LMFDB - Embedded newform 784.2.x.n.373.9

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			373.9
Character	$\chi$	$=$	784.373
Dual form			784.2.x.n.557.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.38135 + 0.303098i) q^{2} +(-2.07072 - 0.554848i) q^{3} +(1.81626 + 0.837371i) q^{4} +(-0.992025 + 0.265812i) q^{5} +(-2.69222 - 1.39407i) q^{6} +(2.25509 + 1.70721i) q^{8} +(1.38196 + 0.797875i) q^{9} +O(q^{10})$	\(q+(1.38135 + 0.303098i) q^{2} +(-2.07072 - 0.554848i) q^{3} +(1.81626 + 0.837371i) q^{4} +(-0.992025 + 0.265812i) q^{5} +(-2.69222 - 1.39407i) q^{6} +(2.25509 + 1.70721i) q^{8} +(1.38196 + 0.797875i) q^{9} +(-1.45090 + 0.0664989i) q^{10} +(-0.340839 + 1.27203i) q^{11} +(-3.29636 - 2.74171i) q^{12} +(3.98199 - 3.98199i) q^{13} +2.20169 q^{15} +(2.59762 + 3.04177i) q^{16} +(2.81402 + 4.87403i) q^{17} +(1.66714 + 1.52102i) q^{18} +(1.25764 + 4.69357i) q^{19} +(-2.02436 - 0.347908i) q^{20} +(-0.856369 + 1.65381i) q^{22} +(0.495945 + 0.286334i) q^{23} +(-3.72243 - 4.78639i) q^{24} +(-3.41667 + 1.97262i) q^{25} +(6.70746 - 4.29359i) q^{26} +(2.12867 + 2.12867i) q^{27} +(5.81867 - 5.81867i) q^{29} +(3.04131 + 0.667330i) q^{30} +(1.27227 + 2.20364i) q^{31} +(2.66627 + 4.98909i) q^{32} +(1.41157 - 2.44491i) q^{33} +(2.40984 + 7.58567i) q^{34} +(1.84188 + 2.60636i) q^{36} +(7.52705 - 2.01687i) q^{37} +(0.314626 + 6.86465i) q^{38} +(-10.4550 + 6.03619i) q^{39} +(-2.69090 - 1.09416i) q^{40} +4.12387i q^{41} +(0.783403 + 0.783403i) q^{43} +(-1.68421 + 2.02493i) q^{44} +(-1.58302 - 0.424170i) q^{45} +(0.598287 + 0.545848i) q^{46} +(-4.77165 + 8.26474i) q^{47} +(-3.69123 - 7.73995i) q^{48} +(-5.31752 + 1.68929i) q^{50} +(-3.12271 - 11.6541i) q^{51} +(10.5667 - 3.89794i) q^{52} +(-1.26508 + 4.72136i) q^{53} +(2.29524 + 3.58563i) q^{54} -1.35248i q^{55} -10.4169i q^{57} +(9.80126 - 6.27400i) q^{58} +(3.71739 - 13.8735i) q^{59} +(3.99885 + 1.84363i) q^{60} +(-2.32582 - 8.68008i) q^{61} +(1.08954 + 3.42963i) q^{62} +(2.17087 + 7.69983i) q^{64} +(-2.89177 + 5.00869i) q^{65} +(2.69092 - 2.94943i) q^{66} +(-8.24686 - 2.20974i) q^{67} +(1.02963 + 11.2089i) q^{68} +(-0.868093 - 0.868093i) q^{69} +9.57512i q^{71} +(1.75431 + 4.15858i) q^{72} +(10.9611 - 6.32838i) q^{73} +(11.0088 - 0.504564i) q^{74} +(8.16948 - 2.18901i) q^{75} +(-1.64606 + 9.57786i) q^{76} +(-16.2716 + 5.16921i) q^{78} +(4.29142 - 7.43296i) q^{79} +(-3.38544 - 2.32703i) q^{80} +(-5.62042 - 9.73485i) q^{81} +(-1.24994 + 5.69651i) q^{82} +(-2.65975 + 2.65975i) q^{83} +(-4.08716 - 4.08716i) q^{85} +(0.844706 + 1.31960i) q^{86} +(-15.2773 + 8.82037i) q^{87} +(-2.94025 + 2.28666i) q^{88} +(-2.44491 - 1.41157i) q^{89} +(-2.05815 - 1.06574i) q^{90} +(0.660999 + 0.935348i) q^{92} +(-1.41184 - 5.26905i) q^{93} +(-9.09636 + 9.97023i) q^{94} +(-2.49521 - 4.32184i) q^{95} +(-2.75292 - 11.8104i) 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 $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.38135	+	0.303098i	0.976763	+	0.214323i
$2$	1.38135	+	0.303098i	0.976763	+	0.214323i
$3$	−2.07072	−	0.554848i	−1.19553	−	0.320342i	−0.394462	−	0.918912i	$-0.629069\pi$
$3$	−2.07072	−	0.554848i	−1.19553	−	0.320342i	−0.801070	+	0.598570i	$0.795736\pi$
$4$	1.81626	+	0.837371i	0.908131	+	0.418685i
$5$	−0.992025	+	0.265812i	−0.443647	+	0.118875i	−0.473725	−	0.880673i	$-0.657091\pi$
$5$	−0.992025	+	0.265812i	−0.443647	+	0.118875i	0.0300783	+	0.999548i	$0.490424\pi$
$6$	−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
$10$	−1.45090	+	0.0664989i	−0.458815	+	0.0210288i
$11$	−0.340839	+	1.27203i	−0.102767	+	0.383531i	−0.998082	−	0.0619014i	$-0.980284\pi$
$11$	−0.340839	+	1.27203i	−0.102767	+	0.383531i	0.895315	+	0.445433i	$0.146950\pi$
$12$	−3.29636	−	2.74171i	−0.951578	−	0.791465i
$13$	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
$16$	2.59762	+	3.04177i	0.649405	+	0.760443i
$17$	2.81402	+	4.87403i	0.682501	+	1.18213i	0.974215	+	0.225620i	$0.0724409\pi$
$17$	2.81402	+	4.87403i	0.682501	+	1.18213i	−0.291715	+	0.956505i	$0.594226\pi$
$18$	1.66714	+	1.52102i	0.392948	+	0.358507i
$19$	1.25764	+	4.69357i	0.288522	+	1.07678i	0.946227	+	0.323503i	$0.104860\pi$
$19$	1.25764	+	4.69357i	0.288522	+	1.07678i	−0.657706	+	0.753275i	$0.728473\pi$
$20$	−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	$-0.314317\pi$
$23$	0.495945	+	0.286334i	0.103412	+	0.0597048i	−0.447402	+	0.894333i	$0.647651\pi$
$24$	−3.72243	−	4.78639i	−0.759837	−	0.977018i
$25$	−3.41667	+	1.97262i	−0.683334	+	0.394523i
$26$	6.70746	−	4.29359i	1.31544	−	0.842042i
$27$	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	$-0.0267815\pi$
$30$	3.04131	+	0.667330i	0.555265	+	0.121837i
$31$	1.27227	+	2.20364i	0.228507	+	0.395786i	0.957366	−	0.288878i	$-0.0932823\pi$
$31$	1.27227	+	2.20364i	0.228507	+	0.395786i	−0.728859	+	0.684664i	$0.759949\pi$
$32$	2.66627	+	4.98909i	0.471334	+	0.881955i
$33$	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
$37$	7.52705	−	2.01687i	1.23744	−	0.331571i	0.419967	−	0.907539i	$-0.362042\pi$
$37$	7.52705	−	2.01687i	1.23744	−	0.331571i	0.817472	+	0.575968i	$0.195375\pi$
$38$	0.314626	+	6.86465i	0.0510391	+	1.11359i
$39$	−10.4550	+	6.03619i	−1.67414	+	0.966565i
$40$	−2.69090	−	1.09416i	−0.425469	−	0.173002i
$41$			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	$0.723078\pi$
$44$	−1.68421	+	2.02493i	−0.253905	+	0.305270i
$45$	−1.58302	−	0.424170i	−0.235983	−	0.0632315i
$46$	0.598287	+	0.545848i	0.0882126	+	0.0804809i
$47$	−4.77165	+	8.26474i	−0.696017	+	1.20554i	0.273820	+	0.961781i	$0.411713\pi$
$47$	−4.77165	+	8.26474i	−0.696017	+	1.20554i	−0.969837	+	0.243755i	$0.921621\pi$
$48$	−3.69123	−	7.73995i	−0.532783	−	1.11717i
$49$		0			0
$50$	−5.31752	+	1.68929i	−0.752011	+	0.238901i
$51$	−3.12271	−	11.6541i	−0.437267	−	1.63190i
$52$	10.5667	−	3.89794i	1.46534	−	0.540546i
$53$	−1.26508	+	4.72136i	−0.173773	+	0.648529i	0.822985	+	0.568064i	$0.192307\pi$
$53$	−1.26508	+	4.72136i	−0.173773	+	0.648529i	−0.996757	+	0.0804652i	$0.974359\pi$
$54$	2.29524	+	3.58563i	0.312343	+	0.487943i
$55$		−	1.35248i		−	0.182369i
$56$		0			0
$57$		−	10.4169i		−	1.37975i
$58$	9.80126	−	6.27400i	1.28697	−	0.823816i
$59$	3.71739	−	13.8735i	0.483963	−	1.80617i	−0.100724	−	0.994914i	$-0.532116\pi$
$59$	3.71739	−	13.8735i	0.483963	−	1.80617i	0.584687	−	0.811259i	$-0.301217\pi$
$60$	3.99885	+	1.84363i	0.516250	+	0.238012i
$61$	−2.32582	−	8.68008i	−0.297791	−	1.11137i	−0.938976	−	0.343984i	$-0.888224\pi$
$61$	−2.32582	−	8.68008i	−0.297791	−	1.11137i	0.641185	−	0.767386i	$-0.278443\pi$
$62$	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
$66$	2.69092	−	2.94943i	0.331229	−	0.363050i
$67$	−8.24686	−	2.20974i	−1.00751	−	0.269963i	−0.282924	−	0.959142i	$-0.591304\pi$
$67$	−8.24686	−	2.20974i	−1.00751	−	0.269963i	−0.724591	+	0.689180i	$0.757971\pi$
$68$	1.02963	+	11.2089i	0.124861	+	1.35928i
$69$	−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	$0.807648\pi$
$72$	1.75431	+	4.15858i	0.206747	+	0.490093i
$73$	10.9611	−	6.32838i	1.28290	−	0.740681i	0.305520	−	0.952186i	$-0.401170\pi$
$73$	10.9611	−	6.32838i	1.28290	−	0.740681i	0.977377	+	0.211504i	$0.0678363\pi$
$74$	11.0088	−	0.504564i	1.27975	−	0.0586544i
$75$	8.16948	−	2.18901i	0.943330	−	0.252765i
$76$	−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	−0.516983	−	0.855996i	$-0.672945\pi$
$79$	4.29142	−	7.43296i	0.482822	−	0.836273i	0.999805	+	0.0197228i	$0.00627836\pi$
$80$	−3.38544	−	2.32703i	−0.378504	−	0.260170i
$81$	−5.62042	−	9.73485i	−0.624491	−	1.08165i
$82$	−1.24994	+	5.69651i	−0.138033	+	0.629075i
$83$	−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
$86$	0.844706	+	1.31960i	0.0910870	+	0.142296i
$87$	−15.2773	+	8.82037i	−1.63790	+	0.945643i
$88$	−2.94025	+	2.28666i	−0.313431	+	0.243759i
$89$	−2.44491	−	1.41157i	−0.259160	−	0.149626i	0.364792	−	0.931089i	$-0.381140\pi$
$89$	−2.44491	−	1.41157i	−0.259160	−	0.149626i	−0.623951	+	0.781463i	$0.714474\pi$
$90$	−2.05815	−	1.06574i	−0.216948	−	0.112339i
$91$		0			0
$92$	0.660999	+	0.935348i	0.0689139	+	0.0975168i
$93$	−1.41184	−	5.26905i	−0.146401	−	0.546375i
$94$	−9.09636	+	9.97023i	−0.938218	+	1.02835i
$95$	−2.49521	−	4.32184i	−0.256004	−	0.443411i
$96$	−2.75292	−	11.8104i	−0.280968	−	1.20539i
$97$	−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
$100$	−7.85738	+	0.721768i	−0.785738	+	0.0721768i
$101$	−1.61690	+	6.03434i	−0.160887	+	0.600439i	0.837642	+	0.546220i	$0.183934\pi$
$101$	−1.61690	+	6.03434i	−0.160887	+	0.600439i	−0.998529	+	0.0542192i	$0.982733\pi$
$102$	−0.781216	−	17.0449i	−0.0773519	−	1.68770i
$103$	−3.01360	−	1.73990i	−0.296939	−	0.171438i	0.344128	−	0.938923i	$-0.388175\pi$
$103$	−3.01360	−	1.73990i	−0.296939	−	0.171438i	−0.641067	+	0.767485i	$0.721508\pi$
$104$	15.7778	−	2.18166i	1.54714	−	0.213929i
$105$		0			0
$106$	−3.17856	+	6.13841i	−0.308729	+	0.596215i
$107$	−19.8543	+	5.31996i	−1.91939	+	0.514300i	−0.930349	+	0.366676i	$0.880496\pi$
$107$	−19.8543	+	5.31996i	−1.91939	+	0.514300i	−0.989044	+	0.147623i	$0.952838\pi$
$108$	2.08373	+	5.64870i	0.200507	+	0.543547i
$109$	3.99291	+	1.06990i	0.382451	+	0.102478i	0.444922	−	0.895569i	$-0.353231\pi$
$109$	3.99291	+	1.06990i	0.382451	+	0.102478i	−0.0624707	+	0.998047i	$0.519898\pi$
$110$	0.409936	−	1.86826i	0.0390859	−	0.178131i
$111$	−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	$0.534929\pi$
$114$	3.15734	−	14.3894i	0.295712	−	1.34769i
$115$	−0.568101	−	0.152222i	−0.0529757	−	0.0141948i
$116$	15.4406	−	5.69585i	1.43363	−	0.528846i
$117$	8.68008	−	2.32582i	0.802473	−	0.215022i
$118$	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
$122$	−0.581856	−	12.6952i	−0.0526788	−	1.14937i
$123$	2.28812	−	8.53939i	0.206313	−	0.769971i
$124$	0.465517	+	5.06776i	0.0418046	+	0.455098i
$125$	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	$0.575355\pi$
$128$	0.664928	+	11.2942i	0.0587719	+	0.998271i
$129$	−1.18754	−	2.05688i	−0.104557	−	0.181098i
$130$	−5.51268	+	6.04227i	−0.483494	+	0.529942i
$131$	−4.00149	−	14.9338i	−0.349612	−	1.30477i	−0.887131	−	0.461518i	$-0.847305\pi$
$131$	−4.00149	−	14.9338i	−0.349612	−	1.30477i	0.537519	−	0.843252i	$-0.319362\pi$
$132$	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
$136$	−1.97512	+	15.7955i	−0.169365	+	1.35445i
$137$	7.97102	−	4.60207i	0.681010	−	0.393182i	−0.119225	−	0.992867i	$-0.538041\pi$
$137$	7.97102	−	4.60207i	0.681010	−	0.393182i	0.800236	+	0.599686i	$0.204708\pi$
$138$	−0.936024	−	1.46226i	−0.0796796	−	0.124476i
$139$	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
$142$	−2.90220	+	13.2266i	−0.243548	+	1.10995i
$143$	3.70799	+	6.42243i	0.310078	+	0.537070i
$144$	1.16285	+	6.27618i	0.0969045	+	0.523015i
$145$	−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
$149$	6.68624	−	1.79157i	0.547758	−	0.146771i	0.0256818	−	0.999670i	$-0.491824\pi$
$149$	6.68624	−	1.79157i	0.547758	−	0.146771i	0.522076	+	0.852899i	$0.325158\pi$
$150$	11.9484	−	0.547629i	0.975583	−	0.0447137i
$151$	−15.2728	+	8.81774i	−1.24288	+	0.717578i	−0.969680	−	0.244379i	$-0.921416\pi$
$151$	−15.2728	+	8.81774i	−1.24288	+	0.717578i	−0.273201	+	0.961957i	$0.588083\pi$
$152$	−5.17682	+	12.7315i	−0.419895	+	1.03266i
$153$			8.98095i			0.726067i
$154$		0			0
$155$	−1.84788	−	1.84788i	−0.148425	−	0.148425i
$156$	−24.0436	+	2.20861i	−1.92502	+	0.176830i
$157$	−21.4104	−	5.73691i	−1.70874	−	0.457855i	−0.733624	−	0.679555i	$-0.762173\pi$
$157$	−21.4104	−	5.73691i	−1.70874	−	0.457855i	−0.975115	+	0.221700i	$0.928839\pi$
$158$	8.18087	−	8.96680i	0.650835	−	0.713360i
$159$	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
$163$	−4.96202	−	18.5185i	−0.388655	−	1.45048i	−0.832324	−	0.554290i	$-0.812990\pi$
$163$	−4.96202	−	18.5185i	−0.388655	−	1.45048i	0.443669	−	0.896191i	$-0.353677\pi$
$164$	−3.45321	+	7.49003i	−0.269650	+	0.584873i
$165$	−0.750424	+	2.80062i	−0.0584204	+	0.218028i
$166$	−4.48021	+	2.86788i	−0.347732	+	0.222591i
$167$		−	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
$170$	−4.40699	−	6.88461i	−0.338001	−	0.528025i
$171$	−2.00687	+	7.48976i	−0.153469	+	0.572756i
$172$	0.766866	+	2.07886i	0.0584730	+	0.158512i
$173$	2.16746	+	8.08908i	0.164789	+	0.615001i	0.998067	+	0.0621469i	$0.0197947\pi$
$173$	2.16746	+	8.08908i	0.164789	+	0.615001i	−0.833278	+	0.552854i	$0.813539\pi$
$174$	−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
$178$	−2.94943	−	2.69092i	−0.221069	−	0.201693i
$179$	14.4907	+	3.88277i	1.08309	+	0.290212i	0.755860	−	0.654734i	$-0.227219\pi$
$179$	14.4907	+	3.88277i	1.08309	+	0.290212i	0.327227	+	0.944946i	$0.393886\pi$
$180$	−2.52000	−	2.09598i	−0.187830	−	0.156225i
$181$	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
$184$	0.629569	+	1.49239i	0.0464124	+	0.110021i
$185$	−6.93091	+	4.00156i	−0.509571	+	0.294201i
$186$	−0.353203	−	7.70633i	−0.0258981	−	0.565056i
$187$	−7.15904	+	1.91826i	−0.523521	+	0.140277i
$188$	−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	−0.998965	−	0.0454904i	$-0.985515\pi$
$191$	−6.35852	+	11.0133i	−0.460087	+	0.796893i	0.538878	+	0.842384i	$0.318848\pi$
$192$	−0.223032	−	17.1487i	−0.0160959	−	1.23760i
$193$	−9.26433	−	16.0463i	−0.666861	−	1.15504i	−0.978777	−	0.204928i	$-0.934304\pi$
$193$	−9.26433	−	16.0463i	−0.666861	−	1.15504i	0.311916	−	0.950110i	$-0.399029\pi$
$194$	−12.4058	−	2.72211i	−0.890688	−	0.195436i
$195$	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	$0.713602\pi$
$198$	−2.50300	+	1.60223i	−0.177881	+	0.113865i
$199$	19.3572	−	11.1759i	1.37219	−	0.792237i	0.380991	−	0.924579i	$-0.375583\pi$
$199$	19.3572	−	11.1759i	1.37219	−	0.792237i	0.991204	+	0.132342i	$0.0422497\pi$
$200$	−11.0726	−	1.38455i	−0.782949	−	0.0979022i
$201$	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
$205$	−1.09617	−	4.09098i	−0.0765602	−	0.285726i
$206$	−3.63548	−	3.31683i	−0.253296	−	0.231095i
$207$	0.456917	+	0.791404i	0.0317580	+	0.0550064i
$208$	22.4560	+	1.76860i	1.55704	+	0.122631i
$209$	−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	$0.220070\pi$
$212$	−6.25126	+	7.51589i	−0.429338	+	0.516193i
$213$	5.31274	−	19.8274i	0.364023	−	1.35855i
$214$	−29.0383	+	1.33091i	−1.98502	+	0.0909789i
$215$	−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
$219$	−26.2086	+	7.02259i	−1.77102	+	0.474542i
$220$	1.13253	−	2.45647i	0.0763552	−	0.165615i
$221$	30.6137	+	8.20293i	2.05930	+	0.551789i
$222$	−23.0761	−	5.06341i	−1.54877	−	0.339834i
$223$	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
$226$	−3.21614	−	0.705690i	−0.213934	−	0.0469418i
$227$	8.05786	+	2.15910i	0.534819	+	0.143304i	0.516113	−	0.856521i	$-0.327379\pi$
$227$	8.05786	+	2.15910i	0.534819	+	0.143304i	0.0187062	+	0.999825i	$0.494045\pi$
$228$	8.72278	−	18.9198i	0.577681	−	1.25299i
$229$	−19.4264	+	5.20529i	−1.28373	+	0.343975i	−0.835277	−	0.549830i	$-0.814692\pi$
$229$	−19.4264	+	5.20529i	−1.28373	+	0.343975i	−0.448456	+	0.893805i	$0.648026\pi$
$230$	−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	$-0.234258\pi$
$233$	8.09687	+	4.67473i	0.530443	+	0.306252i	−0.210754	+	0.977539i	$0.567592\pi$
$234$	12.6952	−	0.581856i	0.829910	−	0.0380371i
$235$	2.53673	−	9.46719i	0.165478	−	0.617571i
$236$	18.3690	−	22.0851i	1.19572	−	1.43761i
$237$	−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	$0.576647\pi$
$240$	5.71916	+	6.69705i	0.369170	+	0.432293i
$241$	4.70190	+	8.14393i	0.302876	+	0.524597i	0.976786	−	0.214217i	$-0.0687199\pi$
$241$	4.70190	+	8.14393i	0.302876	+	0.524597i	−0.673910	+	0.738813i	$0.735387\pi$
$242$	9.68028	+	8.83182i	0.622272	+	0.567731i
$243$	3.89952	+	14.5532i	0.250154	+	0.933589i
$244$	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
$248$	−0.892987	+	7.14145i	−0.0567047	+	0.453482i
$249$	6.98335	−	4.03184i	0.442552	−	0.255507i
$250$	10.9424	−	7.00448i	0.692059	−	0.443002i
$251$	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
$254$	−7.30183	−	1.60218i	−0.458157	−	0.100530i
$255$	6.19561	+	10.7311i	0.387984	+	0.672009i
$256$	−2.50474	+	15.8027i	−0.156546	+	0.987671i
$257$	−3.04716	+	5.27784i	−0.190077	+	0.329223i	−0.945276	−	0.326273i	$-0.894207\pi$
$257$	−3.04716	+	5.27784i	−0.190077	+	0.329223i	0.755199	+	0.655496i	$0.227540\pi$
$258$	−1.01697	−	3.20121i	−0.0633140	−	0.199299i
$259$		0			0
$260$	−9.44635	+	6.67562i	−0.585838	+	0.414004i
$261$	12.6837	−	3.39860i	0.785104	−	0.210368i
$262$	−1.00106	−	21.8416i	−0.0618459	−	1.34938i
$263$	0.869755	−	0.502153i	0.0536314	−	0.0309641i	−0.472945	−	0.881092i	$-0.656809\pi$
$263$	0.869755	−	0.502153i	0.0536314	−	0.0309641i	0.526576	+	0.850128i	$0.323476\pi$
$264$	7.35718	−	3.10365i	0.452803	−	0.191016i
$265$		−	5.01998i		−	0.308375i
$266$		0			0
$267$	4.27952	+	4.27952i	0.261902	+	0.261902i
$268$	−13.1281	−	10.9192i	−0.801926	−	0.666993i
$269$	14.2923	+	3.82962i	0.871419	+	0.233496i	0.666701	−	0.745325i	$-0.267706\pi$
$269$	14.2923	+	3.82962i	0.871419	+	0.233496i	0.204718	+	0.978821i	$0.434372\pi$
$270$	−3.23004	−	2.94693i	−0.196574	−	0.179345i
$271$	5.38725	−	9.33100i	0.327252	−	0.566818i	−0.654713	−	0.755877i	$-0.727211\pi$
$271$	5.38725	−	9.33100i	0.327252	−	0.566818i	0.981966	+	0.189060i	$0.0605439\pi$
$272$	−7.51592	+	21.2205i	−0.455720	+	1.28668i
$273$		0			0
$274$	12.4057	−	3.94107i	0.749454	−	0.238089i
$275$	−1.34469	−	5.01845i	−0.0810879	−	0.302624i
$276$	−0.849769	−	2.30360i	−0.0511501	−	0.138660i
$277$	1.00389	−	3.74656i	0.0603178	−	0.225109i	−0.929187	−	0.369610i	$-0.879491\pi$
$277$	1.00389	−	3.74656i	0.0603178	−	0.225109i	0.989505	+	0.144501i	$0.0461578\pi$
$278$	3.31630	+	5.18074i	0.198899	+	0.310720i
$279$			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	$0.843761\pi$
$282$	24.3680	−	15.5985i	1.45109	−	0.928876i
$283$	−1.48622	+	5.54664i	−0.0883464	+	0.329713i	−0.995927	−	0.0901649i	$-0.971261\pi$
$283$	−1.48622	+	5.54664i	−0.0883464	+	0.329713i	0.907580	+	0.419878i	$0.137927\pi$
$284$	−8.01793	+	17.3909i	−0.475776	+	1.03196i
$285$	2.76893	+	10.3338i	0.164017	+	0.612121i
$286$	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
$290$	−8.05538	+	8.82925i	−0.473028	+	0.518472i
$291$	18.5971	+	4.98307i	1.09018	+	0.292113i
$292$	25.2074	−	2.31551i	1.47515	−	0.135505i
$293$	−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
$296$	20.4174	+	8.30203i	1.18674	+	0.482546i
$297$	−3.43326	+	1.98219i	−0.199218	+	0.115019i
$298$	9.77907	−	0.448202i	0.566486	−	0.0259636i
$299$	3.11503	−	0.834669i	0.180147	−	0.0482702i
$300$	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
$304$	−11.0099	+	16.0175i	−0.631460	+	0.918669i
$305$	4.61454	+	7.99262i	0.264228	+	0.457656i
$306$	−2.72211	+	12.4058i	−0.155613	+	0.709195i
$307$	−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
$310$	−1.99248	−	3.11266i	−0.113165	−	0.176787i
$311$	7.82255	−	4.51635i	0.443576	−	0.256099i	−0.261537	−	0.965193i	$-0.584229\pi$
$311$	7.82255	−	4.51635i	0.443576	−	0.256099i	0.705113	+	0.709095i	$0.250896\pi$
$312$	−33.8820	−	4.23670i	−1.91819	−	0.239856i
$313$	−2.04109	−	1.17843i	−0.115369	−	0.0666086i	0.441205	−	0.897406i	$-0.354551\pi$
$313$	−2.04109	−	1.17843i	−0.115369	−	0.0666086i	−0.556574	+	0.830798i	$0.687885\pi$
$314$	−27.8365	−	14.4142i	−1.57090	−	0.813438i
$315$		0			0
$316$	14.0185	−	9.90669i	0.788601	−	0.557295i
$317$	−1.82168	−	6.79860i	−0.102316	−	0.381847i	0.895711	−	0.444636i	$-0.146667\pi$
$317$	−1.82168	−	6.79860i	−0.102316	−	0.381847i	−0.998027	+	0.0627892i	$0.980000\pi$
$318$	9.98781	−	10.9473i	0.560089	−	0.613896i
$319$	5.41829	+	9.38475i	0.303366	+	0.525445i
$320$	−4.20026	−	7.06137i	−0.234802	−	0.394743i
$321$	44.0646			2.45945
$322$		0			0
$323$	−19.3376	+	19.3376i	−1.07597	+	1.07597i
$324$	−2.05647	−	22.3874i	−0.114249	−	1.24375i
$325$	−5.75021	+	21.4601i	−0.318964	+	1.19039i
$326$	−1.24136	−	27.0845i	−0.0687525	−	1.50007i
$327$	−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
$331$	21.5320	−	5.76948i	1.18350	−	0.317119i	0.387189	−	0.922000i	$-0.373446\pi$
$331$	21.5320	−	5.76948i	1.18350	−	0.317119i	0.796316	+	0.604881i	$0.206779\pi$
$332$	−7.05799	+	2.60360i	−0.387358	+	0.142891i
$333$	12.0113	+	3.21841i	0.658214	+	0.176368i
$334$	2.81563	−	12.8321i	0.154065	−	0.702140i
$335$	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	$0.753184\pi$
$338$	5.67172	−	25.8485i	0.308501	−	1.40597i
$339$	4.82117	+	1.29183i	0.261850	+	0.0701625i
$340$	−4.00088	−	10.8458i	−0.216978	−	0.588197i
$341$	−3.23674	+	0.867281i	−0.175279	+	0.0469659i
$342$	−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
$346$	0.542239	+	11.8308i	0.0291510	+	0.636028i
$347$	5.58960	−	20.8607i	0.300066	−	1.11986i	−0.637045	−	0.770827i	$-0.719843\pi$
$347$	5.58960	−	20.8607i	0.300066	−	1.11986i	0.937110	−	0.349033i	$-0.113490\pi$
$348$	−35.1336	+	3.22732i	−1.88336	+	0.173002i
$349$	−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
$352$	−7.25504	+	1.69110i	−0.386695	+	0.0901358i
$353$	−16.0394	−	27.7811i	−0.853693	−	1.47864i	−0.877852	−	0.478932i	$-0.841024\pi$
$353$	−16.0394	−	27.7811i	−0.853693	−	1.47864i	0.0241588	−	0.999708i	$-0.492309\pi$
$354$	−29.3487	+	32.1682i	−1.55987	+	1.70972i
$355$	−2.54518	−	9.49875i	−0.135084	−	0.504142i
$356$	−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	$-0.207131\pi$
$359$	12.6732	+	7.31687i	0.668865	+	0.386169i	−0.126781	+	0.991931i	$0.540465\pi$
$360$	−2.84571	−	3.65909i	−0.149982	−	0.192851i
$361$	−3.99342	+	2.30560i	−0.210180	+	0.121348i
$362$	2.71089	+	4.23496i	0.142481	+	0.222584i
$363$	−14.0457	−	14.0457i	−0.737210	−	0.737210i
$364$		0			0
$365$	−9.19150	+	9.19150i	−0.481105	+	0.481105i
$366$	−5.83904	+	26.6111i	−0.305212	+	1.39098i
$367$	−15.6885	−	27.1733i	−0.818934	−	1.41843i	−0.906469	−	0.422273i	$-0.861232\pi$
$367$	−15.6885	−	27.1733i	−0.818934	−	1.41843i	0.0875349	−	0.996161i	$-0.472101\pi$
$368$	0.417314	+	2.25234i	0.0217540	+	0.117411i
$369$	−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
$373$	27.7029	−	7.42298i	1.43440	−	0.384347i	0.543833	−	0.839193i	$-0.316973\pi$
$373$	27.7029	−	7.42298i	1.43440	−	0.384347i	0.890570	+	0.454846i	$0.150306\pi$
$374$	−10.4706	+	0.479896i	−0.541420	+	0.0248148i
$375$	−17.0561	+	9.84733i	−0.880772	+	0.508514i
$376$	−24.8702	+	10.4915i	−1.28258	+	0.541060i
$377$		−	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	$0.938932\pi$
$380$	−0.912983	−	9.93901i	−0.0468350	−	0.509861i
$381$	10.9458	+	2.93293i	0.560773	+	0.150259i
$382$	−12.1215	+	13.2860i	−0.620188	+	0.679769i
$383$	−1.42396	+	2.46638i	−0.0727612	+	0.126026i	−0.900110	−	0.435662i	$-0.856514\pi$
$383$	−1.42396	+	2.46638i	−0.0727612	+	0.126026i	0.827349	+	0.561688i	$0.189848\pi$
$384$	4.88966	−	23.7560i	0.249525	−	1.21229i
$385$		0			0
$386$	−7.93369	−	24.9736i	−0.403814	−	1.27112i
$387$	0.457574	+	1.70769i	0.0232598	+	0.0868067i
$388$	−16.3118	−	7.52039i	−0.828104	−	0.381790i
$389$	−7.00385	+	26.1387i	−0.355109	+	1.32529i	0.525238	+	0.850956i	$0.323976\pi$
$389$	−7.00385	+	26.1387i	−0.355109	+	1.32529i	−0.880347	+	0.474330i	$0.842690\pi$
$390$	14.7678	−	9.45317i	0.747795	−	0.478680i
$391$			3.22300i			0.162994i
$392$		0			0
$393$			33.1439i			1.67189i
$394$	2.44200	+	3.81490i	0.123026	+	0.192192i
$395$	−2.28142	+	8.51439i	−0.114791	+	0.428405i
$396$	−3.94316	+	1.45458i	−0.198151	+	0.0730955i
$397$	0.369676	+	1.37965i	0.0185535	+	0.0692426i	0.974582	−	0.224031i	$-0.0719218\pi$
$397$	0.369676	+	1.37965i	0.0185535	+	0.0692426i	−0.956028	+	0.293274i	$0.905255\pi$
$398$	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	−0.835812	−	0.549015i	$-0.815003\pi$
$401$	1.15254	−	1.99626i	0.0575550	−	0.0996882i	0.893367	+	0.449327i	$0.148336\pi$
$402$	19.1218	+	17.4458i	0.953711	+	0.870120i
$403$	13.8411	+	3.70870i	0.689472	+	0.184743i
$404$	−7.98969	+	9.60600i	−0.397502	+	0.477916i
$405$	8.16323	+	8.16323i	0.405634	+	0.405634i
$406$		0			0
$407$			10.2621i			0.508671i
$408$	12.8540	−	31.6122i	0.636369	−	1.56504i
$409$	−24.9640	+	14.4130i	−1.23439	+	0.712675i	−0.967942	−	0.251175i	$-0.919183\pi$
$409$	−24.9640	+	14.4130i	−1.23439	+	0.712675i	−0.266447	+	0.963849i	$0.585850\pi$
$410$	−0.274233	−	5.98333i	−0.0135434	−	0.295496i
$411$	−19.0592	+	5.10691i	−0.940123	+	0.251905i
$412$	−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
$416$	30.4836	+	9.24944i	1.49458	+	0.453491i
$417$	−4.66226	−	8.07527i	−0.228312	−	0.395448i
$418$	−8.83928	−	1.93953i	−0.432343	−	0.0948655i
$419$	−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	$0.688956\pi$
$422$	3.24886	−	2.07967i	0.158152	−	0.101237i
$423$	−13.1885	+	7.61436i	−0.641245	+	0.370223i
$424$	−10.9132	+	8.48733i	−0.529994	+	0.412181i
$425$	−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
$429$	−4.11475	−	15.3564i	−0.198662	−	0.741416i
$430$	−1.18874	−	1.08454i	−0.0573259	−	0.0523014i
$431$	7.85427	+	13.6040i	0.378327	+	0.655281i	0.990819	−	0.135195i	$-0.0431662\pi$
$431$	7.85427	+	13.6040i	0.378327	+	0.655281i	−0.612492	+	0.790477i	$0.709833\pi$
$432$	−0.945450	+	12.0044i	−0.0454880	+	0.577561i
$433$	−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
$436$	6.35627	+	5.28676i	0.304410	+	0.253190i
$437$	−0.720209	+	2.68786i	−0.0344523	+	0.128578i
$438$	−38.3319	+	1.75686i	−1.83157	+	0.0839459i
$439$	24.7473	+	14.2878i	1.18112	+	0.681921i	0.956274	−	0.292472i	$-0.0944780\pi$
$439$	24.7473	+	14.2878i	1.18112	+	0.681921i	0.224848	+	0.974394i	$0.427811\pi$
$440$	2.30897	−	3.04998i	0.110076	−	0.145402i
$441$		0			0
$442$	39.8020	+	20.6101i	1.89319	+	0.980323i
$443$	−19.9278	+	5.33964i	−0.946799	+	0.253694i	−0.699003	−	0.715118i	$-0.746373\pi$
$443$	−19.9278	+	5.33964i	−0.946799	+	0.253694i	−0.247795	+	0.968812i	$0.579706\pi$
$444$	−30.3415	−	13.9887i	−1.43995	−	0.663874i
$445$	2.80062	+	0.750424i	0.132762	+	0.0355735i
$446$	28.8784	+	6.33655i	1.36743	+	0.300044i
$447$	−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	$0.480208\pi$
$450$	−8.69644	−	1.90819i	−0.409954	−	0.0899528i
$451$	−5.24569	−	1.40558i	−0.247010	−	0.0661860i
$452$	−4.22872	−	1.94961i	−0.198902	−	0.0917021i
$453$	36.5182	−	9.78502i	1.71577	−	0.459740i
$454$	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	$-0.391081\pi$
$457$	−6.68069	−	3.85710i	−0.312510	−	0.180428i	−0.648049	+	0.761599i	$0.724415\pi$
$458$	−28.4124	+	1.30222i	−1.32762	+	0.0608487i
$459$	−4.38507	+	16.3653i	−0.204678	+	0.763867i
$460$	−0.904354	−	0.752187i	−0.0421657	−	0.0350709i
$461$	−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	$0.595923\pi$
$464$	32.8138	+	2.58437i	1.52334	+	0.119976i
$465$	2.80115	+	4.85174i	0.129900	+	0.224994i
$466$	9.76771	+	8.91159i	0.452481	+	0.412821i
$467$	−2.47581	−	9.23985i	−0.114567	−	0.427569i	0.884687	−	0.466185i	$-0.154372\pi$
$467$	−2.47581	−	9.23985i	−0.114567	−	0.427569i	−0.999254	+	0.0386156i	$0.987705\pi$
$468$	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
$472$	32.0680	−	24.9396i	1.47605	−	1.14794i
$473$	−1.26353	+	0.729497i	−0.0580970	+	0.0335423i
$474$	−21.9155	+	14.0286i	−1.00661	+	0.644355i
$475$	−13.5555	−	13.5555i	−0.621970	−	0.621970i
$476$		0			0
$477$	−5.51535	+	5.51535i	−0.252531	+	0.252531i
$478$	−10.1853	−	2.23487i	−0.465864	−	0.102221i
$479$	−17.0112	−	29.4642i	−0.777261	−	1.34626i	−0.933515	−	0.358539i	$-0.883275\pi$
$479$	−17.0112	−	29.4642i	−0.777261	−	1.34626i	0.156254	−	0.987717i	$-0.450058\pi$
$480$	5.87031	+	10.9844i	0.267942	+	0.501369i
$481$	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
$485$	8.90932	−	2.38725i	0.404552	−	0.108399i
$486$	0.975552	+	21.2850i	0.0442519	+	0.965509i
$487$	15.8637	−	9.15891i	0.718853	−	0.415030i	−0.0954776	−	0.995432i	$-0.530438\pi$
$487$	15.8637	−	9.15891i	0.718853	−	0.415030i	0.814330	+	0.580402i	$0.197104\pi$
$488$	9.57378	−	23.5450i	0.433385	−	1.06583i
$489$			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	$0.717067\pi$
$492$	11.3065	−	13.5938i	0.509735	−	0.612854i
$493$	44.7342	+	11.9865i	2.01473	+	0.539845i
$494$	28.5878	+	26.0821i	1.28623	+	1.17349i
$495$	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
$499$	−3.06599	−	11.4424i	−0.137252	−	0.512233i	−0.999978	−	0.00656149i	$-0.997911\pi$
$499$	−3.06599	−	11.4424i	−0.137252	−	0.512233i	0.862726	−	0.505672i	$-0.168755\pi$
$500$	17.2384	−	6.35902i	0.770923	−	0.284384i
$501$	−5.15427	+	19.2360i	−0.230276	+	0.859401i
$502$	7.81071	+	12.2019i	0.348609	+	0.544598i
$503$			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
$506$	−0.898255	+	0.574993i	−0.0399323	+	0.0255615i
$507$	−10.3826	+	38.7483i	−0.461107	+	1.72087i
$508$	−9.60077	−	4.42635i	−0.425965	−	0.196387i
$509$	−5.72030	−	21.3485i	−0.253548	−	0.946254i	−0.968893	−	0.247482i	$-0.920397\pi$
$509$	−5.72030	−	21.3485i	−0.253548	−	0.946254i	0.715345	−	0.698772i	$-0.246270\pi$
$510$	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
$514$	−5.80891	+	6.36696i	−0.256220	+	0.280835i
$515$	3.45205	+	0.924974i	0.152116	+	0.0407592i
$516$	−0.434513	−	4.73024i	−0.0191284	−	0.208237i
$517$	−8.88663	−	8.88663i	−0.390834	−	0.390834i
$518$		0			0
$519$		−	17.9529i		−	0.788043i
$520$	−15.0721	+	6.35820i	−0.660955	+	0.278825i
$521$	19.3677	−	11.1820i	0.848516	−	0.489891i	−0.0116337	−	0.999932i	$-0.503703\pi$
$521$	19.3677	−	11.1820i	0.848516	−	0.489891i	0.860150	+	0.510041i	$0.170370\pi$
$522$	18.5508	−	0.850235i	0.811947	−	0.0372138i
$523$	−2.28802	+	0.613074i	−0.100048	+	0.0268079i	−0.308496	−	0.951226i	$-0.599826\pi$
$523$	−2.28802	+	0.613074i	−0.100048	+	0.0268079i	0.208448	+	0.978034i	$0.433159\pi$
$524$	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
$528$	11.1036	−	2.05727i	0.483221	−	0.0895313i
$529$	−11.3360	−	19.6346i	−0.492871	−	0.853677i
$530$	1.52155	−	6.93436i	0.0660919	−	0.301209i
$531$	16.2066	−	16.2066i	0.703306	−	0.703306i
$532$		0			0
$533$	16.4212	+	16.4212i	0.711281	+	0.711281i
$534$	4.61440	+	7.20863i	0.199685	+	0.311948i
$535$	18.2819	−	10.5551i	0.790395	−	0.456335i
$536$	−14.8249	−	19.0623i	−0.640340	−	0.823365i
$537$	−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
$541$	−2.23514	−	8.34164i	−0.0960960	−	0.358635i	0.901087	−	0.433638i	$-0.142770\pi$
$541$	−2.23514	−	8.34164i	−0.0960960	−	0.358635i	−0.997183	+	0.0750025i	$0.976104\pi$
$542$	10.2699	−	11.2565i	0.441130	−	0.483509i
$543$	−3.81113	−	6.60108i	−0.163551	−	0.283279i
$544$	−16.8140	+	27.0349i	−0.720895	+	1.15911i
$545$	−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	$-0.0296044\pi$
$548$	18.3311	−	1.68387i	0.783066	−	0.0719313i
$549$	3.71143	−	13.8512i	0.158400	−	0.591156i
$550$	−0.336404	−	7.33982i	−0.0143443	−	0.312971i
$551$	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
$555$	16.5723	−	4.44052i	0.703453	−	0.188490i
$556$	3.01070	+	8.16158i	0.127682	+	0.346128i
$557$	3.69563	+	0.990242i	0.156589	+	0.0419579i	0.336262	−	0.941769i	$-0.390837\pi$
$557$	3.69563	+	0.990242i	0.156589	+	0.0419579i	−0.179673	+	0.983726i	$0.557504\pi$
$558$	−1.23072	+	5.60892i	−0.0521005	+	0.237444i
$559$	6.23900			0.263882
$560$		0			0
$561$	15.8887			0.670823
$562$	−4.78988	+	21.8295i	−0.202049	+	0.920824i
$563$	−17.7758	−	4.76300i	−0.749159	−	0.200736i	−0.136014	−	0.990707i	$-0.543429\pi$
$563$	−17.7758	−	4.76300i	−0.749159	−	0.200736i	−0.613145	+	0.789970i	$0.710096\pi$
$564$	38.3886	−	14.1611i	1.61645	−	0.596289i
$565$	2.30969	−	0.618878i	0.0971692	−	0.0260364i
$566$	−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	$-0.382481\pi$
$569$	−6.35393	−	3.66845i	−0.266371	−	0.153789i	−0.627237	+	0.778828i	$0.715814\pi$
$570$	0.692710	+	15.1139i	0.0290144	+	0.633050i
$571$	6.49973	−	24.2573i	0.272005	−	1.01514i	−0.685816	−	0.727775i	$-0.740555\pi$
$571$	6.49973	−	24.2573i	0.272005	−	1.01514i	0.957822	−	0.287363i	$-0.0927787\pi$
$572$	1.35673	+	14.7698i	0.0567277	+	0.617556i
$573$	19.2774	−	19.2774i	0.805327	−	0.805327i
$574$		0			0
$575$	−2.25931			−0.0942197
$576$	−3.14344	+	12.3729i	−0.130977	+	0.515539i
$577$	−4.46876	−	7.74012i	−0.186037	−	0.322225i	0.757889	−	0.652384i	$-0.226231\pi$
$577$	−4.46876	−	7.74012i	−0.186037	−	0.322225i	−0.943925	+	0.330159i	$0.892898\pi$
$578$	−13.9876	+	15.3314i	−0.581808	+	0.637702i
$579$	10.2806	+	38.3677i	0.427247	+	1.59451i
$580$	−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
$584$	35.5221	+	4.44179i	1.46992	+	0.183802i
$585$	−7.99262	+	4.61454i	−0.330454	+	0.190788i
$586$	−6.91033	−	10.7953i	−0.285463	−	0.445951i
$587$	−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
$590$	−4.47099	+	20.3763i	−0.184068	+	0.838877i
$591$	−3.43312	−	5.94633i	−0.141220	−	0.244599i
$592$	25.6873	+	17.6565i	1.05574	+	0.725678i
$593$	7.45619	−	12.9145i	0.306189	−	0.530335i	−0.671336	−	0.741153i	$-0.734279\pi$
$593$	7.45619	−	12.9145i	0.306189	−	0.530335i	0.977525	+	0.210818i	$0.0676127\pi$
$594$	−5.34334	+	1.69749i	−0.219240	+	0.0696489i
$595$		0			0
$596$	13.6442	+	2.34490i	0.558887	+	0.0960507i
$597$	−46.2843	+	12.4018i	−1.89429	+	0.507573i
$598$	4.55593	−	0.208811i	0.186306	−	0.00853892i
$599$	−3.14899	+	1.81807i	−0.128664	+	0.0742844i	−0.562951	−	0.826490i	$-0.690334\pi$
$599$	−3.14899	+	1.81807i	−0.128664	+	0.0742844i	0.434286	+	0.900775i	$0.357001\pi$
$600$	22.1600	+	9.01061i	0.904679	+	0.367857i
$601$		−	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
$604$	−35.1231	+	3.22636i	−1.42914	+	0.131279i
$605$	−9.19187	−	2.46295i	−0.373703	−	0.100133i
$606$	12.7654	−	13.9917i	0.518557	−	0.568374i
$607$	−17.3000	+	29.9645i	−0.702186	+	1.21622i	0.265512	+	0.964108i	$0.414459\pi$
$607$	−17.3000	+	29.9645i	−0.702186	+	1.21622i	−0.967698	+	0.252114i	$0.918874\pi$
$608$	−20.0634	+	18.7888i	−0.813679	+	0.761985i
$609$		0			0
$610$	3.95175	+	12.4393i	0.160002	+	0.503651i
$611$	13.9094	+	51.9108i	0.562716	+	2.10009i
$612$	−7.52039	+	16.3118i	−0.303994	+	0.659364i
$613$	10.5417	−	39.3423i	0.425777	−	1.58902i	−0.336444	−	0.941703i	$-0.609224\pi$
$613$	10.5417	−	39.3423i	0.425777	−	1.58902i	0.762221	−	0.647317i	$-0.224109\pi$
$614$	−1.59510	+	1.02106i	−0.0643731	+	0.0412066i
$615$			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	$0.864220\pi$
$618$	5.68773	+	8.88538i	0.228794	+	0.357422i
$619$	6.48686	−	24.2093i	0.260729	−	0.973053i	−0.704084	−	0.710116i	$-0.748642\pi$
$619$	6.48686	−	24.2093i	0.260729	−	0.973053i	0.964813	−	0.262937i	$-0.0846910\pi$
$620$	−1.80888	−	4.90360i	−0.0726462	−	0.196933i
$621$	0.446192	+	1.66521i	0.0179051	+	0.0668227i
$622$	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
$626$	−2.46229	−	2.24647i	−0.0984129	−	0.0897871i
$627$	13.2506	+	3.55048i	0.529177	+	0.141793i
$628$	−34.0831	−	28.3482i	−1.36006	−	1.13122i
$629$	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	$-0.292054\pi$
$632$	22.3672	−	9.43564i	0.889718	−	0.375329i
$633$	−5.06404	+	2.92373i	−0.201278	+	0.116208i
$634$	−0.455734	−	9.94340i	−0.0180995	−	0.394903i
$635$	5.24385	−	1.40508i	0.208096	−	0.0557591i
$636$	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
$640$	−3.66175	−	11.0273i	−0.144743	−	0.435894i
$641$	8.94810	+	15.4986i	0.353429	+	0.612157i	0.986848	−	0.161652i	$-0.0516823\pi$
$641$	8.94810	+	15.4986i	0.353429	+	0.612157i	−0.633419	+	0.773809i	$0.718349\pi$
$642$	60.8687	+	13.3559i	2.40230	+	0.527116i
$643$	−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
$646$	−32.5731	+	20.8508i	−1.28157	+	0.820363i
$647$	−2.97970	+	1.72033i	−0.117144	+	0.0676331i	−0.557427	−	0.830226i	$-0.688211\pi$
$647$	−2.97970	+	1.72033i	−0.117144	+	0.0676331i	0.440283	+	0.897859i	$0.354878\pi$
$648$	3.94488	−	31.5482i	0.154969	−	1.23933i
$649$	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
$653$	−7.49623	−	27.9763i	−0.293350	−	1.09480i	−0.942519	−	0.334153i	$-0.891550\pi$
$653$	−7.49623	−	27.9763i	−0.293350	−	1.09480i	0.649169	−	0.760645i	$-0.275117\pi$
$654$	−9.25828	−	8.44681i	−0.362028	−	0.330296i
$655$	7.93916	+	13.7510i	0.310208	+	0.537297i
$656$	−12.5439	+	10.7122i	−0.489756	+	0.418243i
$657$	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	$0.0536414\pi$
$660$	−3.70812	+	4.45828i	−0.144339	+	0.173538i
$661$	7.08235	−	26.4317i	0.275472	−	1.02807i	−0.680053	−	0.733163i	$-0.738043\pi$
$661$	7.08235	−	26.4317i	0.275472	−	1.02807i	0.955525	−	0.294911i	$-0.0952900\pi$
$662$	31.4920	−	1.44336i	1.22397	−	0.0560979i
$663$	−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
$667$	4.55182	−	1.21966i	0.176247	−	0.0472253i
$668$	7.77876	−	16.8722i	0.300969	−	0.652804i
$669$	−43.2903	−	11.5996i	−1.67370	−	0.448467i
$670$	12.1123	+	2.65771i	0.467940	+	0.102676i
$671$	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	$0.669465\pi$
$674$	−36.2189	−	7.94721i	−1.39510	−	0.306115i
$675$	−11.4720	−	3.07391i	−0.441557	−	0.118315i
$676$	15.6693	−	33.9868i	0.602665	−	1.30718i
$677$	−32.4507	+	8.69514i	−1.24718	+	0.334181i	−0.821247	−	0.570573i	$-0.806721\pi$
$677$	−32.4507	+	8.69514i	−1.24718	+	0.334181i	−0.425934	+	0.904754i	$0.640055\pi$
$678$	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
$682$	−4.73394	+	0.216970i	−0.181272	+	0.00830821i
$683$	−1.81082	+	6.75807i	−0.0692890	+	0.258590i	−0.991878	−	0.127195i	$-0.959403\pi$
$683$	−1.81082	+	6.75807i	−0.0692890	+	0.258590i	0.922589	+	0.385785i	$0.126069\pi$
$684$	−9.91671	+	11.9229i	−0.379175	+	0.455882i
$685$	−6.68416	+	6.68416i	−0.255389	+	0.255389i
$686$		0			0
$687$	43.1148			1.64493
$688$	−0.347949	+	4.41791i	−0.0132654	+	0.168431i
$689$	13.7629	+	23.8380i	0.524323	+	0.908154i
$690$	1.31724	+	1.20179i	0.0501466	+	0.0457514i
$691$	−2.26807	−	8.46454i	−0.0862813	−	0.322006i	0.909272	−	0.416201i	$-0.136639\pi$
$691$	−2.26807	−	8.46454i	−0.0862813	−	0.322006i	−0.995554	+	0.0941952i	$0.969972\pi$
$692$	−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
$696$	−49.5100	−	6.19087i	−1.87667	−	0.234664i
$697$	−20.0999	+	11.6047i	−0.761337	+	0.439558i
$698$	−6.70272	+	4.29056i	−0.253702	+	0.162400i
$699$	−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	$0.198221\pi$
$702$	23.4176	+	5.13832i	0.883839	+	0.193934i
$703$	18.9326	+	32.7922i	0.714056	+	1.23678i
$704$	−10.5343	+	0.137007i	−0.397027	+	0.00516364i
$705$	−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
$709$	−37.4930	+	10.0462i	−1.40808	+	0.377294i	−0.881240	−	0.472670i	$-0.843290\pi$
$709$	−37.4930	+	10.0462i	−1.40808	+	0.377294i	−0.526841	+	0.849964i	$0.676624\pi$
$710$	−0.636735	−	13.8926i	−0.0238962	−	0.521378i
$711$	11.8611	−	6.84803i	0.444827	−	0.256821i
$712$	−3.10365	−	7.35718i	−0.116314	−	0.275722i
$713$			1.45718i			0.0545718i
$714$		0			0
$715$	−5.38558	−	5.38558i	−0.201409	−	0.201409i
$716$	23.0676	+	19.1862i	0.862077	+	0.717023i
$717$	15.2683	+	4.09113i	0.570206	+	0.152786i
$718$	15.2884	+	13.9484i	0.570558	+	0.520549i
$719$	13.7596	−	23.8323i	0.513145	−	0.888794i	−0.486738	−	0.873548i	$-0.661813\pi$
$719$	13.7596	−	23.8323i	0.513145	−	0.888794i	0.999884	−	0.0152461i	$-0.00485318\pi$
$720$	−2.82186	−	5.91702i	−0.105165	−	0.220514i
$721$		0			0
$722$	−6.21515	+	1.97445i	−0.231304	+	0.0734814i
$723$	−5.21768	−	19.4727i	−0.194048	−	0.724196i
$724$	2.46108	+	6.67163i	0.0914653	+	0.247949i
$725$	−8.40248	+	31.3585i	−0.312060	+	1.16462i
$726$	−15.1449	−	23.6593i	−0.562078	−	0.878081i
$727$		−	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
$730$	−15.4826	+	9.91076i	−0.573037	+	0.366814i
$731$	−1.61382	+	6.02284i	−0.0596891	+	0.222763i
$732$	−16.1315	+	34.9894i	−0.596239	+	1.29325i
$733$	5.58317	+	20.8367i	0.206219	+	0.769620i	0.989075	+	0.147416i	$0.0470957\pi$
$733$	5.58317	+	20.8367i	0.206219	+	0.769620i	−0.782856	+	0.622203i	$0.786238\pi$
$734$	−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
$738$	−6.27247	+	6.87506i	−0.230893	+	0.253074i
$739$	−39.5654	−	10.6015i	−1.45544	−	0.389983i	−0.557525	−	0.830160i	$-0.688249\pi$
$739$	−39.5654	−	10.6015i	−1.45544	−	0.389983i	−0.897911	+	0.440177i	$0.854916\pi$
$740$	−15.9391	+	1.46415i	−0.585935	+	0.0538231i
$741$	−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	$-0.232204\pi$
$744$	5.81155	−	14.2925i	0.213062	−	0.523988i
$745$	−6.15669	+	3.55457i	−0.225564	+	0.130229i
$746$	40.5174	−	1.85702i	1.48345	−	0.0679905i
$747$	−5.79781	+	1.55352i	−0.212131	+	0.0568402i
$748$	−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	−0.341545	−	0.939866i	$-0.610950\pi$
$751$	17.6258	−	30.5288i	0.643175	−	1.11401i	0.984720	−	0.174146i	$-0.0557166\pi$
$752$	−37.5344	+	6.95439i	−1.36874	+	0.253600i
$753$	−10.9808	−	19.0193i	−0.400162	−	0.693101i
$754$	14.0455	−	64.0115i	0.511507	−	2.33116i
$755$	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	$0.884811\pi$
$758$	−16.6036	−	25.9383i	−0.603071	−	0.942120i
$759$	1.40012	−	0.808360i	0.0508212	−	0.0293416i
$760$	1.75135	−	14.0060i	0.0635281	−	0.508051i
$761$	27.7326	+	16.0115i	1.00531	+	0.580415i	0.909814	−	0.415015i	$-0.136224\pi$
$761$	27.7326	+	16.0115i	1.00531	+	0.580415i	0.0954932	+	0.995430i	$0.469557\pi$
$762$	14.2311	+	7.36908i	0.515538	+	0.266954i
$763$		0			0
$764$	−20.7710	+	14.6786i	−0.751467	+	0.531052i
$765$	−2.38725	−	8.90932i	−0.0863111	−	0.322117i
$766$	−2.71455	+	2.97533i	−0.0980807	+	0.107503i
$767$	−40.4415	−	70.0467i	−1.46026	−	2.52924i
$768$	13.9547	−	31.3333i	0.503549	−	1.13064i
$769$	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
$772$	−3.38976	−	36.9020i	−0.122000	−	1.32813i
$773$	−13.2301	+	49.3755i	−0.475855	+	1.77591i	0.142263	+	0.989829i	$0.454562\pi$
$773$	−13.2301	+	49.3755i	−0.475855	+	1.77591i	−0.618118	+	0.786085i	$0.712105\pi$
$774$	0.114472	+	2.49761i	0.00411462	+	0.0897746i
$775$	−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
$779$	−19.3557	+	5.18633i	−0.693488	+	0.185820i
$780$	23.2647	−	8.58206i	0.833011	−	0.307287i
$781$	−12.1798	−	3.26358i	−0.435829	−	0.116780i
$782$	−0.976887	+	4.45210i	−0.0349334	+	0.159207i
$783$	24.7720			0.885280
$784$		0			0
$785$	22.7646			0.812504
$786$	−10.0459	+	45.7834i	−0.358324	+	1.63304i
$787$	9.16210	+	2.45498i	0.326593	+	0.0875105i	0.418390	−	0.908267i	$-0.362594\pi$
$787$	9.16210	+	2.45498i	0.326593	+	0.0875105i	−0.0917969	+	0.995778i	$0.529261\pi$
$788$	2.21697	+	6.00989i	0.0789763	+	0.214093i
$789$	−2.07964	+	0.557238i	−0.0740371	+	0.0198382i
$790$	−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
$794$	0.0924827	+	2.01783i	0.00328209	+	0.0716101i
$795$	−2.78533	+	10.3950i	−0.0987854	+	0.368672i
$796$	44.5161	−	4.08918i	1.57783	−	0.144937i
$797$	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
$800$	−18.9513	−	11.7865i	−0.670030	−	0.416717i
$801$	−2.25251	−	3.90146i	−0.0795885	−	0.137851i
$802$	2.19712	−	2.40820i	0.0775831	−	0.0850364i
$803$	4.31392	+	16.0998i	0.152235	+	0.568149i
$804$	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
$808$	−13.9481	+	10.8476i	−0.490693	+	0.381617i
$809$	−6.68666	+	3.86054i	−0.235090	+	0.135729i	−0.612918	−	0.790146i	$-0.710004\pi$
$809$	−6.68666	+	3.86054i	−0.235090	+	0.135729i	0.377828	+	0.925876i	$0.376671\pi$
$810$	8.80203	+	13.7506i	0.309272	+	0.483145i
$811$	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
$814$	−3.11041	+	14.1755i	−0.109020	+	0.496851i
$815$	9.84489	+	17.0518i	0.344851	+	0.597300i
$816$	27.3375	−	39.7716i	0.957006	−	1.39228i
$817$	−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
$821$	18.0969	−	4.84905i	0.631586	−	0.169233i	0.0711970	−	0.997462i	$-0.477318\pi$
$821$	18.0969	−	4.84905i	0.631586	−	0.169233i	0.560390	+	0.828229i	$0.310651\pi$
$822$	−27.8754	+	1.27761i	−0.972266	+	0.0445617i
$823$	−1.88654	+	1.08919i	−0.0657606	+	0.0379669i	−0.532520	−	0.846418i	$-0.678755\pi$
$823$	−1.88654	+	1.08919i	−0.0657606	+	0.0379669i	0.466759	+	0.884384i	$0.345421\pi$
$824$	−3.82556	−	9.06848i	−0.133270	−	0.315916i
$825$			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	$0.886602\pi$
$828$	0.167183	+	1.82001i	0.00581002	+	0.0632496i
$829$	−24.4687	−	6.55637i	−0.849833	−	0.227712i	−0.192486	−	0.981300i	$-0.561655\pi$
$829$	−24.4687	−	6.55637i	−0.849833	−	0.227712i	−0.657347	+	0.753588i	$0.728322\pi$
$830$	3.68216	−	4.03590i	0.127810	−	0.140088i
$831$	−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
$835$	2.46926	+	9.21542i	0.0854524	+	0.318913i
$836$	−11.6223	−	5.35834i	−0.401965	−	0.185322i
$837$	−1.98257	+	7.39906i	−0.0685278	+	0.255749i
$838$	−23.6593	+	15.1449i	−0.817298	+	0.523170i
$839$		−	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
$842$	5.96359	+	9.31633i	0.205519	+	0.321062i
$843$	8.76829	−	32.7237i	0.301996	−	1.12706i
$844$	5.11817	−	1.88803i	0.176175	−	0.0649886i
$845$	4.97400	+	18.5632i	0.171111	+	0.638595i
$846$	−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
$850$	−23.1973	−	21.1641i	−0.795659	−	0.725921i
$851$	4.31050	+	1.15500i	0.147762	+	0.0395927i
$852$	26.2522	−	31.5631i	0.899387	−	1.08133i
$853$	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
$856$	−53.8556	−	21.8986i	−1.84075	−	0.748477i
$857$	−16.6790	+	9.62961i	−0.569743	+	0.328941i	−0.757047	−	0.653361i	$-0.773358\pi$
$857$	−16.6790	+	9.62961i	−0.569743	+	0.328941i	0.187304	+	0.982302i	$0.440025\pi$
$858$	−1.02940	−	22.4598i	−0.0351430	−	0.766765i
$859$	40.6558	−	10.8937i	1.38716	−	0.371687i	0.513441	−	0.858125i	$-0.328371\pi$
$859$	40.6558	−	10.8937i	1.38716	−	0.371687i	0.873715	+	0.486437i	$0.161704\pi$
$860$	−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	0.142424	+	0.989806i	$0.454510\pi$
$863$	−23.0898	+	39.9927i	−0.785985	+	1.36137i	−0.928409	+	0.371560i	$0.878823\pi$
$864$	−4.94451	+	16.2957i	−0.168216	+	0.554391i
$865$	−4.30035	−	7.44843i	−0.146216	−	0.253254i
$866$	−38.3857	−	8.42267i	−1.30440	−	0.286214i
$867$	22.2453	−	22.2453i	0.755490	−	0.755490i
$868$		0			0
$869$	7.99226	+	7.99226i	0.271119	+	0.271119i
$870$	21.5794	−	13.8134i	0.731609	−	0.468319i
$871$	−41.6381	+	24.0398i	−1.41085	+	0.814556i
$872$	7.17784	+	9.22945i	0.243072	+	0.312549i
$873$	−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
$877$	3.24285	+	12.1025i	0.109503	+	0.408672i	0.998817	−	0.0486255i	$-0.0154841\pi$
$877$	3.24285	+	12.1025i	0.109503	+	0.408672i	−0.889314	+	0.457298i	$0.848817\pi$
$878$	29.8540	+	27.2374i	1.00753	+	0.919217i
$879$	9.71496	+	16.8268i	0.327678	+	0.567554i
$880$	4.11395	−	3.51324i	0.138681	−	0.118431i
$881$	−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	$0.247452\pi$
$884$	48.7337	+	40.5337i	1.63909	+	1.36330i
$885$	8.18455	−	30.5452i	0.275121	−	1.02676i
$886$	−29.1457	+	1.33583i	−0.979170	+	0.0448781i
$887$	12.1158	+	6.99504i	0.406808	+	0.234870i	0.689417	−	0.724365i	$-0.257867\pi$
$887$	12.1158	+	6.99504i	0.406808	+	0.234870i	−0.282610	+	0.959235i	$0.591200\pi$
$888$	−37.6724	−	28.5198i	−1.26420	−	0.957061i
$889$		0			0
$890$	3.64119	+	1.88546i	0.122053	+	0.0632009i
$891$	14.2987	−	3.83132i	0.479024	−	0.128354i
$892$	37.9706	+	17.5060i	1.27135	+	0.586144i
$893$	−44.7921	−	12.0020i	−1.49891	−	0.401632i
$894$	−20.4984	−	4.49780i	−0.685570	−	0.150429i
$895$	−15.4072			−0.515007
$896$		0			0
$897$	−6.91347			−0.230834
$898$	3.63756	+	0.798159i	0.121387	+	0.0266349i
$899$	20.2252	+	5.41933i	0.674548	+	0.180745i
$900$	−11.4345	−	5.27175i	−0.381149	−	0.175725i
$901$	−26.5720	+	7.11995i	−0.885243	+	0.237200i
$902$	−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
$906$	53.4103	−	2.44794i	1.77444	−	0.0813274i
$907$	3.74438	−	13.9742i	0.124330	−	0.464006i	−0.875485	−	0.483246i	$-0.839458\pi$
$907$	3.74438	−	13.9742i	0.124330	−	0.464006i	0.999815	+	0.0192393i	$0.00612444\pi$
$908$	12.8272	+	10.6689i	0.425686	+	0.354060i
$909$	−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	$0.221450\pi$
$912$	31.6857	−	27.0591i	1.04922	−	0.896015i
$913$	−2.47673	−	4.28982i	−0.0819678	−	0.141972i
$914$	−8.05930	−	7.35292i	−0.266578	−	0.243213i
$915$	−5.12074	−	19.1109i	−0.169287	−	0.631786i
$916$	−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	$-0.347708\pi$
$919$	−2.37039	−	1.36854i	−0.0781918	−	0.0451441i	−0.538586	+	0.842570i	$0.681041\pi$
$920$	−1.02124	−	1.31314i	−0.0336694	−	0.0432930i
$921$	2.48630	−	1.43547i	0.0819265	−	0.0473003i
$922$	−32.0231	+	20.4987i	−1.05462	+	0.675088i
$923$	38.1280	+	38.1280i	1.25500	+	1.25500i
$924$		0			0
$925$	−21.7389	+	21.7389i	−0.714772	+	0.714772i
$926$	−17.6443	−	3.87154i	−0.579827	−	0.127227i
$927$	−2.77645	−	4.80895i	−0.0911905	−	0.157947i
$928$	44.5440	+	13.5157i	1.46223	+	0.443675i
$929$	−6.91731	+	11.9811i	−0.226949	+	0.393088i	−0.956903	−	0.290409i	$-0.906209\pi$
$929$	−6.91731	+	11.9811i	−0.226949	+	0.393088i	0.729953	+	0.683497i	$0.239542\pi$
$930$	2.39882	+	7.55099i	0.0786605	+	0.247607i
$931$		0			0
$932$	10.7916	+	15.2706i	0.353489	+	0.500206i
$933$	−18.7042	+	5.01178i	−0.612349	+	0.164078i
$934$	−0.619380	−	13.5139i	−0.0202667	−	0.442188i
$935$	6.59205	−	3.80592i	0.215583	−	0.124467i
$936$	23.5450	+	9.57378i	0.769593	+	0.312929i
$937$			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
$940$	12.5349	−	15.0707i	0.408844	−	0.491553i
$941$	−42.8390	−	11.4787i	−1.39651	−	0.374194i	−0.519420	−	0.854519i	$-0.673852\pi$
$941$	−42.8390	−	11.4787i	−1.39651	−	0.374194i	−0.877090	+	0.480325i	$0.840519\pi$
$942$	49.6440	+	45.2928i	1.61749	+	1.47572i
$943$	−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
$947$	0.265913	+	0.992401i	0.00864101	+	0.0322487i	0.970112	−	0.242659i	$-0.0780195\pi$
$947$	0.265913	+	0.992401i	0.00864101	+	0.0322487i	−0.961471	+	0.274907i	$0.911353\pi$
$948$	−34.5251	+	12.7359i	−1.12132	+	0.413642i
$949$	18.4473	−	68.8464i	0.598826	−	2.23485i
$950$	−14.6163	−	22.8336i	−0.474215	−	0.740820i
$951$			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	$0.799199\pi$
$954$	−9.29033	+	5.94694i	−0.300786	+	0.192539i
$955$	3.38035	−	12.6156i	0.109385	−	0.408232i
$956$	−13.3921	−	6.17429i	−0.433131	−	0.199691i
$957$	−6.01266	−	22.4396i	−0.194362	−	0.725368i
$958$	−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
$962$	41.8278	−	45.8461i	1.34858	−	1.47814i
$963$	−31.6826	−	8.48932i	−1.02096	−	0.273564i
$964$	1.72040	+	18.7287i	0.0554102	+	0.603212i
$965$	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	$-0.234381\pi$
$968$	10.1864	+	24.1469i	0.327404	+	0.776111i
$969$	50.7721	−	29.3133i	1.63104	−	0.941679i
$970$	13.0305	−	0.597223i	0.418383	−	0.0191757i
$971$	−15.7410	+	4.21780i	−0.505154	+	0.135356i	−0.502391	−	0.864641i	$-0.667546\pi$
$971$	−15.7410	+	4.21780i	−0.505154	+	0.135356i	−0.00276313	+	0.999996i	$0.500880\pi$
$972$	−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
$976$	20.3612	−	29.6222i	0.651746	−	0.948182i
$977$	26.8666	+	46.5343i	0.859538	+	1.48876i	0.872370	+	0.488846i	$0.162582\pi$
$977$	26.8666	+	46.5343i	0.859538	+	1.48876i	−0.0128319	+	0.999918i	$0.504085\pi$
$978$	−12.4573	+	56.7733i	−0.398341	+	1.81541i
$979$	2.62888	−	2.62888i	0.0840193	−	0.0840193i
$980$		0			0
$981$	4.66440	+	4.66440i	0.148923	+	0.148923i
$982$	3.48962	+	5.45149i	0.111358	+	0.173964i
$983$	27.0344	−	15.6083i	0.862263	−	0.497827i	−0.00250678	−	0.999997i	$-0.500798\pi$
$983$	27.0344	−	15.6083i	0.862263	−	0.497827i	0.864769	+	0.502169i	$0.167465\pi$
$984$	19.7385	−	15.3508i	0.629239	−	0.489365i
$985$	−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
$989$	0.164210	+	0.612840i	0.00522157	+	0.0194872i
$990$	2.05715	−	2.25478i	0.0653805	−	0.0716615i
$991$	21.7139	+	37.6096i	0.689764	+	1.19471i	0.971914	+	0.235336i	$0.0756192\pi$
$991$	21.7139	+	37.6096i	0.689764	+	1.19471i	−0.282150	+	0.959370i	$0.591047\pi$
$992$	−7.60194	+	12.2230i	−0.241362	+	0.388080i
$993$	−47.7880			−1.51650
$994$		0			0
$995$	−16.2321	+	16.2321i	−0.514593	+	0.514593i
$996$	16.0597	−	1.47522i	0.508873	−	0.0467443i
$997$	−6.60392	+	24.6462i	−0.209148	+	0.780552i	0.778997	+	0.627028i	$0.215729\pi$
$997$	−6.60392	+	24.6462i	−0.209148	+	0.780552i	−0.988145	+	0.153524i	$0.950938\pi$
$998$	−0.767025	−	16.7353i	−0.0242798	−	0.529747i
$999$	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.373.9		40
7.2	even	3		784.2.m.i.197.4	yes	20
7.3	odd	6	inner	784.2.x.n.165.3		40
7.4	even	3	inner	784.2.x.n.165.4		40
7.5	odd	6		784.2.m.i.197.3	✓	20
7.6	odd	2	inner	784.2.x.n.373.10		40
16.13	even	4	inner	784.2.x.n.765.4		40
112.13	odd	4	inner	784.2.x.n.765.3		40
112.45	odd	12	inner	784.2.x.n.557.10		40
112.61	odd	12		784.2.m.i.589.3	yes	20
112.93	even	12		784.2.m.i.589.4	yes	20
112.109	even	12	inner	784.2.x.n.557.9		40

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.38135 + 0.303098i) q^{2} +(-2.07072 - 0.554848i) q^{3} +(1.81626 + 0.837371i) q^{4} +(-0.992025 + 0.265812i) q^{5} +(-2.69222 - 1.39407i) q^{6} +(2.25509 + 1.70721i) q^{8} +(1.38196 + 0.797875i) q^{9} +O(q^{10})\)	\(q+(1.38135 + 0.303098i) q^{2} +(-2.07072 - 0.554848i) q^{3} +(1.81626 + 0.837371i) q^{4} +(-0.992025 + 0.265812i) q^{5} +(-2.69222 - 1.39407i) q^{6} +(2.25509 + 1.70721i) q^{8} +(1.38196 + 0.797875i) q^{9} +(-1.45090 + 0.0664989i) q^{10} +(-0.340839 + 1.27203i) q^{11} +(-3.29636 - 2.74171i) q^{12} +(3.98199 - 3.98199i) q^{13} +2.20169 q^{15} +(2.59762 + 3.04177i) q^{16} +(2.81402 + 4.87403i) q^{17} +(1.66714 + 1.52102i) q^{18} +(1.25764 + 4.69357i) q^{19} +(-2.02436 - 0.347908i) q^{20} +(-0.856369 + 1.65381i) q^{22} +(0.495945 + 0.286334i) q^{23} +(-3.72243 - 4.78639i) q^{24} +(-3.41667 + 1.97262i) q^{25} +(6.70746 - 4.29359i) q^{26} +(2.12867 + 2.12867i) q^{27} +(5.81867 - 5.81867i) q^{29} +(3.04131 + 0.667330i) q^{30} +(1.27227 + 2.20364i) q^{31} +(2.66627 + 4.98909i) q^{32} +(1.41157 - 2.44491i) q^{33} +(2.40984 + 7.58567i) q^{34} +(1.84188 + 2.60636i) q^{36} +(7.52705 - 2.01687i) q^{37} +(0.314626 + 6.86465i) q^{38} +(-10.4550 + 6.03619i) q^{39} +(-2.69090 - 1.09416i) q^{40} +4.12387i q^{41} +(0.783403 + 0.783403i) q^{43} +(-1.68421 + 2.02493i) q^{44} +(-1.58302 - 0.424170i) q^{45} +(0.598287 + 0.545848i) q^{46} +(-4.77165 + 8.26474i) q^{47} +(-3.69123 - 7.73995i) q^{48} +(-5.31752 + 1.68929i) q^{50} +(-3.12271 - 11.6541i) q^{51} +(10.5667 - 3.89794i) q^{52} +(-1.26508 + 4.72136i) q^{53} +(2.29524 + 3.58563i) q^{54} -1.35248i q^{55} -10.4169i q^{57} +(9.80126 - 6.27400i) q^{58} +(3.71739 - 13.8735i) q^{59} +(3.99885 + 1.84363i) q^{60} +(-2.32582 - 8.68008i) q^{61} +(1.08954 + 3.42963i) q^{62} +(2.17087 + 7.69983i) q^{64} +(-2.89177 + 5.00869i) q^{65} +(2.69092 - 2.94943i) q^{66} +(-8.24686 - 2.20974i) q^{67} +(1.02963 + 11.2089i) q^{68} +(-0.868093 - 0.868093i) q^{69} +9.57512i q^{71} +(1.75431 + 4.15858i) q^{72} +(10.9611 - 6.32838i) q^{73} +(11.0088 - 0.504564i) q^{74} +(8.16948 - 2.18901i) q^{75} +(-1.64606 + 9.57786i) q^{76} +(-16.2716 + 5.16921i) q^{78} +(4.29142 - 7.43296i) q^{79} +(-3.38544 - 2.32703i) q^{80} +(-5.62042 - 9.73485i) q^{81} +(-1.24994 + 5.69651i) q^{82} +(-2.65975 + 2.65975i) q^{83} +(-4.08716 - 4.08716i) q^{85} +(0.844706 + 1.31960i) q^{86} +(-15.2773 + 8.82037i) q^{87} +(-2.94025 + 2.28666i) q^{88} +(-2.44491 - 1.41157i) q^{89} +(-2.05815 - 1.06574i) q^{90} +(0.660999 + 0.935348i) q^{92} +(-1.41184 - 5.26905i) q^{93} +(-9.09636 + 9.97023i) q^{94} +(-2.49521 - 4.32184i) q^{95} +(-2.75292 - 11.8104i) 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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