LMFDB - Embedded newform 784.2.w.f.19.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [784,2,Mod(19,784)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("784.19"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(784, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 10])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [56,-2,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			19.6
Character	$\chi$	$=$	784.19
Dual form			784.2.w.f.619.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.482479 + 1.32937i) q^{2} +(-0.449868 + 1.67893i) q^{3} +(-1.53443 - 1.28278i) q^{4} +(-0.731029 + 0.195879i) q^{5} +(-2.01486 - 1.40809i) q^{6} +(2.44562 - 1.42090i) q^{8} +(-0.0183525 - 0.0105958i) q^{9} +(0.0923119 - 1.06631i) q^{10} +(1.18531 - 4.42364i) q^{11} +(2.84399 - 1.99912i) q^{12} +(2.89529 - 2.89529i) q^{13} -1.31547i q^{15} +(0.708938 + 3.93667i) q^{16} +(2.28427 - 1.31882i) q^{17} +(0.0229404 - 0.0192849i) q^{18} +(5.38016 - 1.44161i) q^{19} +(1.37298 + 0.637190i) q^{20} +(5.30875 + 3.71003i) q^{22} +(1.01143 - 1.75184i) q^{23} +(1.28539 + 4.74524i) q^{24} +(-3.83409 + 2.21361i) q^{25} +(2.45199 + 5.24582i) q^{26} +(-3.66114 + 3.66114i) q^{27} +(-0.209526 - 0.209526i) q^{29} +(1.74874 + 0.634686i) q^{30} +(-3.33052 - 5.76864i) q^{31} +(-5.57533 - 0.956926i) q^{32} +(6.89376 + 3.98011i) q^{33} +(0.651087 + 3.67293i) q^{34} +(0.0145684 + 0.0398007i) q^{36} +(1.02406 + 3.82183i) q^{37} +(-0.679388 + 7.84774i) q^{38} +(3.55850 + 6.16350i) q^{39} +(-1.50949 + 1.51776i) q^{40} +5.04472 q^{41} +(-3.79454 - 3.79454i) q^{43} +(-7.49334 + 5.26726i) q^{44} +(0.0154917 + 0.00415099i) q^{45} +(1.84085 + 2.18978i) q^{46} +(2.53993 - 4.39928i) q^{47} +(-6.92833 - 0.580727i) q^{48} +(-1.09283 - 6.16493i) q^{50} +(1.18659 + 4.42843i) q^{51} +(-8.15665 + 0.728587i) q^{52} +(10.7333 + 2.87599i) q^{53} +(-3.10057 - 6.63342i) q^{54} +3.46599i q^{55} +9.68145i q^{57} +(0.379629 - 0.177445i) q^{58} +(5.23198 + 1.40190i) q^{59} +(-1.68746 + 2.01849i) q^{60} +(1.56694 + 5.84791i) q^{61} +(9.27554 - 1.64424i) q^{62} +(3.96208 - 6.94996i) q^{64} +(-1.54942 + 2.68367i) q^{65} +(-8.61712 + 7.24400i) q^{66} +(9.24005 + 2.47586i) q^{67} +(-5.19681 - 0.906581i) q^{68} +(2.48621 + 2.48621i) q^{69} -7.25507 q^{71} +(-0.0599387 + 0.000163756i) q^{72} +(-3.29633 - 5.70940i) q^{73} +(-5.57470 - 0.482607i) q^{74} +(-1.99167 - 7.43301i) q^{75} +(-10.1047 - 4.68953i) q^{76} +(-9.91044 + 1.75679i) q^{78} +(-13.0615 - 7.54108i) q^{79} +(-1.28936 - 2.73896i) q^{80} +(-4.53156 - 7.84890i) q^{81} +(-2.43397 + 6.70628i) q^{82} +(8.00548 + 8.00548i) q^{83} +(-1.41154 + 1.41154i) q^{85} +(6.87511 - 3.21354i) q^{86} +(0.446039 - 0.257521i) q^{87} +(-3.38674 - 12.5027i) q^{88} +(-3.92536 + 6.79892i) q^{89} +(-0.0129926 + 0.0185914i) q^{90} +(-3.79919 + 1.39063i) q^{92} +(11.1834 - 2.99659i) q^{93} +(4.62279 + 5.49905i) q^{94} +(-3.65067 + 2.10772i) q^{95} +(4.11478 - 8.93010i) q^{96} +8.79532i q^{97} +(-0.0686254 + 0.0686254i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 2 q^{2} + 6 q^{3} - 4 q^{4} + 6 q^{5} + 4 q^{8} + 24 q^{10} + 2 q^{11} + 6 q^{12} + 8 q^{16} + 12 q^{17} - 30 q^{18} + 6 q^{19} - 28 q^{22} - 12 q^{23} + 6 q^{24} + 6 q^{26} - 24 q^{29} - 18 q^{30}+ \cdots - 16 q^{99}+O(q^{100}) $ 56 * q - 2 * q^2 + 6 * q^3 - 4 * q^4 + 6 * q^5 + 4 * q^8 + 24 * q^10 + 2 * q^11 + 6 * q^12 + 8 * q^16 + 12 * q^17 - 30 * q^18 + 6 * q^19 - 28 * q^22 - 12 * q^23 + 6 * q^24 + 6 * q^26 - 24 * q^29 - 18 * q^30 - 12 * q^32 + 12 * q^33 + 16 * q^36 + 6 * q^37 + 6 * q^38 - 4 * q^39 + 66 * q^40 + 26 * q^44 - 12 * q^45 + 16 * q^46 - 34 * q^51 - 84 * q^52 + 6 * q^53 - 42 * q^54 + 18 * q^58 - 42 * q^59 + 78 * q^60 + 6 * q^61 - 16 * q^64 - 4 * q^65 - 126 * q^66 + 6 * q^67 - 24 * q^68 - 80 * q^71 - 4 * q^72 + 62 * q^74 - 24 * q^75 + 4 * q^78 - 12 * q^80 - 8 * q^81 - 42 * q^82 - 28 * q^85 + 12 * q^87 + 30 * q^88 - 20 * q^92 + 10 * q^93 + 42 * q^94 - 36 * q^96 - 16 * q^99

Character values

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

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.482479	+	1.32937i	−0.341164	+	0.940004i
$2$	−0.482479	+	1.32937i	−0.341164	+	0.940004i
$3$	−0.449868	+	1.67893i	−0.259732	+	0.969331i	0.705665	+	0.708546i	$0.250648\pi$
$3$	−0.449868	+	1.67893i	−0.259732	+	0.969331i	−0.965397	+	0.260786i	$0.916018\pi$
$4$	−1.53443	−	1.28278i	−0.767214	−	0.641391i
$5$	−0.731029	+	0.195879i	−0.326926	+	0.0875996i	−0.418549	−	0.908194i	$-0.637461\pi$
$5$	−0.731029	+	0.195879i	−0.326926	+	0.0875996i	0.0916229	+	0.995794i	$0.470795\pi$
$6$	−2.01486	−	1.40809i	−0.822564	−	0.574850i
$7$		0			0
$7$		0			0
$8$	2.44562	−	1.42090i	0.864656	−	0.502364i
$9$	−0.0183525	−	0.0105958i	−0.00611749	−	0.00353194i
$10$	0.0923119	−	1.06631i	0.0291916	−	0.337198i
$11$	1.18531	−	4.42364i	0.357385	−	1.33378i	−0.520072	−	0.854122i	$-0.674095\pi$
$11$	1.18531	−	4.42364i	0.357385	−	1.33378i	0.877457	−	0.479656i	$-0.159238\pi$
$12$	2.84399	−	1.99912i	0.820990	−	0.577095i
$13$	2.89529	−	2.89529i	0.803010	−	0.803010i	−0.180555	−	0.983565i	$-0.557789\pi$
$13$	2.89529	−	2.89529i	0.803010	−	0.803010i	0.983565	+	0.180555i	$0.0577895\pi$
$14$		0			0
$15$		−	1.31547i		−	0.339652i
$16$	0.708938	+	3.93667i	0.177234	+	0.984169i
$17$	2.28427	−	1.31882i	0.554017	−	0.319862i	−0.196724	−	0.980459i	$-0.563030\pi$
$17$	2.28427	−	1.31882i	0.554017	−	0.319862i	0.750740	+	0.660597i	$0.229697\pi$
$18$	0.0229404	−	0.0192849i	0.00540710	−	0.00454549i
$19$	5.38016	−	1.44161i	1.23429	−	0.330728i	0.418043	−	0.908427i	$-0.362716\pi$
$19$	5.38016	−	1.44161i	1.23429	−	0.330728i	0.816249	+	0.577700i	$0.196049\pi$
$20$	1.37298	+	0.637190i	0.307008	+	0.142480i
$21$		0			0
$22$	5.30875	+	3.71003i	1.13183	+	0.790980i
$23$	1.01143	−	1.75184i	0.210897	−	0.365284i	−0.741099	−	0.671396i	$-0.765695\pi$
$23$	1.01143	−	1.75184i	0.210897	−	0.365284i	0.951995	+	0.306112i	$0.0990283\pi$
$24$	1.28539	+	4.74524i	0.262379	+	0.968618i
$25$	−3.83409	+	2.21361i	−0.766818	+	0.442723i
$26$	2.45199	+	5.24582i	0.480874	+	1.02879i
$27$	−3.66114	+	3.66114i	−0.704587	+	0.704587i
$28$		0			0
$29$	−0.209526	−	0.209526i	−0.0389080	−	0.0389080i	0.687385	−	0.726293i	$-0.258758\pi$
$29$	−0.209526	−	0.209526i	−0.0389080	−	0.0389080i	−0.726293	+	0.687385i	$0.758758\pi$
$30$	1.74874	+	0.634686i	0.319274	+	0.115877i
$31$	−3.33052	−	5.76864i	−0.598180	−	1.03608i	−0.993090	−	0.117358i	$-0.962558\pi$
$31$	−3.33052	−	5.76864i	−0.598180	−	1.03608i	0.394910	−	0.918720i	$-0.370776\pi$
$32$	−5.57533	−	0.956926i	−0.985588	−	0.169162i
$33$	6.89376	+	3.98011i	1.20005	+	0.692849i
$34$	0.651087	+	3.67293i	0.111660	+	0.629903i
$35$		0			0
$36$	0.0145684	+	0.0398007i	0.00242807	+	0.00663346i
$37$	1.02406	+	3.82183i	0.168354	+	0.628305i	0.997589	+	0.0694046i	$0.0221099\pi$
$37$	1.02406	+	3.82183i	0.168354	+	0.628305i	−0.829235	+	0.558900i	$0.811223\pi$
$38$	−0.679388	+	7.84774i	−0.110211	+	1.27307i
$39$	3.55850	+	6.16350i	0.569815	+	0.986949i
$40$	−1.50949	+	1.51776i	−0.238672	+	0.239980i
$41$	5.04472			0.787853			0.393926	−	0.919142i	$-0.371117\pi$
$41$	5.04472			0.787853			0.393926	+	0.919142i	$0.371117\pi$
$42$		0			0
$43$	−3.79454	−	3.79454i	−0.578662	−	0.578662i	0.355873	−	0.934534i	$-0.384184\pi$
$43$	−3.79454	−	3.79454i	−0.578662	−	0.578662i	−0.934534	+	0.355873i	$0.884184\pi$
$44$	−7.49334	+	5.26726i	−1.12966	+	0.794070i
$45$	0.0154917	+	0.00415099i	0.00230936	+	0.000618792i
$46$	1.84085	+	2.18978i	0.271418	+	0.322866i
$47$	2.53993	−	4.39928i	0.370486	−	0.641701i	−0.619154	−	0.785270i	$-0.712524\pi$
$47$	2.53993	−	4.39928i	0.370486	−	0.641701i	0.989640	+	0.143568i	$0.0458577\pi$
$48$	−6.92833	−	0.580727i	−1.00002	−	0.0838208i
$49$		0			0
$50$	−1.09283	−	6.16493i	−0.154550	−	0.871853i
$51$	1.18659	+	4.42843i	0.166156	+	0.620104i
$52$	−8.15665	+	0.728587i	−1.13112	+	0.101037i
$53$	10.7333	+	2.87599i	1.47434	+	0.395047i	0.904416	−	0.426652i	$-0.140307\pi$
$53$	10.7333	+	2.87599i	1.47434	+	0.395047i	0.569921	+	0.821699i	$0.306974\pi$
$54$	−3.10057	−	6.63342i	−0.421935	−	0.902695i
$55$			3.46599i			0.467354i
$56$		0			0
$57$			9.68145i			1.28234i
$58$	0.379629	−	0.177445i	0.0498477	−	0.0232997i
$59$	5.23198	+	1.40190i	0.681145	+	0.182512i	0.582770	−	0.812637i	$-0.301969\pi$
$59$	5.23198	+	1.40190i	0.681145	+	0.182512i	0.0983751	+	0.995149i	$0.468635\pi$
$60$	−1.68746	+	2.01849i	−0.217850	+	0.260586i
$61$	1.56694	+	5.84791i	0.200626	+	0.748748i	0.990738	+	0.135785i	$0.0433557\pi$
$61$	1.56694	+	5.84791i	0.200626	+	0.748748i	−0.790112	+	0.612962i	$0.789978\pi$
$62$	9.27554	−	1.64424i	1.17799	−	0.208818i
$63$		0			0
$64$	3.96208	−	6.94996i	0.495261	−	0.868745i
$65$	−1.54942	+	2.68367i	−0.192182	+	0.332868i
$66$	−8.61712	+	7.24400i	−1.06069	+	0.891675i
$67$	9.24005	+	2.47586i	1.12885	+	0.302475i	0.774461	−	0.632622i	$-0.218021\pi$
$67$	9.24005	+	2.47586i	1.12885	+	0.302475i	0.354392	+	0.935097i	$0.384688\pi$
$68$	−5.19681	−	0.906581i	−0.630206	−	0.109939i
$69$	2.48621	+	2.48621i	0.299305	+	0.299305i
$70$		0			0
$71$	−7.25507			−0.861018			−0.430509	−	0.902586i	$-0.641666\pi$
$71$	−7.25507			−0.861018			−0.430509	+	0.902586i	$0.641666\pi$
$72$	−0.0599387		0.000163756i	−0.00706384		1.92989e-5i
$73$	−3.29633	−	5.70940i	−0.385806	−	0.668235i	0.606075	−	0.795408i	$-0.292743\pi$
$73$	−3.29633	−	5.70940i	−0.385806	−	0.668235i	−0.991881	+	0.127172i	$0.959410\pi$
$74$	−5.57470	−	0.482607i	−0.648045	−	0.0561020i
$75$	−1.99167	−	7.43301i	−0.229978	−	0.858290i
$76$	−10.1047	−	4.68953i	−1.15909	−	0.537926i
$77$		0			0
$78$	−9.91044	+	1.75679i	−1.12214	+	0.198917i
$79$	−13.0615	−	7.54108i	−1.46954	−	0.848437i	−0.470121	−	0.882602i	$-0.655790\pi$
$79$	−13.0615	−	7.54108i	−1.46954	−	0.848437i	−0.999416	+	0.0341648i	$0.989123\pi$
$80$	−1.28936	−	2.73896i	−0.144155	−	0.306225i
$81$	−4.53156	−	7.84890i	−0.503507	−	0.872100i
$82$	−2.43397	+	6.70628i	−0.268787	+	0.740584i
$83$	8.00548	+	8.00548i	0.878715	+	0.878715i	0.993402	−	0.114687i	$-0.0365864\pi$
$83$	8.00548	+	8.00548i	0.878715	+	0.878715i	−0.114687	+	0.993402i	$0.536586\pi$
$84$		0			0
$85$	−1.41154	+	1.41154i	−0.153103	+	0.153103i
$86$	6.87511	−	3.21354i	0.741363	−	0.346525i
$87$	0.446039	−	0.257521i	0.0478204	−	0.0276091i
$88$	−3.38674	−	12.5027i	−0.361027	−	1.33280i
$89$	−3.92536	+	6.79892i	−0.416087	+	0.720684i	−0.995542	−	0.0943203i	$-0.969932\pi$
$89$	−3.92536	+	6.79892i	−0.416087	+	0.720684i	0.579455	+	0.815004i	$0.303266\pi$
$90$	−0.0129926	+	0.0185914i	−0.00136954	+	0.00195970i
$91$		0			0
$92$	−3.79919	+	1.39063i	−0.396093	+	0.144984i
$93$	11.1834	−	2.99659i	1.15967	−	0.310732i
$94$	4.62279	+	5.49905i	0.476805	+	0.567184i
$95$	−3.65067	+	2.10772i	−0.374551	+	0.216247i
$96$	4.11478	−	8.93010i	0.419963	−	0.911425i
$97$			8.79532i			0.893029i	0.894776	+	0.446514i	$0.147335\pi$
$97$			8.79532i			0.893029i	−0.894776	+	0.446514i	$0.852665\pi$
$98$		0			0
$99$	−0.0686254	+	0.0686254i	−0.00689712	+	0.00689712i
$100$	8.72272	+	1.52168i	0.872272	+	0.152168i
$101$	−0.597042	+	2.22819i	−0.0594079	+	0.221713i	−0.989247	−	0.146252i	$-0.953279\pi$
$101$	−0.597042	+	2.22819i	−0.0594079	+	0.221713i	0.929839	+	0.367966i	$0.119946\pi$
$102$	−6.45951	−	0.559207i	−0.639587	−	0.0553697i
$103$	−11.8007	−	6.81315i	−1.16276	−	0.671319i	−0.210795	−	0.977530i	$-0.567605\pi$
$103$	−11.8007	−	6.81315i	−1.16276	−	0.671319i	−0.951964	+	0.306211i	$0.900939\pi$
$104$	2.96685	−	11.1947i	0.290924	−	1.09773i
$105$		0			0
$106$	−9.00185	+	12.8809i	−0.874337	+	1.25111i
$107$	4.56363	−	1.22282i	0.441183	−	0.118215i	−0.0313881	−	0.999507i	$-0.509993\pi$
$107$	4.56363	−	1.22282i	0.441183	−	0.118215i	0.472571	+	0.881293i	$0.343326\pi$
$108$	10.3142	−	0.921309i	0.992485	−	0.0886530i
$109$	−2.13269	+	7.95931i	−0.204275	+	0.762364i	0.785395	+	0.618995i	$0.212460\pi$
$109$	−2.13269	+	7.95931i	−0.204275	+	0.762364i	−0.989669	+	0.143368i	$0.954207\pi$
$110$	−4.60757	−	1.67227i	−0.439314	−	0.159444i
$111$	−6.87728			−0.652763
$112$		0			0
$113$	18.4851			1.73893			0.869467	−	0.493990i	$-0.164462\pi$
$113$	18.4851			1.73893			0.869467	+	0.493990i	$0.164462\pi$
$114$	−12.8702	−	4.67110i	−1.20540	−	0.437488i
$115$	−0.396233	+	1.47876i	−0.0369490	+	0.137895i
$116$	0.0527263	+	0.590279i	0.00489551	+	0.0548060i
$117$	−0.0838137	+	0.0224578i	−0.00774858	+	0.00207623i
$118$	−4.38796	+	6.27882i	−0.403945	+	0.578012i
$119$		0			0
$120$	−1.86915	−	3.21713i	−0.170629	−	0.293682i
$121$	−8.63736	−	4.98678i	−0.785215	−	0.453344i
$122$	−8.53002	−	0.738453i	−0.772272	−	0.0668564i
$123$	−2.26946	+	8.46974i	−0.204630	+	0.763690i
$124$	−2.28946	+	13.1239i	−0.205599	+	1.17856i
$125$	5.04499	−	5.04499i	0.451237	−	0.451237i
$126$		0			0
$127$		−	13.0667i		−	1.15948i	−0.814802	−	0.579739i	$-0.803154\pi$
$127$		−	13.0667i		−	1.15948i	0.814802	−	0.579739i	$-0.196846\pi$
$128$	7.32741	+	8.62027i	0.647658	+	0.761931i
$129$	8.07781	−	4.66373i	0.711212	−	0.410618i
$130$	−2.82002	−	3.35456i	−0.247332	−	0.294214i
$131$	8.29942	−	2.22382i	0.725124	−	0.194296i	0.122667	−	0.992448i	$-0.460855\pi$
$131$	8.29942	−	2.22382i	0.725124	−	0.194296i	0.602457	+	0.798152i	$0.294189\pi$
$132$	−5.47235	−	14.9504i	−0.476307	−	1.30126i
$133$		0			0
$134$	−7.74946	+	11.0889i	−0.669452	+	0.957932i
$135$	1.95926	−	3.39354i	0.168626	−	0.292070i
$136$	3.71253	−	6.47106i	0.318347	−	0.554888i
$137$	19.9938	−	11.5434i	1.70818	−	0.986221i	0.771376	−	0.636380i	$-0.219569\pi$
$137$	19.9938	−	11.5434i	1.70818	−	0.986221i	0.936809	−	0.349841i	$-0.113764\pi$
$138$	−4.50463	+	2.10554i	−0.383460	+	0.179235i
$139$	−6.09369	+	6.09369i	−0.516860	+	0.516860i	−0.916620	−	0.399760i	$-0.869093\pi$
$139$	−6.09369	+	6.09369i	−0.516860	+	0.516860i	0.399760	+	0.916620i	$0.369093\pi$
$140$		0			0
$141$	6.24346	+	6.24346i	0.525794	+	0.525794i
$142$	3.50042	−	9.64464i	0.293749	−	0.809360i
$143$	−9.37591	−	16.2396i	−0.784053	−	1.35802i
$144$	0.0287015	−	0.0797595i	0.00239179	−	0.00664662i
$145$	0.194211	+	0.112128i	0.0161284	+	0.00931173i
$146$	9.18030	−	1.62736i	0.759767	−	0.134681i
$147$		0			0
$148$	3.33124	−	7.17796i	0.273826	−	0.590025i
$149$	−3.12680	−	11.6694i	−0.256157	−	0.955992i	−0.967443	−	0.253089i	$-0.918553\pi$
$149$	−3.12680	−	11.6694i	−0.256157	−	0.955992i	0.711286	−	0.702903i	$-0.248113\pi$
$150$	10.8421	+	0.938615i	0.885256	+	0.0766376i
$151$	−0.813682	−	1.40934i	−0.0662165	−	0.114690i	0.831016	−	0.556248i	$-0.187759\pi$
$151$	−0.813682	−	1.40934i	−0.0662165	−	0.114690i	−0.897233	+	0.441557i	$0.854426\pi$
$152$	11.1094	−	11.1703i	0.901093	−	0.906030i
$153$	−0.0558960			−0.00451892
$154$		0			0
$155$	3.56466	+	3.56466i	0.286321	+	0.286321i
$156$	2.44617	−	14.0222i	0.195850	−	1.12268i
$157$	23.2350	+	6.22579i	1.85435	+	0.496872i	0.999749	−	0.0224085i	$-0.00713343\pi$
$157$	23.2350	+	6.22579i	1.85435	+	0.496872i	0.854604	+	0.519281i	$0.173800\pi$
$158$	16.3268	−	13.7251i	1.29889	−	1.09191i
$159$	−9.65717	+	16.7267i	−0.765864	+	1.32651i
$160$	4.26317	−	0.392548i	0.337033	−	0.0310336i
$161$		0			0
$162$	12.6204	−	2.23718i	0.991556	−	0.175769i
$163$	2.36008	+	8.80794i	0.184856	+	0.689891i	0.994661	+	0.103193i	$0.0329059\pi$
$163$	2.36008	+	8.80794i	0.184856	+	0.689891i	−0.809806	+	0.586698i	$0.800427\pi$
$164$	−7.74076	−	6.47128i	−0.604452	−	0.505322i
$165$	−5.81916	−	1.55924i	−0.453021	−	0.121387i
$166$	−14.5047	+	6.77973i	−1.12578	+	0.526209i
$167$			3.18749i			0.246656i	0.992366	+	0.123328i	$0.0393566\pi$
$167$			3.18749i			0.246656i	−0.992366	+	0.123328i	$0.960643\pi$
$168$		0			0
$169$		−	3.76544i		−	0.289649i
$170$	−1.19541	−	2.55749i	−0.0916840	−	0.196150i
$171$	−0.114014	−	0.0305500i	−0.00871888	−	0.00233622i
$172$	0.954877	+	10.6900i	0.0728087	+	0.815106i
$173$	−4.98693	−	18.6115i	−0.379149	−	1.41500i	−0.847187	−	0.531295i	$-0.821706\pi$
$173$	−4.98693	−	18.6115i	−0.379149	−	1.41500i	0.468038	−	0.883708i	$-0.344961\pi$
$174$	0.127135	+	0.717198i	0.00963807	+	0.0543706i
$175$		0			0
$176$	18.2547	+	1.53010i	1.37600	+	0.115336i
$177$	−4.70740	+	8.15345i	−0.353830	+	0.612851i
$178$	−7.14435	−	8.49858i	−0.535492	−	0.636995i
$179$	−7.03090	−	1.88392i	−0.525514	−	0.140811i	−0.0136980	−	0.999906i	$-0.504360\pi$
$179$	−7.03090	−	1.88392i	−0.525514	−	0.140811i	−0.511816	+	0.859095i	$0.671027\pi$
$180$	−0.0184461	−	0.0262419i	−0.00137489	−	0.00195595i
$181$	−5.59617	−	5.59617i	−0.415960	−	0.415960i	0.467849	−	0.883809i	$-0.345029\pi$
$181$	−5.59617	−	5.59617i	−0.415960	−	0.415960i	−0.883809	+	0.467849i	$0.845029\pi$
$182$		0			0
$183$	−10.5231			−0.777894
$184$	−0.0156314	−	5.72147i	−0.00115236	−	0.421792i
$185$	−1.49723	−	2.59328i	−0.110079	−	0.190662i
$186$	−1.41221	+	16.3127i	−0.103548	+	1.19610i
$187$	−3.12643	−	11.6680i	−0.228627	−	0.853249i
$188$	−9.54065	+	3.49221i	−0.695824	+	0.254695i
$189$		0			0
$190$	−1.04055	−	5.87001i	−0.0754897	−	0.425855i
$191$	4.12735	+	2.38292i	0.298644	+	0.172422i	0.641834	−	0.766844i	$-0.278174\pi$
$191$	4.12735	+	2.38292i	0.298644	+	0.172422i	−0.343189	+	0.939266i	$0.611507\pi$
$192$	9.88608	+	9.77863i	0.713467	+	0.705712i
$193$	2.67050	+	4.62543i	0.192226	+	0.332946i	0.945988	−	0.324202i	$-0.105096\pi$
$193$	2.67050	+	4.62543i	0.192226	+	0.332946i	−0.753761	+	0.657148i	$0.771763\pi$
$194$	−11.6922	−	4.24356i	−0.839451	−	0.304670i
$195$	−3.80866	−	3.80866i	−0.272744	−	0.272744i
$196$		0			0
$197$	−11.6754	+	11.6754i	−0.831838	+	0.831838i	−0.987768	−	0.155930i	$-0.950163\pi$
$197$	−11.6754	+	11.6754i	−0.831838	+	0.831838i	0.155930	+	0.987768i	$0.450163\pi$
$198$	−0.0581180	−	0.124339i	−0.00413027	−	0.00883636i
$199$	9.02919	−	5.21301i	0.640062	−	0.369540i	−0.144576	−	0.989494i	$-0.546182\pi$
$199$	9.02919	−	5.21301i	0.640062	−	0.369540i	0.784639	+	0.619953i	$0.212849\pi$
$200$	−6.23139	+	10.8615i	−0.440626	+	0.768025i
$201$	−8.31361	+	14.3996i	−0.586397	+	1.01567i
$202$	−2.67402	−	1.86874i	−0.188143	−	0.131484i
$203$		0			0
$204$	3.85997	−	8.31724i	0.270252	−	0.582324i
$205$	−3.68784	+	0.988153i	−0.257570	+	0.0690156i
$206$	14.7508	−	12.4003i	1.02773	−	0.863968i
$207$	−0.0371243	+	0.0214337i	−0.00258032	+	0.00148975i
$208$	13.4504	+	9.34524i	0.932618	+	0.647976i
$209$		−	25.5086i		−	1.76447i
$210$		0			0
$211$	−0.716512	+	0.716512i	−0.0493267	+	0.0493267i	−0.731340	−	0.682013i	$-0.761105\pi$
$211$	−0.716512	+	0.716512i	−0.0493267	+	0.0493267i	0.682013	+	0.731340i	$0.261105\pi$
$212$	−12.7803	−	18.1815i	−0.877752	−	1.24871i
$213$	3.26383	−	12.1808i	0.223634	−	0.834612i
$214$	−0.576279	+	6.65672i	−0.0393936	+	0.455044i
$215$	3.51719	+	2.03065i	0.239870	+	0.138489i
$216$	−3.75163	+	14.1559i	−0.255266	+	0.963185i
$217$		0			0
$218$	−9.55186	−	6.67533i	−0.646933	−	0.452110i
$219$	11.0686	−	2.96583i	0.747947	−	0.200412i
$220$	4.44611	−	5.31831i	0.299757	−	0.358560i
$221$	2.79525	−	10.4320i	0.188029	−	0.701733i
$222$	3.31814	−	9.14242i	0.222699	−	0.613599i
$223$	−12.9181			−0.865062			−0.432531	−	0.901619i	$-0.642379\pi$
$223$	−12.9181			−0.865062			−0.432531	+	0.901619i	$0.642379\pi$
$224$		0			0
$225$	0.0938201			0.00625467
$226$	−8.91869	+	24.5735i	−0.593262	+	1.63461i
$227$	−4.02569	+	15.0241i	−0.267195	+	0.997184i	0.693699	+	0.720265i	$0.255980\pi$
$227$	−4.02569	+	15.0241i	−0.267195	+	0.997184i	−0.960893	+	0.276919i	$0.910687\pi$
$228$	12.4192	−	14.8555i	0.822481	−	0.983828i
$229$	13.3759	−	3.58406i	0.883903	−	0.236841i	0.211813	−	0.977310i	$-0.432063\pi$
$229$	13.3759	−	3.58406i	0.883903	−	0.236841i	0.672090	+	0.740469i	$0.265397\pi$
$230$	−1.77464	−	1.24021i	−0.117017	−	0.0817771i
$231$		0			0
$232$	−0.810136	−	0.214705i	−0.0531881	−	0.0140961i
$233$	−10.6523	−	6.15010i	−0.697854	−	0.402906i	0.108694	−	0.994075i	$-0.465333\pi$
$233$	−10.6523	−	6.15010i	−0.697854	−	0.402906i	−0.806548	+	0.591169i	$0.798667\pi$
$234$	0.0105837	−	0.122255i	0.000691879	−	0.00799203i
$235$	−0.995035	+	3.71352i	−0.0649089	+	0.242243i
$236$	−6.22975	−	8.86261i	−0.405522	−	0.576907i
$237$	18.5369	−	18.5369i	1.20410	−	1.20410i
$238$		0			0
$239$			7.20218i			0.465870i	0.972492	+	0.232935i	$0.0748329\pi$
$239$			7.20218i			0.465870i	−0.972492	+	0.232935i	$0.925167\pi$
$240$	5.17857	−	0.932584i	0.334275	−	0.0601981i
$241$	−20.7383	+	11.9733i	−1.33587	+	0.771265i	−0.986192	−	0.165605i	$-0.947042\pi$
$241$	−20.7383	+	11.9733i	−1.33587	+	0.771265i	−0.349678	+	0.936870i	$0.613709\pi$
$242$	10.7966	−	9.07620i	0.694032	−	0.583440i
$243$	0.212722	−	0.0569986i	0.0136461	−	0.00365646i
$244$	5.09723	−	10.9832i	0.326317	−	0.703130i
$245$		0			0
$246$	−10.1644	−	7.10341i	−0.648059	−	0.452897i
$247$	11.4032	−	19.7510i	0.725571	−	1.25673i
$248$	−16.3418	−	9.37553i	−1.03771	−	0.595347i
$249$	−17.0421	+	9.83923i	−1.08000	+	0.623536i
$250$	4.27253	+	9.14073i	0.270219	+	0.578111i
$251$	6.11266	−	6.11266i	0.385828	−	0.385828i	−0.487369	−	0.873196i	$-0.662043\pi$
$251$	6.11266	−	6.11266i	0.385828	−	0.385828i	0.873196	+	0.487369i	$0.162043\pi$
$252$		0			0
$253$	−6.55066	−	6.55066i	−0.411837	−	0.411837i
$254$	17.3704	+	6.30439i	1.08991	+	0.395573i
$255$	−1.73487	−	3.00488i	−0.108642	−	0.188173i
$256$	−14.9948	+	5.58171i	−0.937176	+	0.348857i
$257$	19.7315	+	11.3920i	1.23082	+	0.710613i	0.967200	−	0.254015i	$-0.0817512\pi$
$257$	19.7315	+	11.3920i	1.23082	+	0.710613i	0.263617	+	0.964627i	$0.415085\pi$
$258$	2.30242	+	12.9885i	0.143343	+	0.808630i
$259$		0			0
$260$	5.82003	−	2.13033i	0.360943	−	0.132118i
$261$	0.00162522	+	0.00606542i	0.000100599	+	0.000375440i
$262$	−1.04802	+	12.1059i	−0.0647470	+	0.747906i
$263$	−5.28788	−	9.15888i	−0.326065	−	0.564761i	0.655662	−	0.755054i	$-0.272389\pi$
$263$	−5.28788	−	9.15888i	−0.326065	−	0.564761i	−0.981727	+	0.190293i	$0.939056\pi$
$264$	22.5148	−	0.0615119i	1.38569	−	0.00378580i
$265$	−8.40973			−0.516605
$266$		0			0
$267$	−9.64903	−	9.64903i	−0.590511	−	0.590511i
$268$	−11.0022	−	15.6520i	−0.672066	−	0.956099i
$269$	−10.0057	−	2.68103i	−0.610061	−	0.163465i	−0.0594553	−	0.998231i	$-0.518936\pi$
$269$	−10.0057	−	2.68103i	−0.610061	−	0.163465i	−0.550605	+	0.834766i	$0.685603\pi$
$270$	3.56596	+	4.24189i	0.217017	+	0.258153i
$271$	−12.3322	+	21.3601i	−0.749131	+	1.29753i	0.199109	+	0.979977i	$0.436195\pi$
$271$	−12.3322	+	21.3601i	−0.749131	+	1.29753i	−0.948240	+	0.317555i	$0.897138\pi$
$272$	6.81118	+	8.05746i	0.412989	+	0.488555i
$273$		0			0
$274$	5.69884	+	32.1485i	0.344280	+	1.94216i
$275$	5.24764	+	19.5845i	0.316445	+	1.18099i
$276$	−0.625643	−	7.00418i	−0.0376593	−	0.421602i
$277$	−10.3610	−	2.77622i	−0.622531	−	0.166807i	−0.0662529	−	0.997803i	$-0.521104\pi$
$277$	−10.3610	−	2.77622i	−0.622531	−	0.166807i	−0.556278	+	0.830996i	$0.687771\pi$
$278$	−5.16066	−	11.0408i	−0.309516	−	0.662184i
$279$			0.141158i			0.00845093i
$280$		0			0
$281$		−	6.46396i		−	0.385608i	−0.981237	−	0.192804i	$-0.938242\pi$
$281$		−	6.46396i		−	0.385608i	0.981237	−	0.192804i	$-0.0617581\pi$
$282$	−11.3122	+	5.28750i	−0.673630	+	0.314866i
$283$	−19.0327	−	5.09979i	−1.13138	−	0.303151i	−0.355897	−	0.934525i	$-0.615825\pi$
$283$	−19.0327	−	5.09979i	−1.13138	−	0.303151i	−0.775478	+	0.631374i	$0.782491\pi$
$284$	11.1324	+	9.30668i	0.660585	+	0.552250i
$285$	−1.89639	−	7.07742i	−0.112332	−	0.419230i
$286$	26.1120	−	4.62877i	1.54403	−	0.273705i
$287$		0			0
$288$	0.0921817	+	0.0766371i	0.00543186	+	0.00451588i
$289$	−5.02141	+	8.69734i	−0.295377	+	0.511608i
$290$	−0.242762	+	0.204079i	−0.0142555	+	0.0119839i
$291$	−14.7667	−	3.95673i	−0.865641	−	0.231948i
$292$	−2.26595	+	12.9891i	−0.132605	+	0.760132i
$293$	−2.96394	−	2.96394i	−0.173155	−	0.173155i	0.615209	−	0.788364i	$-0.289072\pi$
$293$	−2.96394	−	2.96394i	−0.173155	−	0.173155i	−0.788364	+	0.615209i	$0.789072\pi$
$294$		0			0
$295$	−4.09933			−0.238672
$296$	7.93489	+	7.89165i	0.461206	+	0.458693i
$297$	11.8560	+	20.5352i	0.687954	+	1.19157i
$298$	17.0215	+	1.47357i	0.986028	+	0.0853615i
$299$	−2.14372	−	8.00046i	−0.123974	−	0.462679i
$300$	−6.47886	+	13.9603i	−0.374057	+	0.805998i
$301$		0			0
$302$	2.26611	−	0.401705i	0.130400	−	0.0231155i
$303$	−3.47239	−	2.00479i	−0.199484	−	0.115172i
$304$	9.48934	+	20.1579i	0.544251	+	1.15614i
$305$	−2.29096	−	3.96806i	−0.131180	−	0.227210i
$306$	0.0269686	−	0.0743062i	0.00154169	−	0.00424780i
$307$	−8.60981	−	8.60981i	−0.491388	−	0.491388i	0.417356	−	0.908743i	$-0.362957\pi$
$307$	−8.60981	−	8.60981i	−0.491388	−	0.491388i	−0.908743	+	0.417356i	$0.862957\pi$
$308$		0			0
$309$	16.7476	−	16.7476i	0.952736	−	0.952736i
$310$	−6.45862	+	3.01887i	−0.366825	+	0.171460i
$311$	−4.98997	+	2.88096i	−0.282955	+	0.163364i	−0.634760	−	0.772709i	$-0.718901\pi$
$311$	−4.98997	+	2.88096i	−0.282955	+	0.163364i	0.351805	+	0.936073i	$0.385568\pi$
$312$	17.4604	+	10.0173i	0.988502	+	0.567117i
$313$	4.01618	−	6.95623i	0.227008	−	0.393190i	−0.729912	−	0.683541i	$-0.760439\pi$
$313$	4.01618	−	6.95623i	0.227008	−	0.393190i	0.956920	+	0.290352i	$0.0937723\pi$
$314$	−19.4867	+	27.8840i	−1.09970	+	1.57358i
$315$		0			0
$316$	10.3684	+	28.3263i	0.583269	+	1.59348i
$317$	9.01190	−	2.41473i	0.506159	−	0.135625i	0.00330181	−	0.999995i	$-0.498949\pi$
$317$	9.01190	−	2.41473i	0.506159	−	0.135625i	0.502857	+	0.864370i	$0.332282\pi$
$318$	−17.5765	−	20.9082i	−0.985644	−	1.17247i
$319$	−1.17522	+	0.678515i	−0.0657998	+	0.0379895i
$320$	−1.53505	+	5.85671i	−0.0858120	+	0.327400i
$321$			8.21213i			0.458356i
$322$		0			0
$323$	10.3885	−	10.3885i	0.578031	−	0.578031i
$324$	−3.11507	+	17.8566i	−0.173060	+	0.992032i
$325$	−4.69176	+	17.5099i	−0.260252	+	0.971273i
$326$	−12.8477	−	1.11224i	−0.711566	−	0.0616011i
$327$	−12.4037	−	7.16128i	−0.685926	−	0.396020i
$328$	12.3374	−	7.16804i	0.681222	−	0.395789i
$329$		0			0
$330$	4.88042	−	6.98349i	0.268658	−	0.384428i
$331$	4.96046	−	1.32915i	0.272652	−	0.0730568i	−0.119903	−	0.992786i	$-0.538258\pi$
$331$	4.96046	−	1.32915i	0.272652	−	0.0730568i	0.392554	+	0.919729i	$0.371592\pi$
$332$	−2.01454	−	22.5531i	−0.110562	−	1.23776i
$333$	0.0217014	−	0.0809907i	0.00118923	−	0.00443827i
$334$	−4.23734	−	1.53790i	−0.231857	−	0.0841500i
$335$	−7.23972			−0.395548
$336$		0			0
$337$	1.50446			0.0819532			0.0409766	−	0.999160i	$-0.486953\pi$
$337$	1.50446			0.0819532			0.0409766	+	0.999160i	$0.486953\pi$
$338$	5.00564	+	1.81674i	0.272271	+	0.0988178i
$339$	−8.31587	+	31.0353i	−0.451656	+	1.68560i
$340$	3.97660	−	0.355207i	0.215661	−	0.0192638i
$341$	−29.4661	+	7.89541i	−1.59568	+	0.427561i
$342$	0.0956216	−	0.136827i	0.00517062	−	0.00739875i
$343$		0			0
$344$	−14.6716	−	3.88833i	−0.791042	−	0.209644i
$345$	−2.30449	−	1.33050i	−0.124070	−	0.0716316i
$346$	27.1475	+	2.35019i	1.45946	+	0.126347i
$347$	2.24815	−	8.39020i	0.120687	−	0.450410i	−0.878962	−	0.476891i	$-0.841764\pi$
$347$	2.24815	−	8.39020i	0.120687	−	0.450410i	0.999649	+	0.0264814i	$0.00843029\pi$
$348$	−1.01476	−	0.177024i	−0.0543967	−	0.00948949i
$349$	−15.6677	+	15.6677i	−0.838672	+	0.838672i	−0.988684	−	0.150012i	$-0.952069\pi$
$349$	−15.6677	+	15.6677i	−0.838672	+	0.838672i	0.150012	+	0.988684i	$0.452069\pi$
$350$		0			0
$351$			21.2002i			1.13158i
$352$	−10.8416	+	23.5290i	−0.577859	+	1.25410i
$353$	−21.5439	+	12.4384i	−1.14666	+	0.662027i	−0.948072	−	0.318056i	$-0.896970\pi$
$353$	−21.5439	+	12.4384i	−1.14666	+	0.662027i	−0.198592	+	0.980082i	$0.563637\pi$
$354$	−8.56770	−	10.1917i	−0.455368	−	0.541684i
$355$	5.30367	−	1.42111i	0.281490	−	0.0754249i
$356$	14.7447	−	5.39707i	0.781468	−	0.286044i
$357$		0			0
$358$	5.89668	−	8.43768i	0.311649	−	0.445945i
$359$	−4.32864	+	7.49742i	−0.228457	+	0.395699i	−0.957351	−	0.288928i	$-0.906701\pi$
$359$	−4.32864	+	7.49742i	−0.228457	+	0.395699i	0.728894	+	0.684626i	$0.240035\pi$
$360$	0.0437849	−	0.0118604i	0.00230767	−	0.000625099i
$361$	10.4134	−	6.01216i	0.548072	−	0.316429i
$362$	10.1394	−	4.73932i	0.532915	−	0.249093i
$363$	12.2581	−	12.2581i	0.643386	−	0.643386i
$364$		0			0
$365$	3.52806	+	3.52806i	0.184667	+	0.184667i
$366$	5.07720	−	13.9891i	0.265389	−	0.731223i
$367$	11.9671	+	20.7276i	0.624676	+	1.08197i	0.988603	+	0.150543i	$0.0481022\pi$
$367$	11.9671	+	20.7276i	0.624676	+	1.08197i	−0.363928	+	0.931427i	$0.618564\pi$
$368$	7.61346	+	2.73971i	0.396879	+	0.142817i
$369$	−0.0925831	−	0.0534529i	−0.00481968	−	0.00278264i
$370$	4.16980	−	0.739164i	0.216778	−	0.0384273i
$371$		0			0
$372$	−21.0042	−	9.74787i	−1.08901	−	0.505403i
$373$	0.612436	+	2.28564i	0.0317107	+	0.118346i	0.979967	−	0.199160i	$-0.0638213\pi$
$373$	0.612436	+	2.28564i	0.0317107	+	0.118346i	−0.948256	+	0.317506i	$0.897155\pi$
$374$	17.0195	+	1.47340i	0.880057	+	0.0761875i
$375$	6.20061	+	10.7398i	0.320198	+	0.554599i
$376$	−0.0392541	−	14.3679i	−0.00202438	−	0.740970i
$377$	−1.21328			−0.0624870
$378$		0			0
$379$	−5.34619	−	5.34619i	−0.274615	−	0.274615i	0.556340	−	0.830955i	$-0.312205\pi$
$379$	−5.34619	−	5.34619i	−0.274615	−	0.274615i	−0.830955	+	0.556340i	$0.812205\pi$
$380$	8.30543	+	1.44888i	0.426060	+	0.0743259i
$381$	21.9380	+	5.87828i	1.12392	+	0.301153i
$382$	−5.15914	+	4.33704i	−0.263964	+	0.221902i
$383$	12.5700	−	21.7718i	0.642296	−	1.11249i	−0.342623	−	0.939473i	$-0.611315\pi$
$383$	12.5700	−	21.7718i	0.642296	−	1.11249i	0.984919	−	0.173016i	$-0.0553514\pi$
$384$	−17.7692	+	8.42424i	−0.906781	+	0.429898i
$385$		0			0
$386$	−7.43735	+	1.31839i	−0.378551	+	0.0671043i
$387$	0.0294330	+	0.109845i	0.00149616	+	0.00558375i
$388$	11.2825	−	13.4958i	0.572781	−	0.685144i
$389$	−6.08010	−	1.62916i	−0.308273	−	0.0826016i	0.101366	−	0.994849i	$-0.467679\pi$
$389$	−6.08010	−	1.62916i	−0.308273	−	0.0826016i	−0.409639	+	0.912248i	$0.634345\pi$
$390$	6.90071	−	3.22551i	0.349431	−	0.163330i
$391$		−	5.33557i		−	0.269831i
$392$		0			0
$393$			14.9346i			0.753350i
$394$	−9.88775	−	21.1540i	−0.498138	−	1.06572i
$395$	11.0255	+	2.95427i	0.554753	+	0.148646i
$396$	0.193332	−	0.0172693i	0.00971531	−	0.000867813i
$397$	−4.67347	−	17.4416i	−0.234555	−	0.875371i	−0.978349	−	0.206962i	$-0.933642\pi$
$397$	−4.67347	−	17.4416i	−0.234555	−	0.875371i	0.743794	−	0.668409i	$-0.233024\pi$
$398$	2.57360	+	14.5183i	0.129003	+	0.727735i
$399$		0			0
$400$	−11.4324	−	13.5243i	−0.571620	−	0.676213i
$401$	−7.88832	+	13.6630i	−0.393924	+	0.682296i	−0.992963	−	0.118423i	$-0.962216\pi$
$401$	−7.88832	+	13.6630i	−0.393924	+	0.682296i	0.599039	+	0.800720i	$0.295549\pi$
$402$	−15.1312	−	17.9993i	−0.754675	−	0.897726i
$403$	−26.3447	−	7.05905i	−1.31232	−	0.351636i
$404$	3.77440	−	2.65312i	0.187784	−	0.131998i
$405$	4.85014	+	4.85014i	0.241005	+	0.241005i
$406$		0			0
$407$	18.1202			0.898186
$408$	9.19431	+	9.14421i	0.455186	+	0.452706i
$409$	−14.9850	−	25.9548i	−0.740963	−	1.28338i	−0.952057	−	0.305919i	$-0.901036\pi$
$409$	−14.9850	−	25.9548i	−0.740963	−	1.28338i	0.211095	−	0.977466i	$-0.432297\pi$
$410$	0.465687	−	5.37925i	0.0229987	−	0.265662i
$411$	10.3860	+	38.7612i	0.512305	+	1.91195i
$412$	9.36756	+	25.5920i	0.461507	+	1.26083i
$413$		0			0
$414$	−0.0105816	−	0.0596931i	−0.000520056	−	0.00293376i
$415$	−7.42034	−	4.28413i	−0.364250	−	0.210300i
$416$	−18.9128	+	13.3716i	−0.927276	+	0.655598i
$417$	−7.48953	−	12.9722i	−0.366764	−	0.635253i
$418$	33.9103	+	12.3074i	1.65861	+	0.601974i
$419$	19.0681	+	19.0681i	0.931537	+	0.931537i	0.997802	−	0.0662653i	$-0.0211084\pi$
$419$	19.0681	+	19.0681i	0.931537	+	0.931537i	−0.0662653	+	0.997802i	$0.521108\pi$
$420$		0			0
$421$	1.12116	−	1.12116i	0.0546418	−	0.0546418i	−0.679258	−	0.733900i	$-0.737698\pi$
$421$	1.12116	−	1.12116i	0.0546418	−	0.0546418i	0.733900	+	0.679258i	$0.237698\pi$
$422$	−0.606805	−	1.29821i	−0.0295388	−	0.0631958i
$423$	−0.0932279	+	0.0538251i	−0.00453289	+	0.00261707i
$424$	30.3361	−	8.21743i	1.47325	−	0.399074i
$425$	−5.83873	+	10.1130i	−0.283220	+	0.490552i
$426$	14.6180	+	10.2158i	0.708243	+	0.494956i
$427$		0			0
$428$	−8.57117	−	3.97781i	−0.414303	−	0.192275i
$429$	31.4830	−	8.43585i	1.52001	−	0.407287i
$430$	−4.39645	+	3.69588i	−0.212015	+	0.178231i
$431$	14.2383	−	8.22048i	0.685834	−	0.395966i	−0.116216	−	0.993224i	$-0.537076\pi$
$431$	14.2383	−	8.22048i	0.685834	−	0.395966i	0.802049	+	0.597258i	$0.203743\pi$
$432$	−17.0083	−	11.8172i	−0.818310	−	0.568556i
$433$			34.3709i			1.65176i	0.563847	+	0.825879i	$0.309321\pi$
$433$			34.3709i			1.65176i	−0.563847	+	0.825879i	$0.690679\pi$
$434$		0			0
$435$	−0.275625	+	0.275625i	−0.0132152	+	0.0132152i
$436$	13.4825	−	9.47721i	0.645696	−	0.453876i
$437$	2.91616	−	10.8833i	0.139499	−	0.520617i
$438$	−1.39771	+	16.1452i	−0.0667850	+	0.771447i
$439$	−8.37299	−	4.83415i	−0.399621	−	0.230721i	0.286699	−	0.958021i	$-0.407442\pi$
$439$	−8.37299	−	4.83415i	−0.399621	−	0.230721i	−0.686321	+	0.727299i	$0.740775\pi$
$440$	4.92482	+	8.47648i	0.234782	+	0.404100i
$441$		0			0
$442$	12.5193	+	8.74913i	0.595483	+	0.416154i
$443$	−33.5974	+	9.00239i	−1.59626	+	0.427717i	−0.943910	−	0.330202i	$-0.892883\pi$
$443$	−33.5974	+	9.00239i	−1.59626	+	0.427717i	−0.652350	+	0.757918i	$0.726217\pi$
$444$	10.5527	+	8.82206i	0.500809	+	0.418676i
$445$	1.53779	−	5.73910i	0.0728982	−	0.272060i
$446$	6.23273	−	17.1729i	0.295128	−	0.813162i
$447$	20.9987			0.993205
$448$		0			0
$449$	−35.5072			−1.67569			−0.837844	−	0.545910i	$-0.816184\pi$
$449$	−35.5072			−1.67569			−0.837844	+	0.545910i	$0.816184\pi$
$450$	−0.0452662	+	0.124721i	−0.00213387	+	0.00587942i
$451$	5.97956	−	22.3160i	0.281567	−	1.05082i
$452$	−28.3641	−	23.7124i	−1.33414	−	1.11534i
$453$	2.73223	−	0.732100i	0.128372	−	0.0343970i
$454$	−18.0302	−	12.6004i	−0.846200	−	0.591368i
$455$		0			0
$456$	13.7564	+	23.6771i	0.644201	+	1.10878i
$457$	26.0860	+	15.0607i	1.22025	+	0.704512i	0.964971	−	0.262356i	$-0.0844993\pi$
$457$	26.0860	+	15.0607i	1.22025	+	0.704512i	0.255279	+	0.966867i	$0.417833\pi$
$458$	−1.68906	+	19.5107i	−0.0789246	+	0.911674i
$459$	−3.53464	+	13.1914i	−0.164983	+	0.615724i
$460$	2.50492	−	1.76077i	0.116793	−	0.0820965i
$461$	−2.37946	+	2.37946i	−0.110822	+	0.110822i	−0.760344	−	0.649521i	$-0.774969\pi$
$461$	−2.37946	+	2.37946i	−0.110822	+	0.110822i	0.649521	+	0.760344i	$0.274969\pi$
$462$		0			0
$463$			1.23324i			0.0573136i	0.999589	+	0.0286568i	$0.00912299\pi$
$463$			1.23324i			0.0573136i	−0.999589	+	0.0286568i	$0.990877\pi$
$464$	0.676295	−	0.973377i	0.0313962	−	0.0451879i
$465$	−7.58845	+	4.38120i	−0.351906	+	0.203173i
$466$	13.3152	−	11.1935i	0.616816	−	0.518528i
$467$	30.7990	−	8.25258i	1.42521	−	0.381884i	0.537881	−	0.843021i	$-0.319225\pi$
$467$	30.7990	−	8.25258i	1.42521	−	0.381884i	0.887329	+	0.461137i	$0.152558\pi$
$468$	0.157415	+	0.0730549i	0.00727649	+	0.00337696i
$469$		0			0
$470$	−4.45654	−	3.11446i	−0.205565	−	0.143659i
$471$	−20.9054	+	36.2091i	−0.963268	+	1.66843i
$472$	14.7874	−	4.00560i	0.680644	−	0.184373i
$473$	−21.2834	+	12.2880i	−0.978611	+	0.565001i
$474$	15.6987	+	33.5860i	0.721064	+	1.54266i
$475$	−17.4368	+	17.4368i	−0.800057	+	0.800057i
$476$		0			0
$477$	−0.166510	−	0.166510i	−0.00762396	−	0.00762396i
$478$	−9.57433	−	3.47490i	−0.437920	−	0.158938i
$479$	6.64611	+	11.5114i	0.303668	+	0.525969i	0.976964	−	0.213404i	$-0.0684552\pi$
$479$	6.64611	+	11.5114i	0.303668	+	0.525969i	−0.673296	+	0.739373i	$0.735122\pi$
$480$	−1.25880	+	7.33416i	−0.0574563	+	0.334757i
$481$	14.0303	+	8.10037i	0.639725	+	0.369345i
$482$	−5.91105	−	33.3456i	−0.269241	−	1.51885i
$483$		0			0
$484$	6.85645	+	18.7317i	0.311657	+	0.851442i
$485$	−1.72281	−	6.42963i	−0.0782290	−	0.291955i
$486$	−0.0268617	+	0.310285i	−0.00121847	+	0.0140748i
$487$	0.642044	+	1.11205i	0.0290938	+	0.0503919i	0.880206	−	0.474592i	$-0.157405\pi$
$487$	0.642044	+	1.11205i	0.0290938	+	0.0503919i	−0.851112	+	0.524984i	$0.824071\pi$
$488$	12.1414	+	12.0753i	0.549617	+	0.546622i
$489$	−15.8497			−0.716746
$490$		0			0
$491$	7.08341	+	7.08341i	0.319670	+	0.319670i	0.848640	−	0.528970i	$-0.177422\pi$
$491$	7.08341	+	7.08341i	0.319670	+	0.319670i	−0.528970	+	0.848640i	$0.677422\pi$
$492$	14.3472	−	10.0850i	0.646819	−	0.454666i
$493$	−0.754942	−	0.202286i	−0.0340009	−	0.00911051i
$494$	20.7545	+	24.6885i	0.933788	+	1.11079i
$495$	0.0367249	−	0.0636095i	0.00165066	−	0.00285903i
$496$	20.3481	−	17.2008i	0.913657	−	0.772338i
$497$		0			0
$498$	−4.85751	−	27.4023i	−0.217670	−	1.22793i
$499$	5.87786	+	21.9365i	0.263129	+	0.982011i	0.963386	+	0.268120i	$0.0864024\pi$
$499$	5.87786	+	21.9365i	0.263129	+	0.982011i	−0.700256	+	0.713891i	$0.746931\pi$
$500$	−14.2128	+	1.26955i	−0.635615	+	0.0567759i
$501$	−5.35158	−	1.43395i	−0.239091	−	0.0640642i
$502$	5.17673	+	11.0752i	0.231049	+	0.494310i
$503$		−	36.0928i		−	1.60930i	−0.593751	−	0.804649i	$-0.702354\pi$
$503$		−	36.0928i		−	1.60930i	0.593751	−	0.804649i	$-0.297646\pi$
$504$		0			0
$505$		−	1.74582i		−	0.0776880i
$506$	11.8688	−	5.54767i	0.527632	−	0.246624i
$507$	6.32191	+	1.69395i	0.280766	+	0.0752310i
$508$	−16.7617	+	20.0499i	−0.743680	+	0.889568i
$509$	1.40903	+	5.25856i	0.0624540	+	0.233081i	0.990097	−	0.140388i	$-0.0448349\pi$
$509$	1.40903	+	5.25856i	0.0624540	+	0.233081i	−0.927643	+	0.373469i	$0.878168\pi$
$510$	4.83163	−	0.856484i	0.213948	−	0.0379257i
$511$		0			0
$512$	−0.185456	−	22.6267i	−0.00819607	−	0.999966i
$513$	−14.4196	+	24.9755i	−0.636640	+	1.10269i
$514$	−24.6642	+	20.7340i	−1.08789	+	0.914537i
$515$	9.96122	+	2.66910i	0.438944	+	0.117615i
$516$	−18.3774	−	3.20592i	−0.809018	−	0.141133i
$517$	−16.4502	−	16.4502i	−0.723481	−	0.723481i
$518$		0			0
$519$	33.4908			1.47008
$520$	0.0239460	+	8.76480i	0.00105010	+	0.384362i
$521$	−2.57861	−	4.46629i	−0.112971	−	0.195672i	0.803996	−	0.594635i	$-0.202703\pi$
$521$	−2.57861	−	4.46629i	−0.112971	−	0.195672i	−0.916967	+	0.398963i	$0.869370\pi$
$522$	−0.00884730		0.000765920i	−0.000387236		3.35234e-5i
$523$	−1.98945	−	7.42474i	−0.0869928	−	0.324661i	0.908691	−	0.417469i	$-0.137083\pi$
$523$	−1.98945	−	7.42474i	−0.0869928	−	0.324661i	−0.995684	+	0.0928072i	$0.970416\pi$
$524$	−15.5875	−	7.23406i	−0.680945	−	0.316021i
$525$		0			0
$526$	14.7268	−	2.61056i	0.642119	−	0.113826i
$527$	−15.2156	−	8.78475i	−0.662803	−	0.382670i
$528$	−10.7812	+	29.9601i	−0.469190	+	1.30385i
$529$	9.45404	+	16.3749i	0.411045	+	0.711951i
$530$	4.05752	−	11.1796i	0.176247	−	0.485611i
$531$	−0.0811654	−	0.0811654i	−0.00352228	−	0.00352228i
$532$		0			0
$533$	14.6059	−	14.6059i	0.632653	−	0.632653i
$534$	17.4825	−	8.17163i	0.756544	−	0.353621i
$535$	−3.09662	+	1.78784i	−0.133879	+	0.0772949i
$536$	26.1156	−	7.07418i	1.12802	−	0.305558i
$537$	6.32595	−	10.9569i	0.272985	−	0.472824i
$538$	8.39163	−	12.0077i	0.361789	−	0.517691i
$539$		0			0
$540$	−7.35952	+	2.69384i	−0.316704	+	0.115924i
$541$	7.55039	−	2.02312i	0.324617	−	0.0869808i	−0.0928305	−	0.995682i	$-0.529591\pi$
$541$	7.55039	−	2.02312i	0.324617	−	0.0869808i	0.417447	+	0.908701i	$0.362925\pi$
$542$	−22.4453	−	26.6999i	−0.964109	−	1.14686i
$543$	11.9131	−	6.87805i	0.511241	−	0.295165i
$544$	−13.9976	+	5.16700i	−0.600141	+	0.221533i
$545$		−	6.23624i		−	0.267131i
$546$		0			0
$547$	3.45431	−	3.45431i	0.147696	−	0.147696i	−0.629392	−	0.777088i	$-0.716696\pi$
$547$	3.45431	−	3.45431i	0.147696	−	0.147696i	0.777088	+	0.629392i	$0.216696\pi$
$548$	−45.4867	−	7.93514i	−1.94310	−	0.338972i
$549$	0.0332060	−	0.123927i	0.00141720	−	0.00528906i
$550$	−28.5668	−	2.47306i	−1.21809	−	0.105452i
$551$	−1.42934	−	0.825229i	−0.0608918	−	0.0351559i
$552$	9.61298	+	2.54766i	0.409156	+	0.108436i
$553$		0			0
$554$	8.68956	−	12.4341i	0.369184	−	0.528273i
$555$	5.02749	−	1.34711i	0.213405	−	0.0571817i
$556$	17.1672	−	1.53345i	0.728052	−	0.0650327i
$557$	−7.47554	+	27.8991i	−0.316749	+	1.18212i	0.605602	+	0.795768i	$0.292933\pi$
$557$	−7.47554	+	27.8991i	−0.316749	+	1.18212i	−0.922350	+	0.386354i	$0.873734\pi$
$558$	−0.187651	−	0.0681059i	−0.00794390	−	0.00288315i
$559$	−21.9726			−0.929342
$560$		0			0
$561$	20.9963			0.886463
$562$	8.59297	+	3.11873i	0.362473	+	0.131556i
$563$	−0.243342	+	0.908166i	−0.0102557	+	0.0382746i	−0.970864	−	0.239631i	$-0.922974\pi$
$563$	−0.243342	+	0.908166i	−0.0102557	+	0.0382746i	0.960608	+	0.277906i	$0.0896402\pi$
$564$	−1.57114	−	17.5891i	−0.0661568	−	0.740636i
$565$	−13.5132	+	3.62084i	−0.568503	+	0.152330i
$566$	15.9624	−	22.8409i	0.670948	−	0.960073i
$567$		0			0
$568$	−17.7431	+	10.3087i	−0.744485	+	0.432545i
$569$	−11.5141	−	6.64769i	−0.482698	−	0.278686i	0.238842	−	0.971058i	$-0.423232\pi$
$569$	−11.5141	−	6.64769i	−0.482698	−	0.278686i	−0.721540	+	0.692373i	$0.756565\pi$
$570$	10.3235	+	0.893712i	0.432402	+	0.0374335i
$571$	2.11813	−	7.90497i	0.0886410	−	0.330813i	−0.907338	−	0.420402i	$-0.861889\pi$
$571$	2.11813	−	7.90497i	0.0886410	−	0.330813i	0.995979	+	0.0895898i	$0.0285556\pi$
$572$	−6.44516	+	36.9457i	−0.269486	+	1.54478i
$573$	−5.85753	+	5.85753i	−0.244702	+	0.244702i
$574$		0			0
$575$			8.95562i			0.373475i
$576$	−0.146354	+	0.0855674i	−0.00609810	+	0.00356531i
$577$	−23.0378	+	13.3009i	−0.959077	+	0.553724i	−0.895889	−	0.444278i	$-0.853460\pi$
$577$	−23.0378	+	13.3009i	−0.959077	+	0.553724i	−0.0631883	+	0.998002i	$0.520127\pi$
$578$	−9.13922	−	10.8716i	−0.380141	−	0.452198i
$579$	−8.96716	+	2.40274i	−0.372662	+	0.0998546i
$580$	−0.154168	−	0.421183i	−0.00640146	−	0.0174887i
$581$		0			0
$582$	12.3846	−	17.7213i	0.513358	−	0.734573i
$583$	25.4447	−	44.0715i	1.05381	−	1.82525i
$584$	−16.1740	−	9.27926i	−0.669287	−	0.383979i
$585$	0.0568713	−	0.0328347i	0.00235134	−	0.00135755i
$586$	5.37021	−	2.51013i	0.221841	−	0.103692i
$587$	9.30074	−	9.30074i	0.383883	−	0.383883i	−0.488616	−	0.872499i	$-0.662498\pi$
$587$	9.30074	−	9.30074i	0.383883	−	0.383883i	0.872499	+	0.488616i	$0.162498\pi$
$588$		0			0
$589$	−26.2349	−	26.2349i	−1.08099	−	1.08099i
$590$	1.97784	−	5.44951i	0.0814264	−	0.224353i
$591$	−14.3498	−	24.8546i	−0.590272	−	1.02238i
$592$	−14.3193	+	6.74082i	−0.588520	+	0.277046i
$593$	−12.2162	−	7.05302i	−0.501659	−	0.289633i	0.227739	−	0.973722i	$-0.426867\pi$
$593$	−12.2162	−	7.05302i	−0.501659	−	0.289633i	−0.729398	+	0.684089i	$0.760200\pi$
$594$	−33.0190	+	5.85316i	−1.35479	+	0.240158i
$595$		0			0
$596$	−10.1714	+	21.9168i	−0.416638	+	0.897748i
$597$	4.69033	+	17.5046i	0.191963	+	0.716414i
$598$	11.6698	+	1.01027i	0.477215	+	0.0413131i
$599$	−14.7397	−	25.5299i	−0.602247	−	1.04312i	−0.992480	−	0.122406i	$-0.960939\pi$
$599$	−14.7397	−	25.5299i	−0.602247	−	1.04312i	0.390233	−	0.920716i	$-0.372394\pi$
$600$	−15.4324	−	15.3483i	−0.630026	−	0.626593i
$601$	23.6858			0.966164			0.483082	−	0.875575i	$-0.339517\pi$
$601$	23.6858			0.966164			0.483082	+	0.875575i	$0.339517\pi$
$602$		0			0
$603$	−0.143344	−	0.143344i	−0.00583742	−	0.00583742i
$604$	−0.559339	+	3.20631i	−0.0227592	+	0.130463i
$605$	7.29097	+	1.95361i	0.296420	+	0.0794255i
$606$	4.34045	−	3.64881i	0.176319	−	0.148223i
$607$	2.86300	−	4.95886i	0.116206	−	0.201274i	−0.802055	−	0.597250i	$-0.796260\pi$
$607$	2.86300	−	4.95886i	0.116206	−	0.201274i	0.918261	+	0.395976i	$0.129593\pi$
$608$	−31.3757	+	2.88903i	−1.27245	+	0.117166i
$609$		0			0
$610$	6.38034	−	1.13102i	0.258333	−	0.0457936i
$611$	−5.38338	−	20.0910i	−0.217788	−	0.812796i
$612$	0.0857684	+	0.0717024i	0.00346698	+	0.00289840i
$613$	2.17496	+	0.582780i	0.0878459	+	0.0235383i	0.302474	−	0.953158i	$-0.402187\pi$
$613$	2.17496	+	0.582780i	0.0878459	+	0.0235383i	−0.214628	+	0.976696i	$0.568854\pi$
$614$	15.5996	−	7.29153i	0.629550	−	0.294262i
$615$		−	6.63616i		−	0.267596i
$616$		0			0
$617$			12.2572i			0.493457i	0.969085	+	0.246729i	$0.0793556\pi$
$617$			12.2572i			0.493457i	−0.969085	+	0.246729i	$0.920644\pi$
$618$	14.1833	+	30.3440i	0.570536	+	1.22062i
$619$	7.21445	+	1.93311i	0.289973	+	0.0776981i	0.400873	−	0.916133i	$-0.368707\pi$
$619$	7.21445	+	1.93311i	0.289973	+	0.0776981i	−0.110900	+	0.993832i	$0.535373\pi$
$620$	−0.897031	−	10.0424i	−0.0360256	−	0.403313i
$621$	2.71077	+	10.1167i	0.108779	+	0.405970i
$622$	−1.42229	−	8.02350i	−0.0570288	−	0.321713i
$623$		0			0
$624$	−21.7409	+	18.3782i	−0.870334	+	0.735716i
$625$	8.36824	−	14.4942i	0.334730	−	0.579769i
$626$	7.30966	+	8.69521i	0.292153	+	0.347531i
$627$	42.8272	+	11.4755i	1.71036	+	0.458288i
$628$	−27.6661	−	39.3584i	−1.10400	−	1.57057i
$629$	7.37954	+	7.37954i	0.294241	+	0.294241i
$630$		0			0
$631$	−10.1046			−0.402257			−0.201129	−	0.979565i	$-0.564461\pi$
$631$	−10.1046			−0.402257			−0.201129	+	0.979565i	$0.564461\pi$
$632$	−42.6586	+	0.116546i	−1.69687	+	0.00463595i
$633$	−0.880639	−	1.52531i	−0.0350022	−	0.0606257i
$634$	−1.13799	+	13.1452i	−0.0451954	+	0.522061i
$635$	2.55948	+	9.55211i	0.101570	+	0.379064i
$636$	36.2750	−	13.2779i	1.43840	−	0.526502i
$637$		0			0
$638$	−0.334974	−	1.88967i	−0.0132618	−	0.0748127i
$639$	0.133148	+	0.0768733i	0.00526727	+	0.00304106i
$640$	−7.04508	−	4.86638i	−0.278481	−	0.192361i
$641$	11.1392	+	19.2937i	0.439973	+	0.762056i	0.997687	−	0.0679772i	$-0.0216545\pi$
$641$	11.1392	+	19.2937i	0.439973	+	0.762056i	−0.557713	+	0.830034i	$0.688321\pi$
$642$	−10.9169	−	3.96218i	−0.430856	−	0.156375i
$643$	−2.94059	−	2.94059i	−0.115965	−	0.115965i	0.646743	−	0.762708i	$-0.276131\pi$
$643$	−2.94059	−	2.94059i	−0.115965	−	0.115965i	−0.762708	+	0.646743i	$0.776131\pi$
$644$		0			0
$645$	−4.99159	+	4.99159i	−0.196544	+	0.196544i
$646$	8.79788	+	18.8223i	0.346148	+	0.740555i
$647$	13.6596	−	7.88639i	0.537015	−	0.310046i	−0.206853	−	0.978372i	$-0.566322\pi$
$647$	13.6596	−	7.88639i	0.537015	−	0.310046i	0.743869	+	0.668326i	$0.232989\pi$
$648$	−22.2350	−	12.7565i	−0.873472	−	0.501122i
$649$	12.4030	−	21.4827i	0.486862	−	0.843269i
$650$	−21.0134	−	14.6852i	−0.824212	−	0.576001i
$651$		0			0
$652$	7.67730	−	16.5426i	0.300666	−	0.647859i
$653$	−11.8827	+	3.18397i	−0.465007	+	0.124598i	−0.483713	−	0.875227i	$-0.660712\pi$
$653$	−11.8827	+	3.18397i	−0.465007	+	0.124598i	0.0187058	+	0.999825i	$0.494045\pi$
$654$	15.5045	−	13.0339i	0.606274	−	0.509666i
$655$	−5.63152	+	3.25136i	−0.220042	+	0.127041i
$656$	3.57639	+	19.8594i	0.139635	+	0.775380i
$657$			0.139709i			0.00545056i
$658$		0			0
$659$	22.1996	−	22.1996i	0.864775	−	0.864775i	−0.127114	−	0.991888i	$-0.540571\pi$
$659$	22.1996	−	22.1996i	0.864775	−	0.864775i	0.991888	+	0.127114i	$0.0405713\pi$
$660$	6.92891	+	9.85725i	0.269708	+	0.383693i
$661$	0.253956	−	0.947777i	0.00987774	−	0.0368642i	−0.960811	−	0.277204i	$-0.910592\pi$
$661$	0.253956	−	0.947777i	0.00987774	−	0.0368642i	0.970689	+	0.240340i	$0.0772589\pi$
$662$	−0.626390	+	7.23556i	−0.0243453	+	0.281218i
$663$	16.2571	+	9.38606i	0.631375	+	0.364524i
$664$	30.9533	+	8.20334i	1.20122	+	0.318351i
$665$		0			0
$666$	0.0971959	+	0.0679254i	0.00376626	+	0.00263206i
$667$	−0.578976	+	0.155136i	−0.0224181	+	0.00600690i
$668$	4.08886	−	4.89098i	0.158203	−	0.189238i
$669$	5.81146	−	21.6887i	0.224684	−	0.838532i
$670$	3.49301	−	9.62424i	0.134947	−	0.371817i
$671$	27.7264			1.07036
$672$		0			0
$673$	−28.5560			−1.10075			−0.550376	−	0.834917i	$-0.685516\pi$
$673$	−28.5560			−1.10075			−0.550376	+	0.834917i	$0.685516\pi$
$674$	−0.725871	+	1.99998i	−0.0279595	+	0.0770363i
$675$	5.93280	−	22.1415i	0.228354	−	0.852227i
$676$	−4.83024	+	5.77779i	−0.185778	+	0.222223i
$677$	−7.13755	+	1.91250i	−0.274318	+	0.0735033i	−0.393356	−	0.919386i	$-0.628686\pi$
$677$	−7.13755	+	1.91250i	−0.274318	+	0.0735033i	0.119037	+	0.992890i	$0.462019\pi$
$678$	−37.2450	−	26.0287i	−1.43039	−	0.999627i
$679$		0			0
$680$	−1.44643	+	5.45774i	−0.0554679	+	0.209295i
$681$	−23.4134	−	13.5177i	−0.897203	−	0.518001i
$682$	3.72088	−	42.9806i	0.142480	−	1.64581i
$683$	0.510463	−	1.90507i	0.0195323	−	0.0728956i	−0.955472	−	0.295083i	$-0.904653\pi$
$683$	0.510463	−	1.90507i	0.0195323	−	0.0728956i	0.975004	+	0.222187i	$0.0713195\pi$
$684$	0.135758	+	0.193132i	0.00519082	+	0.00738459i
$685$	−12.3549	+	12.3549i	−0.472058	+	0.472058i
$686$		0			0
$687$			24.0695i			0.918310i
$688$	12.2478	−	17.6280i	0.466942	−	0.672059i
$689$	39.4030	−	22.7493i	1.50113	−	0.866680i
$690$	2.88059	−	2.42157i	0.109662	−	0.0921877i
$691$	0.216289	−	0.0579544i	0.00822801	−	0.00220469i	−0.254703	−	0.967019i	$-0.581978\pi$
$691$	0.216289	−	0.0579544i	0.00822801	−	0.00220469i	0.262931	+	0.964815i	$0.415311\pi$
$692$	−16.2224	+	34.9551i	−0.616682	+	1.32879i
$693$		0			0
$694$	10.0690	+	7.03671i	0.382213	+	0.267110i
$695$	3.26104	−	5.64829i	0.123698	−	0.214252i
$696$	0.724929	−	1.26357i	0.0274784	−	0.0478957i
$697$	11.5235	−	6.65309i	0.436484	−	0.252004i
$698$	−13.2688	−	28.3874i	−0.502230	−	1.07448i
$699$	15.1177	−	15.1177i	0.571804	−	0.571804i
$700$		0			0
$701$	18.2761	+	18.2761i	0.690279	+	0.690279i	0.962293	−	0.272014i	$-0.0876898\pi$
$701$	18.2761	+	18.2761i	0.690279	+	0.690279i	−0.272014	+	0.962293i	$0.587690\pi$
$702$	−28.1828	−	10.2286i	−1.06369	−	0.386055i
$703$	11.0192	+	19.0858i	0.415596	+	0.719833i
$704$	−26.0478	−	25.7647i	−0.981714	−	0.971044i
$705$	−5.78711	−	3.34119i	−0.217955	−	0.125837i
$706$	−6.14066	−	34.6409i	−0.231107	−	1.30373i
$707$		0			0
$708$	17.6823	−	6.47232i	0.664541	−	0.243245i
$709$	0.446105	+	1.66489i	0.0167538	+	0.0625261i	0.973797	−	0.227420i	$-0.0730292\pi$
$709$	0.446105	+	1.66489i	0.0167538	+	0.0625261i	−0.957043	+	0.289946i	$0.906362\pi$
$710$	−0.669729	+	7.73617i	−0.0251345	+	0.290333i
$711$	0.159808	+	0.276795i	0.00599325	+	0.0103806i
$712$	0.0606657	+	22.2051i	0.00227354	+	0.832171i
$713$	−13.4743			−0.504617
$714$		0			0
$715$	10.0351	+	10.0351i	0.375290	+	0.375290i
$716$	8.37174	+	11.9099i	0.312867	+	0.445092i
$717$	−12.0920	−	3.24003i	−0.451582	−	0.121001i
$718$	−7.87834	−	9.37169i	−0.294017	−	0.349748i
$719$	−25.5064	+	44.1784i	−0.951229	+	1.64758i	−0.208457	+	0.978031i	$0.566844\pi$
$719$	−25.5064	+	44.1784i	−0.951229	+	1.64758i	−0.742771	+	0.669545i	$0.766489\pi$
$720$	−0.00535844	+	0.0639285i	−0.000199697	+	0.00238248i
$721$		0			0
$722$	2.96813	+	16.7439i	0.110462	+	0.623144i
$723$	−10.7728	−	40.2045i	−0.400644	−	1.49522i
$724$	1.40825	+	15.7656i	0.0523372	+	0.585924i
$725$	1.26715	+	0.339532i	0.0470609	+	0.0126099i
$726$	10.3813	+	22.2099i	0.385285	+	0.824285i
$727$			31.5017i			1.16833i	0.811634	+	0.584166i	$0.198578\pi$
$727$			31.5017i			1.16833i	−0.811634	+	0.584166i	$0.801422\pi$
$728$		0			0
$729$		−	26.8066i		−	0.992837i
$730$	−6.39230	+	2.98787i	−0.236590	+	0.110586i
$731$	−13.6721	−	3.66342i	−0.505680	−	0.135496i
$732$	16.1470	+	13.4989i	0.596811	+	0.498934i
$733$	−10.8083	−	40.3371i	−0.399213	−	1.48988i	−0.814484	−	0.580186i	$-0.802980\pi$
$733$	−10.8083	−	40.3371i	−0.399213	−	1.48988i	0.415271	−	0.909698i	$-0.363687\pi$
$734$	−33.3284	+	5.90799i	−1.23017	+	0.218068i
$735$		0			0
$736$	−7.31541	+	8.79923i	−0.269650	+	0.324344i
$737$	21.9047	−	37.9400i	0.806869	−	1.39754i
$738$	0.115728	−	0.0972869i	0.00426000	−	0.00358118i
$739$	−17.3991	−	4.66207i	−0.640036	−	0.171497i	−0.0758162	−	0.997122i	$-0.524156\pi$
$739$	−17.3991	−	4.66207i	−0.640036	−	0.171497i	−0.564220	+	0.825625i	$0.690823\pi$
$740$	−1.02922	+	5.89982i	−0.0378349	+	0.216882i
$741$	28.0306	+	28.0306i	1.02973	+	1.02973i
$742$		0			0
$743$	−23.0128			−0.844256			−0.422128	−	0.906536i	$-0.638717\pi$
$743$	−23.0128			−0.844256			−0.422128	+	0.906536i	$0.638717\pi$
$744$	23.0925	−	23.2191i	0.846614	−	0.851253i
$745$	4.57156	+	7.91818i	0.167489	+	0.290100i
$746$	−3.33394	−	0.288623i	−0.122064	−	0.0105672i
$747$	−0.0620958	−	0.231745i	−0.00227197	−	0.00847910i
$748$	−10.1702	+	21.9142i	−0.371860	+	0.801264i
$749$		0			0
$750$	−17.2687	+	3.06116i	−0.630565	+	0.111778i
$751$	0.399765	+	0.230804i	0.0145876	+	0.00842217i	0.507276	−	0.861784i	$-0.330652\pi$
$751$	0.399765	+	0.230804i	0.0145876	+	0.00842217i	−0.492688	+	0.870206i	$0.663986\pi$
$752$	19.1192	+	6.88005i	0.697205	+	0.250889i
$753$	7.51284	+	13.0126i	0.273783	+	0.474206i
$754$	0.585382	−	1.61289i	0.0213183	−	0.0587380i
$755$	0.870885	+	0.870885i	0.0316947	+	0.0316947i
$756$		0			0
$757$	−5.23204	+	5.23204i	−0.190162	+	0.190162i	−0.795766	−	0.605604i	$-0.792931\pi$
$757$	−5.23204	+	5.23204i	−0.190162	+	0.190162i	0.605604	+	0.795766i	$0.292931\pi$
$758$	9.68647	−	4.52762i	0.351828	−	0.164450i
$759$	13.9450	−	8.05117i	0.506173	−	0.292239i
$760$	−5.93329	+	10.3419i	−0.215223	+	0.375140i
$761$	−10.6052	+	18.3687i	−0.384437	+	0.665864i	−0.991691	−	0.128644i	$-0.958938\pi$
$761$	−10.6052	+	18.3687i	−0.384437	+	0.665864i	0.607254	+	0.794508i	$0.292271\pi$
$762$	−18.3990	+	26.3275i	−0.666526	+	0.953746i
$763$		0			0
$764$	−3.27634	−	8.95091i	−0.118534	−	0.323833i
$765$	0.0408616	−	0.0109488i	0.00147735	−	0.000395856i
$766$	22.8780	+	27.2146i	0.826616	+	0.983302i
$767$	19.2070	−	11.0892i	0.693525	−	0.400407i
$768$	−2.62562	−	27.6863i	−0.0947440	−	0.999043i
$769$		−	10.8533i		−	0.391379i	−0.980666	−	0.195689i	$-0.937306\pi$
$769$		−	10.8533i		−	0.391379i	0.980666	−	0.195689i	$-0.0626944\pi$
$770$		0			0
$771$	−28.0029	+	28.0029i	−1.00850	+	1.00850i
$772$	1.83574	−	10.5231i	0.0660699	−	0.378733i
$773$	12.5926	−	46.9962i	0.452924	−	1.69034i	−0.241196	−	0.970476i	$-0.577540\pi$
$773$	12.5926	−	46.9962i	0.452924	−	1.69034i	0.694120	−	0.719859i	$-0.255794\pi$
$774$	−0.160225	−	0.0138709i	−0.00575919	−	0.000498579i
$775$	25.5391	+	14.7450i	0.917390	+	0.529656i
$776$	12.4973	+	21.5100i	0.448626	+	0.772163i
$777$		0			0
$778$	5.09927	−	7.29665i	0.182818	−	0.261597i
$779$	27.1414	−	7.27251i	0.972441	−	0.260565i
$780$	0.958432	+	10.7298i	0.0343174	+	0.384189i
$781$	−8.59952	+	32.0938i	−0.307715	+	1.14841i
$782$	7.09292	+	2.57430i	0.253642	+	0.0920568i
$783$	1.53421			0.0548282
$784$		0			0
$785$	−18.2049			−0.649762
$786$	−19.8535	−	7.20563i	−0.708152	−	0.257016i
$787$	3.47299	−	12.9614i	0.123799	−	0.462023i	−0.875995	−	0.482319i	$-0.839794\pi$
$787$	3.47299	−	12.9614i	0.123799	−	0.462023i	0.999794	+	0.0202968i	$0.00646112\pi$
$788$	32.8921	−	2.93806i	1.17173	−	0.104664i
$789$	17.7560	−	4.75770i	0.632130	−	0.169379i
$790$	−9.24688	+	13.2315i	−0.328989	+	0.470757i
$791$		0			0
$792$	−0.0703216	+	0.265341i	−0.00249877	+	0.00942850i
$793$	21.4682	+	12.3946i	0.762356	+	0.440147i
$794$	25.4412	+	2.20247i	0.902874	+	0.0781628i
$795$	3.78327	−	14.1194i	0.134179	−	0.500762i
$796$	−20.5418	−	3.58351i	−0.728085	−	0.127014i
$797$	6.22856	−	6.22856i	0.220627	−	0.220627i	−0.588135	−	0.808762i	$-0.700138\pi$
$797$	6.22856	−	6.22856i	0.220627	−	0.220627i	0.808762	+	0.588135i	$0.200138\pi$
$798$		0			0
$799$		−	13.3989i		−	0.474017i
$800$	23.4946	−	8.67269i	0.830659	−	0.306626i
$801$	0.144080	−	0.0831847i	0.00509082	−	0.00293919i
$802$	−14.3571	−	17.0786i	−0.506968	−	0.603065i
$803$	−29.1635	+	7.81434i	−1.02916	+	0.275762i
$804$	31.2282	−	11.4306i	1.10133	−	0.403126i
$805$		0			0
$806$	22.0948	−	31.6159i	0.778258	−	1.11362i
$807$	9.00253	−	15.5928i	0.316904	−	0.548894i
$808$	1.70590	+	6.29764i	0.0600134	+	0.221550i
$809$	1.49336	−	0.862190i	0.0525036	−	0.0303130i	−0.473518	−	0.880784i	$-0.657016\pi$
$809$	1.49336	−	0.862190i	0.0525036	−	0.0303130i	0.526022	+	0.850471i	$0.323683\pi$
$810$	−8.78770	+	4.10752i	−0.308768	+	0.144323i
$811$	29.5809	−	29.5809i	1.03872	−	1.03872i	0.0395050	−	0.999219i	$-0.487422\pi$
$811$	29.5809	−	29.5809i	1.03872	−	1.03872i	0.999219	−	0.0395050i	$-0.0125781\pi$
$812$		0			0
$813$	−30.3142	−	30.3142i	−1.06317	−	1.06317i
$814$	−8.74263	+	24.0884i	−0.306429	+	0.844299i
$815$	−3.45058	−	5.97657i	−0.120868	−	0.209350i
$816$	−16.5921	+	7.81071i	−0.580838	+	0.273430i
$817$	−25.8854	−	14.9450i	−0.905617	−	0.522858i
$818$	41.7335	−	7.39793i	1.45918	−	0.258663i
$819$		0			0
$820$	6.92631	+	3.21444i	0.241877	+	0.112253i
$821$	−9.77105	−	36.4661i	−0.341012	−	1.27267i	−0.897202	−	0.441620i	$-0.854404\pi$
$821$	−9.77105	−	36.4661i	−0.341012	−	1.27267i	0.556190	−	0.831055i	$-0.312263\pi$
$822$	−56.5389	−	4.89463i	−1.97202	−	0.170720i
$823$	18.3778	+	31.8313i	0.640609	+	1.10957i	0.985297	+	0.170850i	$0.0546515\pi$
$823$	18.3778	+	31.8313i	0.640609	+	1.10957i	−0.344688	+	0.938717i	$0.612015\pi$
$824$	−38.5408	+	0.105296i	−1.34263	+	0.00366816i
$825$	−35.2417			−1.22696
$826$		0			0
$827$	25.1791	+	25.1791i	0.875565	+	0.875565i	0.993072	−	0.117507i	$-0.0374904\pi$
$827$	25.1791	+	25.1791i	0.875565	+	0.875565i	−0.117507	+	0.993072i	$0.537490\pi$
$828$	0.0844594	+	0.0147339i	0.00293517	+	0.000512039i
$829$	−22.7086	−	6.08475i	−0.788702	−	0.211332i	−0.158084	−	0.987426i	$-0.550532\pi$
$829$	−22.7086	−	6.08475i	−0.788702	−	0.211332i	−0.630618	+	0.776094i	$0.717198\pi$
$830$	9.27534	−	7.79734i	0.321952	−	0.270650i
$831$	9.32215	−	16.1464i	0.323382	−	0.560114i
$832$	−8.65076	−	31.5935i	−0.299911	−	1.09531i
$833$		0			0
$834$	20.8584	−	3.69749i	0.722267	−	0.128034i
$835$	−0.624362	−	2.33015i	−0.0216069	−	0.0806382i
$836$	−32.7220	+	39.1412i	−1.13172	+	1.35373i
$837$	33.3133	+	8.92628i	1.15148	+	0.308537i
$838$	−34.5484	+	16.1485i	−1.19346	+	0.557841i
$839$		−	13.7267i		−	0.473899i	−0.971522	−	0.236949i	$-0.923852\pi$
$839$		−	13.7267i		−	0.473899i	0.971522	−	0.236949i	$-0.0761475\pi$
$840$		0			0
$841$		−	28.9122i		−	0.996972i
$842$	0.949493	+	2.03136i	0.0327217	+	0.0700054i
$843$	10.8525	+	2.90793i	0.373782	+	0.100154i
$844$	2.01857	−	0.180307i	0.0694819	−	0.00620642i
$845$	0.737569	+	2.75264i	0.0253731	+	0.0946938i
$846$	−0.0265728	−	0.149903i	−0.000913592	−	0.00515379i
$847$		0			0
$848$	−3.71257	+	44.2925i	−0.127490	+	1.52101i
$849$	17.1244	−	29.6603i	0.587708	−	1.01794i
$850$	−10.6268	−	12.6411i	−0.364496	−	0.433587i
$851$	7.73099	+	2.07151i	0.265015	+	0.0710106i
$852$	−20.6334	+	14.5037i	−0.706888	+	0.496889i
$853$	2.88131	+	2.88131i	0.0986542	+	0.0986542i	0.754711	−	0.656057i	$-0.227777\pi$
$853$	2.88131	+	2.88131i	0.0986542	+	0.0986542i	−0.656057	+	0.754711i	$0.727777\pi$
$854$		0			0
$855$	0.0893318			0.00305508
$856$	9.42338	−	9.47501i	0.322084	−	0.323849i
$857$	−7.75242	−	13.4276i	−0.264817	−	0.458677i	0.702698	−	0.711488i	$-0.251978\pi$
$857$	−7.75242	−	13.4276i	−0.264817	−	0.458677i	−0.967516	+	0.252811i	$0.918645\pi$
$858$	−3.97557	+	45.9226i	−0.135724	+	1.56777i
$859$	−6.34616	−	23.6842i	−0.216528	−	0.808094i	−0.985623	−	0.168960i	$-0.945959\pi$
$859$	−6.34616	−	23.6842i	−0.216528	−	0.808094i	0.769095	−	0.639135i	$-0.220707\pi$
$860$	−2.79199	−	7.62767i	−0.0952060	−	0.260101i
$861$		0			0
$862$	4.05835	+	22.8941i	0.138228	+	0.779776i
$863$	40.7734	+	23.5405i	1.38794	+	0.801329i	0.993083	−	0.117412i	$-0.0374598\pi$
$863$	40.7734	+	23.5405i	1.38794	+	0.801329i	0.394860	+	0.918741i	$0.370793\pi$
$864$	23.9155	−	16.9086i	0.813622	−	0.575243i
$865$	7.29118	+	12.6287i	0.247907	+	0.429388i
$866$	−45.6915	−	16.5832i	−1.55266	−	0.563521i
$867$	−12.3433	−	12.3433i	−0.419199	−	0.419199i
$868$		0			0
$869$	−48.8410	+	48.8410i	−1.65682	+	1.65682i
$870$	−0.233423	−	0.499389i	−0.00791378	−	0.0169309i
$871$	33.9210	−	19.5843i	1.14937	−	0.663589i
$872$	6.09364	+	22.4958i	0.206357	+	0.761803i
$873$	0.0931935	−	0.161416i	0.00315412	−	0.00546310i
$874$	13.0608	+	9.12759i	0.441790	+	0.308745i
$875$		0			0
$876$	−20.7885	−	9.64778i	−0.702378	−	0.325968i
$877$	−19.5661	+	5.24273i	−0.660701	+	0.177034i	−0.573563	−	0.819162i	$-0.694439\pi$
$877$	−19.5661	+	5.24273i	−0.660701	+	0.177034i	−0.0871389	+	0.996196i	$0.527772\pi$
$878$	10.4661	−	8.79840i	0.353215	−	0.296931i
$879$	6.30964	−	3.64287i	0.212819	−	0.122871i
$880$	−13.6445	+	2.45717i	−0.459955	+	0.0828312i
$881$			29.7191i			1.00126i	0.865660	+	0.500632i	$0.166899\pi$
$881$			29.7191i			1.00126i	−0.865660	+	0.500632i	$0.833101\pi$
$882$		0			0
$883$	−10.1351	+	10.1351i	−0.341074	+	0.341074i	−0.856771	−	0.515697i	$-0.827533\pi$
$883$	−10.1351	+	10.1351i	−0.341074	+	0.341074i	0.515697	+	0.856771i	$0.327533\pi$
$884$	−17.6711	+	12.4215i	−0.594343	+	0.417779i
$885$	1.84416	−	6.88249i	0.0619907	−	0.231352i
$886$	4.24256	−	49.0067i	0.142532	−	1.64641i
$887$	29.8863	+	17.2549i	1.00348	+	0.579362i	0.909277	−	0.416191i	$-0.136635\pi$
$887$	29.8863	+	17.2549i	1.00348	+	0.579362i	0.0942069	+	0.995553i	$0.469968\pi$
$888$	−16.8192	+	9.77193i	−0.564415	+	0.327925i
$889$		0			0
$890$	6.88742	+	4.81328i	0.230867	+	0.161342i
$891$	−40.0920	+	10.7426i	−1.34313	+	0.359891i
$892$	19.8219	+	16.5712i	0.663688	+	0.554843i
$893$	7.32316	−	27.3304i	0.245060	−	0.914577i
$894$	−10.1314	+	27.9150i	−0.338846	+	0.933617i
$895$	5.50881			0.184139
$896$		0			0
$897$	14.3966			0.480689
$898$	17.1315	−	47.2020i	0.571685	−	1.57515i
$899$	−0.510848	+	1.90651i	−0.0170377	+	0.0635857i
$900$	−0.143960	−	0.120351i	−0.00479867	−	0.00401169i
$901$	28.3107	−	7.58584i	0.943168	−	0.252721i
$902$	26.7812	+	18.7160i	0.891715	+	0.623176i
$903$		0			0
$904$	45.2076	−	26.2655i	1.50358	−	0.873579i
$905$	5.18714	+	2.99479i	0.172426	+	0.0995503i
$906$	−0.345017	+	3.98536i	−0.0114624	+	0.132405i
$907$	2.16076	−	8.06405i	0.0717467	−	0.267762i	−0.920729	−	0.390202i	$-0.872405\pi$
$907$	2.16076	−	8.06405i	0.0717467	−	0.267762i	0.992476	+	0.122440i	$0.0390718\pi$
$908$	25.4498	−	17.8893i	0.844581	−	0.593677i
$909$	0.0345667	−	0.0345667i	0.00114650	−	0.00114650i
$910$		0			0
$911$			8.93090i			0.295894i	0.988995	+	0.147947i	$0.0472665\pi$
$911$			8.93090i			0.295894i	−0.988995	+	0.147947i	$0.952734\pi$
$912$	−38.1127	+	6.86354i	−1.26204	+	0.227275i
$913$	44.9023	−	25.9244i	1.48605	−	0.857972i
$914$	−32.6072	+	27.4113i	−1.07855	+	0.906686i
$915$	7.69273	−	2.06126i	0.254314	−	0.0681432i
$916$	−25.1219	−	11.6589i	−0.830050	−	0.385220i
$917$		0			0
$918$	−15.8309	−	11.0634i	−0.522496	−	0.365147i
$919$	−26.6631	+	46.1818i	−0.879533	+	1.52340i	−0.0276794	+	0.999617i	$0.508812\pi$
$919$	−26.6631	+	46.1818i	−0.879533	+	1.52340i	−0.851854	+	0.523779i	$0.824522\pi$
$920$	1.13214	+	4.17950i	0.0373256	+	0.137794i
$921$	18.3286	−	10.5820i	0.603946	−	0.348689i
$922$	−2.01513	−	4.31121i	−0.0663648	−	0.141982i
$923$	−21.0055	+	21.0055i	−0.691406	+	0.691406i
$924$		0			0
$925$	−12.3864	−	12.3864i	−0.407262	−	0.407262i
$926$	−1.63943	−	0.595013i	−0.0538750	−	0.0195533i
$927$	0.144382	+	0.250076i	0.00474211	+	0.00821358i
$928$	0.967676	+	1.36868i	0.0317655	+	0.0449291i
$929$	−33.5814	−	19.3882i	−1.10177	−	0.636107i	−0.165084	−	0.986280i	$-0.552789\pi$
$929$	−33.5814	−	19.3882i	−1.10177	−	0.636107i	−0.936685	+	0.350173i	$0.886123\pi$
$930$	−2.16294	−	12.2017i	−0.0709257	−	0.400108i
$931$		0			0
$932$	8.45592	+	23.1014i	0.276983	+	0.756713i
$933$	−2.59210	−	9.67386i	−0.0848617	−	0.316708i
$934$	−3.88920	+	44.9249i	−0.127258	+	1.46999i
$935$	4.57103	+	7.91725i	0.149489	+	0.258922i
$936$	−0.173066	+	0.174014i	−0.00565684	+	0.00568783i
$937$	−14.3493			−0.468771			−0.234385	−	0.972144i	$-0.575308\pi$
$937$	−14.3493			−0.468771			−0.234385	+	0.972144i	$0.575308\pi$
$938$		0			0
$939$	9.87228	+	9.87228i	0.322170	+	0.322170i
$940$	6.29045	−	4.42172i	0.205172	−	0.144220i
$941$	−31.7588	−	8.50975i	−1.03531	−	0.277410i	−0.299141	−	0.954209i	$-0.596700\pi$
$941$	−31.7588	−	8.50975i	−1.03531	−	0.277410i	−0.736168	+	0.676799i	$0.763367\pi$
$942$	−38.0488	−	45.2610i	−1.23970	−	1.47468i
$943$	5.10236	−	8.83754i	0.166156	−	0.287790i
$944$	−1.80969	+	21.5904i	−0.0589005	+	0.702709i
$945$		0			0
$946$	−6.06642	−	34.2221i	−0.197236	−	1.11266i
$947$	13.0783	+	48.8089i	0.424988	+	1.58608i	0.763950	+	0.645276i	$0.223258\pi$
$947$	13.0783	+	48.8089i	0.424988	+	1.58608i	−0.338962	+	0.940800i	$0.610076\pi$
$948$	−52.2224	+	4.66473i	−1.69610	+	0.151503i
$949$	−26.0742	−	6.98657i	−0.846405	−	0.226794i
$950$	−14.7670	−	31.5929i	−0.479106	−	1.02501i
$951$			16.2167i			0.525861i
$952$		0			0
$953$		−	12.5441i		−	0.406345i	−0.979143	−	0.203172i	$-0.934875\pi$
$953$		−	12.5441i		−	0.406345i	0.979143	−	0.203172i	$-0.0651252\pi$
$954$	0.301690	−	0.141015i	0.00976758	−	0.00456553i
$955$	−3.48398	−	0.933528i	−0.112739	−	0.0302083i
$956$	9.23883	−	11.0512i	0.298805	−	0.357422i
$957$	−0.610485	−	2.27836i	−0.0197342	−	0.0736489i
$958$	−18.5095	+	3.28110i	−0.598013	+	0.106008i
$959$		0			0
$960$	−9.14244	−	5.21199i	−0.295071	−	0.168216i
$961$	−6.68477	+	11.5784i	−0.215638	+	0.373496i
$962$	−17.5377	+	14.7431i	−0.565437	+	0.475336i
$963$	−0.0967106	−	0.0259135i	−0.00311646	−	0.000835052i
$964$	47.1805	+	8.23061i	1.51958	+	0.265090i
$965$	−2.85823	−	2.85823i	−0.0920098	−	0.0920098i
$966$		0			0
$967$	−19.7015			−0.633559			−0.316779	−	0.948499i	$-0.602601\pi$
$967$	−19.7015			−0.633559			−0.316779	+	0.948499i	$0.602601\pi$
$968$	−28.2094	+	0.0770698i	−0.906685	+	0.00247712i
$969$	12.7681	+	22.1150i	0.410171	+	0.710437i
$970$	9.37856	+	0.811912i	0.301127	+	0.0260689i
$971$	5.14459	+	19.1999i	0.165098	+	0.616153i	0.998028	+	0.0627745i	$0.0199949\pi$
$971$	5.14459	+	19.1999i	0.165098	+	0.616153i	−0.832930	+	0.553378i	$0.813338\pi$
$972$	−0.399523	−	0.185415i	−0.0128147	−	0.00594720i
$973$		0			0
$974$	−1.78810	+	0.316969i	−0.0572943	+	0.0101563i
$975$	−27.2872	−	15.7543i	−0.873890	−	0.504541i
$976$	−21.9104	+	10.3143i	−0.701336	+	0.330154i
$977$	−22.0366	−	38.1686i	−0.705015	−	1.22112i	−0.966686	−	0.255965i	$-0.917607\pi$
$977$	−22.0366	−	38.1686i	−0.705015	−	1.22112i	0.261671	−	0.965157i	$-0.415726\pi$
$978$	7.64713	−	21.0700i	0.244528	−	0.673744i
$979$	25.4232	+	25.4232i	0.812530	+	0.812530i
$980$		0			0
$981$	0.123475	−	0.123475i	0.00394227	−	0.00394227i
$982$	−12.8340	+	5.99885i	−0.409551	+	0.191431i
$983$	−38.9733	+	22.5013i	−1.24306	+	0.717678i	−0.969715	−	0.244239i	$-0.921462\pi$
$983$	−38.9733	+	22.5013i	−1.24306	+	0.717678i	−0.273340	+	0.961917i	$0.588129\pi$
$984$	6.48442	+	23.9384i	0.206716	+	0.763128i
$985$	6.24810	−	10.8220i	0.199081	−	0.344818i
$986$	0.633156	−	0.905995i	0.0201638	−	0.0288528i
$987$		0			0
$988$	−42.8337	+	15.6786i	−1.36272	+	0.498803i
$989$	−10.4853	+	2.80953i	−0.333414	+	0.0893379i
$990$	0.0668412	+	0.0795111i	0.00212435	+	0.00252703i
$991$	−32.1531	+	18.5636i	−1.02138	+	0.589693i	−0.914503	−	0.404579i	$-0.867418\pi$
$991$	−32.1531	+	18.5636i	−1.02138	+	0.589693i	−0.106875	+	0.994272i	$0.534085\pi$
$992$	13.0486	+	35.3491i	0.414294	+	1.12234i
$993$			8.92622i			0.283265i
$994$		0			0
$995$	−5.57949	+	5.57949i	−0.176882	+	0.176882i
$996$	38.7714	+	6.76365i	1.22852	+	0.214315i
$997$	−14.9373	+	55.7466i	−0.473067	+	1.76551i	0.155582	+	0.987823i	$0.450275\pi$
$997$	−14.9373	+	55.7466i	−0.473067	+	1.76551i	−0.628649	+	0.777689i	$0.716392\pi$
$998$	−31.9975	−	2.77006i	−1.01286	−	0.0876848i
$999$	−17.7415	−	10.2430i	−0.561316	−	0.324076i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.w.f.19.6		56
7.2	even	3		784.2.j.a.195.25		56
7.3	odd	6	inner	784.2.w.f.227.5		56
7.4	even	3		112.2.v.a.3.5	✓	56
7.5	odd	6		784.2.j.a.195.26		56
7.6	odd	2		112.2.v.a.19.6	yes	56
16.11	odd	4	inner	784.2.w.f.411.5		56
28.11	odd	6		448.2.z.a.367.4		56
28.27	even	2		448.2.z.a.47.4		56
56.11	odd	6		896.2.z.a.479.11		56
56.13	odd	2		896.2.z.b.607.4		56
56.27	even	2		896.2.z.a.607.11		56
56.53	even	6		896.2.z.b.479.4		56
112.11	odd	12		112.2.v.a.59.6	yes	56
112.13	odd	4		896.2.z.a.159.11		56
112.27	even	4		112.2.v.a.75.5	yes	56
112.53	even	12		448.2.z.a.143.4		56
112.59	even	12	inner	784.2.w.f.619.6		56
112.67	odd	12		896.2.z.b.31.4		56
112.69	odd	4		448.2.z.a.271.4		56
112.75	even	12		784.2.j.a.587.25		56
112.83	even	4		896.2.z.b.159.4		56
112.107	odd	12		784.2.j.a.587.26		56
112.109	even	12		896.2.z.a.31.11		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.v.a.3.5	✓	56	7.4	even	3
112.2.v.a.19.6	yes	56	7.6	odd	2
112.2.v.a.59.6	yes	56	112.11	odd	12
112.2.v.a.75.5	yes	56	112.27	even	4
448.2.z.a.47.4		56	28.27	even	2
448.2.z.a.143.4		56	112.53	even	12
448.2.z.a.271.4		56	112.69	odd	4
448.2.z.a.367.4		56	28.11	odd	6
784.2.j.a.195.25		56	7.2	even	3
784.2.j.a.195.26		56	7.5	odd	6
784.2.j.a.587.25		56	112.75	even	12
784.2.j.a.587.26		56	112.107	odd	12
784.2.w.f.19.6		56	1.1	even	1	trivial
784.2.w.f.227.5		56	7.3	odd	6	inner
784.2.w.f.411.5		56	16.11	odd	4	inner
784.2.w.f.619.6		56	112.59	even	12	inner
896.2.z.a.31.11		56	112.109	even	12
896.2.z.a.159.11		56	112.13	odd	4
896.2.z.a.479.11		56	56.11	odd	6
896.2.z.a.607.11		56	56.27	even	2
896.2.z.b.31.4		56	112.67	odd	12
896.2.z.b.159.4		56	112.83	even	4
896.2.z.b.479.4		56	56.53	even	6
896.2.z.b.607.4		56	56.13	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.482479 + 1.32937i) q^{2} +(-0.449868 + 1.67893i) q^{3} +(-1.53443 - 1.28278i) q^{4} +(-0.731029 + 0.195879i) q^{5} +(-2.01486 - 1.40809i) q^{6} +(2.44562 - 1.42090i) q^{8} +(-0.0183525 - 0.0105958i) q^{9} +(0.0923119 - 1.06631i) q^{10} +(1.18531 - 4.42364i) q^{11} +(2.84399 - 1.99912i) q^{12} +(2.89529 - 2.89529i) q^{13} -1.31547i q^{15} +(0.708938 + 3.93667i) q^{16} +(2.28427 - 1.31882i) q^{17} +(0.0229404 - 0.0192849i) q^{18} +(5.38016 - 1.44161i) q^{19} +(1.37298 + 0.637190i) q^{20} +(5.30875 + 3.71003i) q^{22} +(1.01143 - 1.75184i) q^{23} +(1.28539 + 4.74524i) q^{24} +(-3.83409 + 2.21361i) q^{25} +(2.45199 + 5.24582i) q^{26} +(-3.66114 + 3.66114i) q^{27} +(-0.209526 - 0.209526i) q^{29} +(1.74874 + 0.634686i) q^{30} +(-3.33052 - 5.76864i) q^{31} +(-5.57533 - 0.956926i) q^{32} +(6.89376 + 3.98011i) q^{33} +(0.651087 + 3.67293i) q^{34} +(0.0145684 + 0.0398007i) q^{36} +(1.02406 + 3.82183i) q^{37} +(-0.679388 + 7.84774i) q^{38} +(3.55850 + 6.16350i) q^{39} +(-1.50949 + 1.51776i) q^{40} +5.04472 q^{41} +(-3.79454 - 3.79454i) q^{43} +(-7.49334 + 5.26726i) q^{44} +(0.0154917 + 0.00415099i) q^{45} +(1.84085 + 2.18978i) q^{46} +(2.53993 - 4.39928i) q^{47} +(-6.92833 - 0.580727i) q^{48} +(-1.09283 - 6.16493i) q^{50} +(1.18659 + 4.42843i) q^{51} +(-8.15665 + 0.728587i) q^{52} +(10.7333 + 2.87599i) q^{53} +(-3.10057 - 6.63342i) q^{54} +3.46599i q^{55} +9.68145i q^{57} +(0.379629 - 0.177445i) q^{58} +(5.23198 + 1.40190i) q^{59} +(-1.68746 + 2.01849i) q^{60} +(1.56694 + 5.84791i) q^{61} +(9.27554 - 1.64424i) q^{62} +(3.96208 - 6.94996i) q^{64} +(-1.54942 + 2.68367i) q^{65} +(-8.61712 + 7.24400i) q^{66} +(9.24005 + 2.47586i) q^{67} +(-5.19681 - 0.906581i) q^{68} +(2.48621 + 2.48621i) q^{69} -7.25507 q^{71} +(-0.0599387 + 0.000163756i) q^{72} +(-3.29633 - 5.70940i) q^{73} +(-5.57470 - 0.482607i) q^{74} +(-1.99167 - 7.43301i) q^{75} +(-10.1047 - 4.68953i) q^{76} +(-9.91044 + 1.75679i) q^{78} +(-13.0615 - 7.54108i) q^{79} +(-1.28936 - 2.73896i) q^{80} +(-4.53156 - 7.84890i) q^{81} +(-2.43397 + 6.70628i) q^{82} +(8.00548 + 8.00548i) q^{83} +(-1.41154 + 1.41154i) q^{85} +(6.87511 - 3.21354i) q^{86} +(0.446039 - 0.257521i) q^{87} +(-3.38674 - 12.5027i) q^{88} +(-3.92536 + 6.79892i) q^{89} +(-0.0129926 + 0.0185914i) q^{90} +(-3.79919 + 1.39063i) q^{92} +(11.1834 - 2.99659i) q^{93} +(4.62279 + 5.49905i) q^{94} +(-3.65067 + 2.10772i) q^{95} +(4.11478 - 8.93010i) q^{96} +8.79532i q^{97} +(-0.0686254 + 0.0686254i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 2 q^{2} + 6 q^{3} - 4 q^{4} + 6 q^{5} + 4 q^{8} + 24 q^{10} + 2 q^{11} + 6 q^{12} + 8 q^{16} + 12 q^{17} - 30 q^{18} + 6 q^{19} - 28 q^{22} - 12 q^{23} + 6 q^{24} + 6 q^{26} - 24 q^{29} - 18 q^{30}+ \cdots - 16 q^{99}+O(q^{100}) \) 56 * q - 2 * q^2 + 6 * q^3 - 4 * q^4 + 6 * q^5 + 4 * q^8 + 24 * q^10 + 2 * q^11 + 6 * q^12 + 8 * q^16 + 12 * q^17 - 30 * q^18 + 6 * q^19 - 28 * q^22 - 12 * q^23 + 6 * q^24 + 6 * q^26 - 24 * q^29 - 18 * q^30 - 12 * q^32 + 12 * q^33 + 16 * q^36 + 6 * q^37 + 6 * q^38 - 4 * q^39 + 66 * q^40 + 26 * q^44 - 12 * q^45 + 16 * q^46 - 34 * q^51 - 84 * q^52 + 6 * q^53 - 42 * q^54 + 18 * q^58 - 42 * q^59 + 78 * q^60 + 6 * q^61 - 16 * q^64 - 4 * q^65 - 126 * q^66 + 6 * q^67 - 24 * q^68 - 80 * q^71 - 4 * q^72 + 62 * q^74 - 24 * q^75 + 4 * q^78 - 12 * q^80 - 8 * q^81 - 42 * q^82 - 28 * q^85 + 12 * q^87 + 30 * q^88 - 20 * q^92 + 10 * q^93 + 42 * q^94 - 36 * q^96 - 16 * q^99

Introduction

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