LMFDB - Embedded newform 507.2.k.d.488.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("507.80");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

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

Embedding invariants

Embedding label			488.1
Root			$0.500000 + 1.19293i$ of defining polynomial
Character	$\chi$	$=$	507.488
Dual form			507.2.k.d.80.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.619657 - 2.31259i) q^{2} +(-1.28311 - 1.16345i) q^{3} +(-3.23205 + 1.86603i) q^{4} +(-1.69293 + 1.69293i) q^{5} +(-1.89551 + 3.68825i) q^{6} +(1.36603 + 0.366025i) q^{7} +(2.93225 + 2.93225i) q^{8} +(0.292748 + 2.98568i) q^{9} +O(q^{10})$	\(q+(-0.619657 - 2.31259i) q^{2} +(-1.28311 - 1.16345i) q^{3} +(-3.23205 + 1.86603i) q^{4} +(-1.69293 + 1.69293i) q^{5} +(-1.89551 + 3.68825i) q^{6} +(1.36603 + 0.366025i) q^{7} +(2.93225 + 2.93225i) q^{8} +(0.292748 + 2.98568i) q^{9} +(4.96410 + 2.86603i) q^{10} +(1.69293 - 0.453620i) q^{11} +(6.31812 + 1.36603i) q^{12} -3.38587i q^{14} +(4.14187 - 0.202571i) q^{15} +(1.23205 - 2.13397i) q^{16} +(1.07328 + 1.85897i) q^{17} +(6.72326 - 2.52711i) q^{18} +(0.267949 - 1.00000i) q^{19} +(2.31259 - 8.63071i) q^{20} +(-1.32691 - 2.05896i) q^{21} +(-2.09808 - 3.63397i) q^{22} +(-0.350863 - 7.17394i) q^{24} -0.732051i q^{25} +(3.09808 - 4.17156i) q^{27} +(-5.09808 + 1.36603i) q^{28} +(4.79122 + 2.76621i) q^{29} +(-3.03500 - 9.45293i) q^{30} +(-4.46410 - 4.46410i) q^{31} +(2.31259 + 0.619657i) q^{32} +(-2.69999 - 1.38761i) q^{33} +(3.63397 - 3.63397i) q^{34} +(-2.93225 + 1.69293i) q^{35} +(-6.51754 - 9.10360i) q^{36} +(1.76795 + 6.59808i) q^{37} -2.47863 q^{38} -9.92820 q^{40} +(0.166037 + 0.619657i) q^{41} +(-3.93930 + 4.34444i) q^{42} +(7.09808 - 4.09808i) q^{43} +(-4.62518 + 4.62518i) q^{44} +(-5.55017 - 4.55896i) q^{45} +(6.77174 + 6.77174i) q^{47} +(-4.06364 + 1.30469i) q^{48} +(-4.33013 - 2.50000i) q^{49} +(-1.69293 + 0.453620i) q^{50} +(0.785693 - 3.63397i) q^{51} +4.62518i q^{53} +(-11.5669 - 4.57965i) q^{54} +(-2.09808 + 3.63397i) q^{55} +(2.93225 + 5.07880i) q^{56} +(-1.50726 + 0.971364i) q^{57} +(3.42820 - 12.7942i) q^{58} +(-1.23931 + 4.62518i) q^{59} +(-13.0087 + 8.38356i) q^{60} +(3.50000 + 6.06218i) q^{61} +(-7.55743 + 13.0899i) q^{62} +(-0.692934 + 4.18567i) 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} +(-7.89635 + 9.61317i) q^{72} +(6.09808 - 6.09808i) q^{73} +(14.1631 - 8.17709i) q^{74} +(-0.851708 + 0.939303i) q^{75} +(1.00000 + 3.73205i) q^{76} +2.47863 q^{77} +2.00000 q^{79} +(1.52690 + 5.69846i) q^{80} +(-8.82860 + 1.74811i) q^{81} +(1.33013 - 0.767949i) q^{82} +(1.23931 - 1.23931i) q^{83} +(8.13071 + 4.17862i) q^{84} +(-4.96410 - 1.33013i) q^{85} +(-13.8755 - 13.8755i) q^{86} +(-2.92931 - 9.12372i) q^{87} +(6.29423 + 3.63397i) q^{88} +(9.70398 - 2.60017i) q^{89} +(-7.10381 + 15.6603i) q^{90} +(0.534160 + 10.9217i) q^{93} +(11.4641 - 19.8564i) q^{94} +(1.23931 + 2.14655i) q^{95} +(-2.24637 - 3.48568i) q^{96} +(-3.36603 + 12.5622i) q^{97} +(-3.09828 + 11.5630i) q^{98} +(1.84997 + 4.92177i) 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	$-0.762059\pi$
$2$	−0.619657	−	2.31259i	−0.438164	−	1.63525i	0.295217	−	0.955430i	$-0.404608\pi$
$3$	−1.28311	−	1.16345i	−0.740805	−	0.671721i
$3$	−1.28311	−	1.16345i	−0.740805	−	0.671721i
$4$	−3.23205	+	1.86603i	−1.61603	+	0.933013i
$5$	−1.69293	+	1.69293i	−0.757103	+	0.757103i	−0.975794	−	0.218691i	$-0.929821\pi$
$5$	−1.69293	+	1.69293i	−0.757103	+	0.757103i	0.218691	+	0.975794i	$0.429821\pi$
$6$	−1.89551	+	3.68825i	−0.773837	+	1.50572i
$7$	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
$9$	0.292748	+	2.98568i	0.0975828	+	0.995227i
$10$	4.96410	+	2.86603i	1.56979	+	0.906317i
$11$	1.69293	−	0.453620i	0.510439	−	0.136772i	0.00559833	−	0.999984i	$-0.498218\pi$
$11$	1.69293	−	0.453620i	0.510439	−	0.136772i	0.504840	+	0.863213i	$0.331551\pi$
$12$	6.31812	+	1.36603i	1.82388	+	0.394338i
$13$		0			0
$13$		0			0
$14$		−	3.38587i		−	0.904911i
$15$	4.14187	−	0.202571i	1.06943	−	0.0523036i
$16$	1.23205	−	2.13397i	0.308013	−	0.533494i
$17$	1.07328	+	1.85897i	0.260308	+	0.450867i	0.966324	−	0.257330i	$-0.0828426\pi$
$17$	1.07328	+	1.85897i	0.260308	+	0.450867i	−0.706016	+	0.708196i	$0.749509\pi$
$18$	6.72326	−	2.52711i	1.58469	−	0.595644i
$19$	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
$21$	−1.32691	−	2.05896i	−0.289555	−	0.449302i
$22$	−2.09808	−	3.63397i	−0.447311	−	0.774766i
$23$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$	−0.350863	−	7.17394i	−0.0716197	−	1.46437i
$25$		−	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	$-0.161618\pi$
$29$	4.79122	+	2.76621i	0.889707	+	0.513673i	0.0158603	+	0.999874i	$0.494951\pi$
$30$	−3.03500	−	9.45293i	−0.554113	−	1.72586i
$31$	−4.46410	−	4.46410i	−0.801776	−	0.801776i	0.181597	−	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
$33$	−2.69999	−	1.38761i	−0.470008	−	0.241551i
$34$	3.63397	−	3.63397i	0.623222	−	0.623222i
$35$	−2.93225	+	1.69293i	−0.495640	+	0.286158i
$36$	−6.51754	−	9.10360i	−1.08626	−	1.51727i
$37$	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	0.977678	−	0.210107i	$-0.0673812\pi$
$41$	0.166037	+	0.619657i	0.0259306	+	0.0967741i	−0.951748	+	0.306881i	$0.900715\pi$
$42$	−3.93930	+	4.34444i	−0.607848	+	0.670362i
$43$	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
$45$	−5.55017	−	4.55896i	−0.827370	−	0.679610i
$46$		0			0
$47$	6.77174	+	6.77174i	0.987759	+	0.987759i	0.999926	−	0.0121668i	$-0.00387290\pi$
$47$	6.77174	+	6.77174i	0.987759	+	0.987759i	−0.0121668	+	0.999926i	$0.503873\pi$
$48$	−4.06364	+	1.30469i	−0.586536	+	0.188316i
$49$	−4.33013	−	2.50000i	−0.618590	−	0.357143i
$50$	−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	$0.897103\pi$
$54$	−11.5669	−	4.57965i	−1.57405	−	0.623211i
$55$	−2.09808	+	3.63397i	−0.282905	+	0.490005i
$56$	2.93225	+	5.07880i	0.391838	+	0.678683i
$57$	−1.50726	+	0.971364i	−0.199642	+	0.128660i
$58$	3.42820	−	12.7942i	0.450145	−	1.67996i
$59$	−1.23931	+	4.62518i	−0.161345	+	0.602147i	0.837133	+	0.546999i	$0.184230\pi$
$59$	−1.23931	+	4.62518i	−0.161345	+	0.602147i	−0.998478	+	0.0551484i	$0.982437\pi$
$60$	−13.0087	+	8.38356i	−1.67942	+	1.08231i
$61$	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
$63$	−0.692934	+	4.18567i	−0.0873015	+	0.527345i
$64$		−	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	−0.0263025	−	0.999654i	$-0.508373\pi$
$71$	−4.62518	−	1.23931i	−0.548908	−	0.147079i	−0.522606	+	0.852575i	$0.675040\pi$
$72$	−7.89635	+	9.61317i	−0.930594	+	1.13292i
$73$	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
$75$	−0.851708	+	0.939303i	−0.0983467	+	0.108461i
$76$	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
$81$	−8.82860	+	1.74811i	−0.980955	+	0.194234i
$82$	1.33013	−	0.767949i	0.146888	−	0.0848058i
$83$	1.23931	−	1.23931i	0.136032	−	0.136032i	−0.635812	−	0.771844i	$-0.719335\pi$
$83$	1.23931	−	1.23931i	0.136032	−	0.136032i	0.771844	+	0.635812i	$0.219335\pi$
$84$	8.13071	+	4.17862i	0.887133	+	0.455924i
$85$	−4.96410	−	1.33013i	−0.538432	−	0.144273i
$86$	−13.8755	−	13.8755i	−1.49624	−	1.49624i
$87$	−2.92931	−	9.12372i	−0.314054	−	0.978165i
$88$	6.29423	+	3.63397i	0.670967	+	0.387383i
$89$	9.70398	−	2.60017i	1.02862	−	0.275618i	0.295230	−	0.955426i	$-0.404604\pi$
$89$	9.70398	−	2.60017i	1.02862	−	0.275618i	0.733390	+	0.679808i	$0.237937\pi$
$90$	−7.10381	+	15.6603i	−0.748807	+	1.65074i
$91$		0			0
$92$		0			0
$93$	0.534160	+	10.9217i	0.0553898	+	1.13253i
$94$	11.4641	−	19.8564i	1.18243	−	2.04803i
$95$	1.23931	+	2.14655i	0.127151	+	0.220232i
$96$	−2.24637	−	3.48568i	−0.229269	−	0.355756i
$97$	−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
$99$	1.84997	+	4.92177i	0.185929	+	0.494656i
$100$	1.36603	+	2.36603i	0.136603	+	0.236603i
$101$	9.87002	−	17.0954i	0.982104	−	1.70105i	0.327944	−	0.944697i	$-0.393644\pi$
$101$	9.87002	−	17.0954i	0.982104	−	1.70105i	0.654160	−	0.756356i	$-0.273022\pi$
$102$	−8.89076	+	0.434830i	−0.880316	+	0.0430546i
$103$			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	0.994078	−	0.108673i	$-0.0346600\pi$
$107$	14.4507	+	8.34312i	1.39700	+	0.806560i	0.402925	+	0.915233i	$0.367993\pi$
$108$	−2.22890	+	19.2638i	−0.214476	+	1.85366i
$109$	2.80385	+	2.80385i	0.268560	+	0.268560i	0.828520	−	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
$111$	5.40808	−	10.5230i	0.513313	−	0.998798i
$112$	2.46410	−	2.46410i	0.232836	−	0.232836i
$113$	−11.2309	+	6.48415i	−1.05651	+	0.609978i	−0.924465	−	0.381266i	$-0.875488\pi$
$113$	−11.2309	+	6.48415i	−1.05651	+	0.609978i	−0.132047	+	0.991243i	$0.542155\pi$
$114$	3.18035	+	2.88377i	0.297867	+	0.270090i
$115$		0			0
$116$	−20.6473			−1.91705
$117$		0			0
$118$	11.4641			1.05536
$119$	0.785693	+	2.93225i	0.0720244	+	0.268799i
$120$	12.7390	+	11.5510i	1.16291	+	1.05446i
$121$	−6.86603	+	3.96410i	−0.624184	+	0.360373i
$122$	11.8505	−	11.8505i	1.07290	−	1.07290i
$123$	0.507899	−	0.988265i	0.0457957	−	0.0891088i
$124$	22.7583	+	6.09808i	2.04376	+	0.547623i
$125$	−7.22536	−	7.22536i	−0.646255	−	0.646255i
$126$	10.1091	−	0.991207i	0.900592	−	0.0883037i
$127$	13.0981	+	7.56218i	1.16227	+	0.671035i	0.951846	−	0.306576i	$-0.0991834\pi$
$127$	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	$0.0126189\pi$
$131$			0.907241i			0.0792660i	−0.999214	+	0.0396330i	$0.987381\pi$
$132$	11.3158	−	0.553435i	0.984915	−	0.0481703i
$133$	0.732051	−	1.26795i	0.0634769	−	0.109945i
$134$	−10.4897	−	18.1687i	−0.906170	−	1.56953i
$135$	1.81734	+	12.3070i	0.156412	+	1.05922i
$136$	−2.30385	+	8.59808i	−0.197553	+	0.737279i
$137$	−1.52690	+	5.69846i	−0.130452	+	0.486852i	−0.999975	−	0.00703925i	$-0.997759\pi$
$137$	−1.52690	+	5.69846i	−0.130452	+	0.486852i	0.869524	+	0.493891i	$0.164426\pi$
$138$		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
$141$	−0.810284	−	16.5675i	−0.0682383	−	1.39523i
$142$			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
$147$	2.64740	+	8.24568i	0.218354	+	0.680092i
$148$	−18.0263	−	18.0263i	−1.48175	−	1.48175i
$149$	5.24484	+	1.40535i	0.429674	+	0.115131i	0.467173	−	0.884166i	$-0.345272\pi$
$149$	5.24484	+	1.40535i	0.429674	+	0.115131i	−0.0374992	+	0.999297i	$0.511939\pi$
$150$	2.69999	+	1.38761i	0.220453	+	0.113298i
$151$	−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
$153$	−5.23610	+	3.74867i	−0.423313	+	0.303062i
$154$	−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
$159$	5.38119	−	5.93462i	0.426756	−	0.470646i
$160$	−4.96410	+	2.86603i	−0.392447	+	0.226579i
$161$		0			0
$162$	9.51336	+	19.3337i	0.747440	+	1.51900i
$163$	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
$165$	6.92003	−	2.22178i	0.538723	−	0.172965i
$166$	−3.63397	−	2.09808i	−0.282051	−	0.162842i
$167$	−11.3969	+	3.05379i	−0.881920	+	0.236310i	−0.671235	−	0.741244i	$-0.734236\pi$
$167$	−11.3969	+	3.05379i	−0.881920	+	0.236310i	−0.210685	+	0.977554i	$0.567569\pi$
$168$	2.14655	−	9.92820i	0.165610	−	0.765978i
$169$		0			0
$170$			12.3042i			0.943686i
$171$	3.06412	+	0.507263i	0.234319	+	0.0387914i
$172$	−15.2942	+	26.4904i	−1.16617	+	2.01987i
$173$	3.71794	+	6.43966i	0.282670	+	0.489598i	0.972041	−	0.234809i	$-0.0754466\pi$
$173$	3.71794	+	6.43966i	0.282670	+	0.489598i	−0.689372	+	0.724408i	$0.742113\pi$
$174$	−19.2843	+	12.4279i	−1.46194	+	0.942154i
$175$	0.267949	−	1.00000i	0.0202551	−	0.0755929i
$176$	1.11777	−	4.17156i	0.0842548	−	0.314443i
$177$	6.97136	−	4.49274i	0.524000	−	0.337695i
$178$	−12.0263	−	20.8301i	−0.901408	−	1.56128i
$179$	−9.37191	+	16.2326i	−0.700489	+	1.21328i	0.267805	+	0.963473i	$0.413702\pi$
$179$	−9.37191	+	16.2326i	−0.700489	+	1.21328i	−0.968295	+	0.249810i	$0.919632\pi$
$180$	26.4456	+	4.37804i	1.97114	+	0.326320i
$181$		−	3.00000i		−	0.222988i	−0.993765	−	0.111494i	$-0.964436\pi$
$181$		−	3.00000i		−	0.222988i	0.993765	−	0.111494i	$-0.0355636\pi$
$182$		0			0
$183$	2.56218	−	11.8505i	0.189402	−	0.876017i
$184$		0			0
$185$	−14.1631	−	8.17709i	−1.04129	−	0.601191i
$186$	24.9265	−	8.00301i	1.82770	−	0.586809i
$187$	2.66025	+	2.66025i	0.194537	+	0.194537i
$188$	−34.5228	−	9.25036i	−2.51784	−	0.674652i
$189$	5.75895	−	4.56448i	0.418902	−	0.332017i
$190$	4.19615	−	4.19615i	0.304421	−	0.304421i
$191$	−16.8078	+	9.70398i	−1.21617	+	0.702156i	−0.964096	−	0.265553i	$-0.914446\pi$
$191$	−16.8078	+	9.70398i	−1.21617	+	0.702156i	−0.252073	+	0.967708i	$0.581112\pi$
$192$	−12.4027	+	13.6783i	−0.895089	+	0.987146i
$193$	−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	0.980201	−	0.198006i	$-0.0634465\pi$
$197$	0.453620	+	1.69293i	0.0323191	+	0.120617i	−0.947882	+	0.318622i	$0.896780\pi$
$198$	10.2357	−	7.32803i	0.727418	−	0.520780i
$199$	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
$201$	−13.4990	−	6.93756i	−0.952149	−	0.489338i
$202$	−45.6506	−	12.2321i	−3.21197	−	0.860644i
$203$	5.53242	+	5.53242i	0.388300	+	0.388300i
$204$	4.24169	+	13.2113i	0.296978	+	0.924977i
$205$	−1.33013	−	0.767949i	−0.0929001	−	0.0536359i
$206$	16.0221	−	4.29311i	1.11631	−	0.299115i
$207$		0			0
$208$		0			0
$209$		−	1.81448i		−	0.125510i
$210$	−0.685879	−	14.0238i	−0.0473302	−	0.967737i
$211$	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
$213$	4.49274	+	6.97136i	0.307837	+	0.477670i
$214$	10.3397	−	38.5885i	0.706810	−	2.63785i
$215$	−5.07880	+	18.9543i	−0.346371	+	1.29268i
$216$	21.3164	−	3.14772i	1.45040	−	0.214176i
$217$	−4.46410	−	7.73205i	−0.303043	−	0.524886i
$218$	4.74673	−	8.22158i	0.321489	−	0.556835i
$219$	−14.9193	+	0.729677i	−1.00816	+	0.0493070i
$220$		−	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
$225$	2.18567	−	0.214307i	0.145711	−	0.0142871i
$226$	21.9545	+	21.9545i	1.46039	+	1.46039i
$227$	15.1149	+	4.05001i	1.00321	+	0.268809i	0.722789	−	0.691069i	$-0.242860\pi$
$227$	15.1149	+	4.05001i	1.00321	+	0.268809i	0.280419	+	0.959878i	$0.409526\pi$
$228$	3.05896	−	5.95209i	0.202585	−	0.394187i
$229$	−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
$231$	−3.18035	−	2.88377i	−0.209252	−	0.189738i
$232$	5.93782	+	22.1603i	0.389837	+	1.45489i
$233$	−7.43588			−0.487141			−0.243570	−	0.969883i	$-0.578319\pi$
$233$	−7.43588			−0.487141			−0.243570	+	0.969883i	$0.578319\pi$
$234$		0			0
$235$	−22.9282			−1.49567
$236$	−4.62518	−	17.2614i	−0.301074	−	1.12362i
$237$	−2.56622	−	2.32691i	−0.166694	−	0.151149i
$238$	6.29423	−	3.63397i	0.407994	−	0.235556i
$239$	7.10381	−	7.10381i	0.459507	−	0.459507i	−0.438986	−	0.898494i	$-0.644662\pi$
$239$	7.10381	−	7.10381i	0.459507	−	0.459507i	0.898494	+	0.438986i	$0.144662\pi$
$240$	4.67072	−	9.08823i	0.301493	−	0.586643i
$241$	−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
$243$	13.3619	+	8.02865i	0.857167	+	0.515038i
$244$	−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
$249$	−3.03206	+	0.148292i	−0.192149	+	0.00939765i
$250$	−12.2321	+	21.1865i	−0.773623	+	1.33995i
$251$	−10.9433	−	18.9543i	−0.690735	−	1.19639i	−0.971597	−	0.236640i	$-0.923954\pi$
$251$	−10.9433	−	18.9543i	−0.690735	−	1.19639i	0.280863	−	0.959748i	$-0.409379\pi$
$252$	−5.57097	−	14.8213i	−0.350938	−	0.933656i
$253$		0			0
$254$	9.37191	−	34.9764i	0.588046	−	2.19462i
$255$	4.82195	+	7.48221i	0.301962	+	0.468554i
$256$	14.1603	+	24.5263i	0.885016	+	1.53289i
$257$	8.29863	−	14.3737i	0.517655	−	0.896604i	−0.482135	−	0.876097i	$-0.660139\pi$
$257$	8.29863	−	14.3737i	0.517655	−	0.896604i	0.999790	−	0.0205071i	$-0.00652807\pi$
$258$	1.66030	+	33.9474i	0.103366	+	2.11347i
$259$			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	$-0.212994\pi$
$263$	10.3681	+	5.98604i	0.639326	+	0.369115i	−0.145029	+	0.989427i	$0.546327\pi$
$264$	−3.84823	−	11.9858i	−0.236842	−	0.737677i
$265$	−7.83013	−	7.83013i	−0.481001	−	0.481001i
$266$	−3.38587	−	0.907241i	−0.207601	−	0.0556265i
$267$	−15.4765	−	7.95383i	−0.947145	−	0.486766i
$268$	−23.1244	+	23.1244i	−1.41254	+	1.41254i
$269$	9.58244	−	5.53242i	0.584251	−	0.337318i	−0.178570	−	0.983927i	$-0.557147\pi$
$269$	9.58244	−	5.53242i	0.584251	−	0.337318i	0.762821	+	0.646610i	$0.223814\pi$
$270$	27.3350	−	11.8289i	1.66355	−	0.719883i
$271$	−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
$279$	12.0215	−	14.6352i	0.719710	−	0.876189i
$280$	−13.5622	−	3.63397i	−0.810495	−	0.217172i
$281$	−15.9006	−	15.9006i	−0.948547	−	0.948547i	0.0501922	−	0.998740i	$-0.484017\pi$
$281$	−15.9006	−	15.9006i	−0.948547	−	0.948547i	−0.998740	+	0.0501922i	$0.984017\pi$
$282$	−37.8117	+	12.1400i	−2.25166	+	0.722928i
$283$	−21.2942	−	12.2942i	−1.26581	−	0.730816i	−0.291618	−	0.956535i	$-0.594194\pi$
$283$	−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
$288$	−1.17309	+	7.08606i	−0.0691251	+	0.417550i
$289$	6.19615	−	10.7321i	0.364480	−	0.631297i
$290$	15.8561	+	27.4635i	0.931100	+	1.61271i
$291$	18.9345	−	12.2025i	1.10996	−	0.715320i
$292$	−8.33013	+	31.0885i	−0.487484	+	1.81931i
$293$	5.69846	−	21.2669i	0.332908	−	1.24243i	−0.573212	−	0.819407i	$-0.694303\pi$
$293$	5.69846	−	21.2669i	0.332908	−	1.24243i	0.906120	−	0.423021i	$-0.139030\pi$
$294$	17.4284	−	11.2318i	1.01645	−	0.655054i
$295$	−5.73205	−	9.92820i	−0.333733	−	0.578042i
$296$	−14.1631	+	24.5313i	−0.823215	+	1.42585i
$297$	3.35253	−	8.46753i	0.194534	−	0.491336i
$298$		−	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
$303$	−32.5540	+	10.4520i	−1.87018	+	0.600449i
$304$	−1.80385	−	1.80385i	−0.103458	−	0.103458i
$305$	−16.1881	−	4.33760i	−0.926930	−	0.248370i
$306$	11.9137	+	9.78605i	0.681063	+	0.559431i
$307$	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
$309$	8.06065	−	8.88965i	0.458554	−	0.505715i
$310$	−9.36603	−	34.9545i	−0.531954	−	1.98528i
$311$	4.29311			0.243440			0.121720	−	0.992564i	$-0.461159\pi$
$311$	4.29311			0.243440			0.121720	+	0.992564i	$0.461159\pi$
$312$		0			0
$313$	2.00000			0.113047			0.0565233	−	0.998401i	$-0.481998\pi$
$313$	2.00000			0.113047			0.0565233	+	0.998401i	$0.481998\pi$
$314$	9.41640	+	35.1425i	0.531398	+	1.98321i
$315$	−5.91297	−	8.25916i	−0.333158	−	0.465351i
$316$	−6.46410	+	3.73205i	−0.363634	+	0.209944i
$317$	−11.2754	+	11.2754i	−0.633288	+	0.633288i	−0.948891	−	0.315603i	$-0.897793\pi$
$317$	−11.2754	+	11.2754i	−0.633288	+	0.633288i	0.315603	+	0.948891i	$0.397793\pi$
$318$	−17.0588	−	8.76706i	−0.956612	−	0.491632i
$319$	9.36603	+	2.50962i	0.524397	+	0.140512i
$320$	18.0471	+	18.0471i	1.00886	+	1.00886i
$321$	−8.83503	−	27.5179i	−0.493123	−	1.53590i
$322$		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
$327$	−0.335500	−	6.85980i	−0.0185532	−	0.379348i
$328$	−1.33013	+	2.30385i	−0.0734440	+	0.127209i
$329$	6.77174	+	11.7290i	0.373338	+	0.646640i
$330$	−9.42610	−	14.6265i	−0.518890	−	0.805160i
$331$	−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
$333$	−19.1822	+	7.21011i	−1.05118	+	0.395112i
$334$	14.1244	+	24.4641i	0.772850	+	1.33862i
$335$	−10.4897	+	18.1687i	−0.573112	+	0.992660i
$336$	−6.02859	+	0.294847i	−0.328886	+	0.0160852i
$337$			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
$342$	−0.725614	−	7.40039i	−0.0392367	−	0.400167i
$343$	−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	$-0.421550\pi$
$347$	22.4618	−	12.9683i	1.20581	−	0.696175i	0.961841	+	0.273608i	$0.0882171\pi$
$348$	26.4928	+	24.0222i	1.42016	+	1.28772i
$349$	−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	$-0.824778\pi$
$353$	−7.05932	−	26.3457i	−0.375730	−	1.40224i	0.476546	−	0.879149i	$-0.341889\pi$
$354$	−14.7097	−	13.3380i	−0.781813	−	0.708904i
$355$	9.92820	−	5.73205i	0.526934	−	0.304226i
$356$	−26.5118	+	26.5118i	−1.40512	+	1.40512i
$357$	2.40340	−	4.67652i	0.127202	−	0.247508i
$358$	43.3468	+	11.6147i	2.29095	+	0.613858i
$359$	12.0611	+	12.0611i	0.636559	+	0.636559i	0.949705	−	0.313146i	$-0.101383\pi$
$359$	12.0611	+	12.0611i	0.636559	+	0.636559i	−0.313146	+	0.949705i	$0.601383\pi$
$360$	−2.90646	−	29.6425i	−0.153184	−	1.56229i
$361$	15.5263	+	8.96410i	0.817173	+	0.471795i
$362$	−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
$366$	−28.9931	+	1.41800i	−1.51549	+	0.0741199i
$367$	−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
$369$	−1.80149	+	0.677136i	−0.0937819	+	0.0352503i
$370$	−10.1340	+	37.8205i	−0.526840	+	1.96619i
$371$	−1.69293	+	6.31812i	−0.0878928	+	0.328020i
$372$	−22.1066	−	34.3028i	−1.14618	−	1.77852i
$373$	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
$375$	0.864563	+	17.6773i	0.0446459	+	0.912852i
$376$			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
$381$	−8.00804	−	24.9421i	−0.410264	−	1.27782i
$382$	32.8564	+	32.8564i	1.68108	+	1.68108i
$383$	13.5435	+	3.62896i	0.692039	+	0.185431i	0.587662	−	0.809106i	$-0.300048\pi$
$383$	13.5435	+	3.62896i	0.692039	+	0.185431i	0.104377	+	0.994538i	$0.466715\pi$
$384$	31.9412	+	16.4156i	1.62999	+	0.837703i
$385$	−4.19615	+	4.19615i	−0.213856	+	0.213856i
$386$	−14.9488	+	8.63071i	−0.760875	+	0.439291i
$387$	14.3135	+	19.9929i	0.727596	+	1.01630i
$388$	−12.5622	−	46.8827i	−0.637748	−	2.38011i
$389$	−5.28933			−0.268180			−0.134090	−	0.990969i	$-0.542811\pi$
$389$	−5.28933			−0.268180			−0.134090	+	0.990969i	$0.542811\pi$
$390$		0			0
$391$		0			0
$392$	−5.36639	−	20.0276i	−0.271043	−	1.01155i
$393$	1.05553	−	1.16409i	0.0532446	−	0.0587206i
$394$	3.63397	−	2.09808i	0.183077	−	0.105700i
$395$	−3.38587	+	3.38587i	−0.170362	+	0.170362i
$396$	−15.1633	−	12.4553i	−0.761986	−	0.625903i
$397$	−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
$399$	−2.41450	+	0.775212i	−0.120876	+	0.0388091i
$400$	−1.56218	−	0.901924i	−0.0781089	−	0.0450962i
$401$	−27.1314	+	7.26985i	−1.35488	+	0.363039i	−0.861933	−	0.507021i	$-0.830747\pi$
$401$	−27.1314	+	7.26985i	−1.35488	+	0.363039i	−0.492946	+	0.870060i	$0.664080\pi$
$402$	−7.67898	+	35.5167i	−0.382993	+	1.77141i
$403$		0			0
$404$			73.6708i			3.66526i
$405$	11.9868	−	17.9057i	0.595629	−	0.889739i
$406$	9.36603	−	16.2224i	0.464828	−	0.805106i
$407$	5.98604	+	10.3681i	0.296717	+	0.513929i
$408$	12.9596	−	8.35187i	0.641594	−	0.413479i
$409$	−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
$411$	8.58908	−	5.53528i	0.423668	−	0.273035i
$412$	−12.9282	−	22.3923i	−0.636927	−	1.10319i
$413$	−3.38587	+	5.86450i	−0.166608	+	0.288573i
$414$		0			0
$415$			4.19615i			0.205981i
$416$		0			0
$417$	0.875644	−	4.05001i	0.0428805	−	0.198330i
$418$	−4.19615	+	1.12436i	−0.205241	+	0.0549940i
$419$	−7.22536	−	4.17156i	−0.352982	−	0.203794i	0.313016	−	0.949748i	$-0.398661\pi$
$419$	−7.22536	−	4.17156i	−0.352982	−	0.203794i	−0.665998	+	0.745954i	$0.731994\pi$
$420$	−20.8389	+	6.69063i	−1.01683	+	0.326469i
$421$	−0.830127	−	0.830127i	−0.0404579	−	0.0404579i	0.686588	−	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
$423$	−18.2358	+	22.2007i	−0.886657	+	1.07943i
$424$	−13.5622	+	13.5622i	−0.658638	+	0.658638i
$425$	1.36086	−	0.785693i	0.0660114	−	0.0381117i
$426$	13.3380	−	14.7097i	0.646226	−	0.712688i
$427$	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	$-0.0994120\pi$
$431$	−0.542599	−	2.02501i	−0.0261361	−	0.0975412i	−0.977762	+	0.209718i	$0.932745\pi$
$432$	−5.08502	−	11.7508i	−0.244653	−	0.565360i
$433$	−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
$435$	20.4050	+	10.4867i	0.978344	+	0.502800i
$436$	−14.2942	−	3.83013i	−0.684569	−	0.183430i
$437$		0			0
$438$	10.9323	+	34.0502i	0.522366	+	1.62698i
$439$	−4.09808	−	2.36603i	−0.195591	−	0.112924i	0.399007	−	0.916948i	$-0.369355\pi$
$439$	−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	$-0.752134\pi$
$443$		−	29.5656i		−	1.40470i	0.711830	−	0.702351i	$-0.247866\pi$
$444$	2.15697	+	44.1025i	0.102365	+	2.09301i
$445$	−12.0263	+	20.8301i	−0.570100	+	0.987443i
$446$	27.6295	+	47.8558i	1.30830	+	2.26604i
$447$	−5.09465	−	7.90535i	−0.240969	−	0.373910i
$448$	3.90192	−	14.5622i	0.184349	−	0.687998i
$449$	2.26810	−	8.46467i	0.107038	−	0.399472i	−0.891530	−	0.452961i	$-0.850368\pi$
$449$	2.26810	−	8.46467i	0.107038	−	0.399472i	0.998568	+	0.0534890i	$0.0170342\pi$
$450$	−1.84997	−	4.92177i	−0.0872084	−	0.232014i
$451$	0.562178	+	0.973721i	0.0264719	+	0.0458507i
$452$	24.1992	−	41.9142i	1.13823	−	1.97148i
$453$	18.2614	−	0.893131i	0.857996	−	0.0419629i
$454$		−	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
$459$	11.0799	+	1.28199i	0.517166	+	0.0598382i
$460$		0			0
$461$	23.4135	+	6.27363i	1.09048	+	0.292192i	0.758880	−	0.651230i	$-0.225747\pi$
$461$	23.4135	+	6.27363i	1.09048	+	0.292192i	0.331595	+	0.943422i	$0.392413\pi$
$462$	−4.69825	+	9.14181i	−0.218582	+	0.425315i
$463$	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
$465$	−19.3940	−	17.5854i	−0.899377	−	0.815506i
$466$	4.60770	+	17.1962i	0.213447	+	0.796596i
$467$	−30.4728			−1.41011			−0.705057	−	0.709151i	$-0.749079\pi$
$467$	−30.4728			−1.41011			−0.705057	+	0.709151i	$0.749079\pi$
$468$		0			0
$469$	12.3923			0.572223
$470$	14.2076	+	53.0236i	0.655349	+	2.44579i
$471$	19.4984	+	17.6800i	0.898437	+	0.814653i
$472$	−17.1962	+	9.92820i	−0.791517	+	0.456983i
$473$	10.1576	−	10.1576i	0.467047	−	0.467047i
$474$	−3.79101	+	7.37651i	−0.174127	+	0.338814i
$475$	−0.732051	−	0.196152i	−0.0335888	−	0.00900009i
$476$	−8.01105	−	8.01105i	−0.367186	−	0.367186i
$477$	−13.8093	+	1.35401i	−0.632285	+	0.0619960i
$478$	−20.8301	−	12.0263i	−0.952748	−	0.550069i
$479$	−8.46467	+	2.26810i	−0.386761	+	0.103632i	−0.446959	−	0.894554i	$-0.647493\pi$
$479$	−8.46467	+	2.26810i	−0.386761	+	0.103632i	0.0601988	+	0.998186i	$0.480827\pi$
$480$	9.70398	+	2.09808i	0.442924	+	0.0957636i
$481$		0			0
$482$			17.9256i			0.816487i
$483$		0			0
$484$	14.7942	−	25.6244i	0.672465	−	1.16474i
$485$	−15.5685	−	26.9654i	−0.706928	−	1.22444i
$486$	10.2872	−	35.8756i	0.466636	−	1.62735i
$487$	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
$489$	−14.5007	−	22.5007i	−0.655746	−	1.01752i
$490$	−14.3301	−	24.8205i	−0.647369	−	1.12128i
$491$	−12.5147	+	21.6761i	−0.564780	+	0.978227i	0.432290	+	0.901734i	$0.357706\pi$
$491$	−12.5147	+	21.6761i	−0.564780	+	0.978227i	−0.997070	+	0.0764928i	$0.975628\pi$
$492$	0.202571	+	4.14187i	0.00913261	+	0.186730i
$493$			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
$498$	2.22178	+	6.92003i	0.0995602	+	0.310094i
$499$	−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
$501$	18.1765	+	9.34143i	0.812064	+	0.417345i
$502$	−37.0526	+	37.0526i	−1.65374	+	1.65374i
$503$	24.8188	−	14.3292i	1.10662	−	0.638906i	0.168666	−	0.985673i	$-0.446054\pi$
$503$	24.8188	−	14.3292i	1.10662	−	0.638906i	0.937951	+	0.346767i	$0.112721\pi$
$504$	−14.3053	+	10.2416i	−0.637208	+	0.456196i
$505$	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	$0.0245846\pi$
$509$	3.88398	+	14.4952i	0.172154	+	0.642489i	−0.824865	+	0.565330i	$0.808749\pi$
$510$	14.3153	−	15.7876i	0.633893	−	0.699087i
$511$	10.5622	−	6.09808i	0.467243	−	0.269763i
$512$	18.6223	−	18.6223i	0.822996	−	0.822996i
$513$	−3.34143	−	4.21584i	−0.147528	−	0.186134i
$514$	−38.3827	−	10.2846i	−1.69299	−	0.453635i
$515$	−11.7290	−	11.7290i	−0.516841	−	0.516841i
$516$	50.4445	−	16.1960i	2.22070	−	0.712988i
$517$	14.5359	+	8.39230i	0.639288	+	0.369093i
$518$	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	$-0.260056\pi$
$522$	39.2031	+	6.49004i	1.71587	+	0.284061i
$523$	−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
$525$	−1.50726	+	0.971364i	−0.0657823	+	0.0423938i
$526$	7.41858	−	27.6865i	0.323466	−	1.20719i
$527$	3.50742	−	13.0899i	0.152785	−	0.570203i
$528$	−6.28764	+	4.05211i	−0.273634	+	0.176345i
$529$	11.5000	+	19.9186i	0.500000	+	0.866025i
$530$	−13.2559	+	22.9599i	−0.575799	+	0.997313i
$531$	−14.1721	−	2.34618i	−0.615018	−	0.101816i
$532$			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
$537$	30.9111	−	9.92447i	1.33391	−	0.428273i
$538$	−18.7321	−	18.7321i	−0.807596	−	0.807596i
$539$	−8.46467	−	2.26810i	−0.364599	−	0.0976940i
$540$	−28.8389	−	36.3857i	−1.24103	−	1.56579i
$541$	−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
$543$	−3.49036	+	3.84933i	−0.149786	+	0.165191i
$544$	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
$549$	−17.0751	+	12.2246i	−0.728748	+	0.521732i
$550$	−2.66025	+	1.53590i	−0.113434	+	0.0654909i
$551$	4.05001	−	4.05001i	0.172536	−	0.172536i
$552$		0			0
$553$	2.73205	+	0.732051i	0.116179	+	0.0311300i
$554$	−6.07502	−	6.07502i	−0.258103	−	0.258103i
$555$	8.65920	+	26.9703i	0.367563	+	1.14482i
$556$	−7.73205	−	4.46410i	−0.327912	−	0.189320i
$557$	39.3140	−	10.5342i	1.66579	−	0.446347i	0.701819	−	0.712355i	$-0.252372\pi$
$557$	39.3140	−	10.5342i	1.66579	−	0.446347i	0.963971	+	0.266009i	$0.0857049\pi$
$558$	−41.2946	−	18.7321i	−1.74814	−	0.792991i
$559$		0			0
$560$			8.34312i			0.352561i
$561$	−0.318318	−	6.50849i	−0.0134394	−	0.274788i
$562$	−26.9186	+	46.6244i	−1.13549	+	1.96673i
$563$	2.14655	+	3.71794i	0.0904665	+	0.156693i	0.907708	−	0.419603i	$-0.137831\pi$
$563$	2.14655	+	3.71794i	0.0904665	+	0.156693i	−0.817241	+	0.576296i	$0.804498\pi$
$564$	33.5342	+	52.0350i	1.41205	+	2.19107i
$565$	8.03590	−	29.9904i	0.338073	−	1.26170i
$566$	−15.2364	+	56.8630i	−0.640434	+	2.39013i
$567$	−12.6999	−	0.843533i	−0.533347	−	0.0354250i
$568$	−9.92820	−	17.1962i	−0.416578	−	0.721535i
$569$	8.01105	−	13.8755i	0.335841	−	0.581693i	−0.647805	−	0.761806i	$-0.724313\pi$
$569$	8.01105	−	13.8755i	0.335841	−	0.581693i	0.983646	+	0.180113i	$0.0576463\pi$
$570$	−10.2662	+	0.502098i	−0.430002	+	0.0210306i
$571$		−	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
$576$	31.8281	−	3.12077i	1.32617	−	0.130032i
$577$	−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
$579$	−5.70810	+	11.1068i	−0.237220	+	0.461581i
$580$	34.9545	−	34.9545i	1.45141	−	1.45141i
$581$	2.14655	−	1.23931i	0.0890541	−	0.0514154i
$582$	−39.9522	−	36.2264i	−1.65607	−	1.50163i
$583$	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	$-0.947235\pi$
$587$	−5.20035	−	19.4080i	−0.214641	−	0.801053i	0.771651	−	0.636046i	$-0.219431\pi$
$588$	−23.9432	−	21.7104i	−0.987400	−	0.895320i
$589$	−5.66025	+	3.26795i	−0.233227	+	0.134654i
$590$	−19.4080	+	19.4080i	−0.799013	+	0.799013i
$591$	1.38761	−	2.69999i	0.0570785	−	0.111063i
$592$	16.2583	+	4.35641i	0.668213	+	0.179047i
$593$	−10.6112	−	10.6112i	−0.435751	−	0.435751i	0.454828	−	0.890579i	$-0.349701\pi$
$593$	−10.6112	−	10.6112i	−0.435751	−	0.435751i	−0.890579	+	0.454828i	$0.849701\pi$
$594$	−21.6593	−	2.50608i	−0.888694	−	0.102826i
$595$	−6.29423	−	3.63397i	−0.258038	−	0.148978i
$596$	−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	$0.857256\pi$
$600$	−5.25169	+	0.256850i	−0.214399	+	0.0104859i
$601$	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
$603$	9.24923	+	24.6072i	0.376658	+	1.00208i
$604$	10.1962	−	38.0526i	0.414876	−	1.54834i
$605$	4.91277	−	18.3347i	0.199732	−	0.745411i
$606$	44.3434	+	68.8075i	1.80133	+	2.79511i
$607$	−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
$609$	−0.661992	−	13.5354i	−0.0268253	−	0.548483i
$610$			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
$615$	0.813227	+	2.53291i	0.0327925	+	0.102137i
$616$	7.26795	+	7.26795i	0.292834	+	0.292834i
$617$	−36.3818	−	9.74847i	−1.46468	−	0.392459i	−0.563574	−	0.826066i	$-0.690574\pi$
$617$	−36.3818	−	9.74847i	−1.46468	−	0.392459i	−0.901102	+	0.433607i	$0.857241\pi$
$618$	−25.5530	−	13.1324i	−1.02789	−	0.528264i
$619$	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
$627$	−2.11107	+	2.32818i	−0.0843078	+	0.0929786i
$628$	49.1147	−	28.3564i	1.95989	−	1.13154i
$629$	−10.3681	+	10.3681i	−0.413404	+	0.413404i
$630$	−15.4360	+	18.7921i	−0.614986	+	0.748696i
$631$	−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
$633$	−20.1131	+	6.45761i	−0.799425	+	0.256667i
$634$	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
$639$	2.34618	−	14.1721i	0.0928136	−	0.560641i
$640$	24.8205	−	42.9904i	0.981117	−	1.69934i
$641$	−9.65949	−	16.7307i	−0.381527	−	0.660824i	0.609754	−	0.792591i	$-0.291268\pi$
$641$	−9.65949	−	16.7307i	−0.381527	−	0.660824i	−0.991281	+	0.131767i	$0.957935\pi$
$642$	−58.1629	+	37.4835i	−2.29551	+	1.47935i
$643$	−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
$645$	28.5692	−	18.4116i	1.12491	−	0.724955i
$646$	−2.66025	−	4.60770i	−0.104666	−	0.181287i
$647$	7.22536	−	12.5147i	0.284058	−	0.492003i	−0.688322	−	0.725405i	$-0.741652\pi$
$647$	7.22536	−	12.5147i	0.284058	−	0.492003i	0.972380	+	0.233402i	$0.0749858\pi$
$648$	−31.0135	−	20.7618i	−1.21833	−	0.815599i
$649$			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	$-0.607886\pi$
$653$	−33.6156	−	19.4080i	−1.31548	−	0.759492i	−0.982998	+	0.183617i	$0.941219\pi$
$654$	−15.6560	+	5.02659i	−0.612198	+	0.196555i
$655$	−1.53590	−	1.53590i	−0.0600125	−	0.0600125i
$656$	1.52690	+	0.409131i	0.0596153	+	0.0159739i
$657$	19.9921	+	16.4217i	0.779967	+	0.640672i
$658$	22.9282	−	22.9282i	0.893834	−	0.893834i
$659$	27.1759	−	15.6900i	1.05862	−	0.611197i	0.133572	−	0.991039i	$-0.457355\pi$
$659$	27.1759	−	15.6900i	1.05862	−	0.611197i	0.925051	+	0.379842i	$0.124022\pi$
$660$	−18.2200	+	20.0938i	−0.709212	+	0.782152i
$661$	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
$666$	28.5604	+	39.8928i	1.10669	+	1.54581i
$667$		0			0
$668$	31.1370	−	31.1370i	1.20473	−	1.20473i
$669$	35.5561	+	18.2734i	1.37468	+	0.706489i
$670$	48.5167	+	13.0000i	1.87436	+	0.502234i
$671$	8.67520	+	8.67520i	0.334902	+	0.334902i
$672$	−1.79275	−	5.58376i	−0.0691568	−	0.215398i
$673$	−11.0096	−	6.35641i	−0.424390	−	0.245021i	0.272564	−	0.962138i	$-0.412128\pi$
$673$	−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	$0.267985\pi$
$677$			38.8159i			1.49182i	−0.666048	+	0.745909i	$0.732015\pi$
$678$	−2.62700	−	53.7131i	−0.100889	−	2.06284i
$679$	−9.19615	+	15.9282i	−0.352916	+	0.611268i
$680$	−10.6557	−	18.4562i	−0.408628	−	0.707764i
$681$	−14.6820	−	22.7821i	−0.562617	−	0.873011i
$682$	−6.85641	+	25.5885i	−0.262545	+	0.979833i
$683$	4.26054	−	15.9006i	0.163025	−	0.608418i	−0.835259	−	0.549857i	$-0.814682\pi$
$683$	4.26054	−	15.9006i	0.163025	−	0.608418i	0.998284	−	0.0585607i	$-0.0186511\pi$
$684$	−10.8500	+	4.07823i	−0.414859	+	0.155935i
$685$	−7.06218	−	12.2321i	−0.269832	−	0.467363i
$686$	−20.3152	+	35.1870i	−0.775638	+	1.34344i
$687$	24.7699	−	1.21145i	0.945031	−	0.0462196i
$688$		−	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
$693$	0.725614	+	7.40039i	0.0275638	+	0.281118i
$694$	−43.9090	−	43.9090i	−1.66676	−	1.66676i
$695$	−5.53242	−	1.48241i	−0.209857	−	0.0562309i
$696$	18.1636	−	35.3425i	0.688488	−	1.33965i
$697$	−0.973721	+	0.973721i	−0.0368823	+	0.0368823i
$698$	−12.0936	+	6.98226i	−0.457751	+	0.264283i
$699$	9.54106	+	8.65131i	0.360876	+	0.327223i
$700$	1.00000	+	3.73205i	0.0377964	+	0.141058i
$701$	20.3152			0.767295			0.383647	−	0.923480i	$-0.374668\pi$
$701$	20.3152			0.767295			0.383647	+	0.923480i	$0.374668\pi$
$702$		0			0
$703$	7.07180			0.266718
$704$	−4.83571	−	18.0471i	−0.182253	−	0.680176i
$705$	29.4194	+	26.6759i	1.10800	+	1.00467i
$706$	−56.5526	+	32.6506i	−2.12838	+	1.22882i
$707$	19.7400	−	19.7400i	0.742401	−	0.742401i
$708$	−14.1482	+	27.5295i	−0.531724	+	1.03462i
$709$	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
$711$	0.585497	+	5.97136i	0.0219578	+	0.223944i
$712$	36.0788	+	20.8301i	1.35211	+	0.780642i
$713$		0			0
$714$	−12.3042	−	2.66025i	−0.460472	−	0.0995575i
$715$		0			0
$716$		−	69.9529i		−	2.61426i
$717$	−17.3799	+	0.850019i	−0.649065	+	0.0317446i
$718$	20.4186	−	35.3660i	0.762015	−	1.31985i
$719$	−5.86450	−	10.1576i	−0.218709	−	0.378815i	0.735705	−	0.677302i	$-0.236851\pi$
$719$	−5.86450	−	10.1576i	−0.218709	−	0.378815i	−0.954413	+	0.298488i	$0.903518\pi$
$720$	−16.5668	+	6.22704i	−0.617408	+	0.232068i
$721$	−2.53590	+	9.46410i	−0.0944418	+	0.352462i
$722$	11.1093	−	41.4606i	0.413447	−	1.54300i
$723$	7.02496	+	10.9006i	0.261261	+	0.405398i
$724$	5.59808	+	9.69615i	0.208051	+	0.360355i
$725$	2.02501	−	3.50742i	0.0752069	−	0.130262i
$726$	−1.60603	−	32.8376i	−0.0596052	−	1.21872i
$727$		−	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
$732$	13.8323	+	43.0826i	0.511257	+	1.59238i
$733$	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
$735$	−18.4413	−	9.47753i	−0.680216	−	0.349584i
$736$		0			0
$737$	13.3004	−	7.67898i	0.489926	−	0.282859i
$738$	2.68224	+	3.74652i	0.0987348	+	0.137911i
$739$	−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	$0.326177\pi$
$743$	13.5435	+	50.5449i	0.496862	+	1.85431i	−0.0224808	+	0.999747i	$0.507156\pi$
$744$	−30.4589	+	33.5915i	−1.11668	+	1.23152i
$745$	−11.2583	+	6.50000i	−0.412473	+	0.238142i
$746$	33.1620	−	33.1620i	1.21415	−	1.21415i
$747$	4.06300	+	3.33739i	0.148658	+	0.122109i
$748$	−13.5622	−	3.63397i	−0.495882	−	0.132871i
$749$	16.6862	+	16.6862i	0.609702	+	0.609702i
$750$	40.3446	−	12.9532i	1.47318	−	0.472986i
$751$	38.2750	+	22.0981i	1.39667	+	0.806370i	0.994043	−	0.108992i	$-0.0347622\pi$
$751$	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
$756$	−10.0958	+	25.4990i	−0.367180	+	0.927389i
$757$	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	−0.942703	−	0.333634i	$-0.891725\pi$
$761$	1.11777	−	4.17156i	0.0405190	−	0.151219i	0.983222	+	0.182415i	$0.0583916\pi$
$762$	−52.7187	+	33.9749i	−1.90980	+	1.23078i
$763$	2.80385	+	4.85641i	0.101506	+	0.175814i
$764$	36.2158	−	62.7275i	1.31024	−	2.26940i
$765$	2.51810	−	15.2106i	0.0910423	−	0.549941i
$766$		−	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
$771$	−27.3712	+	8.78792i	−0.985748	+	0.316489i
$772$	19.0263	+	19.0263i	0.684771	+	0.684771i
$773$	−5.98604	−	1.60396i	−0.215303	−	0.0576903i	0.149555	−	0.988753i	$-0.452216\pi$
$773$	−5.98604	−	1.60396i	−0.215303	−	0.0576903i	−0.364858	+	0.931063i	$0.618883\pi$
$774$	37.3659	−	45.4900i	1.34309	−	1.63510i
$775$	−3.26795	+	3.26795i	−0.117388	+	0.117388i
$776$	−46.7054	+	26.9654i	−1.67663	+	0.968001i
$777$	11.2393	−	12.3952i	0.403206	−	0.444675i
$778$	3.27757	+	12.2321i	0.117507	+	0.438540i
$779$	0.664146			0.0237955
$780$		0			0
$781$	−8.39230			−0.300300
$782$		0			0
$783$	26.3830	−	11.4169i	0.942851	−	0.408008i
$784$	−10.6699	+	6.16025i	−0.381067	+	0.220009i
$785$	25.7261	−	25.7261i	0.918203	−	0.918203i
$786$	−3.34613	−	1.71968i	−0.119353	−	0.0613389i
$787$	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
$789$	−6.33898	−	19.7436i	−0.225674	−	0.702891i
$790$	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
$795$	0.936928	+	19.1569i	0.0332294	+	0.679426i
$796$	−1.73205	+	3.00000i	−0.0613909	+	0.106332i
$797$	8.58622	+	14.8718i	0.304139	+	0.526785i	0.977069	−	0.212921i	$-0.0682978\pi$
$797$	8.58622	+	14.8718i	0.304139	+	0.526785i	−0.672930	+	0.739706i	$0.734964\pi$
$798$	3.28891	+	5.10339i	0.116426	+	0.180658i
$799$	−5.32051	+	19.8564i	−0.188226	+	0.702469i
$800$	0.453620	−	1.69293i	0.0160379	−	0.0598543i
$801$	10.6041	+	28.2118i	0.374678	+	0.996815i
$802$	33.6244	+	58.2391i	1.18732	+	2.05649i
$803$	7.55743	−	13.0899i	0.266696	−	0.461931i
$804$	56.5752	−	2.76699i	1.99526	−	0.0975841i
$805$		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	$-0.216558\pi$
$809$	17.6705	+	10.2021i	0.621263	+	0.358686i	−0.156097	+	0.987742i	$0.549891\pi$
$810$	−48.8362	−	16.6252i	−1.71593	−	0.584150i
$811$	−19.0000	−	19.0000i	−0.667180	−	0.667180i	0.289882	−	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
$813$	−1.63929	+	3.18972i	−0.0574925	+	0.111868i
$814$	20.2679	−	20.2679i	0.710391	−	0.710391i
$815$	−32.0442	+	18.5007i	−1.12246	+	0.648052i
$816$	−6.78680	−	6.15389i	−0.237585	−	0.215429i
$817$	−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	$-0.0488432\pi$
$821$	1.60396	+	5.98604i	0.0559784	+	0.208914i	−0.932272	+	0.361758i	$0.882177\pi$
$822$	−18.1231	−	16.4330i	−0.632116	−	0.573168i
$823$	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
$825$	−1.01580	+	1.97653i	−0.0353656	+	0.0688139i
$826$	15.6603	+	4.19615i	0.544890	+	0.146003i
$827$	3.62896	+	3.62896i	0.126191	+	0.126191i	0.767382	−	0.641190i	$-0.221559\pi$
$827$	3.62896	+	3.62896i	0.126191	+	0.126191i	−0.641190	+	0.767382i	$0.721559\pi$
$828$		0			0
$829$	−20.6769	−	11.9378i	−0.718139	−	0.414618i	0.0959284	−	0.995388i	$-0.469418\pi$
$829$	−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
$834$	−9.90862	+	0.484612i	−0.343108	+	0.0167807i
$835$	14.1244	−	24.4641i	0.488793	−	0.846615i
$836$	3.38587	+	5.86450i	0.117103	+	0.202828i
$837$	−32.4524	+	4.79215i	−1.12172	+	0.165641i
$838$	−5.16987	+	19.2942i	−0.178590	+	0.666508i
$839$	−2.02501	+	7.55743i	−0.0699110	+	0.260911i	−0.992031	−	0.125992i	$-0.959789\pi$
$839$	−2.02501	+	7.55743i	−0.0699110	+	0.260911i	0.922120	+	0.386903i	$0.126455\pi$
$840$	13.1738	+	20.4418i	0.454540	+	0.705308i
$841$	0.803848	+	1.39230i	0.0277189	+	0.0480105i
$842$	−1.40535	+	2.43414i	−0.0484316	+	0.0838859i
$843$	1.90261	+	38.9017i	0.0655294	+	1.33985i
$844$			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
$849$	13.0191	+	40.5497i	0.446814	+	1.39166i
$850$	−2.66025	−	2.66025i	−0.0912460	−	0.0912460i
$851$		0			0
$852$	−27.5295	−	14.1482i	−0.943145	−	0.484711i
$853$	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
$855$	−6.04612	+	4.32860i	−0.206773	+	0.148035i
$856$	17.9090	+	66.8372i	0.612116	+	2.28445i
$857$	−35.7621			−1.22161			−0.610806	−	0.791781i	$-0.709154\pi$
$857$	−35.7621			−1.22161			−0.610806	+	0.791781i	$0.709154\pi$
$858$		0			0
$859$	−23.1769			−0.790786			−0.395393	−	0.918512i	$-0.629392\pi$
$859$	−23.1769			−0.790786			−0.395393	+	0.918512i	$0.629392\pi$
$860$	−18.9543	−	70.7386i	−0.646338	−	2.41217i
$861$	1.05553	−	1.16409i	0.0359725	−	0.0396721i
$862$	−4.34679	+	2.50962i	−0.148052	+	0.0854780i
$863$	−12.0611	+	12.0611i	−0.410563	+	0.410563i	−0.881935	−	0.471371i	$-0.843759\pi$
$863$	−12.0611	+	12.0611i	−0.410563	+	0.410563i	0.471371	+	0.881935i	$0.343759\pi$
$864$	9.74952	−	7.72737i	0.331685	−	0.262890i
$865$	−17.1962	−	4.60770i	−0.584687	−	0.156666i
$866$	11.9395	+	11.9395i	0.405721	+	0.405721i
$867$	−20.4366	+	6.56147i	−0.694063	+	0.222839i
$868$	28.8564	+	16.6603i	0.979450	+	0.565486i
$869$	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
$873$	−38.4921	−	6.37233i	−1.30276	−	0.215671i
$874$		0			0
$875$	−7.22536	−	12.5147i	−0.244262	−	0.423074i
$876$	46.8585	−	30.1982i	1.58320	−	1.02030i
$877$	−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
$879$	−32.0549	+	20.6579i	−1.08118	+	0.696775i
$880$	5.16987	+	8.95448i	0.174276	+	0.301856i
$881$	−13.5880	+	23.5350i	−0.457790	+	0.792916i	−0.998844	−	0.0480724i	$-0.984692\pi$
$881$	−13.5880	+	23.5350i	−0.457790	+	0.792916i	0.541054	+	0.840988i	$0.318026\pi$
$882$	−35.4303	−	5.86546i	−1.19300	−	0.197500i
$883$			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	$-0.975927\pi$
$887$	−46.4949	−	26.8438i	−1.56115	−	0.901328i	−0.564005	−	0.825772i	$-0.690740\pi$
$888$	46.7139	−	14.9982i	1.56761	−	0.503306i
$889$	15.1244	+	15.1244i	0.507255	+	0.507255i
$890$	55.6237	+	14.9043i	1.86451	+	0.499594i
$891$	−14.1533	+	6.96426i	−0.474152	+	0.233311i
$892$	60.9090	−	60.9090i	2.03938	−	2.03938i
$893$	8.58622	−	4.95725i	0.287327	−	0.165888i
$894$	−15.1249	+	16.6804i	−0.505853	+	0.557878i
$895$	−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
$900$	−6.66430	+	4.77117i	−0.222143	+	0.159039i
$901$	−8.59808	+	4.96410i	−0.286443	+	0.165378i
$902$	1.90346	−	1.90346i	0.0633783	−	0.0633783i
$903$	−17.8563	−	9.17688i	−0.594219	−	0.305387i
$904$	−51.9449	−	13.9186i	−1.72766	−	0.462925i
$905$	5.07880	+	5.07880i	0.168825	+	0.168825i
$906$	−13.3813	−	41.6777i	−0.444562	−	1.38465i
$907$	−15.0000	−	8.66025i	−0.498067	−	0.287559i	0.229848	−	0.973227i	$-0.426177\pi$
$907$	−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	$-0.951030\pi$
$911$		−	9.25036i		−	0.306478i	0.988189	−	0.153239i	$-0.0489705\pi$
$912$	0.215843	+	4.41323i	0.00714727	+	0.146137i
$913$	1.53590	−	2.66025i	0.0508308	−	0.0880416i
$914$	−33.4495	−	57.9363i	−1.10641	−	1.91636i
$915$	15.7246	+	24.3998i	0.519839	+	0.806632i
$916$	13.8301	−	51.6147i	0.456960	−	1.70540i
$917$	−0.332073	+	1.23931i	−0.0109660	+	0.0409257i
$918$	−3.90102	−	26.4177i	−0.128753	−	0.871913i
$919$	−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
$921$	−30.3186	+	1.48282i	−0.999031	+	0.0488607i
$922$		−	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
$927$	−20.6854	+	2.02822i	−0.679398	+	0.0666155i
$928$	9.36603	+	9.36603i	0.307455	+	0.307455i
$929$	−47.3251	−	12.6807i	−1.55269	−	0.416041i	−0.622347	−	0.782742i	$-0.713821\pi$
$929$	−47.3251	−	12.6807i	−1.55269	−	0.416041i	−0.930339	+	0.366701i	$0.880487\pi$
$930$	−28.6503	+	55.7474i	−0.939480	+	1.82803i
$931$	−3.66025	+	3.66025i	−0.119960	+	0.119960i
$932$	24.0331	−	13.8755i	0.787232	−	0.454509i
$933$	−5.50854	−	4.99484i	−0.180341	−	0.163524i
$934$	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
$939$	−2.56622	−	2.32691i	−0.0837455	−	0.0759358i
$940$	74.1051	−	42.7846i	2.41704	−	1.39548i
$941$	−38.2408	+	38.2408i	−1.24661	+	1.24661i	−0.289407	+	0.957206i	$0.593458\pi$
$941$	−38.2408	+	38.2408i	−1.24661	+	1.24661i	−0.957206	+	0.289407i	$0.906542\pi$
$942$	28.8044	−	56.0473i	0.938498	−	1.82612i
$943$		0			0
$944$	8.34312	+	8.34312i	0.271546	+	0.271546i
$945$	−2.02215	+	17.4769i	−0.0657805	+	0.568523i
$946$	−29.7846	−	17.1962i	−0.968381	−	0.559095i
$947$	39.6016	−	10.6112i	1.28688	−	0.344818i	0.450405	−	0.892824i	$-0.351279\pi$
$947$	39.6016	−	10.6112i	1.28688	−	0.344818i	0.836475	+	0.548006i	$0.184613\pi$
$948$	12.6362	+	2.73205i	0.410406	+	0.0887329i
$949$		0			0
$950$			1.81448i			0.0588695i
$951$	27.5859	−	1.34918i	0.894535	−	0.0437500i
$952$	−6.29423	+	10.9019i	−0.203997	+	0.353333i
$953$	21.8866	+	37.9087i	0.708976	+	1.22798i	0.965237	+	0.261375i	$0.0841760\pi$
$953$	21.8866	+	37.9087i	0.708976	+	1.22798i	−0.256261	+	0.966608i	$0.582491\pi$
$954$	11.6883	+	31.0963i	0.378423	+	1.00678i
$955$	12.0263	−	44.8827i	0.389161	−	1.45237i
$956$	−9.70398	+	36.2158i	−0.313849	+	1.17130i
$957$	−9.09782	−	14.1171i	−0.294091	−	0.456340i
$958$	10.4904	+	18.1699i	0.338929	+	0.587042i
$959$	−4.17156	+	7.22536i	−0.134707	+	0.233319i
$960$	−2.15946	−	44.1534i	−0.0696963	−	1.42505i
$961$			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
$969$	−3.42345	−	1.75941i	−0.109977	−	0.0565205i
$970$	−52.7128	+	52.7128i	−1.69251	+	1.69251i
$971$	−45.5551	+	26.3013i	−1.46193	+	0.844047i	−0.999101	−	0.0423987i	$-0.986500\pi$
$971$	−45.5551	+	26.3013i	−1.46193	+	0.844047i	−0.462832	+	0.886446i	$0.653167\pi$
$972$	−58.1681	−	1.01535i	−1.86574	−	0.0325673i
$973$	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	$0.0723550\pi$
$977$	7.60192	+	28.3707i	0.243207	+	0.907661i	−0.731069	+	0.682303i	$0.760978\pi$
$978$	−43.0495	+	47.4770i	−1.37657	+	1.51815i
$979$	15.2487	−	8.80385i	0.487351	−	0.281372i
$980$	−31.5906	+	31.5906i	−1.00912	+	1.00912i
$981$	−7.55058	+	9.19222i	−0.241071	+	0.293485i
$982$	57.8827	+	15.5096i	1.84711	+	0.494932i
$983$	−4.38209	−	4.38209i	−0.139767	−	0.139767i	0.633762	−	0.773528i	$-0.281510\pi$
$983$	−4.38209	−	4.38209i	−0.139767	−	0.139767i	−0.773528	+	0.633762i	$0.781510\pi$
$984$	4.38712	−	1.40855i	0.139856	−	0.0449029i
$985$	−3.63397	−	2.09808i	−0.115788	−	0.0668503i
$986$	27.4635	−	7.35882i	0.874616	−	0.234353i
$987$	4.95725	−	22.9282i	0.157791	−	0.729813i
$988$		0			0
$989$		0			0
$990$	−4.92247	+	29.7342i	−0.156446	+	0.945015i
$991$	−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
$993$	28.4216	−	18.3164i	0.901931	−	0.581255i
$994$	−4.19615	+	15.6603i	−0.133094	+	0.496713i
$995$	−0.575167	+	2.14655i	−0.0182340	+	0.0680503i
$996$	9.52306	−	6.13719i	0.301750	−	0.194464i
$997$	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
$999$	33.0015	+	13.0662i	1.04412	+	0.413397i

Twists

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

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

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