LMFDB - Embedded newform 507.2.k.e.89.2

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			89.2
Root			$0.500000 + 1.19293i$ of defining polynomial
Character	$\chi$	$=$	507.89
Dual form			507.2.k.e.188.2

$q$-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 $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$-1$	$e\left(\frac{7}{12}\right)$

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	$-0.0953919\pi$
$2$	2.31259	+	0.619657i	1.63525	+	0.438164i	0.679818	+	0.733380i	$0.262059\pi$
$3$	−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	$-0.929821\pi$
$5$	−1.69293	+	1.69293i	−0.757103	+	0.757103i	0.218691	+	0.975794i	$0.429821\pi$
$6$	−3.68825	+	1.89551i	−1.50572	+	0.773837i
$7$	0.366025	+	1.36603i	0.138345	+	0.516309i	0.999962	+	0.00875026i	$0.00278533\pi$
$7$	0.366025	+	1.36603i	0.138345	+	0.516309i	−0.861617	+	0.507559i	$0.830548\pi$
$8$	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	0.863213	+	0.504840i	$0.168449\pi$
$11$	−0.453620	+	1.69293i	−0.136772	+	0.510439i	−0.999984	+	0.00559833i	$0.998218\pi$
$12$	−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	−0.966324	−	0.257330i	$-0.917157\pi$
$17$	−1.07328	+	1.85897i	−0.260308	+	0.450867i	0.706016	+	0.708196i	$0.250491\pi$
$18$	2.52711	−	6.72326i	0.595644	−	1.58469i
$19$	1.00000	−	0.267949i	0.229416	−	0.0614718i	−0.142280	−	0.989826i	$-0.545443\pi$
$19$	1.00000	−	0.267949i	0.229416	−	0.0614718i	0.371695	+	0.928355i	$0.378777\pi$
$20$	−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	$-0.166667\pi$
$23$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$24$	−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	0.0158603	−	0.999874i	$-0.494951\pi$
$29$	4.79122	−	2.76621i	0.889707	−	0.513673i	0.873847	+	0.486202i	$0.161618\pi$
$30$	3.03500	−	9.45293i	0.554113	−	1.72586i
$31$	4.46410	+	4.46410i	0.801776	+	0.801776i	0.983373	−	0.181597i	$-0.0581266\pi$
$31$	4.46410	+	4.46410i	0.801776	+	0.801776i	−0.181597	+	0.983373i	$0.558127\pi$
$32$	−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	$-0.226895\pi$
$37$	6.59808	+	1.76795i	1.08472	+	0.290649i	0.328190	+	0.944612i	$0.393561\pi$
$38$	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	$-0.432619\pi$
$41$	−0.619657	−	0.166037i	−0.0967741	−	0.0259306i	−0.306881	+	0.951748i	$0.599285\pi$
$42$	−3.93930	−	4.34444i	−0.607848	−	0.670362i
$43$	−7.09808	−	4.09808i	−1.08245	−	0.624951i	−0.150891	−	0.988550i	$-0.548214\pi$
$43$	−7.09808	−	4.09808i	−1.08245	−	0.624951i	−0.931555	+	0.363600i	$0.881548\pi$
$44$	−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	$-0.00387290\pi$
$47$	6.77174	+	6.77174i	0.987759	+	0.987759i	−0.0121668	+	0.999926i	$0.503873\pi$
$48$	−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	$-0.897103\pi$
$53$		−	4.62518i		−	0.635318i	0.948205	−	0.317659i	$-0.102897\pi$
$54$	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	$-0.482437\pi$
$59$	4.62518	−	1.23931i	0.602147	−	0.161345i	0.546999	+	0.837133i	$0.315770\pi$
$60$	8.38356	−	13.0087i	1.08231	−	1.67942i
$61$	3.50000	−	6.06218i	0.448129	−	0.776182i	−0.550135	−	0.835076i	$-0.685424\pi$
$61$	3.50000	−	6.06218i	0.448129	−	0.776182i	0.998264	+	0.0588933i	$0.0187572\pi$
$62$	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	−0.677365	−	0.735647i	$-0.736878\pi$
$67$	2.26795	−	8.46410i	0.277074	−	1.03405i	0.954439	−	0.298407i	$-0.0964553\pi$
$68$	−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	0.999654	+	0.0263025i	$0.00837330\pi$
$71$	1.23931	+	4.62518i	0.147079	+	0.548908i	−0.852575	+	0.522606i	$0.824960\pi$
$72$	9.61317	−	7.89635i	1.13292	−	0.930594i
$73$	−6.09808	+	6.09808i	−0.713726	+	0.713726i	−0.967313	−	0.253587i	$-0.918390\pi$
$73$	−6.09808	+	6.09808i	−0.713726	+	0.713726i	0.253587	+	0.967313i	$0.418390\pi$
$74$	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	$-0.719335\pi$
$83$	1.23931	−	1.23931i	0.136032	−	0.136032i	0.771844	+	0.635812i	$0.219335\pi$
$84$	−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	0.679808	+	0.733390i	$0.262063\pi$
$89$	−2.60017	+	9.70398i	−0.275618	+	1.02862i	−0.955426	+	0.295230i	$0.904604\pi$
$90$	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	$-0.812881\pi$
$97$	−12.5622	+	3.36603i	−1.27550	+	0.341768i	−0.443362	+	0.896343i	$0.646214\pi$
$98$	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	−0.654160	−	0.756356i	$-0.726978\pi$
$101$	−9.87002	−	17.0954i	−0.982104	−	1.70105i	−0.327944	−	0.944697i	$-0.606356\pi$
$102$	0.434830	−	8.89076i	0.0430546	−	0.880316i
$103$			6.92820i			0.682656i	0.939944	+	0.341328i	$0.110877\pi$
$103$			6.92820i			0.682656i	−0.939944	+	0.341328i	$0.889123\pi$
$104$		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	0.402925	−	0.915233i	$-0.367993\pi$
$107$	14.4507	−	8.34312i	1.39700	−	0.806560i	0.994078	+	0.108673i	$0.0346600\pi$
$108$	2.22890	+	19.2638i	0.214476	+	1.85366i
$109$	−2.80385	−	2.80385i	−0.268560	−	0.268560i	0.559960	−	0.828520i	$-0.310817\pi$
$109$	−2.80385	−	2.80385i	−0.268560	−	0.268560i	−0.828520	+	0.559960i	$0.810817\pi$
$110$	−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	−0.132047	−	0.991243i	$-0.542155\pi$
$113$	−11.2309	−	6.48415i	−1.05651	−	0.609978i	−0.924465	+	0.381266i	$0.875488\pi$
$114$	−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	−0.951846	−	0.306576i	$-0.900817\pi$
$127$	−13.0981	+	7.56218i	−1.16227	+	0.671035i	−0.210420	+	0.977611i	$0.567483\pi$
$128$	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	$-0.987381\pi$
$131$		−	0.907241i		−	0.0792660i	0.999214	−	0.0396330i	$-0.0126189\pi$
$132$	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	$-0.502241\pi$
$137$	5.69846	−	1.52690i	0.486852	−	0.130452i	0.493891	+	0.869524i	$0.335574\pi$
$138$		0			0
$139$	1.19615	−	2.07180i	0.101456	−	0.175728i	−0.810829	−	0.585284i	$-0.800983\pi$
$139$	1.19615	−	2.07180i	0.101456	−	0.175728i	0.912285	+	0.409556i	$0.134316\pi$
$140$	−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	$-0.154728\pi$
$149$	−1.40535	−	5.24484i	−0.115131	−	0.429674i	−0.999297	+	0.0374992i	$0.988061\pi$
$150$	1.38761	+	2.69999i	0.113298	+	0.220453i
$151$	7.46410	−	7.46410i	0.607420	−	0.607420i	−0.334851	−	0.942271i	$-0.608686\pi$
$151$	7.46410	−	7.46410i	0.607420	−	0.607420i	0.942271	+	0.334851i	$0.108686\pi$
$152$	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	0.925558	+	0.378606i	$0.123596\pi$
$163$	4.00000	+	14.9282i	0.313304	+	1.16927i	−0.612254	+	0.790661i	$0.709737\pi$
$164$	−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	−0.741244	−	0.671235i	$-0.765764\pi$
$167$	3.05379	−	11.3969i	0.236310	−	0.881920i	0.977554	−	0.210685i	$-0.0675693\pi$
$168$	−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	−0.972041	−	0.234809i	$-0.924553\pi$
$173$	−3.71794	+	6.43966i	−0.282670	+	0.489598i	0.689372	+	0.724408i	$0.257887\pi$
$174$	−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	0.968295	+	0.249810i	$0.0803683\pi$
$179$	9.37191	+	16.2326i	0.700489	+	1.21328i	−0.267805	+	0.963473i	$0.586298\pi$
$180$	4.37804	+	26.4456i	0.326320	+	1.97114i
$181$		−	3.00000i		−	0.222988i	−0.993765	−	0.111494i	$-0.964436\pi$
$181$		−	3.00000i		−	0.222988i	0.993765	−	0.111494i	$-0.0355636\pi$
$182$		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	−0.252073	−	0.967708i	$-0.581112\pi$
$191$	−16.8078	−	9.70398i	−1.21617	−	0.702156i	−0.964096	+	0.265553i	$0.914446\pi$
$192$	12.4027	+	13.6783i	0.895089	+	0.987146i
$193$	−6.96410	−	1.86603i	−0.501287	−	0.134319i	−0.000689767	−	1.00000i	$-0.500220\pi$
$193$	−6.96410	−	1.86603i	−0.501287	−	0.134319i	−0.500597	+	0.865680i	$0.666886\pi$
$194$	−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	$-0.436554\pi$
$197$	−1.69293	−	0.453620i	−0.120617	−	0.0323191i	−0.318622	+	0.947882i	$0.603220\pi$
$198$	10.2357	+	7.32803i	0.727418	+	0.520780i
$199$	−0.803848	−	0.464102i	−0.0569832	−	0.0328993i	0.471238	−	0.882006i	$-0.343807\pi$
$199$	−0.803848	−	0.464102i	−0.0569832	−	0.0328993i	−0.528221	+	0.849107i	$0.677141\pi$
$200$	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	0.995920	−	0.0902411i	$-0.0287638\pi$
$211$	6.09808	+	10.5622i	0.419809	+	0.727130i	−0.576111	+	0.817371i	$0.695430\pi$
$212$	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	0.413011	+	0.910726i	$0.364477\pi$
$223$	−5.97372	+	22.2942i	−0.400030	+	1.49293i	−0.813041	+	0.582206i	$0.802190\pi$
$224$	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	−0.959878	−	0.280419i	$-0.909526\pi$
$227$	−4.05001	−	15.1149i	−0.268809	−	1.00321i	0.691069	−	0.722789i	$-0.257140\pi$
$228$	−5.95209	+	3.05896i	−0.394187	+	0.202585i
$229$	10.1244	−	10.1244i	0.669036	−	0.669036i	−0.288457	−	0.957493i	$-0.593142\pi$
$229$	10.1244	−	10.1244i	0.669036	−	0.669036i	0.957493	+	0.288457i	$0.0931421\pi$
$230$		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	$-0.644662\pi$
$239$	7.10381	−	7.10381i	0.459507	−	0.459507i	0.898494	+	0.438986i	$0.144662\pi$
$240$	9.08823	−	4.67072i	0.586643	−	0.301493i
$241$	−1.93782	−	7.23205i	−0.124826	−	0.465857i	0.875007	−	0.484110i	$-0.160856\pi$
$241$	−1.93782	−	7.23205i	−0.124826	−	0.465857i	−0.999833	+	0.0182524i	$0.994190\pi$
$242$	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	−0.280863	−	0.959748i	$-0.590621\pi$
$251$	10.9433	−	18.9543i	0.690735	−	1.19639i	0.971597	−	0.236640i	$-0.0760461\pi$
$252$	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	−0.999790	−	0.0205071i	$-0.993472\pi$
$257$	−8.29863	−	14.3737i	−0.517655	−	0.896604i	0.482135	−	0.876097i	$-0.339861\pi$
$258$	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	−0.145029	−	0.989427i	$-0.546327\pi$
$263$	10.3681	−	5.98604i	0.639326	−	0.369115i	0.784355	+	0.620312i	$0.212994\pi$
$264$	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	0.762821	−	0.646610i	$-0.223814\pi$
$269$	9.58244	+	5.53242i	0.584251	+	0.337318i	−0.178570	+	0.983927i	$0.557147\pi$
$270$	−27.3350	−	11.8289i	−1.66355	−	0.719883i
$271$	−2.00000	−	0.535898i	−0.121491	−	0.0325535i	0.197561	−	0.980291i	$-0.436698\pi$
$271$	−2.00000	−	0.535898i	−0.121491	−	0.0325535i	−0.319052	+	0.947737i	$0.603365\pi$
$272$	−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	0.403724	−	0.914881i	$-0.367715\pi$
$277$	−3.10770	−	1.79423i	−0.186723	−	0.107805i	−0.590448	+	0.807076i	$0.701049\pi$
$278$	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	$-0.484017\pi$
$281$	−15.9006	−	15.9006i	−0.948547	−	0.948547i	−0.998740	+	0.0501922i	$0.984017\pi$
$282$	−37.8117	−	12.1400i	−2.25166	−	0.722928i
$283$	21.2942	−	12.2942i	1.26581	−	0.730816i	0.291618	−	0.956535i	$-0.405806\pi$
$283$	21.2942	−	12.2942i	1.26581	−	0.730816i	0.974192	+	0.225719i	$0.0724731\pi$
$284$	−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	$-0.805697\pi$
$293$	−21.2669	+	5.69846i	−1.24243	+	0.332908i	−0.423021	+	0.906120i	$0.639030\pi$
$294$	−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	$-0.916708\pi$
$307$	−12.3923	+	12.3923i	−0.707266	+	0.707266i	0.258693	+	0.965960i	$0.416708\pi$
$308$	−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	$-0.897793\pi$
$317$	−11.2754	+	11.2754i	−0.633288	+	0.633288i	0.315603	+	0.948891i	$0.397793\pi$
$318$	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	$-0.763588\pi$
$331$	−18.8564	+	5.05256i	−1.03644	+	0.277714i	−0.299804	+	0.954001i	$0.596921\pi$
$332$	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	$0.101736\pi$
$337$			11.5359i			0.628400i	−0.949357	+	0.314200i	$0.898264\pi$
$338$		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	0.961841	−	0.273608i	$-0.0882171\pi$
$347$	22.4618	+	12.9683i	1.20581	+	0.696175i	0.243969	+	0.969783i	$0.421550\pi$
$348$	−26.4928	+	24.0222i	−1.42016	+	1.28772i
$349$	−5.63397	−	1.50962i	−0.301580	−	0.0808080i	0.104856	−	0.994487i	$-0.466562\pi$
$349$	−5.63397	−	1.50962i	−0.301580	−	0.0808080i	−0.406436	+	0.913679i	$0.633228\pi$
$350$	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	$-0.158111\pi$
$353$	26.3457	+	7.05932i	1.40224	+	0.375730i	0.523093	+	0.852276i	$0.324778\pi$
$354$	−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	$-0.101383\pi$
$359$	12.0611	+	12.0611i	0.636559	+	0.636559i	−0.313146	+	0.949705i	$0.601383\pi$
$360$	−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	0.712976	−	0.701188i	$-0.247347\pi$
$367$	−4.80385	−	8.32051i	−0.250759	−	0.434327i	−0.963735	+	0.266861i	$0.914013\pi$
$368$		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	−0.492840	−	0.870120i	$-0.664041\pi$
$373$	9.79423	−	16.9641i	0.507126	−	0.878368i	0.999966	−	0.00824796i	$-0.00262544\pi$
$374$	−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	$-0.875673\pi$
$379$	1.29423	−	4.83013i	0.0664801	−	0.248107i	0.991167	+	0.132622i	$0.0423397\pi$
$380$	−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	−0.994538	−	0.104377i	$-0.966715\pi$
$383$	−3.62896	−	13.5435i	−0.185431	−	0.692039i	0.809106	−	0.587662i	$-0.199952\pi$
$384$	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	$-0.154736\pi$
$397$	−2.29423	−	8.56218i	−0.115144	−	0.429723i	−0.999298	+	0.0374729i	$0.988069\pi$
$398$	−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	−0.507021	−	0.861933i	$-0.669253\pi$
$401$	7.26985	−	27.1314i	0.363039	−	1.35488i	0.870060	−	0.492946i	$-0.164080\pi$
$402$	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	$-0.676154\pi$
$409$	−11.2321	+	3.00962i	−0.555389	+	0.148816i	−0.0298020	+	0.999556i	$0.509488\pi$
$410$	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	−0.665998	−	0.745954i	$-0.731994\pi$
$419$	−7.22536	+	4.17156i	−0.352982	+	0.203794i	0.313016	+	0.949748i	$0.398661\pi$
$420$	20.8389	+	6.69063i	1.01683	+	0.326469i
$421$	0.830127	+	0.830127i	0.0404579	+	0.0404579i	0.727046	−	0.686588i	$-0.240893\pi$
$421$	0.830127	+	0.830127i	0.0404579	+	0.0404579i	−0.686588	+	0.727046i	$0.740893\pi$
$422$	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	$-0.400588\pi$
$431$	2.02501	+	0.542599i	0.0975412	+	0.0261361i	−0.209718	+	0.977762i	$0.567255\pi$
$432$	−5.08502	+	11.7508i	−0.244653	+	0.565360i
$433$	6.10770	+	3.52628i	0.293517	+	0.169462i	0.639527	−	0.768769i	$-0.279130\pi$
$433$	6.10770	+	3.52628i	0.293517	+	0.169462i	−0.346010	+	0.938231i	$0.612464\pi$
$434$	−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	−0.399007	−	0.916948i	$-0.630645\pi$
$439$	4.09808	−	2.36603i	0.195591	−	0.112924i	0.594597	+	0.804024i	$0.297312\pi$
$440$	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	$0.247866\pi$
$443$			29.5656i			1.40470i	−0.711830	+	0.702351i	$0.752134\pi$
$444$	−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	$-0.649632\pi$
$449$	−8.46467	+	2.26810i	−0.399472	+	0.107038i	0.0534890	+	0.998568i	$0.482966\pi$
$450$	−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	−0.561945	−	0.827175i	$-0.689947\pi$
$457$	7.23205	−	26.9904i	0.338301	−	1.26256i	0.900246	−	0.435382i	$-0.143387\pi$
$458$	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	−0.943422	−	0.331595i	$-0.892413\pi$
$461$	−6.27363	−	23.4135i	−0.292192	−	1.09048i	0.651230	−	0.758880i	$-0.274253\pi$
$462$	9.14181	−	4.69825i	0.425315	−	0.218582i
$463$	−15.0526	+	15.0526i	−0.699552	+	0.699552i	−0.964314	−	0.264762i	$-0.914707\pi$
$463$	−15.0526	+	15.0526i	−0.699552	+	0.699552i	0.264762	+	0.964314i	$0.414707\pi$
$464$	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	$-0.852507\pi$
$479$	2.26810	−	8.46467i	0.103632	−	0.386761i	0.998186	+	0.0601988i	$0.0191735\pi$
$480$	−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	$-0.388547\pi$
$487$	24.4904	−	6.56218i	1.10977	−	0.297361i	0.766735	+	0.641964i	$0.221880\pi$
$488$	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	0.997070	+	0.0764928i	$0.0243722\pi$
$491$	12.5147	+	21.6761i	0.564780	+	0.978227i	−0.432290	+	0.901734i	$0.642294\pi$
$492$	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	$-0.204869\pi$
$499$	4.46410	+	4.46410i	0.199841	+	0.199841i	−0.600091	+	0.799932i	$0.704869\pi$
$500$	−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	0.937951	−	0.346767i	$-0.112721\pi$
$503$	24.8188	+	14.3292i	1.10662	+	0.638906i	0.168666	+	0.985673i	$0.446054\pi$
$504$	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	$-0.524585\pi$
$509$	−14.4952	−	3.88398i	−0.642489	−	0.172154i	−0.565330	+	0.824865i	$0.691251\pi$
$510$	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	$0.260056\pi$
$521$			33.2835i			1.45818i	−0.684419	+	0.729089i	$0.739944\pi$
$522$	−6.49004	−	39.2031i	−0.284061	−	1.71587i
$523$	−6.49038	−	11.2417i	−0.283805	−	0.491564i	0.688514	−	0.725223i	$-0.258263\pi$
$523$	−6.49038	−	11.2417i	−0.283805	−	0.491564i	−0.972319	+	0.233659i	$0.924930\pi$
$524$	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	0.0185354	−	0.999828i	$-0.494100\pi$
$541$	23.6865	−	23.6865i	1.01836	−	1.01836i	0.999828	−	0.0185354i	$-0.00590034\pi$
$542$	−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	0.266009	+	0.963971i	$0.414295\pi$
$557$	−10.5342	+	39.3140i	−0.446347	+	1.66579i	−0.712355	+	0.701819i	$0.752372\pi$
$558$	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	−0.907708	−	0.419603i	$-0.862169\pi$
$563$	−2.14655	+	3.71794i	−0.0904665	+	0.156693i	0.817241	+	0.576296i	$0.195502\pi$
$564$	−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	0.647805	−	0.761806i	$-0.275687\pi$
$569$	−8.01105	−	13.8755i	−0.335841	−	0.581693i	−0.983646	+	0.180113i	$0.942354\pi$
$570$	0.502098	−	10.2662i	0.0210306	−	0.430002i
$571$		−	40.0526i		−	1.67615i	−0.545557	−	0.838074i	$-0.683682\pi$
$571$		−	40.0526i		−	1.67615i	0.545557	−	0.838074i	$-0.316318\pi$
$572$		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	$-0.217237\pi$
$577$	3.49038	+	3.49038i	0.145306	+	0.145306i	−0.630711	+	0.776018i	$0.717237\pi$
$578$	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	$-0.280569\pi$
$587$	19.4080	+	5.20035i	0.801053	+	0.214641i	0.165006	+	0.986292i	$0.447235\pi$
$588$	−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	$-0.349701\pi$
$593$	−10.6112	−	10.6112i	−0.435751	−	0.435751i	−0.890579	+	0.454828i	$0.849701\pi$
$594$	−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	$-0.857256\pi$
$599$		−	21.2224i		−	0.867126i	0.901123	−	0.433563i	$-0.142744\pi$
$600$	−0.256850	+	5.25169i	−0.0104859	+	0.214399i
$601$	3.79423	+	6.57180i	0.154770	+	0.268069i	0.932975	−	0.359941i	$-0.117203\pi$
$601$	3.79423	+	6.57180i	0.154770	+	0.268069i	−0.778205	+	0.628010i	$0.783870\pi$
$602$	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	−0.950744	−	0.309977i	$-0.899679\pi$
$607$	−5.09808	+	8.83013i	−0.206925	+	0.358404i	0.743820	+	0.668380i	$0.233012\pi$
$608$	−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	0.819185	+	0.573530i	$0.194426\pi$
$613$	−4.38269	+	16.3564i	−0.177015	+	0.660629i	−0.996200	+	0.0870991i	$0.972240\pi$
$614$	−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	0.826066	+	0.563574i	$0.190574\pi$
$617$	9.74847	+	36.3818i	0.392459	+	1.46468i	−0.433607	+	0.901102i	$0.642759\pi$
$618$	−13.1324	−	25.5530i	−0.528264	−	1.02789i
$619$	−14.3397	+	14.3397i	−0.576363	+	0.576363i	−0.933899	−	0.357536i	$-0.883617\pi$
$619$	−14.3397	+	14.3397i	−0.576363	+	0.576363i	0.357536	+	0.933899i	$0.383617\pi$
$620$	−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	$-0.0982151\pi$
$631$	−0.607695	−	2.26795i	−0.0241920	−	0.0902856i	−0.976966	+	0.213393i	$0.931548\pi$
$632$	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	−0.609754	−	0.792591i	$-0.708732\pi$
$641$	9.65949	−	16.7307i	0.381527	−	0.660824i	0.991281	+	0.131767i	$0.0420650\pi$
$642$	−37.4835	+	58.1629i	−1.47935	+	2.29551i
$643$	−26.1244	+	7.00000i	−1.03024	+	0.276053i	−0.734065	−	0.679079i	$-0.762379\pi$
$643$	−26.1244	+	7.00000i	−1.03024	+	0.276053i	−0.296179	+	0.955132i	$0.595713\pi$
$644$		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	0.688322	−	0.725405i	$-0.258348\pi$
$647$	−7.22536	−	12.5147i	−0.284058	−	0.492003i	−0.972380	+	0.233402i	$0.925014\pi$
$648$	−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	−0.982998	−	0.183617i	$-0.941219\pi$
$653$	−33.6156	+	19.4080i	−1.31548	+	0.759492i	−0.332482	+	0.943110i	$0.607886\pi$
$654$	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	0.925051	−	0.379842i	$-0.124022\pi$
$659$	27.1759	+	15.6900i	1.05862	+	0.611197i	0.133572	+	0.991039i	$0.457355\pi$
$660$	18.2200	+	20.0938i	0.709212	+	0.782152i
$661$	16.5263	+	4.42820i	0.642798	+	0.172237i	0.565470	−	0.824769i	$-0.308695\pi$
$661$	16.5263	+	4.42820i	0.642798	+	0.172237i	0.0773274	+	0.997006i	$0.475361\pi$
$662$	−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	−0.272564	−	0.962138i	$-0.587872\pi$
$673$	11.0096	−	6.35641i	0.424390	−	0.245021i	0.696954	+	0.717116i	$0.254538\pi$
$674$	−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	$-0.732015\pi$
$677$		−	38.8159i		−	1.49182i	0.666048	−	0.745909i	$-0.267985\pi$
$678$	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	$-0.685318\pi$
$683$	−15.9006	+	4.26054i	−0.608418	+	0.163025i	−0.0585607	+	0.998284i	$0.518651\pi$
$684$	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	−0.332770	−	0.943008i	$-0.607983\pi$
$691$	11.2224	−	41.8827i	0.426921	−	1.59329i	0.759691	−	0.650284i	$-0.225350\pi$
$692$	−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	$-0.0212828\pi$
$709$	2.66987	+	9.96410i	0.100269	+	0.374210i	−0.897496	+	0.441022i	$0.854616\pi$
$710$	−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	−0.735705	−	0.677302i	$-0.763149\pi$
$719$	5.86450	−	10.1576i	0.218709	−	0.378815i	0.954413	+	0.298488i	$0.0964822\pi$
$720$	−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	$-0.843106\pi$
$727$		−	25.5167i		−	0.946361i	0.880966	−	0.473180i	$-0.156894\pi$
$728$		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	−0.898086	−	0.439820i	$-0.855042\pi$
$733$	−36.2224	−	36.2224i	−1.33791	−	1.33791i	−0.439820	−	0.898086i	$-0.644958\pi$
$734$	−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	$-0.799197\pi$
$739$	−48.9808	−	13.1244i	−1.80179	−	0.482787i	−0.994255	+	0.107037i	$0.965864\pi$
$740$	−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	$-0.826177\pi$
$743$	−50.5449	−	13.5435i	−1.85431	−	0.496862i	−0.999747	+	0.0224808i	$0.992844\pi$
$744$	−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	−0.994043	−	0.108992i	$-0.965238\pi$
$751$	−38.2750	+	22.0981i	−1.39667	+	0.806370i	−0.402632	+	0.915362i	$0.631904\pi$
$752$	−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	0.998411	−	0.0563489i	$-0.0179459\pi$
$757$	12.3923	+	21.4641i	0.450406	+	0.780126i	−0.548005	+	0.836475i	$0.684613\pi$
$758$	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	$-0.608275\pi$
$761$	−4.17156	+	1.11777i	−0.151219	+	0.0405190i	0.182415	+	0.983222i	$0.441608\pi$
$762$	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	$-0.903770\pi$
$769$	0.581416	−	2.16987i	0.0209664	−	0.0782476i	0.975616	+	0.219483i	$0.0704370\pi$
$770$	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	$-0.0477842\pi$
$773$	1.60396	+	5.98604i	0.0576903	+	0.215303i	−0.931063	+	0.364858i	$0.881117\pi$
$774$	−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	$-0.0165081\pi$
$787$	3.02628	+	11.2942i	0.107875	+	0.402596i	−0.890780	+	0.454434i	$0.849841\pi$
$788$	−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	−0.977069	−	0.212921i	$-0.931702\pi$
$797$	−8.58622	+	14.8718i	−0.304139	+	0.526785i	0.672930	+	0.739706i	$0.265036\pi$
$798$	−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	−0.156097	−	0.987742i	$-0.549891\pi$
$809$	17.6705	−	10.2021i	0.621263	−	0.358686i	0.777361	+	0.629055i	$0.216558\pi$
$810$	48.8362	−	16.6252i	1.71593	−	0.584150i
$811$	19.0000	+	19.0000i	0.667180	+	0.667180i	0.957062	−	0.289882i	$-0.0936161\pi$
$811$	19.0000	+	19.0000i	0.667180	+	0.667180i	−0.289882	+	0.957062i	$0.593616\pi$
$812$	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	$-0.451157\pi$
$821$	−5.98604	−	1.60396i	−0.208914	−	0.0559784i	−0.361758	+	0.932272i	$0.617823\pi$
$822$	−18.1231	+	16.4330i	−0.632116	+	0.573168i
$823$	−13.3923	−	7.73205i	−0.466826	−	0.269522i	0.248084	−	0.968739i	$-0.420199\pi$
$823$	−13.3923	−	7.73205i	−0.466826	−	0.269522i	−0.714910	+	0.699216i	$0.753532\pi$
$824$	−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	$-0.221559\pi$
$827$	3.62896	+	3.62896i	0.126191	+	0.126191i	−0.641190	+	0.767382i	$0.721559\pi$
$828$		0			0
$829$	20.6769	−	11.9378i	0.718139	−	0.414618i	−0.0959284	−	0.995388i	$-0.530582\pi$
$829$	20.6769	−	11.9378i	0.718139	−	0.414618i	0.814067	+	0.580771i	$0.197249\pi$
$830$	−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	$-0.540211\pi$
$839$	7.55743	−	2.02501i	0.260911	−	0.0699110i	0.386903	+	0.922120i	$0.373545\pi$
$840$	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	$-0.916507\pi$
$853$	−20.6340	+	20.6340i	−0.706494	+	0.706494i	0.259302	+	0.965796i	$0.416507\pi$
$854$	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	$-0.843759\pi$
$863$	−12.0611	+	12.0611i	−0.410563	+	0.410563i	0.471371	+	0.881935i	$0.343759\pi$
$864$	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	$-0.646236\pi$
$877$	−11.2321	+	3.00962i	−0.379279	+	0.101628i	0.0641422	+	0.997941i	$0.479569\pi$
$878$	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	0.998844	−	0.0480724i	$-0.0153078\pi$
$881$	13.5880	+	23.5350i	0.457790	+	0.792916i	−0.541054	+	0.840988i	$0.681974\pi$
$882$	−5.86546	−	35.4303i	−0.197500	−	1.19300i
$883$			39.3731i			1.32501i	0.749058	+	0.662505i	$0.230506\pi$
$883$			39.3731i			1.32501i	−0.749058	+	0.662505i	$0.769494\pi$
$884$		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	−0.564005	+	0.825772i	$0.690740\pi$
$887$	−46.4949	+	26.8438i	−1.56115	+	0.901328i	−0.997142	+	0.0755567i	$0.975927\pi$
$888$	−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	−0.229848	−	0.973227i	$-0.573823\pi$
$907$	15.0000	−	8.66025i	0.498067	−	0.287559i	0.727915	+	0.685668i	$0.240490\pi$
$908$	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	$0.0489705\pi$
$911$			9.25036i			0.306478i	−0.988189	+	0.153239i	$0.951030\pi$
$912$	−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	0.219121	+	0.975698i	$0.429681\pi$
$919$	−22.2942	+	38.6147i	−0.735419	+	1.27378i	−0.954539	+	0.298085i	$0.903652\pi$
$920$		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	0.782742	+	0.622347i	$0.213821\pi$
$929$	12.6807	+	47.3251i	0.416041	+	1.55269i	−0.366701	+	0.930339i	$0.619513\pi$
$930$	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	−0.289407	+	0.957206i	$0.593458\pi$
$941$	−38.2408	+	38.2408i	−1.24661	+	1.24661i	−0.957206	+	0.289407i	$0.906542\pi$
$942$	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	0.548006	+	0.836475i	$0.315387\pi$
$947$	−10.6112	+	39.6016i	−0.344818	+	1.28688i	−0.892824	+	0.450405i	$0.851279\pi$
$948$	−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	0.256261	+	0.966608i	$0.417509\pi$
$953$	−21.8866	+	37.9087i	−0.708976	+	1.22798i	−0.965237	+	0.261375i	$0.915824\pi$
$954$	−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	$-0.251039\pi$
$967$	−0.143594	−	0.143594i	−0.00461766	−	0.00461766i	−0.709412	+	0.704794i	$0.751039\pi$
$968$	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	−0.462832	−	0.886446i	$-0.653167\pi$
$971$	−45.5551	−	26.3013i	−1.46193	−	0.844047i	−0.999101	+	0.0423987i	$0.986500\pi$
$972$	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	$-0.572355\pi$
$977$	−28.3707	−	7.60192i	−0.907661	−	0.243207i	−0.682303	+	0.731069i	$0.739022\pi$
$978$	−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	$-0.281510\pi$
$983$	−4.38209	−	4.38209i	−0.139767	−	0.139767i	−0.773528	+	0.633762i	$0.781510\pi$
$984$	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	0.588334	−	0.808618i	$-0.299784\pi$
$991$	−12.7846	−	22.1436i	−0.406117	−	0.703414i	−0.994451	+	0.105203i	$0.966451\pi$
$992$	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	−0.805266	−	0.592914i	$-0.797977\pi$
$997$	3.50000	−	6.06218i	0.110846	−	0.191991i	0.916112	+	0.400923i	$0.131311\pi$
$998$	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.e.89.2		8
3.2	odd	2	inner	507.2.k.e.89.1		8
13.2	odd	12		507.2.f.f.239.4		8
13.3	even	3		507.2.f.f.437.1		8
13.4	even	6		507.2.k.d.488.2		8
13.5	odd	4		39.2.k.b.2.2	yes	8
13.6	odd	12	inner	507.2.k.e.188.1		8
13.7	odd	12		507.2.k.f.188.2		8
13.8	odd	4		507.2.k.d.80.1		8
13.9	even	3		39.2.k.b.20.1	yes	8
13.10	even	6		507.2.f.e.437.4		8
13.11	odd	12		507.2.f.e.239.1		8
13.12	even	2		507.2.k.f.89.1		8
39.2	even	12		507.2.f.f.239.1		8
39.5	even	4		39.2.k.b.2.1	✓	8
39.8	even	4		507.2.k.d.80.2		8
39.11	even	12		507.2.f.e.239.4		8
39.17	odd	6		507.2.k.d.488.1		8
39.20	even	12		507.2.k.f.188.1		8
39.23	odd	6		507.2.f.e.437.1		8
39.29	odd	6		507.2.f.f.437.4		8
39.32	even	12	inner	507.2.k.e.188.2		8
39.35	odd	6		39.2.k.b.20.2	yes	8
39.38	odd	2		507.2.k.f.89.2		8
52.31	even	4		624.2.cn.c.353.2		8
52.35	odd	6		624.2.cn.c.449.1		8
65.9	even	6		975.2.bo.d.176.2		8
65.18	even	4		975.2.bp.e.899.1		8
65.22	odd	12		975.2.bp.e.449.2		8
65.44	odd	4		975.2.bo.d.626.1		8
65.48	odd	12		975.2.bp.f.449.1		8
65.57	even	4		975.2.bp.f.899.2		8
156.35	even	6		624.2.cn.c.449.2		8
156.83	odd	4		624.2.cn.c.353.1		8
195.44	even	4		975.2.bo.d.626.2		8
195.74	odd	6		975.2.bo.d.176.1		8
195.83	odd	4		975.2.bp.e.899.2		8
195.113	even	12		975.2.bp.f.449.2		8
195.122	odd	4		975.2.bp.f.899.1		8
195.152	even	12		975.2.bp.e.449.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.2.k.b.2.1	✓	8	39.5	even	4
39.2.k.b.2.2	yes	8	13.5	odd	4
39.2.k.b.20.1	yes	8	13.9	even	3
39.2.k.b.20.2	yes	8	39.35	odd	6
507.2.f.e.239.1		8	13.11	odd	12
507.2.f.e.239.4		8	39.11	even	12
507.2.f.e.437.1		8	39.23	odd	6
507.2.f.e.437.4		8	13.10	even	6
507.2.f.f.239.1		8	39.2	even	12
507.2.f.f.239.4		8	13.2	odd	12
507.2.f.f.437.1		8	13.3	even	3
507.2.f.f.437.4		8	39.29	odd	6
507.2.k.d.80.1		8	13.8	odd	4
507.2.k.d.80.2		8	39.8	even	4
507.2.k.d.488.1		8	39.17	odd	6
507.2.k.d.488.2		8	13.4	even	6
507.2.k.e.89.1		8	3.2	odd	2	inner
507.2.k.e.89.2		8	1.1	even	1	trivial
507.2.k.e.188.1		8	13.6	odd	12	inner
507.2.k.e.188.2		8	39.32	even	12	inner
507.2.k.f.89.1		8	13.12	even	2
507.2.k.f.89.2		8	39.38	odd	2
507.2.k.f.188.1		8	39.20	even	12
507.2.k.f.188.2		8	13.7	odd	12
624.2.cn.c.353.1		8	156.83	odd	4
624.2.cn.c.353.2		8	52.31	even	4
624.2.cn.c.449.1		8	52.35	odd	6
624.2.cn.c.449.2		8	156.35	even	6
975.2.bo.d.176.1		8	195.74	odd	6
975.2.bo.d.176.2		8	65.9	even	6
975.2.bo.d.626.1		8	65.44	odd	4
975.2.bo.d.626.2		8	195.44	even	4
975.2.bp.e.449.1		8	195.152	even	12
975.2.bp.e.449.2		8	65.22	odd	12
975.2.bp.e.899.1		8	65.18	even	4
975.2.bp.e.899.2		8	195.83	odd	4
975.2.bp.f.449.1		8	65.48	odd	12
975.2.bp.f.449.2		8	195.113	even	12
975.2.bp.f.899.1		8	195.122	odd	4
975.2.bp.f.899.2		8	65.57	even	4

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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