LMFDB - Embedded newform 544.2.cc.c.175.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [544,2,Mod(79,544)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("544.79"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(544, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([8, 8, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 544 = 2^{5} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	544.cc (of order $16$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [112,0,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$4.34386186996$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 136)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			175.12
Character	$\chi$	$=$	544.175
Dual form			544.2.cc.c.143.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.25761 + 1.88214i) q^{3} +(1.55757 + 0.309820i) q^{5} +(-3.91750 + 0.779239i) q^{7} +(-0.812832 + 1.96235i) q^{9} +(2.04236 + 1.36466i) q^{11} +(-1.67634 + 1.67634i) q^{13} +(1.37568 + 3.32120i) q^{15} +(-0.0531197 + 4.12276i) q^{17} +(1.36178 + 3.28763i) q^{19} +(-6.39331 - 6.39331i) q^{21} +(5.72685 + 3.82656i) q^{23} +(-2.28937 - 0.948286i) q^{25} +(1.94477 - 0.386838i) q^{27} +(-0.362301 + 1.82141i) q^{29} +(-5.41149 - 8.09887i) q^{31} +5.56021i q^{33} -6.34320 q^{35} +(5.16270 - 3.44961i) q^{37} +(-5.26329 - 1.04693i) q^{39} +(-0.977918 - 4.91633i) q^{41} +(1.08459 - 2.61842i) q^{43} +(-1.87402 + 2.80466i) q^{45} +(2.87182 - 2.87182i) q^{47} +(8.27242 - 3.42655i) q^{49} +(-7.82643 + 5.08484i) q^{51} +(3.16997 - 1.31304i) q^{53} +(2.75831 + 2.75831i) q^{55} +(-4.47520 + 6.69761i) q^{57} +(-6.57678 - 2.72419i) q^{59} +(1.72880 + 8.69128i) q^{61} +(1.65513 - 8.32089i) q^{63} +(-3.13038 + 2.09165i) q^{65} +6.11894i q^{67} +15.5911i q^{69} +(5.58989 - 3.73504i) q^{71} +(2.78015 - 13.9768i) q^{73} +(-1.09431 - 5.50148i) q^{75} +(-9.06432 - 3.75456i) q^{77} +(-7.05875 + 10.5642i) q^{79} +(7.67959 + 7.67959i) q^{81} +(16.0062 - 6.62999i) q^{83} +(-1.36005 + 6.40503i) q^{85} +(-3.88378 + 1.60871i) q^{87} +(0.443072 - 0.443072i) q^{89} +(5.26080 - 7.87334i) q^{91} +(8.43769 - 20.3704i) q^{93} +(1.10249 + 5.54261i) q^{95} +(9.17174 + 1.82437i) q^{97} +(-4.33803 + 2.89858i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 16 q^{3} - 16 q^{9} + 16 q^{11} - 16 q^{17} + 16 q^{19} - 16 q^{25} - 32 q^{27} + 32 q^{35} - 16 q^{41} + 96 q^{43} - 16 q^{49} + 16 q^{51} + 32 q^{57} + 16 q^{59} + 64 q^{65} - 96 q^{73} + 16 q^{75}+ \cdots - 48 q^{99}+O(q^{100}) $ 112 * q + 16 * q^3 - 16 * q^9 + 16 * q^11 - 16 * q^17 + 16 * q^19 - 16 * q^25 - 32 * q^27 + 32 * q^35 - 16 * q^41 + 96 * q^43 - 16 * q^49 + 16 * q^51 + 32 * q^57 + 16 * q^59 + 64 * q^65 - 96 * q^73 + 16 * q^75 - 96 * q^81 - 128 * q^83 - 16 * q^89 + 16 * q^91 - 16 * q^97 - 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/544\mathbb{Z}\right)^\times$.

$n$	$69$	$511$	$513$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{16}\right)$

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
$3$	1.25761	+	1.88214i	0.726080	+	1.08666i	0.992434	+	0.122780i	$0.0391809\pi$
$3$	1.25761	+	1.88214i	0.726080	+	1.08666i	−0.266354	+	0.963875i	$0.585819\pi$
$4$		0			0
$5$	1.55757	+	0.309820i	0.696566	+	0.138556i	0.530658	−	0.847586i	$-0.321945\pi$
$5$	1.55757	+	0.309820i	0.696566	+	0.138556i	0.165907	+	0.986141i	$0.446945\pi$
$6$		0			0
$7$	−3.91750	+	0.779239i	−1.48068	+	0.294525i	−0.868299	−	0.496042i	$-0.834786\pi$
$7$	−3.91750	+	0.779239i	−1.48068	+	0.294525i	−0.612376	+	0.790566i	$0.709786\pi$
$8$		0			0
$9$	−0.812832	+	1.96235i	−0.270944	+	0.654117i
$10$		0			0
$11$	2.04236	+	1.36466i	0.615793	+	0.411460i	0.823972	−	0.566631i	$-0.191753\pi$
$11$	2.04236	+	1.36466i	0.615793	+	0.411460i	−0.208178	+	0.978091i	$0.566753\pi$
$12$		0			0
$13$	−1.67634	+	1.67634i	−0.464934	+	0.464934i	−0.900269	−	0.435335i	$-0.856630\pi$
$13$	−1.67634	+	1.67634i	−0.464934	+	0.464934i	0.435335	+	0.900269i	$0.356630\pi$
$14$		0			0
$15$	1.37568	+	3.32120i	0.355200	+	0.857529i
$16$		0			0
$17$	−0.0531197	+	4.12276i	−0.0128834	+	0.999917i
$17$	−0.0531197	+	4.12276i	−0.0128834	+	0.999917i
$18$		0			0
$19$	1.36178	+	3.28763i	0.312414	+	0.754233i	0.999614	+	0.0277659i	$0.00883928\pi$
$19$	1.36178	+	3.28763i	0.312414	+	0.754233i	−0.687201	+	0.726468i	$0.741161\pi$
$20$		0			0
$21$	−6.39331	−	6.39331i	−1.39513	−	1.39513i
$22$		0			0
$23$	5.72685	+	3.82656i	1.19413	+	0.797893i	0.983718	−	0.179719i	$-0.0575190\pi$
$23$	5.72685	+	3.82656i	1.19413	+	0.797893i	0.210413	+	0.977612i	$0.432519\pi$
$24$		0			0
$25$	−2.28937	−	0.948286i	−0.457873	−	0.189657i
$26$		0			0
$27$	1.94477	−	0.386838i	0.374271	−	0.0744471i
$28$		0			0
$29$	−0.362301	+	1.82141i	−0.0672775	+	0.338227i	−0.999734	−	0.0230549i	$-0.992661\pi$
$29$	−0.362301	+	1.82141i	−0.0672775	+	0.338227i	0.932457	+	0.361282i	$0.117661\pi$
$30$		0			0
$31$	−5.41149	−	8.09887i	−0.971933	−	1.45460i	−0.888926	−	0.458051i	$-0.848548\pi$
$31$	−5.41149	−	8.09887i	−0.971933	−	1.45460i	−0.0830072	−	0.996549i	$-0.526452\pi$
$32$		0			0
$33$			5.56021i			0.967907i
$34$		0			0
$35$	−6.34320			−1.07220
$36$		0			0
$37$	5.16270	−	3.44961i	0.848743	−	0.567112i	−0.0533879	−	0.998574i	$-0.517002\pi$
$37$	5.16270	−	3.44961i	0.848743	−	0.567112i	0.902131	+	0.431462i	$0.142002\pi$
$38$		0			0
$39$	−5.26329	−	1.04693i	−0.842801	−	0.167644i
$40$		0			0
$41$	−0.977918	−	4.91633i	−0.152725	−	0.767801i	−0.978892	−	0.204376i	$-0.934483\pi$
$41$	−0.977918	−	4.91633i	−0.152725	−	0.767801i	0.826167	−	0.563425i	$-0.190517\pi$
$42$		0			0
$43$	1.08459	−	2.61842i	0.165398	−	0.399306i	−0.819350	−	0.573294i	$-0.805665\pi$
$43$	1.08459	−	2.61842i	0.165398	−	0.399306i	0.984748	+	0.173988i	$0.0556654\pi$
$44$		0			0
$45$	−1.87402	+	2.80466i	−0.279362	+	0.418095i
$46$		0			0
$47$	2.87182	−	2.87182i	0.418898	−	0.418898i	−0.465926	−	0.884824i	$-0.654279\pi$
$47$	2.87182	−	2.87182i	0.418898	−	0.418898i	0.884824	+	0.465926i	$0.154279\pi$
$48$		0			0
$49$	8.27242	−	3.42655i	1.18177	−	0.489507i
$50$		0			0
$51$	−7.82643	+	5.08484i	−1.09592	+	0.712020i
$52$		0			0
$53$	3.16997	−	1.31304i	0.435428	−	0.180360i	−0.154192	−	0.988041i	$-0.549277\pi$
$53$	3.16997	−	1.31304i	0.435428	−	0.180360i	0.589620	+	0.807681i	$0.299277\pi$
$54$		0			0
$55$	2.75831	+	2.75831i	0.371930	+	0.371930i
$56$		0			0
$57$	−4.47520	+	6.69761i	−0.592754	+	0.887120i
$58$		0			0
$59$	−6.57678	−	2.72419i	−0.856224	−	0.354660i	−0.0889946	−	0.996032i	$-0.528365\pi$
$59$	−6.57678	−	2.72419i	−0.856224	−	0.354660i	−0.767230	+	0.641372i	$0.778365\pi$
$60$		0			0
$61$	1.72880	+	8.69128i	0.221351	+	1.11280i	0.918361	+	0.395744i	$0.129513\pi$
$61$	1.72880	+	8.69128i	0.221351	+	1.11280i	−0.697010	+	0.717061i	$0.745487\pi$
$62$		0			0
$63$	1.65513	−	8.32089i	0.208527	−	1.04833i
$64$		0			0
$65$	−3.13038	+	2.09165i	−0.388276	+	0.259438i
$66$		0			0
$67$			6.11894i			0.747548i	0.927520	+	0.373774i	$0.121936\pi$
$67$			6.11894i			0.747548i	−0.927520	+	0.373774i	$0.878064\pi$
$68$		0			0
$69$			15.5911i			1.87694i
$70$		0			0
$71$	5.58989	−	3.73504i	0.663398	−	0.443268i	−0.177749	−	0.984076i	$-0.556881\pi$
$71$	5.58989	−	3.73504i	0.663398	−	0.443268i	0.841146	+	0.540808i	$0.181881\pi$
$72$		0			0
$73$	2.78015	−	13.9768i	0.325392	−	1.63586i	−0.378538	−	0.925586i	$-0.623573\pi$
$73$	2.78015	−	13.9768i	0.325392	−	1.63586i	0.703930	−	0.710270i	$-0.251427\pi$
$74$		0			0
$75$	−1.09431	−	5.50148i	−0.126360	−	0.635256i
$76$		0			0
$77$	−9.06432	−	3.75456i	−1.03297	−	0.427872i
$78$		0			0
$79$	−7.05875	+	10.5642i	−0.794171	+	1.18856i	0.184440	+	0.982844i	$0.440953\pi$
$79$	−7.05875	+	10.5642i	−0.794171	+	1.18856i	−0.978611	+	0.205717i	$0.934047\pi$
$80$		0			0
$81$	7.67959	+	7.67959i	0.853288	+	0.853288i
$82$		0			0
$83$	16.0062	−	6.62999i	1.75691	−	0.727736i	0.759936	−	0.649998i	$-0.225230\pi$
$83$	16.0062	−	6.62999i	1.75691	−	0.727736i	0.996974	−	0.0777381i	$-0.0247698\pi$
$84$		0			0
$85$	−1.36005	+	6.40503i	−0.147518	+	0.694723i
$86$		0			0
$87$	−3.88378	+	1.60871i	−0.416385	+	0.172472i
$88$		0			0
$89$	0.443072	−	0.443072i	0.0469655	−	0.0469655i	−0.683234	−	0.730200i	$-0.739427\pi$
$89$	0.443072	−	0.443072i	0.0469655	−	0.0469655i	0.730200	+	0.683234i	$0.239427\pi$
$90$		0			0
$91$	5.26080	−	7.87334i	0.551481	−	0.825350i
$92$		0			0
$93$	8.43769	−	20.3704i	0.874948	−	2.11231i
$94$		0			0
$95$	1.10249	+	5.54261i	0.113113	+	0.568660i
$96$		0			0
$97$	9.17174	+	1.82437i	0.931249	+	0.185237i	0.637328	−	0.770593i	$-0.280040\pi$
$97$	9.17174	+	1.82437i	0.931249	+	0.185237i	0.293921	+	0.955830i	$0.405040\pi$
$98$		0			0
$99$	−4.33803	+	2.89858i	−0.435988	+	0.291318i
$100$		0			0
$101$	5.10512			0.507978			0.253989	−	0.967207i	$-0.418257\pi$
$101$	5.10512			0.507978			0.253989	+	0.967207i	$0.418257\pi$
$102$		0			0
$103$		−	0.265102i		−	0.0261212i	−0.999915	−	0.0130606i	$-0.995843\pi$
$103$		−	0.265102i		−	0.0261212i	0.999915	−	0.0130606i	$-0.00415744\pi$
$104$		0			0
$105$	−7.97725	−	11.9388i	−0.778500	−	1.16511i
$106$		0			0
$107$	1.02449	−	5.15045i	0.0990410	−	0.497913i	−0.899142	−	0.437657i	$-0.855808\pi$
$107$	1.02449	−	5.15045i	0.0990410	−	0.497913i	0.998183	−	0.0602556i	$-0.0191916\pi$
$108$		0			0
$109$	9.58462	−	1.90650i	0.918040	−	0.182609i	0.286614	−	0.958046i	$-0.407470\pi$
$109$	9.58462	−	1.90650i	0.918040	−	0.182609i	0.631425	+	0.775437i	$0.282470\pi$
$110$		0			0
$111$	12.9853	+	5.37869i	1.23251	+	0.510523i
$112$		0			0
$113$	−6.70304	−	4.47883i	−0.630569	−	0.421333i	0.198795	−	0.980041i	$-0.436297\pi$
$113$	−6.70304	−	4.47883i	−0.630569	−	0.421333i	−0.829364	+	0.558708i	$0.811297\pi$
$114$		0			0
$115$	7.73442	+	7.73442i	0.721239	+	0.721239i
$116$		0			0
$117$	−1.92699	−	4.65216i	−0.178150	−	0.430092i
$118$		0			0
$119$	−3.00452	−	16.1923i	−0.275424	−	1.48435i
$120$		0			0
$121$	−1.90059	−	4.58844i	−0.172781	−	0.417131i
$122$		0			0
$123$	8.02339	−	8.02339i	0.723445	−	0.723445i
$124$		0			0
$125$	−9.87426	−	6.59777i	−0.883181	−	0.590123i
$126$		0			0
$127$	0.215916	−	0.521267i	0.0191594	−	0.0462550i	−0.914010	−	0.405691i	$-0.867031\pi$
$127$	0.215916	−	0.521267i	0.0191594	−	0.0462550i	0.933170	+	0.359436i	$0.117031\pi$
$128$		0			0
$129$	6.29223	−	1.25160i	0.554000	−	0.110197i
$130$		0			0
$131$	−19.6039	−	3.89946i	−1.71280	−	0.340697i	−0.761313	−	0.648385i	$-0.775445\pi$
$131$	−19.6039	−	3.89946i	−1.71280	−	0.340697i	−0.951487	+	0.307688i	$0.900445\pi$
$132$		0			0
$133$	−7.89662	−	11.8181i	−0.684723	−	1.02476i
$134$		0			0
$135$	3.14896			0.271019
$136$		0			0
$137$	−3.05874			−0.261326			−0.130663	−	0.991427i	$-0.541711\pi$
$137$	−3.05874			−0.261326			−0.130663	+	0.991427i	$0.541711\pi$
$138$		0			0
$139$	−4.93873	−	7.39132i	−0.418897	−	0.626924i	0.560670	−	0.828039i	$-0.310543\pi$
$139$	−4.93873	−	7.39132i	−0.418897	−	0.626924i	−0.979568	+	0.201115i	$0.935543\pi$
$140$		0			0
$141$	9.01678	+	1.79355i	0.759350	+	0.151044i
$142$		0			0
$143$	−5.71132	+	1.13605i	−0.477605	+	0.0950015i
$144$		0			0
$145$	−1.12862	+	2.72472i	−0.0937264	+	0.226276i
$146$		0			0
$147$	16.8527	+	11.2606i	1.38999	+	0.928760i
$148$		0			0
$149$	−8.62399	+	8.62399i	−0.706505	+	0.706505i	−0.965798	−	0.259294i	$-0.916510\pi$
$149$	−8.62399	+	8.62399i	−0.706505	+	0.706505i	0.259294	+	0.965798i	$0.416510\pi$
$150$		0			0
$151$	3.92551	+	9.47701i	0.319453	+	0.771228i	0.999283	+	0.0378583i	$0.0120535\pi$
$151$	3.92551	+	9.47701i	0.319453	+	0.771228i	−0.679830	+	0.733370i	$0.737946\pi$
$152$		0			0
$153$	−8.04713	−	3.45535i	−0.650572	−	0.279349i
$154$		0			0
$155$	−5.91958	−	14.2911i	−0.475472	−	1.14789i
$156$		0			0
$157$	13.4869	+	13.4869i	1.07637	+	1.07637i	0.996832	+	0.0795382i	$0.0253446\pi$
$157$	13.4869	+	13.4869i	1.07637	+	1.07637i	0.0795382	+	0.996832i	$0.474655\pi$
$158$		0			0
$159$	6.45790	+	4.31503i	0.512145	+	0.342204i
$160$		0			0
$161$	−25.4167	−	10.5280i	−2.00312	−	0.829719i
$162$		0			0
$163$	−3.46089	+	0.688413i	−0.271078	+	0.0539207i	−0.328757	−	0.944414i	$-0.606630\pi$
$163$	−3.46089	+	0.688413i	−0.271078	+	0.0539207i	0.0576797	+	0.998335i	$0.481630\pi$
$164$		0			0
$165$	−1.72266	+	8.66040i	−0.134109	+	0.674211i
$166$		0			0
$167$	7.07994	+	10.5959i	0.547863	+	0.819934i	0.997304	−	0.0733754i	$-0.0233771\pi$
$167$	7.07994	+	10.5959i	0.547863	+	0.819934i	−0.449442	+	0.893310i	$0.648377\pi$
$168$		0			0
$169$			7.37975i			0.567673i
$170$		0			0
$171$	−7.55837			−0.578003
$172$		0			0
$173$	9.27081	−	6.19456i	0.704847	−	0.470964i	−0.150773	−	0.988568i	$-0.548176\pi$
$173$	9.27081	−	6.19456i	0.704847	−	0.470964i	0.855620	+	0.517605i	$0.173176\pi$
$174$		0			0
$175$	9.70753	+	1.93095i	0.733820	+	0.145966i
$176$		0			0
$177$	−3.14369	−	15.8044i	−0.236294	−	1.18793i
$178$		0			0
$179$	−1.32051	+	3.18798i	−0.0986992	+	0.238281i	−0.965515	−	0.260348i	$-0.916163\pi$
$179$	−1.32051	+	3.18798i	−0.0986992	+	0.238281i	0.866816	+	0.498629i	$0.166163\pi$
$180$		0			0
$181$	7.57255	−	11.3331i	0.562863	−	0.842385i	−0.435464	−	0.900206i	$-0.643416\pi$
$181$	7.57255	−	11.3331i	0.562863	−	0.842385i	0.998327	+	0.0578218i	$0.0184155\pi$
$182$		0			0
$183$	−14.1841	+	14.1841i	−1.04852	+	1.04852i
$184$		0			0
$185$	9.11002	−	3.77350i	0.669782	−	0.277433i
$186$		0			0
$187$	−5.73465	+	8.34766i	−0.419359	+	0.610441i
$188$		0			0
$189$	−7.31719	+	3.03088i	−0.532247	+	0.220464i
$190$		0			0
$191$	−15.5081	−	15.5081i	−1.12212	−	1.12212i	−0.991422	−	0.130703i	$-0.958276\pi$
$191$	−15.5081	−	15.5081i	−1.12212	−	1.12212i	−0.130703	−	0.991422i	$-0.541724\pi$
$192$		0			0
$193$	0.764638	−	1.14436i	0.0550398	−	0.0823730i	−0.802929	−	0.596075i	$-0.796726\pi$
$193$	0.764638	−	1.14436i	0.0550398	−	0.0823730i	0.857969	+	0.513702i	$0.171726\pi$
$194$		0			0
$195$	−7.87358	−	3.26134i	−0.563839	−	0.233550i
$196$		0			0
$197$	−2.05749	−	10.3437i	−0.146590	−	0.736957i	−0.982230	−	0.187680i	$-0.939903\pi$
$197$	−2.05749	−	10.3437i	−0.146590	−	0.736957i	0.835641	−	0.549277i	$-0.185097\pi$
$198$		0			0
$199$	3.58491	−	18.0226i	0.254128	−	1.27759i	−0.617169	−	0.786831i	$-0.711721\pi$
$199$	3.58491	−	18.0226i	0.254128	−	1.27759i	0.871297	−	0.490756i	$-0.163279\pi$
$200$		0			0
$201$	−11.5167	+	7.69523i	−0.812327	+	0.542779i
$202$		0			0
$203$		−	7.41768i		−	0.520619i
$204$		0			0
$205$		−	7.96050i		−	0.555985i
$206$		0			0
$207$	−12.1640	+	8.12774i	−0.845458	+	0.564917i
$208$		0			0
$209$	−1.70525	+	8.57287i	−0.117955	+	0.592998i
$210$		0			0
$211$	0.365262	+	1.83630i	0.0251457	+	0.126416i	0.991319	−	0.131477i	$-0.0419719\pi$
$211$	0.365262	+	1.83630i	0.0251457	+	0.126416i	−0.966174	+	0.257893i	$0.916972\pi$
$212$		0			0
$213$	14.0598	+	5.82374i	0.963359	+	0.399036i
$214$		0			0
$215$	2.50056	−	3.74235i	0.170537	−	0.255226i
$216$		0			0
$217$	27.5105	+	27.5105i	1.86753	+	1.86753i
$218$		0			0
$219$	29.8026	−	12.3446i	2.01387	−	0.834173i
$220$		0			0
$221$	−6.82212	−	7.00021i	−0.458905	−	0.470885i
$222$		0			0
$223$	12.4584	−	5.16043i	0.834275	−	0.345568i	0.0756812	−	0.997132i	$-0.475887\pi$
$223$	12.4584	−	5.16043i	0.834275	−	0.345568i	0.758594	+	0.651564i	$0.225887\pi$
$224$		0			0
$225$	3.72174	−	3.72174i	0.248116	−	0.248116i
$226$		0			0
$227$	−11.5521	+	17.2889i	−0.766738	+	1.14750i	0.218420	+	0.975855i	$0.429910\pi$
$227$	−11.5521	+	17.2889i	−0.766738	+	1.14750i	−0.985158	+	0.171650i	$0.945090\pi$
$228$		0			0
$229$	−9.64260	+	23.2793i	−0.637201	+	1.53834i	0.193193	+	0.981161i	$0.438116\pi$
$229$	−9.64260	+	23.2793i	−0.637201	+	1.53834i	−0.830393	+	0.557178i	$0.811884\pi$
$230$		0			0
$231$	−4.33273	−	21.7821i	−0.285073	−	1.43316i
$232$		0			0
$233$	−2.27157	−	0.451844i	−0.148816	−	0.0296013i	0.120120	−	0.992759i	$-0.461672\pi$
$233$	−2.27157	−	0.451844i	−0.148816	−	0.0296013i	−0.268936	+	0.963158i	$0.586672\pi$
$234$		0			0
$235$	5.36280	−	3.58331i	0.349830	−	0.233749i
$236$		0			0
$237$	−28.7604			−1.86819
$238$		0			0
$239$		−	11.2231i		−	0.725965i	−0.931796	−	0.362982i	$-0.881759\pi$
$239$		−	11.2231i		−	0.725965i	0.931796	−	0.362982i	$-0.118241\pi$
$240$		0			0
$241$	−3.12364	−	4.67486i	−0.201211	−	0.301134i	0.717118	−	0.696952i	$-0.245461\pi$
$241$	−3.12364	−	4.67486i	−0.201211	−	0.301134i	−0.918329	+	0.395818i	$0.870461\pi$
$242$		0			0
$243$	−3.63566	+	18.2777i	−0.233228	+	1.17251i
$244$		0			0
$245$	13.9465	−	2.77413i	0.891008	−	0.177232i
$246$		0			0
$247$	−7.79400	−	3.22838i	−0.495920	−	0.205417i
$248$		0			0
$249$	32.6081	+	21.7880i	2.06645	+	1.38076i
$250$		0			0
$251$	11.1300	+	11.1300i	0.702519	+	0.702519i	0.964951	−	0.262432i	$-0.0845244\pi$
$251$	11.1300	+	11.1300i	0.702519	+	0.702519i	−0.262432	+	0.964951i	$0.584524\pi$
$252$		0			0
$253$	6.47432	+	15.6304i	0.407037	+	0.982674i
$254$		0			0
$255$	−13.7656	+	5.49520i	−0.862034	+	0.344123i
$256$		0			0
$257$	1.55502	+	3.75414i	0.0969992	+	0.234177i	0.964929	−	0.262509i	$-0.0845500\pi$
$257$	1.55502	+	3.75414i	0.0969992	+	0.234177i	−0.867930	+	0.496686i	$0.834550\pi$
$258$		0			0
$259$	−17.5368	+	17.5368i	−1.08968	+	1.08968i
$260$		0			0
$261$	−3.27975	−	2.19146i	−0.203011	−	0.135648i
$262$		0			0
$263$	−5.20634	+	12.5692i	−0.321037	+	0.775051i	0.678158	+	0.734916i	$0.262779\pi$
$263$	−5.20634	+	12.5692i	−0.321037	+	0.775051i	−0.999194	+	0.0401344i	$0.987221\pi$
$264$		0			0
$265$	5.34425	−	1.06304i	0.328294	−	0.0653018i
$266$		0			0
$267$	1.39113	+	0.276714i	0.0851360	+	0.0169346i
$268$		0			0
$269$	0.757121	+	1.13311i	0.0461625	+	0.0690871i	0.853833	−	0.520547i	$-0.174272\pi$
$269$	0.757121	+	1.13311i	0.0461625	+	0.0690871i	−0.807670	+	0.589634i	$0.799272\pi$
$270$		0			0
$271$	−1.17410			−0.0713212			−0.0356606	−	0.999364i	$-0.511354\pi$
$271$	−1.17410			−0.0713212			−0.0356606	+	0.999364i	$0.511354\pi$
$272$		0			0
$273$	21.4348			1.29729
$274$		0			0
$275$	−3.38161	−	5.06094i	−0.203919	−	0.305186i
$276$		0			0
$277$	−25.2299	−	5.01854i	−1.51592	−	0.301535i	−0.634147	−	0.773212i	$-0.718649\pi$
$277$	−25.2299	−	5.01854i	−1.51592	−	0.301535i	−0.881771	+	0.471677i	$0.843649\pi$
$278$		0			0
$279$	20.2915	−	4.03622i	1.21482	−	0.241642i
$280$		0			0
$281$	−1.11240	+	2.68556i	−0.0663600	+	0.160207i	−0.953580	−	0.301139i	$-0.902633\pi$
$281$	−1.11240	+	2.68556i	−0.0663600	+	0.160207i	0.887220	+	0.461346i	$0.152633\pi$
$282$		0			0
$283$	5.74499	+	3.83868i	0.341504	+	0.228186i	0.714481	−	0.699655i	$-0.246663\pi$
$283$	5.74499	+	3.83868i	0.341504	+	0.228186i	−0.372977	+	0.927841i	$0.621663\pi$
$284$		0			0
$285$	−9.04548	+	9.04548i	−0.535808	+	0.535808i
$286$		0			0
$287$	7.66199	+	18.4977i	0.452273	+	1.09188i
$288$		0			0
$289$	−16.9944	−	0.438000i	−0.999668	−	0.0257647i
$290$		0			0
$291$	8.10072	+	19.5569i	0.474872	+	1.14644i
$292$		0			0
$293$	10.3468	+	10.3468i	0.604467	+	0.604467i	0.941495	−	0.337028i	$-0.109422\pi$
$293$	10.3468	+	10.3468i	0.604467	+	0.604467i	−0.337028	+	0.941495i	$0.609422\pi$
$294$		0			0
$295$	−9.39978	−	6.28073i	−0.547277	−	0.365678i
$296$		0			0
$297$	4.49981	+	1.86388i	0.261105	+	0.108153i
$298$		0			0
$299$	−16.0148	+	3.18554i	−0.926159	+	0.184225i
$300$		0			0
$301$	−2.20849	+	11.1028i	−0.127295	+	0.639956i
$302$		0			0
$303$	6.42023	+	9.60855i	0.368833	+	0.551997i
$304$		0			0
$305$			14.0729i			0.805811i
$306$		0			0
$307$	26.5174			1.51343			0.756715	−	0.653745i	$-0.226803\pi$
$307$	26.5174			1.51343			0.756715	+	0.653745i	$0.226803\pi$
$308$		0			0
$309$	0.498959	−	0.333394i	0.0283848	−	0.0189661i
$310$		0			0
$311$	−6.62139	−	1.31708i	−0.375465	−	0.0746846i	0.00375083	−	0.999993i	$-0.498806\pi$
$311$	−6.62139	−	1.31708i	−0.375465	−	0.0746846i	−0.379215	+	0.925308i	$0.623806\pi$
$312$		0			0
$313$	−0.830614	−	4.17578i	−0.0469491	−	0.236029i	0.950185	−	0.311687i	$-0.100894\pi$
$313$	−0.830614	−	4.17578i	−0.0469491	−	0.236029i	−0.997134	+	0.0756583i	$0.975894\pi$
$314$		0			0
$315$	5.15595	−	12.4476i	0.290505	−	0.701341i
$316$		0			0
$317$	−6.65233	+	9.95591i	−0.373632	+	0.559180i	−0.969868	−	0.243629i	$-0.921662\pi$
$317$	−6.65233	+	9.95591i	−0.373632	+	0.559180i	0.596237	+	0.802809i	$0.296662\pi$
$318$		0			0
$319$	−3.22555	+	3.22555i	−0.180596	+	0.180596i
$320$		0			0
$321$	10.9823	−	4.54901i	0.612971	−	0.253901i
$322$		0			0
$323$	−13.6264	+	5.43966i	−0.758196	+	0.302671i
$324$		0			0
$325$	5.42741	−	2.24811i	0.301059	−	0.124703i
$326$		0			0
$327$	15.6420	+	15.6420i	0.865004	+	0.865004i
$328$		0			0
$329$	−9.01250	+	13.4882i	−0.496875	+	0.743627i
$330$		0			0
$331$	−7.49253	−	3.10351i	−0.411827	−	0.170584i	0.167144	−	0.985932i	$-0.446545\pi$
$331$	−7.49253	−	3.10351i	−0.411827	−	0.170584i	−0.578971	+	0.815348i	$0.696545\pi$
$332$		0			0
$333$	2.57293	+	12.9350i	0.140996	+	0.708833i
$334$		0			0
$335$	−1.89577	+	9.53068i	−0.103577	+	0.520717i
$336$		0			0
$337$	−22.3238	+	14.9163i	−1.21605	+	0.812541i	−0.986976	−	0.160868i	$-0.948571\pi$
$337$	−22.3238	+	14.9163i	−1.21605	+	0.812541i	−0.229077	+	0.973408i	$0.573571\pi$
$338$		0			0
$339$		−	18.2487i		−	0.991133i
$340$		0			0
$341$		−	23.9256i		−	1.29564i
$342$		0			0
$343$	−6.48943	+	4.33610i	−0.350396	+	0.234127i
$344$		0			0
$345$	−4.83042	+	24.2841i	−0.260061	+	1.30741i
$346$		0			0
$347$	0.808226	+	4.06323i	0.0433878	+	0.218125i	0.996396	−	0.0848177i	$-0.0270308\pi$
$347$	0.808226	+	4.06323i	0.0433878	+	0.218125i	−0.953009	+	0.302943i	$0.902031\pi$
$348$		0			0
$349$	−10.7699	−	4.46102i	−0.576497	−	0.238793i	0.0753324	−	0.997158i	$-0.475998\pi$
$349$	−10.7699	−	4.46102i	−0.576497	−	0.238793i	−0.651829	+	0.758366i	$0.725998\pi$
$350$		0			0
$351$	−2.61162	+	3.90857i	−0.139398	+	0.208624i
$352$		0			0
$353$	−14.2069	−	14.2069i	−0.756155	−	0.756155i	0.219466	−	0.975620i	$-0.429569\pi$
$353$	−14.2069	−	14.2069i	−0.756155	−	0.756155i	−0.975620	+	0.219466i	$0.929569\pi$
$354$		0			0
$355$	9.86382	−	4.08573i	0.523517	−	0.216848i
$356$		0			0
$357$	26.6977	−	26.0185i	1.41299	−	1.37704i
$358$		0			0
$359$	−7.57532	+	3.13780i	−0.399810	+	0.165607i	−0.573523	−	0.819190i	$-0.694424\pi$
$359$	−7.57532	+	3.13780i	−0.399810	+	0.165607i	0.173713	+	0.984796i	$0.444424\pi$
$360$		0			0
$361$	4.48098	−	4.48098i	0.235841	−	0.235841i
$362$		0			0
$363$	6.24590	−	9.34765i	0.327825	−	0.490624i
$364$		0			0
$365$	8.66055	−	20.9084i	0.453314	−	1.09440i
$366$		0			0
$367$	−2.36264	−	11.8778i	−0.123329	−	0.620017i	−0.992167	−	0.124920i	$-0.960133\pi$
$367$	−2.36264	−	11.8778i	−0.123329	−	0.620017i	0.868838	−	0.495097i	$-0.164867\pi$
$368$		0			0
$369$	10.4424	+	2.07713i	0.543612	+	0.108131i
$370$		0			0
$371$	−11.3952	+	7.61400i	−0.591607	+	0.395299i
$372$		0			0
$373$	−26.2968			−1.36160			−0.680798	−	0.732471i	$-0.738367\pi$
$373$	−26.2968			−1.36160			−0.680798	+	0.732471i	$0.738367\pi$
$374$		0			0
$375$		−	26.8822i		−	1.38819i
$376$		0			0
$377$	−2.44596	−	3.66064i	−0.125974	−	0.188533i
$378$		0			0
$379$	−1.94490	+	9.77769i	−0.0999030	+	0.502246i	0.898140	+	0.439710i	$0.144919\pi$
$379$	−1.94490	+	9.77769i	−0.0999030	+	0.502246i	−0.998043	+	0.0625360i	$0.980081\pi$
$380$		0			0
$381$	1.25264	−	0.249165i	0.0641745	−	0.0127651i
$382$		0			0
$383$	−10.5148	−	4.35536i	−0.537280	−	0.222549i	0.0975084	−	0.995235i	$-0.468913\pi$
$383$	−10.5148	−	4.35536i	−0.537280	−	0.222549i	−0.634788	+	0.772686i	$0.718913\pi$
$384$		0			0
$385$	−12.9551	−	8.65629i	−0.660251	−	0.441166i
$386$		0			0
$387$	4.25668	+	4.25668i	0.216379	+	0.216379i
$388$		0			0
$389$	−7.68665	−	18.5572i	−0.389729	−	0.940889i	−0.989997	−	0.141090i	$-0.954939\pi$
$389$	−7.68665	−	18.5572i	−0.389729	−	0.940889i	0.600268	−	0.799799i	$-0.295061\pi$
$390$		0			0
$391$	−16.0802	+	23.4072i	−0.813211	+	1.18375i
$392$		0			0
$393$	−17.3147	−	41.8013i	−0.873409	−	2.10860i
$394$		0			0
$395$	−14.2675	+	14.2675i	−0.717874	+	0.717874i
$396$		0			0
$397$	2.64896	+	1.76998i	0.132948	+	0.0888328i	0.620266	−	0.784392i	$-0.287025\pi$
$397$	2.64896	+	1.76998i	0.132948	+	0.0888328i	−0.487318	+	0.873225i	$0.662025\pi$
$398$		0			0
$399$	12.3125	−	29.7251i	0.616398	−	1.48812i
$400$		0			0
$401$	−25.1811	+	5.00882i	−1.25748	+	0.250129i	−0.778471	−	0.627680i	$-0.784005\pi$
$401$	−25.1811	+	5.00882i	−1.25748	+	0.250129i	−0.479011	+	0.877809i	$0.659005\pi$
$402$		0			0
$403$	22.6480	+	4.50497i	1.12818	+	0.224408i
$404$		0			0
$405$	9.58220	+	14.3408i	0.476144	+	0.712599i
$406$		0			0
$407$	15.2516			0.755994
$408$		0			0
$409$	6.70044			0.331316			0.165658	−	0.986183i	$-0.447025\pi$
$409$	6.70044			0.331316			0.165658	+	0.986183i	$0.447025\pi$
$410$		0			0
$411$	−3.84669	−	5.75699i	−0.189743	−	0.283971i
$412$		0			0
$413$	27.8873	+	5.54714i	1.37225	+	0.272957i
$414$		0			0
$415$	26.9849	−	5.36763i	1.32464	−	0.263486i
$416$		0			0
$417$	7.70055	−	18.5908i	0.377097	−	0.910393i
$418$		0			0
$419$	−5.44403	−	3.63759i	−0.265958	−	0.177708i	0.415440	−	0.909621i	$-0.363628\pi$
$419$	−5.44403	−	3.63759i	−0.265958	−	0.177708i	−0.681398	+	0.731913i	$0.738628\pi$
$420$		0			0
$421$	21.5388	−	21.5388i	1.04973	−	1.04973i	0.0510380	−	0.998697i	$-0.483747\pi$
$421$	21.5388	−	21.5388i	1.04973	−	1.04973i	0.998697	−	0.0510380i	$-0.0162530\pi$
$422$		0			0
$423$	3.30121	+	7.96981i	0.160510	+	0.387506i
$424$		0			0
$425$	4.03117	−	9.38814i	0.195541	−	0.455392i
$426$		0			0
$427$	−13.5452	−	32.7009i	−0.655497	−	1.58251i
$428$		0			0
$429$	−9.32081	−	9.32081i	−0.450013	−	0.450013i
$430$		0			0
$431$	−17.7741	−	11.8762i	−0.856146	−	0.572059i	0.0482099	−	0.998837i	$-0.484648\pi$
$431$	−17.7741	−	11.8762i	−0.856146	−	0.572059i	−0.904356	+	0.426779i	$0.859648\pi$
$432$		0			0
$433$	6.61056	+	2.73819i	0.317683	+	0.131589i	0.535827	−	0.844328i	$-0.320000\pi$
$433$	6.61056	+	2.73819i	0.317683	+	0.131589i	−0.218143	+	0.975917i	$0.570000\pi$
$434$		0			0
$435$	−6.54766	+	1.30241i	−0.313936	+	0.0624458i
$436$		0			0
$437$	−4.78159	+	24.0387i	−0.228735	+	1.14993i
$438$		0			0
$439$	3.66708	+	5.48817i	0.175020	+	0.261936i	0.908600	−	0.417667i	$-0.137152\pi$
$439$	3.66708	+	5.48817i	0.175020	+	0.261936i	−0.733580	+	0.679603i	$0.762152\pi$
$440$		0			0
$441$			19.0186i			0.905647i
$442$		0			0
$443$	0.0876330			0.00416357			0.00208179	−	0.999998i	$-0.499337\pi$
$443$	0.0876330			0.00416357			0.00208179	+	0.999998i	$0.499337\pi$
$444$		0			0
$445$	0.827387	−	0.552843i	0.0392219	−	0.0262072i
$446$		0			0
$447$	−27.0772	−	5.38598i	−1.28071	−	0.254748i
$448$		0			0
$449$	−7.14374	−	35.9140i	−0.337134	−	1.69489i	−0.662308	−	0.749232i	$-0.730423\pi$
$449$	−7.14374	−	35.9140i	−0.337134	−	1.69489i	0.325174	−	0.945654i	$-0.394577\pi$
$450$		0			0
$451$	4.71185	−	11.3754i	0.221872	−	0.535647i
$452$		0			0
$453$	−12.9003	+	19.3067i	−0.606110	+	0.907108i
$454$		0			0
$455$	10.6334	−	10.6334i	0.498500	−	0.498500i
$456$		0			0
$457$	−6.50023	+	2.69248i	−0.304068	+	0.125949i	−0.529500	−	0.848310i	$-0.677621\pi$
$457$	−6.50023	+	2.69248i	−0.304068	+	0.125949i	0.225432	+	0.974259i	$0.427621\pi$
$458$		0			0
$459$	1.49154	+	8.03837i	0.0696190	+	0.375199i
$460$		0			0
$461$	12.8491	−	5.32227i	0.598442	−	0.247883i	−0.0628356	−	0.998024i	$-0.520014\pi$
$461$	12.8491	−	5.32227i	0.598442	−	0.247883i	0.661278	+	0.750141i	$0.270014\pi$
$462$		0			0
$463$	−7.89732	−	7.89732i	−0.367019	−	0.367019i	0.499370	−	0.866389i	$-0.333565\pi$
$463$	−7.89732	−	7.89732i	−0.367019	−	0.367019i	−0.866389	+	0.499370i	$0.833565\pi$
$464$		0			0
$465$	19.4534	−	29.1141i	0.902131	−	1.35014i
$466$		0			0
$467$	20.6714	+	8.56237i	0.956557	+	0.396219i	0.805692	−	0.592335i	$-0.201794\pi$
$467$	20.6714	+	8.56237i	0.956557	+	0.396219i	0.150866	+	0.988554i	$0.451794\pi$
$468$		0			0
$469$	−4.76812	−	23.9710i	−0.220171	−	1.10688i
$470$		0			0
$471$	−8.42303	+	42.3454i	−0.388113	+	1.95117i
$472$		0			0
$473$	5.78837	−	3.86766i	0.266149	−	0.177835i
$474$		0			0
$475$		−	8.81794i		−	0.404595i
$476$		0			0
$477$			7.28787i			0.333689i
$478$		0			0
$479$	13.6534	−	9.12292i	0.623841	−	0.416837i	−0.203075	−	0.979163i	$-0.565093\pi$
$479$	13.6534	−	9.12292i	0.623841	−	0.416837i	0.826916	+	0.562326i	$0.190093\pi$
$480$		0			0
$481$	−2.87173	+	14.4372i	−0.130940	+	0.658279i
$482$		0			0
$483$	−12.1492	−	61.0779i	−0.552806	−	2.77914i
$484$		0			0
$485$	13.7204	+	5.68317i	0.623011	+	0.258060i
$486$		0			0
$487$	−1.02911	+	1.54017i	−0.0466334	+	0.0697918i	−0.854054	−	0.520185i	$-0.825863\pi$
$487$	−1.02911	+	1.54017i	−0.0466334	+	0.0697918i	0.807420	+	0.589977i	$0.200863\pi$
$488$		0			0
$489$	−5.64813	−	5.64813i	−0.255417	−	0.255417i
$490$		0			0
$491$	8.00880	−	3.31735i	0.361432	−	0.149710i	−0.194575	−	0.980888i	$-0.562333\pi$
$491$	8.00880	−	3.31735i	0.361432	−	0.149710i	0.556007	+	0.831178i	$0.312333\pi$
$492$		0			0
$493$	−7.48999	−	1.59043i	−0.337332	−	0.0716295i
$494$		0			0
$495$	−7.65481	+	3.17073i	−0.344058	+	0.142514i
$496$		0			0
$497$	−18.9879	+	18.9879i	−0.851723	+	0.851723i
$498$		0			0
$499$	−15.5586	+	23.2852i	−0.696501	+	1.04239i	0.299592	+	0.954068i	$0.403150\pi$
$499$	−15.5586	+	23.2852i	−0.696501	+	1.04239i	−0.996092	+	0.0883192i	$0.971850\pi$
$500$		0			0
$501$	−11.0392	+	26.6509i	−0.493194	+	1.19068i
$502$		0			0
$503$	1.42171	+	7.14743i	0.0633910	+	0.318688i	0.999450	−	0.0331543i	$-0.0105553\pi$
$503$	1.42171	+	7.14743i	0.0633910	+	0.318688i	−0.936059	+	0.351842i	$0.885555\pi$
$504$		0			0
$505$	7.95157	+	1.58167i	0.353840	+	0.0703832i
$506$		0			0
$507$	−13.8897	+	9.28083i	−0.616865	+	0.412176i
$508$		0			0
$509$	21.5629			0.955760			0.477880	−	0.878425i	$-0.341405\pi$
$509$	21.5629			0.955760			0.477880	+	0.878425i	$0.341405\pi$
$510$		0			0
$511$			56.9203i			2.51801i
$512$		0			0
$513$	3.92013	+	5.86688i	0.173078	+	0.259029i
$514$		0			0
$515$	0.0821337	−	0.412914i	0.00361924	−	0.0181952i
$516$		0			0
$517$	9.78432	−	1.94622i	0.430314	−	0.0855947i
$518$		0			0
$519$	23.3181	+	9.65866i	1.02355	+	0.423968i
$520$		0			0
$521$	4.85313	+	3.24276i	0.212619	+	0.142068i	0.657320	−	0.753611i	$-0.271690\pi$
$521$	4.85313	+	3.24276i	0.212619	+	0.142068i	−0.444701	+	0.895679i	$0.646690\pi$
$522$		0			0
$523$	0.928399	+	0.928399i	0.0405961	+	0.0405961i	0.727113	−	0.686517i	$-0.240861\pi$
$523$	0.928399	+	0.928399i	0.0405961	+	0.0405961i	−0.686517	+	0.727113i	$0.740861\pi$
$524$		0			0
$525$	8.57394	+	20.6993i	0.374197	+	0.903392i
$526$		0			0
$527$	33.6772	−	21.8801i	1.46700	−	0.953112i
$528$		0			0
$529$	9.35256	+	22.5791i	0.406633	+	0.981699i
$530$		0			0
$531$	10.6916	−	10.6916i	0.463978	−	0.463978i
$532$		0			0
$533$	9.88077	+	6.60212i	0.427984	+	0.285970i
$534$		0			0
$535$	3.19142	−	7.70477i	0.137977	−	0.333106i
$536$		0			0
$537$	−7.66091	+	1.52385i	−0.330593	+	0.0657590i
$538$		0			0
$539$	21.5713	+	4.29080i	0.929141	+	0.184818i
$540$		0			0
$541$	−20.1913	−	30.2184i	−0.868092	−	1.29919i	−0.953052	−	0.302807i	$-0.902076\pi$
$541$	−20.1913	−	30.2184i	−0.868092	−	1.29919i	0.0849601	−	0.996384i	$-0.472924\pi$
$542$		0			0
$543$	30.8538			1.32406
$544$		0			0
$545$	15.5194			0.664777
$546$		0			0
$547$	4.20366	+	6.29123i	0.179736	+	0.268993i	0.910387	−	0.413757i	$-0.135784\pi$
$547$	4.20366	+	6.29123i	0.179736	+	0.268993i	−0.730652	+	0.682750i	$0.760784\pi$
$548$		0			0
$549$	−18.4606	−	3.67204i	−0.787878	−	0.156719i
$550$		0			0
$551$	−6.48148	+	1.28925i	−0.276120	+	0.0549238i
$552$		0			0
$553$	19.4206	−	46.8855i	0.825849	−	1.99378i
$554$		0			0
$555$	18.5591	+	12.4008i	0.787789	+	0.526384i
$556$		0			0
$557$	−26.1434	+	26.1434i	−1.10773	+	1.10773i	−0.114283	+	0.993448i	$0.536457\pi$
$557$	−26.1434	+	26.1434i	−1.10773	+	1.10773i	−0.993448	+	0.114283i	$0.963543\pi$
$558$		0			0
$559$	2.57124	+	6.20751i	0.108752	+	0.262550i
$560$		0			0
$561$	−22.9234	−	0.295356i	−0.967827	−	0.0124700i
$562$		0			0
$563$	−9.43760	−	22.7844i	−0.397748	−	0.960248i	−0.988199	−	0.153175i	$-0.951050\pi$
$563$	−9.43760	−	22.7844i	−0.397748	−	0.960248i	0.590452	−	0.807073i	$-0.298950\pi$
$564$		0			0
$565$	−9.05282	−	9.05282i	−0.380855	−	0.380855i
$566$		0			0
$567$	−36.0690	−	24.1006i	−1.51476	−	1.01213i
$568$		0			0
$569$	21.6080	+	8.95034i	0.905856	+	0.375218i	0.786469	−	0.617630i	$-0.211907\pi$
$569$	21.6080	+	8.95034i	0.905856	+	0.375218i	0.119387	+	0.992848i	$0.461907\pi$
$570$		0			0
$571$	−7.43083	+	1.47808i	−0.310971	+	0.0618559i	−0.348109	−	0.937454i	$-0.613176\pi$
$571$	−7.43083	+	1.47808i	−0.310971	+	0.0618559i	0.0371378	+	0.999310i	$0.488176\pi$
$572$		0			0
$573$	9.68533	−	48.6915i	0.404611	−	2.03411i
$574$		0			0
$575$	−9.48219	−	14.1911i	−0.395434	−	0.591810i
$576$		0			0
$577$		−	15.4426i		−	0.642884i	−0.946929	−	0.321442i	$-0.895832\pi$
$577$		−	15.4426i		−	0.642884i	0.946929	−	0.321442i	$-0.104168\pi$
$578$		0			0
$579$	3.11546			0.129474
$580$		0			0
$581$	−57.5380	+	38.4456i	−2.38708	+	1.59499i
$582$		0			0
$583$	8.26605	+	1.64422i	0.342345	+	0.0680966i
$584$		0			0
$585$	−1.56008	−	7.84307i	−0.0645015	−	0.324271i
$586$		0			0
$587$	4.61264	−	11.1359i	0.190384	−	0.459628i	−0.799648	−	0.600469i	$-0.794981\pi$
$587$	4.61264	−	11.1359i	0.190384	−	0.459628i	0.990032	+	0.140841i	$0.0449807\pi$
$588$		0			0
$589$	19.2568	−	28.8199i	0.793463	−	1.18750i
$590$		0			0
$591$	16.8808	−	16.8808i	0.694382	−	0.694382i
$592$		0			0
$593$	27.8859	−	11.5507i	1.14514	−	0.474332i	0.272237	−	0.962230i	$-0.412236\pi$
$593$	27.8859	−	11.5507i	1.14514	−	0.474332i	0.872900	+	0.487898i	$0.162236\pi$
$594$		0			0
$595$	0.336949	−	26.1515i	0.0138136	−	1.07211i
$596$		0			0
$597$	38.4295	−	15.9180i	1.57281	−	0.651481i
$598$		0			0
$599$	−11.1432	−	11.1432i	−0.455299	−	0.455299i	0.441810	−	0.897109i	$-0.354337\pi$
$599$	−11.1432	−	11.1432i	−0.455299	−	0.455299i	−0.897109	+	0.441810i	$0.854337\pi$
$600$		0			0
$601$	−24.8557	+	37.1992i	−1.01389	+	1.51739i	−0.166759	+	0.985998i	$0.553330\pi$
$601$	−24.8557	+	37.1992i	−1.01389	+	1.51739i	−0.847127	+	0.531390i	$0.821670\pi$
$602$		0			0
$603$	−12.0075	−	4.97367i	−0.488984	−	0.202544i
$604$		0			0
$605$	−1.53872	−	7.73566i	−0.0625578	−	0.314499i
$606$		0			0
$607$	2.44705	−	12.3021i	0.0993225	−	0.499328i	−0.898815	−	0.438328i	$-0.855571\pi$
$607$	2.44705	−	12.3021i	0.0993225	−	0.499328i	0.998138	−	0.0610004i	$-0.0194291\pi$
$608$		0			0
$609$	13.9611	−	9.32853i	0.565733	−	0.378011i
$610$		0			0
$611$			9.62830i			0.389519i
$612$		0			0
$613$			37.9509i			1.53282i	0.642351	+	0.766411i	$0.277959\pi$
$613$			37.9509i			1.53282i	−0.642351	+	0.766411i	$0.722041\pi$
$614$		0			0
$615$	14.9828	−	10.0112i	0.604164	−	0.403690i
$616$		0			0
$617$	−1.83441	+	9.22219i	−0.0738505	+	0.371272i	−0.999982	−	0.00592821i	$-0.998113\pi$
$617$	−1.83441	+	9.22219i	−0.0738505	+	0.371272i	0.926132	+	0.377200i	$0.123113\pi$
$618$		0			0
$619$	−7.07536	−	35.5702i	−0.284383	−	1.42969i	−0.813710	−	0.581271i	$-0.802556\pi$
$619$	−7.07536	−	35.5702i	−0.284383	−	1.42969i	0.529328	−	0.848418i	$-0.322444\pi$
$620$		0			0
$621$	12.6177	+	5.22641i	0.506329	+	0.209729i
$622$		0			0
$623$	−1.39047	+	2.08099i	−0.0557082	+	0.0833732i
$624$		0			0
$625$	−4.57470	−	4.57470i	−0.182988	−	0.182988i
$626$		0			0
$627$	−18.2799	+	7.57178i	−0.730028	+	0.302388i
$628$		0			0
$629$	13.9477	+	21.4679i	0.556130	+	0.855979i
$630$		0			0
$631$	31.6304	−	13.1018i	1.25919	−	0.521573i	0.349528	−	0.936926i	$-0.386342\pi$
$631$	31.6304	−	13.1018i	1.25919	−	0.521573i	0.909660	+	0.415353i	$0.136342\pi$
$632$		0			0
$633$	−2.99681	+	2.99681i	−0.119113	+	0.119113i
$634$		0			0
$635$	0.497803	−	0.745015i	0.0197547	−	0.0295650i
$636$		0			0
$637$	−8.12334	+	19.6115i	−0.321858	+	0.777035i
$638$		0			0
$639$	2.78582	+	14.0053i	0.110205	+	0.554040i
$640$		0			0
$641$	41.0725	+	8.16982i	1.62226	+	0.322688i	0.920806	−	0.390022i	$-0.127532\pi$
$641$	41.0725	+	8.16982i	1.62226	+	0.322688i	0.701459	+	0.712710i	$0.252532\pi$
$642$		0			0
$643$	12.8831	−	8.60823i	0.508061	−	0.339475i	−0.274976	−	0.961451i	$-0.588670\pi$
$643$	12.8831	−	8.60823i	0.508061	−	0.339475i	0.783037	+	0.621976i	$0.213670\pi$
$644$		0			0
$645$	10.1883			0.401166
$646$		0			0
$647$			4.31868i			0.169785i	0.996390	+	0.0848923i	$0.0270546\pi$
$647$			4.31868i			0.169785i	−0.996390	+	0.0848923i	$0.972945\pi$
$648$		0			0
$649$	−9.71454	−	14.5388i	−0.381329	−	0.570699i
$650$		0			0
$651$	−17.1812	+	86.3760i	−0.673386	+	3.38534i
$652$		0			0
$653$	−16.4937	+	3.28079i	−0.645447	+	0.128387i	−0.506950	−	0.861975i	$-0.669227\pi$
$653$	−16.4937	+	3.28079i	−0.645447	+	0.128387i	−0.138497	+	0.990363i	$0.544227\pi$
$654$		0			0
$655$	−29.3263	−	12.1473i	−1.14587	−	0.474636i
$656$		0			0
$657$	25.1675	+	16.8164i	0.981877	+	0.656070i
$658$		0			0
$659$	−24.3424	−	24.3424i	−0.948246	−	0.948246i	0.0504793	−	0.998725i	$-0.483925\pi$
$659$	−24.3424	−	24.3424i	−0.948246	−	0.948246i	−0.998725	+	0.0504793i	$0.983925\pi$
$660$		0			0
$661$	13.8353	+	33.4013i	0.538130	+	1.29916i	0.926027	+	0.377457i	$0.123202\pi$
$661$	13.8353	+	33.4013i	0.538130	+	1.29916i	−0.387897	+	0.921703i	$0.626798\pi$
$662$		0			0
$663$	4.59585	−	21.6437i	0.178488	−	0.840572i
$664$		0			0
$665$	−8.63804	−	20.8541i	−0.334969	−	0.808686i
$666$		0			0
$667$	−9.04457	+	9.04457i	−0.350207	+	0.350207i
$668$		0			0
$669$	25.3804	+	16.9586i	0.981263	+	0.655659i
$670$		0			0
$671$	−8.32980	+	20.1099i	−0.321568	+	0.776335i
$672$		0			0
$673$	−37.1218	+	7.38398i	−1.43094	+	0.284631i	−0.848910	−	0.528537i	$-0.822741\pi$
$673$	−37.1218	+	7.38398i	−1.43094	+	0.284631i	−0.582028	+	0.813168i	$0.697741\pi$
$674$		0			0
$675$	−4.81912	−	0.958583i	−0.185488	−	0.0368959i
$676$		0			0
$677$	−5.75120	−	8.60728i	−0.221037	−	0.330805i	0.704334	−	0.709869i	$-0.251246\pi$
$677$	−5.75120	−	8.60728i	−0.221037	−	0.330805i	−0.925370	+	0.379064i	$0.876246\pi$
$678$		0			0
$679$	−37.3519			−1.43343
$680$		0			0
$681$	−47.0681			−1.80366
$682$		0			0
$683$	2.82528	+	4.22832i	0.108106	+	0.161792i	0.881578	−	0.472038i	$-0.156482\pi$
$683$	2.82528	+	4.22832i	0.108106	+	0.161792i	−0.773472	+	0.633831i	$0.781482\pi$
$684$		0			0
$685$	−4.76420	−	0.947658i	−0.182031	−	0.0362082i
$686$		0			0
$687$	−55.9415	+	11.1275i	−2.13430	+	0.424539i
$688$		0			0
$689$	−3.11284	+	7.51506i	−0.118590	+	0.286301i
$690$		0			0
$691$	1.80294	+	1.20468i	0.0685870	+	0.0458283i	0.589391	−	0.807848i	$-0.299368\pi$
$691$	1.80294	+	1.20468i	0.0685870	+	0.0458283i	−0.520804	+	0.853676i	$0.674368\pi$
$692$		0			0
$693$	14.7355	−	14.7355i	0.559757	−	0.559757i
$694$		0			0
$695$	−5.40243	−	13.0426i	−0.204926	−	0.494734i
$696$		0			0
$697$	20.3208	−	3.77057i	0.769705	−	0.142821i
$698$		0			0
$699$	−2.00631	−	4.84366i	−0.0758856	−	0.183204i
$700$		0			0
$701$	−29.0858	−	29.0858i	−1.09856	−	1.09856i	−0.994580	−	0.103977i	$-0.966843\pi$
$701$	−29.0858	−	29.0858i	−1.09856	−	1.09856i	−0.103977	−	0.994580i	$-0.533157\pi$
$702$		0			0
$703$	18.3715	+	12.2754i	0.692894	+	0.462977i
$704$		0			0
$705$	13.4886	+	5.58715i	0.508009	+	0.210424i
$706$		0			0
$707$	−19.9993	+	3.97810i	−0.752150	+	0.149612i
$708$		0			0
$709$	2.89581	−	14.5582i	0.108754	−	0.546745i	−0.887540	−	0.460731i	$-0.847587\pi$
$709$	2.89581	−	14.5582i	0.108754	−	0.546745i	0.996294	−	0.0860136i	$-0.0274128\pi$
$710$		0			0
$711$	−14.9930	−	22.4386i	−0.562282	−	0.841514i
$712$		0			0
$713$		−	67.0885i		−	2.51248i
$714$		0			0
$715$	−9.24775			−0.345846
$716$		0			0
$717$	21.1235	−	14.1143i	0.788873	−	0.527108i
$718$		0			0
$719$	−17.5647	−	3.49383i	−0.655052	−	0.130298i	−0.143635	−	0.989631i	$-0.545879\pi$
$719$	−17.5647	−	3.49383i	−0.655052	−	0.130298i	−0.511417	+	0.859333i	$0.670879\pi$
$720$		0			0
$721$	0.206578	+	1.03854i	0.00769335	+	0.0386771i
$722$		0			0
$723$	4.87043	−	11.7583i	0.181133	−	0.437294i
$724$		0			0
$725$	2.55665	−	3.82630i	0.0949518	−	0.142105i
$726$		0			0
$727$	9.14200	−	9.14200i	0.339058	−	0.339058i	−0.516955	−	0.856013i	$-0.672934\pi$
$727$	9.14200	−	9.14200i	0.339058	−	0.339058i	0.856013	+	0.516955i	$0.172934\pi$
$728$		0			0
$729$	−8.87181	+	3.67482i	−0.328585	+	0.136105i
$730$		0			0
$731$	10.7375	+	4.61058i	0.397142	+	0.170529i
$732$		0			0
$733$	−12.0200	+	4.97884i	−0.443968	+	0.183898i	−0.593457	−	0.804866i	$-0.702237\pi$
$733$	−12.0200	+	4.97884i	−0.443968	+	0.183898i	0.149489	+	0.988763i	$0.452237\pi$
$734$		0			0
$735$	22.7605	+	22.7605i	0.839533	+	0.839533i
$736$		0			0
$737$	−8.35027	+	12.4971i	−0.307586	+	0.460335i
$738$		0			0
$739$	27.1906	+	11.2627i	1.00022	+	0.414305i	0.821878	−	0.569663i	$-0.192926\pi$
$739$	27.1906	+	11.2627i	1.00022	+	0.414305i	0.178343	+	0.983968i	$0.442926\pi$
$740$		0			0
$741$	−3.72552	−	18.7294i	−0.136860	−	0.688043i
$742$		0			0
$743$	−1.16420	+	5.85282i	−0.0427103	+	0.214719i	−0.996247	−	0.0865584i	$-0.972413\pi$
$743$	−1.16420	+	5.85282i	−0.0427103	+	0.214719i	0.953536	+	0.301278i	$0.0974131\pi$
$744$		0			0
$745$	−16.1043	+	10.7606i	−0.590017	+	0.394237i
$746$		0			0
$747$			36.7989i			1.34640i
$748$		0			0
$749$			20.9752i			0.766417i
$750$		0			0
$751$	4.76539	−	3.18413i	0.173891	−	0.116191i	−0.465579	−	0.885007i	$-0.654154\pi$
$751$	4.76539	−	3.18413i	0.173891	−	0.116191i	0.639470	+	0.768816i	$0.279154\pi$
$752$		0			0
$753$	−6.95107	+	34.9454i	−0.253311	+	1.27348i
$754$		0			0
$755$	3.17808	+	15.9773i	0.115662	+	0.581473i
$756$		0			0
$757$	5.74019	+	2.37766i	0.208631	+	0.0864177i	0.484552	−	0.874763i	$-0.338983\pi$
$757$	5.74019	+	2.37766i	0.208631	+	0.0864177i	−0.275921	+	0.961180i	$0.588983\pi$
$758$		0			0
$759$	−21.2765	+	31.8425i	−0.772287	+	1.15581i
$760$		0			0
$761$	34.6524	+	34.6524i	1.25615	+	1.25615i	0.952917	+	0.303231i	$0.0980654\pi$
$761$	34.6524	+	34.6524i	1.25615	+	1.25615i	0.303231	+	0.952917i	$0.401935\pi$
$762$		0			0
$763$	−36.0621	+	14.9374i	−1.30554	+	0.540771i
$764$		0			0
$765$	−11.4634	−	7.87511i	−0.414461	−	0.284725i
$766$		0			0
$767$	15.5916	−	6.45826i	0.562981	−	0.233194i
$768$		0			0
$769$	−20.7436	+	20.7436i	−0.748035	+	0.748035i	−0.974110	−	0.226075i	$-0.927410\pi$
$769$	−20.7436	+	20.7436i	−0.748035	+	0.748035i	0.226075	+	0.974110i	$0.427410\pi$
$770$		0			0
$771$	−5.11023	+	7.64799i	−0.184040	+	0.275436i
$772$		0			0
$773$	15.5416	−	37.5208i	0.558994	−	1.34953i	−0.351570	−	0.936162i	$-0.614352\pi$
$773$	15.5416	−	37.5208i	0.558994	−	1.34953i	0.910564	−	0.413369i	$-0.135648\pi$
$774$		0			0
$775$	4.70884	+	23.6729i	0.169146	+	0.850357i
$776$		0			0
$777$	−55.0612	−	10.9524i	−1.97531	−	0.392913i
$778$		0			0
$779$	14.8313	−	9.90999i	0.531388	−	0.355062i
$780$		0			0
$781$	16.5136			0.590903
$782$		0			0
$783$			3.68237i			0.131597i
$784$		0			0
$785$	16.8282	+	25.1852i	0.600626	+	0.898900i
$786$		0			0
$787$	6.57472	−	33.0533i	0.234363	−	1.17822i	−0.666965	−	0.745089i	$-0.732407\pi$
$787$	6.57472	−	33.0533i	0.234363	−	1.17822i	0.901329	−	0.433136i	$-0.142593\pi$
$788$		0			0
$789$	−30.2046	+	6.00806i	−1.07531	+	0.213893i
$790$		0			0
$791$	29.7492	+	12.3225i	1.05776	+	0.438139i
$792$		0			0
$793$	−17.4676	−	11.6715i	−0.620294	−	0.414467i
$794$		0			0
$795$	8.72175	+	8.72175i	0.309329	+	0.309329i
$796$		0			0
$797$	3.63700	+	8.78050i	0.128829	+	0.311021i	0.975112	−	0.221713i	$-0.0711647\pi$
$797$	3.63700	+	8.78050i	0.128829	+	0.311021i	−0.846283	+	0.532734i	$0.821165\pi$
$798$		0			0
$799$	11.6873	+	11.9924i	0.413466	+	0.424260i
$800$		0			0
$801$	0.509319	+	1.22961i	0.0179959	+	0.0434460i
$802$		0			0
$803$	24.7515	−	24.7515i	0.873463	−	0.873463i
$804$		0			0
$805$	−36.3265	−	24.2726i	−1.28034	−	0.855498i
$806$		0			0
$807$	−1.18052	+	2.85002i	−0.0415562	+	0.100325i
$808$		0			0
$809$	−19.9757	+	3.97341i	−0.702308	+	0.139698i	−0.533311	−	0.845919i	$-0.679053\pi$
$809$	−19.9757	+	3.97341i	−0.702308	+	0.139698i	−0.168996	+	0.985617i	$0.554053\pi$
$810$		0			0
$811$	43.7391	+	8.70024i	1.53589	+	0.305507i	0.889296	−	0.457331i	$-0.151195\pi$
$811$	43.7391	+	8.70024i	1.53589	+	0.305507i	0.646590	+	0.762838i	$0.276195\pi$
$812$		0			0
$813$	−1.47655	−	2.20981i	−0.0517849	−	0.0775016i
$814$		0			0
$815$	−5.60385			−0.196294
$816$		0			0
$817$	10.0854			0.352842
$818$		0			0
$819$	11.1741	+	16.7232i	0.390455	+	0.584357i
$820$		0			0
$821$	−46.0889	−	9.16766i	−1.60851	−	0.319953i	−0.692599	−	0.721323i	$-0.743534\pi$
$821$	−46.0889	−	9.16766i	−1.60851	−	0.319953i	−0.915916	+	0.401370i	$0.868534\pi$
$822$		0			0
$823$	49.8672	−	9.91920i	1.73826	−	0.345762i	0.778729	−	0.627360i	$-0.215865\pi$
$823$	49.8672	−	9.91920i	1.73826	−	0.345762i	0.959532	+	0.281599i	$0.0908647\pi$
$824$		0			0
$825$	5.27267	−	12.7293i	0.183571	−	0.443179i
$826$		0			0
$827$	4.87246	+	3.25567i	0.169432	+	0.113211i	0.637395	−	0.770537i	$-0.280012\pi$
$827$	4.87246	+	3.25567i	0.169432	+	0.113211i	−0.467963	+	0.883748i	$0.655012\pi$
$828$		0			0
$829$	−1.74130	+	1.74130i	−0.0604779	+	0.0604779i	−0.736699	−	0.676221i	$-0.763616\pi$
$829$	−1.74130	+	1.74130i	−0.0604779	+	0.0604779i	0.676221	+	0.736699i	$0.263616\pi$
$830$		0			0
$831$	−22.2837	−	53.7976i	−0.773013	−	1.86622i
$832$		0			0
$833$	13.6874	+	34.2872i	0.474241	+	1.18798i
$834$		0			0
$835$	7.74469	+	18.6973i	0.268016	+	0.647048i
$836$		0			0
$837$	−13.6571	−	13.6571i	−0.472057	−	0.472057i
$838$		0			0
$839$	25.9855	+	17.3630i	0.897120	+	0.599436i	0.916350	−	0.400379i	$-0.131122\pi$
$839$	25.9855	+	17.3630i	0.897120	+	0.599436i	−0.0192301	+	0.999815i	$0.506122\pi$
$840$		0			0
$841$	23.6062	+	9.77803i	0.814008	+	0.337173i
$842$		0			0
$843$	−6.45356	+	1.28369i	−0.222272	+	0.0442127i
$844$		0			0
$845$	−2.28639	+	11.4945i	−0.0786543	+	0.395422i
$846$		0			0
$847$	11.0211	+	16.4942i	0.378688	+	0.566747i
$848$		0			0
$849$			15.6404i			0.536779i
$850$		0			0
$851$	42.7662			1.46601
$852$		0			0
$853$	29.0938	−	19.4398i	0.996152	−	0.665608i	0.0532168	−	0.998583i	$-0.483053\pi$
$853$	29.0938	−	19.4398i	0.996152	−	0.665608i	0.942936	+	0.332975i	$0.108053\pi$
$854$		0			0
$855$	−11.7727	−	2.34173i	−0.402617	−	0.0800856i
$856$		0			0
$857$	4.73913	+	23.8252i	0.161886	+	0.813854i	0.973327	+	0.229421i	$0.0736831\pi$
$857$	4.73913	+	23.8252i	0.161886	+	0.813854i	−0.811442	+	0.584433i	$0.801317\pi$
$858$		0			0
$859$	−8.98480	+	21.6912i	−0.306557	+	0.740095i	0.693254	+	0.720693i	$0.256176\pi$
$859$	−8.98480	+	21.6912i	−0.306557	+	0.740095i	−0.999812	+	0.0194021i	$0.993824\pi$
$860$		0			0
$861$	−25.1795	+	37.6837i	−0.858114	+	1.28426i
$862$		0			0
$863$	−39.7230	+	39.7230i	−1.35219	+	1.35219i	−0.468979	+	0.883210i	$0.655378\pi$
$863$	−39.7230	+	39.7230i	−1.35219	+	1.35219i	−0.883210	+	0.468979i	$0.844622\pi$
$864$		0			0
$865$	16.3591	−	6.77617i	0.556227	−	0.230397i
$866$		0			0
$867$	−20.5478	−	32.5366i	−0.697841	−	1.10500i
$868$		0			0
$869$	−28.8329	+	11.9430i	−0.978090	+	0.405138i
$870$		0			0
$871$	−10.2574	−	10.2574i	−0.347560	−	0.347560i
$872$		0			0
$873$	−11.0351	+	16.5153i	−0.373483	+	0.558957i
$874$		0			0
$875$	43.8236	+	18.1523i	1.48151	+	0.613661i
$876$		0			0
$877$	0.834949	+	4.19757i	0.0281942	+	0.141742i	0.992318	−	0.123709i	$-0.0394790\pi$
$877$	0.834949	+	4.19757i	0.0281942	+	0.141742i	−0.964124	+	0.265451i	$0.914479\pi$
$878$		0			0
$879$	−6.46194	+	32.4864i	−0.217956	+	1.09574i
$880$		0			0
$881$	30.0537	−	20.0813i	1.01254	−	0.676555i	0.0655561	−	0.997849i	$-0.479118\pi$
$881$	30.0537	−	20.0813i	1.01254	−	0.676555i	0.946979	+	0.321294i	$0.104118\pi$
$882$		0			0
$883$		−	11.1632i		−	0.375672i	−0.982200	−	0.187836i	$-0.939853\pi$
$883$		−	11.1632i		−	0.375672i	0.982200	−	0.187836i	$-0.0601474\pi$
$884$		0			0
$885$		−	25.5904i		−	0.860212i
$886$		0			0
$887$	−24.1279	+	16.1217i	−0.810135	+	0.541315i	−0.890251	−	0.455471i	$-0.849471\pi$
$887$	−24.1279	+	16.1217i	−0.810135	+	0.541315i	0.0801157	+	0.996786i	$0.474471\pi$
$888$		0			0
$889$	−0.439659	+	2.21031i	−0.0147457	+	0.0741316i
$890$		0			0
$891$	5.20444	+	26.1645i	0.174355	+	0.876543i
$892$		0			0
$893$	13.3522	+	5.53068i	0.446816	+	0.185077i
$894$		0			0
$895$	−3.04448	+	4.55638i	−0.101766	+	0.152303i
$896$		0			0
$897$	−26.1360	−	26.1360i	−0.872654	−	0.872654i
$898$		0			0
$899$	16.7119	−	6.92231i	0.557374	−	0.230872i
$900$		0			0
$901$	5.24498	+	13.1388i	0.174736	+	0.437716i
$902$		0			0
$903$	−23.6745	+	9.80630i	−0.787838	+	0.326333i
$904$		0			0
$905$	15.3060	−	15.3060i	0.508788	−	0.508788i
$906$		0			0
$907$	−28.9723	+	43.3602i	−0.962011	+	1.43975i	−0.0649269	+	0.997890i	$0.520681\pi$
$907$	−28.9723	+	43.3602i	−0.962011	+	1.43975i	−0.897084	+	0.441861i	$0.854319\pi$
$908$		0			0
$909$	−4.14960	+	10.0180i	−0.137634	+	0.332277i
$910$		0			0
$911$	0.592380	+	2.97809i	0.0196264	+	0.0986687i	0.989357	−	0.145509i	$-0.0464820\pi$
$911$	0.592380	+	2.97809i	0.0196264	+	0.0986687i	−0.969731	+	0.244178i	$0.921482\pi$
$912$		0			0
$913$	41.7380	+	8.30221i	1.38133	+	0.274763i
$914$		0			0
$915$	−26.4872	+	17.6982i	−0.875639	+	0.585083i
$916$		0			0
$917$	79.8368			2.63644
$918$		0			0
$919$			6.84897i			0.225927i	0.993599	+	0.112963i	$0.0360343\pi$
$919$			6.84897i			0.225927i	−0.993599	+	0.112963i	$0.963966\pi$
$920$		0			0
$921$	33.3485	+	49.9096i	1.09887	+	1.64458i
$922$		0			0
$923$	−3.10935	+	15.6318i	−0.102346	+	0.514526i
$924$		0			0
$925$	−15.0905	+	3.00169i	−0.496174	+	0.0986951i
$926$		0			0
$927$	0.520222	+	0.215483i	0.0170863	+	0.00707740i
$928$		0			0
$929$	−13.6512	−	9.12141i	−0.447880	−	0.299264i	0.311101	−	0.950377i	$-0.399302\pi$
$929$	−13.6512	−	9.12141i	−0.447880	−	0.299264i	−0.758981	+	0.651113i	$0.774302\pi$
$930$		0			0
$931$	22.5304	+	22.5304i	0.738405	+	0.738405i
$932$		0			0
$933$	−5.84818	−	14.1188i	−0.191461	−	0.462227i
$934$		0			0
$935$	−11.5184	+	11.2253i	−0.376691	+	0.367108i
$936$		0			0
$937$	−12.9063	−	31.1586i	−0.421631	−	1.01791i	−0.981866	−	0.189575i	$-0.939289\pi$
$937$	−12.9063	−	31.1586i	−0.421631	−	1.01791i	0.560235	−	0.828334i	$-0.310711\pi$
$938$		0			0
$939$	6.81482	−	6.81482i	0.222393	−	0.222393i
$940$		0			0
$941$	1.56839	+	1.04797i	0.0511281	+	0.0341627i	0.580872	−	0.813995i	$-0.302712\pi$
$941$	1.56839	+	1.04797i	0.0511281	+	0.0341627i	−0.529744	+	0.848158i	$0.677712\pi$
$942$		0			0
$943$	13.2122	−	31.8971i	0.430249	−	1.03871i
$944$		0			0
$945$	−12.3360	+	2.45379i	−0.401292	+	0.0798219i
$946$		0			0
$947$	−22.7008	−	4.51548i	−0.737678	−	0.146733i	−0.188070	−	0.982156i	$-0.560223\pi$
$947$	−22.7008	−	4.51548i	−0.737678	−	0.146733i	−0.549609	+	0.835422i	$0.685223\pi$
$948$		0			0
$949$	18.7693	+	28.0903i	0.609279	+	0.911850i
$950$		0			0
$951$	−27.1045			−0.878922
$952$		0			0
$953$	22.0527			0.714358			0.357179	−	0.934036i	$-0.383739\pi$
$953$	22.0527			0.714358			0.357179	+	0.934036i	$0.383739\pi$
$954$		0			0
$955$	−19.3502	−	28.9596i	−0.626157	−	0.937111i
$956$		0			0
$957$	−10.1274	−	2.01447i	−0.327372	−	0.0651184i
$958$		0			0
$959$	11.9826	−	2.38349i	0.386939	−	0.0769669i
$960$		0			0
$961$	−24.4443	+	59.0137i	−0.788525	+	1.90367i
$962$		0			0
$963$	9.27425	+	6.19685i	0.298858	+	0.199691i
$964$		0			0
$965$	1.54552	−	1.54552i	0.0497521	−	0.0497521i
$966$		0			0
$967$	−21.2143	−	51.2160i	−0.682207	−	1.64699i	−0.759919	−	0.650018i	$-0.774761\pi$
$967$	−21.2143	−	51.2160i	−0.682207	−	1.64699i	0.0777115	−	0.996976i	$-0.475239\pi$
$968$		0			0
$969$	−27.3749	−	18.8060i	−0.879409	−	0.604134i
$970$		0			0
$971$	0.393875	+	0.950898i	0.0126401	+	0.0305158i	0.930074	−	0.367373i	$-0.119743\pi$
$971$	0.393875	+	0.950898i	0.0126401	+	0.0305158i	−0.917434	+	0.397889i	$0.869743\pi$
$972$		0			0
$973$	25.1071	+	25.1071i	0.804895	+	0.804895i
$974$		0			0
$975$	11.0568	+	7.38792i	0.354101	+	0.236603i
$976$		0			0
$977$	11.0562	+	4.57961i	0.353718	+	0.146515i	0.552465	−	0.833536i	$-0.313687\pi$
$977$	11.0562	+	4.57961i	0.353718	+	0.146515i	−0.198747	+	0.980051i	$0.563687\pi$
$978$		0			0
$979$	1.50955	−	0.300269i	0.0482455	−	0.00959662i
$980$		0			0
$981$	−4.04947	+	20.3580i	−0.129289	+	0.649982i
$982$		0			0
$983$	−11.5932	−	17.3504i	−0.369765	−	0.553393i	0.599197	−	0.800602i	$-0.295487\pi$
$983$	−11.5932	−	17.3504i	−0.369765	−	0.553393i	−0.968962	+	0.247209i	$0.920487\pi$
$984$		0			0
$985$		−	16.7484i		−	0.533650i
$986$		0			0
$987$	−36.7208			−1.16884
$988$		0			0
$989$	16.2308	−	10.8451i	0.516110	−	0.344854i
$990$		0			0
$991$	−32.6899	−	6.50243i	−1.03843	−	0.206557i	−0.353704	−	0.935357i	$-0.615078\pi$
$991$	−32.6899	−	6.50243i	−1.03843	−	0.206557i	−0.684726	+	0.728801i	$0.740078\pi$
$992$		0			0
$993$	−3.58142	−	18.0050i	−0.113653	−	0.571371i
$994$		0			0
$995$	11.1675	−	26.9607i	0.354034	−	0.854713i
$996$		0			0
$997$	−3.46448	+	5.18496i	−0.109721	+	0.164209i	−0.882267	−	0.470750i	$-0.843983\pi$
$997$	−3.46448	+	5.18496i	−0.109721	+	0.164209i	0.772545	+	0.634960i	$0.218983\pi$
$998$		0			0
$999$	8.70582	−	8.70582i	0.275440	−	0.275440i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	544.2.cc.c.175.12		112
4.3	odd	2		136.2.s.c.107.10	yes	112
8.3	odd	2	inner	544.2.cc.c.175.11		112
8.5	even	2		136.2.s.c.107.8	yes	112
17.7	odd	16	inner	544.2.cc.c.143.11		112
68.7	even	16		136.2.s.c.75.8	✓	112
136.75	even	16	inner	544.2.cc.c.143.12		112
136.109	odd	16		136.2.s.c.75.10	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.2.s.c.75.8	✓	112	68.7	even	16
136.2.s.c.75.10	yes	112	136.109	odd	16
136.2.s.c.107.8	yes	112	8.5	even	2
136.2.s.c.107.10	yes	112	4.3	odd	2
544.2.cc.c.143.11		112	17.7	odd	16	inner
544.2.cc.c.143.12		112	136.75	even	16	inner
544.2.cc.c.175.11		112	8.3	odd	2	inner
544.2.cc.c.175.12		112	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 544 = 2^{5} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	544.cc (of order \(16\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.25761 + 1.88214i) q^{3} +(1.55757 + 0.309820i) q^{5} +(-3.91750 + 0.779239i) q^{7} +(-0.812832 + 1.96235i) q^{9} +(2.04236 + 1.36466i) q^{11} +(-1.67634 + 1.67634i) q^{13} +(1.37568 + 3.32120i) q^{15} +(-0.0531197 + 4.12276i) q^{17} +(1.36178 + 3.28763i) q^{19} +(-6.39331 - 6.39331i) q^{21} +(5.72685 + 3.82656i) q^{23} +(-2.28937 - 0.948286i) q^{25} +(1.94477 - 0.386838i) q^{27} +(-0.362301 + 1.82141i) q^{29} +(-5.41149 - 8.09887i) q^{31} +5.56021i q^{33} -6.34320 q^{35} +(5.16270 - 3.44961i) q^{37} +(-5.26329 - 1.04693i) q^{39} +(-0.977918 - 4.91633i) q^{41} +(1.08459 - 2.61842i) q^{43} +(-1.87402 + 2.80466i) q^{45} +(2.87182 - 2.87182i) q^{47} +(8.27242 - 3.42655i) q^{49} +(-7.82643 + 5.08484i) q^{51} +(3.16997 - 1.31304i) q^{53} +(2.75831 + 2.75831i) q^{55} +(-4.47520 + 6.69761i) q^{57} +(-6.57678 - 2.72419i) q^{59} +(1.72880 + 8.69128i) q^{61} +(1.65513 - 8.32089i) q^{63} +(-3.13038 + 2.09165i) q^{65} +6.11894i q^{67} +15.5911i q^{69} +(5.58989 - 3.73504i) q^{71} +(2.78015 - 13.9768i) q^{73} +(-1.09431 - 5.50148i) q^{75} +(-9.06432 - 3.75456i) q^{77} +(-7.05875 + 10.5642i) q^{79} +(7.67959 + 7.67959i) q^{81} +(16.0062 - 6.62999i) q^{83} +(-1.36005 + 6.40503i) q^{85} +(-3.88378 + 1.60871i) q^{87} +(0.443072 - 0.443072i) q^{89} +(5.26080 - 7.87334i) q^{91} +(8.43769 - 20.3704i) q^{93} +(1.10249 + 5.54261i) q^{95} +(9.17174 + 1.82437i) q^{97} +(-4.33803 + 2.89858i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 16 q^{3} - 16 q^{9} + 16 q^{11} - 16 q^{17} + 16 q^{19} - 16 q^{25} - 32 q^{27} + 32 q^{35} - 16 q^{41} + 96 q^{43} - 16 q^{49} + 16 q^{51} + 32 q^{57} + 16 q^{59} + 64 q^{65} - 96 q^{73} + 16 q^{75}+ \cdots - 48 q^{99}+O(q^{100}) \) 112 * q + 16 * q^3 - 16 * q^9 + 16 * q^11 - 16 * q^17 + 16 * q^19 - 16 * q^25 - 32 * q^27 + 32 * q^35 - 16 * q^41 + 96 * q^43 - 16 * q^49 + 16 * q^51 + 32 * q^57 + 16 * q^59 + 64 * q^65 - 96 * q^73 + 16 * q^75 - 96 * q^81 - 128 * q^83 - 16 * q^89 + 16 * q^91 - 16 * q^97 - 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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