LMFDB - Embedded newform 1512.2.c.f.757.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(757,1512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))

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

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

chi := DirichletCharacter("1512.757");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			757.21
Character	$\chi$	$=$	1512.757
Dual form			1512.2.c.f.757.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.29659 - 0.564669i) q^{2} +(1.36230 - 1.46429i) q^{4} +1.53368i q^{5} +1.00000 q^{7} +(0.939505 - 2.66783i) q^{8} +O(q^{10})$	\(q+(1.29659 - 0.564669i) q^{2} +(1.36230 - 1.46429i) q^{4} +1.53368i q^{5} +1.00000 q^{7} +(0.939505 - 2.66783i) q^{8} +(0.866019 + 1.98855i) q^{10} -2.28335i q^{11} +7.10447i q^{13} +(1.29659 - 0.564669i) q^{14} +(-0.288288 - 3.98960i) q^{16} +6.81307 q^{17} -1.60676i q^{19} +(2.24575 + 2.08932i) q^{20} +(-1.28934 - 2.96057i) q^{22} +1.16757 q^{23} +2.64784 q^{25} +(4.01168 + 9.21160i) q^{26} +(1.36230 - 1.46429i) q^{28} +4.07059i q^{29} -7.90568 q^{31} +(-2.62659 - 5.01009i) q^{32} +(8.83376 - 3.84713i) q^{34} +1.53368i q^{35} -7.04836i q^{37} +(-0.907287 - 2.08331i) q^{38} +(4.09159 + 1.44090i) q^{40} +10.1710 q^{41} +0.344719i q^{43} +(-3.34348 - 3.11060i) q^{44} +(1.51386 - 0.659289i) q^{46} +3.10859 q^{47} +1.00000 q^{49} +(3.43317 - 1.49515i) q^{50} +(10.4030 + 9.67841i) q^{52} -5.66835i q^{53} +3.50191 q^{55} +(0.939505 - 2.66783i) q^{56} +(2.29853 + 5.27789i) q^{58} -1.38165i q^{59} +5.50516i q^{61} +(-10.2504 + 4.46409i) q^{62} +(-6.23466 - 5.01288i) q^{64} -10.8960 q^{65} +8.35907i q^{67} +(9.28143 - 9.97630i) q^{68} +(0.866019 + 1.98855i) q^{70} +12.2819 q^{71} -5.95132 q^{73} +(-3.97999 - 9.13885i) q^{74} +(-2.35276 - 2.18889i) q^{76} -2.28335i q^{77} -15.0027 q^{79} +(6.11875 - 0.442140i) q^{80} +(13.1876 - 5.74322i) q^{82} -14.7419i q^{83} +10.4490i q^{85} +(0.194652 + 0.446959i) q^{86} +(-6.09159 - 2.14522i) q^{88} -11.8923 q^{89} +7.10447i q^{91} +(1.59058 - 1.70966i) q^{92} +(4.03057 - 1.75532i) q^{94} +2.46425 q^{95} -2.60256 q^{97} +(1.29659 - 0.564669i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{7}+O(q^{10}) $ 24 * q + 24 * q^7	$ 24 q + 24 q^{7} + 20 q^{10} - 4 q^{16} + 4 q^{22} - 24 q^{25} - 16 q^{31} + 4 q^{34} + 12 q^{40} - 52 q^{46} + 24 q^{49} + 12 q^{52} - 8 q^{55} - 28 q^{58} + 24 q^{64} + 20 q^{70} - 24 q^{76} + 32 q^{79} + 44 q^{82} - 60 q^{88} + 12 q^{94}+O(q^{100}) $ 24 * q + 24 * q^7 + 20 * q^10 - 4 * q^16 + 4 * q^22 - 24 * q^25 - 16 * q^31 + 4 * q^34 + 12 * q^40 - 52 * q^46 + 24 * q^49 + 12 * q^52 - 8 * q^55 - 28 * q^58 + 24 * q^64 + 20 * q^70 - 24 * q^76 + 32 * q^79 + 44 * q^82 - 60 * q^88 + 12 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$-1$	$1$	$1$	$1$

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 $

$2$	1.29659	−	0.564669i	0.916829	−	0.399281i
$2$	1.29659	−	0.564669i	0.916829	−	0.399281i
$3$		0			0
$3$		0			0
$4$	1.36230	−	1.46429i	0.681149	−	0.732145i
$5$			1.53368i			0.685881i	0.939357	+	0.342940i	$0.111423\pi$
$5$			1.53368i			0.685881i	−0.939357	+	0.342940i	$0.888577\pi$
$6$		0			0
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	0.939505	−	2.66783i	0.332165	−	0.943221i
$9$		0			0
$10$	0.866019	+	1.98855i	0.273859	+	0.628835i
$11$		−	2.28335i		−	0.688455i	−0.938886	−	0.344228i	$-0.888141\pi$
$11$		−	2.28335i		−	0.688455i	0.938886	−	0.344228i	$-0.111859\pi$
$12$		0			0
$13$			7.10447i			1.97043i	0.171333	+	0.985213i	$0.445193\pi$
$13$			7.10447i			1.97043i	−0.171333	+	0.985213i	$0.554807\pi$
$14$	1.29659	−	0.564669i	0.346529	−	0.150914i
$15$		0			0
$16$	−0.288288	−	3.98960i	−0.0720720	−	0.997399i
$17$	6.81307			1.65241			0.826206	−	0.563368i	$-0.190495\pi$
$17$	6.81307			1.65241			0.826206	+	0.563368i	$0.190495\pi$
$18$		0			0
$19$		−	1.60676i		−	0.368616i	−0.982869	−	0.184308i	$-0.940996\pi$
$19$		−	1.60676i		−	0.368616i	0.982869	−	0.184308i	$-0.0590044\pi$
$20$	2.24575	+	2.08932i	0.502164	+	0.467187i
$21$		0			0
$22$	−1.28934	−	2.96057i	−0.274887	−	0.631195i
$23$	1.16757			0.243455			0.121727	−	0.992564i	$-0.461157\pi$
$23$	1.16757			0.243455			0.121727	+	0.992564i	$0.461157\pi$
$24$		0			0
$25$	2.64784			0.529568
$26$	4.01168	+	9.21160i	0.786754	+	1.80654i
$27$		0			0
$28$	1.36230	−	1.46429i	0.257450	−	0.276725i
$29$			4.07059i			0.755889i	0.925828	+	0.377944i	$0.123369\pi$
$29$			4.07059i			0.755889i	−0.925828	+	0.377944i	$0.876631\pi$
$30$		0			0
$31$	−7.90568			−1.41990			−0.709951	−	0.704251i	$-0.751283\pi$
$31$	−7.90568			−1.41990			−0.709951	+	0.704251i	$0.751283\pi$
$32$	−2.62659	−	5.01009i	−0.464321	−	0.885667i
$33$		0			0
$34$	8.83376	−	3.84713i	1.51498	−	0.659777i
$35$			1.53368i			0.259238i
$36$		0			0
$37$		−	7.04836i		−	1.15874i	−0.815063	−	0.579372i	$-0.803298\pi$
$37$		−	7.04836i		−	1.15874i	0.815063	−	0.579372i	$-0.196702\pi$
$38$	−0.907287	−	2.08331i	−0.147181	−	0.337958i
$39$		0			0
$40$	4.09159	+	1.44090i	0.646937	+	0.227826i
$41$	10.1710			1.58844			0.794218	−	0.607633i	$-0.207881\pi$
$41$	10.1710			1.58844			0.794218	+	0.607633i	$0.207881\pi$
$42$		0			0
$43$			0.344719i			0.0525691i	0.999655	+	0.0262846i	$0.00836760\pi$
$43$			0.344719i			0.0525691i	−0.999655	+	0.0262846i	$0.991632\pi$
$44$	−3.34348	−	3.11060i	−0.504049	−	0.468941i
$45$		0			0
$46$	1.51386	−	0.659289i	0.223206	−	0.0972069i
$47$	3.10859			0.453434			0.226717	−	0.973961i	$-0.427201\pi$
$47$	3.10859			0.453434			0.226717	+	0.973961i	$0.427201\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$	3.43317	−	1.49515i	0.485523	−	0.211447i
$51$		0			0
$52$	10.4030	+	9.67841i	1.44264	+	1.34215i
$53$		−	5.66835i		−	0.778608i	−0.921109	−	0.389304i	$-0.872716\pi$
$53$		−	5.66835i		−	0.778608i	0.921109	−	0.389304i	$-0.127284\pi$
$54$		0			0
$55$	3.50191			0.472198
$56$	0.939505	−	2.66783i	0.125547	−	0.356504i
$57$		0			0
$58$	2.29853	+	5.27789i	0.301812	+	0.693020i
$59$		−	1.38165i		−	0.179875i	−0.995947	−	0.0899374i	$-0.971333\pi$
$59$		−	1.38165i		−	0.179875i	0.995947	−	0.0899374i	$-0.0286667\pi$
$60$		0			0
$61$			5.50516i			0.704863i	0.935838	+	0.352431i	$0.114645\pi$
$61$			5.50516i			0.704863i	−0.935838	+	0.352431i	$0.885355\pi$
$62$	−10.2504	+	4.46409i	−1.30181	+	0.566940i
$63$		0			0
$64$	−6.23466	−	5.01288i	−0.779333	−	0.626611i
$65$	−10.8960			−1.35148
$66$		0			0
$67$			8.35907i			1.02122i	0.859811	+	0.510612i	$0.170581\pi$
$67$			8.35907i			1.02122i	−0.859811	+	0.510612i	$0.829419\pi$
$68$	9.28143	−	9.97630i	1.12554	−	1.20980i
$69$		0			0
$70$	0.866019	+	1.98855i	0.103509	+	0.237677i
$71$	12.2819			1.45759			0.728795	−	0.684732i	$-0.240081\pi$
$71$	12.2819			1.45759			0.728795	+	0.684732i	$0.240081\pi$
$72$		0			0
$73$	−5.95132			−0.696549			−0.348275	−	0.937393i	$-0.613232\pi$
$73$	−5.95132			−0.696549			−0.348275	+	0.937393i	$0.613232\pi$
$74$	−3.97999	−	9.13885i	−0.462665	−	1.06237i
$75$		0			0
$76$	−2.35276	−	2.18889i	−0.269880	−	0.251082i
$77$		−	2.28335i		−	0.260212i
$78$		0			0
$79$	−15.0027			−1.68794			−0.843968	−	0.536393i	$-0.819787\pi$
$79$	−15.0027			−1.68794			−0.843968	+	0.536393i	$0.819787\pi$
$80$	6.11875	−	0.442140i	0.684097	−	0.0494328i
$81$		0			0
$82$	13.1876	−	5.74322i	1.45632	−	0.634233i
$83$		−	14.7419i		−	1.61814i	−0.587715	−	0.809068i	$-0.699973\pi$
$83$		−	14.7419i		−	1.61814i	0.587715	−	0.809068i	$-0.300027\pi$
$84$		0			0
$85$			10.4490i			1.13336i
$86$	0.194652	+	0.446959i	0.0209899	+	0.0481969i
$87$		0			0
$88$	−6.09159	−	2.14522i	−0.649366	−	0.228681i
$89$	−11.8923			−1.26058			−0.630290	−	0.776360i	$-0.717064\pi$
$89$	−11.8923			−1.26058			−0.630290	+	0.776360i	$0.717064\pi$
$90$		0			0
$91$			7.10447i			0.744751i
$92$	1.59058	−	1.70966i	0.165829	−	0.178244i
$93$		0			0
$94$	4.03057	−	1.75532i	0.415722	−	0.181048i
$95$	2.46425			0.252827
$96$		0			0
$97$	−2.60256			−0.264250			−0.132125	−	0.991233i	$-0.542180\pi$
$97$	−2.60256			−0.264250			−0.132125	+	0.991233i	$0.542180\pi$
$98$	1.29659	−	0.564669i	0.130976	−	0.0570402i
$99$		0			0
$100$	3.60715	−	3.87720i	0.360715	−	0.387720i
$101$			9.58182i			0.953427i	0.879059	+	0.476713i	$0.158172\pi$
$101$			9.58182i			0.953427i	−0.879059	+	0.476713i	$0.841828\pi$
$102$		0			0
$103$	9.44175			0.930323			0.465162	−	0.885226i	$-0.345996\pi$
$103$	9.44175			0.930323			0.465162	+	0.885226i	$0.345996\pi$
$104$	18.9535	+	6.67469i	1.85855	+	0.654507i
$105$		0			0
$106$	−3.20074	−	7.34954i	−0.310884	−	0.713850i
$107$			5.04240i			0.487467i	0.969842	+	0.243733i	$0.0783722\pi$
$107$			5.04240i			0.487467i	−0.969842	+	0.243733i	$0.921628\pi$
$108$		0			0
$109$		−	2.35923i		−	0.225973i	−0.993597	−	0.112987i	$-0.963958\pi$
$109$		−	2.35923i		−	0.225973i	0.993597	−	0.112987i	$-0.0360417\pi$
$110$	4.54055	−	1.97742i	0.432925	−	0.188540i
$111$		0			0
$112$	−0.288288	−	3.98960i	−0.0272407	−	0.376982i
$113$	−14.0317			−1.31999			−0.659994	−	0.751271i	$-0.729441\pi$
$113$	−14.0317			−1.31999			−0.659994	+	0.751271i	$0.729441\pi$
$114$		0			0
$115$			1.79067i			0.166981i
$116$	5.96052	+	5.54535i	0.553420	+	0.514873i
$117$		0			0
$118$	−0.780172	−	1.79143i	−0.0718207	−	0.164914i
$119$	6.81307			0.624553
$120$		0			0
$121$	5.78632			0.526029
$122$	3.10859	+	7.13794i	0.281439	+	0.646238i
$123$		0			0
$124$	−10.7699	+	11.5762i	−0.967165	+	1.03957i
$125$			11.7293i			1.04910i
$126$		0			0
$127$	−17.0218			−1.51044			−0.755220	−	0.655472i	$-0.772470\pi$
$127$	−17.0218			−1.51044			−0.755220	+	0.655472i	$0.772470\pi$
$128$	−10.9144	−	2.97914i	−0.964708	−	0.263322i
$129$		0			0
$130$	−14.1276	+	6.15261i	−1.23907	+	0.539619i
$131$		−	17.8861i		−	1.56272i	−0.624082	−	0.781359i	$-0.714527\pi$
$131$		−	17.8861i		−	1.56272i	0.624082	−	0.781359i	$-0.285473\pi$
$132$		0			0
$133$		−	1.60676i		−	0.139324i
$134$	4.72011	+	10.8383i	0.407755	+	0.936287i
$135$		0			0
$136$	6.40091	−	18.1761i	0.548874	−	1.55859i
$137$	9.18009			0.784308			0.392154	−	0.919900i	$-0.371730\pi$
$137$	9.18009			0.784308			0.392154	+	0.919900i	$0.371730\pi$
$138$		0			0
$139$			12.0518i			1.02222i	0.859516	+	0.511108i	$0.170765\pi$
$139$			12.0518i			1.02222i	−0.859516	+	0.511108i	$0.829235\pi$
$140$	2.24575	+	2.08932i	0.189800	+	0.176580i
$141$		0			0
$142$	15.9246	−	6.93519i	1.33636	−	0.581988i
$143$	16.2220			1.35655
$144$		0			0
$145$	−6.24296			−0.518449
$146$	−7.71643	+	3.36053i	−0.638616	+	0.278119i
$147$		0			0
$148$	−10.3208	−	9.60197i	−0.848368	−	0.789277i
$149$			7.71091i			0.631702i	0.948809	+	0.315851i	$0.102290\pi$
$149$			7.71091i			0.631702i	−0.948809	+	0.315851i	$0.897710\pi$
$150$		0			0
$151$	5.91312			0.481203			0.240601	−	0.970624i	$-0.422655\pi$
$151$	5.91312			0.481203			0.240601	+	0.970624i	$0.422655\pi$
$152$	−4.28657	−	1.50956i	−0.347686	−	0.122441i
$153$		0			0
$154$	−1.28934	−	2.96057i	−0.103898	−	0.238569i
$155$		−	12.1247i		−	0.973883i
$156$		0			0
$157$			0.906198i			0.0723225i	0.999346	+	0.0361612i	$0.0115130\pi$
$157$			0.906198i			0.0723225i	−0.999346	+	0.0361612i	$0.988487\pi$
$158$	−19.4524	+	8.47156i	−1.54755	+	0.673961i
$159$		0			0
$160$	7.68385	−	4.02834i	0.607462	−	0.318468i
$161$	1.16757			0.0920172
$162$		0			0
$163$		−	4.46083i		−	0.349400i	−0.984622	−	0.174700i	$-0.944105\pi$
$163$		−	4.46083i		−	0.349400i	0.984622	−	0.174700i	$-0.0558955\pi$
$164$	13.8559	−	14.8932i	1.08196	−	1.16297i
$165$		0			0
$166$	−8.32430	−	19.1142i	−0.646091	−	1.48355i
$167$	−22.6885			−1.75569			−0.877845	−	0.478944i	$-0.841020\pi$
$167$	−22.6885			−1.75569			−0.877845	+	0.478944i	$0.841020\pi$
$168$		0			0
$169$	−37.4735			−2.88258
$170$	5.90025	+	13.5481i	0.452528	+	1.03909i
$171$		0			0
$172$	0.504768	+	0.469610i	0.0384882	+	0.0358074i
$173$		−	24.2316i		−	1.84229i	−0.389218	−	0.921145i	$-0.627255\pi$
$173$		−	24.2316i		−	1.84229i	0.389218	−	0.921145i	$-0.372745\pi$
$174$		0			0
$175$	2.64784			0.200158
$176$	−9.10964	+	0.658262i	−0.686665	+	0.0496183i
$177$		0			0
$178$	−15.4194	+	6.71520i	−1.15574	+	0.503326i
$179$		−	8.82249i		−	0.659424i	−0.944082	−	0.329712i	$-0.893048\pi$
$179$		−	8.82249i		−	0.659424i	0.944082	−	0.329712i	$-0.106952\pi$
$180$		0			0
$181$			4.29583i			0.319306i	0.987173	+	0.159653i	$0.0510376\pi$
$181$			4.29583i			0.319306i	−0.987173	+	0.159653i	$0.948962\pi$
$182$	4.01168	+	9.21160i	0.297365	+	0.682809i
$183$		0			0
$184$	1.09694	−	3.11488i	0.0808672	−	0.229632i
$185$	10.8099			0.794760
$186$		0			0
$187$		−	15.5566i		−	1.13761i
$188$	4.23483	−	4.55188i	0.308856	−	0.331980i
$189$		0			0
$190$	3.19512	−	1.39148i	0.231799	−	0.100949i
$191$	−0.224849			−0.0162695			−0.00813476	−	0.999967i	$-0.502589\pi$
$191$	−0.224849			−0.0162695			−0.00813476	+	0.999967i	$0.502589\pi$
$192$		0			0
$193$	−11.7447			−0.845404			−0.422702	−	0.906269i	$-0.638918\pi$
$193$	−11.7447			−0.845404			−0.422702	+	0.906269i	$0.638918\pi$
$194$	−3.37446	+	1.46958i	−0.242272	+	0.105510i
$195$		0			0
$196$	1.36230	−	1.46429i	0.0973070	−	0.104592i
$197$			14.7998i			1.05444i	0.849729	+	0.527220i	$0.176766\pi$
$197$			14.7998i			1.05444i	−0.849729	+	0.527220i	$0.823234\pi$
$198$		0			0
$199$	−19.6242			−1.39112			−0.695561	−	0.718467i	$-0.744844\pi$
$199$	−19.6242			−1.39112			−0.695561	+	0.718467i	$0.744844\pi$
$200$	2.48766	−	7.06399i	0.175904	−	0.499500i
$201$		0			0
$202$	5.41056	+	12.4237i	0.380685	+	0.874129i
$203$			4.07059i			0.285699i
$204$		0			0
$205$			15.5989i			1.08948i
$206$	12.2421	−	5.33146i	0.852947	−	0.371461i
$207$		0			0
$208$	28.3440	−	2.04813i	1.96530	−	0.142013i
$209$	−3.66879			−0.253776
$210$		0			0
$211$			0.913482i			0.0628867i	0.999506	+	0.0314434i	$0.0100104\pi$
$211$			0.913482i			0.0628867i	−0.999506	+	0.0314434i	$0.989990\pi$
$212$	−8.30011	−	7.72199i	−0.570054	−	0.530348i
$213$		0			0
$214$	2.84728	+	6.53793i	0.194636	+	0.446924i
$215$	−0.528687			−0.0360561
$216$		0			0
$217$	−7.90568			−0.536673
$218$	−1.33218	−	3.05896i	−0.0902269	−	0.207179i
$219$		0			0
$220$	4.77065	−	5.12782i	0.321637	−	0.345717i
$221$			48.4033i			3.25596i
$222$		0			0
$223$	−11.8646			−0.794512			−0.397256	−	0.917708i	$-0.630037\pi$
$223$	−11.8646			−0.794512			−0.397256	+	0.917708i	$0.630037\pi$
$224$	−2.62659	−	5.01009i	−0.175497	−	0.334751i
$225$		0			0
$226$	−18.1933	+	7.92324i	−1.21020	+	0.527046i
$227$		−	19.2403i		−	1.27702i	−0.769613	−	0.638510i	$-0.779551\pi$
$227$		−	19.2403i		−	1.27702i	0.769613	−	0.638510i	$-0.220449\pi$
$228$		0			0
$229$			7.11176i			0.469958i	0.972000	+	0.234979i	$0.0755022\pi$
$229$			7.11176i			0.469958i	−0.972000	+	0.234979i	$0.924498\pi$
$230$	1.01114	+	2.32177i	0.0666723	+	0.153093i
$231$		0			0
$232$	10.8596	+	3.82434i	0.712970	+	0.251080i
$233$	−18.5527			−1.21542			−0.607712	−	0.794157i	$-0.707913\pi$
$233$	−18.5527			−1.21542			−0.607712	+	0.794157i	$0.707913\pi$
$234$		0			0
$235$			4.76757i			0.311002i
$236$	−2.02313	−	1.88221i	−0.131694	−	0.122522i
$237$		0			0
$238$	8.83376	−	3.84713i	0.572608	−	0.249372i
$239$	3.86610			0.250077			0.125039	−	0.992152i	$-0.460095\pi$
$239$	3.86610			0.250077			0.125039	+	0.992152i	$0.460095\pi$
$240$		0			0
$241$	−11.5687			−0.745205			−0.372603	−	0.927991i	$-0.621535\pi$
$241$	−11.5687			−0.745205			−0.372603	+	0.927991i	$0.621535\pi$
$242$	7.50250	−	3.26736i	0.482279	−	0.210034i
$243$		0			0
$244$	8.06114	+	7.49966i	0.516062	+	0.480117i
$245$			1.53368i			0.0979829i
$246$		0			0
$247$	11.4152			0.726331
$248$	−7.42743	+	21.0910i	−0.471642	+	1.33928i
$249$		0			0
$250$	6.62317	+	15.2081i	0.418886	+	0.961846i
$251$			13.5653i			0.856235i	0.903723	+	0.428117i	$0.140823\pi$
$251$			13.5653i			0.856235i	−0.903723	+	0.428117i	$0.859177\pi$
$252$		0			0
$253$		−	2.66596i		−	0.167608i
$254$	−22.0703	+	9.61167i	−1.38481	+	0.603090i
$255$		0			0
$256$	−15.8338	+	2.30031i	−0.989611	+	0.143769i
$257$	11.1567			0.695938			0.347969	−	0.937506i	$-0.386871\pi$
$257$	11.1567			0.695938			0.347969	+	0.937506i	$0.386871\pi$
$258$		0			0
$259$		−	7.04836i		−	0.437964i
$260$	−14.8435	+	15.9548i	−0.920557	+	0.989477i
$261$		0			0
$262$	−10.0997	−	23.1910i	−0.623964	−	1.43274i
$263$	−13.9609			−0.860864			−0.430432	−	0.902623i	$-0.641639\pi$
$263$	−13.9609			−0.860864			−0.430432	+	0.902623i	$0.641639\pi$
$264$		0			0
$265$	8.69341			0.534032
$266$	−0.907287	−	2.08331i	−0.0556294	−	0.127736i
$267$		0			0
$268$	12.2401	+	11.3875i	0.747683	+	0.695605i
$269$			16.1185i			0.982761i	0.870945	+	0.491380i	$0.163507\pi$
$269$			16.1185i			0.982761i	−0.870945	+	0.491380i	$0.836493\pi$
$270$		0			0
$271$	8.91716			0.541679			0.270840	−	0.962624i	$-0.412699\pi$
$271$	8.91716			0.541679			0.270840	+	0.962624i	$0.412699\pi$
$272$	−1.96413	−	27.1814i	−0.119093	−	1.64811i
$273$		0			0
$274$	11.9028	−	5.18371i	0.719076	−	0.313159i
$275$		−	6.04594i		−	0.364584i
$276$		0			0
$277$		−	26.8189i		−	1.61139i	−0.592328	−	0.805697i	$-0.701791\pi$
$277$		−	26.8189i		−	1.61139i	0.592328	−	0.805697i	$-0.298209\pi$
$278$	6.80525	+	15.6262i	0.408152	+	0.937197i
$279$		0			0
$280$	4.09159	+	1.44090i	0.244519	+	0.0861100i
$281$	−11.0688			−0.660306			−0.330153	−	0.943927i	$-0.607100\pi$
$281$	−11.0688			−0.660306			−0.330153	+	0.943927i	$0.607100\pi$
$282$		0			0
$283$			21.7405i			1.29234i	0.763194	+	0.646170i	$0.223630\pi$
$283$			21.7405i			1.29234i	−0.763194	+	0.646170i	$0.776370\pi$
$284$	16.7316	−	17.9842i	0.992836	−	1.06717i
$285$		0			0
$286$	21.0333	−	9.16005i	1.24372	−	0.541645i
$287$	10.1710			0.600373
$288$		0			0
$289$	29.4179			1.73046
$290$	−8.09456	+	3.52520i	−0.475329	+	0.207007i
$291$		0			0
$292$	−8.10747	+	8.71446i	−0.474454	+	0.509975i
$293$			8.80042i			0.514126i	0.966395	+	0.257063i	$0.0827548\pi$
$293$			8.80042i			0.514126i	−0.966395	+	0.257063i	$0.917245\pi$
$294$		0			0
$295$	2.11900			0.123373
$296$	−18.8039	−	6.62197i	−1.09295	−	0.384894i
$297$		0			0
$298$	4.35411	+	9.99789i	0.252227	+	0.579162i
$299$			8.29496i			0.479710i
$300$		0			0
$301$			0.344719i			0.0198693i
$302$	7.66690	−	3.33896i	0.441181	−	0.192135i
$303$		0			0
$304$	−6.41033	+	0.463210i	−0.367657	+	0.0265669i
$305$	−8.44312			−0.483452
$306$		0			0
$307$			3.11170i			0.177594i	0.996050	+	0.0887971i	$0.0283023\pi$
$307$			3.11170i			0.177594i	−0.996050	+	0.0887971i	$0.971698\pi$
$308$	−3.34348	−	3.11060i	−0.190513	−	0.177243i
$309$		0			0
$310$	−6.84647	−	15.7208i	−0.388853	−	0.892884i
$311$	0.443815			0.0251664			0.0125832	−	0.999921i	$-0.495995\pi$
$311$	0.443815			0.0251664			0.0125832	+	0.999921i	$0.495995\pi$
$312$		0			0
$313$	19.1601			1.08299			0.541497	−	0.840703i	$-0.317858\pi$
$313$	19.1601			1.08299			0.541497	+	0.840703i	$0.317858\pi$
$314$	0.511702	+	1.17497i	0.0288770	+	0.0663073i
$315$		0			0
$316$	−20.4382	+	21.9683i	−1.14974	+	1.23581i
$317$			11.2142i			0.629854i	0.949116	+	0.314927i	$0.101980\pi$
$317$			11.2142i			0.629854i	−0.949116	+	0.314927i	$0.898020\pi$
$318$		0			0
$319$	9.29456			0.520396
$320$	7.68814	−	9.56195i	0.429780	−	0.534529i
$321$		0			0
$322$	1.51386	−	0.659289i	0.0843640	−	0.0367408i
$323$		−	10.9470i		−	0.609105i
$324$		0			0
$325$			18.8115i			1.04347i
$326$	−2.51889	−	5.78388i	−0.139509	−	0.320339i
$327$		0			0
$328$	9.55566	−	27.1344i	0.527623	−	1.49825i
$329$	3.10859			0.171382
$330$		0			0
$331$			17.8007i			0.978414i	0.872168	+	0.489207i	$0.162714\pi$
$331$			17.8007i			0.978414i	−0.872168	+	0.489207i	$0.837286\pi$
$332$	−21.5864	−	20.0829i	−1.18471	−	1.10219i
$333$		0			0
$334$	−29.4177	+	12.8115i	−1.60967	+	0.701014i
$335$	−12.8201			−0.700437
$336$		0			0
$337$	−3.46393			−0.188692			−0.0943461	−	0.995539i	$-0.530076\pi$
$337$	−3.46393			−0.188692			−0.0943461	+	0.995539i	$0.530076\pi$
$338$	−48.5879	+	21.1601i	−2.64283	+	1.15096i
$339$		0			0
$340$	15.3004	+	14.2347i	0.829781	+	0.771985i
$341$			18.0514i			0.977539i
$342$		0			0
$343$	1.00000			0.0539949
$344$	0.919652	+	0.323865i	0.0495843	+	0.0174616i
$345$		0			0
$346$	−13.6828	−	31.4184i	−0.735592	−	1.68906i
$347$		−	27.3962i		−	1.47070i	−0.677686	−	0.735352i	$-0.737017\pi$
$347$		−	27.3962i		−	1.47070i	0.677686	−	0.735352i	$-0.262983\pi$
$348$		0			0
$349$		−	1.62149i		−	0.0867961i	−0.999058	−	0.0433981i	$-0.986182\pi$
$349$		−	1.62149i		−	0.0867961i	0.999058	−	0.0433981i	$-0.0138184\pi$
$350$	3.43317	−	1.49515i	0.183510	−	0.0799193i
$351$		0			0
$352$	−11.4398	+	5.99743i	−0.609742	+	0.319664i
$353$	−16.5882			−0.882903			−0.441452	−	0.897285i	$-0.645536\pi$
$353$	−16.5882			−0.882903			−0.441452	+	0.897285i	$0.645536\pi$
$354$		0			0
$355$			18.8364i			0.999732i
$356$	−16.2008	+	17.4137i	−0.858642	+	0.922927i
$357$		0			0
$358$	−4.98178	−	11.4392i	−0.263296	−	0.604578i
$359$	−7.84388			−0.413984			−0.206992	−	0.978343i	$-0.566367\pi$
$359$	−7.84388			−0.413984			−0.206992	+	0.978343i	$0.566367\pi$
$360$		0			0
$361$	16.4183			0.864122
$362$	2.42572	+	5.56993i	0.127493	+	0.292749i
$363$		0			0
$364$	10.4030	+	9.67841i	0.545266	+	0.507287i
$365$		−	9.12740i		−	0.477750i
$366$		0			0
$367$	0.761448			0.0397472			0.0198736	−	0.999803i	$-0.493674\pi$
$367$	0.761448			0.0397472			0.0198736	+	0.999803i	$0.493674\pi$
$368$	−0.336596	−	4.65813i	−0.0175463	−	0.242822i
$369$		0			0
$370$	14.0160	−	6.10402i	0.728659	−	0.317333i
$371$		−	5.66835i		−	0.294286i
$372$		0			0
$373$			13.3240i			0.689888i	0.938623	+	0.344944i	$0.112102\pi$
$373$			13.3240i			0.689888i	−0.938623	+	0.344944i	$0.887898\pi$
$374$	−8.78433	−	20.1706i	−0.454227	−	1.04299i
$375$		0			0
$376$	2.92054	−	8.29320i	0.150615	−	0.427689i
$377$	−28.9194			−1.48942
$378$		0			0
$379$			13.6595i			0.701640i	0.936443	+	0.350820i	$0.114097\pi$
$379$			13.6595i			0.701640i	−0.936443	+	0.350820i	$0.885903\pi$
$380$	3.35704	−	3.60837i	0.172213	−	0.185106i
$381$		0			0
$382$	−0.291538	+	0.126965i	−0.0149164	+	0.00649612i
$383$	9.70332			0.495816			0.247908	−	0.968784i	$-0.420257\pi$
$383$	9.70332			0.495816			0.247908	+	0.968784i	$0.420257\pi$
$384$		0			0
$385$	3.50191			0.178474
$386$	−15.2281	+	6.63188i	−0.775090	+	0.337554i
$387$		0			0
$388$	−3.54546	+	3.81090i	−0.179994	+	0.193469i
$389$		−	24.7223i		−	1.25347i	−0.779233	−	0.626734i	$-0.784391\pi$
$389$		−	24.7223i		−	1.25347i	0.779233	−	0.626734i	$-0.215609\pi$
$390$		0			0
$391$	7.95472			0.402287
$392$	0.939505	−	2.66783i	0.0474522	−	0.134746i
$393$		0			0
$394$	8.35697	+	19.1892i	0.421018	+	0.966740i
$395$		−	23.0093i		−	1.15772i
$396$		0			0
$397$		−	29.1070i		−	1.46084i	−0.682999	−	0.730420i	$-0.739325\pi$
$397$		−	29.1070i		−	1.46084i	0.682999	−	0.730420i	$-0.260675\pi$
$398$	−25.4446	+	11.0812i	−1.27542	+	0.555449i
$399$		0			0
$400$	−0.763340	−	10.5638i	−0.0381670	−	0.528191i
$401$	−13.7247			−0.685380			−0.342690	−	0.939449i	$-0.611338\pi$
$401$	−13.7247			−0.685380			−0.342690	+	0.939449i	$0.611338\pi$
$402$		0			0
$403$		−	56.1657i		−	2.79781i
$404$	14.0306	+	13.0533i	0.698046	+	0.649426i
$405$		0			0
$406$	2.29853	+	5.27789i	0.114074	+	0.261937i
$407$	−16.0939			−0.797743
$408$		0			0
$409$	18.1707			0.898486			0.449243	−	0.893410i	$-0.351694\pi$
$409$	18.1707			0.898486			0.449243	+	0.893410i	$0.351694\pi$
$410$	8.80824	+	20.2255i	0.435008	+	0.998864i
$411$		0			0
$412$	12.8625	−	13.8255i	0.633689	−	0.681131i
$413$		−	1.38165i		−	0.0679863i
$414$		0			0
$415$	22.6093			1.10985
$416$	35.5941	−	18.6606i	1.74514	−	0.914909i
$417$		0			0
$418$	−4.75692	+	2.07165i	−0.232669	+	0.101328i
$419$			32.9489i			1.60966i	0.593507	+	0.804829i	$0.297743\pi$
$419$			32.9489i			1.60966i	−0.593507	+	0.804829i	$0.702257\pi$
$420$		0			0
$421$		−	27.5222i		−	1.34135i	−0.741751	−	0.670675i	$-0.766004\pi$
$421$		−	27.5222i		−	1.34135i	0.741751	−	0.670675i	$-0.233996\pi$
$422$	0.515815	+	1.18441i	0.0251095	+	0.0576563i
$423$		0			0
$424$	−15.1222	−	5.32545i	−0.734400	−	0.258626i
$425$	18.0399			0.875064
$426$		0			0
$427$			5.50516i			0.266413i
$428$	7.38353	+	6.86925i	0.356896	+	0.332038i
$429$		0			0
$430$	−0.685491	+	0.298533i	−0.0330573	+	0.0143965i
$431$	40.3524			1.94371			0.971855	−	0.235582i	$-0.0756996\pi$
$431$	40.3524			1.94371			0.971855	+	0.235582i	$0.0756996\pi$
$432$		0			0
$433$	−38.5928			−1.85465			−0.927327	−	0.374253i	$-0.877899\pi$
$433$	−38.5928			−1.85465			−0.927327	+	0.374253i	$0.877899\pi$
$434$	−10.2504	+	4.46409i	−0.492037	+	0.214283i
$435$		0			0
$436$	−3.45460	−	3.21397i	−0.165445	−	0.153921i
$437$		−	1.87600i		−	0.0897413i
$438$		0			0
$439$	−1.68908			−0.0806152			−0.0403076	−	0.999187i	$-0.512834\pi$
$439$	−1.68908			−0.0806152			−0.0403076	+	0.999187i	$0.512834\pi$
$440$	3.29007	−	9.34252i	0.156848	−	0.445387i
$441$		0			0
$442$	27.3318	+	62.7592i	1.30004	+	2.98515i
$443$			18.3190i			0.870361i	0.900343	+	0.435180i	$0.143315\pi$
$443$			18.3190i			0.870361i	−0.900343	+	0.435180i	$0.856685\pi$
$444$		0			0
$445$		−	18.2389i		−	0.864607i
$446$	−15.3835	+	6.69956i	−0.728431	+	0.317234i
$447$		0			0
$448$	−6.23466	−	5.01288i	−0.294560	−	0.236837i
$449$	−34.2644			−1.61704			−0.808518	−	0.588471i	$-0.799730\pi$
$449$	−34.2644			−1.61704			−0.808518	+	0.588471i	$0.799730\pi$
$450$		0			0
$451$		−	23.2238i		−	1.09357i
$452$	−19.1153	+	20.5464i	−0.899108	+	0.966422i
$453$		0			0
$454$	−10.8644	−	24.9467i	−0.509890	−	1.17081i
$455$	−10.8960			−0.510810
$456$		0			0
$457$	3.08541			0.144330			0.0721648	−	0.997393i	$-0.477009\pi$
$457$	3.08541			0.144330			0.0721648	+	0.997393i	$0.477009\pi$
$458$	4.01579	+	9.22104i	0.187645	+	0.430871i
$459$		0			0
$460$	2.62206	+	2.43943i	0.122254	+	0.113739i
$461$		−	8.62369i		−	0.401645i	−0.979628	−	0.200823i	$-0.935639\pi$
$461$		−	8.62369i		−	0.401645i	0.979628	−	0.200823i	$-0.0643615\pi$
$462$		0			0
$463$	3.29178			0.152982			0.0764910	−	0.997070i	$-0.475628\pi$
$463$	3.29178			0.152982			0.0764910	+	0.997070i	$0.475628\pi$
$464$	16.2400	−	1.17350i	0.753923	−	0.0544784i
$465$		0			0
$466$	−24.0552	+	10.4761i	−1.11434	+	0.485296i
$467$			31.3473i			1.45058i	0.688443	+	0.725290i	$0.258294\pi$
$467$			31.3473i			1.45058i	−0.688443	+	0.725290i	$0.741706\pi$
$468$		0			0
$469$			8.35907i			0.385986i
$470$	2.69210	+	6.18159i	0.124177	+	0.285135i
$471$		0			0
$472$	−3.68600	−	1.29806i	−0.169662	−	0.0597482i
$473$	0.787113			0.0361915
$474$		0			0
$475$		−	4.25444i		−	0.195207i
$476$	9.28143	−	9.97630i	0.425414	−	0.457263i
$477$		0			0
$478$	5.01275	−	2.18307i	0.229278	−	0.0998512i
$479$	23.7139			1.08351			0.541757	−	0.840535i	$-0.317759\pi$
$479$	23.7139			1.08351			0.541757	+	0.840535i	$0.317759\pi$
$480$		0			0
$481$	50.0749			2.28322
$482$	−14.9999	+	6.53248i	−0.683225	+	0.297546i
$483$		0			0
$484$	7.88270	−	8.47285i	0.358304	−	0.385130i
$485$		−	3.99148i		−	0.181244i
$486$		0			0
$487$	35.7317			1.61916			0.809580	−	0.587010i	$-0.199695\pi$
$487$	35.7317			1.61916			0.809580	+	0.587010i	$0.199695\pi$
$488$	14.6868	+	5.17212i	0.664842	+	0.234131i
$489$		0			0
$490$	0.866019	+	1.98855i	0.0391227	+	0.0898335i
$491$		−	40.3543i		−	1.82116i	−0.413330	−	0.910581i	$-0.635634\pi$
$491$		−	40.3543i		−	1.82116i	0.413330	−	0.910581i	$-0.364366\pi$
$492$		0			0
$493$			27.7332i			1.24904i
$494$	14.8008	−	6.44580i	0.665921	−	0.290010i
$495$		0			0
$496$	2.27911	+	31.5405i	0.102335	+	1.41621i
$497$	12.2819			0.550917
$498$		0			0
$499$		−	41.0646i		−	1.83831i	−0.393902	−	0.919153i	$-0.628875\pi$
$499$		−	41.0646i		−	1.83831i	0.393902	−	0.919153i	$-0.371125\pi$
$500$	17.1751	+	15.9788i	0.768094	+	0.714594i
$501$		0			0
$502$	7.65991	+	17.5887i	0.341879	+	0.785021i
$503$	13.5744			0.605252			0.302626	−	0.953109i	$-0.402137\pi$
$503$	13.5744			0.605252			0.302626	+	0.953109i	$0.402137\pi$
$504$		0			0
$505$	−14.6954			−0.653937
$506$	−1.50539	−	3.45667i	−0.0669226	−	0.153668i
$507$		0			0
$508$	−23.1887	+	24.9248i	−1.02883	+	1.10586i
$509$		−	13.3591i		−	0.592132i	−0.955167	−	0.296066i	$-0.904325\pi$
$509$		−	13.3591i		−	0.592132i	0.955167	−	0.296066i	$-0.0956749\pi$
$510$		0			0
$511$	−5.95132			−0.263271
$512$	−19.2310	+	11.9234i	−0.849899	+	0.526945i
$513$		0			0
$514$	14.4657	−	6.29986i	0.638056	−	0.277875i
$515$			14.4806i			0.638091i
$516$		0			0
$517$		−	7.09799i		−	0.312169i
$518$	−3.97999	−	9.13885i	−0.174871	−	0.401538i
$519$		0			0
$520$	−10.2368	+	29.0686i	−0.448914	+	1.27474i
$521$	−20.5338			−0.899600			−0.449800	−	0.893129i	$-0.648505\pi$
$521$	−20.5338			−0.899600			−0.449800	+	0.893129i	$0.648505\pi$
$522$		0			0
$523$		−	4.37298i		−	0.191217i	−0.995419	−	0.0956086i	$-0.969520\pi$
$523$		−	4.37298i		−	0.191217i	0.995419	−	0.0956086i	$-0.0304797\pi$
$524$	−26.1905	−	24.3662i	−1.14414	−	1.06444i
$525$		0			0
$526$	−18.1015	+	7.88327i	−0.789264	+	0.343727i
$527$	−53.8619			−2.34626
$528$		0			0
$529$	−21.6368			−0.940730
$530$	11.2718	−	4.90890i	0.489616	−	0.213229i
$531$		0			0
$532$	−2.35276	−	2.18889i	−0.102005	−	0.0949002i
$533$			72.2593i			3.12990i
$534$		0			0
$535$	−7.73340			−0.334344
$536$	22.3006	+	7.85339i	0.963239	+	0.339215i
$537$		0			0
$538$	9.10160	+	20.8991i	0.392398	+	0.901023i
$539$		−	2.28335i		−	0.0983507i
$540$		0			0
$541$		−	11.8762i		−	0.510598i	−0.966862	−	0.255299i	$-0.917826\pi$
$541$		−	11.8762i		−	0.510598i	0.966862	−	0.255299i	$-0.0821740\pi$
$542$	11.5619	−	5.03525i	0.496627	−	0.216282i
$543$		0			0
$544$	−17.8952	−	34.1341i	−0.767249	−	1.46349i
$545$	3.61829			0.154991
$546$		0			0
$547$			5.50044i			0.235182i	0.993062	+	0.117591i	$0.0375171\pi$
$547$			5.50044i			0.235182i	−0.993062	+	0.117591i	$0.962483\pi$
$548$	12.5060	−	13.4423i	0.534231	−	0.574227i
$549$		0			0
$550$	−3.41395	−	7.83911i	−0.145571	−	0.334261i
$551$	6.54045			0.278633
$552$		0			0
$553$	−15.0027			−0.637980
$554$	−15.1438	−	34.7732i	−0.643399	−	1.47737i
$555$		0			0
$556$	17.6473	+	16.4181i	0.748410	+	0.696282i
$557$		−	8.19596i		−	0.347274i	−0.984810	−	0.173637i	$-0.944448\pi$
$557$		−	8.19596i		−	0.347274i	0.984810	−	0.173637i	$-0.0555519\pi$
$558$		0			0
$559$	−2.44905			−0.103584
$560$	6.11875	−	0.442140i	0.258564	−	0.0186838i
$561$		0			0
$562$	−14.3516	+	6.25018i	−0.605388	+	0.263648i
$563$		−	0.145215i		−	0.00612008i	−0.999995	−	0.00306004i	$-0.999026\pi$
$563$		−	0.145215i		−	0.00612008i	0.999995	−	0.00306004i	$-0.000974043\pi$
$564$		0			0
$565$		−	21.5200i		−	0.905354i
$566$	12.2762	+	28.1886i	0.516007	+	1.18485i
$567$		0			0
$568$	11.5389	−	32.7660i	0.484160	−	1.37483i
$569$	5.09548			0.213613			0.106807	−	0.994280i	$-0.465937\pi$
$569$	5.09548			0.213613			0.106807	+	0.994280i	$0.465937\pi$
$570$		0			0
$571$		−	25.3061i		−	1.05903i	−0.848301	−	0.529514i	$-0.822374\pi$
$571$		−	25.3061i		−	1.05903i	0.848301	−	0.529514i	$-0.177626\pi$
$572$	22.0992	−	23.7537i	0.924013	−	0.993191i
$573$		0			0
$574$	13.1876	−	5.74322i	0.550439	−	0.239717i
$575$	3.09153			0.128926
$576$		0			0
$577$	19.5004			0.811814			0.405907	−	0.913914i	$-0.366956\pi$
$577$	19.5004			0.811814			0.405907	+	0.913914i	$0.366956\pi$
$578$	38.1430	−	16.6114i	1.58654	−	0.690942i
$579$		0			0
$580$	−8.50477	+	9.14150i	−0.353141	+	0.379580i
$581$		−	14.7419i		−	0.611598i
$582$		0			0
$583$	−12.9428			−0.536037
$584$	−5.59130	+	15.8771i	−0.231369	+	0.657000i
$585$		0			0
$586$	4.96932	+	11.4105i	0.205281	+	0.471365i
$587$		−	36.0783i		−	1.48911i	−0.667561	−	0.744555i	$-0.732662\pi$
$587$		−	36.0783i		−	1.48911i	0.667561	−	0.744555i	$-0.267338\pi$
$588$		0			0
$589$			12.7025i			0.523399i
$590$	2.74747	−	1.19653i	0.113112	−	0.0492604i
$591$		0			0
$592$	−28.1201	+	2.03196i	−1.15573	+	0.0835130i
$593$	16.7669			0.688535			0.344268	−	0.938872i	$-0.388127\pi$
$593$	16.7669			0.688535			0.344268	+	0.938872i	$0.388127\pi$
$594$		0			0
$595$			10.4490i			0.428369i
$596$	11.2910	+	10.5046i	0.462497	+	0.430283i
$597$		0			0
$598$	4.68390	+	10.7552i	0.191539	+	0.439811i
$599$	31.1008			1.27074			0.635372	−	0.772206i	$-0.280847\pi$
$599$	31.1008			1.27074			0.635372	+	0.772206i	$0.280847\pi$
$600$		0			0
$601$	17.1858			0.701022			0.350511	−	0.936559i	$-0.386008\pi$
$601$	17.1858			0.701022			0.350511	+	0.936559i	$0.386008\pi$
$602$	0.194652	+	0.446959i	0.00793342	+	0.0182167i
$603$		0			0
$604$	8.05543	−	8.65852i	0.327771	−	0.352310i
$605$			8.87434i			0.360793i
$606$		0			0
$607$	12.9692			0.526404			0.263202	−	0.964741i	$-0.415221\pi$
$607$	12.9692			0.526404			0.263202	+	0.964741i	$0.415221\pi$
$608$	−8.05001	+	4.22030i	−0.326471	+	0.171156i
$609$		0			0
$610$	−10.9473	+	4.76757i	−0.443242	+	0.193033i
$611$			22.0849i			0.893459i
$612$		0			0
$613$			26.5265i			1.07139i	0.844410	+	0.535697i	$0.179951\pi$
$613$			26.5265i			1.07139i	−0.844410	+	0.535697i	$0.820049\pi$
$614$	1.75708	+	4.03460i	0.0709100	+	0.162823i
$615$		0			0
$616$	−6.09159	−	2.14522i	−0.245437	−	0.0864332i
$617$	37.3263			1.50270			0.751350	−	0.659904i	$-0.229403\pi$
$617$	37.3263			1.50270			0.751350	+	0.659904i	$0.229403\pi$
$618$		0			0
$619$			10.8774i			0.437200i	0.975815	+	0.218600i	$0.0701489\pi$
$619$			10.8774i			0.437200i	−0.975815	+	0.218600i	$0.929851\pi$
$620$	−17.7541	−	16.5175i	−0.713023	−	0.663360i
$621$		0			0
$622$	0.575446	−	0.250608i	0.0230733	−	0.0100485i
$623$	−11.8923			−0.476454
$624$		0			0
$625$	−4.74975			−0.189990
$626$	24.8428	−	10.8191i	0.992920	−	0.432419i
$627$		0			0
$628$	1.32694	+	1.23451i	0.0529505	+	0.0492624i
$629$		−	48.0210i		−	1.91472i
$630$		0			0
$631$	−24.2943			−0.967140			−0.483570	−	0.875306i	$-0.660660\pi$
$631$	−24.2943			−0.967140			−0.483570	+	0.875306i	$0.660660\pi$
$632$	−14.0951	+	40.0247i	−0.560674	+	1.59210i
$633$		0			0
$634$	6.33233	+	14.5403i	0.251489	+	0.577468i
$635$		−	26.1059i		−	1.03598i
$636$		0			0
$637$			7.10447i			0.281489i
$638$	12.0512	−	5.24835i	0.477113	−	0.207784i
$639$		0			0
$640$	4.56904	−	16.7392i	0.180607	−	0.661675i
$641$	16.5765			0.654731			0.327365	−	0.944898i	$-0.393839\pi$
$641$	16.5765			0.654731			0.327365	+	0.944898i	$0.393839\pi$
$642$		0			0
$643$			7.15319i			0.282094i	0.990003	+	0.141047i	$0.0450469\pi$
$643$			7.15319i			0.282094i	−0.990003	+	0.141047i	$0.954953\pi$
$644$	1.59058	−	1.70966i	0.0626775	−	0.0673699i
$645$		0			0
$646$	−6.18141	−	14.1937i	−0.243204	−	0.558445i
$647$	7.94968			0.312534			0.156267	−	0.987715i	$-0.450054\pi$
$647$	7.94968			0.312534			0.156267	+	0.987715i	$0.450054\pi$
$648$		0			0
$649$	−3.15478			−0.123836
$650$	10.6223	+	24.3908i	0.416640	+	0.956687i
$651$		0			0
$652$	−6.53195	−	6.07699i	−0.255811	−	0.237993i
$653$			7.45217i			0.291626i	0.989312	+	0.145813i	$0.0465798\pi$
$653$			7.45217i			0.291626i	−0.989312	+	0.145813i	$0.953420\pi$
$654$		0			0
$655$	27.4315			1.07184
$656$	−2.93216	−	40.5780i	−0.114482	−	1.58431i
$657$		0			0
$658$	4.03057	−	1.75532i	0.157128	−	0.0684297i
$659$		−	26.2741i		−	1.02349i	−0.859136	−	0.511747i	$-0.828999\pi$
$659$		−	26.2741i		−	1.02349i	0.859136	−	0.511747i	$-0.171001\pi$
$660$		0			0
$661$		−	3.98821i		−	0.155123i	−0.996988	−	0.0775617i	$-0.975287\pi$
$661$		−	3.98821i		−	0.155123i	0.996988	−	0.0775617i	$-0.0247135\pi$
$662$	10.0515	+	23.0802i	0.390662	+	0.897038i
$663$		0			0
$664$	−39.3290	−	13.8501i	−1.52626	−	0.537488i
$665$	2.46425			0.0955594
$666$		0			0
$667$			4.75268i			0.184025i
$668$	−30.9085	+	33.2226i	−1.19589	+	1.28542i
$669$		0			0
$670$	−16.6224	+	7.23911i	−0.642181	+	0.279671i
$671$	12.5702			0.485267
$672$		0			0
$673$	30.5709			1.17842			0.589211	−	0.807979i	$-0.299439\pi$
$673$	30.5709			1.17842			0.589211	+	0.807979i	$0.299439\pi$
$674$	−4.49130	+	1.95597i	−0.172998	+	0.0753413i
$675$		0			0
$676$	−51.0501	+	54.8721i	−1.96347	+	2.11047i
$677$			21.9032i			0.841808i	0.907105	+	0.420904i	$0.138287\pi$
$677$			21.9032i			0.841808i	−0.907105	+	0.420904i	$0.861713\pi$
$678$		0			0
$679$	−2.60256			−0.0998770
$680$	27.8763	+	9.81692i	1.06901	+	0.376462i
$681$		0			0
$682$	10.1931	+	23.4053i	0.390313	+	0.896236i
$683$			13.0423i			0.499051i	0.968368	+	0.249525i	$0.0802746\pi$
$683$			13.0423i			0.499051i	−0.968368	+	0.249525i	$0.919725\pi$
$684$		0			0
$685$			14.0793i			0.537942i
$686$	1.29659	−	0.564669i	0.0495041	−	0.0215592i
$687$		0			0
$688$	1.37529	−	0.0993783i	0.0524324	−	0.00378876i
$689$	40.2707			1.53419
$690$		0			0
$691$			3.25399i			0.123788i	0.998083	+	0.0618938i	$0.0197140\pi$
$691$			3.25399i			0.123788i	−0.998083	+	0.0618938i	$0.980286\pi$
$692$	−35.4820	−	33.0106i	−1.34882	−	1.25487i
$693$		0			0
$694$	−15.4698	−	35.5216i	−0.587224	−	1.34838i
$695$	−18.4835			−0.701118
$696$		0			0
$697$	69.2954			2.62475
$698$	−0.915603	−	2.10240i	−0.0346561	−	0.0795772i
$699$		0			0
$700$	3.60715	−	3.87720i	0.136337	−	0.146545i
$701$			2.70404i			0.102130i	0.998695	+	0.0510650i	$0.0162616\pi$
$701$			2.70404i			0.102130i	−0.998695	+	0.0510650i	$0.983738\pi$
$702$		0			0
$703$	−11.3250			−0.427132
$704$	−11.4462	+	14.2359i	−0.431393	+	0.536536i
$705$		0			0
$706$	−21.5082	+	9.36687i	−0.809471	+	0.352527i
$707$			9.58182i			0.360361i
$708$		0			0
$709$		−	49.0447i		−	1.84191i	−0.389668	−	0.920955i	$-0.627410\pi$
$709$		−	49.0447i		−	1.84191i	0.389668	−	0.920955i	$-0.372590\pi$
$710$	10.6363	+	24.4231i	0.399174	+	0.916583i
$711$		0			0
$712$	−11.1729	+	31.7266i	−0.418721	+	1.18901i
$713$	−9.23042			−0.345682
$714$		0			0
$715$			24.8793i			0.930431i
$716$	−12.9187	−	12.0189i	−0.482794	−	0.449166i
$717$		0			0
$718$	−10.1703	+	4.42920i	−0.379553	+	0.165296i
$719$	21.3291			0.795442			0.397721	−	0.917506i	$-0.369801\pi$
$719$	21.3291			0.795442			0.397721	+	0.917506i	$0.369801\pi$
$720$		0			0
$721$	9.44175			0.351629
$722$	21.2879	−	9.27092i	0.792252	−	0.345028i
$723$		0			0
$724$	6.29033	+	5.85219i	0.233778	+	0.217495i
$725$			10.7783i			0.400294i
$726$		0			0
$727$	−23.5713			−0.874210			−0.437105	−	0.899411i	$-0.643996\pi$
$727$	−23.5713			−0.874210			−0.437105	+	0.899411i	$0.643996\pi$
$728$	18.9535	+	6.67469i	0.702465	+	0.247380i
$729$		0			0
$730$	−5.15396	−	11.8345i	−0.190756	−	0.438015i
$731$			2.34859i			0.0868658i
$732$		0			0
$733$		−	2.28803i		−	0.0845105i	−0.999107	−	0.0422552i	$-0.986546\pi$
$733$		−	2.28803i		−	0.0845105i	0.999107	−	0.0422552i	$-0.0134543\pi$
$734$	0.987286	−	0.429966i	0.0364414	−	0.0158703i
$735$		0			0
$736$	−3.06673	−	5.84962i	−0.113041	−	0.215620i
$737$	19.0867			0.703067
$738$		0			0
$739$		−	33.6953i		−	1.23950i	−0.784798	−	0.619751i	$-0.787234\pi$
$739$		−	33.6953i		−	1.23950i	0.784798	−	0.619751i	$-0.212766\pi$
$740$	14.7263	−	15.8288i	0.541350	−	0.581879i
$741$		0			0
$742$	−3.20074	−	7.34954i	−0.117503	−	0.269810i
$743$	−35.7898			−1.31300			−0.656501	−	0.754326i	$-0.727964\pi$
$743$	−35.7898			−1.31300			−0.656501	+	0.754326i	$0.727964\pi$
$744$		0			0
$745$	−11.8260			−0.433272
$746$	7.52362	+	17.2757i	0.275459	+	0.632509i
$747$		0			0
$748$	−22.7794	−	21.1927i	−0.832896	−	0.774883i
$749$			5.04240i			0.184245i
$750$		0			0
$751$	7.35858			0.268518			0.134259	−	0.990946i	$-0.457135\pi$
$751$	7.35858			0.268518			0.134259	+	0.990946i	$0.457135\pi$
$752$	−0.896169	−	12.4020i	−0.0326799	−	0.452255i
$753$		0			0
$754$	−37.4966	+	16.3299i	−1.36555	+	0.594699i
$755$			9.06881i			0.330048i
$756$		0			0
$757$			23.2086i			0.843530i	0.906705	+	0.421765i	$0.138589\pi$
$757$			23.2086i			0.843530i	−0.906705	+	0.421765i	$0.861411\pi$
$758$	7.71308	+	17.7108i	0.280152	+	0.643283i
$759$		0			0
$760$	2.31517	−	6.57420i	0.0839802	−	0.238471i
$761$	22.1491			0.802902			0.401451	−	0.915880i	$-0.368506\pi$
$761$	22.1491			0.802902			0.401451	+	0.915880i	$0.368506\pi$
$762$		0			0
$763$		−	2.35923i		−	0.0854099i
$764$	−0.306312	+	0.329245i	−0.0110820	+	0.0119117i
$765$		0			0
$766$	12.5812	−	5.47916i	0.454579	−	0.197970i
$767$	9.81586			0.354430
$768$		0			0
$769$	−27.4818			−0.991020			−0.495510	−	0.868602i	$-0.665019\pi$
$769$	−27.4818			−0.991020			−0.495510	+	0.868602i	$0.665019\pi$
$770$	4.54055	−	1.97742i	0.163630	−	0.0712613i
$771$		0			0
$772$	−15.9998	+	17.1977i	−0.575846	+	0.618958i
$773$		−	39.9693i		−	1.43760i	−0.695219	−	0.718798i	$-0.744692\pi$
$773$		−	39.9693i		−	1.43760i	0.695219	−	0.718798i	$-0.255308\pi$
$774$		0			0
$775$	−20.9330			−0.751935
$776$	−2.44512	+	6.94319i	−0.0877746	+	0.249246i
$777$		0			0
$778$	−13.9599	−	32.0547i	−0.500487	−	1.14922i
$779$		−	16.3423i		−	0.585523i
$780$		0			0
$781$		−	28.0438i		−	1.00348i
$782$	10.3140	−	4.49178i	0.368829	−	0.160626i
$783$		0			0
$784$	−0.288288	−	3.98960i	−0.0102960	−	0.142486i
$785$	−1.38981			−0.0496046
$786$		0			0
$787$		−	34.5651i		−	1.23211i	−0.787702	−	0.616057i	$-0.788729\pi$
$787$		−	34.5651i		−	1.23211i	0.787702	−	0.616057i	$-0.211271\pi$
$788$	21.6711	+	20.1617i	0.772002	+	0.718230i
$789$		0			0
$790$	−12.9926	−	29.8336i	−0.462257	−	1.06143i
$791$	−14.0317			−0.498908
$792$		0			0
$793$	−39.1112			−1.38888
$794$	−16.4358	−	37.7399i	−0.583286	−	1.33934i
$795$		0			0
$796$	−26.7340	+	28.7355i	−0.947562	+	1.01850i
$797$		−	16.9968i		−	0.602059i	−0.953615	−	0.301029i	$-0.902670\pi$
$797$		−	16.9968i		−	0.602059i	0.953615	−	0.301029i	$-0.0973302\pi$
$798$		0			0
$799$	21.1790			0.749260
$800$	−6.95480	−	13.2659i	−0.245889	−	0.469021i
$801$		0			0
$802$	−17.7953	+	7.74992i	−0.628376	+	0.273659i
$803$			13.5889i			0.479543i
$804$		0			0
$805$			1.79067i			0.0631128i
$806$	−31.7150	−	72.8239i	−1.11711	−	2.56511i
$807$		0			0
$808$	25.5627	+	9.00217i	0.899292	+	0.316695i
$809$	−2.33018			−0.0819249			−0.0409624	−	0.999161i	$-0.513042\pi$
$809$	−2.33018			−0.0819249			−0.0409624	+	0.999161i	$0.513042\pi$
$810$		0			0
$811$			8.79524i			0.308843i	0.988005	+	0.154421i	$0.0493513\pi$
$811$			8.79524i			0.308843i	−0.988005	+	0.154421i	$0.950649\pi$
$812$	5.96052	+	5.54535i	0.209173	+	0.194604i
$813$		0			0
$814$	−20.8672	+	9.08771i	−0.731394	+	0.318524i
$815$	6.84147			0.239646
$816$		0			0
$817$	0.553880			0.0193778
$818$	23.5600	−	10.2605i	0.823757	−	0.358748i
$819$		0			0
$820$	22.8414	+	21.2504i	0.797655	+	0.742097i
$821$		−	14.1689i		−	0.494497i	−0.968952	−	0.247249i	$-0.920474\pi$
$821$		−	14.1689i		−	0.494497i	0.968952	−	0.247249i	$-0.0795265\pi$
$822$		0			0
$823$	5.53482			0.192932			0.0964659	−	0.995336i	$-0.469246\pi$
$823$	5.53482			0.192932			0.0964659	+	0.995336i	$0.469246\pi$
$824$	8.87057	−	25.1890i	0.309021	−	0.877501i
$825$		0			0
$826$	−0.780172	−	1.79143i	−0.0271457	−	0.0623318i
$827$		−	7.32030i		−	0.254552i	−0.991867	−	0.127276i	$-0.959377\pi$
$827$		−	7.32030i		−	0.254552i	0.991867	−	0.127276i	$-0.0406234\pi$
$828$		0			0
$829$		−	32.7046i		−	1.13588i	−0.823071	−	0.567939i	$-0.807741\pi$
$829$		−	32.7046i		−	1.13588i	0.823071	−	0.567939i	$-0.192259\pi$
$830$	29.3150	−	12.7668i	1.01754	−	0.443141i
$831$		0			0
$832$	35.6139	−	44.2940i	1.23469	−	1.53562i
$833$	6.81307			0.236059
$834$		0			0
$835$		−	34.7968i		−	1.20419i
$836$	−4.99799	+	5.37217i	−0.172859	+	0.185800i
$837$		0			0
$838$	18.6052	+	42.7212i	0.642706	+	1.47578i
$839$	19.2836			0.665744			0.332872	−	0.942972i	$-0.391982\pi$
$839$	19.2836			0.665744			0.332872	+	0.942972i	$0.391982\pi$
$840$		0			0
$841$	12.4303			0.428632
$842$	−15.5409	−	35.6851i	−0.535576	−	1.22979i
$843$		0			0
$844$	1.33760	+	1.24444i	0.0460422	+	0.0428352i
$845$		−	57.4723i		−	1.97711i
$846$		0			0
$847$	5.78632			0.198820
$848$	−22.6144	+	1.63412i	−0.776583	+	0.0561158i
$849$		0			0
$850$	23.3904	−	10.1866i	0.802284	−	0.349397i
$851$		−	8.22944i		−	0.282102i
$852$		0			0
$853$		−	24.5003i		−	0.838874i	−0.907784	−	0.419437i	$-0.862228\pi$
$853$		−	24.5003i		−	0.838874i	0.907784	−	0.419437i	$-0.137772\pi$
$854$	3.10859	+	7.13794i	0.106374	+	0.244255i
$855$		0			0
$856$	13.4523	+	4.73736i	0.459789	+	0.161920i
$857$	−24.0113			−0.820211			−0.410105	−	0.912038i	$-0.634508\pi$
$857$	−24.0113			−0.820211			−0.410105	+	0.912038i	$0.634508\pi$
$858$		0			0
$859$			2.15328i			0.0734689i	0.999325	+	0.0367344i	$0.0116956\pi$
$859$			2.15328i			0.0734689i	−0.999325	+	0.0367344i	$0.988304\pi$
$860$	−0.720229	+	0.774151i	−0.0245596	+	0.0263983i
$861$		0			0
$862$	52.3206	−	22.7858i	1.78205	−	0.776087i
$863$	−6.94727			−0.236488			−0.118244	−	0.992985i	$-0.537726\pi$
$863$	−6.94727			−0.236488			−0.118244	+	0.992985i	$0.537726\pi$
$864$		0			0
$865$	37.1633			1.26359
$866$	−50.0391	+	21.7922i	−1.70040	+	0.740528i
$867$		0			0
$868$	−10.7699	+	11.5762i	−0.365554	+	0.392922i
$869$			34.2564i			1.16207i
$870$		0			0
$871$	−59.3868			−2.01225
$872$	−6.29403	−	2.21651i	−0.213143	−	0.0750604i
$873$		0			0
$874$	−1.05932	−	2.43241i	−0.0358320	−	0.0822774i
$875$			11.7293i			0.396523i
$876$		0			0
$877$			24.2307i			0.818211i	0.912487	+	0.409106i	$0.134159\pi$
$877$			24.2307i			0.818211i	−0.912487	+	0.409106i	$0.865841\pi$
$878$	−2.19004	+	0.953769i	−0.0739103	+	0.0321881i
$879$		0			0
$880$	−1.00956	−	13.9712i	−0.0340323	−	0.470970i
$881$	−42.4462			−1.43005			−0.715024	−	0.699100i	$-0.753584\pi$
$881$	−42.4462			−1.43005			−0.715024	+	0.699100i	$0.753584\pi$
$882$		0			0
$883$		−	0.397509i		−	0.0133773i	−0.999978	−	0.00668863i	$-0.997871\pi$
$883$		−	0.397509i		−	0.0133773i	0.999978	−	0.00668863i	$-0.00212907\pi$
$884$	70.8764	+	65.9397i	2.38383	+	2.21779i
$885$		0			0
$886$	10.3442	+	23.7522i	0.347519	+	0.797971i
$887$	−36.3698			−1.22118			−0.610590	−	0.791947i	$-0.709068\pi$
$887$	−36.3698			−1.22118			−0.610590	+	0.791947i	$0.709068\pi$
$888$		0			0
$889$	−17.0218			−0.570892
$890$	−10.2989	−	23.6484i	−0.345221	−	0.792696i
$891$		0			0
$892$	−16.1631	+	17.3732i	−0.541181	+	0.581698i
$893$		−	4.99476i		−	0.167143i
$894$		0			0
$895$	13.5308			0.452286
$896$	−10.9144	−	2.97914i	−0.364625	−	0.0995262i
$897$		0			0
$898$	−44.4269	+	19.3480i	−1.48254	+	0.645652i
$899$		−	32.1807i		−	1.07329i
$900$		0			0
$901$		−	38.6189i		−	1.28658i
$902$	−13.1138	−	30.1118i	−0.436641	−	1.00261i
$903$		0			0
$904$	−13.1828	+	37.4341i	−0.438454	+	1.24504i
$905$	−6.58840			−0.219006
$906$		0			0
$907$			52.1212i			1.73066i	0.501205	+	0.865329i	$0.332890\pi$
$907$			52.1212i			1.73066i	−0.501205	+	0.865329i	$0.667110\pi$
$908$	−28.1733	−	26.2110i	−0.934964	−	0.869841i
$909$		0			0
$910$	−14.1276	+	6.15261i	−0.468325	+	0.203957i
$911$	25.8160			0.855322			0.427661	−	0.903939i	$-0.359338\pi$
$911$	25.8160			0.855322			0.427661	+	0.903939i	$0.359338\pi$
$912$		0			0
$913$	−33.6609			−1.11401
$914$	4.00052	−	1.74224i	0.132326	−	0.0576281i
$915$		0			0
$916$	10.4137	+	9.68833i	0.344077	+	0.320112i
$917$		−	17.8861i		−	0.590652i
$918$		0			0
$919$	−4.71609			−0.155569			−0.0777847	−	0.996970i	$-0.524785\pi$
$919$	−4.71609			−0.155569			−0.0777847	+	0.996970i	$0.524785\pi$
$920$	4.77721	+	1.68234i	0.157500	+	0.0554652i
$921$		0			0
$922$	−4.86953	−	11.1814i	−0.160369	−	0.368240i
$923$			87.2562i			2.87207i
$924$		0			0
$925$		−	18.6629i		−	0.613634i
$926$	4.26810	−	1.85877i	0.140258	−	0.0610829i
$927$		0			0
$928$	20.3940	−	10.6918i	0.669466	−	0.350975i
$929$	48.4774			1.59049			0.795246	−	0.606287i	$-0.207342\pi$
$929$	48.4774			1.59049			0.795246	+	0.606287i	$0.207342\pi$
$930$		0			0
$931$		−	1.60676i		−	0.0526594i
$932$	−25.2742	+	27.1665i	−0.827885	+	0.889867i
$933$		0			0
$934$	17.7008	+	40.6446i	0.579189	+	1.32993i
$935$	23.8588			0.780266
$936$		0			0
$937$	11.5193			0.376319			0.188159	−	0.982138i	$-0.439748\pi$
$937$	11.5193			0.376319			0.188159	+	0.982138i	$0.439748\pi$
$938$	4.72011	+	10.8383i	0.154117	+	0.353883i
$939$		0			0
$940$	6.98110	+	6.49485i	0.227698	+	0.211839i
$941$			32.3390i			1.05422i	0.849796	+	0.527111i	$0.176725\pi$
$941$			32.3390i			1.05422i	−0.849796	+	0.527111i	$0.823275\pi$
$942$		0			0
$943$	11.8753			0.386712
$944$	−5.51221	+	0.398312i	−0.179407	+	0.0129639i
$945$		0			0
$946$	1.02056	−	0.444458i	0.0331814	−	0.0144506i
$947$			37.4382i			1.21658i	0.793715	+	0.608289i	$0.208144\pi$
$947$			37.4382i			1.21658i	−0.793715	+	0.608289i	$0.791856\pi$
$948$		0			0
$949$		−	42.2810i		−	1.37250i
$950$	−2.40235	−	5.51627i	−0.0779426	−	0.178972i
$951$		0			0
$952$	6.40091	−	18.1761i	0.207455	−	0.589092i
$953$	−18.4974			−0.599190			−0.299595	−	0.954066i	$-0.596852\pi$
$953$	−18.4974			−0.599190			−0.299595	+	0.954066i	$0.596852\pi$
$954$		0			0
$955$		−	0.344846i		−	0.0111590i
$956$	5.26678	−	5.66109i	0.170340	−	0.183093i
$957$		0			0
$958$	30.7472	−	13.3905i	0.993397	−	0.432627i
$959$	9.18009			0.296441
$960$		0			0
$961$	31.4998			1.01612
$962$	64.9267	−	28.2757i	2.09332	−	0.911647i
$963$		0			0
$964$	−15.7600	+	16.9399i	−0.507596	+	0.545598i
$965$		−	18.0126i		−	0.579846i
$966$		0			0
$967$	44.4221			1.42852			0.714259	−	0.699882i	$-0.246764\pi$
$967$	44.4221			1.42852			0.714259	+	0.699882i	$0.246764\pi$
$968$	5.43628	−	15.4369i	0.174729	−	0.496162i
$969$		0			0
$970$	−2.25387	−	5.17532i	−0.0723672	−	0.166169i
$971$			37.5434i			1.20482i	0.798185	+	0.602412i	$0.205794\pi$
$971$			37.5434i			1.20482i	−0.798185	+	0.602412i	$0.794206\pi$
$972$		0			0
$973$			12.0518i			0.386361i
$974$	46.3295	−	20.1766i	1.48449	−	0.646500i
$975$		0			0
$976$	21.9634	−	1.58707i	0.703030	−	0.0508009i
$977$	−6.89949			−0.220734			−0.110367	−	0.993891i	$-0.535203\pi$
$977$	−6.89949			−0.220734			−0.110367	+	0.993891i	$0.535203\pi$
$978$		0			0
$979$			27.1542i			0.867853i
$980$	2.24575	+	2.08932i	0.0717377	+	0.0667410i
$981$		0			0
$982$	−22.7868	−	52.3230i	−0.727156	−	1.66969i
$983$	28.9252			0.922571			0.461285	−	0.887252i	$-0.347388\pi$
$983$	28.9252			0.922571			0.461285	+	0.887252i	$0.347388\pi$
$984$		0			0
$985$	−22.6980			−0.723220
$986$	15.6601	+	35.9586i	0.498718	+	1.14515i
$987$		0			0
$988$	15.5509	−	16.7151i	0.494739	−	0.531779i
$989$			0.402483i			0.0127982i
$990$		0			0
$991$	37.7278			1.19846			0.599232	−	0.800575i	$-0.295473\pi$
$991$	37.7278			1.19846			0.599232	+	0.800575i	$0.295473\pi$
$992$	20.7650	+	39.6082i	0.659290	+	1.25756i
$993$		0			0
$994$	15.9246	−	6.93519i	0.505096	−	0.219971i
$995$		−	30.0971i		−	0.954144i
$996$		0			0
$997$			53.0914i			1.68142i	0.541484	+	0.840711i	$0.317863\pi$
$997$			53.0914i			1.68142i	−0.541484	+	0.840711i	$0.682137\pi$
$998$	−23.1879	−	53.2440i	−0.734001	−	1.68541i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.c.f.757.21	yes	24
3.2	odd	2	inner	1512.2.c.f.757.4	yes	24
4.3	odd	2		6048.2.c.g.3025.16		24
8.3	odd	2		6048.2.c.g.3025.9		24
8.5	even	2	inner	1512.2.c.f.757.22	yes	24
12.11	even	2		6048.2.c.g.3025.10		24
24.5	odd	2	inner	1512.2.c.f.757.3	✓	24
24.11	even	2		6048.2.c.g.3025.15		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1512.2.c.f.757.3	✓	24	24.5	odd	2	inner
1512.2.c.f.757.4	yes	24	3.2	odd	2	inner
1512.2.c.f.757.21	yes	24	1.1	even	1	trivial
1512.2.c.f.757.22	yes	24	8.5	even	2	inner
6048.2.c.g.3025.9		24	8.3	odd	2
6048.2.c.g.3025.10		24	12.11	even	2
6048.2.c.g.3025.15		24	24.11	even	2
6048.2.c.g.3025.16		24	4.3	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.29659 - 0.564669i) q^{2} +(1.36230 - 1.46429i) q^{4} +1.53368i q^{5} +1.00000 q^{7} +(0.939505 - 2.66783i) q^{8} +O(q^{10})\)	\(q+(1.29659 - 0.564669i) q^{2} +(1.36230 - 1.46429i) q^{4} +1.53368i q^{5} +1.00000 q^{7} +(0.939505 - 2.66783i) q^{8} +(0.866019 + 1.98855i) q^{10} -2.28335i q^{11} +7.10447i q^{13} +(1.29659 - 0.564669i) q^{14} +(-0.288288 - 3.98960i) q^{16} +6.81307 q^{17} -1.60676i q^{19} +(2.24575 + 2.08932i) q^{20} +(-1.28934 - 2.96057i) q^{22} +1.16757 q^{23} +2.64784 q^{25} +(4.01168 + 9.21160i) q^{26} +(1.36230 - 1.46429i) q^{28} +4.07059i q^{29} -7.90568 q^{31} +(-2.62659 - 5.01009i) q^{32} +(8.83376 - 3.84713i) q^{34} +1.53368i q^{35} -7.04836i q^{37} +(-0.907287 - 2.08331i) q^{38} +(4.09159 + 1.44090i) q^{40} +10.1710 q^{41} +0.344719i q^{43} +(-3.34348 - 3.11060i) q^{44} +(1.51386 - 0.659289i) q^{46} +3.10859 q^{47} +1.00000 q^{49} +(3.43317 - 1.49515i) q^{50} +(10.4030 + 9.67841i) q^{52} -5.66835i q^{53} +3.50191 q^{55} +(0.939505 - 2.66783i) q^{56} +(2.29853 + 5.27789i) q^{58} -1.38165i q^{59} +5.50516i q^{61} +(-10.2504 + 4.46409i) q^{62} +(-6.23466 - 5.01288i) q^{64} -10.8960 q^{65} +8.35907i q^{67} +(9.28143 - 9.97630i) q^{68} +(0.866019 + 1.98855i) q^{70} +12.2819 q^{71} -5.95132 q^{73} +(-3.97999 - 9.13885i) q^{74} +(-2.35276 - 2.18889i) q^{76} -2.28335i q^{77} -15.0027 q^{79} +(6.11875 - 0.442140i) q^{80} +(13.1876 - 5.74322i) q^{82} -14.7419i q^{83} +10.4490i q^{85} +(0.194652 + 0.446959i) q^{86} +(-6.09159 - 2.14522i) q^{88} -11.8923 q^{89} +7.10447i q^{91} +(1.59058 - 1.70966i) q^{92} +(4.03057 - 1.75532i) q^{94} +2.46425 q^{95} -2.60256 q^{97} +(1.29659 - 0.564669i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{7}+O(q^{10}) \) 24 * q + 24 * q^7	\( 24 q + 24 q^{7} + 20 q^{10} - 4 q^{16} + 4 q^{22} - 24 q^{25} - 16 q^{31} + 4 q^{34} + 12 q^{40} - 52 q^{46} + 24 q^{49} + 12 q^{52} - 8 q^{55} - 28 q^{58} + 24 q^{64} + 20 q^{70} - 24 q^{76} + 32 q^{79} + 44 q^{82} - 60 q^{88} + 12 q^{94}+O(q^{100}) \) 24 * q + 24 * q^7 + 20 * q^10 - 4 * q^16 + 4 * q^22 - 24 * q^25 - 16 * q^31 + 4 * q^34 + 12 * q^40 - 52 * q^46 + 24 * q^49 + 12 * q^52 - 8 * q^55 - 28 * q^58 + 24 * q^64 + 20 * q^70 - 24 * q^76 + 32 * q^79 + 44 * q^82 - 60 * q^88 + 12 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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