LMFDB - Embedded newform 950.2.f.d.493.6

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			493.6
Character	$\chi$	$=$	950.493
Dual form			950.2.f.d.607.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(1.16084 - 1.16084i) q^{3} +1.00000i q^{4} -1.64167 q^{6} +(2.19318 - 2.19318i) q^{7} +(0.707107 - 0.707107i) q^{8} +0.304919i q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(1.16084 - 1.16084i) q^{3} +1.00000i q^{4} -1.64167 q^{6} +(2.19318 - 2.19318i) q^{7} +(0.707107 - 0.707107i) q^{8} +0.304919i q^{9} +4.06726 q^{11} +(1.16084 + 1.16084i) q^{12} +(-0.238119 + 0.238119i) q^{13} -3.10163 q^{14} -1.00000 q^{16} +(2.63204 - 2.63204i) q^{17} +(0.215610 - 0.215610i) q^{18} +(0.420721 + 4.33855i) q^{19} -5.09185i q^{21} +(-2.87599 - 2.87599i) q^{22} +(2.60562 + 2.60562i) q^{23} -1.64167i q^{24} +0.336751 q^{26} +(3.83647 + 3.83647i) q^{27} +(2.19318 + 2.19318i) q^{28} -6.78652 q^{29} -3.46410i q^{31} +(0.707107 + 0.707107i) q^{32} +(4.72142 - 4.72142i) q^{33} -3.72227 q^{34} -0.304919 q^{36} +(3.07634 + 3.07634i) q^{37} +(2.77032 - 3.36531i) q^{38} +0.552835i q^{39} -8.82591i q^{41} +(-3.60048 + 3.60048i) q^{42} +(-4.02125 - 4.02125i) q^{43} +4.06726i q^{44} -3.68490i q^{46} +(-1.81973 + 1.81973i) q^{47} +(-1.16084 + 1.16084i) q^{48} -2.62009i q^{49} -6.11074i q^{51} +(-0.238119 - 0.238119i) q^{52} +(6.19591 - 6.19591i) q^{53} -5.42559i q^{54} -3.10163i q^{56} +(5.52473 + 4.54795i) q^{57} +(4.79880 + 4.79880i) q^{58} +0.737138 q^{59} -2.00000 q^{61} +(-2.44949 + 2.44949i) q^{62} +(0.668743 + 0.668743i) q^{63} -1.00000i q^{64} -6.67709 q^{66} +(-8.99636 - 8.99636i) q^{67} +(2.63204 + 2.63204i) q^{68} +6.04939 q^{69} +11.3502i q^{71} +(0.215610 + 0.215610i) q^{72} +(3.94750 + 3.94750i) q^{73} -4.35060i q^{74} +(-4.33855 + 0.420721i) q^{76} +(8.92023 - 8.92023i) q^{77} +(0.390913 - 0.390913i) q^{78} -2.73915 q^{79} +7.99227 q^{81} +(-6.24086 + 6.24086i) q^{82} +(-10.2621 - 10.2621i) q^{83} +5.09185 q^{84} +5.68691i q^{86} +(-7.87804 + 7.87804i) q^{87} +(2.87599 - 2.87599i) q^{88} +6.52835 q^{89} +1.04448i q^{91} +(-2.60562 + 2.60562i) q^{92} +(-4.02125 - 4.02125i) q^{93} +2.57349 q^{94} +1.64167 q^{96} +(-8.40975 - 8.40975i) q^{97} +(-1.85268 + 1.85268i) q^{98} +1.24018i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	−0.158426	−	0.987371i	$-0.550642\pi$
$7$	2.19318	−	2.19318i	0.828945	−	0.828945i	0.987371	+	0.158426i	$0.0506420\pi$
$8$	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	−0.311787	−	0.950152i	$-0.600928\pi$
$17$	2.63204	−	2.63204i	0.638364	−	0.638364i	0.950152	+	0.311787i	$0.100928\pi$
$18$	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	0.924497	−	0.381189i	$-0.124485\pi$
$23$	2.60562	+	2.60562i	0.543309	+	0.543309i	−0.381189	+	0.924497i	$0.624485\pi$
$24$		−	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	$-0.716991\pi$
$29$	−6.78652			−1.26023			−0.630113	+	0.776503i	$0.716991\pi$
$30$		0			0
$31$		−	3.46410i		−	0.622171i	−0.950382	−	0.311086i	$-0.899307\pi$
$31$		−	3.46410i		−	0.622171i	0.950382	−	0.311086i	$-0.100693\pi$
$32$	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	$0.633589\pi$
$38$	2.77032	−	3.36531i	0.449406	−	0.545926i
$39$			0.552835i			0.0885244i
$40$		0			0
$41$		−	8.82591i		−	1.37838i	−0.724582	−	0.689188i	$-0.757967\pi$
$41$		−	8.82591i		−	1.37838i	0.724582	−	0.689188i	$-0.242033\pi$
$42$	−3.60048	+	3.60048i	−0.555566	+	0.555566i
$43$	−4.02125	−	4.02125i	−0.613236	−	0.613236i	0.330552	−	0.943788i	$-0.392765\pi$
$43$	−4.02125	−	4.02125i	−0.613236	−	0.613236i	−0.943788	+	0.330552i	$0.892765\pi$
$44$			4.06726i			0.613162i
$45$		0			0
$46$		−	3.68490i		−	0.543309i
$47$	−1.81973	+	1.81973i	−0.265435	+	0.265435i	−0.827258	−	0.561822i	$-0.810100\pi$
$47$	−1.81973	+	1.81973i	−0.265435	+	0.265435i	0.561822	+	0.827258i	$0.310100\pi$
$48$	−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
$57$	5.52473	+	4.54795i	0.731768	+	0.602391i
$58$	4.79880	+	4.79880i	0.630113	+	0.630113i
$59$	0.737138			0.0959672			0.0479836	−	0.998848i	$-0.484720\pi$
$59$	0.737138			0.0959672			0.0479836	+	0.998848i	$0.484720\pi$
$60$		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	$0.235215\pi$
$71$			11.3502i			1.34703i	−0.739176	+	0.673513i	$0.764785\pi$
$72$	0.215610	+	0.215610i	0.0254099	+	0.0254099i
$73$	3.94750	+	3.94750i	0.462020	+	0.462020i	0.899317	−	0.437297i	$-0.144064\pi$
$73$	3.94750	+	3.94750i	0.462020	+	0.462020i	−0.437297	+	0.899317i	$0.644064\pi$
$74$		−	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	$-0.549244\pi$
$79$	−2.73915			−0.308179			−0.154089	+	0.988057i	$0.549244\pi$
$80$		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	$-0.956685\pi$
$83$	−10.2621	−	10.2621i	−1.12641	−	1.12641i	−0.135658	−	0.990756i	$-0.543315\pi$
$84$	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	$-0.387539\pi$
$89$	6.52835			0.692004			0.346002	+	0.938234i	$0.387539\pi$
$90$		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	$-0.845076\pi$
$109$	−18.4559			−1.76775			−0.883877	+	0.467719i	$0.845076\pi$
$110$		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
$133$	10.4379	+	8.59251i	0.905084	+	0.745065i
$134$			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	$-0.458323\pi$
$137$	13.1327	−	13.1327i	1.12200	−	1.12200i	0.991441	−	0.130558i	$-0.0416770\pi$
$138$	−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	$0.378192\pi$
$151$			22.7988i			1.85534i	−0.373400	+	0.927671i	$0.621808\pi$
$152$	3.36531	+	2.77032i	0.272963	+	0.224703i
$153$	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	−0.894146	−	0.447775i	$-0.852217\pi$
$157$	−5.59302	+	5.59302i	−0.446372	+	0.446372i	0.447775	+	0.894146i	$0.352217\pi$
$158$	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	0.421941	−	0.906623i	$-0.361349\pi$
$163$	−6.18801	−	6.18801i	−0.484682	−	0.484682i	−0.906623	+	0.421941i	$0.861349\pi$
$164$	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	$-0.221249\pi$
$179$	20.5504			1.53601			0.768005	+	0.640443i	$0.221249\pi$
$180$		0			0
$181$			4.87105i			0.362063i	0.983477	+	0.181031i	$0.0579435\pi$
$181$			4.87105i			0.362063i	−0.983477	+	0.181031i	$0.942056\pi$
$182$	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	−0.646860	−	0.762609i	$-0.723918\pi$
$197$	1.62462	−	1.62462i	0.115749	−	0.115749i	0.762609	+	0.646860i	$0.223918\pi$
$198$	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	$0.443179\pi$
$211$			28.5900i			1.96822i	−0.177563	+	0.984109i	$0.556821\pi$
$212$	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	$0.706214\pi$
$228$	−4.54795	+	5.52473i	−0.301196	+	0.365884i
$229$			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	0.525586	−	0.850740i	$-0.323846\pi$
$233$	−4.96326	−	4.96326i	−0.325154	−	0.325154i	−0.850740	+	0.525586i	$0.823846\pi$
$234$			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	$0.154819\pi$
$241$			14.5128i			0.934853i	−0.884032	+	0.467427i	$0.845181\pi$
$242$	−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
$247$	−1.13327	−	0.932910i	−0.0721084	−	0.0593596i
$248$	−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	0.484747	−	0.874654i	$-0.338912\pi$
$263$	−6.32324	−	6.32324i	−0.389907	−	0.389907i	−0.874654	+	0.484747i	$0.838912\pi$
$264$		−	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	$-0.180473\pi$
$269$	27.6699			1.68706			0.843531	+	0.537081i	$0.180473\pi$
$270$		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	$0.507202\pi$
$277$	−17.0156	+	17.0156i	−1.02237	+	1.02237i	−0.999744	+	0.0226242i	$0.992798\pi$
$278$	−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	$-0.947753\pi$
$281$		−	5.47831i		−	0.326808i	0.986559	−	0.163404i	$-0.0522475\pi$
$282$	2.98740	−	2.98740i	0.177897	−	0.177897i
$283$	−7.26610	−	7.26610i	−0.431925	−	0.431925i	0.457358	−	0.889283i	$-0.348796\pi$
$283$	−7.26610	−	7.26610i	−0.431925	−	0.431925i	−0.889283	+	0.457358i	$0.848796\pi$
$284$	−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	$0.145421\pi$
$313$	23.6817	+	23.6817i	1.33857	+	1.33857i	0.441125	+	0.897445i	$0.354579\pi$
$314$	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
$323$	12.5266	+	10.3119i	0.696999	+	0.573769i
$324$			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	$-0.982150\pi$
$331$		−	2.03939i		−	0.112095i	0.998428	−	0.0560475i	$-0.0178498\pi$
$332$	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
$342$	1.02615	+	0.844723i	0.0554877	+	0.0456774i
$343$	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	$0.612783\pi$
$347$	−23.9338	+	23.9338i	−1.28484	+	1.28484i	−0.937883	+	0.346952i	$0.887217\pi$
$348$	−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	0.161846	−	0.986816i	$-0.448255\pi$
$353$	−15.4998	−	15.4998i	−0.824970	−	0.824970i	−0.986816	+	0.161846i	$0.948255\pi$
$354$	−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	−0.757129	−	0.653266i	$-0.773398\pi$
$367$	−1.98973	+	1.98973i	−0.103863	+	0.103863i	0.653266	+	0.757129i	$0.273398\pi$
$368$	−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	$-0.686405\pi$
$379$	−21.5201			−1.10542			−0.552708	+	0.833375i	$0.686405\pi$
$380$		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	−0.350935	−	0.936400i	$-0.614136\pi$
$397$	11.6653	−	11.6653i	0.585465	−	0.585465i	0.936400	+	0.350935i	$0.114136\pi$
$398$	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	$0.188921\pi$
$401$			22.3990i			1.11855i	−0.828982	+	0.559275i	$0.811079\pi$
$402$	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	$-0.311433\pi$
$409$	22.5840			1.11671			0.558353	+	0.829603i	$0.311433\pi$
$410$		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
$418$	11.2676	−	13.6876i	0.551117	−	0.669482i
$419$		−	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	$-0.828953\pi$
$421$		−	21.0054i		−	1.02374i	0.859063	−	0.511870i	$-0.171047\pi$
$422$	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	$0.158879\pi$
$431$			19.8746i			0.957328i	−0.877998	+	0.478664i	$0.841121\pi$
$432$	−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
$437$	−10.2084	+	12.4008i	−0.488332	+	0.593212i
$438$	−6.48049	−	6.48049i	−0.309650	−	0.309650i
$439$	−36.0050			−1.71843			−0.859213	−	0.511618i	$-0.829046\pi$
$439$	−36.0050			−1.71843			−0.859213	+	0.511618i	$0.829046\pi$
$440$		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	0.759578	−	0.650416i	$-0.225406\pi$
$443$	2.29758	+	2.29758i	0.109161	+	0.109161i	−0.650416	+	0.759578i	$0.725406\pi$
$444$			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	$-0.293484\pi$
$449$	25.6065			1.20845			0.604223	+	0.796816i	$0.293484\pi$
$450$		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	−0.0619238	−	0.998081i	$-0.519724\pi$
$457$	20.0128	−	20.0128i	0.936157	−	0.936157i	0.998081	+	0.0619238i	$0.0197236\pi$
$458$	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	$-0.933281\pi$
$463$	−25.5237	−	25.5237i	−1.18619	−	1.18619i	−0.208073	−	0.978113i	$-0.566719\pi$
$464$	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	$0.531133\pi$
$467$	−23.6172	+	23.6172i	−1.09287	+	1.09287i	−0.995221	+	0.0976518i	$0.968867\pi$
$468$	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	0.0937637	−	0.995594i	$-0.470110\pi$
$503$	−20.2260	−	20.2260i	−0.901831	−	0.901831i	−0.995594	+	0.0937637i	$0.970110\pi$
$504$	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	$-0.871144\pi$
$509$	−41.4751			−1.83835			−0.919176	+	0.393847i	$0.871144\pi$
$510$		0			0
$511$	17.3152			0.765978
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−15.0306	+	18.2588i	−0.663618	+	0.806145i
$514$		−	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	$0.0331603\pi$
$521$			4.74714i			0.207976i	−0.994579	+	0.103988i	$0.966840\pi$
$522$	−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
$532$	−8.59251	+	10.4379i	−0.372532	+	0.452542i
$533$	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	−0.921882	−	0.387471i	$-0.873349\pi$
$557$	−12.6126	+	12.6126i	−0.534411	+	0.534411i	0.387471	+	0.921882i	$0.373349\pi$
$558$	−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	$-0.514400\pi$
$569$	−2.15748			−0.0904464			−0.0452232	+	0.998977i	$0.514400\pi$
$570$		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	−0.525752	−	0.850638i	$-0.676216\pi$
$577$	7.80401	−	7.80401i	0.324885	−	0.324885i	0.850638	+	0.525752i	$0.176216\pi$
$578$	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	−0.987776	−	0.155878i	$-0.950179\pi$
$587$	−20.1553	+	20.1553i	−0.831898	+	0.831898i	0.155878	+	0.987776i	$0.450179\pi$
$588$	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	0.369306	−	0.929308i	$-0.379595\pi$
$593$	−13.6369	−	13.6369i	−0.560002	−	0.560002i	−0.929308	+	0.369306i	$0.879595\pi$
$594$		−	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	$-0.670612\pi$
$599$	−24.9980			−1.02139			−0.510696	+	0.859761i	$0.670612\pi$
$600$		0			0
$601$		−	23.1239i		−	0.943244i	−0.881801	−	0.471622i	$-0.843669\pi$
$601$		−	23.1239i		−	0.943244i	0.881801	−	0.471622i	$-0.156331\pi$
$602$	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	$-0.550851\pi$
$608$	−2.77032	+	3.36531i	−0.112351	+	0.136481i
$609$			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	$0.0125940\pi$
$613$	25.7188	+	25.7188i	1.03877	+	1.03877i	0.0395548	+	0.999217i	$0.487406\pi$
$614$		−	28.4610i		−	1.14859i
$615$		0			0
$616$		−	12.6151i		−	0.508277i
$617$	1.29044	−	1.29044i	0.0519512	−	0.0519512i	−0.680654	−	0.732605i	$-0.738304\pi$
$617$	1.29044	−	1.29044i	0.0519512	−	0.0519512i	0.732605	+	0.680654i	$0.238304\pi$
$618$	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
$627$	22.4705	+	18.4977i	0.897385	+	0.738727i
$628$	−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	$0.0435397\pi$
$641$			6.90462i			0.272716i	−0.990660	+	0.136358i	$0.956460\pi$
$642$	−18.9184	−	18.9184i	−0.746648	−	0.746648i
$643$	−11.5345	−	11.5345i	−0.454875	−	0.454875i	0.442094	−	0.896969i	$-0.354236\pi$
$643$	−11.5345	−	11.5345i	−0.454875	−	0.454875i	−0.896969	+	0.442094i	$0.854236\pi$
$644$			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	−0.825357	−	0.564611i	$-0.809026\pi$
$647$	−6.63240	+	6.63240i	−0.260747	+	0.260747i	0.564611	+	0.825357i	$0.309026\pi$
$648$	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	0.757666	−	0.652642i	$-0.226340\pi$
$653$	2.68377	+	2.68377i	0.105024	+	0.105024i	−0.652642	+	0.757666i	$0.726340\pi$
$654$	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	$-0.597401\pi$
$659$	−15.4664			−0.602485			−0.301243	+	0.953548i	$0.597401\pi$
$660$		0			0
$661$			32.0168i			1.24531i	0.782497	+	0.622654i	$0.213945\pi$
$661$			32.0168i			1.24531i	−0.782497	+	0.622654i	$0.786055\pi$
$662$	−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
$703$	−12.0526	+	14.6411i	−0.454571	+	0.552200i
$704$		−	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
$722$	15.7661	+	10.6033i	0.586753	+	0.394615i
$723$	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	−0.657303	−	0.753627i	$-0.728303\pi$
$727$	2.59718	−	2.59718i	0.0963240	−	0.0963240i	0.753627	+	0.657303i	$0.228303\pi$
$728$	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	0.844123	−	0.536149i	$-0.180122\pi$
$733$	8.33808	+	8.33808i	0.307974	+	0.307974i	−0.536149	+	0.844123i	$0.680122\pi$
$734$	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	$0.0404872\pi$
$751$			6.95258i			0.253703i	−0.991922	+	0.126852i	$0.959513\pi$
$752$	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	−0.981266	−	0.192656i	$-0.938290\pi$
$757$	−21.6975	+	21.6975i	−0.788610	+	0.788610i	0.192656	+	0.981266i	$0.438290\pi$
$758$	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	$0.627817\pi$
$798$	−17.1357	−	14.1061i	−0.606596	−	0.499349i
$799$			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	$0.0322798\pi$
$811$			5.76603i			0.202473i	−0.994862	+	0.101236i	$0.967720\pi$
$812$	−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
$817$	15.7546	−	19.1382i	0.551183	−	0.669562i
$818$	−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	0.939777	−	0.341789i	$-0.111033\pi$
$823$	17.1550	+	17.1550i	0.597987	+	0.597987i	−0.341789	+	0.939777i	$0.611033\pi$
$824$			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	$-0.298613\pi$
$829$	34.0502			1.18261			0.591306	+	0.806447i	$0.298613\pi$
$830$		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	$-0.385787\pi$
$839$	20.3430			0.702319			0.351159	+	0.936316i	$0.385787\pi$
$840$		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	0.341932	−	0.939725i	$-0.388919\pi$
$853$	−17.4592	−	17.4592i	−0.597793	−	0.597793i	−0.939725	+	0.341932i	$0.888919\pi$
$854$	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	0.533482	−	0.845811i	$-0.320883\pi$
$883$	−9.28094	−	9.28094i	−0.312329	−	0.312329i	−0.845811	+	0.533482i	$0.820883\pi$
$884$	−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
$893$	−8.66060	−	7.12940i	−0.289816	−	0.238576i
$894$		−	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	$-0.867077\pi$
$911$		−	24.4817i		−	0.811115i	0.914070	−	0.405557i	$-0.132923\pi$
$912$	−5.52473	−	4.54795i	−0.182942	−	0.150598i
$913$	−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	$-0.458757\pi$
$937$	34.3090	−	34.3090i	1.12082	−	1.12082i	0.991618	−	0.129207i	$-0.0412433\pi$
$938$	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	$-0.946754\pi$
$941$		−	10.2149i		−	0.332995i	0.986042	−	0.166497i	$-0.0532457\pi$
$942$	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	−0.316578	−	0.948566i	$-0.602534\pi$
$947$	19.4484	−	19.4484i	0.631988	−	0.631988i	0.948566	+	0.316578i	$0.102534\pi$
$948$	−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	−0.0997585	−	0.995012i	$-0.531807\pi$
$967$	27.8394	−	27.8394i	0.895253	−	0.895253i	0.995012	+	0.0997585i	$0.0318070\pi$
$968$	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	$0.237288\pi$
$971$			42.2736i			1.35662i	−0.734774	+	0.678312i	$0.762712\pi$
$972$	−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
$988$	0.932910	−	1.13327i	0.0296798	−	0.0360542i
$989$		−	20.9557i		−	0.666352i
$990$		0			0
$991$			9.77763i			0.310597i	0.987868	+	0.155298i	$0.0496339\pi$
$991$			9.77763i			0.310597i	−0.987868	+	0.155298i	$0.950366\pi$
$992$	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	$0.702533\pi$
$997$	−44.1586	+	44.1586i	−1.39852	+	1.39852i	−0.804314	+	0.594204i	$0.797467\pi$
$998$	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.493.6	yes	32
5.2	odd	4	inner	950.2.f.d.607.12	yes	32
5.3	odd	4	inner	950.2.f.d.607.5	yes	32
5.4	even	2	inner	950.2.f.d.493.11	yes	32
19.18	odd	2	inner	950.2.f.d.493.12	yes	32
95.18	even	4	inner	950.2.f.d.607.11	yes	32
95.37	even	4	inner	950.2.f.d.607.6	yes	32
95.94	odd	2	inner	950.2.f.d.493.5	✓	32

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

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