LMFDB - Embedded newform 425.2.k.c.86.8

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			86.8
Character	$\chi$	$=$	425.86
Dual form			425.2.k.c.341.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.422163 + 0.306719i) q^{2} +(0.519515 - 1.59890i) q^{3} +(-0.533889 + 1.64314i) q^{4} +(0.360883 - 2.20675i) q^{5} +(0.271094 + 0.834342i) q^{6} +3.01247 q^{7} +(-0.601098 - 1.84999i) q^{8} +(0.140459 + 0.102050i) q^{9} +(0.524502 + 1.04230i) q^{10} +(-0.154244 + 0.112065i) q^{11} +(2.34986 + 1.70727i) q^{12} +(-1.29480 - 0.940726i) q^{13} +(-1.27175 + 0.923982i) q^{14} +(-3.34090 - 1.72346i) q^{15} +(-1.97429 - 1.43441i) q^{16} +(-0.309017 - 0.951057i) q^{17} -0.0905972 q^{18} +(0.536719 + 1.65185i) q^{19} +(3.43334 + 1.77114i) q^{20} +(1.56502 - 4.81665i) q^{21} +(0.0307436 - 0.0946191i) q^{22} +(6.98691 - 5.07629i) q^{23} -3.27023 q^{24} +(-4.73953 - 1.59276i) q^{25} +0.835154 q^{26} +(4.31646 - 3.13609i) q^{27} +(-1.60833 + 4.94992i) q^{28} +(0.527659 - 1.62397i) q^{29} +(1.93902 - 0.297138i) q^{30} +(-0.469509 - 1.44500i) q^{31} +5.16382 q^{32} +(0.0990486 + 0.304840i) q^{33} +(0.422163 + 0.306719i) q^{34} +(1.08715 - 6.64778i) q^{35} +(-0.242672 + 0.176311i) q^{36} +(3.62369 + 2.63276i) q^{37} +(-0.733237 - 0.532728i) q^{38} +(-2.17680 + 1.58153i) q^{39} +(-4.29940 + 0.658847i) q^{40} +(2.44169 + 1.77399i) q^{41} +(0.816663 + 2.51343i) q^{42} -8.55826 q^{43} +(-0.101789 - 0.313275i) q^{44} +(0.275888 - 0.273131i) q^{45} +(-1.39262 + 4.28604i) q^{46} +(2.17809 - 6.70347i) q^{47} +(-3.31915 + 2.41150i) q^{48} +2.07499 q^{49} +(2.48938 - 0.781300i) q^{50} -1.68118 q^{51} +(2.23703 - 1.62529i) q^{52} +(-4.32916 + 13.3238i) q^{53} +(-0.860349 + 2.64788i) q^{54} +(0.191636 + 0.380821i) q^{55} +(-1.81079 - 5.57305i) q^{56} +2.91998 q^{57} +(0.275344 + 0.847421i) q^{58} +(-7.67463 - 5.57594i) q^{59} +(4.61556 - 4.56944i) q^{60} +(4.25901 - 3.09435i) q^{61} +(0.641418 + 0.466017i) q^{62} +(0.423129 + 0.307421i) q^{63} +(1.76861 - 1.28497i) q^{64} +(-2.54322 + 2.51781i) q^{65} +(-0.135315 - 0.0983121i) q^{66} +(3.96079 + 12.1901i) q^{67} +1.72770 q^{68} +(-4.48668 - 13.8086i) q^{69} +(1.58005 + 3.13989i) q^{70} +(-2.25975 + 6.95479i) q^{71} +(0.104361 - 0.321190i) q^{72} +(-0.877455 + 0.637508i) q^{73} -2.33730 q^{74} +(-5.00892 + 6.75058i) q^{75} -3.00077 q^{76} +(-0.464656 + 0.337592i) q^{77} +(0.433875 - 1.33533i) q^{78} +(-5.18563 + 15.9597i) q^{79} +(-3.87787 + 3.83912i) q^{80} +(-2.61089 - 8.03548i) q^{81} -1.57491 q^{82} +(3.37649 + 10.3918i) q^{83} +(7.07889 + 5.14311i) q^{84} +(-2.21027 + 0.338705i) q^{85} +(3.61298 - 2.62498i) q^{86} +(-2.32244 - 1.68735i) q^{87} +(0.300035 + 0.217988i) q^{88} +(3.84664 - 2.79475i) q^{89} +(-0.0326949 + 0.199926i) q^{90} +(-3.90054 - 2.83391i) q^{91} +(4.61082 + 14.1907i) q^{92} -2.55433 q^{93} +(1.13657 + 3.49802i) q^{94} +(3.83892 - 0.588282i) q^{95} +(2.68268 - 8.25645i) q^{96} +(0.257510 - 0.792536i) q^{97} +(-0.875981 + 0.636438i) q^{98} -0.0331012 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 $

$2$	−0.422163	+	0.306719i	−0.298514	+	0.216883i	−0.726952	−	0.686688i	$-0.759064\pi$
$2$	−0.422163	+	0.306719i	−0.298514	+	0.216883i	0.428438	+	0.903571i	$0.359064\pi$
$3$	0.519515	−	1.59890i	0.299942	−	0.923126i	−0.681574	−	0.731749i	$-0.738704\pi$
$3$	0.519515	−	1.59890i	0.299942	−	0.923126i	0.981516	−	0.191378i	$-0.0612955\pi$
$4$	−0.533889	+	1.64314i	−0.266945	+	0.821571i
$5$	0.360883	−	2.20675i	0.161392	−	0.986890i
$5$	0.360883	−	2.20675i	0.161392	−	0.986890i
$6$	0.271094	+	0.834342i	0.110674	+	0.340619i
$7$	3.01247			1.13861			0.569304	−	0.822127i	$-0.307213\pi$
$7$	3.01247			1.13861			0.569304	+	0.822127i	$0.307213\pi$
$8$	−0.601098	−	1.84999i	−0.212520	−	0.654071i
$9$	0.140459	+	0.102050i	0.0468197	+	0.0340165i
$10$	0.524502	+	1.04230i	0.165862	+	0.329604i
$11$	−0.154244	+	0.112065i	−0.0465063	+	0.0337888i	−0.610796	−	0.791788i	$-0.709150\pi$
$11$	−0.154244	+	0.112065i	−0.0465063	+	0.0337888i	0.564289	+	0.825577i	$0.309150\pi$
$12$	2.34986	+	1.70727i	0.678346	+	0.492847i
$13$	−1.29480	−	0.940726i	−0.359112	−	0.260910i	0.393569	−	0.919295i	$-0.371240\pi$
$13$	−1.29480	−	0.940726i	−0.359112	−	0.260910i	−0.752682	+	0.658384i	$0.771240\pi$
$14$	−1.27175	+	0.923982i	−0.339890	+	0.246945i
$15$	−3.34090	−	1.72346i	−0.862617	−	0.444995i
$16$	−1.97429	−	1.43441i	−0.493573	−	0.358602i
$17$	−0.309017	−	0.951057i	−0.0749476	−	0.230665i
$17$	−0.309017	−	0.951057i	−0.0749476	−	0.230665i
$18$	−0.0905972			−0.0213540
$19$	0.536719	+	1.65185i	0.123132	+	0.378961i	0.993556	−	0.113342i	$-0.0361555\pi$
$19$	0.536719	+	1.65185i	0.123132	+	0.378961i	−0.870424	+	0.492302i	$0.836155\pi$
$20$	3.43334	+	1.77114i	0.767718	+	0.396040i
$21$	1.56502	−	4.81665i	0.341516	−	1.05108i
$22$	0.0307436	−	0.0946191i	0.00655456	−	0.0201729i
$23$	6.98691	−	5.07629i	1.45687	−	1.05848i	0.472707	−	0.881220i	$-0.343277\pi$
$23$	6.98691	−	5.07629i	1.45687	−	1.05848i	0.984164	−	0.177259i	$-0.0567230\pi$
$24$	−3.27023			−0.667534
$25$	−4.73953	−	1.59276i	−0.947905	−	0.318552i
$26$	0.835154			0.163787
$27$	4.31646	−	3.13609i	0.830703	−	0.603541i
$28$	−1.60833	+	4.94992i	−0.303945	+	0.935447i
$29$	0.527659	−	1.62397i	0.0979838	−	0.301563i	−0.890036	−	0.455890i	$-0.849321\pi$
$29$	0.527659	−	1.62397i	0.0979838	−	0.301563i	0.988020	+	0.154327i	$0.0493210\pi$
$30$	1.93902	−	0.297138i	0.354015	−	0.0542498i
$31$	−0.469509	−	1.44500i	−0.0843262	−	0.259529i	0.899999	−	0.435892i	$-0.143567\pi$
$31$	−0.469509	−	1.44500i	−0.0843262	−	0.259529i	−0.984325	+	0.176362i	$0.943567\pi$
$32$	5.16382			0.912844
$33$	0.0990486	+	0.304840i	0.0172422	+	0.0530659i
$34$	0.422163	+	0.306719i	0.0724003	+	0.0526019i
$35$	1.08715	−	6.64778i	0.183762	−	1.12368i
$36$	−0.242672	+	0.176311i	−0.0404453	+	0.0293852i
$37$	3.62369	+	2.63276i	0.595731	+	0.432824i	0.844361	−	0.535775i	$-0.179980\pi$
$37$	3.62369	+	2.63276i	0.595731	+	0.432824i	−0.248630	+	0.968599i	$0.579980\pi$
$38$	−0.733237	−	0.532728i	−0.118947	−	0.0864198i
$39$	−2.17680	+	1.58153i	−0.348566	+	0.253248i
$40$	−4.29940	+	0.658847i	−0.679795	+	0.104173i
$41$	2.44169	+	1.77399i	0.381329	+	0.277051i	0.761893	−	0.647703i	$-0.224270\pi$
$41$	2.44169	+	1.77399i	0.381329	+	0.277051i	−0.380564	+	0.924754i	$0.624270\pi$
$42$	0.816663	+	2.51343i	0.126014	+	0.387831i
$43$	−8.55826			−1.30512			−0.652561	−	0.757736i	$-0.726305\pi$
$43$	−8.55826			−1.30512			−0.652561	+	0.757736i	$0.726305\pi$
$44$	−0.101789	−	0.313275i	−0.0153453	−	0.0472280i
$45$	0.275888	−	0.273131i	0.0411269	−	0.0407160i
$46$	−1.39262	+	4.28604i	−0.205330	+	0.631941i
$47$	2.17809	−	6.70347i	0.317707	−	0.977802i	−0.656919	−	0.753961i	$-0.728141\pi$
$47$	2.17809	−	6.70347i	0.317707	−	0.977802i	0.974626	−	0.223840i	$-0.0718594\pi$
$48$	−3.31915	+	2.41150i	−0.479078	+	0.348071i
$49$	2.07499			0.296426
$50$	2.48938	−	0.781300i	0.352052	−	0.110493i
$51$	−1.68118			−0.235413
$52$	2.23703	−	1.62529i	0.310220	−	0.225388i
$53$	−4.32916	+	13.3238i	−0.594656	+	1.83016i	−0.0382250	+	0.999269i	$0.512170\pi$
$53$	−4.32916	+	13.3238i	−0.594656	+	1.83016i	−0.556431	+	0.830894i	$0.687830\pi$
$54$	−0.860349	+	2.64788i	−0.117079	+	0.360331i
$55$	0.191636	+	0.380821i	0.0258401	+	0.0513499i
$56$	−1.81079	−	5.57305i	−0.241977	−	0.744729i
$57$	2.91998			0.386761
$58$	0.275344	+	0.847421i	0.0361544	+	0.111272i
$59$	−7.67463	−	5.57594i	−0.999151	−	0.725926i	−0.0372451	−	0.999306i	$-0.511858\pi$
$59$	−7.67463	−	5.57594i	−0.999151	−	0.725926i	−0.961906	+	0.273380i	$0.911858\pi$
$60$	4.61556	−	4.56944i	0.595866	−	0.589912i
$61$	4.25901	−	3.09435i	0.545310	−	0.396191i	−0.280743	−	0.959783i	$-0.590581\pi$
$61$	4.25901	−	3.09435i	0.545310	−	0.396191i	0.826053	+	0.563592i	$0.190581\pi$
$62$	0.641418	+	0.466017i	0.0814601	+	0.0591842i
$63$	0.423129	+	0.307421i	0.0533093	+	0.0387315i
$64$	1.76861	−	1.28497i	0.221076	−	0.160621i
$65$	−2.54322	+	2.51781i	−0.315448	+	0.312296i
$66$	−0.135315	−	0.0983121i	−0.0166561	−	0.0121014i
$67$	3.96079	+	12.1901i	0.483887	+	1.48925i	0.833586	+	0.552390i	$0.186284\pi$
$67$	3.96079	+	12.1901i	0.483887	+	1.48925i	−0.349699	+	0.936862i	$0.613716\pi$
$68$	1.72770			0.209515
$69$	−4.48668	−	13.8086i	−0.540133	−	1.66236i
$70$	1.58005	+	3.13989i	0.188852	+	0.375289i
$71$	−2.25975	+	6.95479i	−0.268183	+	0.825381i	0.722760	+	0.691099i	$0.242873\pi$
$71$	−2.25975	+	6.95479i	−0.268183	+	0.825381i	−0.990943	+	0.134283i	$0.957127\pi$
$72$	0.104361	−	0.321190i	0.0122991	−	0.0378526i
$73$	−0.877455	+	0.637508i	−0.102698	+	0.0746147i	−0.637949	−	0.770078i	$-0.720217\pi$
$73$	−0.877455	+	0.637508i	−0.102698	+	0.0746147i	0.535251	+	0.844693i	$0.320217\pi$
$74$	−2.33730			−0.271706
$75$	−5.00892	+	6.75058i	−0.578380	+	0.779490i
$76$	−3.00077			−0.344212
$77$	−0.464656	+	0.337592i	−0.0529524	+	0.0384722i
$78$	0.433875	−	1.33533i	0.0491266	−	0.151196i
$79$	−5.18563	+	15.9597i	−0.583429	+	1.79561i	0.0220602	+	0.999757i	$0.492977\pi$
$79$	−5.18563	+	15.9597i	−0.583429	+	1.79561i	−0.605489	+	0.795853i	$0.707023\pi$
$80$	−3.87787	+	3.83912i	−0.433559	+	0.429227i
$81$	−2.61089	−	8.03548i	−0.290098	−	0.892831i
$82$	−1.57491			−0.173920
$83$	3.37649	+	10.3918i	0.370618	+	1.14064i	0.946388	+	0.323032i	$0.104702\pi$
$83$	3.37649	+	10.3918i	0.370618	+	1.14064i	−0.575770	+	0.817611i	$0.695298\pi$
$84$	7.07889	+	5.14311i	0.772370	+	0.561160i
$85$	−2.21027	+	0.338705i	−0.239737	+	0.0367377i
$86$	3.61298	−	2.62498i	0.389597	−	0.283059i
$87$	−2.32244	−	1.68735i	−0.248991	−	0.180903i
$88$	0.300035	+	0.217988i	0.0319838	+	0.0232376i
$89$	3.84664	−	2.79475i	0.407743	−	0.296243i	−0.364944	−	0.931029i	$-0.618912\pi$
$89$	3.84664	−	2.79475i	0.407743	−	0.296243i	0.772687	+	0.634787i	$0.218912\pi$
$90$	−0.0326949	+	0.199926i	−0.00344635	+	0.0210740i
$91$	−3.90054	−	2.83391i	−0.408888	−	0.297074i
$92$	4.61082	+	14.1907i	0.480712	+	1.47948i
$93$	−2.55433			−0.264871
$94$	1.13657	+	3.49802i	0.117229	+	0.360793i
$95$	3.83892	−	0.588282i	0.393865	−	0.0603565i
$96$	2.68268	−	8.25645i	0.273800	−	0.842670i
$97$	0.257510	−	0.792536i	0.0261462	−	0.0804698i	−0.937132	−	0.348975i	$-0.886530\pi$
$97$	0.257510	−	0.792536i	0.0261462	−	0.0804698i	0.963278	+	0.268505i	$0.0865297\pi$
$98$	−0.875981	+	0.636438i	−0.0884875	+	0.0642899i
$99$	−0.0331012			−0.00332679
$100$	5.14751	−	6.93736i	0.514751	−	0.693736i
$101$	10.6199			1.05672			0.528358	−	0.849022i	$-0.322808\pi$
$101$	10.6199			1.05672			0.528358	+	0.849022i	$0.322808\pi$
$102$	0.709733	−	0.515651i	0.0702741	−	0.0510571i
$103$	−1.84277	+	5.67145i	−0.181573	+	0.558825i	−0.999873	−	0.0159675i	$-0.994917\pi$
$103$	−1.84277	+	5.67145i	−0.181573	+	0.558825i	0.818299	+	0.574792i	$0.194917\pi$
$104$	−0.962033	+	2.96083i	−0.0943351	+	0.290334i
$105$	−10.0644	−	5.19187i	−0.982181	−	0.506674i
$106$	−2.25905	−	6.95264i	−0.219418	−	0.675300i
$107$	−16.7652			−1.62075			−0.810375	−	0.585912i	$-0.800736\pi$
$107$	−16.7652			−1.62075			−0.810375	+	0.585912i	$0.800736\pi$
$108$	2.84853	+	8.76688i	0.274100	+	0.843594i
$109$	−6.85323	−	4.97917i	−0.656421	−	0.476918i	0.209032	−	0.977909i	$-0.432969\pi$
$109$	−6.85323	−	4.97917i	−0.656421	−	0.476918i	−0.865452	+	0.500991i	$0.832969\pi$
$110$	−0.197706	−	0.101990i	−0.0188506	−	0.00972437i
$111$	6.09209	−	4.42616i	0.578236	−	0.420113i
$112$	−5.94750	−	4.32111i	−0.561986	−	0.408307i
$113$	−1.90544	−	1.38438i	−0.179249	−	0.130232i	0.494543	−	0.869153i	$-0.335336\pi$
$113$	−1.90544	−	1.38438i	−0.179249	−	0.130232i	−0.673792	+	0.738921i	$0.735336\pi$
$114$	−1.23271	+	0.895614i	−0.115454	+	0.0838819i
$115$	−8.68066	−	17.2503i	−0.809476	−	1.60860i
$116$	2.38670	+	1.73404i	0.221599	+	0.161001i
$117$	−0.0858656	−	0.264267i	−0.00793828	−	0.0244315i
$118$	4.95019			0.455702
$119$	−0.930905	−	2.86503i	−0.0853359	−	0.262637i
$120$	−1.18017	+	7.21660i	−0.107734	+	0.658783i
$121$	−3.38795	+	10.4271i	−0.307996	+	0.947914i
$122$	−0.848897	+	2.61264i	−0.0768555	+	0.236537i
$123$	4.10494	−	2.98241i	0.370130	−	0.268915i
$124$	2.62500			0.235732
$125$	−5.22524	+	9.88417i	−0.467360	+	0.884067i
$126$	−0.272921			−0.0243138
$127$	−1.16808	+	0.848662i	−0.103651	+	0.0753066i	−0.638403	−	0.769702i	$-0.720405\pi$
$127$	−1.16808	+	0.848662i	−0.103651	+	0.0753066i	0.534753	+	0.845009i	$0.320405\pi$
$128$	−3.54393	+	10.9071i	−0.313243	+	0.964061i
$129$	−4.44614	+	13.6838i	−0.391461	+	1.20479i
$130$	0.301393	−	1.84298i	0.0264339	−	0.161640i
$131$	1.36125	+	4.18950i	0.118933	+	0.366038i	0.992747	−	0.120222i	$-0.0383607\pi$
$131$	1.36125	+	4.18950i	0.118933	+	0.366038i	−0.873814	+	0.486260i	$0.838361\pi$
$132$	−0.553777			−0.0482001
$133$	1.61685	+	4.97615i	0.140199	+	0.431487i
$134$	−5.41102	−	3.93133i	−0.467441	−	0.339616i
$135$	−5.36285	−	10.6571i	−0.461560	−	0.917219i
$136$	−1.57370	+	1.14336i	−0.134943	+	0.0980421i
$137$	6.81825	+	4.95375i	0.582522	+	0.423227i	0.839633	−	0.543155i	$-0.182770\pi$
$137$	6.81825	+	4.95375i	0.582522	+	0.423227i	−0.257110	+	0.966382i	$0.582770\pi$
$138$	6.12946	+	4.45332i	0.521775	+	0.379092i
$139$	−5.90693	+	4.29164i	−0.501019	+	0.364012i	−0.809406	−	0.587249i	$-0.800211\pi$
$139$	−5.90693	+	4.29164i	−0.501019	+	0.364012i	0.308387	+	0.951261i	$0.400211\pi$
$140$	10.3428	+	5.33552i	0.874129	+	0.450934i
$141$	−9.58664	−	6.96510i	−0.807341	−	0.586567i
$142$	−1.17919	−	3.62916i	−0.0989550	−	0.304552i
$143$	0.305137			0.0255168
$144$	−0.130927	−	0.402951i	−0.0109106	−	0.0335793i
$145$	−3.39327	−	1.75047i	−0.281796	−	0.145369i
$146$	0.174893	−	0.538264i	0.0144742	−	0.0445471i
$147$	1.07799	−	3.31770i	0.0889107	−	0.273639i
$148$	−6.26066	+	4.54863i	−0.514623	+	0.373895i
$149$	−7.86147			−0.644037			−0.322018	−	0.946733i	$-0.604361\pi$
$149$	−7.86147			−0.644037			−0.322018	+	0.946733i	$0.604361\pi$
$150$	0.0440473	−	4.38617i	0.00359644	−	0.358129i
$151$	−1.53233			−0.124699			−0.0623497	−	0.998054i	$-0.519859\pi$
$151$	−1.53233			−0.124699			−0.0623497	+	0.998054i	$0.519859\pi$
$152$	2.73329	−	1.98585i	0.221699	−	0.161074i
$153$	0.0536506	−	0.165120i	0.00433740	−	0.0133491i
$154$	0.0926143	−	0.285038i	0.00746307	−	0.0229690i
$155$	−3.35819	+	0.514615i	−0.269737	+	0.0413349i
$156$	−1.43652	−	4.42115i	−0.115014	−	0.353975i
$157$	−5.44739			−0.434749			−0.217375	−	0.976088i	$-0.569749\pi$
$157$	−5.44739			−0.434749			−0.217375	+	0.976088i	$0.569749\pi$
$158$	−2.70597	−	8.32813i	−0.215276	−	0.662551i
$159$	19.0544	+	13.8438i	1.51111	+	1.09789i
$160$	1.86353	−	11.3953i	0.147325	−	0.900877i
$161$	21.0479	−	15.2922i	1.65880	−	1.20519i
$162$	3.56685	+	2.59147i	0.280239	+	0.203605i
$163$	1.70290	+	1.23723i	0.133381	+	0.0969071i	0.652475	−	0.757810i	$-0.273731\pi$
$163$	1.70290	+	1.23723i	0.133381	+	0.0969071i	−0.519094	+	0.854717i	$0.673731\pi$
$164$	−4.21852	+	3.06493i	−0.329411	+	0.239331i
$165$	0.708453	−	0.108564i	0.0551530	−	0.00845173i
$166$	−4.61278	−	3.35138i	−0.358021	−	0.260117i
$167$	3.52565	+	10.8508i	0.272823	+	0.839662i	0.989787	+	0.142552i	$0.0455309\pi$
$167$	3.52565	+	10.8508i	0.272823	+	0.839662i	−0.716965	+	0.697110i	$0.754469\pi$
$168$	−9.85149			−0.760059
$169$	−3.22568	−	9.92763i	−0.248130	−	0.763664i
$170$	0.829205	−	0.820919i	0.0635971	−	0.0629616i
$171$	−0.0931836	+	0.286790i	−0.00712593	+	0.0219313i
$172$	4.56916	−	14.0624i	0.348395	−	1.07225i
$173$	11.7604	−	8.54440i	0.894123	−	0.649618i	−0.0428267	−	0.999083i	$-0.513636\pi$
$173$	11.7604	−	8.54440i	0.894123	−	0.649618i	0.936950	+	0.349464i	$0.113636\pi$
$174$	1.49799			0.113562
$175$	−14.2777	−	4.79814i	−1.07929	−	0.362705i
$176$	0.465269			0.0350710
$177$	−12.9025	+	9.37419i	−0.969809	+	0.704607i
$178$	−0.766705	+	2.35968i	−0.0574670	+	0.176865i
$179$	4.16051	−	12.8047i	0.310971	−	0.957070i	−0.666410	−	0.745585i	$-0.732170\pi$
$179$	4.16051	−	12.8047i	0.310971	−	0.957070i	0.977381	−	0.211485i	$-0.0678299\pi$
$180$	0.301500	+	0.599144i	0.0224725	+	0.0446576i
$181$	1.84930	+	5.69156i	0.137457	+	0.423051i	0.995964	−	0.0897517i	$-0.0286074\pi$
$181$	1.84930	+	5.69156i	0.137457	+	0.423051i	−0.858507	+	0.512802i	$0.828607\pi$
$182$	2.51588			0.186489
$183$	−2.73494	−	8.41729i	−0.202173	−	0.622224i
$184$	−13.5909	−	9.87437i	−1.00193	−	0.727948i
$185$	7.11759	−	7.04647i	0.523296	−	0.518067i
$186$	1.07834	−	0.783461i	0.0790678	−	0.0574462i
$187$	0.154244	+	0.112065i	0.0112794	+	0.00819499i
$188$	9.85190	+	7.15782i	0.718523	+	0.522038i
$189$	13.0032	−	9.44739i	0.945844	−	0.687196i
$190$	−1.44021	+	1.42582i	−0.104484	+	0.103440i
$191$	16.8851	+	12.2678i	1.22176	+	0.887664i	0.996245	−	0.0865745i	$-0.0275921\pi$
$191$	16.8851	+	12.2678i	1.22176	+	0.887664i	0.225520	+	0.974239i	$0.427592\pi$
$192$	−1.13572	−	3.49540i	−0.0819638	−	0.252259i
$193$	21.1184			1.52013			0.760067	−	0.649845i	$-0.225166\pi$
$193$	21.1184			1.52013			0.760067	+	0.649845i	$0.225166\pi$
$194$	0.134374	+	0.413562i	0.00964753	+	0.0296920i
$195$	2.70449	+	5.37440i	0.193673	+	0.384869i
$196$	−1.10781	+	3.40950i	−0.0791295	+	0.243535i
$197$	7.05754	−	21.7209i	0.502829	−	1.54755i	−0.301561	−	0.953447i	$-0.597508\pi$
$197$	7.05754	−	21.7209i	0.502829	−	1.54755i	0.804390	−	0.594102i	$-0.202492\pi$
$198$	0.0139741	−	0.0101528i	0.000993094	−	0.000721525i
$199$	−13.4544			−0.953755			−0.476878	−	0.878970i	$-0.658232\pi$
$199$	−13.4544			−0.953755			−0.476878	+	0.878970i	$0.658232\pi$
$200$	−0.0976663	+	9.72549i	−0.00690605	+	0.687696i
$201$	21.5484			1.51991
$202$	−4.48331	+	3.25732i	−0.315445	+	0.229184i
$203$	1.58956	−	4.89215i	0.111565	−	0.343362i
$204$	0.897567	−	2.76243i	0.0628422	−	0.193409i
$205$	4.79594	−	4.74801i	0.334963	−	0.331616i
$206$	−0.961596	−	2.95949i	−0.0669975	−	0.206197i
$207$	1.49941			0.104216
$208$	1.20693	+	3.71454i	0.0836852	+	0.257557i
$209$	−0.267900	−	0.194641i	−0.0185310	−	0.0134636i
$210$	5.84124	−	0.895121i	0.403084	−	0.0617692i
$211$	−1.41524	+	1.02824i	−0.0974295	+	0.0707866i	−0.635433	−	0.772156i	$-0.719179\pi$
$211$	−1.41524	+	1.02824i	−0.0974295	+	0.0707866i	0.538004	+	0.842942i	$0.319179\pi$
$212$	−19.5816	−	14.2269i	−1.34487	−	0.977105i
$213$	9.94605	+	7.22623i	0.681492	+	0.495133i
$214$	7.07762	−	5.14219i	0.483816	−	0.351513i
$215$	−3.08853	+	18.8860i	−0.210636	+	1.28801i
$216$	−8.39636	−	6.10031i	−0.571300	−	0.415074i
$217$	−1.41438	−	4.35302i	−0.0960145	−	0.295502i
$218$	4.42038			0.299386
$219$	0.563463	+	1.73416i	0.0380753	+	0.117184i
$220$	−0.728055	+	0.111568i	−0.0490855	+	0.00752193i
$221$	−0.494569	+	1.52213i	−0.0332683	+	0.102389i
$222$	−1.21426	+	3.73712i	−0.0814961	+	0.250819i
$223$	16.5791	−	12.0455i	1.11022	−	0.806623i	0.127523	−	0.991836i	$-0.459297\pi$
$223$	16.5791	−	12.0455i	1.11022	−	0.806623i	0.982699	+	0.185212i	$0.0592973\pi$
$224$	15.5559			1.03937
$225$	−0.503170	−	0.707384i	−0.0335447	−	0.0471590i
$226$	1.22902			0.0817534
$227$	−0.517514	+	0.375996i	−0.0343486	+	0.0249557i	−0.604827	−	0.796357i	$-0.706758\pi$
$227$	−0.517514	+	0.375996i	−0.0343486	+	0.0249557i	0.570478	+	0.821313i	$0.306758\pi$
$228$	−1.55895	+	4.79794i	−0.103244	+	0.317752i
$229$	−2.21042	+	6.80299i	−0.146069	+	0.449554i	−0.997147	−	0.0754854i	$-0.975949\pi$
$229$	−2.21042	+	6.80299i	−0.146069	+	0.449554i	0.851078	+	0.525039i	$0.175949\pi$
$230$	8.95565	+	4.61992i	0.590518	+	0.304628i
$231$	0.298381	+	0.918323i	0.0196320	+	0.0604212i
$232$	−3.32150			−0.218067
$233$	−3.22632	−	9.92959i	−0.211363	−	0.650509i	−0.999392	−	0.0348703i	$-0.988898\pi$
$233$	−3.22632	−	9.92959i	−0.211363	−	0.650509i	0.788029	−	0.615638i	$-0.211102\pi$
$234$	0.117305	+	0.0852271i	0.00766847	+	0.00557147i
$235$	−14.0069	−	7.22567i	−0.913708	−	0.471351i
$236$	13.2595	−	9.63357i	0.863118	−	0.627092i
$237$	22.8240	+	16.5826i	1.48258	+	1.07716i
$238$	1.27175	+	0.923982i	0.0824355	+	0.0598929i
$239$	−20.2708	+	14.7276i	−1.31121	+	0.952650i	−0.311213	+	0.950340i	$0.600735\pi$
$239$	−20.2708	+	14.7276i	−1.31121	+	0.952650i	−0.999997	+	0.00230969i	$0.999265\pi$
$240$	4.12377	+	8.19482i	0.266188	+	0.528973i
$241$	0.0398106	+	0.0289241i	0.00256443	+	0.00186317i	0.589067	−	0.808084i	$-0.299496\pi$
$241$	0.0398106	+	0.0289241i	0.00256443	+	0.00186317i	−0.586502	+	0.809948i	$0.699496\pi$
$242$	−1.76791	−	5.44106i	−0.113645	−	0.349765i
$243$	1.80197			0.115596
$244$	2.81062	+	8.65020i	0.179931	+	0.553772i
$245$	0.748826	−	4.57898i	0.0478408	−	0.292540i
$246$	−0.818189	+	2.51813i	−0.0521658	+	0.160550i
$247$	0.858996	−	2.64372i	0.0546566	−	0.168216i
$248$	−2.39101	+	1.73717i	−0.151830	+	0.110311i
$249$	18.3695			1.16412
$250$	−0.825763	−	5.77541i	−0.0522259	−	0.365269i
$251$	−5.98924			−0.378038			−0.189019	−	0.981973i	$-0.560531\pi$
$251$	−5.98924			−0.378038			−0.189019	+	0.981973i	$0.560531\pi$
$252$	−0.731041	+	0.531133i	−0.0460513	+	0.0334582i
$253$	−0.508816	+	1.56597i	−0.0319890	+	0.0984519i
$254$	0.232820	−	0.716547i	0.0146084	−	0.0449601i
$255$	−0.606711	+	3.70996i	−0.0379937	+	0.232327i
$256$	−0.498203	−	1.53331i	−0.0311377	−	0.0958319i
$257$	24.7621			1.54462			0.772309	−	0.635247i	$-0.219102\pi$
$257$	24.7621			1.54462			0.772309	+	0.635247i	$0.219102\pi$
$258$	−2.32009	−	7.14051i	−0.144443	−	0.444549i
$259$	10.9163	+	7.93113i	0.678303	+	0.492816i
$260$	−2.77932	−	5.52311i	−0.172366	−	0.342528i
$261$	0.239840	−	0.174254i	0.0148457	−	0.0107860i
$262$	−1.85967	−	1.35113i	−0.114891	−	0.0834730i
$263$	−3.09561	−	2.24909i	−0.190883	−	0.138685i	0.488239	−	0.872710i	$-0.337639\pi$
$263$	−3.09561	−	2.24909i	−0.190883	−	0.138685i	−0.679122	+	0.734025i	$0.737639\pi$
$264$	0.504414	−	0.366478i	0.0310445	−	0.0225552i
$265$	27.8400	+	14.3617i	1.71020	+	0.882233i
$266$	−2.20885	−	1.60483i	−0.135434	−	0.0983982i
$267$	−2.47014	−	7.60231i	−0.151170	−	0.465254i
$268$	−22.1446			−1.35270
$269$	−7.00420	−	21.5567i	−0.427053	−	1.31434i	−0.901014	−	0.433789i	$-0.857176\pi$
$269$	−7.00420	−	21.5567i	−0.427053	−	1.31434i	0.473961	−	0.880546i	$-0.342824\pi$
$270$	5.53274	+	2.85415i	0.336712	+	0.173698i
$271$	−8.14743	+	25.0752i	−0.494921	+	1.52321i	0.322158	+	0.946686i	$0.395592\pi$
$271$	−8.14743	+	25.0752i	−0.494921	+	1.52321i	−0.817079	+	0.576525i	$0.804408\pi$
$272$	−0.754113	+	2.32092i	−0.0457248	+	0.140726i
$273$	−6.55753	+	4.76433i	−0.396880	+	0.288350i
$274$	−4.39782			−0.265682
$275$	0.909536	−	0.285461i	0.0548471	−	0.0172139i
$276$	25.0849			1.50993
$277$	13.3585	−	9.70555i	0.802637	−	0.583150i	−0.109049	−	0.994036i	$-0.534781\pi$
$277$	13.3585	−	9.70555i	0.802637	−	0.583150i	0.911687	+	0.410886i	$0.134781\pi$
$278$	1.17736	−	3.62354i	0.0706133	−	0.217325i
$279$	0.0815147	−	0.250877i	0.00488016	−	0.0150196i
$280$	−12.9518	+	1.98476i	−0.774020	+	0.118612i
$281$	6.04600	+	18.6077i	0.360674	+	1.11004i	0.952646	+	0.304082i	$0.0983498\pi$
$281$	6.04600	+	18.6077i	0.360674	+	1.11004i	−0.591972	+	0.805959i	$0.701650\pi$
$282$	6.18345			0.368219
$283$	−6.35002	−	19.5433i	−0.377469	−	1.16173i	−0.941798	−	0.336181i	$-0.890865\pi$
$283$	−6.35002	−	19.5433i	−0.377469	−	1.16173i	0.564328	−	0.825550i	$-0.309135\pi$
$284$	−10.2213	−	7.42617i	−0.606520	−	0.440662i
$285$	1.05377	−	6.44368i	0.0624200	−	0.381691i
$286$	−0.128817	+	0.0935914i	−0.00761714	+	0.00553417i
$287$	7.35553	+	5.34411i	0.434183	+	0.315453i
$288$	0.725306	+	0.526966i	0.0427391	+	0.0310518i
$289$	−0.809017	+	0.587785i	−0.0475892	+	0.0345756i
$290$	1.96942	−	0.301796i	0.115648	−	0.0177221i
$291$	−1.13341	−	0.823468i	−0.0664414	−	0.0482725i
$292$	−0.579053	−	1.78214i	−0.0338865	−	0.104292i
$293$	−23.9442			−1.39884			−0.699419	−	0.714712i	$-0.746558\pi$
$293$	−23.9442			−1.39884			−0.699419	+	0.714712i	$0.746558\pi$
$294$	0.562516	+	1.73125i	0.0328066	+	0.100968i
$295$	−15.0744	+	14.9238i	−0.877664	+	0.868894i
$296$	2.69240	−	8.28634i	0.156492	−	0.481634i
$297$	−0.314342	+	0.967447i	−0.0182400	+	0.0561369i
$298$	3.31882	−	2.41126i	0.192254	−	0.139681i
$299$	−13.8220			−0.799349
$300$	−8.41795	−	11.8344i	−0.486011	−	0.683261i
$301$	−25.7815			−1.48602
$302$	0.646894	−	0.469996i	0.0372245	−	0.0270452i
$303$	5.51718	−	16.9801i	0.316954	−	0.975483i
$304$	1.30979	−	4.03111i	0.0751214	−	0.231200i
$305$	−5.29147	−	10.5153i	−0.302989	−	0.602103i
$306$	0.0279961	+	0.0861630i	0.00160043	+	0.00492561i
$307$	−23.0608			−1.31615			−0.658073	−	0.752954i	$-0.728628\pi$
$307$	−23.0608			−1.31615			−0.658073	+	0.752954i	$0.728628\pi$
$308$	−0.306637	−	0.943732i	−0.0174723	−	0.0537741i
$309$	8.11075	+	5.89281i	0.461405	+	0.335230i
$310$	1.25986	−	1.24727i	0.0715553	−	0.0708404i
$311$	−16.0849	+	11.6864i	−0.912094	+	0.662675i	−0.941543	−	0.336891i	$-0.890624\pi$
$311$	−16.0849	+	11.6864i	−0.912094	+	0.662675i	0.0294499	+	0.999566i	$0.490624\pi$
$312$	4.23429	+	3.07639i	0.239720	+	0.174166i
$313$	−6.32364	−	4.59439i	−0.357433	−	0.259690i	0.394548	−	0.918876i	$-0.370901\pi$
$313$	−6.32364	−	4.59439i	−0.357433	−	0.259690i	−0.751981	+	0.659185i	$0.770901\pi$
$314$	2.29968	−	1.67082i	0.129779	−	0.0942898i
$315$	0.831104	−	0.822799i	0.0468274	−	0.0463595i
$316$	−23.4556	−	17.0415i	−1.31948	−	0.958657i
$317$	−5.39894	−	16.6162i	−0.303235	−	0.933260i	−0.980330	−	0.197365i	$-0.936762\pi$
$317$	−5.39894	−	16.6162i	−0.303235	−	0.933260i	0.677095	−	0.735895i	$-0.263238\pi$
$318$	−12.2902			−0.689200
$319$	0.100601	+	0.309619i	0.00563260	+	0.0173353i
$320$	−2.19735	−	4.36661i	−0.122836	−	0.244101i
$321$	−8.70975	+	26.8058i	−0.486131	+	1.49616i
$322$	−4.19522	+	12.9116i	−0.233790	+	0.719533i
$323$	1.40515	−	1.02090i	0.0781845	−	0.0568044i
$324$	14.5974			0.810965
$325$	4.63838	+	6.52090i	0.257291	+	0.361714i
$326$	−1.09838			−0.0608337
$327$	−11.5216	+	8.37090i	−0.637143	+	0.462912i
$328$	1.81418	−	5.58346i	0.100171	−	0.308295i
$329$	6.56143	−	20.1940i	0.361743	−	1.11333i
$330$	−0.265783	+	0.263128i	−0.0146309	+	0.0144847i
$331$	−6.43047	−	19.7909i	−0.353450	−	1.08781i	−0.956903	−	0.290409i	$-0.906209\pi$
$331$	−6.43047	−	19.7909i	−0.353450	−	1.08781i	0.603452	−	0.797399i	$-0.293791\pi$
$332$	−18.8778			−1.03605
$333$	0.240308	+	0.739592i	0.0131688	+	0.0405294i
$334$	−4.81655	−	3.49943i	−0.263550	−	0.191480i
$335$	28.3298	−	4.34131i	1.54782	−	0.237191i
$336$	−9.99885	+	7.26459i	−0.545482	+	0.396316i
$337$	5.90894	+	4.29310i	0.321881	+	0.233860i	0.736977	−	0.675917i	$-0.236252\pi$
$337$	5.90894	+	4.29310i	0.321881	+	0.233860i	−0.415097	+	0.909777i	$0.636252\pi$
$338$	4.40676	+	3.20170i	0.239696	+	0.174149i
$339$	−3.20340	+	2.32741i	−0.173985	+	0.126407i
$340$	0.623498	−	3.81261i	0.0338139	−	0.206768i
$341$	0.234352	+	0.170267i	0.0126909	+	0.00922048i
$342$	−0.0486252	−	0.149653i	−0.00262935	−	0.00809231i
$343$	−14.8365			−0.801094
$344$	5.14435	+	15.8327i	0.277365	+	0.853642i
$345$	−32.0913	+	4.91772i	−1.72774	+	0.264761i
$346$	−2.34405	+	7.21425i	−0.126017	+	0.387840i
$347$	3.84952	−	11.8476i	0.206653	−	0.636012i	−0.792989	−	0.609236i	$-0.791476\pi$
$347$	3.84952	−	11.8476i	0.206653	−	0.636012i	0.999641	−	0.0267756i	$-0.00852396\pi$
$348$	4.01248	−	2.91524i	0.215092	−	0.156273i
$349$	−21.3676			−1.14378			−0.571892	−	0.820329i	$-0.693790\pi$
$349$	−21.3676			−1.14378			−0.571892	+	0.820329i	$0.693790\pi$
$350$	7.49919	−	2.35364i	0.400848	−	0.125808i
$351$	−8.53915			−0.455786
$352$	−0.796489	+	0.578683i	−0.0424530	+	0.0308439i
$353$	2.01903	−	6.21395i	0.107462	−	0.330735i	−0.882838	−	0.469677i	$-0.844370\pi$
$353$	2.01903	−	6.21395i	0.107462	−	0.330735i	0.990300	+	0.138942i	$0.0443702\pi$
$354$	2.57170	−	7.91486i	0.136684	−	0.420670i
$355$	14.5320	+	7.49657i	0.771279	+	0.397877i
$356$	2.53849	+	7.81266i	0.134540	+	0.414070i
$357$	−5.06452			−0.268043
$358$	2.17104	+	6.68178i	0.114743	+	0.353143i
$359$	−21.5743	−	15.6747i	−1.13865	−	0.827277i	−0.151718	−	0.988424i	$-0.548481\pi$
$359$	−21.5743	−	15.6747i	−1.13865	−	0.827277i	−0.986930	+	0.161147i	$0.948481\pi$
$360$	−0.671125	−	0.346211i	−0.0353714	−	0.0182469i
$361$	12.9308	−	9.39476i	0.680567	−	0.494461i
$362$	−2.52642	−	1.83555i	−0.132786	−	0.0964743i
$363$	14.9117	+	10.8340i	0.782663	+	0.568638i
$364$	6.73898	−	4.89615i	0.353218	−	0.256628i
$365$	1.09017	+	2.16639i	0.0570619	+	0.113394i
$366$	3.73634	+	2.71461i	0.195301	+	0.141895i
$367$	8.57661	+	26.3961i	0.447695	+	1.37786i	0.879501	+	0.475897i	$0.157877\pi$
$367$	8.57661	+	26.3961i	0.447695	+	1.37786i	−0.431806	+	0.901967i	$0.642123\pi$
$368$	−21.0757			−1.09864
$369$	0.161923	+	0.498348i	0.00842937	+	0.0259429i
$370$	−0.843493	+	5.15786i	−0.0438511	+	0.268144i
$371$	−13.0415	+	40.1375i	−0.677080	+	2.08384i
$372$	1.36373	−	4.19712i	0.0707060	−	0.217611i
$373$	17.6828	−	12.8473i	0.915580	−	0.665208i	−0.0268402	−	0.999640i	$-0.508545\pi$
$373$	17.6828	−	12.8473i	0.915580	−	0.665208i	0.942420	+	0.334432i	$0.108545\pi$
$374$	−0.0994885			−0.00514443
$375$	13.0892	+	13.4896i	0.675925	+	0.696601i
$376$	−13.7106			−0.707070
$377$	−2.21092	+	1.60633i	−0.113868	+	0.0827301i
$378$	−2.59178	+	7.97667i	−0.133307	+	0.410275i
$379$	−3.65213	+	11.2401i	−0.187597	+	0.577364i	−0.999983	−	0.00575513i	$-0.998168\pi$
$379$	−3.65213	+	11.2401i	−0.187597	+	0.577364i	0.812386	+	0.583120i	$0.198168\pi$
$380$	−1.08293	+	6.62197i	−0.0555530	+	0.339700i
$381$	0.750091	+	2.30854i	0.0384283	+	0.118270i
$382$	−10.8910			−0.557233
$383$	−4.59536	−	14.1431i	−0.234812	−	0.722677i	−0.997146	−	0.0754933i	$-0.975947\pi$
$383$	−4.59536	−	14.1431i	−0.234812	−	0.722677i	0.762334	−	0.647183i	$-0.224053\pi$
$384$	15.5983	+	11.3328i	0.795996	+	0.578325i
$385$	0.577297	+	1.14721i	0.0294218	+	0.0584673i
$386$	−8.91538	+	6.47741i	−0.453781	+	0.329691i
$387$	−1.20209	−	0.873366i	−0.0611054	−	0.0443957i
$388$	1.16477	+	0.846253i	0.0591321	+	0.0429620i
$389$	−7.00097	+	5.08650i	−0.354963	+	0.257896i	−0.750948	−	0.660361i	$-0.770403\pi$
$389$	−7.00097	+	5.08650i	−0.354963	+	0.257896i	0.395985	+	0.918257i	$0.370403\pi$
$390$	−2.79016	−	1.43935i	−0.141285	−	0.0728844i
$391$	−6.98691	−	5.07629i	−0.353343	−	0.256719i
$392$	−1.24727	−	3.83870i	−0.0629967	−	0.193884i
$393$	7.40579			0.373573
$394$	3.68278	+	11.3344i	0.185536	+	0.571020i
$395$	33.3478	+	17.2030i	1.67791	+	0.865577i
$396$	0.0176724	−	0.0543899i	0.000888069	−	0.00273320i
$397$	−0.538092	+	1.65608i	−0.0270060	+	0.0831161i	−0.963651	−	0.267164i	$-0.913914\pi$
$397$	−0.538092	+	1.65608i	−0.0270060	+	0.0831161i	0.936645	+	0.350280i	$0.113914\pi$
$398$	5.67993	−	4.12671i	0.284709	−	0.206853i
$399$	8.79636			0.440369
$400$	7.07255	+	9.94298i	0.353627	+	0.497149i
$401$	15.9398			0.795997			0.397999	−	0.917386i	$-0.369705\pi$
$401$	15.9398			0.795997			0.397999	+	0.917386i	$0.369705\pi$
$402$	−9.09692	+	6.60930i	−0.453713	+	0.329642i
$403$	−0.751429	+	2.31266i	−0.0374313	+	0.115202i
$404$	−5.66983	+	17.4500i	−0.282085	+	0.868168i
$405$	−18.6746	+	2.86172i	−0.927946	+	0.142200i
$406$	0.829465	+	2.55283i	0.0411657	+	0.126695i
$407$	−0.853973			−0.0423299
$408$	1.01056	+	3.11018i	0.0500301	+	0.153977i
$409$	20.4509	+	14.8584i	1.01123	+	0.734703i	0.964467	−	0.264203i	$-0.0851089\pi$
$409$	20.4509	+	14.8584i	1.01123	+	0.734703i	0.0467648	+	0.998906i	$0.485109\pi$
$410$	−0.568358	+	3.47544i	−0.0280692	+	0.171640i
$411$	11.4627	−	8.32817i	0.565415	−	0.410798i
$412$	−8.33517	−	6.05586i	−0.410644	−	0.298351i
$413$	−23.1196	−	16.7974i	−1.13764	−	0.826544i
$414$	−0.632994	+	0.459897i	−0.0311100	+	0.0226027i
$415$	24.1506	−	3.70087i	1.18550	−	0.181669i
$416$	−6.68611	−	4.85774i	−0.327813	−	0.238170i
$417$	3.79317	+	11.6742i	0.185752	+	0.571687i
$418$	0.172797			0.00845180
$419$	5.90523	+	18.1744i	0.288489	+	0.887878i	0.985331	+	0.170654i	$0.0545879\pi$
$419$	5.90523	+	18.1744i	0.288489	+	0.887878i	−0.696842	+	0.717225i	$0.745412\pi$
$420$	13.9042	−	13.7653i	0.678457	−	0.671678i
$421$	−11.3096	+	34.8074i	−0.551197	+	1.69641i	0.154585	+	0.987980i	$0.450596\pi$
$421$	−11.3096	+	34.8074i	−0.551197	+	1.69641i	−0.705781	+	0.708430i	$0.749404\pi$
$422$	0.282084	−	0.868165i	0.0137316	−	0.0422616i
$423$	0.990019	−	0.719291i	0.0481364	−	0.0349731i
$424$	27.2511			1.32343
$425$	−0.0502090	+	4.99975i	−0.00243549	+	0.242523i
$426$	−6.41527			−0.310821
$427$	12.8301	−	9.32164i	0.620894	−	0.451106i
$428$	8.95074	−	27.5475i	0.432650	−	1.33156i
$429$	0.158523	−	0.487884i	0.00765357	−	0.0235553i
$430$	−4.48883	−	8.92026i	−0.216470	−	0.430173i
$431$	−0.454116	−	1.39763i	−0.0218740	−	0.0673213i	0.939524	−	0.342484i	$-0.111268\pi$
$431$	−0.454116	−	1.39763i	−0.0218740	−	0.0673213i	−0.961398	+	0.275163i	$0.911268\pi$
$432$	−13.0204			−0.626444
$433$	10.0583	+	30.9563i	0.483371	+	1.48766i	0.834327	+	0.551270i	$0.185857\pi$
$433$	10.0583	+	30.9563i	0.483371	+	1.48766i	−0.350956	+	0.936392i	$0.614143\pi$
$434$	1.93225	+	1.40386i	0.0927511	+	0.0673876i
$435$	−4.56169	+	4.51611i	−0.218716	+	0.216531i
$436$	11.8403	−	8.60252i	0.567050	−	0.411986i
$437$	12.1353	+	8.81679i	0.580509	+	0.421764i
$438$	−0.769772	−	0.559272i	−0.0367812	−	0.0267231i
$439$	33.1297	−	24.0702i	1.58120	−	1.14881i	0.665889	−	0.746051i	$-0.268052\pi$
$439$	33.1297	−	24.0702i	1.58120	−	1.14881i	0.915307	−	0.402756i	$-0.131948\pi$
$440$	0.589323	−	0.583435i	0.0280949	−	0.0278142i
$441$	0.291451	+	0.211751i	0.0138786	+	0.0100834i
$442$	−0.258077	−	0.794278i	−0.0122755	−	0.0377800i
$443$	−13.8692			−0.658944			−0.329472	−	0.944165i	$-0.606871\pi$
$443$	−13.8692			−0.658944			−0.329472	+	0.944165i	$0.606871\pi$
$444$	4.02031	+	12.3733i	0.190796	+	0.587209i
$445$	−4.77913	−	9.49716i	−0.226553	−	0.450209i
$446$	−3.30452	+	10.1703i	−0.156474	+	0.481577i
$447$	−4.08415	+	12.5697i	−0.193174	+	0.594527i
$448$	5.32789	−	3.87094i	0.251719	−	0.182885i
$449$	3.70055			0.174640			0.0873198	−	0.996180i	$-0.472170\pi$
$449$	3.70055			0.174640			0.0873198	+	0.996180i	$0.472170\pi$
$450$	0.429388	+	0.144299i	0.0202415	+	0.00680234i
$451$	−0.575419			−0.0270954
$452$	3.29204	−	2.39180i	0.154844	−	0.112501i
$453$	−0.796069	+	2.45005i	−0.0374026	+	0.115113i
$454$	0.103150	−	0.317463i	0.00484107	−	0.0148993i
$455$	−7.66138	+	7.58483i	−0.359171	+	0.355582i
$456$	−1.75520	−	5.40194i	−0.0821946	−	0.252969i
$457$	17.6048			0.823520			0.411760	−	0.911292i	$-0.364914\pi$
$457$	17.6048			0.823520			0.411760	+	0.911292i	$0.364914\pi$
$458$	−1.15345	−	3.54994i	−0.0538970	−	0.165878i
$459$	−4.31646	−	3.13609i	−0.201475	−	0.146380i
$460$	32.9793	−	5.05379i	1.53767	−	0.235634i
$461$	−14.9707	+	10.8769i	−0.697256	+	0.506586i	−0.879037	−	0.476753i	$-0.841814\pi$
$461$	−14.9707	+	10.8769i	−0.697256	+	0.506586i	0.181781	+	0.983339i	$0.441814\pi$
$462$	−0.407633	−	0.296162i	−0.0189648	−	0.0137787i
$463$	−3.35841	−	2.44003i	−0.156078	−	0.113398i	0.507005	−	0.861943i	$-0.330753\pi$
$463$	−3.35841	−	2.44003i	−0.156078	−	0.113398i	−0.663083	+	0.748545i	$0.730753\pi$
$464$	−3.37118	+	2.44931i	−0.156503	+	0.113706i
$465$	−0.921813	+	5.63677i	−0.0427480	+	0.261399i
$466$	4.40762	+	3.20233i	0.204179	+	0.148345i
$467$	−9.71449	−	29.8981i	−0.449533	−	1.38352i	−0.877435	−	0.479695i	$-0.840747\pi$
$467$	−9.71449	−	29.8981i	−0.449533	−	1.38352i	0.427902	−	0.903825i	$-0.359253\pi$
$468$	0.480071			0.0221913
$469$	11.9318	+	36.7222i	0.550958	+	1.69567i
$470$	8.12943	−	1.24577i	0.374983	−	0.0574629i
$471$	−2.83000	+	8.70985i	−0.130400	+	0.401329i
$472$	−5.70224	+	17.5497i	−0.262467	+	0.807789i
$473$	1.32006	−	0.959079i	0.0606964	−	0.0440985i
$474$	−14.7217			−0.676188
$475$	0.0872059	−	8.68385i	0.00400128	−	0.398443i
$476$	5.20465			0.238555
$477$	−1.96776	+	1.42966i	−0.0900974	+	0.0654596i
$478$	4.04034	−	12.4349i	0.184801	−	0.568759i
$479$	2.13519	−	6.57143i	0.0975592	−	0.300256i	−0.890353	−	0.455271i	$-0.849542\pi$
$479$	2.13519	−	6.57143i	0.0975592	−	0.300256i	0.987912	+	0.155015i	$0.0495424\pi$
$480$	−17.2518	−	8.89963i	−0.787434	−	0.406211i
$481$	−2.21524	−	6.81780i	−0.101006	−	0.310865i
$482$	−0.0256781			−0.00116961
$483$	−13.5160	−	41.5980i	−0.614999	−	1.89277i
$484$	−15.3243	−	11.1338i	−0.696561	−	0.506081i
$485$	−1.65600	−	0.854274i	−0.0751951	−	0.0387906i
$486$	−0.760725	+	0.552699i	−0.0345072	+	0.0250709i
$487$	−10.8751	−	7.90122i	−0.492797	−	0.358038i	0.313462	−	0.949601i	$-0.398511\pi$
$487$	−10.8751	−	7.90122i	−0.492797	−	0.358038i	−0.806259	+	0.591563i	$0.798511\pi$
$488$	−8.28460	−	6.01912i	−0.375026	−	0.272473i
$489$	2.86289	−	2.08001i	0.129464	−	0.0940612i
$490$	1.08833	+	2.16275i	0.0491660	+	0.0977033i
$491$	−24.1537	−	17.5487i	−1.09004	−	0.791961i	−0.110635	−	0.993861i	$-0.535288\pi$
$491$	−24.1537	−	17.5487i	−1.09004	−	0.791961i	−0.979406	+	0.201900i	$0.935288\pi$
$492$	2.70895	+	8.33728i	0.122129	+	0.375874i
$493$	−1.70754			−0.0769037
$494$	0.448243	+	1.37955i	0.0201674	+	0.0620689i
$495$	−0.0119456	+	0.0730461i	−0.000536916	+	0.00328318i
$496$	−1.14577	+	3.52632i	−0.0514466	+	0.158336i
$497$	−6.80742	+	20.9511i	−0.305355	+	0.939785i
$498$	−7.75493	+	5.63429i	−0.347507	+	0.252478i
$499$	8.96941			0.401526			0.200763	−	0.979640i	$-0.435658\pi$
$499$	8.96941			0.401526			0.200763	+	0.979640i	$0.435658\pi$
$500$	−13.4514	−	13.8629i	−0.601565	−	0.619966i
$501$	19.1810			0.856945
$502$	2.52843	−	1.83701i	0.112850	−	0.0819900i
$503$	−1.69781	+	5.22533i	−0.0757017	+	0.232986i	−0.981746	−	0.190197i	$-0.939087\pi$
$503$	−1.69781	+	5.22533i	−0.0757017	+	0.232986i	0.906044	+	0.423183i	$0.139087\pi$
$504$	0.314384	−	0.967576i	0.0140038	−	0.0430993i
$505$	3.83253	−	23.4354i	0.170545	−	1.04286i
$506$	−0.265511	−	0.817159i	−0.0118034	−	0.0363271i
$507$	−17.5491			−0.779383
$508$	−0.770845	−	2.37242i	−0.0342007	−	0.105259i
$509$	23.4946	+	17.0698i	1.04138	+	0.756605i	0.970554	−	0.240883i	$-0.0774372\pi$
$509$	23.4946	+	17.0698i	1.04138	+	0.756605i	0.0708239	+	0.997489i	$0.477437\pi$
$510$	−0.881785	−	1.75230i	−0.0390461	−	0.0775930i
$511$	−2.64331	+	1.92048i	−0.116933	+	0.0849568i
$512$	−17.8757	−	12.9874i	−0.790000	−	0.573969i
$513$	7.49708	+	5.44695i	0.331004	+	0.240489i
$514$	−10.4536	+	7.59501i	−0.461090	+	0.335002i
$515$	11.8505	+	6.11326i	0.522195	+	0.269383i
$516$	−20.1107	−	14.6113i	−0.885324	−	0.643226i
$517$	0.415266	+	1.27806i	0.0182634	+	0.0562089i
$518$	−7.04106			−0.309367
$519$	−7.55198	−	23.2426i	−0.331495	−	1.02024i
$520$	6.18665	+	3.19148i	0.271303	+	0.139956i
$521$	6.33525	−	19.4979i	0.277552	−	0.854218i	−0.710980	−	0.703212i	$-0.751749\pi$
$521$	6.33525	−	19.4979i	0.277552	−	0.854218i	0.988533	−	0.151007i	$-0.0482514\pi$
$522$	−0.0478044	+	0.147127i	−0.00209234	+	0.00643957i
$523$	4.04112	−	2.93605i	0.176706	−	0.128384i	−0.495917	−	0.868370i	$-0.665168\pi$
$523$	4.04112	−	2.93605i	0.176706	−	0.128384i	0.672622	+	0.739986i	$0.265168\pi$
$524$	−7.61070			−0.332475
$525$	−15.0892	+	20.3359i	−0.658548	+	0.887533i
$526$	1.99669			0.0870597
$527$	−1.22919	+	0.893058i	−0.0535443	+	0.0389022i
$528$	0.241714	−	0.743920i	0.0105193	−	0.0323750i
$529$	15.9408	−	49.0608i	0.693079	−	2.13308i
$530$	−16.1580	+	2.47608i	−0.701860	+	0.107554i
$531$	−0.508949	−	1.56638i	−0.0220865	−	0.0679753i
$532$	−9.03975			−0.391923
$533$	−1.49266	−	4.59393i	−0.0646542	−	0.198985i
$534$	3.37457	+	2.45177i	0.146032	+	0.106099i
$535$	−6.05026	+	36.9966i	−0.261575	+	1.59950i
$536$	20.1707	−	14.6548i	0.871240	−	0.632993i
$537$	−18.3121	−	13.3045i	−0.790224	−	0.574131i
$538$	9.56876	+	6.95211i	0.412538	+	0.299727i
$539$	−0.320054	+	0.232533i	−0.0137857	+	0.0100159i
$540$	20.3743	−	3.12220i	0.876772	−	0.134358i
$541$	−18.3219	−	13.3116i	−0.787718	−	0.572311i	0.119567	−	0.992826i	$-0.461849\pi$
$541$	−18.3219	−	13.3116i	−0.787718	−	0.572311i	−0.907286	+	0.420515i	$0.861849\pi$
$542$	−4.25151	−	13.0848i	−0.182618	−	0.562040i
$543$	10.0610			0.431759
$544$	−1.59571	−	4.91109i	−0.0684155	−	0.210561i
$545$	−13.4610	+	13.3265i	−0.576606	+	0.570845i
$546$	1.30704	−	4.02264i	0.0559359	−	0.172153i
$547$	−11.4925	+	35.3702i	−0.491382	+	1.51232i	0.331137	+	0.943583i	$0.392568\pi$
$547$	−11.4925	+	35.3702i	−0.491382	+	1.51232i	−0.822520	+	0.568737i	$0.807432\pi$
$548$	−11.7799	+	8.55860i	−0.503213	+	0.365605i
$549$	0.913994			0.0390083
$550$	−0.296416	+	0.399483i	−0.0126392	+	0.0170340i
$551$	2.96576			0.126345
$552$	−22.8488	+	16.6006i	−0.972510	+	0.706570i
$553$	−15.6216	+	48.0782i	−0.664297	+	2.04449i
$554$	−2.66260	+	8.19464i	−0.113123	+	0.348157i
$555$	−7.56893	−	15.0411i	−0.321283	−	0.638458i
$556$	−3.89812	−	11.9972i	−0.165317	−	0.508794i
$557$	−6.49658			−0.275269			−0.137634	−	0.990483i	$-0.543950\pi$
$557$	−6.49658			−0.275269			−0.137634	+	0.990483i	$0.543950\pi$
$558$	0.0425361	+	0.130913i	0.00180070	+	0.00554198i
$559$	11.0812	+	8.05097i	0.468685	+	0.340520i
$560$	−11.6820	+	11.5653i	−0.493654	+	0.488721i
$561$	0.259313	−	0.188402i	0.0109482	−	0.00795433i
$562$	−8.25973	−	6.00104i	−0.348416	−	0.253139i
$563$	13.6555	+	9.92132i	0.575512	+	0.418134i	0.837103	−	0.547045i	$-0.184247\pi$
$563$	13.6555	+	9.92132i	0.575512	+	0.418134i	−0.261592	+	0.965179i	$0.584247\pi$
$564$	16.5629	−	12.0336i	0.697422	−	0.506707i
$565$	−3.74264	+	3.70524i	−0.157454	+	0.155881i
$566$	8.67505	+	6.30280i	0.364640	+	0.264926i
$567$	−7.86522	−	24.2067i	−0.330308	−	1.01658i
$568$	14.2246			0.596852
$569$	−7.70764	−	23.7217i	−0.323121	−	0.994464i	−0.972282	−	0.233813i	$-0.924880\pi$
$569$	−7.70764	−	23.7217i	−0.323121	−	0.994464i	0.649161	−	0.760651i	$-0.275120\pi$
$570$	1.53154	+	3.04349i	0.0641490	+	0.127478i
$571$	−7.47234	+	22.9975i	−0.312708	+	0.962415i	0.663980	+	0.747750i	$0.268866\pi$
$571$	−7.47234	+	22.9975i	−0.312708	+	0.962415i	−0.976688	+	0.214665i	$0.931134\pi$
$572$	−0.162909	+	0.501384i	−0.00681159	+	0.0209639i
$573$	28.3870	−	20.6244i	1.18588	−	0.861596i
$574$	−4.74437			−0.198026
$575$	−41.1999	+	12.9307i	−1.71816	+	0.539249i
$576$	0.379549			0.0158145
$577$	23.0931	−	16.7782i	0.961380	−	0.698484i	0.00790944	−	0.999969i	$-0.497482\pi$
$577$	23.0931	−	16.7782i	0.961380	−	0.698484i	0.953471	+	0.301485i	$0.0974823\pi$
$578$	0.161252	−	0.496282i	0.00670719	−	0.0206426i
$579$	10.9713	−	33.7662i	0.455952	−	1.40328i
$580$	4.68791	−	4.64107i	0.194655	−	0.192710i
$581$	10.1716	+	31.3049i	0.421988	+	1.29875i
$582$	0.731055			0.0303032
$583$	−0.825381	−	2.54026i	−0.0341838	−	0.105207i
$584$	1.70682	+	1.24008i	0.0706288	+	0.0513148i
$585$	−0.614160	+	0.0941148i	−0.0253924	+	0.00389117i
$586$	10.1084	−	7.34416i	0.417573	−	0.303384i
$587$	−15.3728	−	11.1690i	−0.634505	−	0.460995i	0.223453	−	0.974715i	$-0.428267\pi$
$587$	−15.3728	−	11.1690i	−0.634505	−	0.460995i	−0.857958	+	0.513720i	$0.828267\pi$
$588$	4.87593	+	3.54257i	0.201080	+	0.146093i
$589$	2.13493	−	1.55112i	0.0879682	−	0.0639126i
$590$	1.78644	−	10.9238i	0.0735464	−	0.449728i
$591$	−31.0631	−	22.5686i	−1.27776	−	0.928350i
$592$	−3.37777	−	10.3957i	−0.138825	−	0.427260i
$593$	−2.57778			−0.105857			−0.0529283	−	0.998598i	$-0.516855\pi$
$593$	−2.57778			−0.105857			−0.0529283	+	0.998598i	$0.516855\pi$
$594$	−0.164031	−	0.504835i	−0.00673026	−	0.0207136i
$595$	−6.65837	+	1.02034i	−0.272966	+	0.0418298i
$596$	4.19716	−	12.9175i	0.171922	−	0.529122i
$597$	−6.98975	+	21.5122i	−0.286071	+	0.880437i
$598$	5.83514	−	4.23948i	0.238617	−	0.173365i
$599$	15.8717			0.648500			0.324250	−	0.945971i	$-0.394888\pi$
$599$	15.8717			0.648500			0.324250	+	0.945971i	$0.394888\pi$
$600$	15.4994	+	5.20869i	0.632759	+	0.212644i
$601$	31.1604			1.27106			0.635529	−	0.772077i	$-0.280782\pi$
$601$	31.1604			1.27106			0.635529	+	0.772077i	$0.280782\pi$
$602$	10.8840	−	7.90768i	0.443598	−	0.322293i
$603$	−0.687661	+	2.11640i	−0.0280037	+	0.0861865i
$604$	0.818096	−	2.51784i	0.0332879	−	0.102449i
$605$	21.7873	+	11.2393i	0.885779	+	0.456943i
$606$	2.87898	+	8.86060i	0.116951	+	0.359937i
$607$	34.5808			1.40359			0.701795	−	0.712379i	$-0.252382\pi$
$607$	34.5808			1.40359			0.701795	+	0.712379i	$0.252382\pi$
$608$	2.77152	+	8.52986i	0.112400	+	0.345932i
$609$	−6.99628	−	5.08309i	−0.283503	−	0.205977i
$610$	5.45910	+	2.81616i	0.221032	+	0.114023i
$611$	−9.12631	+	6.63065i	−0.369211	+	0.268248i
$612$	0.242672	+	0.176311i	0.00980942	+	0.00712696i
$613$	−9.25334	−	6.72294i	−0.373739	−	0.271537i	0.385021	−	0.922908i	$-0.374194\pi$
$613$	−9.25334	−	6.72294i	−0.373739	−	0.271537i	−0.758760	+	0.651371i	$0.774194\pi$
$614$	9.73539	−	7.07317i	0.392888	−	0.285450i
$615$	−5.10005	−	10.1349i	−0.205654	−	0.408678i
$616$	0.903846	+	0.656683i	0.0364170	+	0.0264585i
$617$	−8.37789	−	25.7845i	−0.337281	−	1.03804i	−0.965587	−	0.260078i	$-0.916252\pi$
$617$	−8.37789	−	25.7845i	−0.337281	−	1.03804i	0.628306	−	0.777966i	$-0.283748\pi$
$618$	−5.23149			−0.210441
$619$	−10.2702	−	31.6083i	−0.412793	−	1.27045i	−0.914210	−	0.405240i	$-0.867188\pi$
$619$	−10.2702	−	31.6083i	−0.412793	−	1.27045i	0.501417	−	0.865206i	$-0.332812\pi$
$620$	0.947319	−	5.79274i	0.0380452	−	0.232642i
$621$	14.2390	−	43.8232i	0.571392	−	1.75856i
$622$	3.20602	−	9.86712i	0.128550	−	0.395635i
$623$	11.5879	−	8.41910i	0.464259	−	0.337304i
$624$	6.56619			0.262858
$625$	19.9262	+	15.0978i	0.797050	+	0.603914i
$626$	4.07879			0.163021
$627$	−0.450389	+	0.327227i	−0.0179868	+	0.0130682i
$628$	2.90830	−	8.95084i	0.116054	−	0.357177i
$629$	1.38413	−	4.25990i	0.0551887	−	0.169853i
$630$	−0.0984926	+	0.602270i	−0.00392404	+	0.0239950i
$631$	9.48485	+	29.1914i	0.377586	+	1.16209i	0.941717	+	0.336405i	$0.109211\pi$
$631$	9.48485	+	29.1914i	0.377586	+	1.16209i	−0.564131	+	0.825685i	$0.690789\pi$
$632$	32.6424			1.29845
$633$	0.908807	+	2.79702i	0.0361218	+	0.111172i
$634$	7.37574	+	5.35879i	0.292928	+	0.212825i
$635$	1.45125	+	2.88394i	0.0575910	+	0.114446i
$636$	−32.9203	+	23.9180i	−1.30537	+	0.948409i
$637$	−2.68669	−	1.95199i	−0.106450	−	0.0773408i
$638$	−0.137436	−	0.0998533i	−0.00544115	−	0.00395323i
$639$	−1.02714	+	0.746258i	−0.0406328	+	0.0295215i
$640$	22.7904	+	11.7568i	0.900868	+	0.464728i
$641$	−1.67074	−	1.21386i	−0.0659901	−	0.0479446i	0.554301	−	0.832316i	$-0.312986\pi$
$641$	−1.67074	−	1.21386i	−0.0659901	−	0.0479446i	−0.620291	+	0.784372i	$0.712986\pi$
$642$	−4.54493	−	13.9879i	−0.179374	−	0.552057i
$643$	39.7836			1.56891			0.784455	−	0.620185i	$-0.212943\pi$
$643$	39.7836			1.56891			0.784455	+	0.620185i	$0.212943\pi$
$644$	13.8900	+	42.7490i	0.547342	+	1.68454i
$645$	28.5923	+	14.7498i	1.12582	+	0.580772i
$646$	−0.280071	+	0.861971i	−0.0110193	+	0.0339138i
$647$	6.44075	−	19.8226i	0.253212	−	0.779306i	−0.740965	−	0.671544i	$-0.765631\pi$
$647$	6.44075	−	19.8226i	0.253212	−	0.779306i	0.994177	−	0.107762i	$-0.0343685\pi$
$648$	−13.2962	+	9.66023i	−0.522323	+	0.379490i
$649$	1.80863			0.0709950
$650$	−3.95823	−	1.33020i	−0.155255	−	0.0521747i
$651$	−7.69484			−0.301585
$652$	−2.94210	+	2.13756i	−0.115221	+	0.0837133i
$653$	−5.28082	+	16.2527i	−0.206654	+	0.636017i	0.792987	+	0.609238i	$0.208525\pi$
$653$	−5.28082	+	16.2527i	−0.206654	+	0.636017i	−0.999641	+	0.0267782i	$0.991475\pi$
$654$	2.29645	−	7.06776i	0.0897985	−	0.276371i
$655$	9.73645	−	1.49203i	0.380435	−	0.0582984i
$656$	−2.27599	−	7.00477i	−0.0888624	−	0.273490i
$657$	−0.188304			−0.00734644
$658$	3.42390	+	10.5377i	0.133477	+	0.410801i
$659$	11.0240	+	8.00938i	0.429433	+	0.312001i	0.781422	−	0.624003i	$-0.214495\pi$
$659$	11.0240	+	8.00938i	0.429433	+	0.312001i	−0.351989	+	0.936004i	$0.614495\pi$
$660$	−0.199849	+	1.22205i	−0.00777910	+	0.0475682i
$661$	−4.25188	+	3.08917i	−0.165379	+	0.120155i	−0.667396	−	0.744703i	$-0.732591\pi$
$661$	−4.25188	+	3.08917i	−0.165379	+	0.120155i	0.502018	+	0.864857i	$0.332591\pi$
$662$	8.78496	+	6.38265i	0.341437	+	0.248069i
$663$	2.17680	+	1.58153i	0.0845397	+	0.0614217i
$664$	17.1951	−	12.4929i	0.667298	−	0.484820i
$665$	11.5646	−	1.77218i	0.448457	−	0.0687223i
$666$	−0.328296	−	0.238521i	−0.0127212	−	0.00924250i
$667$	−4.55702	−	14.0251i	−0.176448	−	0.543052i
$668$	−19.7117			−0.762670
$669$	−10.6464	−	32.7662i	−0.411613	−	1.26682i
$670$	−10.6282	+	10.5220i	−0.410604	+	0.406502i
$671$	−0.310159	+	0.954570i	−0.0119735	+	0.0368508i
$672$	8.08150	−	24.8723i	0.311751	−	0.959470i
$673$	−38.6923	+	28.1116i	−1.49148	+	1.08362i	−0.517856	+	0.855468i	$0.673270\pi$
$673$	−38.6923	+	28.1116i	−1.49148	+	1.08362i	−0.973625	+	0.228156i	$0.926730\pi$
$674$	−3.81131			−0.146806
$675$	−25.4530	+	7.98851i	−0.979687	+	0.307478i
$676$	18.0347			0.693641
$677$	−16.8843	+	12.2672i	−0.648916	+	0.471465i	−0.862902	−	0.505371i	$-0.831355\pi$
$677$	−16.8843	+	12.2672i	−0.648916	+	0.471465i	0.213985	+	0.976837i	$0.431355\pi$
$678$	0.638496	−	1.96509i	0.0245213	−	0.0754688i
$679$	0.775743	−	2.38749i	0.0297703	−	0.0916235i
$680$	1.95519	+	3.88538i	0.0749781	+	0.148997i
$681$	0.332325	+	1.02279i	0.0127347	+	0.0391934i
$682$	−0.151159			−0.00578818
$683$	−8.92004	−	27.4530i	−0.341316	−	1.05046i	−0.963527	−	0.267612i	$-0.913765\pi$
$683$	−8.92004	−	27.4530i	−0.341316	−	1.05046i	0.622211	−	0.782850i	$-0.286235\pi$
$684$	−0.421486	−	0.306228i	−0.0161159	−	0.0117089i
$685$	13.3923	−	13.2585i	0.511693	−	0.506581i
$686$	6.26340	−	4.55063i	0.239138	−	0.173744i
$687$	9.72896	+	7.06850i	0.371183	+	0.269680i
$688$	16.8965	+	12.2760i	0.644173	+	0.468019i
$689$	18.1394	−	13.1791i	0.691057	−	0.502082i
$690$	12.0394	−	11.9191i	0.458332	−	0.453752i
$691$	−30.5998	−	22.2320i	−1.16407	−	0.845747i	−0.173783	−	0.984784i	$-0.555599\pi$
$691$	−30.5998	−	22.2320i	−1.16407	−	0.845747i	−0.990287	+	0.139037i	$0.955599\pi$
$692$	7.76093	+	23.8857i	0.295026	+	0.907998i
$693$	−0.0997163			−0.00378791
$694$	2.00876	+	6.18233i	0.0762515	+	0.234678i
$695$	7.33888	+	14.5839i	0.278380	+	0.553200i
$696$	−1.72557	+	5.31075i	−0.0654075	+	0.201304i
$697$	0.932644	−	2.87038i	0.0353264	−	0.108724i
$698$	9.02062	−	6.55386i	0.341436	−	0.248067i
$699$	−17.5526			−0.663899
$700$	15.5067	−	20.8986i	0.586100	−	0.789893i
$701$	46.0639			1.73981			0.869904	−	0.493221i	$-0.164181\pi$
$701$	46.0639			1.73981			0.869904	+	0.493221i	$0.164181\pi$
$702$	3.60491	−	2.61912i	0.136058	−	0.0988523i
$703$	−2.40403	+	7.39885i	−0.0906698	+	0.279053i
$704$	−0.128798	+	0.396398i	−0.00485424	+	0.0149398i
$705$	−18.8299	+	18.6418i	−0.709176	+	0.702090i
$706$	1.05358	+	3.24257i	0.0396519	+	0.122036i
$707$	31.9921			1.20318
$708$	−8.51464	−	26.2054i	−0.320000	−	0.984858i
$709$	−8.99096	−	6.53231i	−0.337662	−	0.245326i	0.406012	−	0.913868i	$-0.366919\pi$
$709$	−8.99096	−	6.53231i	−0.337662	−	0.245326i	−0.743675	+	0.668541i	$0.766919\pi$
$710$	−8.43421	+	1.29247i	−0.316530	+	0.0485056i
$711$	−2.35705	+	1.71250i	−0.0883964	+	0.0642238i
$712$	−7.48247	−	5.43633i	−0.280417	−	0.203735i
$713$	−10.6156	−	7.71271i	−0.397559	−	0.288843i
$714$	2.13805	−	1.55339i	0.0800146	−	0.0581340i
$715$	0.110119	−	0.673363i	0.00411821	−	0.0251823i
$716$	18.8187	+	13.6726i	0.703289	+	0.510970i
$717$	13.0170	+	40.0623i	0.486129	+	1.49615i
$718$	13.9156			0.519325
$719$	−0.309560	−	0.952727i	−0.0115446	−	0.0355307i	0.945118	−	0.326728i	$-0.105946\pi$
$719$	−0.309560	−	0.952727i	−0.0115446	−	0.0355307i	−0.956663	+	0.291198i	$0.905946\pi$
$720$	−0.936464	+	0.143505i	−0.0348999	+	0.00534812i
$721$	−5.55128	+	17.0851i	−0.206741	+	0.636282i
$722$	−2.57734	+	7.93223i	−0.0959186	+	0.295207i
$723$	0.0669290	−	0.0486268i	0.00248912	−	0.00180845i
$724$	−10.3394			−0.384260
$725$	−5.08744	+	6.85640i	−0.188943	+	0.254640i
$726$	−9.61818			−0.356964
$727$	19.6766	−	14.2959i	0.729766	−	0.530206i	−0.159723	−	0.987162i	$-0.551060\pi$
$727$	19.6766	−	14.2959i	0.729766	−	0.530206i	0.889489	+	0.456956i	$0.151060\pi$
$728$	−2.89810	+	8.91943i	−0.107411	+	0.330576i
$729$	8.76881	−	26.9876i	0.324771	−	0.999541i
$730$	−1.12470	−	0.580195i	−0.0416271	−	0.0214740i
$731$	2.64465	+	8.13938i	0.0978158	+	0.301046i
$732$	15.2910			0.565171
$733$	6.52839	+	20.0923i	0.241132	+	0.742127i	0.996249	+	0.0865367i	$0.0275800\pi$
$733$	6.52839	+	20.0923i	0.241132	+	0.742127i	−0.755117	+	0.655590i	$0.772420\pi$
$734$	−11.7169	−	8.51283i	−0.432479	−	0.314214i
$735$	−6.93232	−	3.57615i	−0.255702	−	0.131908i
$736$	36.0792	−	26.2130i	1.32990	−	0.966226i
$737$	−1.97700	−	1.43638i	−0.0728239	−	0.0529096i
$738$	−0.221211	−	0.160719i	−0.00814287	−	0.00591614i
$739$	0.718571	−	0.522072i	0.0264331	−	0.0192047i	−0.574490	−	0.818511i	$-0.694800\pi$
$739$	0.718571	−	0.522072i	0.0264331	−	0.0192047i	0.600923	+	0.799307i	$0.294800\pi$
$740$	7.77835	+	15.4573i	0.285938	+	0.568220i
$741$	−3.78079	−	2.74690i	−0.138891	−	0.100910i
$742$	−6.80532	−	20.9446i	−0.249831	−	0.768902i
$743$	−30.3798			−1.11453			−0.557264	−	0.830335i	$-0.688149\pi$
$743$	−30.3798			−1.11453			−0.557264	+	0.830335i	$0.688149\pi$
$744$	1.53540	+	4.72548i	0.0562906	+	0.173245i
$745$	−2.83707	+	17.3483i	−0.103942	+	0.635594i
$746$	−3.52450	+	10.8473i	−0.129041	+	0.397148i
$747$	−0.586216	+	1.80419i	−0.0214485	+	0.0660118i
$748$	−0.266488	+	0.193615i	−0.00974376	+	0.00707925i
$749$	−50.5046			−1.84540
$750$	−9.66331	−	1.68009i	−0.352854	−	0.0613484i
$751$	−18.8449			−0.687662			−0.343831	−	0.939032i	$-0.611725\pi$
$751$	−18.8449			−0.687662			−0.343831	+	0.939032i	$0.611725\pi$
$752$	−13.9157	+	10.1103i	−0.507453	+	0.368686i
$753$	−3.11150	+	9.57621i	−0.113389	+	0.348976i
$754$	0.440676	−	1.35626i	0.0160485	−	0.0493922i
$755$	−0.552992	+	3.38148i	−0.0201255	+	0.123065i
$756$	8.58113	+	26.4100i	0.312093	+	0.960522i
$757$	−38.6184			−1.40361			−0.701805	−	0.712369i	$-0.747622\pi$
$757$	−38.6184			−1.40361			−0.701805	+	0.712369i	$0.747622\pi$
$758$	−1.90576	−	5.86532i	−0.0692202	−	0.213038i
$759$	2.23950	+	1.62709i	0.0812887	+	0.0590597i
$760$	−3.39589	−	6.74835i	−0.123182	−	0.244788i
$761$	−11.2863	+	8.19995i	−0.409127	+	0.297248i	−0.773248	−	0.634103i	$-0.781369\pi$
$761$	−11.2863	+	8.19995i	−0.409127	+	0.297248i	0.364121	+	0.931351i	$0.381369\pi$
$762$	−1.02473	−	0.744513i	−0.0371222	−	0.0269709i
$763$	−20.6452	−	14.9996i	−0.747406	−	0.543022i
$764$	−29.1725	+	21.1950i	−1.05542	+	0.766810i
$765$	−0.345017	−	0.177983i	−0.0124741	−	0.00643497i
$766$	6.27793	+	4.56119i	0.226831	+	0.164802i
$767$	4.69166	+	14.4394i	0.169406	+	0.521378i
$768$	−2.71044			−0.0978045
$769$	−12.2394	−	37.6690i	−0.441364	−	1.35838i	−0.886423	−	0.462876i	$-0.846817\pi$
$769$	−12.2394	−	37.6690i	−0.441364	−	1.35838i	0.445059	−	0.895501i	$-0.353183\pi$
$770$	−0.595585	−	0.307242i	−0.0214634	−	0.0110722i
$771$	12.8643	−	39.5922i	0.463296

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+(-0.422163 + 0.306719i) q^{2} +(0.519515 - 1.59890i) q^{3} +(-0.533889 + 1.64314i) q^{4} +(0.360883 - 2.20675i) q^{5} +(0.271094 + 0.834342i) q^{6} +3.01247 q^{7} +(-0.601098 - 1.84999i) q^{8} +(0.140459 + 0.102050i) q^{9} +(0.524502 + 1.04230i) q^{10} +(-0.154244 + 0.112065i) q^{11} +(2.34986 + 1.70727i) q^{12} +(-1.29480 - 0.940726i) q^{13} +(-1.27175 + 0.923982i) q^{14} +(-3.34090 - 1.72346i) q^{15} +(-1.97429 - 1.43441i) q^{16} +(-0.309017 - 0.951057i) q^{17} -0.0905972 q^{18} +(0.536719 + 1.65185i) q^{19} +(3.43334 + 1.77114i) q^{20} +(1.56502 - 4.81665i) q^{21} +(0.0307436 - 0.0946191i) q^{22} +(6.98691 - 5.07629i) q^{23} -3.27023 q^{24} +(-4.73953 - 1.59276i) q^{25} +0.835154 q^{26} +(4.31646 - 3.13609i) q^{27} +(-1.60833 + 4.94992i) q^{28} +(0.527659 - 1.62397i) q^{29} +(1.93902 - 0.297138i) q^{30} +(-0.469509 - 1.44500i) q^{31} +5.16382 q^{32} +(0.0990486 + 0.304840i) q^{33} +(0.422163 + 0.306719i) q^{34} +(1.08715 - 6.64778i) q^{35} +(-0.242672 + 0.176311i) q^{36} +(3.62369 + 2.63276i) q^{37} +(-0.733237 - 0.532728i) q^{38} +(-2.17680 + 1.58153i) q^{39} +(-4.29940 + 0.658847i) q^{40} +(2.44169 + 1.77399i) q^{41} +(0.816663 + 2.51343i) q^{42} -8.55826 q^{43} +(-0.101789 - 0.313275i) q^{44} +(0.275888 - 0.273131i) q^{45} +(-1.39262 + 4.28604i) q^{46} +(2.17809 - 6.70347i) q^{47} +(-3.31915 + 2.41150i) q^{48} +2.07499 q^{49} +(2.48938 - 0.781300i) q^{50} -1.68118 q^{51} +(2.23703 - 1.62529i) q^{52} +(-4.32916 + 13.3238i) q^{53} +(-0.860349 + 2.64788i) q^{54} +(0.191636 + 0.380821i) q^{55} +(-1.81079 - 5.57305i) q^{56} +2.91998 q^{57} +(0.275344 + 0.847421i) q^{58} +(-7.67463 - 5.57594i) q^{59} +(4.61556 - 4.56944i) q^{60} +(4.25901 - 3.09435i) q^{61} +(0.641418 + 0.466017i) q^{62} +(0.423129 + 0.307421i) q^{63} +(1.76861 - 1.28497i) q^{64} +(-2.54322 + 2.51781i) q^{65} +(-0.135315 - 0.0983121i) q^{66} +(3.96079 + 12.1901i) q^{67} +1.72770 q^{68} +(-4.48668 - 13.8086i) q^{69} +(1.58005 + 3.13989i) q^{70} +(-2.25975 + 6.95479i) q^{71} +(0.104361 - 0.321190i) q^{72} +(-0.877455 + 0.637508i) q^{73} -2.33730 q^{74} +(-5.00892 + 6.75058i) q^{75} -3.00077 q^{76} +(-0.464656 + 0.337592i) q^{77} +(0.433875 - 1.33533i) q^{78} +(-5.18563 + 15.9597i) q^{79} +(-3.87787 + 3.83912i) q^{80} +(-2.61089 - 8.03548i) q^{81} -1.57491 q^{82} +(3.37649 + 10.3918i) q^{83} +(7.07889 + 5.14311i) q^{84} +(-2.21027 + 0.338705i) q^{85} +(3.61298 - 2.62498i) q^{86} +(-2.32244 - 1.68735i) q^{87} +(0.300035 + 0.217988i) q^{88} +(3.84664 - 2.79475i) q^{89} +(-0.0326949 + 0.199926i) q^{90} +(-3.90054 - 2.83391i) q^{91} +(4.61082 + 14.1907i) q^{92} -2.55433 q^{93} +(1.13657 + 3.49802i) q^{94} +(3.83892 - 0.588282i) q^{95} +(2.68268 - 8.25645i) q^{96} +(0.257510 - 0.792536i) q^{97} +(-0.875981 + 0.636438i) q^{98} -0.0331012 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

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