LMFDB - Embedded newform 1674.2.g.b.1369.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1674,2,Mod(955,1674)] 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("1674.955"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1674, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1674 = 2 \cdot 3^{3} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1674.g (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$13.3669572984$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 558)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1369.13
Character	$\chi$	$=$	1674.1369
Dual form			1674.2.g.b.955.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.38064 - 2.39134i) q^{5} +(-0.281122 - 0.486917i) q^{7} -1.00000 q^{8} +(-1.38064 - 2.39134i) q^{10} +3.99186 q^{11} +(0.735188 - 1.27338i) q^{13} -0.562243 q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.03355 - 1.79016i) q^{17} +(1.45518 - 2.52045i) q^{19} -2.76129 q^{20} +(1.99593 - 3.45705i) q^{22} +(1.12187 + 1.94313i) q^{23} +(-1.31235 - 2.27306i) q^{25} +(-0.735188 - 1.27338i) q^{26} +(-0.281122 + 0.486917i) q^{28} +(-2.14333 + 3.71236i) q^{29} +(3.62516 - 4.22590i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.03355 - 1.79016i) q^{34} -1.55251 q^{35} +(1.82864 - 3.16730i) q^{37} +(-1.45518 - 2.52045i) q^{38} +(-1.38064 + 2.39134i) q^{40} +(-3.11925 + 5.40270i) q^{41} +(-5.87561 - 10.1769i) q^{43} +(-1.99593 - 3.45705i) q^{44} +2.24373 q^{46} +(-2.96852 + 5.14163i) q^{47} +(3.34194 - 5.78841i) q^{49} -2.62470 q^{50} -1.47038 q^{52} +(-0.731740 - 1.26741i) q^{53} +(5.51133 - 9.54590i) q^{55} +(0.281122 + 0.486917i) q^{56} +(2.14333 + 3.71236i) q^{58} +1.27123 q^{59} +(-6.92283 + 11.9907i) q^{61} +(-1.84716 - 5.25243i) q^{62} +1.00000 q^{64} +(-2.03006 - 3.51617i) q^{65} +(-2.84476 + 4.92726i) q^{67} -2.06710 q^{68} +(-0.776257 + 1.34452i) q^{70} +(-2.14830 - 3.72096i) q^{71} +(-4.67244 - 8.09290i) q^{73} +(-1.82864 - 3.16730i) q^{74} -2.91037 q^{76} +(-1.12220 - 1.94370i) q^{77} +(0.516125 + 0.893955i) q^{79} +(1.38064 + 2.39134i) q^{80} +(3.11925 + 5.40270i) q^{82} +2.04433 q^{83} +(-2.85393 - 4.94316i) q^{85} -11.7512 q^{86} -3.99186 q^{88} +3.63785 q^{89} -0.826708 q^{91} +(1.12187 - 1.94313i) q^{92} +(2.96852 + 5.14163i) q^{94} +(-4.01818 - 6.95968i) q^{95} +(-7.94907 + 13.7682i) q^{97} +(-3.34194 - 5.78841i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{2} - 16 q^{4} + q^{5} + q^{7} - 32 q^{8} - q^{10} - 4 q^{11} - 10 q^{13} + 2 q^{14} - 16 q^{16} + 4 q^{17} + 4 q^{19} - 2 q^{20} - 2 q^{22} + q^{23} - 19 q^{25} + 10 q^{26} + q^{28} + 3 q^{29}+ \cdots + 13 q^{98}+O(q^{100}) $ 32 * q + 16 * q^2 - 16 * q^4 + q^5 + q^7 - 32 * q^8 - q^10 - 4 * q^11 - 10 * q^13 + 2 * q^14 - 16 * q^16 + 4 * q^17 + 4 * q^19 - 2 * q^20 - 2 * q^22 + q^23 - 19 * q^25 + 10 * q^26 + q^28 + 3 * q^29 - q^31 + 16 * q^32 - 4 * q^34 - 19 * q^37 - 4 * q^38 - q^40 - 10 * q^41 - 13 * q^43 + 2 * q^44 + 2 * q^46 + 6 * q^47 - 13 * q^49 - 38 * q^50 + 20 * q^52 + 7 * q^53 - 11 * q^55 - q^56 - 3 * q^58 - 12 * q^59 + 7 * q^61 - 11 * q^62 + 32 * q^64 + 8 * q^65 - 8 * q^67 - 8 * q^68 - 7 * q^71 + 7 * q^73 + 19 * q^74 - 8 * q^76 + q^77 - 34 * q^79 + q^80 + 10 * q^82 + 28 * q^83 + 13 * q^85 - 26 * q^86 + 4 * q^88 - 2 * q^89 + 24 * q^91 + q^92 - 6 * q^94 - 21 * q^95 + 10 * q^97 + 13 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1674\mathbb{Z}\right)^\times$.

$n$	$1055$	$1243$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.38064	−	2.39134i	0.617442	−	1.06944i	−0.372509	−	0.928029i	$-0.621502\pi$
$5$	1.38064	−	2.39134i	0.617442	−	1.06944i	0.989951	−	0.141413i	$-0.0451644\pi$
$6$		0			0
$7$	−0.281122	−	0.486917i	−0.106254	−	0.184037i	0.807996	−	0.589188i	$-0.200552\pi$
$7$	−0.281122	−	0.486917i	−0.106254	−	0.184037i	−0.914250	+	0.405151i	$0.867219\pi$
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−1.38064	−	2.39134i	−0.436598	−	0.756209i
$11$	3.99186			1.20359			0.601795	−	0.798651i	$-0.294452\pi$
$11$	3.99186			1.20359			0.601795	+	0.798651i	$0.294452\pi$
$12$		0			0
$13$	0.735188	−	1.27338i	0.203904	−	0.353173i	−0.745879	−	0.666082i	$-0.767970\pi$
$13$	0.735188	−	1.27338i	0.203904	−	0.353173i	0.949783	+	0.312909i	$0.101304\pi$
$14$	−0.562243			−0.150266
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.03355	−	1.79016i	0.250673	−	0.434179i	−0.713038	−	0.701125i	$-0.752681\pi$
$17$	1.03355	−	1.79016i	0.250673	−	0.434179i	0.963711	+	0.266946i	$0.0860147\pi$
$18$		0			0
$19$	1.45518	−	2.52045i	0.333842	−	0.578231i	−0.649420	−	0.760430i	$-0.724988\pi$
$19$	1.45518	−	2.52045i	0.333842	−	0.578231i	0.983262	+	0.182199i	$0.0583215\pi$
$20$	−2.76129			−0.617442
$21$		0			0
$22$	1.99593	−	3.45705i	0.425533	−	0.737045i
$23$	1.12187	+	1.94313i	0.233925	+	0.405170i	0.958960	−	0.283542i	$-0.0915096\pi$
$23$	1.12187	+	1.94313i	0.233925	+	0.405170i	−0.725035	+	0.688712i	$0.758176\pi$
$24$		0			0
$25$	−1.31235	−	2.27306i	−0.262470	−	0.454611i
$26$	−0.735188	−	1.27338i	−0.144182	−	0.249731i
$27$		0			0
$28$	−0.281122	+	0.486917i	−0.0531270	+	0.0920186i
$29$	−2.14333	+	3.71236i	−0.398007	+	0.689368i	−0.993480	−	0.114007i	$-0.963631\pi$
$29$	−2.14333	+	3.71236i	−0.398007	+	0.689368i	0.595473	+	0.803375i	$0.296965\pi$
$30$		0			0
$31$	3.62516	−	4.22590i	0.651098	−	0.758994i
$31$	3.62516	−	4.22590i	0.651098	−	0.758994i
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	−1.03355	−	1.79016i	−0.177253	−	0.307011i
$35$	−1.55251			−0.262423
$36$		0			0
$37$	1.82864	−	3.16730i	0.300627	−	0.520701i	−0.675651	−	0.737221i	$-0.736137\pi$
$37$	1.82864	−	3.16730i	0.300627	−	0.520701i	0.976278	+	0.216520i	$0.0694708\pi$
$38$	−1.45518	−	2.52045i	−0.236062	−	0.408871i
$39$		0			0
$40$	−1.38064	+	2.39134i	−0.218299	+	0.378105i
$41$	−3.11925	+	5.40270i	−0.487145	+	0.843759i	−0.999891	−	0.0147809i	$-0.995295\pi$
$41$	−3.11925	+	5.40270i	−0.487145	+	0.843759i	0.512746	+	0.858540i	$0.328628\pi$
$42$		0			0
$43$	−5.87561	−	10.1769i	−0.896023	−	1.55196i	−0.832534	−	0.553974i	$-0.813111\pi$
$43$	−5.87561	−	10.1769i	−0.896023	−	1.55196i	−0.0634887	−	0.997983i	$-0.520223\pi$
$44$	−1.99593	−	3.45705i	−0.300897	−	0.521170i
$45$		0			0
$46$	2.24373			0.330820
$47$	−2.96852	+	5.14163i	−0.433003	+	0.749983i	−0.997130	−	0.0757045i	$-0.975879\pi$
$47$	−2.96852	+	5.14163i	−0.433003	+	0.749983i	0.564127	+	0.825688i	$0.309213\pi$
$48$		0			0
$49$	3.34194	−	5.78841i	0.477420	−	0.826916i
$50$	−2.62470			−0.371188
$51$		0			0
$52$	−1.47038			−0.203904
$53$	−0.731740	−	1.26741i	−0.100512	−	0.174092i	0.811384	−	0.584514i	$-0.198715\pi$
$53$	−0.731740	−	1.26741i	−0.100512	−	0.174092i	−0.911896	+	0.410422i	$0.865381\pi$
$54$		0			0
$55$	5.51133	−	9.54590i	0.743147	−	1.28717i
$56$	0.281122	+	0.486917i	0.0375664	+	0.0650670i
$57$		0			0
$58$	2.14333	+	3.71236i	0.281433	+	0.487457i
$59$	1.27123			0.165501			0.0827503	−	0.996570i	$-0.473630\pi$
$59$	1.27123			0.165501			0.0827503	+	0.996570i	$0.473630\pi$
$60$		0			0
$61$	−6.92283	+	11.9907i	−0.886378	+	1.53525i	−0.0422512	+	0.999107i	$0.513453\pi$
$61$	−6.92283	+	11.9907i	−0.886378	+	1.53525i	−0.844126	+	0.536144i	$0.819880\pi$
$62$	−1.84716	−	5.25243i	−0.234589	−	0.667059i
$63$		0			0
$64$	1.00000			0.125000
$65$	−2.03006	−	3.51617i	−0.251798	−	0.436127i
$66$		0			0
$67$	−2.84476	+	4.92726i	−0.347542	+	0.601961i	−0.985812	−	0.167852i	$-0.946317\pi$
$67$	−2.84476	+	4.92726i	−0.347542	+	0.601961i	0.638270	+	0.769813i	$0.279650\pi$
$68$	−2.06710			−0.250673
$69$		0			0
$70$	−0.776257	+	1.34452i	−0.0927804	+	0.160700i
$71$	−2.14830	−	3.72096i	−0.254956	−	0.441596i	0.709928	−	0.704275i	$-0.248728\pi$
$71$	−2.14830	−	3.72096i	−0.254956	−	0.441596i	−0.964884	+	0.262678i	$0.915394\pi$
$72$		0			0
$73$	−4.67244	−	8.09290i	−0.546868	−	0.947202i	−0.998487	−	0.0549916i	$-0.982487\pi$
$73$	−4.67244	−	8.09290i	−0.546868	−	0.947202i	0.451619	−	0.892211i	$-0.350847\pi$
$74$	−1.82864	−	3.16730i	−0.212575	−	0.368191i
$75$		0			0
$76$	−2.91037			−0.333842
$77$	−1.12220	−	1.94370i	−0.127886	−	0.221505i
$78$		0			0
$79$	0.516125	+	0.893955i	0.0580686	+	0.100578i	0.893598	−	0.448867i	$-0.148172\pi$
$79$	0.516125	+	0.893955i	0.0580686	+	0.100578i	−0.835530	+	0.549445i	$0.814839\pi$
$80$	1.38064	+	2.39134i	0.154361	+	0.267360i
$81$		0			0
$82$	3.11925	+	5.40270i	0.344463	+	0.596628i
$83$	2.04433			0.224394			0.112197	−	0.993686i	$-0.464211\pi$
$83$	2.04433			0.224394			0.112197	+	0.993686i	$0.464211\pi$
$84$		0			0
$85$	−2.85393	−	4.94316i	−0.309552	−	0.536161i
$86$	−11.7512			−1.26717
$87$		0			0
$88$	−3.99186			−0.425533
$89$	3.63785			0.385611			0.192805	−	0.981237i	$-0.438241\pi$
$89$	3.63785			0.385611			0.192805	+	0.981237i	$0.438241\pi$
$90$		0			0
$91$	−0.826708			−0.0866626
$92$	1.12187	−	1.94313i	0.116963	−	0.202585i
$93$		0			0
$94$	2.96852	+	5.14163i	0.306179	+	0.530318i
$95$	−4.01818	−	6.95968i	−0.412256	−	0.714049i
$96$		0			0
$97$	−7.94907	+	13.7682i	−0.807106	+	1.39795i	0.107754	+	0.994178i	$0.465634\pi$
$97$	−7.94907	+	13.7682i	−0.807106	+	1.39795i	−0.914860	+	0.403771i	$0.867699\pi$
$98$	−3.34194	−	5.78841i	−0.337587	−	0.584718i
$99$		0			0
$100$	−1.31235	+	2.27306i	−0.131235	+	0.227306i
$101$	−1.05409	+	1.82574i	−0.104886	+	0.181668i	−0.913692	−	0.406408i	$-0.866781\pi$
$101$	−1.05409	+	1.82574i	−0.104886	+	0.181668i	0.808806	+	0.588076i	$0.200114\pi$
$102$		0			0
$103$	5.89275	−	10.2065i	0.580630	−	1.00568i	−0.414775	−	0.909924i	$-0.636140\pi$
$103$	5.89275	−	10.2065i	0.580630	−	1.00568i	0.995405	−	0.0957562i	$-0.0305269\pi$
$104$	−0.735188	+	1.27338i	−0.0720911	+	0.124865i
$105$		0			0
$106$	−1.46348			−0.142146
$107$	3.06844	−	5.31470i	0.296638	−	0.513792i	−0.678727	−	0.734391i	$-0.737468\pi$
$107$	3.06844	−	5.31470i	0.296638	−	0.513792i	0.975365	+	0.220599i	$0.0708013\pi$
$108$		0			0
$109$	12.8643			1.23218			0.616088	−	0.787677i	$-0.288716\pi$
$109$	12.8643			1.23218			0.616088	+	0.787677i	$0.288716\pi$
$110$	−5.51133	−	9.54590i	−0.525484	−	0.910166i
$111$		0			0
$112$	0.562243			0.0531270
$113$	−6.85988	+	11.8817i	−0.645323	+	1.11773i	0.338903	+	0.940821i	$0.389944\pi$
$113$	−6.85988	+	11.8817i	−0.645323	+	1.11773i	−0.984227	+	0.176912i	$0.943389\pi$
$114$		0			0
$115$	6.19558			0.577741
$116$	4.28667			0.398007
$117$		0			0
$118$	0.635617	−	1.10092i	0.0585133	−	0.101348i
$119$	−1.16222			−0.106540
$120$		0			0
$121$	4.93492			0.448629
$122$	6.92283	+	11.9907i	0.626764	+	1.08559i
$123$		0			0
$124$	−5.47232	−	1.02653i	−0.491428	−	0.0921852i
$125$	6.55889			0.586645
$126$		0			0
$127$	−3.57207	+	6.18701i	−0.316970	+	0.549008i	−0.979854	−	0.199714i	$-0.935999\pi$
$127$	−3.57207	+	6.18701i	−0.316970	+	0.549008i	0.662884	+	0.748722i	$0.269332\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	−4.06013			−0.356097
$131$	−3.48452			−0.304444			−0.152222	−	0.988346i	$-0.548643\pi$
$131$	−3.48452			−0.304444			−0.152222	+	0.988346i	$0.548643\pi$
$132$		0			0
$133$	−1.63633			−0.141888
$134$	2.84476	+	4.92726i	0.245749	+	0.425651i
$135$		0			0
$136$	−1.03355	+	1.79016i	−0.0886264	+	0.153505i
$137$	−1.66890			−0.142584			−0.0712918	−	0.997456i	$-0.522712\pi$
$137$	−1.66890			−0.142584			−0.0712918	+	0.997456i	$0.522712\pi$
$138$		0			0
$139$	−8.28078	−	14.3427i	−0.702366	−	1.21653i	−0.967634	−	0.252359i	$-0.918793\pi$
$139$	−8.28078	−	14.3427i	−0.702366	−	1.21653i	0.265267	−	0.964175i	$-0.414540\pi$
$140$	0.776257	+	1.34452i	0.0656057	+	0.113632i
$141$		0			0
$142$	−4.29659			−0.360562
$143$	2.93476	−	5.08316i	0.245417	−	0.425075i
$144$		0			0
$145$	5.91835	+	10.2509i	0.491493	+	0.851290i
$146$	−9.34488			−0.773387
$147$		0			0
$148$	−3.65728			−0.300627
$149$	12.7433			1.04397			0.521987	−	0.852953i	$-0.325191\pi$
$149$	12.7433			1.04397			0.521987	+	0.852953i	$0.325191\pi$
$150$		0			0
$151$	−2.16532	+	3.75045i	−0.176212	+	0.305207i	−0.940580	−	0.339573i	$-0.889718\pi$
$151$	−2.16532	+	3.75045i	−0.176212	+	0.305207i	0.764368	+	0.644780i	$0.223051\pi$
$152$	−1.45518	+	2.52045i	−0.118031	+	0.204436i
$153$		0			0
$154$	−2.24439			−0.180858
$155$	−5.10052	−	14.5035i	−0.409684	−	1.16495i
$156$		0			0
$157$	−11.0809	−	19.1927i	−0.884353	−	1.53174i	−0.846454	−	0.532463i	$-0.821267\pi$
$157$	−11.0809	−	19.1927i	−0.884353	−	1.53174i	−0.0378993	−	0.999282i	$-0.512067\pi$
$158$	1.03225			0.0821214
$159$		0			0
$160$	2.76129			0.218299
$161$	0.630761	−	1.09251i	0.0497109	−	0.0861019i
$162$		0			0
$163$	1.82322			0.142806			0.0714029	−	0.997448i	$-0.477252\pi$
$163$	1.82322			0.142806			0.0714029	+	0.997448i	$0.477252\pi$
$164$	6.23850			0.487145
$165$		0			0
$166$	1.02216	−	1.77044i	0.0793354	−	0.137413i
$167$	6.41709			0.496569			0.248285	−	0.968687i	$-0.420133\pi$
$167$	6.41709			0.496569			0.248285	+	0.968687i	$0.420133\pi$
$168$		0			0
$169$	5.41900	+	9.38598i	0.416846	+	0.721999i
$170$	−5.70787			−0.437773
$171$		0			0
$172$	−5.87561	+	10.1769i	−0.448011	+	0.775978i
$173$	21.0217			1.59825			0.799127	−	0.601163i	$-0.205296\pi$
$173$	21.0217			1.59825			0.799127	+	0.601163i	$0.205296\pi$
$174$		0			0
$175$	−0.737859	+	1.27801i	−0.0557769	+	0.0966084i
$176$	−1.99593	+	3.45705i	−0.150449	+	0.260585i
$177$		0			0
$178$	1.81892	−	3.15047i	0.136334	−	0.236137i
$179$	−7.59632	+	13.1572i	−0.567775	+	0.983416i	0.429010	+	0.903300i	$0.358862\pi$
$179$	−7.59632	+	13.1572i	−0.567775	+	0.983416i	−0.996786	+	0.0801160i	$0.974471\pi$
$180$		0			0
$181$	−1.37767	−	2.38619i	−0.102401	−	0.177364i	0.810272	−	0.586054i	$-0.199319\pi$
$181$	−1.37767	−	2.38619i	−0.102401	−	0.177364i	−0.912674	+	0.408689i	$0.865986\pi$
$182$	−0.413354	+	0.715950i	−0.0306398	+	0.0530698i
$183$		0			0
$184$	−1.12187	−	1.94313i	−0.0827050	−	0.143249i
$185$	−5.04940	−	8.74582i	−0.371239	−	0.643005i
$186$		0			0
$187$	4.12579	−	7.14608i	0.301708	−	0.522573i
$188$	5.93704			0.433003
$189$		0			0
$190$	−8.03635			−0.583018
$191$	−17.6085			−1.27411			−0.637054	−	0.770819i	$-0.719847\pi$
$191$	−17.6085			−1.27411			−0.637054	+	0.770819i	$0.719847\pi$
$192$		0			0
$193$	4.22580			0.304180			0.152090	−	0.988367i	$-0.451400\pi$
$193$	4.22580			0.304180			0.152090	+	0.988367i	$0.451400\pi$
$194$	7.94907	+	13.7682i	0.570710	+	0.988499i
$195$		0			0
$196$	−6.68388			−0.477420
$197$	11.0548	+	19.1475i	0.787624	+	1.36421i	0.927419	+	0.374025i	$0.122022\pi$
$197$	11.0548	+	19.1475i	0.787624	+	1.36421i	−0.139794	+	0.990181i	$0.544644\pi$
$198$		0			0
$199$	−4.22595	−	7.31956i	−0.299570	−	0.518870i	0.676468	−	0.736472i	$-0.263510\pi$
$199$	−4.22595	−	7.31956i	−0.299570	−	0.518870i	−0.976038	+	0.217602i	$0.930176\pi$
$200$	1.31235	+	2.27306i	0.0927971	+	0.160729i
$201$		0			0
$202$	1.05409	+	1.82574i	0.0741655	+	0.128458i
$203$	2.41015			0.169159
$204$		0			0
$205$	8.61313	+	14.9184i	0.601567	+	1.04195i
$206$	−5.89275	−	10.2065i	−0.410567	−	0.711123i
$207$		0			0
$208$	0.735188	+	1.27338i	0.0509761	+	0.0882932i
$209$	5.80888	−	10.0613i	0.401809	−	0.695953i
$210$		0			0
$211$	26.7357			1.84056			0.920280	−	0.391261i	$-0.127961\pi$
$211$	26.7357			1.84056			0.920280	+	0.391261i	$0.127961\pi$
$212$	−0.731740	+	1.26741i	−0.0502561	+	0.0870461i
$213$		0			0
$214$	−3.06844	−	5.31470i	−0.209755	−	0.363306i
$215$	−32.4485			−2.21297
$216$		0			0
$217$	−3.07677	−	0.577160i	−0.208865	−	0.0391802i
$218$	6.43215	−	11.1408i	0.435640	−	0.754551i
$219$		0			0
$220$	−11.0227			−0.743147
$221$	−1.51971	−	2.63221i	−0.102227	−	0.177062i
$222$		0			0
$223$	−10.6257	−	18.4043i	−0.711551	−	1.23244i	−0.964275	−	0.264904i	$-0.914660\pi$
$223$	−10.6257	−	18.4043i	−0.711551	−	1.23244i	0.252723	−	0.967539i	$-0.418674\pi$
$224$	0.281122	−	0.486917i	0.0187832	−	0.0325335i
$225$		0			0
$226$	6.85988	+	11.8817i	0.456312	+	0.790356i
$227$	26.5385			1.76142			0.880711	−	0.473655i	$-0.157066\pi$
$227$	26.5385			1.76142			0.880711	+	0.473655i	$0.157066\pi$
$228$		0			0
$229$	−2.02883			−0.134069			−0.0670344	−	0.997751i	$-0.521354\pi$
$229$	−2.02883			−0.134069			−0.0670344	+	0.997751i	$0.521354\pi$
$230$	3.09779	−	5.36553i	0.204262	−	0.353793i
$231$		0			0
$232$	2.14333	−	3.71236i	0.140717	−	0.243728i
$233$	−12.9457			−0.848098			−0.424049	−	0.905639i	$-0.639392\pi$
$233$	−12.9457			−0.848098			−0.424049	+	0.905639i	$0.639392\pi$
$234$		0			0
$235$	8.19693	+	14.1975i	0.534709	+	0.926143i
$236$	−0.635617	−	1.10092i	−0.0413751	−	0.0716638i
$237$		0			0
$238$	−0.581108	+	1.00651i	−0.0376676	+	0.0652422i
$239$	6.91699	−	11.9806i	0.447423	−	0.774959i	−0.550795	−	0.834641i	$-0.685675\pi$
$239$	6.91699	−	11.9806i	0.447423	−	0.774959i	0.998217	+	0.0596818i	$0.0190086\pi$
$240$		0			0
$241$	13.9301	+	24.1277i	0.897317	+	1.55420i	0.830910	+	0.556407i	$0.187820\pi$
$241$	13.9301	+	24.1277i	0.897317	+	1.55420i	0.0664072	+	0.997793i	$0.478846\pi$
$242$	2.46746	−	4.27376i	0.158614	−	0.274728i
$243$		0			0
$244$	13.8457			0.886378
$245$	−9.22805	−	15.9835i	−0.589559	−	1.02115i
$246$		0			0
$247$	−2.13966	−	3.70601i	−0.136144	−	0.235808i
$248$	−3.62516	+	4.22590i	−0.230198	+	0.268345i
$249$		0			0
$250$	3.27944	−	5.68016i	0.207410	−	0.359245i
$251$	−4.36267	+	7.55637i	−0.275370	+	0.476954i	−0.970228	−	0.242192i	$-0.922134\pi$
$251$	−4.36267	+	7.55637i	−0.275370	+	0.476954i	0.694859	+	0.719146i	$0.255467\pi$
$252$		0			0
$253$	4.47833	+	7.75669i	0.281550	+	0.487659i
$254$	3.57207	+	6.18701i	0.224132	+	0.388208i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	3.24025	−	5.61228i	0.202121	−	0.350084i	−0.747090	−	0.664722i	$-0.768550\pi$
$257$	3.24025	−	5.61228i	0.202121	−	0.350084i	0.949212	+	0.314638i	$0.101883\pi$
$258$		0			0
$259$	−2.05628			−0.127771
$260$	−2.03006	+	3.51617i	−0.125899	+	0.218064i
$261$		0			0
$262$	−1.74226	+	3.01768i	−0.107637	+	0.186433i
$263$	−7.90071	+	13.6844i	−0.487178	+	0.843818i	−0.999891	−	0.0147424i	$-0.995307\pi$
$263$	−7.90071	+	13.6844i	−0.487178	+	0.843818i	0.512713	+	0.858560i	$0.328641\pi$
$264$		0			0
$265$	−4.04109			−0.248242
$266$	−0.818166	+	1.41711i	−0.0501650	+	0.0868883i
$267$		0			0
$268$	5.68951			0.347542
$269$	5.24517	+	9.08490i	0.319804	+	0.553916i	0.980447	−	0.196784i	$-0.0630497\pi$
$269$	5.24517	+	9.08490i	0.319804	+	0.553916i	−0.660643	+	0.750700i	$0.729716\pi$
$270$		0			0
$271$	19.1276			1.16192			0.580959	−	0.813933i	$-0.302678\pi$
$271$	19.1276			1.16192			0.580959	+	0.813933i	$0.302678\pi$
$272$	1.03355	+	1.79016i	0.0626683	+	0.108545i
$273$		0			0
$274$	−0.834449	+	1.44531i	−0.0504109	+	0.0873143i
$275$	−5.23871	−	9.07371i	−0.315906	−	0.547165i
$276$		0			0
$277$	−2.65245	+	4.59418i	−0.159370	+	0.276038i	−0.934642	−	0.355591i	$-0.884280\pi$
$277$	−2.65245	+	4.59418i	−0.159370	+	0.276038i	0.775271	+	0.631628i	$0.217613\pi$
$278$	−16.5616			−0.993296
$279$		0			0
$280$	1.55251			0.0927804
$281$	−11.3592	+	19.6748i	−0.677635	+	1.17370i	0.298057	+	0.954548i	$0.403662\pi$
$281$	−11.3592	+	19.6748i	−0.677635	+	1.17370i	−0.975691	+	0.219149i	$0.929672\pi$
$282$		0			0
$283$	12.8023	+	22.1743i	0.761019	+	1.31812i	0.942326	+	0.334697i	$0.108634\pi$
$283$	12.8023	+	22.1743i	0.761019	+	1.31812i	−0.181307	+	0.983427i	$0.558033\pi$
$284$	−2.14830	+	3.72096i	−0.127478	+	0.220798i
$285$		0			0
$286$	−2.93476	−	5.08316i	−0.173536	−	0.300573i
$287$	3.50755			0.207044
$288$		0			0
$289$	6.36354	+	11.0220i	0.374326	+	0.648351i
$290$	11.8367			0.695076
$291$		0			0
$292$	−4.67244	+	8.09290i	−0.273434	+	0.473601i
$293$	6.34563			0.370715			0.185358	−	0.982671i	$-0.440656\pi$
$293$	6.34563			0.370715			0.185358	+	0.982671i	$0.440656\pi$
$294$		0			0
$295$	1.75512	−	3.03996i	0.102187	−	0.176993i
$296$	−1.82864	+	3.16730i	−0.106288	+	0.184096i
$297$		0			0
$298$	6.37166	−	11.0360i	0.369101	−	0.639301i
$299$	3.29913			0.190793
$300$		0			0
$301$	−3.30352	+	5.72187i	−0.190412	+	0.329803i
$302$	2.16532	+	3.75045i	0.124600	+	0.215814i
$303$		0			0
$304$	1.45518	+	2.52045i	0.0834605	+	0.144558i
$305$	19.1159	+	33.1097i	1.09457	+	1.89586i
$306$		0			0
$307$	2.68363	−	4.64819i	0.153163	−	0.265286i	−0.779226	−	0.626743i	$-0.784387\pi$
$307$	2.68363	−	4.64819i	0.153163	−	0.265286i	0.932389	+	0.361457i	$0.117721\pi$
$308$	−1.12220	+	1.94370i	−0.0639431	+	0.110753i
$309$		0			0
$310$	−15.1106	−	2.83455i	−0.858226	−	0.160991i
$311$	14.3458	+	24.8477i	0.813476	+	1.40898i	0.910417	+	0.413691i	$0.135761\pi$
$311$	14.3458	+	24.8477i	0.813476	+	1.40898i	−0.0969413	+	0.995290i	$0.530906\pi$
$312$		0			0
$313$	−3.51471	−	6.08766i	−0.198663	−	0.344095i	0.749432	−	0.662081i	$-0.230327\pi$
$313$	−3.51471	−	6.08766i	−0.198663	−	0.344095i	−0.948095	+	0.317986i	$0.896993\pi$
$314$	−22.1618			−1.25066
$315$		0			0
$316$	0.516125	−	0.893955i	0.0290343	−	0.0502889i
$317$	2.92859	+	5.07247i	0.164486	+	0.284898i	0.936473	−	0.350741i	$-0.114070\pi$
$317$	2.92859	+	5.07247i	0.164486	+	0.284898i	−0.771987	+	0.635639i	$0.780737\pi$
$318$		0			0
$319$	−8.55588	+	14.8192i	−0.479037	+	0.829717i
$320$	1.38064	−	2.39134i	0.0771803	−	0.133680i
$321$		0			0
$322$	−0.630761	−	1.09251i	−0.0351509	−	0.0608832i
$323$	−3.00802	−	5.21004i	−0.167370	−	0.289894i
$324$		0			0
$325$	−3.85929			−0.214075
$326$	0.911611	−	1.57896i	0.0504895	−	0.0874503i
$327$		0			0
$328$	3.11925	−	5.40270i	0.172232	−	0.298314i
$329$	3.33806			0.184033
$330$		0			0
$331$	−14.4242			−0.792828			−0.396414	−	0.918072i	$-0.629745\pi$
$331$	−14.4242			−0.792828			−0.396414	+	0.918072i	$0.629745\pi$
$332$	−1.02216	−	1.77044i	−0.0560986	−	0.0971656i
$333$		0			0
$334$	3.20854	−	5.55736i	0.175564	−	0.304085i
$335$	7.85518	+	13.6056i	0.429175	+	0.743352i
$336$		0			0
$337$	13.7311	+	23.7829i	0.747978	+	1.29554i	0.948790	+	0.315907i	$0.102309\pi$
$337$	13.7311	+	23.7829i	0.747978	+	1.29554i	−0.200812	+	0.979630i	$0.564358\pi$
$338$	10.8380			0.589509
$339$		0			0
$340$	−2.85393	+	4.94316i	−0.154776	+	0.268080i
$341$	14.4711	−	16.8692i	0.783655	−	0.913517i
$342$		0			0
$343$	−7.69367			−0.415419
$344$	5.87561	+	10.1769i	0.316792	+	0.548700i
$345$		0			0
$346$	10.5109	−	18.2054i	0.565068	−	0.978726i
$347$	9.86345			0.529498			0.264749	−	0.964317i	$-0.414711\pi$
$347$	9.86345			0.529498			0.264749	+	0.964317i	$0.414711\pi$
$348$		0			0
$349$	5.34850	−	9.26388i	0.286299	−	0.495884i	−0.686624	−	0.727012i	$-0.740908\pi$
$349$	5.34850	−	9.26388i	0.286299	−	0.495884i	0.972923	+	0.231128i	$0.0742417\pi$
$350$	0.737859	+	1.27801i	0.0394402	+	0.0683125i
$351$		0			0
$352$	1.99593	+	3.45705i	0.106383	+	0.184261i
$353$	14.5379	+	25.1803i	0.773773	+	1.34021i	0.935481	+	0.353376i	$0.114966\pi$
$353$	14.5379	+	25.1803i	0.773773	+	1.34021i	−0.161708	+	0.986839i	$0.551700\pi$
$354$		0			0
$355$	−11.8641			−0.629682
$356$	−1.81892	−	3.15047i	−0.0964027	−	0.166974i
$357$		0			0
$358$	7.59632	+	13.1572i	0.401478	+	0.695380i
$359$	−1.79467	−	3.10846i	−0.0947189	−	0.164058i	0.814772	−	0.579781i	$-0.196862\pi$
$359$	−1.79467	−	3.10846i	−0.0947189	−	0.164058i	−0.909491	+	0.415723i	$0.863529\pi$
$360$		0			0
$361$	5.26489	+	9.11905i	0.277099	+	0.479950i
$362$	−2.75534			−0.144817
$363$		0			0
$364$	0.413354	+	0.715950i	0.0216656	+	0.0375260i
$365$	−25.8039			−1.35064
$366$		0			0
$367$	−14.6889			−0.766754			−0.383377	−	0.923592i	$-0.625239\pi$
$367$	−14.6889			−0.766754			−0.383377	+	0.923592i	$0.625239\pi$
$368$	−2.24373			−0.116963
$369$		0			0
$370$	−10.0988			−0.525012
$371$	−0.411416	+	0.712593i	−0.0213596	+	0.0369960i
$372$		0			0
$373$	−19.2242	−	33.2973i	−0.995392	−	1.72407i	−0.580741	−	0.814088i	$-0.697237\pi$
$373$	−19.2242	−	33.2973i	−0.995392	−	1.72407i	−0.414651	−	0.909981i	$-0.636096\pi$
$374$	−4.12579	−	7.14608i	−0.213340	−	0.369515i
$375$		0			0
$376$	2.96852	−	5.14163i	0.153090	−	0.265159i
$377$	3.15150	+	5.45856i	0.162311	+	0.281130i
$378$		0			0
$379$	−13.8582	+	24.0031i	−0.711849	+	1.23296i	0.252313	+	0.967646i	$0.418809\pi$
$379$	−13.8582	+	24.0031i	−0.711849	+	1.23296i	−0.964162	+	0.265313i	$0.914525\pi$
$380$	−4.01818	+	6.95968i	−0.206128	+	0.357024i
$381$		0			0
$382$	−8.80426	+	15.2494i	−0.450465	+	0.780229i
$383$	11.0303	−	19.1051i	0.563624	−	0.976225i	−0.433552	−	0.901128i	$-0.642740\pi$
$383$	11.0303	−	19.1051i	0.563624	−	0.976225i	0.997176	−	0.0750969i	$-0.0239266\pi$
$384$		0			0
$385$	−6.19741			−0.315849
$386$	2.11290	−	3.65965i	0.107544	−	0.186272i
$387$		0			0
$388$	15.8981			0.807106
$389$	−1.37490	−	2.38140i	−0.0697103	−	0.120742i	0.829063	−	0.559154i	$-0.188874\pi$
$389$	−1.37490	−	2.38140i	−0.0697103	−	0.120742i	−0.898774	+	0.438413i	$0.855541\pi$
$390$		0			0
$391$	4.63803			0.234555
$392$	−3.34194	+	5.78841i	−0.168794	+	0.292359i
$393$		0			0
$394$	22.1097			1.11387
$395$	2.85034			0.143416
$396$		0			0
$397$	−0.820424	+	1.42102i	−0.0411759	+	0.0713187i	−0.885879	−	0.463917i	$-0.846444\pi$
$397$	−0.820424	+	1.42102i	−0.0411759	+	0.0713187i	0.844703	+	0.535235i	$0.179777\pi$
$398$	−8.45190			−0.423656
$399$		0			0
$400$	2.62470			0.131235
$401$	4.89561	+	8.47944i	0.244475	+	0.423443i	0.961984	−	0.273106i	$-0.0880510\pi$
$401$	4.89561	+	8.47944i	0.244475	+	0.423443i	−0.717509	+	0.696549i	$0.754718\pi$
$402$		0			0
$403$	−2.71601	−	7.72304i	−0.135294	−	0.384712i
$404$	2.10818			0.104886
$405$		0			0
$406$	1.20507	−	2.08725i	0.0598068	−	0.103588i
$407$	7.29967	−	12.6434i	0.361831	−	0.626710i
$408$		0			0
$409$	16.7776			0.829599			0.414799	−	0.909913i	$-0.363852\pi$
$409$	16.7776			0.829599			0.414799	+	0.909913i	$0.363852\pi$
$410$	17.2263			0.850745
$411$		0			0
$412$	−11.7855			−0.580630
$413$	−0.357371	−	0.618985i	−0.0175851	−	0.0304583i
$414$		0			0
$415$	2.82249	−	4.88869i	0.138551	−	0.239977i
$416$	1.47038			0.0720911
$417$		0			0
$418$	−5.80888	−	10.0613i	−0.284122	−	0.492113i
$419$	−11.7683	−	20.3833i	−0.574919	−	0.995789i	−0.996050	−	0.0887895i	$-0.971700\pi$
$419$	−11.7683	−	20.3833i	−0.574919	−	0.995789i	0.421131	−	0.907000i	$-0.361633\pi$
$420$		0			0
$421$	35.4521			1.72783			0.863915	−	0.503638i	$-0.168005\pi$
$421$	35.4521			1.72783			0.863915	+	0.503638i	$0.168005\pi$
$422$	13.3678	−	23.1538i	0.650736	−	1.12711i
$423$		0			0
$424$	0.731740	+	1.26741i	0.0355364	+	0.0615509i
$425$	−5.42553			−0.263177
$426$		0			0
$427$	7.78463			0.376724
$428$	−6.13689			−0.296638
$429$		0			0
$430$	−16.2242	+	28.1012i	−0.782403	+	1.35516i
$431$	10.4796	−	18.1512i	0.504785	−	0.874314i	−0.495199	−	0.868779i	$-0.664905\pi$
$431$	10.4796	−	18.1512i	0.504785	−	0.874314i	0.999985	−	0.00553455i	$-0.00176171\pi$
$432$		0			0
$433$	−6.09639			−0.292974			−0.146487	−	0.989213i	$-0.546797\pi$
$433$	−6.09639			−0.292974			−0.146487	+	0.989213i	$0.546797\pi$
$434$	−2.03822	+	2.37598i	−0.0978377	+	0.114051i
$435$		0			0
$436$	−6.43215	−	11.1408i	−0.308044	−	0.533548i
$437$	6.53008			0.312376
$438$		0			0
$439$	−27.7751			−1.32563			−0.662817	−	0.748781i	$-0.730639\pi$
$439$	−27.7751			−1.32563			−0.662817	+	0.748781i	$0.730639\pi$
$440$	−5.51133	+	9.54590i	−0.262742	+	0.455083i
$441$		0			0
$442$	−3.03942			−0.144570
$443$	−3.02353			−0.143652			−0.0718262	−	0.997417i	$-0.522883\pi$
$443$	−3.02353			−0.143652			−0.0718262	+	0.997417i	$0.522883\pi$
$444$		0			0
$445$	5.02257	−	8.69934i	0.238092	−	0.412388i
$446$	−21.2515			−1.00629
$447$		0			0
$448$	−0.281122	−	0.486917i	−0.0132817	−	0.0230047i
$449$	26.6291			1.25671			0.628353	−	0.777928i	$-0.283729\pi$
$449$	26.6291			1.25671			0.628353	+	0.777928i	$0.283729\pi$
$450$		0			0
$451$	−12.4516	+	21.5668i	−0.586322	+	1.01554i
$452$	13.7198			0.645323
$453$		0			0
$454$	13.2692	−	22.9830i	0.622756	−	1.07865i
$455$	−1.14139	+	1.97694i	−0.0535091	+	0.0926805i
$456$		0			0
$457$	6.35410	−	11.0056i	0.297232	−	0.514822i	−0.678269	−	0.734813i	$-0.737270\pi$
$457$	6.35410	−	11.0056i	0.297232	−	0.514822i	0.975502	+	0.219992i	$0.0706030\pi$
$458$	−1.01441	+	1.75702i	−0.0474005	+	0.0821000i
$459$		0			0
$460$	−3.09779	−	5.36553i	−0.144435	−	0.250169i
$461$	−10.5442	+	18.2631i	−0.491093	+	0.850597i	−0.999947	−	0.0102549i	$-0.996736\pi$
$461$	−10.5442	+	18.2631i	−0.491093	+	0.850597i	0.508855	+	0.860852i	$0.330069\pi$
$462$		0			0
$463$	−8.33955	−	14.4445i	−0.387572	−	0.671294i	0.604551	−	0.796567i	$-0.293353\pi$
$463$	−8.33955	−	14.4445i	−0.387572	−	0.671294i	−0.992122	+	0.125273i	$0.960019\pi$
$464$	−2.14333	−	3.71236i	−0.0995017	−	0.172342i
$465$		0			0
$466$	−6.47283	+	11.2113i	−0.299848	+	0.519352i
$467$	34.4397			1.59368			0.796840	−	0.604191i	$-0.206504\pi$
$467$	34.4397			1.59368			0.796840	+	0.604191i	$0.206504\pi$
$468$		0			0
$469$	3.19889			0.147711
$470$	16.3939			0.756193
$471$		0			0
$472$	−1.27123			−0.0585133
$473$	−23.4546	−	40.6246i	−1.07844	−	1.86792i
$474$		0			0
$475$	−7.63883			−0.350494
$476$	0.581108	+	1.00651i	0.0266350	+	0.0461332i
$477$		0			0
$478$	−6.91699	−	11.9806i	−0.316376	−	0.547979i
$479$	12.6337	+	21.8823i	0.577250	+	0.999826i	0.995793	+	0.0916290i	$0.0292074\pi$
$479$	12.6337	+	21.8823i	0.577250	+	0.999826i	−0.418544	+	0.908197i	$0.637459\pi$
$480$		0			0
$481$	−2.68879	−	4.65712i	−0.122598	−	0.212346i
$482$	27.8602			1.26900
$483$		0			0
$484$	−2.46746	−	4.27376i	−0.112157	−	0.194262i
$485$	21.9497	+	38.0179i	0.996683	+	1.72630i
$486$		0			0
$487$	−13.9395	−	24.1440i	−0.631660	−	1.09407i	−0.987212	−	0.159411i	$-0.949040\pi$
$487$	−13.9395	−	24.1440i	−0.631660	−	1.09407i	0.355552	−	0.934657i	$-0.384293\pi$
$488$	6.92283	−	11.9907i	0.313382	−	0.542793i
$489$		0			0
$490$	−18.4561			−0.833762
$491$	1.00378	−	1.73860i	0.0452999	−	0.0784618i	−0.842486	−	0.538718i	$-0.818909\pi$
$491$	1.00378	−	1.73860i	0.0452999	−	0.0784618i	0.887786	+	0.460256i	$0.152242\pi$
$492$		0			0
$493$	4.43049	+	7.67384i	0.199539	+	0.345612i
$494$	−4.27933			−0.192536
$495$		0			0
$496$	1.84716	+	5.25243i	0.0829397	+	0.235841i
$497$	−1.20786	+	2.09208i	−0.0541801	+	0.0938427i
$498$		0			0
$499$	−20.5227			−0.918720			−0.459360	−	0.888250i	$-0.651921\pi$
$499$	−20.5227			−0.918720			−0.459360	+	0.888250i	$0.651921\pi$
$500$	−3.27944	−	5.68016i	−0.146661	−	0.254025i
$501$		0			0
$502$	4.36267	+	7.55637i	0.194716	+	0.337257i
$503$	16.3446	−	28.3097i	0.728771	−	1.26227i	−0.228632	−	0.973513i	$-0.573425\pi$
$503$	16.3446	−	28.3097i	0.728771	−	1.26227i	0.957403	−	0.288755i	$-0.0932413\pi$
$504$		0			0
$505$	2.91064	+	5.04138i	0.129522	+	0.224339i
$506$	8.95665			0.398172
$507$		0			0
$508$	7.14415			0.316970
$509$	15.4177	−	26.7042i	0.683376	−	1.18364i	−0.290568	−	0.956854i	$-0.593844\pi$
$509$	15.4177	−	26.7042i	0.683376	−	1.18364i	0.973944	−	0.226788i	$-0.0728223\pi$
$510$		0			0
$511$	−2.62705	+	4.55018i	−0.116214	+	0.201288i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−3.24025	−	5.61228i	−0.142921	−	0.247547i
$515$	−16.2716	−	28.1832i	−0.717011	−	1.24190i
$516$		0			0
$517$	−11.8499	+	20.5246i	−0.521158	+	0.902673i
$518$	−1.02814	+	1.78079i	−0.0451739	+	0.0782435i
$519$		0			0
$520$	2.03006	+	3.51617i	0.0890241	+	0.154194i
$521$	−4.71147	+	8.16051i	−0.206413	+	0.357519i	−0.950582	−	0.310473i	$-0.899513\pi$
$521$	−4.71147	+	8.16051i	−0.206413	+	0.357519i	0.744169	+	0.667992i	$0.232846\pi$
$522$		0			0
$523$	40.0302			1.75040			0.875200	−	0.483761i	$-0.160730\pi$
$523$	40.0302			1.75040			0.875200	+	0.483761i	$0.160730\pi$
$524$	1.74226	+	3.01768i	0.0761109	+	0.131828i
$525$		0			0
$526$	7.90071	+	13.6844i	0.344487	+	0.596669i
$527$	−3.81826	−	10.8573i	−0.166326	−	0.472952i
$528$		0			0
$529$	8.98284	−	15.5587i	0.390558	−	0.676466i
$530$	−2.02054	+	3.49968i	−0.0877668	+	0.152016i
$531$		0			0
$532$	0.818166	+	1.41711i	0.0354720	+	0.0614393i
$533$	4.58646	+	7.94399i	0.198662	+	0.344092i
$534$		0			0
$535$	−8.47285	−	14.6754i	−0.366313	−	0.634473i
$536$	2.84476	−	4.92726i	0.122875	−	0.212825i
$537$		0			0
$538$	10.4903			0.452271
$539$	13.3405	−	23.1065i	0.574618	−	0.995268i
$540$		0			0
$541$	−7.70912	+	13.3526i	−0.331441	+	0.574073i	−0.982795	−	0.184702i	$-0.940868\pi$
$541$	−7.70912	+	13.3526i	−0.331441	+	0.574073i	0.651354	+	0.758774i	$0.274201\pi$
$542$	9.56379	−	16.5650i	0.410800	−	0.711527i
$543$		0			0
$544$	2.06710			0.0886264
$545$	17.7610	−	30.7630i	0.760798	−	1.31774i
$546$		0			0
$547$	−5.40646			−0.231164			−0.115582	−	0.993298i	$-0.536873\pi$
$547$	−5.40646			−0.231164			−0.115582	+	0.993298i	$0.536873\pi$
$548$	0.834449	+	1.44531i	0.0356459	+	0.0617405i
$549$		0			0
$550$	−10.4774			−0.446759
$551$	6.23788	+	10.8043i	0.265743	+	0.460280i
$552$		0			0
$553$	0.290188	−	0.502620i	0.0123400	−	0.0213736i
$554$	2.65245	+	4.59418i	0.112692	+	0.195188i
$555$		0			0
$556$	−8.28078	+	14.3427i	−0.351183	+	0.608267i
$557$	−27.1620			−1.15089			−0.575445	−	0.817840i	$-0.695171\pi$
$557$	−27.1620			−1.15089			−0.575445	+	0.817840i	$0.695171\pi$
$558$		0			0
$559$	−17.2787			−0.730812
$560$	0.776257	−	1.34452i	0.0328028	−	0.0568162i
$561$		0			0
$562$	11.3592	+	19.6748i	0.479160	+	0.829929i
$563$	2.45043	−	4.24427i	0.103273	−	0.178874i	−0.809758	−	0.586764i	$-0.800402\pi$
$563$	2.45043	−	4.24427i	0.103273	−	0.178874i	0.913031	+	0.407889i	$0.133735\pi$
$564$		0			0
$565$	18.9421	+	32.8087i	0.796900	+	1.38027i
$566$	25.6046			1.07624
$567$		0			0
$568$	2.14830	+	3.72096i	0.0901405	+	0.156128i
$569$	−26.8565			−1.12589			−0.562943	−	0.826496i	$-0.690331\pi$
$569$	−26.8565			−1.12589			−0.562943	+	0.826496i	$0.690331\pi$
$570$		0			0
$571$	−19.4371	+	33.6661i	−0.813419	+	1.40888i	0.0970391	+	0.995281i	$0.469063\pi$
$571$	−19.4371	+	33.6661i	−0.813419	+	1.40888i	−0.910458	+	0.413602i	$0.864271\pi$
$572$	−5.86953			−0.245417
$573$		0			0
$574$	1.75378	−	3.03763i	0.0732012	−	0.126788i
$575$	2.94456	−	5.10013i	0.122797	−	0.212690i
$576$		0			0
$577$	3.68743	−	6.38682i	0.153510	−	0.265887i	−0.779006	−	0.627017i	$-0.784276\pi$
$577$	3.68743	−	6.38682i	0.153510	−	0.265887i	0.932515	+	0.361130i	$0.117609\pi$
$578$	12.7271			0.529377
$579$		0			0
$580$	5.91835	−	10.2509i	0.245746	−	0.425645i
$581$	−0.574705	−	0.995418i	−0.0238428	−	0.0412969i
$582$		0			0
$583$	−2.92100	−	5.05932i	−0.120975	−	0.209536i
$584$	4.67244	+	8.09290i	0.193347	+	0.334887i
$585$		0			0
$586$	3.17281	−	5.49547i	0.131068	−	0.227016i
$587$	−17.2870	+	29.9420i	−0.713511	+	1.23584i	0.250019	+	0.968241i	$0.419563\pi$
$587$	−17.2870	+	29.9420i	−0.713511	+	1.23584i	−0.963531	+	0.267597i	$0.913770\pi$
$588$		0			0
$589$	−5.37590	−	15.2865i	−0.221510	−	0.629869i
$590$	−1.75512	−	3.03996i	−0.0722571	−	0.125153i
$591$		0			0
$592$	1.82864	+	3.16730i	0.0751567	+	0.130175i
$593$	−20.4038			−0.837884			−0.418942	−	0.908013i	$-0.637599\pi$
$593$	−20.4038			−0.837884			−0.418942	+	0.908013i	$0.637599\pi$
$594$		0			0
$595$	−1.60460	+	2.77926i	−0.0657823	+	0.113938i
$596$	−6.37166	−	11.0360i	−0.260994	−	0.452054i
$597$		0			0
$598$	1.64956	−	2.85713i	0.0674557	−	0.116837i
$599$	−18.7854	+	32.5373i	−0.767551	+	1.32944i	0.171337	+	0.985213i	$0.445191\pi$
$599$	−18.7854	+	32.5373i	−0.767551	+	1.32944i	−0.938887	+	0.344224i	$0.888142\pi$
$600$		0			0
$601$	−7.88826	−	13.6629i	−0.321769	−	0.557320i	0.659084	−	0.752069i	$-0.270944\pi$
$601$	−7.88826	−	13.6629i	−0.321769	−	0.557320i	−0.980853	+	0.194749i	$0.937611\pi$
$602$	3.30352	+	5.72187i	0.134642	+	0.233206i
$603$		0			0
$604$	4.33065			0.176212
$605$	6.81336	−	11.8011i	0.277002	−	0.479782i
$606$		0			0
$607$	−3.23359	+	5.60074i	−0.131247	+	0.227327i	−0.924158	−	0.382011i	$-0.875232\pi$
$607$	−3.23359	+	5.60074i	−0.131247	+	0.227327i	0.792910	+	0.609338i	$0.208565\pi$
$608$	2.91037			0.118031
$609$		0			0
$610$	38.2318			1.54796
$611$	4.36484	+	7.56012i	0.176582	+	0.305850i
$612$		0			0
$613$	−9.79127	+	16.9590i	−0.395466	+	0.684967i	−0.993160	−	0.116757i	$-0.962750\pi$
$613$	−9.79127	+	16.9590i	−0.395466	+	0.684967i	0.597695	+	0.801724i	$0.296083\pi$
$614$	−2.68363	−	4.64819i	−0.108303	−	0.187586i
$615$		0			0
$616$	1.12220	+	1.94370i	0.0452146	+	0.0783140i
$617$	−10.6772			−0.429846			−0.214923	−	0.976631i	$-0.568950\pi$
$617$	−10.6772			−0.429846			−0.214923	+	0.976631i	$0.568950\pi$
$618$		0			0
$619$	4.27984	−	7.41290i	0.172021	−	0.297950i	−0.767105	−	0.641521i	$-0.778304\pi$
$619$	4.27984	−	7.41290i	0.172021	−	0.297950i	0.939126	+	0.343572i	$0.111637\pi$
$620$	−10.0101	+	11.6689i	−0.402015	+	0.468635i
$621$		0			0
$622$	28.6916			1.15043
$623$	−1.02268	−	1.77133i	−0.0409727	−	0.0709668i
$624$		0			0
$625$	15.6172	−	27.0498i	0.624689	−	1.08199i
$626$	−7.02943			−0.280953
$627$		0			0
$628$	−11.0809	+	19.1927i	−0.442176	+	0.765872i
$629$	−3.77999	−	6.54714i	−0.150718	−	0.261052i
$630$		0			0
$631$	−8.95079	−	15.5032i	−0.356325	−	0.617174i	0.631018	−	0.775768i	$-0.282637\pi$
$631$	−8.95079	−	15.5032i	−0.356325	−	0.617174i	−0.987344	+	0.158594i	$0.949304\pi$
$632$	−0.516125	−	0.893955i	−0.0205303	−	0.0355596i
$633$		0			0
$634$	5.85718			0.232619
$635$	9.86351	+	17.0841i	0.391422	+	0.677962i
$636$		0			0
$637$	−4.91391	−	8.51114i	−0.194696	−	0.337224i
$638$	8.55588	+	14.8192i	0.338730	+	0.586698i
$639$		0			0
$640$	−1.38064	−	2.39134i	−0.0545747	−	0.0945262i
$641$	1.27105			0.0502034			0.0251017	−	0.999685i	$-0.492009\pi$
$641$	1.27105			0.0502034			0.0251017	+	0.999685i	$0.492009\pi$
$642$		0			0
$643$	21.4808	+	37.2058i	0.847119	+	1.46725i	0.883769	+	0.467924i	$0.154998\pi$
$643$	21.4808	+	37.2058i	0.847119	+	1.46725i	−0.0366500	+	0.999328i	$0.511669\pi$
$644$	−1.26152			−0.0497109
$645$		0			0
$646$	−6.01603			−0.236698
$647$	−31.9389			−1.25565			−0.627824	−	0.778355i	$-0.716054\pi$
$647$	−31.9389			−1.25565			−0.627824	+	0.778355i	$0.716054\pi$
$648$		0			0
$649$	5.07458			0.199195
$650$	−1.92965	+	3.34224i	−0.0756869	+	0.131094i
$651$		0			0
$652$	−0.911611	−	1.57896i	−0.0357014	−	0.0618367i
$653$	−1.74521	−	3.02279i	−0.0682953	−	0.118291i	0.829856	−	0.557978i	$-0.188423\pi$
$653$	−1.74521	−	3.02279i	−0.0682953	−	0.118291i	−0.898151	+	0.439687i	$0.855089\pi$
$654$		0			0
$655$	−4.81087	+	8.33268i	−0.187976	+	0.325585i
$656$	−3.11925	−	5.40270i	−0.121786	−	0.210940i
$657$		0			0
$658$	1.66903	−	2.89084i	0.0650656	−	0.112697i
$659$	5.41504	−	9.37912i	0.210940	−	0.365359i	−0.741069	−	0.671429i	$-0.765681\pi$
$659$	5.41504	−	9.37912i	0.210940	−	0.365359i	0.952009	+	0.306070i	$0.0990142\pi$
$660$		0			0
$661$	14.6983	−	25.4582i	0.571698	−	0.990209i	−0.424694	−	0.905337i	$-0.639618\pi$
$661$	14.6983	−	25.4582i	0.571698	−	0.990209i	0.996392	−	0.0848723i	$-0.0270482\pi$
$662$	−7.21212	+	12.4918i	−0.280307	+	0.485506i
$663$		0			0
$664$	−2.04433			−0.0793354
$665$	−2.25919	+	3.91303i	−0.0876077	+	0.151741i
$666$		0			0
$667$	−9.61813			−0.372415
$668$	−3.20854	−	5.55736i	−0.124142	−	0.215021i
$669$		0			0
$670$	15.7104			0.606944
$671$	−27.6349	+	47.8651i	−1.06684	+	1.84781i
$672$		0			0
$673$	13.8437			0.533634			0.266817	−	0.963747i	$-0.414028\pi$
$673$	13.8437			0.533634			0.266817	+	0.963747i	$0.414028\pi$
$674$	27.4621			1.05780
$675$		0			0
$676$	5.41900	−	9.38598i	0.208423	−	0.360999i
$677$	−48.5912			−1.86751			−0.933755	−	0.357912i	$-0.883489\pi$
$677$	−48.5912			−1.86751			−0.933755	+	0.357912i	$0.883489\pi$
$678$		0			0
$679$	8.93862			0.343033
$680$	2.85393	+	4.94316i	0.109443	+	0.189561i
$681$		0			0
$682$	−7.37358	−	20.9669i	−0.282349	−	0.802866i
$683$	−12.4018			−0.474540			−0.237270	−	0.971444i	$-0.576253\pi$
$683$	−12.4018			−0.474540			−0.237270	+	0.971444i	$0.576253\pi$
$684$		0			0
$685$	−2.30415	+	3.99091i	−0.0880371	+	0.152485i
$686$	−3.84683	+	6.66291i	−0.146873	+	0.254391i
$687$		0			0
$688$	11.7512			0.448011
$689$	−2.15186			−0.0819795
$690$		0			0
$691$	−19.2775			−0.733351			−0.366675	−	0.930349i	$-0.619504\pi$
$691$	−19.2775			−0.733351			−0.366675	+	0.930349i	$0.619504\pi$
$692$	−10.5109	−	18.2054i	−0.399563	−	0.692064i
$693$		0			0
$694$	4.93173	−	8.54200i	0.187206	−	0.324250i
$695$	−45.7312			−1.73468
$696$		0			0
$697$	6.44781	+	11.1679i	0.244228	+	0.423016i
$698$	−5.34850	−	9.26388i	−0.202444	−	0.350643i
$699$		0			0
$700$	1.47572			0.0557769
$701$	21.8284	−	37.8079i	0.824447	−	1.42798i	−0.0778936	−	0.996962i	$-0.524819\pi$
$701$	21.8284	−	37.8079i	0.824447	−	1.42798i	0.902341	−	0.431023i	$-0.141847\pi$
$702$		0			0
$703$	−5.32202	−	9.21800i	−0.200724	−	0.347664i
$704$	3.99186			0.150449
$705$		0			0
$706$	29.0758			1.09428
$707$	1.18531			0.0445781
$708$		0			0
$709$	0.117091	−	0.202808i	0.00439746	−	0.00761662i	−0.863818	−	0.503803i	$-0.831934\pi$
$709$	0.117091	−	0.202808i	0.00439746	−	0.00761662i	0.868216	+	0.496187i	$0.165267\pi$
$710$	−5.93206	+	10.2746i	−0.222626	+	0.385600i
$711$		0			0
$712$	−3.63785			−0.136334
$713$	12.2784	+	2.30326i	0.459830	+	0.0862578i
$714$		0			0
$715$	−8.10372	−	14.0361i	−0.303062	−	0.524919i
$716$	15.1926			0.567775
$717$		0			0
$718$	−3.58934			−0.133953
$719$	22.2177	−	38.4822i	0.828580	−	1.43514i	−0.0705720	−	0.997507i	$-0.522482\pi$
$719$	22.2177	−	38.4822i	0.828580	−	1.43514i	0.899152	−	0.437636i	$-0.144184\pi$
$720$		0			0
$721$	−6.62631			−0.246777
$722$	10.5298			0.391877
$723$		0			0
$724$	−1.37767	+	2.38619i	−0.0512007	+	0.0886822i
$725$	11.2512			0.417859
$726$		0			0
$727$	−5.06156	−	8.76688i	−0.187723	−	0.325145i	0.756768	−	0.653684i	$-0.226777\pi$
$727$	−5.06156	−	8.76688i	−0.187723	−	0.325145i	−0.944491	+	0.328538i	$0.893444\pi$
$728$	0.826708			0.0306398
$729$		0			0
$730$	−12.9019	+	22.3468i	−0.477522	+	0.827093i
$731$	−24.2910			−0.898436
$732$		0			0
$733$	−16.8826	+	29.2415i	−0.623574	+	1.08006i	0.365241	+	0.930913i	$0.380986\pi$
$733$	−16.8826	+	29.2415i	−0.623574	+	1.08006i	−0.988815	+	0.149148i	$0.952347\pi$
$734$	−7.34444	+	12.7209i	−0.271088	+	0.469539i
$735$		0			0
$736$	−1.12187	+	1.94313i	−0.0413525	+	0.0716247i
$737$	−11.3559	+	19.6689i	−0.418298	+	0.724514i
$738$		0			0
$739$	12.3038	+	21.3109i	0.452604	+	0.783934i	0.998547	−	0.0538888i	$-0.0171616\pi$
$739$	12.3038	+	21.3109i	0.452604	+	0.783934i	−0.545943	+	0.837823i	$0.683828\pi$
$740$	−5.04940	+	8.74582i	−0.185620	+	0.321503i
$741$		0			0
$742$	0.411416	+	0.712593i	0.0151035	+	0.0261601i
$743$	−7.66651	−	13.2788i	−0.281257	−	0.487152i	0.690438	−	0.723392i	$-0.257418\pi$
$743$	−7.66651	−	13.2788i	−0.281257	−	0.487152i	−0.971695	+	0.236240i	$0.924085\pi$
$744$		0			0
$745$	17.5940	−	30.4737i	0.644594	−	1.11647i
$746$	−38.4484			−1.40770
$747$		0			0
$748$	−8.25158			−0.301708
$749$	−3.45042			−0.126076
$750$		0			0
$751$	−35.9315			−1.31116			−0.655580	−	0.755126i	$-0.727576\pi$
$751$	−35.9315			−1.31116			−0.655580	+	0.755126i	$0.727576\pi$
$752$	−2.96852	−	5.14163i	−0.108251	−	0.187496i
$753$		0			0
$754$	6.30301			0.229542
$755$	5.97908	+	10.3561i	0.217601	+	0.376896i
$756$		0			0
$757$	−6.91512	−	11.9773i	−0.251334	−	0.435324i	0.712559	−	0.701612i	$-0.247536\pi$
$757$	−6.91512	−	11.9773i	−0.251334	−	0.435324i	−0.963893	+	0.266288i	$0.914203\pi$
$758$	13.8582	+	24.0031i	0.503353	+	0.871833i
$759$		0			0
$760$	4.01818	+	6.95968i	0.145755	+	0.252454i
$761$	−21.8022			−0.790331			−0.395165	−	0.918610i	$-0.629313\pi$
$761$	−21.8022			−0.790331			−0.395165	+	0.918610i	$0.629313\pi$
$762$		0			0
$763$	−3.61643	−	6.26385i	−0.130924	−	0.226766i
$764$	8.80426	+	15.2494i	0.318527	+	0.551705i
$765$		0			0
$766$	−11.0303	−	19.1051i	−0.398542	−	0.690295i
$767$	0.934595	−	1.61877i	0.0337463	−	0.0584503i
$768$		0			0
$769$	−11.3437			−0.409066			−0.204533	−	0.978860i	$-0.565568\pi$
$769$	−11.3437			−0.409066			−0.204533	+	0.978860i	$0.565568\pi$
$770$	−3.09871	+	5.36712i	−0.111670	+	0.193417i
$771$		0			0
$772$	−2.11290	−	3.65965i	−0.0760450	−	0.131714i
$773$	−45.7918			−1.64702			−0.823509	−	0.567303i	$-0.807987\pi$
$773$	−45.7918			−1.64702			−0.823509	+	0.567303i	$0.807987\pi$
$774$		0			0
$775$	−14.3632	−	2.69433i	−0.515941	−	0.0967834i
$776$	7.94907	−	13.7682i	0.285355	−	0.494249i
$777$		0			0
$778$	−2.74980			−0.0985852
$779$	9.07815	+	15.7238i	0.325259	+	0.563364i
$780$		0			0
$781$	−8.57569	−	14.8535i	−0.306862	−	0.531501i
$782$	2.31901	−	4.01665i	0.0829277	−	0.143635i
$783$		0			0
$784$	3.34194	+	5.78841i	0.119355	+	0.206729i
$785$	−61.1951			−2.18415
$786$		0			0
$787$	7.58536			0.270389			0.135194	−	0.990819i	$-0.456834\pi$
$787$	7.58536			0.270389			0.135194	+	0.990819i	$0.456834\pi$
$788$	11.0548	−	19.1475i	0.393812	−	0.682103i
$789$		0			0
$790$	1.42517	−	2.46846i	0.0507052	−	0.0878240i
$791$	7.71384			0.274273
$792$		0			0
$793$	10.1792	+	17.6308i	0.361472	+	0.626089i
$794$	0.820424	+	1.42102i	0.0291158	+	0.0504300i
$795$		0			0
$796$	−4.22595	+	7.31956i	−0.149785	+	0.259435i
$797$	−14.8039	+	25.6410i	−0.524380	+	0.908253i	0.475217	+	0.879869i	$0.342369\pi$
$797$	−14.8039	+	25.6410i	−0.524380	+	0.908253i	−0.999597	+	0.0283841i	$0.990964\pi$
$798$		0			0
$799$	6.13624	+	10.6283i	0.217085	+	0.376002i
$800$	1.31235	−	2.27306i	0.0463986	−	0.0803647i
$801$		0			0
$802$	9.79122			0.345740
$803$	−18.6517	−	32.3057i	−0.658204	−	1.14004i
$804$		0			0
$805$	−1.74171	−	3.01673i	−0.0613873	−	0.106326i
$806$	−8.04636	−	1.50939i	−0.283421	−	0.0531658i
$807$		0			0
$808$	1.05409	−	1.82574i	0.0370827	−	0.0642292i
$809$	−21.6194	+	37.4460i	−0.760099	+	1.31653i	0.182700	+	0.983169i	$0.441516\pi$
$809$	−21.6194	+	37.4460i	−0.760099	+	1.31653i	−0.942799	+	0.333361i	$0.891817\pi$
$810$		0			0
$811$	−22.3906	−	38.7817i	−0.786241	−	1.36181i	−0.928255	−	0.371944i	$-0.878691\pi$
$811$	−22.3906	−	38.7817i	−0.786241	−	1.36181i	0.142015	−	0.989865i	$-0.454642\pi$
$812$	−1.20507	−	2.08725i	−0.0422898	−	0.0732481i
$813$		0			0
$814$	−7.29967	−	12.6434i	−0.255853	−	0.443151i
$815$	2.51722	−	4.35995i	0.0881743	−	0.152722i
$816$		0			0
$817$	−34.2004			−1.19652
$818$	8.38880	−	14.5298i	0.293308	−	0.508024i
$819$		0			0
$820$	8.61313	−	14.9184i	0.300784	−	0.520973i
$821$	−0.261194	+	0.452402i	−0.00911574	+	0.0157889i	−0.870547	−	0.492085i	$-0.836235\pi$
$821$	−0.261194	+	0.452402i	−0.00911574	+	0.0157889i	0.861432	+	0.507874i	$0.169568\pi$
$822$		0			0
$823$	5.13594			0.179028			0.0895138	−	0.995986i	$-0.471469\pi$
$823$	5.13594			0.179028			0.0895138	+	0.995986i	$0.471469\pi$
$824$	−5.89275	+	10.2065i	−0.205284	+	0.355562i
$825$		0			0
$826$	−0.714742			−0.0248691
$827$	18.1801	+	31.4889i	0.632185	+	1.09498i	0.987104	+	0.160079i	$0.0511749\pi$
$827$	18.1801	+	31.4889i	0.632185	+	1.09498i	−0.354919	+	0.934897i	$0.615492\pi$
$828$		0			0
$829$	36.4298			1.26526			0.632630	−	0.774454i	$-0.281975\pi$
$829$	36.4298			1.26526			0.632630	+	0.774454i	$0.281975\pi$
$830$	−2.82249	−	4.88869i	−0.0979700	−	0.169689i
$831$		0			0
$832$	0.735188	−	1.27338i	0.0254880	−	0.0441466i
$833$	−6.90814	−	11.9653i	−0.239353	−	0.414571i
$834$		0			0
$835$	8.85971	−	15.3455i	0.306603	−	0.531052i
$836$	−11.6178			−0.401809
$837$		0			0
$838$	−23.5366			−0.813058
$839$	−2.42087	+	4.19306i	−0.0835776	+	0.144761i	−0.904784	−	0.425870i	$-0.859968\pi$
$839$	−2.42087	+	4.19306i	−0.0835776	+	0.144761i	0.821207	+	0.570631i	$0.193301\pi$
$840$		0			0
$841$	5.31225	+	9.20108i	0.183181	+	0.317279i
$842$	17.7261	−	30.7024i	0.610880	−	1.05808i
$843$		0			0
$844$	−13.3678	−	23.1538i	−0.460140	−	0.796985i
$845$	29.9268			1.02951
$846$		0			0
$847$	−1.38731	−	2.40289i	−0.0476686	−	0.0825644i
$848$	1.46348			0.0502561
$849$		0			0
$850$	−2.71276	+	4.69864i	−0.0930470	+	0.161162i
$851$	8.20596			0.281297
$852$		0			0
$853$	−4.69259	+	8.12781i	−0.160671	+	0.278291i	−0.935110	−	0.354359i	$-0.884699\pi$
$853$	−4.69259	+	8.12781i	−0.160671	+	0.278291i	0.774438	+	0.632649i	$0.218033\pi$
$854$	3.89231	−	6.74168i	0.133192	−	0.230696i
$855$		0			0
$856$	−3.06844	+	5.31470i	−0.104877	+	0.181653i
$857$	39.3604			1.34453			0.672263	−	0.740312i	$-0.265322\pi$
$857$	39.3604			1.34453			0.672263	+	0.740312i	$0.265322\pi$
$858$		0			0
$859$	−2.24672	+	3.89143i	−0.0766570	+	0.132774i	−0.901806	−	0.432142i	$-0.857758\pi$
$859$	−2.24672	+	3.89143i	−0.0766570	+	0.132774i	0.825149	+	0.564916i	$0.191091\pi$
$860$	16.2242	+	28.1012i	0.553242	+	0.958244i
$861$		0			0
$862$	−10.4796	−	18.1512i	−0.356937	−	0.618233i
$863$	−11.5510	−	20.0070i	−0.393202	−	0.681045i	0.599668	−	0.800249i	$-0.295299\pi$
$863$	−11.5510	−	20.0070i	−0.393202	−	0.681045i	−0.992870	+	0.119203i	$0.961966\pi$
$864$		0			0
$865$	29.0235	−	50.2702i	0.986829	−	1.70924i
$866$	−3.04820	+	5.27963i	−0.103582	+	0.179409i
$867$		0			0
$868$	1.03855	+	2.95314i	0.0352507	+	0.100236i
$869$	2.06030	+	3.56854i	0.0698908	+	0.121054i
$870$		0			0
$871$	4.18286	+	7.24492i	0.141731	+	0.245485i
$872$	−12.8643			−0.435640
$873$		0			0
$874$	3.26504	−	5.65521i	0.110442	−	0.191290i
$875$	−1.84384	−	3.19363i	−0.0623333	−	0.107964i
$876$		0			0
$877$	−23.7542	+	41.1436i	−0.802124	+	1.38932i	0.116092	+	0.993238i	$0.462963\pi$
$877$	−23.7542	+	41.1436i	−0.802124	+	1.38932i	−0.918216	+	0.396081i	$0.870370\pi$
$878$	−13.8876	+	24.0540i	−0.468683	+	0.811782i
$879$		0			0
$880$	5.51133	+	9.54590i	0.185787	+	0.321792i
$881$	27.7949	+	48.1423i	0.936435	+	1.62195i	0.772054	+	0.635557i	$0.219229\pi$
$881$	27.7949	+	48.1423i	0.936435	+	1.62195i	0.164381	+	0.986397i	$0.447437\pi$
$882$		0			0
$883$	1.92102			0.0646475			0.0323238	−	0.999477i	$-0.489709\pi$
$883$	1.92102			0.0646475			0.0323238	+	0.999477i	$0.489709\pi$
$884$	−1.51971	+	2.63221i	−0.0511134	+	0.0885309i
$885$		0			0
$886$	−1.51177	+	2.61845i	−0.0507888	+	0.0879687i
$887$	24.1943			0.812366			0.406183	−	0.913792i	$-0.366860\pi$
$887$	24.1943			0.812366			0.406183	+	0.913792i	$0.366860\pi$
$888$		0			0
$889$	4.01675			0.134717
$890$	−5.02257	−	8.69934i	−0.168357	−	0.291603i
$891$		0			0
$892$	−10.6257	+	18.4043i	−0.355776	+	0.616222i
$893$	8.63948	+	14.9640i	0.289109	+	0.500752i
$894$		0			0
$895$	20.9756	+	36.3308i	0.701137	+	1.21440i
$896$	−0.562243			−0.0187832
$897$		0			0
$898$	13.3146	−	23.0615i	0.444313	−	0.769572i
$899$	7.91814	+	22.5154i	0.264085	+	0.750931i
$900$		0			0
$901$	−3.02516			−0.100783
$902$	12.4516	+	21.5668i	0.414593	+	0.718095i
$903$		0			0
$904$	6.85988	−	11.8817i	0.228156	−	0.395178i
$905$	−7.60828			−0.252908
$906$		0			0
$907$	9.28510	−	16.0823i	0.308307	−	0.534003i	−0.669685	−	0.742645i	$-0.733571\pi$
$907$	9.28510	−	16.0823i	0.308307	−	0.534003i	0.977992	+	0.208642i	$0.0669043\pi$
$908$	−13.2692	−	22.9830i	−0.440355	−	0.762718i
$909$		0			0
$910$	1.14139	+	1.97694i	0.0378367	+	0.0655350i
$911$	−20.8285	−	36.0760i	−0.690079	−	1.19525i	−0.971811	−	0.235759i	$-0.924242\pi$
$911$	−20.8285	−	36.0760i	−0.690079	−	1.19525i	0.281732	−	0.959493i	$-0.409091\pi$
$912$		0			0
$913$	8.16067			0.270079
$914$	−6.35410	−	11.0056i	−0.210175	−	0.364034i
$915$		0			0
$916$	1.01441	+	1.75702i	0.0335172	+	0.0580535i
$917$	0.979572	+	1.69667i	0.0323483	+	0.0560290i
$918$		0			0
$919$	−17.9232	−	31.0439i	−0.591231	−	1.02404i	−0.994067	−	0.108770i	$-0.965309\pi$
$919$	−17.9232	−	31.0439i	−0.591231	−	1.02404i	0.402836	−	0.915272i	$-0.368025\pi$
$920$	−6.19558			−0.204262
$921$		0			0
$922$	10.5442	+	18.2631i	0.347255	+	0.601463i
$923$	−6.31760			−0.207946
$924$		0			0
$925$	−9.59927			−0.315622
$926$	−16.6791			−0.548109
$927$		0			0
$928$	−4.28667			−0.140717
$929$	14.7317	−	25.5161i	0.483333	−	0.837157i	−0.516484	−	0.856297i	$-0.672759\pi$
$929$	14.7317	−	25.5161i	0.483333	−	0.837157i	0.999817	+	0.0191398i	$0.00609277\pi$
$930$		0			0
$931$	−9.72627	−	16.8464i	−0.318766	−	0.552118i
$932$	6.47283	+	11.2113i	0.212024	+	0.367237i
$933$		0			0
$934$	17.2199	−	29.8257i	0.563451	−	0.975925i
$935$	−11.3925	−	19.7324i	−0.372574	−	0.645318i
$936$		0			0
$937$	6.46800	−	11.2029i	0.211300	−	0.365983i	−0.740821	−	0.671702i	$-0.765563\pi$
$937$	6.46800	−	11.2029i	0.211300	−	0.365983i	0.952122	+	0.305719i	$0.0988968\pi$
$938$	1.59944	−	2.77032i	0.0522237	−	0.0904541i
$939$		0			0
$940$	8.19693	−	14.1975i	0.267354	−	0.463071i
$941$	−26.5819	+	46.0413i	−0.866546	+	1.50090i	−0.00104283	+	0.999999i	$0.500332\pi$
$941$	−26.5819	+	46.0413i	−0.866546	+	1.50090i	−0.865504	+	0.500903i	$0.833001\pi$
$942$		0			0
$943$	−13.9975			−0.455822
$944$	−0.635617	+	1.10092i	−0.0206876	+	0.0358319i
$945$		0			0
$946$	−46.9092			−1.52515
$947$	−22.3097	−	38.6415i	−0.724968	−	1.25568i	−0.958987	−	0.283450i	$-0.908521\pi$
$947$	−22.3097	−	38.6415i	−0.724968	−	1.25568i	0.234019	−	0.972232i	$-0.424812\pi$
$948$		0			0
$949$	−13.7405			−0.446035
$950$	−3.81942	+	6.61542i	−0.123918	+	0.214633i
$951$		0			0
$952$	1.16222			0.0376676
$953$	−28.5363			−0.924382			−0.462191	−	0.886780i	$-0.652937\pi$
$953$	−28.5363			−0.924382			−0.462191	+	0.886780i	$0.652937\pi$
$954$		0			0
$955$	−24.3111	+	42.1080i	−0.786688	+	1.36258i
$956$	−13.8340			−0.447423
$957$		0			0
$958$	25.2674			0.816354
$959$	0.469163	+	0.812615i	0.0151501	+	0.0262407i
$960$		0			0
$961$	−4.71644	−	30.6391i	−0.152143	−	0.988358i
$962$	−5.37758			−0.173380
$963$		0			0
$964$	13.9301	−	24.1277i	0.448659	−	0.777100i
$965$	5.83433	−	10.1054i	0.187814	−	0.325303i
$966$		0			0
$967$	−12.6640			−0.407245			−0.203623	−	0.979049i	$-0.565272\pi$
$967$	−12.6640			−0.407245			−0.203623	+	0.979049i	$0.565272\pi$
$968$	−4.93492			−0.158614
$969$		0			0
$970$	43.8993			1.40952
$971$	−18.7126	−	32.4111i	−0.600515	−	1.04012i	−0.992743	−	0.120255i	$-0.961629\pi$
$971$	−18.7126	−	32.4111i	−0.600515	−	1.04012i	0.392228	−	0.919868i	$-0.371705\pi$
$972$		0			0
$973$	−4.65581	+	8.06410i	−0.149258	+	0.258523i
$974$	−27.8791			−0.893303
$975$		0			0
$976$	−6.92283	−	11.9907i	−0.221594	−	0.383813i
$977$	−20.4535	−	35.4264i	−0.654364	−	1.13339i	−0.982053	−	0.188606i	$-0.939603\pi$
$977$	−20.4535	−	35.4264i	−0.654364	−	1.13339i	0.327689	−	0.944786i	$-0.393730\pi$
$978$		0			0
$979$	14.5218			0.464117
$980$	−9.22805	+	15.9835i	−0.294779	+	0.510573i
$981$		0			0
$982$	−1.00378	−	1.73860i	−0.0320319	−	0.0554809i
$983$	−19.5580			−0.623802			−0.311901	−	0.950115i	$-0.600966\pi$
$983$	−19.5580			−0.623802			−0.311901	+	0.950115i	$0.600966\pi$
$984$		0			0
$985$	61.0511			1.94525
$986$	8.86099			0.282191
$987$		0			0
$988$	−2.13966	+	3.70601i	−0.0680718	+	0.117904i
$989$	13.1833	−	22.8341i	0.419204	−	0.726083i
$990$		0			0
$991$	17.9448			0.570035			0.285018	−	0.958522i	$-0.408001\pi$
$991$	17.9448			0.570035			0.285018	+	0.958522i	$0.408001\pi$
$992$	5.47232	+	1.02653i	0.173746	+	0.0325924i
$993$		0			0
$994$	1.20786	+	2.09208i	0.0383111	+	0.0663568i
$995$	−23.3381			−0.739868
$996$		0			0
$997$	13.6427			0.432070			0.216035	−	0.976386i	$-0.430688\pi$
$997$	13.6427			0.432070			0.216035	+	0.976386i	$0.430688\pi$
$998$	−10.2613	+	17.7731i	−0.324817	+	0.562599i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1674.2.g.b.1369.13		32
3.2	odd	2		558.2.g.a.439.3	yes	32
9.4	even	3		1674.2.h.b.253.4		32
9.5	odd	6		558.2.h.a.67.14	yes	32
31.25	even	3		1674.2.h.b.397.4		32
93.56	odd	6		558.2.h.a.25.14	yes	32
279.149	odd	6		558.2.g.a.211.3	✓	32
279.211	even	3	inner	1674.2.g.b.955.13		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
558.2.g.a.211.3	✓	32	279.149	odd	6
558.2.g.a.439.3	yes	32	3.2	odd	2
558.2.h.a.25.14	yes	32	93.56	odd	6
558.2.h.a.67.14	yes	32	9.5	odd	6
1674.2.g.b.955.13		32	279.211	even	3	inner
1674.2.g.b.1369.13		32	1.1	even	1	trivial
1674.2.h.b.253.4		32	9.4	even	3
1674.2.h.b.397.4		32	31.25	even	3

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:	\( N \)	\(=\)	\( 1674 = 2 \cdot 3^{3} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1674.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.38064 - 2.39134i) q^{5} +(-0.281122 - 0.486917i) q^{7} -1.00000 q^{8} +(-1.38064 - 2.39134i) q^{10} +3.99186 q^{11} +(0.735188 - 1.27338i) q^{13} -0.562243 q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.03355 - 1.79016i) q^{17} +(1.45518 - 2.52045i) q^{19} -2.76129 q^{20} +(1.99593 - 3.45705i) q^{22} +(1.12187 + 1.94313i) q^{23} +(-1.31235 - 2.27306i) q^{25} +(-0.735188 - 1.27338i) q^{26} +(-0.281122 + 0.486917i) q^{28} +(-2.14333 + 3.71236i) q^{29} +(3.62516 - 4.22590i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.03355 - 1.79016i) q^{34} -1.55251 q^{35} +(1.82864 - 3.16730i) q^{37} +(-1.45518 - 2.52045i) q^{38} +(-1.38064 + 2.39134i) q^{40} +(-3.11925 + 5.40270i) q^{41} +(-5.87561 - 10.1769i) q^{43} +(-1.99593 - 3.45705i) q^{44} +2.24373 q^{46} +(-2.96852 + 5.14163i) q^{47} +(3.34194 - 5.78841i) q^{49} -2.62470 q^{50} -1.47038 q^{52} +(-0.731740 - 1.26741i) q^{53} +(5.51133 - 9.54590i) q^{55} +(0.281122 + 0.486917i) q^{56} +(2.14333 + 3.71236i) q^{58} +1.27123 q^{59} +(-6.92283 + 11.9907i) q^{61} +(-1.84716 - 5.25243i) q^{62} +1.00000 q^{64} +(-2.03006 - 3.51617i) q^{65} +(-2.84476 + 4.92726i) q^{67} -2.06710 q^{68} +(-0.776257 + 1.34452i) q^{70} +(-2.14830 - 3.72096i) q^{71} +(-4.67244 - 8.09290i) q^{73} +(-1.82864 - 3.16730i) q^{74} -2.91037 q^{76} +(-1.12220 - 1.94370i) q^{77} +(0.516125 + 0.893955i) q^{79} +(1.38064 + 2.39134i) q^{80} +(3.11925 + 5.40270i) q^{82} +2.04433 q^{83} +(-2.85393 - 4.94316i) q^{85} -11.7512 q^{86} -3.99186 q^{88} +3.63785 q^{89} -0.826708 q^{91} +(1.12187 - 1.94313i) q^{92} +(2.96852 + 5.14163i) q^{94} +(-4.01818 - 6.95968i) q^{95} +(-7.94907 + 13.7682i) q^{97} +(-3.34194 - 5.78841i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{2} - 16 q^{4} + q^{5} + q^{7} - 32 q^{8} - q^{10} - 4 q^{11} - 10 q^{13} + 2 q^{14} - 16 q^{16} + 4 q^{17} + 4 q^{19} - 2 q^{20} - 2 q^{22} + q^{23} - 19 q^{25} + 10 q^{26} + q^{28} + 3 q^{29}+ \cdots + 13 q^{98}+O(q^{100}) \) 32 * q + 16 * q^2 - 16 * q^4 + q^5 + q^7 - 32 * q^8 - q^10 - 4 * q^11 - 10 * q^13 + 2 * q^14 - 16 * q^16 + 4 * q^17 + 4 * q^19 - 2 * q^20 - 2 * q^22 + q^23 - 19 * q^25 + 10 * q^26 + q^28 + 3 * q^29 - q^31 + 16 * q^32 - 4 * q^34 - 19 * q^37 - 4 * q^38 - q^40 - 10 * q^41 - 13 * q^43 + 2 * q^44 + 2 * q^46 + 6 * q^47 - 13 * q^49 - 38 * q^50 + 20 * q^52 + 7 * q^53 - 11 * q^55 - q^56 - 3 * q^58 - 12 * q^59 + 7 * q^61 - 11 * q^62 + 32 * q^64 + 8 * q^65 - 8 * q^67 - 8 * q^68 - 7 * q^71 + 7 * q^73 + 19 * q^74 - 8 * q^76 + q^77 - 34 * q^79 + q^80 + 10 * q^82 + 28 * q^83 + 13 * q^85 - 26 * q^86 + 4 * q^88 - 2 * q^89 + 24 * q^91 + q^92 - 6 * q^94 - 21 * q^95 + 10 * q^97 + 13 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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