LMFDB - Embedded newform 931.2.f.o.324.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [931,2,Mod(324,931)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("931.324"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(931, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 931 = 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	931.f (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$7.43407242818$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.2672476416.4
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 5x^{6} - 4x^{5} + 24x^{4} - 10x^{3} + 9x^{2} + 2x + 1 $ x^8 + 5x^6 - 4x^5 + 24x^4 - 10x^3 + 9x^2 + 2x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			324.2
Root			$-0.145683 + 0.252331i$ of defining polynomial
Character	$\chi$	$=$	931.324
Dual form			931.2.f.o.704.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.145683 + 0.252331i) q^{2} +(-1.21605 - 2.10626i) q^{3} +(0.957553 + 1.65853i) q^{4} +(1.03287 - 1.78898i) q^{5} +0.708633 q^{6} -1.14073 q^{8} +(-1.45755 + 2.52456i) q^{9} +(0.300944 + 0.521251i) q^{10} +(2.47455 + 4.28604i) q^{11} +(2.32886 - 4.03371i) q^{12} +1.62374 q^{13} -5.02408 q^{15} +(-1.74892 + 3.02922i) q^{16} +(3.49505 + 6.05360i) q^{17} +(-0.424683 - 0.735572i) q^{18} +(-0.500000 + 0.866025i) q^{19} +3.95611 q^{20} -1.44200 q^{22} +(3.70647 - 6.41980i) q^{23} +(1.38719 + 2.40268i) q^{24} +(0.366359 + 0.634552i) q^{25} +(-0.236552 + 0.409720i) q^{26} -0.206472 q^{27} +3.88335 q^{29} +(0.731926 - 1.26773i) q^{30} +(-0.404180 - 0.700061i) q^{31} +(-1.65031 - 2.85842i) q^{32} +(6.01834 - 10.4241i) q^{33} -2.03668 q^{34} -5.58273 q^{36} +(-2.05337 + 3.55655i) q^{37} +(-0.145683 - 0.252331i) q^{38} +(-1.97455 - 3.42001i) q^{39} +(-1.17823 + 2.04075i) q^{40} -8.50709 q^{41} +7.31545 q^{43} +(-4.73902 + 8.20822i) q^{44} +(3.01093 + 5.21508i) q^{45} +(1.07994 + 1.87052i) q^{46} +(2.70975 - 4.69343i) q^{47} +8.50709 q^{48} -0.213490 q^{50} +(8.50030 - 14.7230i) q^{51} +(1.55482 + 2.69302i) q^{52} +(0.995049 + 1.72347i) q^{53} +(0.0300796 - 0.0520994i) q^{54} +10.2235 q^{55} +2.43210 q^{57} +(-0.565740 + 0.979891i) q^{58} +(2.87761 + 4.98417i) q^{59} +(-4.81083 - 8.33259i) q^{60} +(5.69060 - 9.85640i) q^{61} +0.235529 q^{62} -6.03399 q^{64} +(1.67711 - 2.90484i) q^{65} +(1.75355 + 3.03723i) q^{66} +(-6.99751 - 12.1200i) q^{67} +(-6.69339 + 11.5933i) q^{68} -18.0290 q^{69} +6.51969 q^{71} +(1.66268 - 2.87984i) q^{72} +(1.04491 + 1.80984i) q^{73} +(-0.598285 - 1.03626i) q^{74} +(0.891021 - 1.54329i) q^{75} -1.91511 q^{76} +1.15063 q^{78} +(1.15989 - 2.00898i) q^{79} +(3.61281 + 6.25758i) q^{80} +(4.62374 + 8.00855i) q^{81} +(1.23934 - 2.14660i) q^{82} +5.01753 q^{83} +14.4397 q^{85} +(-1.06574 + 1.84592i) q^{86} +(-4.72235 - 8.17935i) q^{87} +(-2.82279 - 4.88922i) q^{88} +(-3.34720 + 5.79753i) q^{89} -1.75457 q^{90} +14.1966 q^{92} +(-0.983006 + 1.70262i) q^{93} +(0.789532 + 1.36751i) q^{94} +(1.03287 + 1.78898i) q^{95} +(-4.01372 + 6.95196i) q^{96} +14.0663 q^{97} -14.4271 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{3} - 2 q^{4} + 8 q^{5} + 8 q^{6} + 12 q^{8} - 2 q^{9} + 10 q^{10} + 6 q^{11} + 6 q^{12} - 4 q^{13} + 8 q^{15} - 2 q^{16} + 8 q^{17} + 6 q^{18} - 4 q^{19} - 28 q^{22} + 8 q^{23} + 12 q^{24} - 20 q^{25}+ \cdots + 16 q^{99}+O(q^{100}) $ 8 * q + 2 * q^3 - 2 * q^4 + 8 * q^5 + 8 * q^6 + 12 * q^8 - 2 * q^9 + 10 * q^10 + 6 * q^11 + 6 * q^12 - 4 * q^13 + 8 * q^15 - 2 * q^16 + 8 * q^17 + 6 * q^18 - 4 * q^19 - 28 * q^22 + 8 * q^23 + 12 * q^24 - 20 * q^25 + 16 * q^26 + 20 * q^27 + 4 * q^29 - 2 * q^30 - 2 * q^32 + 18 * q^33 + 44 * q^34 - 40 * q^36 - 10 * q^37 - 2 * q^39 + 22 * q^40 - 24 * q^41 + 8 * q^43 + 14 * q^44 + 8 * q^45 + 8 * q^46 + 16 * q^47 + 24 * q^48 + 24 * q^50 + 10 * q^51 + 28 * q^52 - 12 * q^53 + 4 * q^54 + 16 * q^55 - 4 * q^57 - 4 * q^58 + 14 * q^59 + 2 * q^60 + 20 * q^61 + 40 * q^62 - 40 * q^64 - 10 * q^65 - 8 * q^66 - 2 * q^67 - 24 * q^68 - 28 * q^69 - 4 * q^71 + 8 * q^72 - 16 * q^73 + 26 * q^74 + 36 * q^75 + 4 * q^76 + 28 * q^78 + 8 * q^79 + 28 * q^80 + 20 * q^81 - 12 * q^82 - 40 * q^83 - 28 * q^85 - 8 * q^86 - 20 * q^87 + 2 * q^88 + 16 * q^89 + 64 * q^90 + 52 * q^92 - 12 * q^93 + 10 * q^94 + 8 * q^95 - 12 * q^96 - 4 * q^97 + 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/931\mathbb{Z}\right)^\times$.

$n$	$248$	$344$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−0.145683	+	0.252331i	−0.103014	+	0.178425i	−0.912925	−	0.408127i	$-0.866182\pi$
$2$	−0.145683	+	0.252331i	−0.103014	+	0.178425i	0.809911	+	0.586552i	$0.199515\pi$
$3$	−1.21605	−	2.10626i	−0.702086	−	1.21605i	−0.967733	−	0.251979i	$-0.918919\pi$
$3$	−1.21605	−	2.10626i	−0.702086	−	1.21605i	0.265646	−	0.964071i	$-0.414415\pi$
$4$	0.957553	+	1.65853i	0.478776	+	0.829265i
$5$	1.03287	−	1.78898i	0.461914	−	0.800058i	−0.537143	−	0.843491i	$-0.680496\pi$
$5$	1.03287	−	1.78898i	0.461914	−	0.800058i	0.999056	+	0.0434336i	$0.0138297\pi$
$6$	0.708633			0.289298
$7$		0			0
$7$		0			0
$8$	−1.14073			−0.403310
$9$	−1.45755	+	2.52456i	−0.485851	+	0.841518i
$10$	0.300944	+	0.521251i	0.0951669	+	0.164834i
$11$	2.47455	+	4.28604i	0.746104	+	1.29229i	0.949677	+	0.313230i	$0.101411\pi$
$11$	2.47455	+	4.28604i	0.746104	+	1.29229i	−0.203574	+	0.979060i	$0.565256\pi$
$12$	2.32886	−	4.03371i	0.672285	−	1.16443i
$13$	1.62374			0.450344			0.225172	−	0.974319i	$-0.427706\pi$
$13$	1.62374			0.450344			0.225172	+	0.974319i	$0.427706\pi$
$14$		0			0
$15$	−5.02408			−1.29721
$16$	−1.74892	+	3.02922i	−0.437230	+	0.757304i
$17$	3.49505	+	6.05360i	0.847674	+	1.46821i	0.883279	+	0.468848i	$0.155331\pi$
$17$	3.49505	+	6.05360i	0.847674	+	1.46821i	−0.0356050	+	0.999366i	$0.511336\pi$
$18$	−0.424683	−	0.735572i	−0.100099	−	0.173376i
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i
$20$	3.95611			0.884613
$21$		0			0
$22$	−1.44200			−0.307436
$23$	3.70647	−	6.41980i	0.772853	−	1.33862i	−0.163140	−	0.986603i	$-0.552162\pi$
$23$	3.70647	−	6.41980i	0.772853	−	1.33862i	0.935993	−	0.352018i	$-0.114504\pi$
$24$	1.38719	+	2.40268i	0.283158	+	0.490445i
$25$	0.366359	+	0.634552i	0.0732718	+	0.126910i
$26$	−0.236552	+	0.409720i	−0.0463916	+	0.0803527i
$27$	−0.206472			−0.0397356
$28$		0			0
$29$	3.88335			0.721120			0.360560	−	0.932736i	$-0.382586\pi$
$29$	3.88335			0.721120			0.360560	+	0.932736i	$0.382586\pi$
$30$	0.731926	−	1.26773i	0.133631	−	0.231455i
$31$	−0.404180	−	0.700061i	−0.0725929	−	0.125735i	0.827444	−	0.561548i	$-0.189794\pi$
$31$	−0.404180	−	0.700061i	−0.0725929	−	0.125735i	−0.900037	+	0.435814i	$0.856461\pi$
$32$	−1.65031	−	2.85842i	−0.291736	−	0.505302i
$33$	6.01834	−	10.4241i	1.04766	−	1.81460i
$34$	−2.03668			−0.349288
$35$		0			0
$36$	−5.58273			−0.930456
$37$	−2.05337	+	3.55655i	−0.337572	+	0.584692i	−0.983976	−	0.178304i	$-0.942939\pi$
$37$	−2.05337	+	3.55655i	−0.337572	+	0.584692i	0.646403	+	0.762996i	$0.276272\pi$
$38$	−0.145683	−	0.252331i	−0.0236330	−	0.0409335i
$39$	−1.97455	−	3.42001i	−0.316180	−	0.547641i
$40$	−1.17823	+	2.04075i	−0.186294	+	0.322671i
$41$	−8.50709			−1.32858			−0.664292	−	0.747473i	$-0.731267\pi$
$41$	−8.50709			−1.32858			−0.664292	+	0.747473i	$0.731267\pi$
$42$		0			0
$43$	7.31545			1.11560			0.557798	−	0.829977i	$-0.311646\pi$
$43$	7.31545			1.11560			0.557798	+	0.829977i	$0.311646\pi$
$44$	−4.73902	+	8.20822i	−0.714434	+	1.23744i
$45$	3.01093	+	5.21508i	0.448842	+	0.777418i
$46$	1.07994	+	1.87052i	0.159229	+	0.275793i
$47$	2.70975	−	4.69343i	0.395258	−	0.684606i	−0.597876	−	0.801588i	$-0.703989\pi$
$47$	2.70975	−	4.69343i	0.395258	−	0.684606i	0.993134	+	0.116982i	$0.0373220\pi$
$48$	8.50709			1.22789
$49$		0			0
$50$	−0.213490			−0.0301920
$51$	8.50030	−	14.7230i	1.19028	−	2.06163i
$52$	1.55482	+	2.69302i	0.215614	+	0.373455i
$53$	0.995049	+	1.72347i	0.136680	+	0.236737i	0.926238	−	0.376939i	$-0.123023\pi$
$53$	0.995049	+	1.72347i	0.136680	+	0.236737i	−0.789558	+	0.613676i	$0.789690\pi$
$54$	0.0300796	−	0.0520994i	0.00409331	−	0.00708983i
$55$	10.2235			1.37854
$56$		0			0
$57$	2.43210			0.322139
$58$	−0.565740	+	0.979891i	−0.0742853	+	0.128666i
$59$	2.87761	+	4.98417i	0.374633	+	0.648883i	0.990272	−	0.139145i	$-0.0444354\pi$
$59$	2.87761	+	4.98417i	0.374633	+	0.648883i	−0.615639	+	0.788028i	$0.711102\pi$
$60$	−4.81083	−	8.33259i	−0.621075	−	1.07573i
$61$	5.69060	−	9.85640i	0.728606	−	1.26198i	−0.228866	−	0.973458i	$-0.573502\pi$
$61$	5.69060	−	9.85640i	0.728606	−	1.26198i	0.957472	−	0.288525i	$-0.0931648\pi$
$62$	0.235529			0.0299123
$63$		0			0
$64$	−6.03399			−0.754248
$65$	1.67711	−	2.90484i	0.208020	−	0.360301i
$66$	1.75355	+	3.03723i	0.215847	+	0.373857i
$67$	−6.99751	−	12.1200i	−0.854882	−	1.48070i	−0.876754	−	0.480939i	$-0.840296\pi$
$67$	−6.99751	−	12.1200i	−0.854882	−	1.48070i	0.0218718	−	0.999761i	$-0.493037\pi$
$68$	−6.69339	+	11.5933i	−0.811692	+	1.40589i
$69$	−18.0290			−2.17044
$70$		0			0
$71$	6.51969			0.773745			0.386872	−	0.922133i	$-0.373555\pi$
$71$	6.51969			0.773745			0.386872	+	0.922133i	$0.373555\pi$
$72$	1.66268	−	2.87984i	0.195948	−	0.339393i
$73$	1.04491	+	1.80984i	0.122298	+	0.211826i	0.920673	−	0.390334i	$-0.127640\pi$
$73$	1.04491	+	1.80984i	0.122298	+	0.211826i	−0.798376	+	0.602160i	$0.794307\pi$
$74$	−0.598285	−	1.03626i	−0.0695492	−	0.120463i
$75$	0.891021	−	1.54329i	0.102886	−	0.178204i
$76$	−1.91511			−0.219678
$77$		0			0
$78$	1.15063			0.130284
$79$	1.15989	−	2.00898i	0.130497	−	0.226028i	−0.793371	−	0.608738i	$-0.791676\pi$
$79$	1.15989	−	2.00898i	0.130497	−	0.226028i	0.923868	+	0.382710i	$0.125009\pi$
$80$	3.61281	+	6.25758i	0.403925	+	0.699618i
$81$	4.62374	+	8.00855i	0.513749	+	0.889839i
$82$	1.23934	−	2.14660i	0.136862	−	0.237053i
$83$	5.01753			0.550745			0.275373	−	0.961338i	$-0.411199\pi$
$83$	5.01753			0.550745			0.275373	+	0.961338i	$0.411199\pi$
$84$		0			0
$85$	14.4397			1.56621
$86$	−1.06574	+	1.84592i	−0.114922	+	0.199050i
$87$	−4.72235	−	8.17935i	−0.506289	−	0.876918i
$88$	−2.82279	−	4.88922i	−0.300911	−	0.521193i
$89$	−3.34720	+	5.79753i	−0.354803	+	0.614537i	−0.987084	−	0.160202i	$-0.948785\pi$
$89$	−3.34720	+	5.79753i	−0.354803	+	0.614537i	0.632281	+	0.774739i	$0.282119\pi$
$90$	−1.75457			−0.184948
$91$		0			0
$92$	14.1966			1.48009
$93$	−0.983006	+	1.70262i	−0.101933	+	0.176553i
$94$	0.789532	+	1.36751i	0.0814340	+	0.141048i
$95$	1.03287	+	1.78898i	0.105970	+	0.183546i
$96$	−4.01372	+	6.95196i	−0.409648	+	0.709531i
$97$	14.0663			1.42822			0.714111	−	0.700033i	$-0.246831\pi$
$97$	14.0663			1.42822			0.714111	+	0.700033i	$0.246831\pi$
$98$		0			0
$99$	−14.4271			−1.44998
$100$	−0.701616	+	1.21523i	−0.0701616	+	0.121523i
$101$	−0.897068	−	1.55377i	−0.0892616	−	0.154606i	0.817938	−	0.575307i	$-0.195117\pi$
$101$	−0.897068	−	1.55377i	−0.0892616	−	0.154606i	−0.907199	+	0.420701i	$0.861784\pi$
$102$	2.47671	+	4.28978i	0.245231	+	0.424752i
$103$	8.45044	−	14.6366i	0.832647	−	1.44219i	−0.0632856	−	0.997995i	$-0.520158\pi$
$103$	8.45044	−	14.6366i	0.832647	−	1.44219i	0.895932	−	0.444191i	$-0.146509\pi$
$104$	−1.85225			−0.181628
$105$		0			0
$106$	−0.579848			−0.0563199
$107$	−4.50463	+	7.80224i	−0.435479	+	0.754271i	−0.997335	−	0.0729640i	$-0.976754\pi$
$107$	−4.50463	+	7.80224i	−0.435479	+	0.754271i	0.561856	+	0.827235i	$0.310088\pi$
$108$	−0.197708	−	0.342440i	−0.0190245	−	0.0329513i
$109$	−3.50463	−	6.07019i	−0.335682	−	0.581419i	0.647933	−	0.761697i	$-0.275634\pi$
$109$	−3.50463	−	6.07019i	−0.335682	−	0.581419i	−0.983616	+	0.180278i	$0.942300\pi$
$110$	−1.48940	+	2.57972i	−0.142009	+	0.245966i
$111$	9.98801			0.948020
$112$		0			0
$113$	−0.261701			−0.0246188			−0.0123094	−	0.999924i	$-0.503918\pi$
$113$	−0.261701			−0.0246188			−0.0123094	+	0.999924i	$0.503918\pi$
$114$	−0.354317	+	0.613694i	−0.0331848	+	0.0574777i
$115$	−7.65661	−	13.2616i	−0.713982	−	1.23665i
$116$	3.71851	+	6.44066i	0.345255	+	0.598000i
$117$	−2.36668	+	4.09922i	−0.218800	+	0.378973i
$118$	−1.67688			−0.154369
$119$		0			0
$120$	5.73113			0.523179
$121$	−6.74676	+	11.6857i	−0.613342	+	1.06234i
$122$	1.65805	+	2.87183i	0.150113	+	0.260003i
$123$	10.3450	+	17.9181i	0.932781	+	1.61562i
$124$	0.774048	−	1.34069i	0.0695115	−	0.120398i
$125$	11.8423			1.05921
$126$		0			0
$127$	−8.07337			−0.716395			−0.358198	−	0.933646i	$-0.616609\pi$
$127$	−8.07337			−0.716395			−0.358198	+	0.933646i	$0.616609\pi$
$128$	4.17967	−	7.23940i	0.369434	−	0.639879i
$129$	−8.89595	−	15.4082i	−0.783245	−	1.35662i
$130$	0.488655	+	0.846375i	0.0428578	+	0.0742320i
$131$	−9.71635	+	16.8292i	−0.848922	+	1.47038i	0.0332496	+	0.999447i	$0.489414\pi$
$131$	−9.71635	+	16.8292i	−0.848922	+	1.47038i	−0.882171	+	0.470929i	$0.843919\pi$
$132$	23.0515			2.00638
$133$		0			0
$134$	4.07769			0.352259
$135$	−0.213259	+	0.369375i	−0.0183544	+	0.0317908i
$136$	−3.98691	−	6.90554i	−0.341875	−	0.592145i
$137$	3.14073	+	5.43991i	0.268331	+	0.464763i	0.968431	−	0.249282i	$-0.0801946\pi$
$137$	3.14073	+	5.43991i	0.268331	+	0.464763i	−0.700100	+	0.714045i	$0.746861\pi$
$138$	2.62653	−	4.54928i	0.223585	−	0.387261i
$139$	−18.1959			−1.54336			−0.771679	−	0.636012i	$-0.780583\pi$
$139$	−18.1959			−1.54336			−0.771679	+	0.636012i	$0.780583\pi$
$140$		0			0
$141$	−13.1808			−1.11002
$142$	−0.949811	+	1.64512i	−0.0797064	+	0.138055i
$143$	4.01802	+	6.95941i	0.336003	+	0.581975i
$144$	−5.09828	−	8.83049i	−0.424857	−	0.735874i
$145$	4.01100	−	6.94725i	0.333095	−	0.576938i
$146$	−0.608906			−0.0503934
$147$		0			0
$148$	−7.86485			−0.646487
$149$	−4.37903	+	7.58470i	−0.358744	+	0.621363i	−0.987751	−	0.156036i	$-0.950128\pi$
$149$	−4.37903	+	7.58470i	−0.358744	+	0.621363i	0.629007	+	0.777400i	$0.283462\pi$
$150$	0.259614	+	0.449665i	0.0211974	+	0.0367150i
$151$	6.02225	+	10.4308i	0.490084	+	0.848850i	0.999935	−	0.0114128i	$-0.00363288\pi$
$151$	6.02225	+	10.4308i	0.490084	+	0.848850i	−0.509851	+	0.860263i	$0.670300\pi$
$152$	0.570366	−	0.987903i	0.0462628	−	0.0801295i
$153$	−20.3769			−1.64737
$154$		0			0
$155$	−1.66986			−0.134127
$156$	3.78146	−	6.54969i	0.302759	−	0.524395i
$157$	−2.13794	−	3.70302i	−0.170626	−	0.295533i	0.768013	−	0.640435i	$-0.221246\pi$
$157$	−2.13794	−	3.70302i	−0.170626	−	0.295533i	−0.938639	+	0.344901i	$0.887912\pi$
$158$	0.337953	+	0.585351i	0.0268861	+	0.0465680i
$159$	2.42006	−	4.19166i	0.191923	−	0.332420i
$160$	−6.81822			−0.539028
$161$		0			0
$162$	−2.69441			−0.211693
$163$	4.51339	−	7.81742i	0.353516	−	0.612308i	−0.633347	−	0.773868i	$-0.718319\pi$
$163$	4.51339	−	7.81742i	0.353516	−	0.612308i	0.986863	+	0.161560i	$0.0516527\pi$
$164$	−8.14599	−	14.1093i	−0.636095	−	1.10175i
$165$	−12.4323	−	21.5334i	−0.967856	−	1.67637i
$166$	−0.730971	+	1.26608i	−0.0567343	+	0.0982668i
$167$	−21.2318			−1.64297			−0.821484	−	0.570232i	$-0.806853\pi$
$167$	−21.2318			−1.64297			−0.821484	+	0.570232i	$0.806853\pi$
$168$		0			0
$169$	−10.3635			−0.797190
$170$	−2.10363	+	3.64359i	−0.161341	+	0.279451i
$171$	−1.45755	−	2.52456i	−0.111462	−	0.193058i
$172$	7.00493	+	12.1329i	0.534121	+	0.925125i
$173$	−3.40035	+	5.88957i	−0.258524	+	0.447776i	−0.965847	−	0.259115i	$-0.916569\pi$
$173$	−3.40035	+	5.88957i	−0.258524	+	0.447776i	0.707323	+	0.706890i	$0.249903\pi$
$174$	2.75187			0.208619
$175$		0			0
$176$	−17.3111			−1.30488
$177$	6.99863	−	12.1220i	0.526049	−	0.911144i
$178$	−0.975265	−	1.68921i	−0.0730992	−	0.126611i
$179$	−9.63608	−	16.6902i	−0.720235	−	1.24748i	−0.960906	−	0.276876i	$-0.910701\pi$
$179$	−9.63608	−	16.6902i	−0.720235	−	1.24748i	0.240671	−	0.970607i	$-0.422633\pi$
$180$	−5.76624	+	9.98742i	−0.429790	+	0.744418i
$181$	−20.5508			−1.52753			−0.763764	−	0.645495i	$-0.776651\pi$
$181$	−20.5508			−1.52753			−0.763764	+	0.645495i	$0.776651\pi$
$182$		0			0
$183$	−27.6802			−2.04618
$184$	−4.22809	+	7.32327i	−0.311699	+	0.539879i
$185$	4.24173	+	7.34690i	0.311858	+	0.540155i
$186$	−0.286416	−	0.496086i	−0.0210010	−	0.0363748i
$187$	−17.2973	+	29.9598i	−1.26491	+	2.19088i
$188$	10.3789			0.756960
$189$		0			0
$190$	−0.601888			−0.0436656
$191$	2.24183	−	3.88296i	0.162213	−	0.280961i	−0.773449	−	0.633858i	$-0.781470\pi$
$191$	2.24183	−	3.88296i	0.162213	−	0.280961i	0.935662	+	0.352897i	$0.114803\pi$
$192$	7.33763	+	12.7091i	0.529548	+	0.917203i
$193$	12.5145	+	21.6758i	0.900814	+	1.56026i	0.826440	+	0.563025i	$0.190363\pi$
$193$	12.5145	+	21.6758i	0.900814	+	1.56026i	0.0743742	+	0.997230i	$0.476304\pi$
$194$	−2.04923	+	3.54938i	−0.147126	+	0.254830i
$195$	−8.15780			−0.584192
$196$		0			0
$197$	−0.100378			−0.00715167			−0.00357583	−	0.999994i	$-0.501138\pi$
$197$	−0.100378			−0.00715167			−0.00357583	+	0.999994i	$0.501138\pi$
$198$	2.10179	−	3.64041i	0.149368	−	0.258713i
$199$	−13.4650	−	23.3220i	−0.954506	−	1.65325i	−0.735494	−	0.677531i	$-0.763050\pi$
$199$	−13.4650	−	23.3220i	−0.954506	−	1.65325i	−0.219013	−	0.975722i	$-0.570284\pi$
$200$	−0.417917	−	0.723854i	−0.0295512	−	0.0511842i
$201$	−17.0186	+	29.4772i	−1.20040	+	2.07916i
$202$	0.522752			0.0367807
$203$		0			0
$204$	32.5580			2.27951
$205$	−8.78672	+	15.2190i	−0.613691	+	1.06294i
$206$	2.46218	+	4.26462i	0.171548	+	0.297130i
$207$	10.8048	+	18.7144i	0.750983	+	1.30074i
$208$	−2.83979	+	4.91866i	−0.196904	+	0.341047i
$209$	−4.94909			−0.342336
$210$		0			0
$211$	14.5345			1.00060			0.500299	−	0.865853i	$-0.333223\pi$
$211$	14.5345			1.00060			0.500299	+	0.865853i	$0.333223\pi$
$212$	−1.90562	+	3.30064i	−0.130879	+	0.226689i
$213$	−7.92826	−	13.7322i	−0.543236	−	0.940912i
$214$	−1.31250	−	2.27331i	−0.0897206	−	0.155401i
$215$	7.55591	−	13.0872i	0.515309	−	0.892541i
$216$	0.235529			0.0160258
$217$		0			0
$218$	2.04226			0.138320
$219$	2.54133	−	4.40171i	0.171727	−	0.297440i
$220$	9.78958	+	16.9560i	0.660013	+	1.14318i
$221$	5.67504	+	9.82947i	0.381745	+	0.661201i
$222$	−1.45509	+	2.52029i	−0.0976591	+	0.169151i
$223$	2.30829			0.154574			0.0772872	−	0.997009i	$-0.475374\pi$
$223$	2.30829			0.154574			0.0772872	+	0.997009i	$0.475374\pi$
$224$		0			0
$225$	−2.13595			−0.142397
$226$	0.0381256	−	0.0660354i	0.00253607	−	0.00439261i
$227$	9.92610	+	17.1925i	0.658819	+	1.14111i	0.980922	+	0.194403i	$0.0622769\pi$
$227$	9.92610	+	17.1925i	0.658819	+	1.14111i	−0.322103	+	0.946705i	$0.604390\pi$
$228$	2.32886	+	4.03371i	0.154233	+	0.267139i
$229$	8.71356	−	15.0923i	0.575808	−	0.997330i	−0.420145	−	0.907457i	$-0.638021\pi$
$229$	8.71356	−	15.0923i	0.575808	−	0.997330i	0.995953	−	0.0898724i	$-0.0286459\pi$
$230$	4.46176			0.294200
$231$		0			0
$232$	−4.42986			−0.290835
$233$	−4.44614	+	7.70094i	−0.291276	+	0.504505i	−0.974112	−	0.226067i	$-0.927413\pi$
$233$	−4.44614	+	7.70094i	−0.291276	+	0.504505i	0.682835	+	0.730572i	$0.260747\pi$
$234$	−0.689573	−	1.19438i	−0.0450788	−	0.0780788i
$235$	−5.59764	−	9.69540i	−0.365150	−	0.632458i
$236$	−5.51093	+	9.54520i	−0.358731	+	0.621340i
$237$	−5.64192			−0.366482
$238$		0			0
$239$	−10.9234			−0.706575			−0.353287	−	0.935515i	$-0.614936\pi$
$239$	−10.9234			−0.706575			−0.353287	+	0.935515i	$0.614936\pi$
$240$	8.78672	−	15.2190i	0.567180	−	0.982385i
$241$	2.59199	+	4.48945i	0.166964	+	0.289191i	0.937351	−	0.348386i	$-0.113270\pi$
$241$	2.59199	+	4.48945i	0.166964	+	0.289191i	−0.770387	+	0.637577i	$0.779937\pi$
$242$	−1.96578	−	3.40483i	−0.126365	−	0.218871i
$243$	10.9357	−	18.9412i	0.701524	−	1.21508i
$244$	21.7962			1.39536
$245$		0			0
$246$	−6.02841			−0.384357
$247$	−0.811869	+	1.40620i	−0.0516580	+	0.0894743i
$248$	0.461061	+	0.798582i	0.0292774	+	0.0507100i
$249$	−6.10156	−	10.5682i	−0.386671	−	0.669734i
$250$	−1.72523	+	2.98818i	−0.109113	+	0.188989i
$251$	−12.2672			−0.774301			−0.387151	−	0.922016i	$-0.626541\pi$
$251$	−12.2672			−0.774301			−0.387151	+	0.922016i	$0.626541\pi$
$252$		0			0
$253$	36.6873			2.30651
$254$	1.17616	−	2.03716i	0.0737986	−	0.127823i
$255$	−17.5594	−	30.4138i	−1.09961	−	1.90459i
$256$	−4.81617	−	8.34185i	−0.301011	−	0.521366i
$257$	−11.1870	+	19.3764i	−0.697825	+	1.20867i	0.271393	+	0.962468i	$0.412516\pi$
$257$	−11.1870	+	19.3764i	−0.697825	+	1.20867i	−0.969219	+	0.246201i	$0.920818\pi$
$258$	5.18397			0.322740
$259$		0			0
$260$	6.42369			0.398380
$261$	−5.66019	+	9.80374i	−0.350357	+	0.606836i
$262$	−2.83102	−	4.90348i	−0.174901	−	0.302938i
$263$	−4.53813	−	7.86026i	−0.279833	−	0.484685i	0.691510	−	0.722367i	$-0.256946\pi$
$263$	−4.53813	−	7.86026i	−0.279833	−	0.484685i	−0.971343	+	0.237682i	$0.923612\pi$
$264$	−6.86532	+	11.8911i	−0.422531	+	0.731845i
$265$	4.11102			0.252538
$266$		0			0
$267$	16.2815			0.996409
$268$	13.4010	−	23.2112i	0.818595	−	1.41785i
$269$	9.40992	+	16.2985i	0.573733	+	0.993735i	0.996178	+	0.0873463i	$0.0278387\pi$
$269$	9.40992	+	16.2985i	0.573733	+	0.993735i	−0.422445	+	0.906389i	$0.638828\pi$
$270$	−0.0621366	−	0.107624i	−0.00378151	−	0.00654977i
$271$	12.4907	−	21.6346i	0.758758	−	1.31421i	−0.184727	−	0.982790i	$-0.559140\pi$
$271$	12.4907	−	21.6346i	0.758758	−	1.31421i	0.943484	−	0.331417i	$-0.107527\pi$
$272$	−24.4502			−1.48251
$273$		0			0
$274$	−1.83021			−0.110567
$275$	−1.81314	+	3.14046i	−0.109337	+	0.189377i
$276$	−17.2637	−	29.9017i	−1.03915	−	1.79987i
$277$	−10.4370	−	18.0775i	−0.627100	−	1.08617i	−0.988131	−	0.153616i	$-0.950908\pi$
$277$	−10.4370	−	18.0775i	−0.627100	−	1.08617i	0.361030	−	0.932554i	$-0.382425\pi$
$278$	2.65084	−	4.59140i	0.158987	−	0.275374i
$279$	2.35646			0.141077
$280$		0			0
$281$	29.3117			1.74859			0.874296	−	0.485393i	$-0.161324\pi$
$281$	29.3117			1.74859			0.874296	+	0.485393i	$0.161324\pi$
$282$	1.92022	−	3.32592i	0.114347	−	0.198055i
$283$	0.283137	+	0.490408i	0.0168308	+	0.0291518i	0.874318	−	0.485353i	$-0.161309\pi$
$283$	0.283137	+	0.490408i	0.0168308	+	0.0291518i	−0.857487	+	0.514505i	$0.827976\pi$
$284$	6.24295	+	10.8131i	0.370451	+	0.641639i
$285$	2.51204	−	4.35098i	0.148801	−	0.257730i
$286$	−2.34143			−0.138452
$287$		0			0
$288$	9.62165			0.566961
$289$	−15.9307	+	27.5928i	−0.937102	+	1.62311i
$290$	1.16867	+	2.02420i	0.0686268	+	0.118865i
$291$	−17.1054	−	29.6274i	−1.00273	−	1.73679i
$292$	−2.00112	+	3.46604i	−0.117107	+	0.202834i
$293$	−25.2701			−1.47630			−0.738148	−	0.674639i	$-0.764300\pi$
$293$	−25.2701			−1.47630			−0.738148	+	0.674639i	$0.764300\pi$
$294$		0			0
$295$	11.8888			0.692192
$296$	2.34235	−	4.05707i	0.136146	−	0.235812i
$297$	−0.510925	−	0.884948i	−0.0296469	−	0.0513499i
$298$	−1.27590	−	2.20993i	−0.0739112	−	0.128018i
$299$	6.01834	−	10.4241i	0.348050	−	0.602840i
$300$	3.41280			0.197038
$301$		0			0
$302$	−3.50937			−0.201941
$303$	−2.18176	+	3.77892i	−0.125339	+	0.217093i
$304$	−1.74892	−	3.02922i	−0.100307	−	0.173738i
$305$	−11.7553	−	20.3608i	−0.673106	−	1.16585i
$306$	2.96857	−	5.14172i	0.169702	−	0.293932i
$307$	6.37114			0.363620			0.181810	−	0.983334i	$-0.441804\pi$
$307$	6.37114			0.363620			0.181810	+	0.983334i	$0.441804\pi$
$308$		0			0
$309$	−41.1046			−2.33836
$310$	0.243271	−	0.421358i	0.0138169	−	0.0239315i
$311$	0.147844	+	0.256074i	0.00838348	+	0.0145206i	0.870187	−	0.492722i	$-0.163998\pi$
$311$	0.147844	+	0.256074i	0.00838348	+	0.0145206i	−0.861803	+	0.507243i	$0.830665\pi$
$312$	2.25243	+	3.90132i	0.127519	+	0.220869i
$313$	−10.1840	+	17.6392i	−0.575632	+	0.997024i	0.420341	+	0.907366i	$0.361911\pi$
$313$	−10.1840	+	17.6392i	−0.575632	+	0.997024i	−0.995973	+	0.0896576i	$0.971423\pi$
$314$	1.24585			0.0703074
$315$		0			0
$316$	4.44261			0.249916
$317$	15.2580	−	26.4276i	0.856974	−	1.48432i	−0.0178276	−	0.999841i	$-0.505675\pi$
$317$	15.2580	−	26.4276i	0.856974	−	1.48432i	0.874802	−	0.484481i	$-0.160992\pi$
$318$	0.705124	+	1.22131i	0.0395414	+	0.0684877i
$319$	9.60954	+	16.6442i	0.538031	+	0.931896i
$320$	−6.23232	+	10.7947i	−0.348398	+	0.603442i
$321$	21.9114			1.22297
$322$		0			0
$323$	−6.99010			−0.388939
$324$	−8.85495	+	15.3372i	−0.491941	+	0.852068i
$325$	0.594871	+	1.03035i	0.0329975	+	0.0571533i
$326$	1.31505	+	2.27774i	0.0728340	+	0.126152i
$327$	−8.52360	+	14.7633i	−0.471356	+	0.816413i
$328$	9.70431			0.535831
$329$		0			0
$330$	7.24474			0.398810
$331$	14.1407	−	24.4924i	0.777244	−	1.34623i	−0.156281	−	0.987713i	$-0.549951\pi$
$331$	14.1407	−	24.4924i	0.777244	−	1.34623i	0.933525	−	0.358513i	$-0.116716\pi$
$332$	4.80455	+	8.32172i	0.263684	+	0.456714i
$333$	−5.98580	−	10.3677i	−0.328020	−	0.568147i
$334$	3.09312	−	5.35745i	0.169248	−	0.293147i
$335$	−28.9101			−1.57953
$336$		0			0
$337$	0.0981441			0.00534625			0.00267312	−	0.999996i	$-0.499149\pi$
$337$	0.0981441			0.00534625			0.00267312	+	0.999996i	$0.499149\pi$
$338$	1.50979	−	2.61503i	0.0821216	−	0.142239i
$339$	0.318242	+	0.551211i	0.0172845	+	0.0299377i
$340$	13.8268	+	23.9487i	0.749863	+	1.29880i
$341$	2.00033	−	3.46467i	0.108324	−	0.187622i
$342$	0.849365			0.0459284
$343$		0			0
$344$	−8.34497			−0.449931
$345$	−18.6216	+	32.2536i	−1.00255	+	1.73648i
$346$	−0.990748	−	1.71603i	−0.0532630	−	0.0922541i
$347$	0.536866	+	0.929880i	0.0288205	+	0.0499186i	0.880076	−	0.474833i	$-0.157492\pi$
$347$	0.536866	+	0.929880i	0.0288205	+	0.0499186i	−0.851255	+	0.524752i	$0.824158\pi$
$348$	9.04380	−	15.6643i	0.484798	−	0.839695i
$349$	7.94431			0.425249			0.212625	−	0.977134i	$-0.431799\pi$
$349$	7.94431			0.425249			0.212625	+	0.977134i	$0.431799\pi$
$350$		0			0
$351$	−0.335257			−0.0178947
$352$	8.16753	−	14.1466i	0.435331	−	0.754015i
$353$	4.37905	+	7.58474i	0.233073	+	0.403695i	0.958711	−	0.284382i	$-0.0917884\pi$
$353$	4.37905	+	7.58474i	0.233073	+	0.403695i	−0.725638	+	0.688077i	$0.758455\pi$
$354$	2.03917	+	3.53194i	0.108381	+	0.187721i
$355$	6.73399	−	11.6636i	0.357403	−	0.619040i
$356$	−12.8205			−0.679485
$357$		0			0
$358$	5.61527			0.296776
$359$	−4.44279	+	7.69514i	−0.234482	+	0.406134i	−0.959122	−	0.282993i	$-0.908673\pi$
$359$	−4.44279	+	7.69514i	−0.234482	+	0.406134i	0.724640	+	0.689127i	$0.242006\pi$
$360$	−3.43466	−	5.94900i	−0.181022	−	0.313540i
$361$	−0.500000	−	0.866025i	−0.0263158	−	0.0455803i
$362$	2.99391	−	5.18560i	0.157356	−	0.272549i
$363$	32.8176			1.72248
$364$		0			0
$365$	4.31703			0.225964
$366$	4.03254	−	6.98457i	0.210784	−	0.365089i
$367$	−7.03222	−	12.1802i	−0.367079	−	0.635799i	0.622029	−	0.782995i	$-0.286309\pi$
$367$	−7.03222	−	12.1802i	−0.367079	−	0.635799i	−0.989107	+	0.147195i	$0.952975\pi$
$368$	12.9646	+	22.4554i	0.675829	+	1.17057i
$369$	12.3995	−	21.4766i	0.645494	−	1.11803i
$370$	−2.47180			−0.128503
$371$		0			0
$372$	−3.76512			−0.195212
$373$	18.4284	−	31.9189i	0.954187	−	1.65270i	0.217968	−	0.975956i	$-0.430057\pi$
$373$	18.4284	−	31.9189i	0.954187	−	1.65270i	0.736218	−	0.676744i	$-0.236610\pi$
$374$	−5.03987	−	8.72930i	−0.260605	−	0.451382i
$375$	−14.4008	−	24.9430i	−0.743656	−	1.28805i
$376$	−3.09110	+	5.35394i	−0.159411	+	0.276108i
$377$	6.30555			0.324752
$378$		0			0
$379$	−17.2907			−0.888164			−0.444082	−	0.895986i	$-0.646470\pi$
$379$	−17.2907			−0.888164			−0.444082	+	0.895986i	$0.646470\pi$
$380$	−1.97805	+	3.42609i	−0.101472	+	0.175755i
$381$	9.81761	+	17.0046i	0.502972	+	0.871172i
$382$	0.653195	+	1.13137i	0.0334203	+	0.0578857i
$383$	11.8112	−	20.4576i	0.603525	−	1.04534i	−0.388758	−	0.921340i	$-0.627096\pi$
$383$	11.8112	−	20.4576i	0.603525	−	1.04534i	0.992283	−	0.123996i	$-0.0395710\pi$
$384$	−20.3307			−1.03750
$385$		0			0
$386$	−7.29263			−0.371185
$387$	−10.6627	+	18.4683i	−0.542013	+	0.938794i
$388$	13.4693	+	23.3295i	0.683799	+	1.18437i
$389$	1.40881	+	2.44012i	0.0714293	+	0.123719i	0.899528	−	0.436863i	$-0.143911\pi$
$389$	1.40881	+	2.44012i	0.0714293	+	0.123719i	−0.828099	+	0.560582i	$0.810577\pi$
$390$	1.18846	−	2.05847i	0.0601798	−	0.104235i
$391$	51.8172			2.62051
$392$		0			0
$393$	47.2623			2.38407
$394$	0.0146235	−	0.0253286i	0.000736720	−	0.00127604i
$395$	−2.39602	−	4.15004i	−0.120557	−	0.208811i
$396$	−13.8147	−	23.9278i	−0.694216	−	1.20242i
$397$	−12.0006	+	20.7857i	−0.602293	+	1.04320i	0.390180	+	0.920739i	$0.372413\pi$
$397$	−12.0006	+	20.7857i	−0.602293	+	1.04320i	−0.992473	+	0.122464i	$0.960920\pi$
$398$	7.84649			0.393309
$399$		0			0
$400$	−2.56293			−0.128146
$401$	−16.6870	+	28.9027i	−0.833309	+	1.44333i	0.0620915	+	0.998070i	$0.480223\pi$
$401$	−16.6870	+	28.9027i	−0.833309	+	1.44333i	−0.895400	+	0.445262i	$0.853110\pi$
$402$	−4.95867	−	8.58867i	−0.247316	−	0.428364i
$403$	−0.656283	−	1.13672i	−0.0326918	−	0.0566238i
$404$	1.71798	−	2.97563i	0.0854727	−	0.148043i
$405$	19.1029			0.949230
$406$		0			0
$407$	−20.3247			−1.00746
$408$	−9.69657	+	16.7950i	−0.480052	+	0.831474i
$409$	14.2074	+	24.6079i	0.702511	+	1.21678i	0.967582	+	0.252556i	$0.0812712\pi$
$409$	14.2074	+	24.6079i	0.702511	+	1.21678i	−0.265071	+	0.964229i	$0.585395\pi$
$410$	−2.56016	−	4.43433i	−0.126437	−	0.218996i
$411$	7.63857	−	13.2304i	0.376783	−	0.652607i
$412$	32.3670			1.59461
$413$		0			0
$414$	−6.29630			−0.309446
$415$	5.18245	−	8.97628i	0.254397	−	0.440628i
$416$	−2.67967	−	4.64133i	−0.131382	−	0.227560i
$417$	22.1271	+	38.3253i	1.08357	+	1.87680i
$418$	0.721001	−	1.24881i	0.0352653	−	0.0610813i
$419$	5.95276			0.290812			0.145406	−	0.989372i	$-0.453551\pi$
$419$	5.95276			0.290812			0.145406	+	0.989372i	$0.453551\pi$
$420$		0			0
$421$	−2.95244			−0.143893			−0.0719465	−	0.997408i	$-0.522921\pi$
$421$	−2.95244			−0.143893			−0.0719465	+	0.997408i	$0.522921\pi$
$422$	−2.11744	+	3.66751i	−0.103075	+	0.178532i
$423$	7.89921	+	13.6818i	0.384073	+	0.665233i
$424$	−1.13508	−	1.96602i	−0.0551245	−	0.0954785i
$425$	−2.56088	+	4.43558i	−0.124221	+	0.215157i
$426$	4.62007			0.223843
$427$		0			0
$428$	−17.2537			−0.833987
$429$	9.77221	−	16.9260i	0.471807	−	0.817193i
$430$	2.20154	+	3.81318i	0.106168	+	0.183888i
$431$	−4.98517	−	8.63456i	−0.240127	−	0.415912i	0.720623	−	0.693327i	$-0.243856\pi$
$431$	−4.98517	−	8.63456i	−0.240127	−	0.415912i	−0.960750	+	0.277415i	$0.910522\pi$
$432$	0.361103	−	0.625449i	0.0173736	−	0.0300919i
$433$	−19.1090			−0.918319			−0.459159	−	0.888354i	$-0.651849\pi$
$433$	−19.1090			−0.918319			−0.459159	+	0.888354i	$0.651849\pi$
$434$		0			0
$435$	−19.5103			−0.935447
$436$	6.71173	−	11.6251i	0.321433	−	0.556739i
$437$	3.70647	+	6.41980i	0.177305	+	0.307101i
$438$	0.740459	+	1.28251i	0.0353805	+	0.0612809i
$439$	−3.65340	+	6.32788i	−0.174367	+	0.302013i	−0.939942	−	0.341334i	$-0.889121\pi$
$439$	−3.65340	+	6.32788i	−0.174367	+	0.302013i	0.765575	+	0.643347i	$0.222455\pi$
$440$	−11.6623			−0.555979
$441$		0			0
$442$	−3.30704			−0.157300
$443$	8.23193	−	14.2581i	0.391111	−	0.677423i	−0.601486	−	0.798884i	$-0.705424\pi$
$443$	8.23193	−	14.2581i	0.391111	−	0.677423i	0.992596	+	0.121460i	$0.0387577\pi$
$444$	9.56405	+	16.5654i	0.453890	+	0.786160i
$445$	6.91445	+	11.9762i	0.327777	+	0.567726i
$446$	−0.336279	+	0.582453i	−0.0159233	+	0.0275799i
$447$	21.3005			1.00748
$448$		0			0
$449$	−9.71849			−0.458644			−0.229322	−	0.973351i	$-0.573651\pi$
$449$	−9.71849			−0.458644			−0.229322	+	0.973351i	$0.573651\pi$
$450$	0.311172	−	0.538966i	0.0146688	−	0.0254071i
$451$	−21.0512	−	36.4617i	−0.991262	−	1.71692i
$452$	−0.250593	−	0.434040i	−0.0117869	−	0.0204155i
$453$	14.6467	−	25.3688i	0.688162	−	1.19193i
$454$	−5.78428			−0.271470
$455$		0			0
$456$	−2.77437			−0.129922
$457$	5.50079	−	9.52765i	0.257316	−	0.445685i	−0.708206	−	0.706006i	$-0.750495\pi$
$457$	5.50079	−	9.52765i	0.257316	−	0.445685i	0.965522	+	0.260321i	$0.0838285\pi$
$458$	2.53884	+	4.39741i	0.118632	+	0.205477i
$459$	−0.721630	−	1.24990i	−0.0336828	−	0.0583404i
$460$	14.6632	−	25.3974i	0.683676	−	1.18416i
$461$	−28.6779			−1.33567			−0.667833	−	0.744311i	$-0.732778\pi$
$461$	−28.6779			−1.33567			−0.667833	+	0.744311i	$0.732778\pi$
$462$		0			0
$463$	−33.7722			−1.56953			−0.784765	−	0.619794i	$-0.787216\pi$
$463$	−33.7722			−1.56953			−0.784765	+	0.619794i	$0.787216\pi$
$464$	−6.79167	+	11.7635i	−0.315295	+	0.546108i
$465$	2.03064	+	3.51716i	0.0941685	+	0.163105i
$466$	−1.29546	−	2.24380i	−0.0600109	−	0.103942i
$467$	8.42387	−	14.5906i	0.389810	−	0.675171i	−0.602614	−	0.798033i	$-0.705874\pi$
$467$	8.42387	−	14.5906i	0.389810	−	0.675171i	0.992424	+	0.122862i	$0.0392073\pi$
$468$	−9.06490			−0.419025
$469$		0			0
$470$	3.26193			0.150462
$471$	−5.19969	+	9.00612i	−0.239589	+	0.414980i
$472$	−3.28258	−	5.68560i	−0.151093	−	0.261701i
$473$	18.1024	+	31.3543i	0.832350	+	1.44167i
$474$	0.821934	−	1.42363i	0.0377527	−	0.0653896i
$475$	−0.732718			−0.0336194
$476$		0			0
$477$	−5.80134			−0.265625
$478$	1.59136	−	2.75631i	0.0727869	−	0.126071i
$479$	11.5225	+	19.9575i	0.526476	+	0.911882i	0.999524	+	0.0308461i	$0.00982016\pi$
$479$	11.5225	+	19.9575i	0.526476	+	0.911882i	−0.473049	+	0.881036i	$0.656847\pi$
$480$	8.29129	+	14.3609i	0.378444	+	0.655484i
$481$	−3.33414	+	5.77490i	−0.152024	+	0.263313i
$482$	−1.51044			−0.0687985
$483$		0			0
$484$	−25.8415			−1.17461
$485$	14.5287	−	25.1645i	0.659715	−	1.14266i
$486$	3.18630	+	5.51883i	0.144533	+	0.250339i
$487$	10.9734	+	19.0065i	0.497253	+	0.861267i	0.999995	−	0.00316956i	$-0.00100890\pi$
$487$	10.9734	+	19.0065i	0.497253	+	0.861267i	−0.502742	+	0.864436i	$0.667676\pi$
$488$	−6.49145	+	11.2435i	−0.293854	+	0.508970i
$489$	−21.9540			−0.992795
$490$		0			0
$491$	10.1883			0.459791			0.229896	−	0.973215i	$-0.426162\pi$
$491$	10.1883			0.459791			0.229896	+	0.973215i	$0.426162\pi$
$492$	−19.8118	+	34.3151i	−0.893187	+	1.54705i
$493$	13.5725	+	23.5083i	0.611275	+	1.05876i
$494$	−0.236552	−	0.409720i	−0.0106430	−	0.0184342i
$495$	−14.9013	+	25.8099i	−0.669766	+	1.16007i
$496$	2.82752			0.126959
$497$		0			0
$498$	3.55559			0.159330
$499$	−8.21501	+	14.2288i	−0.367754	+	0.636969i	−0.989214	−	0.146477i	$-0.953207\pi$
$499$	−8.21501	+	14.2288i	−0.367754	+	0.636969i	0.621460	+	0.783446i	$0.286540\pi$
$500$	11.3396	+	19.6408i	0.507124	+	0.878364i
$501$	25.8189	+	44.7197i	1.15351	+	1.99793i
$502$	1.78713	−	3.09541i	0.0797637	−	0.138155i
$503$	2.13595			0.0952373			0.0476186	−	0.998866i	$-0.484837\pi$
$503$	2.13595			0.0952373			0.0476186	+	0.998866i	$0.484837\pi$
$504$		0			0
$505$	−3.70622			−0.164925
$506$	−5.34474	+	9.25736i	−0.237603	+	0.411540i
$507$	12.6025	+	21.8282i	0.559697	+	0.969423i
$508$	−7.73067	−	13.3899i	−0.342993	−	0.594082i
$509$	12.1123	−	20.9792i	0.536869	−	0.929885i	−0.462201	−	0.886775i	$-0.652940\pi$
$509$	12.1123	−	20.9792i	0.536869	−	0.929885i	0.999070	−	0.0431099i	$-0.0137265\pi$
$510$	10.2325			0.453101
$511$		0			0
$512$	19.5252			0.862901
$513$	0.103236	−	0.178810i	0.00455799	−	0.00789466i
$514$	−3.25952	−	5.64565i	−0.143771	−	0.249019i
$515$	−17.4564	−	30.2354i	−0.769222	−	1.33233i
$516$	17.0367	−	29.5084i	0.749998	−	1.29903i
$517$	26.8216			1.17961
$518$		0			0
$519$	16.5400			0.726023
$520$	−1.91313	+	3.31365i	−0.0838965	+	0.145313i
$521$	3.78220	+	6.55097i	0.165701	+	0.287003i	0.936904	−	0.349586i	$-0.113678\pi$
$521$	3.78220	+	6.55097i	0.165701	+	0.287003i	−0.771203	+	0.636590i	$0.780345\pi$
$522$	−1.64919	−	2.85648i	−0.0721832	−	0.125025i
$523$	5.87203	−	10.1707i	0.256766	−	0.444732i	−0.708608	−	0.705603i	$-0.750676\pi$
$523$	5.87203	−	10.1707i	0.256766	−	0.444732i	0.965374	+	0.260871i	$0.0840097\pi$
$524$	−37.2157			−1.62577
$525$		0			0
$526$	2.64452			0.115307
$527$	2.82526	−	4.89349i	0.123070	−	0.213164i
$528$	21.0512	+	36.4617i	0.916135	+	1.58679i
$529$	−15.9759	−	27.6710i	−0.694603	−	1.20309i
$530$	−0.598908	+	1.03734i	−0.0260149	+	0.0450591i
$531$	−16.7771			−0.728063
$532$		0			0
$533$	−13.8133			−0.598320
$534$	−2.37194	+	4.10832i	−0.102644	+	0.177784i
$535$	9.30539	+	16.1174i	0.402307	+	0.696816i
$536$	7.98229	+	13.8257i	0.344782	+	0.597181i
$537$	−23.4359	+	40.5922i	−1.01133	+	1.75168i
$538$	−5.48348			−0.236410
$539$		0			0
$540$	−0.816827			−0.0351506
$541$	2.22196	−	3.84854i	0.0955293	−	0.165462i	−0.814300	−	0.580444i	$-0.802879\pi$
$541$	2.22196	−	3.84854i	0.0955293	−	0.165462i	0.909829	+	0.414982i	$0.136212\pi$
$542$	3.63938	+	6.30360i	0.156325	+	0.270763i
$543$	24.9908	+	43.2853i	1.07246	+	1.85755i
$544$	11.5358	−	19.9806i	0.494594	−	0.856662i
$545$	−14.4793			−0.620225
$546$		0			0
$547$	−8.15542			−0.348700			−0.174350	−	0.984684i	$-0.555782\pi$
$547$	−8.15542			−0.348700			−0.174350	+	0.984684i	$0.555782\pi$
$548$	−6.01483	+	10.4180i	−0.256941	+	0.445035i
$549$	16.5887	+	28.7324i	0.707988	+	1.22627i
$550$	−0.528290	−	0.915025i	−0.0225264	−	0.0390168i
$551$	−1.94168	+	3.36308i	−0.0827182	+	0.143272i
$552$	20.5663			0.875359
$553$		0			0
$554$	6.08201			0.258400
$555$	10.3163	−	17.8684i	0.437903	−	0.758471i
$556$	−17.4236	−	30.1785i	−0.738923	−	1.27985i
$557$	−2.61737	−	4.53341i	−0.110901	−	0.192087i	0.805233	−	0.592959i	$-0.202040\pi$
$557$	−2.61737	−	4.53341i	−0.110901	−	0.192087i	−0.916134	+	0.400872i	$0.868707\pi$
$558$	−0.343297	+	0.594607i	−0.0145329	+	0.0251717i
$559$	11.8784			0.502402
$560$		0			0
$561$	84.1376			3.55229
$562$	−4.27023	+	7.39626i	−0.180129	+	0.311993i
$563$	−12.6952	−	21.9888i	−0.535040	−	0.926716i	−0.999161	−	0.0409446i	$-0.986963\pi$
$563$	−12.6952	−	21.9888i	−0.535040	−	0.926716i	0.464122	−	0.885771i	$-0.346370\pi$
$564$	−12.6213	−	21.8607i	−0.531451	−	0.920501i
$565$	−0.270304	+	0.468180i	−0.0113718	+	0.0196965i
$566$	−0.164994			−0.00693521
$567$		0			0
$568$	−7.43722			−0.312059
$569$	3.59078	−	6.21941i	0.150533	−	0.260731i	−0.780890	−	0.624668i	$-0.785234\pi$
$569$	3.59078	−	6.21941i	0.150533	−	0.260731i	0.931424	+	0.363937i	$0.118568\pi$
$570$	0.731926	+	1.26773i	0.0306570	+	0.0530995i
$571$	−4.47094	−	7.74390i	−0.187103	−	0.324072i	0.757180	−	0.653206i	$-0.226577\pi$
$571$	−4.47094	−	7.74390i	−0.187103	−	0.324072i	−0.944283	+	0.329134i	$0.893243\pi$
$572$	−7.69492	+	13.3280i	−0.321741	+	0.557272i
$573$	−10.9047			−0.455550
$574$		0			0
$575$	5.43159			0.226513
$576$	8.79485	−	15.2331i	0.366452	−	0.634714i
$577$	−6.38221	−	11.0543i	−0.265695	−	0.460197i	0.702050	−	0.712127i	$-0.252268\pi$
$577$	−6.38221	−	11.0543i	−0.265695	−	0.460197i	−0.967745	+	0.251930i	$0.918935\pi$
$578$	−4.64169	−	8.03964i	−0.193069	−	0.334405i
$579$	30.4365	−	52.7176i	1.26490	−	2.19087i
$580$	15.3630			0.637913
$581$		0			0
$582$	9.96788			0.413182
$583$	−4.92459	+	8.52964i	−0.203956	+	0.353261i
$584$	−1.19196	−	2.06454i	−0.0493239	−	0.0854314i
$585$	4.88895	+	8.46792i	0.202133	+	0.350105i
$586$	3.68144	−	6.37644i	0.152079	−	0.263408i
$587$	24.2518			1.00098			0.500489	−	0.865743i	$-0.333153\pi$
$587$	24.2518			1.00098			0.500489	+	0.865743i	$0.333153\pi$
$588$		0			0
$589$	0.808361			0.0333079
$590$	−1.73200	+	2.99991i	−0.0713053	+	0.123504i
$591$	0.122065	+	0.211423i	0.00502109	+	0.00869678i
$592$	−7.18237	−	12.4402i	−0.295193	−	0.511290i
$593$	1.92547	−	3.33502i	0.0790698	−	0.136953i	−0.823779	−	0.566911i	$-0.808138\pi$
$593$	1.92547	−	3.33502i	0.0790698	−	0.136953i	0.902849	+	0.429958i	$0.141472\pi$
$594$	0.297733			0.0122161
$595$		0			0
$596$	−16.7726			−0.687033
$597$	−32.7481	+	56.7214i	−1.34029	+	2.32145i
$598$	1.75355	+	3.03723i	0.0717078	+	0.124202i
$599$	−18.6359	−	32.2782i	−0.761440	−	1.31885i	−0.942108	−	0.335309i	$-0.891159\pi$
$599$	−18.6359	−	32.2782i	−0.761440	−	1.31885i	0.180668	−	0.983544i	$-0.442174\pi$
$600$	−1.01642	+	1.76048i	−0.0414950	+	0.0718715i
$601$	−2.99633			−0.122223			−0.0611114	−	0.998131i	$-0.519464\pi$
$601$	−2.99633			−0.122223			−0.0611114	+	0.998131i	$0.519464\pi$
$602$		0			0
$603$	40.7970			1.66138
$604$	−11.5332	+	19.9762i	−0.469281	+	0.812818i
$605$	13.9371	+	24.1397i	0.566622	+	0.981418i
$606$	−0.635692	−	1.10105i	−0.0258232	−	0.0447271i
$607$	−12.6711	+	21.9471i	−0.514306	+	0.890803i	0.485557	+	0.874205i	$0.338617\pi$
$607$	−12.6711	+	21.9471i	−0.514306	+	0.890803i	−0.999862	+	0.0165982i	$0.994716\pi$
$608$	3.30062			0.133858
$609$		0			0
$610$	6.85021			0.277357
$611$	4.39993	−	7.62089i	0.178002	−	0.308308i
$612$	−19.5119	−	33.7956i	−0.788723	−	1.36611i
$613$	−5.61967	−	9.73356i	−0.226976	−	0.393135i	0.729934	−	0.683518i	$-0.239551\pi$
$613$	−5.61967	−	9.73356i	−0.226976	−	0.393135i	−0.956911	+	0.290383i	$0.906217\pi$
$614$	−0.928170	+	1.60764i	−0.0374579	+	0.0648790i
$615$	42.7403			1.72346
$616$		0			0
$617$	−16.1879			−0.651701			−0.325851	−	0.945421i	$-0.605651\pi$
$617$	−16.1879			−0.651701			−0.325851	+	0.945421i	$0.605651\pi$
$618$	5.98826	−	10.3720i	0.240883	−	0.417222i
$619$	−7.32638	−	12.6897i	−0.294472	−	0.510040i	0.680390	−	0.732850i	$-0.261810\pi$
$619$	−7.32638	−	12.6897i	−0.294472	−	0.510040i	−0.974862	+	0.222810i	$0.928477\pi$
$620$	−1.59898	−	2.76952i	−0.0642166	−	0.111226i
$621$	−0.765284	+	1.32551i	−0.0307098	+	0.0531909i
$622$	−0.0861539			−0.00345446
$623$		0			0
$624$	13.8133			0.552974
$625$	10.3998	−	18.0129i	0.415991	−	0.720517i
$626$	−2.96727	−	5.13947i	−0.118596	−	0.205414i
$627$	6.01834	+	10.4241i	0.240349	+	0.416297i
$628$	4.09438	−	7.09168i	0.163384	−	0.282989i
$629$	−28.7065			−1.14460
$630$		0			0
$631$	−23.3309			−0.928790			−0.464395	−	0.885628i	$-0.653728\pi$
$631$	−23.3309			−0.928790			−0.464395	+	0.885628i	$0.653728\pi$
$632$	−1.32312	+	2.29171i	−0.0526309	+	0.0911594i
$633$	−17.6747	−	30.6135i	−0.702506	−	1.21678i
$634$	4.44567	+	7.70013i	0.176560	+	0.305811i
$635$	−8.33874	+	14.4431i	−0.330913	+	0.573158i
$636$	9.26933			0.367553
$637$		0			0
$638$	−5.59980			−0.221698
$639$	−9.50279	+	16.4593i	−0.375925	+	0.651120i
$640$	−8.63411	−	14.9547i	−0.341293	−	0.591137i
$641$	−7.59159	−	13.1490i	−0.299850	−	0.519355i	0.676252	−	0.736671i	$-0.263603\pi$
$641$	−7.59159	−	13.1490i	−0.299850	−	0.519355i	−0.976101	+	0.217316i	$0.930270\pi$
$642$	−3.19213	+	5.52893i	−0.125983	+	0.218209i
$643$	−31.7842			−1.25345			−0.626723	−	0.779242i	$-0.715604\pi$
$643$	−31.7842			−1.25345			−0.626723	+	0.779242i	$0.715604\pi$
$644$		0			0
$645$	−36.7534			−1.44717
$646$	1.01834	−	1.76382i	0.0400661	−	0.0693965i
$647$	6.68836	+	11.5846i	0.262947	+	0.455437i	0.967024	−	0.254687i	$-0.0819724\pi$
$647$	6.68836	+	11.5846i	0.262947	+	0.455437i	−0.704077	+	0.710124i	$0.748639\pi$
$648$	−5.27445	−	9.13561i	−0.207200	−	0.358881i
$649$	−14.2416	+	24.6671i	−0.559030	+	0.968268i
$650$	−0.346651			−0.0135968
$651$		0			0
$652$	17.2872			0.677020
$653$	13.6852	−	23.7035i	0.535544	−	0.927590i	−0.463592	−	0.886049i	$-0.653440\pi$
$653$	13.6852	−	23.7035i	0.535544	−	0.927590i	0.999137	−	0.0415416i	$-0.0132269\pi$
$654$	−2.48349	−	4.30154i	−0.0971123	−	0.168203i
$655$	20.0715	+	34.7648i	0.784257	+	1.35837i
$656$	14.8782	−	25.7698i	0.580897	−	1.00614i
$657$	−6.09206			−0.237674
$658$		0			0
$659$	47.6905			1.85776			0.928879	−	0.370383i	$-0.120774\pi$
$659$	47.6905			1.85776			0.928879	+	0.370383i	$0.120774\pi$
$660$	23.8092	−	41.2388i	0.926773	−	1.60522i
$661$	−8.41086	−	14.5680i	−0.327144	−	0.566631i	0.654800	−	0.755803i	$-0.272753\pi$
$661$	−8.41086	−	14.5680i	−0.327144	−	0.566631i	−0.981944	+	0.189172i	$0.939420\pi$
$662$	4.12013	+	7.13628i	0.160134	+	0.277360i
$663$	13.8023	−	23.9062i	0.536036	−	0.928441i
$664$	−5.72366			−0.222121
$665$		0			0
$666$	3.48813			0.135162
$667$	14.3935	−	24.9303i	0.557320	−	0.965307i
$668$	−20.3306	−	35.2136i	−0.786614	−	1.36246i
$669$	−2.80699	−	4.86185i	−0.108525	−	0.187970i
$670$	4.21172	−	7.29492i	0.162713	−	0.281827i
$671$	56.3266			2.17446
$672$		0			0
$673$	14.1611			0.545870			0.272935	−	0.962032i	$-0.412006\pi$
$673$	14.1611			0.545870			0.272935	+	0.962032i	$0.412006\pi$
$674$	−0.0142980	+	0.0247648i	−0.000550737	+	0.000953905i
$675$	−0.0756429	−	0.131017i	−0.00291150	−	0.00504286i
$676$	−9.92357	−	17.1881i	−0.381676	−	0.661082i
$677$	−2.52657	+	4.37615i	−0.0971040	+	0.168189i	−0.910485	−	0.413543i	$-0.864291\pi$
$677$	−2.52657	+	4.37615i	−0.0971040	+	0.168189i	0.813381	+	0.581732i	$0.197625\pi$
$678$	−0.185450			−0.00712218
$679$		0			0
$680$	−16.4719			−0.631667
$681$	24.1413	−	41.8139i	0.925095	−	1.60231i
$682$	0.582829	+	1.00949i	0.0223177	+	0.0386553i
$683$	−10.1679	−	17.6114i	−0.389065	−	0.673881i	0.603259	−	0.797545i	$-0.293869\pi$
$683$	−10.1679	−	17.6114i	−0.389065	−	0.673881i	−0.992324	+	0.123665i	$0.960535\pi$
$684$	2.79137	−	4.83479i	0.106731	−	0.184863i
$685$	12.9759			0.495783
$686$		0			0
$687$	−42.3845			−1.61707
$688$	−12.7941	+	22.1601i	−0.487772	+	0.844846i
$689$	1.61570	+	2.79847i	0.0615532	+	0.106613i
$690$	−5.42573	−	9.39763i	−0.206554	−	0.357762i
$691$	−11.5570	+	20.0174i	−0.439650	+	0.761496i	−0.997662	−	0.0683367i	$-0.978231\pi$
$691$	−11.5570	+	20.0174i	−0.439650	+	0.761496i	0.558012	+	0.829833i	$0.311564\pi$
$692$	−13.0240			−0.495100
$693$		0			0
$694$	−0.312850			−0.0118756
$695$	−18.7940	+	32.5522i	−0.712898	+	1.23478i
$696$	5.38693	+	9.33044i	0.204191	+	0.353670i
$697$	−29.7327	−	51.4985i	−1.12621	−	1.95065i
$698$	−1.15735	+	2.00460i	−0.0438065	+	0.0758751i
$699$	21.6269			0.818005
$700$		0			0
$701$	−50.1400			−1.89376			−0.946882	−	0.321583i	$-0.895785\pi$
$701$	−50.1400			−1.89376			−0.946882	+	0.321583i	$0.895785\pi$
$702$	0.0488414	−	0.0845957i	0.00184340	−	0.00319286i
$703$	−2.05337	−	3.55655i	−0.0774444	−	0.134138i
$704$	−14.9314	−	25.8619i	−0.562748	−	0.974707i
$705$	−13.6140	+	23.5802i	−0.512733	+	0.888080i
$706$	−2.55182			−0.0960391
$707$		0			0
$708$	26.8062			1.00744
$709$	1.90369	−	3.29729i	0.0714947	−	0.123832i	−0.828062	−	0.560637i	$-0.810556\pi$
$709$	1.90369	−	3.29729i	0.0714947	−	0.123832i	0.899557	+	0.436804i	$0.143890\pi$
$710$	1.96206	+	3.39839i	0.0736349	+	0.127539i
$711$	3.38119	+	5.85640i	0.126805	+	0.219632i
$712$	3.81826	−	6.61343i	0.143095	−	0.247849i
$713$	−5.99233			−0.224415
$714$		0			0
$715$	16.6004			0.620818
$716$	18.4541	−	31.9635i	0.689663	−	1.19453i
$717$	13.2834	+	23.0075i	0.496077	+	0.859230i
$718$	−1.29448	−	2.24211i	−0.0483097	−	0.0836748i
$719$	−5.35088	+	9.26799i	−0.199554	+	0.345638i	−0.948384	−	0.317125i	$-0.897283\pi$
$719$	−5.35088	+	9.26799i	−0.199554	+	0.345638i	0.748830	+	0.662762i	$0.230616\pi$
$720$	−21.0635			−0.784989
$721$		0			0
$722$	0.291367			0.0108436
$723$	6.30397	−	10.9188i	0.234447	−	0.406074i
$724$	−19.6785	−	34.0841i	−0.731344	−	1.26673i
$725$	1.42270	+	2.46419i	0.0528378	+	0.0915177i
$726$	−4.78098	+	8.28089i	−0.177439	+	0.307333i
$727$	22.1589			0.821829			0.410914	−	0.911674i	$-0.365210\pi$
$727$	22.1589			0.821829			0.410914	+	0.911674i	$0.365210\pi$
$728$		0			0
$729$	−25.4509			−0.942625
$730$	−0.628920	+	1.08932i	−0.0232774	+	0.0403176i
$731$	25.5679	+	44.2848i	0.945661	+	1.63793i
$732$	−26.5052	−	45.9084i	−0.979662	−	1.69682i
$733$	18.6709	−	32.3390i	0.689627	−	1.19447i	−0.282332	−	0.959317i	$-0.591108\pi$
$733$	18.6709	−	32.3390i	0.689627	−	1.19447i	0.971959	−	0.235152i	$-0.0755587\pi$
$734$	4.09791			0.151257
$735$		0			0
$736$	−24.4673			−0.901877
$737$	34.6313	−	59.9832i	1.27566	−	2.20951i
$738$	3.61281	+	6.25758i	0.132989	+	0.230345i
$739$	8.02690	+	13.9030i	0.295274	+	0.511430i	0.975049	−	0.221991i	$-0.0712557\pi$
$739$	8.02690	+	13.9030i	0.295274	+	0.511430i	−0.679774	+	0.733421i	$0.737922\pi$
$740$	−8.12337	+	14.0701i	−0.298621	+	0.517227i
$741$	3.94909			0.145074
$742$		0			0
$743$	24.6993			0.906131			0.453065	−	0.891477i	$-0.350330\pi$
$743$	24.6993			0.906131			0.453065	+	0.891477i	$0.350330\pi$
$744$	1.12135	−	1.94223i	0.0411106	−	0.0712056i
$745$	9.04594	+	15.6680i	0.331418	+	0.574032i
$746$	5.36943	+	9.30012i	0.196589	+	0.340502i
$747$	−7.31331	+	12.6670i	−0.267580	+	0.463462i
$748$	−66.2524			−2.42243
$749$		0			0
$750$	8.39185			0.306427
$751$	−13.0960	+	22.6830i	−0.477881	+	0.827714i	−0.999679	−	0.0253551i	$-0.991928\pi$
$751$	−13.0960	+	22.6830i	−0.477881	+	0.827714i	0.521797	+	0.853069i	$0.325262\pi$
$752$	9.47827	+	16.4168i	0.345637	+	0.598661i
$753$	14.9176	+	25.8380i	0.543626	+	0.941589i
$754$	−0.918614	+	1.59109i	−0.0334540	+	0.0579439i
$755$	24.8808			0.905505
$756$		0			0
$757$	23.2718			0.845826			0.422913	−	0.906170i	$-0.361008\pi$
$757$	23.2718			0.845826			0.422913	+	0.906170i	$0.361008\pi$
$758$	2.51897	−	4.36299i	0.0914931	−	0.158471i
$759$	−44.6136	−	77.2731i	−1.61937	−	2.80483i
$760$	−1.17823	−	2.04075i	−0.0427388	−	0.0740258i
$761$	17.2717	−	29.9155i	0.626099	−	1.08443i	−0.362229	−	0.932089i	$-0.617984\pi$
$761$	17.2717	−	29.9155i	0.626099	−	1.08443i	0.988327	−	0.152346i	$-0.0486827\pi$
$762$	−5.72105			−0.207252
$763$		0			0
$764$	8.58668			0.310655
$765$	−21.0467	+	36.4539i	−0.760944	+	1.31799i
$766$	3.44140	+	5.96068i	0.124343	+	0.215368i
$767$	4.67248	+	8.09298i	0.168714	+	0.292221i
$768$	−11.7134	+	20.2882i	−0.422671	+	0.732088i
$769$	−11.1106			−0.400659			−0.200329	−	0.979729i	$-0.564201\pi$
$769$	−11.1106			−0.400659			−0.200329	+	0.979729i	$0.564201\pi$
$770$		0			0
$771$	54.4157			1.95974
$772$	−23.9666	+	41.5114i	−0.862577	+	1.49403i
$773$	4.15207	+	7.19160i	0.149340	+	0.258664i	0.930984	−	0.365061i	$-0.118952\pi$
$773$	4.15207	+	7.19160i	0.149340	+	0.258664i	−0.781644	+	0.623725i	$0.785619\pi$
$774$	−3.10674	−	5.38104i	−0.111670	−	0.193417i
$775$	0.296150	−	0.512947i	0.0106380	−	0.0184256i
$776$	−16.0459			−0.576015
$777$		0			0
$778$	−0.820959			−0.0294328
$779$	4.25355	−	7.36736i	0.152399	−	0.263963i
$780$	−7.81152	−	13.5300i	−0.279697	−	0.484450i
$781$	16.1333	+	27.9436i	0.577294	+	0.999902i
$782$	−7.54891	+	13.0751i	−0.269948	+	0.467564i
$783$	−0.801804			−0.0286542
$784$		0			0
$785$	−8.83286			−0.315258
$786$	−6.88533	+	11.9257i	−0.245592	+	0.425377i
$787$	−8.30955	−	14.3926i	−0.296203	−	0.513039i	0.679061	−	0.734082i	$-0.262387\pi$
$787$	−8.30955	−	14.3926i	−0.296203	−	0.513039i	−0.975264	+	0.221043i	$0.929054\pi$
$788$	−0.0961176	−	0.166481i	−0.00342405	−	0.00593063i
$789$	−11.0372	+	19.1169i	−0.392934	+	0.680581i
$790$	1.39624			0.0496761
$791$		0			0
$792$	16.4575			0.584791
$793$	9.24004	−	16.0042i	0.328123	−	0.568326i
$794$	−3.49658	−	6.05625i	−0.124089	−	0.214928i
$795$	−4.99921	−	8.65888i	−0.177304	−	0.307099i
$796$	25.7868	−	44.6641i	0.913990	−	1.58308i
$797$	−24.5479			−0.869532			−0.434766	−	0.900543i	$-0.643169\pi$
$797$	−24.5479			−0.869532			−0.434766	+	0.900543i	$0.643169\pi$
$798$		0			0
$799$	37.8828			1.34020
$800$	1.20921	−	2.09441i	0.0427521	−	0.0740487i
$801$	−9.75745	−	16.9004i	−0.344763	−	0.597146i
$802$	−4.86204	−	8.42130i	−0.171684	−	0.297366i
$803$	−5.17137	+	8.95707i	−0.182494	+	0.316088i
$804$	−65.1850			−2.29890
$805$		0			0
$806$	0.382438			0.0134708
$807$	22.8859	−	39.6395i	0.805621	−	1.39538i
$808$	1.02331	+	1.77243i	0.0360001	+	0.0623539i
$809$	1.99514	+	3.45569i	0.0701455	+	0.121496i	0.898965	−	0.438021i	$-0.144320\pi$
$809$	1.99514	+	3.45569i	0.0701455	+	0.121496i	−0.828819	+	0.559516i	$0.810987\pi$
$810$	−2.78297	+	4.82025i	−0.0977837	+	0.169366i
$811$	−41.1357			−1.44447			−0.722235	−	0.691648i	$-0.756885\pi$
$811$	−41.1357			−1.44447			−0.722235	+	0.691648i	$0.756885\pi$
$812$		0			0
$813$	−60.7574			−2.13085
$814$	2.96097	−	5.12854i	0.103782	−	0.179755i
$815$	−9.32349	−	16.1488i	−0.326588	−	0.565666i
$816$	29.7327	+	51.4985i	1.04085	+	1.80281i
$817$	−3.65773	+	6.33537i	−0.127968	+	0.221646i
$818$	−8.27914			−0.289473
$819$		0			0
$820$	−33.6550			−1.17528
$821$	1.21907	−	2.11149i	0.0425459	−	0.0736916i	−0.843968	−	0.536393i	$-0.819786\pi$
$821$	1.21907	−	2.11149i	0.0425459	−	0.0736916i	0.886514	+	0.462701i	$0.153120\pi$
$822$	2.22563	+	3.85490i	0.0776276	+	0.134455i
$823$	−17.9009	−	31.0052i	−0.623985	−	1.08077i	−0.988736	−	0.149669i	$-0.952179\pi$
$823$	−17.9009	−	31.0052i	−0.623985	−	1.08077i	0.364751	−	0.931105i	$-0.381154\pi$
$824$	−9.63969	+	16.6964i	−0.335814	+	0.581648i
$825$	8.81949			0.307055
$826$		0			0
$827$	3.66665			0.127502			0.0637510	−	0.997966i	$-0.479694\pi$
$827$	3.66665			0.127502			0.0637510	+	0.997966i	$0.479694\pi$
$828$	−20.6922	+	35.8400i	−0.719105	+	1.24553i
$829$	24.2953	+	42.0807i	0.843811	+	1.46152i	0.886649	+	0.462442i	$0.153027\pi$
$829$	24.2953	+	42.0807i	0.843811	+	1.46152i	−0.0428380	+	0.999082i	$0.513640\pi$
$830$	1.51000	+	2.61539i	0.0524127	+	0.0907815i
$831$	−25.3839	+	43.9662i	−0.880557	+	1.52517i
$832$	−9.79762			−0.339671
$833$		0			0
$834$	−12.8942			−0.446491
$835$	−21.9297	+	37.9834i	−0.758909	+	1.31447i
$836$	−4.73902	−	8.20822i	−0.163902	−	0.283887i
$837$	0.0834520	+	0.144543i	0.00288452	+	0.00499614i
$838$	−0.867219	+	1.50207i	−0.0299576	+	0.0518881i
$839$	9.11600			0.314719			0.157360	−	0.987541i	$-0.449702\pi$
$839$	9.11600			0.314719			0.157360	+	0.987541i	$0.449702\pi$
$840$		0			0
$841$	−13.9196			−0.479985
$842$	0.430122	−	0.744992i	0.0148230	−	0.0256741i
$843$	−35.6445	−	61.7381i	−1.22766	−	2.12637i
$844$	13.9176	+	24.1059i	0.479063	+	0.829761i
$845$	−10.7041	+	18.5401i	−0.368233	+	0.637798i
$846$	−4.60314			−0.158259
$847$		0			0
$848$	−6.96104			−0.239043
$849$	0.688618	−	1.19272i	0.0236333	−	0.0409341i
$850$	−0.746157	−	1.29238i	−0.0255930	−	0.0443283i
$851$	15.2215	+	26.3645i	0.521788	+	0.903762i
$852$	15.1835	−	26.2985i	0.520177	−	0.900973i
$853$	1.01631			0.0347979			0.0173989	−	0.999849i	$-0.494461\pi$
$853$	1.01631			0.0347979			0.0173989	+	0.999849i	$0.494461\pi$
$854$		0			0
$855$	−6.02185			−0.205943
$856$	5.13857	−	8.90027i	0.175633	−	0.304205i
$857$	−7.94256	−	13.7569i	−0.271313	−	0.469928i	0.697885	−	0.716209i	$-0.254124\pi$
$857$	−7.94256	−	13.7569i	−0.271313	−	0.469928i	−0.969198	+	0.246282i	$0.920791\pi$
$858$	2.84730	+	4.93167i	0.0972052	+	0.168364i
$859$	−2.86206	+	4.95723i	−0.0976522	+	0.169139i	−0.910712	−	0.413041i	$-0.864467\pi$
$859$	−2.86206	+	4.95723i	−0.0976522	+	0.169139i	0.813060	+	0.582180i	$0.197800\pi$
$860$	28.9407			0.986871
$861$		0			0
$862$	2.90503			0.0989456
$863$	−6.94749	+	12.0334i	−0.236495	+	0.409622i	−0.959706	−	0.281005i	$-0.909332\pi$
$863$	−6.94749	+	12.0334i	−0.236495	+	0.409622i	0.723211	+	0.690627i	$0.242665\pi$
$864$	0.340743	+	0.590184i	0.0115923	+	0.0200785i
$865$	7.02423	+	12.1663i	0.238831	+	0.413667i
$866$	2.78386	−	4.82179i	0.0945995	−	0.163851i
$867$	77.4902			2.63171
$868$		0			0
$869$	11.4808			0.389459
$870$	2.84233	−	4.92305i	0.0963639	−	0.166907i
$871$	−11.3621	−	19.6798i	−0.384991	−	0.666824i
$872$	3.99784	+	6.92446i	0.135384	+	0.234492i
$873$	−20.5024	+	35.5113i	−0.693903	+	1.20187i
$874$	−2.15989			−0.0730593
$875$		0			0
$876$	9.73383			0.328876
$877$	20.0105	−	34.6592i	0.675707	−	1.17036i	−0.300555	−	0.953765i	$-0.597172\pi$
$877$	20.0105	−	34.6592i	0.675707	−	1.17036i	0.976262	−	0.216594i	$-0.0694948\pi$
$878$	−1.06448	−	1.84374i	−0.0359245	−	0.0622230i
$879$	30.7297	+	53.2254i	1.03649	+	1.79525i
$880$	−17.8801	+	30.9693i	−0.602740	+	1.04398i
$881$	−8.38440			−0.282478			−0.141239	−	0.989976i	$-0.545109\pi$
$881$	−8.38440			−0.282478			−0.141239	+	0.989976i	$0.545109\pi$
$882$		0			0
$883$	−20.0109			−0.673421			−0.336711	−	0.941608i	$-0.609314\pi$
$883$	−20.0109			−0.673421			−0.336711	+	0.941608i	$0.609314\pi$
$884$	−10.8683	+	18.8245i	−0.365541	+	0.633135i
$885$	−14.4574	−	25.0409i	−0.485979	−	0.841740i
$886$	2.39851	+	4.15434i	0.0805795	+	0.139568i
$887$	−14.5790	+	25.2516i	−0.489516	+	0.847867i	−0.999927	−	0.0120638i	$-0.996160\pi$
$887$	−14.5790	+	25.2516i	−0.489516	+	0.847867i	0.510411	+	0.859931i	$0.329493\pi$
$888$	−11.3936			−0.382346
$889$		0			0
$890$	−4.02929			−0.135062
$891$	−22.8833	+	39.6351i	−0.766620	+	1.32782i
$892$	2.21031	+	3.82836i	0.0740065	+	0.128183i
$893$	2.70975	+	4.69343i	0.0906783	+	0.157059i
$894$	−3.10313	+	5.37477i	−0.103784	+	0.179759i
$895$	−39.8113			−1.33074
$896$		0			0
$897$	−29.2744			−0.977444
$898$	1.41582	−	2.45228i	0.0472466	−	0.0818336i
$899$	−1.56957	−	2.71858i	−0.0523482	−	0.0906698i
$900$	−2.04528	−	3.54254i	−0.0681761	−	0.118085i
$901$	−6.95549	+	12.0473i	−0.231721	+	0.401352i
$902$	12.2672			0.408454
$903$		0			0
$904$	0.298531			0.00992900
$905$	−21.2263	+	36.7650i	−0.705586	+	1.22211i
$906$	4.26757	+	7.39164i	0.141780	+	0.245571i
$907$	−25.3305	−	43.8737i	−0.841086	−	1.45680i	−0.888977	−	0.457951i	$-0.848583\pi$
$907$	−25.3305	−	43.8737i	−0.841086	−	1.45680i	0.0478915	−	0.998853i	$-0.484750\pi$
$908$	−19.0095	+	32.9255i	−0.630854	+	1.09267i
$909$	5.23010			0.173471
$910$		0			0
$911$	−28.9746			−0.959970			−0.479985	−	0.877277i	$-0.659358\pi$
$911$	−28.9746			−0.959970			−0.479985	+	0.877277i	$0.659358\pi$
$912$	−4.25355	+	7.36736i	−0.140849	+	0.243958i
$913$	12.4161	+	21.5053i	0.410913	+	0.711722i
$914$	1.60275	+	2.77604i	0.0530142	+	0.0918233i
$915$	−28.5900	+	49.5194i	−0.945157	+	1.63706i
$916$	33.3748			1.10273
$917$		0			0
$918$	0.420518			0.0138792
$919$	−25.0947	+	43.4653i	−0.827797	+	1.43379i	0.0719655	+	0.997407i	$0.477073\pi$
$919$	−25.0947	+	43.4653i	−0.827797	+	1.43379i	−0.899763	+	0.436380i	$0.856260\pi$
$920$	8.73414	+	15.1280i	0.287956	+	0.498754i
$921$	−7.74762	−	13.4193i	−0.255293	−	0.442180i
$922$	4.17790	−	7.23634i	0.137592	−	0.238316i
$923$	10.5863			0.348451
$924$		0			0
$925$	−3.00908			−0.0989381
$926$	4.92006	−	8.52179i	0.161683	−	0.280043i
$927$	24.6339	+	42.6672i	0.809084	+	1.40137i
$928$	−6.40873	−	11.1003i	−0.210377	−	0.364384i
$929$	16.9550	−	29.3670i	0.556277	−	0.963500i	−0.441526	−	0.897248i	$-0.645563\pi$
$929$	16.9550	−	29.3670i	0.556277	−	0.963500i	0.997803	−	0.0662515i	$-0.0211040\pi$
$930$	−1.18332			−0.0388026
$931$		0			0
$932$	−17.0297			−0.557825
$933$	0.359572	−	0.622797i	0.0117719	−	0.0203895i
$934$	2.45444	+	4.25121i	0.0803116	+	0.139104i
$935$	35.7318	+	61.8892i	1.16855	+	2.02399i
$936$	2.69975	−	4.67611i	0.0882442	−	0.152843i
$937$	17.4372			0.569648			0.284824	−	0.958580i	$-0.408065\pi$
$937$	17.4372			0.569648			0.284824	+	0.958580i	$0.408065\pi$
$938$		0			0
$939$	49.5369			1.61657
$940$	10.7201	−	18.5677i	0.349650	−	0.605612i
$941$	0.299182	+	0.518199i	0.00975306	+	0.0168928i	0.870861	−	0.491530i	$-0.163562\pi$
$941$	0.299182	+	0.518199i	0.00975306	+	0.0168928i	−0.861108	+	0.508423i	$0.830229\pi$
$942$	−1.51502	−	2.62409i	−0.0493619	−	0.0854973i
$943$	−31.5313	+	54.6138i	−1.02680	+	1.77847i
$944$	−20.1308			−0.655203
$945$		0			0
$946$	−10.5489			−0.342974
$947$	−16.6568	+	28.8505i	−0.541274	+	0.937514i	0.457557	+	0.889180i	$0.348724\pi$
$947$	−16.6568	+	28.8505i	−0.541274	+	0.937514i	−0.998831	+	0.0483337i	$0.984609\pi$
$948$	−5.40243	−	9.35729i	−0.175463	−	0.303911i
$949$	1.69666	+	2.93871i	0.0550761	+	0.0953945i
$950$	0.106745	−	0.184887i	0.00346326	−	0.00599854i
$951$	−74.2179			−2.40668
$952$		0			0
$953$	8.41792			0.272683			0.136342	−	0.990662i	$-0.456466\pi$
$953$	8.41792			0.272683			0.136342	+	0.990662i	$0.456466\pi$
$954$	0.845160	−	1.46386i	0.0273631	−	0.0473942i
$955$	−4.63104	−	8.02119i	−0.149857	−	0.259560i
$956$	−10.4597	−	18.1168i	−0.338291	−	0.585938i
$957$	23.3713	−	40.4803i	0.755488	−	1.30854i
$958$	−6.71454			−0.216937
$959$		0			0
$960$	30.3153			0.978421
$961$	15.1733	−	26.2809i	0.489461	−	0.847771i
$962$	−0.971458	−	1.68261i	−0.0313211	−	0.0542497i
$963$	−13.1315	−	22.7444i	−0.423155	−	0.732927i
$964$	−4.96393	+	8.59777i	−0.159877	+	0.276916i
$965$	51.7034			1.66439
$966$		0			0
$967$	−17.5459			−0.564237			−0.282118	−	0.959380i	$-0.591037\pi$
$967$	−17.5459			−0.564237			−0.282118	+	0.959380i	$0.591037\pi$
$968$	7.69624	−	13.3303i	0.247367	−	0.428452i
$969$	8.50030	+	14.7230i	0.273069	+	0.472970i
$970$	4.23319	+	7.33209i	0.135919	+	0.235419i
$971$	−4.93633	+	8.54998i	−0.158414	+	0.274382i	−0.934297	−	0.356495i	$-0.883972\pi$
$971$	−4.93633	+	8.54998i	−0.158414	+	0.274382i	0.775883	+	0.630877i	$0.217305\pi$
$972$	41.8860			1.34349
$973$		0			0
$974$	−6.39458			−0.204895
$975$	1.44678	−	2.50590i	0.0463342	−	0.0802532i
$976$	19.9048	+	34.4761i	0.637137	+	1.10355i
$977$	7.48203	+	12.9593i	0.239371	+	0.414603i	0.960534	−	0.278162i	$-0.0897253\pi$
$977$	7.48203	+	12.9593i	0.239371	+	0.414603i	−0.721163	+	0.692766i	$0.756392\pi$
$978$	3.19834	−	5.53968i	0.102272	−	0.177140i
$979$	−33.1312			−1.05888
$980$		0			0
$981$	20.4327			0.652366
$982$	−1.48427	+	2.57082i	−0.0473648	+	0.0820383i
$983$	−3.29055	−	5.69941i	−0.104952	−	0.181783i	0.808766	−	0.588130i	$-0.200136\pi$
$983$	−3.29055	−	5.69941i	−0.104952	−	0.181783i	−0.913719	+	0.406347i	$0.866802\pi$
$984$	−11.8009	−	20.4398i	−0.376200	−	0.651597i
$985$	−0.103678	+	0.179575i	−0.00330345	+	0.00572175i
$986$	−7.90916			−0.251879
$987$		0			0
$988$	−3.10963			−0.0989305
$989$	27.1145	−	46.9637i	0.862191	−	1.49336i
$990$	−4.34176	−	7.52015i	−0.137990	−	0.239006i
$991$	−7.56502	−	13.1030i	−0.240311	−	0.416230i	0.720492	−	0.693463i	$-0.243916\pi$
$991$	−7.56502	−	13.1030i	−0.240311	−	0.416230i	−0.960803	+	0.277233i	$0.910583\pi$
$992$	−1.33404	+	2.31063i	−0.0423560	+	0.0733627i
$993$	−68.7832			−2.18277
$994$		0			0
$995$	−55.6303			−1.76360
$996$	11.6851	−	20.2392i	0.370258	−	0.641305i
$997$	−14.2273	−	24.6423i	−0.450582	−	0.780430i	0.547840	−	0.836583i	$-0.315450\pi$
$997$	−14.2273	−	24.6423i	−0.450582	−	0.780430i	−0.998422	+	0.0561523i	$0.982117\pi$
$998$	−2.39358	−	4.14580i	−0.0757675	−	0.131233i
$999$	0.423964	−	0.734328i	0.0134136	−	0.0232331i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	931.2.f.o.324.2		8
7.2	even	3		931.2.a.l.1.3	✓	4
7.3	odd	6		931.2.f.n.704.2		8
7.4	even	3	inner	931.2.f.o.704.2		8
7.5	odd	6		931.2.a.m.1.3	yes	4
7.6	odd	2		931.2.f.n.324.2		8
21.2	odd	6		8379.2.a.bv.1.2		4
21.5	even	6		8379.2.a.bu.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
931.2.a.l.1.3	✓	4	7.2	even	3
931.2.a.m.1.3	yes	4	7.5	odd	6
931.2.f.n.324.2		8	7.6	odd	2
931.2.f.n.704.2		8	7.3	odd	6
931.2.f.o.324.2		8	1.1	even	1	trivial
931.2.f.o.704.2		8	7.4	even	3	inner
8379.2.a.bu.1.2		4	21.5	even	6
8379.2.a.bv.1.2		4	21.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 931 = 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	931.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.145683 + 0.252331i) q^{2} +(-1.21605 - 2.10626i) q^{3} +(0.957553 + 1.65853i) q^{4} +(1.03287 - 1.78898i) q^{5} +0.708633 q^{6} -1.14073 q^{8} +(-1.45755 + 2.52456i) q^{9} +(0.300944 + 0.521251i) q^{10} +(2.47455 + 4.28604i) q^{11} +(2.32886 - 4.03371i) q^{12} +1.62374 q^{13} -5.02408 q^{15} +(-1.74892 + 3.02922i) q^{16} +(3.49505 + 6.05360i) q^{17} +(-0.424683 - 0.735572i) q^{18} +(-0.500000 + 0.866025i) q^{19} +3.95611 q^{20} -1.44200 q^{22} +(3.70647 - 6.41980i) q^{23} +(1.38719 + 2.40268i) q^{24} +(0.366359 + 0.634552i) q^{25} +(-0.236552 + 0.409720i) q^{26} -0.206472 q^{27} +3.88335 q^{29} +(0.731926 - 1.26773i) q^{30} +(-0.404180 - 0.700061i) q^{31} +(-1.65031 - 2.85842i) q^{32} +(6.01834 - 10.4241i) q^{33} -2.03668 q^{34} -5.58273 q^{36} +(-2.05337 + 3.55655i) q^{37} +(-0.145683 - 0.252331i) q^{38} +(-1.97455 - 3.42001i) q^{39} +(-1.17823 + 2.04075i) q^{40} -8.50709 q^{41} +7.31545 q^{43} +(-4.73902 + 8.20822i) q^{44} +(3.01093 + 5.21508i) q^{45} +(1.07994 + 1.87052i) q^{46} +(2.70975 - 4.69343i) q^{47} +8.50709 q^{48} -0.213490 q^{50} +(8.50030 - 14.7230i) q^{51} +(1.55482 + 2.69302i) q^{52} +(0.995049 + 1.72347i) q^{53} +(0.0300796 - 0.0520994i) q^{54} +10.2235 q^{55} +2.43210 q^{57} +(-0.565740 + 0.979891i) q^{58} +(2.87761 + 4.98417i) q^{59} +(-4.81083 - 8.33259i) q^{60} +(5.69060 - 9.85640i) q^{61} +0.235529 q^{62} -6.03399 q^{64} +(1.67711 - 2.90484i) q^{65} +(1.75355 + 3.03723i) q^{66} +(-6.99751 - 12.1200i) q^{67} +(-6.69339 + 11.5933i) q^{68} -18.0290 q^{69} +6.51969 q^{71} +(1.66268 - 2.87984i) q^{72} +(1.04491 + 1.80984i) q^{73} +(-0.598285 - 1.03626i) q^{74} +(0.891021 - 1.54329i) q^{75} -1.91511 q^{76} +1.15063 q^{78} +(1.15989 - 2.00898i) q^{79} +(3.61281 + 6.25758i) q^{80} +(4.62374 + 8.00855i) q^{81} +(1.23934 - 2.14660i) q^{82} +5.01753 q^{83} +14.4397 q^{85} +(-1.06574 + 1.84592i) q^{86} +(-4.72235 - 8.17935i) q^{87} +(-2.82279 - 4.88922i) q^{88} +(-3.34720 + 5.79753i) q^{89} -1.75457 q^{90} +14.1966 q^{92} +(-0.983006 + 1.70262i) q^{93} +(0.789532 + 1.36751i) q^{94} +(1.03287 + 1.78898i) q^{95} +(-4.01372 + 6.95196i) q^{96} +14.0663 q^{97} -14.4271 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} - 2 q^{4} + 8 q^{5} + 8 q^{6} + 12 q^{8} - 2 q^{9} + 10 q^{10} + 6 q^{11} + 6 q^{12} - 4 q^{13} + 8 q^{15} - 2 q^{16} + 8 q^{17} + 6 q^{18} - 4 q^{19} - 28 q^{22} + 8 q^{23} + 12 q^{24} - 20 q^{25}+ \cdots + 16 q^{99}+O(q^{100}) \) 8 * q + 2 * q^3 - 2 * q^4 + 8 * q^5 + 8 * q^6 + 12 * q^8 - 2 * q^9 + 10 * q^10 + 6 * q^11 + 6 * q^12 - 4 * q^13 + 8 * q^15 - 2 * q^16 + 8 * q^17 + 6 * q^18 - 4 * q^19 - 28 * q^22 + 8 * q^23 + 12 * q^24 - 20 * q^25 + 16 * q^26 + 20 * q^27 + 4 * q^29 - 2 * q^30 - 2 * q^32 + 18 * q^33 + 44 * q^34 - 40 * q^36 - 10 * q^37 - 2 * q^39 + 22 * q^40 - 24 * q^41 + 8 * q^43 + 14 * q^44 + 8 * q^45 + 8 * q^46 + 16 * q^47 + 24 * q^48 + 24 * q^50 + 10 * q^51 + 28 * q^52 - 12 * q^53 + 4 * q^54 + 16 * q^55 - 4 * q^57 - 4 * q^58 + 14 * q^59 + 2 * q^60 + 20 * q^61 + 40 * q^62 - 40 * q^64 - 10 * q^65 - 8 * q^66 - 2 * q^67 - 24 * q^68 - 28 * q^69 - 4 * q^71 + 8 * q^72 - 16 * q^73 + 26 * q^74 + 36 * q^75 + 4 * q^76 + 28 * q^78 + 8 * q^79 + 28 * q^80 + 20 * q^81 - 12 * q^82 - 40 * q^83 - 28 * q^85 - 8 * q^86 - 20 * q^87 + 2 * q^88 + 16 * q^89 + 64 * q^90 + 52 * q^92 - 12 * q^93 + 10 * q^94 + 8 * q^95 - 12 * q^96 - 4 * q^97 + 16 * q^99

Introduction

L-functions

Modular forms

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Database

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