LMFDB - Embedded newform 930.2.bk.a.47.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(47,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 5, 4]))

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

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

chi := DirichletCharacter("930.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bk (of order $20$, degree $8$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$512$
Relative dimension:	$64$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			47.7
Character	$\chi$	$=$	930.47
Dual form			930.2.bk.a.653.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.156434 + 0.987688i) q^{2} +(-1.22292 - 1.22657i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(2.20307 - 0.382712i) q^{5} +(1.40277 - 1.01599i) q^{6} +(-0.157227 + 0.0801110i) q^{7} +(0.453990 - 0.891007i) q^{8} +(-0.00893248 + 2.99999i) q^{9} +O(q^{10})$	\(q+(-0.156434 + 0.987688i) q^{2} +(-1.22292 - 1.22657i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(2.20307 - 0.382712i) q^{5} +(1.40277 - 1.01599i) q^{6} +(-0.157227 + 0.0801110i) q^{7} +(0.453990 - 0.891007i) q^{8} +(-0.00893248 + 2.99999i) q^{9} +(0.0333634 + 2.23582i) q^{10} +(-5.09677 - 1.65604i) q^{11} +(0.784036 + 1.54444i) q^{12} +(-5.04492 + 0.799037i) q^{13} +(-0.0545290 - 0.167823i) q^{14} +(-3.16360 - 2.23419i) q^{15} +(0.809017 + 0.587785i) q^{16} +(3.92721 + 2.00102i) q^{17} +(-2.96165 - 0.478124i) q^{18} +(-0.594594 - 0.818388i) q^{19} +(-2.21351 - 0.316807i) q^{20} +(0.290537 + 0.0948797i) q^{21} +(2.43296 - 4.77496i) q^{22} +(-1.76185 + 3.45782i) q^{23} +(-1.64807 + 0.532780i) q^{24} +(4.70706 - 1.68628i) q^{25} -5.10781i q^{26} +(3.69061 - 3.65779i) q^{27} +(0.174287 - 0.0276044i) q^{28} +(-8.50746 + 6.18103i) q^{29} +(2.70158 - 2.77515i) q^{30} +(2.41008 + 5.01911i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(4.20170 + 8.27674i) q^{33} +(-2.59073 + 3.56584i) q^{34} +(-0.315722 + 0.236663i) q^{35} +(0.935542 - 2.85040i) q^{36} +(-3.93226 - 3.93226i) q^{37} +(0.901327 - 0.459249i) q^{38} +(7.14961 + 5.21078i) q^{39} +(0.659176 - 2.13670i) q^{40} +(5.37941 + 7.40412i) q^{41} +(-0.139162 + 0.272118i) q^{42} +(1.39520 - 8.80898i) q^{43} +(4.33558 + 3.14998i) q^{44} +(1.12845 + 6.61261i) q^{45} +(-3.13963 - 2.28108i) q^{46} +(-5.34865 + 0.847143i) q^{47} +(-0.268405 - 1.71113i) q^{48} +(-4.09619 + 5.63793i) q^{49} +(0.929176 + 4.91290i) q^{50} +(-2.34829 - 7.26407i) q^{51} +(5.04492 + 0.799037i) q^{52} +(-3.89285 + 7.64014i) q^{53} +(3.03542 + 4.21737i) q^{54} +(-11.8624 - 1.69779i) q^{55} +0.176460i q^{56} +(-0.276667 + 1.73013i) q^{57} +(-4.77407 - 9.36964i) q^{58} +(4.29599 + 3.12122i) q^{59} +(2.31836 + 3.10245i) q^{60} +0.961240 q^{61} +(-5.33434 + 1.59525i) q^{62} +(-0.238927 - 0.472394i) q^{63} +(-0.587785 - 0.809017i) q^{64} +(-10.8085 + 3.69109i) q^{65} +(-8.83213 + 2.85520i) q^{66} +(-5.45621 - 5.45621i) q^{67} +(-3.11666 - 3.11666i) q^{68} +(6.39584 - 2.06761i) q^{69} +(-0.184359 - 0.348858i) q^{70} +(-10.4580 + 3.39802i) q^{71} +(2.66895 + 1.36992i) q^{72} +(-0.457301 - 0.897503i) q^{73} +(4.49899 - 3.26871i) q^{74} +(-7.82470 - 3.71134i) q^{75} +(0.312596 + 0.962073i) q^{76} +(0.934016 - 0.147934i) q^{77} +(-6.26507 + 6.24644i) q^{78} +(-9.93524 + 3.22815i) q^{79} +(2.00728 + 0.985314i) q^{80} +(-8.99984 - 0.0535947i) q^{81} +(-8.15449 + 4.15492i) q^{82} +(-3.61359 - 0.572337i) q^{83} +(-0.246998 - 0.180017i) q^{84} +(9.41775 + 2.90539i) q^{85} +(8.48227 + 2.75606i) q^{86} +(17.9854 + 2.87606i) q^{87} +(-3.78943 + 3.78943i) q^{88} +(0.391788 - 1.20580i) q^{89} +(-6.70773 + 0.0801183i) q^{90} +(0.729185 - 0.529784i) q^{91} +(2.74414 - 2.74414i) q^{92} +(3.20894 - 9.09410i) q^{93} -5.41532i q^{94} +(-1.62314 - 1.57541i) q^{95} +(1.73205 + 0.00257859i) q^{96} +(0.426442 - 0.217283i) q^{97} +(-4.92773 - 4.92773i) q^{98} +(5.01363 - 15.2755i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 512 q + 8 q^{3} - 12 q^{7}+O(q^{10}) $ 512 * q + 8 * q^3 - 12 * q^7	$ 512 q + 8 q^{3} - 12 q^{7} - 8 q^{10} - 8 q^{12} + 8 q^{15} + 128 q^{16} + 28 q^{22} + 32 q^{25} + 44 q^{27} + 8 q^{28} + 24 q^{30} + 8 q^{31} + 28 q^{33} + 176 q^{37} + 24 q^{42} - 40 q^{45} - 24 q^{46} + 12 q^{48} - 16 q^{51} - 40 q^{55} + 40 q^{57} + 56 q^{58} + 12 q^{60} - 32 q^{61} - 224 q^{63} + 32 q^{66} + 48 q^{67} + 24 q^{70} + 40 q^{73} - 32 q^{75} + 48 q^{76} - 76 q^{78} - 96 q^{81} + 24 q^{85} - 80 q^{87} - 72 q^{88} + 16 q^{90} + 80 q^{91} - 168 q^{93} - 112 q^{97}+O(q^{100}) $ 512 * q + 8 * q^3 - 12 * q^7 - 8 * q^10 - 8 * q^12 + 8 * q^15 + 128 * q^16 + 28 * q^22 + 32 * q^25 + 44 * q^27 + 8 * q^28 + 24 * q^30 + 8 * q^31 + 28 * q^33 + 176 * q^37 + 24 * q^42 - 40 * q^45 - 24 * q^46 + 12 * q^48 - 16 * q^51 - 40 * q^55 + 40 * q^57 + 56 * q^58 + 12 * q^60 - 32 * q^61 - 224 * q^63 + 32 * q^66 + 48 * q^67 + 24 * q^70 + 40 * q^73 - 32 * q^75 + 48 * q^76 - 76 * q^78 - 96 * q^81 + 24 * q^85 - 80 * q^87 - 72 * q^88 + 16 * q^90 + 80 * q^91 - 168 * q^93 - 112 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$	−0.156434	+	0.987688i	−0.110616	+	0.698401i
$2$	−0.156434	+	0.987688i	−0.110616	+	0.698401i
$3$	−1.22292	−	1.22657i	−0.706053	−	0.708159i
$3$	−1.22292	−	1.22657i	−0.706053	−	0.708159i
$4$	−0.951057	−	0.309017i	−0.475528	−	0.154508i
$5$	2.20307	−	0.382712i	0.985244	−	0.171154i
$5$	2.20307	−	0.382712i	0.985244	−	0.171154i
$6$	1.40277	−	1.01599i	0.572680	−	0.414775i
$7$	−0.157227	+	0.0801110i	−0.0594261	+	0.0302791i	−0.483451	−	0.875371i	$-0.660617\pi$
$7$	−0.157227	+	0.0801110i	−0.0594261	+	0.0302791i	0.424025	+	0.905651i	$0.360617\pi$
$8$	0.453990	−	0.891007i	0.160510	−	0.315018i
$9$	−0.00893248	+	2.99999i	−0.00297749	+	0.999996i
$10$	0.0333634	+	2.23582i	0.0105504	+	0.707028i
$11$	−5.09677	−	1.65604i	−1.53674	−	0.499316i	−0.586262	−	0.810122i	$-0.699401\pi$
$11$	−5.09677	−	1.65604i	−1.53674	−	0.499316i	−0.950473	+	0.310806i	$0.899401\pi$
$12$	0.784036	+	1.54444i	0.226332	+	0.445841i
$13$	−5.04492	+	0.799037i	−1.39921	+	0.221613i	−0.810030	−	0.586389i	$-0.800549\pi$
$13$	−5.04492	+	0.799037i	−1.39921	+	0.221613i	−0.589180	+	0.808002i	$0.700549\pi$
$14$	−0.0545290	−	0.167823i	−0.0145735	−	0.0448526i
$15$	−3.16360	−	2.23419i	−0.816839	−	0.576866i
$16$	0.809017	+	0.587785i	0.202254	+	0.146946i
$17$	3.92721	+	2.00102i	0.952489	+	0.485318i	0.859943	−	0.510391i	$-0.170499\pi$
$17$	3.92721	+	2.00102i	0.952489	+	0.485318i	0.0925468	+	0.995708i	$0.470499\pi$
$18$	−2.96165	−	0.478124i	−0.698069	−	0.112695i
$19$	−0.594594	−	0.818388i	−0.136409	−	0.187751i	0.735347	−	0.677690i	$-0.237019\pi$
$19$	−0.594594	−	0.818388i	−0.136409	−	0.187751i	−0.871757	+	0.489939i	$0.837019\pi$
$20$	−2.21351	−	0.316807i	−0.494956	−	0.0708401i
$21$	0.290537	+	0.0948797i	0.0634004	+	0.0207044i
$22$	2.43296	−	4.77496i	0.518710	−	1.01803i
$23$	−1.76185	+	3.45782i	−0.367370	+	0.721005i	−0.998505	−	0.0546686i	$-0.982590\pi$
$23$	−1.76185	+	3.45782i	−0.367370	+	0.721005i	0.631134	+	0.775674i	$0.282590\pi$
$24$	−1.64807	+	0.532780i	−0.336412	+	0.108753i
$25$	4.70706	−	1.68628i	0.941413	−	0.337257i
$26$		−	5.10781i		−	1.00172i
$27$	3.69061	−	3.65779i	0.710258	−	0.703942i
$28$	0.174287	−	0.0276044i	0.0329372	−	0.00521673i
$29$	−8.50746	+	6.18103i	−1.57980	+	1.14779i	−0.662866	+	0.748738i	$0.730660\pi$
$29$	−8.50746	+	6.18103i	−1.57980	+	1.14779i	−0.916929	+	0.399050i	$0.869340\pi$
$30$	2.70158	−	2.77515i	0.493239	−	0.506671i
$31$	2.41008	+	5.01911i	0.432864	+	0.901459i
$31$	2.41008	+	5.01911i	0.432864	+	0.901459i
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	4.20170	+	8.27674i	0.731422	+	1.44080i
$34$	−2.59073	+	3.56584i	−0.444307	+	0.611536i
$35$	−0.315722	+	0.236663i	−0.0533668	+	0.0400033i
$36$	0.935542	−	2.85040i	0.155924	−	0.475066i
$37$	−3.93226	−	3.93226i	−0.646460	−	0.646460i	0.305675	−	0.952136i	$-0.401118\pi$
$37$	−3.93226	−	3.93226i	−0.646460	−	0.646460i	−0.952136	+	0.305675i	$0.901118\pi$
$38$	0.901327	−	0.459249i	0.146215	−	0.0745001i
$39$	7.14961	+	5.21078i	1.14485	+	0.834392i
$40$	0.659176	−	2.13670i	0.104225	−	0.337842i
$41$	5.37941	+	7.40412i	0.840122	+	1.15633i	0.985954	+	0.167020i	$0.0534143\pi$
$41$	5.37941	+	7.40412i	0.840122	+	1.15633i	−0.145831	+	0.989309i	$0.546586\pi$
$42$	−0.139162	+	0.272118i	−0.0214731	+	0.0419887i
$43$	1.39520	−	8.80898i	0.212767	−	1.34336i	−0.617755	−	0.786371i	$-0.711958\pi$
$43$	1.39520	−	8.80898i	0.212767	−	1.34336i	0.830522	−	0.556986i	$-0.188042\pi$
$44$	4.33558	+	3.14998i	0.653613	+	0.474877i
$45$	1.12845	+	6.61261i	0.168220	+	0.985750i
$46$	−3.13963	−	2.28108i	−0.462914	−	0.336327i
$47$	−5.34865	+	0.847143i	−0.780181	+	0.123568i	−0.533807	−	0.845606i	$-0.679239\pi$
$47$	−5.34865	+	0.847143i	−0.780181	+	0.123568i	−0.246374	+	0.969175i	$0.579239\pi$
$48$	−0.268405	−	1.71113i	−0.0387410	−	0.246980i
$49$	−4.09619	+	5.63793i	−0.585171	+	0.805418i
$50$	0.929176	+	4.91290i	0.131405	+	0.694790i
$51$	−2.34829	−	7.26407i	−0.328826	−	1.01717i
$52$	5.04492	+	0.799037i	0.699605	+	0.110807i
$53$	−3.89285	+	7.64014i	−0.534724	+	1.04945i	0.452745	+	0.891640i	$0.350445\pi$
$53$	−3.89285	+	7.64014i	−0.534724	+	1.04945i	−0.987469	+	0.157815i	$0.949555\pi$
$54$	3.03542	+	4.21737i	0.413068	+	0.573912i
$55$	−11.8624	−	1.69779i	−1.59952	−	0.228930i
$56$			0.176460i			0.0235804i
$57$	−0.276667	+	1.73013i	−0.0366454	+	0.229162i
$58$	−4.77407	−	9.36964i	−0.626866	−	1.23029i
$59$	4.29599	+	3.12122i	0.559291	+	0.406349i	0.831199	−	0.555975i	$-0.187655\pi$
$59$	4.29599	+	3.12122i	0.559291	+	0.406349i	−0.271909	+	0.962323i	$0.587655\pi$
$60$	2.31836	+	3.10245i	0.299299	+	0.400524i
$61$	0.961240			0.123074			0.0615371	−	0.998105i	$-0.480400\pi$
$61$	0.961240			0.123074			0.0615371	+	0.998105i	$0.480400\pi$
$62$	−5.33434	+	1.59525i	−0.677462	+	0.202597i
$63$	−0.238927	−	0.472394i	−0.0301020	−	0.0595160i
$64$	−0.587785	−	0.809017i	−0.0734732	−	0.101127i
$65$	−10.8085	+	3.69109i	−1.34063	+	0.457823i
$66$	−8.83213	+	2.85520i	−1.08716	+	0.351451i
$67$	−5.45621	−	5.45621i	−0.666582	−	0.666582i	0.290341	−	0.956923i	$-0.406231\pi$
$67$	−5.45621	−	5.45621i	−0.666582	−	0.666582i	−0.956923	+	0.290341i	$0.906231\pi$
$68$	−3.11666	−	3.11666i	−0.377950	−	0.377950i
$69$	6.39584	−	2.06761i	0.769969	−	0.248911i
$70$	−0.184359	−	0.348858i	−0.0220352	−	0.0416965i
$71$	−10.4580	+	3.39802i	−1.24114	+	0.403271i	−0.854738	−	0.519059i	$-0.826283\pi$
$71$	−10.4580	+	3.39802i	−1.24114	+	0.403271i	−0.386403	+	0.922330i	$0.626283\pi$
$72$	2.66895	+	1.36992i	0.314539	+	0.161447i
$73$	−0.457301	−	0.897503i	−0.0535230	−	0.105045i	0.862696	−	0.505723i	$-0.168774\pi$
$73$	−0.457301	−	0.897503i	−0.0535230	−	0.105045i	−0.916219	+	0.400679i	$0.868774\pi$
$74$	4.49899	−	3.26871i	0.522997	−	0.379980i
$75$	−7.82470	−	3.71134i	−0.903519	−	0.428548i
$76$	0.312596	+	0.962073i	0.0358573	+	0.110357i
$77$	0.934016	−	0.147934i	0.106441	−	0.0168586i
$78$	−6.26507	+	6.24644i	−0.709379	+	0.707270i
$79$	−9.93524	+	3.22815i	−1.11780	+	0.363196i	−0.808928	−	0.587907i	$-0.799952\pi$
$79$	−9.93524	+	3.22815i	−1.11780	+	0.363196i	−0.308873	+	0.951103i	$0.599952\pi$
$80$	2.00728	+	0.985314i	0.224420	+	0.110161i
$81$	−8.99984	−	0.0535947i	−0.999982	−	0.00595496i
$82$	−8.15449	+	4.15492i	−0.900512	+	0.458834i
$83$	−3.61359	−	0.572337i	−0.396643	−	0.0628222i	−0.0450733	−	0.998984i	$-0.514352\pi$
$83$	−3.61359	−	0.572337i	−0.396643	−	0.0628222i	−0.351570	+	0.936162i	$0.614352\pi$
$84$	−0.246998	−	0.180017i	−0.0269497	−	0.0196414i
$85$	9.41775	+	2.90539i	1.02150	+	0.315134i
$86$	8.48227	+	2.75606i	0.914666	+	0.297193i
$87$	17.9854	+	2.87606i	1.92824	+	0.308346i
$88$	−3.78943	+	3.78943i	−0.403955	+	0.403955i
$89$	0.391788	−	1.20580i	0.0415295	−	0.127815i	−0.928142	−	0.372226i	$-0.878595\pi$
$89$	0.391788	−	1.20580i	0.0415295	−	0.127815i	0.969672	+	0.244411i	$0.0785947\pi$
$90$	−6.70773	+	0.0801183i	−0.707056	+	0.00844521i
$91$	0.729185	−	0.529784i	0.0764393	−	0.0555364i
$92$	2.74414	−	2.74414i	0.286096	−	0.286096i
$93$	3.20894	−	9.09410i	0.332751	−	0.943015i
$94$		−	5.41532i		−	0.558548i
$95$	−1.62314	−	1.57541i	−0.166531	−	0.161634i
$96$	1.73205	+	0.00257859i	0.176776	+	0.000263176i
$97$	0.426442	−	0.217283i	0.0432986	−	0.0220617i	−0.432207	−	0.901774i	$-0.642265\pi$
$97$	0.426442	−	0.217283i	0.0432986	−	0.0220617i	0.475506	+	0.879713i	$0.342265\pi$
$98$	−4.92773	−	4.92773i	−0.497776	−	0.497776i
$99$	5.01363	−	15.2755i	0.503889	−	1.53524i
$100$	−4.99777	+	0.149189i	−0.499777	+	0.0149189i
$101$	−15.9122	+	5.17018i	−1.58332	+	0.514452i	−0.962909	−	0.269826i	$-0.913034\pi$
$101$	−15.9122	+	5.17018i	−1.58332	+	0.514452i	−0.620410	+	0.784277i	$0.713034\pi$
$102$	7.54199	−	1.18303i	0.746769	−	0.117137i
$103$	1.21370	−	7.66299i	0.119589	−	0.755057i	−0.852894	−	0.522084i	$-0.825155\pi$
$103$	1.21370	−	7.66299i	0.119589	−	0.755057i	0.972483	−	0.232973i	$-0.0748454\pi$
$104$	−1.57840	+	4.85781i	−0.154775	+	0.476348i
$105$	0.676386	+	0.0978349i	0.0660085	+	0.00954771i
$106$	−6.93711	−	5.04010i	−0.673791	−	0.489538i
$107$	−0.194118	−	0.0989080i	−0.0187661	−	0.00956180i	0.444582	−	0.895738i	$-0.353352\pi$
$107$	−0.194118	−	0.0989080i	−0.0187661	−	0.00956180i	−0.463348	+	0.886176i	$0.653352\pi$
$108$	−4.64030	+	2.33830i	−0.446513	+	0.225003i
$109$	1.71268	−	2.35730i	0.164045	−	0.225788i	−0.719079	−	0.694928i	$-0.755436\pi$
$109$	1.71268	−	2.35730i	0.164045	−	0.225788i	0.883124	+	0.469140i	$0.155436\pi$
$110$	3.53257	−	11.4507i	0.336817	−	1.09178i
$111$	−0.0143397	+	9.63203i	−0.00136106	+	0.914232i
$112$	−0.174287	−	0.0276044i	−0.0164686	−	0.00260837i
$113$	9.28327	−	4.73006i	0.873296	−	0.444967i	0.0409102	−	0.999163i	$-0.486974\pi$
$113$	9.28327	−	4.73006i	0.873296	−	0.444967i	0.832386	+	0.554196i	$0.186974\pi$
$114$	−1.66555	−	0.543913i	−0.155993	−	0.0509421i
$115$	−2.55813	+	8.29211i	−0.238547	+	0.773243i
$116$	10.0011	−	3.24956i	0.928580	−	0.301714i
$117$	−2.35204	−	15.1418i	−0.217446	−	1.39986i
$118$	−3.75484	+	3.75484i	−0.345661	+	0.345661i
$119$	−0.777766			−0.0712977
$120$	−3.42692	+	1.80449i	−0.312834	+	0.164727i
$121$	14.3354	+	10.4153i	1.30322	+	0.946846i
$122$	−0.150371	+	0.949405i	−0.0136139	+	0.0859551i
$123$	2.50306	−	15.6528i	0.225693	−	1.41137i
$124$	−0.741134	−	5.51822i	−0.0665558	−	0.495551i
$125$	9.72464	−	5.51646i	0.869799	−	0.493407i
$126$	0.503954	−	0.162087i	0.0448958	−	0.0144399i
$127$	1.42444	+	8.99355i	0.126399	+	0.798049i	0.966697	+	0.255924i	$0.0823798\pi$
$127$	1.42444	+	8.99355i	0.126399	+	0.798049i	−0.840298	+	0.542124i	$0.817620\pi$
$128$	0.891007	−	0.453990i	0.0787546	−	0.0401275i
$129$	−12.5110	+	9.06136i	−1.10153	+	0.797809i
$130$	−1.95482	−	11.2529i	−0.171449	−	0.986942i
$131$	19.7390	+	6.41358i	1.72460	+	0.560357i	0.992652	−	0.121002i	$-0.0386106\pi$
$131$	19.7390	+	6.41358i	1.72460	+	0.560357i	0.731950	+	0.681359i	$0.238611\pi$
$132$	−1.43840	−	9.17005i	−0.125197	−	0.798150i
$133$	0.159048	+	0.0810389i	0.0137912	+	0.00702697i
$134$	6.24257	−	4.53549i	0.539276	−	0.391807i
$135$	6.73080	−	9.47081i	0.579295	−	0.815118i
$136$	3.56584	−	2.59073i	0.305768	−	0.222153i
$137$	14.4817	−	2.29368i	1.23726	−	0.195963i	0.496681	−	0.867933i	$-0.334552\pi$
$137$	14.4817	−	2.29368i	1.23726	−	0.195963i	0.740578	+	0.671970i	$0.234552\pi$
$138$	1.04163	+	6.64055i	0.0886692	+	0.565281i
$139$	−4.27542	+	5.88462i	−0.362637	+	0.499127i	−0.950881	−	0.309557i	$-0.899819\pi$
$139$	−4.27542	+	5.88462i	−0.362637	+	0.499127i	0.588244	+	0.808683i	$0.299819\pi$
$140$	0.373403	−	0.127516i	0.0315583	−	0.0107771i
$141$	7.58005	+	5.52449i	0.638355	+	0.465246i
$142$	−1.72019	−	10.8609i	−0.144355	−	0.911423i
$143$	27.0361	+	4.28209i	2.26087	+	0.358087i
$144$	−1.77057	+	2.42179i	−0.147548	+	0.201816i
$145$	−16.3770	+	16.8732i	−1.36004	+	1.40124i
$146$	0.957991	−	0.311270i	0.0792839	−	0.0257609i
$147$	11.9246	−	1.87048i	0.983526	−	0.154275i
$148$	2.52467	+	4.95494i	0.207527	+	0.407294i
$149$	−14.0055			−1.14737			−0.573687	−	0.819075i	$-0.694487\pi$
$149$	−14.0055			−1.14737			−0.573687	+	0.819075i	$0.694487\pi$
$150$	4.88970	−	7.14779i	0.399242	−	0.583614i
$151$	−1.24059	+	3.81813i	−0.100957	+	0.310715i	−0.988760	−	0.149509i	$-0.952231\pi$
$151$	−1.24059	+	3.81813i	−0.100957	+	0.310715i	0.887803	+	0.460224i	$0.152231\pi$
$152$	−0.999129	+	0.158246i	−0.0810401	+	0.0128355i
$153$	−6.03810	+	11.7637i	−0.488151	+	0.951040i
$154$			0.945659i			0.0762033i
$155$	7.23046	+	10.1351i	0.580765	+	0.814071i
$156$	−5.18946	−	7.16509i	−0.415490	−	0.573667i
$157$	16.5473	+	2.62084i	1.32062	+	0.209166i	0.776647	−	0.629936i	$-0.216919\pi$
$157$	16.5473	+	2.62084i	1.32062	+	0.209166i	0.543975	+	0.839102i	$0.316919\pi$
$158$	−1.63420	−	10.3179i	−0.130010	−	0.820849i
$159$	14.1318	−	4.56845i	1.12072	−	0.362302i
$160$	−1.28719	+	1.82843i	−0.101761	+	0.144550i
$161$		−	0.684805i		−	0.0539702i
$162$	1.46082	−	8.88065i	0.114773	−	0.697730i
$163$	−17.7874	−	9.06312i	−1.39322	−	0.709879i	−0.413543	−	0.910485i	$-0.635709\pi$
$163$	−17.7874	−	9.06312i	−1.39322	−	0.709879i	−0.979672	+	0.200606i	$0.935709\pi$
$164$	−2.82812	−	8.70406i	−0.220839	−	0.679673i
$165$	12.4243	+	16.6262i	0.967228	+	1.29435i
$166$	1.13058	−	3.47957i	0.0877501	−	0.270067i
$167$	1.70990	−	10.7959i	0.132316	−	0.835411i	−0.828856	−	0.559462i	$-0.811008\pi$
$167$	1.70990	−	10.7959i	0.132316	−	0.835411i	0.961172	−	0.275949i	$-0.0889922\pi$
$168$	0.216440	−	0.215796i	0.0166987	−	0.0166490i
$169$	12.4490	−	4.04494i	0.957619	−	0.311149i
$170$	−4.34288	+	8.84730i	−0.333084	+	0.678557i
$171$	2.46046	−	1.77646i	0.188156	−	0.135850i
$172$	−4.04904	+	7.94669i	−0.308737	+	0.605930i
$173$	−3.37601	−	21.3153i	−0.256673	−	1.62057i	−0.693107	−	0.720835i	$-0.743759\pi$
$173$	−3.37601	−	21.3153i	−0.256673	−	1.62057i	0.436434	−	0.899736i	$-0.356241\pi$
$174$	−5.65418	+	17.3140i	−0.428643	+	1.31257i
$175$	−0.604986	+	0.642216i	−0.0457326	+	0.0485470i
$176$	−3.14998	−	4.33558i	−0.237439	−	0.326806i
$177$	−1.42527	−	9.08633i	−0.107130	−	0.682970i
$178$	1.12967	+	0.575594i	0.0846720	+	0.0431426i
$179$	−2.65970	+	8.18572i	−0.198796	+	0.611830i	0.801116	+	0.598509i	$0.204240\pi$
$179$	−2.65970	+	8.18572i	−0.198796	+	0.611830i	−0.999911	+	0.0133203i	$0.995760\pi$
$180$	0.970188	−	6.63768i	0.0723135	−	0.494743i
$181$	−9.99779			−0.743130			−0.371565	−	0.928407i	$-0.621179\pi$
$181$	−9.99779			−0.743130			−0.371565	+	0.928407i	$0.621179\pi$
$182$	0.409192	+	0.803084i	0.0303313	+	0.0595285i
$183$	−1.17552	−	1.17902i	−0.0868969	−	0.0871560i
$184$	2.28108	+	3.13963i	0.168163	+	0.231457i
$185$	−10.1680	−	7.15814i	−0.747566	−	0.526277i
$186$	8.48015	+	4.59206i	0.621795	+	0.336706i
$187$	−16.7024	−	16.7024i	−1.22140	−	1.22140i
$188$	5.34865	+	0.847143i	0.390090	+	0.0617842i
$189$	−0.287233	+	0.870760i	−0.0208931	+	0.0633385i
$190$	1.80993	−	1.35671i	0.131306	−	0.0984260i
$191$		−	13.0384i		−	0.943429i	−0.881751	−	0.471714i	$-0.843635\pi$
$191$		−	13.0384i		−	0.943429i	0.881751	−	0.471714i	$-0.156365\pi$
$192$	−0.273499	+	1.71032i	−0.0197381	+	0.123432i
$193$	−1.33598	−	2.62200i	−0.0961657	−	0.188736i	0.837912	−	0.545805i	$-0.183776\pi$
$193$	−1.33598	−	2.62200i	−0.0961657	−	0.188736i	−0.934078	+	0.357069i	$0.883776\pi$
$194$	0.147898	+	0.455182i	0.0106184	+	0.0326802i
$195$	17.7453	+	8.74348i	1.27077	+	0.626134i
$196$	5.63793	−	4.09619i	0.402709	−	0.292585i
$197$	8.53031	+	16.7417i	0.607760	+	1.19280i	0.965848	+	0.259108i	$0.0834285\pi$
$197$	8.53031	+	16.7417i	0.607760	+	1.19280i	−0.358089	+	0.933688i	$0.616571\pi$
$198$	14.3031	+	7.34151i	1.01648	+	0.521739i
$199$	13.4903	−	18.5678i	0.956303	−	1.31624i	0.00763243	−	0.999971i	$-0.497570\pi$
$199$	13.4903	−	18.5678i	0.956303	−	1.31624i	0.948670	−	0.316267i	$-0.102430\pi$
$200$	0.634472	−	4.95958i	0.0448639	−	0.350695i
$201$	−0.0198970	+	13.3649i	−0.00140343	+	0.942688i
$202$	−2.61731	−	16.5251i	−0.184153	−	1.16270i
$203$	0.842431	−	1.65336i	0.0591270	−	0.116043i
$204$	−0.0113654	+	7.63421i	−0.000795739	+	0.534501i
$205$	14.6849	+	14.2531i	1.02564	+	0.995476i
$206$	7.37878	+	2.39751i	0.514104	+	0.167043i
$207$	−10.3577	−	5.31640i	−0.719908	−	0.369516i
$208$	−4.55109	−	2.31890i	−0.315561	−	0.160787i
$209$	1.67522	+	5.15581i	0.115878	+	0.356635i
$210$	−0.202440	+	0.652754i	−0.0139697	+	0.0450443i
$211$	4.61055			0.317403			0.158702	−	0.987327i	$-0.449269\pi$
$211$	4.61055			0.317403			0.158702	+	0.987327i	$0.449269\pi$
$212$	6.06325	−	6.06325i	0.416426	−	0.416426i
$213$	16.9573	+	8.67198i	1.16189	+	0.594194i
$214$	0.128057	−	0.176255i	0.00875380	−	0.0120486i
$215$	−0.297561	−	19.9408i	−0.0202935	−	1.35995i
$216$	−1.58361	−	4.94896i	−0.107751	−	0.336734i
$217$	−0.781015	−	0.596064i	−0.0530188	−	0.0404635i
$218$	2.06035	+	2.06035i	0.139545	+	0.139545i
$219$	−0.541605	+	1.65848i	−0.0365983	+	0.112070i
$220$	10.7571	+	5.28036i	0.725245	+	0.356002i
$221$	−21.4114	−	6.95698i	−1.44029	−	0.467977i
$222$	−9.51120	−	1.52094i	−0.638350	−	0.102079i
$223$	−2.82617	+	2.82617i	−0.189254	+	0.189254i	−0.795374	−	0.606119i	$-0.792725\pi$
$223$	−2.82617	+	2.82617i	−0.189254	+	0.189254i	0.606119	+	0.795374i	$0.292725\pi$
$224$	0.0545290	−	0.167823i	0.00364337	−	0.0112132i
$225$	5.01678	+	14.1362i	0.334452	+	0.942413i
$226$	3.21960	+	9.90892i	0.214165	+	0.659131i
$227$	−3.08534	+	19.4801i	−0.204781	+	1.29294i	0.644339	+	0.764740i	$0.277133\pi$
$227$	−3.08534	+	19.4801i	−0.204781	+	1.29294i	−0.849121	+	0.528199i	$0.822867\pi$
$228$	0.797766	−	1.55996i	0.0528334	−	0.103311i
$229$	−10.7553	−	14.8034i	−0.710732	−	0.978239i	−0.999781	−	0.0209247i	$-0.993339\pi$
$229$	−10.7553	−	14.8034i	−0.710732	−	0.978239i	0.289049	−	0.957314i	$-0.406661\pi$
$230$	−7.78984	−	3.82381i	−0.513647	−	0.252134i
$231$	−1.32368	−	0.964722i	−0.0870916	−	0.0634741i
$232$	1.64503	+	10.3863i	0.108002	+	0.681896i
$233$	−2.25099	−	14.2122i	−0.147467	−	0.931072i	−0.944828	−	0.327568i	$-0.893771\pi$
$233$	−2.25099	−	14.2122i	−0.147467	−	0.931072i	0.797360	−	0.603504i	$-0.206229\pi$
$234$	15.3234	+	0.0456254i	1.00172	+	0.00298263i
$235$	−11.4593	+	3.91331i	−0.747519	+	0.255276i
$236$	−3.12122	−	4.29599i	−0.203174	−	0.279645i
$237$	16.1095	+	8.23846i	1.04643	+	0.535145i
$238$	0.121669	−	0.768191i	0.00788666	−	0.0497944i
$239$	−3.24491	−	9.98681i	−0.209896	−	0.645993i	−0.999477	−	0.0323465i	$-0.989702\pi$
$239$	−3.24491	−	9.98681i	−0.209896	−	0.645993i	0.789581	−	0.613647i	$-0.210298\pi$
$240$	−1.24619	−	3.66702i	−0.0804409	−	0.236705i
$241$	4.54882	−	13.9998i	0.293015	−	0.901808i	−0.690866	−	0.722983i	$-0.742770\pi$
$241$	4.54882	−	13.9998i	0.293015	−	0.901808i	0.983881	−	0.178825i	$-0.0572296\pi$
$242$	−12.5296	+	12.5296i	−0.805436	+	0.805436i
$243$	10.9403	+	11.1044i	0.701824	+	0.712351i
$244$	−0.914193	−	0.297039i	−0.0585252	−	0.0190160i
$245$	−6.86651	+	13.9884i	−0.438686	+	0.893688i
$246$	15.0686	+	4.92089i	0.960737	+	0.313744i
$247$	3.65360	+	3.65360i	0.232473	+	0.232473i
$248$	5.56622	+	0.131230i	0.353455	+	0.00833313i
$249$	3.71713	+	5.13224i	0.235563	+	0.325242i
$250$	3.92727	+	10.4679i	0.248382	+	0.662047i
$251$	−11.2190	+	15.4417i	−0.708140	+	0.974671i	0.291695	+	0.956511i	$0.405781\pi$
$251$	−11.2190	+	15.4417i	−0.708140	+	0.974671i	−0.999835	+	0.0181594i	$0.994219\pi$
$252$	0.0812559	+	0.523106i	0.00511864	+	0.0329526i
$253$	14.7060	−	14.7060i	0.924560	−	0.924560i
$254$	−9.10566			−0.571340
$255$	−7.95350	−	15.1046i	−0.498068	−	0.945885i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	5.30885	+	2.70499i	0.331157	+	0.168733i	0.611661	−	0.791120i	$-0.290502\pi$
$257$	5.30885	+	2.70499i	0.331157	+	0.168733i	−0.280504	+	0.959853i	$0.590502\pi$
$258$	−6.99265	−	13.7745i	−0.435343	−	0.857563i
$259$	0.933275	+	0.303239i	0.0579909	+	0.0188424i
$260$	11.4201	−	0.170414i	0.708247	−	0.0105686i
$261$	−18.4670	−	25.5775i	−1.14308	−	1.58321i
$262$	−9.42247	+	18.4926i	−0.582122	+	1.14248i
$263$	−3.05293	−	19.2754i	−0.188252	−	1.18857i	−0.883018	−	0.469339i	$-0.844492\pi$
$263$	−3.05293	−	19.2754i	−0.188252	−	1.18857i	0.694766	−	0.719236i	$-0.255508\pi$
$264$	9.28216	+	0.0138188i	0.571278	+	0.000850490i
$265$	−5.65226	+	18.3216i	−0.347215	+	1.12549i
$266$	−0.104922	+	0.144412i	−0.00643317	+	0.00885449i
$267$	−1.95812	+	0.994043i	−0.119835	+	0.0608345i
$268$	3.50310	+	6.87522i	0.213986	+	0.419971i
$269$	17.6080	−	12.7929i	1.07358	−	0.779999i	0.0970245	−	0.995282i	$-0.469067\pi$
$269$	17.6080	−	12.7929i	1.07358	−	0.779999i	0.976552	+	0.215283i	$0.0690675\pi$
$270$	8.30128	+	8.12950i	0.505200	+	0.494745i
$271$	−2.52974	−	7.78573i	−0.153671	−	0.472949i	0.844353	−	0.535787i	$-0.179985\pi$
$271$	−2.52974	−	7.78573i	−0.153671	−	0.472949i	−0.998024	+	0.0628376i	$0.979985\pi$
$272$	2.00102	+	3.92721i	0.121329	+	0.238122i
$273$	−1.54155	−	0.246511i	−0.0932988	−	0.0149195i
$274$			14.6623i			0.885780i
$275$	−26.7834	+	0.799514i	−1.61510	+	0.0482125i
$276$	−6.72174	−	0.0100070i	−0.404601	−	0.000602350i
$277$	1.93774	+	0.306907i	0.116427	+	0.0184403i	0.214376	−	0.976751i	$-0.431228\pi$
$277$	1.93774	+	0.306907i	0.116427	+	0.0184403i	−0.0979489	+	0.995191i	$0.531228\pi$
$278$	−5.14334	−	5.14334i	−0.308477	−	0.308477i
$279$	−15.0788	+	7.18538i	−0.902744	+	0.430178i
$280$	0.0675332	+	0.388753i	0.00403588	+	0.0232325i
$281$	13.3639	+	18.3939i	0.797225	+	1.09729i	0.993171	+	0.116671i	$0.0372223\pi$
$281$	13.3639	+	18.3939i	0.797225	+	1.09729i	−0.195946	+	0.980615i	$0.562778\pi$
$282$	−6.64225	+	6.62251i	−0.395540	+	0.394364i
$283$	0.781019	+	1.53284i	0.0464268	+	0.0911177i	0.913054	−	0.407838i	$-0.133717\pi$
$283$	0.781019	+	1.53284i	0.0464268	+	0.0911177i	−0.866628	+	0.498955i	$0.833717\pi$
$284$	10.9962			0.652507
$285$	0.0526243	+	3.91749i	0.00311720	+	0.232052i
$286$	−8.45875	+	26.0333i	−0.500176	+	1.53938i
$287$	−1.43894	−	0.733175i	−0.0849378	−	0.0432780i
$288$	−2.11499	−	2.12763i	−0.124627	−	0.125372i
$289$	1.42660	+	1.96355i	0.0839177	+	0.115503i
$290$	−14.1035	−	18.8149i	−0.828186	−	1.10485i
$291$	−0.788016	−	0.257340i	−0.0461943	−	0.0150855i
$292$	0.157575	+	0.994890i	0.00922138	+	0.0582215i
$293$	−13.5108	+	26.5165i	−0.789311	+	1.54911i	0.0457496	+	0.998953i	$0.485432\pi$
$293$	−13.5108	+	26.5165i	−0.789311	+	1.54911i	−0.835061	+	0.550158i	$0.814568\pi$
$294$	−0.0179698	+	12.0704i	−0.00104802	+	0.703961i
$295$	10.6589	+	5.23215i	0.620586	+	0.304628i
$296$	−5.28888	+	1.71846i	−0.307410	+	0.0998836i
$297$	−24.8676	+	12.5311i	−1.44297	+	0.727129i
$298$	2.19094	−	13.8331i	0.126918	−	0.801327i
$299$	6.12545	−	18.8522i	0.354244	−	1.09025i
$300$	6.29487	+	5.94766i	0.363434	+	0.343388i
$301$	0.486332	+	1.49678i	0.0280317	+	0.0862728i
$302$	−3.57705	−	1.82260i	−0.205836	−	0.104879i
$303$	25.8009	+	13.1946i	1.48222	+	0.758011i
$304$		−	1.01158i		−	0.0580183i
$305$	2.11768	−	0.367878i	0.121258	−	0.0210646i
$306$	−10.6743	−	7.80401i	−0.610210	−	0.446126i
$307$	−0.423441	−	2.67350i	−0.0241670	−	0.152585i	0.972654	−	0.232259i	$-0.0746118\pi$
$307$	−0.423441	−	2.67350i	−0.0241670	−	0.152585i	−0.996821	+	0.0796748i	$0.974612\pi$
$308$	−0.934016	−	0.147934i	−0.0532205	−	0.00842930i
$309$	−10.8834	+	7.88255i	−0.619137	+	0.448422i
$310$	−11.1414	+	5.55596i	−0.632790	+	0.315558i
$311$			26.8522i			1.52265i	0.648372	+	0.761324i	$0.275450\pi$
$311$			26.8522i			1.52265i	−0.648372	+	0.761324i	$0.724550\pi$
$312$	7.88869	−	4.00471i	0.446609	−	0.226722i
$313$	5.83216	−	0.923723i	0.329653	−	0.0522119i	0.0105857	−	0.999944i	$-0.496630\pi$
$313$	5.83216	−	0.923723i	0.329653	−	0.0522119i	0.319067	+	0.947732i	$0.396630\pi$
$314$	−5.17715	+	15.9336i	−0.292164	+	0.899187i
$315$	−0.707165	−	0.949277i	−0.0398443	−	0.0534857i
$316$	10.4465			0.587663
$317$	−5.51509	−	10.8240i	−0.309758	−	0.607934i	0.682675	−	0.730722i	$-0.260817\pi$
$317$	−5.51509	−	10.8240i	−0.309758	−	0.607934i	−0.992433	+	0.122788i	$0.960817\pi$
$318$	2.30150	+	14.6725i	0.129062	+	0.822791i
$319$	53.5966	−	17.4146i	3.00084	−	0.975031i
$320$	−1.60455	−	1.55737i	−0.0896973	−	0.0870597i
$321$	0.116073	+	0.359055i	0.00647858	+	0.0200405i
$322$	0.676374	+	0.107127i	0.0376928	+	0.00596996i
$323$	−0.697490	−	4.40378i	−0.0388094	−	0.245033i
$324$	8.54280	+	2.83208i	0.474600	+	0.157338i
$325$	−22.3994	+	12.2683i	−1.24249	+	0.680522i
$326$	11.7341	−	16.1506i	0.649892	−	0.894499i
$327$	−4.98585	+	0.782074i	−0.275718	+	0.0432488i
$328$	9.03932	−	1.43169i	0.499113	−	0.0790517i
$329$	0.773085	−	0.561679i	0.0426215	−	0.0309664i
$330$	−18.3651	+	9.67038i	−1.01097	+	0.532337i
$331$	−8.13905	+	5.91337i	−0.447363	+	0.325028i	−0.788554	−	0.614966i	$-0.789170\pi$
$331$	−8.13905	+	5.91337i	−0.447363	+	0.325028i	0.341191	+	0.939994i	$0.389170\pi$
$332$	3.25987	+	1.66099i	0.178909	+	0.0911585i
$333$	11.8319	−	11.7616i	0.648382	−	0.644533i
$334$	10.3955	+	3.37770i	0.568816	+	0.184820i
$335$	−14.1086	−	9.93227i	−0.770834	−	0.542658i
$336$	0.179281	+	0.247533i	0.00978056	+	0.0135040i
$337$	6.17639	−	3.14703i	0.336450	−	0.171430i	−0.277601	−	0.960697i	$-0.589539\pi$
$337$	6.17639	−	3.14703i	0.336450	−	0.171430i	0.614050	+	0.789267i	$0.289539\pi$
$338$	2.04768	+	12.9285i	0.111379	+	0.703220i
$339$	−17.1544	−	5.60206i	−0.931701	−	0.304262i
$340$	−8.05900	−	5.67344i	−0.437061	−	0.307685i
$341$	−3.97178	−	29.5725i	−0.215084	−	1.60144i
$342$	1.36969	+	2.70807i	0.0740644	+	0.146436i
$343$	0.385602	−	2.43459i	0.0208205	−	0.131456i
$344$	−7.21545	−	5.24233i	−0.389031	−	0.282647i
$345$	13.2992	−	7.00287i	0.716006	−	0.377022i
$346$	21.5810			1.16020
$347$	6.70312	−	6.70312i	0.359842	−	0.359842i	−0.503913	−	0.863755i	$-0.668107\pi$
$347$	6.70312	−	6.70312i	0.359842	−	0.359842i	0.863755	+	0.503913i	$0.168107\pi$
$348$	−16.2164	−	8.29309i	−0.869289	−	0.444556i
$349$	11.5511	−	3.75318i	0.618316	−	0.200903i	0.0169235	−	0.999857i	$-0.494613\pi$
$349$	11.5511	−	3.75318i	0.618316	−	0.200903i	0.601393	+	0.798954i	$0.294613\pi$
$350$	−0.539669	−	0.698002i	−0.0288465	−	0.0373098i
$351$	−15.6961	+	21.4022i	−0.837797	+	1.14236i
$352$	4.77496	−	2.43296i	0.254506	−	0.129677i
$353$	−10.8404	−	1.71695i	−0.576975	−	0.0913838i	−0.138875	−	0.990310i	$-0.544348\pi$
$353$	−10.8404	−	1.71695i	−0.576975	−	0.0913838i	−0.438100	+	0.898926i	$0.644348\pi$
$354$	9.19742	+	0.0136927i	0.488838	+	0.000727757i
$355$	−21.7394	+	11.4885i	−1.15381	+	0.609747i
$356$	−0.745226	+	1.02572i	−0.0394969	+	0.0543628i
$357$	0.951146	+	0.953982i	0.0503400	+	0.0504901i
$358$	−7.66887	−	3.90749i	−0.405313	−	0.206517i
$359$	21.9405	+	15.9407i	1.15797	+	0.841317i	0.989521	−	0.144392i	$-0.0461228\pi$
$359$	21.9405	+	15.9407i	1.15797	+	0.841317i	0.168453	+	0.985710i	$0.446123\pi$
$360$	6.40418	+	1.99660i	0.337530	+	0.105230i
$361$	5.55511	−	17.0969i	0.292374	−	0.899835i
$362$	1.56400	−	9.87470i	0.0822020	−	0.519003i
$363$	−4.75603	−	30.3205i	−0.249627	−	1.59141i
$364$	−0.857208	+	0.278524i	−0.0449299	+	0.0145986i
$365$	−1.35095	−	1.80225i	−0.0707121	−	0.0943341i
$366$	1.34840	−	0.976607i	0.0704820	−	0.0510480i
$367$	−21.5816	−	21.5816i	−1.12655	−	1.12655i	−0.990734	−	0.135819i	$-0.956633\pi$
$367$	−21.5816	−	21.5816i	−1.12655	−	1.12655i	−0.135819	−	0.990734i	$-0.543367\pi$
$368$	−3.45782	+	1.76185i	−0.180251	+	0.0918426i
$369$	−22.2603	+	16.0720i	−1.15883	+	0.836675i
$370$	8.66064	−	8.92303i	0.450245	−	0.463886i
$371$		−	1.51309i		−	0.0785560i
$372$	−5.86211	+	7.65739i	−0.303936	+	0.397017i
$373$	1.73443	−	1.73443i	0.0898056	−	0.0898056i	−0.660777	−	0.750582i	$-0.729773\pi$
$373$	1.73443	−	1.73443i	0.0898056	−	0.0898056i	0.750582	+	0.660777i	$0.229773\pi$
$374$	19.1096	−	13.8839i	0.988131	−	0.717919i
$375$	−18.6588	−	5.18174i	−0.963535	−	0.267584i
$376$	−1.67343	+	5.15028i	−0.0863004	+	0.265605i
$377$	37.9806	−	37.9806i	1.95610	−	1.95610i
$378$	−0.815106	−	0.419914i	−0.0419246	−	0.0215980i
$379$	24.4703	+	7.95089i	1.25696	+	0.408410i	0.860409	−	0.509605i	$-0.170208\pi$
$379$	24.4703	+	7.95089i	1.25696	+	0.408410i	0.396547	+	0.918014i	$0.370208\pi$
$380$	1.05687	+	1.99988i	0.0542163	+	0.102592i
$381$	9.28922	−	12.7456i	0.475901	−	0.652975i
$382$	12.8779	+	2.03966i	0.658892	+	0.104358i
$383$	−10.2860	+	5.24098i	−0.525590	+	0.267802i	−0.696590	−	0.717469i	$-0.745300\pi$
$383$	−10.2860	+	5.24098i	−0.525590	+	0.267802i	0.171000	+	0.985271i	$0.445300\pi$
$384$	−1.64648	−	0.537685i	−0.0840216	−	0.0274386i
$385$	2.00109	−	0.683368i	0.101985	−	0.0348276i
$386$	2.79871	−	0.909357i	0.142451	−	0.0462851i
$387$	26.4144	+	4.26428i	1.34272	+	0.216766i
$388$	−0.472714	+	0.0748706i	−0.0239984	+	0.00380098i
$389$	1.66222	+	5.11579i	0.0842779	+	0.259381i	0.984311	−	0.176440i	$-0.0564582\pi$
$389$	1.66222	+	5.11579i	0.0842779	+	0.259381i	−0.900033	+	0.435821i	$0.856458\pi$
$390$	−11.4118	+	16.1591i	−0.577860	+	0.818247i
$391$	−13.8383	+	10.0541i	−0.699833	+	0.508458i
$392$	3.16380	+	6.20930i	0.159796	+	0.313617i
$393$	−16.2725	−	32.0545i	−0.820839	−	1.61693i
$394$	−17.8700	+	5.80631i	−0.900277	+	0.292518i
$395$	−20.6526	+	10.9142i	−1.03915	+	0.549153i
$396$	−9.48862	+	12.9785i	−0.476821	+	0.652196i
$397$	−1.23506	−	1.23506i	−0.0619859	−	0.0619859i	0.675434	−	0.737420i	$-0.263956\pi$
$397$	−1.23506	−	1.23506i	−0.0619859	−	0.0619859i	−0.737420	+	0.675434i	$0.763956\pi$
$398$	16.2289	+	16.2289i	0.813480	+	0.813480i
$399$	−0.0951032	−	0.294187i	−0.00476111	−	0.0147278i
$400$	4.79927	+	1.40251i	0.239963	+	0.0701255i
$401$	5.65080	+	7.77766i	0.282188	+	0.388398i	0.926457	−	0.376401i	$-0.122838\pi$
$401$	5.65080	+	7.77766i	0.282188	+	0.388398i	−0.644269	+	0.764799i	$0.722838\pi$
$402$	−13.1973	−	2.11038i	−0.658219	−	0.105256i
$403$	−16.1691	−	23.3953i	−0.805442	−	1.16540i
$404$	16.7310			0.832400
$405$	−19.8478	+	3.32627i	−0.986246	+	0.165284i
$406$	1.50122	+	1.09070i	0.0745044	+	0.0541306i
$407$	13.5299	+	26.5539i	0.670651	+	1.31623i
$408$	−7.53844	−	1.20548i	−0.373208	−	0.0596801i
$409$			11.5349i			0.570366i	0.958473	+	0.285183i	$0.0920544\pi$
$409$			11.5349i			0.570366i	−0.958473	+	0.285183i	$0.907946\pi$
$410$	−16.3748	+	12.2744i	−0.808693	+	0.606190i
$411$	−20.5234	−	14.9578i	−1.01234	−	0.737816i
$412$	−3.52229	+	6.91289i	−0.173531	+	0.340573i
$413$	−0.925489	−	0.146583i	−0.0455403	−	0.00721288i
$414$	6.87125	−	9.39848i	0.337703	−	0.461910i
$415$	−8.18005	+	0.122065i	−0.401543	+	0.00599191i
$416$	3.00229	−	4.13230i	0.147200	−	0.202603i
$417$	12.4464	−	1.95232i	0.609502	−	0.0956057i
$418$	−5.35440	+	0.848053i	−0.261892	+	0.0414796i
$419$	−2.51548	−	1.82761i	−0.122889	−	0.0892844i	0.524643	−	0.851322i	$-0.324199\pi$
$419$	−2.51548	−	1.82761i	−0.122889	−	0.0892844i	−0.647532	+	0.762038i	$0.724199\pi$
$420$	−0.613049	−	0.302061i	−0.0299137	−	0.0147391i
$421$	−18.7063	−	13.5909i	−0.911691	−	0.662382i	0.0297509	−	0.999557i	$-0.490529\pi$
$421$	−18.7063	−	13.5909i	−0.911691	−	0.662382i	−0.941442	+	0.337175i	$0.890529\pi$
$422$	−0.721249	+	4.55378i	−0.0351098	+	0.221675i
$423$	−2.49364	−	16.0534i	−0.121245	−	0.780545i
$424$	5.04010	+	6.93711i	0.244769	+	0.336896i
$425$	21.8599	+	2.79651i	1.06036	+	0.135651i
$426$	−11.2179	+	15.3919i	−0.543509	+	0.745739i
$427$	−0.151132	+	0.0770058i	−0.00731381	+	0.00372657i
$428$	0.154053	+	0.154053i	0.00744642	+	0.00744642i
$429$	−27.8107	−	38.3982i	−1.34271	−	1.85388i
$430$	19.7418	+	2.82553i	0.952036	+	0.136259i
$431$	−19.9872	+	27.5100i	−0.962747	+	1.32511i	−0.0171208	+	0.999853i	$0.505450\pi$
$431$	−19.9872	+	27.5100i	−0.962747	+	1.32511i	−0.945627	+	0.325255i	$0.894550\pi$
$432$	5.13576	−	0.789928i	0.247094	−	0.0380054i
$433$	−19.8329	+	19.8329i	−0.953109	+	0.953109i	−0.998949	−	0.0458400i	$-0.985404\pi$
$433$	−19.8329	+	19.8329i	−0.953109	+	0.953109i	0.0458400	+	0.998949i	$0.485404\pi$
$434$	0.710904	−	0.678155i	0.0341245	−	0.0325525i
$435$	40.7238	−	0.547050i	1.95256	−	0.0262291i
$436$	−2.35730	+	1.71268i	−0.112894	+	0.0820223i
$437$	3.87742	−	0.614123i	0.185482	−	0.0293775i
$438$	−1.55334	−	0.794382i	−0.0742215	−	0.0379570i
$439$		−	12.5519i		−	0.599069i	−0.954085	−	0.299535i	$-0.903169\pi$
$439$		−	12.5519i		−	0.599069i	0.954085	−	0.299535i	$-0.0968314\pi$
$440$	−6.89814	+	9.79866i	−0.328856	+	0.467133i
$441$	−16.8771	−	12.3389i	−0.803672	−	0.587566i
$442$	10.2208	−	20.0595i	0.486154	−	0.954131i
$443$	17.2902	−	33.9339i	0.821481	−	1.61225i	0.0311919	−	0.999513i	$-0.490070\pi$
$443$	17.2902	−	33.9339i	0.821481	−	1.61225i	0.790289	−	0.612734i	$-0.209930\pi$
$444$	2.99010	−	9.15618i	0.141904	−	0.434533i
$445$	0.401664	−	2.80641i	0.0190407	−	0.133037i
$446$	−2.34927	−	3.23349i	−0.111241	−	0.153110i
$447$	17.1276	+	17.1787i	0.810107	+	0.812523i
$448$	0.157227	+	0.0801110i	0.00742826	+	0.00378489i
$449$	−5.00505	−	3.63638i	−0.236203	−	0.171611i	0.463387	−	0.886156i	$-0.346634\pi$
$449$	−5.00505	−	3.63638i	−0.236203	−	0.171611i	−0.699590	+	0.714545i	$0.746634\pi$
$450$	−14.7469	+	2.74363i	−0.695178	+	0.129336i
$451$	−15.1561	−	46.6456i	−0.713672	−	2.19646i
$452$	−10.2906	+	1.62987i	−0.484028	+	0.0766625i
$453$	6.20033	−	3.14761i	0.291317	−	0.147888i
$454$	−18.7576	−	6.09472i	−0.880338	−	0.286039i
$455$	1.40369	−	1.44622i	0.0658061	−	0.0677998i
$456$	1.41595	+	1.03198i	0.0663082	+	0.0483267i
$457$	−8.74178	+	17.1567i	−0.408923	+	0.802557i	−0.999992	−	0.00406442i	$-0.998706\pi$
$457$	−8.74178	+	17.1567i	−0.408923	+	0.802557i	0.591069	+	0.806621i	$0.298706\pi$
$458$	16.3037	−	8.30715i	0.761822	−	0.388167i
$459$	21.8131	−	6.97995i	1.01815	−	0.325796i
$460$	4.99533	−	7.09576i	0.232908	−	0.330841i
$461$	20.0248	+	6.50646i	0.932649	+	0.303036i	0.735646	−	0.677367i	$-0.236879\pi$
$461$	20.0248	+	6.50646i	0.932649	+	0.303036i	0.197004	+	0.980403i	$0.436879\pi$
$462$	1.15991	−	1.15647i	0.0539641	−	0.0538036i
$463$	4.14253	−	26.1549i	0.192520	−	1.21552i	−0.682300	−	0.731073i	$-0.739020\pi$
$463$	4.14253	−	26.1549i	0.192520	−	1.21552i	0.874819	−	0.484449i	$-0.160980\pi$
$464$	−10.5158			−0.488184
$465$	3.58911	−	21.2631i	0.166441	−	0.986051i
$466$	14.3894			0.666574
$467$	−4.00237	+	25.2700i	−0.185208	+	1.16935i	0.703437	+	0.710758i	$0.251648\pi$
$467$	−4.00237	+	25.2700i	−0.185208	+	1.16935i	−0.888644	+	0.458597i	$0.848352\pi$
$468$	−2.44216	+	15.1276i	−0.112889	+	0.699272i
$469$	1.29496	+	0.420759i	0.0597959	+	0.0194289i
$470$	−2.07251	−	11.9303i	−0.0955976	−	0.550306i
$471$	−17.0214	−	23.5015i	−0.784307	−	1.08289i
$472$	4.73137	−	2.41075i	0.217779	−	0.110964i
$473$	−21.6991	+	42.5869i	−0.997725	+	1.95815i
$474$	−10.6571	+	14.6224i	−0.489498	+	0.671631i
$475$	−4.17883	−	2.84955i	−0.191738	−	0.130746i
$476$	0.739700	+	0.240343i	0.0339041	+	0.0110161i
$477$	−22.8856	−	11.7467i	−1.04786	−	0.537846i
$478$	10.3715	−	1.64268i	0.474380	−	0.0751344i
$479$	−11.2529	−	34.6328i	−0.514157	−	1.58241i	−0.784811	−	0.619736i	$-0.787240\pi$
$479$	−11.2529	−	34.6328i	−0.514157	−	1.58241i	0.270653	−	0.962677i	$-0.412760\pi$
$480$	3.81682	−	0.657195i	0.174213	−	0.0299967i
$481$	22.9800	+	16.6959i	1.04780	+	0.761270i
$482$	13.1159	+	6.68287i	0.597412	+	0.304396i
$483$	−0.839959	+	0.837461i	−0.0382194	+	0.0381058i
$484$	−10.4153	−	14.3354i	−0.473423	−	0.651611i
$485$	0.856325	−	0.641894i	0.0388837	−	0.0291469i
$486$	−12.6792	+	9.06854i	−0.575139	+	0.411357i
$487$	−4.72839	+	9.27999i	−0.214264	+	0.420516i	−0.972975	−	0.230911i	$-0.925829\pi$
$487$	−4.72839	+	9.27999i	−0.214264	+	0.420516i	0.758711	+	0.651427i	$0.225829\pi$
$488$	0.436394	−	0.856471i	0.0197546	−	0.0387706i
$489$	10.6360	+	32.9009i	0.480977	+	1.48783i
$490$	−12.7420	−	8.97025i	−0.575627	−	0.405235i
$491$		−	1.95041i		−	0.0880208i	−0.999031	−	0.0440104i	$-0.985987\pi$
$491$		−	1.95041i		−	0.0880208i	0.999031	−	0.0440104i	$-0.0140135\pi$
$492$	−7.21755	+	14.1133i	−0.325392	+	0.636275i
$493$	−45.7789	+	7.25067i	−2.06178	+	0.326554i
$494$	−4.18017	+	3.03707i	−0.188075	+	0.136644i
$495$	5.19930	−	35.5717i	0.233691	−	1.59883i
$496$	−1.00036	+	5.47716i	−0.0449176	+	0.245932i
$497$	1.37206	−	1.37206i	0.0615455	−	0.0615455i
$498$	−5.65054	+	2.86850i	−0.253207	+	0.128541i
$499$	−17.0850	+	23.5155i	−0.764829	+	1.05270i	0.231968	+	0.972724i	$0.425484\pi$
$499$	−17.0850	+	23.5155i	−0.764829	+	1.05270i	−0.996797	+	0.0799738i	$0.974516\pi$
$500$	−10.9534	+	2.24138i	−0.489849	+	0.100238i
$501$	−15.3330	+	11.1052i	−0.685026	+	0.496144i
$502$	−13.4965	−	13.4965i	−0.602380	−	0.602380i
$503$	−21.6946	+	11.0539i	−0.967313	+	0.492871i	−0.864940	−	0.501875i	$-0.832644\pi$
$503$	−21.6946	+	11.0539i	−0.967313	+	0.492871i	−0.102373	+	0.994746i	$0.532644\pi$
$504$	−0.529377	−	0.00157622i	−0.0235803	−	7.02105e-5i
$505$	−33.0770	+	17.4800i	−1.47191	+	0.777852i
$506$	12.2244	+	16.8255i	0.543443	+	0.747985i
$507$	−20.1856	−	10.3229i	−0.896473	−	0.458458i
$508$	1.42444	−	8.99355i	0.0631993	−	0.399024i
$509$	6.71216	+	4.87667i	0.297511	+	0.216155i	0.726519	−	0.687146i	$-0.241137\pi$
$509$	6.71216	+	4.87667i	0.297511	+	0.216155i	−0.429008	+	0.903301i	$0.641137\pi$
$510$	16.1628	−	5.49271i	0.715701	−	0.243221i
$511$	0.143800	+	0.104477i	0.00636133	+	0.00462177i
$512$	−0.987688	+	0.156434i	−0.0436501	+	0.00691349i
$513$	−5.18790	−	0.845452i	−0.229051	−	0.0373276i
$514$	−3.50218	+	4.82034i	−0.154474	+	0.212616i
$515$	−0.258850	−	17.3466i	−0.0114063	−	0.764384i
$516$	14.6988	−	4.75175i	0.647079	−	0.209184i
$517$	28.6638	+	4.53989i	1.26063	+	0.199664i
$518$	−0.445502	+	0.874347i	−0.0195742	+	0.0384166i
$519$	−22.0160	+	30.2078i	−0.966397	+	1.32598i
$520$	−1.61819	+	11.3062i	−0.0709622	+	0.495809i
$521$		−	6.36377i		−	0.278802i	−0.990236	−	0.139401i	$-0.955482\pi$
$521$		−	6.36377i		−	0.278802i	0.990236	−	0.139401i	$-0.0445177\pi$
$522$	28.1514	−	14.2385i	1.23216	−	0.623200i
$523$	17.4486	+	34.2448i	0.762973	+	1.49742i	0.864526	+	0.502589i	$0.167619\pi$
$523$	17.4486	+	34.2448i	0.762973	+	1.49742i	−0.101553	+	0.994830i	$0.532381\pi$
$524$	−16.7910	−	12.1994i	−0.733517	−	0.532931i
$525$	1.52757	−	0.0433236i	0.0666687	−	0.00189080i
$526$	19.5157			0.850926
$527$	−0.578412	+	24.5337i	−0.0251960	+	1.06871i
$528$	−1.46570	+	9.16572i	−0.0637864	+	0.398887i
$529$	4.66665	+	6.42310i	0.202898	+	0.279265i
$530$	−17.2119	−	8.44880i	−0.747635	−	0.366993i
$531$	−9.40200	+	12.8600i	−0.408012	+	0.558078i
$532$	−0.126221	−	0.126221i	−0.00547238	−	0.00547238i
$533$	−33.0549	−	33.0549i	−1.43176	−	1.43176i
$534$	−0.675487	−	2.08952i	−0.0292312	−	0.0904222i
$535$	−0.465509	−	0.143610i	−0.0201257	−	0.00620882i
$536$	−7.33858	+	2.38445i	−0.316979	+	0.102993i
$537$	13.2929	−	6.74818i	0.573633	−	0.291206i
$538$	9.88094	+	19.3924i	0.425997	+	0.836067i
$539$	30.2140	−	21.9518i	1.30141	−	0.945530i
$540$	−9.32801	+	6.92735i	−0.401414	+	0.298106i
$541$	−1.64538	−	5.06396i	−0.0707405	−	0.217717i	0.909436	−	0.415844i	$-0.136514\pi$
$541$	−1.64538	−	5.06396i	−0.0707405	−	0.217717i	−0.980176	+	0.198128i	$0.936514\pi$
$542$	8.08561	−	1.28064i	0.347307	−	0.0550080i
$543$	12.2265	+	12.2630i	0.524689	+	0.526254i
$544$	−4.19189	+	1.36203i	−0.179726	+	0.0583965i
$545$	2.87099	−	5.84876i	0.122980	−	0.250533i
$546$	0.484627	−	1.48401i	0.0207401	−	0.0635097i
$547$	3.58237	−	1.82531i	0.153171	−	0.0780446i	−0.375725	−	0.926731i	$-0.622606\pi$
$547$	3.58237	−	1.82531i	0.153171	−	0.0780446i	0.528896	+	0.848687i	$0.322606\pi$
$548$	−14.4817	−	2.29368i	−0.618630	−	0.0979813i
$549$	−0.00858626	+	2.88371i	−0.000366452	+	0.123074i
$550$	3.40018	−	26.5787i	0.144984	−	1.13332i
$551$	10.1170	+	3.28720i	0.430997	+	0.140039i
$552$	1.06140	−	6.63742i	0.0451760	−	0.282507i
$553$	1.30347	−	1.30347i	0.0554293	−	0.0554293i
$554$	−0.606257	+	1.86587i	−0.0257574	+	0.0792732i
$555$	3.65470	+	21.2256i	0.155133	+	0.900975i
$556$	5.88462	−	4.27542i	0.249563	−	0.181318i
$557$	−22.5094	+	22.5094i	−0.953754	+	0.953754i	−0.998977	−	0.0452233i	$-0.985600\pi$
$557$	−22.5094	+	22.5094i	−0.953754	+	0.953754i	0.0452233	+	0.998977i	$0.485600\pi$
$558$	−4.73808	−	16.0172i	−0.200579	−	0.678062i
$559$			45.5554i			1.92679i
$560$	−0.394532	+	0.00588729i	−0.0166720	+	0.000248783i
$561$	−0.0609081	+	40.9122i	−0.00257154	+	1.72731i
$562$	−20.2580	+	10.3220i	−0.854531	+	0.435405i
$563$	3.19650	+	3.19650i	0.134716	+	0.134716i	0.771249	−	0.636533i	$-0.219632\pi$
$563$	3.19650	+	3.19650i	0.134716	+	0.134716i	−0.636533	+	0.771249i	$0.719632\pi$
$564$	−5.50189	−	7.59646i	−0.231672	−	0.319869i
$565$	18.6415	−	13.9735i	0.784252	−	0.587869i
$566$	−1.63614	+	0.531615i	−0.0687722	+	0.0223455i
$567$	1.41931	−	0.712560i	0.0596054	−	0.0299247i
$568$	−1.72019	+	10.8609i	−0.0721776	+	0.455711i
$569$	2.39055	−	7.35736i	0.100217	−	0.308437i	−0.888361	−	0.459146i	$-0.848156\pi$
$569$	2.39055	−	7.35736i	0.100217	−	0.308437i	0.988578	+	0.150709i	$0.0481556\pi$
$570$	−3.87749	−	0.560854i	−0.162410	−	0.0234916i
$571$	−0.530103	−	0.385142i	−0.0221841	−	0.0161177i	0.576638	−	0.817000i	$-0.304364\pi$
$571$	−0.530103	−	0.385142i	−0.0221841	−	0.0161177i	−0.598822	+	0.800882i	$0.704364\pi$
$572$	−24.3896	−	12.4271i	−1.01978	−	0.519604i
$573$	−15.9925	+	15.9450i	−0.668097	+	0.666111i
$574$	0.949248	−	1.30653i	0.0396208	−	0.0545334i
$575$	−2.46226	+	19.2471i	−0.102683	+	0.802662i
$576$	2.43229	−	1.75612i	0.101345	−	0.0731717i
$577$	5.40133	+	0.855487i	0.224860	+	0.0356144i	0.267848	−	0.963461i	$-0.413688\pi$
$577$	5.40133	+	0.855487i	0.224860	+	0.0356144i	−0.0429875	+	0.999076i	$0.513688\pi$
$578$	−2.16254	+	1.10187i	−0.0899499	+	0.0458318i
$579$	−1.58227	+	4.84516i	−0.0657568	+	0.201358i
$580$	20.7895	−	10.9866i	0.863239	−	0.456192i
$581$	0.614004	−	0.199502i	0.0254732	−	0.00827674i
$582$	0.377444	−	0.738057i	0.0156456	−	0.0305935i
$583$	32.4934	−	32.4934i	1.34574	−	1.34574i
$584$	−1.00729			−0.0416820
$585$	−10.9767	−	32.4584i	−0.453829	−	1.34199i
$586$	−24.0765	−	17.4926i	−0.994590	−	0.722612i
$587$	−5.20394	+	32.8564i	−0.214790	+	1.35613i	0.610768	+	0.791810i	$0.290861\pi$
$587$	−5.20394	+	32.8564i	−0.214790	+	1.35613i	−0.825557	+	0.564318i	$0.809139\pi$
$588$	−11.9190	−	1.90598i	−0.491531	−	0.0786012i
$589$	2.67456	−	4.95672i	0.110203	−	0.204238i
$590$	−6.83516	+	9.70920i	−0.281399	+	0.399721i
$591$	10.1029	−	30.9367i	0.415578	−	1.27257i
$592$	−0.869942	−	5.49260i	−0.0357544	−	0.225744i
$593$	−27.2871	+	13.9035i	−1.12055	+	0.570947i	−0.913278	−	0.407337i	$-0.866457\pi$
$593$	−27.2871	+	13.9035i	−1.12055	+	0.570947i	−0.207268	+	0.978284i	$0.566457\pi$
$594$	−8.48668	−	26.5218i	−0.348213	−	1.08820i
$595$	−1.71348	+	0.297660i	−0.0702457	+	0.0122029i
$596$	13.3200	+	4.32793i	0.545609	+	0.177279i
$597$	−39.2722	+	6.16019i	−1.60731	+	0.252120i
$598$	17.6619	+	8.99917i	0.722248	+	0.368004i
$599$	−13.4722	+	9.78815i	−0.550461	+	0.399933i	−0.827955	−	0.560794i	$-0.810496\pi$
$599$	−13.4722	+	9.78815i	−0.550461	+	0.399933i	0.277495	+	0.960727i	$0.410496\pi$
$600$	−6.85917	+	5.28695i	−0.280024	+	0.215839i
$601$	−19.0985	+	13.8759i	−0.779045	+	0.566009i	−0.904692	−	0.426066i	$-0.859899\pi$
$601$	−19.0985	+	13.8759i	−0.779045	+	0.566009i	0.125648	+	0.992075i	$0.459899\pi$
$602$	−1.55443	+	0.246197i	−0.0633538	+	0.0100343i
$603$	16.4173	−	16.3198i	0.668564	−	0.664594i
$604$	2.35974	−	3.24790i	0.0960163	−	0.132155i
$605$	35.5681	+	17.4593i	1.44605	+	0.709823i
$606$	−17.0683	+	23.4191i	−0.693353	+	0.951337i
$607$	1.23359	+	7.78858i	0.0500699	+	0.316129i	0.999993	+	0.00364616i	$0.00116061\pi$
$607$	1.23359	+	7.78858i	0.0500699	+	0.316129i	−0.949923	+	0.312483i	$0.898839\pi$
$608$	0.999129	+	0.158246i	0.0405200	+	0.00641774i
$609$	−3.05819	+	0.988634i	−0.123924	+	0.0400615i
$610$	0.0320702	+	2.14916i	0.00129848	+	0.0870168i
$611$	26.3066	−	8.54754i	1.06425	−	0.345796i
$612$	9.37776	−	9.32208i	0.379074	−	0.376823i
$613$	17.9103	+	35.1510i	0.723392	+	1.41974i	0.900194	+	0.435490i	$0.143425\pi$
$613$	17.9103	+	35.1510i	0.723392	+	1.41974i	−0.176802	+	0.984246i	$0.556575\pi$
$614$	2.70682			0.109239
$615$	−0.476103	−	35.4423i	−0.0191983	−	1.42917i
$616$	0.292225	−	0.899375i	0.0117741	−	0.0362368i
$617$	3.64537	−	0.577369i	0.146757	−	0.0232440i	−0.0826237	−	0.996581i	$-0.526330\pi$
$617$	3.64537	−	0.577369i	0.146757	−	0.0232440i	0.229381	+	0.973337i	$0.426330\pi$
$618$	−6.08296	−	11.9825i	−0.244692	−	0.482008i
$619$			7.99396i			0.321304i	0.987011	+	0.160652i	$0.0513597\pi$
$619$			7.99396i			0.321304i	−0.987011	+	0.160652i	$0.948640\pi$
$620$	−3.74466	−	11.8734i	−0.150389	−	0.476847i
$621$	6.14568	+	19.2059i	0.246618	+	0.770707i
$622$	−26.5216	−	4.20061i	−1.06342	−	0.168429i
$623$	0.0349983	+	0.220971i	0.00140218	+	0.00885300i
$624$	2.72134	+	8.41804i	0.108941	+	0.336991i
$625$	19.3129	−	15.8749i	0.772516	−	0.634996i
$626$			5.90486i			0.236006i
$627$	4.27528	−	8.35992i	0.170738	−	0.333863i
$628$	−14.9276	−	7.60598i	−0.595675	−	0.303512i
$629$	−7.57432	−	23.3114i	−0.302008	−	0.929485i
$630$	1.04821	−	0.549959i	0.0417619	−	0.0219109i
$631$	−6.38183	+	19.6412i	−0.254057	+	0.781906i	0.739958	+	0.672654i	$0.234846\pi$
$631$	−6.38183	+	19.6412i	−0.254057	+	0.781906i	−0.994014	+	0.109252i	$0.965154\pi$
$632$	−1.63420	+	10.3179i	−0.0650049	+	0.410425i
$633$	−5.63833	−	5.65515i	−0.224104	−	0.224772i
$634$	11.5535	−	3.75394i	0.458846	−	0.149088i
$635$	6.58008	+	19.2683i	0.261123	+	0.764639i
$636$	−14.8519	−	0.0221107i	−0.588915	−	0.000876747i
$637$	16.1601	−	31.7159i	0.640285	−	1.25663i
$638$	8.81584	+	55.6610i	0.349022	+	2.20364i
$639$	−10.1006	−	31.4043i	−0.399574	−	1.24234i
$640$	1.78921	−	1.34117i	0.0707245	−	0.0530145i
$641$	−3.64619	−	5.01855i	−0.144016	−	0.198221i	0.730915	−	0.682468i	$-0.239093\pi$
$641$	−3.64619	−	5.01855i	−0.144016	−	0.198221i	−0.874931	+	0.484247i	$0.839093\pi$
$642$	−0.372792	+	0.0584757i	−0.0147129	+	0.00230785i
$643$	5.78576	+	2.94799i	0.228168	+	0.116257i	0.564338	−	0.825544i	$-0.309132\pi$
$643$	5.78576	+	2.94799i	0.228168	+	0.116257i	−0.336170	+	0.941801i	$0.609132\pi$
$644$	−0.211616	+	0.651288i	−0.00833885	+	0.0256643i
$645$	−24.0948	+	24.7510i	−0.948732	+	0.974568i
$646$	4.45867			0.175424
$647$	−11.5936	−	22.7537i	−0.455791	−	0.894540i	−0.998507	−	0.0546241i	$-0.982604\pi$
$647$	−11.5936	−	22.7537i	−0.455791	−	0.894540i	0.542716	−	0.839916i	$-0.317396\pi$
$648$	−4.13360	+	7.99459i	−0.162383	+	0.314057i
$649$	−16.7268	−	23.0225i	−0.656586	−	0.903713i
$650$	−8.61322	−	24.0428i	−0.337838	−	0.943035i
$651$	0.224007	+	1.68691i	0.00877952	+	0.0661151i
$652$	14.1161	+	14.1161i	0.552831	+	0.552831i
$653$	39.7906	+	6.30221i	1.55713	+	0.246625i	0.874823	−	0.484444i	$-0.160978\pi$
$653$	39.7906	+	6.30221i	1.55713	+	0.246625i	0.682304	+	0.731068i	$0.260978\pi$
$654$	0.00751344	−	5.04681i	0.000293799	−	0.197346i
$655$	45.9410	+	6.57525i	1.79506	+	0.256916i
$656$			9.15199i			0.357325i
$657$	2.69658	−	1.36388i	0.105204	−	0.0532100i
$658$	0.433827	+	0.851433i	0.0169123	+	0.0331923i
$659$	6.30382	+	19.4012i	0.245562	+	0.755762i	0.995544	+	0.0943032i	$0.0300623\pi$
$659$	6.30382	+	19.4012i	0.245562	+	0.755762i	−0.749982	+	0.661459i	$0.769938\pi$
$660$	−6.67839	−	19.6518i	−0.259956	−	0.764945i
$661$	−14.6447	+	10.6400i	−0.569613	+	0.413848i	−0.834965	−	0.550304i	$-0.814512\pi$
$661$	−14.6447	+	10.6400i	−0.569613	+	0.413848i	0.265352	+	0.964152i	$0.414512\pi$
$662$	−4.56734	−	8.96390i	−0.177515	−	0.348392i
$663$	17.6512	+	34.7703i	0.685516	+	1.35037i
$664$	−2.15049	+	2.95990i	−0.0834553	+	0.114866i
$665$	0.381409	+	0.117665i	0.0147904	+	0.00456286i
$666$	9.76590	+	13.5261i	0.378421	+	0.524126i
$667$	−6.38404	−	40.3073i	−0.247191	−	1.56070i
$668$	−4.96233	+	9.73912i	−0.191998	+	0.376818i
$669$	6.92267	+	0.0103061i	0.267646	+	0.000398458i
$670$	12.0171	−	12.3811i	0.464259	−	0.478325i
$671$	−4.89922	−	1.59185i	−0.189132	−	0.0614528i
$672$	−0.272531	+	0.138351i	−0.0105131	+	0.00533700i
$673$	15.5342	+	7.91509i	0.598801	+	0.305104i	0.726993	−	0.686645i	$-0.240917\pi$
$673$	15.5342	+	7.91509i	0.598801	+	0.305104i	−0.128192	+	0.991749i	$0.540917\pi$
$674$	2.14208	+	6.59266i	0.0825100	+	0.253940i
$675$	11.2039	−	23.4409i	0.431237	−	0.902239i
$676$	−13.0897			−0.503450
$677$	−21.8524	+	21.8524i	−0.839858	+	0.839858i	−0.988840	−	0.148982i	$-0.952400\pi$
$677$	−21.8524	+	21.8524i	−0.839858	+	0.839858i	0.148982	+	0.988840i	$0.452400\pi$
$678$	8.21663	−	16.0669i	0.315558	−	0.617045i
$679$	−0.0496413	+	0.0683253i	−0.00190506	+	0.00262209i
$680$	6.86429	−	7.07226i	0.263234	−	0.271209i
$681$	27.6668	−	20.0382i	1.06019	−	0.767866i
$682$	29.8297	+	0.703271i	1.14224	+	0.0269296i
$683$	13.0673	+	13.0673i	0.500006	+	0.500006i	0.911440	−	0.411434i	$-0.134972\pi$
$683$	13.0673	+	13.0673i	0.500006	+	0.500006i	−0.411434	+	0.911440i	$0.634972\pi$
$684$	−2.88900	+	0.929191i	−0.110464	+	0.0355285i
$685$	31.0265	−	10.5955i	1.18546	−	0.404833i
$686$	2.34430	+	0.761708i	0.0895057	+	0.0290822i
$687$	−5.00450	+	31.2956i	−0.190934	+	1.19400i
$688$	6.30653	−	6.30653i	0.240434	−	0.240434i
$689$	13.5344	−	41.6545i	0.515618	−	1.58691i
$690$	4.83620	+	14.2310i	0.184111	+	0.541764i
$691$	−1.41970	−	4.36937i	−0.0540078	−	0.166219i	0.920414	−	0.390944i	$-0.127851\pi$
$691$	−1.41970	−	4.36937i	−0.0540078	−	0.166219i	−0.974422	+	0.224725i	$0.927851\pi$
$692$	−3.37601	+	21.3153i	−0.128337	+	0.810286i
$693$	0.435456	+	2.80336i	0.0165416	+	0.106491i
$694$	5.57199	+	7.66919i	0.211510	+	0.291118i
$695$	−7.16696	+	14.6005i	−0.271858	+	0.553828i
$696$	10.7278	−	14.7194i	0.406636	−	0.557937i
$697$	6.31033	+	39.8418i	0.239021	+	1.50912i
$698$	1.89998	+	11.9960i	0.0719154	+	0.454056i
$699$	−14.6794	+	20.1414i	−0.555227	+	0.761817i
$700$	0.773832	−	0.423833i	0.0292481	−	0.0160194i
$701$	−7.91712	−	10.8970i	−0.299025	−	0.411573i	0.632894	−	0.774238i	$-0.281867\pi$
$701$	−7.91712	−	10.8970i	−0.299025	−	0.411573i	−0.931920	+	0.362665i	$0.881867\pi$
$702$	−18.6833	−	18.8509i	−0.705155	−	0.711482i
$703$	−0.880019	+	5.55622i	−0.0331905	+	0.209557i
$704$	1.65604	+	5.09677i	0.0624144	+	0.192092i
$705$	18.8137	+	9.26988i	0.708565	+	0.349124i
$706$	3.39161	−	10.4383i	0.127645	−	0.392851i
$707$	2.08763	−	2.08763i	0.0785134	−	0.0785134i
$708$	−1.45232	+	9.08205i	−0.0545815	+	0.341324i
$709$	22.0346	+	7.15947i	0.827526	+	0.268880i	0.692003	−	0.721895i	$-0.256728\pi$
$709$	22.0346	+	7.15947i	0.827526	+	0.268880i	0.135523	+	0.990774i	$0.456728\pi$
$710$	−7.94628	−	23.2689i	−0.298219	−	0.873267i
$711$	−9.59567	−	29.8344i	−0.359866	−	1.11888i
$712$	−0.896508	−	0.896508i	−0.0335981	−	0.0335981i
$713$	−21.6014	−	0.509278i	−0.808978	−	0.0190726i
$714$	−1.09103	+	0.790200i	−0.0408307	+	0.0295725i
$715$	61.2012	−	0.913259i	2.28880	−	0.0341539i
$716$	5.05906	−	6.96319i	0.189066	−	0.260227i
$717$	−8.28122	+	16.1932i	−0.309268	+	0.604745i
$718$	−19.1767	+	19.1767i	−0.715667	+	0.715667i
$719$	4.10354			0.153036			0.0765180	−	0.997068i	$-0.475620\pi$
$719$	4.10354			0.153036			0.0765180	+	0.997068i	$0.475620\pi$
$720$	−2.97386	+	6.01300i	−0.110829	+	0.224091i
$721$	0.423064	+	1.30206i	0.0157557	+	0.0484912i
$722$	16.0174	+	8.16125i	0.596104	+	0.303730i
$723$	−22.7346	+	11.5412i	−0.845508	+	0.429223i
$724$	9.50847	+	3.08949i	0.353379	+	0.114820i
$725$	−29.6222	+	43.4405i	−1.10014	+	1.61334i
$726$	30.6912	+	0.0456915i	1.13906	+	0.00169577i
$727$	−3.81183	+	7.48113i	−0.141373	+	0.277460i	−0.950827	−	0.309724i	$-0.899763\pi$
$727$	−3.81183	+	7.48113i	−0.141373	+	0.277460i	0.809454	+	0.587184i	$0.199763\pi$
$728$	−0.140998	−	0.890225i	−0.00522573	−	0.0329939i
$729$	0.241174	−	26.9989i	0.00893238	−	0.999960i
$730$	1.99140	−	1.05239i	0.0737049	−	0.0389505i
$731$	23.1062	−	31.8029i	0.854613	−	1.17627i
$732$	0.753647	+	1.48457i	0.0278556	+	0.0548714i
$733$	−8.72603	−	17.1258i	−0.322303	−	0.632556i	0.671831	−	0.740704i	$-0.265508\pi$
$733$	−8.72603	−	17.1258i	−0.322303	−	0.632556i	−0.994135	+	0.108148i	$0.965508\pi$
$734$	24.6921	−	17.9398i	0.911400	−	0.662171i
$735$	25.5549	−	8.68449i	0.942608	−	0.320332i
$736$	−1.19923	−	3.69086i	−0.0442043	−	0.136047i
$737$	18.7733	+	36.8448i	0.691525	+	1.35719i
$738$	−12.3919	−	24.5005i	−0.456151	−	0.901874i
$739$			29.6102i			1.08923i	0.838687	+	0.544614i	$0.183324\pi$
$739$			29.6102i			1.08923i	−0.838687	+	0.544614i	$0.816676\pi$
$740$	7.45835	+	9.94988i	0.274174	+	0.365765i
$741$	0.0133235	−	8.94945i	0.000489451	−	0.328766i
$742$	1.49447	+	0.236700i	0.0548636	+	0.00868953i
$743$	−2.02574	−	2.02574i	−0.0743171	−	0.0743171i	0.668971	−	0.743288i	$-0.266735\pi$
$743$	−2.02574	−	2.02574i	−0.0743171	−	0.0743171i	−0.743288	+	0.668971i	$0.766735\pi$
$744$	−6.64608	−	6.98782i	−0.243657	−	0.256186i
$745$	−30.8551	+	5.36006i	−1.13044	+	0.196378i
$746$	1.44175	+	1.98440i	0.0527864	+	0.0726542i
$747$	1.74928	−	10.8356i	0.0640029	−	0.396455i
$748$	10.7236	+	21.0462i	0.392093	+	0.769525i
$749$	0.0384441			0.00140472
$750$	8.03682	−	17.6184i	0.293463	−	0.643335i
$751$	−15.3385	+	47.2070i	−0.559710	+	1.72261i	0.123460	+	0.992350i	$0.460601\pi$
$751$	−15.3385	+	47.2070i	−0.559710	+	1.72261i	−0.683169	+	0.730260i	$0.739399\pi$
$752$	−4.82509	−	2.45850i	−0.175953	−	0.0896524i
$753$	32.6603	−	5.12305i	1.19021	−	0.186694i
$754$	31.5715	+	43.4545i	1.14977	+	1.58252i
$755$	−1.27186	+	8.88641i	−0.0462877	+	0.323410i
$756$	0.542254	−	0.739382i	0.0197216	−	0.0268911i
$757$	−0.00999264	−	0.0630911i	−0.000363189	−	0.00229308i	0.987506	−	0.157581i	$-0.0503695\pi$
$757$	−0.00999264	−	0.0630911i	−0.000363189	−	0.00229308i	−0.987869	+	0.155288i	$0.950370\pi$
$758$	−11.6810	+	22.9253i	−0.424273	+	0.832683i
$759$	−36.0222	−	0.0536281i	−1.30752	−	0.00194658i
$760$	−2.14059	+	0.731007i	−0.0776474	+	0.0265164i
$761$	35.9601	−	11.6841i	1.30355	−	0.423550i	0.426737	−	0.904376i	$-0.359663\pi$
$761$	35.9601	−	11.6841i	1.30355	−	0.423550i	0.876816	+	0.480826i	$0.159663\pi$
$762$	11.1355	+	11.1687i	0.403396	+	0.404599i
$763$	−0.0804330	+	0.507834i	−0.00291187	+	0.0183848i
$764$	−4.02910	+	12.4003i	−0.145768	+	0.448627i
$765$	−8.80026	+	28.2272i	−0.318174	+	1.02056i
$766$	−3.56737	−	10.9792i	−0.128894	−	0.396696i
$767$	−24.1669	−	12.3137i	−0.872617	−	0.444621i
$768$	0.788631	−	1.54210i	0.0284573	−	0.0556456i
$769$		−	12.3985i		−	0.447102i	−0.974692	−	0.223551i	$-0.928235\pi$
$769$		−	12.3985i		−	0.447102i	0.974692	−	0.223551i	$-0.0717650\pi$
$770$	0.361915	+	2.08336i	0.0130425	+	0.0750789i
$771$	−3.17444	−	9.81965i	−0.114325	−	0.353646i
$772$	0.460346	+	2.90651i	0.0165682	+	0.104608i
$773$	−11.7059	−	1.85404i	−0.421034	−	0.0666852i	−0.0576770	−	0.998335i	$-0.518369\pi$
$773$	−11.7059	−	1.85404i	−0.421034	−	0.0666852i	−0.363357	+	0.931650i	$0.618369\pi$
$774$	−8.34390	+	25.4221i	−0.299915	+	0.913777i
$775$	19.8081	+	19.5612i	0.711527	+	0.702659i
$776$		−	0.478607i		−	0.0171810i
$777$	−0.769377	−	1.51556i	−0.0276012	−	0.0543705i
$778$	−5.31283	+	0.841470i	−0.190474	+	0.0301682i
$779$	2.86088	−	8.80488i	0.102502	−	0.315468i
$780$	−14.1749	−	13.7992i	−0.507544	−	0.494089i
$781$	58.9295			2.10867
$782$	−7.76554	−	15.2407i	−0.277695	−	0.545008i
$783$	−8.78879	+	53.9302i	−0.314086	+	1.92731i
$784$	−6.62778	+	2.15350i	−0.236706	+	0.0769106i
$785$	37.4580	−	0.558957i	1.33694	−	0.0199500i
$786$	34.2054	−	11.0577i	1.22007	−	0.394416i
$787$	−10.7214	−	1.69810i	−0.382176	−	0.0605308i	−0.0376094	−	0.999293i	$-0.511974\pi$
$787$	−10.7214	−	1.69810i	−0.382176	−	0.0605308i	−0.344567	+	0.938762i	$0.611974\pi$
$788$	−2.93935	−	18.5583i	−0.104710	−	0.661112i
$789$	−19.9091	+	27.3170i	−0.708784	+	0.972509i
$790$	−7.54904	−	22.1057i	−0.268583	−	0.786485i
$791$	−1.08065	+	1.48738i	−0.0384234	+	0.0528853i
$792$	−11.3344	−	11.4021i	−0.402750	−	0.405156i
$793$	−4.84938	+	0.768066i	−0.172206	+	0.0272748i
$794$	1.41306	−	1.02665i	0.0501476	−	0.0364344i
$795$	29.3850	−	15.4730i	1.04218	−	0.548772i
$796$	−18.5678	+	13.4903i	−0.658119	+	0.478151i
$797$	−21.6476	−	11.0300i	−0.766797	−	0.390703i	0.0264126	−	0.999651i	$-0.491592\pi$
$797$	−21.6476	−	11.0300i	−0.766797	−	0.390703i	−0.793210	+	0.608948i	$0.791592\pi$
$798$	0.305442	−	0.0479113i	0.0108125	−	0.00169604i
$799$	−22.7004	−	7.37582i	−0.803084	−	0.260938i
$800$	−2.13601	+	4.52078i	−0.0755195	+	0.159834i
$801$	3.61389	+	1.18613i	0.127690	+	0.0419099i
$802$	−8.56589	+	4.36454i	−0.302472	+	0.154117i
$803$	0.844455	+	5.33168i	0.0298002	+	0.188151i
$804$	4.14891	−	12.7046i	0.146321	−	0.448058i
$805$	−0.262083	−	1.50867i	−0.00923721	−	0.0531738i
$806$	25.6367	−	12.3102i	0.903013	−	0.433610i
$807$	−37.2245	−	5.95261i	−1.31036	−	0.209542i
$808$	−2.61731	+	16.5251i	−0.0920767	+	0.581349i
$809$	−32.0026	−	23.2512i	−1.12515	−	0.817469i	−0.140168	−	0.990128i	$-0.544764\pi$
$809$	−32.0026	−	23.2512i	−1.12515	−	0.817469i	−0.984982	+	0.172658i	$0.944764\pi$
$810$	−0.180437	−	20.1238i	−0.00633992	−	0.707078i
$811$	−33.8207			−1.18760			−0.593802	−	0.804611i	$-0.702374\pi$
$811$	−33.8207			−1.18760			−0.593802	+	0.804611i	$0.702374\pi$
$812$	−1.31212	+	1.31212i	−0.0460463	+	0.0460463i
$813$	−6.45605	+	12.6242i	−0.226424	+	0.442751i
$814$	−28.3435	+	9.20935i	−0.993438	+	0.322788i
$815$	−42.6555	−	13.1593i	−1.49416	−	0.460950i
$816$	2.36991	−	7.25705i	0.0829634	−	0.254048i
$817$	−8.03874	+	4.09594i	−0.281240	+	0.143299i
$818$	−11.3929	−	1.80446i	−0.398344	−	0.0630916i
$819$	1.58283	+	2.19228i	0.0553086	+	0.0766043i
$820$	−9.56171	−	18.0933i	−0.333909	−	0.631847i
$821$	−12.3551	+	17.0054i	−0.431197	+	0.593492i	−0.968228	−	0.250071i	$-0.919546\pi$
$821$	−12.3551	+	17.0054i	−0.431197	+	0.593492i	0.537030	+	0.843563i	$0.319546\pi$
$822$	17.9842	−	17.9308i	0.627273	−	0.625408i
$823$	0.845421	+	0.430763i	0.0294695	+	0.0150155i	0.468663	−	0.883377i	$-0.344736\pi$
$823$	0.845421	+	0.430763i	0.0294695	+	0.0150155i	−0.439194	+	0.898392i	$0.644736\pi$
$824$	−6.27677	−	4.56034i	−0.218662	−	0.158867i
$825$	33.7346	+	31.8739i	1.17449	+	1.10971i
$826$	0.289557	−	0.891164i	0.0100750	−	0.0310076i
$827$	−0.461539	+	2.91404i	−0.0160493	+	0.101331i	−0.994413	−	0.105563i	$-0.966336\pi$
$827$	−0.461539	+	2.91404i	−0.0160493	+	0.101331i	0.978363	+	0.206894i	$0.0663356\pi$
$828$	8.20787	+	8.25690i	0.285243	+	0.286947i
$829$	21.9316	−	7.12601i	0.761716	−	0.247497i	0.0977012	−	0.995216i	$-0.468851\pi$
$829$	21.9316	−	7.12601i	0.761716	−	0.247497i	0.664015	+	0.747719i	$0.268851\pi$
$830$	1.15908	−	8.09844i	0.0402323	−	0.281101i
$831$	−1.99325	−	2.75209i	−0.0691452	−	0.0954688i
$832$	3.61177	+	3.61177i	0.125215	+	0.125215i
$833$	−27.3682	+	13.9448i	−0.948253	+	0.483159i
$834$	−0.0187561	+	12.5986i	−0.000649471	+	0.436252i
$835$	−0.364677	−	24.4385i	−0.0126202	−	0.845731i
$836$		−	5.42114i		−	0.187494i
$837$	27.2535	+	9.70801i	0.942020	+	0.335558i
$838$	2.19861	−	2.19861i	0.0759498	−	0.0759498i
$839$	32.1401	−	23.3511i	1.10960	−	0.806171i	0.126999	−	0.991903i	$-0.459466\pi$
$839$	32.1401	−	23.3511i	1.10960	−	0.806171i	0.982600	+	0.185732i	$0.0594656\pi$
$840$	0.394244	−	0.558248i	0.0136027	−	0.0192614i
$841$	25.2102	−	77.5890i	0.869318	−	2.67548i
$842$	16.3499	−	16.3499i	0.563456	−	0.563456i
$843$	6.21829	−	38.8860i	0.214169	−	1.33930i
$844$	−4.38489	−	1.42474i	−0.150934	−	0.0490415i
$845$	25.8781	−	13.6757i	0.890234	−	0.470458i
$846$	16.2459	+	0.0483723i	0.558545	+	0.00166307i
$847$	−3.08830	−	0.489138i	−0.106115	−	0.0168070i
$848$	−7.64014	+	3.89285i	−0.262364	+	0.133681i
$849$	0.925002	−	2.83251i	0.0317460	−	0.0972115i
$850$	−6.18172	+	21.1533i	−0.212031	+	0.725553i
$851$	20.5251	−	6.66901i	0.703592	−	0.228611i
$852$	−13.4475	−	13.4876i	−0.460704	−	0.462078i
$853$	−20.5083	+	3.24819i	−0.702190	+	0.111216i	−0.497312	−	0.867572i	$-0.665680\pi$
$853$	−20.5083	+	3.24819i	−0.702190	+	0.111216i	−0.204878	+	0.978788i	$0.565680\pi$
$854$	−0.0524154	−	0.161318i	−0.00179362	−	0.00552019i
$855$	4.74071	−	4.85533i	0.162129	−	0.166049i
$856$	−0.176255	+	0.128057i	−0.00602428	+	0.00437690i
$857$	−25.0916	−	49.2449i	−0.857111	−	1.68218i	−0.722603	−	0.691263i	$-0.757055\pi$
$857$	−25.0916	−	49.2449i	−0.857111	−	1.68218i	−0.134508	−	0.990913i	$-0.542945\pi$
$858$	42.2760	−	21.4615i	1.44328	−	0.732683i
$859$	30.8436	−	10.0217i	1.05237	−	0.341935i	0.268771	−	0.963204i	$-0.413382\pi$
$859$	30.8436	−	10.0217i	1.05237	−	0.341935i	0.783598	+	0.621269i	$0.213382\pi$
$860$	−5.87904	+	19.0568i	−0.200474	+	0.649830i
$861$	0.860417	+	2.66157i	0.0293229	+	0.0907060i
$862$	−24.0446	−	24.0446i	−0.818962	−	0.818962i
$863$	−17.3743	−	17.3743i	−0.591427	−	0.591427i	0.346590	−	0.938017i	$-0.387340\pi$
$863$	−17.3743	−	17.3743i	−0.591427	−	0.591427i	−0.938017	+	0.346590i	$0.887340\pi$
$864$	−0.0232072	+	5.19610i	−0.000789526	+	0.176775i
$865$	−15.5952	−	45.6671i	−0.530253	−	1.55273i
$866$	−16.4862	−	22.6913i	−0.560223	−	0.771081i
$867$	0.663804	−	4.15108i	0.0225440	−	0.140978i
$868$	0.558596	+	0.808238i	0.0189600	+	0.0274334i
$869$	55.9836			1.89911
$870$	−5.83029	+	40.3080i	−0.197666	+	1.36657i
$871$	31.8859	+	23.1664i	1.08041	+	0.784965i
$872$	−1.32283	−	2.59620i	−0.0447966	−	0.0879183i
$873$	0.648037	+	1.28126i	0.0219327	+	0.0433641i
$874$			3.92575i			0.132791i
$875$	−1.08704	+	1.64638i	−0.0367488	+	0.0556580i
$876$	1.02760	−	1.40995i	0.0347193	−	0.0476377i
$877$	11.6738	−	22.9112i	0.394197	−	0.773655i	−0.605558	−	0.795801i	$-0.707050\pi$
$877$	11.6738	−	22.9112i	0.394197	−	0.773655i	0.999755	+	0.0221460i	$0.00704987\pi$
$878$	12.3974	+	1.96355i	0.418391	+	0.0662666i
$879$	49.0469	−	15.8556i	1.65431	−	0.534797i
$880$	−8.59891	−	8.34606i	−0.289869	−	0.281345i
$881$	−0.177421	+	0.244200i	−0.00597748	+	0.00822730i	−0.811995	−	0.583664i	$-0.801619\pi$
$881$	−0.177421	+	0.244200i	−0.00597748	+	0.00822730i	0.806018	+	0.591891i	$0.201619\pi$
$882$	14.8271	−	14.7391i	0.499256	−	0.496292i
$883$	48.3305	−	7.65480i	1.62645	−	0.257605i	0.724447	−	0.689331i	$-0.242095\pi$
$883$	48.3305	−	7.65480i	1.62645	−	0.257605i	0.902005	+	0.431726i	$0.142095\pi$
$884$	18.2136	+	13.2330i	0.612590	+	0.445073i
$885$	−6.61742	−	19.4724i	−0.222442	−	0.654557i
$886$	30.8113	+	22.3857i	1.03513	+	0.752063i
$887$	−3.45723	+	21.8281i	−0.116082	+	0.732915i	0.859149	+	0.511726i	$0.170994\pi$
$887$	−3.45723	+	21.8281i	−0.116082	+	0.732915i	−0.975231	+	0.221189i	$0.929006\pi$
$888$	8.57569	+	4.38563i	0.287781	+	0.147172i
$889$	−0.944442	−	1.29991i	−0.0316756	−	0.0435977i
$890$	2.70902	+	0.835738i	0.0908067	+	0.0280140i
$891$	45.7814	+	15.1773i	1.53373	+	0.508458i
$892$	3.56118	−	1.81451i	0.119237	−	0.0607544i
$893$	3.87356	+	3.87356i	0.129624	+	0.129624i
$894$	−19.6465	+	14.2294i	−0.657078	+	0.475902i
$895$	−2.72675	+	19.0516i	−0.0911451	+	0.636826i
$896$	−0.103720	+	0.142759i	−0.00346505	+	0.00476924i
$897$	−30.6144	+	15.5415i	−1.02219	+	0.518914i
$898$	4.37457	−	4.37457i	0.145981	−	0.145981i
$899$	−51.5270	−	27.8031i	−1.71852	−	0.927285i
$900$	−0.402923	−	14.9946i	−0.0134308	−	0.499820i
$901$	−30.5761	+	22.2148i	−1.01864	+	0.740084i
$902$	48.4423	−	7.67251i	1.61295	−	0.255466i
$903$	1.24115	−	2.42696i	0.0413029	−	0.0807641i
$904$		−	10.4189i		−	0.346526i
$905$	−22.0259	+	3.82627i	−0.732165	+	0.127190i
$906$	2.13891	+	6.61639i	0.0710605	+	0.219815i
$907$	−14.6424	+	28.7373i	−0.486193	+	0.954207i	0.509409	+	0.860524i	$0.329864\pi$
$907$	−14.6424	+	28.7373i	−0.486193	+	0.954207i	−0.995602	+	0.0936829i	$0.970136\pi$
$908$	8.95401	−	17.5732i	0.297149	−	0.583189i
$909$	−15.3683	−	47.7825i	−0.509735	−	1.58484i
$910$	1.20883	+	1.61265i	0.0400723	+	0.0534588i
$911$	27.9575	+	38.4802i	0.926274	+	1.27491i	0.961295	+	0.275521i	$0.0888502\pi$
$911$	27.9575	+	38.4802i	0.926274	+	1.27491i	−0.0350210	+	0.999387i	$0.511150\pi$
$912$	−1.24077	+	1.23709i	−0.0410861	+	0.0409640i
$913$	17.4699	+	8.90134i	0.578168	+	0.294591i
$914$	−15.5780	−	11.3181i	−0.515273	−	0.374368i
$915$	−3.04098	−	2.14759i	−0.100532	−	0.0709972i
$916$	5.65441	+	17.4025i	0.186827	+	0.574995i
$917$	−3.61729	+	0.572923i	−0.119453	+	0.0189196i
$918$	3.48170	+	22.6365i	0.114913	+	0.747114i
$919$	−33.6719	−	10.9407i	−1.11073	−	0.360899i	−0.304509	−	0.952510i	$-0.598492\pi$
$919$	−33.6719	−	10.9407i	−1.11073	−	0.360899i	−0.806224	+	0.591611i	$0.798492\pi$
$920$	6.22696	+	6.04385i	0.205297	+	0.199260i
$921$	−2.76139	+	3.78885i	−0.0909909	+	0.124847i
$922$	−9.55893	+	18.7605i	−0.314806	+	0.617843i
$923$	50.0449	−	25.4991i	1.64725	−	0.839314i
$924$	0.960777	+	1.32654i	0.0316072	+	0.0436401i
$925$	−25.1403	−	11.8785i	−0.826609	−	0.390563i
$926$	25.1849	+	8.18306i	0.827626	+	0.268912i
$927$	22.9780	+	3.70953i	0.754698	+	0.121837i
$928$	1.64503	−	10.3863i	0.0540008	−	0.340948i
$929$	−36.3554			−1.19278			−0.596390	−	0.802695i	$-0.703399\pi$
$929$	−36.3554			−1.19278			−0.596390	+	0.802695i	$0.703399\pi$
$930$	20.4398	+	6.87120i	0.670248	+	0.225315i
$931$	7.04958			0.231041
$932$	−2.25099	+	14.2122i	−0.0737337	+	0.465536i
$933$	32.9360	−	32.8381i	1.07828	−	1.07507i
$934$	−24.3327	−	7.90619i	−0.796192	−	0.258698i
$935$	−43.1887	−	30.4043i	−1.41242	−	0.994328i
$936$	−14.5593	−	4.77857i	−0.475885	−	0.156192i
$937$	−28.9360	+	14.7436i	−0.945298	+	0.481653i	−0.857499	−	0.514485i	$-0.827983\pi$
$937$	−28.9360	+	14.7436i	−0.945298	+	0.481653i	−0.0877982	+	0.996138i	$0.527983\pi$
$938$	−0.618156	+	1.21320i	−0.0201835	+	0.0396124i
$939$	−8.26527	−	6.02389i	−0.269727	−	0.196582i
$940$	12.1077	−	0.180673i	0.394909	−	0.00589292i
$941$	−10.2533	−	3.33149i	−0.334247	−	0.108603i	0.137085	−	0.990559i	$-0.456227\pi$
$941$	−10.2533	−	3.33149i	−0.334247	−	0.108603i	−0.471332	+	0.881956i	$0.656227\pi$
$942$	25.8749	−	13.1354i	0.843050	−	0.427976i
$943$	−35.0798	+	5.55609i	−1.14236	+	0.180931i
$944$	1.64092	+	5.05024i	0.0534075	+	0.164371i
$945$	−0.299545	+	2.02828i	−0.00974420	+	0.0659798i
$946$	−38.6681	−	28.0940i	−1.25721	−	0.913414i
$947$	−17.7999	−	9.06951i	−0.578420	−	0.294720i	0.140200	−	0.990123i	$-0.455226\pi$
$947$	−17.7999	−	9.06951i	−0.578420	−	0.294720i	−0.718619	+	0.695404i	$0.755226\pi$
$948$	−12.7753	−	12.8134i	−0.414921	−	0.416159i
$949$	3.02418	+	4.16243i	0.0981692	+	0.135118i
$950$	3.46818	−	3.68161i	0.112523	−	0.119447i
$951$	−6.53181	+	20.0015i	−0.211808	+	0.648592i
$952$	−0.353098	+	0.692995i	−0.0114440	+	0.0224601i
$953$	11.9780	−	23.5082i	0.388006	−	0.761505i	−0.611552	−	0.791204i	$-0.709455\pi$
$953$	11.9780	−	23.5082i	0.388006	−	0.761505i	0.999559	+	0.0296984i	$0.00945468\pi$
$954$	15.1822	−	20.7662i	0.491542	−	0.672331i
$955$	−4.98997	−	28.7246i	−0.161471	−	0.929508i
$956$			10.5008i			0.339619i
$957$	−86.9046	−	44.4432i	−2.80923	−	1.43664i
$958$	35.9667	−	5.69657i	1.16203	−	0.184048i
$959$	−2.09317	+	1.52078i	−0.0675919	+	0.0491084i
$960$	0.0520218	+	3.87263i	0.00167900	+	0.124989i
$961$	−19.3830	+	24.1930i	−0.625258	+	0.780418i
$962$	−20.0853	+	20.0853i	−0.647575	+	0.647575i
$963$	0.298457	−	0.581468i	0.00961763	−	0.0187375i
$964$	−8.65237	+	11.9090i	−0.278674	+	0.383562i
$965$	−3.94673	−	5.26517i	−0.127050	−	0.169492i
$966$	−0.695752	−	0.960625i	−0.0223855	−	0.0309076i
$967$	14.1668	+	14.1668i	0.455575	+	0.455575i	0.897200	−	0.441625i	$-0.145598\pi$
$967$	14.1668	+	14.1668i	0.455575	+	0.455575i	−0.441625	+	0.897200i	$0.645598\pi$
$968$	15.7883	−	8.04452i	0.507454	−	0.258561i
$969$	−4.54855	+	6.24099i	−0.146121	+	0.200489i
$970$	0.500033	+	0.946197i	0.0160551	+	0.0303806i
$971$	−0.559061	−	0.769482i	−0.0179411	−	0.0246939i	0.799952	−	0.600064i	$-0.204858\pi$
$971$	−0.559061	−	0.769482i	−0.0179411	−	0.0246939i	−0.817893	+	0.575370i	$0.804858\pi$
$972$	−6.97343	−	13.9417i	−0.223673	−	0.447181i
$973$	0.200788	−	1.26773i	0.00643698	−	0.0406415i
$974$	−8.42605	−	6.12189i	−0.269988	−	0.196158i
$975$	42.4405	+	12.4712i	1.35918	+	0.399397i
$976$	0.777659	+	0.565002i	0.0248923	+	0.0180853i
$977$	37.1961	−	5.89128i	1.19001	−	0.188479i	0.470141	−	0.882591i	$-0.344203\pi$
$977$	37.1961	−	5.89128i	1.19001	−	0.188479i	0.719867	+	0.694113i	$0.244203\pi$
$978$	−34.1597	+	5.35824i	−1.09231	+	0.171338i
$979$	−3.99371	+	5.49688i	−0.127640	+	0.175681i
$980$	10.8531	−	11.1819i	0.346690	−	0.357193i
$981$	7.05656	+	5.15906i	0.225299	+	0.164716i
$982$	1.92640	+	0.305111i	0.0614738	+	0.00973650i
$983$	4.63716	−	9.10094i	0.147902	−	0.290275i	−0.805155	−	0.593064i	$-0.797918\pi$
$983$	4.63716	−	9.10094i	0.147902	−	0.290275i	0.953057	+	0.302790i	$0.0979179\pi$
$984$	−12.8104	−	9.33649i	−0.408381	−	0.297636i
$985$	25.2001	+	33.6185i	0.802943	+	1.07117i
$986$		−	46.3496i		−	1.47607i
$987$	−1.63436	−	0.261352i	−0.0520222	−	0.00831891i
$988$	−2.34576	−	4.60381i	−0.0746285	−	0.146467i
$989$	28.0017	+	20.3444i	0.890403	+	0.646915i
$990$	34.3204	+	10.6999i	1.09078	+	0.340066i
$991$	5.89442			0.187243			0.0936213	−	0.995608i	$-0.470156\pi$
$991$	5.89442			0.187243			0.0936213	+	0.995608i	$0.470156\pi$
$992$	−5.25324	−	1.84486i	−0.166790	−	0.0585745i
$993$	17.2066	+	2.75152i	0.546033	+	0.0873167i
$994$	1.14053	+	1.56981i	0.0361755	+	0.0497913i
$995$	22.6140	−	46.0692i	0.716913	−	1.46049i
$996$	−1.94925	−	6.02970i	−0.0617643	−	0.191058i
$997$	27.6919	+	27.6919i	0.877010	+	0.877010i	0.993224	−	0.116214i	$-0.0370758\pi$
$997$	27.6919	+	27.6919i	0.877010	+	0.877010i	−0.116214	+	0.993224i	$0.537076\pi$
$998$	−20.5533	−	20.5533i	−0.650603	−	0.650603i
$999$	−28.8958	−	0.129057i	−0.914224	−	0.00408318i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bk.a.47.7	✓	512
3.2	odd	2	inner	930.2.bk.a.47.43	yes	512
5.3	odd	4	inner	930.2.bk.a.233.56	yes	512
15.8	even	4	inner	930.2.bk.a.233.6	yes	512
31.2	even	5	inner	930.2.bk.a.467.6	yes	512
93.2	odd	10	inner	930.2.bk.a.467.56	yes	512
155.33	odd	20	inner	930.2.bk.a.653.43	yes	512
465.188	even	20	inner	930.2.bk.a.653.7	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bk.a.47.7	✓	512	1.1	even	1	trivial
930.2.bk.a.47.43	yes	512	3.2	odd	2	inner
930.2.bk.a.233.6	yes	512	15.8	even	4	inner
930.2.bk.a.233.56	yes	512	5.3	odd	4	inner
930.2.bk.a.467.6	yes	512	31.2	even	5	inner
930.2.bk.a.467.56	yes	512	93.2	odd	10	inner
930.2.bk.a.653.7	yes	512	465.188	even	20	inner
930.2.bk.a.653.43	yes	512	155.33	odd	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bk (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.156434 + 0.987688i) q^{2} +(-1.22292 - 1.22657i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(2.20307 - 0.382712i) q^{5} +(1.40277 - 1.01599i) q^{6} +(-0.157227 + 0.0801110i) q^{7} +(0.453990 - 0.891007i) q^{8} +(-0.00893248 + 2.99999i) q^{9} +O(q^{10})\)	\(q+(-0.156434 + 0.987688i) q^{2} +(-1.22292 - 1.22657i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(2.20307 - 0.382712i) q^{5} +(1.40277 - 1.01599i) q^{6} +(-0.157227 + 0.0801110i) q^{7} +(0.453990 - 0.891007i) q^{8} +(-0.00893248 + 2.99999i) q^{9} +(0.0333634 + 2.23582i) q^{10} +(-5.09677 - 1.65604i) q^{11} +(0.784036 + 1.54444i) q^{12} +(-5.04492 + 0.799037i) q^{13} +(-0.0545290 - 0.167823i) q^{14} +(-3.16360 - 2.23419i) q^{15} +(0.809017 + 0.587785i) q^{16} +(3.92721 + 2.00102i) q^{17} +(-2.96165 - 0.478124i) q^{18} +(-0.594594 - 0.818388i) q^{19} +(-2.21351 - 0.316807i) q^{20} +(0.290537 + 0.0948797i) q^{21} +(2.43296 - 4.77496i) q^{22} +(-1.76185 + 3.45782i) q^{23} +(-1.64807 + 0.532780i) q^{24} +(4.70706 - 1.68628i) q^{25} -5.10781i q^{26} +(3.69061 - 3.65779i) q^{27} +(0.174287 - 0.0276044i) q^{28} +(-8.50746 + 6.18103i) q^{29} +(2.70158 - 2.77515i) q^{30} +(2.41008 + 5.01911i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(4.20170 + 8.27674i) q^{33} +(-2.59073 + 3.56584i) q^{34} +(-0.315722 + 0.236663i) q^{35} +(0.935542 - 2.85040i) q^{36} +(-3.93226 - 3.93226i) q^{37} +(0.901327 - 0.459249i) q^{38} +(7.14961 + 5.21078i) q^{39} +(0.659176 - 2.13670i) q^{40} +(5.37941 + 7.40412i) q^{41} +(-0.139162 + 0.272118i) q^{42} +(1.39520 - 8.80898i) q^{43} +(4.33558 + 3.14998i) q^{44} +(1.12845 + 6.61261i) q^{45} +(-3.13963 - 2.28108i) q^{46} +(-5.34865 + 0.847143i) q^{47} +(-0.268405 - 1.71113i) q^{48} +(-4.09619 + 5.63793i) q^{49} +(0.929176 + 4.91290i) q^{50} +(-2.34829 - 7.26407i) q^{51} +(5.04492 + 0.799037i) q^{52} +(-3.89285 + 7.64014i) q^{53} +(3.03542 + 4.21737i) q^{54} +(-11.8624 - 1.69779i) q^{55} +0.176460i q^{56} +(-0.276667 + 1.73013i) q^{57} +(-4.77407 - 9.36964i) q^{58} +(4.29599 + 3.12122i) q^{59} +(2.31836 + 3.10245i) q^{60} +0.961240 q^{61} +(-5.33434 + 1.59525i) q^{62} +(-0.238927 - 0.472394i) q^{63} +(-0.587785 - 0.809017i) q^{64} +(-10.8085 + 3.69109i) q^{65} +(-8.83213 + 2.85520i) q^{66} +(-5.45621 - 5.45621i) q^{67} +(-3.11666 - 3.11666i) q^{68} +(6.39584 - 2.06761i) q^{69} +(-0.184359 - 0.348858i) q^{70} +(-10.4580 + 3.39802i) q^{71} +(2.66895 + 1.36992i) q^{72} +(-0.457301 - 0.897503i) q^{73} +(4.49899 - 3.26871i) q^{74} +(-7.82470 - 3.71134i) q^{75} +(0.312596 + 0.962073i) q^{76} +(0.934016 - 0.147934i) q^{77} +(-6.26507 + 6.24644i) q^{78} +(-9.93524 + 3.22815i) q^{79} +(2.00728 + 0.985314i) q^{80} +(-8.99984 - 0.0535947i) q^{81} +(-8.15449 + 4.15492i) q^{82} +(-3.61359 - 0.572337i) q^{83} +(-0.246998 - 0.180017i) q^{84} +(9.41775 + 2.90539i) q^{85} +(8.48227 + 2.75606i) q^{86} +(17.9854 + 2.87606i) q^{87} +(-3.78943 + 3.78943i) q^{88} +(0.391788 - 1.20580i) q^{89} +(-6.70773 + 0.0801183i) q^{90} +(0.729185 - 0.529784i) q^{91} +(2.74414 - 2.74414i) q^{92} +(3.20894 - 9.09410i) q^{93} -5.41532i q^{94} +(-1.62314 - 1.57541i) q^{95} +(1.73205 + 0.00257859i) q^{96} +(0.426442 - 0.217283i) q^{97} +(-4.92773 - 4.92773i) q^{98} +(5.01363 - 15.2755i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 512 q + 8 q^{3} - 12 q^{7}+O(q^{10}) \) 512 * q + 8 * q^3 - 12 * q^7	\( 512 q + 8 q^{3} - 12 q^{7} - 8 q^{10} - 8 q^{12} + 8 q^{15} + 128 q^{16} + 28 q^{22} + 32 q^{25} + 44 q^{27} + 8 q^{28} + 24 q^{30} + 8 q^{31} + 28 q^{33} + 176 q^{37} + 24 q^{42} - 40 q^{45} - 24 q^{46} + 12 q^{48} - 16 q^{51} - 40 q^{55} + 40 q^{57} + 56 q^{58} + 12 q^{60} - 32 q^{61} - 224 q^{63} + 32 q^{66} + 48 q^{67} + 24 q^{70} + 40 q^{73} - 32 q^{75} + 48 q^{76} - 76 q^{78} - 96 q^{81} + 24 q^{85} - 80 q^{87} - 72 q^{88} + 16 q^{90} + 80 q^{91} - 168 q^{93} - 112 q^{97}+O(q^{100}) \) 512 * q + 8 * q^3 - 12 * q^7 - 8 * q^10 - 8 * q^12 + 8 * q^15 + 128 * q^16 + 28 * q^22 + 32 * q^25 + 44 * q^27 + 8 * q^28 + 24 * q^30 + 8 * q^31 + 28 * q^33 + 176 * q^37 + 24 * q^42 - 40 * q^45 - 24 * q^46 + 12 * q^48 - 16 * q^51 - 40 * q^55 + 40 * q^57 + 56 * q^58 + 12 * q^60 - 32 * q^61 - 224 * q^63 + 32 * q^66 + 48 * q^67 + 24 * q^70 + 40 * q^73 - 32 * q^75 + 48 * q^76 - 76 * q^78 - 96 * q^81 + 24 * q^85 - 80 * q^87 - 72 * q^88 + 16 * q^90 + 80 * q^91 - 168 * q^93 - 112 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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