LMFDB - Embedded newform 507.2.k.d.488.2

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			488.2
Root			$0.500000 - 2.19293i$ of defining polynomial
Character	$\chi$	$=$	507.488
Dual form			507.2.k.d.80.2

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

$n$	$170$	$340$
$\chi(n)$	$-1$	$e\left(\frac{11}{12}\right)$

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	0.733380	+	0.679818i	$0.237941\pi$
$2$	0.619657	+	2.31259i	0.438164	+	1.63525i	−0.295217	+	0.955430i	$0.595392\pi$
$3$	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	−0.218691	−	0.975794i	$-0.570179\pi$
$5$	1.69293	−	1.69293i	0.757103	−	0.757103i	0.975794	+	0.218691i	$0.0701787\pi$
$6$	−0.202571	+	4.14187i	−0.0826993	+	1.69091i
$7$	1.36603	+	0.366025i	0.516309	+	0.138345i	0.507559	−	0.861617i	$-0.330548\pi$
$7$	1.36603	+	0.366025i	0.516309	+	0.138345i	0.00875026	+	0.999962i	$0.497215\pi$
$8$	−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	−0.504840	−	0.863213i	$-0.668449\pi$
$11$	−1.69293	+	0.453620i	−0.510439	+	0.136772i	−0.00559833	+	0.999984i	$0.501782\pi$
$12$	−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	0.706016	−	0.708196i	$-0.250491\pi$
$17$	−1.07328	−	1.85897i	−0.260308	−	0.450867i	−0.966324	+	0.257330i	$0.917157\pi$
$18$	−2.52711	+	6.72326i	−0.595644	+	1.58469i
$19$	0.267949	−	1.00000i	0.0614718	−	0.229416i	−0.928355	−	0.371695i	$-0.878777\pi$
$19$	0.267949	−	1.00000i	0.0614718	−	0.229416i	0.989826	+	0.142280i	$0.0454432\pi$
$20$	−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	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$	−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	−0.0158603	−	0.999874i	$-0.505049\pi$
$29$	−4.79122	−	2.76621i	−0.889707	−	0.513673i	−0.873847	+	0.486202i	$0.838382\pi$
$30$	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	$0.941873\pi$
$32$	−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	0.944612	+	0.328190i	$0.106439\pi$
$37$	1.76795	+	6.59808i	0.290649	+	1.08472i	−0.653963	+	0.756527i	$0.726895\pi$
$38$	2.47863			0.402086
$39$		0			0
$40$	−9.92820			−1.56979
$41$	−0.166037	−	0.619657i	−0.0259306	−	0.0967741i	0.951748	−	0.306881i	$-0.0992854\pi$
$41$	−0.166037	−	0.619657i	−0.0259306	−	0.0967741i	−0.977678	+	0.210107i	$0.932619\pi$
$42$	−1.79275	+	5.58376i	−0.276627	+	0.861593i
$43$	7.09808	−	4.09808i	1.08245	−	0.624951i	0.150891	−	0.988550i	$-0.451786\pi$
$43$	7.09808	−	4.09808i	1.08245	−	0.624951i	0.931555	+	0.363600i	$0.118452\pi$
$44$	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	0.0121668	−	0.999926i	$-0.496127\pi$
$47$	−6.77174	−	6.77174i	−0.987759	−	0.987759i	−0.999926	+	0.0121668i	$0.996127\pi$
$48$	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	$-0.897103\pi$
$53$		−	4.62518i		−	0.635318i	0.948205	−	0.317659i	$-0.102897\pi$
$54$	−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	−0.837133	−	0.546999i	$-0.815770\pi$
$59$	1.23931	−	4.62518i	0.161345	−	0.602147i	0.998478	−	0.0551484i	$-0.0175632\pi$
$60$	−8.38356	+	13.0087i	−1.08231	+	1.67942i
$61$	3.50000	+	6.06218i	0.448129	+	0.776182i	0.998264	−	0.0588933i	$-0.0187572\pi$
$61$	3.50000	+	6.06218i	0.448129	+	0.776182i	−0.550135	+	0.835076i	$0.685424\pi$
$62$	7.55743	−	13.0899i	0.959794	−	1.66241i
$63$	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	0.298407	−	0.954439i	$-0.403545\pi$
$67$	8.46410	−	2.26795i	1.03405	−	0.277074i	0.735647	+	0.677365i	$0.236878\pi$
$68$	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	0.522606	−	0.852575i	$-0.324960\pi$
$71$	4.62518	+	1.23931i	0.548908	+	0.147079i	0.0263025	+	0.999654i	$0.491627\pi$
$72$	−2.03185	−	12.2734i	−0.239456	−	1.44644i
$73$	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
$76$	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	−0.771844	−	0.635812i	$-0.780665\pi$
$83$	−1.23931	+	1.23931i	−0.136032	+	0.136032i	0.635812	+	0.771844i	$0.280665\pi$
$84$	−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	−0.733390	−	0.679808i	$-0.762063\pi$
$89$	−9.70398	+	2.60017i	−1.02862	+	0.275618i	−0.295230	+	0.955426i	$0.595396\pi$
$90$	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	0.554575	+	0.832134i	$0.312881\pi$
$97$	−3.36603	+	12.5622i	−0.341768	+	1.27550i	−0.896343	+	0.443362i	$0.853786\pi$
$98$	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	−0.327944	+	0.944697i	$0.606356\pi$
$101$	−9.87002	+	17.0954i	−0.982104	+	1.70105i	−0.654160	+	0.756356i	$0.726978\pi$
$102$	7.91704	−	4.06880i	0.783903	−	0.402872i
$103$			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
$106$	10.6962	−	2.86603i	1.03890	−	0.278373i
$107$	−14.4507	−	8.34312i	−1.39700	−	0.806560i	−0.402925	−	0.915233i	$-0.632007\pi$
$107$	−14.4507	−	8.34312i	−1.39700	−	0.806560i	−0.994078	+	0.108673i	$0.965340\pi$
$108$	−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	$0.689183\pi$
$110$	−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	0.132047	−	0.991243i	$-0.457845\pi$
$113$	11.2309	−	6.48415i	1.05651	−	0.609978i	0.924465	+	0.381266i	$0.124512\pi$
$114$	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	0.951846	−	0.306576i	$-0.0991834\pi$
$127$	13.0981	+	7.56218i	1.16227	+	0.671035i	0.210420	+	0.977611i	$0.432517\pi$
$128$	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	$-0.987381\pi$
$131$		−	0.907241i		−	0.0792660i	0.999214	−	0.0396330i	$-0.0126189\pi$
$132$	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	−0.869524	−	0.493891i	$-0.835574\pi$
$137$	1.52690	−	5.69846i	0.130452	−	0.486852i	0.999975	+	0.00703925i	$0.00224068\pi$
$138$		0			0
$139$	1.19615	+	2.07180i	0.101456	+	0.175728i	0.912285	−	0.409556i	$-0.134316\pi$
$139$	1.19615	+	2.07180i	0.101456	+	0.175728i	−0.810829	+	0.585284i	$0.800983\pi$
$140$	−6.31812	+	10.9433i	−0.533978	+	0.924877i
$141$	−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	0.0374992	−	0.999297i	$-0.488061\pi$
$149$	−5.24484	−	1.40535i	−0.429674	−	0.115131i	−0.467173	+	0.884166i	$0.654728\pi$
$150$	3.03206	+	0.148292i	0.247567	+	0.0121080i
$151$	−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
$154$	−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	0.790661	−	0.612254i	$-0.209737\pi$
$163$	14.9282	+	4.00000i	1.16927	+	0.313304i	0.378606	+	0.925558i	$0.376404\pi$
$164$	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	0.210685	−	0.977554i	$-0.432431\pi$
$167$	11.3969	−	3.05379i	0.881920	−	0.236310i	0.671235	+	0.741244i	$0.265764\pi$
$168$	−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	0.689372	−	0.724408i	$-0.257887\pi$
$173$	−3.71794	−	6.43966i	−0.282670	−	0.489598i	−0.972041	+	0.234809i	$0.924553\pi$
$174$	12.4279	−	19.2843i	0.942154	−	1.46194i
$175$	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	−0.267805	−	0.963473i	$-0.586298\pi$
$179$	9.37191	−	16.2326i	0.700489	−	1.21328i	0.968295	−	0.249810i	$-0.0803683\pi$
$180$	−20.7135	+	17.0143i	−1.54389	+	1.26817i
$181$		−	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
$188$	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	0.252073	−	0.967708i	$-0.418888\pi$
$191$	16.8078	−	9.70398i	1.21617	−	0.702156i	0.964096	+	0.265553i	$0.0855544\pi$
$192$	5.64439	−	17.5802i	0.407349	−	1.26874i
$193$	−1.86603	−	6.96410i	−0.134319	−	0.501287i	−1.00000		0.000689767i	$-0.999780\pi$
$193$	−1.86603	−	6.96410i	−0.134319	−	0.501287i	0.865680	−	0.500597i	$-0.166886\pi$
$194$	−31.1370			−2.23550
$195$		0			0
$196$	18.6603			1.33288
$197$	−0.453620	−	1.69293i	−0.0323191	−	0.120617i	0.947882	−	0.318622i	$-0.103220\pi$
$197$	−0.453620	−	1.69293i	−0.0323191	−	0.120617i	−0.980201	+	0.198006i	$0.936554\pi$
$198$	1.22842	−	12.5284i	0.0872998	−	0.890353i
$199$	0.803848	−	0.464102i	0.0569832	−	0.0328993i	−0.471238	−	0.882006i	$-0.656193\pi$
$199$	0.803848	−	0.464102i	0.0569832	−	0.0328993i	0.528221	+	0.849107i	$0.322859\pi$
$200$	−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	−0.576111	−	0.817371i	$-0.695430\pi$
$211$	6.09808	−	10.5622i	0.419809	−	0.727130i	0.995920	+	0.0902411i	$0.0287638\pi$
$212$	8.63071	+	14.9488i	0.592759	+	1.02669i
$213$	6.97136	+	4.49274i	0.477670	+	0.307837i
$214$	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	−0.910726	−	0.413011i	$-0.864477\pi$
$223$	−22.2942	+	5.97372i	−1.49293	+	0.400030i	−0.582206	+	0.813041i	$0.697810\pi$
$224$	−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	−0.280419	−	0.959878i	$-0.590474\pi$
$227$	−15.1149	−	4.05001i	−1.00321	−	0.268809i	−0.722789	+	0.691069i	$0.757140\pi$
$228$	−0.326909	+	6.68414i	−0.0216500	+	0.442668i
$229$	−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
$232$	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	−0.898494	−	0.438986i	$-0.855338\pi$
$239$	−7.10381	+	7.10381i	−0.459507	+	0.459507i	0.438986	+	0.898494i	$0.355338\pi$
$240$	0.499156	−	10.2060i	0.0322204	−	0.658794i
$241$	−7.23205	−	1.93782i	−0.465857	−	0.124826i	0.0182524	−	0.999833i	$-0.494190\pi$
$241$	−7.23205	−	1.93782i	−0.465857	−	0.124826i	−0.484110	+	0.875007i	$0.660856\pi$
$242$	−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	0.971597	+	0.236640i	$0.0760461\pi$
$251$	10.9433	+	18.9543i	0.690735	+	1.19639i	−0.280863	+	0.959748i	$0.590621\pi$
$252$	−14.8213	−	5.57097i	−0.933656	−	0.350938i
$253$		0			0
$254$	−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	0.482135	+	0.876097i	$0.339861\pi$
$257$	−8.29863	+	14.3737i	−0.517655	+	0.896604i	−0.999790	+	0.0205071i	$0.993472\pi$
$258$	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	0.145029	−	0.989427i	$-0.453673\pi$
$263$	−10.3681	−	5.98604i	−0.639326	−	0.369115i	−0.784355	+	0.620312i	$0.787006\pi$
$264$	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	−0.762821	−	0.646610i	$-0.776186\pi$
$269$	−9.58244	+	5.53242i	−0.584251	+	0.337318i	0.178570	+	0.983927i	$0.442853\pi$
$270$	3.42336	+	29.5872i	0.208339	+	1.80062i
$271$	−0.535898	−	2.00000i	−0.0325535	−	0.121491i	0.947737	−	0.319052i	$-0.103365\pi$
$271$	−0.535898	−	2.00000i	−0.0325535	−	0.121491i	−0.980291	+	0.197561i	$0.936698\pi$
$272$	−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	−0.403724	−	0.914881i	$-0.632285\pi$
$277$	3.10770	−	1.79423i	0.186723	−	0.107805i	0.590448	+	0.807076i	$0.298951\pi$
$278$	−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	0.998740	−	0.0501922i	$-0.0159834\pi$
$281$	15.9006	+	15.9006i	0.948547	+	0.948547i	−0.0501922	+	0.998740i	$0.515983\pi$
$282$	29.4194	−	26.6759i	1.75190	−	1.58853i
$283$	−21.2942	−	12.2942i	−1.26581	−	0.730816i	−0.291618	−	0.956535i	$-0.594194\pi$
$283$	−21.2942	−	12.2942i	−1.26581	−	0.730816i	−0.974192	+	0.225719i	$0.927527\pi$
$284$	−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	0.573212	+	0.819407i	$0.305697\pi$
$293$	−5.69846	+	21.2669i	−0.332908	+	1.24243i	−0.906120	+	0.423021i	$0.860970\pi$
$294$	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	−0.258693	−	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
$310$	−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	−0.315603	−	0.948891i	$-0.602207\pi$
$317$	11.2754	−	11.2754i	0.633288	−	0.633288i	0.948891	+	0.315603i	$0.102207\pi$
$318$	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	0.676287	+	0.736638i	$0.263588\pi$
$331$	−5.05256	+	18.8564i	−0.277714	+	1.03644i	−0.954001	+	0.299804i	$0.903079\pi$
$332$	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	$0.101736\pi$
$337$			11.5359i			0.628400i	−0.949357	+	0.314200i	$0.898264\pi$
$338$		0			0
$339$	21.9545	−	4.74673i	1.19240	−	0.257807i
$340$	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	−0.961841	−	0.273608i	$-0.911783\pi$
$347$	−22.4618	+	12.9683i	−1.20581	+	0.696175i	−0.243969	+	0.969783i	$0.578450\pi$
$348$	34.0502	+	10.9323i	1.82528	+	0.586034i
$349$	−1.50962	−	5.63397i	−0.0808080	−	0.301580i	0.913679	−	0.406436i	$-0.133228\pi$
$349$	−1.50962	−	5.63397i	−0.0808080	−	0.301580i	−0.994487	+	0.104856i	$0.966562\pi$
$350$	2.47863			0.132488
$351$		0			0
$352$	4.19615			0.223656
$353$	7.05932	+	26.3457i	0.375730	+	1.40224i	0.852276	+	0.523093i	$0.175222\pi$
$353$	7.05932	+	26.3457i	0.375730	+	1.40224i	−0.476546	+	0.879149i	$0.658111\pi$
$354$	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	0.313146	−	0.949705i	$-0.398617\pi$
$359$	−12.0611	−	12.0611i	−0.636559	−	0.636559i	−0.949705	+	0.313146i	$0.898617\pi$
$360$	−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	−0.963735	−	0.266861i	$-0.914013\pi$
$367$	−4.80385	+	8.32051i	−0.250759	+	0.434327i	0.712976	+	0.701188i	$0.247347\pi$
$368$		0			0
$369$	0.677136	−	1.80149i	0.0352503	−	0.0937819i
$370$	−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	0.999966	+	0.00824796i	$0.00262544\pi$
$373$	9.79423	+	16.9641i	0.507126	+	0.878368i	−0.492840	+	0.870120i	$0.664041\pi$
$374$	−4.50363	+	7.80052i	−0.232877	+	0.403355i
$375$	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	−0.132622	−	0.991167i	$-0.542340\pi$
$379$	4.83013	−	1.29423i	0.248107	−	0.0664801i	0.380729	+	0.924687i	$0.375673\pi$
$380$	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	−0.104377	−	0.994538i	$-0.533285\pi$
$383$	−13.5435	−	3.62896i	−0.692039	−	0.185431i	−0.587662	+	0.809106i	$0.699952\pi$
$384$	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	0.0374729	−	0.999298i	$-0.488069\pi$
$397$	−8.56218	−	2.29423i	−0.429723	−	0.115144i	−0.467196	+	0.884154i	$0.654736\pi$
$398$	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	0.492946	−	0.870060i	$-0.335920\pi$
$401$	27.1314	−	7.26985i	1.35488	−	0.363039i	0.861933	+	0.507021i	$0.169253\pi$
$402$	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	0.850740	+	0.525587i	$0.176154\pi$
$409$	−3.00962	+	11.2321i	−0.148816	+	0.555389i	−0.999556	+	0.0298020i	$0.990512\pi$
$410$	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	0.665998	−	0.745954i	$-0.268006\pi$
$419$	7.22536	+	4.17156i	0.352982	+	0.203794i	−0.313016	+	0.949748i	$0.601339\pi$
$420$	−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	$0.759107\pi$
$422$	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	0.977762	−	0.209718i	$-0.0672547\pi$
$431$	0.542599	+	2.02501i	0.0261361	+	0.0975412i	−0.951626	+	0.307260i	$0.900588\pi$
$432$	12.7190	−	1.47164i	0.611943	−	0.0708043i
$433$	−6.10770	+	3.52628i	−0.293517	+	0.169462i	−0.639527	−	0.768769i	$-0.720870\pi$
$433$	−6.10770	+	3.52628i	−0.293517	+	0.169462i	0.346010	+	0.938231i	$0.387536\pi$
$434$	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	0.399007	−	0.916948i	$-0.369355\pi$
$439$	−4.09808	−	2.36603i	−0.195591	−	0.112924i	−0.594597	+	0.804024i	$0.702688\pi$
$440$	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	$0.247866\pi$
$443$			29.5656i			1.40470i	−0.711830	+	0.702351i	$0.752134\pi$
$444$	−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	−0.998568	−	0.0534890i	$-0.982966\pi$
$449$	−2.26810	+	8.46467i	−0.107038	+	0.399472i	0.891530	+	0.452961i	$0.149632\pi$
$450$	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	0.435382	−	0.900246i	$-0.356613\pi$
$457$	26.9904	−	7.23205i	1.26256	−	0.338301i	0.827175	+	0.561945i	$0.189947\pi$
$458$	−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	−0.331595	−	0.943422i	$-0.607587\pi$
$461$	−23.4135	−	6.27363i	−1.09048	−	0.292192i	−0.758880	+	0.651230i	$0.774253\pi$
$462$	0.502098	−	10.2662i	0.0233597	−	0.477625i
$463$	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
$466$	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	−0.0601988	−	0.998186i	$-0.519173\pi$
$479$	8.46467	−	2.26810i	0.386761	−	0.103632i	0.446959	+	0.894554i	$0.352507\pi$
$480$	−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	−0.641964	−	0.766735i	$-0.721880\pi$
$487$	6.56218	−	24.4904i	0.297361	−	1.10977i	0.939324	−	0.343030i	$-0.111453\pi$
$488$	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	−0.432290	−	0.901734i	$-0.642294\pi$
$491$	12.5147	−	21.6761i	0.564780	−	0.978227i	0.997070	−	0.0764928i	$-0.0243722\pi$
$492$	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	0.600091	−	0.799932i	$-0.295131\pi$
$499$	−4.46410	−	4.46410i	−0.199841	−	0.199841i	−0.799932	+	0.600091i	$0.795131\pi$
$500$	−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	−0.937951	−	0.346767i	$-0.887279\pi$
$503$	−24.8188	+	14.3292i	−1.10662	+	0.638906i	−0.168666	+	0.985673i	$0.553946\pi$
$504$	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	−0.997019	−	0.0771582i	$-0.975415\pi$
$509$	−3.88398	−	14.4952i	−0.172154	−	0.642489i	0.824865	−	0.565330i	$-0.191251\pi$
$510$	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	$0.260056\pi$
$521$			33.2835i			1.45818i	−0.684419	+	0.729089i	$0.739944\pi$
$522$	30.7059	−	25.2221i	1.34396	−	1.10394i
$523$	−6.49038	+	11.2417i	−0.283805	+	0.491564i	−0.972319	−	0.233659i	$-0.924930\pi$
$523$	−6.49038	+	11.2417i	−0.283805	+	0.491564i	0.688514	+	0.725223i	$0.258263\pi$
$524$	1.69293	+	2.93225i	0.0739562	+	0.128096i
$525$	0.971364	−	1.50726i	0.0423938	−	0.0657823i
$526$	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	−0.0185354	+	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
$544$	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	−0.963971	−	0.266009i	$-0.914295\pi$
$557$	−39.3140	+	10.5342i	−1.66579	+	0.446347i	−0.701819	+	0.712355i	$0.747628\pi$
$558$	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	0.817241	−	0.576296i	$-0.195502\pi$
$563$	−2.14655	−	3.71794i	−0.0904665	−	0.156693i	−0.907708	+	0.419603i	$0.862169\pi$
$564$	52.0350	+	33.5342i	2.19107	+	1.41205i
$565$	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	−0.983646	−	0.180113i	$-0.942354\pi$
$569$	−8.01105	+	13.8755i	−0.335841	+	0.581693i	0.647805	+	0.761806i	$0.275687\pi$
$570$	9.14181	−	4.69825i	0.382908	−	0.196788i
$571$		−	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
$574$	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	0.630711	−	0.776018i	$-0.282763\pi$
$577$	−3.49038	−	3.49038i	−0.145306	−	0.145306i	−0.776018	+	0.630711i	$0.782763\pi$
$578$	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	0.986292	+	0.165006i	$0.0527645\pi$
$587$	5.20035	+	19.4080i	0.214641	+	0.801053i	−0.771651	+	0.636046i	$0.780569\pi$
$588$	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	0.890579	−	0.454828i	$-0.150299\pi$
$593$	10.6112	+	10.6112i	0.435751	+	0.435751i	−0.454828	+	0.890579i	$0.650299\pi$
$594$	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	$-0.857256\pi$
$599$		−	21.2224i		−	0.867126i	0.901123	−	0.433563i	$-0.142744\pi$
$600$	−4.67652	+	2.40340i	−0.190918	+	0.0981186i
$601$	3.79423	−	6.57180i	0.154770	−	0.268069i	−0.778205	−	0.628010i	$-0.783870\pi$
$601$	3.79423	−	6.57180i	0.154770	−	0.268069i	0.932975	+	0.359941i	$0.117203\pi$
$602$	13.8755	+	24.0331i	0.565525	+	0.979518i
$603$	24.6072	+	9.24923i	1.00208	+	0.376658i
$604$	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	0.743820	−	0.668380i	$-0.233012\pi$
$607$	−5.09808	−	8.83013i	−0.206925	−	0.358404i	−0.950744	+	0.309977i	$0.899679\pi$
$608$	−1.23931	+	2.14655i	−0.0502608	+	0.0870543i
$609$	−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	−0.573530	−	0.819185i	$-0.694426\pi$
$613$	−16.3564	+	4.38269i	−0.660629	+	0.177015i	−0.0870991	+	0.996200i	$0.527760\pi$
$614$	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	0.901102	−	0.433607i	$-0.142759\pi$
$617$	36.3818	+	9.74847i	1.46468	+	0.392459i	0.563574	+	0.826066i	$0.309426\pi$
$618$	−28.6957	−	1.40345i	−1.15431	−	0.0564552i
$619$	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
$622$	−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	0.213393	−	0.976966i	$-0.431548\pi$
$631$	−2.26795	−	0.607695i	−0.0902856	−	0.0241920i	−0.303679	+	0.952774i	$0.598215\pi$
$632$	−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	0.991281	−	0.131767i	$-0.0420650\pi$
$641$	9.65949	+	16.7307i	0.381527	+	0.660824i	−0.609754	+	0.792591i	$0.708732\pi$
$642$	37.4835	−	58.1629i	1.47935	−	2.29551i
$643$	−7.00000	+	26.1244i	−0.276053	+	1.03024i	0.679079	+	0.734065i	$0.262379\pi$
$643$	−7.00000	+	26.1244i	−0.276053	+	1.03024i	−0.955132	+	0.296179i	$0.904287\pi$
$644$		0			0
$645$	18.4116	−	28.5692i	0.724955	−	1.12491i
$646$	−2.66025	−	4.60770i	−0.104666	−	0.181287i
$647$	−7.22536	+	12.5147i	−0.284058	+	0.492003i	−0.972380	−	0.233402i	$-0.925014\pi$
$647$	−7.22536	+	12.5147i	−0.284058	+	0.492003i	0.688322	+	0.725405i	$0.258348\pi$
$648$	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	0.982998	−	0.183617i	$-0.0587807\pi$
$653$	33.6156	+	19.4080i	1.31548	+	0.759492i	0.332482	+	0.943110i	$0.392114\pi$
$654$	−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	−0.925051	−	0.379842i	$-0.875978\pi$
$659$	−27.1759	+	15.6900i	−1.05862	+	0.611197i	−0.133572	+	0.991039i	$0.542645\pi$
$660$	8.29179	−	25.8259i	0.322757	−	1.00527i
$661$	4.42820	+	16.5263i	0.172237	+	0.642798i	0.997006	+	0.0773274i	$0.0246387\pi$
$661$	4.42820	+	16.5263i	0.172237	+	0.642798i	−0.824769	+	0.565470i	$0.808695\pi$
$662$	−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	0.272564	−	0.962138i	$-0.412128\pi$
$673$	−11.0096	−	6.35641i	−0.424390	−	0.245021i	−0.696954	+	0.717116i	$0.745462\pi$
$674$	−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	$-0.732015\pi$
$677$		−	38.8159i		−	1.49182i	0.666048	−	0.745909i	$-0.267985\pi$
$678$	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	0.835259	+	0.549857i	$0.185318\pi$
$683$	−4.26054	+	15.9006i	−0.163025	+	0.608418i	−0.998284	+	0.0585607i	$0.981349\pi$
$684$	−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	0.650284	−	0.759691i	$-0.274650\pi$
$691$	41.8827	−	11.2224i	1.59329	−	0.426921i	0.943008	+	0.332770i	$0.107983\pi$
$692$	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	0.441022	−	0.897496i	$-0.354616\pi$
$709$	9.96410	+	2.66987i	0.374210	+	0.100269i	−0.0668121	+	0.997766i	$0.521283\pi$
$710$	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	0.954413	−	0.298488i	$-0.0964822\pi$
$719$	5.86450	+	10.1576i	0.218709	+	0.378815i	−0.735705	+	0.677302i	$0.763149\pi$
$720$	6.22704	−	16.5668i	0.232068	−	0.617408i
$721$	−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	$-0.843106\pi$
$727$		−	25.5167i		−	0.946361i	0.880966	−	0.473180i	$-0.156894\pi$
$728$		0			0
$729$	−7.80385	+	25.8476i	−0.289031	+	0.957320i
$730$	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	0.898086	+	0.439820i	$0.144958\pi$
$733$	36.2224	+	36.2224i	1.33791	+	1.33791i	0.439820	+	0.898086i	$0.355042\pi$
$734$	−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	−0.589825	−	0.807531i	$-0.700803\pi$
$739$	−13.1244	−	48.9808i	−0.482787	−	1.80179i	0.107037	−	0.994255i	$-0.465864\pi$
$740$	−61.0346			−2.24368
$741$		0			0
$742$	15.6603			0.574906
$743$	−13.5435	−	50.5449i	−0.496862	−	1.85431i	−0.519343	−	0.854566i	$-0.673823\pi$
$743$	−13.5435	−	50.5449i	−0.496862	−	1.85431i	0.0224808	−	0.999747i	$-0.492844\pi$
$744$	−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	0.994043	−	0.108992i	$-0.0347622\pi$
$751$	38.2750	+	22.0981i	1.39667	+	0.806370i	0.402632	+	0.915362i	$0.368096\pi$
$752$	−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	−0.548005	−	0.836475i	$-0.684613\pi$
$757$	12.3923	−	21.4641i	0.450406	−	0.780126i	0.998411	+	0.0563489i	$0.0179459\pi$
$758$	5.98604	+	10.3681i	0.217423	+	0.376587i
$759$		0			0
$760$	−2.66025	+	9.92820i	−0.0964976	+	0.360134i
$761$	−1.11777	+	4.17156i	−0.0405190	+	0.151219i	−0.983222	−	0.182415i	$-0.941608\pi$
$761$	−1.11777	+	4.17156i	−0.0405190	+	0.151219i	0.942703	+	0.333634i	$0.108275\pi$
$762$	−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	−0.219483	−	0.975616i	$-0.570437\pi$
$769$	2.16987	−	0.581416i	0.0782476	−	0.0209664i	0.297730	+	0.954650i	$0.403770\pi$
$770$	−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	0.364858	−	0.931063i	$-0.381117\pi$
$773$	5.98604	+	1.60396i	0.215303	+	0.0576903i	−0.149555	+	0.988753i	$0.547784\pi$
$774$	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	0.454434	−	0.890780i	$-0.349841\pi$
$787$	11.2942	+	3.02628i	0.402596	+	0.107875i	−0.0518385	+	0.998655i	$0.516508\pi$
$788$	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	0.672930	−	0.739706i	$-0.265036\pi$
$797$	−8.58622	−	14.8718i	−0.304139	−	0.526785i	−0.977069	+	0.212921i	$0.931702\pi$
$798$	5.10339	+	3.28891i	0.180658	+	0.116426i
$799$	−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	0.156097	−	0.987742i	$-0.450109\pi$
$809$	−17.6705	−	10.2021i	−0.621263	−	0.358686i	−0.777361	+	0.629055i	$0.783442\pi$
$810$	−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	$0.906384\pi$
$812$	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	0.932272	−	0.361758i	$-0.117823\pi$
$821$	−1.60396	−	5.98604i	−0.0559784	−	0.208914i	−0.988250	+	0.152844i	$0.951157\pi$
$822$	23.2930	+	7.47856i	0.812436	+	0.260845i
$823$	13.3923	−	7.73205i	0.466826	−	0.269522i	−0.248084	−	0.968739i	$-0.579801\pi$
$823$	13.3923	−	7.73205i	0.466826	−	0.269522i	0.714910	+	0.699216i	$0.246468\pi$
$824$	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	0.641190	−	0.767382i	$-0.278441\pi$
$827$	−3.62896	−	3.62896i	−0.126191	−	0.126191i	−0.767382	+	0.641190i	$0.778441\pi$
$828$		0			0
$829$	−20.6769	−	11.9378i	−0.718139	−	0.414618i	0.0959284	−	0.995388i	$-0.469418\pi$
$829$	−20.6769	−	11.9378i	−0.718139	−	0.414618i	−0.814067	+	0.580771i	$0.802751\pi$
$830$	−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	−0.922120	−	0.386903i	$-0.873545\pi$
$839$	2.02501	−	7.55743i	0.0699110	−	0.260911i	0.992031	+	0.125992i	$0.0402114\pi$
$840$	−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	−0.259302	−	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
$856$	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	−0.471371	−	0.881935i	$-0.656241\pi$
$863$	12.0611	−	12.0611i	0.410563	−	0.410563i	0.881935	+	0.471371i	$0.156241\pi$
$864$	−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	−0.997941	−	0.0641422i	$-0.979569\pi$
$877$	−3.00962	+	11.2321i	−0.101628	+	0.379279i	0.896313	+	0.443422i	$0.146236\pi$
$878$	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	−0.541054	−	0.840988i	$-0.681974\pi$
$881$	13.5880	−	23.5350i	0.457790	−	0.792916i	0.998844	+	0.0480724i	$0.0153078\pi$
$882$	27.7508	−	22.7948i	0.934419	−	0.767541i
$883$			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
$886$	−68.3731	+	18.3205i	−2.29704	+	0.615490i
$887$	46.4949	+	26.8438i	1.56115	+	0.901328i	0.997142	+	0.0755567i	$0.0240734\pi$
$887$	46.4949	+	26.8438i	1.56115	+	0.901328i	0.564005	+	0.825772i	$0.309260\pi$
$888$	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	0.229848	−	0.973227i	$-0.426177\pi$
$907$	−15.0000	−	8.66025i	−0.498067	−	0.287559i	−0.727915	+	0.685668i	$0.759510\pi$
$908$	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	$0.0489705\pi$
$911$			9.25036i			0.306478i	−0.988189	+	0.153239i	$0.951030\pi$
$912$	−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	−0.954539	−	0.298085i	$-0.903652\pi$
$919$	−22.2942	−	38.6147i	−0.735419	−	1.27378i	0.219121	−	0.975698i	$-0.429681\pi$
$920$		0			0
$921$	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	0.930339	−	0.366701i	$-0.119513\pi$
$929$	47.3251	+	12.6807i	1.55269	+	0.416041i	0.622347	+	0.782742i	$0.286179\pi$
$930$	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	0.289407	−	0.957206i	$-0.406542\pi$
$941$	38.2408	−	38.2408i	1.24661	−	1.24661i	0.957206	−	0.289407i	$-0.0934582\pi$
$942$	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	−0.836475	−	0.548006i	$-0.815387\pi$
$947$	−39.6016	+	10.6112i	−1.28688	+	0.344818i	−0.450405	+	0.892824i	$0.648721\pi$
$948$	−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	−0.965237	−	0.261375i	$-0.915824\pi$
$953$	−21.8866	−	37.9087i	−0.708976	−	1.22798i	0.256261	−	0.966608i	$-0.417509\pi$
$954$	31.0963	+	11.6883i	1.00678	+	0.378423i
$955$	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	0.709412	−	0.704794i	$-0.248961\pi$
$967$	0.143594	+	0.143594i	0.00461766	+	0.00461766i	−0.704794	+	0.709412i	$0.748961\pi$
$968$	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	0.462832	−	0.886446i	$-0.346833\pi$
$971$	45.5551	−	26.3013i	1.46193	−	0.844047i	0.999101	+	0.0423987i	$0.0135000\pi$
$972$	−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	−0.974276	−	0.225357i	$-0.927645\pi$
$977$	−7.60192	−	28.3707i	−0.243207	−	0.907661i	0.731069	−	0.682303i	$-0.239022\pi$
$978$	−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	0.773528	−	0.633762i	$-0.218490\pi$
$983$	4.38209	+	4.38209i	0.139767	+	0.139767i	−0.633762	+	0.773528i	$0.718490\pi$
$984$	−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	−0.994451	−	0.105203i	$-0.966451\pi$
$991$	−12.7846	+	22.1436i	−0.406117	+	0.703414i	0.588334	+	0.808618i	$0.299784\pi$
$992$	7.55743	+	13.0899i	0.239949	+	0.415603i
$993$	−18.3164	+	28.4216i	−0.581255	+	0.901931i
$994$	−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	0.916112	−	0.400923i	$-0.131311\pi$
$997$	3.50000	+	6.06218i	0.110846	+	0.191991i	−0.805266	+	0.592914i	$0.797977\pi$
$998$	7.55743	−	13.0899i	0.239226	−	0.414352i
$999$	−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.488.2		8
3.2	odd	2	inner	507.2.k.d.488.1		8
13.2	odd	12	inner	507.2.k.d.80.1		8
13.3	even	3		507.2.k.f.89.1		8
13.4	even	6		507.2.f.f.437.1		8
13.5	odd	4		507.2.k.f.188.2		8
13.6	odd	12		507.2.f.e.239.1		8
13.7	odd	12		507.2.f.f.239.4		8
13.8	odd	4		507.2.k.e.188.1		8
13.9	even	3		507.2.f.e.437.4		8
13.10	even	6		507.2.k.e.89.2		8
13.11	odd	12		39.2.k.b.2.2	yes	8
13.12	even	2		39.2.k.b.20.1	yes	8
39.2	even	12	inner	507.2.k.d.80.2		8
39.5	even	4		507.2.k.f.188.1		8
39.8	even	4		507.2.k.e.188.2		8
39.11	even	12		39.2.k.b.2.1	✓	8
39.17	odd	6		507.2.f.f.437.4		8
39.20	even	12		507.2.f.f.239.1		8
39.23	odd	6		507.2.k.e.89.1		8
39.29	odd	6		507.2.k.f.89.2		8
39.32	even	12		507.2.f.e.239.4		8
39.35	odd	6		507.2.f.e.437.1		8
39.38	odd	2		39.2.k.b.20.2	yes	8
52.11	even	12		624.2.cn.c.353.2		8
52.51	odd	2		624.2.cn.c.449.1		8
65.12	odd	4		975.2.bp.e.449.2		8
65.24	odd	12		975.2.bo.d.626.1		8
65.37	even	12		975.2.bp.f.899.2		8
65.38	odd	4		975.2.bp.f.449.1		8
65.63	even	12		975.2.bp.e.899.1		8
65.64	even	2		975.2.bo.d.176.2		8
156.11	odd	12		624.2.cn.c.353.1		8
156.155	even	2		624.2.cn.c.449.2		8
195.38	even	4		975.2.bp.f.449.2		8
195.77	even	4		975.2.bp.e.449.1		8
195.89	even	12		975.2.bo.d.626.2		8
195.128	odd	12		975.2.bp.e.899.2		8
195.167	odd	12		975.2.bp.f.899.1		8
195.194	odd	2		975.2.bo.d.176.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.2.k.b.2.1	✓	8	39.11	even	12
39.2.k.b.2.2	yes	8	13.11	odd	12
39.2.k.b.20.1	yes	8	13.12	even	2
39.2.k.b.20.2	yes	8	39.38	odd	2
507.2.f.e.239.1		8	13.6	odd	12
507.2.f.e.239.4		8	39.32	even	12
507.2.f.e.437.1		8	39.35	odd	6
507.2.f.e.437.4		8	13.9	even	3
507.2.f.f.239.1		8	39.20	even	12
507.2.f.f.239.4		8	13.7	odd	12
507.2.f.f.437.1		8	13.4	even	6
507.2.f.f.437.4		8	39.17	odd	6
507.2.k.d.80.1		8	13.2	odd	12	inner
507.2.k.d.80.2		8	39.2	even	12	inner
507.2.k.d.488.1		8	3.2	odd	2	inner
507.2.k.d.488.2		8	1.1	even	1	trivial
507.2.k.e.89.1		8	39.23	odd	6
507.2.k.e.89.2		8	13.10	even	6
507.2.k.e.188.1		8	13.8	odd	4
507.2.k.e.188.2		8	39.8	even	4
507.2.k.f.89.1		8	13.3	even	3
507.2.k.f.89.2		8	39.29	odd	6
507.2.k.f.188.1		8	39.5	even	4
507.2.k.f.188.2		8	13.5	odd	4
624.2.cn.c.353.1		8	156.11	odd	12
624.2.cn.c.353.2		8	52.11	even	12
624.2.cn.c.449.1		8	52.51	odd	2
624.2.cn.c.449.2		8	156.155	even	2
975.2.bo.d.176.1		8	195.194	odd	2
975.2.bo.d.176.2		8	65.64	even	2
975.2.bo.d.626.1		8	65.24	odd	12
975.2.bo.d.626.2		8	195.89	even	12
975.2.bp.e.449.1		8	195.77	even	4
975.2.bp.e.449.2		8	65.12	odd	4
975.2.bp.e.899.1		8	65.63	even	12
975.2.bp.e.899.2		8	195.128	odd	12
975.2.bp.f.449.1		8	65.38	odd	4
975.2.bp.f.449.2		8	195.38	even	4
975.2.bp.f.899.1		8	195.167	odd	12
975.2.bp.f.899.2		8	65.37	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.619657 + 2.31259i) q^{2} +(1.64914 + 0.529480i) q^{3} +(-3.23205 + 1.86603i) q^{4} +(1.69293 - 1.69293i) q^{5} +(-0.202571 + 4.14187i) q^{6} +(1.36603 + 0.366025i) q^{7} +(-2.93225 - 2.93225i) q^{8} +(2.43930 + 1.74637i) q^{9} +O(q^{10})\)	\(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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more