LMFDB - Embedded newform 672.2.bd.a.431.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,2,Mod(431,672)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(672, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 3, 4]))

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

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

chi := DirichletCharacter("672.431");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	672.bd (of order $6$, degree $2$, not 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:	$5.36594701583$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			431.4
Character	$\chi$	$=$	672.431
Dual form			672.2.bd.a.527.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.66017 + 0.493786i) q^{3} +(1.09212 + 1.89161i) q^{5} +(0.451847 - 2.60688i) q^{7} +(2.51235 - 1.63954i) q^{9} +(1.45052 + 0.837460i) q^{11} -1.56085i q^{13} +(-2.74716 - 2.60112i) q^{15} +(-0.278795 - 0.160963i) q^{17} +(-2.87437 - 4.97856i) q^{19} +(0.537096 + 4.55099i) q^{21} +(3.26717 + 5.65891i) q^{23} +(0.114544 - 0.198397i) q^{25} +(-3.36136 + 3.96248i) q^{27} +7.04205 q^{29} +(7.76983 + 4.48591i) q^{31} +(-2.82165 - 0.674082i) q^{33} +(5.42467 - 1.99231i) q^{35} +(0.946173 - 0.546273i) q^{37} +(0.770727 + 2.59129i) q^{39} -3.44933i q^{41} +11.6570 q^{43} +(5.84516 + 2.96181i) q^{45} +(2.25371 + 3.90354i) q^{47} +(-6.59167 - 2.35583i) q^{49} +(0.542330 + 0.129561i) q^{51} +(-4.42876 + 7.67084i) q^{53} +3.65843i q^{55} +(7.23030 + 6.84595i) q^{57} +(-5.37016 - 3.10046i) q^{59} +(3.80578 - 2.19727i) q^{61} +(-3.13889 - 7.29023i) q^{63} +(2.95253 - 1.70464i) q^{65} +(-0.716072 + 1.24027i) q^{67} +(-8.21836 - 7.78149i) q^{69} +6.37080 q^{71} +(-4.49012 + 7.77711i) q^{73} +(-0.0921980 + 0.385933i) q^{75} +(2.83858 - 3.40294i) q^{77} +(3.58799 - 2.07153i) q^{79} +(3.62382 - 8.23820i) q^{81} -9.06459i q^{83} -0.703162i q^{85} +(-11.6910 + 3.47726i) q^{87} +(4.57586 - 2.64187i) q^{89} +(-4.06896 - 0.705268i) q^{91} +(-15.1143 - 3.61076i) q^{93} +(6.27833 - 10.8744i) q^{95} +4.23153 q^{97} +(5.01728 - 0.274197i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 2 q^{3} - 2 q^{9} + 4 q^{19} - 16 q^{25} + 8 q^{27} - 14 q^{33} + 16 q^{43} - 16 q^{49} + 34 q^{51} + 4 q^{57} + 36 q^{67} + 4 q^{73} - 10 q^{81} - 72 q^{91} - 32 q^{97} + 44 q^{99}+O(q^{100}) $ 56 * q + 2 * q^3 - 2 * q^9 + 4 * q^19 - 16 * q^25 + 8 * q^27 - 14 * q^33 + 16 * q^43 - 16 * q^49 + 34 * q^51 + 4 * q^57 + 36 * q^67 + 4 * q^73 - 10 * q^81 - 72 * q^91 - 32 * q^97 + 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$-1$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.66017	+	0.493786i	−0.958502	+	0.285087i
$3$	−1.66017	+	0.493786i	−0.958502	+	0.285087i
$4$		0			0
$5$	1.09212	+	1.89161i	0.488411	+	0.845953i	0.999911	−	0.0133302i	$-0.00424327\pi$
$5$	1.09212	+	1.89161i	0.488411	+	0.845953i	−0.511500	+	0.859283i	$0.670910\pi$
$6$		0			0
$7$	0.451847	−	2.60688i	0.170782	−	0.985309i
$7$	0.451847	−	2.60688i	0.170782	−	0.985309i
$8$		0			0
$9$	2.51235	−	1.63954i	0.837450	−	0.546513i
$10$		0			0
$11$	1.45052	+	0.837460i	0.437349	+	0.252504i	0.702473	−	0.711711i	$-0.252079\pi$
$11$	1.45052	+	0.837460i	0.437349	+	0.252504i	−0.265123	+	0.964215i	$0.585413\pi$
$12$		0			0
$13$		−	1.56085i		−	0.432903i	−0.976293	−	0.216452i	$-0.930552\pi$
$13$		−	1.56085i		−	0.432903i	0.976293	−	0.216452i	$-0.0694483\pi$
$14$		0			0
$15$	−2.74716	−	2.60112i	−0.709313	−	0.671608i
$16$		0			0
$17$	−0.278795	−	0.160963i	−0.0676178	−	0.0390392i	0.465810	−	0.884885i	$-0.345763\pi$
$17$	−0.278795	−	0.160963i	−0.0676178	−	0.0390392i	−0.533428	+	0.845846i	$0.679096\pi$
$18$		0			0
$19$	−2.87437	−	4.97856i	−0.659427	−	1.14216i	−0.980764	−	0.195196i	$-0.937466\pi$
$19$	−2.87437	−	4.97856i	−0.659427	−	1.14216i	0.321337	−	0.946965i	$-0.395868\pi$
$20$		0			0
$21$	0.537096	+	4.55099i	0.117204	+	0.993108i
$22$		0			0
$23$	3.26717	+	5.65891i	0.681252	+	1.17996i	0.974599	+	0.223958i	$0.0718977\pi$
$23$	3.26717	+	5.65891i	0.681252	+	1.17996i	−0.293346	+	0.956006i	$0.594769\pi$
$24$		0			0
$25$	0.114544	−	0.198397i	0.0229089	−	0.0396793i
$26$		0			0
$27$	−3.36136	+	3.96248i	−0.646894	+	0.762580i
$28$		0			0
$29$	7.04205			1.30768			0.653838	−	0.756635i	$-0.273158\pi$
$29$	7.04205			1.30768			0.653838	+	0.756635i	$0.273158\pi$
$30$		0			0
$31$	7.76983	+	4.48591i	1.39550	+	0.805694i	0.993917	−	0.110128i	$-0.0351259\pi$
$31$	7.76983	+	4.48591i	1.39550	+	0.805694i	0.401585	+	0.915822i	$0.368459\pi$
$32$		0			0
$33$	−2.82165	−	0.674082i	−0.491186	−	0.117343i
$34$		0			0
$35$	5.42467	−	1.99231i	0.916937	−	0.336762i
$36$		0			0
$37$	0.946173	−	0.546273i	0.155550	−	0.0898068i	−0.420205	−	0.907429i	$-0.638042\pi$
$37$	0.946173	−	0.546273i	0.155550	−	0.0898068i	0.575755	+	0.817623i	$0.304708\pi$
$38$		0			0
$39$	0.770727	+	2.59129i	0.123415	+	0.414938i
$40$		0			0
$41$		−	3.44933i		−	0.538694i	−0.963043	−	0.269347i	$-0.913192\pi$
$41$		−	3.44933i		−	0.538694i	0.963043	−	0.269347i	$-0.0868079\pi$
$42$		0			0
$43$	11.6570			1.77768			0.888841	−	0.458215i	$-0.151511\pi$
$43$	11.6570			1.77768			0.888841	+	0.458215i	$0.151511\pi$
$44$		0			0
$45$	5.84516	+	2.96181i	0.871345	+	0.441521i
$46$		0			0
$47$	2.25371	+	3.90354i	0.328737	+	0.569390i	0.982262	−	0.187516i	$-0.0600436\pi$
$47$	2.25371	+	3.90354i	0.328737	+	0.569390i	−0.653524	+	0.756906i	$0.726710\pi$
$48$		0			0
$49$	−6.59167	−	2.35583i	−0.941667	−	0.336546i
$50$		0			0
$51$	0.542330	+	0.129561i	0.0759413	+	0.0181421i
$52$		0			0
$53$	−4.42876	+	7.67084i	−0.608337	+	1.05367i	0.383177	+	0.923675i	$0.374830\pi$
$53$	−4.42876	+	7.67084i	−0.608337	+	1.05367i	−0.991515	+	0.129996i	$0.958504\pi$
$54$		0			0
$55$			3.65843i			0.493303i
$56$		0			0
$57$	7.23030	+	6.84595i	0.957677	+	0.906769i
$58$		0			0
$59$	−5.37016	−	3.10046i	−0.699135	−	0.403646i	0.107890	−	0.994163i	$-0.465591\pi$
$59$	−5.37016	−	3.10046i	−0.699135	−	0.403646i	−0.807025	+	0.590517i	$0.798924\pi$
$60$		0			0
$61$	3.80578	−	2.19727i	0.487280	−	0.281331i	−0.236165	−	0.971713i	$-0.575891\pi$
$61$	3.80578	−	2.19727i	0.487280	−	0.281331i	0.723445	+	0.690382i	$0.242557\pi$
$62$		0			0
$63$	−3.13889	−	7.29023i	−0.395463	−	0.918482i
$64$		0			0
$65$	2.95253	−	1.70464i	0.366216	−	0.211435i
$66$		0			0
$67$	−0.716072	+	1.24027i	−0.0874821	+	0.151523i	−0.906446	−	0.422321i	$-0.861215\pi$
$67$	−0.716072	+	1.24027i	−0.0874821	+	0.151523i	0.818964	+	0.573845i	$0.194549\pi$
$68$		0			0
$69$	−8.21836	−	7.78149i	−0.989374	−	0.936781i
$70$		0			0
$71$	6.37080			0.756074			0.378037	−	0.925790i	$-0.376599\pi$
$71$	6.37080			0.756074			0.378037	+	0.925790i	$0.376599\pi$
$72$		0			0
$73$	−4.49012	+	7.77711i	−0.525528	+	0.910242i	0.474030	+	0.880509i	$0.342799\pi$
$73$	−4.49012	+	7.77711i	−0.525528	+	0.910242i	−0.999558	+	0.0297328i	$0.990534\pi$
$74$		0			0
$75$	−0.0921980	+	0.385933i	−0.0106461	+	0.0445637i
$76$		0			0
$77$	2.83858	−	3.40294i	0.323486	−	0.387801i
$78$		0			0
$79$	3.58799	−	2.07153i	0.403681	−	0.233065i	−0.284390	−	0.958709i	$-0.591791\pi$
$79$	3.58799	−	2.07153i	0.403681	−	0.233065i	0.688071	+	0.725643i	$0.258458\pi$
$80$		0			0
$81$	3.62382	−	8.23820i	0.402647	−	0.915356i
$82$		0			0
$83$		−	9.06459i		−	0.994968i	−0.867473	−	0.497484i	$-0.834257\pi$
$83$		−	9.06459i		−	0.994968i	0.867473	−	0.497484i	$-0.165743\pi$
$84$		0			0
$85$		−	0.703162i		−	0.0762687i
$86$		0			0
$87$	−11.6910	+	3.47726i	−1.25341	+	0.372802i
$88$		0			0
$89$	4.57586	−	2.64187i	0.485040	−	0.280038i	−0.237474	−	0.971394i	$-0.576320\pi$
$89$	4.57586	−	2.64187i	0.485040	−	0.280038i	0.722515	+	0.691356i	$0.242986\pi$
$90$		0			0
$91$	−4.06896	−	0.705268i	−0.426543	−	0.0739322i
$92$		0			0
$93$	−15.1143	−	3.61076i	−1.56728	−	0.374419i
$94$		0			0
$95$	6.27833	−	10.8744i	0.644143	−	1.11569i
$96$		0			0
$97$	4.23153			0.429647			0.214823	−	0.976653i	$-0.431082\pi$
$97$	4.23153			0.429647			0.214823	+	0.976653i	$0.431082\pi$
$98$		0			0
$99$	5.01728	−	0.274197i	0.504255	−	0.0275578i
$100$		0			0
$101$	2.47136	−	4.28052i	0.245909	−	0.425927i	−0.716478	−	0.697610i	$-0.754247\pi$
$101$	2.47136	−	4.28052i	0.245909	−	0.425927i	0.962387	+	0.271683i	$0.0875802\pi$
$102$		0			0
$103$	−15.8817	+	9.16928i	−1.56487	+	0.903476i	−0.568114	+	0.822950i	$0.692327\pi$
$103$	−15.8817	+	9.16928i	−1.56487	+	0.903476i	−0.996752	+	0.0805264i	$0.974340\pi$
$104$		0			0
$105$	−8.02212	+	5.98621i	−0.782879	+	0.584194i
$106$		0			0
$107$	3.83045	−	2.21151i	0.370303	−	0.213795i	−0.303288	−	0.952899i	$-0.598084\pi$
$107$	3.83045	−	2.21151i	0.370303	−	0.213795i	0.673591	+	0.739104i	$0.264751\pi$
$108$		0			0
$109$	−7.04986	−	4.07024i	−0.675255	−	0.389858i	0.122810	−	0.992430i	$-0.460809\pi$
$109$	−7.04986	−	4.07024i	−0.675255	−	0.389858i	−0.798065	+	0.602572i	$0.794143\pi$
$110$		0			0
$111$	−1.30107	+	1.37411i	−0.123492	+	0.130425i
$112$		0			0
$113$			13.4000i			1.26056i	0.776367	+	0.630281i	$0.217060\pi$
$113$			13.4000i			1.26056i	−0.776367	+	0.630281i	$0.782940\pi$
$114$		0			0
$115$	−7.13629	+	12.3604i	−0.665463	+	1.15262i
$116$		0			0
$117$	−2.55908	−	3.92141i	−0.236587	−	0.362535i
$118$		0			0
$119$	−0.545583	+	0.654056i	−0.0500136	+	0.0599572i
$120$		0			0
$121$	−4.09732	−	7.09677i	−0.372484	−	0.645161i
$122$		0			0
$123$	1.70323	+	5.72648i	0.153575	+	0.516339i
$124$		0			0
$125$	11.4216			1.02158
$126$		0			0
$127$		−	12.5356i		−	1.11236i	−0.831063	−	0.556178i	$-0.812267\pi$
$127$		−	12.5356i		−	1.11236i	0.831063	−	0.556178i	$-0.187733\pi$
$128$		0			0
$129$	−19.3527	+	5.75608i	−1.70391	+	0.506795i
$130$		0			0
$131$	−14.8145	+	8.55318i	−1.29435	+	0.747295i	−0.979423	−	0.201820i	$-0.935315\pi$
$131$	−14.8145	+	8.55318i	−1.29435	+	0.747295i	−0.314930	+	0.949115i	$0.601981\pi$
$132$		0			0
$133$	−14.2773	+	5.24361i	−1.23800	+	0.454678i
$134$		0			0
$135$	−11.1665	−	2.03086i	−0.961057	−	0.174789i
$136$		0			0
$137$	−17.9399	−	10.3576i	−1.53271	−	0.884909i	−0.999236	−	0.0390917i	$-0.987554\pi$
$137$	−17.9399	−	10.3576i	−1.53271	−	0.884909i	−0.533472	−	0.845818i	$-0.679113\pi$
$138$		0			0
$139$	−1.27255			−0.107936			−0.0539682	−	0.998543i	$-0.517187\pi$
$139$	−1.27255			−0.107936			−0.0539682	+	0.998543i	$0.517187\pi$
$140$		0			0
$141$	−5.66906	−	5.36770i	−0.477421	−	0.452042i
$142$		0			0
$143$	1.30715	−	2.26406i	0.109310	−	0.189330i
$144$		0			0
$145$	7.69077	+	13.3208i	0.638684	+	1.10623i
$146$		0			0
$147$	12.1066	+	0.656207i	0.998534	+	0.0541230i
$148$		0			0
$149$	2.47136	+	4.28052i	0.202461	+	0.350674i	0.949321	−	0.314308i	$-0.101773\pi$
$149$	2.47136	+	4.28052i	0.202461	+	0.350674i	−0.746859	+	0.664982i	$0.768439\pi$
$150$		0			0
$151$	−5.48605	−	3.16737i	−0.446448	−	0.257757i	0.259881	−	0.965641i	$-0.416317\pi$
$151$	−5.48605	−	3.16737i	−0.446448	−	0.257757i	−0.706329	+	0.707884i	$0.749650\pi$
$152$		0			0
$153$	−0.964337	+	0.0527015i	−0.0779620	+	0.00426066i
$154$		0			0
$155$			19.5966i			1.57404i
$156$		0			0
$157$	2.09256	+	1.20814i	0.167004	+	0.0964199i	0.581172	−	0.813780i	$-0.302594\pi$
$157$	2.09256	+	1.20814i	0.167004	+	0.0964199i	−0.414168	+	0.910200i	$0.635928\pi$
$158$		0			0
$159$	3.56476	−	14.9218i	0.282704	−	1.18337i
$160$		0			0
$161$	16.2284	−	5.96017i	1.27897	−	0.469727i
$162$		0			0
$163$	−4.46077	−	7.72628i	−0.349395	−	0.605169i	0.636747	−	0.771072i	$-0.280279\pi$
$163$	−4.46077	−	7.72628i	−0.349395	−	0.605169i	−0.986142	+	0.165903i	$0.946946\pi$
$164$		0			0
$165$	−1.80648	−	6.07363i	−0.140634	−	0.472832i
$166$		0			0
$167$	−7.01131			−0.542551			−0.271276	−	0.962502i	$-0.587445\pi$
$167$	−7.01131			−0.542551			−0.271276	+	0.962502i	$0.587445\pi$
$168$		0			0
$169$	10.5637			0.812595
$170$		0			0
$171$	−15.3840	−	7.79525i	−1.17644	−	0.596118i
$172$		0			0
$173$	−7.11660	−	12.3263i	−0.541065	−	0.937152i	−0.998843	−	0.0480854i	$-0.984688\pi$
$173$	−7.11660	−	12.3263i	−0.541065	−	0.937152i	0.457778	−	0.889066i	$-0.348645\pi$
$174$		0			0
$175$	−0.465440	−	0.388249i	−0.0351840	−	0.0293488i
$176$		0			0
$177$	10.4464	+	2.49560i	0.785196	+	0.187581i
$178$		0			0
$179$	−1.07613	−	0.621304i	−0.0804338	−	0.0464384i	0.459244	−	0.888310i	$-0.348120\pi$
$179$	−1.07613	−	0.621304i	−0.0804338	−	0.0464384i	−0.539677	+	0.841872i	$0.681454\pi$
$180$		0			0
$181$			20.9487i			1.55710i	0.627580	+	0.778552i	$0.284046\pi$
$181$			20.9487i			1.55710i	−0.627580	+	0.778552i	$0.715954\pi$
$182$		0			0
$183$	−5.23327	+	5.52709i	−0.386855	+	0.408574i
$184$		0			0
$185$	2.06667	+	1.19319i	0.151945	+	0.0877253i
$186$		0			0
$187$	−0.269600	−	0.466960i	−0.0197151	−	0.0341475i
$188$		0			0
$189$	8.81091	+	10.5531i	0.640899	+	0.767625i
$190$		0			0
$191$	−12.2119	−	21.1516i	−0.883621	−	1.53048i	−0.847287	−	0.531136i	$-0.821765\pi$
$191$	−12.2119	−	21.1516i	−0.883621	−	1.53048i	−0.0363339	−	0.999340i	$-0.511568\pi$
$192$		0			0
$193$	0.00662606	−	0.0114767i	0.000476954	−	0.000826109i	−0.865787	−	0.500413i	$-0.833182\pi$
$193$	0.00662606	−	0.0114767i	0.000476954	−	0.000826109i	0.866264	+	0.499587i	$0.166515\pi$
$194$		0			0
$195$	−4.05998	+	4.28792i	−0.290741	+	0.307064i
$196$		0			0
$197$	6.48422			0.461981			0.230991	−	0.972956i	$-0.425803\pi$
$197$	6.48422			0.461981			0.230991	+	0.972956i	$0.425803\pi$
$198$		0			0
$199$	−4.47013	−	2.58083i	−0.316879	−	0.182950i	0.333121	−	0.942884i	$-0.391898\pi$
$199$	−4.47013	−	2.58083i	−0.316879	−	0.182950i	−0.650001	+	0.759934i	$0.725231\pi$
$200$		0			0
$201$	0.576375	−	2.41265i	0.0406543	−	0.170175i
$202$		0			0
$203$	3.18193	−	18.3578i	0.223328	−	1.28846i
$204$		0			0
$205$	6.52478	−	3.76708i	0.455710	−	0.263104i
$206$		0			0
$207$	17.4863	+	8.86051i	1.21538	+	0.615848i
$208$		0			0
$209$		−	9.62870i		−	0.666031i
$210$		0			0
$211$	16.8357			1.15902			0.579509	−	0.814966i	$-0.303244\pi$
$211$	16.8357			1.15902			0.579509	+	0.814966i	$0.303244\pi$
$212$		0			0
$213$	−10.5766	+	3.14581i	−0.724698	+	0.215547i
$214$		0			0
$215$	12.7309	+	22.0506i	0.868240	+	1.50384i
$216$		0			0
$217$	15.2050	−	18.2281i	1.03218	−	1.23740i
$218$		0			0
$219$	3.61415	−	15.1285i	0.244221	−	1.02229i
$220$		0			0
$221$	−0.251239	+	0.435159i	−0.0169002	+	0.0292720i
$222$		0			0
$223$			1.80170i			0.120651i	0.998179	+	0.0603254i	$0.0192138\pi$
$223$			1.80170i			0.120651i	−0.998179	+	0.0603254i	$0.980786\pi$
$224$		0			0
$225$	−0.0375035	−	0.686242i	−0.00250023	−	0.0457495i
$226$		0			0
$227$	10.0476	+	5.80096i	0.666879	+	0.385023i	0.794893	−	0.606749i	$-0.207527\pi$
$227$	10.0476	+	5.80096i	0.666879	+	0.385023i	−0.128014	+	0.991772i	$0.540860\pi$
$228$		0			0
$229$	8.50697	−	4.91150i	0.562156	−	0.324561i	−0.191854	−	0.981423i	$-0.561450\pi$
$229$	8.50697	−	4.91150i	0.562156	−	0.324561i	0.754010	+	0.656862i	$0.228117\pi$
$230$		0			0
$231$	−3.03220	+	7.05112i	−0.199504	+	0.463930i
$232$		0			0
$233$	−6.94161	+	4.00774i	−0.454760	+	0.262556i	−0.709838	−	0.704365i	$-0.751232\pi$
$233$	−6.94161	+	4.00774i	−0.454760	+	0.262556i	0.255079	+	0.966920i	$0.417899\pi$
$234$		0			0
$235$	−4.92265	+	8.52627i	−0.321118	+	0.556193i
$236$		0			0
$237$	−4.93380	+	5.21080i	−0.320485	+	0.338478i
$238$		0			0
$239$	6.02441			0.389686			0.194843	−	0.980834i	$-0.437580\pi$
$239$	6.02441			0.389686			0.194843	+	0.980834i	$0.437580\pi$
$240$		0			0
$241$	5.11917	−	8.86666i	0.329755	−	0.571152i	−0.652708	−	0.757609i	$-0.726367\pi$
$241$	5.11917	−	8.86666i	0.329755	−	0.571152i	0.982463	+	0.186457i	$0.0597006\pi$
$242$		0			0
$243$	−1.94826	+	15.4662i	−0.124981	+	0.992159i
$244$		0			0
$245$	−2.74260	−	15.0417i	−0.175218	−	0.960979i
$246$		0			0
$247$	−7.77081	+	4.48648i	−0.494445	+	0.285468i
$248$		0			0
$249$	4.47597	+	15.0488i	0.283653	+	0.953678i
$250$		0			0
$251$		−	9.97684i		−	0.629733i	−0.949136	−	0.314866i	$-0.898040\pi$
$251$		−	9.97684i		−	0.629733i	0.949136	−	0.314866i	$-0.101960\pi$
$252$		0			0
$253$			10.9445i			0.688075i
$254$		0			0
$255$	0.347212	+	1.16737i	0.0217432	+	0.0731036i
$256$		0			0
$257$	−17.1555	+	9.90475i	−1.07013	+	0.617841i	−0.928218	−	0.372038i	$-0.878659\pi$
$257$	−17.1555	+	9.90475i	−1.07013	+	0.617841i	−0.141915	+	0.989879i	$0.545326\pi$
$258$		0			0
$259$	−0.996544	−	2.71339i	−0.0619222	−	0.168602i
$260$		0			0
$261$	17.6921	−	11.5457i	1.09511	−	0.714662i
$262$		0			0
$263$	−3.41780	+	5.91981i	−0.210751	+	0.365031i	−0.951950	−	0.306254i	$-0.900924\pi$
$263$	−3.41780	+	5.91981i	−0.210751	+	0.365031i	0.741199	+	0.671285i	$0.234258\pi$
$264$		0			0
$265$	−19.3470			−1.18847
$266$		0			0
$267$	−6.29220	+	6.64546i	−0.385077	+	0.406696i
$268$		0			0
$269$	−12.0822	+	20.9270i	−0.736665	+	1.27594i	0.217324	+	0.976099i	$0.430267\pi$
$269$	−12.0822	+	20.9270i	−0.736665	+	1.27594i	−0.953989	+	0.299842i	$0.903066\pi$
$270$		0			0
$271$	15.2835	−	8.82392i	0.928405	−	0.536015i	0.0420983	−	0.999113i	$-0.486596\pi$
$271$	15.2835	−	8.82392i	0.928405	−	0.536015i	0.886307	+	0.463099i	$0.153262\pi$
$272$		0			0
$273$	7.10344	−	0.838329i	0.429919	−	0.0507380i
$274$		0			0
$275$	0.332299	−	0.191853i	0.0200384	−	0.0115692i
$276$		0			0
$277$	12.9250	+	7.46224i	0.776587	+	0.448363i	0.835219	−	0.549917i	$-0.185341\pi$
$277$	12.9250	+	7.46224i	0.776587	+	0.448363i	−0.0586324	+	0.998280i	$0.518674\pi$
$278$		0			0
$279$	26.8754	−	1.46875i	1.60899	−	0.0879320i
$280$		0			0
$281$			13.8890i			0.828547i	0.910152	+	0.414273i	$0.135964\pi$
$281$			13.8890i			0.828547i	−0.910152	+	0.414273i	$0.864036\pi$
$282$		0			0
$283$	−2.88865	+	5.00329i	−0.171712	+	0.297415i	−0.939019	−	0.343866i	$-0.888263\pi$
$283$	−2.88865	+	5.00329i	−0.171712	+	0.297415i	0.767306	+	0.641281i	$0.221597\pi$
$284$		0			0
$285$	−5.05350	+	21.1535i	−0.299343	+	1.25303i
$286$		0			0
$287$	−8.99199	−	1.55857i	−0.530780	−	0.0919994i
$288$		0			0
$289$	−8.44818	−	14.6327i	−0.496952	−	0.860746i
$290$		0			0
$291$	−7.02508	+	2.08947i	−0.411817	+	0.122487i
$292$		0			0
$293$	−15.6381			−0.913587			−0.456794	−	0.889573i	$-0.651002\pi$
$293$	−15.6381			−0.913587			−0.456794	+	0.889573i	$0.651002\pi$
$294$		0			0
$295$		−	13.5443i		−	0.788581i
$296$		0			0
$297$	−8.19415	+	2.93267i	−0.475473	+	0.170171i
$298$		0			0
$299$	8.83273	−	5.09958i	0.510810	−	0.294916i
$300$		0			0
$301$	5.26720	−	30.3885i	0.303597	−	1.75157i
$302$		0			0
$303$	−1.98922	+	8.32672i	−0.114278	+	0.478358i
$304$		0			0
$305$	8.31274	+	4.79936i	0.475986	+	0.274811i
$306$		0			0
$307$	−7.19887			−0.410861			−0.205430	−	0.978672i	$-0.565859\pi$
$307$	−7.19887			−0.410861			−0.205430	+	0.978672i	$0.565859\pi$
$308$		0			0
$309$	21.8387	−	23.0647i	1.24236	−	1.31211i
$310$		0			0
$311$	−4.35089	+	7.53597i	−0.246717	+	0.427326i	−0.962613	−	0.270881i	$-0.912685\pi$
$311$	−4.35089	+	7.53597i	−0.246717	+	0.427326i	0.715896	+	0.698207i	$0.246018\pi$
$312$		0			0
$313$	9.57541	+	16.5851i	0.541234	+	0.937445i	0.998834	+	0.0482863i	$0.0153760\pi$
$313$	9.57541	+	16.5851i	0.541234	+	0.937445i	−0.457600	+	0.889158i	$0.651291\pi$
$314$		0			0
$315$	10.3622	−	13.8994i	0.583844	−	0.783140i
$316$		0			0
$317$	1.83178	+	3.17274i	0.102883	+	0.178199i	0.912871	−	0.408247i	$-0.133860\pi$
$317$	1.83178	+	3.17274i	0.102883	+	0.178199i	−0.809988	+	0.586446i	$0.800527\pi$
$318$		0			0
$319$	10.2147	+	5.89744i	0.571911	+	0.330193i
$320$		0			0
$321$	−5.26720	+	5.56291i	−0.293986	+	0.310491i
$322$		0			0
$323$			1.85067i			0.102974i
$324$		0			0
$325$	−0.309668	−	0.178787i	−0.0171773	−	0.00991732i
$326$		0			0
$327$	13.7138	+	3.27618i	0.758376	+	0.181173i
$328$		0			0
$329$	11.1944	−	4.11135i	0.617167	−	0.226666i
$330$		0			0
$331$	−5.41365	−	9.37672i	−0.297561	−	0.515391i	0.678016	−	0.735047i	$-0.262840\pi$
$331$	−5.41365	−	9.37672i	−0.297561	−	0.515391i	−0.975577	+	0.219656i	$0.929507\pi$
$332$		0			0
$333$	1.48148	−	2.92372i	0.0811847	−	0.160219i
$334$		0			0
$335$	−3.12815			−0.170909
$336$		0			0
$337$	−20.0426			−1.09179			−0.545894	−	0.837854i	$-0.683810\pi$
$337$	−20.0426			−1.09179			−0.545894	+	0.837854i	$0.683810\pi$
$338$		0			0
$339$	−6.61670	−	22.2462i	−0.359370	−	1.20825i
$340$		0			0
$341$	7.51355	+	13.0139i	0.406882	+	0.704740i
$342$		0			0
$343$	−9.11979	+	16.1192i	−0.492422	+	0.870357i
$344$		0			0
$345$	5.74408	−	24.0442i	0.309251	−	1.29450i
$346$		0			0
$347$	−5.06136	−	2.92218i	−0.271708	−	0.156871i	0.357955	−	0.933739i	$-0.383474\pi$
$347$	−5.06136	−	2.92218i	−0.271708	−	0.156871i	−0.629664	+	0.776868i	$0.716807\pi$
$348$		0			0
$349$		−	18.6166i		−	0.996526i	−0.867026	−	0.498263i	$-0.833971\pi$
$349$		−	18.6166i		−	0.996526i	0.867026	−	0.498263i	$-0.166029\pi$
$350$		0			0
$351$	6.18486	+	5.24659i	0.330123	+	0.280042i
$352$		0			0
$353$	−5.78219	−	3.33835i	−0.307755	−	0.177682i	0.338167	−	0.941086i	$-0.390193\pi$
$353$	−5.78219	−	3.33835i	−0.307755	−	0.177682i	−0.645921	+	0.763404i	$0.723527\pi$
$354$		0			0
$355$	6.95768	+	12.0511i	0.369275	+	0.639603i
$356$		0			0
$357$	0.582800	−	1.35525i	0.0308450	−	0.0717273i
$358$		0			0
$359$	12.1282	+	21.0067i	0.640102	+	1.10869i	0.985410	+	0.170200i	$0.0544414\pi$
$359$	12.1282	+	21.0067i	0.640102	+	1.10869i	−0.345307	+	0.938490i	$0.612225\pi$
$360$		0			0
$361$	−7.02406	+	12.1660i	−0.369687	+	0.640317i
$362$		0			0
$363$	10.3065	+	9.75866i	0.540953	+	0.512197i
$364$		0			0
$365$	−19.6150			−1.02670
$366$		0			0
$367$	6.54864	+	3.78086i	0.341836	+	0.197359i	0.661084	−	0.750312i	$-0.270097\pi$
$367$	6.54864	+	3.78086i	0.341836	+	0.197359i	−0.319248	+	0.947671i	$0.603430\pi$
$368$		0			0
$369$	−5.65531	−	8.66592i	−0.294404	−	0.451130i
$370$		0			0
$371$	17.9958	+	15.0113i	0.934298	+	0.779348i
$372$		0			0
$373$	−16.9620	+	9.79302i	−0.878260	+	0.507063i	−0.870084	−	0.492903i	$-0.835936\pi$
$373$	−16.9620	+	9.79302i	−0.878260	+	0.507063i	−0.00817543	+	0.999967i	$0.502602\pi$
$374$		0			0
$375$	−18.9618	+	5.63982i	−0.979184	+	0.291239i
$376$		0			0
$377$		−	10.9916i		−	0.566097i
$378$		0			0
$379$	−4.99759			−0.256709			−0.128354	−	0.991728i	$-0.540969\pi$
$379$	−4.99759			−0.256709			−0.128354	+	0.991728i	$0.540969\pi$
$380$		0			0
$381$	6.18991	+	20.8113i	0.317119	+	1.06620i
$382$		0			0
$383$	−15.1532	−	26.2461i	−0.774292	−	1.34111i	−0.935192	−	0.354142i	$-0.884773\pi$
$383$	−15.1532	−	26.2461i	−0.774292	−	1.34111i	0.160900	−	0.986971i	$-0.448560\pi$
$384$		0			0
$385$	9.53710	+	1.65305i	0.486056	+	0.0842474i
$386$		0			0
$387$	29.2866	−	19.1122i	1.48872	−	0.971527i
$388$		0			0
$389$	2.13059	−	3.69030i	0.108025	−	0.187106i	−0.806945	−	0.590627i	$-0.798881\pi$
$389$	2.13059	−	3.69030i	0.108025	−	0.187106i	0.914970	+	0.403521i	$0.132214\pi$
$390$		0			0
$391$		−	2.10357i		−	0.106382i
$392$		0			0
$393$	20.3713	−	21.5150i	1.02760	−	1.08529i
$394$		0			0
$395$	7.83704	+	4.52472i	0.394324	+	0.227663i
$396$		0			0
$397$	17.1398	−	9.89568i	0.860223	−	0.496650i	−0.00386406	−	0.999993i	$-0.501230\pi$
$397$	17.1398	−	9.89568i	0.860223	−	0.496650i	0.864087	+	0.503343i	$0.167897\pi$
$398$		0			0
$399$	21.1136	−	15.7552i	1.05700	−	0.788748i
$400$		0			0
$401$	−1.98773	+	1.14762i	−0.0992627	+	0.0573094i	−0.548810	−	0.835947i	$-0.684919\pi$
$401$	−1.98773	+	1.14762i	−0.0992627	+	0.0573094i	0.449547	+	0.893257i	$0.351585\pi$
$402$		0			0
$403$	7.00186	−	12.1276i	0.348787	−	0.604118i
$404$		0			0
$405$	19.5411	−	2.14226i	0.971005	−	0.106450i
$406$		0			0
$407$	1.82993			0.0907062
$408$		0			0
$409$	−0.750621	+	1.30011i	−0.0371158	+	0.0642865i	−0.883987	−	0.467512i	$-0.845150\pi$
$409$	−0.750621	+	1.30011i	−0.0371158	+	0.0642865i	0.846871	+	0.531799i	$0.178484\pi$
$410$		0			0
$411$	34.8978	+	8.33695i	1.72138	+	0.411231i
$412$		0			0
$413$	−10.5090	+	12.5984i	−0.517116	+	0.619928i
$414$		0			0
$415$	17.1467	−	9.89963i	0.841696	−	0.485954i
$416$		0			0
$417$	2.11265	−	0.628367i	0.103457	−	0.0307713i
$418$		0			0
$419$		−	8.44514i		−	0.412572i	−0.978492	−	0.206286i	$-0.933862\pi$
$419$		−	8.44514i		−	0.412572i	0.978492	−	0.206286i	$-0.0661378\pi$
$420$		0			0
$421$			13.9326i			0.679032i	0.940600	+	0.339516i	$0.110263\pi$
$421$			13.9326i			0.679032i	−0.940600	+	0.339516i	$0.889737\pi$
$422$		0			0
$423$	12.0621	+	6.11202i	0.586480	+	0.297176i
$424$		0			0
$425$	−0.0638689	+	0.0368747i	−0.00309809	+	0.00178869i
$426$		0			0
$427$	−4.00839	−	10.9140i	−0.193979	−	0.528168i
$428$		0			0
$429$	−1.05214	+	4.40418i	−0.0507979	+	0.212636i
$430$		0			0
$431$	−16.9743	+	29.4004i	−0.817624	+	1.41617i	0.0898039	+	0.995959i	$0.471376\pi$
$431$	−16.9743	+	29.4004i	−0.817624	+	1.41617i	−0.907428	+	0.420207i	$0.861957\pi$
$432$		0			0
$433$	4.44336			0.213534			0.106767	−	0.994284i	$-0.465950\pi$
$433$	4.44336			0.213534			0.106767	+	0.994284i	$0.465950\pi$
$434$		0			0
$435$	−19.3456	−	18.3173i	−0.927552	−	0.878245i
$436$		0			0
$437$	18.7822	−	32.5316i	0.898472	−	1.55620i
$438$		0			0
$439$	7.55680	−	4.36292i	0.360667	−	0.208231i	−0.308707	−	0.951157i	$-0.599896\pi$
$439$	7.55680	−	4.36292i	0.360667	−	0.208231i	0.669373	+	0.742926i	$0.266563\pi$
$440$		0			0
$441$	−20.4231	+	4.88864i	−0.972526	+	0.232792i
$442$		0			0
$443$	−32.0121	+	18.4822i	−1.52094	+	0.878115i	−0.521244	+	0.853407i	$0.674532\pi$
$443$	−32.0121	+	18.4822i	−1.52094	+	0.878115i	−0.999695	+	0.0247072i	$0.992135\pi$
$444$		0			0
$445$	9.99478	+	5.77049i	0.473798	+	0.273548i
$446$		0			0
$447$	−6.21654	−	5.88608i	−0.294032	−	0.278402i
$448$		0			0
$449$			23.4269i			1.10559i	0.833319	+	0.552793i	$0.186438\pi$
$449$			23.4269i			1.10559i	−0.833319	+	0.552793i	$0.813562\pi$
$450$		0			0
$451$	2.88868	−	5.00333i	0.136022	−	0.235598i
$452$		0			0
$453$	10.6718	+	2.54945i	0.501405	+	0.119784i
$454$		0			0
$455$	−3.10971	−	8.46712i	−0.145785	−	0.396945i
$456$		0			0
$457$	0.661376	+	1.14554i	0.0309378	+	0.0535859i	0.881080	−	0.472968i	$-0.156817\pi$
$457$	0.661376	+	1.14554i	0.0309378	+	0.0535859i	−0.850142	+	0.526554i	$0.823484\pi$
$458$		0			0
$459$	1.57494	−	0.563669i	0.0735120	−	0.0263098i
$460$		0			0
$461$	−23.5461			−1.09665			−0.548325	−	0.836266i	$-0.684734\pi$
$461$	−23.5461			−1.09665			−0.548325	+	0.836266i	$0.684734\pi$
$462$		0			0
$463$			14.4502i			0.671557i	0.941941	+	0.335778i	$0.108999\pi$
$463$			14.4502i			0.671557i	−0.941941	+	0.335778i	$0.891001\pi$
$464$		0			0
$465$	−9.67654	−	32.5338i	−0.448739	−	1.50872i
$466$		0			0
$467$	−13.0084	+	7.51039i	−0.601956	+	0.347540i	−0.769811	−	0.638272i	$-0.779649\pi$
$467$	−13.0084	+	7.51039i	−0.601956	+	0.347540i	0.167855	+	0.985812i	$0.446316\pi$
$468$		0			0
$469$	2.90969	+	2.42713i	0.134357	+	0.112074i
$470$		0			0
$471$	−4.07057	−	0.972444i	−0.187562	−	0.0448079i
$472$		0			0
$473$	16.9088	+	9.76231i	0.777468	+	0.448872i
$474$		0			0
$475$	−1.31697			−0.0604269
$476$		0			0
$477$	1.45004	+	26.5330i	0.0663928	+	1.21486i
$478$		0			0
$479$	10.9550	−	18.9745i	0.500545	−	0.866969i	−0.499455	−	0.866340i	$-0.666466\pi$
$479$	10.9550	−	18.9745i	0.500545	−	0.866969i	1.00000		0.000629369i	$-0.000200335\pi$
$480$		0			0
$481$	−0.852653	−	1.47684i	−0.0388776	−	0.0673380i
$482$		0			0
$483$	−23.9989	+	17.9083i	−1.09199	+	0.814854i
$484$		0			0
$485$	4.62134	+	8.00440i	0.209844	+	0.363461i
$486$		0			0
$487$	−9.51388	−	5.49284i	−0.431115	−	0.248904i	0.268707	−	0.963222i	$-0.413404\pi$
$487$	−9.51388	−	5.49284i	−0.431115	−	0.248904i	−0.699821	+	0.714318i	$0.746737\pi$
$488$		0			0
$489$	11.2208	+	10.6243i	0.507421	+	0.480448i
$490$		0			0
$491$			32.3525i			1.46005i	0.683422	+	0.730024i	$0.260491\pi$
$491$			32.3525i			1.46005i	−0.683422	+	0.730024i	$0.739509\pi$
$492$		0			0
$493$	−1.96329	−	1.13351i	−0.0884222	−	0.0510506i
$494$		0			0
$495$	5.99814	+	9.19127i	0.269597	+	0.413117i
$496$		0			0
$497$	2.87863	−	16.6079i	0.129124	−	0.744967i
$498$		0			0
$499$	7.10372	+	12.3040i	0.318006	+	0.550803i	0.980072	−	0.198643i	$-0.0636534\pi$
$499$	7.10372	+	12.3040i	0.318006	+	0.550803i	−0.662066	+	0.749446i	$0.730320\pi$
$500$		0			0
$501$	11.6400	−	3.46208i	0.520036	−	0.154674i
$502$		0			0
$503$	−33.4106			−1.48970			−0.744852	−	0.667229i	$-0.767480\pi$
$503$	−33.4106			−1.48970			−0.744852	+	0.667229i	$0.767480\pi$
$504$		0			0
$505$	10.7961			0.480419
$506$		0			0
$507$	−17.5376	+	5.21622i	−0.778873	+	0.231660i
$508$		0			0
$509$	8.44815	+	14.6326i	0.374458	+	0.648580i	0.990246	−	0.139332i	$-0.0444956\pi$
$509$	8.44815	+	14.6326i	0.374458	+	0.648580i	−0.615788	+	0.787912i	$0.711162\pi$
$510$		0			0
$511$	18.2452	+	15.2193i	0.807118	+	0.673261i
$512$		0			0
$513$	29.3893	+	5.34507i	1.29757	+	0.235991i
$514$		0			0
$515$	−34.6894	−	20.0279i	−1.52860	−	0.882536i
$516$		0			0
$517$			7.54957i			0.332030i
$518$		0			0
$519$	17.9013	+	16.9497i	0.785781	+	0.744011i
$520$		0			0
$521$	31.0684	+	17.9374i	1.36113	+	0.785850i	0.989775	−	0.142639i	$-0.0455589\pi$
$521$	31.0684	+	17.9374i	1.36113	+	0.785850i	0.371358	+	0.928490i	$0.378892\pi$
$522$		0			0
$523$	1.10840	+	1.91980i	0.0484669	+	0.0839471i	0.889241	−	0.457439i	$-0.151233\pi$
$523$	1.10840	+	1.91980i	0.0484669	+	0.0839471i	−0.840774	+	0.541386i	$0.817900\pi$
$524$		0			0
$525$	0.964423	+	0.414732i	0.0420909	+	0.0181004i
$526$		0			0
$527$	−1.44413	−	2.50130i	−0.0629072	−	0.108959i
$528$		0			0
$529$	−9.84883	+	17.0587i	−0.428210	+	0.741681i
$530$		0			0
$531$	−18.5751	+	1.01514i	−0.806089	+	0.0440532i
$532$		0			0
$533$	−5.38390			−0.233202
$534$		0			0
$535$	8.36662	+	4.83047i	0.361721	+	0.208840i
$536$		0			0
$537$	2.09335	+	0.500095i	0.0903349	+	0.0215807i
$538$		0			0
$539$	−7.58846	−	8.93744i	−0.326858	−	0.384963i
$540$		0			0
$541$	−32.2404	+	18.6140i	−1.38612	+	0.800279i	−0.992876	−	0.119153i	$-0.961982\pi$
$541$	−32.2404	+	18.6140i	−1.38612	+	0.800279i	−0.393248	+	0.919432i	$0.628649\pi$
$542$		0			0
$543$	−10.3442	−	34.7785i	−0.443911	−	1.49249i
$544$		0			0
$545$		−	17.7808i		−	0.761645i
$546$		0			0
$547$	−12.2271			−0.522792			−0.261396	−	0.965232i	$-0.584183\pi$
$547$	−12.2271			−0.522792			−0.261396	+	0.965232i	$0.584183\pi$
$548$		0			0
$549$	5.95895	−	11.7600i	0.254322	−	0.501906i
$550$		0			0
$551$	−20.2415	−	35.0593i	−0.862317	−	1.49358i
$552$		0			0
$553$	−3.77901	−	10.2895i	−0.160700	−	0.437554i
$554$		0			0
$555$	−4.02021	−	0.960414i	−0.170649	−	0.0407673i
$556$		0			0
$557$	0.649106	−	1.12428i	0.0275035	−	0.0476375i	−0.851946	−	0.523630i	$-0.824578\pi$
$557$	0.649106	−	1.12428i	0.0275035	−	0.0476375i	0.879450	+	0.475992i	$0.157911\pi$
$558$		0			0
$559$		−	18.1949i		−	0.769564i
$560$		0			0
$561$	0.678160	+	0.642111i	0.0286320	+	0.0271099i
$562$		0			0
$563$	24.2080	+	13.9765i	1.02024	+	0.589038i	0.914175	−	0.405320i	$-0.132840\pi$
$563$	24.2080	+	13.9765i	1.02024	+	0.589038i	0.106070	+	0.994359i	$0.466173\pi$
$564$		0			0
$565$	−25.3475	+	14.6344i	−1.06638	+	0.615672i
$566$		0			0
$567$	−19.8386	−	13.1693i	−0.833143	−	0.553058i
$568$		0			0
$569$	−26.1457	+	15.0952i	−1.09608	+	0.632825i	−0.935190	−	0.354147i	$-0.884771\pi$
$569$	−26.1457	+	15.0952i	−1.09608	+	0.632825i	−0.160895	+	0.986972i	$0.551438\pi$
$570$		0			0
$571$	16.0016	−	27.7156i	0.669646	−	1.15986i	−0.308357	−	0.951271i	$-0.599779\pi$
$571$	16.0016	−	27.7156i	0.669646	−	1.15986i	0.978003	−	0.208591i	$-0.0668877\pi$
$572$		0			0
$573$	30.7182	+	29.0853i	1.28327	+	1.21505i
$574$		0			0
$575$	1.49694			0.0624269
$576$		0			0
$577$	7.72204	−	13.3750i	0.321473	−	0.556807i	−0.659319	−	0.751863i	$-0.729155\pi$
$577$	7.72204	−	13.3750i	0.321473	−	0.556807i	0.980792	+	0.195056i	$0.0624888\pi$
$578$		0			0
$579$	−0.00533339	+	0.0223251i	−0.000221648	+	0.000927800i
$580$		0			0
$581$	−23.6303	−	4.09581i	−0.980351	−	0.169923i
$582$		0			0
$583$	−12.8480	+	7.41782i	−0.532112	+	0.307215i
$584$		0			0
$585$	4.62295	−	9.12344i	0.191136	−	0.377208i
$586$		0			0
$587$			1.97510i			0.0815212i	0.999169	+	0.0407606i	$0.0129781\pi$
$587$			1.97510i			0.0815212i	−0.999169	+	0.0407606i	$0.987022\pi$
$588$		0			0
$589$		−	51.5768i		−	2.12518i
$590$		0			0
$591$	−10.7649	+	3.20181i	−0.442810	+	0.131705i
$592$		0			0
$593$	−14.0265	+	8.09823i	−0.576001	+	0.332554i	−0.759543	−	0.650458i	$-0.774577\pi$
$593$	−14.0265	+	8.09823i	−0.576001	+	0.332554i	0.183542	+	0.983012i	$0.441244\pi$
$594$		0			0
$595$	−1.83306	−	0.317722i	−0.0751482	−	0.0130253i
$596$		0			0
$597$	8.69558	+	2.07734i	0.355886	+	0.0850200i
$598$		0			0
$599$	7.00327	−	12.1300i	0.286146	−	0.495619i	−0.686741	−	0.726903i	$-0.740959\pi$
$599$	7.00327	−	12.1300i	0.286146	−	0.495619i	0.972886	+	0.231283i	$0.0742925\pi$
$600$		0			0
$601$	−15.5923			−0.636024			−0.318012	−	0.948087i	$-0.603015\pi$
$601$	−15.5923			−0.636024			−0.318012	+	0.948087i	$0.603015\pi$
$602$		0			0
$603$	0.234452	+	4.29003i	0.00954764	+	0.174704i
$604$		0			0
$605$	8.94954	−	15.5011i	0.363850	−	0.630207i
$606$		0			0
$607$	−28.3416	+	16.3630i	−1.15035	+	0.664155i	−0.948973	−	0.315359i	$-0.897875\pi$
$607$	−28.3416	+	16.3630i	−1.15035	+	0.664155i	−0.201378	+	0.979514i	$0.564542\pi$
$608$		0			0
$609$	3.78226	+	32.0483i	0.153265	+	1.29866i
$610$		0			0
$611$	6.09286	−	3.51771i	0.246491	−	0.142311i
$612$		0			0
$613$	−0.287887	−	0.166212i	−0.0116277	−	0.00671323i	0.494175	−	0.869363i	$-0.335470\pi$
$613$	−0.287887	−	0.166212i	−0.0116277	−	0.00671323i	−0.505803	+	0.862649i	$0.668804\pi$
$614$		0			0
$615$	−8.97213	+	9.47585i	−0.361791	+	0.382103i
$616$		0			0
$617$		−	39.1386i		−	1.57566i	−0.615893	−	0.787830i	$-0.711205\pi$
$617$		−	39.1386i		−	1.57566i	0.615893	−	0.787830i	$-0.288795\pi$
$618$		0			0
$619$	−1.61116	+	2.79062i	−0.0647581	+	0.112164i	−0.896587	−	0.442868i	$-0.853961\pi$
$619$	−1.61116	+	2.79062i	−0.0647581	+	0.112164i	0.831829	+	0.555033i	$0.187294\pi$
$620$		0			0
$621$	−33.4055	−	6.07550i	−1.34052	−	0.243801i
$622$		0			0
$623$	−4.81946	−	13.1225i	−0.193088	−	0.525740i
$624$		0			0
$625$	11.9010	+	20.6132i	0.476042	+	0.824528i
$626$		0			0
$627$	4.75451	+	15.9853i	0.189877	+	0.638392i
$628$		0			0
$629$	−0.351718			−0.0140239
$630$		0			0
$631$			10.2850i			0.409441i	0.978820	+	0.204721i	$0.0656286\pi$
$631$			10.2850i			0.409441i	−0.978820	+	0.204721i	$0.934371\pi$
$632$		0			0
$633$	−27.9502	+	8.31323i	−1.11092	+	0.330421i
$634$		0			0
$635$	23.7125	−	13.6904i	0.941002	−	0.543287i
$636$		0			0
$637$	−3.67710	+	10.2886i	−0.145692	+	0.407650i
$638$		0			0
$639$	16.0057	−	10.4452i	0.633175	−	0.413205i
$640$		0			0
$641$	−26.2428	−	15.1513i	−1.03653	−	0.598439i	−0.117680	−	0.993052i	$-0.537546\pi$
$641$	−26.2428	−	15.1513i	−1.03653	−	0.598439i	−0.918848	+	0.394612i	$0.870879\pi$
$642$		0			0
$643$	37.4668			1.47755			0.738773	−	0.673955i	$-0.235406\pi$
$643$	37.4668			1.47755			0.738773	+	0.673955i	$0.235406\pi$
$644$		0			0
$645$	−32.0238	−	30.3214i	−1.26093	−	1.19390i
$646$		0			0
$647$	−0.130900	+	0.226726i	−0.00514622	+	0.00891351i	−0.868587	−	0.495537i	$-0.834971\pi$
$647$	−0.130900	+	0.226726i	−0.00514622	+	0.00891351i	0.863441	+	0.504450i	$0.168305\pi$
$648$		0			0
$649$	−5.19303	−	8.99459i	−0.203844	−	0.353069i
$650$		0			0
$651$	−16.2422	+	37.7698i	−0.636583	+	1.48032i
$652$		0			0
$653$	−22.1548	−	38.3732i	−0.866984	−	1.50166i	−0.865064	−	0.501662i	$-0.832722\pi$
$653$	−22.1548	−	38.3732i	−0.866984	−	1.50166i	−0.00192051	−	0.999998i	$-0.500611\pi$
$654$		0			0
$655$	−32.3586	−	18.6822i	−1.26435	−	0.729975i
$656$		0			0
$657$	1.47013	+	26.9006i	0.0573552	+	1.04949i
$658$		0			0
$659$		−	23.4513i		−	0.913534i	−0.889586	−	0.456767i	$-0.849007\pi$
$659$		−	23.4513i		−	0.913534i	0.889586	−	0.456767i	$-0.150993\pi$
$660$		0			0
$661$	−29.3695	−	16.9565i	−1.14234	−	0.659531i	−0.195332	−	0.980737i	$-0.562578\pi$
$661$	−29.3695	−	16.9565i	−1.14234	−	0.659531i	−0.947009	+	0.321206i	$0.895912\pi$
$662$		0			0
$663$	0.202225	−	0.846498i	0.00785378	−	0.0328752i
$664$		0			0
$665$	−25.5114	−	21.2804i	−0.989289	−	0.825219i
$666$		0			0
$667$	23.0076	+	39.8503i	0.890857	+	1.54301i
$668$		0			0
$669$	−0.889654	−	2.99114i	−0.0343960	−	0.115644i
$670$		0			0
$671$	7.36050			0.284149
$672$		0			0
$673$	−13.3855			−0.515973			−0.257986	−	0.966149i	$-0.583059\pi$
$673$	−13.3855			−0.515973			−0.257986	+	0.966149i	$0.583059\pi$
$674$		0			0
$675$	0.401119	+	1.12076i	0.0154391	+	0.0431381i
$676$		0			0
$677$	−13.0777	−	22.6513i	−0.502618	−	0.870559i	−0.999995	−	0.00302522i	$-0.999037\pi$
$677$	−13.0777	−	22.6513i	−0.502618	−	0.870559i	0.497378	−	0.867534i	$-0.334296\pi$
$678$		0			0
$679$	1.91201	−	11.0311i	0.0733761	−	0.423335i
$680$		0			0
$681$	−19.5451	−	4.66926i	−0.748970	−	0.178926i
$682$		0			0
$683$	19.0543	+	11.0010i	0.729092	+	0.420942i	0.818090	−	0.575090i	$-0.195033\pi$
$683$	19.0543	+	11.0010i	0.729092	+	0.420942i	−0.0889978	+	0.996032i	$0.528366\pi$
$684$		0			0
$685$		−	45.2470i		−	1.72880i
$686$		0			0
$687$	−11.6978	+	12.3546i	−0.446299	+	0.471356i
$688$		0			0
$689$	11.9731	+	6.91265i	0.456137	+	0.263351i
$690$		0			0
$691$	−17.0852	−	29.5924i	−0.649952	−	1.12575i	−0.983134	−	0.182887i	$-0.941456\pi$
$691$	−17.0852	−	29.5924i	−0.649952	−	1.12575i	0.333182	−	0.942862i	$-0.391878\pi$
$692$		0			0
$693$	1.55224	−	13.2033i	0.0589649	−	0.501553i
$694$		0			0
$695$	−1.38978	−	2.40717i	−0.0527173	−	0.0913091i
$696$		0			0
$697$	−0.555213	+	0.961656i	−0.0210302	+	0.0364253i
$698$		0			0
$699$	9.54531	−	10.0812i	0.361037	−	0.381306i
$700$		0			0
$701$	25.6168			0.967533			0.483767	−	0.875197i	$-0.339268\pi$
$701$	25.6168			0.967533			0.483767	+	0.875197i	$0.339268\pi$
$702$		0			0
$703$	−5.43931	−	3.14039i	−0.205147	−	0.118442i
$704$		0			0
$705$	3.96229	−	16.5858i	0.149229	−	0.624658i
$706$		0			0
$707$	−10.0421	−	8.37668i	−0.377673	−	0.315037i
$708$		0			0
$709$	−0.228674	+	0.132025i	−0.00858802	+	0.00495830i	−0.504288	−	0.863536i	$-0.668245\pi$
$709$	−0.228674	+	0.132025i	−0.00858802	+	0.00495830i	0.495700	+	0.868494i	$0.334912\pi$
$710$		0			0
$711$	5.61795	−	11.0871i	0.210689	−	0.415797i
$712$		0			0
$713$			58.6250i			2.19552i
$714$		0			0
$715$	5.71028			0.213552
$716$		0			0
$717$	−10.0016	+	2.97477i	−0.373515	+	0.111095i
$718$		0			0
$719$	19.9630	+	34.5770i	0.744496	+	1.28950i	0.950430	+	0.310939i	$0.100643\pi$
$719$	19.9630	+	34.5770i	0.744496	+	1.28950i	−0.205934	+	0.978566i	$0.566023\pi$
$720$		0			0
$721$	16.7271	+	45.5447i	0.622952	+	1.69617i
$722$		0			0
$723$	−4.12048	+	17.2480i	−0.153242	+	0.641459i
$724$		0			0
$725$	0.806627	−	1.39712i	0.0299574	−	0.0518877i
$726$		0			0
$727$			4.46181i			0.165479i	0.996571	+	0.0827397i	$0.0263670\pi$
$727$			4.46181i			0.165479i	−0.996571	+	0.0827397i	$0.973633\pi$
$728$		0			0
$729$	−4.40255	−	26.6386i	−0.163057	−	0.986617i
$730$		0			0
$731$	−3.24993	−	1.87635i	−0.120203	−	0.0693992i
$732$		0			0
$733$	−3.91514	+	2.26041i	−0.144609	+	0.0834900i	−0.570559	−	0.821257i	$-0.693273\pi$
$733$	−3.91514	+	2.26041i	−0.144609	+	0.0834900i	0.425950	+	0.904747i	$0.359940\pi$
$734$		0			0
$735$	11.9806	+	23.6176i	0.441910	+	0.871148i
$736$		0			0
$737$	−2.07736	+	1.19936i	−0.0765205	+	0.0441791i
$738$		0			0
$739$	0.571921	−	0.990596i	0.0210384	−	0.0364397i	−0.855315	−	0.518109i	$-0.826636\pi$
$739$	0.571921	−	0.990596i	0.0210384	−	0.0364397i	0.876353	+	0.481670i	$0.159969\pi$
$740$		0			0
$741$	10.6855	−	11.2854i	0.392543	−	0.414581i
$742$		0			0
$743$	−13.5335			−0.496495			−0.248248	−	0.968697i	$-0.579855\pi$
$743$	−13.5335			−0.496495			−0.248248	+	0.968697i	$0.579855\pi$
$744$		0			0
$745$	−5.39804	+	9.34968i	−0.197769	+	0.342546i
$746$		0			0
$747$	−14.8618	−	22.7734i	−0.543763	−	0.833237i
$748$		0			0
$749$	−4.03437	−	10.9848i	−0.147413	−	0.401375i
$750$		0			0
$751$	−13.7335	+	7.92906i	−0.501144	+	0.289336i	−0.729186	−	0.684316i	$-0.760101\pi$
$751$	−13.7335	+	7.92906i	−0.501144	+	0.289336i	0.228042	+	0.973651i	$0.426768\pi$
$752$		0			0
$753$	4.92642	+	16.5633i	0.179529	+	0.603600i
$754$		0			0
$755$		−	13.8366i		−	0.503566i
$756$		0			0
$757$			41.0141i			1.49068i	0.666683	+	0.745341i	$0.267713\pi$
$757$			41.0141i			1.49068i	−0.666683	+	0.745341i	$0.732287\pi$
$758$		0			0
$759$	−5.40424	−	18.1698i	−0.196162	−	0.659521i
$760$		0			0
$761$	−8.79472	+	5.07763i	−0.318808	+	0.184064i	−0.650861	−	0.759197i	$-0.725592\pi$
$761$	−8.79472	+	5.07763i	−0.318808	+	0.184064i	0.332053	+	0.943261i	$0.392259\pi$
$762$		0			0
$763$	−13.7961	+	16.5390i	−0.499452	+	0.598753i
$764$		0			0
$765$	−1.15286	−	1.76659i	−0.0416818	−	0.0638712i
$766$		0			0
$767$	−4.83937	+	8.38203i	−0.174740	+	0.302658i
$768$		0			0
$769$	15.2996			0.551719			0.275859	−	0.961198i	$-0.411038\pi$
$769$	15.2996			0.551719			0.275859	+	0.961198i	$0.411038\pi$
$770$		0			0
$771$	23.5903	−	24.9148i	0.849585	−	0.897283i
$772$		0			0
$773$	−18.3453	+	31.7750i	−0.659835	+	1.14287i	0.320823	+	0.947139i	$0.396040\pi$
$773$	−18.3453	+	31.7750i	−0.659835	+	1.14287i	−0.980658	+	0.195728i	$0.937293\pi$
$774$		0			0
$775$	1.77998	−	1.02767i	0.0639388	−	0.0369151i
$776$		0			0
$777$	2.99427	+	4.01262i	0.107419	+	0.143952i
$778$		0			0
$779$	−17.1727	+	9.91466i	−0.615276	+	0.355230i
$780$		0			0
$781$	9.24099	+	5.33529i	0.330669	+	0.190912i
$782$		0			0
$783$	−23.6709	+	27.9040i	−0.845927	+	0.997208i
$784$		0			0
$785$			5.27773i			0.188370i
$786$		0			0
$787$	−14.6430	+	25.3624i	−0.521965	+	0.904071i	0.477708	+	0.878519i	$0.341468\pi$
$787$	−14.6430	+	25.3624i	−0.521965	+	0.904071i	−0.999673	+	0.0255520i	$0.991866\pi$
$788$		0			0
$789$	2.75103	−	11.5156i	0.0979393	−	0.409965i
$790$		0			0
$791$	34.9321	+	6.05473i	1.24204	+	0.215281i
$792$		0			0
$793$	−3.42962	−	5.94027i	−0.121789	−	0.210945i
$794$		0			0
$795$	32.1193	−	9.55326i	1.13915	−	0.338819i
$796$		0			0
$797$	18.4577			0.653805			0.326903	−	0.945058i	$-0.393995\pi$
$797$	18.4577			0.653805			0.326903	+	0.945058i	$0.393995\pi$
$798$		0			0
$799$		−	1.45105i		−	0.0513345i
$800$		0			0
$801$	7.16471	−	14.1396i	0.253153	−	0.499599i
$802$		0			0
$803$	−13.0260	+	7.52059i	−0.459679	+	0.265396i
$804$		0			0
$805$	28.9976	+	24.1885i	1.02203	+	0.852533i
$806$		0			0
$807$	9.72510	−	40.7084i	0.342340	−	1.43301i
$808$		0			0
$809$	12.9060	+	7.45126i	0.453750	+	0.261972i	0.709412	−	0.704794i	$-0.248960\pi$
$809$	12.9060	+	7.45126i	0.453750	+	0.261972i	−0.255663	+	0.966766i	$0.582294\pi$
$810$		0			0
$811$	−29.7496			−1.04465			−0.522325	−	0.852747i	$-0.674935\pi$
$811$	−29.7496			−1.04465			−0.522325	+	0.852747i	$0.674935\pi$
$812$		0			0
$813$	−21.0161	+	22.1960i	−0.737067	+	0.778448i
$814$		0			0
$815$	9.74341	−	16.8761i	0.341297	−	0.591143i
$816$		0			0
$817$	−33.5067	−	58.0353i	−1.17225	−	2.03040i
$818$		0			0
$819$	−11.3790	+	4.89935i	−0.397614	+	0.171197i
$820$		0			0
$821$	7.25813	+	12.5715i	0.253311	+	0.438747i	0.964435	−	0.264319i	$-0.0851472\pi$
$821$	7.25813	+	12.5715i	0.253311	+	0.438747i	−0.711125	+	0.703066i	$0.751814\pi$
$822$		0			0
$823$	42.5817	+	24.5846i	1.48431	+	0.856965i	0.999841	−	0.0178459i	$-0.00568083\pi$
$823$	42.5817	+	24.5846i	1.48431	+	0.856965i	0.484465	+	0.874810i	$0.339014\pi$
$824$		0			0
$825$	−0.456939	+	0.482593i	−0.0159086	+	0.0168017i
$826$		0			0
$827$			0.00653186i			0.000227135i	1.00000		0.000113567i	$3.61496e-5\pi$
$827$			0.00653186i			0.000227135i	−1.00000		0.000113567i	$0.999964\pi$
$828$		0			0
$829$	7.61159	+	4.39455i	0.264361	+	0.152629i	0.626322	−	0.779564i	$-0.284559\pi$
$829$	7.61159	+	4.39455i	0.264361	+	0.152629i	−0.361961	+	0.932193i	$0.617893\pi$
$830$		0			0
$831$	−25.1425	−	6.00645i	−0.872182	−	0.208361i
$832$		0			0
$833$	1.45853	+	1.71781i	0.0505350	+	0.0595184i
$834$		0			0
$835$	−7.65719	−	13.2626i	−0.264988	−	0.458973i
$836$		0			0
$837$	−43.8925	+	15.7091i	−1.51715	+	0.542985i
$838$		0			0
$839$	35.4452			1.22371			0.611853	−	0.790972i	$-0.290425\pi$
$839$	35.4452			1.22371			0.611853	+	0.790972i	$0.290425\pi$
$840$		0			0
$841$	20.5905			0.710017
$842$		0			0
$843$	−6.85818	−	23.0581i	−0.236208	−	0.794164i
$844$		0			0
$845$	11.5369	+	19.9825i	0.396881	+	0.687417i
$846$		0			0
$847$	−20.3518	+	7.47458i	−0.699296	+	0.256829i
$848$		0			0
$849$	2.32511	−	9.73270i	0.0797975	−	0.334025i
$850$		0			0
$851$	6.18262	+	3.56954i	0.211937	+	0.122362i
$852$		0			0
$853$			23.8784i			0.817581i	0.912628	+	0.408791i	$0.134049\pi$
$853$			23.8784i			0.817581i	−0.912628	+	0.408791i	$0.865951\pi$
$854$		0			0
$855$	−2.05562	−	37.6138i	−0.0703006	−	1.28637i
$856$		0			0
$857$	46.6784	+	26.9498i	1.59451	+	0.920588i	0.992520	+	0.122081i	$0.0389567\pi$
$857$	46.6784	+	26.9498i	1.59451	+	0.920588i	0.601985	+	0.798507i	$0.294377\pi$
$858$		0			0
$859$	−9.18799	−	15.9141i	−0.313490	−	0.542981i	0.665625	−	0.746286i	$-0.268165\pi$
$859$	−9.18799	−	15.9141i	−0.313490	−	0.542981i	−0.979115	+	0.203305i	$0.934832\pi$
$860$		0			0
$861$	15.6979	−	1.85262i	0.534982	−	0.0631371i
$862$		0			0
$863$	24.6737	+	42.7360i	0.839901	+	1.45475i	0.889977	+	0.456006i	$0.150721\pi$
$863$	24.6737	+	42.7360i	0.839901	+	1.45475i	−0.0500753	+	0.998745i	$0.515946\pi$
$864$		0			0
$865$	15.5444	−	26.9236i	0.528524	−	0.915431i
$866$		0			0
$867$	21.2509	+	20.1212i	0.721717	+	0.683352i
$868$		0			0
$869$	6.93929			0.235399
$870$		0			0
$871$	1.93589	+	1.11768i	0.0655950	+	0.0378713i
$872$		0			0
$873$	10.6311	−	6.93776i	0.359808	−	0.234808i
$874$		0			0
$875$	5.16082	−	29.7747i	0.174467	−	1.00657i
$876$		0			0
$877$	51.2316	−	29.5786i	1.72997	−	0.998797i	0.840467	−	0.541863i	$-0.182281\pi$
$877$	51.2316	−	29.5786i	1.72997	−	0.998797i	0.889500	−	0.456935i	$-0.151053\pi$
$878$		0			0
$879$	25.9620	−	7.72187i	0.875675	−	0.260452i
$880$		0			0
$881$		−	51.0955i		−	1.72145i	−0.509068	−	0.860726i	$-0.670010\pi$
$881$		−	51.0955i		−	1.72145i	0.509068	−	0.860726i	$-0.329990\pi$
$882$		0			0
$883$	−10.4148			−0.350486			−0.175243	−	0.984525i	$-0.556071\pi$
$883$	−10.4148			−0.350486			−0.175243	+	0.984525i	$0.556071\pi$
$884$		0			0
$885$	6.68799	+	22.4859i	0.224814	+	0.755856i
$886$		0			0
$887$	−12.2631	−	21.2404i	−0.411756	−	0.713183i	0.583326	−	0.812238i	$-0.301751\pi$
$887$	−12.2631	−	21.2404i	−0.411756	−	0.713183i	−0.995082	+	0.0990557i	$0.968418\pi$
$888$		0			0
$889$	−32.6789	−	5.66419i	−1.09601	−	0.189971i
$890$		0			0
$891$	12.1556	−	8.91490i	0.407228	−	0.298660i
$892$		0			0
$893$	12.9560	−	22.4405i	0.433556	−	0.750942i
$894$		0			0
$895$		−	2.71416i		−	0.0907242i
$896$		0			0
$897$	−12.1458	+	12.8277i	−0.405535	+	0.428303i
$898$		0			0
$899$	54.7155	+	31.5900i	1.82487	+	1.05359i
$900$		0			0
$901$	2.46944	−	1.42573i	0.0822688	−	0.0474979i
$902$		0			0
$903$	6.26095	+	53.0511i	0.208351	+	1.76543i
$904$		0			0
$905$	−39.6267	+	22.8785i	−1.31724	+	0.760507i
$906$		0			0
$907$	−14.6718	+	25.4124i	−0.487170	+	0.843803i	−0.999891	−	0.0147518i	$-0.995304\pi$
$907$	−14.6718	+	25.4124i	−0.487170	+	0.843803i	0.512721	+	0.858555i	$0.328638\pi$
$908$		0			0
$909$	−0.809158	−	14.8060i	−0.0268381	−	0.491086i
$910$		0			0
$911$	−21.9953			−0.728738			−0.364369	−	0.931255i	$-0.618715\pi$
$911$	−21.9953			−0.728738			−0.364369	+	0.931255i	$0.618715\pi$
$912$		0			0
$913$	7.59124	−	13.1484i	0.251233	−	0.435149i
$914$		0			0
$915$	−16.1705	−	3.86306i	−0.534579	−	0.127709i
$916$		0			0
$917$	15.6032	+	42.4845i	0.515264	+	1.40296i
$918$		0			0
$919$	32.9464	−	19.0216i	1.08680	−	0.627464i	0.154077	−	0.988059i	$-0.450759\pi$
$919$	32.9464	−	19.0216i	1.08680	−	0.627464i	0.932723	+	0.360594i	$0.117426\pi$
$920$		0			0
$921$	11.9514	−	3.55470i	0.393811	−	0.117131i
$922$		0			0
$923$		−	9.94388i		−	0.327307i
$924$		0			0
$925$		−	0.250290i		−	0.00822948i
$926$		0			0
$927$	−24.8669	+	49.0751i	−0.816737	+	1.61184i
$928$		0			0
$929$	26.6079	−	15.3621i	0.872978	−	0.504014i	0.00464125	−	0.999989i	$-0.498523\pi$
$929$	26.6079	−	15.3621i	0.872978	−	0.504014i	0.868337	+	0.495975i	$0.165189\pi$
$930$		0			0
$931$	7.21830	+	39.5886i	0.236570	+	1.29746i
$932$		0			0
$933$	3.50209	−	14.6594i	0.114653	−	0.479928i
$934$		0			0
$935$	0.588871	−	1.01995i	0.0192581	−	0.0333561i
$936$		0			0
$937$	37.2804			1.21790			0.608949	−	0.793210i	$-0.291592\pi$
$937$	37.2804			1.21790			0.608949	+	0.793210i	$0.291592\pi$
$938$		0			0
$939$	−24.0863	−	22.8059i	−0.786027	−	0.744243i
$940$		0			0
$941$	16.0848	−	27.8596i	0.524348	−	0.908198i	−0.475250	−	0.879851i	$-0.657642\pi$
$941$	16.0848	−	27.8596i	0.524348	−	0.908198i	0.999598	−	0.0283471i	$-0.00902436\pi$
$942$		0			0
$943$	19.5194	−	11.2695i	0.635640	−	0.366987i
$944$		0			0
$945$	−10.3398	+	28.1920i	−0.336353	+	0.917087i
$946$		0			0
$947$	−33.3248	+	19.2401i	−1.08291	+	0.625219i	−0.931680	−	0.363279i	$-0.881657\pi$
$947$	−33.3248	+	19.2401i	−1.08291	+	0.625219i	−0.151231	+	0.988498i	$0.548324\pi$
$948$		0			0
$949$	12.1389	+	7.00842i	0.394046	+	0.227503i
$950$		0			0
$951$	−4.60773	−	4.36279i	−0.149416	−	0.141473i
$952$		0			0
$953$		−	37.1213i		−	1.20248i	−0.799070	−	0.601238i	$-0.794674\pi$
$953$		−	37.1213i		−	1.20248i	0.799070	−	0.601238i	$-0.205326\pi$
$954$		0			0
$955$	26.6737	−	46.2002i	0.863140	−	1.49500i
$956$		0			0
$957$	−19.8702	−	4.74692i	−0.642312	−	0.153446i
$958$		0			0
$959$	−35.1071	+	42.0871i	−1.13367	+	1.35906i
$960$		0			0
$961$	24.7469	+	42.8628i	0.798286	+	1.38267i
$962$		0			0
$963$	5.99757	−	11.8363i	0.193269	−	0.381418i
$964$		0			0
$965$	0.0289458			0.000931799
$966$		0			0
$967$		−	28.7342i		−	0.924030i	−0.886872	−	0.462015i	$-0.847127\pi$
$967$		−	28.7342i		−	0.924030i	0.886872	−	0.462015i	$-0.152873\pi$
$968$		0			0
$969$	−0.913833	−	3.07243i	−0.0293565	−	0.0987006i
$970$		0			0
$971$	17.2557	−	9.96261i	0.553763	−	0.319715i	−0.196875	−	0.980429i	$-0.563079\pi$
$971$	17.2557	−	9.96261i	0.553763	−	0.319715i	0.750638	+	0.660713i	$0.229746\pi$
$972$		0			0
$973$	−0.574998	+	3.31739i	−0.0184336	+	0.106351i
$974$		0			0
$975$	0.602385	+	0.143908i	0.0192918	+	0.00460874i
$976$		0			0
$977$	−11.6105	−	6.70332i	−0.371453	−	0.214458i	0.302640	−	0.953105i	$-0.402132\pi$
$977$	−11.6105	−	6.70332i	−0.371453	−	0.214458i	−0.674093	+	0.738647i	$0.735465\pi$
$978$		0			0
$979$	8.84986			0.282843
$980$		0			0
$981$	−24.3851	+	1.33266i	−0.778555	+	0.0425484i
$982$		0			0
$983$	10.2774	−	17.8010i	0.327799	−	0.567765i	−0.654276	−	0.756256i	$-0.727026\pi$
$983$	10.2774	−	17.8010i	0.327799	−	0.567765i	0.982075	+	0.188491i	$0.0603597\pi$
$984$		0			0
$985$	7.08155	+	12.2656i	0.225637	+	0.390814i
$986$		0			0
$987$	−16.5545	+	12.3532i	−0.526936	+	0.393206i
$988$		0			0
$989$	38.0856	+	65.9661i	1.21105	+	2.09760i
$990$		0			0
$991$	4.87181	+	2.81274i	0.154758	+	0.0893497i	0.575379	−	0.817887i	$-0.304854\pi$
$991$	4.87181	+	2.81274i	0.154758	+	0.0893497i	−0.420621	+	0.907236i	$0.638188\pi$
$992$		0			0
$993$	13.6177	+	12.8938i	0.432144	+	0.409172i
$994$		0			0
$995$		−	11.2743i		−	0.357420i
$996$		0			0
$997$	−2.03245	−	1.17343i	−0.0643683	−	0.0371631i	0.467470	−	0.884009i	$-0.345165\pi$
$997$	−2.03245	−	1.17343i	−0.0643683	−	0.0371631i	−0.531839	+	0.846846i	$0.678499\pi$
$998$		0			0
$999$	−1.01583	+	5.58541i	−0.0321394	+	0.176715i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.bd.a.431.4		56
3.2	odd	2	inner	672.2.bd.a.431.17		56
4.3	odd	2		168.2.v.a.11.2	✓	56
7.2	even	3	inner	672.2.bd.a.527.18		56
8.3	odd	2	inner	672.2.bd.a.431.3		56
8.5	even	2		168.2.v.a.11.9	yes	56
12.11	even	2		168.2.v.a.11.27	yes	56
21.2	odd	6	inner	672.2.bd.a.527.3		56
24.5	odd	2		168.2.v.a.11.20	yes	56
24.11	even	2	inner	672.2.bd.a.431.18		56
28.23	odd	6		168.2.v.a.107.20	yes	56
56.37	even	6		168.2.v.a.107.27	yes	56
56.51	odd	6	inner	672.2.bd.a.527.17		56
84.23	even	6		168.2.v.a.107.9	yes	56
168.107	even	6	inner	672.2.bd.a.527.4		56
168.149	odd	6		168.2.v.a.107.2	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.v.a.11.2	✓	56	4.3	odd	2
168.2.v.a.11.9	yes	56	8.5	even	2
168.2.v.a.11.20	yes	56	24.5	odd	2
168.2.v.a.11.27	yes	56	12.11	even	2
168.2.v.a.107.2	yes	56	168.149	odd	6
168.2.v.a.107.9	yes	56	84.23	even	6
168.2.v.a.107.20	yes	56	28.23	odd	6
168.2.v.a.107.27	yes	56	56.37	even	6
672.2.bd.a.431.3		56	8.3	odd	2	inner
672.2.bd.a.431.4		56	1.1	even	1	trivial
672.2.bd.a.431.17		56	3.2	odd	2	inner
672.2.bd.a.431.18		56	24.11	even	2	inner
672.2.bd.a.527.3		56	21.2	odd	6	inner
672.2.bd.a.527.4		56	168.107	even	6	inner
672.2.bd.a.527.17		56	56.51	odd	6	inner
672.2.bd.a.527.18		56	7.2	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.bd (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.66017 + 0.493786i) q^{3} +(1.09212 + 1.89161i) q^{5} +(0.451847 - 2.60688i) q^{7} +(2.51235 - 1.63954i) q^{9} +(1.45052 + 0.837460i) q^{11} -1.56085i q^{13} +(-2.74716 - 2.60112i) q^{15} +(-0.278795 - 0.160963i) q^{17} +(-2.87437 - 4.97856i) q^{19} +(0.537096 + 4.55099i) q^{21} +(3.26717 + 5.65891i) q^{23} +(0.114544 - 0.198397i) q^{25} +(-3.36136 + 3.96248i) q^{27} +7.04205 q^{29} +(7.76983 + 4.48591i) q^{31} +(-2.82165 - 0.674082i) q^{33} +(5.42467 - 1.99231i) q^{35} +(0.946173 - 0.546273i) q^{37} +(0.770727 + 2.59129i) q^{39} -3.44933i q^{41} +11.6570 q^{43} +(5.84516 + 2.96181i) q^{45} +(2.25371 + 3.90354i) q^{47} +(-6.59167 - 2.35583i) q^{49} +(0.542330 + 0.129561i) q^{51} +(-4.42876 + 7.67084i) q^{53} +3.65843i q^{55} +(7.23030 + 6.84595i) q^{57} +(-5.37016 - 3.10046i) q^{59} +(3.80578 - 2.19727i) q^{61} +(-3.13889 - 7.29023i) q^{63} +(2.95253 - 1.70464i) q^{65} +(-0.716072 + 1.24027i) q^{67} +(-8.21836 - 7.78149i) q^{69} +6.37080 q^{71} +(-4.49012 + 7.77711i) q^{73} +(-0.0921980 + 0.385933i) q^{75} +(2.83858 - 3.40294i) q^{77} +(3.58799 - 2.07153i) q^{79} +(3.62382 - 8.23820i) q^{81} -9.06459i q^{83} -0.703162i q^{85} +(-11.6910 + 3.47726i) q^{87} +(4.57586 - 2.64187i) q^{89} +(-4.06896 - 0.705268i) q^{91} +(-15.1143 - 3.61076i) q^{93} +(6.27833 - 10.8744i) q^{95} +4.23153 q^{97} +(5.01728 - 0.274197i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 2 q^{3} - 2 q^{9} + 4 q^{19} - 16 q^{25} + 8 q^{27} - 14 q^{33} + 16 q^{43} - 16 q^{49} + 34 q^{51} + 4 q^{57} + 36 q^{67} + 4 q^{73} - 10 q^{81} - 72 q^{91} - 32 q^{97} + 44 q^{99}+O(q^{100}) \) 56 * q + 2 * q^3 - 2 * q^9 + 4 * q^19 - 16 * q^25 + 8 * q^27 - 14 * q^33 + 16 * q^43 - 16 * q^49 + 34 * q^51 + 4 * q^57 + 36 * q^67 + 4 * q^73 - 10 * q^81 - 72 * q^91 - 32 * q^97 + 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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