LMFDB - Embedded newform 450.2.p.a.443.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,2,Mod(257,450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(450, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 3]))

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

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

chi := DirichletCharacter("450.257");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	450.p (of order $12$, degree $4$, 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:	$3.59326809096$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			443.2
Root			$-0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	450.443
Dual form			450.2.p.a.257.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 - 0.258819i) q^{2} +(-0.599900 - 1.62484i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-1.00000 - 1.41421i) q^{6} +(-1.18034 - 4.40508i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.28024 + 1.94949i) q^{9} +O(q^{10})$	\(q+(0.965926 - 0.258819i) q^{2} +(-0.599900 - 1.62484i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-1.00000 - 1.41421i) q^{6} +(-1.18034 - 4.40508i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.28024 + 1.94949i) q^{9} +(-0.550510 - 0.317837i) q^{11} +(-1.33195 - 1.10721i) q^{12} +(-0.896575 + 3.34607i) q^{13} +(-2.28024 - 3.94949i) q^{14} +(0.500000 - 0.866025i) q^{16} +(0.317837 + 0.317837i) q^{17} +(-1.69798 + 2.47323i) q^{18} -6.44949i q^{19} +(-6.44949 + 4.56048i) q^{21} +(-0.614014 - 0.164525i) q^{22} +(0.965926 + 0.258819i) q^{23} +(-1.57313 - 0.724745i) q^{24} +3.46410i q^{26} +(4.53553 + 2.53553i) q^{27} +(-3.22474 - 3.22474i) q^{28} +(0.158919 - 0.275255i) q^{29} +(-0.224745 - 0.389270i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-0.186185 + 1.08516i) q^{33} +(0.389270 + 0.224745i) q^{34} +(-1.00000 + 2.82843i) q^{36} +(3.00000 - 3.00000i) q^{37} +(-1.66925 - 6.22973i) q^{38} +(5.97469 - 0.550510i) q^{39} +(6.39898 - 3.69445i) q^{41} +(-5.04939 + 6.07433i) q^{42} +(-3.34607 + 0.896575i) q^{43} -0.635674 q^{44} +1.00000 q^{46} +(8.69333 - 2.32937i) q^{47} +(-1.70711 - 0.292893i) q^{48} +(-11.9494 + 6.89898i) q^{49} +(0.325765 - 0.707107i) q^{51} +(0.896575 + 3.34607i) q^{52} +(3.78194 - 3.78194i) q^{53} +(5.03723 + 1.27526i) q^{54} +(-3.94949 - 2.28024i) q^{56} +(-10.4794 + 3.86905i) q^{57} +(0.0822623 - 0.307007i) q^{58} +(4.48905 + 7.77526i) q^{59} +(0.275255 - 0.476756i) q^{61} +(-0.317837 - 0.317837i) q^{62} +(11.2791 + 7.74358i) q^{63} -1.00000i q^{64} +(0.101021 + 1.09638i) q^{66} +(-6.38512 - 1.71089i) q^{67} +(0.434174 + 0.116337i) q^{68} +(-0.158919 - 1.72474i) q^{69} +6.29253i q^{71} +(-0.233875 + 2.99087i) q^{72} +(6.89898 + 6.89898i) q^{73} +(2.12132 - 3.67423i) q^{74} +(-3.22474 - 5.58542i) q^{76} +(-0.750311 + 2.80020i) q^{77} +(5.62863 - 2.07812i) q^{78} +(2.12132 + 1.22474i) q^{79} +(1.39898 - 8.89060i) q^{81} +(5.22474 - 5.22474i) q^{82} +(-1.41043 - 5.26380i) q^{83} +(-3.30518 + 7.17423i) q^{84} +(-3.00000 + 1.73205i) q^{86} +(-0.542582 - 0.0930924i) q^{87} +(-0.614014 + 0.164525i) q^{88} +8.02458 q^{89} +15.7980 q^{91} +(0.965926 - 0.258819i) q^{92} +(-0.497678 + 0.598698i) q^{93} +(7.79423 - 4.50000i) q^{94} +(-1.72474 + 0.158919i) q^{96} +(-0.695075 - 2.59405i) q^{97} +(-9.75663 + 9.75663i) q^{98} +(1.87492 - 0.348469i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} - 8 q^{6} + 8 q^{7}+O(q^{10}) $ 8 * q - 4 * q^3 - 8 * q^6 + 8 * q^7	$ 8 q - 4 q^{3} - 8 q^{6} + 8 q^{7} - 24 q^{11} + 4 q^{12} + 4 q^{16} + 8 q^{18} - 32 q^{21} + 8 q^{22} + 8 q^{27} - 16 q^{28} + 8 q^{31} - 16 q^{33} - 8 q^{36} + 24 q^{37} - 12 q^{38} + 12 q^{41} - 20 q^{42} + 8 q^{46} - 8 q^{48} + 32 q^{51} - 12 q^{56} - 28 q^{57} + 4 q^{58} + 12 q^{61} + 32 q^{63} + 40 q^{66} - 4 q^{67} + 12 q^{68} - 8 q^{72} + 16 q^{73} - 16 q^{76} - 24 q^{77} + 24 q^{78} - 28 q^{81} + 32 q^{82} - 12 q^{83} - 24 q^{86} + 8 q^{87} + 8 q^{88} + 48 q^{91} + 20 q^{93} - 4 q^{96} - 12 q^{97}+O(q^{100}) $ 8 * q - 4 * q^3 - 8 * q^6 + 8 * q^7 - 24 * q^11 + 4 * q^12 + 4 * q^16 + 8 * q^18 - 32 * q^21 + 8 * q^22 + 8 * q^27 - 16 * q^28 + 8 * q^31 - 16 * q^33 - 8 * q^36 + 24 * q^37 - 12 * q^38 + 12 * q^41 - 20 * q^42 + 8 * q^46 - 8 * q^48 + 32 * q^51 - 12 * q^56 - 28 * q^57 + 4 * q^58 + 12 * q^61 + 32 * q^63 + 40 * q^66 - 4 * q^67 + 12 * q^68 - 8 * q^72 + 16 * q^73 - 16 * q^76 - 24 * q^77 + 24 * q^78 - 28 * q^81 + 32 * q^82 - 12 * q^83 - 24 * q^86 + 8 * q^87 + 8 * q^88 + 48 * q^91 + 20 * q^93 - 4 * q^96 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$3$	−0.599900	−	1.62484i	−0.346353	−	0.938104i
$3$	−0.599900	−	1.62484i	−0.346353	−	0.938104i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$		0			0
$5$		0			0
$6$	−1.00000	−	1.41421i	−0.408248	−	0.577350i
$7$	−1.18034	−	4.40508i	−0.446126	−	1.66497i	−0.712946	−	0.701219i	$-0.752640\pi$
$7$	−1.18034	−	4.40508i	−0.446126	−	1.66497i	0.266820	−	0.963746i	$-0.414027\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−2.28024	+	1.94949i	−0.760080	+	0.649830i
$10$		0			0
$11$	−0.550510	−	0.317837i	−0.165985	−	0.0958315i	0.414706	−	0.909955i	$-0.363884\pi$
$11$	−0.550510	−	0.317837i	−0.165985	−	0.0958315i	−0.580691	+	0.814124i	$0.697218\pi$
$12$	−1.33195	−	1.10721i	−0.384501	−	0.319623i
$13$	−0.896575	+	3.34607i	−0.248665	+	0.928032i	0.722840	+	0.691015i	$0.242836\pi$
$13$	−0.896575	+	3.34607i	−0.248665	+	0.928032i	−0.971506	+	0.237016i	$0.923830\pi$
$14$	−2.28024	−	3.94949i	−0.609419	−	1.05555i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	0.317837	+	0.317837i	0.0770869	+	0.0770869i	0.744599	−	0.667512i	$-0.232641\pi$
$17$	0.317837	+	0.317837i	0.0770869	+	0.0770869i	−0.667512	+	0.744599i	$0.732641\pi$
$18$	−1.69798	+	2.47323i	−0.400217	+	0.582946i
$19$		−	6.44949i		−	1.47961i	−0.672819	−	0.739807i	$-0.734917\pi$
$19$		−	6.44949i		−	1.47961i	0.672819	−	0.739807i	$-0.265083\pi$
$20$		0			0
$21$	−6.44949	+	4.56048i	−1.40739	+	0.995178i
$22$	−0.614014	−	0.164525i	−0.130908	−	0.0350768i
$23$	0.965926	+	0.258819i	0.201409	+	0.0539675i	0.358113	−	0.933678i	$-0.383420\pi$
$23$	0.965926	+	0.258819i	0.201409	+	0.0539675i	−0.156704	+	0.987646i	$0.550087\pi$
$24$	−1.57313	−	0.724745i	−0.321114	−	0.147938i
$25$		0			0
$26$			3.46410i			0.679366i
$27$	4.53553	+	2.53553i	0.872864	+	0.487964i
$28$	−3.22474	−	3.22474i	−0.609419	−	0.609419i
$29$	0.158919	−	0.275255i	0.0295104	−	0.0511136i	−0.850893	−	0.525339i	$-0.823939\pi$
$29$	0.158919	−	0.275255i	0.0295104	−	0.0511136i	0.880403	+	0.474225i	$0.157272\pi$
$30$		0			0
$31$	−0.224745	−	0.389270i	−0.0403654	−	0.0699149i	0.845137	−	0.534550i	$-0.179519\pi$
$31$	−0.224745	−	0.389270i	−0.0403654	−	0.0699149i	−0.885502	+	0.464635i	$0.846186\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$	−0.186185	+	1.08516i	−0.0324106	+	0.188903i
$34$	0.389270	+	0.224745i	0.0667592	+	0.0385434i
$35$		0			0
$36$	−1.00000	+	2.82843i	−0.166667	+	0.471405i
$37$	3.00000	−	3.00000i	0.493197	−	0.493197i	−0.416115	−	0.909312i	$-0.636609\pi$
$37$	3.00000	−	3.00000i	0.493197	−	0.493197i	0.909312	+	0.416115i	$0.136609\pi$
$38$	−1.66925	−	6.22973i	−0.270788	−	1.01060i
$39$	5.97469	−	0.550510i	0.956716	−	0.0881522i
$40$		0			0
$41$	6.39898	−	3.69445i	0.999353	−	0.576977i	0.0912960	−	0.995824i	$-0.470899\pi$
$41$	6.39898	−	3.69445i	0.999353	−	0.576977i	0.908057	+	0.418847i	$0.137566\pi$
$42$	−5.04939	+	6.07433i	−0.779138	+	0.937290i
$43$	−3.34607	+	0.896575i	−0.510270	+	0.136726i	−0.504762	−	0.863258i	$-0.668420\pi$
$43$	−3.34607	+	0.896575i	−0.510270	+	0.136726i	−0.00550783	+	0.999985i	$0.501753\pi$
$44$	−0.635674			−0.0958315
$45$		0			0
$46$	1.00000			0.147442
$47$	8.69333	−	2.32937i	1.26805	−	0.339774i	0.438768	−	0.898600i	$-0.355415\pi$
$47$	8.69333	−	2.32937i	1.26805	−	0.339774i	0.829285	+	0.558827i	$0.188748\pi$
$48$	−1.70711	−	0.292893i	−0.246400	−	0.0422755i
$49$	−11.9494	+	6.89898i	−1.70705	+	0.985568i
$50$		0			0
$51$	0.325765	−	0.707107i	0.0456163	−	0.0990148i
$52$	0.896575	+	3.34607i	0.124333	+	0.464016i
$53$	3.78194	−	3.78194i	0.519489	−	0.519489i	−0.397928	−	0.917417i	$-0.630270\pi$
$53$	3.78194	−	3.78194i	0.519489	−	0.519489i	0.917417	+	0.397928i	$0.130270\pi$
$54$	5.03723	+	1.27526i	0.685481	+	0.173540i
$55$		0			0
$56$	−3.94949	−	2.28024i	−0.527773	−	0.304710i
$57$	−10.4794	+	3.86905i	−1.38803	+	0.512468i
$58$	0.0822623	−	0.307007i	0.0108016	−	0.0403120i
$59$	4.48905	+	7.77526i	0.584424	+	1.01225i	0.994947	+	0.100402i	$0.0320128\pi$
$59$	4.48905	+	7.77526i	0.584424	+	1.01225i	−0.410523	+	0.911850i	$0.634654\pi$
$60$		0			0
$61$	0.275255	−	0.476756i	0.0352428	−	0.0610423i	−0.847866	−	0.530211i	$-0.822113\pi$
$61$	0.275255	−	0.476756i	0.0352428	−	0.0610423i	0.883109	+	0.469168i	$0.155446\pi$
$62$	−0.317837	−	0.317837i	−0.0403654	−	0.0403654i
$63$	11.2791	+	7.74358i	1.42104	+	0.975600i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$	0.101021	+	1.09638i	0.0124348	+	0.134955i
$67$	−6.38512	−	1.71089i	−0.780067	−	0.209018i	−0.153253	−	0.988187i	$-0.548975\pi$
$67$	−6.38512	−	1.71089i	−0.780067	−	0.209018i	−0.626814	+	0.779169i	$0.715642\pi$
$68$	0.434174	+	0.116337i	0.0526513	+	0.0141079i
$69$	−0.158919	−	1.72474i	−0.0191316	−	0.207635i
$70$		0			0
$71$			6.29253i			0.746786i	0.927673	+	0.373393i	$0.121806\pi$
$71$			6.29253i			0.746786i	−0.927673	+	0.373393i	$0.878194\pi$
$72$	−0.233875	+	2.99087i	−0.0275624	+	0.352477i
$73$	6.89898	+	6.89898i	0.807464	+	0.807464i	0.984249	−	0.176785i	$-0.0565697\pi$
$73$	6.89898	+	6.89898i	0.807464	+	0.807464i	−0.176785	+	0.984249i	$0.556570\pi$
$74$	2.12132	−	3.67423i	0.246598	−	0.427121i
$75$		0			0
$76$	−3.22474	−	5.58542i	−0.369904	−	0.640692i
$77$	−0.750311	+	2.80020i	−0.0855059	+	0.319112i
$78$	5.62863	−	2.07812i	0.637316	−	0.235300i
$79$	2.12132	+	1.22474i	0.238667	+	0.137795i	0.614564	−	0.788867i	$-0.289332\pi$
$79$	2.12132	+	1.22474i	0.238667	+	0.137795i	−0.375897	+	0.926662i	$0.622665\pi$
$80$		0			0
$81$	1.39898	−	8.89060i	0.155442	−	0.987845i
$82$	5.22474	−	5.22474i	0.576977	−	0.576977i
$83$	−1.41043	−	5.26380i	−0.154815	−	0.577777i	−0.999121	−	0.0419163i	$-0.986654\pi$
$83$	−1.41043	−	5.26380i	−0.154815	−	0.577777i	0.844306	−	0.535861i	$-0.180013\pi$
$84$	−3.30518	+	7.17423i	−0.360625	+	0.782773i
$85$		0			0
$86$	−3.00000	+	1.73205i	−0.323498	+	0.186772i
$87$	−0.542582	−	0.0930924i	−0.0581709	−	0.00998055i
$88$	−0.614014	+	0.164525i	−0.0654542	+	0.0175384i
$89$	8.02458			0.850604			0.425302	−	0.905052i	$-0.360168\pi$
$89$	8.02458			0.850604			0.425302	+	0.905052i	$0.360168\pi$
$90$		0			0
$91$	15.7980			1.65608
$92$	0.965926	−	0.258819i	0.100705	−	0.0269838i
$93$	−0.497678	+	0.598698i	−0.0516068	+	0.0620821i
$94$	7.79423	−	4.50000i	0.803913	−	0.464140i
$95$		0			0
$96$	−1.72474	+	0.158919i	−0.176031	+	0.0162196i
$97$	−0.695075	−	2.59405i	−0.0705741	−	0.263386i	0.921619	−	0.388095i	$-0.126867\pi$
$97$	−0.695075	−	2.59405i	−0.0705741	−	0.263386i	−0.992193	+	0.124709i	$0.960200\pi$
$98$	−9.75663	+	9.75663i	−0.985568	+	0.985568i
$99$	1.87492	−	0.348469i	0.188436	−	0.0350225i
$100$		0			0
$101$	10.8990	+	6.29253i	1.08449	+	0.626130i	0.932104	−	0.362191i	$-0.117971\pi$
$101$	10.8990	+	6.29253i	1.08449	+	0.626130i	0.152385	+	0.988321i	$0.451305\pi$
$102$	0.131652	−	0.767327i	0.0130355	−	0.0759767i
$103$	2.52520	−	9.42418i	0.248816	−	0.928592i	−0.722612	−	0.691254i	$-0.757058\pi$
$103$	2.52520	−	9.42418i	0.248816	−	0.928592i	0.971427	−	0.237338i	$-0.0762749\pi$
$104$	1.73205	+	3.00000i	0.169842	+	0.294174i
$105$		0			0
$106$	2.67423	−	4.63191i	0.259745	−	0.449891i
$107$	13.6100	+	13.6100i	1.31573	+	1.31573i	0.917122	+	0.398606i	$0.130506\pi$
$107$	13.6100	+	13.6100i	1.31573	+	1.31573i	0.398606	+	0.917122i	$0.369494\pi$
$108$	5.19565	−	0.0719302i	0.499952	−	0.00692148i
$109$			5.65153i			0.541318i	0.962675	+	0.270659i	$0.0872417\pi$
$109$			5.65153i			0.541318i	−0.962675	+	0.270659i	$0.912758\pi$
$110$		0			0
$111$	−6.67423	−	3.07483i	−0.633490	−	0.291850i
$112$	−4.40508	−	1.18034i	−0.416241	−	0.111532i
$113$	5.60040	+	1.50062i	0.526841	+	0.141167i	0.512429	−	0.858729i	$-0.328746\pi$
$113$	5.60040	+	1.50062i	0.526841	+	0.141167i	0.0144120	+	0.999896i	$0.495412\pi$
$114$	−9.12096	+	6.44949i	−0.854256	+	0.604050i
$115$		0			0
$116$		−	0.317837i		−	0.0295104i
$117$	−4.47871	−	9.37769i	−0.414057	−	0.866968i
$118$	6.34847	+	6.34847i	0.584424	+	0.584424i
$119$	1.02494	−	1.77526i	0.0939565	−	0.162737i
$120$		0			0
$121$	−5.29796	−	9.17633i	−0.481633	−	0.834212i
$122$	0.142483	−	0.531752i	0.0128998	−	0.0481426i
$123$	−9.84166	−	8.18104i	−0.887393	−	0.737660i
$124$	−0.389270	−	0.224745i	−0.0349574	−	0.0201827i
$125$		0			0
$126$	12.8990	+	4.56048i	1.14913	+	0.406280i
$127$	−1.87628	+	1.87628i	−0.166493	+	0.166493i	−0.785436	−	0.618943i	$-0.787561\pi$
$127$	−1.87628	+	1.87628i	−0.166493	+	0.166493i	0.618943	+	0.785436i	$0.287561\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$	3.46410	+	4.89898i	0.304997	+	0.431331i
$130$		0			0
$131$	−3.12372	+	1.80348i	−0.272921	+	0.157571i	−0.630214	−	0.776421i	$-0.717033\pi$
$131$	−3.12372	+	1.80348i	−0.272921	+	0.157571i	0.357293	+	0.933992i	$0.383700\pi$
$132$	0.381341	+	1.03287i	0.0331915	+	0.0899000i
$133$	−28.4105	+	7.61258i	−2.46351	+	0.660095i
$134$	−6.61037			−0.571049
$135$		0			0
$136$	0.449490			0.0385434
$137$	−21.0552	+	5.64173i	−1.79887	+	0.482005i	−0.993801	−	0.111178i	$-0.964538\pi$
$137$	−21.0552	+	5.64173i	−1.79887	+	0.482005i	−0.805068	+	0.593183i	$0.797871\pi$
$138$	−0.599900	−	1.62484i	−0.0510669	−	0.138316i
$139$	−2.68556	+	1.55051i	−0.227786	+	0.131513i	−0.609550	−	0.792747i	$-0.708650\pi$
$139$	−2.68556	+	1.55051i	−0.227786	+	0.131513i	0.381764	+	0.924260i	$0.375317\pi$
$140$		0			0
$141$	−9.00000	−	12.7279i	−0.757937	−	1.07188i
$142$	1.62863	+	6.07812i	0.136671	+	0.510064i
$143$	1.55708	−	1.55708i	0.130209	−	0.130209i
$144$	0.548188	+	2.94949i	0.0456823	+	0.245791i
$145$		0			0
$146$	8.44949	+	4.87832i	0.699285	+	0.403732i
$147$	18.3782	+	15.2772i	1.51581	+	1.26004i
$148$	1.09808	−	4.09808i	0.0902613	−	0.336860i
$149$	−2.20881	−	3.82577i	−0.180952	−	0.313419i	0.761253	−	0.648455i	$-0.224585\pi$
$149$	−2.20881	−	3.82577i	−0.180952	−	0.313419i	−0.942205	+	0.335036i	$0.891251\pi$
$150$		0			0
$151$	−8.79796	+	15.2385i	−0.715968	+	1.24009i	0.246617	+	0.969113i	$0.420681\pi$
$151$	−8.79796	+	15.2385i	−0.715968	+	1.24009i	−0.962585	+	0.270980i	$0.912652\pi$
$152$	−4.56048	−	4.56048i	−0.369904	−	0.369904i
$153$	−1.34437	−	0.105124i	−0.108685	−	0.00849881i
$154$			2.89898i			0.233606i
$155$		0			0
$156$	4.89898	−	3.46410i	0.392232	−	0.277350i
$157$	−14.1363	−	3.78780i	−1.12820	−	0.302300i	−0.354001	−	0.935245i	$-0.615179\pi$
$157$	−14.1363	−	3.78780i	−1.12820	−	0.302300i	−0.774196	+	0.632945i	$0.781846\pi$
$158$	2.36603	+	0.633975i	0.188231	+	0.0504363i
$159$	−8.41385	−	3.87628i	−0.667262	−	0.307409i
$160$		0			0
$161$		−	4.56048i		−	0.359416i
$162$	−0.949747	−	8.94975i	−0.0746192	−	0.703159i
$163$	−4.44949	−	4.44949i	−0.348511	−	0.348511i	0.511044	−	0.859555i	$-0.329259\pi$
$163$	−4.44949	−	4.44949i	−0.348511	−	0.348511i	−0.859555	+	0.511044i	$0.829259\pi$
$164$	3.69445	−	6.39898i	0.288488	−	0.499676i
$165$		0			0
$166$	−2.72474	−	4.71940i	−0.211481	−	0.366296i
$167$	2.27708	−	8.49818i	0.176206	−	0.657609i	−0.820137	−	0.572167i	$-0.806103\pi$
$167$	2.27708	−	8.49818i	0.176206	−	0.657609i	0.996343	−	0.0854420i	$-0.0272302\pi$
$168$	−1.33573	+	7.78522i	−0.103054	+	0.600643i
$169$	0.866025	+	0.500000i	0.0666173	+	0.0384615i
$170$		0			0
$171$	12.5732	+	14.7064i	0.961498	+	1.12462i
$172$	−2.44949	+	2.44949i	−0.186772	+	0.186772i
$173$	3.33850	+	12.4595i	0.253822	+	0.947275i	0.968742	+	0.248069i	$0.0797961\pi$
$173$	3.33850	+	12.4595i	0.253822	+	0.947275i	−0.714921	+	0.699206i	$0.753537\pi$
$174$	−0.548188	+	0.0505103i	−0.0415580	+	0.00382917i
$175$		0			0
$176$	−0.550510	+	0.317837i	−0.0414963	+	0.0239579i
$177$	9.94060	−	11.9584i	0.747181	−	0.898847i
$178$	7.75115	−	2.07691i	0.580973	−	0.155671i
$179$	−10.6780			−0.798114			−0.399057	−	0.916926i	$-0.630662\pi$
$179$	−10.6780			−0.798114			−0.399057	+	0.916926i	$0.630662\pi$
$180$		0			0
$181$	−15.4495			−1.14835			−0.574176	−	0.818732i	$-0.694677\pi$
$181$	−15.4495			−1.14835			−0.574176	+	0.818732i	$0.694677\pi$
$182$	15.2597	−	4.08881i	1.13112	−	0.303083i
$183$	−0.939780	−	0.161241i	−0.0694705	−	0.0119193i
$184$	0.866025	−	0.500000i	0.0638442	−	0.0368605i
$185$		0			0
$186$	−0.325765	+	0.707107i	−0.0238863	+	0.0518476i
$187$	−0.0739521	−	0.275993i	−0.00540792	−	0.0201826i
$188$	6.36396	−	6.36396i	0.464140	−	0.464140i
$189$	5.81577	−	22.9722i	0.423035	−	1.67098i
$190$		0			0
$191$	−15.1237	−	8.73169i	−1.09431	−	0.631803i	−0.159593	−	0.987183i	$-0.551018\pi$
$191$	−15.1237	−	8.73169i	−1.09431	−	0.631803i	−0.934722	+	0.355380i	$0.884351\pi$
$192$	−1.62484	+	0.599900i	−0.117263	+	0.0432941i
$193$	4.48288	−	16.7303i	0.322685	−	1.20428i	−0.593934	−	0.804513i	$-0.702426\pi$
$193$	4.48288	−	16.7303i	0.322685	−	1.20428i	0.916619	−	0.399762i	$-0.130907\pi$
$194$	−1.34278	−	2.32577i	−0.0964061	−	0.166980i
$195$		0			0
$196$	−6.89898	+	11.9494i	−0.492784	+	0.853527i
$197$	6.92820	+	6.92820i	0.493614	+	0.493614i	0.909443	−	0.415829i	$-0.136508\pi$
$197$	6.92820	+	6.92820i	0.493614	+	0.493614i	−0.415829	+	0.909443i	$0.636508\pi$
$198$	1.72084	−	0.821859i	0.122295	−	0.0584070i
$199$		−	8.44949i		−	0.598968i	−0.954101	−	0.299484i	$-0.903185\pi$
$199$		−	8.44949i		−	0.598968i	0.954101	−	0.299484i	$-0.0968146\pi$
$200$		0			0
$201$	1.05051	+	11.4012i	0.0740973	+	0.804178i
$202$	12.1562	+	3.25725i	0.855310	+	0.229179i
$203$	−1.40010	−	0.375156i	−0.0982677	−	0.0263308i
$204$	−0.0714323	−	0.775255i	−0.00500126	−	0.0542787i
$205$		0			0
$206$		−	9.75663i		−	0.679777i
$207$	−2.70711	+	1.29289i	−0.188157	+	0.0898623i
$208$	2.44949	+	2.44949i	0.169842	+	0.169842i
$209$	−2.04989	+	3.55051i	−0.141794	+	0.245594i
$210$		0			0
$211$	−4.55051	−	7.88171i	−0.313270	−	0.542600i	0.665798	−	0.746132i	$-0.268091\pi$
$211$	−4.55051	−	7.88171i	−0.313270	−	0.542600i	−0.979068	+	0.203532i	$0.934758\pi$
$212$	1.38429	−	5.16622i	0.0950731	−	0.354818i
$213$	10.2244	−	3.77489i	0.700563	−	0.258651i
$214$	16.6688	+	9.62372i	1.13945	+	0.657864i
$215$		0			0
$216$	5.00000	−	1.41421i	0.340207	−	0.0962250i
$217$	−1.44949	+	1.44949i	−0.0983978	+	0.0983978i
$218$	1.46272	+	5.45896i	0.0990682	+	0.369727i
$219$	7.07107	−	15.3485i	0.477818	−	1.03715i
$220$		0			0
$221$	−1.34847	+	0.778539i	−0.0907079	+	0.0523702i
$222$	−7.24264	−	1.24264i	−0.486094	−	0.0834006i
$223$	24.7575	−	6.63374i	1.65788	−	0.444228i	0.696078	−	0.717966i	$-0.254927\pi$
$223$	24.7575	−	6.63374i	1.65788	−	0.444228i	0.961804	+	0.273738i	$0.0882600\pi$
$224$	−4.56048			−0.304710
$225$		0			0
$226$	5.79796			0.385674
$227$	−24.0506	+	6.44433i	−1.59629	+	0.427725i	−0.943920	−	0.330174i	$-0.892893\pi$
$227$	−24.0506	+	6.44433i	−1.59629	+	0.427725i	−0.652372	+	0.757899i	$0.726226\pi$
$228$	−7.14092	+	8.59041i	−0.472919	+	0.568914i
$229$	1.43027	−	0.825765i	0.0945147	−	0.0545681i	−0.451998	−	0.892019i	$-0.649288\pi$
$229$	1.43027	−	0.825765i	0.0945147	−	0.0545681i	0.546512	+	0.837451i	$0.315955\pi$
$230$		0			0
$231$	5.00000	−	0.460702i	0.328976	−	0.0303120i
$232$	−0.0822623	−	0.307007i	−0.00540079	−	0.0201560i
$233$	−14.4600	+	14.4600i	−0.947304	+	0.947304i	−0.998679	−	0.0513751i	$-0.983640\pi$
$233$	−14.4600	+	14.4600i	−0.947304	+	0.947304i	0.0513751	+	0.998679i	$0.483640\pi$
$234$	−6.75323	−	7.89898i	−0.441472	−	0.516372i
$235$		0			0
$236$	7.77526	+	4.48905i	0.506126	+	0.292212i
$237$	0.717439	−	4.18154i	0.0466027	−	0.271620i
$238$	0.530550	−	1.98004i	0.0343905	−	0.128347i
$239$	8.48528	+	14.6969i	0.548867	+	0.950666i	0.998353	+	0.0573782i	$0.0182741\pi$
$239$	8.48528	+	14.6969i	0.548867	+	0.950666i	−0.449485	+	0.893288i	$0.648393\pi$
$240$		0			0
$241$	−9.50000	+	16.4545i	−0.611949	+	1.05993i	0.378963	+	0.925412i	$0.376281\pi$
$241$	−9.50000	+	16.4545i	−0.611949	+	1.05993i	−0.990912	+	0.134515i	$0.957053\pi$
$242$	−7.49245	−	7.49245i	−0.481633	−	0.481633i
$243$	−15.2851	+	3.06035i	−0.980540	+	0.196322i
$244$		−	0.550510i		−	0.0352428i
$245$		0			0
$246$	−11.6237	−	5.35507i	−0.741102	−	0.341427i
$247$	21.5804	+	5.78245i	1.37313	+	0.367929i
$248$	−0.434174	−	0.116337i	−0.0275701	−	0.00738738i
$249$	−7.70674	+	5.44949i	−0.488395	+	0.345347i
$250$		0			0
$251$			2.68556i			0.169511i	0.996402	+	0.0847556i	$0.0270110\pi$
$251$			2.68556i			0.169511i	−0.996402	+	0.0847556i	$0.972989\pi$
$252$	13.6398	+	1.06658i	0.859226	+	0.0671883i
$253$	−0.449490	−	0.449490i	−0.0282592	−	0.0282592i
$254$	−1.32673	+	2.29796i	−0.0832463	+	0.144187i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	4.67050	−	17.4305i	0.291337	−	1.08729i	−0.652745	−	0.757578i	$-0.726383\pi$
$257$	4.67050	−	17.4305i	0.291337	−	1.08729i	0.944083	−	0.329709i	$-0.106951\pi$
$258$	4.61401	+	3.83548i	0.287256	+	0.238786i
$259$	−16.7563	−	9.67423i	−1.04118	−	0.601128i
$260$		0			0
$261$	0.174235	+	0.937458i	0.0107849	+	0.0580272i
$262$	−2.55051	+	2.55051i	−0.157571	+	0.157571i
$263$	−4.32149	−	16.1280i	−0.266474	−	0.994495i	−0.961342	−	0.275358i	$-0.911204\pi$
$263$	−4.32149	−	16.1280i	−0.266474	−	0.994495i	0.694868	−	0.719138i	$-0.255463\pi$
$264$	0.635674	+	0.898979i	0.0391231	+	0.0553284i
$265$		0			0
$266$	−25.4722	+	14.7064i	−1.56180	+	0.901706i
$267$	−4.81395	−	13.0387i	−0.294609	−	0.797955i
$268$	−6.38512	+	1.71089i	−0.390033	+	0.104509i
$269$	15.0956			0.920398			0.460199	−	0.887816i	$-0.347778\pi$
$269$	15.0956			0.920398			0.460199	+	0.887816i	$0.347778\pi$
$270$		0			0
$271$	28.0454			1.70364			0.851819	−	0.523837i	$-0.175500\pi$
$271$	28.0454			1.70364			0.851819	+	0.523837i	$0.175500\pi$
$272$	0.434174	−	0.116337i	0.0263257	−	0.00705394i
$273$	−9.47720	−	25.6692i	−0.573586	−	1.55357i
$274$	−18.8776	+	10.8990i	−1.14044	+	0.658431i
$275$		0			0
$276$	−1.00000	−	1.41421i	−0.0601929	−	0.0851257i
$277$	7.28353	+	27.1825i	0.437625	+	1.63324i	0.734705	+	0.678386i	$0.237320\pi$
$277$	7.28353	+	27.1825i	0.437625	+	1.63324i	−0.297080	+	0.954852i	$0.596013\pi$
$278$	−2.19275	+	2.19275i	−0.131513	+	0.131513i
$279$	1.27135	+	0.449490i	0.0761137	+	0.0269102i
$280$		0			0
$281$	−14.8485	−	8.57277i	−0.885785	−	0.511408i	−0.0132238	−	0.999913i	$-0.504209\pi$
$281$	−14.8485	−	8.57277i	−0.885785	−	0.511408i	−0.872562	+	0.488504i	$0.837543\pi$
$282$	−11.9876	−	9.96486i	−0.713849	−	0.593399i
$283$	−6.26772	+	23.3914i	−0.372577	+	1.39048i	0.484275	+	0.874916i	$0.339083\pi$
$283$	−6.26772	+	23.3914i	−0.372577	+	1.39048i	−0.856853	+	0.515561i	$0.827583\pi$
$284$	3.14626	+	5.44949i	0.186696	+	0.323368i
$285$		0			0
$286$	1.10102	−	1.90702i	0.0651047	−	0.112765i
$287$	−23.8273	−	23.8273i	−1.40648	−	1.40648i
$288$	1.29289	+	2.70711i	0.0761845	+	0.159518i
$289$		−	16.7980i		−	0.988115i
$290$		0			0
$291$	−3.79796	+	2.68556i	−0.222640	+	0.157430i
$292$	9.42418	+	2.52520i	0.551508	+	0.147776i
$293$	−21.2942	−	5.70577i	−1.24402	−	0.333335i	−0.423998	−	0.905663i	$-0.639374\pi$
$293$	−21.2942	−	5.70577i	−1.24402	−	0.333335i	−0.820024	+	0.572329i	$0.806040\pi$
$294$	21.7060	+	10.0000i	1.26592	+	0.583212i
$295$		0			0
$296$		−	4.24264i		−	0.246598i
$297$	−1.69097	−	2.83740i	−0.0981201	−	0.164643i
$298$	−3.12372	−	3.12372i	−0.180952	−	0.180952i
$299$	−1.73205	+	3.00000i	−0.100167	+	0.173494i
$300$		0			0
$301$	7.89898	+	13.6814i	0.455290	+	0.788585i
$302$	−4.55416	+	16.9964i	−0.262062	+	0.978030i
$303$	3.68608	−	21.4840i	0.211760	−	1.23423i
$304$	−5.58542	−	3.22474i	−0.320346	−	0.184952i
$305$		0			0
$306$	−1.32577	+	0.246405i	−0.0757890	+	0.0140860i
$307$	6.67423	−	6.67423i	0.380919	−	0.380919i	−0.490514	−	0.871433i	$-0.663191\pi$
$307$	6.67423	−	6.67423i	0.380919	−	0.380919i	0.871433	+	0.490514i	$0.163191\pi$
$308$	0.750311	+	2.80020i	0.0427529	+	0.159556i
$309$	−16.8277	+	1.55051i	−0.957294	+	0.0882054i
$310$		0			0
$311$	23.8207	−	13.7529i	1.35075	−	0.779853i	0.362392	−	0.932026i	$-0.381960\pi$
$311$	23.8207	−	13.7529i	1.35075	−	0.779853i	0.988354	+	0.152172i	$0.0486269\pi$
$312$	3.83548	−	4.61401i	0.217141	−	0.261217i
$313$	11.5422	−	3.09273i	0.652405	−	0.174811i	0.0825888	−	0.996584i	$-0.473681\pi$
$313$	11.5422	−	3.09273i	0.652405	−	0.174811i	0.569816	+	0.821772i	$0.307015\pi$
$314$	−14.6349			−0.825898
$315$		0			0
$316$	2.44949			0.137795
$317$	10.5276	−	2.82086i	0.591289	−	0.158435i	0.0492469	−	0.998787i	$-0.484318\pi$
$317$	10.5276	−	2.82086i	0.591289	−	0.158435i	0.542042	+	0.840351i	$0.317651\pi$
$318$	−9.13041	−	1.56653i	−0.512008	−	0.0878467i
$319$	−0.174973	+	0.101021i	−0.00979659	+	0.00565606i
$320$		0			0
$321$	13.9495	−	30.2788i	0.778585	−	1.69000i
$322$	−1.18034	−	4.40508i	−0.0657777	−	0.245486i
$323$	2.04989	−	2.04989i	0.114059	−	0.114059i
$324$	−3.23375	−	8.39898i	−0.179653	−	0.466610i
$325$		0			0
$326$	−5.44949	−	3.14626i	−0.301819	−	0.174255i
$327$	9.18286	−	3.39036i	0.507813	−	0.187487i
$328$	1.91239	−	7.13713i	0.105594	−	0.394082i
$329$	−20.5222	−	35.5454i	−1.13142	−	1.95968i
$330$		0			0
$331$	−0.224745	+	0.389270i	−0.0123531	+	0.0213962i	−0.872136	−	0.489264i	$-0.837266\pi$
$331$	−0.224745	+	0.389270i	−0.0123531	+	0.0213962i	0.859783	+	0.510660i	$0.170599\pi$
$332$	−3.85337	−	3.85337i	−0.211481	−	0.211481i
$333$	−0.992248	+	12.6892i	−0.0543748	+	0.695363i
$334$		−	8.79796i		−	0.481403i
$335$		0			0
$336$	0.724745	+	7.86566i	0.0395381	+	0.429107i
$337$	−3.00804	−	0.806003i	−0.163859	−	0.0439058i	0.175957	−	0.984398i	$-0.443698\pi$
$337$	−3.00804	−	0.806003i	−0.163859	−	0.0439058i	−0.339816	+	0.940492i	$0.610365\pi$
$338$	0.965926	+	0.258819i	0.0525394	+	0.0140779i
$339$	−0.921404	−	10.0000i	−0.0500438	−	0.543125i
$340$		0			0
$341$			0.285729i			0.0154731i
$342$	15.9511	+	10.9511i	0.862536	+	0.592167i
$343$	21.9217	+	21.9217i	1.18366	+	1.18366i
$344$	−1.73205	+	3.00000i	−0.0933859	+	0.161749i
$345$		0			0
$346$	6.44949	+	11.1708i	0.346727	+	0.600548i
$347$	−6.15937	+	22.9871i	−0.330652	+	1.23401i	0.577855	+	0.816140i	$0.303890\pi$
$347$	−6.15937	+	22.9871i	−0.330652	+	1.23401i	−0.908507	+	0.417870i	$0.862777\pi$
$348$	−0.516436	+	0.190671i	−0.0276839	+	0.0102210i
$349$	25.1541	+	14.5227i	1.34647	+	0.777383i	0.987747	−	0.156063i	$-0.0498803\pi$
$349$	25.1541	+	14.5227i	1.34647	+	0.777383i	0.358719	+	0.933446i	$0.383214\pi$
$350$		0			0
$351$	−12.5505	+	12.9029i	−0.669897	+	0.688706i
$352$	−0.449490	+	0.449490i	−0.0239579	+	0.0239579i
$353$	8.87564	+	33.1244i	0.472403	+	1.76303i	0.631097	+	0.775704i	$0.282605\pi$
$353$	8.87564	+	33.1244i	0.472403	+	1.76303i	−0.158694	+	0.987328i	$0.550728\pi$
$354$	6.50683	−	14.1237i	0.345834	−	0.750667i
$355$		0			0
$356$	6.94949	−	4.01229i	0.368322	−	0.212651i
$357$	−3.49938	−	0.600398i	−0.185207	−	0.0317764i
$358$	−10.3142	+	2.76368i	−0.545122	+	0.146065i
$359$	−3.32124			−0.175288			−0.0876441	−	0.996152i	$-0.527934\pi$
$359$	−3.32124			−0.175288			−0.0876441	+	0.996152i	$0.527934\pi$
$360$		0			0
$361$	−22.5959			−1.18926
$362$	−14.9231	+	3.99862i	−0.784339	+	0.210163i
$363$	−11.7319	+	14.1132i	−0.615763	+	0.740753i
$364$	13.6814	−	7.89898i	0.717102	−	0.414019i
$365$		0			0
$366$	−0.949490	+	0.0874863i	−0.0496306	+	0.00457298i
$367$	1.06110	+	3.96008i	0.0553890	+	0.206714i	0.988075	−	0.153976i	$-0.0492078\pi$
$367$	1.06110	+	3.96008i	0.0553890	+	0.206714i	−0.932686	+	0.360690i	$0.882541\pi$
$368$	0.707107	−	0.707107i	0.0368605	−	0.0368605i
$369$	−7.38891	+	20.8990i	−0.384651	+	1.08796i
$370$		0			0
$371$	−21.1237	−	12.1958i	−1.09669	−	0.633174i
$372$	−0.131652	+	0.767327i	−0.00682586	+	0.0397841i
$373$	0.127549	−	0.476018i	0.00660422	−	0.0246473i	−0.962545	−	0.271122i	$-0.912605\pi$
$373$	0.127549	−	0.476018i	0.00660422	−	0.0246473i	0.969149	+	0.246474i	$0.0792721\pi$
$374$	−0.142865	−	0.247449i	−0.00738735	−	0.0127953i
$375$		0			0
$376$	4.50000	−	7.79423i	0.232070	−	0.401957i
$377$	0.778539	+	0.778539i	0.0400968	+	0.0400968i
$378$	−0.328036	−	23.6947i	−0.0168724	−	1.21872i
$379$			21.3485i			1.09660i	0.836283	+	0.548299i	$0.184724\pi$
$379$			21.3485i			1.09660i	−0.836283	+	0.548299i	$0.815276\pi$
$380$		0			0
$381$	4.17423	+	1.92308i	0.213853	+	0.0985222i
$382$	−16.8683	−	4.51985i	−0.863058	−	0.231256i
$383$	7.92256	+	2.12284i	0.404824	+	0.108472i	0.455485	−	0.890244i	$-0.349466\pi$
$383$	7.92256	+	2.12284i	0.404824	+	0.108472i	−0.0506606	+	0.998716i	$0.516133\pi$
$384$	−1.41421	+	1.00000i	−0.0721688	+	0.0510310i
$385$		0			0
$386$		−	17.3205i		−	0.881591i
$387$	5.88196	−	8.56753i	0.298997	−	0.435512i
$388$	−1.89898	−	1.89898i	−0.0964061	−	0.0964061i
$389$	−18.4008	+	31.8712i	−0.932959	+	1.61593i	−0.154726	+	0.987957i	$0.549449\pi$
$389$	−18.4008	+	31.8712i	−0.932959	+	1.61593i	−0.778233	+	0.627975i	$0.783884\pi$
$390$		0			0
$391$	0.224745	+	0.389270i	0.0113658	+	0.0196862i
$392$	−3.57117	+	13.3278i	−0.180372	+	0.673156i
$393$	4.80430	+	3.99366i	0.242345	+	0.201453i
$394$	8.48528	+	4.89898i	0.427482	+	0.246807i
$395$		0			0
$396$	1.44949	−	1.23924i	0.0728396	−	0.0622742i
$397$	−10.5505	+	10.5505i	−0.529515	+	0.529515i	−0.920428	−	0.390913i	$-0.872159\pi$
$397$	−10.5505	+	10.5505i	−0.529515	+	0.529515i	0.390913	+	0.920428i	$0.372159\pi$
$398$	−2.18689	−	8.16158i	−0.109619	−	0.409103i
$399$	29.4128	+	41.5959i	1.47248	+	2.08240i
$400$		0			0
$401$	7.65153	−	4.41761i	0.382099	−	0.220605i	−0.296632	−	0.954992i	$-0.595863\pi$
$401$	7.65153	−	4.41761i	0.382099	−	0.220605i	0.678731	+	0.734387i	$0.262530\pi$
$402$	3.96556	+	10.7408i	0.197784	+	0.535703i
$403$	1.50402	−	0.403001i	0.0749207	−	0.0200749i
$404$	12.5851			0.626130
$405$		0			0
$406$	−1.44949			−0.0719370
$407$	−2.60504	+	0.698019i	−0.129127	+	0.0345995i
$408$	−0.269649	−	0.730351i	−0.0133496	−	0.0361578i
$409$	25.0273	−	14.4495i	1.23752	−	0.714481i	0.268932	−	0.963159i	$-0.413329\pi$
$409$	25.0273	−	14.4495i	1.23752	−	0.714481i	0.968586	+	0.248678i	$0.0799961\pi$
$410$		0			0
$411$	21.7980	+	30.8270i	1.07521	+	1.52058i
$412$	−2.52520	−	9.42418i	−0.124408	−	0.464296i
$413$	28.9521	−	28.9521i	1.42464	−	1.42464i
$414$	−2.28024	+	1.94949i	−0.112068	+	0.0958122i
$415$		0			0
$416$	3.00000	+	1.73205i	0.147087	+	0.0849208i
$417$	4.13041	+	3.43347i	0.202267	+	0.168138i
$418$	−1.06110	+	3.96008i	−0.0519001	+	0.193694i
$419$	−2.51059	−	4.34847i	−0.122650	−	0.212437i	0.798162	−	0.602443i	$-0.205806\pi$
$419$	−2.51059	−	4.34847i	−0.122650	−	0.212437i	−0.920812	+	0.390007i	$0.872473\pi$
$420$		0			0
$421$	2.55051	−	4.41761i	0.124304	−	0.215301i	−0.797157	−	0.603773i	$-0.793663\pi$
$421$	2.55051	−	4.41761i	0.124304	−	0.215301i	0.921461	+	0.388471i	$0.126997\pi$
$422$	−6.43539	−	6.43539i	−0.313270	−	0.313270i
$423$	−15.2818	+	22.2591i	−0.743026	+	1.08227i
$424$		−	5.34847i		−	0.259745i
$425$		0			0
$426$	8.89898	−	6.29253i	0.431157	−	0.304874i
$427$	−2.42504	−	0.649788i	−0.117356	−	0.0314455i
$428$	18.5916	+	4.98161i	0.898659	+	0.240795i
$429$	−3.46410	−	1.59592i	−0.167248	−	0.0770516i
$430$		0			0
$431$		−	15.5563i		−	0.749323i	−0.927162	−	0.374661i	$-0.877759\pi$
$431$		−	15.5563i		−	0.749323i	0.927162	−	0.374661i	$-0.122241\pi$
$432$	4.46360	−	2.66012i	0.214755	−	0.127985i
$433$	−13.4495	−	13.4495i	−0.646341	−	0.646341i	0.305766	−	0.952107i	$-0.401088\pi$
$433$	−13.4495	−	13.4495i	−0.646341	−	0.646341i	−0.952107	+	0.305766i	$0.901088\pi$
$434$	−1.02494	+	1.77526i	−0.0491989	+	0.0852150i
$435$		0			0
$436$	2.82577	+	4.89437i	0.135330	+	0.234398i
$437$	1.66925	−	6.22973i	0.0798511	−	0.298008i
$438$	2.85765	−	16.6556i	0.136544	−	0.795836i
$439$	25.8058	+	14.8990i	1.23164	+	0.711089i	0.967372	−	0.253359i	$-0.0815354\pi$
$439$	25.8058	+	14.8990i	1.23164	+	0.711089i	0.264271	+	0.964449i	$0.414869\pi$
$440$		0			0
$441$	13.7980	−	39.0265i	0.657046	−	1.85841i
$442$	−1.10102	+	1.10102i	−0.0523702	+	0.0523702i
$443$	1.41043	+	5.26380i	0.0670116	+	0.250091i	0.991303	−	0.131596i	$-0.0420101\pi$
$443$	1.41043	+	5.26380i	0.0670116	+	0.250091i	−0.924292	+	0.381687i	$0.875343\pi$
$444$	−7.31747	+	0.674235i	−0.347272	+	0.0319978i
$445$		0			0
$446$	22.1969	−	12.8154i	1.05106	−	0.606827i
$447$	−4.89121	+	5.88405i	−0.231346	+	0.278306i
$448$	−4.40508	+	1.18034i	−0.208121	+	0.0557658i
$449$	−0.921404			−0.0434837			−0.0217419	−	0.999764i	$-0.506921\pi$
$449$	−0.921404			−0.0434837			−0.0217419	+	0.999764i	$0.506921\pi$
$450$		0			0
$451$	−4.69694			−0.221170
$452$	5.60040	−	1.50062i	0.263421	−	0.0705833i
$453$	30.0381	+	5.15373i	1.41131	+	0.242143i
$454$	−21.5631	+	12.4495i	−1.01201	+	0.584284i
$455$		0			0
$456$	−4.67423	+	10.1459i	−0.218891	+	0.475125i
$457$	3.78780	+	14.1363i	0.177186	+	0.661267i	0.996169	+	0.0874492i	$0.0278715\pi$
$457$	3.78780	+	14.1363i	0.177186	+	0.661267i	−0.818983	+	0.573818i	$0.805462\pi$
$458$	1.16781	−	1.16781i	0.0545681	−	0.0545681i
$459$	0.635674	+	2.24745i	0.0296707	+	0.104902i
$460$		0			0
$461$	28.6237	+	16.5259i	1.33314	+	0.769689i	0.985780	−	0.168043i	$-0.0537448\pi$
$461$	28.6237	+	16.5259i	1.33314	+	0.769689i	0.347360	+	0.937732i	$0.387078\pi$
$462$	4.71039	−	1.73910i	0.219147	−	0.0809102i
$463$	3.16668	−	11.8182i	0.147168	−	0.549239i	−0.852481	−	0.522758i	$-0.824903\pi$
$463$	3.16668	−	11.8182i	0.147168	−	0.549239i	0.999649	−	0.0264810i	$-0.00843014\pi$
$464$	−0.158919	−	0.275255i	−0.00737761	−	0.0127784i
$465$		0			0
$466$	−10.2247	+	17.7098i	−0.473652	+	0.820390i
$467$	2.82843	+	2.82843i	0.130884	+	0.130884i	0.769514	−	0.638630i	$-0.220499\pi$
$467$	2.82843	+	2.82843i	0.130884	+	0.130884i	−0.638630	+	0.769514i	$0.720499\pi$
$468$	−8.56753	−	5.88196i	−0.396034	−	0.271894i
$469$			30.1464i			1.39203i
$470$		0			0
$471$	2.32577	+	25.2415i	0.107166	+	1.16307i
$472$	8.67217	+	2.32370i	0.399169	+	0.106957i
$473$	2.12701	+	0.569930i	0.0977999	+	0.0262054i
$474$	−0.389270	−	4.22474i	−0.0178797	−	0.194049i
$475$		0			0
$476$		−	2.04989i		−	0.0939565i
$477$	−1.25087	+	15.9966i	−0.0572736	+	0.732433i
$478$	12.0000	+	12.0000i	0.548867	+	0.548867i
$479$	3.53553	−	6.12372i	0.161543	−	0.279800i	−0.773879	−	0.633333i	$-0.781686\pi$
$479$	3.53553	−	6.12372i	0.161543	−	0.279800i	0.935422	+	0.353533i	$0.115020\pi$
$480$		0			0
$481$	7.34847	+	12.7279i	0.335061	+	0.580343i
$482$	−4.91756	+	18.3526i	−0.223989	+	0.835938i
$483$	−7.41007	+	2.73583i	−0.337170	+	0.124485i
$484$	−9.17633	−	5.29796i	−0.417106	−	0.240816i
$485$		0			0
$486$	−13.9722	+	6.91215i	−0.633792	+	0.313541i
$487$	12.0000	−	12.0000i	0.543772	−	0.543772i	−0.380861	−	0.924632i	$-0.624372\pi$
$487$	12.0000	−	12.0000i	0.543772	−	0.543772i	0.924632	+	0.380861i	$0.124372\pi$
$488$	−0.142483	−	0.531752i	−0.00644988	−	0.0240713i
$489$	−4.56048	+	9.89898i	−0.206232	+	0.447647i
$490$		0			0
$491$	−24.2474	+	13.9993i	−1.09427	+	0.631778i	−0.934711	−	0.355410i	$-0.884341\pi$
$491$	−24.2474	+	13.9993i	−1.09427	+	0.631778i	−0.159561	+	0.987188i	$0.551008\pi$
$492$	−12.6136	−	2.16416i	−0.568667	−	0.0975679i
$493$	0.137997	−	0.0369761i	0.00621505	−	0.00166532i
$494$	22.3417			1.00520
$495$		0			0
$496$	−0.449490			−0.0201827
$497$	27.7191	−	7.42731i	1.24337	−	0.333161i
$498$	−6.03371	+	7.25845i	−0.270377	+	0.325259i
$499$	−0.778539	+	0.449490i	−0.0348522	+	0.0201219i	−0.517325	−	0.855789i	$-0.673072\pi$
$499$	−0.778539	+	0.449490i	−0.0348522	+	0.0201219i	0.482473	+	0.875911i	$0.339739\pi$
$500$		0			0
$501$	−15.1742	+	1.39816i	−0.677935	+	0.0624652i
$502$	0.695075	+	2.59405i	0.0310227	+	0.115778i
$503$	4.02834	−	4.02834i	0.179615	−	0.179615i	−0.611573	−	0.791188i	$-0.709463\pi$
$503$	4.02834	−	4.02834i	0.179615	−	0.179615i	0.791188	+	0.611573i	$0.209463\pi$
$504$	13.4511	−	2.50000i	0.599159	−	0.111359i
$505$		0			0
$506$	−0.550510	−	0.317837i	−0.0244732	−	0.0141296i
$507$	0.292893	−	1.70711i	0.0130078	−	0.0758153i
$508$	−0.686765	+	2.56304i	−0.0304702	+	0.113717i
$509$	4.22659	+	7.32066i	0.187340	+	0.324483i	0.944363	−	0.328906i	$-0.106680\pi$
$509$	4.22659	+	7.32066i	0.187340	+	0.324483i	−0.757022	+	0.653389i	$0.773347\pi$
$510$		0			0
$511$	22.2474	−	38.5337i	0.984169	−	1.70463i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	16.3529	−	29.2519i	0.721998	−	1.29150i
$514$		−	18.0454i		−	0.795949i
$515$		0			0
$516$	5.44949	+	2.51059i	0.239900	+	0.110523i
$517$	−5.52613	−	1.48072i	−0.243039	−	0.0651221i
$518$	−18.6892	−	5.00775i	−0.821156	−	0.220028i
$519$	18.2419	−	12.8990i	0.800731	−	0.566202i
$520$		0			0
$521$			29.4449i			1.29000i	0.764181	+	0.645001i	$0.223143\pi$
$521$			29.4449i			1.29000i	−0.764181	+	0.645001i	$0.776857\pi$
$522$	0.410930	+	0.860419i	0.0179859	+	0.0376595i
$523$	−4.22474	−	4.22474i	−0.184735	−	0.184735i	0.608680	−	0.793416i	$-0.291699\pi$
$523$	−4.22474	−	4.22474i	−0.184735	−	0.184735i	−0.793416	+	0.608680i	$0.791699\pi$
$524$	−1.80348	+	3.12372i	−0.0787855	+	0.136461i
$525$		0			0
$526$	−8.34847	−	14.4600i	−0.364011	−	0.630485i
$527$	0.0522921	−	0.195157i	0.00227788	−	0.00850116i
$528$	0.846687	+	0.703823i	0.0368473	+	0.0306300i
$529$	−19.0526	−	11.0000i	−0.828372	−	0.478261i
$530$		0			0
$531$	−25.3939	−	8.97809i	−1.10200	−	0.389616i
$532$	−20.7980	+	20.7980i	−0.901706	+	0.901706i
$533$	6.62471	+	24.7238i	0.286948	+	1.07090i
$534$	−8.02458	−	11.3485i	−0.347258	−	0.491096i
$535$		0			0
$536$	−5.72474	+	3.30518i	−0.247271	+	0.142762i
$537$	6.40576	+	17.3501i	0.276429	+	0.748714i
$538$	14.5813	−	3.90704i	0.628643	−	0.168444i
$539$	8.77101			0.377794
$540$		0			0
$541$	27.9444			1.20142			0.600712	−	0.799466i	$-0.294884\pi$
$541$	27.9444			1.20142			0.600712	+	0.799466i	$0.294884\pi$
$542$	27.0898	−	7.25869i	1.16361	−	0.311787i
$543$	9.26816	+	25.1030i	0.397735	+	1.07727i
$544$	0.389270	−	0.224745i	0.0166898	−	0.00963586i
$545$		0			0
$546$	−15.7980	−	22.3417i	−0.676090	−	0.956136i
$547$	1.05279	+	3.92907i	0.0450140	+	0.167995i	0.984774	−	0.173841i	$-0.0556180\pi$
$547$	1.05279	+	3.92907i	0.0450140	+	0.167995i	−0.939760	+	0.341836i	$0.888951\pi$
$548$	−15.4135	+	15.4135i	−0.658431	+	0.658431i
$549$	0.301783	+	1.62372i	0.0128798	+	0.0692989i
$550$		0			0
$551$	−1.77526	−	1.02494i	−0.0756284	−	0.0436641i
$552$	−1.33195	−	1.10721i	−0.0566916	−	0.0471258i
$553$	2.89123	−	10.7902i	0.122947	−	0.458846i
$554$	14.0707	+	24.3712i	0.597807	+	1.03543i
$555$		0			0
$556$	−1.55051	+	2.68556i	−0.0657563	+	0.113893i
$557$	−7.88171	−	7.88171i	−0.333959	−	0.333959i	0.520129	−	0.854088i	$-0.325884\pi$
$557$	−7.88171	−	7.88171i	−0.333959	−	0.333959i	−0.854088	+	0.520129i	$0.825884\pi$
$558$	1.34437	+	0.105124i	0.0569115	+	0.00445027i
$559$		−	12.0000i		−	0.507546i
$560$		0			0
$561$	−0.404082	+	0.285729i	−0.0170604	+	0.0120635i
$562$	−16.5613	−	4.43759i	−0.698597	−	0.187188i
$563$	−18.9819	−	5.08619i	−0.799993	−	0.214357i	−0.164412	−	0.986392i	$-0.552573\pi$
$563$	−18.9819	−	5.08619i	−0.799993	−	0.214357i	−0.635581	+	0.772034i	$0.719239\pi$
$564$	−14.1582	−	6.52270i	−0.596167	−	0.274655i
$565$		0			0
$566$			24.2166i			1.01790i
$567$	−40.8151	+	4.33130i	−1.71407	+	0.181898i
$568$	4.44949	+	4.44949i	0.186696	+	0.186696i
$569$	9.58166	−	16.5959i	0.401684	−	0.695737i	−0.592245	−	0.805758i	$-0.701758\pi$
$569$	9.58166	−	16.5959i	0.401684	−	0.695737i	0.993929	+	0.110021i	$0.0350917\pi$
$570$		0			0
$571$	−18.4495	−	31.9555i	−0.772087	−	1.33729i	−0.936417	−	0.350889i	$-0.885880\pi$
$571$	−18.4495	−	31.9555i	−0.772087	−	1.33729i	0.164330	−	0.986405i	$-0.447454\pi$
$572$	0.569930	−	2.12701i	0.0238300	−	0.0889347i
$573$	−5.11490	+	29.8118i	−0.213678	+	1.24541i
$574$	−29.1824	−	16.8485i	−1.21805	−	0.703242i
$575$		0			0
$576$	1.94949	+	2.28024i	0.0812287	+	0.0950100i
$577$	17.0000	−	17.0000i	0.707719	−	0.707719i	−0.258336	−	0.966055i	$-0.583174\pi$
$577$	17.0000	−	17.0000i	0.707719	−	0.707719i	0.966055	+	0.258336i	$0.0831741\pi$
$578$	−4.34763	−	16.2256i	−0.180838	−	0.674895i
$579$	−29.8735	+	2.75255i	−1.24150	+	0.114392i
$580$		0			0
$581$	−21.5227	+	12.4261i	−0.892912	+	0.515523i
$582$	−2.97347	+	3.57704i	−0.123254	+	0.148273i
$583$	−3.28404	+	0.879955i	−0.136011	+	0.0364440i
$584$	9.75663			0.403732
$585$		0			0
$586$	−22.0454			−0.910687
$587$	−12.6009	+	3.37640i	−0.520095	+	0.139359i	−0.509310	−	0.860583i	$-0.670099\pi$
$587$	−12.6009	+	3.37640i	−0.520095	+	0.139359i	−0.0107843	+	0.999942i	$0.503433\pi$
$588$	23.5546	+	4.04133i	0.971375	+	0.166662i
$589$	−2.51059	+	1.44949i	−0.103447	+	0.0597252i
$590$		0			0
$591$	7.10102	−	15.4135i	0.292097	−	0.634026i
$592$	−1.09808	−	4.09808i	−0.0451307	−	0.168430i
$593$	−7.24604	+	7.24604i	−0.297559	+	0.297559i	−0.840057	−	0.542498i	$-0.817479\pi$
$593$	−7.24604	+	7.24604i	−0.297559	+	0.297559i	0.542498	+	0.840057i	$0.317479\pi$
$594$	−2.36773	−	2.30306i	−0.0971489	−	0.0944958i
$595$		0			0
$596$	−3.82577	−	2.20881i	−0.156709	−	0.0904762i
$597$	−13.7291	+	5.06885i	−0.561895	+	0.207454i
$598$	−0.896575	+	3.34607i	−0.0366637	+	0.136831i
$599$	−9.97093	−	17.2702i	−0.407401	−	0.705639i	0.587197	−	0.809444i	$-0.300232\pi$
$599$	−9.97093	−	17.2702i	−0.407401	−	0.705639i	−0.994598	+	0.103805i	$0.966898\pi$
$600$		0			0
$601$	−2.65153	+	4.59259i	−0.108158	+	0.187335i	−0.915024	−	0.403399i	$-0.867829\pi$
$601$	−2.65153	+	4.59259i	−0.108158	+	0.187335i	0.806866	+	0.590735i	$0.201162\pi$
$602$	11.1708	+	11.1708i	0.455290	+	0.455290i
$603$	17.8950	−	8.54650i	0.728739	−	0.348040i
$604$			17.5959i			0.715968i
$605$		0			0
$606$	−2.00000	−	21.7060i	−0.0812444	−	0.881747i
$607$	11.3732	+	3.04744i	0.461624	+	0.123692i	0.482133	−	0.876098i	$-0.339862\pi$
$607$	11.3732	+	3.04744i	0.461624	+	0.123692i	−0.0205092	+	0.999790i	$0.506529\pi$
$608$	−6.22973	−	1.66925i	−0.252649	−	0.0676971i
$609$	0.230351	+	2.50000i	0.00933429	+	0.101305i
$610$		0			0
$611$			31.1769i			1.26128i
$612$	−1.21682	+	0.581142i	−0.0491869	+	0.0234913i
$613$	−6.79796	−	6.79796i	−0.274567	−	0.274567i	0.556369	−	0.830936i	$-0.312194\pi$
$613$	−6.79796	−	6.79796i	−0.274567	−	0.274567i	−0.830936	+	0.556369i	$0.812194\pi$
$614$	4.71940	−	8.17423i	0.190459	−	0.329885i
$615$		0			0
$616$	1.44949	+	2.51059i	0.0584016	+	0.101155i
$617$	4.37378	−	16.3232i	0.176082	−	0.657146i	−0.820283	−	0.571958i	$-0.806184\pi$
$617$	4.37378	−	16.3232i	0.176082	−	0.657146i	0.996365	−	0.0851882i	$-0.0271491\pi$
$618$	−15.8530	+	5.85301i	−0.637701	+	0.235442i
$619$	−42.2121	−	24.3712i	−1.69665	−	0.979560i	−0.948900	−	0.315578i	$-0.897802\pi$
$619$	−42.2121	−	24.3712i	−1.69665	−	0.979560i	−0.747748	−	0.663982i	$-0.768865\pi$
$620$		0			0
$621$	3.72474	+	3.62302i	0.149469	+	0.145387i
$622$	19.4495	−	19.4495i	0.779853	−	0.779853i
$623$	−9.47172	−	35.3489i	−0.379476	−	1.41623i
$624$	2.51059	−	5.44949i	0.100504	−	0.218154i
$625$		0			0
$626$	10.3485	−	5.97469i	0.413608	−	0.238797i
$627$	6.99876	+	1.20080i	0.279503	+	0.0479552i
$628$	−14.1363	+	3.78780i	−0.564099	+	0.151150i
$629$	1.90702			0.0760380
$630$		0			0
$631$	−3.10102			−0.123450			−0.0617248	−	0.998093i	$-0.519660\pi$
$631$	−3.10102			−0.123450			−0.0617248	+	0.998093i	$0.519660\pi$
$632$	2.36603	−	0.633975i	0.0941154	−	0.0252182i
$633$	−10.0767	+	12.1221i	−0.400513	+	0.481811i
$634$	9.43879	−	5.44949i	0.374862	−	0.216427i
$635$		0			0
$636$	−9.22474	+	0.849971i	−0.365785	+	0.0337036i
$637$	−12.3709	−	46.1689i	−0.490153	−	1.82928i
$638$	−0.142865	+	0.142865i	−0.00565606	+	0.00565606i
$639$	−12.2672	−	14.3485i	−0.485284	−	0.567617i
$640$		0			0
$641$	16.7474	+	9.66914i	0.661484	+	0.381908i	0.792842	−	0.609427i	$-0.208600\pi$
$641$	16.7474	+	9.66914i	0.661484	+	0.381908i	−0.131358	+	0.991335i	$0.541934\pi$
$642$	5.63745	−	32.8575i	0.222492	−	1.29678i
$643$	−1.63694	+	6.10913i	−0.0645545	+	0.240921i	−0.990662	−	0.136338i	$-0.956467\pi$
$643$	−1.63694	+	6.10913i	−0.0645545	+	0.240921i	0.926108	+	0.377259i	$0.123133\pi$
$644$	−2.28024	−	3.94949i	−0.0898540	−	0.155632i
$645$		0			0
$646$	1.44949	−	2.51059i	0.0570294	−	0.0987778i
$647$	23.5416	+	23.5416i	0.925516	+	0.925516i	0.997412	−	0.0718961i	$-0.0229050\pi$
$647$	23.5416	+	23.5416i	0.925516	+	0.925516i	−0.0718961	+	0.997412i	$0.522905\pi$
$648$	−5.29738	−	7.27583i	−0.208101	−	0.285822i
$649$		−	5.70714i		−	0.224025i
$650$		0			0
$651$	3.22474	+	1.48565i	0.126388	+	0.0582271i
$652$	−6.07812	−	1.62863i	−0.238037	−	0.0637819i
$653$	−25.5482	−	6.84563i	−0.999780	−	0.267890i	−0.278427	−	0.960457i	$-0.589813\pi$
$653$	−25.5482	−	6.84563i	−0.999780	−	0.267890i	−0.721353	+	0.692567i	$0.756480\pi$
$654$	7.99247	−	5.65153i	0.312530	−	0.220992i
$655$		0			0
$656$		−	7.38891i		−	0.288488i
$657$	−29.1808	−	2.28183i	−1.13845	−	0.0890227i
$658$	−29.0227	−	29.0227i	−1.13142	−	1.13142i
$659$	−5.65685	+	9.79796i	−0.220360	+	0.381674i	−0.954917	−	0.296872i	$-0.904056\pi$
$659$	−5.65685	+	9.79796i	−0.220360	+	0.381674i	0.734557	+	0.678546i	$0.237390\pi$
$660$		0			0
$661$	0.651531	+	1.12848i	0.0253416	+	0.0438930i	0.878418	−	0.477893i	$-0.158599\pi$
$661$	0.651531	+	1.12848i	0.0253416	+	0.0438930i	−0.853076	+	0.521786i	$0.825266\pi$
$662$	−0.116337	+	0.434174i	−0.00452155	+	0.0168746i
$663$	2.07395	+	1.72401i	0.0805456	+	0.0669549i
$664$	−4.71940	−	2.72474i	−0.183148	−	0.105741i
$665$		0			0
$666$	2.32577	+	12.5136i	0.0901216	+	0.484893i
$667$	0.224745	−	0.224745i	0.00870216	−	0.00870216i
$668$	−2.27708	−	8.49818i	−0.0881028	−	0.328804i
$669$	−25.6308	−	36.2474i	−0.990945	−	1.40141i
$670$		0			0
$671$	−0.303062	+	0.174973i	−0.0116996	+	0.00675474i
$672$	2.73583	+	7.41007i	0.105537	+	0.285850i
$673$	−22.4704	+	6.02093i	−0.866171	+	0.232090i	−0.664431	−	0.747349i	$-0.731326\pi$
$673$	−22.4704	+	6.02093i	−0.866171	+	0.232090i	−0.201740	+	0.979439i	$0.564660\pi$
$674$	−3.11416			−0.119953
$675$		0			0
$676$	1.00000			0.0384615
$677$	44.0423	−	11.8011i	1.69268	−	0.453553i	0.721602	−	0.692308i	$-0.243406\pi$
$677$	44.0423	−	11.8011i	1.69268	−	0.453553i	0.971080	+	0.238755i	$0.0767393\pi$
$678$	−3.47820	−	9.42078i	−0.133579	−	0.361803i
$679$	−10.6066	+	6.12372i	−0.407044	+	0.235007i
$680$		0			0
$681$	24.8990	+	35.2125i	0.954131	+	1.34934i
$682$	0.0739521	+	0.275993i	0.00283177	+	0.0105683i
$683$	−13.8564	+	13.8564i	−0.530201	+	0.530201i	−0.920632	−	0.390431i	$-0.872326\pi$
$683$	−13.8564	+	13.8564i	−0.530201	+	0.530201i	0.390431	+	0.920632i	$0.372326\pi$
$684$	18.2419	+	6.44949i	0.697497	+	0.246602i
$685$		0			0
$686$	26.8485	+	15.5010i	1.02508	+	0.591830i
$687$	−2.19976	−	1.82859i	−0.0839260	−	0.0697649i
$688$	−0.896575	+	3.34607i	−0.0341816	+	0.127568i
$689$	9.26382	+	16.0454i	0.352923	+	0.611281i
$690$		0			0
$691$	10.4722	−	18.1384i	0.398381	−	0.690016i	−0.595145	−	0.803618i	$-0.702906\pi$
$691$	10.4722	−	18.1384i	0.398381	−	0.690016i	0.993526	+	0.113602i	$0.0362388\pi$
$692$	9.12096	+	9.12096i	0.346727	+	0.346727i
$693$	−3.74807	−	7.84785i	−0.142377	−	0.298115i
$694$			23.7980i			0.903358i
$695$		0			0
$696$	−0.449490	+	0.317837i	−0.0170379	+	0.0120476i
$697$	3.20807	+	0.859599i	0.121514	+	0.0325596i
$698$	28.0557	+	7.51750i	1.06192	+	0.284542i
$699$	32.1698	+	14.8207i	1.21677	+	0.560569i
$700$		0			0
$701$		−	21.1024i		−	0.797028i	−0.917162	−	0.398514i	$-0.869526\pi$
$701$		−	21.1024i		−	0.797028i	0.917162	−	0.398514i	$-0.130474\pi$
$702$	−8.78335	+	15.7116i	−0.331506	+	0.592994i
$703$	−19.3485	−	19.3485i	−0.729741	−	0.729741i
$704$	−0.317837	+	0.550510i	−0.0119789	+	0.0207481i
$705$		0			0
$706$	17.1464	+	29.6985i	0.645314	+	1.11772i
$707$	14.8546	−	55.4382i	0.558666	−	2.08497i
$708$	2.62962	−	15.3266i	0.0988272	−	0.576007i
$709$	25.6790	+	14.8258i	0.964394	+	0.556793i	0.897523	−	0.440968i	$-0.145365\pi$
$709$	25.6790	+	14.8258i	0.964394	+	0.556793i	0.0668716	+	0.997762i	$0.478698\pi$
$710$		0			0
$711$	−7.22474	+	1.34278i	−0.270949	+	0.0503582i
$712$	5.67423	−	5.67423i	0.212651	−	0.212651i
$713$	−0.116337	−	0.434174i	−0.00435684	−	0.0162599i
$714$	−3.53553	+	0.325765i	−0.132314	+	0.0121915i
$715$		0			0
$716$	−9.24745	+	5.33902i	−0.345593	+	0.199528i
$717$	18.7899	−	22.6040i	0.701722	−	0.844160i
$718$	−3.20807	+	0.859599i	−0.119724	+	0.0320800i
$719$	−32.5269			−1.21305			−0.606525	−	0.795065i	$-0.707437\pi$
$719$	−32.5269			−1.21305			−0.606525	+	0.795065i	$0.707437\pi$
$720$		0			0
$721$	−44.4949			−1.65708
$722$	−21.8260	+	5.84825i	−0.812279	+	0.217649i
$723$	32.4350	+	5.56497i	1.20627	+	0.206964i
$724$	−13.3797	+	7.72474i	−0.497251	+	0.287088i
$725$		0			0
$726$	−7.67934	+	16.6688i	−0.285007	+	0.618636i
$727$	−12.5068	−	46.6759i	−0.463850	−	1.73111i	−0.660673	−	0.750674i	$-0.729729\pi$
$727$	−12.5068	−	46.6759i	−0.463850	−	1.73111i	0.196822	−	0.980439i	$-0.436938\pi$
$728$	11.1708	−	11.1708i	0.414019	−	0.414019i
$729$	14.1421	+	23.0000i	0.523783	+	0.851852i
$730$		0			0
$731$	−1.34847	−	0.778539i	−0.0498749	−	0.0287953i
$732$	−0.894494	+	0.330251i	−0.0330614	+	0.0122064i
$733$	−8.83821	+	32.9846i	−0.326447	+	1.21832i	0.586403	+	0.810019i	$0.300543\pi$
$733$	−8.83821	+	32.9846i	−0.326447	+	1.21832i	−0.912850	+	0.408296i	$0.866123\pi$
$734$	2.04989	+	3.55051i	0.0756627	+	0.131052i
$735$		0			0
$736$	0.500000	−	0.866025i	0.0184302	−	0.0319221i
$737$	2.97129	+	2.97129i	0.109449	+	0.109449i
$738$	−1.72808	+	22.0993i	−0.0636115	+	0.813485i
$739$		−	28.9444i		−	1.06474i	−0.846513	−	0.532368i	$-0.821302\pi$
$739$		−	28.9444i		−	1.06474i	0.846513	−	0.532368i	$-0.178698\pi$
$740$		0			0
$741$	−3.55051	−	38.5337i	−0.130431	−	1.41557i
$742$	−23.5605	−	6.31300i	−0.864931	−	0.231758i
$743$	9.56168	+	2.56204i	0.350784	+	0.0939923i	0.429909	−	0.902872i	$-0.358546\pi$
$743$	9.56168	+	2.56204i	0.350784	+	0.0939923i	−0.0791245	+	0.996865i	$0.525212\pi$
$744$	0.0714323	+	0.775255i	0.00261883	+	0.0284222i
$745$		0			0
$746$		−	0.492810i		−	0.0180431i
$747$	13.4779	+	9.25311i	0.493129	+	0.338553i
$748$	−0.202041	−	0.202041i	−0.00738735	−	0.00738735i
$749$	43.8888	−	76.0176i	1.60366	−	2.77762i
$750$		0			0
$751$	−10.3485	−	17.9241i	−0.377621	−	0.654059i	0.613095	−	0.790010i	$-0.289924\pi$
$751$	−10.3485	−	17.9241i	−0.377621	−	0.654059i	−0.990716	+	0.135951i	$0.956591\pi$
$752$	2.32937	−	8.69333i	0.0849434	−	0.317013i
$753$	4.36362	−	1.61107i	0.159019	−	0.0587107i
$754$	0.953512	+	0.550510i	0.0347248	+	0.0200484i
$755$		0			0
$756$	−6.44949	−	22.8024i	−0.234566	−	0.829315i
$757$	−22.0454	+	22.0454i	−0.801254	+	0.801254i	−0.983292	−	0.182038i	$-0.941731\pi$
$757$	−22.0454	+	22.0454i	−0.801254	+	0.801254i	0.182038	+	0.983292i	$0.441731\pi$
$758$	5.52539	+	20.6210i	0.200691	+	0.748990i
$759$	−0.460702	+	1.00000i	−0.0167224	+	0.0362977i
$760$		0			0
$761$	−5.60102	+	3.23375i	−0.203037	+	0.117223i	−0.598071	−	0.801443i	$-0.704066\pi$
$761$	−5.60102	+	3.23375i	−0.203037	+	0.117223i	0.395034	+	0.918666i	$0.370733\pi$
$762$	4.52973	+	0.777179i	0.164095	+	0.0281542i
$763$	24.8955	−	6.67072i	0.901276	−	0.241496i
$764$	−17.4634			−0.631803
$765$		0			0
$766$	8.20204			0.296352
$767$	−30.0413	+	8.04954i	−1.08473	+	0.290652i
$768$	−1.10721	+	1.33195i	−0.0399529	+	0.0480627i
$769$	8.39780	−	4.84847i	0.302832	−	0.174840i	−0.340882	−	0.940106i	$-0.610726\pi$
$769$	8.39780	−	4.84847i	0.302832	−	0.174840i	0.643715	+	0.765266i	$0.277392\pi$
$770$		0			0
$771$	−31.1237	+	2.86775i	−1.12089	+	0.103280i
$772$	−4.48288	−	16.7303i	−0.161342	−	0.602138i
$773$	30.8270	−	30.8270i	1.10877	−	1.10877i	0.115456	−	0.993313i	$-0.463167\pi$
$773$	30.8270	−	30.8270i	1.10877	−	1.10877i	0.993313	−	0.115456i	$-0.0368331\pi$
$774$	3.46410	−	9.79796i	0.124515	−	0.352180i
$775$		0			0
$776$	−2.32577	−	1.34278i	−0.0834901	−	0.0482030i
$777$	−5.66704	+	33.0299i	−0.203304	+	1.18494i
$778$	−9.52497	+	35.5477i	−0.341487	+	1.27445i
$779$	−23.8273	−	41.2702i	−0.853703	−	1.47866i
$780$		0			0
$781$	2.00000	−	3.46410i	0.0715656	−	0.123955i
$782$	0.317837	+	0.317837i	0.0113658	+	0.0113658i
$783$	1.41870	−	0.845485i	0.0507002	−	0.0302152i
$784$			13.7980i			0.492784i
$785$		0			0
$786$	5.67423	+	2.61413i	0.202393	+	0.0932429i
$787$	−9.42418	−	2.52520i	−0.335936	−	0.0900137i	0.0869079	−	0.996216i	$-0.472301\pi$
$787$	−9.42418	−	2.52520i	−0.335936	−	0.0900137i	−0.422844	+	0.906203i	$0.638968\pi$
$788$	9.46410	+	2.53590i	0.337145	+	0.0903376i
$789$	−23.6130	+	16.6969i	−0.840646	+	0.594427i
$790$		0			0
$791$		−	26.4415i		−	0.940150i
$792$	1.07936	−	1.57217i	0.0383534	−	0.0558646i
$793$	1.34847	+	1.34847i	0.0478855	+	0.0478855i
$794$	−7.46034	+	12.9217i	−0.264757	+	0.458573i
$795$		0			0
$796$	−4.22474	−	7.31747i	−0.149742	−	0.259361i
$797$	−10.3005	+	38.4419i	−0.364861	+	1.36168i	0.502747	+	0.864433i	$0.332323\pi$
$797$	−10.3005	+	38.4419i	−0.364861	+	1.36168i	−0.867609	+	0.497248i	$0.834344\pi$
$798$	39.1764	+	32.5660i	1.38683	+	1.15282i
$799$	3.50343	+	2.02270i	0.123942	+	0.0715581i
$800$		0			0
$801$	−18.2980	+	15.6438i	−0.646527	+	0.552748i
$802$	6.24745	−	6.24745i	0.220605	−	0.220605i
$803$	−1.60521	−	5.99071i	−0.0566465	−	0.211408i
$804$	6.61037	+	9.34847i	0.233130	+	0.329695i
$805$		0			0
$806$	1.34847	−	0.778539i	0.0474978	−	0.0274229i
$807$	−9.05589	−	24.5281i	−0.318782	−	0.863429i
$808$	12.1562	−	3.25725i	0.427655	−	0.114590i
$809$	19.4490			0.683792			0.341896	−	0.939738i	$-0.388931\pi$
$809$	19.4490			0.683792			0.341896	+	0.939738i	$0.388931\pi$
$810$		0			0
$811$	−39.6413			−1.39200			−0.695998	−	0.718044i	$-0.745038\pi$
$811$	−39.6413			−1.39200			−0.695998	+	0.718044i	$0.745038\pi$
$812$	−1.40010	+	0.375156i	−0.0491339	+	0.0131654i
$813$	−16.8245	−	45.5694i	−0.590059	−	1.59819i
$814$	−2.33562	+	1.34847i	−0.0818633	+	0.0472638i
$815$		0			0
$816$	−0.449490	−	0.635674i	−0.0157353	−	0.0222531i
$817$	5.78245	+	21.5804i	0.202302	+	0.755003i
$818$	20.4347	−	20.4347i	0.714481	−	0.714481i
$819$	−36.0231	+	30.7980i	−1.25875	+	1.07617i
$820$		0			0
$821$	19.3207	+	11.1548i	0.674296	+	0.389305i	0.797702	−	0.603051i	$-0.206049\pi$
$821$	19.3207	+	11.1548i	0.674296	+	0.389305i	−0.123407	+	0.992356i	$0.539382\pi$
$822$	29.0338	+	24.1348i	1.01267	+	0.841799i
$823$	−0.867910	+	3.23908i	−0.0302534	+	0.112907i	−0.979401	−	0.201923i	$-0.935281\pi$
$823$	−0.867910	+	3.23908i	−0.0302534	+	0.112907i	0.949148	+	0.314830i	$0.101948\pi$
$824$	−4.87832	−	8.44949i	−0.169944	−	0.294352i
$825$		0			0
$826$	20.4722	−	35.4589i	0.712319	−	1.23377i
$827$	31.5662	+	31.5662i	1.09766	+	1.09766i	0.994683	+	0.102980i	$0.0328379\pi$
$827$	31.5662	+	31.5662i	1.09766	+	1.09766i	0.102980	+	0.994683i	$0.467162\pi$
$828$	−1.69798	+	2.47323i	−0.0590088	+	0.0859507i
$829$			10.5505i			0.366434i	0.983072	+	0.183217i	$0.0586512\pi$
$829$			10.5505i			0.366434i	−0.983072	+	0.183217i	$0.941349\pi$
$830$		0			0
$831$	39.7980	−	28.1414i	1.38058	−	0.976215i
$832$	3.34607	+	0.896575i	0.116004	+	0.0310832i
$833$	−5.99071	−	1.60521i	−0.207566	−	0.0556171i
$834$	4.87832	+	2.24745i	0.168922	+	0.0778228i
$835$		0			0
$836$			4.09978i			0.141794i
$837$	−0.0323319	−	2.33539i	−0.00111755	−	0.0807230i
$838$	−3.55051	−	3.55051i	−0.122650	−	0.122650i
$839$	−0.246405	+	0.426786i	−0.00850684	+	0.0147343i	−0.870247	−	0.492615i	$-0.836041\pi$
$839$	−0.246405	+	0.426786i	−0.00850684	+	0.0147343i	0.861741	+	0.507349i	$0.169375\pi$
$840$		0			0
$841$	14.4495	+	25.0273i	0.498258	+	0.863009i
$842$	1.32024	−	4.92721i	0.0454985	−	0.169803i
$843$	−5.02181	+	29.2693i	−0.172960	+	1.00809i
$844$	−7.88171	−	4.55051i	−0.271300	−	0.156635i
$845$		0			0
$846$	−9.00000	+	25.4558i	−0.309426	+	0.875190i
$847$	−34.1691	+	34.1691i	−1.17407	+	1.17407i
$848$	−1.38429	−	5.16622i	−0.0475366	−	0.177409i
$849$	41.7675	−	3.84847i	1.43346	−	0.132079i
$850$		0			0
$851$	3.67423	−	2.12132i	0.125951	−	0.0727179i
$852$	6.96713	−	8.38134i	0.238690	−	0.287140i
$853$	−2.39403	+	0.641478i	−0.0819700	+	0.0219638i	−0.299571	−	0.954074i	$-0.596844\pi$
$853$	−2.39403	+	0.641478i	−0.0819700	+	0.0219638i	0.217601	+	0.976038i	$0.430177\pi$
$854$	−2.51059			−0.0859106
$855$		0			0
$856$	19.2474			0.657864
$857$	−15.2597	+	4.08881i	−0.521260	+	0.139671i	−0.509849	−	0.860264i	$-0.670299\pi$
$857$	−15.2597	+	4.08881i	−0.521260	+	0.139671i	−0.0114106	+	0.999935i	$0.503632\pi$
$858$	−3.75912	−	0.644963i	−0.128334	−	0.0220187i
$859$	40.2658	−	23.2474i	1.37385	−	0.793193i	0.382440	−	0.923980i	$-0.375084\pi$
$859$	40.2658	−	23.2474i	1.37385	−	0.793193i	0.991410	+	0.130788i	$0.0417506\pi$
$860$		0			0
$861$	−24.4217	+	53.0097i	−0.832289	+	1.80657i
$862$	−4.02628	−	15.0263i	−0.137136	−	0.511797i
$863$	−20.7132	+	20.7132i	−0.705085	+	0.705085i	−0.965497	−	0.260413i	$-0.916141\pi$
$863$	−20.7132	+	20.7132i	−0.705085	+	0.705085i	0.260413	+	0.965497i	$0.416141\pi$
$864$	3.62302	−	3.72474i	0.123258	−	0.126718i
$865$		0			0
$866$	−16.4722	−	9.51023i	−0.559748	−	0.323171i
$867$	−27.2941	+	10.0771i	−0.926955	+	0.342236i
$868$	−0.530550	+	1.98004i	−0.0180080	+	0.0672069i
$869$	−0.778539	−	1.34847i	−0.0264101	−	0.0457437i
$870$		0			0
$871$	11.4495	−	19.8311i	0.387951	−	0.671951i
$872$	3.99624	+	3.99624i	0.135330	+	0.135330i
$873$	6.64202	+	4.56002i	0.224798	+	0.154333i
$874$		−	6.44949i		−	0.218157i
$875$		0			0
$876$	−1.55051	−	16.8277i	−0.0523869	−	0.568555i
$877$	41.3188	+	11.0713i	1.39524	+	0.373852i	0.876632	−	0.481162i	$-0.159785\pi$
$877$	41.3188	+	11.0713i	1.39524	+	0.373852i	0.518604	+	0.855014i	$0.326452\pi$
$878$	28.7826	+	7.71228i	0.971366	+	0.260277i
$879$	3.50343	+	38.0227i	0.118168	+	1.28247i
$880$		0			0
$881$			54.8365i			1.84749i	0.383010	+	0.923744i	$0.374887\pi$
$881$			54.8365i			1.84749i	−0.383010	+	0.923744i	$0.625113\pi$
$882$	3.22700	−	41.2679i	0.108659	−	1.38956i
$883$	−6.27015	−	6.27015i	−0.211007	−	0.211007i	0.593688	−	0.804695i	$-0.297671\pi$
$883$	−6.27015	−	6.27015i	−0.211007	−	0.211007i	−0.804695	+	0.593688i	$0.797671\pi$
$884$	−0.778539	+	1.34847i	−0.0261851	+	0.0453539i
$885$		0			0
$886$	2.72474	+	4.71940i	0.0915396	+	0.158551i
$887$	2.12284	−	7.92256i	0.0712781	−	0.266014i	−0.921085	−	0.389360i	$-0.872696\pi$
$887$	2.12284	−	7.92256i	0.0712781	−	0.266014i	0.992364	+	0.123347i	$0.0393627\pi$
$888$	−6.89363	+	2.54516i	−0.231335	+	0.0854100i
$889$	10.4798	+	6.05051i	0.351481	+	0.202928i
$890$		0			0
$891$	−3.59592	+	4.44972i	−0.120468	+	0.149071i
$892$	18.1237	−	18.1237i	0.606827	−	0.606827i
$893$	−15.0233	−	56.0676i	−0.502734	−	1.87623i
$894$	−3.20164	+	6.94949i	−0.107079	+	0.232426i
$895$		0			0
$896$	−3.94949	+	2.28024i	−0.131943	+	0.0761774i
$897$	5.91359	+	1.01461i	0.197449	+	0.0338769i
$898$	−0.890008	+	0.238477i	−0.0296999	+	0.00795807i
$899$	−0.142865			−0.00476480
$900$		0			0
$901$	2.40408			0.0800916
$902$	−4.53689	+	1.21566i	−0.151062	+	0.0404770i
$903$	17.4916	−	21.0421i	0.582084	−	0.700238i
$904$	5.02118	−	2.89898i	0.167002	−	0.0964186i
$905$		0			0
$906$	30.3485	−	2.79632i	1.00826	−	0.0929015i
$907$	0.978838	+	3.65307i	0.0325018	+	0.121298i	0.980271	−	0.197659i	$-0.0633339\pi$
$907$	0.978838	+	3.65307i	0.0325018	+	0.121298i	−0.947769	+	0.318957i	$0.896667\pi$
$908$	−17.6062	+	17.6062i	−0.584284	+	0.584284i
$909$	−37.1195	+	6.89898i	−1.23118	+	0.228825i
$910$		0			0
$911$	−6.12372	−	3.53553i	−0.202888	−	0.117137i	0.395114	−	0.918632i	$-0.370705\pi$
$911$	−6.12372	−	3.53553i	−0.202888	−	0.117137i	−0.598002	+	0.801495i	$0.704038\pi$
$912$	−1.88901	+	11.0100i	−0.0625514	+	0.364576i
$913$	−0.896575	+	3.34607i	−0.0296723	+	0.110739i
$914$	7.31747	+	12.6742i	0.242040	+	0.419226i
$915$		0			0
$916$	0.825765	−	1.43027i	0.0272841	−	0.0472574i
$917$	11.6315	+	11.6315i	0.384107	+	0.384107i
$918$	1.19570	+	2.00634i	0.0394639	+	0.0662192i
$919$		−	12.6515i		−	0.417335i	−0.977987	−	0.208668i	$-0.933087\pi$
$919$		−	12.6515i		−	0.417335i	0.977987	−	0.208668i	$-0.0669127\pi$
$920$		0			0
$921$	−14.8485	−	6.84072i	−0.489274	−	0.225409i
$922$	31.9256	+	8.55444i	1.05141	+	0.281726i
$923$	−21.0552	−	5.64173i	−0.693041	−	0.185700i
$924$	4.09978	−	2.89898i	0.134873	−	0.0953694i
$925$		0			0
$926$		−	12.2351i		−	0.402071i
$927$	12.6143	+	26.4122i	0.414307	+	0.867492i
$928$	−0.224745	−	0.224745i	−0.00737761	−	0.00737761i
$929$	−21.1024	+	36.5505i	−0.692349	+	1.19918i	0.278717	+	0.960373i	$0.410091\pi$
$929$	−21.1024	+	36.5505i	−0.692349	+	1.19918i	−0.971066	+	0.238810i	$0.923243\pi$
$930$		0			0
$931$	44.4949	+	77.0674i	1.45826	+	2.52578i
$932$	−5.29272	+	19.7527i	−0.173369	+	0.647021i
$933$	−36.6363	−	30.4545i	−1.19942	−	0.997036i
$934$	3.46410	+	2.00000i	0.113349	+	0.0654420i
$935$		0			0
$936$	−9.79796	−	3.46410i	−0.320256	−	0.113228i
$937$	3.10102	−	3.10102i	0.101306	−	0.101306i	−0.654637	−	0.755943i	$-0.727179\pi$
$937$	3.10102	−	3.10102i	0.101306	−	0.101306i	0.755943	+	0.654637i	$0.227179\pi$
$938$	7.80247	+	29.1192i	0.254760	+	0.950776i
$939$	−11.9494	−	16.8990i	−0.389953	−	0.551477i
$940$		0			0
$941$	27.5227	−	15.8902i	0.897215	−	0.518007i	0.0209191	−	0.999781i	$-0.493341\pi$
$941$	27.5227	−	15.8902i	0.897215	−	0.518007i	0.876295	+	0.481774i	$0.160007\pi$
$942$	8.77951	+	23.7795i	0.286052	+	0.774778i
$943$	7.13713	−	1.91239i	0.232417	−	0.0622760i
$944$	8.97809			0.292212
$945$		0			0
$946$	2.20204			0.0715945
$947$	−2.94164	+	0.788210i	−0.0955904	+	0.0256134i	−0.306297	−	0.951936i	$-0.599090\pi$
$947$	−2.94164	+	0.788210i	−0.0955904	+	0.0256134i	0.210707	+	0.977549i	$0.432423\pi$
$948$	−1.46945	−	3.98004i	−0.0477255	−	0.129266i
$949$	−29.2699	+	16.8990i	−0.950141	+	0.548564i
$950$		0			0
$951$	−10.8990	−	15.4135i	−0.353424	−	0.499816i
$952$	−0.530550	−	1.98004i	−0.0171952	−	0.0641735i
$953$	−5.79972	+	5.79972i	−0.187871	+	0.187871i	−0.794775	−	0.606904i	$-0.792411\pi$
$953$	−5.79972	+	5.79972i	−0.187871	+	0.187871i	0.606904	+	0.794775i	$0.292411\pi$
$954$	2.93197	+	15.7753i	0.0949260	+	0.510743i
$955$		0			0
$956$	14.6969	+	8.48528i	0.475333	+	0.274434i
$957$	0.269109	+	0.223701i	0.00869905	+	0.00723123i
$958$	1.83013	−	6.83013i	0.0591287	−	0.220671i
$959$	49.7046	+	86.0908i	1.60504	+	2.78002i
$960$		0			0
$961$	15.3990	−	26.6718i	0.496741	−	0.860381i
$962$	10.3923	+	10.3923i	0.335061	+	0.335061i
$963$	−57.5666	−	4.50150i	−1.85506	−	0.145059i
$964$			19.0000i			0.611949i
$965$		0			0
$966$	−6.44949	+	4.56048i	−0.207509	+	0.146731i
$967$	−38.6937	−	10.3679i	−1.24431	−	0.333411i	−0.424172	−	0.905582i	$-0.639435\pi$
$967$	−38.6937	−	10.3679i	−1.24431	−	0.333411i	−0.820134	+	0.572171i	$0.806101\pi$
$968$	−10.2349	−	2.74243i	−0.328961	−	0.0881449i
$969$	−4.56048	−	2.10102i	−0.146504	−	0.0674945i
$970$		0			0
$971$		−	21.4989i		−	0.689934i	−0.938615	−	0.344967i	$-0.887890\pi$
$971$		−	21.4989i		−	0.689934i	0.938615	−	0.344967i	$-0.112110\pi$
$972$	−11.7071	+	10.2929i	−0.375506	+	0.330145i
$973$	10.0000	+	10.0000i	0.320585	+	0.320585i
$974$	8.48528	−	14.6969i	0.271886	−	0.470920i
$975$		0			0
$976$	−0.275255	−	0.476756i	−0.00881070	−	0.0152606i
$977$	−1.68100	+	6.27359i	−0.0537801	+	0.200710i	−0.987589	−	0.157063i	$-0.949797\pi$
$977$	−1.68100	+	6.27359i	−0.0537801	+	0.200710i	0.933808	+	0.357773i	$0.116464\pi$
$978$	−1.84304	+	10.7420i	−0.0589339	+	0.343492i
$979$	−4.41761	−	2.55051i	−0.141188	−	0.0815147i
$980$		0			0
$981$	−11.0176	−	12.8868i	−0.351765	−	0.411445i
$982$	−19.7980	+	19.7980i	−0.631778	+	0.631778i
$983$	7.04041	+	26.2752i	0.224554	+	0.838047i	0.982583	+	0.185826i	$0.0594961\pi$
$983$	7.04041	+	26.2752i	0.224554	+	0.838047i	−0.758029	+	0.652221i	$0.773837\pi$
$984$	−12.7440	+	1.17423i	−0.406263	+	0.0374332i
$985$		0			0
$986$	0.123724	−	0.0714323i	0.00394019	−	0.00227487i
$987$	−45.4445	+	54.6690i	−1.44651	+	1.74013i
$988$	21.5804	−	5.78245i	0.686564	−	0.183964i
$989$	−3.46410			−0.110152
$990$		0			0
$991$	16.7423			0.531838			0.265919	−	0.963995i	$-0.414325\pi$
$991$	16.7423			0.531838			0.265919	+	0.963995i	$0.414325\pi$
$992$	−0.434174	+	0.116337i	−0.0137850	+	0.00369369i
$993$	0.767327	+	0.131652i	0.0243504	+	0.00417787i
$994$	24.8523	−	14.3485i	0.788266	−	0.455106i
$995$		0			0
$996$	−3.94949	+	8.57277i	−0.125144	+	0.271639i
$997$	1.73955	+	6.49211i	0.0550922	+	0.205607i	0.987986	−	0.154545i	$-0.0493913\pi$
$997$	1.73955	+	6.49211i	0.0550922	+	0.205607i	−0.932893	+	0.360153i	$0.882725\pi$
$998$	−0.635674	+	0.635674i	−0.0201219	+	0.0201219i
$999$	21.2132	−	6.00000i	0.671156	−	0.189832i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.p.a.443.2		8
3.2	odd	2		1350.2.q.g.143.1		8
5.2	odd	4	inner	450.2.p.a.407.2		8
5.3	odd	4		90.2.l.a.47.1	yes	8
5.4	even	2		90.2.l.a.83.1	yes	8
9.4	even	3		1350.2.q.g.1043.1		8
9.5	odd	6	inner	450.2.p.a.293.2		8
15.2	even	4		1350.2.q.g.1007.1		8
15.8	even	4		270.2.m.a.197.2		8
15.14	odd	2		270.2.m.a.143.2		8
20.3	even	4		720.2.cu.a.497.1		8
20.19	odd	2		720.2.cu.a.353.1		8
45.4	even	6		270.2.m.a.233.2		8
45.13	odd	12		270.2.m.a.17.2		8
45.14	odd	6		90.2.l.a.23.1	✓	8
45.22	odd	12		1350.2.q.g.557.1		8
45.23	even	12		90.2.l.a.77.1	yes	8
45.29	odd	6		810.2.f.b.323.1		8
45.32	even	12	inner	450.2.p.a.257.2		8
45.34	even	6		810.2.f.b.323.4		8
45.38	even	12		810.2.f.b.647.3		8
45.43	odd	12		810.2.f.b.647.2		8
180.23	odd	12		720.2.cu.a.257.1		8
180.59	even	6		720.2.cu.a.113.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.l.a.23.1	✓	8	45.14	odd	6
90.2.l.a.47.1	yes	8	5.3	odd	4
90.2.l.a.77.1	yes	8	45.23	even	12
90.2.l.a.83.1	yes	8	5.4	even	2
270.2.m.a.17.2		8	45.13	odd	12
270.2.m.a.143.2		8	15.14	odd	2
270.2.m.a.197.2		8	15.8	even	4
270.2.m.a.233.2		8	45.4	even	6
450.2.p.a.257.2		8	45.32	even	12	inner
450.2.p.a.293.2		8	9.5	odd	6	inner
450.2.p.a.407.2		8	5.2	odd	4	inner
450.2.p.a.443.2		8	1.1	even	1	trivial
720.2.cu.a.113.1		8	180.59	even	6
720.2.cu.a.257.1		8	180.23	odd	12
720.2.cu.a.353.1		8	20.19	odd	2
720.2.cu.a.497.1		8	20.3	even	4
810.2.f.b.323.1		8	45.29	odd	6
810.2.f.b.323.4		8	45.34	even	6
810.2.f.b.647.2		8	45.43	odd	12
810.2.f.b.647.3		8	45.38	even	12
1350.2.q.g.143.1		8	3.2	odd	2
1350.2.q.g.557.1		8	45.22	odd	12
1350.2.q.g.1007.1		8	15.2	even	4
1350.2.q.g.1043.1		8	9.4	even	3

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:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	450.p (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{2} +(-0.599900 - 1.62484i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-1.00000 - 1.41421i) q^{6} +(-1.18034 - 4.40508i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.28024 + 1.94949i) q^{9} +O(q^{10})\)	\(q+(0.965926 - 0.258819i) q^{2} +(-0.599900 - 1.62484i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-1.00000 - 1.41421i) q^{6} +(-1.18034 - 4.40508i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.28024 + 1.94949i) q^{9} +(-0.550510 - 0.317837i) q^{11} +(-1.33195 - 1.10721i) q^{12} +(-0.896575 + 3.34607i) q^{13} +(-2.28024 - 3.94949i) q^{14} +(0.500000 - 0.866025i) q^{16} +(0.317837 + 0.317837i) q^{17} +(-1.69798 + 2.47323i) q^{18} -6.44949i q^{19} +(-6.44949 + 4.56048i) q^{21} +(-0.614014 - 0.164525i) q^{22} +(0.965926 + 0.258819i) q^{23} +(-1.57313 - 0.724745i) q^{24} +3.46410i q^{26} +(4.53553 + 2.53553i) q^{27} +(-3.22474 - 3.22474i) q^{28} +(0.158919 - 0.275255i) q^{29} +(-0.224745 - 0.389270i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-0.186185 + 1.08516i) q^{33} +(0.389270 + 0.224745i) q^{34} +(-1.00000 + 2.82843i) q^{36} +(3.00000 - 3.00000i) q^{37} +(-1.66925 - 6.22973i) q^{38} +(5.97469 - 0.550510i) q^{39} +(6.39898 - 3.69445i) q^{41} +(-5.04939 + 6.07433i) q^{42} +(-3.34607 + 0.896575i) q^{43} -0.635674 q^{44} +1.00000 q^{46} +(8.69333 - 2.32937i) q^{47} +(-1.70711 - 0.292893i) q^{48} +(-11.9494 + 6.89898i) q^{49} +(0.325765 - 0.707107i) q^{51} +(0.896575 + 3.34607i) q^{52} +(3.78194 - 3.78194i) q^{53} +(5.03723 + 1.27526i) q^{54} +(-3.94949 - 2.28024i) q^{56} +(-10.4794 + 3.86905i) q^{57} +(0.0822623 - 0.307007i) q^{58} +(4.48905 + 7.77526i) q^{59} +(0.275255 - 0.476756i) q^{61} +(-0.317837 - 0.317837i) q^{62} +(11.2791 + 7.74358i) q^{63} -1.00000i q^{64} +(0.101021 + 1.09638i) q^{66} +(-6.38512 - 1.71089i) q^{67} +(0.434174 + 0.116337i) q^{68} +(-0.158919 - 1.72474i) q^{69} +6.29253i q^{71} +(-0.233875 + 2.99087i) q^{72} +(6.89898 + 6.89898i) q^{73} +(2.12132 - 3.67423i) q^{74} +(-3.22474 - 5.58542i) q^{76} +(-0.750311 + 2.80020i) q^{77} +(5.62863 - 2.07812i) q^{78} +(2.12132 + 1.22474i) q^{79} +(1.39898 - 8.89060i) q^{81} +(5.22474 - 5.22474i) q^{82} +(-1.41043 - 5.26380i) q^{83} +(-3.30518 + 7.17423i) q^{84} +(-3.00000 + 1.73205i) q^{86} +(-0.542582 - 0.0930924i) q^{87} +(-0.614014 + 0.164525i) q^{88} +8.02458 q^{89} +15.7980 q^{91} +(0.965926 - 0.258819i) q^{92} +(-0.497678 + 0.598698i) q^{93} +(7.79423 - 4.50000i) q^{94} +(-1.72474 + 0.158919i) q^{96} +(-0.695075 - 2.59405i) q^{97} +(-9.75663 + 9.75663i) q^{98} +(1.87492 - 0.348469i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} - 8 q^{6} + 8 q^{7}+O(q^{10}) \) 8 * q - 4 * q^3 - 8 * q^6 + 8 * q^7	\( 8 q - 4 q^{3} - 8 q^{6} + 8 q^{7} - 24 q^{11} + 4 q^{12} + 4 q^{16} + 8 q^{18} - 32 q^{21} + 8 q^{22} + 8 q^{27} - 16 q^{28} + 8 q^{31} - 16 q^{33} - 8 q^{36} + 24 q^{37} - 12 q^{38} + 12 q^{41} - 20 q^{42} + 8 q^{46} - 8 q^{48} + 32 q^{51} - 12 q^{56} - 28 q^{57} + 4 q^{58} + 12 q^{61} + 32 q^{63} + 40 q^{66} - 4 q^{67} + 12 q^{68} - 8 q^{72} + 16 q^{73} - 16 q^{76} - 24 q^{77} + 24 q^{78} - 28 q^{81} + 32 q^{82} - 12 q^{83} - 24 q^{86} + 8 q^{87} + 8 q^{88} + 48 q^{91} + 20 q^{93} - 4 q^{96} - 12 q^{97}+O(q^{100}) \) 8 * q - 4 * q^3 - 8 * q^6 + 8 * q^7 - 24 * q^11 + 4 * q^12 + 4 * q^16 + 8 * q^18 - 32 * q^21 + 8 * q^22 + 8 * q^27 - 16 * q^28 + 8 * q^31 - 16 * q^33 - 8 * q^36 + 24 * q^37 - 12 * q^38 + 12 * q^41 - 20 * q^42 + 8 * q^46 - 8 * q^48 + 32 * q^51 - 12 * q^56 - 28 * q^57 + 4 * q^58 + 12 * q^61 + 32 * q^63 + 40 * q^66 - 4 * q^67 + 12 * q^68 - 8 * q^72 + 16 * q^73 - 16 * q^76 - 24 * q^77 + 24 * q^78 - 28 * q^81 + 32 * q^82 - 12 * q^83 - 24 * q^86 + 8 * q^87 + 8 * q^88 + 48 * q^91 + 20 * q^93 - 4 * q^96 - 12 * q^97

Introduction

L-functions

Modular forms

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