LMFDB - Embedded newform 950.2.f.d.493.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(493,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 2]))

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

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

chi := DirichletCharacter("950.493");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.f (of order $4$, degree $2$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			493.5
Character	$\chi$	$=$	950.493
Dual form			950.2.f.d.607.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(1.16084 - 1.16084i) q^{3} +1.00000i q^{4} -1.64167 q^{6} +(-2.19318 + 2.19318i) q^{7} +(0.707107 - 0.707107i) q^{8} +0.304919i q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(1.16084 - 1.16084i) q^{3} +1.00000i q^{4} -1.64167 q^{6} +(-2.19318 + 2.19318i) q^{7} +(0.707107 - 0.707107i) q^{8} +0.304919i q^{9} +4.06726 q^{11} +(1.16084 + 1.16084i) q^{12} +(-0.238119 + 0.238119i) q^{13} +3.10163 q^{14} -1.00000 q^{16} +(-2.63204 + 2.63204i) q^{17} +(0.215610 - 0.215610i) q^{18} +(-0.420721 + 4.33855i) q^{19} +5.09185i q^{21} +(-2.87599 - 2.87599i) q^{22} +(-2.60562 - 2.60562i) q^{23} -1.64167i q^{24} +0.336751 q^{26} +(3.83647 + 3.83647i) q^{27} +(-2.19318 - 2.19318i) q^{28} +6.78652 q^{29} +3.46410i q^{31} +(0.707107 + 0.707107i) q^{32} +(4.72142 - 4.72142i) q^{33} +3.72227 q^{34} -0.304919 q^{36} +(3.07634 + 3.07634i) q^{37} +(3.36531 - 2.77032i) q^{38} +0.552835i q^{39} +8.82591i q^{41} +(3.60048 - 3.60048i) q^{42} +(4.02125 + 4.02125i) q^{43} +4.06726i q^{44} +3.68490i q^{46} +(1.81973 - 1.81973i) q^{47} +(-1.16084 + 1.16084i) q^{48} -2.62009i q^{49} +6.11074i q^{51} +(-0.238119 - 0.238119i) q^{52} +(6.19591 - 6.19591i) q^{53} -5.42559i q^{54} +3.10163i q^{56} +(4.54795 + 5.52473i) q^{57} +(-4.79880 - 4.79880i) q^{58} -0.737138 q^{59} -2.00000 q^{61} +(2.44949 - 2.44949i) q^{62} +(-0.668743 - 0.668743i) q^{63} -1.00000i q^{64} -6.67709 q^{66} +(-8.99636 - 8.99636i) q^{67} +(-2.63204 - 2.63204i) q^{68} -6.04939 q^{69} -11.3502i q^{71} +(0.215610 + 0.215610i) q^{72} +(-3.94750 - 3.94750i) q^{73} -4.35060i q^{74} +(-4.33855 - 0.420721i) q^{76} +(-8.92023 + 8.92023i) q^{77} +(0.390913 - 0.390913i) q^{78} +2.73915 q^{79} +7.99227 q^{81} +(6.24086 - 6.24086i) q^{82} +(10.2621 + 10.2621i) q^{83} -5.09185 q^{84} -5.68691i q^{86} +(7.87804 - 7.87804i) q^{87} +(2.87599 - 2.87599i) q^{88} -6.52835 q^{89} -1.04448i q^{91} +(2.60562 - 2.60562i) q^{92} +(4.02125 + 4.02125i) q^{93} -2.57349 q^{94} +1.64167 q^{96} +(-8.40975 - 8.40975i) q^{97} +(-1.85268 + 1.85268i) q^{98} +1.24018i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 8 q^{6}+O(q^{10}) $ 32 * q - 8 * q^6	$ 32 q - 8 q^{6} - 24 q^{11} - 32 q^{16} + 32 q^{26} + 56 q^{36} - 64 q^{61} + 72 q^{66} + 4 q^{76} - 32 q^{81} + 8 q^{96}+O(q^{100}) $ 32 * q - 8 * q^6 - 24 * q^11 - 32 * q^16 + 32 * q^26 + 56 * q^36 - 64 * q^61 + 72 * q^66 + 4 * q^76 - 32 * q^81 + 8 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	1.16084	−	1.16084i	0.670209	−	0.670209i	−0.287555	−	0.957764i	$-0.592842\pi$
$3$	1.16084	−	1.16084i	0.670209	−	0.670209i	0.957764	+	0.287555i	$0.0928424\pi$
$4$			1.00000i			0.500000i
$5$		0			0
$5$		0			0
$6$	−1.64167			−0.670209
$7$	−2.19318	+	2.19318i	−0.828945	+	0.828945i	−0.987371	−	0.158426i	$-0.949358\pi$
$7$	−2.19318	+	2.19318i	−0.828945	+	0.828945i	0.158426	+	0.987371i	$0.449358\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$			0.304919i			0.101640i
$10$		0			0
$11$	4.06726			1.22632			0.613162	−	0.789957i	$-0.289897\pi$
$11$	4.06726			1.22632			0.613162	+	0.789957i	$0.289897\pi$
$12$	1.16084	+	1.16084i	0.335105	+	0.335105i
$13$	−0.238119	+	0.238119i	−0.0660424	+	0.0660424i	−0.739357	−	0.673314i	$-0.764870\pi$
$13$	−0.238119	+	0.238119i	−0.0660424	+	0.0660424i	0.673314	+	0.739357i	$0.264870\pi$
$14$	3.10163			0.828945
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−2.63204	+	2.63204i	−0.638364	+	0.638364i	−0.950152	−	0.311787i	$-0.899072\pi$
$17$	−2.63204	+	2.63204i	−0.638364	+	0.638364i	0.311787	+	0.950152i	$0.399072\pi$
$18$	0.215610	−	0.215610i	0.0508198	−	0.0508198i
$19$	−0.420721	+	4.33855i	−0.0965200	+	0.995331i
$19$	−0.420721	+	4.33855i	−0.0965200	+	0.995331i
$20$		0			0
$21$			5.09185i			1.11113i
$22$	−2.87599	−	2.87599i	−0.613162	−	0.613162i
$23$	−2.60562	−	2.60562i	−0.543309	−	0.543309i	0.381189	−	0.924497i	$-0.375515\pi$
$23$	−2.60562	−	2.60562i	−0.543309	−	0.543309i	−0.924497	+	0.381189i	$0.875515\pi$
$24$		−	1.64167i		−	0.335105i
$25$		0			0
$26$	0.336751			0.0660424
$27$	3.83647	+	3.83647i	0.738329	+	0.738329i
$28$	−2.19318	−	2.19318i	−0.414472	−	0.414472i
$29$	6.78652			1.26023			0.630113	−	0.776503i	$-0.283009\pi$
$29$	6.78652			1.26023			0.630113	+	0.776503i	$0.283009\pi$
$30$		0			0
$31$			3.46410i			0.622171i	0.950382	+	0.311086i	$0.100693\pi$
$31$			3.46410i			0.622171i	−0.950382	+	0.311086i	$0.899307\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	4.72142	−	4.72142i	0.821894	−	0.821894i
$34$	3.72227			0.638364
$35$		0			0
$36$	−0.304919			−0.0508198
$37$	3.07634	+	3.07634i	0.505747	+	0.505747i	0.913218	−	0.407471i	$-0.133589\pi$
$37$	3.07634	+	3.07634i	0.505747	+	0.505747i	−0.407471	+	0.913218i	$0.633589\pi$
$38$	3.36531	−	2.77032i	0.545926	−	0.449406i
$39$			0.552835i			0.0885244i
$40$		0			0
$41$			8.82591i			1.37838i	0.724582	+	0.689188i	$0.242033\pi$
$41$			8.82591i			1.37838i	−0.724582	+	0.689188i	$0.757967\pi$
$42$	3.60048	−	3.60048i	0.555566	−	0.555566i
$43$	4.02125	+	4.02125i	0.613236	+	0.613236i	0.943788	−	0.330552i	$-0.107235\pi$
$43$	4.02125	+	4.02125i	0.613236	+	0.613236i	−0.330552	+	0.943788i	$0.607235\pi$
$44$			4.06726i			0.613162i
$45$		0			0
$46$			3.68490i			0.543309i
$47$	1.81973	−	1.81973i	0.265435	−	0.265435i	−0.561822	−	0.827258i	$-0.689900\pi$
$47$	1.81973	−	1.81973i	0.265435	−	0.265435i	0.827258	+	0.561822i	$0.189900\pi$
$48$	−1.16084	+	1.16084i	−0.167552	+	0.167552i
$49$		−	2.62009i		−	0.374299i
$50$		0			0
$51$			6.11074i			0.855675i
$52$	−0.238119	−	0.238119i	−0.0330212	−	0.0330212i
$53$	6.19591	−	6.19591i	0.851074	−	0.851074i	−0.139192	−	0.990265i	$-0.544450\pi$
$53$	6.19591	−	6.19591i	0.851074	−	0.851074i	0.990265	+	0.139192i	$0.0444505\pi$
$54$		−	5.42559i		−	0.738329i
$55$		0			0
$56$			3.10163i			0.414472i
$57$	4.54795	+	5.52473i	0.602391	+	0.731768i
$58$	−4.79880	−	4.79880i	−0.630113	−	0.630113i
$59$	−0.737138			−0.0959672			−0.0479836	−	0.998848i	$-0.515280\pi$
$59$	−0.737138			−0.0959672			−0.0479836	+	0.998848i	$0.515280\pi$
$60$		0			0
$61$	−2.00000			−0.256074			−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000			−0.256074			−0.128037	+	0.991769i	$0.540868\pi$
$62$	2.44949	−	2.44949i	0.311086	−	0.311086i
$63$	−0.668743	−	0.668743i	−0.0842536	−	0.0842536i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$	−6.67709			−0.821894
$67$	−8.99636	−	8.99636i	−1.09908	−	1.09908i	−0.994518	−	0.104562i	$-0.966656\pi$
$67$	−8.99636	−	8.99636i	−1.09908	−	1.09908i	−0.104562	−	0.994518i	$-0.533344\pi$
$68$	−2.63204	−	2.63204i	−0.319182	−	0.319182i
$69$	−6.04939			−0.728261
$70$		0			0
$71$		−	11.3502i		−	1.34703i	−0.739176	−	0.673513i	$-0.764785\pi$
$71$		−	11.3502i		−	1.34703i	0.739176	−	0.673513i	$-0.235215\pi$
$72$	0.215610	+	0.215610i	0.0254099	+	0.0254099i
$73$	−3.94750	−	3.94750i	−0.462020	−	0.462020i	0.437297	−	0.899317i	$-0.355936\pi$
$73$	−3.94750	−	3.94750i	−0.462020	−	0.462020i	−0.899317	+	0.437297i	$0.855936\pi$
$74$		−	4.35060i		−	0.505747i
$75$		0			0
$76$	−4.33855	−	0.420721i	−0.497666	−	0.0482600i
$77$	−8.92023	+	8.92023i	−1.01655	+	1.01655i
$78$	0.390913	−	0.390913i	0.0442622	−	0.0442622i
$79$	2.73915			0.308179			0.154089	−	0.988057i	$-0.450756\pi$
$79$	2.73915			0.308179			0.154089	+	0.988057i	$0.450756\pi$
$80$		0			0
$81$	7.99227			0.888030
$82$	6.24086	−	6.24086i	0.689188	−	0.689188i
$83$	10.2621	+	10.2621i	1.12641	+	1.12641i	0.990756	+	0.135658i	$0.0433149\pi$
$83$	10.2621	+	10.2621i	1.12641	+	1.12641i	0.135658	+	0.990756i	$0.456685\pi$
$84$	−5.09185			−0.555566
$85$		0			0
$86$		−	5.68691i		−	0.613236i
$87$	7.87804	−	7.87804i	0.844615	−	0.844615i
$88$	2.87599	−	2.87599i	0.306581	−	0.306581i
$89$	−6.52835			−0.692004			−0.346002	−	0.938234i	$-0.612461\pi$
$89$	−6.52835			−0.692004			−0.346002	+	0.938234i	$0.612461\pi$
$90$		0			0
$91$		−	1.04448i		−	0.109491i
$92$	2.60562	−	2.60562i	0.271654	−	0.271654i
$93$	4.02125	+	4.02125i	0.416985	+	0.416985i
$94$	−2.57349			−0.265435
$95$		0			0
$96$	1.64167			0.167552
$97$	−8.40975	−	8.40975i	−0.853880	−	0.853880i	0.136728	−	0.990609i	$-0.456341\pi$
$97$	−8.40975	−	8.40975i	−0.853880	−	0.853880i	−0.990609	+	0.136728i	$0.956341\pi$
$98$	−1.85268	+	1.85268i	−0.187149	+	0.187149i
$99$			1.24018i			0.124643i
$100$		0			0
$101$	−6.00000			−0.597022			−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000			−0.597022			−0.298511	+	0.954406i	$0.596490\pi$
$102$	4.32095	−	4.32095i	0.427838	−	0.427838i
$103$	−4.16711	+	4.16711i	−0.410597	+	0.410597i	−0.881947	−	0.471349i	$-0.843767\pi$
$103$	−4.16711	+	4.16711i	−0.410597	+	0.410597i	0.471349	+	0.881947i	$0.343767\pi$
$104$			0.336751i			0.0330212i
$105$		0			0
$106$	−8.76234			−0.851074
$107$	11.5239	+	11.5239i	1.11405	+	1.11405i	0.992597	+	0.121456i	$0.0387563\pi$
$107$	11.5239	+	11.5239i	1.11405	+	1.11405i	0.121456	+	0.992597i	$0.461244\pi$
$108$	−3.83647	+	3.83647i	−0.369164	+	0.369164i
$109$	18.4559			1.76775			0.883877	−	0.467719i	$-0.154924\pi$
$109$	18.4559			1.76775			0.883877	+	0.467719i	$0.154924\pi$
$110$		0			0
$111$	7.14225			0.677912
$112$	2.19318	−	2.19318i	0.207236	−	0.207236i
$113$	−1.36666	+	1.36666i	−0.128564	+	0.128564i	−0.768461	−	0.639897i	$-0.778977\pi$
$113$	−1.36666	+	1.36666i	−0.128564	+	0.128564i	0.639897	+	0.768461i	$0.278977\pi$
$114$	0.690685	−	7.12246i	0.0646885	−	0.667080i
$115$		0			0
$116$			6.78652i			0.630113i
$117$	−0.0726070	−	0.0726070i	−0.00671252	−	0.00671252i
$118$	0.521235	+	0.521235i	0.0479836	+	0.0479836i
$119$		−	11.5451i		−	1.05834i
$120$		0			0
$121$	5.54258			0.503871
$122$	1.41421	+	1.41421i	0.128037	+	0.128037i
$123$	10.2454	+	10.2454i	0.923800	+	0.923800i
$124$	−3.46410			−0.311086
$125$		0			0
$126$			0.945745i			0.0842536i
$127$	−7.19670	−	7.19670i	−0.638604	−	0.638604i	0.311607	−	0.950211i	$-0.399133\pi$
$127$	−7.19670	−	7.19670i	−0.638604	−	0.638604i	−0.950211	+	0.311607i	$0.899133\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	9.33603			0.821992
$130$		0			0
$131$	8.60984			0.752245			0.376123	−	0.926570i	$-0.377257\pi$
$131$	8.60984			0.752245			0.376123	+	0.926570i	$0.377257\pi$
$132$	4.72142	+	4.72142i	0.410947	+	0.410947i
$133$	−8.59251	−	10.4379i	−0.745065	−	0.905084i
$134$			12.7228i			1.09908i
$135$		0			0
$136$			3.72227i			0.319182i
$137$	−13.1327	+	13.1327i	−1.12200	+	1.12200i	−0.130558	+	0.991441i	$0.541677\pi$
$137$	−13.1327	+	13.1327i	−1.12200	+	1.12200i	−0.991441	+	0.130558i	$0.958323\pi$
$138$	4.27756	+	4.27756i	0.364130	+	0.364130i
$139$		−	12.8116i		−	1.08667i	−0.839517	−	0.543333i	$-0.817162\pi$
$139$		−	12.8116i		−	1.08667i	0.839517	−	0.543333i	$-0.182838\pi$
$140$		0			0
$141$		−	4.22483i		−	0.355795i
$142$	−8.02583	+	8.02583i	−0.673513	+	0.673513i
$143$	−0.968492	+	0.968492i	−0.0809894	+	0.0809894i
$144$		−	0.304919i		−	0.0254099i
$145$		0			0
$146$			5.58261i			0.462020i
$147$	−3.04150	−	3.04150i	−0.250858	−	0.250858i
$148$	−3.07634	+	3.07634i	−0.252873	+	0.252873i
$149$			14.1345i			1.15794i	0.815347	+	0.578972i	$0.196546\pi$
$149$			14.1345i			1.15794i	−0.815347	+	0.578972i	$0.803454\pi$
$150$		0			0
$151$		−	22.7988i		−	1.85534i	−0.373400	−	0.927671i	$-0.621808\pi$
$151$		−	22.7988i		−	1.85534i	0.373400	−	0.927671i	$-0.378192\pi$
$152$	2.77032	+	3.36531i	0.224703	+	0.272963i
$153$	−0.802560	−	0.802560i	−0.0648831	−	0.0648831i
$154$	12.6151			1.01655
$155$		0			0
$156$	−0.552835			−0.0442622
$157$	5.59302	−	5.59302i	0.446372	−	0.446372i	−0.447775	−	0.894146i	$-0.647783\pi$
$157$	5.59302	−	5.59302i	0.446372	−	0.446372i	0.894146	+	0.447775i	$0.147783\pi$
$158$	−1.93687	−	1.93687i	−0.154089	−	0.154089i
$159$		−	14.3849i		−	1.14079i
$160$		0			0
$161$	11.4292			0.900746
$162$	−5.65139	−	5.65139i	−0.444015	−	0.444015i
$163$	6.18801	+	6.18801i	0.484682	+	0.484682i	0.906623	−	0.421941i	$-0.138651\pi$
$163$	6.18801	+	6.18801i	0.484682	+	0.484682i	−0.421941	+	0.906623i	$0.638651\pi$
$164$	−8.82591			−0.689188
$165$		0			0
$166$		−	14.5128i		−	1.12641i
$167$	−3.36570	−	3.36570i	−0.260446	−	0.260446i	0.564789	−	0.825235i	$-0.308957\pi$
$167$	−3.36570	−	3.36570i	−0.260446	−	0.260446i	−0.825235	+	0.564789i	$0.808957\pi$
$168$	3.60048	+	3.60048i	0.277783	+	0.277783i
$169$			12.8866i			0.991277i
$170$		0			0
$171$	−1.32291	−	0.128286i	−0.101165	−	0.00981025i
$172$	−4.02125	+	4.02125i	−0.306618	+	0.306618i
$173$	−3.47704	+	3.47704i	−0.264355	+	0.264355i	−0.826820	−	0.562466i	$-0.809853\pi$
$173$	−3.47704	+	3.47704i	−0.264355	+	0.264355i	0.562466	+	0.826820i	$0.309853\pi$
$174$	−11.1412			−0.844615
$175$		0			0
$176$	−4.06726			−0.306581
$177$	−0.855697	+	0.855697i	−0.0643181	+	0.0643181i
$178$	4.61624	+	4.61624i	0.346002	+	0.346002i
$179$	−20.5504			−1.53601			−0.768005	−	0.640443i	$-0.778751\pi$
$179$	−20.5504			−1.53601			−0.768005	+	0.640443i	$0.778751\pi$
$180$		0			0
$181$		−	4.87105i		−	0.362063i	−0.983477	−	0.181031i	$-0.942056\pi$
$181$		−	4.87105i		−	0.362063i	0.983477	−	0.181031i	$-0.0579435\pi$
$182$	−0.738557	+	0.738557i	−0.0547455	+	0.0547455i
$183$	−2.32167	+	2.32167i	−0.171623	+	0.171623i
$184$	−3.68490			−0.271654
$185$		0			0
$186$		−	5.68691i		−	0.416985i
$187$	−10.7052	+	10.7052i	−0.782842	+	0.782842i
$188$	1.81973	+	1.81973i	0.132718	+	0.132718i
$189$	−16.8281			−1.22407
$190$		0			0
$191$	11.1422			0.806225			0.403112	−	0.915151i	$-0.367928\pi$
$191$	11.1422			0.806225			0.403112	+	0.915151i	$0.367928\pi$
$192$	−1.16084	−	1.16084i	−0.0837761	−	0.0837761i
$193$	−8.15172	+	8.15172i	−0.586773	+	0.586773i	−0.936756	−	0.349983i	$-0.886187\pi$
$193$	−8.15172	+	8.15172i	−0.586773	+	0.586773i	0.349983	+	0.936756i	$0.386187\pi$
$194$			11.8932i			0.853880i
$195$		0			0
$196$	2.62009			0.187149
$197$	−1.62462	+	1.62462i	−0.115749	+	0.115749i	−0.762609	−	0.646860i	$-0.776082\pi$
$197$	−1.62462	+	1.62462i	−0.115749	+	0.115749i	0.646860	+	0.762609i	$0.276082\pi$
$198$	0.876942	−	0.876942i	0.0623216	−	0.0623216i
$199$			11.2222i			0.795520i	0.917489	+	0.397760i	$0.130212\pi$
$199$			11.2222i			0.795520i	−0.917489	+	0.397760i	$0.869788\pi$
$200$		0			0
$201$	−20.8866			−1.47323
$202$	4.24264	+	4.24264i	0.298511	+	0.298511i
$203$	−14.8841	+	14.8841i	−1.04466	+	1.04466i
$204$	−6.11074			−0.427838
$205$		0			0
$206$	5.89318			0.410597
$207$	0.794502	−	0.794502i	0.0552217	−	0.0552217i
$208$	0.238119	−	0.238119i	0.0165106	−	0.0165106i
$209$	−1.71118	+	17.6460i	−0.118365	+	1.22060i
$210$		0			0
$211$		−	28.5900i		−	1.96822i	−0.177563	−	0.984109i	$-0.556821\pi$
$211$		−	28.5900i		−	1.96822i	0.177563	−	0.984109i	$-0.443179\pi$
$212$	6.19591	+	6.19591i	0.425537	+	0.425537i
$213$	−13.1758	−	13.1758i	−0.902789	−	0.902789i
$214$		−	16.2972i		−	1.11405i
$215$		0			0
$216$	5.42559			0.369164
$217$	−7.59740	−	7.59740i	−0.515745	−	0.515745i
$218$	−13.0503	−	13.0503i	−0.883877	−	0.883877i
$219$	−9.16480			−0.619300
$220$		0			0
$221$		−	1.25348i		−	0.0843182i
$222$	−5.05033	−	5.05033i	−0.338956	−	0.338956i
$223$	4.64334	−	4.64334i	0.310941	−	0.310941i	−0.534333	−	0.845274i	$-0.679437\pi$
$223$	4.64334	−	4.64334i	0.310941	−	0.310941i	0.845274	+	0.534333i	$0.179437\pi$
$224$	−3.10163			−0.207236
$225$		0			0
$226$	1.93274			0.128564
$227$	2.92176	+	2.92176i	0.193924	+	0.193924i	0.797389	−	0.603465i	$-0.206214\pi$
$227$	2.92176	+	2.92176i	0.193924	+	0.193924i	−0.603465	+	0.797389i	$0.706214\pi$
$228$	−5.52473	+	4.54795i	−0.365884	+	0.301196i
$229$			20.4599i			1.35203i	0.736890	+	0.676013i	$0.236294\pi$
$229$			20.4599i			1.35203i	−0.736890	+	0.676013i	$0.763706\pi$
$230$		0			0
$231$			20.7099i			1.36261i
$232$	4.79880	−	4.79880i	0.315057	−	0.315057i
$233$	4.96326	+	4.96326i	0.325154	+	0.325154i	0.850740	−	0.525586i	$-0.176154\pi$
$233$	4.96326	+	4.96326i	0.325154	+	0.325154i	−0.525586	+	0.850740i	$0.676154\pi$
$234$			0.102682i			0.00671252i
$235$		0			0
$236$		−	0.737138i		−	0.0479836i
$237$	3.17971	−	3.17971i	0.206544	−	0.206544i
$238$	−8.16362	+	8.16362i	−0.529169	+	0.529169i
$239$		−	26.2119i		−	1.69551i	−0.530388	−	0.847755i	$-0.677954\pi$
$239$		−	26.2119i		−	1.69551i	0.530388	−	0.847755i	$-0.322046\pi$
$240$		0			0
$241$		−	14.5128i		−	0.934853i	−0.884032	−	0.467427i	$-0.845181\pi$
$241$		−	14.5128i		−	0.934853i	0.884032	−	0.467427i	$-0.154819\pi$
$242$	−3.91920	−	3.91920i	−0.251935	−	0.251935i
$243$	−2.23169	+	2.23169i	−0.143163	+	0.143163i
$244$		−	2.00000i		−	0.128037i
$245$		0			0
$246$		−	14.4892i		−	0.923800i
$247$	−0.932910	−	1.13327i	−0.0593596	−	0.0721084i
$248$	2.44949	+	2.44949i	0.155543	+	0.155543i
$249$	23.8253			1.50987
$250$		0			0
$251$	−20.8116			−1.31362			−0.656809	−	0.754057i	$-0.728094\pi$
$251$	−20.8116			−1.31362			−0.656809	+	0.754057i	$0.728094\pi$
$252$	0.668743	−	0.668743i	0.0421268	−	0.0421268i
$253$	−10.5977	−	10.5977i	−0.666272	−	0.666272i
$254$			10.1777i			0.638604i
$255$		0			0
$256$	1.00000			0.0625000
$257$	15.7466	+	15.7466i	0.982245	+	0.982245i	0.999845	−	0.0176004i	$-0.00560266\pi$
$257$	15.7466	+	15.7466i	0.982245	+	0.982245i	−0.0176004	+	0.999845i	$0.505603\pi$
$258$	−6.60157	−	6.60157i	−0.410996	−	0.410996i
$259$	−13.4939			−0.838472
$260$		0			0
$261$			2.06934i			0.128089i
$262$	−6.08807	−	6.08807i	−0.376123	−	0.376123i
$263$	6.32324	+	6.32324i	0.389907	+	0.389907i	0.874654	−	0.484747i	$-0.161088\pi$
$263$	6.32324	+	6.32324i	0.389907	+	0.389907i	−0.484747	+	0.874654i	$0.661088\pi$
$264$		−	6.67709i		−	0.410947i
$265$		0			0
$266$	−1.30492	+	13.4566i	−0.0800097	+	0.825074i
$267$	−7.57835	+	7.57835i	−0.463787	+	0.463787i
$268$	8.99636	−	8.99636i	0.549540	−	0.549540i
$269$	−27.6699			−1.68706			−0.843531	−	0.537081i	$-0.819527\pi$
$269$	−27.6699			−1.68706			−0.843531	+	0.537081i	$0.819527\pi$
$270$		0			0
$271$	−21.1268			−1.28336			−0.641680	−	0.766972i	$-0.721762\pi$
$271$	−21.1268			−1.28336			−0.641680	+	0.766972i	$0.721762\pi$
$272$	2.63204	−	2.63204i	0.159591	−	0.159591i
$273$	−1.21247	−	1.21247i	−0.0733818	−	0.0733818i
$274$	18.5724			1.12200
$275$		0			0
$276$		−	6.04939i		−	0.364130i
$277$	17.0156	−	17.0156i	1.02237	−	1.02237i	0.0226242	−	0.999744i	$-0.492798\pi$
$277$	17.0156	−	17.0156i	1.02237	−	1.02237i	0.999744	−	0.0226242i	$-0.00720212\pi$
$278$	−9.05918	+	9.05918i	−0.543333	+	0.543333i
$279$	−1.05627			−0.0632372
$280$		0			0
$281$			5.47831i			0.326808i	0.986559	+	0.163404i	$0.0522475\pi$
$281$			5.47831i			0.326808i	−0.986559	+	0.163404i	$0.947753\pi$
$282$	−2.98740	+	2.98740i	−0.177897	+	0.177897i
$283$	7.26610	+	7.26610i	0.431925	+	0.431925i	0.889283	−	0.457358i	$-0.151204\pi$
$283$	7.26610	+	7.26610i	0.431925	+	0.431925i	−0.457358	+	0.889283i	$0.651204\pi$
$284$	11.3502			0.673513
$285$		0			0
$286$	1.36965			0.0809894
$287$	−19.3568	−	19.3568i	−1.14260	−	1.14260i
$288$	−0.215610	+	0.215610i	−0.0127050	+	0.0127050i
$289$			3.14469i			0.184982i
$290$		0			0
$291$	−19.5247			−1.14456
$292$	3.94750	−	3.94750i	0.231010	−	0.231010i
$293$	−14.9516	+	14.9516i	−0.873482	+	0.873482i	−0.992850	−	0.119368i	$-0.961913\pi$
$293$	−14.9516	+	14.9516i	−0.873482	+	0.873482i	0.119368	+	0.992850i	$0.461913\pi$
$294$			4.30133i			0.250858i
$295$		0			0
$296$	4.35060			0.252873
$297$	15.6039	+	15.6039i	0.905431	+	0.905431i
$298$	9.99461	−	9.99461i	0.578972	−	0.578972i
$299$	1.24089			0.0717628
$300$		0			0
$301$	−17.6387			−1.01668
$302$	−16.1212	+	16.1212i	−0.927671	+	0.927671i
$303$	−6.96502	+	6.96502i	−0.400130	+	0.400130i
$304$	0.420721	−	4.33855i	0.0241300	−	0.248833i
$305$		0			0
$306$			1.13499i			0.0648831i
$307$	20.1250	+	20.1250i	1.14859	+	1.14859i	0.986830	+	0.161763i	$0.0517181\pi$
$307$	20.1250	+	20.1250i	1.14859	+	1.14859i	0.161763	+	0.986830i	$0.448282\pi$
$308$	−8.92023	−	8.92023i	−0.508277	−	0.508277i
$309$			9.67466i			0.550372i
$310$		0			0
$311$	12.6124			0.715181			0.357591	−	0.933878i	$-0.383598\pi$
$311$	12.6124			0.715181			0.357591	+	0.933878i	$0.383598\pi$
$312$	0.390913	+	0.390913i	0.0221311	+	0.0221311i
$313$	−23.6817	−	23.6817i	−1.33857	−	1.33857i	−0.897445	−	0.441125i	$-0.854579\pi$
$313$	−23.6817	−	23.6817i	−1.33857	−	1.33857i	−0.441125	−	0.897445i	$-0.645421\pi$
$314$	−7.90972			−0.446372
$315$		0			0
$316$			2.73915i			0.154089i
$317$	−4.84916	−	4.84916i	−0.272356	−	0.272356i	0.557692	−	0.830048i	$-0.311687\pi$
$317$	−4.84916	−	4.84916i	−0.272356	−	0.272356i	−0.830048	+	0.557692i	$0.811687\pi$
$318$	−10.1716	+	10.1716i	−0.570397	+	0.570397i
$319$	27.6025			1.54545
$320$		0			0
$321$	26.7546			1.49330
$322$	−8.08165	−	8.08165i	−0.450373	−	0.450373i
$323$	−10.3119	−	12.5266i	−0.573769	−	0.696999i
$324$			7.99227i			0.444015i
$325$		0			0
$326$		−	8.75116i		−	0.484682i
$327$	21.4243	−	21.4243i	1.18476	−	1.18476i
$328$	6.24086	+	6.24086i	0.344594	+	0.344594i
$329$			7.98201i			0.440063i
$330$		0			0
$331$			2.03939i			0.112095i	0.998428	+	0.0560475i	$0.0178498\pi$
$331$			2.03939i			0.112095i	−0.998428	+	0.0560475i	$0.982150\pi$
$332$	−10.2621	+	10.2621i	−0.563207	+	0.563207i
$333$	−0.938033	+	0.938033i	−0.0514039	+	0.0514039i
$334$			4.75982i			0.260446i
$335$		0			0
$336$		−	5.09185i		−	0.277783i
$337$	−6.97849	−	6.97849i	−0.380143	−	0.380143i	0.491011	−	0.871153i	$-0.336628\pi$
$337$	−6.97849	−	6.97849i	−0.380143	−	0.380143i	−0.871153	+	0.491011i	$0.836628\pi$
$338$	9.11220	−	9.11220i	0.495638	−	0.495638i
$339$			3.17293i			0.172330i
$340$		0			0
$341$			14.0894i			0.762983i
$342$	0.844723	+	1.02615i	0.0456774	+	0.0554877i
$343$	−9.60593	−	9.60593i	−0.518672	−	0.518672i
$344$	5.68691			0.306618
$345$		0			0
$346$	4.91728			0.264355
$347$	23.9338	−	23.9338i	1.28484	−	1.28484i	0.346952	−	0.937883i	$-0.387217\pi$
$347$	23.9338	−	23.9338i	1.28484	−	1.28484i	0.937883	−	0.346952i	$-0.112783\pi$
$348$	7.87804	+	7.87804i	0.422307	+	0.422307i
$349$		−	28.8994i		−	1.54695i	−0.633828	−	0.773474i	$-0.718517\pi$
$349$		−	28.8994i		−	1.54695i	0.633828	−	0.773474i	$-0.281483\pi$
$350$		0			0
$351$	−1.82707			−0.0975220
$352$	2.87599	+	2.87599i	0.153291	+	0.153291i
$353$	15.4998	+	15.4998i	0.824970	+	0.824970i	0.986816	−	0.161846i	$-0.0517448\pi$
$353$	15.4998	+	15.4998i	0.824970	+	0.824970i	−0.161846	+	0.986816i	$0.551745\pi$
$354$	1.21014			0.0643181
$355$		0			0
$356$		−	6.52835i		−	0.346002i
$357$	−13.4020	−	13.4020i	−0.709308	−	0.709308i
$358$	14.5313	+	14.5313i	0.768005	+	0.768005i
$359$		−	14.3644i		−	0.758126i	−0.925371	−	0.379063i	$-0.876246\pi$
$359$		−	14.3644i		−	0.758126i	0.925371	−	0.379063i	$-0.123754\pi$
$360$		0			0
$361$	−18.6460	−	3.65063i	−0.981368	−	0.192139i
$362$	−3.44435	+	3.44435i	−0.181031	+	0.181031i
$363$	6.43403	−	6.43403i	0.337699	−	0.337699i
$364$	1.04448			0.0547455
$365$		0			0
$366$	3.28334			0.171623
$367$	1.98973	−	1.98973i	0.103863	−	0.103863i	−0.653266	−	0.757129i	$-0.726602\pi$
$367$	1.98973	−	1.98973i	0.103863	−	0.103863i	0.757129	+	0.653266i	$0.226602\pi$
$368$	2.60562	+	2.60562i	0.135827	+	0.135827i
$369$	−2.69119			−0.140098
$370$		0			0
$371$			27.1775i			1.41099i
$372$	−4.02125	+	4.02125i	−0.208492	+	0.208492i
$373$	9.23702	−	9.23702i	0.478275	−	0.478275i	−0.426305	−	0.904580i	$-0.640185\pi$
$373$	9.23702	−	9.23702i	0.478275	−	0.478275i	0.904580	+	0.426305i	$0.140185\pi$
$374$	15.1394			0.782842
$375$		0			0
$376$		−	2.57349i		−	0.132718i
$377$	−1.61600	+	1.61600i	−0.0832283	+	0.0832283i
$378$	11.8993	+	11.8993i	0.612034	+	0.612034i
$379$	21.5201			1.10542			0.552708	−	0.833375i	$-0.313595\pi$
$379$	21.5201			1.10542			0.552708	+	0.833375i	$0.313595\pi$
$380$		0			0
$381$	−16.7084			−0.855996
$382$	−7.87876	−	7.87876i	−0.403112	−	0.403112i
$383$	23.3440	−	23.3440i	1.19282	−	1.19282i	0.216551	−	0.976271i	$-0.430519\pi$
$383$	23.3440	−	23.3440i	1.19282	−	1.19282i	0.976271	−	0.216551i	$-0.0694806\pi$
$384$			1.64167i			0.0837761i
$385$		0			0
$386$	11.5283			0.586773
$387$	−1.22616	+	1.22616i	−0.0623290	+	0.0623290i
$388$	8.40975	−	8.40975i	0.426940	−	0.426940i
$389$		−	9.50417i		−	0.481880i	−0.970540	−	0.240940i	$-0.922544\pi$
$389$		−	9.50417i		−	0.481880i	0.970540	−	0.240940i	$-0.0774558\pi$
$390$		0			0
$391$	13.7162			0.693658
$392$	−1.85268	−	1.85268i	−0.0935747	−	0.0935747i
$393$	9.99461	−	9.99461i	0.504161	−	0.504161i
$394$	2.29756			0.115749
$395$		0			0
$396$	−1.24018			−0.0623216
$397$	−11.6653	+	11.6653i	−0.585465	+	0.585465i	−0.936400	−	0.350935i	$-0.885864\pi$
$397$	−11.6653	+	11.6653i	−0.585465	+	0.585465i	0.350935	+	0.936400i	$0.385864\pi$
$398$	7.93529	−	7.93529i	0.397760	−	0.397760i
$399$	−22.0912	−	2.14225i	−1.10594	−	0.107246i
$400$		0			0
$401$		−	22.3990i		−	1.11855i	−0.828982	−	0.559275i	$-0.811079\pi$
$401$		−	22.3990i		−	1.11855i	0.828982	−	0.559275i	$-0.188921\pi$
$402$	14.7691	+	14.7691i	0.736614	+	0.736614i
$403$	−0.824869	−	0.824869i	−0.0410896	−	0.0410896i
$404$		−	6.00000i		−	0.298511i
$405$		0			0
$406$	21.0493			1.04466
$407$	12.5123	+	12.5123i	0.620209	+	0.620209i
$408$	4.32095	+	4.32095i	0.213919	+	0.213919i
$409$	−22.5840			−1.11671			−0.558353	−	0.829603i	$-0.688567\pi$
$409$	−22.5840			−1.11671			−0.558353	+	0.829603i	$0.688567\pi$
$410$		0			0
$411$			30.4897i			1.50395i
$412$	−4.16711	−	4.16711i	−0.205299	−	0.205299i
$413$	1.61668	−	1.61668i	0.0795515	−	0.0795515i
$414$	−1.12359			−0.0552217
$415$		0			0
$416$	−0.336751			−0.0165106
$417$	−14.8722	−	14.8722i	−0.728294	−	0.728294i
$418$	13.6876	−	11.2676i	0.669482	−	0.551117i
$419$		−	13.5714i		−	0.663008i	−0.943454	−	0.331504i	$-0.892444\pi$
$419$		−	13.5714i		−	0.663008i	0.943454	−	0.331504i	$-0.107556\pi$
$420$		0			0
$421$			21.0054i			1.02374i	0.859063	+	0.511870i	$0.171047\pi$
$421$			21.0054i			1.02374i	−0.859063	+	0.511870i	$0.828953\pi$
$422$	−20.2162	+	20.2162i	−0.984109	+	0.984109i
$423$	0.554871	+	0.554871i	0.0269788	+	0.0269788i
$424$		−	8.76234i		−	0.425537i
$425$		0			0
$426$			18.6333i			0.902789i
$427$	4.38636	−	4.38636i	0.212271	−	0.212271i
$428$	−11.5239	+	11.5239i	−0.557026	+	0.557026i
$429$			2.24852i			0.108560i
$430$		0			0
$431$		−	19.8746i		−	0.957328i	−0.877998	−	0.478664i	$-0.841121\pi$
$431$		−	19.8746i		−	0.957328i	0.877998	−	0.478664i	$-0.158879\pi$
$432$	−3.83647	−	3.83647i	−0.184582	−	0.184582i
$433$	14.3442	−	14.3442i	0.689339	−	0.689339i	−0.272747	−	0.962086i	$-0.587932\pi$
$433$	14.3442	−	14.3442i	0.689339	−	0.689339i	0.962086	+	0.272747i	$0.0879322\pi$
$434$			10.7444i			0.515745i
$435$		0			0
$436$			18.4559i			0.883877i
$437$	12.4008	−	10.2084i	0.593212	−	0.488332i
$438$	6.48049	+	6.48049i	0.309650	+	0.309650i
$439$	36.0050			1.71843			0.859213	−	0.511618i	$-0.170954\pi$
$439$	36.0050			1.71843			0.859213	+	0.511618i	$0.170954\pi$
$440$		0			0
$441$	0.798915			0.0380436
$442$	−0.886344	+	0.886344i	−0.0421591	+	0.0421591i
$443$	−2.29758	−	2.29758i	−0.109161	−	0.109161i	0.650416	−	0.759578i	$-0.274594\pi$
$443$	−2.29758	−	2.29758i	−0.109161	−	0.109161i	−0.759578	+	0.650416i	$0.774594\pi$
$444$			7.14225i			0.338956i
$445$		0			0
$446$	−6.56668			−0.310941
$447$	16.4079	+	16.4079i	0.776065	+	0.776065i
$448$	2.19318	+	2.19318i	0.103618	+	0.103618i
$449$	−25.6065			−1.20845			−0.604223	−	0.796816i	$-0.706516\pi$
$449$	−25.6065			−1.20845			−0.604223	+	0.796816i	$0.706516\pi$
$450$		0			0
$451$			35.8973i			1.69034i
$452$	−1.36666	−	1.36666i	−0.0642821	−	0.0642821i
$453$	−26.4657	−	26.4657i	−1.24347	−	1.24347i
$454$		−	4.13199i		−	0.193924i
$455$		0			0
$456$	7.12246	+	0.690685i	0.333540	+	0.0323443i
$457$	−20.0128	+	20.0128i	−0.936157	+	0.936157i	−0.998081	−	0.0619238i	$-0.980276\pi$
$457$	−20.0128	+	20.0128i	−0.936157	+	0.936157i	0.0619238	+	0.998081i	$0.480276\pi$
$458$	14.4673	−	14.4673i	0.676013	−	0.676013i
$459$	−20.1955			−0.942646
$460$		0			0
$461$	18.4035			0.857138			0.428569	−	0.903509i	$-0.359018\pi$
$461$	18.4035			0.857138			0.428569	+	0.903509i	$0.359018\pi$
$462$	14.6441	−	14.6441i	0.681304	−	0.681304i
$463$	25.5237	+	25.5237i	1.18619	+	1.18619i	0.978113	+	0.208073i	$0.0667190\pi$
$463$	25.5237	+	25.5237i	1.18619	+	1.18619i	0.208073	+	0.978113i	$0.433281\pi$
$464$	−6.78652			−0.315057
$465$		0			0
$466$		−	7.01911i		−	0.325154i
$467$	23.6172	−	23.6172i	1.09287	−	1.09287i	0.0976518	−	0.995221i	$-0.468867\pi$
$467$	23.6172	−	23.6172i	1.09287	−	1.09287i	0.995221	−	0.0976518i	$-0.0311331\pi$
$468$	0.0726070	−	0.0726070i	0.00335626	−	0.00335626i
$469$	39.4613			1.82215
$470$		0			0
$471$		−	12.9852i		−	0.598324i
$472$	−0.521235	+	0.521235i	−0.0239918	+	0.0239918i
$473$	16.3555	+	16.3555i	0.752026	+	0.752026i
$474$	−4.49679			−0.206544
$475$		0			0
$476$	11.5451			0.529169
$477$	1.88925	+	1.88925i	0.0865028	+	0.0865028i
$478$	−18.5346	+	18.5346i	−0.847755	+	0.847755i
$479$		−	8.89677i		−	0.406504i	−0.979126	−	0.203252i	$-0.934849\pi$
$479$		−	8.89677i		−	0.406504i	0.979126	−	0.203252i	$-0.0651510\pi$
$480$		0			0
$481$	−1.46507			−0.0668014
$482$	−10.2621	+	10.2621i	−0.467427	+	0.467427i
$483$	13.2674	−	13.2674i	0.603688	−	0.603688i
$484$			5.54258i			0.251935i
$485$		0			0
$486$	3.15609			0.143163
$487$	−17.1048	−	17.1048i	−0.775094	−	0.775094i	0.203898	−	0.978992i	$-0.434639\pi$
$487$	−17.1048	−	17.1048i	−0.775094	−	0.775094i	−0.978992	+	0.203898i	$0.934639\pi$
$488$	−1.41421	+	1.41421i	−0.0640184	+	0.0640184i
$489$	14.3665			0.649677
$490$		0			0
$491$	17.5247			0.790878			0.395439	−	0.918492i	$-0.370593\pi$
$491$	17.5247			0.790878			0.395439	+	0.918492i	$0.370593\pi$
$492$	−10.2454	+	10.2454i	−0.461900	+	0.461900i
$493$	−17.8624	+	17.8624i	−0.804484	+	0.804484i
$494$	−0.141678	+	1.46101i	−0.00637441	+	0.0657340i
$495$		0			0
$496$		−	3.46410i		−	0.155543i
$497$	24.8931	+	24.8931i	1.11661	+	1.11661i
$498$	−16.8470	−	16.8470i	−0.754933	−	0.754933i
$499$			5.36965i			0.240379i	0.992751	+	0.120189i	$0.0383502\pi$
$499$			5.36965i			0.240379i	−0.992751	+	0.120189i	$0.961650\pi$
$500$		0			0
$501$	−7.81405			−0.349106
$502$	14.7160	+	14.7160i	0.656809	+	0.656809i
$503$	20.2260	+	20.2260i	0.901831	+	0.901831i	0.995594	−	0.0937637i	$-0.0298898\pi$
$503$	20.2260	+	20.2260i	0.901831	+	0.901831i	−0.0937637	+	0.995594i	$0.529890\pi$
$504$	−0.945745			−0.0421268
$505$		0			0
$506$			14.9874i			0.666272i
$507$	14.9592	+	14.9592i	0.664363	+	0.664363i
$508$	7.19670	−	7.19670i	0.319302	−	0.319302i
$509$	41.4751			1.83835			0.919176	−	0.393847i	$-0.128856\pi$
$509$	41.4751			1.83835			0.919176	+	0.393847i	$0.128856\pi$
$510$		0			0
$511$	17.3152			0.765978
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−18.2588	+	15.0306i	−0.806145	+	0.663618i
$514$		−	22.2690i		−	0.982245i
$515$		0			0
$516$			9.33603i			0.410996i
$517$	7.40133	−	7.40133i	0.325510	−	0.325510i
$518$	9.54165	+	9.54165i	0.419236	+	0.419236i
$519$			8.07255i			0.354346i
$520$		0			0
$521$		−	4.74714i		−	0.207976i	−0.994579	−	0.103988i	$-0.966840\pi$
$521$		−	4.74714i		−	0.207976i	0.994579	−	0.103988i	$-0.0331603\pi$
$522$	1.46324	−	1.46324i	0.0640445	−	0.0640445i
$523$	22.1301	−	22.1301i	0.967680	−	0.967680i	−0.0318136	−	0.999494i	$-0.510128\pi$
$523$	22.1301	−	22.1301i	0.967680	−	0.967680i	0.999494	+	0.0318136i	$0.0101283\pi$
$524$			8.60984i			0.376123i
$525$		0			0
$526$		−	8.94241i		−	0.389907i
$527$	−9.11767	−	9.11767i	−0.397172	−	0.397172i
$528$	−4.72142	+	4.72142i	−0.205473	+	0.205473i
$529$		−	9.42153i		−	0.409632i
$530$		0			0
$531$		−	0.224767i		−	0.00975407i
$532$	10.4379	−	8.59251i	0.452542	−	0.372532i
$533$	−2.10162	−	2.10162i	−0.0910312	−	0.0910312i
$534$	10.7174			0.463787
$535$		0			0
$536$	−12.7228			−0.549540
$537$	−23.8557	+	23.8557i	−1.02945	+	1.02945i
$538$	19.5656	+	19.5656i	0.843531	+	0.843531i
$539$		−	10.6566i		−	0.459012i
$540$		0			0
$541$	−7.85002			−0.337499			−0.168749	−	0.985659i	$-0.553973\pi$
$541$	−7.85002			−0.337499			−0.168749	+	0.985659i	$0.553973\pi$
$542$	14.9389	+	14.9389i	0.641680	+	0.641680i
$543$	−5.65449	−	5.65449i	−0.242658	−	0.242658i
$544$	−3.72227			−0.159591
$545$		0			0
$546$			1.71469i			0.0733818i
$547$	−22.0927	−	22.0927i	−0.944615	−	0.944615i	0.0539297	−	0.998545i	$-0.482825\pi$
$547$	−22.0927	−	22.0927i	−0.944615	−	0.944615i	−0.998545	+	0.0539297i	$0.982825\pi$
$548$	−13.1327	−	13.1327i	−0.561000	−	0.561000i
$549$		−	0.609838i		−	0.0260272i
$550$		0			0
$551$	−2.85523	+	29.4437i	−0.121637	+	1.25434i
$552$	−4.27756	+	4.27756i	−0.182065	+	0.182065i
$553$	−6.00746	+	6.00746i	−0.255463	+	0.255463i
$554$	−24.0637			−1.02237
$555$		0			0
$556$	12.8116			0.543333
$557$	12.6126	−	12.6126i	0.534411	−	0.534411i	−0.387471	−	0.921882i	$-0.626651\pi$
$557$	12.6126	−	12.6126i	0.534411	−	0.534411i	0.921882	+	0.387471i	$0.126651\pi$
$558$	0.746896	+	0.746896i	0.0316186	+	0.0316186i
$559$	−1.91508			−0.0809991
$560$		0			0
$561$			24.8540i			1.04934i
$562$	3.87375	−	3.87375i	0.163404	−	0.163404i
$563$	−13.2271	+	13.2271i	−0.557456	+	0.557456i	−0.928582	−	0.371127i	$-0.878972\pi$
$563$	−13.2271	+	13.2271i	−0.557456	+	0.557456i	0.371127	+	0.928582i	$0.378972\pi$
$564$	4.22483			0.177897
$565$		0			0
$566$		−	10.2758i		−	0.431925i
$567$	−17.5285	+	17.5285i	−0.736128	+	0.736128i
$568$	−8.02583	−	8.02583i	−0.336756	−	0.336756i
$569$	2.15748			0.0904464			0.0452232	−	0.998977i	$-0.485600\pi$
$569$	2.15748			0.0904464			0.0452232	+	0.998977i	$0.485600\pi$
$570$		0			0
$571$	11.9640			0.500679			0.250339	−	0.968158i	$-0.419458\pi$
$571$	11.9640			0.500679			0.250339	+	0.968158i	$0.419458\pi$
$572$	−0.968492	−	0.968492i	−0.0404947	−	0.0404947i
$573$	12.9343	−	12.9343i	0.540339	−	0.540339i
$574$			27.3747i			1.14260i
$575$		0			0
$576$	0.304919			0.0127050
$577$	−7.80401	+	7.80401i	−0.324885	+	0.324885i	−0.850638	−	0.525752i	$-0.823784\pi$
$577$	−7.80401	+	7.80401i	−0.324885	+	0.324885i	0.525752	+	0.850638i	$0.323784\pi$
$578$	2.22363	−	2.22363i	0.0924908	−	0.0924908i
$579$			18.9256i			0.786522i
$580$		0			0
$581$	−45.0134			−1.86747
$582$	13.8060	+	13.8060i	0.572278	+	0.572278i
$583$	25.2004	−	25.2004i	1.04369	−	1.04369i
$584$	−5.58261			−0.231010
$585$		0			0
$586$	21.1448			0.873482
$587$	20.1553	−	20.1553i	0.831898	−	0.831898i	−0.155878	−	0.987776i	$-0.549821\pi$
$587$	20.1553	−	20.1553i	0.831898	−	0.831898i	0.987776	+	0.155878i	$0.0498208\pi$
$588$	3.04150	−	3.04150i	0.125429	−	0.125429i
$589$	−15.0292	−	1.45742i	−0.619266	−	0.0600519i
$590$		0			0
$591$			3.77184i			0.155153i
$592$	−3.07634	−	3.07634i	−0.126437	−	0.126437i
$593$	13.6369	+	13.6369i	0.560002	+	0.560002i	0.929308	−	0.369306i	$-0.120405\pi$
$593$	13.6369	+	13.6369i	0.560002	+	0.560002i	−0.369306	+	0.929308i	$0.620405\pi$
$594$		−	22.0673i		−	0.905431i
$595$		0			0
$596$	−14.1345			−0.578972
$597$	13.0271	+	13.0271i	0.533165	+	0.533165i
$598$	−0.877445	−	0.877445i	−0.0358814	−	0.0358814i
$599$	24.9980			1.02139			0.510696	−	0.859761i	$-0.329388\pi$
$599$	24.9980			1.02139			0.510696	+	0.859761i	$0.329388\pi$
$600$		0			0
$601$			23.1239i			0.943244i	0.881801	+	0.471622i	$0.156331\pi$
$601$			23.1239i			0.943244i	−0.881801	+	0.471622i	$0.843669\pi$
$602$	12.4724	+	12.4724i	0.508338	+	0.508338i
$603$	2.74316	−	2.74316i	0.111710	−	0.111710i
$604$	22.7988			0.927671
$605$		0			0
$606$	9.85002			0.400130
$607$	−28.2428	−	28.2428i	−1.14634	−	1.14634i	−0.987267	−	0.159074i	$-0.949149\pi$
$607$	−28.2428	−	28.2428i	−1.14634	−	1.14634i	−0.159074	−	0.987267i	$-0.550851\pi$
$608$	−3.36531	+	2.77032i	−0.136481	+	0.112351i
$609$			34.5560i			1.40028i
$610$		0			0
$611$			0.866627i			0.0350600i
$612$	0.802560	−	0.802560i	0.0324416	−	0.0324416i
$613$	−25.7188	−	25.7188i	−1.03877	−	1.03877i	−0.999217	−	0.0395548i	$-0.987406\pi$
$613$	−25.7188	−	25.7188i	−1.03877	−	1.03877i	−0.0395548	−	0.999217i	$-0.512594\pi$
$614$		−	28.4610i		−	1.14859i
$615$		0			0
$616$			12.6151i			0.508277i
$617$	−1.29044	+	1.29044i	−0.0519512	+	0.0519512i	−0.732605	−	0.680654i	$-0.761696\pi$
$617$	−1.29044	+	1.29044i	−0.0519512	+	0.0519512i	0.680654	+	0.732605i	$0.261696\pi$
$618$	6.84101	−	6.84101i	0.275186	−	0.275186i
$619$		−	26.8943i		−	1.08097i	−0.841352	−	0.540487i	$-0.818240\pi$
$619$		−	26.8943i		−	1.08097i	0.841352	−	0.540487i	$-0.181760\pi$
$620$		0			0
$621$		−	19.9927i		−	0.802281i
$622$	−8.91828	−	8.91828i	−0.357591	−	0.357591i
$623$	14.3179	−	14.3179i	0.573633	−	0.573633i
$624$		−	0.552835i		−	0.0221311i
$625$		0			0
$626$			33.4910i			1.33857i
$627$	18.4977	+	22.4705i	0.738727	+	0.897385i
$628$	5.59302	+	5.59302i	0.223186	+	0.223186i
$629$	−16.1941			−0.645701
$630$		0			0
$631$	−8.59193			−0.342039			−0.171020	−	0.985268i	$-0.554706\pi$
$631$	−8.59193			−0.342039			−0.171020	+	0.985268i	$0.554706\pi$
$632$	1.93687	−	1.93687i	0.0770447	−	0.0770447i
$633$	−33.1883	−	33.1883i	−1.31912	−	1.31912i
$634$			6.85775i			0.272356i
$635$		0			0
$636$	14.3849			0.570397
$637$	0.623894	+	0.623894i	0.0247196	+	0.0247196i
$638$	−19.5179	−	19.5179i	−0.772723	−	0.772723i
$639$	3.46090			0.136911
$640$		0			0
$641$		−	6.90462i		−	0.272716i	−0.990660	−	0.136358i	$-0.956460\pi$
$641$		−	6.90462i		−	0.272716i	0.990660	−	0.136358i	$-0.0435397\pi$
$642$	−18.9184	−	18.9184i	−0.746648	−	0.746648i
$643$	11.5345	+	11.5345i	0.454875	+	0.454875i	0.896969	−	0.442094i	$-0.145764\pi$
$643$	11.5345	+	11.5345i	0.454875	+	0.454875i	−0.442094	+	0.896969i	$0.645764\pi$
$644$			11.4292i			0.450373i
$645$		0			0
$646$	−1.56604	+	16.1493i	−0.0616149	+	0.635384i
$647$	6.63240	−	6.63240i	0.260747	−	0.260747i	−0.564611	−	0.825357i	$-0.690974\pi$
$647$	6.63240	−	6.63240i	0.260747	−	0.260747i	0.825357	+	0.564611i	$0.190974\pi$
$648$	5.65139	−	5.65139i	0.222007	−	0.222007i
$649$	−2.99813			−0.117687
$650$		0			0
$651$	−17.6387			−0.691314
$652$	−6.18801	+	6.18801i	−0.242341	+	0.242341i
$653$	−2.68377	−	2.68377i	−0.105024	−	0.105024i	0.652642	−	0.757666i	$-0.273660\pi$
$653$	−2.68377	−	2.68377i	−0.105024	−	0.105024i	−0.757666	+	0.652642i	$0.773660\pi$
$654$	−30.2985			−1.18476
$655$		0			0
$656$		−	8.82591i		−	0.344594i
$657$	1.20367	−	1.20367i	0.0469595	−	0.0469595i
$658$	5.64414	−	5.64414i	0.220031	−	0.220031i
$659$	15.4664			0.602485			0.301243	−	0.953548i	$-0.402599\pi$
$659$	15.4664			0.602485			0.301243	+	0.953548i	$0.402599\pi$
$660$		0			0
$661$		−	32.0168i		−	1.24531i	−0.782497	−	0.622654i	$-0.786055\pi$
$661$		−	32.0168i		−	1.24531i	0.782497	−	0.622654i	$-0.213945\pi$
$662$	1.44207	−	1.44207i	0.0560475	−	0.0560475i
$663$	−1.45509	−	1.45509i	−0.0565108	−	0.0565108i
$664$	14.5128			0.563207
$665$		0			0
$666$	1.32658			0.0514039
$667$	−17.6831	−	17.6831i	−0.684692	−	0.684692i
$668$	3.36570	−	3.36570i	0.130223	−	0.130223i
$669$		−	10.7803i		−	0.416791i
$670$		0			0
$671$	−8.13451			−0.314029
$672$	−3.60048	+	3.60048i	−0.138892	+	0.138892i
$673$	−0.481319	+	0.481319i	−0.0185535	+	0.0185535i	−0.716323	−	0.697769i	$-0.754176\pi$
$673$	−0.481319	+	0.481319i	−0.0185535	+	0.0185535i	0.697769	+	0.716323i	$0.254176\pi$
$674$			9.86908i			0.380143i
$675$		0			0
$676$	−12.8866			−0.495638
$677$	12.6201	+	12.6201i	0.485029	+	0.485029i	0.906733	−	0.421704i	$-0.138568\pi$
$677$	12.6201	+	12.6201i	0.485029	+	0.485029i	−0.421704	+	0.906733i	$0.638568\pi$
$678$	2.24360	−	2.24360i	0.0861649	−	0.0861649i
$679$	36.8882			1.41564
$680$		0			0
$681$	6.78337			0.259939
$682$	9.96270	−	9.96270i	0.381492	−	0.381492i
$683$	18.7448	−	18.7448i	0.717252	−	0.717252i	−0.250790	−	0.968042i	$-0.580690\pi$
$683$	18.7448	−	18.7448i	0.717252	−	0.717252i	0.968042	+	0.250790i	$0.0806904\pi$
$684$	0.128286	−	1.32291i	0.00490513	−	0.0505825i
$685$		0			0
$686$			13.5848i			0.518672i
$687$	23.7505	+	23.7505i	0.906140	+	0.906140i
$688$	−4.02125	−	4.02125i	−0.153309	−	0.153309i
$689$			2.95073i			0.112414i
$690$		0			0
$691$	−2.21724			−0.0843476			−0.0421738	−	0.999110i	$-0.513428\pi$
$691$	−2.21724			−0.0843476			−0.0421738	+	0.999110i	$0.513428\pi$
$692$	−3.47704	−	3.47704i	−0.132177	−	0.132177i
$693$	−2.71995	−	2.71995i	−0.103322	−	0.103322i
$694$	−33.8475			−1.28484
$695$		0			0
$696$		−	11.1412i		−	0.422307i
$697$	−23.2302	−	23.2302i	−0.879906	−	0.879906i
$698$	−20.4349	+	20.4349i	−0.773474	+	0.773474i
$699$	11.5231			0.435843
$700$		0			0
$701$	−44.5789			−1.68372			−0.841861	−	0.539694i	$-0.818540\pi$
$701$	−44.5789			−1.68372			−0.841861	+	0.539694i	$0.818540\pi$
$702$	1.29194	+	1.29194i	0.0487610	+	0.0487610i
$703$	−14.6411	+	12.0526i	−0.552200	+	0.454571i
$704$		−	4.06726i		−	0.153291i
$705$		0			0
$706$		−	21.9200i		−	0.824970i
$707$	13.1591	−	13.1591i	0.494899	−	0.494899i
$708$	−0.855697	−	0.855697i	−0.0321590	−	0.0321590i
$709$			34.4444i			1.29359i	0.762665	+	0.646793i	$0.223890\pi$
$709$			34.4444i			1.29359i	−0.762665	+	0.646793i	$0.776110\pi$
$710$		0			0
$711$			0.835219i			0.0313232i
$712$	−4.61624	+	4.61624i	−0.173001	+	0.173001i
$713$	9.02612	−	9.02612i	0.338031	−	0.338031i
$714$			18.9533i			0.709308i
$715$		0			0
$716$		−	20.5504i		−	0.768005i
$717$	−30.4278	−	30.4278i	−1.13635	−	1.13635i
$718$	−10.1572	+	10.1572i	−0.379063	+	0.379063i
$719$			11.1422i			0.415536i	0.978178	+	0.207768i	$0.0666199\pi$
$719$			11.1422i			0.415536i	−0.978178	+	0.207768i	$0.933380\pi$
$720$		0			0
$721$		−	18.2784i		−	0.680725i
$722$	10.6033	+	15.7661i	0.394615	+	0.586753i
$723$	−16.8470	−	16.8470i	−0.626547	−	0.626547i
$724$	4.87105			0.181031
$725$		0			0
$726$	−9.09909			−0.337699
$727$	−2.59718	+	2.59718i	−0.0963240	+	0.0963240i	−0.753627	−	0.657303i	$-0.771697\pi$
$727$	−2.59718	+	2.59718i	−0.0963240	+	0.0963240i	0.657303	+	0.753627i	$0.271697\pi$
$728$	−0.738557	−	0.738557i	−0.0273727	−	0.0273727i
$729$			29.1581i			1.07993i
$730$		0			0
$731$	−21.1682			−0.782936
$732$	−2.32167	−	2.32167i	−0.0858115	−	0.0858115i
$733$	−8.33808	−	8.33808i	−0.307974	−	0.307974i	0.536149	−	0.844123i	$-0.319878\pi$
$733$	−8.33808	−	8.33808i	−0.307974	−	0.307974i	−0.844123	+	0.536149i	$0.819878\pi$
$734$	−2.81390			−0.103863
$735$		0			0
$736$		−	3.68490i		−	0.135827i
$737$	−36.5905	−	36.5905i	−1.34783	−	1.34783i
$738$	1.90296	+	1.90296i	0.0700488	+	0.0700488i
$739$		−	8.15502i		−	0.299987i	−0.988687	−	0.149994i	$-0.952075\pi$
$739$		−	8.15502i		−	0.299987i	0.988687	−	0.149994i	$-0.0479253\pi$
$740$		0			0
$741$	−2.39850	−	0.232589i	−0.0881111	−	0.00854437i
$742$	19.2174	−	19.2174i	0.705493	−	0.705493i
$743$	−13.5939	+	13.5939i	−0.498713	+	0.498713i	−0.911037	−	0.412324i	$-0.864717\pi$
$743$	−13.5939	+	13.5939i	−0.498713	+	0.498713i	0.412324	+	0.911037i	$0.364717\pi$
$744$	5.68691			0.208492
$745$		0			0
$746$	−13.0631			−0.478275
$747$	−3.12911	+	3.12911i	−0.114488	+	0.114488i
$748$	−10.7052	−	10.7052i	−0.391421	−	0.391421i
$749$	−50.5478			−1.84698
$750$		0			0
$751$		−	6.95258i		−	0.253703i	−0.991922	−	0.126852i	$-0.959513\pi$
$751$		−	6.95258i		−	0.253703i	0.991922	−	0.126852i	$-0.0404872\pi$
$752$	−1.81973	+	1.81973i	−0.0663589	+	0.0663589i
$753$	−24.1589	+	24.1589i	−0.880398	+	0.880398i
$754$	2.28537			0.0832283
$755$		0			0
$756$		−	16.8281i		−	0.612034i
$757$	21.6975	−	21.6975i	0.788610	−	0.788610i	−0.192656	−	0.981266i	$-0.561710\pi$
$757$	21.6975	−	21.6975i	0.788610	−	0.788610i	0.981266	+	0.192656i	$0.0617101\pi$
$758$	−15.2170	−	15.2170i	−0.552708	−	0.552708i
$759$	−24.6044			−0.893084
$760$		0			0
$761$	46.8711			1.69907			0.849537	−	0.527529i	$-0.176881\pi$
$761$	46.8711			1.69907			0.849537	+	0.527529i	$0.176881\pi$
$762$	11.8146	+	11.8146i	0.427998	+	0.427998i
$763$	−40.4771	+	40.4771i	−1.46537	+	1.46537i
$764$			11.1422i			0.403112i
$765$		0			0
$766$	−33.0134			−1.19282
$767$	0.175527	−	0.175527i	0.00633790	−	0.00633790i
$768$	1.16084	−	1.16084i	0.0418881	−	0.0418881i
$769$		−	9.38235i		−	0.338336i	−0.985587	−	0.169168i	$-0.945892\pi$
$769$		−	9.38235i		−	0.338336i	0.985587	−	0.169168i	$-0.0541081\pi$
$770$		0			0
$771$	36.5584			1.31662
$772$	−8.15172	−	8.15172i	−0.293387	−	0.293387i
$773$	−3.63612	+	3.63612i	−0.130782	+	0.130782i	−0.769468	−	0.638686i	$-0.779478\pi$
$773$	−3.63612	+	3.63612i	−0.130782	+	0.130782i	0.638686	+	0.769468i	$0.279478\pi$
$774$	1.73405			0.0623290
$775$		0			0
$776$	−11.8932			−0.426940
$777$	−15.6642	+	15.6642i	−0.561952	+	0.561952i
$778$	−6.72046	+	6.72046i	−0.240940	+	0.240940i
$779$	−38.2916	−	3.71325i	−1.37194	−	0.133041i
$780$		0			0
$781$		−	46.1643i		−	1.65189i
$782$	−9.69881	−	9.69881i	−0.346829	−	0.346829i
$783$	26.0363	+	26.0363i	0.930461	+	0.930461i
$784$			2.62009i			0.0935747i
$785$		0			0
$786$	−14.1345			−0.504161
$787$	33.2695	+	33.2695i	1.18593	+	1.18593i	0.978183	+	0.207747i	$0.0666130\pi$
$787$	33.2695	+	33.2695i	1.18593	+	1.18593i	0.207747	+	0.978183i	$0.433387\pi$
$788$	−1.62462	−	1.62462i	−0.0578747	−	0.0578747i
$789$	14.6805			0.522639
$790$		0			0
$791$		−	5.99465i		−	0.213145i
$792$	0.876942	+	0.876942i	0.0311608	+	0.0311608i
$793$	0.476238	−	0.476238i	0.0169117	−	0.0169117i
$794$	16.4972			0.585465
$795$		0			0
$796$	−11.2222			−0.397760
$797$	14.9516	+	14.9516i	0.529613	+	0.529613i	0.920457	−	0.390844i	$-0.127817\pi$
$797$	14.9516	+	14.9516i	0.529613	+	0.529613i	−0.390844	+	0.920457i	$0.627817\pi$
$798$	14.1061	+	17.1357i	0.499349	+	0.606596i
$799$			9.57924i			0.338889i
$800$		0			0
$801$		−	1.99062i		−	0.0703350i
$802$	−15.8385	+	15.8385i	−0.559275	+	0.559275i
$803$	−16.0555	−	16.0555i	−0.566586	−	0.566586i
$804$		−	20.8866i		−	0.736614i
$805$		0			0
$806$			1.16654i			0.0410896i
$807$	−32.1202	+	32.1202i	−1.13068	+	1.13068i
$808$	−4.24264	+	4.24264i	−0.149256	+	0.149256i
$809$		−	38.8609i		−	1.36628i	−0.730289	−	0.683138i	$-0.760615\pi$
$809$		−	38.8609i		−	1.36628i	0.730289	−	0.683138i	$-0.239385\pi$
$810$		0			0
$811$		−	5.76603i		−	0.202473i	−0.994862	−	0.101236i	$-0.967720\pi$
$811$		−	5.76603i		−	0.202473i	0.994862	−	0.101236i	$-0.0322798\pi$
$812$	−14.8841	−	14.8841i	−0.522329	−	0.522329i
$813$	−24.5247	+	24.5247i	−0.860120	+	0.860120i
$814$		−	17.6950i		−	0.620209i
$815$		0			0
$816$		−	6.11074i		−	0.213919i
$817$	−19.1382	+	15.7546i	−0.669562	+	0.551183i
$818$	15.9693	+	15.9693i	0.558353	+	0.558353i
$819$	0.318481			0.0111286
$820$		0			0
$821$	51.3438			1.79191			0.895955	−	0.444145i	$-0.146492\pi$
$821$	51.3438			1.79191			0.895955	+	0.444145i	$0.146492\pi$
$822$	21.5595	−	21.5595i	0.751974	−	0.751974i
$823$	−17.1550	−	17.1550i	−0.597987	−	0.597987i	0.341789	−	0.939777i	$-0.388967\pi$
$823$	−17.1550	−	17.1550i	−0.597987	−	0.597987i	−0.939777	+	0.341789i	$0.888967\pi$
$824$			5.89318i			0.205299i
$825$		0			0
$826$	−2.28633			−0.0795515
$827$	−1.40880	−	1.40880i	−0.0489889	−	0.0489889i	0.682188	−	0.731177i	$-0.261029\pi$
$827$	−1.40880	−	1.40880i	−0.0489889	−	0.0489889i	−0.731177	+	0.682188i	$0.761029\pi$
$828$	0.794502	+	0.794502i	0.0276108	+	0.0276108i
$829$	−34.0502			−1.18261			−0.591306	−	0.806447i	$-0.701387\pi$
$829$	−34.0502			−1.18261			−0.591306	+	0.806447i	$0.701387\pi$
$830$		0			0
$831$		−	39.5046i		−	1.37040i
$832$	0.238119	+	0.238119i	0.00825530	+	0.00825530i
$833$	6.89620	+	6.89620i	0.238939	+	0.238939i
$834$			21.0324i			0.728294i
$835$		0			0
$836$	−17.6460	−	1.71118i	−0.610299	−	0.0591824i
$837$	−13.2899	+	13.2899i	−0.459367	+	0.459367i
$838$	−9.59645	+	9.59645i	−0.331504	+	0.331504i
$839$	−20.3430			−0.702319			−0.351159	−	0.936316i	$-0.614213\pi$
$839$	−20.3430			−0.702319			−0.351159	+	0.936316i	$0.614213\pi$
$840$		0			0
$841$	17.0569			0.588170
$842$	14.8531	−	14.8531i	0.511870	−	0.511870i
$843$	6.35942	+	6.35942i	0.219030	+	0.219030i
$844$	28.5900			0.984109
$845$		0			0
$846$		−	0.784706i		−	0.0269788i
$847$	−12.1559	+	12.1559i	−0.417681	+	0.417681i
$848$	−6.19591	+	6.19591i	−0.212768	+	0.212768i
$849$	16.8695			0.578960
$850$		0			0
$851$		−	16.0315i		−	0.549553i
$852$	13.1758	−	13.1758i	0.451394	−	0.451394i
$853$	17.4592	+	17.4592i	0.597793	+	0.597793i	0.939725	−	0.341932i	$-0.111081\pi$
$853$	17.4592	+	17.4592i	0.597793	+	0.597793i	−0.341932	+	0.939725i	$0.611081\pi$
$854$	−6.20325			−0.212271
$855$		0			0
$856$	16.2972			0.557026
$857$	18.9477	+	18.9477i	0.647242	+	0.647242i	0.952326	−	0.305083i	$-0.0986843\pi$
$857$	18.9477	+	18.9477i	0.647242	+	0.647242i	−0.305083	+	0.952326i	$0.598684\pi$
$858$	1.58994	−	1.58994i	0.0542798	−	0.0542798i
$859$		−	48.0518i		−	1.63951i	−0.572717	−	0.819753i	$-0.694111\pi$
$859$		−	48.0518i		−	1.63951i	0.572717	−	0.819753i	$-0.305889\pi$
$860$		0			0
$861$	−44.9402			−1.53156
$862$	−14.0535	+	14.0535i	−0.478664	+	0.478664i
$863$	−34.9684	+	34.9684i	−1.19034	+	1.19034i	−0.213364	+	0.976973i	$0.568442\pi$
$863$	−34.9684	+	34.9684i	−1.19034	+	1.19034i	−0.976973	+	0.213364i	$0.931558\pi$
$864$			5.42559i			0.184582i
$865$		0			0
$866$	−20.2858			−0.689339
$867$	3.65047	+	3.65047i	0.123976	+	0.123976i
$868$	7.59740	−	7.59740i	0.257873	−	0.257873i
$869$	11.1408			0.377927
$870$		0			0
$871$	4.28441			0.145172
$872$	13.0503	−	13.0503i	0.441939	−	0.441939i
$873$	2.56429	−	2.56429i	0.0867881	−	0.0867881i
$874$	−15.9871	−	1.55031i	−0.540772	−	0.0524401i
$875$		0			0
$876$		−	9.16480i		−	0.309650i
$877$	31.4187	+	31.4187i	1.06093	+	1.06093i	0.998019	+	0.0629157i	$0.0200399\pi$
$877$	31.4187	+	31.4187i	1.06093	+	1.06093i	0.0629157	+	0.998019i	$0.479960\pi$
$878$	−25.4594	−	25.4594i	−0.859213	−	0.859213i
$879$			34.7127i			1.17083i
$880$		0			0
$881$	32.8968			1.10832			0.554160	−	0.832410i	$-0.313040\pi$
$881$	32.8968			1.10832			0.554160	+	0.832410i	$0.313040\pi$
$882$	−0.564919	−	0.564919i	−0.0190218	−	0.0190218i
$883$	9.28094	+	9.28094i	0.312329	+	0.312329i	0.845811	−	0.533482i	$-0.179117\pi$
$883$	9.28094	+	9.28094i	0.312329	+	0.312329i	−0.533482	+	0.845811i	$0.679117\pi$
$884$	1.25348			0.0421591
$885$		0			0
$886$			3.24927i			0.109161i
$887$	−14.8696	−	14.8696i	−0.499274	−	0.499274i	0.411938	−	0.911212i	$-0.364852\pi$
$887$	−14.8696	−	14.8696i	−0.499274	−	0.499274i	−0.911212	+	0.411938i	$0.864852\pi$
$888$	5.05033	−	5.05033i	0.169478	−	0.169478i
$889$	31.5673			1.05873
$890$		0			0
$891$	32.5066			1.08901
$892$	4.64334	+	4.64334i	0.155471	+	0.155471i
$893$	7.12940	+	8.66060i	0.238576	+	0.289816i
$894$		−	23.2042i		−	0.776065i
$895$		0			0
$896$		−	3.10163i		−	0.103618i
$897$	1.44047	−	1.44047i	0.0480961	−	0.0480961i
$898$	18.1065	+	18.1065i	0.604223	+	0.604223i
$899$			23.5092i			0.784076i
$900$		0			0
$901$			32.6158i			1.08659i
$902$	25.3832	−	25.3832i	0.845168	−	0.845168i
$903$	−20.4756	+	20.4756i	−0.681386	+	0.681386i
$904$			1.93274i			0.0642821i
$905$		0			0
$906$			37.4281i			1.24347i
$907$	−5.87582	−	5.87582i	−0.195103	−	0.195103i	0.602794	−	0.797897i	$-0.294054\pi$
$907$	−5.87582	−	5.87582i	−0.195103	−	0.195103i	−0.797897	+	0.602794i	$0.794054\pi$
$908$	−2.92176	+	2.92176i	−0.0969620	+	0.0969620i
$909$		−	1.82951i		−	0.0606811i
$910$		0			0
$911$			24.4817i			0.811115i	0.914070	+	0.405557i	$0.132923\pi$
$911$			24.4817i			0.811115i	−0.914070	+	0.405557i	$0.867077\pi$
$912$	−4.54795	−	5.52473i	−0.150598	−	0.182942i
$913$	41.7387	+	41.7387i	1.38135	+	1.38135i
$914$	28.3023			0.936157
$915$		0			0
$916$	−20.4599			−0.676013
$917$	−18.8829	+	18.8829i	−0.623570	+	0.623570i
$918$	14.2804	+	14.2804i	0.471323	+	0.471323i
$919$			57.8737i			1.90908i	0.298090	+	0.954538i	$0.403651\pi$
$919$			57.8737i			1.90908i	−0.298090	+	0.954538i	$0.596349\pi$
$920$		0			0
$921$	46.7236			1.53959
$922$	−13.0133	−	13.0133i	−0.428569	−	0.428569i
$923$	2.70271	+	2.70271i	0.0889608	+	0.0889608i
$924$	−20.7099			−0.681304
$925$		0			0
$926$		−	36.0959i		−	1.18619i
$927$	−1.27063	−	1.27063i	−0.0417329	−	0.0417329i
$928$	4.79880	+	4.79880i	0.157528	+	0.157528i
$929$			24.3670i			0.799454i	0.916634	+	0.399727i	$0.130895\pi$
$929$			24.3670i			0.799454i	−0.916634	+	0.399727i	$0.869105\pi$
$930$		0			0
$931$	11.3674	+	1.10233i	0.372551	+	0.0361273i
$932$	−4.96326	+	4.96326i	−0.162577	+	0.162577i
$933$	14.6409	−	14.6409i	0.479321	−	0.479321i
$934$	−33.3997			−1.09287
$935$		0			0
$936$	−0.102682			−0.00335626
$937$	−34.3090	+	34.3090i	−1.12082	+	1.12082i	−0.129207	+	0.991618i	$0.541243\pi$
$937$	−34.3090	+	34.3090i	−1.12082	+	1.12082i	−0.991618	+	0.129207i	$0.958757\pi$
$938$	−27.9034	−	27.9034i	−0.911077	−	0.911077i
$939$	−54.9812			−1.79424
$940$		0			0
$941$			10.2149i			0.332995i	0.986042	+	0.166497i	$0.0532457\pi$
$941$			10.2149i			0.332995i	−0.986042	+	0.166497i	$0.946754\pi$
$942$	−9.18189	+	9.18189i	−0.299162	+	0.299162i
$943$	22.9969	−	22.9969i	0.748884	−	0.748884i
$944$	0.737138			0.0239918
$945$		0			0
$946$		−	23.1301i		−	0.752026i
$947$	−19.4484	+	19.4484i	−0.631988	+	0.631988i	−0.948566	−	0.316578i	$-0.897466\pi$
$947$	−19.4484	+	19.4484i	−0.631988	+	0.631988i	0.316578	+	0.948566i	$0.397466\pi$
$948$	3.17971	+	3.17971i	0.103272	+	0.103272i
$949$	1.87995			0.0610258
$950$		0			0
$951$	−11.2582			−0.365071
$952$	−8.16362	−	8.16362i	−0.264584	−	0.264584i
$953$	−4.76124	+	4.76124i	−0.154232	+	0.154232i	−0.780005	−	0.625773i	$-0.784784\pi$
$953$	−4.76124	+	4.76124i	−0.154232	+	0.154232i	0.625773	+	0.780005i	$0.284784\pi$
$954$		−	2.67180i		−	0.0865028i
$955$		0			0
$956$	26.2119			0.847755
$957$	32.0420	−	32.0420i	1.03577	−	1.03577i
$958$	−6.29097	+	6.29097i	−0.203252	+	0.203252i
$959$		−	57.6046i		−	1.86015i
$960$		0			0
$961$	19.0000			0.612903
$962$	1.03596	+	1.03596i	0.0334007	+	0.0334007i
$963$	−3.51384	+	3.51384i	−0.113232	+	0.113232i
$964$	14.5128			0.467427
$965$		0			0
$966$	−18.7629			−0.603688
$967$	−27.8394	+	27.8394i	−0.895253	+	0.895253i	−0.995012	−	0.0997585i	$-0.968193\pi$
$967$	−27.8394	+	27.8394i	−0.895253	+	0.895253i	0.0997585	+	0.995012i	$0.468193\pi$
$968$	3.91920	−	3.91920i	0.125968	−	0.125968i
$969$	−26.5118	−	2.57092i	−0.851680	−	0.0825897i
$970$		0			0
$971$		−	42.2736i		−	1.35662i	−0.734774	−	0.678312i	$-0.762712\pi$
$971$		−	42.2736i		−	1.35662i	0.734774	−	0.678312i	$-0.237288\pi$
$972$	−2.23169	−	2.23169i	−0.0715816	−	0.0715816i
$973$	28.0982	+	28.0982i	0.900787	+	0.900787i
$974$			24.1899i			0.775094i
$975$		0			0
$976$	2.00000			0.0640184
$977$	−5.93447	−	5.93447i	−0.189860	−	0.189860i	0.605775	−	0.795636i	$-0.292863\pi$
$977$	−5.93447	−	5.93447i	−0.189860	−	0.189860i	−0.795636	+	0.605775i	$0.792863\pi$
$978$	−10.1587	−	10.1587i	−0.324838	−	0.324838i
$979$	−26.5525			−0.848621
$980$		0			0
$981$			5.62755i			0.179674i
$982$	−12.3918	−	12.3918i	−0.395439	−	0.395439i
$983$	21.9442	−	21.9442i	0.699910	−	0.699910i	−0.264481	−	0.964391i	$-0.585201\pi$
$983$	21.9442	−	21.9442i	0.699910	−	0.699910i	0.964391	+	0.264481i	$0.0852006\pi$
$984$	14.4892			0.461900
$985$		0			0
$986$	25.2613			0.804484
$987$	9.26581	+	9.26581i	0.294934	+	0.294934i
$988$	1.13327	−	0.932910i	0.0360542	−	0.0296798i
$989$		−	20.9557i		−	0.666352i
$990$		0			0
$991$		−	9.77763i		−	0.310597i	−0.987868	−	0.155298i	$-0.950366\pi$
$991$		−	9.77763i		−	0.310597i	0.987868	−	0.155298i	$-0.0496339\pi$
$992$	−2.44949	+	2.44949i	−0.0777714	+	0.0777714i
$993$	2.36740	+	2.36740i	0.0751271	+	0.0751271i
$994$		−	35.2042i		−	1.11661i
$995$		0			0
$996$			23.8253i			0.754933i
$997$	44.1586	−	44.1586i	1.39852	−	1.39852i	0.594204	−	0.804314i	$-0.297467\pi$
$997$	44.1586	−	44.1586i	1.39852	−	1.39852i	0.804314	−	0.594204i	$-0.202533\pi$
$998$	3.79692	−	3.79692i	0.120189	−	0.120189i
$999$			23.6045i			0.746815i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.f.d.493.5	✓	32
5.2	odd	4	inner	950.2.f.d.607.11	yes	32
5.3	odd	4	inner	950.2.f.d.607.6	yes	32
5.4	even	2	inner	950.2.f.d.493.12	yes	32
19.18	odd	2	inner	950.2.f.d.493.11	yes	32
95.18	even	4	inner	950.2.f.d.607.12	yes	32
95.37	even	4	inner	950.2.f.d.607.5	yes	32
95.94	odd	2	inner	950.2.f.d.493.6	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.f.d.493.5	✓	32	1.1	even	1	trivial
950.2.f.d.493.6	yes	32	95.94	odd	2	inner
950.2.f.d.493.11	yes	32	19.18	odd	2	inner
950.2.f.d.493.12	yes	32	5.4	even	2	inner
950.2.f.d.607.5	yes	32	95.37	even	4	inner
950.2.f.d.607.6	yes	32	5.3	odd	4	inner
950.2.f.d.607.11	yes	32	5.2	odd	4	inner
950.2.f.d.607.12	yes	32	95.18	even	4	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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(1.16084 - 1.16084i) q^{3} +1.00000i q^{4} -1.64167 q^{6} +(-2.19318 + 2.19318i) q^{7} +(0.707107 - 0.707107i) q^{8} +0.304919i q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(1.16084 - 1.16084i) q^{3} +1.00000i q^{4} -1.64167 q^{6} +(-2.19318 + 2.19318i) q^{7} +(0.707107 - 0.707107i) q^{8} +0.304919i q^{9} +4.06726 q^{11} +(1.16084 + 1.16084i) q^{12} +(-0.238119 + 0.238119i) q^{13} +3.10163 q^{14} -1.00000 q^{16} +(-2.63204 + 2.63204i) q^{17} +(0.215610 - 0.215610i) q^{18} +(-0.420721 + 4.33855i) q^{19} +5.09185i q^{21} +(-2.87599 - 2.87599i) q^{22} +(-2.60562 - 2.60562i) q^{23} -1.64167i q^{24} +0.336751 q^{26} +(3.83647 + 3.83647i) q^{27} +(-2.19318 - 2.19318i) q^{28} +6.78652 q^{29} +3.46410i q^{31} +(0.707107 + 0.707107i) q^{32} +(4.72142 - 4.72142i) q^{33} +3.72227 q^{34} -0.304919 q^{36} +(3.07634 + 3.07634i) q^{37} +(3.36531 - 2.77032i) q^{38} +0.552835i q^{39} +8.82591i q^{41} +(3.60048 - 3.60048i) q^{42} +(4.02125 + 4.02125i) q^{43} +4.06726i q^{44} +3.68490i q^{46} +(1.81973 - 1.81973i) q^{47} +(-1.16084 + 1.16084i) q^{48} -2.62009i q^{49} +6.11074i q^{51} +(-0.238119 - 0.238119i) q^{52} +(6.19591 - 6.19591i) q^{53} -5.42559i q^{54} +3.10163i q^{56} +(4.54795 + 5.52473i) q^{57} +(-4.79880 - 4.79880i) q^{58} -0.737138 q^{59} -2.00000 q^{61} +(2.44949 - 2.44949i) q^{62} +(-0.668743 - 0.668743i) q^{63} -1.00000i q^{64} -6.67709 q^{66} +(-8.99636 - 8.99636i) q^{67} +(-2.63204 - 2.63204i) q^{68} -6.04939 q^{69} -11.3502i q^{71} +(0.215610 + 0.215610i) q^{72} +(-3.94750 - 3.94750i) q^{73} -4.35060i q^{74} +(-4.33855 - 0.420721i) q^{76} +(-8.92023 + 8.92023i) q^{77} +(0.390913 - 0.390913i) q^{78} +2.73915 q^{79} +7.99227 q^{81} +(6.24086 - 6.24086i) q^{82} +(10.2621 + 10.2621i) q^{83} -5.09185 q^{84} -5.68691i q^{86} +(7.87804 - 7.87804i) q^{87} +(2.87599 - 2.87599i) q^{88} -6.52835 q^{89} -1.04448i q^{91} +(2.60562 - 2.60562i) q^{92} +(4.02125 + 4.02125i) q^{93} -2.57349 q^{94} +1.64167 q^{96} +(-8.40975 - 8.40975i) q^{97} +(-1.85268 + 1.85268i) q^{98} +1.24018i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{6}+O(q^{10}) \) 32 * q - 8 * q^6	\( 32 q - 8 q^{6} - 24 q^{11} - 32 q^{16} + 32 q^{26} + 56 q^{36} - 64 q^{61} + 72 q^{66} + 4 q^{76} - 32 q^{81} + 8 q^{96}+O(q^{100}) \) 32 * q - 8 * q^6 - 24 * q^11 - 32 * q^16 + 32 * q^26 + 56 * q^36 - 64 * q^61 + 72 * q^66 + 4 * q^76 - 32 * q^81 + 8 * q^96

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