LMFDB - Embedded newform 80.12.j.a.67.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [80,12,Mod(43,80)] 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("80.43"); S:= CuspForms(chi, 12); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(80, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1, 3])) N = Newforms(chi, 12, names="a")

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	80.j (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:	$61.4674544448$
Analytic rank:	$0$
Dimension:	$260$
Relative dimension:	$130$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			67.10
Character	$\chi$	$=$	80.67
Dual form			80.12.j.a.43.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-43.6367 - 11.9933i) q^{2} +219.501i q^{3} +(1760.32 + 1046.69i) q^{4} +(5720.85 - 4012.48i) q^{5} +(2632.53 - 9578.30i) q^{6} +(37491.7 + 37491.7i) q^{7} +(-64261.4 - 66786.2i) q^{8} +128966. q^{9} +(-297762. + 106480. i) q^{10} +(274026. + 274026. i) q^{11} +(-229750. + 386393. i) q^{12} +2.13499e6 q^{13} +(-1.18637e6 - 2.08566e6i) q^{14} +(880743. + 1.25573e6i) q^{15} +(2.00317e6 + 3.68504e6i) q^{16} +(3.59002e6 + 3.59002e6i) q^{17} +(-5.62766e6 - 1.54673e6i) q^{18} +(9.47032e6 + 9.47032e6i) q^{19} +(1.42704e7 - 1.07528e6i) q^{20} +(-8.22948e6 + 8.22948e6i) q^{21} +(-8.67112e6 - 1.52440e7i) q^{22} +(3.19384e7 - 3.19384e7i) q^{23} +(1.46597e7 - 1.41055e7i) q^{24} +(1.66282e7 - 4.59096e7i) q^{25} +(-9.31641e7 - 2.56055e7i) q^{26} +6.71922e7i q^{27} +(2.67552e7 + 1.05240e8i) q^{28} +(-1.49568e7 + 1.49568e7i) q^{29} +(-2.33724e7 - 6.53590e7i) q^{30} -1.30278e8i q^{31} +(-4.32163e7 - 1.84827e8i) q^{32} +(-6.01490e7 + 6.01490e7i) q^{33} +(-1.13600e8 - 1.99712e8i) q^{34} +(3.64919e8 + 6.40500e7i) q^{35} +(2.27022e8 + 1.34988e8i) q^{36} -6.16927e8 q^{37} +(-2.99673e8 - 5.26833e8i) q^{38} +4.68633e8i q^{39} +(-6.35608e8 - 1.24227e8i) q^{40} -5.21271e8i q^{41} +(4.57805e8 - 2.60409e8i) q^{42} -1.02727e9 q^{43} +(1.95553e8 + 7.69195e8i) q^{44} +(7.37797e8 - 5.17474e8i) q^{45} +(-1.77673e9 + 1.01064e9i) q^{46} +(-1.16750e9 + 1.16750e9i) q^{47} +(-8.08869e8 + 4.39699e8i) q^{48} +8.33932e8i q^{49} +(-1.27620e9 + 1.80392e9i) q^{50} +(-7.88012e8 + 7.88012e8i) q^{51} +(3.75828e9 + 2.23468e9i) q^{52} -1.52042e9i q^{53} +(8.05854e8 - 2.93205e9i) q^{54} +(2.66718e9 + 4.68139e8i) q^{55} +(9.46584e7 - 4.91320e9i) q^{56} +(-2.07874e9 + 2.07874e9i) q^{57} +(8.32045e8 - 4.73284e8i) q^{58} +(4.99146e9 - 4.99146e9i) q^{59} +(2.36026e8 + 3.13236e9i) q^{60} +(-6.16017e9 - 6.16017e9i) q^{61} +(-1.56246e9 + 5.68491e9i) q^{62} +(4.83517e9 + 4.83517e9i) q^{63} +(-3.30867e8 + 8.58356e9i) q^{64} +(1.22140e10 - 8.56661e9i) q^{65} +(3.34608e9 - 1.90332e9i) q^{66} +8.23483e9 q^{67} +(2.56195e9 + 1.00772e10i) q^{68} +(7.01052e9 + 7.01052e9i) q^{69} +(-1.51557e10 - 7.17150e9i) q^{70} +9.46380e9 q^{71} +(-8.28756e9 - 8.61317e9i) q^{72} +(-7.38240e9 - 7.38240e9i) q^{73} +(2.69207e10 + 7.39896e9i) q^{74} +(1.00772e10 + 3.64990e9i) q^{75} +(6.75831e9 + 2.65833e10i) q^{76} +2.05474e10i q^{77} +(5.62044e9 - 2.04496e10i) q^{78} +3.36197e9 q^{79} +(2.62460e10 + 1.30439e10i) q^{80} +8.09723e9 q^{81} +(-6.25174e9 + 2.27466e10i) q^{82} -1.55858e10i q^{83} +(-2.31003e10 + 5.87281e9i) q^{84} +(3.49428e10 + 6.13310e9i) q^{85} +(4.48265e10 + 1.23203e10i) q^{86} +(-3.28303e9 - 3.28303e9i) q^{87} +(6.91855e8 - 3.59104e10i) q^{88} -8.17382e10 q^{89} +(-3.84012e10 + 1.37323e10i) q^{90} +(8.00446e10 + 8.00446e10i) q^{91} +(8.96517e10 - 2.27923e10i) q^{92} +2.85962e10 q^{93} +(6.49483e10 - 3.69439e10i) q^{94} +(9.21777e10 + 1.61789e10i) q^{95} +(4.05698e10 - 9.48602e9i) q^{96} +(7.86089e10 + 7.86089e10i) q^{97} +(1.00016e10 - 3.63901e10i) q^{98} +(3.53401e10 + 3.53401e10i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 260 q - 2 q^{2} - 3956 q^{4} - 2 q^{5} - 4 q^{6} - 4 q^{7} - 74840 q^{8} - 14880348 q^{9} - 4098 q^{10} - 4 q^{11} - 114212 q^{12} - 4 q^{13} + 708588 q^{15} + 5740152 q^{16} - 4 q^{17} - 6791722 q^{18}+ \cdots - 189350900660 q^{99}+O(q^{100}) $ 260 * q - 2 * q^2 - 3956 * q^4 - 2 * q^5 - 4 * q^6 - 4 * q^7 - 74840 * q^8 - 14880348 * q^9 - 4098 * q^10 - 4 * q^11 - 114212 * q^12 - 4 * q^13 + 708588 * q^15 + 5740152 * q^16 - 4 * q^17 - 6791722 * q^18 - 11291288 * q^19 + 27599212 * q^20 - 4 * q^21 + 11921800 * q^22 - 4 * q^23 + 708588 * q^24 - 196875380 * q^26 + 185066800 * q^28 - 534157704 * q^30 - 894200972 * q^32 - 4 * q^33 - 122727336 * q^34 + 434731680 * q^35 + 917614156 * q^36 - 4 * q^37 - 169550316 * q^38 - 1417066568 * q^40 - 1572161236 * q^42 - 4763690660 * q^43 - 1456070840 * q^44 - 97301958 * q^45 - 3653567828 * q^46 + 5707353192 * q^47 - 447163780 * q^48 + 429408694 * q^50 + 112221284 * q^51 - 4957065880 * q^52 - 10995087044 * q^54 - 4 * q^55 - 8945492140 * q^56 + 708588 * q^57 + 33722126388 * q^58 - 11496390224 * q^59 - 6670533420 * q^60 - 2150827028 * q^61 + 15717297108 * q^62 + 708588 * q^63 - 11018267024 * q^64 - 4 * q^65 - 9909115916 * q^66 + 44333852084 * q^67 - 74998571352 * q^68 + 16194123612 * q^69 + 50947270608 * q^70 - 43677902056 * q^71 - 56634399632 * q^72 + 12278087704 * q^73 - 99553151276 * q^74 + 85400572304 * q^75 + 46613107196 * q^76 + 205137826492 * q^78 + 130159671844 * q^80 + 794986843420 * q^81 + 83904972628 * q^82 + 216982878048 * q^84 - 97656252 * q^85 + 56725646132 * q^86 - 50128110092 * q^87 + 346072249440 * q^88 + 174291105374 * q^90 - 46617621428 * q^91 - 51820450984 * q^92 + 708584 * q^93 - 82977932908 * q^94 - 20580862760 * q^95 - 62470624376 * q^96 - 4 * q^97 - 155418407946 * q^98 - 189350900660 * q^99

Character values

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

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

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 $

$2$	−43.6367	−	11.9933i	−0.964244	−	0.265016i
$2$	−43.6367	−	11.9933i	−0.964244	−	0.265016i
$3$			219.501i			0.521519i	0.965404	+	0.260759i	$0.0839729\pi$
$3$			219.501i			0.521519i	−0.965404	+	0.260759i	$0.916027\pi$
$4$	1760.32	+	1046.69i	0.859533	+	0.511080i
$5$	5720.85	−	4012.48i	0.818702	−	0.574219i
$5$	5720.85	−	4012.48i	0.818702	−	0.574219i
$6$	2632.53	−	9578.30i	0.138211	−	0.502871i
$7$	37491.7	+	37491.7i	0.843133	+	0.843133i	0.989265	−	0.146132i	$-0.0466824\pi$
$7$	37491.7	+	37491.7i	0.843133	+	0.843133i	−0.146132	+	0.989265i	$0.546682\pi$
$8$	−64261.4	−	66786.2i	−0.693355	−	0.720596i
$9$	128966.			0.728018
$10$	−297762.	+	106480.i	−0.941606	+	0.336718i
$11$	274026.	+	274026.i	0.513017	+	0.513017i	0.915450	−	0.402433i	$-0.131835\pi$
$11$	274026.	+	274026.i	0.513017	+	0.513017i	−0.402433	+	0.915450i	$0.631835\pi$
$12$	−229750.	+	386393.i	−0.266538	+	0.448262i
$13$	2.13499e6			1.59481			0.797403	−	0.603447i	$-0.206206\pi$
$13$	2.13499e6			1.59481			0.797403	+	0.603447i	$0.206206\pi$
$14$	−1.18637e6	−	2.08566e6i	−0.589542	−	1.03643i
$15$	880743.	+	1.25573e6i	0.299466	+	0.426968i
$16$	2.00317e6	+	3.68504e6i	0.477594	+	0.878581i
$17$	3.59002e6	+	3.59002e6i	0.613236	+	0.613236i	0.943788	−	0.330552i	$-0.107235\pi$
$17$	3.59002e6	+	3.59002e6i	0.613236	+	0.613236i	−0.330552	+	0.943788i	$0.607235\pi$
$18$	−5.62766e6	−	1.54673e6i	−0.701987	−	0.192937i
$19$	9.47032e6	+	9.47032e6i	0.877445	+	0.877445i	0.993270	−	0.115825i	$-0.0369512\pi$
$19$	9.47032e6	+	9.47032e6i	0.877445	+	0.877445i	−0.115825	+	0.993270i	$0.536951\pi$
$20$	1.42704e7	−	1.07528e6i	0.997173	−	0.0751376i
$21$	−8.22948e6	+	8.22948e6i	−0.439710	+	0.439710i
$22$	−8.67112e6	−	1.52440e7i	−0.358716	−	0.630631i
$23$	3.19384e7	−	3.19384e7i	1.03469	−	1.03469i	0.0353147	−	0.999376i	$-0.488757\pi$
$23$	3.19384e7	−	3.19384e7i	1.03469	−	1.03469i	0.999376	−	0.0353147i	$-0.0112433\pi$
$24$	1.46597e7	−	1.41055e7i	0.375804	−	0.361597i
$25$	1.66282e7	−	4.59096e7i	0.340545	−	0.940228i
$26$	−9.31641e7	−	2.56055e7i	−1.53778	−	0.422649i
$27$			6.71922e7i			0.901194i
$28$	2.67552e7	+	1.05240e8i	0.293792	+	1.15561i
$29$	−1.49568e7	+	1.49568e7i	−0.135410	+	0.135410i	−0.771563	−	0.636153i	$-0.780525\pi$
$29$	−1.49568e7	+	1.49568e7i	−0.135410	+	0.135410i	0.636153	+	0.771563i	$0.280525\pi$
$30$	−2.33724e7	−	6.53590e7i	−0.175605	−	0.491065i
$31$		−	1.30278e8i		−	0.817301i	−0.912691	−	0.408650i	$-0.866000\pi$
$31$		−	1.30278e8i		−	0.817301i	0.912691	−	0.408650i	$-0.134000\pi$
$32$	−4.32163e7	−	1.84827e8i	−0.227679	−	0.973736i
$33$	−6.01490e7	+	6.01490e7i	−0.267548	+	0.267548i
$34$	−1.13600e8	−	1.99712e8i	−0.428791	−	0.753826i
$35$	3.64919e8	+	6.40500e7i	1.17442	+	0.206132i
$36$	2.27022e8	+	1.34988e8i	0.625756	+	0.372076i
$37$	−6.16927e8			−1.46260			−0.731298	−	0.682059i	$-0.761085\pi$
$37$	−6.16927e8			−1.46260			−0.731298	+	0.682059i	$0.761085\pi$
$38$	−2.99673e8	−	5.26833e8i	−0.613534	−	1.07861i
$39$			4.68633e8i			0.831721i
$40$	−6.35608e8	−	1.24227e8i	−0.981431	−	0.191816i
$41$		−	5.21271e8i		−	0.702672i	−0.936249	−	0.351336i	$-0.885727\pi$
$41$		−	5.21271e8i		−	0.702672i	0.936249	−	0.351336i	$-0.114273\pi$
$42$	4.57805e8	−	2.60409e8i	0.540518	−	0.307457i
$43$	−1.02727e9			−1.06563			−0.532815	−	0.846232i	$-0.678866\pi$
$43$	−1.02727e9			−1.06563			−0.532815	+	0.846232i	$0.678866\pi$
$44$	1.95553e8	+	7.69195e8i	0.178762	+	0.703148i
$45$	7.37797e8	−	5.17474e8i	0.596030	−	0.418042i
$46$	−1.77673e9	+	1.01064e9i	−1.27190	+	0.723485i
$47$	−1.16750e9	+	1.16750e9i	−0.742541	+	0.742541i	−0.973066	−	0.230525i	$-0.925956\pi$
$47$	−1.16750e9	+	1.16750e9i	−0.742541	+	0.742541i	0.230525	+	0.973066i	$0.425956\pi$
$48$	−8.08869e8	+	4.39699e8i	−0.458196	+	0.249074i
$49$			8.33932e8i			0.421747i
$50$	−1.27620e9	+	1.80392e9i	−0.577544	+	0.816359i
$51$	−7.88012e8	+	7.88012e8i	−0.319814	+	0.319814i
$52$	3.75828e9	+	2.23468e9i	1.37079	+	0.815074i
$53$		−	1.52042e9i		−	0.499398i	−0.968323	−	0.249699i	$-0.919668\pi$
$53$		−	1.52042e9i		−	0.499398i	0.968323	−	0.249699i	$-0.0803317\pi$
$54$	8.05854e8	−	2.93205e9i	0.238831	−	0.868971i
$55$	2.66718e9	+	4.68139e8i	0.714592	+	0.125424i
$56$	9.46584e7	−	4.91320e9i	0.0229681	−	1.19215i
$57$	−2.07874e9	+	2.07874e9i	−0.457604	+	0.457604i
$58$	8.32045e8	−	4.73284e8i	0.166454	−	0.0946821i
$59$	4.99146e9	−	4.99146e9i	0.908954	−	0.908954i	−0.0872339	−	0.996188i	$-0.527803\pi$
$59$	4.99146e9	−	4.99146e9i	0.908954	−	0.908954i	0.996188	+	0.0872339i	$0.0278028\pi$
$60$	2.36026e8	+	3.13236e9i	0.0391857	+	0.520044i
$61$	−6.16017e9	−	6.16017e9i	−0.933854	−	0.933854i	0.0640902	−	0.997944i	$-0.479585\pi$
$61$	−6.16017e9	−	6.16017e9i	−0.933854	−	0.933854i	−0.997944	+	0.0640902i	$0.979585\pi$
$62$	−1.56246e9	+	5.68491e9i	−0.216598	+	0.788078i
$63$	4.83517e9	+	4.83517e9i	0.613816	+	0.613816i
$64$	−3.30867e8	+	8.58356e9i	−0.0385180	+	0.999258i
$65$	1.22140e10	−	8.56661e9i	1.30567	−	0.915768i
$66$	3.34608e9	−	1.90332e9i	0.328886	−	0.187077i
$67$	8.23483e9			0.745149			0.372575	−	0.928002i	$-0.378475\pi$
$67$	8.23483e9			0.745149			0.372575	+	0.928002i	$0.378475\pi$
$68$	2.56195e9	+	1.00772e10i	0.213683	+	0.840509i
$69$	7.01052e9	+	7.01052e9i	0.539611	+	0.539611i
$70$	−1.51557e10	−	7.17150e9i	−1.07780	−	0.510001i
$71$	9.46380e9			0.622507			0.311254	−	0.950327i	$-0.399251\pi$
$71$	9.46380e9			0.622507			0.311254	+	0.950327i	$0.399251\pi$
$72$	−8.28756e9	−	8.61317e9i	−0.504775	−	0.524607i
$73$	−7.38240e9	−	7.38240e9i	−0.416794	−	0.416794i	0.467303	−	0.884097i	$-0.345226\pi$
$73$	−7.38240e9	−	7.38240e9i	−0.416794	−	0.416794i	−0.884097	+	0.467303i	$0.845226\pi$
$74$	2.69207e10	+	7.39896e9i	1.41030	+	0.387611i
$75$	1.00772e10	+	3.64990e9i	0.490346	+	0.177601i
$76$	6.75831e9	+	2.65833e10i	0.305748	+	1.20264i
$77$			2.05474e10i			0.865083i
$78$	5.62044e9	−	2.04496e10i	0.220420	−	0.801982i
$79$	3.36197e9			0.122926			0.0614631	−	0.998109i	$-0.480423\pi$
$79$	3.36197e9			0.122926			0.0614631	+	0.998109i	$0.480423\pi$
$80$	2.62460e10	+	1.30439e10i	0.895505	+	0.445052i
$81$	8.09723e9			0.258029
$82$	−6.25174e9	+	2.27466e10i	−0.186219	+	0.677547i
$83$		−	1.55858e10i		−	0.434309i	−0.976137	−	0.217155i	$-0.930322\pi$
$83$		−	1.55858e10i		−	0.434309i	0.976137	−	0.217155i	$-0.0696776\pi$
$84$	−2.31003e10	+	5.87281e9i	−0.602672	+	0.153218i
$85$	3.49428e10	+	6.13310e9i	0.854188	+	0.149926i
$86$	4.48265e10	+	1.23203e10i	1.02753	+	0.282409i
$87$	−3.28303e9	−	3.28303e9i	−0.0706186	−	0.0706186i
$88$	6.91855e8	−	3.59104e10i	0.0139753	−	0.725381i
$89$	−8.17382e10			−1.55160			−0.775801	−	0.630978i	$-0.782654\pi$
$89$	−8.17382e10			−1.55160			−0.775801	+	0.630978i	$0.782654\pi$
$90$	−3.84012e10	+	1.37323e10i	−0.685506	+	0.245137i
$91$	8.00446e10	+	8.00446e10i	1.34463	+	1.34463i
$92$	8.96517e10	−	2.27923e10i	1.41816	−	0.360541i
$93$	2.85962e10			0.426238
$94$	6.49483e10	−	3.69439e10i	0.912776	−	0.519205i
$95$	9.21777e10	+	1.61789e10i	1.22221	+	0.214520i
$96$	4.05698e10	−	9.48602e9i	0.507822	−	0.118739i
$97$	7.86089e10	+	7.86089e10i	0.929452	+	0.929452i	0.997670	−	0.0682182i	$-0.0217314\pi$
$97$	7.86089e10	+	7.86089e10i	0.929452	+	0.929452i	−0.0682182	+	0.997670i	$0.521731\pi$
$98$	1.00016e10	−	3.63901e10i	0.111770	−	0.406667i
$99$	3.53401e10	+	3.53401e10i	0.373486	+	0.373486i
$100$	7.73242e10	−	6.34111e10i	0.773242	−	0.634111i
$101$	2.91874e10	−	2.91874e10i	0.276330	−	0.276330i	−0.555312	−	0.831642i	$-0.687401\pi$
$101$	2.91874e10	−	2.91874e10i	0.276330	−	0.276330i	0.831642	+	0.555312i	$0.187401\pi$
$102$	4.38371e10	−	2.49354e10i	0.393134	−	0.223623i
$103$	−1.29983e11	+	1.29983e11i	−1.10479	+	1.10479i	−0.110971	+	0.993824i	$0.535396\pi$
$103$	−1.29983e11	+	1.29983e11i	−1.10479	+	1.10479i	−0.993824	+	0.110971i	$0.964604\pi$
$104$	−1.37198e11	−	1.42588e11i	−1.10577	−	1.14921i
$105$	−1.40590e10	+	8.01002e10i	−0.107501	+	0.612481i
$106$	−1.82348e10	+	6.63462e10i	−0.132349	+	0.481542i
$107$			1.23644e10i			0.0852242i	0.999092	+	0.0426121i	$0.0135680\pi$
$107$			1.23644e10i			0.0852242i	−0.999092	+	0.0426121i	$0.986432\pi$
$108$	−7.03296e10	+	1.18280e11i	−0.460582	+	0.774606i
$109$	−1.02864e11	+	1.02864e11i	−0.640352	+	0.640352i	−0.950642	−	0.310290i	$-0.899574\pi$
$109$	−1.02864e11	+	1.02864e11i	−0.640352	+	0.640352i	0.310290	+	0.950642i	$0.399574\pi$
$110$	−1.10773e11	−	5.24163e10i	−0.655802	−	0.310318i
$111$		−	1.35416e11i		−	0.762771i
$112$	−6.30559e10	+	2.13261e11i	−0.338086	+	1.14344i
$113$	−8.70997e10	+	8.70997e10i	−0.444719	+	0.444719i	−0.893594	−	0.448876i	$-0.851825\pi$
$113$	−8.70997e10	+	8.70997e10i	−0.444719	+	0.444719i	0.448876	+	0.893594i	$0.351825\pi$
$114$	1.15641e11	−	6.57786e10i	0.562514	−	0.319969i
$115$	5.45629e10	−	3.10867e11i	0.252964	−	1.44124i
$116$	−4.19839e10	+	1.06736e10i	−0.185594	+	0.0471838i
$117$	2.75342e11			1.16105
$118$	−2.77675e11	+	1.57947e11i	−1.11734	+	0.635566i
$119$			2.69192e11i			1.03408i
$120$	2.72679e10	−	1.39517e11i	0.100036	−	0.511834i
$121$		−	1.35131e11i		−	0.473627i
$122$	1.94929e11	+	3.42690e11i	0.652977	+	1.14795i
$123$	1.14420e11			0.366457
$124$	1.36361e11	−	2.29332e11i	0.417707	−	0.702497i
$125$	−8.90837e10	−	3.29362e11i	−0.261092	−	0.965314i
$126$	−1.53001e11	−	2.68980e11i	−0.429198	−	0.754540i
$127$	−3.98169e11	+	3.98169e11i	−1.06942	+	1.06942i	−0.0720139	+	0.997404i	$0.522943\pi$
$127$	−3.98169e11	+	3.98169e11i	−1.06942	+	1.06942i	−0.997404	+	0.0720139i	$0.977057\pi$
$128$	1.17383e11	−	3.70590e11i	0.301960	−	0.953321i
$129$		−	2.25486e11i		−	0.555746i
$130$	−6.35719e11	+	2.27333e11i	−1.50168	+	0.537000i
$131$	1.68591e11	−	1.68591e11i	0.381806	−	0.381806i	−0.489946	−	0.871753i	$-0.662984\pi$
$131$	1.68591e11	−	1.68591e11i	0.381806	−	0.381806i	0.871753	+	0.489946i	$0.162984\pi$
$132$	−1.68839e11	+	4.29241e10i	−0.366705	+	0.0932277i
$133$			7.10117e11i			1.47961i
$134$	−3.59341e11	−	9.87625e10i	−0.718506	−	0.197477i
$135$	2.69607e11	+	3.84397e11i	0.517482	+	0.737809i
$136$	9.06401e9	−	4.70463e11i	0.0167054	−	0.867085i
$137$	5.87796e11	−	5.87796e11i	1.04055	−	1.04055i	0.0414099	−	0.999142i	$-0.486815\pi$
$137$	5.87796e11	−	5.87796e11i	1.04055	−	1.04055i	0.999142	−	0.0414099i	$-0.0131850\pi$
$138$	−2.21837e11	−	3.89995e11i	−0.377311	−	0.663322i
$139$	−4.90208e10	+	4.90208e10i	−0.0801307	+	0.0801307i	−0.746036	−	0.665905i	$-0.768045\pi$
$139$	−4.90208e10	+	4.90208e10i	−0.0801307	+	0.0801307i	0.665905	+	0.746036i	$0.268045\pi$
$140$	5.75335e11	+	4.94707e11i	0.904101	+	0.777399i
$141$	−2.56269e11	−	2.56269e11i	−0.387249	−	0.387249i
$142$	−4.12969e11	−	1.13502e11i	−0.600249	−	0.164975i
$143$	5.85043e11	+	5.85043e11i	0.818163	+	0.818163i
$144$	2.58342e11	+	4.75245e11i	0.347697	+	0.639623i
$145$	−2.55518e10	+	1.45579e11i	−0.0331053	+	0.188615i
$146$	2.33605e11	+	4.10683e11i	0.291434	+	0.512349i
$147$	−1.83049e11			−0.219949
$148$	−1.08599e12	−	6.45733e11i	−1.25715	−	0.747504i
$149$	−7.86027e11	−	7.86027e11i	−0.876825	−	0.876825i	0.116380	−	0.993205i	$-0.462871\pi$
$149$	−7.86027e11	−	7.86027e11i	−0.876825	−	0.876825i	−0.993205	+	0.116380i	$0.962871\pi$
$150$	−3.95962e11	−	2.80128e11i	−0.425747	−	0.301200i
$151$	−1.27493e12			−1.32164			−0.660822	−	0.750542i	$-0.729792\pi$
$151$	−1.27493e12			−1.32164			−0.660822	+	0.750542i	$0.729792\pi$
$152$	2.39105e10	−	1.24106e12i	0.0239028	−	1.24066i
$153$	4.62991e11	+	4.62991e11i	0.446447	+	0.446447i
$154$	2.46430e11	−	8.96621e11i	0.229261	−	0.834151i
$155$	−5.22738e11	−	7.45302e11i	−0.469310	−	0.669126i
$156$	−4.90515e11	+	8.24946e11i	−0.425076	+	0.714892i
$157$			5.50363e11i			0.460470i	0.973135	+	0.230235i	$0.0739495\pi$
$157$			5.50363e11i			0.460470i	−0.973135	+	0.230235i	$0.926051\pi$
$158$	−1.46705e11	−	4.03209e10i	−0.118531	−	0.0325774i
$159$	3.33734e11			0.260445
$160$	−9.88849e11	−	8.83966e11i	−0.745539	−	0.666462i
$161$	2.39485e12			1.74476
$162$	−3.53336e11	−	9.71121e10i	−0.248803	−	0.0683819i
$163$		−	7.16541e10i		−	0.0487763i	−0.999703	−	0.0243882i	$-0.992236\pi$
$163$		−	7.16541e10i		−	0.0487763i	0.999703	−	0.0243882i	$-0.00776376\pi$
$164$	5.45611e11	−	9.17606e11i	0.359122	−	0.603970i
$165$	−1.02757e11	+	5.85450e11i	−0.0654109	+	0.372673i
$166$	−1.86924e11	+	6.80112e11i	−0.115099	+	0.418780i
$167$	1.00628e12	+	1.00628e12i	0.599485	+	0.599485i	0.940175	−	0.340691i	$-0.110661\pi$
$167$	1.00628e12	+	1.00628e12i	0.599485	+	0.599485i	−0.340691	+	0.940175i	$0.610661\pi$
$168$	1.07845e12	+	2.07776e10i	0.621728	+	0.0119783i
$169$	2.76604e12			1.54341
$170$	−1.45123e12	−	6.86706e11i	−0.783913	−	0.370939i
$171$	1.22135e12	+	1.22135e12i	0.638796	+	0.638796i
$172$	−1.80832e12	−	1.07523e12i	−0.915944	−	0.544623i
$173$	−3.19594e12			−1.56800			−0.783998	−	0.620763i	$-0.786823\pi$
$173$	−3.19594e12			−1.56800			−0.783998	+	0.620763i	$0.786823\pi$
$174$	1.03886e11	+	1.82635e11i	0.0493785	+	0.0868086i
$175$	2.34465e12	−	1.09781e12i	1.07986	−	0.505613i
$176$	−4.60874e11	+	1.55872e12i	−0.205713	+	0.695740i
$177$	1.09563e12	+	1.09563e12i	0.474036	+	0.474036i
$178$	3.56679e12	+	9.80308e11i	1.49612	+	0.411199i
$179$	1.55787e12	+	1.55787e12i	0.633637	+	0.633637i	0.948978	−	0.315341i	$-0.102119\pi$
$179$	1.55787e12	+	1.55787e12i	0.633637	+	0.633637i	−0.315341	+	0.948978i	$0.602119\pi$
$180$	1.84040e12	−	1.38675e11i	0.725960	−	0.0547016i
$181$	1.14219e12	−	1.14219e12i	0.437025	−	0.437025i	−0.453985	−	0.891010i	$-0.649998\pi$
$181$	1.14219e12	−	1.14219e12i	0.437025	−	0.437025i	0.891010	+	0.453985i	$0.149998\pi$
$182$	−2.53289e12	−	4.45288e12i	−0.940206	−	1.65291i
$183$	1.35217e12	−	1.35217e12i	0.487022	−	0.487022i
$184$	−4.18546e12	−	8.06376e10i	−1.46300	−	0.0281864i
$185$	−3.52935e12	+	2.47540e12i	−1.19743	+	0.839850i
$186$	−1.24784e12	−	3.42961e11i	−0.410997	−	0.112960i
$187$			1.96751e12i			0.629200i
$188$	−3.27721e12	+	8.33167e11i	−1.01774	+	0.258740i
$189$	−2.51915e12	+	2.51915e12i	−0.759826	+	0.759826i
$190$	−3.82829e12	−	1.81150e12i	−1.12166	−	0.530755i
$191$		−	2.36741e12i		−	0.673892i	−0.941524	−	0.336946i	$-0.890606\pi$
$191$		−	2.36741e12i		−	0.673892i	0.941524	−	0.336946i	$-0.109394\pi$
$192$	−1.88410e12	−	7.26256e10i	−0.521132	−	0.0200878i
$193$	−4.55912e12	+	4.55912e12i	−1.22551	+	1.22551i	−0.259861	+	0.965646i	$0.583677\pi$
$193$	−4.55912e12	+	4.55912e12i	−1.22551	+	1.22551i	−0.965646	+	0.259861i	$0.916323\pi$
$194$	−2.48746e12	−	4.37301e12i	−0.649899	−	1.14254i
$195$	1.88038e12	+	2.68098e12i	0.477590	+	0.680932i
$196$	−8.72871e11	+	1.46799e12i	−0.215547	+	0.362506i
$197$	5.66064e11			0.135926			0.0679628	−	0.997688i	$-0.478350\pi$
$197$	5.66064e11			0.135926			0.0679628	+	0.997688i	$0.478350\pi$
$198$	−1.11828e12	−	1.96597e12i	−0.261152	−	0.459111i
$199$		−	7.10121e12i		−	1.61302i	−0.591219	−	0.806511i	$-0.701353\pi$
$199$		−	7.10121e12i		−	1.61302i	0.591219	−	0.806511i	$-0.298647\pi$
$200$	−4.13468e12	+	1.83968e12i	−0.913644	+	0.406516i
$201$			1.80755e12i			0.388609i
$202$	−1.62370e12	+	9.23590e11i	−0.339682	+	0.193218i
$203$	−1.12151e12			−0.228337
$204$	−2.21196e12	+	5.62350e11i	−0.438341	+	0.111440i
$205$	−2.09159e12	−	2.98212e12i	−0.403488	−	0.575279i
$206$	7.23095e12	−	4.11311e12i	1.35808	−	0.772503i
$207$	4.11898e12	−	4.11898e12i	0.753274	−	0.753274i
$208$	4.27676e12	+	7.86752e12i	0.761670	+	1.40117i
$209$			5.19022e12i			0.900288i
$210$	1.57415e12	−	3.32669e12i	0.265975	−	0.562091i
$211$	2.61617e12	−	2.61617e12i	0.430638	−	0.430638i	−0.458207	−	0.888845i	$-0.651508\pi$
$211$	2.61617e12	−	2.61617e12i	0.430638	−	0.430638i	0.888845	+	0.458207i	$0.151508\pi$
$212$	1.59141e12	−	2.67643e12i	0.255233	−	0.429249i
$213$			2.07731e12i			0.324649i
$214$	1.48290e11	−	5.39542e11i	0.0225858	−	0.0821769i
$215$	−5.87684e12	+	4.12188e12i	−0.872433	+	0.611905i
$216$	4.48751e12	−	4.31787e12i	0.649397	−	0.624847i
$217$	4.88435e12	−	4.88435e12i	0.689094	−	0.689094i
$218$	5.72234e12	−	3.25498e12i	0.787160	−	0.447752i
$219$	1.62044e12	−	1.62044e12i	0.217366	−	0.217366i
$220$	4.20511e12	+	3.61580e12i	0.550114	+	0.473020i
$221$	7.66466e12	+	7.66466e12i	0.977992	+	0.977992i
$222$	−1.62408e12	+	5.90911e12i	−0.202147	+	0.735497i
$223$	9.73168e11	+	9.73168e11i	0.118171	+	0.118171i	0.763719	−	0.645548i	$-0.223371\pi$
$223$	9.73168e11	+	9.73168e11i	0.118171	+	0.118171i	−0.645548	+	0.763719i	$0.723371\pi$
$224$	5.30924e12	−	8.54975e12i	0.629026	−	1.01295i
$225$	2.14447e12	−	5.92079e12i	0.247923	−	0.684503i
$226$	4.84536e12	−	2.75614e12i	0.546675	−	0.310960i
$227$	5.32358e12			0.586222			0.293111	−	0.956078i	$-0.405310\pi$
$227$	5.32358e12			0.586222			0.293111	+	0.956078i	$0.405310\pi$
$228$	−5.83507e12	+	1.48346e12i	−0.627198	+	0.159453i
$229$	4.31708e12	+	4.31708e12i	0.452997	+	0.452997i	0.896348	−	0.443351i	$-0.146211\pi$
$229$	4.31708e12	+	4.31708e12i	0.452997	+	0.452997i	−0.443351	+	0.896348i	$0.646211\pi$
$230$	−6.10926e12	+	1.29108e13i	−0.625872	+	1.32267i
$231$	−4.51018e12			−0.451157
$232$	1.96005e12	+	3.77626e10i	0.191462	+	0.00368874i
$233$	−1.08243e13	−	1.08243e13i	−1.03263	−	1.03263i	−0.999449	−	0.0331791i	$-0.989437\pi$
$233$	−1.08243e13	−	1.08243e13i	−1.03263	−	1.03263i	−0.0331791	−	0.999449i	$-0.510563\pi$
$234$	−1.20150e13	−	3.30225e12i	−1.11953	−	0.307697i
$235$	−1.99454e12	+	1.13637e13i	−0.181539	+	1.03430i
$236$	1.40111e13	−	3.56206e12i	1.24582	−	0.316727i
$237$			7.37955e11i			0.0641083i
$238$	3.22849e12	−	1.17466e13i	0.274047	−	0.997104i
$239$	−9.08678e12			−0.753740			−0.376870	−	0.926266i	$-0.623000\pi$
$239$	−9.08678e12			−0.753740			−0.376870	+	0.926266i	$0.623000\pi$
$240$	−2.86314e12	+	5.76102e12i	−0.232103	+	0.467022i
$241$	1.34521e12			0.106585			0.0532923	−	0.998579i	$-0.483028\pi$
$241$	1.34521e12			0.106585			0.0532923	+	0.998579i	$0.483028\pi$
$242$	−1.62067e12	+	5.89669e12i	−0.125519	+	0.456692i
$243$			1.36802e13i			1.03576i
$244$	−4.39609e12	−	1.72917e13i	−0.325404	−	1.27995i
$245$	3.34613e12	+	4.77080e12i	0.242175	+	0.345285i
$246$	−4.99290e12	−	1.37226e12i	−0.353354	−	0.0971169i
$247$	2.02191e13	+	2.02191e13i	1.39935	+	1.39935i
$248$	−8.70078e12	+	8.37186e12i	−0.588944	+	0.566680i
$249$	3.42110e12			0.226500
$250$	−6.28061e10	+	1.54407e13i	−0.00406754	+	0.999992i
$251$	1.27148e13	+	1.27148e13i	0.805571	+	0.805571i	0.983960	−	0.178389i	$-0.0570886\pi$
$251$	1.27148e13	+	1.27148e13i	0.805571	+	0.805571i	−0.178389	+	0.983960i	$0.557089\pi$
$252$	3.45052e12	+	1.35724e13i	0.213886	+	0.841305i
$253$	1.75039e13			1.06163
$254$	2.21501e13	−	1.25994e13i	1.31459	−	0.747767i
$255$	−1.34622e12	+	7.66998e12i	−0.0781890	+	0.445475i
$256$	−9.56678e12	+	1.47635e13i	−0.543809	+	0.839209i
$257$	2.28542e13	+	2.28542e13i	1.27155	+	1.27155i	0.945276	+	0.326273i	$0.105793\pi$
$257$	2.28542e13	+	2.28542e13i	1.27155	+	1.27155i	0.326273	+	0.945276i	$0.394207\pi$
$258$	−2.70431e12	+	9.83947e12i	−0.147282	+	0.535875i
$259$	−2.31297e13	−	2.31297e13i	−1.23316	−	1.23316i
$260$	3.04672e13	−	2.29572e12i	1.59030	−	0.119830i
$261$	−1.92892e12	+	1.92892e12i	−0.0985806	+	0.0985806i
$262$	−9.37873e12	+	5.33481e12i	−0.469339	+	0.266970i
$263$	2.06390e13	−	2.06390e13i	1.01142	−	1.01142i	0.0114851	−	0.999934i	$-0.496344\pi$
$263$	2.06390e13	−	2.06390e13i	1.01142	−	1.01142i	0.999934	−	0.0114851i	$-0.00365591\pi$
$264$	7.88238e12	+	1.51863e11i	0.378300	+	0.00728837i
$265$	−6.10066e12	−	8.69811e12i	−0.286764	−	0.408858i
$266$	8.51662e12	−	3.09872e13i	0.392119	−	1.42670i
$267$		−	1.79416e13i		−	0.809189i
$268$	1.44960e13	+	8.61934e12i	0.640481	+	0.380831i
$269$	−1.44221e12	+	1.44221e12i	−0.0624297	+	0.0624297i	−0.737632	−	0.675203i	$-0.764056\pi$
$269$	−1.44221e12	+	1.44221e12i	−0.0624297	+	0.0624297i	0.675203	+	0.737632i	$0.264056\pi$
$270$	−7.15460e12	−	2.00073e13i	−0.303448	−	0.848569i
$271$		−	1.37742e13i		−	0.572447i	−0.958163	−	0.286223i	$-0.907600\pi$
$271$		−	1.37742e13i		−	0.572447i	0.958163	−	0.286223i	$-0.0923999\pi$
$272$	−6.03791e12	+	2.04208e13i	−0.245900	+	0.831654i
$273$	−1.75699e13	+	1.75699e13i	−0.701252	+	0.701252i
$274$	−3.26991e13	+	1.85999e13i	−1.27911	+	0.727583i
$275$	1.71370e13	−	8.02386e12i	0.657058	−	0.307647i
$276$	5.00293e12	+	1.96787e13i	0.188029	+	0.739597i
$277$	−4.22567e13			−1.55689			−0.778444	−	0.627714i	$-0.783991\pi$
$277$	−4.22567e13			−1.55689			−0.778444	+	0.627714i	$0.783991\pi$
$278$	2.72702e12	−	1.55119e12i	0.0985015	−	0.0560296i
$279$		−	1.68015e13i		−	0.595010i
$280$	−1.91726e13	−	2.84875e13i	−0.665751	−	0.989203i
$281$		−	1.56751e13i		−	0.533735i	−0.963733	−	0.266868i	$-0.914011\pi$
$281$		−	1.56751e13i		−	0.533735i	0.963733	−	0.266868i	$-0.0859886\pi$
$282$	8.10922e12	+	1.42562e13i	0.270775	+	0.476030i
$283$	2.17360e13			0.711794			0.355897	−	0.934525i	$-0.384175\pi$
$283$	2.17360e13			0.711794			0.355897	+	0.934525i	$0.384175\pi$
$284$	1.66593e13	+	9.90569e12i	0.535066	+	0.318151i
$285$	−3.55128e12	+	2.02331e13i	−0.111876	+	0.637406i
$286$	−1.85128e13	−	3.25459e13i	−0.572082	−	1.00573i
$287$	1.95434e13	−	1.95434e13i	0.592446	−	0.592446i
$288$	−5.57344e12	−	2.38365e13i	−0.165754	−	0.708898i
$289$		−	8.49547e12i		−	0.247884i
$290$	2.86097e12	−	6.04615e12i	0.0819075	−	0.173097i
$291$	−1.72547e13	+	1.72547e13i	−0.484727	+	0.484727i
$292$	−5.26831e12	−	2.07225e13i	−0.145233	−	0.571264i
$293$			5.11073e13i			1.38265i	0.722545	+	0.691324i	$0.242972\pi$
$293$			5.11073e13i			1.38265i	−0.722545	+	0.691324i	$0.757028\pi$
$294$	7.98766e12	+	2.19536e12i	0.212085	+	0.0582901i
$295$	8.52730e12	−	4.85836e13i	0.222224	−	1.26610i
$296$	3.96446e13	+	4.12022e13i	1.01410	+	1.05394i
$297$	−1.84124e13	+	1.84124e13i	−0.462328	+	0.462328i
$298$	2.48726e13	+	4.37267e13i	0.613101	+	1.07785i
$299$	6.81884e13	−	6.81884e13i	1.65013	−	1.65013i
$300$	1.39188e13	+	1.69727e13i	0.330701	+	0.403260i
$301$	−3.85140e13	−	3.85140e13i	−0.898468	−	0.898468i
$302$	5.56339e13	+	1.52906e13i	1.27439	+	0.350257i
$303$	6.40667e12	+	6.40667e12i	0.144111	+	0.144111i
$304$	−1.59278e13	+	5.38691e13i	−0.351844	+	1.18997i
$305$	−5.99590e13	−	1.05239e13i	−1.30078	−	0.228311i
$306$	−1.46506e13	−	2.57562e13i	−0.312168	−	0.548799i
$307$	−7.90047e13			−1.65345			−0.826726	−	0.562604i	$-0.809799\pi$
$307$	−7.90047e13			−1.65345			−0.826726	+	0.562604i	$0.809799\pi$
$308$	−2.15068e13	+	3.61701e13i	−0.442127	+	0.743567i
$309$	−2.85314e13	−	2.85314e13i	−0.576171	−	0.576171i
$310$	1.38720e13	+	3.87918e13i	0.275200	+	0.769575i
$311$	−9.35622e13			−1.82355			−0.911776	−	0.410688i	$-0.865289\pi$
$311$	−9.35622e13			−1.82355			−0.911776	+	0.410688i	$0.865289\pi$
$312$	3.12983e13	−	3.01151e13i	0.599335	−	0.576678i
$313$	−5.41442e13	−	5.41442e13i	−1.01873	−	1.01873i	−0.999821	−	0.0189067i	$-0.993981\pi$
$313$	−5.41442e13	−	5.41442e13i	−1.01873	−	1.01873i	−0.0189067	−	0.999821i	$-0.506019\pi$
$314$	6.60065e12	−	2.40160e13i	0.122032	−	0.444005i
$315$	4.70623e13	+	8.26028e12i	0.854998	+	0.150068i
$316$	5.91815e12	+	3.51894e12i	0.105659	+	0.0628251i
$317$			3.26764e12i			0.0573335i	0.999589	+	0.0286668i	$0.00912616\pi$
$317$			3.26764e12i			0.0573335i	−0.999589	+	0.0286668i	$0.990874\pi$
$318$	−1.45631e13	−	4.00256e12i	−0.251133	−	0.0690222i
$319$	−8.19709e12			−0.138935
$320$	3.25485e13	+	5.04329e13i	0.542258	+	0.840212i
$321$	−2.71400e12			−0.0444460
$322$	−1.04504e14	−	2.87221e13i	−1.68238	−	0.462391i
$323$			6.79972e13i			1.07616i
$324$	1.42537e13	+	8.47531e12i	0.221784	+	0.131874i
$325$	3.55011e13	−	9.80166e13i	0.543104	−	1.49948i
$326$	−8.59366e11	+	3.12675e12i	−0.0129265	+	0.0470323i
$327$	−2.25788e13	−	2.25788e13i	−0.333956	−	0.333956i
$328$	−3.48138e13	+	3.34977e13i	−0.506343	+	0.487201i
$329$	−8.75436e13			−1.25212
$330$	1.15054e13	−	2.43147e13i	0.161836	−	0.342013i
$331$	−1.91717e13	−	1.91717e13i	−0.265220	−	0.265220i	0.561951	−	0.827171i	$-0.310051\pi$
$331$	−1.91717e13	−	1.91717e13i	−0.265220	−	0.265220i	−0.827171	+	0.561951i	$0.810051\pi$
$332$	1.63135e13	−	2.74360e13i	0.221967	−	0.373303i
$333$	−7.95627e13			−1.06480
$334$	−3.18421e13	−	5.59793e13i	−0.419176	−	0.736922i
$335$	4.71103e13	−	3.30421e13i	0.610055	−	0.427879i
$336$	−4.68110e13	−	1.38408e13i	−0.596323	−	0.176318i
$337$	−3.72581e13	−	3.72581e13i	−0.466935	−	0.466935i	0.433985	−	0.900920i	$-0.357107\pi$
$337$	−3.72581e13	−	3.72581e13i	−0.466935	−	0.466935i	−0.900920	+	0.433985i	$0.857107\pi$
$338$	−1.20701e14	−	3.31738e13i	−1.48822	−	0.409028i
$339$	−1.91185e13	−	1.91185e13i	−0.231929	−	0.231929i
$340$	5.50912e13	+	4.73706e13i	0.657579	+	0.565425i
$341$	3.56996e13	−	3.56996e13i	0.419289	−	0.419289i
$342$	−3.86478e13	−	6.79437e13i	−0.446664	−	0.785246i
$343$	4.28678e13	−	4.28678e13i	0.487544	−	0.487544i
$344$	6.60136e13	+	6.86072e13i	0.738860	+	0.767889i
$345$	6.82357e13	+	1.19766e13i	0.751635	+	0.131926i
$346$	1.39460e14	+	3.83297e13i	1.51193	+	0.415544i
$347$			4.76375e13i			0.508320i	0.967162	+	0.254160i	$0.0817990\pi$
$347$			4.76375e13i			0.508320i	−0.967162	+	0.254160i	$0.918201\pi$
$348$	−2.34287e12	−	9.21552e12i	−0.0246072	−	0.0967908i
$349$	−9.64986e13	+	9.64986e13i	−0.997656	+	0.997656i	−0.999997	−	0.00234087i	$-0.999255\pi$
$349$	−9.64986e13	+	9.64986e13i	−0.997656	+	0.997656i	0.00234087	+	0.999997i	$0.499255\pi$
$350$	−1.15479e14	+	1.97848e13i	−1.17525	+	0.201353i
$351$			1.43455e14i			1.43723i
$352$	3.88051e13	−	6.24898e13i	0.382740	−	0.616346i
$353$	−1.22828e14	+	1.22828e14i	−1.19271	+	1.19271i	−0.216411	+	0.976302i	$0.569435\pi$
$353$	−1.22828e14	+	1.22828e14i	−1.19271	+	1.19271i	−0.976302	+	0.216411i	$0.930565\pi$
$354$	−3.46696e13	−	6.09500e13i	−0.331459	−	0.582714i
$355$	5.41410e13	−	3.79733e13i	0.509648	−	0.357456i
$356$	−1.43886e14	−	8.55548e13i	−1.33365	−	0.792993i
$357$	−5.90879e13			−0.539291
$358$	−4.92965e13	−	8.66645e13i	−0.443057	−	0.778905i
$359$		−	1.50723e14i		−	1.33401i	−0.745053	−	0.667005i	$-0.767576\pi$
$359$		−	1.50723e14i		−	1.33401i	0.745053	−	0.667005i	$-0.232424\pi$
$360$	−8.19721e13	−	1.60210e13i	−0.714500	−	0.139646i
$361$			6.28835e13i			0.539818i
$362$	−6.35400e13	+	3.61428e13i	−0.537217	+	0.305580i
$363$	2.96615e13			0.247005
$364$	5.71223e13	+	2.24686e14i	0.468541	+	1.84297i
$365$	−7.18553e13	−	1.26119e13i	−0.580561	−	0.101899i
$366$	−7.52209e13	+	4.27872e13i	−0.598677	+	0.340539i
$367$	3.85971e13	−	3.85971e13i	0.302616	−	0.302616i	−0.539421	−	0.842036i	$-0.681357\pi$
$367$	3.85971e13	−	3.85971e13i	0.302616	−	0.302616i	0.842036	+	0.539421i	$0.181357\pi$
$368$	1.81673e14	+	5.37161e13i	1.40322	+	0.414898i
$369$		−	6.72264e13i		−	0.511558i
$370$	1.83697e14	−	6.56901e13i	1.37719	−	0.492482i
$371$	5.70032e13	−	5.70032e13i	0.421059	−	0.421059i
$372$	5.03385e13	+	2.99314e13i	0.366365	+	0.217842i
$373$			1.20625e14i			0.865044i	0.901623	+	0.432522i	$0.142376\pi$
$373$			1.20625e14i			0.865044i	−0.901623	+	0.432522i	$0.857624\pi$
$374$	2.35969e13	−	8.58558e13i	0.166748	−	0.606703i
$375$	7.22954e13	−	1.95540e13i	0.503429	−	0.136164i
$376$	1.52999e14	+	2.94770e12i	1.04992	+	0.0202278i
$377$	−3.19326e13	+	3.19326e13i	−0.215952	+	0.215952i
$378$	1.40140e14	−	7.97146e13i	0.934024	−	0.531292i
$379$	4.75331e13	−	4.75331e13i	0.312234	−	0.312234i	−0.533540	−	0.845775i	$-0.679139\pi$
$379$	4.75331e13	−	4.75331e13i	0.312234	−	0.312234i	0.845775	+	0.533540i	$0.179139\pi$
$380$	1.45328e14	+	1.24962e14i	0.940893	+	0.809035i
$381$	−8.73986e13	−	8.73986e13i	−0.557721	−	0.557721i
$382$	−2.83930e13	+	1.03306e14i	−0.178592	+	0.649796i
$383$	1.65331e14	+	1.65331e14i	1.02509	+	1.02509i	0.999677	+	0.0254090i	$0.00808879\pi$
$383$	1.65331e14	+	1.65331e14i	1.02509	+	1.02509i	0.0254090	+	0.999677i	$0.491911\pi$
$384$	8.13449e13	+	2.57657e13i	0.497174	+	0.157478i
$385$	8.24460e13	+	1.17549e14i	0.496747	+	0.708245i
$386$	2.53624e14	−	1.44266e14i	1.50647	−	0.856908i
$387$	−1.32483e14			−0.775798
$388$	5.60977e13	+	2.20656e14i	0.323870	+	1.27392i
$389$	−1.01563e14	−	1.01563e14i	−0.578111	−	0.578111i	0.356272	−	0.934382i	$-0.384048\pi$
$389$	−1.01563e14	−	1.01563e14i	−0.578111	−	0.578111i	−0.934382	+	0.356272i	$0.884048\pi$
$390$	−4.98999e13	−	1.39541e14i	−0.280056	−	0.783153i
$391$	2.29319e14			1.26902
$392$	5.56952e13	−	5.35897e13i	0.303910	−	0.292421i
$393$	3.70060e13	+	3.70060e13i	0.199119	+	0.199119i
$394$	−2.47012e13	−	6.78895e12i	−0.131065	−	0.0360225i
$395$	1.92333e13	−	1.34898e13i	0.100640	−	0.0705865i
$396$	2.52198e13	+	9.92002e13i	0.130142	+	0.511904i
$397$			7.29538e13i			0.371279i	0.982618	+	0.185639i	$0.0594356\pi$
$397$			7.29538e13i			0.371279i	−0.982618	+	0.185639i	$0.940564\pi$
$398$	−8.51666e13	+	3.09873e14i	−0.427477	+	1.55535i
$399$	−1.55871e14			−0.771642
$400$	2.02488e14	−	3.06894e13i	0.988709	−	0.149850i
$401$	9.15313e13			0.440834			0.220417	−	0.975406i	$-0.429258\pi$
$401$	9.15313e13			0.440834			0.220417	+	0.975406i	$0.429258\pi$
$402$	2.16785e13	−	7.88757e13i	0.102988	−	0.374714i
$403$		−	2.78143e14i		−	1.30344i
$404$	8.19296e13	−	2.08290e13i	0.378742	−	0.0962879i
$405$	4.63230e13	−	3.24899e13i	0.211249	−	0.148165i
$406$	4.89391e13	+	1.34506e13i	0.220172	+	0.0605129i
$407$	−1.69054e14	−	1.69054e14i	−0.750336	−	0.750336i
$408$	1.03267e14	+	1.98956e12i	0.452201	+	0.00871217i
$409$	−4.84099e13			−0.209149			−0.104575	−	0.994517i	$-0.533348\pi$
$409$	−4.84099e13			−0.209149			−0.104575	+	0.994517i	$0.533348\pi$
$410$	5.55048e13	+	1.55215e14i	0.236602	+	0.661640i
$411$	1.29022e14	+	1.29022e14i	0.542667	+	0.542667i
$412$	−3.64864e14	+	9.27598e13i	−1.51425	+	0.384968i
$413$	3.74277e14			1.53274
$414$	−2.29139e14	+	1.30339e14i	−0.925970	+	0.526710i
$415$	−6.25376e13	−	8.91639e13i	−0.249389	−	0.355570i
$416$	−9.22665e13	−	3.94605e14i	−0.363104	−	1.55292i
$417$	−1.07601e13	−	1.07601e13i	−0.0417896	−	0.0417896i
$418$	6.22477e13	−	2.26484e14i	0.238591	−	0.868097i
$419$	3.23723e14	+	3.23723e14i	1.22461	+	1.22461i	0.965977	+	0.258628i	$0.0832705\pi$
$419$	3.23723e14	+	3.23723e14i	1.22461	+	1.22461i	0.258628	+	0.965977i	$0.416729\pi$
$420$	−1.08589e14	+	1.26287e14i	−0.405428	+	0.471505i
$421$	1.40343e13	−	1.40343e13i	0.0517176	−	0.0517176i	−0.680775	−	0.732493i	$-0.738357\pi$
$421$	1.40343e13	−	1.40343e13i	0.0517176	−	0.0517176i	0.732493	+	0.680775i	$0.238357\pi$
$422$	−1.45538e14	+	8.27847e13i	−0.529367	+	0.301114i
$423$	−1.50569e14	+	1.50569e14i	−0.540584	+	0.540584i
$424$	−1.01543e14	+	9.77045e13i	−0.359864	+	0.346260i
$425$	2.24512e14	−	1.05121e14i	0.785416	−	0.367747i
$426$	2.49138e13	−	9.06471e13i	0.0860373	−	0.313041i
$427$		−	4.61911e14i		−	1.57473i
$428$	−1.29417e13	+	2.17654e13i	−0.0435564	+	0.0732530i
$429$	−1.28418e14	+	1.28418e14i	−0.426687	+	0.426687i
$430$	3.05881e14	−	1.09383e14i	1.00340	−	0.358817i
$431$		−	1.22169e14i		−	0.395673i	−0.980235	−	0.197836i	$-0.936609\pi$
$431$		−	1.22169e14i		−	0.395673i	0.980235	−	0.197836i	$-0.0633915\pi$
$432$	−2.47606e14	+	1.34598e14i	−0.791772	+	0.430404i
$433$	−2.33605e14	+	2.33605e14i	−0.737563	+	0.737563i	−0.972106	−	0.234543i	$-0.924641\pi$
$433$	−2.33605e14	+	2.33605e14i	−0.737563	+	0.737563i	0.234543	+	0.972106i	$0.424641\pi$
$434$	−2.71716e14	+	1.54558e14i	−0.847075	+	0.481833i
$435$	−3.19548e13	−	5.60865e12i	−0.0983661	−	0.0172650i
$436$	−2.88742e14	+	7.34072e13i	−0.877676	+	0.223132i
$437$	6.04934e14			1.81577
$438$	−9.01453e13	+	5.12764e13i	−0.267199	+	0.151988i
$439$			1.20184e14i			0.351795i	0.984408	+	0.175898i	$0.0562828\pi$
$439$			1.20184e14i			0.351795i	−0.984408	+	0.175898i	$0.943717\pi$
$440$	−1.40132e14	−	2.08214e14i	−0.405086	−	0.601895i
$441$			1.07549e14i			0.307040i
$442$	−2.42536e14	−	4.26385e14i	−0.683839	−	1.20221i
$443$	2.86919e14			0.798987			0.399493	−	0.916736i	$-0.369186\pi$
$443$	2.86919e14			0.798987			0.399493	+	0.916736i	$0.369186\pi$
$444$	1.41739e14	−	2.38376e14i	0.389837	−	0.655626i
$445$	−4.67612e14	+	3.27973e14i	−1.27030	+	0.890959i
$446$	−3.07944e13	−	5.41373e13i	−0.0826285	−	0.145263i
$447$	1.72534e14	−	1.72534e14i	0.457281	−	0.457281i
$448$	−3.34217e14	+	3.09408e14i	−0.874983	+	0.810032i
$449$			4.24253e14i			1.09716i	0.836098	+	0.548580i	$0.184832\pi$
$449$			4.24253e14i			1.09716i	−0.836098	+	0.548580i	$0.815168\pi$
$450$	−1.64587e14	+	2.32644e14i	−0.420463	+	0.594325i
$451$	1.42842e14	−	1.42842e14i	0.360483	−	0.360483i
$452$	−2.44490e14	+	6.21571e13i	−0.609537	+	0.154963i
$453$		−	2.79850e14i		−	0.689262i
$454$	−2.32304e14	−	6.38471e13i	−0.565261	−	0.155358i
$455$	7.79100e14	+	1.36746e14i	1.87297	+	0.328740i
$456$	2.72415e14	+	5.24838e12i	0.647029	+	0.0124658i
$457$	−3.81937e14	+	3.81937e14i	−0.896299	+	0.896299i	−0.995107	−	0.0988077i	$-0.968497\pi$
$457$	−3.81937e14	+	3.81937e14i	−0.896299	+	0.896299i	0.0988077	+	0.995107i	$0.468497\pi$
$458$	−1.36607e14	−	2.40159e14i	−0.316748	−	0.556851i
$459$	−2.41221e14	+	2.41221e14i	−0.552644	+	0.552644i
$460$	4.21431e14	−	4.90117e14i	0.954022	−	1.10951i
$461$	4.39751e14	+	4.39751e14i	0.983676	+	0.983676i	0.999869	−	0.0161930i	$-0.00515463\pi$
$461$	4.39751e14	+	4.39751e14i	0.983676	+	0.983676i	−0.0161930	+	0.999869i	$0.505155\pi$
$462$	1.96809e14	+	5.40917e13i	0.435025	+	0.119564i
$463$	−3.06705e14	−	3.06705e14i	−0.669924	−	0.669924i	0.287774	−	0.957698i	$-0.407085\pi$
$463$	−3.06705e14	−	3.06705e14i	−0.669924	−	0.669924i	−0.957698	+	0.287774i	$0.907085\pi$
$464$	−8.50773e13	−	2.51552e13i	−0.183639	−	0.0542975i
$465$	1.63595e14	−	1.14742e14i	0.348962	−	0.244754i
$466$	3.42520e14	+	6.02158e14i	0.722043	+	1.26937i
$467$	−6.22178e14			−1.29620			−0.648100	−	0.761555i	$-0.724436\pi$
$467$	−6.22178e14			−1.29620			−0.648100	+	0.761555i	$0.724436\pi$
$468$	4.84691e14	+	2.88199e14i	0.997959	+	0.593389i
$469$	3.08738e14	+	3.08738e14i	0.628260	+	0.628260i
$470$	2.23323e14	−	4.71954e14i	0.449154	−	0.949208i
$471$	−1.20805e14			−0.240144
$472$	−6.54120e14	−	1.26024e13i	−1.28522	−	0.0247612i
$473$	−2.81497e14	−	2.81497e14i	−0.546686	−	0.546686i
$474$	8.85049e12	−	3.22019e13i	0.0169897	−	0.0618160i
$475$	5.92252e14	−	2.77304e14i	1.12381	−	0.526189i
$476$	−2.81761e14	+	4.73865e14i	−0.528497	+	0.888825i
$477$		−	1.96083e14i		−	0.363571i
$478$	3.96517e14	+	1.08980e14i	0.726789	+	0.199753i
$479$	−1.69488e14			−0.307110			−0.153555	−	0.988140i	$-0.549072\pi$
$479$	−1.69488e14			−0.307110			−0.153555	+	0.988140i	$0.549072\pi$
$480$	1.94031e14	−	2.17054e14i	0.347572	−	0.388812i
$481$	−1.31713e15			−2.33256
$482$	−5.87003e13	−	1.61334e13i	−0.102774	−	0.0282467i
$483$			5.25673e14i			0.909927i
$484$	1.41441e14	−	2.37875e14i	0.242062	−	0.407098i
$485$	7.65126e14	+	1.34294e14i	1.29465	+	0.227235i
$486$	1.64071e14	−	5.96961e14i	0.274493	−	0.998726i
$487$	4.10928e14	+	4.10928e14i	0.679761	+	0.679761i	0.959946	−	0.280185i	$-0.0903959\pi$
$487$	4.10928e14	+	4.10928e14i	0.679761	+	0.679761i	−0.280185	+	0.959946i	$0.590396\pi$
$488$	−1.55531e13	+	8.07277e14i	−0.0254395	+	1.32042i
$489$	1.57281e13			0.0254378
$490$	−8.87968e13	−	2.48313e14i	−0.142010	−	0.397120i
$491$	−1.03218e13	−	1.03218e13i	−0.0163232	−	0.0163232i	0.698898	−	0.715221i	$-0.253674\pi$
$491$	−1.03218e13	−	1.03218e13i	−0.0163232	−	0.0163232i	−0.715221	+	0.698898i	$0.753674\pi$
$492$	2.01416e14	+	1.19762e14i	0.314982	+	0.187289i
$493$	−1.07390e14			−0.166076
$494$	−6.39801e14	−	1.12479e15i	−0.978468	−	1.72017i
$495$	3.43977e14	+	6.03741e13i	0.520236	+	0.0913108i
$496$	4.80079e14	−	2.60970e14i	0.718065	−	0.390338i
$497$	3.54814e14	+	3.54814e14i	0.524857	+	0.524857i
$498$	−1.49285e14	−	4.10301e13i	−0.218402	−	0.0600262i
$499$	3.11363e14	+	3.11363e14i	0.450519	+	0.450519i	0.895527	−	0.445007i	$-0.146799\pi$
$499$	3.11363e14	+	3.11363e14i	0.450519	+	0.450519i	−0.445007	+	0.895527i	$0.646799\pi$
$500$	1.87925e14	−	6.73027e14i	0.268936	−	0.963158i
$501$	−2.20879e14	+	2.20879e14i	−0.312642	+	0.312642i
$502$	−4.02340e14	−	7.07323e14i	−0.563277	−	0.990256i
$503$	−5.50095e14	+	5.50095e14i	−0.761752	+	0.761752i	−0.976639	−	0.214887i	$-0.931062\pi$
$503$	−5.50095e14	+	5.50095e14i	−0.761752	+	0.761752i	0.214887	+	0.976639i	$0.431062\pi$
$504$	1.22077e13	−	6.33638e14i	0.0167212	−	0.867907i
$505$	4.98631e13	−	2.84091e14i	0.0675580	−	0.384906i
$506$	−7.63813e14	−	2.09929e14i	−1.02367	−	0.281348i
$507$			6.07148e14i			0.804916i
$508$	−1.11767e15	+	2.84146e14i	−1.46576	+	0.372641i
$509$	8.30122e14	−	8.30122e14i	1.07695	−	1.07695i	0.0801646	−	0.996782i	$-0.474455\pi$
$509$	8.30122e14	−	8.30122e14i	1.07695	−	1.07695i	0.996782	−	0.0801646i	$-0.0255446\pi$
$510$	1.50733e14	−	3.18547e14i	0.193451	−	0.408825i
$511$		−	5.53558e14i		−	0.702826i
$512$	5.94526e14	−	5.29495e14i	0.746768	−	0.665084i
$513$	−6.36331e14	+	6.36331e14i	−0.790748	+	0.790748i
$514$	−7.23184e14	−	1.27138e15i	−0.889102	−	1.56306i
$515$	−2.22060e14	+	1.26517e15i	−0.270103	+	1.53889i
$516$	2.36015e14	−	3.96928e14i	0.284031	−	0.477682i
$517$	−6.39853e14			−0.761872
$518$	7.31902e14	+	1.28670e15i	0.862262	+	1.51588i
$519$		−	7.01512e14i		−	0.817739i
$520$	−1.35702e15	−	2.65223e14i	−1.56519	−	0.305909i
$521$		−	1.44764e15i		−	1.65216i	−0.563553	−	0.826080i	$-0.690566\pi$
$521$		−	1.44764e15i		−	1.65216i	0.563553	−	0.826080i	$-0.309434\pi$
$522$	1.07306e14	−	6.10377e13i	0.121181	−	0.0689303i
$523$	3.75792e14			0.419941			0.209971	−	0.977708i	$-0.432663\pi$
$523$	3.75792e14			0.419941			0.209971	+	0.977708i	$0.432663\pi$
$524$	4.73239e14	−	1.20312e14i	0.523309	−	0.133041i
$525$	2.40970e14	+	5.14653e14i	0.263686	+	0.563168i
$526$	−1.14814e15	+	6.53088e14i	−1.24330	+	0.707212i
$527$	4.67700e14	−	4.67700e14i	0.501198	−	0.501198i
$528$	−3.42140e14	−	1.01162e14i	−0.362842	−	0.107283i
$529$		−	1.08732e15i		−	1.14117i
$530$	1.61894e14	+	4.52724e14i	0.168156	+	0.470236i
$531$	6.43730e14	−	6.43730e14i	0.661735	−	0.661735i
$532$	−7.43274e14	+	1.25004e15i	−0.756197	+	1.27177i
$533$		−	1.11291e15i		−	1.12063i
$534$	−2.15179e14	+	7.82913e14i	−0.214448	+	0.780256i
$535$	4.96119e13	+	7.07350e13i	0.0489373	+	0.0697732i
$536$	−5.29182e14	−	5.49973e14i	−0.516653	−	0.536952i
$537$	−3.41955e14	+	3.41955e14i	−0.330454	+	0.330454i
$538$	8.02301e13	−	4.56365e13i	0.0767423	−	0.0436526i
$539$	−2.28519e14	+	2.28519e14i	−0.216364	+	0.216364i
$540$	7.22506e13	+	9.58858e14i	0.0677136	+	0.898646i
$541$	1.30073e15	+	1.30073e15i	1.20671	+	1.20671i	0.972087	+	0.234620i	$0.0753846\pi$
$541$	1.30073e15	+	1.30073e15i	1.20671	+	1.20671i	0.234620	+	0.972087i	$0.424615\pi$
$542$	−1.65198e14	+	6.01060e14i	−0.151708	+	0.551978i
$543$	2.50712e14	+	2.50712e14i	0.227917	+	0.227917i
$544$	5.08386e14	−	8.18680e14i	0.457509	−	0.736750i
$545$	−1.75731e14	+	1.00121e15i	−0.156555	+	0.891960i
$546$	9.77411e14	−	5.55971e14i	0.862021	−	0.490335i
$547$	−3.08467e14			−0.269326			−0.134663	−	0.990891i	$-0.542995\pi$
$547$	−3.08467e14			−0.269326			−0.134663	+	0.990891i	$0.542995\pi$
$548$	1.64995e15	−	4.19470e14i	1.42619	−	0.362583i
$549$	−7.94455e14	−	7.94455e14i	−0.679863	−	0.679863i
$550$	−8.44033e14	+	1.44607e14i	−0.715096	+	0.122516i
$551$	−2.83291e14			−0.237629
$552$	1.77000e13	−	9.18713e14i	0.0146997	−	0.762983i
$553$	1.26046e14	+	1.26046e14i	0.103643	+	0.103643i
$554$	1.84394e15	+	5.06796e14i	1.50122	+	0.412600i
$555$	−5.43354e14	−	7.74696e14i	−0.437997	−	0.624482i
$556$	−1.37602e14	+	3.49827e13i	−0.109828	+	0.0279217i
$557$		−	1.12989e15i		−	0.892961i	−0.894793	−	0.446480i	$-0.852677\pi$
$557$		−	1.12989e15i		−	0.892961i	0.894793	−	0.446480i	$-0.147323\pi$
$558$	−2.01504e14	+	7.33161e14i	−0.157687	+	0.573735i
$559$	−2.19321e15			−1.69947
$560$	4.94970e14	+	1.47304e15i	0.379791	+	1.13027i
$561$	−4.31871e14			−0.328140
$562$	−1.87996e14	+	6.84010e14i	−0.141448	+	0.514651i
$563$			2.50654e15i			1.86757i	0.357829	+	0.933787i	$0.383517\pi$
$563$			2.50654e15i			1.86757i	−0.357829	+	0.933787i	$0.616483\pi$
$564$	−1.82881e14	−	7.19350e14i	−0.134938	−	0.530769i
$565$	−1.48799e14	+	8.47771e14i	−0.108726	+	0.619458i
$566$	−9.48487e14	−	2.60686e14i	−0.686343	−	0.188637i
$567$	3.03579e14	+	3.03579e14i	0.217553	+	0.217553i
$568$	−6.08157e14	−	6.32051e14i	−0.431619	−	0.448577i
$569$	−4.37661e14			−0.307624			−0.153812	−	0.988100i	$-0.549155\pi$
$569$	−4.37661e14			−0.307624			−0.153812	+	0.988100i	$0.549155\pi$
$570$	3.97627e14	−	8.40315e14i	0.276799	−	0.584966i
$571$	6.63342e14	+	6.63342e14i	0.457340	+	0.457340i	0.897781	−	0.440442i	$-0.145178\pi$
$571$	6.63342e14	+	6.63342e14i	0.457340	+	0.457340i	−0.440442	+	0.897781i	$0.645178\pi$
$572$	4.17505e14	+	1.64223e15i	0.285091	+	1.12138i
$573$	5.19649e14			0.351447
$574$	−1.08720e15	+	6.18419e14i	−0.728271	+	0.414255i
$575$	−9.35202e14	−	1.99736e15i	−0.620486	−	1.32520i
$576$	−4.26707e13	+	1.10699e15i	−0.0280418	+	0.727478i
$577$	−5.56171e14	−	5.56171e14i	−0.362028	−	0.362028i	0.502531	−	0.864559i	$-0.332402\pi$
$577$	−5.56171e14	−	5.56171e14i	−0.362028	−	0.362028i	−0.864559	+	0.502531i	$0.832402\pi$
$578$	−1.01888e14	+	3.70714e14i	−0.0656933	+	0.239021i
$579$	−1.00073e15	−	1.00073e15i	−0.639125	−	0.639125i
$580$	−1.97356e14	+	2.29522e14i	−0.124852	+	0.145201i
$581$	5.84338e14	−	5.84338e14i	0.366181	−	0.366181i
$582$	9.59880e14	−	5.45999e14i	0.595855	−	0.338934i
$583$	4.16635e14	−	4.16635e14i	0.256200	−	0.256200i
$584$	−1.86390e13	+	9.67446e14i	−0.0113540	+	0.589327i
$585$	1.57519e15	−	1.10480e15i	0.950553	−	0.666696i
$586$	6.12944e14	−	2.23016e15i	0.366424	−	1.33321i
$587$		−	2.74075e14i		−	0.162315i	−0.996701	−	0.0811577i	$-0.974138\pi$
$587$		−	2.74075e14i		−	0.162315i	0.996701	−	0.0811577i	$-0.0258617\pi$
$588$	−3.22226e14	−	1.91596e14i	−0.189053	−	0.112412i
$589$	1.23377e15	−	1.23377e15i	0.717136	−	0.717136i
$590$	−9.54778e14	+	2.01776e15i	−0.549815	+	1.16194i
$591$			1.24252e14i			0.0708877i
$592$	−1.23581e15	−	2.27340e15i	−0.698526	−	1.28501i
$593$	−8.16854e14	+	8.16854e14i	−0.457450	+	0.457450i	−0.897818	−	0.440368i	$-0.854848\pi$
$593$	−8.16854e14	+	8.16854e14i	−0.457450	+	0.457450i	0.440368	+	0.897818i	$0.354848\pi$
$594$	1.02428e15	−	5.82632e14i	0.568321	−	0.323272i
$595$	1.08013e15	+	1.54001e15i	0.593787	+	0.846602i
$596$	−5.60933e14	−	2.20639e15i	−0.305532	−	1.20179i
$597$	1.55872e15			0.841221
$598$	−3.79332e15	+	2.15771e15i	−2.02844	+	1.15382i
$599$		−	1.61734e15i		−	0.856949i	−0.903554	−	0.428475i	$-0.859051\pi$
$599$		−	1.61734e15i		−	0.856949i	0.903554	−	0.428475i	$-0.140949\pi$
$600$	−4.03812e14	−	9.07567e14i	−0.212006	−	0.476482i
$601$			1.63672e15i			0.851460i	0.904850	+	0.425730i	$0.139983\pi$
$601$			1.63672e15i			0.851460i	−0.904850	+	0.425730i	$0.860017\pi$
$602$	1.21871e15	+	2.14253e15i	0.628234	+	1.10445i
$603$	1.06202e15			0.542482
$604$	−2.24430e15	−	1.33446e15i	−1.13600	−	0.675467i
$605$	−5.42212e14	−	7.73067e14i	−0.271966	−	0.387760i
$606$	−2.02729e14	−	3.56403e14i	−0.100767	−	0.177150i
$607$	3.10856e14	−	3.10856e14i	0.153116	−	0.153116i	−0.626392	−	0.779508i	$-0.715469\pi$
$607$	3.10856e14	−	3.10856e14i	0.153116	−	0.153116i	0.779508	+	0.626392i	$0.215469\pi$
$608$	1.34110e15	−	2.15965e15i	0.654624	−	1.05418i
$609$		−	2.46173e14i		−	0.119082i
$610$	2.49020e15	+	1.17833e15i	1.19377	+	0.564877i
$611$	−2.49262e15	+	2.49262e15i	−1.18421	+	1.18421i
$612$	3.30405e14	+	1.29962e15i	0.155565	+	0.611906i
$613$		−	1.01443e15i		−	0.473359i	−0.971588	−	0.236680i	$-0.923941\pi$
$613$		−	1.01443e15i		−	0.473359i	0.971588	−	0.236680i	$-0.0760592\pi$
$614$	3.44750e15	+	9.47524e14i	1.59433	+	0.438192i
$615$	6.54578e14	−	4.59106e14i	0.300019	−	0.210426i
$616$	1.37228e15	−	1.32041e15i	0.623376	−	0.599810i
$617$	6.46866e13	−	6.46866e13i	0.0291237	−	0.0291237i	−0.692395	−	0.721519i	$-0.743444\pi$
$617$	6.46866e13	−	6.46866e13i	0.0291237	−	0.0291237i	0.721519	+	0.692395i	$0.243444\pi$
$618$	9.02832e14	+	1.58720e15i	0.402875	+	0.708264i
$619$	−2.80073e15	+	2.80073e15i	−1.23872	+	1.23872i	−0.278192	+	0.960525i	$0.589735\pi$
$619$	−2.80073e15	+	2.80073e15i	−1.23872	+	1.23872i	−0.960525	+	0.278192i	$0.910265\pi$
$620$	−1.40086e14	−	1.85912e15i	−0.0614101	−	0.814991i
$621$	2.14601e15	+	2.14601e15i	0.932457	+	0.932457i
$622$	4.08274e15	+	1.12212e15i	1.75835	+	0.483271i
$623$	−3.06451e15	−	3.06451e15i	−1.30821	−	1.30821i
$624$	−1.72693e15	+	9.38754e14i	−0.730734	+	0.397225i
$625$	−1.83119e15	−	1.52679e15i	−0.768058	−	0.640380i
$626$	1.71331e15	+	3.01204e15i	0.712323	+	1.25228i
$627$	−1.13926e15			−0.469517
$628$	−5.76061e14	+	9.68817e14i	−0.235337	+	0.395789i
$629$	−2.21478e15	−	2.21478e15i	−0.896915	−	0.896915i
$630$	−1.95458e15	−	9.24882e14i	−0.784656	−	0.371290i
$631$	−2.65721e15			−1.05746			−0.528731	−	0.848790i	$-0.677332\pi$
$631$	−2.65721e15			−1.05746			−0.528731	+	0.848790i	$0.677332\pi$
$632$	−2.16045e14	−	2.24533e14i	−0.0852314	−	0.0885801i
$633$	5.74253e14	+	5.74253e14i	0.224586	+	0.224586i
$634$	3.91897e13	−	1.42589e14i	0.0151943	−	0.0552835i
$635$	−6.80223e14	+	3.87551e15i	−0.261454	+	1.48961i
$636$	5.87480e14	+	3.49317e14i	0.223861	+	0.133109i
$637$			1.78044e15i			0.672606i
$638$	3.57694e14	+	9.83098e13i	0.133967	+	0.0368199i
$639$	1.22051e15			0.453197
$640$	−8.15454e14	−	2.59109e15i	−0.300199	−	0.953876i
$641$	2.51916e15			0.919467			0.459733	−	0.888057i	$-0.347945\pi$
$641$	2.51916e15			0.919467			0.459733	+	0.888057i	$0.347945\pi$
$642$	1.18430e14	+	3.25497e13i	0.0428568	+	0.0117789i
$643$		−	4.94539e15i		−	1.77435i	−0.461430	−	0.887177i	$-0.652663\pi$
$643$		−	4.94539e15i		−	1.77435i	0.461430	−	0.887177i	$-0.347337\pi$
$644$	4.21572e15	+	2.50668e15i	1.49968	+	0.891715i
$645$	−9.04758e14	−	1.28997e15i	−0.319120	−	0.454990i
$646$	8.15508e14	−	2.96717e15i	0.285200	−	1.03768i
$647$	−6.17209e14	−	6.17209e14i	−0.214022	−	0.214022i	0.591951	−	0.805974i	$-0.298358\pi$
$647$	−6.17209e14	−	6.17209e14i	−0.214022	−	0.214022i	−0.805974	+	0.591951i	$0.798358\pi$
$648$	−5.20339e14	−	5.40783e14i	−0.178906	−	0.185935i
$649$	2.73558e15			0.932617
$650$	−2.72469e15	+	3.85135e15i	−0.921072	+	1.30194i
$651$	1.07212e15	+	1.07212e15i	0.359375	+	0.359375i
$652$	7.49998e13	−	1.26134e14i	0.0249286	−	0.0419249i
$653$	3.82266e15			1.25992			0.629961	−	0.776627i	$-0.283071\pi$
$653$	3.82266e15			1.25992			0.629961	+	0.776627i	$0.283071\pi$
$654$	7.14472e14	+	1.25606e15i	0.233511	+	0.410518i
$655$	2.88017e14	−	1.64096e15i	0.0933451	−	0.531826i
$656$	1.92090e15	−	1.04420e15i	0.617354	−	0.335592i
$657$	−9.52080e14	−	9.52080e14i	−0.303434	−	0.303434i
$658$	3.82011e15	+	1.04993e15i	1.20735	+	0.331833i
$659$	−6.70617e14	−	6.70617e14i	−0.210187	−	0.210187i	0.594160	−	0.804347i	$-0.297485\pi$
$659$	−6.70617e14	−	6.70617e14i	−0.210187	−	0.210187i	−0.804347	+	0.594160i	$0.797485\pi$
$660$	−7.93671e14	+	9.23026e14i	−0.246689	+	0.286894i
$661$	3.69386e15	−	3.69386e15i	1.13860	−	1.13860i	0.149902	−	0.988701i	$-0.452104\pi$
$661$	3.69386e15	−	3.69386e15i	1.13860	−	1.13860i	0.988701	−	0.149902i	$-0.0478958\pi$
$662$	6.06658e14	+	1.06652e15i	0.185449	+	0.326025i
$663$	−1.68240e15	+	1.68240e15i	−0.510041	+	0.510041i
$664$	−1.04092e15	+	1.00156e15i	−0.312962	+	0.301130i
$665$	2.84933e15	+	4.06247e15i	0.849617	+	1.21136i
$666$	3.47186e15	+	9.54217e14i	1.02672	+	0.282188i
$667$			9.55393e14i			0.280214i
$668$	7.18112e14	+	2.82464e15i	0.208892	+	0.821661i
$669$	−2.13612e14	+	2.13612e14i	−0.0616284	+	0.0616284i
$670$	−2.45202e15	+	8.76842e14i	−0.701637	+	0.250905i
$671$		−	3.37609e15i		−	0.958166i
$672$	1.87668e15	+	1.16538e15i	0.528274	+	0.328049i
$673$	1.54983e15	−	1.54983e15i	0.432713	−	0.432713i	−0.456837	−	0.889550i	$-0.651018\pi$
$673$	1.54983e15	−	1.54983e15i	0.432713	−	0.432713i	0.889550	+	0.456837i	$0.151018\pi$
$674$	1.17898e15	+	2.07267e15i	0.326494	+	0.573985i
$675$	3.08477e15	+	1.11728e15i	0.847328	+	0.306897i
$676$	4.86912e15	+	2.89519e15i	1.32661	+	0.788806i
$677$	−4.74071e15			−1.28117			−0.640584	−	0.767888i	$-0.721308\pi$
$677$	−4.74071e15			−1.28117			−0.640584	+	0.767888i	$0.721308\pi$
$678$	6.04975e14	+	1.06356e15i	0.162171	+	0.285101i
$679$			5.89437e15i			1.56730i
$680$	−1.83587e15	−	2.72782e15i	−0.484220	−	0.719477i
$681$			1.16853e15i			0.305725i
$682$	−1.98596e15	+	1.12966e15i	−0.515415	+	0.293179i
$683$	2.15812e15			0.555600			0.277800	−	0.960639i	$-0.410395\pi$
$683$	2.15812e15			0.555600			0.277800	+	0.960639i	$0.410395\pi$
$684$	8.71594e14	+	3.42835e15i	0.222590	+	0.875542i
$685$	1.00418e15	−	5.72122e15i	0.254397	−	1.44941i
$686$	−2.38474e15	+	1.35649e15i	−0.599318	+	0.340904i
$687$	−9.47604e14	+	9.47604e14i	−0.236246	+	0.236246i
$688$	−2.05779e15	−	3.78551e15i	−0.508938	−	0.936242i
$689$		−	3.24609e15i		−	0.796443i
$690$	−2.83394e15	−	1.34099e15i	−0.689797	−	0.326404i
$691$	−5.24960e15	+	5.24960e15i	−1.26764	+	1.26764i	−0.320340	+	0.947303i	$0.603797\pi$
$691$	−5.24960e15	+	5.24960e15i	−1.26764	+	1.26764i	−0.947303	+	0.320340i	$0.896203\pi$
$692$	−5.62589e15	−	3.34517e15i	−1.34774	−	0.801372i
$693$			2.64992e15i			0.629796i
$694$	5.71329e14	−	2.07874e15i	0.134713	−	0.490144i
$695$	−8.37459e13	+	4.77135e14i	−0.0195906	+	0.111616i
$696$	−8.28894e12	+	4.30234e14i	−0.00192375	+	0.0998512i
$697$	1.87137e15	−	1.87137e15i	0.430904	−	0.430904i
$698$	5.36821e15	−	3.05355e15i	1.22638	−	0.697589i
$699$	2.37596e15	−	2.37596e15i	0.538535	−	0.538535i
$700$	5.27641e15	+	5.21626e14i	1.18659	+	0.117306i
$701$	3.35996e15	+	3.35996e15i	0.749696	+	0.749696i	0.974422	−	0.224726i	$-0.0721488\pi$
$701$	3.35996e15	+	3.35996e15i	0.749696	+	0.749696i	−0.224726	+	0.974422i	$0.572149\pi$
$702$	1.72049e15	−	6.25990e15i	0.380889	−	1.38584i
$703$	−5.84249e15	−	5.84249e15i	−1.28335	−	1.28335i
$704$	−2.44278e15	+	2.26145e15i	−0.532397	+	0.492876i
$705$	−2.49435e15	−	4.37803e14i	−0.539407	−	0.0946757i
$706$	6.83291e15	−	3.88670e15i	1.46615	−	0.833978i
$707$	2.18857e15			0.465966
$708$	7.81877e14	+	3.07546e15i	0.165179	+	0.649721i
$709$	−3.10846e15	−	3.10846e15i	−0.651615	−	0.651615i	0.301766	−	0.953382i	$-0.402424\pi$
$709$	−3.10846e15	−	3.10846e15i	−0.651615	−	0.651615i	−0.953382	+	0.301766i	$0.902424\pi$
$710$	−2.81796e15	+	1.00770e15i	−0.586156	+	0.209609i
$711$	4.33580e14			0.0894925
$712$	5.25262e15	+	5.45899e15i	1.07581	+	1.11808i
$713$	−4.16088e15	−	4.16088e15i	−0.845654	−	0.845654i
$714$	2.57840e15	+	7.08657e14i	0.520008	+	0.142921i
$715$	5.69442e15	+	9.99474e14i	1.13964	+	0.200027i
$716$	1.11175e15	+	4.37298e15i	0.220793	+	0.868472i
$717$		−	1.99456e15i		−	0.393089i
$718$	−1.80766e15	+	6.57704e15i	−0.353534	+	1.28631i
$719$	−5.00760e15			−0.971897			−0.485949	−	0.873987i	$-0.661526\pi$
$719$	−5.00760e15			−0.971897			−0.485949	+	0.873987i	$0.661526\pi$
$720$	3.38485e15	+	1.68222e15i	0.651944	+	0.324006i
$721$	−9.74657e15			−1.86298
$722$	7.54179e14	−	2.74403e15i	0.143060	−	0.520516i
$723$			2.95274e14i			0.0555859i
$724$	3.20615e15	−	8.15102e14i	0.598992	−	0.152282i
$725$	4.37955e14	+	9.35364e14i	0.0812028	+	0.173429i
$726$	−1.29433e15	−	3.55738e14i	−0.238174	−	0.0654604i
$727$	1.21944e15	+	1.21944e15i	0.222700	+	0.222700i	0.809635	−	0.586934i	$-0.199665\pi$
$727$	1.21944e15	+	1.21944e15i	0.222700	+	0.222700i	−0.586934	+	0.809635i	$0.699665\pi$
$728$	2.02095e14	−	1.04897e16i	0.0366297	−	1.90125i
$729$	−1.56843e15			−0.282139
$730$	2.98427e15	+	1.41212e15i	0.532798	+	0.252114i
$731$	−3.68790e15	−	3.68790e15i	−0.653482	−	0.653482i
$732$	3.79555e15	−	9.64947e14i	0.667519	−	0.169704i
$733$	7.56214e15			1.32000			0.659998	−	0.751267i	$-0.270557\pi$
$733$	7.56214e15			1.32000			0.659998	+	0.751267i	$0.270557\pi$
$734$	−2.14715e15	+	1.22134e15i	−0.371993	+	0.211597i
$735$	−1.04720e15	+	7.34480e14i	−0.180073	+	0.126299i
$736$	−7.28336e15	−	4.52284e15i	−1.24309	−	0.771939i
$737$	2.25656e15	+	2.25656e15i	0.382274	+	0.382274i
$738$	−8.06264e14	+	2.93354e15i	−0.135571	+	0.493267i
$739$	−1.25837e15	−	1.25837e15i	−0.210022	−	0.210022i	0.594255	−	0.804277i	$-0.297447\pi$
$739$	−1.25837e15	−	1.25837e15i	−0.210022	−	0.210022i	−0.804277	+	0.594255i	$0.797447\pi$
$740$	−8.80378e15	+	6.63371e14i	−1.45846	+	0.109896i
$741$	−4.43811e15	+	4.43811e15i	−0.729789	+	0.729789i
$742$	−3.17109e15	+	1.80378e15i	−0.517591	+	0.294416i
$743$	−4.80916e14	+	4.80916e14i	−0.0779167	+	0.0779167i	−0.744991	−	0.667074i	$-0.767546\pi$
$743$	−4.80916e14	+	4.80916e14i	−0.0779167	+	0.0779167i	0.667074	+	0.744991i	$0.267546\pi$
$744$	−1.83763e15	−	1.90983e15i	−0.295534	−	0.307145i
$745$	−7.65066e15	−	1.34283e15i	−1.22135	−	0.214369i
$746$	1.44669e15	−	5.26367e15i	0.229251	−	0.834114i
$747$		−	2.01004e15i		−	0.316185i
$748$	−2.05938e15	+	3.46346e15i	−0.321572	+	0.540818i
$749$	−4.63563e14	+	4.63563e14i	−0.0718553	+	0.0718553i
$750$	−3.38925e15	−	1.37860e13i	−0.521514	−	0.00212130i
$751$			1.45650e15i			0.222480i	0.993794	+	0.111240i	$0.0354823\pi$
$751$			1.45650e15i			0.222480i	−0.993794	+	0.111240i	$0.964518\pi$
$752$	−6.64101e15	−	1.96358e15i	−1.00702	−	0.297749i
$753$	−2.79091e15	+	2.79091e15i	−0.420120	+	0.420120i
$754$	1.77641e15	−	1.01046e15i	0.265461	−	0.151000i
$755$	−7.29371e15	+	5.11565e15i	−1.08203	+	0.758913i
$756$	−7.07130e15	+	1.79774e15i	−1.04143	+	0.264763i
$757$	8.47927e15			1.23974			0.619871	−	0.784704i	$-0.287185\pi$
$757$	8.47927e15			1.23974			0.619871	+	0.784704i	$0.287185\pi$
$758$	−2.64426e15	+	1.50411e15i	−0.383817	+	0.218323i
$759$			3.84213e15i			0.553659i
$760$	−4.84295e15	−	7.19588e15i	−0.692843	−	1.02946i
$761$			6.92694e15i			0.983843i	0.870640	+	0.491922i	$0.163705\pi$
$761$			6.92694e15i			0.983843i	−0.870640	+	0.491922i	$0.836295\pi$
$762$	2.76559e15	+	4.86198e15i	0.389974	+	0.685584i
$763$	−7.71312e15			−1.07980
$764$	2.47795e15	−	4.16741e15i	0.344413	−	0.579232i
$765$	4.50644e15	+	7.90963e14i	0.621865	+	0.109149i
$766$	−5.23163e15	−	9.19734e15i	−0.716769	−	1.26010i
$767$	1.06567e16	−	1.06567e16i	1.44961	−	1.44961i
$768$	−3.24061e15	−	2.09992e15i	−0.437663	−	0.283606i
$769$			9.47266e15i			1.27021i	0.772424	+	0.635107i	$0.219044\pi$
$769$			9.47266e15i			1.27021i	−0.772424	+	0.635107i	$0.780956\pi$
$770$	−2.18788e15	−	6.11823e15i	−0.291289	−	0.814567i
$771$	−5.01651e15	+	5.01651e15i	−0.663136	+	0.663136i
$772$	−1.27975e16	+	3.25353e15i	−1.67970	+	0.427031i
$773$		−	8.28252e15i		−	1.07938i	−0.841863	−	0.539691i	$-0.818541\pi$
$773$		−	8.28252e15i		−	1.07938i	0.841863	−	0.539691i	$-0.181459\pi$
$774$	5.78111e15	+	1.58890e15i	0.748059	+	0.205599i
$775$	−5.98101e15	−	2.16629e15i	−0.768449	−	0.278328i
$776$	1.98470e14	−	1.03015e16i	0.0253196	−	1.31420i
$777$	5.07698e15	−	5.07698e15i	0.643117	−	0.643117i
$778$	3.21379e15	+	5.64992e15i	0.404231	+	0.710648i
$779$	4.93661e15	−	4.93661e15i	0.616556	−	0.616556i
$780$	5.03913e14	+	6.68758e15i	0.0624936	+	0.829370i
$781$	2.59332e15	+	2.59332e15i	0.319357	+	0.319357i
$782$	−1.00067e16	−	2.75028e15i	−1.22364	−	0.336310i
$783$	−1.00498e15	−	1.00498e15i	−0.122030	−	0.122030i
$784$	−3.07307e15	+	1.67051e15i	−0.370539	+	0.201424i
$785$	2.20832e15	+	3.14855e15i	0.264411	+	0.376988i
$786$	−1.17100e15	−	2.05864e15i	−0.139230	−	0.244769i
$787$	7.81317e15			0.922500			0.461250	−	0.887270i	$-0.347401\pi$
$787$	7.81317e15			0.922500			0.461250	+	0.887270i	$0.347401\pi$
$788$	9.96455e14	+	5.92495e14i	0.116833	+	0.0694689i
$789$	4.53027e15	+	4.53027e15i	0.527474	+	0.527474i
$790$	−1.00106e15	+	3.57981e14i	−0.115748	+	0.0413914i
$791$	−6.53104e15			−0.749914
$792$	8.92260e13	−	4.63124e15i	0.0101743	−	0.528091i
$793$	−1.31519e16	−	1.31519e16i	−1.48932	−	1.48932i
$794$	8.74954e14	−	3.18346e15i	0.0983949	−	0.358003i
$795$	1.90924e15	−	1.33910e15i	0.213227	−	0.149553i
$796$	7.43278e15	−	1.25004e16i	0.824384	−	1.38645i
$797$			5.21237e15i			0.574135i	0.957910	+	0.287068i	$0.0926805\pi$
$797$			5.21237e15i			0.574135i	−0.957910	+	0.287068i	$0.907320\pi$
$798$	6.80172e15	+	1.86941e15i	0.744051	+	0.204497i
$799$	−8.38272e15			−0.910705
$800$	−9.20395e15	−	1.08930e15i	−0.993069	−	0.117531i
$801$	−1.05415e16			−1.12959
$802$	−3.99412e15	−	1.09776e15i	−0.425072	−	0.116828i
$803$		−	4.04594e15i		−	0.427645i
$804$	−1.89195e15	+	3.18188e15i	−0.198611	+	0.334022i
$805$	1.37006e16	−	9.60930e15i	1.42844	−	1.00188i
$806$	−3.33584e15	+	1.21372e16i	−0.345432	+	1.25683i
$807$	−3.16567e14	−	3.16567e14i	−0.0325582	−	0.0325582i
$808$	−3.82494e15	−	7.36919e13i	−0.390717	−	0.00752761i
$809$	1.64951e16			1.67354			0.836772	−	0.547552i	$-0.184440\pi$
$809$	1.64951e16			1.67354			0.836772	+	0.547552i	$0.184440\pi$
$810$	−2.41104e15	+	8.62189e14i	−0.242962	+	0.0868830i
$811$	9.90917e15	+	9.90917e15i	0.991797	+	0.991797i	0.999967	−	0.00816976i	$-0.00260054\pi$
$811$	9.90917e15	+	9.90917e15i	0.991797	+	0.991797i	−0.00816976	+	0.999967i	$0.502601\pi$
$812$	−1.97422e15	−	1.17388e15i	−0.196263	−	0.116698i
$813$	3.02345e15			0.298542
$814$	5.34945e15	+	9.40446e15i	0.524656	+	0.922358i
$815$	−2.87510e14	−	4.09922e14i	−0.0280083	−	0.0399333i
$816$	−4.48238e15	−	1.32533e15i	−0.433723	−	0.128241i
$817$	−9.72854e15	−	9.72854e15i	−0.935031	−	0.935031i
$818$	2.11245e15	+	5.80593e14i	0.201671	+	0.0554279i
$819$	1.03231e16	+	1.03231e16i	0.978919	+	0.978919i
$820$	−5.60514e14	−	7.43874e15i	−0.0527971	−	0.700686i
$821$	−5.02987e15	+	5.02987e15i	−0.470619	+	0.470619i	−0.902115	−	0.431496i	$-0.857986\pi$
$821$	−5.02987e15	+	5.02987e15i	−0.470619	+	0.470619i	0.431496	+	0.902115i	$0.357986\pi$
$822$	−4.08270e15	−	7.17749e15i	−0.379448	−	0.667079i
$823$	1.33810e16	−	1.33810e16i	1.23535	−	1.23535i	0.273473	−	0.961880i	$-0.411828\pi$
$823$	1.33810e16	−	1.33810e16i	1.23535	−	1.23535i	0.961880	−	0.273473i	$-0.0881724\pi$
$824$	1.70340e16	+	3.28179e14i	1.56213	+	0.0300961i
$825$	1.76125e15	+	3.76158e15i	0.160444	+	0.342668i
$826$	−1.63322e16	−	4.48880e15i	−1.47793	−	0.406200i
$827$			1.69728e16i			1.52572i	0.646566	+	0.762858i	$0.276204\pi$
$827$			1.69728e16i			1.52572i	−0.646566	+	0.762858i	$0.723796\pi$
$828$	1.15620e16	−	2.93943e15i	1.03245	−	0.262480i
$829$	−3.92349e15	+	3.92349e15i	−0.348035	+	0.348035i	−0.859377	−	0.511342i	$-0.829148\pi$
$829$	−3.92349e15	+	3.92349e15i	−0.348035	+	0.348035i	0.511342	+	0.859377i	$0.329148\pi$
$830$	1.65957e15	+	4.64085e15i	0.146240	+	0.408948i
$831$		−	9.27540e15i		−	0.811946i
$832$	−7.06398e14	+	1.83258e16i	−0.0614287	+	1.59362i
$833$	−2.99383e15	+	2.99383e15i	−0.258630	+	0.258630i
$834$	3.40487e14	+	5.98585e14i	0.0292205	+	0.0513703i
$835$	9.79445e15	+	1.71910e15i	0.835034	+	0.146564i
$836$	−5.43257e15	+	9.13647e15i	−0.460119	+	0.773827i
$837$	8.75367e15			0.736547
$838$	−1.02437e16	−	1.80087e16i	−0.856278	−	1.50536i
$839$		−	6.33325e15i		−	0.525939i	−0.964804	−	0.262970i	$-0.915298\pi$
$839$		−	6.33325e15i		−	0.525939i	0.964804	−	0.262970i	$-0.0847019\pi$
$840$	6.25304e15	−	4.20840e15i	0.515888	−	0.347201i
$841$			1.17531e16i			0.963329i
$842$	−7.80726e14	+	4.44093e14i	−0.0635744	+	0.0361624i
$843$	3.44070e15			0.278353
$844$	7.34364e15	−	1.86698e15i	0.590239	−	0.150057i
$845$	1.58241e16	−	1.10987e16i	1.26359	−	0.886254i
$846$	8.37613e15	−	4.76451e15i	0.664518	−	0.377991i
$847$	5.06631e15	−	5.06631e15i	0.399331	−	0.399331i
$848$	5.60281e15	−	3.04567e15i	0.438762	−	0.238509i
$849$			4.77108e15i			0.371214i
$850$	−1.10577e16	+	1.89449e15i	−0.854791	+	0.146450i
$851$	−1.97037e16	+	1.97037e16i	−1.51333	+	1.51333i
$852$	−2.17431e15	+	3.65674e15i	−0.165922	+	0.279047i
$853$		−	1.63191e16i		−	1.23730i	−0.785665	−	0.618652i	$-0.787679\pi$
$853$		−	1.63191e16i		−	1.23730i	0.785665	−	0.618652i	$-0.212321\pi$
$854$	−5.53982e15	+	2.01563e16i	−0.417328	+	1.51842i
$855$	1.18878e16	+	2.08653e15i	0.889792	+	0.156175i
$856$	8.25773e14	−	7.94555e14i	0.0614122	−	0.0590906i
$857$	3.05233e15	−	3.05233e15i	0.225547	−	0.225547i	−0.585282	−	0.810830i	$-0.699016\pi$
$857$	3.05233e15	−	3.05233e15i	0.225547	−	0.225547i	0.810830	+	0.585282i	$0.199016\pi$
$858$	7.14387e15	−	4.06358e15i	0.524509	−	0.298351i
$859$	−1.13771e16	+	1.13771e16i	−0.829982	+	0.829982i	−0.987514	−	0.157532i	$-0.949646\pi$
$859$	−1.13771e16	+	1.13771e16i	−0.829982	+	0.829982i	0.157532	+	0.987514i	$0.449646\pi$
$860$	−1.46595e16	+	1.10460e15i	−1.06262	+	0.0800689i
$861$	4.28979e15	+	4.28979e15i	0.308972	+	0.308972i
$862$	−1.46521e15	+	5.33106e15i	−0.104860	+	0.381525i
$863$	−6.07377e15	−	6.07377e15i	−0.431916	−	0.431916i	0.457364	−	0.889280i	$-0.348794\pi$
$863$	−6.07377e15	−	6.07377e15i	−0.431916	−	0.431916i	−0.889280	+	0.457364i	$0.848794\pi$
$864$	1.24190e16	−	2.90380e15i	0.877525	−	0.205183i
$865$	−1.82835e16	+	1.28236e16i	−1.28372	+	0.900373i
$866$	1.29954e16	−	7.39207e15i	0.906656	−	0.515724i
$867$	1.86476e15			0.129276
$868$	1.37104e16	−	3.48562e15i	0.944481	−	0.240116i
$869$	9.21265e14	+	9.21265e14i	0.0630632	+	0.0630632i
$870$	1.32714e15	+	6.27985e14i	0.0902734	+	0.0427163i
$871$	1.75813e16			1.18837
$872$	1.34801e16	+	2.59710e14i	0.905427	+	0.0174441i
$873$	1.01379e16	+	1.01379e16i	0.676658	+	0.676658i
$874$	−2.63973e16	−	7.25513e15i	−1.75084	−	0.481208i
$875$	9.00845e15	−	1.56883e16i	0.593753	−	1.03402i
$876$	4.54861e15	−	1.15640e15i	0.297925	−	0.0757417i
$877$			1.87090e16i			1.21773i	0.793273	+	0.608866i	$0.208375\pi$
$877$			1.87090e16i			1.21773i	−0.793273	+	0.608866i	$0.791625\pi$
$878$	1.44139e15	−	5.24441e15i	0.0932314	−	0.339217i
$879$	−1.12181e16			−0.721076
$880$	3.61772e15	+	1.07664e16i	0.231090	+	0.687728i
$881$	−1.09617e16			−0.695839			−0.347919	−	0.937524i	$-0.613112\pi$
$881$	−1.09617e16			−0.695839			−0.347919	+	0.937524i	$0.613112\pi$
$882$	1.28986e15	−	4.69309e15i	0.0813705	−	0.296061i
$883$			2.19499e16i			1.37610i	0.725665	+	0.688048i	$0.241532\pi$
$883$			2.19499e16i			1.37610i	−0.725665	+	0.688048i	$0.758468\pi$
$884$	5.46974e15	+	2.15148e16i	0.340784	+	1.34045i
$885$	1.06641e16	+	1.87175e15i	0.660295	+	0.115894i
$886$	−1.25202e16	−	3.44110e15i	−0.770418	−	0.211744i
$887$	1.82218e16	+	1.82218e16i	1.11433	+	1.11433i	0.992559	+	0.121768i	$0.0388563\pi$
$887$	1.82218e16	+	1.82218e16i	1.11433	+	1.11433i	0.121768	+	0.992559i	$0.461144\pi$
$888$	−9.04393e15	+	8.70204e15i	−0.549650	+	0.528871i
$889$	−2.98561e16			−1.80332
$890$	2.43385e16	−	8.70345e15i	1.46100	−	0.522452i
$891$	2.21885e15	+	2.21885e15i	0.132373	+	0.132373i
$892$	6.94483e14	+	2.73170e15i	0.0411770	+	0.161967i
$893$	−2.21133e16			−1.30308
$894$	−9.59805e15	+	5.45956e15i	−0.562117	+	0.319743i
$895$	1.51633e16	+	2.66144e15i	0.882607	+	0.154913i
$896$	1.82949e16	−	9.49318e15i	1.05837	−	0.549184i
$897$	1.49674e16	+	1.49674e16i	0.860575	+	0.860575i
$898$	5.08818e15	−	1.85130e16i	0.290765	−	1.05793i
$899$	1.94854e15	+	1.94854e15i	0.110670	+	0.110670i
$900$	9.97221e15	−	8.17789e15i	0.562934	−	0.461644i
$901$	5.45834e15	−	5.45834e15i	0.306249	−	0.306249i
$902$	−7.94628e15	+	4.52001e15i	−0.443127	+	0.252060i
$903$	8.45386e15	−	8.45386e15i	0.468568	−	0.468568i
$904$	1.14142e16	+	2.19908e14i	0.628811	+	0.0121148i
$905$	1.95129e15	−	1.11173e16i	0.106845	−	0.608741i
$906$	−3.35631e15	+	1.22117e16i	−0.182666	+	0.664617i
$907$		−	1.19941e16i		−	0.648824i	−0.945916	−	0.324412i	$-0.894834\pi$
$907$		−	1.19941e16i		−	0.648824i	0.945916	−	0.324412i	$-0.105166\pi$
$908$	9.37123e15	+	5.57215e15i	0.503877	+	0.299606i
$909$	3.76419e15	−	3.76419e15i	0.201173	−	0.201173i
$910$	−3.23573e16	−	1.53111e16i	−1.71888	−	0.813353i
$911$			7.39016e15i			0.390214i	0.980782	+	0.195107i	$0.0625054\pi$
$911$			7.39016e15i			0.390214i	−0.980782	+	0.195107i	$0.937495\pi$
$912$	−1.18243e16	−	3.49616e15i	−0.620590	−	0.183493i
$913$	4.27091e15	−	4.27091e15i	0.222808	−	0.222808i
$914$	2.12472e16	−	1.20858e16i	1.10178	−	0.626717i
$915$	2.31001e15	−	1.31611e16i	0.119069	−	0.678383i
$916$	3.08080e15	+	1.21181e16i	0.157848	+	0.620883i
$917$	1.26416e16			0.643827
$918$	1.34191e16	−	7.63306e15i	0.679343	−	0.386424i
$919$		−	4.71287e15i		−	0.237165i	−0.992944	−	0.118582i	$-0.962165\pi$
$919$		−	4.71287e15i		−	0.237165i	0.992944	−	0.118582i	$-0.0378350\pi$
$920$	−2.42679e16	+	1.63327e16i	−1.21395	+	0.817007i
$921$		−	1.73416e16i		−	0.862306i
$922$	−1.39152e16	−	2.44633e16i	−0.687814	−	1.20919i
$923$	2.02051e16			0.992779
$924$	−7.93937e15	−	4.72077e15i	−0.387784	−	0.230577i
$925$	−1.02584e16	+	2.83228e16i	−0.498080	+	1.37517i
$926$	9.70520e15	+	1.70620e16i	0.468429	+	0.823511i
$927$	−1.67634e16	+	1.67634e16i	−0.804311	+	0.804311i
$928$	3.41080e15	+	2.11805e15i	0.162683	+	0.101023i
$929$			2.22338e16i			1.05421i	0.849799	+	0.527106i	$0.176723\pi$
$929$			2.22338e16i			1.05421i	−0.849799	+	0.527106i	$0.823277\pi$
$930$	−8.51485e15	+	3.04491e15i	−0.401348	+	0.143522i
$931$	−7.89760e15	+	7.89760e15i	−0.370060	+	0.370060i
$932$	−7.72459e15	−	3.03841e16i	−0.359822	−	1.41533i
$933$		−	2.05370e16i		−	0.951016i
$934$	2.71498e16	+	7.46195e15i	1.24985	+	0.343514i
$935$	7.89460e15	+	1.12559e16i	0.361299	+	0.515127i
$936$	−1.76939e16	−	1.83891e16i	−0.805019	−	0.836647i
$937$	1.00250e16	−	1.00250e16i	0.453435	−	0.453435i	−0.443058	−	0.896493i	$-0.646106\pi$
$937$	1.00250e16	−	1.00250e16i	0.453435	−	0.453435i	0.896493	+	0.443058i	$0.146106\pi$
$938$	−9.76954e15	−	1.71751e16i	−0.439297	−	0.772295i
$939$	1.18847e16	−	1.18847e16i	0.531286	−	0.531286i
$940$	−1.54053e16	+	1.79161e16i	−0.684649	+	0.796235i
$941$	−8.80653e15	−	8.80653e15i	−0.389100	−	0.389100i	0.485266	−	0.874367i	$-0.338723\pi$
$941$	−8.80653e15	−	8.80653e15i	−0.389100	−	0.389100i	−0.874367	+	0.485266i	$0.838723\pi$
$942$	5.27155e15	+	1.44885e15i	0.231557	+	0.0636419i
$943$	−1.66486e16	−	1.66486e16i	−0.727048	−	0.727048i
$944$	2.83925e16	+	8.39495e15i	1.23270	+	0.364479i
$945$	−4.30366e15	+	2.45197e16i	−0.185765	+	1.05838i
$946$	8.90755e15	+	1.56597e16i	0.382258	+	0.672020i
$947$	2.77151e16			1.18247			0.591236	−	0.806499i	$-0.298640\pi$
$947$	2.77151e16			1.18247			0.591236	+	0.806499i	$0.298640\pi$
$948$	−7.72412e14	+	1.29904e15i	−0.0327645	+	0.0551032i
$949$	−1.57614e16	−	1.57614e16i	−0.664706	−	0.664706i
$950$	−2.91697e16	+	4.99760e15i	−1.22307	+	0.209547i
$951$	−7.17251e14			−0.0299005
$952$	1.79783e16	−	1.72987e16i	0.745153	−	0.716983i
$953$	−4.31612e15	−	4.31612e15i	−0.177862	−	0.177862i	0.612561	−	0.790423i	$-0.290139\pi$
$953$	−4.31612e15	−	4.31612e15i	−0.177862	−	0.177862i	−0.790423	+	0.612561i	$0.790139\pi$
$954$	−2.35168e15	+	8.55642e15i	−0.0963522	+	0.350571i
$955$	−9.49918e15	−	1.35436e16i	−0.386962	−	0.551717i
$956$	−1.59957e16	−	9.51106e15i	−0.647864	−	0.385222i
$957$		−	1.79927e15i		−	0.0724571i
$958$	7.39591e15	+	2.03272e15i	0.296129	+	0.0813891i
$959$	4.40750e16			1.75465
$960$	−1.10701e16	+	7.14443e15i	−0.438186	+	0.282798i
$961$	8.43610e15			0.332019
$962$	5.74754e16	+	1.57967e16i	2.24915	+	0.618165i
$963$			1.59459e15i			0.0620448i
$964$	2.36800e15	+	1.40802e15i	0.0916130	+	0.0544733i
$965$	−7.78869e15	+	4.43754e16i	−0.299615	+	1.70703i
$966$	6.30454e15	−	2.29386e16i	0.241145	−	0.877392i
$967$	−3.55753e16	−	3.55753e16i	−1.35302	−	1.35302i	−0.882267	−	0.470749i	$-0.843984\pi$
$967$	−3.55753e16	−	3.55753e16i	−1.35302	−	1.35302i	−0.470749	−	0.882267i	$-0.656016\pi$
$968$	−9.02492e15	+	8.68374e15i	−0.341294	+	0.328392i
$969$	−1.49255e16			−0.561238
$970$	−3.17770e16	−	1.50365e16i	−1.18814	−	0.562214i
$971$	9.45298e15	+	9.45298e15i	0.351450	+	0.351450i	0.860649	−	0.509199i	$-0.170058\pi$
$971$	9.45298e15	+	9.45298e15i	0.351450	+	0.351450i	−0.509199	+	0.860649i	$0.670058\pi$
$972$	−1.43190e16	+	2.40817e16i	−0.529357	+	0.890270i
$973$	−3.67575e15			−0.135122
$974$	−1.30032e16	−	2.28599e16i	−0.475308	−	0.835603i
$975$	2.15148e16	+	7.79252e15i	0.782008	+	0.283239i
$976$	1.03606e16	−	3.50404e16i	0.374463	−	1.26647i
$977$	−5.71986e15	−	5.71986e15i	−0.205573	−	0.205573i	0.596810	−	0.802383i	$-0.296435\pi$
$977$	−5.71986e15	−	5.71986e15i	−0.205573	−	0.205573i	−0.802383	+	0.596810i	$0.796435\pi$
$978$	−6.86325e14	−	1.88632e14i	−0.0245282	−	0.00674142i
$979$	−2.23984e16	−	2.23984e16i	−0.795998	−	0.795998i
$980$	8.96713e14	+	1.19005e16i	0.0316891	+	0.420555i
$981$	−1.32660e16	+	1.32660e16i	−0.466188	+	0.466188i
$982$	3.26616e14	+	5.74199e14i	0.0114136	+	0.0200655i
$983$	−2.43221e16	+	2.43221e16i	−0.845195	+	0.845195i	−0.989529	−	0.144334i	$-0.953896\pi$
$983$	−2.43221e16	+	2.43221e16i	−0.845195	+	0.845195i	0.144334	+	0.989529i	$0.453896\pi$
$984$	−7.35277e15	−	7.64166e15i	−0.254084	−	0.264067i
$985$	3.23837e15	−	2.27132e15i	0.111283	−	0.0780510i
$986$	4.68615e15	+	1.28796e15i	0.160138	+	0.0440128i
$987$		−	1.92159e16i		−	0.653005i
$988$	1.44289e16	+	5.67552e16i	0.487609	+	1.91797i
$989$	−3.28093e16	+	3.28093e16i	−1.10260	+	1.10260i
$990$	−1.42859e16	−	6.75993e15i	−0.477436	−	0.225917i
$991$			1.84922e16i			0.614589i	0.951615	+	0.307294i	$0.0994236\pi$
$991$			1.84922e16i			0.614589i	−0.951615	+	0.307294i	$0.900576\pi$
$992$	−2.40790e16	+	5.63013e15i	−0.795836	+	0.186082i
$993$	4.20821e15	−	4.20821e15i	0.138317	−	0.138317i
$994$	−1.12275e16	−	1.97383e16i	−0.366994	−	0.645185i
$995$	−2.84934e16	−	4.06250e16i	−0.926228	−	1.32058i
$996$	6.02223e15	+	3.58084e15i	0.194684	+	0.115760i
$997$	−4.31283e16			−1.38656			−0.693281	−	0.720668i	$-0.743835\pi$
$997$	−4.31283e16			−1.38656			−0.693281	+	0.720668i	$0.743835\pi$
$998$	−9.85258e15	−	1.73211e16i	−0.315016	−	0.553806i
$999$		−	4.14527e16i		−	1.31808i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.12.j.a.67.10	yes	260
5.3	odd	4		80.12.s.a.3.55	yes	260
16.11	odd	4		80.12.s.a.27.55	yes	260
80.43	even	4	inner	80.12.j.a.43.10	✓	260

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.12.j.a.43.10	✓	260	80.43	even	4	inner
80.12.j.a.67.10	yes	260	1.1	even	1	trivial
80.12.s.a.3.55	yes	260	5.3	odd	4
80.12.s.a.27.55	yes	260	16.11	odd	4

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:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	80.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-43.6367 - 11.9933i) q^{2} +219.501i q^{3} +(1760.32 + 1046.69i) q^{4} +(5720.85 - 4012.48i) q^{5} +(2632.53 - 9578.30i) q^{6} +(37491.7 + 37491.7i) q^{7} +(-64261.4 - 66786.2i) q^{8} +128966. q^{9} +(-297762. + 106480. i) q^{10} +(274026. + 274026. i) q^{11} +(-229750. + 386393. i) q^{12} +2.13499e6 q^{13} +(-1.18637e6 - 2.08566e6i) q^{14} +(880743. + 1.25573e6i) q^{15} +(2.00317e6 + 3.68504e6i) q^{16} +(3.59002e6 + 3.59002e6i) q^{17} +(-5.62766e6 - 1.54673e6i) q^{18} +(9.47032e6 + 9.47032e6i) q^{19} +(1.42704e7 - 1.07528e6i) q^{20} +(-8.22948e6 + 8.22948e6i) q^{21} +(-8.67112e6 - 1.52440e7i) q^{22} +(3.19384e7 - 3.19384e7i) q^{23} +(1.46597e7 - 1.41055e7i) q^{24} +(1.66282e7 - 4.59096e7i) q^{25} +(-9.31641e7 - 2.56055e7i) q^{26} +6.71922e7i q^{27} +(2.67552e7 + 1.05240e8i) q^{28} +(-1.49568e7 + 1.49568e7i) q^{29} +(-2.33724e7 - 6.53590e7i) q^{30} -1.30278e8i q^{31} +(-4.32163e7 - 1.84827e8i) q^{32} +(-6.01490e7 + 6.01490e7i) q^{33} +(-1.13600e8 - 1.99712e8i) q^{34} +(3.64919e8 + 6.40500e7i) q^{35} +(2.27022e8 + 1.34988e8i) q^{36} -6.16927e8 q^{37} +(-2.99673e8 - 5.26833e8i) q^{38} +4.68633e8i q^{39} +(-6.35608e8 - 1.24227e8i) q^{40} -5.21271e8i q^{41} +(4.57805e8 - 2.60409e8i) q^{42} -1.02727e9 q^{43} +(1.95553e8 + 7.69195e8i) q^{44} +(7.37797e8 - 5.17474e8i) q^{45} +(-1.77673e9 + 1.01064e9i) q^{46} +(-1.16750e9 + 1.16750e9i) q^{47} +(-8.08869e8 + 4.39699e8i) q^{48} +8.33932e8i q^{49} +(-1.27620e9 + 1.80392e9i) q^{50} +(-7.88012e8 + 7.88012e8i) q^{51} +(3.75828e9 + 2.23468e9i) q^{52} -1.52042e9i q^{53} +(8.05854e8 - 2.93205e9i) q^{54} +(2.66718e9 + 4.68139e8i) q^{55} +(9.46584e7 - 4.91320e9i) q^{56} +(-2.07874e9 + 2.07874e9i) q^{57} +(8.32045e8 - 4.73284e8i) q^{58} +(4.99146e9 - 4.99146e9i) q^{59} +(2.36026e8 + 3.13236e9i) q^{60} +(-6.16017e9 - 6.16017e9i) q^{61} +(-1.56246e9 + 5.68491e9i) q^{62} +(4.83517e9 + 4.83517e9i) q^{63} +(-3.30867e8 + 8.58356e9i) q^{64} +(1.22140e10 - 8.56661e9i) q^{65} +(3.34608e9 - 1.90332e9i) q^{66} +8.23483e9 q^{67} +(2.56195e9 + 1.00772e10i) q^{68} +(7.01052e9 + 7.01052e9i) q^{69} +(-1.51557e10 - 7.17150e9i) q^{70} +9.46380e9 q^{71} +(-8.28756e9 - 8.61317e9i) q^{72} +(-7.38240e9 - 7.38240e9i) q^{73} +(2.69207e10 + 7.39896e9i) q^{74} +(1.00772e10 + 3.64990e9i) q^{75} +(6.75831e9 + 2.65833e10i) q^{76} +2.05474e10i q^{77} +(5.62044e9 - 2.04496e10i) q^{78} +3.36197e9 q^{79} +(2.62460e10 + 1.30439e10i) q^{80} +8.09723e9 q^{81} +(-6.25174e9 + 2.27466e10i) q^{82} -1.55858e10i q^{83} +(-2.31003e10 + 5.87281e9i) q^{84} +(3.49428e10 + 6.13310e9i) q^{85} +(4.48265e10 + 1.23203e10i) q^{86} +(-3.28303e9 - 3.28303e9i) q^{87} +(6.91855e8 - 3.59104e10i) q^{88} -8.17382e10 q^{89} +(-3.84012e10 + 1.37323e10i) q^{90} +(8.00446e10 + 8.00446e10i) q^{91} +(8.96517e10 - 2.27923e10i) q^{92} +2.85962e10 q^{93} +(6.49483e10 - 3.69439e10i) q^{94} +(9.21777e10 + 1.61789e10i) q^{95} +(4.05698e10 - 9.48602e9i) q^{96} +(7.86089e10 + 7.86089e10i) q^{97} +(1.00016e10 - 3.63901e10i) q^{98} +(3.53401e10 + 3.53401e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 260 q - 2 q^{2} - 3956 q^{4} - 2 q^{5} - 4 q^{6} - 4 q^{7} - 74840 q^{8} - 14880348 q^{9} - 4098 q^{10} - 4 q^{11} - 114212 q^{12} - 4 q^{13} + 708588 q^{15} + 5740152 q^{16} - 4 q^{17} - 6791722 q^{18}+ \cdots - 189350900660 q^{99}+O(q^{100}) \) 260 * q - 2 * q^2 - 3956 * q^4 - 2 * q^5 - 4 * q^6 - 4 * q^7 - 74840 * q^8 - 14880348 * q^9 - 4098 * q^10 - 4 * q^11 - 114212 * q^12 - 4 * q^13 + 708588 * q^15 + 5740152 * q^16 - 4 * q^17 - 6791722 * q^18 - 11291288 * q^19 + 27599212 * q^20 - 4 * q^21 + 11921800 * q^22 - 4 * q^23 + 708588 * q^24 - 196875380 * q^26 + 185066800 * q^28 - 534157704 * q^30 - 894200972 * q^32 - 4 * q^33 - 122727336 * q^34 + 434731680 * q^35 + 917614156 * q^36 - 4 * q^37 - 169550316 * q^38 - 1417066568 * q^40 - 1572161236 * q^42 - 4763690660 * q^43 - 1456070840 * q^44 - 97301958 * q^45 - 3653567828 * q^46 + 5707353192 * q^47 - 447163780 * q^48 + 429408694 * q^50 + 112221284 * q^51 - 4957065880 * q^52 - 10995087044 * q^54 - 4 * q^55 - 8945492140 * q^56 + 708588 * q^57 + 33722126388 * q^58 - 11496390224 * q^59 - 6670533420 * q^60 - 2150827028 * q^61 + 15717297108 * q^62 + 708588 * q^63 - 11018267024 * q^64 - 4 * q^65 - 9909115916 * q^66 + 44333852084 * q^67 - 74998571352 * q^68 + 16194123612 * q^69 + 50947270608 * q^70 - 43677902056 * q^71 - 56634399632 * q^72 + 12278087704 * q^73 - 99553151276 * q^74 + 85400572304 * q^75 + 46613107196 * q^76 + 205137826492 * q^78 + 130159671844 * q^80 + 794986843420 * q^81 + 83904972628 * q^82 + 216982878048 * q^84 - 97656252 * q^85 + 56725646132 * q^86 - 50128110092 * q^87 + 346072249440 * q^88 + 174291105374 * q^90 - 46617621428 * q^91 - 51820450984 * q^92 + 708584 * q^93 - 82977932908 * q^94 - 20580862760 * q^95 - 62470624376 * q^96 - 4 * q^97 - 155418407946 * q^98 - 189350900660 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more