LMFDB - Embedded newform 425.2.k.c.86.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(86,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8, 0]))

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

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

chi := DirichletCharacter("425.86");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.k (of order $5$, degree $4$, 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:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			86.11
Character	$\chi$	$=$	425.86
Dual form			425.2.k.c.341.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.364820 - 0.265058i) q^{2} +(-0.632459 + 1.94651i) q^{3} +(-0.555196 + 1.70872i) q^{4} +(-2.23395 + 0.0971993i) q^{5} +(0.285203 + 0.877764i) q^{6} +4.23898 q^{7} +(0.529060 + 1.62828i) q^{8} +(-0.961836 - 0.698814i) q^{9} +(-0.789229 + 0.627587i) q^{10} +(-4.11043 + 2.98640i) q^{11} +(-2.97489 - 2.16138i) q^{12} +(-0.747112 - 0.542808i) q^{13} +(1.54647 - 1.12357i) q^{14} +(1.22368 - 4.40988i) q^{15} +(-2.28244 - 1.65829i) q^{16} +(-0.309017 - 0.951057i) q^{17} -0.536123 q^{18} +(-1.18302 - 3.64096i) q^{19} +(1.07420 - 3.87116i) q^{20} +(-2.68098 + 8.25121i) q^{21} +(-0.708001 + 2.17900i) q^{22} +(-3.44478 + 2.50278i) q^{23} -3.50406 q^{24} +(4.98110 - 0.434278i) q^{25} -0.416437 q^{26} +(-2.99883 + 2.17877i) q^{27} +(-2.35346 + 7.24321i) q^{28} +(1.25887 - 3.87441i) q^{29} +(-0.722448 - 1.93316i) q^{30} +(1.81606 + 5.58927i) q^{31} -4.69637 q^{32} +(-3.21338 - 9.88976i) q^{33} +(-0.364820 - 0.265058i) q^{34} +(-9.46969 + 0.412026i) q^{35} +(1.72808 - 1.25553i) q^{36} +(0.586205 + 0.425903i) q^{37} +(-1.39665 - 1.01473i) q^{38} +(1.52910 - 1.11095i) q^{39} +(-1.34016 - 3.58607i) q^{40} +(4.78305 + 3.47509i) q^{41} +(1.20897 + 3.72082i) q^{42} -1.67707 q^{43} +(-2.82082 - 8.68160i) q^{44} +(2.21662 + 1.46763i) q^{45} +(-0.593346 + 1.82613i) q^{46} +(-0.0592930 + 0.182485i) q^{47} +(4.67143 - 3.39399i) q^{48} +10.9690 q^{49} +(1.70210 - 1.47871i) q^{50} +2.04668 q^{51} +(1.34230 - 0.975237i) q^{52} +(-3.74774 + 11.5344i) q^{53} +(-0.516532 + 1.58972i) q^{54} +(8.89224 - 7.07102i) q^{55} +(2.24267 + 6.90224i) q^{56} +7.83537 q^{57} +(-0.567679 - 1.74714i) q^{58} +(10.2311 + 7.43334i) q^{59} +(6.85585 + 4.53928i) q^{60} +(10.9472 - 7.95360i) q^{61} +(2.14401 + 1.55772i) q^{62} +(-4.07720 - 2.96226i) q^{63} +(2.85155 - 2.07177i) q^{64} +(1.72177 + 1.13999i) q^{65} +(-3.79366 - 2.75626i) q^{66} +(-0.595852 - 1.83385i) q^{67} +1.79665 q^{68} +(-2.69300 - 8.28820i) q^{69} +(-3.34553 + 2.66033i) q^{70} +(-1.10221 + 3.39226i) q^{71} +(0.628996 - 1.93585i) q^{72} +(2.43074 - 1.76604i) q^{73} +0.326748 q^{74} +(-2.30502 + 9.97042i) q^{75} +6.87818 q^{76} +(-17.4240 + 12.6593i) q^{77} +(0.263379 - 0.810598i) q^{78} +(-3.99330 + 12.2901i) q^{79} +(5.26006 + 3.48270i) q^{80} +(-3.44653 - 10.6073i) q^{81} +2.66605 q^{82} +(-1.54328 - 4.74973i) q^{83} +(-12.6105 - 9.16207i) q^{84} +(0.782772 + 2.09458i) q^{85} +(-0.611831 + 0.444521i) q^{86} +(6.74538 + 4.90080i) q^{87} +(-7.03736 - 5.11294i) q^{88} +(6.45514 - 4.68994i) q^{89} +(1.19768 - 0.0521108i) q^{90} +(-3.16699 - 2.30095i) q^{91} +(-2.36402 - 7.27569i) q^{92} -12.0281 q^{93} +(0.0267378 + 0.0822903i) q^{94} +(2.99671 + 8.01875i) q^{95} +(2.97026 - 9.14152i) q^{96} +(-3.56474 + 10.9711i) q^{97} +(4.00170 - 2.90740i) q^{98} +6.04050 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 2 q^{2} + 2 q^{3} - 20 q^{4} - 17 q^{6} - 44 q^{7} + 15 q^{8} - 22 q^{9} - 2 q^{10} + 4 q^{11} + 14 q^{12} + 6 q^{13} - 10 q^{14} + 14 q^{15} - 32 q^{16} + 20 q^{17} - 62 q^{18} - 3 q^{19} + 16 q^{21}+ \cdots + 76 q^{99}+O(q^{100}) $ 80 * q + 2 * q^2 + 2 * q^3 - 20 * q^4 - 17 * q^6 - 44 * q^7 + 15 * q^8 - 22 * q^9 - 2 * q^10 + 4 * q^11 + 14 * q^12 + 6 * q^13 - 10 * q^14 + 14 * q^15 - 32 * q^16 + 20 * q^17 - 62 * q^18 - 3 * q^19 + 16 * q^21 + 17 * q^22 - 5 * q^23 + 30 * q^24 - 14 * q^25 + 18 * q^26 + 17 * q^27 + 32 * q^28 + 20 * q^29 - 114 * q^30 - 21 * q^31 - 88 * q^32 - 2 * q^34 - 2 * q^35 + 47 * q^36 + 6 * q^37 + 22 * q^38 - 46 * q^39 + 59 * q^40 - 26 * q^41 - 3 * q^42 - 102 * q^43 - 44 * q^44 + 74 * q^45 + 2 * q^46 + 2 * q^47 + 72 * q^48 + 108 * q^49 + 7 * q^50 + 18 * q^51 + 65 * q^52 - 18 * q^53 - 29 * q^54 - 49 * q^55 - 117 * q^56 + 2 * q^57 + 42 * q^58 + 21 * q^59 + 112 * q^60 + 4 * q^61 + 15 * q^62 + 41 * q^63 - 11 * q^64 + 8 * q^65 - 156 * q^66 + 21 * q^67 - 80 * q^68 - 67 * q^69 + 32 * q^70 - 4 * q^71 + 83 * q^72 - 2 * q^73 + 78 * q^74 - 68 * q^75 + 16 * q^76 + 2 * q^77 - 2 * q^78 - 53 * q^79 - 54 * q^80 - 21 * q^81 - 72 * q^82 - 42 * q^83 - 52 * q^84 + 42 * q^86 - 8 * q^87 + 68 * q^88 - 73 * q^89 + 97 * q^90 - 83 * q^91 + 117 * q^92 - 120 * q^93 + 80 * q^94 + 16 * q^95 + 88 * q^96 + 57 * q^97 + 17 * q^98 + 76 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	0.364820	−	0.265058i	0.257967	−	0.187424i	−0.451283	−	0.892381i	$-0.649034\pi$
$2$	0.364820	−	0.265058i	0.257967	−	0.187424i	0.709250	+	0.704957i	$0.249034\pi$
$3$	−0.632459	+	1.94651i	−0.365150	+	1.12382i	0.584737	+	0.811223i	$0.301198\pi$
$3$	−0.632459	+	1.94651i	−0.365150	+	1.12382i	−0.949887	+	0.312593i	$0.898802\pi$
$4$	−0.555196	+	1.70872i	−0.277598	+	0.854358i
$5$	−2.23395	+	0.0971993i	−0.999055	+	0.0434689i
$5$	−2.23395	+	0.0971993i	−0.999055	+	0.0434689i
$6$	0.285203	+	0.877764i	0.116434	+	0.358345i
$7$	4.23898			1.60218			0.801092	−	0.598541i	$-0.204253\pi$
$7$	4.23898			1.60218			0.801092	+	0.598541i	$0.204253\pi$
$8$	0.529060	+	1.62828i	0.187051	+	0.575683i
$9$	−0.961836	−	0.698814i	−0.320612	−	0.232938i
$10$	−0.789229	+	0.627587i	−0.249576	+	0.198460i
$11$	−4.11043	+	2.98640i	−1.23934	+	0.900434i	−0.997554	−	0.0698950i	$-0.977734\pi$
$11$	−4.11043	+	2.98640i	−1.23934	+	0.900434i	−0.241787	+	0.970329i	$0.577734\pi$
$12$	−2.97489	−	2.16138i	−0.858777	−	0.623938i
$13$	−0.747112	−	0.542808i	−0.207211	−	0.150548i	0.479340	−	0.877629i	$-0.340876\pi$
$13$	−0.747112	−	0.542808i	−0.207211	−	0.150548i	−0.686551	+	0.727082i	$0.740876\pi$
$14$	1.54647	−	1.12357i	0.413311	−	0.300288i
$15$	1.22368	−	4.40988i	0.315954	−	1.13863i
$16$	−2.28244	−	1.65829i	−0.570611	−	0.414573i
$17$	−0.309017	−	0.951057i	−0.0749476	−	0.230665i
$17$	−0.309017	−	0.951057i	−0.0749476	−	0.230665i
$18$	−0.536123			−0.126365
$19$	−1.18302	−	3.64096i	−0.271403	−	0.835294i	−0.990149	−	0.140020i	$-0.955283\pi$
$19$	−1.18302	−	3.64096i	−0.271403	−	0.835294i	0.718745	−	0.695273i	$-0.244717\pi$
$20$	1.07420	−	3.87116i	0.240197	−	0.865617i
$21$	−2.68098	+	8.25121i	−0.585038	+	1.80056i
$22$	−0.708001	+	2.17900i	−0.150946	+	0.464565i
$23$	−3.44478	+	2.50278i	−0.718287	+	0.521866i	−0.885837	−	0.463997i	$-0.846415\pi$
$23$	−3.44478	+	2.50278i	−0.718287	+	0.521866i	0.167549	+	0.985864i	$0.446415\pi$
$24$	−3.50406			−0.715264
$25$	4.98110	−	0.434278i	0.996221	−	0.0868555i
$26$	−0.416437			−0.0816700
$27$	−2.99883	+	2.17877i	−0.577124	+	0.419305i
$28$	−2.35346	+	7.24321i	−0.444763	+	1.36884i
$29$	1.25887	−	3.87441i	0.233766	−	0.719459i	−0.763516	−	0.645789i	$-0.776529\pi$
$29$	1.25887	−	3.87441i	0.233766	−	0.719459i	0.997283	−	0.0736705i	$-0.0234713\pi$
$30$	−0.722448	−	1.93316i	−0.131900	−	0.352946i
$31$	1.81606	+	5.58927i	0.326175	+	1.00386i	0.970908	+	0.239454i	$0.0769686\pi$
$31$	1.81606	+	5.58927i	0.326175	+	1.00386i	−0.644733	+	0.764408i	$0.723031\pi$
$32$	−4.69637			−0.830209
$33$	−3.21338	−	9.88976i	−0.559377	−	1.72159i
$34$	−0.364820	−	0.265058i	−0.0625662	−	0.0454570i
$35$	−9.46969	+	0.412026i	−1.60067	+	0.0696451i
$36$	1.72808	−	1.25553i	0.288014	−	0.209254i
$37$	0.586205	+	0.425903i	0.0963715	+	0.0700180i	0.634927	−	0.772572i	$-0.281030\pi$
$37$	0.586205	+	0.425903i	0.0963715	+	0.0700180i	−0.538556	+	0.842590i	$0.681030\pi$
$38$	−1.39665	−	1.01473i	−0.226567	−	0.164611i
$39$	1.52910	−	1.11095i	0.244852	−	0.177895i
$40$	−1.34016	−	3.58607i	−0.211898	−	0.567008i
$41$	4.78305	+	3.47509i	0.746987	+	0.542718i	0.894891	−	0.446284i	$-0.147253\pi$
$41$	4.78305	+	3.47509i	0.746987	+	0.542718i	−0.147905	+	0.989002i	$0.547253\pi$
$42$	1.20897	+	3.72082i	0.186548	+	0.574135i
$43$	−1.67707			−0.255752			−0.127876	−	0.991790i	$-0.540816\pi$
$43$	−1.67707			−0.255752			−0.127876	+	0.991790i	$0.540816\pi$
$44$	−2.82082	−	8.68160i	−0.425255	−	1.30880i
$45$	2.21662	+	1.46763i	0.330434	+	0.218781i
$46$	−0.593346	+	1.82613i	−0.0874842	+	0.269249i
$47$	−0.0592930	+	0.182485i	−0.00864877	+	0.0266182i	−0.955288	−	0.295678i	$-0.904455\pi$
$47$	−0.0592930	+	0.182485i	−0.00864877	+	0.0266182i	0.946639	+	0.322296i	$0.104455\pi$
$48$	4.67143	−	3.39399i	0.674262	−	0.489880i
$49$	10.9690			1.56699
$50$	1.70210	−	1.47871i	0.240713	−	0.209122i
$51$	2.04668			0.286592
$52$	1.34230	−	0.975237i	0.186143	−	0.135241i
$53$	−3.74774	+	11.5344i	−0.514792	+	1.58437i	0.268868	+	0.963177i	$0.413350\pi$
$53$	−3.74774	+	11.5344i	−0.514792	+	1.58437i	−0.783660	+	0.621190i	$0.786650\pi$
$54$	−0.516532	+	1.58972i	−0.0702911	+	0.216334i
$55$	8.89224	−	7.07102i	1.19903	−	0.953456i
$56$	2.24267	+	6.90224i	0.299690	+	0.922350i
$57$	7.83537			1.03782
$58$	−0.567679	−	1.74714i	−0.0745399	−	0.229410i
$59$	10.2311	+	7.43334i	1.33198	+	0.967738i	0.999698	+	0.0245574i	$0.00781766\pi$
$59$	10.2311	+	7.43334i	1.33198	+	0.967738i	0.332279	+	0.943181i	$0.392182\pi$
$60$	6.85585	+	4.53928i	0.885087	+	0.586018i
$61$	10.9472	−	7.95360i	1.40164	−	1.01835i	0.407173	−	0.913351i	$-0.366515\pi$
$61$	10.9472	−	7.95360i	1.40164	−	1.01835i	0.994472	−	0.105003i	$-0.0334853\pi$
$62$	2.14401	+	1.55772i	0.272290	+	0.197830i
$63$	−4.07720	−	2.96226i	−0.513679	−	0.373210i
$64$	2.85155	−	2.07177i	0.356444	−	0.258972i
$65$	1.72177	+	1.13999i	0.213560	+	0.141398i
$66$	−3.79366	−	2.75626i	−0.466967	−	0.339272i
$67$	−0.595852	−	1.83385i	−0.0727950	−	0.224040i	0.908039	−	0.418886i	$-0.137579\pi$
$67$	−0.595852	−	1.83385i	−0.0727950	−	0.224040i	−0.980834	+	0.194846i	$0.937579\pi$
$68$	1.79665			0.217876
$69$	−2.69300	−	8.28820i	−0.324199	−	0.997783i
$70$	−3.34553	+	2.66033i	−0.399867	+	0.317970i
$71$	−1.10221	+	3.39226i	−0.130809	+	0.402588i	−0.994915	−	0.100722i	$-0.967885\pi$
$71$	−1.10221	+	3.39226i	−0.130809	+	0.402588i	0.864106	+	0.503310i	$0.167885\pi$
$72$	0.628996	−	1.93585i	0.0741279	−	0.228142i
$73$	2.43074	−	1.76604i	0.284496	−	0.206699i	−0.436380	−	0.899763i	$-0.643740\pi$
$73$	2.43074	−	1.76604i	0.284496	−	0.206699i	0.720876	+	0.693064i	$0.243740\pi$
$74$	0.326748			0.0379837
$75$	−2.30502	+	9.97042i	−0.266160	+	1.15128i
$76$	6.87818			0.788981
$77$	−17.4240	+	12.6593i	−1.98565	+	1.44266i
$78$	0.263379	−	0.810598i	0.0298218	−	0.0917821i
$79$	−3.99330	+	12.2901i	−0.449281	+	1.38274i	0.428439	+	0.903571i	$0.359064\pi$
$79$	−3.99330	+	12.2901i	−0.449281	+	1.38274i	−0.877720	+	0.479174i	$0.840936\pi$
$80$	5.26006	+	3.48270i	0.588092	+	0.389377i
$81$	−3.44653	−	10.6073i	−0.382948	−	1.17859i
$82$	2.66605			0.294416
$83$	−1.54328	−	4.74973i	−0.169397	−	0.521351i	0.829936	−	0.557858i	$-0.188377\pi$
$83$	−1.54328	−	4.74973i	−0.169397	−	0.521351i	−0.999333	+	0.0365075i	$0.988377\pi$
$84$	−12.6105	−	9.16207i	−1.37592	−	0.999663i
$85$	0.782772	+	2.09458i	0.0849035	+	0.227189i
$86$	−0.611831	+	0.444521i	−0.0659755	+	0.0479340i
$87$	6.74538	+	4.90080i	0.723180	+	0.525421i
$88$	−7.03736	−	5.11294i	−0.750185	−	0.545041i
$89$	6.45514	−	4.68994i	0.684244	−	0.497132i	−0.190519	−	0.981683i	$-0.561017\pi$
$89$	6.45514	−	4.68994i	0.684244	−	0.497132i	0.874763	+	0.484551i	$0.161017\pi$
$90$	1.19768	−	0.0521108i	0.126246	−	0.00549296i
$91$	−3.16699	−	2.30095i	−0.331991	−	0.241205i
$92$	−2.36402	−	7.27569i	−0.246466	−	0.758543i
$93$	−12.0281			−1.24726
$94$	0.0267378	+	0.0822903i	0.00275779	+	0.00848760i
$95$	2.99671	+	8.01875i	0.307456	+	0.822707i
$96$	2.97026	−	9.14152i	0.303151	−	0.933002i
$97$	−3.56474	+	10.9711i	−0.361945	+	1.11395i	0.589928	+	0.807456i	$0.299156\pi$
$97$	−3.56474	+	10.9711i	−0.361945	+	1.11395i	−0.951872	+	0.306495i	$0.900844\pi$
$98$	4.00170	−	2.90740i	0.404233	−	0.293692i
$99$	6.04050			0.607093
$100$	−2.02343	+	8.75240i	−0.202343	+	0.875240i
$101$	3.61563			0.359769			0.179884	−	0.983688i	$-0.442428\pi$
$101$	3.61563			0.359769			0.179884	+	0.983688i	$0.442428\pi$
$102$	0.746670	−	0.542488i	0.0739314	−	0.0537143i
$103$	−2.52763	+	7.77923i	−0.249054	+	0.766510i	0.745889	+	0.666071i	$0.232025\pi$
$103$	−2.52763	+	7.77923i	−0.249054	+	0.766510i	−0.994943	+	0.100440i	$0.967975\pi$
$104$	0.488576	−	1.50368i	0.0479088	−	0.147448i
$105$	5.18717	−	18.6934i	0.506216	−	1.82429i
$106$	1.69002	+	5.20134i	0.164149	+	0.505199i
$107$	2.51163			0.242809			0.121404	−	0.992603i	$-0.461260\pi$
$107$	2.51163			0.242809			0.121404	+	0.992603i	$0.461260\pi$
$108$	−2.05797	−	6.33379i	−0.198028	−	0.609469i
$109$	−1.96044	−	1.42434i	−0.187776	−	0.136427i	0.489926	−	0.871764i	$-0.337024\pi$
$109$	−1.96044	−	1.42434i	−0.187776	−	0.136427i	−0.677702	+	0.735337i	$0.737024\pi$
$110$	1.36984	−	4.93661i	0.130609	−	0.470687i
$111$	−1.19977	+	0.871686i	−0.113877	+	0.0827368i
$112$	−9.67523	−	7.02947i	−0.914223	−	0.664222i
$113$	10.4529	+	7.59446i	0.983324	+	0.714427i	0.958449	−	0.285264i	$-0.0920813\pi$
$113$	10.4529	+	7.59446i	0.983324	+	0.714427i	0.0248749	+	0.999691i	$0.492081\pi$
$114$	2.85850	−	2.07682i	0.267723	−	0.194512i
$115$	7.45222	−	5.92593i	0.694923	−	0.552596i
$116$	5.92134	+	4.30211i	0.549783	+	0.399441i
$117$	0.339276	+	1.04418i	0.0313661	+	0.0965349i
$118$	5.70278			0.524984
$119$	−1.30992	−	4.03151i	−0.120080	−	0.369568i
$120$	7.82792	−	0.340593i	0.714588	−	0.0310917i
$121$	4.57785	−	14.0892i	0.416168	−	1.28083i
$122$	1.88560	−	5.80327i	0.170714	−	0.525404i
$123$	−9.78936	+	7.11239i	−0.882677	+	0.641303i
$124$	−10.5587			−0.948203
$125$	−11.0853	+	1.45432i	−0.991504	+	0.130078i
$126$	−2.27262			−0.202461
$127$	9.49182	−	6.89621i	0.842263	−	0.611940i	−0.0807391	−	0.996735i	$-0.525728\pi$
$127$	9.49182	−	6.89621i	0.842263	−	0.611940i	0.923002	+	0.384796i	$0.125728\pi$
$128$	3.39368	−	10.4447i	0.299962	−	0.923188i
$129$	1.06068	−	3.26444i	0.0933877	−	0.287418i
$130$	0.930301	−	0.0404774i	0.0815928	−	0.00355010i
$131$	5.97160	+	18.3787i	0.521741	+	1.60575i	0.770671	+	0.637233i	$0.219921\pi$
$131$	5.97160	+	18.3787i	0.521741	+	1.60575i	−0.248930	+	0.968522i	$0.580079\pi$
$132$	18.6828			1.62613
$133$	−5.01480	−	15.4340i	−0.434838	−	1.33829i
$134$	−0.703454	−	0.511089i	−0.0607691	−	0.0441514i
$135$	6.48746	−	5.15877i	0.558352	−	0.443996i
$136$	1.38510	−	1.00633i	0.118771	−	0.0862922i
$137$	−4.63502	−	3.36754i	−0.395996	−	0.287708i	0.371912	−	0.928268i	$-0.378702\pi$
$137$	−4.63502	−	3.36754i	−0.395996	−	0.287708i	−0.767908	+	0.640560i	$0.778702\pi$
$138$	−3.17931	−	2.30991i	−0.270641	−	0.196632i
$139$	−11.6427	+	8.45894i	−0.987524	+	0.717478i	−0.959377	−	0.282126i	$-0.908960\pi$
$139$	−11.6427	+	8.45894i	−0.987524	+	0.717478i	−0.0281463	+	0.999604i	$0.508960\pi$
$140$	4.55349	−	16.4098i	0.384840	−	1.38688i
$141$	−0.317708	−	0.230828i	−0.0267559	−	0.0194393i
$142$	0.497035	+	1.52972i	0.0417103	+	0.128371i
$143$	4.69199			0.392364
$144$	1.03650	+	3.19001i	0.0863747	+	0.265834i
$145$	−2.43567	+	8.77761i	−0.202271	+	0.728941i
$146$	0.418682	−	1.28857i	0.0346504	−	0.106643i
$147$	−6.93741	+	21.3512i	−0.572188	+	1.76101i
$148$	−1.05320	+	0.765198i	−0.0865729	+	0.0628989i
$149$	−10.1468			−0.831260			−0.415630	−	0.909534i	$-0.636439\pi$
$149$	−10.1468			−0.831260			−0.415630	+	0.909534i	$0.636439\pi$
$150$	1.80182	+	4.24838i	0.147118	+	0.346878i
$151$	9.68629			0.788259			0.394130	−	0.919055i	$-0.371046\pi$
$151$	9.68629			0.788259			0.394130	+	0.919055i	$0.371046\pi$
$152$	5.30261	−	3.85257i	0.430098	−	0.312485i
$153$	−0.367388	+	1.13071i	−0.0297016	+	0.0914121i
$154$	−3.00120	+	9.23675i	−0.241844	+	0.744318i
$155$	−4.60028	−	12.3097i	−0.369503	−	0.988735i
$156$	1.04936	+	3.22959i	0.0840158	+	0.258574i
$157$	−18.8079			−1.50104			−0.750518	−	0.660851i	$-0.770196\pi$
$157$	−18.8079			−1.50104			−0.750518	+	0.660851i	$0.770196\pi$
$158$	1.80075	+	5.54213i	0.143260	+	0.440908i
$159$	−20.0814	−	14.5900i	−1.59256	−	1.15706i
$160$	10.4915	−	0.456484i	0.829424	−	0.0360882i
$161$	−14.6024	+	10.6092i	−1.15083	+	0.836126i
$162$	−4.06892	−	2.95624i	−0.319685	−	0.232264i
$163$	10.0771	+	7.32143i	0.789298	+	0.573458i	0.907755	−	0.419501i	$-0.137795\pi$
$163$	10.0771	+	7.32143i	0.789298	+	0.573458i	−0.118457	+	0.992959i	$0.537795\pi$
$164$	−8.59347	+	6.24352i	−0.671037	+	0.487537i
$165$	8.13982	+	21.7809i	0.633684	+	1.69564i
$166$	−1.82197	−	1.32374i	−0.141413	−	0.102742i
$167$	−3.67114	−	11.2986i	−0.284082	−	0.874313i	−0.986672	−	0.162719i	$-0.947974\pi$
$167$	−3.67114	−	11.2986i	−0.284082	−	0.874313i	0.702591	−	0.711594i	$-0.252026\pi$
$168$	−14.8537			−1.14598
$169$	−3.75369	−	11.5527i	−0.288745	−	0.888666i
$170$	0.840756	+	0.556666i	0.0644830	+	0.0426944i
$171$	−1.40649	+	4.32872i	−0.107557	+	0.331025i
$172$	0.931104	−	2.86564i	0.0709961	−	0.218503i
$173$	11.8342	−	8.59804i	0.899736	−	0.653697i	−0.0386620	−	0.999252i	$-0.512310\pi$
$173$	11.8342	−	8.59804i	0.899736	−	0.653697i	0.938398	+	0.345556i	$0.112310\pi$
$174$	3.75985			0.285033
$175$	21.1148	−	1.84089i	1.59613	−	0.139159i
$176$	14.3341			1.08048
$177$	−20.9398	+	15.2137i	−1.57393	+	1.14353i
$178$	1.11187	−	3.42197i	0.0833378	−	0.256487i
$179$	4.60377	−	14.1689i	0.344102	−	1.05904i	−0.617961	−	0.786209i	$-0.712041\pi$
$179$	4.60377	−	14.1689i	0.344102	−	1.05904i	0.962063	−	0.272828i	$-0.0879590\pi$
$180$	−3.73842	+	2.97275i	−0.278645	+	0.221576i
$181$	0.798698	+	2.45814i	0.0593667	+	0.182712i	0.976342	−	0.216232i	$-0.0693768\pi$
$181$	0.798698	+	2.45814i	0.0593667	+	0.182712i	−0.916975	+	0.398944i	$0.869377\pi$
$182$	−1.76527			−0.130850
$183$	8.55810	+	26.3391i	0.632633	+	1.94704i
$184$	−5.89772	−	4.28495i	−0.434786	−	0.315890i
$185$	−1.35095	−	0.894468i	−0.0993240	−	0.0657626i
$186$	−4.38811	+	3.18815i	−0.321752	+	0.233766i
$187$	4.11043	+	2.98640i	0.300584	+	0.218387i
$188$	−0.278896	−	0.202630i	−0.0203406	−	0.0147783i
$189$	−12.7120	+	9.23578i	−0.924659	+	0.671804i
$190$	3.21869	+	2.13110i	0.233509	+	0.154607i
$191$	−21.4921	−	15.6149i	−1.55512	−	1.12986i	−0.939875	−	0.341518i	$-0.889059\pi$
$191$	−21.4921	−	15.6149i	−1.55512	−	1.12986i	−0.615241	−	0.788339i	$-0.710941\pi$
$192$	2.22924	+	6.86088i	0.160881	+	0.495141i
$193$	−11.4461			−0.823907			−0.411954	−	0.911205i	$-0.635153\pi$
$193$	−11.4461			−0.823907			−0.411954	+	0.911205i	$0.635153\pi$
$194$	1.60749	+	4.94736i	0.115411	+	0.355200i
$195$	−3.30795	+	2.63045i	−0.236887	+	0.188370i
$196$	−6.08992	+	18.7428i	−0.434994	+	1.33877i
$197$	−8.42851	+	25.9403i	−0.600506	+	1.84817i	−0.0753590	+	0.997156i	$0.524010\pi$
$197$	−8.42851	+	25.9403i	−0.600506	+	1.84817i	−0.525147	+	0.851011i	$0.675990\pi$
$198$	2.20370	−	1.60108i	0.156610	−	0.113784i
$199$	22.9595			1.62756			0.813778	−	0.581176i	$-0.197407\pi$
$199$	22.9595			1.62756			0.813778	+	0.581176i	$0.197407\pi$
$200$	3.34243	+	7.88086i	0.236345	+	0.557261i
$201$	3.94644			0.278361
$202$	1.31906	−	0.958351i	0.0928085	−	0.0674293i
$203$	5.33633	−	16.4235i	0.374537	−	1.15271i
$204$	−1.13631	+	3.49719i	−0.0795574	+	0.244852i
$205$	−11.0229	−	7.29828i	−0.769872	−	0.509734i
$206$	1.13981	+	3.50799i	0.0794147	+	0.244413i
$207$	5.06230			0.351854
$208$	0.805105	+	2.47786i	0.0558240	+	0.171809i
$209$	15.7361	+	11.4329i	1.08849	+	0.790833i
$210$	−3.06244	−	8.19464i	−0.211329	−	0.565484i
$211$	14.6727	−	10.6603i	1.01011	−	0.733887i	0.0458772	−	0.998947i	$-0.485392\pi$
$211$	14.6727	−	10.6603i	1.01011	−	0.733887i	0.964232	+	0.265060i	$0.0853917\pi$
$212$	−17.6282	−	12.8077i	−1.21071	−	0.879634i
$213$	−5.90596	−	4.29093i	−0.404670	−	0.294010i
$214$	0.916296	−	0.665728i	0.0626367	−	0.0455082i
$215$	3.74651	−	0.163011i	0.255510	−	0.0111172i
$216$	−5.13421	−	3.73022i	−0.349339	−	0.253809i
$217$	7.69826	+	23.6928i	0.522592	+	1.60837i
$218$	−1.09274			−0.0740098
$219$	1.90026	+	5.84840i	0.128408	+	0.395198i
$220$	7.14543	+	19.1201i	0.481745	+	1.28908i
$221$	−0.285371	+	0.878282i	−0.0191961	+	0.0590797i
$222$	−0.206655	+	0.636018i	−0.0138698	+	0.0426867i
$223$	−5.98115	+	4.34556i	−0.400527	+	0.291000i	−0.769756	−	0.638339i	$-0.779622\pi$
$223$	−5.98115	+	4.34556i	−0.400527	+	0.291000i	0.369228	+	0.929339i	$0.379622\pi$
$224$	−19.9078			−1.33015
$225$	−5.09448	−	3.06316i	−0.339632	−	0.204211i
$226$	5.82639			0.387566
$227$	5.35101	−	3.88773i	0.355159	−	0.258038i	−0.395871	−	0.918306i	$-0.629557\pi$
$227$	5.35101	−	3.88773i	0.355159	−	0.258038i	0.751030	+	0.660268i	$0.229557\pi$
$228$	−4.35016	+	13.3884i	−0.288096	+	0.886670i
$229$	5.96170	−	18.3482i	0.393960	−	1.21248i	−0.535808	−	0.844340i	$-0.679993\pi$
$229$	5.96170	−	18.3482i	0.393960	−	1.21248i	0.929768	−	0.368145i	$-0.120007\pi$
$230$	1.14801	−	4.13717i	0.0756975	−	0.272797i
$231$	−13.6214	−	41.9225i	−0.896225	−	2.75830i
$232$	6.97463			0.457907
$233$	−5.39359	−	16.5998i	−0.353346	−	1.08749i	−0.956963	−	0.290211i	$-0.906274\pi$
$233$	−5.39359	−	16.5998i	−0.353346	−	1.08749i	0.603617	−	0.797274i	$-0.293726\pi$
$234$	0.400544	+	0.291012i	0.0261844	+	0.0190241i
$235$	0.114720	−	0.413427i	0.00748353	−	0.0269690i
$236$	−18.3817	+	13.3551i	−1.19655	+	0.869344i
$237$	−21.3972	−	15.5460i	−1.38990	−	1.00982i
$238$	−1.54647	−	1.12357i	−0.100243	−	0.0728305i
$239$	9.75616	−	7.08827i	0.631074	−	0.458502i	−0.225698	−	0.974197i	$-0.572466\pi$
$239$	9.75616	−	7.08827i	0.631074	−	0.458502i	0.856772	+	0.515695i	$0.172466\pi$
$240$	−10.1059	+	8.03608i	−0.652331	+	0.518727i
$241$	9.61379	+	6.98483i	0.619279	+	0.449932i	0.852670	−	0.522451i	$-0.174982\pi$
$241$	9.61379	+	6.98483i	0.619279	+	0.449932i	−0.233391	+	0.972383i	$0.574982\pi$
$242$	−2.06435	−	6.35342i	−0.132701	−	0.408413i
$243$	11.7068			0.750991
$244$	7.51262	+	23.1215i	0.480946	+	1.48020i
$245$	−24.5041	+	1.06618i	−1.56551	+	0.0681154i
$246$	−1.68617	+	5.18949i	−0.107506	+	0.330870i
$247$	−1.09250	+	3.36236i	−0.0695139	+	0.213942i
$248$	−8.14008	+	5.91411i	−0.516895	+	0.375546i
$249$	10.2214			0.647758
$250$	−3.65868	+	3.46882i	−0.231396	+	0.219387i
$251$	19.5464			1.23376			0.616879	−	0.787058i	$-0.288397\pi$
$251$	19.5464			1.23376			0.616879	+	0.787058i	$0.288397\pi$
$252$	7.32531	−	5.32215i	0.461451	−	0.335264i
$253$	6.68523	−	20.5750i	0.420297	−	1.29354i
$254$	1.63492	−	5.03176i	0.102584	−	0.315721i
$255$	−4.57219	+	0.198936i	−0.286321	+	0.0124578i
$256$	0.648036	+	1.99445i	0.0405023	+	0.124653i
$257$	13.8743			0.865454			0.432727	−	0.901525i	$-0.357551\pi$
$257$	13.8743			0.865454			0.432727	+	0.901525i	$0.357551\pi$
$258$	−0.478306	−	1.47208i	−0.0297780	−	0.0916474i
$259$	2.48491	+	1.80539i	0.154405	+	0.112182i
$260$	−2.90384	+	2.30911i	−0.180089	+	0.143205i
$261$	−3.91832	+	2.84682i	−0.242538	+	0.176214i
$262$	7.04998	+	5.12211i	0.435549	+	0.316445i
$263$	11.4518	+	8.32019i	0.706146	+	0.513045i	0.881928	−	0.471384i	$-0.156245\pi$
$263$	11.4518	+	8.32019i	0.706146	+	0.513045i	−0.175782	+	0.984429i	$0.556245\pi$
$264$	14.4032	−	10.4645i	0.886456	−	0.644048i
$265$	7.25115	−	26.1315i	0.445435	−	1.60525i
$266$	−5.92039	−	4.30141i	−0.363002	−	0.263737i
$267$	5.04638	+	15.5312i	0.308834	+	0.950492i
$268$	3.46434			0.211618
$269$	0.874306	+	2.69084i	0.0533074	+	0.164063i	0.974166	−	0.225834i	$-0.0725106\pi$
$269$	0.874306	+	2.69084i	0.0533074	+	0.164063i	−0.920858	+	0.389897i	$0.872511\pi$
$270$	0.999390	−	3.60157i	0.0608209	−	0.219185i
$271$	−2.12479	+	6.53943i	−0.129072	+	0.397242i	−0.994621	−	0.103582i	$-0.966970\pi$
$271$	−2.12479	+	6.53943i	−0.129072	+	0.397242i	0.865549	+	0.500824i	$0.166970\pi$
$272$	−0.871815	+	2.68317i	−0.0528616	+	0.162691i
$273$	6.48181	−	4.70931i	0.392297	−	0.285021i
$274$	−2.58354			−0.156077
$275$	−19.1776	+	16.6607i	−1.15645	+	1.00468i
$276$	15.6573			0.942461
$277$	−19.9213	+	14.4737i	−1.19695	+	0.869639i	−0.993982	−	0.109546i	$-0.965060\pi$
$277$	−19.9213	+	14.4737i	−1.19695	+	0.869639i	−0.202973	+	0.979184i	$0.565060\pi$
$278$	−2.00540	+	6.17199i	−0.120276	+	0.370171i
$279$	2.15911	−	6.64505i	0.129262	−	0.397829i
$280$	−5.68092	−	15.2013i	−0.339500	−	0.908451i
$281$	−6.91170	−	21.2720i	−0.412318	−	1.26898i	−0.914628	−	0.404296i	$-0.867517\pi$
$281$	−6.91170	−	21.2720i	−0.412318	−	1.26898i	0.502311	−	0.864687i	$-0.332483\pi$
$282$	−0.177089			−0.0105455
$283$	7.90975	+	24.3437i	0.470186	+	1.44708i	0.852341	+	0.522986i	$0.175182\pi$
$283$	7.90975	+	24.3437i	0.470186	+	1.44708i	−0.382155	+	0.924098i	$0.624818\pi$
$284$	−5.18447	−	3.76674i	−0.307642	−	0.223515i
$285$	−17.5039	+	0.761592i	−1.03684	+	0.0451128i
$286$	1.71174	−	1.24365i	0.101217	−	0.0735385i
$287$	20.2752	+	14.7308i	1.19681	+	0.869533i
$288$	4.51714	+	3.28189i	0.266175	+	0.193387i
$289$	−0.809017	+	0.587785i	−0.0475892	+	0.0345756i
$290$	1.43799	+	3.84784i	0.0844416	+	0.225953i
$291$	−19.1009	−	13.8776i	−1.11971	−	0.813519i
$292$	1.66812	+	5.13394i	0.0976192	+	0.300441i
$293$	−6.75387			−0.394565			−0.197283	−	0.980347i	$-0.563212\pi$
$293$	−6.75387			−0.394565			−0.197283	+	0.980347i	$0.563212\pi$
$294$	3.12838	+	9.62815i	0.182451	+	0.561525i
$295$	−23.5784	−	15.6113i	−1.37279	−	0.908924i
$296$	−0.383351	+	1.17983i	−0.0222818	+	0.0685763i
$297$	5.81977	−	17.9114i	0.337697	−	1.03932i
$298$	−3.70177	+	2.68949i	−0.214438	+	0.155798i
$299$	3.93217			0.227403
$300$	−15.7569	−	9.47415i	−0.909724	−	0.546990i
$301$	−7.10909			−0.409761
$302$	3.53376	−	2.56742i	0.203345	−	0.147739i
$303$	−2.28674	+	7.03786i	−0.131370	+	0.404314i
$304$	−3.33760	+	10.2721i	−0.191424	+	0.589144i
$305$	−23.6824	+	18.8320i	−1.35605	+	1.07832i
$306$	0.165671	+	0.509884i	0.00947079	+	0.0291481i
$307$	4.89101			0.279145			0.139572	−	0.990212i	$-0.455427\pi$
$307$	4.89101			0.279145			0.139572	+	0.990212i	$0.455427\pi$
$308$	−11.9574	−	36.8011i	−0.681337	−	2.09694i
$309$	−13.5437	−	9.84008i	−0.770475	−	0.559783i
$310$	−4.94104	−	3.27147i	−0.280632	−	0.185807i
$311$	7.67988	−	5.57976i	0.435486	−	0.316399i	−0.348353	−	0.937364i	$-0.613259\pi$
$311$	7.67988	−	5.57976i	0.435486	−	0.316399i	0.783839	+	0.620964i	$0.213259\pi$
$312$	2.61793	+	1.90203i	0.148211	+	0.107681i
$313$	12.9093	+	9.37916i	0.729677	+	0.530141i	0.889461	−	0.457011i	$-0.151080\pi$
$313$	12.9093	+	9.37916i	0.729677	+	0.530141i	−0.159784	+	0.987152i	$0.551080\pi$
$314$	−6.86151	+	4.98518i	−0.387218	+	0.281330i
$315$	9.39621	+	6.22125i	0.529417	+	0.350528i
$316$	−18.7832	−	13.6468i	−1.05664	−	0.767693i
$317$	−7.99018	−	24.5913i	−0.448773	−	1.38118i	−0.878292	−	0.478125i	$-0.841317\pi$
$317$	−7.99018	−	24.5913i	−0.448773	−	1.38118i	0.429519	−	0.903058i	$-0.358683\pi$
$318$	−11.1933			−0.627690
$319$	6.39604	+	19.6850i	0.358109	+	1.10215i
$320$	−6.16886	+	4.90542i	−0.344850	+	0.274221i
$321$	−1.58850	+	4.88891i	−0.0886617	+	0.272873i
$322$	−2.51518	+	7.74094i	−0.140166	+	0.431386i
$323$	−3.09719	+	2.25024i	−0.172332	+	0.125207i
$324$	20.0384			1.11325
$325$	−3.95717	−	2.37933i	−0.219504	−	0.131982i
$326$	5.61692			0.311093
$327$	4.01239	−	2.91517i	0.221886	−	0.161209i
$328$	−3.12789	+	9.62666i	−0.172709	+	0.531543i
$329$	−0.251342	+	0.773551i	−0.0138569	+	0.0426472i
$330$	8.74277	+	5.78861i	0.481274	+	0.318652i
$331$	4.65536	+	14.3277i	0.255881	+	0.787522i	0.993655	+	0.112474i	$0.0358774\pi$
$331$	4.65536	+	14.3277i	0.255881	+	0.787522i	−0.737773	+	0.675049i	$0.764123\pi$
$332$	8.97276			0.492444
$333$	−0.266206	−	0.819297i	−0.0145880	−	0.0448972i
$334$	−4.33409	−	3.14890i	−0.237151	−	0.172300i
$335$	1.50936	+	4.03881i	0.0824649	+	0.220664i
$336$	19.8021	−	14.3871i	1.08029	−	0.784878i
$337$	0.681986	+	0.495492i	0.0371501	+	0.0269912i	0.606205	−	0.795308i	$-0.292691\pi$
$337$	0.681986	+	0.495492i	0.0371501	+	0.0269912i	−0.569055	+	0.822299i	$0.692691\pi$
$338$	−4.43154	−	3.21970i	−0.241044	−	0.175129i
$339$	−21.3937	+	15.5434i	−1.16195	+	0.844203i
$340$	−4.01364	+	0.174633i	−0.217670	+	0.00947082i
$341$	−24.1566	−	17.5508i	−1.30815	−	0.950429i
$342$	0.634245	+	1.95200i	0.0342960	+	0.105552i
$343$	16.8243			0.908428
$344$	−0.887272	−	2.73074i	−0.0478385	−	0.147232i
$345$	6.82165	+	18.2537i	0.367265	+	0.982747i
$346$	2.03838	−	6.27348i	0.109584	−	0.337264i
$347$	4.97896	−	15.3237i	0.267284	−	0.822617i	−0.723874	−	0.689932i	$-0.757640\pi$
$347$	4.97896	−	15.3237i	0.267284	−	0.822617i	0.991158	−	0.132685i	$-0.0423597\pi$
$348$	−12.1191	+	8.80503i	−0.649651	+	0.471999i
$349$	24.6462			1.31928			0.659641	−	0.751581i	$-0.270709\pi$
$349$	24.6462			1.31928			0.659641	+	0.751581i	$0.270709\pi$
$350$	7.21517	−	6.26824i	0.385667	−	0.335051i
$351$	3.42311			0.182712
$352$	19.3041	−	14.0253i	1.02891	−	0.747548i
$353$	8.35119	−	25.7023i	0.444489	−	1.36800i	−0.438554	−	0.898705i	$-0.644509\pi$
$353$	8.35119	−	25.7023i	0.444489	−	1.36800i	0.883043	−	0.469292i	$-0.155491\pi$
$354$	−3.60677	+	11.1005i	−0.191698	+	0.589985i
$355$	2.13257	−	7.68529i	0.113185	−	0.407893i
$356$	4.42990	+	13.6338i	0.234784	+	0.722592i
$357$	8.67583			0.459174
$358$	−2.07604	−	6.38939i	−0.109722	−	0.337690i
$359$	5.09190	+	3.69948i	0.268740	+	0.195251i	0.713991	−	0.700155i	$-0.246886\pi$
$359$	5.09190	+	3.69948i	0.268740	+	0.195251i	−0.445251	+	0.895406i	$0.646886\pi$
$360$	−1.21698	+	4.38574i	−0.0641407	+	0.231149i
$361$	3.51426	−	2.55326i	0.184961	−	0.134382i
$362$	0.942929	+	0.685078i	0.0495593	+	0.0360069i
$363$	24.5294	+	17.8216i	1.28746	+	0.935394i
$364$	5.68998	−	4.13401i	0.298236	−	0.216681i
$365$	−5.25850	+	4.18151i	−0.275243	+	0.218870i
$366$	10.1036	+	7.34066i	0.528121	+	0.383702i
$367$	−10.7060	−	32.9496i	−0.558847	−	1.71995i	−0.685562	−	0.728015i	$-0.740443\pi$
$367$	−10.7060	−	32.9496i	−0.558847	−	1.71995i	0.126715	−	0.991939i	$-0.459557\pi$
$368$	12.0129			0.626214
$369$	−2.17206	−	6.68493i	−0.113073	−	0.348003i
$370$	−0.729941	+	0.0317597i	−0.0379478	+	0.00165111i
$371$	−15.8866	+	48.8940i	−0.824792	+	2.53845i
$372$	6.67797	−	20.5527i	0.346236	−	1.06561i
$373$	10.6100	−	7.70860i	0.549364	−	0.399136i	−0.278187	−	0.960527i	$-0.589733\pi$
$373$	10.6100	−	7.70860i	0.549364	−	0.399136i	0.827551	+	0.561391i	$0.189733\pi$
$374$	2.29114			0.118472
$375$	4.18019	−	22.4975i	0.215864	−	1.16177i
$376$	−0.328506			−0.0169414
$377$	−3.04358	+	2.21129i	−0.156752	+	0.113887i
$378$	−2.18957	+	6.73880i	−0.112619	+	0.346607i
$379$	1.19405	−	3.67491i	0.0613343	−	0.188768i	−0.915694	−	0.401875i	$-0.868359\pi$
$379$	1.19405	−	3.67491i	0.0613343	−	0.188768i	0.977029	+	0.213108i	$0.0683585\pi$
$380$	−15.3655	+	0.668554i	−0.788235	+	0.0342961i
$381$	7.42034	+	22.8375i	0.380156	+	1.17000i
$382$	−11.9796			−0.612931
$383$	−5.91215	−	18.1957i	−0.302097	−	0.929758i	−0.980745	−	0.195294i	$-0.937434\pi$
$383$	−5.91215	−	18.1957i	−0.302097	−	0.929758i	0.678648	−	0.734464i	$-0.262566\pi$
$384$	18.1843	+	13.2117i	0.927963	+	0.674204i
$385$	37.6940	−	29.9739i	1.92107	−	1.52761i
$386$	−4.17577	+	3.03387i	−0.212541	+	0.154420i
$387$	1.61307	+	1.17196i	0.0819970	+	0.0595743i
$388$	−16.7674	−	12.1823i	−0.851238	−	0.618461i
$389$	22.0762	−	16.0393i	1.11931	−	0.813224i	0.135203	−	0.990818i	$-0.456831\pi$
$389$	22.0762	−	16.0393i	1.11931	−	0.813224i	0.984104	+	0.177594i	$0.0568314\pi$
$390$	−0.509587	+	1.83644i	−0.0258040	+	0.0929917i
$391$	3.44478	+	2.50278i	0.174210	+	0.126571i
$392$	5.80323	+	17.8605i	0.293107	+	0.902092i
$393$	−39.5511			−1.99509
$394$	3.80077	+	11.6976i	0.191480	+	0.589316i
$395$	7.72625	−	27.8437i	0.388750	−	1.40097i
$396$	−3.35366	+	10.3215i	−0.168528	+	0.518675i
$397$	9.05126	−	27.8569i	0.454270	−	1.39810i	−0.417721	−	0.908576i	$-0.637171\pi$
$397$	9.05126	−	27.8569i	0.454270	−	1.39810i	0.871990	−	0.489523i	$-0.162829\pi$
$398$	8.37610	−	6.08559i	0.419856	−	0.305043i
$399$	33.2140			1.66278
$400$	−12.0892	−	7.26891i	−0.604462	−	0.363445i
$401$	−16.5901			−0.828471			−0.414236	−	0.910170i	$-0.635951\pi$
$401$	−16.5901			−0.828471			−0.414236	+	0.910170i	$0.635951\pi$
$402$	1.43974	−	1.04604i	0.0718079	−	0.0521715i
$403$	1.67710	−	5.16158i	0.0835423	−	0.257117i
$404$	−2.00738	+	6.17809i	−0.0998711	+	0.307371i
$405$	8.73042	+	23.3613i	0.433818	+	1.16083i
$406$	−2.40638	−	7.40608i	−0.119427	−	0.367557i
$407$	−3.68147			−0.182484
$408$	1.08281	+	3.33256i	0.0536073	+	0.164986i
$409$	8.46382	+	6.14932i	0.418509	+	0.304065i	0.777038	−	0.629454i	$-0.216721\pi$
$409$	8.46382	+	6.14932i	0.418509	+	0.304065i	−0.358529	+	0.933519i	$0.616721\pi$
$410$	−5.95584	+	0.259138i	−0.294138	+	0.0127979i
$411$	9.48639	−	6.89227i	0.467929	−	0.339971i
$412$	−11.8892	−	8.63799i	−0.585738	−	0.425563i
$413$	43.3695	+	31.5098i	2.13407	+	1.55050i
$414$	1.84683	−	1.34180i	0.0907667	−	0.0659459i
$415$	3.90929	+	10.4607i	0.191900	+	0.513494i
$416$	3.50871	+	2.54923i	0.172029	+	0.124986i
$417$	−9.10184	−	28.0126i	−0.445719	−	1.37178i
$418$	8.77124			0.429015
$419$	0.304859	+	0.938259i	0.0148933	+	0.0458370i	0.958227	−	0.286009i	$-0.0923287\pi$
$419$	0.304859	+	0.938259i	0.0148933	+	0.0458370i	−0.943334	+	0.331846i	$0.892329\pi$
$420$	29.0618	+	19.2419i	1.41807	+	0.938909i
$421$	−8.97334	+	27.6171i	−0.437334	+	1.34597i	0.453343	+	0.891336i	$0.350231\pi$
$421$	−8.97334	+	27.6171i	−0.437334	+	1.34597i	−0.890676	+	0.454638i	$0.849769\pi$
$422$	2.52729	−	7.77821i	0.123027	−	0.378637i
$423$	0.184553	−	0.134086i	0.00897329	−	0.00651948i
$424$	−20.7639			−1.00839
$425$	−1.95227	−	4.60311i	−0.0946989	−	0.223284i
$426$	−3.29196			−0.159496
$427$	46.4049	−	33.7152i	2.24569	−	1.63159i
$428$	−1.39445	+	4.29167i	−0.0674032	+	0.207446i
$429$	−2.96749	+	9.13300i	−0.143272	+	0.440945i
$430$	1.32360	−	1.05251i	0.0638295	−	0.0507565i
$431$	2.99954	+	9.23163i	0.144483	+	0.444672i	0.996944	−	0.0781183i	$-0.0248912\pi$
$431$	2.99954	+	9.23163i	0.144483	+	0.444672i	−0.852461	+	0.522790i	$0.824891\pi$
$432$	10.4577			0.503146
$433$	7.37399	+	22.6948i	0.354371	+	1.09064i	0.956373	+	0.292148i	$0.0943699\pi$
$433$	7.37399	+	22.6948i	0.354371	+	1.09064i	−0.602002	+	0.798495i	$0.705630\pi$
$434$	9.08844	+	6.60314i	0.436259	+	0.316961i
$435$	−15.5452	−	10.2925i	−0.745336	−	0.493489i
$436$	3.52223	−	2.55905i	0.168684	−	0.122556i
$437$	13.1878	+	9.58148i	0.630857	+	0.458345i
$438$	2.24341	+	1.62994i	0.107195	+	0.0778814i
$439$	−3.33121	+	2.42027i	−0.158990	+	0.115513i	−0.664436	−	0.747345i	$-0.731328\pi$
$439$	−3.33121	+	2.42027i	−0.158990	+	0.115513i	0.505446	+	0.862858i	$0.331328\pi$
$440$	16.2181	+	10.7380i	0.773168	+	0.511916i
$441$	−10.5503	−	7.66526i	−0.502397	−	0.365013i
$442$	0.128686	+	0.396055i	0.00612097	+	0.0188384i
$443$	−6.74185			−0.320315			−0.160157	−	0.987091i	$-0.551200\pi$
$443$	−6.74185			−0.320315			−0.160157	+	0.987091i	$0.551200\pi$
$444$	−0.823355	−	2.53403i	−0.0390747	−	0.120260i
$445$	−13.9646	+	11.1045i	−0.661987	+	0.526406i
$446$	−1.03022	+	3.17070i	−0.0487824	+	0.150137i
$447$	6.41744	−	19.7509i	0.303535	−	0.934184i
$448$	12.0877	−	8.78221i	0.571089	−	0.414921i
$449$	−24.0188			−1.13352			−0.566758	−	0.823884i	$-0.691803\pi$
$449$	−24.0188			−1.13352			−0.566758	+	0.823884i	$0.691803\pi$
$450$	−2.67049	+	0.232826i	−0.125888	+	0.0109755i
$451$	−30.0384			−1.41445
$452$	−18.7802	+	13.6446i	−0.883345	+	0.641787i
$453$	−6.12618	+	18.8544i	−0.287833	+	0.885858i
$454$	0.921683	−	2.83665i	0.0432567	−	0.133131i
$455$	7.29857	+	4.83240i	0.342162	+	0.226546i
$456$	4.14538	+	12.7582i	0.194125	+	0.597455i
$457$	−41.8241			−1.95645			−0.978225	−	0.207547i	$-0.933452\pi$
$457$	−41.8241			−1.95645			−0.978225	+	0.207547i	$0.933452\pi$
$458$	−2.68839	−	8.27400i	−0.125620	−	0.386619i
$459$	2.99883	+	2.17877i	0.139973	+	0.101696i
$460$	5.98830	+	16.0238i	0.279206	+	0.747113i
$461$	15.1805	−	11.0293i	0.707027	−	0.513685i	−0.175186	−	0.984535i	$-0.556053\pi$
$461$	15.1805	−	11.0293i	0.707027	−	0.513685i	0.882213	+	0.470850i	$0.156053\pi$
$462$	−16.0813	−	11.6837i	−0.748168	−	0.543576i
$463$	20.9796	+	15.2425i	0.975003	+	0.708381i	0.956586	−	0.291449i	$-0.0941374\pi$
$463$	20.9796	+	15.2425i	0.975003	+	0.708381i	0.0184169	+	0.999830i	$0.494137\pi$
$464$	−9.29820	+	6.75553i	−0.431658	+	0.313618i
$465$	26.8703	−	1.16913i	1.24608	−	0.0542170i
$466$	−6.36758	−	4.62632i	−0.294972	−	0.214310i
$467$	4.84737	+	14.9187i	0.224309	+	0.690354i	0.998361	+	0.0572310i	$0.0182271\pi$
$467$	4.84737	+	14.9187i	0.224309	+	0.690354i	−0.774051	+	0.633123i	$0.781773\pi$
$468$	−1.97258			−0.0911825
$469$	−2.52581	−	7.77363i	−0.116631	−	0.358953i
$470$	−0.0677295	−	0.181234i	−0.00312413	−	0.00835970i
$471$	11.8952	−	36.6097i	0.548103	−	1.68689i
$472$	−6.69067	+	20.5918i	−0.307963	+	0.947813i
$473$	6.89350	−	5.00842i	0.316963	−	0.230287i
$474$	−11.9267			−0.547812
$475$	−7.47393	−	17.6222i	−0.342928	−	0.808564i
$476$	7.61597			0.349077
$477$	11.6651	−	8.47519i	0.534108	−	0.388052i
$478$	1.68045	−	5.17189i	0.0768619	−	0.236557i
$479$	7.29044	−	22.4377i	0.333109	−	1.02520i	−0.634537	−	0.772892i	$-0.718809\pi$
$479$	7.29044	−	22.4377i	0.333109	−	1.02520i	0.967646	−	0.252311i	$-0.0811906\pi$
$480$	−5.74687	+	20.7104i	−0.262308	+	0.945298i
$481$	−0.206777	−	0.636394i	−0.00942821	−	0.0290170i
$482$	5.35869			0.244082
$483$	−11.4156	−	35.1335i	−0.519427	−	1.59863i
$484$	21.5328	+	15.6445i	0.978764	+	0.711114i
$485$	6.89708	−	24.8555i	0.313180	−	1.12863i
$486$	4.27088	−	3.10297i	0.193731	−	0.140754i
$487$	−16.7248	−	12.1513i	−0.757871	−	0.550626i	0.140385	−	0.990097i	$-0.455166\pi$
$487$	−16.7248	−	12.1513i	−0.757871	−	0.550626i	−0.898257	+	0.439471i	$0.855166\pi$
$488$	18.7424	+	13.6171i	0.848428	+	0.616419i
$489$	−20.6245	+	14.9846i	−0.932674	+	0.677627i
$490$	−8.65702	+	6.88397i	−0.391084	+	0.310986i
$491$	−28.7068	−	20.8567i	−1.29552	−	0.941250i	−0.295619	−	0.955306i	$-0.595526\pi$
$491$	−28.7068	−	20.8567i	−1.29552	−	0.941250i	−0.999901	+	0.0140555i	$0.995526\pi$
$492$	−6.71804	−	20.6760i	−0.302873	−	0.932147i
$493$	−4.07379			−0.183474
$494$	0.492653	+	1.51623i	0.0221655	+	0.0682185i
$495$	−13.4942	+	0.587133i	−0.606519	+	0.0263896i
$496$	5.12358	−	15.7687i	0.230055	−	0.708038i
$497$	−4.67226	+	14.3797i	−0.209579	+	0.645019i
$498$	3.72899	−	2.70927i	0.167100	−	0.121405i
$499$	−15.3872			−0.688824			−0.344412	−	0.938819i	$-0.611922\pi$
$499$	−15.3872			−0.688824			−0.344412	+	0.938819i	$0.611922\pi$
$500$	3.66952	−	19.7491i	0.164106	−	0.883209i
$501$	24.3147			1.08630
$502$	7.13093	−	5.18092i	0.318269	−	0.231236i
$503$	−3.29116	+	10.1291i	−0.146745	+	0.451636i	−0.997231	−	0.0743618i	$-0.976308\pi$
$503$	−3.29116	+	10.1291i	−0.146745	+	0.451636i	0.850486	+	0.525998i	$0.176308\pi$
$504$	2.66630	−	8.20603i	0.118766	−	0.365526i
$505$	−8.07716	+	0.351437i	−0.359429	+	0.0156387i
$506$	−3.01466	−	9.27816i	−0.134018	−	0.412465i
$507$	24.8614			1.10413
$508$	6.51385	+	20.0476i	0.289005	+	0.889467i
$509$	−18.2069	−	13.2281i	−0.807007	−	0.586325i	0.105954	−	0.994371i	$-0.466210\pi$
$509$	−18.2069	−	13.2281i	−0.807007	−	0.586325i	−0.912961	+	0.408046i	$0.866210\pi$
$510$	−1.61530	+	1.28447i	−0.0715266	+	0.0568772i
$511$	10.3039	−	7.48619i	0.455816	−	0.331169i
$512$	18.5346	+	13.4662i	0.819122	+	0.595127i
$513$	11.4805	+	8.34107i	0.506877	+	0.368267i
$514$	5.06162	−	3.67748i	0.223259	−	0.162207i
$515$	4.89046	−	17.6241i	0.215500	−	0.776612i
$516$	4.98911	+	3.62480i	0.219633	+	0.159573i
$517$	−0.301254	−	0.927165i	−0.0132491	−	0.0407767i
$518$	1.38508			0.0608569
$519$	9.25151	+	28.4732i	0.406096	+	1.24984i
$520$	−0.945300	+	3.40665i	−0.0414541	+	0.149391i
$521$	7.32885	−	22.5559i	0.321083	−	0.988191i	−0.652095	−	0.758137i	$-0.726110\pi$
$521$	7.32885	−	22.5559i	0.321083	−	0.988191i	0.973178	−	0.230054i	$-0.0738902\pi$
$522$	−0.674910	+	2.07716i	−0.0295400	+	0.0909148i
$523$	−34.7403	+	25.2403i	−1.51909	+	1.10368i	−0.557147	+	0.830414i	$0.688104\pi$
$523$	−34.7403	+	25.2403i	−1.51909	+	1.10368i	−0.961938	+	0.273266i	$0.911896\pi$
$524$	−34.7194			−1.51672
$525$	−9.77092	+	42.2644i	−0.426438	+	1.84457i
$526$	6.38317			0.278319
$527$	4.75452	−	3.45436i	0.207110	−	0.150474i
$528$	−9.06575	+	27.9015i	−0.394536	+	1.21426i
$529$	−1.50477	+	4.63121i	−0.0654248	+	0.201357i
$530$	−4.28099	−	11.4553i	−0.185954	−	0.497586i
$531$	−4.64612	−	14.2993i	−0.201625	−	0.620537i
$532$	29.1565			1.26409
$533$	−1.68716	−	5.19256i	−0.0730792	−	0.224915i
$534$	5.95768	+	4.32851i	0.257814	+	0.187313i
$535$	−5.61088	+	0.244129i	−0.242579	+	0.0105546i
$536$	2.67077	−	1.94043i	0.115360	−	0.0838137i
$537$	24.6683	+	17.9225i	1.06451	+	0.773415i
$538$	1.03219	+	0.749931i	0.0445009	+	0.0323318i
$539$	−45.0871	+	32.7577i	−1.94204	+	1.41097i
$540$	5.21306	+	13.9494i	0.224334	+	0.600285i
$541$	22.8961	+	16.6350i	0.984381	+	0.715195i	0.958683	−	0.284475i	$-0.0918192\pi$
$541$	22.8961	+	16.6350i	0.984381	+	0.715195i	0.0256978	+	0.999670i	$0.491819\pi$
$542$	0.958159	+	2.94891i	0.0411564	+	0.126667i
$543$	−5.28993			−0.227013
$544$	1.45126	+	4.46651i	0.0622222	+	0.191500i
$545$	4.51798	+	2.99136i	0.193529	+	0.128136i
$546$	1.11646	−	3.43611i	0.0477800	−	0.147052i
$547$	8.66964	−	26.6824i	0.370687	−	1.14086i	−0.575656	−	0.817692i	$-0.695253\pi$
$547$	8.66964	−	26.6824i	0.370687	−	1.14086i	0.946343	−	0.323165i	$-0.104747\pi$
$548$	8.32751	−	6.05029i	0.355734	−	0.258456i
$549$	−16.0875			−0.686597
$550$	−2.58033	+	11.1613i	−0.110026	+	0.475920i
$551$	−15.5958			−0.664405
$552$	12.0707	−	8.76991i	0.513765	−	0.373272i
$553$	−16.9275	+	52.0975i	−0.719831	+	2.21541i
$554$	−3.43134	+	10.5606i	−0.145784	+	0.448676i
$555$	2.59551	−	2.06392i	0.110173	−	0.0876087i
$556$	−7.98994	−	24.5905i	−0.338849	−	1.04287i
$557$	−31.7949			−1.34719			−0.673596	−	0.739099i	$-0.735251\pi$
$557$	−31.7949			−1.34719			−0.673596	+	0.739099i	$0.735251\pi$
$558$	−0.973634	−	2.99654i	−0.0412172	−	0.126854i
$559$	1.25296	+	0.910330i	0.0529946	+	0.0385029i
$560$	22.2973	+	14.7631i	0.942232	+	0.623854i
$561$	−8.41273	+	6.11221i	−0.355186	+	0.258058i
$562$	−8.15984	−	5.92847i	−0.344202	−	0.250078i
$563$	6.96384	+	5.05953i	0.293491	+	0.213234i	0.724780	−	0.688980i	$-0.241941\pi$
$563$	6.96384	+	5.05953i	0.293491	+	0.213234i	−0.431289	+	0.902214i	$0.641941\pi$
$564$	0.570810	−	0.414718i	0.0240355	−	0.0174628i
$565$	−24.0894	−	15.9497i	−1.01345	−	0.671007i
$566$	9.33813	+	6.78455i	0.392511	+	0.285176i
$567$	−14.6098	−	44.9643i	−0.613553	−	1.88832i
$568$	−6.10668			−0.256231
$569$	6.54218	+	20.1347i	0.274262	+	0.844093i	0.989414	+	0.145123i	$0.0463578\pi$
$569$	6.54218	+	20.1347i	0.274262	+	0.844093i	−0.715151	+	0.698970i	$0.753642\pi$
$570$	−6.18390	+	4.91737i	−0.259015	+	0.205966i
$571$	−13.6910	+	42.1367i	−0.572952	+	1.76336i	0.0700972	+	0.997540i	$0.477669\pi$
$571$	−13.6910	+	42.1367i	−0.572952	+	1.76336i	−0.643049	+	0.765825i	$0.722331\pi$
$572$	−2.60497	+	8.01729i	−0.108919	+	0.335220i
$573$	43.9875	−	31.9588i	1.83760	−	1.33510i
$574$	11.3013			0.471709
$575$	−16.0719	+	13.9626i	−0.670246	+	0.582281i
$576$	−4.19051			−0.174605
$577$	15.1457	−	11.0040i	0.630524	−	0.458103i	−0.226058	−	0.974114i	$-0.572584\pi$
$577$	15.1457	−	11.0040i	0.630524	−	0.458103i	0.856582	+	0.516011i	$0.172584\pi$
$578$	−0.139349	+	0.428872i	−0.00579615	+	0.0178387i
$579$	7.23917	−	22.2799i	0.300850	−	0.925920i
$580$	−13.6462	−	9.03516i	−0.566626	−	0.375165i
$581$	−6.54194	−	20.1340i	−0.271405	−	0.835300i
$582$	−10.6467			−0.441322
$583$	−19.0414	−	58.6035i	−0.788615	−	2.42711i
$584$	4.16160	+	3.02358i	0.172208	+	0.125117i
$585$	−0.859422	−	2.29968i	−0.0355327	−	0.0950802i
$586$	−2.46395	+	1.79016i	−0.101785	+	0.0739510i
$587$	23.8252	+	17.3100i	0.983371	+	0.714461i	0.958459	−	0.285229i	$-0.0920697\pi$
$587$	23.8252	+	17.3100i	0.983371	+	0.714461i	0.0249113	+	0.999690i	$0.492070\pi$
$588$	−32.6314	−	23.7081i	−1.34570	−	0.977707i
$589$	18.2019	−	13.2244i	0.749995	−	0.544903i
$590$	−12.7398	+	0.554307i	−0.524488	+	0.0228204i
$591$	−45.1622	−	32.8123i	−1.85773	−	1.34972i
$592$	−0.631708	−	1.94420i	−0.0259630	−	0.0799060i
$593$	18.5976			0.763713			0.381857	−	0.924222i	$-0.375285\pi$
$593$	18.5976			0.763713			0.381857	+	0.924222i	$0.375285\pi$
$594$	−2.62438	−	8.07702i	−0.107680	−	0.331404i
$595$	3.31815	+	8.87889i	0.136031	+	0.363999i
$596$	5.63347	−	17.3380i	0.230756	−	0.710194i
$597$	−14.5209	+	44.6908i	−0.594302	+	1.82907i
$598$	1.43454	−	1.04225i	0.0586625	−	0.0426208i
$599$	4.80784			0.196443			0.0982216	−	0.995165i	$-0.468685\pi$
$599$	4.80784			0.196443			0.0982216	+	0.995165i	$0.468685\pi$
$600$	−17.4541	+	1.52174i	−0.712561	+	0.0621246i
$601$	−32.0693			−1.30813			−0.654066	−	0.756437i	$-0.726938\pi$
$601$	−32.0693			−1.30813			−0.654066	+	0.756437i	$0.726938\pi$
$602$	−2.59354	+	1.88432i	−0.105705	+	0.0767990i
$603$	−0.708405	+	2.18025i	−0.0288485	+	0.0887866i
$604$	−5.37778	+	16.5511i	−0.218819	+	0.673455i
$605$	−8.85726	+	31.9196i	−0.360099	+	1.29771i
$606$	1.03119	+	3.17367i	0.0418892	+	0.128922i
$607$	−36.5676			−1.48423			−0.742116	−	0.670271i	$-0.766178\pi$
$607$	−36.5676			−1.48423			−0.742116	+	0.670271i	$0.766178\pi$
$608$	5.55590	+	17.0993i	0.225321	+	0.693468i
$609$	28.5935	+	20.7744i	1.15867	+	0.841821i
$610$	−3.64827	+	13.1475i	−0.147714	+	0.532328i
$611$	0.143353	−	0.104152i	0.00579944	−	0.00421354i
$612$	−1.72808	−	1.25553i	−0.0698536	−	0.0507516i
$613$	−12.8568	−	9.34103i	−0.519282	−	0.377281i	0.297051	−	0.954862i	$-0.403997\pi$
$613$	−12.8568	−	9.34103i	−0.519282	−	0.377281i	−0.816334	+	0.577581i	$0.803997\pi$
$614$	1.78434	−	1.29640i	0.0720101	−	0.0523184i
$615$	21.1777	−	16.8403i	0.853966	−	0.679065i
$616$	−29.8312	−	21.6736i	−1.20193	−	0.873256i
$617$	4.18624	+	12.8839i	0.168532	+	0.518688i	0.999279	−	0.0379620i	$-0.0120866\pi$
$617$	4.18624	+	12.8839i	0.168532	+	0.518688i	−0.830747	+	0.556650i	$0.812087\pi$
$618$	−7.54921			−0.303674
$619$	−6.91489	−	21.2819i	−0.277933	−	0.855390i	−0.988428	−	0.151688i	$-0.951529\pi$
$619$	−6.91489	−	21.2819i	−0.277933	−	0.855390i	0.710495	−	0.703702i	$-0.248471\pi$
$620$	23.5878	−	1.02630i	0.947307	−	0.0412173i
$621$	4.87731	−	15.0108i	0.195720	−	0.602363i
$622$	1.32282	−	4.07122i	0.0530402	−	0.163241i
$623$	27.3632	−	19.8805i	1.09628	−	0.796497i
$624$	−5.33236			−0.213465
$625$	24.6228	−	4.32637i	0.984912	−	0.173055i
$626$	7.19560			0.287594
$627$	−32.2067	+	23.3996i	−1.28621	+	0.934489i
$628$	10.4421	−	32.1374i	0.416684	−	1.28242i
$629$	0.223910	−	0.689125i	0.00892789	−	0.0274772i
$630$	5.07692	−	0.220897i	0.202269	−	0.00880074i
$631$	4.24447	+	13.0631i	0.168970	+	0.520035i	0.999307	−	0.0372263i	$-0.0118522\pi$
$631$	4.24447	+	13.0631i	0.168970	+	0.520035i	−0.830337	+	0.557261i	$0.811852\pi$
$632$	−22.1244			−0.880061
$633$	11.4705	+	35.3027i	0.455913	+	1.40316i
$634$	−9.43308	−	6.85354i	−0.374636	−	0.272189i
$635$	−20.5340	+	16.3284i	−0.814866	+	0.647973i
$636$	36.0793	−	26.2132i	1.43064	−	1.03942i
$637$	−8.19503	−	5.95404i	−0.324699	−	0.235908i
$638$	7.55106	+	5.48616i	0.298949	+	0.217199i
$639$	3.43071	−	2.49256i	0.135717	−	0.0986040i
$640$	−6.56611	+	23.6628i	−0.259548	+	0.935354i
$641$	−13.9807	−	10.1576i	−0.552205	−	0.401200i	0.276393	−	0.961045i	$-0.410861\pi$
$641$	−13.9807	−	10.1576i	−0.552205	−	0.401200i	−0.828598	+	0.559844i	$0.810861\pi$
$642$	0.716325	+	2.20462i	0.0282711	+	0.0870095i
$643$	−15.8309			−0.624309			−0.312155	−	0.950031i	$-0.601051\pi$
$643$	−15.8309			−0.624309			−0.312155	+	0.950031i	$0.601051\pi$
$644$	−10.0210	−	30.8415i	−0.394883	−	1.21533i
$645$	−2.05221	+	7.39570i	−0.0808057	+	0.291206i
$646$	−0.533474	+	1.64187i	−0.0209893	+	0.0645983i
$647$	−3.11594	+	9.58989i	−0.122500	+	0.377017i	−0.993437	−	0.114377i	$-0.963513\pi$
$647$	−3.11594	+	9.58989i	−0.122500	+	0.377017i	0.870937	+	0.491395i	$0.163513\pi$
$648$	15.4483	−	11.2238i	0.606865	−	0.440913i
$649$	−64.2532			−2.52216
$650$	−2.07432	+	0.180849i	−0.0813614	+	0.00709349i
$651$	−50.9870			−1.99834
$652$	−18.1050	+	13.1540i	−0.709046	+	0.515152i
$653$	6.70847	−	20.6466i	0.262523	−	0.807962i	−0.729731	−	0.683734i	$-0.760355\pi$
$653$	6.70847	−	20.6466i	0.262523	−	0.807962i	0.992254	−	0.124228i	$-0.0396453\pi$
$654$	0.691114	−	2.12703i	0.0270247	−	0.0831734i
$655$	−15.1267	−	40.4767i	−0.591048	−	1.58156i
$656$	−5.15432	−	15.8634i	−0.201243	−	0.619361i
$657$	−3.57210			−0.139361
$658$	0.113341	+	0.348827i	0.00441848	+	0.0135987i
$659$	−2.10900	−	1.53228i	−0.0821551	−	0.0596892i	0.545950	−	0.837818i	$-0.316169\pi$
$659$	−2.10900	−	1.53228i	−0.0821551	−	0.0596892i	−0.628105	+	0.778129i	$0.716169\pi$
$660$	−41.7366	+	1.81596i	−1.62460	+	0.0706861i
$661$	25.6405	−	18.6289i	0.997299	−	0.724580i	0.0357913	−	0.999359i	$-0.488605\pi$
$661$	25.6405	−	18.6289i	0.997299	−	0.724580i	0.961507	+	0.274779i	$0.0886048\pi$
$662$	5.49604	+	3.99310i	0.213610	+	0.155196i
$663$	−1.52910	−	1.11095i	−0.0593852	−	0.0431459i
$664$	6.91739	−	5.02578i	0.268447	−	0.195038i
$665$	12.7030	+	33.9913i	0.492601	+	1.31813i
$666$	−0.314278	−	0.228336i	−0.0121780	−	0.00884785i
$667$	5.36026	+	16.4972i	0.207550	+	0.638773i
$668$	21.3443			0.825837
$669$	−4.67583	−	14.3907i	−0.180778	−	0.556378i
$670$	1.62116	+	1.07337i	0.0626309	+	0.0414681i
$671$	−21.2450	+	65.3855i	−0.820155	+	2.52418i
$672$	12.5909	−	38.7507i	0.485703	−	1.49484i
$673$	−4.96411	+	3.60664i	−0.191352	+	0.139026i	−0.679337	−	0.733827i	$-0.737732\pi$
$673$	−4.96411	+	3.60664i	−0.191352	+	0.139026i	0.487984	+	0.872852i	$0.337732\pi$
$674$	0.380136			0.0146423
$675$	−13.9913	+	12.1550i	−0.538524	+	0.467847i
$676$	21.8242			0.839394
$677$	19.0400	−	13.8334i	0.731767	−	0.531660i	−0.158355	−	0.987382i	$-0.550619\pi$
$677$	19.0400	−	13.8334i	0.731767	−	0.531660i	0.890122	+	0.455722i	$0.150619\pi$
$678$	−3.68495	+	11.3411i	−0.141520	+	0.435553i
$679$	−15.1109	+	46.5065i	−0.579902	+	1.78475i
$680$	−2.99643	+	2.38273i	−0.114908	+	0.0913734i
$681$	4.18321	+	12.8746i	0.160301	+	0.493356i
$682$	−13.4648			−0.515594
$683$	8.29369	+	25.5253i	0.317349	+	0.976700i	0.974777	+	0.223182i	$0.0716445\pi$
$683$	8.29369	+	25.5253i	0.317349	+	0.976700i	−0.657428	+	0.753518i	$0.728355\pi$
$684$	−6.61567	−	4.80657i	−0.252957	−	0.183784i
$685$	10.6817	+	7.07241i	0.408128	+	0.270223i
$686$	6.13786	−	4.45941i	0.234344	−	0.170261i
$687$	31.9444	+	23.2090i	1.21876	+	0.885478i
$688$	3.82783	+	2.78108i	0.145935	+	0.106028i
$689$	9.06093	−	6.58315i	0.345194	−	0.250798i
$690$	7.32696	+	4.85120i	0.278933	+	0.184682i
$691$	−1.81751	−	1.32050i	−0.0691414	−	0.0502342i	0.552678	−	0.833395i	$-0.313606\pi$
$691$	−1.81751	−	1.32050i	−0.0691414	−	0.0502342i	−0.621819	+	0.783161i	$0.713606\pi$
$692$	8.12132	+	24.9949i	0.308726	+	0.950162i
$693$	25.6056			0.972675
$694$	−2.24523	−	6.91009i	−0.0852276	−	0.262304i
$695$	25.1871	−	20.0286i	0.955402	−	0.759726i
$696$	−4.41116	+	13.5762i	−0.167205	+	0.514603i
$697$	1.82696	−	5.62281i	0.0692011	−	0.212979i
$698$	8.99144	−	6.53266i	0.340331	−	0.247265i
$699$	35.7228			1.35116
$700$	−8.57728	+	37.1013i	−0.324191	+	1.40230i
$701$	13.7916			0.520900			0.260450	−	0.965487i	$-0.416129\pi$
$701$	13.7916			0.520900			0.260450	+	0.965487i	$0.416129\pi$
$702$	1.24882	−	0.907322i	0.0471337	−	0.0342447i
$703$	0.857203	−	2.63820i	0.0323300	−	0.0995016i
$704$	−5.53396	+	17.0318i	−0.208569	+	0.641909i
$705$	0.732182	+	0.484779i	0.0275756	+	0.0182578i
$706$	−3.76591	−	11.5903i	−0.141732	−	0.436206i
$707$	15.3266			0.576416
$708$	−14.3701	−	44.2267i	−0.540063	−	1.66214i
$709$	−13.3179	−	9.67601i	−0.500164	−	0.363390i	0.308916	−	0.951089i	$-0.400034\pi$
$709$	−13.3179	−	9.67601i	−0.500164	−	0.363390i	−0.809079	+	0.587699i	$0.800034\pi$
$710$	−1.25904	−	3.36901i	−0.0472510	−	0.126437i
$711$	12.4294	−	9.03048i	0.466139	−	0.338670i
$712$	11.0517	+	8.02951i	0.414179	+	0.300919i
$713$	−20.2447	−	14.7086i	−0.758169	−	0.550842i
$714$	3.16512	−	2.29959i	0.118452	−	0.0860602i
$715$	−10.4817	+	0.456059i	−0.391993	+	0.0170556i
$716$	21.6547	+	15.7331i	0.809275	+	0.587972i
$717$	7.62699	+	23.4735i	0.284835	+	0.876633i
$718$	2.83820			0.105921
$719$	9.56039	+	29.4238i	0.356542	+	1.09732i	0.955110	+	0.296252i	$0.0957368\pi$
$719$	9.56039	+	29.4238i	0.356542	+	1.09732i	−0.598567	+	0.801072i	$0.704263\pi$
$720$	−2.62555	−	7.02558i	−0.0978485	−	0.261828i
$721$	−10.7146	+	32.9760i	−0.399031	+	1.22809i
$722$	0.605314	−	1.86296i	0.0225274	−	0.0693323i
$723$	−19.6763	+	14.2957i	−0.731771	+	0.531663i
$724$	−4.64369			−0.172582
$725$	4.58800	−	19.8455i	0.170394	−	0.737044i
$726$	13.6726			0.507437
$727$	−37.5682	+	27.2949i	−1.39333	+	1.01231i	−0.397838	+	0.917456i	$0.630239\pi$
$727$	−37.5682	+	27.2949i	−1.39333	+	1.01231i	−0.995491	+	0.0948566i	$0.969761\pi$
$728$	2.07107	−	6.37408i	0.0767588	−	0.236239i
$729$	2.93554	−	9.03466i	0.108724	−	0.334617i
$730$	−0.810069	+	2.91931i	−0.0299820	+	0.108048i
$731$	0.518245	+	1.59499i	0.0191680	+	0.0589929i
$732$	−49.7575			−1.83909
$733$	8.73530	+	26.8845i	0.322646	+	0.993001i	0.972492	+	0.232936i	$0.0748332\pi$
$733$	8.73530	+	26.8845i	0.322646	+	0.993001i	−0.649846	+	0.760065i	$0.725167\pi$
$734$	−12.6393	−	9.18298i	−0.466525	−	0.338950i
$735$	13.4225	−	48.3718i	0.495098	−	1.78422i
$736$	16.1780	−	11.7540i	0.596328	−	0.433258i
$737$	7.92581	+	5.75844i	0.291951	+	0.212115i
$738$	−2.56430	−	1.86308i	−0.0943933	−	0.0685808i
$739$	7.89158	−	5.73357i	0.290297	−	0.210913i	−0.433099	−	0.901346i	$-0.642580\pi$
$739$	7.89158	−	5.73357i	0.290297	−	0.210913i	0.723396	+	0.690433i	$0.242580\pi$
$740$	2.27843	−	1.81179i	0.0837569	−	0.0666027i
$741$	−5.85389	−	4.25310i	−0.215048	−	0.156242i
$742$	7.16395	+	22.0484i	0.262997	+	0.809422i
$743$	24.0625			0.882767			0.441383	−	0.897319i	$-0.354488\pi$
$743$	24.0625			0.882767			0.441383	+	0.897319i	$0.354488\pi$
$744$	−6.36360	−	19.5851i	−0.233301	−	0.718026i
$745$	22.6675	−	0.986264i	0.830474	−	0.0361339i
$746$	1.82751	−	5.62451i	0.0669101	−	0.205928i
$747$	−1.83480	+	5.64693i	−0.0671317	+	0.206610i
$748$	−7.38501	+	5.36552i	−0.270023	+	0.196183i
$749$	10.6468			0.389024
$750$	−4.43812	−	9.31554i	−0.162057	−	0.340155i
$751$	20.6672			0.754155			0.377078	−	0.926182i	$-0.376929\pi$
$751$	20.6672			0.754155			0.377078	+	0.926182i	$0.376929\pi$
$752$	0.437946	−	0.318187i	0.0159703	−	0.0116031i
$753$	−12.3623	+	38.0472i	−0.450507	+	1.38652i
$754$	−0.524240	+	1.61345i	−0.0190917	+	0.0587582i
$755$	−21.6387	+	0.941501i	−0.787514	+	0.0342647i
$756$	−8.72370	−	26.8488i	−0.317278	−	0.976481i
$757$	−19.0715			−0.693165			−0.346582	−	0.938020i	$-0.612658\pi$
$757$	−19.0715			−0.693165			−0.346582	+	0.938020i	$0.612658\pi$
$758$	−0.538449	−	1.65718i	−0.0195574	−	0.0601914i
$759$	35.8213	+	26.0257i	1.30023	+	0.944673i
$760$	−11.4713	+	9.12188i	−0.416108	+	0.330885i
$761$	−24.1141	+	17.5199i	−0.874134	+	0.635095i	−0.931693	−	0.363247i	$-0.881668\pi$
$761$	−24.1141	+	17.5199i	−0.874134	+	0.635095i	0.0575593	+	0.998342i	$0.481668\pi$
$762$	8.76033	+	6.36476i	0.317353	+	0.230571i
$763$	−8.31027	−	6.03776i	−0.300852	−	0.218582i
$764$	38.6138	−	28.0546i	1.39700	−	1.01498i
$765$	0.710825	−	2.56165i	0.0256999	−	0.0926168i
$766$	−6.97979	−	5.07111i	−0.252190	−	0.183227i
$767$	−3.60891	−	11.1071i	−0.130310	−	0.401053i
$768$	−4.29207			−0.154877
$769$	15.3536	+	47.2535i	0.553665	+	1.70400i	0.699444	+	0.714688i	$0.253431\pi$
$769$	15.3536	+	47.2535i	0.553665	+	1.70400i	−0.145779	+	0.989317i	$0.546569\pi$
$770$	5.80674	−	20.9262i	0.209260	−	0.754127i
$771$	−8.77491	+	27.0064i	−0.316021	+	0.972611i
$772$	6.35481	−

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.364820 - 0.265058i) q^{2} +(-0.632459 + 1.94651i) q^{3} +(-0.555196 + 1.70872i) q^{4} +(-2.23395 + 0.0971993i) q^{5} +(0.285203 + 0.877764i) q^{6} +4.23898 q^{7} +(0.529060 + 1.62828i) q^{8} +(-0.961836 - 0.698814i) q^{9} +(-0.789229 + 0.627587i) q^{10} +(-4.11043 + 2.98640i) q^{11} +(-2.97489 - 2.16138i) q^{12} +(-0.747112 - 0.542808i) q^{13} +(1.54647 - 1.12357i) q^{14} +(1.22368 - 4.40988i) q^{15} +(-2.28244 - 1.65829i) q^{16} +(-0.309017 - 0.951057i) q^{17} -0.536123 q^{18} +(-1.18302 - 3.64096i) q^{19} +(1.07420 - 3.87116i) q^{20} +(-2.68098 + 8.25121i) q^{21} +(-0.708001 + 2.17900i) q^{22} +(-3.44478 + 2.50278i) q^{23} -3.50406 q^{24} +(4.98110 - 0.434278i) q^{25} -0.416437 q^{26} +(-2.99883 + 2.17877i) q^{27} +(-2.35346 + 7.24321i) q^{28} +(1.25887 - 3.87441i) q^{29} +(-0.722448 - 1.93316i) q^{30} +(1.81606 + 5.58927i) q^{31} -4.69637 q^{32} +(-3.21338 - 9.88976i) q^{33} +(-0.364820 - 0.265058i) q^{34} +(-9.46969 + 0.412026i) q^{35} +(1.72808 - 1.25553i) q^{36} +(0.586205 + 0.425903i) q^{37} +(-1.39665 - 1.01473i) q^{38} +(1.52910 - 1.11095i) q^{39} +(-1.34016 - 3.58607i) q^{40} +(4.78305 + 3.47509i) q^{41} +(1.20897 + 3.72082i) q^{42} -1.67707 q^{43} +(-2.82082 - 8.68160i) q^{44} +(2.21662 + 1.46763i) q^{45} +(-0.593346 + 1.82613i) q^{46} +(-0.0592930 + 0.182485i) q^{47} +(4.67143 - 3.39399i) q^{48} +10.9690 q^{49} +(1.70210 - 1.47871i) q^{50} +2.04668 q^{51} +(1.34230 - 0.975237i) q^{52} +(-3.74774 + 11.5344i) q^{53} +(-0.516532 + 1.58972i) q^{54} +(8.89224 - 7.07102i) q^{55} +(2.24267 + 6.90224i) q^{56} +7.83537 q^{57} +(-0.567679 - 1.74714i) q^{58} +(10.2311 + 7.43334i) q^{59} +(6.85585 + 4.53928i) q^{60} +(10.9472 - 7.95360i) q^{61} +(2.14401 + 1.55772i) q^{62} +(-4.07720 - 2.96226i) q^{63} +(2.85155 - 2.07177i) q^{64} +(1.72177 + 1.13999i) q^{65} +(-3.79366 - 2.75626i) q^{66} +(-0.595852 - 1.83385i) q^{67} +1.79665 q^{68} +(-2.69300 - 8.28820i) q^{69} +(-3.34553 + 2.66033i) q^{70} +(-1.10221 + 3.39226i) q^{71} +(0.628996 - 1.93585i) q^{72} +(2.43074 - 1.76604i) q^{73} +0.326748 q^{74} +(-2.30502 + 9.97042i) q^{75} +6.87818 q^{76} +(-17.4240 + 12.6593i) q^{77} +(0.263379 - 0.810598i) q^{78} +(-3.99330 + 12.2901i) q^{79} +(5.26006 + 3.48270i) q^{80} +(-3.44653 - 10.6073i) q^{81} +2.66605 q^{82} +(-1.54328 - 4.74973i) q^{83} +(-12.6105 - 9.16207i) q^{84} +(0.782772 + 2.09458i) q^{85} +(-0.611831 + 0.444521i) q^{86} +(6.74538 + 4.90080i) q^{87} +(-7.03736 - 5.11294i) q^{88} +(6.45514 - 4.68994i) q^{89} +(1.19768 - 0.0521108i) q^{90} +(-3.16699 - 2.30095i) q^{91} +(-2.36402 - 7.27569i) q^{92} -12.0281 q^{93} +(0.0267378 + 0.0822903i) q^{94} +(2.99671 + 8.01875i) q^{95} +(2.97026 - 9.14152i) q^{96} +(-3.56474 + 10.9711i) q^{97} +(4.00170 - 2.90740i) q^{98} +6.04050 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 2 q^{2} + 2 q^{3} - 20 q^{4} - 17 q^{6} - 44 q^{7} + 15 q^{8} - 22 q^{9} - 2 q^{10} + 4 q^{11} + 14 q^{12} + 6 q^{13} - 10 q^{14} + 14 q^{15} - 32 q^{16} + 20 q^{17} - 62 q^{18} - 3 q^{19} + 16 q^{21}+ \cdots + 76 q^{99}+O(q^{100}) \) 80 * q + 2 * q^2 + 2 * q^3 - 20 * q^4 - 17 * q^6 - 44 * q^7 + 15 * q^8 - 22 * q^9 - 2 * q^10 + 4 * q^11 + 14 * q^12 + 6 * q^13 - 10 * q^14 + 14 * q^15 - 32 * q^16 + 20 * q^17 - 62 * q^18 - 3 * q^19 + 16 * q^21 + 17 * q^22 - 5 * q^23 + 30 * q^24 - 14 * q^25 + 18 * q^26 + 17 * q^27 + 32 * q^28 + 20 * q^29 - 114 * q^30 - 21 * q^31 - 88 * q^32 - 2 * q^34 - 2 * q^35 + 47 * q^36 + 6 * q^37 + 22 * q^38 - 46 * q^39 + 59 * q^40 - 26 * q^41 - 3 * q^42 - 102 * q^43 - 44 * q^44 + 74 * q^45 + 2 * q^46 + 2 * q^47 + 72 * q^48 + 108 * q^49 + 7 * q^50 + 18 * q^51 + 65 * q^52 - 18 * q^53 - 29 * q^54 - 49 * q^55 - 117 * q^56 + 2 * q^57 + 42 * q^58 + 21 * q^59 + 112 * q^60 + 4 * q^61 + 15 * q^62 + 41 * q^63 - 11 * q^64 + 8 * q^65 - 156 * q^66 + 21 * q^67 - 80 * q^68 - 67 * q^69 + 32 * q^70 - 4 * q^71 + 83 * q^72 - 2 * q^73 + 78 * q^74 - 68 * q^75 + 16 * q^76 + 2 * q^77 - 2 * q^78 - 53 * q^79 - 54 * q^80 - 21 * q^81 - 72 * q^82 - 42 * q^83 - 52 * q^84 + 42 * q^86 - 8 * q^87 + 68 * q^88 - 73 * q^89 + 97 * q^90 - 83 * q^91 + 117 * q^92 - 120 * q^93 + 80 * q^94 + 16 * q^95 + 88 * q^96 + 57 * q^97 + 17 * q^98 + 76 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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