LMFDB - Embedded newform 450.2.p.a.407.2

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			407.2
Root			$-0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	450.407
Dual form			450.2.p.a.293.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 + 0.965926i) q^{2} +(-1.62484 + 0.599900i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-1.00000 - 1.41421i) q^{6} +(4.40508 - 1.18034i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.28024 - 1.94949i) q^{9} +O(q^{10})$	\(q+(0.258819 + 0.965926i) q^{2} +(-1.62484 + 0.599900i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-1.00000 - 1.41421i) q^{6} +(4.40508 - 1.18034i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.28024 - 1.94949i) q^{9} +(-0.550510 - 0.317837i) q^{11} +(1.10721 - 1.33195i) q^{12} +(3.34607 + 0.896575i) q^{13} +(2.28024 + 3.94949i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-0.317837 + 0.317837i) q^{17} +(2.47323 + 1.69798i) q^{18} +6.44949i q^{19} +(-6.44949 + 4.56048i) q^{21} +(0.164525 - 0.614014i) q^{22} +(0.258819 - 0.965926i) q^{23} +(1.57313 + 0.724745i) q^{24} +3.46410i q^{26} +(-2.53553 + 4.53553i) q^{27} +(-3.22474 + 3.22474i) q^{28} +(-0.158919 + 0.275255i) q^{29} +(-0.224745 - 0.389270i) q^{31} +(0.965926 + 0.258819i) q^{32} +(1.08516 + 0.186185i) q^{33} +(-0.389270 - 0.224745i) q^{34} +(-1.00000 + 2.82843i) q^{36} +(3.00000 + 3.00000i) q^{37} +(-6.22973 + 1.66925i) q^{38} +(-5.97469 + 0.550510i) q^{39} +(6.39898 - 3.69445i) q^{41} +(-6.07433 - 5.04939i) q^{42} +(0.896575 + 3.34607i) q^{43} +0.635674 q^{44} +1.00000 q^{46} +(2.32937 + 8.69333i) q^{47} +(-0.292893 + 1.70711i) q^{48} +(11.9494 - 6.89898i) q^{49} +(0.325765 - 0.707107i) q^{51} +(-3.34607 + 0.896575i) q^{52} +(-3.78194 - 3.78194i) q^{53} +(-5.03723 - 1.27526i) q^{54} +(-3.94949 - 2.28024i) q^{56} +(-3.86905 - 10.4794i) q^{57} +(-0.307007 - 0.0822623i) q^{58} +(-4.48905 - 7.77526i) q^{59} +(0.275255 - 0.476756i) q^{61} +(0.317837 - 0.317837i) q^{62} +(7.74358 - 11.2791i) q^{63} +1.00000i q^{64} +(0.101021 + 1.09638i) q^{66} +(1.71089 - 6.38512i) q^{67} +(0.116337 - 0.434174i) q^{68} +(0.158919 + 1.72474i) q^{69} +6.29253i q^{71} +(-2.99087 - 0.233875i) q^{72} +(6.89898 - 6.89898i) q^{73} +(-2.12132 + 3.67423i) q^{74} +(-3.22474 - 5.58542i) q^{76} +(-2.80020 - 0.750311i) q^{77} +(-2.07812 - 5.62863i) q^{78} +(-2.12132 - 1.22474i) q^{79} +(1.39898 - 8.89060i) q^{81} +(5.22474 + 5.22474i) q^{82} +(-5.26380 + 1.41043i) q^{83} +(3.30518 - 7.17423i) q^{84} +(-3.00000 + 1.73205i) q^{86} +(0.0930924 - 0.542582i) q^{87} +(0.164525 + 0.614014i) q^{88} -8.02458 q^{89} +15.7980 q^{91} +(0.258819 + 0.965926i) q^{92} +(0.598698 + 0.497678i) q^{93} +(-7.79423 + 4.50000i) q^{94} +(-1.72474 + 0.158919i) q^{96} +(2.59405 - 0.695075i) 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 $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$3$	−1.62484	+	0.599900i	−0.938104	+	0.346353i
$3$	−1.62484	+	0.599900i	−0.938104	+	0.346353i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$	−1.00000	−	1.41421i	−0.408248	−	0.577350i
$7$	4.40508	−	1.18034i	1.66497	−	0.446126i	0.701219	−	0.712946i	$-0.252640\pi$
$7$	4.40508	−	1.18034i	1.66497	−	0.446126i	0.963746	+	0.266820i	$0.0859730\pi$
$8$	−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	$0.697218\pi$
$12$	1.10721	−	1.33195i	0.319623	−	0.384501i
$13$	3.34607	+	0.896575i	0.928032	+	0.248665i	0.691015	−	0.722840i	$-0.257164\pi$
$13$	3.34607	+	0.896575i	0.928032	+	0.248665i	0.237016	+	0.971506i	$0.423830\pi$
$14$	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	$-0.767359\pi$
$17$	−0.317837	+	0.317837i	−0.0770869	+	0.0770869i	0.667512	+	0.744599i	$0.267359\pi$
$18$	2.47323	+	1.69798i	0.582946	+	0.400217i
$19$			6.44949i			1.47961i	0.672819	+	0.739807i	$0.265083\pi$
$19$			6.44949i			1.47961i	−0.672819	+	0.739807i	$0.734917\pi$
$20$		0			0
$21$	−6.44949	+	4.56048i	−1.40739	+	0.995178i
$22$	0.164525	−	0.614014i	0.0350768	−	0.130908i
$23$	0.258819	−	0.965926i	0.0539675	−	0.201409i	−0.933678	−	0.358113i	$-0.883420\pi$
$23$	0.258819	−	0.965926i	0.0539675	−	0.201409i	0.987646	+	0.156704i	$0.0500868\pi$
$24$	1.57313	+	0.724745i	0.321114	+	0.147938i
$25$		0			0
$26$			3.46410i			0.679366i
$27$	−2.53553	+	4.53553i	−0.487964	+	0.872864i
$28$	−3.22474	+	3.22474i	−0.609419	+	0.609419i
$29$	−0.158919	+	0.275255i	−0.0295104	+	0.0511136i	−0.880403	−	0.474225i	$-0.842728\pi$
$29$	−0.158919	+	0.275255i	−0.0295104	+	0.0511136i	0.850893	+	0.525339i	$0.176061\pi$
$30$		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	$0.846186\pi$
$32$	0.965926	+	0.258819i	0.170753	+	0.0457532i
$33$	1.08516	+	0.186185i	0.188903	+	0.0324106i
$34$	−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	0.909312	−	0.416115i	$-0.136609\pi$
$37$	3.00000	+	3.00000i	0.493197	+	0.493197i	−0.416115	+	0.909312i	$0.636609\pi$
$38$	−6.22973	+	1.66925i	−1.01060	+	0.270788i
$39$	−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	$0.137566\pi$
$42$	−6.07433	−	5.04939i	−0.937290	−	0.779138i
$43$	0.896575	+	3.34607i	0.136726	+	0.510270i	0.999985	+	0.00550783i	$0.00175320\pi$
$43$	0.896575	+	3.34607i	0.136726	+	0.510270i	−0.863258	+	0.504762i	$0.831580\pi$
$44$	0.635674			0.0958315
$45$		0			0
$46$	1.00000			0.147442
$47$	2.32937	+	8.69333i	0.339774	+	1.26805i	0.898600	+	0.438768i	$0.144585\pi$
$47$	2.32937	+	8.69333i	0.339774	+	1.26805i	−0.558827	+	0.829285i	$0.688748\pi$
$48$	−0.292893	+	1.70711i	−0.0422755	+	0.246400i
$49$	11.9494	−	6.89898i	1.70705	−	0.985568i
$50$		0			0
$51$	0.325765	−	0.707107i	0.0456163	−	0.0990148i
$52$	−3.34607	+	0.896575i	−0.464016	+	0.124333i
$53$	−3.78194	−	3.78194i	−0.519489	−	0.519489i	0.397928	−	0.917417i	$-0.369730\pi$
$53$	−3.78194	−	3.78194i	−0.519489	−	0.519489i	−0.917417	+	0.397928i	$0.869730\pi$
$54$	−5.03723	−	1.27526i	−0.685481	−	0.173540i
$55$		0			0
$56$	−3.94949	−	2.28024i	−0.527773	−	0.304710i
$57$	−3.86905	−	10.4794i	−0.512468	−	1.38803i
$58$	−0.307007	−	0.0822623i	−0.0403120	−	0.0108016i
$59$	−4.48905	−	7.77526i	−0.584424	−	1.01225i	−0.994947	−	0.100402i	$-0.967987\pi$
$59$	−4.48905	−	7.77526i	−0.584424	−	1.01225i	0.410523	−	0.911850i	$-0.365346\pi$
$60$		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
$63$	7.74358	−	11.2791i	0.975600	−	1.42104i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	0.101021	+	1.09638i	0.0124348	+	0.134955i
$67$	1.71089	−	6.38512i	0.209018	−	0.780067i	−0.779169	−	0.626814i	$-0.784358\pi$
$67$	1.71089	−	6.38512i	0.209018	−	0.780067i	0.988187	−	0.153253i	$-0.0489748\pi$
$68$	0.116337	−	0.434174i	0.0141079	−	0.0526513i
$69$	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	$0.878194\pi$
$72$	−2.99087	−	0.233875i	−0.352477	−	0.0275624i
$73$	6.89898	−	6.89898i	0.807464	−	0.807464i	−0.176785	−	0.984249i	$-0.556570\pi$
$73$	6.89898	−	6.89898i	0.807464	−	0.807464i	0.984249	+	0.176785i	$0.0565697\pi$
$74$	−2.12132	+	3.67423i	−0.246598	+	0.427121i
$75$		0			0
$76$	−3.22474	−	5.58542i	−0.369904	−	0.640692i
$77$	−2.80020	−	0.750311i	−0.319112	−	0.0855059i
$78$	−2.07812	−	5.62863i	−0.235300	−	0.637316i
$79$	−2.12132	−	1.22474i	−0.238667	−	0.137795i	0.375897	−	0.926662i	$-0.377335\pi$
$79$	−2.12132	−	1.22474i	−0.238667	−	0.137795i	−0.614564	+	0.788867i	$0.710668\pi$
$80$		0			0
$81$	1.39898	−	8.89060i	0.155442	−	0.987845i
$82$	5.22474	+	5.22474i	0.576977	+	0.576977i
$83$	−5.26380	+	1.41043i	−0.577777	+	0.154815i	−0.535861	−	0.844306i	$-0.680013\pi$
$83$	−5.26380	+	1.41043i	−0.577777	+	0.154815i	−0.0419163	+	0.999121i	$0.513346\pi$
$84$	3.30518	−	7.17423i	0.360625	−	0.782773i
$85$		0			0
$86$	−3.00000	+	1.73205i	−0.323498	+	0.186772i
$87$	0.0930924	−	0.542582i	0.00998055	−	0.0581709i
$88$	0.164525	+	0.614014i	0.0175384	+	0.0654542i
$89$	−8.02458			−0.850604			−0.425302	−	0.905052i	$-0.639832\pi$
$89$	−8.02458			−0.850604			−0.425302	+	0.905052i	$0.639832\pi$
$90$		0			0
$91$	15.7980			1.65608
$92$	0.258819	+	0.965926i	0.0269838	+	0.100705i
$93$	0.598698	+	0.497678i	0.0620821	+	0.0516068i
$94$	−7.79423	+	4.50000i	−0.803913	+	0.464140i
$95$		0			0
$96$	−1.72474	+	0.158919i	−0.176031	+	0.0162196i
$97$	2.59405	−	0.695075i	0.263386	−	0.0705741i	−0.124709	−	0.992193i	$-0.539800\pi$
$97$	2.59405	−	0.695075i	0.263386	−	0.0705741i	0.388095	+	0.921619i	$0.373133\pi$
$98$	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	$0.451305\pi$
$102$	0.767327	+	0.131652i	0.0759767	+	0.0130355i
$103$	−9.42418	−	2.52520i	−0.928592	−	0.248816i	−0.237338	−	0.971427i	$-0.576275\pi$
$103$	−9.42418	−	2.52520i	−0.928592	−	0.248816i	−0.691254	+	0.722612i	$0.742942\pi$
$104$	−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	−0.398606	+	0.917122i	$0.630506\pi$
$107$	−13.6100	+	13.6100i	−1.31573	+	1.31573i	−0.917122	+	0.398606i	$0.869494\pi$
$108$	−0.0719302	−	5.19565i	−0.00692148	−	0.499952i
$109$		−	5.65153i		−	0.541318i	−0.962675	−	0.270659i	$-0.912758\pi$
$109$		−	5.65153i		−	0.541318i	0.962675	−	0.270659i	$-0.0872417\pi$
$110$		0			0
$111$	−6.67423	−	3.07483i	−0.633490	−	0.291850i
$112$	1.18034	−	4.40508i	0.111532	−	0.416241i
$113$	1.50062	−	5.60040i	0.141167	−	0.526841i	−0.858729	−	0.512429i	$-0.828746\pi$
$113$	1.50062	−	5.60040i	0.141167	−	0.526841i	0.999896	−	0.0144120i	$-0.00458763\pi$
$114$	9.12096	−	6.44949i	0.854256	−	0.604050i
$115$		0			0
$116$		−	0.317837i		−	0.0295104i
$117$	9.37769	−	4.47871i	0.866968	−	0.414057i
$118$	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
$122$	0.531752	+	0.142483i	0.0481426	+	0.0128998i
$123$	−8.18104	+	9.84166i	−0.737660	+	0.887393i
$124$	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	0.618943	−	0.785436i	$-0.287561\pi$
$127$	−1.87628	−	1.87628i	−0.166493	−	0.166493i	−0.785436	+	0.618943i	$0.787561\pi$
$128$	−0.965926	+	0.258819i	−0.0853766	+	0.0228766i
$129$	−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	$0.383700\pi$
$132$	−1.03287	+	0.381341i	−0.0899000	+	0.0331915i
$133$	7.61258	+	28.4105i	0.660095	+	2.46351i
$134$	6.61037			0.571049
$135$		0			0
$136$	0.449490			0.0385434
$137$	−5.64173	−	21.0552i	−0.482005	−	1.79887i	−0.593183	−	0.805068i	$-0.702129\pi$
$137$	−5.64173	−	21.0552i	−0.482005	−	1.79887i	0.111178	−	0.993801i	$-0.464538\pi$
$138$	−1.62484	+	0.599900i	−0.138316	+	0.0510669i
$139$	2.68556	−	1.55051i	0.227786	−	0.131513i	−0.381764	−	0.924260i	$-0.624683\pi$
$139$	2.68556	−	1.55051i	0.227786	−	0.131513i	0.609550	+	0.792747i	$0.291350\pi$
$140$		0			0
$141$	−9.00000	−	12.7279i	−0.757937	−	1.07188i
$142$	−6.07812	+	1.62863i	−0.510064	+	0.136671i
$143$	−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
$147$	−15.2772	+	18.3782i	−1.26004	+	1.51581i
$148$	−4.09808	−	1.09808i	−0.336860	−	0.0902613i
$149$	2.20881	+	3.82577i	0.180952	+	0.313419i	0.942205	−	0.335036i	$-0.108749\pi$
$149$	2.20881	+	3.82577i	0.180952	+	0.313419i	−0.761253	+	0.648455i	$0.775415\pi$
$150$		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
$153$	−0.105124	+	1.34437i	−0.00849881	+	0.108685i
$154$		−	2.89898i		−	0.233606i
$155$		0			0
$156$	4.89898	−	3.46410i	0.392232	−	0.277350i
$157$	3.78780	−	14.1363i	0.302300	−	1.12820i	−0.632945	−	0.774196i	$-0.718154\pi$
$157$	3.78780	−	14.1363i	0.302300	−	1.12820i	0.935245	−	0.354001i	$-0.115179\pi$
$158$	0.633975	−	2.36603i	0.0504363	−	0.188231i
$159$	8.41385	+	3.87628i	0.667262	+	0.307409i
$160$		0			0
$161$		−	4.56048i		−	0.359416i
$162$	8.94975	−	0.949747i	0.703159	−	0.0746192i
$163$	−4.44949	+	4.44949i	−0.348511	+	0.348511i	−0.859555	−	0.511044i	$-0.829259\pi$
$163$	−4.44949	+	4.44949i	−0.348511	+	0.348511i	0.511044	+	0.859555i	$0.329259\pi$
$164$	−3.69445	+	6.39898i	−0.288488	+	0.499676i
$165$		0			0
$166$	−2.72474	−	4.71940i	−0.211481	−	0.366296i
$167$	8.49818	+	2.27708i	0.657609	+	0.176206i	0.572167	−	0.820137i	$-0.306103\pi$
$167$	8.49818	+	2.27708i	0.657609	+	0.176206i	0.0854420	+	0.996343i	$0.472770\pi$
$168$	7.78522	+	1.33573i	0.600643	+	0.103054i
$169$	−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
$173$	12.4595	−	3.33850i	0.947275	−	0.253822i	0.248069	−	0.968742i	$-0.420204\pi$
$173$	12.4595	−	3.33850i	0.947275	−	0.253822i	0.699206	+	0.714921i	$0.253537\pi$
$174$	0.548188	−	0.0505103i	0.0415580	−	0.00382917i
$175$		0			0
$176$	−0.550510	+	0.317837i	−0.0414963	+	0.0239579i
$177$	11.9584	+	9.94060i	0.898847	+	0.747181i
$178$	−2.07691	−	7.75115i	−0.155671	−	0.580973i
$179$	10.6780			0.798114			0.399057	−	0.916926i	$-0.369338\pi$
$179$	10.6780			0.798114			0.399057	+	0.916926i	$0.369338\pi$
$180$		0			0
$181$	−15.4495			−1.14835			−0.574176	−	0.818732i	$-0.694677\pi$
$181$	−15.4495			−1.14835			−0.574176	+	0.818732i	$0.694677\pi$
$182$	4.08881	+	15.2597i	0.303083	+	1.13112i
$183$	−0.161241	+	0.939780i	−0.0119193	+	0.0694705i
$184$	−0.866025	+	0.500000i	−0.0638442	+	0.0368605i
$185$		0			0
$186$	−0.325765	+	0.707107i	−0.0238863	+	0.0518476i
$187$	0.275993	−	0.0739521i	0.0201826	−	0.00540792i
$188$	−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	$0.884351\pi$
$192$	−0.599900	−	1.62484i	−0.0432941	−	0.117263i
$193$	−16.7303	−	4.48288i	−1.20428	−	0.322685i	−0.399762	−	0.916619i	$-0.630907\pi$
$193$	−16.7303	−	4.48288i	−1.20428	−	0.322685i	−0.804513	+	0.593934i	$0.797574\pi$
$194$	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	$-0.863492\pi$
$197$	−6.92820	+	6.92820i	−0.493614	+	0.493614i	0.415829	+	0.909443i	$0.363492\pi$
$198$	−0.821859	−	1.72084i	−0.0584070	−	0.122295i
$199$			8.44949i			0.598968i	0.954101	+	0.299484i	$0.0968146\pi$
$199$			8.44949i			0.598968i	−0.954101	+	0.299484i	$0.903185\pi$
$200$		0			0
$201$	1.05051	+	11.4012i	0.0740973	+	0.804178i
$202$	−3.25725	+	12.1562i	−0.229179	+	0.855310i
$203$	−0.375156	+	1.40010i	−0.0263308	+	0.0982677i
$204$	0.0714323	+	0.775255i	0.00500126	+	0.0542787i
$205$		0			0
$206$		−	9.75663i		−	0.679777i
$207$	−1.29289	−	2.70711i	−0.0898623	−	0.188157i
$208$	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	$0.934758\pi$
$212$	5.16622	+	1.38429i	0.354818	+	0.0950731i
$213$	−3.77489	−	10.2244i	−0.258651	−	0.700563i
$214$	−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
$218$	5.45896	−	1.46272i	0.369727	−	0.0990682i
$219$	−7.07107	+	15.3485i	−0.477818	+	1.03715i
$220$		0			0
$221$	−1.34847	+	0.778539i	−0.0907079	+	0.0523702i
$222$	1.24264	−	7.24264i	0.0834006	−	0.486094i
$223$	−6.63374	−	24.7575i	−0.444228	−	1.65788i	−0.717966	−	0.696078i	$-0.754927\pi$
$223$	−6.63374	−	24.7575i	−0.444228	−	1.65788i	0.273738	−	0.961804i	$-0.411740\pi$
$224$	4.56048			0.304710
$225$		0			0
$226$	5.79796			0.385674
$227$	−6.44433	−	24.0506i	−0.427725	−	1.59629i	−0.757899	−	0.652372i	$-0.773774\pi$
$227$	−6.44433	−	24.0506i	−0.427725	−	1.59629i	0.330174	−	0.943920i	$-0.392893\pi$
$228$	8.59041	+	7.14092i	0.568914	+	0.472919i
$229$	−1.43027	+	0.825765i	−0.0945147	+	0.0545681i	−0.546512	−	0.837451i	$-0.684045\pi$
$229$	−1.43027	+	0.825765i	−0.0945147	+	0.0545681i	0.451998	+	0.892019i	$0.350712\pi$
$230$		0			0
$231$	5.00000	−	0.460702i	0.328976	−	0.0303120i
$232$	0.307007	−	0.0822623i	0.0201560	−	0.00540079i
$233$	14.4600	+	14.4600i	0.947304	+	0.947304i	0.998679	−	0.0513751i	$-0.0163604\pi$
$233$	14.4600	+	14.4600i	0.947304	+	0.947304i	−0.0513751	+	0.998679i	$0.516360\pi$
$234$	6.75323	+	7.89898i	0.441472	+	0.516372i
$235$		0			0
$236$	7.77526	+	4.48905i	0.506126	+	0.292212i
$237$	4.18154	+	0.717439i	0.271620	+	0.0466027i
$238$	−1.98004	−	0.530550i	−0.128347	−	0.0343905i
$239$	−8.48528	−	14.6969i	−0.548867	−	0.950666i	−0.998353	−	0.0573782i	$-0.981726\pi$
$239$	−8.48528	−	14.6969i	−0.548867	−	0.950666i	0.449485	−	0.893288i	$-0.351607\pi$
$240$		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
$243$	3.06035	+	15.2851i	0.196322	+	0.980540i
$244$			0.550510i			0.0352428i
$245$		0			0
$246$	−11.6237	−	5.35507i	−0.741102	−	0.341427i
$247$	−5.78245	+	21.5804i	−0.367929	+	1.37313i
$248$	−0.116337	+	0.434174i	−0.00738738	+	0.0275701i
$249$	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	$0.972989\pi$
$252$	−1.06658	+	13.6398i	−0.0671883	+	0.859226i
$253$	−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
$257$	17.4305	+	4.67050i	1.08729	+	0.291337i	0.757578	−	0.652745i	$-0.226383\pi$
$257$	17.4305	+	4.67050i	1.08729	+	0.291337i	0.329709	+	0.944083i	$0.393049\pi$
$258$	3.83548	−	4.61401i	0.238786	−	0.287256i
$259$	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
$263$	−16.1280	+	4.32149i	−0.994495	+	0.266474i	−0.719138	−	0.694868i	$-0.755463\pi$
$263$	−16.1280	+	4.32149i	−0.994495	+	0.266474i	−0.275358	+	0.961342i	$0.588796\pi$
$264$	−0.635674	−	0.898979i	−0.0391231	−	0.0553284i
$265$		0			0
$266$	−25.4722	+	14.7064i	−1.56180	+	0.901706i
$267$	13.0387	−	4.81395i	0.797955	−	0.294609i
$268$	1.71089	+	6.38512i	0.104509	+	0.390033i
$269$	−15.0956			−0.920398			−0.460199	−	0.887816i	$-0.652222\pi$
$269$	−15.0956			−0.920398			−0.460199	+	0.887816i	$0.652222\pi$
$270$		0			0
$271$	28.0454			1.70364			0.851819	−	0.523837i	$-0.175500\pi$
$271$	28.0454			1.70364			0.851819	+	0.523837i	$0.175500\pi$
$272$	0.116337	+	0.434174i	0.00705394	+	0.0263257i
$273$	−25.6692	+	9.47720i	−1.55357	+	0.573586i
$274$	18.8776	−	10.8990i	1.14044	−	0.658431i
$275$		0			0
$276$	−1.00000	−	1.41421i	−0.0601929	−	0.0851257i
$277$	−27.1825	+	7.28353i	−1.63324	+	0.437625i	−0.954852	−	0.297080i	$-0.903987\pi$
$277$	−27.1825	+	7.28353i	−1.63324	+	0.437625i	−0.678386	+	0.734705i	$0.737320\pi$
$278$	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	$0.837543\pi$
$282$	9.96486	−	11.9876i	0.593399	−	0.713849i
$283$	23.3914	+	6.26772i	1.39048	+	0.372577i	0.874916	−	0.484275i	$-0.160917\pi$
$283$	23.3914	+	6.26772i	1.39048	+	0.372577i	0.515561	+	0.856853i	$0.327583\pi$
$284$	−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
$288$	2.70711	−	1.29289i	0.159518	−	0.0761845i
$289$			16.7980i			0.988115i
$290$		0			0
$291$	−3.79796	+	2.68556i	−0.222640	+	0.157430i
$292$	−2.52520	+	9.42418i	−0.147776	+	0.551508i
$293$	−5.70577	+	21.2942i	−0.333335	+	1.24402i	0.572329	+	0.820024i	$0.306040\pi$
$293$	−5.70577	+	21.2942i	−0.333335	+	1.24402i	−0.905663	+	0.423998i	$0.860626\pi$
$294$	−21.7060	−	10.0000i	−1.26592	−	0.583212i
$295$		0			0
$296$		−	4.24264i		−	0.246598i
$297$	2.83740	−	1.69097i	0.164643	−	0.0981201i
$298$	−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
$302$	−16.9964	−	4.55416i	−0.978030	−	0.262062i
$303$	−21.4840	−	3.68608i	−1.23423	−	0.211760i
$304$	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	0.871433	−	0.490514i	$-0.163191\pi$
$307$	6.67423	+	6.67423i	0.380919	+	0.380919i	−0.490514	+	0.871433i	$0.663191\pi$
$308$	2.80020	−	0.750311i	0.159556	−	0.0427529i
$309$	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	$0.0486269\pi$
$312$	4.61401	+	3.83548i	0.261217	+	0.217141i
$313$	−3.09273	−	11.5422i	−0.174811	−	0.652405i	−0.996584	−	0.0825888i	$-0.973681\pi$
$313$	−3.09273	−	11.5422i	−0.174811	−	0.652405i	0.821772	−	0.569816i	$-0.192985\pi$
$314$	14.6349			0.825898
$315$		0			0
$316$	2.44949			0.137795
$317$	2.82086	+	10.5276i	0.158435	+	0.591289i	0.998787	+	0.0492469i	$0.0156821\pi$
$317$	2.82086	+	10.5276i	0.158435	+	0.591289i	−0.840351	+	0.542042i	$0.817651\pi$
$318$	−1.56653	+	9.13041i	−0.0878467	+	0.512008i
$319$	0.174973	−	0.101021i	0.00979659	−	0.00565606i
$320$		0			0
$321$	13.9495	−	30.2788i	0.778585	−	1.69000i
$322$	4.40508	−	1.18034i	0.245486	−	0.0657777i
$323$	−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
$327$	3.39036	+	9.18286i	0.187487	+	0.507813i
$328$	−7.13713	−	1.91239i	−0.394082	−	0.105594i
$329$	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
$333$	12.6892	+	0.992248i	0.695363	+	0.0543748i
$334$			8.79796i			0.481403i
$335$		0			0
$336$	0.724745	+	7.86566i	0.0395381	+	0.429107i
$337$	0.806003	−	3.00804i	0.0439058	−	0.163859i	−0.940492	−	0.339816i	$-0.889635\pi$
$337$	0.806003	−	3.00804i	0.0439058	−	0.163859i	0.984398	+	0.175957i	$0.0563020\pi$
$338$	0.258819	−	0.965926i	0.0140779	−	0.0525394i
$339$	0.921404	+	10.0000i	0.0500438	+	0.543125i
$340$		0			0
$341$			0.285729i			0.0154731i
$342$	−10.9511	+	15.9511i	−0.592167	+	0.862536i
$343$	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
$347$	−22.9871	−	6.15937i	−1.23401	−	0.330652i	−0.417870	−	0.908507i	$-0.637223\pi$
$347$	−22.9871	−	6.15937i	−1.23401	−	0.330652i	−0.816140	+	0.577855i	$0.803890\pi$
$348$	0.190671	+	0.516436i	0.0102210	+	0.0276839i
$349$	−25.1541	−	14.5227i	−1.34647	−	0.777383i	−0.358719	−	0.933446i	$-0.616786\pi$
$349$	−25.1541	−	14.5227i	−1.34647	−	0.777383i	−0.987747	+	0.156063i	$0.950120\pi$
$350$		0			0
$351$	−12.5505	+	12.9029i	−0.669897	+	0.688706i
$352$	−0.449490	−	0.449490i	−0.0239579	−	0.0239579i
$353$	33.1244	−	8.87564i	1.76303	−	0.472403i	0.775704	−	0.631097i	$-0.217395\pi$
$353$	33.1244	−	8.87564i	1.76303	−	0.472403i	0.987328	+	0.158694i	$0.0507284\pi$
$354$	−6.50683	+	14.1237i	−0.345834	+	0.750667i
$355$		0			0
$356$	6.94949	−	4.01229i	0.368322	−	0.212651i
$357$	0.600398	−	3.49938i	0.0317764	−	0.185207i
$358$	2.76368	+	10.3142i	0.146065	+	0.545122i
$359$	3.32124			0.175288			0.0876441	−	0.996152i	$-0.472066\pi$
$359$	3.32124			0.175288			0.0876441	+	0.996152i	$0.472066\pi$
$360$		0			0
$361$	−22.5959			−1.18926
$362$	−3.99862	−	14.9231i	−0.210163	−	0.784339i
$363$	14.1132	+	11.7319i	0.740753	+	0.615763i
$364$	−13.6814	+	7.89898i	−0.717102	+	0.414019i
$365$		0			0
$366$	−0.949490	+	0.0874863i	−0.0496306	+	0.00457298i
$367$	−3.96008	+	1.06110i	−0.206714	+	0.0553890i	−0.360690	−	0.932686i	$-0.617459\pi$
$367$	−3.96008	+	1.06110i	−0.206714	+	0.0553890i	0.153976	+	0.988075i	$0.450792\pi$
$368$	−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
$372$	−0.767327	−	0.131652i	−0.0397841	−	0.00682586i
$373$	−0.476018	−	0.127549i	−0.0246473	−	0.00660422i	0.246474	−	0.969149i	$-0.420728\pi$
$373$	−0.476018	−	0.127549i	−0.0246473	−	0.00660422i	−0.271122	+	0.962545i	$0.587395\pi$
$374$	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
$378$	−23.6947	+	0.328036i	−1.21872	+	0.0168724i
$379$		−	21.3485i		−	1.09660i	−0.836283	−	0.548299i	$-0.815276\pi$
$379$		−	21.3485i		−	1.09660i	0.836283	−	0.548299i	$-0.184724\pi$
$380$		0			0
$381$	4.17423	+	1.92308i	0.213853	+	0.0985222i
$382$	4.51985	−	16.8683i	0.231256	−	0.863058i
$383$	2.12284	−	7.92256i	0.108472	−	0.404824i	−0.890244	−	0.455485i	$-0.849466\pi$
$383$	2.12284	−	7.92256i	0.108472	−	0.404824i	0.998716	+	0.0506606i	$0.0161327\pi$
$384$	1.41421	−	1.00000i	0.0721688	−	0.0510310i
$385$		0			0
$386$		−	17.3205i		−	0.881591i
$387$	8.56753	+	5.88196i	0.435512	+	0.298997i
$388$	−1.89898	+	1.89898i	−0.0964061	+	0.0964061i
$389$	18.4008	−	31.8712i	0.932959	−	1.61593i	0.154726	−	0.987957i	$-0.450551\pi$
$389$	18.4008	−	31.8712i	0.932959	−	1.61593i	0.778233	−	0.627975i	$-0.216116\pi$
$390$		0			0
$391$	0.224745	+	0.389270i	0.0113658	+	0.0196862i
$392$	−13.3278	−	3.57117i	−0.673156	−	0.180372i
$393$	3.99366	−	4.80430i	0.201453	−	0.242345i
$394$	−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	0.390913	−	0.920428i	$-0.372159\pi$
$397$	−10.5505	−	10.5505i	−0.529515	−	0.529515i	−0.920428	+	0.390913i	$0.872159\pi$
$398$	−8.16158	+	2.18689i	−0.409103	+	0.109619i
$399$	−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	$0.262530\pi$
$402$	−10.7408	+	3.96556i	−0.535703	+	0.197784i
$403$	−0.403001	−	1.50402i	−0.0200749	−	0.0749207i
$404$	−12.5851			−0.626130
$405$		0			0
$406$	−1.44949			−0.0719370
$407$	−0.698019	−	2.60504i	−0.0345995	−	0.129127i
$408$	−0.730351	+	0.269649i	−0.0361578	+	0.0133496i
$409$	−25.0273	+	14.4495i	−1.23752	+	0.714481i	−0.968586	−	0.248678i	$-0.920004\pi$
$409$	−25.0273	+	14.4495i	−1.23752	+	0.714481i	−0.268932	+	0.963159i	$0.586671\pi$
$410$		0			0
$411$	21.7980	+	30.8270i	1.07521	+	1.52058i
$412$	9.42418	−	2.52520i	0.464296	−	0.124408i
$413$	−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
$417$	−3.43347	+	4.13041i	−0.168138	+	0.202267i
$418$	3.96008	+	1.06110i	0.193694	+	0.0519001i
$419$	2.51059	+	4.34847i	0.122650	+	0.212437i	0.920812	−	0.390007i	$-0.127527\pi$
$419$	2.51059	+	4.34847i	0.122650	+	0.212437i	−0.798162	+	0.602443i	$0.794194\pi$
$420$		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
$423$	22.2591	+	15.2818i	1.08227	+	0.743026i
$424$			5.34847i			0.259745i
$425$		0			0
$426$	8.89898	−	6.29253i	0.431157	−	0.304874i
$427$	0.649788	−	2.42504i	0.0314455	−	0.117356i
$428$	4.98161	−	18.5916i	0.240795	−	0.898659i
$429$	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	$-0.122241\pi$
$432$	2.66012	+	4.46360i	0.127985	+	0.214755i
$433$	−13.4495	+	13.4495i	−0.646341	+	0.646341i	−0.952107	−	0.305766i	$-0.901088\pi$
$433$	−13.4495	+	13.4495i	−0.646341	+	0.646341i	0.305766	+	0.952107i	$0.401088\pi$
$434$	1.02494	−	1.77526i	0.0491989	−	0.0852150i
$435$		0			0
$436$	2.82577	+	4.89437i	0.135330	+	0.234398i
$437$	6.22973	+	1.66925i	0.298008	+	0.0798511i
$438$	−16.6556	−	2.85765i	−0.795836	−	0.136544i
$439$	−25.8058	−	14.8990i	−1.23164	−	0.711089i	−0.264271	−	0.964449i	$-0.585131\pi$
$439$	−25.8058	−	14.8990i	−1.23164	−	0.711089i	−0.967372	+	0.253359i	$0.918465\pi$
$440$		0			0
$441$	13.7980	−	39.0265i	0.657046	−	1.85841i
$442$	−1.10102	−	1.10102i	−0.0523702	−	0.0523702i
$443$	5.26380	−	1.41043i	0.250091	−	0.0670116i	−0.131596	−	0.991303i	$-0.542010\pi$
$443$	5.26380	−	1.41043i	0.250091	−	0.0670116i	0.381687	+	0.924292i	$0.375343\pi$
$444$	7.31747	−	0.674235i	0.347272	−	0.0319978i
$445$		0			0
$446$	22.1969	−	12.8154i	1.05106	−	0.606827i
$447$	−5.88405	−	4.89121i	−0.278306	−	0.231346i
$448$	1.18034	+	4.40508i	0.0557658	+	0.208121i
$449$	0.921404			0.0434837			0.0217419	−	0.999764i	$-0.493079\pi$
$449$	0.921404			0.0434837			0.0217419	+	0.999764i	$0.493079\pi$
$450$		0			0
$451$	−4.69694			−0.221170
$452$	1.50062	+	5.60040i	0.0705833	+	0.263421i
$453$	5.15373	−	30.0381i	0.242143	−	1.41131i
$454$	21.5631	−	12.4495i	1.01201	−	0.584284i
$455$		0			0
$456$	−4.67423	+	10.1459i	−0.218891	+	0.475125i
$457$	−14.1363	+	3.78780i	−0.661267	+	0.177186i	−0.573818	−	0.818983i	$-0.694538\pi$
$457$	−14.1363	+	3.78780i	−0.661267	+	0.177186i	−0.0874492	+	0.996169i	$0.527872\pi$
$458$	−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	$0.387078\pi$
$462$	1.73910	+	4.71039i	0.0809102	+	0.219147i
$463$	−11.8182	−	3.16668i	−0.549239	−	0.147168i	−0.0264810	−	0.999649i	$-0.508430\pi$
$463$	−11.8182	−	3.16668i	−0.549239	−	0.147168i	−0.522758	+	0.852481i	$0.675097\pi$
$464$	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	$-0.779501\pi$
$467$	−2.82843	+	2.82843i	−0.130884	+	0.130884i	0.638630	+	0.769514i	$0.279501\pi$
$468$	−5.88196	+	8.56753i	−0.271894	+	0.396034i
$469$		−	30.1464i		−	1.39203i
$470$		0			0
$471$	2.32577	+	25.2415i	0.107166	+	1.16307i
$472$	−2.32370	+	8.67217i	−0.106957	+	0.399169i
$473$	0.569930	−	2.12701i	0.0262054	−	0.0977999i
$474$	0.389270	+	4.22474i	0.0178797	+	0.194049i
$475$		0			0
$476$		−	2.04989i		−	0.0939565i
$477$	−15.9966	−	1.25087i	−0.732433	−	0.0572736i
$478$	12.0000	−	12.0000i	0.548867	−	0.548867i
$479$	−3.53553	+	6.12372i	−0.161543	+	0.279800i	−0.935422	−	0.353533i	$-0.884980\pi$
$479$	−3.53553	+	6.12372i	−0.161543	+	0.279800i	0.773879	+	0.633333i	$0.218314\pi$
$480$		0			0
$481$	7.34847	+	12.7279i	0.335061	+	0.580343i
$482$	−18.3526	−	4.91756i	−0.835938	−	0.223989i
$483$	2.73583	+	7.41007i	0.124485	+	0.337170i
$484$	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	0.924632	−	0.380861i	$-0.124372\pi$
$487$	12.0000	+	12.0000i	0.543772	+	0.543772i	−0.380861	+	0.924632i	$0.624372\pi$
$488$	−0.531752	+	0.142483i	−0.0240713	+	0.00644988i
$489$	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	$0.551008\pi$
$492$	2.16416	−	12.6136i	0.0975679	−	0.568667i
$493$	−0.0369761	−	0.137997i	−0.00166532	−	0.00621505i
$494$	−22.3417			−1.00520
$495$		0			0
$496$	−0.449490			−0.0201827
$497$	7.42731	+	27.7191i	0.333161	+	1.24337i
$498$	7.25845	+	6.03371i	0.325259	+	0.270377i
$499$	0.778539	−	0.449490i	0.0348522	−	0.0201219i	−0.482473	−	0.875911i	$-0.660261\pi$
$499$	0.778539	−	0.449490i	0.0348522	−	0.0201219i	0.517325	+	0.855789i	$0.326928\pi$
$500$		0			0
$501$	−15.1742	+	1.39816i	−0.677935	+	0.0624652i
$502$	−2.59405	+	0.695075i	−0.115778	+	0.0310227i
$503$	−4.02834	−	4.02834i	−0.179615	−	0.179615i	0.611573	−	0.791188i	$-0.290537\pi$
$503$	−4.02834	−	4.02834i	−0.179615	−	0.179615i	−0.791188	+	0.611573i	$0.790537\pi$
$504$	−13.4511	+	2.50000i	−0.599159	+	0.111359i
$505$		0			0
$506$	−0.550510	−	0.317837i	−0.0244732	−	0.0141296i
$507$	1.70711	+	0.292893i	0.0758153	+	0.0130078i
$508$	2.56304	+	0.686765i	0.113717	+	0.0304702i
$509$	−4.22659	−	7.32066i	−0.187340	−	0.324483i	0.757022	−	0.653389i	$-0.226653\pi$
$509$	−4.22659	−	7.32066i	−0.187340	−	0.324483i	−0.944363	+	0.328906i	$0.893320\pi$
$510$		0			0
$511$	22.2474	−	38.5337i	0.984169	−	1.70463i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−29.2519	−	16.3529i	−1.29150	−	0.721998i
$514$			18.0454i			0.795949i
$515$		0			0
$516$	5.44949	+	2.51059i	0.239900	+	0.110523i
$517$	1.48072	−	5.52613i	0.0651221	−	0.243039i
$518$	−5.00775	+	18.6892i	−0.220028	+	0.821156i
$519$	−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	$0.776857\pi$
$522$	−0.860419	+	0.410930i	−0.0376595	+	0.0179859i
$523$	−4.22474	+	4.22474i	−0.184735	+	0.184735i	−0.793416	−	0.608680i	$-0.791699\pi$
$523$	−4.22474	+	4.22474i	−0.184735	+	0.184735i	0.608680	+	0.793416i	$0.291699\pi$
$524$	1.80348	−	3.12372i	0.0787855	−	0.136461i
$525$		0			0
$526$	−8.34847	−	14.4600i	−0.364011	−	0.630485i
$527$	0.195157	+	0.0522921i	0.00850116	+	0.00227788i
$528$	0.703823	−	0.846687i	0.0306300	−	0.0368473i
$529$	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
$533$	24.7238	−	6.62471i	1.07090	−	0.286948i
$534$	8.02458	+	11.3485i	0.347258	+	0.491096i
$535$		0			0
$536$	−5.72474	+	3.30518i	−0.247271	+	0.142762i
$537$	−17.3501	+	6.40576i	−0.748714	+	0.276429i
$538$	−3.90704	−	14.5813i	−0.168444	−	0.628643i
$539$	−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	$0.294884\pi$
$542$	7.25869	+	27.0898i	0.311787	+	1.16361i
$543$	25.1030	−	9.26816i	1.07727	−	0.397735i
$544$	−0.389270	+	0.224745i	−0.0166898	+	0.00963586i
$545$		0			0
$546$	−15.7980	−	22.3417i	−0.676090	−	0.956136i
$547$	−3.92907	+	1.05279i	−0.167995	+	0.0450140i	−0.341836	−	0.939760i	$-0.611049\pi$
$547$	−3.92907	+	1.05279i	−0.167995	+	0.0450140i	0.173841	+	0.984774i	$0.444382\pi$
$548$	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
$552$	1.10721	−	1.33195i	0.0471258	−	0.0566916i
$553$	−10.7902	−	2.89123i	−0.458846	−	0.122947i
$554$	−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	$-0.674116\pi$
$557$	7.88171	−	7.88171i	0.333959	−	0.333959i	0.854088	+	0.520129i	$0.174116\pi$
$558$	0.105124	−	1.34437i	0.00445027	−	0.0569115i
$559$			12.0000i			0.507546i
$560$		0			0
$561$	−0.404082	+	0.285729i	−0.0170604	+	0.0120635i
$562$	4.43759	−	16.5613i	0.187188	−	0.698597i
$563$	−5.08619	+	18.9819i	−0.214357	+	0.799993i	0.772034	+	0.635581i	$0.219239\pi$
$563$	−5.08619	+	18.9819i	−0.214357	+	0.799993i	−0.986392	+	0.164412i	$0.947427\pi$
$564$	14.1582	+	6.52270i	0.596167	+	0.274655i
$565$		0			0
$566$			24.2166i			1.01790i
$567$	−4.33130	−	40.8151i	−0.181898	−	1.71407i
$568$	4.44949	−	4.44949i	0.186696	−	0.186696i
$569$	−9.58166	+	16.5959i	−0.401684	+	0.695737i	−0.993929	−	0.110021i	$-0.964908\pi$
$569$	−9.58166	+	16.5959i	−0.401684	+	0.695737i	0.592245	+	0.805758i	$0.298242\pi$
$570$		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	$-0.447454\pi$
$572$	2.12701	+	0.569930i	0.0889347	+	0.0238300i
$573$	29.8118	+	5.11490i	1.24541	+	0.213678i
$574$	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	0.966055	−	0.258336i	$-0.0831741\pi$
$577$	17.0000	+	17.0000i	0.707719	+	0.707719i	−0.258336	+	0.966055i	$0.583174\pi$
$578$	−16.2256	+	4.34763i	−0.674895	+	0.180838i
$579$	29.8735	−	2.75255i	1.24150	−	0.114392i
$580$		0			0
$581$	−21.5227	+	12.4261i	−0.892912	+	0.515523i
$582$	−3.57704	−	2.97347i	−0.148273	−	0.123254i
$583$	0.879955	+	3.28404i	0.0364440	+	0.136011i
$584$	−9.75663			−0.403732
$585$		0			0
$586$	−22.0454			−0.910687
$587$	−3.37640	−	12.6009i	−0.139359	−	0.520095i	−0.999942	−	0.0107843i	$-0.996567\pi$
$587$	−3.37640	−	12.6009i	−0.139359	−	0.520095i	0.860583	−	0.509310i	$-0.170099\pi$
$588$	4.04133	−	23.5546i	0.166662	−	0.971375i
$589$	2.51059	−	1.44949i	0.103447	−	0.0597252i
$590$		0			0
$591$	7.10102	−	15.4135i	0.292097	−	0.634026i
$592$	4.09808	−	1.09808i	0.168430	−	0.0451307i
$593$	7.24604	+	7.24604i	0.297559	+	0.297559i	0.840057	−	0.542498i	$-0.182521\pi$
$593$	7.24604	+	7.24604i	0.297559	+	0.297559i	−0.542498	+	0.840057i	$0.682521\pi$
$594$	2.36773	+	2.30306i	0.0971489	+	0.0944958i
$595$		0			0
$596$	−3.82577	−	2.20881i	−0.156709	−	0.0904762i
$597$	−5.06885	−	13.7291i	−0.207454	−	0.561895i
$598$	3.34607	+	0.896575i	0.136831	+	0.0366637i
$599$	9.97093	+	17.2702i	0.407401	+	0.705639i	0.994598	−	0.103805i	$-0.0331018\pi$
$599$	9.97093	+	17.2702i	0.407401	+	0.705639i	−0.587197	+	0.809444i	$0.699768\pi$
$600$		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
$603$	−8.54650	−	17.8950i	−0.348040	−	0.728739i
$604$		−	17.5959i		−	0.715968i
$605$		0			0
$606$	−2.00000	−	21.7060i	−0.0812444	−	0.881747i
$607$	−3.04744	+	11.3732i	−0.123692	+	0.461624i	−0.999790	−	0.0205092i	$-0.993471\pi$
$607$	−3.04744	+	11.3732i	−0.123692	+	0.461624i	0.876098	+	0.482133i	$0.160138\pi$
$608$	−1.66925	+	6.22973i	−0.0676971	+	0.252649i
$609$	−0.230351	−	2.50000i	−0.00933429	−	0.101305i
$610$		0			0
$611$			31.1769i			1.26128i
$612$	−0.581142	−	1.21682i	−0.0234913	−	0.0491869i
$613$	−6.79796	+	6.79796i	−0.274567	+	0.274567i	−0.830936	−	0.556369i	$-0.812194\pi$
$613$	−6.79796	+	6.79796i	−0.274567	+	0.274567i	0.556369	+	0.830936i	$0.312194\pi$
$614$	−4.71940	+	8.17423i	−0.190459	+	0.329885i
$615$		0			0
$616$	1.44949	+	2.51059i	0.0584016	+	0.101155i
$617$	16.3232	+	4.37378i	0.657146	+	0.176082i	0.571958	−	0.820283i	$-0.306184\pi$
$617$	16.3232	+	4.37378i	0.657146	+	0.176082i	0.0851882	+	0.996365i	$0.472851\pi$
$618$	5.85301	+	15.8530i	0.235442	+	0.637701i
$619$	42.2121	+	24.3712i	1.69665	+	0.979560i	0.948900	+	0.315578i	$0.102198\pi$
$619$	42.2121	+	24.3712i	1.69665	+	0.979560i	0.747748	+	0.663982i	$0.231135\pi$
$620$		0			0
$621$	3.72474	+	3.62302i	0.149469	+	0.145387i
$622$	19.4495	+	19.4495i	0.779853	+	0.779853i
$623$	−35.3489	+	9.47172i	−1.41623	+	0.379476i
$624$	−2.51059	+	5.44949i	−0.100504	+	0.218154i
$625$		0			0
$626$	10.3485	−	5.97469i	0.413608	−	0.238797i
$627$	−1.20080	+	6.99876i	−0.0479552	+	0.279503i
$628$	3.78780	+	14.1363i	0.151150	+	0.564099i
$629$	−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	$0.519660\pi$
$632$	0.633975	+	2.36603i	0.0252182	+	0.0941154i
$633$	12.1221	+	10.0767i	0.481811	+	0.400513i
$634$	−9.43879	+	5.44949i	−0.374862	+	0.216427i
$635$		0			0
$636$	−9.22474	+	0.849971i	−0.365785	+	0.0337036i
$637$	46.1689	−	12.3709i	1.82928	−	0.490153i
$638$	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	$0.541934\pi$
$642$	32.8575	+	5.63745i	1.29678	+	0.222492i
$643$	6.10913	+	1.63694i	0.240921	+	0.0645545i	0.377259	−	0.926108i	$-0.376867\pi$
$643$	6.10913	+	1.63694i	0.240921	+	0.0645545i	−0.136338	+	0.990662i	$0.543533\pi$
$644$	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	$-0.977095\pi$
$647$	−23.5416	+	23.5416i	−0.925516	+	0.925516i	0.0718961	+	0.997412i	$0.477095\pi$
$648$	−7.27583	+	5.29738i	−0.285822	+	0.208101i
$649$			5.70714i			0.224025i
$650$		0			0
$651$	3.22474	+	1.48565i	0.126388	+	0.0582271i
$652$	1.62863	−	6.07812i	0.0637819	−	0.238037i
$653$	−6.84563	+	25.5482i	−0.267890	+	0.999780i	0.692567	+	0.721353i	$0.256480\pi$
$653$	−6.84563	+	25.5482i	−0.267890	+	0.999780i	−0.960457	+	0.278427i	$0.910187\pi$
$654$	−7.99247	+	5.65153i	−0.312530	+	0.220992i
$655$		0			0
$656$		−	7.38891i		−	0.288488i
$657$	2.28183	−	29.1808i	0.0890227	−	1.13845i
$658$	−29.0227	+	29.0227i	−1.13142	+	1.13142i
$659$	5.65685	−	9.79796i	0.220360	−	0.381674i	−0.734557	−	0.678546i	$-0.762610\pi$
$659$	5.65685	−	9.79796i	0.220360	−	0.381674i	0.954917	+	0.296872i	$0.0959435\pi$
$660$		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	$0.825266\pi$
$662$	−0.434174	−	0.116337i	−0.0168746	−	0.00452155i
$663$	1.72401	−	2.07395i	0.0669549	−	0.0805456i
$664$	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
$668$	−8.49818	+	2.27708i	−0.328804	+	0.0881028i
$669$	25.6308	+	36.2474i	0.990945	+	1.40141i
$670$		0			0
$671$	−0.303062	+	0.174973i	−0.0116996	+	0.00675474i
$672$	−7.41007	+	2.73583i	−0.285850	+	0.105537i
$673$	6.02093	+	22.4704i	0.232090	+	0.866171i	0.979439	+	0.201740i	$0.0646595\pi$
$673$	6.02093	+	22.4704i	0.232090	+	0.866171i	−0.747349	+	0.664431i	$0.768674\pi$
$674$	3.11416			0.119953
$675$		0			0
$676$	1.00000			0.0384615
$677$	11.8011	+	44.0423i	0.453553	+	1.69268i	0.692308	+	0.721602i	$0.256594\pi$
$677$	11.8011	+	44.0423i	0.453553	+	1.69268i	−0.238755	+	0.971080i	$0.576739\pi$
$678$	−9.42078	+	3.47820i	−0.361803	+	0.133579i
$679$	10.6066	−	6.12372i	0.407044	−	0.235007i
$680$		0			0
$681$	24.8990	+	35.2125i	0.954131	+	1.34934i
$682$	−0.275993	+	0.0739521i	−0.0105683	+	0.00283177i
$683$	13.8564	+	13.8564i	0.530201	+	0.530201i	0.920632	−	0.390431i	$-0.127674\pi$
$683$	13.8564	+	13.8564i	0.530201	+	0.530201i	−0.390431	+	0.920632i	$0.627674\pi$
$684$	−18.2419	−	6.44949i	−0.697497	−	0.246602i
$685$		0			0
$686$	26.8485	+	15.5010i	1.02508	+	0.591830i
$687$	1.82859	−	2.19976i	0.0697649	−	0.0839260i
$688$	3.34607	+	0.896575i	0.127568	+	0.0341816i
$689$	−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
$693$	−7.84785	+	3.74807i	−0.298115	+	0.142377i
$694$		−	23.7980i		−	0.903358i
$695$		0			0
$696$	−0.449490	+	0.317837i	−0.0170379	+	0.0120476i
$697$	−0.859599	+	3.20807i	−0.0325596	+	0.121514i
$698$	7.51750	−	28.0557i	0.284542	−	1.06192i
$699$	−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	$-0.130474\pi$
$702$	−15.7116	−	8.78335i	−0.592994	−	0.331506i
$703$	−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
$707$	55.4382	+	14.8546i	2.08497	+	0.558666i
$708$	−15.3266	−	2.62962i	−0.576007	−	0.0988272i
$709$	−25.6790	−	14.8258i	−0.964394	−	0.556793i	−0.0668716	−	0.997762i	$-0.521302\pi$
$709$	−25.6790	−	14.8258i	−0.964394	−	0.556793i	−0.897523	+	0.440968i	$0.854635\pi$
$710$		0			0
$711$	−7.22474	+	1.34278i	−0.270949	+	0.0503582i
$712$	5.67423	+	5.67423i	0.212651	+	0.212651i
$713$	−0.434174	+	0.116337i	−0.0162599	+	0.00435684i
$714$	3.53553	−	0.325765i	0.132314	−	0.0121915i
$715$		0			0
$716$	−9.24745	+	5.33902i	−0.345593	+	0.199528i
$717$	22.6040	+	18.7899i	0.844160	+	0.701722i
$718$	0.859599	+	3.20807i	0.0320800	+	0.119724i
$719$	32.5269			1.21305			0.606525	−	0.795065i	$-0.292563\pi$
$719$	32.5269			1.21305			0.606525	+	0.795065i	$0.292563\pi$
$720$		0			0
$721$	−44.4949			−1.65708
$722$	−5.84825	−	21.8260i	−0.217649	−	0.812279i
$723$	5.56497	−	32.4350i	0.206964	−	1.20627i
$724$	13.3797	−	7.72474i	0.497251	−	0.287088i
$725$		0			0
$726$	−7.67934	+	16.6688i	−0.285007	+	0.618636i
$727$	46.6759	−	12.5068i	1.73111	−	0.463850i	0.750674	−	0.660673i	$-0.229729\pi$
$727$	46.6759	−	12.5068i	1.73111	−	0.463850i	0.980439	+	0.196822i	$0.0630622\pi$
$728$	−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
$732$	−0.330251	−	0.894494i	−0.0122064	−	0.0330614i
$733$	32.9846	+	8.83821i	1.21832	+	0.326447i	0.810019	−	0.586403i	$-0.199457\pi$
$733$	32.9846	+	8.83821i	1.21832	+	0.326447i	0.408296	+	0.912850i	$0.366123\pi$
$734$	−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
$738$	22.0993	+	1.72808i	0.813485	+	0.0636115i
$739$			28.9444i			1.06474i	0.846513	+	0.532368i	$0.178698\pi$
$739$			28.9444i			1.06474i	−0.846513	+	0.532368i	$0.821302\pi$
$740$		0			0
$741$	−3.55051	−	38.5337i	−0.130431	−	1.41557i
$742$	6.31300	−	23.5605i	0.231758	−	0.864931i
$743$	2.56204	−	9.56168i	0.0939923	−	0.350784i	−0.902872	−	0.429909i	$-0.858546\pi$
$743$	2.56204	−	9.56168i	0.0939923	−	0.350784i	0.996865	+	0.0791245i	$0.0252125\pi$
$744$	−0.0714323	−	0.775255i	−0.00261883	−	0.0284222i
$745$		0			0
$746$		−	0.492810i		−	0.0180431i
$747$	−9.25311	+	13.4779i	−0.338553	+	0.493129i
$748$	−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	$0.956591\pi$
$752$	8.69333	+	2.32937i	0.317013	+	0.0849434i
$753$	−1.61107	−	4.36362i	−0.0587107	−	0.159019i
$754$	−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	0.182038	−	0.983292i	$-0.441731\pi$
$757$	−22.0454	−	22.0454i	−0.801254	−	0.801254i	−0.983292	+	0.182038i	$0.941731\pi$
$758$	20.6210	−	5.52539i	0.748990	−	0.200691i
$759$	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	$0.370733\pi$
$762$	−0.777179	+	4.52973i	−0.0281542	+	0.164095i
$763$	−6.67072	−	24.8955i	−0.241496	−	0.901276i
$764$	17.4634			0.631803
$765$		0			0
$766$	8.20204			0.296352
$767$	−8.04954	−	30.0413i	−0.290652	−	1.08473i
$768$	1.33195	+	1.10721i	0.0480627	+	0.0399529i
$769$	−8.39780	+	4.84847i	−0.302832	+	0.174840i	−0.643715	−	0.765266i	$-0.722608\pi$
$769$	−8.39780	+	4.84847i	−0.302832	+	0.174840i	0.340882	+	0.940106i	$0.389274\pi$
$770$		0			0
$771$	−31.1237	+	2.86775i	−1.12089	+	0.103280i
$772$	16.7303	−	4.48288i	0.602138	−	0.161342i
$773$	−30.8270	−	30.8270i	−1.10877	−	1.10877i	−0.993313	−	0.115456i	$-0.963167\pi$
$773$	−30.8270	−	30.8270i	−1.10877	−	1.10877i	−0.115456	−	0.993313i	$-0.536833\pi$
$774$	−3.46410	+	9.79796i	−0.124515	+	0.352180i
$775$		0			0
$776$	−2.32577	−	1.34278i	−0.0834901	−	0.0482030i
$777$	−33.0299	−	5.66704i	−1.18494	−	0.203304i
$778$	35.5477	+	9.52497i	1.27445	+	0.341487i
$779$	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
$783$	−0.845485	−	1.41870i	−0.0302152	−	0.0507002i
$784$		−	13.7980i		−	0.492784i
$785$		0			0
$786$	5.67423	+	2.61413i	0.202393	+	0.0932429i
$787$	2.52520	−	9.42418i	0.0900137	−	0.335936i	−0.906203	−	0.422844i	$-0.861032\pi$
$787$	2.52520	−	9.42418i	0.0900137	−	0.335936i	0.996216	+	0.0869079i	$0.0276986\pi$
$788$	2.53590	−	9.46410i	0.0903376	−	0.337145i
$789$	23.6130	−	16.6969i	0.840646	−	0.594427i
$790$		0			0
$791$		−	26.4415i		−	0.940150i
$792$	1.57217	+	1.07936i	0.0558646	+	0.0383534i
$793$	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
$797$	−38.4419	−	10.3005i	−1.36168	−	0.364861i	−0.497248	−	0.867609i	$-0.665656\pi$
$797$	−38.4419	−	10.3005i	−1.36168	−	0.364861i	−0.864433	+	0.502747i	$0.832323\pi$
$798$	32.5660	−	39.1764i	1.15282	−	1.38683i
$799$	−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
$803$	−5.99071	+	1.60521i	−0.211408	+	0.0566465i
$804$	−6.61037	−	9.34847i	−0.233130	−	0.329695i
$805$		0			0
$806$	1.34847	−	0.778539i	0.0474978	−	0.0274229i
$807$	24.5281	−	9.05589i	0.863429	−	0.318782i
$808$	−3.25725	−	12.1562i	−0.114590	−	0.427655i
$809$	−19.4490			−0.683792			−0.341896	−	0.939738i	$-0.611069\pi$
$809$	−19.4490			−0.683792			−0.341896	+	0.939738i	$0.611069\pi$
$810$		0			0
$811$	−39.6413			−1.39200			−0.695998	−	0.718044i	$-0.745038\pi$
$811$	−39.6413			−1.39200			−0.695998	+	0.718044i	$0.745038\pi$
$812$	−0.375156	−	1.40010i	−0.0131654	−	0.0491339i
$813$	−45.5694	+	16.8245i	−1.59819	+	0.590059i
$814$	2.33562	−	1.34847i	0.0818633	−	0.0472638i
$815$		0			0
$816$	−0.449490	−	0.635674i	−0.0157353	−	0.0222531i
$817$	−21.5804	+	5.78245i	−0.755003	+	0.202302i
$818$	−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	$0.539382\pi$
$822$	−24.1348	+	29.0338i	−0.841799	+	1.01267i
$823$	3.23908	+	0.867910i	0.112907	+	0.0302534i	0.314830	−	0.949148i	$-0.398052\pi$
$823$	3.23908	+	0.867910i	0.112907	+	0.0302534i	−0.201923	+	0.979401i	$0.564719\pi$
$824$	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	−0.102980	+	0.994683i	$0.532838\pi$
$827$	−31.5662	+	31.5662i	−1.09766	+	1.09766i	−0.994683	+	0.102980i	$0.967162\pi$
$828$	2.47323	+	1.69798i	0.0859507	+	0.0590088i
$829$		−	10.5505i		−	0.366434i	−0.983072	−	0.183217i	$-0.941349\pi$
$829$		−	10.5505i		−	0.366434i	0.983072	−	0.183217i	$-0.0586512\pi$
$830$		0			0
$831$	39.7980	−	28.1414i	1.38058	−	0.976215i
$832$	−0.896575	+	3.34607i	−0.0310832	+	0.116004i
$833$	−1.60521	+	5.99071i	−0.0556171	+	0.207566i
$834$	−4.87832	−	2.24745i	−0.168922	−	0.0778228i
$835$		0			0
$836$			4.09978i			0.141794i
$837$	2.33539	−	0.0323319i	0.0807230	−	0.00111755i
$838$	−3.55051	+	3.55051i	−0.122650	+	0.122650i
$839$	0.246405	−	0.426786i	0.00850684	−	0.0147343i	−0.861741	−	0.507349i	$-0.830625\pi$
$839$	0.246405	−	0.426786i	0.00850684	−	0.0147343i	0.870247	+	0.492615i	$0.163959\pi$
$840$		0			0
$841$	14.4495	+	25.0273i	0.498258	+	0.863009i
$842$	4.92721	+	1.32024i	0.169803	+	0.0454985i
$843$	29.2693	+	5.02181i	1.00809	+	0.172960i
$844$	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
$848$	−5.16622	+	1.38429i	−0.177409	+	0.0475366i
$849$	−41.7675	+	3.84847i	−1.43346	+	0.132079i
$850$		0			0
$851$	3.67423	−	2.12132i	0.125951	−	0.0727179i
$852$	8.38134	+	6.96713i	0.287140	+	0.238690i
$853$	0.641478	+	2.39403i	0.0219638	+	0.0819700i	0.976038	−	0.217601i	$-0.0698231\pi$
$853$	0.641478	+	2.39403i	0.0219638	+	0.0819700i	−0.954074	+	0.299571i	$0.903156\pi$
$854$	2.51059			0.0859106
$855$		0			0
$856$	19.2474			0.657864
$857$	−4.08881	−	15.2597i	−0.139671	−	0.521260i	−0.999935	−	0.0114106i	$-0.996368\pi$
$857$	−4.08881	−	15.2597i	−0.139671	−	0.521260i	0.860264	−	0.509849i	$-0.170299\pi$
$858$	−0.644963	+	3.75912i	−0.0220187	+	0.128334i
$859$	−40.2658	+	23.2474i	−1.37385	+	0.793193i	−0.991410	−	0.130788i	$-0.958249\pi$
$859$	−40.2658	+	23.2474i	−1.37385	+	0.793193i	−0.382440	+	0.923980i	$0.624916\pi$
$860$		0			0
$861$	−24.4217	+	53.0097i	−0.832289	+	1.80657i
$862$	15.0263	−	4.02628i	0.511797	−	0.137136i
$863$	20.7132	+	20.7132i	0.705085	+	0.705085i	0.965497	−	0.260413i	$-0.0838586\pi$
$863$	20.7132	+	20.7132i	0.705085	+	0.705085i	−0.260413	+	0.965497i	$0.583859\pi$
$864$	−3.62302	+	3.72474i	−0.123258	+	0.126718i
$865$		0			0
$866$	−16.4722	−	9.51023i	−0.559748	−	0.323171i
$867$	−10.0771	−	27.2941i	−0.342236	−	0.926955i
$868$	1.98004	+	0.530550i	0.0672069	+	0.0180080i
$869$	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
$873$	4.56002	−	6.64202i	0.154333	−	0.224798i
$874$			6.44949i			0.218157i
$875$		0			0
$876$	−1.55051	−	16.8277i	−0.0523869	−	0.568555i
$877$	−11.0713	+	41.3188i	−0.373852	+	1.39524i	0.481162	+	0.876632i	$0.340215\pi$
$877$	−11.0713	+	41.3188i	−0.373852	+	1.39524i	−0.855014	+	0.518604i	$0.826452\pi$
$878$	7.71228	−	28.7826i	0.260277	−	0.971366i
$879$	−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	$0.625113\pi$
$882$	41.2679	+	3.22700i	1.38956	+	0.108659i
$883$	−6.27015	+	6.27015i	−0.211007	+	0.211007i	−0.804695	−	0.593688i	$-0.797671\pi$
$883$	−6.27015	+	6.27015i	−0.211007	+	0.211007i	0.593688	+	0.804695i	$0.297671\pi$
$884$	0.778539	−	1.34847i	0.0261851	−	0.0453539i
$885$		0			0
$886$	2.72474	+	4.71940i	0.0915396	+	0.158551i
$887$	7.92256	+	2.12284i	0.266014	+	0.0712781i	0.389360	−	0.921085i	$-0.372696\pi$
$887$	7.92256	+	2.12284i	0.266014	+	0.0712781i	−0.123347	+	0.992364i	$0.539363\pi$
$888$	2.54516	+	6.89363i	0.0854100	+	0.231335i
$889$	−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
$893$	−56.0676	+	15.0233i	−1.87623	+	0.502734i
$894$	3.20164	−	6.94949i	0.107079	−	0.232426i
$895$		0			0
$896$	−3.94949	+	2.28024i	−0.131943	+	0.0761774i
$897$	−1.01461	+	5.91359i	−0.0338769	+	0.197449i
$898$	0.238477	+	0.890008i	0.00795807	+	0.0296999i
$899$	0.142865			0.00476480
$900$		0			0
$901$	2.40408			0.0800916
$902$	−1.21566	−	4.53689i	−0.0404770	−	0.151062i
$903$	−21.0421	−	17.4916i	−0.700238	−	0.582084i
$904$	−5.02118	+	2.89898i	−0.167002	+	0.0964186i
$905$		0			0
$906$	30.3485	−	2.79632i	1.00826	−	0.0929015i
$907$	−3.65307	+	0.978838i	−0.121298	+	0.0325018i	−0.318957	−	0.947769i	$-0.603333\pi$
$907$	−3.65307	+	0.978838i	−0.121298	+	0.0325018i	0.197659	+	0.980271i	$0.436666\pi$
$908$	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	$0.704038\pi$
$912$	−11.0100	−	1.88901i	−0.364576	−	0.0625514i
$913$	3.34607	+	0.896575i	0.110739	+	0.0296723i
$914$	−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
$918$	2.00634	−	1.19570i	0.0662192	−	0.0394639i
$919$			12.6515i			0.417335i	0.977987	+	0.208668i	$0.0669127\pi$
$919$			12.6515i			0.417335i	−0.977987	+	0.208668i	$0.933087\pi$
$920$		0			0
$921$	−14.8485	−	6.84072i	−0.489274	−	0.225409i
$922$	−8.55444	+	31.9256i	−0.281726	+	1.05141i
$923$	−5.64173	+	21.0552i	−0.185700	+	0.693041i
$924$	−4.09978	+	2.89898i	−0.134873	+	0.0953694i
$925$		0			0
$926$		−	12.2351i		−	0.402071i
$927$	−26.4122	+	12.6143i	−0.867492	+	0.414307i
$928$	−0.224745	+	0.224745i	−0.00737761	+	0.00737761i
$929$	21.1024	−	36.5505i	0.692349	−	1.19918i	−0.278717	−	0.960373i	$-0.589909\pi$
$929$	21.1024	−	36.5505i	0.692349	−	1.19918i	0.971066	−	0.238810i	$-0.0767574\pi$
$930$		0			0
$931$	44.4949	+	77.0674i	1.45826	+	2.52578i
$932$	−19.7527	−	5.29272i	−0.647021	−	0.173369i
$933$	−30.4545	+	36.6363i	−0.997036	+	1.19942i
$934$	−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	0.755943	−	0.654637i	$-0.227179\pi$
$937$	3.10102	+	3.10102i	0.101306	+	0.101306i	−0.654637	+	0.755943i	$0.727179\pi$
$938$	29.1192	−	7.80247i	0.950776	−	0.254760i
$939$	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	$0.160007\pi$
$942$	−23.7795	+	8.77951i	−0.774778	+	0.286052i
$943$	−1.91239	−	7.13713i	−0.0622760	−	0.232417i
$944$	−8.97809			−0.292212
$945$		0			0
$946$	2.20204			0.0715945
$947$	−0.788210	−	2.94164i	−0.0256134	−	0.0955904i	0.951936	−	0.306297i	$-0.0990901\pi$
$947$	−0.788210	−	2.94164i	−0.0256134	−	0.0955904i	−0.977549	+	0.210707i	$0.932423\pi$
$948$	−3.98004	+	1.46945i	−0.129266	+	0.0477255i
$949$	29.2699	−	16.8990i	0.950141	−	0.548564i
$950$		0			0
$951$	−10.8990	−	15.4135i	−0.353424	−	0.499816i
$952$	1.98004	−	0.530550i	0.0641735	−	0.0171952i
$953$	5.79972	+	5.79972i	0.187871	+	0.187871i	0.794775	−	0.606904i	$-0.207589\pi$
$953$	5.79972	+	5.79972i	0.187871	+	0.187871i	−0.606904	+	0.794775i	$0.707589\pi$
$954$	−2.93197	−	15.7753i	−0.0949260	−	0.510743i
$955$		0			0
$956$	14.6969	+	8.48528i	0.475333	+	0.274434i
$957$	−0.223701	+	0.269109i	−0.00723123	+	0.00869905i
$958$	−6.83013	−	1.83013i	−0.220671	−	0.0591287i
$959$	−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
$963$	−4.50150	+	57.5666i	−0.145059	+	1.85506i
$964$		−	19.0000i		−	0.611949i
$965$		0			0
$966$	−6.44949	+	4.56048i	−0.207509	+	0.146731i
$967$	10.3679	−	38.6937i	0.333411	−	1.24431i	−0.572171	−	0.820134i	$-0.693899\pi$
$967$	10.3679	−	38.6937i	0.333411	−	1.24431i	0.905582	−	0.424172i	$-0.139435\pi$
$968$	−2.74243	+	10.2349i	−0.0881449	+	0.328961i
$969$	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	$-0.112110\pi$
$972$	−10.2929	−	11.7071i	−0.330145	−	0.375506i
$973$	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
$977$	−6.27359	−	1.68100i	−0.200710	−	0.0537801i	0.157063	−	0.987589i	$-0.449797\pi$
$977$	−6.27359	−	1.68100i	−0.200710	−	0.0537801i	−0.357773	+	0.933808i	$0.616464\pi$
$978$	10.7420	+	1.84304i	0.343492	+	0.0589339i
$979$	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
$983$	26.2752	−	7.04041i	0.838047	−	0.224554i	0.185826	−	0.982583i	$-0.440504\pi$
$983$	26.2752	−	7.04041i	0.838047	−	0.224554i	0.652221	+	0.758029i	$0.273837\pi$
$984$	12.7440	−	1.17423i	0.406263	−	0.0374332i
$985$		0			0
$986$	0.123724	−	0.0714323i	0.00394019	−	0.00227487i
$987$	−54.6690	−	45.4445i	−1.74013	−	1.44651i
$988$	−5.78245	−	21.5804i	−0.183964	−	0.686564i
$989$	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	$0.414325\pi$
$992$	−0.116337	−	0.434174i	−0.00369369	−	0.0137850i
$993$	0.131652	−	0.767327i	0.00417787	−	0.0243504i
$994$	−24.8523	+	14.3485i	−0.788266	+	0.455106i
$995$		0			0
$996$	−3.94949	+	8.57277i	−0.125144	+	0.271639i
$997$	−6.49211	+	1.73955i	−0.205607	+	0.0550922i	−0.360153	−	0.932893i	$-0.617275\pi$
$997$	−6.49211	+	1.73955i	−0.205607	+	0.0550922i	0.154545	+	0.987986i	$0.450609\pi$
$998$	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.407.2		8
3.2	odd	2		1350.2.q.g.1007.1		8
5.2	odd	4		90.2.l.a.83.1	yes	8
5.3	odd	4	inner	450.2.p.a.443.2		8
5.4	even	2		90.2.l.a.47.1	yes	8
9.4	even	3		1350.2.q.g.557.1		8
9.5	odd	6	inner	450.2.p.a.257.2		8
15.2	even	4		270.2.m.a.143.2		8
15.8	even	4		1350.2.q.g.143.1		8
15.14	odd	2		270.2.m.a.197.2		8
20.7	even	4		720.2.cu.a.353.1		8
20.19	odd	2		720.2.cu.a.497.1		8
45.2	even	12		810.2.f.b.323.1		8
45.4	even	6		270.2.m.a.17.2		8
45.7	odd	12		810.2.f.b.323.4		8
45.13	odd	12		1350.2.q.g.1043.1		8
45.14	odd	6		90.2.l.a.77.1	yes	8
45.22	odd	12		270.2.m.a.233.2		8
45.23	even	12	inner	450.2.p.a.293.2		8
45.29	odd	6		810.2.f.b.647.3		8
45.32	even	12		90.2.l.a.23.1	✓	8
45.34	even	6		810.2.f.b.647.2		8
180.59	even	6		720.2.cu.a.257.1		8
180.167	odd	12		720.2.cu.a.113.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.l.a.23.1	✓	8	45.32	even	12
90.2.l.a.47.1	yes	8	5.4	even	2
90.2.l.a.77.1	yes	8	45.14	odd	6
90.2.l.a.83.1	yes	8	5.2	odd	4
270.2.m.a.17.2		8	45.4	even	6
270.2.m.a.143.2		8	15.2	even	4
270.2.m.a.197.2		8	15.14	odd	2
270.2.m.a.233.2		8	45.22	odd	12
450.2.p.a.257.2		8	9.5	odd	6	inner
450.2.p.a.293.2		8	45.23	even	12	inner
450.2.p.a.407.2		8	1.1	even	1	trivial
450.2.p.a.443.2		8	5.3	odd	4	inner
720.2.cu.a.113.1		8	180.167	odd	12
720.2.cu.a.257.1		8	180.59	even	6
720.2.cu.a.353.1		8	20.7	even	4
720.2.cu.a.497.1		8	20.19	odd	2
810.2.f.b.323.1		8	45.2	even	12
810.2.f.b.323.4		8	45.7	odd	12
810.2.f.b.647.2		8	45.34	even	6
810.2.f.b.647.3		8	45.29	odd	6
1350.2.q.g.143.1		8	15.8	even	4
1350.2.q.g.557.1		8	9.4	even	3
1350.2.q.g.1007.1		8	3.2	odd	2
1350.2.q.g.1043.1		8	45.13	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:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	450.p (of order \(12\), degree \(4\), minimal)

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