LMFDB - Embedded newform 920.2.bv.a.17.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [920,2,Mod(17,920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(920, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 0, 11, 14]))

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

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

chi := DirichletCharacter("920.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 920 = 2^{3} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	920.bv (of order $44$, degree $20$, 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:	$7.34623698596$
Analytic rank:	$0$
Dimension:	$720$
Relative dimension:	$36$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			17.11
Character	$\chi$	$=$	920.17
Dual form			920.2.bv.a.433.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.25117 + 0.683192i) q^{3} +(-2.21439 + 0.310585i) q^{5} +(1.08006 + 1.44279i) q^{7} +(-0.523240 + 0.814177i) q^{9} +(-0.838110 + 0.382752i) q^{11} +(-2.55861 - 1.91535i) q^{13} +(2.55840 - 1.90145i) q^{15} +(0.172280 + 2.40878i) q^{17} +(-2.33469 - 2.69438i) q^{19} +(-2.33704 - 1.06729i) q^{21} +(2.67427 - 3.98099i) q^{23} +(4.80707 - 1.37551i) q^{25} +(0.403516 - 5.64190i) q^{27} +(5.38824 + 4.66893i) q^{29} +(-3.38961 + 0.995279i) q^{31} +(0.787127 - 1.05148i) q^{33} +(-2.83978 - 2.85945i) q^{35} +(-5.63382 + 1.22556i) q^{37} +(4.50981 + 0.648413i) q^{39} +(4.48092 - 2.87971i) q^{41} +(-4.50132 - 8.24355i) q^{43} +(0.905787 - 1.96542i) q^{45} +(-7.74918 - 7.74918i) q^{47} +(1.05702 - 3.59987i) q^{49} +(-1.86121 - 2.89611i) q^{51} +(-0.873743 + 0.654076i) q^{53} +(1.73703 - 1.10787i) q^{55} +(4.76188 + 1.77609i) q^{57} +(5.72104 - 0.822561i) q^{59} +(-2.47142 - 8.41688i) q^{61} +(-1.73981 + 0.124434i) q^{63} +(6.26064 + 3.44667i) q^{65} +(-3.47499 - 9.31680i) q^{67} +(-0.626195 + 6.80795i) q^{69} +(3.57510 - 7.82838i) q^{71} +(-9.21950 - 0.659392i) q^{73} +(-5.07474 + 5.00516i) q^{75} +(-1.45744 - 0.795820i) q^{77} +(0.194438 + 1.35234i) q^{79} +(2.14350 + 4.69360i) q^{81} +(0.760562 + 3.49625i) q^{83} +(-1.12963 - 5.28049i) q^{85} +(-9.93140 - 2.16044i) q^{87} +(6.35945 + 1.86730i) q^{89} -5.76021i q^{91} +(3.56102 - 3.56102i) q^{93} +(6.00676 + 5.24129i) q^{95} +(-3.95701 + 18.1901i) q^{97} +(0.126905 - 0.882640i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) $ 720 * q - 20 * q^23 + 16 * q^25 - 24 * q^27 - 16 * q^31 + 88 * q^37 - 32 * q^41 + 56 * q^47 - 40 * q^55 + 88 * q^57 + 16 * q^73 - 140 * q^75 - 48 * q^77 + 40 * q^81 - 92 * q^85 - 88 * q^87 + 72 * q^93 - 248 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$.

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$1$	$e\left(\frac{7}{22}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	−1.25117	+	0.683192i	−0.722365	+	0.394441i	−0.797970	−	0.602697i	$-0.794093\pi$
$3$	−1.25117	+	0.683192i	−0.722365	+	0.394441i	0.0756053	+	0.997138i	$0.475911\pi$
$4$		0			0
$5$	−2.21439	+	0.310585i	−0.990307	+	0.138898i
$5$	−2.21439	+	0.310585i	−0.990307	+	0.138898i
$6$		0			0
$7$	1.08006	+	1.44279i	0.408223	+	0.545322i	0.956788	−	0.290786i	$-0.0939166\pi$
$7$	1.08006	+	1.44279i	0.408223	+	0.545322i	−0.548565	+	0.836108i	$0.684826\pi$
$8$		0			0
$9$	−0.523240	+	0.814177i	−0.174413	+	0.271392i
$10$		0			0
$11$	−0.838110	+	0.382752i	−0.252700	+	0.115404i	−0.537738	−	0.843112i	$-0.680721\pi$
$11$	−0.838110	+	0.382752i	−0.252700	+	0.115404i	0.285038	+	0.958516i	$0.407994\pi$
$12$		0			0
$13$	−2.55861	−	1.91535i	−0.709630	−	0.531222i	0.182386	−	0.983227i	$-0.441618\pi$
$13$	−2.55861	−	1.91535i	−0.709630	−	0.531222i	−0.892015	+	0.452005i	$0.850709\pi$
$14$		0			0
$15$	2.55840	−	1.90145i	0.660576	−	0.490953i
$16$		0			0
$17$	0.172280	+	2.40878i	0.0417840	+	0.584216i	0.974613	+	0.223897i	$0.0718778\pi$
$17$	0.172280	+	2.40878i	0.0417840	+	0.584216i	−0.932829	+	0.360320i	$0.882668\pi$
$18$		0			0
$19$	−2.33469	−	2.69438i	−0.535615	−	0.618133i	0.421856	−	0.906663i	$-0.361379\pi$
$19$	−2.33469	−	2.69438i	−0.535615	−	0.618133i	−0.957471	+	0.288530i	$0.906833\pi$
$20$		0			0
$21$	−2.33704	−	1.06729i	−0.509984	−	0.232902i
$22$		0			0
$23$	2.67427	−	3.98099i	0.557624	−	0.830094i
$23$	2.67427	−	3.98099i	0.557624	−	0.830094i
$24$		0			0
$25$	4.80707	−	1.37551i	0.961415	−	0.275103i
$26$		0			0
$27$	0.403516	−	5.64190i	0.0776568	−	1.08578i
$28$		0			0
$29$	5.38824	+	4.66893i	1.00057	+	0.866999i	0.991122	−	0.132956i	$-0.0424469\pi$
$29$	5.38824	+	4.66893i	1.00057	+	0.866999i	0.00944858	+	0.999955i	$0.496992\pi$
$30$		0			0
$31$	−3.38961	+	0.995279i	−0.608792	+	0.178757i	−0.571575	−	0.820550i	$-0.693667\pi$
$31$	−3.38961	+	0.995279i	−0.608792	+	0.178757i	−0.0372167	+	0.999307i	$0.511849\pi$
$32$		0			0
$33$	0.787127	−	1.05148i	0.137021	−	0.183039i
$34$		0			0
$35$	−2.83978	−	2.85945i	−0.480010	−	0.483335i
$36$		0			0
$37$	−5.63382	+	1.22556i	−0.926194	+	0.201481i	−0.650274	−	0.759700i	$-0.725346\pi$
$37$	−5.63382	+	1.22556i	−0.926194	+	0.201481i	−0.275920	+	0.961181i	$0.588982\pi$
$38$		0			0
$39$	4.50981	+	0.648413i	0.722148	+	0.103829i
$40$		0			0
$41$	4.48092	−	2.87971i	0.699802	−	0.449735i	−0.141757	−	0.989902i	$-0.545275\pi$
$41$	4.48092	−	2.87971i	0.699802	−	0.449735i	0.841558	+	0.540166i	$0.181639\pi$
$42$		0			0
$43$	−4.50132	−	8.24355i	−0.686445	−	1.25713i	−0.955780	−	0.294083i	$-0.904986\pi$
$43$	−4.50132	−	8.24355i	−0.686445	−	1.25713i	0.269335	−	0.963047i	$-0.413196\pi$
$44$		0			0
$45$	0.905787	−	1.96542i	0.135027	−	0.292987i
$46$		0			0
$47$	−7.74918	−	7.74918i	−1.13033	−	1.13033i	−0.990121	−	0.140213i	$-0.955221\pi$
$47$	−7.74918	−	7.74918i	−1.13033	−	1.13033i	−0.140213	−	0.990121i	$-0.544779\pi$
$48$		0			0
$49$	1.05702	−	3.59987i	0.151002	−	0.514267i
$50$		0			0
$51$	−1.86121	−	2.89611i	−0.260622	−	0.405536i
$52$		0			0
$53$	−0.873743	+	0.654076i	−0.120018	+	0.0898442i	−0.657601	−	0.753367i	$-0.728429\pi$
$53$	−0.873743	+	0.654076i	−0.120018	+	0.0898442i	0.537583	+	0.843211i	$0.319338\pi$
$54$		0			0
$55$	1.73703	−	1.10787i	0.234221	−	0.149385i
$56$		0			0
$57$	4.76188	+	1.77609i	0.630727	+	0.235249i
$58$		0			0
$59$	5.72104	−	0.822561i	0.744816	−	0.107088i	0.240550	−	0.970637i	$-0.422672\pi$
$59$	5.72104	−	0.822561i	0.744816	−	0.107088i	0.504266	+	0.863548i	$0.331763\pi$
$60$		0			0
$61$	−2.47142	−	8.41688i	−0.316433	−	1.07767i	−0.952120	−	0.305724i	$-0.901101\pi$
$61$	−2.47142	−	8.41688i	−0.316433	−	1.07767i	0.635687	−	0.771947i	$-0.280717\pi$
$62$		0			0
$63$	−1.73981	+	0.124434i	−0.219196	+	0.0156772i
$64$		0			0
$65$	6.26064	+	3.44667i	0.776536	+	0.427507i
$66$		0			0
$67$	−3.47499	−	9.31680i	−0.424537	−	1.13823i	−0.956569	−	0.291504i	$-0.905844\pi$
$67$	−3.47499	−	9.31680i	−0.424537	−	1.13823i	0.532032	−	0.846724i	$-0.321429\pi$
$68$		0			0
$69$	−0.626195	+	6.80795i	−0.0753850	+	0.819581i
$70$		0			0
$71$	3.57510	−	7.82838i	0.424287	−	0.929058i	−0.569933	−	0.821691i	$-0.693031\pi$
$71$	3.57510	−	7.82838i	0.424287	−	0.929058i	0.994219	−	0.107367i	$-0.0342419\pi$
$72$		0			0
$73$	−9.21950	−	0.659392i	−1.07906	−	0.0771759i	−0.479528	−	0.877526i	$-0.659192\pi$
$73$	−9.21950	−	0.659392i	−1.07906	−	0.0771759i	−0.599532	+	0.800350i	$0.704647\pi$
$74$		0			0
$75$	−5.07474	+	5.00516i	−0.585981	+	0.577946i
$76$		0			0
$77$	−1.45744	−	0.795820i	−0.166090	−	0.0906921i
$78$		0			0
$79$	0.194438	+	1.35234i	0.0218759	+	0.152151i	0.997832	−	0.0658186i	$-0.0209659\pi$
$79$	0.194438	+	1.35234i	0.0218759	+	0.152151i	−0.975956	+	0.217969i	$0.930057\pi$
$80$		0			0
$81$	2.14350	+	4.69360i	0.238166	+	0.521512i
$82$		0			0
$83$	0.760562	+	3.49625i	0.0834825	+	0.383763i	0.999863	−	0.0165451i	$-0.00526672\pi$
$83$	0.760562	+	3.49625i	0.0834825	+	0.383763i	−0.916381	+	0.400308i	$0.868903\pi$
$84$		0			0
$85$	−1.12963	−	5.28049i	−0.122525	−	0.572749i
$86$		0			0
$87$	−9.93140	−	2.16044i	−1.06476	−	0.231624i
$88$		0			0
$89$	6.35945	+	1.86730i	0.674100	+	0.197934i	0.600828	−	0.799378i	$-0.294838\pi$
$89$	6.35945	+	1.86730i	0.674100	+	0.197934i	0.0732721	+	0.997312i	$0.476656\pi$
$90$		0			0
$91$		−	5.76021i		−	0.603834i
$92$		0			0
$93$	3.56102	−	3.56102i	0.369261	−	0.369261i
$94$		0			0
$95$	6.00676	+	5.24129i	0.616281	+	0.537745i
$96$		0			0
$97$	−3.95701	+	18.1901i	−0.401773	+	1.84692i	0.118544	+	0.992949i	$0.462177\pi$
$97$	−3.95701	+	18.1901i	−0.401773	+	1.84692i	−0.520317	+	0.853973i	$0.674186\pi$
$98$		0			0
$99$	0.126905	−	0.882640i	0.0127544	−	0.0887087i
$100$		0			0
$101$	0.755886	+	0.485778i	0.0752134	+	0.0483367i	0.577707	−	0.816244i	$-0.303948\pi$
$101$	0.755886	+	0.485778i	0.0752134	+	0.0483367i	−0.502494	+	0.864581i	$0.667584\pi$
$102$		0			0
$103$	1.78867	−	4.79562i	0.176243	−	0.472527i	−0.818550	−	0.574435i	$-0.805222\pi$
$103$	1.78867	−	4.79562i	0.176243	−	0.472527i	0.994794	+	0.101908i	$0.0324947\pi$
$104$		0			0
$105$	5.50661	+	1.63755i	0.537390	+	0.159809i
$106$		0			0
$107$	4.42829	−	8.10981i	0.428099	−	0.784005i	−0.571224	−	0.820794i	$-0.693531\pi$
$107$	4.42829	−	8.10981i	0.428099	−	0.784005i	0.999323	+	0.0367890i	$0.0117130\pi$
$108$		0			0
$109$	−3.04348	+	3.51236i	−0.291512	+	0.336423i	−0.882548	−	0.470222i	$-0.844174\pi$
$109$	−3.04348	+	3.51236i	−0.291512	+	0.336423i	0.591036	+	0.806645i	$0.298719\pi$
$110$		0			0
$111$	6.21159	−	5.38237i	0.589578	−	0.510872i
$112$		0			0
$113$	16.4525	−	6.13645i	1.54772	−	0.577269i	0.576843	−	0.816855i	$-0.304284\pi$
$113$	16.4525	−	6.13645i	1.54772	−	0.577269i	0.970875	+	0.239586i	$0.0770117\pi$
$114$		0			0
$115$	−4.68545	+	9.64606i	−0.436921	+	0.899500i
$116$		0			0
$117$	2.89820	−	1.08097i	0.267938	−	0.0999358i
$118$		0			0
$119$	−3.28929	+	2.85019i	−0.301529	+	0.261276i
$120$		0			0
$121$	−6.64754	+	7.67167i	−0.604322	+	0.697424i
$122$		0			0
$123$	−3.63901	+	6.66435i	−0.328118	+	0.600904i
$124$		0			0
$125$	−10.2175	+	4.53893i	−0.913884	+	0.405975i
$126$		0			0
$127$	−2.05910	+	5.52066i	−0.182715	+	0.489879i	−0.995725	−	0.0923718i	$-0.970555\pi$
$127$	−2.05910	+	5.52066i	−0.182715	+	0.489879i	0.813009	+	0.582251i	$0.197828\pi$
$128$		0			0
$129$	11.2639	+	7.23884i	0.991727	+	0.637345i
$130$		0			0
$131$	−1.41728	+	9.85737i	−0.123828	+	0.861242i	0.829328	+	0.558762i	$0.188724\pi$
$131$	−1.41728	+	9.85737i	−0.123828	+	0.861242i	−0.953156	+	0.302480i	$0.902185\pi$
$132$		0			0
$133$	1.36581	−	6.27855i	0.118431	−	0.544419i
$134$		0			0
$135$	0.858744	+	12.6187i	0.0739089	+	1.08604i
$136$		0			0
$137$	−11.1812	+	11.1812i	−0.955277	+	0.955277i	−0.999042	−	0.0437647i	$-0.986065\pi$
$137$	−11.1812	+	11.1812i	−0.955277	+	0.955277i	0.0437647	+	0.999042i	$0.486065\pi$
$138$		0			0
$139$			7.93759i			0.673257i	0.941637	+	0.336629i	$0.109287\pi$
$139$			7.93759i			0.673257i	−0.941637	+	0.336629i	$0.890713\pi$
$140$		0			0
$141$	14.9898	+	4.40139i	1.26237	+	0.370664i
$142$		0			0
$143$	2.87749	+	0.625961i	0.240628	+	0.0523455i
$144$		0			0
$145$	−13.3818	−	8.66535i	−1.11130	−	0.719618i
$146$		0			0
$147$	1.13689	+	5.22620i	0.0937692	+	0.431050i
$148$		0			0
$149$	−0.539036	−	1.18032i	−0.0441596	−	0.0966959i	0.886266	−	0.463176i	$-0.153290\pi$
$149$	−0.539036	−	1.18032i	−0.0441596	−	0.0966959i	−0.930426	+	0.366480i	$0.880563\pi$
$150$		0			0
$151$	1.27342	+	8.85683i	0.103629	+	0.720759i	0.973700	+	0.227832i	$0.0731638\pi$
$151$	1.27342	+	8.85683i	0.103629	+	0.720759i	−0.870071	+	0.492926i	$0.835927\pi$
$152$		0			0
$153$	−2.05132	−	1.12011i	−0.165839	−	0.0905552i
$154$		0			0
$155$	7.19681	−	3.25670i	0.578061	−	0.261584i
$156$		0			0
$157$	−13.8103	−	0.987735i	−1.10218	−	0.0788298i	−0.491630	−	0.870804i	$-0.663599\pi$
$157$	−13.8103	−	0.987735i	−1.10218	−	0.0788298i	−0.610555	+	0.791974i	$0.709053\pi$
$158$		0			0
$159$	0.646344	−	1.41530i	0.0512584	−	0.112240i
$160$		0			0
$161$	8.63208	−	0.441291i	0.680304	−	0.0347786i
$162$		0			0
$163$	−5.31017	−	14.2371i	−0.415925	−	1.11514i	−0.960951	−	0.276719i	$-0.910753\pi$
$163$	−5.31017	−	14.2371i	−0.415925	−	1.11514i	0.545026	−	0.838419i	$-0.316520\pi$
$164$		0			0
$165$	−1.41644	+	2.57286i	−0.110269	+	0.200297i
$166$		0			0
$167$	−19.8464	+	1.41944i	−1.53576	+	0.109840i	−0.813412	−	0.581688i	$-0.802392\pi$
$167$	−19.8464	+	1.41944i	−1.53576	+	0.109840i	−0.722350	+	0.691528i	$0.756938\pi$
$168$		0			0
$169$	−0.784619	−	2.67217i	−0.0603553	−	0.205551i
$170$		0			0
$171$	3.41530	−	0.491047i	0.261175	−	0.0375513i
$172$		0			0
$173$	−18.1716	−	6.77764i	−1.38156	−	0.515295i	−0.454680	−	0.890655i	$-0.650246\pi$
$173$	−18.1716	−	6.77764i	−1.38156	−	0.515295i	−0.926879	+	0.375360i	$0.877519\pi$
$174$		0			0
$175$	7.17649	+	5.44995i	0.542491	+	0.411978i
$176$		0			0
$177$	−6.59605	+	4.93774i	−0.495789	+	0.371143i
$178$		0			0
$179$	−0.0841560	−	0.130949i	−0.00629011	−	0.00978761i	0.838094	−	0.545525i	$-0.183670\pi$
$179$	−0.0841560	−	0.130949i	−0.00629011	−	0.00978761i	−0.844384	+	0.535738i	$0.820034\pi$
$180$		0			0
$181$	2.79815	−	9.52964i	0.207985	−	0.708332i	−0.787743	−	0.616004i	$-0.788751\pi$
$181$	2.79815	−	9.52964i	0.207985	−	0.708332i	0.995729	−	0.0923289i	$-0.0294311\pi$
$182$		0			0
$183$	8.84252	+	8.84252i	0.653658	+	0.653658i
$184$		0			0
$185$	12.0948	−	4.46365i	0.889231	−	0.328174i
$186$		0			0
$187$	−1.06636	−	1.95288i	−0.0779797	−	0.142809i
$188$		0			0
$189$	8.57588	−	5.51138i	0.623803	−	0.400894i
$190$		0			0
$191$	0.324078	+	0.0465954i	0.0234495	+	0.00337153i	0.154030	−	0.988066i	$-0.450775\pi$
$191$	0.324078	+	0.0465954i	0.0234495	+	0.00337153i	−0.130580	+	0.991438i	$0.541684\pi$
$192$		0			0
$193$	20.5529	−	4.47102i	1.47943	−	0.321831i	0.600827	−	0.799379i	$-0.294838\pi$
$193$	20.5529	−	4.47102i	1.47943	−	0.321831i	0.878605	+	0.477549i	$0.158475\pi$
$194$		0			0
$195$	−10.1879	−	0.0351621i	−0.729569	−	0.00251801i
$196$		0			0
$197$	−8.02053	+	10.7142i	−0.571439	+	0.763353i	−0.989416	−	0.145104i	$-0.953648\pi$
$197$	−8.02053	+	10.7142i	−0.571439	+	0.763353i	0.417977	+	0.908457i	$0.362739\pi$
$198$		0			0
$199$	−5.25073	+	1.54175i	−0.372214	+	0.109292i	−0.462489	−	0.886625i	$-0.653044\pi$
$199$	−5.25073	+	1.54175i	−0.372214	+	0.109292i	0.0902750	+	0.995917i	$0.471225\pi$
$200$		0			0
$201$	10.7130	+	9.28285i	0.755635	+	0.654762i
$202$		0			0
$203$	−0.916675	+	12.8168i	−0.0643380	+	0.899563i
$204$		0			0
$205$	−9.02812	+	7.76852i	−0.630551	+	0.542577i
$206$		0			0
$207$	1.84194	+	4.26034i	0.128024	+	0.296114i
$208$		0			0
$209$	2.98801	+	1.36458i	0.206685	+	0.0943897i
$210$		0			0
$211$	−0.175427	−	0.202454i	−0.0120769	−	0.0139375i	0.749679	−	0.661802i	$-0.230208\pi$
$211$	−0.175427	−	0.202454i	−0.0120769	−	0.0139375i	−0.761756	+	0.647864i	$0.775662\pi$
$212$		0			0
$213$	0.875218	+	12.2371i	0.0599689	+	0.838475i
$214$		0			0
$215$	12.5280	+	16.8564i	0.854403	+	1.14960i
$216$		0			0
$217$	−5.09694	−	3.81553i	−0.346003	−	0.259015i
$218$		0			0
$219$	11.9857	−	5.47368i	0.809917	−	0.369877i
$220$		0			0
$221$	4.17287	−	6.49311i	0.280697	−	0.436774i
$222$		0			0
$223$	−8.90492	−	11.8956i	−0.596318	−	0.796587i	0.396268	−	0.918135i	$-0.370305\pi$
$223$	−8.90492	−	11.8956i	−0.596318	−	0.796587i	−0.992586	+	0.121548i	$0.961214\pi$
$224$		0			0
$225$	−1.39534	+	4.63353i	−0.0930227	+	0.308902i
$226$		0			0
$227$	0.406569	−	0.222004i	0.0269849	−	0.0147349i	−0.465700	−	0.884943i	$-0.654197\pi$
$227$	0.406569	−	0.222004i	0.0269849	−	0.0147349i	0.492685	+	0.870208i	$0.336016\pi$
$228$		0			0
$229$	−20.8758			−1.37951			−0.689754	−	0.724043i	$-0.742282\pi$
$229$	−20.8758			−1.37951			−0.689754	+	0.724043i	$0.742282\pi$
$230$		0			0
$231$	2.36720			0.155750
$232$		0			0
$233$	0.590738	−	0.322567i	0.0387005	−	0.0211321i	−0.459782	−	0.888032i	$-0.652073\pi$
$233$	0.590738	−	0.322567i	0.0387005	−	0.0211321i	0.498483	+	0.866900i	$0.333891\pi$
$234$		0			0
$235$	19.5665	+	14.7530i	1.27638	+	0.962377i
$236$		0			0
$237$	−1.16719	−	1.55918i	−0.0758169	−	0.101279i
$238$		0			0
$239$	−3.09736	+	4.81959i	−0.200352	+	0.311753i	−0.926862	−	0.375402i	$-0.877505\pi$
$239$	−3.09736	+	4.81959i	−0.200352	+	0.311753i	0.726510	+	0.687156i	$0.241141\pi$
$240$		0			0
$241$	−8.90636	+	4.06740i	−0.573709	+	0.262004i	−0.681073	−	0.732216i	$-0.738486\pi$
$241$	−8.90636	+	4.06740i	−0.573709	+	0.262004i	0.107364	+	0.994220i	$0.465759\pi$
$242$		0			0
$243$	7.69580	+	5.76101i	0.493686	+	0.369569i
$244$		0			0
$245$	−1.22259	+	8.29981i	−0.0781081	+	0.530256i
$246$		0			0
$247$	0.812884	+	11.3656i	0.0517226	+	0.723176i
$248$		0			0
$249$	−3.34020	−	3.85480i	−0.211677	−	0.244288i
$250$		0			0
$251$	−7.11609	−	3.24981i	−0.449164	−	0.205126i	0.177973	−	0.984035i	$-0.443046\pi$
$251$	−7.11609	−	3.24981i	−0.449164	−	0.205126i	−0.627137	+	0.778909i	$0.715773\pi$
$252$		0			0
$253$	−0.717601	+	4.36009i	−0.0451152	+	0.274116i
$254$		0			0
$255$	5.02095	+	5.83505i	0.314424	+	0.365405i
$256$		0			0
$257$	1.38235	−	19.3278i	0.0862289	−	1.20564i	−0.751568	−	0.659655i	$-0.770702\pi$
$257$	1.38235	−	19.3278i	0.0862289	−	1.20564i	0.837797	−	0.545982i	$-0.183843\pi$
$258$		0			0
$259$	−7.85307	−	6.80472i	−0.487966	−	0.422825i
$260$		0			0
$261$	−6.62068	+	1.94401i	−0.409810	+	0.120331i
$262$		0			0
$263$	−7.79069	+	10.4071i	−0.480394	+	0.641732i	−0.973622	−	0.228169i	$-0.926726\pi$
$263$	−7.79069	+	10.4071i	−0.480394	+	0.641732i	0.493227	+	0.869901i	$0.335817\pi$
$264$		0			0
$265$	1.73166	−	1.71975i	0.106375	−	0.105644i
$266$		0			0
$267$	−9.23250	+	2.00841i	−0.565020	+	0.122912i
$268$		0			0
$269$	15.0088	+	2.15793i	0.915100	+	0.131572i	0.583747	−	0.811935i	$-0.301586\pi$
$269$	15.0088	+	2.15793i	0.915100	+	0.131572i	0.331353	+	0.943507i	$0.392495\pi$
$270$		0			0
$271$	17.9864	−	11.5591i	1.09259	−	0.702168i	0.135162	−	0.990824i	$-0.456845\pi$
$271$	17.9864	−	11.5591i	1.09259	−	0.702168i	0.957433	+	0.288655i	$0.0932082\pi$
$272$		0			0
$273$	3.93533	+	7.20702i	0.238177	+	0.436189i
$274$		0			0
$275$	−3.50237	+	2.99275i	−0.211201	+	0.180469i
$276$		0			0
$277$	7.89093	+	7.89093i	0.474120	+	0.474120i	0.903245	−	0.429125i	$-0.141178\pi$
$277$	7.89093	+	7.89093i	0.474120	+	0.474120i	−0.429125	+	0.903245i	$0.641178\pi$
$278$		0			0
$279$	0.963245	−	3.28051i	0.0576680	−	0.196399i
$280$		0			0
$281$	8.22119	+	12.7924i	0.490435	+	0.763132i	0.994961	−	0.100265i	$-0.0319689\pi$
$281$	8.22119	+	12.7924i	0.490435	+	0.763132i	−0.504526	+	0.863397i	$0.668333\pi$
$282$		0			0
$283$	15.0376	−	11.2570i	0.893890	−	0.669158i	−0.0502376	−	0.998737i	$-0.515998\pi$
$283$	15.0376	−	11.2570i	0.893890	−	0.669158i	0.944128	+	0.329579i	$0.106907\pi$
$284$		0			0
$285$	−11.0963	−	2.45399i	−0.657289	−	0.145362i
$286$		0			0
$287$	8.99446	+	3.35476i	0.530926	+	0.198025i
$288$		0			0
$289$	11.0544	−	1.58938i	0.650259	−	0.0934931i
$290$		0			0
$291$	−7.47641	−	25.4623i	−0.438275	−	1.49263i
$292$		0			0
$293$	5.04255	−	0.360650i	0.294589	−	0.0210694i	0.0767374	−	0.997051i	$-0.475550\pi$
$293$	5.04255	−	0.360650i	0.294589	−	0.0210694i	0.217851	+	0.975982i	$0.430095\pi$
$294$		0			0
$295$	−12.4132	+	3.59834i	−0.722722	+	0.209504i
$296$		0			0
$297$	1.82126	+	4.88297i	0.105680	+	0.283339i
$298$		0			0
$299$	−14.4674	+	5.06362i	−0.836670	+	0.292837i
$300$		0			0
$301$	7.03201	−	15.3979i	0.405318	−	0.887523i
$302$		0			0
$303$	−1.27762	−	0.0913774i	−0.0733976	−	0.00524950i
$304$		0			0
$305$	8.08685	+	17.8707i	0.463052	+	1.02327i
$306$		0			0
$307$	−12.5117	−	6.83191i	−0.714081	−	0.389918i	0.0807618	−	0.996733i	$-0.474265\pi$
$307$	−12.5117	−	6.83191i	−0.714081	−	0.389918i	−0.794842	+	0.606816i	$0.792447\pi$
$308$		0			0
$309$	1.03839	+	7.22216i	0.0590720	+	0.410855i
$310$		0			0
$311$	−14.0200	−	30.6994i	−0.794999	−	1.74081i	−0.661752	−	0.749723i	$-0.730187\pi$
$311$	−14.0200	−	30.6994i	−0.794999	−	1.74081i	−0.133248	−	0.991083i	$-0.542541\pi$
$312$		0			0
$313$	−1.76838	−	8.12910i	−0.0999546	−	0.459484i	−0.999732	−	0.0231354i	$-0.992635\pi$
$313$	−1.76838	−	8.12910i	−0.0999546	−	0.459484i	0.899778	−	0.436349i	$-0.143729\pi$
$314$		0			0
$315$	3.81398	−	0.815905i	0.214894	−	0.0459710i
$316$		0			0
$317$	−3.89967	−	0.848321i	−0.219027	−	0.0476465i	0.101712	−	0.994814i	$-0.467568\pi$
$317$	−3.89967	−	0.848321i	−0.219027	−	0.0476465i	−0.320740	+	0.947167i	$0.603931\pi$
$318$		0			0
$319$	−6.30298	−	1.85072i	−0.352899	−	0.103620i
$320$		0			0
$321$			13.1722i			0.735198i
$322$		0			0
$323$	6.08796	−	6.08796i	0.338743	−	0.338743i
$324$		0			0
$325$	−14.9340	−	5.68782i	−0.828389	−	0.315504i
$326$		0			0
$327$	1.40830	−	6.47385i	0.0778792	−	0.358005i
$328$		0			0
$329$	2.81086	−	19.5500i	0.154968	−	1.07783i
$330$		0			0
$331$	30.5478	+	19.6319i	1.67906	+	1.07906i	0.874131	+	0.485691i	$0.161432\pi$
$331$	30.5478	+	19.6319i	1.67906	+	1.07906i	0.804927	+	0.593374i	$0.202205\pi$
$332$		0			0
$333$	1.95001	−	5.22819i	0.106860	−	0.286503i
$334$		0			0
$335$	10.5886	+	19.5518i	0.578520	+	1.06823i
$336$		0			0
$337$	0.815261	−	1.49304i	0.0444101	−	0.0813310i	−0.854531	−	0.519400i	$-0.826156\pi$
$337$	0.815261	−	1.49304i	0.0444101	−	0.0813310i	0.898941	+	0.438069i	$0.144337\pi$
$338$		0			0
$339$	−16.3925	+	18.9180i	−0.890319	+	1.02748i
$340$		0			0
$341$	2.45992	−	2.13153i	0.133212	−	0.115429i
$342$		0			0
$343$	18.1559	−	6.77180i	0.980326	−	0.365643i
$344$		0			0
$345$	−0.727803	−	15.2700i	−0.0391836	−	0.822107i
$346$		0			0
$347$	16.4586	−	6.13875i	0.883545	−	0.329545i	0.133592	−	0.991036i	$-0.457349\pi$
$347$	16.4586	−	6.13875i	0.883545	−	0.329545i	0.749953	+	0.661491i	$0.230076\pi$
$348$		0			0
$349$	−3.14997	+	2.72947i	−0.168614	+	0.146105i	−0.735080	−	0.677980i	$-0.762856\pi$
$349$	−3.14997	+	2.72947i	−0.168614	+	0.146105i	0.566466	+	0.824085i	$0.308310\pi$
$350$		0			0
$351$	−11.8386	+	13.6625i	−0.631900	+	0.729251i
$352$		0			0
$353$	−7.15925	+	13.1112i	−0.381048	+	0.697838i	−0.995866	−	0.0908311i	$-0.971048\pi$
$353$	−7.15925	+	13.1112i	−0.381048	+	0.697838i	0.614818	+	0.788669i	$0.289229\pi$
$354$		0			0
$355$	−5.48530	+	18.4455i	−0.291130	+	0.978985i
$356$		0			0
$357$	2.16825	−	5.81330i	0.114756	−	0.307672i
$358$		0			0
$359$	−16.3017	−	10.4765i	−0.860371	−	0.552927i	0.0344223	−	0.999407i	$-0.489041\pi$
$359$	−16.3017	−	10.4765i	−0.860371	−	0.552927i	−0.894793	+	0.446480i	$0.852677\pi$
$360$		0			0
$361$	0.895094	−	6.22552i	0.0471102	−	0.327659i
$362$		0			0
$363$	3.07600	−	14.1401i	0.161448	−	0.742165i
$364$		0			0
$365$	20.6204	−	1.40328i	1.07932	−	0.0734513i
$366$		0			0
$367$	12.4880	−	12.4880i	0.651867	−	0.651867i	−0.301575	−	0.953442i	$-0.597512\pi$
$367$	12.4880	−	12.4880i	0.651867	−	0.651867i	0.953442	+	0.301575i	$0.0975125\pi$
$368$		0			0
$369$			5.15504i			0.268361i
$370$		0			0
$371$	−1.88738	−	0.554186i	−0.0979881	−	0.0287719i
$372$		0			0
$373$	−29.7955	−	6.48162i	−1.54275	−	0.335606i	−0.640893	−	0.767631i	$-0.721436\pi$
$373$	−29.7955	−	6.48162i	−1.54275	−	0.335606i	−0.901862	+	0.432025i	$0.857799\pi$
$374$		0			0
$375$	9.68295	−	12.6595i	0.500025	−	0.653736i
$376$		0			0
$377$	−4.84374	−	22.2663i	−0.249465	−	1.14677i
$378$		0			0
$379$	8.36153	+	18.3092i	0.429503	+	0.940480i	0.993407	+	0.114640i	$0.0365715\pi$
$379$	8.36153	+	18.3092i	0.429503	+	0.940480i	−0.563904	+	0.825840i	$0.690701\pi$
$380$		0			0
$381$	−1.19538	−	8.31406i	−0.0612412	−	0.425942i
$382$		0			0
$383$	−30.0261	−	16.3955i	−1.53426	−	0.837772i	−0.534293	−	0.845299i	$-0.679422\pi$
$383$	−30.0261	−	16.3955i	−1.53426	−	0.837772i	−0.999972	+	0.00752762i	$0.997604\pi$
$384$		0			0
$385$	3.47450	+	1.30960i	0.177077	+	0.0667434i
$386$		0			0
$387$	9.06698	+	0.648483i	0.460900	+	0.0329642i
$388$		0			0
$389$	3.98230	−	8.72001i	0.201910	−	0.442122i	−0.781407	−	0.624022i	$-0.785497\pi$
$389$	3.98230	−	8.72001i	0.201910	−	0.442122i	0.983317	+	0.181900i	$0.0582247\pi$
$390$		0			0
$391$	10.0501	+	5.75590i	0.508254	+	0.291088i
$392$		0			0
$393$	−4.96122	−	13.3015i	−0.250261	−	0.670974i
$394$		0			0
$395$	−0.850579	−	2.93423i	−0.0427973	−	0.147637i
$396$		0			0
$397$	0.833700	−	0.0596274i	0.0418422	−	0.00299261i	−0.0504024	−	0.998729i	$-0.516050\pi$
$397$	0.833700	−	0.0596274i	0.0418422	−	0.00299261i	0.0922446	+	0.995736i	$0.470596\pi$
$398$		0			0
$399$	2.58058	+	8.78866i	0.129191	+	0.439983i
$400$		0			0
$401$	−34.6591	+	4.98323i	−1.73079	+	0.248851i	−0.934476	−	0.356027i	$-0.884131\pi$
$401$	−34.6591	+	4.98323i	−1.73079	+	0.248851i	−0.796319	+	0.604877i	$0.793222\pi$
$402$		0			0
$403$	10.5790	+	3.94575i	0.526976	+	0.196552i
$404$		0			0
$405$	−6.20431	−	9.72775i	−0.308295	−	0.483376i
$406$		0			0
$407$	4.25267	−	3.18351i	0.210797	−	0.157801i
$408$		0			0
$409$	−12.6757	−	19.7237i	−0.626772	−	0.975276i	−0.998891	−	0.0470909i	$-0.985005\pi$
$409$	−12.6757	−	19.7237i	−0.626772	−	0.975276i	0.372119	−	0.928185i	$-0.378631\pi$
$410$		0			0
$411$	6.35073	−	21.6286i	0.313258	−	1.06686i
$412$		0			0
$413$	7.36583	+	7.36583i	0.362449	+	0.362449i
$414$		0			0
$415$	−2.77006	−	7.50585i	−0.135977	−	0.368448i
$416$		0			0
$417$	−5.42290	−	9.93130i	−0.265561	−	0.486338i
$418$		0			0
$419$	−17.0307	+	10.9449i	−0.832003	+	0.534696i	−0.885914	−	0.463850i	$-0.846468\pi$
$419$	−17.0307	+	10.9449i	−0.832003	+	0.534696i	0.0539111	+	0.998546i	$0.482831\pi$
$420$		0			0
$421$	−30.3729	−	4.36697i	−1.48029	−	0.212833i	−0.645650	−	0.763634i	$-0.723413\pi$
$421$	−30.3729	−	4.36697i	−1.48029	−	0.212833i	−0.834637	+	0.550801i	$0.814322\pi$
$422$		0			0
$423$	10.3639	−	2.25453i	0.503910	−	0.109619i
$424$		0			0
$425$	4.14148	+	11.3422i	0.200891	+	0.550179i
$426$		0			0
$427$	9.47449	−	12.6564i	0.458503	−	0.612488i
$428$		0			0
$429$	−4.02790	+	1.18270i	−0.194469	+	0.0571011i
$430$		0			0
$431$	−15.4078	−	13.3510i	−0.742169	−	0.643093i	0.199398	−	0.979919i	$-0.436101\pi$
$431$	−15.4078	−	13.3510i	−0.742169	−	0.643093i	−0.941567	+	0.336826i	$0.890647\pi$
$432$		0			0
$433$	1.29937	−	18.1676i	0.0624438	−	0.873078i	−0.865631	−	0.500683i	$-0.833082\pi$
$433$	1.29937	−	18.1676i	0.0624438	−	0.873078i	0.928074	−	0.372395i	$-0.121463\pi$
$434$		0			0
$435$	22.6630	+	1.69953i	1.08661	+	0.0814862i
$436$		0			0
$437$	−16.9699	+	2.08889i	−0.811780	+	0.0999250i
$438$		0			0
$439$	−31.7035	−	14.4785i	−1.51312	−	0.691021i	−0.525928	−	0.850529i	$-0.676282\pi$
$439$	−31.7035	−	14.4785i	−1.51312	−	0.691021i	−0.987197	+	0.159509i	$0.949009\pi$
$440$		0			0
$441$	2.37786	+	2.74419i	0.113231	+	0.130676i
$442$		0			0
$443$	0.241664	+	3.37890i	0.0114818	+	0.160536i	0.999958	+	0.00916038i	$0.00291588\pi$
$443$	0.241664	+	3.37890i	0.0114818	+	0.160536i	−0.988476	+	0.151376i	$0.951630\pi$
$444$		0			0
$445$	−14.6623	−	2.15979i	−0.695058	−	0.102384i
$446$		0			0
$447$	1.48082	+	1.10852i	0.0700402	+	0.0524314i
$448$		0			0
$449$	31.2167	−	14.2562i	1.47320	−	0.672790i	0.492865	−	0.870106i	$-0.335950\pi$
$449$	31.2167	−	14.2562i	1.47320	−	0.672790i	0.980340	+	0.197316i	$0.0632224\pi$
$450$		0			0
$451$	−2.65329	+	4.12859i	−0.124938	+	0.194408i
$452$		0			0
$453$	−7.64419	−	10.2114i	−0.359155	−	0.479775i
$454$		0			0
$455$	1.78903	+	12.7554i	0.0838712	+	0.597981i
$456$		0			0
$457$	−29.5264	+	16.1227i	−1.38119	+	0.754186i	−0.986365	−	0.164571i	$-0.947376\pi$
$457$	−29.5264	+	16.1227i	−1.38119	+	0.754186i	−0.394823	+	0.918757i	$0.629194\pi$
$458$		0			0
$459$	13.6596			0.637577
$460$		0			0
$461$	23.4006			1.08988			0.544938	−	0.838477i	$-0.316553\pi$
$461$	23.4006			1.08988			0.544938	+	0.838477i	$0.316553\pi$
$462$		0			0
$463$	−9.19881	+	5.02293i	−0.427505	+	0.233435i	−0.678571	−	0.734534i	$-0.737401\pi$
$463$	−9.19881	+	5.02293i	−0.427505	+	0.233435i	0.251066	+	0.967970i	$0.419219\pi$
$464$		0			0
$465$	−6.77950	+	8.99150i	−0.314392	+	0.416971i
$466$		0			0
$467$	14.7991	+	19.7693i	0.684820	+	0.914813i	0.999408	−	0.0344157i	$-0.0109570\pi$
$467$	14.7991	+	19.7693i	0.684820	+	0.914813i	−0.314587	+	0.949229i	$0.601866\pi$
$468$		0			0
$469$	9.68898	−	15.0763i	0.447395	−	0.696161i
$470$		0			0
$471$	17.9539	−	8.19929i	0.827274	−	0.377803i
$472$		0			0
$473$	6.92783	+	5.18611i	0.318542	+	0.238458i
$474$		0			0
$475$	−14.9292	−	9.74068i	−0.684998	−	0.446933i
$476$		0			0
$477$	−0.0753564	−	1.05362i	−0.00345033	−	0.0482419i
$478$		0			0
$479$	22.0621	+	25.4610i	1.00804	+	1.16334i	0.986531	+	0.163573i	$0.0523019\pi$
$479$	22.0621	+	25.4610i	1.00804	+	1.16334i	0.0215100	+	0.999769i	$0.493153\pi$
$480$		0			0
$481$	16.7621	+	7.65499i	0.764286	+	0.349038i
$482$		0			0
$483$	−10.4987	+	6.44951i	−0.477710	+	0.293463i
$484$		0			0
$485$	3.11281	−	41.5090i	0.141345	−	1.88482i
$486$		0			0
$487$	−0.478308	+	6.68762i	−0.0216742	+	0.303045i	0.975039	+	0.222034i	$0.0712695\pi$
$487$	−0.478308	+	6.68762i	−0.0216742	+	0.303045i	−0.996713	+	0.0810113i	$0.974185\pi$
$488$		0			0
$489$	16.3706	+	14.1852i	0.740306	+	0.641479i
$490$		0			0
$491$	−2.66596	+	0.782795i	−0.120313	+	0.0353271i	−0.341335	−	0.939942i	$-0.610879\pi$
$491$	−2.66596	+	0.782795i	−0.120313	+	0.0353271i	0.221022	+	0.975269i	$0.429061\pi$
$492$		0			0
$493$	−10.3182	+	13.7835i	−0.464707	+	0.620776i
$494$		0			0
$495$	−0.00688178	+	1.99393i	−0.000309313	+	0.0896204i
$496$		0			0
$497$	15.1560	−	3.29699i	0.679840	−	0.147890i
$498$		0			0
$499$	−27.0099	−	3.88343i	−1.20913	−	0.173846i	−0.491879	−	0.870664i	$-0.663690\pi$
$499$	−27.0099	−	3.88343i	−1.20913	−	0.173846i	−0.717249	+	0.696817i	$0.754599\pi$
$500$		0			0
$501$	23.8615	−	15.3349i	1.06606	−	0.685112i
$502$		0			0
$503$	2.09915	+	3.84430i	0.0935963	+	0.171409i	0.920283	−	0.391254i	$-0.127959\pi$
$503$	2.09915	+	3.84430i	0.0935963	+	0.171409i	−0.826686	+	0.562663i	$0.809777\pi$
$504$		0			0
$505$	−1.82470	−	0.840937i	−0.0811982	−	0.0374212i
$506$		0			0
$507$	2.80730	+	2.80730i	0.124676	+	0.124676i
$508$		0			0
$509$	0.0825841	−	0.281256i	0.00366048	−	0.0124664i	−0.957642	−	0.287960i	$-0.907023\pi$
$509$	0.0825841	−	0.281256i	0.00366048	−	0.0124664i	0.961303	+	0.275493i	$0.0888412\pi$
$510$		0			0
$511$	−9.00622	−	14.0140i	−0.398412	−	0.619941i
$512$		0			0
$513$	−16.1435	+	12.0849i	−0.712753	+	0.533560i
$514$		0			0
$515$	−2.47138	+	11.1749i	−0.108902	+	0.492426i
$516$		0			0
$517$	9.46068	+	3.52865i	0.416080	+	0.155190i
$518$		0			0
$519$	27.3662	−	3.93467i	1.20124	−	0.172713i
$520$		0			0
$521$	−0.569516	−	1.93959i	−0.0249510	−	0.0849752i	0.946076	−	0.323944i	$-0.105009\pi$
$521$	−0.569516	−	1.93959i	−0.0249510	−	0.0849752i	−0.971027	+	0.238969i	$0.923191\pi$
$522$		0			0
$523$	4.77067	−	0.341205i	0.208607	−	0.0149199i	0.0333553	−	0.999444i	$-0.489381\pi$
$523$	4.77067	−	0.341205i	0.208607	−	0.0149199i	0.175251	+	0.984524i	$0.443926\pi$
$524$		0			0
$525$	−12.7024	−	1.91591i	−0.554378	−	0.0836173i
$526$		0			0
$527$	−2.98137	−	7.99337i	−0.129871	−	0.348197i
$528$		0			0
$529$	−8.69655	−	21.2925i	−0.378111	−	0.925760i
$530$		0			0
$531$	−2.32377	+	5.08834i	−0.100843	+	0.220815i
$532$		0			0
$533$	−16.9805	−	1.21447i	−0.735509	−	0.0526047i
$534$		0			0
$535$	−7.28720	+	19.3337i	−0.315053	+	0.835868i
$536$		0			0
$537$	0.194757	+	0.106346i	0.00840440	+	0.00458915i
$538$		0			0
$539$	0.491960	+	3.42166i	0.0211902	+	0.147381i
$540$		0			0
$541$	−3.02631	−	6.62670i	−0.130111	−	0.284904i	0.833353	−	0.552741i	$-0.186418\pi$
$541$	−3.02631	−	6.62670i	−0.130111	−	0.284904i	−0.963464	+	0.267837i	$0.913691\pi$
$542$		0			0
$543$	3.00960	+	13.8349i	0.129154	+	0.593713i
$544$		0			0
$545$	5.64857	−	8.72300i	0.241958	−	0.373652i
$546$		0			0
$547$	−3.59252	−	0.781505i	−0.153605	−	0.0334147i	0.135105	−	0.990831i	$-0.456863\pi$
$547$	−3.59252	−	0.781505i	−0.153605	−	0.0334147i	−0.288710	+	0.957417i	$0.593226\pi$
$548$		0			0
$549$	8.14598	+	2.39187i	0.347662	+	0.102083i
$550$		0			0
$551$		−	25.4185i		−	1.08286i
$552$		0			0
$553$	−1.74114	+	1.74114i	−0.0740408	+	0.0740408i
$554$		0			0
$555$	−12.0832	+	13.8479i	−0.512904	+	0.587811i
$556$		0			0
$557$	−1.31361	+	6.03856i	−0.0556593	+	0.255862i	−0.996566	−	0.0828047i	$-0.973612\pi$
$557$	−1.31361	+	6.03856i	−0.0556593	+	0.255862i	0.940906	+	0.338667i	$0.109976\pi$
$558$		0			0
$559$	−4.27217	+	29.7136i	−0.180693	+	1.25675i
$560$		0			0
$561$	2.66839	+	1.71487i	0.112660	+	0.0724019i
$562$		0			0
$563$	−7.58760	+	20.3431i	−0.319779	+	0.857361i	0.673242	+	0.739422i	$0.264901\pi$
$563$	−7.58760	+	20.3431i	−0.319779	+	0.857361i	−0.993021	+	0.117939i	$0.962371\pi$
$564$		0			0
$565$	−34.5264	+	18.6984i	−1.45253	+	0.786648i
$566$		0			0
$567$	−4.45677	+	8.16197i	−0.187167	+	0.342771i
$568$		0			0
$569$	16.4652	−	19.0019i	0.690259	−	0.796601i	−0.297143	−	0.954833i	$-0.596034\pi$
$569$	16.4652	−	19.0019i	0.690259	−	0.796601i	0.987402	+	0.158232i	$0.0505794\pi$
$570$		0			0
$571$	−5.92243	+	5.13181i	−0.247846	+	0.214760i	−0.769920	−	0.638140i	$-0.779704\pi$
$571$	−5.92243	+	5.13181i	−0.247846	+	0.214760i	0.522074	+	0.852900i	$0.325158\pi$
$572$		0			0
$573$	−0.437312	+	0.163109i	−0.0182690	+	0.00681397i
$574$		0			0
$575$	7.37951	−	22.8154i	0.307747	−	0.951468i
$576$		0			0
$577$	27.2661	−	10.1697i	1.13510	−	0.423371i	0.289495	−	0.957179i	$-0.406512\pi$
$577$	27.2661	−	10.1697i	1.13510	−	0.423371i	0.845605	+	0.533809i	$0.179240\pi$
$578$		0			0
$579$	−22.6607	+	19.6356i	−0.941747	+	0.816028i
$580$		0			0
$581$	−4.22289	+	4.87348i	−0.175195	+	0.202186i
$582$		0			0
$583$	0.481944	−	0.882614i	0.0199601	−	0.0365541i
$584$		0			0
$585$	−6.08201	+	3.29383i	−0.251460	+	0.136183i
$586$		0			0
$587$	0.101574	−	0.272330i	0.00419240	−	0.0112403i	−0.934837	−	0.355078i	$-0.884454\pi$
$587$	0.101574	−	0.272330i	0.00419240	−	0.0112403i	0.939029	+	0.343838i	$0.111727\pi$
$588$		0			0
$589$	10.5953	+	6.80922i	0.436574	+	0.280569i
$590$		0			0
$591$	2.71523	−	18.8848i	0.111690	−	0.776819i
$592$		0			0
$593$	8.52880	−	39.2063i	0.350236	−	1.61001i	−0.378764	−	0.925493i	$-0.623651\pi$
$593$	8.52880	−	39.2063i	0.350236	−	1.61001i	0.728999	−	0.684514i	$-0.239986\pi$
$594$		0			0
$595$	6.39856	−	7.33304i	0.262315	−	0.300625i
$596$		0			0
$597$	5.51626	−	5.51626i	0.225765	−	0.225765i
$598$		0			0
$599$		−	7.63499i		−	0.311957i	−0.987760	−	0.155979i	$-0.950147\pi$
$599$		−	7.63499i		−	0.311957i	0.987760	−	0.155979i	$-0.0498531\pi$
$600$		0			0
$601$	14.6692	+	4.30727i	0.598369	+	0.175697i	0.566871	−	0.823807i	$-0.308154\pi$
$601$	14.6692	+	4.30727i	0.598369	+	0.175697i	0.0314984	+	0.999504i	$0.489972\pi$
$602$		0			0
$603$	9.40378	+	2.04567i	0.382951	+	0.0833060i
$604$		0			0
$605$	12.3376	−	19.0527i	0.501593	−	0.774603i
$606$		0			0
$607$	−1.89539	−	8.71298i	−0.0769316	−	0.353649i	0.922549	−	0.385880i	$-0.126102\pi$
$607$	−1.89539	−	8.71298i	−0.0769316	−	0.353649i	−0.999480	+	0.0322315i	$0.989739\pi$
$608$		0			0
$609$	−7.60941	−	16.6623i	−0.308349	−	0.675190i
$610$		0			0
$611$	4.98472	+	34.6695i	0.201660	+	1.40258i
$612$		0			0
$613$	−18.8179	−	10.2753i	−0.760046	−	0.415017i	0.0519722	−	0.998649i	$-0.483449\pi$
$613$	−18.8179	−	10.2753i	−0.760046	−	0.415017i	−0.812018	+	0.583632i	$0.801631\pi$
$614$		0			0
$615$	5.98835	−	15.8877i	0.241474	−	0.640654i
$616$		0			0
$617$	10.8897	+	0.778846i	0.438403	+	0.0313552i	0.288797	−	0.957391i	$-0.406745\pi$
$617$	10.8897	+	0.778846i	0.438403	+	0.0313552i	0.149606	+	0.988746i	$0.452199\pi$
$618$		0			0
$619$	11.6839	−	25.5841i	0.469614	−	1.02831i	−0.515575	−	0.856844i	$-0.672422\pi$
$619$	11.6839	−	25.5841i	0.469614	−	1.02831i	0.985190	−	0.171468i	$-0.0548509\pi$
$620$		0			0
$621$	−21.3812	−	16.6944i	−0.857999	−	0.669921i
$622$		0			0
$623$	4.17445	+	11.1921i	0.167246	+	0.448403i
$624$		0			0
$625$	21.2159	−	13.2244i	0.848637	−	0.528976i
$626$		0			0
$627$	−4.67078	+	0.334061i	−0.186533	+	0.0133411i
$628$		0			0
$629$	−3.92271	−	13.3595i	−0.156409	−	0.532679i
$630$		0			0
$631$	−22.3845	+	3.21840i	−0.891112	+	0.128123i	−0.572637	−	0.819809i	$-0.694080\pi$
$631$	−22.3845	+	3.21840i	−0.891112	+	0.128123i	−0.318475	+	0.947931i	$0.603171\pi$
$632$		0			0
$633$	0.357805	+	0.133454i	0.0142215	+	0.00530434i
$634$		0			0
$635$	2.84502	−	12.8644i	0.112901	−	0.510509i
$636$		0			0
$637$	−9.59948	+	7.18608i	−0.380345	+	0.284723i
$638$		0			0
$639$	4.50305	+	7.00689i	0.178138	+	0.277188i
$640$		0			0
$641$	−12.2560	+	41.7402i	−0.484084	+	1.64864i	0.249003	+	0.968503i	$0.419897\pi$
$641$	−12.2560	+	41.7402i	−0.484084	+	1.64864i	−0.733087	+	0.680135i	$0.761921\pi$
$642$		0			0
$643$	7.08203	+	7.08203i	0.279288	+	0.279288i	0.832825	−	0.553537i	$-0.186722\pi$
$643$	7.08203	+	7.08203i	0.279288	+	0.279288i	−0.553537	+	0.832825i	$0.686722\pi$
$644$		0			0
$645$	−27.1909	−	12.5313i	−1.07064	−	0.493418i
$646$		0			0
$647$	−2.34065	−	4.28658i	−0.0920204	−	0.168523i	0.827615	−	0.561297i	$-0.189697\pi$
$647$	−2.34065	−	4.28658i	−0.0920204	−	0.168523i	−0.919635	+	0.392774i	$0.871516\pi$
$648$		0			0
$649$	−4.48002	+	2.87914i	−0.175856	+	0.113016i
$650$		0			0
$651$	8.98390	+	1.29169i	0.352107	+	0.0506253i
$652$		0			0
$653$	12.1846	−	2.65060i	0.476822	−	0.103726i	0.0322695	−	0.999479i	$-0.489727\pi$
$653$	12.1846	−	2.65060i	0.476822	−	0.103726i	0.444552	+	0.895753i	$0.353363\pi$
$654$		0			0
$655$	0.0768560	−	22.2683i	0.00300301	−	0.870094i
$656$		0			0
$657$	5.36087	−	7.16128i	0.209147	−	0.279388i
$658$		0			0
$659$	−0.527434	+	0.154868i	−0.0205459	+	0.00603282i	−0.291989	−	0.956422i	$-0.594317\pi$
$659$	−0.527434	+	0.154868i	−0.0205459	+	0.00603282i	0.271443	+	0.962454i	$0.412499\pi$
$660$		0			0
$661$	−10.8643	−	9.41395i	−0.422572	−	0.366160i	0.417462	−	0.908694i	$-0.362920\pi$
$661$	−10.8643	−	9.41395i	−0.422572	−	0.366160i	−0.840034	+	0.542534i	$0.817465\pi$
$662$		0			0
$663$	−0.784938	+	10.9749i	−0.0304845	+	0.426229i
$664$		0			0
$665$	−1.07443	+	14.3274i	−0.0416645	+	0.555592i
$666$		0			0
$667$	32.9966	−	8.96452i	1.27763	−	0.347108i
$668$		0			0
$669$	19.2686	+	8.79966i	0.744966	+	0.340215i
$670$		0			0
$671$	5.29290	+	6.10833i	0.204330	+	0.235809i
$672$		0			0
$673$	−1.42407	−	19.9110i	−0.0548937	−	0.767514i	−0.948121	−	0.317909i	$-0.897019\pi$
$673$	−1.42407	−	19.9110i	−0.0548937	−	0.767514i	0.893227	−	0.449605i	$-0.148435\pi$
$674$		0			0
$675$	−5.82077	−	27.6761i	−0.224042	−	1.06525i
$676$		0			0
$677$	−20.6787	−	15.4799i	−0.794748	−	0.594941i	0.122861	−	0.992424i	$-0.460793\pi$
$677$	−20.6787	−	15.4799i	−0.794748	−	0.594941i	−0.917610	+	0.397483i	$0.869884\pi$
$678$		0			0
$679$	−30.5182	+	13.9372i	−1.17118	+	0.534860i
$680$		0			0
$681$	−0.357017	+	0.555530i	−0.0136809	+	0.0212880i
$682$		0			0
$683$	16.0019	+	21.3760i	0.612294	+	0.817929i	0.994343	−	0.106213i	$-0.0338726\pi$
$683$	16.0019	+	21.3760i	0.612294	+	0.817929i	−0.382050	+	0.924142i	$0.624782\pi$
$684$		0			0
$685$	21.2869	−	28.2324i	0.813332	−	1.07870i
$686$		0			0
$687$	26.1192	−	14.2622i	0.996509	−	0.544135i
$688$		0			0
$689$	3.48835			0.132895
$690$		0			0
$691$	−35.7365			−1.35948			−0.679739	−	0.733454i	$-0.737907\pi$
$691$	−35.7365			−1.35948			−0.679739	+	0.733454i	$0.737907\pi$
$692$		0			0
$693$	1.41053	−	0.770206i	0.0535815	−	0.0292577i
$694$		0			0
$695$	−2.46529	−	17.5769i	−0.0935140	−	0.666731i
$696$		0			0
$697$	7.70857	+	10.2974i	0.291983	+	0.390044i
$698$		0			0
$699$	−0.518740	+	0.807175i	−0.0196206	+	0.0305302i
$700$		0			0
$701$	−9.89360	+	4.51825i	−0.373676	+	0.170652i	−0.593396	−	0.804911i	$-0.702213\pi$
$701$	−9.89360	+	4.51825i	−0.373676	+	0.170652i	0.219720	+	0.975563i	$0.429486\pi$
$702$		0			0
$703$	16.4554	+	12.3183i	0.620626	+	0.464594i
$704$		0			0
$705$	−34.5602	−	5.09082i	−1.30161	−	0.191731i
$706$		0			0
$707$	0.115525	+	1.61525i	0.00434476	+	0.0607477i
$708$		0			0
$709$	31.3359	+	36.1635i	1.17684	+	1.35815i	0.920107	+	0.391667i	$0.128102\pi$
$709$	31.3359	+	36.1635i	1.17684	+	1.35815i	0.256736	+	0.966482i	$0.417353\pi$
$710$		0			0
$711$	−1.20278	−	0.549293i	−0.0451079	−	0.0206001i
$712$		0			0
$713$	−5.10254	+	16.1556i	−0.191091	+	0.605033i
$714$		0			0
$715$	−6.56632	−	0.492417i	−0.245566	−	0.0184153i
$716$		0			0
$717$	0.582630	−	8.14624i	0.0217587	−	0.304227i
$718$		0			0
$719$	−0.100895	−	0.0874262i	−0.00376276	−	0.00326045i	0.652977	−	0.757377i	$-0.273520\pi$
$719$	−0.100895	−	0.0874262i	−0.00376276	−	0.00326045i	−0.656740	+	0.754117i	$0.728065\pi$
$720$		0			0
$721$	8.85093	−	2.59887i	0.329626	−	0.0967869i
$722$		0			0
$723$	8.36458	−	11.1738i	0.311082	−	0.415557i
$724$		0			0
$725$	32.3238	+	15.0323i	1.20048	+	0.558286i
$726$		0			0
$727$	−24.8184	+	5.39891i	−0.920463	+	0.200234i	−0.647743	−	0.761859i	$-0.724287\pi$
$727$	−24.8184	+	5.39891i	−0.920463	+	0.200234i	−0.272720	+	0.962093i	$0.587923\pi$
$728$		0			0
$729$	−28.8868	−	4.15329i	−1.06988	−	0.153826i
$730$		0			0
$731$	19.0815	−	12.2629i	0.705753	−	0.453560i
$732$		0			0
$733$	11.6817	+	21.3934i	0.431473	+	0.790183i	0.999460	−	0.0328541i	$-0.0104597\pi$
$733$	11.6817	+	21.3934i	0.431473	+	0.790183i	−0.567988	+	0.823037i	$0.692278\pi$
$734$		0			0
$735$	−4.14070	−	11.2198i	−0.152732	−	0.413847i
$736$		0			0
$737$	6.47844	+	6.47844i	0.238637	+	0.238637i
$738$		0			0
$739$	7.40865	−	25.2316i	0.272532	−	0.928158i	−0.703530	−	0.710665i	$-0.748394\pi$
$739$	7.40865	−	25.2316i	0.272532	−	0.928158i	0.976062	−	0.217493i	$-0.0697878\pi$
$740$		0			0
$741$	−8.78195	−	13.6650i	−0.322613	−	0.501996i
$742$		0			0
$743$	−14.3916	+	10.7734i	−0.527976	+	0.395238i	−0.829745	−	0.558143i	$-0.811514\pi$
$743$	−14.3916	+	10.7734i	−0.527976	+	0.395238i	0.301768	+	0.953381i	$0.402423\pi$
$744$		0			0
$745$	1.56023	+	2.44629i	0.0571624	+	0.0896250i
$746$		0			0
$747$	−3.24452	−	1.21014i	−0.118711	−	0.0442768i
$748$		0			0
$749$	16.4835	−	2.36998i	0.602296	−	0.0865970i
$750$		0			0
$751$	−3.99362	−	13.6010i	−0.145729	−	0.496309i	0.853983	−	0.520301i	$-0.174180\pi$
$751$	−3.99362	−	13.6010i	−0.145729	−	0.496309i	−0.999712	+	0.0239927i	$0.992362\pi$
$752$		0			0
$753$	11.1237	−	0.795583i	0.405371	−	0.0289927i
$754$		0			0
$755$	−5.57065	−	19.2170i	−0.202737	−	0.699378i
$756$		0			0
$757$	8.54567	+	22.9118i	0.310598	+	0.832745i	0.994649	+	0.103311i	$0.0329436\pi$
$757$	8.54567	+	22.9118i	0.310598	+	0.832745i	−0.684051	+	0.729434i	$0.739784\pi$
$758$		0			0
$759$	−2.08093	−	5.94548i	−0.0755331	−	0.215807i
$760$		0			0
$761$	−17.1072	+	37.4595i	−0.620135	+	1.35791i	0.295286	+	0.955409i	$0.404585\pi$
$761$	−17.1072	+	37.4595i	−0.620135	+	1.35791i	−0.915421	+	0.402497i	$0.868142\pi$
$762$		0			0
$763$	−8.35472	−	0.597541i	−0.302461	−	0.0216324i
$764$		0			0
$765$	4.89032	+	1.84325i	0.176810	+	0.0666427i
$766$		0			0
$767$	−16.2134	−	8.85317i	−0.585431	−	0.319670i
$768$		0			0
$769$	5.26278	+	36.6034i	0.189781	+	1.31995i	0.832574	+	0.553913i	$0.186866\pi$
$769$	5.26278	+	36.6034i	0.189781	+	1.31995i	−0.642794	+	0.766039i	$0.722225\pi$
$770$		0			0
$771$	11.4751	+	25.1269i	0.413264	+	0.904922i
$772$		0			0
$773$	4.96366	+	22.8176i	0.178531	+	0.820692i	0.976075	+	0.217432i	$0.0697681\pi$
$773$	4.96366	+	22.8176i	0.178531	+	0.820692i	−0.797545	+	0.603260i	$0.793868\pi$
$774$		0			0
$775$	−14.9251	+	9.44683i	−0.536125	+	0.339340i
$776$		0			0
$777$	14.4745	+	3.14873i	0.519269	+	0.112960i
$778$		0			0
$779$	−18.2206	−	5.35005i	−0.652821	−	0.191685i
$780$		0			0
$781$			7.92942i			0.283737i
$782$		0			0
$783$	28.5159	−	28.5159i	1.01907	−	1.01907i
$784$		0			0
$785$	30.8883	−	2.10205i	1.10245	−	0.0750253i
$786$		0			0
$787$	0.220900	−	1.01546i	0.00787423	−	0.0361973i	−0.973042	−	0.230627i	$-0.925922\pi$
$787$	0.220900	−	1.01546i	0.00787423	−	0.0361973i	0.980916	+	0.194430i	$0.0622858\pi$
$788$		0			0
$789$	2.63742	−	18.3437i	0.0938947	−	0.653052i
$790$		0			0
$791$	26.6232	+	17.1097i	0.946612	+	0.608351i
$792$		0			0
$793$	−9.79787	+	26.2691i	−0.347933	+	0.932843i
$794$		0			0
$795$	−0.991691	+	3.33477i	−0.0351716	+	0.118272i
$796$		0			0
$797$	−20.7982	+	38.0890i	−0.736708	+	1.34918i	0.193115	+	0.981176i	$0.438141\pi$
$797$	−20.7982	+	38.0890i	−0.736708	+	1.34918i	−0.929824	+	0.368005i	$0.880041\pi$
$798$		0			0
$799$	17.3311	−	20.0011i	0.613130	−	0.707590i
$800$		0			0
$801$	−4.84783	+	4.20067i	−0.171290	+	0.148423i
$802$		0			0
$803$	7.97933	−	2.97614i	0.281585	−	0.105026i
$804$		0			0
$805$	−18.9778	+	3.65819i	−0.668879	+	0.128934i
$806$		0			0
$807$	−20.2528	+	7.55392i	−0.712934	+	0.265911i
$808$		0			0
$809$	−6.55456	+	5.67956i	−0.230446	+	0.199683i	−0.762428	−	0.647073i	$-0.775993\pi$
$809$	−6.55456	+	5.67956i	−0.230446	+	0.199683i	0.531982	+	0.846756i	$0.321447\pi$
$810$		0			0
$811$	−35.3251	+	40.7674i	−1.24043	+	1.43154i	−0.377661	+	0.925944i	$0.623272\pi$
$811$	−35.3251	+	40.7674i	−1.24043	+	1.43154i	−0.862772	+	0.505593i	$0.831274\pi$
$812$		0			0
$813$	−14.6070	+	26.7507i	−0.512288	+	0.938186i
$814$		0			0
$815$	16.1807	+	29.8773i	0.566783	+	1.04656i
$816$		0			0
$817$	−11.7021	+	31.3744i	−0.409403	+	1.09765i
$818$		0			0
$819$	4.68983	+	3.01397i	0.163876	+	0.105317i
$820$		0			0
$821$	−4.70891	+	32.7512i	−0.164342	+	1.14303i	0.725987	+	0.687708i	$0.241383\pi$
$821$	−4.70891	+	32.7512i	−0.164342	+	1.14303i	−0.890329	+	0.455317i	$0.849526\pi$
$822$		0			0
$823$	7.72968	−	35.5327i	0.269440	−	1.23859i	−0.621116	−	0.783719i	$-0.713320\pi$
$823$	7.72968	−	35.5327i	0.269440	−	1.23859i	0.890555	−	0.454875i	$-0.150316\pi$
$824$		0			0
$825$	2.33745	−	6.13724i	0.0813797	−	0.213671i
$826$		0			0
$827$	36.2765	−	36.2765i	1.26146	−	1.26146i	0.311069	−	0.950387i	$-0.399313\pi$
$827$	36.2765	−	36.2765i	1.26146	−	1.26146i	0.950387	−	0.311069i	$-0.100687\pi$
$828$		0			0
$829$		−	17.9104i		−	0.622054i	−0.950401	−	0.311027i	$-0.899327\pi$
$829$		−	17.9104i		−	0.622054i	0.950401	−	0.311027i	$-0.100673\pi$
$830$		0			0
$831$	−15.2639	−	4.48190i	−0.529500	−	0.155475i
$832$		0			0
$833$	8.85340	+	1.92594i	0.306752	+	0.0667299i
$834$		0			0
$835$	43.5069	−	9.30720i	1.50562	−	0.322089i
$836$		0			0
$837$	4.24750	+	19.5254i	0.146815	+	0.674898i
$838$		0			0
$839$	−6.77228	−	14.8292i	−0.233805	−	0.511961i	0.755969	−	0.654608i	$-0.227166\pi$
$839$	−6.77228	−	14.8292i	−0.233805	−	0.511961i	−0.989774	+	0.142646i	$0.954439\pi$
$840$		0			0
$841$	3.10702	+	21.6098i	0.107139	+	0.745166i
$842$		0			0
$843$	−19.0258	−	10.3889i	−0.655284	−	0.357812i
$844$		0			0
$845$	2.56739	+	5.67354i	0.0883209	+	0.195176i
$846$		0			0
$847$	−18.2483	−	1.30514i	−0.627019	−	0.0448453i
$848$		0			0
$849$	−11.1239	+	24.3580i	−0.381772	+	0.835964i
$850$		0			0
$851$	−10.1874	+	25.7056i	−0.349220	+	0.881178i
$852$		0			0
$853$	−10.7179	−	28.7359i	−0.366975	−	0.983898i	−0.980896	−	0.194531i	$-0.937682\pi$
$853$	−10.7179	−	28.7359i	−0.366975	−	0.983898i	0.613921	−	0.789367i	$-0.289591\pi$
$854$		0			0
$855$	−7.41032	+	2.14811i	−0.253427	+	0.0734639i
$856$		0			0
$857$	23.7225	−	1.69667i	0.810345	−	0.0579570i	0.339984	−	0.940431i	$-0.389578\pi$
$857$	23.7225	−	1.69667i	0.810345	−	0.0579570i	0.470361	+	0.882474i	$0.344124\pi$
$858$		0			0
$859$	2.73970	+	9.33055i	0.0934773	+	0.318354i	0.992936	−	0.118651i	$-0.0378571\pi$
$859$	2.73970	+	9.33055i	0.0934773	+	0.318354i	−0.899459	+	0.437006i	$0.856039\pi$
$860$		0			0
$861$	−13.5456	+	1.94756i	−0.461632	+	0.0663726i
$862$		0			0
$863$	17.0522	+	6.36014i	0.580463	+	0.216502i	0.622507	−	0.782614i	$-0.286114\pi$
$863$	17.0522	+	6.36014i	0.580463	+	0.216502i	−0.0420437	+	0.999116i	$0.513387\pi$
$864$		0			0
$865$	42.3440	+	9.36455i	1.43974	+	0.318404i
$866$		0			0
$867$	−12.7451	+	9.54088i	−0.432847	+	0.324025i
$868$		0			0
$869$	−0.680572	−	1.05899i	−0.0230868	−	0.0359238i
$870$		0			0
$871$	−8.95380	+	30.4938i	−0.303388	+	1.03324i
$872$		0			0
$873$	−12.7395	−	12.7395i	−0.431166	−	0.431166i
$874$		0			0
$875$	−17.5842	−	9.83943i	−0.594456	−	0.332633i
$876$		0			0
$877$	−8.17785	−	14.9766i	−0.276146	−	0.505724i	0.702392	−	0.711791i	$-0.252116\pi$
$877$	−8.17785	−	14.9766i	−0.276146	−	0.505724i	−0.978538	+	0.206066i	$0.933934\pi$
$878$		0			0
$879$	−6.06271	+	3.89627i	−0.204490	+	0.131418i
$880$		0			0
$881$	58.4975	+	8.41068i	1.97083	+	0.283363i	0.998828	+	0.0483984i	$0.0154117\pi$
$881$	58.4975	+	8.41068i	1.97083	+	0.283363i	0.972004	+	0.234965i	$0.0754974\pi$
$882$		0			0
$883$	34.7706	−	7.56388i	1.17012	−	0.254545i	0.414810	−	0.909908i	$-0.363848\pi$
$883$	34.7706	−	7.56388i	1.17012	−	0.254545i	0.755314	+	0.655363i	$0.227484\pi$
$884$		0			0
$885$	13.0727	−	12.9827i	0.439432	−	0.436410i
$886$		0			0
$887$	−26.9058	+	35.9419i	−0.903408	+	1.20681i	0.0743831	+	0.997230i	$0.476301\pi$
$887$	−26.9058	+	35.9419i	−0.903408	+	1.20681i	−0.977791	+	0.209582i	$0.932790\pi$
$888$		0			0
$889$	−10.1891	+	2.99178i	−0.341731	+	0.100341i
$890$		0			0
$891$	−3.59297	−	3.11333i	−0.120369	−	0.104300i
$892$		0			0
$893$	−2.78728	+	38.9712i	−0.0932726	+	1.30412i
$894$		0			0
$895$	0.227025	+	0.263836i	0.00758862	+	0.00881905i
$896$		0			0
$897$	14.6418	−	16.2195i	0.488875	−	0.541552i
$898$		0			0
$899$	−22.9109	−	10.4631i	−0.764121	−	0.348963i
$900$		0			0
$901$	−1.72606	−	1.99197i	−0.0575033	−	0.0663623i
$902$		0			0
$903$	1.72150	+	24.0697i	0.0572879	+	0.800990i
$904$		0			0
$905$	−3.23645	+	21.9714i	−0.107583	+	0.730355i
$906$		0			0
$907$	8.73618	+	6.53982i	0.290080	+	0.217151i	0.734400	−	0.678717i	$-0.237464\pi$
$907$	8.73618	+	6.53982i	0.290080	+	0.217151i	−0.444320	+	0.895868i	$0.646555\pi$
$908$		0			0
$909$	−0.791019	+	0.361246i	−0.0262364	+	0.0119818i
$910$		0			0
$911$	0.603802	−	0.939534i	0.0200049	−	0.0311282i	−0.831107	−	0.556112i	$-0.812292\pi$
$911$	0.603802	−	0.939534i	0.0200049	−	0.0311282i	0.851112	+	0.524984i	$0.175929\pi$
$912$		0			0
$913$	−1.97563	−	2.63913i	−0.0653838	−	0.0873425i
$914$		0			0
$915$	−22.3272	−	16.8345i	−0.738114	−	0.556530i
$916$		0			0
$917$	−15.7528	+	8.60169i	−0.520204	+	0.284053i
$918$		0			0
$919$	5.65057			0.186395			0.0931976	−	0.995648i	$-0.470291\pi$
$919$	5.65057			0.186395			0.0931976	+	0.995648i	$0.470291\pi$
$920$		0			0
$921$	20.3218			0.669627
$922$		0			0
$923$	−24.1414	+	13.1822i	−0.794622	+	0.433897i
$924$		0			0
$925$	−25.3964	+	13.6408i	−0.835028	+	0.448505i
$926$		0			0
$927$	2.96858	+	3.96556i	0.0975010	+	0.130246i
$928$		0			0
$929$	−11.1843	+	17.4032i	−0.366946	+	0.570980i	−0.974803	−	0.223067i	$-0.928393\pi$
$929$	−11.1843	+	17.4032i	−0.366946	+	0.570980i	0.607857	+	0.794047i	$0.292029\pi$
$930$		0			0
$931$	−12.1672	+	5.55658i	−0.398764	+	0.182110i
$932$		0			0
$933$	38.5150	+	28.8320i	1.26093	+	0.943917i
$934$		0			0
$935$	2.96787	+	3.99326i	0.0970597	+	0.130594i
$936$		0			0
$937$	1.39733	+	19.5372i	0.0456487	+	0.638252i	0.967848	+	0.251536i	$0.0809358\pi$
$937$	1.39733	+	19.5372i	0.0456487	+	0.638252i	−0.922199	+	0.386715i	$0.873610\pi$
$938$		0			0
$939$	7.76629	+	8.96277i	0.253443	+	0.292489i
$940$		0			0
$941$	42.0234	+	19.1915i	1.36992	+	0.625624i	0.958309	−	0.285734i	$-0.0922374\pi$
$941$	42.0234	+	19.1915i	1.36992	+	0.625624i	0.411616	+	0.911358i	$0.364965\pi$
$942$		0			0
$943$	0.519090	−	25.5396i	0.0169039	−	0.831684i
$944$		0			0
$945$	−17.2786	+	14.8679i	−0.562073	+	0.483653i
$946$		0			0
$947$	0.708908	−	9.91183i	0.0230364	−	0.322091i	−0.972847	−	0.231449i	$-0.925653\pi$
$947$	0.708908	−	9.91183i	0.0230364	−	0.322091i	0.995883	−	0.0906425i	$-0.0288920\pi$
$948$		0			0
$949$	22.3261	+	19.3457i	0.724736	+	0.627987i
$950$		0			0
$951$	5.45873	−	1.60283i	0.177011	−	0.0519752i
$952$		0			0
$953$	−16.5785	+	22.1462i	−0.537029	+	0.717387i	−0.984200	−	0.177062i	$-0.943341\pi$
$953$	−16.5785	+	22.1462i	−0.537029	+	0.717387i	0.447171	+	0.894449i	$0.352432\pi$
$954$		0			0
$955$	−0.732108	−	0.00252678i	−0.0236905	−	8.17646e-5i
$956$		0			0
$957$	9.15051	−	1.99057i	0.295794	−	0.0643461i
$958$		0			0
$959$	−28.2085	−	4.05577i	−0.910900	−	0.130968i
$960$		0			0
$961$	−15.5800	+	10.0127i	−0.502581	+	0.322989i
$962$		0			0
$963$	4.28576	+	7.84879i	0.138107	+	0.252924i
$964$		0			0
$965$	−44.1236	+	16.2840i	−1.42039	+	0.524201i
$966$		0			0
$967$	17.8258	+	17.8258i	0.573238	+	0.573238i	0.933032	−	0.359794i	$-0.117153\pi$
$967$	17.8258	+	17.8258i	0.573238	+	0.573238i	−0.359794	+	0.933032i	$0.617153\pi$
$968$		0			0
$969$	−3.45784	+	11.7763i	−0.111082	+	0.378310i
$970$		0			0
$971$	−30.3226	−	47.1828i	−0.973098	−	1.51417i	−0.853332	−	0.521367i	$-0.825422\pi$
$971$	−30.3226	−	47.1828i	−0.973098	−	1.51417i	−0.119765	−	0.992802i	$-0.538214\pi$
$972$		0			0
$973$	−11.4523	+	8.57305i	−0.367142	+	0.274839i
$974$		0			0
$975$	22.5709	−	3.08634i	0.722847	−	0.0988419i
$976$		0			0
$977$	42.3640	+	15.8009i	1.35534	+	0.505517i	0.918998	−	0.394263i	$-0.129000\pi$
$977$	42.3640	+	15.8009i	1.35534	+	0.505517i	0.436345	+	0.899779i	$0.356273\pi$
$978$		0			0
$979$	−6.04463	+	0.869086i	−0.193187	+	0.0277761i
$980$		0			0
$981$	−1.26721	−	4.31574i	−0.0404590	−	0.137791i
$982$		0			0
$983$	−8.42607	+	0.602644i	−0.268750	+	0.0192214i	−0.205064	−	0.978749i	$-0.565740\pi$
$983$	−8.42607	+	0.602644i	−0.268750	+	0.0192214i	−0.0636860	+	0.997970i	$0.520286\pi$
$984$		0			0
$985$	14.4329	−	26.2164i	0.459872	−	0.835325i
$986$		0			0
$987$	9.83952	+	26.3808i	0.313195	+	0.839709i
$988$		0			0
$989$	−44.8552	−	4.12578i	−1.42631	−	0.131192i
$990$		0			0
$991$	−22.8764	+	50.0922i	−0.726692	+	1.59123i	0.0775907	+	0.996985i	$0.475277\pi$
$991$	−22.8764	+	50.0922i	−0.726692	+	1.59123i	−0.804282	+	0.594247i	$0.797450\pi$
$992$		0			0
$993$	−51.6329	−	3.69286i	−1.63852	−	0.117189i
$994$		0			0
$995$	11.1483	−	5.04484i	0.353426	−	0.159932i
$996$		0			0
$997$	8.15055	+	4.45054i	0.258130	+	0.140950i	0.603104	−	0.797662i	$-0.293930\pi$
$997$	8.15055	+	4.45054i	0.258130	+	0.140950i	−0.344974	+	0.938612i	$0.612112\pi$
$998$		0			0
$999$	4.64116	+	32.2799i	0.146840	+	1.02129i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bv.a.17.11	✓	720
5.3	odd	4	inner	920.2.bv.a.753.11	yes	720
23.19	odd	22	inner	920.2.bv.a.617.11	yes	720
115.88	even	44	inner	920.2.bv.a.433.11	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bv.a.17.11	✓	720	1.1	even	1	trivial
920.2.bv.a.433.11	yes	720	115.88	even	44	inner
920.2.bv.a.617.11	yes	720	23.19	odd	22	inner
920.2.bv.a.753.11	yes	720	5.3	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:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	920.bv (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.25117 + 0.683192i) q^{3} +(-2.21439 + 0.310585i) q^{5} +(1.08006 + 1.44279i) q^{7} +(-0.523240 + 0.814177i) q^{9} +(-0.838110 + 0.382752i) q^{11} +(-2.55861 - 1.91535i) q^{13} +(2.55840 - 1.90145i) q^{15} +(0.172280 + 2.40878i) q^{17} +(-2.33469 - 2.69438i) q^{19} +(-2.33704 - 1.06729i) q^{21} +(2.67427 - 3.98099i) q^{23} +(4.80707 - 1.37551i) q^{25} +(0.403516 - 5.64190i) q^{27} +(5.38824 + 4.66893i) q^{29} +(-3.38961 + 0.995279i) q^{31} +(0.787127 - 1.05148i) q^{33} +(-2.83978 - 2.85945i) q^{35} +(-5.63382 + 1.22556i) q^{37} +(4.50981 + 0.648413i) q^{39} +(4.48092 - 2.87971i) q^{41} +(-4.50132 - 8.24355i) q^{43} +(0.905787 - 1.96542i) q^{45} +(-7.74918 - 7.74918i) q^{47} +(1.05702 - 3.59987i) q^{49} +(-1.86121 - 2.89611i) q^{51} +(-0.873743 + 0.654076i) q^{53} +(1.73703 - 1.10787i) q^{55} +(4.76188 + 1.77609i) q^{57} +(5.72104 - 0.822561i) q^{59} +(-2.47142 - 8.41688i) q^{61} +(-1.73981 + 0.124434i) q^{63} +(6.26064 + 3.44667i) q^{65} +(-3.47499 - 9.31680i) q^{67} +(-0.626195 + 6.80795i) q^{69} +(3.57510 - 7.82838i) q^{71} +(-9.21950 - 0.659392i) q^{73} +(-5.07474 + 5.00516i) q^{75} +(-1.45744 - 0.795820i) q^{77} +(0.194438 + 1.35234i) q^{79} +(2.14350 + 4.69360i) q^{81} +(0.760562 + 3.49625i) q^{83} +(-1.12963 - 5.28049i) q^{85} +(-9.93140 - 2.16044i) q^{87} +(6.35945 + 1.86730i) q^{89} -5.76021i q^{91} +(3.56102 - 3.56102i) q^{93} +(6.00676 + 5.24129i) q^{95} +(-3.95701 + 18.1901i) q^{97} +(0.126905 - 0.882640i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) \) 720 * q - 20 * q^23 + 16 * q^25 - 24 * q^27 - 16 * q^31 + 88 * q^37 - 32 * q^41 + 56 * q^47 - 40 * q^55 + 88 * q^57 + 16 * q^73 - 140 * q^75 - 48 * q^77 + 40 * q^81 - 92 * q^85 - 88 * q^87 + 72 * q^93 - 248 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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