	−	0.352723i
$649$	9.41995e14	+	5.43861e14i	0.321146	+	0.185414i
$650$	−2.19136e15			−0.740783
$651$	2.80221e14	−	4.40394e15i	0.0939303	−	1.47620i
$652$	−5.40172e14			−0.179544
$653$	−2.88256e15	−	1.66425e15i	−0.950072	−	0.548524i	−0.0569686	−	0.998376i	$-0.518143\pi$
$653$	−2.88256e15	−	1.66425e15i	−0.950072	−	0.548524i	−0.893103	+	0.449852i	$0.851477\pi$
$654$	1.44758e13	−	8.44607e14i	0.00473113	−	0.276043i
$655$	4.31817e14	+	7.47929e14i	0.139950	+	0.242400i
$656$	−5.05285e14	+	8.75179e14i	−0.162392	+	0.281271i
$657$	3.71907e15	−	1.98048e15i	1.18529	−	0.631191i
$658$	6.75694e13	−	1.45498e15i	0.0213554	−	0.459849i
$659$		−	1.50528e15i		−	0.471788i	−0.971779	−	0.235894i	$-0.924198\pi$
$659$		−	1.50528e15i		−	0.471788i	0.971779	−	0.235894i	$-0.0758018\pi$
$660$	4.06467e14	−	2.25476e14i	0.126338	−	0.0700824i
$661$	4.25359e15	−	2.45581e15i	1.31114	−	0.756985i	0.328852	−	0.944381i	$-0.393338\pi$
$661$	4.25359e15	−	2.45581e15i	1.31114	−	0.756985i	0.982284	+	0.187396i	$0.0600048\pi$
$662$	−1.96721e15	+	1.13577e15i	−0.601357	+	0.347194i
$663$	5.27645e15	−	2.92696e15i	1.59962	−	0.887346i
$664$			1.80156e15i			0.541657i
$665$	5.84520e13	−	1.25866e15i	0.0174293	−	0.375308i
$666$	−3.49337e15	+	1.86029e15i	−1.03309	+	0.550139i
$667$	4.14818e15	−	7.18486e15i	1.21665	−	2.10730i
$668$	−5.13673e14	−	8.89707e14i	−0.149422	−	0.258807i
$669$	−7.81143e13	+	4.55767e15i	−0.0225365	+	1.31492i
$670$	5.01560e14	+	2.89576e14i	0.143520	+	0.0828612i
$671$	5.86762e13			0.0166528
$672$	−3.98785e13	+	6.26727e14i	−0.0112256	+	0.176420i
$673$	1.89585e15			0.529323			0.264662	−	0.964341i	$-0.414740\pi$
$673$	1.89585e15			0.529323			0.264662	+	0.964341i	$0.414740\pi$
$674$	4.25840e15	+	2.45859e15i	1.17928	+	0.680858i
$675$	1.12684e15	+	2.20637e15i	0.309521	+	0.606049i
$676$	−1.25705e15	−	2.17727e15i	−0.342487	−	0.593206i
$677$	−1.62589e15	+	2.81613e15i	−0.439395	+	0.761054i	−0.997643	−	0.0686202i	$-0.978140\pi$
$677$	−1.62589e15	+	2.81613e15i	−0.439395	+	0.761054i	0.558248	+	0.829674i	$0.311474\pi$
$678$	5.55140e14	−	9.24569e14i	0.148812	−	0.247843i
$679$	−5.47175e14	−	3.50726e14i	−0.145493	−	0.0932576i
$680$		−	9.00296e14i		−	0.237458i
$681$	1.21939e15	+	2.19821e15i	0.319032	+	0.575121i
$682$	1.78421e15	−	1.03012e15i	0.463055	−	0.267345i
$683$	−2.43784e15	+	1.40749e15i	−0.627611	+	0.362351i	−0.779826	−	0.625996i	$-0.784693\pi$
$683$	−2.43784e15	+	1.40749e15i	−0.627611	+	0.362351i	0.152215	+	0.988347i	$0.451359\pi$
$684$	4.45962e13	−	1.30063e15i	0.0113891	−	0.332158i
$685$			8.81858e14i			0.223409i
$686$	−2.21788e15	−	1.73135e15i	−0.557385	−	0.435112i
$687$	1.24721e15	+	7.48863e14i	0.310940	+	0.186698i
$688$	−7.20147e14	+	1.24733e15i	−0.178109	+	0.308493i
$689$	−1.42349e15	−	2.46556e15i	−0.349261	−	0.604938i
$690$	−2.47332e15	−	4.23904e13i	−0.602019	−	0.0103181i
$691$	5.88307e14	+	3.39659e14i	0.142061	+	0.0820189i	0.569346	−	0.822098i	$-0.307197\pi$
$691$	5.88307e14	+	3.39659e14i	0.142061	+	0.0820189i	−0.427285	+	0.904117i	$0.640530\pi$
$692$	−2.87723e15			−0.689273
$693$	−1.73352e14	+	2.14394e15i	−0.0411999	+	0.509541i
$694$	8.75881e14			0.206523
$695$	2.31651e14	+	1.33744e14i	0.0541897	+	0.0312865i
$696$	−2.46023e15	−	4.21660e13i	−0.570984	−	0.00978615i
$697$	3.35205e15	+	5.80592e15i	0.771845	+	1.33687i
$698$	−1.30103e15	+	2.25344e15i	−0.297222	+	0.514804i
$699$	1.83376e15	+	1.10104e15i	0.415640	+	0.249563i
$700$	−6.94912e14	−	1.34400e15i	−0.156275	−	0.302246i
$701$			2.01138e15i			0.448791i	0.974498	+	0.224396i	$0.0720408\pi$
$701$			2.01138e15i			0.448791i	−0.974498	+	0.224396i	$0.927959\pi$
$702$	−2.67413e15	+	4.12636e15i	−0.592010	+	0.913509i
$703$	−4.33788e15	+	2.50447e15i	−0.952846	+	0.550126i
$704$	−2.53913e14	+	1.46596e14i	−0.0553394	+	0.0319502i
$705$	−8.25435e14	−	1.48802e15i	−0.178502	−	0.321786i
$706$		−	4.91959e15i		−	1.05561i
$707$	−2.91511e15	−	1.35378e14i	−0.620652	−	0.0288231i
$708$	−8.83776e14	+	1.47190e15i	−0.186706	+	0.310954i
$709$	−1.99383e15	+	3.45341e15i	−0.417959	+	0.723926i	−0.995734	−	0.0922702i	$-0.970588\pi$
$709$	−1.99383e15	+	3.45341e15i	−0.417959	+	0.723926i	0.577775	+	0.816196i	$0.303921\pi$
$710$	9.66971e14	+	1.67484e15i	0.201137	+	0.348380i
$711$	−1.95794e15	+	3.13776e15i	−0.404125	+	0.647645i
$712$	−1.70233e14	−	9.82839e13i	−0.0348661	−	0.0201299i
$713$	−1.09642e16			−2.22836
$714$	3.46839e15	+	2.30796e15i	0.699501	+	0.465466i
$715$	−2.22266e15			−0.444826
$716$	−3.94759e15	−	2.27914e15i	−0.783989	−	0.452636i
$717$	1.62199e14	−	9.46368e15i	0.0319663	−	1.86511i
$718$	1.06563e15	+	1.84573e15i	0.208412	+	0.360981i
$719$	−2.12007e15	+	3.67208e15i	−0.411474	+	0.712693i	−0.995051	−	0.0993642i	$-0.968319\pi$
$719$	−2.12007e15	+	3.67208e15i	−0.411474	+	0.712693i	0.583577	+	0.812057i	$0.301652\pi$
$720$	3.44842e14	+	6.47566e14i	0.0664188	+	0.124726i
$721$	9.88440e14	−	5.11070e14i	0.188932	−	0.0976869i
$722$			2.08067e15i			0.394683i
$723$	−4.57713e15	+	2.53904e15i	−0.861654	+	0.477979i
$724$	−1.54787e15	+	8.93662e14i	−0.289182	+	0.166959i
$725$	5.13404e15	−	2.96414e15i	0.951920	−	0.549591i
$726$	2.48216e15	−	1.37691e15i	0.456751	−	0.253370i
$727$			6.87819e15i			1.25613i	0.778160	+	0.628066i	$0.216153\pi$
$727$			6.87819e15i			1.25613i	−0.778160	+	0.628066i	$0.783847\pi$
$728$	1.62050e15	−	2.52817e15i	0.293715	−	0.458231i
$729$	5.52970e15	+	5.70600e14i	0.994718	+	0.102643i
$730$	−1.50312e15	+	2.60348e15i	−0.268360	+	0.464812i
$731$	4.77744e15	+	8.27477e15i	0.846544	+	1.46626i
$732$	−1.58708e12	+	9.26001e13i	−0.000279118	+	0.0162855i
$733$	−9.46338e15	−	5.46368e15i	−1.65186	−	0.953704i	−0.976305	−	0.216399i	$-0.930569\pi$
$733$	−9.46338e15	−	5.46368e15i	−1.65186	−	0.953704i	−0.675559	−	0.737306i	$-0.736098\pi$
$734$	7.11363e15			1.23243
$735$	−3.26720e15	−	3.60686e14i	−0.561818	−	0.0620225i
$736$	1.56033e15			0.266310
$737$	−1.08359e15	−	6.25612e14i	−0.183567	−	0.105982i
$738$	−4.63492e15	−	2.89215e15i	−0.779349	−	0.486307i
$739$	7.99991e14	+	1.38562e15i	0.133518	+	0.231260i	0.925030	−	0.379893i	$-0.124039\pi$
$739$	7.99991e14	+	1.38562e15i	0.133518	+	0.231260i	−0.791512	+	0.611153i	$0.790706\pi$
$740$	1.41190e15	−	2.44548e15i	0.233899	−	0.405126i
$741$	−3.20339e15	+	5.33516e15i	−0.526757	+	0.877298i
$742$	1.06076e15	−	1.65492e15i	0.173140	−	0.270119i
$743$		−	3.20246e15i		−	0.518855i	−0.965763	−	0.259427i	$-0.916466\pi$
$743$		−	3.20246e15i		−	0.518855i	0.965763	−	0.259427i	$-0.0835338\pi$
$744$	1.57742e15	+	2.84362e15i	0.253686	+	0.457321i
$745$	1.64590e15	−	9.50259e14i	0.262750	−	0.151699i
$746$	−4.56633e15	+	2.63637e15i	−0.723609	+	0.417776i
$747$	−9.73369e15	−	3.33751e14i	−1.53114	−	0.0525000i
$748$			1.94504e15i			0.303717i
$749$	5.29439e13	−	2.73745e13i	0.00820665	−	0.00424322i
$750$	−3.74230e15	−	2.24699e15i	−0.575839	−	0.345752i
$751$	2.16617e15	−	3.75191e15i	0.330881	−	0.573103i	−0.651804	−	0.758388i	$-0.725987\pi$
$751$	2.16617e15	−	3.75191e15i	0.330881	−	0.573103i	0.982685	+	0.185285i	$0.0593207\pi$
$752$	5.36669e14	+	9.29537e14i	0.0813782	+	0.140951i
$753$	6.73107e15	+	1.15364e14i	1.01324	+	0.0173660i
$754$	1.01897e16	+	5.88301e15i	1.52271	+	0.879139i
$755$	1.17841e15			0.174819
$756$	−3.37877e15	−	3.31566e14i	−0.497610	−	0.0488315i
$757$	−7.49524e15			−1.09587			−0.547934	−	0.836522i	$-0.684585\pi$
$757$	−7.49524e15			−1.09587			−0.547934	+	0.836522i	$0.684585\pi$
$758$	1.94238e15	+	1.12143e15i	0.281937	+	0.162777i
$759$	5.34346e15	+	9.15820e13i	0.770004	+	0.0131972i
$760$	4.64254e14	+	8.04112e14i	0.0664173	+	0.115038i
$761$	−3.35657e14	+	5.81375e14i	−0.0476738	+	0.0825735i	−0.888878	−	0.458145i	$-0.848514\pi$
$761$	−3.35657e14	+	5.81375e14i	−0.0476738	+	0.0825735i	0.841204	+	0.540718i	$0.181847\pi$
$762$	5.51487e15	+	3.31130e15i	0.777648	+	0.466924i
$763$	−2.78595e15	−	1.29380e14i	−0.390021	−	0.0181126i
$764$			3.36762e15i			0.468069i
$765$	4.86423e15	+	1.66786e14i	0.671237	+	0.0230155i
$766$	7.26431e15	−	4.19405e15i	0.995259	−	0.574613i
$767$	7.10973e15	−	4.10480e15i	0.967116	−	0.558364i
$768$	−2.24484e14	−	4.04678e14i	−0.0303179	−	0.0546542i
$769$		−	8.72203e15i		−	1.16956i	−0.811192	−	0.584780i	$-0.801181\pi$
$769$		−	8.72203e15i		−	1.16956i	0.811192	−	0.584780i	$-0.198819\pi$
$770$	−7.04836e14	−	1.36320e15i	−0.0938403	−	0.181493i
$771$	−1.32288e15	+	2.20323e15i	−0.174873	+	0.291246i
$772$	1.79906e15	−	3.11606e15i	0.236130	−	0.408989i
$773$	3.52896e15	+	6.11233e15i	0.459896	+	0.796562i	0.998955	−	0.0457053i	$-0.0145535\pi$
$773$	3.52896e15	+	6.11233e15i	0.459896	+	0.796562i	−0.539059	+	0.842268i	$0.681220\pi$
$774$	−6.60582e15	−	4.12198e15i	−0.854775	−	0.533372i
$775$	−6.78500e15	−	3.91732e15i	−0.871747	−	0.503303i
$776$	4.78936e14			0.0610995
$777$	5.80174e15	+	1.17085e16i	0.734925	+	1.48315i
$778$	−1.72822e15			−0.217375
$779$	−5.98786e15	−	3.45709e15i	−0.747851	−	0.431772i
$780$	6.01188e13	−	3.50770e15i	0.00745572	−	0.435013i
$781$	−2.08908e15	−	3.61840e15i	−0.257262	−	0.445590i
$782$	5.17559e15	−	8.96438e15i	0.632881	−	1.09618i
$783$	6.83593e14	−	1.32846e16i	0.0830057	−	1.61309i
$784$	2.06445e15	+	1.92161e14i	0.248924	+	0.0231700i
$785$		−	2.06740e15i		−	0.247537i
$786$	2.57530e15	−	1.42858e15i	0.306199	−	0.169856i
$787$	6.73990e13	−	3.89128e13i	0.00795778	−	0.00459443i	−0.496016	−	0.868313i	$-0.665204\pi$
$787$	6.73990e13	−	3.89128e13i	0.00795778	−	0.00459443i	0.503974	+	0.863719i	$0.331871\pi$
$788$	4.30015e15	−	2.48269e15i	0.504184	−	0.291091i
$789$	−1.29765e15	+	7.19836e14i	−0.151090	+	0.0838128i
$790$		−	2.63880e15i		−	0.305110i
$791$	−2.99760e15	−	1.92139e15i	−0.344193	−	0.220620i
$792$	−7.45010e14	−	1.39903e15i	−0.0849520	−	0.159528i
$793$	2.21430e14	−	3.83528e14i	0.0250746	−	0.0434305i
$794$	1.94130e15	+	3.36244e15i	0.218314	+	0.378130i
$795$	3.93532e13	−	2.29611e15i	0.00439502	−	0.256432i
$796$	3.03059e15	+	1.74971e15i	0.336129	+	0.194064i
$797$	−1.08837e15			−0.119882			−0.0599412	−	0.998202i	$-0.519091\pi$
$797$	−1.08837e15			−0.119882			−0.0599412	+	0.998202i	$0.519091\pi$
$798$	−4.28798e15	−	2.72843e14i	−0.469069	−	0.0298468i
$799$	7.12049e15			0.773576
$800$	9.65578e14	+	5.57477e14i	0.104182	+	0.0601495i
$801$	5.62557e14	−	9.01547e14i	0.0602820	−	0.0966072i
$802$	1.32698e15	+	2.29840e15i	0.141223	+	0.244605i
$803$	3.24740e15	−	5.62465e15i	0.343241	−	0.594512i
$804$	1.01662e15	−	1.69315e15i	0.106721	−	0.177741i
$805$	−3.78871e14	+	8.15828e15i	−0.0395015	+	0.850592i
$806$		−	1.55496e16i		−	1.61019i
$807$	−2.55237e15	−	4.60117e15i	−0.262506	−	0.473221i
$808$	1.86236e15	−	1.07524e15i	0.190240	−	0.109835i
$809$	1.60388e16	−	9.25999e15i	1.62725	−	0.939493i	0.642342	−	0.766418i	$-0.277963\pi$
$809$	1.60388e16	−	9.25999e15i	1.62725	−	0.939493i	0.984909	−	0.173075i	$-0.0553704\pi$
$810$	−3.56263e15	+	1.74319e15i	−0.359007	+	0.175662i
$811$			6.99229e15i			0.699849i	0.936778	+	0.349925i	$0.113793\pi$
$811$			6.99229e15i			0.699849i	−0.936778	+	0.349925i	$0.886207\pi$
$812$	−3.76865e14	+	8.11509e15i	−0.0374652	+	0.806743i
$813$	−6.58663e15	−	3.95482e15i	−0.650377	−	0.390507i
$814$	−3.05032e15	+	5.28331e15i	−0.299166	+	0.518170i
$815$	1.04175e15	+	1.80436e15i	0.101484	+	0.175775i
$816$	−3.06957e15	−	5.26095e13i	−0.297017	−	0.00509059i
$817$	−8.53407e15	−	4.92715e15i	−0.820229	−	0.473559i
$818$	−1.12686e16			−1.07578
$819$	1.33593e16	+	9.22379e15i	1.26684	+	0.874677i
$820$	3.89787e15			0.367157
$821$	1.54066e16	+	8.89499e15i	1.44151	+	0.832258i	0.997951	−	0.0639853i	$-0.0203811\pi$
$821$	1.54066e16	+	8.89499e15i	1.44151	+	0.832258i	0.443563	+	0.896243i	$0.353714\pi$
$822$	3.00670e15	+	5.15321e13i	0.279444	+	0.00478942i
$823$	1.22769e15	+	2.12642e15i	0.113342	+	0.196314i	0.917116	−	0.398621i	$-0.130511\pi$
$823$	1.22769e15	+	2.12642e15i	0.113342	+	0.196314i	−0.803774	+	0.594935i	$0.797178\pi$
$824$	−4.09994e14	+	7.10130e14i	−0.0375991	+	0.0651236i
$825$	3.27397e15	+	1.96580e15i	0.298249	+	0.179078i
$826$	4.77214e15	+	3.05883e15i	0.431840	+	0.276799i
$827$			2.32536e15i			0.209031i	0.994523	+	0.104515i	$0.0333292\pi$
$827$			2.32536e15i			0.209031i	−0.994523	+	0.104515i	$0.966671\pi$
$828$	−2.89061e14	+	8.43033e15i	−0.0258121	+	0.752796i
$829$	4.70008e13	−	2.71359e13i	0.00416923	−	0.00240711i	−0.497914	−	0.867226i	$-0.665900\pi$
$829$	4.70008e13	−	2.71359e13i	0.00416923	−	0.00240711i	0.502083	+	0.864819i	$0.332567\pi$
$830$	6.01784e15	−	3.47440e15i	0.530288	−	0.306162i
$831$	−2.76638e15	−	4.98697e15i	−0.242162	−	0.436547i
$832$			2.21288e15i			0.192433i
$833$	7.95177e15	−	1.12233e16i	0.686936	−	0.969555i
$834$	4.69536e14	−	7.81999e14i	0.0402955	−	0.0671109i
$835$	−1.98129e15	+	3.43169e15i	−0.168917	+	0.292572i
$836$	−1.00299e15	−	1.73724e15i	−0.0849500	−	0.147138i
$837$	−1.56561e16	+	7.99588e15i	−1.31733	+	0.672785i
$838$	−1.54671e14	−	8.92994e13i	−0.0129291	−	0.00746460i
$839$	−1.15476e16			−0.958963			−0.479482	−	0.877552i	$-0.659175\pi$
$839$	−1.15476e16			−0.958963			−0.479482	+	0.877552i	$0.659175\pi$
$840$	2.17040e15	−	1.07547e15i	0.179062	−	0.0887282i
$841$	−1.96300e16			−1.60895
$842$	−3.93599e14	−	2.27244e14i	−0.0320507	−	0.0185045i
$843$	2.53035e14	−	1.47636e16i	0.0204705	−	1.19438i
$844$	−5.01171e15	−	8.68054e15i	−0.402812	−	0.697692i
$845$	−4.84856e15	+	8.39795e15i	−0.387169	+	0.670597i
$846$	−5.12164e15	+	2.72738e15i	−0.406324	+	0.216375i
$847$	−4.30421e15	−	8.32460e15i	−0.339262	−	0.656153i
$848$			1.44853e15i			0.113436i
$849$	−7.81471e14	+	4.33499e14i	−0.0608024	+	0.0337284i
$850$	6.40562e15	−	3.69829e15i	0.495173	−	0.285888i
$851$	2.81170e16	−	1.62333e16i	2.15951	−	1.24680i
$852$	5.76690e15	−	3.19902e15i	0.440073	−	0.244118i
$853$			7.22643e15i			0.547904i	0.961743	+	0.273952i	$0.0883309\pi$
$853$			7.22643e15i			0.547904i	−0.961743	+	0.273952i	$0.911669\pi$
$854$	3.05443e14	+	1.41848e13i	0.0230097	+	0.00106857i
$855$	−4.43056e15	+	2.35936e15i	−0.331623	+	0.176596i
$856$	−2.19605e13	+	3.80367e13i	−0.00163319	+	0.00282877i
$857$	−1.21752e15	−	2.10881e15i	−0.0899668	−	0.155827i	0.817530	−	0.575886i	$-0.195343\pi$
$857$	−1.21752e15	−	2.10881e15i	−0.0899668	−	0.155827i	−0.907497	+	0.420059i	$0.862009\pi$
$858$	−1.29883e14	+	7.57818e15i	−0.00953613	+	0.556397i
$859$	1.28644e16	+	7.42728e15i	0.938487	+	0.541836i	0.889486	−	0.456963i	$-0.151063\pi$
$859$	1.28644e16	+	7.42728e15i	0.938487	+	0.541836i	0.0490014	+	0.998799i	$0.484396\pi$
$860$	5.55537e15			0.402690
$861$	−9.99241e15	+	1.50166e16i	−0.719702	+	1.08157i
$862$	−1.62507e16			−1.16301
$863$	−1.02127e16	−	5.89630e15i	−0.726242	−	0.419296i	0.0908040	−	0.995869i	$-0.471056\pi$
$863$	−1.02127e16	−	5.89630e15i	−0.726242	−	0.419296i	−0.817046	+	0.576573i	$0.804390\pi$
$864$	2.22803e15	−	1.13790e15i	0.157433	−	0.0804042i
$865$	5.54889e15	+	9.61096e15i	0.389599	+	0.674805i
$866$	1.12069e15	−	1.94110e15i	0.0781876	−	0.135425i
$867$	−3.05863e15	+	5.09406e15i	−0.212042	+	0.353150i
$868$	9.53686e15	−	4.93100e15i	0.656972	−	0.339685i
$869$			5.70096e15i			0.390247i
$870$	4.60383e15	+	8.29934e15i	0.313158	+	0.564531i
$871$	−8.17843e15	+	4.72182e15i	−0.552803	+	0.319161i
$872$	1.77985e15	−	1.02759e15i	0.119548	−	0.0690210i
$873$	−8.87260e13	+	2.58765e15i	−0.00592206	+	0.172714i
$874$			1.06755e16i			0.708072i
$875$	−7.77703e15	+	1.21331e16i	−0.512590	+	0.799701i
$876$	8.78873e15	+	5.27703e15i	0.575644	+	0.345634i
$877$	7.69360e15	−	1.33257e16i	0.500763	−	0.867347i	−0.499237	−	0.866466i	$-0.666386\pi$
$877$	7.69360e15	−	1.33257e16i	0.500763	−	0.867347i	1.00000		0.000881075i	$-0.000280455\pi$
$878$	−3.27738e15	−	5.67660e15i	−0.211986	−	0.367171i
$879$	−2.55310e16	−	4.37577e14i	−1.64108	−	0.0281265i
$880$	9.79367e14	+	5.65438e14i	0.0625592	+	0.0361185i
$881$	−2.41065e16			−1.53026			−0.765132	−	0.643874i	$-0.777326\pi$
$881$	−2.41065e16			−1.53026			−0.765132	+	0.643874i	$0.777326\pi$
$882$	−1.42068e15	+	1.11185e16i	−0.0896232	+	0.701404i
$883$	−1.28473e16			−0.805428			−0.402714	−	0.915326i	$-0.631933\pi$
$883$	−1.28473e16			−0.805428			−0.402714	+	0.915326i	$0.631933\pi$
$884$	1.27134e16	+	7.34010e15i	0.792091	+	0.457314i
$885$	6.62108e15	+	1.13479e14i	0.409959	+	0.00702633i
$886$	−3.49341e15	−	6.05076e15i	−0.214963	−	0.372327i
$887$	6.59547e15	−	1.14237e16i	0.403335	−	0.698597i	−0.590791	−	0.806825i	$-0.701184\pi$
$887$	6.59547e15	−	1.14237e16i	0.403335	−	0.698597i	0.994126	+	0.108228i	$0.0345176\pi$
$888$	−8.25538e15	−	4.95678e15i	−0.501725	−	0.301251i
$889$	1.14607e16	−	1.78801e16i	0.692232	−	1.07996i
$890$			7.58183e14i			0.0455123i
$891$	7.69686e15	−	3.76605e15i	0.459183	−	0.224677i
$892$	−9.60441e15	+	5.54511e15i	−0.569461	+	0.328779i
$893$	−6.35977e15	+	3.67181e15i	−0.374764	+	0.216370i
$894$	−3.14374e15	−	5.66723e15i	−0.184115	−	0.331905i
$895$			1.75818e16i			1.02338i
$896$	−1.35720e15	+	7.01735e14i	−0.0785143	+	0.0405956i
$897$	2.07635e16	−	3.45811e16i	1.19383	−	1.98829i
$898$	5.74155e15	−	9.94465e15i	0.328102	−	0.568289i
$899$	2.10331e16	+	3.64305e16i	1.19461	+	2.06912i
$900$	−3.19088e15	+	5.11367e15i	−0.180126	+	0.288668i
$901$	8.32208e15	+	4.80476e15i	0.466924	+	0.269578i
$902$	−8.42112e15			−0.469606
$903$	−1.42415e16	+	2.14021e16i	−0.789356	+	1.18624i
$904$	2.62376e15			0.144543
$905$	5.97029e15	+	3.44695e15i	0.326910	+	0.188741i
$906$	6.88615e13	−	4.01781e15i	0.00374776	−	0.218667i
$907$	3.04050e15	+	5.26630e15i	0.164477	+	0.284882i	0.936469	−	0.350749i	$-0.114073\pi$
$907$	3.04050e15	+	5.26630e15i	0.164477	+	0.284882i	−0.771993	+	0.635632i	$0.780740\pi$
$908$	−3.05794e15	+	5.29650e15i	−0.164421	+	0.284785i
$909$	5.46440e15	+	1.02614e16i	0.292039	+	0.548409i
$910$	−1.15702e16	−	5.37320e14i	−0.614629	−	0.0285434i
$911$		−	2.11794e16i		−	1.11831i	−0.829063	−	0.559155i	$-0.811126\pi$
$911$		−	2.11794e16i		−	1.11831i	0.829063	−	0.559155i	$-0.188874\pi$
$912$	2.76875e15	−	1.53589e15i	0.145316	−	0.0806099i
$913$	−1.30012e16	+	7.50624e15i	−0.678257	+	0.391592i
$914$	−9.75006e15	+	5.62920e15i	−0.505596	+	0.291906i
$915$	3.12378e14	−	1.73283e14i	0.0161014	−	0.00893181i
$916$			3.53936e15i			0.181342i
$917$	−4.46572e15	−	8.63697e15i	−0.227436	−	0.439876i
$918$	8.52903e14	−	1.65749e16i	0.0431782	−	0.839104i
$919$	1.21029e16	−	2.09629e16i	0.609054	−	1.05491i	−0.382343	−	0.924021i	$-0.624883\pi$
$919$	1.21029e16	−	2.09629e16i	0.609054	−	1.05491i	0.991397	−	0.130892i	$-0.0417840\pi$
$920$	−3.00917e15	−	5.21204e15i	−0.150527	−	0.260720i
$921$	−2.45462e14	+	1.43218e16i	−0.0122055	+	0.712145i
$922$	1.06771e16	+	6.16443e15i	0.527757	+	0.304700i
$923$	−3.15348e16			−1.54946
$924$	−4.68901e15	+	2.32349e15i	−0.229026	+	0.113486i
$925$	2.31995e16			1.12642
$926$	−1.23960e16	−	7.15683e15i	−0.598303	−	0.345430i
$927$	−3.76082e15	−	2.34672e15i	−0.180445	−	0.112596i
$928$	−2.99324e15	−	5.18445e15i	−0.142767	−	0.247280i
$929$	−1.79422e16	+	3.10767e16i	−0.850723	+	1.47350i	0.0298337	+	0.999555i	$0.490502\pi$
$929$	−1.79422e16	+	3.10767e16i	−0.850723	+	1.47350i	−0.880557	+	0.473941i	$0.842831\pi$
$930$	6.45656e15	−	1.07532e16i	0.304330	−	0.506853i
$931$	−1.31474e15	+	1.41247e16i	−0.0616051	+	0.661845i
$932$			5.20388e15i			0.242404i
$933$	1.34303e16	+	2.42108e16i	0.621921	+	1.12114i
$934$	−2.13513e16	+	1.23272e16i	−0.982918	+	0.567488i
$935$	6.49710e15	−	3.75110e15i	0.297342	−	0.171670i
$936$	−1.19560e16	−	4.09951e14i	−0.543963	−	0.0186515i
$937$		−	6.53149e14i		−	0.0295423i	−0.999891	−	0.0147712i	$-0.995298\pi$
$937$		−	6.53149e14i		−	0.0295423i	0.999891	−	0.0147712i	$-0.00470198\pi$
$938$	−5.48946e15	−	3.51862e15i	−0.246839	−	0.158218i
$939$	−3.07707e16	−	1.84757e16i	−1.37555	−	0.825922i
$940$	2.06999e15	−	3.58532e15i	0.0919950	−	0.159340i
$941$	−1.75758e16	−	3.04422e16i	−0.776557	−	1.34504i	−0.933915	−	0.357494i	$-0.883631\pi$
$941$	−1.75758e16	−	3.04422e16i	−0.776557	−	1.34504i	0.157359	−	0.987541i	$-0.449702\pi$
$942$	−7.04880e15	−	1.20810e14i	−0.309624	−	0.00530668i
$943$	3.88117e16	+	2.24079e16i	1.69492	+	0.978561i
$944$	−4.17700e15			−0.181350
$945$	5.40859e15	+	1.19257e16i	0.233458	+	0.514766i
$946$	−1.20020e16			−0.515055
$947$	−5.68686e15	−	3.28331e15i	−0.242632	−	0.140084i	0.373754	−	0.927528i	$-0.378070\pi$
$947$	−5.68686e15	−	3.28331e15i	−0.242632	−	0.140084i	−0.616386	+	0.787444i	$0.711404\pi$
$948$	−8.99699e15	−	1.54200e14i	−0.381638	−	0.00654092i
$949$	−2.45098e16	−	4.24522e16i	−1.03365	−	1.79034i
$950$	−3.81418e15	+	6.60635e15i	−0.159927	+	0.277001i
$951$	3.00621e16	+	1.80502e16i	1.25322	+	0.752471i
$952$	−4.70205e14	+	1.01250e16i	−0.0194888	+	0.419655i
$953$		−	2.19339e16i		−	0.903868i	−0.892051	−	0.451934i	$-0.850734\pi$
$953$		−	2.19339e16i		−	0.903868i	0.892051	−	0.451934i	$-0.149266\pi$
$954$	−7.82630e15	−	2.68350e14i	−0.320657	−	0.0109947i
$955$	1.12490e16	−	6.49464e15i	0.458244	−	0.264567i
$956$	1.99429e16	−	1.15140e16i	0.807736	−	0.466346i
$957$	−9.94629e15	−	1.79302e16i	−0.400540	−	0.722055i
$958$			4.15912e15i			0.166529i
$959$	4.60576e14	−	9.91765e15i	0.0183358	−	0.394827i
$960$	−9.18838e14	+	1.53030e15i	−0.0363703	+	0.0605737i
$961$	1.50925e16	−	2.61410e16i	0.593996	−	1.02883i
$962$	2.30224e16	+	3.98759e16i	0.900922	+	1.56044i
$963$	−2.01441e14	−	1.25698e14i	−0.00783797	−	0.00489083i
$964$	−1.10284e16	−	6.36727e15i	−0.426668	−	0.246337i
$965$	−1.38783e16			−0.533872
$966$	2.77936e16	+	1.76850e15i	1.06309	+	0.0676442i
$967$	3.38779e16			1.28846			0.644231	−	0.764831i	$-0.277178\pi$
$967$	3.38779e16			1.28846			0.644231	+	0.764831i	$0.277178\pi$
$968$	5.98069e15	+	3.45295e15i	0.226171	+	0.130580i
$969$	3.59947e14	−	2.10015e16i	0.0135350	−	0.789715i
$970$	−9.23653e14	−	1.59981e15i	−0.0345354	−	0.0598170i
$971$	6.09515e15	−	1.05571e16i	0.226610	−	0.392500i	−0.730191	−	0.683243i	$-0.760569\pi$
$971$	6.09515e15	−	1.05571e16i	0.226610	−	0.392500i	0.956801	+	0.290743i	$0.0939024\pi$
$972$	5.73523e15	+	1.22487e16i	0.212025	+	0.452820i
$973$	−2.53536e15	−	1.62511e15i	−0.0932008	−	0.0597395i
$974$			1.65477e16i			0.604872i
$975$	2.52043e16	−	1.39814e16i	0.916114	−	0.508189i
$976$	−1.95137e14	+	1.12662e14i	−0.00705286	+	0.00407197i
$977$	−1.02157e16	+	5.89801e15i	−0.367152	+	0.211975i	−0.672214	−	0.740357i	$-0.734656\pi$
$977$	−1.02157e16	+	5.89801e15i	−0.367152	+	0.211975i	0.305061	+	0.952333i	$0.401323\pi$
$978$	6.21287e15	−	3.44642e15i	0.222039	−	0.123170i
$979$		−	1.63801e15i		−	0.0582119i
$980$	−3.33952e15	−	7.26659e15i	−0.118016	−	0.256795i
$981$	5.22228e15	+	9.80674e15i	0.183519	+	0.344624i
$982$	1.29571e16	−	2.24423e16i	0.452787	−	0.784250i
$983$	2.72447e16	+	4.71892e16i	0.946756	+	1.63983i	0.752198	+	0.658938i	$0.228994\pi$
$983$	2.72447e16	+	4.71892e16i	0.946756	+	1.63983i	0.194558	+	0.980891i	$0.437673\pi$
$984$	2.27775e14	−	1.32898e16i	0.00787107	−	0.459247i
$985$	−1.65861e16	−	9.57600e15i	−0.569962	−	0.329067i
$986$	−3.97142e16			−1.35713
$987$	8.50594e15	+	1.71658e16i	0.289053	+	0.583337i
$988$	−1.51402e16			−0.511645
$989$	5.53156e16	+	3.19365e16i	1.85895	+	1.07327i
$990$	−3.23645e15	+	5.18669e15i	−0.108162	+	0.173339i
$991$	1.26052e16	+	2.18329e16i	0.418933	+	0.725614i	0.995832	−	0.0912017i	$-0.0290708\pi$
$991$	1.26052e16	+	2.18329e16i	0.418933	+	0.725614i	−0.576899	+	0.816815i	$0.695737\pi$
$992$	−3.95578e15	+	6.85161e15i	−0.130743	+	0.226453i
$993$	1.53797e16	−	2.56145e16i	0.505508	−	0.841908i
$994$	−1.00001e16	−	1.93408e16i	−0.326874	−	0.632193i
$995$		−	1.34977e16i		−	0.438765i
$996$	−1.14944e16	−	2.07209e16i	−0.371585	−	0.669858i
$997$	−2.66098e16	+	1.53632e16i	−0.855497	+	0.493921i	−0.862502	−	0.506054i	$-0.831104\pi$
$997$	−2.66098e16	+	1.53632e16i	−0.855497	+	0.493921i	0.00700498	+	0.999975i	$0.497770\pi$
$998$	8.41602e15	−	4.85899e15i	0.269085	−	0.155356i
$999$	2.83105e16	−	4.36849e16i	0.900196	−	1.38906i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	42.12.f.a.5.15	✓	60
3.2	odd	2	inner	42.12.f.a.5.25	yes	60
7.3	odd	6	inner	42.12.f.a.17.25	yes	60
21.17	even	6	inner	42.12.f.a.17.15	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.12.f.a.5.15	✓	60	1.1	even	1	trivial
42.12.f.a.5.25	yes	60	3.2	odd	2	inner
42.12.f.a.17.15	yes	60	21.17	even	6	inner
42.12.f.a.17.25	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} +(420.827 + 7.21258i) q^{3} +(512.000 + 886.810i) q^{4} +(1974.84 - 3420.52i) q^{5} +(-11546.9 - 6933.11i) q^{6} +(-23996.1 + 37436.8i) q^{7} -32768.0i q^{8} +(177043. + 6070.49i) q^{9} +(-109457. + 63194.8i) q^{10} +(236474. - 136529. i) q^{11} +(209067. + 376886. i) q^{12} -2.06091e6i q^{13} +(1.26399e6 - 653541. i) q^{14} +(855735. - 1.42520e6i) q^{15} +(-524288. + 908093. i) q^{16} +(3.47811e6 + 6.02427e6i) q^{17} +(-4.80923e6 - 3.00092e6i) q^{18} +(-6.21305e6 - 3.58711e6i) q^{19} +4.04447e6 q^{20} +(-1.03682e7 + 1.55813e7i) q^{21} -8.73783e6 q^{22} +(4.02714e7 + 2.32507e7i) q^{23} +(236342. - 1.37896e7i) q^{24} +(1.66141e7 + 2.87765e7i) q^{25} +(-3.29745e7 + 5.71135e7i) q^{26} +(7.44606e7 + 3.83156e6i) q^{27} +(-4.54853e7 - 2.11234e6i) q^{28} -1.78411e8i q^{29} +(-4.65180e7 + 2.58046e7i) q^{30} +(-2.04194e8 + 1.17891e8i) q^{31} +(2.90590e7 - 1.67772e7i) q^{32} +(1.00499e8 - 5.57493e7i) q^{33} -2.22599e8i q^{34} +(8.06649e7 + 1.56011e8i) q^{35} +(8.52626e7 + 1.60112e8i) q^{36} +(3.49094e8 - 6.04648e8i) q^{37} +(1.14787e8 + 1.98818e8i) q^{38} +(1.48644e7 - 8.67284e8i) q^{39} +(-1.12084e8 - 6.47115e7i) q^{40} +9.63754e8 q^{41} +(5.36634e8 - 2.65911e8i) q^{42} +1.37357e9 q^{43} +(2.42150e8 + 1.39805e8i) q^{44} +(3.70395e8 - 5.93591e8i) q^{45} +(-7.44022e8 - 1.28868e9i) q^{46} +(5.11807e8 - 8.86476e8i) q^{47} +(-2.27184e8 + 3.78368e8i) q^{48} +(-8.25701e8 - 1.79667e9i) q^{49} -1.06330e9i q^{50} +(1.42023e9 + 2.56026e9i) q^{51} +(1.82763e9 - 1.05518e9i) q^{52} +(1.19635e9 - 6.90713e8i) q^{53} +(-2.00221e9 - 1.29755e9i) q^{54} -1.07849e9i q^{55} +(1.22673e9 + 7.86304e8i) q^{56} +(-2.58875e9 - 1.55436e9i) q^{57} +(-2.85458e9 + 4.94427e9i) q^{58} +(1.99175e9 + 3.44981e9i) q^{59} +(1.70202e9 + 2.91710e7i) q^{60} +(1.86097e8 + 1.07443e8i) q^{61} +7.54505e9 q^{62} +(-4.47560e9 + 6.48225e9i) q^{63} -1.07374e9 q^{64} +(-7.04936e9 - 4.06995e9i) q^{65} +(-3.67711e9 - 6.30223e7i) q^{66} +(-2.29114e9 - 3.96837e9i) q^{67} +(-3.56159e9 + 6.16885e9i) q^{68} +(1.67796e10 + 1.00750e10i) q^{69} +(2.60721e8 - 5.61413e9i) q^{70} -1.53014e10i q^{71} +(1.98918e8 - 5.80134e9i) q^{72} +(2.05988e10 - 1.18927e10i) q^{73} +(-1.93487e10 + 1.11710e10i) q^{74} +(6.78410e9 + 1.22297e10i) q^{75} -7.34640e9i q^{76} +(-5.63271e8 + 1.21290e10i) q^{77} +(-1.42885e10 + 2.37970e10i) q^{78} +(-1.04391e10 + 1.80811e10i) q^{79} +(2.07077e9 + 3.58667e9i) q^{80} +(3.13074e10 + 2.14948e9i) q^{81} +(-2.67083e10 - 1.54201e10i) q^{82} -5.49793e10 q^{83} +(-1.91262e10 - 1.21700e9i) q^{84} +2.74748e10 q^{85} +(-3.80655e10 - 2.19772e10i) q^{86} +(1.28680e9 - 7.50801e10i) q^{87} +(-4.47377e9 - 7.74880e9i) q^{88} +(2.99939e9 - 5.19509e9i) q^{89} +(-1.97621e10 + 1.05237e10i) q^{90} +(7.71537e10 + 4.94537e10i) q^{91} +4.76174e10i q^{92} +(-8.67805e10 + 4.81391e10i) q^{93} +(-2.83672e10 + 1.63778e10i) q^{94} +(-2.45395e10 + 1.41679e10i) q^{95} +(1.23498e10 - 6.85071e9i) q^{96} +1.46160e10i q^{97} +(-5.86429e9 + 6.30021e10i) q^{98} +(4.26949e10 - 2.27359e10i) 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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