LMFDB - Embedded newform 1674.2.h.b.397.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1674,2,Mod(253,1674)] 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("1674.253"); 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, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1674 = 2 \cdot 3^{3} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1674.h (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			397.4
Character	$\chi$	$=$	1674.397
Dual form			1674.2.h.b.253.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} -2.76129 q^{5} +0.562243 q^{7} -1.00000 q^{8} +(-1.38064 + 2.39134i) q^{10} +(-1.99593 - 3.45705i) q^{11} -1.47038 q^{13} +(0.281122 - 0.486917i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.03355 + 1.79016i) q^{17} +(1.45518 + 2.52045i) q^{19} +(1.38064 + 2.39134i) q^{20} -3.99186 q^{22} +(1.12187 + 1.94313i) q^{23} +2.62470 q^{25} +(-0.735188 + 1.27338i) q^{26} +(-0.281122 - 0.486917i) q^{28} +(-2.14333 + 3.71236i) q^{29} +(-5.47232 + 1.02653i) q^{31} +(0.500000 + 0.866025i) q^{32} +2.06710 q^{34} -1.55251 q^{35} +(1.82864 + 3.16730i) q^{37} +2.91037 q^{38} +2.76129 q^{40} +6.23850 q^{41} +11.7512 q^{43} +(-1.99593 + 3.45705i) q^{44} +2.24373 q^{46} +(-2.96852 + 5.14163i) q^{47} -6.68388 q^{49} +(1.31235 - 2.27306i) q^{50} +(0.735188 + 1.27338i) q^{52} +(-0.731740 + 1.26741i) q^{53} +(5.51133 + 9.54590i) q^{55} -0.562243 q^{56} +(2.14333 + 3.71236i) q^{58} +(-0.635617 + 1.10092i) q^{59} +(-6.92283 + 11.9907i) q^{61} +(-1.84716 + 5.25243i) q^{62} +1.00000 q^{64} +4.06013 q^{65} +5.68951 q^{67} +(1.03355 - 1.79016i) q^{68} +(-0.776257 + 1.34452i) q^{70} +(-2.14830 + 3.72096i) q^{71} +(-4.67244 + 8.09290i) q^{73} +3.65728 q^{74} +(1.45518 - 2.52045i) q^{76} +(-1.12220 - 1.94370i) q^{77} -1.03225 q^{79} +(1.38064 - 2.39134i) q^{80} +(3.11925 - 5.40270i) q^{82} +(-1.02216 - 1.77044i) q^{83} +(-2.85393 - 4.94316i) q^{85} +(5.87561 - 10.1769i) q^{86} +(1.99593 + 3.45705i) q^{88} +3.63785 q^{89} -0.826708 q^{91} +(1.12187 - 1.94313i) q^{92} +(2.96852 + 5.14163i) q^{94} +(-4.01818 - 6.95968i) q^{95} +(-7.94907 + 13.7682i) q^{97} +(-3.34194 + 5.78841i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{2} - 16 q^{4} - 2 q^{5} - 2 q^{7} - 32 q^{8} - q^{10} + 2 q^{11} + 20 q^{13} - q^{14} - 16 q^{16} + 4 q^{17} + 4 q^{19} + q^{20} + 4 q^{22} + q^{23} + 38 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 - 2 * q^5 - 2 * q^7 - 32 * q^8 - q^10 + 2 * q^11 + 20 * q^13 - q^14 - 16 * q^16 + 4 * q^17 + 4 * q^19 + q^20 + 4 * q^22 + q^23 + 38 * q^25 + 10 * q^26 + q^28 + 3 * q^29 - 10 * q^31 + 16 * q^32 + 8 * q^34 - 19 * q^37 + 8 * q^38 + 2 * q^40 + 20 * q^41 + 26 * q^43 + 2 * q^44 + 2 * q^46 + 6 * q^47 + 26 * q^49 + 19 * q^50 - 10 * q^52 + 7 * q^53 - 11 * q^55 + 2 * q^56 - 3 * q^58 + 6 * q^59 + 7 * q^61 - 11 * q^62 + 32 * q^64 - 16 * q^65 + 16 * q^67 + 4 * q^68 - 7 * q^71 + 7 * q^73 - 38 * q^74 + 4 * q^76 + q^77 + 68 * q^79 + q^80 + 10 * q^82 - 14 * q^83 + 13 * q^85 + 13 * q^86 - 2 * 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 $\left(\mathbb{Z}/1674\mathbb{Z}\right)^\times$.

$n$	$1055$	$1243$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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
$5$	−2.76129			−1.23488			−0.617442	−	0.786616i	$-0.711831\pi$
$5$	−2.76129			−1.23488			−0.617442	+	0.786616i	$0.711831\pi$
$6$		0			0
$7$	0.562243			0.212508			0.106254	−	0.994339i	$-0.466114\pi$
$7$	0.562243			0.212508			0.106254	+	0.994339i	$0.466114\pi$
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−1.38064	+	2.39134i	−0.436598	+	0.756209i
$11$	−1.99593	−	3.45705i	−0.601795	−	1.04234i	−0.992549	−	0.121844i	$-0.961119\pi$
$11$	−1.99593	−	3.45705i	−0.601795	−	1.04234i	0.390754	−	0.920495i	$-0.372214\pi$
$12$		0			0
$13$	−1.47038			−0.407809			−0.203904	−	0.978991i	$-0.565363\pi$
$13$	−1.47038			−0.407809			−0.203904	+	0.978991i	$0.565363\pi$
$14$	0.281122	−	0.486917i	0.0751329	−	0.130134i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.03355	+	1.79016i	0.250673	+	0.434179i	0.963711	−	0.266946i	$-0.0860147\pi$
$17$	1.03355	+	1.79016i	0.250673	+	0.434179i	−0.713038	+	0.701125i	$0.752681\pi$
$18$		0			0
$19$	1.45518	+	2.52045i	0.333842	+	0.578231i	0.983262	−	0.182199i	$-0.0583215\pi$
$19$	1.45518	+	2.52045i	0.333842	+	0.578231i	−0.649420	+	0.760430i	$0.724988\pi$
$20$	1.38064	+	2.39134i	0.308721	+	0.534721i
$21$		0			0
$22$	−3.99186			−0.851067
$23$	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
$25$	2.62470			0.524940
$26$	−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
$31$	−5.47232	+	1.02653i	−0.982857	+	0.184370i
$31$	−5.47232	+	1.02653i	−0.982857	+	0.184370i
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	2.06710			0.354505
$35$	−1.55251			−0.262423
$36$		0			0
$37$	1.82864	+	3.16730i	0.300627	+	0.520701i	0.976278	−	0.216520i	$-0.0694708\pi$
$37$	1.82864	+	3.16730i	0.300627	+	0.520701i	−0.675651	+	0.737221i	$0.736137\pi$
$38$	2.91037			0.472124
$39$		0			0
$40$	2.76129			0.436598
$41$	6.23850			0.974289			0.487145	−	0.873321i	$-0.338038\pi$
$41$	6.23850			0.974289			0.487145	+	0.873321i	$0.338038\pi$
$42$		0			0
$43$	11.7512			1.79205			0.896023	−	0.444008i	$-0.146444\pi$
$43$	11.7512			1.79205			0.896023	+	0.444008i	$0.146444\pi$
$44$	−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
$49$	−6.68388			−0.954840
$50$	1.31235	−	2.27306i	0.185594	−	0.321459i
$51$		0			0
$52$	0.735188	+	1.27338i	0.101952	+	0.176586i
$53$	−0.731740	+	1.26741i	−0.100512	+	0.174092i	−0.911896	−	0.410422i	$-0.865381\pi$
$53$	−0.731740	+	1.26741i	−0.100512	+	0.174092i	0.811384	+	0.584514i	$0.198715\pi$
$54$		0			0
$55$	5.51133	+	9.54590i	0.743147	+	1.28717i
$56$	−0.562243			−0.0751329
$57$		0			0
$58$	2.14333	+	3.71236i	0.281433	+	0.487457i
$59$	−0.635617	+	1.10092i	−0.0827503	+	0.143328i	−0.904430	−	0.426621i	$-0.859704\pi$
$59$	−0.635617	+	1.10092i	−0.0827503	+	0.143328i	0.821680	+	0.569949i	$0.193037\pi$
$60$		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
$65$	4.06013			0.503597
$66$		0			0
$67$	5.68951			0.695084			0.347542	−	0.937664i	$-0.387016\pi$
$67$	5.68951			0.695084			0.347542	+	0.937664i	$0.387016\pi$
$68$	1.03355	−	1.79016i	0.125337	−	0.217089i
$69$		0			0
$70$	−0.776257	+	1.34452i	−0.0927804	+	0.160700i
$71$	−2.14830	+	3.72096i	−0.254956	+	0.441596i	−0.964884	−	0.262678i	$-0.915394\pi$
$71$	−2.14830	+	3.72096i	−0.254956	+	0.441596i	0.709928	+	0.704275i	$0.248728\pi$
$72$		0			0
$73$	−4.67244	+	8.09290i	−0.546868	+	0.947202i	0.451619	+	0.892211i	$0.350847\pi$
$73$	−4.67244	+	8.09290i	−0.546868	+	0.947202i	−0.998487	+	0.0549916i	$0.982487\pi$
$74$	3.65728			0.425151
$75$		0			0
$76$	1.45518	−	2.52045i	0.166921	−	0.289116i
$77$	−1.12220	−	1.94370i	−0.127886	−	0.221505i
$78$		0			0
$79$	−1.03225			−0.116137			−0.0580686	−	0.998313i	$-0.518494\pi$
$79$	−1.03225			−0.116137			−0.0580686	+	0.998313i	$0.518494\pi$
$80$	1.38064	−	2.39134i	0.154361	−	0.267360i
$81$		0			0
$82$	3.11925	−	5.40270i	0.344463	−	0.596628i
$83$	−1.02216	−	1.77044i	−0.112197	−	0.194331i	0.804459	−	0.594009i	$-0.202455\pi$
$83$	−1.02216	−	1.77044i	−0.112197	−	0.194331i	−0.916656	+	0.399677i	$0.869122\pi$
$84$		0			0
$85$	−2.85393	−	4.94316i	−0.309552	−	0.536161i
$86$	5.87561	−	10.1769i	0.633584	−	1.09740i
$87$		0			0
$88$	1.99593	+	3.45705i	0.212767	+	0.368523i
$89$	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
$103$	−11.7855			−1.16126			−0.580630	−	0.814168i	$-0.697194\pi$
$103$	−11.7855			−1.16126			−0.580630	+	0.814168i	$0.697194\pi$
$104$	1.47038			0.144182
$105$		0			0
$106$	0.731740	+	1.26741i	0.0710728	+	0.123102i
$107$	3.06844	+	5.31470i	0.296638	+	0.513792i	0.975365	−	0.220599i	$-0.0708013\pi$
$107$	3.06844	+	5.31470i	0.296638	+	0.513792i	−0.678727	+	0.734391i	$0.737468\pi$
$108$		0			0
$109$	12.8643			1.23218			0.616088	−	0.787677i	$-0.288716\pi$
$109$	12.8643			1.23218			0.616088	+	0.787677i	$0.288716\pi$
$110$	11.0227			1.05097
$111$		0			0
$112$	−0.281122	+	0.486917i	−0.0265635	+	0.0460093i
$113$	13.7198			1.29065			0.645323	−	0.763910i	$-0.276723\pi$
$113$	13.7198			1.29065			0.645323	+	0.763910i	$0.276723\pi$
$114$		0			0
$115$	−3.09779	−	5.36553i	−0.288871	−	0.500338i
$116$	4.28667			0.398007
$117$		0			0
$118$	0.635617	+	1.10092i	0.0585133	+	0.101348i
$119$	0.581108	+	1.00651i	0.0532700	+	0.0922664i
$120$		0			0
$121$	−2.46746	+	4.27376i	−0.224314	+	0.388524i
$122$	6.92283	+	11.9907i	0.626764	+	1.08559i
$123$		0			0
$124$	3.62516	+	4.22590i	0.325549	+	0.379497i
$125$	6.55889			0.586645
$126$		0			0
$127$	−3.57207	−	6.18701i	−0.316970	−	0.549008i	0.662884	−	0.748722i	$-0.269332\pi$
$127$	−3.57207	−	6.18701i	−0.316970	−	0.549008i	−0.979854	+	0.199714i	$0.935999\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	2.03006	−	3.51617i	0.178048	−	0.308389i
$131$	1.74226	−	3.01768i	0.152222	−	0.263656i	−0.779822	−	0.626001i	$-0.784691\pi$
$131$	1.74226	−	3.01768i	0.152222	−	0.263656i	0.932044	+	0.362345i	$0.118024\pi$
$132$		0			0
$133$	0.818166	+	1.41711i	0.0709440	+	0.122879i
$134$	2.84476	−	4.92726i	0.245749	−	0.425651i
$135$		0			0
$136$	−1.03355	−	1.79016i	−0.0886264	−	0.153505i
$137$	0.834449	+	1.44531i	0.0712918	+	0.123481i	0.899468	−	0.436987i	$-0.143955\pi$
$137$	0.834449	+	1.44531i	0.0712918	+	0.123481i	−0.828176	+	0.560468i	$0.810621\pi$
$138$		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
$142$	2.14830	+	3.72096i	0.180281	+	0.312256i
$143$	2.93476	+	5.08316i	0.245417	+	0.425075i
$144$		0			0
$145$	5.91835	−	10.2509i	0.491493	−	0.851290i
$146$	4.67244	+	8.09290i	0.386694	+	0.669773i
$147$		0			0
$148$	1.82864	−	3.16730i	0.150313	−	0.260350i
$149$	−6.37166	+	11.0360i	−0.521987	+	0.904108i	0.477686	+	0.878531i	$0.341476\pi$
$149$	−6.37166	+	11.0360i	−0.521987	+	0.904108i	−0.999673	+	0.0255774i	$0.991858\pi$
$150$		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
$155$	15.1106	−	2.83455i	1.21371	−	0.227676i
$156$		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	$-0.512067\pi$
$158$	−0.516125	+	0.893955i	−0.0410607	+	0.0711192i
$159$		0			0
$160$	−1.38064	−	2.39134i	−0.109149	−	0.189052i
$161$	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	$0.477252\pi$
$164$	−3.11925	−	5.40270i	−0.243572	−	0.421880i
$165$		0			0
$166$	−2.04433			−0.158671
$167$	−3.20854	+	5.55736i	−0.248285	+	0.430041i	−0.963050	−	0.269323i	$-0.913200\pi$
$167$	−3.20854	+	5.55736i	−0.248285	+	0.430041i	0.714765	+	0.699364i	$0.246533\pi$
$168$		0			0
$169$	−10.8380			−0.833692
$170$	−5.70787			−0.437773
$171$		0			0
$172$	−5.87561	−	10.1769i	−0.448011	−	0.775978i
$173$	−10.5109	−	18.2054i	−0.799127	−	1.38413i	−0.920185	−	0.391483i	$-0.871962\pi$
$173$	−10.5109	−	18.2054i	−0.799127	−	1.38413i	0.121059	−	0.992645i	$-0.461371\pi$
$174$		0			0
$175$	1.47572			0.111554
$176$	3.99186			0.300897
$177$		0			0
$178$	1.81892	−	3.15047i	0.136334	−	0.236137i
$179$	−7.59632	−	13.1572i	−0.567775	−	0.983416i	−0.996786	−	0.0801160i	$-0.974471\pi$
$179$	−7.59632	−	13.1572i	−0.567775	−	0.983416i	0.429010	−	0.903300i	$-0.358862\pi$
$180$		0			0
$181$	−1.37767	+	2.38619i	−0.102401	+	0.177364i	−0.912674	−	0.408689i	$-0.865986\pi$
$181$	−1.37767	+	2.38619i	−0.102401	+	0.177364i	0.810272	+	0.586054i	$0.199319\pi$
$182$	−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
$191$	8.80426	+	15.2494i	0.637054	+	1.10341i	0.986076	+	0.166295i	$0.0531805\pi$
$191$	8.80426	+	15.2494i	0.637054	+	1.10341i	−0.349022	+	0.937115i	$0.613486\pi$
$192$		0			0
$193$	−2.11290	+	3.65965i	−0.152090	+	0.263428i	−0.931996	−	0.362469i	$-0.881934\pi$
$193$	−2.11290	+	3.65965i	−0.152090	+	0.263428i	0.779906	+	0.625897i	$0.215267\pi$
$194$	7.94907	+	13.7682i	0.570710	+	0.988499i
$195$		0			0
$196$	3.34194	+	5.78841i	0.238710	+	0.413458i
$197$	11.0548	−	19.1475i	0.787624	−	1.36421i	−0.139794	−	0.990181i	$-0.544644\pi$
$197$	11.0548	−	19.1475i	0.787624	−	1.36421i	0.927419	−	0.374025i	$-0.122022\pi$
$198$		0			0
$199$	−4.22595	+	7.31956i	−0.299570	+	0.518870i	−0.976038	−	0.217602i	$-0.930176\pi$
$199$	−4.22595	+	7.31956i	−0.299570	+	0.518870i	0.676468	+	0.736472i	$0.263510\pi$
$200$	−2.62470			−0.185594
$201$		0			0
$202$	1.05409	+	1.82574i	0.0741655	+	0.128458i
$203$	−1.20507	+	2.08725i	−0.0845796	+	0.146496i
$204$		0			0
$205$	−17.2263			−1.20313
$206$	−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
$211$	−13.3678	+	23.1538i	−0.920280	+	1.59397i	−0.121297	+	0.992616i	$0.538705\pi$
$211$	−13.3678	+	23.1538i	−0.920280	+	1.59397i	−0.798982	+	0.601355i	$0.794628\pi$
$212$	1.46348			0.100512
$213$		0			0
$214$	6.13689			0.419509
$215$	−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
$220$	5.51133	−	9.54590i	0.371574	−	0.643584i
$221$	−1.51971	−	2.63221i	−0.102227	−	0.177062i
$222$		0			0
$223$	21.2515			1.42310			0.711551	−	0.702634i	$-0.247993\pi$
$223$	21.2515			1.42310			0.711551	+	0.702634i	$0.247993\pi$
$224$	0.281122	+	0.486917i	0.0187832	+	0.0325335i
$225$		0			0
$226$	6.85988	−	11.8817i	0.456312	−	0.790356i
$227$	−13.2692	−	22.9830i	−0.880711	−	1.52544i	−0.850552	−	0.525890i	$-0.823732\pi$
$227$	−13.2692	−	22.9830i	−0.880711	−	1.52544i	−0.0301581	−	0.999545i	$-0.509601\pi$
$228$		0			0
$229$	1.01441	−	1.75702i	0.0670344	−	0.116107i	−0.830560	−	0.556929i	$-0.811980\pi$
$229$	1.01441	−	1.75702i	0.0670344	−	0.116107i	0.897595	+	0.440822i	$0.145313\pi$
$230$	−6.19558			−0.408525
$231$		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
$236$	1.27123			0.0827503
$237$		0			0
$238$	1.16222			0.0753352
$239$	−13.8340			−0.894846			−0.447423	−	0.894323i	$-0.647658\pi$
$239$	−13.8340			−0.894846			−0.447423	+	0.894323i	$0.647658\pi$
$240$		0			0
$241$	−27.8602			−1.79463			−0.897317	−	0.441386i	$-0.854487\pi$
$241$	−27.8602			−1.79463			−0.897317	+	0.441386i	$0.854487\pi$
$242$	2.46746	+	4.27376i	0.158614	+	0.274728i
$243$		0			0
$244$	13.8457			0.886378
$245$	18.4561			1.17912
$246$		0			0
$247$	−2.13966	−	3.70601i	−0.136144	−	0.235808i
$248$	5.47232	−	1.02653i	0.347492	−	0.0651848i
$249$		0			0
$250$	3.27944	−	5.68016i	0.207410	−	0.359245i
$251$	−4.36267	−	7.55637i	−0.275370	−	0.476954i	0.694859	−	0.719146i	$-0.255467\pi$
$251$	−4.36267	−	7.55637i	−0.275370	−	0.476954i	−0.970228	+	0.242192i	$0.922134\pi$
$252$		0			0
$253$	4.47833	−	7.75669i	0.281550	−	0.487659i
$254$	−7.14415			−0.448264
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−6.48050			−0.404242			−0.202121	−	0.979361i	$-0.564783\pi$
$257$	−6.48050			−0.404242			−0.202121	+	0.979361i	$0.564783\pi$
$258$		0			0
$259$	1.02814	+	1.78079i	0.0638856	+	0.110653i
$260$	−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
$265$	2.02054	−	3.49968i	0.124121	−	0.214984i
$266$	1.63633			0.100330
$267$		0			0
$268$	−2.84476	−	4.92726i	−0.173771	−	0.300980i
$269$	5.24517	−	9.08490i	0.319804	−	0.553916i	−0.660643	−	0.750700i	$-0.729716\pi$
$269$	5.24517	−	9.08490i	0.319804	−	0.553916i	0.980447	+	0.196784i	$0.0630497\pi$
$270$		0			0
$271$	19.1276			1.16192			0.580959	−	0.813933i	$-0.302678\pi$
$271$	19.1276			1.16192			0.580959	+	0.813933i	$0.302678\pi$
$272$	−2.06710			−0.125337
$273$		0			0
$274$	1.66890			0.100822
$275$	−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	$0.558033\pi$
$284$	4.29659			0.254956
$285$		0			0
$286$	5.86953			0.347072
$287$	3.50755			0.207044
$288$		0			0
$289$	6.36354	−	11.0220i	0.374326	−	0.648351i
$290$	−5.91835	−	10.2509i	−0.347538	−	0.601953i
$291$		0			0
$292$	9.34488			0.546868
$293$	−3.17281	+	5.49547i	−0.185358	+	0.321049i	−0.943697	−	0.330811i	$-0.892678\pi$
$293$	−3.17281	+	5.49547i	−0.185358	+	0.321049i	0.758339	+	0.651860i	$0.226011\pi$
$294$		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
$299$	−1.64956	−	2.85713i	−0.0953967	−	0.165232i
$300$		0			0
$301$	6.60704			0.380824
$302$	2.16532	+	3.75045i	0.124600	+	0.215814i
$303$		0			0
$304$	−2.91037			−0.166921
$305$	19.1159	−	33.1097i	1.09457	−	1.89586i
$306$		0			0
$307$	2.68363	+	4.64819i	0.153163	+	0.265286i	0.932389	−	0.361457i	$-0.117721\pi$
$307$	2.68363	+	4.64819i	0.153163	+	0.265286i	−0.779226	+	0.626743i	$0.784387\pi$
$308$	−1.12220	+	1.94370i	−0.0639431	+	0.110753i
$309$		0			0
$310$	5.10052	−	14.5035i	0.289690	−	0.823741i
$311$	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
$313$	7.02943			0.397327			0.198663	−	0.980068i	$-0.436340\pi$
$313$	7.02943			0.397327			0.198663	+	0.980068i	$0.436340\pi$
$314$	−22.1618			−1.25066
$315$		0			0
$316$	0.516125	+	0.893955i	0.0290343	+	0.0502889i
$317$	−5.85718			−0.328972			−0.164486	−	0.986379i	$-0.552597\pi$
$317$	−5.85718			−0.328972			−0.164486	+	0.986379i	$0.552597\pi$
$318$		0			0
$319$	17.1118			0.958074
$320$	−2.76129			−0.154361
$321$		0			0
$322$	1.26152			0.0703019
$323$	−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
$328$	−6.23850			−0.344463
$329$	−1.66903	+	2.89084i	−0.0920166	+	0.159377i
$330$		0			0
$331$	7.21212	+	12.4918i	0.396414	+	0.686609i	0.993281	−	0.115731i	$-0.0369212\pi$
$331$	7.21212	+	12.4918i	0.396414	+	0.686609i	−0.596867	+	0.802341i	$0.703588\pi$
$332$	−1.02216	+	1.77044i	−0.0560986	+	0.0971656i
$333$		0			0
$334$	3.20854	+	5.55736i	0.175564	+	0.304085i
$335$	−15.7104			−0.858349
$336$		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	$0.564358\pi$
$338$	−5.41900	+	9.38598i	−0.294755	+	0.510530i
$339$		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
$344$	−11.7512			−0.633584
$345$		0			0
$346$	−21.0217			−1.13014
$347$	−4.93173	+	8.54200i	−0.264749	+	0.458559i	−0.967498	−	0.252879i	$-0.918622\pi$
$347$	−4.93173	+	8.54200i	−0.264749	+	0.458559i	0.702749	+	0.711438i	$0.251956\pi$
$348$		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
$353$	−29.0758			−1.54755			−0.773773	−	0.633463i	$-0.781633\pi$
$353$	−29.0758			−1.54755			−0.773773	+	0.633463i	$0.781633\pi$
$354$		0			0
$355$	5.93206	−	10.2746i	0.314841	−	0.545321i
$356$	−1.81892	−	3.15047i	−0.0964027	−	0.166974i
$357$		0			0
$358$	−15.1926			−0.802955
$359$	−1.79467	+	3.10846i	−0.0947189	+	0.164058i	−0.909491	−	0.415723i	$-0.863529\pi$
$359$	−1.79467	+	3.10846i	−0.0947189	+	0.164058i	0.814772	+	0.579781i	$0.196862\pi$
$360$		0			0
$361$	5.26489	−	9.11905i	0.277099	−	0.479950i
$362$	1.37767	+	2.38619i	0.0724087	+	0.125416i
$363$		0			0
$364$	0.413354	+	0.715950i	0.0216656	+	0.0375260i
$365$	12.9019	−	22.3468i	0.675318	−	1.16969i
$366$		0			0
$367$	7.34444	+	12.7209i	0.383377	+	0.664028i	0.991543	−	0.129782i	$-0.0414277\pi$
$367$	7.34444	+	12.7209i	0.383377	+	0.664028i	−0.608166	+	0.793810i	$0.708094\pi$
$368$	−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	−0.964162	−	0.265313i	$-0.914525\pi$
$379$	−13.8582	−	24.0031i	−0.711849	−	1.23296i	0.252313	−	0.967646i	$-0.418809\pi$
$380$	−4.01818	+	6.95968i	−0.206128	+	0.357024i
$381$		0			0
$382$	17.6085			0.900930
$383$	−22.0607			−1.12725			−0.563624	−	0.826032i	$-0.690593\pi$
$383$	−22.0607			−1.12725			−0.563624	+	0.826032i	$0.690593\pi$
$384$		0			0
$385$	3.09871	+	5.36712i	0.157925	+	0.273534i
$386$	2.11290	+	3.65965i	0.107544	+	0.186272i
$387$		0			0
$388$	15.8981			0.807106
$389$	2.74980			0.139421			0.0697103	−	0.997567i	$-0.477793\pi$
$389$	2.74980			0.139421			0.0697103	+	0.997567i	$0.477793\pi$
$390$		0			0
$391$	−2.31901	+	4.01665i	−0.117278	+	0.203131i
$392$	6.68388			0.337587
$393$		0			0
$394$	−11.0548	−	19.1475i	−0.556934	−	0.964639i
$395$	2.85034			0.143416
$396$		0			0
$397$	−0.820424	−	1.42102i	−0.0411759	−	0.0713187i	0.844703	−	0.535235i	$-0.179777\pi$
$397$	−0.820424	−	1.42102i	−0.0411759	−	0.0713187i	−0.885879	+	0.463917i	$0.846444\pi$
$398$	4.22595	+	7.31956i	0.211828	+	0.366896i
$399$		0			0
$400$	−1.31235	+	2.27306i	−0.0656175	+	0.113653i
$401$	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
$403$	8.04636	−	1.50939i	0.400818	−	0.0751879i
$404$	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
$409$	−8.38880	+	14.5298i	−0.414799	+	0.718454i	−0.995407	−	0.0957295i	$-0.969482\pi$
$409$	−8.38880	+	14.5298i	−0.414799	+	0.718454i	0.580608	+	0.814183i	$0.302815\pi$
$410$	−8.61313	+	14.9184i	−0.425372	+	0.736767i
$411$		0			0
$412$	5.89275	+	10.2065i	0.290315	+	0.502840i
$413$	−0.357371	+	0.618985i	−0.0175851	+	0.0304583i
$414$		0			0
$415$	2.82249	+	4.88869i	0.138551	+	0.239977i
$416$	−0.735188	−	1.27338i	−0.0360455	−	0.0624327i
$417$		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
$421$	−17.7261	−	30.7024i	−0.863915	−	1.49634i	−0.868121	−	0.496353i	$-0.834672\pi$
$421$	−17.7261	−	30.7024i	−0.863915	−	1.49634i	0.00420582	−	0.999991i	$-0.498661\pi$
$422$	13.3678	+	23.1538i	0.650736	+	1.12711i
$423$		0			0
$424$	0.731740	−	1.26741i	0.0355364	−	0.0615509i
$425$	2.71276	+	4.69864i	0.131588	+	0.227918i
$426$		0			0
$427$	−3.89231	+	6.74168i	−0.188362	+	0.326253i
$428$	3.06844	−	5.31470i	0.148319	−	0.256896i
$429$		0			0
$430$	−16.2242	+	28.1012i	−0.782403	+	1.35516i
$431$	10.4796	+	18.1512i	0.504785	+	0.874314i	0.999985	+	0.00553455i	$0.00176171\pi$
$431$	10.4796	+	18.1512i	0.504785	+	0.874314i	−0.495199	+	0.868779i	$0.664905\pi$
$432$		0			0
$433$	−6.09639			−0.292974			−0.146487	−	0.989213i	$-0.546797\pi$
$433$	−6.09639			−0.292974			−0.146487	+	0.989213i	$0.546797\pi$
$434$	−1.03855	+	2.95314i	−0.0498520	+	0.141755i
$435$		0			0
$436$	−6.43215	−	11.1408i	−0.308044	−	0.533548i
$437$	−3.26504	+	5.65521i	−0.156188	+	0.270526i
$438$		0			0
$439$	13.8876	+	24.0540i	0.662817	+	1.14803i	0.979872	+	0.199626i	$0.0639727\pi$
$439$	13.8876	+	24.0540i	0.662817	+	1.14803i	−0.317055	+	0.948407i	$0.602694\pi$
$440$	−5.51133	−	9.54590i	−0.262742	−	0.455083i
$441$		0			0
$442$	−3.03942			−0.144570
$443$	1.51177	+	2.61845i	0.0718262	+	0.124407i	0.899702	−	0.436505i	$-0.143784\pi$
$443$	1.51177	+	2.61845i	0.0718262	+	0.124407i	−0.827876	+	0.560912i	$0.810451\pi$
$444$		0			0
$445$	−10.0451			−0.476185
$446$	10.6257	−	18.4043i	0.503143	−	0.871469i
$447$		0			0
$448$	0.562243			0.0265635
$449$	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
$452$	−6.85988	−	11.8817i	−0.322662	−	0.558866i
$453$		0			0
$454$	−26.5385			−1.24551
$455$	2.28278			0.107018
$456$		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
$470$	−8.19693	−	14.1975i	−0.378096	−	0.654882i
$471$		0			0
$472$	0.635617	−	1.10092i	0.0292566	−	0.0506740i
$473$	−23.4546	−	40.6246i	−1.07844	−	1.86792i
$474$		0			0
$475$	3.81942	+	6.61542i	0.175247	+	0.303536i
$476$	0.581108	−	1.00651i	0.0266350	−	0.0461332i
$477$		0			0
$478$	−6.91699	+	11.9806i	−0.316376	+	0.547979i
$479$	−25.2674			−1.15450			−0.577250	−	0.816568i	$-0.695874\pi$
$479$	−25.2674			−1.15450			−0.577250	+	0.816568i	$0.695874\pi$
$480$		0			0
$481$	−2.68879	−	4.65712i	−0.122598	−	0.212346i
$482$	−13.9301	+	24.1277i	−0.634499	+	1.09898i
$483$		0			0
$484$	4.93492			0.224314
$485$	21.9497	−	38.0179i	0.996683	−	1.72630i
$486$		0			0
$487$	−13.9395	+	24.1440i	−0.631660	+	1.09407i	0.355552	+	0.934657i	$0.384293\pi$
$487$	−13.9395	+	24.1440i	−0.631660	+	1.09407i	−0.987212	+	0.159411i	$0.949040\pi$
$488$	6.92283	−	11.9907i	0.313382	−	0.542793i
$489$		0			0
$490$	9.22805	−	15.9835i	0.416881	−	0.722059i
$491$	−2.00756			−0.0905999			−0.0452999	−	0.998973i	$-0.514424\pi$
$491$	−2.00756			−0.0905999			−0.0452999	+	0.998973i	$0.514424\pi$
$492$		0			0
$493$	−8.86099			−0.399079
$494$	−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
$499$	10.2613	−	17.7731i	0.459360	−	0.795635i	−0.539567	−	0.841943i	$-0.681412\pi$
$499$	10.2613	−	17.7731i	0.459360	−	0.795635i	0.998927	+	0.0463077i	$0.0147455\pi$
$500$	−3.27944	−	5.68016i	−0.146661	−	0.254025i
$501$		0			0
$502$	−8.72535			−0.389431
$503$	16.3446	+	28.3097i	0.728771	+	1.26227i	0.957403	+	0.288755i	$0.0932413\pi$
$503$	16.3446	+	28.3097i	0.728771	+	1.26227i	−0.228632	+	0.973513i	$0.573425\pi$
$504$		0			0
$505$	2.91064	−	5.04138i	0.129522	−	0.224339i
$506$	−4.47833	−	7.75669i	−0.199086	−	0.344827i
$507$		0			0
$508$	−3.57207	+	6.18701i	−0.158485	+	0.274504i
$509$	−30.8353			−1.36675			−0.683376	−	0.730067i	$-0.739489\pi$
$509$	−30.8353			−1.36675			−0.683376	+	0.730067i	$0.739489\pi$
$510$		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
$515$	32.5431			1.43402
$516$		0			0
$517$	23.6998			1.04232
$518$	2.05628			0.0903478
$519$		0			0
$520$	−4.06013			−0.178048
$521$	−4.71147	−	8.16051i	−0.206413	−	0.357519i	0.744169	−	0.667992i	$-0.232846\pi$
$521$	−4.71147	−	8.16051i	−0.206413	−	0.357519i	−0.950582	+	0.310473i	$0.899513\pi$
$522$		0			0
$523$	40.0302			1.75040			0.875200	−	0.483761i	$-0.160730\pi$
$523$	40.0302			1.75040			0.875200	+	0.483761i	$0.160730\pi$
$524$	−3.48452			−0.152222
$525$		0			0
$526$	7.90071	+	13.6844i	0.344487	+	0.596669i
$527$	−7.49358	−	8.73537i	−0.326426	−	0.380519i
$528$		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
$533$	−9.17293			−0.397324
$534$		0			0
$535$	−8.47285	−	14.6754i	−0.366313	−	0.634473i
$536$	−5.68951			−0.245749
$537$		0			0
$538$	−5.24517	−	9.08490i	−0.226135	−	0.391678i
$539$	13.3405	+	23.1065i	0.574618	+	0.995268i
$540$		0			0
$541$	−7.70912	−	13.3526i	−0.331441	−	0.574073i	0.651354	−	0.758774i	$-0.274201\pi$
$541$	−7.70912	−	13.3526i	−0.331441	−	0.574073i	−0.982795	+	0.184702i	$0.940868\pi$
$542$	9.56379	−	16.5650i	0.410800	−	0.711527i
$543$		0			0
$544$	−1.03355	+	1.79016i	−0.0443132	+	0.0767527i
$545$	−35.5220			−1.52160
$546$		0			0
$547$	2.70323	+	4.68213i	0.115582	+	0.200194i	0.918012	−	0.396552i	$-0.129793\pi$
$547$	2.70323	+	4.68213i	0.115582	+	0.200194i	−0.802430	+	0.596746i	$0.796460\pi$
$548$	0.834449	−	1.44531i	0.0356459	−	0.0617405i
$549$		0			0
$550$	−10.4774			−0.446759
$551$	−12.4758			−0.531486
$552$		0			0
$553$	−0.580375			−0.0246801
$554$	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
$563$	−4.90086			−0.206546			−0.103273	−	0.994653i	$-0.532932\pi$
$563$	−4.90086			−0.206546			−0.103273	+	0.994653i	$0.532932\pi$
$564$		0			0
$565$	−37.8842			−1.59380
$566$	25.6046			1.07624
$567$		0			0
$568$	2.14830	−	3.72096i	0.0901405	−	0.156128i
$569$	13.4283	+	23.2585i	0.562943	+	0.975045i	0.997238	+	0.0742745i	$0.0236641\pi$
$569$	13.4283	+	23.2585i	0.562943	+	0.975045i	−0.434295	+	0.900771i	$0.643003\pi$
$570$		0			0
$571$	38.8743			1.62684			0.813419	−	0.581679i	$-0.197604\pi$
$571$	38.8743			1.62684			0.813419	+	0.581679i	$0.197604\pi$
$572$	2.93476	−	5.08316i	0.122709	−	0.212538i
$573$		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	0.932515	−	0.361130i	$-0.117609\pi$
$577$	3.68743	+	6.38682i	0.153510	+	0.265887i	−0.779006	+	0.627017i	$0.784276\pi$
$578$	−6.36354	−	11.0220i	−0.264688	−	0.458454i
$579$		0			0
$580$	−11.8367			−0.491493
$581$	−0.574705	−	0.995418i	−0.0238428	−	0.0412969i
$582$		0			0
$583$	5.84200			0.241951
$584$	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
$589$	−10.5505	−	12.2989i	−0.434727	−	0.506768i
$590$	−1.75512	−	3.03996i	−0.0722571	−	0.125153i
$591$		0			0
$592$	−3.65728			−0.150313
$593$	−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
$596$	12.7433			0.521987
$597$		0			0
$598$	−3.29913			−0.134911
$599$	37.5708			1.53510			0.767551	−	0.640988i	$-0.221475\pi$
$599$	37.5708			1.53510			0.767551	+	0.640988i	$0.221475\pi$
$600$		0			0
$601$	15.7765			0.643538			0.321769	−	0.946818i	$-0.395723\pi$
$601$	15.7765			0.643538			0.321769	+	0.946818i	$0.395723\pi$
$602$	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
$607$	6.46718			0.262495			0.131247	−	0.991350i	$-0.458102\pi$
$607$	6.46718			0.262495			0.131247	+	0.991350i	$0.458102\pi$
$608$	−1.45518	+	2.52045i	−0.0590155	+	0.102218i
$609$		0			0
$610$	−19.1159	−	33.1097i	−0.773981	−	1.34057i
$611$	4.36484	−	7.56012i	0.176582	−	0.305850i
$612$		0			0
$613$	−9.79127	−	16.9590i	−0.395466	−	0.684967i	0.597695	−	0.801724i	$-0.296083\pi$
$613$	−9.79127	−	16.9590i	−0.395466	−	0.684967i	−0.993160	+	0.116757i	$0.962750\pi$
$614$	5.36726			0.216605
$615$		0			0
$616$	1.12220	+	1.94370i	0.0452146	+	0.0783140i
$617$	5.33858	−	9.24669i	0.214923	−	0.372258i	−0.738326	−	0.674444i	$-0.764383\pi$
$617$	5.33858	−	9.24669i	0.214923	−	0.372258i	0.953249	+	0.302187i	$0.0977166\pi$
$618$		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
$623$	2.04535			0.0819454
$624$		0			0
$625$	−31.2345			−1.24938
$626$	3.51471	−	6.08766i	0.140476	−	0.243312i
$627$		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	−0.987344	−	0.158594i	$-0.949304\pi$
$631$	−8.95079	+	15.5032i	−0.356325	+	0.617174i	0.631018	+	0.775768i	$0.282637\pi$
$632$	1.03225			0.0410607
$633$		0			0
$634$	−2.92859	+	5.07247i	−0.116309	+	0.201454i
$635$	9.86351	+	17.0841i	0.391422	+	0.677962i
$636$		0			0
$637$	9.82781			0.389392
$638$	8.55588	−	14.8192i	0.338730	−	0.586698i
$639$		0			0
$640$	−1.38064	+	2.39134i	−0.0545747	+	0.0945262i
$641$	−0.635524	−	1.10076i	−0.0251017	−	0.0434774i	0.853202	−	0.521581i	$-0.174658\pi$
$641$	−0.635524	−	1.10076i	−0.0251017	−	0.0434774i	−0.878303	+	0.478104i	$0.841324\pi$
$642$		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	$0.511669\pi$
$644$	0.630761	−	1.09251i	0.0248555	−	0.0430509i
$645$		0			0
$646$	3.00802	+	5.21004i	0.118349	+	0.204986i
$647$	−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
$661$	−29.3966			−1.14340			−0.571698	−	0.820464i	$-0.693715\pi$
$661$	−29.3966			−1.14340			−0.571698	+	0.820464i	$0.693715\pi$
$662$	14.4242			0.560614
$663$		0			0
$664$	1.02216	+	1.77044i	0.0396677	+	0.0687065i
$665$	−2.25919	−	3.91303i	−0.0876077	−	0.151741i
$666$		0			0
$667$	−9.61813			−0.372415
$668$	6.41709			0.248285
$669$		0			0
$670$	−7.85518	+	13.6056i	−0.303472	+	0.525629i
$671$	55.2699			2.13367
$672$		0			0
$673$	−6.92184	−	11.9890i	−0.266817	−	0.462141i	0.701221	−	0.712944i	$-0.252639\pi$
$673$	−6.92184	−	11.9890i	−0.266817	−	0.462141i	−0.968038	+	0.250803i	$0.919305\pi$
$674$	27.4621			1.05780
$675$		0			0
$676$	5.41900	+	9.38598i	0.208423	+	0.360999i
$677$	24.2956	+	42.0812i	0.933755	+	1.61731i	0.776838	+	0.629700i	$0.216822\pi$
$677$	24.2956	+	42.0812i	0.933755	+	1.61731i	0.156917	+	0.987612i	$0.449844\pi$
$678$		0			0
$679$	−4.46931	+	7.74107i	−0.171516	+	0.297075i
$680$	2.85393	+	4.94316i	0.109443	+	0.189561i
$681$		0			0
$682$	21.8447	−	4.09776i	0.836477	−	0.156912i
$683$	−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
$688$	−5.87561	+	10.1769i	−0.224006	+	0.387989i
$689$	1.07593	−	1.86357i	0.0409897	−	0.0709963i
$690$		0			0
$691$	9.63875	+	16.6948i	0.366675	+	0.635101i	0.989044	−	0.147624i	$-0.0471626\pi$
$691$	9.63875	+	16.6948i	0.366675	+	0.635101i	−0.622368	+	0.782725i	$0.713829\pi$
$692$	−10.5109	+	18.2054i	−0.399563	+	0.692064i
$693$		0			0
$694$	4.93173	+	8.54200i	0.187206	+	0.324250i
$695$	22.8656	+	39.6044i	0.867341	+	1.50228i
$696$		0			0
$697$	6.44781	+	11.1679i	0.244228	+	0.423016i
$698$	−5.34850	−	9.26388i	−0.202444	−	0.350643i
$699$		0			0
$700$	−0.737859	−	1.27801i	−0.0278885	−	0.0483042i
$701$	21.8284	+	37.8079i	0.824447	+	1.42798i	0.902341	+	0.431023i	$0.141847\pi$
$701$	21.8284	+	37.8079i	0.824447	+	1.42798i	−0.0778936	+	0.996962i	$0.524819\pi$
$702$		0			0
$703$	−5.32202	+	9.21800i	−0.200724	+	0.347664i
$704$	−1.99593	−	3.45705i	−0.0752244	−	0.130292i
$705$		0			0
$706$	−14.5379	+	25.1803i	−0.547140	+	0.947675i
$707$	−0.592655	+	1.02651i	−0.0222891	+	0.0386058i
$708$		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
$713$	−8.13388	−	9.48178i	−0.304616	−	0.355095i
$714$		0			0
$715$	−8.10372	−	14.0361i	−0.303062	−	0.524919i
$716$	−7.59632	+	13.1572i	−0.283888	+	0.491708i
$717$		0			0
$718$	1.79467	+	3.10846i	0.0669764	+	0.116007i
$719$	22.2177	+	38.4822i	0.828580	+	1.43514i	0.899152	+	0.437636i	$0.144184\pi$
$719$	22.2177	+	38.4822i	0.828580	+	1.43514i	−0.0705720	+	0.997507i	$0.522482\pi$
$720$		0			0
$721$	−6.62631			−0.246777
$722$	−5.26489	−	9.11905i	−0.195939	−	0.339376i
$723$		0			0
$724$	2.75534			0.102401
$725$	−5.62560	+	9.74383i	−0.208930	+	0.361877i
$726$		0			0
$727$	10.1231			0.375446			0.187723	−	0.982222i	$-0.439889\pi$
$727$	10.1231			0.375446			0.187723	+	0.982222i	$0.439889\pi$
$728$	0.826708			0.0306398
$729$		0			0
$730$	−12.9019	−	22.3468i	−0.477522	−	0.827093i
$731$	12.1455	+	21.0366i	0.449218	+	0.778068i
$732$		0			0
$733$	33.7652			1.24715			0.623574	−	0.781765i	$-0.285680\pi$
$733$	33.7652			1.24715			0.623574	+	0.781765i	$0.285680\pi$
$734$	14.6889			0.542177
$735$		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	−0.545943	−	0.837823i	$-0.683828\pi$
$739$	12.3038	−	21.3109i	0.452604	−	0.783934i	0.998547	+	0.0538888i	$0.0171616\pi$
$740$	−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
$749$	1.72521	+	2.98815i	0.0630379	+	0.109185i
$750$		0			0
$751$	17.9658	−	31.1176i	0.655580	−	1.13550i	−0.326168	−	0.945312i	$-0.605758\pi$
$751$	17.9658	−	31.1176i	0.655580	−	1.13550i	0.981748	−	0.190186i	$-0.0609091\pi$
$752$	−2.96852	−	5.14163i	−0.108251	−	0.187496i
$753$		0			0
$754$	−3.15150	−	5.45856i	−0.114771	−	0.198789i
$755$	5.97908	−	10.3561i	0.217601	−	0.376896i
$756$		0			0
$757$	−6.91512	+	11.9773i	−0.251334	+	0.435324i	−0.963893	−	0.266288i	$-0.914203\pi$
$757$	−6.91512	+	11.9773i	−0.251334	+	0.435324i	0.712559	+	0.701612i	$0.247536\pi$
$758$	−27.7164			−1.00671
$759$		0			0
$760$	4.01818	+	6.95968i	0.145755	+	0.252454i
$761$	10.9011	−	18.8813i	0.395165	−	0.684447i	−0.597957	−	0.801528i	$-0.704021\pi$
$761$	10.9011	−	18.8813i	0.395165	−	0.684447i	0.993122	+	0.117082i	$0.0373539\pi$
$762$		0			0
$763$	7.23287			0.261847
$764$	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
$769$	5.67187	−	9.82397i	0.204533	−	0.354261i	−0.745451	−	0.666560i	$-0.767766\pi$
$769$	5.67187	−	9.82397i	0.204533	−	0.354261i	0.949984	+	0.312299i	$0.101099\pi$
$770$	6.19741			0.223339
$771$		0			0
$772$	4.22580			0.152090
$773$	−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
$778$	1.37490	−	2.38140i	0.0492926	−	0.0853773i
$779$	9.07815	+	15.7238i	0.325259	+	0.563364i
$780$		0			0
$781$	17.1514			0.613725
$782$	2.31901	+	4.01665i	0.0829277	+	0.143635i
$783$		0			0
$784$	3.34194	−	5.78841i	0.119355	−	0.206729i
$785$	30.5976	+	52.9965i	1.09207	+	1.89153i
$786$		0			0
$787$	−3.79268	+	6.56912i	−0.135194	+	0.234164i	−0.925672	−	0.378328i	$-0.876499\pi$
$787$	−3.79268	+	6.56912i	−0.135194	+	0.234164i	0.790477	+	0.612491i	$0.209833\pi$
$788$	−22.1097			−0.787624
$789$		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
$794$	−1.64085			−0.0582315
$795$		0			0
$796$	8.45190			0.299570
$797$	29.6077			1.04876			0.524380	−	0.851484i	$-0.324297\pi$
$797$	29.6077			1.04876			0.524380	+	0.851484i	$0.324297\pi$
$798$		0			0
$799$	−12.2725			−0.434169
$800$	1.31235	+	2.27306i	0.0463986	+	0.0803647i
$801$		0			0
$802$	9.79122			0.345740
$803$	37.3034			1.31641
$804$		0			0
$805$	−1.74171	−	3.01673i	−0.0613873	−	0.106326i
$806$	2.71601	−	7.72304i	0.0956674	−	0.272033i
$807$		0			0
$808$	1.05409	−	1.82574i	0.0370827	−	0.0642292i
$809$	−21.6194	−	37.4460i	−0.760099	−	1.31653i	−0.942799	−	0.333361i	$-0.891817\pi$
$809$	−21.6194	−	37.4460i	−0.760099	−	1.31653i	0.182700	−	0.983169i	$-0.441516\pi$
$810$		0			0
$811$	−22.3906	+	38.7817i	−0.786241	+	1.36181i	0.142015	+	0.989865i	$0.454642\pi$
$811$	−22.3906	+	38.7817i	−0.786241	+	1.36181i	−0.928255	+	0.371944i	$0.878691\pi$
$812$	2.41015			0.0845796
$813$		0			0
$814$	−7.29967	−	12.6434i	−0.255853	−	0.443151i
$815$	−5.03444			−0.176349
$816$		0			0
$817$	17.1002	+	29.6184i	0.598260	+	1.03622i
$818$	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
$823$	−2.56797	+	4.44785i	−0.0895138	+	0.155042i	−0.907306	−	0.420472i	$-0.861865\pi$
$823$	−2.56797	+	4.44785i	−0.0895138	+	0.155042i	0.817792	+	0.575514i	$0.195198\pi$
$824$	11.7855			0.410567
$825$		0			0
$826$	0.357371	+	0.618985i	0.0124345	+	0.0215372i
$827$	18.1801	−	31.4889i	0.632185	−	1.09498i	−0.354919	−	0.934897i	$-0.615492\pi$
$827$	18.1801	−	31.4889i	0.632185	−	1.09498i	0.987104	−	0.160079i	$-0.0511749\pi$
$828$		0			0
$829$	36.4298			1.26526			0.632630	−	0.774454i	$-0.281975\pi$
$829$	36.4298			1.26526			0.632630	+	0.774454i	$0.281975\pi$
$830$	5.64498			0.195940
$831$		0			0
$832$	−1.47038			−0.0509761
$833$	−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
$842$	−35.4521			−1.22176
$843$		0			0
$844$	26.7357			0.920280
$845$	29.9268			1.02951
$846$		0			0
$847$	−1.38731	+	2.40289i	−0.0476686	+	0.0825644i
$848$	−0.731740	−	1.26741i	−0.0251280	−	0.0435231i
$849$		0			0
$850$	5.42553			0.186094
$851$	−4.10298	+	7.10657i	−0.140648	+	0.243610i
$852$		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
$857$	−19.6802	−	34.0871i	−0.672263	−	1.16439i	−0.977261	−	0.212041i	$-0.931989\pi$
$857$	−19.6802	−	34.0871i	−0.672263	−	1.16439i	0.304998	−	0.952353i	$-0.401344\pi$
$858$		0			0
$859$	4.49343			0.153314			0.0766570	−	0.997058i	$-0.475575\pi$
$859$	4.49343			0.153314			0.0766570	+	0.997058i	$0.475575\pi$
$860$	16.2242	+	28.1012i	0.553242	+	0.958244i
$861$		0			0
$862$	20.9592			0.713874
$863$	−11.5510	+	20.0070i	−0.393202	+	0.681045i	−0.992870	−	0.119203i	$-0.961966\pi$
$863$	−11.5510	+	20.0070i	−0.393202	+	0.681045i	0.599668	+	0.800249i	$0.295299\pi$
$864$		0			0
$865$	29.0235	+	50.2702i	0.986829	+	1.70924i
$866$	−3.04820	+	5.27963i	−0.103582	+	0.179409i
$867$		0			0
$868$	2.03822	+	2.37598i	0.0691817	+	0.0806461i
$869$	2.06030	+	3.56854i	0.0698908	+	0.121054i
$870$		0			0
$871$	−8.36572			−0.283461
$872$	−12.8643			−0.435640
$873$		0			0
$874$	3.26504	+	5.65521i	0.110442	+	0.191290i
$875$	3.68769			0.124667
$876$		0			0
$877$	47.5085			1.60425			0.802124	−	0.597158i	$-0.203703\pi$
$877$	47.5085			1.60425			0.802124	+	0.597158i	$0.203703\pi$
$878$	27.7751			0.937365
$879$		0			0
$880$	−11.0227			−0.371574
$881$	27.7949	−	48.1423i	0.936435	−	1.62195i	0.164381	−	0.986397i	$-0.447437\pi$
$881$	27.7949	−	48.1423i	0.936435	−	1.62195i	0.772054	−	0.635557i	$-0.219229\pi$
$882$		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
$886$	3.02353			0.101578
$887$	−12.0972	+	20.9529i	−0.406183	+	0.703530i	−0.994458	−	0.105131i	$-0.966474\pi$
$887$	−12.0972	+	20.9529i	−0.406183	+	0.703530i	0.588275	+	0.808661i	$0.299807\pi$
$888$		0			0
$889$	−2.00837	−	3.47860i	−0.0673587	−	0.116669i
$890$	−5.02257	+	8.69934i	−0.168357	+	0.291603i
$891$		0			0
$892$	−10.6257	−	18.4043i	−0.355776	−	0.616222i
$893$	−17.2790			−0.578218
$894$		0			0
$895$	20.9756	+	36.3308i	0.701137	+	1.21440i
$896$	0.281122	−	0.486917i	0.00939161	−	0.0162667i
$897$		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
$902$	−24.9032			−0.829185
$903$		0			0
$904$	−13.7198			−0.456312
$905$	3.80414	−	6.58896i	0.126454	−	0.219024i
$906$		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
$911$	41.6570			1.38016			0.690079	−	0.723734i	$-0.257576\pi$
$911$	41.6570			1.38016			0.690079	+	0.723734i	$0.257576\pi$
$912$		0			0
$913$	−4.08033	+	7.06735i	−0.135039	+	0.233895i
$914$	−6.35410	−	11.0056i	−0.210175	−	0.364034i
$915$		0			0
$916$	−2.02883			−0.0670344
$917$	0.979572	−	1.69667i	0.0323483	−	0.0560290i
$918$		0			0
$919$	−17.9232	+	31.0439i	−0.591231	+	1.02404i	0.402836	+	0.915272i	$0.368025\pi$
$919$	−17.9232	+	31.0439i	−0.591231	+	1.02404i	−0.994067	+	0.108770i	$0.965309\pi$
$920$	3.09779	+	5.36553i	0.102131	+	0.176896i
$921$		0			0
$922$	10.5442	+	18.2631i	0.347255	+	0.601463i
$923$	3.15880	−	5.47120i	0.103973	−	0.180087i
$924$		0			0
$925$	4.79963	+	8.31321i	0.157811	+	0.273337i
$926$	−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	0.952122	−	0.305719i	$-0.0988968\pi$
$937$	6.46800	+	11.2029i	0.211300	+	0.365983i	−0.740821	+	0.671702i	$0.765563\pi$
$938$	1.59944	−	2.77032i	0.0522237	−	0.0904541i
$939$		0			0
$940$	−16.3939			−0.534709
$941$	53.1639			1.73309			0.866546	−	0.499097i	$-0.166335\pi$
$941$	53.1639			1.73309			0.866546	+	0.499097i	$0.166335\pi$
$942$		0			0
$943$	6.99875	+	12.1222i	0.227911	+	0.394753i
$944$	−0.635617	−	1.10092i	−0.0206876	−	0.0358319i
$945$		0			0
$946$	−46.9092			−1.52515
$947$	44.6194			1.44994			0.724968	−	0.688782i	$-0.241854\pi$
$947$	44.6194			1.44994			0.724968	+	0.688782i	$0.241854\pi$
$948$		0			0
$949$	6.87024	−	11.8996i	0.223017	−	0.386277i
$950$	7.63883			0.247836
$951$		0			0
$952$	−0.581108	−	1.00651i	−0.0188338	−	0.0326211i
$953$	−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
$956$	6.91699	+	11.9806i	0.223711	+	0.387479i
$957$		0			0
$958$	−12.6337	+	21.8823i	−0.408177	+	0.706984i
$959$	0.469163	+	0.812615i	0.0151501	+	0.0262407i
$960$		0			0
$961$	28.8925	−	11.2350i	0.932015	−	0.362419i
$962$	−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
$967$	6.33198	−	10.9673i	0.203623	−	0.352685i	−0.746070	−	0.665867i	$-0.768062\pi$
$967$	6.33198	−	10.9673i	0.203623	−	0.352685i	0.949693	+	0.313182i	$0.101395\pi$
$968$	2.46746	−	4.27376i	0.0793071	−	0.137364i
$969$		0			0
$970$	−21.9497	−	38.0179i	−0.704761	−	1.22068i
$971$	−18.7126	+	32.4111i	−0.600515	+	1.04012i	0.392228	+	0.919868i	$0.371705\pi$
$971$	−18.7126	+	32.4111i	−0.600515	+	1.04012i	−0.992743	+	0.120255i	$0.961629\pi$
$972$		0			0
$973$	−4.65581	−	8.06410i	−0.149258	−	0.258523i
$974$	13.9395	+	24.1440i	0.446651	+	0.773623i
$975$		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
$979$	−7.26088	−	12.5762i	−0.232059	−	0.401937i
$980$	−9.22805	−	15.9835i	−0.294779	−	0.510573i
$981$		0			0
$982$	−1.00378	+	1.73860i	−0.0320319	+	0.0554809i
$983$	9.77898	+	16.9377i	0.311901	+	0.540228i	0.978774	−	0.204943i	$-0.0657010\pi$
$983$	9.77898	+	16.9377i	0.311901	+	0.540228i	−0.666873	+	0.745171i	$0.732368\pi$
$984$		0			0
$985$	−30.5256	+	52.8718i	−0.972625	+	1.68464i
$986$	−4.43049	+	7.67384i	−0.141096	+	0.244385i
$987$		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	$0.408001\pi$
$992$	−3.62516	−	4.22590i	−0.115099	−	0.134172i
$993$		0			0
$994$	1.20786	+	2.09208i	0.0383111	+	0.0663568i
$995$	11.6691	−	20.2114i	0.369934	−	0.640744i
$996$		0			0
$997$	−6.82137	−	11.8150i	−0.216035	−	0.374183i	0.737557	−	0.675284i	$-0.235979\pi$
$997$	−6.82137	−	11.8150i	−0.216035	−	0.374183i	−0.953592	+	0.301101i	$0.902646\pi$
$998$	−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.h.b.397.4		32
3.2	odd	2		558.2.h.a.25.14	yes	32
9.4	even	3		1674.2.g.b.955.13		32
9.5	odd	6		558.2.g.a.211.3	✓	32
31.5	even	3		1674.2.g.b.1369.13		32
93.5	odd	6		558.2.g.a.439.3	yes	32
279.5	odd	6		558.2.h.a.67.14	yes	32
279.67	even	3	inner	1674.2.h.b.253.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
558.2.g.a.211.3	✓	32	9.5	odd	6
558.2.g.a.439.3	yes	32	93.5	odd	6
558.2.h.a.25.14	yes	32	3.2	odd	2
558.2.h.a.67.14	yes	32	279.5	odd	6
1674.2.g.b.955.13		32	9.4	even	3
1674.2.g.b.1369.13		32	31.5	even	3
1674.2.h.b.253.4		32	279.67	even	3	inner
1674.2.h.b.397.4		32	1.1	even	1	trivial

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.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} -2.76129 q^{5} +0.562243 q^{7} -1.00000 q^{8} +(-1.38064 + 2.39134i) q^{10} +(-1.99593 - 3.45705i) q^{11} -1.47038 q^{13} +(0.281122 - 0.486917i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.03355 + 1.79016i) q^{17} +(1.45518 + 2.52045i) q^{19} +(1.38064 + 2.39134i) q^{20} -3.99186 q^{22} +(1.12187 + 1.94313i) q^{23} +2.62470 q^{25} +(-0.735188 + 1.27338i) q^{26} +(-0.281122 - 0.486917i) q^{28} +(-2.14333 + 3.71236i) q^{29} +(-5.47232 + 1.02653i) q^{31} +(0.500000 + 0.866025i) q^{32} +2.06710 q^{34} -1.55251 q^{35} +(1.82864 + 3.16730i) q^{37} +2.91037 q^{38} +2.76129 q^{40} +6.23850 q^{41} +11.7512 q^{43} +(-1.99593 + 3.45705i) q^{44} +2.24373 q^{46} +(-2.96852 + 5.14163i) q^{47} -6.68388 q^{49} +(1.31235 - 2.27306i) q^{50} +(0.735188 + 1.27338i) q^{52} +(-0.731740 + 1.26741i) q^{53} +(5.51133 + 9.54590i) q^{55} -0.562243 q^{56} +(2.14333 + 3.71236i) q^{58} +(-0.635617 + 1.10092i) q^{59} +(-6.92283 + 11.9907i) q^{61} +(-1.84716 + 5.25243i) q^{62} +1.00000 q^{64} +4.06013 q^{65} +5.68951 q^{67} +(1.03355 - 1.79016i) q^{68} +(-0.776257 + 1.34452i) q^{70} +(-2.14830 + 3.72096i) q^{71} +(-4.67244 + 8.09290i) q^{73} +3.65728 q^{74} +(1.45518 - 2.52045i) q^{76} +(-1.12220 - 1.94370i) q^{77} -1.03225 q^{79} +(1.38064 - 2.39134i) q^{80} +(3.11925 - 5.40270i) q^{82} +(-1.02216 - 1.77044i) q^{83} +(-2.85393 - 4.94316i) q^{85} +(5.87561 - 10.1769i) q^{86} +(1.99593 + 3.45705i) q^{88} +3.63785 q^{89} -0.826708 q^{91} +(1.12187 - 1.94313i) q^{92} +(2.96852 + 5.14163i) q^{94} +(-4.01818 - 6.95968i) q^{95} +(-7.94907 + 13.7682i) q^{97} +(-3.34194 + 5.78841i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{2} - 16 q^{4} - 2 q^{5} - 2 q^{7} - 32 q^{8} - q^{10} + 2 q^{11} + 20 q^{13} - q^{14} - 16 q^{16} + 4 q^{17} + 4 q^{19} + q^{20} + 4 q^{22} + q^{23} + 38 q^{25} + 10 q^{26} + q^{28} + 3 q^{29}+ \cdots + 13 q^{98}+O(q^{100}) \) 32 * q + 16 * q^2 - 16 * q^4 - 2 * q^5 - 2 * q^7 - 32 * q^8 - q^10 + 2 * q^11 + 20 * q^13 - q^14 - 16 * q^16 + 4 * q^17 + 4 * q^19 + q^20 + 4 * q^22 + q^23 + 38 * q^25 + 10 * q^26 + q^28 + 3 * q^29 - 10 * q^31 + 16 * q^32 + 8 * q^34 - 19 * q^37 + 8 * q^38 + 2 * q^40 + 20 * q^41 + 26 * q^43 + 2 * q^44 + 2 * q^46 + 6 * q^47 + 26 * q^49 + 19 * q^50 - 10 * q^52 + 7 * q^53 - 11 * q^55 + 2 * q^56 - 3 * q^58 + 6 * q^59 + 7 * q^61 - 11 * q^62 + 32 * q^64 - 16 * q^65 + 16 * q^67 + 4 * q^68 - 7 * q^71 + 7 * q^73 - 38 * q^74 + 4 * q^76 + q^77 + 68 * q^79 + q^80 + 10 * q^82 - 14 * q^83 + 13 * q^85 + 13 * q^86 - 2 * 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

Fields

Representations

Groups

Database

Properties

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