LMFDB - Embedded newform 276.2.i.a.133.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [276,2,Mod(13,276)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(276, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 14]))

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

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

chi := DirichletCharacter("276.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 276 = 2^{2} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	276.i (of order $11$, degree $10$, 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:	$2.20387109579$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 8 x^{19} + 43 x^{18} - 165 x^{17} + 538 x^{16} - 1433 x^{15} + 3444 x^{14} - 7370 x^{13} + \cdots + 529 $ x^20 - 8x^19 + 43x^18 - 165x^17 + 538x^16 - 1433x^15 + 3444x^14 - 7370x^13 + 15500x^12 - 28190x^11 + 41920x^10 - 33520x^9 - 13837x^8 + 78980x^7 - 92652x^6 - 52852x^5 + 177374x^4 + 151360x^3 + 115323x^2 + 12834*x + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			133.1
Root			$-0.262998 - 0.575885i$ of defining polynomial
Character	$\chi$	$=$	276.133
Dual form			276.2.i.a.193.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.654861 + 0.755750i) q^{3} +(-0.149019 + 1.03645i) q^{5} +(0.607780 + 1.33085i) q^{7} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})$	\(q+(-0.654861 + 0.755750i) q^{3} +(-0.149019 + 1.03645i) q^{5} +(0.607780 + 1.33085i) q^{7} +(-0.142315 - 0.989821i) q^{9} +(1.96481 - 0.576921i) q^{11} +(-2.86365 + 6.27053i) q^{13} +(-0.685708 - 0.791349i) q^{15} +(-6.54296 + 4.20490i) q^{17} +(5.36057 + 3.44503i) q^{19} +(-1.40380 - 0.412194i) q^{21} +(-0.692970 - 4.74550i) q^{23} +(3.74545 + 1.09976i) q^{25} +(0.841254 + 0.540641i) q^{27} +(3.48875 - 2.24209i) q^{29} +(-0.595921 - 0.687730i) q^{31} +(-0.850671 + 1.86271i) q^{33} +(-1.46993 + 0.431610i) q^{35} +(-0.580529 - 4.03767i) q^{37} +(-2.86365 - 6.27053i) q^{39} +(-0.696437 + 4.84382i) q^{41} +(2.29407 - 2.64750i) q^{43} +1.04710 q^{45} -1.92699 q^{47} +(3.18225 - 3.67251i) q^{49} +(1.10687 - 7.69846i) q^{51} +(-3.25236 - 7.12168i) q^{53} +(0.305154 + 2.12240i) q^{55} +(-6.11401 + 1.79523i) q^{57} +(6.00809 - 13.1559i) q^{59} +(4.93456 + 5.69479i) q^{61} +(1.23081 - 0.790994i) q^{63} +(-6.07233 - 3.90245i) q^{65} +(9.68609 + 2.84409i) q^{67} +(4.04021 + 2.58393i) q^{69} +(0.189483 + 0.0556372i) q^{71} +(-6.69670 - 4.30371i) q^{73} +(-3.28389 + 2.11043i) q^{75} +(1.96197 + 2.26424i) q^{77} +(-1.92232 + 4.20928i) q^{79} +(-0.959493 + 0.281733i) q^{81} +(-1.17882 - 8.19891i) q^{83} +(-3.38314 - 7.40803i) q^{85} +(-0.590193 + 4.10488i) q^{87} +(0.180249 - 0.208018i) q^{89} -10.0856 q^{91} +0.909997 q^{93} +(-4.36941 + 5.04257i) q^{95} +(1.04696 - 7.28177i) q^{97} +(-0.850671 - 1.86271i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{3} - 4 q^{5} - 2 q^{9}+O(q^{10}) $ 20 * q - 2 * q^3 - 4 * q^5 - 2 * q^9	$ 20 q - 2 q^{3} - 4 q^{5} - 2 q^{9} - 22 q^{13} + 7 q^{15} + 7 q^{17} + 19 q^{19} + 20 q^{23} + 20 q^{25} - 2 q^{27} + 32 q^{29} - 3 q^{31} + 11 q^{33} - 26 q^{35} - 10 q^{37} - 22 q^{39} - 40 q^{41} + 8 q^{43} - 4 q^{45} - 18 q^{47} - 34 q^{49} - 26 q^{51} - 34 q^{53} - 17 q^{55} - 3 q^{57} - 32 q^{59} + 32 q^{61} + 49 q^{65} + 35 q^{67} - 2 q^{69} + 33 q^{71} - q^{73} - 2 q^{75} - 50 q^{77} + 22 q^{79} - 2 q^{81} - 14 q^{83} - 9 q^{85} - 12 q^{87} + 10 q^{89} - 72 q^{91} + 30 q^{93} - 51 q^{95} - 4 q^{97} + 11 q^{99}+O(q^{100}) $ 20 * q - 2 * q^3 - 4 * q^5 - 2 * q^9 - 22 * q^13 + 7 * q^15 + 7 * q^17 + 19 * q^19 + 20 * q^23 + 20 * q^25 - 2 * q^27 + 32 * q^29 - 3 * q^31 + 11 * q^33 - 26 * q^35 - 10 * q^37 - 22 * q^39 - 40 * q^41 + 8 * q^43 - 4 * q^45 - 18 * q^47 - 34 * q^49 - 26 * q^51 - 34 * q^53 - 17 * q^55 - 3 * q^57 - 32 * q^59 + 32 * q^61 + 49 * q^65 + 35 * q^67 - 2 * q^69 + 33 * q^71 - q^73 - 2 * q^75 - 50 * q^77 + 22 * q^79 - 2 * q^81 - 14 * q^83 - 9 * q^85 - 12 * q^87 + 10 * q^89 - 72 * q^91 + 30 * q^93 - 51 * q^95 - 4 * q^97 + 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/276\mathbb{Z}\right)^\times$.

$n$	$97$	$139$	$185$
$\chi(n)$	$e\left(\frac{6}{11}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.654861	+	0.755750i	−0.378084	+	0.436332i
$3$	−0.654861	+	0.755750i	−0.378084	+	0.436332i
$4$		0			0
$5$	−0.149019	+	1.03645i	−0.0666431	+	0.463513i	0.928986	+	0.370115i	$0.120682\pi$
$5$	−0.149019	+	1.03645i	−0.0666431	+	0.463513i	−0.995629	+	0.0933976i	$0.970227\pi$
$6$		0			0
$7$	0.607780	+	1.33085i	0.229719	+	0.503015i	0.989030	−	0.147713i	$-0.0471911\pi$
$7$	0.607780	+	1.33085i	0.229719	+	0.503015i	−0.759311	+	0.650728i	$0.774464\pi$
$8$		0			0
$9$	−0.142315	−	0.989821i	−0.0474383	−	0.329940i
$10$		0			0
$11$	1.96481	−	0.576921i	0.592413	−	0.173948i	0.0282350	−	0.999601i	$-0.491011\pi$
$11$	1.96481	−	0.576921i	0.592413	−	0.173948i	0.564178	+	0.825653i	$0.309193\pi$
$12$		0			0
$13$	−2.86365	+	6.27053i	−0.794235	+	1.73913i	−0.130123	+	0.991498i	$0.541537\pi$
$13$	−2.86365	+	6.27053i	−0.794235	+	1.73913i	−0.664112	+	0.747633i	$0.731190\pi$
$14$		0			0
$15$	−0.685708	−	0.791349i	−0.177049	−	0.204325i
$16$		0			0
$17$	−6.54296	+	4.20490i	−1.58690	+	1.01984i	−0.613798	+	0.789463i	$0.710359\pi$
$17$	−6.54296	+	4.20490i	−1.58690	+	1.01984i	−0.973102	+	0.230375i	$0.926005\pi$
$18$		0			0
$19$	5.36057	+	3.44503i	1.22980	+	0.790344i	0.983860	−	0.178941i	$-0.0572672\pi$
$19$	5.36057	+	3.44503i	1.22980	+	0.790344i	0.245939	+	0.969285i	$0.420904\pi$
$20$		0			0
$21$	−1.40380	−	0.412194i	−0.306335	−	0.0899481i
$22$		0			0
$23$	−0.692970	−	4.74550i	−0.144494	−	0.989506i
$23$	−0.692970	−	4.74550i	−0.144494	−	0.989506i
$24$		0			0
$25$	3.74545	+	1.09976i	0.749090	+	0.219953i
$26$		0			0
$27$	0.841254	+	0.540641i	0.161899	+	0.104046i
$28$		0			0
$29$	3.48875	−	2.24209i	0.647845	−	0.416345i	−0.175033	−	0.984563i	$-0.556003\pi$
$29$	3.48875	−	2.24209i	0.647845	−	0.416345i	0.822878	+	0.568218i	$0.192367\pi$
$30$		0			0
$31$	−0.595921	−	0.687730i	−0.107031	−	0.123520i	0.699707	−	0.714430i	$-0.253314\pi$
$31$	−0.595921	−	0.687730i	−0.107031	−	0.123520i	−0.806737	+	0.590910i	$0.798769\pi$
$32$		0			0
$33$	−0.850671	+	1.86271i	−0.148083	+	0.324256i
$34$		0			0
$35$	−1.46993	+	0.431610i	−0.248463	+	0.0729554i
$36$		0			0
$37$	−0.580529	−	4.03767i	−0.0954384	−	0.663789i	−0.980239	−	0.197818i	$-0.936614\pi$
$37$	−0.580529	−	4.03767i	−0.0954384	−	0.663789i	0.884800	−	0.465970i	$-0.154295\pi$
$38$		0			0
$39$	−2.86365	−	6.27053i	−0.458552	−	1.00409i
$40$		0			0
$41$	−0.696437	+	4.84382i	−0.108765	+	0.756478i	0.860321	+	0.509753i	$0.170263\pi$
$41$	−0.696437	+	4.84382i	−0.108765	+	0.756478i	−0.969086	+	0.246725i	$0.920646\pi$
$42$		0			0
$43$	2.29407	−	2.64750i	0.349842	−	0.403740i	−0.553369	−	0.832937i	$-0.686658\pi$
$43$	2.29407	−	2.64750i	0.349842	−	0.403740i	0.903211	+	0.429197i	$0.141203\pi$
$44$		0			0
$45$	1.04710			0.156093
$46$		0			0
$47$	−1.92699			−0.281080			−0.140540	−	0.990075i	$-0.544884\pi$
$47$	−1.92699			−0.281080			−0.140540	+	0.990075i	$0.544884\pi$
$48$		0			0
$49$	3.18225	−	3.67251i	0.454607	−	0.524645i
$50$		0			0
$51$	1.10687	−	7.69846i	0.154993	−	1.07800i
$52$		0			0
$53$	−3.25236	−	7.12168i	−0.446746	−	0.978238i	−0.990311	−	0.138870i	$-0.955653\pi$
$53$	−3.25236	−	7.12168i	−0.446746	−	0.978238i	0.543564	−	0.839368i	$-0.317074\pi$
$54$		0			0
$55$	0.305154	+	2.12240i	0.0411470	+	0.286184i
$56$		0			0
$57$	−6.11401	+	1.79523i	−0.809820	+	0.237785i
$58$		0			0
$59$	6.00809	−	13.1559i	0.782187	−	1.71275i	0.0844153	−	0.996431i	$-0.473098\pi$
$59$	6.00809	−	13.1559i	0.782187	−	1.71275i	0.697772	−	0.716320i	$-0.254175\pi$
$60$		0			0
$61$	4.93456	+	5.69479i	0.631806	+	0.729143i	0.977904	−	0.209056i	$-0.0670390\pi$
$61$	4.93456	+	5.69479i	0.631806	+	0.729143i	−0.346098	+	0.938198i	$0.612494\pi$
$62$		0			0
$63$	1.23081	−	0.790994i	0.155068	−	0.0996559i
$64$		0			0
$65$	−6.07233	−	3.90245i	−0.753180	−	0.484039i
$66$		0			0
$67$	9.68609	+	2.84409i	1.18334	+	0.347461i	0.813462	−	0.581618i	$-0.197580\pi$
$67$	9.68609	+	2.84409i	1.18334	+	0.347461i	0.369882	+	0.929079i	$0.379398\pi$
$68$		0			0
$69$	4.04021	+	2.58393i	0.486384	+	0.311069i
$70$		0			0
$71$	0.189483	+	0.0556372i	0.0224875	+	0.00660292i	0.292957	−	0.956126i	$-0.405361\pi$
$71$	0.189483	+	0.0556372i	0.0224875	+	0.00660292i	−0.270469	+	0.962729i	$0.587179\pi$
$72$		0			0
$73$	−6.69670	−	4.30371i	−0.783789	−	0.503711i	0.0864999	−	0.996252i	$-0.472432\pi$
$73$	−6.69670	−	4.30371i	−0.783789	−	0.503711i	−0.870289	+	0.492541i	$0.836068\pi$
$74$		0			0
$75$	−3.28389	+	2.11043i	−0.379191	+	0.243691i
$76$		0			0
$77$	1.96197	+	2.26424i	0.223587	+	0.258034i
$78$		0			0
$79$	−1.92232	+	4.20928i	−0.216277	+	0.473581i	−0.986410	−	0.164302i	$-0.947463\pi$
$79$	−1.92232	+	4.20928i	−0.216277	+	0.473581i	0.770133	+	0.637884i	$0.220190\pi$
$80$		0			0
$81$	−0.959493	+	0.281733i	−0.106610	+	0.0313036i
$82$		0			0
$83$	−1.17882	−	8.19891i	−0.129393	−	0.899947i	−0.946326	−	0.323214i	$-0.895237\pi$
$83$	−1.17882	−	8.19891i	−0.129393	−	0.899947i	0.816933	−	0.576733i	$-0.195673\pi$
$84$		0			0
$85$	−3.38314	−	7.40803i	−0.366953	−	0.803514i
$86$		0			0
$87$	−0.590193	+	4.10488i	−0.0632753	+	0.440089i
$88$		0			0
$89$	0.180249	−	0.208018i	0.0191063	−	0.0220499i	−0.746116	−	0.665816i	$-0.768084\pi$
$89$	0.180249	−	0.208018i	0.0191063	−	0.0220499i	0.765222	+	0.643766i	$0.222629\pi$
$90$		0			0
$91$	−10.0856			−1.05726
$92$		0			0
$93$	0.909997			0.0943623
$94$		0			0
$95$	−4.36941	+	5.04257i	−0.448292	+	0.517357i
$96$		0			0
$97$	1.04696	−	7.28177i	0.106303	−	0.739351i	−0.865046	−	0.501693i	$-0.832711\pi$
$97$	1.04696	−	7.28177i	0.106303	−	0.739351i	0.971349	−	0.237659i	$-0.0763800\pi$
$98$		0			0
$99$	−0.850671	−	1.86271i	−0.0854956	−	0.187209i
$100$		0			0
$101$	2.03748	+	14.1710i	0.202737	+	1.41006i	0.796117	+	0.605143i	$0.206884\pi$
$101$	2.03748	+	14.1710i	0.202737	+	1.41006i	−0.593380	+	0.804922i	$0.702207\pi$
$102$		0			0
$103$	3.85204	−	1.13106i	0.379553	−	0.111447i	−0.0863903	−	0.996261i	$-0.527533\pi$
$103$	3.85204	−	1.13106i	0.379553	−	0.111447i	0.465943	+	0.884815i	$0.345715\pi$
$104$		0			0
$105$	0.636410	−	1.39354i	0.0621072	−	0.135996i
$106$		0			0
$107$	8.52969	+	9.84379i	0.824596	+	0.951635i	0.999457	−	0.0329585i	$-0.0104929\pi$
$107$	8.52969	+	9.84379i	0.824596	+	0.951635i	−0.174861	+	0.984593i	$0.555947\pi$
$108$		0			0
$109$	−2.98252	+	1.91675i	−0.285674	+	0.183592i	−0.675628	−	0.737243i	$-0.736127\pi$
$109$	−2.98252	+	1.91675i	−0.285674	+	0.183592i	0.389954	+	0.920834i	$0.372491\pi$
$110$		0			0
$111$	3.43163	+	2.20538i	0.325716	+	0.209325i
$112$		0			0
$113$	14.6873	+	4.31258i	1.38166	+	0.405693i	0.886348	−	0.463019i	$-0.153234\pi$
$113$	14.6873	+	4.31258i	1.38166	+	0.405693i	0.495316	+	0.868713i	$0.335052\pi$
$114$		0			0
$115$	5.02173	−	0.0110588i	0.468278	−	0.00103124i
$116$		0			0
$117$	6.61424	+	1.94212i	0.611487	+	0.179549i
$118$		0			0
$119$	−9.57279	−	6.15206i	−0.877536	−	0.563958i
$120$		0			0
$121$	−5.72614	+	3.67997i	−0.520558	+	0.334542i
$122$		0			0
$123$	−3.20465	−	3.69836i	−0.288953	−	0.333470i
$124$		0			0
$125$	−3.87290	+	8.48047i	−0.346403	+	0.758517i
$126$		0			0
$127$	−13.2206	+	3.88193i	−1.17314	+	0.344466i	−0.809527	−	0.587083i	$-0.800276\pi$
$127$	−13.2206	+	3.88193i	−1.17314	+	0.344466i	−0.363616	+	0.931549i	$0.618458\pi$
$128$		0			0
$129$	0.498549	+	3.46748i	0.0438948	+	0.305295i
$130$		0			0
$131$	−3.99409	−	8.74584i	−0.348966	−	0.764128i	−0.999987	−	0.00506875i	$-0.998387\pi$
$131$	−3.99409	−	8.74584i	−0.348966	−	0.764128i	0.651022	−	0.759059i	$-0.274341\pi$
$132$		0			0
$133$	−1.32678	+	9.22796i	−0.115046	+	0.800165i
$134$		0			0
$135$	−0.685708	+	0.791349i	−0.0590163	+	0.0681085i
$136$		0			0
$137$	3.53079			0.301656			0.150828	−	0.988560i	$-0.451806\pi$
$137$	3.53079			0.301656			0.150828	+	0.988560i	$0.451806\pi$
$138$		0			0
$139$	2.28333			0.193670			0.0968349	−	0.995300i	$-0.469128\pi$
$139$	2.28333			0.193670			0.0968349	+	0.995300i	$0.469128\pi$
$140$		0			0
$141$	1.26191	−	1.45632i	0.106272	−	0.122644i
$142$		0			0
$143$	−2.00894	+	13.9725i	−0.167996	+	1.16844i
$144$		0			0
$145$	1.80391	+	3.95002i	0.149807	+	0.328031i
$146$		0			0
$147$	0.691569	+	4.80997i	0.0570397	+	0.396720i
$148$		0			0
$149$	12.9656	−	3.80706i	1.06219	−	0.311886i	0.296456	−	0.955047i	$-0.404195\pi$
$149$	12.9656	−	3.80706i	1.06219	−	0.311886i	0.765732	+	0.643160i	$0.222377\pi$
$150$		0			0
$151$	−0.959780	+	2.10162i	−0.0781058	+	0.171028i	−0.944656	−	0.328061i	$-0.893605\pi$
$151$	−0.959780	+	2.10162i	−0.0781058	+	0.171028i	0.866551	+	0.499089i	$0.166332\pi$
$152$		0			0
$153$	5.09326	+	5.87794i	0.411766	+	0.475203i
$154$		0			0
$155$	0.801598	−	0.515156i	0.0643859	−	0.0413783i
$156$		0			0
$157$	−10.1745	−	6.53877i	−0.812015	−	0.521851i	0.0675010	−	0.997719i	$-0.478497\pi$
$157$	−10.1745	−	6.53877i	−0.812015	−	0.521851i	−0.879516	+	0.475869i	$0.842134\pi$
$158$		0			0
$159$	7.51205	+	2.20574i	0.595744	+	0.174926i
$160$		0			0
$161$	5.89439	−	3.80646i	0.464543	−	0.299991i
$162$		0			0
$163$	20.7606	+	6.09585i	1.62609	+	0.477464i	0.962647	−	0.270759i	$-0.0872748\pi$
$163$	20.7606	+	6.09585i	1.62609	+	0.477464i	0.663447	+	0.748224i	$0.269093\pi$
$164$		0			0
$165$	−1.80383	−	1.15925i	−0.140428	−	0.0902477i
$166$		0			0
$167$	−4.66020	+	2.99493i	−0.360617	+	0.231755i	−0.708385	−	0.705826i	$-0.750576\pi$
$167$	−4.66020	+	2.99493i	−0.360617	+	0.231755i	0.347768	+	0.937581i	$0.386940\pi$
$168$		0			0
$169$	−22.6058	−	26.0885i	−1.73891	−	2.00681i
$170$		0			0
$171$	2.64708	−	5.79629i	0.202427	−	0.443253i
$172$		0			0
$173$	−10.5327	+	3.09267i	−0.800783	+	0.235131i	−0.656422	−	0.754394i	$-0.727931\pi$
$173$	−10.5327	+	3.09267i	−0.800783	+	0.235131i	−0.144361	+	0.989525i	$0.546113\pi$
$174$		0			0
$175$	0.812787	+	5.65306i	0.0614409	+	0.427331i
$176$		0			0
$177$	6.00809	+	13.1559i	0.451596	+	0.988857i
$178$		0			0
$179$	−2.69832	+	18.7672i	−0.201682	+	1.40273i	0.597611	+	0.801786i	$0.296117\pi$
$179$	−2.69832	+	18.7672i	−0.201682	+	1.40273i	−0.799293	+	0.600942i	$0.794792\pi$
$180$		0			0
$181$	10.9386	−	12.6238i	0.813060	−	0.938322i	−0.185961	−	0.982557i	$-0.559540\pi$
$181$	10.9386	−	12.6238i	0.813060	−	0.938322i	0.999021	+	0.0442355i	$0.0140852\pi$
$182$		0			0
$183$	−7.53528			−0.557024
$184$		0			0
$185$	4.27134			0.314035
$186$		0			0
$187$	−10.4298	+	12.0366i	−0.762701	+	0.880204i
$188$		0			0
$189$	−0.208216	+	1.44818i	−0.0151455	+	0.105339i
$190$		0			0
$191$	4.20633	+	9.21058i	0.304359	+	0.666454i	0.998578	−	0.0533102i	$-0.0169772\pi$
$191$	4.20633	+	9.21058i	0.304359	+	0.666454i	−0.694219	+	0.719764i	$0.744250\pi$
$192$		0			0
$193$	−2.01479	−	14.0132i	−0.145028	−	1.00869i	−0.924207	−	0.381891i	$-0.875273\pi$
$193$	−2.01479	−	14.0132i	−0.145028	−	1.00869i	0.779180	−	0.626801i	$-0.215636\pi$
$194$		0			0
$195$	6.92580	−	2.03360i	0.495967	−	0.145629i
$196$		0			0
$197$	−10.5317	+	23.0613i	−0.750356	+	1.64305i	0.0153688	+	0.999882i	$0.495108\pi$
$197$	−10.5317	+	23.0613i	−0.750356	+	1.64305i	−0.765725	+	0.643168i	$0.777620\pi$
$198$		0			0
$199$	−8.66657	−	10.0018i	−0.614357	−	0.709005i	0.360269	−	0.932849i	$-0.382685\pi$
$199$	−8.66657	−	10.0018i	−0.614357	−	0.709005i	−0.974625	+	0.223843i	$0.928140\pi$
$200$		0			0
$201$	−8.49246	+	5.45777i	−0.599012	+	0.384961i
$202$		0			0
$203$	5.10428	+	3.28032i	0.358251	+	0.230234i
$204$		0			0
$205$	−4.91658	−	1.44364i	−0.343389	−	0.100828i
$206$		0			0
$207$	−4.59858	+	1.36127i	−0.319623	+	0.0946150i
$208$		0			0
$209$	12.5200	+	3.67621i	0.866028	+	0.254289i
$210$		0			0
$211$	−1.09064	−	0.700911i	−0.0750826	−	0.0482527i	0.502561	−	0.864542i	$-0.332391\pi$
$211$	−1.09064	−	0.700911i	−0.0750826	−	0.0482527i	−0.577644	+	0.816289i	$0.696028\pi$
$212$		0			0
$213$	−0.166133	+	0.106767i	−0.0113832	+	0.00731555i
$214$		0			0
$215$	2.40213	+	2.77221i	0.163824	+	0.189063i
$216$		0			0
$217$	0.553078	−	1.21107i	0.0375454	−	0.0822129i
$218$		0			0
$219$	7.63793	−	2.24270i	0.516123	−	0.151548i
$220$		0			0
$221$	−7.63019	−	53.0692i	−0.513262	−	3.56982i
$222$		0			0
$223$	−5.04981	−	11.0575i	−0.338160	−	0.740468i	0.661797	−	0.749683i	$-0.269794\pi$
$223$	−5.04981	−	11.0575i	−0.338160	−	0.740468i	−0.999958	+	0.00921525i	$0.997067\pi$
$224$		0			0
$225$	0.555536	−	3.86384i	0.0370357	−	0.257589i
$226$		0			0
$227$	15.4515	−	17.8319i	1.02555	−	1.18355i	0.0427099	−	0.999088i	$-0.486401\pi$
$227$	15.4515	−	17.8319i	1.02555	−	1.18355i	0.982840	−	0.184460i	$-0.0590537\pi$
$228$		0			0
$229$	15.4803			1.02296			0.511482	−	0.859294i	$-0.329097\pi$
$229$	15.4803			1.02296			0.511482	+	0.859294i	$0.329097\pi$
$230$		0			0
$231$	−2.99601			−0.197123
$232$		0			0
$233$	−8.18474	+	9.44569i	−0.536200	+	0.618808i	−0.957612	−	0.288062i	$-0.906989\pi$
$233$	−8.18474	+	9.44569i	−0.536200	+	0.618808i	0.421412	+	0.906869i	$0.361535\pi$
$234$		0			0
$235$	0.287157	−	1.99722i	0.0187320	−	0.130284i
$236$		0			0
$237$	−1.92232	−	4.20928i	−0.124868	−	0.273422i
$238$		0			0
$239$	−2.97190	−	20.6700i	−0.192236	−	1.33703i	−0.826073	−	0.563564i	$-0.809430\pi$
$239$	−2.97190	−	20.6700i	−0.192236	−	1.33703i	0.633837	−	0.773467i	$-0.281479\pi$
$240$		0			0
$241$	−2.47491	+	0.726700i	−0.159423	+	0.0468109i	−0.360470	−	0.932771i	$-0.617384\pi$
$241$	−2.47491	+	0.726700i	−0.159423	+	0.0468109i	0.201047	+	0.979582i	$0.435566\pi$
$242$		0			0
$243$	0.415415	−	0.909632i	0.0266489	−	0.0583529i
$244$		0			0
$245$	3.33215	+	3.84551i	0.212883	+	0.245680i
$246$		0			0
$247$	−36.9530	+	23.7482i	−2.35126	+	1.51106i
$248$		0			0
$249$	6.96829	+	4.47825i	0.441597	+	0.283797i
$250$		0			0
$251$	−6.05809	−	1.77882i	−0.382383	−	0.112278i	0.0848910	−	0.996390i	$-0.472946\pi$
$251$	−6.05809	−	1.77882i	−0.382383	−	0.112278i	−0.467274	+	0.884112i	$0.654764\pi$
$252$		0			0
$253$	−4.09934	−	8.92423i	−0.257723	−	0.561062i
$254$		0			0
$255$	7.81410	+	2.29443i	0.489338	+	0.143683i
$256$		0			0
$257$	10.3497	+	6.65137i	0.645599	+	0.414901i	0.822056	−	0.569407i	$-0.192827\pi$
$257$	10.3497	+	6.65137i	0.645599	+	0.414901i	−0.176457	+	0.984308i	$0.556464\pi$
$258$		0			0
$259$	5.02071	−	3.22661i	0.311972	−	0.200492i
$260$		0			0
$261$	−2.71577	−	3.13416i	−0.168102	−	0.194000i
$262$		0			0
$263$	2.94567	−	6.45011i	0.181638	−	0.397731i	−0.796809	−	0.604231i	$-0.793480\pi$
$263$	2.94567	−	6.45011i	0.181638	−	0.397731i	0.978447	+	0.206500i	$0.0662075\pi$
$264$		0			0
$265$	7.86590	−	2.30964i	0.483199	−	0.141880i
$266$		0			0
$267$	0.0391718	+	0.272446i	0.00239728	+	0.0166734i
$268$		0			0
$269$	−6.22048	−	13.6209i	−0.379269	−	0.830484i	−0.998958	−	0.0456362i	$-0.985469\pi$
$269$	−6.22048	−	13.6209i	−0.379269	−	0.830484i	0.619689	−	0.784848i	$-0.287259\pi$
$270$		0			0
$271$	−2.61485	+	18.1867i	−0.158841	+	1.10476i	0.741933	+	0.670474i	$0.233909\pi$
$271$	−2.61485	+	18.1867i	−0.158841	+	1.10476i	−0.900774	+	0.434288i	$0.857000\pi$
$272$		0			0
$273$	6.60468	−	7.62221i	0.399733	−	0.461317i
$274$		0			0
$275$	7.99358			0.482031
$276$		0			0
$277$	13.9414			0.837657			0.418829	−	0.908065i	$-0.362441\pi$
$277$	13.9414			0.837657			0.418829	+	0.908065i	$0.362441\pi$
$278$		0			0
$279$	−0.595921	+	0.687730i	−0.0356769	+	0.0411733i
$280$		0			0
$281$	1.10403	−	7.67872i	0.0658611	−	0.458074i	−0.930028	−	0.367490i	$-0.880217\pi$
$281$	1.10403	−	7.67872i	0.0658611	−	0.458074i	0.995889	−	0.0905846i	$-0.0288736\pi$
$282$		0			0
$283$	−13.5340	−	29.6354i	−0.804514	−	1.76164i	−0.629385	−	0.777093i	$-0.716693\pi$
$283$	−13.5340	−	29.6354i	−0.804514	−	1.76164i	−0.175128	−	0.984546i	$-0.556034\pi$
$284$		0			0
$285$	−0.949564	−	6.60437i	−0.0562473	−	0.391209i
$286$		0			0
$287$	−6.86970	+	2.01713i	−0.405506	+	0.119067i
$288$		0			0
$289$	18.0670	−	39.5612i	1.06277	−	2.32713i
$290$		0			0
$291$	4.81758	+	5.55978i	0.282411	+	0.325920i
$292$		0			0
$293$	18.0543	−	11.6028i	1.05475	−	0.677844i	0.106155	−	0.994350i	$-0.466146\pi$
$293$	18.0543	−	11.6028i	1.05475	−	0.677844i	0.948591	+	0.316506i	$0.102510\pi$
$294$		0			0
$295$	12.7401	+	8.18754i	0.741755	+	0.476697i
$296$		0			0
$297$	1.96481	+	0.576921i	0.114010	+	0.0334763i
$298$		0			0
$299$	31.7412	+	9.24419i	1.83564	+	0.534605i
$300$		0			0
$301$	4.91772	+	1.44397i	0.283453	+	0.0832293i
$302$		0			0
$303$	−12.0440	−	7.74019i	−0.691908	−	0.444662i
$304$		0			0
$305$	−6.63768	+	4.26578i	−0.380073	+	0.244258i
$306$		0			0
$307$	2.82498	+	3.26020i	0.161230	+	0.186070i	0.830616	−	0.556845i	$-0.187988\pi$
$307$	2.82498	+	3.26020i	0.161230	+	0.186070i	−0.669386	+	0.742915i	$0.733443\pi$
$308$		0			0
$309$	−1.66775	+	3.65187i	−0.0948751	+	0.207748i
$310$		0			0
$311$	−12.4182	+	3.64631i	−0.704171	+	0.206763i	−0.614165	−	0.789178i	$-0.710507\pi$
$311$	−12.4182	+	3.64631i	−0.704171	+	0.206763i	−0.0900065	+	0.995941i	$0.528689\pi$
$312$		0			0
$313$	−0.525717	−	3.65644i	−0.0297153	−	0.206674i	0.969555	−	0.244874i	$-0.0787467\pi$
$313$	−0.525717	−	3.65644i	−0.0297153	−	0.206674i	−0.999270	+	0.0382000i	$0.987838\pi$
$314$		0			0
$315$	0.636410	+	1.39354i	0.0358576	+	0.0785172i
$316$		0			0
$317$	−2.66225	+	18.5164i	−0.149527	+	1.03998i	0.767469	+	0.641087i	$0.221516\pi$
$317$	−2.66225	+	18.5164i	−0.149527	+	1.03998i	−0.916996	+	0.398897i	$0.869393\pi$
$318$		0			0
$319$	5.56124	−	6.41801i	0.311370	−	0.359340i
$320$		0			0
$321$	−13.0252			−0.726996
$322$		0			0
$323$	−49.5600			−2.75759
$324$		0			0
$325$	−17.6218	+	20.3366i	−0.977480	+	1.12807i
$326$		0			0
$327$	0.504553	−	3.50925i	0.0279019	−	0.194062i
$328$		0			0
$329$	−1.17118	−	2.56454i	−0.0645695	−	0.141387i
$330$		0			0
$331$	0.646147	+	4.49405i	0.0355154	+	0.247015i	0.999843	−	0.0176950i	$-0.00563279\pi$
$331$	0.646147	+	4.49405i	0.0355154	+	0.247015i	−0.964328	+	0.264710i	$0.914724\pi$
$332$		0			0
$333$	−3.91395	+	1.14924i	−0.214483	+	0.0629780i
$334$		0			0
$335$	−4.39116	+	9.61529i	−0.239914	+	0.525339i
$336$		0			0
$337$	14.8054	+	17.0864i	0.806503	+	0.930754i	0.998719	−	0.0505986i	$-0.0161129\pi$
$337$	14.8054	+	17.0864i	0.806503	+	0.930754i	−0.192216	+	0.981353i	$0.561567\pi$
$338$		0			0
$339$	−12.8774	+	8.27578i	−0.699402	+	0.449479i
$340$		0			0
$341$	−1.56764	−	1.00746i	−0.0848924	−	0.0545570i
$342$		0			0
$343$	16.6483	+	4.88839i	0.898924	+	0.263948i
$344$		0			0
$345$	−3.28017	+	3.80241i	−0.176599	+	0.204715i
$346$		0			0
$347$	−17.3095	−	5.08253i	−0.929222	−	0.272844i	−0.218111	−	0.975924i	$-0.569990\pi$
$347$	−17.3095	−	5.08253i	−0.929222	−	0.272844i	−0.711111	+	0.703080i	$0.751808\pi$
$348$		0			0
$349$	−4.22571	−	2.71570i	−0.226197	−	0.145368i	0.422634	−	0.906300i	$-0.361106\pi$
$349$	−4.22571	−	2.71570i	−0.226197	−	0.145368i	−0.648831	+	0.760932i	$0.724742\pi$
$350$		0			0
$351$	−5.79916	+	3.72689i	−0.309536	+	0.198927i
$352$		0			0
$353$	−8.32044	−	9.60230i	−0.442852	−	0.511079i	0.489810	−	0.871829i	$-0.337066\pi$
$353$	−8.32044	−	9.60230i	−0.442852	−	0.511079i	−0.932662	+	0.360750i	$0.882521\pi$
$354$		0			0
$355$	−0.0859014	+	0.188098i	−0.00455917	+	0.00998320i
$356$		0			0
$357$	10.9183	−	3.20589i	0.577855	−	0.169674i
$358$		0			0
$359$	−0.759247	−	5.28068i	−0.0400715	−	0.278703i	0.959927	−	0.280249i	$-0.0904171\pi$
$359$	−0.759247	−	5.28068i	−0.0400715	−	0.278703i	−0.999999	+	0.00154569i	$0.999508\pi$
$360$		0			0
$361$	8.97460	+	19.6516i	0.472348	+	1.03430i
$362$		0			0
$363$	0.968691	−	6.73739i	0.0508431	−	0.353621i
$364$		0			0
$365$	5.45849	−	6.29944i	0.285711	−	0.329728i
$366$		0			0
$367$	−1.47822			−0.0771624			−0.0385812	−	0.999255i	$-0.512284\pi$
$367$	−1.47822			−0.0771624			−0.0385812	+	0.999255i	$0.512284\pi$
$368$		0			0
$369$	4.89363			0.254752
$370$		0			0
$371$	7.50119	−	8.65683i	0.389442	−	0.449440i
$372$		0			0
$373$	−2.50047	+	17.3912i	−0.129470	+	0.900480i	0.816758	+	0.576980i	$0.195769\pi$
$373$	−2.50047	+	17.3912i	−0.129470	+	0.900480i	−0.946228	+	0.323501i	$0.895140\pi$
$374$		0			0
$375$	−3.87290	−	8.48047i	−0.199996	−	0.437930i
$376$		0			0
$377$	4.06848	+	28.2969i	0.209537	+	1.45736i
$378$		0			0
$379$	4.96855	−	1.45890i	0.255218	−	0.0749386i	−0.151621	−	0.988439i	$-0.548449\pi$
$379$	4.96855	−	1.45890i	0.255218	−	0.0749386i	0.406839	+	0.913500i	$0.366631\pi$
$380$		0			0
$381$	5.72391	−	12.5336i	0.293245	−	0.642117i
$382$		0			0
$383$	18.1398	+	20.9345i	0.926901	+	1.06970i	0.997391	+	0.0721881i	$0.0229982\pi$
$383$	18.1398	+	20.9345i	0.926901	+	1.06970i	−0.0704902	+	0.997512i	$0.522456\pi$
$384$		0			0
$385$	−2.63913	+	1.69607i	−0.134503	+	0.0864395i
$386$		0			0
$387$	−2.94703	−	1.89394i	−0.149806	−	0.0962745i
$388$		0			0
$389$	−5.15517	−	1.51370i	−0.261378	−	0.0767474i	0.148418	−	0.988925i	$-0.452582\pi$
$389$	−5.15517	−	1.51370i	−0.261378	−	0.0767474i	−0.409796	+	0.912177i	$0.634400\pi$
$390$		0			0
$391$	24.4884	+	28.1357i	1.23843	+	1.42289i
$392$		0			0
$393$	9.22524	+	2.70878i	0.465352	+	0.136640i
$394$		0			0
$395$	−4.07624	−	2.61964i	−0.205098	−	0.131808i
$396$		0			0
$397$	−30.4469	+	19.5670i	−1.52808	+	0.982040i	−0.537786	+	0.843081i	$0.680739\pi$
$397$	−30.4469	+	19.5670i	−1.52808	+	0.982040i	−0.990298	+	0.138959i	$0.955624\pi$
$398$		0			0
$399$	−6.10517	−	7.04574i	−0.305641	−	0.352728i
$400$		0			0
$401$	−3.81908	+	8.36262i	−0.190716	+	0.417609i	−0.980700	−	0.195518i	$-0.937361\pi$
$401$	−3.81908	+	8.36262i	−0.190716	+	0.417609i	0.789984	+	0.613127i	$0.210089\pi$
$402$		0			0
$403$	6.01894	−	1.76732i	0.299825	−	0.0880365i
$404$		0			0
$405$	−0.149019	−	1.03645i	−0.00740479	−	0.0515015i
$406$		0			0
$407$	−3.47005	−	7.59834i	−0.172004	−	0.376636i
$408$		0			0
$409$	0.120756	−	0.839879i	0.00597102	−	0.0415293i	−0.986618	−	0.163048i	$-0.947867\pi$
$409$	0.120756	−	0.839879i	0.00597102	−	0.0415293i	0.992589	+	0.121519i	$0.0387765\pi$
$410$		0			0
$411$	−2.31218	+	2.66839i	−0.114051	+	0.131622i
$412$		0			0
$413$	21.1602			1.04122
$414$		0			0
$415$	8.67340			0.425760
$416$		0			0
$417$	−1.49527	+	1.72563i	−0.0732235	+	0.0845044i
$418$		0			0
$419$	−3.51724	+	24.4629i	−0.171828	+	1.19509i	0.703190	+	0.711002i	$0.251758\pi$
$419$	−3.51724	+	24.4629i	−0.171828	+	1.19509i	−0.875018	+	0.484090i	$0.839151\pi$
$420$		0			0
$421$	6.50485	+	14.2436i	0.317027	+	0.694192i	0.999319	−	0.0368873i	$-0.0117443\pi$
$421$	6.50485	+	14.2436i	0.317027	+	0.694192i	−0.682293	+	0.731079i	$0.739017\pi$
$422$		0			0
$423$	0.274239	+	1.90737i	0.0133339	+	0.0927396i
$424$		0			0
$425$	−29.1307	+	8.55355i	−1.41305	+	0.414908i
$426$		0			0
$427$	−4.57980	+	10.0284i	−0.221632	+	0.485306i
$428$		0			0
$429$	−9.24414	−	10.6683i	−0.446311	−	0.515071i
$430$		0			0
$431$	−5.59612	+	3.59641i	−0.269555	+	0.173233i	−0.668435	−	0.743771i	$-0.733036\pi$
$431$	−5.59612	+	3.59641i	−0.269555	+	0.173233i	0.398880	+	0.917003i	$0.369399\pi$
$432$		0			0
$433$	17.0259	+	10.9419i	0.818214	+	0.525834i	0.881513	−	0.472160i	$-0.156526\pi$
$433$	17.0259	+	10.9419i	0.818214	+	0.525834i	−0.0632987	+	0.997995i	$0.520162\pi$
$434$		0			0
$435$	−4.16654	−	1.22341i	−0.199770	−	0.0586578i
$436$		0			0
$437$	12.6337	−	27.8259i	0.604351	−	1.33109i
$438$		0			0
$439$	−3.95674	−	1.16180i	−0.188845	−	0.0554498i	0.185943	−	0.982561i	$-0.440466\pi$
$439$	−3.95674	−	1.16180i	−0.188845	−	0.0554498i	−0.374787	+	0.927111i	$0.622284\pi$
$440$		0			0
$441$	−4.08801	−	2.62721i	−0.194667	−	0.125105i
$442$		0			0
$443$	25.8064	−	16.5847i	1.22610	−	0.787965i	0.242819	−	0.970072i	$-0.421928\pi$
$443$	25.8064	−	16.5847i	1.22610	−	0.787965i	0.983279	+	0.182106i	$0.0582916\pi$
$444$		0			0
$445$	0.188739	+	0.217817i	0.00894710	+	0.0103255i
$446$		0			0
$447$	−5.61351	+	12.2919i	−0.265510	+	0.581386i
$448$		0			0
$449$	−21.7635	+	6.39035i	−1.02709	+	0.301579i	−0.751525	−	0.659704i	$-0.770682\pi$
$449$	−21.7635	+	6.39035i	−1.02709	+	0.301579i	−0.275560	+	0.961284i	$0.588863\pi$
$450$		0			0
$451$	1.42614	+	9.91899i	0.0671541	+	0.467067i
$452$		0			0
$453$	−0.959780	−	2.10162i	−0.0450944	−	0.0987429i
$454$		0			0
$455$	1.50294	−	10.4532i	0.0704591	−	0.490054i
$456$		0			0
$457$	18.4108	−	21.2472i	0.861222	−	0.993903i	−0.138772	−	0.990324i	$-0.544315\pi$
$457$	18.4108	−	21.2472i	0.861222	−	0.993903i	0.999994	−	0.00357885i	$-0.00113919\pi$
$458$		0			0
$459$	−7.77763			−0.363029
$460$		0			0
$461$	−4.98643			−0.232241			−0.116121	−	0.993235i	$-0.537046\pi$
$461$	−4.98643			−0.232241			−0.116121	+	0.993235i	$0.537046\pi$
$462$		0			0
$463$	17.2211	−	19.8742i	0.800333	−	0.923634i	−0.198066	−	0.980189i	$-0.563466\pi$
$463$	17.2211	−	19.8742i	0.800333	−	0.923634i	0.998400	+	0.0565546i	$0.0180115\pi$
$464$		0			0
$465$	−0.135606	+	0.943163i	−0.00628859	+	0.0437381i
$466$		0			0
$467$	14.8145	+	32.4393i	0.685534	+	1.50111i	0.856671	+	0.515863i	$0.172529\pi$
$467$	14.8145	+	32.4393i	0.685534	+	1.50111i	−0.171137	+	0.985247i	$0.554744\pi$
$468$		0			0
$469$	2.10194	+	14.6193i	0.0970588	+	0.675059i
$470$		0			0
$471$	11.6046	−	3.40741i	0.534710	−	0.157005i
$472$		0			0
$473$	2.98002	−	6.52533i	0.137021	−	0.300035i
$474$		0			0
$475$	16.2890	+	18.7985i	0.747392	+	0.862536i
$476$		0			0
$477$	−6.58633	+	4.23278i	−0.301567	+	0.193806i
$478$		0			0
$479$	−35.6477	−	22.9094i	−1.62878	−	1.04676i	−0.949921	−	0.312490i	$-0.898837\pi$
$479$	−35.6477	−	22.9094i	−1.62878	−	1.04676i	−0.678863	−	0.734265i	$-0.737527\pi$
$480$		0			0
$481$	26.9807	+	7.92226i	1.23022	+	0.361224i
$482$		0			0
$483$	−0.983273	+	6.94739i	−0.0447405	+	0.316117i
$484$		0			0
$485$	7.39115	+	2.17024i	0.335615	+	0.0985454i
$486$		0			0
$487$	−25.0812	−	16.1187i	−1.13654	−	0.730407i	−0.169622	−	0.985509i	$-0.554255\pi$
$487$	−25.0812	−	16.1187i	−1.13654	−	0.730407i	−0.966914	+	0.255102i	$0.917891\pi$
$488$		0			0
$489$	−18.2022	+	11.6979i	−0.823133	+	0.528995i
$490$		0			0
$491$	−8.55804	−	9.87650i	−0.386219	−	0.445720i	0.529034	−	0.848601i	$-0.322554\pi$
$491$	−8.55804	−	9.87650i	−0.386219	−	0.445720i	−0.915253	+	0.402880i	$0.868009\pi$
$492$		0			0
$493$	−13.3990	+	29.3397i	−0.603461	+	1.32140i
$494$		0			0
$495$	2.05736	−	0.604097i	0.0924716	−	0.0271521i
$496$		0			0
$497$	0.0411190	+	0.285989i	0.00184444	+	0.0128284i
$498$		0			0
$499$	−9.02701	−	19.7664i	−0.404104	−	0.884865i	−0.996838	−	0.0794664i	$-0.974678\pi$
$499$	−9.02701	−	19.7664i	−0.404104	−	0.884865i	0.592733	−	0.805399i	$-0.298049\pi$
$500$		0			0
$501$	0.788367	−	5.48321i	0.0352216	−	0.244972i
$502$		0			0
$503$	11.9282	−	13.7659i	0.531852	−	0.613790i	−0.424706	−	0.905331i	$-0.639623\pi$
$503$	11.9282	−	13.7659i	0.531852	−	0.613790i	0.956558	+	0.291541i	$0.0941680\pi$
$504$		0			0
$505$	−14.9911			−0.667094
$506$		0			0
$507$	34.5200			1.53309
$508$		0			0
$509$	0.994643	−	1.14788i	0.0440868	−	0.0508788i	−0.733278	−	0.679929i	$-0.762011\pi$
$509$	0.994643	−	1.14788i	0.0440868	−	0.0508788i	0.777365	+	0.629050i	$0.216556\pi$
$510$		0			0
$511$	1.65748	−	11.5280i	0.0733226	−	0.509970i
$512$		0			0
$513$	2.64708	+	5.79629i	0.116871	+	0.255912i
$514$		0			0
$515$	0.598260	+	4.16099i	0.0263625	+	0.183355i
$516$		0			0
$517$	−3.78617	+	1.11172i	−0.166515	+	0.0488933i
$518$		0			0
$519$	4.56014	−	9.98532i	0.200168	−	0.438307i
$520$		0			0
$521$	−9.68764	−	11.1801i	−0.424423	−	0.489810i	0.502756	−	0.864428i	$-0.332319\pi$
$521$	−9.68764	−	11.1801i	−0.424423	−	0.489810i	−0.927179	+	0.374618i	$0.877774\pi$
$522$		0			0
$523$	16.4684	−	10.5836i	0.720114	−	0.462789i	−0.128563	−	0.991701i	$-0.541036\pi$
$523$	16.4684	−	10.5836i	0.720114	−	0.462789i	0.848677	+	0.528912i	$0.177400\pi$
$524$		0			0
$525$	−4.80456	−	3.08770i	−0.209688	−	0.134758i
$526$		0			0
$527$	6.79092	+	1.99399i	0.295817	+	0.0868597i
$528$		0			0
$529$	−22.0396	+	6.57698i	−0.958243	+	0.285956i
$530$		0			0
$531$	−13.8770	−	4.07466i	−0.602211	−	0.176825i
$532$		0			0
$533$	−28.3790	−	18.2381i	−1.22923	−	0.789978i
$534$		0			0
$535$	−11.4736	+	7.37366i	−0.496049	+	0.318791i
$536$		0			0
$537$	−12.4163	−	14.3292i	−0.535803	−	0.618349i
$538$		0			0
$539$	4.13378	−	9.05171i	0.178054	−	0.389885i
$540$		0			0
$541$	1.35451	−	0.397719i	0.0582349	−	0.0170993i	−0.252485	−	0.967601i	$-0.581248\pi$
$541$	1.35451	−	0.397719i	0.0582349	−	0.0170993i	0.310720	+	0.950501i	$0.399430\pi$
$542$		0			0
$543$	2.37719	+	16.5337i	0.102015	+	0.709529i
$544$		0			0
$545$	−1.54216	−	3.37686i	−0.0660589	−	0.144649i
$546$		0			0
$547$	3.19234	−	22.2032i	0.136494	−	0.949340i	−0.800335	−	0.599553i	$-0.795345\pi$
$547$	3.19234	−	22.2032i	0.136494	−	0.949340i	0.936829	−	0.349787i	$-0.113746\pi$
$548$		0			0
$549$	4.93456	−	5.69479i	0.210602	−	0.243048i
$550$		0			0
$551$	26.4258			1.12578
$552$		0			0
$553$	−6.77028			−0.287902
$554$		0			0
$555$	−2.79713	+	3.22806i	−0.118732	+	0.137024i
$556$		0			0
$557$	−4.95373	+	34.4539i	−0.209896	+	1.45986i	0.563594	+	0.826052i	$0.309418\pi$
$557$	−4.95373	+	34.4539i	−0.209896	+	1.45986i	−0.773490	+	0.633808i	$0.781491\pi$
$558$		0			0
$559$	10.0318	+	21.9665i	0.424299	+	0.929086i
$560$		0			0
$561$	−2.26661	−	15.7646i	−0.0956963	−	0.665582i
$562$		0			0
$563$	44.9036	−	13.1849i	1.89246	−	0.555677i	0.899553	−	0.436812i	$-0.143893\pi$
$563$	44.9036	−	13.1849i	1.89246	−	0.555677i	0.992910	−	0.118865i	$-0.0379256\pi$
$564$		0			0
$565$	−6.65844	+	14.5799i	−0.280123	+	0.613383i
$566$		0			0
$567$	−0.958106	−	1.10571i	−0.0402367	−	0.0464356i
$568$		0			0
$569$	−7.35168	+	4.72464i	−0.308198	+	0.198067i	−0.685592	−	0.727986i	$-0.740457\pi$
$569$	−7.35168	+	4.72464i	−0.308198	+	0.198067i	0.377394	+	0.926053i	$0.376820\pi$
$570$		0			0
$571$	16.5741	+	10.6516i	0.693606	+	0.445754i	0.839366	−	0.543566i	$-0.182926\pi$
$571$	16.5741	+	10.6516i	0.693606	+	0.445754i	−0.145760	+	0.989320i	$0.546563\pi$
$572$		0			0
$573$	−9.71545	−	2.85271i	−0.405869	−	0.119174i
$574$		0			0
$575$	2.62344	−	18.5361i	0.109405	−	0.773011i
$576$		0			0
$577$	16.5543	+	4.86079i	0.689165	+	0.202357i	0.607520	−	0.794304i	$-0.292164\pi$
$577$	16.5543	+	4.86079i	0.689165	+	0.202357i	0.0816453	+	0.996661i	$0.473983\pi$
$578$		0			0
$579$	11.9099	+	7.65401i	0.494957	+	0.318090i
$580$		0			0
$581$	10.1951	−	6.55198i	0.422963	−	0.271822i
$582$		0			0
$583$	−10.4989	−	12.1164i	−0.434821	−	0.501810i
$584$		0			0
$585$	−2.99854	+	6.56590i	−0.123975	+	0.271466i
$586$		0			0
$587$	−22.4307	+	6.58626i	−0.925815	+	0.271844i	−0.709684	−	0.704520i	$-0.751162\pi$
$587$	−22.4307	+	6.58626i	−0.925815	+	0.271844i	−0.216131	+	0.976364i	$0.569344\pi$
$588$		0			0
$589$	−0.825228	−	5.73959i	−0.0340029	−	0.236496i
$590$		0			0
$591$	−10.5317	−	23.0613i	−0.433218	−	0.948616i
$592$		0			0
$593$	−2.08335	+	14.4900i	−0.0855529	+	0.595034i	0.901273	+	0.433251i	$0.142634\pi$
$593$	−2.08335	+	14.4900i	−0.0855529	+	0.595034i	−0.986826	+	0.161783i	$0.948276\pi$
$594$		0			0
$595$	7.80280	−	9.00491i	0.319884	−	0.369166i
$596$		0			0
$597$	13.2342			0.541640
$598$		0			0
$599$	−18.2295			−0.744838			−0.372419	−	0.928065i	$-0.621472\pi$
$599$	−18.2295			−0.744838			−0.372419	+	0.928065i	$0.621472\pi$
$600$		0			0
$601$	22.2399	−	25.6662i	0.907185	−	1.04695i	−0.0915063	−	0.995804i	$-0.529168\pi$
$601$	22.2399	−	25.6662i	0.907185	−	1.04695i	0.998691	−	0.0511429i	$-0.0162864\pi$
$602$		0			0
$603$	1.43667	−	9.99225i	0.0585057	−	0.406916i
$604$		0			0
$605$	−2.96079	−	6.48322i	−0.120373	−	0.263580i
$606$		0			0
$607$	−6.97050	−	48.4809i	−0.282924	−	1.96778i	−0.249664	−	0.968333i	$-0.580320\pi$
$607$	−6.97050	−	48.4809i	−0.282924	−	1.96778i	−0.0332604	−	0.999447i	$-0.510589\pi$
$608$		0			0
$609$	−5.82170	+	1.70941i	−0.235907	+	0.0692686i
$610$		0			0
$611$	5.51822	−	12.0832i	0.223243	−	0.488835i
$612$		0			0
$613$	−13.5055	−	15.5862i	−0.545482	−	0.629519i	0.414343	−	0.910121i	$-0.364012\pi$
$613$	−13.5055	−	15.5862i	−0.545482	−	0.629519i	−0.959824	+	0.280601i	$0.909466\pi$
$614$		0			0
$615$	4.31071	−	2.77032i	0.173824	−	0.111710i
$616$		0			0
$617$	−22.7181	−	14.6000i	−0.914597	−	0.587776i	−0.00351174	−	0.999994i	$-0.501118\pi$
$617$	−22.7181	−	14.6000i	−0.914597	−	0.587776i	−0.911085	+	0.412218i	$0.864754\pi$
$618$		0			0
$619$	−26.2222	−	7.69954i	−1.05396	−	0.309471i	−0.291544	−	0.956557i	$-0.594169\pi$
$619$	−26.2222	−	7.69954i	−1.05396	−	0.309471i	−0.762416	+	0.647087i	$0.775987\pi$
$620$		0			0
$621$	1.98265	−	4.36682i	0.0795610	−	0.175234i
$622$		0			0
$623$	0.386393	+	0.113455i	0.0154805	+	0.00454549i
$624$		0			0
$625$	8.20704	+	5.27435i	0.328282	+	0.210974i
$626$		0			0
$627$	−10.9772	+	7.05460i	−0.438386	+	0.281733i
$628$		0			0
$629$	20.7764	+	23.9772i	0.828408	+	0.956034i
$630$		0			0
$631$	16.7273	−	36.6276i	0.665903	−	1.45812i	−0.211015	−	0.977483i	$-0.567677\pi$
$631$	16.7273	−	36.6276i	0.665903	−	1.45812i	0.876918	−	0.480640i	$-0.159596\pi$
$632$		0			0
$633$	1.24393	−	0.365250i	0.0494417	−	0.0145174i
$634$		0			0
$635$	−2.05329	−	14.2810i	−0.0814825	−	0.566723i
$636$		0			0
$637$	13.9157	+	30.4712i	0.551361	+	1.20731i
$638$		0			0
$639$	0.0281046	−	0.195472i	0.00111180	−	0.00773276i
$640$		0			0
$641$	2.25845	−	2.60639i	0.0892035	−	0.102946i	−0.709393	−	0.704813i	$-0.751031\pi$
$641$	2.25845	−	2.60639i	0.0892035	−	0.102946i	0.798596	+	0.601867i	$0.205576\pi$
$642$		0			0
$643$	−23.4827			−0.926065			−0.463033	−	0.886341i	$-0.653239\pi$
$643$	−23.4827			−0.926065			−0.463033	+	0.886341i	$0.653239\pi$
$644$		0			0
$645$	−3.66816			−0.144434
$646$		0			0
$647$	−25.6644	+	29.6183i	−1.00897	+	1.16442i	−0.0226236	+	0.999744i	$0.507202\pi$
$647$	−25.6644	+	29.6183i	−1.00897	+	1.16442i	−0.986348	+	0.164672i	$0.947344\pi$
$648$		0			0
$649$	4.21487	−	29.3150i	0.165448	−	1.15072i
$650$		0			0
$651$	0.553078	+	1.21107i	0.0216768	+	0.0474657i
$652$		0			0
$653$	0.626064	+	4.35437i	0.0244998	+	0.170400i	0.998398	−	0.0565867i	$-0.0180217\pi$
$653$	0.626064	+	4.35437i	0.0244998	+	0.170400i	−0.973898	+	0.226987i	$0.927113\pi$
$654$		0			0
$655$	9.65980	−	2.83637i	0.377439	−	0.110826i
$656$		0			0
$657$	−3.30686	+	7.24102i	−0.129013	+	0.282499i
$658$		0			0
$659$	−10.1304	−	11.6911i	−0.394623	−	0.455419i	0.523317	−	0.852138i	$-0.324694\pi$
$659$	−10.1304	−	11.6911i	−0.394623	−	0.455419i	−0.917940	+	0.396719i	$0.870149\pi$
$660$		0			0
$661$	−21.5003	+	13.8174i	−0.836264	+	0.537434i	−0.887263	−	0.461264i	$-0.847396\pi$
$661$	−21.5003	+	13.8174i	−0.836264	+	0.537434i	0.0509984	+	0.998699i	$0.483760\pi$
$662$		0			0
$663$	45.1037	+	28.9864i	1.75168	+	1.12574i
$664$		0			0
$665$	−9.36657	−	2.75027i	−0.363220	−	0.106651i
$666$		0			0
$667$	−13.0574	−	15.0022i	−0.505586	−	0.580887i
$668$		0			0
$669$	11.6637	+	3.42476i	0.450943	+	0.132409i
$670$		0			0
$671$	12.9809	+	8.34233i	0.501123	+	0.322052i
$672$		0			0
$673$	−13.8361	+	8.89193i	−0.533343	+	0.342759i	−0.779430	−	0.626489i	$-0.784491\pi$
$673$	−13.8361	+	8.89193i	−0.533343	+	0.342759i	0.246087	+	0.969248i	$0.420855\pi$
$674$		0			0
$675$	2.55630	+	2.95012i	0.0983919	+	0.113550i
$676$		0			0
$677$	18.6868	−	40.9185i	0.718193	−	1.57262i	−0.0982256	−	0.995164i	$-0.531317\pi$
$677$	18.6868	−	40.9185i	0.718193	−	1.57262i	0.816419	−	0.577460i	$-0.195956\pi$
$678$		0			0
$679$	10.3273	−	3.03236i	0.396325	−	0.116371i
$680$		0			0
$681$	3.35792	+	23.3549i	0.128676	+	0.894961i
$682$		0			0
$683$	2.20603	+	4.83054i	0.0844115	+	0.184836i	0.947131	−	0.320848i	$-0.103968\pi$
$683$	2.20603	+	4.83054i	0.0844115	+	0.184836i	−0.862719	+	0.505683i	$0.831240\pi$
$684$		0			0
$685$	−0.526153	+	3.65948i	−0.0201033	+	0.139821i
$686$		0			0
$687$	−10.1374	+	11.6992i	−0.386767	+	0.446353i
$688$		0			0
$689$	53.9703			2.05611
$690$		0			0
$691$	−22.2506			−0.846454			−0.423227	−	0.906024i	$-0.639103\pi$
$691$	−22.2506			−0.846454			−0.423227	+	0.906024i	$0.639103\pi$
$692$		0			0
$693$	1.96197	−	2.26424i	0.0745291	−	0.0860112i
$694$		0			0
$695$	−0.340259	+	2.36655i	−0.0129068	+	0.0897685i
$696$		0			0
$697$	−15.8110	−	34.6214i	−0.598886	−	1.31138i
$698$		0			0
$699$	−1.77871	−	12.3712i	−0.0672771	−	0.467923i
$700$		0			0
$701$	−29.8621	+	8.76829i	−1.12787	+	0.331174i	−0.791872	−	0.610687i	$-0.790893\pi$
$701$	−29.8621	+	8.76829i	−1.12787	+	0.331174i	−0.336003	+	0.941861i	$0.609075\pi$
$702$		0			0
$703$	10.7979	−	23.6441i	0.407251	−	0.891756i
$704$		0			0
$705$	1.32135	+	1.52492i	0.0497649	+	0.0574318i
$706$		0			0
$707$	−17.6212	+	11.3244i	−0.662712	+	0.425899i
$708$		0			0
$709$	19.2880	+	12.3956i	0.724376	+	0.465528i	0.850157	−	0.526530i	$-0.176507\pi$
$709$	19.2880	+	12.3956i	0.724376	+	0.465528i	−0.125781	+	0.992058i	$0.540144\pi$
$710$		0			0
$711$	4.44001	+	1.30371i	0.166513	+	0.0488928i
$712$		0			0
$713$	−2.85067	+	3.30452i	−0.106758	+	0.123755i
$714$		0			0
$715$	−14.1824	−	4.16433i	−0.530391	−	0.155737i
$716$		0			0
$717$	17.5675	+	11.2900i	0.656071	+	0.421631i
$718$		0			0
$719$	38.6336	−	24.8283i	1.44079	−	0.925939i	0.441197	−	0.897410i	$-0.354554\pi$
$719$	38.6336	−	24.8283i	1.44079	−	0.925939i	0.999593	−	0.0285287i	$-0.00908221\pi$
$720$		0			0
$721$	3.84647	+	4.43907i	0.143250	+	0.165320i
$722$		0			0
$723$	1.07152	−	2.34630i	0.0398503	−	0.0872599i
$724$		0			0
$725$	15.5327	−	4.56082i	0.576871	−	0.169385i
$726$		0			0
$727$	−2.94326	−	20.4708i	−0.109159	−	0.759221i	−0.968715	−	0.248178i	$-0.920168\pi$
$727$	−2.94326	−	20.4708i	−0.109159	−	0.759221i	0.859555	−	0.511043i	$-0.170741\pi$
$728$		0			0
$729$	0.415415	+	0.909632i	0.0153857	+	0.0336901i
$730$		0			0
$731$	−3.87753	+	26.9688i	−0.143416	+	0.997477i
$732$		0			0
$733$	−25.5114	+	29.4417i	−0.942284	+	1.08745i	0.0537563	+	0.998554i	$0.482881\pi$
$733$	−25.5114	+	29.4417i	−0.942284	+	1.08745i	−0.996041	+	0.0888999i	$0.971665\pi$
$734$		0			0
$735$	−5.08833			−0.187686
$736$		0			0
$737$	20.6722			0.761469
$738$		0			0
$739$	−19.0924	+	22.0338i	−0.702324	+	0.810525i	−0.989065	−	0.147483i	$-0.952883\pi$
$739$	−19.0924	+	22.0338i	−0.702324	+	0.810525i	0.286740	+	0.958008i	$0.407428\pi$
$740$		0			0
$741$	6.25133	−	43.4790i	0.229648	−	1.59724i
$742$		0			0
$743$	−1.03328	−	2.26256i	−0.0379073	−	0.0830054i	0.889731	−	0.456485i	$-0.150892\pi$
$743$	−1.03328	−	2.26256i	−0.0379073	−	0.0830054i	−0.927638	+	0.373480i	$0.878165\pi$
$744$		0			0
$745$	2.01369	+	14.0055i	0.0737759	+	0.513123i
$746$		0			0
$747$	−7.94769	+	2.33365i	−0.290791	+	0.0853839i
$748$		0			0
$749$	−7.91646	+	17.3346i	−0.289261	+	0.633393i
$750$		0			0
$751$	17.6256	+	20.3411i	0.643169	+	0.742256i	0.979932	−	0.199333i	$-0.0638775\pi$
$751$	17.6256	+	20.3411i	0.643169	+	0.742256i	−0.336763	+	0.941589i	$0.609332\pi$
$752$		0			0
$753$	5.31155	−	3.41352i	0.193564	−	0.124396i
$754$		0			0
$755$	−2.03520	−	1.30794i	−0.0740684	−	0.0476009i
$756$		0			0
$757$	−14.4648	−	4.24725i	−0.525733	−	0.154369i	0.00808709	−	0.999967i	$-0.497426\pi$
$757$	−14.4648	−	4.24725i	−0.525733	−	0.154369i	−0.533820	+	0.845598i	$0.679244\pi$
$758$		0			0
$759$	9.42898	+	2.74606i	0.342250	+	0.0996756i
$760$		0			0
$761$	−19.3488	−	5.68132i	−0.701394	−	0.205948i	−0.0884574	−	0.996080i	$-0.528194\pi$
$761$	−19.3488	−	5.68132i	−0.701394	−	0.205948i	−0.612937	+	0.790132i	$0.710012\pi$
$762$		0			0
$763$	−4.36364	−	2.80434i	−0.157974	−	0.101524i
$764$		0			0
$765$	−6.85116	+	4.40297i	−0.247704	+	0.159190i
$766$		0			0
$767$	65.2892	+	75.3478i	2.35746	+	2.72065i
$768$		0			0
$769$	−12.8841	+	28.2123i	−0.464613	+	1.01736i	0.521798	+	0.853069i	$0.325261\pi$
$769$	−12.8841	+	28.2123i	−0.464613	+	1.01736i	−0.986412	+	0.164293i	$0.947466\pi$
$770$		0			0
$771$	−11.8044	+	3.46609i	−0.425126	+	0.124828i
$772$		0			0
$773$	−2.11398	−	14.7030i	−0.0760344	−	0.528831i	−0.991868	−	0.127273i	$-0.959378\pi$
$773$	−2.11398	−	14.7030i	−0.0760344	−	0.528831i	0.915833	−	0.401559i	$-0.131531\pi$
$774$		0			0
$775$	−1.47565	−	3.23123i	−0.0530070	−	0.116069i
$776$		0			0
$777$	−0.849353	+	5.90738i	−0.0304704	+	0.211926i
$778$		0			0
$779$	−20.4204	+	23.5664i	−0.731637	+	0.844354i
$780$		0			0
$781$	0.404396			0.0144704
$782$		0			0
$783$	4.14709			0.148205
$784$		0			0
$785$	8.29328	−	9.57095i	0.296000	−	0.341602i
$786$		0			0
$787$	3.39324	−	23.6005i	0.120956	−	0.841268i	−0.835521	−	0.549459i	$-0.814834\pi$
$787$	3.39324	−	23.6005i	0.120956	−	0.841268i	0.956477	−	0.291809i	$-0.0942571\pi$
$788$		0			0
$789$	2.94567	+	6.45011i	0.104869	+	0.229630i
$790$		0			0
$791$	3.18724	+	22.1677i	0.113325	+	0.788194i
$792$		0			0
$793$	−49.8402	+	14.6344i	−1.76988	+	0.519683i
$794$		0			0
$795$	−3.40556	+	7.45714i	−0.120783	+	0.264478i
$796$		0			0
$797$	0.00998140	+	0.0115191i	0.000353559	+	0.000408029i	0.755926	−	0.654657i	$-0.227187\pi$
$797$	0.00998140	+	0.0115191i	0.000353559	+	0.000408029i	−0.755573	+	0.655065i	$0.772641\pi$
$798$		0			0
$799$	12.6082	−	8.10279i	0.446046	−	0.286656i
$800$		0			0
$801$	−0.231553	−	0.148810i	−0.00818152	−	0.00525794i
$802$		0			0
$803$	−15.6407	−	4.59251i	−0.551947	−	0.162066i
$804$		0			0
$805$	3.06682	+	6.67646i	0.108091	+	0.235314i
$806$		0			0
$807$	14.3676	+	4.21870i	0.505762	+	0.148505i
$808$		0			0
$809$	−28.8969	−	18.5709i	−1.01596	−	0.652917i	−0.0770303	−	0.997029i	$-0.524544\pi$
$809$	−28.8969	−	18.5709i	−1.01596	−	0.652917i	−0.938929	+	0.344111i	$0.888180\pi$
$810$		0			0
$811$	−29.9953	+	19.2768i	−1.05328	+	0.676899i	−0.948235	−	0.317568i	$-0.897134\pi$
$811$	−29.9953	+	19.2768i	−1.05328	+	0.676899i	−0.105041	+	0.994468i	$0.533497\pi$
$812$		0			0
$813$	−12.0322	−	13.8859i	−0.421988	−	0.487000i
$814$		0			0
$815$	−9.41174	+	20.6088i	−0.329679	+	0.721896i
$816$		0			0
$817$	21.4182	−	6.28896i	0.749329	−	0.220023i
$818$		0			0
$819$	1.43533	+	9.98297i	0.0501546	+	0.348833i
$820$		0			0
$821$	14.4238	+	31.5837i	0.503393	+	1.10228i	0.975352	+	0.220657i	$0.0708200\pi$
$821$	14.4238	+	31.5837i	0.503393	+	1.10228i	−0.471958	+	0.881621i	$0.656453\pi$
$822$		0			0
$823$	3.76747	−	26.2033i	0.131326	−	0.913390i	−0.812504	−	0.582956i	$-0.801896\pi$
$823$	3.76747	−	26.2033i	0.131326	−	0.913390i	0.943829	−	0.330434i	$-0.107195\pi$
$824$		0			0
$825$	−5.23468	+	6.04115i	−0.182248	+	0.210326i
$826$		0			0
$827$	−25.7194			−0.894351			−0.447176	−	0.894446i	$-0.647570\pi$
$827$	−25.7194			−0.894351			−0.447176	+	0.894446i	$0.647570\pi$
$828$		0			0
$829$	2.78348			0.0966741			0.0483371	−	0.998831i	$-0.484608\pi$
$829$	2.78348			0.0966741			0.0483371	+	0.998831i	$0.484608\pi$
$830$		0			0
$831$	−9.12967	+	10.5362i	−0.316705	+	0.365497i
$832$		0			0
$833$	−5.37877	+	37.4102i	−0.186363	+	1.29618i
$834$		0			0
$835$	−2.40963	−	5.27635i	−0.0833887	−	0.182596i
$836$		0			0
$837$	−0.129506	−	0.900734i	−0.00447638	−	0.0311339i
$838$		0			0
$839$	40.0523	−	11.7604i	1.38276	−	0.406014i	0.496030	−	0.868306i	$-0.334791\pi$
$839$	40.0523	−	11.7604i	1.38276	−	0.406014i	0.886728	+	0.462291i	$0.152972\pi$
$840$		0			0
$841$	−4.90258	+	10.7352i	−0.169054	+	0.370178i
$842$		0			0
$843$	5.08020	+	5.86287i	0.174972	+	0.201928i
$844$		0			0
$845$	30.4080	−	19.5420i	1.04607	−	0.672267i
$846$		0			0
$847$	−8.37773	−	5.38404i	−0.287862	−	0.184998i
$848$		0			0
$849$	31.2598	+	9.17871i	1.07283	+	0.315012i
$850$		0			0
$851$	−18.7585	+	5.55289i	−0.643032	+	0.190350i
$852$		0			0
$853$	25.9788	+	7.62807i	0.889498	+	0.261180i	0.694388	−	0.719601i	$-0.255675\pi$
$853$	25.9788	+	7.62807i	0.889498	+	0.261180i	0.195110	+	0.980781i	$0.437493\pi$
$854$		0			0
$855$	5.61308	+	3.60731i	0.191963	+	0.123367i
$856$		0			0
$857$	26.7373	−	17.1830i	0.913330	−	0.586961i	0.00261458	−	0.999997i	$-0.499168\pi$
$857$	26.7373	−	17.1830i	0.913330	−	0.586961i	0.910715	+	0.413035i	$0.135531\pi$
$858$		0			0
$859$	−10.1980	−	11.7692i	−0.347952	−	0.401558i	0.554615	−	0.832107i	$-0.312866\pi$
$859$	−10.1980	−	11.7692i	−0.347952	−	0.401558i	−0.902567	+	0.430549i	$0.858320\pi$
$860$		0			0
$861$	2.97425	−	6.51271i	0.101362	−	0.221953i
$862$		0			0
$863$	−3.00864	+	0.883417i	−0.102415	+	0.0300719i	−0.332539	−	0.943090i	$-0.607905\pi$
$863$	−3.00864	+	0.883417i	−0.102415	+	0.0300719i	0.230123	+	0.973161i	$0.426087\pi$
$864$		0			0
$865$	−1.63582	−	11.3774i	−0.0556197	−	0.386843i
$866$		0			0
$867$	18.0670	+	39.5612i	0.613588	+	1.34357i
$868$		0			0
$869$	−1.34856	+	9.37947i	−0.0457469	+	0.318177i
$870$		0			0
$871$	−45.5715	+	52.5924i	−1.54413	+	1.78202i
$872$		0			0
$873$	−7.35665			−0.248985
$874$		0			0
$875$	−13.6401			−0.461121
$876$		0			0
$877$	4.94937	−	5.71188i	0.167128	−	0.192877i	−0.666007	−	0.745945i	$-0.731998\pi$
$877$	4.94937	−	5.71188i	0.167128	−	0.192877i	0.833136	+	0.553069i	$0.186543\pi$
$878$		0			0
$879$	−3.05425	+	21.2428i	−0.103017	+	0.716501i
$880$		0			0
$881$	−9.06153	−	19.8420i	−0.305291	−	0.668493i	0.693351	−	0.720600i	$-0.256134\pi$
$881$	−9.06153	−	19.8420i	−0.305291	−	0.668493i	−0.998642	+	0.0521069i	$0.983406\pi$
$882$		0			0
$883$	−0.282773	−	1.96673i	−0.00951608	−	0.0661858i	0.984510	−	0.175328i	$-0.0560986\pi$
$883$	−0.282773	−	1.96673i	−0.00951608	−	0.0661858i	−0.994026	+	0.109142i	$0.965190\pi$
$884$		0			0
$885$	−14.5307	+	4.26660i	−0.488444	+	0.143420i
$886$		0			0
$887$	−6.13496	+	13.4337i	−0.205992	+	0.451059i	−0.984226	−	0.176915i	$-0.943388\pi$
$887$	−6.13496	+	13.4337i	−0.205992	+	0.451059i	0.778234	+	0.627974i	$0.216116\pi$
$888$		0			0
$889$	−13.2015	−	15.2354i	−0.442765	−	0.510978i
$890$		0			0
$891$	−1.72269	+	1.10710i	−0.0577122	+	0.0370893i
$892$		0			0
$893$	−10.3297	−	6.63852i	−0.345672	−	0.222150i
$894$		0			0
$895$	−19.0491	−	5.59333i	−0.636742	−	0.186964i
$896$		0			0
$897$	−27.7724	+	17.9348i	−0.927292	+	0.598824i
$898$		0			0
$899$	−3.62097	−	1.06321i	−0.120766	−	0.0354601i
$900$		0			0
$901$	51.2260	+	32.9210i	1.70659	+	1.09676i
$902$		0			0
$903$	−4.31171	+	2.77097i	−0.143485	+	0.0922119i
$904$		0			0
$905$	11.4539	+	13.2185i	0.380739	+	0.439397i
$906$		0			0
$907$	3.30569	−	7.23846i	0.109764	−	0.240349i	−0.846777	−	0.531948i	$-0.821460\pi$
$907$	3.30569	−	7.23846i	0.109764	−	0.240349i	0.956541	+	0.291599i	$0.0941873\pi$
$908$		0			0
$909$	13.7368	−	4.03348i	0.455620	−	0.133782i
$910$		0			0
$911$	−4.07719	−	28.3575i	−0.135083	−	0.939524i	−0.938788	−	0.344496i	$-0.888050\pi$
$911$	−4.07719	−	28.3575i	−0.135083	−	0.939524i	0.803705	−	0.595029i	$-0.202859\pi$
$912$		0			0
$913$	−7.04629	−	15.4292i	−0.233198	−	0.510633i
$914$		0			0
$915$	1.12290	−	7.80992i	0.0371218	−	0.258188i
$916$		0			0
$917$	9.21190	−	10.6311i	0.304204	−	0.351070i
$918$		0			0
$919$	−33.7887			−1.11458			−0.557292	−	0.830316i	$-0.688160\pi$
$919$	−33.7887			−1.11458			−0.557292	+	0.830316i	$0.688160\pi$
$920$		0			0
$921$	−4.31387			−0.142147
$922$		0			0
$923$	−0.891487	+	1.02883i	−0.0293437	+	0.0338644i
$924$		0			0
$925$	2.26614	−	15.7613i	0.0745101	−	0.518229i
$926$		0			0
$927$	−1.66775	−	3.65187i	−0.0547762	−	0.119943i
$928$		0			0
$929$	4.77544	+	33.2139i	0.156677	+	1.08971i	0.904703	+	0.426043i	$0.140093\pi$
$929$	4.77544	+	33.2139i	0.156677	+	1.08971i	−0.748026	+	0.663670i	$0.768998\pi$
$930$		0			0
$931$	29.7106	−	8.72382i	0.973726	−	0.285912i
$932$		0			0
$933$	5.37649	−	11.7729i	0.176018	−	0.385427i
$934$		0			0
$935$	−10.9211	−	12.6036i	−0.357157	−	0.412182i
$936$		0			0
$937$	18.4646	−	11.8665i	0.603212	−	0.387661i	−0.203094	−	0.979159i	$-0.565100\pi$
$937$	18.4646	−	11.8665i	0.603212	−	0.387661i	0.806306	+	0.591499i	$0.201463\pi$
$938$		0			0
$939$	3.10763	+	1.99715i	0.101414	+	0.0651745i
$940$		0			0
$941$	−31.4102	−	9.22286i	−1.02394	−	0.300657i	−0.273697	−	0.961816i	$-0.588246\pi$
$941$	−31.4102	−	9.22286i	−1.02394	−	0.300657i	−0.750245	+	0.661159i	$0.770065\pi$
$942$		0			0
$943$	23.4690	−	0.0516832i	0.764255	−	0.00168304i
$944$		0			0
$945$	−1.46993	−	0.431610i	−0.0478168	−	0.0140403i
$946$		0			0
$947$	26.9781	+	17.3378i	0.876672	+	0.563403i	0.899787	−	0.436330i	$-0.143722\pi$
$947$	26.9781	+	17.3378i	0.876672	+	0.563403i	−0.0231147	+	0.999733i	$0.507358\pi$
$948$		0			0
$949$	46.1635	−	29.6675i	1.49853	−	0.963048i
$950$		0			0
$951$	−12.2503	−	14.1376i	−0.397245	−	0.458445i
$952$		0			0
$953$	−10.1659	+	22.2603i	−0.329307	+	0.721081i	−0.999783	−	0.0208504i	$-0.993363\pi$
$953$	−10.1659	+	22.2603i	−0.329307	+	0.721081i	0.670476	+	0.741931i	$0.266090\pi$
$954$		0			0
$955$	−10.1731	+	2.98709i	−0.329194	+	0.0966600i
$956$		0			0
$957$	1.20857	+	8.40581i	0.0390676	+	0.271721i
$958$		0			0
$959$	2.14594	+	4.69896i	0.0692962	+	0.151737i
$960$		0			0
$961$	4.29391	−	29.8648i	0.138513	−	0.963381i
$962$		0			0
$963$	8.52969	−	9.84379i	0.274865	−	0.317212i
$964$		0			0
$965$	14.8242			0.477207
$966$		0			0
$967$	17.6787			0.568508			0.284254	−	0.958749i	$-0.408254\pi$
$967$	17.6787			0.568508			0.284254	+	0.958749i	$0.408254\pi$
$968$		0			0
$969$	32.4549	−	37.4549i	1.04260	−	1.20323i
$970$		0			0
$971$	−0.739698	+	5.14471i	−0.0237380	+	0.165102i	−0.998242	−	0.0592682i	$-0.981123\pi$
$971$	−0.739698	+	5.14471i	−0.0237380	+	0.165102i	0.974504	+	0.224370i	$0.0720324\pi$
$972$		0			0
$973$	1.38777	+	3.03878i	0.0444897	+	0.0974189i
$974$		0			0
$975$	−3.82958	−	26.6353i	−0.122645	−	0.853012i
$976$		0			0
$977$	22.4267	−	6.58506i	0.717492	−	0.210675i	0.0974469	−	0.995241i	$-0.468932\pi$
$977$	22.4267	−	6.58506i	0.717492	−	0.210675i	0.620045	+	0.784566i	$0.287114\pi$
$978$		0			0
$979$	0.234145	−	0.512706i	0.00748330	−	0.0163862i
$980$		0			0
$981$	2.32170	+	2.67938i	0.0741262	+	0.0855461i
$982$		0			0
$983$	28.1221	−	18.0730i	0.896956	−	0.576438i	−0.00893018	−	0.999960i	$-0.502843\pi$
$983$	28.1221	−	18.0730i	0.896956	−	0.576438i	0.905886	+	0.423522i	$0.139206\pi$
$984$		0			0
$985$	−22.3324	−	14.3522i	−0.711569	−	0.457298i
$986$		0			0
$987$	2.70511	+	0.794292i	0.0861046	+	0.0252826i
$988$		0			0
$989$	−14.1534	−	9.05188i	−0.450053	−	0.287833i
$990$		0			0
$991$	−0.861200	−	0.252871i	−0.0273569	−	0.00803271i	0.268025	−	0.963412i	$-0.413629\pi$
$991$	−0.861200	−	0.252871i	−0.0273569	−	0.00803271i	−0.295382	+	0.955379i	$0.595447\pi$
$992$		0			0
$993$	−3.81951	−	2.45465i	−0.121209	−	0.0778960i
$994$		0			0
$995$	11.6578	−	7.49199i	0.369576	−	0.237512i
$996$		0			0
$997$	−32.7655	−	37.8134i	−1.03770	−	1.19756i	−0.979952	−	0.199232i	$-0.936155\pi$
$997$	−32.7655	−	37.8134i	−1.03770	−	1.19756i	−0.0577428	−	0.998331i	$-0.518390\pi$
$998$		0			0
$999$	1.69456	−	3.71056i	0.0536134	−	0.117397i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.2.i.a.133.1	✓	20
3.2	odd	2		828.2.q.c.685.2		20
23.3	even	11		6348.2.a.s.1.7		10
23.9	even	11	inner	276.2.i.a.193.1	yes	20
23.20	odd	22		6348.2.a.t.1.4		10
69.32	odd	22		828.2.q.c.469.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.i.a.133.1	✓	20	1.1	even	1	trivial
276.2.i.a.193.1	yes	20	23.9	even	11	inner
828.2.q.c.469.2		20	69.32	odd	22
828.2.q.c.685.2		20	3.2	odd	2
6348.2.a.s.1.7		10	23.3	even	11
6348.2.a.t.1.4		10	23.20	odd	22

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:	\( N \)	\(=\)	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	276.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.654861 + 0.755750i) q^{3} +(-0.149019 + 1.03645i) q^{5} +(0.607780 + 1.33085i) q^{7} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})\)	\(q+(-0.654861 + 0.755750i) q^{3} +(-0.149019 + 1.03645i) q^{5} +(0.607780 + 1.33085i) q^{7} +(-0.142315 - 0.989821i) q^{9} +(1.96481 - 0.576921i) q^{11} +(-2.86365 + 6.27053i) q^{13} +(-0.685708 - 0.791349i) q^{15} +(-6.54296 + 4.20490i) q^{17} +(5.36057 + 3.44503i) q^{19} +(-1.40380 - 0.412194i) q^{21} +(-0.692970 - 4.74550i) q^{23} +(3.74545 + 1.09976i) q^{25} +(0.841254 + 0.540641i) q^{27} +(3.48875 - 2.24209i) q^{29} +(-0.595921 - 0.687730i) q^{31} +(-0.850671 + 1.86271i) q^{33} +(-1.46993 + 0.431610i) q^{35} +(-0.580529 - 4.03767i) q^{37} +(-2.86365 - 6.27053i) q^{39} +(-0.696437 + 4.84382i) q^{41} +(2.29407 - 2.64750i) q^{43} +1.04710 q^{45} -1.92699 q^{47} +(3.18225 - 3.67251i) q^{49} +(1.10687 - 7.69846i) q^{51} +(-3.25236 - 7.12168i) q^{53} +(0.305154 + 2.12240i) q^{55} +(-6.11401 + 1.79523i) q^{57} +(6.00809 - 13.1559i) q^{59} +(4.93456 + 5.69479i) q^{61} +(1.23081 - 0.790994i) q^{63} +(-6.07233 - 3.90245i) q^{65} +(9.68609 + 2.84409i) q^{67} +(4.04021 + 2.58393i) q^{69} +(0.189483 + 0.0556372i) q^{71} +(-6.69670 - 4.30371i) q^{73} +(-3.28389 + 2.11043i) q^{75} +(1.96197 + 2.26424i) q^{77} +(-1.92232 + 4.20928i) q^{79} +(-0.959493 + 0.281733i) q^{81} +(-1.17882 - 8.19891i) q^{83} +(-3.38314 - 7.40803i) q^{85} +(-0.590193 + 4.10488i) q^{87} +(0.180249 - 0.208018i) q^{89} -10.0856 q^{91} +0.909997 q^{93} +(-4.36941 + 5.04257i) q^{95} +(1.04696 - 7.28177i) q^{97} +(-0.850671 - 1.86271i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{3} - 4 q^{5} - 2 q^{9}+O(q^{10}) \) 20 * q - 2 * q^3 - 4 * q^5 - 2 * q^9	\( 20 q - 2 q^{3} - 4 q^{5} - 2 q^{9} - 22 q^{13} + 7 q^{15} + 7 q^{17} + 19 q^{19} + 20 q^{23} + 20 q^{25} - 2 q^{27} + 32 q^{29} - 3 q^{31} + 11 q^{33} - 26 q^{35} - 10 q^{37} - 22 q^{39} - 40 q^{41} + 8 q^{43} - 4 q^{45} - 18 q^{47} - 34 q^{49} - 26 q^{51} - 34 q^{53} - 17 q^{55} - 3 q^{57} - 32 q^{59} + 32 q^{61} + 49 q^{65} + 35 q^{67} - 2 q^{69} + 33 q^{71} - q^{73} - 2 q^{75} - 50 q^{77} + 22 q^{79} - 2 q^{81} - 14 q^{83} - 9 q^{85} - 12 q^{87} + 10 q^{89} - 72 q^{91} + 30 q^{93} - 51 q^{95} - 4 q^{97} + 11 q^{99}+O(q^{100}) \) 20 * q - 2 * q^3 - 4 * q^5 - 2 * q^9 - 22 * q^13 + 7 * q^15 + 7 * q^17 + 19 * q^19 + 20 * q^23 + 20 * q^25 - 2 * q^27 + 32 * q^29 - 3 * q^31 + 11 * q^33 - 26 * q^35 - 10 * q^37 - 22 * q^39 - 40 * q^41 + 8 * q^43 - 4 * q^45 - 18 * q^47 - 34 * q^49 - 26 * q^51 - 34 * q^53 - 17 * q^55 - 3 * q^57 - 32 * q^59 + 32 * q^61 + 49 * q^65 + 35 * q^67 - 2 * q^69 + 33 * q^71 - q^73 - 2 * q^75 - 50 * q^77 + 22 * q^79 - 2 * q^81 - 14 * q^83 - 9 * q^85 - 12 * q^87 + 10 * q^89 - 72 * q^91 + 30 * q^93 - 51 * q^95 - 4 * q^97 + 11 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more