LMFDB - Embedded newform 420.2.bv.c.233.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [420,2,Mod(53,420)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(420, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 9, 8]))

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

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

chi := DirichletCharacter("420.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	420.bv (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:	$3.35371688489$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			233.8
Character	$\chi$	$=$	420.233
Dual form			420.2.bv.c.137.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.735650 - 1.56806i) q^{3} +(1.16077 - 1.91118i) q^{5} +(-1.34070 + 2.28090i) q^{7} +(-1.91764 - 2.30709i) q^{9} +O(q^{10})$	\(q+(0.735650 - 1.56806i) q^{3} +(1.16077 - 1.91118i) q^{5} +(-1.34070 + 2.28090i) q^{7} +(-1.91764 - 2.30709i) q^{9} +(4.85929 - 2.80551i) q^{11} +(0.354801 + 0.354801i) q^{13} +(-2.14293 - 3.22612i) q^{15} +(0.959140 - 3.57956i) q^{17} +(-2.40962 - 1.39119i) q^{19} +(2.59031 + 3.78025i) q^{21} +(1.06092 + 3.95939i) q^{23} +(-2.30523 - 4.43688i) q^{25} +(-5.02837 + 1.30977i) q^{27} -8.44181 q^{29} +(-0.730482 - 1.26523i) q^{31} +(-0.824484 - 9.68354i) q^{33} +(2.80298 + 5.20992i) q^{35} +(1.95515 + 7.29673i) q^{37} +(0.817359 - 0.295341i) q^{39} -1.89242i q^{41} +(7.19023 + 7.19023i) q^{43} +(-6.63520 + 0.986960i) q^{45} +(10.7725 - 2.88649i) q^{47} +(-3.40505 - 6.11602i) q^{49} +(-4.90738 - 4.13729i) q^{51} +(2.37622 + 0.636707i) q^{53} +(0.278670 - 12.5435i) q^{55} +(-3.95411 + 2.75500i) q^{57} +(5.64924 + 9.78477i) q^{59} +(1.67588 - 2.90270i) q^{61} +(7.83323 - 1.28084i) q^{63} +(1.08993 - 0.266247i) q^{65} +(3.43889 + 0.921448i) q^{67} +(6.98904 + 1.24914i) q^{69} +10.5611i q^{71} +(-2.79345 + 10.4253i) q^{73} +(-8.65315 + 0.350755i) q^{75} +(-0.115747 + 14.8449i) q^{77} +(1.42483 + 0.822628i) q^{79} +(-1.64532 + 8.84833i) q^{81} +(0.481281 - 0.481281i) q^{83} +(-5.72785 - 5.98813i) q^{85} +(-6.21021 + 13.2373i) q^{87} +(7.37227 - 12.7691i) q^{89} +(-1.28495 + 0.333585i) q^{91} +(-2.52134 + 0.214674i) q^{93} +(-5.45583 + 2.99036i) q^{95} +(-5.38134 + 5.38134i) q^{97} +(-15.7909 - 5.83085i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 2 q^{3} - 8 q^{7}+O(q^{10}) $ 48 * q - 2 * q^3 - 8 * q^7	$ 48 q - 2 q^{3} - 8 q^{7} + 32 q^{13} - 16 q^{21} + 16 q^{25} - 32 q^{27} - 64 q^{31} + 34 q^{33} - 40 q^{37} - 24 q^{43} + 30 q^{45} + 36 q^{51} + 92 q^{57} - 18 q^{63} + 28 q^{67} - 8 q^{73} - 38 q^{75} + 20 q^{81} - 56 q^{85} - 24 q^{87} - 24 q^{91} + 6 q^{93} + 56 q^{97}+O(q^{100}) $ 48 * q - 2 * q^3 - 8 * q^7 + 32 * q^13 - 16 * q^21 + 16 * q^25 - 32 * q^27 - 64 * q^31 + 34 * q^33 - 40 * q^37 - 24 * q^43 + 30 * q^45 + 36 * q^51 + 92 * q^57 - 18 * q^63 + 28 * q^67 - 8 * q^73 - 38 * q^75 + 20 * q^81 - 56 * q^85 - 24 * q^87 - 24 * q^91 + 6 * q^93 + 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/420\mathbb{Z}\right)^\times$.

$n$	$211$	$241$	$281$	$337$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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
$3$	0.735650	−	1.56806i	0.424727	−	0.905321i
$3$	0.735650	−	1.56806i	0.424727	−	0.905321i
$4$		0			0
$5$	1.16077	−	1.91118i	0.519112	−	0.854706i
$5$	1.16077	−	1.91118i	0.519112	−	0.854706i
$6$		0			0
$7$	−1.34070	+	2.28090i	−0.506737	+	0.862101i
$7$	−1.34070	+	2.28090i	−0.506737	+	0.862101i
$8$		0			0
$9$	−1.91764	−	2.30709i	−0.639213	−	0.769030i
$10$		0			0
$11$	4.85929	−	2.80551i	1.46513	−	0.845893i	0.465889	−	0.884843i	$-0.345735\pi$
$11$	4.85929	−	2.80551i	1.46513	−	0.845893i	0.999241	+	0.0389498i	$0.0124012\pi$
$12$		0			0
$13$	0.354801	+	0.354801i	0.0984040	+	0.0984040i	0.754595	−	0.656191i	$-0.227833\pi$
$13$	0.354801	+	0.354801i	0.0984040	+	0.0984040i	−0.656191	+	0.754595i	$0.727833\pi$
$14$		0			0
$15$	−2.14293	−	3.22612i	−0.553303	−	0.832980i
$16$		0			0
$17$	0.959140	−	3.57956i	0.232626	−	0.868171i	−0.746579	−	0.665297i	$-0.768305\pi$
$17$	0.959140	−	3.57956i	0.232626	−	0.868171i	0.979205	−	0.202874i	$-0.0650282\pi$
$18$		0			0
$19$	−2.40962	−	1.39119i	−0.552804	−	0.319161i	0.197448	−	0.980313i	$-0.436735\pi$
$19$	−2.40962	−	1.39119i	−0.552804	−	0.319161i	−0.750252	+	0.661152i	$0.770068\pi$
$20$		0			0
$21$	2.59031	+	3.78025i	0.565253	+	0.824918i
$22$		0			0
$23$	1.06092	+	3.95939i	0.221216	+	0.825591i	0.983885	+	0.178802i	$0.0572220\pi$
$23$	1.06092	+	3.95939i	0.221216	+	0.825591i	−0.762669	+	0.646789i	$0.776111\pi$
$24$		0			0
$25$	−2.30523	−	4.43688i	−0.461046	−	0.887376i
$26$		0			0
$27$	−5.02837	+	1.30977i	−0.967710	+	0.252065i
$28$		0			0
$29$	−8.44181			−1.56760			−0.783802	−	0.621010i	$-0.786722\pi$
$29$	−8.44181			−1.56760			−0.783802	+	0.621010i	$0.786722\pi$
$30$		0			0
$31$	−0.730482	−	1.26523i	−0.131198	−	0.227242i	0.792940	−	0.609299i	$-0.208549\pi$
$31$	−0.730482	−	1.26523i	−0.131198	−	0.227242i	−0.924139	+	0.382057i	$0.875216\pi$
$32$		0			0
$33$	−0.824484	−	9.68354i	−0.143524	−	1.68569i
$34$		0			0
$35$	2.80298	+	5.20992i	0.473790	+	0.880638i
$36$		0			0
$37$	1.95515	+	7.29673i	0.321425	+	1.19958i	0.917857	+	0.396911i	$0.129918\pi$
$37$	1.95515	+	7.29673i	0.321425	+	1.19958i	−0.596432	+	0.802664i	$0.703415\pi$
$38$		0			0
$39$	0.817359	−	0.295341i	0.130882	−	0.0472924i
$40$		0			0
$41$		−	1.89242i		−	0.295547i	−0.989021	−	0.147773i	$-0.952789\pi$
$41$		−	1.89242i		−	0.295547i	0.989021	−	0.147773i	$-0.0472106\pi$
$42$		0			0
$43$	7.19023	+	7.19023i	1.09650	+	1.09650i	0.994817	+	0.101682i	$0.0324225\pi$
$43$	7.19023	+	7.19023i	1.09650	+	1.09650i	0.101682	+	0.994817i	$0.467578\pi$
$44$		0			0
$45$	−6.63520	+	0.986960i	−0.989118	+	0.147127i
$46$		0			0
$47$	10.7725	−	2.88649i	1.57133	−	0.421038i	0.635104	−	0.772426i	$-0.280957\pi$
$47$	10.7725	−	2.88649i	1.57133	−	0.421038i	0.936230	+	0.351389i	$0.114290\pi$
$48$		0			0
$49$	−3.40505	−	6.11602i	−0.486435	−	0.873717i
$50$		0			0
$51$	−4.90738	−	4.13729i	−0.687171	−	0.579337i
$52$		0			0
$53$	2.37622	+	0.636707i	0.326399	+	0.0874584i	0.418298	−	0.908310i	$-0.362627\pi$
$53$	2.37622	+	0.636707i	0.326399	+	0.0874584i	−0.0918986	+	0.995768i	$0.529294\pi$
$54$		0			0
$55$	0.278670	−	12.5435i	0.0375759	−	1.69137i
$56$		0			0
$57$	−3.95411	+	2.75500i	−0.523734	+	0.364908i
$58$		0			0
$59$	5.64924	+	9.78477i	0.735468	+	1.27387i	0.954518	+	0.298155i	$0.0963712\pi$
$59$	5.64924	+	9.78477i	0.735468	+	1.27387i	−0.219049	+	0.975714i	$0.570296\pi$
$60$		0			0
$61$	1.67588	−	2.90270i	0.214574	−	0.371653i	−0.738567	−	0.674180i	$-0.764497\pi$
$61$	1.67588	−	2.90270i	0.214574	−	0.371653i	0.953141	+	0.302527i	$0.0978304\pi$
$62$		0			0
$63$	7.83323	−	1.28084i	0.986894	−	0.161370i
$64$		0			0
$65$	1.08993	−	0.266247i	0.135189	−	0.0330239i
$66$		0			0
$67$	3.43889	+	0.921448i	0.420127	+	0.112573i	0.462688	−	0.886521i	$-0.346885\pi$
$67$	3.43889	+	0.921448i	0.420127	+	0.112573i	−0.0425609	+	0.999094i	$0.513552\pi$
$68$		0			0
$69$	6.98904	+	1.24914i	0.841382	+	0.150379i
$70$		0			0
$71$			10.5611i			1.25337i	0.779273	+	0.626685i	$0.215589\pi$
$71$			10.5611i			1.25337i	−0.779273	+	0.626685i	$0.784411\pi$
$72$		0			0
$73$	−2.79345	+	10.4253i	−0.326948	+	1.22019i	0.585391	+	0.810751i	$0.300941\pi$
$73$	−2.79345	+	10.4253i	−0.326948	+	1.22019i	−0.912339	+	0.409436i	$0.865726\pi$
$74$		0			0
$75$	−8.65315	+	0.350755i	−0.999179	+	0.0405017i
$76$		0			0
$77$	−0.115747	+	14.8449i	−0.0131907	+	1.69174i
$78$		0			0
$79$	1.42483	+	0.822628i	0.160306	+	0.0925529i	0.578007	−	0.816032i	$-0.303831\pi$
$79$	1.42483	+	0.822628i	0.160306	+	0.0925529i	−0.417701	+	0.908585i	$0.637164\pi$
$80$		0			0
$81$	−1.64532	+	8.84833i	−0.182813	+	0.983148i
$82$		0			0
$83$	0.481281	−	0.481281i	0.0528275	−	0.0528275i	−0.680200	−	0.733027i	$-0.738107\pi$
$83$	0.481281	−	0.481281i	0.0528275	−	0.0528275i	0.733027	+	0.680200i	$0.238107\pi$
$84$		0			0
$85$	−5.72785	−	5.98813i	−0.621272	−	0.649504i
$86$		0			0
$87$	−6.21021	+	13.2373i	−0.665805	+	1.41919i
$88$		0			0
$89$	7.37227	−	12.7691i	0.781459	−	1.35353i	−0.149633	−	0.988742i	$-0.547809\pi$
$89$	7.37227	−	12.7691i	0.781459	−	1.35353i	0.931092	−	0.364785i	$-0.118858\pi$
$90$		0			0
$91$	−1.28495	+	0.333585i	−0.134699	+	0.0349692i
$92$		0			0
$93$	−2.52134	+	0.214674i	−0.261451	+	0.0222607i
$94$		0			0
$95$	−5.45583	+	2.99036i	−0.559756	+	0.306804i
$96$		0			0
$97$	−5.38134	+	5.38134i	−0.546392	+	0.546392i	−0.925395	−	0.379003i	$-0.876267\pi$
$97$	−5.38134	+	5.38134i	−0.546392	+	0.546392i	0.379003	+	0.925395i	$0.376267\pi$
$98$		0			0
$99$	−15.7909	−	5.83085i	−1.58705	−	0.586022i
$100$		0			0
$101$	0.640605	−	0.369854i	0.0637426	−	0.0368018i	−0.467790	−	0.883840i	$-0.654950\pi$
$101$	0.640605	−	0.369854i	0.0637426	−	0.0368018i	0.531533	+	0.847038i	$0.321616\pi$
$102$		0			0
$103$	4.33168	−	1.16067i	0.426813	−	0.114364i	−0.0390165	−	0.999239i	$-0.512422\pi$
$103$	4.33168	−	1.16067i	0.426813	−	0.114364i	0.465830	+	0.884874i	$0.345756\pi$
$104$		0			0
$105$	10.2315	−	0.562566i	0.998492	−	0.0549008i
$106$		0			0
$107$	−13.7674	+	3.68897i	−1.33095	+	0.356626i	−0.853068	−	0.521800i	$-0.825261\pi$
$107$	−13.7674	+	3.68897i	−1.33095	+	0.356626i	−0.477879	+	0.878426i	$0.658594\pi$
$108$		0			0
$109$	−0.798292	+	0.460894i	−0.0764625	+	0.0441456i	−0.537744	−	0.843108i	$-0.680723\pi$
$109$	−0.798292	+	0.460894i	−0.0764625	+	0.0441456i	0.461281	+	0.887254i	$0.347390\pi$
$110$		0			0
$111$	12.8800	+	2.30203i	1.22252	+	0.218499i
$112$		0			0
$113$	−2.37995	+	2.37995i	−0.223887	+	0.223887i	−0.810133	−	0.586246i	$-0.800605\pi$
$113$	−2.37995	+	2.37995i	−0.223887	+	0.223887i	0.586246	+	0.810133i	$0.300605\pi$
$114$		0			0
$115$	8.79860	+	2.56834i	0.820474	+	0.239499i
$116$		0			0
$117$	0.138177	−	1.49894i	0.0127745	−	0.138577i
$118$		0			0
$119$	6.87871	+	6.98682i	0.630570	+	0.640481i
$120$		0			0
$121$	10.2418	−	17.7393i	0.931071	−	1.61266i
$122$		0			0
$123$	−2.96743	−	1.39216i	−0.267565	−	0.125527i
$124$		0			0
$125$	−11.1555	−	0.744482i	−0.997781	−	0.0665885i
$126$		0			0
$127$	−10.0614	+	10.0614i	−0.892806	+	0.892806i	−0.994786	−	0.101980i	$-0.967482\pi$
$127$	−10.0614	+	10.0614i	−0.892806	+	0.892806i	0.101980	+	0.994786i	$0.467482\pi$
$128$		0			0
$129$	16.5642	−	5.98524i	1.45840	−	0.526971i
$130$		0			0
$131$	6.97835	+	4.02895i	0.609701	+	0.352011i	0.772848	−	0.634591i	$-0.218831\pi$
$131$	6.97835	+	4.02895i	0.609701	+	0.352011i	−0.163147	+	0.986602i	$0.552165\pi$
$132$		0			0
$133$	6.40375	−	3.63093i	0.555275	−	0.314841i
$134$		0			0
$135$	−3.33357	+	11.1305i	−0.286908	+	0.957958i
$136$		0			0
$137$	3.12759	−	11.6723i	0.267208	−	0.997235i	−0.693677	−	0.720287i	$-0.744010\pi$
$137$	3.12759	−	11.6723i	0.267208	−	0.997235i	0.960885	−	0.276948i	$-0.0893231\pi$
$138$		0			0
$139$			16.3972i			1.39079i	0.718628	+	0.695395i	$0.244771\pi$
$139$			16.3972i			1.39079i	−0.718628	+	0.695395i	$0.755229\pi$
$140$		0			0
$141$	3.39861	−	19.0154i	0.286214	−	1.60139i
$142$		0			0
$143$	2.71948	+	0.728682i	0.227414	+	0.0609354i
$144$		0			0
$145$	−9.79899	+	16.1338i	−0.813762	+	1.33984i
$146$		0			0
$147$	−12.0952	+	0.840078i	−0.997597	+	0.0692885i
$148$		0			0
$149$	−4.18906	+	7.25567i	−0.343181	+	0.594407i	−0.985022	−	0.172431i	$-0.944838\pi$
$149$	−4.18906	+	7.25567i	−0.343181	+	0.594407i	0.641840	+	0.766838i	$0.278171\pi$
$150$		0			0
$151$	−0.350603	−	0.607261i	−0.0285316	−	0.0494182i	0.851407	−	0.524506i	$-0.175750\pi$
$151$	−0.350603	−	0.607261i	−0.0285316	−	0.0494182i	−0.879939	+	0.475087i	$0.842416\pi$
$152$		0			0
$153$	−10.0976	+	4.65148i	−0.816346	+	0.376050i
$154$		0			0
$155$	−3.26601	−	0.0725584i	−0.262332	−	0.00582803i
$156$		0			0
$157$	0.781369	+	0.209367i	0.0623600	+	0.0167093i	0.289864	−	0.957068i	$-0.406390\pi$
$157$	0.781369	+	0.209367i	0.0623600	+	0.0167093i	−0.227504	+	0.973777i	$0.573057\pi$
$158$		0			0
$159$	2.74646	−	3.25767i	0.217809	−	0.258350i
$160$		0			0
$161$	−10.4534	−	2.88851i	−0.823841	−	0.227647i
$162$		0			0
$163$	−3.40268	+	0.911747i	−0.266519	+	0.0714135i	−0.389604	−	0.920983i	$-0.627388\pi$
$163$	−3.40268	+	0.911747i	−0.266519	+	0.0714135i	0.123085	+	0.992396i	$0.460721\pi$
$164$		0			0
$165$	−19.4640	−	9.66462i	−1.51527	−	0.752389i
$166$		0			0
$167$	4.96146	+	4.96146i	0.383929	+	0.383929i	0.872516	−	0.488586i	$-0.162487\pi$
$167$	4.96146	+	4.96146i	0.383929	+	0.383929i	−0.488586	+	0.872516i	$0.662487\pi$
$168$		0			0
$169$		−	12.7482i		−	0.980633i
$170$		0			0
$171$	1.41117	+	8.22700i	0.107915	+	0.629134i
$172$		0			0
$173$	−1.66150	−	6.20080i	−0.126322	−	0.471438i	0.873562	−	0.486713i	$-0.161804\pi$
$173$	−1.66150	−	6.20080i	−0.126322	−	0.471438i	−0.999883	+	0.0152749i	$0.995138\pi$
$174$		0			0
$175$	13.2107	+	0.690520i	0.998637	+	0.0521984i
$176$		0			0
$177$	19.4990	−	1.66020i	1.46563	−	0.124788i
$178$		0			0
$179$	−10.8624	−	18.8143i	−0.811896	−	1.40625i	−0.911535	−	0.411222i	$-0.865102\pi$
$179$	−10.8624	−	18.8143i	−0.811896	−	1.40625i	0.0996392	−	0.995024i	$-0.468231\pi$
$180$		0			0
$181$	6.70675			0.498509			0.249254	−	0.968438i	$-0.419814\pi$
$181$	6.70675			0.498509			0.249254	+	0.968438i	$0.419814\pi$
$182$		0			0
$183$	−3.31876	−	4.76325i	−0.245330	−	0.352110i
$184$		0			0
$185$	16.2149	+	4.73317i	1.19214	+	0.347989i
$186$		0			0
$187$	−5.38176	−	20.0850i	−0.393553	−	1.46876i
$188$		0			0
$189$	3.75408	−	13.2252i	0.273069	−	0.961994i
$190$		0			0
$191$	−7.73525	−	4.46595i	−0.559703	−	0.323145i	0.193323	−	0.981135i	$-0.438073\pi$
$191$	−7.73525	−	4.46595i	−0.559703	−	0.323145i	−0.753026	+	0.657990i	$0.771407\pi$
$192$		0			0
$193$	−5.42747	+	20.2556i	−0.390678	+	1.45803i	0.438340	+	0.898809i	$0.355566\pi$
$193$	−5.42747	+	20.2556i	−0.390678	+	1.45803i	−0.829018	+	0.559221i	$0.811100\pi$
$194$		0			0
$195$	0.384315	−	1.90494i	0.0275214	−	0.136416i
$196$		0			0
$197$	−6.77027	−	6.77027i	−0.482362	−	0.482362i	0.423524	−	0.905885i	$-0.360793\pi$
$197$	−6.77027	−	6.77027i	−0.482362	−	0.482362i	−0.905885	+	0.423524i	$0.860793\pi$
$198$		0			0
$199$	−6.41199	+	3.70197i	−0.454534	+	0.262425i	−0.709743	−	0.704461i	$-0.751189\pi$
$199$	−6.41199	+	3.70197i	−0.454534	+	0.262425i	0.255209	+	0.966886i	$0.417856\pi$
$200$		0			0
$201$	3.97471	−	4.71453i	0.280354	−	0.332537i
$202$		0			0
$203$	11.3179	−	19.2550i	0.794363	−	1.35143i
$204$		0			0
$205$	−3.61676	−	2.19666i	−0.252606	−	0.153422i
$206$		0			0
$207$	7.10022	−	10.0403i	0.493499	−	0.697850i
$208$		0			0
$209$	−15.6120			−1.07991
$210$		0			0
$211$	−15.0795			−1.03812			−0.519058	−	0.854739i	$-0.673717\pi$
$211$	−15.0795			−1.03812			−0.519058	+	0.854739i	$0.673717\pi$
$212$		0			0
$213$	16.5604	+	7.76925i	1.13470	+	0.532340i
$214$		0			0
$215$	22.0880	−	5.39563i	1.50639	−	0.367979i
$216$		0			0
$217$	3.86523	+	0.0301376i	0.262389	+	0.00204587i
$218$		0			0
$219$	14.2925	+	12.0497i	0.965798	+	0.814240i
$220$		0			0
$221$	1.61033	−	0.929727i	0.108323	−	0.0625402i
$222$		0			0
$223$	−11.8910	−	11.8910i	−0.796283	−	0.796283i	0.186224	−	0.982507i	$-0.440375\pi$
$223$	−11.8910	−	11.8910i	−0.796283	−	0.796283i	−0.982507	+	0.186224i	$0.940375\pi$
$224$		0			0
$225$	−5.81568	+	13.8267i	−0.387712	+	0.921781i
$226$		0			0
$227$	3.06435	−	11.4363i	0.203388	−	0.759055i	−0.786547	−	0.617531i	$-0.788133\pi$
$227$	3.06435	−	11.4363i	0.203388	−	0.759055i	0.989935	−	0.141524i	$-0.0452003\pi$
$228$		0			0
$229$	14.0898	+	8.13475i	0.931080	+	0.537559i	0.887153	−	0.461476i	$-0.152680\pi$
$229$	14.0898	+	8.13475i	0.931080	+	0.537559i	0.0439269	+	0.999035i	$0.486013\pi$
$230$		0			0
$231$	23.1926	+	11.1022i	1.52596	+	0.730468i
$232$		0			0
$233$	1.88095	+	7.01982i	0.123225	+	0.459884i	0.999770	−	0.0214368i	$-0.00682407\pi$
$233$	1.88095	+	7.01982i	0.123225	+	0.459884i	−0.876545	+	0.481320i	$0.840157\pi$
$234$		0			0
$235$	6.98781	−	23.9388i	0.455834	−	1.56159i
$236$		0			0
$237$	2.33811	−	1.62906i	0.151877	−	0.105819i
$238$		0			0
$239$	22.9991			1.48769			0.743845	−	0.668352i	$-0.233000\pi$
$239$	22.9991			1.48769			0.743845	+	0.668352i	$0.233000\pi$
$240$		0			0
$241$	−12.7879	−	22.1493i	−0.823740	−	1.42676i	−0.902878	−	0.429897i	$-0.858550\pi$
$241$	−12.7879	−	22.1493i	−0.823740	−	1.42676i	0.0791378	−	0.996864i	$-0.474783\pi$
$242$		0			0
$243$	12.6644	+	9.08923i	0.812419	+	0.583074i
$244$		0			0
$245$	−15.6413	−	0.591624i	−0.999285	−	0.0377975i
$246$		0			0
$247$	−0.361337	−	1.34853i	−0.0229913	−	0.0858049i
$248$		0			0
$249$	−0.400625	−	1.10873i	−0.0253886	−	0.0702631i
$250$		0			0
$251$		−	27.8607i		−	1.75855i	−0.476313	−	0.879276i	$-0.658027\pi$
$251$		−	27.8607i		−	1.75855i	0.476313	−	0.879276i	$-0.341973\pi$
$252$		0			0
$253$	16.2634	+	16.2634i	1.02247	+	1.02247i
$254$		0			0
$255$	−13.6035	+	4.57646i	−0.851881	+	0.286589i
$256$		0			0
$257$	−7.65810	+	2.05198i	−0.477699	+	0.127999i	−0.489631	−	0.871930i	$-0.662869\pi$
$257$	−7.65810	+	2.05198i	−0.477699	+	0.127999i	0.0119320	+	0.999929i	$0.496202\pi$
$258$		0			0
$259$	−19.2644	−	5.32321i	−1.19703	−	0.330768i
$260$		0			0
$261$	16.1883	+	19.4760i	1.00203	+	1.20553i
$262$		0			0
$263$	−19.7406	−	5.28947i	−1.21726	−	0.326163i	−0.407651	−	0.913138i	$-0.633652\pi$
$263$	−19.7406	−	5.28947i	−1.21726	−	0.326163i	−0.809605	+	0.586975i	$0.800319\pi$
$264$		0			0
$265$	3.97511	−	3.80232i	0.244189	−	0.233575i
$266$		0			0
$267$	−14.5994	−	20.9538i	−0.893470	−	1.28235i
$268$		0			0
$269$	−9.59686	−	16.6223i	−0.585131	−	1.01348i	−0.994859	−	0.101269i	$-0.967710\pi$
$269$	−9.59686	−	16.6223i	−0.585131	−	1.01348i	0.409728	−	0.912208i	$-0.365624\pi$
$270$		0			0
$271$	2.31420	−	4.00831i	0.140578	−	0.243488i	−0.787137	−	0.616779i	$-0.788437\pi$
$271$	2.31420	−	4.00831i	0.140578	−	0.243488i	0.927714	+	0.373291i	$0.121771\pi$
$272$		0			0
$273$	−0.422189	+	2.26028i	−0.0255521	+	0.136798i
$274$		0			0
$275$	−23.6495	−	15.0927i	−1.42612	−	0.910126i
$276$		0			0
$277$	27.9277	+	7.48322i	1.67802	+	0.449623i	0.967254	−	0.253810i	$-0.0816838\pi$
$277$	27.9277	+	7.48322i	1.67802	+	0.449623i	0.710762	+	0.703433i	$0.248350\pi$
$278$		0			0
$279$	−1.51820	+	4.11154i	−0.0908923	+	0.246152i
$280$		0			0
$281$			2.69129i			0.160549i	0.996773	+	0.0802743i	$0.0255796\pi$
$281$			2.69129i			0.160549i	−0.996773	+	0.0802743i	$0.974420\pi$
$282$		0			0
$283$	3.72033	−	13.8845i	0.221151	−	0.825346i	−0.762759	−	0.646682i	$-0.776156\pi$
$283$	3.72033	−	13.8845i	0.221151	−	0.825346i	0.983910	−	0.178664i	$-0.0571774\pi$
$284$		0			0
$285$	0.675493	+	10.7549i	0.0400128	+	0.637067i
$286$		0			0
$287$	4.31643	+	2.53717i	0.254791	+	0.149764i
$288$		0			0
$289$	2.82913	+	1.63340i	0.166420	+	0.0960825i
$290$		0			0
$291$	4.47949	+	12.3971i	0.262593	+	0.726728i
$292$		0			0
$293$	−4.68014	+	4.68014i	−0.273417	+	0.273417i	−0.830474	−	0.557057i	$-0.811930\pi$
$293$	−4.68014	+	4.68014i	−0.273417	+	0.273417i	0.557057	+	0.830474i	$0.311930\pi$
$294$		0			0
$295$	25.2579	+	0.561137i	1.47057	+	0.0326706i
$296$		0			0
$297$	−20.7597	+	20.4717i	−1.20460	+	1.18789i
$298$		0			0
$299$	−1.02838	+	1.78121i	−0.0594729	+	0.103010i
$300$		0			0
$301$	−26.0402	+	6.76028i	−1.50093	+	0.389656i
$302$		0			0
$303$	−0.108693	−	1.27659i	−0.00624423	−	0.0733383i
$304$		0			0
$305$	−3.60229	−	6.57227i	−0.206266	−	0.376327i
$306$		0			0
$307$	−0.468035	+	0.468035i	−0.0267122	+	0.0267122i	−0.720337	−	0.693625i	$-0.756013\pi$
$307$	−0.468035	+	0.468035i	−0.0267122	+	0.0267122i	0.693625	+	0.720337i	$0.256013\pi$
$308$		0			0
$309$	1.36660	−	7.64620i	0.0777430	−	0.434977i
$310$		0			0
$311$	−10.8991	+	6.29258i	−0.618029	+	0.356819i	−0.776101	−	0.630608i	$-0.782805\pi$
$311$	−10.8991	+	6.29258i	−0.618029	+	0.356819i	0.158072	+	0.987428i	$0.449472\pi$
$312$		0			0
$313$	−15.4699	+	4.14514i	−0.874408	+	0.234297i	−0.667993	−	0.744168i	$-0.732846\pi$
$313$	−15.4699	+	4.14514i	−0.874408	+	0.234297i	−0.206415	+	0.978465i	$0.566180\pi$
$314$		0			0
$315$	6.64466	−	16.4575i	0.374384	−	0.927274i
$316$		0			0
$317$	−10.9034	+	2.92155i	−0.612394	+	0.164091i	−0.551668	−	0.834064i	$-0.686008\pi$
$317$	−10.9034	+	2.92155i	−0.612394	+	0.164091i	−0.0607264	+	0.998154i	$0.519342\pi$
$318$		0			0
$319$	−41.0212	+	23.6836i	−2.29675	+	1.32603i
$320$		0			0
$321$	−4.34346	+	24.3020i	−0.242428	+	1.35640i
$322$		0			0
$323$	−7.29101	+	7.29101i	−0.405683	+	0.405683i
$324$		0			0
$325$	0.756312	−	2.39211i	0.0419526	−	0.132690i
$326$		0			0
$327$	0.135448	+	1.59083i	0.00749026	+	0.0879730i
$328$		0			0
$329$	−7.85892	+	28.4410i	−0.433276	+	1.56800i
$330$		0			0
$331$	−15.2057	+	26.3371i	−0.835782	+	1.44762i	0.0576098	+	0.998339i	$0.481652\pi$
$331$	−15.2057	+	26.3371i	−0.835782	+	1.44762i	−0.893392	+	0.449278i	$0.851681\pi$
$332$		0			0
$333$	13.0849	−	18.5032i	0.717050	−	1.01397i
$334$		0			0
$335$	5.75281	−	5.50275i	0.314310	−	0.300648i
$336$		0			0
$337$	6.99764	−	6.99764i	0.381186	−	0.381186i	−0.490343	−	0.871529i	$-0.663129\pi$
$337$	6.99764	−	6.99764i	0.381186	−	0.381186i	0.871529	+	0.490343i	$0.163129\pi$
$338$		0			0
$339$	1.98110	+	5.48272i	0.107599	+	0.297781i
$340$		0			0
$341$	−7.09924	−	4.09875i	−0.384445	−	0.221960i
$342$		0			0
$343$	18.5152	+	0.433165i	0.999726	+	0.0233887i
$344$		0			0
$345$	10.5000	−	11.9074i	0.565301	−	0.641071i
$346$		0			0
$347$	−4.73743	+	17.6803i	−0.254319	+	0.949130i	0.714150	+	0.699993i	$0.246814\pi$
$347$	−4.73743	+	17.6803i	−0.254319	+	0.949130i	−0.968468	+	0.249137i	$0.919853\pi$
$348$		0			0
$349$			21.3176i			1.14110i	0.821262	+	0.570552i	$0.193271\pi$
$349$			21.3176i			1.14110i	−0.821262	+	0.570552i	$0.806729\pi$
$350$		0			0
$351$	−2.24878	−	1.31936i	−0.120031	−	0.0704224i
$352$		0			0
$353$	0.0780276	+	0.0209074i	0.00415299	+	0.00111279i	0.260895	−	0.965367i	$-0.415982\pi$
$353$	0.0780276	+	0.0209074i	0.00415299	+	0.00111279i	−0.256742	+	0.966480i	$0.582649\pi$
$354$		0			0
$355$	20.1841	+	12.2590i	1.07126	+	0.650639i
$356$		0			0
$357$	16.0161	−	5.64640i	0.847662	−	0.298839i
$358$		0			0
$359$	2.75276	−	4.76793i	0.145285	−	0.251642i	−0.784194	−	0.620516i	$-0.786923\pi$
$359$	2.75276	−	4.76793i	0.145285	−	0.251642i	0.929479	+	0.368874i	$0.120257\pi$
$360$		0			0
$361$	−5.62917	−	9.75001i	−0.296272	−	0.513158i
$362$		0			0
$363$	−20.2819	−	29.1097i	−1.06453	−	1.52786i
$364$		0			0
$365$	16.6821	+	17.4401i	0.873179	+	0.912858i
$366$		0			0
$367$	23.4871	+	6.29334i	1.22601	+	0.328510i	0.813026	−	0.582227i	$-0.197818\pi$
$367$	23.4871	+	6.29334i	1.22601	+	0.328510i	0.412988	+	0.910736i	$0.364485\pi$
$368$		0			0
$369$	−4.36598	+	3.62898i	−0.227284	+	0.188917i
$370$		0			0
$371$	−4.63807	+	4.56630i	−0.240796	+	0.237070i
$372$		0			0
$373$	−18.9361	+	5.07391i	−0.980474	+	0.262717i	−0.713244	−	0.700916i	$-0.752775\pi$
$373$	−18.9361	+	5.07391i	−0.980474	+	0.262717i	−0.267230	+	0.963633i	$0.586108\pi$
$374$		0			0
$375$	−9.37395	+	16.9449i	−0.484069	+	0.875030i
$376$		0			0
$377$	−2.99516	−	2.99516i	−0.154259	−	0.154259i
$378$		0			0
$379$		−	15.7804i		−	0.810583i	−0.914188	−	0.405291i	$-0.867170\pi$
$379$		−	15.7804i		−	0.810583i	0.914188	−	0.405291i	$-0.132830\pi$
$380$		0			0
$381$	8.37525	+	23.1786i	0.429077	+	1.18748i
$382$		0			0
$383$	0.235352	+	0.878346i	0.0120259	+	0.0448814i	0.971678	−	0.236308i	$-0.0759376\pi$
$383$	0.235352	+	0.878346i	0.0120259	+	0.0448814i	−0.959652	+	0.281190i	$0.909271\pi$
$384$		0			0
$385$	28.2370	+	17.4527i	1.43909	+	0.889474i
$386$		0			0
$387$	2.80023	−	30.3767i	0.142344	−	1.54414i
$388$		0			0
$389$	14.2750	+	24.7251i	0.723772	+	1.25361i	0.959477	+	0.281785i	$0.0909266\pi$
$389$	14.2750	+	24.7251i	0.723772	+	1.25361i	−0.235705	+	0.971825i	$0.575740\pi$
$390$		0			0
$391$	15.1905			0.768214
$392$		0			0
$393$	11.4513	−	7.97859i	0.577640	−	0.402466i
$394$		0			0
$395$	3.22610	−	1.76824i	0.162322	−	0.0889696i
$396$		0			0
$397$	−7.43161	−	27.7352i	−0.372982	−	1.39199i	−0.856271	−	0.516527i	$-0.827225\pi$
$397$	−7.43161	−	27.7352i	−0.372982	−	1.39199i	0.483289	−	0.875461i	$-0.339442\pi$
$398$		0			0
$399$	−0.982610	−	12.7126i	−0.0491920	−	0.636424i
$400$		0			0
$401$	0.256628	+	0.148164i	0.0128154	+	0.00739896i	0.506394	−	0.862302i	$-0.330978\pi$
$401$	0.256628	+	0.148164i	0.0128154	+	0.00739896i	−0.493579	+	0.869701i	$0.664311\pi$
$402$		0			0
$403$	0.189730	−	0.708081i	0.00945111	−	0.0352720i
$404$		0			0
$405$	15.0009	+	13.4154i	0.745402	+	0.666615i
$406$		0			0
$407$	29.9717	+	29.9717i	1.48564	+	1.48564i
$408$		0			0
$409$	20.8175	−	12.0190i	1.02936	−	0.594301i	0.112558	−	0.993645i	$-0.464095\pi$
$409$	20.8175	−	12.0190i	1.02936	−	0.594301i	0.916801	+	0.399344i	$0.130762\pi$
$410$		0			0
$411$	−16.0021	−	13.4910i	−0.789327	−	0.665462i
$412$		0			0
$413$	−29.8921	−	0.233072i	−1.47089	−	0.0114687i
$414$		0			0
$415$	−0.361160	−	1.47847i	−0.0177286	−	0.0725754i
$416$		0			0
$417$	25.7118	+	12.0626i	1.25911	+	0.590707i
$418$		0			0
$419$	24.1241			1.17854			0.589269	−	0.807937i	$-0.299416\pi$
$419$	24.1241			1.17854			0.589269	+	0.807937i	$0.299416\pi$
$420$		0			0
$421$	−25.5203			−1.24378			−0.621891	−	0.783104i	$-0.713635\pi$
$421$	−25.5203			−1.24378			−0.621891	+	0.783104i	$0.713635\pi$
$422$		0			0
$423$	−27.3172	−	19.3179i	−1.32821	−	0.939270i
$424$		0			0
$425$	−18.0931	+	3.99612i	−0.877645	+	0.193840i
$426$		0			0
$427$	4.37394	+	7.71417i	0.211670	+	0.373315i
$428$		0			0
$429$	3.14320	−	3.72825i	0.151755	−	0.180002i
$430$		0			0
$431$	−11.8878	+	6.86340i	−0.572613	+	0.330598i	−0.758192	−	0.652031i	$-0.773917\pi$
$431$	−11.8878	+	6.86340i	−0.572613	+	0.330598i	0.185579	+	0.982629i	$0.440584\pi$
$432$		0			0
$433$	−1.57386	−	1.57386i	−0.0756350	−	0.0756350i	0.668277	−	0.743912i	$-0.267032\pi$
$433$	−1.57386	−	1.57386i	−0.0756350	−	0.0756350i	−0.743912	+	0.668277i	$0.767032\pi$
$434$		0			0
$435$	18.0902	+	27.2343i	0.867360	+	1.30578i
$436$		0			0
$437$	2.95188	−	11.0166i	0.141207	−	0.526993i
$438$		0			0
$439$	3.53021	+	2.03816i	0.168487	+	0.0972763i	0.581872	−	0.813280i	$-0.302320\pi$
$439$	3.53021	+	2.03816i	0.168487	+	0.0972763i	−0.413385	+	0.910556i	$0.635654\pi$
$440$		0			0
$441$	−7.58055	+	19.5841i	−0.360978	+	0.932574i
$442$		0			0
$443$	−5.71070	−	21.3126i	−0.271323	−	1.01259i	−0.958265	−	0.285880i	$-0.907714\pi$
$443$	−5.71070	−	21.3126i	−0.271323	−	1.01259i	0.686942	−	0.726712i	$-0.258953\pi$
$444$		0			0
$445$	−15.8467	−	28.9118i	−0.751203	−	1.37055i
$446$		0			0
$447$	8.29566	+	11.9063i	0.392371	+	0.563151i
$448$		0			0
$449$	−0.0268595			−0.00126758			−0.000633788	−	1.00000i	$-0.500202\pi$
$449$	−0.0268595			−0.00126758			−0.000633788		1.00000i	$0.500202\pi$
$450$		0			0
$451$	−5.30921	−	9.19582i	−0.250001	−	0.433014i
$452$		0			0
$453$	−1.21014	+	0.103035i	−0.0568575	+	0.00484101i
$454$		0			0
$455$	−0.853987	+	2.84298i	−0.0400355	+	0.133281i
$456$		0			0
$457$	−0.454415	−	1.69590i	−0.0212566	−	0.0793309i	0.954483	−	0.298266i	$-0.0964083\pi$
$457$	−0.454415	−	1.69590i	−0.0212566	−	0.0793309i	−0.975739	+	0.218935i	$0.929742\pi$
$458$		0			0
$459$	−0.134513	+	19.2556i	−0.00627853	+	0.898775i
$460$		0			0
$461$			27.4449i			1.27824i	0.769108	+	0.639119i	$0.220701\pi$
$461$			27.4449i			1.27824i	−0.769108	+	0.639119i	$0.779299\pi$
$462$		0			0
$463$	−15.0804	−	15.0804i	−0.700846	−	0.700846i	0.263746	−	0.964592i	$-0.415042\pi$
$463$	−15.0804	−	15.0804i	−0.700846	−	0.700846i	−0.964592	+	0.263746i	$0.915042\pi$
$464$		0			0
$465$	−2.51641	+	5.06793i	−0.116696	+	0.235019i
$466$		0			0
$467$	−6.28196	+	1.68325i	−0.290695	+	0.0778914i	−0.401219	−	0.915982i	$-0.631414\pi$
$467$	−6.28196	+	1.68325i	−0.290695	+	0.0778914i	0.110525	+	0.993873i	$0.464747\pi$
$468$		0			0
$469$	−6.71225	+	6.60839i	−0.309943	+	0.305147i
$470$		0			0
$471$	0.903114	−	1.07121i	0.0416133	−	0.0493589i
$472$		0			0
$473$	55.1116	+	14.7671i	2.53404	+	0.678993i
$474$		0			0
$475$	−0.617836	+	13.8982i	−0.0283483	+	0.637693i
$476$		0			0
$477$	−3.08780	−	6.70313i	−0.141381	−	0.306915i
$478$		0			0
$479$	−14.1306	−	24.4749i	−0.645643	−	1.11829i	−0.984153	−	0.177324i	$-0.943256\pi$
$479$	−14.1306	−	24.4749i	−0.645643	−	1.11829i	0.338509	−	0.940963i	$-0.390077\pi$
$480$		0			0
$481$	−1.89520	+	3.28258i	−0.0864135	+	0.149673i
$482$		0			0
$483$	−12.2194	+	14.2666i	−0.556001	+	0.649153i
$484$		0			0
$485$	4.03822	+	16.5312i	0.183366	+	0.750643i
$486$		0			0
$487$	20.8911	+	5.59776i	0.946667	+	0.253659i	0.698947	−	0.715173i	$-0.253652\pi$
$487$	20.8911	+	5.59776i	0.946667	+	0.253659i	0.247720	+	0.968832i	$0.420319\pi$
$488$		0			0
$489$	−1.07351	+	6.00635i	−0.0485457	+	0.271616i
$490$		0			0
$491$			19.7036i			0.889213i	0.895726	+	0.444606i	$0.146656\pi$
$491$			19.7036i			0.889213i	−0.895726	+	0.444606i	$0.853344\pi$
$492$		0			0
$493$	−8.09688	+	30.2180i	−0.364665	+	1.36095i
$494$		0			0
$495$	−29.4734	+	23.4111i	−1.32473	+	1.05225i
$496$		0			0
$497$	−24.0888	−	14.1592i	−1.08053	−	0.635129i
$498$		0			0
$499$	10.1127	+	5.83855i	0.452705	+	0.261370i	0.708972	−	0.705237i	$-0.249159\pi$
$499$	10.1127	+	5.83855i	0.452705	+	0.261370i	−0.256267	+	0.966606i	$0.582493\pi$
$500$		0			0
$501$	11.4298	−	4.12998i	0.510645	−	0.184514i
$502$		0			0
$503$	1.01611	−	1.01611i	0.0453059	−	0.0453059i	−0.684091	−	0.729397i	$-0.739801\pi$
$503$	1.01611	−	1.01611i	0.0453059	−	0.0453059i	0.729397	+	0.684091i	$0.239801\pi$
$504$		0			0
$505$	0.0367374	−	1.65363i	0.00163479	−	0.0735855i
$506$		0			0
$507$	−19.9900	−	9.37823i	−0.887788	−	0.416502i
$508$		0			0
$509$	−0.920899	+	1.59504i	−0.0408181	+	0.0706991i	−0.885713	−	0.464234i	$-0.846330\pi$
$509$	−0.920899	+	1.59504i	−0.0408181	+	0.0706991i	0.844895	+	0.534933i	$0.179663\pi$
$510$		0			0
$511$	−20.0339	−	20.3488i	−0.886247	−	0.900176i
$512$		0			0
$513$	13.9386	+	3.83939i	0.615403	+	0.169513i
$514$		0			0
$515$	2.80983	−	9.62591i	0.123816	−	0.424168i
$516$		0			0
$517$	44.2487	−	44.2487i	1.94606	−	1.94606i
$518$		0			0
$519$	−10.9455	−	1.95628i	−0.480455	−	0.0858712i
$520$		0			0
$521$	33.3936	−	19.2798i	1.46300	−	0.844664i	0.463851	−	0.885913i	$-0.346467\pi$
$521$	33.3936	−	19.2798i	1.46300	−	0.844664i	0.999149	+	0.0412494i	$0.0131338\pi$
$522$		0			0
$523$	−34.3552	+	9.20544i	−1.50225	+	0.402526i	−0.913852	−	0.406048i	$-0.866907\pi$
$523$	−34.3552	+	9.20544i	−1.50225	+	0.402526i	−0.588395	+	0.808574i	$0.700240\pi$
$524$		0			0
$525$	10.8012	−	20.2073i	0.471405	−	0.881917i
$526$		0			0
$527$	−5.22960	+	1.40127i	−0.227805	+	0.0610402i
$528$		0			0
$529$	5.36732	−	3.09883i	0.233362	−	0.134732i
$530$		0			0
$531$	11.7411	−	31.7970i	0.509522	−	1.37987i
$532$		0			0
$533$	0.671433	−	0.671433i	0.0290830	−	0.0290830i
$534$		0			0
$535$	−8.93051	+	30.5941i	−0.386100	+	1.32270i
$536$		0			0
$537$	−37.4929	+	3.19225i	−1.61794	+	0.137756i
$538$		0			0
$539$	−33.7046	−	20.1666i	−1.45176	−	0.868637i
$540$		0			0
$541$	11.4999	−	19.9184i	0.494420	−	0.856361i	−0.505559	−	0.862792i	$-0.668714\pi$
$541$	11.4999	−	19.9184i	0.494420	−	0.856361i	0.999979	+	0.00643114i	$0.00204711\pi$
$542$		0			0
$543$	4.93382	−	10.5166i	0.211730	−	0.451311i
$544$		0			0
$545$	−0.0457804	+	2.06067i	−0.00196102	+	0.0882695i
$546$		0			0
$547$	−11.2947	+	11.2947i	−0.482926	+	0.482926i	−0.906065	−	0.423139i	$-0.860928\pi$
$547$	−11.2947	+	11.2947i	−0.482926	+	0.482926i	0.423139	+	0.906065i	$0.360928\pi$
$548$		0			0
$549$	−9.91052	+	1.69994i	−0.422971	+	0.0725518i
$550$		0			0
$551$	20.3415	+	11.7442i	0.866578	+	0.500319i
$552$		0			0
$553$	−3.78661	+	2.14701i	−0.161023	+	0.0913002i
$554$		0			0
$555$	19.3504	−	21.9440i	0.821377	−	0.931469i
$556$		0			0
$557$	7.62097	−	28.4418i	0.322911	−	1.20512i	−0.593485	−	0.804845i	$-0.702248\pi$
$557$	7.62097	−	28.4418i	0.322911	−	1.20512i	0.916395	−	0.400274i	$-0.131085\pi$
$558$		0			0
$559$			5.10220i			0.215800i
$560$		0			0
$561$	−35.4536	−	6.33658i	−1.49685	−	0.267531i
$562$		0			0
$563$	4.69011	+	1.25671i	0.197664	+	0.0529640i	0.356293	−	0.934374i	$-0.384041\pi$
$563$	4.69011	+	1.25671i	0.197664	+	0.0529640i	−0.158628	+	0.987338i	$0.550707\pi$
$564$		0			0
$565$	1.78595	+	7.31110i	0.0751353	+	0.307580i
$566$		0			0
$567$	−17.9763	−	15.6158i	−0.754934	−	0.655801i
$568$		0			0
$569$	7.18242	−	12.4403i	0.301103	−	0.521525i	−0.675283	−	0.737558i	$-0.735979\pi$
$569$	7.18242	−	12.4403i	0.301103	−	0.521525i	0.976386	+	0.216033i	$0.0693120\pi$
$570$		0			0
$571$	13.1239	+	22.7312i	0.549218	+	0.951273i	0.998328	+	0.0577969i	$0.0184076\pi$
$571$	13.1239	+	22.7312i	0.549218	+	0.951273i	−0.449111	+	0.893476i	$0.648259\pi$
$572$		0			0
$573$	−12.6933	+	8.84398i	−0.530271	+	0.369463i
$574$		0			0
$575$	15.1217	−	13.8345i	0.630619	−	0.576938i
$576$		0			0
$577$	−10.9827	−	2.94280i	−0.457215	−	0.122510i	0.0228586	−	0.999739i	$-0.492723\pi$
$577$	−10.9827	−	2.94280i	−0.457215	−	0.122510i	−0.480073	+	0.877228i	$0.659390\pi$
$578$		0			0
$579$	27.7693	+	23.4116i	1.15405	+	0.972955i
$580$		0			0
$581$	0.452503	+	1.74301i	0.0187730	+	0.0723123i
$582$		0			0
$583$	13.3330	−	3.57257i	0.552198	−	0.147961i
$584$		0			0
$585$	−2.70435	−	2.00400i	−0.111811	−	0.0828552i
$586$		0			0
$587$	−32.7234	−	32.7234i	−1.35064	−	1.35064i	−0.884944	−	0.465697i	$-0.845804\pi$
$587$	−32.7234	−	32.7234i	−1.35064	−	1.35064i	−0.465697	−	0.884944i	$-0.654196\pi$
$588$		0			0
$589$			4.06496i			0.167494i
$590$		0			0
$591$	−15.5967	+	5.63566i	−0.641564	+	0.231820i
$592$		0			0
$593$	1.27068	+	4.74225i	0.0521807	+	0.194741i	0.987096	−	0.160130i	$-0.0511914\pi$
$593$	1.27068	+	4.74225i	0.0521807	+	0.194741i	−0.934915	+	0.354871i	$0.884525\pi$
$594$		0			0
$595$	21.3377	−	5.03638i	0.874760	−	0.206471i
$596$		0			0
$597$	1.08793	+	12.7778i	0.0445262	+	0.522959i
$598$		0			0
$599$	11.3589	+	19.6742i	0.464113	+	0.803868i	0.999161	−	0.0409541i	$-0.0130398\pi$
$599$	11.3589	+	19.6742i	0.464113	+	0.803868i	−0.535048	+	0.844822i	$0.679706\pi$
$600$		0			0
$601$	−38.7931			−1.58240			−0.791202	−	0.611555i	$-0.790544\pi$
$601$	−38.7931			−1.58240			−0.791202	+	0.611555i	$0.790544\pi$
$602$		0			0
$603$	−4.46869	−	9.70083i	−0.181979	−	0.395048i
$604$		0			0
$605$	−22.0147	−	40.1651i	−0.895023	−	1.63294i
$606$		0			0
$607$	−5.08531	−	18.9786i	−0.206406	−	0.770319i	−0.989016	−	0.147806i	$-0.952779\pi$
$607$	−5.08531	−	18.9786i	−0.206406	−	0.770319i	0.782610	−	0.622512i	$-0.213888\pi$
$608$		0			0
$609$	−21.8669	−	31.9121i	−0.886093	−	1.29314i
$610$		0			0
$611$	4.84623	+	2.79797i	0.196057	+	0.113194i
$612$		0			0
$613$	6.04692	−	22.5674i	0.244233	−	0.911490i	−0.729535	−	0.683944i	$-0.760263\pi$
$613$	6.04692	−	22.5674i	0.244233	−	0.911490i	0.973767	−	0.227546i	$-0.0730701\pi$
$614$		0			0
$615$	−6.10518	+	4.05533i	−0.246184	+	0.163527i
$616$		0			0
$617$	26.0352	+	26.0352i	1.04814	+	1.04814i	0.998781	+	0.0493563i	$0.0157170\pi$
$617$	26.0352	+	26.0352i	1.04814	+	1.04814i	0.0493563	+	0.998781i	$0.484283\pi$
$618$		0			0
$619$	−8.79293	+	5.07660i	−0.353418	+	0.204046i	−0.666190	−	0.745782i	$-0.732076\pi$
$619$	−8.79293	+	5.07660i	−0.353418	+	0.204046i	0.312772	+	0.949828i	$0.398743\pi$
$620$		0			0
$621$	−10.5206	−	18.5197i	−0.422176	−	0.743172i
$622$		0			0
$623$	19.2412	+	33.9350i	0.770882	+	1.35958i
$624$		0			0
$625$	−14.3718	+	20.4561i	−0.574873	+	0.818243i
$626$		0			0
$627$	−11.4850	+	24.4806i	−0.458666	+	0.977662i
$628$		0			0
$629$	27.9943			1.11621
$630$		0			0
$631$	10.7854			0.429360			0.214680	−	0.976684i	$-0.431129\pi$
$631$	10.7854			0.429360			0.214680	+	0.976684i	$0.431129\pi$
$632$		0			0
$633$	−11.0932	+	23.6456i	−0.440916	+	0.939828i
$634$		0			0
$635$	7.55021	+	30.9082i	0.299621	+	1.22655i
$636$		0			0
$637$	0.961855	−	3.37808i	0.0381101	−	0.133844i
$638$		0			0
$639$	24.3653	−	20.2523i	0.963878	−	0.801170i
$640$		0			0
$641$	27.2771	−	15.7485i	1.07738	−	0.622026i	0.147193	−	0.989108i	$-0.452976\pi$
$641$	27.2771	−	15.7485i	1.07738	−	0.622026i	0.930189	+	0.367081i	$0.119643\pi$
$642$		0			0
$643$	2.24828	+	2.24828i	0.0886636	+	0.0886636i	0.750048	−	0.661384i	$-0.230031\pi$
$643$	2.24828	+	2.24828i	0.0886636	+	0.0886636i	−0.661384	+	0.750048i	$0.730031\pi$
$644$		0			0
$645$	7.78835	−	38.6047i	0.306666	−	1.52006i
$646$		0			0
$647$	9.72936	−	36.3105i	0.382501	−	1.42751i	−0.459569	−	0.888142i	$-0.651996\pi$
$647$	9.72936	−	36.3105i	0.382501	−	1.42751i	0.842069	−	0.539369i	$-0.181337\pi$
$648$		0			0
$649$	54.9026	+	31.6980i	2.15511	+	1.24426i
$650$		0			0
$651$	2.89071	−	6.03875i	0.113296	−	0.236677i
$652$		0			0
$653$	0.610173	+	2.27720i	0.0238779	+	0.0891135i	0.976837	−	0.213987i	$-0.0686449\pi$
$653$	0.610173	+	2.27720i	0.0238779	+	0.0891135i	−0.952959	+	0.303100i	$0.901978\pi$
$654$		0			0
$655$	15.8003	−	8.66020i	0.617369	−	0.338382i
$656$		0			0
$657$	29.4089	−	13.5472i	1.14735	−	0.528527i
$658$		0			0
$659$	0.552796			0.0215339			0.0107669	−	0.999942i	$-0.496573\pi$
$659$	0.552796			0.0215339			0.0107669	+	0.999942i	$0.496573\pi$
$660$		0			0
$661$	−14.6334	−	25.3458i	−0.569173	−	0.985837i	−0.996648	−	0.0818098i	$-0.973930\pi$
$661$	−14.6334	−	25.3458i	−0.569173	−	0.985837i	0.427475	−	0.904027i	$-0.359403\pi$
$662$		0			0
$663$	−0.273228	−	3.20906i	−0.0106113	−	0.124629i
$664$		0			0
$665$	0.493907	−	16.4534i	0.0191529	−	0.638035i
$666$		0			0
$667$	−8.95606	−	33.4245i	−0.346780	−	1.29420i
$668$		0			0
$669$	−27.3935	+	9.89826i	−1.05910	+	0.382689i
$670$		0			0
$671$		−	18.8068i		−	0.726027i
$672$		0			0
$673$	13.7634	+	13.7634i	0.530542	+	0.530542i	0.920734	−	0.390192i	$-0.127591\pi$
$673$	13.7634	+	13.7634i	0.530542	+	0.530542i	−0.390192	+	0.920734i	$0.627591\pi$
$674$		0			0
$675$	17.4028	+	19.2910i	0.669836	+	0.742509i
$676$		0			0
$677$	7.44300	−	1.99434i	0.286058	−	0.0766489i	−0.112937	−	0.993602i	$-0.536026\pi$
$677$	7.44300	−	1.99434i	0.286058	−	0.0766489i	0.398995	+	0.916953i	$0.369359\pi$
$678$		0			0
$679$	−5.05955	−	19.4891i	−0.194168	−	0.747922i
$680$		0			0
$681$	−15.6786	−	13.2182i	−0.600804	−	0.506523i
$682$		0			0
$683$	−22.6346	−	6.06492i	−0.866089	−	0.232068i	−0.201693	−	0.979449i	$-0.564644\pi$
$683$	−22.6346	−	6.06492i	−0.866089	−	0.232068i	−0.664396	+	0.747381i	$0.731311\pi$
$684$		0			0
$685$	−18.6775	−	19.5263i	−0.713632	−	0.746061i
$686$		0			0
$687$	23.1209	−	16.1094i	0.882119	−	0.614610i
$688$		0			0
$689$	0.617181	+	1.06899i	0.0235127	+	0.0407252i
$690$		0			0
$691$	−0.318591	+	0.551815i	−0.0121198	+	0.0209920i	−0.872022	−	0.489467i	$-0.837191\pi$
$691$	−0.318591	+	0.551815i	−0.0121198	+	0.0209920i	0.859902	+	0.510459i	$0.170525\pi$
$692$		0			0
$693$	34.4705	−	28.2002i	1.30943	−	1.07124i
$694$		0			0
$695$	31.3380	+	19.0333i	1.18872	+	0.721975i
$696$		0			0
$697$	−6.77404	−	1.81510i	−0.256585	−	0.0687517i
$698$		0			0
$699$	12.3912	+	2.21467i	0.468680	+	0.0837666i
$700$		0			0
$701$			33.7903i			1.27624i	0.769937	+	0.638120i	$0.220288\pi$
$701$			33.7903i			1.27624i	−0.769937	+	0.638120i	$0.779712\pi$
$702$		0			0
$703$	5.43999	−	20.3023i	0.205173	−	0.765716i
$704$		0			0
$705$	−32.3969	−	28.5679i	−1.22014	−	1.07593i
$706$		0			0
$707$	−0.0152591	+	1.95702i	−0.000573878	+	0.0736014i
$708$		0			0
$709$	−9.01238	−	5.20330i	−0.338467	−	0.195414i	0.321127	−	0.947036i	$-0.395938\pi$
$709$	−9.01238	−	5.20330i	−0.338467	−	0.195414i	−0.659594	+	0.751622i	$0.729272\pi$
$710$		0			0
$711$	−0.834441	−	4.86472i	−0.0312940	−	0.182441i
$712$		0			0
$713$	4.23457	−	4.23457i	0.158586	−	0.158586i
$714$		0			0
$715$	4.54933	−	4.35158i	0.170135	−	0.162740i
$716$		0			0
$717$	16.9193	−	36.0641i	0.631863	−	1.34684i
$718$		0			0
$719$	−22.3999	+	38.7978i	−0.835376	+	1.44691i	0.0583487	+	0.998296i	$0.481416\pi$
$719$	−22.3999	+	38.7978i	−0.835376	+	1.44691i	−0.893724	+	0.448617i	$0.851917\pi$
$720$		0			0
$721$	−3.16011	+	11.4363i	−0.117689	+	0.425909i
$722$		0			0
$723$	−44.1389	+	3.75811i	−1.64154	+	0.139765i
$724$		0			0
$725$	19.4603	+	37.4553i	0.722738	+	1.39106i
$726$		0			0
$727$	−29.2716	+	29.2716i	−1.08562	+	1.08562i	−0.0896504	+	0.995973i	$0.528575\pi$
$727$	−29.2716	+	29.2716i	−1.08562	+	1.08562i	−0.995973	+	0.0896504i	$0.971425\pi$
$728$		0			0
$729$	23.5690	−	13.1720i	0.872926	−	0.487852i
$730$		0			0
$731$	32.6343	−	18.8414i	1.20702	−	0.696875i
$732$		0			0
$733$	−18.8330	+	5.04628i	−0.695611	+	0.186388i	−0.589264	−	0.807941i	$-0.700582\pi$
$733$	−18.8330	+	5.04628i	−0.695611	+	0.186388i	−0.106347	+	0.994329i	$0.533916\pi$
$734$		0			0
$735$	−12.4342	+	24.0913i	−0.458643	+	0.888621i
$736$		0			0
$737$	19.2957	−	5.17026i	0.710766	−	0.190449i
$738$		0			0
$739$	−33.6491	+	19.4273i	−1.23780	+	0.714645i	−0.968644	−	0.248452i	$-0.920078\pi$
$739$	−33.6491	+	19.4273i	−1.23780	+	0.714645i	−0.269156	+	0.963096i	$0.586745\pi$
$740$		0			0
$741$	−2.38040	−	0.425445i	−0.0874460	−	0.0156291i
$742$		0			0
$743$	16.5948	−	16.5948i	0.608805	−	0.608805i	−0.333829	−	0.942634i	$-0.608341\pi$
$743$	16.5948	−	16.5948i	0.608805	−	0.608805i	0.942634	+	0.333829i	$0.108341\pi$
$744$		0			0
$745$	9.00436	+	16.4282i	0.329894	+	0.601883i
$746$		0			0
$747$	−2.03328	−	0.187435i	−0.0743939	−	0.00685788i
$748$		0			0
$749$	10.0438	−	36.3480i	0.366993	−	1.32813i
$750$		0			0
$751$	7.45444	−	12.9115i	0.272017	−	0.471146i	−0.697362	−	0.716720i	$-0.745643\pi$
$751$	7.45444	−	12.9115i	0.272017	−	0.471146i	0.969378	+	0.245573i	$0.0789761\pi$
$752$		0			0
$753$	−43.6873	−	20.4957i	−1.59205	−	0.746905i
$754$		0			0
$755$	−1.56756	−	0.0348252i	−0.0570492	−	0.00126742i
$756$		0			0
$757$	−24.0812	+	24.0812i	−0.875244	+	0.875244i	−0.993038	−	0.117794i	$-0.962418\pi$
$757$	−24.0812	+	24.0812i	−0.875244	+	0.875244i	0.117794	+	0.993038i	$0.462418\pi$
$758$		0			0
$759$	37.4662	−	13.5379i	1.35994	−	0.491394i
$760$		0			0
$761$	−8.45249	−	4.88005i	−0.306403	−	0.176902i	0.338913	−	0.940818i	$-0.389941\pi$
$761$	−8.45249	−	4.88005i	−0.306403	−	0.176902i	−0.645316	+	0.763916i	$0.723274\pi$
$762$		0			0
$763$	0.0190152	−	2.43875i	0.000688396	−	0.0882886i
$764$		0			0
$765$	−2.83121	+	24.6977i	−0.102363	+	0.892948i
$766$		0			0
$767$	−1.46729	+	5.47600i	−0.0529808	+	0.197727i
$768$		0			0
$769$			21.7405i			0.783983i	0.919969	+	0.391992i	$0.128214\pi$
$769$			21.7405i			0.783983i	−0.919969	+	0.391992i	$0.871786\pi$
$770$		0			0
$771$	−2.41604	+	13.5179i	−0.0870116	+	0.486836i
$772$		0			0
$773$	−19.7897	−	5.30264i	−0.711787	−	0.190723i	−0.115283	−	0.993333i	$-0.536777\pi$
$773$	−19.7897	−	5.30264i	−0.711787	−	0.190723i	−0.596504	+	0.802610i	$0.703444\pi$
$774$		0			0
$775$	−3.92975	+	6.15771i	−0.141161	+	0.221191i
$776$		0			0
$777$	−22.5190	+	26.2918i	−0.807864	+	0.943213i
$778$		0			0
$779$	−2.63272	+	4.56001i	−0.0943270	+	0.163379i
$780$		0			0
$781$	29.6292	+	51.3193i	1.06022	+	1.83635i
$782$		0			0
$783$	42.4485	−	11.0568i	1.51699	−	0.395139i
$784$		0			0
$785$	1.30713	−	1.25031i	0.0466534	−	0.0446255i
$786$		0			0
$787$	−5.65540	−	1.51536i	−0.201593	−	0.0540167i	0.156609	−	0.987661i	$-0.449944\pi$
$787$	−5.65540	−	1.51536i	−0.201593	−	0.0540167i	−0.358203	+	0.933644i	$0.616610\pi$
$788$		0			0
$789$	−22.8164	+	27.0633i	−0.812285	+	0.963478i
$790$		0			0
$791$	−2.23764	−	8.61924i	−0.0795613	−	0.306465i
$792$		0			0
$793$	1.62448	−	0.435279i	0.0576871	−	0.0154572i
$794$		0			0
$795$	−3.03799	−	9.03039i	−0.107746	−	0.320275i
$796$		0			0
$797$	23.9839	+	23.9839i	0.849554	+	0.849554i	0.990077	−	0.140523i	$-0.0448785\pi$
$797$	23.9839	+	23.9839i	0.849554	+	0.849554i	−0.140523	+	0.990077i	$0.544878\pi$
$798$		0			0
$799$		−	41.3294i		−	1.46213i
$800$		0			0
$801$	−43.5969	+	7.47814i	−1.54042	+	0.264227i
$802$		0			0
$803$	15.6741	+	58.4965i	0.553127	+	2.06430i
$804$		0			0
$805$	−17.6544	+	16.6254i	−0.622237	+	0.585968i
$806$		0			0
$807$	−33.1247	+	2.82033i	−1.16604	+	0.0992802i
$808$		0			0
$809$	−3.46923	−	6.00888i	−0.121972	−	0.211261i	0.798573	−	0.601897i	$-0.205588\pi$
$809$	−3.46923	−	6.00888i	−0.121972	−	0.211261i	−0.920545	+	0.390636i	$0.872255\pi$
$810$		0			0
$811$	21.4448			0.753029			0.376515	−	0.926411i	$-0.377122\pi$
$811$	21.4448			0.753029			0.376515	+	0.926411i	$0.377122\pi$
$812$		0			0
$813$	−4.58284	−	6.57752i	−0.160727	−	0.230684i
$814$		0			0
$815$	−2.20722	+	7.56147i	−0.0773155	+	0.264867i
$816$		0			0
$817$	−7.32269	−	27.3287i	−0.256189	−	0.956109i
$818$		0			0
$819$	3.23368	+	2.32479i	0.112994	+	0.0812349i
$820$		0			0
$821$	−40.9600	−	23.6483i	−1.42951	−	0.825330i	−0.432431	−	0.901667i	$-0.642344\pi$
$821$	−40.9600	−	23.6483i	−1.42951	−	0.825330i	−0.997082	+	0.0763370i	$0.975678\pi$
$822$		0			0
$823$	9.96943	−	37.2064i	0.347512	−	1.29693i	−0.542137	−	0.840290i	$-0.682385\pi$
$823$	9.96943	−	37.2064i	0.347512	−	1.29693i	0.889650	−	0.456644i	$-0.150949\pi$
$824$		0			0
$825$	−41.0641	+	25.9809i	−1.42967	+	0.904540i
$826$		0			0
$827$	17.2898	+	17.2898i	0.601225	+	0.601225i	0.940638	−	0.339413i	$-0.110228\pi$
$827$	17.2898	+	17.2898i	0.601225	+	0.601225i	−0.339413	+	0.940638i	$0.610228\pi$
$828$		0			0
$829$	5.14316	−	2.96940i	0.178629	−	0.103132i	−0.408019	−	0.912973i	$-0.633780\pi$
$829$	5.14316	−	2.96940i	0.178629	−	0.103132i	0.586648	+	0.809842i	$0.300447\pi$
$830$		0			0
$831$	32.2792	−	38.2874i	1.11975	−	1.32818i
$832$		0			0
$833$	−25.1586	+	6.32244i	−0.871693	+	0.219060i
$834$		0			0
$835$	15.2414	−	3.72314i	0.527449	−	0.128845i
$836$		0			0
$837$	5.33029	+	5.40529i	0.184242	+	0.186834i
$838$		0			0
$839$	−46.8893			−1.61880			−0.809400	−	0.587258i	$-0.800207\pi$
$839$	−46.8893			−1.61880			−0.809400	+	0.587258i	$0.800207\pi$
$840$		0			0
$841$	42.2642			1.45738
$842$		0			0
$843$	4.22010	+	1.97984i	0.145348	+	0.0681894i
$844$		0			0
$845$	−24.3642	−	14.7978i	−0.838154	−	0.509058i
$846$		0			0
$847$	26.7304	+	47.1436i	0.918469	+	1.61987i
$848$		0			0
$849$	−19.0349	−	16.0478i	−0.653274	−	0.550760i
$850$		0			0
$851$	−26.8164	+	15.4824i	−0.919254	+	0.530731i
$852$		0			0
$853$	17.1149	+	17.1149i	0.586004	+	0.586004i	0.936547	−	0.350543i	$-0.114003\pi$
$853$	17.1149	+	17.1149i	0.586004	+	0.586004i	−0.350543	+	0.936547i	$0.614003\pi$
$854$		0			0
$855$	17.3613	+	6.85265i	0.593745	+	0.234356i
$856$		0			0
$857$	−9.83221	+	36.6943i	−0.335862	+	1.25345i	0.567070	+	0.823670i	$0.308077\pi$
$857$	−9.83221	+	36.6943i	−0.335862	+	1.25345i	−0.902932	+	0.429784i	$0.858590\pi$
$858$		0			0
$859$	40.6274	+	23.4562i	1.38619	+	0.800317i	0.992883	−	0.119091i	$-0.0379980\pi$
$859$	40.6274	+	23.4562i	1.38619	+	0.800317i	0.393306	+	0.919408i	$0.371331\pi$
$860$		0			0
$861$	7.15382	−	4.90197i	0.243802	−	0.167059i
$862$		0			0
$863$	6.48160	+	24.1896i	0.220636	+	0.823425i	0.984106	+	0.177582i	$0.0568274\pi$
$863$	6.48160	+	24.1896i	0.220636	+	0.823425i	−0.763470	+	0.645843i	$0.776506\pi$
$864$		0			0
$865$	−13.7795	−	4.02227i	−0.468516	−	0.136761i
$866$		0			0
$867$	4.64253	−	3.23465i	0.157669	−	0.109854i
$868$		0			0
$869$	9.23157			0.313160
$870$		0			0
$871$	0.893190	+	1.54705i	0.0302646	+	0.0524198i
$872$		0			0
$873$	22.7347	+	2.09576i	0.769453	+	0.0709307i
$874$		0			0
$875$	16.6543	−	24.4466i	0.563018	−	0.826444i
$876$		0			0
$877$	6.96471	+	25.9927i	0.235182	+	0.877710i	0.978067	+	0.208291i	$0.0667901\pi$
$877$	6.96471	+	25.9927i	0.235182	+	0.877710i	−0.742885	+	0.669419i	$0.766543\pi$
$878$		0			0
$879$	3.89581	+	10.7817i	0.131402	+	0.363658i
$880$		0			0
$881$			23.4482i			0.789991i	0.918683	+	0.394996i	$0.129254\pi$
$881$			23.4482i			0.789991i	−0.918683	+	0.394996i	$0.870746\pi$
$882$		0			0
$883$	13.3238	+	13.3238i	0.448382	+	0.448382i	0.894816	−	0.446434i	$-0.147306\pi$
$883$	13.3238	+	13.3238i	0.448382	+	0.448382i	−0.446434	+	0.894816i	$0.647306\pi$
$884$		0			0
$885$	19.4609	−	39.1932i	0.654171	−	1.31747i
$886$		0			0
$887$	−40.9386	+	10.9695i	−1.37458	+	0.368319i	−0.869151	−	0.494547i	$-0.835334\pi$
$887$	−40.9386	+	10.9695i	−1.37458	+	0.368319i	−0.505433	+	0.862866i	$0.668667\pi$
$888$		0			0
$889$	−9.45978	−	36.4385i	−0.317271	−	1.22211i
$890$		0			0
$891$	16.8290	+	47.6125i	0.563793	+	1.59508i
$892$		0			0
$893$	−29.9733	−	8.03132i	−1.00302	−	0.268758i
$894$		0			0
$895$	−48.5663	−	1.07896i	−1.62339	−	0.0360657i
$896$		0			0
$897$	2.03652	+	2.92291i	0.0679974	+	0.0975933i
$898$		0			0
$899$	6.16659	+	10.6808i	0.205667	+	0.356226i
$900$		0			0
$901$	4.55826	−	7.89513i	0.151858	−	0.263025i
$902$		0			0
$903$	−8.55589	+	45.8058i	−0.284722	+	1.52432i
$904$		0			0
$905$	7.78499	−	12.8178i	0.258782	−	0.426079i
$906$		0			0
$907$	−8.95873	−	2.40049i	−0.297470	−	0.0797068i	0.106997	−	0.994259i	$-0.465876\pi$
$907$	−8.95873	−	2.40049i	−0.297470	−	0.0797068i	−0.404467	+	0.914552i	$0.632543\pi$
$908$		0			0
$909$	−2.08174	−	0.768687i	−0.0690468	−	0.0254958i
$910$		0			0
$911$		−	25.2501i		−	0.836573i	−0.908315	−	0.418286i	$-0.862631\pi$
$911$		−	25.2501i		−	0.836573i	0.908315	−	0.418286i	$-0.137369\pi$
$912$		0			0
$913$	0.988444	−	3.68893i	0.0327127	−	0.122086i
$914$		0			0
$915$	−12.9558	+	0.813722i	−0.428304	+	0.0269008i
$916$		0			0
$917$	−18.5455	+	10.5153i	−0.612427	+	0.347247i
$918$		0			0
$919$	−16.7217	−	9.65429i	−0.551599	−	0.318466i	0.198168	−	0.980168i	$-0.436501\pi$
$919$	−16.7217	−	9.65429i	−0.551599	−	0.318466i	−0.749767	+	0.661702i	$0.769834\pi$
$920$		0			0
$921$	0.389599	+	1.07822i	0.0128377	+	0.0355285i
$922$		0			0
$923$	−3.74708	+	3.74708i	−0.123337	+	0.123337i
$924$		0			0
$925$	27.8676	−	25.4954i	0.916283	−	0.838284i
$926$		0			0
$927$	−10.9844	−	7.76783i	−0.360774	−	0.255129i
$928$		0			0
$929$	19.3847	−	33.5754i	0.635993	−	1.10157i	−0.350311	−	0.936633i	$-0.613924\pi$
$929$	19.3847	−	33.5754i	0.635993	−	1.10157i	0.986304	−	0.164938i	$-0.0527425\pi$
$930$		0			0
$931$	−0.303705	+	19.4743i	−0.00995354	+	0.638245i
$932$		0			0
$933$	1.84926	+	21.7195i	0.0605421	+	0.711066i
$934$		0			0
$935$	−44.6330	−	13.0285i	−1.45966	−	0.426078i
$936$		0			0
$937$	5.52036	−	5.52036i	0.180342	−	0.180342i	−0.611163	−	0.791505i	$-0.709298\pi$
$937$	5.52036	−	5.52036i	0.180342	−	0.180342i	0.791505	+	0.611163i	$0.209298\pi$
$938$		0			0
$939$	−4.88056	+	27.3071i	−0.159271	+	0.891132i
$940$		0			0
$941$	−11.0638	+	6.38770i	−0.360670	+	0.208233i	−0.669375	−	0.742925i	$-0.733438\pi$
$941$	−11.0638	+	6.38770i	−0.360670	+	0.208233i	0.308704	+	0.951158i	$0.400105\pi$
$942$		0			0
$943$	7.49284	−	2.00770i	0.244001	−	0.0653797i
$944$		0			0
$945$	−20.9182	−	22.5262i	−0.680469	−	0.732776i
$946$		0			0
$947$	25.3411	−	6.79014i	0.823477	−	0.220650i	0.177611	−	0.984101i	$-0.443163\pi$
$947$	25.3411	−	6.79014i	0.823477	−	0.220650i	0.645866	+	0.763451i	$0.276497\pi$
$948$		0			0
$949$	−4.69002	+	2.70778i	−0.152244	+	0.0878983i
$950$		0			0
$951$	−3.43989	+	19.2464i	−0.111546	+	0.624107i
$952$		0			0
$953$	40.2920	−	40.2920i	1.30518	−	1.30518i	0.380336	−	0.924848i	$-0.375808\pi$
$953$	40.2920	−	40.2920i	1.30518	−	1.30518i	0.924848	−	0.380336i	$-0.124192\pi$
$954$		0			0
$955$	−17.5141	+	9.59953i	−0.566742	+	0.310634i
$956$		0			0
$957$	6.96013	+	81.7466i	0.224989	+	2.64249i
$958$		0			0
$959$	22.4303	+	22.7828i	0.724312	+	0.735696i
$960$		0			0
$961$	14.4328	−	24.9983i	0.465574	−	0.806398i
$962$		0			0
$963$	34.9117	+	24.6886i	1.12501	+	0.795577i
$964$		0			0
$965$	32.4121	+	33.8850i	1.04338	+	1.09080i
$966$		0			0
$967$	−36.8309	+	36.8309i	−1.18440	+	1.18440i	−0.205810	+	0.978592i	$0.565983\pi$
$967$	−36.8309	+	36.8309i	−1.18440	+	1.18440i	−0.978592	+	0.205810i	$0.934017\pi$
$968$		0			0
$969$	6.06913	+	16.7964i	0.194969	+	0.539578i
$970$		0			0
$971$	2.79105	+	1.61141i	0.0895690	+	0.0517127i	0.544115	−	0.839010i	$-0.316865\pi$
$971$	2.79105	+	1.61141i	0.0895690	+	0.0517127i	−0.454547	+	0.890723i	$0.650199\pi$
$972$		0			0
$973$	−37.4004	−	21.9837i	−1.19900	−	0.704765i
$974$		0			0
$975$	−3.19459	−	2.94570i	−0.102309	−	0.0943378i
$976$		0			0
$977$	−0.825778	+	3.08185i	−0.0264190	+	0.0985970i	−0.977876	−	0.209183i	$-0.932919\pi$
$977$	−0.825778	+	3.08185i	−0.0264190	+	0.0985970i	0.951457	+	0.307780i	$0.0995862\pi$
$978$		0			0
$979$		−	82.7319i		−	2.64412i
$980$		0			0
$981$	2.59416	+	0.957901i	0.0828251	+	0.0305834i
$982$		0			0
$983$	9.84111	+	2.63692i	0.313883	+	0.0841046i	0.412321	−	0.911038i	$-0.364718\pi$
$983$	9.84111	+	2.63692i	0.313883	+	0.0841046i	−0.0984385	+	0.995143i	$0.531385\pi$
$984$		0			0
$985$	−20.7979	+	5.08049i	−0.662677	+	0.161878i
$986$		0			0
$987$	38.8159	+	33.2459i	1.23552	+	1.05823i
$988$		0			0
$989$	−20.8407	+	36.0972i	−0.662696	+	1.14782i
$990$		0			0
$991$	20.4323	+	35.3898i	0.649054	+	1.12419i	0.983349	+	0.181726i	$0.0581684\pi$
$991$	20.4323	+	35.3898i	0.649054	+	1.12419i	−0.334295	+	0.942468i	$0.608498\pi$
$992$		0			0
$993$	30.1121	+	43.2184i	0.955579	+	1.37149i
$994$		0			0
$995$	−0.367715	+	16.5516i	−0.0116573	+	0.524721i
$996$		0			0
$997$	−19.9314	−	5.34061i	−0.631234	−	0.169139i	−0.0710045	−	0.997476i	$-0.522620\pi$
$997$	−19.9314	−	5.34061i	−0.631234	−	0.169139i	−0.560230	+	0.828337i	$0.689287\pi$
$998$		0			0
$999$	−19.3883	−	34.1299i	−0.613418	−	1.07982i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	420.2.bv.c.233.8	yes	48
3.2	odd	2	inner	420.2.bv.c.233.6	yes	48
5.2	odd	4	inner	420.2.bv.c.317.3	yes	48
7.4	even	3	inner	420.2.bv.c.53.1	✓	48
15.2	even	4	inner	420.2.bv.c.317.1	yes	48
21.11	odd	6	inner	420.2.bv.c.53.3	yes	48
35.32	odd	12	inner	420.2.bv.c.137.6	yes	48
105.32	even	12	inner	420.2.bv.c.137.8	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bv.c.53.1	✓	48	7.4	even	3	inner
420.2.bv.c.53.3	yes	48	21.11	odd	6	inner
420.2.bv.c.137.6	yes	48	35.32	odd	12	inner
420.2.bv.c.137.8	yes	48	105.32	even	12	inner
420.2.bv.c.233.6	yes	48	3.2	odd	2	inner
420.2.bv.c.233.8	yes	48	1.1	even	1	trivial
420.2.bv.c.317.1	yes	48	15.2	even	4	inner
420.2.bv.c.317.3	yes	48	5.2	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:	\( N \)	\(=\)	\( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	420.bv (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.735650 - 1.56806i) q^{3} +(1.16077 - 1.91118i) q^{5} +(-1.34070 + 2.28090i) q^{7} +(-1.91764 - 2.30709i) q^{9} +O(q^{10})\)	\(q+(0.735650 - 1.56806i) q^{3} +(1.16077 - 1.91118i) q^{5} +(-1.34070 + 2.28090i) q^{7} +(-1.91764 - 2.30709i) q^{9} +(4.85929 - 2.80551i) q^{11} +(0.354801 + 0.354801i) q^{13} +(-2.14293 - 3.22612i) q^{15} +(0.959140 - 3.57956i) q^{17} +(-2.40962 - 1.39119i) q^{19} +(2.59031 + 3.78025i) q^{21} +(1.06092 + 3.95939i) q^{23} +(-2.30523 - 4.43688i) q^{25} +(-5.02837 + 1.30977i) q^{27} -8.44181 q^{29} +(-0.730482 - 1.26523i) q^{31} +(-0.824484 - 9.68354i) q^{33} +(2.80298 + 5.20992i) q^{35} +(1.95515 + 7.29673i) q^{37} +(0.817359 - 0.295341i) q^{39} -1.89242i q^{41} +(7.19023 + 7.19023i) q^{43} +(-6.63520 + 0.986960i) q^{45} +(10.7725 - 2.88649i) q^{47} +(-3.40505 - 6.11602i) q^{49} +(-4.90738 - 4.13729i) q^{51} +(2.37622 + 0.636707i) q^{53} +(0.278670 - 12.5435i) q^{55} +(-3.95411 + 2.75500i) q^{57} +(5.64924 + 9.78477i) q^{59} +(1.67588 - 2.90270i) q^{61} +(7.83323 - 1.28084i) q^{63} +(1.08993 - 0.266247i) q^{65} +(3.43889 + 0.921448i) q^{67} +(6.98904 + 1.24914i) q^{69} +10.5611i q^{71} +(-2.79345 + 10.4253i) q^{73} +(-8.65315 + 0.350755i) q^{75} +(-0.115747 + 14.8449i) q^{77} +(1.42483 + 0.822628i) q^{79} +(-1.64532 + 8.84833i) q^{81} +(0.481281 - 0.481281i) q^{83} +(-5.72785 - 5.98813i) q^{85} +(-6.21021 + 13.2373i) q^{87} +(7.37227 - 12.7691i) q^{89} +(-1.28495 + 0.333585i) q^{91} +(-2.52134 + 0.214674i) q^{93} +(-5.45583 + 2.99036i) q^{95} +(-5.38134 + 5.38134i) q^{97} +(-15.7909 - 5.83085i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 2 q^{3} - 8 q^{7}+O(q^{10}) \) 48 * q - 2 * q^3 - 8 * q^7	\( 48 q - 2 q^{3} - 8 q^{7} + 32 q^{13} - 16 q^{21} + 16 q^{25} - 32 q^{27} - 64 q^{31} + 34 q^{33} - 40 q^{37} - 24 q^{43} + 30 q^{45} + 36 q^{51} + 92 q^{57} - 18 q^{63} + 28 q^{67} - 8 q^{73} - 38 q^{75} + 20 q^{81} - 56 q^{85} - 24 q^{87} - 24 q^{91} + 6 q^{93} + 56 q^{97}+O(q^{100}) \) 48 * q - 2 * q^3 - 8 * q^7 + 32 * q^13 - 16 * q^21 + 16 * q^25 - 32 * q^27 - 64 * q^31 + 34 * q^33 - 40 * q^37 - 24 * q^43 + 30 * q^45 + 36 * q^51 + 92 * q^57 - 18 * q^63 + 28 * q^67 - 8 * q^73 - 38 * q^75 + 20 * q^81 - 56 * q^85 - 24 * q^87 - 24 * q^91 + 6 * q^93 + 56 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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