LMFDB - Embedded newform 132.3.m.a.125.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [132,3,Mod(5,132)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(132, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 5, 4])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("132.5"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 132 = 2^{2} \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	132.m (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.59673948956$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			125.4
Character	$\chi$	$=$	132.125
Dual form			132.3.m.a.113.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.296378 + 2.98532i) q^{3} +(3.94591 + 5.43107i) q^{5} +(-0.935402 - 2.87887i) q^{7} +(-8.82432 - 1.76957i) q^{9} +(-6.22292 + 9.07057i) q^{11} +(-0.130232 - 0.0946188i) q^{13} +(-17.3830 + 10.1702i) q^{15} +(14.3517 + 19.7534i) q^{17} +(-0.192298 + 0.591833i) q^{19} +(8.87160 - 1.93924i) q^{21} -6.09109i q^{23} +(-6.20096 + 19.0846i) q^{25} +(7.89807 - 25.8190i) q^{27} +(49.6551 - 16.1339i) q^{29} +(-36.1042 - 26.2312i) q^{31} +(-25.2343 - 21.2657i) q^{33} +(11.9444 - 16.4400i) q^{35} +(9.51197 + 29.2748i) q^{37} +(0.321066 - 0.360741i) q^{39} +(-1.80114 - 0.585225i) q^{41} +79.5435 q^{43} +(-25.2093 - 54.9081i) q^{45} +(-14.0524 - 4.56591i) q^{47} +(32.2289 - 23.4157i) q^{49} +(-63.2237 + 36.9899i) q^{51} +(28.0492 - 38.6064i) q^{53} +(-73.8180 + 1.99452i) q^{55} +(-1.70982 - 0.749479i) q^{57} +(-20.8550 + 6.77621i) q^{59} +(49.8894 - 36.2468i) q^{61} +(3.15993 + 27.0594i) q^{63} -1.08065i q^{65} -56.3242 q^{67} +(18.1839 + 1.80527i) q^{69} +(52.9951 + 72.9415i) q^{71} +(-21.7702 - 67.0016i) q^{73} +(-55.1359 - 24.1681i) q^{75} +(31.9340 + 9.43034i) q^{77} +(79.8792 + 58.0357i) q^{79} +(74.7373 + 31.2305i) q^{81} +(-60.8336 - 83.7303i) q^{83} +(-50.6517 + 155.890i) q^{85} +(33.4483 + 153.018i) q^{87} +165.487i q^{89} +(-0.150577 + 0.463427i) q^{91} +(89.0093 - 100.008i) q^{93} +(-3.97308 + 1.29093i) q^{95} +(-79.1668 - 57.5180i) q^{97} +(70.9640 - 69.0298i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 5 q^{3} - 8 q^{7} - 7 q^{9} - 4 q^{13} + 29 q^{15} + 56 q^{19} + 2 q^{21} + 20 q^{25} + 47 q^{27} - 40 q^{31} + 36 q^{33} - 120 q^{37} - 109 q^{39} - 100 q^{43} + 34 q^{45} - 176 q^{49} - 124 q^{51}+ \cdots + 515 q^{99}+O(q^{100}) $ 32 * q + 5 * q^3 - 8 * q^7 - 7 * q^9 - 4 * q^13 + 29 * q^15 + 56 * q^19 + 2 * q^21 + 20 * q^25 + 47 * q^27 - 40 * q^31 + 36 * q^33 - 120 * q^37 - 109 * q^39 - 100 * q^43 + 34 * q^45 - 176 * q^49 - 124 * q^51 - 246 * q^55 - 310 * q^57 + 120 * q^61 - 325 * q^63 + 88 * q^67 + 70 * q^69 + 280 * q^73 + 282 * q^75 + 512 * q^79 + 573 * q^81 + 740 * q^85 + 354 * q^87 + 156 * q^91 + 563 * q^93 - 62 * q^97 + 515 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/132\mathbb{Z}\right)^\times$.

$n$	$13$	$67$	$89$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.296378	+	2.98532i	−0.0987927	+	0.995108i
$3$	−0.296378	+	2.98532i	−0.0987927	+	0.995108i
$4$		0			0
$5$	3.94591	+	5.43107i	0.789181	+	1.08621i	0.994210	+	0.107459i	$0.0342714\pi$
$5$	3.94591	+	5.43107i	0.789181	+	1.08621i	−0.205028	+	0.978756i	$0.565729\pi$
$6$		0			0
$7$	−0.935402	−	2.87887i	−0.133629	−	0.411268i	0.861745	−	0.507341i	$-0.169372\pi$
$7$	−0.935402	−	2.87887i	−0.133629	−	0.411268i	−0.995374	+	0.0960736i	$0.969372\pi$
$8$		0			0
$9$	−8.82432	−	1.76957i	−0.980480	−	0.196619i
$10$		0			0
$11$	−6.22292	+	9.07057i	−0.565720	+	0.824598i
$11$	−6.22292	+	9.07057i	−0.565720	+	0.824598i
$12$		0			0
$13$	−0.130232	−	0.0946188i	−0.0100178	−	0.00727837i	0.582765	−	0.812641i	$-0.301971\pi$
$13$	−0.130232	−	0.0946188i	−0.0100178	−	0.00727837i	−0.592783	+	0.805362i	$0.701971\pi$
$14$		0			0
$15$	−17.3830	+	10.1702i	−1.15887	+	0.678011i
$16$		0			0
$17$	14.3517	+	19.7534i	0.844215	+	1.16196i	0.985108	+	0.171938i	$0.0550028\pi$
$17$	14.3517	+	19.7534i	0.844215	+	1.16196i	−0.140892	+	0.990025i	$0.544997\pi$
$18$		0			0
$19$	−0.192298	+	0.591833i	−0.0101210	+	0.0311491i	−0.955989	−	0.293401i	$-0.905213\pi$
$19$	−0.192298	+	0.591833i	−0.0101210	+	0.0311491i	0.945869	+	0.324550i	$0.105213\pi$
$20$		0			0
$21$	8.87160	−	1.93924i	0.422457	−	0.0923450i
$22$		0			0
$23$		−	6.09109i		−	0.264830i	−0.991194	−	0.132415i	$-0.957727\pi$
$23$		−	6.09109i		−	0.264830i	0.991194	−	0.132415i	$-0.0422732\pi$
$24$		0			0
$25$	−6.20096	+	19.0846i	−0.248039	+	0.763384i
$26$		0			0
$27$	7.89807	−	25.8190i	0.292521	−	0.956259i
$28$		0			0
$29$	49.6551	−	16.1339i	1.71224	−	0.556342i	0.721539	−	0.692373i	$-0.243435\pi$
$29$	49.6551	−	16.1339i	1.71224	−	0.556342i	0.990704	+	0.136032i	$0.0434349\pi$
$30$		0			0
$31$	−36.1042	−	26.2312i	−1.16465	−	0.846169i	−0.174293	−	0.984694i	$-0.555764\pi$
$31$	−36.1042	−	26.2312i	−1.16465	−	0.846169i	−0.990359	+	0.138525i	$0.955764\pi$
$32$		0			0
$33$	−25.2343	−	21.2657i	−0.764675	−	0.644416i
$34$		0			0
$35$	11.9444	−	16.4400i	0.341267	−	0.469714i
$36$		0			0
$37$	9.51197	+	29.2748i	0.257080	+	0.791211i	0.993413	+	0.114592i	$0.0365559\pi$
$37$	9.51197	+	29.2748i	0.257080	+	0.791211i	−0.736333	+	0.676620i	$0.763444\pi$
$38$		0			0
$39$	0.321066	−	0.360741i	0.00823245	−	0.00924976i
$40$		0			0
$41$	−1.80114	−	0.585225i	−0.0439302	−	0.0142738i	0.286969	−	0.957940i	$-0.407352\pi$
$41$	−1.80114	−	0.585225i	−0.0439302	−	0.0142738i	−0.330900	+	0.943666i	$0.607352\pi$
$42$		0			0
$43$	79.5435			1.84985			0.924924	−	0.380152i	$-0.124128\pi$
$43$	79.5435			1.84985			0.924924	+	0.380152i	$0.124128\pi$
$44$		0			0
$45$	−25.2093	−	54.9081i	−0.560206	−	1.22018i
$46$		0			0
$47$	−14.0524	−	4.56591i	−0.298988	−	0.0971471i	0.155682	−	0.987807i	$-0.450243\pi$
$47$	−14.0524	−	4.56591i	−0.298988	−	0.0971471i	−0.454670	+	0.890660i	$0.650243\pi$
$48$		0			0
$49$	32.2289	−	23.4157i	0.657733	−	0.477871i
$50$		0			0
$51$	−63.2237	+	36.9899i	−1.23968	+	0.725292i
$52$		0			0
$53$	28.0492	−	38.6064i	0.529230	−	0.728422i	−0.457783	−	0.889064i	$-0.651356\pi$
$53$	28.0492	−	38.6064i	0.529230	−	0.728422i	0.987013	+	0.160642i	$0.0513564\pi$
$54$		0			0
$55$	−73.8180	+	1.99452i	−1.34215	+	0.0362641i
$56$		0			0
$57$	−1.70982	−	0.749479i	−0.0299969	−	0.0131488i
$58$		0			0
$59$	−20.8550	+	6.77621i	−0.353475	+	0.114851i	−0.480372	−	0.877065i	$-0.659498\pi$
$59$	−20.8550	+	6.77621i	−0.353475	+	0.114851i	0.126897	+	0.991916i	$0.459498\pi$
$60$		0			0
$61$	49.8894	−	36.2468i	0.817859	−	0.594209i	−0.0982396	−	0.995163i	$-0.531321\pi$
$61$	49.8894	−	36.2468i	0.817859	−	0.594209i	0.916098	+	0.400954i	$0.131321\pi$
$62$		0			0
$63$	3.15993	+	27.0594i	0.0501576	+	0.429514i
$64$		0			0
$65$		−	1.08065i		−	0.0166255i
$66$		0			0
$67$	−56.3242			−0.840659			−0.420330	−	0.907371i	$-0.638086\pi$
$67$	−56.3242			−0.840659			−0.420330	+	0.907371i	$0.638086\pi$
$68$		0			0
$69$	18.1839	+	1.80527i	0.263534	+	0.0261633i
$70$		0			0
$71$	52.9951	+	72.9415i	0.746410	+	1.02734i	0.998224	+	0.0595694i	$0.0189728\pi$
$71$	52.9951	+	72.9415i	0.746410	+	1.02734i	−0.251814	+	0.967776i	$0.581027\pi$
$72$		0			0
$73$	−21.7702	−	67.0016i	−0.298221	−	0.917831i	−0.982120	−	0.188254i	$-0.939717\pi$
$73$	−21.7702	−	67.0016i	−0.298221	−	0.917831i	0.683899	−	0.729577i	$-0.260283\pi$
$74$		0			0
$75$	−55.1359	−	24.1681i	−0.735145	−	0.322242i
$76$		0			0
$77$	31.9340	+	9.43034i	0.414727	+	0.122472i
$78$		0			0
$79$	79.8792	+	58.0357i	1.01113	+	0.734629i	0.964446	−	0.264281i	$-0.0851346\pi$
$79$	79.8792	+	58.0357i	1.01113	+	0.734629i	0.0466840	+	0.998910i	$0.485135\pi$
$80$		0			0
$81$	74.7373	+	31.2305i	0.922682	+	0.385562i
$82$		0			0
$83$	−60.8336	−	83.7303i	−0.732935	−	1.00880i	−0.998994	−	0.0448419i	$-0.985722\pi$
$83$	−60.8336	−	83.7303i	−0.732935	−	1.00880i	0.266059	−	0.963957i	$-0.414278\pi$
$84$		0			0
$85$	−50.6517	+	155.890i	−0.595902	+	1.83400i
$86$		0			0
$87$	33.4483	+	153.018i	0.384463	+	1.75883i
$88$		0			0
$89$			165.487i			1.85940i	0.368312	+	0.929702i	$0.379936\pi$
$89$			165.487i			1.85940i	−0.368312	+	0.929702i	$0.620064\pi$
$90$		0			0
$91$	−0.150577	+	0.463427i	−0.00165469	+	0.00509261i
$92$		0			0
$93$	89.0093	−	100.008i	0.957089	−	1.07536i
$94$		0			0
$95$	−3.97308	+	1.29093i	−0.0418219	+	0.0135888i
$96$		0			0
$97$	−79.1668	−	57.5180i	−0.816152	−	0.592969i	0.0994555	−	0.995042i	$-0.468290\pi$
$97$	−79.1668	−	57.5180i	−0.816152	−	0.592969i	−0.915608	+	0.402073i	$0.868290\pi$
$98$		0			0
$99$	70.9640	−	69.0298i	0.716808	−	0.697270i
$100$		0			0
$101$	−88.6783	+	122.055i	−0.878003	+	1.20847i	0.0989666	+	0.995091i	$0.468446\pi$
$101$	−88.6783	+	122.055i	−0.878003	+	1.20847i	−0.976970	+	0.213377i	$0.931554\pi$
$102$		0			0
$103$	6.58597	+	20.2695i	0.0639415	+	0.196792i	0.977924	−	0.208963i	$-0.0670088\pi$
$103$	6.58597	+	20.2695i	0.0639415	+	0.196792i	−0.913982	+	0.405755i	$0.867009\pi$
$104$		0			0
$105$	45.5387	+	40.5302i	0.433702	+	0.386002i
$106$		0			0
$107$	−112.194	−	36.4542i	−1.04855	−	0.340693i	−0.266449	−	0.963849i	$-0.585850\pi$
$107$	−112.194	−	36.4542i	−1.04855	−	0.340693i	−0.782098	+	0.623156i	$0.785850\pi$
$108$		0			0
$109$	−101.381			−0.930102			−0.465051	−	0.885284i	$-0.653964\pi$
$109$	−101.381			−0.930102			−0.465051	+	0.885284i	$0.653964\pi$
$110$		0			0
$111$	−90.2140	+	19.7199i	−0.812738	+	0.177657i
$112$		0			0
$113$	−142.057	−	46.1570i	−1.25714	−	0.408469i	−0.396665	−	0.917964i	$-0.629832\pi$
$113$	−142.057	−	46.1570i	−1.25714	−	0.408469i	−0.860474	+	0.509495i	$0.829832\pi$
$114$		0			0
$115$	33.0812	−	24.0349i	0.287662	−	0.208999i
$116$		0			0
$117$	0.981771	+	1.06540i	0.00839121	+	0.00910599i
$118$		0			0
$119$	43.4428	−	59.7940i	0.365066	−	0.502470i
$120$		0			0
$121$	−43.5507	−	112.891i	−0.359923	−	0.932982i
$122$		0			0
$123$	2.28090	−	5.20353i	0.0185439	−	0.0423051i
$124$		0			0
$125$	31.4970	−	10.2340i	0.251976	−	0.0818718i
$126$		0			0
$127$	157.846	−	114.682i	1.24288	−	0.903004i	0.245092	−	0.969500i	$-0.421182\pi$
$127$	157.846	−	114.682i	1.24288	−	0.903004i	0.997787	+	0.0664953i	$0.0211817\pi$
$128$		0			0
$129$	−23.5749	+	237.463i	−0.182751	+	1.84080i
$130$		0			0
$131$		−	132.420i		−	1.01084i	−0.862873	−	0.505420i	$-0.831337\pi$
$131$		−	132.420i		−	1.01084i	0.862873	−	0.505420i	$-0.168663\pi$
$132$		0			0
$133$	1.88369			0.0141631
$134$		0			0
$135$	171.390	−	58.9843i	1.26955	−	0.436921i
$136$		0			0
$137$	−45.3714	−	62.4484i	−0.331178	−	0.455828i	0.610661	−	0.791892i	$-0.290904\pi$
$137$	−45.3714	−	62.4484i	−0.331178	−	0.455828i	−0.941839	+	0.336065i	$0.890904\pi$
$138$		0			0
$139$	4.63361	+	14.2608i	0.0333353	+	0.102596i	0.966340	−	0.257269i	$-0.0828228\pi$
$139$	4.63361	+	14.2608i	0.0333353	+	0.102596i	−0.933004	+	0.359865i	$0.882823\pi$
$140$		0			0
$141$	17.7956	−	40.5978i	0.126210	−	0.287928i
$142$		0			0
$143$	1.66867	−	0.592471i	0.0116690	−	0.00414315i
$144$		0			0
$145$	283.559	+	206.017i	1.95558	+	1.42081i
$146$		0			0
$147$	60.3514	+	103.154i	0.410554	+	0.701725i
$148$		0			0
$149$	−3.02024	−	4.15701i	−0.0202701	−	0.0278994i	0.798762	−	0.601648i	$-0.205489\pi$
$149$	−3.02024	−	4.15701i	−0.0202701	−	0.0278994i	−0.819032	+	0.573748i	$0.805489\pi$
$150$		0			0
$151$	−52.4433	+	161.404i	−0.347307	+	1.06890i	0.613031	+	0.790059i	$0.289950\pi$
$151$	−52.4433	+	161.404i	−0.347307	+	1.06890i	−0.960337	+	0.278841i	$0.910050\pi$
$152$		0			0
$153$	−91.6887	−	199.706i	−0.599273	−	1.30527i
$154$		0			0
$155$		−	299.591i		−	1.93284i
$156$		0			0
$157$	16.0439	−	49.3779i	0.102190	−	0.314509i	−0.886871	−	0.462018i	$-0.847126\pi$
$157$	16.0439	−	49.3779i	0.102190	−	0.314509i	0.989061	+	0.147509i	$0.0471255\pi$
$158$		0			0
$159$	106.939	+	95.1779i	0.672575	+	0.598603i
$160$		0			0
$161$	−17.5355	+	5.69762i	−0.108916	+	0.0353889i
$162$		0			0
$163$	−78.7195	−	57.1931i	−0.482942	−	0.350878i	0.319522	−	0.947579i	$-0.396478\pi$
$163$	−78.7195	−	57.1931i	−0.482942	−	0.350878i	−0.802464	+	0.596701i	$0.796478\pi$
$164$		0			0
$165$	15.9237	−	220.962i	0.0965075	−	1.33916i
$166$		0			0
$167$	95.4091	−	131.319i	0.571312	−	0.786344i	−0.421397	−	0.906876i	$-0.638460\pi$
$167$	95.4091	−	131.319i	0.571312	−	0.786344i	0.992709	+	0.120532i	$0.0384602\pi$
$168$		0			0
$169$	−52.2159	−	160.704i	−0.308970	−	0.950911i
$170$		0			0
$171$	2.74419	−	4.88224i	0.0160479	−	0.0285511i
$172$		0			0
$173$	−188.563	−	61.2678i	−1.08996	−	0.354149i	−0.291729	−	0.956501i	$-0.594230\pi$
$173$	−188.563	−	61.2678i	−1.08996	−	0.354149i	−0.798231	+	0.602352i	$0.794230\pi$
$174$		0			0
$175$	60.7425			0.347100
$176$		0			0
$177$	−14.0482	−	64.2673i	−0.0793684	−	0.363092i
$178$		0			0
$179$	185.458	+	60.2590i	1.03608	+	0.336643i	0.777191	−	0.629265i	$-0.216644\pi$
$179$	185.458	+	60.2590i	1.03608	+	0.336643i	0.258888	+	0.965907i	$0.416644\pi$
$180$		0			0
$181$	−19.2475	+	13.9841i	−0.106340	+	0.0772603i	−0.639684	−	0.768638i	$-0.720935\pi$
$181$	−19.2475	+	13.9841i	−0.106340	+	0.0772603i	0.533345	+	0.845898i	$0.320935\pi$
$182$		0			0
$183$	93.4222	+	159.679i	0.510504	+	0.872561i
$184$		0			0
$185$	−121.460	+	167.176i	−0.656543	+	0.903653i
$186$		0			0
$187$	−268.484	+	7.25429i	−1.43574	+	0.0387930i
$188$		0			0
$189$	−81.7175	+	1.41361i	−0.432368	+	0.00747940i
$190$		0			0
$191$	−144.795	+	47.0467i	−0.758088	+	0.246318i	−0.662458	−	0.749099i	$-0.730487\pi$
$191$	−144.795	+	47.0467i	−0.758088	+	0.246318i	−0.0956300	+	0.995417i	$0.530487\pi$
$192$		0			0
$193$	104.155	−	75.6733i	0.539665	−	0.392090i	−0.284296	−	0.958737i	$-0.591760\pi$
$193$	104.155	−	75.6733i	0.539665	−	0.392090i	0.823961	+	0.566647i	$0.191760\pi$
$194$		0			0
$195$	3.22611	+	0.320282i	0.0165441	+	0.00164247i
$196$		0			0
$197$			141.406i			0.717798i	0.933376	+	0.358899i	$0.116848\pi$
$197$			141.406i			0.717798i	−0.933376	+	0.358899i	$0.883152\pi$
$198$		0			0
$199$	−162.261			−0.815381			−0.407690	−	0.913120i	$-0.633666\pi$
$199$	−162.261			−0.815381			−0.407690	+	0.913120i	$0.633666\pi$
$200$		0			0
$201$	16.6932	−	168.146i	0.0830510	−	0.836547i
$202$		0			0
$203$	−92.8950	−	127.859i	−0.457611	−	0.629847i
$204$		0			0
$205$	−3.92872	−	12.0913i	−0.0191645	−	0.0589822i
$206$		0			0
$207$	−10.7786	+	53.7497i	−0.0520705	+	0.259660i
$208$		0			0
$209$	−4.17161	−	5.42718i	−0.0199599	−	0.0259674i
$210$		0			0
$211$	202.696	+	147.268i	0.960647	+	0.697951i	0.953301	−	0.302022i	$-0.0976617\pi$
$211$	202.696	+	147.268i	0.960647	+	0.697951i	0.00734596	+	0.999973i	$0.497662\pi$
$212$		0			0
$213$	−233.461	+	136.589i	−1.09606	+	0.641264i
$214$		0			0
$215$	313.871	+	432.006i	1.45987	+	2.00933i
$216$		0			0
$217$	−41.7444	+	128.476i	−0.192371	+	0.592056i
$218$		0			0
$219$	206.474	−	45.1332i	0.942803	−	0.206087i
$220$		0			0
$221$		−	3.93045i		−	0.0177848i
$222$		0			0
$223$	−22.8305	+	70.2650i	−0.102379	+	0.315090i	−0.989106	−	0.147203i	$-0.952973\pi$
$223$	−22.8305	+	70.2650i	−0.102379	+	0.315090i	0.886728	+	0.462292i	$0.152973\pi$
$224$		0			0
$225$	88.4908	−	157.436i	0.393292	−	0.699714i
$226$		0			0
$227$	26.0651	−	8.46905i	0.114824	−	0.0373086i	−0.251041	−	0.967976i	$-0.580773\pi$
$227$	26.0651	−	8.46905i	0.114824	−	0.0373086i	0.365865	+	0.930668i	$0.380773\pi$
$228$		0			0
$229$	−7.28457	−	5.29255i	−0.0318104	−	0.0231116i	0.571766	−	0.820416i	$-0.306258\pi$
$229$	−7.28457	−	5.29255i	−0.0318104	−	0.0231116i	−0.603577	+	0.797305i	$0.706258\pi$
$230$		0			0
$231$	−37.6172	+	92.5383i	−0.162845	+	0.400599i
$232$		0			0
$233$	−69.9579	+	96.2887i	−0.300248	+	0.413256i	−0.932309	−	0.361662i	$-0.882209\pi$
$233$	−69.9579	+	96.2887i	−0.300248	+	0.413256i	0.632061	+	0.774919i	$0.282209\pi$
$234$		0			0
$235$	−30.6518	−	94.3365i	−0.130433	−	0.401432i
$236$		0			0
$237$	−196.930	+	221.265i	−0.830927	+	0.933607i
$238$		0			0
$239$	349.506	+	113.561i	1.46237	+	0.475152i	0.928792	−	0.370601i	$-0.120848\pi$
$239$	349.506	+	113.561i	1.46237	+	0.475152i	0.533575	+	0.845753i	$0.320848\pi$
$240$		0			0
$241$	−237.557			−0.985713			−0.492856	−	0.870111i	$-0.664047\pi$
$241$	−237.557			−0.985713			−0.492856	+	0.870111i	$0.664047\pi$
$242$		0			0
$243$	−115.384	+	213.859i	−0.474830	+	0.880078i
$244$		0			0
$245$	254.344	+	82.6415i	1.03814	+	0.337312i
$246$		0			0
$247$	0.0810419	−	0.0588804i	0.000328105	−	0.000238382i
$248$		0			0
$249$	267.992	−	156.792i	1.07627	−	0.629688i
$250$		0			0
$251$	−36.8500	+	50.7197i	−0.146813	+	0.202071i	−0.876090	−	0.482148i	$-0.839857\pi$
$251$	−36.8500	+	50.7197i	−0.146813	+	0.202071i	0.729277	+	0.684219i	$0.239857\pi$
$252$		0			0
$253$	55.2497	+	37.9043i	0.218378	+	0.149819i
$254$		0			0
$255$	−450.370	−	197.414i	−1.76616	−	0.774173i
$256$		0			0
$257$	200.555	−	65.1643i	0.780370	−	0.253558i	0.108372	−	0.994110i	$-0.465436\pi$
$257$	200.555	−	65.1643i	0.780370	−	0.253558i	0.671998	+	0.740553i	$0.265436\pi$
$258$		0			0
$259$	75.3810	−	54.7675i	0.291046	−	0.211457i
$260$		0			0
$261$	−466.722	+	54.5027i	−1.78821	+	0.208823i
$262$		0			0
$263$			113.017i			0.429723i	0.976645	+	0.214861i	$0.0689300\pi$
$263$			113.017i			0.429723i	−0.976645	+	0.214861i	$0.931070\pi$
$264$		0			0
$265$	320.353			1.20888
$266$		0			0
$267$	−494.032	−	49.0467i	−1.85031	−	0.183696i
$268$		0			0
$269$	279.218	+	384.310i	1.03798	+	1.42866i	0.898781	+	0.438397i	$0.144454\pi$
$269$	279.218	+	384.310i	1.03798	+	1.42866i	0.139202	+	0.990264i	$0.455546\pi$
$270$		0			0
$271$	−81.9833	−	252.319i	−0.302521	−	0.931065i	−0.980591	−	0.196067i	$-0.937183\pi$
$271$	−81.9833	−	252.319i	−0.302521	−	0.931065i	0.678069	−	0.734998i	$-0.262817\pi$
$272$		0			0
$273$	−1.33885	−	0.586870i	−0.00490422	−	0.00214971i
$274$		0			0
$275$	−134.520	−	175.008i	−0.489165	−	0.636393i
$276$		0			0
$277$	122.544	+	89.0332i	0.442396	+	0.321420i	0.786586	−	0.617480i	$-0.211847\pi$
$277$	122.544	+	89.0332i	0.442396	+	0.321420i	−0.344190	+	0.938900i	$0.611847\pi$
$278$		0			0
$279$	272.177	+	295.362i	0.975545	+	1.05864i
$280$		0			0
$281$	−225.243	−	310.020i	−0.801576	−	1.10327i	−0.992569	−	0.121683i	$-0.961171\pi$
$281$	−225.243	−	310.020i	−0.801576	−	1.10327i	0.190993	−	0.981591i	$-0.438829\pi$
$282$		0			0
$283$	128.017	−	393.996i	0.452357	−	1.39221i	−0.421854	−	0.906664i	$-0.638620\pi$
$283$	128.017	−	393.996i	0.452357	−	1.39221i	0.874210	−	0.485547i	$-0.161380\pi$
$284$		0			0
$285$	−2.67632	−	12.2435i	−0.00939059	−	0.0429598i
$286$		0			0
$287$			5.73266i			0.0199744i
$288$		0			0
$289$	−94.9194	+	292.132i	−0.328441	+	1.01084i
$290$		0			0
$291$	195.173	−	219.291i	0.670698	−	0.753579i
$292$		0			0
$293$	−330.857	+	107.502i	−1.12920	+	0.366901i	−0.813273	−	0.581882i	$-0.802317\pi$
$293$	−330.857	+	107.502i	−1.12920	+	0.366901i	−0.315930	+	0.948782i	$0.602317\pi$
$294$		0			0
$295$	−119.094	−	86.5269i	−0.403709	−	0.293312i
$296$		0			0
$297$	185.044	+	232.309i	0.623044	+	0.782187i
$298$		0			0
$299$	−0.576332	+	0.793253i	−0.00192753	+	0.00265302i
$300$		0			0
$301$	−74.4051	−	228.995i	−0.247193	−	0.760782i
$302$		0			0
$303$	−338.092	−	300.908i	−1.11582	−	0.993096i
$304$		0			0
$305$	393.718	+	127.927i	1.29088	+	0.419432i
$306$		0			0
$307$	507.760			1.65394			0.826971	−	0.562245i	$-0.190062\pi$
$307$	507.760			1.65394			0.826971	+	0.562245i	$0.190062\pi$
$308$		0			0
$309$	−62.4631	+	13.6538i	−0.202146	+	0.0441871i
$310$		0			0
$311$	−86.9099	−	28.2388i	−0.279453	−	0.0907998i	0.165937	−	0.986136i	$-0.446935\pi$
$311$	−86.9099	−	28.2388i	−0.279453	−	0.0907998i	−0.445390	+	0.895336i	$0.646935\pi$
$312$		0			0
$313$	−387.262	+	281.363i	−1.23726	+	0.898922i	−0.997413	−	0.0718884i	$-0.977097\pi$
$313$	−387.262	+	281.363i	−1.23726	+	0.898922i	−0.239848	+	0.970811i	$0.577097\pi$
$314$		0			0
$315$	−134.493	+	123.935i	−0.426961	+	0.393446i
$316$		0			0
$317$	295.722	−	407.026i	0.932876	−	1.28399i	−0.0258512	−	0.999666i	$-0.508230\pi$
$317$	295.722	−	407.026i	0.932876	−	1.28399i	0.958727	−	0.284328i	$-0.0917704\pi$
$318$		0			0
$319$	−162.655	+	550.800i	−0.509892	+	1.72665i
$320$		0			0
$321$	142.080	−	324.133i	0.442615	−	1.00976i
$322$		0			0
$323$	−14.4505	+	4.69525i	−0.0447384	+	0.0145364i
$324$		0			0
$325$	2.61332	−	1.89869i	0.00804100	−	0.00584213i
$326$		0			0
$327$	30.0471	−	302.656i	0.0918873	−	0.925552i
$328$		0			0
$329$			44.7261i			0.135946i
$330$		0			0
$331$	154.468			0.466670			0.233335	−	0.972396i	$-0.425036\pi$
$331$	154.468			0.466670			0.233335	+	0.972396i	$0.425036\pi$
$332$		0			0
$333$	−32.1328	−	275.162i	−0.0964949	−	0.826314i
$334$		0			0
$335$	−222.250	−	305.901i	−0.663432	−	0.913136i
$336$		0			0
$337$	−93.7345	−	288.485i	−0.278144	−	0.856039i	−0.988370	−	0.152066i	$-0.951407\pi$
$337$	−93.7345	−	288.485i	−0.278144	−	0.856039i	0.710226	−	0.703973i	$-0.248593\pi$
$338$		0			0
$339$	179.896	−	410.405i	0.530667	−	1.21063i
$340$		0			0
$341$	462.606	−	164.251i	1.35662	−	0.481675i
$342$		0			0
$343$	−217.555	−	158.063i	−0.634270	−	0.460824i
$344$		0			0
$345$	61.9473	+	105.881i	0.179558	+	0.306903i
$346$		0			0
$347$	−190.035	−	261.561i	−0.547651	−	0.753777i	0.442040	−	0.896995i	$-0.354255\pi$
$347$	−190.035	−	261.561i	−0.547651	−	0.753777i	−0.989691	+	0.143218i	$0.954255\pi$
$348$		0			0
$349$	172.352	−	530.445i	0.493845	−	1.51990i	−0.324903	−	0.945747i	$-0.605332\pi$
$349$	172.352	−	530.445i	0.493845	−	1.51990i	0.818748	−	0.574152i	$-0.194668\pi$
$350$		0			0
$351$	−3.47154	+	2.61514i	−0.00989043	+	0.00745055i
$352$		0			0
$353$			31.0942i			0.0880857i	0.999030	+	0.0440428i	$0.0140238\pi$
$353$			31.0942i			0.0880857i	−0.999030	+	0.0440428i	$0.985976\pi$
$354$		0			0
$355$	−187.037	+	575.641i	−0.526865	+	1.62152i
$356$		0			0
$357$	165.629	+	147.413i	0.463946	+	0.412920i
$358$		0			0
$359$	99.5764	−	32.3543i	0.277371	−	0.0901234i	−0.167028	−	0.985952i	$-0.553417\pi$
$359$	99.5764	−	32.3543i	0.277371	−	0.0901234i	0.444400	+	0.895829i	$0.353417\pi$
$360$		0			0
$361$	291.742	+	211.963i	0.808149	+	0.587155i
$362$		0			0
$363$	349.923	−	96.5544i	0.963976	−	0.265990i
$364$		0			0
$365$	277.988	−	382.618i	0.761611	−	1.04827i
$366$		0			0
$367$	41.8989	+	128.951i	0.114166	+	0.351366i	0.991772	−	0.128016i	$-0.0408608\pi$
$367$	41.8989	+	128.951i	0.114166	+	0.351366i	−0.877606	+	0.479382i	$0.840861\pi$
$368$		0			0
$369$	14.8582	+	8.35145i	0.0402662	+	0.0226326i
$370$		0			0
$371$	−137.380	−	44.6375i	−0.370297	−	0.120317i
$372$		0			0
$373$	−275.618			−0.738921			−0.369461	−	0.929246i	$-0.620457\pi$
$373$	−275.618			−0.738921			−0.369461	+	0.929246i	$0.620457\pi$
$374$		0			0
$375$	21.2167	+	97.0617i	0.0565780	+	0.258831i
$376$		0			0
$377$	−7.99324	−	2.59716i	−0.0212022	−	0.00688902i
$378$		0			0
$379$	−227.546	+	165.322i	−0.600385	+	0.436205i	−0.846015	−	0.533158i	$-0.821005\pi$
$379$	−227.546	+	165.322i	−0.600385	+	0.436205i	0.245631	+	0.969363i	$0.421005\pi$
$380$		0			0
$381$	295.580	+	505.209i	0.775800	+	1.32601i
$382$		0			0
$383$	−233.294	+	321.102i	−0.609123	+	0.838386i	−0.996505	−	0.0835335i	$-0.973379\pi$
$383$	−233.294	+	321.102i	−0.609123	+	0.838386i	0.387382	+	0.921919i	$0.373379\pi$
$384$		0			0
$385$	74.7915	+	210.647i	0.194264	+	0.547135i
$386$		0			0
$387$	−701.917	−	140.758i	−1.81374	−	0.363715i
$388$		0			0
$389$	79.1447	−	25.7157i	0.203457	−	0.0661072i	−0.205516	−	0.978654i	$-0.565887\pi$
$389$	79.1447	−	25.7157i	0.203457	−	0.0661072i	0.408973	+	0.912547i	$0.365887\pi$
$390$		0			0
$391$	120.320	−	87.4172i	0.307723	−	0.223574i
$392$		0			0
$393$	395.317	+	39.2464i	1.00590	+	0.0998637i
$394$		0			0
$395$			662.833i			1.67806i
$396$		0			0
$397$	173.738			0.437627			0.218813	−	0.975767i	$-0.429781\pi$
$397$	173.738			0.437627			0.218813	+	0.975767i	$0.429781\pi$
$398$		0			0
$399$	−0.558284	+	5.62342i	−0.00139921	+	0.0140938i
$400$		0			0
$401$	−325.191	−	447.587i	−0.810950	−	1.11618i	−0.991176	−	0.132552i	$-0.957683\pi$
$401$	−325.191	−	447.587i	−0.810950	−	1.11618i	0.180226	−	0.983625i	$-0.442317\pi$
$402$		0			0
$403$	2.21994	+	6.83228i	0.00550854	+	0.0169535i
$404$		0			0
$405$	125.291	+	529.136i	0.309361	+	1.30651i
$406$		0			0
$407$	−324.732	−	95.8957i	−0.797866	−	0.235616i
$408$		0			0
$409$	120.270	+	87.3813i	0.294059	+	0.213646i	0.725026	−	0.688721i	$-0.241828\pi$
$409$	120.270	+	87.3813i	0.294059	+	0.213646i	−0.430968	+	0.902367i	$0.641828\pi$
$410$		0			0
$411$	199.876	−	116.940i	0.486316	−	0.284526i
$412$		0			0
$413$	39.0157	+	53.7005i	0.0944690	+	0.130025i
$414$		0			0
$415$	214.702	−	660.784i	0.517353	−	1.59225i
$416$		0			0
$417$	−43.9464	+	9.60625i	−0.105387	+	0.0230366i
$418$		0			0
$419$			326.983i			0.780389i	0.920732	+	0.390195i	$0.127592\pi$
$419$			326.983i			0.780389i	−0.920732	+	0.390195i	$0.872408\pi$
$420$		0			0
$421$	145.745	−	448.557i	0.346188	−	1.06546i	−0.614757	−	0.788716i	$-0.710746\pi$
$421$	145.745	−	448.557i	0.346188	−	1.06546i	0.960945	−	0.276740i	$-0.0892539\pi$
$422$		0			0
$423$	115.924	+	65.1578i	0.274051	+	0.154037i
$424$		0			0
$425$	−465.979	+	151.406i	−1.09642	+	0.356249i
$426$		0			0
$427$	−151.016	−	109.720i	−0.353669	−	0.256955i
$428$		0			0
$429$	1.27416	+	5.15711i	0.00297007	+	0.0120212i
$430$		0			0
$431$	−332.586	+	457.765i	−0.771661	+	1.06210i	0.224492	+	0.974476i	$0.427928\pi$
$431$	−332.586	+	457.765i	−0.771661	+	1.06210i	−0.996154	+	0.0876247i	$0.972072\pi$
$432$		0			0
$433$	−177.300	−	545.673i	−0.409468	−	1.26021i	−0.917106	−	0.398643i	$-0.869481\pi$
$433$	−177.300	−	545.673i	−0.409468	−	1.26021i	0.507638	−	0.861571i	$-0.330519\pi$
$434$		0			0
$435$	−699.069	+	785.456i	−1.60706	+	1.80565i
$436$		0			0
$437$	3.60491	+	1.17131i	0.00824922	+	0.00268033i
$438$		0			0
$439$	262.112			0.597066			0.298533	−	0.954399i	$-0.403503\pi$
$439$	262.112			0.597066			0.298533	+	0.954399i	$0.403503\pi$
$440$		0			0
$441$	−325.834	+	149.596i	−0.738852	+	0.339220i
$442$		0			0
$443$	−389.672	−	126.612i	−0.879622	−	0.285806i	−0.165821	−	0.986156i	$-0.553028\pi$
$443$	−389.672	−	126.612i	−0.879622	−	0.285806i	−0.713800	+	0.700349i	$0.753028\pi$
$444$		0			0
$445$	−898.772	+	652.996i	−2.01971	+	1.46741i
$446$		0			0
$447$	13.3052	−	7.78436i	0.0297654	−	0.0174147i
$448$		0			0
$449$	−123.881	+	170.508i	−0.275905	+	0.379751i	−0.924372	−	0.381492i	$-0.875410\pi$
$449$	−123.881	+	170.508i	−0.275905	+	0.379751i	0.648467	+	0.761243i	$0.275410\pi$
$450$		0			0
$451$	16.5166	−	12.6955i	0.0366223	−	0.0281498i
$452$		0			0
$453$	−466.300	−	204.397i	−1.02936	−	0.451207i
$454$		0			0
$455$	−3.11107	+	1.01085i	−0.00683751	+	0.00222164i
$456$		0			0
$457$	78.0919	−	56.7371i	0.170879	−	0.124151i	−0.499058	−	0.866568i	$-0.666321\pi$
$457$	78.0919	−	56.7371i	0.170879	−	0.124151i	0.669938	+	0.742417i	$0.266321\pi$
$458$		0			0
$459$	623.363	−	214.532i	1.35809	−	0.467390i
$460$		0			0
$461$		−	542.354i		−	1.17647i	−0.808689	−	0.588237i	$-0.799822\pi$
$461$		−	542.354i		−	1.17647i	0.808689	−	0.588237i	$-0.200178\pi$
$462$		0			0
$463$	488.061			1.05413			0.527064	−	0.849826i	$-0.323293\pi$
$463$	488.061			1.05413			0.527064	+	0.849826i	$0.323293\pi$
$464$		0			0
$465$	894.375	+	88.7921i	1.92339	+	0.190951i
$466$		0			0
$467$	314.910	+	433.437i	0.674326	+	0.928130i	0.999849	−	0.0174039i	$-0.00554013\pi$
$467$	314.910	+	433.437i	0.674326	+	0.928130i	−0.325522	+	0.945534i	$0.605540\pi$
$468$		0			0
$469$	52.6858	+	162.150i	0.112336	+	0.345736i
$470$		0			0
$471$	142.654	+	62.5307i	0.302875	+	0.132761i
$472$		0			0
$473$	−494.992	+	721.505i	−1.04650	+	1.52538i
$474$		0			0
$475$	−10.1025	−	7.33987i	−0.0212684	−	0.0154524i
$476$		0			0
$477$	−315.831	+	291.040i	−0.662120	+	0.610147i
$478$		0			0
$479$	326.911	+	449.955i	0.682487	+	0.939363i	0.999960	−	0.00890429i	$-0.00283436\pi$
$479$	326.911	+	449.955i	0.682487	+	0.939363i	−0.317473	+	0.948267i	$0.602834\pi$
$480$		0			0
$481$	1.53119	−	4.71252i	0.00318335	−	0.00979734i
$482$		0			0
$483$	−11.8121	−	54.0377i	−0.0244557	−	0.111879i
$484$		0			0
$485$		−	656.921i		−	1.35448i
$486$		0			0
$487$	−151.085	+	464.991i	−0.310235	+	0.954807i	0.667436	+	0.744667i	$0.267392\pi$
$487$	−151.085	+	464.991i	−0.310235	+	0.954807i	−0.977671	+	0.210139i	$0.932608\pi$
$488$		0			0
$489$	194.071	−	218.053i	0.396872	−	0.445915i
$490$		0			0
$491$	400.794	−	130.226i	0.816282	−	0.265226i	0.129026	−	0.991641i	$-0.458815\pi$
$491$	400.794	−	130.226i	0.816282	−	0.265226i	0.687256	+	0.726415i	$0.258815\pi$
$492$		0			0
$493$	1031.33	+	749.306i	2.09195	+	1.51989i
$494$		0			0
$495$	654.923	+	113.026i	1.32308	+	0.228335i
$496$		0			0
$497$	160.418	−	220.796i	0.322772	−	0.444257i
$498$		0			0
$499$	−167.289	−	514.863i	−0.335249	−	1.03179i	−0.966599	−	0.256292i	$-0.917499\pi$
$499$	−167.289	−	514.863i	−0.335249	−	1.03179i	0.631351	−	0.775497i	$-0.282501\pi$
$500$		0			0
$501$	363.754	+	323.747i	0.726056	+	0.646202i
$502$		0			0
$503$	−453.350	−	147.302i	−0.901293	−	0.292848i	−0.178522	−	0.983936i	$-0.557132\pi$
$503$	−453.350	−	147.302i	−0.901293	−	0.292848i	−0.722771	+	0.691088i	$0.757132\pi$
$504$		0			0
$505$	−1012.81			−2.00556
$506$		0			0
$507$	495.229	−	108.252i	0.976783	−	0.213515i
$508$		0			0
$509$	−56.2723	−	18.2840i	−0.110555	−	0.0359214i	0.253217	−	0.967409i	$-0.418511\pi$
$509$	−56.2723	−	18.2840i	−0.110555	−	0.0359214i	−0.363772	+	0.931488i	$0.618511\pi$
$510$		0			0
$511$	−172.525	+	125.347i	−0.337623	+	0.245297i
$512$		0			0
$513$	13.7618	+	9.63929i	0.0268260	+	0.0187900i
$514$		0			0
$515$	−84.0977	+	115.751i	−0.163297	+	0.224758i
$516$		0			0
$517$	128.863	−	99.0504i	0.249251	−	0.191587i
$518$		0			0
$519$	238.790	−	544.763i	0.460097	−	1.04964i
$520$		0			0
$521$	−330.109	+	107.259i	−0.633607	+	0.205871i	−0.608172	−	0.793805i	$-0.708097\pi$
$521$	−330.109	+	107.259i	−0.633607	+	0.205871i	−0.0254349	+	0.999676i	$0.508097\pi$
$522$		0			0
$523$	−621.557	+	451.587i	−1.18844	+	0.863456i	−0.993099	−	0.117279i	$-0.962583\pi$
$523$	−621.557	+	451.587i	−1.18844	+	0.863456i	−0.195346	+	0.980734i	$0.562583\pi$
$524$		0			0
$525$	−18.0028	+	181.336i	−0.0342910	+	0.345402i
$526$		0			0
$527$		−	1089.64i		−	2.06763i
$528$		0			0
$529$	491.899			0.929865
$530$		0			0
$531$	196.022	−	22.8910i	0.369157	−	0.0431093i
$532$		0			0
$533$	0.179192	+	0.246636i	0.000336195	+	0.000462732i
$534$		0			0
$535$	−244.723	−	753.181i	−0.457427	−	1.40782i
$536$		0			0
$537$	−234.858	+	535.793i	−0.437353	+	0.997753i
$538$		0			0
$539$	11.8358	+	438.048i	0.0219589	+	0.812706i
$540$		0			0
$541$	385.903	+	280.375i	0.713315	+	0.518253i	0.884241	−	0.467030i	$-0.154676\pi$
$541$	385.903	+	280.375i	0.713315	+	0.518253i	−0.170927	+	0.985284i	$0.554676\pi$
$542$		0			0
$543$	−36.0426	−	61.6045i	−0.0663768	−	0.113452i
$544$		0			0
$545$	−400.040	−	550.609i	−0.734019	−	1.01029i
$546$		0			0
$547$	10.0893	−	31.0516i	0.0184447	−	0.0567670i	−0.941411	−	0.337263i	$-0.890499\pi$
$547$	10.0893	−	31.0516i	0.0184447	−	0.0567670i	0.959855	+	0.280496i	$0.0904989\pi$
$548$		0			0
$549$	−504.381	+	231.570i	−0.918727	+	0.421804i
$550$		0			0
$551$			32.4901i			0.0589656i
$552$		0			0
$553$	92.3581	−	284.249i	0.167013	−	0.514012i
$554$		0			0
$555$	−463.076	−	412.146i	−0.834371	−	0.742605i
$556$		0			0
$557$	753.009	−	244.667i	1.35190	−	0.439259i	0.458570	−	0.888658i	$-0.348362\pi$
$557$	753.009	−	244.667i	1.35190	−	0.439259i	0.893331	+	0.449399i	$0.148362\pi$
$558$		0			0
$559$	−10.3591	−	7.52631i	−0.0185314	−	0.0134639i
$560$		0			0
$561$	57.9162	−	803.660i	0.103238	−	1.43255i
$562$		0			0
$563$	309.395	−	425.846i	0.549547	−	0.756387i	−0.440403	−	0.897800i	$-0.645165\pi$
$563$	309.395	−	425.846i	0.549547	−	0.756387i	0.989951	+	0.141413i	$0.0451645\pi$
$564$		0			0
$565$	−309.860	−	953.651i	−0.548425	−	1.68788i
$566$		0			0
$567$	19.9992	−	244.372i	0.0352719	−	0.430991i
$568$		0			0
$569$	−690.404	−	224.326i	−1.21336	−	0.394246i	−0.368703	−	0.929547i	$-0.620198\pi$
$569$	−690.404	−	224.326i	−1.21336	−	0.394246i	−0.844661	+	0.535302i	$0.820198\pi$
$570$		0			0
$571$	−227.235			−0.397959			−0.198980	−	0.980004i	$-0.563763\pi$
$571$	−227.235			−0.397959			−0.198980	+	0.980004i	$0.563763\pi$
$572$		0			0
$573$	−97.5356	−	446.203i	−0.170219	−	0.778714i
$574$		0			0
$575$	116.246	+	37.7706i	0.202167	+	0.0656880i
$576$		0			0
$577$	−402.346	+	292.322i	−0.697307	+	0.506623i	−0.879054	−	0.476722i	$-0.841825\pi$
$577$	−402.346	+	292.322i	−0.697307	+	0.506623i	0.181747	+	0.983345i	$0.441825\pi$
$578$		0			0
$579$	195.040	+	333.365i	0.336857	+	0.575761i
$580$		0			0
$581$	−184.145	+	253.454i	−0.316945	+	0.436237i
$582$		0			0
$583$	175.634	+	494.666i	0.301260	+	0.848484i
$584$		0			0
$585$	−1.91229	+	9.53604i	−0.00326888	+	0.0163009i
$586$		0			0
$587$	−214.156	+	69.5836i	−0.364832	+	0.118541i	−0.485695	−	0.874128i	$-0.661434\pi$
$587$	−214.156	+	69.5836i	−0.364832	+	0.118541i	0.120864	+	0.992669i	$0.461434\pi$
$588$		0			0
$589$	22.4673	−	16.3235i	0.0381448	−	0.0277138i
$590$		0			0
$591$	−422.143	−	41.9097i	−0.714287	−	0.0709132i
$592$		0			0
$593$		−	418.371i		−	0.705516i	−0.935715	−	0.352758i	$-0.885244\pi$
$593$		−	418.371i		−	0.705516i	0.935715	−	0.352758i	$-0.114756\pi$
$594$		0			0
$595$	496.167			0.833894
$596$		0			0
$597$	48.0905	−	484.401i	0.0805537	−	0.811392i
$598$		0			0
$599$	−250.864	−	345.285i	−0.418805	−	0.576436i	0.546533	−	0.837437i	$-0.315947\pi$
$599$	−250.864	−	345.285i	−0.418805	−	0.576436i	−0.965338	+	0.261002i	$0.915947\pi$
$600$		0			0
$601$	192.876	+	593.610i	0.320924	+	0.987704i	0.973247	+	0.229762i	$0.0737948\pi$
$601$	192.876	+	593.610i	0.320924	+	0.987704i	−0.652322	+	0.757942i	$0.726205\pi$
$602$		0			0
$603$	497.022	+	99.6695i	0.824250	+	0.165289i
$604$		0			0
$605$	441.272	−	681.983i	0.729375	−	1.12725i
$606$		0			0
$607$	71.8971	+	52.2363i	0.118447	+	0.0860565i	0.645432	−	0.763818i	$-0.276678\pi$
$607$	71.8971	+	52.2363i	0.118447	+	0.0860565i	−0.526985	+	0.849875i	$0.676678\pi$
$608$		0			0
$609$	409.232	−	239.427i	0.671974	−	0.393148i
$610$		0			0
$611$	1.39805	+	1.92425i	0.00228814	+	0.00314935i
$612$		0			0
$613$	231.825	−	713.485i	0.378182	−	1.16392i	−0.563125	−	0.826372i	$-0.690401\pi$
$613$	231.825	−	713.485i	0.378182	−	1.16392i	0.941307	−	0.337552i	$-0.109599\pi$
$614$		0			0
$615$	37.2610	−	8.14488i	0.0605870	−	0.0132437i
$616$		0			0
$617$			996.446i			1.61499i	0.589878	+	0.807493i	$0.299176\pi$
$617$			996.446i			1.61499i	−0.589878	+	0.807493i	$0.700824\pi$
$618$		0			0
$619$	−85.3058	+	262.544i	−0.137812	+	0.424143i	−0.996017	−	0.0891652i	$-0.971580\pi$
$619$	−85.3058	+	262.544i	−0.137812	+	0.424143i	0.858205	+	0.513308i	$0.171580\pi$
$620$		0			0
$621$	−157.266	−	48.1079i	−0.253246	−	0.0774684i
$622$		0			0
$623$	476.416	−	154.797i	0.764713	−	0.248470i
$624$		0			0
$625$	585.724	+	425.553i	0.937158	+	0.680885i
$626$		0			0
$627$	17.4383	−	10.8451i	0.0278122	−	0.0172968i
$628$		0			0
$629$	−441.764	+	608.036i	−0.702327	+	0.966670i
$630$		0			0
$631$	175.851	+	541.213i	0.278686	+	0.857706i	0.988221	+	0.153036i	$0.0489050\pi$
$631$	175.851	+	541.213i	0.278686	+	0.857706i	−0.709535	+	0.704670i	$0.751095\pi$
$632$		0			0
$633$	−499.716	+	561.468i	−0.789441	+	0.886995i
$634$		0			0
$635$	1245.69	+	404.749i	1.96171	+	0.637399i
$636$		0			0
$637$	−6.41279			−0.0100672
$638$		0			0
$639$	−338.571	−	737.438i	−0.529845	−	1.15405i
$640$		0			0
$641$	−232.830	−	75.6509i	−0.363229	−	0.118020i	0.121716	−	0.992565i	$-0.461160\pi$
$641$	−232.830	−	75.6509i	−0.363229	−	0.118020i	−0.484945	+	0.874545i	$0.661160\pi$
$642$		0			0
$643$	247.364	−	179.720i	0.384703	−	0.279503i	−0.378579	−	0.925569i	$-0.623587\pi$
$643$	247.364	−	179.720i	0.384703	−	0.279503i	0.763281	+	0.646066i	$0.223587\pi$
$644$		0			0
$645$	−1382.70	+	808.969i	−2.14373	+	1.25422i
$646$		0			0
$647$	598.342	−	823.547i	0.924794	−	1.27287i	−0.0370619	−	0.999313i	$-0.511800\pi$
$647$	598.342	−	823.547i	0.924794	−	1.27287i	0.961856	−	0.273557i	$-0.0882001\pi$
$648$		0			0
$649$	68.3150	−	231.335i	0.105262	−	0.356448i
$650$		0			0
$651$	−371.171	−	162.698i	−0.570155	−	0.249920i
$652$		0			0
$653$	605.849	−	196.852i	0.927794	−	0.301458i	0.194134	−	0.980975i	$-0.437811\pi$
$653$	605.849	−	196.852i	0.927794	−	0.301458i	0.733660	+	0.679517i	$0.237811\pi$
$654$		0			0
$655$	719.183	−	522.517i	1.09799	−	0.797736i
$656$		0			0
$657$	73.5428	+	629.768i	0.111937	+	0.958551i
$658$		0			0
$659$			163.018i			0.247373i	0.992321	+	0.123686i	$0.0394716\pi$
$659$			163.018i			0.247373i	−0.992321	+	0.123686i	$0.960528\pi$
$660$		0			0
$661$	−361.095			−0.546285			−0.273143	−	0.961974i	$-0.588063\pi$
$661$	−361.095			−0.546285			−0.273143	+	0.961974i	$0.588063\pi$
$662$		0			0
$663$	11.7337	+	1.16490i	0.0176978	+	0.00175701i
$664$		0			0
$665$	7.43286	+	10.2305i	0.0111772	+	0.0153841i
$666$		0			0
$667$	−98.2731	−	302.453i	−0.147336	−	0.453454i
$668$		0			0
$669$	−202.997	−	88.9814i	−0.303434	−	0.133007i
$670$		0			0
$671$	18.3215	+	678.086i	0.0273048	+	1.01056i
$672$		0			0
$673$	−336.391	−	244.402i	−0.499837	−	0.363153i	0.309117	−	0.951024i	$-0.399966\pi$
$673$	−336.391	−	244.402i	−0.499837	−	0.363153i	−0.808955	+	0.587871i	$0.799966\pi$
$674$		0			0
$675$	443.770	+	310.834i	0.657436	+	0.460495i
$676$		0			0
$677$	263.727	+	362.989i	0.389553	+	0.536173i	0.958084	−	0.286489i	$-0.0924880\pi$
$677$	263.727	+	362.989i	0.389553	+	0.536173i	−0.568531	+	0.822662i	$0.692488\pi$
$678$		0			0
$679$	−91.5343	+	281.714i	−0.134807	+	0.414895i
$680$		0			0
$681$	17.5578	+	80.3227i	0.0257823	+	0.117948i
$682$		0			0
$683$			759.557i			1.11209i	0.831152	+	0.556045i	$0.187682\pi$
$683$			759.557i			1.11209i	−0.831152	+	0.556045i	$0.812318\pi$
$684$		0			0
$685$	160.131	−	492.831i	0.233767	−	0.719462i
$686$		0			0
$687$	17.9590	−	20.1782i	0.0261412	−	0.0293715i
$688$		0			0
$689$	−7.30578	+	2.37379i	−0.0106035	+	0.00344527i
$690$		0			0
$691$	−912.455	−	662.937i	−1.32048	−	0.959388i	−0.999926	−	0.0121593i	$-0.996129\pi$
$691$	−912.455	−	662.937i	−1.32048	−	0.959388i	−0.320558	−	0.947229i	$-0.603871\pi$
$692$		0			0
$693$	−265.108	−	139.726i	−0.382551	−	0.201624i
$694$		0			0
$695$	−59.1676	+	81.4372i	−0.0851332	+	0.117176i
$696$		0			0
$697$	−14.2891	−	43.9775i	−0.0205009	−	0.0630954i
$698$		0			0
$699$	−266.719	−	237.385i	−0.381572	−	0.339606i
$700$		0			0
$701$	−261.087	−	84.8322i	−0.372449	−	0.121016i	0.116811	−	0.993154i	$-0.462733\pi$
$701$	−261.087	−	84.8322i	−0.372449	−	0.121016i	−0.489260	+	0.872138i	$0.662733\pi$
$702$		0			0
$703$	−19.1550			−0.0272474
$704$		0			0
$705$	290.710	−	63.5462i	0.412354	−	0.0901365i
$706$		0			0
$707$	434.331	+	141.123i	0.614330	+	0.199608i
$708$		0			0
$709$	−664.060	+	482.468i	−0.936615	+	0.680491i	−0.947604	−	0.319449i	$-0.896502\pi$
$709$	−664.060	+	482.468i	−0.936615	+	0.680491i	0.0109882	+	0.999940i	$0.496502\pi$
$710$		0			0
$711$	−602.182	−	653.477i	−0.846951	−	0.919096i
$712$		0			0
$713$	−159.777	+	219.914i	−0.224091	+	0.308435i
$714$		0			0
$715$	9.80216	+	6.72482i	0.0137093	+	0.00940535i
$716$		0			0
$717$	−442.603	+	1009.73i	−0.617298	+	1.40827i
$718$		0			0
$719$	84.2931	−	27.3885i	0.117237	−	0.0380925i	−0.249811	−	0.968295i	$-0.580369\pi$
$719$	84.2931	−	27.3885i	0.117237	−	0.0380925i	0.367048	+	0.930202i	$0.380369\pi$
$720$		0			0
$721$	52.1929	−	37.9204i	0.0723896	−	0.0525941i
$722$		0			0
$723$	70.4066	−	709.184i	0.0973812	−	0.980891i
$724$		0			0
$725$			1047.69i			1.44509i
$726$		0			0
$727$	−1060.77			−1.45910			−0.729552	−	0.683925i	$-0.760272\pi$
$727$	−1060.77			−1.45910			−0.729552	+	0.683925i	$0.760272\pi$
$728$		0			0
$729$	−604.241	−	407.841i	−0.828863	−	0.559452i
$730$		0			0
$731$	1141.58	+	1571.25i	1.56167	+	2.14945i
$732$		0			0
$733$	277.962	+	855.480i	0.379212	+	1.16709i	0.940593	+	0.339537i	$0.110270\pi$
$733$	277.962	+	855.480i	0.379212	+	1.16709i	−0.561381	+	0.827558i	$0.689730\pi$
$734$		0			0
$735$	−322.094	+	734.807i	−0.438223	+	0.999738i
$736$		0			0
$737$	350.501	−	510.893i	0.475577	−	0.693206i
$738$		0			0
$739$	777.319	+	564.755i	1.05185	+	0.764215i	0.972564	−	0.232636i	$-0.0747352\pi$
$739$	777.319	+	564.755i	1.05185	+	0.764215i	0.0792884	+	0.996852i	$0.474735\pi$
$740$		0			0
$741$	0.151758	+	0.259387i	0.000204802	+	0.000350050i
$742$		0			0
$743$	−560.693	−	771.727i	−0.754634	−	1.03866i	−0.997642	−	0.0686397i	$-0.978134\pi$
$743$	−560.693	−	771.727i	−0.754634	−	1.03866i	0.243008	−	0.970024i	$-0.421866\pi$
$744$		0			0
$745$	10.6594	−	32.8063i	0.0143080	−	0.0440354i
$746$		0			0
$747$	388.649	+	846.512i	0.520279	+	1.13322i
$748$		0			0
$749$			357.093i			0.476760i
$750$		0			0
$751$	−115.245	+	354.687i	−0.153455	+	0.472287i	−0.998001	−	0.0631965i	$-0.979871\pi$
$751$	−115.245	+	354.687i	−0.153455	+	0.472287i	0.844546	+	0.535483i	$0.179871\pi$
$752$		0			0
$753$	−140.493	−	125.041i	−0.186578	−	0.166058i
$754$		0			0
$755$	−1083.53	+	352.061i	−1.43514	+	0.466306i
$756$		0			0
$757$	18.7633	+	13.6324i	0.0247864	+	0.0180084i	0.600110	−	0.799918i	$-0.295124\pi$
$757$	18.7633	+	13.6324i	0.0247864	+	0.0180084i	−0.575323	+	0.817926i	$0.695124\pi$
$758$		0			0
$759$	−129.532	+	153.704i	−0.170661	+	0.202509i
$760$		0			0
$761$	−121.840	+	167.698i	−0.160105	+	0.220366i	−0.881531	−	0.472126i	$-0.843487\pi$
$761$	−121.840	+	167.698i	−0.160105	+	0.220366i	0.721426	+	0.692491i	$0.243487\pi$
$762$		0			0
$763$	94.8322	+	291.863i	0.124289	+	0.382521i
$764$		0			0
$765$	722.825	−	1285.99i	0.944869	−	1.68103i
$766$		0			0
$767$	3.35714	+	1.09080i	0.00437698	+	0.00142217i
$768$		0			0
$769$	−140.439			−0.182626			−0.0913130	−	0.995822i	$-0.529106\pi$
$769$	−140.439			−0.182626			−0.0913130	+	0.995822i	$0.529106\pi$
$770$		0			0
$771$	135.096	+	618.035i	0.175222	+	0.801602i
$772$		0			0
$773$	239.002	+	77.6565i	0.309188	+	0.100461i	0.459501	−	0.888177i	$-0.348028\pi$
$773$	239.002	+	77.6565i	0.309188	+	0.100461i	−0.150313	+	0.988638i	$0.548028\pi$
$774$		0			0
$775$	724.494	−	526.376i	0.934831	−	0.679194i
$776$		0			0
$777$	141.157	+	241.269i	0.181670	+	0.310513i
$778$		0			0
$779$	0.692711	−	0.953435i	0.000889231	−	0.00122392i
$780$		0			0
$781$	−991.405	+	26.7873i	−1.26940	+	0.0342987i
$782$		0			0
$783$	−24.3820	−	1409.47i	−0.0311392	−	1.80009i
$784$		0			0
$785$	331.483	−	107.705i	0.422271	−	0.137204i
$786$		0			0
$787$	150.499	−	109.344i	0.191231	−	0.138937i	−0.488050	−	0.872816i	$-0.662292\pi$
$787$	150.499	−	109.344i	0.191231	−	0.138937i	0.679281	+	0.733878i	$0.262292\pi$
$788$		0			0
$789$	−337.393	−	33.4958i	−0.427621	−	0.0424535i
$790$		0			0
$791$			452.138i			0.571604i
$792$		0			0
$793$	−9.92680			−0.0125180
$794$		0			0
$795$	−94.9457	+	956.359i	−0.119429	+	1.20297i
$796$		0			0
$797$	−462.837	−	637.040i	−0.580724	−	0.799298i	0.413051	−	0.910708i	$-0.364463\pi$
$797$	−462.837	−	637.040i	−0.580724	−	0.799298i	−0.993774	+	0.111410i	$0.964463\pi$
$798$		0			0
$799$	−111.484	−	343.111i	−0.139529	−	0.429426i
$800$		0			0
$801$	292.841	−	1460.31i	0.365594	−	1.82311i
$802$		0			0
$803$	743.217	+	219.478i	0.925551	+	0.273322i
$804$		0			0
$805$	−100.138	−	72.7542i	−0.124394	−	0.0903778i
$806$		0			0
$807$	−1230.04	+	719.654i	−1.52422	+	0.891764i
$808$		0			0
$809$	204.853	+	281.956i	0.253218	+	0.348524i	0.916635	−	0.399725i	$-0.130894\pi$
$809$	204.853	+	281.956i	0.253218	+	0.348524i	−0.663417	+	0.748250i	$0.730894\pi$
$810$		0			0
$811$	−323.730	+	996.340i	−0.399174	+	1.22853i	0.526488	+	0.850183i	$0.323508\pi$
$811$	−323.730	+	996.340i	−0.399174	+	1.22853i	−0.925663	+	0.378350i	$0.876492\pi$
$812$		0			0
$813$	777.551	−	169.965i	0.956397	−	0.209059i
$814$		0			0
$815$		−	653.210i		−	0.801485i
$816$		0			0
$817$	−15.2961	+	47.0765i	−0.0187222	+	0.0576211i
$818$		0			0
$819$	2.14880	−	3.82297i	0.00262369	−	0.00466786i
$820$		0			0
$821$	334.935	−	108.827i	0.407960	−	0.132554i	−0.0978461	−	0.995202i	$-0.531195\pi$
$821$	334.935	−	108.827i	0.407960	−	0.132554i	0.505806	+	0.862647i	$0.331195\pi$
$822$		0			0
$823$	−768.207	−	558.135i	−0.933422	−	0.678171i	0.0134060	−	0.999910i	$-0.495733\pi$
$823$	−768.207	−	558.135i	−0.933422	−	0.678171i	−0.946828	+	0.321739i	$0.895733\pi$
$824$		0			0
$825$	562.325	−	349.718i	0.681606	−	0.423901i
$826$		0			0
$827$	488.020	−	671.702i	0.590109	−	0.812215i	−0.404649	−	0.914472i	$-0.632606\pi$
$827$	488.020	−	671.702i	0.590109	−	0.812215i	0.994758	+	0.102257i	$0.0326064\pi$
$828$		0			0
$829$	−15.5344	−	47.8100i	−0.0187387	−	0.0576718i	0.941250	−	0.337711i	$-0.109653\pi$
$829$	−15.5344	−	47.8100i	−0.0187387	−	0.0576718i	−0.959989	+	0.280039i	$0.909653\pi$
$830$		0			0
$831$	−302.112	+	339.445i	−0.363553	+	0.408478i
$832$		0			0
$833$	925.077	+	300.576i	1.11054	+	0.360835i
$834$		0			0
$835$	1089.68			1.30501
$836$		0			0
$837$	−962.418	+	724.998i	−1.14984	+	0.866187i
$838$		0			0
$839$	−1000.90	−	325.211i	−1.19296	−	0.387617i	−0.355796	−	0.934564i	$-0.615790\pi$
$839$	−1000.90	−	325.211i	−1.19296	−	0.387617i	−0.837168	+	0.546946i	$0.815790\pi$
$840$		0			0
$841$	1524.94	−	1107.93i	1.81325	−	1.31740i
$842$		0			0
$843$	992.267	−	580.540i	1.17707	−	0.688659i
$844$		0			0
$845$	666.756	−	917.711i	0.789060	−	1.08605i
$846$		0			0
$847$	−284.261	+	230.975i	−0.335609	+	0.272698i
$848$		0			0
$849$	1138.26	+	498.944i	1.34071	+	0.587684i
$850$		0			0
$851$	178.316	−	57.9382i	0.209537	−	0.0680825i
$852$		0			0
$853$	−494.172	+	359.037i	−0.579334	+	0.420911i	−0.838484	−	0.544926i	$-0.816558\pi$
$853$	−494.172	+	359.037i	−0.579334	+	0.420911i	0.259150	+	0.965837i	$0.416558\pi$
$854$		0			0
$855$	37.3441	−	4.36096i	0.0436774	−	0.00510054i
$856$		0			0
$857$		−	125.921i		−	0.146932i	−0.997298	−	0.0734661i	$-0.976594\pi$
$857$		−	125.921i		−	0.146932i	0.997298	−	0.0734661i	$-0.0234061\pi$
$858$		0			0
$859$	382.660			0.445472			0.222736	−	0.974879i	$-0.428501\pi$
$859$	382.660			0.445472			0.222736	+	0.974879i	$0.428501\pi$
$860$		0			0
$861$	−17.1139	−	1.69904i	−0.0198767	−	0.00197333i
$862$		0			0
$863$	−206.116	−	283.695i	−0.238837	−	0.328731i	0.672726	−	0.739892i	$-0.265123\pi$
$863$	−206.116	−	283.695i	−0.238837	−	0.328731i	−0.911563	+	0.411161i	$0.865123\pi$
$864$		0			0
$865$	−411.302	−	1265.86i	−0.475493	−	1.46342i
$866$		0			0
$867$	−843.976	−	369.947i	−0.973444	−	0.426697i
$868$		0			0
$869$	−1023.50	+	363.400i	−1.17779	+	0.418181i
$870$		0			0
$871$	7.33519	+	5.32933i	0.00842157	+	0.00611863i
$872$		0			0
$873$	596.811	+	647.649i	0.683632	+	0.741865i
$874$		0			0
$875$	−58.9247	−	81.1028i	−0.0673425	−	0.0926889i
$876$		0			0
$877$	−163.941	+	504.559i	−0.186934	+	0.575324i	−0.999976	−	0.00688082i	$-0.997810\pi$
$877$	−163.941	+	504.559i	−0.186934	+	0.575324i	0.813042	+	0.582205i	$0.197810\pi$
$878$		0			0
$879$	−222.869	−	1019.58i	−0.253549	−	1.15993i
$880$		0			0
$881$		−	1455.22i		−	1.65179i	−0.563826	−	0.825893i	$-0.690671\pi$
$881$		−	1455.22i		−	1.65179i	0.563826	−	0.825893i	$-0.309329\pi$
$882$		0			0
$883$	−227.256	+	699.421i	−0.257368	+	0.792096i	0.735986	+	0.676996i	$0.236719\pi$
$883$	−227.256	+	699.421i	−0.257368	+	0.792096i	−0.993354	+	0.115100i	$0.963281\pi$
$884$		0			0
$885$	293.608	−	329.890i	0.331760	−	0.372757i
$886$		0			0
$887$	235.954	−	76.6659i	0.266013	−	0.0864329i	−0.172974	−	0.984926i	$-0.555338\pi$
$887$	235.954	−	76.6659i	0.266013	−	0.0864329i	0.438987	+	0.898494i	$0.355338\pi$
$888$		0			0
$889$	−477.803	−	347.144i	−0.537461	−	0.390488i
$890$		0			0
$891$	−748.362	+	483.565i	−0.839913	+	0.542722i
$892$		0			0
$893$	5.40452	−	7.43868i	0.00605209	−	0.00832999i
$894$		0			0
$895$	404.529	+	1245.01i	0.451988	+	1.39108i
$896$		0			0
$897$	−2.19730	−	1.95564i	−0.00244961	−	0.00218020i
$898$		0			0
$899$	−2215.97	−	720.012i	−2.46493	−	0.800903i
$900$		0			0
$901$	1165.16			1.29318
$902$		0			0
$903$	705.678	−	154.254i	0.781481	−	0.170824i
$904$		0			0
$905$	−151.897	−	49.3545i	−0.167843	−	0.0545353i
$906$		0			0
$907$	784.360	−	569.871i	0.864785	−	0.628303i	−0.0643973	−	0.997924i	$-0.520512\pi$
$907$	784.360	−	569.871i	0.864785	−	0.628303i	0.929183	+	0.369621i	$0.120512\pi$
$908$		0			0
$909$	998.511	−	920.132i	1.09847	−	1.01225i
$910$		0			0
$911$	−148.796	+	204.801i	−0.163333	+	0.224808i	−0.882837	−	0.469680i	$-0.844369\pi$
$911$	−148.796	+	204.801i	−0.163333	+	0.224808i	0.719504	+	0.694489i	$0.244369\pi$
$912$		0			0
$913$	1138.04	−	30.7494i	1.24649	−	0.0336795i
$914$		0			0
$915$	−498.592	+	1137.46i	−0.544909	+	1.24313i
$916$		0			0
$917$	−381.221	+	123.866i	−0.415726	+	0.135078i
$918$		0			0
$919$	976.948	−	709.795i	1.06306	−	0.772355i	0.0884046	−	0.996085i	$-0.471823\pi$
$919$	976.948	−	709.795i	1.06306	−	0.772355i	0.974651	+	0.223729i	$0.0718232\pi$
$920$		0			0
$921$	−150.489	+	1515.83i	−0.163397	+	1.64585i
$922$		0			0
$923$		−	14.5136i		−	0.0157244i
$924$		0			0
$925$	−617.682			−0.667764
$926$		0			0
$927$	−22.2484	−	190.519i	−0.0240004	−	0.205522i
$928$		0			0
$929$	31.5339	+	43.4027i	0.0339439	+	0.0467198i	0.825652	−	0.564180i	$-0.190808\pi$
$929$	31.5339	+	43.4027i	0.0339439	+	0.0467198i	−0.791708	+	0.610900i	$0.790808\pi$
$930$		0			0
$931$	7.66061	+	23.5769i	0.00822837	+	0.0253243i
$932$		0			0
$933$	110.060	−	251.085i	0.117964	−	0.269116i
$934$		0			0
$935$	−1098.81	−	1429.53i	−1.17520	−	1.52891i
$936$		0			0
$937$	−310.002	−	225.229i	−0.330845	−	0.240373i	0.409944	−	0.912111i	$-0.365548\pi$
$937$	−310.002	−	225.229i	−0.330845	−	0.240373i	−0.740789	+	0.671738i	$0.765548\pi$
$938$		0			0
$939$	−725.183	−	1239.49i	−0.772292	−	1.32001i
$940$		0			0
$941$	719.245	+	989.955i	0.764341	+	1.05202i	0.996841	+	0.0794283i	$0.0253095\pi$
$941$	719.245	+	989.955i	0.764341	+	1.05202i	−0.232500	+	0.972596i	$0.574691\pi$
$942$		0			0
$943$	−3.56466	+	10.9709i	−0.00378012	+	0.0116340i
$944$		0			0
$945$	−330.127	−	438.236i	−0.349341	−	0.463741i
$946$		0			0
$947$		−	1190.44i		−	1.25707i	−0.777782	−	0.628534i	$-0.783655\pi$
$947$		−	1190.44i		−	1.25707i	0.777782	−	0.628534i	$-0.216345\pi$
$948$		0			0
$949$	−3.50445	+	10.7856i	−0.00369279	+	0.0113652i
$950$		0			0
$951$	1127.46	+	1003.46i	1.18555	+	1.05516i
$952$		0			0
$953$	111.747	−	36.3089i	0.117259	−	0.0380996i	−0.249800	−	0.968297i	$-0.580365\pi$
$953$	111.747	−	36.3089i	0.117259	−	0.0380996i	0.367059	+	0.930198i	$0.380365\pi$
$954$		0			0
$955$	−826.860	−	600.749i	−0.865822	−	0.629057i
$956$		0			0
$957$	−1596.11	−	648.824i	−1.66783	−	0.677977i
$958$		0			0
$959$	−137.340	+	189.033i	−0.143212	+	0.197115i
$960$		0			0
$961$	318.471	+	980.152i	0.331395	+	1.01993i
$962$		0			0
$963$	925.532	+	520.219i	0.961092	+	0.540207i
$964$		0			0
$965$	821.974	+	267.076i	0.851787	+	0.276762i
$966$		0			0
$967$	488.396			0.505063			0.252531	−	0.967589i	$-0.418737\pi$
$967$	488.396			0.505063			0.252531	+	0.967589i	$0.418737\pi$
$968$		0			0
$969$	−9.73404	−	44.5310i	−0.0100454	−	0.0459556i
$970$		0			0
$971$	125.133	+	40.6583i	0.128871	+	0.0418726i	0.372742	−	0.927935i	$-0.378418\pi$
$971$	125.133	+	40.6583i	0.128871	+	0.0418726i	−0.243872	+	0.969808i	$0.578418\pi$
$972$		0			0
$973$	36.7207	−	26.6792i	0.0377397	−	0.0274195i
$974$		0			0
$975$	4.89368	+	8.36435i	0.00501916	+	0.00857882i
$976$		0			0
$977$	−733.587	+	1009.70i	−0.750856	+	1.03346i	0.247064	+	0.968999i	$0.420534\pi$
$977$	−733.587	+	1009.70i	−0.750856	+	1.03346i	−0.997920	+	0.0644657i	$0.979466\pi$
$978$		0			0
$979$	−1501.06	−	1029.81i	−1.53326	−	1.05190i
$980$		0			0
$981$	894.620	+	179.401i	0.911947	+	0.182876i
$982$		0			0
$983$	−791.093	+	257.042i	−0.804774	+	0.261487i	−0.682383	−	0.730995i	$-0.739056\pi$
$983$	−791.093	+	257.042i	−0.804774	+	0.261487i	−0.122391	+	0.992482i	$0.539056\pi$
$984$		0			0
$985$	−767.987	+	557.976i	−0.779683	+	0.566473i
$986$		0			0
$987$	−133.522	−	13.2558i	−0.135281	−	0.0134304i
$988$		0			0
$989$		−	484.506i		−	0.489895i
$990$		0			0
$991$	−1450.80			−1.46397			−0.731986	−	0.681319i	$-0.761407\pi$
$991$	−1450.80			−1.46397			−0.731986	+	0.681319i	$0.761407\pi$
$992$		0			0
$993$	−45.7808	+	461.136i	−0.0461036	+	0.464387i
$994$		0			0
$995$	−640.266	−	881.250i	−0.643483	−	0.885679i
$996$		0			0
$997$	410.589	+	1263.66i	0.411824	+	1.26746i	0.915061	+	0.403316i	$0.132143\pi$
$997$	410.589	+	1263.66i	0.411824	+	1.26746i	−0.503236	+	0.864149i	$0.667857\pi$
$998$		0			0
$999$	830.973	−	14.3747i	0.831804	−	0.0143891i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	132.3.m.a.125.4	yes	32
3.2	odd	2	inner	132.3.m.a.125.3	yes	32
11.3	even	5	inner	132.3.m.a.113.3	✓	32
11.5	even	5		1452.3.e.l.485.2		16
11.6	odd	10		1452.3.e.m.485.2		16
33.5	odd	10		1452.3.e.l.485.1		16
33.14	odd	10	inner	132.3.m.a.113.4	yes	32
33.17	even	10		1452.3.e.m.485.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
132.3.m.a.113.3	✓	32	11.3	even	5	inner
132.3.m.a.113.4	yes	32	33.14	odd	10	inner
132.3.m.a.125.3	yes	32	3.2	odd	2	inner
132.3.m.a.125.4	yes	32	1.1	even	1	trivial
1452.3.e.l.485.1		16	33.5	odd	10
1452.3.e.l.485.2		16	11.5	even	5
1452.3.e.m.485.1		16	33.17	even	10
1452.3.e.m.485.2		16	11.6	odd	10

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:	\( N \)	\(=\)	\( 132 = 2^{2} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	132.m (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.296378 + 2.98532i) q^{3} +(3.94591 + 5.43107i) q^{5} +(-0.935402 - 2.87887i) q^{7} +(-8.82432 - 1.76957i) q^{9} +(-6.22292 + 9.07057i) q^{11} +(-0.130232 - 0.0946188i) q^{13} +(-17.3830 + 10.1702i) q^{15} +(14.3517 + 19.7534i) q^{17} +(-0.192298 + 0.591833i) q^{19} +(8.87160 - 1.93924i) q^{21} -6.09109i q^{23} +(-6.20096 + 19.0846i) q^{25} +(7.89807 - 25.8190i) q^{27} +(49.6551 - 16.1339i) q^{29} +(-36.1042 - 26.2312i) q^{31} +(-25.2343 - 21.2657i) q^{33} +(11.9444 - 16.4400i) q^{35} +(9.51197 + 29.2748i) q^{37} +(0.321066 - 0.360741i) q^{39} +(-1.80114 - 0.585225i) q^{41} +79.5435 q^{43} +(-25.2093 - 54.9081i) q^{45} +(-14.0524 - 4.56591i) q^{47} +(32.2289 - 23.4157i) q^{49} +(-63.2237 + 36.9899i) q^{51} +(28.0492 - 38.6064i) q^{53} +(-73.8180 + 1.99452i) q^{55} +(-1.70982 - 0.749479i) q^{57} +(-20.8550 + 6.77621i) q^{59} +(49.8894 - 36.2468i) q^{61} +(3.15993 + 27.0594i) q^{63} -1.08065i q^{65} -56.3242 q^{67} +(18.1839 + 1.80527i) q^{69} +(52.9951 + 72.9415i) q^{71} +(-21.7702 - 67.0016i) q^{73} +(-55.1359 - 24.1681i) q^{75} +(31.9340 + 9.43034i) q^{77} +(79.8792 + 58.0357i) q^{79} +(74.7373 + 31.2305i) q^{81} +(-60.8336 - 83.7303i) q^{83} +(-50.6517 + 155.890i) q^{85} +(33.4483 + 153.018i) q^{87} +165.487i q^{89} +(-0.150577 + 0.463427i) q^{91} +(89.0093 - 100.008i) q^{93} +(-3.97308 + 1.29093i) q^{95} +(-79.1668 - 57.5180i) q^{97} +(70.9640 - 69.0298i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 5 q^{3} - 8 q^{7} - 7 q^{9} - 4 q^{13} + 29 q^{15} + 56 q^{19} + 2 q^{21} + 20 q^{25} + 47 q^{27} - 40 q^{31} + 36 q^{33} - 120 q^{37} - 109 q^{39} - 100 q^{43} + 34 q^{45} - 176 q^{49} - 124 q^{51}+ \cdots + 515 q^{99}+O(q^{100}) \) 32 * q + 5 * q^3 - 8 * q^7 - 7 * q^9 - 4 * q^13 + 29 * q^15 + 56 * q^19 + 2 * q^21 + 20 * q^25 + 47 * q^27 - 40 * q^31 + 36 * q^33 - 120 * q^37 - 109 * q^39 - 100 * q^43 + 34 * q^45 - 176 * q^49 - 124 * q^51 - 246 * q^55 - 310 * q^57 + 120 * q^61 - 325 * q^63 + 88 * q^67 + 70 * q^69 + 280 * q^73 + 282 * q^75 + 512 * q^79 + 573 * q^81 + 740 * q^85 + 354 * q^87 + 156 * q^91 + 563 * q^93 - 62 * q^97 + 515 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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