LMFDB - Embedded newform 784.2.x.n.165.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(165,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

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

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

chi := DirichletCharacter("784.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.x (of order $12$, degree $4$, not 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:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			165.4
Character	$\chi$	$=$	784.165
Dual form			784.2.x.n.765.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.953167 + 1.04474i) q^{2} +(0.554848 + 2.07072i) q^{3} +(-0.182947 - 1.99162i) q^{4} +(0.265812 - 0.992025i) q^{5} +(-2.69222 - 1.39407i) q^{6} +(2.25509 + 1.70721i) q^{8} +(-1.38196 + 0.797875i) q^{9} +O(q^{10})$	\(q+(-0.953167 + 1.04474i) q^{2} +(0.554848 + 2.07072i) q^{3} +(-0.182947 - 1.99162i) q^{4} +(0.265812 - 0.992025i) q^{5} +(-2.69222 - 1.39407i) q^{6} +(2.25509 + 1.70721i) q^{8} +(-1.38196 + 0.797875i) q^{9} +(0.783041 + 1.22327i) q^{10} +(1.27203 - 0.340839i) q^{11} +(4.02257 - 1.48388i) q^{12} +(3.98199 - 3.98199i) q^{13} +2.20169 q^{15} +(-3.93306 + 0.728719i) q^{16} +(2.81402 - 4.87403i) q^{17} +(0.483669 - 2.20429i) q^{18} +(-4.69357 - 1.25764i) q^{19} +(-2.02436 - 0.347908i) q^{20} +(-0.856369 + 1.65381i) q^{22} +(-0.495945 + 0.286334i) q^{23} +(-2.28392 + 5.61691i) q^{24} +(3.41667 + 1.97262i) q^{25} +(0.364629 + 7.95563i) q^{26} +(2.12867 + 2.12867i) q^{27} +(5.81867 - 5.81867i) q^{29} +(-2.09858 + 2.30019i) q^{30} +(1.27227 - 2.20364i) q^{31} +(2.98754 - 4.80360i) q^{32} +(1.41157 + 2.44491i) q^{33} +(2.40984 + 7.58567i) q^{34} +(1.84188 + 2.60636i) q^{36} +(-2.01687 + 7.52705i) q^{37} +(5.78765 - 3.70480i) q^{38} +(10.4550 + 6.03619i) q^{39} +(2.29302 - 1.78331i) q^{40} +4.12387i q^{41} +(0.783403 + 0.783403i) q^{43} +(-0.911535 - 2.47104i) q^{44} +(0.424170 + 1.58302i) q^{45} +(0.173575 - 0.791056i) q^{46} +(-4.77165 - 8.26474i) q^{47} +(-3.69123 - 7.73995i) q^{48} +(-5.31752 + 1.68929i) q^{50} +(11.6541 + 3.12271i) q^{51} +(-8.65908 - 7.20210i) q^{52} +(4.72136 - 1.26508i) q^{53} +(-4.25287 + 0.194921i) q^{54} -1.35248i q^{55} -10.4169i q^{57} +(0.532812 + 11.6251i) q^{58} +(-13.8735 + 3.71739i) q^{59} +(-0.402793 - 4.38493i) q^{60} +(8.68008 + 2.32582i) q^{61} +(1.08954 + 3.42963i) q^{62} +(2.17087 + 7.69983i) q^{64} +(-2.89177 - 5.00869i) q^{65} +(-3.89974 - 0.855688i) q^{66} +(2.20974 + 8.24686i) q^{67} +(-10.2220 - 4.71276i) q^{68} +(-0.868093 - 0.868093i) q^{69} +9.57512i q^{71} +(-4.47858 - 0.560015i) q^{72} +(-10.9611 - 6.32838i) q^{73} +(-5.94137 - 9.28162i) q^{74} +(-2.18901 + 8.16948i) q^{75} +(-1.64606 + 9.57786i) q^{76} +(-16.2716 + 5.16921i) q^{78} +(4.29142 + 7.43296i) q^{79} +(-0.322548 + 4.09540i) q^{80} +(-5.62042 + 9.73485i) q^{81} +(-4.30836 - 3.93073i) q^{82} +(-2.65975 + 2.65975i) q^{83} +(-4.08716 - 4.08716i) q^{85} +(-1.56516 + 0.0717357i) q^{86} +(15.2773 + 8.82037i) q^{87} +(3.45043 + 1.40300i) q^{88} +(2.44491 - 1.41157i) q^{89} +(-2.05815 - 1.06574i) q^{90} +(0.660999 + 0.935348i) q^{92} +(5.26905 + 1.41184i) q^{93} +(13.1827 + 2.89256i) q^{94} +(-2.49521 + 4.32184i) q^{95} +(11.6046 + 3.52110i) q^{96} -8.98095 q^{97} +(-1.48595 + 1.48595i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 8 q^{4}+O(q^{10}) $ 40 * q + 8 * q^4	$ 40 q + 8 q^{4} - 4 q^{11} - 32 q^{15} - 16 q^{18} - 8 q^{29} - 8 q^{30} + 40 q^{32} + 80 q^{36} + 20 q^{37} + 120 q^{43} - 56 q^{44} + 64 q^{46} - 112 q^{50} + 16 q^{51} - 28 q^{53} + 72 q^{58} + 24 q^{60} - 64 q^{64} - 16 q^{65} - 12 q^{67} - 16 q^{72} + 16 q^{74} - 176 q^{78} + 72 q^{79} - 12 q^{81} + 64 q^{85} + 40 q^{86} - 80 q^{88} - 48 q^{92} - 48 q^{93} - 64 q^{95} - 216 q^{99}+O(q^{100}) $ 40 * q + 8 * q^4 - 4 * q^11 - 32 * q^15 - 16 * q^18 - 8 * q^29 - 8 * q^30 + 40 * q^32 + 80 * q^36 + 20 * q^37 + 120 * q^43 - 56 * q^44 + 64 * q^46 - 112 * q^50 + 16 * q^51 - 28 * q^53 + 72 * q^58 + 24 * q^60 - 64 * q^64 - 16 * q^65 - 12 * q^67 - 16 * q^72 + 16 * q^74 - 176 * q^78 + 72 * q^79 - 12 * q^81 + 64 * q^85 + 40 * q^86 - 80 * q^88 - 48 * q^92 - 48 * q^93 - 64 * q^95 - 216 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.953167	+	1.04474i	−0.673991	+	0.738740i
$2$	−0.953167	+	1.04474i	−0.673991	+	0.738740i
$3$	0.554848	+	2.07072i	0.320342	+	1.19553i	0.918912	+	0.394462i	$0.129069\pi$
$3$	0.554848	+	2.07072i	0.320342	+	1.19553i	−0.598570	+	0.801070i	$0.704264\pi$
$4$	−0.182947	−	1.99162i	−0.0914734	−	0.995808i
$5$	0.265812	−	0.992025i	0.118875	−	0.443647i	−0.880673	−	0.473725i	$-0.842909\pi$
$5$	0.265812	−	0.992025i	0.118875	−	0.443647i	0.999548	+	0.0300783i	$0.00957567\pi$
$6$	−2.69222	−	1.39407i	−1.09909	−	0.569128i
$7$		0			0
$7$		0			0
$8$	2.25509	+	1.70721i	0.797295	+	0.603590i
$9$	−1.38196	+	0.797875i	−0.460653	+	0.265958i
$10$	0.783041	+	1.22327i	0.247619	+	0.386831i
$11$	1.27203	−	0.340839i	0.383531	−	0.102767i	−0.0619014	−	0.998082i	$-0.519716\pi$
$11$	1.27203	−	0.340839i	0.383531	−	0.102767i	0.445433	+	0.895315i	$0.353050\pi$
$12$	4.02257	−	1.48388i	1.16122	−	0.428358i
$13$	3.98199	−	3.98199i	1.10441	−	1.10441i	0.110533	−	0.993873i	$-0.464744\pi$
$13$	3.98199	−	3.98199i	1.10441	−	1.10441i	0.993873	−	0.110533i	$-0.0352556\pi$
$14$		0			0
$15$	2.20169			0.568475
$16$	−3.93306	+	0.728719i	−0.983265	+	0.182180i
$17$	2.81402	−	4.87403i	0.682501	−	1.18213i	−0.291715	−	0.956505i	$-0.594226\pi$
$17$	2.81402	−	4.87403i	0.682501	−	1.18213i	0.974215	−	0.225620i	$-0.0724409\pi$
$18$	0.483669	−	2.20429i	0.114002	−	0.519556i
$19$	−4.69357	−	1.25764i	−1.07678	−	0.288522i	−0.323503	−	0.946227i	$-0.604860\pi$
$19$	−4.69357	−	1.25764i	−1.07678	−	0.288522i	−0.753275	+	0.657706i	$0.771527\pi$
$20$	−2.02436	−	0.347908i	−0.452661	−	0.0777945i
$21$		0			0
$22$	−0.856369	+	1.65381i	−0.182579	+	0.352594i
$23$	−0.495945	+	0.286334i	−0.103412	+	0.0597048i	−0.550814	−	0.834628i	$-0.685683\pi$
$23$	−0.495945	+	0.286334i	−0.103412	+	0.0597048i	0.447402	+	0.894333i	$0.352349\pi$
$24$	−2.28392	+	5.61691i	−0.466204	+	1.14655i
$25$	3.41667	+	1.97262i	0.683334	+	0.394523i
$26$	0.364629	+	7.95563i	0.0715095	+	1.56023i
$27$	2.12867	+	2.12867i	0.409662	+	0.409662i
$28$		0			0
$29$	5.81867	−	5.81867i	1.08050	−	1.08050i	0.0840373	−	0.996463i	$-0.473219\pi$
$29$	5.81867	−	5.81867i	1.08050	−	1.08050i	0.996463	−	0.0840373i	$-0.0267815\pi$
$30$	−2.09858	+	2.30019i	−0.383147	+	0.419955i
$31$	1.27227	−	2.20364i	0.228507	−	0.395786i	−0.728859	−	0.684664i	$-0.759949\pi$
$31$	1.27227	−	2.20364i	0.228507	−	0.395786i	0.957366	+	0.288878i	$0.0932823\pi$
$32$	2.98754	−	4.80360i	0.528128	−	0.849165i
$33$	1.41157	+	2.44491i	0.245722	+	0.425604i
$34$	2.40984	+	7.58567i	0.413285	+	1.30093i
$35$		0			0
$36$	1.84188	+	2.60636i	0.306981	+	0.434394i
$37$	−2.01687	+	7.52705i	−0.331571	+	1.23744i	0.575968	+	0.817472i	$0.304625\pi$
$37$	−2.01687	+	7.52705i	−0.331571	+	1.23744i	−0.907539	+	0.419967i	$0.862042\pi$
$38$	5.78765	−	3.70480i	0.938881	−	0.600998i
$39$	10.4550	+	6.03619i	1.67414	+	0.966565i
$40$	2.29302	−	1.78331i	0.362559	−	0.281966i
$41$			4.12387i			0.644040i	0.946733	+	0.322020i	$0.104362\pi$
$41$			4.12387i			0.644040i	−0.946733	+	0.322020i	$0.895638\pi$
$42$		0			0
$43$	0.783403	+	0.783403i	0.119468	+	0.119468i	0.764313	−	0.644845i	$-0.223078\pi$
$43$	0.783403	+	0.783403i	0.119468	+	0.119468i	−0.644845	+	0.764313i	$0.723078\pi$
$44$	−0.911535	−	2.47104i	−0.137419	−	0.372523i
$45$	0.424170	+	1.58302i	0.0632315	+	0.235983i
$46$	0.173575	−	0.791056i	0.0255922	−	0.116635i
$47$	−4.77165	−	8.26474i	−0.696017	−	1.20554i	−0.969837	−	0.243755i	$-0.921621\pi$
$47$	−4.77165	−	8.26474i	−0.696017	−	1.20554i	0.273820	−	0.961781i	$-0.411713\pi$
$48$	−3.69123	−	7.73995i	−0.532783	−	1.11717i
$49$		0			0
$50$	−5.31752	+	1.68929i	−0.752011	+	0.238901i
$51$	11.6541	+	3.12271i	1.63190	+	0.437267i
$52$	−8.65908	−	7.20210i	−1.20080	−	0.998751i
$53$	4.72136	−	1.26508i	0.648529	−	0.173773i	0.0804652	−	0.996757i	$-0.474359\pi$
$53$	4.72136	−	1.26508i	0.648529	−	0.173773i	0.568064	+	0.822985i	$0.307693\pi$
$54$	−4.25287	+	0.194921i	−0.578742	+	0.0265254i
$55$		−	1.35248i		−	0.182369i
$56$		0			0
$57$		−	10.4169i		−	1.37975i
$58$	0.532812	+	11.6251i	0.0699617	+	1.52646i
$59$	−13.8735	+	3.71739i	−1.80617	+	0.483963i	−0.994914	−	0.100724i	$-0.967884\pi$
$59$	−13.8735	+	3.71739i	−1.80617	+	0.483963i	−0.811259	+	0.584687i	$0.801217\pi$
$60$	−0.402793	−	4.38493i	−0.0520003	−	0.566091i
$61$	8.68008	+	2.32582i	1.11137	+	0.297791i	0.767386	−	0.641185i	$-0.221557\pi$
$61$	8.68008	+	2.32582i	1.11137	+	0.297791i	0.343984	+	0.938976i	$0.388224\pi$
$62$	1.08954	+	3.42963i	0.138371	+	0.435563i
$63$		0			0
$64$	2.17087	+	7.69983i	0.271359	+	0.962478i
$65$	−2.89177	−	5.00869i	−0.358680	−	0.621252i
$66$	−3.89974	−	0.855688i	−0.480025	−	0.105328i
$67$	2.20974	+	8.24686i	0.269963	+	1.00751i	0.959142	+	0.282924i	$0.0913044\pi$
$67$	2.20974	+	8.24686i	0.269963	+	1.00751i	−0.689180	+	0.724591i	$0.742029\pi$
$68$	−10.2220	−	4.71276i	−1.23960	−	0.571506i
$69$	−0.868093	−	0.868093i	−0.104506	−	0.104506i
$70$		0			0
$71$			9.57512i			1.13636i	0.822905	+	0.568179i	$0.192352\pi$
$71$			9.57512i			1.13636i	−0.822905	+	0.568179i	$0.807648\pi$
$72$	−4.47858	−	0.560015i	−0.527806	−	0.0659984i
$73$	−10.9611	−	6.32838i	−1.28290	−	0.740681i	−0.305520	−	0.952186i	$-0.598830\pi$
$73$	−10.9611	−	6.32838i	−1.28290	−	0.740681i	−0.977377	+	0.211504i	$0.932164\pi$
$74$	−5.94137	−	9.28162i	−0.690670	−	1.07897i
$75$	−2.18901	+	8.16948i	−0.252765	+	0.943330i
$76$	−1.64606	+	9.57786i	−0.188816	+	1.09866i
$77$		0			0
$78$	−16.2716	+	5.16921i	−1.84239	+	0.585298i
$79$	4.29142	+	7.43296i	0.482822	+	0.836273i	0.999805	−	0.0197228i	$-0.00627836\pi$
$79$	4.29142	+	7.43296i	0.482822	+	0.836273i	−0.516983	+	0.855996i	$0.672945\pi$
$80$	−0.322548	+	4.09540i	−0.0360620	+	0.457879i
$81$	−5.62042	+	9.73485i	−0.624491	+	1.08165i
$82$	−4.30836	−	3.93073i	−0.475778	−	0.434077i
$83$	−2.65975	+	2.65975i	−0.291945	+	0.291945i	−0.837848	−	0.545903i	$-0.816187\pi$
$83$	−2.65975	+	2.65975i	−0.291945	+	0.291945i	0.545903	+	0.837848i	$0.316187\pi$
$84$		0			0
$85$	−4.08716	−	4.08716i	−0.443314	−	0.443314i
$86$	−1.56516	+	0.0717357i	−0.168776	+	0.00773546i
$87$	15.2773	+	8.82037i	1.63790	+	0.945643i
$88$	3.45043	+	1.40300i	0.367817	+	0.149560i
$89$	2.44491	−	1.41157i	0.259160	−	0.149626i	−0.364792	−	0.931089i	$-0.618860\pi$
$89$	2.44491	−	1.41157i	0.259160	−	0.149626i	0.623951	+	0.781463i	$0.285526\pi$
$90$	−2.05815	−	1.06574i	−0.216948	−	0.112339i
$91$		0			0
$92$	0.660999	+	0.935348i	0.0689139	+	0.0975168i
$93$	5.26905	+	1.41184i	0.546375	+	0.146401i
$94$	13.1827	+	2.89256i	1.35969	+	0.298345i
$95$	−2.49521	+	4.32184i	−0.256004	+	0.443411i
$96$	11.6046	+	3.52110i	1.18439	+	0.359371i
$97$	−8.98095			−0.911877			−0.455939	−	0.890011i	$-0.650696\pi$
$97$	−8.98095			−0.911877			−0.455939	+	0.890011i	$0.650696\pi$
$98$		0			0
$99$	−1.48595	+	1.48595i	−0.149343	+	0.149343i
$100$	3.30362	−	7.16558i	0.330362	−	0.716558i
$101$	6.03434	−	1.61690i	0.600439	−	0.160887i	0.0542192	−	0.998529i	$-0.482733\pi$
$101$	6.03434	−	1.61690i	0.600439	−	0.160887i	0.546220	+	0.837642i	$0.316066\pi$
$102$	−14.3707	+	9.19902i	−1.42291	+	0.910838i
$103$	3.01360	−	1.73990i	0.296939	−	0.171438i	−0.344128	−	0.938923i	$-0.611825\pi$
$103$	3.01360	−	1.73990i	0.296939	−	0.171438i	0.641067	+	0.767485i	$0.278492\pi$
$104$	15.7778	−	2.18166i	1.54714	−	0.213929i
$105$		0			0
$106$	−3.17856	+	6.13841i	−0.308729	+	0.596215i
$107$	5.31996	−	19.8543i	0.514300	−	1.91939i	0.147623	−	0.989044i	$-0.452838\pi$
$107$	5.31996	−	19.8543i	0.514300	−	1.91939i	0.366676	−	0.930349i	$-0.380496\pi$
$108$	3.85005	−	4.62892i	0.370471	−	0.445418i
$109$	−1.06990	−	3.99291i	−0.102478	−	0.382451i	0.895569	−	0.444922i	$-0.146769\pi$
$109$	−1.06990	−	3.99291i	−0.102478	−	0.382451i	−0.998047	+	0.0624707i	$0.980102\pi$
$110$	1.41299	+	1.28914i	0.134723	+	0.122915i
$111$	−16.7055			−1.58561
$112$		0			0
$113$	−2.32825			−0.219024			−0.109512	−	0.993985i	$-0.534929\pi$
$113$	−2.32825			−0.219024			−0.109512	+	0.993985i	$0.534929\pi$
$114$	10.8829	+	9.92901i	1.01928	+	0.929937i
$115$	0.152222	+	0.568101i	0.0141948	+	0.0529757i
$116$	−12.6531	−	10.5240i	−1.17481	−	0.977133i
$117$	−2.32582	+	8.68008i	−0.215022	+	0.802473i
$118$	9.34005	−	18.0374i	0.859821	−	1.66048i
$119$		0			0
$120$	4.96502	+	3.75875i	0.453242	+	0.343126i
$121$	−8.02439	+	4.63288i	−0.729490	+	0.421171i
$122$	−10.7034	+	6.85150i	−0.969043	+	0.620305i
$123$	−8.53939	+	2.28812i	−0.769971	+	0.206313i
$124$	−4.62156	−	2.13073i	−0.415029	−	0.191345i
$125$	6.49614	−	6.49614i	0.581032	−	0.581032i
$126$		0			0
$127$	−5.28600			−0.469057			−0.234528	−	0.972109i	$-0.575355\pi$
$127$	−5.28600			−0.469057			−0.234528	+	0.972109i	$0.575355\pi$
$128$	−10.1135	−	5.07123i	−0.893914	−	0.448238i
$129$	−1.18754	+	2.05688i	−0.104557	+	0.181098i
$130$	7.98910	+	1.75298i	0.700690	+	0.153747i
$131$	14.9338	+	4.00149i	1.30477	+	0.349612i	0.843252	−	0.537519i	$-0.180638\pi$
$131$	14.9338	+	4.00149i	1.30477	+	0.349612i	0.461518	+	0.887131i	$0.347305\pi$
$132$	4.61107	−	3.25859i	0.401342	−	0.283624i
$133$		0			0
$134$	−10.7220	−	5.55204i	−0.926244	−	0.479623i
$135$	2.67752	−	1.54586i	0.230444	−	0.133047i
$136$	14.6669	−	6.18725i	1.25767	−	0.530553i
$137$	−7.97102	−	4.60207i	−0.681010	−	0.393182i	0.119225	−	0.992867i	$-0.461959\pi$
$137$	−7.97102	−	4.60207i	−0.681010	−	0.393182i	−0.800236	+	0.599686i	$0.795292\pi$
$138$	1.73437	−	0.0794908i	0.147639	−	0.00676670i
$139$	3.07562	+	3.07562i	0.260871	+	0.260871i	0.825408	−	0.564537i	$-0.190945\pi$
$139$	3.07562	+	3.07562i	0.260871	+	0.260871i	−0.564537	+	0.825408i	$0.690945\pi$
$140$		0			0
$141$	14.4664	−	14.4664i	1.21829	−	1.21829i
$142$	−10.0035	−	9.12668i	−0.839473	−	0.765894i
$143$	3.70799	−	6.42243i	0.310078	−	0.537070i
$144$	4.85390	−	4.14515i	0.404492	−	0.345429i
$145$	−4.22559	−	7.31894i	−0.350916	−	0.607805i
$146$	17.0592	−	5.41943i	1.41183	−	0.448515i
$147$		0			0
$148$	15.3600	+	2.63977i	1.26258	+	0.216988i
$149$	−1.79157	+	6.68624i	−0.146771	+	0.547758i	0.852899	+	0.522076i	$0.174842\pi$
$149$	−1.79157	+	6.68624i	−0.146771	+	0.547758i	−0.999670	+	0.0256818i	$0.991824\pi$
$150$	−6.44846	−	10.0738i	−0.526515	−	0.822523i
$151$	15.2728	+	8.81774i	1.24288	+	0.717578i	0.969680	−	0.244379i	$-0.0785842\pi$
$151$	15.2728	+	8.81774i	1.24288	+	0.717578i	0.273201	+	0.961957i	$0.411917\pi$
$152$	−8.43737	−	10.8490i	−0.684361	−	0.879969i
$153$			8.98095i			0.726067i
$154$		0			0
$155$	−1.84788	−	1.84788i	−0.148425	−	0.148425i
$156$	10.1091	−	21.9266i	0.809373	−	1.75554i
$157$	5.73691	+	21.4104i	0.457855	+	1.70874i	0.679555	+	0.733624i	$0.262173\pi$
$157$	5.73691	+	21.4104i	0.457855	+	1.70874i	−0.221700	+	0.975115i	$0.571161\pi$
$158$	−11.8559	−	2.60144i	−0.943206	−	0.206960i
$159$	5.23928	+	9.07470i	0.415502	+	0.719670i
$160$	−3.97117	−	4.24057i	−0.313948	−	0.335247i
$161$		0			0
$162$	−4.81315	−	15.1508i	−0.378157	−	1.19036i
$163$	18.5185	+	4.96202i	1.45048	+	0.388655i	0.896191	−	0.443669i	$-0.146323\pi$
$163$	18.5185	+	4.96202i	1.45048	+	0.388655i	0.554290	+	0.832324i	$0.312990\pi$
$164$	8.21316	−	0.754449i	0.641340	−	0.0589126i
$165$	2.80062	−	0.750424i	0.218028	−	0.0584204i
$166$	−0.243551	−	5.31391i	−0.0189033	−	0.412440i
$167$		−	9.28950i		−	0.718843i	−0.933175	−	0.359422i	$-0.882974\pi$
$167$		−	9.28950i		−	0.718843i	0.933175	−	0.359422i	$-0.117026\pi$
$168$		0			0
$169$		−	18.7125i		−	1.43942i
$170$	8.16574	−	0.374259i	0.626284	−	0.0287043i
$171$	7.48976	−	2.00687i	0.572756	−	0.153469i
$172$	1.41692	−	1.70356i	0.108039	−	0.129895i
$173$	−8.08908	−	2.16746i	−0.615001	−	0.164789i	−0.0621469	−	0.998067i	$-0.519795\pi$
$173$	−8.08908	−	2.16746i	−0.615001	−	0.164789i	−0.552854	+	0.833278i	$0.686461\pi$
$174$	−23.7768	+	7.55350i	−1.80251	+	0.572629i
$175$		0			0
$176$	−4.75460	+	2.26750i	−0.358391	+	0.170919i
$177$	−15.3954	−	26.6655i	−1.15719	−	2.00431i
$178$	−0.855688	+	3.89974i	−0.0641365	+	0.292298i
$179$	−3.88277	−	14.4907i	−0.290212	−	1.08309i	−0.944946	−	0.327227i	$-0.893886\pi$
$179$	−3.88277	−	14.4907i	−0.290212	−	1.08309i	0.654734	−	0.755860i	$-0.272781\pi$
$180$	3.07517	−	1.13439i	0.229210	−	0.0845526i
$181$	2.51415	+	2.51415i	0.186875	+	0.186875i	0.794344	−	0.607469i	$-0.207815\pi$
$181$	2.51415	+	2.51415i	0.186875	+	0.186875i	−0.607469	+	0.794344i	$0.707815\pi$
$182$		0			0
$183$			19.2645i			1.42407i
$184$	−1.60723	−	0.200973i	−0.118487	−	0.0148159i
$185$	6.93091	+	4.00156i	0.509571	+	0.294201i
$186$	−6.49728	+	4.15905i	−0.476404	+	0.304956i
$187$	1.91826	−	7.15904i	0.140277	−	0.523521i
$188$	−15.5872	+	11.0153i	−1.13682	+	0.803373i
$189$		0			0
$190$	−2.13682	−	6.72627i	−0.155022	−	0.487975i
$191$	−6.35852	−	11.0133i	−0.460087	−	0.796893i	0.538878	−	0.842384i	$-0.318848\pi$
$191$	−6.35852	−	11.0133i	−0.460087	−	0.796893i	−0.998965	+	0.0454904i	$0.985515\pi$
$192$	−14.7397	+	8.76751i	−1.06375	+	0.632740i
$193$	−9.26433	+	16.0463i	−0.666861	+	1.15504i	0.311916	+	0.950110i	$0.399029\pi$
$193$	−9.26433	+	16.0463i	−0.666861	+	1.15504i	−0.978777	+	0.204928i	$0.934304\pi$
$194$	8.56034	−	9.38272i	0.614597	−	0.673640i
$195$	8.76712	−	8.76712i	0.627826	−	0.627826i
$196$		0			0
$197$	2.26478	+	2.26478i	0.161359	+	0.161359i	0.783168	−	0.621810i	$-0.213602\pi$
$197$	2.26478	+	2.26478i	0.161359	+	0.161359i	−0.621810	+	0.783168i	$0.713602\pi$
$198$	−0.136067	−	2.96878i	−0.00966989	−	0.210982i
$199$	−19.3572	−	11.1759i	−1.37219	−	0.792237i	−0.380991	−	0.924579i	$-0.624417\pi$
$199$	−19.3572	−	11.1759i	−1.37219	−	0.792237i	−0.991204	+	0.132342i	$0.957750\pi$
$200$	4.33723	+	10.2814i	0.306689	+	0.727005i
$201$	−15.8509	+	9.15152i	−1.11804	+	0.645498i
$202$	−4.06250	+	7.84546i	−0.285836	+	0.552005i
$203$		0			0
$204$	4.08716	−	23.7818i	0.286158	−	1.66506i
$205$	4.09098	+	1.09617i	0.285726	+	0.0765602i
$206$	−1.05472	+	4.80683i	−0.0734861	+	0.334908i
$207$	0.456917	−	0.791404i	0.0317580	−	0.0550064i
$208$	−12.7597	+	18.5632i	−0.884723	+	1.28712i
$209$	−6.39901			−0.442629
$210$		0			0
$211$	1.92874	−	1.92874i	0.132780	−	0.132780i	−0.637593	−	0.770373i	$-0.720070\pi$
$211$	1.92874	−	1.92874i	0.132780	−	0.132780i	0.770373	+	0.637593i	$0.220070\pi$
$212$	−3.38332	−	9.17169i	−0.232367	−	0.629914i
$213$	−19.8274	+	5.31274i	−1.35855	+	0.364023i
$214$	15.6717	+	24.4825i	1.07130	+	1.67359i
$215$	0.985393	−	0.568917i	0.0672032	−	0.0387998i
$216$	1.16626	+	8.43442i	0.0793537	+	0.573890i
$217$		0			0
$218$	5.19133	+	2.68815i	0.351601	+	0.182064i
$219$	7.02259	−	26.2086i	0.474542	−	1.77102i
$220$	−2.69363	+	0.247433i	−0.181604	+	0.0166819i
$221$	−8.20293	−	30.6137i	−0.551789	−	2.05930i
$222$	15.9231	−	17.4528i	1.06869	−	1.17136i
$223$	20.9059			1.39996			0.699981	−	0.714161i	$-0.253192\pi$
$223$	20.9059			1.39996			0.699981	+	0.714161i	$0.253192\pi$
$224$		0			0
$225$	−6.29560			−0.419707
$226$	2.21921	−	2.43241i	0.147620	−	0.161802i
$227$	−2.15910	−	8.05786i	−0.143304	−	0.534819i	−0.999825	−	0.0187062i	$-0.994045\pi$
$227$	−2.15910	−	8.05786i	−0.143304	−	0.534819i	0.856521	−	0.516113i	$-0.172621\pi$
$228$	−20.7464	+	1.90573i	−1.37396	+	0.126210i
$229$	5.20529	−	19.4264i	0.343975	−	1.28373i	−0.549830	−	0.835277i	$-0.685308\pi$
$229$	5.20529	−	19.4264i	0.343975	−	1.28373i	0.893805	−	0.448456i	$-0.148026\pi$
$230$	−0.738609	−	0.382463i	−0.0487024	−	0.0252189i
$231$		0			0
$232$	23.0553	−	3.18794i	1.51366	−	0.209298i
$233$	−8.09687	+	4.67473i	−0.530443	+	0.306252i	−0.741197	−	0.671288i	$-0.765742\pi$
$233$	−8.09687	+	4.67473i	−0.530443	+	0.306252i	0.210754	+	0.977539i	$0.432408\pi$
$234$	−6.85150	−	10.7034i	−0.447896	−	0.699705i
$235$	−9.46719	+	2.53673i	−0.617571	+	0.165478i
$236$	9.94172	+	26.9506i	0.647151	+	1.75433i
$237$	−13.0105	+	13.0105i	−0.845123	+	0.845123i
$238$		0			0
$239$	−7.37343			−0.476947			−0.238474	−	0.971149i	$-0.576647\pi$
$239$	−7.37343			−0.476947			−0.238474	+	0.971149i	$0.576647\pi$
$240$	−8.65939	+	1.60442i	−0.558962	+	0.103565i
$241$	4.70190	−	8.14393i	0.302876	−	0.524597i	−0.673910	−	0.738813i	$-0.735387\pi$
$241$	4.70190	−	8.14393i	0.302876	−	0.524597i	0.976786	+	0.214217i	$0.0687199\pi$
$242$	2.80844	−	12.7993i	0.180533	−	0.822769i
$243$	−14.5532	−	3.89952i	−0.933589	−	0.250154i
$244$	3.04414	−	17.7129i	0.194881	−	1.13395i
$245$		0			0
$246$	5.74898	−	11.1024i	0.366541	−	0.707861i
$247$	−23.6976	+	13.6818i	−1.50784	+	0.870554i
$248$	6.63117	−	2.79737i	0.421080	−	0.177633i
$249$	−6.98335	−	4.03184i	−0.442552	−	0.255507i
$250$	0.594848	+	12.9787i	0.0376215	+	0.820842i
$251$	7.24386	+	7.24386i	0.457228	+	0.457228i	0.897745	−	0.440516i	$-0.145205\pi$
$251$	7.24386	+	7.24386i	0.457228	+	0.457228i	−0.440516	+	0.897745i	$0.645205\pi$
$252$		0			0
$253$	−0.533263	+	0.533263i	−0.0335260	+	0.0335260i
$254$	5.03844	−	5.52248i	0.316140	−	0.346511i
$255$	6.19561	−	10.7311i	0.387984	−	0.672009i
$256$	14.9379	−	5.73220i	0.933621	−	0.358262i
$257$	−3.04716	−	5.27784i	−0.190077	−	0.329223i	0.755199	−	0.655496i	$-0.227540\pi$
$257$	−3.04716	−	5.27784i	−0.190077	−	0.329223i	−0.945276	+	0.326273i	$0.894207\pi$
$258$	−1.01697	−	3.20121i	−0.0633140	−	0.199299i
$259$		0			0
$260$	−9.44635	+	6.67562i	−0.585838	+	0.414004i
$261$	−3.39860	+	12.6837i	−0.210368	+	0.785104i
$262$	−18.4149	+	11.7878i	−1.13767	+	0.728250i
$263$	−0.869755	−	0.502153i	−0.0536314	−	0.0309641i	0.472945	−	0.881092i	$-0.343191\pi$
$263$	−0.869755	−	0.502153i	−0.0536314	−	0.0309641i	−0.526576	+	0.850128i	$0.676524\pi$
$264$	−0.990756	+	7.92333i	−0.0609768	+	0.487647i
$265$		−	5.01998i		−	0.308375i
$266$		0			0
$267$	4.27952	+	4.27952i	0.261902	+	0.261902i
$268$	16.0203	−	5.90969i	0.978596	−	0.360992i
$269$	−3.82962	−	14.2923i	−0.233496	−	0.871419i	−0.978821	−	0.204718i	$-0.934372\pi$
$269$	−3.82962	−	14.2923i	−0.233496	−	0.871419i	0.745325	−	0.666701i	$-0.232294\pi$
$270$	−0.937098	+	4.27076i	−0.0570300	+	0.259910i
$271$	5.38725	+	9.33100i	0.327252	+	0.566818i	0.981966	−	0.189060i	$-0.0605439\pi$
$271$	5.38725	+	9.33100i	0.327252	+	0.566818i	−0.654713	+	0.755877i	$0.727211\pi$
$272$	−7.51592	+	21.2205i	−0.455720	+	1.28668i
$273$		0			0
$274$	12.4057	−	3.94107i	0.749454	−	0.238089i
$275$	5.01845	+	1.34469i	0.302624	+	0.0810879i
$276$	−1.57009	+	1.88772i	−0.0945084	+	0.113627i
$277$	−3.74656	+	1.00389i	−0.225109	+	0.0603178i	−0.369610	−	0.929187i	$-0.620509\pi$
$277$	−3.74656	+	1.00389i	−0.225109	+	0.0603178i	0.144501	+	0.989505i	$0.453842\pi$
$278$	−6.14480	+	0.281633i	−0.368541	+	0.0168912i
$279$			4.06046i			0.243093i
$280$		0			0
$281$			15.8030i			0.942730i	0.881938	+	0.471365i	$0.156239\pi$
$281$			15.8030i			0.942730i	−0.881938	+	0.471365i	$0.843761\pi$
$282$	1.32468	+	28.9025i	0.0788838	+	1.72112i
$283$	5.54664	−	1.48622i	0.329713	−	0.0883464i	−0.0901649	−	0.995927i	$-0.528739\pi$
$283$	5.54664	−	1.48622i	0.329713	−	0.0883464i	0.419878	+	0.907580i	$0.362073\pi$
$284$	19.0700	−	1.75174i	1.13159	−	0.103947i
$285$	−10.3338	−	2.76893i	−0.612121	−	0.164017i
$286$	3.17541	+	9.99552i	0.187766	+	0.591047i
$287$		0			0
$288$	−0.295991	+	9.02207i	−0.0174415	+	0.531631i
$289$	−7.33745	−	12.7088i	−0.431614	−	0.747578i
$290$	11.6740	+	2.56154i	0.685524	+	0.150419i
$291$	−4.98307	−	18.5971i	−0.292113	−	1.09018i
$292$	−10.5984	+	22.9880i	−0.620225	+	1.34527i
$293$	−6.40882	−	6.40882i	−0.374407	−	0.374407i	0.494672	−	0.869080i	$-0.335288\pi$
$293$	−6.40882	−	6.40882i	−0.374407	−	0.374407i	−0.869080	+	0.494672i	$0.835288\pi$
$294$		0			0
$295$			14.7510i			0.858834i
$296$	−17.3985	+	13.5310i	−1.01127	+	0.786471i
$297$	3.43326	+	1.98219i	0.199218	+	0.115019i
$298$	−5.27769	−	8.24482i	−0.305728	−	0.477610i
$299$	−0.834669	+	3.11503i	−0.0482702	+	0.180147i
$300$	16.6709	+	2.86508i	0.962497	+	0.165415i
$301$		0			0
$302$	−23.7697	+	7.55124i	−1.36779	+	0.434525i
$303$	6.69629	+	11.5983i	0.384692	+	0.666305i
$304$	19.3765	+	1.52607i	1.11132	+	0.0875262i
$305$	4.61454	−	7.99262i	0.264228	−	0.457656i
$306$	−9.38272	−	8.56034i	−0.536375	−	0.489362i
$307$	−0.946958	+	0.946958i	−0.0540457	+	0.0540457i	−0.733613	−	0.679567i	$-0.762168\pi$
$307$	−0.946958	+	0.946958i	−0.0540457	+	0.0540457i	0.679567	+	0.733613i	$0.262168\pi$
$308$		0			0
$309$	5.27495	+	5.27495i	0.300081	+	0.300081i
$310$	3.69189	−	0.169209i	0.209685	−	0.00961045i
$311$	−7.82255	−	4.51635i	−0.443576	−	0.256099i	0.261537	−	0.965193i	$-0.415771\pi$
$311$	−7.82255	−	4.51635i	−0.443576	−	0.256099i	−0.705113	+	0.709095i	$0.749104\pi$
$312$	13.2719	+	31.4610i	0.751374	+	1.78113i
$313$	2.04109	−	1.17843i	0.115369	−	0.0666086i	−0.441205	−	0.897406i	$-0.645449\pi$
$313$	2.04109	−	1.17843i	0.115369	−	0.0666086i	0.556574	+	0.830798i	$0.312115\pi$
$314$	−27.8365	−	14.4142i	−1.57090	−	0.813438i
$315$		0			0
$316$	14.0185	−	9.90669i	0.788601	−	0.557295i
$317$	6.79860	+	1.82168i	0.381847	+	0.102316i	0.444636	−	0.895711i	$-0.353333\pi$
$317$	6.79860	+	1.82168i	0.381847	+	0.102316i	−0.0627892	+	0.998027i	$0.520000\pi$
$318$	−14.4746	−	3.17604i	−0.811694	−	0.178103i
$319$	5.41829	−	9.38475i	0.303366	−	0.525445i
$320$	8.21546	−	0.106848i	0.459258	−	0.00597300i
$321$	44.0646			2.45945
$322$		0			0
$323$	−19.3376	+	19.3376i	−1.07597	+	1.07597i
$324$	20.4163	+	9.41275i	1.13424	+	0.522930i
$325$	21.4601	−	5.75021i	1.19039	−	0.318964i
$326$	−22.8352	+	14.6173i	−1.26473	+	0.809578i
$327$	7.67458	−	4.43092i	0.424405	−	0.245030i
$328$	−7.04031	+	9.29970i	−0.388736	+	0.513490i
$329$		0			0
$330$	−1.88546	+	3.64119i	−0.103791	+	0.200441i
$331$	−5.76948	+	21.5320i	−0.317119	+	1.18350i	0.604881	+	0.796316i	$0.293221\pi$
$331$	−5.76948	+	21.5320i	−0.317119	+	1.18350i	−0.922000	+	0.387189i	$0.873446\pi$
$332$	5.78378	+	4.81060i	0.317426	+	0.264016i
$333$	−3.21841	−	12.0113i	−0.176368	−	0.658214i
$334$	9.70508	+	8.85444i	0.531038	+	0.484494i
$335$	8.76847			0.479072
$336$		0			0
$337$	−26.2199			−1.42829			−0.714145	−	0.699998i	$-0.753184\pi$
$337$	−26.2199			−1.42829			−0.714145	+	0.699998i	$0.753184\pi$
$338$	19.5496	+	17.8361i	1.06336	+	0.970156i
$339$	−1.29183	−	4.82117i	−0.0701625	−	0.261850i
$340$	−7.39231	+	8.88777i	−0.400904	+	0.482007i
$341$	0.867281	−	3.23674i	0.0469659	−	0.175279i
$342$	−5.04233	+	9.73770i	−0.272658	+	0.526555i
$343$		0			0
$344$	0.429211	+	3.10408i	0.0231415	+	0.167361i
$345$	−1.09192	+	0.630420i	−0.0587870	+	0.0339407i
$346$	9.97467	−	6.38500i	0.536241	−	0.343260i
$347$	−20.8607	+	5.58960i	−1.11986	+	0.300066i	−0.770827	−	0.637045i	$-0.780157\pi$
$347$	−20.8607	+	5.58960i	−1.11986	+	0.300066i	−0.349033	+	0.937110i	$0.613490\pi$
$348$	14.7718	−	32.0402i	0.791854	−	1.71754i
$349$	−3.97918	+	3.97918i	−0.213000	+	0.213000i	−0.805541	−	0.592540i	$-0.798125\pi$
$349$	−3.97918	+	3.97918i	−0.213000	+	0.213000i	0.592540	+	0.805541i	$0.298125\pi$
$350$		0			0
$351$	16.9527			0.904866
$352$	2.16299	−	7.12860i	0.115288	−	0.379956i
$353$	−16.0394	+	27.7811i	−0.853693	+	1.47864i	0.0241588	+	0.999708i	$0.492309\pi$
$353$	−16.0394	+	27.7811i	−0.853693	+	1.47864i	−0.877852	+	0.478932i	$0.841024\pi$
$354$	42.5328	+	9.33262i	2.26059	+	0.496023i
$355$	9.49875	+	2.54518i	0.504142	+	0.135084i
$356$	−3.25859	−	4.61107i	−0.172705	−	0.244386i
$357$		0			0
$358$	18.8399	+	9.75559i	0.995719	+	0.515599i
$359$	−12.6732	+	7.31687i	−0.668865	+	0.386169i	−0.795646	−	0.605761i	$-0.792869\pi$
$359$	−12.6732	+	7.31687i	−0.668865	+	0.386169i	0.126781	+	0.991931i	$0.459535\pi$
$360$	−1.74601	+	4.29401i	−0.0920229	+	0.226314i
$361$	3.99342	+	2.30560i	0.210180	+	0.121348i
$362$	−5.02302	+	0.230219i	−0.264004	+	0.0121001i
$363$	−14.0457	−	14.0457i	−0.737210	−	0.737210i
$364$		0			0
$365$	−9.19150	+	9.19150i	−0.481105	+	0.481105i
$366$	−20.1263	−	18.3623i	−1.05202	−	0.959812i
$367$	−15.6885	+	27.1733i	−0.818934	+	1.41843i	0.0875349	+	0.996161i	$0.472101\pi$
$367$	−15.6885	+	27.1733i	−0.818934	+	1.41843i	−0.906469	+	0.422273i	$0.861232\pi$
$368$	1.74193	−	1.48757i	0.0908041	−	0.0775452i
$369$	−3.29033	−	5.69902i	−0.171288	−	0.296679i
$370$	−10.7869	+	3.42682i	−0.560784	+	0.178152i
$371$		0			0
$372$	1.84788	−	10.7522i	0.0958082	−	0.557476i
$373$	−7.42298	+	27.7029i	−0.384347	+	1.43440i	0.454846	+	0.890570i	$0.349694\pi$
$373$	−7.42298	+	27.7029i	−0.384347	+	1.43440i	−0.839193	+	0.543833i	$0.816973\pi$
$374$	5.65089	+	8.82783i	0.292200	+	0.456476i
$375$	17.0561	+	9.84733i	0.880772	+	0.508514i
$376$	3.34914	−	26.7840i	0.172719	−	1.38128i
$377$		−	46.3398i		−	2.38662i
$378$		0			0
$379$	−15.3987	−	15.3987i	−0.790976	−	0.790976i	0.190677	−	0.981653i	$-0.438932\pi$
$379$	−15.3987	−	15.3987i	−0.790976	−	0.790976i	−0.981653	+	0.190677i	$0.938932\pi$
$380$	9.06393	+	4.17884i	0.464970	+	0.214370i
$381$	−2.93293	−	10.9458i	−0.150259	−	0.560773i
$382$	17.5667	+	3.85452i	0.898791	+	0.197214i
$383$	−1.42396	−	2.46638i	−0.0727612	−	0.126026i	0.827349	−	0.561688i	$-0.189848\pi$
$383$	−1.42396	−	2.46638i	−0.0727612	−	0.126026i	−0.900110	+	0.435662i	$0.856514\pi$
$384$	4.88966	−	23.7560i	0.249525	−	1.21229i
$385$		0			0
$386$	−7.93369	−	24.9736i	−0.403814	−	1.27112i
$387$	−1.70769	−	0.457574i	−0.0868067	−	0.0232598i
$388$	1.64304	+	17.8866i	0.0834125	+	0.908054i
$389$	26.1387	−	7.00385i	1.32529	−	0.355109i	0.474330	−	0.880347i	$-0.342690\pi$
$389$	26.1387	−	7.00385i	1.32529	−	0.355109i	0.850956	+	0.525238i	$0.176024\pi$
$390$	0.802800	+	17.5159i	0.0406514	+	0.886950i
$391$			3.22300i			0.162994i
$392$		0			0
$393$			33.1439i			1.67189i
$394$	−4.52480	+	0.207384i	−0.227956	+	0.0104479i
$395$	8.51439	−	2.28142i	0.428405	−	0.114791i
$396$	3.23128	+	2.68759i	0.162378	+	0.135056i
$397$	−1.37965	−	0.369676i	−0.0692426	−	0.0185535i	0.224031	−	0.974582i	$-0.428078\pi$
$397$	−1.37965	−	0.369676i	−0.0692426	−	0.0185535i	−0.293274	+	0.956028i	$0.594745\pi$
$398$	30.1265	−	9.57068i	1.51010	−	0.479735i
$399$		0			0
$400$	−14.8755	−	5.26862i	−0.743773	−	0.263431i
$401$	1.15254	+	1.99626i	0.0575550	+	0.0996882i	0.893367	−	0.449327i	$-0.148336\pi$
$401$	1.15254	+	1.99626i	0.0575550	+	0.0996882i	−0.835812	+	0.549015i	$0.815003\pi$
$402$	5.54762	−	25.2829i	0.276690	−	1.26100i
$403$	−3.70870	−	13.8411i	−0.184743	−	0.689472i
$404$	−4.32420	−	11.7223i	−0.215137	−	0.583205i
$405$	8.16323	+	8.16323i	0.405634	+	0.405634i
$406$		0			0
$407$			10.2621i			0.508671i
$408$	20.9500	+	26.9380i	1.03718	+	1.33363i
$409$	24.9640	+	14.4130i	1.23439	+	0.712675i	0.967942	−	0.251175i	$-0.0808168\pi$
$409$	24.9640	+	14.4130i	1.23439	+	0.712675i	0.266447	+	0.963849i	$0.414150\pi$
$410$	−5.04460	+	3.22916i	−0.249135	+	0.159477i
$411$	5.10691	−	19.0592i	0.251905	−	0.940123i
$412$	−4.01654	−	5.68362i	−0.197881	−	0.280012i
$413$		0			0
$414$	0.391290	+	1.23170i	0.0192309	+	0.0605347i
$415$	1.93154	+	3.34553i	0.0948156	+	0.164225i
$416$	−7.23153	−	31.0243i	−0.354555	−	1.52109i
$417$	−4.66226	+	8.07527i	−0.228312	+	0.395448i
$418$	6.09932	−	6.68528i	0.298328	−	0.326987i
$419$	−14.0457	+	14.0457i	−0.686179	+	0.686179i	−0.961385	−	0.275206i	$-0.911254\pi$
$419$	−14.0457	+	14.0457i	−0.686179	+	0.686179i	0.275206	+	0.961385i	$0.411254\pi$
$420$		0			0
$421$	5.53079	+	5.53079i	0.269554	+	0.269554i	0.828920	−	0.559366i	$-0.188956\pi$
$421$	5.53079	+	5.53079i	0.269554	+	0.269554i	−0.559366	+	0.828920i	$0.688956\pi$
$422$	0.176614	+	3.85343i	0.00859741	+	0.187582i
$423$	13.1885	+	7.61436i	0.641245	+	0.370223i
$424$	12.8069	+	5.20747i	0.621956	+	0.252897i
$425$	19.2292	−	11.1020i	0.932752	−	0.538525i
$426$	13.3484	−	25.7783i	0.646733	−	1.24896i
$427$		0			0
$428$	−40.5155	−	6.96302i	−1.95839	−	0.336570i
$429$	15.3564	+	4.11475i	0.741416	+	0.198662i
$430$	−0.344876	+	1.57175i	−0.0166314	+	0.0757964i
$431$	7.85427	−	13.6040i	0.378327	−	0.655281i	−0.612492	−	0.790477i	$-0.709833\pi$
$431$	7.85427	−	13.6040i	0.378327	−	0.655281i	0.990819	+	0.135195i	$0.0431662\pi$
$432$	−9.92338	−	6.82098i	−0.477439	−	0.328174i
$433$	−27.7885			−1.33543			−0.667716	−	0.744416i	$-0.732728\pi$
$433$	−27.7885			−1.33543			−0.667716	+	0.744416i	$0.732728\pi$
$434$		0			0
$435$	12.8109	−	12.8109i	0.614237	−	0.614237i
$436$	−7.75661	+	2.86131i	−0.371474	+	0.137032i
$437$	2.68786	−	0.720209i	0.128578	−	0.0344523i
$438$	20.6874	+	32.3180i	0.988483	+	1.54421i
$439$	−24.7473	+	14.2878i	−1.18112	+	0.681921i	−0.956274	−	0.292472i	$-0.905522\pi$
$439$	−24.7473	+	14.2878i	−1.18112	+	0.681921i	−0.224848	+	0.974394i	$0.572189\pi$
$440$	2.30897	−	3.04998i	0.110076	−	0.145402i
$441$		0			0
$442$	39.8020	+	20.6101i	1.89319	+	0.980323i
$443$	5.33964	−	19.9278i	0.253694	−	0.946799i	−0.715118	−	0.699003i	$-0.753627\pi$
$443$	5.33964	−	19.9278i	0.253694	−	0.946799i	0.968812	−	0.247795i	$-0.0797061\pi$
$444$	3.05622	+	33.2709i	0.145042	+	1.57897i
$445$	−0.750424	−	2.80062i	−0.0355735	−	0.132762i
$446$	−19.9268	+	21.8411i	−0.943562	+	1.03421i
$447$	−14.8394			−0.701879
$448$		0			0
$449$	2.63333			0.124275			0.0621373	−	0.998068i	$-0.480208\pi$
$449$	2.63333			0.124275			0.0621373	+	0.998068i	$0.480208\pi$
$450$	6.00076	−	6.57724i	0.282878	−	0.310054i
$451$	1.40558	+	5.24569i	0.0661860	+	0.247010i
$452$	0.425947	+	4.63699i	0.0200349	+	0.218106i
$453$	−9.78502	+	36.5182i	−0.459740	+	1.71577i
$454$	10.4763	+	5.42479i	0.491678	+	0.254598i
$455$		0			0
$456$	17.7838	−	23.4910i	0.832802	−	1.10007i
$457$	6.68069	−	3.85710i	0.312510	−	0.180428i	−0.335539	−	0.942026i	$-0.608919\pi$
$457$	6.68069	−	3.85710i	0.312510	−	0.180428i	0.648049	+	0.761599i	$0.275585\pi$
$458$	15.3339	+	23.9547i	0.716508	+	1.11933i
$459$	16.3653	−	4.38507i	0.763867	−	0.204678i
$460$	1.10359	−	0.407100i	0.0514551	−	0.0189811i
$461$	−19.0110	+	19.0110i	−0.885432	+	0.885432i	−0.994080	−	0.108649i	$-0.965348\pi$
$461$	−19.0110	+	19.0110i	−0.885432	+	0.885432i	0.108649	+	0.994080i	$0.465348\pi$
$462$		0			0
$463$	−12.7732			−0.593621			−0.296811	−	0.954936i	$-0.595923\pi$
$463$	−12.7732			−0.593621			−0.296811	+	0.954936i	$0.595923\pi$
$464$	−18.6450	+	27.1254i	−0.865573	+	1.25926i
$465$	2.80115	−	4.85174i	0.129900	−	0.224994i
$466$	2.83381	−	12.9149i	0.131274	−	0.598270i
$467$	9.23985	+	2.47581i	0.427569	+	0.114567i	0.466185	−	0.884687i	$-0.345628\pi$
$467$	9.23985	+	2.47581i	0.427569	+	0.114567i	−0.0386156	+	0.999254i	$0.512295\pi$
$468$	17.7129	+	3.04414i	0.818778	+	0.140716i
$469$		0			0
$470$	6.37360	−	12.3086i	0.293992	−	0.567755i
$471$	−41.1520	+	23.7591i	−1.89618	+	1.09476i
$472$	−37.6323	−	15.3019i	−1.73217	−	0.704327i
$473$	1.26353	+	0.729497i	0.0580970	+	0.0335423i
$474$	−1.19136	−	25.9937i	−0.0547212	−	1.19393i
$475$	−13.5555	−	13.5555i	−0.621970	−	0.621970i
$476$		0			0
$477$	−5.51535	+	5.51535i	−0.252531	+	0.252531i
$478$	7.02810	−	7.70328i	0.321458	−	0.352340i
$479$	−17.0112	+	29.4642i	−0.777261	+	1.34626i	0.156254	+	0.987717i	$0.450058\pi$
$479$	−17.0112	+	29.4642i	−0.777261	+	1.34626i	−0.933515	+	0.358539i	$0.883275\pi$
$480$	6.57765	−	10.5761i	0.300227	−	0.482729i
$481$	21.9415	+	38.0038i	1.00045	+	1.73282i
$482$	4.02656	+	12.6748i	0.183405	+	0.577320i
$483$		0			0
$484$	10.6950	+	15.1339i	0.486134	+	0.687906i
$485$	−2.38725	+	8.90932i	−0.108399	+	0.404552i
$486$	17.9456	−	11.4874i	0.814029	−	0.521078i
$487$	−15.8637	−	9.15891i	−0.718853	−	0.415030i	0.0954776	−	0.995432i	$-0.469562\pi$
$487$	−15.8637	−	9.15891i	−0.718853	−	0.415030i	−0.814330	+	0.580402i	$0.802896\pi$
$488$	15.6037	+	20.0636i	0.706346	+	0.908239i
$489$			41.0998i			1.85860i
$490$		0			0
$491$	3.23636	+	3.23636i	0.146055	+	0.146055i	0.776353	−	0.630298i	$-0.217067\pi$
$491$	3.23636	+	3.23636i	0.146055	+	0.146055i	−0.630298	+	0.776353i	$0.717067\pi$
$492$	6.11931	+	16.5886i	0.275880	+	0.747871i
$493$	−11.9865	−	44.7342i	−0.539845	−	2.01473i
$494$	8.29388	−	37.7988i	0.373159	−	1.70065i
$495$	1.07911	+	1.86908i	0.0485025	+	0.0840088i
$496$	−3.39809	+	9.59419i	−0.152579	+	0.430792i
$497$		0			0
$498$	10.8685	−	3.45274i	0.487029	−	0.154721i
$499$	11.4424	+	3.06599i	0.512233	+	0.137252i	0.505672	−	0.862726i	$-0.331245\pi$
$499$	11.4424	+	3.06599i	0.512233	+	0.137252i	0.00656149	+	0.999978i	$0.497911\pi$
$500$	−14.1263	−	11.7494i	−0.631745	−	0.525447i
$501$	19.2360	−	5.15427i	0.859401	−	0.230276i
$502$	−14.4725	+	0.663316i	−0.645940	+	0.0296053i
$503$			33.5509i			1.49596i	0.663720	+	0.747981i	$0.268977\pi$
$503$			33.5509i			1.49596i	−0.663720	+	0.747981i	$0.731023\pi$
$504$		0			0
$505$		−	6.41600i		−	0.285508i
$506$	−0.0488306	−	1.06541i	−0.00217079	−	0.0473632i
$507$	38.7483	−	10.3826i	1.72087	−	0.461107i
$508$	0.967058	+	10.5277i	0.0429062	+	0.467090i
$509$	21.3485	+	5.72030i	0.946254	+	0.253548i	0.698772	−	0.715345i	$-0.253730\pi$
$509$	21.3485	+	5.72030i	0.946254	+	0.253548i	0.247482	+	0.968893i	$0.420397\pi$
$510$	5.30573	+	16.7013i	0.234942	+	0.739547i
$511$		0			0
$512$	−8.24971	+	21.0699i	−0.364589	+	0.931168i
$513$	−7.31395	−	12.6681i	−0.322919	−	0.559312i
$514$	8.41841	+	1.84718i	0.371320	+	0.0814757i
$515$	−0.924974	−	3.45205i	−0.0407592	−	0.152116i
$516$	4.31377	+	1.98882i	0.189903	+	0.0875530i
$517$	−8.88663	−	8.88663i	−0.390834	−	0.390834i
$518$		0			0
$519$		−	17.9529i		−	0.788043i
$520$	2.02968	−	16.2319i	0.0890076	−	0.711817i
$521$	−19.3677	−	11.1820i	−0.848516	−	0.489891i	0.0116337	−	0.999932i	$-0.496297\pi$
$521$	−19.3677	−	11.1820i	−0.848516	−	0.489891i	−0.860150	+	0.510041i	$0.829630\pi$
$522$	−10.0117	−	15.6404i	−0.438201	−	0.684560i
$523$	0.613074	−	2.28802i	0.0268079	−	0.100048i	−0.951226	−	0.308496i	$-0.900174\pi$
$523$	0.613074	−	2.28802i	0.0268079	−	0.100048i	0.978034	+	0.208448i	$0.0668411\pi$
$524$	5.23734	−	30.4744i	0.228794	−	1.33128i
$525$		0			0
$526$	1.35364	−	0.430029i	0.0590215	−	0.0187501i
$527$	−7.16041	−	12.4022i	−0.311912	−	0.540248i
$528$	−7.33343	−	8.58733i	−0.319147	−	0.373716i
$529$	−11.3360	+	19.6346i	−0.492871	+	0.853677i
$530$	5.24456	+	4.78488i	0.227809	+	0.207842i
$531$	16.2066	−	16.2066i	0.703306	−	0.703306i
$532$		0			0
$533$	16.4212	+	16.4212i	0.711281	+	0.711281i
$534$	−8.55006	+	0.391873i	−0.369997	+	0.0169580i
$535$	−18.2819	−	10.5551i	−0.790395	−	0.456335i
$536$	−9.09596	+	22.3699i	−0.392886	+	0.966233i
$537$	27.8519	−	16.0803i	1.20190	−	0.693916i
$538$	18.5820	+	9.62203i	0.801126	+	0.414835i
$539$		0			0
$540$	−3.56861	−	5.04977i	−0.153569	−	0.217307i
$541$	8.34164	+	2.23514i	0.358635	+	0.0960960i	0.433638	−	0.901087i	$-0.357230\pi$
$541$	8.34164	+	2.23514i	0.358635	+	0.0960960i	−0.0750025	+	0.997183i	$0.523896\pi$
$542$	−14.8834	−	3.26574i	−0.639296	−	0.140275i
$543$	−3.81113	+	6.60108i	−0.163551	+	0.283279i
$544$	−15.0059	−	28.0788i	−0.643372	−	1.20387i
$545$	−4.24546			−0.181855
$546$		0			0
$547$	25.4590	−	25.4590i	1.08855	−	1.08855i	0.0928708	−	0.995678i	$-0.470396\pi$
$547$	25.4590	−	25.4590i	1.08855	−	1.08855i	0.995678	−	0.0928708i	$-0.0296044\pi$
$548$	−7.70728	+	16.7171i	−0.329239	+	0.714121i
$549$	−13.8512	+	3.71143i	−0.591156	+	0.158400i
$550$	−6.18827	+	3.96124i	−0.263869	+	0.168908i
$551$	−34.6281	+	19.9925i	−1.47521	+	0.851711i
$552$	−0.475612	−	3.43965i	−0.0202434	−	0.146401i
$553$		0			0
$554$	2.52230	−	4.87104i	0.107162	−	0.206951i
$555$	−4.44052	+	16.5723i	−0.188490	+	0.703453i
$556$	5.56278	−	6.68814i	0.235915	−	0.283640i
$557$	−0.990242	−	3.69563i	−0.0419579	−	0.156589i	0.941769	−	0.336262i	$-0.109163\pi$
$557$	−0.990242	−	3.69563i	−0.0419579	−	0.156589i	−0.983726	+	0.179673i	$0.942496\pi$
$558$	−4.24211	−	3.87029i	−0.179583	−	0.163843i
$559$	6.23900			0.263882
$560$		0			0
$561$	15.8887			0.670823
$562$	−16.5100	−	15.0629i	−0.696433	−	0.635391i
$563$	4.76300	+	17.7758i	0.200736	+	0.749159i	0.990707	+	0.136014i	$0.0434291\pi$
$563$	4.76300	+	17.7758i	0.200736	+	0.749159i	−0.789970	+	0.613145i	$0.789904\pi$
$564$	−31.4582	−	26.1650i	−1.32463	−	1.10175i
$565$	−0.618878	+	2.30969i	−0.0260364	+	0.0971692i
$566$	−3.73416	+	7.21138i	−0.156959	+	0.303117i
$567$		0			0
$568$	−16.3467	+	21.5928i	−0.685894	+	0.906012i
$569$	6.35393	−	3.66845i	0.266371	−	0.153789i	−0.360866	−	0.932618i	$-0.617519\pi$
$569$	6.35393	−	3.66845i	0.266371	−	0.153789i	0.627237	+	0.778828i	$0.284186\pi$
$570$	12.7426	−	8.15683i	0.533730	−	0.341652i
$571$	−24.2573	+	6.49973i	−1.01514	+	0.272005i	−0.727775	−	0.685816i	$-0.759445\pi$
$571$	−24.2573	+	6.49973i	−1.01514	+	0.272005i	−0.287363	+	0.957822i	$0.592779\pi$
$572$	−13.4694	−	6.20993i	−0.563183	−	0.259650i
$573$	19.2774	−	19.2774i	0.805327	−	0.805327i
$574$		0			0
$575$	−2.25931			−0.0942197
$576$	−9.14355	−	8.90877i	−0.380981	−	0.371199i
$577$	−4.46876	+	7.74012i	−0.186037	+	0.322225i	−0.943925	−	0.330159i	$-0.892898\pi$
$577$	−4.46876	+	7.74012i	−0.186037	+	0.322225i	0.757889	+	0.652384i	$0.226231\pi$
$578$	20.2712	+	4.44794i	0.843170	+	0.185010i
$579$	−38.3677	−	10.2806i	−1.59451	−	0.427247i
$580$	−13.8034	+	9.75473i	−0.573157	+	0.405043i
$581$		0			0
$582$	24.1787	+	12.5201i	1.00224	+	0.518975i
$583$	5.57452	−	3.21845i	0.230873	−	0.133295i
$584$	−13.9144	−	32.9839i	−0.575780	−	1.36489i
$585$	7.99262	+	4.61454i	0.330454	+	0.190788i
$586$	12.8042	−	0.586852i	0.528937	−	0.0242426i
$587$	−12.3651	−	12.3651i	−0.510363	−	0.510363i	0.404274	−	0.914638i	$-0.367524\pi$
$587$	−12.3651	−	12.3651i	−0.510363	−	0.510363i	−0.914638	+	0.404274i	$0.867524\pi$
$588$		0			0
$589$	−8.74288	+	8.74288i	−0.360244	+	0.360244i
$590$	−15.4109	−	14.0601i	−0.634455	−	0.578846i
$591$	−3.43312	+	5.94633i	−0.141220	+	0.244599i
$592$	2.44735	−	31.0741i	0.100586	−	1.27714i
$593$	7.45619	+	12.9145i	0.306189	+	0.530335i	0.977525	−	0.210818i	$-0.0676127\pi$
$593$	7.45619	+	12.9145i	0.306189	+	0.530335i	−0.671336	+	0.741153i	$0.734279\pi$
$594$	−5.34334	+	1.69749i	−0.219240	+	0.0696489i
$595$		0			0
$596$	13.6442	+	2.34490i	0.558887	+	0.0960507i
$597$	12.4018	−	46.2843i	0.507573	−	1.89429i
$598$	−2.45880	−	3.84115i	−0.100548	−	0.157076i
$599$	3.14899	+	1.81807i	0.128664	+	0.0742844i	0.562951	−	0.826490i	$-0.309666\pi$
$599$	3.14899	+	1.81807i	0.128664	+	0.0742844i	−0.434286	+	0.900775i	$0.642999\pi$
$600$	−18.8834	+	14.6858i	−0.770912	+	0.599546i
$601$		−	24.4392i		−	0.996896i	−0.866920	−	0.498448i	$-0.833903\pi$
$601$		−	24.4392i		−	0.996896i	0.866920	−	0.498448i	$-0.166097\pi$
$602$		0			0
$603$	−9.63374	−	9.63374i	−0.392316	−	0.392316i
$604$	14.7674	−	32.0307i	0.600879	−	1.30331i
$605$	2.46295	+	9.19187i	0.100133	+	0.373703i
$606$	−18.4998	−	4.05927i	−0.751505	−	0.164896i
$607$	−17.3000	−	29.9645i	−0.702186	−	1.21622i	−0.967698	−	0.252114i	$-0.918874\pi$
$607$	−17.3000	−	29.9645i	−0.702186	−	1.21622i	0.265512	−	0.964108i	$-0.414459\pi$
$608$	−20.0634	+	18.7888i	−0.813679	+	0.761985i
$609$		0			0
$610$	3.95175	+	12.4393i	0.160002	+	0.503651i
$611$	−51.9108	−	13.9094i	−2.10009	−	0.562716i
$612$	17.8866	−	1.64304i	0.723023	−	0.0664158i
$613$	−39.3423	+	10.5417i	−1.58902	+	0.425777i	−0.941703	−	0.336444i	$-0.890776\pi$
$613$	−39.3423	+	10.5417i	−1.58902	+	0.425777i	−0.647317	+	0.762221i	$0.724109\pi$
$614$	−0.0867124	−	1.89193i	−0.00349943	−	0.0763520i
$615$			9.07950i			0.366121i
$616$		0			0
$617$			20.5545i			0.827493i	0.910392	+	0.413746i	$0.135780\pi$
$617$			20.5545i			0.827493i	−0.910392	+	0.413746i	$0.864220\pi$
$618$	−10.5388	+	0.483024i	−0.423934	+	0.0194301i
$619$	−24.2093	+	6.48686i	−0.973053	+	0.260729i	−0.710116	−	0.704084i	$-0.751358\pi$
$619$	−24.2093	+	6.48686i	−0.973053	+	0.260729i	−0.262937	+	0.964813i	$0.584691\pi$
$620$	−3.34220	+	4.01833i	−0.134226	+	0.161380i
$621$	−1.66521	−	0.446192i	−0.0668227	−	0.0179051i
$622$	12.1746	−	3.86766i	0.488156	−	0.155079i
$623$		0			0
$624$	−45.5188	−	16.1220i	−1.82221	−	0.645395i
$625$	5.14550	+	8.91227i	0.205820	+	0.356491i
$626$	−0.714359	+	3.25564i	−0.0285515	+	0.130122i
$627$	−3.55048	−	13.2506i	−0.141793	−	0.529177i
$628$	41.5918	−	15.3427i	1.65969	−	0.612240i
$629$	31.0116	+	31.0116i	1.23651	+	1.23651i
$630$		0			0
$631$		−	39.8948i		−	1.58819i	−0.607795	−	0.794094i	$-0.707946\pi$
$631$		−	39.8948i		−	1.58819i	0.607795	−	0.794094i	$-0.292054\pi$
$632$	−3.01207	+	24.0883i	−0.119814	+	0.958183i
$633$	5.06404	+	2.92373i	0.201278	+	0.116208i
$634$	−8.38337	+	5.36638i	−0.332946	+	0.213126i
$635$	−1.40508	+	5.24385i	−0.0557591	+	0.208096i
$636$	17.1148	−	12.0948i	0.678646	−	0.479591i
$637$		0			0
$638$	4.64006	+	14.6059i	0.183702	+	0.578254i
$639$	−7.63975	−	13.2324i	−0.302224	−	0.523467i
$640$	−7.71907	+	8.68483i	−0.305123	+	0.343298i
$641$	8.94810	−	15.4986i	0.353429	−	0.612157i	−0.633419	−	0.773809i	$-0.718349\pi$
$641$	8.94810	−	15.4986i	0.353429	−	0.612157i	0.986848	+	0.161652i	$0.0516823\pi$
$642$	−42.0009	+	46.0359i	−1.65764	+	1.81689i
$643$	−30.0202	+	30.0202i	−1.18388	+	1.18388i	−0.205152	+	0.978730i	$0.565769\pi$
$643$	−30.0202	+	30.0202i	−1.18388	+	1.18388i	−0.978730	+	0.205152i	$0.934231\pi$
$644$		0			0
$645$	1.72481	+	1.72481i	0.0679144	+	0.0679144i
$646$	−1.77073	−	38.6346i	−0.0696684	−	1.52006i
$647$	2.97970	+	1.72033i	0.117144	+	0.0676331i	0.557427	−	0.830226i	$-0.311789\pi$
$647$	2.97970	+	1.72033i	0.117144	+	0.0676331i	−0.440283	+	0.897859i	$0.645122\pi$
$648$	−29.2940	+	12.3577i	−1.15078	+	0.485458i
$649$	−16.3805	+	9.45726i	−0.642989	+	0.371230i
$650$	−14.4476	+	27.9010i	−0.566681	+	1.09437i
$651$		0			0
$652$	6.49453	−	37.7895i	0.254345	−	1.47995i
$653$	27.9763	+	7.49623i	1.09480	+	0.293350i	0.760645	−	0.649169i	$-0.224883\pi$
$653$	27.9763	+	7.49623i	1.09480	+	0.293350i	0.334153	+	0.942519i	$0.391550\pi$
$654$	−2.68601	+	12.2413i	−0.105031	+	0.478673i
$655$	7.93916	−	13.7510i	0.310208	−	0.537297i
$656$	−3.00514	−	16.2194i	−0.117331	−	0.633262i
$657$	20.1970			0.787961
$658$		0			0
$659$	21.0017	−	21.0017i	0.818111	−	0.818111i	−0.167723	−	0.985834i	$-0.553641\pi$
$659$	21.0017	−	21.0017i	0.818111	−	0.818111i	0.985834	+	0.167723i	$0.0536414\pi$
$660$	−2.00692	−	5.44047i	−0.0781193	−	0.211770i
$661$	−26.4317	+	7.08235i	−1.02807	+	0.275472i	−0.733163	−	0.680053i	$-0.761957\pi$
$661$	−26.4317	+	7.08235i	−1.02807	+	0.275472i	−0.294911	+	0.955525i	$0.595290\pi$
$662$	−16.9960	−	26.5511i	−0.660567	−	1.03194i
$663$	58.8412	−	33.9720i	2.28520	−	1.31936i
$664$	−10.5387	+	1.45722i	−0.408981	+	0.0565513i
$665$		0			0
$666$	15.6163	+	8.08636i	0.605120	+	0.313340i
$667$	−1.21966	+	4.55182i	−0.0472253	+	0.176247i
$668$	−18.5011	+	1.69949i	−0.715830	+	0.0657551i
$669$	11.5996	+	43.2903i	0.448467	+	1.67370i
$670$	−8.35781	+	9.16073i	−0.322890	+	0.353910i
$671$	11.8340			0.456848
$672$		0			0
$673$	−26.3363			−1.01519			−0.507594	−	0.861596i	$-0.669465\pi$
$673$	−26.3363			−1.01519			−0.507594	+	0.861596i	$0.669465\pi$
$674$	24.9919	−	27.3929i	0.962654	−	1.05513i
$675$	3.07391	+	11.4720i	0.118315	+	0.441557i
$676$	−37.2680	+	3.42339i	−1.43339	+	0.131669i
$677$	8.69514	−	32.4507i	0.334181	−	1.24718i	−0.570573	−	0.821247i	$-0.693279\pi$
$677$	8.69514	−	32.4507i	0.334181	−	1.24718i	0.904754	−	0.425934i	$-0.140055\pi$
$678$	6.26818	+	3.24576i	0.240728	+	0.124653i
$679$		0			0
$680$	−2.23928	−	16.1945i	−0.0858723	−	0.621032i
$681$	15.4876	−	8.94178i	0.593487	−	0.342650i
$682$	2.55487	+	3.99123i	0.0978312	+	0.152832i
$683$	6.75807	−	1.81082i	0.258590	−	0.0692890i	−0.127195	−	0.991878i	$-0.540597\pi$
$683$	6.75807	−	1.81082i	0.258590	−	0.0692890i	0.385785	+	0.922589i	$0.373931\pi$
$684$	−5.36715	−	14.5496i	−0.205218	−	0.556316i
$685$	−6.68416	+	6.68416i	−0.255389	+	0.255389i
$686$		0			0
$687$	43.1148			1.64493
$688$	−3.65205	−	2.51029i	−0.139233	−	0.0957039i
$689$	13.7629	−	23.8380i	0.524323	−	0.908154i
$690$	0.382159	−	1.74166i	0.0145485	−	0.0663040i
$691$	8.46454	+	2.26807i	0.322006	+	0.0862813i	0.416201	−	0.909272i	$-0.363361\pi$
$691$	8.46454	+	2.26807i	0.322006	+	0.0862813i	−0.0941952	+	0.995554i	$0.530028\pi$
$692$	−2.83688	+	16.5069i	−0.107842	+	0.627497i
$693$		0			0
$694$	14.0440	−	27.1217i	0.533105	−	1.02953i
$695$	3.86863	−	2.23356i	0.146746	−	0.0847236i
$696$	19.3935	+	45.9724i	0.735111	+	1.74258i
$697$	20.0999	+	11.6047i	0.761337	+	0.439558i
$698$	−0.364371	−	7.95001i	−0.0137916	−	0.300912i
$699$	−14.1726	−	14.1726i	−0.536057	−	0.536057i
$700$		0			0
$701$	6.06405	−	6.06405i	0.229036	−	0.229036i	−0.583254	−	0.812290i	$-0.698221\pi$
$701$	6.06405	−	6.06405i	0.229036	−	0.229036i	0.812290	+	0.583254i	$0.198221\pi$
$702$	−16.1587	+	17.7111i	−0.609871	+	0.668461i
$703$	18.9326	−	32.7922i	0.714056	−	1.23678i
$704$	5.38582	+	9.05449i	0.202986	+	0.341254i
$705$	−10.5057	−	18.1964i	−0.395668	−	0.685317i
$706$	−13.7357	−	43.2370i	−0.516949	−	1.62725i
$707$		0			0
$708$	−50.2910	+	35.5400i	−1.89005	+	1.33568i
$709$	10.0462	−	37.4930i	0.377294	−	1.40808i	−0.472670	−	0.881240i	$-0.656710\pi$
$709$	10.0462	−	37.4930i	0.377294	−	1.40808i	0.849964	−	0.526841i	$-0.176624\pi$
$710$	−11.7129	+	7.49771i	−0.439579	+	0.281384i
$711$	−11.8611	−	6.84803i	−0.444827	−	0.256821i
$712$	7.92333	+	0.990756i	0.296939	+	0.0371301i
$713$			1.45718i			0.0545718i
$714$		0			0
$715$	−5.38558	−	5.38558i	−0.201409	−	0.201409i
$716$	−28.1496	+	10.3840i	−1.05200	+	0.388069i
$717$	−4.09113	−	15.2683i	−0.152786	−	0.570206i
$718$	4.43546	−	20.2143i	0.165530	−	0.754392i
$719$	13.7596	+	23.8323i	0.513145	+	0.888794i	0.999884	+	0.0152461i	$0.00485318\pi$
$719$	13.7596	+	23.8323i	0.513145	+	0.888794i	−0.486738	+	0.873548i	$0.661813\pi$
$720$	−2.82186	−	5.91702i	−0.105165	−	0.220514i
$721$		0			0
$722$	−6.21515	+	1.97445i	−0.231304	+	0.0734814i
$723$	19.4727	+	5.21768i	0.724196	+	0.194048i
$724$	4.54726	−	5.46717i	0.168998	−	0.203186i
$725$	31.3585	−	8.40248i	1.16462	−	0.312060i
$726$	28.0620	−	1.28616i	1.04148	−	0.0477339i
$727$		−	22.9836i		−	0.852416i	−0.904625	−	0.426208i	$-0.859849\pi$
$727$		−	22.9836i		−	0.852416i	0.904625	−	0.426208i	$-0.140151\pi$
$728$		0			0
$729$			1.42320i			0.0527110i
$730$	−0.841660	−	18.3637i	−0.0311513	−	0.679672i
$731$	6.02284	−	1.61382i	0.222763	−	0.0596891i
$732$	38.3675	−	3.52438i	1.41810	−	0.130265i
$733$	−20.8367	−	5.58317i	−0.769620	−	0.206219i	−0.147416	−	0.989075i	$-0.547096\pi$
$733$	−20.8367	−	5.58317i	−0.769620	−	0.206219i	−0.622203	+	0.782856i	$0.713762\pi$
$734$	−13.4352	−	42.2910i	−0.495901	−	1.56099i
$735$		0			0
$736$	−0.106223	+	3.23776i	−0.00391542	+	0.119345i
$737$	5.62171	+	9.73709i	0.207078	+	0.358670i
$738$	9.09021	+	1.99459i	0.334615	+	0.0734218i
$739$	10.6015	+	39.5654i	0.389983	+	1.45544i	0.830160	+	0.557525i	$0.188249\pi$
$739$	10.6015	+	39.5654i	0.389983	+	1.45544i	−0.440177	+	0.897911i	$0.645084\pi$
$740$	6.70158	−	14.5358i	0.246355	−	0.534346i
$741$	−41.4799	−	41.4799i	−1.52380	−	1.52380i
$742$		0			0
$743$		−	36.3344i		−	1.33298i	−0.745514	−	0.666490i	$-0.767796\pi$
$743$		−	36.3344i		−	1.33298i	0.745514	−	0.666490i	$-0.232204\pi$
$744$	9.47188	+	12.1792i	0.347256	+	0.446511i
$745$	6.15669	+	3.55457i	0.225564	+	0.130229i
$746$	−21.8669	−	34.1605i	−0.800604	−	1.25071i
$747$	1.55352	−	5.79781i	0.0568402	−	0.212131i
$748$	−14.6090	−	2.51071i	−0.534158	−	0.0918007i
$749$		0			0
$750$	−26.5451	+	8.43295i	−0.969291	+	0.307928i
$751$	17.6258	+	30.5288i	0.643175	+	1.11401i	0.984720	+	0.174146i	$0.0557166\pi$
$751$	17.6258	+	30.5288i	0.643175	+	1.11401i	−0.341545	+	0.939866i	$0.610950\pi$
$752$	24.7899	+	29.0285i	0.903994	+	1.05856i
$753$	−10.9808	+	19.0193i	−0.400162	+	0.693101i
$754$	48.4128	+	44.1695i	1.76309	+	1.60856i
$755$	12.8071	−	12.8071i	0.466098	−	0.466098i
$756$		0			0
$757$	−15.9910	−	15.9910i	−0.581203	−	0.581203i	0.354031	−	0.935234i	$-0.384811\pi$
$757$	−15.9910	−	15.9910i	−0.581203	−	0.581203i	−0.935234	+	0.354031i	$0.884811\pi$
$758$	30.7650	−	1.41005i	1.11744	−	0.0512152i
$759$	−1.40012	−	0.808360i	−0.0508212	−	0.0293416i
$760$	−13.0052	+	5.48628i	−0.471749	+	0.199008i
$761$	−27.7326	+	16.0115i	−1.00531	+	0.580415i	−0.909814	−	0.415015i	$-0.863776\pi$
$761$	−27.7326	+	16.0115i	−1.00531	+	0.580415i	−0.0954932	+	0.995430i	$0.530443\pi$
$762$	14.2311	+	7.36908i	0.515538	+	0.266954i
$763$		0			0
$764$	−20.7710	+	14.6786i	−0.751467	+	0.531052i
$765$	8.90932	+	2.38725i	0.322117	+	0.0863111i
$766$	3.93399	+	0.863203i	0.142141	+	0.0311888i
$767$	−40.4415	+	70.0467i	−1.46026	+	2.52924i
$768$	20.1581	+	27.7518i	0.727392	+	1.00141i
$769$	45.1390			1.62775			0.813876	−	0.581038i	$-0.197353\pi$
$769$	45.1390			1.62775			0.813876	+	0.581038i	$0.197353\pi$
$770$		0			0
$771$	9.23823	−	9.23823i	0.332707	−	0.332707i
$772$	33.6529	+	15.5154i	1.21120	+	0.558410i
$773$	49.3755	−	13.2301i	1.77591	−	0.475855i	0.786085	−	0.618118i	$-0.212105\pi$
$773$	49.3755	−	13.2301i	1.77591	−	0.475855i	0.989829	+	0.142263i	$0.0454379\pi$
$774$	2.10575	−	1.34794i	0.0756898	−	0.0484507i
$775$	8.69387	−	5.01941i	0.312293	−	0.180303i
$776$	−20.2529	−	15.3324i	−0.727035	−	0.550400i
$777$		0			0
$778$	−17.5974	+	33.9839i	−0.630897	+	1.21838i
$779$	5.18633	−	19.3557i	0.185820	−	0.693488i
$780$	−19.0646	−	15.8568i	−0.682624	−	0.567765i
$781$	3.26358	+	12.1798i	0.116780	+	0.435829i
$782$	−3.36719	−	3.07206i	−0.120410	−	0.109857i
$783$	24.7720			0.885280
$784$		0			0
$785$	22.7646			0.812504
$786$	−34.6266	−	31.5917i	−1.23509	−	1.12684i
$787$	−2.45498	−	9.16210i	−0.0875105	−	0.326593i	0.908267	−	0.418390i	$-0.137406\pi$
$787$	−2.45498	−	9.16210i	−0.0875105	−	0.326593i	−0.995778	+	0.0917969i	$0.970739\pi$
$788$	4.09623	−	4.92490i	0.145922	−	0.175442i
$789$	0.557238	−	2.07964i	0.0198382	−	0.0740371i
$790$	−5.73214	+	11.0699i	−0.203941	+	0.393848i
$791$		0			0
$792$	−5.88777	+	0.814122i	−0.209213	+	0.0289286i
$793$	43.8254	−	25.3026i	1.55628	−	0.898521i
$794$	1.70125	−	1.08901i	0.0603751	−	0.0386474i
$795$	10.3950	−	2.78533i	0.368672	−	0.0987854i
$796$	−18.7167	+	40.5967i	−0.663396	+	1.43891i
$797$	23.5858	−	23.5858i	0.835450	−	0.835450i	−0.152806	−	0.988256i	$-0.548831\pi$
$797$	23.5858	−	23.5858i	0.835450	−	0.835450i	0.988256	+	0.152806i	$0.0488309\pi$
$798$		0			0
$799$	−53.7101			−1.90013
$800$	19.6831	−	10.5190i	0.695903	−	0.371905i
$801$	−2.25251	+	3.90146i	−0.0795885	+	0.137851i
$802$	−3.18412	−	0.698665i	−0.112435	−	0.0246707i
$803$	−16.0998	−	4.31392i	−0.568149	−	0.152235i
$804$	21.1262	+	29.8946i	0.745063	+	1.05430i
$805$		0			0
$806$	17.9953	+	9.31822i	0.633856	+	0.328220i
$807$	27.4706	−	15.8602i	0.967011	−	0.558304i
$808$	16.3684	+	6.65563i	0.575837	+	0.234144i
$809$	6.68666	+	3.86054i	0.235090	+	0.135729i	0.612918	−	0.790146i	$-0.289996\pi$
$809$	6.68666	+	3.86054i	0.235090	+	0.135729i	−0.377828	+	0.925876i	$0.623329\pi$
$810$	−16.3093	+	0.747503i	−0.573052	+	0.0262646i
$811$	29.6043	+	29.6043i	1.03955	+	1.03955i	0.999185	+	0.0403642i	$0.0128518\pi$
$811$	29.6043	+	29.6043i	1.03955	+	1.03955i	0.0403642	+	0.999185i	$0.487148\pi$
$812$		0			0
$813$	−16.3328	+	16.3328i	−0.572816	+	0.572816i
$814$	−10.7211	−	9.78145i	−0.375776	−	0.342840i
$815$	9.84489	−	17.0518i	0.344851	−	0.597300i
$816$	−48.1119	−	3.78923i	−1.68426	−	0.132650i
$817$	−2.69172	−	4.66219i	−0.0941712	−	0.163109i
$818$	−38.8526	+	12.3428i	−1.35845	+	0.431556i
$819$		0			0
$820$	1.43473	−	8.34820i	0.0501028	−	0.291532i
$821$	−4.84905	+	18.0969i	−0.169233	+	0.631586i	0.828229	+	0.560390i	$0.189349\pi$
$821$	−4.84905	+	18.0969i	−0.169233	+	0.631586i	−0.997462	+	0.0711970i	$0.977318\pi$
$822$	15.0441	+	23.5020i	0.524724	+	0.819726i
$823$	1.88654	+	1.08919i	0.0657606	+	0.0379669i	0.532520	−	0.846418i	$-0.321245\pi$
$823$	1.88654	+	1.08919i	0.0657606	+	0.0379669i	−0.466759	+	0.884384i	$0.654579\pi$
$824$	9.76632	+	1.22121i	0.340226	+	0.0425428i
$825$			11.1379i			0.387773i
$826$		0			0
$827$	−16.9223	−	16.9223i	−0.588448	−	0.588448i	0.348763	−	0.937211i	$-0.386602\pi$
$827$	−16.9223	−	16.9223i	−0.588448	−	0.588448i	−0.937211	+	0.348763i	$0.886602\pi$
$828$	−1.65976	−	0.765219i	−0.0576808	−	0.0265932i
$829$	6.55637	+	24.4687i	0.227712	+	0.849833i	0.981300	+	0.192486i	$0.0616549\pi$
$829$	6.55637	+	24.4687i	0.227712	+	0.849833i	−0.753588	+	0.657347i	$0.771678\pi$
$830$	−5.33627	−	1.17089i	−0.185225	−	0.0406423i
$831$	−4.15755	−	7.20109i	−0.144224	−	0.249803i
$832$	39.3050	+	22.0162i	1.36266	+	0.763276i
$833$		0			0
$834$	−3.99262	−	12.5679i	−0.138253	−	0.435191i
$835$	−9.21542	−	2.46926i	−0.318913	−	0.0854524i
$836$	1.17068	+	12.7444i	0.0404888	+	0.440773i
$837$	7.39906	−	1.98257i	0.255749	−	0.0685278i
$838$	−1.28616	−	28.0620i	−0.0444297	−	0.969386i
$839$		−	37.1837i		−	1.28372i	−0.766820	−	0.641862i	$-0.778162\pi$
$839$		−	37.1837i		−	1.28372i	0.766820	−	0.641862i	$-0.221838\pi$
$840$		0			0
$841$		−	38.7138i		−	1.33496i
$842$	−11.0500	+	0.506451i	−0.380807	+	0.0174535i
$843$	−32.7237	+	8.76829i	−1.12706	+	0.301996i
$844$	−4.19416	−	3.48845i	−0.144369	−	0.120077i
$845$	−18.5632	−	4.97400i	−0.638595	−	0.171111i
$846$	−20.5258	+	6.52070i	−0.705691	+	0.224186i
$847$		0			0
$848$	−17.6475	+	8.41620i	−0.606018	+	0.289014i
$849$	6.15509	+	10.6609i	0.211242	+	0.365882i
$850$	−6.72998	+	30.6714i	−0.230836	+	1.05202i
$851$	−1.15500	−	4.31050i	−0.0395927	−	0.147762i
$852$	14.2083	+	38.5166i	0.486768	+	1.31956i
$853$	10.9925	+	10.9925i	0.376375	+	0.376375i	0.869793	−	0.493417i	$-0.164252\pi$
$853$	10.9925	+	10.9925i	0.376375	+	0.376375i	−0.493417	+	0.869793i	$0.664252\pi$
$854$		0			0
$855$		−	7.96347i		−	0.272345i
$856$	45.8925	−	35.6911i	1.56857	−	1.21990i
$857$	16.6790	+	9.62961i	0.569743	+	0.328941i	0.757047	−	0.653361i	$-0.226642\pi$
$857$	16.6790	+	9.62961i	0.569743	+	0.328941i	−0.187304	+	0.982302i	$0.559975\pi$
$858$	−18.9361	+	12.1214i	−0.646467	+	0.413817i
$859$	−10.8937	+	40.6558i	−0.371687	+	1.38716i	0.486437	+	0.873715i	$0.338296\pi$
$859$	−10.8937	+	40.6558i	−0.371687	+	1.38716i	−0.858125	+	0.513441i	$0.828371\pi$
$860$	−1.31334	−	1.85844i	−0.0447844	−	0.0633723i
$861$		0			0
$862$	6.72615	+	21.1725i	0.229094	+	0.721138i
$863$	−23.0898	−	39.9927i	−0.785985	−	1.36137i	−0.928409	−	0.371560i	$-0.878823\pi$
$863$	−23.0898	−	39.9927i	−0.785985	−	1.36137i	0.142424	−	0.989806i	$-0.454510\pi$
$864$	16.5848	−	3.86578i	0.564225	−	0.131517i
$865$	−4.30035	+	7.44843i	−0.146216	+	0.253254i
$866$	26.4871	−	29.0317i	0.900069	−	0.986537i
$867$	22.2453	−	22.2453i	0.755490	−	0.755490i
$868$		0			0
$869$	7.99226	+	7.99226i	0.271119	+	0.271119i
$870$	1.17309	+	25.5950i	0.0397715	+	0.867751i
$871$	41.6381	+	24.0398i	1.41085	+	0.814556i
$872$	4.40402	−	10.8309i	0.149139	−	0.366781i
$873$	12.4113	−	7.16567i	0.420059	−	0.242521i
$874$	−1.80955	+	3.49458i	−0.0612088	+	0.118206i
$875$		0			0
$876$	−53.4823	−	9.19150i	−1.80700	−	0.310552i
$877$	−12.1025	−	3.24285i	−0.408672	−	0.109503i	0.0486255	−	0.998817i	$-0.484516\pi$
$877$	−12.1025	−	3.24285i	−0.408672	−	0.109503i	−0.457298	+	0.889314i	$0.651183\pi$
$878$	8.66124	−	39.4730i	0.292303	−	1.33215i
$879$	9.71496	−	16.8268i	0.327678	−	0.567554i
$880$	0.985582	+	5.31940i	0.0332239	+	0.179317i
$881$	−55.9288			−1.88429			−0.942144	−	0.335208i	$-0.891193\pi$
$881$	−55.9288			−1.88429			−0.942144	+	0.335208i	$0.891193\pi$
$882$		0			0
$883$	0.336329	−	0.336329i	0.0113184	−	0.0113184i	−0.701425	−	0.712743i	$-0.747452\pi$
$883$	0.336329	−	0.336329i	0.0113184	−	0.0113184i	0.712743	+	0.701425i	$0.247452\pi$
$884$	−59.4701	+	21.9378i	−2.00020	+	0.737847i
$885$	−30.5452	+	8.18455i	−1.02676	+	0.275121i
$886$	15.7297	+	24.5730i	0.528451	+	0.825547i
$887$	−12.1158	+	6.99504i	−0.406808	+	0.234870i	−0.689417	−	0.724365i	$-0.742133\pi$
$887$	−12.1158	+	6.99504i	−0.406808	+	0.234870i	0.282610	+	0.959235i	$0.408800\pi$
$888$	−37.6724	−	28.5198i	−1.26420	−	0.957061i
$889$		0			0
$890$	3.64119	+	1.88546i	0.122053	+	0.0632009i
$891$	−3.83132	+	14.2987i	−0.128354	+	0.479024i
$892$	−3.82467	−	41.6365i	−0.128059	−	1.39409i
$893$	12.0020	+	44.7921i	0.401632	+	1.49891i
$894$	14.1444	−	15.5033i	0.473060	−	0.518506i
$895$	−15.4072			−0.515007
$896$		0			0
$897$	−6.91347			−0.230834
$898$	−2.51000	+	2.75114i	−0.0837599	+	0.0918066i
$899$	−5.41933	−	20.2252i	−0.180745	−	0.674548i
$900$	1.15176	+	12.5384i	0.0383920	+	0.417947i
$901$	7.11995	−	26.5720i	0.237200	−	0.885243i
$902$	−6.82011	−	3.53156i	−0.227085	−	0.117588i
$903$		0			0
$904$	−5.25043	−	3.97482i	−0.174627	−	0.132201i
$905$	3.16239	−	1.82581i	0.105121	−	0.0606919i
$906$	−28.8251	−	45.0307i	−0.957651	−	1.49604i
$907$	−13.9742	+	3.74438i	−0.464006	+	0.124330i	−0.483246	−	0.875485i	$-0.660542\pi$
$907$	−13.9742	+	3.74438i	−0.464006	+	0.124330i	0.0192393	+	0.999815i	$0.493876\pi$
$908$	−15.6531	+	5.77425i	−0.519468	+	0.191625i
$909$	−7.04913	+	7.04913i	−0.233805	+	0.233805i
$910$		0			0
$911$	46.3367			1.53520			0.767602	−	0.640927i	$-0.221450\pi$
$911$	46.3367			1.53520			0.767602	+	0.640927i	$0.221450\pi$
$912$	7.59098	+	40.9702i	0.251362	+	1.35666i
$913$	−2.47673	+	4.28982i	−0.0819678	+	0.141972i
$914$	−2.33816	+	10.6560i	−0.0773395	+	0.352470i
$915$	19.1109	+	5.12074i	0.631786	+	0.169287i
$916$	−39.6422	−	6.81293i	−1.30981	−	0.225106i
$917$		0			0
$918$	−11.0176	+	21.2771i	−0.363636	+	0.702250i
$919$	2.37039	−	1.36854i	0.0781918	−	0.0451441i	−0.460394	−	0.887715i	$-0.652292\pi$
$919$	2.37039	−	1.36854i	0.0781918	−	0.0451441i	0.538586	+	0.842570i	$0.318959\pi$
$920$	−0.626593	+	1.54099i	−0.0206581	+	0.0508051i
$921$	−2.48630	−	1.43547i	−0.0819265	−	0.0473003i
$922$	−1.74083	−	37.9822i	−0.0573311	−	1.25088i
$923$	38.1280	+	38.1280i	1.25500	+	1.25500i
$924$		0			0
$925$	−21.7389	+	21.7389i	−0.714772	+	0.714772i
$926$	12.1750	−	13.3446i	0.400095	−	0.438532i
$927$	−2.77645	+	4.80895i	−0.0911905	+	0.157947i
$928$	−10.5670	−	45.3341i	−0.346880	−	1.48816i
$929$	−6.91731	−	11.9811i	−0.226949	−	0.393088i	0.729953	−	0.683497i	$-0.239542\pi$
$929$	−6.91731	−	11.9811i	−0.226949	−	0.393088i	−0.956903	+	0.290409i	$0.906209\pi$
$930$	2.39882	+	7.55099i	0.0786605	+	0.247607i
$931$		0			0
$932$	10.7916	+	15.2706i	0.353489	+	0.500206i
$933$	5.01178	−	18.7042i	0.164078	−	0.612349i
$934$	−11.3937	+	7.29335i	−0.372813	+	0.238646i
$935$	−6.59205	−	3.80592i	−0.215583	−	0.124467i
$936$	−20.0636	+	15.6037i	−0.655801	+	0.510023i
$937$			22.0600i			0.720670i	0.932823	+	0.360335i	$0.117338\pi$
$937$			22.0600i			0.720670i	−0.932823	+	0.360335i	$0.882662\pi$
$938$		0			0
$939$	3.57269	+	3.57269i	0.116590	+	0.116590i
$940$	6.78417	+	18.3909i	0.221275	+	0.599845i
$941$	11.4787	+	42.8390i	0.374194	+	1.39651i	0.854519	+	0.519420i	$0.173852\pi$
$941$	11.4787	+	42.8390i	0.374194	+	1.39651i	−0.480325	+	0.877090i	$0.659481\pi$
$942$	14.4027	−	65.6393i	0.469265	−	2.13865i
$943$	−1.18080	−	2.04521i	−0.0384523	−	0.0666013i
$944$	51.8563	−	24.7306i	1.68778	−	0.804912i
$945$		0			0
$946$	−1.96648	+	0.624719i	−0.0639359	+	0.0203114i
$947$	−0.992401	−	0.265913i	−0.0322487	−	0.00864101i	0.242659	−	0.970112i	$-0.421981\pi$
$947$	−0.992401	−	0.265913i	−0.0322487	−	0.00864101i	−0.274907	+	0.961471i	$0.588647\pi$
$948$	28.2921	+	23.5317i	0.918886	+	0.764273i
$949$	−68.8464	+	18.4473i	−2.23485	+	0.598826i
$950$	27.0826	−	1.24127i	0.878677	−	0.0402722i
$951$			15.0888i			0.489287i
$952$		0			0
$953$			36.4163i			1.17964i	0.807535	+	0.589820i	$0.200801\pi$
$953$			36.4163i			1.17964i	−0.807535	+	0.589820i	$0.799199\pi$
$954$	−0.505038	−	11.0191i	−0.0163512	−	0.356758i
$955$	−12.6156	+	3.38035i	−0.408232	+	0.109385i
$956$	1.34895	+	14.6850i	0.0436280	+	0.474948i
$957$	22.4396	+	6.01266i	0.725368	+	0.194362i
$958$	−14.5679	−	45.8565i	−0.470666	−	1.48156i
$959$		0			0
$960$	4.77959	+	16.9527i	0.154261	+	0.547145i
$961$	12.2626	+	21.2395i	0.395569	+	0.685146i
$962$	−60.6178	−	13.3009i	−1.95440	−	0.428837i
$963$	8.48932	+	31.6826i	0.273564	+	1.02096i
$964$	−17.0798	−	7.87447i	−0.550102	−	0.253620i
$965$	13.4557	+	13.4557i	0.433156	+	0.433156i
$966$		0			0
$967$		−	41.7673i		−	1.34315i	−0.740938	−	0.671574i	$-0.765619\pi$
$967$		−	41.7673i		−	1.34315i	0.740938	−	0.671574i	$-0.234381\pi$
$968$	−26.0050	−	3.25174i	−0.835833	−	0.104515i
$969$	−50.7721	−	29.3133i	−1.63104	−	0.941679i
$970$	−7.03245	−	10.9861i	−0.225798	−	0.352743i
$971$	4.21780	−	15.7410i	0.135356	−	0.505154i	−0.864641	−	0.502391i	$-0.832454\pi$
$971$	4.21780	−	15.7410i	0.135356	−	0.505154i	0.999996	−	0.00276313i	$-0.000879532\pi$
$972$	−5.10388	+	29.6978i	−0.163707	+	0.952557i
$973$		0			0
$974$	24.6894	−	7.84341i	0.791099	−	0.251319i
$975$	23.8142	+	41.2474i	0.762664	+	1.32097i
$976$	−35.8341	−	2.82225i	−1.14702	−	0.0903380i
$977$	26.8666	−	46.5343i	0.859538	−	1.48876i	−0.0128319	−	0.999918i	$-0.504085\pi$
$977$	26.8666	−	46.5343i	0.859538	−	1.48876i	0.872370	−	0.488846i	$-0.162582\pi$
$978$	−42.9385	−	39.1750i	−1.37302	−	1.25268i
$979$	2.62888	−	2.62888i	0.0840193	−	0.0840193i
$980$		0			0
$981$	4.66440	+	4.66440i	0.148923	+	0.148923i
$982$	−6.46594	+	0.296352i	−0.206336	+	0.00945697i
$983$	−27.0344	−	15.6083i	−0.862263	−	0.497827i	0.00250678	−	0.999997i	$-0.499202\pi$
$983$	−27.0344	−	15.6083i	−0.862263	−	0.497827i	−0.864769	+	0.502169i	$0.832535\pi$
$984$	−23.1634	−	9.41861i	−0.738422	−	0.300254i
$985$	2.84872	−	1.64471i	0.0907678	−	0.0524048i
$986$	58.1606	+	30.1165i	1.85221	+	0.959103i
$987$		0			0
$988$	31.5843	+	44.6935i	1.00483	+	1.42189i
$989$	−0.612840	−	0.164210i	−0.0194872	−	0.00522157i
$990$	−2.98127	−	0.654155i	−0.0947509	−	0.0207904i
$991$	21.7139	−	37.6096i	0.689764	−	1.19471i	−0.282150	−	0.959370i	$-0.591047\pi$
$991$	21.7139	−	37.6096i	0.689764	−	1.19471i	0.971914	−	0.235336i	$-0.0756192\pi$
$992$	−6.78444	−	12.6950i	−0.215406	−	0.403066i
$993$	−47.7880			−1.51650
$994$		0			0
$995$	−16.2321	+	16.2321i	−0.514593	+	0.514593i
$996$	−6.75229	+	14.6458i	−0.213955	+	0.464069i
$997$	24.6462	−	6.60392i	0.780552	−	0.209148i	0.153524	−	0.988145i	$-0.450938\pi$
$997$	24.6462	−	6.60392i	0.780552	−	0.209148i	0.627028	+	0.778997i	$0.284271\pi$
$998$	−14.1097	+	9.03191i	−0.446634	+	0.285900i
$999$	−20.3158	+	11.7293i	−0.642764	+	0.371100i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.x.n.165.4		40
7.2	even	3	inner	784.2.x.n.373.9		40
7.3	odd	6		784.2.m.i.197.3	✓	20
7.4	even	3		784.2.m.i.197.4	yes	20
7.5	odd	6	inner	784.2.x.n.373.10		40
7.6	odd	2	inner	784.2.x.n.165.3		40
16.13	even	4	inner	784.2.x.n.557.9		40
112.13	odd	4	inner	784.2.x.n.557.10		40
112.45	odd	12		784.2.m.i.589.3	yes	20
112.61	odd	12	inner	784.2.x.n.765.3		40
112.93	even	12	inner	784.2.x.n.765.4		40
112.109	even	12		784.2.m.i.589.4	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
784.2.m.i.197.3	✓	20	7.3	odd	6
784.2.m.i.197.4	yes	20	7.4	even	3
784.2.m.i.589.3	yes	20	112.45	odd	12
784.2.m.i.589.4	yes	20	112.109	even	12
784.2.x.n.165.3		40	7.6	odd	2	inner
784.2.x.n.165.4		40	1.1	even	1	trivial
784.2.x.n.373.9		40	7.2	even	3	inner
784.2.x.n.373.10		40	7.5	odd	6	inner
784.2.x.n.557.9		40	16.13	even	4	inner
784.2.x.n.557.10		40	112.13	odd	4	inner
784.2.x.n.765.3		40	112.61	odd	12	inner
784.2.x.n.765.4		40	112.93	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.953167 + 1.04474i) q^{2} +(0.554848 + 2.07072i) q^{3} +(-0.182947 - 1.99162i) q^{4} +(0.265812 - 0.992025i) q^{5} +(-2.69222 - 1.39407i) q^{6} +(2.25509 + 1.70721i) q^{8} +(-1.38196 + 0.797875i) q^{9} +O(q^{10})\)	\(q+(-0.953167 + 1.04474i) q^{2} +(0.554848 + 2.07072i) q^{3} +(-0.182947 - 1.99162i) q^{4} +(0.265812 - 0.992025i) q^{5} +(-2.69222 - 1.39407i) q^{6} +(2.25509 + 1.70721i) q^{8} +(-1.38196 + 0.797875i) q^{9} +(0.783041 + 1.22327i) q^{10} +(1.27203 - 0.340839i) q^{11} +(4.02257 - 1.48388i) q^{12} +(3.98199 - 3.98199i) q^{13} +2.20169 q^{15} +(-3.93306 + 0.728719i) q^{16} +(2.81402 - 4.87403i) q^{17} +(0.483669 - 2.20429i) q^{18} +(-4.69357 - 1.25764i) q^{19} +(-2.02436 - 0.347908i) q^{20} +(-0.856369 + 1.65381i) q^{22} +(-0.495945 + 0.286334i) q^{23} +(-2.28392 + 5.61691i) q^{24} +(3.41667 + 1.97262i) q^{25} +(0.364629 + 7.95563i) q^{26} +(2.12867 + 2.12867i) q^{27} +(5.81867 - 5.81867i) q^{29} +(-2.09858 + 2.30019i) q^{30} +(1.27227 - 2.20364i) q^{31} +(2.98754 - 4.80360i) q^{32} +(1.41157 + 2.44491i) q^{33} +(2.40984 + 7.58567i) q^{34} +(1.84188 + 2.60636i) q^{36} +(-2.01687 + 7.52705i) q^{37} +(5.78765 - 3.70480i) q^{38} +(10.4550 + 6.03619i) q^{39} +(2.29302 - 1.78331i) q^{40} +4.12387i q^{41} +(0.783403 + 0.783403i) q^{43} +(-0.911535 - 2.47104i) q^{44} +(0.424170 + 1.58302i) q^{45} +(0.173575 - 0.791056i) q^{46} +(-4.77165 - 8.26474i) q^{47} +(-3.69123 - 7.73995i) q^{48} +(-5.31752 + 1.68929i) q^{50} +(11.6541 + 3.12271i) q^{51} +(-8.65908 - 7.20210i) q^{52} +(4.72136 - 1.26508i) q^{53} +(-4.25287 + 0.194921i) q^{54} -1.35248i q^{55} -10.4169i q^{57} +(0.532812 + 11.6251i) q^{58} +(-13.8735 + 3.71739i) q^{59} +(-0.402793 - 4.38493i) q^{60} +(8.68008 + 2.32582i) q^{61} +(1.08954 + 3.42963i) q^{62} +(2.17087 + 7.69983i) q^{64} +(-2.89177 - 5.00869i) q^{65} +(-3.89974 - 0.855688i) q^{66} +(2.20974 + 8.24686i) q^{67} +(-10.2220 - 4.71276i) q^{68} +(-0.868093 - 0.868093i) q^{69} +9.57512i q^{71} +(-4.47858 - 0.560015i) q^{72} +(-10.9611 - 6.32838i) q^{73} +(-5.94137 - 9.28162i) q^{74} +(-2.18901 + 8.16948i) q^{75} +(-1.64606 + 9.57786i) q^{76} +(-16.2716 + 5.16921i) q^{78} +(4.29142 + 7.43296i) q^{79} +(-0.322548 + 4.09540i) q^{80} +(-5.62042 + 9.73485i) q^{81} +(-4.30836 - 3.93073i) q^{82} +(-2.65975 + 2.65975i) q^{83} +(-4.08716 - 4.08716i) q^{85} +(-1.56516 + 0.0717357i) q^{86} +(15.2773 + 8.82037i) q^{87} +(3.45043 + 1.40300i) q^{88} +(2.44491 - 1.41157i) q^{89} +(-2.05815 - 1.06574i) q^{90} +(0.660999 + 0.935348i) q^{92} +(5.26905 + 1.41184i) q^{93} +(13.1827 + 2.89256i) q^{94} +(-2.49521 + 4.32184i) q^{95} +(11.6046 + 3.52110i) q^{96} -8.98095 q^{97} +(-1.48595 + 1.48595i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 8 q^{4}+O(q^{10}) \) 40 * q + 8 * q^4	\( 40 q + 8 q^{4} - 4 q^{11} - 32 q^{15} - 16 q^{18} - 8 q^{29} - 8 q^{30} + 40 q^{32} + 80 q^{36} + 20 q^{37} + 120 q^{43} - 56 q^{44} + 64 q^{46} - 112 q^{50} + 16 q^{51} - 28 q^{53} + 72 q^{58} + 24 q^{60} - 64 q^{64} - 16 q^{65} - 12 q^{67} - 16 q^{72} + 16 q^{74} - 176 q^{78} + 72 q^{79} - 12 q^{81} + 64 q^{85} + 40 q^{86} - 80 q^{88} - 48 q^{92} - 48 q^{93} - 64 q^{95} - 216 q^{99}+O(q^{100}) \) 40 * q + 8 * q^4 - 4 * q^11 - 32 * q^15 - 16 * q^18 - 8 * q^29 - 8 * q^30 + 40 * q^32 + 80 * q^36 + 20 * q^37 + 120 * q^43 - 56 * q^44 + 64 * q^46 - 112 * q^50 + 16 * q^51 - 28 * q^53 + 72 * q^58 + 24 * q^60 - 64 * q^64 - 16 * q^65 - 12 * q^67 - 16 * q^72 + 16 * q^74 - 176 * q^78 + 72 * q^79 - 12 * q^81 + 64 * q^85 + 40 * q^86 - 80 * q^88 - 48 * q^92 - 48 * q^93 - 64 * q^95 - 216 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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