LMFDB - Embedded newform 380.3.bc.a.249.18

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			249.18
Character	$\chi$	$=$	380.249
Dual form			380.3.bc.a.29.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.70131 + 3.10577i) q^{3} +(-1.84618 + 4.64668i) q^{5} +(5.39353 - 3.11396i) q^{7} +(2.49107 + 14.1276i) q^{9} +O(q^{10})$	\(q+(3.70131 + 3.10577i) q^{3} +(-1.84618 + 4.64668i) q^{5} +(5.39353 - 3.11396i) q^{7} +(2.49107 + 14.1276i) q^{9} +(-5.50250 + 9.53061i) q^{11} +(-2.18533 + 1.83371i) q^{13} +(-21.2648 + 11.4650i) q^{15} +(10.0440 + 1.77103i) q^{17} +(6.50913 - 17.8502i) q^{19} +(29.6344 + 5.22534i) q^{21} +(-11.1915 + 30.7484i) q^{23} +(-18.1832 - 17.1572i) q^{25} +(-12.9140 + 22.3677i) q^{27} +(35.2028 - 6.20721i) q^{29} +(-32.0389 + 18.4977i) q^{31} +(-49.9664 + 18.1863i) q^{33} +(4.51212 + 30.8109i) q^{35} -19.2462 q^{37} -13.7837 q^{39} +(20.3488 - 24.2508i) q^{41} +(-16.3688 - 44.9730i) q^{43} +(-70.2453 - 14.5069i) q^{45} +(73.4155 - 12.9451i) q^{47} +(-5.10654 + 8.84478i) q^{49} +(31.6756 + 37.7495i) q^{51} +(-68.3938 - 24.8933i) q^{53} +(-34.1271 - 43.1636i) q^{55} +(79.5311 - 45.8535i) q^{57} +(-1.75422 - 0.309316i) q^{59} +(99.4120 + 36.1830i) q^{61} +(57.4283 + 68.4404i) q^{63} +(-4.48614 - 13.5399i) q^{65} +(2.73000 + 15.4826i) q^{67} +(-136.921 + 79.0513i) q^{69} +(29.4037 + 80.7861i) q^{71} +(-0.964646 + 1.14962i) q^{73} +(-14.0154 - 119.977i) q^{75} +68.5382i q^{77} +(23.0023 - 27.4131i) q^{79} +(4.05556 - 1.47610i) q^{81} +(96.0430 - 55.4504i) q^{83} +(-26.7725 + 43.4016i) q^{85} +(149.575 + 86.3571i) q^{87} +(-9.32264 - 11.1103i) q^{89} +(-6.07655 + 16.6952i) q^{91} +(-176.036 - 31.0398i) q^{93} +(70.9273 + 63.2006i) q^{95} +(17.0891 - 96.9169i) q^{97} +(-148.352 - 53.9955i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

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

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	0.997985	+	0.0634514i	$0.0202108\pi$
$3$	3.70131	+	3.10577i	1.23377	+	1.03526i	0.235786	+	0.971805i	$0.424234\pi$
$4$		0			0
$5$	−1.84618	+	4.64668i	−0.369236	+	0.929336i
$5$	−1.84618	+	4.64668i	−0.369236	+	0.929336i
$6$		0			0
$7$	5.39353	−	3.11396i	0.770505	−	0.444851i	−0.0625499	−	0.998042i	$-0.519923\pi$
$7$	5.39353	−	3.11396i	0.770505	−	0.444851i	0.833055	+	0.553191i	$0.186590\pi$
$8$		0			0
$9$	2.49107	+	14.1276i	0.276786	+	1.56973i
$10$		0			0
$11$	−5.50250	+	9.53061i	−0.500227	+	0.866419i	0.499773	+	0.866157i	$0.333417\pi$
$11$	−5.50250	+	9.53061i	−0.500227	+	0.866419i	−1.00000		0.000262521i	$0.999916\pi$
$12$		0			0
$13$	−2.18533	+	1.83371i	−0.168102	+	0.141055i	−0.722958	−	0.690892i	$-0.757218\pi$
$13$	−2.18533	+	1.83371i	−0.168102	+	0.141055i	0.554856	+	0.831947i	$0.312774\pi$
$14$		0			0
$15$	−21.2648	+	11.4650i	−1.41765	+	0.764333i
$16$		0			0
$17$	10.0440	+	1.77103i	0.590824	+	0.104178i	0.461064	−	0.887367i	$-0.347468\pi$
$17$	10.0440	+	1.77103i	0.590824	+	0.104178i	0.129761	+	0.991545i	$0.458579\pi$
$18$		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	0.417164	+	0.908831i	$0.363024\pi$
$23$	−11.1915	+	30.7484i	−0.486588	+	1.33689i	−0.903751	+	0.428058i	$0.859198\pi$
$24$		0			0
$25$	−18.1832	−	17.1572i	−0.727329	−	0.686289i
$26$		0			0
$27$	−12.9140	+	22.3677i	−0.478297	+	0.828434i
$28$		0			0
$29$	35.2028	−	6.20721i	1.21389	−	0.214042i	0.470197	−	0.882562i	$-0.344183\pi$
$29$	35.2028	−	6.20721i	1.21389	−	0.214042i	0.743694	+	0.668520i	$0.233072\pi$
$30$		0			0
$31$	−32.0389	+	18.4977i	−1.03351	+	0.596699i	−0.917989	−	0.396605i	$-0.870188\pi$
$31$	−32.0389	+	18.4977i	−1.03351	+	0.596699i	−0.115524	+	0.993305i	$0.536855\pi$
$32$		0			0
$33$	−49.9664	+	18.1863i	−1.51413	+	0.551099i
$34$		0			0
$35$	4.51212	+	30.8109i	0.128918	+	0.880313i
$36$		0			0
$37$	−19.2462			−0.520166			−0.260083	−	0.965586i	$-0.583750\pi$
$37$	−19.2462			−0.520166			−0.260083	+	0.965586i	$0.583750\pi$
$38$		0			0
$39$	−13.7837			−0.353427
$40$		0			0
$41$	20.3488	−	24.2508i	0.496313	−	0.591483i	−0.458498	−	0.888695i	$-0.651613\pi$
$41$	20.3488	−	24.2508i	0.496313	−	0.591483i	0.954811	+	0.297212i	$0.0960569\pi$
$42$		0			0
$43$	−16.3688	−	44.9730i	−0.380671	−	1.04588i	−0.971075	−	0.238777i	$-0.923254\pi$
$43$	−16.3688	−	44.9730i	−0.380671	−	1.04588i	0.590404	−	0.807108i	$-0.298969\pi$
$44$		0			0
$45$	−70.2453	−	14.5069i	−1.56101	−	0.322374i
$46$		0			0
$47$	73.4155	−	12.9451i	1.56203	−	0.275428i	0.675241	−	0.737598i	$-0.264040\pi$
$47$	73.4155	−	12.9451i	1.56203	−	0.275428i	0.886792	+	0.462169i	$0.152929\pi$
$48$		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	$-0.629801\pi$
$53$	−68.3938	−	24.8933i	−1.29045	−	0.469685i	−0.893874	+	0.448318i	$0.852023\pi$
$54$		0			0
$55$	−34.1271	−	43.1636i	−0.620492	−	0.784792i
$56$		0			0
$57$	79.5311	−	45.8535i	1.39528	−	0.804447i
$58$		0			0
$59$	−1.75422	−	0.309316i	−0.0297325	−	0.00524264i	0.158762	−	0.987317i	$-0.449250\pi$
$59$	−1.75422	−	0.309316i	−0.0297325	−	0.00524264i	−0.188495	+	0.982074i	$0.560361\pi$
$60$		0			0
$61$	99.4120	+	36.1830i	1.62971	+	0.593164i	0.985196	−	0.171432i	$-0.0548395\pi$
$61$	99.4120	+	36.1830i	1.62971	+	0.593164i	0.644509	+	0.764596i	$0.277062\pi$
$62$		0			0
$63$	57.4283	+	68.4404i	0.911561	+	1.08636i
$64$		0			0
$65$	−4.48614	−	13.5399i	−0.0690176	−	0.208306i
$66$		0			0
$67$	2.73000	+	15.4826i	0.0407463	+	0.231084i	0.998379	−	0.0569071i	$-0.0181239\pi$
$67$	2.73000	+	15.4826i	0.0407463	+	0.231084i	−0.957633	+	0.287991i	$0.907013\pi$
$68$		0			0
$69$	−136.921	+	79.0513i	−1.98436	+	1.14567i
$70$		0			0
$71$	29.4037	+	80.7861i	0.414137	+	1.13783i	0.954970	+	0.296702i	$0.0958869\pi$
$71$	29.4037	+	80.7861i	0.414137	+	1.13783i	−0.540833	+	0.841130i	$0.681891\pi$
$72$		0			0
$73$	−0.964646	+	1.14962i	−0.0132143	+	0.0157482i	−0.772611	−	0.634880i	$-0.781050\pi$
$73$	−0.964646	+	1.14962i	−0.0132143	+	0.0157482i	0.759397	+	0.650628i	$0.225494\pi$
$74$		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	−0.600554	−	0.799584i	$-0.705053\pi$
$79$	23.0023	−	27.4131i	0.291168	−	0.347001i	0.891722	+	0.452584i	$0.149498\pi$
$80$		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	$-0.433784\pi$
$83$	96.0430	−	55.4504i	1.15714	−	0.668077i	0.950618	+	0.310364i	$0.100451\pi$
$84$		0			0
$85$	−26.7725	+	43.4016i	−0.314970	+	0.510607i
$86$		0			0
$87$	149.575	+	86.3571i	1.71925	+	0.992610i
$88$		0			0
$89$	−9.32264	−	11.1103i	−0.104749	−	0.124835i	0.711123	−	0.703068i	$-0.248187\pi$
$89$	−9.32264	−	11.1103i	−0.104749	−	0.124835i	−0.815872	+	0.578233i	$0.803742\pi$
$90$		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
$95$	70.9273	+	63.2006i	0.746603	+	0.665270i
$96$		0			0
$97$	17.0891	−	96.9169i	0.176176	−	0.999143i	−0.760602	−	0.649218i	$-0.775096\pi$
$97$	17.0891	−	96.9169i	0.176176	−	0.999143i	0.936778	−	0.349925i	$-0.113793\pi$
$98$		0			0
$99$	−148.352	−	53.9955i	−1.49850	−	0.545410i
$100$		0			0
$101$	−10.6708	+	8.95385i	−0.105651	+	0.0886520i	−0.694083	−	0.719895i	$-0.744190\pi$
$101$	−10.6708	+	8.95385i	−0.105651	+	0.0886520i	0.588432	+	0.808547i	$0.299746\pi$
$102$		0			0
$103$	20.5158	−	35.5344i	0.199182	−	0.344994i	−0.749081	−	0.662478i	$-0.769505\pi$
$103$	20.5158	−	35.5344i	0.199182	−	0.344994i	0.948264	+	0.317484i	$0.102838\pi$
$104$		0			0
$105$	−78.9909	+	128.055i	−0.752294	+	1.21957i
$106$		0			0
$107$	−22.8431	−	39.5654i	−0.213487	−	0.369770i	0.739317	−	0.673358i	$-0.235149\pi$
$107$	−22.8431	−	39.5654i	−0.213487	−	0.369770i	−0.952803	+	0.303588i	$0.901815\pi$
$108$		0			0
$109$	28.7117	+	78.8848i	0.263410	+	0.723714i	0.998932	+	0.0462122i	$0.0147150\pi$
$109$	28.7117	+	78.8848i	0.263410	+	0.723714i	−0.735521	+	0.677501i	$0.763063\pi$
$110$		0			0
$111$	−71.2360	−	59.7741i	−0.641766	−	0.538506i
$112$		0			0
$113$	100.441			0.888859			0.444430	−	0.895814i	$-0.353406\pi$
$113$	100.441			0.888859			0.444430	+	0.895814i	$0.353406\pi$
$114$		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
$125$	113.294	−	52.8163i	0.906349	−	0.422530i
$126$		0			0
$127$	97.0632	−	81.4457i	0.764277	−	0.641304i	−0.174960	−	0.984576i	$-0.555979\pi$
$127$	97.0632	−	81.4457i	0.764277	−	0.641304i	0.939236	+	0.343271i	$0.111535\pi$
$128$		0			0
$129$	79.0897	−	217.297i	0.613098	−	1.68447i
$130$		0			0
$131$	44.6821	−	253.405i	0.341085	−	1.93439i	−0.0148787	−	0.999889i	$-0.504736\pi$
$131$	44.6821	−	253.405i	0.341085	−	1.93439i	0.355964	−	0.934500i	$-0.384153\pi$
$132$		0			0
$133$	−20.4777	−	116.545i	−0.153968	−	0.876278i
$134$		0			0
$135$	−80.0940	−	101.302i	−0.593289	−	0.750386i
$136$		0			0
$137$	−36.1609	+	99.3513i	−0.263948	+	0.725192i	0.734944	+	0.678128i	$0.237209\pi$
$137$	−36.1609	+	99.3513i	−0.263948	+	0.725192i	−0.998892	+	0.0470637i	$0.985014\pi$
$138$		0			0
$139$	177.969	−	149.334i	1.28035	−	1.07434i	0.287157	−	0.957884i	$-0.407290\pi$
$139$	177.969	−	149.334i	1.28035	−	1.07434i	0.993195	−	0.116460i	$-0.0371546\pi$
$140$		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
$145$	−36.1479	+	175.036i	−0.249296	+	1.20714i
$146$		0			0
$147$	−46.3707	+	16.8776i	−0.315447	+	0.114813i
$148$		0			0
$149$	−99.6722	−	83.6349i	−0.668941	−	0.561308i	0.243811	−	0.969823i	$-0.421602\pi$
$149$	−99.6722	−	83.6349i	−0.668941	−	0.561308i	−0.912752	+	0.408515i	$0.866047\pi$
$150$		0			0
$151$			83.6396i			0.553905i	0.960884	+	0.276952i	$0.0893244\pi$
$151$			83.6396i			0.553905i	−0.960884	+	0.276952i	$0.910676\pi$
$152$		0			0
$153$			146.309i			0.956270i
$154$		0			0
$155$	−26.8031	−	183.025i	−0.172923	−	1.18080i
$156$		0			0
$157$	−48.8046	−	134.090i	−0.310857	−	0.854074i	−0.992484	−	0.122374i	$-0.960949\pi$
$157$	−48.8046	−	134.090i	−0.310857	−	0.854074i	0.681627	−	0.731700i	$-0.261273\pi$
$158$		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	$-0.474882\pi$
$163$	−121.449	−	70.1187i	−0.745087	−	0.430176i	−0.823916	+	0.566712i	$0.808215\pi$
$164$		0			0
$165$	7.74123	−	265.753i	0.0469166	−	1.61062i
$166$		0			0
$167$	−272.922	−	99.3354i	−1.63426	−	0.594823i	−0.648240	−	0.761436i	$-0.724495\pi$
$167$	−272.922	−	99.3354i	−1.63426	−	0.594823i	−0.986022	+	0.166613i	$0.946717\pi$
$168$		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	−0.920489	−	0.390769i	$-0.872209\pi$
$173$	13.5180	−	76.6642i	0.0781385	−	0.443146i	0.998627	−	0.0523768i	$-0.0166797\pi$
$174$		0			0
$175$	−151.499	−	35.9162i	−0.865707	−	0.205236i
$176$		0			0
$177$	−5.53224	−	6.59307i	−0.0312556	−	0.0372490i
$178$		0			0
$179$	−117.256	−	67.6978i	−0.655061	−	0.378200i	0.135331	−	0.990800i	$-0.456790\pi$
$179$	−117.256	−	67.6978i	−0.655061	−	0.378200i	−0.790393	+	0.612601i	$0.790123\pi$
$180$		0			0
$181$	−338.236	+	59.6401i	−1.86871	+	0.329503i	−0.989222	−	0.146424i	$-0.953224\pi$
$181$	−338.236	+	59.6401i	−1.86871	+	0.329503i	−0.879485	+	0.475927i	$0.842113\pi$
$182$		0			0
$183$	255.579	+	442.675i	1.39661	+	2.41899i
$184$		0			0
$185$	35.5319	−	89.4307i	0.192064	−	0.483409i
$186$		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	$-0.355428\pi$
$193$	−71.4194	−	59.9280i	−0.370049	−	0.310508i	−0.808781	+	0.588110i	$0.799872\pi$
$194$		0			0
$195$	25.4471	−	64.0482i	0.130498	−	0.328453i
$196$		0			0
$197$	−136.779	+	78.9693i	−0.694309	+	0.400859i	−0.805224	−	0.592970i	$-0.797955\pi$
$197$	−136.779	+	78.9693i	−0.694309	+	0.400859i	0.110915	+	0.993830i	$0.464622\pi$
$198$		0			0
$199$	15.2690	+	86.5949i	0.0767288	+	0.435150i	0.998837	+	0.0482180i	$0.0153542\pi$
$199$	15.2690	+	86.5949i	0.0767288	+	0.435150i	−0.922108	+	0.386932i	$0.873535\pi$
$200$		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
$205$	75.1180	+	139.326i	0.366429	+	0.679638i
$206$		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	0.854729	−	0.519074i	$-0.173723\pi$
$211$	312.360	+	55.0775i	1.48038	+	0.261031i	0.625649	+	0.780105i	$0.284834\pi$
$212$		0			0
$213$	−142.071	+	390.336i	−0.666998	+	1.83256i
$214$		0			0
$215$	239.195	+	6.96762i	1.11254	+	0.0324075i
$216$		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	$-0.345178\pi$
$223$	310.807	−	113.124i	1.39375	−	0.507284i	0.926318	+	0.376743i	$0.122956\pi$
$224$		0			0
$225$	197.094	−	299.625i	0.875974	−	1.33167i
$226$		0			0
$227$	−5.57972			−0.0245803			−0.0122901	−	0.999924i	$-0.503912\pi$
$227$	−5.57972			−0.0245803			−0.0122901	+	0.999924i	$0.503912\pi$
$228$		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	$-0.147740\pi$
$233$	−18.3000	−	50.2789i	−0.0785408	−	0.215789i	−0.972748	+	0.231864i	$0.925518\pi$
$234$		0			0
$235$	−75.3865	+	365.037i	−0.320794	+	1.55335i
$236$		0			0
$237$	170.277	−	30.0245i	0.718470	−	0.126686i
$238$		0			0
$239$	−187.445	+	324.665i	−0.784290	+	1.35843i	0.145132	+	0.989412i	$0.453639\pi$
$239$	−187.445	+	324.665i	−0.784290	+	1.35843i	−0.929422	+	0.369018i	$0.879694\pi$
$240$		0			0
$241$	112.767	+	134.391i	0.467914	+	0.557639i	0.947458	−	0.319879i	$-0.103642\pi$
$241$	112.767	+	134.391i	0.467914	+	0.557639i	−0.479544	+	0.877518i	$0.659198\pi$
$242$		0			0
$243$	238.029	+	86.6355i	0.979543	+	0.356525i
$244$		0			0
$245$	−31.6712	−	40.0575i	−0.129270	−	0.163500i
$246$		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	0.848559	−	0.529100i	$-0.177471\pi$
$251$	290.782	+	105.836i	1.15849	+	0.421657i	0.309935	+	0.950758i	$0.399693\pi$
$252$		0			0
$253$	−231.470	−	275.855i	−0.914902	−	1.09034i
$254$		0			0
$255$	−233.889	+	77.4939i	−0.917211	+	0.303898i
$256$		0			0
$257$	78.4041	+	444.652i	0.305075	+	1.73016i	0.623154	+	0.782099i	$0.285851\pi$
$257$	78.4041	+	444.652i	0.305075	+	1.73016i	−0.318079	+	0.948064i	$0.603038\pi$
$258$		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	$-0.807925\pi$
$263$	−31.9739	+	38.1050i	−0.121574	+	0.144886i	0.701824	+	0.712350i	$0.252369\pi$
$264$		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	−0.943062	−	0.332617i	$-0.892068\pi$
$269$	−121.517	+	144.819i	−0.451737	+	0.538359i	0.491325	+	0.870976i	$0.336513\pi$
$270$		0			0
$271$	−161.727	+	58.8637i	−0.596778	+	0.217209i	−0.622708	−	0.782454i	$-0.713968\pi$
$271$	−161.727	+	58.8637i	−0.596778	+	0.217209i	0.0259301	+	0.999664i	$0.491745\pi$
$272$		0			0
$273$	−74.3426	+	42.9217i	−0.272317	+	0.157223i
$274$		0			0
$275$	263.572	−	78.8897i	0.958444	−	0.286872i
$276$		0			0
$277$	−309.467	−	178.671i	−1.11721	−	0.645021i	−0.176523	−	0.984297i	$-0.556485\pi$
$277$	−309.467	−	178.671i	−1.11721	−	0.645021i	−0.940687	+	0.339275i	$0.889818\pi$
$278$		0			0
$279$	−341.139	−	406.553i	−1.22272	−	1.45718i
$280$		0			0
$281$	155.851	−	428.198i	0.554631	−	1.52384i	−0.272686	−	0.962103i	$-0.587912\pi$
$281$	155.851	−	428.198i	0.554631	−	1.52384i	0.827318	−	0.561734i	$-0.189866\pi$
$282$		0			0
$283$	−353.971	−	62.4146i	−1.25078	−	0.220546i	−0.491250	−	0.871018i	$-0.663460\pi$
$283$	−353.971	−	62.4146i	−1.25078	−	0.220546i	−0.759530	+	0.650472i	$0.774571\pi$
$284$		0			0
$285$	66.2376	+	454.209i	0.232412	+	1.59372i
$286$		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	$-0.909130\pi$
$293$	−69.1119	+	119.705i	−0.235877	+	0.408551i	0.723650	+	0.690167i	$0.242463\pi$
$294$		0			0
$295$	4.67590	−	7.58023i	0.0158505	−	0.0256957i
$296$		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	$-0.389307\pi$
$307$	−161.450	−	135.473i	−0.525895	−	0.441279i	−0.866681	+	0.498862i	$0.833751\pi$
$308$		0			0
$309$	186.297	−	67.8065i	0.602903	−	0.219439i
$310$		0			0
$311$	265.110	+	459.184i	0.852444	+	1.47648i	0.878996	+	0.476828i	$0.158214\pi$
$311$	265.110	+	459.184i	0.852444	+	1.47648i	−0.0265526	+	0.999647i	$0.508453\pi$
$312$		0			0
$313$	−411.512	+	72.5606i	−1.31473	+	0.231823i	−0.786666	−	0.617379i	$-0.788194\pi$
$313$	−411.512	+	72.5606i	−1.31473	+	0.231823i	−0.528068	+	0.849202i	$0.677083\pi$
$314$		0			0
$315$	−424.044	+	140.498i	−1.34617	+	0.446024i
$316$		0			0
$317$	−102.814	+	86.2708i	−0.324333	+	0.272148i	−0.790386	−	0.612609i	$-0.790120\pi$
$317$	−102.814	+	86.2708i	−0.324333	+	0.272148i	0.466053	+	0.884757i	$0.345676\pi$
$318$		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
$325$	71.1977	+	4.15142i	0.219070	+	0.0127736i
$326$		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	0.379069	−	0.925368i	$-0.376244\pi$
$331$	−77.0531	−	44.4866i	−0.232789	−	0.134401i	−0.611858	+	0.790968i	$0.709578\pi$
$332$		0			0
$333$	−47.9436	−	271.901i	−0.143975	−	0.816521i
$334$		0			0
$335$	−76.9828	−	15.8983i	−0.229799	−	0.0474575i
$336$		0			0
$337$	239.236	−	87.0749i	0.709900	−	0.258383i	0.0382682	−	0.999268i	$-0.487816\pi$
$337$	239.236	−	87.0749i	0.709900	−	0.258383i	0.671632	+	0.740885i	$0.265594\pi$
$338$		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
$345$	−114.545	−	782.170i	−0.332015	−	2.26716i
$346$		0			0
$347$	101.149	+	277.905i	0.291496	+	0.800879i	0.995848	+	0.0910283i	$0.0290154\pi$
$347$	101.149	+	277.905i	0.291496	+	0.800879i	−0.704352	+	0.709851i	$0.748762\pi$
$348$		0			0
$349$	−65.4118	−	113.297i	−0.187426	−	0.324632i	0.756965	−	0.653455i	$-0.226681\pi$
$349$	−65.4118	−	113.297i	−0.187426	−	0.324632i	−0.944391	+	0.328823i	$0.893348\pi$
$350$		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	$-0.437915\pi$
$353$	−197.288	−	113.904i	−0.558888	−	0.322674i	−0.752699	+	0.658365i	$0.771249\pi$
$354$		0			0
$355$	−429.672	−	12.5161i	−1.21034	−	0.0352566i
$356$		0			0
$357$	288.394	+	104.967i	0.807826	+	0.294025i
$358$		0			0
$359$	46.7510	−	265.138i	0.130226	−	0.738547i	−0.847840	−	0.530252i	$-0.822097\pi$
$359$	46.7510	−	265.138i	0.130226	−	0.738547i	0.978066	−	0.208295i	$-0.0667914\pi$
$360$		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
$365$	−3.56100	−	6.60481i	−0.00975618	−	0.0180954i
$366$		0			0
$367$	131.716	+	156.973i	0.358899	+	0.427719i	0.915036	−	0.403371i	$-0.132162\pi$
$367$	131.716	+	156.973i	0.358899	+	0.427719i	−0.556138	+	0.831090i	$0.687717\pi$
$368$		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	$-0.292844\pi$
$373$	−144.014	−	249.440i	−0.386098	−	0.668741i	−0.991921	+	0.126859i	$0.959511\pi$
$374$		0			0
$375$	583.370	+	156.374i	1.55565	+	0.416998i
$376$		0			0
$377$	−65.5476	+	78.1166i	−0.173866	+	0.207206i
$378$		0			0
$379$		−	374.063i		−	0.986975i	−0.869753	−	0.493487i	$-0.835722\pi$
$379$		−	374.063i		−	0.986975i	0.869753	−	0.493487i	$-0.164278\pi$
$380$		0			0
$381$	612.212			1.60686
$382$		0			0
$383$	−4.66590	−	3.91515i	−0.0121825	−	0.0102223i	0.636676	−	0.771131i	$-0.280309\pi$
$383$	−4.66590	−	3.91515i	−0.0121825	−	0.0102223i	−0.648859	+	0.760909i	$0.724753\pi$
$384$		0			0
$385$	−318.475	−	126.534i	−0.827208	−	0.328660i
$386$		0			0
$387$	594.584	−	343.283i	1.53639	−	0.887037i
$388$		0			0
$389$	30.4427	+	172.649i	0.0782589	+	0.443828i	0.998609	+	0.0527320i	$0.0167929\pi$
$389$	30.4427	+	172.649i	0.0782589	+	0.443828i	−0.920350	+	0.391096i	$0.872096\pi$
$390$		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
$395$	84.9133	+	157.494i	0.214970	+	0.398718i
$396$		0			0
$397$	23.0745	+	4.06865i	0.0581221	+	0.0102485i	0.202634	−	0.979255i	$-0.435050\pi$
$397$	23.0745	+	4.06865i	0.0581221	+	0.0102485i	−0.144511	+	0.989503i	$0.546161\pi$
$398$		0			0
$399$	286.168	−	494.969i	0.717212	−	1.24052i
$400$		0			0
$401$	−673.256	−	118.713i	−1.67894	−	0.296043i	−0.748679	−	0.662933i	$-0.769311\pi$
$401$	−673.256	−	118.713i	−1.67894	−	0.296043i	−0.930264	+	0.366890i	$0.880423\pi$
$402$		0			0
$403$	36.0962	−	99.1736i	0.0895688	−	0.246088i
$404$		0			0
$405$	−0.628324	+	21.5701i	−0.00155142	+	0.0532594i
$406$		0			0
$407$	105.902	−	183.428i	0.260201	−	0.450682i
$408$		0			0
$409$	−152.896	+	26.9598i	−0.373830	+	0.0659163i	−0.357407	−	0.933949i	$-0.616339\pi$
$409$	−152.896	+	26.9598i	−0.373830	+	0.0659163i	−0.0164231	+	0.999865i	$0.505228\pi$
$410$		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
$415$	80.3476	+	548.652i	0.193609	+	1.32205i
$416$		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	−0.00525979	+	0.999986i	$0.501674\pi$
$421$	−416.428	+	496.280i	−0.989141	+	1.17881i	−0.983881	+	0.178826i	$0.942770\pi$
$422$		0			0
$423$	365.767	+	1004.94i	0.864697	+	2.37573i
$424$		0			0
$425$	−152.247	−	204.530i	−0.358227	−	0.481248i
$426$		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	0.584191	−	0.811616i	$-0.301412\pi$
$431$	−136.428	−	162.589i	−0.316539	−	0.377236i	−0.900730	+	0.434380i	$0.856967\pi$
$432$		0			0
$433$	−465.015	−	169.252i	−1.07394	−	0.390881i	−0.256290	−	0.966600i	$-0.582500\pi$
$433$	−465.015	−	169.252i	−1.07394	−	0.390881i	−0.817648	+	0.575718i	$0.804722\pi$
$434$		0			0
$435$	−677.416	+	535.595i	−1.55728	+	1.23125i
$436$		0			0
$437$	476.020	+	399.917i	1.08929	+	0.915142i
$438$		0			0
$439$	−183.802	−	32.4092i	−0.418683	−	0.0738251i	−0.0396619	−	0.999213i	$-0.512628\pi$
$439$	−183.802	−	32.4092i	−0.418683	−	0.0738251i	−0.379021	+	0.925388i	$0.623739\pi$
$440$		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	$-0.183159\pi$
$443$	69.7156	+	83.0838i	0.157371	+	0.187548i	−0.681597	+	0.731727i	$0.738714\pi$
$444$		0			0
$445$	68.8372	−	22.8077i	0.154690	−	0.0512533i
$446$		0			0
$447$	−109.167	−	619.118i	−0.244222	−	1.38505i
$448$		0			0
$449$	−6.26444	+	3.61678i	−0.0139520	+	0.00805518i	−0.506960	−	0.861970i	$-0.669231\pi$
$449$	−6.26444	+	3.61678i	−0.0139520	+	0.00805518i	0.493008	+	0.870025i	$0.335897\pi$
$450$		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	−0.150582	−	0.988598i	$-0.548115\pi$
$461$	170.351	−	62.0025i	0.369524	−	0.134496i	0.520106	+	0.854102i	$0.325892\pi$
$462$		0			0
$463$	389.839	−	225.074i	0.841986	−	0.486121i	−0.0159531	−	0.999873i	$-0.505078\pi$
$463$	389.839	−	225.074i	0.841986	−	0.486121i	0.857939	+	0.513752i	$0.171745\pi$
$464$		0			0
$465$	469.226	−	760.675i	1.00909	−	1.63586i
$466$		0			0
$467$	599.198	+	345.947i	1.28308	+	0.740786i	0.977410	−	0.211351i	$-0.0677864\pi$
$467$	599.198	+	345.947i	1.28308	+	0.740786i	0.305670	+	0.952138i	$0.401120\pi$
$468$		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
$475$	−424.618	+	212.897i	−0.893932	+	0.448203i
$476$		0			0
$477$	181.308	−	1028.25i	0.380101	−	2.15566i
$478$		0			0
$479$	639.439	+	232.737i	1.33495	+	0.485880i	0.908217	−	0.418500i	$-0.137444\pi$
$479$	639.439	+	232.737i	1.33495	+	0.485880i	0.426728	+	0.904380i	$0.359666\pi$
$480$		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
$485$	418.792	+	258.333i	0.863489	+	0.532646i
$486$		0			0
$487$	−418.424	−	724.731i	−0.859186	−	1.48815i	−0.872706	−	0.488246i	$-0.837637\pi$
$487$	−418.424	−	724.731i	−0.859186	−	1.48815i	0.0135198	−	0.999909i	$-0.495696\pi$
$488$		0			0
$489$	−231.749	−	636.724i	−0.473924	−	1.30209i
$490$		0			0
$491$	−245.424	−	205.935i	−0.499845	−	0.419420i	0.357694	−	0.933839i	$-0.383563\pi$
$491$	−245.424	−	205.935i	−0.499845	−	0.419420i	−0.857539	+	0.514419i	$0.828008\pi$
$492$		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	−0.316150	−	0.948709i	$-0.602390\pi$
$499$	25.6903	−	9.35050i	0.0514835	−	0.0187385i	0.367634	+	0.929971i	$0.380168\pi$
$500$		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	$-0.731633\pi$
$503$	−520.504	+	91.7789i	−1.03480	+	0.182463i	−0.369648	+	0.929172i	$0.620522\pi$
$504$		0			0
$505$	−21.9055	−	66.1141i	−0.0433772	−	0.130919i
$506$		0			0
$507$	−595.400	+	499.600i	−1.17436	+	0.985404i
$508$		0			0
$509$	−302.530	+	831.194i	−0.594361	+	1.63299i	0.167959	+	0.985794i	$0.446282\pi$
$509$	−302.530	+	831.194i	−0.594361	+	1.63299i	−0.762320	+	0.647200i	$0.775940\pi$
$510$		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
$515$	127.241	+	160.933i	0.247070	+	0.312492i
$516$		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	0.960338	−	0.278839i	$-0.0899496\pi$
$521$	624.692	+	360.666i	1.19903	+	0.692257i	0.238687	+	0.971097i	$0.423283\pi$
$522$		0			0
$523$	−168.483	−	955.513i	−0.322147	−	1.82698i	−0.529011	−	0.848615i	$-0.677437\pi$
$523$	−168.483	−	955.513i	−0.322147	−	1.82698i	0.206865	−	0.978370i	$-0.433674\pi$
$524$		0			0
$525$	−449.196	−	603.457i	−0.855612	−	1.14944i
$526$		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
$535$	226.020	−	33.0996i	0.422468	−	0.0618684i
$536$		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	−0.795766	−	0.605604i	$-0.792932\pi$
$541$	−138.020	−	782.748i	−0.255119	−	1.44685i	0.540647	−	0.841250i	$-0.318180\pi$
$542$		0			0
$543$	−1437.15	−	829.736i	−2.64668	−	1.52806i
$544$		0			0
$545$	−419.559	−	12.2215i	−0.769833	−	0.0224248i
$546$		0			0
$547$	552.475	+	201.084i	1.01001	+	0.367613i	0.793436	−	0.608653i	$-0.208290\pi$
$547$	552.475	+	201.084i	1.01001	+	0.367613i	0.216573	+	0.976266i	$0.430512\pi$
$548$		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
$555$	409.266	−	220.657i	0.737416	−	0.397580i
$556$		0			0
$557$	8.14290	+	9.70434i	0.0146192	+	0.0174225i	0.773305	−	0.634035i	$-0.218602\pi$
$557$	8.14290	+	9.70434i	0.0146192	+	0.0174225i	−0.758685	+	0.651457i	$0.774158\pi$
$558$		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	−0.948291	−	0.317401i	$-0.897190\pi$
$563$	−421.700	−	730.406i	−0.749023	−	1.29735i	0.199268	−	0.979945i	$-0.436143\pi$
$564$		0			0
$565$	−185.432	+	466.717i	−0.328199	+	0.826049i
$566$		0			0
$567$	17.2773	−	20.5903i	0.0304714	−	0.0363144i
$568$		0			0
$569$			166.474i			0.292572i	0.989242	+	0.146286i	$0.0467320\pi$
$569$			166.474i			0.292572i	−0.989242	+	0.146286i	$0.953268\pi$
$570$		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
$575$	731.056	−	367.091i	1.27140	−	0.638419i
$576$		0			0
$577$	91.4934	−	52.8238i	0.158567	−	0.0915490i	−0.418617	−	0.908163i	$-0.637485\pi$
$577$	91.4934	−	52.8238i	0.158567	−	0.0915490i	0.577184	+	0.816614i	$0.304152\pi$
$578$		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
$585$	180.110	−	97.1071i	0.307881	−	0.165995i
$586$		0			0
$587$	−149.284	−	26.3228i	−0.254317	−	0.0448430i	0.0450359	−	0.998985i	$-0.485660\pi$
$587$	−149.284	−	26.3228i	−0.254317	−	0.0448430i	−0.299353	+	0.954142i	$0.596771\pi$
$588$		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	0.428207	+	0.903681i	$0.359145\pi$
$593$	−285.051	+	783.171i	−0.480693	+	1.32069i	−0.908900	+	0.417013i	$0.863077\pi$
$594$		0			0
$595$	−9.24734	+	317.456i	−0.0155417	+	0.533540i
$596$		0			0
$597$	−212.428	+	367.937i	−0.355827	+	0.616310i
$598$		0			0
$599$	54.8231	−	9.66679i	0.0915243	−	0.0161382i	−0.127698	−	0.991813i	$-0.540759\pi$
$599$	54.8231	−	9.66679i	0.0915243	−	0.0161382i	0.219223	+	0.975675i	$0.429648\pi$
$600$		0			0
$601$	244.702	−	141.279i	0.407157	−	0.235072i	−0.282410	−	0.959294i	$-0.591134\pi$
$601$	244.702	−	141.279i	0.407157	−	0.235072i	0.689568	+	0.724221i	$0.257801\pi$
$602$		0			0
$603$	−211.931	+	77.1366i	−0.351461	+	0.127921i
$604$		0			0
$605$	0.544462	−	0.0797339i	0.000899937	−	0.000131792i
$606$		0			0
$607$	−1205.30			−1.98566			−0.992832	−	0.119520i	$-0.961864\pi$
$607$	−1205.30			−1.98566			−0.992832	+	0.119520i	$0.961864\pi$
$608$		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	0.967269	+	0.253755i	$0.0816655\pi$
$613$	238.707	+	655.843i	0.389408	+	1.06989i	−0.577861	+	0.816136i	$0.696112\pi$
$614$		0			0
$615$	−154.679	+	748.988i	−0.251510	+	1.21787i
$616$		0			0
$617$	21.3727	−	3.76858i	0.0346396	−	0.00610790i	−0.156302	−	0.987709i	$-0.549957\pi$
$617$	21.3727	−	3.76858i	0.0346396	−	0.00610790i	0.190941	+	0.981601i	$0.438846\pi$
$618$		0			0
$619$	523.107	−	906.048i	0.845084	−	1.46373i	−0.0404644	−	0.999181i	$-0.512884\pi$
$619$	523.107	−	906.048i	0.845084	−	1.46373i	0.885548	−	0.464547i	$-0.153783\pi$
$620$		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
$625$	36.2596	+	623.947i	0.0580154	+	0.998316i
$626$		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	0.992551	−	0.121827i	$-0.0388752\pi$
$631$	1056.66	+	384.593i	1.67458	+	0.609498i	0.682030	+	0.731324i	$0.261097\pi$
$632$		0			0
$633$	985.083	+	1173.98i	1.55621	+	1.85462i
$634$		0			0
$635$	199.256	+	601.385i	0.313788	+	0.947062i
$636$		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	−0.995055	−	0.0993261i	$-0.968331\pi$
$641$	−190.149	−	522.430i	−0.296644	−	0.815023i	0.698411	−	0.715697i	$-0.253891\pi$
$642$		0			0
$643$	−21.8161	+	25.9994i	−0.0339287	+	0.0404346i	−0.782742	−	0.622346i	$-0.786180\pi$
$643$	−21.8161	+	25.9994i	−0.0339287	+	0.0404346i	0.748813	+	0.662781i	$0.230624\pi$
$644$		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	$-0.524705\pi$
$653$	487.866	−	281.670i	0.747115	−	0.431347i	0.824651	+	0.565643i	$0.191372\pi$
$654$		0			0
$655$	1095.00	+	675.455i	1.67176	+	1.03123i
$656$		0			0
$657$	−18.6444	−	10.7643i	−0.0283780	−	0.0163841i
$658$		0			0
$659$	360.097	+	429.147i	0.546429	+	0.651209i	0.966616	−	0.256229i	$-0.0824800\pi$
$659$	360.097	+	429.147i	0.546429	+	0.651209i	−0.420187	+	0.907437i	$0.638036\pi$
$660$		0			0
$661$	−204.329	+	561.390i	−0.309122	+	0.849305i	0.683707	+	0.729757i	$0.260367\pi$
$661$	−204.329	+	561.390i	−0.309122	+	0.849305i	−0.992828	+	0.119548i	$0.961855\pi$
$662$		0			0
$663$	−138.443	−	24.4113i	−0.208813	−	0.0368194i
$664$		0			0
$665$	579.353	+	120.010i	0.871207	+	0.180466i
$666$		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	−0.0403372	−	0.999186i	$-0.512843\pi$
$673$	568.787	−	985.168i	0.845152	−	1.46385i	0.885489	−	0.464660i	$-0.153823\pi$
$674$		0			0
$675$	618.587	−	185.149i	0.916424	−	0.274295i
$676$		0			0
$677$	−455.681	−	789.262i	−0.673088	−	1.16582i	−0.977024	−	0.213130i	$-0.931634\pi$
$677$	−455.681	−	789.262i	−0.673088	−	1.16582i	0.303936	−	0.952692i	$-0.401699\pi$
$678$		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	$-0.660967\pi$
$683$	−661.708			−0.968826			−0.484413	+	0.874839i	$0.660967\pi$
$684$		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	0.900449	−	0.434961i	$-0.143238\pi$
$691$	50.8141	+	88.0125i	0.0735370	+	0.127370i	−0.826912	+	0.562331i	$0.809905\pi$
$692$		0			0
$693$	−968.279	+	170.734i	−1.39723	+	0.246369i
$694$		0			0
$695$	365.343	+	1102.66i	0.525673	+	1.58656i
$696$		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	0.592477	+	0.805588i	$0.298150\pi$
$701$	−168.097	+	953.327i	−0.239797	+	1.35995i	−0.832273	+	0.554366i	$0.812961\pi$
$702$		0			0
$703$	−125.276	+	343.549i	−0.178202	+	0.488689i
$704$		0			0
$705$	−1412.75	+	1116.98i	−2.00390	+	1.58437i
$706$		0			0
$707$	−29.6713	+	81.5213i	−0.0419679	+	0.115306i
$708$		0			0
$709$	88.1291	−	73.9491i	0.124301	−	0.104301i	−0.578518	−	0.815669i	$-0.696369\pi$
$709$	88.1291	−	73.9491i	0.124301	−	0.104301i	0.702819	+	0.711369i	$0.251924\pi$
$710$		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
$715$	153.728	+	31.7475i	0.215005	+	0.0444022i
$716$		0			0
$717$	−1702.13	+	619.524i	−2.37396	+	0.864050i
$718$		0			0
$719$	508.673	+	426.827i	0.707473	+	0.593640i	0.923889	−	0.382661i	$-0.124992\pi$
$719$	508.673	+	426.827i	0.707473	+	0.593640i	−0.216416	+	0.976301i	$0.569437\pi$
$720$		0			0
$721$		−	255.541i		−	0.354426i
$722$		0			0
$723$			847.652i			1.17241i
$724$		0			0
$725$	−746.600	−	491.116i	−1.02979	−	0.677401i
$726$		0			0
$727$	58.6097	+	161.029i	0.0806186	+	0.221498i	0.973453	−	0.228888i	$-0.0735088\pi$
$727$	58.6097	+	161.029i	0.0806186	+	0.221498i	−0.892834	+	0.450385i	$0.851287\pi$
$728$		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	$-0.601722\pi$
$733$	−948.075	−	547.371i	−1.29342	−	0.746755i	−0.979258	+	0.202616i	$0.935056\pi$
$734$		0			0
$735$	7.18416	−	246.629i	0.00977437	−	0.335549i
$736$		0			0
$737$	−162.581	−	59.1745i	−0.220598	−	0.0802910i
$738$		0			0
$739$	−134.060	+	760.292i	−0.181407	+	1.02881i	0.749078	+	0.662482i	$0.230497\pi$
$739$	−134.060	+	760.292i	−0.181407	+	1.02881i	−0.930485	+	0.366330i	$0.880614\pi$
$740$		0			0
$741$	−89.7196	+	246.042i	−0.121079	+	0.332040i
$742$		0			0
$743$	205.976	−	1168.15i	0.277222	−	1.57221i	−0.454591	−	0.890700i	$-0.650215\pi$
$743$	205.976	−	1168.15i	0.277222	−	1.57221i	0.731814	−	0.681505i	$-0.238674\pi$
$744$		0			0
$745$	572.637	−	308.739i	0.768641	−	0.414415i
$746$		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	0.879322	−	0.476228i	$-0.157996\pi$
$751$	1403.24	−	247.429i	1.86849	−	0.329466i	0.989172	+	0.146762i	$0.0468850\pi$
$752$		0			0
$753$	747.573	+	1294.83i	0.992793	+	1.71957i
$754$		0			0
$755$	−388.646	−	154.414i	−0.514763	−	0.204522i
$756$		0			0
$757$	−242.035	+	288.446i	−0.319730	+	0.381039i	−0.901839	−	0.432071i	$-0.857783\pi$
$757$	−242.035	+	288.446i	−0.319730	+	0.381039i	0.582110	+	0.813110i	$0.302227\pi$
$758$		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
$765$	−679.852	−	270.113i	−0.888695	−	0.353089i
$766$		0			0
$767$	4.40074	−	2.54077i	0.00573760	−	0.00331260i
$768$		0			0
$769$	28.1475	+	159.632i	0.0366027	+	0.207584i	0.997624	−	0.0688889i	$-0.0219454\pi$
$769$	28.1475	+	159.632i	0.0366027	+	0.207584i	−0.961022	+	0.276473i	$0.910834\pi$
$770$		0			0
$771$	−1090.79	+	1889.30i	−1.41477	+	2.45046i
$772$		0			0
$773$	951.125	−	798.088i	1.23043	−	1.03246i	0.232222	−	0.972663i	$-0.425400\pi$
$773$	951.125	−	798.088i	1.23043	−	1.03246i	0.998211	−	0.0597932i	$-0.0190441\pi$
$774$		0			0
$775$	899.940	+	213.351i	1.16121	+	0.275292i
$776$		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
$785$	713.173	+	20.7743i	0.908501	+	0.0264641i
$786$		0			0
$787$	−347.181	+	601.335i	−0.441145	+	0.764085i	−0.997775	−	0.0666752i	$-0.978761\pi$
$787$	−347.181	+	601.335i	−0.441145	+	0.764085i	0.556630	+	0.830761i	$0.312094\pi$
$788$		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
$795$	1739.78	−	254.783i	2.18840	−	0.320482i
$796$		0			0
$797$	−223.303			−0.280179			−0.140089	−	0.990139i	$-0.544739\pi$
$797$	−223.303			−0.280179			−0.140089	+	0.990139i	$0.544739\pi$
$798$		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
$805$	−997.886	−	206.081i	−1.23961	−	0.256001i
$806$		0			0
$807$	−899.547	+	158.614i	−1.11468	+	0.196548i
$808$		0			0
$809$	−413.014	+	715.361i	−0.510524	+	0.884253i	0.489402	+	0.872058i	$0.337215\pi$
$809$	−413.014	+	715.361i	−0.510524	+	0.884253i	−0.999926	+	0.0121948i	$0.996118\pi$
$810$		0			0
$811$	−546.655	−	651.478i	−0.674051	−	0.803302i	0.315279	−	0.948999i	$-0.397902\pi$
$811$	−546.655	−	651.478i	−0.674051	−	0.803302i	−0.989329	+	0.145697i	$0.953458\pi$
$812$		0			0
$813$	−781.419	−	284.413i	−0.961154	−	0.349832i
$814$		0			0
$815$	550.036	−	434.883i	0.674891	−	0.533599i
$816$		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	0.217348	−	0.976094i	$-0.430259\pi$
$821$	−199.975	−	72.7850i	−0.243575	−	0.0886541i	−0.460923	+	0.887440i	$0.652482\pi$
$822$		0			0
$823$	138.657	+	165.245i	0.168478	+	0.200784i	0.843676	−	0.536852i	$-0.180387\pi$
$823$	138.657	+	165.245i	0.168478	+	0.200784i	−0.675199	+	0.737636i	$0.735942\pi$
$824$		0			0
$825$	1220.58	+	526.599i	1.47949	+	0.638301i
$826$		0			0
$827$	−36.9515	−	209.562i	−0.0446813	−	0.253401i	0.954283	−	0.298905i	$-0.0966215\pi$
$827$	−36.9515	−	209.562i	−0.0446813	−	0.253401i	−0.998964	+	0.0455048i	$0.985510\pi$
$828$		0			0
$829$	1416.47	−	817.797i	1.70864	−	0.986486i	0.772399	−	0.635138i	$-0.219057\pi$
$829$	1416.47	−	817.797i	1.70864	−	0.986486i	0.936245	−	0.351348i	$-0.114277\pi$
$830$		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	−0.999793	−	0.0203528i	$-0.993521\pi$
$839$	−676.349	+	806.041i	−0.806137	+	0.960717i	0.193656	+	0.981070i	$0.437965\pi$
$840$		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
$845$	−684.547	−	422.266i	−0.810115	−	0.499723i
$846$		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	$-0.356684\pi$
$853$	457.367	+	80.6462i	0.536187	+	0.0945442i	0.101003	+	0.994886i	$0.467795\pi$
$854$		0			0
$855$	−716.186	+	1159.47i	−0.837645	+	1.35610i
$856$		0			0
$857$	−35.4066	+	200.801i	−0.0413146	+	0.234307i	−0.998472	−	0.0552616i	$-0.982401\pi$
$857$	−35.4066	+	200.801i	−0.0413146	+	0.234307i	0.957157	+	0.289569i	$0.0935118\pi$
$858$		0			0
$859$	642.546	+	233.868i	0.748017	+	0.272256i	0.687771	−	0.725928i	$-0.258589\pi$
$859$	642.546	+	233.868i	0.748017	+	0.272256i	0.0602457	+	0.998184i	$0.480812\pi$
$860$		0			0
$861$	729.744	−	612.328i	0.847554	−	0.711182i
$862$		0			0
$863$	−606.102	+	1049.80i	−0.702320	+	1.21645i	0.265331	+	0.964157i	$0.414519\pi$
$863$	−606.102	+	1049.80i	−0.702320	+	1.21645i	−0.967650	+	0.252296i	$0.918814\pi$
$864$		0			0
$865$	331.277	+	204.350i	0.382979	+	0.236242i
$866$		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	$-0.382450\pi$
$877$	−433.920	−	364.102i	−0.494778	−	0.415168i	−0.855735	+	0.517414i	$0.826895\pi$
$878$		0			0
$879$	−627.582	+	228.421i	−0.713973	+	0.259865i
$880$		0			0
$881$	309.992	+	536.922i	0.351864	+	0.609446i	0.986576	−	0.163303i	$-0.0522148\pi$
$881$	309.992	+	536.922i	0.351864	+	0.609446i	−0.634712	+	0.772748i	$0.718881\pi$
$882$		0			0
$883$	−1323.69	+	233.403i	−1.49909	+	0.264329i	−0.862176	−	0.506609i	$-0.830899\pi$
$883$	−1323.69	+	233.403i	−1.49909	+	0.264329i	−0.636910	+	0.770938i	$0.719788\pi$
$884$		0			0
$885$	40.8494	−	13.5345i	0.0461575	−	0.0152933i
$886$		0			0
$887$	1174.09	−	985.177i	1.32366	−	1.11068i	0.338148	−	0.941093i	$-0.390200\pi$
$887$	1174.09	−	985.177i	1.32366	−	1.11068i	0.985514	−	0.169591i	$-0.0542448\pi$
$888$		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
$895$	531.046	−	419.868i	0.593347	−	0.469127i
$896$		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
$905$	347.316	−	1681.78i	0.383775	−	1.85832i
$906$		0			0
$907$	1257.80	−	457.803i	1.38677	−	0.504744i	0.462548	−	0.886594i	$-0.346935\pi$
$907$	1257.80	−	457.803i	1.38677	−	0.504744i	0.924224	+	0.381851i	$0.124713\pi$
$908$		0			0
$909$	−153.078	−	128.448i	−0.168403	−	0.141307i
$910$		0			0
$911$		−	658.221i		−	0.722526i	−0.932464	−	0.361263i	$-0.882346\pi$
$911$		−	658.221i		−	0.722526i	0.932464	−	0.361263i	$-0.117654\pi$
$912$		0			0
$913$			1220.46i			1.33676i
$914$		0			0
$915$	−2528.81	+	370.333i	−2.76373	+	0.404736i
$916$		0			0
$917$	−548.098	−	1505.89i	−0.597708	−	1.64219i
$918$		0			0
$919$	−370.964	−	642.529i	−0.403661	−	0.699161i	0.590504	−	0.807035i	$-0.298929\pi$
$919$	−370.964	−	642.529i	−0.403661	−	0.699161i	−0.994165	+	0.107874i	$0.965596\pi$
$920$		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
$925$	349.957	+	330.210i	0.378332	+	0.356984i
$926$		0			0
$927$	553.121	+	201.320i	0.596679	+	0.217173i
$928$		0			0
$929$	−227.922	+	1292.61i	−0.245341	+	1.39140i	0.574358	+	0.818604i	$0.305252\pi$
$929$	−227.922	+	1292.61i	−0.245341	+	1.39140i	−0.819699	+	0.572794i	$0.805860\pi$
$930$		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
$935$	−266.329	−	493.975i	−0.284843	−	0.528316i
$936$		0			0
$937$	720.434	+	858.580i	0.768873	+	0.916308i	0.998374	−	0.0570008i	$-0.0181538\pi$
$937$	720.434	+	858.580i	0.768873	+	0.916308i	−0.229501	+	0.973309i	$0.573709\pi$
$938$		0			0
$939$	−1748.49	−	1009.49i	−1.86208	−	1.07507i
$940$		0			0
$941$	495.539	−	87.3769i	0.526609	−	0.0928554i	0.0959781	−	0.995383i	$-0.469402\pi$
$941$	495.539	−	87.3769i	0.526609	−	0.0928554i	0.430631	+	0.902528i	$0.358291\pi$
$942$		0			0
$943$	517.940	+	897.098i	0.549247	+	0.951324i
$944$		0			0
$945$	−747.440	−	296.967i	−0.790942	−	0.314251i
$946$		0			0
$947$	299.919	−	357.430i	0.316704	−	0.377434i	−0.584083	−	0.811694i	$-0.698546\pi$
$947$	299.919	−	357.430i	0.316704	−	0.377434i	0.900787	+	0.434260i	$0.142990\pi$
$948$		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	$-0.146036\pi$
$953$	587.190	+	492.711i	0.616149	+	0.517011i	−0.280441	+	0.959871i	$0.590481\pi$
$954$		0			0
$955$	−275.946	+	694.532i	−0.288949	+	0.727259i
$956$		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
$965$	410.319	−	221.225i	0.425202	−	0.229249i
$966$		0			0
$967$	833.913	+	147.041i	0.862371	+	0.152059i	0.587305	−	0.809366i	$-0.300189\pi$
$967$	833.913	+	147.041i	0.862371	+	0.152059i	0.275067	+	0.961425i	$0.411300\pi$
$968$		0			0
$969$	880.019	−	319.701i	0.908172	−	0.329929i
$970$		0			0
$971$	894.877	+	157.791i	0.921603	+	0.162504i	0.614268	−	0.789098i	$-0.289452\pi$
$971$	894.877	+	157.791i	0.921603	+	0.162504i	0.307335	+	0.951601i	$0.400563\pi$
$972$		0			0
$973$	494.863	−	1359.62i	0.508595	−	1.39735i
$974$		0			0
$975$	250.632	+	236.489i	0.257058	+	0.242553i
$976$		0			0
$977$	207.038	−	358.601i	0.211912	−	0.367043i	−0.740401	−	0.672166i	$-0.765364\pi$
$977$	207.038	−	358.601i	0.211912	−	0.367043i	0.952313	+	0.305123i	$0.0986976\pi$
$978$		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	$-0.744538\pi$
$983$	−751.916	+	273.675i	−0.764919	+	0.278408i	−0.0700495	+	0.997544i	$0.522316\pi$
$984$		0			0
$985$	−114.426	−	781.359i	−0.116169	−	0.793258i
$986$		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	−0.682998	−	0.730420i	$-0.739324\pi$
$991$	153.532	−	182.973i	0.154927	−	0.184635i	0.837925	+	0.545786i	$0.183769\pi$
$992$		0			0
$993$	−147.032	−	403.968i	−0.148069	−	0.406816i
$994$		0			0
$995$	−430.568	−	88.9197i	−0.432732	−	0.0893665i
$996$		0			0
$997$	1577.80	−	278.208i	1.58255	−	0.279046i	0.687895	−	0.725810i	$-0.258535\pi$
$997$	1577.80	−	278.208i	1.58255	−	0.279046i	0.894651	+	0.446765i	$0.147424\pi$
$998$		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.249.18	yes	120
5.4	even	2	inner	380.3.bc.a.249.3	yes	120
19.10	odd	18	inner	380.3.bc.a.29.3	✓	120
95.29	odd	18	inner	380.3.bc.a.29.18	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.3.bc.a.29.3	✓	120	19.10	odd	18	inner
380.3.bc.a.29.18	yes	120	95.29	odd	18	inner
380.3.bc.a.249.3	yes	120	5.4	even	2	inner
380.3.bc.a.249.18	yes	120	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(3.70131 + 3.10577i) q^{3} +(-1.84618 + 4.64668i) q^{5} +(5.39353 - 3.11396i) q^{7} +(2.49107 + 14.1276i) q^{9} +O(q^{10})\)	\(q+(3.70131 + 3.10577i) q^{3} +(-1.84618 + 4.64668i) q^{5} +(5.39353 - 3.11396i) q^{7} +(2.49107 + 14.1276i) q^{9} +(-5.50250 + 9.53061i) q^{11} +(-2.18533 + 1.83371i) q^{13} +(-21.2648 + 11.4650i) q^{15} +(10.0440 + 1.77103i) q^{17} +(6.50913 - 17.8502i) q^{19} +(29.6344 + 5.22534i) q^{21} +(-11.1915 + 30.7484i) q^{23} +(-18.1832 - 17.1572i) q^{25} +(-12.9140 + 22.3677i) q^{27} +(35.2028 - 6.20721i) q^{29} +(-32.0389 + 18.4977i) q^{31} +(-49.9664 + 18.1863i) q^{33} +(4.51212 + 30.8109i) q^{35} -19.2462 q^{37} -13.7837 q^{39} +(20.3488 - 24.2508i) q^{41} +(-16.3688 - 44.9730i) q^{43} +(-70.2453 - 14.5069i) q^{45} +(73.4155 - 12.9451i) q^{47} +(-5.10654 + 8.84478i) q^{49} +(31.6756 + 37.7495i) q^{51} +(-68.3938 - 24.8933i) q^{53} +(-34.1271 - 43.1636i) q^{55} +(79.5311 - 45.8535i) q^{57} +(-1.75422 - 0.309316i) q^{59} +(99.4120 + 36.1830i) q^{61} +(57.4283 + 68.4404i) q^{63} +(-4.48614 - 13.5399i) q^{65} +(2.73000 + 15.4826i) q^{67} +(-136.921 + 79.0513i) q^{69} +(29.4037 + 80.7861i) q^{71} +(-0.964646 + 1.14962i) q^{73} +(-14.0154 - 119.977i) q^{75} +68.5382i q^{77} +(23.0023 - 27.4131i) q^{79} +(4.05556 - 1.47610i) q^{81} +(96.0430 - 55.4504i) q^{83} +(-26.7725 + 43.4016i) q^{85} +(149.575 + 86.3571i) q^{87} +(-9.32264 - 11.1103i) q^{89} +(-6.07655 + 16.6952i) q^{91} +(-176.036 - 31.0398i) q^{93} +(70.9273 + 63.2006i) q^{95} +(17.0891 - 96.9169i) q^{97} +(-148.352 - 53.9955i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q+O(q^{10}) \) 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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