LMFDB - Embedded newform 125.2.h.a.4.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [125,2,Mod(4,125)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(125, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("125.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 125 = 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	125.h (of order $50$, degree $20$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$0.998130025266$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{50})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label			4.11
Character	$\chi$	$=$	125.4
Dual form			125.2.h.a.94.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.07048 + 0.130264i) q^{2} +(-0.974456 - 0.458544i) q^{3} +(2.28570 + 0.288751i) q^{4} +(0.707806 + 2.12109i) q^{5} +(-1.95786 - 1.07634i) q^{6} +(1.45498 - 2.00261i) q^{7} +(0.619230 + 0.118124i) q^{8} +(-1.17297 - 1.41788i) q^{9} +O(q^{10})$	\(q+(2.07048 + 0.130264i) q^{2} +(-0.974456 - 0.458544i) q^{3} +(2.28570 + 0.288751i) q^{4} +(0.707806 + 2.12109i) q^{5} +(-1.95786 - 1.07634i) q^{6} +(1.45498 - 2.00261i) q^{7} +(0.619230 + 0.118124i) q^{8} +(-1.17297 - 1.41788i) q^{9} +(1.18920 + 4.48388i) q^{10} +(-0.0607221 + 0.965150i) q^{11} +(-2.09491 - 1.32947i) q^{12} +(-4.33827 + 3.58893i) q^{13} +(3.27338 - 3.95683i) q^{14} +(0.282886 - 2.39147i) q^{15} +(-3.19626 - 0.820659i) q^{16} +(-0.640649 - 5.07126i) q^{17} +(-2.24392 - 3.08849i) q^{18} +(1.70464 + 3.62254i) q^{19} +(1.00537 + 5.05255i) q^{20} +(-2.33610 + 1.28428i) q^{21} +(-0.251448 + 1.99042i) q^{22} +(1.67761 - 4.23716i) q^{23} +(-0.549247 - 0.399051i) q^{24} +(-3.99802 + 3.00264i) q^{25} +(-9.44983 + 6.86570i) q^{26} +(1.29633 + 5.04887i) q^{27} +(3.90390 - 4.15723i) q^{28} +(2.82179 + 2.64984i) q^{29} +(0.897233 - 4.91464i) q^{30} +(2.08257 - 0.263089i) q^{31} +(-7.70998 - 2.50512i) q^{32} +(0.501735 - 0.912652i) q^{33} +(-0.665852 - 10.5834i) q^{34} +(5.27755 + 1.66868i) q^{35} +(-2.27164 - 3.57954i) q^{36} +(-0.235804 + 0.918396i) q^{37} +(3.05754 + 7.72246i) q^{38} +(5.87314 - 1.50797i) q^{39} +(0.187742 + 1.39705i) q^{40} +(1.57651 - 0.624185i) q^{41} +(-5.00414 + 2.35477i) q^{42} +(7.92164 - 2.57390i) q^{43} +(-0.417480 + 2.18851i) q^{44} +(2.17721 - 3.49155i) q^{45} +(4.02541 - 8.55443i) q^{46} +(8.83092 - 1.68459i) q^{47} +(2.73830 + 2.26532i) q^{48} +(0.269649 + 0.829893i) q^{49} +(-8.66897 + 5.69611i) q^{50} +(-1.70111 + 5.23549i) q^{51} +(-10.9523 + 6.95054i) q^{52} +(-6.04722 - 10.9999i) q^{53} +(2.02634 + 10.6225i) q^{54} +(-2.09015 + 0.554342i) q^{55} +(1.13752 - 1.06821i) q^{56} -4.31166i q^{57} +(5.49729 + 5.85402i) q^{58} +(-5.19682 + 8.18888i) q^{59} +(1.33713 - 5.38449i) q^{60} +(9.62343 + 3.81019i) q^{61} +(4.34619 - 0.273439i) q^{62} +(-4.54610 + 0.286016i) q^{63} +(-9.50065 - 3.76157i) q^{64} +(-10.6831 - 6.66159i) q^{65} +(1.15772 - 1.82427i) q^{66} +(-4.88802 - 5.20522i) q^{67} -11.7764i q^{68} +(-3.57768 + 3.35967i) q^{69} +(10.7097 + 4.14245i) q^{70} +(0.533807 + 2.79831i) q^{71} +(-0.558852 - 1.01655i) q^{72} +(-7.76605 + 4.92849i) q^{73} +(-0.607862 + 1.87081i) q^{74} +(5.27274 - 1.09267i) q^{75} +(2.85028 + 8.77226i) q^{76} +(1.84447 + 1.52587i) q^{77} +(12.3567 - 2.35716i) q^{78} +(-1.00490 + 2.13553i) q^{79} +(-0.521640 - 7.36041i) q^{80} +(0.0174734 - 0.0915987i) q^{81} +(3.34545 - 1.08700i) q^{82} +(5.63120 - 2.64984i) q^{83} +(-5.71046 + 2.26093i) q^{84} +(10.3031 - 4.94834i) q^{85} +(16.7369 - 4.29731i) q^{86} +(-1.53464 - 3.87606i) q^{87} +(-0.151609 + 0.590477i) q^{88} +(2.94749 + 4.64449i) q^{89} +(4.96269 - 6.94559i) q^{90} +(0.875123 + 13.9097i) q^{91} +(5.05800 - 9.20046i) q^{92} +(-2.15001 - 0.698580i) q^{93} +(18.5037 - 2.33756i) q^{94} +(-6.47717 + 6.17974i) q^{95} +(6.36432 + 5.97650i) q^{96} +(-3.95475 + 4.21138i) q^{97} +(0.450198 + 1.75341i) q^{98} +(1.43969 - 1.04599i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9}+O(q^{10}) $ 240 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 25 * q^5 - 20 * q^6 - 25 * q^7 - 35 * q^8 - 20 * q^9	\( 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9} - 20 q^{10} - 25 q^{11} + 60 q^{12} - 20 q^{13} - 30 q^{14} - 40 q^{15} - 40 q^{16} - 15 q^{17} - 25 q^{18} - 10 q^{19} - 10 q^{20} - 35 q^{21} - 25 q^{22} + 70 q^{23} + 15 q^{24} + 35 q^{25} - 45 q^{26} - 20 q^{27} - 10 q^{28} - 10 q^{29} - 40 q^{30} - 30 q^{31} - 25 q^{32} - 35 q^{33} - 20 q^{34} - 40 q^{35} + 170 q^{36} - 55 q^{37} - 40 q^{38} - 35 q^{40} - 35 q^{41} - 10 q^{42} - 25 q^{43} + 15 q^{44} + 140 q^{45} - 40 q^{46} + 100 q^{47} + 5 q^{48} + 35 q^{49} - 10 q^{50} - 55 q^{51} - 15 q^{52} - 15 q^{53} + 30 q^{54} - 15 q^{55} + 65 q^{56} + 255 q^{58} + 5 q^{59} + 135 q^{60} - 40 q^{61} + 5 q^{62} - 35 q^{63} + 25 q^{64} - 30 q^{65} - 95 q^{66} + 105 q^{67} - 10 q^{69} - 55 q^{70} + 45 q^{71} - 30 q^{72} - 40 q^{73} + 35 q^{74} - 15 q^{75} - 65 q^{76} - 35 q^{77} + 100 q^{78} + 430 q^{80} - 95 q^{81} + 175 q^{82} + 20 q^{83} + 45 q^{84} - 10 q^{85} - 80 q^{86} - 5 q^{87} - 5 q^{88} + 30 q^{89} + 65 q^{91} - 55 q^{92} + 275 q^{93} + 60 q^{94} + 10 q^{95} - 135 q^{96} + 35 q^{97} - 15 q^{98} + 45 q^{99}+O(q^{100}) \) 240 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 25 * q^5 - 20 * q^6 - 25 * q^7 - 35 * q^8 - 20 * q^9 - 20 * q^10 - 25 * q^11 + 60 * q^12 - 20 * q^13 - 30 * q^14 - 40 * q^15 - 40 * q^16 - 15 * q^17 - 25 * q^18 - 10 * q^19 - 10 * q^20 - 35 * q^21 - 25 * q^22 + 70 * q^23 + 15 * q^24 + 35 * q^25 - 45 * q^26 - 20 * q^27 - 10 * q^28 - 10 * q^29 - 40 * q^30 - 30 * q^31 - 25 * q^32 - 35 * q^33 - 20 * q^34 - 40 * q^35 + 170 * q^36 - 55 * q^37 - 40 * q^38 - 35 * q^40 - 35 * q^41 - 10 * q^42 - 25 * q^43 + 15 * q^44 + 140 * q^45 - 40 * q^46 + 100 * q^47 + 5 * q^48 + 35 * q^49 - 10 * q^50 - 55 * q^51 - 15 * q^52 - 15 * q^53 + 30 * q^54 - 15 * q^55 + 65 * q^56 + 255 * q^58 + 5 * q^59 + 135 * q^60 - 40 * q^61 + 5 * q^62 - 35 * q^63 + 25 * q^64 - 30 * q^65 - 95 * q^66 + 105 * q^67 - 10 * q^69 - 55 * q^70 + 45 * q^71 - 30 * q^72 - 40 * q^73 + 35 * q^74 - 15 * q^75 - 65 * q^76 - 35 * q^77 + 100 * q^78 + 430 * q^80 - 95 * q^81 + 175 * q^82 + 20 * q^83 + 45 * q^84 - 10 * q^85 - 80 * q^86 - 5 * q^87 - 5 * q^88 + 30 * q^89 + 65 * q^91 - 55 * q^92 + 275 * q^93 + 60 * q^94 + 10 * q^95 - 135 * q^96 + 35 * q^97 - 15 * q^98 + 45 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/125\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{50}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	2.07048	+	0.130264i	1.46405	+	0.0921104i	0.774706	−	0.632322i	$-0.217898\pi$
$2$	2.07048	+	0.130264i	1.46405	+	0.0921104i	0.689346	+	0.724432i	$0.257898\pi$
$3$	−0.974456	−	0.458544i	−0.562603	−	0.264741i	0.123379	−	0.992360i	$-0.460627\pi$
$3$	−0.974456	−	0.458544i	−0.562603	−	0.264741i	−0.685982	+	0.727619i	$0.740627\pi$
$4$	2.28570	+	0.288751i	1.14285	+	0.144376i
$5$	0.707806	+	2.12109i	0.316540	+	0.948579i
$5$	0.707806	+	2.12109i	0.316540	+	0.948579i
$6$	−1.95786	−	1.07634i	−0.799294	−	0.439416i
$7$	1.45498	−	2.00261i	0.549930	−	0.756914i	−0.440072	−	0.897962i	$-0.645047\pi$
$7$	1.45498	−	2.00261i	0.549930	−	0.756914i	0.990003	+	0.141048i	$0.0450472\pi$
$8$	0.619230	+	0.118124i	0.218931	+	0.0417633i
$9$	−1.17297	−	1.41788i	−0.390990	−	0.472626i
$10$	1.18920	+	4.48388i	0.376058	+	1.41793i
$11$	−0.0607221	+	0.965150i	−0.0183084	+	0.291004i	0.978209	+	0.207621i	$0.0665722\pi$
$11$	−0.0607221	+	0.965150i	−0.0183084	+	0.291004i	−0.996518	+	0.0833821i	$0.973428\pi$
$12$	−2.09491	−	1.32947i	−0.604748	−	0.383785i
$13$	−4.33827	+	3.58893i	−1.20322	+	0.995391i	−0.203353	+	0.979105i	$0.565184\pi$
$13$	−4.33827	+	3.58893i	−1.20322	+	0.995391i	−0.999867	+	0.0162855i	$0.994816\pi$
$14$	3.27338	−	3.95683i	0.874847	−	1.05751i
$15$	0.282886	−	2.39147i	0.0730409	−	0.617474i
$16$	−3.19626	−	0.820659i	−0.799064	−	0.205165i
$17$	−0.640649	−	5.07126i	−0.155380	−	1.22996i	−0.856208	−	0.516631i	$-0.827186\pi$
$17$	−0.640649	−	5.07126i	−0.155380	−	1.22996i	0.700828	−	0.713330i	$-0.252814\pi$
$18$	−2.24392	−	3.08849i	−0.528896	−	0.727963i
$19$	1.70464	+	3.62254i	0.391071	+	0.831068i	0.999304	+	0.0373093i	$0.0118787\pi$
$19$	1.70464	+	3.62254i	0.391071	+	0.831068i	−0.608233	+	0.793759i	$0.708121\pi$
$20$	1.00537	+	5.05255i	0.224807	+	1.12978i
$21$	−2.33610	+	1.28428i	−0.509778	+	0.280253i
$22$	−0.251448	+	1.99042i	−0.0536089	+	0.424358i
$23$	1.67761	−	4.23716i	0.349806	−	0.883509i	−0.643228	−	0.765675i	$-0.722405\pi$
$23$	1.67761	−	4.23716i	0.349806	−	0.883509i	0.993033	−	0.117833i	$-0.0375949\pi$
$24$	−0.549247	−	0.399051i	−0.112115	−	0.0814560i
$25$	−3.99802	+	3.00264i	−0.799604	+	0.600527i
$26$	−9.44983	+	6.86570i	−1.85326	+	1.34648i
$27$	1.29633	+	5.04887i	0.249479	+	0.971656i
$28$	3.90390	−	4.15723i	0.737768	−	0.785643i
$29$	2.82179	+	2.64984i	0.523993	+	0.492062i	0.900803	−	0.434229i	$-0.142979\pi$
$29$	2.82179	+	2.64984i	0.523993	+	0.492062i	−0.376810	+	0.926291i	$0.622979\pi$
$30$	0.897233	−	4.91464i	0.163812	−	0.897287i
$31$	2.08257	−	0.263089i	0.374040	−	0.0472522i	0.0639337	−	0.997954i	$-0.479635\pi$
$31$	2.08257	−	0.263089i	0.374040	−	0.0472522i	0.310106	+	0.950702i	$0.399635\pi$
$32$	−7.70998	−	2.50512i	−1.36294	−	0.442847i
$33$	0.501735	−	0.912652i	0.0873408	−	0.158872i
$34$	−0.665852	−	10.5834i	−0.114193	−	1.81504i
$35$	5.27755	+	1.66868i	0.892068	+	0.282058i
$36$	−2.27164	−	3.57954i	−0.378607	−	0.596590i
$37$	−0.235804	+	0.918396i	−0.0387659	+	0.150983i	−0.985020	−	0.172442i	$-0.944834\pi$
$37$	−0.235804	+	0.918396i	−0.0387659	+	0.150983i	0.946254	+	0.323425i	$0.104834\pi$
$38$	3.05754	+	7.72246i	0.495998	+	1.25275i
$39$	5.87314	−	1.50797i	0.940456	−	0.241468i
$40$	0.187742	+	1.39705i	0.0296847	+	0.220893i
$41$	1.57651	−	0.624185i	0.246210	−	0.0974813i	−0.241779	−	0.970331i	$-0.577731\pi$
$41$	1.57651	−	0.624185i	0.246210	−	0.0974813i	0.487988	+	0.872850i	$0.337731\pi$
$42$	−5.00414	+	2.35477i	−0.772156	+	0.363349i
$43$	7.92164	−	2.57390i	1.20804	−	0.392516i	0.365326	−	0.930879i	$-0.380957\pi$
$43$	7.92164	−	2.57390i	1.20804	−	0.392516i	0.842712	+	0.538364i	$0.180957\pi$
$44$	−0.417480	+	2.18851i	−0.0629376	+	0.329930i
$45$	2.17721	−	3.49155i	0.324559	−	0.520490i
$46$	4.02541	−	8.55443i	0.593514	−	1.26128i
$47$	8.83092	−	1.68459i	1.28812	−	0.245722i	0.502580	−	0.864531i	$-0.332384\pi$
$47$	8.83092	−	1.68459i	1.28812	−	0.245722i	0.785542	+	0.618808i	$0.212384\pi$
$48$	2.73830	+	2.26532i	0.395240	+	0.326971i
$49$	0.269649	+	0.829893i	0.0385212	+	0.118556i
$50$	−8.66897	+	5.69611i	−1.22598	+	0.805552i
$51$	−1.70111	+	5.23549i	−0.238203	+	0.733115i
$52$	−10.9523	+	6.95054i	−1.51881	+	0.963867i
$53$	−6.04722	−	10.9999i	−0.830650	−	1.51095i	−0.859367	−	0.511359i	$-0.829142\pi$
$53$	−6.04722	−	10.9999i	−0.830650	−	1.51095i	0.0287169	−	0.999588i	$-0.490858\pi$
$54$	2.02634	+	10.6225i	0.275751	+	1.44554i
$55$	−2.09015	+	0.554342i	−0.281835	+	0.0747475i
$56$	1.13752	−	1.06821i	0.152008	−	0.142745i
$57$		−	4.31166i		−	0.571093i
$58$	5.49729	+	5.85402i	0.721829	+	0.768670i
$59$	−5.19682	+	8.18888i	−0.676569	+	1.06610i	0.316503	+	0.948592i	$0.397491\pi$
$59$	−5.19682	+	8.18888i	−0.676569	+	1.06610i	−0.993072	+	0.117510i	$0.962509\pi$
$60$	1.33713	−	5.38449i	0.172623	−	0.695135i
$61$	9.62343	+	3.81019i	1.23215	+	0.487844i	0.891790	−	0.452449i	$-0.149450\pi$
$61$	9.62343	+	3.81019i	1.23215	+	0.487844i	0.340364	+	0.940294i	$0.389450\pi$
$62$	4.34619	−	0.273439i	0.551967	−	0.0347268i
$63$	−4.54610	+	0.286016i	−0.572754	+	0.0360346i
$64$	−9.50065	−	3.76157i	−1.18758	−	0.470197i
$65$	−10.6831	−	6.66159i	−1.32508	−	0.826269i
$66$	1.15772	−	1.82427i	0.142505	−	0.224552i
$67$	−4.88802	−	5.20522i	−0.597167	−	0.635919i	0.357387	−	0.933956i	$-0.383668\pi$
$67$	−4.88802	−	5.20522i	−0.597167	−	0.635919i	−0.954554	+	0.298038i	$0.903668\pi$
$68$		−	11.7764i		−	1.42809i
$69$	−3.57768	+	3.35967i	−0.430702	+	0.404456i
$70$	10.7097	+	4.14245i	1.28005	+	0.495117i
$71$	0.533807	+	2.79831i	0.0633513	+	0.332099i	0.999826	−	0.0186352i	$-0.00593211\pi$
$71$	0.533807	+	2.79831i	0.0633513	+	0.332099i	−0.936475	+	0.350734i	$0.885932\pi$
$72$	−0.558852	−	1.01655i	−0.0658614	−	0.119801i
$73$	−7.76605	+	4.92849i	−0.908948	+	0.576836i	−0.906055	−	0.423160i	$-0.860921\pi$
$73$	−7.76605	+	4.92849i	−0.908948	+	0.576836i	−0.00289284	+	0.999996i	$0.500921\pi$
$74$	−0.607862	+	1.87081i	−0.0706625	+	0.217477i
$75$	5.27274	−	1.09267i	0.608843	−	0.126170i
$76$	2.85028	+	8.77226i	0.326950	+	1.00625i
$77$	1.84447	+	1.52587i	0.210196	+	0.173890i
$78$	12.3567	−	2.35716i	1.39912	−	0.266896i
$79$	−1.00490	+	2.13553i	−0.113060	+	0.240266i	−0.953347	−	0.301877i	$-0.902387\pi$
$79$	−1.00490	+	2.13553i	−0.113060	+	0.240266i	0.840286	+	0.542143i	$0.182387\pi$
$80$	−0.521640	−	7.36041i	−0.0583211	−	0.822918i
$81$	0.0174734	−	0.0915987i	0.00194149	−	0.0101776i
$82$	3.34545	−	1.08700i	0.369443	−	0.120039i
$83$	5.63120	−	2.64984i	0.618104	−	0.290858i	−0.0911208	−	0.995840i	$-0.529045\pi$
$83$	5.63120	−	2.64984i	0.618104	−	0.290858i	0.709225	+	0.704982i	$0.249045\pi$
$84$	−5.71046	+	2.26093i	−0.623062	+	0.246688i
$85$	10.3031	−	4.94834i	1.11753	−	0.536723i
$86$	16.7369	−	4.29731i	1.80479	−	0.463391i
$87$	−1.53464	−	3.87606i	−0.164531	−	0.415558i
$88$	−0.151609	+	0.590477i	−0.0161615	+	0.0629450i
$89$	2.94749	+	4.64449i	0.312433	+	0.492315i	0.963865	−	0.266392i	$-0.0858314\pi$
$89$	2.94749	+	4.64449i	0.312433	+	0.492315i	−0.651432	+	0.758707i	$0.725831\pi$
$90$	4.96269	−	6.94559i	0.523113	−	0.732129i
$91$	0.875123	+	13.9097i	0.0917378	+	1.45813i
$92$	5.05800	−	9.20046i	0.527333	−	0.959215i
$93$	−2.15001	−	0.698580i	−0.222945	−	0.0724394i
$94$	18.5037	−	2.33756i	1.90851	−	0.241101i
$95$	−6.47717	+	6.17974i	−0.664544	+	0.634028i
$96$	6.36432	+	5.97650i	0.649556	+	0.609974i
$97$	−3.95475	+	4.21138i	−0.401544	+	0.427601i	−0.897683	−	0.440642i	$-0.854751\pi$
$97$	−3.95475	+	4.21138i	−0.401544	+	0.427601i	0.496139	+	0.868243i	$0.334751\pi$
$98$	0.450198	+	1.75341i	0.0454769	+	0.177121i
$99$	1.43969	−	1.04599i	0.144694	−	0.105126i
$100$	−10.0053	+	5.70870i	−1.00053	+	0.570870i
$101$	−5.05771	−	3.67464i	−0.503261	−	0.365641i	0.307000	−	0.951709i	$-0.400675\pi$
$101$	−5.05771	−	3.67464i	−0.503261	−	0.365641i	−0.810261	+	0.586069i	$0.800675\pi$
$102$	−4.20412	+	10.6184i	−0.416270	+	1.05138i
$103$	−0.965134	+	7.63982i	−0.0950974	+	0.752774i	0.870397	+	0.492350i	$0.163862\pi$
$103$	−0.965134	+	7.63982i	−0.0950974	+	0.752774i	−0.965495	+	0.260423i	$0.916138\pi$
$104$	−3.11033	+	1.70992i	−0.304993	+	0.167671i
$105$	−4.37757	−	4.04604i	−0.427208	−	0.394854i
$106$	−11.0878	−	23.5628i	−1.07694	−	2.28862i
$107$	−6.37642	−	8.77639i	−0.616432	−	0.848446i	0.380655	−	0.924717i	$-0.375698\pi$
$107$	−6.37642	−	8.77639i	−0.616432	−	0.848446i	−0.997087	+	0.0762714i	$0.975698\pi$
$108$	1.50516	+	11.9145i	0.144834	+	1.14648i
$109$	−12.6819	−	3.25617i	−1.21471	−	0.311884i	−0.413631	−	0.910445i	$-0.635740\pi$
$109$	−12.6819	−	3.25617i	−1.21471	−	0.311884i	−0.801078	+	0.598560i	$0.795740\pi$
$110$	−4.39982	+	0.875485i	−0.419507	+	0.0834742i
$111$	0.650906	−	0.786810i	0.0617813	−	0.0746807i
$112$	−6.29394	+	5.20680i	−0.594722	+	0.491997i
$113$	−17.3574	−	11.0154i	−1.63285	−	1.03624i	−0.953037	−	0.302854i	$-0.902061\pi$
$113$	−17.3574	−	11.0154i	−1.63285	−	1.03624i	−0.679814	−	0.733385i	$-0.737939\pi$
$114$	0.561653	−	8.92722i	0.0526036	−	0.836111i
$115$	10.1748	+	0.559270i	0.948805	+	0.0521522i
$116$	5.68462	+	6.87153i	0.527804	+	0.638005i
$117$	10.1773	+	1.94143i	0.940895	+	0.179485i
$118$	−11.8266	+	16.2780i	−1.08873	+	1.49851i
$119$	−11.0879	−	6.09561i	−1.01642	−	0.558784i
$120$	0.457662	−	1.44745i	0.0417787	−	0.132134i
$121$	9.98544	+	1.26145i	0.907767	+	0.114678i
$122$	19.4288	+	9.14251i	1.75900	+	0.827724i
$123$	−1.82246	−	0.114659i	−0.164326	−	0.0103385i
$124$	4.83609			0.434294
$125$	−9.19868	−	6.35487i	−0.822755	−	0.568397i
$126$	−9.44987			−0.841862
$127$	−1.56071	−	0.0981913i	−0.138490	−	0.00871307i	−0.00660591	−	0.999978i	$-0.502103\pi$
$127$	−1.56071	−	0.0981913i	−0.138490	−	0.00871307i	−0.131884	+	0.991265i	$0.542103\pi$
$128$	−4.51053	−	2.12249i	−0.398678	−	0.187604i
$129$	−8.89954	−	1.12427i	−0.783561	−	0.0989867i
$130$	−21.2514	−	15.1843i	−1.86387	−	1.33175i
$131$	−18.8627	−	10.3699i	−1.64804	−	0.906020i	−0.987938	−	0.154847i	$-0.950511\pi$
$131$	−18.8627	−	10.3699i	−1.64804	−	0.906020i	−0.660106	−	0.751173i	$-0.729489\pi$
$132$	1.41035	−	1.94117i	0.122755	−	0.168957i
$133$	9.73474	+	1.85700i	0.844109	+	0.161022i
$134$	−9.44252	−	11.4140i	−0.815709	−	0.986023i
$135$	−9.79155	+	6.32325i	−0.842722	+	0.544219i
$136$	0.202331	−	3.21595i	0.0173497	−	0.275766i
$137$	17.2148	+	10.9248i	1.47076	+	0.933372i	0.998656	+	0.0518286i	$0.0165049\pi$
$137$	17.2148	+	10.9248i	1.47076	+	0.933372i	0.472103	+	0.881543i	$0.343495\pi$
$138$	−7.84517	+	6.49009i	−0.667825	+	0.552473i
$139$	3.37337	−	4.07770i	0.286125	−	0.345866i	−0.607793	−	0.794095i	$-0.707945\pi$
$139$	3.37337	−	4.07770i	0.286125	−	0.345866i	0.893919	+	0.448229i	$0.147945\pi$
$140$	11.5811	+	5.33800i	0.978778	+	0.451143i
$141$	−9.37780	−	2.40781i	−0.789754	−	0.202774i
$142$	0.740719	+	5.86340i	0.0621598	+	0.492045i
$143$	−3.20043	−	4.40501i	−0.267633	−	0.368366i
$144$	2.58552	+	5.49451i	0.215460	+	0.457876i
$145$	−3.62325	+	7.86083i	−0.300895	+	0.652806i
$146$	−16.7215	+	9.19271i	−1.38388	+	0.760794i
$147$	0.117782	−	0.932341i	0.00971450	−	0.0768982i
$148$	−0.804165	+	2.03109i	−0.0661020	+	0.166955i
$149$	3.82680	+	2.78033i	0.313503	+	0.227774i	0.733398	−	0.679799i	$-0.237933\pi$
$149$	3.82680	+	2.78033i	0.313503	+	0.227774i	−0.419895	+	0.907573i	$0.637933\pi$
$150$	11.0594	−	1.57550i	0.903000	−	0.128639i
$151$	13.8281	−	10.0467i	1.12531	−	0.817586i	0.140305	−	0.990108i	$-0.455192\pi$
$151$	13.8281	−	10.0467i	1.12531	−	0.817586i	0.985006	+	0.172522i	$0.0551916\pi$
$152$	0.627653	+	2.44455i	0.0509093	+	0.198279i
$153$	−6.43896	+	6.85680i	−0.520559	+	0.554339i
$154$	3.62017	+	3.39956i	0.291721	+	0.273945i
$155$	2.03209	+	4.23109i	0.163221	+	0.339849i
$156$	13.8597	−	1.75088i	1.10966	−	0.140183i
$157$	−5.21672	−	1.69501i	−0.416339	−	0.135277i	0.0933541	−	0.995633i	$-0.470241\pi$
$157$	−5.21672	−	1.69501i	−0.416339	−	0.135277i	−0.509693	+	0.860356i	$0.670241\pi$
$158$	−2.35882	+	4.29067i	−0.187657	+	0.341348i
$159$	0.848832	+	13.4918i	0.0673168	+	1.06997i
$160$	−0.143584	−	18.1267i	−0.0113513	−	1.43304i
$161$	−6.04448	−	9.52457i	−0.476371	−	0.750641i
$162$	0.0481103	−	0.187377i	0.00377991	−	0.0147218i
$163$	8.35545	+	21.1035i	0.654450	+	1.65295i	0.753162	+	0.657835i	$0.228528\pi$
$163$	8.35545	+	21.1035i	0.654450	+	1.65295i	−0.0987125	+	0.995116i	$0.531472\pi$
$164$	3.78367	−	0.971481i	0.295455	−	0.0758599i
$165$	2.29095	+	0.418242i	0.178350	+	0.0325601i
$166$	12.0045	−	4.75291i	0.931728	−	0.368897i
$167$	3.97833	−	1.87206i	0.307852	−	0.144864i	−0.265647	−	0.964070i	$-0.585586\pi$
$167$	3.97833	−	1.87206i	0.307852	−	0.144864i	0.573499	+	0.819206i	$0.305586\pi$
$168$	−1.59829	+	0.519315i	−0.123310	+	0.0400660i
$169$	3.50423	−	18.3698i	0.269556	−	1.41306i
$170$	21.9770	−	8.90333i	1.68556	−	0.682854i
$171$	3.13683	−	6.66610i	0.239879	−	0.509769i
$172$	18.8497	−	3.59578i	1.43728	−	0.274175i
$173$	−2.52148	−	2.08595i	−0.191705	−	0.158592i	0.536620	−	0.843824i	$-0.319701\pi$
$173$	−2.52148	−	2.08595i	−0.191705	−	0.158592i	−0.728325	+	0.685232i	$0.759701\pi$
$174$	−2.67254	−	8.22523i	−0.202605	−	0.623553i
$175$	0.196064	+	12.3752i	0.0148210	+	0.935480i
$176$	0.986142	−	3.03503i	0.0743333	−	0.228774i
$177$	8.81904	−	5.59673i	0.662880	−	0.420676i
$178$	5.49771	+	10.0003i	0.412071	+	0.749554i
$179$	−3.45804	−	18.1277i	−0.258466	−	1.35493i	−0.840522	−	0.541777i	$-0.817752\pi$
$179$	−3.45804	−	18.1277i	−0.258466	−	1.35493i	0.582056	−	0.813148i	$-0.302248\pi$
$180$	5.98463	−	7.35197i	0.446068	−	0.547984i
$181$	0.249418	−	0.234219i	0.0185391	−	0.0174094i	−0.675222	−	0.737614i	$-0.735952\pi$
$181$	0.249418	−	0.234219i	0.0185391	−	0.0174094i	0.693761	+	0.720205i	$0.255952\pi$
$182$			28.9137i			2.14323i
$183$	−7.63047	−	8.12563i	−0.564061	−	0.600664i
$184$	1.53934	−	2.42561i	0.113481	−	0.178818i
$185$	−2.11490	+	0.149885i	−0.155491	+	0.0110198i
$186$	−4.36055	−	1.72647i	−0.319731	−	0.126591i
$187$	4.93343	−	0.310385i	0.360768	−	0.0226976i
$188$	20.6713	−	1.30053i	1.50761	−	0.0948506i
$189$	11.9970	+	4.74997i	0.872656	+	0.345509i
$190$	−14.2159	+	11.9513i	−1.03133	+	0.867039i
$191$	5.85454	−	9.22529i	0.423620	−	0.667518i	−0.563751	−	0.825945i	$-0.690642\pi$
$191$	5.85454	−	9.22529i	0.423620	−	0.667518i	0.987371	+	0.158427i	$0.0506422\pi$
$192$	7.53312	+	8.02196i	0.543656	+	0.578935i
$193$			15.0520i			1.08347i	0.840550	+	0.541735i	$0.182232\pi$
$193$			15.0520i			1.08347i	−0.840550	+	0.541735i	$0.817768\pi$
$194$	−8.73683	+	8.20443i	−0.627268	+	0.589044i
$195$	7.35558	+	11.3901i	0.526744	+	0.815662i
$196$	0.376704	+	1.97475i	0.0269074	+	0.141054i
$197$	−1.98117	−	3.60373i	−0.141152	−	0.256755i	0.796276	−	0.604934i	$-0.206800\pi$
$197$	−1.98117	−	3.60373i	−0.141152	−	0.256755i	−0.937428	+	0.348178i	$0.886800\pi$
$198$	3.11711	−	1.97818i	0.221523	−	0.140583i
$199$	3.06530	−	9.43402i	0.217293	−	0.668760i	−0.781690	−	0.623668i	$-0.785642\pi$
$199$	3.06530	−	9.43402i	0.217293	−	0.668760i	0.998983	−	0.0450921i	$-0.0143581\pi$
$200$	−2.83038	+	1.38706i	−0.200138	+	0.0980798i
$201$	2.37634	+	7.31363i	0.167614	+	0.515864i
$202$	−9.99323	−	8.26712i	−0.703121	−	0.581673i
$203$	9.41222	−	1.79548i	0.660608	−	0.126018i
$204$	−5.39999	+	11.4756i	−0.378075	+	0.803450i
$205$	2.43982	+	2.90212i	0.170404	+	0.202693i
$206$	−2.99348	+	15.6924i	−0.208566	+	1.09334i
$207$	−7.97555	+	2.59141i	−0.554339	+	0.180116i
$208$	16.8115	−	7.91091i	1.16567	−	0.548523i
$209$	−3.59980	+	1.42526i	−0.249004	+	0.0985875i
$210$	−8.53664	−	8.94750i	−0.589084	−	0.617436i
$211$	1.41052	−	0.362161i	0.0971045	−	0.0249322i	−0.199825	−	0.979832i	$-0.564037\pi$
$211$	1.41052	−	0.362161i	0.0971045	−	0.0249322i	0.296929	+	0.954899i	$0.404037\pi$
$212$	−10.6459	−	26.8885i	−0.731165	−	1.84671i
$213$	0.762980	−	2.97161i	0.0522785	−	0.203611i
$214$	−12.0590	−	19.0020i	−0.824338	−	1.29895i
$215$	11.0664	+	14.9807i	0.754725	+	1.02167i
$216$	0.206331	+	3.27954i	0.0140391	+	0.223145i
$217$	2.50323	−	4.55335i	0.169930	−	0.309102i
$218$	−25.8336	−	8.39383i	−1.74967	−	0.568502i
$219$	9.82761	−	1.24152i	0.664088	−	0.0838939i
$220$	−4.93751	+	0.663528i	−0.332887	+	0.0447350i
$221$	20.9797	+	19.7013i	1.41125	+	1.32525i
$222$	1.45018	−	1.54429i	0.0973299	−	0.103646i
$223$	−6.27790	−	24.4508i	−0.420399	−	1.63735i	−0.727817	−	0.685772i	$-0.759465\pi$
$223$	−6.27790	−	24.4508i	−0.420399	−	1.63735i	0.307418	−	0.951575i	$-0.400535\pi$
$224$	−16.2346	+	11.7951i	−1.08472	+	0.788097i
$225$	8.94693	+	2.14670i	0.596462	+	0.143113i
$226$	−34.5034	−	25.0682i	−2.29513	−	1.66751i
$227$	−2.20611	+	5.57200i	−0.146425	+	0.369827i	−0.984416	−	0.175857i	$-0.943730\pi$
$227$	−2.20611	+	5.57200i	−0.146425	+	0.369827i	0.837991	+	0.545684i	$0.183730\pi$
$228$	1.24500	−	9.85516i	0.0824519	−	0.652674i
$229$	−25.4968	+	14.0170i	−1.68488	+	0.926269i	−0.709801	+	0.704402i	$0.751215\pi$
$229$	−25.4968	+	14.0170i	−1.68488	+	0.926269i	−0.975077	+	0.221867i	$0.928785\pi$
$230$	20.9939	+	2.48337i	1.38430	+	0.163748i
$231$	−1.09767	−	2.33267i	−0.0722214	−	0.153478i
$232$	1.43433	+	1.97418i	0.0941681	+	0.129611i
$233$	3.28038	+	25.9669i	0.214905	+	1.70115i	0.618153	+	0.786058i	$0.287881\pi$
$233$	3.28038	+	25.9669i	0.214905	+	1.70115i	−0.403248	+	0.915091i	$0.632119\pi$
$234$	20.8191	+	5.34543i	1.36099	+	0.349442i
$235$	9.82374	+	17.5388i	0.640830	+	1.14410i
$236$	−14.2429	+	17.2167i	−0.927136	+	1.12071i
$237$	1.95847	−	1.62019i	0.127216	−	0.105242i
$238$	−22.1632	−	14.0652i	−1.43663	−	0.911712i
$239$	−0.0203514	+	0.323477i	−0.00131642	+	0.0209240i	−0.998630	−	0.0523251i	$-0.983337\pi$
$239$	−0.0203514	+	0.323477i	−0.00131642	+	0.0209240i	0.997314	+	0.0732490i	$0.0233368\pi$
$240$	−2.86676	+	7.41159i	−0.185048	+	0.478416i
$241$	−2.89804	−	3.50313i	−0.186679	−	0.225656i	0.668868	−	0.743381i	$-0.266779\pi$
$241$	−2.89804	−	3.50313i	−0.186679	−	0.225656i	−0.855547	+	0.517725i	$0.826779\pi$
$242$	20.5103	+	3.91256i	1.31846	+	0.251509i
$243$	9.13271	−	12.5701i	0.585863	−	0.806372i
$244$	20.8961	+	11.4877i	1.33773	+	0.735426i
$245$	−1.56942	+	1.15935i	−0.100266	+	0.0740683i
$246$	−3.75843	−	0.474800i	−0.239629	−	0.0302722i
$247$	−20.3962	−	9.59775i	−1.29778	−	0.610690i
$248$	1.32066	+	0.0830892i	0.0838623	+	0.00527617i
$249$	−6.70243			−0.424749
$250$	−18.2179	−	14.3559i	−1.15220	−	0.907947i
$251$	29.9788			1.89224			0.946122	−	0.323810i	$-0.104964\pi$
$251$	29.9788			1.89224			0.946122	+	0.323810i	$0.104964\pi$
$252$	−10.4736	−	0.658943i	−0.659775	−	0.0415095i
$253$	3.98762	+	1.87643i	0.250700	+	0.117970i
$254$	−3.21862	−	0.406607i	−0.201954	−	0.0255128i
$255$	−12.3090	+	0.0975010i	−0.770818	+	0.00610575i
$256$	8.84609	+	4.86318i	0.552881	+	0.303949i
$257$	−7.74487	+	10.6599i	−0.483112	+	0.664946i	−0.979099	−	0.203383i	$-0.934806\pi$
$257$	−7.74487	+	10.6599i	−0.483112	+	0.664946i	0.495987	+	0.868330i	$0.334806\pi$
$258$	−18.2799	−	3.48708i	−1.13806	−	0.217096i
$259$	1.49610	+	1.80847i	0.0929629	+	0.112373i
$260$	−22.4948	−	18.3112i	−1.39507	−	1.13561i
$261$	0.447268	−	7.10913i	0.0276852	−	0.440044i
$262$	−37.7041	−	23.9278i	−2.32937	−	1.47826i
$263$	3.22408	−	2.66719i	0.198805	−	0.164466i	−0.532695	−	0.846307i	$-0.678821\pi$
$263$	3.22408	−	2.66719i	0.198805	−	0.164466i	0.731500	+	0.681841i	$0.238821\pi$
$264$	0.418496	−	0.505874i	0.0257566	−	0.0311344i
$265$	19.0514	−	20.6125i	1.17032	−	1.26621i
$266$	19.9137	+	5.11297i	1.22099	+	0.313496i
$267$	−0.742489	−	5.87741i	−0.0454396	−	0.359692i
$268$	−9.66955	−	13.3090i	−0.590662	−	0.812976i
$269$	−2.62134	−	5.57062i	−0.159826	−	0.339647i	0.808835	−	0.588036i	$-0.200099\pi$
$269$	−2.62134	−	5.57062i	−0.159826	−	0.339647i	−0.968660	+	0.248389i	$0.920099\pi$
$270$	−21.0969	+	11.8167i	−1.28392	+	0.719142i
$271$	−23.1446	+	12.7239i	−1.40593	+	0.772919i	−0.990605	−	0.136752i	$-0.956334\pi$
$271$	−23.1446	+	12.7239i	−1.40593	+	0.772919i	−0.415329	+	0.909671i	$0.636334\pi$
$272$	−2.11410	+	16.7348i	−0.128186	+	1.01470i
$273$	5.52544	−	13.9557i	0.334415	−	0.844635i
$274$	34.2198	+	24.8622i	2.06729	+	1.50198i
$275$	−2.65523	−	4.04101i	−0.160116	−	0.243682i
$276$	−9.14762	+	6.64613i	−0.550622	+	0.400050i
$277$	−0.0853708	−	0.332497i	−0.00512943	−	0.0199778i	0.965967	−	0.258666i	$-0.0832828\pi$
$277$	−0.0853708	−	0.332497i	−0.00512943	−	0.0199778i	−0.971096	+	0.238688i	$0.923283\pi$
$278$	7.51568	−	8.00338i	0.450760	−	0.480011i
$279$	−2.81582	−	2.64423i	−0.168578	−	0.158306i
$280$	3.07090	+	1.65670i	0.183522	+	0.0990070i
$281$	5.37410	−	0.678906i	0.320592	−	0.0405002i	0.0366094	−	0.999330i	$-0.488344\pi$
$281$	5.37410	−	0.678906i	0.320592	−	0.0405002i	0.283982	+	0.958829i	$0.408344\pi$
$282$	−19.1029	−	6.20692i	−1.13756	−	0.369617i
$283$	3.04738	−	5.54317i	0.181148	−	0.329507i	−0.770106	−	0.637916i	$-0.779797\pi$
$283$	3.04738	−	5.54317i	0.181148	−	0.329507i	0.951254	+	0.308409i	$0.0997966\pi$
$284$	0.412107	+	6.55025i	0.0244540	+	0.388686i
$285$	9.14541	−	3.05182i	0.541727	−	0.180774i
$286$	−6.05262	−	9.53740i	−0.357899	−	0.563958i
$287$	1.04379	−	4.06531i	0.0616132	−	0.239968i
$288$	5.49161	+	13.8702i	0.323596	+	0.817311i
$289$	−8.84134	+	2.27007i	−0.520079	+	0.133534i
$290$	−8.52586	+	15.8037i	−0.500656	+	0.928027i
$291$	5.78484	−	2.29038i	0.339113	−	0.134264i
$292$	−19.1740	+	9.02259i	−1.12207	+	0.528007i
$293$	−2.21595	+	0.720007i	−0.129457	+	0.0420633i	−0.373029	−	0.927820i	$-0.621681\pi$
$293$	−2.21595	+	0.720007i	−0.129457	+	0.0420633i	0.243572	+	0.969883i	$0.421681\pi$
$294$	0.365316	−	1.91505i	0.0213057	−	0.111688i
$295$	−21.0477	−	5.22677i	−1.22544	−	0.304314i
$296$	−0.254502	+	0.540844i	−0.0147926	+	0.0314359i
$297$	−4.95163	+	0.944575i	−0.287323	+	0.0548098i
$298$	7.56114	+	6.25512i	0.438005	+	0.362349i
$299$	7.92894	+	24.4028i	0.458543	+	1.41125i
$300$	12.3674	−	0.975003i	0.714033	−	0.0562918i
$301$	6.37132	−	19.6089i	0.367237	−	1.13024i
$302$	29.9395	−	19.0002i	1.72282	−	1.09334i
$303$	3.24353	+	5.89996i	0.186336	+	0.338944i
$304$	−2.47559	−	12.9775i	−0.141985	−	0.744311i
$305$	−1.27021	+	23.1090i	−0.0727322	+	1.32322i
$306$	−14.2250	+	13.3581i	−0.813186	+	0.763633i
$307$			19.0428i			1.08683i	0.839464	+	0.543416i	$0.182869\pi$
$307$			19.0428i			1.08683i	−0.839464	+	0.543416i	$0.817131\pi$
$308$	3.77530	+	4.02028i	0.215118	+	0.229077i
$309$	4.44368	−	7.00211i	0.252792	−	0.398336i
$310$	3.65625	+	9.02510i	0.207661	+	0.512591i
$311$	−1.84698	−	0.731272i	−0.104733	−	0.0414666i	0.315174	−	0.949034i	$-0.397937\pi$
$311$	−1.84698	−	0.731272i	−0.104733	−	0.0414666i	−0.419907	+	0.907567i	$0.637937\pi$
$312$	3.81495	−	0.240017i	0.215979	−	0.0135883i
$313$	23.5612	−	1.48235i	1.33176	−	0.0837872i	0.619108	−	0.785306i	$-0.287494\pi$
$313$	23.5612	−	1.48235i	1.33176	−	0.0837872i	0.712651	+	0.701519i	$0.247494\pi$
$314$	−10.5803	−	4.18904i	−0.597082	−	0.236401i
$315$	−3.82442	−	9.44022i	−0.215482	−	0.531896i
$316$	−2.91354	+	4.59101i	−0.163900	+	0.258265i
$317$	−5.62830	−	5.99354i	−0.316117	−	0.336631i	0.551212	−	0.834365i	$-0.314165\pi$
$317$	−5.62830	−	5.99354i	−0.316117	−	0.336631i	−0.867329	+	0.497734i	$0.834165\pi$
$318$			28.0451i			1.57269i
$319$	−2.72883	+	2.56254i	−0.152785	+	0.143475i
$320$	1.25401	−	22.8142i	0.0701011	−	1.27535i
$321$	2.18918	+	11.4761i	0.122188	+	0.640532i
$322$	−11.2743	−	20.5078i	−0.628291	−	1.14286i
$323$	17.2788	−	10.9654i	0.961417	−	0.610134i
$324$	0.0663882	−	0.204322i	0.00368823	−	0.0113512i
$325$	6.56825	−	27.3749i	0.364341	−	1.51849i
$326$	14.5508	+	44.7828i	0.805895	+	2.48029i
$327$	10.8649	+	8.98822i	0.600830	+	0.497050i
$328$	1.04995	−	0.200290i	0.0579740	−	0.0110591i
$329$	9.47524	−	20.1359i	0.522387	−	1.11013i
$330$	4.68888	+	1.16439i	0.258114	+	0.0640976i
$331$	−4.95887	+	25.9953i	−0.272564	+	1.42883i	0.537882	+	0.843020i	$0.319225\pi$
$331$	−4.95887	+	25.9953i	−0.272564	+	1.42883i	−0.810447	+	0.585813i	$0.800775\pi$
$332$	13.6364	−	4.43073i	0.748394	−	0.243168i
$333$	1.57876	−	0.742910i	0.0865157	−	0.0407112i
$334$	8.48092	−	3.35783i	0.464055	−	0.183733i
$335$	7.58095	−	14.0522i	0.414191	−	0.767754i
$336$	8.52072	−	2.18775i	0.464844	−	0.119352i
$337$	0.589518	+	1.48895i	0.0321131	+	0.0811085i	0.944948	−	0.327220i	$-0.106112\pi$
$337$	0.589518	+	1.48895i	0.0321131	+	0.0811085i	−0.912835	+	0.408328i	$0.866112\pi$
$338$	9.64837	−	37.5779i	0.524802	−	2.04397i
$339$	11.8630	+	18.6931i	0.644312	+	1.01527i
$340$	24.9787	−	8.33539i	1.35466	−	0.452050i
$341$	0.127463	+	2.02596i	0.00690250	+	0.109712i
$342$	7.36310	−	13.3934i	0.398151	−	0.724234i
$343$	18.5337	+	6.02197i	1.00073	+	0.325156i
$344$	5.20936	−	0.658095i	0.280870	−	0.0354821i
$345$	−9.65845	−	5.21058i	−0.519994	−	0.280528i
$346$	−4.94896	−	4.64738i	−0.266058	−	0.249845i
$347$	−14.8985	+	15.8653i	−0.799795	+	0.851695i	−0.991547	−	0.129749i	$-0.958583\pi$
$347$	−14.8985	+	15.8653i	−0.799795	+	0.851695i	0.191752	+	0.981443i	$0.438583\pi$
$348$	−2.38851	−	9.30265i	−0.128038	−	0.498674i
$349$	−3.51231	+	2.55184i	−0.188010	+	0.136597i	−0.677809	−	0.735238i	$-0.737070\pi$
$349$	−3.51231	+	2.55184i	−0.188010	+	0.136597i	0.489799	+	0.871835i	$0.337070\pi$
$350$	−1.20610	+	25.6483i	−0.0644686	+	1.37096i
$351$	−23.7439	−	17.2510i	−1.26736	−	0.920788i
$352$	2.88598	−	7.28916i	0.153823	−	0.388514i
$353$	−0.972216	+	7.69588i	−0.0517458	+	0.409610i	0.944872	+	0.327439i	$0.106186\pi$
$353$	−0.972216	+	7.69588i	−0.0517458	+	0.409610i	−0.996618	+	0.0821715i	$0.973814\pi$
$354$	18.9887	−	10.4391i	1.00924	−	0.554834i
$355$	−5.55764	+	3.11292i	−0.294969	+	0.165216i
$356$	5.39597	+	11.4670i	0.285986	+	0.607750i
$357$	8.00954	+	11.0242i	0.423910	+	0.583462i
$358$	−4.79843	−	37.9835i	−0.253605	−	2.00749i
$359$	2.36327	+	0.606785i	0.124729	+	0.0320249i	0.310538	−	0.950561i	$-0.399491\pi$
$359$	2.36327	+	0.606785i	0.124729	+	0.0320249i	−0.185810	+	0.982586i	$0.559491\pi$
$360$	1.76063	−	1.90489i	0.0927933	−	0.100397i
$361$	1.89404	−	2.28950i	0.0996865	−	0.120500i
$362$	0.546926	−	0.452456i	0.0287458	−	0.0237806i
$363$	−9.15194	−	5.80800i	−0.480352	−	0.304841i
$364$	−2.01617	+	32.0461i	−0.105676	+	1.67967i
$365$	−15.9506	−	12.9841i	−0.834893	−	0.679617i
$366$	−14.7403	−	17.8179i	−0.770487	−	0.931359i
$367$	−24.5602	−	4.68511i	−1.28203	−	0.244561i	−0.499033	−	0.866583i	$-0.666312\pi$
$367$	−24.5602	−	4.68511i	−1.28203	−	0.244561i	−0.783000	+	0.622022i	$0.786312\pi$
$368$	−8.83933	+	12.1663i	−0.460782	+	0.634212i
$369$	−2.73422	−	1.50315i	−0.142338	−	0.0782508i
$370$	−4.39839	+	0.0348402i	−0.228661	+	0.00181126i
$371$	−30.8270	−	3.89435i	−1.60046	−	0.202185i
$372$	−4.71256	−	2.21756i	−0.244335	−	0.114975i
$373$	−3.08182	−	0.193892i	−0.159571	−	0.0100393i	−0.0171958	−	0.999852i	$-0.505474\pi$
$373$	−3.08182	−	0.193892i	−0.159571	−	0.0100393i	−0.142375	+	0.989813i	$0.545474\pi$
$374$	10.2550			0.530274
$375$	6.04972	+	10.4105i	0.312406	+	0.537598i
$376$	5.66736			0.292272
$377$	−21.7518	−	1.36851i	−1.12027	−	0.0704816i
$378$	24.2209	+	11.3975i	1.24579	+	0.586224i
$379$	24.8799	+	3.14306i	1.27799	+	0.161448i	0.734872	−	0.678206i	$-0.237242\pi$
$379$	24.8799	+	3.14306i	1.27799	+	0.161448i	0.543121	+	0.839654i	$0.317242\pi$
$380$	−16.5893	+	12.2548i	−0.851012	+	0.628656i
$381$	1.47581	+	0.811336i	0.0756083	+	0.0415660i
$382$	13.3235	−	18.3382i	0.681687	−	0.938262i
$383$	−14.7083	−	2.80576i	−0.751561	−	0.143368i	−0.202653	−	0.979251i	$-0.564956\pi$
$383$	−14.7083	−	2.80576i	−0.751561	−	0.143368i	−0.548908	+	0.835883i	$0.684956\pi$
$384$	3.42205	+	4.13655i	0.174631	+	0.211093i
$385$	−1.93099	+	4.99230i	−0.0984123	+	0.254431i
$386$	−1.96073	+	31.1650i	−0.0997987	+	1.58626i
$387$	−12.9413	−	8.21281i	−0.657844	−	0.417481i
$388$	−10.2554	+	8.48402i	−0.520640	+	0.430711i
$389$	3.71308	−	4.48835i	0.188261	−	0.227568i	−0.667935	−	0.744220i	$-0.732822\pi$
$389$	3.71308	−	4.48835i	0.188261	−	0.227568i	0.856196	+	0.516651i	$0.172822\pi$
$390$	13.7459	+	24.5412i	0.696049	+	1.24269i
$391$	−22.5625	−	5.79306i	−1.14103	−	0.292968i
$392$	0.0689439	+	0.545747i	0.00348219	+	0.0275644i
$393$	13.6259	+	18.7544i	0.687334	+	0.946033i
$394$	−3.63254	−	7.71954i	−0.183005	−	0.388905i
$395$	−5.24092	−	0.619948i	−0.263699	−	0.0311930i
$396$	3.59273	−	1.97512i	0.180541	−	0.0992535i
$397$	−3.01660	+	23.8789i	−0.151399	+	1.19845i	0.715011	+	0.699113i	$0.246422\pi$
$397$	−3.01660	+	23.8789i	−0.151399	+	1.19845i	−0.866410	+	0.499333i	$0.833578\pi$
$398$	7.57556	−	19.1337i	0.379728	−	0.959084i
$399$	−8.63456	−	6.27338i	−0.432269	−	0.314062i
$400$	15.2428	−	6.31618i	0.762142	−	0.315809i
$401$	12.0128	−	8.72778i	0.599888	−	0.435844i	−0.245951	−	0.969282i	$-0.579100\pi$
$401$	12.0128	−	8.72778i	0.599888	−	0.435844i	0.845839	+	0.533438i	$0.179100\pi$
$402$	3.96748	+	15.4523i	0.197880	+	0.770691i
$403$	−8.09053	+	8.61554i	−0.403018	+	0.429171i
$404$	−10.4994	−	9.85955i	−0.522363	−	0.490531i
$405$	0.206657	−	0.0277715i	0.0102689	−	0.00137998i
$406$	19.7217	−	2.49143i	0.978773	−	0.123648i
$407$	−0.872071	−	0.283353i	−0.0432269	−	0.0140453i
$408$	−1.67182	+	3.04103i	−0.0827674	+	0.150553i
$409$	−1.29390	−	20.5660i	−0.0639794	−	1.01692i	−0.890782	−	0.454431i	$-0.849842\pi$
$409$	−1.29390	−	20.5660i	−0.0639794	−	1.01692i	0.826802	−	0.562493i	$-0.190158\pi$
$410$	4.67355	+	6.32660i	0.230810	+	0.312449i
$411$	−11.7655	−	18.5395i	−0.580351	−	0.914487i
$412$	−4.41201	+	17.1837i	−0.217364	+	0.846578i
$413$	8.83784	+	22.3218i	0.434882	+	1.09839i
$414$	−16.8508	+	4.32655i	−0.828172	+	0.212639i
$415$	9.60634	+	10.0687i	0.471557	+	0.494253i
$416$	42.4387	−	16.8027i	2.08073	−	0.823819i
$417$	−5.15701	+	2.42670i	−0.252540	+	0.118836i
$418$	−7.63899	+	2.48206i	−0.373635	+	0.121401i
$419$	5.17607	−	27.1339i	0.252868	−	1.32558i	−0.598548	−	0.801087i	$-0.704255\pi$
$419$	5.17607	−	27.1339i	0.252868	−	1.32558i	0.851415	−	0.524492i	$-0.175745\pi$
$420$	−8.83753	−	10.5121i	−0.431227	−	0.512937i
$421$	−7.09738	+	15.0827i	−0.345905	+	0.735086i	−0.999768	−	0.0215269i	$-0.993147\pi$
$421$	−7.09738	+	15.0827i	−0.345905	+	0.735086i	0.653863	+	0.756613i	$0.273147\pi$
$422$	2.96764	−	0.566108i	0.144463	−	0.0275577i
$423$	−12.7469	−	10.5452i	−0.619777	−	0.512725i
$424$	−2.44527	−	7.52577i	−0.118753	−	0.365484i
$425$	17.7885	+	18.3514i	0.862868	+	0.890172i
$426$	1.96683	−	6.05328i	0.0952932	−	0.293282i
$427$	21.6322	−	13.7282i	1.04686	−	0.664355i
$428$	−12.0404	−	21.9014i	−0.581994	−	1.05864i
$429$	1.09878	+	5.76003i	0.0530498	+	0.278097i
$430$	20.9614	+	32.4588i	1.01085	+	1.56530i
$431$	−2.17462	+	2.04211i	−0.104748	+	0.0983649i	−0.735152	−	0.677902i	$-0.762889\pi$
$431$	−2.17462	+	2.04211i	−0.104748	+	0.0983649i	0.630404	+	0.776267i	$0.282889\pi$
$432$		−	17.2013i		−	0.827600i
$433$	−10.0071	−	10.6564i	−0.480909	−	0.512116i	0.442063	−	0.896984i	$-0.354247\pi$
$433$	−10.0071	−	10.6564i	−0.480909	−	0.512116i	−0.922971	+	0.384868i	$0.874247\pi$
$434$	5.77602	−	9.10156i	0.277258	−	0.436889i
$435$	7.13524	−	5.99861i	0.342109	−	0.287611i
$436$	−28.0469	−	11.1045i	−1.34320	−	0.531811i
$437$	18.2090	−	1.14561i	0.871054	−	0.0548021i
$438$	20.5096	−	1.29036i	0.979988	−	0.0616556i
$439$	−10.5295	−	4.16891i	−0.502544	−	0.198971i	0.103155	−	0.994665i	$-0.467106\pi$
$439$	−10.5295	−	4.16891i	−0.502544	−	0.198971i	−0.605699	+	0.795694i	$0.707106\pi$
$440$	−1.35976	+	0.0963678i	−0.0648241	+	0.00459416i
$441$	0.860397	−	1.35577i	0.0409713	−	0.0645604i
$442$	40.8718	+	43.5240i	1.94407	+	2.07023i
$443$		−	16.9234i		−	0.804056i	−0.915627	−	0.402028i	$-0.868305\pi$
$443$		−	16.9234i		−	0.804056i	0.915627	−	0.402028i	$-0.131695\pi$
$444$	1.71497	−	1.61046i	0.0813888	−	0.0764292i
$445$	−7.76513	+	9.53927i	−0.368102	+	0.452205i
$446$	−9.81322	−	51.4427i	−0.464670	−	2.43588i
$447$	−2.45414	−	4.46407i	−0.116077	−	0.211143i
$448$	−21.3562	+	13.5531i	−1.00899	+	0.640322i
$449$	−8.52440	+	26.2354i	−0.402291	+	1.23813i	0.520844	+	0.853652i	$0.325617\pi$
$449$	−8.52440	+	26.2354i	−0.402291	+	1.23813i	−0.923136	+	0.384474i	$0.874383\pi$
$450$	18.2448	+	5.61016i	0.860069	+	0.264466i
$451$	0.506703	+	1.55947i	0.0238597	+	0.0734326i
$452$	−36.4932	−	30.1898i	−1.71650	−	1.42001i
$453$	−18.0817	+	3.44926i	−0.849551	+	0.162061i
$454$	−5.29355	+	11.2494i	−0.248439	+	0.527959i
$455$	−28.8842	+	11.7016i	−1.35411	+	0.548578i
$456$	0.509312	−	2.66991i	0.0238507	−	0.125030i
$457$	32.5715	−	10.5831i	1.52363	−	0.495058i	0.576826	−	0.816867i	$-0.304291\pi$
$457$	32.5715	−	10.5831i	1.52363	−	0.495058i	0.946805	+	0.321809i	$0.104291\pi$
$458$	−54.6167	+	25.7006i	−2.55207	+	1.20091i
$459$	24.7737	−	9.80859i	1.15634	−	0.457826i
$460$	23.0951	+	4.21631i	1.07681	+	0.196586i
$461$	22.4971	−	5.77628i	1.04779	−	0.269028i	0.314726	−	0.949183i	$-0.398087\pi$
$461$	22.4971	−	5.77628i	1.04779	−	0.269028i	0.733069	+	0.680155i	$0.238087\pi$
$462$	−1.96884	−	4.97273i	−0.0915990	−	0.231353i
$463$	2.03747	−	7.93544i	0.0946895	−	0.368791i	−0.903524	−	0.428537i	$-0.859029\pi$
$463$	2.03747	−	7.93544i	0.0946895	−	0.368791i	0.998214	+	0.0597460i	$0.0190291\pi$
$464$	−6.84455	−	10.7853i	−0.317750	−	0.500694i
$465$	−0.0400398	−	5.05481i	−0.00185680	−	0.234411i
$466$	3.40943	+	54.1913i	0.157939	+	2.51037i
$467$	13.5913	−	24.7225i	0.628931	−	1.14402i	−0.349400	−	0.936974i	$-0.613615\pi$
$467$	13.5913	−	24.7225i	0.628931	−	1.14402i	0.978331	−	0.207047i	$-0.0663853\pi$
$468$	22.7017	+	7.37624i	1.04939	+	0.340967i
$469$	−17.5360	+	2.21531i	−0.809736	+	0.102293i
$470$	18.0552	+	37.5934i	0.832825	+	1.73406i
$471$	4.30622	+	4.04381i	0.198420	+	0.186329i
$472$	−4.18533	+	4.45693i	−0.192646	+	0.205147i
$473$	2.00318	+	7.80186i	0.0921062	+	0.358730i
$474$	4.26603	−	3.09945i	0.195945	−	0.142362i
$475$	−17.6924	−	9.36459i	−0.811781	−	0.429677i
$476$	−23.5834	−	17.1344i	−1.08095	−	0.785353i
$477$	−8.50324	+	21.4767i	−0.389336	+	0.983352i
$478$	−0.0842745	+	0.667102i	−0.00385463	+	0.0305125i
$479$	−13.2280	+	7.27215i	−0.604402	+	0.332273i	−0.754402	−	0.656413i	$-0.772073\pi$
$479$	−13.2280	+	7.27215i	−0.604402	+	0.332273i	0.149999	+	0.988686i	$0.452073\pi$
$480$	−8.17197	+	17.7295i	−0.372998	+	0.809237i
$481$	−2.27308	−	4.83054i	−0.103643	−	0.220254i
$482$	−5.54401	−	7.63067i	−0.252523	−	0.347568i
$483$	1.52264	+	12.0529i	0.0692825	+	0.548428i
$484$	22.4595	+	5.76661i	1.02088	+	0.262119i
$485$	−11.7319	−	5.40753i	−0.532718	−	0.245543i
$486$	20.5465	−	24.8365i	0.932010	−	1.12661i
$487$	8.25163	−	6.82635i	0.373917	−	0.309331i	−0.431417	−	0.902153i	$-0.641986\pi$
$487$	8.25163	−	6.82635i	0.373917	−	0.309331i	0.805334	+	0.592822i	$0.201986\pi$
$488$	5.50904	+	3.49614i	0.249383	+	0.158263i
$489$	1.53485	−	24.3957i	0.0694083	−	1.10321i
$490$	−3.40047	+	2.19598i	−0.153618	+	0.0992043i
$491$	−13.3963	−	16.1933i	−0.604565	−	0.730794i	0.376080	−	0.926587i	$-0.377272\pi$
$491$	−13.3963	−	16.1933i	−0.604565	−	0.730794i	−0.980645	+	0.195793i	$0.937272\pi$
$492$	−4.13249	−	0.788314i	−0.186307	−	0.0355399i
$493$	11.6302	−	16.0076i	0.523799	−	0.720948i
$494$	−40.9798	−	22.5289i	−1.84377	−	1.01362i
$495$	3.23767	+	2.31334i	0.145522	+	0.103977i
$496$	−6.87232	−	0.868176i	−0.308576	−	0.0389823i
$497$	6.38060	+	3.00248i	0.286209	+	0.134680i
$498$	−13.8773	−	0.873083i	−0.621855	−	0.0391238i
$499$	1.98167			0.0887118			0.0443559	−	0.999016i	$-0.485876\pi$
$499$	1.98167			0.0887118			0.0443559	+	0.999016i	$0.485876\pi$
$500$	−19.1904	−	17.1815i	−0.858223	−	0.768378i
$501$	−4.73513			−0.211550
$502$	62.0706	+	3.90515i	2.77034	+	0.174295i
$503$	−10.8563	−	5.10857i	−0.484057	−	0.227780i	0.168236	−	0.985747i	$-0.446193\pi$
$503$	−10.8563	−	5.10857i	−0.484057	−	0.227780i	−0.652293	+	0.757967i	$0.726193\pi$
$504$	−2.84886	−	0.359895i	−0.126899	−	0.0160310i
$505$	4.21436	−	13.3288i	0.187536	−	0.593123i
$506$	8.01187	+	4.40457i	0.356171	+	0.195807i
$507$	−11.8381	+	16.2937i	−0.525748	+	0.723630i
$508$	−3.53895	−	0.675091i	−0.157016	−	0.0299523i
$509$	16.5598	+	20.0174i	0.734000	+	0.887253i	0.996989	−	0.0775454i	$-0.0247083\pi$
$509$	16.5598	+	20.0174i	0.734000	+	0.887253i	−0.262989	+	0.964799i	$0.584708\pi$
$510$	−25.4982	−	1.40154i	−1.12908	−	0.0620612i
$511$	−1.42962	+	22.7232i	−0.0632428	+	1.00522i
$512$	26.1001	+	16.5636i	1.15347	+	0.732015i
$513$	−16.0800	+	13.3025i	−0.709948	+	0.587320i
$514$	−17.4242	+	21.0623i	−0.768549	+	0.929017i
$515$	−16.8878	+	3.36038i	−0.744168	+	0.148076i
$516$	−20.0170	−	5.13950i	−0.881201	−	0.226254i
$517$	1.08965	+	8.62545i	0.0479227	+	0.379347i
$518$	2.86206	+	3.93929i	0.125752	+	0.173083i
$519$	1.50057	+	3.18888i	0.0658678	+	0.139976i
$520$	−5.82840	−	5.38699i	−0.255592	−	0.236235i
$521$	−0.613325	+	0.337178i	−0.0268703	+	0.0147720i	−0.495132	−	0.868818i	$-0.664880\pi$
$521$	−0.613325	+	0.337178i	−0.0268703	+	0.0147720i	0.468262	+	0.883590i	$0.344880\pi$
$522$	1.85212	−	14.6611i	0.0810652	−	0.641697i
$523$	−12.5244	+	31.6329i	−0.547652	+	1.38321i	0.347596	+	0.937644i	$0.386998\pi$
$523$	−12.5244	+	31.6329i	−0.547652	+	1.38321i	−0.895249	+	0.445567i	$0.853002\pi$
$524$	−40.1202	−	29.1491i	−1.75266	−	1.27338i
$525$	5.48354	−	12.1490i	0.239321	−	0.530227i
$526$	7.02284	−	5.10239i	0.306210	−	0.222475i
$527$	−2.66839	−	10.3927i	−0.116237	−	0.452713i
$528$	−2.35265	+	2.50532i	−0.102386	+	0.109030i
$529$	1.62714	+	1.52799i	0.0707454	+	0.0664343i
$530$	42.1306	−	40.1960i	1.83004	−	1.74600i
$531$	17.7065	−	2.23686i	0.768399	−	0.0970713i
$532$	21.7145	+	7.05547i	0.941442	+	0.305893i
$533$	−4.59918	+	8.36588i	−0.199213	+	0.362366i
$534$	−0.771698	−	12.2658i	−0.0333946	−	0.530793i
$535$	14.1022	−	19.7369i	0.609692	−	0.853302i
$536$	−2.41195	−	3.80062i	−0.104180	−	0.164162i
$537$	−4.94263	+	19.2503i	−0.213290	+	0.830711i
$538$	−4.70178	−	11.8753i	−0.202708	−	0.511983i
$539$	−0.817345	+	0.209859i	−0.0352055	+	0.00903925i
$540$	−24.2064	+	11.6257i	−1.04168	+	0.500292i
$541$	−1.34570	+	0.532801i	−0.0578562	+	0.0229069i	−0.396874	−	0.917873i	$-0.629905\pi$
$541$	−1.34570	+	0.532801i	−0.0578562	+	0.0229069i	0.339018	+	0.940780i	$0.389905\pi$
$542$	−49.5780	+	23.3296i	−2.12956	+	1.00209i
$543$	−0.350447	+	0.113867i	−0.0150391	+	0.00488650i
$544$	−7.76474	+	40.7042i	−0.332911	+	1.74518i
$545$	−2.06974	−	29.2042i	−0.0886577	−	1.25097i
$546$	13.2582	−	28.1752i	0.567400	−	1.20579i
$547$	−21.3197	+	4.06695i	−0.911565	+	0.173890i	−0.621771	−	0.783199i	$-0.713587\pi$
$547$	−21.3197	+	4.06695i	−0.911565	+	0.173890i	−0.289794	+	0.957089i	$0.593587\pi$
$548$	36.1933	+	29.9417i	1.54610	+	1.27905i
$549$	−5.88562	−	18.1141i	−0.251192	−	0.773090i
$550$	−4.97120	−	8.71273i	−0.211973	−	0.371512i
$551$	−4.78901	+	14.7391i	−0.204019	+	0.627905i
$552$	−2.61227	+	1.65779i	−0.111185	+	0.0705604i
$553$	2.81451	+	5.11958i	0.119685	+	0.217706i
$554$	−0.133446	−	0.699550i	−0.00566959	−	0.0297211i
$555$	2.12961	+	0.823719i	0.0903968	+	0.0349649i
$556$	8.88795	−	8.34634i	0.376933	−	0.353964i
$557$			10.5129i			0.445445i	0.974882	+	0.222723i	$0.0714944\pi$
$557$			10.5129i			0.445445i	−0.974882	+	0.222723i	$0.928506\pi$
$558$	−5.48565	−	5.84163i	−0.232226	−	0.247296i
$559$	−25.1287	+	39.5965i	−1.06283	+	1.67475i
$560$	−15.4990	−	9.66460i	−0.654951	−	0.408404i
$561$	−4.94973	−	1.95974i	−0.208978	−	0.0827402i
$562$	11.2154	−	0.705614i	0.473094	−	0.0297645i
$563$	19.4200	−	1.22180i	0.818454	−	0.0514928i	0.351958	−	0.936016i	$-0.385516\pi$
$563$	19.4200	−	1.22180i	0.818454	−	0.0514928i	0.466496	+	0.884523i	$0.345516\pi$
$564$	−20.7396	−	8.21139i	−0.873294	−	0.345762i
$565$	11.0789	−	44.6134i	0.466091	−	1.87690i
$566$	7.03162	−	11.0801i	0.295561	−	0.465730i
$567$	−0.158013	−	0.168267i	−0.00663591	−	0.00706653i
$568$			1.79586i			0.0753524i
$569$	23.5411	−	22.1066i	0.986894	−	0.926755i	−0.0104240	−	0.999946i	$-0.503318\pi$
$569$	23.5411	−	22.1066i	0.986894	−	0.926755i	0.997318	+	0.0731906i	$0.0233181\pi$
$570$	19.3329	−	5.12742i	0.809768	−	0.214764i
$571$	−1.07735	−	5.64768i	−0.0450858	−	0.236348i	0.952610	−	0.304194i	$-0.0983873\pi$
$571$	−1.07735	−	5.64768i	−0.0450858	−	0.236348i	−0.997696	+	0.0678463i	$0.978387\pi$
$572$	−6.04327	−	10.9927i	−0.252682	−	0.459626i
$573$	−9.93520	+	6.30507i	−0.415049	+	0.263398i
$574$	2.69072	−	8.28118i	0.112308	−	0.345650i
$575$	6.01553	+	21.9775i	0.250865	+	0.916525i
$576$	5.81053	+	17.8830i	0.242105	+	0.745124i
$577$	−3.61362	−	2.98945i	−0.150437	−	0.124452i	0.559161	−	0.829059i	$-0.311123\pi$
$577$	−3.61362	−	2.98945i	−0.150437	−	0.124452i	−0.709598	+	0.704607i	$0.751123\pi$
$578$	−18.6015	+	3.54843i	−0.773722	+	0.147595i
$579$	6.90202	−	14.6675i	0.286838	−	0.609562i
$580$	−10.5515	+	16.9213i	−0.438127	+	0.702618i
$581$	2.88669	−	15.1325i	0.119760	−	0.627804i
$582$	12.2758	−	3.98863i	0.508846	−	0.165334i
$583$	10.9837	−	5.16854i	0.454899	−	0.214059i
$584$	−5.39115	+	2.13451i	−0.223087	+	0.0883265i
$585$	3.08563	+	22.9612i	0.127575	+	0.949327i
$586$	−4.68189	+	1.20210i	−0.193407	+	0.0496585i
$587$	4.05346	+	10.2379i	0.167304	+	0.422562i	0.989105	−	0.147213i	$-0.0470304\pi$
$587$	4.05346	+	10.2379i	0.167304	+	0.422562i	−0.821801	+	0.569775i	$0.807030\pi$
$588$	0.538429	−	2.09704i	0.0222044	−	0.0864806i
$589$	4.50307	+	7.09571i	0.185546	+	0.292374i
$590$	−42.8980	−	13.5637i	−1.76608	−	0.558408i
$591$	0.278091	+	4.42014i	0.0114391	+	0.181820i
$592$	1.50738	−	2.74191i	0.0619529	−	0.112692i
$593$	14.7499	+	4.79255i	0.605708	+	0.196806i	0.595784	−	0.803144i	$-0.296841\pi$
$593$	14.7499	+	4.79255i	0.605708	+	0.196806i	0.00992334	+	0.999951i	$0.496841\pi$
$594$	−10.3753	+	1.31071i	−0.425704	+	0.0537790i
$595$	5.08126	−	27.8329i	0.208311	−	1.14104i
$596$	7.94409	+	7.45999i	0.325403	+	0.305573i
$597$	−7.31291	+	7.78746i	−0.299298	+	0.318720i
$598$	13.2379	+	51.5584i	0.541340	+	2.10838i
$599$	23.2023	−	16.8574i	0.948018	−	0.688776i	−0.00231907	−	0.999997i	$-0.500738\pi$
$599$	23.2023	−	16.8574i	0.948018	−	0.688776i	0.950337	+	0.311222i	$0.100738\pi$
$600$	3.39411	−	0.0537737i	0.138564	−	0.00219530i
$601$	12.6726	+	9.20720i	0.516927	+	0.375569i	0.815445	−	0.578835i	$-0.196492\pi$
$601$	12.6726	+	9.20720i	0.516927	+	0.375569i	−0.298518	+	0.954404i	$0.596492\pi$
$602$	15.7460	−	39.7699i	0.641760	−	1.62090i
$603$	−1.64685	+	13.0362i	−0.0670650	+	0.530874i
$604$	34.5078	−	18.9708i	1.40410	−	0.771911i
$605$	4.39210	+	22.0728i	0.178564	+	0.897389i
$606$	5.94713	+	12.6383i	0.241586	+	0.513395i
$607$	−12.3244	−	16.9631i	−0.500233	−	0.688512i	0.482001	−	0.876171i	$-0.339910\pi$
$607$	−12.3244	−	16.9631i	−0.500233	−	0.688512i	−0.982234	+	0.187659i	$0.939910\pi$
$608$	−4.06781	−	32.2000i	−0.164972	−	1.30588i
$609$	−9.99510	−	2.56631i	−0.405022	−	0.103992i
$610$	−5.64022	+	47.6813i	−0.228366	+	1.93056i
$611$	−32.2651	+	39.0018i	−1.30531	+	1.57784i
$612$	−16.6974	+	13.8133i	−0.674954	+	0.558371i
$613$	9.73322	+	6.17689i	0.393121	+	0.249482i	0.717665	−	0.696388i	$-0.245211\pi$
$613$	9.73322	+	6.17689i	0.393121	+	0.249482i	−0.324544	+	0.945871i	$0.605211\pi$
$614$	−2.48059	+	39.4278i	−0.100108	+	1.59118i
$615$	−1.04674	−	3.94675i	−0.0422088	−	0.159148i
$616$	0.961905	+	1.16274i	0.0387563	+	0.0468483i
$617$	8.80250	+	1.67917i	0.354375	+	0.0676007i	0.361495	−	0.932374i	$-0.382266\pi$
$617$	8.80250	+	1.67917i	0.354375	+	0.0676007i	−0.00711987	+	0.999975i	$0.502266\pi$
$618$	10.1127	−	13.9189i	0.406791	−	0.559900i
$619$	39.6032	+	21.7721i	1.59179	+	0.875093i	0.997487	+	0.0708504i	$0.0225713\pi$
$619$	39.6032	+	21.7721i	1.59179	+	0.875093i	0.594301	+	0.804243i	$0.297429\pi$
$620$	3.42301	+	10.2578i	0.137472	+	0.411962i
$621$	23.5676	+	2.97728i	0.945736	+	0.119474i
$622$	−3.72889	−	1.75468i	−0.149515	−	0.0703563i
$623$	13.5896	+	0.854987i	0.544457	+	0.0342543i
$624$	−20.0096			−0.801025
$625$	6.96835	−	24.0092i	0.278734	−	0.960368i
$626$	48.9762			1.95748
$627$	4.16140	+	0.261813i	0.166190	+	0.0104558i
$628$	−11.4344	−	5.38063i	−0.456283	−	0.214710i
$629$	4.80849	+	0.607454i	0.191727	+	0.0242208i
$630$	−6.68868	−	20.0440i	−0.266483	−	0.798572i
$631$	8.61720	+	4.73735i	0.343045	+	0.188591i	0.643958	−	0.765061i	$-0.277291\pi$
$631$	8.61720	+	4.73735i	0.343045	+	0.188591i	−0.300912	+	0.953652i	$0.597291\pi$
$632$	−0.874524	+	1.20368i	−0.0347867	+	0.0478798i
$633$	−1.54056	−	0.293878i	−0.0612318	−	0.0116806i
$634$	−10.8726	−	13.1427i	−0.431805	−	0.521962i
$635$	−0.896405	−	3.37989i	−0.0355727	−	0.134127i
$636$	−1.95560	+	31.0833i	−0.0775445	+	1.23253i
$637$	−4.14824	−	2.63255i	−0.164359	−	0.104306i
$638$	−5.98381	+	4.95024i	−0.236901	+	0.195982i
$639$	3.34153	−	4.03921i	0.132189	−	0.159789i
$640$	1.30941	−	11.0695i	0.0517591	−	0.437562i
$641$	−10.4634	−	2.68653i	−0.413278	−	0.106112i	0.0363255	−	0.999340i	$-0.488435\pi$
$641$	−10.4634	−	2.68653i	−0.413278	−	0.106112i	−0.449603	+	0.893228i	$0.648435\pi$
$642$	3.03774	+	24.0462i	0.119890	+	0.949028i
$643$	−4.34403	−	5.97904i	−0.171312	−	0.235790i	0.714725	−	0.699406i	$-0.246552\pi$
$643$	−4.34403	−	5.97904i	−0.171312	−	0.235790i	−0.886037	+	0.463615i	$0.846552\pi$
$644$	−11.0656	−	23.5157i	−0.436047	−	0.926647i
$645$	−3.91447	−	19.6725i	−0.154132	−	0.774602i
$646$	37.2038	−	20.4530i	1.46376	−	0.804711i
$647$	3.32066	−	26.2857i	0.130549	−	1.03340i	−0.781669	−	0.623693i	$-0.785631\pi$
$647$	3.32066	−	26.2857i	0.130549	−	1.03340i	0.912218	−	0.409706i	$-0.134369\pi$
$648$	0.0216401	−	0.0546566i	0.000850103	−	0.00214712i
$649$	−7.58793	−	5.51296i	−0.297852	−	0.216402i
$650$	17.1654	−	55.8236i	0.673283	−	2.18958i
$651$	−4.52720	+	3.28920i	−0.177435	+	0.128914i
$652$	13.0044	+	50.6489i	0.509292	+	1.98356i
$653$	4.21733	−	4.49100i	0.165037	−	0.175746i	−0.641135	−	0.767428i	$-0.721536\pi$
$653$	4.21733	−	4.49100i	0.165037	−	0.175746i	0.806171	+	0.591682i	$0.201536\pi$
$654$	21.3247	+	20.0253i	0.833863	+	0.783049i
$655$	8.64425	−	47.3493i	0.337759	−	1.85009i
$656$	−5.55118	+	0.701277i	−0.216737	+	0.0273803i
$657$	16.0973	+	5.23034i	0.628017	+	0.204055i
$658$	22.2413	−	40.4568i	0.867056	−	1.57717i
$659$	0.950656	+	15.1102i	0.0370323	+	0.588611i	0.972163	+	0.234307i	$0.0752822\pi$
$659$	0.950656	+	15.1102i	0.0370323	+	0.588611i	−0.935130	+	0.354304i	$0.884718\pi$
$660$	5.11565	+	1.61749i	0.199126	+	0.0629607i
$661$	−15.9806	−	25.1814i	−0.621573	−	0.979442i	−0.998582	−	0.0532328i	$-0.983047\pi$
$661$	−15.9806	−	25.1814i	−0.621573	−	0.979442i	0.377009	−	0.926210i	$-0.376953\pi$
$662$	−13.6535	+	53.1769i	−0.530659	+	2.06678i
$663$	−11.4099	−	28.8182i	−0.443125	−	1.11920i
$664$	3.80002	−	0.975679i	0.147469	−	0.0378637i
$665$	2.95145	+	21.9626i	0.114452	+	0.851674i
$666$	3.36558	−	1.33253i	0.130413	−	0.0516343i
$667$	15.9616	−	7.51097i	0.618037	−	0.290826i
$668$	9.63383	−	3.13022i	0.372744	−	0.121112i
$669$	−5.09424	+	26.7049i	−0.196955	+	1.03247i
$670$	17.5267	−	28.1073i	0.677116	−	1.08588i
$671$	−4.26175	+	9.05669i	−0.164523	+	0.349630i
$672$	21.2285	−	4.04956i	0.818909	−	0.156215i
$673$	−23.0174	−	19.0416i	−0.887255	−	0.734001i	0.0775444	−	0.996989i	$-0.475292\pi$
$673$	−23.0174	−	19.0416i	−0.887255	−	0.734001i	−0.964799	+	0.262988i	$0.915292\pi$
$674$	1.02663	+	3.15965i	0.0395444	+	0.121705i
$675$	−20.3427	−	16.2931i	−0.782990	−	0.627121i
$676$	13.3139	−	40.9761i	0.512074	−	1.57600i
$677$	−2.02289	+	1.28376i	−0.0777458	+	0.0493390i	−0.574132	−	0.818763i	$-0.694660\pi$
$677$	−2.02289	+	1.28376i	−0.0777458	+	0.0493390i	0.496386	+	0.868102i	$0.334660\pi$
$678$	22.1272	+	40.2492i	0.849789	+	1.54576i
$679$	2.67966	+	14.0473i	0.102836	+	0.539085i
$680$	6.96453	−	1.84711i	0.267077	−	0.0708334i
$681$	4.70477	−	4.41807i	0.180287	−	0.169301i
$682$			4.21133i			0.161260i
$683$	19.0897	+	20.3285i	0.730447	+	0.777847i	0.981773	−	0.190056i	$-0.0608669\pi$
$683$	19.0897	+	20.3285i	0.730447	+	0.777847i	−0.251327	+	0.967902i	$0.580867\pi$
$684$	9.09469	−	14.3309i	0.347744	−	0.547957i
$685$	−10.9878	+	44.2467i	−0.419822	+	1.69058i
$686$	37.5893	+	14.8827i	1.43517	+	0.568223i
$687$	31.2730	−	1.96753i	1.19314	−	0.0750659i
$688$	−27.4319	+	1.72587i	−1.04583	+	0.0657981i
$689$	65.7123	+	26.0173i	2.50344	+	0.991181i
$690$	−19.3189	−	12.0466i	−0.735458	−	0.458605i
$691$	−20.8055	+	32.7842i	−0.791477	+	1.24717i	0.173500	+	0.984834i	$0.444492\pi$
$691$	−20.8055	+	32.7842i	−0.791477	+	1.24717i	−0.964977	+	0.262335i	$0.915508\pi$
$692$	−5.16103	−	5.49594i	−0.196193	−	0.208924i
$693$		−	4.40503i		−	0.167333i
$694$	−32.9138	+	30.9081i	−1.24939	+	1.17326i
$695$	11.0369	+	4.26899i	0.418652	+	0.161932i
$696$	−0.492439	−	2.58145i	−0.0186658	−	0.0978497i
$697$	−4.17540	−	7.59502i	−0.158154	−	0.287682i
$698$	−7.60459	+	4.82602i	−0.287838	+	0.182668i
$699$	8.71039	−	26.8078i	0.329457	−	1.01396i
$700$	−3.12522	+	28.3427i	−0.118122	+	1.07125i
$701$	4.75074	+	14.6213i	0.179433	+	0.552238i	0.999808	−	0.0195877i	$-0.00623535\pi$
$701$	4.75074	+	14.6213i	0.179433	+	0.552238i	−0.820375	+	0.571826i	$0.806235\pi$
$702$	−46.9142	−	38.8108i	−1.77066	−	1.46482i
$703$	−3.72889	+	0.711323i	−0.140638	+	0.0268281i
$704$	4.20738	−	8.94114i	0.158572	−	0.336982i
$705$	−1.53049	−	21.5954i	−0.0576416	−	0.813330i
$706$	−3.01545	+	15.8075i	−0.113488	+	0.594925i
$707$	−14.7177	+	4.78208i	−0.553517	+	0.179849i
$708$	21.7738	−	10.2460i	0.818308	−	0.385066i
$709$	−26.2668	+	10.3998i	−0.986472	+	0.390572i	−0.805292	−	0.592878i	$-0.797991\pi$
$709$	−26.2668	+	10.3998i	−0.986472	+	0.390572i	−0.181179	+	0.983450i	$0.557991\pi$
$710$	−11.9125	+	5.72128i	−0.447068	+	0.214716i
$711$	4.20664	−	1.08008i	0.157761	−	0.0405062i
$712$	1.27654	+	3.22418i	0.0478405	+	0.120831i
$713$	2.37898	−	9.26552i	0.0890936	−	0.346997i
$714$	15.1476	+	23.8687i	0.566883	+	0.893265i
$715$	7.07813	−	9.90628i	0.264707	−	0.370474i
$716$	−2.66965	−	42.4329i	−0.0997696	−	1.58579i
$717$	0.168160	−	0.305882i	0.00628005	−	0.0114234i
$718$	4.81407	+	1.56419i	0.179659	+	0.0583749i
$719$	−34.6980	+	4.38337i	−1.29402	+	0.163472i	−0.742022	−	0.670376i	$-0.766133\pi$
$719$	−34.6980	+	4.38337i	−1.29402	+	0.163472i	−0.551994	+	0.833848i	$0.686133\pi$
$720$	−9.82428	+	9.37316i	−0.366129	+	0.349317i
$721$	13.8953	+	13.0486i	0.517488	+	0.485954i
$722$	4.21982	−	4.49366i	0.157046	−	0.167237i
$723$	1.21767	+	4.74252i	0.0452857	+	0.176376i
$724$	0.637726	−	0.463335i	0.0237009	−	0.0172197i
$725$	−19.2381	−	2.12129i	−0.714484	−	0.0787829i
$726$	−18.1924	−	13.2175i	−0.675182	−	0.490548i
$727$	−13.3368	+	33.6850i	−0.494635	+	1.24931i	0.441371	+	0.897325i	$0.354492\pi$
$727$	−13.3368	+	33.6850i	−0.494635	+	1.24931i	−0.936007	+	0.351982i	$0.885508\pi$
$728$	−1.10117	+	8.71666i	−0.0408121	+	0.323061i
$729$	−14.9085	+	8.19603i	−0.552167	+	0.303557i
$730$	−31.3341	−	28.9611i	−1.15973	−	1.07190i
$731$	−18.1279	−	38.5237i	−0.670484	−	1.42485i
$732$	−15.0947	−	20.7761i	−0.557916	−	0.767905i
$733$	−1.22522	−	9.69860i	−0.0452544	−	0.358226i	−0.998440	−	0.0558391i	$-0.982217\pi$
$733$	−1.22522	−	9.69860i	−0.0452544	−	0.358226i	0.953185	−	0.302387i	$-0.0977834\pi$
$734$	−50.2412	−	12.8998i	−1.85444	−	0.476139i
$735$	2.06094	−	0.410091i	0.0760190	−	0.0151264i
$736$	−23.5489	+	28.4658i	−0.868025	+	1.04926i
$737$	5.32062	−	4.40160i	0.195988	−	0.162135i
$738$	−5.46535	−	3.46841i	−0.201182	−	0.127674i
$739$	−0.423253	+	6.72741i	−0.0155696	+	0.247472i	0.982542	+	0.186042i	$0.0595661\pi$
$739$	−0.423253	+	6.72741i	−0.0155696	+	0.247472i	−0.998111	+	0.0614299i	$0.980434\pi$
$740$	−4.87731	−	0.268087i	−0.179294	−	0.00985507i
$741$	15.4743	+	18.7052i	0.568461	+	0.687151i
$742$	−63.3194	−	12.0788i	−2.32453	−	0.443428i
$743$	9.71459	−	13.3710i	0.356394	−	0.490534i	−0.592746	−	0.805390i	$-0.701956\pi$
$743$	9.71459	−	13.3710i	0.356394	−	0.490534i	0.949140	+	0.314856i	$0.101956\pi$
$744$	−1.24883	−	0.686550i	−0.0457843	−	0.0251701i
$745$	−3.18869	+	10.0849i	−0.116825	+	0.369482i
$746$	−6.35560	−	0.802899i	−0.232695	−	0.0293962i
$747$	−10.3624	−	4.87616i	−0.379139	−	0.178409i
$748$	11.3660	+	0.715086i	0.415581	+	0.0261461i
$749$	−26.8532			−0.981195
$750$	11.1697	+	22.3429i	0.407861	+	0.815848i
$751$	25.1100			0.916278			0.458139	−	0.888881i	$-0.348516\pi$
$751$	25.1100			0.916278			0.458139	+	0.888881i	$0.348516\pi$
$752$	−29.6084	−	1.86280i	−1.07971	−	0.0679293i
$753$	−29.2130	−	13.7466i	−1.06458	−	0.500954i
$754$	−44.8584	−	5.66693i	−1.63365	−	0.206378i
$755$	31.0974	+	22.2194i	1.13175	+	0.808647i
$756$	26.0501	+	14.3212i	0.947433	+	0.520855i
$757$	14.0754	−	19.3731i	0.511579	−	0.704128i	−0.472606	−	0.881274i	$-0.656687\pi$
$757$	14.0754	−	19.3731i	0.511579	−	0.704128i	0.984185	+	0.177146i	$0.0566866\pi$
$758$	51.1039	+	9.74859i	1.85618	+	0.354085i
$759$	−3.02534	−	3.65700i	−0.109813	−	0.132741i
$760$	−4.74084	+	3.06157i	−0.171968	+	0.111055i
$761$	0.848707	−	13.4898i	0.0307656	−	0.489005i	−0.952231	−	0.305380i	$-0.901217\pi$
$761$	0.848707	−	13.4898i	0.0307656	−	0.489005i	0.982996	−	0.183626i	$-0.0587834\pi$
$762$	2.94996	+	1.87210i	0.106866	+	0.0678191i
$763$	−24.9728	+	20.6593i	−0.904075	+	0.747916i
$764$	16.0455	−	19.3957i	0.580508	−	0.701713i
$765$	−19.1014	−	8.80432i	−0.690613	−	0.318321i
$766$	−30.0879	−	7.72525i	−1.08712	−	0.279125i
$767$	−6.84410	−	54.1767i	−0.247126	−	1.95621i
$768$	−6.39014	−	8.79528i	−0.230584	−	0.317372i
$769$	2.69683	+	5.73105i	0.0972501	+	0.206667i	0.947532	−	0.319660i	$-0.103569\pi$
$769$	2.69683	+	5.73105i	0.0972501	+	0.206667i	−0.850282	+	0.526327i	$0.823569\pi$
$770$	−4.64840	+	10.0849i	−0.167517	+	0.363435i
$771$	12.4351	−	6.83624i	0.447838	−	0.246201i
$772$	−4.34629	+	34.4044i	−0.156426	+	1.23824i
$773$	−10.4784	+	26.4655i	−0.376883	+	0.951897i	0.610281	+	0.792185i	$0.291057\pi$
$773$	−10.4784	+	26.4655i	−0.376883	+	0.951897i	−0.987164	+	0.159712i	$0.948943\pi$
$774$	−25.7249	−	18.6903i	−0.924664	−	0.671808i
$775$	−7.53618	+	7.30503i	−0.270708	+	0.262404i
$776$	−2.94637	+	2.14066i	−0.105768	+	0.0768452i
$777$	−0.628617	−	2.44830i	−0.0225515	−	0.0878323i
$778$	8.27254	−	8.80936i	0.296585	−	0.315831i
$779$	4.94852	+	4.64697i	0.177299	+	0.166495i
$780$	13.5237	+	28.1583i	0.484228	+	1.00823i
$781$	−2.73321	+	0.345284i	−0.0978018	+	0.0123552i
$782$	−45.9606	−	14.9335i	−1.64355	−	0.534021i
$783$	−9.72071	+	17.6819i	−0.347390	+	0.631900i
$784$	−0.180807	−	2.87384i	−0.00645739	−	0.102637i
$785$	−0.0971514	−	12.2648i	−0.00346748	−	0.437751i
$786$	25.7691	+	40.6056i	0.919153	+	1.44835i
$787$	−7.92796	+	30.8774i	−0.282601	+	1.10066i	0.655750	+	0.754978i	$0.272352\pi$
$787$	−7.92796	+	30.8774i	−0.282601	+	1.10066i	−0.938352	+	0.345682i	$0.887648\pi$
$788$	−3.48778	−	8.80912i	−0.124247	−	0.313812i
$789$	−4.36475	+	1.12068i	−0.155389	+	0.0398972i
$790$	−10.7705	−	1.96629i	−0.383196	−	0.0699575i
$791$	−47.3142	+	18.7330i	−1.68230	+	0.666069i
$792$	1.01506	−	0.477649i	0.0360684	−	0.0169725i
$793$	−55.4236	+	18.0082i	−1.96815	+	0.639490i
$794$	−9.35637	+	49.0478i	−0.332045	+	1.74064i
$795$	−28.0165	+	11.3500i	−0.993642	+	0.402544i
$796$	9.73044	−	20.6782i	0.344886	−	0.732920i
$797$	30.2465	−	5.76983i	1.07139	−	0.204378i	0.378629	−	0.925549i	$-0.376396\pi$
$797$	30.2465	−	5.76983i	1.07139	−	0.204378i	0.692757	+	0.721171i	$0.256396\pi$
$798$	−17.0605	−	14.1137i	−0.603936	−	0.499619i
$799$	−14.2005	−	43.7047i	−0.502378	−	1.54616i
$800$	38.3466	−	13.1347i	1.35576	−	0.464383i
$801$	3.12801	−	9.62702i	0.110523	−	0.340154i
$802$	26.0091	−	16.5059i	0.918414	−	0.582843i
$803$	−4.28516	−	7.79467i	−0.151220	−	0.275068i
$804$	3.31979	+	17.4029i	0.117080	+	0.613755i
$805$	15.9241	−	19.5624i	0.561252	−	0.689484i
$806$	−17.8736	+	16.7844i	−0.629571	+	0.591206i
$807$			6.63033i			0.233399i
$808$	−2.69782	−	2.87289i	−0.0949090	−	0.101068i
$809$	−9.69071	+	15.2701i	−0.340707	+	0.536869i	−0.970874	−	0.239591i	$-0.922987\pi$
$809$	−9.69071	+	15.2701i	−0.340707	+	0.536869i	0.630167	+	0.776460i	$0.282987\pi$
$810$	0.431497	−	0.0305806i	0.0151612	−	0.00107449i
$811$	−2.88824	−	1.14353i	−0.101420	−	0.0401549i	0.316867	−	0.948470i	$-0.397369\pi$
$811$	−2.88824	−	1.14353i	−0.101420	−	0.0401549i	−0.418287	+	0.908315i	$0.637369\pi$
$812$	22.0320	−	1.38613i	0.773170	−	0.0486438i
$813$	28.3879	−	1.78601i	0.995605	−	0.0626382i
$814$	−1.76870	−	0.700277i	−0.0619928	−	0.0245447i
$815$	−38.8482	+	32.6598i	−1.36079	+	1.14402i
$816$	9.73375	−	15.3379i	0.340749	−	0.536935i
$817$	22.8276	+	24.3089i	0.798636	+	0.850461i
$818$		−	42.7501i		−	1.49472i
$819$	18.6957	−	17.5565i	0.653281	−	0.613472i
$820$	4.73870	+	7.33787i	0.165483	+	0.256249i
$821$	−8.86985	−	46.4974i	−0.309560	−	1.62277i	−0.708443	−	0.705768i	$-0.750602\pi$
$821$	−8.86985	−	46.4974i	−0.309560	−	1.62277i	0.398883	−	0.917002i	$-0.369398\pi$
$822$	−21.9453	−	39.9184i	−0.765431	−	1.39231i
$823$	35.8553	−	22.7544i	1.24984	−	0.793170i	0.264598	−	0.964359i	$-0.414761\pi$
$823$	35.8553	−	22.7544i	1.24984	−	0.793170i	0.985238	+	0.171189i	$0.0547608\pi$
$824$	−1.50009	+	4.61680i	−0.0522581	+	0.160834i
$825$	0.734417	+	5.15533i	0.0255691	+	0.179486i
$826$	15.3909	+	47.3682i	0.535517	+	1.64815i
$827$	8.99822	+	7.44398i	0.312899	+	0.258852i	0.780595	−	0.625037i	$-0.214916\pi$
$827$	8.99822	+	7.44398i	0.312899	+	0.258852i	−0.467697	+	0.883889i	$0.654916\pi$
$828$	−18.9780	+	3.62025i	−0.659531	+	0.125812i
$829$	14.0318	−	29.8191i	0.487345	−	1.03566i	−0.498327	−	0.866989i	$-0.666052\pi$
$829$	14.0318	−	29.8191i	0.487345	−	1.03566i	0.985672	−	0.168672i	$-0.0539479\pi$
$830$	18.5782	+	22.0984i	0.644858	+	0.767047i
$831$	−0.0692746	+	0.363150i	−0.00240311	+	0.0125975i
$832$	54.7165	−	17.7785i	1.89695	−	0.616357i
$833$	4.03586	−	1.89913i	0.139834	−	0.0658009i
$834$	−10.9936	+	4.35268i	−0.380677	+	0.150721i
$835$	6.78669	+	7.11333i	0.234863	+	0.246167i
$836$	−8.63962	+	2.21828i	−0.298807	+	0.0767207i
$837$	4.02800	+	10.1736i	0.139228	+	0.351650i
$838$	14.2515	−	55.5061i	0.492311	−	1.91743i
$839$	10.6669	+	16.8084i	0.368263	+	0.580289i	0.977041	−	0.213051i	$-0.0683401\pi$
$839$	10.6669	+	16.8084i	0.368263	+	0.580289i	−0.608778	+	0.793340i	$0.708340\pi$
$840$	−2.23279	−	3.02253i	−0.0770385	−	0.104287i
$841$	−0.880065	−	13.9882i	−0.0303471	−	0.482353i
$842$	−16.6597	+	30.3039i	−0.574132	+	1.04434i
$843$	−5.54813	−	1.80270i	−0.191088	−	0.0620882i
$844$	3.32861	−	0.420501i	0.114575	−	0.0144742i
$845$	41.4443	−	5.56949i	1.42573	−	0.191596i
$846$	−25.0187	−	23.4941i	−0.860159	−	0.807743i
$847$	17.0548	−	18.1615i	0.586010	−	0.624037i
$848$	10.3013	+	40.1211i	0.353750	+	1.37776i
$849$	−5.51133	+	4.00421i	−0.189148	+	0.137424i
$850$	34.4402	+	40.3134i	1.18129	+	1.38274i
$851$	3.49580	+	2.53985i	0.119835	+	0.0870649i
$852$	2.60200	−	6.57190i	0.0891430	−	0.225150i
$853$	4.05553	−	32.1028i	0.138859	−	1.09918i	−0.756551	−	0.653935i	$-0.773117\pi$
$853$	4.05553	−	32.1028i	0.138859	−	1.09918i	0.895409	−	0.445244i	$-0.146883\pi$
$854$	46.5774	−	25.6061i	1.59384	−	0.876224i
$855$	16.3596	+	1.93518i	0.559488	+	0.0661818i
$856$	−2.91176	−	6.18781i	−0.0995220	−	0.211495i
$857$	20.7271	+	28.5284i	0.708025	+	0.974512i	0.999837	+	0.0180367i	$0.00574158\pi$
$857$	20.7271	+	28.5284i	0.708025	+	0.974512i	−0.291813	+	0.956475i	$0.594258\pi$
$858$	1.52469	+	12.0692i	0.0520521	+	0.412035i
$859$	46.0459	+	11.8226i	1.57107	+	0.403381i	0.931024	−	0.364958i	$-0.118917\pi$
$859$	46.0459	+	11.8226i	1.57107	+	0.403381i	0.640043	+	0.768339i	$0.278917\pi$
$860$	20.9689	+	37.4368i	0.715033	+	1.27658i
$861$	−2.88126	+	3.48284i	−0.0981929	+	0.118695i
$862$	−4.76853	+	3.94487i	−0.162417	+	0.134363i
$863$	21.4954	+	13.6414i	0.731712	+	0.464358i	0.848767	−	0.528767i	$-0.177345\pi$
$863$	21.4954	+	13.6414i	0.731712	+	0.464358i	−0.117055	+	0.993125i	$0.537345\pi$
$864$	2.65337	−	42.1742i	0.0902696	−	1.43479i
$865$	2.63976	−	6.82473i	0.0897546	−	0.232048i
$866$	−19.3313	−	23.3675i	−0.656904	−	0.794061i
$867$	9.65643	+	1.84206i	0.327949	+	0.0625597i
$868$	7.03641	−	9.68479i	0.238831	−	0.328723i
$869$	−2.00008	−	1.09956i	−0.0678482	−	0.0372999i
$870$	15.5548	−	11.4906i	0.527357	−	0.389566i
$871$	39.8868	+	5.03887i	1.35151	+	0.170736i
$872$	−7.46840	−	3.51436i	−0.252912	−	0.119011i
$873$	10.6100	+	0.667526i	0.359095	+	0.0225923i
$874$	37.8506			1.28032
$875$	−26.1102	+	9.17514i	−0.882685	+	0.310176i
$876$	22.8215			0.771066
$877$	−51.5839	−	3.24538i	−1.74186	−	0.109589i	−0.840268	−	0.542171i	$-0.817603\pi$
$877$	−51.5839	−	3.24538i	−1.74186	−	0.109589i	−0.901595	+	0.432582i	$0.857603\pi$
$878$	−21.2580	−	10.0033i	−0.717423	−	0.337594i
$879$	2.48951	+	0.314498i	0.0839689	+	0.0106077i
$880$	7.13557	−	0.0565217i	0.240540	−	0.00190535i
$881$	−42.3007	−	23.2550i	−1.42515	−	0.783481i	−0.432170	−	0.901792i	$-0.642252\pi$
$881$	−42.3007	−	23.2550i	−1.42515	−	0.783481i	−0.992977	+	0.118311i	$0.962252\pi$
$882$	1.95804	−	2.69502i	0.0659308	−	0.0907459i
$883$	4.04458	+	0.771545i	0.136111	+	0.0259646i	0.254987	−	0.966945i	$-0.417929\pi$
$883$	4.04458	+	0.771545i	0.136111	+	0.0259646i	−0.118876	+	0.992909i	$0.537929\pi$
$884$	42.2646	+	51.0891i	1.42151	+	1.71831i
$885$	18.1133	+	14.7446i	0.608873	+	0.495633i
$886$	2.20451	−	35.0397i	0.0740619	−	1.17718i
$887$	1.51800	+	0.963351i	0.0509694	+	0.0323462i	0.561067	−	0.827770i	$-0.310391\pi$
$887$	1.51800	+	0.963351i	0.0509694	+	0.0323462i	−0.510098	+	0.860116i	$0.670391\pi$
$888$	0.496002	−	0.410328i	0.0166447	−	0.0137697i
$889$	−2.46743	+	2.98261i	−0.0827550	+	0.100034i
$890$	−17.3202	+	18.7394i	−0.580574	+	0.628146i
$891$	0.0873455	+	0.0224265i	0.00292618	+	0.000751316i
$892$	−7.28920	−	57.6999i	−0.244060	−	1.93194i
$893$	21.1560	+	29.1188i	0.707959	+	0.974422i
$894$	−4.49975	−	9.56246i	−0.150494	−	0.319816i
$895$	36.0027	−	20.1657i	1.20344	−	0.674064i
$896$	−10.8132	+	5.94463i	−0.361245	+	0.198596i
$897$	3.46335	−	27.4152i	0.115638	−	0.915367i
$898$	−21.0671	+	53.2095i	−0.703020	+	1.77563i
$899$	6.57370	+	4.77608i	0.219245	+	0.159291i
$900$	19.8301	+	7.49015i	0.661005	+	0.249672i
$901$	−51.9090	+	37.7141i	−1.72934	+	1.25644i
$902$	0.845977	+	3.29486i	0.0281680	+	0.109707i
$903$	−15.2001	+	16.1865i	−0.505828	+	0.538652i
$904$	−9.44706	−	8.87138i	−0.314205	−	0.295058i
$905$	0.673339	+	0.363256i	0.0223825	+	0.0120750i
$906$	−37.8871	+	4.78626i	−1.25871	+	0.159013i
$907$	6.38336	+	2.07408i	0.211956	+	0.0688687i	0.413070	−	0.910699i	$-0.364456\pi$
$907$	6.38336	+	2.07408i	0.211956	+	0.0688687i	−0.201114	+	0.979568i	$0.564456\pi$
$908$	−6.65144	+	12.0989i	−0.220736	+	0.401517i
$909$	0.722352	+	11.4815i	0.0239589	+	0.380816i
$910$	−61.3286	+	20.4653i	−2.03302	+	0.678419i
$911$	17.9128	+	28.2260i	0.593477	+	0.935169i	0.999770	+	0.0214269i	$0.00682092\pi$
$911$	17.9128	+	28.2260i	0.593477	+	0.935169i	−0.406294	+	0.913742i	$0.633179\pi$
$912$	−3.53840	+	13.7812i	−0.117168	+	0.456340i
$913$	2.21555	+	5.59585i	0.0733242	+	0.185196i
$914$	68.8173	−	17.6693i	2.27628	−	0.584448i
$915$	11.8343	−	21.9363i	0.391229	−	0.725191i
$916$	−62.3255	+	24.6764i	−2.05929	+	0.815332i
$917$	−48.2116	+	22.6867i	−1.59209	+	0.749180i
$918$	52.5711	−	17.0814i	1.73511	−	0.563770i
$919$	−0.0421051	+	0.220722i	−0.00138892	+	0.00728096i	−0.982975	−	0.183740i	$-0.941180\pi$
$919$	−0.0421051	+	0.220722i	−0.00138892	+	0.00728096i	0.981586	+	0.191021i	$0.0611797\pi$
$920$	6.23448	+	1.54821i	0.205545	+	0.0510430i
$921$	8.73198	−	18.5564i	0.287729	−	0.611454i
$922$	47.3323	−	9.02912i	1.55881	−	0.297358i
$923$	−12.3588	−	10.2241i	−0.406794	−	0.336529i
$924$	−1.83538	−	5.64873i	−0.0603797	−	0.185830i
$925$	−1.81486	−	4.37980i	−0.0596722	−	0.144007i
$926$	5.25226	−	16.1648i	0.172600	−	0.531208i
$927$	11.9644	−	7.59284i	0.392962	−	0.249381i
$928$	−15.1178	−	27.4991i	−0.496265	−	0.902702i
$929$	−2.24738	−	11.7812i	−0.0737343	−	0.386529i	−0.999954	−	0.00954555i	$-0.996962\pi$
$929$	−2.24738	−	11.7812i	−0.0737343	−	0.386529i	0.926220	−	0.376983i	$-0.123038\pi$
$930$	0.575557	−	10.4711i	0.0188733	−	0.343362i
$931$	−2.54667	+	2.39148i	−0.0834637	+	0.0783777i
$932$			60.2998i			1.97519i
$933$	1.46448	+	1.55952i	0.0479450	+	0.0510562i
$934$	31.3610	−	49.4170i	1.02616	−	1.61698i
$935$	4.15026	+	10.2445i	0.135728	+	0.335032i
$936$	6.07278	+	2.40438i	0.198495	+	0.0785897i
$937$	6.68193	−	0.420391i	0.218289	−	0.0137336i	0.0467306	−	0.998908i	$-0.485120\pi$
$937$	6.68193	−	0.420391i	0.218289	−	0.0137336i	0.171558	+	0.985174i	$0.445120\pi$
$938$	−36.5965	+	2.30246i	−1.19492	+	0.0751779i
$939$	−23.6391	−	9.35938i	−0.771433	−	0.305432i
$940$	17.3898	+	42.9250i	0.567192	+	1.40006i
$941$	−7.87448	+	12.4082i	−0.256701	+	0.404496i	−0.948098	−	0.317980i	$-0.896996\pi$
$941$	−7.87448	+	12.4082i	−0.256701	+	0.404496i	0.691397	+	0.722475i	$0.256996\pi$
$942$	8.38920	+	8.93359i	0.273335	+	0.291072i
$943$		−	7.72707i		−	0.251628i
$944$	23.3307	−	21.9089i	0.759348	−	0.713076i
$945$	−1.58351	+	28.8088i	−0.0515116	+	0.937151i
$946$	3.13124	+	16.4146i	0.101806	+	0.533683i
$947$	6.64264	+	12.0829i	0.215857	+	0.392642i	0.961961	−	0.273187i	$-0.0880779\pi$
$947$	6.64264	+	12.0829i	0.215857	+	0.392642i	−0.746104	+	0.665829i	$0.768078\pi$
$948$	4.94430	−	3.13775i	0.160584	−	0.101909i
$949$	16.0033	−	49.2530i	0.519488	−	1.59882i
$950$	−35.4119	−	21.6939i	−1.14891	−	0.703843i
$951$	2.73624	+	8.42127i	0.0887285	+	0.273078i
$952$	−6.14590	−	5.08433i	−0.199190	−	0.164784i
$953$	−4.59958	+	0.877417i	−0.148995	+	0.0284223i	−0.261339	−	0.965247i	$-0.584164\pi$
$953$	−4.59958	+	0.877417i	−0.148995	+	0.0284223i	0.112344	+	0.993669i	$0.464164\pi$
$954$	−20.4034	+	43.3595i	−0.660586	+	1.40382i
$955$	23.7115	+	5.88829i	0.767287	+	0.190540i
$956$	−0.139921	+	0.733494i	−0.00452538	+	0.0237229i
$957$	3.83417	−	1.24580i	0.123941	−	0.0402709i
$958$	−28.3356	+	13.3337i	−0.915482	+	0.430793i
$959$	46.9253	−	18.5790i	1.51530	−	0.599949i
$960$	−11.6833	+	21.6564i	−0.377076	+	0.698957i
$961$	−25.7582	+	6.61358i	−0.830910	+	0.213341i
$962$	−4.07713	−	10.2976i	−0.131452	−	0.332009i
$963$	−4.96449	+	19.3354i	−0.159979	+	0.623075i
$964$	−5.61252	−	8.84391i	−0.180767	−	0.284843i
$965$	−31.9267	+	10.6539i	−1.02776	+	0.342962i
$966$	1.58254	+	25.1537i	0.0509174	+	0.809308i
$967$	−10.7077	+	19.4772i	−0.344335	+	0.626344i	−0.990603	−	0.136767i	$-0.956329\pi$
$967$	−10.7077	+	19.4772i	−0.344335	+	0.626344i	0.646268	+	0.763111i	$0.276329\pi$
$968$	6.03427	+	1.96065i	0.193949	+	0.0630178i
$969$	−21.8656	+	2.76226i	−0.702423	+	0.0887366i
$970$	−23.5863	−	12.7244i	−0.757310	−	0.408557i
$971$	−13.8856	−	13.0395i	−0.445610	−	0.418456i	0.428983	−	0.903312i	$-0.358872\pi$
$971$	−13.8856	−	13.0395i	−0.445610	−	0.418456i	−0.874594	+	0.484856i	$0.838872\pi$
$972$	24.5043	−	26.0944i	0.785975	−	0.836978i
$973$	−3.25785	−	12.6885i	−0.104442	−	0.406775i
$974$	17.9741	−	13.0589i	0.575927	−	0.418436i
$975$	−18.9531	+	23.6638i	−0.606984	+	0.757848i
$976$	−27.6321	−	20.0759i	−0.884482	−	0.642614i
$977$	−2.93344	+	7.40903i	−0.0938491	+	0.237036i	−0.969116	−	0.246604i	$-0.920685\pi$
$977$	−2.93344	+	7.40903i	−0.0938491	+	0.237036i	0.875267	+	0.483639i	$0.160685\pi$
$978$	6.35576	−	50.3110i	0.203235	−	1.60877i
$979$	−4.66161	+	2.56274i	−0.148986	+	0.0819056i
$980$	−3.92198	+	2.19676i	−0.125283	+	0.0701729i
$981$	10.2587	+	21.8008i	0.327534	+	0.696046i
$982$	−25.6274	−	35.2730i	−0.817802	−	1.12561i
$983$	−3.09697	−	24.5151i	−0.0987781	−	0.781909i	−0.961226	−	0.275763i	$-0.911070\pi$
$983$	−3.09697	−	24.5151i	−0.0987781	−	0.781909i	0.862448	−	0.506146i	$-0.168930\pi$
$984$	−1.11498	−	0.286277i	−0.0355441	−	0.00912619i
$985$	6.24155	−	6.75298i	0.198872	−	0.215168i
$986$	26.1654	−	31.6285i	0.833276	−	1.00726i
$987$	−18.4664	+	15.2767i	−0.587792	+	0.486264i
$988$	−43.8484	−	27.8270i	−1.39500	−	0.885295i
$989$	2.38341	−	37.8832i	0.0757881	−	1.20462i
$990$	6.40219	+	5.21149i	0.203475	+	0.165632i
$991$	1.06950	+	1.29281i	0.0339739	+	0.0410674i	0.787227	−	0.616664i	$-0.211516\pi$
$991$	1.06950	+	1.29281i	0.0339739	+	0.0410674i	−0.753253	+	0.657731i	$0.771516\pi$
$992$	−16.7156	−	3.18867i	−0.530721	−	0.101240i
$993$	16.7522	−	23.0574i	0.531616	−	0.731706i
$994$	12.8198	+	7.04775i	0.406620	+	0.223541i
$995$	22.1800	−	0.175691i	0.703153	−	0.00556977i
$996$	−15.3197	−	1.93533i	−0.485425	−	0.0613234i
$997$	−1.21303	−	0.570809i	−0.0384171	−	0.0180777i	0.406475	−	0.913662i	$-0.366758\pi$
$997$	−1.21303	−	0.570809i	−0.0384171	−	0.0180777i	−0.444892	+	0.895584i	$0.646758\pi$
$998$	4.10301	+	0.258140i	0.129879	+	0.00817127i
$999$	−4.94254			−0.156375

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	125.2.h.a.4.11	✓	240
5.2	odd	4		625.2.g.b.226.4		480
5.3	odd	4		625.2.g.b.226.21		480
5.4	even	2		625.2.h.a.399.2		240
125.17	odd	100		625.2.g.b.401.4		480
125.31	even	25		625.2.h.a.224.2		240
125.94	even	50	inner	125.2.h.a.94.11	yes	240
125.108	odd	100		625.2.g.b.401.21		480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
125.2.h.a.4.11	✓	240	1.1	even	1	trivial
125.2.h.a.94.11	yes	240	125.94	even	50	inner
625.2.g.b.226.4		480	5.2	odd	4
625.2.g.b.226.21		480	5.3	odd	4
625.2.g.b.401.4		480	125.17	odd	100
625.2.g.b.401.21		480	125.108	odd	100
625.2.h.a.224.2		240	125.31	even	25
625.2.h.a.399.2		240	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 125 = 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	125.h (of order \(50\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(2.07048 + 0.130264i) q^{2} +(-0.974456 - 0.458544i) q^{3} +(2.28570 + 0.288751i) q^{4} +(0.707806 + 2.12109i) q^{5} +(-1.95786 - 1.07634i) q^{6} +(1.45498 - 2.00261i) q^{7} +(0.619230 + 0.118124i) q^{8} +(-1.17297 - 1.41788i) q^{9} +O(q^{10})\)	\(q+(2.07048 + 0.130264i) q^{2} +(-0.974456 - 0.458544i) q^{3} +(2.28570 + 0.288751i) q^{4} +(0.707806 + 2.12109i) q^{5} +(-1.95786 - 1.07634i) q^{6} +(1.45498 - 2.00261i) q^{7} +(0.619230 + 0.118124i) q^{8} +(-1.17297 - 1.41788i) q^{9} +(1.18920 + 4.48388i) q^{10} +(-0.0607221 + 0.965150i) q^{11} +(-2.09491 - 1.32947i) q^{12} +(-4.33827 + 3.58893i) q^{13} +(3.27338 - 3.95683i) q^{14} +(0.282886 - 2.39147i) q^{15} +(-3.19626 - 0.820659i) q^{16} +(-0.640649 - 5.07126i) q^{17} +(-2.24392 - 3.08849i) q^{18} +(1.70464 + 3.62254i) q^{19} +(1.00537 + 5.05255i) q^{20} +(-2.33610 + 1.28428i) q^{21} +(-0.251448 + 1.99042i) q^{22} +(1.67761 - 4.23716i) q^{23} +(-0.549247 - 0.399051i) q^{24} +(-3.99802 + 3.00264i) q^{25} +(-9.44983 + 6.86570i) q^{26} +(1.29633 + 5.04887i) q^{27} +(3.90390 - 4.15723i) q^{28} +(2.82179 + 2.64984i) q^{29} +(0.897233 - 4.91464i) q^{30} +(2.08257 - 0.263089i) q^{31} +(-7.70998 - 2.50512i) q^{32} +(0.501735 - 0.912652i) q^{33} +(-0.665852 - 10.5834i) q^{34} +(5.27755 + 1.66868i) q^{35} +(-2.27164 - 3.57954i) q^{36} +(-0.235804 + 0.918396i) q^{37} +(3.05754 + 7.72246i) q^{38} +(5.87314 - 1.50797i) q^{39} +(0.187742 + 1.39705i) q^{40} +(1.57651 - 0.624185i) q^{41} +(-5.00414 + 2.35477i) q^{42} +(7.92164 - 2.57390i) q^{43} +(-0.417480 + 2.18851i) q^{44} +(2.17721 - 3.49155i) q^{45} +(4.02541 - 8.55443i) q^{46} +(8.83092 - 1.68459i) q^{47} +(2.73830 + 2.26532i) q^{48} +(0.269649 + 0.829893i) q^{49} +(-8.66897 + 5.69611i) q^{50} +(-1.70111 + 5.23549i) q^{51} +(-10.9523 + 6.95054i) q^{52} +(-6.04722 - 10.9999i) q^{53} +(2.02634 + 10.6225i) q^{54} +(-2.09015 + 0.554342i) q^{55} +(1.13752 - 1.06821i) q^{56} -4.31166i q^{57} +(5.49729 + 5.85402i) q^{58} +(-5.19682 + 8.18888i) q^{59} +(1.33713 - 5.38449i) q^{60} +(9.62343 + 3.81019i) q^{61} +(4.34619 - 0.273439i) q^{62} +(-4.54610 + 0.286016i) q^{63} +(-9.50065 - 3.76157i) q^{64} +(-10.6831 - 6.66159i) q^{65} +(1.15772 - 1.82427i) q^{66} +(-4.88802 - 5.20522i) q^{67} -11.7764i q^{68} +(-3.57768 + 3.35967i) q^{69} +(10.7097 + 4.14245i) q^{70} +(0.533807 + 2.79831i) q^{71} +(-0.558852 - 1.01655i) q^{72} +(-7.76605 + 4.92849i) q^{73} +(-0.607862 + 1.87081i) q^{74} +(5.27274 - 1.09267i) q^{75} +(2.85028 + 8.77226i) q^{76} +(1.84447 + 1.52587i) q^{77} +(12.3567 - 2.35716i) q^{78} +(-1.00490 + 2.13553i) q^{79} +(-0.521640 - 7.36041i) q^{80} +(0.0174734 - 0.0915987i) q^{81} +(3.34545 - 1.08700i) q^{82} +(5.63120 - 2.64984i) q^{83} +(-5.71046 + 2.26093i) q^{84} +(10.3031 - 4.94834i) q^{85} +(16.7369 - 4.29731i) q^{86} +(-1.53464 - 3.87606i) q^{87} +(-0.151609 + 0.590477i) q^{88} +(2.94749 + 4.64449i) q^{89} +(4.96269 - 6.94559i) q^{90} +(0.875123 + 13.9097i) q^{91} +(5.05800 - 9.20046i) q^{92} +(-2.15001 - 0.698580i) q^{93} +(18.5037 - 2.33756i) q^{94} +(-6.47717 + 6.17974i) q^{95} +(6.36432 + 5.97650i) q^{96} +(-3.95475 + 4.21138i) q^{97} +(0.450198 + 1.75341i) q^{98} +(1.43969 - 1.04599i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9}+O(q^{10}) \) 240 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 25 * q^5 - 20 * q^6 - 25 * q^7 - 35 * q^8 - 20 * q^9	\( 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9} - 20 q^{10} - 25 q^{11} + 60 q^{12} - 20 q^{13} - 30 q^{14} - 40 q^{15} - 40 q^{16} - 15 q^{17} - 25 q^{18} - 10 q^{19} - 10 q^{20} - 35 q^{21} - 25 q^{22} + 70 q^{23} + 15 q^{24} + 35 q^{25} - 45 q^{26} - 20 q^{27} - 10 q^{28} - 10 q^{29} - 40 q^{30} - 30 q^{31} - 25 q^{32} - 35 q^{33} - 20 q^{34} - 40 q^{35} + 170 q^{36} - 55 q^{37} - 40 q^{38} - 35 q^{40} - 35 q^{41} - 10 q^{42} - 25 q^{43} + 15 q^{44} + 140 q^{45} - 40 q^{46} + 100 q^{47} + 5 q^{48} + 35 q^{49} - 10 q^{50} - 55 q^{51} - 15 q^{52} - 15 q^{53} + 30 q^{54} - 15 q^{55} + 65 q^{56} + 255 q^{58} + 5 q^{59} + 135 q^{60} - 40 q^{61} + 5 q^{62} - 35 q^{63} + 25 q^{64} - 30 q^{65} - 95 q^{66} + 105 q^{67} - 10 q^{69} - 55 q^{70} + 45 q^{71} - 30 q^{72} - 40 q^{73} + 35 q^{74} - 15 q^{75} - 65 q^{76} - 35 q^{77} + 100 q^{78} + 430 q^{80} - 95 q^{81} + 175 q^{82} + 20 q^{83} + 45 q^{84} - 10 q^{85} - 80 q^{86} - 5 q^{87} - 5 q^{88} + 30 q^{89} + 65 q^{91} - 55 q^{92} + 275 q^{93} + 60 q^{94} + 10 q^{95} - 135 q^{96} + 35 q^{97} - 15 q^{98} + 45 q^{99}+O(q^{100}) \) 240 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 25 * q^5 - 20 * q^6 - 25 * q^7 - 35 * q^8 - 20 * q^9 - 20 * q^10 - 25 * q^11 + 60 * q^12 - 20 * q^13 - 30 * q^14 - 40 * q^15 - 40 * q^16 - 15 * q^17 - 25 * q^18 - 10 * q^19 - 10 * q^20 - 35 * q^21 - 25 * q^22 + 70 * q^23 + 15 * q^24 + 35 * q^25 - 45 * q^26 - 20 * q^27 - 10 * q^28 - 10 * q^29 - 40 * q^30 - 30 * q^31 - 25 * q^32 - 35 * q^33 - 20 * q^34 - 40 * q^35 + 170 * q^36 - 55 * q^37 - 40 * q^38 - 35 * q^40 - 35 * q^41 - 10 * q^42 - 25 * q^43 + 15 * q^44 + 140 * q^45 - 40 * q^46 + 100 * q^47 + 5 * q^48 + 35 * q^49 - 10 * q^50 - 55 * q^51 - 15 * q^52 - 15 * q^53 + 30 * q^54 - 15 * q^55 + 65 * q^56 + 255 * q^58 + 5 * q^59 + 135 * q^60 - 40 * q^61 + 5 * q^62 - 35 * q^63 + 25 * q^64 - 30 * q^65 - 95 * q^66 + 105 * q^67 - 10 * q^69 - 55 * q^70 + 45 * q^71 - 30 * q^72 - 40 * q^73 + 35 * q^74 - 15 * q^75 - 65 * q^76 - 35 * q^77 + 100 * q^78 + 430 * q^80 - 95 * q^81 + 175 * q^82 + 20 * q^83 + 45 * q^84 - 10 * q^85 - 80 * q^86 - 5 * q^87 - 5 * q^88 + 30 * q^89 + 65 * q^91 - 55 * q^92 + 275 * q^93 + 60 * q^94 + 10 * q^95 - 135 * q^96 + 35 * q^97 - 15 * q^98 + 45 * q^99

Introduction

L-functions

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