LMFDB - Embedded newform 572.2.bc.a.241.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(197,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 1]))

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

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

chi := DirichletCharacter("572.197");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bc (of order $12$, degree $4$, 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:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			241.4
Character	$\chi$	$=$	572.241
Dual form			572.2.bc.a.197.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.02435 + 1.77422i) q^{3} +(-1.58636 - 1.58636i) q^{5} +(0.799284 - 2.98297i) q^{7} +(-0.598575 - 1.03676i) q^{9} +O(q^{10})$	\(q+(-1.02435 + 1.77422i) q^{3} +(-1.58636 - 1.58636i) q^{5} +(0.799284 - 2.98297i) q^{7} +(-0.598575 - 1.03676i) q^{9} +(1.70209 + 2.84656i) q^{11} +(-1.18584 + 3.40496i) q^{13} +(4.43955 - 1.18957i) q^{15} +(1.93590 + 3.35307i) q^{17} +(6.50958 + 1.74424i) q^{19} +(4.47370 + 4.47370i) q^{21} +(-1.73090 - 0.999337i) q^{23} +0.0330985i q^{25} -3.69349 q^{27} +(2.33549 + 1.34839i) q^{29} +(-1.14818 - 1.14818i) q^{31} +(-6.79396 + 0.104020i) q^{33} +(-6.00003 + 3.46412i) q^{35} +(2.99876 + 11.1915i) q^{37} +(-4.82645 - 5.59181i) q^{39} +(2.90482 + 10.8409i) q^{41} +(1.86515 + 3.23054i) q^{43} +(-0.695124 + 2.59424i) q^{45} +(1.75021 - 1.75021i) q^{47} +(-2.19707 - 1.26848i) q^{49} -7.93212 q^{51} -3.56986 q^{53} +(1.81554 - 7.21581i) q^{55} +(-9.76274 + 9.76274i) q^{57} +(-7.03470 - 1.88494i) q^{59} +(10.4661 - 6.04262i) q^{61} +(-3.57106 + 0.956863i) q^{63} +(7.28268 - 3.52034i) q^{65} +(7.89800 - 2.11626i) q^{67} +(3.54609 - 2.04734i) q^{69} +(-0.464798 + 1.73465i) q^{71} +(-8.57365 - 8.57365i) q^{73} +(-0.0587241 - 0.0339044i) q^{75} +(9.85165 - 2.80207i) q^{77} -9.94056i q^{79} +(5.57914 - 9.66336i) q^{81} +(3.21672 - 3.21672i) q^{83} +(2.24815 - 8.39022i) q^{85} +(-4.78470 + 2.76245i) q^{87} +(3.64193 + 13.5919i) q^{89} +(9.20908 + 6.25886i) q^{91} +(3.21325 - 0.860988i) q^{93} +(-7.55957 - 13.0936i) q^{95} +(-2.31410 + 8.63632i) q^{97} +(1.93238 - 3.46854i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 28 q^{9}+O(q^{10}) $ 56 * q - 28 * q^9	$ 56 q - 28 q^{9} + 4 q^{11} + 8 q^{15} - 12 q^{23} - 24 q^{27} - 4 q^{31} - 10 q^{33} - 12 q^{37} - 64 q^{45} - 8 q^{47} + 40 q^{53} + 22 q^{55} + 48 q^{59} - 36 q^{67} - 48 q^{71} + 120 q^{75} + 28 q^{81} + 28 q^{89} + 36 q^{91} + 20 q^{93} - 68 q^{97} - 44 q^{99}+O(q^{100}) $ 56 * q - 28 * q^9 + 4 * q^11 + 8 * q^15 - 12 * q^23 - 24 * q^27 - 4 * q^31 - 10 * q^33 - 12 * q^37 - 64 * q^45 - 8 * q^47 + 40 * q^53 + 22 * q^55 + 48 * q^59 - 36 * q^67 - 48 * q^71 + 120 * q^75 + 28 * q^81 + 28 * q^89 + 36 * q^91 + 20 * q^93 - 68 * q^97 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{11}{12}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.02435	+	1.77422i	−0.591407	+	1.02435i	0.402636	+	0.915360i	$0.368094\pi$
$3$	−1.02435	+	1.77422i	−0.591407	+	1.02435i	−0.994043	+	0.108987i	$0.965239\pi$
$4$		0			0
$5$	−1.58636	−	1.58636i	−0.709443	−	0.709443i	0.256975	−	0.966418i	$-0.417274\pi$
$5$	−1.58636	−	1.58636i	−0.709443	−	0.709443i	−0.966418	+	0.256975i	$0.917274\pi$
$6$		0			0
$7$	0.799284	−	2.98297i	0.302101	−	1.12746i	−0.633311	−	0.773897i	$-0.718305\pi$
$7$	0.799284	−	2.98297i	0.302101	−	1.12746i	0.935412	−	0.353559i	$-0.115029\pi$
$8$		0			0
$9$	−0.598575	−	1.03676i	−0.199525	−	0.345587i
$10$		0			0
$11$	1.70209	+	2.84656i	0.513199	+	0.858269i
$11$	1.70209	+	2.84656i	0.513199	+	0.858269i
$12$		0			0
$13$	−1.18584	+	3.40496i	−0.328893	+	0.944367i
$13$	−1.18584	+	3.40496i	−0.328893	+	0.944367i
$14$		0			0
$15$	4.43955	−	1.18957i	1.14629	−	0.307146i
$16$		0			0
$17$	1.93590	+	3.35307i	0.469524	+	0.813239i	0.999393	−	0.0348403i	$-0.0110923\pi$
$17$	1.93590	+	3.35307i	0.469524	+	0.813239i	−0.529869	+	0.848079i	$0.677759\pi$
$18$		0			0
$19$	6.50958	+	1.74424i	1.49340	+	0.400155i	0.910884	−	0.412663i	$-0.135401\pi$
$19$	6.50958	+	1.74424i	1.49340	+	0.400155i	0.582517	+	0.812819i	$0.302068\pi$
$20$		0			0
$21$	4.47370	+	4.47370i	0.976242	+	0.976242i
$22$		0			0
$23$	−1.73090	−	0.999337i	−0.360918	−	0.208376i	0.308565	−	0.951203i	$-0.400151\pi$
$23$	−1.73090	−	0.999337i	−0.360918	−	0.208376i	−0.669483	+	0.742827i	$0.733484\pi$
$24$		0			0
$25$			0.0330985i			0.00661971i
$26$		0			0
$27$	−3.69349			−0.710812
$28$		0			0
$29$	2.33549	+	1.34839i	0.433689	+	0.250391i	0.700917	−	0.713243i	$-0.252774\pi$
$29$	2.33549	+	1.34839i	0.433689	+	0.250391i	−0.267228	+	0.963633i	$0.586108\pi$
$30$		0			0
$31$	−1.14818	−	1.14818i	−0.206219	−	0.206219i	0.596439	−	0.802658i	$-0.296582\pi$
$31$	−1.14818	−	1.14818i	−0.206219	−	0.206219i	−0.802658	+	0.596439i	$0.796582\pi$
$32$		0			0
$33$	−6.79396	+	0.104020i	−1.18268	+	0.0181075i
$34$		0			0
$35$	−6.00003	+	3.46412i	−1.01419	+	0.585543i
$36$		0			0
$37$	2.99876	+	11.1915i	0.492993	+	1.83987i	0.540994	+	0.841026i	$0.318048\pi$
$37$	2.99876	+	11.1915i	0.492993	+	1.83987i	−0.0480014	+	0.998847i	$0.515285\pi$
$38$		0			0
$39$	−4.82645	−	5.59181i	−0.772851	−	0.895406i
$40$		0			0
$41$	2.90482	+	10.8409i	0.453657	+	1.69307i	0.692006	+	0.721892i	$0.256727\pi$
$41$	2.90482	+	10.8409i	0.453657	+	1.69307i	−0.238349	+	0.971180i	$0.576606\pi$
$42$		0			0
$43$	1.86515	+	3.23054i	0.284433	+	0.492653i	0.972472	−	0.233021i	$-0.0748612\pi$
$43$	1.86515	+	3.23054i	0.284433	+	0.492653i	−0.688038	+	0.725674i	$0.741528\pi$
$44$		0			0
$45$	−0.695124	+	2.59424i	−0.103623	+	0.386726i
$46$		0			0
$47$	1.75021	−	1.75021i	0.255295	−	0.255295i	−0.567842	−	0.823137i	$-0.692222\pi$
$47$	1.75021	−	1.75021i	0.255295	−	0.255295i	0.823137	+	0.567842i	$0.192222\pi$
$48$		0			0
$49$	−2.19707	−	1.26848i	−0.313867	−	0.181211i
$50$		0			0
$51$	−7.93212			−1.11072
$52$		0			0
$53$	−3.56986			−0.490359			−0.245179	−	0.969478i	$-0.578847\pi$
$53$	−3.56986			−0.490359			−0.245179	+	0.969478i	$0.578847\pi$
$54$		0			0
$55$	1.81554	−	7.21581i	0.244808	−	0.972979i
$56$		0			0
$57$	−9.76274	+	9.76274i	−1.29311	+	1.29311i
$58$		0			0
$59$	−7.03470	−	1.88494i	−0.915840	−	0.245398i	−0.230033	−	0.973183i	$-0.573884\pi$
$59$	−7.03470	−	1.88494i	−0.915840	−	0.245398i	−0.685806	+	0.727784i	$0.740550\pi$
$60$		0			0
$61$	10.4661	−	6.04262i	1.34005	−	0.773678i	0.353235	−	0.935535i	$-0.385082\pi$
$61$	10.4661	−	6.04262i	1.34005	−	0.773678i	0.986814	+	0.161857i	$0.0517482\pi$
$62$		0			0
$63$	−3.57106	+	0.956863i	−0.449911	+	0.120553i
$64$		0			0
$65$	7.28268	−	3.52034i	0.903306	−	0.436644i
$66$		0			0
$67$	7.89800	−	2.11626i	0.964894	−	0.258543i	0.258223	−	0.966085i	$-0.416863\pi$
$67$	7.89800	−	2.11626i	0.964894	−	0.258543i	0.706671	+	0.707543i	$0.250196\pi$
$68$		0			0
$69$	3.54609	−	2.04734i	0.426899	−	0.246470i
$70$		0			0
$71$	−0.464798	+	1.73465i	−0.0551614	+	0.205865i	−0.988006	−	0.154413i	$-0.950651\pi$
$71$	−0.464798	+	1.73465i	−0.0551614	+	0.205865i	0.932845	+	0.360278i	$0.117318\pi$
$72$		0			0
$73$	−8.57365	−	8.57365i	−1.00347	−	1.00347i	−0.999994	−	0.00347616i	$-0.998894\pi$
$73$	−8.57365	−	8.57365i	−1.00347	−	1.00347i	−0.00347616	−	0.999994i	$-0.501106\pi$
$74$		0			0
$75$	−0.0587241	−	0.0339044i	−0.00678088	−	0.00391494i
$76$		0			0
$77$	9.85165	−	2.80207i	1.12270	−	0.319326i
$78$		0			0
$79$		−	9.94056i		−	1.11840i	−0.829033	−	0.559200i	$-0.811108\pi$
$79$		−	9.94056i		−	1.11840i	0.829033	−	0.559200i	$-0.188892\pi$
$80$		0			0
$81$	5.57914	−	9.66336i	0.619905	−	1.07371i
$82$		0			0
$83$	3.21672	−	3.21672i	0.353080	−	0.353080i	−0.508174	−	0.861254i	$-0.669679\pi$
$83$	3.21672	−	3.21672i	0.353080	−	0.353080i	0.861254	+	0.508174i	$0.169679\pi$
$84$		0			0
$85$	2.24815	−	8.39022i	0.243847	−	0.910048i
$86$		0			0
$87$	−4.78470	+	2.76245i	−0.512974	+	0.296166i
$88$		0			0
$89$	3.64193	+	13.5919i	0.386044	+	1.44073i	0.836515	+	0.547943i	$0.184589\pi$
$89$	3.64193	+	13.5919i	0.386044	+	1.44073i	−0.450472	+	0.892791i	$0.648744\pi$
$90$		0			0
$91$	9.20908	+	6.25886i	0.965374	+	0.656107i
$92$		0			0
$93$	3.21325	−	0.860988i	0.333199	−	0.0892803i
$94$		0			0
$95$	−7.55957	−	13.0936i	−0.775595	−	1.34337i
$96$		0			0
$97$	−2.31410	+	8.63632i	−0.234961	+	0.876886i	0.743206	+	0.669063i	$0.233304\pi$
$97$	−2.31410	+	8.63632i	−0.234961	+	0.876886i	−0.978166	+	0.207823i	$0.933362\pi$
$98$		0			0
$99$	1.93238	−	3.46854i	0.194211	−	0.348601i
$100$		0			0
$101$	−6.09392	+	10.5550i	−0.606367	+	1.05026i	0.385466	+	0.922722i	$0.374041\pi$
$101$	−6.09392	+	10.5550i	−0.606367	+	1.05026i	−0.991834	+	0.127537i	$0.959293\pi$
$102$		0			0
$103$		−	4.35617i		−	0.429226i	−0.976699	−	0.214613i	$-0.931151\pi$
$103$		−	4.35617i		−	0.429226i	0.976699	−	0.214613i	$-0.0688490\pi$
$104$		0			0
$105$		−	14.1938i		−	1.38518i
$106$		0			0
$107$	6.48225	+	3.74253i	0.626663	+	0.361804i	0.779459	−	0.626454i	$-0.215494\pi$
$107$	6.48225	+	3.74253i	0.626663	+	0.361804i	−0.152795	+	0.988258i	$0.548828\pi$
$108$		0			0
$109$	12.6751	−	12.6751i	1.21405	−	1.21405i	0.244372	−	0.969682i	$-0.421418\pi$
$109$	12.6751	−	12.6751i	1.21405	−	1.21405i	0.969682	−	0.244372i	$-0.0785817\pi$
$110$		0			0
$111$	−22.9280	−	6.14354i	−2.17623	−	0.583119i
$112$		0			0
$113$	−4.01472	−	6.95370i	−0.377673	−	0.654149i	0.613050	−	0.790044i	$-0.289942\pi$
$113$	−4.01472	−	6.95370i	−0.377673	−	0.654149i	−0.990723	+	0.135895i	$0.956609\pi$
$114$		0			0
$115$	1.16053	+	4.33115i	0.108220	+	0.403882i
$116$		0			0
$117$	4.23995	−	0.808692i	0.391984	−	0.0747636i
$118$		0			0
$119$	11.5494	−	3.09466i	1.05874	−	0.283687i
$120$		0			0
$121$	−5.20578	+	9.69019i	−0.473253	+	0.880927i
$122$		0			0
$123$	−22.2098	−	5.95109i	−2.00259	−	0.536592i
$124$		0			0
$125$	−7.87931	+	7.87931i	−0.704747	+	0.704747i
$126$		0			0
$127$	8.18180	−	14.1713i	0.726017	−	1.25750i	−0.232537	−	0.972588i	$-0.574703\pi$
$127$	8.18180	−	14.1713i	0.726017	−	1.25750i	0.958554	−	0.284911i	$-0.0919639\pi$
$128$		0			0
$129$	−7.64226			−0.672864
$130$		0			0
$131$			1.67923i			0.146715i	0.997306	+	0.0733577i	$0.0233715\pi$
$131$			1.67923i			0.146715i	−0.997306	+	0.0733577i	$0.976629\pi$
$132$		0			0
$133$	10.4060	−	18.0237i	0.902316	−	1.56286i
$134$		0			0
$135$	5.85922	+	5.85922i	0.504281	+	0.504281i
$136$		0			0
$137$	11.9134	+	3.19217i	1.01783	+	0.272726i	0.728896	−	0.684624i	$-0.240034\pi$
$137$	11.9134	+	3.19217i	1.01783	+	0.272726i	0.288931	+	0.957350i	$0.406700\pi$
$138$		0			0
$139$	−3.54119	+	2.04450i	−0.300359	+	0.173413i	−0.642604	−	0.766198i	$-0.722146\pi$
$139$	−3.54119	+	2.04450i	−0.300359	+	0.173413i	0.342245	+	0.939611i	$0.388813\pi$
$140$		0			0
$141$	1.31244	+	4.89809i	0.110527	+	0.412494i
$142$		0			0
$143$	−11.7108	+	2.41999i	−0.979309	+	0.202370i
$144$		0			0
$145$	−1.56589	−	5.84398i	−0.130040	−	0.485316i
$146$		0			0
$147$	4.50113	−	2.59873i	0.371247	−	0.214339i
$148$		0			0
$149$	4.21005	+	1.12808i	0.344901	+	0.0924159i	0.427111	−	0.904199i	$-0.359531\pi$
$149$	4.21005	+	1.12808i	0.344901	+	0.0924159i	−0.0822104	+	0.996615i	$0.526198\pi$
$150$		0			0
$151$	1.84146	+	1.84146i	0.149856	+	0.149856i	0.778054	−	0.628198i	$-0.216207\pi$
$151$	1.84146	+	1.84146i	0.149856	+	0.149856i	−0.628198	+	0.778054i	$0.716207\pi$
$152$		0			0
$153$	2.31756	−	4.01413i	0.187363	−	0.324523i
$154$		0			0
$155$			3.64285i			0.292601i
$156$		0			0
$157$	−10.2014			−0.814162			−0.407081	−	0.913392i	$-0.633453\pi$
$157$	−10.2014			−0.814162			−0.407081	+	0.913392i	$0.633453\pi$
$158$		0			0
$159$	3.65678	−	6.33373i	0.290002	−	0.502297i
$160$		0			0
$161$	−4.36447	+	4.36447i	−0.343969	+	0.343969i
$162$		0			0
$163$	−3.01716	−	0.808447i	−0.236323	−	0.0633224i	0.138714	−	0.990332i	$-0.455703\pi$
$163$	−3.01716	−	0.808447i	−0.236323	−	0.0633224i	−0.375036	+	0.927010i	$0.622370\pi$
$164$		0			0
$165$	10.9427	+	10.6127i	0.851888	+	0.826195i
$166$		0			0
$167$	−19.3312	+	5.17979i	−1.49590	+	0.400824i	−0.911723	−	0.410806i	$-0.865247\pi$
$167$	−19.3312	+	5.17979i	−1.49590	+	0.400824i	−0.584172	+	0.811630i	$0.698581\pi$
$168$		0			0
$169$	−10.1876	−	8.07549i	−0.783659	−	0.621191i
$170$		0			0
$171$	−2.08811	−	7.79294i	−0.159682	−	0.595941i
$172$		0			0
$173$	−3.06802	−	5.31396i	−0.233257	−	0.404013i	0.725508	−	0.688214i	$-0.241605\pi$
$173$	−3.06802	−	5.31396i	−0.233257	−	0.404013i	−0.958765	+	0.284201i	$0.908272\pi$
$174$		0			0
$175$	0.0987319	+	0.0264551i	0.00746343	+	0.00199982i
$176$		0			0
$177$	10.5503	−	10.5503i	0.793007	−	0.793007i
$178$		0			0
$179$	−20.1632	−	11.6412i	−1.50707	−	0.870106i	−0.999966	−	0.00821967i	$-0.997384\pi$
$179$	−20.1632	−	11.6412i	−1.50707	−	0.870106i	−0.507102	−	0.861886i	$-0.669283\pi$
$180$		0			0
$181$		−	4.51284i		−	0.335436i	−0.985835	−	0.167718i	$-0.946360\pi$
$181$		−	4.51284i		−	0.335436i	0.985835	−	0.167718i	$-0.0536399\pi$
$182$		0			0
$183$			24.7590i			1.83023i
$184$		0			0
$185$	12.9967	−	22.5109i	0.955536	−	1.65504i
$186$		0			0
$187$	−6.24964	+	11.2179i	−0.457019	+	0.820332i
$188$		0			0
$189$	−2.95215	+	11.0176i	−0.214737	+	0.801410i
$190$		0			0
$191$	2.07977	+	3.60227i	0.150487	+	0.260651i	0.931407	−	0.363980i	$-0.118583\pi$
$191$	2.07977	+	3.60227i	0.150487	+	0.260651i	−0.780920	+	0.624632i	$0.785249\pi$
$192$		0			0
$193$	−18.8748	+	5.05749i	−1.35864	+	0.364046i	−0.863316	−	0.504663i	$-0.831617\pi$
$193$	−18.8748	+	5.05749i	−1.35864	+	0.364046i	−0.495322	+	0.868709i	$0.664950\pi$
$194$		0			0
$195$	−1.21414	+	16.5271i	−0.0869462	+	1.18353i
$196$		0			0
$197$	−2.42150	−	9.03715i	−0.172524	−	0.643870i	−0.996960	−	0.0779143i	$-0.975174\pi$
$197$	−2.42150	−	9.03715i	−0.172524	−	0.643870i	0.824436	−	0.565956i	$-0.191493\pi$
$198$		0			0
$199$	−15.6223	+	9.01952i	−1.10743	+	0.639377i	−0.938163	−	0.346193i	$-0.887474\pi$
$199$	−15.6223	+	9.01952i	−1.10743	+	0.639377i	−0.169270	+	0.985570i	$0.554141\pi$
$200$		0			0
$201$	−4.33558	+	16.1806i	−0.305808	+	1.14129i
$202$		0			0
$203$	5.88894	−	5.88894i	0.413322	−	0.413322i
$204$		0			0
$205$	12.5896	−	21.8058i	0.879294	−	1.52298i
$206$		0			0
$207$			2.39271i			0.166305i
$208$		0			0
$209$	6.11482	+	21.4987i	0.422971	+	1.48710i
$210$		0			0
$211$	8.90378	+	5.14060i	0.612962	+	0.353894i	0.774124	−	0.633034i	$-0.218191\pi$
$211$	8.90378	+	5.14060i	0.612962	+	0.353894i	−0.161162	+	0.986928i	$0.551524\pi$
$212$		0			0
$213$	−2.60154	−	2.60154i	−0.178255	−	0.178255i
$214$		0			0
$215$	2.16600	−	8.08363i	0.147720	−	0.551299i
$216$		0			0
$217$	−4.34269	+	2.50726i	−0.294801	+	0.170204i
$218$		0			0
$219$	23.9940	−	6.42916i	1.62136	−	0.434442i
$220$		0			0
$221$	−13.7128	+	2.61545i	−0.922419	+	0.175934i
$222$		0			0
$223$	15.5695	−	4.17184i	1.04261	−	0.279367i	0.303416	−	0.952858i	$-0.401873\pi$
$223$	15.5695	−	4.17184i	1.04261	−	0.279367i	0.739195	+	0.673491i	$0.235206\pi$
$224$		0			0
$225$	0.0343153	−	0.0198119i	0.00228769	−	0.00132080i
$226$		0			0
$227$	4.22539	+	1.13219i	0.280449	+	0.0751461i	0.396302	−	0.918120i	$-0.370293\pi$
$227$	4.22539	+	1.13219i	0.280449	+	0.0751461i	−0.115853	+	0.993266i	$0.536960\pi$
$228$		0			0
$229$	−4.43616	+	4.43616i	−0.293150	+	0.293150i	−0.838323	−	0.545174i	$-0.816464\pi$
$229$	−4.43616	+	4.43616i	−0.293150	+	0.293150i	0.545174	+	0.838323i	$0.316464\pi$
$230$		0			0
$231$	−5.12001	+	20.3493i	−0.336872	+	1.33889i
$232$		0			0
$233$	−14.1297			−0.925667			−0.462833	−	0.886445i	$-0.653167\pi$
$233$	−14.1297			−0.925667			−0.462833	+	0.886445i	$0.653167\pi$
$234$		0			0
$235$	−5.55295			−0.362234
$236$		0			0
$237$	17.6368	+	10.1826i	1.14563	+	0.661430i
$238$		0			0
$239$	14.5038	−	14.5038i	0.938170	−	0.938170i	−0.0600266	−	0.998197i	$-0.519119\pi$
$239$	14.5038	−	14.5038i	0.938170	−	0.938170i	0.998197	+	0.0600266i	$0.0191185\pi$
$240$		0			0
$241$	6.23243	−	23.2597i	0.401466	−	1.49829i	−0.409016	−	0.912527i	$-0.634128\pi$
$241$	6.23243	−	23.2597i	0.401466	−	1.49829i	0.810482	−	0.585764i	$-0.199205\pi$
$242$		0			0
$243$	5.88972	+	10.2013i	0.377826	+	0.654413i
$244$		0			0
$245$	1.47308	+	5.49762i	0.0941118	+	0.351230i
$246$		0			0
$247$	−13.6584	+	20.0965i	−0.869062	+	1.27871i
$248$		0			0
$249$	2.41213	+	9.00220i	0.152863	+	0.570491i
$250$		0			0
$251$	−0.100928	+	0.0582708i	−0.00637052	+	0.00367802i	−0.503182	−	0.864181i	$-0.667837\pi$
$251$	−0.100928	+	0.0582708i	−0.00637052	+	0.00367802i	0.496811	+	0.867859i	$0.334504\pi$
$252$		0			0
$253$	−0.101480	−	6.62807i	−0.00638000	−	0.416703i
$254$		0			0
$255$	12.5832	+	12.5832i	0.787992	+	0.787992i
$256$		0			0
$257$	−6.19880	−	3.57888i	−0.386670	−	0.223244i	0.294046	−	0.955791i	$-0.404998\pi$
$257$	−6.19880	−	3.57888i	−0.386670	−	0.223244i	−0.680716	+	0.732547i	$0.738331\pi$
$258$		0			0
$259$	35.7808			2.22331
$260$		0			0
$261$		−	3.22846i		−	0.199837i
$262$		0			0
$263$	−17.7638	−	10.2559i	−1.09536	−	0.632407i	−0.160362	−	0.987058i	$-0.551266\pi$
$263$	−17.7638	−	10.2559i	−1.09536	−	0.632407i	−0.934999	+	0.354652i	$0.884600\pi$
$264$		0			0
$265$	5.66310	+	5.66310i	0.347882	+	0.347882i
$266$		0			0
$267$	−27.8456	−	7.46120i	−1.70412	−	0.456618i
$268$		0			0
$269$	11.6870	+	20.2425i	0.712569	+	1.23421i	0.963890	+	0.266302i	$0.0858019\pi$
$269$	11.6870	+	20.2425i	0.712569	+	1.23421i	−0.251320	+	0.967904i	$0.580865\pi$
$270$		0			0
$271$	19.8951	−	5.33087i	1.20854	−	0.323828i	0.402352	−	0.915485i	$-0.368193\pi$
$271$	19.8951	−	5.33087i	1.20854	−	0.323828i	0.806189	+	0.591658i	$0.201526\pi$
$272$		0			0
$273$	−20.5379	+	9.92771i	−1.24301	+	0.600852i
$274$		0			0
$275$	−0.0942169	+	0.0563367i	−0.00568149	+	0.00339723i
$276$		0			0
$277$	5.68007	+	9.83818i	0.341283	+	0.591119i	0.984671	−	0.174421i	$-0.0558053\pi$
$277$	5.68007	+	9.83818i	0.341283	+	0.591119i	−0.643389	+	0.765540i	$0.722472\pi$
$278$		0			0
$279$	−0.503116	+	1.87765i	−0.0301208	+	0.112412i
$280$		0			0
$281$	14.5489	+	14.5489i	0.867917	+	0.867917i	0.992242	−	0.124325i	$-0.0396765\pi$
$281$	14.5489	+	14.5489i	0.867917	+	0.867917i	−0.124325	+	0.992242i	$0.539677\pi$
$282$		0			0
$283$	−6.41051	+	11.1033i	−0.381065	+	0.660024i	−0.991215	−	0.132262i	$-0.957776\pi$
$283$	−6.41051	+	11.1033i	−0.381065	+	0.660024i	0.610150	+	0.792286i	$0.291109\pi$
$284$		0			0
$285$	30.9745			1.83477
$286$		0			0
$287$	34.6600			2.04591
$288$		0			0
$289$	1.00461	−	1.74004i	0.0590947	−	0.102355i
$290$		0			0
$291$	−12.9523	−	12.9523i	−0.759278	−	0.759278i
$292$		0			0
$293$	−4.92240	+	18.3706i	−0.287570	+	1.07322i	0.659372	+	0.751817i	$0.270822\pi$
$293$	−4.92240	+	18.3706i	−0.287570	+	1.07322i	−0.946941	+	0.321407i	$0.895844\pi$
$294$		0			0
$295$	8.16938	+	14.1498i	0.475640	+	0.823833i
$296$		0			0
$297$	−6.28665	−	10.5137i	−0.364788	−	0.610069i
$298$		0			0
$299$	5.45528	−	4.70861i	0.315487	−	0.272306i
$300$		0			0
$301$	11.1274	−	2.98158i	0.641372	−	0.171855i
$302$		0			0
$303$	−12.4846	−	21.6239i	−0.717220	−	1.24226i
$304$		0			0
$305$	−26.1889	−	7.01728i	−1.49957	−	0.401809i
$306$		0			0
$307$	−8.58118	−	8.58118i	−0.489754	−	0.489754i	0.418475	−	0.908228i	$-0.362565\pi$
$307$	−8.58118	−	8.58118i	−0.489754	−	0.489754i	−0.908228	+	0.418475i	$0.862565\pi$
$308$		0			0
$309$	7.72881	+	4.46223i	0.439677	+	0.253847i
$310$		0			0
$311$		−	31.3790i		−	1.77934i	−0.456602	−	0.889671i	$-0.650934\pi$
$311$		−	31.3790i		−	1.77934i	0.456602	−	0.889671i	$-0.349066\pi$
$312$		0			0
$313$	3.77902			0.213603			0.106801	−	0.994280i	$-0.465939\pi$
$313$	3.77902			0.213603			0.106801	+	0.994280i	$0.465939\pi$
$314$		0			0
$315$	7.18293	+	4.14707i	0.404712	+	0.233661i
$316$		0			0
$317$	−16.9565	−	16.9565i	−0.952371	−	0.952371i	0.0465452	−	0.998916i	$-0.485179\pi$
$317$	−16.9565	−	16.9565i	−0.952371	−	0.952371i	−0.998916	+	0.0465452i	$0.985179\pi$
$318$		0			0
$319$	0.136926	+	8.94319i	0.00766638	+	0.500722i
$320$		0			0
$321$	−13.2802	+	7.66730i	−0.741226	+	0.427947i
$322$		0			0
$323$	6.75332	+	25.2038i	0.375765	+	1.40237i
$324$		0			0
$325$	−0.112699	−	0.0392496i	−0.00625143	−	0.00217717i
$326$		0			0
$327$	9.50472	+	35.4721i	0.525612	+	1.96161i
$328$		0			0
$329$	−3.82191	−	6.61975i	−0.210709	−	0.364959i
$330$		0			0
$331$	2.33238	−	8.70457i	0.128199	−	0.478446i	−0.871734	−	0.489979i	$-0.837004\pi$
$331$	2.33238	−	8.70457i	0.128199	−	0.478446i	0.999933	+	0.0115327i	$0.00367105\pi$
$332$		0			0
$333$	9.80796	−	9.80796i	0.537473	−	0.537473i
$334$		0			0
$335$	−15.8863	−	9.17194i	−0.867959	−	0.501116i
$336$		0			0
$337$	−2.21046			−0.120412			−0.0602058	−	0.998186i	$-0.519176\pi$
$337$	−2.21046			−0.120412			−0.0602058	+	0.998186i	$0.519176\pi$
$338$		0			0
$339$	16.4499			0.893435
$340$		0			0
$341$	1.31405	−	5.22265i	0.0711599	−	0.282822i
$342$		0			0
$343$	9.74588	−	9.74588i	0.526228	−	0.526228i
$344$		0			0
$345$	−8.87321	−	2.37757i	−0.477717	−	0.128004i
$346$		0			0
$347$	22.1547	−	12.7910i	1.18933	−	0.686658i	0.231172	−	0.972913i	$-0.425744\pi$
$347$	22.1547	−	12.7910i	1.18933	−	0.686658i	0.958153	+	0.286255i	$0.0924105\pi$
$348$		0			0
$349$	−24.8958	+	6.67080i	−1.33264	+	0.357080i	−0.853699	−	0.520767i	$-0.825646\pi$
$349$	−24.8958	+	6.67080i	−1.33264	+	0.357080i	−0.478941	+	0.877847i	$0.658979\pi$
$350$		0			0
$351$	4.37989	−	12.5762i	0.233781	−	0.671268i
$352$		0			0
$353$	−25.5788	+	6.85382i	−1.36142	+	0.364792i	−0.864338	−	0.502911i	$-0.832262\pi$
$353$	−25.5788	+	6.85382i	−1.36142	+	0.364792i	−0.497083	+	0.867703i	$0.665596\pi$
$354$		0			0
$355$	3.48912	−	2.01445i	0.185184	−	0.106916i
$356$		0			0
$357$	−6.34002	+	23.6613i	−0.335549	+	1.25229i
$358$		0			0
$359$	2.23250	+	2.23250i	0.117827	+	0.117827i	0.763562	−	0.645735i	$-0.223449\pi$
$359$	2.23250	+	2.23250i	0.117827	+	0.117827i	−0.645735	+	0.763562i	$0.723449\pi$
$360$		0			0
$361$	22.8778	+	13.2085i	1.20410	+	0.695185i
$362$		0			0
$363$	−11.8600	−	19.1623i	−0.622489	−	1.00576i
$364$		0			0
$365$			27.2019i			1.42381i
$366$		0			0
$367$	1.70821	−	2.95870i	0.0891677	−	0.154443i	−0.817992	−	0.575230i	$-0.804913\pi$
$367$	1.70821	−	2.95870i	0.0891677	−	0.154443i	0.907160	+	0.420787i	$0.138246\pi$
$368$		0			0
$369$	9.50073	−	9.50073i	0.494588	−	0.494588i
$370$		0			0
$371$	−2.85334	+	10.6488i	−0.148138	+	0.552858i
$372$		0			0
$373$	−9.58773	+	5.53548i	−0.496434	+	0.286616i	−0.727240	−	0.686384i	$-0.759197\pi$
$373$	−9.58773	+	5.53548i	−0.496434	+	0.286616i	0.230806	+	0.973000i	$0.425864\pi$
$374$		0			0
$375$	−5.90849	−	22.0508i	−0.305113	−	1.13870i
$376$		0			0
$377$	−7.36075	+	6.35327i	−0.379098	+	0.327210i
$378$		0			0
$379$	15.9735	−	4.28009i	0.820503	−	0.219853i	0.175937	−	0.984401i	$-0.443705\pi$
$379$	15.9735	−	4.28009i	0.820503	−	0.219853i	0.644567	+	0.764548i	$0.277038\pi$
$380$		0			0
$381$	16.7620	+	29.0326i	0.858743	+	1.48739i
$382$		0			0
$383$	−5.94901	+	22.2020i	−0.303980	+	1.13447i	0.629839	+	0.776725i	$0.283121\pi$
$383$	−5.94901	+	22.2020i	−0.303980	+	1.13447i	−0.933820	+	0.357744i	$0.883546\pi$
$384$		0			0
$385$	−20.0734	−	11.1832i	−1.02304	−	0.569948i
$386$		0			0
$387$	2.23287	−	3.86744i	0.113503	−	0.196593i
$388$		0			0
$389$		−	0.727445i		−	0.0368829i	−0.999830	−	0.0184415i	$-0.994130\pi$
$389$		−	0.727445i		−	0.0368829i	0.999830	−	0.0184415i	$-0.00587043\pi$
$390$		0			0
$391$		−	7.73845i		−	0.391350i
$392$		0			0
$393$	−2.97933	−	1.72012i	−0.150288	−	0.0867686i
$394$		0			0
$395$	−15.7693	+	15.7693i	−0.793442	+	0.793442i
$396$		0			0
$397$	−17.8351	−	4.77890i	−0.895117	−	0.239846i	−0.218199	−	0.975904i	$-0.570018\pi$
$397$	−17.8351	−	4.77890i	−0.895117	−	0.239846i	−0.676918	+	0.736058i	$0.736685\pi$
$398$		0			0
$399$	21.3187	+	36.9251i	1.06727	+	1.84857i
$400$		0			0
$401$	−6.39023	−	23.8487i	−0.319113	−	1.19095i	−0.920099	−	0.391686i	$-0.871892\pi$
$401$	−6.39023	−	23.8487i	−0.319113	−	1.19095i	0.600986	−	0.799259i	$-0.294775\pi$
$402$		0			0
$403$	5.27105	−	2.54795i	0.262570	−	0.126922i
$404$		0			0
$405$	−24.1801	+	6.47905i	−1.20152	+	0.321947i
$406$		0			0
$407$	−26.7531	+	27.5851i	−1.32610	+	1.36734i
$408$		0			0
$409$	26.4937	+	7.09895i	1.31003	+	0.351021i	0.845233	−	0.534398i	$-0.179462\pi$
$409$	26.4937	+	7.09895i	1.31003	+	0.351021i	0.464794	+	0.885419i	$0.346128\pi$
$410$		0			0
$411$	−17.8670	+	17.8670i	−0.881316	+	0.881316i
$412$		0			0
$413$	−11.2454	+	19.4777i	−0.553352	+	0.958434i
$414$		0			0
$415$	−10.2058			−0.500981
$416$		0			0
$417$		−	8.37713i		−	0.410230i
$418$		0			0
$419$	−18.4756	+	32.0006i	−0.902590	+	1.56333i	−0.0784711	+	0.996916i	$0.525004\pi$
$419$	−18.4756	+	32.0006i	−0.902590	+	1.56333i	−0.824119	+	0.566416i	$0.808330\pi$
$420$		0			0
$421$	23.5886	+	23.5886i	1.14964	+	1.14964i	0.986623	+	0.163016i	$0.0521223\pi$
$421$	23.5886	+	23.5886i	1.14964	+	1.14964i	0.163016	+	0.986623i	$0.447878\pi$
$422$		0			0
$423$	−2.86219	−	0.766921i	−0.139164	−	0.0372890i
$424$		0			0
$425$	−0.110982	+	0.0640753i	−0.00538340	+	0.00310811i
$426$		0			0
$427$	−9.65954	−	36.0499i	−0.467458	−	1.74458i
$428$		0			0
$429$	7.70236	−	23.2565i	0.371873	−	1.12284i
$430$		0			0
$431$	1.73372	+	6.47034i	0.0835105	+	0.311665i	0.995028	−	0.0995960i	$-0.0317550\pi$
$431$	1.73372	+	6.47034i	0.0835105	+	0.311665i	−0.911517	+	0.411261i	$0.865088\pi$
$432$		0			0
$433$	34.8496	−	20.1204i	1.67476	−	0.966925i	0.709851	−	0.704352i	$-0.248762\pi$
$433$	34.8496	−	20.1204i	1.67476	−	0.966925i	0.964912	−	0.262573i	$-0.0845710\pi$
$434$		0			0
$435$	11.9725	+	3.20803i	0.574039	+	0.153813i
$436$		0			0
$437$	−9.52437	−	9.52437i	−0.455612	−	0.455612i
$438$		0			0
$439$	0.772635	−	1.33824i	0.0368758	−	0.0638708i	−0.846998	−	0.531595i	$-0.821593\pi$
$439$	0.772635	−	1.33824i	0.0368758	−	0.0638708i	0.883874	+	0.467725i	$0.154926\pi$
$440$		0			0
$441$			3.03712i			0.144625i
$442$		0			0
$443$	20.3180			0.965338			0.482669	−	0.875803i	$-0.339667\pi$
$443$	20.3180			0.965338			0.482669	+	0.875803i	$0.339667\pi$
$444$		0			0
$445$	15.7842	−	27.3390i	0.748243	−	1.29600i
$446$		0			0
$447$	−6.31402	+	6.31402i	−0.298643	+	0.298643i
$448$		0			0
$449$	−2.35178	−	0.630157i	−0.110987	−	0.0297389i	0.202898	−	0.979200i	$-0.434964\pi$
$449$	−2.35178	−	0.630157i	−0.110987	−	0.0297389i	−0.313885	+	0.949461i	$0.601631\pi$
$450$		0			0
$451$	−25.9151	+	26.7210i	−1.22029	+	1.25824i
$452$		0			0
$453$	−5.15344	+	1.38086i	−0.242130	+	0.0648785i
$454$		0			0
$455$	−4.68013	−	24.5378i	−0.219408	−	1.15035i
$456$		0			0
$457$	−1.94068	−	7.24272i	−0.0907813	−	0.338800i	0.905565	−	0.424208i	$-0.139447\pi$
$457$	−1.94068	−	7.24272i	−0.0907813	−	0.338800i	−0.996346	+	0.0854076i	$0.972781\pi$
$458$		0			0
$459$	−7.15021	−	12.3845i	−0.333743	−	0.578061i
$460$		0			0
$461$	−4.95977	−	1.32897i	−0.230999	−	0.0618961i	0.141462	−	0.989944i	$-0.454820\pi$
$461$	−4.95977	−	1.32897i	−0.230999	−	0.0618961i	−0.372462	+	0.928048i	$0.621486\pi$
$462$		0			0
$463$	7.67716	−	7.67716i	0.356788	−	0.356788i	−0.505840	−	0.862628i	$-0.668817\pi$
$463$	7.67716	−	7.67716i	0.356788	−	0.356788i	0.862628	+	0.505840i	$0.168817\pi$
$464$		0			0
$465$	−6.46322	−	3.73154i	−0.299725	−	0.173046i
$466$		0			0
$467$		−	26.9442i		−	1.24683i	−0.781891	−	0.623416i	$-0.785745\pi$
$467$		−	26.9442i		−	1.24683i	0.781891	−	0.623416i	$-0.214255\pi$
$468$		0			0
$469$		−	25.2510i		−	1.16598i
$470$		0			0
$471$	10.4498	−	18.0996i	0.481501	−	0.833985i
$472$		0			0
$473$	−6.02127	+	10.8079i	−0.276858	+	0.496950i
$474$		0			0
$475$	−0.0577317	+	0.215458i	−0.00264891	+	0.00988587i
$476$		0			0
$477$	2.13683	+	3.70110i	0.0978388	+	0.169462i
$478$		0			0
$479$	26.3868	−	7.07033i	1.20565	−	0.323052i	0.400594	−	0.916256i	$-0.368804\pi$
$479$	26.3868	−	7.07033i	1.20565	−	0.323052i	0.805052	+	0.593204i	$0.202137\pi$
$480$		0			0
$481$	−41.6628	−	3.06068i	−1.89966	−	0.139555i
$482$		0			0
$483$	−3.27281	−	12.2143i	−0.148918	−	0.555769i
$484$		0			0
$485$	17.3713	−	10.0294i	0.788792	−	0.455409i
$486$		0			0
$487$	−6.28845	+	23.4688i	−0.284957	+	1.06347i	0.663914	+	0.747809i	$0.268894\pi$
$487$	−6.28845	+	23.4688i	−0.284957	+	1.06347i	−0.948871	+	0.315665i	$0.897772\pi$
$488$		0			0
$489$	4.52499	−	4.52499i	0.204627	−	0.204627i
$490$		0			0
$491$	6.60559	−	11.4412i	0.298106	−	0.516335i	−0.677596	−	0.735434i	$-0.736978\pi$
$491$	6.60559	−	11.4412i	0.298106	−	0.516335i	0.975703	+	0.219099i	$0.0703117\pi$
$492$		0			0
$493$			10.4414i			0.470257i
$494$		0			0
$495$	−8.56781	+	2.43691i	−0.385095	+	0.109531i
$496$		0			0
$497$	4.80290	+	2.77296i	0.215440	+	0.124384i
$498$		0			0
$499$	4.39493	+	4.39493i	0.196744	+	0.196744i	0.798603	−	0.601859i	$-0.205573\pi$
$499$	4.39493	+	4.39493i	0.196744	+	0.196744i	−0.601859	+	0.798603i	$0.705573\pi$
$500$		0			0
$501$	10.6118	−	39.6038i	0.474100	−	1.76937i
$502$		0			0
$503$	−8.27682	+	4.77863i	−0.369045	+	0.213068i	−0.673041	−	0.739605i	$-0.735012\pi$
$503$	−8.27682	+	4.77863i	−0.369045	+	0.213068i	0.303996	+	0.952673i	$0.401679\pi$
$504$		0			0
$505$	26.4112	−	7.07686i	1.17528	−	0.314916i
$506$		0			0
$507$	24.7633	−	9.80290i	1.09978	−	0.435362i
$508$		0			0
$509$	12.5616	−	3.36586i	0.556781	−	0.149189i	0.0305541	−	0.999533i	$-0.490273\pi$
$509$	12.5616	−	3.36586i	0.556781	−	0.149189i	0.526227	+	0.850344i	$0.323606\pi$
$510$		0			0
$511$	−32.4277	+	18.7222i	−1.43452	+	0.828219i
$512$		0			0
$513$	−24.0431	−	6.44232i	−1.06153	−	0.284435i
$514$		0			0
$515$	−6.91047	+	6.91047i	−0.304512	+	0.304512i
$516$		0			0
$517$	7.96110	+	2.00306i	0.350129	+	0.0880947i
$518$		0			0
$519$	12.5709			0.551800
$520$		0			0
$521$	26.2660			1.15074			0.575368	−	0.817895i	$-0.304859\pi$
$521$	26.2660			1.15074			0.575368	+	0.817895i	$0.304859\pi$
$522$		0			0
$523$	18.1351	+	10.4703i	0.792994	+	0.457836i	0.841016	−	0.541011i	$-0.181958\pi$
$523$	18.1351	+	10.4703i	0.792994	+	0.457836i	−0.0480212	+	0.998846i	$0.515292\pi$
$524$		0			0
$525$	−0.148073	+	0.148073i	−0.00646244	+	0.00646244i
$526$		0			0
$527$	1.62717	−	6.07267i	0.0708805	−	0.264530i
$528$		0			0
$529$	−9.50265	−	16.4591i	−0.413159	−	0.715612i
$530$		0			0
$531$	2.25656	+	8.42158i	0.0979262	+	0.365466i
$532$		0			0
$533$	−40.3577	−	2.96481i	−1.74809	−	0.128420i
$534$		0			0
$535$	−4.34620	−	16.2202i	−0.187902	−	0.701262i
$536$		0			0
$537$	41.3082	−	23.8493i	1.78258	−	1.02917i
$538$		0			0
$539$	−0.128811	−	8.41315i	−0.00554827	−	0.362380i
$540$		0			0
$541$	5.31006	+	5.31006i	0.228297	+	0.228297i	0.811981	−	0.583684i	$-0.198389\pi$
$541$	5.31006	+	5.31006i	0.228297	+	0.228297i	−0.583684	+	0.811981i	$0.698389\pi$
$542$		0			0
$543$	8.00677	+	4.62271i	0.343603	+	0.198380i
$544$		0			0
$545$	−40.2146			−1.72260
$546$		0			0
$547$		−	24.2473i		−	1.03674i	−0.855157	−	0.518369i	$-0.826539\pi$
$547$		−	24.2473i		−	1.03674i	0.855157	−	0.518369i	$-0.173461\pi$
$548$		0			0
$549$	−12.5295	−	7.23392i	−0.534747	−	0.308736i
$550$		0			0
$551$	12.8511	+	12.8511i	0.547476	+	0.547476i
$552$		0			0
$553$	−29.6524	−	7.94533i	−1.26095	−	0.337870i
$554$		0			0
$555$	26.6263	+	46.1180i	1.13022	+	1.95760i
$556$		0			0
$557$	21.8339	−	5.85037i	0.925131	−	0.247888i	0.235354	−	0.971910i	$-0.424375\pi$
$557$	21.8339	−	5.85037i	0.925131	−	0.247888i	0.689777	+	0.724022i	$0.257708\pi$
$558$		0			0
$559$	−13.2117	+	2.51988i	−0.558794	+	0.106580i
$560$		0			0
$561$	−13.5012	−	22.5792i	−0.570020	−	0.953296i
$562$		0			0
$563$	−1.97162	−	3.41495i	−0.0830940	−	0.143923i	0.821483	−	0.570232i	$-0.193147\pi$
$563$	−1.97162	−	3.41495i	−0.0830940	−	0.143923i	−0.904577	+	0.426309i	$0.859814\pi$
$564$		0			0
$565$	−4.66229	+	17.3999i	−0.196144	+	0.732020i
$566$		0			0
$567$	−24.3662	−	24.3662i	−1.02328	−	1.02328i
$568$		0			0
$569$	13.8521	−	23.9925i	0.580709	−	1.00582i	−0.414686	−	0.909965i	$-0.636109\pi$
$569$	13.8521	−	23.9925i	0.580709	−	1.00582i	0.995395	−	0.0958536i	$-0.0305581\pi$
$570$		0			0
$571$	−31.7626			−1.32922			−0.664611	−	0.747190i	$-0.731403\pi$
$571$	−31.7626			−1.32922			−0.664611	+	0.747190i	$0.731403\pi$
$572$		0			0
$573$	−8.52163			−0.355996
$574$		0			0
$575$	0.0330766	−	0.0572903i	0.00137939	−	0.00238917i
$576$		0			0
$577$	1.07587	+	1.07587i	0.0447890	+	0.0447890i	0.729147	−	0.684358i	$-0.239917\pi$
$577$	1.07587	+	1.07587i	0.0447890	+	0.0447890i	−0.684358	+	0.729147i	$0.739917\pi$
$578$		0			0
$579$	10.3613	−	38.6687i	0.430599	−	1.60702i
$580$		0			0
$581$	−7.02429	−	12.1664i	−0.291417	−	0.504749i
$582$		0			0
$583$	−6.07623	−	10.1618i	−0.251652	−	0.420860i
$584$		0			0
$585$	−8.00898	−	5.44322i	−0.331131	−	0.225050i
$586$		0			0
$587$	20.6717	−	5.53896i	0.853211	−	0.228617i	0.194397	−	0.980923i	$-0.437725\pi$
$587$	20.6717	−	5.53896i	0.853211	−	0.228617i	0.658814	+	0.752306i	$0.271058\pi$
$588$		0			0
$589$	−5.47146	−	9.47684i	−0.225447	−	0.390486i
$590$		0			0
$591$	18.5144	+	4.96091i	0.761579	+	0.204064i
$592$		0			0
$593$	−10.8335	−	10.8335i	−0.444879	−	0.444879i	0.448769	−	0.893648i	$-0.351863\pi$
$593$	−10.8335	−	10.8335i	−0.444879	−	0.444879i	−0.893648	+	0.448769i	$0.851863\pi$
$594$		0			0
$595$	−23.2309	−	13.4123i	−0.952373	−	0.549853i
$596$		0			0
$597$		−	36.9565i		−	1.51253i
$598$		0			0
$599$	40.9723			1.67408			0.837041	−	0.547141i	$-0.184284\pi$
$599$	40.9723			1.67408			0.837041	+	0.547141i	$0.184284\pi$
$600$		0			0
$601$	−8.52325	−	4.92090i	−0.347671	−	0.200728i	0.315988	−	0.948763i	$-0.397664\pi$
$601$	−8.52325	−	4.92090i	−0.347671	−	0.200728i	−0.663659	+	0.748035i	$0.730997\pi$
$602$		0			0
$603$	−6.92160	−	6.92160i	−0.281869	−	0.281869i
$604$		0			0
$605$	23.6304	−	7.11390i	0.960714	−	0.289221i
$606$		0			0
$607$	11.4683	−	6.62121i	0.465483	−	0.268747i	−0.248864	−	0.968538i	$-0.580057\pi$
$607$	11.4683	−	6.62121i	0.465483	−	0.268747i	0.714347	+	0.699792i	$0.246724\pi$
$608$		0			0
$609$	4.41596	+	16.4806i	0.178944	+	0.667827i
$610$		0			0
$611$	3.88394	+	8.03489i	0.157127	+	0.325057i
$612$		0			0
$613$	−6.12205	−	22.8478i	−0.247267	−	0.922814i	−0.972230	−	0.234026i	$-0.924810\pi$
$613$	−6.12205	−	22.8478i	−0.247267	−	0.922814i	0.724963	−	0.688788i	$-0.241857\pi$
$614$		0			0
$615$	25.7922	+	44.6734i	1.04004	+	1.80141i
$616$		0			0
$617$	−0.505077	+	1.88497i	−0.0203336	+	0.0758861i	−0.975347	−	0.220676i	$-0.929174\pi$
$617$	−0.505077	+	1.88497i	−0.0203336	+	0.0758861i	0.955013	+	0.296562i	$0.0958403\pi$
$618$		0			0
$619$	−15.4508	+	15.4508i	−0.621020	+	0.621020i	−0.945792	−	0.324772i	$-0.894712\pi$
$619$	−15.4508	+	15.4508i	−0.621020	+	0.621020i	0.324772	+	0.945792i	$0.394712\pi$
$620$		0			0
$621$	6.39307	+	3.69104i	0.256545	+	0.148116i
$622$		0			0
$623$	43.4550			1.74099
$624$		0			0
$625$	25.1644			1.00658
$626$		0			0
$627$	−44.4072	−	11.1731i	−1.77345	−	0.446212i
$628$		0			0
$629$	−31.7207	+	31.7207i	−1.26479	+	1.26479i
$630$		0			0
$631$	−13.5843	−	3.63989i	−0.540781	−	0.144902i	−0.0219189	−	0.999760i	$-0.506978\pi$
$631$	−13.5843	−	3.63989i	−0.540781	−	0.144902i	−0.518862	+	0.854858i	$0.673644\pi$
$632$		0			0
$633$	−18.2411	+	10.5315i	−0.725020	+	0.418590i
$634$		0			0
$635$	−35.4601	+	9.50151i	−1.40719	+	0.377056i
$636$		0			0
$637$	6.92450	−	5.97673i	0.274359	−	0.236807i
$638$		0			0
$639$	2.07664	−	0.556433i	0.0821504	−	0.0220121i
$640$		0			0
$641$	11.4509	−	6.61117i	0.452283	−	0.261126i	−0.256511	−	0.966541i	$-0.582573\pi$
$641$	11.4509	−	6.61117i	0.452283	−	0.261126i	0.708794	+	0.705416i	$0.249240\pi$
$642$		0			0
$643$	3.28083	−	12.2442i	0.129384	−	0.482866i	−0.870574	−	0.492037i	$-0.836253\pi$
$643$	3.28083	−	12.2442i	0.129384	−	0.482866i	0.999958	+	0.00917092i	$0.00291924\pi$
$644$		0			0
$645$	12.1234	+	12.1234i	0.477359	+	0.477359i
$646$		0			0
$647$	−20.6593	−	11.9277i	−0.812202	−	0.468925i	0.0355180	−	0.999369i	$-0.488692\pi$
$647$	−20.6593	−	11.9277i	−0.812202	−	0.468925i	−0.847720	+	0.530444i	$0.822025\pi$
$648$		0			0
$649$	−6.60809	−	23.2330i	−0.259390	−	0.911976i
$650$		0			0
$651$		−	10.2732i		−	0.402638i
$652$		0			0
$653$	−15.2258	+	26.3718i	−0.595830	+	1.03201i	0.397599	+	0.917559i	$0.369844\pi$
$653$	−15.2258	+	26.3718i	−0.595830	+	1.03201i	−0.993429	+	0.114449i	$0.963490\pi$
$654$		0			0
$655$	2.66388	−	2.66388i	0.104086	−	0.104086i
$656$		0			0
$657$	−3.75686	+	14.0208i	−0.146569	+	0.547004i
$658$		0			0
$659$	6.07274	−	3.50610i	0.236560	−	0.136578i	−0.377034	−	0.926199i	$-0.623056\pi$
$659$	6.07274	−	3.50610i	0.236560	−	0.136578i	0.613595	+	0.789621i	$0.289723\pi$
$660$		0			0
$661$	8.78365	+	32.7810i	0.341644	+	1.27503i	0.896484	+	0.443076i	$0.146113\pi$
$661$	8.78365	+	32.7810i	0.341644	+	1.27503i	−0.554840	+	0.831957i	$0.687220\pi$
$662$		0			0
$663$	9.40622	−	27.0086i	0.365307	−	1.04893i
$664$		0			0
$665$	−45.0999	+	12.0845i	−1.74890	+	0.468616i
$666$		0			0
$667$	−2.69500	−	4.66788i	−0.104351	−	0.180741i
$668$		0			0
$669$	−8.54682	+	31.8972i	−0.330439	+	1.23322i
$670$		0			0
$671$	35.0149	+	19.5073i	1.35174	+	0.753073i
$672$		0			0
$673$	−3.31369	+	5.73948i	−0.127733	+	0.221241i	−0.922798	−	0.385284i	$-0.874104\pi$
$673$	−3.31369	+	5.73948i	−0.127733	+	0.221241i	0.795065	+	0.606525i	$0.207437\pi$
$674$		0			0
$675$		−	0.122249i		−	0.00470537i
$676$		0			0
$677$		−	21.1112i		−	0.811367i	−0.914014	−	0.405684i	$-0.867033\pi$
$677$		−	21.1112i		−	0.811367i	0.914014	−	0.405684i	$-0.132967\pi$
$678$		0			0
$679$	23.9123	+	13.8058i	0.917669	+	0.529816i
$680$		0			0
$681$	−6.33702	+	6.33702i	−0.242835	+	0.242835i
$682$		0			0
$683$	−8.92806	−	2.39227i	−0.341623	−	0.0915375i	0.0839288	−	0.996472i	$-0.473253\pi$
$683$	−8.92806	−	2.39227i	−0.341623	−	0.0915375i	−0.425551	+	0.904934i	$0.639920\pi$
$684$		0			0
$685$	−13.8350	−	23.9629i	−0.528607	−	0.915574i
$686$		0			0
$687$	−3.32656	−	12.4149i	−0.126916	−	0.473658i
$688$		0			0
$689$	4.23329	−	12.1553i	0.161275	−	0.463079i
$690$		0			0
$691$	−10.7846	+	2.88972i	−0.410265	+	0.109930i	−0.458048	−	0.888928i	$-0.651451\pi$
$691$	−10.7846	+	2.88972i	−0.410265	+	0.109930i	0.0477829	+	0.998858i	$0.484784\pi$
$692$		0			0
$693$	−8.80203	−	8.53656i	−0.334361	−	0.324277i
$694$		0			0
$695$	8.86093	+	2.37428i	0.336114	+	0.0900616i
$696$		0			0
$697$	−30.7270	+	30.7270i	−1.16387	+	1.16387i
$698$		0			0
$699$	14.4737	−	25.0692i	0.547446	−	0.948204i
$700$		0			0
$701$	−6.09309			−0.230133			−0.115066	−	0.993358i	$-0.536708\pi$
$701$	−6.09309			−0.230133			−0.115066	+	0.993358i	$0.536708\pi$
$702$		0			0
$703$			78.0826i			2.94494i
$704$		0			0
$705$	5.68815	−	9.85216i	0.214228	−	0.371054i
$706$		0			0
$707$	26.6144	+	26.6144i	1.00094	+	1.00094i
$708$		0			0
$709$	35.5663	+	9.52995i	1.33572	+	0.357905i	0.854845	−	0.518884i	$-0.173652\pi$
$709$	35.5663	+	9.52995i	1.33572	+	0.357905i	0.480875	+	0.876789i	$0.340319\pi$
$710$		0			0
$711$	−10.3060	+	5.95017i	−0.386505	+	0.223149i
$712$		0			0
$713$	0.839966	+	3.13480i	0.0314570	+	0.117399i
$714$		0			0
$715$	22.4166	+	14.7387i	0.838334	+	0.551194i
$716$		0			0
$717$	10.8760	+	40.5898i	0.406172	+	1.51585i
$718$		0			0
$719$	29.6208	−	17.1016i	1.10467	−	0.637782i	0.167227	−	0.985918i	$-0.446519\pi$
$719$	29.6208	−	17.1016i	1.10467	−	0.637782i	0.937444	+	0.348136i	$0.113185\pi$
$720$		0			0
$721$	−12.9943	−	3.48182i	−0.483934	−	0.129670i
$722$		0			0
$723$	34.8838	+	34.8838i	1.29734	+	1.29734i
$724$		0			0
$725$	−0.0446299	+	0.0773012i	−0.00165751	+	0.00287089i
$726$		0			0
$727$			9.13960i			0.338969i	0.985533	+	0.169485i	$0.0542103\pi$
$727$			9.13960i			0.338969i	−0.985533	+	0.169485i	$0.945790\pi$
$728$		0			0
$729$	9.34237			0.346014
$730$		0			0
$731$	−7.22149	+	12.5080i	−0.267097	+	0.462625i
$732$		0			0
$733$	9.89202	−	9.89202i	0.365370	−	0.365370i	−0.500415	−	0.865785i	$-0.666819\pi$
$733$	9.89202	−	9.89202i	0.365370	−	0.365370i	0.865785	+	0.500415i	$0.166819\pi$
$734$		0			0
$735$	−11.2629	−	3.01790i	−0.415440	−	0.111317i
$736$		0			0
$737$	19.4672	+	18.8800i	0.717082	+	0.695455i
$738$		0			0
$739$	24.0638	−	6.44786i	0.885200	−	0.237188i	0.212550	−	0.977150i	$-0.431823\pi$
$739$	24.0638	−	6.44786i	0.885200	−	0.237188i	0.672649	+	0.739962i	$0.265156\pi$
$740$		0			0
$741$	−21.6647	−	44.8188i	−0.795874	−	1.64646i
$742$		0			0
$743$	12.2681	+	45.7850i	0.450071	+	1.67969i	0.702188	+	0.711991i	$0.252207\pi$
$743$	12.2681	+	45.7850i	0.450071	+	1.67969i	−0.252117	+	0.967697i	$0.581127\pi$
$744$		0			0
$745$	−4.88913	−	8.46822i	−0.179124	−	0.310251i
$746$		0			0
$747$	−5.26041	−	1.40952i	−0.192468	−	0.0515718i
$748$		0			0
$749$	16.3450	−	16.3450i	0.597234	−	0.597234i
$750$		0			0
$751$	−33.4010	−	19.2840i	−1.21882	−	0.703685i	−0.254153	−	0.967164i	$-0.581797\pi$
$751$	−33.4010	−	19.2840i	−1.21882	−	0.703685i	−0.964665	+	0.263479i	$0.915130\pi$
$752$		0			0
$753$		−	0.238758i		−	0.00870083i
$754$		0			0
$755$		−	5.84244i		−	0.212628i
$756$		0			0
$757$	11.8022	−	20.4420i	0.428959	−	0.742978i	−0.567822	−	0.823151i	$-0.692214\pi$
$757$	11.8022	−	20.4420i	0.428959	−	0.742978i	0.996781	+	0.0801731i	$0.0255473\pi$
$758$		0			0
$759$	11.8636	+	6.60940i	0.430622	+	0.239906i
$760$		0			0
$761$	−1.68817	+	6.30035i	−0.0611963	+	0.228388i	−0.989750	−	0.142810i	$-0.954386\pi$
$761$	−1.68817	+	6.30035i	−0.0611963	+	0.228388i	0.928554	+	0.371198i	$0.121053\pi$
$762$		0			0
$763$	−27.6784	−	47.9404i	−1.00203	−	1.73556i
$764$		0			0
$765$	−10.0444	+	2.69138i	−0.363154	+	0.0973069i
$766$		0			0
$767$	14.7602	−	21.7177i	0.532959	−	0.784179i
$768$		0			0
$769$	−0.307483	−	1.14754i	−0.0110881	−	0.0413815i	0.960160	−	0.279450i	$-0.0901523\pi$
$769$	−0.307483	−	1.14754i	−0.0110881	−	0.0413815i	−0.971248	+	0.238069i	$0.923486\pi$
$770$		0			0
$771$	12.6994	−	7.33203i	0.457359	−	0.264057i
$772$		0			0
$773$	10.3265	−	38.5391i	0.371420	−	1.38616i	−0.487087	−	0.873354i	$-0.661940\pi$
$773$	10.3265	−	38.5391i	0.371420	−	1.38616i	0.858506	−	0.512803i	$-0.171393\pi$
$774$		0			0
$775$	0.0380029	−	0.0380029i	0.00136511	−	0.00136511i
$776$		0			0
$777$	−36.6520	+	63.4831i	−1.31488	+	2.27744i
$778$		0			0
$779$			75.6367i			2.70997i
$780$		0			0
$781$	−5.72891	+	1.62945i	−0.204997	+	0.0583065i
$782$		0			0
$783$	−8.62610	−	4.98028i	−0.308272	−	0.177981i
$784$		0			0
$785$	16.1832	+	16.1832i	0.577602	+	0.577602i
$786$		0			0
$787$	−11.5600	+	43.1424i	−0.412068	+	1.53786i	0.378567	+	0.925574i	$0.376417\pi$
$787$	−11.5600	+	43.1424i	−0.412068	+	1.53786i	−0.790636	+	0.612287i	$0.790250\pi$
$788$		0			0
$789$	36.3925	−	21.0112i	1.29561	−	0.748020i
$790$		0			0
$791$	−23.9516	+	6.41781i	−0.851620	+	0.228191i
$792$		0			0
$793$	8.16376	+	42.8024i	0.289904	+	1.51996i
$794$		0			0
$795$	−15.8486	+	4.24661i	−0.562091	+	0.150612i
$796$		0			0
$797$	−1.15655	+	0.667733i	−0.0409670	+	0.0236523i	−0.520344	−	0.853957i	$-0.674196\pi$
$797$	−1.15655	+	0.667733i	−0.0409670	+	0.0236523i	0.479377	+	0.877609i	$0.340863\pi$
$798$		0			0
$799$	9.25682	+	2.48036i	0.327483	+	0.0877487i
$800$		0			0
$801$	11.9116	−	11.9116i	0.420874	−	0.420874i
$802$		0			0
$803$	9.81228	−	38.9985i	0.346268	−	1.37623i
$804$		0			0
$805$	13.8473			0.488053
$806$		0			0
$807$	−47.8862			−1.68567
$808$		0			0
$809$	6.35114	+	3.66683i	0.223294	+	0.128919i	0.607475	−	0.794339i	$-0.292183\pi$
$809$	6.35114	+	3.66683i	0.223294	+	0.128919i	−0.384180	+	0.923258i	$0.625516\pi$
$810$		0			0
$811$	−32.7461	+	32.7461i	−1.14987	+	1.14987i	−0.163293	+	0.986578i	$0.552212\pi$
$811$	−32.7461	+	32.7461i	−1.14987	+	1.14987i	−0.986578	+	0.163293i	$0.947788\pi$
$812$		0			0
$813$	−10.9213	+	40.7590i	−0.383028	+	1.42948i
$814$		0			0
$815$	3.50383	+	6.06881i	0.122734	+	0.212581i
$816$		0			0
$817$	6.50654	+	24.2828i	0.227635	+	0.849546i
$818$		0			0
$819$	0.976622	−	13.2940i	0.0341259	−	0.464531i
$820$		0			0
$821$	−5.21265	−	19.4539i	−0.181923	−	0.678945i	−0.995268	−	0.0971643i	$-0.969023\pi$
$821$	−5.21265	−	19.4539i	−0.181923	−	0.678945i	0.813346	−	0.581781i	$-0.197644\pi$
$822$		0			0
$823$	1.44357	−	0.833443i	0.0503196	−	0.0290520i	−0.474629	−	0.880186i	$-0.657418\pi$
$823$	1.44357	−	0.833443i	0.0503196	−	0.0290520i	0.524949	+	0.851134i	$0.324084\pi$
$824$		0			0
$825$	−0.00344290	−	0.224870i	−0.000119866	−	0.00782897i
$826$		0			0
$827$	−35.5172	−	35.5172i	−1.23505	−	1.23505i	−0.961998	−	0.273055i	$-0.911966\pi$
$827$	−35.5172	−	35.5172i	−1.23505	−	1.23505i	−0.273055	−	0.961998i	$-0.588034\pi$
$828$		0			0
$829$	−17.7306	−	10.2367i	−0.615808	−	0.355537i	0.159427	−	0.987210i	$-0.449035\pi$
$829$	−17.7306	−	10.2367i	−0.615808	−	0.355537i	−0.775235	+	0.631673i	$0.782369\pi$
$830$		0			0
$831$	−23.2735			−0.807348
$832$		0			0
$833$		−	9.82258i		−	0.340332i
$834$		0			0
$835$	38.8834	+	22.4493i	1.34561	+	0.776891i
$836$		0			0
$837$	4.24078	+	4.24078i	0.146583	+	0.146583i
$838$		0			0
$839$	−50.3788	−	13.4990i	−1.73927	−	0.466036i	−0.756985	−	0.653432i	$-0.773328\pi$
$839$	−50.3788	−	13.4990i	−1.73927	−	0.466036i	−0.982284	+	0.187396i	$0.939995\pi$
$840$		0			0
$841$	−10.8637	−	18.8164i	−0.374609	−	0.648842i
$842$		0			0
$843$	−40.7162	+	10.9099i	−1.40234	+	0.375756i
$844$		0			0
$845$	3.35053	+	28.9718i	0.115262	+	0.996662i
$846$		0			0
$847$	24.7446	+	23.2739i	0.850236	+	0.799701i
$848$		0			0
$849$	−13.1332	−	22.7473i	−0.450729	−	0.780686i
$850$		0			0
$851$	5.99354	−	22.3682i	0.205456	−	0.766771i
$852$		0			0
$853$	12.2087	+	12.2087i	0.418019	+	0.418019i	0.884521	−	0.466501i	$-0.154486\pi$
$853$	12.2087	+	12.2087i	0.418019	+	0.418019i	−0.466501	+	0.884521i	$0.654486\pi$
$854$		0			0
$855$	−9.04993	+	15.6749i	−0.309501	+	0.536072i
$856$		0			0
$857$	45.3821			1.55022			0.775111	−	0.631825i	$-0.217694\pi$
$857$	45.3821			1.55022			0.775111	+	0.631825i	$0.217694\pi$
$858$		0			0
$859$	13.6119			0.464433			0.232217	−	0.972664i	$-0.425402\pi$
$859$	13.6119			0.464433			0.232217	+	0.972664i	$0.425402\pi$
$860$		0			0
$861$	−35.5039	+	61.4945i	−1.20997	+	2.09573i
$862$		0			0
$863$	−5.22855	−	5.22855i	−0.177982	−	0.177982i	0.612494	−	0.790475i	$-0.290166\pi$
$863$	−5.22855	−	5.22855i	−0.177982	−	0.177982i	−0.790475	+	0.612494i	$0.790166\pi$
$864$		0			0
$865$	−3.56289	+	13.2969i	−0.121142	+	0.452107i
$866$		0			0
$867$	2.05814	+	3.56480i	0.0698981	+	0.121067i
$868$		0			0
$869$	28.2964	−	16.9197i	0.959889	−	0.573962i
$870$		0			0
$871$	−2.15996	+	29.4020i	−0.0731876	+	0.996247i
$872$		0			0
$873$	10.3390	−	2.77032i	0.349921	−	0.0937611i
$874$		0			0
$875$	17.2059	+	29.8015i	0.581667	+	1.00748i
$876$		0			0
$877$	15.4917	+	4.15099i	0.523118	+	0.140169i	0.510708	−	0.859754i	$-0.329383\pi$
$877$	15.4917	+	4.15099i	0.523118	+	0.140169i	0.0124093	+	0.999923i	$0.496050\pi$
$878$		0			0
$879$	−27.5513	−	27.5513i	−0.929283	−	0.929283i
$880$		0			0
$881$	−29.9116	−	17.2695i	−1.00775	−	0.581823i	−0.0972159	−	0.995263i	$-0.530994\pi$
$881$	−29.9116	−	17.2695i	−1.00775	−	0.581823i	−0.910531	+	0.413440i	$0.864327\pi$
$882$		0			0
$883$			15.2056i			0.511709i	0.966715	+	0.255855i	$0.0823569\pi$
$883$			15.2056i			0.511709i	−0.966715	+	0.255855i	$0.917643\pi$
$884$		0			0
$885$	−33.4731			−1.12519
$886$		0			0
$887$	−46.4920	−	26.8422i	−1.56105	−	0.901271i	−0.997151	−	0.0754260i	$-0.975968\pi$
$887$	−46.4920	−	26.8422i	−1.56105	−	0.901271i	−0.563897	−	0.825845i	$-0.690698\pi$
$888$		0			0
$889$	−35.7329	−	35.7329i	−1.19844	−	1.19844i
$890$		0			0
$891$	37.0035	−	0.566547i	1.23966	−	0.0189800i
$892$		0			0
$893$	14.4459	−	8.34037i	0.483415	−	0.279100i
$894$		0			0
$895$	13.5189	+	50.4534i	0.451888	+	1.68647i
$896$		0			0
$897$	2.76601	+	14.5021i	0.0923544	+	0.484212i
$898$		0			0
$899$	−1.13336	−	4.22975i	−0.0377996	−	0.141070i
$900$		0			0
$901$	−6.91089	−	11.9700i	−0.230235	−	0.398779i
$902$		0			0
$903$	−6.10834	+	22.7966i	−0.203273	+	0.758625i
$904$		0			0
$905$	−7.15900	+	7.15900i	−0.237973	+	0.237973i
$906$		0			0
$907$	42.5804	+	24.5838i	1.41386	+	0.816293i	0.995749	−	0.0921033i	$-0.0293590\pi$
$907$	42.5804	+	24.5838i	1.41386	+	0.816293i	0.418111	+	0.908396i	$0.362692\pi$
$908$		0			0
$909$	14.5907			0.483942
$910$		0			0
$911$	20.1205			0.666620			0.333310	−	0.942817i	$-0.391834\pi$
$911$	20.1205			0.666620			0.333310	+	0.942817i	$0.391834\pi$
$912$		0			0
$913$	14.6317	+	3.68143i	0.484239	+	0.121838i
$914$		0			0
$915$	39.2767	−	39.2767i	1.29845	−	1.29845i
$916$		0			0
$917$	5.00910	+	1.34219i	0.165415	+	0.0443229i
$918$		0			0
$919$	−15.5103	+	8.95488i	−0.511638	+	0.295394i	−0.733507	−	0.679682i	$-0.762118\pi$
$919$	−15.5103	+	8.95488i	−0.511638	+	0.295394i	0.221869	+	0.975076i	$0.428784\pi$
$920$		0			0
$921$	24.0150	−	6.43481i	0.791322	−	0.212034i
$922$		0			0
$923$	−5.35525	−	3.63964i	−0.176270	−	0.119800i
$924$		0			0
$925$	−0.370423	+	0.0992545i	−0.0121794	+	0.00326347i
$926$		0			0
$927$	−4.51631	+	2.60749i	−0.148335	+	0.0856413i
$928$		0			0
$929$	7.24325	−	27.0322i	0.237643	−	0.886897i	−0.739296	−	0.673381i	$-0.764842\pi$
$929$	7.24325	−	27.0322i	0.237643	−	0.886897i	0.976939	−	0.213517i	$-0.0684918\pi$
$930$		0			0
$931$	−12.0895	−	12.0895i	−0.396217	−	0.396217i
$932$		0			0
$933$	55.6734	+	32.1430i	1.82266	+	1.05232i
$934$		0			0
$935$	27.7098	−	7.88141i	0.906208	−	0.257750i
$936$		0			0
$937$			25.9366i			0.847311i	0.905823	+	0.423655i	$0.139253\pi$
$937$			25.9366i			0.847311i	−0.905823	+	0.423655i	$0.860747\pi$
$938$		0			0
$939$	−3.87103	+	6.70482i	−0.126326	+	0.218803i
$940$		0			0
$941$	33.1317	−	33.1317i	1.08006	−	1.08006i	0.0835587	−	0.996503i	$-0.473371\pi$
$941$	33.1317	−	33.1317i	1.08006	−	1.08006i	0.996503	−	0.0835587i	$-0.0266286\pi$
$942$		0			0
$943$	5.80579	−	21.6675i	0.189063	−	0.705591i
$944$		0			0
$945$	22.1610	−	12.7947i	0.720899	−	0.416211i
$946$		0			0
$947$	−12.9297	−	48.2542i	−0.420158	−	1.56805i	−0.774275	−	0.632849i	$-0.781885\pi$
$947$	−12.9297	−	48.2542i	−0.420158	−	1.56805i	0.354118	−	0.935201i	$-0.384781\pi$
$948$		0			0
$949$	39.3600	−	19.0260i	1.27768	−	0.617610i
$950$		0			0
$951$	47.4539	−	12.7152i	1.53880	−	0.412320i
$952$		0			0
$953$	17.0097	+	29.4617i	0.550999	+	0.954358i	0.998203	+	0.0599257i	$0.0190864\pi$
$953$	17.0097	+	29.4617i	0.550999	+	0.954358i	−0.447204	+	0.894432i	$0.647580\pi$
$954$		0			0
$955$	2.41524	−	9.01378i	0.0781552	−	0.291679i
$956$		0			0
$957$	−16.0075	−	8.91799i	−0.517448	−	0.288278i
$958$		0			0
$959$	19.0443	−	32.9857i	0.614973	−	1.06516i
$960$		0			0
$961$		−	28.3634i		−	0.914948i
$962$		0			0
$963$		−	8.96074i		−	0.288756i
$964$		0			0
$965$	37.9653	+	21.9193i	1.22215	+	0.705607i
$966$		0			0
$967$	−13.8902	+	13.8902i	−0.446680	+	0.446680i	−0.894249	−	0.447569i	$-0.852290\pi$
$967$	−13.8902	+	13.8902i	−0.446680	+	0.446680i	0.447569	+	0.894249i	$0.352290\pi$
$968$		0			0
$969$	−51.6348	−	13.8355i	−1.65875	−	0.444460i
$970$		0			0
$971$	−10.0375	−	17.3855i	−0.322120	−	0.557928i	0.658805	−	0.752313i	$-0.271062\pi$
$971$	−10.0375	−	17.3855i	−0.322120	−	0.557928i	−0.980925	+	0.194386i	$0.937729\pi$
$972$		0			0
$973$	3.26828	+	12.1974i	0.104776	+	0.391030i
$974$		0			0
$975$	0.185081	−	0.159748i	0.00592732	−	0.00511604i
$976$		0			0
$977$	1.38110	−	0.370065i	0.0441853	−	0.0118394i	−0.236659	−	0.971593i	$-0.576052\pi$
$977$	1.38110	−	0.370065i	0.0441853	−	0.0118394i	0.280844	+	0.959753i	$0.409386\pi$
$978$		0			0
$979$	−32.4911	+	33.5015i	−1.03842	+	1.07071i
$980$		0			0
$981$	−20.7280	−	5.55406i	−0.661795	−	0.177328i
$982$		0			0
$983$	−27.7638	+	27.7638i	−0.885527	+	0.885527i	−0.994090	−	0.108563i	$-0.965375\pi$
$983$	−27.7638	+	27.7638i	−0.885527	+	0.885527i	0.108563	+	0.994090i	$0.465375\pi$
$984$		0			0
$985$	−10.4948	+	18.1776i	−0.334393	+	0.579186i
$986$		0			0
$987$	15.6599			0.498459
$988$		0			0
$989$		−	7.45567i		−	0.237076i
$990$		0			0
$991$	−0.997301	+	1.72738i	−0.0316803	+	0.0548719i	−0.881431	−	0.472313i	$-0.843419\pi$
$991$	−0.997301	+	1.72738i	−0.0316803	+	0.0548719i	0.849751	+	0.527185i	$0.176753\pi$
$992$		0			0
$993$	13.0547	+	13.0547i	0.414277	+	0.414277i
$994$		0			0
$995$	39.0908	+	10.4744i	1.23926	+	0.332059i
$996$		0			0
$997$	−8.07333	+	4.66114i	−0.255685	+	0.147620i	−0.622365	−	0.782728i	$-0.713828\pi$
$997$	−8.07333	+	4.66114i	−0.255685	+	0.147620i	0.366680	+	0.930347i	$0.380495\pi$
$998$		0			0
$999$	−11.0759	−	41.3357i	−0.350425	−	1.30781i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bc.a.241.4	yes	56
11.10	odd	2	inner	572.2.bc.a.241.3	yes	56
13.2	odd	12	inner	572.2.bc.a.197.3	✓	56
143.54	even	12	inner	572.2.bc.a.197.4	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bc.a.197.3	✓	56	13.2	odd	12	inner
572.2.bc.a.197.4	yes	56	143.54	even	12	inner
572.2.bc.a.241.3	yes	56	11.10	odd	2	inner
572.2.bc.a.241.4	yes	56	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.bc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.02435 + 1.77422i) q^{3} +(-1.58636 - 1.58636i) q^{5} +(0.799284 - 2.98297i) q^{7} +(-0.598575 - 1.03676i) q^{9} +O(q^{10})\)	\(q+(-1.02435 + 1.77422i) q^{3} +(-1.58636 - 1.58636i) q^{5} +(0.799284 - 2.98297i) q^{7} +(-0.598575 - 1.03676i) q^{9} +(1.70209 + 2.84656i) q^{11} +(-1.18584 + 3.40496i) q^{13} +(4.43955 - 1.18957i) q^{15} +(1.93590 + 3.35307i) q^{17} +(6.50958 + 1.74424i) q^{19} +(4.47370 + 4.47370i) q^{21} +(-1.73090 - 0.999337i) q^{23} +0.0330985i q^{25} -3.69349 q^{27} +(2.33549 + 1.34839i) q^{29} +(-1.14818 - 1.14818i) q^{31} +(-6.79396 + 0.104020i) q^{33} +(-6.00003 + 3.46412i) q^{35} +(2.99876 + 11.1915i) q^{37} +(-4.82645 - 5.59181i) q^{39} +(2.90482 + 10.8409i) q^{41} +(1.86515 + 3.23054i) q^{43} +(-0.695124 + 2.59424i) q^{45} +(1.75021 - 1.75021i) q^{47} +(-2.19707 - 1.26848i) q^{49} -7.93212 q^{51} -3.56986 q^{53} +(1.81554 - 7.21581i) q^{55} +(-9.76274 + 9.76274i) q^{57} +(-7.03470 - 1.88494i) q^{59} +(10.4661 - 6.04262i) q^{61} +(-3.57106 + 0.956863i) q^{63} +(7.28268 - 3.52034i) q^{65} +(7.89800 - 2.11626i) q^{67} +(3.54609 - 2.04734i) q^{69} +(-0.464798 + 1.73465i) q^{71} +(-8.57365 - 8.57365i) q^{73} +(-0.0587241 - 0.0339044i) q^{75} +(9.85165 - 2.80207i) q^{77} -9.94056i q^{79} +(5.57914 - 9.66336i) q^{81} +(3.21672 - 3.21672i) q^{83} +(2.24815 - 8.39022i) q^{85} +(-4.78470 + 2.76245i) q^{87} +(3.64193 + 13.5919i) q^{89} +(9.20908 + 6.25886i) q^{91} +(3.21325 - 0.860988i) q^{93} +(-7.55957 - 13.0936i) q^{95} +(-2.31410 + 8.63632i) q^{97} +(1.93238 - 3.46854i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 28 q^{9}+O(q^{10}) \) 56 * q - 28 * q^9	\( 56 q - 28 q^{9} + 4 q^{11} + 8 q^{15} - 12 q^{23} - 24 q^{27} - 4 q^{31} - 10 q^{33} - 12 q^{37} - 64 q^{45} - 8 q^{47} + 40 q^{53} + 22 q^{55} + 48 q^{59} - 36 q^{67} - 48 q^{71} + 120 q^{75} + 28 q^{81} + 28 q^{89} + 36 q^{91} + 20 q^{93} - 68 q^{97} - 44 q^{99}+O(q^{100}) \) 56 * q - 28 * q^9 + 4 * q^11 + 8 * q^15 - 12 * q^23 - 24 * q^27 - 4 * q^31 - 10 * q^33 - 12 * q^37 - 64 * q^45 - 8 * q^47 + 40 * q^53 + 22 * q^55 + 48 * q^59 - 36 * q^67 - 48 * q^71 + 120 * q^75 + 28 * q^81 + 28 * q^89 + 36 * q^91 + 20 * q^93 - 68 * q^97 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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