LMFDB - Embedded newform 931.2.f.n.324.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [931,2,Mod(324,931)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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

Self dual:	no
Analytic conductor:	$7.43407242818$
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.n.704.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.145683 + 0.252331i) q^{2} +(1.21605 + 2.10626i) q^{3} +(0.957553 + 1.65853i) q^{4} +(-1.03287 + 1.78898i) q^{5} -0.708633 q^{6} -1.14073 q^{8} +(-1.45755 + 2.52456i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 8 * q - 2 * q^3 - 2 * q^4 - 8 * q^5 - 8 * q^6 + 12 * q^8 - 2 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

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	$0.0810814\pi$
$3$	1.21605	+	2.10626i	0.702086	+	1.21605i	−0.265646	+	0.964071i	$0.585585\pi$
$4$	0.957553	+	1.65853i	0.478776	+	0.829265i
$5$	−1.03287	+	1.78898i	−0.461914	+	0.800058i	−0.999056	−	0.0434336i	$-0.986170\pi$
$5$	−1.03287	+	1.78898i	−0.461914	+	0.800058i	0.537143	+	0.843491i	$0.319504\pi$
$6$	−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	$-0.572294\pi$
$13$	−1.62374			−0.450344			−0.225172	+	0.974319i	$0.572294\pi$
$14$		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	$-0.844669\pi$
$17$	−3.49505	−	6.05360i	−0.847674	−	1.46821i	0.0356050	−	0.999366i	$-0.488664\pi$
$18$	−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	0.900037	−	0.435814i	$-0.143539\pi$
$31$	0.404180	+	0.700061i	0.0725929	+	0.125735i	−0.827444	+	0.561548i	$0.810206\pi$
$32$	−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	$-0.268733\pi$
$41$	8.50709			1.32858			0.664292	+	0.747473i	$0.268733\pi$
$42$		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	−0.993134	−	0.116982i	$-0.962678\pi$
$47$	−2.70975	+	4.69343i	−0.395258	+	0.684606i	0.597876	+	0.801588i	$0.296011\pi$
$48$	−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	0.615639	−	0.788028i	$-0.288898\pi$
$59$	−2.87761	−	4.98417i	−0.374633	−	0.648883i	−0.990272	+	0.139145i	$0.955565\pi$
$60$	−4.81083	−	8.33259i	−0.621075	−	1.07573i
$61$	−5.69060	+	9.85640i	−0.728606	+	1.26198i	0.228866	+	0.973458i	$0.426498\pi$
$61$	−5.69060	+	9.85640i	−0.728606	+	1.26198i	−0.957472	+	0.288525i	$0.906835\pi$
$62$	−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	0.798376	−	0.602160i	$-0.205693\pi$
$73$	−1.04491	−	1.80984i	−0.122298	−	0.211826i	−0.920673	+	0.390334i	$0.872360\pi$
$74$	−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	$-0.588801\pi$
$83$	−5.01753			−0.550745			−0.275373	+	0.961338i	$0.588801\pi$
$84$		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	−0.632281	−	0.774739i	$-0.717881\pi$
$89$	3.34720	−	5.79753i	0.354803	−	0.614537i	0.987084	+	0.160202i	$0.0512146\pi$
$90$	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	$-0.753169\pi$
$97$	−14.0663			−1.42822			−0.714111	+	0.700033i	$0.753169\pi$
$98$		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	0.907199	−	0.420701i	$-0.138216\pi$
$101$	0.897068	+	1.55377i	0.0892616	+	0.154606i	−0.817938	+	0.575307i	$0.804883\pi$
$102$	2.47671	+	4.28978i	0.245231	+	0.424752i
$103$	−8.45044	+	14.6366i	−0.832647	+	1.44219i	0.0632856	+	0.997995i	$0.479842\pi$
$103$	−8.45044	+	14.6366i	−0.832647	+	1.44219i	−0.895932	+	0.444191i	$0.853491\pi$
$104$	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	$-0.510586\pi$
$131$	9.71635	−	16.8292i	0.848922	−	1.47038i	0.882171	−	0.470929i	$-0.156081\pi$
$132$	−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	$-0.219417\pi$
$139$	18.1959			1.54336			0.771679	+	0.636012i	$0.219417\pi$
$140$		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	0.938639	−	0.344901i	$-0.112088\pi$
$157$	2.13794	+	3.70302i	0.170626	+	0.295533i	−0.768013	+	0.640435i	$0.778754\pi$
$158$	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	$-0.193147\pi$
$167$	21.2318			1.64297			0.821484	+	0.570232i	$0.193147\pi$
$168$		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	−0.707323	−	0.706890i	$-0.750097\pi$
$173$	3.40035	−	5.88957i	0.258524	−	0.447776i	0.965847	+	0.259115i	$0.0834307\pi$
$174$	−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	$-0.223349\pi$
$181$	20.5508			1.52753			0.763764	+	0.645495i	$0.223349\pi$
$182$		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	$0.236950\pi$
$199$	13.4650	+	23.3220i	0.954506	+	1.65325i	0.219013	+	0.975722i	$0.429716\pi$
$200$	−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	$-0.524626\pi$
$223$	−2.30829			−0.154574			−0.0772872	+	0.997009i	$0.524626\pi$
$224$		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	$-0.937723\pi$
$227$	−9.92610	−	17.1925i	−0.658819	−	1.14111i	0.322103	−	0.946705i	$-0.395610\pi$
$228$	2.32886	+	4.03371i	0.154233	+	0.267139i
$229$	−8.71356	+	15.0923i	−0.575808	+	0.997330i	0.420145	+	0.907457i	$0.361979\pi$
$229$	−8.71356	+	15.0923i	−0.575808	+	0.997330i	−0.995953	+	0.0898724i	$0.971354\pi$
$230$	−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	0.770387	−	0.637577i	$-0.220063\pi$
$241$	−2.59199	−	4.48945i	−0.166964	−	0.289191i	−0.937351	+	0.348386i	$0.886730\pi$
$242$	−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	$-0.373459\pi$
$251$	12.2672			0.774301			0.387151	+	0.922016i	$0.373459\pi$
$252$		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	$-0.587484\pi$
$257$	11.1870	−	19.3764i	0.697825	−	1.20867i	0.969219	−	0.246201i	$-0.0791822\pi$
$258$	−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	$-0.972161\pi$
$269$	−9.40992	−	16.2985i	−0.573733	−	0.993735i	0.422445	−	0.906389i	$-0.361172\pi$
$270$	−0.0621366	−	0.107624i	−0.00378151	−	0.00654977i
$271$	−12.4907	+	21.6346i	−0.758758	+	1.31421i	0.184727	+	0.982790i	$0.440860\pi$
$271$	−12.4907	+	21.6346i	−0.758758	+	1.31421i	−0.943484	+	0.331417i	$0.892473\pi$
$272$	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	0.857487	−	0.514505i	$-0.172024\pi$
$283$	−0.283137	−	0.490408i	−0.0168308	−	0.0291518i	−0.874318	+	0.485353i	$0.838691\pi$
$284$	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	$-0.235700\pi$
$293$	25.2701			1.47630			0.738148	+	0.674639i	$0.235700\pi$
$294$		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	$-0.558196\pi$
$307$	−6.37114			−0.363620			−0.181810	+	0.983334i	$0.558196\pi$
$308$		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	0.861803	−	0.507243i	$-0.169335\pi$
$311$	−0.147844	−	0.256074i	−0.00838348	−	0.0145206i	−0.870187	+	0.492722i	$0.836002\pi$
$312$	2.25243	+	3.90132i	0.127519	+	0.220869i
$313$	10.1840	−	17.6392i	0.575632	−	0.997024i	−0.420341	−	0.907366i	$-0.638089\pi$
$313$	10.1840	−	17.6392i	0.575632	−	0.997024i	0.995973	−	0.0896576i	$-0.0285773\pi$
$314$	−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	$-0.568201\pi$
$349$	−7.94431			−0.425249			−0.212625	+	0.977134i	$0.568201\pi$
$350$		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	0.725638	−	0.688077i	$-0.241545\pi$
$353$	−4.37905	−	7.58474i	−0.233073	−	0.403695i	−0.958711	+	0.284382i	$0.908212\pi$
$354$	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	0.989107	−	0.147195i	$-0.0470246\pi$
$367$	7.03222	+	12.1802i	0.367079	+	0.635799i	−0.622029	+	0.782995i	$0.713691\pi$
$368$	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	$0.372904\pi$
$383$	−11.8112	+	20.4576i	−0.603525	+	1.04534i	−0.992283	+	0.123996i	$0.960429\pi$
$384$	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	$-0.627587\pi$
$397$	12.0006	−	20.7857i	0.602293	−	1.04320i	0.992473	−	0.122464i	$-0.0390795\pi$
$398$	−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	$-0.918729\pi$
$409$	−14.2074	−	24.6079i	−0.702511	−	1.21678i	0.265071	−	0.964229i	$-0.414605\pi$
$410$	−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	$-0.546449\pi$
$419$	−5.95276			−0.290812			−0.145406	+	0.989372i	$0.546449\pi$
$420$		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	$-0.348151\pi$
$433$	19.1090			0.918319			0.459159	+	0.888354i	$0.348151\pi$
$434$		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	−0.765575	−	0.643347i	$-0.777545\pi$
$439$	3.65340	−	6.32788i	0.174367	−	0.302013i	0.939942	+	0.341334i	$0.110879\pi$
$440$	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	$-0.267222\pi$
$461$	28.6779			1.33567			0.667833	+	0.744311i	$0.267222\pi$
$462$		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	−0.992424	−	0.122862i	$-0.960793\pi$
$467$	−8.42387	+	14.5906i	−0.389810	+	0.675171i	0.602614	+	0.798033i	$0.294126\pi$
$468$	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	$-0.990180\pi$
$479$	−11.5225	−	19.9575i	−0.526476	−	0.911882i	0.473049	−	0.881036i	$-0.343153\pi$
$480$	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	$-0.515163\pi$
$503$	−2.13595			−0.0952373			−0.0476186	+	0.998866i	$0.515163\pi$
$504$		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	$0.347060\pi$
$509$	−12.1123	+	20.9792i	−0.536869	+	0.929885i	−0.999070	+	0.0431099i	$0.986273\pi$
$510$	−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	0.771203	−	0.636590i	$-0.219655\pi$
$521$	−3.78220	−	6.55097i	−0.165701	−	0.287003i	−0.936904	+	0.349586i	$0.886322\pi$
$522$	−1.64919	−	2.85648i	−0.0721832	−	0.125025i
$523$	−5.87203	+	10.1707i	−0.256766	+	0.444732i	−0.965374	−	0.260871i	$-0.915990\pi$
$523$	−5.87203	+	10.1707i	−0.256766	+	0.444732i	0.708608	+	0.705603i	$0.249324\pi$
$524$	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	$0.0130367\pi$
$563$	12.6952	+	21.9888i	0.535040	+	0.926716i	−0.464122	+	0.885771i	$0.653630\pi$
$564$	−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	0.967745	−	0.251930i	$-0.0810652\pi$
$577$	6.38221	+	11.0543i	0.265695	+	0.460197i	−0.702050	+	0.712127i	$0.747732\pi$
$578$	−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	$-0.666847\pi$
$587$	−24.2518			−1.00098			−0.500489	+	0.865743i	$0.666847\pi$
$588$		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	−0.902849	−	0.429958i	$-0.858528\pi$
$593$	−1.92547	+	3.33502i	−0.0790698	+	0.136953i	0.823779	+	0.566911i	$0.191862\pi$
$594$	−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	$-0.480536\pi$
$601$	2.99633			0.122223			0.0611114	+	0.998131i	$0.480536\pi$
$602$		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	$-0.661383\pi$
$607$	12.6711	−	21.9471i	0.514306	−	0.890803i	0.999862	−	0.0165982i	$-0.00528362\pi$
$608$	−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	0.974862	−	0.222810i	$-0.0715229\pi$
$619$	7.32638	+	12.6897i	0.294472	+	0.510040i	−0.680390	+	0.732850i	$0.738190\pi$
$620$	−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	$-0.284396\pi$
$643$	31.7842			1.25345			0.626723	+	0.779242i	$0.284396\pi$
$644$		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	0.704077	−	0.710124i	$-0.251361\pi$
$647$	−6.68836	−	11.5846i	−0.262947	−	0.455437i	−0.967024	+	0.254687i	$0.918028\pi$
$648$	−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	0.981944	−	0.189172i	$-0.0605803\pi$
$661$	8.41086	+	14.5680i	0.327144	+	0.566631i	−0.654800	+	0.755803i	$0.727247\pi$
$662$	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	−0.813381	−	0.581732i	$-0.802375\pi$
$677$	2.52657	−	4.37615i	0.0971040	−	0.168189i	0.910485	+	0.413543i	$0.135709\pi$
$678$	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	−0.558012	−	0.829833i	$-0.688436\pi$
$691$	11.5570	−	20.0174i	0.439650	−	0.761496i	0.997662	+	0.0683367i	$0.0217692\pi$
$692$	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	−0.748830	−	0.662762i	$-0.769384\pi$
$719$	5.35088	−	9.26799i	0.199554	−	0.345638i	0.948384	+	0.317125i	$0.102717\pi$
$720$	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	$-0.634790\pi$
$727$	−22.1589			−0.821829			−0.410914	+	0.911674i	$0.634790\pi$
$728$		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	$0.408892\pi$
$733$	−18.6709	+	32.3390i	−0.689627	+	1.19447i	−0.971959	+	0.235152i	$0.924441\pi$
$734$	−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	$0.382016\pi$
$761$	−17.2717	+	29.9155i	−0.626099	+	1.08443i	−0.988327	+	0.152346i	$0.951317\pi$
$762$	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	$-0.435799\pi$
$769$	11.1106			0.400659			0.200329	+	0.979729i	$0.435799\pi$
$770$		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	0.781644	−	0.623725i	$-0.214381\pi$
$773$	−4.15207	−	7.19160i	−0.149340	−	0.258664i	−0.930984	+	0.365061i	$0.881048\pi$
$774$	−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	0.975264	−	0.221043i	$-0.0709461\pi$
$787$	8.30955	+	14.3926i	0.296203	+	0.513039i	−0.679061	+	0.734082i	$0.737613\pi$
$788$	−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	$-0.356831\pi$
$797$	24.5479			0.869532			0.434766	+	0.900543i	$0.356831\pi$
$798$		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	$-0.243115\pi$
$811$	41.1357			1.44447			0.722235	+	0.691648i	$0.243115\pi$
$812$		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	$-0.846973\pi$
$829$	−24.2953	−	42.0807i	−0.843811	−	1.46152i	0.0428380	−	0.999082i	$-0.486360\pi$
$830$	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	$-0.550298\pi$
$839$	−9.11600			−0.314719			−0.157360	+	0.987541i	$0.550298\pi$
$840$		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	$-0.505539\pi$
$853$	−1.01631			−0.0347979			−0.0173989	+	0.999849i	$0.505539\pi$
$854$		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	0.969198	−	0.246282i	$-0.0792089\pi$
$857$	7.94256	+	13.7569i	0.271313	+	0.469928i	−0.697885	+	0.716209i	$0.745876\pi$
$858$	2.84730	+	4.93167i	0.0972052	+	0.168364i
$859$	2.86206	−	4.95723i	0.0976522	−	0.169139i	−0.813060	−	0.582180i	$-0.802200\pi$
$859$	2.86206	−	4.95723i	0.0976522	−	0.169139i	0.910712	+	0.413041i	$0.135533\pi$
$860$	−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	$-0.454891\pi$
$881$	8.38440			0.282478			0.141239	+	0.989976i	$0.454891\pi$
$882$		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	−0.510411	−	0.859931i	$-0.670507\pi$
$887$	14.5790	−	25.2516i	0.489516	−	0.847867i	0.999927	+	0.0120638i	$0.00384010\pi$
$888$	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	$0.354437\pi$
$929$	−16.9550	+	29.3670i	−0.556277	+	0.963500i	−0.997803	+	0.0662515i	$0.978896\pi$
$930$	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	$-0.591935\pi$
$937$	−17.4372			−0.569648			−0.284824	+	0.958580i	$0.591935\pi$
$938$		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	0.861108	−	0.508423i	$-0.169771\pi$
$941$	−0.299182	−	0.518199i	−0.00975306	−	0.0168928i	−0.870861	+	0.491530i	$0.836438\pi$
$942$	−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	−0.775883	−	0.630877i	$-0.782695\pi$
$971$	4.93633	−	8.54998i	0.158414	−	0.274382i	0.934297	+	0.356495i	$0.116028\pi$
$972$	−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	0.913719	−	0.406347i	$-0.133198\pi$
$983$	3.29055	+	5.69941i	0.104952	+	0.181783i	−0.808766	+	0.588130i	$0.799864\pi$
$984$	−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	0.998422	−	0.0561523i	$-0.0178832\pi$
$997$	14.2273	+	24.6423i	0.450582	+	0.780430i	−0.547840	+	0.836583i	$0.684550\pi$
$998$	−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.n.324.2		8
7.2	even	3		931.2.a.m.1.3	yes	4
7.3	odd	6		931.2.f.o.704.2		8
7.4	even	3	inner	931.2.f.n.704.2		8
7.5	odd	6		931.2.a.l.1.3	✓	4
7.6	odd	2		931.2.f.o.324.2		8
21.2	odd	6		8379.2.a.bu.1.2		4
21.5	even	6		8379.2.a.bv.1.2		4

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

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

\(f(q)\)	\(=\)	\(q+(-0.145683 + 0.252331i) q^{2} +(1.21605 + 2.10626i) q^{3} +(0.957553 + 1.65853i) q^{4} +(-1.03287 + 1.78898i) q^{5} -0.708633 q^{6} -1.14073 q^{8} +(-1.45755 + 2.52456i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} - 2 q^{4} - 8 q^{5} - 8 q^{6} + 12 q^{8} - 2 q^{9}+O(q^{10}) \) 8 * q - 2 * q^3 - 2 * q^4 - 8 * q^5 - 8 * q^6 + 12 * q^8 - 2 * q^9	\( 8 q - 2 q^{3} - 2 q^{4} - 8 q^{5} - 8 q^{6} + 12 q^{8} - 2 q^{9} - 10 q^{10} + 6 q^{11} - 6 q^{12} + 4 q^{13} + 8 q^{15} - 2 q^{16} - 8 q^{17} + 6 q^{18} + 4 q^{19} - 28 q^{22} + 8 q^{23} - 12 q^{24} - 20 q^{25} - 16 q^{26} - 20 q^{27} + 4 q^{29} - 2 q^{30} - 2 q^{32} - 18 q^{33} - 44 q^{34} - 40 q^{36} - 10 q^{37} - 2 q^{39} - 22 q^{40} + 24 q^{41} + 8 q^{43} + 14 q^{44} - 8 q^{45} + 8 q^{46} - 16 q^{47} - 24 q^{48} + 24 q^{50} + 10 q^{51} - 28 q^{52} - 12 q^{53} - 4 q^{54} - 16 q^{55} - 4 q^{57} - 4 q^{58} - 14 q^{59} + 2 q^{60} - 20 q^{61} - 40 q^{62} - 40 q^{64} - 10 q^{65} + 8 q^{66} - 2 q^{67} + 24 q^{68} + 28 q^{69} - 4 q^{71} + 8 q^{72} + 16 q^{73} + 26 q^{74} - 36 q^{75} - 4 q^{76} + 28 q^{78} + 8 q^{79} - 28 q^{80} + 20 q^{81} + 12 q^{82} + 40 q^{83} - 28 q^{85} - 8 q^{86} + 20 q^{87} + 2 q^{88} - 16 q^{89} - 64 q^{90} + 52 q^{92} - 12 q^{93} - 10 q^{94} + 8 q^{95} + 12 q^{96} + 4 q^{97} + 16 q^{99}+O(q^{100}) \) 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

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