LMFDB - Embedded newform 80.10.q.a.29.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [80,10,Mod(29,80)] 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("80.29"); S:= CuspForms(chi, 10); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(80, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 3, 2])) N = Newforms(chi, 10, names="a")

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	80.q (of order $4$, 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:	$41.2028668931$
Analytic rank:	$0$
Dimension:	$212$
Relative dimension:	$106$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			29.17
Character	$\chi$	$=$	80.29
Dual form			80.10.q.a.69.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-20.0088 - 10.5663i) q^{2} +(47.8279 - 47.8279i) q^{3} +(288.707 + 422.838i) q^{4} +(-1077.67 + 889.809i) q^{5} +(-1462.35 + 451.618i) q^{6} +1025.94 q^{7} +(-1308.86 - 11511.1i) q^{8} +15108.0i q^{9} +(30964.8 - 6417.12i) q^{10} +(-27940.6 + 27940.6i) q^{11} +(34031.7 + 6415.22i) q^{12} +(-73654.0 + 73654.0i) q^{13} +(-20527.8 - 10840.4i) q^{14} +(-8984.79 + 94100.3i) q^{15} +(-95440.4 + 244153. i) q^{16} -126813. i q^{17} +(159635. - 302293. i) q^{18} +(-176308. - 176308. i) q^{19} +(-687375. - 198784. i) q^{20} +(49068.5 - 49068.5i) q^{21} +(854286. - 263830. i) q^{22} +359559. q^{23} +(-613151. - 487950. i) q^{24} +(369603. - 1.91783e6i) q^{25} +(2.25198e6 - 695482. i) q^{26} +(1.66398e6 + 1.66398e6i) q^{27} +(296195. + 433806. i) q^{28} +(695018. + 695018. i) q^{29} +(1.17407e6 - 1.78790e6i) q^{30} +2.67835e6 q^{31} +(4.48944e6 - 3.87676e6i) q^{32} +2.67268e6i q^{33} +(-1.33995e6 + 2.53739e6i) q^{34} +(-1.10562e6 + 912889. i) q^{35} +(-6.38823e6 + 4.36178e6i) q^{36} +(2.57912e6 + 2.57912e6i) q^{37} +(1.66480e6 + 5.39065e6i) q^{38} +7.04544e6i q^{39} +(1.16532e7 + 1.12404e7i) q^{40} -2.75830e7i q^{41} +(-1.50027e6 + 463331. i) q^{42} +(9.51782e6 + 9.51782e6i) q^{43} +(-1.98810e7 - 3.74770e6i) q^{44} +(-1.34432e7 - 1.62814e7i) q^{45} +(-7.19436e6 - 3.79921e6i) q^{46} -3.66538e7i q^{47} +(7.11261e6 + 1.62420e7i) q^{48} -3.93011e7 q^{49} +(-2.76597e7 + 3.44683e7i) q^{50} +(-6.06522e6 - 6.06522e6i) q^{51} +(-5.24082e7 - 9.87930e6i) q^{52} +(-3.90184e7 - 3.90184e7i) q^{53} +(-1.57122e7 - 5.08764e7i) q^{54} +(5.24882e6 - 5.49724e7i) q^{55} +(-1.34281e6 - 1.18096e7i) q^{56} -1.68649e7 q^{57} +(-6.56274e6 - 2.12503e7i) q^{58} +(-2.11344e6 + 2.11344e6i) q^{59} +(-4.23832e7 + 2.33683e7i) q^{60} +(-5.82448e7 - 5.82448e7i) q^{61} +(-5.35906e7 - 2.83002e7i) q^{62} +1.54998e7i q^{63} +(-1.30791e8 + 3.01328e7i) q^{64} +(1.38364e7 - 1.44913e8i) q^{65} +(2.82403e7 - 5.34772e7i) q^{66} +(-7.12248e7 + 7.12248e7i) q^{67} +(5.36216e7 - 3.66119e7i) q^{68} +(1.71970e7 - 1.71970e7i) q^{69} +(3.17680e7 - 6.58357e6i) q^{70} +1.03896e7i q^{71} +(1.73909e8 - 1.97742e7i) q^{72} -1.84558e8 q^{73} +(-2.43534e7 - 7.88568e7i) q^{74} +(-7.40487e7 - 1.09403e8i) q^{75} +(2.36485e7 - 1.25451e8i) q^{76} +(-2.86653e7 + 2.86653e7i) q^{77} +(7.44442e7 - 1.40971e8i) q^{78} -4.59415e8 q^{79} +(-1.14397e8 - 3.48039e8i) q^{80} -1.38201e8 q^{81} +(-2.91450e8 + 5.51904e8i) q^{82} +(4.11154e7 - 4.11154e7i) q^{83} +(3.49144e7 + 6.58161e6i) q^{84} +(1.12840e8 + 1.36662e8i) q^{85} +(-8.98725e7 - 2.91008e8i) q^{86} +6.64825e7 q^{87} +(3.58196e8 + 2.85055e8i) q^{88} +1.42514e8i q^{89} +(9.69497e7 + 4.67816e8i) q^{90} +(-7.55644e7 + 7.55644e7i) q^{91} +(1.03807e8 + 1.52035e8i) q^{92} +(1.28100e8 - 1.28100e8i) q^{93} +(-3.87295e8 + 7.33401e8i) q^{94} +(3.46883e8 + 3.31207e7i) q^{95} +(2.93032e7 - 4.00138e8i) q^{96} -1.21163e9i q^{97} +(7.86368e8 + 4.15266e8i) q^{98} +(-4.22125e8 - 4.22125e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 212 q - 4 q^{4} - 2 q^{5} - 4 q^{6} + 17812 q^{10} - 4 q^{11} + 108500 q^{14} - 4 q^{15} - 534208 q^{16} + 480884 q^{19} + 2372984 q^{20} - 78736 q^{21} - 4888112 q^{24} - 7927240 q^{26} - 4 q^{29} - 34132064 q^{30}+ \cdots + 771348172 q^{99}+O(q^{100}) $ 212 * q - 4 * q^4 - 2 * q^5 - 4 * q^6 + 17812 * q^10 - 4 * q^11 + 108500 * q^14 - 4 * q^15 - 534208 * q^16 + 480884 * q^19 + 2372984 * q^20 - 78736 * q^21 - 4888112 * q^24 - 7927240 * q^26 - 4 * q^29 - 34132064 * q^30 + 22164496 * q^31 - 32890400 * q^34 + 15214056 * q^35 - 72152684 * q^36 + 40955304 * q^40 - 63499328 * q^44 + 3945614 * q^45 + 13956012 * q^46 + 1083782580 * q^49 - 119678604 * q^50 + 90093056 * q^51 + 6659032 * q^54 - 74344568 * q^56 - 144037620 * q^59 - 106324752 * q^60 - 90121108 * q^61 + 74046704 * q^64 - 62806092 * q^65 + 1419462624 * q^66 - 382438912 * q^69 - 127364260 * q^70 + 2153363568 * q^74 + 119613476 * q^75 + 1579189648 * q^76 + 423438896 * q^79 + 425390872 * q^80 - 7748409788 * q^81 + 4494494704 * q^84 + 3906248 * q^85 + 2482762604 * q^86 - 3409730584 * q^90 + 1231623152 * q^91 + 3948740348 * q^94 - 2480993260 * q^95 - 464870984 * q^96 + 771348172 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	−20.0088	−	10.5663i	−0.884274	−	0.466968i
$2$	−20.0088	−	10.5663i	−0.884274	−	0.466968i
$3$	47.8279	−	47.8279i	0.340907	−	0.340907i	−0.515801	−	0.856708i	$-0.672506\pi$
$3$	47.8279	−	47.8279i	0.340907	−	0.340907i	0.856708	+	0.515801i	$0.172506\pi$
$4$	288.707	+	422.838i	0.563881	+	0.825856i
$5$	−1077.67	+	889.809i	−0.771115	+	0.636696i
$5$	−1077.67	+	889.809i	−0.771115	+	0.636696i
$6$	−1462.35	+	451.618i	−0.460648	+	0.142262i
$7$	1025.94			0.161503			0.0807513	−	0.996734i	$-0.474268\pi$
$7$	1025.94			0.161503			0.0807513	+	0.996734i	$0.474268\pi$
$8$	−1308.86	−	11511.1i	−0.112977	−	0.993598i
$9$			15108.0i			0.767565i
$10$	30964.8	−	6417.12i	0.979194	−	0.202927i
$11$	−27940.6	+	27940.6i	−0.575397	+	0.575397i	−0.933632	−	0.358234i	$-0.883379\pi$
$11$	−27940.6	+	27940.6i	−0.575397	+	0.575397i	0.358234	+	0.933632i	$0.383379\pi$
$12$	34031.7	+	6415.22i	0.473771	+	0.0893091i
$13$	−73654.0	+	73654.0i	−0.715239	+	0.715239i	−0.967626	−	0.252387i	$-0.918784\pi$
$13$	−73654.0	+	73654.0i	−0.715239	+	0.715239i	0.252387	+	0.967626i	$0.418784\pi$
$14$	−20527.8	−	10840.4i	−0.142813	−	0.0754167i
$15$	−8984.79	+	94100.3i	−0.0458245	+	0.479933i
$16$	−95440.4	+	244153.i	−0.364076	+	0.931369i
$17$		−	126813.i		−	0.368252i	−0.982903	−	0.184126i	$-0.941055\pi$
$17$		−	126813.i		−	0.368252i	0.982903	−	0.184126i	$-0.0589454\pi$
$18$	159635.	−	302293.i	0.358428	−	0.678738i
$19$	−176308.	−	176308.i	−0.310372	−	0.310372i	0.534682	−	0.845053i	$-0.320431\pi$
$19$	−176308.	−	176308.i	−0.310372	−	0.310372i	−0.845053	+	0.534682i	$0.820431\pi$
$20$	−687375.	−	198784.i	−0.960636	−	0.277809i
$21$	49068.5	−	49068.5i	0.0550574	−	0.0550574i
$22$	854286.	−	263830.i	0.777501	−	0.240117i
$23$	359559.			0.267914			0.133957	−	0.990987i	$-0.457232\pi$
$23$	359559.			0.267914			0.133957	+	0.990987i	$0.457232\pi$
$24$	−613151.	−	487950.i	−0.377239	−	0.300210i
$25$	369603.	−	1.91783e6i	0.189237	−	0.981931i
$26$	2.25198e6	−	695482.i	0.966462	−	0.298473i
$27$	1.66398e6	+	1.66398e6i	0.602575	+	0.602575i
$28$	296195.	+	433806.i	0.0910683	+	0.133378i
$29$	695018.	+	695018.i	0.182476	+	0.182476i	0.792434	−	0.609958i	$-0.208814\pi$
$29$	695018.	+	695018.i	0.182476	+	0.182476i	−0.609958	+	0.792434i	$0.708814\pi$
$30$	1.17407e6	−	1.78790e6i	0.264635	−	0.402993i
$31$	2.67835e6			0.520882			0.260441	−	0.965490i	$-0.416132\pi$
$31$	2.67835e6			0.520882			0.260441	+	0.965490i	$0.416132\pi$
$32$	4.48944e6	−	3.87676e6i	0.756863	−	0.653573i
$33$			2.67268e6i			0.392314i
$34$	−1.33995e6	+	2.53739e6i	−0.171962	+	0.325636i
$35$	−1.10562e6	+	912889.i	−0.124537	+	0.102828i
$36$	−6.38823e6	+	4.36178e6i	−0.633898	+	0.432815i
$37$	2.57912e6	+	2.57912e6i	0.226237	+	0.226237i	0.811119	−	0.584882i	$-0.198859\pi$
$37$	2.57912e6	+	2.57912e6i	0.226237	+	0.226237i	−0.584882	+	0.811119i	$0.698859\pi$
$38$	1.66480e6	+	5.39065e6i	0.129520	+	0.419387i
$39$			7.04544e6i			0.487660i
$40$	1.16532e7	+	1.12404e7i	0.719737	+	0.694246i
$41$		−	2.75830e7i		−	1.52445i	−0.647310	−	0.762227i	$-0.724106\pi$
$41$		−	2.75830e7i		−	1.52445i	0.647310	−	0.762227i	$-0.275894\pi$
$42$	−1.50027e6	+	463331.i	−0.0743959	+	0.0229758i
$43$	9.51782e6	+	9.51782e6i	0.424550	+	0.424550i	0.886767	−	0.462217i	$-0.152946\pi$
$43$	9.51782e6	+	9.51782e6i	0.424550	+	0.424550i	−0.462217	+	0.886767i	$0.652946\pi$
$44$	−1.98810e7	−	3.74770e6i	−0.799651	−	0.150740i
$45$	−1.34432e7	−	1.62814e7i	−0.488705	−	0.591881i
$46$	−7.19436e6	−	3.79921e6i	−0.236909	−	0.125107i
$47$		−	3.66538e7i		−	1.09567i	−0.836587	−	0.547834i	$-0.815452\pi$
$47$		−	3.66538e7i		−	1.09567i	0.836587	−	0.547834i	$-0.184548\pi$
$48$	7.11261e6	+	1.62420e7i	0.193394	+	0.441626i
$49$	−3.93011e7			−0.973917
$50$	−2.76597e7	+	3.44683e7i	−0.625868	+	0.779929i
$51$	−6.06522e6	−	6.06522e6i	−0.125540	−	0.125540i
$52$	−5.24082e7	−	9.87930e6i	−0.993995	−	0.187375i
$53$	−3.90184e7	−	3.90184e7i	−0.679248	−	0.679248i	0.280582	−	0.959830i	$-0.409473\pi$
$53$	−3.90184e7	−	3.90184e7i	−0.679248	−	0.679248i	−0.959830	+	0.280582i	$0.909473\pi$
$54$	−1.57122e7	−	5.08764e7i	−0.251458	−	0.814225i
$55$	5.24882e6	−	5.49724e7i	0.0773445	−	0.810051i
$56$	−1.34281e6	−	1.18096e7i	−0.0182460	−	0.160469i
$57$	−1.68649e7			−0.211616
$58$	−6.56274e6	−	2.12503e7i	−0.0761481	−	0.246569i
$59$	−2.11344e6	+	2.11344e6i	−0.0227068	+	0.0227068i	−0.718369	−	0.695662i	$-0.755111\pi$
$59$	−2.11344e6	+	2.11344e6i	−0.0227068	+	0.0227068i	0.695662	+	0.718369i	$0.255111\pi$
$60$	−4.23832e7	+	2.33683e7i	−0.422195	+	0.232781i
$61$	−5.82448e7	−	5.82448e7i	−0.538608	−	0.538608i	0.384512	−	0.923120i	$-0.374370\pi$
$61$	−5.82448e7	−	5.82448e7i	−0.538608	−	0.538608i	−0.923120	+	0.384512i	$0.874370\pi$
$62$	−5.35906e7	−	2.83002e7i	−0.460602	−	0.243235i
$63$			1.54998e7i			0.123964i
$64$	−1.30791e8	+	3.01328e7i	−0.974473	+	0.224507i
$65$	1.38364e7	−	1.44913e8i	0.0961420	−	1.00692i
$66$	2.82403e7	−	5.34772e7i	0.183198	−	0.346913i
$67$	−7.12248e7	+	7.12248e7i	−0.431812	+	0.431812i	−0.889244	−	0.457433i	$-0.848769\pi$
$67$	−7.12248e7	+	7.12248e7i	−0.431812	+	0.431812i	0.457433	+	0.889244i	$0.348769\pi$
$68$	5.36216e7	−	3.66119e7i	0.304123	−	0.207650i
$69$	1.71970e7	−	1.71970e7i	0.0913338	−	0.0913338i
$70$	3.17680e7	−	6.58357e6i	0.158142	−	0.0327733i
$71$			1.03896e7i			0.0485216i	0.999706	+	0.0242608i	$0.00772321\pi$
$71$			1.03896e7i			0.0485216i	−0.999706	+	0.0242608i	$0.992277\pi$
$72$	1.73909e8	−	1.97742e7i	0.762651	−	0.0867169i
$73$	−1.84558e8			−0.760642			−0.380321	−	0.924855i	$-0.624186\pi$
$73$	−1.84558e8			−0.760642			−0.380321	+	0.924855i	$0.624186\pi$
$74$	−2.43534e7	−	7.88568e7i	−0.0944099	−	0.305701i
$75$	−7.40487e7	−	1.09403e8i	−0.270235	−	0.399260i
$76$	2.36485e7	−	1.25451e8i	0.0813096	−	0.431335i
$77$	−2.86653e7	+	2.86653e7i	−0.0929282	+	0.0929282i
$78$	7.44442e7	−	1.40971e8i	0.227722	−	0.431225i
$79$	−4.59415e8			−1.32704			−0.663518	−	0.748160i	$-0.730938\pi$
$79$	−4.59415e8			−1.32704			−0.663518	+	0.748160i	$0.730938\pi$
$80$	−1.14397e8	−	3.48039e8i	−0.312254	−	0.949999i
$81$	−1.38201e8			−0.356720
$82$	−2.91450e8	+	5.51904e8i	−0.711872	+	1.34804i
$83$	4.11154e7	−	4.11154e7i	0.0950941	−	0.0950941i	−0.657959	−	0.753053i	$-0.728580\pi$
$83$	4.11154e7	−	4.11154e7i	0.0950941	−	0.0950941i	0.753053	+	0.657959i	$0.228580\pi$
$84$	3.49144e7	+	6.58161e6i	0.0765153	+	0.0144237i
$85$	1.12840e8	+	1.36662e8i	0.234464	+	0.283965i
$86$	−8.98725e7	−	2.91008e8i	−0.177167	−	0.573671i
$87$	6.64825e7			0.124414
$88$	3.58196e8	+	2.85055e8i	0.636720	+	0.506707i
$89$			1.42514e8i			0.240771i	0.992727	+	0.120385i	$0.0384130\pi$
$89$			1.42514e8i			0.240771i	−0.992727	+	0.120385i	$0.961587\pi$
$90$	9.69497e7	+	4.67816e8i	0.155760	+	0.751595i
$91$	−7.55644e7	+	7.55644e7i	−0.115513	+	0.115513i
$92$	1.03807e8	+	1.52035e8i	0.151072	+	0.221258i
$93$	1.28100e8	−	1.28100e8i	0.177572	−	0.177572i
$94$	−3.87295e8	+	7.33401e8i	−0.511643	+	0.968871i
$95$	3.46883e8	+	3.31207e7i	0.436944	+	0.0417199i
$96$	2.93032e7	−	4.00138e8i	0.0352123	−	0.480828i
$97$		−	1.21163e9i		−	1.38963i	−0.719190	−	0.694814i	$-0.755487\pi$
$97$		−	1.21163e9i		−	1.38963i	0.719190	−	0.694814i	$-0.244513\pi$
$98$	7.86368e8	+	4.15266e8i	0.861209	+	0.454788i
$99$	−4.22125e8	−	4.22125e8i	−0.441655	−	0.441655i
$100$	9.17641e8	−	3.97410e8i	0.917641	−	0.397410i
$101$	1.63862e8	−	1.63862e8i	0.156687	−	0.156687i	−0.624410	−	0.781097i	$-0.714660\pi$
$101$	1.63862e8	−	1.63862e8i	0.156687	−	0.156687i	0.781097	+	0.624410i	$0.214660\pi$
$102$	5.72712e7	+	1.85445e8i	0.0523884	+	0.169635i
$103$	1.90563e9			1.66829			0.834144	−	0.551547i	$-0.185962\pi$
$103$	1.90563e9			1.66829			0.834144	+	0.551547i	$0.185962\pi$
$104$	9.44239e8	+	7.51433e8i	0.791466	+	0.629855i
$105$	−9.21784e6	+	9.65410e7i	−0.00740078	+	0.0775104i
$106$	3.68433e8	+	1.19299e9i	0.283454	+	0.917829i
$107$	−1.23791e9	−	1.23791e9i	−0.912985	−	0.912985i	0.0835207	−	0.996506i	$-0.473384\pi$
$107$	−1.23791e9	−	1.23791e9i	−0.912985	−	0.912985i	−0.996506	+	0.0835207i	$0.973384\pi$
$108$	−2.23192e8	+	1.18400e9i	−0.157860	+	0.837421i
$109$	1.29556e9	+	1.29556e9i	0.879099	+	0.879099i	0.993441	−	0.114342i	$-0.0364761\pi$
$109$	1.29556e9	+	1.29556e9i	0.879099	+	0.879099i	−0.114342	+	0.993441i	$0.536476\pi$
$110$	−6.85876e8	+	1.04447e9i	−0.446662	+	0.680189i
$111$	2.46708e8			0.154251
$112$	−9.79159e7	+	2.50486e8i	−0.0587993	+	0.150419i
$113$		−	2.77041e9i		−	1.59842i	−0.601050	−	0.799211i	$-0.705251\pi$
$113$		−	2.77041e9i		−	1.59842i	0.601050	−	0.799211i	$-0.294749\pi$
$114$	3.37448e8	+	1.78200e8i	0.187126	+	0.0988178i
$115$	−3.87485e8	+	3.19939e8i	−0.206592	+	0.170580i
$116$	−9.32236e7	+	4.94537e8i	−0.0478041	+	0.253593i
$117$	−1.11276e9	−	1.11276e9i	−0.548993	−	0.548993i
$118$	6.46186e7	−	1.99562e7i	0.0306824	−	0.00947566i
$119$		−	1.30103e8i		−	0.0594737i
$120$	1.09495e9	−	1.97397e7i	0.482037	−	0.00869011i
$121$			7.96599e8i			0.337836i
$122$	5.49979e8	+	1.78084e9i	0.224764	+	0.727790i
$123$	−1.31924e9	−	1.31924e9i	−0.519697	−	0.519697i
$124$	7.73257e8	+	1.13251e9i	0.293715	+	0.430173i
$125$	1.30820e9	+	2.39566e9i	0.479268	+	0.877668i
$126$	1.63776e8	−	3.10134e8i	0.0578872	−	0.109618i
$127$		−	2.91641e9i		−	0.994791i	−0.867524	−	0.497396i	$-0.834290\pi$
$127$		−	2.91641e9i		−	0.994791i	0.867524	−	0.497396i	$-0.165710\pi$
$128$	2.93538e9	+	7.79059e8i	0.966538	+	0.256522i
$129$	9.10435e8			0.289465
$130$	−1.80804e9	+	2.75333e9i	−0.555217	+	0.845500i
$131$	−1.26085e8	−	1.26085e8i	−0.0374062	−	0.0374062i	0.688156	−	0.725562i	$-0.258420\pi$
$131$	−1.26085e8	−	1.26085e8i	−0.0374062	−	0.0374062i	−0.725562	+	0.688156i	$0.758420\pi$
$132$	−1.13011e9	+	7.71621e8i	−0.323995	+	0.221218i
$133$	−1.80881e8	−	1.80881e8i	−0.0501258	−	0.0501258i
$134$	2.17771e9	−	6.72543e8i	0.583482	−	0.180197i
$135$	−3.27384e9	−	3.12590e8i	−0.848312	−	0.0809977i
$136$	−1.45976e9	+	1.65981e8i	−0.365894	+	0.0416039i
$137$	−1.47726e9			−0.358273			−0.179136	−	0.983824i	$-0.557330\pi$
$137$	−1.47726e9			−0.358273			−0.179136	+	0.983824i	$0.557330\pi$
$138$	−5.25800e8	+	1.62383e8i	−0.123414	+	0.0381141i
$139$	2.35043e8	−	2.35043e8i	0.0534049	−	0.0534049i	−0.679900	−	0.733305i	$-0.737977\pi$
$139$	2.35043e8	−	2.35043e8i	0.0534049	−	0.0534049i	0.733305	+	0.679900i	$0.237977\pi$
$140$	−7.05204e8	−	2.03940e8i	−0.155145	−	0.0448670i
$141$	−1.75308e9	−	1.75308e9i	−0.373521	−	0.373521i
$142$	1.09779e8	−	2.07883e8i	0.0226581	−	0.0429064i
$143$		−	4.11587e9i		−	0.823094i
$144$	−3.68866e9	−	1.44191e9i	−0.714886	−	0.279452i
$145$	−1.36743e9	−	1.30564e8i	−0.256891	−	0.0245282i
$146$	3.69279e9	+	1.95009e9i	0.672616	+	0.355196i
$147$	−1.87969e9	+	1.87969e9i	−0.332015	+	0.332015i
$148$	−3.45940e8	+	1.83516e9i	−0.0592684	+	0.314410i
$149$	5.17938e9	−	5.17938e9i	0.860874	−	0.860874i	−0.130566	−	0.991440i	$-0.541679\pi$
$149$	5.17938e9	−	5.17938e9i	0.860874	−	0.860874i	0.991440	+	0.130566i	$0.0416794\pi$
$150$	3.25640e8	+	2.97146e9i	0.0525203	+	0.479246i
$151$			9.06276e9i			1.41861i	0.704899	+	0.709307i	$0.250992\pi$
$151$			9.06276e9i			1.41861i	−0.704899	+	0.709307i	$0.749008\pi$
$152$	−1.79873e9	+	2.26026e9i	−0.273320	+	0.343449i
$153$	1.91589e9			0.282657
$154$	8.76444e8	−	2.70673e8i	0.125569	−	0.0387795i
$155$	−2.88636e9	+	2.38322e9i	−0.401660	+	0.331643i
$156$	−2.97908e9	+	2.03407e9i	−0.402737	+	0.274982i
$157$	−2.10992e9	+	2.10992e9i	−0.277152	+	0.277152i	−0.831971	−	0.554819i	$-0.812787\pi$
$157$	−2.10992e9	+	2.10992e9i	−0.277152	+	0.277152i	0.554819	+	0.831971i	$0.312787\pi$
$158$	9.19235e9	+	4.85431e9i	1.17346	+	0.619684i
$159$	−3.73234e9			−0.463121
$160$	−1.38854e9	+	8.17260e9i	−0.167501	+	0.985872i
$161$	3.68885e8			0.0432688
$162$	2.76524e9	+	1.46027e9i	0.315439	+	0.166577i
$163$	6.70372e9	−	6.70372e9i	0.743826	−	0.743826i	−0.229486	−	0.973312i	$-0.573704\pi$
$163$	6.70372e9	−	6.70372e9i	0.743826	−	0.743826i	0.973312	+	0.229486i	$0.0737045\pi$
$164$	1.16632e10	−	7.96341e9i	1.25898	−	0.859611i
$165$	−2.37817e9	−	2.88025e9i	−0.249785	−	0.302519i
$166$	−1.25711e9	+	3.88235e8i	−0.128495	+	0.0396833i
$167$	2.22645e8			0.0221508			0.0110754	−	0.999939i	$-0.496475\pi$
$167$	2.22645e8			0.0221508			0.0110754	+	0.999939i	$0.496475\pi$
$168$	−6.29054e8	−	5.00607e8i	−0.0609251	−	0.0484847i
$169$		−	2.45336e8i		−	0.0231350i
$170$	−8.13777e8	−	3.92676e9i	−0.0747283	−	0.360590i
$171$	2.66366e9	−	2.66366e9i	0.238230	−	0.238230i
$172$	−1.27664e9	+	6.77236e9i	−0.111222	+	0.590014i
$173$	1.48682e10	−	1.48682e10i	1.26198	−	1.26198i	0.311844	−	0.950133i	$-0.399053\pi$
$173$	1.48682e10	−	1.48682e10i	1.26198	−	1.26198i	0.950133	−	0.311844i	$-0.100947\pi$
$174$	−1.33024e9	−	7.02474e8i	−0.110016	−	0.0580976i
$175$	3.79190e8	−	1.96758e9i	0.0305623	−	0.158585i
$176$	−4.15511e9	−	9.48842e9i	−0.326419	−	0.745396i
$177$			2.02163e8i			0.0154818i
$178$	1.50585e9	−	2.85155e9i	0.112432	−	0.212907i
$179$	−1.20644e10	−	1.20644e10i	−0.878352	−	0.878352i	0.115012	−	0.993364i	$-0.463309\pi$
$179$	−1.20644e10	−	1.20644e10i	−0.878352	−	0.878352i	−0.993364	+	0.115012i	$0.963309\pi$
$180$	3.00323e9	−	1.03849e10i	0.213237	−	0.737351i
$181$	2.50298e9	−	2.50298e9i	0.173342	−	0.173342i	−0.615104	−	0.788446i	$-0.710886\pi$
$181$	2.50298e9	−	2.50298e9i	0.173342	−	0.173342i	0.788446	+	0.615104i	$0.210886\pi$
$182$	2.31039e9	−	7.13521e8i	0.156086	−	0.0482043i
$183$	−5.57145e9			−0.367230
$184$	−4.70613e8	−	4.13891e9i	−0.0302680	−	0.266199i
$185$	−5.07435e9	−	4.84504e8i	−0.318499	−	0.0304106i
$186$	−3.91667e9	+	1.20959e9i	−0.239943	+	0.0741019i
$187$	3.54324e9	+	3.54324e9i	0.211891	+	0.211891i
$188$	1.54986e10	−	1.05822e10i	0.904864	−	0.617827i
$189$	1.70714e9	+	1.70714e9i	0.0973175	+	0.0973175i
$190$	−6.59075e9	−	4.32797e9i	−0.366897	−	0.240931i
$191$	−3.36825e10			−1.83128			−0.915640	−	0.402000i	$-0.868315\pi$
$191$	−3.36825e10			−1.83128			−0.915640	+	0.402000i	$0.868315\pi$
$192$	−4.81430e9	+	7.69668e9i	−0.255669	+	0.408740i
$193$			2.20130e10i			1.14201i	0.820945	+	0.571007i	$0.193447\pi$
$193$			2.20130e10i			1.14201i	−0.820945	+	0.571007i	$0.806553\pi$
$194$	−1.28025e10	+	2.42434e10i	−0.648912	+	1.22881i
$195$	−6.26910e9	−	7.59263e9i	−0.310491	−	0.376042i
$196$	−1.13465e10	−	1.66180e10i	−0.549173	−	0.804315i
$197$	4.72571e9	+	4.72571e9i	0.223547	+	0.223547i	0.809990	−	0.586443i	$-0.199472\pi$
$197$	4.72571e9	+	4.72571e9i	0.223547	+	0.223547i	−0.586443	+	0.809990i	$0.699472\pi$
$198$	3.98594e9	+	1.29065e10i	0.184305	+	0.596783i
$199$		−	1.70335e10i		−	0.769956i	−0.922926	−	0.384978i	$-0.874209\pi$
$199$		−	1.70335e10i		−	0.769956i	0.922926	−	0.384978i	$-0.125791\pi$
$200$	−2.25601e10	−	1.74435e9i	−0.997024	−	0.0770900i
$201$			6.81307e9i			0.294415i
$202$	−5.01011e9	+	1.54728e9i	−0.211722	+	0.0653863i
$203$	7.13045e8	+	7.13045e8i	0.0294703	+	0.0294703i
$204$	8.13536e8	−	4.31568e9i	0.0328883	−	0.174467i
$205$	2.45436e10	+	2.97253e10i	0.970614	+	1.17553i
$206$	−3.81294e10	−	2.01354e10i	−1.47522	−	0.779038i
$207$			5.43221e9i			0.205641i
$208$	−1.09533e10	−	2.50124e10i	−0.405750	−	0.926554i
$209$	9.85231e9			0.357174
$210$	1.20452e9	−	1.83428e9i	0.0427392	−	0.0650845i
$211$	−2.99069e10	−	2.99069e10i	−1.03873	−	1.03873i	−0.999219	−	0.0395068i	$-0.987421\pi$
$211$	−2.99069e10	−	2.99069e10i	−1.03873	−	1.03873i	−0.0395068	−	0.999219i	$-0.512579\pi$
$212$	5.23359e9	−	2.77634e10i	0.177946	−	0.943976i
$213$	4.96912e8	+	4.96912e8i	0.0165414	+	0.0165414i
$214$	1.16891e10	+	3.78494e10i	0.380994	+	1.23366i
$215$	−1.87261e10	−	1.78799e9i	−0.597687	−	0.0570678i
$216$	1.69763e10	−	2.13321e10i	0.530640	−	0.666794i
$217$	2.74782e9			0.0841238
$218$	−1.22334e10	−	3.96119e10i	−0.366853	−	1.18788i
$219$	−8.82703e9	+	8.82703e9i	−0.259308	+	0.259308i
$220$	2.47598e10	−	1.36515e10i	0.712598	−	0.392897i
$221$	9.34032e9	+	9.34032e9i	0.263388	+	0.263388i
$222$	−4.93633e9	−	2.60678e9i	−0.136401	−	0.0720306i
$223$			3.84680e10i			1.04166i	0.853659	+	0.520832i	$0.174378\pi$
$223$			3.84680e10i			1.04166i	−0.853659	+	0.520832i	$0.825622\pi$
$224$	4.60589e9	−	3.97732e9i	0.122235	−	0.105554i
$225$	2.89746e10	+	5.58396e9i	0.753696	+	0.145252i
$226$	−2.92730e10	+	5.54327e10i	−0.746413	+	1.41344i
$227$	−1.14916e10	+	1.14916e10i	−0.287253	+	0.287253i	−0.835993	−	0.548740i	$-0.815108\pi$
$227$	−1.14916e10	+	1.14916e10i	−0.287253	+	0.287253i	0.548740	+	0.835993i	$0.315108\pi$
$228$	−4.86903e9	−	7.13114e9i	−0.119326	−	0.174764i
$229$	1.37335e10	−	1.37335e10i	0.330005	−	0.330005i	−0.522583	−	0.852588i	$-0.675032\pi$
$229$	1.37335e10	−	1.37335e10i	0.330005	−	0.330005i	0.852588	+	0.522583i	$0.175032\pi$
$230$	1.11337e10	−	2.30734e9i	0.262340	−	0.0543670i
$231$			2.74200e9i			0.0633598i
$232$	7.09071e9	−	8.91008e9i	0.160692	−	0.201923i
$233$	−1.68678e10			−0.374935			−0.187468	−	0.982271i	$-0.560028\pi$
$233$	−1.68678e10			−0.374935			−0.187468	+	0.982271i	$0.560028\pi$
$234$	1.05073e10	+	3.40229e10i	0.229098	+	0.741822i
$235$	3.26149e10	+	3.95006e10i	0.697607	+	0.844886i
$236$	−1.50381e9	−	2.83478e8i	−0.0315564	−	0.00594861i
$237$	−2.19729e10	+	2.19729e10i	−0.452396	+	0.452396i
$238$	−1.37470e9	+	2.60320e9i	−0.0277723	+	0.0525910i
$239$	−8.40656e9			−0.166659			−0.0833293	−	0.996522i	$-0.526555\pi$
$239$	−8.40656e9			−0.166659			−0.0833293	+	0.996522i	$0.526555\pi$
$240$	−2.21173e10	−	1.11746e10i	−0.430311	−	0.217412i
$241$	5.67511e10			1.08367			0.541835	−	0.840485i	$-0.317730\pi$
$241$	5.67511e10			1.08367			0.541835	+	0.840485i	$0.317730\pi$
$242$	8.41709e9	−	1.59390e10i	0.157759	−	0.298739i
$243$	−3.93620e10	+	3.93620e10i	−0.724184	+	0.724184i
$244$	7.81244e9	−	4.14438e10i	0.141102	−	0.748523i
$245$	4.23534e10	−	3.49705e10i	0.751002	−	0.620089i
$246$	1.24570e10	+	4.03359e10i	0.216873	+	0.702237i
$247$	2.59717e10			0.443980
$248$	−3.50558e9	−	3.08306e10i	−0.0588475	−	0.517547i
$249$		−	3.93293e9i		−	0.0648365i
$250$	−8.62277e8	−	6.17572e10i	−0.0139610	−	0.999903i
$251$	−2.57904e10	+	2.57904e10i	−0.410135	+	0.410135i	−0.881786	−	0.471651i	$-0.843658\pi$
$251$	−2.57904e10	+	2.57904e10i	−0.410135	+	0.410135i	0.471651	+	0.881786i	$0.343658\pi$
$252$	−6.55393e9	+	4.47491e9i	−0.102376	+	0.0699008i
$253$	−1.00463e10	+	1.00463e10i	−0.154157	+	0.154157i
$254$	−3.08156e10	+	5.83540e10i	−0.464536	+	0.879668i
$255$	1.19332e10	+	1.13939e9i	0.176736	+	0.0168749i
$256$	−5.05017e10	−	4.66041e10i	−0.734897	−	0.678179i
$257$		−	6.23158e10i		−	0.891044i	−0.895271	−	0.445522i	$-0.853018\pi$
$257$		−	6.23158e10i		−	0.891044i	0.895271	−	0.445522i	$-0.146982\pi$
$258$	−1.82167e10	−	9.61992e9i	−0.255966	−	0.135171i
$259$	2.64601e9	+	2.64601e9i	0.0365379	+	0.0365379i
$260$	6.52692e10	−	3.59867e10i	0.885785	−	0.488385i
$261$	−1.05003e10	+	1.05003e10i	−0.140062	+	0.140062i
$262$	1.19057e9	+	3.85507e9i	0.0156098	+	0.0505448i
$263$	1.20133e11			1.54832			0.774161	−	0.632989i	$-0.218172\pi$
$263$	1.20133e11			1.54832			0.774161	+	0.632989i	$0.218172\pi$
$264$	3.07654e10	−	3.49817e9i	0.389802	−	0.0443223i
$265$	7.67678e10	+	7.32987e9i	0.956253	+	0.0913040i
$266$	1.70798e9	+	5.53047e9i	0.0209178	+	0.0677322i
$267$	6.81617e9	+	6.81617e9i	0.0820804	+	0.0820804i
$268$	−5.06796e10	−	9.55346e9i	−0.600105	−	0.113124i
$269$	6.57458e10	+	6.57458e10i	0.765566	+	0.765566i	0.977322	−	0.211757i	$-0.0679184\pi$
$269$	6.57458e10	+	6.57458e10i	0.765566	+	0.765566i	−0.211757	+	0.977322i	$0.567918\pi$
$270$	6.22028e10	+	4.08469e10i	0.712317	+	0.467759i
$271$	−1.34514e11			−1.51498			−0.757488	−	0.652849i	$-0.773574\pi$
$271$	−1.34514e11			−1.51498			−0.757488	+	0.652849i	$0.773574\pi$
$272$	3.09618e10	+	1.21031e10i	0.342978	+	0.134072i
$273$			7.22818e9i			0.0787585i
$274$	2.95582e10	+	1.56091e10i	0.316811	+	0.167302i
$275$	4.32584e10	+	6.39123e10i	0.456114	+	0.673887i
$276$	1.22364e10	+	2.30665e9i	0.126930	+	0.0239272i
$277$	1.08092e11	+	1.08092e11i	1.10315	+	1.10315i	0.994028	+	0.109125i	$0.0348049\pi$
$277$	1.08092e11	+	1.08092e11i	1.10315	+	1.10315i	0.109125	+	0.994028i	$0.465195\pi$
$278$	−7.18647e9	+	2.21941e9i	−0.0721630	+	0.0222862i
$279$			4.04644e10i			0.399810i
$280$	1.19554e10	+	1.15320e10i	0.116240	+	0.112123i
$281$			8.51645e10i			0.814855i	0.913238	+	0.407427i	$0.133574\pi$
$281$			8.51645e10i			0.814855i	−0.913238	+	0.407427i	$0.866426\pi$
$282$	1.65535e10	+	5.36006e10i	0.155872	+	0.504718i
$283$	2.92820e10	+	2.92820e10i	0.271370	+	0.271370i	0.829652	−	0.558282i	$-0.188539\pi$
$283$	2.92820e10	+	2.92820e10i	0.271370	+	0.271370i	−0.558282	+	0.829652i	$0.688539\pi$
$284$	−4.39311e9	+	2.99954e9i	−0.0400719	+	0.0273604i
$285$	1.81748e10	−	1.50066e10i	0.163180	−	0.134735i
$286$	−4.34895e10	+	8.23537e10i	−0.384359	+	0.727841i
$287$		−	2.82985e10i		−	0.246203i
$288$	5.85700e10	+	6.78264e10i	0.501660	+	0.580942i
$289$	1.02506e11			0.864391
$290$	2.59811e10	+	1.70611e10i	0.215708	+	0.141650i
$291$	−5.79499e10	−	5.79499e10i	−0.473734	−	0.473734i
$292$	−5.32832e10	−	7.80382e10i	−0.428911	−	0.628181i
$293$	7.33539e9	+	7.33539e9i	0.0581459	+	0.0581459i	0.735582	−	0.677436i	$-0.236909\pi$
$293$	7.33539e9	+	7.33539e9i	0.0581459	+	0.0581459i	−0.677436	+	0.735582i	$0.736909\pi$
$294$	5.74717e10	−	1.77490e10i	0.448633	−	0.138552i
$295$	3.97023e8	−	4.15814e9i	0.00305223	−	0.0319668i
$296$	2.63127e10	−	3.30641e10i	0.199229	−	0.250348i
$297$	−9.29851e10			−0.693441
$298$	−1.58360e11	+	4.89065e10i	−1.16325	+	0.359247i
$299$	−2.64830e10	+	2.64830e10i	−0.191623	+	0.191623i
$300$	2.48816e10	−	6.28962e10i	0.177350	−	0.448310i
$301$	9.76469e9	+	9.76469e9i	0.0685660	+	0.0685660i
$302$	9.57598e10	−	1.81335e11i	0.662448	−	1.25444i
$303$		−	1.56744e10i		−	0.106831i
$304$	5.98732e10	−	2.62192e10i	0.402069	−	0.176072i
$305$	1.14595e11	+	1.09417e10i	0.758258	+	0.0723993i
$306$	−3.83348e10	−	2.02439e10i	−0.249946	−	0.131992i
$307$	−1.65748e11	+	1.65748e11i	−1.06494	+	1.06494i	−0.0672045	+	0.997739i	$0.521408\pi$
$307$	−1.65748e11	+	1.65748e11i	−1.06494	+	1.06494i	−0.997739	+	0.0672045i	$0.978592\pi$
$308$	−2.03966e10	−	3.84491e9i	−0.129146	−	0.0243449i
$309$	9.11423e10	−	9.11423e10i	0.568731	−	0.568731i
$310$	8.29345e10	−	1.71873e10i	0.510044	−	0.105701i
$311$		−	1.65873e11i		−	1.00543i	−0.864451	−	0.502716i	$-0.832334\pi$
$311$		−	1.65873e11i		−	1.00543i	0.864451	−	0.502716i	$-0.167666\pi$
$312$	8.11005e10	−	9.22151e9i	0.484538	−	0.0550942i
$313$	−2.67581e11			−1.57582			−0.787908	−	0.615793i	$-0.788836\pi$
$313$	−2.67581e11			−1.57582			−0.787908	+	0.615793i	$0.788836\pi$
$314$	6.45111e10	−	1.99230e10i	0.374499	−	0.115657i
$315$	−1.37919e10	−	1.67037e10i	−0.0789272	−	0.0955903i
$316$	−1.32636e11	−	1.94258e11i	−0.748291	−	1.09594i
$317$	3.68356e9	−	3.68356e9i	0.0204881	−	0.0204881i	−0.696789	−	0.717277i	$-0.745388\pi$
$317$	3.68356e9	−	3.68356e9i	0.0204881	−	0.0204881i	0.717277	+	0.696789i	$0.245388\pi$
$318$	7.46798e10	+	3.94370e10i	0.409526	+	0.216263i
$319$	−3.88384e10			−0.209992
$320$	1.14137e11	−	1.48853e11i	0.608488	−	0.793563i
$321$	−1.18414e11			−0.622486
$322$	−7.38097e9	−	3.89775e9i	−0.0382615	−	0.0202052i
$323$	−2.23583e10	+	2.23583e10i	−0.114295	+	0.114295i
$324$	−3.98996e10	−	5.84366e10i	−0.201148	−	0.294600i
$325$	1.14034e11	+	1.68479e11i	0.566966	+	0.837666i
$326$	−2.04967e11	+	6.33002e10i	−1.00509	+	0.310403i
$327$	1.23928e11			0.599382
$328$	−3.17510e11	+	3.61023e10i	−1.51469	+	0.172228i
$329$		−	3.76046e10i		−	0.176953i
$330$	1.71509e10	+	8.27590e10i	0.0796112	+	0.384152i
$331$	−1.88293e11	+	1.88293e11i	−0.862203	+	0.862203i	−0.991594	−	0.129391i	$-0.958698\pi$
$331$	−1.88293e11	+	1.88293e11i	−0.862203	+	0.862203i	0.129391	+	0.991594i	$0.458698\pi$
$332$	2.92555e10	+	5.51486e9i	0.132156	+	0.0249123i
$333$	−3.89652e10	+	3.89652e10i	−0.173651	+	0.173651i
$334$	−4.45487e9	−	2.35253e9i	−0.0195873	−	0.0103437i
$335$	1.33800e10	−	1.40133e11i	0.0580438	−	0.607909i
$336$	7.29709e9	+	1.66633e10i	0.0312337	+	0.0713239i
$337$		−	3.92529e11i		−	1.65782i	−0.559381	−	0.828911i	$-0.688961\pi$
$337$		−	3.92529e11i		−	1.65782i	0.559381	−	0.828911i	$-0.311039\pi$
$338$	−2.59229e9	+	4.90888e9i	−0.0108033	+	0.0204577i
$339$	−1.32503e11	−	1.32503e11i	−0.544913	−	0.544913i
$340$	−2.52085e10	+	8.71684e10i	−0.102304	+	0.353756i
$341$	−7.48344e10	+	7.48344e10i	−0.299714	+	0.299714i
$342$	−8.14419e10	+	2.51518e10i	−0.321907	+	0.0994148i
$343$	−8.17207e10			−0.318793
$344$	9.71027e10	−	1.22018e11i	0.373868	−	0.469797i
$345$	−3.23057e9	+	3.38346e10i	−0.0122770	+	0.128581i
$346$	−4.54598e11	+	1.40394e11i	−1.70524	+	0.526630i
$347$	−2.89324e11	−	2.89324e11i	−1.07128	−	1.07128i	−0.997257	−	0.0740196i	$-0.976417\pi$
$347$	−2.89324e11	−	2.89324e11i	−1.07128	−	1.07128i	−0.0740196	−	0.997257i	$-0.523583\pi$
$348$	1.91940e10	+	2.81114e10i	0.0701550	+	0.102748i
$349$	−2.31908e10	−	2.31908e10i	−0.0836761	−	0.0836761i	0.664030	−	0.747706i	$-0.268845\pi$
$349$	−2.31908e10	−	2.31908e10i	−0.0836761	−	0.0836761i	−0.747706	+	0.664030i	$0.768845\pi$
$350$	−2.83772e10	+	3.53623e10i	−0.101079	+	0.125961i
$351$	−2.45118e11			−0.861971
$352$	−1.71186e10	+	2.33756e11i	−0.0594327	+	0.811562i
$353$		−	1.50647e11i		−	0.516387i	−0.966093	−	0.258194i	$-0.916873\pi$
$353$		−	1.50647e11i		−	0.516387i	0.966093	−	0.258194i	$-0.0831272\pi$
$354$	2.13611e9	−	4.04504e9i	0.00722951	−	0.0136902i
$355$	−9.24474e9	−	1.11965e10i	−0.0308935	−	0.0374157i
$356$	−6.02605e10	+	4.11449e10i	−0.198842	+	0.135766i
$357$	−6.22254e9	−	6.22254e9i	−0.0202750	−	0.0202750i
$358$	1.13919e11	+	3.68872e11i	0.366541	+	1.18687i
$359$		−	3.77960e11i		−	1.20094i	−0.799648	−	0.600469i	$-0.794980\pi$
$359$		−	3.77960e11i		−	1.20094i	0.799648	−	0.600469i	$-0.205020\pi$
$360$	−1.69820e11	+	1.76056e11i	−0.532879	+	0.552445i
$361$		−	2.60518e11i		−	0.807339i
$362$	−7.65290e10	+	2.36345e10i	−0.234227	+	0.0723366i
$363$	3.80997e10	+	3.80997e10i	0.115171	+	0.115171i
$364$	−5.37675e10	−	1.01356e10i	−0.160533	−	0.0302615i
$365$	1.98892e11	−	1.64222e11i	0.586542	−	0.484297i
$366$	1.11478e11	+	5.88696e10i	0.324732	+	0.171485i
$367$		−	5.41942e11i		−	1.55939i	−0.626157	−	0.779697i	$-0.715373\pi$
$367$		−	5.41942e11i		−	1.55939i	0.626157	−	0.779697i	$-0.284627\pi$
$368$	−3.43165e10	+	8.77874e10i	−0.0975411	+	0.249527i
$369$	4.16724e11			1.17012
$370$	9.64124e10	+	6.33114e10i	0.267439	+	0.175620i
$371$	−4.00305e10	−	4.00305e10i	−0.109700	−	0.109700i
$372$	9.11488e10	+	1.71822e10i	0.246779	+	0.0465195i
$373$	1.43603e11	+	1.43603e11i	0.384125	+	0.384125i	0.872586	−	0.488461i	$-0.162442\pi$
$373$	1.43603e11	+	1.43603e11i	0.384125	+	0.384125i	−0.488461	+	0.872586i	$0.662442\pi$
$374$	−3.34572e10	−	1.08335e11i	−0.0884234	−	0.286316i
$375$	1.77148e11	+	5.20111e10i	0.462589	+	0.135817i
$376$	−4.21925e11	+	4.79748e10i	−1.08865	+	0.123785i
$377$	−1.02382e11			−0.261028
$378$	−1.61198e10	−	5.21960e10i	−0.0406112	−	0.131500i
$379$	−4.92500e10	+	4.92500e10i	−0.122611	+	0.122611i	−0.765750	−	0.643139i	$-0.777632\pi$
$379$	−4.92500e10	+	4.92500e10i	−0.122611	+	0.122611i	0.643139	+	0.765750i	$0.277632\pi$
$380$	8.61427e10	+	1.56237e11i	0.211930	+	0.384378i
$381$	−1.39486e11	−	1.39486e11i	−0.339131	−	0.339131i
$382$	6.73948e11	+	3.55899e11i	1.61935	+	0.855150i
$383$		−	4.16644e11i		−	0.989397i	−0.869065	−	0.494699i	$-0.835278\pi$
$383$		−	4.16644e11i		−	0.989397i	0.869065	−	0.494699i	$-0.164722\pi$
$384$	1.77654e11	−	1.03132e11i	0.416950	−	0.242049i
$385$	5.38496e9	−	5.63982e10i	0.0124913	−	0.130825i
$386$	2.32596e11	−	4.40455e11i	0.533284	−	1.00985i
$387$	−1.43795e11	+	1.43795e11i	−0.325870	+	0.325870i
$388$	5.12325e11	−	3.49807e11i	1.14763	−	0.783584i
$389$	−6.21399e10	+	6.21399e10i	−0.137593	+	0.137593i	−0.772549	−	0.634955i	$-0.781018\pi$
$389$	−6.21399e10	+	6.21399e10i	−0.137593	+	0.137593i	0.634955	+	0.772549i	$0.281018\pi$
$390$	4.52115e10	+	2.18161e11i	0.0989596	+	0.477514i
$391$		−	4.55969e10i		−	0.0986598i
$392$	5.14396e10	+	4.52397e11i	0.110030	+	0.967682i
$393$	−1.20608e10			−0.0255041
$394$	−4.46228e10	−	1.44489e11i	−0.0932875	−	0.302066i
$395$	4.95096e11	−	4.08791e11i	1.02330	−	0.844919i
$396$	5.66202e10	−	3.00361e11i	0.115703	−	0.613784i
$397$	1.35891e10	−	1.35891e10i	0.0274558	−	0.0274558i	−0.693246	−	0.720701i	$-0.743820\pi$
$397$	1.35891e10	−	1.35891e10i	0.0274558	−	0.0274558i	0.720701	+	0.693246i	$0.243820\pi$
$398$	−1.79981e11	+	3.40821e11i	−0.359545	+	0.680852i
$399$	−1.73024e10			−0.0341765
$400$	4.32970e11	+	2.73279e11i	0.845644	+	0.533747i
$401$	−5.59336e11			−1.08025			−0.540123	−	0.841586i	$-0.681622\pi$
$401$	−5.59336e11			−1.08025			−0.540123	+	0.841586i	$0.681622\pi$
$402$	7.19888e10	−	1.36322e11i	0.137483	−	0.260344i
$403$	−1.97271e11	+	1.97271e11i	−0.372555	+	0.372555i
$404$	1.16595e11	+	2.19790e10i	0.217754	+	0.0410481i
$405$	1.48934e11	−	1.22972e11i	0.275072	−	0.227122i
$406$	−6.73296e9	−	2.18014e10i	−0.0122981	−	0.0398215i
$407$	−1.44124e11			−0.260352
$408$	−6.18786e10	+	7.77557e10i	−0.110553	+	0.138919i
$409$			7.76620e11i			1.37231i	0.727453	+	0.686157i	$0.240704\pi$
$409$			7.76620e11i			1.37231i	−0.727453	+	0.686157i	$0.759296\pi$
$410$	−1.77004e11	−	8.54103e11i	−0.309353	−	1.49274i
$411$	−7.06542e10	+	7.06542e10i	−0.122138	+	0.122138i
$412$	5.50169e11	+	8.05773e11i	0.940716	+	1.37777i
$413$	−2.16826e9	+	2.16826e9i	−0.00366720	+	0.00366720i
$414$	5.73983e10	−	1.08692e11i	0.0960280	−	0.181843i
$415$	−7.72381e9	+	8.08936e10i	−0.0127825	+	0.133874i
$416$	−4.51263e10	+	6.16205e11i	−0.0738770	+	1.00880i
$417$		−	2.24833e10i		−	0.0364122i
$418$	−1.97133e11	−	1.04102e11i	−0.315840	−	0.166789i
$419$	6.96138e11	+	6.96138e11i	1.10340	+	1.10340i	0.993998	+	0.109400i	$0.0348929\pi$
$419$	6.96138e11	+	6.96138e11i	1.10340	+	1.10340i	0.109400	+	0.993998i	$0.465107\pi$
$420$	−4.34825e10	+	2.39744e10i	−0.0681856	+	0.0375947i
$421$	−2.38187e11	+	2.38187e11i	−0.369529	+	0.369529i	−0.867305	−	0.497776i	$-0.834150\pi$
$421$	−2.38187e11	+	2.38187e11i	−0.369529	+	0.369529i	0.497776	+	0.867305i	$0.334150\pi$
$422$	2.82398e11	+	9.14409e11i	0.433466	+	1.40357i
$423$	5.53765e11			0.840996
$424$	−3.98074e11	+	5.00213e11i	−0.598160	+	0.751638i
$425$	−2.43207e11	−	4.68706e10i	−0.361598	−	0.0696868i
$426$	−4.69211e9	−	1.51931e10i	−0.00690280	−	0.0223514i
$427$	−5.97555e10	−	5.97555e10i	−0.0869866	−	0.0869866i
$428$	1.66043e11	−	8.80833e11i	0.239179	−	1.26881i
$429$	−1.96854e11	−	1.96854e11i	−0.280599	−	0.280599i
$430$	3.55795e11	+	2.33641e11i	0.501870	+	0.329564i
$431$	7.79489e11			1.08808			0.544042	−	0.839058i	$-0.316893\pi$
$431$	7.79489e11			1.08808			0.544042	+	0.839058i	$0.316893\pi$
$432$	−5.65077e11	+	2.47455e11i	−0.780603	+	0.341837i
$433$		−	7.84714e11i		−	1.07279i	−0.843966	−	0.536397i	$-0.819785\pi$
$433$		−	7.84714e11i		−	1.07279i	0.843966	−	0.536397i	$-0.180215\pi$
$434$	−5.49806e10	−	2.90342e10i	−0.0743885	−	0.0392831i
$435$	−7.16460e10	+	5.91568e10i	−0.0959379	+	0.0792142i
$436$	−1.73775e11	+	9.21849e11i	−0.230302	+	1.22172i
$437$	−6.33933e10	−	6.33933e10i	−0.0831529	−	0.0831529i
$438$	2.69888e11	−	8.33497e10i	0.350388	−	0.108211i
$439$			1.55059e12i			1.99254i	0.0863097	+	0.996268i	$0.472493\pi$
$439$			1.55059e12i			1.99254i	−0.0863097	+	0.996268i	$0.527507\pi$
$440$	−6.39660e11	+	1.15317e10i	−0.813603	+	0.0146675i
$441$		−	5.93760e11i		−	0.747544i
$442$	−8.81964e10	−	2.85581e11i	−0.109913	−	0.355901i
$443$	5.47116e11	+	5.47116e11i	0.674936	+	0.674936i	0.958850	−	0.283914i	$-0.0916330\pi$
$443$	5.47116e11	+	5.47116e11i	0.674936	+	0.674936i	−0.283914	+	0.958850i	$0.591633\pi$
$444$	7.12263e10	+	1.04317e11i	0.0869795	+	0.127390i
$445$	−1.26811e11	−	1.53583e11i	−0.153298	−	0.185662i
$446$	4.06464e11	−	7.69700e11i	0.486425	−	0.921117i
$447$		−	4.95438e11i		−	0.586956i
$448$	−1.34184e11	+	3.09144e10i	−0.157380	+	0.0362584i
$449$	−1.06201e12			−1.23316			−0.616580	−	0.787292i	$-0.711482\pi$
$449$	−1.06201e12			−1.23316			−0.616580	+	0.787292i	$0.711482\pi$
$450$	−5.20746e11	−	4.17883e11i	−0.598646	−	0.480394i
$451$	7.70685e11	+	7.70685e11i	0.877167	+	0.877167i
$452$	1.17144e12	−	7.99838e11i	1.32007	−	0.901320i
$453$	4.33453e11	+	4.33453e11i	0.483616	+	0.483616i
$454$	3.51357e11	−	1.08510e11i	0.388148	−	0.119872i
$455$	1.41953e10	−	1.48671e11i	0.0155272	−	0.162621i
$456$	2.20739e10	+	1.94133e11i	0.0239076	+	0.210261i
$457$	−1.83435e12			−1.96725			−0.983623	−	0.180241i	$-0.942312\pi$
$457$	−1.83435e12			−1.96725			−0.983623	+	0.180241i	$0.942312\pi$
$458$	−4.19903e11	+	1.29679e11i	−0.445917	+	0.137713i
$459$	2.11015e11	−	2.11015e11i	0.221900	−	0.221900i
$460$	−2.47152e11	−	7.14747e10i	−0.257368	−	0.0744290i
$461$	−4.01663e10	−	4.01663e10i	−0.0414198	−	0.0414198i	0.686094	−	0.727513i	$-0.259324\pi$
$461$	−4.01663e10	−	4.01663e10i	−0.0414198	−	0.0414198i	−0.727513	+	0.686094i	$0.759324\pi$
$462$	2.89728e10	−	5.48642e10i	0.0295870	−	0.0560274i
$463$		−	8.45075e11i		−	0.854636i	−0.904101	−	0.427318i	$-0.859459\pi$
$463$		−	8.45075e11i		−	0.854636i	0.904101	−	0.427318i	$-0.140541\pi$
$464$	−2.36023e11	+	1.03358e11i	−0.236387	+	0.103517i
$465$	−2.40644e10	+	2.52033e11i	−0.0238691	+	0.249988i
$466$	3.37505e11	+	1.78230e11i	0.331546	+	0.175083i
$467$	−7.86801e11	+	7.86801e11i	−0.765489	+	0.765489i	−0.977309	−	0.211820i	$-0.932061\pi$
$467$	−7.86801e11	+	7.86801e11i	−0.765489	+	0.765489i	0.211820	+	0.977309i	$0.432061\pi$
$468$	1.49256e11	−	7.91782e11i	0.143822	−	0.762955i
$469$	−7.30722e10	+	7.30722e10i	−0.0697387	+	0.0697387i
$470$	−2.35212e11	−	1.13498e12i	−0.222341	−	1.07287i
$471$			2.01826e11i			0.188966i
$472$	2.70941e10	+	2.15617e10i	0.0251267	+	0.0199961i
$473$	−5.31866e11			−0.488570
$474$	6.71823e11	−	2.07480e11i	0.611297	−	0.188787i
$475$	−4.03295e11	+	2.72966e11i	−0.363497	+	0.246030i
$476$	5.50124e10	−	3.75616e10i	0.0491167	−	0.0335361i
$477$	5.89490e11	−	5.89490e11i	0.521367	−	0.521367i
$478$	1.68205e11	+	8.88261e10i	0.147372	+	0.0778243i
$479$	1.39370e12			1.20965			0.604823	−	0.796360i	$-0.293244\pi$
$479$	1.39370e12			1.20965			0.604823	+	0.796360i	$0.293244\pi$
$480$	3.24468e11	+	4.57290e11i	0.278988	+	0.393193i
$481$	−3.79925e11			−0.323627
$482$	−1.13552e12	−	5.99648e11i	−0.958262	−	0.506040i
$483$	1.76430e10	−	1.76430e10i	0.0147506	−	0.0147506i
$484$	−3.36832e11	+	2.29984e11i	−0.279004	+	0.190499i
$485$	1.07812e12	+	1.30574e12i	0.884770	+	1.07156i
$486$	1.20350e12	−	3.71677e11i	0.978548	−	0.302206i
$487$	−5.14867e11			−0.414777			−0.207388	−	0.978259i	$-0.566496\pi$
$487$	−5.14867e11			−0.414777			−0.207388	+	0.978259i	$0.566496\pi$
$488$	−5.94225e11	+	7.46694e11i	−0.474309	+	0.596010i
$489$		−	6.41250e11i		−	0.507151i
$490$	−1.21695e12	+	2.52200e11i	−0.953653	+	0.197634i
$491$	8.46916e11	−	8.46916e11i	0.657618	−	0.657618i	−0.297198	−	0.954816i	$-0.596052\pi$
$491$	8.46916e11	−	8.46916e11i	0.657618	−	0.657618i	0.954816	+	0.297198i	$0.0960522\pi$
$492$	1.76951e11	−	9.38698e11i	0.136148	−	0.722242i
$493$	8.81376e10	−	8.81376e10i	0.0671970	−	0.0671970i
$494$	−5.19663e11	−	2.74424e11i	−0.392600	−	0.207325i
$495$	8.30521e11	+	7.92990e10i	0.621766	+	0.0593669i
$496$	−2.55622e11	+	6.53926e11i	−0.189641	+	0.485133i
$497$			1.06591e10i			0.00783637i
$498$	−4.15565e10	+	7.86934e10i	−0.0302766	+	0.0573332i
$499$	−5.77108e11	−	5.77108e11i	−0.416682	−	0.416682i	0.467377	−	0.884058i	$-0.345199\pi$
$499$	−5.77108e11	−	5.77108e11i	−0.416682	−	0.416682i	−0.884058	+	0.467377i	$0.845199\pi$
$500$	−6.35291e11	+	1.24480e12i	−0.454578	+	0.890707i
$501$	1.06487e10	−	1.06487e10i	0.00755135	−	0.00755135i
$502$	7.88546e11	−	2.43527e11i	0.554192	−	0.171152i
$503$	2.53953e12			1.76888			0.884438	−	0.466658i	$-0.154542\pi$
$503$	2.53953e12			1.76888			0.884438	+	0.466658i	$0.154542\pi$
$504$	1.78420e11	−	2.02871e10i	0.123170	−	0.0140050i
$505$	−3.07826e10	+	3.22395e11i	−0.0210617	+	0.220586i
$506$	3.07166e11	−	9.48625e10i	0.208303	−	0.0643306i
$507$	−1.17339e10	−	1.17339e10i	−0.00788690	−	0.00788690i
$508$	1.23317e12	−	8.41989e11i	0.821555	−	0.560944i
$509$	−2.99006e11	−	2.99006e11i	−0.197446	−	0.197446i	0.601458	−	0.798904i	$-0.294587\pi$
$509$	−2.99006e11	−	2.99006e11i	−0.197446	−	0.197446i	−0.798904	+	0.601458i	$0.794587\pi$
$510$	−2.26730e11	−	1.48887e11i	−0.148403	−	0.0974523i
$511$	−1.89345e11			−0.122846
$512$	5.18048e11	+	1.46611e12i	0.333162	+	0.942870i
$513$		−	5.86748e11i		−	0.374044i
$514$	−6.58447e11	+	1.24687e12i	−0.416089	+	0.787927i
$515$	−2.05363e12	+	1.69565e12i	−1.28644	+	1.06219i
$516$	2.62849e11	+	3.84967e11i	0.163224	+	0.239056i
$517$	1.02413e12	+	1.02413e12i	0.630445	+	0.630445i
$518$	−2.49851e10	−	8.09022e10i	−0.0152475	−	0.0493715i
$519$		−	1.42223e12i		−	0.860434i
$520$	−1.68621e12	+	3.03987e10i	−1.01134	+	0.0182323i
$521$			1.03127e12i			0.613201i	0.951838	+	0.306600i	$0.0991915\pi$
$521$			1.03127e12i			0.613201i	−0.951838	+	0.306600i	$0.900809\pi$
$522$	3.21048e11	−	9.91497e10i	0.189258	−	0.0584486i
$523$	1.49472e12	+	1.49472e12i	0.873577	+	0.873577i	0.992860	−	0.119283i	$-0.0380596\pi$
$523$	1.49472e12	+	1.49472e12i	0.873577	+	0.873577i	−0.119283	+	0.992860i	$0.538060\pi$
$524$	1.69120e10	−	8.97154e10i	0.00979949	−	0.0519848i
$525$	−7.59694e10	−	1.12241e11i	−0.0436437	−	0.0644815i
$526$	−2.40372e12	−	1.26936e12i	−1.36914	−	0.723018i
$527$		−	3.39650e11i		−	0.191816i
$528$	−6.52542e11	−	2.55082e11i	−0.365389	−	0.142832i
$529$	−1.67187e12			−0.928222
$530$	−1.45858e12	−	9.57813e11i	−0.802953	−	0.527278i
$531$	−3.19298e10	−	3.19298e10i	−0.0174289	−	0.0174289i
$532$	2.42618e10	−	1.28705e11i	0.0131317	−	0.0696617i
$533$	2.03160e12	+	2.03160e12i	1.09035	+	1.09035i
$534$	−6.43620e10	−	2.08405e11i	−0.0342526	−	0.110911i
$535$	2.43557e12	+	2.32550e11i	1.28531	+	0.122723i
$536$	9.13096e11	+	7.26649e11i	0.477832	+	0.380262i
$537$	−1.15403e12			−0.598873
$538$	−6.20808e11	−	2.01019e12i	−0.319475	−	1.03447i
$539$	1.09809e12	−	1.09809e12i	0.560389	−	0.560389i
$540$	−8.13006e11	−	1.47455e12i	−0.411455	−	0.746257i
$541$	−6.12381e11	−	6.12381e11i	−0.307351	−	0.307351i	0.536530	−	0.843881i	$-0.319735\pi$
$541$	−6.12381e11	−	6.12381e11i	−0.307351	−	0.307351i	−0.843881	+	0.536530i	$0.819735\pi$
$542$	2.69147e12	+	1.42131e12i	1.33965	+	0.707446i
$543$		−	2.39425e11i		−	0.118187i
$544$	−4.91625e11	−	5.69321e11i	−0.240680	−	0.278716i
$545$	−2.54898e12	−	2.43379e11i	−1.23761	−	0.118168i
$546$	7.63751e10	−	1.44628e11i	0.0367777	−	0.0696441i
$547$	−1.80572e12	+	1.80572e12i	−0.862396	+	0.862396i	−0.991616	−	0.129220i	$-0.958753\pi$
$547$	−1.80572e12	+	1.80572e12i	−0.862396	+	0.862396i	0.129220	+	0.991616i	$0.458753\pi$
$548$	−4.26495e11	−	6.24641e11i	−0.202023	−	0.295882i
$549$	8.79961e11	−	8.79961e11i	0.413416	−	0.413416i
$550$	−1.90236e11	−	1.73589e12i	−0.0886461	−	0.808892i
$551$		−	2.45075e11i		−	0.113270i
$552$	−2.20464e11	−	1.75447e11i	−0.101068	−	0.0804304i
$553$	−4.71331e11			−0.214320
$554$	−1.02067e12	−	3.30494e12i	−0.460352	−	1.49063i
$555$	−2.65869e11	+	2.19523e11i	−0.118946	+	0.0982113i
$556$	1.67244e11	+	3.15266e10i	0.0742188	+	0.0139907i
$557$	−2.10439e12	+	2.10439e12i	−0.926356	+	0.926356i	−0.997468	−	0.0711121i	$-0.977345\pi$
$557$	−2.10439e12	+	2.10439e12i	−0.926356	+	0.926356i	0.0711121	+	0.997468i	$0.477345\pi$
$558$	4.27558e11	−	8.09645e11i	0.186699	−	0.353542i
$559$	−1.40205e12			−0.607311
$560$	−1.17364e11	−	3.57066e11i	−0.0504299	−	0.153427i
$561$	3.38931e11			0.144470
$562$	8.99873e11	−	1.70404e12i	0.380512	−	0.720555i
$563$	−2.18801e12	+	2.18801e12i	−0.917830	+	0.917830i	−0.996871	−	0.0790415i	$-0.974814\pi$
$563$	−2.18801e12	+	2.18801e12i	−0.917830	+	0.917830i	0.0790415	+	0.996871i	$0.474814\pi$
$564$	2.35142e11	−	1.24739e12i	0.0978532	−	0.519096i
$565$	2.46514e12	+	2.98558e12i	1.01771	+	1.23257i
$566$	−2.76497e11	−	8.95301e11i	−0.113244	−	0.366687i
$567$	−1.41785e11			−0.0576113
$568$	1.19595e11	−	1.35985e10i	0.0482110	−	0.00548181i
$569$		−	1.57387e12i		−	0.629453i	−0.949182	−	0.314726i	$-0.898087\pi$
$569$		−	1.57387e12i		−	0.629453i	0.949182	−	0.314726i	$-0.101913\pi$
$570$	−5.22220e11	+	1.08224e11i	−0.207213	+	0.0429426i
$571$	1.85511e12	−	1.85511e12i	0.730312	−	0.730312i	−0.240370	−	0.970681i	$-0.577269\pi$
$571$	1.85511e12	−	1.85511e12i	0.730312	−	0.730312i	0.970681	+	0.240370i	$0.0772687\pi$
$572$	1.74035e12	−	1.18828e12i	0.679757	−	0.464127i
$573$	−1.61097e12	+	1.61097e12i	−0.624296	+	0.624296i
$574$	−2.99010e11	+	5.66219e11i	−0.114969	+	0.217711i
$575$	1.32894e11	−	6.89575e11i	0.0506992	−	0.263073i
$576$	−4.55245e11	−	1.97599e12i	−0.172323	−	0.747971i
$577$		−	2.52034e12i		−	0.946603i	−0.880901	−	0.473301i	$-0.843062\pi$
$577$		−	2.52034e12i		−	0.946603i	0.880901	−	0.473301i	$-0.156938\pi$
$578$	−2.05103e12	−	1.08311e12i	−0.764358	−	0.403643i
$579$	1.05284e12	+	1.05284e12i	0.389321	+	0.389321i
$580$	−3.39580e11	−	6.15897e11i	−0.124599	−	0.225986i
$581$	4.21819e10	−	4.21819e10i	0.0153580	−	0.0153580i
$582$	5.47195e11	+	1.77183e12i	0.197692	+	0.640129i
$583$	2.18039e12			0.781675
$584$	2.41561e11	+	2.12446e12i	0.0859348	+	0.755772i
$585$	2.18934e12	+	2.09040e11i	0.772878	+	0.0737952i
$586$	−6.92648e10	−	2.24281e11i	−0.0242646	−	0.0785692i
$587$	−2.77524e12	−	2.77524e12i	−0.964781	−	0.964781i	0.0346195	−	0.999401i	$-0.488978\pi$
$587$	−2.77524e12	−	2.77524e12i	−0.964781	−	0.964781i	−0.999401	+	0.0346195i	$0.988978\pi$
$588$	−1.33748e12	−	2.52125e11i	−0.461414	−	0.0869797i
$589$	−4.72215e11	−	4.72215e11i	−0.161667	−	0.161667i
$590$	−5.18800e10	+	7.90044e10i	−0.0176265	+	0.0268422i
$591$	4.52042e11			0.152418
$592$	−8.75851e11	+	3.83547e11i	−0.293077	+	0.128343i
$593$		−	1.02544e12i		−	0.340537i	−0.985398	−	0.170269i	$-0.945536\pi$
$593$		−	1.02544e12i		−	0.340537i	0.985398	−	0.170269i	$-0.0544636\pi$
$594$	1.86052e12	+	9.82507e11i	0.613191	+	0.323815i
$595$	1.15767e11	+	1.40207e11i	0.0378666	+	0.0458610i
$596$	3.68536e12	+	6.94716e11i	1.19639	+	0.225527i
$597$	−8.14678e11	−	8.14678e11i	−0.262483	−	0.262483i
$598$	8.09721e11	−	2.50067e11i	0.258929	−	0.0799652i
$599$			1.11839e12i			0.354955i	0.984125	+	0.177478i	$0.0567937\pi$
$599$			1.11839e12i			0.354955i	−0.984125	+	0.177478i	$0.943206\pi$
$600$	−1.16243e12	+	9.95574e11i	−0.366173	+	0.313612i
$601$			3.54229e11i			0.110751i	0.998466	+	0.0553757i	$0.0176357\pi$
$601$			3.54229e11i			0.110751i	−0.998466	+	0.0553757i	$0.982364\pi$
$602$	−9.22035e10	−	2.98557e11i	−0.0286130	−	0.0926494i
$603$	−1.07606e12	−	1.07606e12i	−0.331443	−	0.331443i
$604$	−3.83208e12	+	2.61648e12i	−1.17157	+	0.799930i
$605$	−7.08821e11	−	8.58468e11i	−0.215099	−	0.260510i
$606$	−1.65620e11	+	3.13626e11i	−0.0498869	+	0.0944682i
$607$		−	5.89627e12i		−	1.76290i	−0.472276	−	0.881451i	$-0.656568\pi$
$607$		−	5.89627e12i		−	1.76290i	0.472276	−	0.881451i	$-0.343432\pi$
$608$	−1.47503e12	−	1.08020e11i	−0.437759	−	0.0320582i
$609$	6.82069e10			0.0200933
$610$	−2.17730e12	−	1.42978e12i	−0.636700	−	0.418103i
$611$	2.69970e12	+	2.69970e12i	0.783665	+	0.783665i
$612$	5.53132e11	+	8.10113e11i	0.159385	+	0.233434i
$613$	2.48193e12	+	2.48193e12i	0.709932	+	0.709932i	0.966521	−	0.256589i	$-0.0825986\pi$
$613$	2.48193e12	+	2.48193e12i	0.709932	+	0.709932i	−0.256589	+	0.966521i	$0.582599\pi$
$614$	5.06778e12	−	1.56509e12i	1.43900	−	0.444407i
$615$	2.59557e12	+	2.47828e11i	0.731635	+	0.0698573i
$616$	3.67487e11	+	2.92449e11i	0.102832	+	0.0818345i
$617$	−4.48315e12			−1.24537			−0.622687	−	0.782471i	$-0.713959\pi$
$617$	−4.48315e12			−1.24537			−0.622687	+	0.782471i	$0.713959\pi$
$618$	−2.78669e12	+	8.60616e11i	−0.768493	+	0.237335i
$619$	−4.46860e12	+	4.46860e12i	−1.22339	+	1.22339i	−0.256964	+	0.966421i	$0.582722\pi$
$619$	−4.46860e12	+	4.46860e12i	−1.22339	+	1.22339i	−0.966421	+	0.256964i	$0.917278\pi$
$620$	−1.84103e12	−	5.32413e11i	−0.500378	−	0.144706i
$621$	5.98300e11	+	5.98300e11i	0.161438	+	0.161438i
$622$	−1.75266e12	+	3.31892e12i	−0.469505	+	0.889078i
$623$			1.46211e11i			0.0388851i
$624$	−1.72016e12	−	6.72420e11i	−0.454192	−	0.177546i
$625$	−3.54148e12	−	1.41768e12i	−0.928379	−	0.371635i
$626$	5.35398e12	+	2.82734e12i	1.39345	+	0.735856i
$627$	4.71216e11	−	4.71216e11i	0.121763	−	0.121763i
$628$	−1.50130e12	−	2.83006e11i	−0.385168	−	0.0726068i
$629$	3.27067e11	−	3.27067e11i	0.0833121	−	0.0833121i
$630$	9.94644e10	+	4.79950e11i	0.0251556	+	0.121385i
$631$			6.94902e11i			0.174499i	0.996187	+	0.0872493i	$0.0278077\pi$
$631$			6.94902e11i			0.174499i	−0.996187	+	0.0872493i	$0.972192\pi$
$632$	6.01310e11	+	5.28835e12i	0.149924	+	1.31854i
$633$	−2.86078e12			−0.708218
$634$	−1.12625e11	+	3.47822e10i	−0.0276844	+	0.00854979i
$635$	2.59505e12	+	3.14292e12i	0.633380	+	0.767099i
$636$	−1.07755e12	−	1.57818e12i	−0.261145	−	0.382471i
$637$	2.89468e12	−	2.89468e12i	0.696584	−	0.696584i
$638$	7.77110e11	+	4.10377e11i	0.185690	+	0.0980596i
$639$	−1.56965e11			−0.0372435
$640$	−3.85657e12	+	1.77236e12i	−0.908639	+	0.417583i
$641$	7.50157e12			1.75506			0.877528	−	0.479526i	$-0.159191\pi$
$641$	7.50157e12			1.75506			0.877528	+	0.479526i	$0.159191\pi$
$642$	2.36932e12	+	1.25119e12i	0.550448	+	0.290681i
$643$	−2.55790e12	+	2.55790e12i	−0.590112	+	0.590112i	−0.937662	−	0.347550i	$-0.887014\pi$
$643$	−2.55790e12	+	2.55790e12i	−0.590112	+	0.590112i	0.347550	+	0.937662i	$0.387014\pi$
$644$	1.06500e11	+	1.55979e11i	0.0243985	+	0.0357338i
$645$	−9.81145e11	+	8.10114e11i	−0.223210	+	0.184301i
$646$	6.83607e11	−	2.11119e11i	0.154440	−	0.0476959i
$647$	−3.68851e12			−0.827525			−0.413763	−	0.910385i	$-0.635786\pi$
$647$	−3.68851e12			−0.827525			−0.413763	+	0.910385i	$0.635786\pi$
$648$	1.80886e11	+	1.59084e12i	0.0403011	+	0.354437i
$649$		−	1.18101e11i		−	0.0261308i
$650$	−5.01480e11	−	4.57598e12i	−0.110190	−	1.00548i
$651$	1.31422e11	−	1.31422e11i	0.0286784	−	0.0286784i
$652$	4.77000e12	+	8.99178e11i	1.03372	+	0.194864i
$653$	1.58728e12	−	1.58728e12i	0.341620	−	0.341620i	−0.515356	−	0.856976i	$-0.672340\pi$
$653$	1.58728e12	−	1.58728e12i	0.341620	−	0.341620i	0.856976	+	0.515356i	$0.172340\pi$
$654$	−2.47965e12	−	1.30946e12i	−0.530018	−	0.279893i
$655$	2.48070e11	+	2.36859e10i	0.0526608	+	0.00502811i
$656$	6.73447e12	+	2.63253e12i	1.41983	+	0.555018i
$657$		−	2.78830e12i		−	0.583842i
$658$	−3.97341e11	+	7.52423e11i	−0.0826316	+	0.156475i
$659$	−3.81770e12	−	3.81770e12i	−0.788529	−	0.788529i	0.192724	−	0.981253i	$-0.438268\pi$
$659$	−3.81770e12	−	3.81770e12i	−0.788529	−	0.788529i	−0.981253	+	0.192724i	$0.938268\pi$
$660$	5.31286e11	−	1.83713e12i	0.108989	−	0.376871i
$661$	−1.56265e12	+	1.56265e12i	−0.318387	+	0.318387i	−0.848147	−	0.529761i	$-0.822282\pi$
$661$	−1.56265e12	+	1.56265e12i	−0.318387	+	0.318387i	0.529761	+	0.848147i	$0.322282\pi$
$662$	5.75710e12	−	1.77797e12i	1.16504	−	0.359802i
$663$	8.93456e11			0.179582
$664$	−5.27097e11	−	4.19468e11i	−0.105229	−	0.0837418i
$665$	3.55880e11	+	3.39798e10i	0.0705677	+	0.00673788i
$666$	1.19137e12	−	3.67931e11i	0.234645	−	0.0724657i
$667$	2.49900e11	+	2.49900e11i	0.0488878	+	0.0488878i
$668$	6.42792e10	+	9.41428e10i	0.0124904	+	0.0182933i
$669$	1.83985e12	+	1.83985e12i	0.355111	+	0.355111i
$670$	−1.74840e12	+	2.66252e12i	−0.335201	+	0.510454i
$671$	3.25478e12			0.619827
$672$	3.00632e10	−	4.10517e11i	0.00568687	−	0.0776550i
$673$			1.84020e12i			0.345778i	0.984941	+	0.172889i	$0.0553102\pi$
$673$			1.84020e12i			0.345778i	−0.984941	+	0.172889i	$0.944690\pi$
$674$	−4.14758e12	+	7.85406e12i	−0.774150	+	1.46597i
$675$	3.80625e12	−	2.57623e12i	0.705717	−	0.477658i
$676$	1.03737e11	−	7.08301e10i	0.0191062	−	0.0130454i
$677$	−2.86916e12	−	2.86916e12i	−0.524934	−	0.524934i	0.394123	−	0.919058i	$-0.371048\pi$
$677$	−2.86916e12	−	2.86916e12i	−0.524934	−	0.524934i	−0.919058	+	0.394123i	$0.871048\pi$
$678$	1.25117e12	+	4.05130e12i	0.227395	+	0.736310i
$679$		−	1.24306e12i		−	0.224429i
$680$	1.42544e12	−	1.47778e12i	0.255658	−	0.265045i
$681$			1.09924e12i			0.195853i
$682$	2.28807e12	−	7.06628e11i	0.404986	−	0.125072i
$683$	−3.11130e12	−	3.11130e12i	−0.547078	−	0.547078i	0.378517	−	0.925594i	$-0.376434\pi$
$683$	−3.11130e12	−	3.11130e12i	−0.547078	−	0.547078i	−0.925594	+	0.378517i	$0.876434\pi$
$684$	1.89532e12	+	3.57280e11i	0.331077	+	0.0624104i
$685$	1.59199e12	−	1.31448e12i	0.276269	−	0.228111i
$686$	1.63514e12	+	8.63485e11i	0.281900	+	0.148866i
$687$		−	1.31369e12i		−	0.225002i
$688$	−3.23219e12	+	1.41542e12i	−0.549982	+	0.240844i
$689$	5.74773e12			0.971650
$690$	4.22146e11	−	6.42857e11i	0.0708993	−	0.107968i
$691$	2.30039e12	+	2.30039e12i	0.383839	+	0.383839i	0.872483	−	0.488644i	$-0.162508\pi$
$691$	2.30039e12	+	2.30039e12i	0.383839	+	0.383839i	−0.488644	+	0.872483i	$0.662508\pi$
$692$	1.05794e13	+	1.99429e12i	1.75382	+	0.330607i
$693$	−4.33074e11	−	4.33074e11i	−0.0713284	−	0.0713284i
$694$	2.73195e12	+	8.84611e12i	0.447050	+	1.44755i
$695$	−4.41544e10	+	4.62442e11i	−0.00717865	+	0.0751840i
$696$	−8.70164e10	−	7.65285e11i	−0.0140559	−	0.123618i
$697$	−3.49790e12			−0.561383
$698$	2.18980e11	+	7.09062e11i	0.0349185	+	0.113067i
$699$	−8.06751e11	+	8.06751e11i	−0.127818	+	0.127818i
$700$	9.41443e11	−	4.07718e11i	0.148202	−	0.0641828i
$701$	4.07411e12	+	4.07411e12i	0.637238	+	0.637238i	0.949873	−	0.312635i	$-0.101212\pi$
$701$	4.07411e12	+	4.07411e12i	0.637238	+	0.637238i	−0.312635	+	0.949873i	$0.601212\pi$
$702$	4.90452e12	+	2.58999e12i	0.762219	+	0.402513i
$703$		−	9.09440e11i		−	0.140435i
$704$	2.81246e12	−	4.49631e12i	0.431528	−	0.689890i
$705$	3.44914e12	+	3.29327e11i	0.525847	+	0.0502084i
$706$	−1.59178e12	+	3.01428e12i	−0.241136	+	0.456628i
$707$	1.68112e11	−	1.68112e11i	0.0253054	−	0.0253054i
$708$	−8.54821e10	+	5.83658e10i	−0.0127857	+	0.00872989i
$709$	1.71956e12	−	1.71956e12i	0.255570	−	0.255570i	−0.567680	−	0.823249i	$-0.692159\pi$
$709$	1.71956e12	−	1.71956e12i	0.255570	−	0.255570i	0.823249	+	0.567680i	$0.192159\pi$
$710$	6.66712e10	+	3.21711e11i	0.00984635	+	0.0475121i
$711$		−	6.94083e12i		−	1.01859i
$712$	1.64049e12	−	1.86532e11i	0.239229	−	0.0272015i
$713$	9.63024e11			0.139551
$714$	5.87566e10	+	1.90255e11i	0.00846087	+	0.0273964i
$715$	3.66234e12	+	4.43553e12i	0.524060	+	0.634700i
$716$	1.61822e12	−	8.58439e12i	0.230106	−	1.22068i
$717$	−4.02068e11	+	4.02068e11i	−0.0568151	+	0.0568151i
$718$	−3.99363e12	+	7.56254e12i	−0.560800	+	1.06196i
$719$	−1.12103e13			−1.56437			−0.782183	−	0.623049i	$-0.785894\pi$
$719$	−1.12103e13			−1.56437			−0.782183	+	0.623049i	$0.785894\pi$
$720$	5.25817e12	−	1.72830e12i	0.729185	−	0.239675i
$721$	1.95506e12			0.269433
$722$	−2.75271e12	+	5.21267e12i	−0.377002	+	0.713909i
$723$	2.71429e12	−	2.71429e12i	0.369431	−	0.369431i
$724$	1.78099e12	+	3.35728e11i	0.240900	+	0.0454113i
$725$	1.58981e12	−	1.07605e12i	0.213710	−	0.144647i
$726$	−3.59758e11	−	1.16490e12i	−0.0480613	−	0.155623i
$727$	−4.30906e12			−0.572107			−0.286054	−	0.958214i	$-0.592344\pi$
$727$	−4.30906e12			−0.572107			−0.286054	+	0.958214i	$0.592344\pi$
$728$	9.68731e11	+	7.70924e11i	0.127824	+	0.101723i
$729$			1.04500e12i			0.137038i
$730$	−5.71481e12	+	1.18433e12i	−0.744816	+	0.154355i
$731$	1.20699e12	−	1.20699e12i	0.156342	−	0.156342i
$732$	−1.60852e12	−	2.35582e12i	−0.207074	−	0.303279i
$733$	8.56177e12	−	8.56177e12i	1.09546	−	1.09546i	0.100523	−	0.994935i	$-0.467948\pi$
$733$	8.56177e12	−	8.56177e12i	1.09546	−	1.09546i	0.994935	−	0.100523i	$-0.0320517\pi$
$734$	−5.72632e12	+	1.08436e13i	−0.728188	+	1.37893i
$735$	3.53112e11	−	3.69824e12i	0.0446292	−	0.467415i
$736$	1.61422e12	−	1.39393e12i	0.202774	−	0.175101i
$737$		−	3.98012e12i		−	0.496927i
$738$	−8.33815e12	−	4.40322e12i	−1.03470	−	0.546408i
$739$	−2.70749e12	−	2.70749e12i	−0.333938	−	0.333938i	0.520142	−	0.854080i	$-0.325879\pi$
$739$	−2.70749e12	−	2.70749e12i	−0.333938	−	0.333938i	−0.854080	+	0.520142i	$0.825879\pi$
$740$	−1.26013e12	−	2.28551e12i	−0.154481	−	0.280182i
$741$	1.24217e12	−	1.24217e12i	0.151356	−	0.151356i
$742$	3.77990e11	+	1.22394e12i	0.0457786	+	0.148232i
$743$	−8.33540e12			−1.00341			−0.501703	−	0.865040i	$-0.667293\pi$
$743$	−8.33540e12			−1.00341			−0.501703	+	0.865040i	$0.667293\pi$
$744$	−1.64223e12	−	1.30690e12i	−0.196497	−	0.156374i
$745$	−9.72981e11	+	1.01903e13i	−0.115718	+	1.21195i
$746$	−1.35597e12	−	4.39066e12i	−0.160297	−	0.519046i
$747$	6.21171e11	+	6.21171e11i	0.0729909	+	0.0729909i
$748$	−4.75259e11	+	2.52117e12i	−0.0555102	+	0.294473i
$749$	−1.27002e12	−	1.27002e12i	−0.147450	−	0.147450i
$750$	−2.99496e12	−	2.91248e12i	−0.345633	−	0.336114i
$751$	−1.44761e13			−1.66063			−0.830315	−	0.557294i	$-0.811839\pi$
$751$	−1.44761e13			−1.66063			−0.830315	+	0.557294i	$0.811839\pi$
$752$	8.94914e12	+	3.49826e12i	1.02047	+	0.398907i
$753$			2.46701e12i			0.279636i
$754$	2.04854e12	+	1.08179e12i	0.230820	+	0.121892i
$755$	−8.06413e12	−	9.76663e12i	−0.903226	−	1.09392i
$756$	−2.28981e11	+	1.21471e12i	−0.0254948	+	0.135246i
$757$	−7.48267e12	−	7.48267e12i	−0.828181	−	0.828181i	0.159084	−	0.987265i	$-0.449146\pi$
$757$	−7.48267e12	−	7.48267e12i	−0.828181	−	0.828181i	−0.987265	+	0.159084i	$0.949146\pi$
$758$	1.50583e12	−	4.65046e11i	0.165677	−	0.0511663i
$759$			9.60986e11i			0.105106i
$760$	−7.27666e10	−	4.03634e12i	−0.00791172	−	0.438860i
$761$		−	6.03639e12i		−	0.652448i	−0.945292	−	0.326224i	$-0.894224\pi$
$761$		−	6.03639e12i		−	0.652448i	0.945292	−	0.326224i	$-0.105776\pi$
$762$	1.31710e12	+	4.26480e12i	0.141521	+	0.458249i
$763$	1.32916e12	+	1.32916e12i	0.141977	+	0.141977i
$764$	−9.72439e12	−	1.42423e13i	−1.03262	−	1.51237i
$765$	−2.06469e12	+	1.70478e12i	−0.217961	+	0.179967i
$766$	−4.40238e12	+	8.33656e12i	−0.462017	+	0.874898i
$767$		−	3.11326e11i		−	0.0324816i
$768$	−4.64437e12	+	1.86415e11i	−0.481727	+	0.0193355i
$769$	8.49015e12			0.875482			0.437741	−	0.899101i	$-0.355779\pi$
$769$	8.49015e12			0.875482			0.437741	+	0.899101i	$0.355779\pi$
$770$	−7.03666e11	+	1.07156e12i	−0.0721371	+	0.109852i
$771$	−2.98044e12	−	2.98044e12i	−0.303763	−	0.303763i
$772$	−9.30794e12	+	6.35531e12i	−0.943139	+	0.643960i
$773$	−6.61757e12	−	6.61757e12i	−0.666639	−	0.666639i	0.290297	−	0.956937i	$-0.406246\pi$
$773$	−6.61757e12	−	6.61757e12i	−0.666639	−	0.666639i	−0.956937	+	0.290297i	$0.906246\pi$
$774$	4.39655e12	−	1.35779e12i	0.440329	−	0.135987i
$775$	9.89925e11	−	5.13662e12i	0.0985700	−	0.511470i
$776$	−1.39472e13	+	1.58586e12i	−1.38073	+	0.156995i
$777$	2.53107e11			0.0249120
$778$	1.89994e12	−	5.86759e11i	0.185922	−	0.0574185i
$779$	−4.86312e12	+	4.86312e12i	−0.473147	+	0.473147i
$780$	1.40052e12	−	4.84286e12i	0.135477	−	0.468464i
$781$	−2.90290e11	−	2.90290e11i	−0.0279192	−	0.0279192i
$782$	−4.81790e11	+	9.12342e11i	−0.0460710	+	0.0872423i
$783$			2.31299e12i			0.219911i
$784$	3.75091e12	−	9.59546e12i	0.354580	−	0.907076i
$785$	3.96363e11	−	4.15122e12i	0.0372545	−	0.390177i
$786$	2.41322e11	+	1.27438e11i	0.0225526	+	0.0119096i
$787$	−6.70484e12	+	6.70484e12i	−0.623020	+	0.623020i	−0.946302	−	0.323283i	$-0.895214\pi$
$787$	−6.70484e12	+	6.70484e12i	−0.623020	+	0.623020i	0.323283	+	0.946302i	$0.395214\pi$
$788$	−6.33865e11	+	3.36256e12i	−0.0585638	+	0.310672i
$789$	5.74571e12	−	5.74571e12i	0.527834	−	0.527834i
$790$	−1.42257e13	+	2.94812e12i	−1.29943	+	0.269292i
$791$		−	2.84227e12i		−	0.258149i
$792$	−4.30661e12	+	5.41161e12i	−0.388930	+	0.488724i
$793$	8.57993e12			0.770467
$794$	−4.15489e11	+	1.28316e11i	−0.0370995	+	0.0114575i
$795$	4.02222e12	−	3.32107e12i	0.357119	−	0.294867i
$796$	7.20243e12	−	4.91770e12i	0.635872	−	0.434163i
$797$	−8.78933e12	+	8.78933e12i	−0.771602	+	0.771602i	−0.978387	−	0.206784i	$-0.933700\pi$
$797$	−8.78933e12	+	8.78933e12i	−0.771602	+	0.771602i	0.206784	+	0.978387i	$0.433700\pi$
$798$	3.46200e11	+	1.82822e11i	0.0302214	+	0.0159593i
$799$	−4.64820e12			−0.403482
$800$	−5.77568e12	−	1.00429e13i	−0.498538	−	0.866868i
$801$	−2.15310e12			−0.184807
$802$	1.11917e13	+	5.91010e12i	0.955234	+	0.504441i
$803$	5.15665e12	−	5.15665e12i	0.437671	−	0.437671i
$804$	−2.88083e12	+	1.96698e12i	−0.243145	+	0.166015i
$805$	−3.97535e11	+	3.28238e11i	−0.0333652	+	0.0275491i
$806$	6.03158e12	−	1.86274e12i	0.503412	−	0.155469i
$807$	6.28897e12			0.521974
$808$	−2.10070e12	−	1.67176e12i	−0.173386	−	0.137982i
$809$		−	1.25312e12i		−	0.102855i	−0.998677	−	0.0514274i	$-0.983623\pi$
$809$		−	1.25312e12i		−	0.102855i	0.998677	−	0.0514274i	$-0.0163771\pi$
$810$	−4.27936e12	+	8.86851e11i	−0.349298	+	0.0723883i
$811$	−1.25674e13	+	1.25674e13i	−1.02012	+	1.02012i	−0.0203307	+	0.999793i	$0.506472\pi$
$811$	−1.25674e13	+	1.25674e13i	−1.02012	+	1.02012i	−0.999793	+	0.0203307i	$0.993528\pi$
$812$	−9.56416e10	+	5.07364e11i	−0.00772048	+	0.0409560i
$813$	−6.43353e12	+	6.43353e12i	−0.516466	+	0.516466i
$814$	2.88375e12	+	1.52285e12i	0.230223	+	0.121576i
$815$	−1.25934e12	+	1.31894e13i	−0.0999845	+	1.04717i
$816$	2.05971e12	−	9.01974e11i	0.162630	−	0.0712177i
$817$		−	3.35614e12i		−	0.263537i
$818$	8.20599e12	−	1.55393e13i	0.640828	−	1.21350i
$819$	−1.14163e12	−	1.14163e12i	−0.0886638	−	0.0886638i
$820$	−5.48307e12	+	1.89599e13i	−0.423508	+	1.46445i
$821$	−8.35093e12	+	8.35093e12i	−0.641491	+	0.641491i	−0.950922	−	0.309431i	$-0.899861\pi$
$821$	−8.35093e12	+	8.35093e12i	−0.641491	+	0.641491i	0.309431	+	0.950922i	$0.399861\pi$
$822$	2.16026e12	−	6.67155e11i	0.165038	−	0.0509687i
$823$	7.18203e12			0.545692			0.272846	−	0.962058i	$-0.412035\pi$
$823$	7.18203e12			0.545692			0.272846	+	0.962058i	$0.412035\pi$
$824$	−2.49420e12	−	2.19358e13i	−0.188478	−	1.65761i
$825$	5.12575e12	+	9.87830e11i	0.385226	+	0.0742403i
$826$	6.62947e10	−	2.04739e10i	0.00495528	−	0.00153035i
$827$	−1.24667e13	−	1.24667e13i	−0.926782	−	0.926782i	0.0707148	−	0.997497i	$-0.477472\pi$
$827$	−1.24667e13	−	1.24667e13i	−0.926782	−	0.926782i	−0.997497	+	0.0707148i	$0.977472\pi$
$828$	−2.29695e12	+	1.56832e12i	−0.169830	+	0.115957i
$829$	8.24624e12	+	8.24624e12i	0.606402	+	0.606402i	0.942004	−	0.335602i	$-0.108940\pi$
$829$	8.24624e12	+	8.24624e12i	0.606402	+	0.606402i	−0.335602	+	0.942004i	$0.608940\pi$
$830$	1.00929e12	−	1.53698e12i	0.0738184	−	0.112413i
$831$	1.03397e13			0.752145
$832$	7.41392e12	−	1.18527e13i	0.536405	−	0.857557i
$833$			4.98390e12i			0.358647i
$834$	−2.37565e11	+	4.49864e11i	−0.0170034	+	0.0321984i
$835$	−2.39937e11	+	1.98112e11i	−0.0170808	+	0.0141033i
$836$	2.84443e12	+	4.16593e12i	0.201404	+	0.294974i
$837$	4.45671e12	+	4.45671e12i	0.313870	+	0.313870i
$838$	−6.57331e12	−	2.12845e13i	−0.460454	−	1.49096i
$839$			1.08645e13i			0.756972i	0.925607	+	0.378486i	$0.123555\pi$
$839$			1.08645e13i			0.756972i	−0.925607	+	0.378486i	$0.876445\pi$
$840$	1.12335e12	−	2.02517e10i	0.0778503	−	0.00140348i
$841$		−	1.35410e13i		−	0.933405i
$842$	7.28259e12	−	2.24909e12i	0.499323	−	0.154207i
$843$	4.07324e12	+	4.07324e12i	0.277790	+	0.277790i
$844$	4.01146e12	−	2.12802e13i	0.272120	−	1.44356i
$845$	2.18302e11	+	2.64390e11i	0.0147300	+	0.0178398i
$846$	−1.10802e13	−	5.85124e12i	−0.743671	−	0.392719i
$847$			8.17261e11i			0.0545614i
$848$	1.32504e13	−	5.80252e12i	0.879929	−	0.385332i
$849$	2.80100e12			0.185024
$850$	4.37104e12	+	3.50762e12i	0.287210	+	0.230477i
$851$	9.27346e11	+	9.27346e11i	0.0606120	+	0.0606120i
$852$	−6.66514e10	+	3.53575e11i	−0.00433342	+	0.0229881i
$853$	1.35442e13	+	1.35442e13i	0.875960	+	0.875960i	0.993114	−	0.117154i	$-0.0373771\pi$
$853$	1.35442e13	+	1.35442e13i	0.875960	+	0.875960i	−0.117154	+	0.993114i	$0.537377\pi$
$854$	5.64244e11	+	1.82703e12i	0.0363000	+	0.117540i
$855$	−5.00387e11	+	5.24069e12i	−0.0320227	+	0.335383i
$856$	−1.26295e13	+	1.58700e13i	−0.803994	+	1.01029i
$857$	1.12783e12			0.0714214			0.0357107	−	0.999362i	$-0.488631\pi$
$857$	1.12783e12			0.0714214			0.0357107	+	0.999362i	$0.488631\pi$
$858$	1.85880e12	+	6.01882e12i	0.117095	+	0.379157i
$859$	4.66664e12	−	4.66664e12i	0.292439	−	0.292439i	−0.545604	−	0.838043i	$-0.683700\pi$
$859$	4.66664e12	−	4.66664e12i	0.292439	−	0.292439i	0.838043	+	0.545604i	$0.183700\pi$
$860$	−4.65032e12	−	8.43431e12i	−0.289894	−	0.525783i
$861$	−1.35346e12	−	1.35346e12i	−0.0839325	−	0.0839325i
$862$	−1.55967e13	−	8.23631e12i	−0.962165	−	0.508101i
$863$			2.13509e13i			1.31029i	0.755502	+	0.655146i	$0.227393\pi$
$863$			2.13509e13i			1.31029i	−0.755502	+	0.655146i	$0.772607\pi$
$864$	1.39212e13	+	1.01949e12i	0.849894	+	0.0622399i
$865$	−2.79309e12	+	2.92529e13i	−0.169634	+	1.77663i
$866$	−8.29152e12	+	1.57012e13i	−0.500961	+	0.948643i
$867$	4.90266e12	−	4.90266e12i	0.294677	−	0.294677i
$868$	7.93314e11	+	1.16188e12i	0.0474358	+	0.0694741i
$869$	1.28363e13	−	1.28363e13i	0.763573	−	0.763573i
$870$	2.05862e12	−	4.26626e11i	0.121826	−	0.0252471i
$871$		−	1.04920e13i		−	0.617697i
$872$	1.32176e13	−	1.66090e13i	0.774153	−	0.972789i
$873$	1.83053e13			1.06663
$874$	5.98595e11	+	1.93826e12i	0.0347002	+	0.112360i
$875$	1.34213e12	+	2.45780e12i	0.0774031	+	0.141746i
$876$	−6.28083e12	−	1.18398e12i	−0.360370	−	0.0679323i
$877$	1.02341e12	−	1.02341e12i	0.0584188	−	0.0584188i	−0.677294	−	0.735713i	$-0.736847\pi$
$877$	1.02341e12	−	1.02341e12i	0.0584188	−	0.0584188i	0.735713	+	0.677294i	$0.236847\pi$
$878$	1.63840e13	−	3.10255e13i	0.930452	−	1.76195i
$879$	7.01673e11			0.0396447
$880$	1.29207e13	+	6.52810e12i	0.726297	+	0.366957i
$881$	−6.34741e12			−0.354981			−0.177490	−	0.984123i	$-0.556798\pi$
$881$	−6.34741e12			−0.354981			−0.177490	+	0.984123i	$0.556798\pi$
$882$	−6.27383e12	+	1.18804e13i	−0.349080	+	0.661034i
$883$	2.19540e12	−	2.19540e12i	0.121532	−	0.121532i	−0.643725	−	0.765257i	$-0.722612\pi$
$883$	2.19540e12	−	2.19540e12i	0.121532	−	0.121532i	0.765257	+	0.643725i	$0.222612\pi$
$884$	−1.25283e12	+	6.64606e12i	−0.0690012	+	0.366040i
$885$	−1.79886e11	−	2.17864e11i	−0.00985720	−	0.0119382i
$886$	−5.16617e12	−	1.67281e13i	−0.281655	−	0.912002i
$887$	−8.77083e12			−0.475756			−0.237878	−	0.971295i	$-0.576452\pi$
$887$	−8.77083e12			−0.475756			−0.237878	+	0.971295i	$0.576452\pi$
$888$	−3.22906e11	−	2.83987e12i	−0.0174268	−	0.153264i
$889$		−	2.99206e12i		−	0.160662i
$890$	9.14532e11	+	4.41293e12i	0.0488589	+	0.235761i
$891$	3.86141e12	−	3.86141e12i	0.205256	−	0.205256i
$892$	−1.62658e13	+	1.11060e13i	−0.860265	+	0.587375i
$893$	−6.46238e12	+	6.46238e12i	−0.340064	+	0.340064i
$894$	−5.23494e12	+	9.91314e12i	−0.274090	+	0.519030i
$895$	2.37365e13	+	2.26638e12i	1.23655	+	0.118067i
$896$	3.01151e12	+	7.99266e11i	0.156099	+	0.0414291i
$897$			2.53325e12i			0.130651i
$898$	2.12496e13	+	1.12215e13i	1.09045	+	0.575847i
$899$	1.86150e12	+	1.86150e12i	0.0950482	+	0.0950482i
$900$	6.00406e12	+	1.38637e13i	0.305038	+	0.704349i
$901$	−4.94806e12	+	4.94806e12i	−0.250134	+	0.250134i
$902$	−7.27723e12	−	2.35638e13i	−0.366047	−	1.18527i
$903$	9.34050e11			0.0467493
$904$	−3.18904e13	+	3.62609e12i	−1.58819	+	0.180584i
$905$	−4.70202e11	+	4.92456e12i	−0.0233005	+	0.244033i
$906$	−4.09290e12	−	1.32529e13i	−0.201816	−	0.653482i
$907$	2.82508e12	+	2.82508e12i	0.138611	+	0.138611i	0.773008	−	0.634396i	$-0.218751\pi$
$907$	2.82508e12	+	2.82508e12i	0.138611	+	0.138611i	−0.634396	+	0.773008i	$0.718751\pi$
$908$	−8.17679e12	−	1.54138e12i	−0.399206	−	0.0752530i
$909$	2.47563e12	+	2.47563e12i	0.120267	+	0.120267i
$910$	−1.85493e12	+	2.82475e12i	−0.0896690	+	0.136550i
$911$	−1.73273e13			−0.833484			−0.416742	−	0.909025i	$-0.636828\pi$
$911$	−1.73273e13			−0.833484			−0.416742	+	0.909025i	$0.636828\pi$
$912$	1.60960e12	−	4.11762e12i	0.0770443	−	0.197092i
$913$			2.29758e12i			0.109434i
$914$	3.67031e13	+	1.93822e13i	1.73958	+	0.918641i
$915$	6.00417e12	−	4.95753e12i	0.283177	−	0.233814i
$916$	9.77199e12	+	1.84209e12i	0.458620	+	0.0864531i
$917$	−1.29356e11	−	1.29356e11i	−0.00604120	−	0.00604120i
$918$	−6.45181e12	+	1.99252e12i	−0.299840	+	0.0925999i
$919$			2.31537e13i			1.07078i	0.844605	+	0.535390i	$0.179835\pi$
$919$			2.31537e13i			1.07078i	−0.844605	+	0.535390i	$0.820165\pi$
$920$	4.19001e12	+	4.04161e12i	0.192828	+	0.185998i
$921$			1.58548e13i			0.726094i
$922$	3.79273e11	+	1.22809e12i	0.0172847	+	0.0559682i
$923$	−7.65234e11	−	7.65234e11i	−0.0347046	−	0.0347046i
$924$	−1.15942e12	+	7.91635e11i	−0.0523261	+	0.0357274i
$925$	5.89957e12	−	3.99307e12i	0.264961	−	0.179337i
$926$	−8.92931e12	+	1.69090e13i	−0.399088	+	0.755732i
$927$			2.87902e13i			1.28052i
$928$	5.81466e12	+	4.25822e11i	0.257370	+	0.0188479i
$929$	1.27108e13			0.559890			0.279945	−	0.960016i	$-0.409684\pi$
$929$	1.27108e13			0.559890			0.279945	+	0.960016i	$0.409684\pi$
$930$	3.14455e12	−	4.78862e12i	0.137843	−	0.209912i
$931$	6.92911e12	+	6.92911e12i	0.302276	+	0.302276i
$932$	−4.86985e12	−	7.13235e12i	−0.211419	−	0.309643i
$933$	−7.93335e12	−	7.93335e12i	−0.342759	−	0.342759i
$934$	2.40565e13	−	7.42941e12i	1.03436	−	0.319443i
$935$	−6.97123e12	−	6.65620e11i	−0.298303	−	0.0284823i
$936$	−1.13526e13	+	1.42655e13i	−0.483454	+	0.607501i
$937$	−5.83107e12			−0.247127			−0.123564	−	0.992337i	$-0.539432\pi$
$937$	−5.83107e12			−0.247127			−0.123564	+	0.992337i	$0.539432\pi$
$938$	2.23419e12	−	6.89987e11i	0.0942339	−	0.0291024i
$939$	−1.27978e13	+	1.27978e13i	−0.537207	+	0.537207i
$940$	−7.28620e12	+	2.51949e13i	−0.304387	+	1.05254i
$941$	1.15655e13	+	1.15655e13i	0.480853	+	0.480853i	0.905404	−	0.424551i	$-0.139568\pi$
$941$	1.15655e13	+	1.15655e13i	0.480853	+	0.480853i	−0.424551	+	0.905404i	$0.639568\pi$
$942$	2.13256e12	−	4.03831e12i	0.0882412	−	0.167098i
$943$		−	9.91773e12i		−	0.408423i
$944$	−3.14294e11	−	7.17709e11i	−0.0128814	−	0.0294154i
$945$	−3.35876e12	−	3.20698e11i	−0.137005	−	0.0130813i
$946$	1.06420e13	+	5.61985e12i	0.432030	+	0.228147i
$947$	5.17283e12	−	5.17283e12i	0.209003	−	0.209003i	−0.594840	−	0.803844i	$-0.702785\pi$
$947$	5.17283e12	−	5.17283e12i	0.209003	−	0.209003i	0.803844	+	0.594840i	$0.202785\pi$
$948$	−1.56347e13	−	2.94725e12i	−0.628712	−	0.118516i
$949$	1.35934e13	−	1.35934e13i	0.544041	−	0.544041i
$950$	1.09537e13	−	1.20041e12i	0.436319	−	0.0478160i
$951$		−	3.52354e11i		−	0.0139691i
$952$	−1.49762e12	+	1.70286e11i	−0.0590929	+	0.00671914i
$953$	3.12995e13			1.22919			0.614595	−	0.788843i	$-0.289319\pi$
$953$	3.12995e13			1.22919			0.614595	+	0.788843i	$0.289319\pi$
$954$	−1.80237e13	+	5.56628e12i	−0.704493	+	0.217569i
$955$	3.62985e13	−	2.99710e13i	1.41213	−	1.16597i
$956$	−2.42703e12	−	3.55461e12i	−0.0939756	−	0.137636i
$957$	−1.85756e12	+	1.85756e12i	−0.0715878	+	0.0715878i
$958$	−2.78862e13	−	1.47262e13i	−1.06966	−	0.564866i
$959$	−1.51557e12			−0.0578620
$960$	−1.66037e12	−	1.25783e13i	−0.0630934	−	0.477969i
$961$	−1.92661e13			−0.728682
$962$	7.60185e12	+	4.01440e12i	0.286175	+	0.151124i
$963$	1.87024e13	−	1.87024e13i	0.700775	−	0.700775i
$964$	1.63844e13	+	2.39965e13i	0.611061	+	0.894956i
$965$	−1.95874e13	−	2.37227e13i	−0.727115	−	0.880624i
$966$	−5.39438e11	+	1.66595e11i	−0.0199317	+	0.00615553i
$967$	1.43557e11			0.00527965			0.00263983	−	0.999997i	$-0.499160\pi$
$967$	1.43557e11			0.00527965			0.00263983	+	0.999997i	$0.499160\pi$
$968$	9.16970e12	−	1.04264e12i	0.335673	−	0.0381675i
$969$			2.13870e12i			0.0779279i
$970$	−7.77520e12	−	3.75180e13i	−0.281993	−	1.36071i
$971$	1.72522e13	−	1.72522e13i	0.622814	−	0.622814i	−0.323436	−	0.946250i	$-0.604838\pi$
$971$	1.72522e13	−	1.72522e13i	0.622814	−	0.622814i	0.946250	+	0.323436i	$0.104838\pi$
$972$	−2.80078e13	−	5.27967e12i	−1.00643	−	0.189718i
$973$	2.41140e11	−	2.41140e11i	0.00862503	−	0.00862503i
$974$	1.03019e13	+	5.44023e12i	0.366776	+	0.193688i
$975$	1.35120e13	+	2.60402e12i	0.478849	+	0.0922833i
$976$	1.97795e13	−	8.66172e12i	0.697737	−	0.305548i
$977$			3.66053e13i			1.28534i	0.766143	+	0.642670i	$0.222173\pi$
$977$			3.66053e13i			1.28534i	−0.766143	+	0.642670i	$0.777827\pi$
$978$	−6.77563e12	+	1.28307e13i	−0.236824	+	0.448461i
$979$	−3.98193e12	−	3.98193e12i	−0.138539	−	0.138539i
$980$	2.70146e13	+	7.81243e12i	0.935580	+	0.270563i
$981$	−1.95733e13	+	1.95733e13i	−0.674766	+	0.674766i
$982$	−2.58946e13	+	7.99704e12i	−0.888601	+	0.274428i
$983$	−4.49697e13			−1.53614			−0.768068	−	0.640369i	$-0.778782\pi$
$983$	−4.49697e13			−1.53614			−0.768068	+	0.640369i	$0.778782\pi$
$984$	−1.34591e13	+	1.69125e13i	−0.457656	+	0.575084i
$985$	−9.29772e12	−	8.87756e11i	−0.314712	−	0.0300490i
$986$	−2.69482e12	+	8.32243e11i	−0.0907994	+	0.0280417i
$987$	−1.79855e12	−	1.79855e12i	−0.0603247	−	0.0603247i
$988$	7.49820e12	+	1.09818e13i	0.250352	+	0.366664i
$989$	3.42222e12	+	3.42222e12i	0.113743	+	0.113743i
$990$	−1.57799e13	−	1.03622e13i	−0.522089	−	0.342842i
$991$	6.09221e12			0.200652			0.100326	−	0.994955i	$-0.468011\pi$
$991$	6.09221e12			0.200652			0.100326	+	0.994955i	$0.468011\pi$
$992$	1.20243e13	−	1.03833e13i	0.394236	−	0.340434i
$993$			1.80114e13i			0.587862i
$994$	1.12627e11	−	2.13275e11i	0.00365934	−	0.00692950i
$995$	1.51566e13	+	1.83565e13i	0.490228	+	0.593724i
$996$	1.66299e12	−	1.13547e12i	0.0535456	−	0.0365601i
$997$	−1.92226e13	−	1.92226e13i	−0.616145	−	0.616145i	0.328395	−	0.944540i	$-0.393492\pi$
$997$	−1.92226e13	−	1.92226e13i	−0.616145	−	0.616145i	−0.944540	+	0.328395i	$0.893492\pi$
$998$	5.44937e12	+	1.76451e13i	0.173884	+	0.563038i
$999$			8.58320e12i			0.272649i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.10.q.a.29.17	✓	212
5.4	even	2	inner	80.10.q.a.29.90	yes	212
16.5	even	4	inner	80.10.q.a.69.90	yes	212
80.69	even	4	inner	80.10.q.a.69.17	yes	212

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.10.q.a.29.17	✓	212	1.1	even	1	trivial
80.10.q.a.29.90	yes	212	5.4	even	2	inner
80.10.q.a.69.17	yes	212	80.69	even	4	inner
80.10.q.a.69.90	yes	212	16.5	even	4	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:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	80.q (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-20.0088 - 10.5663i) q^{2} +(47.8279 - 47.8279i) q^{3} +(288.707 + 422.838i) q^{4} +(-1077.67 + 889.809i) q^{5} +(-1462.35 + 451.618i) q^{6} +1025.94 q^{7} +(-1308.86 - 11511.1i) q^{8} +15108.0i q^{9} +(30964.8 - 6417.12i) q^{10} +(-27940.6 + 27940.6i) q^{11} +(34031.7 + 6415.22i) q^{12} +(-73654.0 + 73654.0i) q^{13} +(-20527.8 - 10840.4i) q^{14} +(-8984.79 + 94100.3i) q^{15} +(-95440.4 + 244153. i) q^{16} -126813. i q^{17} +(159635. - 302293. i) q^{18} +(-176308. - 176308. i) q^{19} +(-687375. - 198784. i) q^{20} +(49068.5 - 49068.5i) q^{21} +(854286. - 263830. i) q^{22} +359559. q^{23} +(-613151. - 487950. i) q^{24} +(369603. - 1.91783e6i) q^{25} +(2.25198e6 - 695482. i) q^{26} +(1.66398e6 + 1.66398e6i) q^{27} +(296195. + 433806. i) q^{28} +(695018. + 695018. i) q^{29} +(1.17407e6 - 1.78790e6i) q^{30} +2.67835e6 q^{31} +(4.48944e6 - 3.87676e6i) q^{32} +2.67268e6i q^{33} +(-1.33995e6 + 2.53739e6i) q^{34} +(-1.10562e6 + 912889. i) q^{35} +(-6.38823e6 + 4.36178e6i) q^{36} +(2.57912e6 + 2.57912e6i) q^{37} +(1.66480e6 + 5.39065e6i) q^{38} +7.04544e6i q^{39} +(1.16532e7 + 1.12404e7i) q^{40} -2.75830e7i q^{41} +(-1.50027e6 + 463331. i) q^{42} +(9.51782e6 + 9.51782e6i) q^{43} +(-1.98810e7 - 3.74770e6i) q^{44} +(-1.34432e7 - 1.62814e7i) q^{45} +(-7.19436e6 - 3.79921e6i) q^{46} -3.66538e7i q^{47} +(7.11261e6 + 1.62420e7i) q^{48} -3.93011e7 q^{49} +(-2.76597e7 + 3.44683e7i) q^{50} +(-6.06522e6 - 6.06522e6i) q^{51} +(-5.24082e7 - 9.87930e6i) q^{52} +(-3.90184e7 - 3.90184e7i) q^{53} +(-1.57122e7 - 5.08764e7i) q^{54} +(5.24882e6 - 5.49724e7i) q^{55} +(-1.34281e6 - 1.18096e7i) q^{56} -1.68649e7 q^{57} +(-6.56274e6 - 2.12503e7i) q^{58} +(-2.11344e6 + 2.11344e6i) q^{59} +(-4.23832e7 + 2.33683e7i) q^{60} +(-5.82448e7 - 5.82448e7i) q^{61} +(-5.35906e7 - 2.83002e7i) q^{62} +1.54998e7i q^{63} +(-1.30791e8 + 3.01328e7i) q^{64} +(1.38364e7 - 1.44913e8i) q^{65} +(2.82403e7 - 5.34772e7i) q^{66} +(-7.12248e7 + 7.12248e7i) q^{67} +(5.36216e7 - 3.66119e7i) q^{68} +(1.71970e7 - 1.71970e7i) q^{69} +(3.17680e7 - 6.58357e6i) q^{70} +1.03896e7i q^{71} +(1.73909e8 - 1.97742e7i) q^{72} -1.84558e8 q^{73} +(-2.43534e7 - 7.88568e7i) q^{74} +(-7.40487e7 - 1.09403e8i) q^{75} +(2.36485e7 - 1.25451e8i) q^{76} +(-2.86653e7 + 2.86653e7i) q^{77} +(7.44442e7 - 1.40971e8i) q^{78} -4.59415e8 q^{79} +(-1.14397e8 - 3.48039e8i) q^{80} -1.38201e8 q^{81} +(-2.91450e8 + 5.51904e8i) q^{82} +(4.11154e7 - 4.11154e7i) q^{83} +(3.49144e7 + 6.58161e6i) q^{84} +(1.12840e8 + 1.36662e8i) q^{85} +(-8.98725e7 - 2.91008e8i) q^{86} +6.64825e7 q^{87} +(3.58196e8 + 2.85055e8i) q^{88} +1.42514e8i q^{89} +(9.69497e7 + 4.67816e8i) q^{90} +(-7.55644e7 + 7.55644e7i) q^{91} +(1.03807e8 + 1.52035e8i) q^{92} +(1.28100e8 - 1.28100e8i) q^{93} +(-3.87295e8 + 7.33401e8i) q^{94} +(3.46883e8 + 3.31207e7i) q^{95} +(2.93032e7 - 4.00138e8i) q^{96} -1.21163e9i q^{97} +(7.86368e8 + 4.15266e8i) q^{98} +(-4.22125e8 - 4.22125e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 212 q - 4 q^{4} - 2 q^{5} - 4 q^{6} + 17812 q^{10} - 4 q^{11} + 108500 q^{14} - 4 q^{15} - 534208 q^{16} + 480884 q^{19} + 2372984 q^{20} - 78736 q^{21} - 4888112 q^{24} - 7927240 q^{26} - 4 q^{29} - 34132064 q^{30}+ \cdots + 771348172 q^{99}+O(q^{100}) \) 212 * q - 4 * q^4 - 2 * q^5 - 4 * q^6 + 17812 * q^10 - 4 * q^11 + 108500 * q^14 - 4 * q^15 - 534208 * q^16 + 480884 * q^19 + 2372984 * q^20 - 78736 * q^21 - 4888112 * q^24 - 7927240 * q^26 - 4 * q^29 - 34132064 * q^30 + 22164496 * q^31 - 32890400 * q^34 + 15214056 * q^35 - 72152684 * q^36 + 40955304 * q^40 - 63499328 * q^44 + 3945614 * q^45 + 13956012 * q^46 + 1083782580 * q^49 - 119678604 * q^50 + 90093056 * q^51 + 6659032 * q^54 - 74344568 * q^56 - 144037620 * q^59 - 106324752 * q^60 - 90121108 * q^61 + 74046704 * q^64 - 62806092 * q^65 + 1419462624 * q^66 - 382438912 * q^69 - 127364260 * q^70 + 2153363568 * q^74 + 119613476 * q^75 + 1579189648 * q^76 + 423438896 * q^79 + 425390872 * q^80 - 7748409788 * q^81 + 4494494704 * q^84 + 3906248 * q^85 + 2482762604 * q^86 - 3409730584 * q^90 + 1231623152 * q^91 + 3948740348 * q^94 - 2480993260 * q^95 - 464870984 * q^96 + 771348172 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more