LMFDB - Embedded newform 507.2.k.d.80.2

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			80.2
Root			$0.500000 + 2.19293i$ of defining polynomial
Character	$\chi$	$=$	507.80
Dual form			507.2.k.d.488.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.619657 - 2.31259i) q^{2} +(1.64914 - 0.529480i) q^{3} +(-3.23205 - 1.86603i) q^{4} +(1.69293 + 1.69293i) q^{5} +(-0.202571 - 4.14187i) q^{6} +(1.36603 - 0.366025i) q^{7} +(-2.93225 + 2.93225i) q^{8} +(2.43930 - 1.74637i) q^{9} +O(q^{10})$	\(q+(0.619657 - 2.31259i) q^{2} +(1.64914 - 0.529480i) q^{3} +(-3.23205 - 1.86603i) q^{4} +(1.69293 + 1.69293i) q^{5} +(-0.202571 - 4.14187i) q^{6} +(1.36603 - 0.366025i) q^{7} +(-2.93225 + 2.93225i) q^{8} +(2.43930 - 1.74637i) q^{9} +(4.96410 - 2.86603i) q^{10} +(-1.69293 - 0.453620i) q^{11} +(-6.31812 - 1.36603i) q^{12} -3.38587i q^{14} +(3.68825 + 1.89551i) q^{15} +(1.23205 + 2.13397i) q^{16} +(-1.07328 + 1.85897i) q^{17} +(-2.52711 - 6.72326i) q^{18} +(0.267949 + 1.00000i) q^{19} +(-2.31259 - 8.63071i) q^{20} +(2.05896 - 1.32691i) q^{21} +(-2.09808 + 3.63397i) q^{22} +(-3.28311 + 6.38824i) q^{24} +0.732051i q^{25} +(3.09808 - 4.17156i) q^{27} +(-5.09808 - 1.36603i) q^{28} +(-4.79122 + 2.76621i) q^{29} +(6.66898 - 7.35486i) q^{30} +(-4.46410 + 4.46410i) q^{31} +(-2.31259 + 0.619657i) q^{32} +(-3.03206 + 0.148292i) q^{33} +(3.63397 + 3.63397i) q^{34} +(2.93225 + 1.69293i) q^{35} +(-11.1427 + 1.09255i) q^{36} +(1.76795 - 6.59808i) q^{37} +2.47863 q^{38} -9.92820 q^{40} +(-0.166037 + 0.619657i) q^{41} +(-1.79275 - 5.58376i) q^{42} +(7.09808 + 4.09808i) q^{43} +(4.62518 + 4.62518i) q^{44} +(7.08606 + 1.17309i) q^{45} +(-6.77174 + 6.77174i) q^{47} +(3.16172 + 2.86687i) q^{48} +(-4.33013 + 2.50000i) q^{49} +(1.69293 + 0.453620i) q^{50} +(-0.785693 + 3.63397i) q^{51} +4.62518i q^{53} +(-7.72737 - 9.74952i) q^{54} +(-2.09808 - 3.63397i) q^{55} +(-2.93225 + 5.07880i) q^{56} +(0.971364 + 1.50726i) q^{57} +(3.42820 + 12.7942i) q^{58} +(1.23931 + 4.62518i) q^{59} +(-8.38356 - 13.0087i) q^{60} +(3.50000 - 6.06218i) q^{61} +(7.55743 + 13.0899i) q^{62} +(2.69293 - 3.27843i) q^{63} +10.6603i q^{64} +(-1.53590 + 7.10381i) q^{66} +(8.46410 + 2.26795i) q^{67} +(6.93777 - 4.00552i) q^{68} +(5.73205 - 5.73205i) q^{70} +(4.62518 - 1.23931i) q^{71} +(-2.03185 + 12.2734i) q^{72} +(6.09808 + 6.09808i) q^{73} +(-14.1631 - 8.17709i) q^{74} +(0.387606 + 1.20725i) q^{75} +(1.00000 - 3.73205i) q^{76} -2.47863 q^{77} +2.00000 q^{79} +(-1.52690 + 5.69846i) q^{80} +(2.90039 - 8.51984i) q^{81} +(1.33013 + 0.767949i) q^{82} +(-1.23931 - 1.23931i) q^{83} +(-9.13071 + 0.446565i) q^{84} +(-4.96410 + 1.33013i) q^{85} +(13.8755 - 13.8755i) q^{86} +(-6.43672 + 7.09871i) q^{87} +(6.29423 - 3.63397i) q^{88} +(-9.70398 - 2.60017i) q^{89} +(7.10381 - 15.6603i) q^{90} +(-4.99826 + 9.72556i) q^{93} +(11.4641 + 19.8564i) q^{94} +(-1.23931 + 2.14655i) q^{95} +(-3.48568 + 2.24637i) q^{96} +(-3.36603 - 12.5622i) q^{97} +(3.09828 + 11.5630i) q^{98} +(-4.92177 + 1.84997i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} - 12 q^{4} + 2 q^{6} + 4 q^{7} + 4 q^{9}+O(q^{10}) $ 8 * q - 2 * q^3 - 12 * q^4 + 2 * q^6 + 4 * q^7 + 4 * q^9	$ 8 q - 2 q^{3} - 12 q^{4} + 2 q^{6} + 4 q^{7} + 4 q^{9} + 12 q^{10} + 14 q^{15} - 4 q^{16} - 4 q^{18} + 16 q^{19} - 4 q^{21} + 4 q^{22} - 18 q^{24} + 4 q^{27} - 20 q^{28} + 18 q^{30} - 8 q^{31} - 16 q^{33} + 36 q^{34} - 36 q^{36} + 28 q^{37} - 24 q^{40} - 16 q^{42} + 36 q^{43} + 20 q^{45} - 14 q^{48} - 46 q^{54} + 4 q^{55} - 16 q^{57} - 28 q^{58} - 44 q^{60} + 28 q^{61} + 8 q^{63} - 40 q^{66} + 40 q^{67} + 32 q^{70} - 12 q^{72} + 28 q^{73} + 12 q^{75} + 8 q^{76} + 16 q^{79} + 4 q^{81} - 24 q^{82} - 4 q^{84} - 12 q^{85} - 34 q^{87} - 12 q^{88} - 4 q^{93} + 64 q^{94} - 16 q^{96} - 20 q^{97} - 40 q^{99}+O(q^{100}) $ 8 * q - 2 * q^3 - 12 * q^4 + 2 * q^6 + 4 * q^7 + 4 * q^9 + 12 * q^10 + 14 * q^15 - 4 * q^16 - 4 * q^18 + 16 * q^19 - 4 * q^21 + 4 * q^22 - 18 * q^24 + 4 * q^27 - 20 * q^28 + 18 * q^30 - 8 * q^31 - 16 * q^33 + 36 * q^34 - 36 * q^36 + 28 * q^37 - 24 * q^40 - 16 * q^42 + 36 * q^43 + 20 * q^45 - 14 * q^48 - 46 * q^54 + 4 * q^55 - 16 * q^57 - 28 * q^58 - 44 * q^60 + 28 * q^61 + 8 * q^63 - 40 * q^66 + 40 * q^67 + 32 * q^70 - 12 * q^72 + 28 * q^73 + 12 * q^75 + 8 * q^76 + 16 * q^79 + 4 * q^81 - 24 * q^82 - 4 * q^84 - 12 * q^85 - 34 * q^87 - 12 * q^88 - 4 * q^93 + 64 * q^94 - 16 * q^96 - 20 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.619657	−	2.31259i	0.438164	−	1.63525i	−0.295217	−	0.955430i	$-0.595392\pi$
$2$	0.619657	−	2.31259i	0.438164	−	1.63525i	0.733380	−	0.679818i	$-0.237941\pi$
$3$	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	$-0.0701787\pi$
$5$	1.69293	+	1.69293i	0.757103	+	0.757103i	−0.218691	+	0.975794i	$0.570179\pi$
$6$	−0.202571	−	4.14187i	−0.0826993	−	1.69091i
$7$	1.36603	−	0.366025i	0.516309	−	0.138345i	0.00875026	−	0.999962i	$-0.497215\pi$
$7$	1.36603	−	0.366025i	0.516309	−	0.138345i	0.507559	+	0.861617i	$0.330548\pi$
$8$	−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
$11$	−1.69293	−	0.453620i	−0.510439	−	0.136772i	−0.00559833	−	0.999984i	$-0.501782\pi$
$11$	−1.69293	−	0.453620i	−0.510439	−	0.136772i	−0.504840	+	0.863213i	$0.668449\pi$
$12$	−6.31812	−	1.36603i	−1.82388	−	0.394338i
$13$		0			0
$13$		0			0
$14$		−	3.38587i		−	0.904911i
$15$	3.68825	+	1.89551i	0.952303	+	0.489417i
$16$	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
$19$	0.267949	+	1.00000i	0.0614718	+	0.229416i	0.989826	−	0.142280i	$-0.0454432\pi$
$19$	0.267949	+	1.00000i	0.0614718	+	0.229416i	−0.928355	+	0.371695i	$0.878777\pi$
$20$	−2.31259	−	8.63071i	−0.517111	−	1.92988i
$21$	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	$0.833333\pi$
$24$	−3.28311	+	6.38824i	−0.670162	+	1.30399i
$25$			0.732051i			0.146410i
$26$		0			0
$27$	3.09808	−	4.17156i	0.596225	−	0.802817i
$28$	−5.09808	−	1.36603i	−0.963446	−	0.258155i
$29$	−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	−0.983373	−	0.181597i	$-0.941873\pi$
$31$	−4.46410	+	4.46410i	−0.801776	+	0.801776i	0.181597	+	0.983373i	$0.441873\pi$
$32$	−2.31259	+	0.619657i	−0.408812	+	0.109541i
$33$	−3.03206	+	0.148292i	−0.527814	+	0.0258144i
$34$	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
$37$	1.76795	−	6.59808i	0.290649	−	1.08472i	−0.653963	−	0.756527i	$-0.726895\pi$
$37$	1.76795	−	6.59808i	0.290649	−	1.08472i	0.944612	−	0.328190i	$-0.106439\pi$
$38$	2.47863			0.402086
$39$		0			0
$40$	−9.92820			−1.56979
$41$	−0.166037	+	0.619657i	−0.0259306	+	0.0967741i	−0.977678	−	0.210107i	$-0.932619\pi$
$41$	−0.166037	+	0.619657i	−0.0259306	+	0.0967741i	0.951748	+	0.306881i	$0.0992854\pi$
$42$	−1.79275	−	5.58376i	−0.276627	−	0.861593i
$43$	7.09808	+	4.09808i	1.08245	+	0.624951i	0.931555	−	0.363600i	$-0.118452\pi$
$43$	7.09808	+	4.09808i	1.08245	+	0.624951i	0.150891	+	0.988550i	$0.451786\pi$
$44$	4.62518	+	4.62518i	0.697272	+	0.697272i
$45$	7.08606	+	1.17309i	1.05633	+	0.174874i
$46$		0			0
$47$	−6.77174	+	6.77174i	−0.987759	+	0.987759i	−0.999926	−	0.0121668i	$-0.996127\pi$
$47$	−6.77174	+	6.77174i	−0.987759	+	0.987759i	0.0121668	+	0.999926i	$0.496127\pi$
$48$	3.16172	+	2.86687i	0.456354	+	0.413797i
$49$	−4.33013	+	2.50000i	−0.618590	+	0.357143i
$50$	1.69293	+	0.453620i	0.239417	+	0.0641516i
$51$	−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	$0.897103\pi$
$54$	−7.72737	−	9.74952i	−1.05156	−	1.32674i
$55$	−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
$58$	3.42820	+	12.7942i	0.450145	+	1.67996i
$59$	1.23931	+	4.62518i	0.161345	+	0.602147i	0.998478	+	0.0551484i	$0.0175632\pi$
$59$	1.23931	+	4.62518i	0.161345	+	0.602147i	−0.837133	+	0.546999i	$0.815770\pi$
$60$	−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
$63$	2.69293	−	3.27843i	0.339278	−	0.413043i
$64$			10.6603i			1.33253i
$65$		0			0
$66$	−1.53590	+	7.10381i	−0.189056	+	0.874418i
$67$	8.46410	+	2.26795i	1.03405	+	0.277074i	0.735647	−	0.677365i	$-0.236878\pi$
$67$	8.46410	+	2.26795i	1.03405	+	0.277074i	0.298407	+	0.954439i	$0.403545\pi$
$68$	6.93777	−	4.00552i	0.841328	−	0.485741i
$69$		0			0
$70$	5.73205	−	5.73205i	0.685111	−	0.685111i
$71$	4.62518	−	1.23931i	0.548908	−	0.147079i	0.0263025	−	0.999654i	$-0.491627\pi$
$71$	4.62518	−	1.23931i	0.548908	−	0.147079i	0.522606	+	0.852575i	$0.324960\pi$
$72$	−2.03185	+	12.2734i	−0.239456	+	1.44644i
$73$	6.09808	+	6.09808i	0.713726	+	0.713726i	0.967313	−	0.253587i	$-0.0816103\pi$
$73$	6.09808	+	6.09808i	0.713726	+	0.713726i	−0.253587	+	0.967313i	$0.581610\pi$
$74$	−14.1631	−	8.17709i	−1.64643	−	0.950567i
$75$	0.387606	+	1.20725i	0.0447569	+	0.139401i
$76$	1.00000	−	3.73205i	0.114708	−	0.428096i
$77$	−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	$0.464111\pi$
$80$	−1.52690	+	5.69846i	−0.170712	+	0.637107i
$81$	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	$-0.280665\pi$
$83$	−1.23931	−	1.23931i	−0.136032	−	0.136032i	−0.771844	+	0.635812i	$0.780665\pi$
$84$	−9.13071	+	0.446565i	−0.996242	+	0.0487243i
$85$	−4.96410	+	1.33013i	−0.538432	+	0.144273i
$86$	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
$89$	−9.70398	−	2.60017i	−1.02862	−	0.275618i	−0.295230	−	0.955426i	$-0.595396\pi$
$89$	−9.70398	−	2.60017i	−1.02862	−	0.275618i	−0.733390	+	0.679808i	$0.762063\pi$
$90$	7.10381	−	15.6603i	0.748807	−	1.65074i
$91$		0			0
$92$		0			0
$93$	−4.99826	+	9.72556i	−0.518296	+	1.00849i
$94$	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
$97$	−3.36603	−	12.5622i	−0.341768	−	1.27550i	−0.896343	−	0.443362i	$-0.853786\pi$
$97$	−3.36603	−	12.5622i	−0.341768	−	1.27550i	0.554575	−	0.832134i	$-0.312881\pi$
$98$	3.09828	+	11.5630i	0.312974	+	1.16803i
$99$	−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	$-0.606356\pi$
$102$	7.91704	+	4.06880i	0.783903	+	0.402872i
$103$		−	6.92820i		−	0.682656i	−0.939944	−	0.341328i	$-0.889123\pi$
$103$		−	6.92820i		−	0.682656i	0.939944	−	0.341328i	$-0.110877\pi$
$104$		0			0
$105$	5.73205	+	1.23931i	0.559391	+	0.120945i
$106$	10.6962	+	2.86603i	1.03890	+	0.278373i
$107$	−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	−0.559960	−	0.828520i	$-0.689183\pi$
$109$	2.80385	−	2.80385i	0.268560	−	0.268560i	0.828520	+	0.559960i	$0.189183\pi$
$110$	−9.70398	+	2.60017i	−0.925239	+	0.247917i
$111$	−0.577958	−	11.8172i	−0.0548573	−	1.12164i
$112$	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
$119$	−0.785693	+	2.93225i	−0.0720244	+	0.268799i
$120$	−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
$123$	0.0542788	+	1.10981i	0.00489415	+	0.100068i
$124$	22.7583	−	6.09808i	2.04376	−	0.547623i
$125$	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	0.210420	−	0.977611i	$-0.432517\pi$
$127$	13.0981	−	7.56218i	1.16227	−	0.671035i	0.951846	+	0.306576i	$0.0991834\pi$
$128$	20.0276	+	5.36639i	1.77021	+	0.474326i
$129$	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	$0.987381\pi$
$132$	10.0765	+	5.17862i	0.877046	+	0.450741i
$133$	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
$136$	−2.30385	−	8.59808i	−0.197553	−	0.737279i
$137$	1.52690	+	5.69846i	0.130452	+	0.486852i	0.999975	−	0.00703925i	$-0.00224068\pi$
$137$	1.52690	+	5.69846i	0.130452	+	0.486852i	−0.869524	+	0.493891i	$0.835574\pi$
$138$		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
$141$	−7.58202	+	14.7530i	−0.638521	+	1.24243i
$142$		−	11.4641i		−	0.962046i
$143$		0			0
$144$	6.73205	+	3.05379i	0.561004	+	0.254483i
$145$	−12.7942	−	3.42820i	−1.06250	−	0.284697i
$146$	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
$149$	−5.24484	+	1.40535i	−0.429674	+	0.115131i	−0.467173	−	0.884166i	$-0.654728\pi$
$149$	−5.24484	+	1.40535i	−0.429674	+	0.115131i	0.0374992	+	0.999297i	$0.488061\pi$
$150$	3.03206	−	0.148292i	0.247567	−	0.0121080i
$151$	−7.46410	−	7.46410i	−0.607420	−	0.607420i	0.334851	−	0.942271i	$-0.391314\pi$
$151$	−7.46410	−	7.46410i	−0.607420	−	0.607420i	−0.942271	+	0.334851i	$0.891314\pi$
$152$	−3.71794	−	2.14655i	−0.301565	−	0.174109i
$153$	0.628400	+	6.40893i	0.0508031	+	0.518131i
$154$	−1.53590	+	5.73205i	−0.123766	+	0.461902i
$155$	−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	$0.707384\pi$
$158$	1.23931	−	4.62518i	0.0985945	−	0.367960i
$159$	2.44894	+	7.62756i	0.194214	+	0.604905i
$160$	−4.96410	−	2.86603i	−0.392447	−	0.226579i
$161$		0			0
$162$	−17.9057	−	11.9868i	−1.40680	−	0.941772i
$163$	14.9282	−	4.00000i	1.16927	−	0.313304i	0.378606	−	0.925558i	$-0.376404\pi$
$163$	14.9282	−	4.00000i	1.16927	−	0.313304i	0.790661	+	0.612254i	$0.209737\pi$
$164$	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
$167$	11.3969	+	3.05379i	0.881920	+	0.236310i	0.671235	−	0.741244i	$-0.265764\pi$
$167$	11.3969	+	3.05379i	0.881920	+	0.236310i	0.210685	+	0.977554i	$0.432431\pi$
$168$	−2.14655	+	9.92820i	−0.165610	+	0.765978i
$169$		0			0
$170$			12.3042i			0.943686i
$171$	2.39998	+	1.97136i	0.183531	+	0.150754i
$172$	−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
$175$	0.267949	+	1.00000i	0.0202551	+	0.0755929i
$176$	−1.11777	−	4.17156i	−0.0842548	−	0.314443i
$177$	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	$0.586298\pi$
$180$	−20.7135	−	17.0143i	−1.54389	−	1.26817i
$181$			3.00000i			0.222988i	0.993765	+	0.111494i	$0.0355636\pi$
$181$			3.00000i			0.222988i	−0.993765	+	0.111494i	$0.964436\pi$
$182$		0			0
$183$	2.56218	−	11.8505i	0.189402	−	0.876017i
$184$		0			0
$185$	14.1631	−	8.17709i	1.04129	−	0.601191i
$186$	19.3940	+	17.5854i	1.42204	+	1.28943i
$187$	2.66025	−	2.66025i	0.194537	−	0.194537i
$188$	34.5228	−	9.25036i	2.51784	−	0.674652i
$189$	2.70515	−	6.83243i	0.196771	−	0.496986i
$190$	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
$193$	−1.86603	+	6.96410i	−0.134319	+	0.501287i	0.865680	+	0.500597i	$0.166886\pi$
$193$	−1.86603	+	6.96410i	−0.134319	+	0.501287i	−1.00000		0.000689767i	$0.999780\pi$
$194$	−31.1370			−2.23550
$195$		0			0
$196$	18.6603			1.33288
$197$	−0.453620	+	1.69293i	−0.0323191	+	0.120617i	−0.980201	−	0.198006i	$-0.936554\pi$
$197$	−0.453620	+	1.69293i	−0.0323191	+	0.120617i	0.947882	+	0.318622i	$0.103220\pi$
$198$	1.22842	+	12.5284i	0.0872998	+	0.890353i
$199$	0.803848	+	0.464102i	0.0569832	+	0.0328993i	0.528221	−	0.849107i	$-0.322859\pi$
$199$	0.803848	+	0.464102i	0.0569832	+	0.0328993i	−0.471238	+	0.882006i	$0.656193\pi$
$200$	−2.14655	−	2.14655i	−0.151784	−	0.151784i
$201$	15.1593	−	0.741412i	1.06925	−	0.0522952i
$202$	−45.6506	+	12.2321i	−3.21197	+	0.860644i
$203$	−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
$206$	−16.0221	−	4.29311i	−1.11631	−	0.299115i
$207$		0			0
$208$		0			0
$209$		−	1.81448i		−	0.125510i
$210$	6.41793	−	12.4879i	0.442879	−	0.861750i
$211$	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
$214$	10.3397	+	38.5885i	0.706810	+	2.63785i
$215$	5.07880	+	18.9543i	0.346371	+	1.29268i
$216$	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
$219$	13.2854	+	6.82775i	0.897742	+	0.461377i
$220$			15.6603i			1.05581i
$221$		0			0
$222$	−27.6865	−	5.98604i	−1.85820	−	0.401757i
$223$	−22.2942	−	5.97372i	−1.49293	−	0.400030i	−0.582206	−	0.813041i	$-0.697810\pi$
$223$	−22.2942	−	5.97372i	−1.49293	−	0.400030i	−0.910726	+	0.413011i	$0.864477\pi$
$224$	−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
$227$	−15.1149	+	4.05001i	−1.00321	+	0.268809i	−0.722789	−	0.691069i	$-0.757140\pi$
$227$	−15.1149	+	4.05001i	−1.00321	+	0.268809i	−0.280419	+	0.959878i	$0.590474\pi$
$228$	−0.326909	−	6.68414i	−0.0216500	−	0.442668i
$229$	−10.1244	−	10.1244i	−0.669036	−	0.669036i	0.288457	−	0.957493i	$-0.406858\pi$
$229$	−10.1244	−	10.1244i	−0.669036	−	0.669036i	−0.957493	+	0.288457i	$0.906858\pi$
$230$		0			0
$231$	−4.08759	+	1.31238i	−0.268944	+	0.0863485i
$232$	5.93782	−	22.1603i	0.389837	−	1.45489i
$233$	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
$236$	4.62518	−	17.2614i	0.301074	−	1.12362i
$237$	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	$-0.355338\pi$
$239$	−7.10381	−	7.10381i	−0.459507	−	0.459507i	−0.898494	+	0.438986i	$0.855338\pi$
$240$	0.499156	+	10.2060i	0.0322204	+	0.658794i
$241$	−7.23205	+	1.93782i	−0.465857	+	0.124826i	−0.484110	−	0.875007i	$-0.660856\pi$
$241$	−7.23205	+	1.93782i	−0.465857	+	0.124826i	0.0182524	+	0.999833i	$0.494190\pi$
$242$	−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
$245$	−11.5630	−	3.09828i	−0.738730	−	0.197942i
$246$	2.60017	+	0.562178i	0.165781	+	0.0358431i
$247$		0			0
$248$		−	26.1797i		−	1.66241i
$249$	−2.69999	−	1.38761i	−0.171105	−	0.0879360i
$250$	−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
$254$	−9.37191	−	34.9764i	−0.588046	−	2.19462i
$255$	−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	$-0.339861\pi$
$258$	15.5358	−	30.2295i	0.967220	−	1.88201i
$259$		−	9.66025i		−	0.600259i
$260$		0			0
$261$	−6.85641	+	15.1149i	−0.424401	+	0.935586i
$262$	2.09808	+	0.562178i	0.129620	+	0.0347315i
$263$	−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
$266$	3.38587	−	0.907241i	0.207601	−	0.0556265i
$267$	−17.3799	+	0.850019i	−1.06363	+	0.0520203i
$268$	−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
$271$	−0.535898	+	2.00000i	−0.0325535	+	0.121491i	−0.980291	−	0.197561i	$-0.936698\pi$
$271$	−0.535898	+	2.00000i	−0.0325535	+	0.121491i	0.947737	+	0.319052i	$0.103365\pi$
$272$	−5.28933			−0.320713
$273$		0			0
$274$	14.1244			0.853284
$275$	0.332073	−	1.23931i	0.0200248	−	0.0747334i
$276$		0			0
$277$	3.10770	+	1.79423i	0.186723	+	0.107805i	0.590448	−	0.807076i	$-0.298951\pi$
$277$	3.10770	+	1.79423i	0.186723	+	0.107805i	−0.403724	+	0.914881i	$0.632285\pi$
$278$	−4.05001	−	4.05001i	−0.242904	−	0.242904i
$279$	−3.09333	+	18.6853i	−0.185193	+	1.11866i
$280$	−13.5622	+	3.63397i	−0.810495	+	0.217172i
$281$	15.9006	−	15.9006i	0.948547	−	0.948547i	−0.0501922	−	0.998740i	$-0.515983\pi$
$281$	15.9006	−	15.9006i	0.948547	−	0.948547i	0.998740	+	0.0501922i	$0.0159834\pi$
$282$	29.4194	+	26.6759i	1.75190	+	1.58853i
$283$	−21.2942	+	12.2942i	−1.26581	+	0.730816i	−0.974192	−	0.225719i	$-0.927527\pi$
$283$	−21.2942	+	12.2942i	−1.26581	+	0.730816i	−0.291618	+	0.956535i	$0.594194\pi$
$284$	−17.2614	−	4.62518i	−1.02428	−	0.274454i
$285$	−0.907241	+	4.19615i	−0.0537403	+	0.248559i
$286$		0			0
$287$			0.907241i			0.0535527i
$288$	−4.55896	+	5.55017i	−0.268639	+	0.327047i
$289$	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
$292$	−8.33013	−	31.0885i	−0.487484	−	1.81931i
$293$	−5.69846	−	21.2669i	−0.332908	−	1.24243i	−0.906120	−	0.423021i	$-0.860970\pi$
$293$	−5.69846	−	21.2669i	−0.332908	−	1.24243i	0.573212	−	0.819407i	$-0.305697\pi$
$294$	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
$297$	−7.13714	+	5.65683i	−0.414139	+	0.328242i
$298$			13.0000i			0.753070i
$299$		0			0
$300$	1.00000	−	4.62518i	0.0577350	−	0.267035i
$301$	11.1962	+	3.00000i	0.645335	+	0.172917i
$302$	−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
$305$	16.1881	−	4.33760i	0.926930	−	0.248370i
$306$	15.2106	+	2.51810i	0.869533	+	0.143950i
$307$	12.3923	+	12.3923i	0.707266	+	0.707266i	0.965960	−	0.258693i	$-0.0832919\pi$
$307$	12.3923	+	12.3923i	0.707266	+	0.707266i	−0.258693	+	0.965960i	$0.583292\pi$
$308$	8.01105	+	4.62518i	0.456472	+	0.263544i
$309$	−3.66834	−	11.4256i	−0.208685	−	0.649977i
$310$	−9.36603	+	34.9545i	−0.531954	+	1.98528i
$311$	−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	$0.481998\pi$
$314$	−9.41640	+	35.1425i	−0.531398	+	1.98321i
$315$	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	$-0.102207\pi$
$317$	11.2754	+	11.2754i	0.633288	+	0.633288i	−0.315603	+	0.948891i	$0.602207\pi$
$318$	19.1569	−	0.936928i	1.07427	−	0.0525403i
$319$	9.36603	−	2.50962i	0.524397	−	0.140512i
$320$	−18.0471	+	18.0471i	−1.00886	+	1.00886i
$321$	−19.4137	+	21.4103i	−1.08357	+	1.19501i
$322$		0			0
$323$	−2.14655	−	0.575167i	−0.119437	−	0.0320032i
$324$	−25.2725	+	22.1244i	−1.40403	+	1.22913i
$325$		0			0
$326$		−	37.0015i		−	2.04932i
$327$	3.13935	−	6.10851i	0.173606	−	0.337801i
$328$	−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
$331$	−5.05256	−	18.8564i	−0.277714	−	1.03644i	−0.954001	−	0.299804i	$-0.903079\pi$
$331$	−5.05256	−	18.8564i	−0.277714	−	1.03644i	0.676287	−	0.736638i	$-0.263588\pi$
$332$	1.69293	+	6.31812i	0.0929118	+	0.346752i
$333$	−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
$336$	5.36833	+	2.75895i	0.292867	+	0.150513i
$337$		−	11.5359i		−	0.628400i	−0.949357	−	0.314200i	$-0.898264\pi$
$337$		−	11.5359i		−	0.628400i	0.949357	−	0.314200i	$-0.101736\pi$
$338$		0			0
$339$	21.9545	+	4.74673i	1.19240	+	0.257807i
$340$	18.5263	+	4.96410i	1.00473	+	0.269216i
$341$	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
$344$	−32.8299	+	8.79674i	−1.77007	+	0.474289i
$345$		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
$349$	−1.50962	+	5.63397i	−0.0808080	+	0.301580i	−0.994487	−	0.104856i	$-0.966562\pi$
$349$	−1.50962	+	5.63397i	−0.0808080	+	0.301580i	0.913679	+	0.406436i	$0.133228\pi$
$350$	2.47863			0.132488
$351$		0			0
$352$	4.19615			0.223656
$353$	7.05932	−	26.3457i	0.375730	−	1.40224i	−0.476546	−	0.879149i	$-0.658111\pi$
$353$	7.05932	−	26.3457i	0.375730	−	1.40224i	0.852276	−	0.523093i	$-0.175222\pi$
$354$	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
$357$	0.256850	+	5.25169i	0.0135939	+	0.277949i
$358$	43.3468	−	11.6147i	2.29095	−	0.613858i
$359$	−12.0611	+	12.0611i	−0.636559	+	0.636559i	−0.949705	−	0.313146i	$-0.898617\pi$
$359$	−12.0611	+	12.0611i	−0.636559	+	0.636559i	0.313146	+	0.949705i	$0.398617\pi$
$360$	−24.2179	+	17.3383i	−1.27639	+	0.913809i
$361$	15.5263	−	8.96410i	0.817173	−	0.471795i
$362$	6.93777	+	1.85897i	0.364641	+	0.0977053i
$363$	−13.4219	−	2.90192i	−0.704468	−	0.152311i
$364$		0			0
$365$			20.6473i			1.08073i
$366$	−25.8178	−	13.2685i	−1.34952	−	0.693557i
$367$	−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
$370$	−10.1340	−	37.8205i	−0.526840	−	1.96619i
$371$	1.69293	+	6.31812i	0.0878928	+	0.328020i
$372$	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
$375$	8.08992	−	15.7413i	0.417762	−	0.812876i
$376$		−	39.7128i		−	2.04803i
$377$		0			0
$378$	−14.1244	−	10.4897i	−0.726478	−	0.539531i
$379$	4.83013	+	1.29423i	0.248107	+	0.0664801i	0.380729	−	0.924687i	$-0.375673\pi$
$379$	4.83013	+	1.29423i	0.248107	+	0.0664801i	−0.132622	+	0.991167i	$0.542340\pi$
$380$	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
$383$	−13.5435	+	3.62896i	−0.692039	+	0.185431i	−0.587662	−	0.809106i	$-0.699952\pi$
$383$	−13.5435	+	3.62896i	−0.692039	+	0.185431i	−0.104377	+	0.994538i	$0.533285\pi$
$384$	35.8697	−	1.75432i	1.83047	−	0.0895246i
$385$	−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
$388$	−12.5622	+	46.8827i	−0.637748	+	2.38011i
$389$	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
$392$	5.36639	−	20.0276i	0.271043	−	1.01155i
$393$	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
$396$	19.3595	+	3.20495i	0.972851	+	0.161055i
$397$	−8.56218	+	2.29423i	−0.429723	+	0.115144i	−0.467196	−	0.884154i	$-0.654736\pi$
$397$	−8.56218	+	2.29423i	−0.429723	+	0.115144i	0.0374729	+	0.999298i	$0.488069\pi$
$398$	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
$401$	27.1314	+	7.26985i	1.35488	+	0.363039i	0.861933	−	0.507021i	$-0.169253\pi$
$401$	27.1314	+	7.26985i	1.35488	+	0.363039i	0.492946	+	0.870060i	$0.335920\pi$
$402$	7.67898	−	35.5167i	0.382993	−	1.77141i
$403$		0			0
$404$			73.6708i			3.66526i
$405$	19.3337	−	9.51336i	0.960700	−	0.472722i
$406$	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
$409$	−3.00962	−	11.2321i	−0.148816	−	0.555389i	−0.999556	−	0.0298020i	$-0.990512\pi$
$409$	−3.00962	−	11.2321i	−0.148816	−	0.555389i	0.850740	−	0.525587i	$-0.176154\pi$
$410$	0.951730	+	3.55190i	0.0470026	+	0.175416i
$411$	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
$418$	−4.19615	−	1.12436i	−0.205241	−	0.0549940i
$419$	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	−0.727046	−	0.686588i	$-0.759107\pi$
$421$	−0.830127	+	0.830127i	−0.0404579	+	0.0404579i	0.686588	+	0.727046i	$0.259107\pi$
$422$	28.2047	−	7.55743i	1.37298	−	0.367890i
$423$	−4.69237	+	28.3443i	−0.228151	+	1.37815i
$424$	−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
$427$	2.56218	−	9.56218i	0.123992	−	0.462746i
$428$	62.2739			3.01012
$429$		0			0
$430$	46.9808			2.26561
$431$	0.542599	−	2.02501i	0.0261361	−	0.0975412i	−0.951626	−	0.307260i	$-0.900588\pi$
$431$	0.542599	−	2.02501i	0.0261361	−	0.0975412i	0.977762	+	0.209718i	$0.0672547\pi$
$432$	12.7190	+	1.47164i	0.611943	+	0.0708043i
$433$	−6.10770	−	3.52628i	−0.293517	−	0.169462i	0.346010	−	0.938231i	$-0.387536\pi$
$433$	−6.10770	−	3.52628i	−0.293517	−	0.169462i	−0.639527	+	0.768769i	$0.720870\pi$
$434$	15.1149	+	15.1149i	0.725536	+	0.725536i
$435$	−22.9146	+	1.12071i	−1.09867	+	0.0537339i
$436$	−14.2942	+	3.83013i	−0.684569	+	0.183430i
$437$		0			0
$438$	24.0222	−	26.4928i	1.14782	−	1.26587i
$439$	−4.09808	+	2.36603i	−0.195591	+	0.112924i	−0.594597	−	0.804024i	$-0.702688\pi$
$439$	−4.09808	+	2.36603i	−0.195591	+	0.112924i	0.399007	+	0.916948i	$0.369355\pi$
$440$	16.8078	+	4.50363i	0.801280	+	0.214702i
$441$	−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	$-0.247866\pi$
$444$	−20.1832	+	39.2723i	−0.957855	+	1.86378i
$445$	−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
$448$	3.90192	+	14.5622i	0.184349	+	0.687998i
$449$	−2.26810	−	8.46467i	−0.107038	−	0.399472i	0.891530	−	0.452961i	$-0.149632\pi$
$449$	−2.26810	−	8.46467i	−0.107038	−	0.399472i	−0.998568	+	0.0534890i	$0.982966\pi$
$450$	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
$453$	−16.2614	−	8.35723i	−0.764028	−	0.392657i
$454$			37.4641i			1.75828i
$455$		0			0
$456$	−7.26795	−	1.57139i	−0.340353	−	0.0735869i
$457$	26.9904	+	7.23205i	1.26256	+	0.338301i	0.827175	−	0.561945i	$-0.189947\pi$
$457$	26.9904	+	7.23205i	1.26256	+	0.338301i	0.435382	+	0.900246i	$0.356613\pi$
$458$	−29.6871	+	17.1399i	−1.38719	+	0.800893i
$459$	4.42972	+	10.2365i	0.206761	+	0.477798i
$460$		0			0
$461$	−23.4135	+	6.27363i	−1.09048	+	0.292192i	−0.758880	−	0.651230i	$-0.774253\pi$
$461$	−23.4135	+	6.27363i	−1.09048	+	0.292192i	−0.331595	+	0.943422i	$0.607587\pi$
$462$	0.502098	+	10.2662i	0.0233597	+	0.477625i
$463$	15.0526	+	15.0526i	0.699552	+	0.699552i	0.964314	−	0.264762i	$-0.0852934\pi$
$463$	15.0526	+	15.0526i	0.699552	+	0.699552i	−0.264762	+	0.964314i	$0.585293\pi$
$464$	−11.8060	−	6.81623i	−0.548082	−	0.316435i
$465$	−24.9265	+	8.00301i	−1.15594	+	0.371131i
$466$	4.60770	−	17.1962i	0.213447	−	0.796596i
$467$	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
$470$	−14.2076	+	53.0236i	−0.655349	+	2.44579i
$471$	−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
$474$	−0.405142	−	8.28375i	−0.0186088	−	0.380485i
$475$	−0.732051	+	0.196152i	−0.0335888	+	0.00900009i
$476$	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
$479$	8.46467	+	2.26810i	0.386761	+	0.103632i	0.446959	−	0.894554i	$-0.352507\pi$
$479$	8.46467	+	2.26810i	0.386761	+	0.103632i	−0.0601988	+	0.998186i	$0.519173\pi$
$480$	−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
$487$	6.56218	+	24.4904i	0.297361	+	1.10977i	0.939324	+	0.343030i	$0.111453\pi$
$487$	6.56218	+	24.4904i	0.297361	+	1.10977i	−0.641964	+	0.766735i	$0.721880\pi$
$488$	7.51294	+	28.0387i	0.340095	+	1.26925i
$489$	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	$0.642294\pi$
$492$	1.89551	−	3.68825i	0.0854560	−	0.166279i
$493$		−	11.8756i		−	0.534852i
$494$		0			0
$495$	−11.4641	−	5.20035i	−0.515273	−	0.233738i
$496$	−15.0263	−	4.02628i	−0.674700	−	0.180785i
$497$	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	−0.799932	−	0.600091i	$-0.795131\pi$
$499$	−4.46410	+	4.46410i	−0.199841	+	0.199841i	0.600091	+	0.799932i	$0.295131\pi$
$500$	−36.8354	+	9.87002i	−1.64733	+	0.441401i
$501$	20.4120	−	0.998312i	0.911941	−	0.0446013i
$502$	−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
$505$	12.2321	−	45.6506i	0.544319	−	2.03143i
$506$		0			0
$507$		0			0
$508$	−56.4449			−2.50434
$509$	−3.88398	+	14.4952i	−0.172154	+	0.642489i	0.824865	+	0.565330i	$0.191251\pi$
$509$	−3.88398	+	14.4952i	−0.172154	+	0.642489i	−0.997019	+	0.0771582i	$0.975415\pi$
$510$	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
$513$	5.00169	+	1.98031i	0.220830	+	0.0874328i
$514$	−38.3827	+	10.2846i	−1.69299	+	0.453635i
$515$	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
$518$	−22.3402	−	5.98604i	−0.981573	−	0.263012i
$519$	−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	$-0.260056\pi$
$522$	30.7059	+	25.2221i	1.34396	+	1.10394i
$523$	−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
$526$	7.41858	+	27.6865i	0.323466	+	1.20719i
$527$	−3.50742	−	13.0899i	−0.152785	−	0.570203i
$528$	−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
$531$	11.1003	+	9.11792i	0.481713	+	0.395684i
$532$		−	5.46410i		−	0.236899i
$533$		0			0
$534$	−8.80385	+	40.7194i	−0.380980	+	1.76210i
$535$	−38.5885	−	10.3397i	−1.66832	−	0.447026i
$536$	−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
$539$	8.46467	−	2.26810i	0.364599	−	0.0976940i
$540$	−43.1681	−	17.0915i	−1.85766	−	0.735500i
$541$	−23.6865	−	23.6865i	−1.01836	−	1.01836i	−0.999828	−	0.0185354i	$-0.994100\pi$
$541$	−23.6865	−	23.6865i	−1.01836	−	1.01836i	−0.0185354	−	0.999828i	$-0.505900\pi$
$542$	4.29311	+	2.47863i	0.184405	+	0.106466i
$543$	1.58844	+	4.94741i	0.0681664	+	0.212314i
$544$	1.33013	−	4.96410i	0.0570287	−	0.212834i
$545$	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	$0.486386\pi$
$548$	5.69846	−	21.2669i	0.243426	−	0.908479i
$549$	−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
$553$	2.73205	−	0.732051i	0.116179	−	0.0311300i
$554$	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
$557$	−39.3140	−	10.5342i	−1.66579	−	0.446347i	−0.701819	−	0.712355i	$-0.747628\pi$
$557$	−39.3140	−	10.5342i	−1.66579	−	0.446347i	−0.963971	+	0.266009i	$0.914295\pi$
$558$	41.2946	+	18.7321i	1.74814	+	0.792991i
$559$		0			0
$560$			8.34312i			0.352561i
$561$	2.97857	−	5.79567i	0.125755	−	0.244693i
$562$	−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
$565$	8.03590	+	29.9904i	0.338073	+	1.26170i
$566$	15.2364	+	56.8630i	0.640434	+	2.39013i
$567$	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	$0.942354\pi$
$570$	9.14181	+	4.69825i	0.382908	+	0.196788i
$571$			40.0526i			1.67615i	0.545557	+	0.838074i	$0.316318\pi$
$571$			40.0526i			1.67615i	−0.545557	+	0.838074i	$0.683682\pi$
$572$		0			0
$573$	32.8564	+	7.10381i	1.37260	+	0.296766i
$574$	2.09808	+	0.562178i	0.0875720	+	0.0234648i
$575$		0			0
$576$	18.6167	+	26.0036i	0.775697	+	1.08348i
$577$	−3.49038	+	3.49038i	−0.145306	+	0.145306i	−0.776018	−	0.630711i	$-0.782763\pi$
$577$	−3.49038	+	3.49038i	−0.145306	+	0.145306i	0.630711	+	0.776018i	$0.282763\pi$
$578$	28.6583	−	7.67898i	1.19203	−	0.319403i
$579$	0.610020	+	12.4728i	0.0253516	+	0.518351i
$580$	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
$583$	2.09808	−	7.83013i	0.0868934	−	0.324291i
$584$	−35.7621			−1.47985
$585$		0			0
$586$	−52.7128			−2.17755
$587$	5.20035	−	19.4080i	0.214641	−	0.801053i	−0.771651	−	0.636046i	$-0.780569\pi$
$587$	5.20035	−	19.4080i	0.214641	−	0.801053i	0.986292	−	0.165006i	$-0.0527645\pi$
$588$	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
$591$	0.148292	+	3.03206i	0.00609993	+	0.124722i
$592$	16.2583	−	4.35641i	0.668213	−	0.179047i
$593$	10.6112	−	10.6112i	0.435751	−	0.435751i	−0.454828	−	0.890579i	$-0.650299\pi$
$593$	10.6112	−	10.6112i	0.435751	−	0.435751i	0.890579	+	0.454828i	$0.150299\pi$
$594$	8.65935	+	20.0106i	0.355297	+	0.821044i
$595$	−6.29423	+	3.63397i	−0.258038	+	0.148978i
$596$	19.5740	+	5.24484i	0.801782	+	0.214837i
$597$	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	$0.857256\pi$
$600$	−4.67652	−	2.40340i	−0.190918	−	0.0981186i
$601$	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
$604$	10.1962	+	38.0526i	0.414876	+	1.54834i
$605$	−4.91277	−	18.3347i	−0.199732	−	0.745411i
$606$	−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
$609$	−6.19441	+	12.0530i	−0.251010	+	0.488413i
$610$		−	40.1244i		−	1.62459i
$611$		0			0
$612$	9.92820	−	21.8866i	0.401324	−	0.884713i
$613$	−16.3564	−	4.38269i	−0.660629	−	0.177015i	−0.0870991	−	0.996200i	$-0.527760\pi$
$613$	−16.3564	−	4.38269i	−0.660629	−	0.177015i	−0.573530	+	0.819185i	$0.694426\pi$
$614$	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
$617$	36.3818	−	9.74847i	1.46468	−	0.392459i	0.563574	−	0.826066i	$-0.309426\pi$
$617$	36.3818	−	9.74847i	1.46468	−	0.392459i	0.901102	+	0.433607i	$0.142759\pi$
$618$	−28.6957	+	1.40345i	−1.15431	+	0.0564552i
$619$	14.3397	+	14.3397i	0.576363	+	0.576363i	0.933899	−	0.357536i	$-0.116383\pi$
$619$	14.3397	+	14.3397i	0.576363	+	0.576363i	−0.357536	+	0.933899i	$0.616383\pi$
$620$	48.8520	+	28.2047i	1.96194	+	1.13273i
$621$		0			0
$622$	−2.66025	+	9.92820i	−0.106666	+	0.398085i
$623$	−14.2076			−0.569216
$624$		0			0
$625$	28.1244			1.12497
$626$	1.23931	−	4.62518i	0.0495329	−	0.184859i
$627$	−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
$630$	3.97193	−	23.9925i	0.158246	−	0.955883i
$631$	−2.26795	+	0.607695i	−0.0902856	+	0.0241920i	−0.303679	−	0.952774i	$-0.598215\pi$
$631$	−2.26795	+	0.607695i	−0.0902856	+	0.0241920i	0.213393	+	0.976966i	$0.431548\pi$
$632$	−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
$635$	34.9764	+	9.37191i	1.38800	+	0.371913i
$636$	6.31812	−	29.2224i	0.250530	−	1.15874i
$637$		0			0
$638$		−	23.2149i		−	0.919086i
$639$	9.11792	−	11.1003i	0.360699	−	0.439122i
$640$	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
$643$	−7.00000	−	26.1244i	−0.276053	−	1.03024i	−0.955132	−	0.296179i	$-0.904287\pi$
$643$	−7.00000	−	26.1244i	−0.276053	−	1.03024i	0.679079	−	0.734065i	$-0.262379\pi$
$644$		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	$0.925014\pi$
$648$	16.4776	+	33.4870i	0.647302	+	1.31549i
$649$		−	8.39230i		−	0.329427i
$650$		0			0
$651$	−3.26795	+	15.1149i	−0.128081	+	0.592398i
$652$	−55.7128	−	14.9282i	−2.18188	−	0.584634i
$653$	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
$656$	−1.52690	+	0.409131i	−0.0596153	+	0.0159739i
$657$	25.5245	+	4.22556i	0.995807	+	0.164855i
$658$	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
$661$	4.42820	−	16.5263i	0.172237	−	0.642798i	−0.824769	−	0.565470i	$-0.808695\pi$
$661$	4.42820	−	16.5263i	0.172237	−	0.642798i	0.997006	−	0.0773274i	$-0.0246387\pi$
$662$	−46.7380			−1.81652
$663$		0			0
$664$	7.26795			0.282051
$665$	−0.907241	+	3.38587i	−0.0351813	+	0.131298i
$666$	−48.8284	+	4.78766i	−1.89206	+	0.185518i
$667$		0			0
$668$	−31.1370	−	31.1370i	−1.20473	−	1.20473i
$669$	−39.9292	+	1.95286i	−1.54375	+	0.0755019i
$670$	48.5167	−	13.0000i	1.87436	−	0.502234i
$671$	−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	−0.696954	−	0.717116i	$-0.745462\pi$
$673$	−11.0096	+	6.35641i	−0.424390	+	0.245021i	0.272564	+	0.962138i	$0.412128\pi$
$674$	−26.6778	−	7.14830i	−1.02759	−	0.275342i
$675$	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	$0.732015\pi$
$678$	24.5815	−	47.8304i	0.944046	−	1.83692i
$679$	−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
$682$	−6.85641	−	25.5885i	−0.262545	−	0.979833i
$683$	−4.26054	−	15.9006i	−0.163025	−	0.608418i	−0.998284	−	0.0585607i	$-0.981349\pi$
$683$	−4.26054	−	15.9006i	−0.163025	−	0.608418i	0.835259	−	0.549857i	$-0.185318\pi$
$684$	−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
$687$	−22.0571	−	11.3358i	−0.841530	−	0.432488i
$688$			20.1962i			0.769971i
$689$		0			0
$690$		0			0
$691$	41.8827	+	11.2224i	1.59329	+	0.426921i	0.943008	−	0.332770i	$-0.107983\pi$
$691$	41.8827	+	11.2224i	1.59329	+	0.426921i	0.650284	+	0.759691i	$0.274650\pi$
$692$	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
$695$	5.53242	−	1.48241i	0.209857	−	0.0562309i
$696$	−1.94112	−	39.6892i	−0.0735781	−	1.50442i
$697$	−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
$700$	1.00000	−	3.73205i	0.0377964	−	0.141058i
$701$	−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
$704$	4.83571	−	18.0471i	0.182253	−	0.680176i
$705$	−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
$708$	−1.51201	−	30.9154i	−0.0568249	−	1.16187i
$709$	9.96410	−	2.66987i	0.374210	−	0.100269i	−0.0668121	−	0.997766i	$-0.521283\pi$
$709$	9.96410	−	2.66987i	0.374210	−	0.100269i	0.441022	+	0.897496i	$0.354616\pi$
$710$	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
$717$	−15.4765	−	7.95383i	−0.577979	−	0.297041i
$718$	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
$721$	−2.53590	−	9.46410i	−0.0944418	−	0.352462i
$722$	−11.1093	−	41.4606i	−0.413447	−	1.54300i
$723$	−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
$726$	−15.0279	+	29.2412i	−0.557740	+	1.08524i
$727$			25.5167i			0.946361i	0.880966	+	0.473180i	$0.156894\pi$
$727$			25.5167i			0.946361i	−0.880966	+	0.473180i	$0.843106\pi$
$728$		0			0
$729$	−7.80385	−	25.8476i	−0.289031	−	0.957320i
$730$	47.7487	+	12.7942i	1.76726	+	0.473536i
$731$	−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	0.439820	−	0.898086i	$-0.355042\pi$
$733$	36.2224	−	36.2224i	1.33791	−	1.33791i	0.898086	−	0.439820i	$-0.144958\pi$
$734$	−22.2187	+	5.95347i	−0.820106	+	0.219747i
$735$	−20.7094	+	1.01286i	−0.763877	+	0.0373597i
$736$		0			0
$737$	−13.3004	−	7.67898i	−0.489926	−	0.282859i
$738$	4.58570	−	0.449632i	0.168802	−	0.0165512i
$739$	−13.1244	+	48.9808i	−0.482787	+	1.80179i	0.107037	+	0.994255i	$0.465864\pi$
$739$	−13.1244	+	48.9808i	−0.482787	+	1.80179i	−0.589825	+	0.807531i	$0.700803\pi$
$740$	−61.0346			−2.24368
$741$		0			0
$742$	15.6603			0.574906
$743$	−13.5435	+	50.5449i	−0.496862	+	1.85431i	0.0224808	+	0.999747i	$0.492844\pi$
$743$	−13.5435	+	50.5449i	−0.496862	+	1.85431i	−0.519343	+	0.854566i	$0.673823\pi$
$744$	−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
$747$	−5.18736	−	0.858763i	−0.189796	−	0.0314205i
$748$	−13.5622	+	3.63397i	−0.495882	+	0.132871i
$749$	−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	0.402632	−	0.915362i	$-0.368096\pi$
$751$	38.2750	−	22.0981i	1.39667	−	0.806370i	0.994043	+	0.108992i	$0.0347622\pi$
$752$	−22.7938	−	6.10759i	−0.831206	−	0.222721i
$753$	8.01105	−	37.0526i	0.291939	−	1.35027i
$754$		0			0
$755$		−	25.2725i		−	0.919759i
$756$	−21.4927	+	17.0349i	−0.781681	+	0.619553i
$757$	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
$760$	−2.66025	−	9.92820i	−0.0964976	−	0.360134i
$761$	−1.11777	−	4.17156i	−0.0405190	−	0.151219i	0.942703	−	0.333634i	$-0.108275\pi$
$761$	−1.11777	−	4.17156i	−0.0405190	−	0.151219i	−0.983222	+	0.182415i	$0.941608\pi$
$762$	−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
$765$	−9.78605	+	11.9137i	−0.353816	+	0.430742i
$766$			33.5692i			1.21291i
$767$		0			0
$768$	10.3660	−	47.9447i	0.374052	−	1.73006i
$769$	2.16987	+	0.581416i	0.0782476	+	0.0209664i	0.297730	−	0.954650i	$-0.403770\pi$
$769$	2.16987	+	0.581416i	0.0782476	+	0.0209664i	−0.219483	+	0.975616i	$0.570437\pi$
$770$	−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
$773$	5.98604	−	1.60396i	0.215303	−	0.0576903i	−0.149555	−	0.988753i	$-0.547784\pi$
$773$	5.98604	−	1.60396i	0.215303	−	0.0576903i	0.364858	+	0.931063i	$0.381117\pi$
$774$	9.61484	−	58.0785i	0.345598	−	2.08759i
$775$	−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
$778$	3.27757	−	12.2321i	0.117507	−	0.438540i
$779$	−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
$786$	3.75768	−	0.183781i	0.134032	−	0.00655524i
$787$	11.2942	−	3.02628i	0.402596	−	0.107875i	−0.0518385	−	0.998655i	$-0.516508\pi$
$787$	11.2942	−	3.02628i	0.402596	−	0.107875i	0.454434	+	0.890780i	$0.349841\pi$
$788$	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
$791$	17.7150	+	4.74673i	0.629874	+	0.168774i
$792$	9.00727	−	19.8564i	0.320059	−	0.705567i
$793$		0			0
$794$			21.2224i			0.753157i
$795$	−8.76706	+	17.0588i	−0.310935	+	0.605015i
$796$	−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
$799$	−5.32051	−	19.8564i	−0.188226	−	0.702469i
$800$	−0.453620	−	1.69293i	−0.0160379	−	0.0598543i
$801$	−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
$804$	−50.3791	−	25.8913i	−1.77673	−	0.913117i
$805$		0			0
$806$		0			0
$807$	−18.7321	−	4.05001i	−0.659399	−	0.142567i
$808$	79.0692	+	21.1865i	2.78165	+	0.745340i
$809$	−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	−0.957062	−	0.289882i	$-0.906384\pi$
$811$	−19.0000	+	19.0000i	−0.667180	+	0.667180i	0.289882	+	0.957062i	$0.406384\pi$
$812$	28.2047	−	7.55743i	0.989791	−	0.265214i
$813$	0.175190	+	3.58202i	0.00614417	+	0.125627i
$814$	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
$817$	−2.19615	+	8.19615i	−0.0768336	+	0.286747i
$818$	−27.8401			−0.973405
$819$		0			0
$820$	5.73205			0.200172
$821$	−1.60396	+	5.98604i	−0.0559784	+	0.208914i	−0.988250	−	0.152844i	$-0.951157\pi$
$821$	−1.60396	+	5.98604i	−0.0559784	+	0.208914i	0.932272	+	0.361758i	$0.117823\pi$
$822$	23.2930	−	7.47856i	0.812436	−	0.260845i
$823$	13.3923	+	7.73205i	0.466826	+	0.269522i	0.714910	−	0.699216i	$-0.246468\pi$
$823$	13.3923	+	7.73205i	0.466826	+	0.269522i	−0.248084	+	0.968739i	$0.579801\pi$
$824$	20.3152	+	20.3152i	0.707714	+	0.707714i
$825$	−0.108558	−	2.21962i	−0.00377949	−	0.0772774i
$826$	15.6603	−	4.19615i	0.544890	−	0.146003i
$827$	−3.62896	+	3.62896i	−0.126191	+	0.126191i	−0.767382	−	0.641190i	$-0.778441\pi$
$827$	−3.62896	+	3.62896i	−0.126191	+	0.126191i	0.641190	+	0.767382i	$0.278441\pi$
$828$		0			0
$829$	−20.6769	+	11.9378i	−0.718139	+	0.414618i	−0.814067	−	0.580771i	$-0.802751\pi$
$829$	−20.6769	+	11.9378i	−0.718139	+	0.414618i	0.0959284	+	0.995388i	$0.469418\pi$
$830$	−9.70398	−	2.60017i	−0.336830	−	0.0902534i
$831$	6.07502	+	1.31347i	0.210740	+	0.0455636i
$832$		0			0
$833$		−	10.7328i		−	0.371868i
$834$	−8.82343	−	4.53463i	−0.305530	−	0.157021i
$835$	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
$838$	−5.16987	−	19.2942i	−0.178590	−	0.666508i
$839$	2.02501	+	7.55743i	0.0699110	+	0.260911i	0.992031	−	0.125992i	$-0.0402114\pi$
$839$	2.02501	+	7.55743i	0.0699110	+	0.260911i	−0.922120	+	0.386903i	$0.873545\pi$
$840$	−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
$843$	17.8032	−	34.6412i	0.613173	−	1.19311i
$844$		−	45.5167i		−	1.56675i
$845$		0			0
$846$	62.6410	+	28.4152i	2.15364	+	0.976936i
$847$	−10.8301	−	2.90192i	−0.372128	−	0.0997113i
$848$	−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
$852$	−30.9154	+	1.51201i	−1.05914	+	0.0518007i
$853$	20.6340	+	20.6340i	0.706494	+	0.706494i	0.965796	−	0.259302i	$-0.0834926\pi$
$853$	20.6340	+	20.6340i	0.706494	+	0.706494i	−0.259302	+	0.965796i	$0.583493\pi$
$854$	−20.5257	−	11.8505i	−0.702376	−	0.405517i
$855$	0.725614	+	7.40039i	0.0248155	+	0.253088i
$856$	17.9090	−	66.8372i	0.612116	−	2.28445i
$857$	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	$0.629392\pi$
$860$	18.9543	−	70.7386i	0.646338	−	2.41217i
$861$	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	$-0.156241\pi$
$863$	12.0611	+	12.0611i	0.410563	+	0.410563i	−0.471371	+	0.881935i	$0.656241\pi$
$864$	−4.57965	+	11.5669i	−0.155803	+	0.393513i
$865$	−17.1962	+	4.60770i	−0.584687	+	0.156666i
$866$	−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
$869$	−3.38587	−	0.907241i	−0.114858	−	0.0307760i
$870$	−11.6074	+	53.6865i	−0.393529	+	1.82014i
$871$		0			0
$872$			16.4432i			0.556835i
$873$	−30.1489	−	24.7646i	−1.02039	−	0.838156i
$874$		0			0
$875$	7.22536	−	12.5147i	0.244262	−	0.423074i
$876$	−30.1982	−	46.8585i	−1.02030	−	1.58320i
$877$	−3.00962	−	11.2321i	−0.101628	−	0.379279i	0.896313	−	0.443422i	$-0.146236\pi$
$877$	−3.00962	−	11.2321i	−0.101628	−	0.379279i	−0.997941	+	0.0641422i	$0.979569\pi$
$878$	2.93225	+	10.9433i	0.0989586	+	0.369318i
$879$	−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	$0.681974\pi$
$882$	27.7508	+	22.7948i	0.934419	+	0.767541i
$883$		−	39.3731i		−	1.32501i	−0.749058	−	0.662505i	$-0.769494\pi$
$883$		−	39.3731i		−	1.32501i	0.749058	−	0.662505i	$-0.230506\pi$
$884$		0			0
$885$	−4.19615	+	19.4080i	−0.141052	+	0.652392i
$886$	−68.3731	−	18.3205i	−2.29704	−	0.615490i
$887$	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
$890$	−55.6237	+	14.9043i	−1.86451	+	0.499594i
$891$	−8.77495	+	13.1079i	−0.293972	+	0.439130i
$892$	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
$895$	−11.6147	+	43.3468i	−0.388238	+	1.44892i
$896$	29.3225			0.979595
$897$		0			0
$898$	−20.9808			−0.700137
$899$	9.03984	−	33.7371i	0.301495	−	1.12520i
$900$	−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
$903$	20.0524	−	0.980726i	0.667303	−	0.0326365i
$904$	−51.9449	+	13.9186i	−1.72766	+	0.462925i
$905$	−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	−0.727915	−	0.685668i	$-0.759510\pi$
$907$	−15.0000	+	8.66025i	−0.498067	+	0.287559i	0.229848	+	0.973227i	$0.426177\pi$
$908$	56.4094	+	15.1149i	1.87201	+	0.501604i
$909$	−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	$-0.0489705\pi$
$912$	−2.01969	+	3.92989i	−0.0668786	+	0.130132i
$913$	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
$916$	13.8301	+	51.6147i	0.456960	+	1.70540i
$917$	0.332073	+	1.23931i	0.0109660	+	0.0409257i
$918$	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
$921$	26.9981	+	13.8751i	0.889617	+	0.457201i
$922$			58.0333i			1.91123i
$923$		0			0
$924$	15.6603	+	3.38587i	0.515185	+	0.111387i
$925$	4.83013	+	1.29423i	0.158814	+	0.0425540i
$926$	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
$929$	47.3251	−	12.6807i	1.55269	−	0.416041i	0.622347	−	0.782742i	$-0.286179\pi$
$929$	47.3251	−	12.6807i	1.55269	−	0.416041i	0.930339	+	0.366701i	$0.119513\pi$
$930$	3.06183	+	62.6038i	0.100401	+	2.05286i
$931$	−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
$934$	18.8827	−	70.4711i	0.617860	−	2.30589i
$935$	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	$0.706575\pi$
$938$	7.67898	−	28.6583i	0.250727	−	0.935728i
$939$	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	0.957206	+	0.289407i	$0.0934582\pi$
$941$	38.2408	+	38.2408i	1.24661	+	1.24661i	0.289407	+	0.957206i	$0.406542\pi$
$942$	3.07830	+	62.9405i	0.100296	+	2.05071i
$943$		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
$947$	−39.6016	−	10.6112i	−1.28688	−	0.344818i	−0.450405	−	0.892824i	$-0.648721\pi$
$947$	−39.6016	−	10.6112i	−1.28688	−	0.344818i	−0.836475	+	0.548006i	$0.815387\pi$
$948$	−12.6362	−	2.73205i	−0.410406	−	0.0887329i
$949$		0			0
$950$			1.81448i			0.0588695i
$951$	24.5647	+	12.6245i	0.796565	+	0.409379i
$952$	−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
$955$	12.0263	+	44.8827i	0.389161	+	1.45237i
$956$	9.70398	+	36.2158i	0.313849	+	1.17130i
$957$	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
$960$	−20.2066	+	39.3177i	−0.652164	+	1.26897i
$961$		−	8.85641i		−	0.285691i
$962$		0			0
$963$	−20.6795	+	45.5877i	−0.666387	+	1.46904i
$964$	26.9904	+	7.23205i	0.869302	+	0.232929i
$965$	−14.9488	+	8.63071i	−0.481220	+	0.277832i
$966$		0			0
$967$	0.143594	−	0.143594i	0.00461766	−	0.00461766i	−0.704794	−	0.709412i	$-0.748961\pi$
$967$	0.143594	−	0.143594i	0.00461766	−	0.00461766i	0.709412	+	0.704794i	$0.248961\pi$
$968$	31.7566	−	8.50916i	1.02070	−	0.273495i
$969$	−3.84450	+	0.188027i	−0.123503	+	0.00604030i
$970$	−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
$973$	0.875644	−	3.26795i	0.0280719	−	0.104766i
$974$	60.7025			1.94503
$975$		0			0
$976$	17.2487			0.552118
$977$	−7.60192	+	28.3707i	−0.243207	+	0.907661i	0.731069	+	0.682303i	$0.239022\pi$
$977$	−7.60192	+	28.3707i	−0.243207	+	0.907661i	−0.974276	+	0.225357i	$0.927645\pi$
$978$	−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
$981$	1.94288	−	11.7360i	0.0620314	−	0.374701i
$982$	57.8827	−	15.5096i	1.84711	−	0.494932i
$983$	4.38209	−	4.38209i	0.139767	−	0.139767i	−0.633762	−	0.773528i	$-0.718490\pi$
$983$	4.38209	−	4.38209i	0.139767	−	0.139767i	0.773528	+	0.633762i	$0.218490\pi$
$984$	−3.41340	−	3.09508i	−0.108815	−	0.0986677i
$985$	−3.63397	+	2.09808i	−0.115788	+	0.0668503i
$986$	−27.4635	−	7.35882i	−0.874616	−	0.234353i
$987$	−4.95725	+	22.9282i	−0.157791	+	0.729813i
$988$		0			0
$989$		0			0
$990$	−19.1301	+	23.2893i	−0.607994	+	0.740184i
$991$	−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
$994$	−4.19615	−	15.6603i	−0.133094	−	0.496713i
$995$	0.575167	+	2.14655i	0.0182340	+	0.0680503i
$996$	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
$999$	−22.0470	−	27.8165i	−0.697537	−	0.880074i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.k.d.80.2		8
3.2	odd	2	inner	507.2.k.d.80.1		8
13.2	odd	12		507.2.f.f.437.4		8
13.3	even	3		507.2.f.e.239.4		8
13.4	even	6		507.2.k.e.188.2		8
13.5	odd	4		507.2.k.e.89.1		8
13.6	odd	12		39.2.k.b.20.2	yes	8
13.7	odd	12	inner	507.2.k.d.488.1		8
13.8	odd	4		507.2.k.f.89.2		8
13.9	even	3		507.2.k.f.188.1		8
13.10	even	6		507.2.f.f.239.1		8
13.11	odd	12		507.2.f.e.437.1		8
13.12	even	2		39.2.k.b.2.1	✓	8
39.2	even	12		507.2.f.f.437.1		8
39.5	even	4		507.2.k.e.89.2		8
39.8	even	4		507.2.k.f.89.1		8
39.11	even	12		507.2.f.e.437.4		8
39.17	odd	6		507.2.k.e.188.1		8
39.20	even	12	inner	507.2.k.d.488.2		8
39.23	odd	6		507.2.f.f.239.4		8
39.29	odd	6		507.2.f.e.239.1		8
39.32	even	12		39.2.k.b.20.1	yes	8
39.35	odd	6		507.2.k.f.188.2		8
39.38	odd	2		39.2.k.b.2.2	yes	8
52.19	even	12		624.2.cn.c.449.2		8
52.51	odd	2		624.2.cn.c.353.1		8
65.12	odd	4		975.2.bp.f.899.1		8
65.19	odd	12		975.2.bo.d.176.1		8
65.32	even	12		975.2.bp.e.449.1		8
65.38	odd	4		975.2.bp.e.899.2		8
65.58	even	12		975.2.bp.f.449.2		8
65.64	even	2		975.2.bo.d.626.2		8
156.71	odd	12		624.2.cn.c.449.1		8
156.155	even	2		624.2.cn.c.353.2		8
195.32	odd	12		975.2.bp.e.449.2		8
195.38	even	4		975.2.bp.e.899.1		8
195.77	even	4		975.2.bp.f.899.2		8
195.149	even	12		975.2.bo.d.176.2		8
195.188	odd	12		975.2.bp.f.449.1		8
195.194	odd	2		975.2.bo.d.626.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.2.k.b.2.1	✓	8	13.12	even	2
39.2.k.b.2.2	yes	8	39.38	odd	2
39.2.k.b.20.1	yes	8	39.32	even	12
39.2.k.b.20.2	yes	8	13.6	odd	12
507.2.f.e.239.1		8	39.29	odd	6
507.2.f.e.239.4		8	13.3	even	3
507.2.f.e.437.1		8	13.11	odd	12
507.2.f.e.437.4		8	39.11	even	12
507.2.f.f.239.1		8	13.10	even	6
507.2.f.f.239.4		8	39.23	odd	6
507.2.f.f.437.1		8	39.2	even	12
507.2.f.f.437.4		8	13.2	odd	12
507.2.k.d.80.1		8	3.2	odd	2	inner
507.2.k.d.80.2		8	1.1	even	1	trivial
507.2.k.d.488.1		8	13.7	odd	12	inner
507.2.k.d.488.2		8	39.20	even	12	inner
507.2.k.e.89.1		8	13.5	odd	4
507.2.k.e.89.2		8	39.5	even	4
507.2.k.e.188.1		8	39.17	odd	6
507.2.k.e.188.2		8	13.4	even	6
507.2.k.f.89.1		8	39.8	even	4
507.2.k.f.89.2		8	13.8	odd	4
507.2.k.f.188.1		8	13.9	even	3
507.2.k.f.188.2		8	39.35	odd	6
624.2.cn.c.353.1		8	52.51	odd	2
624.2.cn.c.353.2		8	156.155	even	2
624.2.cn.c.449.1		8	156.71	odd	12
624.2.cn.c.449.2		8	52.19	even	12
975.2.bo.d.176.1		8	65.19	odd	12
975.2.bo.d.176.2		8	195.149	even	12
975.2.bo.d.626.1		8	195.194	odd	2
975.2.bo.d.626.2		8	65.64	even	2
975.2.bp.e.449.1		8	65.32	even	12
975.2.bp.e.449.2		8	195.32	odd	12
975.2.bp.e.899.1		8	195.38	even	4
975.2.bp.e.899.2		8	65.38	odd	4
975.2.bp.f.449.1		8	195.188	odd	12
975.2.bp.f.449.2		8	65.58	even	12
975.2.bp.f.899.1		8	65.12	odd	4
975.2.bp.f.899.2		8	195.77	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)

\(f(q)\)	\(=\)	\(q+(0.619657 - 2.31259i) q^{2} +(1.64914 - 0.529480i) q^{3} +(-3.23205 - 1.86603i) q^{4} +(1.69293 + 1.69293i) q^{5} +(-0.202571 - 4.14187i) q^{6} +(1.36603 - 0.366025i) q^{7} +(-2.93225 + 2.93225i) q^{8} +(2.43930 - 1.74637i) q^{9} +O(q^{10})\)	\(q+(0.619657 - 2.31259i) q^{2} +(1.64914 - 0.529480i) q^{3} +(-3.23205 - 1.86603i) q^{4} +(1.69293 + 1.69293i) q^{5} +(-0.202571 - 4.14187i) q^{6} +(1.36603 - 0.366025i) q^{7} +(-2.93225 + 2.93225i) q^{8} +(2.43930 - 1.74637i) q^{9} +(4.96410 - 2.86603i) q^{10} +(-1.69293 - 0.453620i) q^{11} +(-6.31812 - 1.36603i) q^{12} -3.38587i q^{14} +(3.68825 + 1.89551i) q^{15} +(1.23205 + 2.13397i) q^{16} +(-1.07328 + 1.85897i) q^{17} +(-2.52711 - 6.72326i) q^{18} +(0.267949 + 1.00000i) q^{19} +(-2.31259 - 8.63071i) q^{20} +(2.05896 - 1.32691i) q^{21} +(-2.09808 + 3.63397i) q^{22} +(-3.28311 + 6.38824i) q^{24} +0.732051i q^{25} +(3.09808 - 4.17156i) q^{27} +(-5.09808 - 1.36603i) q^{28} +(-4.79122 + 2.76621i) q^{29} +(6.66898 - 7.35486i) q^{30} +(-4.46410 + 4.46410i) q^{31} +(-2.31259 + 0.619657i) q^{32} +(-3.03206 + 0.148292i) q^{33} +(3.63397 + 3.63397i) q^{34} +(2.93225 + 1.69293i) q^{35} +(-11.1427 + 1.09255i) q^{36} +(1.76795 - 6.59808i) q^{37} +2.47863 q^{38} -9.92820 q^{40} +(-0.166037 + 0.619657i) q^{41} +(-1.79275 - 5.58376i) q^{42} +(7.09808 + 4.09808i) q^{43} +(4.62518 + 4.62518i) q^{44} +(7.08606 + 1.17309i) q^{45} +(-6.77174 + 6.77174i) q^{47} +(3.16172 + 2.86687i) q^{48} +(-4.33013 + 2.50000i) q^{49} +(1.69293 + 0.453620i) q^{50} +(-0.785693 + 3.63397i) q^{51} +4.62518i q^{53} +(-7.72737 - 9.74952i) q^{54} +(-2.09808 - 3.63397i) q^{55} +(-2.93225 + 5.07880i) q^{56} +(0.971364 + 1.50726i) q^{57} +(3.42820 + 12.7942i) q^{58} +(1.23931 + 4.62518i) q^{59} +(-8.38356 - 13.0087i) q^{60} +(3.50000 - 6.06218i) q^{61} +(7.55743 + 13.0899i) q^{62} +(2.69293 - 3.27843i) q^{63} +10.6603i q^{64} +(-1.53590 + 7.10381i) q^{66} +(8.46410 + 2.26795i) q^{67} +(6.93777 - 4.00552i) q^{68} +(5.73205 - 5.73205i) q^{70} +(4.62518 - 1.23931i) q^{71} +(-2.03185 + 12.2734i) q^{72} +(6.09808 + 6.09808i) q^{73} +(-14.1631 - 8.17709i) q^{74} +(0.387606 + 1.20725i) q^{75} +(1.00000 - 3.73205i) q^{76} -2.47863 q^{77} +2.00000 q^{79} +(-1.52690 + 5.69846i) q^{80} +(2.90039 - 8.51984i) q^{81} +(1.33013 + 0.767949i) q^{82} +(-1.23931 - 1.23931i) q^{83} +(-9.13071 + 0.446565i) q^{84} +(-4.96410 + 1.33013i) q^{85} +(13.8755 - 13.8755i) q^{86} +(-6.43672 + 7.09871i) q^{87} +(6.29423 - 3.63397i) q^{88} +(-9.70398 - 2.60017i) q^{89} +(7.10381 - 15.6603i) q^{90} +(-4.99826 + 9.72556i) q^{93} +(11.4641 + 19.8564i) q^{94} +(-1.23931 + 2.14655i) q^{95} +(-3.48568 + 2.24637i) q^{96} +(-3.36603 - 12.5622i) q^{97} +(3.09828 + 11.5630i) q^{98} +(-4.92177 + 1.84997i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} - 12 q^{4} + 2 q^{6} + 4 q^{7} + 4 q^{9}+O(q^{10}) \) 8 * q - 2 * q^3 - 12 * q^4 + 2 * q^6 + 4 * q^7 + 4 * q^9	\( 8 q - 2 q^{3} - 12 q^{4} + 2 q^{6} + 4 q^{7} + 4 q^{9} + 12 q^{10} + 14 q^{15} - 4 q^{16} - 4 q^{18} + 16 q^{19} - 4 q^{21} + 4 q^{22} - 18 q^{24} + 4 q^{27} - 20 q^{28} + 18 q^{30} - 8 q^{31} - 16 q^{33} + 36 q^{34} - 36 q^{36} + 28 q^{37} - 24 q^{40} - 16 q^{42} + 36 q^{43} + 20 q^{45} - 14 q^{48} - 46 q^{54} + 4 q^{55} - 16 q^{57} - 28 q^{58} - 44 q^{60} + 28 q^{61} + 8 q^{63} - 40 q^{66} + 40 q^{67} + 32 q^{70} - 12 q^{72} + 28 q^{73} + 12 q^{75} + 8 q^{76} + 16 q^{79} + 4 q^{81} - 24 q^{82} - 4 q^{84} - 12 q^{85} - 34 q^{87} - 12 q^{88} - 4 q^{93} + 64 q^{94} - 16 q^{96} - 20 q^{97} - 40 q^{99}+O(q^{100}) \) 8 * q - 2 * q^3 - 12 * q^4 + 2 * q^6 + 4 * q^7 + 4 * q^9 + 12 * q^10 + 14 * q^15 - 4 * q^16 - 4 * q^18 + 16 * q^19 - 4 * q^21 + 4 * q^22 - 18 * q^24 + 4 * q^27 - 20 * q^28 + 18 * q^30 - 8 * q^31 - 16 * q^33 + 36 * q^34 - 36 * q^36 + 28 * q^37 - 24 * q^40 - 16 * q^42 + 36 * q^43 + 20 * q^45 - 14 * q^48 - 46 * q^54 + 4 * q^55 - 16 * q^57 - 28 * q^58 - 44 * q^60 + 28 * q^61 + 8 * q^63 - 40 * q^66 + 40 * q^67 + 32 * q^70 - 12 * q^72 + 28 * q^73 + 12 * q^75 + 8 * q^76 + 16 * q^79 + 4 * q^81 - 24 * q^82 - 4 * q^84 - 12 * q^85 - 34 * q^87 - 12 * q^88 - 4 * q^93 + 64 * q^94 - 16 * q^96 - 20 * q^97 - 40 * q^99

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