LMFDB - Embedded newform 507.2.k.f.188.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(80,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 1]))

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

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

chi := DirichletCharacter("507.80");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.k (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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	8.0.56070144.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 16x^{6} - 34x^{5} + 63x^{4} - 74x^{3} + 70x^{2} - 38x + 13 $ x^8 - 4x^7 + 16x^6 - 34x^5 + 63x^4 - 74x^3 + 70x^2 - 38*x + 13
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			188.1
Root			$0.500000 + 2.19293i$ of defining polynomial
Character	$\chi$	$=$	507.188
Dual form			507.2.k.f.89.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.31259 + 0.619657i) q^{2} +(-1.28311 - 1.16345i) q^{3} +(3.23205 - 1.86603i) q^{4} +(1.69293 + 1.69293i) q^{5} +(3.68825 + 1.89551i) q^{6} +(-0.366025 + 1.36603i) q^{7} +(-2.93225 + 2.93225i) q^{8} +(0.292748 + 2.98568i) q^{9} +O(q^{10})$	\(q+(-2.31259 + 0.619657i) q^{2} +(-1.28311 - 1.16345i) q^{3} +(3.23205 - 1.86603i) q^{4} +(1.69293 + 1.69293i) q^{5} +(3.68825 + 1.89551i) q^{6} +(-0.366025 + 1.36603i) q^{7} +(-2.93225 + 2.93225i) q^{8} +(0.292748 + 2.98568i) q^{9} +(-4.96410 - 2.86603i) q^{10} +(0.453620 + 1.69293i) q^{11} +(-6.31812 - 1.36603i) q^{12} -3.38587i q^{14} +(-0.202571 - 4.14187i) q^{15} +(1.23205 - 2.13397i) q^{16} +(-1.07328 - 1.85897i) q^{17} +(-2.52711 - 6.72326i) q^{18} +(-1.00000 - 0.267949i) q^{19} +(8.63071 + 2.31259i) q^{20} +(2.05896 - 1.32691i) q^{21} +(-2.09808 - 3.63397i) q^{22} +(7.17394 - 0.350863i) q^{24} +0.732051i q^{25} +(3.09808 - 4.17156i) q^{27} +(1.36603 + 5.09808i) q^{28} +(4.79122 + 2.76621i) q^{29} +(3.03500 + 9.45293i) q^{30} +(-4.46410 + 4.46410i) q^{31} +(0.619657 - 2.31259i) q^{32} +(1.38761 - 2.69999i) q^{33} +(3.63397 + 3.63397i) q^{34} +(-2.93225 + 1.69293i) q^{35} +(6.51754 + 9.10360i) q^{36} +(-6.59808 + 1.76795i) q^{37} +2.47863 q^{38} -9.92820 q^{40} +(0.619657 - 0.166037i) q^{41} +(-3.93930 + 4.34444i) q^{42} +(-7.09808 + 4.09808i) q^{43} +(4.62518 + 4.62518i) q^{44} +(-4.55896 + 5.55017i) q^{45} +(-6.77174 + 6.77174i) q^{47} +(-4.06364 + 1.30469i) q^{48} +(4.33013 + 2.50000i) q^{49} +(-0.453620 - 1.69293i) q^{50} +(-0.785693 + 3.63397i) q^{51} +4.62518i q^{53} +(-4.57965 + 11.5669i) q^{54} +(-2.09808 + 3.63397i) q^{55} +(-2.93225 - 5.07880i) q^{56} +(0.971364 + 1.50726i) q^{57} +(-12.7942 - 3.42820i) q^{58} +(-4.62518 - 1.23931i) q^{59} +(-8.38356 - 13.0087i) q^{60} +(3.50000 + 6.06218i) q^{61} +(7.55743 - 13.0899i) q^{62} +(-4.18567 - 0.692934i) q^{63} +10.6603i q^{64} +(-1.53590 + 7.10381i) q^{66} +(-2.26795 - 8.46410i) q^{67} +(-6.93777 - 4.00552i) q^{68} +(5.73205 - 5.73205i) q^{70} +(-1.23931 + 4.62518i) q^{71} +(-9.61317 - 7.89635i) q^{72} +(6.09808 + 6.09808i) q^{73} +(14.1631 - 8.17709i) q^{74} +(0.851708 - 0.939303i) q^{75} +(-3.73205 + 1.00000i) q^{76} -2.47863 q^{77} +2.00000 q^{79} +(5.69846 - 1.52690i) q^{80} +(-8.82860 + 1.74811i) q^{81} +(-1.33013 + 0.767949i) q^{82} +(-1.23931 - 1.23931i) q^{83} +(4.17862 - 8.13071i) q^{84} +(1.33013 - 4.96410i) q^{85} +(13.8755 - 13.8755i) q^{86} +(-2.92931 - 9.12372i) q^{87} +(-6.29423 - 3.63397i) q^{88} +(2.60017 + 9.70398i) q^{89} +(7.10381 - 15.6603i) q^{90} +(10.9217 - 0.534160i) q^{93} +(11.4641 - 19.8564i) q^{94} +(-1.23931 - 2.14655i) q^{95} +(-3.48568 + 2.24637i) q^{96} +(12.5622 + 3.36603i) q^{97} +(-11.5630 - 3.09828i) q^{98} +(-4.92177 + 1.84997i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} + 12 q^{4} + 14 q^{6} + 4 q^{7} + 4 q^{9}+O(q^{10}) $ 8 * q - 2 * q^3 + 12 * q^4 + 14 * q^6 + 4 * q^7 + 4 * q^9	$ 8 q - 2 q^{3} + 12 q^{4} + 14 q^{6} + 4 q^{7} + 4 q^{9} - 12 q^{10} + 2 q^{15} - 4 q^{16} - 4 q^{18} - 8 q^{19} - 4 q^{21} + 4 q^{22} + 30 q^{24} + 4 q^{27} + 4 q^{28} - 18 q^{30} - 8 q^{31} + 20 q^{33} + 36 q^{34} + 36 q^{36} - 32 q^{37} - 24 q^{40} - 16 q^{42} - 36 q^{43} - 16 q^{45} - 14 q^{48} + 38 q^{54} + 4 q^{55} - 16 q^{57} - 40 q^{58} - 44 q^{60} + 28 q^{61} - 16 q^{63} - 40 q^{66} - 32 q^{67} + 32 q^{70} - 24 q^{72} + 28 q^{73} - 12 q^{75} - 16 q^{76} + 16 q^{79} + 4 q^{81} + 24 q^{82} + 8 q^{84} - 24 q^{85} - 34 q^{87} + 12 q^{88} - 16 q^{93} + 64 q^{94} - 16 q^{96} + 52 q^{97} - 40 q^{99}+O(q^{100}) $ 8 * q - 2 * q^3 + 12 * q^4 + 14 * q^6 + 4 * q^7 + 4 * q^9 - 12 * q^10 + 2 * q^15 - 4 * q^16 - 4 * q^18 - 8 * q^19 - 4 * q^21 + 4 * q^22 + 30 * q^24 + 4 * q^27 + 4 * q^28 - 18 * q^30 - 8 * q^31 + 20 * q^33 + 36 * q^34 + 36 * q^36 - 32 * q^37 - 24 * q^40 - 16 * q^42 - 36 * q^43 - 16 * q^45 - 14 * q^48 + 38 * q^54 + 4 * q^55 - 16 * q^57 - 40 * q^58 - 44 * q^60 + 28 * q^61 - 16 * q^63 - 40 * q^66 - 32 * q^67 + 32 * q^70 - 24 * q^72 + 28 * q^73 - 12 * q^75 - 16 * q^76 + 16 * q^79 + 4 * q^81 + 24 * q^82 + 8 * q^84 - 24 * q^85 - 34 * q^87 + 12 * q^88 - 16 * q^93 + 64 * q^94 - 16 * q^96 + 52 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$-1$	$e\left(\frac{5}{12}\right)$

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 $

$2$	−2.31259	+	0.619657i	−1.63525	+	0.438164i	−0.955430	−	0.295217i	$-0.904608\pi$
$2$	−2.31259	+	0.619657i	−1.63525	+	0.438164i	−0.679818	+	0.733380i	$0.737941\pi$
$3$	−1.28311	−	1.16345i	−0.740805	−	0.671721i
$3$	−1.28311	−	1.16345i	−0.740805	−	0.671721i
$4$	3.23205	−	1.86603i	1.61603	−	0.933013i
$5$	1.69293	+	1.69293i	0.757103	+	0.757103i	0.975794	−	0.218691i	$-0.0701787\pi$
$5$	1.69293	+	1.69293i	0.757103	+	0.757103i	−0.218691	+	0.975794i	$0.570179\pi$
$6$	3.68825	+	1.89551i	1.50572	+	0.773837i
$7$	−0.366025	+	1.36603i	−0.138345	+	0.516309i	0.861617	+	0.507559i	$0.169452\pi$
$7$	−0.366025	+	1.36603i	−0.138345	+	0.516309i	−0.999962	+	0.00875026i	$0.997215\pi$
$8$	−2.93225	+	2.93225i	−1.03671	+	1.03671i
$9$	0.292748	+	2.98568i	0.0975828	+	0.995227i
$10$	−4.96410	−	2.86603i	−1.56979	−	0.906317i
$11$	0.453620	+	1.69293i	0.136772	+	0.510439i	0.999984	+	0.00559833i	$0.00178201\pi$
$11$	0.453620	+	1.69293i	0.136772	+	0.510439i	−0.863213	+	0.504840i	$0.831551\pi$
$12$	−6.31812	−	1.36603i	−1.82388	−	0.394338i
$13$		0			0
$13$		0			0
$14$		−	3.38587i		−	0.904911i
$15$	−0.202571	−	4.14187i	−0.0523036	−	1.06943i
$16$	1.23205	−	2.13397i	0.308013	−	0.533494i
$17$	−1.07328	−	1.85897i	−0.260308	−	0.450867i	0.706016	−	0.708196i	$-0.250491\pi$
$17$	−1.07328	−	1.85897i	−0.260308	−	0.450867i	−0.966324	+	0.257330i	$0.917157\pi$
$18$	−2.52711	−	6.72326i	−0.595644	−	1.58469i
$19$	−1.00000	−	0.267949i	−0.229416	−	0.0614718i	0.142280	−	0.989826i	$-0.454557\pi$
$19$	−1.00000	−	0.267949i	−0.229416	−	0.0614718i	−0.371695	+	0.928355i	$0.621223\pi$
$20$	8.63071	+	2.31259i	1.92988	+	0.517111i
$21$	2.05896	−	1.32691i	0.449302	−	0.289555i
$22$	−2.09808	−	3.63397i	−0.447311	−	0.774766i
$23$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$	7.17394	−	0.350863i	1.46437	−	0.0716197i
$25$			0.732051i			0.146410i
$26$		0			0
$27$	3.09808	−	4.17156i	0.596225	−	0.802817i
$28$	1.36603	+	5.09808i	0.258155	+	0.963446i
$29$	4.79122	+	2.76621i	0.889707	+	0.513673i	0.873847	−	0.486202i	$-0.161618\pi$
$29$	4.79122	+	2.76621i	0.889707	+	0.513673i	0.0158603	+	0.999874i	$0.494951\pi$
$30$	3.03500	+	9.45293i	0.554113	+	1.72586i
$31$	−4.46410	+	4.46410i	−0.801776	+	0.801776i	−0.983373	−	0.181597i	$-0.941873\pi$
$31$	−4.46410	+	4.46410i	−0.801776	+	0.801776i	0.181597	+	0.983373i	$0.441873\pi$
$32$	0.619657	−	2.31259i	0.109541	−	0.408812i
$33$	1.38761	−	2.69999i	0.241551	−	0.470008i
$34$	3.63397	+	3.63397i	0.623222	+	0.623222i
$35$	−2.93225	+	1.69293i	−0.495640	+	0.286158i
$36$	6.51754	+	9.10360i	1.08626	+	1.51727i
$37$	−6.59808	+	1.76795i	−1.08472	+	0.290649i	−0.756527	−	0.653963i	$-0.773105\pi$
$37$	−6.59808	+	1.76795i	−1.08472	+	0.290649i	−0.328190	+	0.944612i	$0.606439\pi$
$38$	2.47863			0.402086
$39$		0			0
$40$	−9.92820			−1.56979
$41$	0.619657	−	0.166037i	0.0967741	−	0.0259306i	−0.210107	−	0.977678i	$-0.567381\pi$
$41$	0.619657	−	0.166037i	0.0967741	−	0.0259306i	0.306881	+	0.951748i	$0.400715\pi$
$42$	−3.93930	+	4.34444i	−0.607848	+	0.670362i
$43$	−7.09808	+	4.09808i	−1.08245	+	0.624951i	−0.931555	−	0.363600i	$-0.881548\pi$
$43$	−7.09808	+	4.09808i	−1.08245	+	0.624951i	−0.150891	+	0.988550i	$0.548214\pi$
$44$	4.62518	+	4.62518i	0.697272	+	0.697272i
$45$	−4.55896	+	5.55017i	−0.679610	+	0.827370i
$46$		0			0
$47$	−6.77174	+	6.77174i	−0.987759	+	0.987759i	−0.999926	−	0.0121668i	$-0.996127\pi$
$47$	−6.77174	+	6.77174i	−0.987759	+	0.987759i	0.0121668	+	0.999926i	$0.496127\pi$
$48$	−4.06364	+	1.30469i	−0.586536	+	0.188316i
$49$	4.33013	+	2.50000i	0.618590	+	0.357143i
$50$	−0.453620	−	1.69293i	−0.0641516	−	0.239417i
$51$	−0.785693	+	3.63397i	−0.110019	+	0.508858i
$52$		0			0
$53$			4.62518i			0.635318i	0.948205	+	0.317659i	$0.102897\pi$
$53$			4.62518i			0.635318i	−0.948205	+	0.317659i	$0.897103\pi$
$54$	−4.57965	+	11.5669i	−0.623211	+	1.57405i
$55$	−2.09808	+	3.63397i	−0.282905	+	0.490005i
$56$	−2.93225	−	5.07880i	−0.391838	−	0.678683i
$57$	0.971364	+	1.50726i	0.128660	+	0.199642i
$58$	−12.7942	−	3.42820i	−1.67996	−	0.450145i
$59$	−4.62518	−	1.23931i	−0.602147	−	0.161345i	−0.0551484	−	0.998478i	$-0.517563\pi$
$59$	−4.62518	−	1.23931i	−0.602147	−	0.161345i	−0.546999	+	0.837133i	$0.684230\pi$
$60$	−8.38356	−	13.0087i	−1.08231	−	1.67942i
$61$	3.50000	+	6.06218i	0.448129	+	0.776182i	0.998264	−	0.0588933i	$-0.0187572\pi$
$61$	3.50000	+	6.06218i	0.448129	+	0.776182i	−0.550135	+	0.835076i	$0.685424\pi$
$62$	7.55743	−	13.0899i	0.959794	−	1.66241i
$63$	−4.18567	−	0.692934i	−0.527345	−	0.0873015i
$64$			10.6603i			1.33253i
$65$		0			0
$66$	−1.53590	+	7.10381i	−0.189056	+	0.874418i
$67$	−2.26795	−	8.46410i	−0.277074	−	1.03405i	−0.954439	−	0.298407i	$-0.903545\pi$
$67$	−2.26795	−	8.46410i	−0.277074	−	1.03405i	0.677365	−	0.735647i	$-0.263122\pi$
$68$	−6.93777	−	4.00552i	−0.841328	−	0.485741i
$69$		0			0
$70$	5.73205	−	5.73205i	0.685111	−	0.685111i
$71$	−1.23931	+	4.62518i	−0.147079	+	0.548908i	0.852575	+	0.522606i	$0.175040\pi$
$71$	−1.23931	+	4.62518i	−0.147079	+	0.548908i	−0.999654	+	0.0263025i	$0.991627\pi$
$72$	−9.61317	−	7.89635i	−1.13292	−	0.930594i
$73$	6.09808	+	6.09808i	0.713726	+	0.713726i	0.967313	−	0.253587i	$-0.0816103\pi$
$73$	6.09808	+	6.09808i	0.713726	+	0.713726i	−0.253587	+	0.967313i	$0.581610\pi$
$74$	14.1631	−	8.17709i	1.64643	−	0.950567i
$75$	0.851708	−	0.939303i	0.0983467	−	0.108461i
$76$	−3.73205	+	1.00000i	−0.428096	+	0.114708i
$77$	−2.47863			−0.282466
$78$		0			0
$79$	2.00000			0.225018			0.112509	−	0.993651i	$-0.464111\pi$
$79$	2.00000			0.225018			0.112509	+	0.993651i	$0.464111\pi$
$80$	5.69846	−	1.52690i	0.637107	−	0.170712i
$81$	−8.82860	+	1.74811i	−0.980955	+	0.194234i
$82$	−1.33013	+	0.767949i	−0.146888	+	0.0848058i
$83$	−1.23931	−	1.23931i	−0.136032	−	0.136032i	0.635812	−	0.771844i	$-0.280665\pi$
$83$	−1.23931	−	1.23931i	−0.136032	−	0.136032i	−0.771844	+	0.635812i	$0.780665\pi$
$84$	4.17862	−	8.13071i	0.455924	−	0.887133i
$85$	1.33013	−	4.96410i	0.144273	−	0.538432i
$86$	13.8755	−	13.8755i	1.49624	−	1.49624i
$87$	−2.92931	−	9.12372i	−0.314054	−	0.978165i
$88$	−6.29423	−	3.63397i	−0.670967	−	0.387383i
$89$	2.60017	+	9.70398i	0.275618	+	1.02862i	0.955426	+	0.295230i	$0.0953964\pi$
$89$	2.60017	+	9.70398i	0.275618	+	1.02862i	−0.679808	+	0.733390i	$0.737937\pi$
$90$	7.10381	−	15.6603i	0.748807	−	1.65074i
$91$		0			0
$92$		0			0
$93$	10.9217	−	0.534160i	1.13253	−	0.0553898i
$94$	11.4641	−	19.8564i	1.18243	−	2.04803i
$95$	−1.23931	−	2.14655i	−0.127151	−	0.220232i
$96$	−3.48568	+	2.24637i	−0.355756	+	0.229269i
$97$	12.5622	+	3.36603i	1.27550	+	0.341768i	0.832134	−	0.554575i	$-0.187119\pi$
$97$	12.5622	+	3.36603i	1.27550	+	0.341768i	0.443362	+	0.896343i	$0.353786\pi$
$98$	−11.5630	−	3.09828i	−1.16803	−	0.312974i
$99$	−4.92177	+	1.84997i	−0.494656	+	0.185929i
$100$	1.36603	+	2.36603i	0.136603	+	0.236603i
$101$	−9.87002	+	17.0954i	−0.982104	+	1.70105i	−0.327944	+	0.944697i	$0.606356\pi$
$101$	−9.87002	+	17.0954i	−0.982104	+	1.70105i	−0.654160	+	0.756356i	$0.726978\pi$
$102$	−0.434830	−	8.89076i	−0.0430546	−	0.880316i
$103$		−	6.92820i		−	0.682656i	−0.939944	−	0.341328i	$-0.889123\pi$
$103$		−	6.92820i		−	0.682656i	0.939944	−	0.341328i	$-0.110877\pi$
$104$		0			0
$105$	5.73205	+	1.23931i	0.559391	+	0.120945i
$106$	−2.86603	−	10.6962i	−0.278373	−	1.03890i
$107$	14.4507	+	8.34312i	1.39700	+	0.806560i	0.994078	−	0.108673i	$-0.0346600\pi$
$107$	14.4507	+	8.34312i	1.39700	+	0.806560i	0.402925	+	0.915233i	$0.367993\pi$
$108$	2.22890	−	19.2638i	0.214476	−	1.85366i
$109$	2.80385	−	2.80385i	0.268560	−	0.268560i	−0.559960	−	0.828520i	$-0.689183\pi$
$109$	2.80385	−	2.80385i	0.268560	−	0.268560i	0.828520	+	0.559960i	$0.189183\pi$
$110$	2.60017	−	9.70398i	0.247917	−	0.925239i
$111$	10.5230	+	5.40808i	0.998798	+	0.513313i
$112$	2.46410	+	2.46410i	0.232836	+	0.232836i
$113$	−11.2309	+	6.48415i	−1.05651	+	0.609978i	−0.924465	−	0.381266i	$-0.875488\pi$
$113$	−11.2309	+	6.48415i	−1.05651	+	0.609978i	−0.132047	+	0.991243i	$0.542155\pi$
$114$	−3.18035	−	2.88377i	−0.297867	−	0.270090i
$115$		0			0
$116$	20.6473			1.91705
$117$		0			0
$118$	11.4641			1.05536
$119$	2.93225	−	0.785693i	0.268799	−	0.0720244i
$120$	12.7390	+	11.5510i	1.16291	+	1.05446i
$121$	6.86603	−	3.96410i	0.624184	−	0.360373i
$122$	−11.8505	−	11.8505i	−1.07290	−	1.07290i
$123$	−0.988265	−	0.507899i	−0.0891088	−	0.0457957i
$124$	−6.09808	+	22.7583i	−0.547623	+	2.04376i
$125$	7.22536	−	7.22536i	0.646255	−	0.646255i
$126$	10.1091	−	0.991207i	0.900592	−	0.0883037i
$127$	−13.0981	−	7.56218i	−1.16227	−	0.671035i	−0.210420	−	0.977611i	$-0.567483\pi$
$127$	−13.0981	−	7.56218i	−1.16227	−	0.671035i	−0.951846	+	0.306576i	$0.900817\pi$
$128$	−5.36639	−	20.0276i	−0.474326	−	1.77021i
$129$	13.8755	+	3.00000i	1.22167	+	0.264135i
$130$		0			0
$131$			0.907241i			0.0792660i	0.999214	+	0.0396330i	$0.0126189\pi$
$131$			0.907241i			0.0792660i	−0.999214	+	0.0396330i	$0.987381\pi$
$132$	−0.553435	−	11.3158i	−0.0481703	−	0.984915i
$133$	0.732051	−	1.26795i	0.0634769	−	0.109945i
$134$	10.4897	+	18.1687i	0.906170	+	1.56953i
$135$	12.3070	−	1.81734i	1.05922	−	0.156412i
$136$	8.59808	+	2.30385i	0.737279	+	0.197553i
$137$	−5.69846	−	1.52690i	−0.486852	−	0.130452i	0.00703925	−	0.999975i	$-0.497759\pi$
$137$	−5.69846	−	1.52690i	−0.486852	−	0.130452i	−0.493891	+	0.869524i	$0.664426\pi$
$138$		0			0
$139$	1.19615	+	2.07180i	0.101456	+	0.175728i	0.912285	−	0.409556i	$-0.134316\pi$
$139$	1.19615	+	2.07180i	0.101456	+	0.175728i	−0.810829	+	0.585284i	$0.800983\pi$
$140$	−6.31812	+	10.9433i	−0.533978	+	0.924877i
$141$	16.5675	−	0.810284i	1.39523	−	0.0682383i
$142$		−	11.4641i		−	0.962046i
$143$		0			0
$144$	6.73205	+	3.05379i	0.561004	+	0.254483i
$145$	3.42820	+	12.7942i	0.284697	+	1.06250i
$146$	−17.8811	−	10.3236i	−1.47985	−	0.854391i
$147$	−2.64740	−	8.24568i	−0.218354	−	0.680092i
$148$	−18.0263	+	18.0263i	−1.48175	+	1.48175i
$149$	1.40535	−	5.24484i	0.115131	−	0.429674i	−0.884166	−	0.467173i	$-0.845272\pi$
$149$	1.40535	−	5.24484i	0.115131	−	0.429674i	0.999297	+	0.0374992i	$0.0119392\pi$
$150$	−1.38761	+	2.69999i	−0.113298	+	0.220453i
$151$	−7.46410	−	7.46410i	−0.607420	−	0.607420i	0.334851	−	0.942271i	$-0.391314\pi$
$151$	−7.46410	−	7.46410i	−0.607420	−	0.607420i	−0.942271	+	0.334851i	$0.891314\pi$
$152$	3.71794	−	2.14655i	0.301565	−	0.174109i
$153$	5.23610	−	3.74867i	0.423313	−	0.303062i
$154$	5.73205	−	1.53590i	0.461902	−	0.123766i
$155$	−15.1149			−1.21405
$156$		0			0
$157$	−15.1962			−1.21278			−0.606392	−	0.795165i	$-0.707384\pi$
$157$	−15.1962			−1.21278			−0.606392	+	0.795165i	$0.707384\pi$
$158$	−4.62518	+	1.23931i	−0.367960	+	0.0985945i
$159$	5.38119	−	5.93462i	0.426756	−	0.470646i
$160$	4.96410	−	2.86603i	0.392447	−	0.226579i
$161$		0			0
$162$	19.3337	−	9.51336i	1.51900	−	0.747440i
$163$	−4.00000	+	14.9282i	−0.313304	+	1.16927i	0.612254	+	0.790661i	$0.290263\pi$
$163$	−4.00000	+	14.9282i	−0.313304	+	1.16927i	−0.925558	+	0.378606i	$0.876404\pi$
$164$	1.69293	−	1.69293i	0.132196	−	0.132196i
$165$	6.92003	−	2.22178i	0.538723	−	0.172965i
$166$	3.63397	+	2.09808i	0.282051	+	0.162842i
$167$	−3.05379	−	11.3969i	−0.236310	−	0.881920i	−0.977554	−	0.210685i	$-0.932431\pi$
$167$	−3.05379	−	11.3969i	−0.236310	−	0.881920i	0.741244	−	0.671235i	$-0.234236\pi$
$168$	−2.14655	+	9.92820i	−0.165610	+	0.765978i
$169$		0			0
$170$			12.3042i			0.943686i
$171$	0.507263	−	3.06412i	0.0387914	−	0.234319i
$172$	−15.2942	+	26.4904i	−1.16617	+	2.01987i
$173$	−3.71794	−	6.43966i	−0.282670	−	0.489598i	0.689372	−	0.724408i	$-0.257887\pi$
$173$	−3.71794	−	6.43966i	−0.282670	−	0.489598i	−0.972041	+	0.234809i	$0.924553\pi$
$174$	12.4279	+	19.2843i	0.942154	+	1.46194i
$175$	−1.00000	−	0.267949i	−0.0755929	−	0.0202551i
$176$	4.17156	+	1.11777i	0.314443	+	0.0842548i
$177$	4.49274	+	6.97136i	0.337695	+	0.524000i
$178$	−12.0263	−	20.8301i	−0.901408	−	1.56128i
$179$	9.37191	−	16.2326i	0.700489	−	1.21328i	−0.267805	−	0.963473i	$-0.586298\pi$
$179$	9.37191	−	16.2326i	0.700489	−	1.21328i	0.968295	−	0.249810i	$-0.0803683\pi$
$180$	−4.37804	+	26.4456i	−0.326320	+	1.97114i
$181$			3.00000i			0.222988i	0.993765	+	0.111494i	$0.0355636\pi$
$181$			3.00000i			0.222988i	−0.993765	+	0.111494i	$0.964436\pi$
$182$		0			0
$183$	2.56218	−	11.8505i	0.189402	−	0.876017i
$184$		0			0
$185$	−14.1631	−	8.17709i	−1.04129	−	0.601191i
$186$	−24.9265	+	8.00301i	−1.82770	+	0.586809i
$187$	2.66025	−	2.66025i	0.194537	−	0.194537i
$188$	−9.25036	+	34.5228i	−0.674652	+	2.51784i
$189$	4.56448	+	5.75895i	0.332017	+	0.418902i
$190$	4.19615	+	4.19615i	0.304421	+	0.304421i
$191$	−16.8078	+	9.70398i	−1.21617	+	0.702156i	−0.964096	−	0.265553i	$-0.914446\pi$
$191$	−16.8078	+	9.70398i	−1.21617	+	0.702156i	−0.252073	+	0.967708i	$0.581112\pi$
$192$	12.4027	−	13.6783i	0.895089	−	0.987146i
$193$	6.96410	−	1.86603i	0.501287	−	0.134319i	0.000689767	−	1.00000i	$-0.499780\pi$
$193$	6.96410	−	1.86603i	0.501287	−	0.134319i	0.500597	+	0.865680i	$0.333114\pi$
$194$	−31.1370			−2.23550
$195$		0			0
$196$	18.6603			1.33288
$197$	1.69293	−	0.453620i	0.120617	−	0.0323191i	−0.198006	−	0.980201i	$-0.563446\pi$
$197$	1.69293	−	0.453620i	0.120617	−	0.0323191i	0.318622	+	0.947882i	$0.396780\pi$
$198$	10.2357	−	7.32803i	0.727418	−	0.520780i
$199$	−0.803848	+	0.464102i	−0.0569832	+	0.0328993i	−0.528221	−	0.849107i	$-0.677141\pi$
$199$	−0.803848	+	0.464102i	−0.0569832	+	0.0328993i	0.471238	+	0.882006i	$0.343807\pi$
$200$	−2.14655	−	2.14655i	−0.151784	−	0.151784i
$201$	−6.93756	+	13.4990i	−0.489338	+	0.952149i
$202$	12.2321	−	45.6506i	0.860644	−	3.21197i
$203$	−5.53242	+	5.53242i	−0.388300	+	0.388300i
$204$	4.24169	+	13.2113i	0.296978	+	0.924977i
$205$	1.33013	+	0.767949i	0.0929001	+	0.0536359i
$206$	4.29311	+	16.0221i	0.299115	+	1.11631i
$207$		0			0
$208$		0			0
$209$		−	1.81448i		−	0.125510i
$210$	−14.0238	+	0.685879i	−0.967737	+	0.0473302i
$211$	6.09808	−	10.5622i	0.419809	−	0.727130i	−0.576111	−	0.817371i	$-0.695430\pi$
$211$	6.09808	−	10.5622i	0.419809	−	0.727130i	0.995920	+	0.0902411i	$0.0287638\pi$
$212$	8.63071	+	14.9488i	0.592759	+	1.02669i
$213$	6.97136	−	4.49274i	0.477670	−	0.307837i
$214$	−38.5885	−	10.3397i	−2.63785	−	0.706810i
$215$	−18.9543	−	5.07880i	−1.29268	−	0.346371i
$216$	3.14772	+	21.3164i	0.214176	+	1.45040i
$217$	−4.46410	−	7.73205i	−0.303043	−	0.524886i
$218$	−4.74673	+	8.22158i	−0.321489	+	0.556835i
$219$	−0.729677	−	14.9193i	−0.0493070	−	1.00816i
$220$			15.6603i			1.05581i
$221$		0			0
$222$	−27.6865	−	5.98604i	−1.85820	−	0.401757i
$223$	5.97372	+	22.2942i	0.400030	+	1.49293i	0.813041	+	0.582206i	$0.197810\pi$
$223$	5.97372	+	22.2942i	0.400030	+	1.49293i	−0.413011	+	0.910726i	$0.635523\pi$
$224$	2.93225	+	1.69293i	0.195919	+	0.113114i
$225$	−2.18567	+	0.214307i	−0.145711	+	0.0142871i
$226$	21.9545	−	21.9545i	1.46039	−	1.46039i
$227$	4.05001	−	15.1149i	0.268809	−	1.00321i	−0.691069	−	0.722789i	$-0.742860\pi$
$227$	4.05001	−	15.1149i	0.268809	−	1.00321i	0.959878	−	0.280419i	$-0.0904735\pi$
$228$	5.95209	+	3.05896i	0.394187	+	0.202585i
$229$	−10.1244	−	10.1244i	−0.669036	−	0.669036i	0.288457	−	0.957493i	$-0.406858\pi$
$229$	−10.1244	−	10.1244i	−0.669036	−	0.669036i	−0.957493	+	0.288457i	$0.906858\pi$
$230$		0			0
$231$	3.18035	+	2.88377i	0.209252	+	0.189738i
$232$	−22.1603	+	5.93782i	−1.45489	+	0.389837i
$233$	7.43588			0.487141			0.243570	−	0.969883i	$-0.421681\pi$
$233$	7.43588			0.487141			0.243570	+	0.969883i	$0.421681\pi$
$234$		0			0
$235$	−22.9282			−1.49567
$236$	−17.2614	+	4.62518i	−1.12362	+	0.301074i
$237$	−2.56622	−	2.32691i	−0.166694	−	0.151149i
$238$	−6.29423	+	3.63397i	−0.407994	+	0.235556i
$239$	−7.10381	−	7.10381i	−0.459507	−	0.459507i	0.438986	−	0.898494i	$-0.355338\pi$
$239$	−7.10381	−	7.10381i	−0.459507	−	0.459507i	−0.898494	+	0.438986i	$0.855338\pi$
$240$	−9.08823	−	4.67072i	−0.586643	−	0.301493i
$241$	1.93782	−	7.23205i	0.124826	−	0.465857i	−0.875007	−	0.484110i	$-0.839144\pi$
$241$	1.93782	−	7.23205i	0.124826	−	0.465857i	0.999833	+	0.0182524i	$0.00581023\pi$
$242$	−13.4219	+	13.4219i	−0.862794	+	0.862794i
$243$	13.3619	+	8.02865i	0.857167	+	0.515038i
$244$	22.6244	+	13.0622i	1.44838	+	0.836220i
$245$	3.09828	+	11.5630i	0.197942	+	0.738730i
$246$	2.60017	+	0.562178i	0.165781	+	0.0358431i
$247$		0			0
$248$		−	26.1797i		−	1.66241i
$249$	0.148292	+	3.03206i	0.00939765	+	0.192149i
$250$	−12.2321	+	21.1865i	−0.773623	+	1.33995i
$251$	10.9433	+	18.9543i	0.690735	+	1.19639i	0.971597	+	0.236640i	$0.0760461\pi$
$251$	10.9433	+	18.9543i	0.690735	+	1.19639i	−0.280863	+	0.959748i	$0.590621\pi$
$252$	−14.8213	+	5.57097i	−0.933656	+	0.350938i
$253$		0			0
$254$	34.9764	+	9.37191i	2.19462	+	0.588046i
$255$	−7.48221	+	4.82195i	−0.468554	+	0.301962i
$256$	14.1603	+	24.5263i	0.885016	+	1.53289i
$257$	−8.29863	+	14.3737i	−0.517655	+	0.896604i	0.482135	+	0.876097i	$0.339861\pi$
$257$	−8.29863	+	14.3737i	−0.517655	+	0.896604i	−0.999790	+	0.0205071i	$0.993472\pi$
$258$	−33.9474	+	1.66030i	−2.11347	+	0.103366i
$259$		−	9.66025i		−	0.600259i
$260$		0			0
$261$	−6.85641	+	15.1149i	−0.424401	+	0.935586i
$262$	−0.562178	−	2.09808i	−0.0347315	−	0.129620i
$263$	10.3681	+	5.98604i	0.639326	+	0.369115i	0.784355	−	0.620312i	$-0.212994\pi$
$263$	10.3681	+	5.98604i	0.639326	+	0.369115i	−0.145029	+	0.989427i	$0.546327\pi$
$264$	3.84823	+	11.9858i	0.236842	+	0.737677i
$265$	−7.83013	+	7.83013i	−0.481001	+	0.481001i
$266$	−0.907241	+	3.38587i	−0.0556265	+	0.207601i
$267$	7.95383	−	15.4765i	0.486766	−	0.947145i
$268$	−23.1244	−	23.1244i	−1.41254	−	1.41254i
$269$	9.58244	−	5.53242i	0.584251	−	0.337318i	−0.178570	−	0.983927i	$-0.557147\pi$
$269$	9.58244	−	5.53242i	0.584251	−	0.337318i	0.762821	+	0.646610i	$0.223814\pi$
$270$	−27.3350	+	11.8289i	−1.66355	+	0.719883i
$271$	2.00000	−	0.535898i	0.121491	−	0.0325535i	−0.197561	−	0.980291i	$-0.563302\pi$
$271$	2.00000	−	0.535898i	0.121491	−	0.0325535i	0.319052	+	0.947737i	$0.396635\pi$
$272$	−5.28933			−0.320713
$273$		0			0
$274$	14.1244			0.853284
$275$	−1.23931	+	0.332073i	−0.0747334	+	0.0200248i
$276$		0			0
$277$	−3.10770	+	1.79423i	−0.186723	+	0.107805i	−0.590448	−	0.807076i	$-0.701049\pi$
$277$	−3.10770	+	1.79423i	−0.186723	+	0.107805i	0.403724	+	0.914881i	$0.367715\pi$
$278$	−4.05001	−	4.05001i	−0.242904	−	0.242904i
$279$	−14.6352	−	12.0215i	−0.876189	−	0.719710i
$280$	3.63397	−	13.5622i	0.217172	−	0.810495i
$281$	15.9006	−	15.9006i	0.948547	−	0.948547i	−0.0501922	−	0.998740i	$-0.515983\pi$
$281$	15.9006	−	15.9006i	0.948547	−	0.948547i	0.998740	+	0.0501922i	$0.0159834\pi$
$282$	−37.8117	+	12.1400i	−2.25166	+	0.722928i
$283$	21.2942	+	12.2942i	1.26581	+	0.730816i	0.974192	−	0.225719i	$-0.0724731\pi$
$283$	21.2942	+	12.2942i	1.26581	+	0.730816i	0.291618	+	0.956535i	$0.405806\pi$
$284$	4.62518	+	17.2614i	0.274454	+	1.02428i
$285$	−0.907241	+	4.19615i	−0.0537403	+	0.248559i
$286$		0			0
$287$			0.907241i			0.0535527i
$288$	7.08606	+	1.17309i	0.417550	+	0.0691251i
$289$	6.19615	−	10.7321i	0.364480	−	0.631297i
$290$	−15.8561	−	27.4635i	−0.931100	−	1.61271i
$291$	−12.2025	−	18.9345i	−0.715320	−	1.10996i
$292$	31.0885	+	8.33013i	1.81931	+	0.487484i
$293$	21.2669	+	5.69846i	1.24243	+	0.332908i	0.819407	−	0.573212i	$-0.194303\pi$
$293$	21.2669	+	5.69846i	1.24243	+	0.332908i	0.423021	+	0.906120i	$0.360970\pi$
$294$	11.2318	+	17.4284i	0.655054	+	1.01645i
$295$	−5.73205	−	9.92820i	−0.333733	−	0.578042i
$296$	14.1631	−	24.5313i	0.823215	−	1.42585i
$297$	8.46753	+	3.35253i	0.491336	+	0.194534i
$298$			13.0000i			0.753070i
$299$		0			0
$300$	1.00000	−	4.62518i	0.0577350	−	0.267035i
$301$	−3.00000	−	11.1962i	−0.172917	−	0.645335i
$302$	21.8866	+	12.6362i	1.25943	+	0.727133i
$303$	32.5540	−	10.4520i	1.87018	−	0.600449i
$304$	−1.80385	+	1.80385i	−0.103458	+	0.103458i
$305$	−4.33760	+	16.1881i	−0.248370	+	0.926930i
$306$	−9.78605	+	11.9137i	−0.559431	+	0.681063i
$307$	12.3923	+	12.3923i	0.707266	+	0.707266i	0.965960	−	0.258693i	$-0.0832919\pi$
$307$	12.3923	+	12.3923i	0.707266	+	0.707266i	−0.258693	+	0.965960i	$0.583292\pi$
$308$	−8.01105	+	4.62518i	−0.456472	+	0.263544i
$309$	−8.06065	+	8.88965i	−0.458554	+	0.505715i
$310$	34.9545	−	9.36603i	1.98528	−	0.531954i
$311$	−4.29311			−0.243440			−0.121720	−	0.992564i	$-0.538841\pi$
$311$	−4.29311			−0.243440			−0.121720	+	0.992564i	$0.538841\pi$
$312$		0			0
$313$	2.00000			0.113047			0.0565233	−	0.998401i	$-0.481998\pi$
$313$	2.00000			0.113047			0.0565233	+	0.998401i	$0.481998\pi$
$314$	35.1425	−	9.41640i	1.98321	−	0.531398i
$315$	−5.91297	−	8.25916i	−0.333158	−	0.465351i
$316$	6.46410	−	3.73205i	0.363634	−	0.209944i
$317$	11.2754	+	11.2754i	0.633288	+	0.633288i	0.948891	−	0.315603i	$-0.102207\pi$
$317$	11.2754	+	11.2754i	0.633288	+	0.633288i	−0.315603	+	0.948891i	$0.602207\pi$
$318$	−8.76706	+	17.0588i	−0.491632	+	0.956612i
$319$	−2.50962	+	9.36603i	−0.140512	+	0.524397i
$320$	−18.0471	+	18.0471i	−1.00886	+	1.00886i
$321$	−8.83503	−	27.5179i	−0.493123	−	1.53590i
$322$		0			0
$323$	0.575167	+	2.14655i	0.0320032	+	0.119437i
$324$	−25.2725	+	22.1244i	−1.40403	+	1.22913i
$325$		0			0
$326$		−	37.0015i		−	2.04932i
$327$	−6.85980	+	0.335500i	−0.379348	+	0.0185532i
$328$	−1.33013	+	2.30385i	−0.0734440	+	0.127209i
$329$	−6.77174	−	11.7290i	−0.373338	−	0.646640i
$330$	−14.6265	+	9.42610i	−0.805160	+	0.518890i
$331$	18.8564	+	5.05256i	1.03644	+	0.277714i	0.736638	−	0.676287i	$-0.236412\pi$
$331$	18.8564	+	5.05256i	1.03644	+	0.277714i	0.299804	+	0.954001i	$0.403079\pi$
$332$	−6.31812	−	1.69293i	−0.346752	−	0.0929118i
$333$	−7.21011	−	19.1822i	−0.395112	−	1.05118i
$334$	14.1244	+	24.4641i	0.772850	+	1.33862i
$335$	10.4897	−	18.1687i	0.573112	−	0.992660i
$336$	−0.294847	−	6.02859i	−0.0160852	−	0.328886i
$337$		−	11.5359i		−	0.628400i	−0.949357	−	0.314200i	$-0.898264\pi$
$337$		−	11.5359i		−	0.628400i	0.949357	−	0.314200i	$-0.101736\pi$
$338$		0			0
$339$	21.9545	+	4.74673i	1.19240	+	0.257807i
$340$	−4.96410	−	18.5263i	−0.269216	−	1.00473i
$341$	−9.58244	−	5.53242i	−0.518918	−	0.299597i
$342$	0.725614	+	7.40039i	0.0392367	+	0.400167i
$343$	−12.0000	+	12.0000i	−0.647939	+	0.647939i
$344$	8.79674	−	32.8299i	0.474289	−	1.77007i
$345$		0			0
$346$	12.5885	+	12.5885i	0.676760	+	0.676760i
$347$	22.4618	−	12.9683i	1.20581	−	0.696175i	0.243969	−	0.969783i	$-0.421550\pi$
$347$	22.4618	−	12.9683i	1.20581	−	0.696175i	0.961841	+	0.273608i	$0.0882171\pi$
$348$	−26.4928	−	24.0222i	−1.42016	−	1.28772i
$349$	5.63397	−	1.50962i	0.301580	−	0.0808080i	−0.104856	−	0.994487i	$-0.533438\pi$
$349$	5.63397	−	1.50962i	0.301580	−	0.0808080i	0.406436	+	0.913679i	$0.366772\pi$
$350$	2.47863			0.132488
$351$		0			0
$352$	4.19615			0.223656
$353$	−26.3457	+	7.05932i	−1.40224	+	0.375730i	−0.879149	−	0.476546i	$-0.841889\pi$
$353$	−26.3457	+	7.05932i	−1.40224	+	0.375730i	−0.523093	+	0.852276i	$0.675222\pi$
$354$	−14.7097	−	13.3380i	−0.781813	−	0.708904i
$355$	−9.92820	+	5.73205i	−0.526934	+	0.304226i
$356$	26.5118	+	26.5118i	1.40512	+	1.40512i
$357$	−4.67652	−	2.40340i	−0.247508	−	0.127202i
$358$	−11.6147	+	43.3468i	−0.613858	+	2.29095i
$359$	−12.0611	+	12.0611i	−0.636559	+	0.636559i	−0.949705	−	0.313146i	$-0.898617\pi$
$359$	−12.0611	+	12.0611i	−0.636559	+	0.636559i	0.313146	+	0.949705i	$0.398617\pi$
$360$	−2.90646	−	29.6425i	−0.153184	−	1.56229i
$361$	−15.5263	−	8.96410i	−0.817173	−	0.471795i
$362$	−1.85897	−	6.93777i	−0.0977053	−	0.364641i
$363$	−13.4219	−	2.90192i	−0.704468	−	0.152311i
$364$		0			0
$365$			20.6473i			1.08073i
$366$	1.41800	+	28.9931i	0.0741199	+	1.51549i
$367$	−4.80385	+	8.32051i	−0.250759	+	0.434327i	−0.963735	−	0.266861i	$-0.914013\pi$
$367$	−4.80385	+	8.32051i	−0.250759	+	0.434327i	0.712976	+	0.701188i	$0.247347\pi$
$368$		0			0
$369$	0.677136	+	1.80149i	0.0352503	+	0.0937819i
$370$	37.8205	+	10.1340i	1.96619	+	0.526840i
$371$	−6.31812	−	1.69293i	−0.328020	−	0.0878928i
$372$	34.3028	−	22.1066i	1.77852	−	1.14618i
$373$	9.79423	+	16.9641i	0.507126	+	0.878368i	0.999966	+	0.00824796i	$0.00262544\pi$
$373$	9.79423	+	16.9641i	0.507126	+	0.878368i	−0.492840	+	0.870120i	$0.664041\pi$
$374$	−4.50363	+	7.80052i	−0.232877	+	0.403355i
$375$	−17.6773	+	0.864563i	−0.912852	+	0.0446459i
$376$		−	39.7128i		−	2.04803i
$377$		0			0
$378$	−14.1244	−	10.4897i	−0.726478	−	0.539531i
$379$	−1.29423	−	4.83013i	−0.0664801	−	0.248107i	0.924687	−	0.380729i	$-0.124327\pi$
$379$	−1.29423	−	4.83013i	−0.0664801	−	0.248107i	−0.991167	+	0.132622i	$0.957660\pi$
$380$	−8.01105	−	4.62518i	−0.410958	−	0.237267i
$381$	8.00804	+	24.9421i	0.410264	+	1.27782i
$382$	32.8564	−	32.8564i	1.68108	−	1.68108i
$383$	3.62896	−	13.5435i	0.185431	−	0.692039i	−0.809106	−	0.587662i	$-0.800048\pi$
$383$	3.62896	−	13.5435i	0.185431	−	0.692039i	0.994538	−	0.104377i	$-0.0332849\pi$
$384$	−16.4156	+	31.9412i	−0.837703	+	1.62999i
$385$	−4.19615	−	4.19615i	−0.213856	−	0.213856i
$386$	−14.9488	+	8.63071i	−0.760875	+	0.439291i
$387$	−14.3135	−	19.9929i	−0.727596	−	1.01630i
$388$	46.8827	−	12.5622i	2.38011	−	0.637748i
$389$	5.28933			0.268180			0.134090	−	0.990969i	$-0.457189\pi$
$389$	5.28933			0.268180			0.134090	+	0.990969i	$0.457189\pi$
$390$		0			0
$391$		0			0
$392$	−20.0276	+	5.36639i	−1.01155	+	0.271043i
$393$	1.05553	−	1.16409i	0.0532446	−	0.0587206i
$394$	−3.63397	+	2.09808i	−0.183077	+	0.105700i
$395$	3.38587	+	3.38587i	0.170362	+	0.170362i
$396$	−12.4553	+	15.1633i	−0.625903	+	0.761986i
$397$	2.29423	−	8.56218i	0.115144	−	0.429723i	−0.884154	−	0.467196i	$-0.845264\pi$
$397$	2.29423	−	8.56218i	0.115144	−	0.429723i	0.999298	+	0.0374729i	$0.0119308\pi$
$398$	1.57139	−	1.57139i	0.0787665	−	0.0787665i
$399$	−2.41450	+	0.775212i	−0.120876	+	0.0388091i
$400$	1.56218	+	0.901924i	0.0781089	+	0.0450962i
$401$	−7.26985	−	27.1314i	−0.363039	−	1.35488i	−0.870060	−	0.492946i	$-0.835920\pi$
$401$	−7.26985	−	27.1314i	−0.363039	−	1.35488i	0.507021	−	0.861933i	$-0.330747\pi$
$402$	7.67898	−	35.5167i	0.382993	−	1.77141i
$403$		0			0
$404$			73.6708i			3.66526i
$405$	−17.9057	−	11.9868i	−0.889739	−	0.595629i
$406$	9.36603	−	16.2224i	0.464828	−	0.805106i
$407$	−5.98604	−	10.3681i	−0.296717	−	0.513929i
$408$	−8.35187	−	12.9596i	−0.413479	−	0.641594i
$409$	11.2321	+	3.00962i	0.555389	+	0.148816i	0.525587	−	0.850740i	$-0.323846\pi$
$409$	11.2321	+	3.00962i	0.555389	+	0.148816i	0.0298020	+	0.999556i	$0.490512\pi$
$410$	−3.55190	−	0.951730i	−0.175416	−	0.0470026i
$411$	5.53528	+	8.58908i	0.273035	+	0.423668i
$412$	−12.9282	−	22.3923i	−0.636927	−	1.10319i
$413$	3.38587	−	5.86450i	0.166608	−	0.288573i
$414$		0			0
$415$		−	4.19615i		−	0.205981i
$416$		0			0
$417$	0.875644	−	4.05001i	0.0428805	−	0.198330i
$418$	1.12436	+	4.19615i	0.0549940	+	0.205241i
$419$	−7.22536	−	4.17156i	−0.352982	−	0.203794i	0.313016	−	0.949748i	$-0.398661\pi$
$419$	−7.22536	−	4.17156i	−0.352982	−	0.203794i	−0.665998	+	0.745954i	$0.731994\pi$
$420$	20.8389	−	6.69063i	1.01683	−	0.326469i
$421$	−0.830127	+	0.830127i	−0.0404579	+	0.0404579i	−0.727046	−	0.686588i	$-0.759107\pi$
$421$	−0.830127	+	0.830127i	−0.0404579	+	0.0404579i	0.686588	+	0.727046i	$0.259107\pi$
$422$	−7.55743	+	28.2047i	−0.367890	+	1.37298i
$423$	−22.2007	−	18.2358i	−1.07943	−	0.886657i
$424$	−13.5622	−	13.5622i	−0.658638	−	0.658638i
$425$	1.36086	−	0.785693i	0.0660114	−	0.0381117i
$426$	−13.3380	+	14.7097i	−0.646226	+	0.712688i
$427$	−9.56218	+	2.56218i	−0.462746	+	0.123992i
$428$	62.2739			3.01012
$429$		0			0
$430$	46.9808			2.26561
$431$	−2.02501	+	0.542599i	−0.0975412	+	0.0261361i	−0.307260	−	0.951626i	$-0.599412\pi$
$431$	−2.02501	+	0.542599i	−0.0975412	+	0.0261361i	0.209718	+	0.977762i	$0.432745\pi$
$432$	−5.08502	−	11.7508i	−0.244653	−	0.565360i
$433$	6.10770	−	3.52628i	0.293517	−	0.169462i	−0.346010	−	0.938231i	$-0.612464\pi$
$433$	6.10770	−	3.52628i	0.293517	−	0.169462i	0.639527	+	0.768769i	$0.279130\pi$
$434$	15.1149	+	15.1149i	0.725536	+	0.725536i
$435$	10.4867	−	20.4050i	0.502800	−	0.978344i
$436$	3.83013	−	14.2942i	0.183430	−	0.684569i
$437$		0			0
$438$	10.9323	+	34.0502i	0.522366	+	1.62698i
$439$	4.09808	+	2.36603i	0.195591	+	0.112924i	0.594597	−	0.804024i	$-0.297312\pi$
$439$	4.09808	+	2.36603i	0.195591	+	0.112924i	−0.399007	+	0.916948i	$0.630645\pi$
$440$	−4.50363	−	16.8078i	−0.214702	−	0.801280i
$441$	−6.19657	+	13.6603i	−0.295075	+	0.650488i
$442$		0			0
$443$		−	29.5656i		−	1.40470i	−0.711830	−	0.702351i	$-0.752134\pi$
$443$		−	29.5656i		−	1.40470i	0.711830	−	0.702351i	$-0.247866\pi$
$444$	44.1025	−	2.15697i	2.09301	−	0.102365i
$445$	−12.0263	+	20.8301i	−0.570100	+	0.987443i
$446$	−27.6295	−	47.8558i	−1.30830	−	2.26604i
$447$	−7.90535	+	5.09465i	−0.373910	+	0.240969i
$448$	−14.5622	−	3.90192i	−0.687998	−	0.184349i
$449$	8.46467	+	2.26810i	0.399472	+	0.107038i	0.452961	−	0.891530i	$-0.350368\pi$
$449$	8.46467	+	2.26810i	0.399472	+	0.107038i	−0.0534890	+	0.998568i	$0.517034\pi$
$450$	4.92177	−	1.84997i	0.232014	−	0.0872084i
$451$	0.562178	+	0.973721i	0.0264719	+	0.0458507i
$452$	−24.1992	+	41.9142i	−1.13823	+	1.97148i
$453$	0.893131	+	18.2614i	0.0419629	+	0.857996i
$454$			37.4641i			1.75828i
$455$		0			0
$456$	−7.26795	−	1.57139i	−0.340353	−	0.0735869i
$457$	−7.23205	−	26.9904i	−0.338301	−	1.26256i	−0.900246	−	0.435382i	$-0.856613\pi$
$457$	−7.23205	−	26.9904i	−0.338301	−	1.26256i	0.561945	−	0.827175i	$-0.310053\pi$
$458$	29.6871	+	17.1399i	1.38719	+	0.800893i
$459$	−11.0799	−	1.28199i	−0.517166	−	0.0598382i
$460$		0			0
$461$	6.27363	−	23.4135i	0.292192	−	1.09048i	−0.651230	−	0.758880i	$-0.725747\pi$
$461$	6.27363	−	23.4135i	0.292192	−	1.09048i	0.943422	−	0.331595i	$-0.107587\pi$
$462$	−9.14181	−	4.69825i	−0.425315	−	0.218582i
$463$	15.0526	+	15.0526i	0.699552	+	0.699552i	0.964314	−	0.264762i	$-0.0852934\pi$
$463$	15.0526	+	15.0526i	0.699552	+	0.699552i	−0.264762	+	0.964314i	$0.585293\pi$
$464$	11.8060	−	6.81623i	0.548082	−	0.316435i
$465$	19.3940	+	17.5854i	0.899377	+	0.815506i
$466$	−17.1962	+	4.60770i	−0.796596	+	0.213447i
$467$	30.4728			1.41011			0.705057	−	0.709151i	$-0.250921\pi$
$467$	30.4728			1.41011			0.705057	+	0.709151i	$0.250921\pi$
$468$		0			0
$469$	12.3923			0.572223
$470$	53.0236	−	14.2076i	2.44579	−	0.655349i
$471$	19.4984	+	17.6800i	0.898437	+	0.814653i
$472$	17.1962	−	9.92820i	0.791517	−	0.456983i
$473$	−10.1576	−	10.1576i	−0.467047	−	0.467047i
$474$	7.37651	+	3.79101i	0.338814	+	0.174127i
$475$	0.196152	−	0.732051i	0.00900009	−	0.0335888i
$476$	8.01105	−	8.01105i	0.367186	−	0.367186i
$477$	−13.8093	+	1.35401i	−0.632285	+	0.0619960i
$478$	20.8301	+	12.0263i	0.952748	+	0.550069i
$479$	−2.26810	−	8.46467i	−0.103632	−	0.386761i	0.894554	−	0.446959i	$-0.147493\pi$
$479$	−2.26810	−	8.46467i	−0.103632	−	0.386761i	−0.998186	+	0.0601988i	$0.980827\pi$
$480$	−9.70398	−	2.09808i	−0.442924	−	0.0957636i
$481$		0			0
$482$			17.9256i			0.816487i
$483$		0			0
$484$	14.7942	−	25.6244i	0.672465	−	1.16474i
$485$	15.5685	+	26.9654i	0.706928	+	1.22444i
$486$	−35.8756	−	10.2872i	−1.62735	−	0.466636i
$487$	−24.4904	−	6.56218i	−1.10977	−	0.297361i	−0.343030	−	0.939324i	$-0.611453\pi$
$487$	−24.4904	−	6.56218i	−1.10977	−	0.297361i	−0.766735	+	0.641964i	$0.778120\pi$
$488$	−28.0387	−	7.51294i	−1.26925	−	0.340095i
$489$	22.5007	−	14.5007i	1.01752	−	0.655746i
$490$	−14.3301	−	24.8205i	−0.647369	−	1.12128i
$491$	12.5147	−	21.6761i	0.564780	−	0.978227i	−0.432290	−	0.901734i	$-0.642294\pi$
$491$	12.5147	−	21.6761i	0.564780	−	0.978227i	0.997070	−	0.0764928i	$-0.0243722\pi$
$492$	−4.14187	+	0.202571i	−0.186730	+	0.00913261i
$493$		−	11.8756i		−	0.534852i
$494$		0			0
$495$	−11.4641	−	5.20035i	−0.515273	−	0.233738i
$496$	4.02628	+	15.0263i	0.180785	+	0.674700i
$497$	−5.86450	−	3.38587i	−0.263059	−	0.151877i
$498$	−2.22178	−	6.92003i	−0.0995602	−	0.310094i
$499$	−4.46410	+	4.46410i	−0.199841	+	0.199841i	−0.799932	−	0.600091i	$-0.795131\pi$
$499$	−4.46410	+	4.46410i	−0.199841	+	0.199841i	0.600091	+	0.799932i	$0.295131\pi$
$500$	9.87002	−	36.8354i	0.441401	−	1.64733i
$501$	−9.34143	+	18.1765i	−0.417345	+	0.812064i
$502$	−37.0526	−	37.0526i	−1.65374	−	1.65374i
$503$	24.8188	−	14.3292i	1.10662	−	0.638906i	0.168666	−	0.985673i	$-0.446054\pi$
$503$	24.8188	−	14.3292i	1.10662	−	0.638906i	0.937951	+	0.346767i	$0.112721\pi$
$504$	14.3053	−	10.2416i	0.637208	−	0.456196i
$505$	−45.6506	+	12.2321i	−2.03143	+	0.544319i
$506$		0			0
$507$		0			0
$508$	−56.4449			−2.50434
$509$	14.4952	−	3.88398i	0.642489	−	0.172154i	0.0771582	−	0.997019i	$-0.475415\pi$
$509$	14.4952	−	3.88398i	0.642489	−	0.172154i	0.565330	+	0.824865i	$0.308749\pi$
$510$	14.3153	−	15.7876i	0.633893	−	0.699087i
$511$	−10.5622	+	6.09808i	−0.467243	+	0.269763i
$512$	−18.6223	−	18.6223i	−0.822996	−	0.822996i
$513$	−4.21584	+	3.34143i	−0.186134	+	0.147528i
$514$	10.2846	−	38.3827i	0.453635	−	1.69299i
$515$	11.7290	−	11.7290i	0.516841	−	0.516841i
$516$	50.4445	−	16.1960i	2.22070	−	0.712988i
$517$	−14.5359	−	8.39230i	−0.639288	−	0.369093i
$518$	5.98604	+	22.3402i	0.263012	+	0.981573i
$519$	−2.72172	+	12.5885i	−0.119470	+	0.552572i
$520$		0			0
$521$		−	33.2835i		−	1.45818i	−0.684419	−	0.729089i	$-0.739944\pi$
$521$		−	33.2835i		−	1.45818i	0.684419	−	0.729089i	$-0.260056\pi$
$522$	6.49004	−	39.2031i	0.284061	−	1.71587i
$523$	−6.49038	+	11.2417i	−0.283805	+	0.491564i	−0.972319	−	0.233659i	$-0.924930\pi$
$523$	−6.49038	+	11.2417i	−0.283805	+	0.491564i	0.688514	+	0.725223i	$0.258263\pi$
$524$	1.69293	+	2.93225i	0.0739562	+	0.128096i
$525$	0.971364	+	1.50726i	0.0423938	+	0.0657823i
$526$	−27.6865	−	7.41858i	−1.20719	−	0.323466i
$527$	13.0899	+	3.50742i	0.570203	+	0.152785i
$528$	−4.05211	−	6.28764i	−0.176345	−	0.273634i
$529$	11.5000	+	19.9186i	0.500000	+	0.866025i
$530$	13.2559	−	22.9599i	0.575799	−	0.997313i
$531$	2.34618	−	14.1721i	0.101816	−	0.615018i
$532$		−	5.46410i		−	0.236899i
$533$		0			0
$534$	−8.80385	+	40.7194i	−0.380980	+	1.76210i
$535$	10.3397	+	38.5885i	0.447026	+	1.66832i
$536$	31.4690	+	18.1687i	1.35926	+	0.784766i
$537$	−30.9111	+	9.92447i	−1.33391	+	0.428273i
$538$	−18.7321	+	18.7321i	−0.807596	+	0.807596i
$539$	−2.26810	+	8.46467i	−0.0976940	+	0.364599i
$540$	36.3857	−	28.8389i	1.56579	−	1.24103i
$541$	−23.6865	−	23.6865i	−1.01836	−	1.01836i	−0.999828	−	0.0185354i	$-0.994100\pi$
$541$	−23.6865	−	23.6865i	−1.01836	−	1.01836i	−0.0185354	−	0.999828i	$-0.505900\pi$
$542$	−4.29311	+	2.47863i	−0.184405	+	0.106466i
$543$	3.49036	−	3.84933i	0.149786	−	0.165191i
$544$	−4.96410	+	1.33013i	−0.212834	+	0.0570287i
$545$	9.49346			0.406655
$546$		0			0
$547$	2.00000			0.0855138			0.0427569	−	0.999086i	$-0.486386\pi$
$547$	2.00000			0.0855138			0.0427569	+	0.999086i	$0.486386\pi$
$548$	−21.2669	+	5.69846i	−0.908479	+	0.243426i
$549$	−17.0751	+	12.2246i	−0.728748	+	0.521732i
$550$	2.66025	−	1.53590i	0.113434	−	0.0654909i
$551$	−4.05001	−	4.05001i	−0.172536	−	0.172536i
$552$		0			0
$553$	−0.732051	+	2.73205i	−0.0311300	+	0.116179i
$554$	6.07502	−	6.07502i	0.258103	−	0.258103i
$555$	8.65920	+	26.9703i	0.367563	+	1.14482i
$556$	7.73205	+	4.46410i	0.327912	+	0.189320i
$557$	10.5342	+	39.3140i	0.446347	+	1.66579i	0.712355	+	0.701819i	$0.247628\pi$
$557$	10.5342	+	39.3140i	0.446347	+	1.66579i	−0.266009	+	0.963971i	$0.585705\pi$
$558$	41.2946	+	18.7321i	1.74814	+	0.792991i
$559$		0			0
$560$			8.34312i			0.352561i
$561$	−6.50849	+	0.318318i	−0.274788	+	0.0134394i
$562$	−26.9186	+	46.6244i	−1.13549	+	1.96673i
$563$	−2.14655	−	3.71794i	−0.0904665	−	0.156693i	0.817241	−	0.576296i	$-0.195502\pi$
$563$	−2.14655	−	3.71794i	−0.0904665	−	0.156693i	−0.907708	+	0.419603i	$0.862169\pi$
$564$	52.0350	−	33.5342i	2.19107	−	1.41205i
$565$	−29.9904	−	8.03590i	−1.26170	−	0.338073i
$566$	−56.8630	−	15.2364i	−2.39013	−	0.640434i
$567$	0.843533	−	12.6999i	0.0354250	−	0.533347i
$568$	−9.92820	−	17.1962i	−0.416578	−	0.721535i
$569$	−8.01105	+	13.8755i	−0.335841	+	0.581693i	−0.983646	−	0.180113i	$-0.942354\pi$
$569$	−8.01105	+	13.8755i	−0.335841	+	0.581693i	0.647805	+	0.761806i	$0.275687\pi$
$570$	−0.502098	−	10.2662i	−0.0210306	−	0.430002i
$571$			40.0526i			1.67615i	0.545557	+	0.838074i	$0.316318\pi$
$571$			40.0526i			1.67615i	−0.545557	+	0.838074i	$0.683682\pi$
$572$		0			0
$573$	32.8564	+	7.10381i	1.37260	+	0.296766i
$574$	−0.562178	−	2.09808i	−0.0234648	−	0.0875720i
$575$		0			0
$576$	−31.8281	+	3.12077i	−1.32617	+	0.130032i
$577$	−3.49038	+	3.49038i	−0.145306	+	0.145306i	−0.776018	−	0.630711i	$-0.782763\pi$
$577$	−3.49038	+	3.49038i	−0.145306	+	0.145306i	0.630711	+	0.776018i	$0.282763\pi$
$578$	−7.67898	+	28.6583i	−0.319403	+	1.19203i
$579$	−11.1068	−	5.70810i	−0.461581	−	0.237220i
$580$	34.9545	+	34.9545i	1.45141	+	1.45141i
$581$	2.14655	−	1.23931i	0.0890541	−	0.0514154i
$582$	39.9522	+	36.2264i	1.65607	+	1.50163i
$583$	−7.83013	+	2.09808i	−0.324291	+	0.0868934i
$584$	−35.7621			−1.47985
$585$		0			0
$586$	−52.7128			−2.17755
$587$	−19.4080	+	5.20035i	−0.801053	+	0.214641i	−0.636046	−	0.771651i	$-0.719431\pi$
$587$	−19.4080	+	5.20035i	−0.801053	+	0.214641i	−0.165006	+	0.986292i	$0.552765\pi$
$588$	−23.9432	−	21.7104i	−0.987400	−	0.895320i
$589$	5.66025	−	3.26795i	0.233227	−	0.134654i
$590$	19.4080	+	19.4080i	0.799013	+	0.799013i
$591$	−2.69999	−	1.38761i	−0.111063	−	0.0570785i
$592$	−4.35641	+	16.2583i	−0.179047	+	0.668213i
$593$	10.6112	−	10.6112i	0.435751	−	0.435751i	−0.454828	−	0.890579i	$-0.650299\pi$
$593$	10.6112	−	10.6112i	0.435751	−	0.435751i	0.890579	+	0.454828i	$0.150299\pi$
$594$	−21.6593	−	2.50608i	−0.888694	−	0.102826i
$595$	6.29423	+	3.63397i	0.258038	+	0.148978i
$596$	−5.24484	−	19.5740i	−0.214837	−	0.801782i
$597$	1.57139	+	0.339746i	0.0643126	+	0.0139049i
$598$		0			0
$599$			21.2224i			0.867126i	0.901123	+	0.433563i	$0.142744\pi$
$599$			21.2224i			0.867126i	−0.901123	+	0.433563i	$0.857256\pi$
$600$	0.256850	+	5.25169i	0.0104859	+	0.214399i
$601$	3.79423	−	6.57180i	0.154770	−	0.268069i	−0.778205	−	0.628010i	$-0.783870\pi$
$601$	3.79423	−	6.57180i	0.154770	−	0.268069i	0.932975	+	0.359941i	$0.117203\pi$
$602$	13.8755	+	24.0331i	0.565525	+	0.979518i
$603$	24.6072	−	9.24923i	1.00208	−	0.376658i
$604$	−38.0526	−	10.1962i	−1.54834	−	0.414876i
$605$	18.3347	+	4.91277i	0.745411	+	0.199732i
$606$	−68.8075	+	44.3434i	−2.79511	+	1.80133i
$607$	−5.09808	−	8.83013i	−0.206925	−	0.358404i	0.743820	−	0.668380i	$-0.233012\pi$
$607$	−5.09808	−	8.83013i	−0.206925	−	0.358404i	−0.950744	+	0.309977i	$0.899679\pi$
$608$	−1.23931	+	2.14655i	−0.0502608	+	0.0870543i
$609$	13.5354	−	0.661992i	0.548483	−	0.0268253i
$610$		−	40.1244i		−	1.62459i
$611$		0			0
$612$	9.92820	−	21.8866i	0.401324	−	0.884713i
$613$	4.38269	+	16.3564i	0.177015	+	0.660629i	0.996200	+	0.0870991i	$0.0277597\pi$
$613$	4.38269	+	16.3564i	0.177015	+	0.660629i	−0.819185	+	0.573530i	$0.805574\pi$
$614$	−36.3373	−	20.9794i	−1.46645	−	0.846658i
$615$	−0.813227	−	2.53291i	−0.0327925	−	0.102137i
$616$	7.26795	−	7.26795i	0.292834	−	0.292834i
$617$	−9.74847	+	36.3818i	−0.392459	+	1.46468i	0.433607	+	0.901102i	$0.357241\pi$
$617$	−9.74847	+	36.3818i	−0.392459	+	1.46468i	−0.826066	+	0.563574i	$0.809426\pi$
$618$	13.1324	−	25.5530i	0.528264	−	1.02789i
$619$	14.3397	+	14.3397i	0.576363	+	0.576363i	0.933899	−	0.357536i	$-0.116383\pi$
$619$	14.3397	+	14.3397i	0.576363	+	0.576363i	−0.357536	+	0.933899i	$0.616383\pi$
$620$	−48.8520	+	28.2047i	−1.96194	+	1.13273i
$621$		0			0
$622$	9.92820	−	2.66025i	0.398085	−	0.106666i
$623$	−14.2076			−0.569216
$624$		0			0
$625$	28.1244			1.12497
$626$	−4.62518	+	1.23931i	−0.184859	+	0.0495329i
$627$	−2.11107	+	2.32818i	−0.0843078	+	0.0929786i
$628$	−49.1147	+	28.3564i	−1.95989	+	1.13154i
$629$	10.3681	+	10.3681i	0.413404	+	0.413404i
$630$	18.7921	+	15.4360i	0.748696	+	0.614986i
$631$	0.607695	−	2.26795i	0.0241920	−	0.0902856i	−0.952774	−	0.303679i	$-0.901785\pi$
$631$	0.607695	−	2.26795i	0.0241920	−	0.0902856i	0.976966	+	0.213393i	$0.0684516\pi$
$632$	−5.86450	+	5.86450i	−0.233277	+	0.233277i
$633$	−20.1131	+	6.45761i	−0.799425	+	0.256667i
$634$	−33.0622	−	19.0885i	−1.31307	−	0.758099i
$635$	−9.37191	−	34.9764i	−0.371913	−	1.38800i
$636$	6.31812	−	29.2224i	0.250530	−	1.15874i
$637$		0			0
$638$		−	23.2149i		−	0.919086i
$639$	−14.1721	−	2.34618i	−0.560641	−	0.0928136i
$640$	24.8205	−	42.9904i	0.981117	−	1.69934i
$641$	9.65949	+	16.7307i	0.381527	+	0.660824i	0.991281	−	0.131767i	$-0.0420650\pi$
$641$	9.65949	+	16.7307i	0.381527	+	0.660824i	−0.609754	+	0.792591i	$0.708732\pi$
$642$	37.4835	+	58.1629i	1.47935	+	2.29551i
$643$	26.1244	+	7.00000i	1.03024	+	0.276053i	0.734065	−	0.679079i	$-0.237621\pi$
$643$	26.1244	+	7.00000i	1.03024	+	0.276053i	0.296179	+	0.955132i	$0.404287\pi$
$644$		0			0
$645$	18.4116	+	28.5692i	0.724955	+	1.12491i
$646$	−2.66025	−	4.60770i	−0.104666	−	0.181287i
$647$	−7.22536	+	12.5147i	−0.284058	+	0.492003i	−0.972380	−	0.233402i	$-0.925014\pi$
$647$	−7.22536	+	12.5147i	−0.284058	+	0.492003i	0.688322	+	0.725405i	$0.258348\pi$
$648$	20.7618	−	31.0135i	0.815599	−	1.21833i
$649$		−	8.39230i		−	0.329427i
$650$		0			0
$651$	−3.26795	+	15.1149i	−0.128081	+	0.592398i
$652$	14.9282	+	55.7128i	0.584634	+	2.18188i
$653$	−33.6156	−	19.4080i	−1.31548	−	0.759492i	−0.332482	−	0.943110i	$-0.607886\pi$
$653$	−33.6156	−	19.4080i	−1.31548	−	0.759492i	−0.982998	+	0.183617i	$0.941219\pi$
$654$	15.6560	−	5.02659i	0.612198	−	0.196555i
$655$	−1.53590	+	1.53590i	−0.0600125	+	0.0600125i
$656$	0.409131	−	1.52690i	0.0159739	−	0.0596153i
$657$	−16.4217	+	19.9921i	−0.640672	+	0.779967i
$658$	22.9282	+	22.9282i	0.893834	+	0.893834i
$659$	27.1759	−	15.6900i	1.05862	−	0.611197i	0.133572	−	0.991039i	$-0.457355\pi$
$659$	27.1759	−	15.6900i	1.05862	−	0.611197i	0.925051	+	0.379842i	$0.124022\pi$
$660$	18.2200	−	20.0938i	0.709212	−	0.782152i
$661$	−16.5263	+	4.42820i	−0.642798	+	0.172237i	−0.565470	−	0.824769i	$-0.691305\pi$
$661$	−16.5263	+	4.42820i	−0.642798	+	0.172237i	−0.0773274	+	0.997006i	$0.524639\pi$
$662$	−46.7380			−1.81652
$663$		0			0
$664$	7.26795			0.282051
$665$	3.38587	−	0.907241i	0.131298	−	0.0351813i
$666$	28.5604	+	39.8928i	1.10669	+	1.54581i
$667$		0			0
$668$	−31.1370	−	31.1370i	−1.20473	−	1.20473i
$669$	18.2734	−	35.5561i	0.706489	−	1.37468i
$670$	−13.0000	+	48.5167i	−0.502234	+	1.87436i
$671$	−8.67520	+	8.67520i	−0.334902	+	0.334902i
$672$	−1.79275	−	5.58376i	−0.0691568	−	0.215398i
$673$	11.0096	+	6.35641i	0.424390	+	0.245021i	0.696954	−	0.717116i	$-0.254538\pi$
$673$	11.0096	+	6.35641i	0.424390	+	0.245021i	−0.272564	+	0.962138i	$0.587872\pi$
$674$	7.14830	+	26.6778i	0.275342	+	1.02759i
$675$	3.05379	+	2.26795i	0.117541	+	0.0872934i
$676$		0			0
$677$			38.8159i			1.49182i	0.666048	+	0.745909i	$0.267985\pi$
$677$			38.8159i			1.49182i	−0.666048	+	0.745909i	$0.732015\pi$
$678$	−53.7131	+	2.62700i	−2.06284	+	0.100889i
$679$	−9.19615	+	15.9282i	−0.352916	+	0.611268i
$680$	10.6557	+	18.4562i	0.408628	+	0.707764i
$681$	−22.7821	+	14.6820i	−0.873011	+	0.562617i
$682$	25.5885	+	6.85641i	0.979833	+	0.262545i
$683$	15.9006	+	4.26054i	0.608418	+	0.163025i	0.549857	−	0.835259i	$-0.314682\pi$
$683$	15.9006	+	4.26054i	0.608418	+	0.163025i	0.0585607	+	0.998284i	$0.481349\pi$
$684$	−4.07823	−	10.8500i	−0.155935	−	0.414859i
$685$	−7.06218	−	12.2321i	−0.269832	−	0.467363i
$686$	20.3152	−	35.1870i	0.775638	−	1.34344i
$687$	1.21145	+	24.7699i	0.0462196	+	0.945031i
$688$			20.1962i			0.769971i
$689$		0			0
$690$		0			0
$691$	−11.2224	−	41.8827i	−0.426921	−	1.59329i	−0.759691	−	0.650284i	$-0.774650\pi$
$691$	−11.2224	−	41.8827i	−0.426921	−	1.59329i	0.332770	−	0.943008i	$-0.392017\pi$
$692$	−24.0331	−	13.8755i	−0.913603	−	0.527469i
$693$	−0.725614	−	7.40039i	−0.0275638	−	0.281118i
$694$	−43.9090	+	43.9090i	−1.66676	+	1.66676i
$695$	−1.48241	+	5.53242i	−0.0562309	+	0.209857i
$696$	35.3425	+	18.1636i	1.33965	+	0.688488i
$697$	−0.973721	−	0.973721i	−0.0368823	−	0.0368823i
$698$	−12.0936	+	6.98226i	−0.457751	+	0.264283i
$699$	−9.54106	−	8.65131i	−0.360876	−	0.327223i
$700$	−3.73205	+	1.00000i	−0.141058	+	0.0377964i
$701$	−20.3152			−0.767295			−0.383647	−	0.923480i	$-0.625332\pi$
$701$	−20.3152			−0.767295			−0.383647	+	0.923480i	$0.625332\pi$
$702$		0			0
$703$	7.07180			0.266718
$704$	−18.0471	+	4.83571i	−0.680176	+	0.182253i
$705$	29.4194	+	26.6759i	1.10800	+	1.00467i
$706$	56.5526	−	32.6506i	2.12838	−	1.22882i
$707$	−19.7400	−	19.7400i	−0.742401	−	0.742401i
$708$	27.5295	+	14.1482i	1.03462	+	0.531724i
$709$	−2.66987	+	9.96410i	−0.100269	+	0.374210i	−0.997766	−	0.0668121i	$-0.978717\pi$
$709$	−2.66987	+	9.96410i	−0.100269	+	0.374210i	0.897496	+	0.441022i	$0.145384\pi$
$710$	19.4080	−	19.4080i	0.728368	−	0.728368i
$711$	0.585497	+	5.97136i	0.0219578	+	0.223944i
$712$	−36.0788	−	20.8301i	−1.35211	−	0.780642i
$713$		0			0
$714$	12.3042	+	2.66025i	0.460472	+	0.0995575i
$715$		0			0
$716$		−	69.9529i		−	2.61426i
$717$	0.850019	+	17.3799i	0.0317446	+	0.649065i
$718$	20.4186	−	35.3660i	0.762015	−	1.31985i
$719$	5.86450	+	10.1576i	0.218709	+	0.378815i	0.954413	−	0.298488i	$-0.0964822\pi$
$719$	5.86450	+	10.1576i	0.218709	+	0.378815i	−0.735705	+	0.677302i	$0.763149\pi$
$720$	6.22704	+	16.5668i	0.232068	+	0.617408i
$721$	9.46410	+	2.53590i	0.352462	+	0.0944418i
$722$	41.4606	+	11.1093i	1.54300	+	0.413447i
$723$	−10.9006	+	7.02496i	−0.405398	+	0.261261i
$724$	5.59808	+	9.69615i	0.208051	+	0.360355i
$725$	−2.02501	+	3.50742i	−0.0752069	+	0.130262i
$726$	32.8376	−	1.60603i	1.21872	−	0.0596052i
$727$			25.5167i			0.946361i	0.880966	+	0.473180i	$0.156894\pi$
$727$			25.5167i			0.946361i	−0.880966	+	0.473180i	$0.843106\pi$
$728$		0			0
$729$	−7.80385	−	25.8476i	−0.289031	−	0.957320i
$730$	−12.7942	−	47.7487i	−0.473536	−	1.76726i
$731$	15.2364	+	8.79674i	0.563539	+	0.325359i
$732$	−13.8323	−	43.0826i	−0.511257	−	1.59238i
$733$	36.2224	−	36.2224i	1.33791	−	1.33791i	0.439820	−	0.898086i	$-0.355042\pi$
$733$	36.2224	−	36.2224i	1.33791	−	1.33791i	0.898086	−	0.439820i	$-0.144958\pi$
$734$	5.95347	−	22.2187i	0.219747	−	0.820106i
$735$	9.47753	−	18.4413i	0.349584	−	0.680216i
$736$		0			0
$737$	13.3004	−	7.67898i	0.489926	−	0.282859i
$738$	−2.68224	−	3.74652i	−0.0987348	−	0.137911i
$739$	48.9808	−	13.1244i	1.80179	−	0.482787i	0.807531	−	0.589825i	$-0.200803\pi$
$739$	48.9808	−	13.1244i	1.80179	−	0.482787i	0.994255	+	0.107037i	$0.0341364\pi$
$740$	−61.0346			−2.24368
$741$		0			0
$742$	15.6603			0.574906
$743$	50.5449	−	13.5435i	1.85431	−	0.496862i	0.854566	−	0.519343i	$-0.173823\pi$
$743$	50.5449	−	13.5435i	1.85431	−	0.496862i	0.999747	+	0.0224808i	$0.00715645\pi$
$744$	−30.4589	+	33.5915i	−1.11668	+	1.23152i
$745$	11.2583	−	6.50000i	0.412473	−	0.238142i
$746$	−33.1620	−	33.1620i	−1.21415	−	1.21415i
$747$	3.33739	−	4.06300i	0.122109	−	0.148658i
$748$	3.63397	−	13.5622i	0.132871	−	0.495882i
$749$	−16.6862	+	16.6862i	−0.609702	+	0.609702i
$750$	40.3446	−	12.9532i	1.47318	−	0.472986i
$751$	−38.2750	−	22.0981i	−1.39667	−	0.806370i	−0.402632	−	0.915362i	$-0.631904\pi$
$751$	−38.2750	−	22.0981i	−1.39667	−	0.806370i	−0.994043	+	0.108992i	$0.965238\pi$
$752$	6.10759	+	22.7938i	0.222721	+	0.831206i
$753$	8.01105	−	37.0526i	0.291939	−	1.35027i
$754$		0			0
$755$		−	25.2725i		−	0.919759i
$756$	25.4990	+	10.0958i	0.927389	+	0.367180i
$757$	12.3923	−	21.4641i	0.450406	−	0.780126i	−0.548005	−	0.836475i	$-0.684613\pi$
$757$	12.3923	−	21.4641i	0.450406	−	0.780126i	0.998411	+	0.0563489i	$0.0179459\pi$
$758$	5.98604	+	10.3681i	0.217423	+	0.376587i
$759$		0			0
$760$	9.92820	+	2.66025i	0.360134	+	0.0964976i
$761$	4.17156	+	1.11777i	0.151219	+	0.0405190i	0.333634	−	0.942703i	$-0.391725\pi$
$761$	4.17156	+	1.11777i	0.151219	+	0.0405190i	−0.182415	+	0.983222i	$0.558392\pi$
$762$	−33.9749	−	52.7187i	−1.23078	−	1.90980i
$763$	2.80385	+	4.85641i	0.101506	+	0.175814i
$764$	−36.2158	+	62.7275i	−1.31024	+	2.26940i
$765$	15.2106	+	2.51810i	0.549941	+	0.0910423i
$766$			33.5692i			1.21291i
$767$		0			0
$768$	10.3660	−	47.9447i	0.374052	−	1.73006i
$769$	−0.581416	−	2.16987i	−0.0209664	−	0.0782476i	0.954650	−	0.297730i	$-0.0962297\pi$
$769$	−0.581416	−	2.16987i	−0.0209664	−	0.0782476i	−0.975616	+	0.219483i	$0.929563\pi$
$770$	12.3042	+	7.10381i	0.443411	+	0.256004i
$771$	27.3712	−	8.78792i	0.985748	−	0.316489i
$772$	19.0263	−	19.0263i	0.684771	−	0.684771i
$773$	−1.60396	+	5.98604i	−0.0576903	+	0.215303i	−0.988753	−	0.149555i	$-0.952216\pi$
$773$	−1.60396	+	5.98604i	−0.0576903	+	0.215303i	0.931063	+	0.364858i	$0.118883\pi$
$774$	45.4900	+	37.3659i	1.63510	+	1.34309i
$775$	−3.26795	−	3.26795i	−0.117388	−	0.117388i
$776$	−46.7054	+	26.9654i	−1.67663	+	0.968001i
$777$	−11.2393	+	12.3952i	−0.403206	+	0.444675i
$778$	−12.2321	+	3.27757i	−0.438540	+	0.117507i
$779$	−0.664146			−0.0237955
$780$		0			0
$781$	−8.39230			−0.300300
$782$		0			0
$783$	26.3830	−	11.4169i	0.942851	−	0.408008i
$784$	10.6699	−	6.16025i	0.381067	−	0.220009i
$785$	−25.7261	−	25.7261i	−0.918203	−	0.918203i
$786$	−1.71968	+	3.34613i	−0.0613389	+	0.119353i
$787$	−3.02628	+	11.2942i	−0.107875	+	0.402596i	−0.998655	−	0.0518385i	$-0.983492\pi$
$787$	−3.02628	+	11.2942i	−0.107875	+	0.402596i	0.890780	+	0.454434i	$0.150159\pi$
$788$	4.62518	−	4.62518i	0.164765	−	0.164765i
$789$	−6.33898	−	19.7436i	−0.225674	−	0.702891i
$790$	−9.92820	−	5.73205i	−0.353230	−	0.203937i
$791$	−4.74673	−	17.7150i	−0.168774	−	0.629874i
$792$	9.00727	−	19.8564i	0.320059	−	0.705567i
$793$		0			0
$794$			21.2224i			0.753157i
$795$	19.1569	−	0.936928i	0.679426	−	0.0332294i
$796$	−1.73205	+	3.00000i	−0.0613909	+	0.106332i
$797$	−8.58622	−	14.8718i	−0.304139	−	0.526785i	0.672930	−	0.739706i	$-0.265036\pi$
$797$	−8.58622	−	14.8718i	−0.304139	−	0.526785i	−0.977069	+	0.212921i	$0.931702\pi$
$798$	5.10339	−	3.28891i	0.180658	−	0.116426i
$799$	19.8564	+	5.32051i	0.702469	+	0.188226i
$800$	1.69293	+	0.453620i	0.0598543	+	0.0160379i
$801$	−28.2118	+	10.6041i	−0.996815	+	0.374678i
$802$	33.6244	+	58.2391i	1.18732	+	2.05649i
$803$	−7.55743	+	13.0899i	−0.266696	+	0.461931i
$804$	2.76699	+	56.5752i	0.0975841	+	1.99526i
$805$		0			0
$806$		0			0
$807$	−18.7321	−	4.05001i	−0.659399	−	0.142567i
$808$	−21.1865	−	79.0692i	−0.745340	−	2.78165i
$809$	17.6705	+	10.2021i	0.621263	+	0.358686i	0.777361	−	0.629055i	$-0.216558\pi$
$809$	17.6705	+	10.2021i	0.621263	+	0.358686i	−0.156097	+	0.987742i	$0.549891\pi$
$810$	48.8362	+	16.6252i	1.71593	+	0.584150i
$811$	−19.0000	+	19.0000i	−0.667180	+	0.667180i	−0.957062	−	0.289882i	$-0.906384\pi$
$811$	−19.0000	+	19.0000i	−0.667180	+	0.667180i	0.289882	+	0.957062i	$0.406384\pi$
$812$	−7.55743	+	28.2047i	−0.265214	+	0.989791i
$813$	−3.18972	−	1.63929i	−0.111868	−	0.0574925i
$814$	20.2679	+	20.2679i	0.710391	+	0.710391i
$815$	−32.0442	+	18.5007i	−1.12246	+	0.648052i
$816$	6.78680	+	6.15389i	0.237585	+	0.215429i
$817$	8.19615	−	2.19615i	0.286747	−	0.0768336i
$818$	−27.8401			−0.973405
$819$		0			0
$820$	5.73205			0.200172
$821$	5.98604	−	1.60396i	0.208914	−	0.0559784i	−0.152844	−	0.988250i	$-0.548843\pi$
$821$	5.98604	−	1.60396i	0.208914	−	0.0559784i	0.361758	+	0.932272i	$0.382177\pi$
$822$	−18.1231	−	16.4330i	−0.632116	−	0.573168i
$823$	−13.3923	+	7.73205i	−0.466826	+	0.269522i	−0.714910	−	0.699216i	$-0.753532\pi$
$823$	−13.3923	+	7.73205i	−0.466826	+	0.269522i	0.248084	+	0.968739i	$0.420199\pi$
$824$	20.3152	+	20.3152i	0.707714	+	0.707714i
$825$	1.97653	+	1.01580i	0.0688139	+	0.0353656i
$826$	−4.19615	+	15.6603i	−0.146003	+	0.544890i
$827$	−3.62896	+	3.62896i	−0.126191	+	0.126191i	−0.767382	−	0.641190i	$-0.778441\pi$
$827$	−3.62896	+	3.62896i	−0.126191	+	0.126191i	0.641190	+	0.767382i	$0.278441\pi$
$828$		0			0
$829$	20.6769	+	11.9378i	0.718139	+	0.414618i	0.814067	−	0.580771i	$-0.197249\pi$
$829$	20.6769	+	11.9378i	0.718139	+	0.414618i	−0.0959284	+	0.995388i	$0.530582\pi$
$830$	2.60017	+	9.70398i	0.0902534	+	0.336830i
$831$	6.07502	+	1.31347i	0.210740	+	0.0455636i
$832$		0			0
$833$		−	10.7328i		−	0.371868i
$834$	0.484612	+	9.90862i	0.0167807	+	0.343108i
$835$	14.1244	−	24.4641i	0.488793	−	0.846615i
$836$	−3.38587	−	5.86450i	−0.117103	−	0.202828i
$837$	4.79215	+	32.4524i	0.165641	+	1.12172i
$838$	19.2942	+	5.16987i	0.666508	+	0.178590i
$839$	−7.55743	−	2.02501i	−0.260911	−	0.0699110i	0.125992	−	0.992031i	$-0.459789\pi$
$839$	−7.55743	−	2.02501i	−0.260911	−	0.0699110i	−0.386903	+	0.922120i	$0.626455\pi$
$840$	−20.4418	+	13.1738i	−0.705308	+	0.454540i
$841$	0.803848	+	1.39230i	0.0277189	+	0.0480105i
$842$	1.40535	−	2.43414i	0.0484316	−	0.0838859i
$843$	−38.9017	+	1.90261i	−1.33985	+	0.0655294i
$844$		−	45.5167i		−	1.56675i
$845$		0			0
$846$	62.6410	+	28.4152i	2.15364	+	0.976936i
$847$	2.90192	+	10.8301i	0.0997113	+	0.372128i
$848$	9.87002	+	5.69846i	0.338938	+	0.195686i
$849$	−13.0191	−	40.5497i	−0.446814	−	1.39166i
$850$	−2.66025	+	2.66025i	−0.0912460	+	0.0912460i
$851$		0			0
$852$	14.1482	−	27.5295i	0.484711	−	0.943145i
$853$	20.6340	+	20.6340i	0.706494	+	0.706494i	0.965796	−	0.259302i	$-0.0834926\pi$
$853$	20.6340	+	20.6340i	0.706494	+	0.706494i	−0.259302	+	0.965796i	$0.583493\pi$
$854$	20.5257	−	11.8505i	0.702376	−	0.405517i
$855$	6.04612	−	4.32860i	0.206773	−	0.148035i
$856$	−66.8372	+	17.9090i	−2.28445	+	0.612116i
$857$	35.7621			1.22161			0.610806	−	0.791781i	$-0.290846\pi$
$857$	35.7621			1.22161			0.610806	+	0.791781i	$0.290846\pi$
$858$		0			0
$859$	−23.1769			−0.790786			−0.395393	−	0.918512i	$-0.629392\pi$
$859$	−23.1769			−0.790786			−0.395393	+	0.918512i	$0.629392\pi$
$860$	−70.7386	+	18.9543i	−2.41217	+	0.646338i
$861$	1.05553	−	1.16409i	0.0359725	−	0.0396721i
$862$	4.34679	−	2.50962i	0.148052	−	0.0854780i
$863$	12.0611	+	12.0611i	0.410563	+	0.410563i	0.881935	−	0.471371i	$-0.156241\pi$
$863$	12.0611	+	12.0611i	0.410563	+	0.410563i	−0.471371	+	0.881935i	$0.656241\pi$
$864$	−7.72737	−	9.74952i	−0.262890	−	0.331685i
$865$	4.60770	−	17.1962i	0.156666	−	0.584687i
$866$	−11.9395	+	11.9395i	−0.405721	+	0.405721i
$867$	−20.4366	+	6.56147i	−0.694063	+	0.222839i
$868$	−28.8564	−	16.6603i	−0.979450	−	0.565486i
$869$	0.907241	+	3.38587i	0.0307760	+	0.114858i
$870$	−11.6074	+	53.6865i	−0.393529	+	1.82014i
$871$		0			0
$872$			16.4432i			0.556835i
$873$	−6.37233	+	38.4921i	−0.215671	+	1.30276i
$874$		0			0
$875$	7.22536	+	12.5147i	0.244262	+	0.423074i
$876$	−30.1982	−	46.8585i	−1.02030	−	1.58320i
$877$	11.2321	+	3.00962i	0.379279	+	0.101628i	0.443422	−	0.896313i	$-0.353764\pi$
$877$	11.2321	+	3.00962i	0.379279	+	0.101628i	−0.0641422	+	0.997941i	$0.520431\pi$
$878$	−10.9433	−	2.93225i	−0.369318	−	0.0989586i
$879$	−20.6579	−	32.0549i	−0.696775	−	1.08118i
$880$	5.16987	+	8.95448i	0.174276	+	0.301856i
$881$	13.5880	−	23.5350i	0.457790	−	0.792916i	−0.541054	−	0.840988i	$-0.681974\pi$
$881$	13.5880	−	23.5350i	0.457790	−	0.792916i	0.998844	+	0.0480724i	$0.0153078\pi$
$882$	5.86546	−	35.4303i	0.197500	−	1.19300i
$883$		−	39.3731i		−	1.32501i	−0.749058	−	0.662505i	$-0.769494\pi$
$883$		−	39.3731i		−	1.32501i	0.749058	−	0.662505i	$-0.230506\pi$
$884$		0			0
$885$	−4.19615	+	19.4080i	−0.141052	+	0.652392i
$886$	18.3205	+	68.3731i	0.615490	+	2.29704i
$887$	−46.4949	−	26.8438i	−1.56115	−	0.901328i	−0.997142	−	0.0755567i	$-0.975927\pi$
$887$	−46.4949	−	26.8438i	−1.56115	−	0.901328i	−0.564005	−	0.825772i	$-0.690740\pi$
$888$	−46.7139	+	14.9982i	−1.56761	+	0.503306i
$889$	15.1244	−	15.1244i	0.507255	−	0.507255i
$890$	14.9043	−	55.6237i	0.499594	−	1.86451i
$891$	−6.96426	−	14.1533i	−0.233311	−	0.474152i
$892$	60.9090	+	60.9090i	2.03938	+	2.03938i
$893$	8.58622	−	4.95725i	0.287327	−	0.165888i
$894$	15.1249	−	16.6804i	0.505853	−	0.557878i
$895$	43.3468	−	11.6147i	1.44892	−	0.388238i
$896$	29.3225			0.979595
$897$		0			0
$898$	−20.9808			−0.700137
$899$	−33.7371	+	9.03984i	−1.12520	+	0.301495i
$900$	−6.66430	+	4.77117i	−0.222143	+	0.159039i
$901$	8.59808	−	4.96410i	0.286443	−	0.165378i
$902$	−1.90346	−	1.90346i	−0.0633783	−	0.0633783i
$903$	−9.17688	+	17.8563i	−0.305387	+	0.594219i
$904$	13.9186	−	51.9449i	0.462925	−	1.72766i
$905$	−5.07880	+	5.07880i	−0.168825	+	0.168825i
$906$	−13.3813	−	41.6777i	−0.444562	−	1.38465i
$907$	15.0000	+	8.66025i	0.498067	+	0.287559i	0.727915	−	0.685668i	$-0.240490\pi$
$907$	15.0000	+	8.66025i	0.498067	+	0.287559i	−0.229848	+	0.973227i	$0.573823\pi$
$908$	−15.1149	−	56.4094i	−0.501604	−	1.87201i
$909$	−53.9308	−	24.4641i	−1.78877	−	0.811423i
$910$		0			0
$911$		−	9.25036i		−	0.306478i	−0.988189	−	0.153239i	$-0.951030\pi$
$911$		−	9.25036i		−	0.306478i	0.988189	−	0.153239i	$-0.0489705\pi$
$912$	4.41323	−	0.215843i	0.146137	−	0.00714727i
$913$	1.53590	−	2.66025i	0.0508308	−	0.0880416i
$914$	33.4495	+	57.9363i	1.10641	+	1.91636i
$915$	24.3998	−	15.7246i	0.806632	−	0.519839i
$916$	−51.6147	−	13.8301i	−1.70540	−	0.456960i
$917$	−1.23931	−	0.332073i	−0.0409257	−	0.0109660i
$918$	26.4177	−	3.90102i	0.871913	−	0.128753i
$919$	−22.2942	−	38.6147i	−0.735419	−	1.27378i	−0.954539	−	0.298085i	$-0.903652\pi$
$919$	−22.2942	−	38.6147i	−0.735419	−	1.27378i	0.219121	−	0.975698i	$-0.429681\pi$
$920$		0			0
$921$	−1.48282	−	30.3186i	−0.0488607	−	0.999031i
$922$			58.0333i			1.91123i
$923$		0			0
$924$	15.6603	+	3.38587i	0.515185	+	0.111387i
$925$	−1.29423	−	4.83013i	−0.0425540	−	0.158814i
$926$	−44.1378	−	25.4830i	−1.45046	−	0.837423i
$927$	20.6854	−	2.02822i	0.679398	−	0.0666155i
$928$	9.36603	−	9.36603i	0.307455	−	0.307455i
$929$	−12.6807	+	47.3251i	−0.416041	+	1.55269i	0.366701	+	0.930339i	$0.380487\pi$
$929$	−12.6807	+	47.3251i	−0.416041	+	1.55269i	−0.782742	+	0.622347i	$0.786179\pi$
$930$	−55.7474	−	28.6503i	−1.82803	−	0.939480i
$931$	−3.66025	−	3.66025i	−0.119960	−	0.119960i
$932$	24.0331	−	13.8755i	0.787232	−	0.454509i
$933$	5.50854	+	4.99484i	0.180341	+	0.163524i
$934$	−70.4711	+	18.8827i	−2.30589	+	0.617860i
$935$	9.00727			0.294569
$936$		0			0
$937$	−37.0000			−1.20874			−0.604369	−	0.796705i	$-0.706575\pi$
$937$	−37.0000			−1.20874			−0.604369	+	0.796705i	$0.706575\pi$
$938$	−28.6583	+	7.67898i	−0.935728	+	0.250727i
$939$	−2.56622	−	2.32691i	−0.0837455	−	0.0759358i
$940$	−74.1051	+	42.7846i	−2.41704	+	1.39548i
$941$	38.2408	+	38.2408i	1.24661	+	1.24661i	0.957206	+	0.289407i	$0.0934582\pi$
$941$	38.2408	+	38.2408i	1.24661	+	1.24661i	0.289407	+	0.957206i	$0.406542\pi$
$942$	−56.0473	−	28.8044i	−1.82612	−	0.938498i
$943$		0			0
$944$	−8.34312	+	8.34312i	−0.271546	+	0.271546i
$945$	−2.02215	+	17.4769i	−0.0657805	+	0.568523i
$946$	29.7846	+	17.1962i	0.968381	+	0.559095i
$947$	10.6112	+	39.6016i	0.344818	+	1.28688i	0.892824	+	0.450405i	$0.148721\pi$
$947$	10.6112	+	39.6016i	0.344818	+	1.28688i	−0.548006	+	0.836475i	$0.684613\pi$
$948$	−12.6362	−	2.73205i	−0.410406	−	0.0887329i
$949$		0			0
$950$			1.81448i			0.0588695i
$951$	−1.34918	−	27.5859i	−0.0437500	−	0.894535i
$952$	−6.29423	+	10.9019i	−0.203997	+	0.353333i
$953$	−21.8866	−	37.9087i	−0.708976	−	1.22798i	−0.965237	−	0.261375i	$-0.915824\pi$
$953$	−21.8866	−	37.9087i	−0.708976	−	1.22798i	0.256261	−	0.966608i	$-0.417509\pi$
$954$	31.0963	−	11.6883i	1.00678	−	0.378423i
$955$	−44.8827	−	12.0263i	−1.45237	−	0.389161i
$956$	−36.2158	−	9.70398i	−1.17130	−	0.313849i
$957$	14.1171	−	9.09782i	0.456340	−	0.294091i
$958$	10.4904	+	18.1699i	0.338929	+	0.587042i
$959$	4.17156	−	7.22536i	0.134707	−	0.233319i
$960$	44.1534	−	2.15946i	1.42505	−	0.0696963i
$961$		−	8.85641i		−	0.285691i
$962$		0			0
$963$	−20.6795	+	45.5877i	−0.666387	+	1.46904i
$964$	−7.23205	−	26.9904i	−0.232929	−	0.869302i
$965$	14.9488	+	8.63071i	0.481220	+	0.277832i
$966$		0			0
$967$	0.143594	−	0.143594i	0.00461766	−	0.00461766i	−0.704794	−	0.709412i	$-0.748961\pi$
$967$	0.143594	−	0.143594i	0.00461766	−	0.00461766i	0.709412	+	0.704794i	$0.248961\pi$
$968$	−8.50916	+	31.7566i	−0.273495	+	1.02070i
$969$	1.75941	−	3.42345i	0.0565205	−	0.109977i
$970$	−52.7128	−	52.7128i	−1.69251	−	1.69251i
$971$	−45.5551	+	26.3013i	−1.46193	+	0.844047i	−0.999101	−	0.0423987i	$-0.986500\pi$
$971$	−45.5551	+	26.3013i	−1.46193	+	0.844047i	−0.462832	+	0.886446i	$0.653167\pi$
$972$	58.1681	+	1.01535i	1.86574	+	0.0325673i
$973$	−3.26795	+	0.875644i	−0.104766	+	0.0280719i
$974$	60.7025			1.94503
$975$		0			0
$976$	17.2487			0.552118
$977$	28.3707	−	7.60192i	0.907661	−	0.243207i	0.225357	−	0.974276i	$-0.427645\pi$
$977$	28.3707	−	7.60192i	0.907661	−	0.243207i	0.682303	+	0.731069i	$0.260978\pi$
$978$	−43.0495	+	47.4770i	−1.37657	+	1.51815i
$979$	−15.2487	+	8.80385i	−0.487351	+	0.281372i
$980$	31.5906	+	31.5906i	1.00912	+	1.00912i
$981$	9.19222	+	7.55058i	0.293485	+	0.241071i
$982$	−15.5096	+	57.8827i	−0.494932	+	1.84711i
$983$	4.38209	−	4.38209i	0.139767	−	0.139767i	−0.633762	−	0.773528i	$-0.718490\pi$
$983$	4.38209	−	4.38209i	0.139767	−	0.139767i	0.773528	+	0.633762i	$0.218490\pi$
$984$	4.38712	−	1.40855i	0.139856	−	0.0449029i
$985$	3.63397	+	2.09808i	0.115788	+	0.0668503i
$986$	7.35882	+	27.4635i	0.234353	+	0.874616i
$987$	−4.95725	+	22.9282i	−0.157791	+	0.729813i
$988$		0			0
$989$		0			0
$990$	29.7342	+	4.92247i	0.945015	+	0.156446i
$991$	−12.7846	+	22.1436i	−0.406117	+	0.703414i	−0.994451	−	0.105203i	$-0.966451\pi$
$991$	−12.7846	+	22.1436i	−0.406117	+	0.703414i	0.588334	+	0.808618i	$0.299784\pi$
$992$	7.55743	+	13.0899i	0.239949	+	0.415603i
$993$	−18.3164	−	28.4216i	−0.581255	−	0.901931i
$994$	15.6603	+	4.19615i	0.496713	+	0.133094i
$995$	−2.14655	−	0.575167i	−0.0680503	−	0.0182340i
$996$	6.13719	+	9.52306i	0.194464	+	0.301750i
$997$	3.50000	+	6.06218i	0.110846	+	0.191991i	0.916112	−	0.400923i	$-0.131311\pi$
$997$	3.50000	+	6.06218i	0.110846	+	0.191991i	−0.805266	+	0.592914i	$0.797977\pi$
$998$	7.55743	−	13.0899i	0.239226	−	0.414352i
$999$	−13.0662	+	33.0015i	−0.413397	+	1.04412i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.k.f.188.1		8
3.2	odd	2	inner	507.2.k.f.188.2		8
13.2	odd	12		507.2.k.e.89.1		8
13.3	even	3		507.2.k.d.80.2		8
13.4	even	6		507.2.f.f.239.1		8
13.5	odd	4		39.2.k.b.20.2	yes	8
13.6	odd	12		507.2.f.f.437.4		8
13.7	odd	12		507.2.f.e.437.1		8
13.8	odd	4		507.2.k.d.488.1		8
13.9	even	3		507.2.f.e.239.4		8
13.10	even	6		39.2.k.b.2.1	✓	8
13.11	odd	12	inner	507.2.k.f.89.2		8
13.12	even	2		507.2.k.e.188.2		8
39.2	even	12		507.2.k.e.89.2		8
39.5	even	4		39.2.k.b.20.1	yes	8
39.8	even	4		507.2.k.d.488.2		8
39.11	even	12	inner	507.2.k.f.89.1		8
39.17	odd	6		507.2.f.f.239.4		8
39.20	even	12		507.2.f.e.437.4		8
39.23	odd	6		39.2.k.b.2.2	yes	8
39.29	odd	6		507.2.k.d.80.1		8
39.32	even	12		507.2.f.f.437.1		8
39.35	odd	6		507.2.f.e.239.1		8
39.38	odd	2		507.2.k.e.188.1		8
52.23	odd	6		624.2.cn.c.353.1		8
52.31	even	4		624.2.cn.c.449.2		8
65.18	even	4		975.2.bp.f.449.2		8
65.23	odd	12		975.2.bp.e.899.2		8
65.44	odd	4		975.2.bo.d.176.1		8
65.49	even	6		975.2.bo.d.626.2		8
65.57	even	4		975.2.bp.e.449.1		8
65.62	odd	12		975.2.bp.f.899.1		8
156.23	even	6		624.2.cn.c.353.2		8
156.83	odd	4		624.2.cn.c.449.1		8
195.23	even	12		975.2.bp.e.899.1		8
195.44	even	4		975.2.bo.d.176.2		8
195.62	even	12		975.2.bp.f.899.2		8
195.83	odd	4		975.2.bp.f.449.1		8
195.122	odd	4		975.2.bp.e.449.2		8
195.179	odd	6		975.2.bo.d.626.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.2.k.b.2.1	✓	8	13.10	even	6
39.2.k.b.2.2	yes	8	39.23	odd	6
39.2.k.b.20.1	yes	8	39.5	even	4
39.2.k.b.20.2	yes	8	13.5	odd	4
507.2.f.e.239.1		8	39.35	odd	6
507.2.f.e.239.4		8	13.9	even	3
507.2.f.e.437.1		8	13.7	odd	12
507.2.f.e.437.4		8	39.20	even	12
507.2.f.f.239.1		8	13.4	even	6
507.2.f.f.239.4		8	39.17	odd	6
507.2.f.f.437.1		8	39.32	even	12
507.2.f.f.437.4		8	13.6	odd	12
507.2.k.d.80.1		8	39.29	odd	6
507.2.k.d.80.2		8	13.3	even	3
507.2.k.d.488.1		8	13.8	odd	4
507.2.k.d.488.2		8	39.8	even	4
507.2.k.e.89.1		8	13.2	odd	12
507.2.k.e.89.2		8	39.2	even	12
507.2.k.e.188.1		8	39.38	odd	2
507.2.k.e.188.2		8	13.12	even	2
507.2.k.f.89.1		8	39.11	even	12	inner
507.2.k.f.89.2		8	13.11	odd	12	inner
507.2.k.f.188.1		8	1.1	even	1	trivial
507.2.k.f.188.2		8	3.2	odd	2	inner
624.2.cn.c.353.1		8	52.23	odd	6
624.2.cn.c.353.2		8	156.23	even	6
624.2.cn.c.449.1		8	156.83	odd	4
624.2.cn.c.449.2		8	52.31	even	4
975.2.bo.d.176.1		8	65.44	odd	4
975.2.bo.d.176.2		8	195.44	even	4
975.2.bo.d.626.1		8	195.179	odd	6
975.2.bo.d.626.2		8	65.49	even	6
975.2.bp.e.449.1		8	65.57	even	4
975.2.bp.e.449.2		8	195.122	odd	4
975.2.bp.e.899.1		8	195.23	even	12
975.2.bp.e.899.2		8	65.23	odd	12
975.2.bp.f.449.1		8	195.83	odd	4
975.2.bp.f.449.2		8	65.18	even	4
975.2.bp.f.899.1		8	65.62	odd	12
975.2.bp.f.899.2		8	195.62	even	12

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.k (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.31259 + 0.619657i) q^{2} +(-1.28311 - 1.16345i) q^{3} +(3.23205 - 1.86603i) q^{4} +(1.69293 + 1.69293i) q^{5} +(3.68825 + 1.89551i) q^{6} +(-0.366025 + 1.36603i) q^{7} +(-2.93225 + 2.93225i) q^{8} +(0.292748 + 2.98568i) q^{9} +O(q^{10})\)	\(q+(-2.31259 + 0.619657i) q^{2} +(-1.28311 - 1.16345i) q^{3} +(3.23205 - 1.86603i) q^{4} +(1.69293 + 1.69293i) q^{5} +(3.68825 + 1.89551i) q^{6} +(-0.366025 + 1.36603i) q^{7} +(-2.93225 + 2.93225i) q^{8} +(0.292748 + 2.98568i) q^{9} +(-4.96410 - 2.86603i) q^{10} +(0.453620 + 1.69293i) q^{11} +(-6.31812 - 1.36603i) q^{12} -3.38587i q^{14} +(-0.202571 - 4.14187i) q^{15} +(1.23205 - 2.13397i) q^{16} +(-1.07328 - 1.85897i) q^{17} +(-2.52711 - 6.72326i) q^{18} +(-1.00000 - 0.267949i) q^{19} +(8.63071 + 2.31259i) q^{20} +(2.05896 - 1.32691i) q^{21} +(-2.09808 - 3.63397i) q^{22} +(7.17394 - 0.350863i) q^{24} +0.732051i q^{25} +(3.09808 - 4.17156i) q^{27} +(1.36603 + 5.09808i) q^{28} +(4.79122 + 2.76621i) q^{29} +(3.03500 + 9.45293i) q^{30} +(-4.46410 + 4.46410i) q^{31} +(0.619657 - 2.31259i) q^{32} +(1.38761 - 2.69999i) q^{33} +(3.63397 + 3.63397i) q^{34} +(-2.93225 + 1.69293i) q^{35} +(6.51754 + 9.10360i) q^{36} +(-6.59808 + 1.76795i) q^{37} +2.47863 q^{38} -9.92820 q^{40} +(0.619657 - 0.166037i) q^{41} +(-3.93930 + 4.34444i) q^{42} +(-7.09808 + 4.09808i) q^{43} +(4.62518 + 4.62518i) q^{44} +(-4.55896 + 5.55017i) q^{45} +(-6.77174 + 6.77174i) q^{47} +(-4.06364 + 1.30469i) q^{48} +(4.33013 + 2.50000i) q^{49} +(-0.453620 - 1.69293i) q^{50} +(-0.785693 + 3.63397i) q^{51} +4.62518i q^{53} +(-4.57965 + 11.5669i) q^{54} +(-2.09808 + 3.63397i) q^{55} +(-2.93225 - 5.07880i) q^{56} +(0.971364 + 1.50726i) q^{57} +(-12.7942 - 3.42820i) q^{58} +(-4.62518 - 1.23931i) q^{59} +(-8.38356 - 13.0087i) q^{60} +(3.50000 + 6.06218i) q^{61} +(7.55743 - 13.0899i) q^{62} +(-4.18567 - 0.692934i) q^{63} +10.6603i q^{64} +(-1.53590 + 7.10381i) q^{66} +(-2.26795 - 8.46410i) q^{67} +(-6.93777 - 4.00552i) q^{68} +(5.73205 - 5.73205i) q^{70} +(-1.23931 + 4.62518i) q^{71} +(-9.61317 - 7.89635i) q^{72} +(6.09808 + 6.09808i) q^{73} +(14.1631 - 8.17709i) q^{74} +(0.851708 - 0.939303i) q^{75} +(-3.73205 + 1.00000i) q^{76} -2.47863 q^{77} +2.00000 q^{79} +(5.69846 - 1.52690i) q^{80} +(-8.82860 + 1.74811i) q^{81} +(-1.33013 + 0.767949i) q^{82} +(-1.23931 - 1.23931i) q^{83} +(4.17862 - 8.13071i) q^{84} +(1.33013 - 4.96410i) q^{85} +(13.8755 - 13.8755i) q^{86} +(-2.92931 - 9.12372i) q^{87} +(-6.29423 - 3.63397i) q^{88} +(2.60017 + 9.70398i) q^{89} +(7.10381 - 15.6603i) q^{90} +(10.9217 - 0.534160i) q^{93} +(11.4641 - 19.8564i) q^{94} +(-1.23931 - 2.14655i) q^{95} +(-3.48568 + 2.24637i) q^{96} +(12.5622 + 3.36603i) q^{97} +(-11.5630 - 3.09828i) q^{98} +(-4.92177 + 1.84997i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} + 12 q^{4} + 14 q^{6} + 4 q^{7} + 4 q^{9}+O(q^{10}) \) 8 * q - 2 * q^3 + 12 * q^4 + 14 * q^6 + 4 * q^7 + 4 * q^9	\( 8 q - 2 q^{3} + 12 q^{4} + 14 q^{6} + 4 q^{7} + 4 q^{9} - 12 q^{10} + 2 q^{15} - 4 q^{16} - 4 q^{18} - 8 q^{19} - 4 q^{21} + 4 q^{22} + 30 q^{24} + 4 q^{27} + 4 q^{28} - 18 q^{30} - 8 q^{31} + 20 q^{33} + 36 q^{34} + 36 q^{36} - 32 q^{37} - 24 q^{40} - 16 q^{42} - 36 q^{43} - 16 q^{45} - 14 q^{48} + 38 q^{54} + 4 q^{55} - 16 q^{57} - 40 q^{58} - 44 q^{60} + 28 q^{61} - 16 q^{63} - 40 q^{66} - 32 q^{67} + 32 q^{70} - 24 q^{72} + 28 q^{73} - 12 q^{75} - 16 q^{76} + 16 q^{79} + 4 q^{81} + 24 q^{82} + 8 q^{84} - 24 q^{85} - 34 q^{87} + 12 q^{88} - 16 q^{93} + 64 q^{94} - 16 q^{96} + 52 q^{97} - 40 q^{99}+O(q^{100}) \) 8 * q - 2 * q^3 + 12 * q^4 + 14 * q^6 + 4 * q^7 + 4 * q^9 - 12 * q^10 + 2 * q^15 - 4 * q^16 - 4 * q^18 - 8 * q^19 - 4 * q^21 + 4 * q^22 + 30 * q^24 + 4 * q^27 + 4 * q^28 - 18 * q^30 - 8 * q^31 + 20 * q^33 + 36 * q^34 + 36 * q^36 - 32 * q^37 - 24 * q^40 - 16 * q^42 - 36 * q^43 - 16 * q^45 - 14 * q^48 + 38 * q^54 + 4 * q^55 - 16 * q^57 - 40 * q^58 - 44 * q^60 + 28 * q^61 - 16 * q^63 - 40 * q^66 - 32 * q^67 + 32 * q^70 - 24 * q^72 + 28 * q^73 - 12 * q^75 - 16 * q^76 + 16 * q^79 + 4 * q^81 + 24 * q^82 + 8 * q^84 - 24 * q^85 - 34 * q^87 + 12 * q^88 - 16 * q^93 + 64 * q^94 - 16 * q^96 + 52 * q^97 - 40 * q^99

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