LMFDB - Embedded newform 380.3.bc.a.29.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,3,Mod(29,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 9, 17]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("380.29");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	380.bc (of order $18$, degree $6$, 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:	$10.3542500457$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$20$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			29.3
Character	$\chi$	$=$	380.29
Dual form			380.3.bc.a.249.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.70131 + 3.10577i) q^{3} +(-4.40108 + 2.37286i) q^{5} +(-5.39353 - 3.11396i) q^{7} +(2.49107 - 14.1276i) q^{9} +O(q^{10})$	\(q+(-3.70131 + 3.10577i) q^{3} +(-4.40108 + 2.37286i) q^{5} +(-5.39353 - 3.11396i) q^{7} +(2.49107 - 14.1276i) q^{9} +(-5.50250 - 9.53061i) q^{11} +(2.18533 + 1.83371i) q^{13} +(8.92023 - 22.4514i) q^{15} +(-10.0440 + 1.77103i) q^{17} +(6.50913 + 17.8502i) q^{19} +(29.6344 - 5.22534i) q^{21} +(11.1915 + 30.7484i) q^{23} +(13.7391 - 20.8863i) q^{25} +(12.9140 + 22.3677i) q^{27} +(35.2028 + 6.20721i) q^{29} +(-32.0389 - 18.4977i) q^{31} +(49.9664 + 18.1863i) q^{33} +(31.1264 + 0.906694i) q^{35} +19.2462 q^{37} -13.7837 q^{39} +(20.3488 + 24.2508i) q^{41} +(16.3688 - 44.9730i) q^{43} +(22.5593 + 68.0876i) q^{45} +(-73.4155 - 12.9451i) q^{47} +(-5.10654 - 8.84478i) q^{49} +(31.6756 - 37.7495i) q^{51} +(68.3938 - 24.8933i) q^{53} +(46.8318 + 28.8884i) q^{55} +(-79.5311 - 45.8535i) q^{57} +(-1.75422 + 0.309316i) q^{59} +(99.4120 - 36.1830i) q^{61} +(-57.4283 + 68.4404i) q^{63} +(-13.9690 - 2.88483i) q^{65} +(-2.73000 + 15.4826i) q^{67} +(-136.921 - 79.0513i) q^{69} +(29.4037 - 80.7861i) q^{71} +(0.964646 + 1.14962i) q^{73} +(14.0154 + 119.977i) q^{75} +68.5382i q^{77} +(23.0023 + 27.4131i) q^{79} +(4.05556 + 1.47610i) q^{81} +(-96.0430 - 55.4504i) q^{83} +(40.0021 - 31.6275i) q^{85} +(-149.575 + 86.3571i) q^{87} +(-9.32264 + 11.1103i) q^{89} +(-6.07655 - 16.6952i) q^{91} +(176.036 - 31.0398i) q^{93} +(-71.0033 - 63.1152i) q^{95} +(-17.0891 - 96.9169i) q^{97} +(-148.352 + 53.9955i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q+O(q^{10}) $ 120 * q	$ 120 q + 30 q^{11} - 3 q^{15} + 24 q^{19} - 72 q^{21} + 150 q^{25} + 60 q^{29} + 171 q^{35} + 24 q^{39} - 12 q^{41} - 90 q^{45} + 270 q^{49} - 144 q^{51} + 3 q^{55} + 84 q^{59} + 396 q^{61} - 405 q^{65} + 420 q^{71} + 96 q^{79} - 120 q^{81} + 30 q^{85} + 12 q^{89} - 84 q^{91} + 267 q^{95} + 324 q^{99}+O(q^{100}) $ 120 * q + 30 * q^11 - 3 * q^15 + 24 * q^19 - 72 * q^21 + 150 * q^25 + 60 * q^29 + 171 * q^35 + 24 * q^39 - 12 * q^41 - 90 * q^45 + 270 * q^49 - 144 * q^51 + 3 * q^55 + 84 * q^59 + 396 * q^61 - 405 * q^65 + 420 * q^71 + 96 * q^79 - 120 * q^81 + 30 * q^85 + 12 * q^89 - 84 * q^91 + 267 * q^95 + 324 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−3.70131	+	3.10577i	−1.23377	+	1.03526i	−0.235786	+	0.971805i	$0.575766\pi$
$3$	−3.70131	+	3.10577i	−1.23377	+	1.03526i	−0.997985	+	0.0634514i	$0.979789\pi$
$4$		0			0
$5$	−4.40108	+	2.37286i	−0.880217	+	0.474572i
$5$	−4.40108	+	2.37286i	−0.880217	+	0.474572i
$6$		0			0
$7$	−5.39353	−	3.11396i	−0.770505	−	0.444851i	0.0625499	−	0.998042i	$-0.480077\pi$
$7$	−5.39353	−	3.11396i	−0.770505	−	0.444851i	−0.833055	+	0.553191i	$0.813410\pi$
$8$		0			0
$9$	2.49107	−	14.1276i	0.276786	−	1.56973i
$10$		0			0
$11$	−5.50250	−	9.53061i	−0.500227	−	0.866419i	−1.00000		0.000262521i	$-0.999916\pi$
$11$	−5.50250	−	9.53061i	−0.500227	−	0.866419i	0.499773	−	0.866157i	$-0.333417\pi$
$12$		0			0
$13$	2.18533	+	1.83371i	0.168102	+	0.141055i	0.722958	−	0.690892i	$-0.242782\pi$
$13$	2.18533	+	1.83371i	0.168102	+	0.141055i	−0.554856	+	0.831947i	$0.687226\pi$
$14$		0			0
$15$	8.92023	−	22.4514i	0.594682	−	1.49676i
$16$		0			0
$17$	−10.0440	+	1.77103i	−0.590824	+	0.104178i	−0.461064	−	0.887367i	$-0.652532\pi$
$17$	−10.0440	+	1.77103i	−0.590824	+	0.104178i	−0.129761	+	0.991545i	$0.541421\pi$
$18$		0			0
$19$	6.50913	+	17.8502i	0.342586	+	0.939487i
$19$	6.50913	+	17.8502i	0.342586	+	0.939487i
$20$		0			0
$21$	29.6344	−	5.22534i	1.41116	−	0.248826i
$22$		0			0
$23$	11.1915	+	30.7484i	0.486588	+	1.33689i	0.903751	+	0.428058i	$0.140802\pi$
$23$	11.1915	+	30.7484i	0.486588	+	1.33689i	−0.417164	+	0.908831i	$0.636976\pi$
$24$		0			0
$25$	13.7391	−	20.8863i	0.549563	−	0.835452i
$26$		0			0
$27$	12.9140	+	22.3677i	0.478297	+	0.828434i
$28$		0			0
$29$	35.2028	+	6.20721i	1.21389	+	0.214042i	0.743694	−	0.668520i	$-0.233072\pi$
$29$	35.2028	+	6.20721i	1.21389	+	0.214042i	0.470197	+	0.882562i	$0.344183\pi$
$30$		0			0
$31$	−32.0389	−	18.4977i	−1.03351	−	0.596699i	−0.115524	−	0.993305i	$-0.536855\pi$
$31$	−32.0389	−	18.4977i	−1.03351	−	0.596699i	−0.917989	+	0.396605i	$0.870188\pi$
$32$		0			0
$33$	49.9664	+	18.1863i	1.51413	+	0.551099i
$34$		0			0
$35$	31.1264	+	0.906694i	0.889325	+	0.0259056i
$36$		0			0
$37$	19.2462			0.520166			0.260083	−	0.965586i	$-0.416250\pi$
$37$	19.2462			0.520166			0.260083	+	0.965586i	$0.416250\pi$
$38$		0			0
$39$	−13.7837			−0.353427
$40$		0			0
$41$	20.3488	+	24.2508i	0.496313	+	0.591483i	0.954811	−	0.297212i	$-0.0960569\pi$
$41$	20.3488	+	24.2508i	0.496313	+	0.591483i	−0.458498	+	0.888695i	$0.651613\pi$
$42$		0			0
$43$	16.3688	−	44.9730i	0.380671	−	1.04588i	−0.590404	−	0.807108i	$-0.701031\pi$
$43$	16.3688	−	44.9730i	0.380671	−	1.04588i	0.971075	−	0.238777i	$-0.0767463\pi$
$44$		0			0
$45$	22.5593	+	68.0876i	0.501318	+	1.51306i
$46$		0			0
$47$	−73.4155	−	12.9451i	−1.56203	−	0.275428i	−0.675241	−	0.737598i	$-0.735960\pi$
$47$	−73.4155	−	12.9451i	−1.56203	−	0.275428i	−0.886792	+	0.462169i	$0.847071\pi$
$48$		0			0
$49$	−5.10654	−	8.84478i	−0.104215	−	0.180506i
$50$		0			0
$51$	31.6756	−	37.7495i	0.621090	−	0.740187i
$52$		0			0
$53$	68.3938	−	24.8933i	1.29045	−	0.469685i	0.396574	−	0.918003i	$-0.370199\pi$
$53$	68.3938	−	24.8933i	1.29045	−	0.469685i	0.893874	+	0.448318i	$0.147977\pi$
$54$		0			0
$55$	46.8318	+	28.8884i	0.851487	+	0.525243i
$56$		0			0
$57$	−79.5311	−	45.8535i	−1.39528	−	0.804447i
$58$		0			0
$59$	−1.75422	+	0.309316i	−0.0297325	+	0.00524264i	−0.188495	−	0.982074i	$-0.560361\pi$
$59$	−1.75422	+	0.309316i	−0.0297325	+	0.00524264i	0.158762	+	0.987317i	$0.449250\pi$
$60$		0			0
$61$	99.4120	−	36.1830i	1.62971	−	0.593164i	0.644509	−	0.764596i	$-0.277062\pi$
$61$	99.4120	−	36.1830i	1.62971	−	0.593164i	0.985196	+	0.171432i	$0.0548395\pi$
$62$		0			0
$63$	−57.4283	+	68.4404i	−0.911561	+	1.08636i
$64$		0			0
$65$	−13.9690	−	2.88483i	−0.214907	−	0.0443820i
$66$		0			0
$67$	−2.73000	+	15.4826i	−0.0407463	+	0.231084i	−0.998379	−	0.0569071i	$-0.981876\pi$
$67$	−2.73000	+	15.4826i	−0.0407463	+	0.231084i	0.957633	+	0.287991i	$0.0929872\pi$
$68$		0			0
$69$	−136.921	−	79.0513i	−1.98436	−	1.14567i
$70$		0			0
$71$	29.4037	−	80.7861i	0.414137	−	1.13783i	−0.540833	−	0.841130i	$-0.681891\pi$
$71$	29.4037	−	80.7861i	0.414137	−	1.13783i	0.954970	−	0.296702i	$-0.0958869\pi$
$72$		0			0
$73$	0.964646	+	1.14962i	0.0132143	+	0.0157482i	0.772611	−	0.634880i	$-0.218950\pi$
$73$	0.964646	+	1.14962i	0.0132143	+	0.0157482i	−0.759397	+	0.650628i	$0.774506\pi$
$74$		0			0
$75$	14.0154	+	119.977i	0.186872	+	1.59970i
$76$		0			0
$77$			68.5382i			0.890107i
$78$		0			0
$79$	23.0023	+	27.4131i	0.291168	+	0.347001i	0.891722	−	0.452584i	$-0.149498\pi$
$79$	23.0023	+	27.4131i	0.291168	+	0.347001i	−0.600554	+	0.799584i	$0.705053\pi$
$80$		0			0
$81$	4.05556	+	1.47610i	0.0500687	+	0.0182235i
$82$		0			0
$83$	−96.0430	−	55.4504i	−1.15714	−	0.668077i	−0.206526	−	0.978441i	$-0.566216\pi$
$83$	−96.0430	−	55.4504i	−1.15714	−	0.668077i	−0.950618	+	0.310364i	$0.899549\pi$
$84$		0			0
$85$	40.0021	−	31.6275i	0.470613	−	0.372088i
$86$		0			0
$87$	−149.575	+	86.3571i	−1.71925	+	0.992610i
$88$		0			0
$89$	−9.32264	+	11.1103i	−0.104749	+	0.124835i	−0.815872	−	0.578233i	$-0.803742\pi$
$89$	−9.32264	+	11.1103i	−0.104749	+	0.124835i	0.711123	+	0.703068i	$0.248187\pi$
$90$		0			0
$91$	−6.07655	−	16.6952i	−0.0667753	−	0.183464i
$92$		0			0
$93$	176.036	−	31.0398i	1.89286	−	0.333762i
$94$		0			0
$95$	−71.0033	−	63.1152i	−0.747404	−	0.664370i
$96$		0			0
$97$	−17.0891	−	96.9169i	−0.176176	−	0.999143i	−0.936778	−	0.349925i	$-0.886207\pi$
$97$	−17.0891	−	96.9169i	−0.176176	−	0.999143i	0.760602	−	0.649218i	$-0.224904\pi$
$98$		0			0
$99$	−148.352	+	53.9955i	−1.49850	+	0.545410i
$100$		0			0
$101$	−10.6708	−	8.95385i	−0.105651	−	0.0886520i	0.588432	−	0.808547i	$-0.299746\pi$
$101$	−10.6708	−	8.95385i	−0.105651	−	0.0886520i	−0.694083	+	0.719895i	$0.744190\pi$
$102$		0			0
$103$	−20.5158	−	35.5344i	−0.199182	−	0.344994i	0.749081	−	0.662478i	$-0.230495\pi$
$103$	−20.5158	−	35.5344i	−0.199182	−	0.344994i	−0.948264	+	0.317484i	$0.897162\pi$
$104$		0			0
$105$	−118.024	+	93.3154i	−1.12404	+	0.888718i
$106$		0			0
$107$	22.8431	−	39.5654i	0.213487	−	0.369770i	−0.739317	−	0.673358i	$-0.764851\pi$
$107$	22.8431	−	39.5654i	0.213487	−	0.369770i	0.952803	+	0.303588i	$0.0981846\pi$
$108$		0			0
$109$	28.7117	−	78.8848i	0.263410	−	0.723714i	−0.735521	−	0.677501i	$-0.763063\pi$
$109$	28.7117	−	78.8848i	0.263410	−	0.723714i	0.998932	−	0.0462122i	$-0.0147150\pi$
$110$		0			0
$111$	−71.2360	+	59.7741i	−0.641766	+	0.538506i
$112$		0			0
$113$	−100.441			−0.888859			−0.444430	−	0.895814i	$-0.646594\pi$
$113$	−100.441			−0.888859			−0.444430	+	0.895814i	$0.646594\pi$
$114$		0			0
$115$	−122.217	−	108.771i	−1.06275	−	0.945831i
$116$		0			0
$117$	31.3497	−	26.3055i	0.267946	−	0.224833i
$118$		0			0
$119$	59.6876	+	21.7245i	0.501577	+	0.182559i
$120$		0			0
$121$	−0.0550269	+	0.0953094i	−0.000454768	+	0.000787681i
$122$		0			0
$123$	−150.635	−	26.5610i	−1.22467	−	0.215943i
$124$		0			0
$125$	−10.9066	+	124.523i	−0.0872526	+	0.996186i
$126$		0			0
$127$	−97.0632	−	81.4457i	−0.764277	−	0.641304i	0.174960	−	0.984576i	$-0.444021\pi$
$127$	−97.0632	−	81.4457i	−0.764277	−	0.641304i	−0.939236	+	0.343271i	$0.888465\pi$
$128$		0			0
$129$	79.0897	+	217.297i	0.613098	+	1.68447i
$130$		0			0
$131$	44.6821	+	253.405i	0.341085	+	1.93439i	0.355964	+	0.934500i	$0.384153\pi$
$131$	44.6821	+	253.405i	0.341085	+	1.93439i	−0.0148787	+	0.999889i	$0.504736\pi$
$132$		0			0
$133$	20.4777	−	116.545i	0.153968	−	0.876278i
$134$		0			0
$135$	−109.911	−	67.7991i	−0.814157	−	0.502216i
$136$		0			0
$137$	36.1609	+	99.3513i	0.263948	+	0.725192i	0.998892	+	0.0470637i	$0.0149864\pi$
$137$	36.1609	+	99.3513i	0.263948	+	0.725192i	−0.734944	+	0.678128i	$0.762791\pi$
$138$		0			0
$139$	177.969	+	149.334i	1.28035	+	1.07434i	0.993195	+	0.116460i	$0.0371546\pi$
$139$	177.969	+	149.334i	1.28035	+	1.07434i	0.287157	+	0.957884i	$0.407290\pi$
$140$		0			0
$141$	311.938	−	180.098i	2.21233	−	1.27729i
$142$		0			0
$143$	5.45159	−	30.9175i	0.0381230	−	0.216206i
$144$		0			0
$145$	−169.660	+	56.2129i	−1.17007	+	0.387675i
$146$		0			0
$147$	46.3707	+	16.8776i	0.315447	+	0.114813i
$148$		0			0
$149$	−99.6722	+	83.6349i	−0.668941	+	0.561308i	−0.912752	−	0.408515i	$-0.866047\pi$
$149$	−99.6722	+	83.6349i	−0.668941	+	0.561308i	0.243811	+	0.969823i	$0.421602\pi$
$150$		0			0
$151$		−	83.6396i		−	0.553905i	−0.960884	−	0.276952i	$-0.910676\pi$
$151$		−	83.6396i		−	0.553905i	0.960884	−	0.276952i	$-0.0893244\pi$
$152$		0			0
$153$			146.309i			0.956270i
$154$		0			0
$155$	184.898	+	5.38599i	1.19289	+	0.0347483i
$156$		0			0
$157$	48.8046	−	134.090i	0.310857	−	0.854074i	−0.681627	−	0.731700i	$-0.738727\pi$
$157$	48.8046	−	134.090i	0.310857	−	0.854074i	0.992484	−	0.122374i	$-0.0390506\pi$
$158$		0			0
$159$	−175.834	+	304.553i	−1.10587	+	1.91543i
$160$		0			0
$161$	35.3875	−	200.693i	0.219798	−	1.24654i
$162$		0			0
$163$	121.449	−	70.1187i	0.745087	−	0.430176i	−0.0788290	−	0.996888i	$-0.525118\pi$
$163$	121.449	−	70.1187i	0.745087	−	0.430176i	0.823916	+	0.566712i	$0.191785\pi$
$164$		0			0
$165$	−263.060	+	38.5238i	−1.59430	+	0.233478i
$166$		0			0
$167$	272.922	−	99.3354i	1.63426	−	0.594823i	0.648240	−	0.761436i	$-0.275505\pi$
$167$	272.922	−	99.3354i	1.63426	−	0.594823i	0.986022	+	0.166613i	$0.0532832\pi$
$168$		0			0
$169$	−27.9334	−	158.418i	−0.165286	−	0.937385i
$170$		0			0
$171$	268.395	−	47.4919i	1.56956	−	0.277731i
$172$		0			0
$173$	−13.5180	−	76.6642i	−0.0781385	−	0.443146i	−0.998627	−	0.0523768i	$-0.983320\pi$
$173$	−13.5180	−	76.6642i	−0.0781385	−	0.443146i	0.920489	−	0.390769i	$-0.127791\pi$
$174$		0			0
$175$	−139.141	+	69.8681i	−0.795093	+	0.399246i
$176$		0			0
$177$	5.53224	−	6.59307i	0.0312556	−	0.0372490i
$178$		0			0
$179$	−117.256	+	67.6978i	−0.655061	+	0.378200i	−0.790393	−	0.612601i	$-0.790123\pi$
$179$	−117.256	+	67.6978i	−0.655061	+	0.378200i	0.135331	+	0.990800i	$0.456790\pi$
$180$		0			0
$181$	−338.236	−	59.6401i	−1.86871	−	0.329503i	−0.879485	−	0.475927i	$-0.842113\pi$
$181$	−338.236	−	59.6401i	−1.86871	−	0.329503i	−0.989222	+	0.146424i	$0.953224\pi$
$182$		0			0
$183$	−255.579	+	442.675i	−1.39661	+	2.41899i
$184$		0			0
$185$	−84.7039	+	45.6684i	−0.457859	+	0.246856i
$186$		0			0
$187$	72.1462	+	85.9805i	0.385808	+	0.459789i
$188$		0			0
$189$		−	160.855i		−	0.851083i
$190$		0			0
$191$	149.468			0.782558			0.391279	−	0.920272i	$-0.372033\pi$
$191$	149.468			0.782558			0.391279	+	0.920272i	$0.372033\pi$
$192$		0			0
$193$	71.4194	−	59.9280i	0.370049	−	0.310508i	−0.438732	−	0.898618i	$-0.644572\pi$
$193$	71.4194	−	59.9280i	0.370049	−	0.310508i	0.808781	+	0.588110i	$0.200128\pi$
$194$		0			0
$195$	60.6631	−	32.7067i	0.311093	−	0.167727i
$196$		0			0
$197$	136.779	+	78.9693i	0.694309	+	0.400859i	0.805224	−	0.592970i	$-0.202045\pi$
$197$	136.779	+	78.9693i	0.694309	+	0.400859i	−0.110915	+	0.993830i	$0.535378\pi$
$198$		0			0
$199$	15.2690	−	86.5949i	0.0767288	−	0.435150i	−0.922108	−	0.386932i	$-0.873535\pi$
$199$	15.2690	−	86.5949i	0.0767288	−	0.435150i	0.998837	−	0.0482180i	$-0.0153542\pi$
$200$		0			0
$201$	−37.9808	−	65.7847i	−0.188959	−	0.327287i
$202$		0			0
$203$	−170.539	−	143.099i	−0.840092	−	0.704921i
$204$		0			0
$205$	−147.101	−	58.4449i	−0.717564	−	0.285097i
$206$		0			0
$207$	462.280	−	81.5124i	2.23324	−	0.393780i
$208$		0			0
$209$	134.307	−	160.257i	0.642618	−	0.766780i
$210$		0			0
$211$	312.360	−	55.0775i	1.48038	−	0.261031i	0.625649	−	0.780105i	$-0.284834\pi$
$211$	312.360	−	55.0775i	1.48038	−	0.261031i	0.854729	+	0.519074i	$0.173723\pi$
$212$		0			0
$213$	142.071	+	390.336i	0.666998	+	1.83256i
$214$		0			0
$215$	34.6740	+	236.771i	0.161275	+	1.10126i
$216$		0			0
$217$	115.202	+	199.536i	0.530885	+	0.919519i
$218$		0			0
$219$	−7.14091	−	1.25914i	−0.0326069	−	0.00574948i
$220$		0			0
$221$	−25.1970	−	14.5475i	−0.114014	−	0.0658258i
$222$		0			0
$223$	−310.807	−	113.124i	−1.39375	−	0.507284i	−0.467435	−	0.884028i	$-0.654822\pi$
$223$	−310.807	−	113.124i	−1.39375	−	0.507284i	−0.926318	+	0.376743i	$0.877044\pi$
$224$		0			0
$225$	−260.848	−	246.129i	−1.15932	−	1.09391i
$226$		0			0
$227$	5.57972			0.0245803			0.0122901	−	0.999924i	$-0.496088\pi$
$227$	5.57972			0.0245803			0.0122901	+	0.999924i	$0.496088\pi$
$228$		0			0
$229$	−244.828			−1.06912			−0.534559	−	0.845131i	$-0.679522\pi$
$229$	−244.828			−1.06912			−0.534559	+	0.845131i	$0.679522\pi$
$230$		0			0
$231$	−212.864	−	253.681i	−0.921489	−	1.09819i
$232$		0			0
$233$	18.3000	−	50.2789i	0.0785408	−	0.215789i	−0.894208	−	0.447653i	$-0.852260\pi$
$233$	18.3000	−	50.2789i	0.0785408	−	0.215789i	0.972748	+	0.231864i	$0.0744823\pi$
$234$		0			0
$235$	353.825	−	117.232i	1.50564	−	0.498860i
$236$		0			0
$237$	−170.277	−	30.0245i	−0.718470	−	0.126686i
$238$		0			0
$239$	−187.445	−	324.665i	−0.784290	−	1.35843i	−0.929422	−	0.369018i	$-0.879694\pi$
$239$	−187.445	−	324.665i	−0.784290	−	1.35843i	0.145132	−	0.989412i	$-0.453639\pi$
$240$		0			0
$241$	112.767	−	134.391i	0.467914	−	0.557639i	−0.479544	−	0.877518i	$-0.659198\pi$
$241$	112.767	−	134.391i	0.467914	−	0.557639i	0.947458	+	0.319879i	$0.103642\pi$
$242$		0			0
$243$	−238.029	+	86.6355i	−0.979543	+	0.356525i
$244$		0			0
$245$	43.4617	+	26.8095i	0.177395	+	0.109427i
$246$		0			0
$247$	−18.5076	+	50.9445i	−0.0749294	+	0.206253i
$248$		0			0
$249$	527.701	−	93.0480i	2.11928	−	0.373687i
$250$		0			0
$251$	290.782	−	105.836i	1.15849	−	0.421657i	0.309935	−	0.950758i	$-0.399693\pi$
$251$	290.782	−	105.836i	1.15849	−	0.421657i	0.848559	+	0.529100i	$0.177471\pi$
$252$		0			0
$253$	231.470	−	275.855i	0.914902	−	1.09034i
$254$		0			0
$255$	−49.8327	+	241.301i	−0.195422	+	0.946277i
$256$		0			0
$257$	−78.4041	+	444.652i	−0.305075	+	1.73016i	0.318079	+	0.948064i	$0.396962\pi$
$257$	−78.4041	+	444.652i	−0.305075	+	1.73016i	−0.623154	+	0.782099i	$0.714149\pi$
$258$		0			0
$259$	−103.805	−	59.9317i	−0.400791	−	0.231397i
$260$		0			0
$261$	175.386	−	481.868i	0.671976	−	1.84624i
$262$		0			0
$263$	31.9739	+	38.1050i	0.121574	+	0.144886i	0.823398	−	0.567464i	$-0.192075\pi$
$263$	31.9739	+	38.1050i	0.121574	+	0.144886i	−0.701824	+	0.712350i	$0.747631\pi$
$264$		0			0
$265$	−241.938	+	271.846i	−0.912975	+	1.02584i
$266$		0			0
$267$		−	70.0766i		−	0.262459i
$268$		0			0
$269$	−121.517	−	144.819i	−0.451737	−	0.538359i	0.491325	−	0.870976i	$-0.336513\pi$
$269$	−121.517	−	144.819i	−0.451737	−	0.538359i	−0.943062	+	0.332617i	$0.892068\pi$
$270$		0			0
$271$	−161.727	−	58.8637i	−0.596778	−	0.217209i	0.0259301	−	0.999664i	$-0.491745\pi$
$271$	−161.727	−	58.8637i	−0.596778	−	0.217209i	−0.622708	+	0.782454i	$0.713968\pi$
$272$		0			0
$273$	74.3426	+	42.9217i	0.272317	+	0.157223i
$274$		0			0
$275$	−274.659	−	16.0149i	−0.998758	−	0.0582360i
$276$		0			0
$277$	309.467	−	178.671i	1.11721	−	0.645021i	0.176523	−	0.984297i	$-0.443515\pi$
$277$	309.467	−	178.671i	1.11721	−	0.645021i	0.940687	+	0.339275i	$0.110182\pi$
$278$		0			0
$279$	−341.139	+	406.553i	−1.22272	+	1.45718i
$280$		0			0
$281$	155.851	+	428.198i	0.554631	+	1.52384i	0.827318	+	0.561734i	$0.189866\pi$
$281$	155.851	+	428.198i	0.554631	+	1.52384i	−0.272686	+	0.962103i	$0.587912\pi$
$282$		0			0
$283$	353.971	−	62.4146i	1.25078	−	0.220546i	0.491250	−	0.871018i	$-0.336540\pi$
$283$	353.971	−	62.4146i	1.25078	−	0.220546i	0.759530	+	0.650472i	$0.225429\pi$
$284$		0			0
$285$	458.827	+	13.0890i	1.60992	+	0.0459262i
$286$		0			0
$287$	−34.2362	−	194.163i	−0.119290	−	0.676526i
$288$		0			0
$289$	−173.826	+	63.2673i	−0.601473	+	0.218918i
$290$		0			0
$291$	364.253	+	305.645i	1.25173	+	1.05033i
$292$		0			0
$293$	69.1119	+	119.705i	0.235877	+	0.408551i	0.959527	−	0.281616i	$-0.0908705\pi$
$293$	69.1119	+	119.705i	0.235877	+	0.408551i	−0.723650	+	0.690167i	$0.757537\pi$
$294$		0			0
$295$	6.98650	−	5.52384i	0.0236830	−	0.0187249i
$296$		0			0
$297$	142.119	−	246.157i	0.478514	−	0.828811i
$298$		0			0
$299$	−31.9265	+	87.7175i	−0.106778	+	0.293369i
$300$		0			0
$301$	−228.330	+	191.592i	−0.758572	+	0.636517i
$302$		0			0
$303$	67.3045			0.222127
$304$		0			0
$305$	−351.663	+	395.135i	−1.15299	+	1.29553i
$306$		0			0
$307$	161.450	−	135.473i	0.525895	−	0.441279i	−0.340786	−	0.940141i	$-0.610693\pi$
$307$	161.450	−	135.473i	0.525895	−	0.441279i	0.866681	+	0.498862i	$0.166249\pi$
$308$		0			0
$309$	186.297	+	67.8065i	0.602903	+	0.219439i
$310$		0			0
$311$	265.110	−	459.184i	0.852444	−	1.47648i	−0.0265526	−	0.999647i	$-0.508453\pi$
$311$	265.110	−	459.184i	0.852444	−	1.47648i	0.878996	−	0.476828i	$-0.158214\pi$
$312$		0			0
$313$	411.512	+	72.5606i	1.31473	+	0.231823i	0.786666	−	0.617379i	$-0.211806\pi$
$313$	411.512	+	72.5606i	1.31473	+	0.231823i	0.528068	+	0.849202i	$0.322917\pi$
$314$		0			0
$315$	90.3474	−	437.482i	0.286817	−	1.38883i
$316$		0			0
$317$	102.814	+	86.2708i	0.324333	+	0.272148i	0.790386	−	0.612609i	$-0.209880\pi$
$317$	102.814	+	86.2708i	0.324333	+	0.272148i	−0.466053	+	0.884757i	$0.654324\pi$
$318$		0			0
$319$	−134.545	−	369.660i	−0.421772	−	1.15881i
$320$		0			0
$321$	38.3316	+	217.389i	0.119413	+	0.677225i
$322$		0			0
$323$	−96.9911	−	167.760i	−0.300282	−	0.519381i
$324$		0			0
$325$	68.3238	−	20.4500i	0.210227	−	0.0629230i
$326$		0			0
$327$	138.727	+	381.149i	0.424241	+	1.16559i
$328$		0			0
$329$	355.658	+	298.433i	1.08103	+	0.907091i
$330$		0			0
$331$	−77.0531	+	44.4866i	−0.232789	+	0.134401i	−0.611858	−	0.790968i	$-0.709578\pi$
$331$	−77.0531	+	44.4866i	−0.232789	+	0.134401i	0.379069	+	0.925368i	$0.376244\pi$
$332$		0			0
$333$	47.9436	−	271.901i	0.143975	−	0.816521i
$334$		0			0
$335$	−24.7231	−	74.6182i	−0.0738002	−	0.222741i
$336$		0			0
$337$	−239.236	−	87.0749i	−0.709900	−	0.258383i	−0.0382682	−	0.999268i	$-0.512184\pi$
$337$	−239.236	−	87.0749i	−0.709900	−	0.258383i	−0.671632	+	0.740885i	$0.734406\pi$
$338$		0			0
$339$	371.764	−	311.947i	1.09665	−	0.920197i
$340$		0			0
$341$			407.134i			1.19394i
$342$		0			0
$343$			368.774i			1.07514i
$344$		0			0
$345$	790.178	+	23.0175i	2.29037	+	0.0667173i
$346$		0			0
$347$	−101.149	+	277.905i	−0.291496	+	0.800879i	0.704352	+	0.709851i	$0.251238\pi$
$347$	−101.149	+	277.905i	−0.291496	+	0.800879i	−0.995848	+	0.0910283i	$0.970985\pi$
$348$		0			0
$349$	−65.4118	+	113.297i	−0.187426	+	0.324632i	−0.944391	−	0.328823i	$-0.893348\pi$
$349$	−65.4118	+	113.297i	−0.187426	+	0.324632i	0.756965	+	0.653455i	$0.226681\pi$
$350$		0			0
$351$	−12.7945	+	72.5614i	−0.0364517	+	0.206728i
$352$		0			0
$353$	197.288	−	113.904i	0.558888	−	0.322674i	−0.193811	−	0.981039i	$-0.562085\pi$
$353$	197.288	−	113.904i	0.558888	−	0.322674i	0.752699	+	0.658365i	$0.228751\pi$
$354$		0			0
$355$	62.2857	+	425.317i	0.175453	+	1.19808i
$356$		0			0
$357$	−288.394	+	104.967i	−0.807826	+	0.294025i
$358$		0			0
$359$	46.7510	+	265.138i	0.130226	+	0.738547i	0.978066	+	0.208295i	$0.0667914\pi$
$359$	46.7510	+	265.138i	0.130226	+	0.738547i	−0.847840	+	0.530252i	$0.822097\pi$
$360$		0			0
$361$	−276.262	+	232.379i	−0.765270	+	0.643709i
$362$		0			0
$363$	−0.0923373	−	0.523671i	−0.000254373	−	0.00144262i
$364$		0			0
$365$	−6.97338	−	2.77061i	−0.0191051	−	0.00759070i
$366$		0			0
$367$	−131.716	+	156.973i	−0.358899	+	0.427719i	−0.915036	−	0.403371i	$-0.867838\pi$
$367$	−131.716	+	156.973i	−0.358899	+	0.427719i	0.556138	+	0.831090i	$0.312283\pi$
$368$		0			0
$369$	393.295	−	227.069i	1.06584	−	0.615364i
$370$		0			0
$371$	−446.401	−	78.7125i	−1.20324	−	0.212163i
$372$		0			0
$373$	144.014	−	249.440i	0.386098	−	0.668741i	−0.605823	−	0.795599i	$-0.707156\pi$
$373$	144.014	−	249.440i	0.386098	−	0.668741i	0.991921	+	0.126859i	$0.0404895\pi$
$374$		0			0
$375$	−346.372	−	494.773i	−0.923659	−	1.31939i
$376$		0			0
$377$	65.5476	+	78.1166i	0.173866	+	0.207206i
$378$		0			0
$379$			374.063i			0.986975i	0.869753	+	0.493487i	$0.164278\pi$
$379$			374.063i			0.986975i	−0.869753	+	0.493487i	$0.835722\pi$
$380$		0			0
$381$	612.212			1.60686
$382$		0			0
$383$	4.66590	−	3.91515i	0.0121825	−	0.0102223i	−0.636676	−	0.771131i	$-0.719691\pi$
$383$	4.66590	−	3.91515i	0.0121825	−	0.0102223i	0.648859	+	0.760909i	$0.275247\pi$
$384$		0			0
$385$	−162.632	−	301.642i	−0.422420	−	0.783487i
$386$		0			0
$387$	−594.584	−	343.283i	−1.53639	−	0.887037i
$388$		0			0
$389$	30.4427	−	172.649i	0.0782589	−	0.443828i	−0.920350	−	0.391096i	$-0.872096\pi$
$389$	30.4427	−	172.649i	0.0782589	−	0.443828i	0.998609	−	0.0527320i	$-0.0167929\pi$
$390$		0			0
$391$	−166.864	−	289.017i	−0.426763	−	0.739174i
$392$		0			0
$393$	−952.400	−	799.158i	−2.42341	−	2.03348i
$394$		0			0
$395$	−166.282	−	66.0660i	−0.420968	−	0.167256i
$396$		0			0
$397$	−23.0745	+	4.06865i	−0.0581221	+	0.0102485i	−0.202634	−	0.979255i	$-0.564950\pi$
$397$	−23.0745	+	4.06865i	−0.0581221	+	0.0102485i	0.144511	+	0.989503i	$0.453839\pi$
$398$		0			0
$399$	286.168	+	494.969i	0.717212	+	1.24052i
$400$		0			0
$401$	−673.256	+	118.713i	−1.67894	+	0.296043i	−0.930264	−	0.366890i	$-0.880423\pi$
$401$	−673.256	+	118.713i	−1.67894	+	0.296043i	−0.748679	+	0.662933i	$0.769311\pi$
$402$		0			0
$403$	−36.0962	−	99.1736i	−0.0895688	−	0.246088i
$404$		0			0
$405$	−21.3515	+	3.12682i	−0.0527197	+	0.00772055i
$406$		0			0
$407$	−105.902	−	183.428i	−0.260201	−	0.450682i
$408$		0			0
$409$	−152.896	−	26.9598i	−0.373830	−	0.0659163i	−0.0164231	−	0.999865i	$-0.505228\pi$
$409$	−152.896	−	26.9598i	−0.373830	−	0.0659163i	−0.357407	+	0.933949i	$0.616339\pi$
$410$		0			0
$411$	−442.405	−	255.423i	−1.07641	−	0.621466i
$412$		0			0
$413$	10.4246	+	3.79425i	0.0252412	+	0.00918706i
$414$		0			0
$415$	554.269	+	16.1456i	1.33559	+	0.0389050i
$416$		0			0
$417$	−1122.51			−2.69188
$418$		0			0
$419$	−660.535			−1.57646			−0.788228	−	0.615384i	$-0.789001\pi$
$419$	−660.535			−1.57646			−0.788228	+	0.615384i	$0.789001\pi$
$420$		0			0
$421$	−416.428	−	496.280i	−0.989141	−	1.17881i	−0.983881	−	0.178826i	$-0.942770\pi$
$421$	−416.428	−	496.280i	−0.989141	−	1.17881i	−0.00525979	−	0.999986i	$-0.501674\pi$
$422$		0			0
$423$	−365.767	+	1004.94i	−0.864697	+	2.37573i
$424$		0			0
$425$	−101.005	+	234.115i	−0.237659	+	0.550858i
$426$		0			0
$427$	−648.854	−	114.411i	−1.51957	−	0.267940i
$428$		0			0
$429$	75.8446	+	131.367i	0.176794	+	0.306216i
$430$		0			0
$431$	−136.428	+	162.589i	−0.316539	+	0.377236i	−0.900730	−	0.434380i	$-0.856967\pi$
$431$	−136.428	+	162.589i	−0.316539	+	0.377236i	0.584191	+	0.811616i	$0.301412\pi$
$432$		0			0
$433$	465.015	−	169.252i	1.07394	−	0.390881i	0.256290	−	0.966600i	$-0.417500\pi$
$433$	465.015	−	169.252i	1.07394	−	0.390881i	0.817648	+	0.575718i	$0.195278\pi$
$434$		0			0
$435$	453.378	−	734.985i	1.04225	−	1.68962i
$436$		0			0
$437$	−476.020	+	399.917i	−1.08929	+	0.915142i
$438$		0			0
$439$	−183.802	+	32.4092i	−0.418683	+	0.0738251i	−0.379021	−	0.925388i	$-0.623739\pi$
$439$	−183.802	+	32.4092i	−0.418683	+	0.0738251i	−0.0396619	+	0.999213i	$0.512628\pi$
$440$		0			0
$441$	−137.676	+	50.1100i	−0.312191	+	0.113628i
$442$		0			0
$443$	−69.7156	+	83.0838i	−0.157371	+	0.187548i	−0.838969	−	0.544179i	$-0.816841\pi$
$443$	−69.7156	+	83.0838i	−0.157371	+	0.187548i	0.681597	+	0.731727i	$0.261286\pi$
$444$		0			0
$445$	14.6666	−	71.0186i	0.0329586	−	0.159592i
$446$		0			0
$447$	109.167	−	619.118i	0.244222	−	1.38505i
$448$		0			0
$449$	−6.26444	−	3.61678i	−0.0139520	−	0.00805518i	0.493008	−	0.870025i	$-0.335897\pi$
$449$	−6.26444	−	3.61678i	−0.0139520	−	0.00805518i	−0.506960	+	0.861970i	$0.669231\pi$
$450$		0			0
$451$	119.155	−	327.377i	0.264203	−	0.725891i
$452$		0			0
$453$	259.765	+	309.576i	0.573433	+	0.683391i
$454$		0			0
$455$	66.3588	+	59.0581i	0.145843	+	0.129798i
$456$		0			0
$457$		−	212.758i		−	0.465554i	−0.972530	−	0.232777i	$-0.925219\pi$
$457$		−	212.758i		−	0.465554i	0.972530	−	0.232777i	$-0.0747812\pi$
$458$		0			0
$459$	−169.322	−	201.791i	−0.368894	−	0.439631i
$460$		0			0
$461$	170.351	+	62.0025i	0.369524	+	0.134496i	0.520106	−	0.854102i	$-0.325892\pi$
$461$	170.351	+	62.0025i	0.369524	+	0.134496i	−0.150582	+	0.988598i	$0.548115\pi$
$462$		0			0
$463$	−389.839	−	225.074i	−0.841986	−	0.486121i	0.0159531	−	0.999873i	$-0.494922\pi$
$463$	−389.839	−	225.074i	−0.841986	−	0.486121i	−0.857939	+	0.513752i	$0.828255\pi$
$464$		0			0
$465$	−701.094	+	554.316i	−1.50773	+	1.19208i
$466$		0			0
$467$	−599.198	+	345.947i	−1.28308	+	0.740786i	−0.977410	−	0.211351i	$-0.932214\pi$
$467$	−599.198	+	345.947i	−1.28308	+	0.740786i	−0.305670	+	0.952138i	$0.598880\pi$
$468$		0			0
$469$	62.9365	−	75.0048i	0.134193	−	0.159925i
$470$		0			0
$471$	235.810	+	647.883i	0.500659	+	1.37555i
$472$		0			0
$473$	−518.690	+	91.4591i	−1.09660	+	0.193360i
$474$		0			0
$475$	462.255	+	109.294i	0.973169	+	0.230093i
$476$		0			0
$477$	−181.308	−	1028.25i	−0.380101	−	2.15566i
$478$		0			0
$479$	639.439	−	232.737i	1.33495	−	0.485880i	0.426728	−	0.904380i	$-0.359666\pi$
$479$	639.439	−	232.737i	1.33495	−	0.485880i	0.908217	+	0.418500i	$0.137444\pi$
$480$		0			0
$481$	42.0592	+	35.2918i	0.0874411	+	0.0733718i
$482$		0			0
$483$	492.325	+	852.732i	1.01931	+	1.76549i
$484$		0			0
$485$	305.180	+	385.989i	0.629238	+	0.795854i
$486$		0			0
$487$	418.424	−	724.731i	0.859186	−	1.48815i	−0.0135198	−	0.999909i	$-0.504304\pi$
$487$	418.424	−	724.731i	0.859186	−	1.48815i	0.872706	−	0.488246i	$-0.162363\pi$
$488$		0			0
$489$	−231.749	+	636.724i	−0.473924	+	1.30209i
$490$		0			0
$491$	−245.424	+	205.935i	−0.499845	+	0.419420i	−0.857539	−	0.514419i	$-0.828008\pi$
$491$	−245.424	+	205.935i	−0.499845	+	0.419420i	0.357694	+	0.933839i	$0.383563\pi$
$492$		0			0
$493$	−364.571			−0.739495
$494$		0			0
$495$	524.784	−	589.656i	1.06017	−	1.19122i
$496$		0			0
$497$	−410.154	+	344.160i	−0.825260	+	0.692476i
$498$		0			0
$499$	25.6903	+	9.35050i	0.0514835	+	0.0187385i	0.367634	−	0.929971i	$-0.380168\pi$
$499$	25.6903	+	9.35050i	0.0514835	+	0.0187385i	−0.316150	+	0.948709i	$0.602390\pi$
$500$		0			0
$501$	−701.656	+	1215.30i	−1.40051	+	2.42576i
$502$		0			0
$503$	520.504	+	91.7789i	1.03480	+	0.182463i	0.665151	−	0.746709i	$-0.268367\pi$
$503$	520.504	+	91.7789i	1.03480	+	0.182463i	0.369648	+	0.929172i	$0.379478\pi$
$504$		0			0
$505$	68.2093	+	14.0864i	0.135068	+	0.0278938i
$506$		0			0
$507$	595.400	+	499.600i	1.17436	+	0.985404i
$508$		0			0
$509$	−302.530	−	831.194i	−0.594361	−	1.63299i	−0.762320	−	0.647200i	$-0.775940\pi$
$509$	−302.530	−	831.194i	−0.594361	−	1.63299i	0.167959	−	0.985794i	$-0.446282\pi$
$510$		0			0
$511$	−1.62298	−	9.20438i	−0.00317609	−	0.0180125i
$512$		0			0
$513$	−315.210	+	376.113i	−0.614445	+	0.733163i
$514$		0			0
$515$	174.610	+	107.709i	0.339048	+	0.209143i
$516$		0			0
$517$	280.594	+	770.925i	0.542735	+	1.49115i
$518$		0			0
$519$	288.135	+	241.774i	0.555174	+	0.465847i
$520$		0			0
$521$	624.692	−	360.666i	1.19903	−	0.692257i	0.238687	−	0.971097i	$-0.423283\pi$
$521$	624.692	−	360.666i	1.19903	−	0.692257i	0.960338	+	0.278839i	$0.0899496\pi$
$522$		0			0
$523$	168.483	−	955.513i	0.322147	−	1.82698i	−0.206865	−	0.978370i	$-0.566326\pi$
$523$	168.483	−	955.513i	0.322147	−	1.82698i	0.529011	−	0.848615i	$-0.322563\pi$
$524$		0			0
$525$	298.011	−	690.744i	0.567640	−	1.31570i
$526$		0			0
$527$	354.559	+	129.049i	0.672788	+	0.244875i
$528$		0			0
$529$	−414.979	+	348.209i	−0.784460	+	0.658240i
$530$		0			0
$531$			25.5534i			0.0481231i
$532$		0			0
$533$			90.3098i			0.169437i
$534$		0			0
$535$	−6.65125	+	228.334i	−0.0124322	+	0.426793i
$536$		0			0
$537$	223.747	−	614.741i	0.416662	−	1.14477i
$538$		0			0
$539$	−56.1974	+	97.3368i	−0.104262	+	0.180588i
$540$		0			0
$541$	−138.020	+	782.748i	−0.255119	+	1.44685i	0.540647	+	0.841250i	$0.318180\pi$
$541$	−138.020	+	782.748i	−0.255119	+	1.44685i	−0.795766	+	0.605604i	$0.792932\pi$
$542$		0			0
$543$	1437.15	−	829.736i	2.64668	−	1.52806i
$544$		0			0
$545$	60.8198	+	415.307i	0.111596	+	0.762032i
$546$		0			0
$547$	−552.475	+	201.084i	−1.01001	+	0.367613i	−0.793436	−	0.608653i	$-0.791710\pi$
$547$	−552.475	+	201.084i	−1.01001	+	0.367613i	−0.216573	+	0.976266i	$0.569488\pi$
$548$		0			0
$549$	−263.536	−	1494.59i	−0.480029	−	2.72238i
$550$		0			0
$551$	118.340	+	668.783i	0.214772	+	1.21376i
$552$		0			0
$553$	−38.7005	−	219.481i	−0.0699828	−	0.396892i
$554$		0			0
$555$	171.680	−	432.104i	0.309334	−	0.778566i
$556$		0			0
$557$	−8.14290	+	9.70434i	−0.0146192	+	0.0174225i	−0.773305	−	0.634035i	$-0.781398\pi$
$557$	−8.14290	+	9.70434i	−0.0146192	+	0.0174225i	0.758685	+	0.651457i	$0.225842\pi$
$558$		0			0
$559$	118.239	−	68.2652i	0.211518	−	0.122120i
$560$		0			0
$561$	−534.071	−	94.1711i	−0.951998	−	0.167863i
$562$		0			0
$563$	421.700	−	730.406i	0.749023	−	1.29735i	−0.199268	−	0.979945i	$-0.563857\pi$
$563$	421.700	−	730.406i	0.749023	−	1.29735i	0.948291	−	0.317401i	$-0.102810\pi$
$564$		0			0
$565$	442.050	−	238.333i	0.782389	−	0.421828i
$566$		0			0
$567$	−17.2773	−	20.5903i	−0.0304714	−	0.0363144i
$568$		0			0
$569$		−	166.474i		−	0.292572i	−0.989242	−	0.146286i	$-0.953268\pi$
$569$		−	166.474i		−	0.292572i	0.989242	−	0.146286i	$-0.0467320\pi$
$570$		0			0
$571$	−310.342			−0.543506			−0.271753	−	0.962367i	$-0.587603\pi$
$571$	−310.342			−0.543506			−0.271753	+	0.962367i	$0.587603\pi$
$572$		0			0
$573$	−553.229	+	464.215i	−0.965496	+	0.810148i
$574$		0			0
$575$	795.983	+	188.706i	1.38432	+	0.328184i
$576$		0			0
$577$	−91.4934	−	52.8238i	−0.158567	−	0.0915490i	0.418617	−	0.908163i	$-0.362515\pi$
$577$	−91.4934	−	52.8238i	−0.158567	−	0.0915490i	−0.577184	+	0.816614i	$0.695848\pi$
$578$		0			0
$579$	−78.2230	+	443.625i	−0.135100	+	0.766191i
$580$		0			0
$581$	345.341	+	598.147i	0.594390	+	1.02951i
$582$		0			0
$583$	−613.585	−	514.859i	−1.05246	−	0.883120i
$584$		0			0
$585$	−75.5533	+	190.161i	−0.129151	+	0.325062i
$586$		0			0
$587$	149.284	−	26.3228i	0.254317	−	0.0448430i	−0.0450359	−	0.998985i	$-0.514340\pi$
$587$	149.284	−	26.3228i	0.254317	−	0.0448430i	0.299353	+	0.954142i	$0.403229\pi$
$588$		0			0
$589$	121.643	−	692.306i	0.206524	−	1.17539i
$590$		0			0
$591$	−751.522	+	132.514i	−1.27161	+	0.224219i
$592$		0			0
$593$	285.051	+	783.171i	0.480693	+	1.32069i	0.908900	+	0.417013i	$0.136923\pi$
$593$	285.051	+	783.171i	0.480693	+	1.32069i	−0.428207	+	0.903681i	$0.640855\pi$
$594$		0			0
$595$	−314.239	+	46.0189i	−0.528133	+	0.0773427i
$596$		0			0
$597$	212.428	+	367.937i	0.355827	+	0.616310i
$598$		0			0
$599$	54.8231	+	9.66679i	0.0915243	+	0.0161382i	0.219223	−	0.975675i	$-0.429648\pi$
$599$	54.8231	+	9.66679i	0.0915243	+	0.0161382i	−0.127698	+	0.991813i	$0.540759\pi$
$600$		0			0
$601$	244.702	+	141.279i	0.407157	+	0.235072i	0.689568	−	0.724221i	$-0.257801\pi$
$601$	244.702	+	141.279i	0.407157	+	0.235072i	−0.282410	+	0.959294i	$0.591134\pi$
$602$		0			0
$603$	211.931	+	77.1366i	0.351461	+	0.127921i
$604$		0			0
$605$	0.0160222	−	0.550036i	2.64830e−5	−	0.000909150i
$606$		0			0
$607$	1205.30			1.98566			0.992832	−	0.119520i	$-0.0381356\pi$
$607$	1205.30			1.98566			0.992832	+	0.119520i	$0.0381356\pi$
$608$		0			0
$609$	1075.65			1.76626
$610$		0			0
$611$	−136.699	−	162.912i	−0.223731	−	0.266632i
$612$		0			0
$613$	−238.707	+	655.843i	−0.389408	+	1.06989i	0.577861	+	0.816136i	$0.303888\pi$
$613$	−238.707	+	655.843i	−0.389408	+	1.06989i	−0.967269	+	0.253755i	$0.918334\pi$
$614$		0			0
$615$	725.982	−	240.538i	1.18046	−	0.391119i
$616$		0			0
$617$	−21.3727	−	3.76858i	−0.0346396	−	0.00610790i	0.156302	−	0.987709i	$-0.450043\pi$
$617$	−21.3727	−	3.76858i	−0.0346396	−	0.00610790i	−0.190941	+	0.981601i	$0.561154\pi$
$618$		0			0
$619$	523.107	+	906.048i	0.845084	+	1.46373i	0.885548	+	0.464547i	$0.153783\pi$
$619$	523.107	+	906.048i	0.845084	+	1.46373i	−0.0404644	+	0.999181i	$0.512884\pi$
$620$		0			0
$621$	−543.245	+	647.415i	−0.874791	+	1.04254i
$622$		0			0
$623$	84.8790	−	30.8934i	0.136242	−	0.0495881i
$624$		0			0
$625$	−247.475	−	573.917i	−0.395961	−	0.918267i
$626$		0			0
$627$	0.608107	+	1010.29i	0.000969867	+	1.61131i
$628$		0			0
$629$	−193.309	+	34.0855i	−0.307327	+	0.0541900i
$630$		0			0
$631$	1056.66	−	384.593i	1.67458	−	0.609498i	0.682030	−	0.731324i	$-0.261097\pi$
$631$	1056.66	−	384.593i	1.67458	−	0.609498i	0.992551	+	0.121827i	$0.0388752\pi$
$632$		0			0
$633$	−985.083	+	1173.98i	−1.55621	+	1.85462i
$634$		0			0
$635$	620.442	+	128.132i	0.977074	+	0.201783i
$636$		0			0
$637$	5.05929	−	28.6927i	0.00794237	−	0.0450434i
$638$		0			0
$639$	−1068.06	−	616.647i	−1.67146	−	0.965019i
$640$		0			0
$641$	−190.149	+	522.430i	−0.296644	+	0.815023i	0.698411	+	0.715697i	$0.253891\pi$
$641$	−190.149	+	522.430i	−0.296644	+	0.815023i	−0.995055	+	0.0993261i	$0.968331\pi$
$642$		0			0
$643$	21.8161	+	25.9994i	0.0339287	+	0.0404346i	0.782742	−	0.622346i	$-0.213820\pi$
$643$	21.8161	+	25.9994i	0.0339287	+	0.0404346i	−0.748813	+	0.662781i	$0.769376\pi$
$644$		0			0
$645$	−863.696	−	768.674i	−1.33906	−	1.19174i
$646$		0			0
$647$		−	855.878i		−	1.32284i	−0.750015	−	0.661421i	$-0.769954\pi$
$647$		−	855.878i		−	1.32284i	0.750015	−	0.661421i	$-0.230046\pi$
$648$		0			0
$649$	12.6006	+	15.0168i	0.0194153	+	0.0231383i
$650$		0			0
$651$	−1046.11	−	380.753i	−1.60693	−	0.584874i
$652$		0			0
$653$	−487.866	−	281.670i	−0.747115	−	0.431347i	0.0775355	−	0.996990i	$-0.475295\pi$
$653$	−487.866	−	281.670i	−0.747115	−	0.431347i	−0.824651	+	0.565643i	$0.808628\pi$
$654$		0			0
$655$	−797.944	−	1009.23i	−1.21824	−	1.54081i
$656$		0			0
$657$	18.6444	−	10.7643i	0.0283780	−	0.0163841i
$658$		0			0
$659$	360.097	−	429.147i	0.546429	−	0.651209i	−0.420187	−	0.907437i	$-0.638036\pi$
$659$	360.097	−	429.147i	0.546429	−	0.651209i	0.966616	+	0.256229i	$0.0824800\pi$
$660$		0			0
$661$	−204.329	−	561.390i	−0.309122	−	0.849305i	−0.992828	−	0.119548i	$-0.961855\pi$
$661$	−204.329	−	561.390i	−0.309122	−	0.849305i	0.683707	−	0.729757i	$-0.260367\pi$
$662$		0			0
$663$	138.443	−	24.4113i	0.208813	−	0.0368194i
$664$		0			0
$665$	186.421	+	561.515i	0.280332	+	0.844384i
$666$		0			0
$667$	203.111	+	1151.90i	0.304515	+	1.72699i
$668$		0			0
$669$	1501.73	−	546.586i	2.24474	−	0.817019i
$670$		0			0
$671$	−891.861	−	748.360i	−1.32915	−	1.11529i
$672$		0			0
$673$	−568.787	−	985.168i	−0.845152	−	1.46385i	−0.885489	−	0.464660i	$-0.846177\pi$
$673$	−568.787	−	985.168i	−0.845152	−	1.46385i	0.0403372	−	0.999186i	$-0.487157\pi$
$674$		0			0
$675$	644.606	+	37.5859i	0.954972	+	0.0556829i
$676$		0			0
$677$	455.681	−	789.262i	0.673088	−	1.16582i	−0.303936	−	0.952692i	$-0.598301\pi$
$677$	455.681	−	789.262i	0.673088	−	1.16582i	0.977024	−	0.213130i	$-0.0683658\pi$
$678$		0			0
$679$	−209.625	+	575.939i	−0.308725	+	0.848216i
$680$		0			0
$681$	−20.6523	+	17.3293i	−0.0303264	+	0.0254469i
$682$		0			0
$683$	661.708			0.968826			0.484413	−	0.874839i	$-0.339033\pi$
$683$	661.708			0.968826			0.484413	+	0.874839i	$0.339033\pi$
$684$		0			0
$685$	−394.894	−	351.449i	−0.576487	−	0.513064i
$686$		0			0
$687$	906.184	−	760.379i	1.31905	−	1.10681i
$688$		0			0
$689$	195.110	+	71.0142i	0.283179	+	0.103069i
$690$		0			0
$691$	50.8141	−	88.0125i	0.0735370	−	0.127370i	−0.826912	−	0.562331i	$-0.809905\pi$
$691$	50.8141	−	88.0125i	0.0735370	−	0.127370i	0.900449	+	0.434961i	$0.143238\pi$
$692$		0			0
$693$	968.279	+	170.734i	1.39723	+	0.246369i
$694$		0			0
$695$	−1137.60	−	234.935i	−1.63684	−	0.338036i
$696$		0			0
$697$	−247.333	−	207.537i	−0.354853	−	0.297757i
$698$		0			0
$699$	88.4205	+	242.933i	0.126496	+	0.347544i
$700$		0			0
$701$	−168.097	−	953.327i	−0.239797	−	1.35995i	−0.832273	−	0.554366i	$-0.812961\pi$
$701$	−168.097	−	953.327i	−0.239797	−	1.35995i	0.592477	−	0.805588i	$-0.298150\pi$
$702$		0			0
$703$	125.276	+	343.549i	0.178202	+	0.488689i
$704$		0			0
$705$	−945.520	+	1532.81i	−1.34116	+	2.17420i
$706$		0			0
$707$	29.6713	+	81.5213i	0.0419679	+	0.115306i
$708$		0			0
$709$	88.1291	+	73.9491i	0.124301	+	0.104301i	0.702819	−	0.711369i	$-0.251924\pi$
$709$	88.1291	+	73.9491i	0.124301	+	0.104301i	−0.578518	+	0.815669i	$0.696369\pi$
$710$		0			0
$711$	444.581	−	256.679i	0.625289	−	0.361011i
$712$		0			0
$713$	210.211	−	1192.16i	0.294826	−	1.67204i
$714$		0			0
$715$	49.3700	+	149.006i	0.0690489	+	0.208401i
$716$		0			0
$717$	1702.13	+	619.524i	2.37396	+	0.864050i
$718$		0			0
$719$	508.673	−	426.827i	0.707473	−	0.593640i	−0.216416	−	0.976301i	$-0.569437\pi$
$719$	508.673	−	426.827i	0.707473	−	0.593640i	0.923889	+	0.382661i	$0.124992\pi$
$720$		0			0
$721$			255.541i			0.354426i
$722$		0			0
$723$			847.652i			1.17241i
$724$		0			0
$725$	613.300	−	649.976i	0.845932	−	0.896519i
$726$		0			0
$727$	−58.6097	+	161.029i	−0.0806186	+	0.221498i	−0.973453	−	0.228888i	$-0.926491\pi$
$727$	−58.6097	+	161.029i	−0.0806186	+	0.221498i	0.892834	+	0.450385i	$0.148713\pi$
$728$		0			0
$729$	592.529	−	1026.29i	0.812796	−	1.40780i
$730$		0			0
$731$	−84.7603	+	480.699i	−0.115951	+	0.657591i
$732$		0			0
$733$	948.075	−	547.371i	1.29342	−	0.746755i	0.314159	−	0.949370i	$-0.398278\pi$
$733$	948.075	−	547.371i	1.29342	−	0.746755i	0.979258	+	0.202616i	$0.0649443\pi$
$734$		0			0
$735$	−244.130	+	35.7516i	−0.332149	+	0.0486417i
$736$		0			0
$737$	162.581	−	59.1745i	0.220598	−	0.0802910i
$738$		0			0
$739$	−134.060	−	760.292i	−0.181407	−	1.02881i	−0.930485	−	0.366330i	$-0.880614\pi$
$739$	−134.060	−	760.292i	−0.181407	−	1.02881i	0.749078	−	0.662482i	$-0.230497\pi$
$740$		0			0
$741$	−89.7196	−	246.042i	−0.121079	−	0.332040i
$742$		0			0
$743$	−205.976	−	1168.15i	−0.277222	−	1.57221i	−0.731814	−	0.681505i	$-0.761326\pi$
$743$	−205.976	−	1168.15i	−0.277222	−	1.57221i	0.454591	−	0.890700i	$-0.349785\pi$
$744$		0			0
$745$	240.212	−	604.592i	0.322432	−	0.811533i
$746$		0			0
$747$	−1022.63	+	1218.72i	−1.36898	+	1.63149i
$748$		0			0
$749$	−246.410	+	142.265i	−0.328985	+	0.189940i
$750$		0			0
$751$	1403.24	+	247.429i	1.86849	+	0.329466i	0.989172	−	0.146762i	$-0.0468850\pi$
$751$	1403.24	+	247.429i	1.86849	+	0.329466i	0.879322	+	0.476228i	$0.157996\pi$
$752$		0			0
$753$	−747.573	+	1294.83i	−0.992793	+	1.71957i
$754$		0			0
$755$	198.465	+	368.105i	0.262868	+	0.487556i
$756$		0			0
$757$	242.035	+	288.446i	0.319730	+	0.381039i	0.901839	−	0.432071i	$-0.142217\pi$
$757$	242.035	+	288.446i	0.319730	+	0.381039i	−0.582110	+	0.813110i	$0.697773\pi$
$758$		0			0
$759$			1739.92i			2.29238i
$760$		0			0
$761$	−147.483			−0.193802			−0.0969009	−	0.995294i	$-0.530893\pi$
$761$	−147.483			−0.193802			−0.0969009	+	0.995294i	$0.530893\pi$
$762$		0			0
$763$	−400.501	+	336.061i	−0.524904	+	0.440446i
$764$		0			0
$765$	−347.171	−	643.919i	−0.453819	−	0.841725i
$766$		0			0
$767$	−4.40074	−	2.54077i	−0.00573760	−	0.00331260i
$768$		0			0
$769$	28.1475	−	159.632i	0.0366027	−	0.207584i	−0.961022	−	0.276473i	$-0.910834\pi$
$769$	28.1475	−	159.632i	0.0366027	−	0.207584i	0.997624	+	0.0688889i	$0.0219454\pi$
$770$		0			0
$771$	−1090.79	−	1889.30i	−1.41477	−	2.45046i
$772$		0			0
$773$	−951.125	−	798.088i	−1.23043	−	1.03246i	−0.998211	−	0.0597932i	$-0.980956\pi$
$773$	−951.125	−	798.088i	−1.23043	−	1.03246i	−0.232222	−	0.972663i	$-0.574600\pi$
$774$		0			0
$775$	−826.533	+	415.034i	−1.06649	+	0.535527i
$776$		0			0
$777$	570.348	−	100.568i	0.734038	−	0.129431i
$778$		0			0
$779$	−300.430	+	521.083i	−0.385660	+	0.668913i
$780$		0			0
$781$	−931.735	+	164.290i	−1.19300	+	0.210358i
$782$		0			0
$783$	315.769	+	867.568i	0.403281	+	1.10800i
$784$		0			0
$785$	103.382	+	705.946i	0.131697	+	0.899294i
$786$		0			0
$787$	347.181	+	601.335i	0.441145	+	0.764085i	0.997775	−	0.0666752i	$-0.0212391\pi$
$787$	347.181	+	601.335i	0.441145	+	0.764085i	−0.556630	+	0.830761i	$0.687906\pi$
$788$		0			0
$789$	−236.691	−	41.7350i	−0.299989	−	0.0528961i
$790$		0			0
$791$	541.732	+	312.769i	0.684870	+	0.395410i
$792$		0			0
$793$	283.597	+	103.221i	0.357626	+	0.130165i
$794$		0			0
$795$	51.1977	−	1757.59i	0.0643997	−	2.21081i
$796$		0			0
$797$	223.303			0.280179			0.140089	−	0.990139i	$-0.455261\pi$
$797$	223.303			0.280179			0.140089	+	0.990139i	$0.455261\pi$
$798$		0			0
$799$	760.312			0.951580
$800$		0			0
$801$	133.738	+	159.383i	0.166964	+	0.198980i
$802$		0			0
$803$	5.64862	−	15.5195i	0.00703439	−	0.0193268i
$804$		0			0
$805$	320.472	+	967.235i	0.398102	+	1.20153i
$806$		0			0
$807$	899.547	+	158.614i	1.11468	+	0.196548i
$808$		0			0
$809$	−413.014	−	715.361i	−0.510524	−	0.884253i	−0.999926	−	0.0121948i	$-0.996118\pi$
$809$	−413.014	−	715.361i	−0.510524	−	0.884253i	0.489402	−	0.872058i	$-0.337215\pi$
$810$		0			0
$811$	−546.655	+	651.478i	−0.674051	+	0.803302i	−0.989329	−	0.145697i	$-0.953458\pi$
$811$	−546.655	+	651.478i	−0.674051	+	0.803302i	0.315279	+	0.948999i	$0.397902\pi$
$812$		0			0
$813$	781.419	−	284.413i	0.961154	−	0.349832i
$814$		0			0
$815$	−368.126	+	596.780i	−0.451689	+	0.732246i
$816$		0			0
$817$	909.327	−	0.547336i	1.11301	−	0.000669934i
$818$		0			0
$819$	−251.000	+	44.2580i	−0.306471	+	0.0540391i
$820$		0			0
$821$	−199.975	+	72.7850i	−0.243575	+	0.0886541i	−0.460923	−	0.887440i	$-0.652482\pi$
$821$	−199.975	+	72.7850i	−0.243575	+	0.0886541i	0.217348	+	0.976094i	$0.430259\pi$
$822$		0			0
$823$	−138.657	+	165.245i	−0.168478	+	0.200784i	−0.843676	−	0.536852i	$-0.819613\pi$
$823$	−138.657	+	165.245i	−0.168478	+	0.200784i	0.675199	+	0.737636i	$0.264058\pi$
$824$		0			0
$825$	1066.34	−	793.750i	1.29253	−	0.962121i
$826$		0			0
$827$	36.9515	−	209.562i	0.0446813	−	0.253401i	−0.954283	−	0.298905i	$-0.903379\pi$
$827$	36.9515	−	209.562i	0.0446813	−	0.253401i	0.998964	+	0.0455048i	$0.0144896\pi$
$828$		0			0
$829$	1416.47	+	817.797i	1.70864	+	0.986486i	0.936245	+	0.351348i	$0.114277\pi$
$829$	1416.47	+	817.797i	1.70864	+	0.986486i	0.772399	+	0.635138i	$0.219057\pi$
$830$		0			0
$831$	−590.524	+	1622.45i	−0.710618	+	1.95241i
$832$		0			0
$833$	66.9545	+	79.7932i	0.0803775	+	0.0957902i
$834$		0			0
$835$	−965.443	+	1084.79i	−1.15622	+	1.29915i
$836$		0			0
$837$		−	955.517i		−	1.14160i
$838$		0			0
$839$	−676.349	−	806.041i	−0.806137	−	0.960717i	0.193656	−	0.981070i	$-0.437965\pi$
$839$	−676.349	−	806.041i	−0.806137	−	0.960717i	−0.999793	+	0.0203528i	$0.993521\pi$
$840$		0			0
$841$	410.429	+	149.384i	0.488025	+	0.177627i
$842$		0			0
$843$	−1906.74	−	1100.86i	−2.26185	−	1.30588i
$844$		0			0
$845$	498.841	+	630.929i	0.590344	+	0.746661i
$846$		0			0
$847$	0.593579	−	0.342703i	0.000700801	−	0.000404608i
$848$		0			0
$849$	−1116.31	+	1330.37i	−1.31485	+	1.56698i
$850$		0			0
$851$	215.394	+	591.789i	0.253107	+	0.695405i
$852$		0			0
$853$	−457.367	+	80.6462i	−0.536187	+	0.0945442i	−0.435183	−	0.900342i	$-0.643316\pi$
$853$	−457.367	+	80.6462i	−0.536187	+	0.0945442i	−0.101003	+	0.994886i	$0.532205\pi$
$854$		0			0
$855$	−1068.54	+	845.880i	−1.24975	+	0.989334i
$856$		0			0
$857$	35.4066	+	200.801i	0.0413146	+	0.234307i	0.998472	−	0.0552616i	$-0.0175993\pi$
$857$	35.4066	+	200.801i	0.0413146	+	0.234307i	−0.957157	+	0.289569i	$0.906488\pi$
$858$		0			0
$859$	642.546	−	233.868i	0.748017	−	0.272256i	0.0602457	−	0.998184i	$-0.480812\pi$
$859$	642.546	−	233.868i	0.748017	−	0.272256i	0.687771	+	0.725928i	$0.258589\pi$
$860$		0			0
$861$	729.744	+	612.328i	0.847554	+	0.711182i
$862$		0			0
$863$	606.102	+	1049.80i	0.702320	+	1.21645i	0.967650	+	0.252296i	$0.0811856\pi$
$863$	606.102	+	1049.80i	0.702320	+	1.21645i	−0.265331	+	0.964157i	$0.585481\pi$
$864$		0			0
$865$	241.407	+	305.329i	0.279083	+	0.352982i
$866$		0			0
$867$	446.889	−	774.034i	0.515443	−	0.892773i
$868$		0			0
$869$	134.693	−	370.066i	0.154998	−	0.425853i
$870$		0			0
$871$	−34.3565	+	28.8286i	−0.0394449	+	0.0330982i
$872$		0			0
$873$	−1411.77			−1.61715
$874$		0			0
$875$	446.585	−	637.658i	0.510383	−	0.728752i
$876$		0			0
$877$	433.920	−	364.102i	0.494778	−	0.415168i	−0.360957	−	0.932583i	$-0.617550\pi$
$877$	433.920	−	364.102i	0.494778	−	0.415168i	0.855735	+	0.517414i	$0.173105\pi$
$878$		0			0
$879$	−627.582	−	228.421i	−0.713973	−	0.259865i
$880$		0			0
$881$	309.992	−	536.922i	0.351864	−	0.609446i	−0.634712	−	0.772748i	$-0.718881\pi$
$881$	309.992	−	536.922i	0.351864	−	0.609446i	0.986576	+	0.163303i	$0.0522148\pi$
$882$		0			0
$883$	1323.69	+	233.403i	1.49909	+	0.264329i	0.862176	−	0.506609i	$-0.169101\pi$
$883$	1323.69	+	233.403i	1.49909	+	0.264329i	0.636910	+	0.770938i	$0.280212\pi$
$884$		0			0
$885$	−8.70344	+	42.1439i	−0.00983439	+	0.0476202i
$886$		0			0
$887$	−1174.09	−	985.177i	−1.32366	−	1.11068i	−0.985514	−	0.169591i	$-0.945755\pi$
$887$	−1174.09	−	985.177i	−1.32366	−	1.11068i	−0.338148	−	0.941093i	$-0.609800\pi$
$888$		0			0
$889$	269.895	+	741.530i	0.303594	+	0.834117i
$890$		0			0
$891$	−8.24757	−	46.7743i	−0.00925653	−	0.0524964i
$892$		0			0
$893$	−246.797	−	1394.75i	−0.276369	−	1.56187i
$894$		0			0
$895$	355.416	−	576.176i	0.397113	−	0.643772i
$896$		0			0
$897$	−154.260	−	423.826i	−0.171973	−	0.472493i
$898$		0			0
$899$	−1013.04	−	850.043i	−1.12685	−	0.945543i
$900$		0			0
$901$	−642.861	+	371.156i	−0.713497	+	0.411938i
$902$		0			0
$903$	250.081	−	1418.28i	0.276945	−	1.57063i
$904$		0			0
$905$	1630.12	−	540.105i	1.80124	−	0.596801i
$906$		0			0
$907$	−1257.80	−	457.803i	−1.38677	−	0.504744i	−0.462548	−	0.886594i	$-0.653065\pi$
$907$	−1257.80	−	457.803i	−1.38677	−	0.504744i	−0.924224	+	0.381851i	$0.875287\pi$
$908$		0			0
$909$	−153.078	+	128.448i	−0.168403	+	0.141307i
$910$		0			0
$911$			658.221i			0.722526i	0.932464	+	0.361263i	$0.117654\pi$
$911$			658.221i			0.722526i	−0.932464	+	0.361263i	$0.882346\pi$
$912$		0			0
$913$			1220.46i			1.33676i
$914$		0			0
$915$	74.4172	−	2554.70i	0.0813302	−	2.79203i
$916$		0			0
$917$	548.098	−	1505.89i	0.597708	−	1.64219i
$918$		0			0
$919$	−370.964	+	642.529i	−0.403661	+	0.699161i	−0.994165	−	0.107874i	$-0.965596\pi$
$919$	−370.964	+	642.529i	−0.403661	+	0.699161i	0.590504	+	0.807035i	$0.298929\pi$
$920$		0			0
$921$	−176.830	+	1002.85i	−0.191998	+	1.08887i
$922$		0			0
$923$	212.395	−	122.626i	0.230114	−	0.132856i
$924$		0			0
$925$	264.424	−	401.981i	0.285864	−	0.434574i
$926$		0			0
$927$	−553.121	+	201.320i	−0.596679	+	0.217173i
$928$		0			0
$929$	−227.922	−	1292.61i	−0.245341	−	1.39140i	−0.819699	−	0.572794i	$-0.805860\pi$
$929$	−227.922	−	1292.61i	−0.245341	−	1.39140i	0.574358	−	0.818604i	$-0.305252\pi$
$930$		0			0
$931$	124.642	−	148.725i	0.133880	−	0.159747i
$932$		0			0
$933$	444.865	+	2522.95i	0.476811	+	2.70413i
$934$		0			0
$935$	−521.541	−	207.214i	−0.557798	−	0.221620i
$936$		0			0
$937$	−720.434	+	858.580i	−0.768873	+	0.916308i	−0.998374	−	0.0570008i	$-0.981846\pi$
$937$	−720.434	+	858.580i	−0.768873	+	0.916308i	0.229501	+	0.973309i	$0.426291\pi$
$938$		0			0
$939$	−1748.49	+	1009.49i	−1.86208	+	1.07507i
$940$		0			0
$941$	495.539	+	87.3769i	0.526609	+	0.0928554i	0.430631	−	0.902528i	$-0.358291\pi$
$941$	495.539	+	87.3769i	0.526609	+	0.0928554i	0.0959781	+	0.995383i	$0.469402\pi$
$942$		0			0
$943$	−517.940	+	897.098i	−0.549247	+	0.951324i
$944$		0			0
$945$	381.686	+	707.935i	0.403900	+	0.749138i
$946$		0			0
$947$	−299.919	−	357.430i	−0.316704	−	0.377434i	0.584083	−	0.811694i	$-0.301454\pi$
$947$	−299.919	−	357.430i	−0.316704	−	0.377434i	−0.900787	+	0.434260i	$0.857010\pi$
$948$		0			0
$949$			4.28118i			0.00451125i
$950$		0			0
$951$	−648.482			−0.681895
$952$		0			0
$953$	−587.190	+	492.711i	−0.616149	+	0.517011i	−0.896590	−	0.442861i	$-0.853964\pi$
$953$	−587.190	+	492.711i	−0.616149	+	0.517011i	0.280441	+	0.959871i	$0.409519\pi$
$954$		0			0
$955$	−657.823	+	354.668i	−0.688820	+	0.371380i
$956$		0			0
$957$	1646.07	+	950.360i	1.72003	+	0.993062i
$958$		0			0
$959$	114.341	−	648.458i	0.119229	−	0.676182i
$960$		0			0
$961$	203.828	+	353.041i	0.212100	+	0.367368i
$962$		0			0
$963$	−502.059	−	421.278i	−0.521349	−	0.437464i
$964$		0			0
$965$	−172.122	+	433.217i	−0.178365	+	0.448929i
$966$		0			0
$967$	−833.913	+	147.041i	−0.862371	+	0.152059i	−0.587305	−	0.809366i	$-0.699811\pi$
$967$	−833.913	+	147.041i	−0.862371	+	0.152059i	−0.275067	+	0.961425i	$0.588700\pi$
$968$		0			0
$969$	880.019	+	319.701i	0.908172	+	0.329929i
$970$		0			0
$971$	894.877	−	157.791i	0.921603	−	0.162504i	0.307335	−	0.951601i	$-0.400563\pi$
$971$	894.877	−	157.791i	0.921603	−	0.162504i	0.614268	+	0.789098i	$0.289452\pi$
$972$		0			0
$973$	−494.863	−	1359.62i	−0.508595	−	1.39735i
$974$		0			0
$975$	−189.375	+	287.890i	−0.194231	+	0.295272i
$976$		0			0
$977$	−207.038	−	358.601i	−0.211912	−	0.367043i	0.740401	−	0.672166i	$-0.234636\pi$
$977$	−207.038	−	358.601i	−0.211912	−	0.367043i	−0.952313	+	0.305123i	$0.901302\pi$
$978$		0			0
$979$	157.186	+	27.7161i	0.160557	+	0.0283106i
$980$		0			0
$981$	−1042.93	−	602.135i	−1.06313	−	0.613797i
$982$		0			0
$983$	751.916	+	273.675i	0.764919	+	0.278408i	0.694870	−	0.719136i	$-0.255462\pi$
$983$	751.916	+	273.675i	0.764919	+	0.278408i	0.0700495	+	0.997544i	$0.477684\pi$
$984$		0			0
$985$	−789.358	−	22.9936i	−0.801379	−	0.0233437i
$986$		0			0
$987$	−2243.27			−2.27281
$988$		0			0
$989$	1566.04			1.58346
$990$		0			0
$991$	153.532	+	182.973i	0.154927	+	0.184635i	0.837925	−	0.545786i	$-0.183769\pi$
$991$	153.532	+	182.973i	0.154927	+	0.184635i	−0.682998	+	0.730420i	$0.739324\pi$
$992$		0			0
$993$	147.032	−	403.968i	0.148069	−	0.406816i
$994$		0			0
$995$	138.277	+	417.343i	0.138972	+	0.419440i
$996$		0			0
$997$	−1577.80	−	278.208i	−1.58255	−	0.279046i	−0.687895	−	0.725810i	$-0.741465\pi$
$997$	−1577.80	−	278.208i	−1.58255	−	0.279046i	−0.894651	+	0.446765i	$0.852576\pi$
$998$		0			0
$999$	248.545	+	430.493i	0.248794	+	0.430924i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.3.bc.a.29.3	✓	120
5.4	even	2	inner	380.3.bc.a.29.18	yes	120
19.2	odd	18	inner	380.3.bc.a.249.18	yes	120
95.59	odd	18	inner	380.3.bc.a.249.3	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.3.bc.a.29.3	✓	120	1.1	even	1	trivial
380.3.bc.a.29.18	yes	120	5.4	even	2	inner
380.3.bc.a.249.3	yes	120	95.59	odd	18	inner
380.3.bc.a.249.18	yes	120	19.2	odd	18	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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	380.bc (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.70131 + 3.10577i) q^{3} +(-4.40108 + 2.37286i) q^{5} +(-5.39353 - 3.11396i) q^{7} +(2.49107 - 14.1276i) q^{9} +O(q^{10})\)	\(q+(-3.70131 + 3.10577i) q^{3} +(-4.40108 + 2.37286i) q^{5} +(-5.39353 - 3.11396i) q^{7} +(2.49107 - 14.1276i) q^{9} +(-5.50250 - 9.53061i) q^{11} +(2.18533 + 1.83371i) q^{13} +(8.92023 - 22.4514i) q^{15} +(-10.0440 + 1.77103i) q^{17} +(6.50913 + 17.8502i) q^{19} +(29.6344 - 5.22534i) q^{21} +(11.1915 + 30.7484i) q^{23} +(13.7391 - 20.8863i) q^{25} +(12.9140 + 22.3677i) q^{27} +(35.2028 + 6.20721i) q^{29} +(-32.0389 - 18.4977i) q^{31} +(49.9664 + 18.1863i) q^{33} +(31.1264 + 0.906694i) q^{35} +19.2462 q^{37} -13.7837 q^{39} +(20.3488 + 24.2508i) q^{41} +(16.3688 - 44.9730i) q^{43} +(22.5593 + 68.0876i) q^{45} +(-73.4155 - 12.9451i) q^{47} +(-5.10654 - 8.84478i) q^{49} +(31.6756 - 37.7495i) q^{51} +(68.3938 - 24.8933i) q^{53} +(46.8318 + 28.8884i) q^{55} +(-79.5311 - 45.8535i) q^{57} +(-1.75422 + 0.309316i) q^{59} +(99.4120 - 36.1830i) q^{61} +(-57.4283 + 68.4404i) q^{63} +(-13.9690 - 2.88483i) q^{65} +(-2.73000 + 15.4826i) q^{67} +(-136.921 - 79.0513i) q^{69} +(29.4037 - 80.7861i) q^{71} +(0.964646 + 1.14962i) q^{73} +(14.0154 + 119.977i) q^{75} +68.5382i q^{77} +(23.0023 + 27.4131i) q^{79} +(4.05556 + 1.47610i) q^{81} +(-96.0430 - 55.4504i) q^{83} +(40.0021 - 31.6275i) q^{85} +(-149.575 + 86.3571i) q^{87} +(-9.32264 + 11.1103i) q^{89} +(-6.07655 - 16.6952i) q^{91} +(176.036 - 31.0398i) q^{93} +(-71.0033 - 63.1152i) q^{95} +(-17.0891 - 96.9169i) q^{97} +(-148.352 + 53.9955i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q+O(q^{10}) \) 120 * q	\( 120 q + 30 q^{11} - 3 q^{15} + 24 q^{19} - 72 q^{21} + 150 q^{25} + 60 q^{29} + 171 q^{35} + 24 q^{39} - 12 q^{41} - 90 q^{45} + 270 q^{49} - 144 q^{51} + 3 q^{55} + 84 q^{59} + 396 q^{61} - 405 q^{65} + 420 q^{71} + 96 q^{79} - 120 q^{81} + 30 q^{85} + 12 q^{89} - 84 q^{91} + 267 q^{95} + 324 q^{99}+O(q^{100}) \) 120 * q + 30 * q^11 - 3 * q^15 + 24 * q^19 - 72 * q^21 + 150 * q^25 + 60 * q^29 + 171 * q^35 + 24 * q^39 - 12 * q^41 - 90 * q^45 + 270 * q^49 - 144 * q^51 + 3 * q^55 + 84 * q^59 + 396 * q^61 - 405 * q^65 + 420 * q^71 + 96 * q^79 - 120 * q^81 + 30 * q^85 + 12 * q^89 - 84 * q^91 + 267 * q^95 + 324 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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