LMFDB - Embedded newform 495.2.n.c.181.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [495,2,Mod(91,495)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("495.91"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(495, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 495 = 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	495.n (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,-2,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.95259490005$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	$\Q(\zeta_{15})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			181.1
Root			$-0.104528 + 0.994522i$ of defining polynomial
Character	$\chi$	$=$	495.181
Dual form			495.2.n.c.361.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.564602 - 1.73767i) q^{2} +(-1.08268 + 0.786610i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(-1.41355 + 1.02700i) q^{7} +(-0.978148 - 0.710666i) q^{8} +1.82709 q^{10} +(0.384301 - 3.29428i) q^{11} +(-1.65563 - 5.09549i) q^{13} +(2.58268 + 1.87642i) q^{14} +(-1.50973 + 4.64646i) q^{16} +(-2.26531 + 6.97191i) q^{17} +(-4.86606 - 3.53540i) q^{19} +(-0.413545 - 1.27276i) q^{20} +(-5.94135 + 1.19217i) q^{22} -8.35772 q^{23} +(-0.809017 - 0.587785i) q^{25} +(-7.91949 + 5.75385i) q^{26} +(0.722562 - 2.22382i) q^{28} +(4.48048 - 3.25526i) q^{29} +(-0.00660190 - 0.0203186i) q^{31} +6.50828 q^{32} +13.3939 q^{34} +(-0.539926 - 1.66172i) q^{35} +(0.907432 - 0.659288i) q^{37} +(-3.39596 + 10.4517i) q^{38} +(0.978148 - 0.710666i) q^{40} +(-2.96086 - 2.15119i) q^{41} -1.96950 q^{43} +(2.17524 + 3.86894i) q^{44} +(4.71878 + 14.5229i) q^{46} +(3.09007 + 2.24507i) q^{47} +(-1.21974 + 3.75397i) q^{49} +(-0.564602 + 1.73767i) q^{50} +(5.80067 + 4.21443i) q^{52} +(-0.516329 - 1.58910i) q^{53} +(3.01430 + 1.38348i) q^{55} +2.11251 q^{56} +(-8.18625 - 5.94766i) q^{58} +(4.58172 - 3.32882i) q^{59} +(2.86761 - 8.82559i) q^{61} +(-0.0315794 + 0.0229438i) q^{62} +(-0.655137 - 2.01630i) q^{64} +5.35772 q^{65} +0.350489 q^{67} +(-3.03158 - 9.33024i) q^{68} +(-2.58268 + 1.87642i) q^{70} +(-1.40238 + 4.31607i) q^{71} +(-8.20305 + 5.95986i) q^{73} +(-1.65796 - 1.20458i) q^{74} +8.04935 q^{76} +(2.84001 + 5.05130i) q^{77} +(0.792323 + 2.43852i) q^{79} +(-3.95252 - 2.87167i) q^{80} +(-2.06635 + 6.35956i) q^{82} +(4.96915 - 15.2935i) q^{83} +(-5.93066 - 4.30888i) q^{85} +(1.11198 + 3.42233i) q^{86} +(-2.71704 + 2.94919i) q^{88} +14.5062 q^{89} +(7.57337 + 5.50238i) q^{91} +(9.04870 - 6.57426i) q^{92} +(2.15652 - 6.63708i) q^{94} +(4.86606 - 3.53540i) q^{95} +(-0.587045 - 1.80674i) q^{97} +7.21182 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 2 q^{4} + 2 q^{5} - 5 q^{7} + q^{8} + 2 q^{10} + q^{11} - 16 q^{13} + 10 q^{14} + 12 q^{16} + 4 q^{17} + 2 q^{19} + 3 q^{20} - 9 q^{22} - 10 q^{23} - 2 q^{25} - 16 q^{26} - 5 q^{28} + 16 q^{29}+ \cdots - 26 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 + 2 * q^4 + 2 * q^5 - 5 * q^7 + q^8 + 2 * q^10 + q^11 - 16 * q^13 + 10 * q^14 + 12 * q^16 + 4 * q^17 + 2 * q^19 + 3 * q^20 - 9 * q^22 - 10 * q^23 - 2 * q^25 - 16 * q^26 - 5 * q^28 + 16 * q^29 - 5 * q^31 + 34 * q^34 - 5 * q^35 - 5 * q^37 - 28 * q^38 - q^40 - 5 * q^41 - 8 * q^43 + 19 * q^44 + 10 * q^46 + q^47 - 11 * q^49 - 2 * q^50 + 26 * q^52 + 15 * q^53 - q^55 - 20 * q^56 - 24 * q^58 - 3 * q^59 - 11 * q^61 + 15 * q^62 - 9 * q^64 - 14 * q^65 + 6 * q^67 - 9 * q^68 - 10 * q^70 - q^71 - 35 * q^73 - 5 * q^74 + 58 * q^76 + 25 * q^77 - 30 * q^79 + 3 * q^80 - 25 * q^82 - 31 * q^83 - 4 * q^85 + 62 * q^86 + 17 * q^88 + 48 * q^89 + 5 * q^91 + 20 * q^92 - 19 * q^94 - 2 * q^95 + 11 * q^97 - 26 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$397$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$	$1$

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 $

$2$	−0.564602	−	1.73767i	−0.399234	−	1.22872i	−0.925615	−	0.378467i	$-0.876451\pi$
$2$	−0.564602	−	1.73767i	−0.399234	−	1.22872i	0.526381	−	0.850249i	$-0.323549\pi$
$3$		0			0
$3$		0			0
$4$	−1.08268	+	0.786610i	−0.541338	+	0.393305i
$5$	−0.309017	+	0.951057i	−0.138197	+	0.425325i
$5$	−0.309017	+	0.951057i	−0.138197	+	0.425325i
$6$		0			0
$7$	−1.41355	+	1.02700i	−0.534270	+	0.388170i	−0.821953	−	0.569556i	$-0.807115\pi$
$7$	−1.41355	+	1.02700i	−0.534270	+	0.388170i	0.287683	+	0.957726i	$0.407115\pi$
$8$	−0.978148	−	0.710666i	−0.345827	−	0.251258i
$9$		0			0
$10$	1.82709			0.577777
$11$	0.384301	−	3.29428i	0.115871	−	0.993264i
$11$	0.384301	−	3.29428i	0.115871	−	0.993264i
$12$		0			0
$13$	−1.65563	−	5.09549i	−0.459188	−	1.41323i	−0.866147	−	0.499789i	$-0.833411\pi$
$13$	−1.65563	−	5.09549i	−0.459188	−	1.41323i	0.406960	−	0.913446i	$-0.366589\pi$
$14$	2.58268	+	1.87642i	0.690249	+	0.501495i
$15$		0			0
$16$	−1.50973	+	4.64646i	−0.377432	+	1.16162i
$17$	−2.26531	+	6.97191i	−0.549419	+	1.69094i	0.160826	+	0.986983i	$0.448584\pi$
$17$	−2.26531	+	6.97191i	−0.549419	+	1.69094i	−0.710245	+	0.703955i	$0.751416\pi$
$18$		0			0
$19$	−4.86606	−	3.53540i	−1.11635	−	0.811077i	−0.132699	−	0.991156i	$-0.542364\pi$
$19$	−4.86606	−	3.53540i	−1.11635	−	0.811077i	−0.983652	+	0.180080i	$0.942364\pi$
$20$	−0.413545	−	1.27276i	−0.0924716	−	0.284598i
$21$		0			0
$22$	−5.94135	+	1.19217i	−1.26670	+	0.254172i
$23$	−8.35772			−1.74270			−0.871352	−	0.490658i	$-0.836756\pi$
$23$	−8.35772			−1.74270			−0.871352	+	0.490658i	$0.836756\pi$
$24$		0			0
$25$	−0.809017	−	0.587785i	−0.161803	−	0.117557i
$26$	−7.91949	+	5.75385i	−1.55314	+	1.12842i
$27$		0			0
$28$	0.722562	−	2.22382i	0.136551	−	0.420262i
$29$	4.48048	−	3.25526i	0.832005	−	0.604487i	−0.0881210	−	0.996110i	$-0.528086\pi$
$29$	4.48048	−	3.25526i	0.832005	−	0.604487i	0.920126	+	0.391623i	$0.128086\pi$
$30$		0			0
$31$	−0.00660190	−	0.0203186i	−0.00118574	−	0.00364932i	0.950462	−	0.310841i	$-0.100611\pi$
$31$	−0.00660190	−	0.0203186i	−0.00118574	−	0.00364932i	−0.951648	+	0.307192i	$0.900611\pi$
$32$	6.50828			1.15051
$33$		0			0
$34$	13.3939			2.29703
$35$	−0.539926	−	1.66172i	−0.0912642	−	0.280882i
$36$		0			0
$37$	0.907432	−	0.659288i	0.149181	−	0.108386i	−0.510691	−	0.859764i	$-0.670610\pi$
$37$	0.907432	−	0.659288i	0.149181	−	0.108386i	0.659872	+	0.751378i	$0.270610\pi$
$38$	−3.39596	+	10.4517i	−0.550897	+	1.69549i
$39$		0			0
$40$	0.978148	−	0.710666i	0.154659	−	0.112366i
$41$	−2.96086	−	2.15119i	−0.462409	−	0.335960i	0.332066	−	0.943256i	$-0.392254\pi$
$41$	−2.96086	−	2.15119i	−0.462409	−	0.335960i	−0.794476	+	0.607296i	$0.792254\pi$
$42$		0			0
$43$	−1.96950			−0.300346			−0.150173	−	0.988660i	$-0.547983\pi$
$43$	−1.96950			−0.300346			−0.150173	+	0.988660i	$0.547983\pi$
$44$	2.17524	+	3.86894i	0.327930	+	0.583264i
$45$		0			0
$46$	4.71878	+	14.5229i	0.695747	+	2.14129i
$47$	3.09007	+	2.24507i	0.450733	+	0.327476i	0.789885	−	0.613255i	$-0.210140\pi$
$47$	3.09007	+	2.24507i	0.450733	+	0.327476i	−0.339152	+	0.940731i	$0.610140\pi$
$48$		0			0
$49$	−1.21974	+	3.75397i	−0.174248	+	0.536282i
$50$	−0.564602	+	1.73767i	−0.0798468	+	0.245743i
$51$		0			0
$52$	5.80067	+	4.21443i	0.804408	+	0.584437i
$53$	−0.516329	−	1.58910i	−0.0709232	−	0.218279i	0.909312	−	0.416115i	$-0.136609\pi$
$53$	−0.516329	−	1.58910i	−0.0709232	−	0.218279i	−0.980235	+	0.197836i	$0.936609\pi$
$54$		0			0
$55$	3.01430	+	1.38348i	0.406448	+	0.186549i
$56$	2.11251			0.282296
$57$		0			0
$58$	−8.18625	−	5.94766i	−1.07491	−	0.780966i
$59$	4.58172	−	3.32882i	0.596489	−	0.433375i	−0.248142	−	0.968724i	$-0.579820\pi$
$59$	4.58172	−	3.32882i	0.596489	−	0.433375i	0.844631	+	0.535349i	$0.179820\pi$
$60$		0			0
$61$	2.86761	−	8.82559i	0.367160	−	1.13000i	−0.581458	−	0.813576i	$-0.697518\pi$
$61$	2.86761	−	8.82559i	0.367160	−	1.13000i	0.948618	−	0.316425i	$-0.102482\pi$
$62$	−0.0315794	+	0.0229438i	−0.00401059	+	0.00291387i
$63$		0			0
$64$	−0.655137	−	2.01630i	−0.0818921	−	0.252038i
$65$	5.35772			0.664543
$66$		0			0
$67$	0.350489			0.0428190			0.0214095	−	0.999771i	$-0.493185\pi$
$67$	0.350489			0.0428190			0.0214095	+	0.999771i	$0.493185\pi$
$68$	−3.03158	−	9.33024i	−0.367633	−	1.13146i
$69$		0			0
$70$	−2.58268	+	1.87642i	−0.308689	+	0.224276i
$71$	−1.40238	+	4.31607i	−0.166431	+	0.512223i	−0.999139	−	0.0414901i	$-0.986790\pi$
$71$	−1.40238	+	4.31607i	−0.166431	+	0.512223i	0.832708	+	0.553713i	$0.186790\pi$
$72$		0			0
$73$	−8.20305	+	5.95986i	−0.960094	+	0.697549i	−0.953173	−	0.302427i	$-0.902203\pi$
$73$	−8.20305	+	5.95986i	−0.960094	+	0.697549i	−0.00692130	+	0.999976i	$0.502203\pi$
$74$	−1.65796	−	1.20458i	−0.192734	−	0.140029i
$75$		0			0
$76$	8.04935			0.923324
$77$	2.84001	+	5.05130i	0.323649	+	0.575649i
$78$		0			0
$79$	0.792323	+	2.43852i	0.0891433	+	0.274355i	0.985683	−	0.168608i	$-0.0539273\pi$
$79$	0.792323	+	2.43852i	0.0891433	+	0.274355i	−0.896540	+	0.442963i	$0.853927\pi$
$80$	−3.95252	−	2.87167i	−0.441905	−	0.321063i
$81$		0			0
$82$	−2.06635	+	6.35956i	−0.228190	+	0.702296i
$83$	4.96915	−	15.2935i	0.545435	−	1.67868i	−0.174519	−	0.984654i	$-0.555837\pi$
$83$	4.96915	−	15.2935i	0.545435	−	1.67868i	0.719954	−	0.694022i	$-0.244163\pi$
$84$		0			0
$85$	−5.93066	−	4.30888i	−0.643271	−	0.467364i
$86$	1.11198	+	3.42233i	0.119908	+	0.369040i
$87$		0			0
$88$	−2.71704	+	2.94919i	−0.289637	+	0.314384i
$89$	14.5062			1.53765			0.768825	−	0.639459i	$-0.220841\pi$
$89$	14.5062			1.53765			0.768825	+	0.639459i	$0.220841\pi$
$90$		0			0
$91$	7.57337	+	5.50238i	0.793905	+	0.576806i
$92$	9.04870	−	6.57426i	0.943392	−	0.685414i
$93$		0			0
$94$	2.15652	−	6.63708i	0.222428	−	0.684562i
$95$	4.86606	−	3.53540i	0.499247	−	0.362725i
$96$		0			0
$97$	−0.587045	−	1.80674i	−0.0596054	−	0.183446i	0.916820	−	0.399300i	$-0.130747\pi$
$97$	−0.587045	−	1.80674i	−0.0596054	−	0.183446i	−0.976426	+	0.215853i	$0.930747\pi$
$98$	7.21182			0.728504
$99$		0			0
$100$	1.33826			0.133826
$101$	−2.07354	−	6.38170i	−0.206325	−	0.635003i	−0.999656	−	0.0262128i	$-0.991655\pi$
$101$	−2.07354	−	6.38170i	−0.206325	−	0.635003i	0.793332	−	0.608790i	$-0.208345\pi$
$102$		0			0
$103$	3.43572	−	2.49620i	0.338532	−	0.245958i	−0.405510	−	0.914090i	$-0.632906\pi$
$103$	3.43572	−	2.49620i	0.338532	−	0.245958i	0.744042	+	0.668133i	$0.232906\pi$
$104$	−2.00174	+	6.16074i	−0.196287	+	0.604110i
$105$		0			0
$106$	−2.46980	+	1.79442i	−0.239888	+	0.174289i
$107$	−12.7202	−	9.24174i	−1.22970	−	0.893433i	−0.232837	−	0.972516i	$-0.574801\pi$
$107$	−12.7202	−	9.24174i	−1.22970	−	0.893433i	−0.996868	+	0.0790831i	$0.974801\pi$
$108$		0			0
$109$	4.23895			0.406018			0.203009	−	0.979177i	$-0.434928\pi$
$109$	4.23895			0.406018			0.203009	+	0.979177i	$0.434928\pi$
$110$	0.702153	−	6.01896i	0.0669477	−	0.573885i
$111$		0			0
$112$	−2.63785	−	8.11848i	−0.249254	−	0.767124i
$113$	−5.82203	−	4.22996i	−0.547691	−	0.397921i	0.279242	−	0.960221i	$-0.409917\pi$
$113$	−5.82203	−	4.22996i	−0.547691	−	0.397921i	−0.826933	+	0.562300i	$0.809917\pi$
$114$		0			0
$115$	2.58268	−	7.94866i	0.240836	−	0.741216i
$116$	−2.29029	+	7.04879i	−0.212648	+	0.654463i
$117$		0			0
$118$	−8.37122	−	6.08205i	−0.770633	−	0.559898i
$119$	−3.95804	−	12.1816i	−0.362833	−	1.11668i
$120$		0			0
$121$	−10.7046	−	2.53200i	−0.973148	−	0.230181i
$122$	−16.9550			−1.53503
$123$		0			0
$124$	0.0231305	+	0.0168053i	0.00207718	+	0.00150916i
$125$	0.809017	−	0.587785i	0.0723607	−	0.0525731i
$126$		0			0
$127$	3.92051	−	12.0661i	0.347889	−	1.07069i	−0.612130	−	0.790757i	$-0.709687\pi$
$127$	3.92051	−	12.0661i	0.347889	−	1.07069i	0.960019	−	0.279935i	$-0.0903131\pi$
$128$	7.39685	−	5.37413i	0.653796	−	0.475010i
$129$		0			0
$130$	−3.02498	−	9.30992i	−0.265308	−	0.816534i
$131$	0.970102			0.0847582			0.0423791	−	0.999102i	$-0.486506\pi$
$131$	0.970102			0.0847582			0.0423791	+	0.999102i	$0.486506\pi$
$132$		0			0
$133$	10.5093			0.911268
$134$	−0.197887	−	0.609032i	−0.0170948	−	0.0526124i
$135$		0			0
$136$	7.17051	−	5.20968i	0.614866	−	0.446726i
$137$	−1.30416	+	4.01379i	−0.111422	+	0.342921i	−0.991184	−	0.132493i	$-0.957702\pi$
$137$	−1.30416	+	4.01379i	−0.111422	+	0.342921i	0.879762	+	0.475414i	$0.157702\pi$
$138$		0			0
$139$	−7.15855	+	5.20099i	−0.607180	+	0.441142i	−0.848420	−	0.529323i	$-0.822446\pi$
$139$	−7.15855	+	5.20099i	−0.607180	+	0.441142i	0.241240	+	0.970465i	$0.422446\pi$
$140$	1.89169	+	1.37440i	0.159877	+	0.116158i
$141$		0			0
$142$	8.29167			0.695821
$143$	−17.4223	+	3.49590i	−1.45692	+	0.292342i
$144$		0			0
$145$	1.71139	+	5.26712i	0.142123	+	0.437411i
$146$	14.9877	+	10.8892i	1.24039	+	0.901197i
$147$		0			0
$148$	−0.463852	+	1.42759i	−0.0381284	+	0.117347i
$149$	−2.95222	+	9.08598i	−0.241855	+	0.744353i	0.754283	+	0.656549i	$0.227985\pi$
$149$	−2.95222	+	9.08598i	−0.241855	+	0.744353i	−0.996138	+	0.0878033i	$0.972015\pi$
$150$		0			0
$151$	5.46214	+	3.96848i	0.444503	+	0.322950i	0.787422	−	0.616415i	$-0.211416\pi$
$151$	5.46214	+	3.96848i	0.444503	+	0.322950i	−0.342919	+	0.939365i	$0.611416\pi$
$152$	2.24724	+	6.91629i	0.182275	+	0.560985i
$153$		0			0
$154$	7.17400	−	7.78696i	0.578097	−	0.627491i
$155$	0.0213642			0.00171601
$156$		0			0
$157$	10.2425	+	7.44162i	0.817441	+	0.593906i	0.915978	−	0.401228i	$-0.131416\pi$
$157$	10.2425	+	7.44162i	0.817441	+	0.593906i	−0.0985374	+	0.995133i	$0.531416\pi$
$158$	3.78999	−	2.75359i	0.301515	−	0.219064i
$159$		0			0
$160$	−2.01117	+	6.18975i	−0.158997	+	0.489342i
$161$	11.8140	−	8.58338i	0.931074	−	0.676465i
$162$		0			0
$163$	−7.23278	−	22.2602i	−0.566515	−	1.74355i	−0.663407	−	0.748259i	$-0.730890\pi$
$163$	−7.23278	−	22.2602i	−0.566515	−	1.74355i	0.0968923	−	0.995295i	$-0.469110\pi$
$164$	4.89781			0.382454
$165$		0			0
$166$	−29.3805			−2.28037
$167$	−0.943091	−	2.90254i	−0.0729786	−	0.224605i	0.907913	−	0.419158i	$-0.137675\pi$
$167$	−0.943091	−	2.90254i	−0.0729786	−	0.224605i	−0.980892	+	0.194553i	$0.937675\pi$
$168$		0			0
$169$	−12.7057	+	9.23123i	−0.977362	+	0.710095i
$170$	−4.13893	+	12.7383i	−0.317442	+	0.976985i
$171$		0			0
$172$	2.13233	−	1.54923i	0.162589	−	0.118128i
$173$	12.9503	+	9.40893i	0.984592	+	0.715348i	0.958730	−	0.284318i	$-0.0917670\pi$
$173$	12.9503	+	9.40893i	0.984592	+	0.715348i	0.0258617	+	0.999666i	$0.491767\pi$
$174$		0			0
$175$	1.74724			0.132079
$176$	14.7266	+	6.75911i	1.11006	+	0.509487i
$177$		0			0
$178$	−8.19021	−	25.2069i	−0.613883	−	1.88934i
$179$	−15.6133	−	11.3437i	−1.16699	−	0.847870i	−0.176347	−	0.984328i	$-0.556428\pi$
$179$	−15.6133	−	11.3437i	−1.16699	−	0.847870i	−0.990646	+	0.136458i	$0.956428\pi$
$180$		0			0
$181$	−3.76724	+	11.5944i	−0.280017	+	0.861804i	0.707831	+	0.706382i	$0.249674\pi$
$181$	−3.76724	+	11.5944i	−0.280017	+	0.861804i	−0.987848	+	0.155422i	$0.950326\pi$
$182$	5.28536	−	16.2667i	0.391777	−	1.20576i
$183$		0			0
$184$	8.17508	+	5.93954i	0.602675	+	0.437869i
$185$	0.346608	+	1.06675i	0.0254831	+	0.0784290i
$186$		0			0
$187$	22.0969	+	10.1419i	1.61589	+	0.741649i
$188$	−5.11153			−0.372797
$189$		0			0
$190$	−8.89074	−	6.45950i	−0.645002	−	0.468621i
$191$	−10.8605	+	7.89064i	−0.785841	+	0.570947i	−0.906726	−	0.421720i	$-0.861427\pi$
$191$	−10.8605	+	7.89064i	−0.785841	+	0.570947i	0.120885	+	0.992666i	$0.461427\pi$
$192$		0			0
$193$	2.34167	−	7.20693i	0.168557	−	0.518766i	−0.830723	−	0.556685i	$-0.812073\pi$
$193$	2.34167	−	7.20693i	0.168557	−	0.518766i	0.999281	+	0.0379190i	$0.0120729\pi$
$194$	−2.80806	+	2.04018i	−0.201607	+	0.146476i
$195$		0			0
$196$	−1.63233	−	5.02379i	−0.116595	−	0.358842i
$197$	6.89118			0.490976			0.245488	−	0.969400i	$-0.421052\pi$
$197$	6.89118			0.490976			0.245488	+	0.969400i	$0.421052\pi$
$198$		0			0
$199$	0.639398			0.0453257			0.0226629	−	0.999743i	$-0.492786\pi$
$199$	0.639398			0.0453257			0.0226629	+	0.999743i	$0.492786\pi$
$200$	0.373619	+	1.14988i	0.0264189	+	0.0813089i
$201$		0			0
$202$	−9.91854	+	7.20624i	−0.697866	+	0.507029i
$203$	−2.99021	+	9.20292i	−0.209872	+	0.645918i
$204$		0			0
$205$	2.96086	−	2.15119i	0.206796	−	0.150246i
$206$	−6.27737	−	4.56078i	−0.437365	−	0.317765i
$207$		0			0
$208$	26.1755			1.81495
$209$	−13.5167	+	14.6715i	−0.934966	+	1.01485i
$210$		0			0
$211$	−1.18090	−	3.63445i	−0.0812968	−	0.250206i	0.902144	−	0.431435i	$-0.141992\pi$
$211$	−1.18090	−	3.63445i	−0.0812968	−	0.250206i	−0.983441	+	0.181229i	$0.941992\pi$
$212$	1.80902	+	1.31433i	0.124244	+	0.0902684i
$213$		0			0
$214$	−8.87723	+	27.3213i	−0.606835	+	1.86765i
$215$	0.608609	−	1.87310i	0.0415068	−	0.127745i
$216$		0			0
$217$	0.0301993	+	0.0219411i	0.00205006	+	0.00148946i
$218$	−2.39332	−	7.36589i	−0.162096	−	0.498881i
$219$		0			0
$220$	−4.35177	+	0.873212i	−0.293396	+	0.0588720i
$221$	39.2758			2.64198
$222$		0			0
$223$	21.6171	+	15.7057i	1.44758	+	1.05173i	0.986388	+	0.164434i	$0.0525797\pi$
$223$	21.6171	+	15.7057i	1.44758	+	1.05173i	0.461197	+	0.887298i	$0.347420\pi$
$224$	−9.19975	+	6.68401i	−0.614684	+	0.446594i
$225$		0			0
$226$	−4.06312	+	12.5050i	−0.270275	+	0.831820i
$227$	9.90020	−	7.19291i	0.657099	−	0.477411i	−0.208583	−	0.978005i	$-0.566885\pi$
$227$	9.90020	−	7.19291i	0.657099	−	0.477411i	0.865682	+	0.500594i	$0.166885\pi$
$228$		0			0
$229$	−2.06628	−	6.35937i	−0.136544	−	0.420239i	0.859283	−	0.511500i	$-0.170910\pi$
$229$	−2.06628	−	6.35937i	−0.136544	−	0.420239i	−0.995827	+	0.0912615i	$0.970910\pi$
$230$	−15.2703			−1.00689
$231$		0			0
$232$	−6.69598			−0.439612
$233$	2.01399	+	6.19844i	0.131941	+	0.406073i	0.995102	−	0.0988565i	$-0.0315185\pi$
$233$	2.01399	+	6.19844i	0.131941	+	0.406073i	−0.863161	+	0.504930i	$0.831518\pi$
$234$		0			0
$235$	−3.09007	+	2.24507i	−0.201574	+	0.146452i
$236$	−2.34204	+	7.20806i	−0.152454	+	0.469205i
$237$		0			0
$238$	−18.9328	+	13.7555i	−1.22723	+	0.891637i
$239$	−8.77126	−	6.37269i	−0.567366	−	0.412215i	0.266782	−	0.963757i	$-0.414040\pi$
$239$	−8.77126	−	6.37269i	−0.567366	−	0.412215i	−0.834147	+	0.551542i	$0.814040\pi$
$240$		0			0
$241$	27.1803			1.75084			0.875420	−	0.483363i	$-0.160585\pi$
$241$	27.1803			1.75084			0.875420	+	0.483363i	$0.160585\pi$
$242$	1.64409	+	20.0306i	0.105686	+	1.28762i
$243$		0			0
$244$	3.83761	+	11.8109i	0.245678	+	0.756118i
$245$	−3.19332	−	2.32008i	−0.204014	−	0.148225i
$246$		0			0
$247$	−9.95823	+	30.6483i	−0.633627	+	1.95010i
$248$	−0.00798208	+	0.0245663i	−0.000506862	+	0.00155996i
$249$		0			0
$250$	−1.47815	−	1.07394i	−0.0934863	−	0.0679217i
$251$	−1.71332	−	5.27307i	−0.108144	−	0.332833i	0.882311	−	0.470666i	$-0.155986\pi$
$251$	−1.71332	−	5.27307i	−0.108144	−	0.332833i	−0.990455	+	0.137833i	$0.955986\pi$
$252$		0			0
$253$	−3.21188	+	27.5327i	−0.201929	+	1.73097i
$254$	−23.1804			−1.45447
$255$		0			0
$256$	−16.9451	−	12.3113i	−1.05907	−	0.769457i
$257$	−15.3260	+	11.1350i	−0.956008	+	0.694580i	−0.952220	−	0.305413i	$-0.901206\pi$
$257$	−15.3260	+	11.1350i	−0.956008	+	0.694580i	−0.00378765	+	0.999993i	$0.501206\pi$
$258$		0			0
$259$	−0.605607	+	1.86387i	−0.0376306	+	0.115815i
$260$	−5.80067	+	4.21443i	−0.359742	+	0.261368i
$261$		0			0
$262$	−0.547722	−	1.68571i	−0.0338384	−	0.104144i
$263$	−3.20873			−0.197859			−0.0989293	−	0.995094i	$-0.531542\pi$
$263$	−3.20873			−0.197859			−0.0989293	+	0.995094i	$0.531542\pi$
$264$		0			0
$265$	1.67088			0.102641
$266$	−5.93355	−	18.2616i	−0.363809	−	1.11969i
$267$		0			0
$268$	−0.379466	+	0.275698i	−0.0231796	+	0.0168409i
$269$	1.00252	−	3.08544i	0.0611248	−	0.188123i	−0.915831	−	0.401563i	$-0.868467\pi$
$269$	1.00252	−	3.08544i	0.0611248	−	0.188123i	0.976956	+	0.213441i	$0.0684669\pi$
$270$		0			0
$271$	1.64212	−	1.19307i	0.0997517	−	0.0724738i	−0.536791	−	0.843715i	$-0.680364\pi$
$271$	1.64212	−	1.19307i	0.0997517	−	0.0724738i	0.636543	+	0.771241i	$0.280364\pi$
$272$	−28.9747	−	21.0514i	−1.75685	−	1.27643i
$273$		0			0
$274$	7.71096			0.465836
$275$	−2.24724	+	2.43925i	−0.135514	+	0.147092i
$276$		0			0
$277$	3.49701	+	10.7627i	0.210115	+	0.646668i	0.999464	+	0.0327234i	$0.0104180\pi$
$277$	3.49701	+	10.7627i	0.210115	+	0.646668i	−0.789349	+	0.613944i	$0.789582\pi$
$278$	13.0793	+	9.50268i	0.784446	+	0.569933i
$279$		0			0
$280$	−0.652802	+	2.00912i	−0.0390124	+	0.120068i
$281$	3.18835	−	9.81272i	0.190201	−	0.585378i	−0.809798	−	0.586708i	$-0.800424\pi$
$281$	3.18835	−	9.81272i	0.190201	−	0.585378i	0.999999	+	0.00133051i	$0.000423516\pi$
$282$		0			0
$283$	1.70370	+	1.23781i	0.101274	+	0.0735801i	0.637270	−	0.770641i	$-0.280064\pi$
$283$	1.70370	+	1.23781i	0.101274	+	0.0735801i	−0.535996	+	0.844221i	$0.680064\pi$
$284$	−1.87674	−	5.77602i	−0.111364	−	0.342744i
$285$		0			0
$286$	15.9113	+	28.3003i	0.940858	+	1.67343i
$287$	6.39459			0.377461
$288$		0			0
$289$	−29.7227	−	21.5948i	−1.74839	−	1.27028i
$290$	8.18625	−	5.94766i	0.480713	−	0.349259i
$291$		0			0
$292$	4.19315	−	12.9052i	0.245386	−	0.755220i
$293$	−18.9111	+	13.7398i	−1.10480	+	0.802685i	−0.981837	−	0.189726i	$-0.939240\pi$
$293$	−18.9111	+	13.7398i	−1.10480	+	0.802685i	−0.122964	+	0.992411i	$0.539240\pi$
$294$		0			0
$295$	1.75006	+	5.38614i	0.101893	+	0.313593i
$296$	−1.35614			−0.0788238
$297$		0			0
$298$	17.4552			1.01115
$299$	13.8372	+	42.5867i	0.800228	+	2.46285i
$300$		0			0
$301$	2.78398	−	2.02268i	0.160466	−	0.116585i
$302$	3.81196	−	11.7320i	0.219353	−	0.675100i
$303$		0			0
$304$	23.7735	−	17.2725i	1.36351	−	0.990645i
$305$	7.50749	+	5.45451i	0.429878	+	0.312325i
$306$		0			0
$307$	−32.0518			−1.82929			−0.914646	−	0.404256i	$-0.867531\pi$
$307$	−32.0518			−1.82929			−0.914646	+	0.404256i	$0.867531\pi$
$308$	−7.04821	−	3.23494i	−0.401609	−	0.184328i
$309$		0			0
$310$	−0.0120623	−	0.0371239i	−0.000685091	−	0.00210849i
$311$	1.32220	+	0.960634i	0.0749751	+	0.0544726i	0.624641	−	0.780912i	$-0.285245\pi$
$311$	1.32220	+	0.960634i	0.0749751	+	0.0544726i	−0.549666	+	0.835384i	$0.685245\pi$
$312$		0			0
$313$	9.39813	−	28.9245i	0.531214	−	1.63491i	−0.220477	−	0.975392i	$-0.570761\pi$
$313$	9.39813	−	28.9245i	0.531214	−	1.63491i	0.751691	−	0.659516i	$-0.229239\pi$
$314$	7.14811	−	21.9996i	0.403391	−	1.24151i
$315$		0			0
$316$	−2.77599	−	2.01688i	−0.156162	−	0.113458i
$317$	9.09561	+	27.9934i	0.510861	+	1.57227i	0.790690	+	0.612217i	$0.209722\pi$
$317$	9.09561	+	27.9934i	0.510861	+	1.57227i	−0.279829	+	0.960050i	$0.590278\pi$
$318$		0			0
$319$	−9.00190	−	16.0110i	−0.504010	−	0.896443i
$320$	2.12007			0.118515
$321$		0			0
$322$	−21.5853	−	15.6826i	−1.20290	−	0.873958i
$323$	35.6717	−	25.9170i	1.98482	−	1.44206i
$324$		0			0
$325$	−1.65563	+	5.09549i	−0.0918376	+	0.282647i
$326$	−34.5972	+	25.1363i	−1.91616	+	1.39217i
$327$		0			0
$328$	1.36738	+	4.20837i	0.0755010	+	0.232368i
$329$	−6.67364			−0.367929
$330$		0			0
$331$	−22.7902			−1.25266			−0.626332	−	0.779557i	$-0.715444\pi$
$331$	−22.7902			−1.25266			−0.626332	+	0.779557i	$0.715444\pi$
$332$	6.65002	+	20.4666i	0.364967	+	1.12325i
$333$		0			0
$334$	−4.51117	+	3.27756i	−0.246840	+	0.179340i
$335$	−0.108307	+	0.333334i	−0.00591744	+	0.0182120i
$336$		0			0
$337$	11.7227	−	8.51705i	0.638577	−	0.463954i	−0.220784	−	0.975323i	$-0.570862\pi$
$337$	11.7227	−	8.51705i	0.638577	−	0.463954i	0.859361	+	0.511369i	$0.170862\pi$
$338$	23.2145	+	16.8663i	1.26270	+	0.917406i
$339$		0			0
$340$	9.81040			0.532043
$341$	−0.0694723	+	0.0139401i	−0.00376213	+	0.000754899i
$342$		0			0
$343$	−5.91066	−	18.1911i	−0.319146	−	0.982229i
$344$	1.92646	+	1.39966i	0.103868	+	0.0754644i
$345$		0			0
$346$	9.03783	−	27.8156i	0.485877	−	1.49537i
$347$	−1.35574	+	4.17255i	−0.0727802	+	0.223994i	−0.980829	−	0.194870i	$-0.937572\pi$
$347$	−1.35574	+	4.17255i	−0.0727802	+	0.223994i	0.908049	+	0.418864i	$0.137572\pi$
$348$		0			0
$349$	−11.6548	−	8.46769i	−0.623866	−	0.453265i	0.230404	−	0.973095i	$-0.425995\pi$
$349$	−11.6548	−	8.46769i	−0.623866	−	0.453265i	−0.854270	+	0.519830i	$0.825995\pi$
$350$	−0.986494	−	3.03612i	−0.0527303	−	0.162287i
$351$		0			0
$352$	2.50114	−	21.4401i	0.133311	−	1.14276i
$353$	6.01065			0.319914			0.159957	−	0.987124i	$-0.448864\pi$
$353$	6.01065			0.319914			0.159957	+	0.987124i	$0.448864\pi$
$354$		0			0
$355$	−3.67147	−	2.66748i	−0.194861	−	0.141575i
$356$	−15.7055	+	11.4107i	−0.832389	+	0.604766i
$357$		0			0
$358$	−10.8963	+	33.5354i	−0.575888	+	1.77240i
$359$	−1.98787	+	1.44428i	−0.104916	+	0.0762259i	−0.639006	−	0.769201i	$-0.720654\pi$
$359$	−1.98787	+	1.44428i	−0.104916	+	0.0762259i	0.534090	+	0.845427i	$0.320654\pi$
$360$		0			0
$361$	5.30818	+	16.3369i	0.279378	+	0.859836i
$362$	22.2742			1.17070
$363$		0			0
$364$	−12.5277			−0.656632
$365$	−3.13328	−	9.64326i	−0.164004	−	0.504751i
$366$		0			0
$367$	−1.19726	+	0.869862i	−0.0624966	+	0.0454064i	−0.618595	−	0.785710i	$-0.712298\pi$
$367$	−1.19726	+	0.869862i	−0.0624966	+	0.0454064i	0.556098	+	0.831116i	$0.312298\pi$
$368$	12.6179	−	38.8338i	0.657752	−	2.02435i
$369$		0			0
$370$	1.65796	−	1.20458i	0.0861933	−	0.0626231i
$371$	2.36186	+	1.71599i	0.122622	+	0.0890898i
$372$		0			0
$373$	−24.3331			−1.25992			−0.629961	−	0.776627i	$-0.716929\pi$
$373$	−24.3331			−1.25992			−0.629961	+	0.776627i	$0.716929\pi$
$374$	5.14728	−	44.1232i	0.266159	−	2.28156i
$375$		0			0
$376$	−1.42705	−	4.39201i	−0.0735945	−	0.226501i
$377$	−24.0052	−	17.4408i	−1.23633	−	0.898245i
$378$		0			0
$379$	4.92299	−	15.1514i	0.252877	−	0.778276i	−0.741363	−	0.671104i	$-0.765820\pi$
$379$	4.92299	−	15.1514i	0.252877	−	0.778276i	0.994241	−	0.107172i	$-0.0341795\pi$
$380$	−2.48739	+	7.65539i	−0.127600	+	0.392713i
$381$		0			0
$382$	19.8432	+	14.4169i	1.01527	+	0.737634i
$383$	1.21133	+	3.72809i	0.0618960	+	0.190496i	0.977223	−	0.212215i	$-0.0680678\pi$
$383$	1.21133	+	3.72809i	0.0618960	+	0.190496i	−0.915327	+	0.402712i	$0.868068\pi$
$384$		0			0
$385$	−5.68168	+	1.14007i	−0.289565	+	0.0581033i
$386$	−13.8454			−0.704710
$387$		0			0
$388$	2.05678	+	1.49434i	0.104417	+	0.0758635i
$389$	−28.5510	+	20.7435i	−1.44759	+	1.05174i	−0.461209	+	0.887292i	$0.652584\pi$
$389$	−28.5510	+	20.7435i	−1.44759	+	1.05174i	−0.986386	+	0.164447i	$0.947416\pi$
$390$		0			0
$391$	18.9328	−	58.2693i	0.957475	−	2.94680i
$392$	3.86090	−	2.80511i	0.195005	−	0.141679i
$393$		0			0
$394$	−3.89078	−	11.9746i	−0.196015	−	0.603271i
$395$	−2.56401			−0.129009
$396$		0			0
$397$	23.2231			1.16553			0.582767	−	0.812639i	$-0.301970\pi$
$397$	23.2231			1.16553			0.582767	+	0.812639i	$0.301970\pi$
$398$	−0.361006	−	1.11106i	−0.0180956	−	0.0556925i
$399$		0			0
$400$	3.95252	−	2.87167i	0.197626	−	0.143584i
$401$	−1.75973	+	5.41589i	−0.0878766	+	0.270457i	−0.985332	−	0.170649i	$-0.945414\pi$
$401$	−1.75973	+	5.41589i	−0.0878766	+	0.270457i	0.897455	+	0.441106i	$0.145414\pi$
$402$		0			0
$403$	−0.0926028	+	0.0672799i	−0.00461287	+	0.00335145i
$404$	7.26488	+	5.27824i	0.361441	+	0.262602i
$405$		0			0
$406$	17.6799			0.877438
$407$	−1.82315	−	3.24270i	−0.0903704	−	0.160735i
$408$		0			0
$409$	7.86540	+	24.2072i	0.388919	+	1.19697i	0.933597	+	0.358324i	$0.116652\pi$
$409$	7.86540	+	24.2072i	0.388919	+	1.19697i	−0.544679	+	0.838645i	$0.683348\pi$
$410$	−5.40977	−	3.93043i	−0.267169	−	0.194110i
$411$		0			0
$412$	−1.75624	+	5.40515i	−0.0865237	+	0.266292i
$413$	−3.05777	+	9.41086i	−0.150463	+	0.463078i
$414$		0			0
$415$	13.0094	+	9.45188i	0.638606	+	0.463975i
$416$	−10.7753	−	33.1629i	−0.528301	−	1.62594i
$417$		0			0
$418$	33.1258	+	15.2039i	1.62023	+	0.743645i
$419$	13.4850			0.658786			0.329393	−	0.944193i	$-0.393156\pi$
$419$	13.4850			0.658786			0.329393	+	0.944193i	$0.393156\pi$
$420$		0			0
$421$	−2.38633	−	1.73377i	−0.116303	−	0.0844990i	0.528113	−	0.849174i	$-0.322900\pi$
$421$	−2.38633	−	1.73377i	−0.116303	−	0.0844990i	−0.644416	+	0.764675i	$0.722900\pi$
$422$	−5.64872	+	4.10404i	−0.274975	+	0.199781i
$423$		0			0
$424$	−0.624271	+	1.92131i	−0.0303173	+	0.0933070i
$425$	5.93066	−	4.30888i	0.287679	−	0.209011i
$426$		0			0
$427$	5.01039	+	15.4204i	0.242470	+	0.746246i
$428$	21.0415			1.01708
$429$		0			0
$430$	−3.59845			−0.173533
$431$	−3.56072	−	10.9588i	−0.171514	−	0.527866i	0.827943	−	0.560812i	$-0.189511\pi$
$431$	−3.56072	−	10.9588i	−0.171514	−	0.527866i	−0.999457	+	0.0329464i	$0.989511\pi$
$432$		0			0
$433$	−9.03174	+	6.56194i	−0.434038	+	0.315347i	−0.783261	−	0.621693i	$-0.786445\pi$
$433$	−9.03174	+	6.56194i	−0.434038	+	0.315347i	0.349224	+	0.937039i	$0.386445\pi$
$434$	0.0210757	−	0.0648642i	0.00101166	−	0.00311358i
$435$		0			0
$436$	−4.58941	+	3.33440i	−0.219793	+	0.159689i
$437$	40.6692	+	29.5479i	1.94547	+	1.41347i
$438$		0			0
$439$	0.993624			0.0474231			0.0237115	−	0.999719i	$-0.492452\pi$
$439$	0.993624			0.0474231			0.0237115	+	0.999719i	$0.492452\pi$
$440$	−1.96523	−	3.49541i	−0.0936888	−	0.166637i
$441$		0			0
$442$	−22.1752	−	68.2483i	−1.05477	−	3.24624i
$443$	−8.88506	−	6.45537i	−0.422142	−	0.306704i	0.356357	−	0.934350i	$-0.384019\pi$
$443$	−8.88506	−	6.45537i	−0.422142	−	0.306704i	−0.778499	+	0.627646i	$0.784019\pi$
$444$		0			0
$445$	−4.48265	+	13.7962i	−0.212498	+	0.654002i
$446$	15.0863	−	46.4307i	0.714355	−	2.19856i
$447$		0			0
$448$	2.99681	+	2.17731i	0.141586	+	0.102868i
$449$	−8.96777	−	27.5999i	−0.423215	−	1.30252i	−0.904693	−	0.426064i	$-0.859900\pi$
$449$	−8.96777	−	27.5999i	−0.423215	−	1.30252i	0.481478	−	0.876458i	$-0.340100\pi$
$450$		0			0
$451$	−8.22451	+	8.92722i	−0.387277	+	0.420366i
$452$	9.63070			0.452990
$453$		0			0
$454$	−18.0886	−	13.1421i	−0.848938	−	0.616790i
$455$	−7.57337	+	5.50238i	−0.355045	+	0.257955i
$456$		0			0
$457$	−1.09908	+	3.38262i	−0.0514129	+	0.158232i	−0.973466	−	0.228830i	$-0.926510\pi$
$457$	−1.09908	+	3.38262i	−0.0514129	+	0.158232i	0.922054	+	0.387062i	$0.126510\pi$
$458$	−9.88383	+	7.18103i	−0.461841	+	0.335547i
$459$		0			0
$460$	3.45630	+	10.6374i	0.161151	+	0.495971i
$461$	−25.1829			−1.17288			−0.586441	−	0.809992i	$-0.699472\pi$
$461$	−25.1829			−1.17288			−0.586441	+	0.809992i	$0.699472\pi$
$462$		0			0
$463$	−17.8743			−0.830690			−0.415345	−	0.909664i	$-0.636339\pi$
$463$	−17.8743			−0.830690			−0.415345	+	0.909664i	$0.636339\pi$
$464$	8.36114	+	25.7329i	0.388156	+	1.19462i
$465$		0			0
$466$	9.63371	−	6.99930i	0.446273	−	0.324236i
$467$	7.79502	−	23.9906i	0.360711	−	1.11015i	−0.591913	−	0.806002i	$-0.701627\pi$
$467$	7.79502	−	23.9906i	0.360711	−	1.11015i	0.952624	−	0.304151i	$-0.0983729\pi$
$468$		0			0
$469$	−0.495432	+	0.359952i	−0.0228769	+	0.0166210i
$470$	5.64583	+	4.10194i	0.260423	+	0.189208i
$471$		0			0
$472$	−6.84727			−0.315171
$473$	−0.756881	+	6.48809i	−0.0348014	+	0.298323i
$474$		0			0
$475$	1.85867	+	5.72040i	0.0852816	+	0.262470i
$476$	13.8674	+	10.0753i	0.635613	+	0.461800i
$477$		0			0
$478$	−6.12135	+	18.8396i	−0.279984	+	0.861702i
$479$	1.61793	−	4.97948i	0.0739252	−	0.227518i	−0.907266	−	0.420558i	$-0.861834\pi$
$479$	1.61793	−	4.97948i	0.0739252	−	0.227518i	0.981191	+	0.193039i	$0.0618345\pi$
$480$		0			0
$481$	−4.86176	−	3.53228i	−0.221677	−	0.161058i
$482$	−15.3461	−	47.2304i	−0.698995	−	2.15128i
$483$		0			0
$484$	13.5813	−	5.67904i	0.617333	−	0.258138i
$485$	1.89972			0.0862617
$486$		0			0
$487$	−7.31762	−	5.31656i	−0.331593	−	0.240917i	0.409513	−	0.912304i	$-0.365699\pi$
$487$	−7.31762	−	5.31656i	−0.331593	−	0.240917i	−0.741106	+	0.671388i	$0.765699\pi$
$488$	−9.07699	+	6.59482i	−0.410896	+	0.298533i
$489$		0			0
$490$	−2.22857	+	6.85885i	−0.100677	+	0.309851i
$491$	−28.1629	+	20.4615i	−1.27097	+	0.923416i	−0.999241	−	0.0389565i	$-0.987597\pi$
$491$	−28.1629	+	20.4615i	−1.27097	+	0.923416i	−0.271733	+	0.962373i	$0.587597\pi$
$492$		0			0
$493$	12.5457	+	38.6117i	0.565030	+	1.73898i
$494$	58.8789			2.64909
$495$		0			0
$496$	0.104377			0.00468664
$497$	−2.45028	−	7.54120i	−0.109910	−	0.338269i
$498$		0			0
$499$	−15.8561	+	11.5201i	−0.709815	+	0.515711i	−0.883114	−	0.469158i	$-0.844557\pi$
$499$	−15.8561	+	11.5201i	−0.709815	+	0.515711i	0.173299	+	0.984869i	$0.444557\pi$
$500$	−0.413545	+	1.27276i	−0.0184943	+	0.0569196i
$501$		0			0
$502$	−8.19549	+	5.95437i	−0.365783	+	0.265757i
$503$	14.8989	+	10.8247i	0.664307	+	0.482647i	0.868115	−	0.496364i	$-0.165332\pi$
$503$	14.8989	+	10.8247i	0.664307	+	0.482647i	−0.203808	+	0.979011i	$0.565332\pi$
$504$		0			0
$505$	6.71011			0.298596
$506$	49.6561	−	9.96384i	2.20748	−	0.442947i
$507$		0			0
$508$	5.24667	+	16.1476i	0.232783	+	0.716433i
$509$	1.00187	+	0.727900i	0.0444070	+	0.0322636i	0.609767	−	0.792580i	$-0.291263\pi$
$509$	1.00187	+	0.727900i	0.0444070	+	0.0322636i	−0.565360	+	0.824844i	$0.691263\pi$
$510$		0			0
$511$	5.47459	−	16.8491i	0.242182	−	0.745359i
$512$	−6.17504	+	19.0048i	−0.272901	+	0.839902i
$513$		0			0
$514$	28.0019	+	20.3446i	1.23511	+	0.897362i
$515$	1.31233	+	4.03893i	0.0578281	+	0.177977i
$516$		0			0
$517$	8.58340	−	9.31678i	0.377498	−	0.409752i
$518$	3.58071			0.157327
$519$		0			0
$520$	−5.24064	−	3.80755i	−0.229817	−	0.166972i
$521$	26.8472	−	19.5057i	1.17620	−	0.854558i	0.184461	−	0.982840i	$-0.440946\pi$
$521$	26.8472	−	19.5057i	1.17620	−	0.854558i	0.991738	+	0.128282i	$0.0409462\pi$
$522$		0			0
$523$	4.06383	−	12.5072i	0.177699	−	0.546901i	−0.822047	−	0.569419i	$-0.807168\pi$
$523$	4.06383	−	12.5072i	0.177699	−	0.546901i	0.999746	+	0.0225177i	$0.00716820\pi$
$524$	−1.05031	+	0.763092i	−0.0458829	+	0.0333359i
$525$		0			0
$526$	1.81165	+	5.57570i	0.0789919	+	0.243112i
$527$	0.156615			0.00682224
$528$		0			0
$529$	46.8514			2.03702
$530$	−0.943380	−	2.90342i	−0.0409778	−	0.126117i
$531$		0			0
$532$	−11.3781	+	8.26669i	−0.493304	+	0.358407i
$533$	−6.05930	+	18.6486i	−0.262458	+	0.807761i
$534$		0			0
$535$	12.7202	−	9.24174i	0.549941	−	0.399555i
$536$	−0.342830	−	0.249080i	−0.0148080	−	0.0107586i
$537$		0			0
$538$	−5.92750			−0.255553
$539$	11.8979	+	5.46082i	0.512479	+	0.235214i
$540$		0			0
$541$	10.0900	+	31.0538i	0.433802	+	1.33511i	0.894309	+	0.447450i	$0.147668\pi$
$541$	10.0900	+	31.0538i	0.433802	+	1.33511i	−0.460507	+	0.887656i	$0.652332\pi$
$542$	−3.00030	−	2.17985i	−0.128874	−	0.0936324i
$543$		0			0
$544$	−14.7433	+	45.3752i	−0.632114	+	1.94545i
$545$	−1.30991	+	4.03149i	−0.0561103	+	0.172690i
$546$		0			0
$547$	−22.4136	−	16.2845i	−0.958338	−	0.696273i	−0.00557389	−	0.999984i	$-0.501774\pi$
$547$	−22.4136	−	16.2845i	−0.958338	−	0.696273i	−0.952764	+	0.303711i	$0.901774\pi$
$548$	−1.74531	−	5.37150i	−0.0745558	−	0.229459i
$549$		0			0
$550$	5.50739	+	2.52775i	0.234836	+	0.107784i
$551$	−33.3110			−1.41909
$552$		0			0
$553$	−3.62435	−	2.63324i	−0.154123	−	0.111977i
$554$	16.7276	−	12.1533i	0.710686	−	0.516343i
$555$		0			0
$556$	3.65924	−	11.2620i	0.155186	−	0.477614i
$557$	−18.9514	+	13.7690i	−0.802996	+	0.583411i	−0.911792	−	0.410653i	$-0.865301\pi$
$557$	−18.9514	+	13.7690i	−0.802996	+	0.583411i	0.108795	+	0.994064i	$0.465301\pi$
$558$		0			0
$559$	3.26075	+	10.0356i	0.137915	+	0.424459i
$560$	8.53627			0.360723
$561$		0			0
$562$	−18.8514			−0.795198
$563$	−6.82482	−	21.0046i	−0.287632	−	0.885240i	−0.985597	−	0.169108i	$-0.945911\pi$
$563$	−6.82482	−	21.0046i	−0.287632	−	0.885240i	0.697966	−	0.716131i	$-0.254089\pi$
$564$		0			0
$565$	5.82203	−	4.22996i	0.244935	−	0.177956i
$566$	1.18899	−	3.65933i	0.0499769	−	0.153813i
$567$		0			0
$568$	4.43901	−	3.22513i	0.186257	−	0.135323i
$569$	−11.1119	−	8.07328i	−0.465836	−	0.338449i	0.329980	−	0.943988i	$-0.392958\pi$
$569$	−11.1119	−	8.07328i	−0.465836	−	0.338449i	−0.795816	+	0.605538i	$0.792958\pi$
$570$		0			0
$571$	−26.5201			−1.10983			−0.554915	−	0.831907i	$-0.687249\pi$
$571$	−26.5201			−1.10983			−0.554915	+	0.831907i	$0.687249\pi$
$572$	16.1127	−	17.4894i	0.673708	−	0.731271i
$573$		0			0
$574$	−3.61040	−	11.1117i	−0.150695	−	0.463792i
$575$	6.76153	+	4.91254i	0.281975	+	0.204867i
$576$		0			0
$577$	1.75758	−	5.40927i	0.0731690	−	0.225191i	−0.907783	−	0.419439i	$-0.862227\pi$
$577$	1.75758	−	5.40927i	0.0731690	−	0.225191i	0.980952	+	0.194248i	$0.0622267\pi$
$578$	−20.7430	+	63.8405i	−0.862797	+	2.65542i
$579$		0			0
$580$	−5.99606	−	4.35639i	−0.248973	−	0.180889i
$581$	8.68228	+	26.7213i	0.360202	+	1.10859i
$582$		0			0
$583$	−5.43336	+	1.09024i	−0.225027	+	0.0451532i
$584$	12.2593			0.507292
$585$		0			0
$586$	34.5524	+	25.1038i	1.42735	+	1.03703i
$587$	10.9590	−	7.96215i	0.452324	−	0.328633i	−0.338188	−	0.941078i	$-0.609814\pi$
$587$	10.9590	−	7.96215i	0.452324	−	0.328633i	0.790513	+	0.612446i	$0.209814\pi$
$588$		0			0
$589$	−0.0397090	+	0.122212i	−0.00163618	+	0.00503565i
$590$	8.37122	−	6.08205i	0.344638	−	0.250394i
$591$		0			0
$592$	1.69338	+	5.21169i	0.0695975	+	0.214199i
$593$	−21.1786			−0.869702			−0.434851	−	0.900502i	$-0.643199\pi$
$593$	−21.1786			−0.869702			−0.434851	+	0.900502i	$0.643199\pi$
$594$		0			0
$595$	12.8085			0.525097
$596$	−3.95083	−	12.1594i	−0.161833	−	0.498069i
$597$		0			0
$598$	66.1889	−	48.0890i	2.70666	−	1.96651i
$599$	10.4573	−	32.1842i	0.427273	−	1.31501i	−0.473529	−	0.880778i	$-0.657020\pi$
$599$	10.4573	−	32.1842i	0.427273	−	1.31501i	0.900801	−	0.434231i	$-0.142980\pi$
$600$		0			0
$601$	−23.7186	+	17.2325i	−0.967500	+	0.702930i	−0.954880	−	0.296990i	$-0.904017\pi$
$601$	−23.7186	+	17.2325i	−0.967500	+	0.702930i	−0.0126196	+	0.999920i	$0.504017\pi$
$602$	−5.08658	−	3.69562i	−0.207313	−	0.150622i
$603$		0			0
$604$	−9.03538			−0.367644
$605$	5.71598	−	9.39827i	0.232388	−	0.382094i
$606$		0			0
$607$	2.21715	+	6.82370i	0.0899915	+	0.276965i	0.985916	−	0.167241i	$-0.0534857\pi$
$607$	2.21715	+	6.82370i	0.0899915	+	0.276965i	−0.895925	+	0.444206i	$0.853486\pi$
$608$	−31.6697	−	23.0094i	−1.28438	−	0.933154i
$609$		0			0
$610$	5.23938	−	16.1252i	0.212136	−	0.652888i
$611$	6.32372	−	19.4624i	0.255830	−	0.787364i
$612$		0			0
$613$	22.2515	+	16.1667i	0.898731	+	0.652967i	0.938140	−	0.346257i	$-0.112547\pi$
$613$	22.2515	+	16.1667i	0.898731	+	0.652967i	−0.0394084	+	0.999223i	$0.512547\pi$
$614$	18.0965	+	55.6953i	0.730315	+	2.24768i
$615$		0			0
$616$	0.811840	−	6.95921i	0.0327100	−	0.280395i
$617$	−24.0712			−0.969068			−0.484534	−	0.874772i	$-0.661011\pi$
$617$	−24.0712			−0.969068			−0.484534	+	0.874772i	$0.661011\pi$
$618$		0			0
$619$	−21.8216	−	15.8543i	−0.877083	−	0.637238i	0.0553955	−	0.998464i	$-0.482358\pi$
$619$	−21.8216	−	15.8543i	−0.877083	−	0.637238i	−0.932478	+	0.361227i	$0.882358\pi$
$620$	−0.0231305	+	0.0168053i	−0.000928944	+	0.000674917i
$621$		0			0
$622$	0.922745	−	2.83992i	0.0369987	−	0.113870i
$623$	−20.5051	+	14.8978i	−0.821521	+	0.596870i
$624$		0			0
$625$	0.309017	+	0.951057i	0.0123607	+	0.0380423i
$626$	−55.5673			−2.22092
$627$		0			0
$628$	−16.9430			−0.676098
$629$	2.54088	+	7.82003i	0.101312	+	0.311805i
$630$		0			0
$631$	−7.87681	+	5.72284i	−0.313571	+	0.227823i	−0.733427	−	0.679768i	$-0.762080\pi$
$631$	−7.87681	+	5.72284i	−0.313571	+	0.227823i	0.419856	+	0.907591i	$0.362080\pi$
$632$	0.957964	−	2.94831i	0.0381058	−	0.117277i
$633$		0			0
$634$	43.5078	−	31.6103i	1.72792	−	1.25540i
$635$	10.2640	+	7.45726i	0.407316	+	0.295932i
$636$		0			0
$637$	21.1478			0.837904
$638$	−22.7393	+	24.6821i	−0.900256	+	0.977175i
$639$		0			0
$640$	2.82535	+	8.69552i	0.111682	+	0.343721i
$641$	20.3196	+	14.7631i	0.802577	+	0.583107i	0.911669	−	0.410925i	$-0.134794\pi$
$641$	20.3196	+	14.7631i	0.802577	+	0.583107i	−0.109092	+	0.994032i	$0.534794\pi$
$642$		0			0
$643$	−8.32051	+	25.6079i	−0.328129	+	1.00988i	0.641880	+	0.766806i	$0.278155\pi$
$643$	−8.32051	+	25.6079i	−0.328129	+	1.00988i	−0.970008	+	0.243071i	$0.921845\pi$
$644$	−6.03897	+	18.5860i	−0.237969	+	0.732393i
$645$		0			0
$646$	−65.1754	−	47.3527i	−2.56429	−	1.86307i
$647$	8.28198	+	25.4893i	0.325598	+	1.00209i	0.971170	+	0.238389i	$0.0766192\pi$
$647$	8.28198	+	25.4893i	0.325598	+	1.00209i	−0.645572	+	0.763700i	$0.723381\pi$
$648$		0			0
$649$	−9.20530	−	16.3728i	−0.361340	−	0.642687i
$650$	9.78903			0.383957
$651$		0			0
$652$	25.3409	+	18.4112i	0.992425	+	0.721039i
$653$	23.2700	−	16.9066i	0.910625	−	0.661608i	−0.0305480	−	0.999533i	$-0.509725\pi$
$653$	23.2700	−	16.9066i	0.910625	−	0.661608i	0.941173	+	0.337926i	$0.109725\pi$
$654$		0			0
$655$	−0.299778	+	0.922622i	−0.0117133	+	0.0360498i
$656$	14.4655	−	10.5098i	0.564784	−	0.410340i
$657$		0			0
$658$	3.76795	+	11.5966i	0.146890	+	0.452081i
$659$	−36.5327			−1.42311			−0.711556	−	0.702629i	$-0.752009\pi$
$659$	−36.5327			−1.42311			−0.711556	+	0.702629i	$0.752009\pi$
$660$		0			0
$661$	−35.7750			−1.39149			−0.695743	−	0.718291i	$-0.744925\pi$
$661$	−35.7750			−1.39149			−0.695743	+	0.718291i	$0.744925\pi$
$662$	12.8674	+	39.6018i	0.500106	+	1.53917i
$663$		0			0
$664$	−15.7291	+	11.4279i	−0.610408	+	0.443487i
$665$	−3.24754	+	9.99490i	−0.125934	+	0.387586i
$666$		0			0
$667$	−37.4466	+	27.2065i	−1.44994	+	1.05344i
$668$	3.30423	+	2.40066i	0.127844	+	0.0928844i
$669$		0			0
$670$	0.640375			0.0247398
$671$	−27.9720	−	12.8384i	−1.07985	−	0.495621i
$672$		0			0
$673$	−3.48925	−	10.7388i	−0.134501	−	0.413951i	0.861011	−	0.508586i	$-0.169832\pi$
$673$	−3.48925	−	10.7388i	−0.134501	−	0.413951i	−0.995512	+	0.0946349i	$0.969832\pi$
$674$	−21.4185	−	15.5614i	−0.825009	−	0.599404i
$675$		0			0
$676$	6.49478	−	19.9889i	0.249799	−	0.768803i
$677$	13.5527	−	41.7108i	0.520872	−	1.60308i	−0.251466	−	0.967866i	$-0.580913\pi$
$677$	13.5527	−	41.7108i	0.520872	−	1.60308i	0.772338	−	0.635212i	$-0.219087\pi$
$678$		0			0
$679$	2.68534	+	1.95101i	0.103054	+	0.0748729i
$680$	2.73889	+	8.42944i	0.105032	+	0.323254i
$681$		0			0
$682$	0.0634474	+	0.112849i	0.00242953	+	0.00432121i
$683$	18.5355			0.709241			0.354620	−	0.935010i	$-0.384610\pi$
$683$	18.5355			0.709241			0.354620	+	0.935010i	$0.384610\pi$
$684$		0			0
$685$	−3.41434	−	2.48066i	−0.130455	−	0.0947811i
$686$	−28.2730	+	20.5415i	−1.07947	+	0.784279i
$687$		0			0
$688$	2.97341	−	9.15120i	0.113360	−	0.348886i
$689$	−7.24238	+	5.26190i	−0.275913	+	0.200462i
$690$		0			0
$691$	−8.71597	−	26.8250i	−0.331571	−	1.02047i	−0.968386	−	0.249455i	$-0.919749\pi$
$691$	−8.71597	−	26.8250i	−0.331571	−	1.02047i	0.636815	−	0.771017i	$-0.280251\pi$
$692$	−21.4221			−0.814347
$693$		0			0
$694$	8.01596			0.304282
$695$	−2.73432	−	8.41538i	−0.103719	−	0.319214i
$696$		0			0
$697$	21.7052	−	15.7698i	0.822144	−	0.597322i
$698$	−8.13371	+	25.0330i	−0.307865	+	0.947512i
$699$		0			0
$700$	−1.89169	+	1.37440i	−0.0714993	+	0.0519473i
$701$	0.255153	+	0.185379i	0.00963699	+	0.00700168i	0.592593	−	0.805502i	$-0.298104\pi$
$701$	0.255153	+	0.185379i	0.00963699	+	0.00700168i	−0.582956	+	0.812503i	$0.698104\pi$
$702$		0			0
$703$	−6.74647			−0.254448
$704$	−6.89405	+	1.38334i	−0.259829	+	0.0521366i
$705$		0			0
$706$	−3.39362	−	10.4445i	−0.127721	−	0.393084i
$707$	9.48505	+	6.89129i	0.356722	+	0.259174i
$708$		0			0
$709$	12.0593	−	37.1146i	0.452895	−	1.39387i	−0.420693	−	0.907203i	$-0.638213\pi$
$709$	12.0593	−	37.1146i	0.452895	−	1.39387i	0.873589	−	0.486665i	$-0.161787\pi$
$710$	−2.56227	+	7.88585i	−0.0961602	+	0.295951i
$711$		0			0
$712$	−14.1892	−	10.3090i	−0.531762	−	0.386348i
$713$	0.0551768	+	0.169817i	0.00206639	+	0.00635969i
$714$		0			0
$715$	2.05898	−	17.6498i	0.0770014	−	0.660067i
$716$	25.8272			0.965209
$717$		0			0
$718$	3.63203	+	2.63882i	0.135546	+	0.0984800i
$719$	23.0320	−	16.7337i	0.858948	−	0.624062i	−0.0686507	−	0.997641i	$-0.521869\pi$
$719$	23.0320	−	16.7337i	0.858948	−	0.624062i	0.927598	+	0.373579i	$0.121869\pi$
$720$		0			0
$721$	−2.29295	+	7.05698i	−0.0853939	+	0.262816i
$722$	25.3911	−	18.4477i	0.944957	−	0.686552i
$723$		0			0
$724$	−5.04156	−	15.5163i	−0.187368	−	0.576659i
$725$	−5.53818			−0.205683
$726$		0			0
$727$	45.8400			1.70011			0.850057	−	0.526691i	$-0.176568\pi$
$727$	45.8400			1.70011			0.850057	+	0.526691i	$0.176568\pi$
$728$	−3.49753	−	10.7643i	−0.129627	−	0.398951i
$729$		0			0
$730$	−14.9877	+	10.8892i	−0.554720	+	0.403028i
$731$	4.46153	−	13.7312i	0.165016	−	0.507866i
$732$		0			0
$733$	−30.7169	+	22.3171i	−1.13455	+	0.824301i	−0.986351	−	0.164656i	$-0.947349\pi$
$733$	−30.7169	+	22.3171i	−1.13455	+	0.824301i	−0.148202	+	0.988957i	$0.547349\pi$
$734$	2.18751	+	1.58932i	0.0807423	+	0.0586627i
$735$		0			0
$736$	−54.3944			−2.00500
$737$	0.134693	−	1.15461i	0.00496149	−	0.0425306i
$738$		0			0
$739$	6.52725	+	20.0888i	0.240109	+	0.738979i	0.996403	+	0.0847466i	$0.0270081\pi$
$739$	6.52725	+	20.0888i	0.240109	+	0.738979i	−0.756294	+	0.654232i	$0.772992\pi$
$740$	−1.21438	−	0.882299i	−0.0446415	−	0.0324340i
$741$		0			0
$742$	1.64831	−	5.07298i	0.0605113	−	0.186235i
$743$	−2.46606	+	7.58976i	−0.0904711	+	0.278441i	−0.986047	−	0.166467i	$-0.946764\pi$
$743$	−2.46606	+	7.58976i	−0.0904711	+	0.278441i	0.895576	+	0.444909i	$0.146764\pi$
$744$		0			0
$745$	−7.72900	−	5.61545i	−0.283169	−	0.205734i
$746$	13.7385	+	42.2829i	0.503004	+	1.54809i
$747$		0			0
$748$	−31.9015	+	6.40126i	−1.16643	+	0.234053i
$749$	27.4718			1.00380
$750$		0			0
$751$	7.78664	+	5.65733i	0.284139	+	0.206439i	0.720721	−	0.693226i	$-0.243811\pi$
$751$	7.78664	+	5.65733i	0.284139	+	0.206439i	−0.436582	+	0.899664i	$0.643811\pi$
$752$	−15.0968	+	10.9684i	−0.550523	+	0.399978i
$753$		0			0
$754$	−16.7529	+	51.5600i	−0.610104	+	1.87771i
$755$	−5.46214	+	3.96848i	−0.198788	+	0.144428i
$756$		0			0
$757$	−14.4049	−	44.3338i	−0.523555	−	1.61134i	−0.767155	−	0.641462i	$-0.778328\pi$
$757$	−14.4049	−	44.3338i	−0.523555	−	1.61134i	0.243600	−	0.969876i	$-0.421672\pi$
$758$	−29.1076			−1.05724
$759$		0			0
$760$	−7.27222			−0.263791
$761$	6.79661	+	20.9178i	0.246377	+	0.758270i	0.995407	+	0.0957342i	$0.0305199\pi$
$761$	6.79661	+	20.9178i	0.246377	+	0.758270i	−0.749030	+	0.662536i	$0.769480\pi$
$762$		0			0
$763$	−5.99195	+	4.35341i	−0.216923	+	0.157604i
$764$	5.55158	−	17.0860i	0.200849	−	0.618151i
$765$		0			0
$766$	5.79425	−	4.20977i	0.209355	−	0.152105i
$767$	−24.5476	−	17.8348i	−0.886361	−	0.643979i
$768$		0			0
$769$	48.0330			1.73211			0.866057	−	0.499946i	$-0.166647\pi$
$769$	48.0330			1.73211			0.866057	+	0.499946i	$0.166647\pi$
$770$	5.18895	+	9.22918i	0.186997	+	0.332597i
$771$		0			0
$772$	3.13377	+	9.64476i	0.112787	+	0.347123i
$773$	−13.8222	−	10.0424i	−0.497148	−	0.361199i	0.310778	−	0.950482i	$-0.399410\pi$
$773$	−13.8222	−	10.0424i	−0.497148	−	0.361199i	−0.807927	+	0.589283i	$0.799410\pi$
$774$		0			0
$775$	−0.00660190	+	0.0203186i	−0.000237147	+	0.000729864i
$776$	−0.709771	+	2.18445i	−0.0254793	+	0.0784172i
$777$		0			0
$778$	52.1653	+	37.9003i	1.87022	+	1.35879i
$779$	6.80242	+	20.9357i	0.243722	+	0.750099i
$780$		0			0
$781$	13.6794	+	6.27849i	0.489488	+	0.224662i
$782$	−111.942			−4.00304
$783$		0			0
$784$	−15.6012	−	11.3349i	−0.557186	−	0.404819i
$785$	−10.2425	+	7.44162i	−0.365571	+	0.265603i
$786$		0			0
$787$	−6.95034	+	21.3910i	−0.247753	+	0.762505i	0.747418	+	0.664354i	$0.231293\pi$
$787$	−6.95034	+	21.3910i	−0.247753	+	0.762505i	−0.995171	+	0.0981518i	$0.968707\pi$
$788$	−7.46092	+	5.42068i	−0.265784	+	0.193104i
$789$		0			0
$790$	1.44765	+	4.45540i	0.0515050	+	0.158516i
$791$	12.5739			0.447076
$792$		0			0
$793$	−49.7184			−1.76555
$794$	−13.1118	−	40.3540i	−0.465321	−	1.43211i
$795$		0			0
$796$	−0.692261	+	0.502957i	−0.0245365	+	0.0178268i
$797$	1.05615	−	3.25051i	0.0374109	−	0.115139i	−0.930607	−	0.366020i	$-0.880720\pi$
$797$	1.05615	−	3.25051i	0.0374109	−	0.115139i	0.968018	+	0.250881i	$0.0807203\pi$
$798$		0			0
$799$	−22.6524	+	16.4579i	−0.801383	+	0.582239i
$800$	−5.26531	−	3.82547i	−0.186157	−	0.135251i
$801$		0			0
$802$	10.4046			0.367398
$803$	16.4810	+	29.3135i	0.581603	+	1.03445i
$804$		0			0
$805$	4.51255	+	13.8882i	0.159047	+	0.489495i
$806$	0.169194	+	0.122926i	0.00595959	+	0.00432990i
$807$		0			0
$808$	−2.50703	+	7.71584i	−0.0881969	+	0.271442i
$809$	3.12679	−	9.62328i	0.109932	−	0.338336i	−0.880924	−	0.473257i	$-0.843078\pi$
$809$	3.12679	−	9.62328i	0.109932	−	0.338336i	0.990856	+	0.134921i	$0.0430781\pi$
$810$		0			0
$811$	−20.5287	−	14.9150i	−0.720862	−	0.523737i	0.165798	−	0.986160i	$-0.446980\pi$
$811$	−20.5287	−	14.9150i	−0.720862	−	0.523737i	−0.886659	+	0.462423i	$0.846980\pi$
$812$	−4.00168	−	12.3159i	−0.140432	−	0.432204i
$813$		0			0
$814$	−4.60538	+	4.99887i	−0.161419	+	0.175210i
$815$	23.4058			0.819868
$816$		0			0
$817$	9.58370	+	6.96297i	0.335291	+	0.243603i
$818$	37.6232	−	27.3349i	1.31547	−	0.955741i
$819$		0			0
$820$	−1.51351	+	4.65809i	−0.0528539	+	0.162668i
$821$	1.21284	−	0.881177i	0.0423282	−	0.0307533i	−0.566420	−	0.824117i	$-0.691672\pi$
$821$	1.21284	−	0.881177i	0.0423282	−	0.0307533i	0.608748	+	0.793363i	$0.291672\pi$
$822$		0			0
$823$	−5.90982	−	18.1885i	−0.206003	−	0.634013i	−0.999671	−	0.0256610i	$-0.991831\pi$
$823$	−5.90982	−	18.1885i	−0.206003	−	0.634013i	0.793667	−	0.608352i	$-0.208169\pi$
$824$	−5.13460			−0.178872
$825$		0			0
$826$	18.0794			0.629062
$827$	5.13910	+	15.8165i	0.178704	+	0.549994i	0.999783	−	0.0208200i	$-0.00662770\pi$
$827$	5.13910	+	15.8165i	0.178704	+	0.549994i	−0.821079	+	0.570814i	$0.806628\pi$
$828$		0			0
$829$	−20.7881	+	15.1034i	−0.722001	+	0.524564i	−0.887023	−	0.461725i	$-0.847231\pi$
$829$	−20.7881	+	15.1034i	−0.722001	+	0.524564i	0.165022	+	0.986290i	$0.447231\pi$
$830$	9.07908	−	27.9425i	0.315140	−	0.969900i
$831$		0			0
$832$	−9.18940	+	6.67649i	−0.318585	+	0.231466i
$833$	−23.4093	−	17.0078i	−0.811083	−	0.589286i
$834$		0			0
$835$	3.05191			0.105616
$836$	3.09338	−	26.5169i	0.106987	−	0.917105i
$837$		0			0
$838$	−7.61367	−	23.4325i	−0.263010	−	0.809461i
$839$	−22.9737	−	16.6914i	−0.793141	−	0.576250i	0.115753	−	0.993278i	$-0.463072\pi$
$839$	−22.9737	−	16.6914i	−0.793141	−	0.576250i	−0.908894	+	0.417028i	$0.863072\pi$
$840$		0			0
$841$	0.516507	−	1.58965i	0.0178106	−	0.0548154i
$842$	−1.66539	+	5.12555i	−0.0573932	+	0.176638i
$843$		0			0
$844$	4.13743	+	3.00602i	0.142416	+	0.103471i
$845$	−4.85315	−	14.9365i	−0.166953	−	0.513830i
$846$		0			0
$847$	17.7318	−	7.41457i	0.609273	−	0.254768i
$848$	8.16320			0.280325
$849$		0			0
$850$	−10.8359	−	7.87272i	−0.371667	−	0.270032i
$851$	−7.58406	+	5.51014i	−0.259978	+	0.188885i
$852$		0			0
$853$	4.66838	−	14.3678i	0.159842	−	0.491943i	−0.838777	−	0.544475i	$-0.816729\pi$
$853$	4.66838	−	14.3678i	0.159842	−	0.491943i	0.998619	+	0.0525314i	$0.0167290\pi$
$854$	23.9666	−	17.4128i	0.820122	−	0.595853i
$855$		0			0
$856$	5.87441	+	18.0796i	0.200783	+	0.617947i
$857$	−2.37040			−0.0809713			−0.0404856	−	0.999180i	$-0.512891\pi$
$857$	−2.37040			−0.0809713			−0.0404856	+	0.999180i	$0.512891\pi$
$858$		0			0
$859$	45.0423			1.53682			0.768411	−	0.639956i	$-0.221048\pi$
$859$	45.0423			1.53682			0.768411	+	0.639956i	$0.221048\pi$
$860$	0.814477	+	2.50670i	0.0277734	+	0.0854779i
$861$		0			0
$862$	−17.0323	+	12.3747i	−0.580123	+	0.421484i
$863$	7.73191	−	23.7964i	0.263197	−	0.810038i	−0.728906	−	0.684614i	$-0.759971\pi$
$863$	7.73191	−	23.7964i	0.263197	−	0.810038i	0.992103	−	0.125424i	$-0.0400292\pi$
$864$		0			0
$865$	−12.9503	+	9.40893i	−0.440323	+	0.319913i
$866$	16.5018	+	11.9893i	0.560754	+	0.407412i
$867$		0			0
$868$	−0.0499551			−0.00169559
$869$	8.33767	−	1.67301i	0.282836	−	0.0567530i
$870$		0			0
$871$	−0.580278	−	1.78591i	−0.0196620	−	0.0605133i
$872$	−4.14632	−	3.01248i	−0.140412	−	0.102015i
$873$		0			0
$874$	28.3825	−	87.3522i	0.960051	−	2.95473i
$875$	−0.539926	+	1.66172i	−0.0182528	+	0.0561765i
$876$		0			0
$877$	39.5411	+	28.7283i	1.33521	+	0.970085i	0.999606	+	0.0280807i	$0.00893953\pi$
$877$	39.5411	+	28.7283i	1.33521	+	0.970085i	0.335601	+	0.942004i	$0.391060\pi$
$878$	−0.561002	−	1.72659i	−0.0189329	−	0.0582695i
$879$		0			0
$880$	−10.9791	+	11.9171i	−0.370104	+	0.401726i
$881$	−44.5530			−1.50103			−0.750515	−	0.660853i	$-0.770195\pi$
$881$	−44.5530			−1.50103			−0.750515	+	0.660853i	$0.770195\pi$
$882$		0			0
$883$	35.6410	+	25.8947i	1.19941	+	0.871426i	0.994227	−	0.107297i	$-0.0342196\pi$
$883$	35.6410	+	25.8947i	1.19941	+	0.871426i	0.205187	+	0.978723i	$0.434220\pi$
$884$	−42.5230	+	30.8948i	−1.43020	+	1.03910i
$885$		0			0
$886$	−6.20076	+	19.0840i	−0.208319	+	0.641139i
$887$	−9.81279	+	7.12941i	−0.329481	+	0.239382i	−0.740210	−	0.672375i	$-0.765274\pi$
$887$	−9.81279	+	7.12941i	−0.329481	+	0.239382i	0.410729	+	0.911757i	$0.365274\pi$
$888$		0			0
$889$	6.85007	+	21.0823i	0.229744	+	0.707079i
$890$	26.5041			0.888419
$891$		0			0
$892$	−35.7585			−1.19728
$893$	−7.09925	−	21.8493i	−0.237567	−	0.731158i
$894$		0			0
$895$	15.6133	−	11.3437i	0.521895	−	0.379179i
$896$	−4.93655	+	15.1931i	−0.164919	+	0.507567i
$897$		0			0
$898$	−42.8963	+	31.1660i	−1.43147	+	1.04002i
$899$	−0.0957219	−	0.0695461i	−0.00319251	−	0.00231949i
$900$		0			0
$901$	12.2487			0.408063
$902$	20.1561	+	9.25112i	0.671125	+	0.308029i
$903$		0			0
$904$	2.68872	+	8.27504i	0.0894256	+	0.275224i
$905$	−9.86277	−	7.16572i	−0.327850	−	0.238197i
$906$		0			0
$907$	10.1565	−	31.2586i	0.337242	−	1.03793i	−0.628365	−	0.777919i	$-0.716275\pi$
$907$	10.1565	−	31.2586i	0.337242	−	1.03793i	0.965607	−	0.260006i	$-0.0837246\pi$
$908$	−5.06069	+	15.5752i	−0.167945	+	0.516881i
$909$		0			0
$910$	13.8372	+	10.0533i	0.458700	+	0.333265i
$911$	14.4328	+	44.4195i	0.478179	+	1.47168i	0.841622	+	0.540067i	$0.181601\pi$
$911$	14.4328	+	44.4195i	0.478179	+	1.47168i	−0.363443	+	0.931617i	$0.618399\pi$
$912$		0			0
$913$	−48.4714	−	22.2471i	−1.60417	−	0.736271i
$914$	6.49842			0.214949
$915$		0			0
$916$	7.23946	+	5.25978i	0.239199	+	0.173788i
$917$	−1.37128	+	0.996296i	−0.0452838	+	0.0329006i
$918$		0			0
$919$	2.26765	−	6.97910i	0.0748028	−	0.230219i	−0.906663	−	0.421855i	$-0.861379\pi$
$919$	2.26765	−	6.97910i	0.0748028	−	0.230219i	0.981466	+	0.191636i	$0.0613792\pi$
$920$	−8.17508	+	5.93954i	−0.269524	+	0.195821i
$921$		0			0
$922$	14.2183	+	43.7594i	0.468255	+	1.44114i
$923$	24.3143			0.800314
$924$		0			0
$925$	−1.12165			−0.0368795
$926$	10.0919	+	31.0596i	0.331640	+	1.02068i
$927$		0			0
$928$	29.1603	−	21.1862i	0.957232	−	0.695470i
$929$	−3.93333	+	12.1055i	−0.129048	+	0.397170i	−0.994617	−	0.103621i	$-0.966957\pi$
$929$	−3.93333	+	12.1055i	−0.129048	+	0.397170i	0.865569	+	0.500790i	$0.166957\pi$
$930$		0			0
$931$	19.2071	−	13.9548i	0.629488	−	0.457350i
$932$	−7.05626	−	5.12667i	−0.231135	−	0.167930i
$933$		0			0
$934$	−46.0888			−1.50807
$935$	−16.4738	+	17.8814i	−0.538752	+	0.584784i
$936$		0			0
$937$	5.94961	+	18.3110i	0.194365	+	0.598195i	0.999983	+	0.00575961i	$0.00183335\pi$
$937$	5.94961	+	18.3110i	0.194365	+	0.598195i	−0.805618	+	0.592435i	$0.798167\pi$
$938$	0.905199	+	0.657665i	0.0295558	+	0.0214735i
$939$		0			0
$940$	1.57955	−	4.86136i	0.0515193	−	0.158560i
$941$	12.7530	−	39.2496i	0.415735	−	1.27950i	−0.495857	−	0.868404i	$-0.665146\pi$
$941$	12.7530	−	39.2496i	0.415735	−	1.27950i	0.911592	−	0.411096i	$-0.134854\pi$
$942$		0			0
$943$	24.7461	+	17.9791i	0.805842	+	0.585479i
$944$	8.55007	+	26.3144i	0.278281	+	0.856461i
$945$		0			0
$946$	11.7015	−	2.34798i	0.380448	−	0.0763395i
$947$	50.3012			1.63457			0.817285	−	0.576233i	$-0.195478\pi$
$947$	50.3012			1.63457			0.817285	+	0.576233i	$0.195478\pi$
$948$		0			0
$949$	43.9496	+	31.9312i	1.42666	+	1.03653i
$950$	8.89074	−	6.45950i	0.288454	−	0.209574i
$951$		0			0
$952$	−4.78550	+	14.7282i	−0.155099	+	0.477345i
$953$	−7.30203	+	5.30523i	−0.236536	+	0.171853i	−0.699739	−	0.714399i	$-0.746700\pi$
$953$	−7.30203	+	5.30523i	−0.236536	+	0.171853i	0.463203	+	0.886252i	$0.346700\pi$
$954$		0			0
$955$	−4.14836	−	12.7673i	−0.134238	−	0.413141i
$956$	14.5093			0.469263
$957$		0			0
$958$	−9.56617			−0.309069
$959$	−2.27868	−	7.01305i	−0.0735824	−	0.226463i
$960$		0			0
$961$	25.0792	−	18.2211i	0.809005	−	0.587777i
$962$	−3.39296	+	10.4425i	−0.109393	+	0.336678i
$963$		0			0
$964$	−29.4275	+	21.3803i	−0.947796	+	0.688614i
$965$	6.13058	+	4.45413i	0.197350	+	0.143384i
$966$		0			0
$967$	−30.2503			−0.972785			−0.486392	−	0.873740i	$-0.661687\pi$
$967$	−30.2503			−0.972785			−0.486392	+	0.873740i	$0.661687\pi$
$968$	8.67130	+	10.0841i	0.278706	+	0.324114i
$969$		0			0
$970$	−1.07258	−	3.30107i	−0.0344386	−	0.105991i
$971$	10.3785	+	7.54040i	0.333061	+	0.241983i	0.741728	−	0.670700i	$-0.234006\pi$
$971$	10.3785	+	7.54040i	0.333061	+	0.241983i	−0.408667	+	0.912683i	$0.634006\pi$
$972$		0			0
$973$	4.77751	−	14.7037i	0.153160	−	0.471378i
$974$	−5.10687	+	15.7173i	−0.163635	+	0.503616i
$975$		0			0
$976$	36.6785	+	26.6485i	1.17405	+	0.852996i
$977$	4.06641	+	12.5151i	0.130096	+	0.400394i	0.994795	−	0.101896i	$-0.0324909\pi$
$977$	4.06641	+	12.5151i	0.130096	+	0.400394i	−0.864699	+	0.502290i	$0.832491\pi$
$978$		0			0
$979$	5.57474	−	47.7875i	0.178169	−	1.52729i
$980$	5.28233			0.168738
$981$		0			0
$982$	51.4562	+	37.3851i	1.64203	+	1.19301i
$983$	18.1519	−	13.1881i	0.578954	−	0.420635i	−0.259393	−	0.965772i	$-0.583522\pi$
$983$	18.1519	−	13.1881i	0.578954	−	0.420635i	0.838347	+	0.545137i	$0.183522\pi$
$984$		0			0
$985$	−2.12949	+	6.55390i	−0.0678513	+	0.208825i
$986$	60.0110	−	43.6005i	1.91114	−	1.38852i
$987$		0			0
$988$	−13.3267	−	41.0154i	−0.423979	−	1.30487i
$989$	16.4605			0.523414
$990$		0			0
$991$	22.9146			0.727907			0.363953	−	0.931417i	$-0.381427\pi$
$991$	22.9146			0.727907			0.363953	+	0.931417i	$0.381427\pi$
$992$	−0.0429671	−	0.132239i	−0.00136421	−	0.00419859i
$993$		0			0
$994$	−11.7207	+	8.51555i	−0.371757	+	0.270097i
$995$	−0.197585	+	0.608104i	−0.00626386	+	0.0192782i
$996$		0			0
$997$	13.6234	−	9.89794i	0.431456	−	0.313471i	−0.350775	−	0.936460i	$-0.614082\pi$
$997$	13.6234	−	9.89794i	0.431456	−	0.313471i	0.782231	+	0.622989i	$0.214082\pi$
$998$	28.9705	+	21.0483i	0.917045	+	0.666272i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.n.c.181.1		8
3.2	odd	2		165.2.m.c.16.2	✓	8
11.3	even	5		5445.2.a.bj.1.1		4
11.8	odd	10		5445.2.a.bq.1.4		4
11.9	even	5	inner	495.2.n.c.361.1		8
15.2	even	4		825.2.bx.e.49.1		16
15.8	even	4		825.2.bx.e.49.4		16
15.14	odd	2		825.2.n.j.676.1		8
33.8	even	10		1815.2.a.q.1.1		4
33.14	odd	10		1815.2.a.u.1.4		4
33.20	odd	10		165.2.m.c.31.2	yes	8
165.14	odd	10		9075.2.a.co.1.1		4
165.53	even	20		825.2.bx.e.724.1		16
165.74	even	10		9075.2.a.df.1.4		4
165.119	odd	10		825.2.n.j.526.1		8
165.152	even	20		825.2.bx.e.724.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.m.c.16.2	✓	8	3.2	odd	2
165.2.m.c.31.2	yes	8	33.20	odd	10
495.2.n.c.181.1		8	1.1	even	1	trivial
495.2.n.c.361.1		8	11.9	even	5	inner
825.2.n.j.526.1		8	165.119	odd	10
825.2.n.j.676.1		8	15.14	odd	2
825.2.bx.e.49.1		16	15.2	even	4
825.2.bx.e.49.4		16	15.8	even	4
825.2.bx.e.724.1		16	165.53	even	20
825.2.bx.e.724.4		16	165.152	even	20
1815.2.a.q.1.1		4	33.8	even	10
1815.2.a.u.1.4		4	33.14	odd	10
5445.2.a.bj.1.1		4	11.3	even	5
5445.2.a.bq.1.4		4	11.8	odd	10
9075.2.a.co.1.1		4	165.14	odd	10
9075.2.a.df.1.4		4	165.74	even	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	495.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.564602 - 1.73767i) q^{2} +(-1.08268 + 0.786610i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(-1.41355 + 1.02700i) q^{7} +(-0.978148 - 0.710666i) q^{8} +1.82709 q^{10} +(0.384301 - 3.29428i) q^{11} +(-1.65563 - 5.09549i) q^{13} +(2.58268 + 1.87642i) q^{14} +(-1.50973 + 4.64646i) q^{16} +(-2.26531 + 6.97191i) q^{17} +(-4.86606 - 3.53540i) q^{19} +(-0.413545 - 1.27276i) q^{20} +(-5.94135 + 1.19217i) q^{22} -8.35772 q^{23} +(-0.809017 - 0.587785i) q^{25} +(-7.91949 + 5.75385i) q^{26} +(0.722562 - 2.22382i) q^{28} +(4.48048 - 3.25526i) q^{29} +(-0.00660190 - 0.0203186i) q^{31} +6.50828 q^{32} +13.3939 q^{34} +(-0.539926 - 1.66172i) q^{35} +(0.907432 - 0.659288i) q^{37} +(-3.39596 + 10.4517i) q^{38} +(0.978148 - 0.710666i) q^{40} +(-2.96086 - 2.15119i) q^{41} -1.96950 q^{43} +(2.17524 + 3.86894i) q^{44} +(4.71878 + 14.5229i) q^{46} +(3.09007 + 2.24507i) q^{47} +(-1.21974 + 3.75397i) q^{49} +(-0.564602 + 1.73767i) q^{50} +(5.80067 + 4.21443i) q^{52} +(-0.516329 - 1.58910i) q^{53} +(3.01430 + 1.38348i) q^{55} +2.11251 q^{56} +(-8.18625 - 5.94766i) q^{58} +(4.58172 - 3.32882i) q^{59} +(2.86761 - 8.82559i) q^{61} +(-0.0315794 + 0.0229438i) q^{62} +(-0.655137 - 2.01630i) q^{64} +5.35772 q^{65} +0.350489 q^{67} +(-3.03158 - 9.33024i) q^{68} +(-2.58268 + 1.87642i) q^{70} +(-1.40238 + 4.31607i) q^{71} +(-8.20305 + 5.95986i) q^{73} +(-1.65796 - 1.20458i) q^{74} +8.04935 q^{76} +(2.84001 + 5.05130i) q^{77} +(0.792323 + 2.43852i) q^{79} +(-3.95252 - 2.87167i) q^{80} +(-2.06635 + 6.35956i) q^{82} +(4.96915 - 15.2935i) q^{83} +(-5.93066 - 4.30888i) q^{85} +(1.11198 + 3.42233i) q^{86} +(-2.71704 + 2.94919i) q^{88} +14.5062 q^{89} +(7.57337 + 5.50238i) q^{91} +(9.04870 - 6.57426i) q^{92} +(2.15652 - 6.63708i) q^{94} +(4.86606 - 3.53540i) q^{95} +(-0.587045 - 1.80674i) q^{97} +7.21182 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 2 q^{4} + 2 q^{5} - 5 q^{7} + q^{8} + 2 q^{10} + q^{11} - 16 q^{13} + 10 q^{14} + 12 q^{16} + 4 q^{17} + 2 q^{19} + 3 q^{20} - 9 q^{22} - 10 q^{23} - 2 q^{25} - 16 q^{26} - 5 q^{28} + 16 q^{29}+ \cdots - 26 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 + 2 * q^4 + 2 * q^5 - 5 * q^7 + q^8 + 2 * q^10 + q^11 - 16 * q^13 + 10 * q^14 + 12 * q^16 + 4 * q^17 + 2 * q^19 + 3 * q^20 - 9 * q^22 - 10 * q^23 - 2 * q^25 - 16 * q^26 - 5 * q^28 + 16 * q^29 - 5 * q^31 + 34 * q^34 - 5 * q^35 - 5 * q^37 - 28 * q^38 - q^40 - 5 * q^41 - 8 * q^43 + 19 * q^44 + 10 * q^46 + q^47 - 11 * q^49 - 2 * q^50 + 26 * q^52 + 15 * q^53 - q^55 - 20 * q^56 - 24 * q^58 - 3 * q^59 - 11 * q^61 + 15 * q^62 - 9 * q^64 - 14 * q^65 + 6 * q^67 - 9 * q^68 - 10 * q^70 - q^71 - 35 * q^73 - 5 * q^74 + 58 * q^76 + 25 * q^77 - 30 * q^79 + 3 * q^80 - 25 * q^82 - 31 * q^83 - 4 * q^85 + 62 * q^86 + 17 * q^88 + 48 * q^89 + 5 * q^91 + 20 * q^92 - 19 * q^94 - 2 * q^95 + 11 * q^97 - 26 * q^98

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