LMFDB - Embedded newform 1170.2.q.c.629.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1170,2,Mod(359,1170)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1170, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 2, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1170.359"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1170.q (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,0,0,0,0,0,0,0,0,0,-20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	no
Analytic conductor:	$9.34249703649$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			629.3
Character	$\chi$	$=$	1170.629
Dual form			1170.2.q.c.359.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(1.78575 + 1.34577i) q^{5} +(2.75044 - 2.75044i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.21432 + 0.311108i) q^{10} +(-3.15348 + 3.15348i) q^{11} +(-2.69372 + 2.39664i) q^{13} +3.88971i q^{14} -1.00000 q^{16} +5.01449i q^{17} +(-2.53612 + 2.53612i) q^{19} +(1.34577 - 1.78575i) q^{20} -4.45969i q^{22} -4.34164i q^{23} +(1.37778 + 4.80642i) q^{25} +(0.210072 - 3.59943i) q^{26} +(-2.75044 - 2.75044i) q^{28} +5.70547i q^{29} +(-3.60613 + 3.60613i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-3.54578 - 3.54578i) q^{34} +(8.61307 - 1.21012i) q^{35} +(4.13155 - 4.13155i) q^{37} -3.58662i q^{38} +(0.311108 + 2.21432i) q^{40} +(8.67345 + 8.67345i) q^{41} +9.44654 q^{43} +(3.15348 + 3.15348i) q^{44} +(3.07000 + 3.07000i) q^{46} +(2.13745 + 2.13745i) q^{47} -8.12986i q^{49} +(-4.37290 - 2.42441i) q^{50} +(2.39664 + 2.69372i) q^{52} -3.21386 q^{53} +(-9.87517 + 1.38744i) q^{55} +3.88971 q^{56} +(-4.03438 - 4.03438i) q^{58} +(8.59111 - 8.59111i) q^{59} -2.76670 q^{61} -5.09983i q^{62} +1.00000i q^{64} +(-8.03564 + 0.654644i) q^{65} +(-4.81488 - 4.81488i) q^{67} +5.01449 q^{68} +(-5.23467 + 6.94604i) q^{70} +(4.04025 + 4.04025i) q^{71} +(0.0463227 - 0.0463227i) q^{73} +5.84290i q^{74} +(2.53612 + 2.53612i) q^{76} +17.3469i q^{77} -3.04420 q^{79} +(-1.78575 - 1.34577i) q^{80} -12.2661 q^{82} +(-8.43545 + 8.43545i) q^{83} +(-6.74837 + 8.95461i) q^{85} +(-6.67971 + 6.67971i) q^{86} -4.45969 q^{88} +(8.57916 - 8.57916i) q^{89} +(-0.817118 + 14.0007i) q^{91} -4.34164 q^{92} -3.02281 q^{94} +(-7.94192 + 1.11582i) q^{95} +(5.09718 + 5.09718i) q^{97} +(5.74868 + 5.74868i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 20 q^{13} - 24 q^{16} - 48 q^{19} + 32 q^{25} - 8 q^{31} + 16 q^{34} - 32 q^{37} + 8 q^{40} + 80 q^{43} + 8 q^{46} - 12 q^{52} + 16 q^{55} - 24 q^{58} - 16 q^{61} - 8 q^{67} - 24 q^{70} + 48 q^{73}+ \cdots + 64 q^{97}+O(q^{100}) $ 24 * q - 20 * q^13 - 24 * q^16 - 48 * q^19 + 32 * q^25 - 8 * q^31 + 16 * q^34 - 32 * q^37 + 8 * q^40 + 80 * q^43 + 8 * q^46 - 12 * q^52 + 16 * q^55 - 24 * q^58 - 16 * q^61 - 8 * q^67 - 24 * q^70 + 48 * q^73 + 48 * q^76 - 96 * q^79 - 72 * q^82 + 8 * q^85 + 8 * q^88 + 48 * q^91 - 16 * q^94 + 64 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$.

$n$	$911$	$937$	$1081$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$	1.78575	+	1.34577i	0.798610	+	0.601848i
$5$	1.78575	+	1.34577i	0.798610	+	0.601848i
$6$		0			0
$7$	2.75044	−	2.75044i	1.03957	−	1.03957i	0.0403851	−	0.999184i	$-0.487142\pi$
$7$	2.75044	−	2.75044i	1.03957	−	1.03957i	0.999184	−	0.0403851i	$-0.0128585\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$	−2.21432	+	0.311108i	−0.700229	+	0.0983809i
$11$	−3.15348	+	3.15348i	−0.950809	+	0.950809i	−0.998846	−	0.0480369i	$-0.984703\pi$
$11$	−3.15348	+	3.15348i	−0.950809	+	0.950809i	0.0480369	+	0.998846i	$0.484703\pi$
$12$		0			0
$13$	−2.69372	+	2.39664i	−0.747104	+	0.664707i
$13$	−2.69372	+	2.39664i	−0.747104	+	0.664707i
$14$			3.88971i			1.03957i
$15$		0			0
$16$	−1.00000			−0.250000
$17$			5.01449i			1.21619i	0.793863	+	0.608096i	$0.208067\pi$
$17$			5.01449i			1.21619i	−0.793863	+	0.608096i	$0.791933\pi$
$18$		0			0
$19$	−2.53612	+	2.53612i	−0.581826	+	0.581826i	−0.935405	−	0.353579i	$-0.884965\pi$
$19$	−2.53612	+	2.53612i	−0.581826	+	0.581826i	0.353579	+	0.935405i	$0.384965\pi$
$20$	1.34577	−	1.78575i	0.300924	−	0.399305i
$21$		0			0
$22$		−	4.45969i		−	0.950809i
$23$		−	4.34164i		−	0.905295i	−0.891690	−	0.452647i	$-0.850480\pi$
$23$		−	4.34164i		−	0.905295i	0.891690	−	0.452647i	$-0.149520\pi$
$24$		0			0
$25$	1.37778	+	4.80642i	0.275557	+	0.961285i
$26$	0.210072	−	3.59943i	0.0411984	−	0.705906i
$27$		0			0
$28$	−2.75044	−	2.75044i	−0.519785	−	0.519785i
$29$			5.70547i			1.05948i	0.848160	+	0.529739i	$0.177710\pi$
$29$			5.70547i			1.05948i	−0.848160	+	0.529739i	$0.822290\pi$
$30$		0			0
$31$	−3.60613	+	3.60613i	−0.647679	+	0.647679i	−0.952432	−	0.304752i	$-0.901426\pi$
$31$	−3.60613	+	3.60613i	−0.647679	+	0.647679i	0.304752	+	0.952432i	$0.401426\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$		0			0
$34$	−3.54578	−	3.54578i	−0.608096	−	0.608096i
$35$	8.61307	−	1.21012i	1.45587	−	0.204548i
$36$		0			0
$37$	4.13155	−	4.13155i	0.679223	−	0.679223i	−0.280601	−	0.959824i	$-0.590534\pi$
$37$	4.13155	−	4.13155i	0.679223	−	0.679223i	0.959824	+	0.280601i	$0.0905338\pi$
$38$		−	3.58662i		−	0.581826i
$39$		0			0
$40$	0.311108	+	2.21432i	0.0491905	+	0.350115i
$41$	8.67345	+	8.67345i	1.35457	+	1.35457i	0.880478	+	0.474088i	$0.157222\pi$
$41$	8.67345	+	8.67345i	1.35457	+	1.35457i	0.474088	+	0.880478i	$0.342778\pi$
$42$		0			0
$43$	9.44654			1.44058			0.720292	−	0.693671i	$-0.244008\pi$
$43$	9.44654			1.44058			0.720292	+	0.693671i	$0.244008\pi$
$44$	3.15348	+	3.15348i	0.475404	+	0.475404i
$45$		0			0
$46$	3.07000	+	3.07000i	0.452647	+	0.452647i
$47$	2.13745	+	2.13745i	0.311779	+	0.311779i	0.845599	−	0.533819i	$-0.179244\pi$
$47$	2.13745	+	2.13745i	0.311779	+	0.311779i	−0.533819	+	0.845599i	$0.679244\pi$
$48$		0			0
$49$		−	8.12986i		−	1.16141i
$50$	−4.37290	−	2.42441i	−0.618421	−	0.342864i
$51$		0			0
$52$	2.39664	+	2.69372i	0.332354	+	0.373552i
$53$	−3.21386			−0.441458			−0.220729	−	0.975335i	$-0.570844\pi$
$53$	−3.21386			−0.441458			−0.220729	+	0.975335i	$0.570844\pi$
$54$		0			0
$55$	−9.87517	+	1.38744i	−1.33157	+	0.187083i
$56$	3.88971			0.519785
$57$		0			0
$58$	−4.03438	−	4.03438i	−0.529739	−	0.529739i
$59$	8.59111	−	8.59111i	1.11847	−	1.11847i	0.126501	−	0.991966i	$-0.459625\pi$
$59$	8.59111	−	8.59111i	1.11847	−	1.11847i	0.991966	−	0.126501i	$-0.0403747\pi$
$60$		0			0
$61$	−2.76670			−0.354240			−0.177120	−	0.984189i	$-0.556678\pi$
$61$	−2.76670			−0.354240			−0.177120	+	0.984189i	$0.556678\pi$
$62$		−	5.09983i		−	0.647679i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−8.03564	+	0.654644i	−0.996698	+	0.0811986i
$66$		0			0
$67$	−4.81488	−	4.81488i	−0.588231	−	0.588231i	0.348921	−	0.937152i	$-0.386548\pi$
$67$	−4.81488	−	4.81488i	−0.588231	−	0.588231i	−0.937152	+	0.348921i	$0.886548\pi$
$68$	5.01449			0.608096
$69$		0			0
$70$	−5.23467	+	6.94604i	−0.625663	+	0.830211i
$71$	4.04025	+	4.04025i	0.479490	+	0.479490i	0.904968	−	0.425479i	$-0.139894\pi$
$71$	4.04025	+	4.04025i	0.479490	+	0.479490i	−0.425479	+	0.904968i	$0.639894\pi$
$72$		0			0
$73$	0.0463227	−	0.0463227i	0.00542166	−	0.00542166i	−0.704391	−	0.709812i	$-0.748780\pi$
$73$	0.0463227	−	0.0463227i	0.00542166	−	0.00542166i	0.709812	+	0.704391i	$0.248780\pi$
$74$			5.84290i			0.679223i
$75$		0			0
$76$	2.53612	+	2.53612i	0.290913	+	0.290913i
$77$			17.3469i			1.97686i
$78$		0			0
$79$	−3.04420			−0.342499			−0.171250	−	0.985228i	$-0.554780\pi$
$79$	−3.04420			−0.342499			−0.171250	+	0.985228i	$0.554780\pi$
$80$	−1.78575	−	1.34577i	−0.199653	−	0.150462i
$81$		0			0
$82$	−12.2661			−1.35457
$83$	−8.43545	+	8.43545i	−0.925911	+	0.925911i	−0.997439	−	0.0715280i	$-0.977212\pi$
$83$	−8.43545	+	8.43545i	−0.925911	+	0.925911i	0.0715280	+	0.997439i	$0.477212\pi$
$84$		0			0
$85$	−6.74837	+	8.95461i	−0.731964	+	0.971264i
$86$	−6.67971	+	6.67971i	−0.720292	+	0.720292i
$87$		0			0
$88$	−4.45969			−0.475404
$89$	8.57916	−	8.57916i	0.909389	−	0.909389i	−0.0868341	−	0.996223i	$-0.527675\pi$
$89$	8.57916	−	8.57916i	0.909389	−	0.909389i	0.996223	+	0.0868341i	$0.0276750\pi$
$90$		0			0
$91$	−0.817118	+	14.0007i	−0.0856573	+	1.46768i
$92$	−4.34164			−0.452647
$93$		0			0
$94$	−3.02281			−0.311779
$95$	−7.94192	+	1.11582i	−0.814824	+	0.114481i
$96$		0			0
$97$	5.09718	+	5.09718i	0.517540	+	0.517540i	0.916826	−	0.399286i	$-0.130742\pi$
$97$	5.09718	+	5.09718i	0.517540	+	0.517540i	−0.399286	+	0.916826i	$0.630742\pi$
$98$	5.74868	+	5.74868i	0.580704	+	0.580704i
$99$		0			0
$100$	4.80642	−	1.37778i	0.480642	−	0.137778i
$101$	−15.2866			−1.52107			−0.760537	−	0.649294i	$-0.775064\pi$
$101$	−15.2866			−1.52107			−0.760537	+	0.649294i	$0.775064\pi$
$102$		0			0
$103$	8.69475			0.856719			0.428360	−	0.903608i	$-0.359092\pi$
$103$	8.69475			0.856719			0.428360	+	0.903608i	$0.359092\pi$
$104$	−3.59943	−	0.210072i	−0.352953	−	0.0205992i
$105$		0			0
$106$	2.27254	−	2.27254i	0.220729	−	0.220729i
$107$	−13.0857			−1.26504			−0.632519	−	0.774545i	$-0.717979\pi$
$107$	−13.0857			−1.26504			−0.632519	+	0.774545i	$0.717979\pi$
$108$		0			0
$109$	5.05685	−	5.05685i	0.484358	−	0.484358i	−0.422162	−	0.906520i	$-0.638729\pi$
$109$	5.05685	−	5.05685i	0.484358	−	0.484358i	0.906520	+	0.422162i	$0.138729\pi$
$110$	6.00173	−	7.96387i	0.572243	−	0.759326i
$111$		0			0
$112$	−2.75044	+	2.75044i	−0.259892	+	0.259892i
$113$	3.80322			0.357777			0.178888	−	0.983869i	$-0.442750\pi$
$113$	3.80322			0.357777			0.178888	+	0.983869i	$0.442750\pi$
$114$		0			0
$115$	5.84287	−	7.75307i	0.544850	−	0.722978i
$116$	5.70547			0.529739
$117$		0			0
$118$			12.1497i			1.11847i
$119$	13.7921	+	13.7921i	1.26432	+	1.26432i
$120$		0			0
$121$		−	8.88882i		−	0.808074i
$122$	1.95635	−	1.95635i	0.177120	−	0.177120i
$123$		0			0
$124$	3.60613	+	3.60613i	0.323840	+	0.323840i
$125$	−4.00799	+	10.4372i	−0.358485	+	0.933535i
$126$		0			0
$127$	−2.29829			−0.203940			−0.101970	−	0.994787i	$-0.532515\pi$
$127$	−2.29829			−0.203940			−0.101970	+	0.994787i	$0.532515\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$		0			0
$130$	5.21915	−	6.14496i	0.457750	−	0.538948i
$131$			1.82711i			0.159635i	0.996809	+	0.0798175i	$0.0254338\pi$
$131$			1.82711i			0.159635i	−0.996809	+	0.0798175i	$0.974566\pi$
$132$		0			0
$133$			13.9509i			1.20970i
$134$	6.80927			0.588231
$135$		0			0
$136$	−3.54578	+	3.54578i	−0.304048	+	0.304048i
$137$	−14.3312	−	14.3312i	−1.22440	−	1.22440i	−0.966053	−	0.258345i	$-0.916823\pi$
$137$	−14.3312	−	14.3312i	−1.22440	−	1.22440i	−0.258345	−	0.966053i	$-0.583177\pi$
$138$		0			0
$139$	21.6325			1.83485			0.917423	−	0.397914i	$-0.130266\pi$
$139$	21.6325			1.83485			0.917423	+	0.397914i	$0.130266\pi$
$140$	−1.21012	−	8.61307i	−0.102274	−	0.727937i
$141$		0			0
$142$	−5.71378			−0.479490
$143$	0.936854	−	16.0523i	0.0783437	−	1.34236i
$144$		0			0
$145$	−7.67827	+	10.1885i	−0.637646	+	0.846111i
$146$			0.0655102i			0.00542166i
$147$		0			0
$148$	−4.13155	−	4.13155i	−0.339612	−	0.339612i
$149$	3.50428	+	3.50428i	0.287082	+	0.287082i	0.835925	−	0.548843i	$-0.184932\pi$
$149$	3.50428	+	3.50428i	0.287082	+	0.287082i	−0.548843	+	0.835925i	$0.684932\pi$
$150$		0			0
$151$	−1.47277	−	1.47277i	−0.119853	−	0.119853i	0.644637	−	0.764489i	$-0.277009\pi$
$151$	−1.47277	−	1.47277i	−0.119853	−	0.119853i	−0.764489	+	0.644637i	$0.777009\pi$
$152$	−3.58662			−0.290913
$153$		0			0
$154$	−12.2661	−	12.2661i	−0.988431	−	0.988431i
$155$	−11.2927	+	1.58660i	−0.907048	+	0.127439i
$156$		0			0
$157$			18.0021i			1.43672i	0.695671	+	0.718360i	$0.255107\pi$
$157$			18.0021i			1.43672i	−0.695671	+	0.718360i	$0.744893\pi$
$158$	2.15258	−	2.15258i	0.171250	−	0.171250i
$159$		0			0
$160$	2.21432	−	0.311108i	0.175057	−	0.0245952i
$161$	−11.9414	−	11.9414i	−0.941117	−	0.941117i
$162$		0			0
$163$	8.04240	−	8.04240i	0.629929	−	0.629929i	−0.318121	−	0.948050i	$-0.603052\pi$
$163$	8.04240	−	8.04240i	0.629929	−	0.629929i	0.948050	+	0.318121i	$0.103052\pi$
$164$	8.67345	−	8.67345i	0.677283	−	0.677283i
$165$		0			0
$166$		−	11.9295i		−	0.925911i
$167$	−3.84580	−	3.84580i	−0.297597	−	0.297597i	0.542475	−	0.840072i	$-0.317487\pi$
$167$	−3.84580	−	3.84580i	−0.297597	−	0.297597i	−0.840072	+	0.542475i	$0.817487\pi$
$168$		0			0
$169$	1.51228	−	12.9117i	0.116329	−	0.993211i
$170$	−1.56005	−	11.1037i	−0.119650	−	0.851614i
$171$		0			0
$172$		−	9.44654i		−	0.720292i
$173$			5.52237i			0.419858i	0.977717	+	0.209929i	$0.0673233\pi$
$173$			5.52237i			0.419858i	−0.977717	+	0.209929i	$0.932677\pi$
$174$		0			0
$175$	17.0093	+	9.43027i	1.28578	+	0.712862i
$176$	3.15348	−	3.15348i	0.237702	−	0.237702i
$177$		0			0
$178$			12.1328i			0.909389i
$179$	−7.38088			−0.551673			−0.275837	−	0.961205i	$-0.588955\pi$
$179$	−7.38088			−0.551673			−0.275837	+	0.961205i	$0.588955\pi$
$180$		0			0
$181$			20.9149i			1.55459i	0.629135	+	0.777296i	$0.283409\pi$
$181$			20.9149i			1.55459i	−0.629135	+	0.777296i	$0.716591\pi$
$182$	−9.32222	−	10.4778i	−0.691009	−	0.776666i
$183$		0			0
$184$	3.07000	−	3.07000i	0.226324	−	0.226324i
$185$	12.9380	−	1.81777i	0.951224	−	0.133645i
$186$		0			0
$187$	−15.8131	−	15.8131i	−1.15637	−	1.15637i
$188$	2.13745	−	2.13745i	0.155890	−	0.155890i
$189$		0			0
$190$	4.82678	−	6.40479i	0.350171	−	0.464652i
$191$		−	14.3283i		−	1.03676i	−0.855151	−	0.518379i	$-0.826536\pi$
$191$		−	14.3283i		−	1.03676i	0.855151	−	0.518379i	$-0.173464\pi$
$192$		0			0
$193$	7.61561	−	7.61561i	0.548184	−	0.548184i	−0.377731	−	0.925915i	$-0.623296\pi$
$193$	7.61561	−	7.61561i	0.548184	−	0.548184i	0.925915	+	0.377731i	$0.123296\pi$
$194$	−7.20850			−0.517540
$195$		0			0
$196$	−8.12986			−0.580704
$197$	−0.357634	+	0.357634i	−0.0254804	+	0.0254804i	−0.719732	−	0.694252i	$-0.755735\pi$
$197$	−0.357634	+	0.357634i	−0.0254804	+	0.0254804i	0.694252	+	0.719732i	$0.255735\pi$
$198$		0			0
$199$		−	22.2951i		−	1.58046i	−0.612812	−	0.790229i	$-0.709962\pi$
$199$		−	22.2951i		−	1.58046i	0.612812	−	0.790229i	$-0.290038\pi$
$200$	−2.42441	+	4.37290i	−0.171432	+	0.309210i
$201$		0			0
$202$	10.8093	−	10.8093i	0.760537	−	0.760537i
$203$	15.6926	+	15.6926i	1.10140	+	1.10140i
$204$		0			0
$205$	3.81608	+	27.1611i	0.266527	+	1.89701i
$206$	−6.14812	+	6.14812i	−0.428360	+	0.428360i
$207$		0			0
$208$	2.69372	−	2.39664i	0.186776	−	0.166177i
$209$		−	15.9952i		−	1.10641i
$210$		0			0
$211$	16.2996			1.12211			0.561054	−	0.827779i	$-0.310396\pi$
$211$	16.2996			1.12211			0.561054	+	0.827779i	$0.310396\pi$
$212$			3.21386i			0.220729i
$213$		0			0
$214$	9.25296	−	9.25296i	0.632519	−	0.632519i
$215$	16.8691	+	12.7129i	1.15046	+	0.867013i
$216$		0			0
$217$			19.8369i			1.34661i
$218$			7.15147i			0.484358i
$219$		0			0
$220$	1.38744	+	9.87517i	0.0935414	+	0.665784i
$221$	−12.0179	−	13.5076i	−0.808412	−	0.908623i
$222$		0			0
$223$	−17.7721	−	17.7721i	−1.19011	−	1.19011i	−0.977036	−	0.213073i	$-0.931653\pi$
$223$	−17.7721	−	17.7721i	−1.19011	−	1.19011i	−0.213073	−	0.977036i	$-0.568347\pi$
$224$		−	3.88971i		−	0.259892i
$225$		0			0
$226$	−2.68928	+	2.68928i	−0.178888	+	0.178888i
$227$	−10.6055	+	10.6055i	−0.703909	+	0.703909i	−0.965247	−	0.261338i	$-0.915836\pi$
$227$	−10.6055	+	10.6055i	−0.703909	+	0.703909i	0.261338	+	0.965247i	$0.415836\pi$
$228$		0			0
$229$	1.17330	+	1.17330i	0.0775336	+	0.0775336i	0.744810	−	0.667277i	$-0.232540\pi$
$229$	1.17330	+	1.17330i	0.0775336	+	0.0775336i	−0.667277	+	0.744810i	$0.732540\pi$
$230$	1.35072	+	9.61378i	0.0890637	+	0.633914i
$231$		0			0
$232$	−4.03438	+	4.03438i	−0.264870	+	0.264870i
$233$		−	18.0187i		−	1.18044i	−0.807242	−	0.590221i	$-0.799041\pi$
$233$		−	18.0187i		−	1.18044i	0.807242	−	0.590221i	$-0.200959\pi$
$234$		0			0
$235$	0.940420	+	6.69347i	0.0613463	+	0.436634i
$236$	−8.59111	−	8.59111i	−0.559234	−	0.559234i
$237$		0			0
$238$	−19.5049			−1.26432
$239$	−8.29254	−	8.29254i	−0.536400	−	0.536400i	0.386070	−	0.922470i	$-0.373832\pi$
$239$	−8.29254	−	8.29254i	−0.536400	−	0.536400i	−0.922470	+	0.386070i	$0.873832\pi$
$240$		0			0
$241$	−19.8348	−	19.8348i	−1.27767	−	1.27767i	−0.941969	−	0.335700i	$-0.891027\pi$
$241$	−19.8348	−	19.8348i	−1.27767	−	1.27767i	−0.335700	−	0.941969i	$-0.608973\pi$
$242$	6.28534	+	6.28534i	0.404037	+	0.404037i
$243$		0			0
$244$			2.76670i			0.177120i
$245$	10.9410	−	14.5179i	0.698992	−	0.927513i
$246$		0			0
$247$	0.753447	−	12.9098i	0.0479407	−	0.821429i
$248$	−5.09983			−0.323840
$249$		0			0
$250$	−4.54617	−	10.2143i	−0.287525	−	0.646010i
$251$	−0.799071			−0.0504369			−0.0252184	−	0.999682i	$-0.508028\pi$
$251$	−0.799071			−0.0504369			−0.0252184	+	0.999682i	$0.508028\pi$
$252$		0			0
$253$	13.6913	+	13.6913i	0.860762	+	0.860762i
$254$	1.62514	−	1.62514i	0.101970	−	0.101970i
$255$		0			0
$256$	1.00000			0.0625000
$257$			5.27299i			0.328920i	0.986384	+	0.164460i	$0.0525882\pi$
$257$			5.27299i			0.328920i	−0.986384	+	0.164460i	$0.947412\pi$
$258$		0			0
$259$		−	22.7272i		−	1.41220i
$260$	0.654644	+	8.03564i	0.0405993	+	0.498349i
$261$		0			0
$262$	−1.29196	−	1.29196i	−0.0798175	−	0.0798175i
$263$	8.58678			0.529484			0.264742	−	0.964319i	$-0.414713\pi$
$263$	8.58678			0.529484			0.264742	+	0.964319i	$0.414713\pi$
$264$		0			0
$265$	−5.73914	−	4.32513i	−0.352553	−	0.265691i
$266$	−9.86478	−	9.86478i	−0.604849	−	0.604849i
$267$		0			0
$268$	−4.81488	+	4.81488i	−0.294115	+	0.294115i
$269$			20.8259i			1.26978i	0.772604	+	0.634888i	$0.218954\pi$
$269$			20.8259i			1.26978i	−0.772604	+	0.634888i	$0.781046\pi$
$270$		0			0
$271$	12.8558	+	12.8558i	0.780935	+	0.780935i	0.979989	−	0.199053i	$-0.0637867\pi$
$271$	12.8558	+	12.8558i	0.780935	+	0.780935i	−0.199053	+	0.979989i	$0.563787\pi$
$272$		−	5.01449i		−	0.304048i
$273$		0			0
$274$	20.2674			1.22440
$275$	−19.5017	−	10.8121i	−1.17600	−	0.651996i
$276$		0			0
$277$	−27.3255			−1.64183			−0.820915	−	0.571051i	$-0.806536\pi$
$277$	−27.3255			−1.64183			−0.820915	+	0.571051i	$0.806536\pi$
$278$	−15.2965	+	15.2965i	−0.917423	+	0.917423i
$279$		0			0
$280$	6.94604	+	5.23467i	0.415105	+	0.312832i
$281$	8.30339	−	8.30339i	0.495338	−	0.495338i	−0.414645	−	0.909983i	$-0.636094\pi$
$281$	8.30339	−	8.30339i	0.495338	−	0.495338i	0.909983	+	0.414645i	$0.136094\pi$
$282$		0			0
$283$	24.5729			1.46071			0.730355	−	0.683068i	$-0.239355\pi$
$283$	24.5729			1.46071			0.730355	+	0.683068i	$0.239355\pi$
$284$	4.04025	−	4.04025i	0.239745	−	0.239745i
$285$		0			0
$286$	10.6882	+	12.0132i	0.632009	+	0.710353i
$287$	47.7116			2.81633
$288$		0			0
$289$	−8.14513			−0.479125
$290$	−1.77502	−	12.6337i	−0.104233	−	0.741878i
$291$		0			0
$292$	−0.0463227	−	0.0463227i	−0.00271083	−	0.00271083i
$293$	−18.1139	−	18.1139i	−1.05822	−	1.05822i	−0.998197	−	0.0600274i	$-0.980881\pi$
$293$	−18.1139	−	18.1139i	−1.05822	−	1.05822i	−0.0600274	−	0.998197i	$-0.519119\pi$
$294$		0			0
$295$	26.9032	−	3.77986i	1.56637	−	0.220072i
$296$	5.84290			0.339612
$297$		0			0
$298$	−4.95580			−0.287082
$299$	10.4053	+	11.6952i	0.601756	+	0.676349i
$300$		0			0
$301$	25.9821	−	25.9821i	1.49759	−	1.49759i
$302$	2.08282			0.119853
$303$		0			0
$304$	2.53612	−	2.53612i	0.145457	−	0.145457i
$305$	−4.94063	−	3.72336i	−0.282900	−	0.213199i
$306$		0			0
$307$	5.81587	−	5.81587i	0.331929	−	0.331929i	−0.521390	−	0.853319i	$-0.674586\pi$
$307$	5.81587	−	5.81587i	0.331929	−	0.331929i	0.853319	+	0.521390i	$0.174586\pi$
$308$	17.3469			0.988431
$309$		0			0
$310$	6.86322	−	9.10701i	0.389805	−	0.517243i
$311$	11.4481			0.649164			0.324582	−	0.945858i	$-0.394776\pi$
$311$	11.4481			0.649164			0.324582	+	0.945858i	$0.394776\pi$
$312$		0			0
$313$		−	16.2495i		−	0.918474i	−0.888314	−	0.459237i	$-0.848123\pi$
$313$		−	16.2495i		−	0.918474i	0.888314	−	0.459237i	$-0.151877\pi$
$314$	−12.7294	−	12.7294i	−0.718360	−	0.718360i
$315$		0			0
$316$			3.04420i			0.171250i
$317$	1.23365	−	1.23365i	0.0692886	−	0.0692886i	−0.671613	−	0.740902i	$-0.734398\pi$
$317$	1.23365	−	1.23365i	0.0692886	−	0.0692886i	0.740902	+	0.671613i	$0.234398\pi$
$318$		0			0
$319$	−17.9921	−	17.9921i	−1.00736	−	1.00736i
$320$	−1.34577	+	1.78575i	−0.0752311	+	0.0998263i
$321$		0			0
$322$	16.8877			0.941117
$323$	−12.7174	−	12.7174i	−0.707613	−	0.707613i
$324$		0			0
$325$	−15.2306	−	9.64512i	−0.844842	−	0.535015i
$326$			11.3737i			0.629929i
$327$		0			0
$328$			12.2661i			0.677283i
$329$	11.7579			0.648232
$330$		0			0
$331$	−14.9630	+	14.9630i	−0.822443	+	0.822443i	−0.986458	−	0.164015i	$-0.947555\pi$
$331$	−14.9630	+	14.9630i	−0.822443	+	0.822443i	0.164015	+	0.986458i	$0.447555\pi$
$332$	8.43545	+	8.43545i	0.462955	+	0.462955i
$333$		0			0
$334$	5.43879			0.297597
$335$	−2.11842	−	15.0779i	−0.115741	−	0.823793i
$336$		0			0
$337$	20.9471			1.14106			0.570530	−	0.821277i	$-0.306738\pi$
$337$	20.9471			1.14106			0.570530	+	0.821277i	$0.306738\pi$
$338$	8.06064	+	10.1993i	0.438441	+	0.554770i
$339$		0			0
$340$	8.95461	+	6.74837i	0.485632	+	0.365982i
$341$		−	22.7437i		−	1.23164i
$342$		0			0
$343$	−3.10761	−	3.10761i	−0.167795	−	0.167795i
$344$	6.67971	+	6.67971i	0.360146	+	0.360146i
$345$		0			0
$346$	−3.90491	−	3.90491i	−0.209929	−	0.209929i
$347$	11.4795			0.616251			0.308126	−	0.951346i	$-0.400298\pi$
$347$	11.4795			0.616251			0.308126	+	0.951346i	$0.400298\pi$
$348$		0			0
$349$	3.25043	+	3.25043i	0.173991	+	0.173991i	0.788731	−	0.614739i	$-0.210739\pi$
$349$	3.25043	+	3.25043i	0.173991	+	0.173991i	−0.614739	+	0.788731i	$0.710739\pi$
$350$	−18.6956	+	5.35918i	−0.999322	+	0.286460i
$351$		0			0
$352$			4.45969i			0.237702i
$353$	−11.2170	+	11.2170i	−0.597019	+	0.597019i	−0.939518	−	0.342499i	$-0.888727\pi$
$353$	−11.2170	+	11.2170i	−0.597019	+	0.597019i	0.342499	+	0.939518i	$0.388727\pi$
$354$		0			0
$355$	1.77760	+	12.6521i	0.0943453	+	0.671505i
$356$	−8.57916	−	8.57916i	−0.454694	−	0.454694i
$357$		0			0
$358$	5.21907	−	5.21907i	0.275837	−	0.275837i
$359$	−6.74584	+	6.74584i	−0.356032	+	0.356032i	−0.862348	−	0.506316i	$-0.831007\pi$
$359$	−6.74584	+	6.74584i	−0.356032	+	0.356032i	0.506316	+	0.862348i	$0.331007\pi$
$360$		0			0
$361$			6.13617i			0.322956i
$362$	−14.7891	−	14.7891i	−0.777296	−	0.777296i
$363$		0			0
$364$	14.0007	+	0.817118i	0.733838	+	0.0428286i
$365$	0.145061	−	0.0203807i	0.00759281	−	0.00106678i
$366$		0			0
$367$		−	1.34284i		−	0.0700955i	−0.999386	−	0.0350477i	$-0.988842\pi$
$367$		−	1.34284i		−	0.0700955i	0.999386	−	0.0350477i	$-0.0111583\pi$
$368$			4.34164i			0.226324i
$369$		0			0
$370$	−7.86322	+	10.4339i	−0.408789	+	0.542435i
$371$	−8.83953	+	8.83953i	−0.458926	+	0.458926i
$372$		0			0
$373$		−	1.00977i		−	0.0522837i	−0.999658	−	0.0261418i	$-0.991678\pi$
$373$		−	1.00977i		−	0.0522837i	0.999658	−	0.0261418i	$-0.00832216\pi$
$374$	22.3631			1.15637
$375$		0			0
$376$			3.02281i			0.155890i
$377$	−13.6739	−	15.3689i	−0.704243	−	0.791541i
$378$		0			0
$379$	23.5294	−	23.5294i	1.20863	−	1.20863i	0.237153	−	0.971472i	$-0.423786\pi$
$379$	23.5294	−	23.5294i	1.20863	−	1.20863i	0.971472	−	0.237153i	$-0.0762143\pi$
$380$	1.11582	+	7.94192i	0.0572406	+	0.407412i
$381$		0			0
$382$	10.1316	+	10.1316i	0.518379	+	0.518379i
$383$	20.4310	−	20.4310i	1.04398	−	1.04398i	0.0449898	−	0.998987i	$-0.485674\pi$
$383$	20.4310	−	20.4310i	1.04398	−	1.04398i	0.998987	−	0.0449898i	$-0.0143255\pi$
$384$		0			0
$385$	−23.3450	+	30.9772i	−1.18977	+	1.57874i
$386$			10.7701i			0.548184i
$387$		0			0
$388$	5.09718	−	5.09718i	0.258770	−	0.258770i
$389$	−0.672990			−0.0341220			−0.0170610	−	0.999854i	$-0.505431\pi$
$389$	−0.672990			−0.0341220			−0.0170610	+	0.999854i	$0.505431\pi$
$390$		0			0
$391$	21.7711			1.10101
$392$	5.74868	−	5.74868i	0.290352	−	0.290352i
$393$		0			0
$394$		−	0.505771i		−	0.0254804i
$395$	−5.43617	−	4.09681i	−0.273524	−	0.206133i
$396$		0			0
$397$	11.4614	−	11.4614i	0.575230	−	0.575230i	−0.358355	−	0.933585i	$-0.616662\pi$
$397$	11.4614	−	11.4614i	0.575230	−	0.575230i	0.933585	+	0.358355i	$0.116662\pi$
$398$	15.7650	+	15.7650i	0.790229	+	0.790229i
$399$		0			0
$400$	−1.37778	−	4.80642i	−0.0688892	−	0.240321i
$401$	−13.7266	+	13.7266i	−0.685475	+	0.685475i	−0.961228	−	0.275754i	$-0.911073\pi$
$401$	−13.7266	+	13.7266i	−0.685475	+	0.685475i	0.275754	+	0.961228i	$0.411073\pi$
$402$		0			0
$403$	1.07133	−	18.3565i	0.0533668	−	0.914401i
$404$			15.2866i			0.760537i
$405$		0			0
$406$	−22.1926			−1.10140
$407$			26.0575i			1.29162i
$408$		0			0
$409$	15.7819	−	15.7819i	0.780364	−	0.780364i	−0.199528	−	0.979892i	$-0.563941\pi$
$409$	15.7819	−	15.7819i	0.780364	−	0.780364i	0.979892	+	0.199528i	$0.0639409\pi$
$410$	−21.9042	−	16.5074i	−1.08177	−	0.815243i
$411$		0			0
$412$		−	8.69475i		−	0.428360i
$413$		−	47.2587i		−	2.32545i
$414$		0			0
$415$	−26.4158	+	3.71137i	−1.29670	+	0.182184i
$416$	−0.210072	+	3.59943i	−0.0102996	+	0.176476i
$417$		0			0
$418$	11.3103	+	11.3103i	0.553205	+	0.553205i
$419$		−	0.452702i		−	0.0221160i	−0.999939	−	0.0110580i	$-0.996480\pi$
$419$		−	0.452702i		−	0.0221160i	0.999939	−	0.0110580i	$-0.00351994\pi$
$420$		0			0
$421$	−16.8812	+	16.8812i	−0.822739	+	0.822739i	−0.986500	−	0.163761i	$-0.947637\pi$
$421$	−16.8812	+	16.8812i	−0.822739	+	0.822739i	0.163761	+	0.986500i	$0.447637\pi$
$422$	−11.5255	+	11.5255i	−0.561054	+	0.561054i
$423$		0			0
$424$	−2.27254	−	2.27254i	−0.110364	−	0.110364i
$425$	−24.1018	+	6.90889i	−1.16911	+	0.335130i
$426$		0			0
$427$	−7.60966	+	7.60966i	−0.368257	+	0.368257i
$428$			13.0857i			0.632519i
$429$		0			0
$430$	−20.9176	+	2.93889i	−1.00874	+	0.141726i
$431$	16.1075	+	16.1075i	0.775869	+	0.775869i	0.979126	−	0.203256i	$-0.0651524\pi$
$431$	16.1075	+	16.1075i	0.775869	+	0.775869i	−0.203256	+	0.979126i	$0.565152\pi$
$432$		0			0
$433$	−22.0933			−1.06174			−0.530869	−	0.847454i	$-0.678134\pi$
$433$	−22.0933			−1.06174			−0.530869	+	0.847454i	$0.678134\pi$
$434$	−14.0268	−	14.0268i	−0.673307	−	0.673307i
$435$		0			0
$436$	−5.05685	−	5.05685i	−0.242179	−	0.242179i
$437$	11.0109	+	11.0109i	0.526724	+	0.526724i
$438$		0			0
$439$			28.6601i			1.36787i	0.729542	+	0.683936i	$0.239733\pi$
$439$			28.6601i			1.36787i	−0.729542	+	0.683936i	$0.760267\pi$
$440$	−7.96387	−	6.00173i	−0.379663	−	0.286121i
$441$		0			0
$442$	18.0493	+	1.05340i	0.858517	+	0.0501053i
$443$	7.84995			0.372962			0.186481	−	0.982459i	$-0.440292\pi$
$443$	7.84995			0.372962			0.186481	+	0.982459i	$0.440292\pi$
$444$		0			0
$445$	26.8658	−	3.77460i	1.27356	−	0.178933i
$446$	25.1336			1.19011
$447$		0			0
$448$	2.75044	+	2.75044i	0.129946	+	0.129946i
$449$	1.32444	−	1.32444i	0.0625041	−	0.0625041i	−0.675164	−	0.737668i	$-0.735927\pi$
$449$	1.32444	−	1.32444i	0.0625041	−	0.0625041i	0.737668	+	0.675164i	$0.235927\pi$
$450$		0			0
$451$	−54.7030			−2.57587
$452$		−	3.80322i		−	0.178888i
$453$		0			0
$454$		−	14.9984i		−	0.703909i
$455$	−20.3010	+	23.9021i	−0.951725	+	1.12055i
$456$		0			0
$457$	26.4926	+	26.4926i	1.23927	+	1.23927i	0.960300	+	0.278969i	$0.0899928\pi$
$457$	26.4926	+	26.4926i	1.23927	+	1.23927i	0.278969	+	0.960300i	$0.410007\pi$
$458$	−1.65929			−0.0775336
$459$		0			0
$460$	−7.75307	−	5.84287i	−0.361489	−	0.272425i
$461$	−25.6328	−	25.6328i	−1.19384	−	1.19384i	−0.975981	−	0.217858i	$-0.930093\pi$
$461$	−25.6328	−	25.6328i	−1.19384	−	1.19384i	−0.217858	−	0.975981i	$-0.569907\pi$
$462$		0			0
$463$	−1.94829	+	1.94829i	−0.0905447	+	0.0905447i	−0.750928	−	0.660384i	$-0.770394\pi$
$463$	−1.94829	+	1.94829i	−0.0905447	+	0.0905447i	0.660384	+	0.750928i	$0.270394\pi$
$464$		−	5.70547i		−	0.264870i
$465$		0			0
$466$	12.7411	+	12.7411i	0.590221	+	0.590221i
$467$			23.3069i			1.07852i	0.842141	+	0.539258i	$0.181295\pi$
$467$			23.3069i			1.07852i	−0.842141	+	0.539258i	$0.818705\pi$
$468$		0			0
$469$	−26.4861			−1.22301
$470$	−5.39798	−	4.06802i	−0.248990	−	0.187644i
$471$		0			0
$472$	12.1497			0.559234
$473$	−29.7894	+	29.7894i	−1.36972	+	1.36972i
$474$		0			0
$475$	−15.6839	−	8.69545i	−0.719627	−	0.398975i
$476$	13.7921	−	13.7921i	0.632158	−	0.632158i
$477$		0			0
$478$	11.7274			0.536400
$479$	6.77616	−	6.77616i	0.309610	−	0.309610i	−0.535148	−	0.844758i	$-0.679744\pi$
$479$	6.77616	−	6.77616i	0.309610	−	0.309610i	0.844758	+	0.535148i	$0.179744\pi$
$480$		0			0
$481$	−1.22743	+	21.0311i	−0.0559659	+	0.958935i
$482$	28.0506			1.27767
$483$		0			0
$484$	−8.88882			−0.404037
$485$	2.24262	+	15.9619i	0.101832	+	0.724793i
$486$		0			0
$487$	−25.9766	−	25.9766i	−1.17711	−	1.17711i	−0.980476	−	0.196638i	$-0.936998\pi$
$487$	−25.9766	−	25.9766i	−1.17711	−	1.17711i	−0.196638	−	0.980476i	$-0.563002\pi$
$488$	−1.95635	−	1.95635i	−0.0885600	−	0.0885600i
$489$		0			0
$490$	2.52926	+	18.0021i	0.114260	+	0.813252i
$491$	32.4284			1.46347			0.731737	−	0.681587i	$-0.238710\pi$
$491$	32.4284			1.46347			0.731737	+	0.681587i	$0.238710\pi$
$492$		0			0
$493$	−28.6100			−1.28853
$494$	8.59582	+	9.66135i	0.386744	+	0.434685i
$495$		0			0
$496$	3.60613	−	3.60613i	0.161920	−	0.161920i
$497$	22.2250			0.996925
$498$		0			0
$499$	2.06919	−	2.06919i	0.0926295	−	0.0926295i	−0.659274	−	0.751903i	$-0.729136\pi$
$499$	2.06919	−	2.06919i	0.0926295	−	0.0926295i	0.751903	+	0.659274i	$0.229136\pi$
$500$	10.4372	+	4.00799i	0.466768	+	0.179243i
$501$		0			0
$502$	0.565028	−	0.565028i	0.0252184	−	0.0252184i
$503$	−4.56318			−0.203462			−0.101731	−	0.994812i	$-0.532438\pi$
$503$	−4.56318			−0.203462			−0.101731	+	0.994812i	$0.532438\pi$
$504$		0			0
$505$	−27.2980	−	20.5723i	−1.21475	−	0.915456i
$506$	−19.3624			−0.860762
$507$		0			0
$508$			2.29829i			0.101970i
$509$	3.80809	+	3.80809i	0.168791	+	0.168791i	0.786448	−	0.617657i	$-0.211918\pi$
$509$	3.80809	+	3.80809i	0.168791	+	0.168791i	−0.617657	+	0.786448i	$0.711918\pi$
$510$		0			0
$511$		−	0.254816i		−	0.0112724i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$	−3.72857	−	3.72857i	−0.164460	−	0.164460i
$515$	15.5266	+	11.7012i	0.684185	+	0.515615i
$516$		0			0
$517$	−13.4808			−0.592885
$518$	16.0706	+	16.0706i	0.706100	+	0.706100i
$519$		0			0
$520$	−6.14496	−	5.21915i	−0.269474	−	0.228875i
$521$			37.3410i			1.63594i	0.575260	+	0.817970i	$0.304901\pi$
$521$			37.3410i			1.63594i	−0.575260	+	0.817970i	$0.695099\pi$
$522$		0			0
$523$			19.5269i			0.853850i	0.904287	+	0.426925i	$0.140403\pi$
$523$			19.5269i			0.853850i	−0.904287	+	0.426925i	$0.859597\pi$
$524$	1.82711			0.0798175
$525$		0			0
$526$	−6.07177	+	6.07177i	−0.264742	+	0.264742i
$527$	−18.0829	−	18.0829i	−0.787703	−	0.787703i
$528$		0			0
$529$	4.15015			0.180442
$530$	7.11651	−	0.999857i	0.309122	−	0.0434310i
$531$		0			0
$532$	13.9509			0.604849
$533$	−44.1510	−	2.57676i	−1.91239	−	0.111612i
$534$		0			0
$535$	−23.3677	−	17.6103i	−1.01027	−	0.761361i
$536$		−	6.80927i		−	0.294115i
$537$		0			0
$538$	−14.7261	−	14.7261i	−0.634888	−	0.634888i
$539$	25.6373	+	25.6373i	1.10428	+	1.10428i
$540$		0			0
$541$	−12.1877	−	12.1877i	−0.523991	−	0.523991i	0.394783	−	0.918774i	$-0.370820\pi$
$541$	−12.1877	−	12.1877i	−0.523991	−	0.523991i	−0.918774	+	0.394783i	$0.870820\pi$
$542$	−18.1809			−0.780935
$543$		0			0
$544$	3.54578	+	3.54578i	0.152024	+	0.152024i
$545$	15.8356	−	2.22488i	0.678324	−	0.0953033i
$546$		0			0
$547$		−	6.83555i		−	0.292267i	−0.989265	−	0.146133i	$-0.953317\pi$
$547$		−	6.83555i		−	0.292267i	0.989265	−	0.146133i	$-0.0466829\pi$
$548$	−14.3312	+	14.3312i	−0.612199	+	0.612199i
$549$		0			0
$550$	21.4351	−	6.14449i	0.913998	−	0.262002i
$551$	−14.4698	−	14.4698i	−0.616433	−	0.616433i
$552$		0			0
$553$	−8.37290	+	8.37290i	−0.356052	+	0.356052i
$554$	19.3220	−	19.3220i	0.820915	−	0.820915i
$555$		0			0
$556$		−	21.6325i		−	0.917423i
$557$	−24.2541	−	24.2541i	−1.02768	−	1.02768i	−0.999606	−	0.0280755i	$-0.991062\pi$
$557$	−24.2541	−	24.2541i	−1.02768	−	1.02768i	−0.0280755	−	0.999606i	$-0.508938\pi$
$558$		0			0
$559$	−25.4463	+	22.6399i	−1.07627	+	0.957566i
$560$	−8.61307	+	1.21012i	−0.363968	+	0.0511369i
$561$		0			0
$562$			11.7428i			0.495338i
$563$			17.1720i			0.723712i	0.932234	+	0.361856i	$0.117857\pi$
$563$			17.1720i			0.723712i	−0.932234	+	0.361856i	$0.882143\pi$
$564$		0			0
$565$	6.79159	+	5.11827i	0.285724	+	0.215327i
$566$	−17.3757	+	17.3757i	−0.730355	+	0.730355i
$567$		0			0
$568$			5.71378i			0.239745i
$569$	24.1483			1.01235			0.506174	−	0.862431i	$-0.331059\pi$
$569$	24.1483			1.01235			0.506174	+	0.862431i	$0.331059\pi$
$570$		0			0
$571$		−	27.6629i		−	1.15765i	−0.815450	−	0.578827i	$-0.803511\pi$
$571$		−	27.6629i		−	1.15765i	0.815450	−	0.578827i	$-0.196489\pi$
$572$	−16.0523	−	0.936854i	−0.671181	−	0.0391718i
$573$		0			0
$574$	−33.7372	+	33.7372i	−1.40816	+	1.40816i
$575$	20.8678	−	5.98184i	0.870246	−	0.249460i
$576$		0			0
$577$	−24.6548	−	24.6548i	−1.02639	−	1.02639i	−0.999642	−	0.0267515i	$-0.991484\pi$
$577$	−24.6548	−	24.6548i	−1.02639	−	1.02639i	−0.0267515	−	0.999642i	$-0.508516\pi$
$578$	5.75948	−	5.75948i	0.239563	−	0.239563i
$579$		0			0
$580$	10.1885	+	7.67827i	0.423055	+	0.318823i
$581$			46.4024i			1.92510i
$582$		0			0
$583$	10.1348	−	10.1348i	0.419742	−	0.419742i
$584$	0.0655102			0.00271083
$585$		0			0
$586$	25.6169			1.05822
$587$	16.7940	−	16.7940i	0.693164	−	0.693164i	−0.269763	−	0.962927i	$-0.586945\pi$
$587$	16.7940	−	16.7940i	0.693164	−	0.693164i	0.962927	+	0.269763i	$0.0869453\pi$
$588$		0			0
$589$		−	18.2911i		−	0.753674i
$590$	−16.3507	+	21.6962i	−0.673148	+	0.893220i
$591$		0			0
$592$	−4.13155	+	4.13155i	−0.169806	+	0.169806i
$593$	−20.8963	−	20.8963i	−0.858109	−	0.858109i	0.133006	−	0.991115i	$-0.457537\pi$
$593$	−20.8963	−	20.8963i	−0.858109	−	0.858109i	−0.991115	+	0.133006i	$0.957537\pi$
$594$		0			0
$595$	6.06814	+	43.1902i	0.248769	+	1.77062i
$596$	3.50428	−	3.50428i	0.143541	−	0.143541i
$597$		0			0
$598$	−15.6274	−	0.912056i	−0.639053	−	0.0372967i
$599$		−	0.794778i		−	0.0324737i	−0.999868	−	0.0162369i	$-0.994831\pi$
$599$		−	0.794778i		−	0.0324737i	0.999868	−	0.0162369i	$-0.00516858\pi$
$600$		0			0
$601$	10.9711			0.447520			0.223760	−	0.974644i	$-0.428167\pi$
$601$	10.9711			0.447520			0.223760	+	0.974644i	$0.428167\pi$
$602$			36.7443i			1.49759i
$603$		0			0
$604$	−1.47277	+	1.47277i	−0.0599263	+	0.0599263i
$605$	11.9623	−	15.8732i	0.486338	−	0.645336i
$606$		0			0
$607$			34.3813i			1.39549i	0.716345	+	0.697746i	$0.245814\pi$
$607$			34.3813i			1.39549i	−0.716345	+	0.697746i	$0.754186\pi$
$608$			3.58662i			0.145457i
$609$		0			0
$610$	6.12637	−	0.860743i	0.248049	−	0.0348505i
$611$	−10.8804	−	0.635007i	−0.440173	−	0.0256896i
$612$		0			0
$613$	26.1862	+	26.1862i	1.05765	+	1.05765i	0.998233	+	0.0594159i	$0.0189238\pi$
$613$	26.1862	+	26.1862i	1.05765	+	1.05765i	0.0594159	+	0.998233i	$0.481076\pi$
$614$			8.22488i			0.331929i
$615$		0			0
$616$	−12.2661	+	12.2661i	−0.494216	+	0.494216i
$617$	34.4845	−	34.4845i	1.38829	−	1.38829i	0.559390	−	0.828904i	$-0.311035\pi$
$617$	34.4845	−	34.4845i	1.38829	−	1.38829i	0.828904	−	0.559390i	$-0.188965\pi$
$618$		0			0
$619$	7.32352	+	7.32352i	0.294357	+	0.294357i	0.838799	−	0.544442i	$-0.183258\pi$
$619$	7.32352	+	7.32352i	0.294357	+	0.294357i	−0.544442	+	0.838799i	$0.683258\pi$
$620$	1.58660	+	11.2927i	0.0637193	+	0.453524i
$621$		0			0
$622$	−8.09506	+	8.09506i	−0.324582	+	0.324582i
$623$		−	47.1929i		−	1.89075i
$624$		0			0
$625$	−21.2034	+	13.2444i	−0.848137	+	0.529777i
$626$	11.4901	+	11.4901i	0.459237	+	0.459237i
$627$		0			0
$628$	18.0021			0.718360
$629$	20.7176	+	20.7176i	0.826066	+	0.826066i
$630$		0			0
$631$	0.00180587	+	0.00180587i	7.18905e−5	+	7.18905e-5i	0.707143	−	0.707071i	$-0.249984\pi$
$631$	0.00180587	+	0.00180587i	7.18905e−5	+	7.18905e-5i	−0.707071	+	0.707143i	$0.749984\pi$
$632$	−2.15258	−	2.15258i	−0.0856248	−	0.0856248i
$633$		0			0
$634$			1.74464i			0.0692886i
$635$	−4.10417	−	3.09298i	−0.162869	−	0.122741i
$636$		0			0
$637$	19.4843	+	21.8996i	0.771997	+	0.867693i
$638$	25.4446			1.00736
$639$		0			0
$640$	−0.311108	−	2.21432i	−0.0122976	−	0.0875287i
$641$	−9.37820			−0.370417			−0.185208	−	0.982699i	$-0.559296\pi$
$641$	−9.37820			−0.370417			−0.185208	+	0.982699i	$0.559296\pi$
$642$		0			0
$643$	−24.4684	−	24.4684i	−0.964941	−	0.964941i	0.0344651	−	0.999406i	$-0.489027\pi$
$643$	−24.4684	−	24.4684i	−0.964941	−	0.964941i	−0.999406	+	0.0344651i	$0.989027\pi$
$644$	−11.9414	+	11.9414i	−0.470558	+	0.470558i
$645$		0			0
$646$	17.9851			0.707613
$647$		−	48.7901i		−	1.91814i	−0.283174	−	0.959069i	$-0.591387\pi$
$647$		−	48.7901i		−	1.91814i	0.283174	−	0.959069i	$-0.408613\pi$
$648$		0			0
$649$			54.1837i			2.12690i
$650$	17.5898	−	3.94954i	0.689929	−	0.154914i
$651$		0			0
$652$	−8.04240	−	8.04240i	−0.314965	−	0.314965i
$653$	−10.6839			−0.418094			−0.209047	−	0.977906i	$-0.567036\pi$
$653$	−10.6839			−0.418094			−0.209047	+	0.977906i	$0.567036\pi$
$654$		0			0
$655$	−2.45887	+	3.26275i	−0.0960761	+	0.127486i
$656$	−8.67345	−	8.67345i	−0.338641	−	0.338641i
$657$		0			0
$658$	−8.31407	+	8.31407i	−0.324116	+	0.324116i
$659$		−	14.9799i		−	0.583533i	−0.956490	−	0.291767i	$-0.905757\pi$
$659$		−	14.9799i		−	0.583533i	0.956490	−	0.291767i	$-0.0942431\pi$
$660$		0			0
$661$	30.0075	+	30.0075i	1.16715	+	1.16715i	0.982874	+	0.184281i	$0.0589958\pi$
$661$	30.0075	+	30.0075i	1.16715	+	1.16715i	0.184281	+	0.982874i	$0.441004\pi$
$662$		−	21.1609i		−	0.822443i
$663$		0			0
$664$	−11.9295			−0.462955
$665$	−18.7748	+	24.9128i	−0.728055	+	0.966077i
$666$		0			0
$667$	24.7711			0.959141
$668$	−3.84580	+	3.84580i	−0.148799	+	0.148799i
$669$		0			0
$670$	12.1596	+	9.16373i	0.469767	+	0.354026i
$671$	8.72473	−	8.72473i	0.336815	−	0.336815i
$672$		0			0
$673$	31.2419			1.20428			0.602142	−	0.798389i	$-0.294314\pi$
$673$	31.2419			1.20428			0.602142	+	0.798389i	$0.294314\pi$
$674$	−14.8118	+	14.8118i	−0.570530	+	0.570530i
$675$		0			0
$676$	−12.9117	−	1.51228i	−0.496605	−	0.0581644i
$677$	44.2056			1.69896			0.849480	−	0.527621i	$-0.176916\pi$
$677$	44.2056			1.69896			0.849480	+	0.527621i	$0.176916\pi$
$678$		0			0
$679$	28.0390			1.07604
$680$	−11.1037	+	1.56005i	−0.425807	+	0.0598251i
$681$		0			0
$682$	16.0822	+	16.0822i	0.615819	+	0.615819i
$683$	7.36452	+	7.36452i	0.281795	+	0.281795i	0.833825	−	0.552029i	$-0.186146\pi$
$683$	7.36452	+	7.36452i	0.281795	+	0.281795i	−0.552029	+	0.833825i	$0.686146\pi$
$684$		0			0
$685$	−6.30534	−	44.8785i	−0.240915	−	1.71472i
$686$	4.39483			0.167795
$687$		0			0
$688$	−9.44654			−0.360146
$689$	8.65724	−	7.70245i	0.329815	−	0.293440i
$690$		0			0
$691$	−14.0880	+	14.0880i	−0.535932	+	0.535932i	−0.922331	−	0.386400i	$-0.873718\pi$
$691$	−14.0880	+	14.0880i	−0.535932	+	0.535932i	0.386400	+	0.922331i	$0.373718\pi$
$692$	5.52237			0.209929
$693$		0			0
$694$	−8.11722	+	8.11722i	−0.308126	+	0.308126i
$695$	38.6302	+	29.1125i	1.46533	+	1.10430i
$696$		0			0
$697$	−43.4930	+	43.4930i	−1.64741	+	1.64741i
$698$	−4.59680			−0.173991
$699$		0			0
$700$	9.43027	−	17.0093i	0.356431	−	0.642891i
$701$	47.3805			1.78954			0.894769	−	0.446530i	$-0.147340\pi$
$701$	47.3805			1.78954			0.894769	+	0.446530i	$0.147340\pi$
$702$		0			0
$703$			20.9562i			0.790380i
$704$	−3.15348	−	3.15348i	−0.118851	−	0.118851i
$705$		0			0
$706$		−	15.8632i		−	0.597019i
$707$	−42.0449	+	42.0449i	−1.58126	+	1.58126i
$708$		0			0
$709$	−19.6171	−	19.6171i	−0.736736	−	0.736736i	0.235209	−	0.971945i	$-0.424423\pi$
$709$	−19.6171	−	19.6171i	−0.736736	−	0.736736i	−0.971945	+	0.235209i	$0.924423\pi$
$710$	−10.2034	−	7.68945i	−0.382925	−	0.288580i
$711$		0			0
$712$	12.1328			0.454694
$713$	15.6565	+	15.6565i	0.586341	+	0.586341i
$714$		0			0
$715$	23.2758	−	27.4046i	0.870465	−	1.02487i
$716$			7.38088i			0.275837i
$717$		0			0
$718$		−	9.54006i		−	0.356032i
$719$	−12.4156			−0.463022			−0.231511	−	0.972832i	$-0.574367\pi$
$719$	−12.4156			−0.463022			−0.231511	+	0.972832i	$0.574367\pi$
$720$		0			0
$721$	23.9144	−	23.9144i	0.890619	−	0.890619i
$722$	−4.33893	−	4.33893i	−0.161478	−	0.161478i
$723$		0			0
$724$	20.9149			0.777296
$725$	−27.4229	+	7.86091i	−1.01846	+	0.291947i
$726$		0			0
$727$	−10.6658			−0.395571			−0.197786	−	0.980245i	$-0.563375\pi$
$727$	−10.6658			−0.395571			−0.197786	+	0.980245i	$0.563375\pi$
$728$	−10.4778	+	9.32222i	−0.388333	+	0.345505i
$729$		0			0
$730$	−0.0881619	+	0.116985i	−0.00326302	+	0.00432980i
$731$			47.3696i			1.75203i
$732$		0			0
$733$	−15.1798	−	15.1798i	−0.560679	−	0.560679i	0.368821	−	0.929500i	$-0.379761\pi$
$733$	−15.1798	−	15.1798i	−0.560679	−	0.560679i	−0.929500	+	0.368821i	$0.879761\pi$
$734$	0.949529	+	0.949529i	0.0350477	+	0.0350477i
$735$		0			0
$736$	−3.07000	−	3.07000i	−0.113162	−	0.113162i
$737$	30.3672			1.11859
$738$		0			0
$739$	−24.7127	−	24.7127i	−0.909071	−	0.909071i	0.0871259	−	0.996197i	$-0.472232\pi$
$739$	−24.7127	−	24.7127i	−0.909071	−	0.909071i	−0.996197	+	0.0871259i	$0.972232\pi$
$740$	−1.81777	−	12.9380i	−0.0668226	−	0.475612i
$741$		0			0
$742$		−	12.5010i		−	0.458926i
$743$	3.04326	−	3.04326i	0.111646	−	0.111646i	−0.649077	−	0.760723i	$-0.724845\pi$
$743$	3.04326	−	3.04326i	0.111646	−	0.111646i	0.760723	+	0.649077i	$0.224845\pi$
$744$		0			0
$745$	1.54179	+	10.9737i	0.0564867	+	0.402046i
$746$	0.714012	+	0.714012i	0.0261418	+	0.0261418i
$747$		0			0
$748$	−15.8131	+	15.8131i	−0.578183	+	0.578183i
$749$	−35.9913	+	35.9913i	−1.31510	+	1.31510i
$750$		0			0
$751$			4.80106i			0.175193i	0.996156	+	0.0875965i	$0.0279186\pi$
$751$			4.80106i			0.175193i	−0.996156	+	0.0875965i	$0.972081\pi$
$752$	−2.13745	−	2.13745i	−0.0779448	−	0.0779448i
$753$		0			0
$754$	20.5364	+	1.19856i	0.747892	+	0.0436489i
$755$	−0.647980	−	4.61202i	−0.0235824	−	0.167849i
$756$		0			0
$757$			28.0173i			1.01831i	0.860676	+	0.509154i	$0.170041\pi$
$757$			28.0173i			1.01831i	−0.860676	+	0.509154i	$0.829959\pi$
$758$			33.2756i			1.20863i
$759$		0			0
$760$	−6.40479	−	4.82678i	−0.232326	−	0.175086i
$761$	13.1464	−	13.1464i	0.476555	−	0.476555i	−0.427473	−	0.904028i	$-0.640596\pi$
$761$	13.1464	−	13.1464i	0.476555	−	0.476555i	0.904028	+	0.427473i	$0.140596\pi$
$762$		0			0
$763$		−	27.8171i		−	1.00705i
$764$	−14.3283			−0.518379
$765$		0			0
$766$			28.8939i			1.04398i
$767$	−2.55230	+	43.7318i	−0.0921582	+	1.57906i
$768$		0			0
$769$	13.3941	−	13.3941i	0.483005	−	0.483005i	−0.423085	−	0.906090i	$-0.639053\pi$
$769$	13.3941	−	13.3941i	0.483005	−	0.483005i	0.906090	+	0.423085i	$0.139053\pi$
$770$	−5.39676	−	38.4116i	−0.194486	−	1.38426i
$771$		0			0
$772$	−7.61561	−	7.61561i	−0.274092	−	0.274092i
$773$	0.0474609	−	0.0474609i	0.00170705	−	0.00170705i	−0.706253	−	0.707960i	$-0.749616\pi$
$773$	0.0474609	−	0.0474609i	0.00170705	−	0.00170705i	0.707960	+	0.706253i	$0.249616\pi$
$774$		0			0
$775$	−22.3010	−	12.3641i	−0.801077	−	0.444132i
$776$			7.20850i			0.258770i
$777$		0			0
$778$	0.475876	−	0.475876i	0.0170610	−	0.0170610i
$779$	−43.9939			−1.57624
$780$		0			0
$781$	−25.4817			−0.911806
$782$	−15.3945	+	15.3945i	−0.550507	+	0.550507i
$783$		0			0
$784$			8.12986i			0.290352i
$785$	−24.2267	+	32.1471i	−0.864688	+	1.14738i
$786$		0			0
$787$	29.8056	−	29.8056i	1.06246	−	1.06246i	0.0645402	−	0.997915i	$-0.479442\pi$
$787$	29.8056	−	29.8056i	1.06246	−	1.06246i	0.997915	−	0.0645402i	$-0.0205581\pi$
$788$	0.357634	+	0.357634i	0.0127402	+	0.0127402i
$789$		0			0
$790$	6.74083	−	0.947075i	0.239828	−	0.0336954i
$791$	10.4605	−	10.4605i	0.371934	−	0.371934i
$792$		0			0
$793$	7.45273	−	6.63078i	0.264654	−	0.235466i
$794$			16.2088i			0.575230i
$795$		0			0
$796$	−22.2951			−0.790229
$797$		−	44.3374i		−	1.57051i	−0.619173	−	0.785255i	$-0.712532\pi$
$797$		−	44.3374i		−	1.57051i	0.619173	−	0.785255i	$-0.287468\pi$
$798$		0			0
$799$	−10.7182	+	10.7182i	−0.379184	+	0.379184i
$800$	4.37290	+	2.42441i	0.154605	+	0.0857160i
$801$		0			0
$802$		−	19.4124i		−	0.685475i
$803$			0.292155i			0.0103099i
$804$		0			0
$805$	−5.25391	−	37.3948i	−0.185176	−	1.31799i
$806$	12.2224	+	13.7375i	0.430517	+	0.483884i
$807$		0			0
$808$	−10.8093	−	10.8093i	−0.380269	−	0.380269i
$809$		−	12.5026i		−	0.439567i	−0.975549	−	0.219784i	$-0.929465\pi$
$809$		−	12.5026i		−	0.439567i	0.975549	−	0.219784i	$-0.0705352\pi$
$810$		0			0
$811$	21.4521	−	21.4521i	0.753287	−	0.753287i	−0.221804	−	0.975091i	$-0.571195\pi$
$811$	21.4521	−	21.4521i	0.753287	−	0.753287i	0.975091	+	0.221804i	$0.0711946\pi$
$812$	15.6926	−	15.6926i	0.550701	−	0.550701i
$813$		0			0
$814$	−18.4254	−	18.4254i	−0.645811	−	0.645811i
$815$	25.1849	−	3.53844i	0.882190	−	0.123946i
$816$		0			0
$817$	−23.9576	+	23.9576i	−0.838169	+	0.838169i
$818$			22.3190i			0.780364i
$819$		0			0
$820$	27.1611	−	3.81608i	0.948507	−	0.133263i
$821$	2.76036	+	2.76036i	0.0963373	+	0.0963373i	0.753633	−	0.657296i	$-0.228300\pi$
$821$	2.76036	+	2.76036i	0.0963373	+	0.0963373i	−0.657296	+	0.753633i	$0.728300\pi$
$822$		0			0
$823$	−6.80286			−0.237133			−0.118566	−	0.992946i	$-0.537830\pi$
$823$	−6.80286			−0.237133			−0.118566	+	0.992946i	$0.537830\pi$
$824$	6.14812	+	6.14812i	0.214180	+	0.214180i
$825$		0			0
$826$	33.4170	+	33.4170i	1.16272	+	1.16272i
$827$	14.1668	+	14.1668i	0.492627	+	0.492627i	0.909133	−	0.416506i	$-0.136746\pi$
$827$	14.1668	+	14.1668i	0.492627	+	0.492627i	−0.416506	+	0.909133i	$0.636746\pi$
$828$		0			0
$829$			14.3887i			0.499741i	0.968279	+	0.249870i	$0.0803880\pi$
$829$			14.3887i			0.499741i	−0.968279	+	0.249870i	$0.919612\pi$
$830$	16.0544	−	21.3031i	0.557258	−	0.739442i
$831$		0			0
$832$	−2.39664	−	2.69372i	−0.0830884	−	0.0933880i
$833$	40.7671			1.41250
$834$		0			0
$835$	−1.69205	−	12.0432i	−0.0585558	−	0.416773i
$836$	−15.9952			−0.553205
$837$		0			0
$838$	0.320109	+	0.320109i	0.0110580	+	0.0110580i
$839$	18.3654	−	18.3654i	0.634045	−	0.634045i	−0.315035	−	0.949080i	$-0.602016\pi$
$839$	18.3654	−	18.3654i	0.634045	−	0.634045i	0.949080	+	0.315035i	$0.102016\pi$
$840$		0			0
$841$	−3.55237			−0.122496
$842$		−	23.8736i		−	0.822739i
$843$		0			0
$844$		−	16.2996i		−	0.561054i
$845$	20.0768	−	21.0219i	0.690664	−	0.723176i
$846$		0			0
$847$	−24.4482	−	24.4482i	−0.840049	−	0.840049i
$848$	3.21386			0.110364
$849$		0			0
$850$	12.1572	−	21.9279i	0.416989	−	0.752119i
$851$	−17.9377	−	17.9377i	−0.614897	−	0.614897i
$852$		0			0
$853$	−12.3605	+	12.3605i	−0.423215	+	0.423215i	−0.886309	−	0.463094i	$-0.846739\pi$
$853$	−12.3605	+	12.3605i	−0.423215	+	0.423215i	0.463094	+	0.886309i	$0.346739\pi$
$854$		−	10.7617i		−	0.368257i
$855$		0			0
$856$	−9.25296	−	9.25296i	−0.316260	−	0.316260i
$857$			27.0299i			0.923323i	0.887056	+	0.461661i	$0.152746\pi$
$857$			27.0299i			0.923323i	−0.887056	+	0.461661i	$0.847254\pi$
$858$		0			0
$859$	−9.73277			−0.332078			−0.166039	−	0.986119i	$-0.553098\pi$
$859$	−9.73277			−0.332078			−0.166039	+	0.986119i	$0.553098\pi$
$860$	12.7129	−	16.8691i	0.433506	−	0.575232i
$861$		0			0
$862$	−22.7794			−0.775869
$863$	2.37807	−	2.37807i	0.0809503	−	0.0809503i	−0.665472	−	0.746423i	$-0.731770\pi$
$863$	2.37807	−	2.37807i	0.0809503	−	0.0809503i	0.746423	+	0.665472i	$0.231770\pi$
$864$		0			0
$865$	−7.43186	+	9.86156i	−0.252691	+	0.335303i
$866$	15.6223	−	15.6223i	0.530869	−	0.530869i
$867$		0			0
$868$	19.8369			0.673307
$869$	9.59981	−	9.59981i	0.325651	−	0.325651i
$870$		0			0
$871$	24.5095	+	1.43043i	0.830471	+	0.0484684i
$872$	7.15147			0.242179
$873$		0			0
$874$	−15.5718			−0.526724
$875$	17.6833	+	39.7308i	0.597805	+	1.34314i
$876$		0			0
$877$	−0.650965	−	0.650965i	−0.0219815	−	0.0219815i	0.696031	−	0.718012i	$-0.254948\pi$
$877$	−0.650965	−	0.650965i	−0.0219815	−	0.0219815i	−0.718012	+	0.696031i	$0.754948\pi$
$878$	−20.2658	−	20.2658i	−0.683936	−	0.683936i
$879$		0			0
$880$	9.87517	−	1.38744i	0.332892	−	0.0467707i
$881$	−11.5132			−0.387891			−0.193945	−	0.981012i	$-0.562128\pi$
$881$	−11.5132			−0.387891			−0.193945	+	0.981012i	$0.562128\pi$
$882$		0			0
$883$	−1.42033			−0.0477977			−0.0238989	−	0.999714i	$-0.507608\pi$
$883$	−1.42033			−0.0477977			−0.0238989	+	0.999714i	$0.507608\pi$
$884$	−13.5076	+	12.0179i	−0.454311	+	0.404206i
$885$		0			0
$886$	−5.55075	+	5.55075i	−0.186481	+	0.186481i
$887$	−33.3259			−1.11897			−0.559487	−	0.828839i	$-0.689002\pi$
$887$	−33.3259			−1.11897			−0.559487	+	0.828839i	$0.689002\pi$
$888$		0			0
$889$	−6.32132	+	6.32132i	−0.212010	+	0.212010i
$890$	−16.3280	+	21.6660i	−0.547314	+	0.726247i
$891$		0			0
$892$	−17.7721	+	17.7721i	−0.595055	+	0.595055i
$893$	−10.8417			−0.362803
$894$		0			0
$895$	−13.1804	−	9.93300i	−0.440572	−	0.332024i
$896$	−3.88971			−0.129946
$897$		0			0
$898$			1.87304i			0.0625041i
$899$	−20.5746	−	20.5746i	−0.686203	−	0.686203i
$900$		0			0
$901$		−	16.1159i		−	0.536898i
$902$	38.6809	−	38.6809i	1.28793	−	1.28793i
$903$		0			0
$904$	2.68928	+	2.68928i	0.0894442	+	0.0894442i
$905$	−28.1467	+	37.3487i	−0.935629	+	1.24151i
$906$		0			0
$907$	47.4482			1.57549			0.787747	−	0.616000i	$-0.211248\pi$
$907$	47.4482			1.57549			0.787747	+	0.616000i	$0.211248\pi$
$908$	10.6055	+	10.6055i	0.351954	+	0.351954i
$909$		0			0
$910$	−2.54638	−	31.2563i	−0.0844115	−	1.03614i
$911$			15.7988i			0.523438i	0.965144	+	0.261719i	$0.0842893\pi$
$911$			15.7988i			0.523438i	−0.965144	+	0.261719i	$0.915711\pi$
$912$		0			0
$913$		−	53.2019i		−	1.76073i
$914$	−37.4661			−1.23927
$915$		0			0
$916$	1.17330	−	1.17330i	0.0387668	−	0.0387668i
$917$	5.02535	+	5.02535i	0.165952	+	0.165952i
$918$		0			0
$919$	−1.84363			−0.0608156			−0.0304078	−	0.999538i	$-0.509681\pi$
$919$	−1.84363			−0.0608156			−0.0304078	+	0.999538i	$0.509681\pi$
$920$	9.61378	−	1.35072i	0.316957	−	0.0445319i
$921$		0			0
$922$	36.2502			1.19384
$923$	−20.5663	−	1.20030i	−0.676949	−	0.0395085i
$924$		0			0
$925$	25.5504	+	14.1656i	0.840092	+	0.465762i
$926$		−	2.75530i		−	0.0905447i
$927$		0			0
$928$	4.03438	+	4.03438i	0.132435	+	0.132435i
$929$	−18.3335	−	18.3335i	−0.601502	−	0.601502i	0.339209	−	0.940711i	$-0.389841\pi$
$929$	−18.3335	−	18.3335i	−0.601502	−	0.601502i	−0.940711	+	0.339209i	$0.889841\pi$
$930$		0			0
$931$	20.6183	+	20.6183i	0.675738	+	0.675738i
$932$	−18.0187			−0.590221
$933$		0			0
$934$	−16.4805	−	16.4805i	−0.539258	−	0.539258i
$935$	−6.95733	−	49.5190i	−0.227529	−	1.61944i
$936$		0			0
$937$			9.05077i			0.295676i	0.989012	+	0.147838i	$0.0472314\pi$
$937$			9.05077i			0.295676i	−0.989012	+	0.147838i	$0.952769\pi$
$938$	18.7285	−	18.7285i	0.611507	−	0.611507i
$939$		0			0
$940$	6.69347	−	0.940420i	0.218317	−	0.0306731i
$941$	22.6872	+	22.6872i	0.739581	+	0.739581i	0.972497	−	0.232916i	$-0.0748267\pi$
$941$	22.6872	+	22.6872i	0.739581	+	0.739581i	−0.232916	+	0.972497i	$0.574827\pi$
$942$		0			0
$943$	37.6570	−	37.6570i	1.22628	−	1.22628i
$944$	−8.59111	+	8.59111i	−0.279617	+	0.279617i
$945$		0			0
$946$		−	42.1286i		−	1.36972i
$947$	−3.06685	−	3.06685i	−0.0996593	−	0.0996593i	0.655519	−	0.755178i	$-0.272450\pi$
$947$	−3.06685	−	3.06685i	−0.0996593	−	0.0996593i	−0.755178	+	0.655519i	$0.772450\pi$
$948$		0			0
$949$	−0.0137618	+	0.235799i	−0.000446728	+	0.00765436i
$950$	17.2388	−	4.94159i	0.559301	−	0.160326i
$951$		0			0
$952$			19.5049i			0.632158i
$953$		−	16.1232i		−	0.522283i	−0.965301	−	0.261142i	$-0.915901\pi$
$953$		−	16.1232i		−	0.522283i	0.965301	−	0.261142i	$-0.0840990\pi$
$954$		0			0
$955$	19.2826	−	25.5867i	0.623971	−	0.827966i
$956$	−8.29254	+	8.29254i	−0.268200	+	0.268200i
$957$		0			0
$958$			9.58293i			0.309610i
$959$	−78.8343			−2.54569
$960$		0			0
$961$			4.99171i			0.161023i
$962$	−14.0033	−	15.7391i	−0.451484	−	0.507450i
$963$		0			0
$964$	−19.8348	+	19.8348i	−0.638835	+	0.638835i
$965$	23.8485	−	3.35066i	0.767709	−	0.107862i
$966$		0			0
$967$	−41.8600	−	41.8600i	−1.34613	−	1.34613i	−0.889824	−	0.456304i	$-0.849173\pi$
$967$	−41.8600	−	41.8600i	−1.34613	−	1.34613i	−0.456304	−	0.889824i	$-0.650827\pi$
$968$	6.28534	−	6.28534i	0.202019	−	0.202019i
$969$		0			0
$970$	−12.8726	−	9.70101i	−0.413313	−	0.311481i
$971$		−	45.6574i		−	1.46522i	−0.680651	−	0.732608i	$-0.738303\pi$
$971$		−	45.6574i		−	1.46522i	0.680651	−	0.732608i	$-0.261697\pi$
$972$		0			0
$973$	59.4990	−	59.4990i	1.90745	−	1.90745i
$974$	36.7365			1.17711
$975$		0			0
$976$	2.76670			0.0885600
$977$	10.1014	−	10.1014i	0.323174	−	0.323174i	−0.526809	−	0.849983i	$-0.676612\pi$
$977$	10.1014	−	10.1014i	0.323174	−	0.323174i	0.849983	+	0.526809i	$0.176612\pi$
$978$		0			0
$979$			54.1083i			1.72931i
$980$	−14.5179	−	10.9410i	−0.463756	−	0.349496i
$981$		0			0
$982$	−22.9303	+	22.9303i	−0.731737	+	0.731737i
$983$	12.7136	+	12.7136i	0.405501	+	0.405501i	0.880166	−	0.474666i	$-0.157431\pi$
$983$	12.7136	+	12.7136i	0.405501	+	0.405501i	−0.474666	+	0.880166i	$0.657431\pi$
$984$		0			0
$985$	−1.11994	+	0.157349i	−0.0356842	+	0.00501356i
$986$	20.2303	−	20.2303i	0.644265	−	0.644265i
$987$		0			0
$988$	−12.9098	−	0.753447i	−0.410714	−	0.0239703i
$989$		−	41.0135i		−	1.30415i
$990$		0			0
$991$	−42.1864			−1.34009			−0.670047	−	0.742318i	$-0.733726\pi$
$991$	−42.1864			−1.34009			−0.670047	+	0.742318i	$0.733726\pi$
$992$			5.09983i			0.161920i
$993$		0			0
$994$	−15.7154	+	15.7154i	−0.498463	+	0.498463i
$995$	30.0042	−	39.8134i	0.951196	−	1.26217i
$996$		0			0
$997$			18.4366i			0.583892i	0.956435	+	0.291946i	$0.0943028\pi$
$997$			18.4366i			0.583892i	−0.956435	+	0.291946i	$0.905697\pi$
$998$			2.92627i			0.0926295i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.q.c.629.3	yes	24
3.2	odd	2	inner	1170.2.q.c.629.7	yes	24
5.4	even	2		1170.2.q.d.629.10	yes	24
13.8	odd	4		1170.2.q.d.359.6	yes	24
15.14	odd	2		1170.2.q.d.629.6	yes	24
39.8	even	4		1170.2.q.d.359.10	yes	24
65.34	odd	4	inner	1170.2.q.c.359.7	yes	24
195.164	even	4	inner	1170.2.q.c.359.3	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1170.2.q.c.359.3	✓	24	195.164	even	4	inner
1170.2.q.c.359.7	yes	24	65.34	odd	4	inner
1170.2.q.c.629.3	yes	24	1.1	even	1	trivial
1170.2.q.c.629.7	yes	24	3.2	odd	2	inner
1170.2.q.d.359.6	yes	24	13.8	odd	4
1170.2.q.d.359.10	yes	24	39.8	even	4
1170.2.q.d.629.6	yes	24	15.14	odd	2
1170.2.q.d.629.10	yes	24	5.4	even	2

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:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.q (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(1.78575 + 1.34577i) q^{5} +(2.75044 - 2.75044i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.21432 + 0.311108i) q^{10} +(-3.15348 + 3.15348i) q^{11} +(-2.69372 + 2.39664i) q^{13} +3.88971i q^{14} -1.00000 q^{16} +5.01449i q^{17} +(-2.53612 + 2.53612i) q^{19} +(1.34577 - 1.78575i) q^{20} -4.45969i q^{22} -4.34164i q^{23} +(1.37778 + 4.80642i) q^{25} +(0.210072 - 3.59943i) q^{26} +(-2.75044 - 2.75044i) q^{28} +5.70547i q^{29} +(-3.60613 + 3.60613i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-3.54578 - 3.54578i) q^{34} +(8.61307 - 1.21012i) q^{35} +(4.13155 - 4.13155i) q^{37} -3.58662i q^{38} +(0.311108 + 2.21432i) q^{40} +(8.67345 + 8.67345i) q^{41} +9.44654 q^{43} +(3.15348 + 3.15348i) q^{44} +(3.07000 + 3.07000i) q^{46} +(2.13745 + 2.13745i) q^{47} -8.12986i q^{49} +(-4.37290 - 2.42441i) q^{50} +(2.39664 + 2.69372i) q^{52} -3.21386 q^{53} +(-9.87517 + 1.38744i) q^{55} +3.88971 q^{56} +(-4.03438 - 4.03438i) q^{58} +(8.59111 - 8.59111i) q^{59} -2.76670 q^{61} -5.09983i q^{62} +1.00000i q^{64} +(-8.03564 + 0.654644i) q^{65} +(-4.81488 - 4.81488i) q^{67} +5.01449 q^{68} +(-5.23467 + 6.94604i) q^{70} +(4.04025 + 4.04025i) q^{71} +(0.0463227 - 0.0463227i) q^{73} +5.84290i q^{74} +(2.53612 + 2.53612i) q^{76} +17.3469i q^{77} -3.04420 q^{79} +(-1.78575 - 1.34577i) q^{80} -12.2661 q^{82} +(-8.43545 + 8.43545i) q^{83} +(-6.74837 + 8.95461i) q^{85} +(-6.67971 + 6.67971i) q^{86} -4.45969 q^{88} +(8.57916 - 8.57916i) q^{89} +(-0.817118 + 14.0007i) q^{91} -4.34164 q^{92} -3.02281 q^{94} +(-7.94192 + 1.11582i) q^{95} +(5.09718 + 5.09718i) q^{97} +(5.74868 + 5.74868i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 20 q^{13} - 24 q^{16} - 48 q^{19} + 32 q^{25} - 8 q^{31} + 16 q^{34} - 32 q^{37} + 8 q^{40} + 80 q^{43} + 8 q^{46} - 12 q^{52} + 16 q^{55} - 24 q^{58} - 16 q^{61} - 8 q^{67} - 24 q^{70} + 48 q^{73}+ \cdots + 64 q^{97}+O(q^{100}) \) 24 * q - 20 * q^13 - 24 * q^16 - 48 * q^19 + 32 * q^25 - 8 * q^31 + 16 * q^34 - 32 * q^37 + 8 * q^40 + 80 * q^43 + 8 * q^46 - 12 * q^52 + 16 * q^55 - 24 * q^58 - 16 * q^61 - 8 * q^67 - 24 * q^70 + 48 * q^73 + 48 * q^76 - 96 * q^79 - 72 * q^82 + 8 * q^85 + 8 * q^88 + 48 * q^91 - 16 * q^94 + 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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