LMFDB - Embedded newform 507.2.k.f.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.f.188.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.31259 + 0.619657i) q^{2} +(1.64914 - 0.529480i) q^{3} +(3.23205 + 1.86603i) q^{4} +(-1.69293 + 1.69293i) q^{5} +(4.14187 - 0.202571i) q^{6} +(-0.366025 - 1.36603i) q^{7} +(2.93225 + 2.93225i) q^{8} +(2.43930 - 1.74637i) q^{9} +O(q^{10})$	\(q+(2.31259 + 0.619657i) q^{2} +(1.64914 - 0.529480i) q^{3} +(3.23205 + 1.86603i) q^{4} +(-1.69293 + 1.69293i) q^{5} +(4.14187 - 0.202571i) q^{6} +(-0.366025 - 1.36603i) q^{7} +(2.93225 + 2.93225i) q^{8} +(2.43930 - 1.74637i) q^{9} +(-4.96410 + 2.86603i) q^{10} +(-0.453620 + 1.69293i) q^{11} +(6.31812 + 1.36603i) q^{12} -3.38587i q^{14} +(-1.89551 + 3.68825i) q^{15} +(1.23205 + 2.13397i) q^{16} +(1.07328 - 1.85897i) q^{17} +(6.72326 - 2.52711i) q^{18} +(-1.00000 + 0.267949i) q^{19} +(-8.63071 + 2.31259i) q^{20} +(-1.32691 - 2.05896i) q^{21} +(-2.09808 + 3.63397i) q^{22} +(6.38824 + 3.28311i) q^{24} -0.732051i q^{25} +(3.09808 - 4.17156i) q^{27} +(1.36603 - 5.09808i) q^{28} +(-4.79122 + 2.76621i) q^{29} +(-6.66898 + 7.35486i) q^{30} +(-4.46410 - 4.46410i) q^{31} +(-0.619657 - 2.31259i) q^{32} +(0.148292 + 3.03206i) q^{33} +(3.63397 - 3.63397i) q^{34} +(2.93225 + 1.69293i) q^{35} +(11.1427 - 1.09255i) q^{36} +(-6.59808 - 1.76795i) q^{37} -2.47863 q^{38} -9.92820 q^{40} +(-0.619657 - 0.166037i) q^{41} +(-1.79275 - 5.58376i) q^{42} +(-7.09808 - 4.09808i) q^{43} +(-4.62518 + 4.62518i) q^{44} +(-1.17309 + 7.08606i) q^{45} +(6.77174 + 6.77174i) q^{47} +(3.16172 + 2.86687i) q^{48} +(4.33013 - 2.50000i) q^{49} +(0.453620 - 1.69293i) q^{50} +(0.785693 - 3.63397i) q^{51} +4.62518i q^{53} +(9.74952 - 7.72737i) q^{54} +(-2.09808 - 3.63397i) q^{55} +(2.93225 - 5.07880i) q^{56} +(-1.50726 + 0.971364i) q^{57} +(-12.7942 + 3.42820i) q^{58} +(4.62518 - 1.23931i) q^{59} +(-13.0087 + 8.38356i) q^{60} +(3.50000 - 6.06218i) q^{61} +(-7.55743 - 13.0899i) q^{62} +(-3.27843 - 2.69293i) 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} +(12.2734 + 2.03185i) q^{72} +(6.09808 - 6.09808i) q^{73} +(-14.1631 - 8.17709i) q^{74} +(-0.387606 - 1.20725i) q^{75} +(-3.73205 - 1.00000i) q^{76} +2.47863 q^{77} +2.00000 q^{79} +(-5.69846 - 1.52690i) q^{80} +(2.90039 - 8.51984i) q^{81} +(-1.33013 - 0.767949i) q^{82} +(1.23931 - 1.23931i) q^{83} +(-0.446565 - 9.13071i) q^{84} +(1.33013 + 4.96410i) q^{85} +(-13.8755 - 13.8755i) q^{86} +(-6.43672 + 7.09871i) q^{87} +(-6.29423 + 3.63397i) q^{88} +(-2.60017 + 9.70398i) q^{89} +(-7.10381 + 15.6603i) q^{90} +(-9.72556 - 4.99826i) q^{93} +(11.4641 + 19.8564i) q^{94} +(1.23931 - 2.14655i) q^{95} +(-2.24637 - 3.48568i) q^{96} +(12.5622 - 3.36603i) q^{97} +(11.5630 - 3.09828i) q^{98} +(1.84997 + 4.92177i) 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	$0.262059\pi$
$3$	1.64914	−	0.529480i	0.952129	−	0.305695i
$3$	1.64914	−	0.529480i	0.952129	−	0.305695i
$4$	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	$0.429821\pi$
$6$	4.14187	−	0.202571i	1.69091	−	0.0826993i
$7$	−0.366025	−	1.36603i	−0.138345	−	0.516309i	−0.999962	−	0.00875026i	$-0.997215\pi$
$7$	−0.366025	−	1.36603i	−0.138345	−	0.516309i	0.861617	−	0.507559i	$-0.169452\pi$
$8$	2.93225	+	2.93225i	1.03671	+	1.03671i
$9$	2.43930	−	1.74637i	0.813101	−	0.582123i
$10$	−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
$15$	−1.89551	+	3.68825i	−0.489417	+	0.952303i
$16$	1.23205	+	2.13397i	0.308013	+	0.533494i
$17$	1.07328	−	1.85897i	0.260308	−	0.450867i	−0.706016	−	0.708196i	$-0.749509\pi$
$17$	1.07328	−	1.85897i	0.260308	−	0.450867i	0.966324	+	0.257330i	$0.0828426\pi$
$18$	6.72326	−	2.52711i	1.58469	−	0.595644i
$19$	−1.00000	+	0.267949i	−0.229416	+	0.0614718i	−0.371695	−	0.928355i	$-0.621223\pi$
$19$	−1.00000	+	0.267949i	−0.229416	+	0.0614718i	0.142280	+	0.989826i	$0.454557\pi$
$20$	−8.63071	+	2.31259i	−1.92988	+	0.517111i
$21$	−1.32691	−	2.05896i	−0.289555	−	0.449302i
$22$	−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	$0.833333\pi$
$24$	6.38824	+	3.28311i	1.30399	+	0.670162i
$25$		−	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	$-0.838382\pi$
$29$	−4.79122	+	2.76621i	−0.889707	+	0.513673i	−0.0158603	+	0.999874i	$0.505049\pi$
$30$	−6.66898	+	7.35486i	−1.21758	+	1.34281i
$31$	−4.46410	−	4.46410i	−0.801776	−	0.801776i	0.181597	−	0.983373i	$-0.441873\pi$
$31$	−4.46410	−	4.46410i	−0.801776	−	0.801776i	−0.983373	+	0.181597i	$0.941873\pi$
$32$	−0.619657	−	2.31259i	−0.109541	−	0.408812i
$33$	0.148292	+	3.03206i	0.0258144	+	0.527814i
$34$	3.63397	−	3.63397i	0.623222	−	0.623222i
$35$	2.93225	+	1.69293i	0.495640	+	0.286158i
$36$	11.1427	−	1.09255i	1.85712	−	0.182092i
$37$	−6.59808	−	1.76795i	−1.08472	−	0.290649i	−0.328190	−	0.944612i	$-0.606439\pi$
$37$	−6.59808	−	1.76795i	−1.08472	−	0.290649i	−0.756527	+	0.653963i	$0.773105\pi$
$38$	−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	$0.599285\pi$
$42$	−1.79275	−	5.58376i	−0.276627	−	0.861593i
$43$	−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
$45$	−1.17309	+	7.08606i	−0.174874	+	1.05633i
$46$		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	$0.503873\pi$
$48$	3.16172	+	2.86687i	0.456354	+	0.413797i
$49$	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	$0.897103\pi$
$54$	9.74952	−	7.72737i	1.32674	−	1.05156i
$55$	−2.09808	−	3.63397i	−0.282905	−	0.490005i
$56$	2.93225	−	5.07880i	0.391838	−	0.678683i
$57$	−1.50726	+	0.971364i	−0.199642	+	0.128660i
$58$	−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	$0.315770\pi$
$60$	−13.0087	+	8.38356i	−1.67942	+	1.08231i
$61$	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
$63$	−3.27843	−	2.69293i	−0.413043	−	0.339278i
$64$		−	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	$0.263122\pi$
$67$	−2.26795	+	8.46410i	−0.277074	+	1.03405i	−0.954439	+	0.298407i	$0.903545\pi$
$68$	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	$0.824960\pi$
$72$	12.2734	+	2.03185i	1.44644	+	0.239456i
$73$	6.09808	−	6.09808i	0.713726	−	0.713726i	−0.253587	−	0.967313i	$-0.581610\pi$
$73$	6.09808	−	6.09808i	0.713726	−	0.713726i	0.967313	+	0.253587i	$0.0816103\pi$
$74$	−14.1631	−	8.17709i	−1.64643	−	0.950567i
$75$	−0.387606	−	1.20725i	−0.0447569	−	0.139401i
$76$	−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
$81$	2.90039	−	8.51984i	0.322266	−	0.946649i
$82$	−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	$0.219335\pi$
$84$	−0.446565	−	9.13071i	−0.0487243	−	0.996242i
$85$	1.33013	+	4.96410i	0.144273	+	0.538432i
$86$	−13.8755	−	13.8755i	−1.49624	−	1.49624i
$87$	−6.43672	+	7.09871i	−0.690089	+	0.761062i
$88$	−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
$93$	−9.72556	−	4.99826i	−1.00849	−	0.518296i
$94$	11.4641	+	19.8564i	1.18243	+	2.04803i
$95$	1.23931	−	2.14655i	0.127151	−	0.220232i
$96$	−2.24637	−	3.48568i	−0.229269	−	0.355756i
$97$	12.5622	−	3.36603i	1.27550	−	0.341768i	0.443362	−	0.896343i	$-0.353786\pi$
$97$	12.5622	−	3.36603i	1.27550	−	0.341768i	0.832134	+	0.554575i	$0.187119\pi$
$98$	11.5630	−	3.09828i	1.16803	−	0.312974i
$99$	1.84997	+	4.92177i	0.185929	+	0.494656i
$100$	1.36603	−	2.36603i	0.136603	−	0.236603i
$101$	9.87002	+	17.0954i	0.982104	+	1.70105i	0.654160	+	0.756356i	$0.273022\pi$
$101$	9.87002	+	17.0954i	0.982104	+	1.70105i	0.327944	+	0.944697i	$0.393644\pi$
$102$	4.06880	−	7.91704i	0.402872	−	0.783903i
$103$			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	−0.994078	−	0.108673i	$-0.965340\pi$
$107$	−14.4507	+	8.34312i	−1.39700	+	0.806560i	−0.402925	+	0.915233i	$0.632007\pi$
$108$	17.7974	−	7.70161i	1.71255	−	0.741088i
$109$	2.80385	+	2.80385i	0.268560	+	0.268560i	0.828520	−	0.559960i	$-0.189183\pi$
$109$	2.80385	+	2.80385i	0.268560	+	0.268560i	−0.559960	+	0.828520i	$0.689183\pi$
$110$	−2.60017	−	9.70398i	−0.247917	−	0.925239i
$111$	−11.8172	+	0.577958i	−1.12164	+	0.0548573i
$112$	2.46410	−	2.46410i	0.232836	−	0.232836i
$113$	11.2309	+	6.48415i	1.05651	+	0.609978i	0.924465	−	0.381266i	$-0.124512\pi$
$113$	11.2309	+	6.48415i	1.05651	+	0.609978i	0.132047	+	0.991243i	$0.457845\pi$
$114$	−4.08759	+	1.31238i	−0.382838	+	0.122916i
$115$		0			0
$116$	−20.6473			−1.91705
$117$		0			0
$118$	11.4641			1.05536
$119$	−2.93225	−	0.785693i	−0.268799	−	0.0720244i
$120$	−16.3730	+	5.25678i	−1.49464	+	0.479876i
$121$	6.86603	+	3.96410i	0.624184	+	0.360373i
$122$	11.8505	−	11.8505i	1.07290	−	1.07290i
$123$	−1.10981	+	0.0542788i	−0.100068	+	0.00489415i
$124$	−6.09808	−	22.7583i	−0.547623	−	2.04376i
$125$	−7.22536	−	7.22536i	−0.646255	−	0.646255i
$126$	−5.91297	−	8.25916i	−0.526770	−	0.735784i
$127$	−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	$0.0126189\pi$
$131$			0.907241i			0.0792660i	−0.999214	+	0.0396330i	$0.987381\pi$
$132$	−5.17862	+	10.0765i	−0.450741	+	0.877046i
$133$	0.732051	+	1.26795i	0.0634769	+	0.109945i
$134$	−10.4897	+	18.1687i	−0.906170	+	1.56953i
$135$	1.81734	+	12.3070i	0.156412	+	1.05922i
$136$	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
$141$	14.7530	+	7.58202i	1.24243	+	0.638521i
$142$			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
$147$	5.81727	−	6.41556i	0.479800	−	0.529146i
$148$	−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	$0.988061\pi$
$150$	−0.148292	−	3.03206i	−0.0121080	−	0.247567i
$151$	−7.46410	+	7.46410i	−0.607420	+	0.607420i	−0.942271	−	0.334851i	$-0.891314\pi$
$151$	−7.46410	+	7.46410i	−0.607420	+	0.607420i	0.334851	+	0.942271i	$0.391314\pi$
$152$	−3.71794	−	2.14655i	−0.301565	−	0.174109i
$153$	−0.628400	−	6.40893i	−0.0508031	−	0.518131i
$154$	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
$159$	2.44894	+	7.62756i	0.194214	+	0.604905i
$160$	4.96410	+	2.86603i	0.392447	+	0.226579i
$161$		0			0
$162$	11.9868	−	17.9057i	0.941772	−	1.40680i
$163$	−4.00000	−	14.9282i	−0.313304	−	1.16927i	−0.925558	−	0.378606i	$-0.876404\pi$
$163$	−4.00000	−	14.9282i	−0.313304	−	1.16927i	0.612254	−	0.790661i	$-0.290263\pi$
$164$	−1.69293	−	1.69293i	−0.132196	−	0.132196i
$165$	−5.38413	−	4.88203i	−0.419154	−	0.380066i
$166$	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
$171$	−1.97136	+	2.39998i	−0.150754	+	0.183531i
$172$	−15.2942	−	26.4904i	−1.16617	−	2.01987i
$173$	3.71794	−	6.43966i	0.282670	−	0.489598i	−0.689372	−	0.724408i	$-0.742113\pi$
$173$	3.71794	−	6.43966i	0.282670	−	0.489598i	0.972041	+	0.234809i	$0.0754466\pi$
$174$	−19.2843	+	12.4279i	−1.46194	+	0.942154i
$175$	−1.00000	+	0.267949i	−0.0755929	+	0.0202551i
$176$	−4.17156	+	1.11777i	−0.314443	+	0.0842548i
$177$	6.97136	−	4.49274i	0.524000	−	0.337695i
$178$	−12.0263	+	20.8301i	−0.901408	+	1.56128i
$179$	−9.37191	−	16.2326i	−0.700489	−	1.21328i	−0.968295	−	0.249810i	$-0.919632\pi$
$179$	−9.37191	−	16.2326i	−0.700489	−	1.21328i	0.267805	−	0.963473i	$-0.413702\pi$
$180$	−17.0143	+	20.7135i	−1.26817	+	1.54389i
$181$		−	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
$186$	−19.3940	−	17.5854i	−1.42204	−	1.28943i
$187$	2.66025	+	2.66025i	0.194537	+	0.194537i
$188$	9.25036	+	34.5228i	0.674652	+	2.51784i
$189$	−6.83243	−	2.70515i	−0.496986	−	0.196771i
$190$	4.19615	−	4.19615i	0.304421	−	0.304421i
$191$	16.8078	+	9.70398i	1.21617	+	0.702156i	0.964096	−	0.265553i	$-0.0855544\pi$
$191$	16.8078	+	9.70398i	1.21617	+	0.702156i	0.252073	+	0.967708i	$0.418888\pi$
$192$	−5.64439	−	17.5802i	−0.407349	−	1.26874i
$193$	6.96410	+	1.86603i	0.501287	+	0.134319i	0.500597	−	0.865680i	$-0.333114\pi$
$193$	6.96410	+	1.86603i	0.501287	+	0.134319i	0.000689767		1.00000i	$0.499780\pi$
$194$	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	$0.603220\pi$
$198$	1.22842	+	12.5284i	0.0872998	+	0.890353i
$199$	−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
$201$	0.741412	+	15.1593i	0.0522952	+	1.06925i
$202$	12.2321	+	45.6506i	0.860644	+	3.21197i
$203$	5.53242	+	5.53242i	0.388300	+	0.388300i
$204$	9.32049	−	10.2791i	0.652565	−	0.719679i
$205$	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
$210$	12.4879	+	6.41793i	0.861750	+	0.442879i
$211$	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
$213$	4.49274	+	6.97136i	0.307837	+	0.477670i
$214$	−38.5885	+	10.3397i	−2.63785	+	0.706810i
$215$	18.9543	−	5.07880i	1.29268	−	0.346371i
$216$	21.3164	−	3.14772i	1.45040	−	0.214176i
$217$	−4.46410	+	7.73205i	−0.303043	+	0.524886i
$218$	4.74673	+	8.22158i	0.321489	+	0.556835i
$219$	6.82775	−	13.2854i	0.461377	−	0.897742i
$220$		−	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	$-0.635523\pi$
$223$	5.97372	−	22.2942i	0.400030	−	1.49293i	0.813041	−	0.582206i	$-0.197810\pi$
$224$	−2.93225	+	1.69293i	−0.195919	+	0.113114i
$225$	−1.27843	−	1.78569i	−0.0852287	−	0.119046i
$226$	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	$-0.257140\pi$
$228$	−6.68414	+	0.326909i	−0.442668	+	0.0216500i
$229$	−10.1244	+	10.1244i	−0.669036	+	0.669036i	−0.957493	−	0.288457i	$-0.906858\pi$
$229$	−10.1244	+	10.1244i	−0.669036	+	0.669036i	0.288457	+	0.957493i	$0.406858\pi$
$230$		0			0
$231$	4.08759	−	1.31238i	0.268944	−	0.0863485i
$232$	−22.1603	−	5.93782i	−1.45489	−	0.389837i
$233$	−7.43588			−0.487141			−0.243570	−	0.969883i	$-0.578319\pi$
$233$	−7.43588			−0.487141			−0.243570	+	0.969883i	$0.578319\pi$
$234$		0			0
$235$	−22.9282			−1.49567
$236$	17.2614	+	4.62518i	1.12362	+	0.301074i
$237$	3.29827	−	1.05896i	0.214246	−	0.0687868i
$238$	−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	$0.144662\pi$
$240$	−10.2060	+	0.499156i	−0.658794	+	0.0322204i
$241$	1.93782	+	7.23205i	0.124826	+	0.465857i	0.999833	−	0.0182524i	$-0.00581023\pi$
$241$	1.93782	+	7.23205i	0.124826	+	0.465857i	−0.875007	+	0.484110i	$0.839144\pi$
$242$	13.4219	+	13.4219i	0.862794	+	0.862794i
$243$	0.272062	−	15.5861i	0.0174528	−	0.999848i
$244$	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
$249$	1.38761	−	2.69999i	0.0879360	−	0.171105i
$250$	−12.2321	−	21.1865i	−0.773623	−	1.33995i
$251$	−10.9433	+	18.9543i	−0.690735	+	1.19639i	0.280863	+	0.959748i	$0.409379\pi$
$251$	−10.9433	+	18.9543i	−0.690735	+	1.19639i	−0.971597	+	0.236640i	$0.923954\pi$
$252$	−5.57097	−	14.8213i	−0.350938	−	0.933656i
$253$		0			0
$254$	−34.9764	+	9.37191i	−2.19462	+	0.588046i
$255$	4.82195	+	7.48221i	0.301962	+	0.468554i
$256$	14.1603	−	24.5263i	0.885016	−	1.53289i
$257$	8.29863	+	14.3737i	0.517655	+	0.896604i	0.999790	+	0.0205071i	$0.00652807\pi$
$257$	8.29863	+	14.3737i	0.517655	+	0.896604i	−0.482135	+	0.876097i	$0.660139\pi$
$258$	−30.2295	−	15.5358i	−1.88201	−	0.967220i
$259$			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	$-0.787006\pi$
$263$	−10.3681	+	5.98604i	−0.639326	+	0.369115i	0.145029	+	0.989427i	$0.453673\pi$
$264$	−8.45593	+	9.32559i	−0.520426	+	0.573950i
$265$	−7.83013	−	7.83013i	−0.481001	−	0.481001i
$266$	0.907241	+	3.38587i	0.0556265	+	0.207601i
$267$	0.850019	+	17.3799i	0.0520203	+	1.06363i
$268$	−23.1244	+	23.1244i	−1.41254	+	1.41254i
$269$	−9.58244	−	5.53242i	−0.584251	−	0.337318i	0.178570	−	0.983927i	$-0.442853\pi$
$269$	−9.58244	−	5.53242i	−0.584251	−	0.337318i	−0.762821	+	0.646610i	$0.776186\pi$
$270$	−3.42336	+	29.5872i	−0.208339	+	1.80062i
$271$	2.00000	+	0.535898i	0.121491	+	0.0325535i	0.319052	−	0.947737i	$-0.396635\pi$
$271$	2.00000	+	0.535898i	0.121491	+	0.0325535i	−0.197561	+	0.980291i	$0.563302\pi$
$272$	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
$279$	−18.6853	−	3.09333i	−1.11866	−	0.185193i
$280$	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	$0.984017\pi$
$282$	29.4194	+	26.6759i	1.75190	+	1.58853i
$283$	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
$288$	−5.55017	−	4.55896i	−0.327047	−	0.268639i
$289$	6.19615	+	10.7321i	0.364480	+	0.631297i
$290$	15.8561	−	27.4635i	0.931100	−	1.61271i
$291$	18.9345	−	12.2025i	1.10996	−	0.715320i
$292$	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	$0.639030\pi$
$294$	17.4284	−	11.2318i	1.01645	−	0.655054i
$295$	−5.73205	+	9.92820i	−0.333733	+	0.578042i
$296$	−14.1631	−	24.5313i	−0.823215	−	1.42585i
$297$	5.65683	+	7.13714i	0.328242	+	0.414139i
$298$		−	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
$303$	25.3287	+	22.9666i	1.45509	+	1.31940i
$304$	−1.80385	−	1.80385i	−0.103458	−	0.103458i
$305$	4.33760	+	16.1881i	0.248370	+	0.926930i
$306$	2.51810	−	15.2106i	0.143950	−	0.869533i
$307$	12.3923	−	12.3923i	0.707266	−	0.707266i	−0.258693	−	0.965960i	$-0.583292\pi$
$307$	12.3923	−	12.3923i	0.707266	−	0.707266i	0.965960	+	0.258693i	$0.0832919\pi$
$308$	8.01105	+	4.62518i	0.456472	+	0.263544i
$309$	3.66834	+	11.4256i	0.208685	+	0.649977i
$310$	34.9545	+	9.36603i	1.98528	+	0.531954i
$311$	4.29311			0.243440			0.121720	−	0.992564i	$-0.461159\pi$
$311$	4.29311			0.243440			0.121720	+	0.992564i	$0.461159\pi$
$312$		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
$315$	10.1091	−	0.991207i	0.569585	−	0.0558482i
$316$	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	$0.397793\pi$
$318$	0.936928	+	19.1569i	0.0525403	+	1.07427i
$319$	−2.50962	−	9.36603i	−0.140512	−	0.524397i
$320$	18.0471	+	18.0471i	1.00886	+	1.00886i
$321$	−19.4137	+	21.4103i	−1.08357	+	1.19501i
$322$		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
$327$	6.10851	+	3.13935i	0.337801	+	0.173606i
$328$	−1.33013	−	2.30385i	−0.0734440	−	0.127209i
$329$	6.77174	−	11.7290i	0.373338	−	0.646640i
$330$	−9.42610	−	14.6265i	−0.518890	−	0.805160i
$331$	18.8564	−	5.05256i	1.03644	−	0.277714i	0.299804	−	0.954001i	$-0.403079\pi$
$331$	18.8564	−	5.05256i	1.03644	−	0.277714i	0.736638	+	0.676287i	$0.236412\pi$
$332$	6.31812	−	1.69293i	0.346752	−	0.0929118i
$333$	−19.1822	+	7.21011i	−1.05118	+	0.395112i
$334$	14.1244	−	24.4641i	0.772850	−	1.33862i
$335$	−10.4897	−	18.1687i	−0.573112	−	0.992660i
$336$	2.75895	−	5.36833i	0.150513	−	0.292867i
$337$			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
$342$	−6.04612	+	4.32860i	−0.326937	+	0.234064i
$343$	−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	$-0.578450\pi$
$347$	−22.4618	−	12.9683i	−1.20581	−	0.696175i	−0.961841	+	0.273608i	$0.911783\pi$
$348$	−34.0502	+	10.9323i	−1.82528	+	0.586034i
$349$	5.63397	+	1.50962i	0.301580	+	0.0808080i	0.406436	−	0.913679i	$-0.366772\pi$
$349$	5.63397	+	1.50962i	0.301580	+	0.0808080i	−0.104856	+	0.994487i	$0.533438\pi$
$350$	−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	$0.324778\pi$
$354$	18.9059	−	6.07001i	1.00484	−	0.322617i
$355$	−9.92820	−	5.73205i	−0.526934	−	0.304226i
$356$	−26.5118	+	26.5118i	−1.40512	+	1.40512i
$357$	−5.25169	+	0.256850i	−0.277949	+	0.0135939i
$358$	−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	$0.601383\pi$
$360$	−24.2179	+	17.3383i	−1.27639	+	0.913809i
$361$	−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
$366$	13.2685	−	25.8178i	0.693557	−	1.34952i
$367$	−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
$369$	−1.80149	+	0.677136i	−0.0937819	+	0.0352503i
$370$	37.8205	−	10.1340i	1.96619	−	0.526840i
$371$	6.31812	−	1.69293i	0.328020	−	0.0878928i
$372$	−22.1066	−	34.3028i	−1.14618	−	1.77852i
$373$	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
$375$	−15.7413	−	8.08992i	−0.812876	−	0.417762i
$376$			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	−0.991167	−	0.132622i	$-0.957660\pi$
$379$	−1.29423	+	4.83013i	−0.0664801	+	0.248107i	0.924687	+	0.380729i	$0.124327\pi$
$380$	8.01105	−	4.62518i	0.410958	−	0.237267i
$381$	−17.5965	+	19.4062i	−0.901496	+	0.994211i
$382$	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	$-0.199952\pi$
$384$	−1.75432	−	35.8697i	−0.0895246	−	1.83047i
$385$	−4.19615	+	4.19615i	−0.213856	+	0.213856i
$386$	14.9488	+	8.63071i	0.760875	+	0.439291i
$387$	−24.4711	+	2.39941i	−1.24394	+	0.121969i
$388$	46.8827	+	12.5622i	2.38011	+	0.637748i
$389$	−5.28933			−0.268180			−0.134090	−	0.990969i	$-0.542811\pi$
$389$	−5.28933			−0.268180			−0.134090	+	0.990969i	$0.542811\pi$
$390$		0			0
$391$		0			0
$392$	20.0276	+	5.36639i	1.01155	+	0.271043i
$393$	0.480365	+	1.49616i	0.0242312	+	0.0754715i
$394$	−3.63397	−	2.09808i	−0.183077	−	0.105700i
$395$	−3.38587	+	3.38587i	−0.170362	+	0.170362i
$396$	−3.20495	+	19.3595i	−0.161055	+	0.972851i
$397$	2.29423	+	8.56218i	0.115144	+	0.429723i	0.999298	−	0.0374729i	$-0.0119308\pi$
$397$	2.29423	+	8.56218i	0.115144	+	0.429723i	−0.884154	+	0.467196i	$0.845264\pi$
$398$	−1.57139	−	1.57139i	−0.0787665	−	0.0787665i
$399$	1.87861	+	1.70342i	0.0940479	+	0.0852774i
$400$	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
$405$	9.51336	+	19.3337i	0.472722	+	0.960700i
$406$	9.36603	+	16.2224i	0.464828	+	0.805106i
$407$	5.98604	−	10.3681i	0.296717	−	0.513929i
$408$	12.9596	−	8.35187i	0.641594	−	0.413479i
$409$	11.2321	−	3.00962i	0.555389	−	0.148816i	0.0298020	−	0.999556i	$-0.490512\pi$
$409$	11.2321	−	3.00962i	0.555389	−	0.148816i	0.525587	+	0.850740i	$0.323846\pi$
$410$	3.55190	−	0.951730i	0.175416	−	0.0470026i
$411$	8.58908	−	5.53528i	0.423668	−	0.273035i
$412$	−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	$-0.601339\pi$
$419$	7.22536	−	4.17156i	0.352982	−	0.203794i	0.665998	+	0.745954i	$0.268006\pi$
$420$	16.2137	+	14.7017i	0.791147	+	0.717368i
$421$	−0.830127	−	0.830127i	−0.0404579	−	0.0404579i	0.686588	−	0.727046i	$-0.259107\pi$
$421$	−0.830127	−	0.830127i	−0.0404579	−	0.0404579i	−0.727046	+	0.686588i	$0.759107\pi$
$422$	7.55743	+	28.2047i	0.367890	+	1.37298i
$423$	28.3443	+	4.69237i	1.37815	+	0.228151i
$424$	−13.5622	+	13.5622i	−0.658638	+	0.658638i
$425$	−1.36086	−	0.785693i	−0.0660114	−	0.0381117i
$426$	6.07001	+	18.9059i	0.294093	+	0.915992i
$427$	−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	$0.567255\pi$
$432$	12.7190	+	1.47164i	0.611943	+	0.0708043i
$433$	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
$435$	−1.12071	−	22.9146i	−0.0537339	−	1.09867i
$436$	3.83013	+	14.2942i	0.183430	+	0.684569i
$437$		0			0
$438$	24.0222	−	26.4928i	1.14782	−	1.26587i
$439$	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	$-0.752134\pi$
$443$		−	29.5656i		−	1.40470i	0.711830	−	0.702351i	$-0.247866\pi$
$444$	−39.2723	−	20.1832i	−1.86378	−	0.957855i
$445$	−12.0263	−	20.8301i	−0.570100	−	0.987443i
$446$	27.6295	−	47.8558i	1.30830	−	2.26604i
$447$	−5.09465	−	7.90535i	−0.240969	−	0.373910i
$448$	−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	$0.482966\pi$
$450$	−1.84997	−	4.92177i	−0.0872084	−	0.232014i
$451$	0.562178	−	0.973721i	0.0264719	−	0.0458507i
$452$	24.1992	+	41.9142i	1.13823	+	1.97148i
$453$	−8.35723	+	16.2614i	−0.392657	+	0.764028i
$454$		−	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	$0.310053\pi$
$457$	−7.23205	+	26.9904i	−0.338301	+	1.26256i	−0.900246	+	0.435382i	$0.856613\pi$
$458$	−29.6871	+	17.1399i	−1.38719	+	0.800893i
$459$	−4.42972	−	10.2365i	−0.206761	−	0.477798i
$460$		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	$-0.274253\pi$
$462$	10.2662	−	0.502098i	0.477625	−	0.0233597i
$463$	15.0526	−	15.0526i	0.699552	−	0.699552i	−0.264762	−	0.964314i	$-0.585293\pi$
$463$	15.0526	−	15.0526i	0.699552	−	0.699552i	0.964314	+	0.264762i	$0.0852934\pi$
$464$	−11.8060	−	6.81623i	−0.548082	−	0.316435i
$465$	24.9265	−	8.00301i	1.15594	−	0.371131i
$466$	−17.1962	−	4.60770i	−0.796596	−	0.213447i
$467$	−30.4728			−1.41011			−0.705057	−	0.709151i	$-0.749079\pi$
$467$	−30.4728			−1.41011			−0.705057	+	0.709151i	$0.749079\pi$
$468$		0			0
$469$	12.3923			0.572223
$470$	−53.0236	−	14.2076i	−2.44579	−	0.655349i
$471$	−25.0605	+	8.04605i	−1.15473	+	0.370743i
$472$	17.1962	+	9.92820i	0.791517	+	0.456983i
$473$	10.1576	−	10.1576i	0.467047	−	0.467047i
$474$	8.28375	−	0.405142i	0.380485	−	0.0186088i
$475$	0.196152	+	0.732051i	0.00900009	+	0.0335888i
$476$	−8.01105	−	8.01105i	−0.367186	−	0.367186i
$477$	8.07727	+	11.2822i	0.369833	+	0.516577i
$478$	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
$486$	10.2872	−	35.8756i	0.466636	−	1.62735i
$487$	−24.4904	+	6.56218i	−1.10977	+	0.297361i	−0.766735	−	0.641964i	$-0.778120\pi$
$487$	−24.4904	+	6.56218i	−1.10977	+	0.297361i	−0.343030	+	0.939324i	$0.611453\pi$
$488$	28.0387	−	7.51294i	1.26925	−	0.340095i
$489$	−14.5007	−	22.5007i	−0.655746	−	1.01752i
$490$	−14.3301	+	24.8205i	−0.647369	+	1.12128i
$491$	−12.5147	−	21.6761i	−0.564780	−	0.978227i	−0.997070	−	0.0764928i	$-0.975628\pi$
$491$	−12.5147	−	21.6761i	−0.564780	−	0.978227i	0.432290	−	0.901734i	$-0.357706\pi$
$492$	−3.68825	−	1.89551i	−0.166279	−	0.0854560i
$493$			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
$498$	4.88203	−	5.38413i	0.218769	−	0.241269i
$499$	−4.46410	−	4.46410i	−0.199841	−	0.199841i	0.600091	−	0.799932i	$-0.295131\pi$
$499$	−4.46410	−	4.46410i	−0.199841	−	0.199841i	−0.799932	+	0.600091i	$0.795131\pi$
$500$	−9.87002	−	36.8354i	−0.441401	−	1.64733i
$501$	−0.998312	−	20.4120i	−0.0446013	−	0.911941i
$502$	−37.0526	+	37.0526i	−1.65374	+	1.65374i
$503$	−24.8188	−	14.3292i	−1.10662	−	0.638906i	−0.168666	−	0.985673i	$-0.553946\pi$
$503$	−24.8188	−	14.3292i	−1.10662	−	0.638906i	−0.937951	+	0.346767i	$0.887279\pi$
$504$	−1.71682	−	17.5095i	−0.0764733	−	0.779936i
$505$	−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	$0.691251\pi$
$510$	6.51480	+	20.2912i	0.288480	+	0.898511i
$511$	−10.5622	−	6.09808i	−0.467243	−	0.269763i
$512$	18.6223	−	18.6223i	0.822996	−	0.822996i
$513$	−1.98031	+	5.00169i	−0.0874328	+	0.220830i
$514$	10.2846	+	38.3827i	0.453635	+	1.69299i
$515$	−11.7290	−	11.7290i	−0.516841	−	0.516841i
$516$	−39.2484	−	35.5883i	−1.72781	−	1.56669i
$517$	−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	$-0.260056\pi$
$522$	−25.2221	+	30.7059i	−1.10394	+	1.34396i
$523$	−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
$525$	−1.50726	+	0.971364i	−0.0657823	+	0.0423938i
$526$	−27.6865	+	7.41858i	−1.20719	+	0.323466i
$527$	−13.0899	+	3.50742i	−0.570203	+	0.152785i
$528$	−6.28764	+	4.05211i	−0.273634	+	0.176345i
$529$	11.5000	−	19.9186i	0.500000	−	0.866025i
$530$	−13.2559	−	22.9599i	−0.575799	−	0.997313i
$531$	9.11792	−	11.1003i	0.395684	−	0.481713i
$532$			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
$537$	−24.0504	−	21.8076i	−1.03785	−	0.941066i
$538$	−18.7321	−	18.7321i	−0.807596	−	0.807596i
$539$	2.26810	+	8.46467i	0.0976940	+	0.364599i
$540$	−17.0915	+	43.1681i	−0.735500	+	1.85766i
$541$	−23.6865	+	23.6865i	−1.01836	+	1.01836i	−0.0185354	+	0.999828i	$0.505900\pi$
$541$	−23.6865	+	23.6865i	−1.01836	+	1.01836i	−0.999828	+	0.0185354i	$0.994100\pi$
$542$	4.29311	+	2.47863i	0.184405	+	0.106466i
$543$	−1.58844	−	4.94741i	−0.0681664	−	0.212314i
$544$	−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
$549$	−2.04924	−	20.8998i	−0.0874593	−	0.891981i
$550$	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
$555$	19.0273	−	20.9842i	0.807665	−	0.890731i
$556$	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
$561$	5.79567	+	2.97857i	0.244693	+	0.125755i
$562$	−26.9186	−	46.6244i	−1.13549	−	1.96673i
$563$	2.14655	−	3.71794i	0.0904665	−	0.156693i	−0.817241	−	0.576296i	$-0.804498\pi$
$563$	2.14655	−	3.71794i	0.0904665	−	0.156693i	0.907708	+	0.419603i	$0.137831\pi$
$564$	33.5342	+	52.0350i	1.41205	+	2.19107i
$565$	−29.9904	+	8.03590i	−1.26170	+	0.338073i
$566$	56.8630	−	15.2364i	2.39013	−	0.640434i
$567$	−12.6999	−	0.843533i	−0.533347	−	0.0354250i
$568$	−9.92820	+	17.1962i	−0.416578	+	0.721535i
$569$	8.01105	+	13.8755i	0.335841	+	0.581693i	0.983646	−	0.180113i	$-0.0576463\pi$
$569$	8.01105	+	13.8755i	0.335841	+	0.581693i	−0.647805	+	0.761806i	$0.724313\pi$
$570$	4.69825	−	9.14181i	0.196788	−	0.382908i
$571$		−	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
$576$	−18.6167	−	26.0036i	−0.775697	−	1.08348i
$577$	−3.49038	−	3.49038i	−0.145306	−	0.145306i	0.630711	−	0.776018i	$-0.282763\pi$
$577$	−3.49038	−	3.49038i	−0.145306	−	0.145306i	−0.776018	+	0.630711i	$0.782763\pi$
$578$	7.67898	+	28.6583i	0.319403	+	1.19203i
$579$	12.4728	−	0.610020i	0.518351	−	0.0253516i
$580$	34.9545	−	34.9545i	1.45141	−	1.45141i
$581$	−2.14655	−	1.23931i	−0.0890541	−	0.0514154i
$582$	51.3491	−	16.4864i	2.12849	−	0.683383i
$583$	−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	$0.447235\pi$
$588$	30.7733	−	9.88023i	1.26907	−	0.407454i
$589$	5.66025	+	3.26795i	0.233227	+	0.134654i
$590$	−19.4080	+	19.4080i	−0.799013	+	0.799013i
$591$	−3.03206	+	0.148292i	−0.124722	+	0.00609993i
$592$	−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	$0.849701\pi$
$594$	8.65935	+	20.0106i	0.355297	+	0.821044i
$595$	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	$0.857256\pi$
$600$	2.40340	−	4.67652i	0.0981186	−	0.190918i
$601$	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
$603$	9.24923	+	24.6072i	0.376658	+	1.00208i
$604$	−38.0526	+	10.1962i	−1.54834	+	0.414876i
$605$	−18.3347	+	4.91277i	−0.745411	+	0.199732i
$606$	44.3434	+	68.8075i	1.80133	+	2.79511i
$607$	−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
$609$	12.0530	+	6.19441i	0.488413	+	0.251010i
$610$			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	$-0.805574\pi$
$613$	4.38269	−	16.3564i	0.177015	−	0.660629i	0.996200	−	0.0870991i	$-0.0277597\pi$
$614$	36.3373	−	20.9794i	1.46645	−	0.846658i
$615$	1.78695	−	1.97073i	0.0720567	−	0.0794674i
$616$	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	$0.642759\pi$
$618$	1.40345	+	28.6957i	0.0564552	+	1.15431i
$619$	14.3397	−	14.3397i	0.576363	−	0.576363i	−0.357536	−	0.933899i	$-0.616383\pi$
$619$	14.3397	−	14.3397i	0.576363	−	0.576363i	0.933899	+	0.357536i	$0.116383\pi$
$620$	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
$627$	−0.960731	−	2.99233i	−0.0383679	−	0.119502i
$628$	−49.1147	−	28.3564i	−1.95989	−	1.13154i
$629$	−10.3681	+	10.3681i	−0.413404	+	0.413404i
$630$	23.9925	+	3.97193i	0.955883	+	0.158246i
$631$	0.607695	+	2.26795i	0.0241920	+	0.0902856i	0.976966	−	0.213393i	$-0.0684516\pi$
$631$	0.607695	+	2.26795i	0.0241920	+	0.0902856i	−0.952774	+	0.303679i	$0.901785\pi$
$632$	5.86450	+	5.86450i	0.233277	+	0.233277i
$633$	15.6490	+	14.1897i	0.621993	+	0.563989i
$634$	−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
$639$	11.1003	+	9.11792i	0.439122	+	0.360699i
$640$	24.8205	+	42.9904i	0.981117	+	1.69934i
$641$	−9.65949	+	16.7307i	−0.381527	+	0.660824i	−0.991281	−	0.131767i	$-0.957935\pi$
$641$	−9.65949	+	16.7307i	−0.381527	+	0.660824i	0.609754	+	0.792591i	$0.291268\pi$
$642$	−58.1629	+	37.4835i	−2.29551	+	1.47935i
$643$	26.1244	−	7.00000i	1.03024	−	0.276053i	0.296179	−	0.955132i	$-0.404287\pi$
$643$	26.1244	−	7.00000i	1.03024	−	0.276053i	0.734065	+	0.679079i	$0.237621\pi$
$644$		0			0
$645$	28.5692	−	18.4116i	1.12491	−	0.724955i
$646$	−2.66025	+	4.60770i	−0.104666	+	0.181287i
$647$	7.22536	+	12.5147i	0.284058	+	0.492003i	0.972380	−	0.233402i	$-0.0749858\pi$
$647$	7.22536	+	12.5147i	0.284058	+	0.492003i	−0.688322	+	0.725405i	$0.741652\pi$
$648$	33.4870	−	16.4776i	1.31549	−	0.647302i
$649$			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	$-0.392114\pi$
$653$	33.6156	−	19.4080i	1.31548	−	0.759492i	0.982998	+	0.183617i	$0.0587807\pi$
$654$	12.1812	+	11.0452i	0.476321	+	0.431902i
$655$	−1.53590	−	1.53590i	−0.0600125	−	0.0600125i
$656$	−0.409131	−	1.52690i	−0.0159739	−	0.0596153i
$657$	4.22556	−	25.5245i	0.164855	−	0.995807i
$658$	22.9282	−	22.9282i	0.893834	−	0.893834i
$659$	−27.1759	−	15.6900i	−1.05862	−	0.611197i	−0.133572	−	0.991039i	$-0.542645\pi$
$659$	−27.1759	−	15.6900i	−1.05862	−	0.611197i	−0.925051	+	0.379842i	$0.875978\pi$
$660$	−8.29179	−	25.8259i	−0.322757	−	1.00527i
$661$	−16.5263	−	4.42820i	−0.642798	−	0.172237i	−0.0773274	−	0.997006i	$-0.524639\pi$
$661$	−16.5263	−	4.42820i	−0.642798	−	0.172237i	−0.565470	+	0.824769i	$0.691305\pi$
$662$	46.7380			1.81652
$663$		0			0
$664$	7.26795			0.282051
$665$	−3.38587	−	0.907241i	−0.131298	−	0.0351813i
$666$	−48.8284	+	4.78766i	−1.89206	+	0.185518i
$667$		0			0
$668$	31.1370	−	31.1370i	1.20473	−	1.20473i
$669$	−1.95286	−	39.9292i	−0.0755019	−	1.54375i
$670$	−13.0000	−	48.5167i	−0.502234	−	1.87436i
$671$	8.67520	+	8.67520i	0.334902	+	0.334902i
$672$	−3.93930	+	4.34444i	−0.151962	+	0.167591i
$673$	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	$0.267985\pi$
$677$			38.8159i			1.49182i	−0.666048	+	0.745909i	$0.732015\pi$
$678$	47.8304	+	24.5815i	1.83692	+	0.944046i
$679$	−9.19615	−	15.9282i	−0.352916	−	0.611268i
$680$	−10.6557	+	18.4562i	−0.408628	+	0.707764i
$681$	−14.6820	−	22.7821i	−0.562617	−	0.873011i
$682$	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	$0.518651\pi$
$684$	−10.8500	+	4.07823i	−0.414859	+	0.155935i
$685$	−7.06218	+	12.2321i	−0.269832	+	0.467363i
$686$	−20.3152	−	35.1870i	−0.775638	−	1.34344i
$687$	−11.3358	+	22.0571i	−0.432488	+	0.841530i
$688$		−	20.1962i		−	0.769971i
$689$		0			0
$690$		0			0
$691$	−11.2224	+	41.8827i	−0.426921	+	1.59329i	0.332770	+	0.943008i	$0.392017\pi$
$691$	−11.2224	+	41.8827i	−0.426921	+	1.59329i	−0.759691	+	0.650284i	$0.774650\pi$
$692$	24.0331	−	13.8755i	0.913603	−	0.527469i
$693$	6.04612	−	4.32860i	0.229673	−	0.164430i
$694$	−43.9090	−	43.9090i	−1.66676	−	1.66676i
$695$	1.48241	+	5.53242i	0.0562309	+	0.209857i
$696$	−39.6892	+	1.94112i	−1.50442	+	0.0735781i
$697$	−0.973721	+	0.973721i	−0.0368823	+	0.0368823i
$698$	12.0936	+	6.98226i	0.457751	+	0.264283i
$699$	−12.2628	+	3.93715i	−0.463821	+	0.148917i
$700$	−3.73205	−	1.00000i	−0.141058	−	0.0377964i
$701$	20.3152			0.767295			0.383647	−	0.923480i	$-0.374668\pi$
$701$	20.3152			0.767295			0.383647	+	0.923480i	$0.374668\pi$
$702$		0			0
$703$	7.07180			0.266718
$704$	18.0471	+	4.83571i	0.680176	+	0.182253i
$705$	−37.8117	+	12.1400i	−1.42407	+	0.457220i
$706$	56.5526	+	32.6506i	2.12838	+	1.22882i
$707$	19.7400	−	19.7400i	0.742401	−	0.742401i
$708$	30.9154	−	1.51201i	1.16187	−	0.0568249i
$709$	−2.66987	−	9.96410i	−0.100269	−	0.374210i	0.897496	−	0.441022i	$-0.145384\pi$
$709$	−2.66987	−	9.96410i	−0.100269	−	0.374210i	−0.997766	+	0.0668121i	$0.978717\pi$
$710$	−19.4080	−	19.4080i	−0.728368	−	0.728368i
$711$	4.87861	−	3.49274i	0.182962	−	0.130988i
$712$	−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
$717$	7.95383	−	15.4765i	0.297041	−	0.577979i
$718$	20.4186	+	35.3660i	0.762015	+	1.31985i
$719$	−5.86450	+	10.1576i	−0.218709	+	0.378815i	−0.954413	−	0.298488i	$-0.903518\pi$
$719$	−5.86450	+	10.1576i	−0.218709	+	0.378815i	0.735705	+	0.677302i	$0.236851\pi$
$720$	−16.5668	+	6.22704i	−0.617408	+	0.232068i
$721$	9.46410	−	2.53590i	0.352462	−	0.0944418i
$722$	−41.4606	+	11.1093i	−1.54300	+	0.413447i
$723$	7.02496	+	10.9006i	0.261261	+	0.405398i
$724$	5.59808	−	9.69615i	0.208051	−	0.360355i
$725$	2.02501	+	3.50742i	0.0752069	+	0.130262i
$726$	29.2412	+	15.0279i	1.08524	+	0.557740i
$727$		−	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
$732$	30.3945	−	33.5205i	1.12341	−	1.23895i
$733$	36.2224	+	36.2224i	1.33791	+	1.33791i	0.898086	+	0.439820i	$0.144958\pi$
$733$	36.2224	+	36.2224i	1.33791	+	1.33791i	0.439820	+	0.898086i	$0.355042\pi$
$734$	−5.95347	−	22.2187i	−0.219747	−	0.820106i
$735$	1.01286	+	20.7094i	0.0373597	+	0.763877i
$736$		0			0
$737$	−13.3004	−	7.67898i	−0.489926	−	0.282859i
$738$	−4.58570	+	0.449632i	−0.168802	+	0.0165512i
$739$	48.9808	+	13.1244i	1.80179	+	0.482787i	0.994255	−	0.107037i	$-0.0341364\pi$
$739$	48.9808	+	13.1244i	1.80179	+	0.482787i	0.807531	+	0.589825i	$0.200803\pi$
$740$	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	$0.992844\pi$
$744$	−13.8616	−	43.1739i	−0.508192	−	1.58283i
$745$	11.2583	+	6.50000i	0.412473	+	0.238142i
$746$	33.1620	−	33.1620i	1.21415	−	1.21415i
$747$	0.858763	−	5.18736i	0.0314205	−	0.189796i
$748$	3.63397	+	13.5622i	0.132871	+	0.495882i
$749$	16.6862	+	16.6862i	0.609702	+	0.609702i
$750$	−31.3902	−	28.4629i	−1.14621	−	1.03932i
$751$	−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
$756$	−17.0349	−	21.4927i	−0.619553	−	0.781681i
$757$	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	$0.441608\pi$
$762$	−52.7187	+	33.9749i	−1.90980	+	1.23078i
$763$	2.80385	−	4.85641i	0.101506	−	0.175814i
$764$	36.2158	+	62.7275i	1.31024	+	2.26940i
$765$	11.9137	+	9.78605i	0.430742	+	0.353816i
$766$		−	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	−0.975616	−	0.219483i	$-0.929563\pi$
$769$	−0.581416	+	2.16987i	−0.0209664	+	0.0782476i	0.954650	+	0.297730i	$0.0962297\pi$
$770$	−12.3042	+	7.10381i	−0.443411	+	0.256004i
$771$	21.2961	+	19.3102i	0.766962	+	0.695438i
$772$	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	$0.881117\pi$
$774$	−58.0785	−	9.61484i	−2.08759	−	0.345598i
$775$	−3.26795	+	3.26795i	−0.117388	+	0.117388i
$776$	46.7054	+	26.9654i	1.67663	+	0.968001i
$777$	5.11491	+	15.9311i	0.183496	+	0.571524i
$778$	−12.2321	−	3.27757i	−0.438540	−	0.117507i
$779$	0.664146			0.0237955
$780$		0			0
$781$	−8.39230			−0.300300
$782$		0			0
$783$	−3.30414	+	28.5568i	−0.118080	+	1.02054i
$784$	10.6699	+	6.16025i	0.381067	+	0.220009i
$785$	25.7261	−	25.7261i	0.918203	−	0.918203i
$786$	0.183781	+	3.75768i	0.00655524	+	0.134032i
$787$	−3.02628	−	11.2942i	−0.107875	−	0.402596i	0.890780	−	0.454434i	$-0.150159\pi$
$787$	−3.02628	−	11.2942i	−0.107875	−	0.402596i	−0.998655	+	0.0518385i	$0.983492\pi$
$788$	−4.62518	−	4.62518i	−0.164765	−	0.164765i
$789$	−13.9290	+	15.3615i	−0.495885	+	0.546884i
$790$	−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
$795$	−17.0588	−	8.76706i	−0.605015	−	0.310935i
$796$	−1.73205	−	3.00000i	−0.0613909	−	0.106332i
$797$	8.58622	−	14.8718i	0.304139	−	0.526785i	−0.672930	−	0.739706i	$-0.734964\pi$
$797$	8.58622	−	14.8718i	0.304139	−	0.526785i	0.977069	+	0.212921i	$0.0682978\pi$
$798$	3.28891	+	5.10339i	0.116426	+	0.180658i
$799$	19.8564	−	5.32051i	0.702469	−	0.188226i
$800$	−1.69293	+	0.453620i	−0.0598543	+	0.0160379i
$801$	10.6041	+	28.2118i	0.374678	+	0.996815i
$802$	33.6244	−	58.2391i	1.18732	−	2.05649i
$803$	7.55743	+	13.0899i	0.266696	+	0.461931i
$804$	−25.8913	+	50.3791i	−0.913117	+	1.77673i
$805$		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	$-0.783442\pi$
$809$	−17.6705	+	10.2021i	−0.621263	+	0.358686i	0.156097	+	0.987742i	$0.450109\pi$
$810$	10.0202	+	50.6060i	0.352075	+	1.77811i
$811$	−19.0000	−	19.0000i	−0.667180	−	0.667180i	0.289882	−	0.957062i	$-0.406384\pi$
$811$	−19.0000	−	19.0000i	−0.667180	−	0.667180i	−0.957062	+	0.289882i	$0.906384\pi$
$812$	7.55743	+	28.2047i	0.265214	+	0.989791i
$813$	3.58202	−	0.175190i	0.125627	−	0.00614417i
$814$	20.2679	−	20.2679i	0.710391	−	0.710391i
$815$	32.0442	+	18.5007i	1.12246	+	0.648052i
$816$	8.72282	−	2.80059i	0.305360	−	0.0980403i
$817$	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	$0.617823\pi$
$822$	23.2930	−	7.47856i	0.812436	−	0.260845i
$823$	−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
$825$	2.21962	−	0.108558i	0.0772774	−	0.00377949i
$826$	−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
$834$	4.53463	−	8.82343i	0.157021	−	0.305530i
$835$	14.1244	+	24.4641i	0.488793	+	0.846615i
$836$	3.38587	−	5.86450i	0.117103	−	0.202828i
$837$	−32.4524	+	4.79215i	−1.12172	+	0.165641i
$838$	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	$0.373545\pi$
$840$	13.1738	+	20.4418i	0.454540	+	0.705308i
$841$	0.803848	−	1.39230i	0.0277189	−	0.0480105i
$842$	−1.40535	−	2.43414i	−0.0484316	−	0.0838859i
$843$	−34.6412	−	17.8032i	−1.19311	−	0.613173i
$844$			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
$849$	28.6075	−	31.5497i	0.981808	−	1.08278i
$850$	−2.66025	−	2.66025i	−0.0912460	−	0.0912460i
$851$		0			0
$852$	1.51201	+	30.9154i	0.0518007	+	1.05914i
$853$	20.6340	−	20.6340i	0.706494	−	0.706494i	−0.259302	−	0.965796i	$-0.583493\pi$
$853$	20.6340	−	20.6340i	0.706494	−	0.706494i	0.965796	+	0.259302i	$0.0834926\pi$
$854$	−20.5257	−	11.8505i	−0.702376	−	0.405517i
$855$	−0.725614	−	7.40039i	−0.0248155	−	0.253088i
$856$	−66.8372	−	17.9090i	−2.28445	−	0.612116i
$857$	−35.7621			−1.22161			−0.610806	−	0.791781i	$-0.709154\pi$
$857$	−35.7621			−1.22161			−0.610806	+	0.791781i	$0.709154\pi$
$858$		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
$861$	0.480365	+	1.49616i	0.0163708	+	0.0509891i
$862$	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	$0.343759\pi$
$864$	−11.5669	−	4.57965i	−0.393513	−	0.155803i
$865$	4.60770	+	17.1962i	0.156666	+	0.584687i
$866$	11.9395	+	11.9395i	0.405721	+	0.405721i
$867$	15.9007	+	14.4179i	0.540016	+	0.489657i
$868$	−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
$873$	24.7646	−	30.1489i	0.838156	−	1.02039i
$874$		0			0
$875$	−7.22536	+	12.5147i	−0.244262	+	0.423074i
$876$	46.8585	−	30.1982i	1.58320	−	1.02030i
$877$	11.2321	−	3.00962i	0.379279	−	0.101628i	−0.0641422	−	0.997941i	$-0.520431\pi$
$877$	11.2321	−	3.00962i	0.379279	−	0.101628i	0.443422	+	0.896313i	$0.353764\pi$
$878$	10.9433	−	2.93225i	0.369318	−	0.0989586i
$879$	−32.0549	+	20.6579i	−1.08118	+	0.696775i
$880$	5.16987	−	8.95448i	0.174276	−	0.301856i
$881$	−13.5880	−	23.5350i	−0.457790	−	0.792916i	0.541054	−	0.840988i	$-0.318026\pi$
$881$	−13.5880	−	23.5350i	−0.457790	−	0.792916i	−0.998844	+	0.0480724i	$0.984692\pi$
$882$	22.7948	−	27.7508i	0.767541	−	0.934419i
$883$			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	$-0.309260\pi$
$887$	46.4949	−	26.8438i	1.56115	−	0.901328i	0.997142	−	0.0755567i	$-0.0240734\pi$
$888$	−36.3457	−	32.9563i	−1.21968	−	1.10594i
$889$	15.1244	+	15.1244i	0.507255	+	0.507255i
$890$	−14.9043	−	55.6237i	−0.499594	−	1.86451i
$891$	13.1079	+	8.77495i	0.439130	+	0.293972i
$892$	60.9090	−	60.9090i	2.03938	−	2.03938i
$893$	−8.58622	−	4.95725i	−0.287327	−	0.165888i
$894$	−6.88324	−	21.4388i	−0.230210	−	0.717020i
$895$	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
$900$	−0.799803	−	8.15704i	−0.0266601	−	0.271901i
$901$	8.59808	+	4.96410i	0.286443	+	0.165378i
$902$	1.90346	−	1.90346i	0.0633783	−	0.0633783i
$903$	0.980726	+	20.0524i	0.0326365	+	0.667303i
$904$	13.9186	+	51.9449i	0.462925	+	1.72766i
$905$	5.07880	+	5.07880i	0.168825	+	0.168825i
$906$	−29.4034	+	32.4274i	−0.976861	+	1.07733i
$907$	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	$-0.951030\pi$
$911$		−	9.25036i		−	0.306478i	0.988189	−	0.153239i	$-0.0489705\pi$
$912$	−3.92989	−	2.01969i	−0.130132	−	0.0668786i
$913$	1.53590	+	2.66025i	0.0508308	+	0.0880416i
$914$	−33.4495	+	57.9363i	−1.10641	+	1.91636i
$915$	15.7246	+	24.3998i	0.519839	+	0.806632i
$916$	−51.6147	+	13.8301i	−1.70540	+	0.456960i
$917$	1.23931	−	0.332073i	0.0409257	−	0.0109660i
$918$	−3.90102	−	26.4177i	−0.128753	−	0.871913i
$919$	−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
$921$	13.8751	−	26.9981i	0.457201	−	0.889617i
$922$		−	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
$927$	12.0992	+	16.9000i	0.397390	+	0.555068i
$928$	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	$0.619513\pi$
$930$	62.6038	−	3.06183i	2.05286	−	0.100401i
$931$	−3.66025	+	3.66025i	−0.119960	+	0.119960i
$932$	−24.0331	−	13.8755i	−0.787232	−	0.454509i
$933$	7.07992	−	2.27311i	0.231786	−	0.0744184i
$934$	−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
$939$	3.29827	−	1.05896i	0.107635	−	0.0345578i
$940$	−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	$0.906542\pi$
$942$	−62.9405	+	3.07830i	−2.05071	+	0.100296i
$943$		0			0
$944$	8.34312	+	8.34312i	0.271546	+	0.271546i
$945$	16.1465	−	6.98721i	0.525246	−	0.227294i
$946$	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
$951$	−12.6245	+	24.5647i	−0.409379	+	0.796565i
$952$	−6.29423	−	10.9019i	−0.203997	−	0.353333i
$953$	21.8866	−	37.9087i	0.708976	−	1.22798i	−0.256261	−	0.966608i	$-0.582491\pi$
$953$	21.8866	−	37.9087i	0.708976	−	1.22798i	0.965237	−	0.261375i	$-0.0841760\pi$
$954$	11.6883	+	31.0963i	0.378423	+	1.00678i
$955$	−44.8827	+	12.0263i	−1.45237	+	0.389161i
$956$	36.2158	−	9.70398i	1.17130	−	0.313849i
$957$	−9.09782	−	14.1171i	−0.294091	−	0.456340i
$958$	10.4904	−	18.1699i	0.338929	−	0.587042i
$959$	−4.17156	−	7.22536i	−0.134707	−	0.233319i
$960$	39.3177	+	20.2066i	1.26897	+	0.652164i
$961$			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	0.709412	−	0.704794i	$-0.248961\pi$
$967$	0.143594	+	0.143594i	0.00461766	+	0.00461766i	−0.704794	+	0.709412i	$0.748961\pi$
$968$	8.50916	+	31.7566i	0.273495	+	1.02070i
$969$	0.188027	+	3.84450i	0.00604030	+	0.123503i
$970$	−52.7128	+	52.7128i	−1.69251	+	1.69251i
$971$	45.5551	+	26.3013i	1.46193	+	0.844047i	0.999101	−	0.0423987i	$-0.0135000\pi$
$971$	45.5551	+	26.3013i	1.46193	+	0.844047i	0.462832	+	0.886446i	$0.346833\pi$
$972$	29.9633	−	49.8673i	0.961075	−	1.59950i
$973$	−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	$0.739022\pi$
$978$	−19.5915	−	61.0204i	−0.626468	−	1.95122i
$979$	−15.2487	−	8.80385i	−0.487351	−	0.281372i
$980$	−31.5906	+	31.5906i	−1.00912	+	1.00912i
$981$	11.7360	+	1.94288i	0.374701	+	0.0620314i
$982$	−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	$0.781510\pi$
$984$	−3.41340	−	3.09508i	−0.108815	−	0.0986677i
$985$	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
$990$	−23.2893	−	19.1301i	−0.740184	−	0.607994i
$991$	−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
$993$	28.4216	−	18.3164i	0.901931	−	0.581255i
$994$	15.6603	−	4.19615i	0.496713	−	0.133094i
$995$	2.14655	−	0.575167i	0.0680503	−	0.0182340i
$996$	9.52306	−	6.13719i	0.301750	−	0.194464i
$997$	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
$999$	−27.8165	+	22.0470i	−0.880074	+	0.697537i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.k.f.89.2		8
3.2	odd	2	inner	507.2.k.f.89.1		8
13.2	odd	12		507.2.f.e.239.4		8
13.3	even	3		507.2.f.e.437.1		8
13.4	even	6		39.2.k.b.20.2	yes	8
13.5	odd	4		507.2.k.d.80.2		8
13.6	odd	12	inner	507.2.k.f.188.1		8
13.7	odd	12		507.2.k.e.188.2		8
13.8	odd	4		39.2.k.b.2.1	✓	8
13.9	even	3		507.2.k.d.488.1		8
13.10	even	6		507.2.f.f.437.4		8
13.11	odd	12		507.2.f.f.239.1		8
13.12	even	2		507.2.k.e.89.1		8
39.2	even	12		507.2.f.e.239.1		8
39.5	even	4		507.2.k.d.80.1		8
39.8	even	4		39.2.k.b.2.2	yes	8
39.11	even	12		507.2.f.f.239.4		8
39.17	odd	6		39.2.k.b.20.1	yes	8
39.20	even	12		507.2.k.e.188.1		8
39.23	odd	6		507.2.f.f.437.1		8
39.29	odd	6		507.2.f.e.437.4		8
39.32	even	12	inner	507.2.k.f.188.2		8
39.35	odd	6		507.2.k.d.488.2		8
39.38	odd	2		507.2.k.e.89.2		8
52.43	odd	6		624.2.cn.c.449.2		8
52.47	even	4		624.2.cn.c.353.1		8
65.4	even	6		975.2.bo.d.176.1		8
65.8	even	4		975.2.bp.e.899.2		8
65.17	odd	12		975.2.bp.e.449.1		8
65.34	odd	4		975.2.bo.d.626.2		8
65.43	odd	12		975.2.bp.f.449.2		8
65.47	even	4		975.2.bp.f.899.1		8
156.47	odd	4		624.2.cn.c.353.2		8
156.95	even	6		624.2.cn.c.449.1		8
195.8	odd	4		975.2.bp.e.899.1		8
195.17	even	12		975.2.bp.e.449.2		8
195.47	odd	4		975.2.bp.f.899.2		8
195.134	odd	6		975.2.bo.d.176.2		8
195.164	even	4		975.2.bo.d.626.1		8
195.173	even	12		975.2.bp.f.449.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.2.k.b.2.1	✓	8	13.8	odd	4
39.2.k.b.2.2	yes	8	39.8	even	4
39.2.k.b.20.1	yes	8	39.17	odd	6
39.2.k.b.20.2	yes	8	13.4	even	6
507.2.f.e.239.1		8	39.2	even	12
507.2.f.e.239.4		8	13.2	odd	12
507.2.f.e.437.1		8	13.3	even	3
507.2.f.e.437.4		8	39.29	odd	6
507.2.f.f.239.1		8	13.11	odd	12
507.2.f.f.239.4		8	39.11	even	12
507.2.f.f.437.1		8	39.23	odd	6
507.2.f.f.437.4		8	13.10	even	6
507.2.k.d.80.1		8	39.5	even	4
507.2.k.d.80.2		8	13.5	odd	4
507.2.k.d.488.1		8	13.9	even	3
507.2.k.d.488.2		8	39.35	odd	6
507.2.k.e.89.1		8	13.12	even	2
507.2.k.e.89.2		8	39.38	odd	2
507.2.k.e.188.1		8	39.20	even	12
507.2.k.e.188.2		8	13.7	odd	12
507.2.k.f.89.1		8	3.2	odd	2	inner
507.2.k.f.89.2		8	1.1	even	1	trivial
507.2.k.f.188.1		8	13.6	odd	12	inner
507.2.k.f.188.2		8	39.32	even	12	inner
624.2.cn.c.353.1		8	52.47	even	4
624.2.cn.c.353.2		8	156.47	odd	4
624.2.cn.c.449.1		8	156.95	even	6
624.2.cn.c.449.2		8	52.43	odd	6
975.2.bo.d.176.1		8	65.4	even	6
975.2.bo.d.176.2		8	195.134	odd	6
975.2.bo.d.626.1		8	195.164	even	4
975.2.bo.d.626.2		8	65.34	odd	4
975.2.bp.e.449.1		8	65.17	odd	12
975.2.bp.e.449.2		8	195.17	even	12
975.2.bp.e.899.1		8	195.8	odd	4
975.2.bp.e.899.2		8	65.8	even	4
975.2.bp.f.449.1		8	195.173	even	12
975.2.bp.f.449.2		8	65.43	odd	12
975.2.bp.f.899.1		8	65.47	even	4
975.2.bp.f.899.2		8	195.47	odd	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)

\(f(q)\)	\(=\)	\(q+(2.31259 + 0.619657i) q^{2} +(1.64914 - 0.529480i) q^{3} +(3.23205 + 1.86603i) q^{4} +(-1.69293 + 1.69293i) q^{5} +(4.14187 - 0.202571i) q^{6} +(-0.366025 - 1.36603i) q^{7} +(2.93225 + 2.93225i) q^{8} +(2.43930 - 1.74637i) q^{9} +O(q^{10})\)	\(q+(2.31259 + 0.619657i) q^{2} +(1.64914 - 0.529480i) q^{3} +(3.23205 + 1.86603i) q^{4} +(-1.69293 + 1.69293i) q^{5} +(4.14187 - 0.202571i) q^{6} +(-0.366025 - 1.36603i) q^{7} +(2.93225 + 2.93225i) q^{8} +(2.43930 - 1.74637i) q^{9} +(-4.96410 + 2.86603i) q^{10} +(-0.453620 + 1.69293i) q^{11} +(6.31812 + 1.36603i) q^{12} -3.38587i q^{14} +(-1.89551 + 3.68825i) q^{15} +(1.23205 + 2.13397i) q^{16} +(1.07328 - 1.85897i) q^{17} +(6.72326 - 2.52711i) q^{18} +(-1.00000 + 0.267949i) q^{19} +(-8.63071 + 2.31259i) q^{20} +(-1.32691 - 2.05896i) q^{21} +(-2.09808 + 3.63397i) q^{22} +(6.38824 + 3.28311i) q^{24} -0.732051i q^{25} +(3.09808 - 4.17156i) q^{27} +(1.36603 - 5.09808i) q^{28} +(-4.79122 + 2.76621i) q^{29} +(-6.66898 + 7.35486i) q^{30} +(-4.46410 - 4.46410i) q^{31} +(-0.619657 - 2.31259i) q^{32} +(0.148292 + 3.03206i) q^{33} +(3.63397 - 3.63397i) q^{34} +(2.93225 + 1.69293i) q^{35} +(11.1427 - 1.09255i) q^{36} +(-6.59808 - 1.76795i) q^{37} -2.47863 q^{38} -9.92820 q^{40} +(-0.619657 - 0.166037i) q^{41} +(-1.79275 - 5.58376i) q^{42} +(-7.09808 - 4.09808i) q^{43} +(-4.62518 + 4.62518i) q^{44} +(-1.17309 + 7.08606i) q^{45} +(6.77174 + 6.77174i) q^{47} +(3.16172 + 2.86687i) q^{48} +(4.33013 - 2.50000i) q^{49} +(0.453620 - 1.69293i) q^{50} +(0.785693 - 3.63397i) q^{51} +4.62518i q^{53} +(9.74952 - 7.72737i) q^{54} +(-2.09808 - 3.63397i) q^{55} +(2.93225 - 5.07880i) q^{56} +(-1.50726 + 0.971364i) q^{57} +(-12.7942 + 3.42820i) q^{58} +(4.62518 - 1.23931i) q^{59} +(-13.0087 + 8.38356i) q^{60} +(3.50000 - 6.06218i) q^{61} +(-7.55743 - 13.0899i) q^{62} +(-3.27843 - 2.69293i) 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} +(12.2734 + 2.03185i) q^{72} +(6.09808 - 6.09808i) q^{73} +(-14.1631 - 8.17709i) q^{74} +(-0.387606 - 1.20725i) q^{75} +(-3.73205 - 1.00000i) q^{76} +2.47863 q^{77} +2.00000 q^{79} +(-5.69846 - 1.52690i) q^{80} +(2.90039 - 8.51984i) q^{81} +(-1.33013 - 0.767949i) q^{82} +(1.23931 - 1.23931i) q^{83} +(-0.446565 - 9.13071i) q^{84} +(1.33013 + 4.96410i) q^{85} +(-13.8755 - 13.8755i) q^{86} +(-6.43672 + 7.09871i) q^{87} +(-6.29423 + 3.63397i) q^{88} +(-2.60017 + 9.70398i) q^{89} +(-7.10381 + 15.6603i) q^{90} +(-9.72556 - 4.99826i) q^{93} +(11.4641 + 19.8564i) q^{94} +(1.23931 - 2.14655i) q^{95} +(-2.24637 - 3.48568i) q^{96} +(12.5622 - 3.36603i) q^{97} +(11.5630 - 3.09828i) q^{98} +(1.84997 + 4.92177i) 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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