LMFDB - Embedded newform 572.2.bh.a.57.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(57,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 2, 15]))

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

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

chi := DirichletCharacter("572.57");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bh (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			57.12
Character	$\chi$	$=$	572.57
Dual form			572.2.bh.a.281.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.91590 - 1.39198i) q^{3} +(-1.08106 - 0.550829i) q^{5} +(1.99865 - 0.316555i) q^{7} +(0.806006 - 2.48063i) q^{9} +O(q^{10})$	\(q+(1.91590 - 1.39198i) q^{3} +(-1.08106 - 0.550829i) q^{5} +(1.99865 - 0.316555i) q^{7} +(0.806006 - 2.48063i) q^{9} +(3.25177 + 0.652673i) q^{11} +(-1.35257 - 3.34224i) q^{13} +(-2.83796 + 0.449488i) q^{15} +(0.0296827 + 0.0913538i) q^{17} +(0.843340 + 0.133572i) q^{19} +(3.38857 - 3.38857i) q^{21} +0.576573i q^{23} +(-2.07364 - 2.85412i) q^{25} +(0.286656 + 0.882237i) q^{27} +(0.720448 - 0.991612i) q^{29} +(-1.51590 - 2.97511i) q^{31} +(7.13858 - 3.27595i) q^{33} +(-2.33503 - 0.758698i) q^{35} +(0.418926 + 2.64500i) q^{37} +(-7.24373 - 4.52064i) q^{39} +(3.41576 + 0.541003i) q^{41} -1.19636 q^{43} +(-2.23775 + 2.23775i) q^{45} +(-0.265014 - 0.0419741i) q^{47} +(-2.76301 + 0.897758i) q^{49} +(0.184032 + 0.133707i) q^{51} +(-1.33424 + 4.10636i) q^{53} +(-3.15586 - 2.49675i) q^{55} +(1.80168 - 0.918004i) q^{57} +(1.83951 + 11.6142i) q^{59} +(-8.83440 + 2.87047i) q^{61} +(0.825666 - 5.21305i) q^{63} +(-0.378789 + 4.35821i) q^{65} +(-3.79267 + 3.79267i) q^{67} +(0.802580 + 1.10466i) q^{69} +(3.87705 + 1.97546i) q^{71} +(6.86533 - 1.08736i) q^{73} +(-7.94578 - 2.58174i) q^{75} +(6.70575 + 0.275099i) q^{77} +(-4.77870 - 1.55269i) q^{79} +(8.10772 + 5.89060i) q^{81} +(7.34078 - 14.4071i) q^{83} +(0.0182315 - 0.115109i) q^{85} -2.90268i q^{87} +(10.0402 + 10.0402i) q^{89} +(-3.76131 - 6.25179i) q^{91} +(-7.04561 - 3.58992i) q^{93} +(-0.838128 - 0.608936i) q^{95} +(4.55540 + 8.94047i) q^{97} +(4.23999 - 7.54039i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 28 q^{9}+O(q^{10}) $ 112 * q - 28 * q^9	$ 112 q - 28 q^{9} + 8 q^{11} - 10 q^{13} + 4 q^{15} - 24 q^{27} - 20 q^{29} - 16 q^{31} - 54 q^{33} + 100 q^{35} - 12 q^{37} + 40 q^{39} - 20 q^{41} - 4 q^{45} - 10 q^{47} - 76 q^{53} - 20 q^{55} + 18 q^{59} + 40 q^{61} + 80 q^{63} + 92 q^{67} + 8 q^{71} - 30 q^{73} - 80 q^{79} + 12 q^{81} + 40 q^{85} + 32 q^{89} - 12 q^{91} - 114 q^{93} + 54 q^{97} - 90 q^{99}+O(q^{100}) $ 112 * q - 28 * q^9 + 8 * q^11 - 10 * q^13 + 4 * q^15 - 24 * q^27 - 20 * q^29 - 16 * q^31 - 54 * q^33 + 100 * q^35 - 12 * q^37 + 40 * q^39 - 20 * q^41 - 4 * q^45 - 10 * q^47 - 76 * q^53 - 20 * q^55 + 18 * q^59 + 40 * q^61 + 80 * q^63 + 92 * q^67 + 8 * q^71 - 30 * q^73 - 80 * q^79 + 12 * q^81 + 40 * q^85 + 32 * q^89 - 12 * q^91 - 114 * q^93 + 54 * q^97 - 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{10}\right)$

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			0
$2$		0			0
$3$	1.91590	−	1.39198i	1.10615	−	0.803662i	0.124093	−	0.992271i	$-0.460398\pi$
$3$	1.91590	−	1.39198i	1.10615	−	0.803662i	0.982052	+	0.188609i	$0.0603978\pi$
$4$		0			0
$5$	−1.08106	−	0.550829i	−0.483466	−	0.246338i	0.195230	−	0.980758i	$-0.437455\pi$
$5$	−1.08106	−	0.550829i	−0.483466	−	0.246338i	−0.678696	+	0.734419i	$0.737455\pi$
$6$		0			0
$7$	1.99865	−	0.316555i	0.755417	−	0.119646i	0.233165	−	0.972437i	$-0.425092\pi$
$7$	1.99865	−	0.316555i	0.755417	−	0.119646i	0.522253	+	0.852791i	$0.325092\pi$
$8$		0			0
$9$	0.806006	−	2.48063i	0.268669	−	0.826877i
$10$		0			0
$11$	3.25177	+	0.652673i	0.980446	+	0.196788i
$11$	3.25177	+	0.652673i	0.980446	+	0.196788i
$12$		0			0
$13$	−1.35257	−	3.34224i	−0.375135	−	0.926970i
$13$	−1.35257	−	3.34224i	−0.375135	−	0.926970i
$14$		0			0
$15$	−2.83796	+	0.449488i	−0.732757	+	0.116057i
$16$		0			0
$17$	0.0296827	+	0.0913538i	0.00719910	+	0.0221566i	0.954592	−	0.297918i	$-0.0962921\pi$
$17$	0.0296827	+	0.0913538i	0.00719910	+	0.0221566i	−0.947392	+	0.320074i	$0.896292\pi$
$18$		0			0
$19$	0.843340	+	0.133572i	0.193475	+	0.0306435i	0.252420	−	0.967618i	$-0.418774\pi$
$19$	0.843340	+	0.133572i	0.193475	+	0.0306435i	−0.0589446	+	0.998261i	$0.518774\pi$
$20$		0			0
$21$	3.38857	−	3.38857i	0.739446	−	0.739446i
$22$		0			0
$23$			0.576573i			0.120224i	0.998192	+	0.0601119i	$0.0191458\pi$
$23$			0.576573i			0.120224i	−0.998192	+	0.0601119i	$0.980854\pi$
$24$		0			0
$25$	−2.07364	−	2.85412i	−0.414728	−	0.570824i
$26$		0			0
$27$	0.286656	+	0.882237i	0.0551670	+	0.169787i
$28$		0			0
$29$	0.720448	−	0.991612i	0.133784	−	0.184138i	−0.736869	−	0.676035i	$-0.763697\pi$
$29$	0.720448	−	0.991612i	0.133784	−	0.184138i	0.870653	+	0.491898i	$0.163697\pi$
$30$		0			0
$31$	−1.51590	−	2.97511i	−0.272263	−	0.534346i	0.713875	−	0.700273i	$-0.246938\pi$
$31$	−1.51590	−	2.97511i	−0.272263	−	0.534346i	−0.986138	+	0.165927i	$0.946938\pi$
$32$		0			0
$33$	7.13858	−	3.27595i	1.24267	−	0.570271i
$34$		0			0
$35$	−2.33503	−	0.758698i	−0.394692	−	0.128243i
$36$		0			0
$37$	0.418926	+	2.64500i	0.0688711	+	0.434835i	0.997897	+	0.0648202i	$0.0206474\pi$
$37$	0.418926	+	2.64500i	0.0688711	+	0.434835i	−0.929026	+	0.370015i	$0.879353\pi$
$38$		0			0
$39$	−7.24373	−	4.52064i	−1.15992	−	0.723882i
$40$		0			0
$41$	3.41576	+	0.541003i	0.533452	+	0.0844905i	0.417348	−	0.908747i	$-0.362960\pi$
$41$	3.41576	+	0.541003i	0.533452	+	0.0844905i	0.116104	+	0.993237i	$0.462960\pi$
$42$		0			0
$43$	−1.19636			−0.182443			−0.0912217	−	0.995831i	$-0.529077\pi$
$43$	−1.19636			−0.182443			−0.0912217	+	0.995831i	$0.529077\pi$
$44$		0			0
$45$	−2.23775	+	2.23775i	−0.333584	+	0.333584i
$46$		0			0
$47$	−0.265014	−	0.0419741i	−0.0386563	−	0.00612256i	0.137076	−	0.990560i	$-0.456229\pi$
$47$	−0.265014	−	0.0419741i	−0.0386563	−	0.00612256i	−0.175733	+	0.984438i	$0.556229\pi$
$48$		0			0
$49$	−2.76301	+	0.897758i	−0.394716	+	0.128251i
$50$		0			0
$51$	0.184032	+	0.133707i	0.0257696	+	0.0187227i
$52$		0			0
$53$	−1.33424	+	4.10636i	−0.183271	+	0.564052i	−0.999914	−	0.0130918i	$-0.995833\pi$
$53$	−1.33424	+	4.10636i	−0.183271	+	0.564052i	0.816643	+	0.577143i	$0.195833\pi$
$54$		0			0
$55$	−3.15586	−	2.49675i	−0.425536	−	0.336662i
$56$		0			0
$57$	1.80168	−	0.918004i	0.238639	−	0.121593i
$58$		0			0
$59$	1.83951	+	11.6142i	0.239483	+	1.51204i	0.755323	+	0.655353i	$0.227480\pi$
$59$	1.83951	+	11.6142i	0.239483	+	1.51204i	−0.515839	+	0.856685i	$0.672520\pi$
$60$		0			0
$61$	−8.83440	+	2.87047i	−1.13113	+	0.367526i	−0.814005	−	0.580858i	$-0.802717\pi$
$61$	−8.83440	+	2.87047i	−1.13113	+	0.367526i	−0.317124	+	0.948384i	$0.602717\pi$
$62$		0			0
$63$	0.825666	−	5.21305i	0.104024	−	0.656783i
$64$		0			0
$65$	−0.378789	+	4.35821i	−0.0469830	+	0.540569i
$66$		0			0
$67$	−3.79267	+	3.79267i	−0.463348	+	0.463348i	−0.899751	−	0.436403i	$-0.856252\pi$
$67$	−3.79267	+	3.79267i	−0.463348	+	0.463348i	0.436403	+	0.899751i	$0.356252\pi$
$68$		0			0
$69$	0.802580	+	1.10466i	0.0966193	+	0.132985i
$70$		0			0
$71$	3.87705	+	1.97546i	0.460122	+	0.234444i	0.668657	−	0.743571i	$-0.266870\pi$
$71$	3.87705	+	1.97546i	0.460122	+	0.234444i	−0.208535	+	0.978015i	$0.566870\pi$
$72$		0			0
$73$	6.86533	−	1.08736i	0.803526	−	0.127266i	0.258855	−	0.965916i	$-0.416655\pi$
$73$	6.86533	−	1.08736i	0.803526	−	0.127266i	0.544671	+	0.838650i	$0.316655\pi$
$74$		0			0
$75$	−7.94578	−	2.58174i	−0.917499	−	0.298114i
$76$		0			0
$77$	6.70575	+	0.275099i	0.764191	+	0.0313505i
$78$		0			0
$79$	−4.77870	−	1.55269i	−0.537646	−	0.174692i	0.0275926	−	0.999619i	$-0.491216\pi$
$79$	−4.77870	−	1.55269i	−0.537646	−	0.174692i	−0.565239	+	0.824927i	$0.691216\pi$
$80$		0			0
$81$	8.10772	+	5.89060i	0.900858	+	0.654511i
$82$		0			0
$83$	7.34078	−	14.4071i	0.805755	−	1.58138i	−0.00785260	−	0.999969i	$-0.502500\pi$
$83$	7.34078	−	14.4071i	0.805755	−	1.58138i	0.813608	−	0.581414i	$-0.197500\pi$
$84$		0			0
$85$	0.0182315	−	0.115109i	0.00197749	−	0.0124854i
$86$		0			0
$87$		−	2.90268i		−	0.311200i
$88$		0			0
$89$	10.0402	+	10.0402i	1.06426	+	1.06426i	0.997789	+	0.0664667i	$0.0211726\pi$
$89$	10.0402	+	10.0402i	1.06426	+	1.06426i	0.0664667	+	0.997789i	$0.478827\pi$
$90$		0			0
$91$	−3.76131	−	6.25179i	−0.394292	−	0.655366i
$92$		0			0
$93$	−7.04561	−	3.58992i	−0.730596	−	0.372257i
$94$		0			0
$95$	−0.838128	−	0.608936i	−0.0859902	−	0.0624755i
$96$		0			0
$97$	4.55540	+	8.94047i	0.462530	+	0.907767i	0.998000	+	0.0632127i	$0.0201346\pi$
$97$	4.55540	+	8.94047i	0.462530	+	0.907767i	−0.535470	+	0.844554i	$0.679865\pi$
$98$		0			0
$99$	4.23999	−	7.54039i	0.426135	−	0.757838i
$100$		0			0
$101$	0.446522	−	1.37425i	0.0444306	−	0.136743i	−0.926380	−	0.376589i	$-0.877097\pi$
$101$	0.446522	−	1.37425i	0.0444306	−	0.136743i	0.970811	+	0.239846i	$0.0770969\pi$
$102$		0			0
$103$	−3.84181	+	5.28779i	−0.378544	+	0.521022i	−0.955198	−	0.295967i	$-0.904358\pi$
$103$	−3.84181	+	5.28779i	−0.378544	+	0.521022i	0.576654	+	0.816989i	$0.304358\pi$
$104$		0			0
$105$	−5.52978	+	1.79673i	−0.539651	+	0.175343i
$106$		0			0
$107$	5.00625	+	6.89051i	0.483972	+	0.666131i	0.979262	−	0.202597i	$-0.0649382\pi$
$107$	5.00625	+	6.89051i	0.483972	+	0.666131i	−0.495290	+	0.868728i	$0.664938\pi$
$108$		0			0
$109$	−0.332817	−	0.332817i	−0.0318781	−	0.0318781i	0.690988	−	0.722866i	$-0.257176\pi$
$109$	−0.332817	−	0.332817i	−0.0318781	−	0.0318781i	−0.722866	+	0.690988i	$0.757176\pi$
$110$		0			0
$111$	4.48441	+	4.48441i	0.425642	+	0.425642i
$112$		0			0
$113$	−10.0250	+	7.28359i	−0.943072	+	0.685182i	−0.949158	−	0.314799i	$-0.898063\pi$
$113$	−10.0250	+	7.28359i	−0.943072	+	0.685182i	0.00608603	+	0.999981i	$0.498063\pi$
$114$		0			0
$115$	0.317593	−	0.623312i	0.0296157	−	0.0581242i
$116$		0			0
$117$	−9.38104	+	0.661364i	−0.867278	+	0.0611431i
$118$		0			0
$119$	0.0882436	+	0.173188i	0.00808928	+	0.0158761i
$120$		0			0
$121$	10.1480	+	4.24469i	0.922549	+	0.385881i
$122$		0			0
$123$	7.29732	−	3.71817i	0.657977	−	0.335256i
$124$		0			0
$125$	1.61862	+	10.2196i	0.144774	+	0.914064i
$126$		0			0
$127$	−5.49773	−	16.9203i	−0.487844	−	1.50143i	−0.827819	−	0.560996i	$-0.810418\pi$
$127$	−5.49773	−	16.9203i	−0.487844	−	1.50143i	0.339975	−	0.940435i	$-0.389582\pi$
$128$		0			0
$129$	−2.29211	+	1.66532i	−0.201809	+	0.146623i
$130$		0			0
$131$			14.8017i			1.29323i	0.762816	+	0.646615i	$0.223816\pi$
$131$			14.8017i			1.29323i	−0.762816	+	0.646615i	$0.776184\pi$
$132$		0			0
$133$	1.72782			0.149821
$134$		0			0
$135$	0.176069	−	1.11165i	0.0151536	−	0.0956759i
$136$		0			0
$137$	3.05409	−	5.99400i	0.260929	−	0.512102i	−0.722958	−	0.690892i	$-0.757218\pi$
$137$	3.05409	−	5.99400i	0.260929	−	0.512102i	0.983887	+	0.178790i	$0.0572182\pi$
$138$		0			0
$139$	−5.57262	+	7.67006i	−0.472664	+	0.650566i	−0.977074	−	0.212898i	$-0.931710\pi$
$139$	−5.57262	+	7.67006i	−0.472664	+	0.650566i	0.504411	+	0.863464i	$0.331710\pi$
$140$		0			0
$141$	−0.566168	+	0.288477i	−0.0476800	+	0.0242942i
$142$		0			0
$143$	−2.21686	−	11.7510i	−0.185383	−	0.982666i
$144$		0			0
$145$	−1.32506	+	0.675151i	−0.110040	+	0.0560683i
$146$		0			0
$147$	−4.04400	+	5.56608i	−0.333543	+	0.459083i
$148$		0			0
$149$	−4.76904	+	9.35977i	−0.390695	+	0.766782i	−0.999651	−	0.0264218i	$-0.991589\pi$
$149$	−4.76904	+	9.35977i	−0.390695	+	0.766782i	0.608956	+	0.793204i	$0.291589\pi$
$150$		0			0
$151$	1.79276	−	11.3190i	0.145892	−	0.921128i	−0.800787	−	0.598950i	$-0.795585\pi$
$151$	1.79276	−	11.3190i	0.145892	−	0.921128i	0.946679	−	0.322178i	$-0.104415\pi$
$152$		0			0
$153$	0.250540			0.0202549
$154$		0			0
$155$			4.05128i			0.325407i
$156$		0			0
$157$	−14.6630	+	10.6533i	−1.17023	+	0.850225i	−0.991037	−	0.133588i	$-0.957350\pi$
$157$	−14.6630	+	10.6533i	−1.17023	+	0.850225i	−0.179198	+	0.983813i	$0.557350\pi$
$158$		0			0
$159$	3.15972	+	9.72461i	0.250582	+	0.771211i
$160$		0			0
$161$	0.182517	+	1.15237i	0.0143843	+	0.0908192i
$162$		0			0
$163$	−9.48172	+	4.83118i	−0.742665	+	0.378407i	−0.784018	−	0.620738i	$-0.786833\pi$
$163$	−9.48172	+	4.83118i	−0.742665	+	0.378407i	0.0413530	+	0.999145i	$0.486833\pi$
$164$		0			0
$165$	−9.52175	−	0.390624i	−0.741267	−	0.0304100i
$166$		0			0
$167$	−4.11157	−	8.06941i	−0.318163	−	0.624430i	0.675433	−	0.737421i	$-0.263957\pi$
$167$	−4.11157	−	8.06941i	−0.318163	−	0.624430i	−0.993596	+	0.112991i	$0.963957\pi$
$168$		0			0
$169$	−9.34111	+	9.04122i	−0.718547	+	0.695479i
$170$		0			0
$171$	1.01108	−	1.98436i	0.0773192	−	0.151747i
$172$		0			0
$173$	−15.9232	+	11.5689i	−1.21062	+	0.879566i	−0.995287	−	0.0969748i	$-0.969083\pi$
$173$	−15.9232	+	11.5689i	−1.21062	+	0.879566i	−0.215332	+	0.976541i	$0.569083\pi$
$174$		0			0
$175$	−5.04796	−	5.04796i	−0.381590	−	0.381590i
$176$		0			0
$177$	19.6911	+	19.6911i	1.48007	+	1.48007i
$178$		0			0
$179$	−11.5094	−	15.8413i	−0.860251	−	1.18403i	−0.981510	−	0.191413i	$-0.938693\pi$
$179$	−11.5094	−	15.8413i	−0.860251	−	1.18403i	0.121259	−	0.992621i	$-0.461307\pi$
$180$		0			0
$181$	21.8407	−	7.09646i	1.62340	−	0.527476i	0.650663	−	0.759367i	$-0.274491\pi$
$181$	21.8407	−	7.09646i	1.62340	−	0.527476i	0.972742	+	0.231891i	$0.0744912\pi$
$182$		0			0
$183$	−12.9302	+	17.7969i	−0.955826	+	1.31558i
$184$		0			0
$185$	1.00406	−	3.09017i	0.0738197	−	0.227194i
$186$		0			0
$187$	0.0368971	+	0.316435i	0.00269818	+	0.0231400i
$188$		0			0
$189$	0.852201	+	1.67254i	0.0619885	+	0.121659i
$190$		0			0
$191$	0.706009	+	0.512945i	0.0510850	+	0.0371154i	0.613035	−	0.790056i	$-0.289949\pi$
$191$	0.706009	+	0.512945i	0.0510850	+	0.0371154i	−0.561950	+	0.827171i	$0.689949\pi$
$192$		0			0
$193$	−7.86248	−	4.00614i	−0.565954	−	0.288368i	0.147509	−	0.989061i	$-0.452874\pi$
$193$	−7.86248	−	4.00614i	−0.565954	−	0.288368i	−0.713463	+	0.700693i	$0.752874\pi$
$194$		0			0
$195$	5.34083	+	8.87716i	0.382465	+	0.635706i
$196$		0			0
$197$	5.01953	+	5.01953i	0.357627	+	0.357627i	0.862937	−	0.505311i	$-0.168622\pi$
$197$	5.01953	+	5.01953i	0.357627	+	0.357627i	−0.505311	+	0.862937i	$0.668622\pi$
$198$		0			0
$199$			8.41069i			0.596218i	0.954532	+	0.298109i	$0.0963559\pi$
$199$			8.41069i			0.596218i	−0.954532	+	0.298109i	$0.903644\pi$
$200$		0			0
$201$	−1.98704	+	12.5457i	−0.140155	+	0.884906i
$202$		0			0
$203$	1.12602	−	2.20994i	0.0790313	−	0.155108i
$204$		0			0
$205$	−3.39465	−	2.46636i	−0.237093	−	0.172258i
$206$		0			0
$207$	1.43027	+	0.464722i	0.0994104	+	0.0323004i
$208$		0			0
$209$	2.65517	+	0.984770i	0.183662	+	0.0681180i
$210$		0			0
$211$	−13.1258	−	4.26483i	−0.903617	−	0.293603i	−0.179888	−	0.983687i	$-0.557573\pi$
$211$	−13.1258	−	4.26483i	−0.903617	−	0.293603i	−0.723729	+	0.690084i	$0.757573\pi$
$212$		0			0
$213$	10.1779	−	1.61201i	0.697375	−	0.110453i
$214$		0			0
$215$	1.29334	+	0.658991i	0.0882053	+	0.0449428i
$216$		0			0
$217$	−3.97152	−	5.46633i	−0.269605	−	0.371079i
$218$		0			0
$219$	11.6397	−	11.6397i	0.786538	−	0.786538i
$220$		0			0
$221$	0.265178	−	0.222769i	0.0178378	−	0.0149851i
$222$		0			0
$223$	2.42962	−	15.3400i	0.162700	−	1.02724i	−0.762285	−	0.647241i	$-0.775923\pi$
$223$	2.42962	−	15.3400i	0.162700	−	1.02724i	0.924985	−	0.380004i	$-0.124077\pi$
$224$		0			0
$225$	−8.75139	+	2.84350i	−0.583426	+	0.189567i
$226$		0			0
$227$	−0.569520	−	3.59581i	−0.0378004	−	0.238662i	0.961553	−	0.274620i	$-0.0885519\pi$
$227$	−0.569520	−	3.59581i	−0.0378004	−	0.238662i	−0.999353	+	0.0359575i	$0.988552\pi$
$228$		0			0
$229$	6.86797	−	3.49941i	0.453849	−	0.231247i	−0.212096	−	0.977249i	$-0.568029\pi$
$229$	6.86797	−	3.49941i	0.453849	−	0.231247i	0.665944	+	0.746002i	$0.268029\pi$
$230$		0			0
$231$	13.2305	−	8.80723i	0.870502	−	0.579473i
$232$		0			0
$233$	2.21763	−	6.82517i	0.145282	−	0.447132i	−0.851765	−	0.523924i	$-0.824468\pi$
$233$	2.21763	−	6.82517i	0.145282	−	0.447132i	0.997047	+	0.0767917i	$0.0244677\pi$
$234$		0			0
$235$	0.263377	+	0.191354i	0.0171808	+	0.0124826i
$236$		0			0
$237$	−11.3168	+	3.67706i	−0.735108	+	0.238851i
$238$		0			0
$239$	−13.7217	−	2.17330i	−0.887581	−	0.140579i	−0.304037	−	0.952660i	$-0.598334\pi$
$239$	−13.7217	−	2.17330i	−0.887581	−	0.140579i	−0.583544	+	0.812081i	$0.698334\pi$
$240$		0			0
$241$	20.4822	−	20.4822i	1.31938	−	1.31938i	0.405108	−	0.914269i	$-0.367234\pi$
$241$	20.4822	−	20.4822i	1.31938	−	1.31938i	0.914269	−	0.405108i	$-0.132766\pi$
$242$		0			0
$243$	20.9503			1.34396
$244$		0			0
$245$	3.48151	+	0.551416i	0.222425	+	0.0352287i
$246$		0			0
$247$	−0.694247	−	2.99931i	−0.0441739	−	0.190841i
$248$		0			0
$249$	−5.99022	−	37.8208i	−0.379615	−	2.39679i
$250$		0			0
$251$	3.19853	+	1.03927i	0.201890	+	0.0655979i	0.408216	−	0.912885i	$-0.366151\pi$
$251$	3.19853	+	1.03927i	0.201890	+	0.0655979i	−0.206327	+	0.978483i	$0.566151\pi$
$252$		0			0
$253$	−0.376314	+	1.87488i	−0.0236586	+	0.117873i
$254$		0			0
$255$	−0.125300	−	0.245916i	−0.00784662	−	0.0153999i
$256$		0			0
$257$	0.293715	−	0.404264i	0.0183215	−	0.0252173i	−0.799758	−	0.600323i	$-0.795039\pi$
$257$	0.293715	−	0.404264i	0.0183215	−	0.0252173i	0.818079	+	0.575105i	$0.195039\pi$
$258$		0			0
$259$	1.67457	+	5.15380i	0.104053	+	0.320242i
$260$		0			0
$261$	−1.87914	−	2.58641i	−0.116316	−	0.160095i
$262$		0			0
$263$		−	18.4224i		−	1.13597i	−0.823037	−	0.567987i	$-0.807722\pi$
$263$		−	18.4224i		−	1.13597i	0.823037	−	0.567987i	$-0.192278\pi$
$264$		0			0
$265$	3.70430	−	3.70430i	0.227553	−	0.227553i
$266$		0			0
$267$	33.2117	+	5.26022i	2.03252	+	0.321920i
$268$		0			0
$269$	−5.14184	−	15.8250i	−0.313504	−	0.964865i	−0.976366	−	0.216124i	$-0.930659\pi$
$269$	−5.14184	−	15.8250i	−0.313504	−	0.964865i	0.662863	−	0.748741i	$-0.269341\pi$
$270$		0			0
$271$	1.84966	−	0.292958i	0.112359	−	0.0177959i	−0.100002	−	0.994987i	$-0.531885\pi$
$271$	1.84966	−	0.292958i	0.112359	−	0.0177959i	0.212361	+	0.977191i	$0.431885\pi$
$272$		0			0
$273$	−15.9087	−	6.74213i	−0.962837	−	0.408052i
$274$		0			0
$275$	−4.88020	−	10.6344i	−0.294287	−	0.641276i
$276$		0			0
$277$	8.23067	−	25.3314i	0.494533	−	1.52202i	−0.323150	−	0.946348i	$-0.604742\pi$
$277$	8.23067	−	25.3314i	0.494533	−	1.52202i	0.817683	−	0.575669i	$-0.195258\pi$
$278$		0			0
$279$	−8.60198	+	1.36242i	−0.514987	+	0.0815659i
$280$		0			0
$281$	19.7146	+	10.0451i	1.17607	+	0.599240i	0.929117	−	0.369786i	$-0.120569\pi$
$281$	19.7146	+	10.0451i	1.17607	+	0.599240i	0.246958	+	0.969026i	$0.420569\pi$
$282$		0			0
$283$	−15.6633	+	11.3801i	−0.931088	+	0.676475i	−0.946259	−	0.323410i	$-0.895171\pi$
$283$	−15.6633	+	11.3801i	−0.931088	+	0.676475i	0.0151706	+	0.999885i	$0.495171\pi$
$284$		0			0
$285$	−2.45340			−0.145327
$286$		0			0
$287$	6.99815			0.413088
$288$		0			0
$289$	13.7458	−	9.98693i	0.808578	−	0.587466i
$290$		0			0
$291$	21.1727	+	10.7880i	1.24116	+	0.632405i
$292$		0			0
$293$	−10.3283	+	1.63584i	−0.603384	+	0.0955667i	−0.450650	−	0.892701i	$-0.648808\pi$
$293$	−10.3283	+	1.63584i	−0.603384	+	0.0955667i	−0.152734	+	0.988267i	$0.548808\pi$
$294$		0			0
$295$	4.40881	−	13.5689i	0.256691	−	0.790014i
$296$		0			0
$297$	0.356328	+	3.05593i	0.0206763	+	0.177323i
$298$		0			0
$299$	1.92705	−	0.779856i	0.111444	−	0.0451002i
$300$		0			0
$301$	−2.39110	+	0.378714i	−0.137821	+	0.0218287i
$302$		0			0
$303$	−1.05745	−	3.25448i	−0.0607487	−	0.186965i
$304$		0			0
$305$	11.1317	+	1.76309i	0.637398	+	0.100954i
$306$		0			0
$307$	22.5080	−	22.5080i	1.28460	−	1.28460i	0.346583	−	0.938019i	$-0.387342\pi$
$307$	22.5080	−	22.5080i	1.28460	−	1.28460i	0.938019	−	0.346583i	$-0.112658\pi$
$308$		0			0
$309$			15.4786i			0.880548i
$310$		0			0
$311$	15.4450	+	21.2582i	0.875805	+	1.20544i	0.977565	+	0.210634i	$0.0675527\pi$
$311$	15.4450	+	21.2582i	0.875805	+	1.20544i	−0.101760	+	0.994809i	$0.532447\pi$
$312$		0			0
$313$	−4.02362	−	12.3834i	−0.227429	−	0.699953i	−0.998036	−	0.0626432i	$-0.980047\pi$
$313$	−4.02362	−	12.3834i	−0.227429	−	0.699953i	0.770607	−	0.637310i	$-0.219953\pi$
$314$		0			0
$315$	−3.76410	+	5.18084i	−0.212083	+	0.291907i
$316$		0			0
$317$	−3.63973	−	7.14337i	−0.204427	−	0.401211i	0.765916	−	0.642940i	$-0.222286\pi$
$317$	−3.63973	−	7.14337i	−0.204427	−	0.401211i	−0.970344	+	0.241729i	$0.922286\pi$
$318$		0			0
$319$	2.98993	−	2.75428i	0.167404	−	0.154210i
$320$		0			0
$321$	19.1829	+	6.23292i	1.07069	+	0.347888i
$322$		0			0
$323$	0.0128303	+	0.0810071i	0.000713895	+	0.00450735i
$324$		0			0
$325$	−6.73441	+	10.7910i	−0.373558	+	0.598577i
$326$		0			0
$327$	−1.10092	−	0.174369i	−0.0608810	−	0.00964260i
$328$		0			0
$329$	−0.542957			−0.0299342
$330$		0			0
$331$	−15.3200	+	15.3200i	−0.842063	+	0.842063i	−0.989127	−	0.147064i	$-0.953018\pi$
$331$	−15.3200	+	15.3200i	−0.842063	+	0.842063i	0.147064	+	0.989127i	$0.453018\pi$
$332$		0			0
$333$	6.89892	+	1.09268i	0.378059	+	0.0598786i
$334$		0			0
$335$	6.18923	−	2.01100i	0.338154	−	0.109873i
$336$		0			0
$337$	0.216270	+	0.157129i	0.0117810	+	0.00855938i	0.593660	−	0.804716i	$-0.297682\pi$
$337$	0.216270	+	0.157129i	0.0117810	+	0.00855938i	−0.581879	+	0.813275i	$0.697682\pi$
$338$		0			0
$339$	−9.06826	+	27.9092i	−0.492520	+	1.51582i
$340$		0			0
$341$	−2.98757	−	10.6638i	−0.161786	−	0.577475i
$342$		0			0
$343$	−17.8591	+	9.09968i	−0.964303	+	0.491337i
$344$		0			0
$345$	−0.259163	−	1.63629i	−0.0139529	−	0.0880948i
$346$		0			0
$347$	24.1402	−	7.84362i	1.29591	−	0.421068i	0.421756	−	0.906710i	$-0.361414\pi$
$347$	24.1402	−	7.84362i	1.29591	−	0.421068i	0.874158	+	0.485642i	$0.161414\pi$
$348$		0			0
$349$	−0.0839569	+	0.530083i	−0.00449411	+	0.0283747i	−0.989833	−	0.142231i	$-0.954572\pi$
$349$	−0.0839569	+	0.530083i	−0.00449411	+	0.0283747i	0.985339	+	0.170606i	$0.0545724\pi$
$350$		0			0
$351$	2.56092	−	2.15136i	0.136692	−	0.114831i
$352$		0			0
$353$	13.6912	−	13.6912i	0.728710	−	0.728710i	−0.241653	−	0.970363i	$-0.577689\pi$
$353$	13.6912	−	13.6912i	0.728710	−	0.728710i	0.970363	+	0.241653i	$0.0776894\pi$
$354$		0			0
$355$	−3.10320	−	4.27119i	−0.164701	−	0.226691i
$356$		0			0
$357$	0.410140	+	0.208977i	0.0217069	+	0.0110602i
$358$		0			0
$359$	−28.5139	+	4.51617i	−1.50491	+	0.238354i	−0.853788	−	0.520621i	$-0.825701\pi$
$359$	−28.5139	+	4.51617i	−1.50491	+	0.238354i	−0.651120	+	0.758975i	$0.725701\pi$
$360$		0			0
$361$	−17.3767	−	5.64603i	−0.914563	−	0.297159i
$362$		0			0
$363$	25.3512	−	5.99350i	1.33059	−	0.314577i
$364$		0			0
$365$	−8.02081	−	2.60612i	−0.419828	−	0.136410i
$366$		0			0
$367$	−19.9367	−	14.4848i	−1.04069	−	0.756102i	−0.0702660	−	0.997528i	$-0.522385\pi$
$367$	−19.9367	−	14.4848i	−1.04069	−	0.756102i	−0.970419	+	0.241426i	$0.922385\pi$
$368$		0			0
$369$	4.09515	−	8.03719i	0.213185	−	0.418399i
$370$		0			0
$371$	−1.36678	+	8.62952i	−0.0709597	+	0.448022i
$372$		0			0
$373$		−	14.5764i		−	0.754735i	−0.926064	−	0.377367i	$-0.876829\pi$
$373$		−	14.5764i		−	0.754735i	0.926064	−	0.377367i	$-0.123171\pi$
$374$		0			0
$375$	17.3266	+	17.3266i	0.894739	+	0.894739i
$376$		0			0
$377$	−4.28866	−	1.06668i	−0.220877	−	0.0549371i
$378$		0			0
$379$	−21.2093	−	10.8067i	−1.08945	−	0.555103i	−0.185459	−	0.982652i	$-0.559377\pi$
$379$	−21.2093	−	10.8067i	−1.08945	−	0.555103i	−0.903992	+	0.427549i	$0.859377\pi$
$380$		0			0
$381$	−34.0858	−	24.7648i	−1.74627	−	1.26874i
$382$		0			0
$383$	9.63068	+	18.9013i	0.492105	+	0.965810i	0.994848	+	0.101374i	$0.0323239\pi$
$383$	9.63068	+	18.9013i	0.492105	+	0.965810i	−0.502744	+	0.864435i	$0.667676\pi$
$384$		0			0
$385$	−7.09781	−	3.99112i	−0.361738	−	0.203406i
$386$		0			0
$387$	−0.964275	+	2.96773i	−0.0490169	+	0.150858i
$388$		0			0
$389$	9.46823	−	13.0319i	0.480058	−	0.660743i	−0.498458	−	0.866914i	$-0.666100\pi$
$389$	9.46823	−	13.0319i	0.480058	−	0.660743i	0.978516	+	0.206170i	$0.0661001\pi$
$390$		0			0
$391$	−0.0526722	+	0.0171142i	−0.00266375	+	0.000865504i
$392$		0			0
$393$	20.6037	+	28.3586i	1.03932	+	1.43050i
$394$		0			0
$395$	4.31081	+	4.31081i	0.216900	+	0.216900i
$396$		0			0
$397$	−17.9740	−	17.9740i	−0.902087	−	0.902087i	0.0935292	−	0.995617i	$-0.470185\pi$
$397$	−17.9740	−	17.9740i	−0.902087	−	0.902087i	−0.995617	+	0.0935292i	$0.970185\pi$
$398$		0			0
$399$	3.31033	−	2.40510i	0.165724	−	0.120405i
$400$		0			0
$401$	4.37946	−	8.59516i	0.218700	−	0.429222i	−0.755425	−	0.655236i	$-0.772569\pi$
$401$	4.37946	−	8.59516i	0.218700	−	0.429222i	0.974124	+	0.226014i	$0.0725694\pi$
$402$		0			0
$403$	−7.89318	+	9.09053i	−0.393187	+	0.452832i
$404$		0			0
$405$	−5.52024	−	10.8341i	−0.274303	−	0.538350i
$406$		0			0
$407$	−0.364065	+	8.87435i	−0.0180460	+	0.439885i
$408$		0			0
$409$	4.89126	−	2.49222i	0.241857	−	0.123232i	−0.328861	−	0.944378i	$-0.606665\pi$
$409$	4.89126	−	2.49222i	0.241857	−	0.123232i	0.570718	+	0.821146i	$0.306665\pi$
$410$		0			0
$411$	−2.49220	−	15.7351i	−0.122931	−	0.776158i
$412$		0			0
$413$	7.35305	+	22.6304i	0.361820	+	1.11357i
$414$		0			0
$415$	−15.8717	+	11.5315i	−0.779111	+	0.566057i
$416$		0			0
$417$			22.4521i			1.09948i
$418$		0			0
$419$	−31.8271			−1.55485			−0.777427	−	0.628973i	$-0.783476\pi$
$419$	−31.8271			−1.55485			−0.777427	+	0.628973i	$0.783476\pi$
$420$		0			0
$421$	−5.72477	+	36.1448i	−0.279008	+	1.76159i	0.307407	+	0.951578i	$0.400539\pi$
$421$	−5.72477	+	36.1448i	−0.279008	+	1.76159i	−0.586416	+	0.810010i	$0.699461\pi$
$422$		0			0
$423$	−0.317726	+	0.623571i	−0.0154483	+	0.0303191i
$424$		0			0
$425$	0.199184	−	0.274153i	0.00966183	−	0.0132984i
$426$		0			0
$427$	−16.7482	+	8.53362i	−0.810501	+	0.412971i
$428$		0			0
$429$	−20.6044	−	19.4279i	−0.994792	−	0.937987i
$430$		0			0
$431$	2.34615	−	1.19542i	0.113010	−	0.0575816i	−0.396572	−	0.918004i	$-0.629800\pi$
$431$	2.34615	−	1.19542i	0.113010	−	0.0575816i	0.509582	+	0.860422i	$0.329800\pi$
$432$		0			0
$433$	20.2415	−	27.8601i	0.972746	−	1.33887i	0.0320982	−	0.999485i	$-0.489781\pi$
$433$	20.2415	−	27.8601i	0.972746	−	1.33887i	0.940648	−	0.339385i	$-0.110219\pi$
$434$		0			0
$435$	−1.59888	+	3.13798i	−0.0766605	+	0.150455i
$436$		0			0
$437$	−0.0770140	+	0.486247i	−0.00368408	+	0.0232604i
$438$		0			0
$439$	−7.45364			−0.355743			−0.177871	−	0.984054i	$-0.556921\pi$
$439$	−7.45364			−0.355743			−0.177871	+	0.984054i	$0.556921\pi$
$440$		0			0
$441$			7.57762i			0.360839i
$442$		0			0
$443$	2.99958	−	2.17932i	0.142514	−	0.103543i	−0.514244	−	0.857644i	$-0.671927\pi$
$443$	2.99958	−	2.17932i	0.142514	−	0.103543i	0.656758	+	0.754101i	$0.271927\pi$
$444$		0			0
$445$	−5.32364	−	16.3845i	−0.252365	−	0.776699i
$446$		0			0
$447$	3.89163	+	24.5708i	0.184068	+	1.16216i
$448$		0			0
$449$	−25.0143	+	12.7454i	−1.18050	+	0.601494i	−0.930335	−	0.366710i	$-0.880484\pi$
$449$	−25.0143	+	12.7454i	−1.18050	+	0.601494i	−0.250163	+	0.968204i	$0.580484\pi$
$450$		0			0
$451$	10.7542	+	3.98859i	0.506394	+	0.187815i
$452$		0			0
$453$	−12.3211	−	24.1816i	−0.578897	−	1.13615i
$454$		0			0
$455$	0.622545	+	8.83042i	0.0291854	+	0.413977i
$456$		0			0
$457$	3.55650	−	6.98002i	0.166366	−	0.326512i	−0.792740	−	0.609561i	$-0.791346\pi$
$457$	3.55650	−	6.98002i	0.166366	−	0.326512i	0.959105	+	0.283049i	$0.0913459\pi$
$458$		0			0
$459$	−0.0720870	+	0.0523743i	−0.00336473	+	0.00244462i
$460$		0			0
$461$	20.0881	+	20.0881i	0.935594	+	0.935594i	0.998048	−	0.0624538i	$-0.0198926\pi$
$461$	20.0881	+	20.0881i	0.935594	+	0.935594i	−0.0624538	+	0.998048i	$0.519893\pi$
$462$		0			0
$463$	12.5455	+	12.5455i	0.583039	+	0.583039i	0.935737	−	0.352698i	$-0.114736\pi$
$463$	12.5455	+	12.5455i	0.583039	+	0.583039i	−0.352698	+	0.935737i	$0.614736\pi$
$464$		0			0
$465$	5.63932	+	7.76186i	0.261517	+	0.359948i
$466$		0			0
$467$	30.8953	−	10.0385i	1.42966	−	0.464526i	0.511004	−	0.859578i	$-0.329274\pi$
$467$	30.8953	−	10.0385i	1.42966	−	0.464526i	0.918659	+	0.395053i	$0.129274\pi$
$468$		0			0
$469$	−6.37962	+	8.78079i	−0.294583	+	0.405459i
$470$		0			0
$471$	−13.2636	+	40.8213i	−0.611156	+	1.88095i
$472$		0			0
$473$	−3.89030	−	0.780833i	−0.178876	−	0.0359027i
$474$		0			0
$475$	−1.36755	−	2.68397i	−0.0627476	−	0.123149i
$476$		0			0
$477$	9.11096	+	6.61950i	0.417162	+	0.303086i
$478$		0			0
$479$	18.6974	+	9.52681i	0.854307	+	0.435291i	0.825573	−	0.564296i	$-0.190852\pi$
$479$	18.6974	+	9.52681i	0.854307	+	0.435291i	0.0287344	+	0.999587i	$0.490852\pi$
$480$		0			0
$481$	8.27358	−	4.97770i	0.377243	−	0.226963i
$482$		0			0
$483$	1.95376	+	1.95376i	0.0888991	+	0.0888991i
$484$		0			0
$485$		−	12.1745i		−	0.552814i
$486$		0			0
$487$	2.85792	−	18.0442i	0.129505	−	0.817661i	−0.834351	−	0.551234i	$-0.814157\pi$
$487$	2.85792	−	18.0442i	0.129505	−	0.817661i	0.963855	−	0.266426i	$-0.0858430\pi$
$488$		0			0
$489$	−11.4411	+	22.4544i	−0.517385	+	1.01542i
$490$		0			0
$491$	−9.60506	−	6.97848i	−0.433470	−	0.314935i	0.349565	−	0.936912i	$-0.386329\pi$
$491$	−9.60506	−	6.97848i	−0.433470	−	0.314935i	−0.783035	+	0.621978i	$0.786329\pi$
$492$		0			0
$493$	0.111972	+	0.0363820i	0.00504298	+	0.00163856i
$494$		0			0
$495$	−8.73717	+	5.81613i	−0.392706	+	0.261416i
$496$		0			0
$497$	8.37420	+	2.72094i	0.375634	+	0.122051i
$498$		0			0
$499$	−33.8325	+	5.35855i	−1.51455	+	0.239881i	−0.857705	−	0.514142i	$-0.828110\pi$
$499$	−33.8325	+	5.35855i	−1.51455	+	0.239881i	−0.656847	+	0.754024i	$0.728110\pi$
$500$		0			0
$501$	−19.1098	−	9.73695i	−0.853765	−	0.435015i
$502$		0			0
$503$	5.93071	+	8.16292i	0.264437	+	0.363967i	0.920502	−	0.390738i	$-0.127780\pi$
$503$	5.93071	+	8.16292i	0.264437	+	0.363967i	−0.656065	+	0.754705i	$0.727780\pi$
$504$		0			0
$505$	−1.23970	+	1.23970i	−0.0551658	+	0.0551658i
$506$		0			0
$507$	−5.31141	+	30.3247i	−0.235888	+	1.34677i
$508$		0			0
$509$	2.18907	−	13.8213i	0.0970290	−	0.612617i	−0.890476	−	0.455030i	$-0.849629\pi$
$509$	2.18907	−	13.8213i	0.0970290	−	0.612617i	0.987505	−	0.157587i	$-0.0503714\pi$
$510$		0			0
$511$	13.3772	−	4.34650i	0.591771	−	0.192278i
$512$		0			0
$513$	0.123907	+	0.782315i	0.00547061	+	0.0345401i
$514$		0			0
$515$	7.06591	−	3.60026i	0.311361	−	0.158646i
$516$		0			0
$517$	−0.834371	−	0.309458i	−0.0366956	−	0.0136099i
$518$		0			0
$519$	−14.4036	+	44.3297i	−0.632247	+	1.94586i
$520$		0			0
$521$	12.4374	+	9.03633i	0.544894	+	0.395889i	0.825899	−	0.563817i	$-0.190668\pi$
$521$	12.4374	+	9.03633i	0.544894	+	0.395889i	−0.281005	+	0.959706i	$0.590668\pi$
$522$		0			0
$523$	−9.86162	+	3.20423i	−0.431219	+	0.140111i	−0.516581	−	0.856239i	$-0.672795\pi$
$523$	−9.86162	+	3.20423i	−0.431219	+	0.140111i	0.0853620	+	0.996350i	$0.472795\pi$
$524$		0			0
$525$	−16.6981	−	2.64471i	−0.728763	−	0.115425i
$526$		0			0
$527$	0.226792	−	0.226792i	0.00987922	−	0.00987922i
$528$		0			0
$529$	22.6676			0.985546
$530$		0			0
$531$	30.2932	+	4.79797i	1.31461	+	0.208214i
$532$		0			0
$533$	−2.81189	−	12.1480i	−0.121797	−	0.526189i
$534$		0			0
$535$	−1.61658	−	10.2067i	−0.0698907	−	0.441273i
$536$		0			0
$537$	−44.1016	−	14.3295i	−1.90313	−	0.618363i
$538$		0			0
$539$	−9.57063	+	1.11596i	−0.412236	+	0.0480677i
$540$		0			0
$541$	0.734185	+	1.44092i	0.0315651	+	0.0619500i	0.906251	−	0.422741i	$-0.138932\pi$
$541$	0.734185	+	1.44092i	0.0315651	+	0.0619500i	−0.874685	+	0.484691i	$0.838932\pi$
$542$		0			0
$543$	31.9664	−	43.9980i	1.37181	−	1.88813i
$544$		0			0
$545$	0.176471	+	0.543122i	0.00755918	+	0.0232648i
$546$		0			0
$547$	5.47067	+	7.52973i	0.233909	+	0.321948i	0.909795	−	0.415058i	$-0.136239\pi$
$547$	5.47067	+	7.52973i	0.233909	+	0.321948i	−0.675886	+	0.737006i	$0.736239\pi$
$548$		0			0
$549$			24.2285i			1.03405i
$550$		0			0
$551$	0.740034	−	0.740034i	0.0315265	−	0.0315265i
$552$		0			0
$553$	−10.0424	−	1.59057i	−0.427048	−	0.0676378i
$554$		0			0
$555$	−2.37779	−	7.31808i	−0.100932	−	0.310635i
$556$		0			0
$557$	−21.9863	+	3.48229i	−0.931591	+	0.147550i	−0.603741	−	0.797180i	$-0.706324\pi$
$557$	−21.9863	+	3.48229i	−0.931591	+	0.147550i	−0.327850	+	0.944730i	$0.606324\pi$
$558$		0			0
$559$	1.61816	+	3.99853i	0.0684410	+	0.169120i
$560$		0			0
$561$	0.511163	+	0.554897i	0.0215813	+	0.0234278i
$562$		0			0
$563$	2.43765	−	7.50233i	0.102735	−	0.316185i	−0.886457	−	0.462810i	$-0.846841\pi$
$563$	2.43765	−	7.50233i	0.102735	−	0.316185i	0.989192	+	0.146625i	$0.0468411\pi$
$564$		0			0
$565$	14.8497	−	2.35196i	0.624730	−	0.0989476i
$566$		0			0
$567$	18.0692	+	9.20670i	0.758833	+	0.386645i
$568$		0			0
$569$	−33.6106	+	24.4195i	−1.40903	+	1.02372i	−0.415566	+	0.909563i	$0.636417\pi$
$569$	−33.6106	+	24.4195i	−1.40903	+	1.02372i	−0.993463	+	0.114156i	$0.963583\pi$
$570$		0			0
$571$	8.33670			0.348880			0.174440	−	0.984668i	$-0.444189\pi$
$571$	8.33670			0.348880			0.174440	+	0.984668i	$0.444189\pi$
$572$		0			0
$573$	2.06665			0.0863357
$574$		0			0
$575$	1.64561	−	1.19561i	0.0686267	−	0.0498602i
$576$		0			0
$577$	12.9857	+	6.61655i	0.540602	+	0.275451i	0.702897	−	0.711292i	$-0.251890\pi$
$577$	12.9857	+	6.61655i	0.540602	+	0.275451i	−0.162295	+	0.986742i	$0.551890\pi$
$578$		0			0
$579$	−20.6402	+	3.26909i	−0.857778	+	0.135859i
$580$		0			0
$581$	10.1110	−	31.1184i	0.419475	−	1.29101i
$582$		0			0
$583$	−7.01874	+	12.4821i	−0.290687	+	0.516956i
$584$		0			0
$585$	10.5058	+	4.45238i	0.434361	+	0.184083i
$586$		0			0
$587$	−25.7565	+	4.07943i	−1.06309	+	0.168376i	−0.663392	−	0.748272i	$-0.730884\pi$
$587$	−25.7565	+	4.07943i	−1.06309	+	0.168376i	−0.399694	+	0.916649i	$0.630884\pi$
$588$		0			0
$589$	−0.881023	−	2.71151i	−0.0363019	−	0.111726i
$590$		0			0
$591$	16.6040	+	2.62982i	0.682998	+	0.108176i
$592$		0			0
$593$	24.4704	−	24.4704i	1.00488	−	1.00488i	0.00489115	−	0.999988i	$-0.498443\pi$
$593$	24.4704	−	24.4704i	1.00488	−	1.00488i	0.999988	−	0.00489115i	$-0.00155691\pi$
$594$		0			0
$595$		−	0.235834i		−	0.00966826i
$596$		0			0
$597$	11.7075	+	16.1140i	0.479158	+	0.659504i
$598$		0			0
$599$	2.47558	+	7.61905i	0.101149	+	0.311306i	0.988807	−	0.149197i	$-0.0476690\pi$
$599$	2.47558	+	7.61905i	0.101149	+	0.311306i	−0.887658	+	0.460503i	$0.847669\pi$
$600$		0			0
$601$	19.6802	−	27.0874i	0.802771	−	1.10492i	−0.189628	−	0.981856i	$-0.560728\pi$
$601$	19.6802	−	27.0874i	0.802771	−	1.10492i	0.992399	−	0.123063i	$-0.0392717\pi$
$602$		0			0
$603$	6.35130	+	12.4651i	0.258645	+	0.507619i
$604$		0			0
$605$	−8.63257	−	10.1786i	−0.350964	−	0.413819i
$606$		0			0
$607$	44.8728	+	14.5801i	1.82133	+	0.591786i	0.999765	+	0.0216723i	$0.00689906\pi$
$607$	44.8728	+	14.5801i	1.82133	+	0.591786i	0.821566	+	0.570114i	$0.193101\pi$
$608$		0			0
$609$	−0.918857	−	5.80143i	−0.0372340	−	0.235086i
$610$		0			0
$611$	0.218163	+	0.942514i	0.00882592	+	0.0381300i
$612$		0			0
$613$	36.2995	+	5.74928i	1.46612	+	0.232211i	0.837901	−	0.545822i	$-0.183782\pi$
$613$	36.2995	+	5.74928i	1.46612	+	0.232211i	0.628223	+	0.778033i	$0.283782\pi$
$614$		0			0
$615$	−9.93694			−0.400696
$616$		0			0
$617$	−13.3185	+	13.3185i	−0.536184	+	0.536184i	−0.922406	−	0.386222i	$-0.873780\pi$
$617$	−13.3185	+	13.3185i	−0.536184	+	0.536184i	0.386222	+	0.922406i	$0.373780\pi$
$618$		0			0
$619$	−41.6438	−	6.59573i	−1.67381	−	0.265105i	−0.753827	−	0.657073i	$-0.771794\pi$
$619$	−41.6438	−	6.59573i	−1.67381	−	0.265105i	−0.919979	+	0.391968i	$0.871794\pi$
$620$		0			0
$621$	−0.508675	+	0.165278i	−0.0204124	+	0.00663239i
$622$		0			0
$623$	23.2450	+	16.8885i	0.931291	+	0.676623i
$624$		0			0
$625$	−1.57149	+	4.83654i	−0.0628595	+	0.193462i
$626$		0			0
$627$	6.45782	−	1.80923i	0.257901	−	0.0722537i
$628$		0			0
$629$	−0.229196	+	0.116781i	−0.00913863	+	0.00465637i
$630$		0			0
$631$	2.01971	+	12.7520i	0.0804034	+	0.507647i	0.994718	+	0.102643i	$0.0327300\pi$
$631$	2.01971	+	12.7520i	0.0804034	+	0.507647i	−0.914315	+	0.405004i	$0.867270\pi$
$632$		0			0
$633$	−31.0843	+	10.0999i	−1.23549	+	0.401435i
$634$		0			0
$635$	−3.37679	+	21.3202i	−0.134004	+	0.846066i
$636$		0			0
$637$	6.73769	+	8.02037i	0.266957	+	0.317779i
$638$		0			0
$639$	8.02531	−	8.02531i	0.317476	−	0.317476i
$640$		0			0
$641$	−10.4148	−	14.3347i	−0.411358	−	0.566186i	0.552191	−	0.833718i	$-0.313792\pi$
$641$	−10.4148	−	14.3347i	−0.411358	−	0.566186i	−0.963549	+	0.267532i	$0.913792\pi$
$642$		0			0
$643$	15.4822	+	7.88859i	0.610560	+	0.311096i	0.731792	−	0.681528i	$-0.238684\pi$
$643$	15.4822	+	7.88859i	0.610560	+	0.311096i	−0.121232	+	0.992624i	$0.538684\pi$
$644$		0			0
$645$	3.39522	−	0.537750i	0.133687	−	0.0211739i
$646$		0			0
$647$	14.5781	+	4.73673i	0.573126	+	0.186220i	0.581219	−	0.813747i	$-0.302576\pi$
$647$	14.5781	+	4.73673i	0.573126	+	0.186220i	−0.00809277	+	0.999967i	$0.502576\pi$
$648$		0			0
$649$	−1.59861	+	38.9673i	−0.0627509	+	1.52960i
$650$		0			0
$651$	−15.2181	−	4.94466i	−0.596444	−	0.193796i
$652$		0			0
$653$	2.44121	+	1.77364i	0.0955320	+	0.0694081i	0.634526	−	0.772902i	$-0.281195\pi$
$653$	2.44121	+	1.77364i	0.0955320	+	0.0694081i	−0.538994	+	0.842310i	$0.681195\pi$
$654$		0			0
$655$	8.15321	−	16.0016i	0.318572	−	0.625233i
$656$		0			0
$657$	2.83615	−	17.9068i	0.110649	−	0.698610i
$658$		0			0
$659$		−	28.7939i		−	1.12165i	−0.827935	−	0.560825i	$-0.810484\pi$
$659$		−	28.7939i		−	1.12165i	0.827935	−	0.560825i	$-0.189516\pi$
$660$		0			0
$661$	−5.86723	−	5.86723i	−0.228209	−	0.228209i	0.583735	−	0.811944i	$-0.301591\pi$
$661$	−5.86723	−	5.86723i	−0.228209	−	0.228209i	−0.811944	+	0.583735i	$0.801591\pi$
$662$		0			0
$663$	0.197965	−	0.795927i	0.00768831	−	0.0309112i
$664$		0			0
$665$	−1.86788	−	0.951734i	−0.0724334	−	0.0369067i
$666$		0			0
$667$	0.571737	+	0.415391i	0.0221377	+	0.0160840i
$668$		0			0
$669$	−16.6981	−	32.7720i	−0.645588	−	1.26704i
$670$		0			0
$671$	−30.6009	+	3.56814i	−1.18134	+	0.137747i
$672$		0			0
$673$	−8.36772	+	25.7532i	−0.322552	+	0.992713i	0.649982	+	0.759950i	$0.274777\pi$
$673$	−8.36772	+	25.7532i	−0.322552	+	0.992713i	−0.972534	+	0.232763i	$0.925223\pi$
$674$		0			0
$675$	1.92359	−	2.64760i	0.0740390	−	0.101906i
$676$		0			0
$677$	−9.49722	+	3.08583i	−0.365008	+	0.118598i	−0.485778	−	0.874082i	$-0.661464\pi$
$677$	−9.49722	+	3.08583i	−0.365008	+	0.118598i	0.120770	+	0.992680i	$0.461464\pi$
$678$		0			0
$679$	11.9348	+	16.4268i	0.458015	+	0.630403i
$680$		0			0
$681$	−6.09644	−	6.09644i	−0.233616	−	0.233616i
$682$		0			0
$683$	−24.0562	−	24.0562i	−0.920484	−	0.920484i	0.0765793	−	0.997063i	$-0.475600\pi$
$683$	−24.0562	−	24.0562i	−0.920484	−	0.920484i	−0.997063	+	0.0765793i	$0.975600\pi$
$684$		0			0
$685$	−6.60334	+	4.79761i	−0.252301	+	0.183307i
$686$		0			0
$687$	8.28724	−	16.2646i	0.316178	−	0.620534i
$688$		0			0
$689$	15.5291	−	1.09480i	0.591611	−	0.0417086i
$690$		0			0
$691$	2.54732	+	4.99940i	0.0969048	+	0.190186i	0.934370	−	0.356304i	$-0.115963\pi$
$691$	2.54732	+	4.99940i	0.0969048	+	0.190186i	−0.837465	+	0.546491i	$0.815963\pi$
$692$		0			0
$693$	6.08729	−	16.4128i	0.231237	−	0.623469i
$694$		0			0
$695$	10.2493	−	5.22226i	0.388776	−	0.198091i
$696$		0			0
$697$	0.0519661	+	0.328101i	0.00196836	+	0.0124277i
$698$		0			0
$699$	−5.25176	−	16.1633i	−0.198640	−	0.611351i
$700$		0			0
$701$	−41.2013	+	29.9345i	−1.55615	+	1.13061i	−0.617075	+	0.786904i	$0.711683\pi$
$701$	−41.2013	+	29.9345i	−1.55615	+	1.13061i	−0.939077	+	0.343707i	$0.888317\pi$
$702$		0			0
$703$			2.28659i			0.0862403i
$704$		0			0
$705$	0.770966			0.0290362
$706$		0			0
$707$	0.457414	−	2.88800i	0.0172028	−	0.108614i
$708$		0			0
$709$	−1.09710	+	2.15317i	−0.0412023	+	0.0808641i	−0.910690	−	0.413091i	$-0.864449\pi$
$709$	−1.09710	+	2.15317i	−0.0412023	+	0.0808641i	0.869488	+	0.493955i	$0.164449\pi$
$710$		0			0
$711$	−7.70333	+	10.6027i	−0.288897	+	0.397633i
$712$		0			0
$713$	1.71537	−	0.874025i	0.0642411	−	0.0327325i
$714$		0			0
$715$	−4.07622	+	13.9247i	−0.152442	+	0.520753i
$716$		0			0
$717$	−29.3145	+	14.9365i	−1.09477	+	0.557814i
$718$		0			0
$719$	−4.67112	+	6.42925i	−0.174203	+	0.239770i	−0.887187	−	0.461411i	$-0.847344\pi$
$719$	−4.67112	+	6.42925i	−0.174203	+	0.239770i	0.712983	+	0.701181i	$0.247344\pi$
$720$		0			0
$721$	−6.00454	+	11.7846i	−0.223621	+	0.438880i
$722$		0			0
$723$	10.7310	−	67.7529i	0.399090	−	2.51976i
$724$		0			0
$725$	−4.32413			−0.160594
$726$		0			0
$727$		−	6.06155i		−	0.224811i	−0.993662	−	0.112405i	$-0.964145\pi$
$727$		−	6.06155i		−	0.224811i	0.993662	−	0.112405i	$-0.0358555\pi$
$728$		0			0
$729$	15.8155	−	11.4906i	0.585759	−	0.425579i
$730$		0			0
$731$	−0.0355112	−	0.109292i	−0.00131343	−	0.00404232i
$732$		0			0
$733$	5.22320	+	32.9780i	0.192923	+	1.21807i	0.874025	+	0.485881i	$0.161501\pi$
$733$	5.22320	+	32.9780i	0.192923	+	1.21807i	−0.681102	+	0.732189i	$0.738499\pi$
$734$		0			0
$735$	7.43778	−	3.78974i	0.274347	−	0.139787i
$736$		0			0
$737$	−14.8083	+	9.85752i	−0.545469	+	0.363106i
$738$		0			0
$739$	−13.6810	−	26.8505i	−0.503264	−	0.987711i	−0.993251	−	0.115981i	$-0.962999\pi$
$739$	−13.6810	−	26.8505i	−0.503264	−	0.987711i	0.489988	−	0.871729i	$-0.337001\pi$
$740$		0			0
$741$	−5.50509	−	4.77999i	−0.202235	−	0.175597i
$742$		0			0
$743$	1.05160	−	2.06387i	0.0385793	−	0.0757161i	−0.870912	−	0.491439i	$-0.836471\pi$
$743$	1.05160	−	2.06387i	0.0385793	−	0.0757161i	0.909492	+	0.415722i	$0.136471\pi$
$744$		0			0
$745$	10.3113	−	7.49158i	0.377776	−	0.274470i
$746$		0			0
$747$	−29.8220	−	29.8220i	−1.09113	−	1.09113i
$748$		0			0
$749$	12.1869	+	12.1869i	0.445301	+	0.445301i
$750$		0			0
$751$	−16.7763	−	23.0905i	−0.612174	−	0.842586i	0.384580	−	0.923092i	$-0.374346\pi$
$751$	−16.7763	−	23.0905i	−0.612174	−	0.842586i	−0.996754	+	0.0805062i	$0.974346\pi$
$752$		0			0
$753$	7.57471	−	2.46117i	0.276038	−	0.0896901i
$754$		0			0
$755$	−8.17293	+	11.2491i	−0.297443	+	0.409396i
$756$		0			0
$757$	−4.71314	+	14.5056i	−0.171302	+	0.527214i	−0.999445	−	0.0333030i	$-0.989397\pi$
$757$	−4.71314	+	14.5056i	−0.171302	+	0.527214i	0.828143	+	0.560517i	$0.189397\pi$
$758$		0			0
$759$	1.88883	+	4.11591i	0.0685601	+	0.149398i
$760$		0			0
$761$	−1.20722	−	2.36931i	−0.0437618	−	0.0858873i	0.868090	−	0.496407i	$-0.165347\pi$
$761$	−1.20722	−	2.36931i	−0.0437618	−	0.0858873i	−0.911852	+	0.410519i	$0.865347\pi$
$762$		0			0
$763$	−0.770538	−	0.559829i	−0.0278953	−	0.0202672i
$764$		0			0
$765$	−0.270849	−	0.138005i	−0.00979257	−	0.00498957i
$766$		0			0
$767$	36.3293	−	21.8571i	1.31178	−	0.789213i
$768$		0			0
$769$	16.0162	+	16.0162i	0.577560	+	0.577560i	0.934230	−	0.356671i	$-0.116088\pi$
$769$	16.0162	+	16.0162i	0.577560	+	0.577560i	−0.356671	+	0.934230i	$0.616088\pi$
$770$		0			0
$771$		−	1.18338i		−	0.0426183i
$772$		0			0
$773$	−4.26499	+	26.9281i	−0.153401	+	0.968535i	0.784121	+	0.620608i	$0.213114\pi$
$773$	−4.26499	+	26.9281i	−0.153401	+	0.968535i	−0.937522	+	0.347927i	$0.886886\pi$
$774$		0			0
$775$	−5.34791	+	10.4959i	−0.192103	+	0.377023i
$776$		0			0
$777$	10.3823	+	7.54320i	0.372464	+	0.270611i
$778$		0			0
$779$	2.80838	+	0.912498i	0.100621	+	0.0326936i
$780$		0			0
$781$	11.3180	+	8.95418i	0.404989	+	0.320406i
$782$		0			0
$783$	1.08136	+	0.351355i	0.0386446	+	0.0125564i
$784$		0			0
$785$	21.7198	−	3.44008i	0.775212	−	0.122782i
$786$		0			0
$787$	2.42642	+	1.23632i	0.0864926	+	0.0440702i	0.496702	−	0.867921i	$-0.334544\pi$
$787$	2.42642	+	1.23632i	0.0864926	+	0.0440702i	−0.410209	+	0.911991i	$0.634544\pi$
$788$		0			0
$789$	−25.6437	−	35.2955i	−0.912939	−	1.25655i
$790$		0			0
$791$	−17.7308	+	17.7308i	−0.630434	+	0.630434i
$792$		0			0
$793$	21.5429	+	25.6441i	0.765012	+	0.910650i
$794$		0			0
$795$	1.94075	−	12.2534i	0.0688311	−	0.434583i
$796$		0			0
$797$	−21.1900	+	6.88505i	−0.750588	+	0.243881i	−0.659234	−	0.751938i	$-0.729119\pi$
$797$	−21.1900	+	6.88505i	−0.750588	+	0.243881i	−0.0913538	+	0.995819i	$0.529119\pi$
$798$		0			0
$799$	−0.00403183	−	0.0254560i	−0.000142636	−	0.000900567i
$800$		0			0
$801$	32.9984	−	16.8135i	1.16594	−	0.594076i
$802$		0			0
$803$	23.0342	+	0.944963i	0.812858	+	0.0333470i
$804$		0			0
$805$	0.437445	−	1.34632i	0.0154179	−	0.0474514i
$806$		0			0
$807$	−31.8793	−	23.1617i	−1.12221	−	0.815330i
$808$		0			0
$809$	−15.2417	+	4.95233i	−0.535870	+	0.174115i	−0.564436	−	0.825477i	$-0.690906\pi$
$809$	−15.2417	+	4.95233i	−0.535870	+	0.174115i	0.0285653	+	0.999592i	$0.490906\pi$
$810$		0			0
$811$	−31.5935	−	5.00391i	−1.10940	−	0.175711i	−0.425264	−	0.905069i	$-0.639819\pi$
$811$	−31.5935	−	5.00391i	−1.10940	−	0.175711i	−0.684132	+	0.729358i	$0.739819\pi$
$812$		0			0
$813$	3.13598	−	3.13598i	0.109984	−	0.109984i
$814$		0			0
$815$	12.9115			0.452270
$816$		0			0
$817$	−1.00894	−	0.159800i	−0.0352983	−	0.00559071i
$818$		0			0
$819$	−18.5400	+	4.29144i	−0.647841	+	0.149955i
$820$		0			0
$821$	−6.07087	−	38.3300i	−0.211875	−	1.33773i	−0.832678	−	0.553758i	$-0.813193\pi$
$821$	−6.07087	−	38.3300i	−0.211875	−	1.33773i	0.620803	−	0.783967i	$-0.286807\pi$
$822$		0			0
$823$	11.6288	+	3.77843i	0.405355	+	0.131708i	0.504596	−	0.863356i	$-0.331641\pi$
$823$	11.6288	+	3.77843i	0.405355	+	0.131708i	−0.0992410	+	0.995063i	$0.531641\pi$
$824$		0			0
$825$	−24.1528	−	13.5812i	−0.840893	−	0.472837i
$826$		0			0
$827$	−12.6536	−	24.8340i	−0.440008	−	0.863564i	−0.999399	−	0.0346603i	$-0.988965\pi$
$827$	−12.6536	−	24.8340i	−0.440008	−	0.863564i	0.559391	−	0.828904i	$-0.311035\pi$
$828$		0			0
$829$	−17.1353	+	23.5848i	−0.595135	+	0.819132i	−0.995252	−	0.0973314i	$-0.968969\pi$
$829$	−17.1353	+	23.5848i	−0.595135	+	0.819132i	0.400117	+	0.916464i	$0.368969\pi$
$830$		0			0
$831$	−19.4917	−	59.9894i	−0.676161	−	2.08101i
$832$		0			0
$833$	−0.164027	−	0.225764i	−0.00568321	−	0.00782226i
$834$		0			0
$835$			10.9883i			0.380267i
$836$		0			0
$837$	2.19021	−	2.19021i	0.0757049	−	0.0757049i
$838$		0			0
$839$	21.2536	+	3.36624i	0.733755	+	0.116215i	0.512120	−	0.858914i	$-0.328860\pi$
$839$	21.2536	+	3.36624i	0.733755	+	0.116215i	0.221636	+	0.975130i	$0.428860\pi$
$840$		0			0
$841$	8.49724	+	26.1518i	0.293008	+	0.901787i
$842$		0			0
$843$	51.7538	−	8.19700i	1.78250	−	0.282320i
$844$		0			0
$845$	15.0785	−	4.62878i	0.518716	−	0.159235i
$846$		0			0
$847$	21.6260	+	5.27122i	0.743079	+	0.181121i
$848$		0			0
$849$	−14.1685	+	43.6062i	−0.486262	+	1.49656i
$850$		0			0
$851$	−1.52503	+	0.241542i	−0.0522775	+	0.00827995i
$852$		0			0
$853$	34.9164	+	17.7908i	1.19552	+	0.609146i	0.934422	−	0.356168i	$-0.115917\pi$
$853$	34.9164	+	17.7908i	1.19552	+	0.609146i	0.261094	+	0.965313i	$0.415917\pi$
$854$		0			0
$855$	−2.18608	+	1.58828i	−0.0747624	+	0.0543181i
$856$		0			0
$857$	−14.3704			−0.490883			−0.245441	−	0.969411i	$-0.578933\pi$
$857$	−14.3704			−0.490883			−0.245441	+	0.969411i	$0.578933\pi$
$858$		0			0
$859$	8.91642			0.304224			0.152112	−	0.988363i	$-0.451393\pi$
$859$	8.91642			0.304224			0.152112	+	0.988363i	$0.451393\pi$
$860$		0			0
$861$	13.4078	−	9.74130i	0.456935	−	0.331983i
$862$		0			0
$863$	8.70189	+	4.43383i	0.296216	+	0.150929i	0.595782	−	0.803146i	$-0.296842\pi$
$863$	8.70189	+	4.43383i	0.296216	+	0.150929i	−0.299567	+	0.954075i	$0.596842\pi$
$864$		0			0
$865$	23.5865	−	3.73573i	0.801964	−	0.127019i
$866$		0			0
$867$	12.4340	−	38.2679i	0.422281	−	1.29965i
$868$		0			0
$869$	−14.5258	−	8.16794i	−0.492756	−	0.277078i
$870$		0			0
$871$	17.8058	+	7.54615i	0.603328	+	0.255692i
$872$		0			0
$873$	25.8497	−	4.09419i	0.874880	−	0.138567i
$874$		0			0
$875$	6.47009	+	19.9129i	0.218729	+	0.673178i
$876$		0			0
$877$	24.6657	+	3.90666i	0.832901	+	0.131918i	0.558299	−	0.829640i	$-0.311454\pi$
$877$	24.6657	+	3.90666i	0.832901	+	0.131918i	0.274601	+	0.961558i	$0.411454\pi$
$878$		0			0
$879$	−17.5109	+	17.5109i	−0.590628	+	0.590628i
$880$		0			0
$881$		−	29.7110i		−	1.00099i	−0.865740	−	0.500494i	$-0.833152\pi$
$881$		−	29.7110i		−	1.00099i	0.865740	−	0.500494i	$-0.166848\pi$
$882$		0			0
$883$	0.584544	+	0.804556i	0.0196715	+	0.0270755i	0.818739	−	0.574165i	$-0.194673\pi$
$883$	0.584544	+	0.804556i	0.0196715	+	0.0270755i	−0.799068	+	0.601241i	$0.794673\pi$
$884$		0			0
$885$	−10.4409	−	32.1337i	−0.350966	−	1.08016i
$886$		0			0
$887$	27.6338	−	38.0347i	0.927854	−	1.27708i	−0.0328370	−	0.999461i	$-0.510454\pi$
$887$	27.6338	−	38.0347i	0.927854	−	1.27708i	0.960691	−	0.277621i	$-0.0895458\pi$
$888$		0			0
$889$	−16.3442	−	32.0773i	−0.548167	−	1.07584i
$890$		0			0
$891$	22.5198	+	24.4466i	0.754442	+	0.818991i
$892$		0			0
$893$	−0.217890	−	0.0707969i	−0.00729143	−	0.00236913i
$894$		0			0
$895$	3.71651	+	23.4651i	0.124229	+	0.784353i
$896$		0			0
$897$	2.60648	−	4.17654i	0.0870278	−	0.139451i
$898$		0			0
$899$	−4.04228	−	0.640234i	−0.134818	−	0.0213530i
$900$		0			0
$901$	−0.414735			−0.0138168
$902$		0			0
$903$	−4.05396	+	4.05396i	−0.134907	+	0.134907i
$904$		0			0
$905$	−27.5201	−	4.35875i	−0.914799	−	0.144890i
$906$		0			0
$907$	−28.2507	+	9.17920i	−0.938048	+	0.304790i	−0.737850	−	0.674965i	$-0.764159\pi$
$907$	−28.2507	+	9.17920i	−0.938048	+	0.304790i	−0.200199	+	0.979755i	$0.564159\pi$
$908$		0			0
$909$	−3.04912	−	2.21531i	−0.101133	−	0.0734773i
$910$		0			0
$911$	13.2646	−	40.8241i	0.439475	−	1.35256i	−0.448956	−	0.893554i	$-0.648204\pi$
$911$	13.2646	−	40.8241i	0.439475	−	1.35256i	0.888431	−	0.459010i	$-0.151796\pi$
$912$		0			0
$913$	33.2736	−	42.0574i	1.10120	−	1.39190i
$914$		0			0
$915$	23.7814	−	12.1172i	0.786188	−	0.400583i
$916$		0			0
$917$	4.68554	+	29.5834i	0.154730	+	0.976929i
$918$		0			0
$919$	46.3685	−	15.0660i	1.52956	−	0.496983i	0.581084	−	0.813844i	$-0.302629\pi$
$919$	46.3685	−	15.0660i	1.52956	−	0.496983i	0.948472	+	0.316861i	$0.102629\pi$
$920$		0			0
$921$	11.7924	−	74.4540i	0.388571	−	2.45334i
$922$		0			0
$923$	1.35846	−	15.6300i	0.0447143	−	0.514467i
$924$		0			0
$925$	6.68044	−	6.68044i	0.219652	−	0.219652i
$926$		0			0
$927$	10.0205	+	13.7921i	0.329118	+	0.452992i
$928$		0			0
$929$	−3.64996	−	1.85975i	−0.119751	−	0.0610164i	0.393089	−	0.919501i	$-0.371407\pi$
$929$	−3.64996	−	1.85975i	−0.119751	−	0.0610164i	−0.512840	+	0.858484i	$0.671407\pi$
$930$		0			0
$931$	−2.45007	+	0.388054i	−0.0802980	+	0.0127179i
$932$		0			0
$933$	59.1821	+	19.2294i	1.93754	+	0.629544i
$934$		0			0
$935$	0.134414	−	0.362410i	0.00439579	−	0.0118521i
$936$		0			0
$937$	−6.92069	−	2.24867i	−0.226089	−	0.0734608i	0.193782	−	0.981045i	$-0.437925\pi$
$937$	−6.92069	−	2.24867i	−0.226089	−	0.0734608i	−0.419871	+	0.907584i	$0.637925\pi$
$938$		0			0
$939$	−24.9464	−	18.1246i	−0.814095	−	0.591475i
$940$		0			0
$941$	3.11963	−	6.12262i	0.101697	−	0.199592i	−0.834552	−	0.550930i	$-0.814273\pi$
$941$	3.11963	−	6.12262i	0.101697	−	0.199592i	0.936249	+	0.351338i	$0.114273\pi$
$942$		0			0
$943$	−0.311928	+	1.96943i	−0.0101578	+	0.0641336i
$944$		0			0
$945$		−	2.27754i		−	0.0740883i
$946$		0			0
$947$	−12.7366	−	12.7366i	−0.413885	−	0.413885i	0.469205	−	0.883089i	$-0.344541\pi$
$947$	−12.7366	−	12.7366i	−0.413885	−	0.413885i	−0.883089	+	0.469205i	$0.844541\pi$
$948$		0			0
$949$	−12.9201	−	21.4748i	−0.419403	−	0.697103i
$950$		0			0
$951$	−16.9168	−	8.61954i	−0.548565	−	0.279508i
$952$		0			0
$953$	22.0988	+	16.0557i	0.715851	+	0.520096i	0.885056	−	0.465485i	$-0.154120\pi$
$953$	22.0988	+	16.0557i	0.715851	+	0.520096i	−0.169205	+	0.985581i	$0.554120\pi$
$954$		0			0
$955$	−0.480695	−	0.943417i	−0.0155549	−	0.0305283i
$956$		0			0
$957$	1.89450	−	9.43886i	0.0612405	−	0.305115i
$958$		0			0
$959$	4.20663	−	12.9467i	0.135839	−	0.418070i
$960$		0			0
$961$	11.6680	−	16.0596i	0.376387	−	0.518052i
$962$		0			0
$963$	21.1279	−	6.86487i	0.680837	−	0.221217i
$964$		0			0
$965$	6.29315	+	8.66177i	0.202584	+	0.278832i
$966$		0			0
$967$	−36.8401	−	36.8401i	−1.18470	−	1.18470i	−0.978513	−	0.206186i	$-0.933895\pi$
$967$	−36.8401	−	36.8401i	−1.18470	−	1.18470i	−0.206186	−	0.978513i	$-0.566105\pi$
$968$		0			0
$969$	0.137342	+	0.137342i	0.00441206	+	0.00441206i
$970$		0			0
$971$	−40.5748	+	29.4793i	−1.30211	+	0.946036i	−0.999974	−	0.00722910i	$-0.997699\pi$
$971$	−40.5748	+	29.4793i	−1.30211	+	0.946036i	−0.302134	+	0.953266i	$0.597699\pi$
$972$		0			0
$973$	−8.70972	+	17.0938i	−0.279221	+	0.548001i
$974$		0			0
$975$	2.11843	+	30.0487i	0.0678441	+	0.962327i
$976$		0			0
$977$	10.9396	+	21.4701i	0.349987	+	0.686889i	0.997149	−	0.0754643i	$-0.0240439\pi$
$977$	10.9396	+	21.4701i	0.349987	+	0.686889i	−0.647161	+	0.762353i	$0.724044\pi$
$978$		0			0
$979$	26.0954	+	39.2013i	0.834012	+	1.25288i
$980$		0			0
$981$	−1.09385	+	0.557344i	−0.0349239	+	0.0177946i
$982$		0			0
$983$	7.26317	+	45.8578i	0.231659	+	1.46264i	0.779683	+	0.626175i	$0.215380\pi$
$983$	7.26317	+	45.8578i	0.231659	+	1.46264i	−0.548024	+	0.836463i	$0.684620\pi$
$984$		0			0
$985$	−2.66153	−	8.19133i	−0.0848033	−	0.260998i
$986$		0			0
$987$	−1.04025	+	0.755787i	−0.0331116	+	0.0240570i
$988$		0			0
$989$		−	0.689790i		−	0.0219341i
$990$		0			0
$991$	−27.3366			−0.868374			−0.434187	−	0.900823i	$-0.642964\pi$
$991$	−27.3366			−0.868374			−0.434187	+	0.900823i	$0.642964\pi$
$992$		0			0
$993$	−8.02641	+	50.6768i	−0.254710	+	1.60818i
$994$		0			0
$995$	4.63285	−	9.09249i	0.146871	−	0.288251i
$996$		0			0
$997$	−12.7199	+	17.5075i	−0.402844	+	0.554467i	−0.961455	−	0.274963i	$-0.911334\pi$
$997$	−12.7199	+	17.5075i	−0.402844	+	0.554467i	0.558611	+	0.829430i	$0.311334\pi$
$998$		0			0
$999$	−2.21343	+	1.12780i	−0.0700298	+	0.0356819i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bh.a.57.12	✓	112
11.6	odd	10	inner	572.2.bh.a.369.12	yes	112
13.8	odd	4	inner	572.2.bh.a.541.12	yes	112
143.138	even	20	inner	572.2.bh.a.281.12	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bh.a.57.12	✓	112	1.1	even	1	trivial
572.2.bh.a.281.12	yes	112	143.138	even	20	inner
572.2.bh.a.369.12	yes	112	11.6	odd	10	inner
572.2.bh.a.541.12	yes	112	13.8	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.bh (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.91590 - 1.39198i) q^{3} +(-1.08106 - 0.550829i) q^{5} +(1.99865 - 0.316555i) q^{7} +(0.806006 - 2.48063i) q^{9} +O(q^{10})\)	\(q+(1.91590 - 1.39198i) q^{3} +(-1.08106 - 0.550829i) q^{5} +(1.99865 - 0.316555i) q^{7} +(0.806006 - 2.48063i) q^{9} +(3.25177 + 0.652673i) q^{11} +(-1.35257 - 3.34224i) q^{13} +(-2.83796 + 0.449488i) q^{15} +(0.0296827 + 0.0913538i) q^{17} +(0.843340 + 0.133572i) q^{19} +(3.38857 - 3.38857i) q^{21} +0.576573i q^{23} +(-2.07364 - 2.85412i) q^{25} +(0.286656 + 0.882237i) q^{27} +(0.720448 - 0.991612i) q^{29} +(-1.51590 - 2.97511i) q^{31} +(7.13858 - 3.27595i) q^{33} +(-2.33503 - 0.758698i) q^{35} +(0.418926 + 2.64500i) q^{37} +(-7.24373 - 4.52064i) q^{39} +(3.41576 + 0.541003i) q^{41} -1.19636 q^{43} +(-2.23775 + 2.23775i) q^{45} +(-0.265014 - 0.0419741i) q^{47} +(-2.76301 + 0.897758i) q^{49} +(0.184032 + 0.133707i) q^{51} +(-1.33424 + 4.10636i) q^{53} +(-3.15586 - 2.49675i) q^{55} +(1.80168 - 0.918004i) q^{57} +(1.83951 + 11.6142i) q^{59} +(-8.83440 + 2.87047i) q^{61} +(0.825666 - 5.21305i) q^{63} +(-0.378789 + 4.35821i) q^{65} +(-3.79267 + 3.79267i) q^{67} +(0.802580 + 1.10466i) q^{69} +(3.87705 + 1.97546i) q^{71} +(6.86533 - 1.08736i) q^{73} +(-7.94578 - 2.58174i) q^{75} +(6.70575 + 0.275099i) q^{77} +(-4.77870 - 1.55269i) q^{79} +(8.10772 + 5.89060i) q^{81} +(7.34078 - 14.4071i) q^{83} +(0.0182315 - 0.115109i) q^{85} -2.90268i q^{87} +(10.0402 + 10.0402i) q^{89} +(-3.76131 - 6.25179i) q^{91} +(-7.04561 - 3.58992i) q^{93} +(-0.838128 - 0.608936i) q^{95} +(4.55540 + 8.94047i) q^{97} +(4.23999 - 7.54039i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 28 q^{9}+O(q^{10}) \) 112 * q - 28 * q^9	\( 112 q - 28 q^{9} + 8 q^{11} - 10 q^{13} + 4 q^{15} - 24 q^{27} - 20 q^{29} - 16 q^{31} - 54 q^{33} + 100 q^{35} - 12 q^{37} + 40 q^{39} - 20 q^{41} - 4 q^{45} - 10 q^{47} - 76 q^{53} - 20 q^{55} + 18 q^{59} + 40 q^{61} + 80 q^{63} + 92 q^{67} + 8 q^{71} - 30 q^{73} - 80 q^{79} + 12 q^{81} + 40 q^{85} + 32 q^{89} - 12 q^{91} - 114 q^{93} + 54 q^{97} - 90 q^{99}+O(q^{100}) \) 112 * q - 28 * q^9 + 8 * q^11 - 10 * q^13 + 4 * q^15 - 24 * q^27 - 20 * q^29 - 16 * q^31 - 54 * q^33 + 100 * q^35 - 12 * q^37 + 40 * q^39 - 20 * q^41 - 4 * q^45 - 10 * q^47 - 76 * q^53 - 20 * q^55 + 18 * q^59 + 40 * q^61 + 80 * q^63 + 92 * q^67 + 8 * q^71 - 30 * q^73 - 80 * q^79 + 12 * q^81 + 40 * q^85 + 32 * q^89 - 12 * q^91 - 114 * q^93 + 54 * q^97 - 90 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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