LMFDB - Embedded newform 245.2.l.a.227.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [245,2,Mod(68,245)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(245, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 10]))

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

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

chi := DirichletCharacter("245.68");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	245.l (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.95633484952$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			227.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	245.227
Dual form			245.2.l.a.68.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.133975 + 0.500000i) q^{2} +(0.500000 - 0.133975i) q^{3} +(1.50000 + 0.866025i) q^{4} +(1.86603 + 1.23205i) q^{5} +0.267949i q^{6} +(-1.36603 + 1.36603i) q^{8} +(-2.36603 + 1.36603i) q^{9} +O(q^{10})$	\(q+(-0.133975 + 0.500000i) q^{2} +(0.500000 - 0.133975i) q^{3} +(1.50000 + 0.866025i) q^{4} +(1.86603 + 1.23205i) q^{5} +0.267949i q^{6} +(-1.36603 + 1.36603i) q^{8} +(-2.36603 + 1.36603i) q^{9} +(-0.866025 + 0.767949i) q^{10} +(1.36603 - 2.36603i) q^{11} +(0.866025 + 0.232051i) q^{12} +(-2.00000 - 2.00000i) q^{13} +(1.09808 + 0.366025i) q^{15} +(1.23205 + 2.13397i) q^{16} +(-1.00000 - 3.73205i) q^{17} +(-0.366025 - 1.36603i) q^{18} +(0.366025 + 0.633975i) q^{19} +(1.73205 + 3.46410i) q^{20} +(1.00000 + 1.00000i) q^{22} +(-0.133975 - 0.0358984i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(1.96410 + 4.59808i) q^{25} +(1.26795 - 0.732051i) q^{26} +(-2.09808 + 2.09808i) q^{27} -3.00000i q^{29} +(-0.330127 + 0.500000i) q^{30} +(6.46410 + 3.73205i) q^{31} +(-4.96410 + 1.33013i) q^{32} +(0.366025 - 1.36603i) q^{33} +2.00000 q^{34} -4.73205 q^{36} +(1.26795 - 4.73205i) q^{37} +(-0.366025 + 0.0980762i) q^{38} +(-1.26795 - 0.732051i) q^{39} +(-4.23205 + 0.866025i) q^{40} -6.46410i q^{41} +(2.83013 - 2.83013i) q^{43} +(4.09808 - 2.36603i) q^{44} +(-6.09808 - 0.366025i) q^{45} +(0.0358984 - 0.0621778i) q^{46} +(-8.83013 - 2.36603i) q^{47} +(0.901924 + 0.901924i) q^{48} +(-2.56218 + 0.366025i) q^{50} +(-1.00000 - 1.73205i) q^{51} +(-1.26795 - 4.73205i) q^{52} +(-1.83013 - 6.83013i) q^{53} +(-0.767949 - 1.33013i) q^{54} +(5.46410 - 2.73205i) q^{55} +(0.267949 + 0.267949i) q^{57} +(1.50000 + 0.401924i) q^{58} +(-4.09808 + 7.09808i) q^{59} +(1.33013 + 1.50000i) q^{60} +(-1.33013 + 0.767949i) q^{61} +(-2.73205 + 2.73205i) q^{62} +2.26795i q^{64} +(-1.26795 - 6.19615i) q^{65} +(0.633975 + 0.366025i) q^{66} +(-10.6962 + 2.86603i) q^{67} +(1.73205 - 6.46410i) q^{68} -0.0717968 q^{69} +1.26795 q^{71} +(1.36603 - 5.09808i) q^{72} +(12.9282 - 3.46410i) q^{73} +(2.19615 + 1.26795i) q^{74} +(1.59808 + 2.03590i) q^{75} +1.26795i q^{76} +(0.535898 - 0.535898i) q^{78} +(-2.83013 + 1.63397i) q^{79} +(-0.330127 + 5.50000i) q^{80} +(3.33013 - 5.76795i) q^{81} +(3.23205 + 0.866025i) q^{82} +(-2.09808 - 2.09808i) q^{83} +(2.73205 - 8.19615i) q^{85} +(1.03590 + 1.79423i) q^{86} +(-0.401924 - 1.50000i) q^{87} +(1.36603 + 5.09808i) q^{88} +(-0.330127 - 0.571797i) q^{89} +(1.00000 - 3.00000i) q^{90} +(-0.169873 - 0.169873i) q^{92} +(3.73205 + 1.00000i) q^{93} +(2.36603 - 4.09808i) q^{94} +(-0.0980762 + 1.63397i) q^{95} +(-2.30385 + 1.33013i) q^{96} +(-5.92820 + 5.92820i) q^{97} +7.46410i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 2 q^{3} + 6 q^{4} + 4 q^{5} - 2 q^{8} - 6 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 + 2 * q^3 + 6 * q^4 + 4 * q^5 - 2 * q^8 - 6 * q^9	$ 4 q - 4 q^{2} + 2 q^{3} + 6 q^{4} + 4 q^{5} - 2 q^{8} - 6 q^{9} + 2 q^{11} - 8 q^{13} - 6 q^{15} - 2 q^{16} - 4 q^{17} + 2 q^{18} - 2 q^{19} + 4 q^{22} - 4 q^{23} - 2 q^{24} - 6 q^{25} + 12 q^{26} + 2 q^{27} + 16 q^{30} + 12 q^{31} - 6 q^{32} - 2 q^{33} + 8 q^{34} - 12 q^{36} + 12 q^{37} + 2 q^{38} - 12 q^{39} - 10 q^{40} - 6 q^{43} + 6 q^{44} - 14 q^{45} + 14 q^{46} - 18 q^{47} + 14 q^{48} + 14 q^{50} - 4 q^{51} - 12 q^{52} + 10 q^{53} - 10 q^{54} + 8 q^{55} + 8 q^{57} + 6 q^{58} - 6 q^{59} - 12 q^{60} + 12 q^{61} - 4 q^{62} - 12 q^{65} + 6 q^{66} - 22 q^{67} - 28 q^{69} + 12 q^{71} + 2 q^{72} + 24 q^{73} - 12 q^{74} - 4 q^{75} + 16 q^{78} + 6 q^{79} + 16 q^{80} - 4 q^{81} + 6 q^{82} + 2 q^{83} + 4 q^{85} + 18 q^{86} - 12 q^{87} + 2 q^{88} + 16 q^{89} + 4 q^{90} - 18 q^{92} + 8 q^{93} + 6 q^{94} + 10 q^{95} - 30 q^{96} + 4 q^{97}+O(q^{100}) $ 4 * q - 4 * q^2 + 2 * q^3 + 6 * q^4 + 4 * q^5 - 2 * q^8 - 6 * q^9 + 2 * q^11 - 8 * q^13 - 6 * q^15 - 2 * q^16 - 4 * q^17 + 2 * q^18 - 2 * q^19 + 4 * q^22 - 4 * q^23 - 2 * q^24 - 6 * q^25 + 12 * q^26 + 2 * q^27 + 16 * q^30 + 12 * q^31 - 6 * q^32 - 2 * q^33 + 8 * q^34 - 12 * q^36 + 12 * q^37 + 2 * q^38 - 12 * q^39 - 10 * q^40 - 6 * q^43 + 6 * q^44 - 14 * q^45 + 14 * q^46 - 18 * q^47 + 14 * q^48 + 14 * q^50 - 4 * q^51 - 12 * q^52 + 10 * q^53 - 10 * q^54 + 8 * q^55 + 8 * q^57 + 6 * q^58 - 6 * q^59 - 12 * q^60 + 12 * q^61 - 4 * q^62 - 12 * q^65 + 6 * q^66 - 22 * q^67 - 28 * q^69 + 12 * q^71 + 2 * q^72 + 24 * q^73 - 12 * q^74 - 4 * q^75 + 16 * q^78 + 6 * q^79 + 16 * q^80 - 4 * q^81 + 6 * q^82 + 2 * q^83 + 4 * q^85 + 18 * q^86 - 12 * q^87 + 2 * q^88 + 16 * q^89 + 4 * q^90 - 18 * q^92 + 8 * q^93 + 6 * q^94 + 10 * q^95 - 30 * q^96 + 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.133975	+	0.500000i	−0.0947343	+	0.353553i	−0.996979	−	0.0776710i	$-0.975252\pi$
$2$	−0.133975	+	0.500000i	−0.0947343	+	0.353553i	0.902245	+	0.431224i	$0.141918\pi$
$3$	0.500000	−	0.133975i	0.288675	−	0.0773503i	−0.111576	−	0.993756i	$-0.535590\pi$
$3$	0.500000	−	0.133975i	0.288675	−	0.0773503i	0.400251	+	0.916406i	$0.368923\pi$
$4$	1.50000	+	0.866025i	0.750000	+	0.433013i
$5$	1.86603	+	1.23205i	0.834512	+	0.550990i
$5$	1.86603	+	1.23205i	0.834512	+	0.550990i
$6$			0.267949i			0.109390i
$7$		0			0
$7$		0			0
$8$	−1.36603	+	1.36603i	−0.482963	+	0.482963i
$9$	−2.36603	+	1.36603i	−0.788675	+	0.455342i
$10$	−0.866025	+	0.767949i	−0.273861	+	0.242847i
$11$	1.36603	−	2.36603i	0.411872	−	0.713384i	−0.583222	−	0.812313i	$-0.698208\pi$
$11$	1.36603	−	2.36603i	0.411872	−	0.713384i	0.995094	+	0.0989291i	$0.0315417\pi$
$12$	0.866025	+	0.232051i	0.250000	+	0.0669873i
$13$	−2.00000	−	2.00000i	−0.554700	−	0.554700i	0.373094	−	0.927794i	$-0.378297\pi$
$13$	−2.00000	−	2.00000i	−0.554700	−	0.554700i	−0.927794	+	0.373094i	$0.878297\pi$
$14$		0			0
$15$	1.09808	+	0.366025i	0.283522	+	0.0945074i
$16$	1.23205	+	2.13397i	0.308013	+	0.533494i
$17$	−1.00000	−	3.73205i	−0.242536	−	0.905155i	−0.974606	−	0.223926i	$-0.928112\pi$
$17$	−1.00000	−	3.73205i	−0.242536	−	0.905155i	0.732070	−	0.681229i	$-0.238554\pi$
$18$	−0.366025	−	1.36603i	−0.0862730	−	0.321975i
$19$	0.366025	+	0.633975i	0.0839720	+	0.145444i	0.904953	−	0.425512i	$-0.139906\pi$
$19$	0.366025	+	0.633975i	0.0839720	+	0.145444i	−0.820981	+	0.570956i	$0.806573\pi$
$20$	1.73205	+	3.46410i	0.387298	+	0.774597i
$21$		0			0
$22$	1.00000	+	1.00000i	0.213201	+	0.213201i
$23$	−0.133975	−	0.0358984i	−0.0279356	−	0.00748533i	0.244824	−	0.969567i	$-0.421270\pi$
$23$	−0.133975	−	0.0358984i	−0.0279356	−	0.00748533i	−0.272760	+	0.962082i	$0.587936\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	1.96410	+	4.59808i	0.392820	+	0.919615i
$26$	1.26795	−	0.732051i	0.248665	−	0.143567i
$27$	−2.09808	+	2.09808i	−0.403775	+	0.403775i
$28$		0			0
$29$		−	3.00000i		−	0.557086i	−0.960424	−	0.278543i	$-0.910149\pi$
$29$		−	3.00000i		−	0.557086i	0.960424	−	0.278543i	$-0.0898515\pi$
$30$	−0.330127	+	0.500000i	−0.0602727	+	0.0912871i
$31$	6.46410	+	3.73205i	1.16099	+	0.670296i	0.951540	−	0.307524i	$-0.0995004\pi$
$31$	6.46410	+	3.73205i	1.16099	+	0.670296i	0.209447	+	0.977820i	$0.432834\pi$
$32$	−4.96410	+	1.33013i	−0.877537	+	0.235135i
$33$	0.366025	−	1.36603i	0.0637168	−	0.237795i
$34$	2.00000			0.342997
$35$		0			0
$36$	−4.73205			−0.788675
$37$	1.26795	−	4.73205i	0.208450	−	0.777944i	−0.779921	−	0.625878i	$-0.784741\pi$
$37$	1.26795	−	4.73205i	0.208450	−	0.777944i	0.988370	−	0.152066i	$-0.0485927\pi$
$38$	−0.366025	+	0.0980762i	−0.0593772	+	0.0159101i
$39$	−1.26795	−	0.732051i	−0.203034	−	0.117222i
$40$	−4.23205	+	0.866025i	−0.669146	+	0.136931i
$41$		−	6.46410i		−	1.00952i	−0.863259	−	0.504762i	$-0.831580\pi$
$41$		−	6.46410i		−	1.00952i	0.863259	−	0.504762i	$-0.168420\pi$
$42$		0			0
$43$	2.83013	−	2.83013i	0.431590	−	0.431590i	−0.457579	−	0.889169i	$-0.651283\pi$
$43$	2.83013	−	2.83013i	0.431590	−	0.431590i	0.889169	+	0.457579i	$0.151283\pi$
$44$	4.09808	−	2.36603i	0.617808	−	0.356692i
$45$	−6.09808	−	0.366025i	−0.909048	−	0.0545638i
$46$	0.0358984	−	0.0621778i	0.00529293	−	0.00916762i
$47$	−8.83013	−	2.36603i	−1.28801	−	0.345120i	−0.451103	−	0.892472i	$-0.648969\pi$
$47$	−8.83013	−	2.36603i	−1.28801	−	0.345120i	−0.836903	+	0.547351i	$0.815636\pi$
$48$	0.901924	+	0.901924i	0.130181	+	0.130181i
$49$		0			0
$50$	−2.56218	+	0.366025i	−0.362347	+	0.0517638i
$51$	−1.00000	−	1.73205i	−0.140028	−	0.242536i
$52$	−1.26795	−	4.73205i	−0.175833	−	0.656217i
$53$	−1.83013	−	6.83013i	−0.251387	−	0.938190i	−0.970065	−	0.242846i	$-0.921919\pi$
$53$	−1.83013	−	6.83013i	−0.251387	−	0.938190i	0.718677	−	0.695344i	$-0.244748\pi$
$54$	−0.767949	−	1.33013i	−0.104505	−	0.181007i
$55$	5.46410	−	2.73205i	0.736779	−	0.368390i
$56$		0			0
$57$	0.267949	+	0.267949i	0.0354907	+	0.0354907i
$58$	1.50000	+	0.401924i	0.196960	+	0.0527752i
$59$	−4.09808	+	7.09808i	−0.533524	+	0.924091i	0.465709	+	0.884938i	$0.345799\pi$
$59$	−4.09808	+	7.09808i	−0.533524	+	0.924091i	−0.999233	+	0.0391530i	$0.987534\pi$
$60$	1.33013	+	1.50000i	0.171719	+	0.193649i
$61$	−1.33013	+	0.767949i	−0.170305	+	0.0983258i	−0.582730	−	0.812666i	$-0.698015\pi$
$61$	−1.33013	+	0.767949i	−0.170305	+	0.0983258i	0.412424	+	0.910992i	$0.364682\pi$
$62$	−2.73205	+	2.73205i	−0.346971	+	0.346971i
$63$		0			0
$64$			2.26795i			0.283494i
$65$	−1.26795	−	6.19615i	−0.157270	−	0.768538i
$66$	0.633975	+	0.366025i	0.0780369	+	0.0450546i
$67$	−10.6962	+	2.86603i	−1.30674	+	0.350141i	−0.843996	−	0.536350i	$-0.819803\pi$
$67$	−10.6962	+	2.86603i	−1.30674	+	0.350141i	−0.462747	+	0.886490i	$0.653136\pi$
$68$	1.73205	−	6.46410i	0.210042	−	0.783887i
$69$	−0.0717968			−0.00864332
$70$		0			0
$71$	1.26795			0.150478			0.0752389	−	0.997166i	$-0.476028\pi$
$71$	1.26795			0.150478			0.0752389	+	0.997166i	$0.476028\pi$
$72$	1.36603	−	5.09808i	0.160988	−	0.600814i
$73$	12.9282	−	3.46410i	1.51313	−	0.405442i	0.595658	−	0.803238i	$-0.296891\pi$
$73$	12.9282	−	3.46410i	1.51313	−	0.405442i	0.917474	+	0.397796i	$0.130225\pi$
$74$	2.19615	+	1.26795i	0.255298	+	0.147396i
$75$	1.59808	+	2.03590i	0.184530	+	0.235085i
$76$			1.26795i			0.145444i
$77$		0			0
$78$	0.535898	−	0.535898i	0.0606785	−	0.0606785i
$79$	−2.83013	+	1.63397i	−0.318414	+	0.183837i	−0.650686	−	0.759347i	$-0.725518\pi$
$79$	−2.83013	+	1.63397i	−0.318414	+	0.183837i	0.332271	+	0.943184i	$0.392185\pi$
$80$	−0.330127	+	5.50000i	−0.0369093	+	0.614919i
$81$	3.33013	−	5.76795i	0.370014	−	0.640883i
$82$	3.23205	+	0.866025i	0.356920	+	0.0956365i
$83$	−2.09808	−	2.09808i	−0.230294	−	0.230294i	0.582522	−	0.812815i	$-0.302066\pi$
$83$	−2.09808	−	2.09808i	−0.230294	−	0.230294i	−0.812815	+	0.582522i	$0.802066\pi$
$84$		0			0
$85$	2.73205	−	8.19615i	0.296333	−	0.888998i
$86$	1.03590	+	1.79423i	0.111704	+	0.193477i
$87$	−0.401924	−	1.50000i	−0.0430908	−	0.160817i
$88$	1.36603	+	5.09808i	0.145619	+	0.543457i
$89$	−0.330127	−	0.571797i	−0.0349934	−	0.0606103i	0.847998	−	0.529999i	$-0.177808\pi$
$89$	−0.330127	−	0.571797i	−0.0349934	−	0.0606103i	−0.882992	+	0.469389i	$0.844474\pi$
$90$	1.00000	−	3.00000i	0.105409	−	0.316228i
$91$		0			0
$92$	−0.169873	−	0.169873i	−0.0177105	−	0.0177105i
$93$	3.73205	+	1.00000i	0.386996	+	0.103695i
$94$	2.36603	−	4.09808i	0.244037	−	0.422684i
$95$	−0.0980762	+	1.63397i	−0.0100624	+	0.167642i
$96$	−2.30385	+	1.33013i	−0.235135	+	0.135756i
$97$	−5.92820	+	5.92820i	−0.601918	+	0.601918i	−0.940821	−	0.338903i	$-0.889944\pi$
$97$	−5.92820	+	5.92820i	−0.601918	+	0.601918i	0.338903	+	0.940821i	$0.389944\pi$
$98$		0			0
$99$			7.46410i			0.750170i
$100$	−1.03590	+	8.59808i	−0.103590	+	0.859808i
$101$	−7.16025	−	4.13397i	−0.712472	−	0.411346i	0.0995037	−	0.995037i	$-0.468274\pi$
$101$	−7.16025	−	4.13397i	−0.712472	−	0.411346i	−0.811976	+	0.583691i	$0.801608\pi$
$102$	1.00000	−	0.267949i	0.0990148	−	0.0265309i
$103$	−1.23205	+	4.59808i	−0.121398	+	0.453062i	−0.999686	−	0.0250698i	$-0.992019\pi$
$103$	−1.23205	+	4.59808i	−0.121398	+	0.453062i	0.878288	+	0.478132i	$0.158686\pi$
$104$	5.46410			0.535799
$105$		0			0
$106$	3.66025			0.355515
$107$	−3.40192	+	12.6962i	−0.328876	+	1.22738i	0.581481	+	0.813560i	$0.302474\pi$
$107$	−3.40192	+	12.6962i	−0.328876	+	1.22738i	−0.910357	+	0.413823i	$0.864193\pi$
$108$	−4.96410	+	1.33013i	−0.477671	+	0.127992i
$109$	8.76795	+	5.06218i	0.839817	+	0.484869i	0.857202	−	0.514980i	$-0.172201\pi$
$109$	8.76795	+	5.06218i	0.839817	+	0.484869i	−0.0173849	+	0.999849i	$0.505534\pi$
$110$	0.633975	+	3.09808i	0.0604471	+	0.295390i
$111$		−	2.53590i		−	0.240697i
$112$		0			0
$113$	−7.73205	+	7.73205i	−0.727370	+	0.727370i	−0.970095	−	0.242725i	$-0.921959\pi$
$113$	−7.73205	+	7.73205i	−0.727370	+	0.727370i	0.242725	+	0.970095i	$0.421959\pi$
$114$	−0.169873	+	0.0980762i	−0.0159101	+	0.00918568i
$115$	−0.205771	−	0.232051i	−0.0191883	−	0.0216388i
$116$	2.59808	−	4.50000i	0.241225	−	0.417815i
$117$	7.46410	+	2.00000i	0.690056	+	0.184900i
$118$	−3.00000	−	3.00000i	−0.276172	−	0.276172i
$119$		0			0
$120$	−2.00000	+	1.00000i	−0.182574	+	0.0912871i
$121$	1.76795	+	3.06218i	0.160723	+	0.278380i
$122$	−0.205771	−	0.767949i	−0.0186297	−	0.0695269i
$123$	−0.866025	−	3.23205i	−0.0780869	−	0.291424i
$124$	6.46410	+	11.1962i	0.580493	+	1.00544i
$125$	−2.00000	+	11.0000i	−0.178885	+	0.983870i
$126$		0			0
$127$	0.464102	+	0.464102i	0.0411824	+	0.0411824i	0.727398	−	0.686216i	$-0.240729\pi$
$127$	0.464102	+	0.464102i	0.0411824	+	0.0411824i	−0.686216	+	0.727398i	$0.740729\pi$
$128$	−11.0622	−	2.96410i	−0.977768	−	0.261992i
$129$	1.03590	−	1.79423i	0.0912058	−	0.157973i
$130$	3.26795	+	0.196152i	0.286618	+	0.0172037i
$131$	13.3923	−	7.73205i	1.17009	−	0.675552i	0.216390	−	0.976307i	$-0.430572\pi$
$131$	13.3923	−	7.73205i	1.17009	−	0.675552i	0.953702	+	0.300755i	$0.0972385\pi$
$132$	1.73205	−	1.73205i	0.150756	−	0.150756i
$133$		0			0
$134$		−	5.73205i		−	0.495174i
$135$	−6.50000	+	1.33013i	−0.559431	+	0.114479i
$136$	6.46410	+	3.73205i	0.554292	+	0.320021i
$137$	13.1962	−	3.53590i	1.12742	−	0.302092i	0.353539	−	0.935420i	$-0.384978\pi$
$137$	13.1962	−	3.53590i	1.12742	−	0.302092i	0.773884	+	0.633327i	$0.218311\pi$
$138$	0.00961894	−	0.0358984i	0.000818819	−	0.00305587i
$139$	−5.66025			−0.480096			−0.240048	−	0.970761i	$-0.577163\pi$
$139$	−5.66025			−0.480096			−0.240048	+	0.970761i	$0.577163\pi$
$140$		0			0
$141$	−4.73205			−0.398511
$142$	−0.169873	+	0.633975i	−0.0142554	+	0.0532020i
$143$	−7.46410	+	2.00000i	−0.624180	+	0.167248i
$144$	−5.83013	−	3.36603i	−0.485844	−	0.280502i
$145$	3.69615	−	5.59808i	0.306949	−	0.464895i
$146$			6.92820i			0.573382i
$147$		0			0
$148$	6.00000	−	6.00000i	0.493197	−	0.493197i
$149$	−0.696152	+	0.401924i	−0.0570310	+	0.0329269i	−0.528244	−	0.849092i	$-0.677150\pi$
$149$	−0.696152	+	0.401924i	−0.0570310	+	0.0329269i	0.471213	+	0.882019i	$0.343816\pi$
$150$	−1.23205	+	0.526279i	−0.100597	+	0.0429705i
$151$	−6.92820	+	12.0000i	−0.563809	+	0.976546i	0.433350	+	0.901226i	$0.357331\pi$
$151$	−6.92820	+	12.0000i	−0.563809	+	0.976546i	−0.997159	+	0.0753205i	$0.976002\pi$
$152$	−1.36603	−	0.366025i	−0.110799	−	0.0296886i
$153$	7.46410	+	7.46410i	0.603437	+	0.603437i
$154$		0			0
$155$	7.46410	+	14.9282i	0.599531	+	1.19906i
$156$	−1.26795	−	2.19615i	−0.101517	−	0.175833i
$157$	1.24167	+	4.63397i	0.0990960	+	0.369831i	0.997609	−	0.0691164i	$-0.0220180\pi$
$157$	1.24167	+	4.63397i	0.0990960	+	0.369831i	−0.898513	+	0.438948i	$0.855351\pi$
$158$	−0.437822	−	1.63397i	−0.0348313	−	0.129992i
$159$	−1.83013	−	3.16987i	−0.145139	−	0.251387i
$160$	−10.9019	−	3.63397i	−0.861873	−	0.287291i
$161$		0			0
$162$	2.43782	+	2.43782i	0.191533	+	0.191533i
$163$	13.5622	+	3.63397i	1.06227	+	0.284635i	0.747314	−	0.664471i	$-0.231343\pi$
$163$	13.5622	+	3.63397i	1.06227	+	0.284635i	0.314958	+	0.949106i	$0.398010\pi$
$164$	5.59808	−	9.69615i	0.437136	−	0.757142i
$165$	2.36603	−	2.09808i	0.184195	−	0.163335i
$166$	1.33013	−	0.767949i	0.103238	−	0.0596044i
$167$	11.7583	−	11.7583i	0.909887	−	0.909887i	−0.0863757	−	0.996263i	$-0.527529\pi$
$167$	11.7583	−	11.7583i	0.909887	−	0.909887i	0.996263	+	0.0863757i	$0.0275285\pi$
$168$		0			0
$169$		−	5.00000i		−	0.384615i
$170$	3.73205	+	2.46410i	0.286235	+	0.188988i
$171$	−1.73205	−	1.00000i	−0.132453	−	0.0764719i
$172$	6.69615	−	1.79423i	0.510577	−	0.136809i
$173$	−5.33975	+	19.9282i	−0.405973	+	1.51511i	0.396280	+	0.918130i	$0.370301\pi$
$173$	−5.33975	+	19.9282i	−0.405973	+	1.51511i	−0.802253	+	0.596984i	$0.796366\pi$
$174$	0.803848			0.0609395
$175$		0			0
$176$	6.73205			0.507447
$177$	−1.09808	+	4.09808i	−0.0825365	+	0.308030i
$178$	0.330127	−	0.0884573i	0.0247441	−	0.00663015i
$179$	−6.80385	−	3.92820i	−0.508543	−	0.293608i	0.223691	−	0.974660i	$-0.428189\pi$
$179$	−6.80385	−	3.92820i	−0.508543	−	0.293608i	−0.732235	+	0.681052i	$0.761523\pi$
$180$	−8.83013	−	5.83013i	−0.658159	−	0.434552i
$181$		−	1.19615i		−	0.0889093i	−0.999011	−	0.0444547i	$-0.985845\pi$
$181$		−	1.19615i		−	0.0889093i	0.999011	−	0.0444547i	$-0.0141550\pi$
$182$		0			0
$183$	−0.562178	+	0.562178i	−0.0415574	+	0.0415574i
$184$	0.232051	−	0.133975i	0.0171070	−	0.00987674i
$185$	8.19615	−	7.26795i	0.602593	−	0.534350i
$186$	−1.00000	+	1.73205i	−0.0733236	+	0.127000i
$187$	−10.1962	−	2.73205i	−0.745617	−	0.199787i
$188$	−11.1962	−	11.1962i	−0.816563	−	0.816563i
$189$		0			0
$190$	−0.803848	−	0.267949i	−0.0583172	−	0.0194391i
$191$	−6.63397	−	11.4904i	−0.480018	−	0.831415i	0.519720	−	0.854337i	$-0.326036\pi$
$191$	−6.63397	−	11.4904i	−0.480018	−	0.831415i	−0.999737	+	0.0229220i	$0.992703\pi$
$192$	0.303848	+	1.13397i	0.0219283	+	0.0818376i
$193$	2.09808	+	7.83013i	0.151023	+	0.563625i	0.999413	+	0.0342537i	$0.0109054\pi$
$193$	2.09808	+	7.83013i	0.151023	+	0.563625i	−0.848390	+	0.529371i	$0.822428\pi$
$194$	−2.16987	−	3.75833i	−0.155788	−	0.269832i
$195$	−1.46410	−	2.92820i	−0.104846	−	0.209693i
$196$		0			0
$197$	−10.1244	−	10.1244i	−0.721330	−	0.721330i	0.247546	−	0.968876i	$-0.420376\pi$
$197$	−10.1244	−	10.1244i	−0.721330	−	0.721330i	−0.968876	+	0.247546i	$0.920376\pi$
$198$	−3.73205	−	1.00000i	−0.265225	−	0.0710669i
$199$	−5.53590	+	9.58846i	−0.392429	+	0.679708i	−0.992769	−	0.120037i	$-0.961699\pi$
$199$	−5.53590	+	9.58846i	−0.392429	+	0.679708i	0.600340	+	0.799745i	$0.295032\pi$
$200$	−8.96410	−	3.59808i	−0.633858	−	0.254422i
$201$	−4.96410	+	2.86603i	−0.350141	+	0.202154i
$202$	3.02628	−	3.02628i	0.212928	−	0.212928i
$203$		0			0
$204$		−	3.46410i		−	0.242536i
$205$	7.96410	−	12.0622i	0.556237	−	0.842459i
$206$	−2.13397	−	1.23205i	−0.148681	−	0.0858410i
$207$	0.366025	−	0.0980762i	0.0254405	−	0.00681677i
$208$	1.80385	−	6.73205i	0.125074	−	0.466784i
$209$	2.00000			0.138343
$210$		0			0
$211$	−0.196152			−0.0135037			−0.00675184	−	0.999977i	$-0.502149\pi$
$211$	−0.196152			−0.0135037			−0.00675184	+	0.999977i	$0.502149\pi$
$212$	3.16987	−	11.8301i	0.217708	−	0.812496i
$213$	0.633975	−	0.169873i	0.0434392	−	0.0116395i
$214$	−5.89230	−	3.40192i	−0.402790	−	0.232551i
$215$	8.76795	−	1.79423i	0.597969	−	0.122365i
$216$		−	5.73205i		−	0.390017i
$217$		0			0
$218$	−3.70577	+	3.70577i	−0.250987	+	0.250987i
$219$	6.00000	−	3.46410i	0.405442	−	0.234082i
$220$	10.5622	+	0.633975i	0.712102	+	0.0427426i
$221$	−5.46410	+	9.46410i	−0.367555	+	0.636624i
$222$	1.26795	+	0.339746i	0.0850992	+	0.0228023i
$223$	18.1244	+	18.1244i	1.21370	+	1.21370i	0.969802	+	0.243895i	$0.0784252\pi$
$223$	18.1244	+	18.1244i	1.21370	+	1.21370i	0.243895	+	0.969802i	$0.421575\pi$
$224$		0			0
$225$	−10.9282	−	8.19615i	−0.728547	−	0.546410i
$226$	−2.83013	−	4.90192i	−0.188257	−	0.326071i
$227$	5.09808	+	19.0263i	0.338371	+	1.26282i	0.900168	+	0.435543i	$0.143444\pi$
$227$	5.09808	+	19.0263i	0.338371	+	1.26282i	−0.561797	+	0.827275i	$0.689890\pi$
$228$	0.169873	+	0.633975i	0.0112501	+	0.0419860i
$229$	−9.19615	−	15.9282i	−0.607699	−	1.05257i	−0.991619	−	0.129199i	$-0.958759\pi$
$229$	−9.19615	−	15.9282i	−0.607699	−	1.05257i	0.383920	−	0.923366i	$-0.374574\pi$
$230$	0.143594	−	0.0717968i	0.00946828	−	0.00473414i
$231$		0			0
$232$	4.09808	+	4.09808i	0.269052	+	0.269052i
$233$	6.46410	+	1.73205i	0.423477	+	0.113470i	0.464263	−	0.885698i	$-0.346319\pi$
$233$	6.46410	+	1.73205i	0.423477	+	0.113470i	−0.0407854	+	0.999168i	$0.512986\pi$
$234$	−2.00000	+	3.46410i	−0.130744	+	0.226455i
$235$	−13.5622	−	15.2942i	−0.884699	−	0.997685i
$236$	−12.2942	+	7.09808i	−0.800286	+	0.462045i
$237$	−1.19615	+	1.19615i	−0.0776984	+	0.0776984i
$238$		0			0
$239$			2.39230i			0.154745i	0.997002	+	0.0773727i	$0.0246531\pi$
$239$			2.39230i			0.154745i	−0.997002	+	0.0773727i	$0.975347\pi$
$240$	0.571797	+	2.79423i	0.0369093	+	0.180367i
$241$	−21.4641	−	12.3923i	−1.38262	−	0.798259i	−0.390155	−	0.920749i	$-0.627578\pi$
$241$	−21.4641	−	12.3923i	−1.38262	−	0.798259i	−0.992470	+	0.122491i	$0.960912\pi$
$242$	−1.76795	+	0.473721i	−0.113648	+	0.0304519i
$243$	3.19615	−	11.9282i	0.205033	−	0.765195i
$244$	−2.66025			−0.170305
$245$		0			0
$246$	1.73205			0.110432
$247$	0.535898	−	2.00000i	0.0340984	−	0.127257i
$248$	−13.9282	+	3.73205i	−0.884442	+	0.236985i
$249$	−1.33013	−	0.767949i	−0.0842934	−	0.0486668i
$250$	−5.23205	−	2.47372i	−0.330904	−	0.156452i
$251$			21.8564i			1.37956i	0.724017	+	0.689782i	$0.242294\pi$
$251$			21.8564i			1.37956i	−0.724017	+	0.689782i	$0.757706\pi$
$252$		0			0
$253$	−0.267949	+	0.267949i	−0.0168458	+	0.0168458i
$254$	−0.294229	+	0.169873i	−0.0184615	+	0.0106588i
$255$	0.267949	−	4.46410i	0.0167796	−	0.279553i
$256$	0.696152	−	1.20577i	0.0435095	−	0.0753607i
$257$	2.73205	+	0.732051i	0.170421	+	0.0456641i	0.343020	−	0.939328i	$-0.388550\pi$
$257$	2.73205	+	0.732051i	0.170421	+	0.0456641i	−0.172600	+	0.984992i	$0.555217\pi$
$258$	0.758330	+	0.758330i	0.0472116	+	0.0472116i
$259$		0			0
$260$	3.46410	−	10.3923i	0.214834	−	0.644503i
$261$	4.09808	+	7.09808i	0.253665	+	0.439360i
$262$	2.07180	+	7.73205i	0.127996	+	0.477688i
$263$	4.06218	+	15.1603i	0.250485	+	0.934821i	0.970547	+	0.240912i	$0.0774465\pi$
$263$	4.06218	+	15.1603i	0.250485	+	0.934821i	−0.720062	+	0.693909i	$0.755887\pi$
$264$	1.36603	+	2.36603i	0.0840731	+	0.145619i
$265$	5.00000	−	15.0000i	0.307148	−	0.921443i
$266$		0			0
$267$	−0.241670	−	0.241670i	−0.0147899	−	0.0147899i
$268$	−18.5263	−	4.96410i	−1.13167	−	0.303231i
$269$	11.4282	−	19.7942i	0.696790	−	1.20688i	−0.272784	−	0.962075i	$-0.587944\pi$
$269$	11.4282	−	19.7942i	0.696790	−	1.20688i	0.969574	−	0.244800i	$-0.0787223\pi$
$270$	0.205771	−	3.42820i	0.0125228	−	0.208634i
$271$	−18.4186	+	10.6340i	−1.11885	+	0.645968i	−0.941107	−	0.338109i	$-0.890213\pi$
$271$	−18.4186	+	10.6340i	−1.11885	+	0.645968i	−0.177742	+	0.984077i	$0.556879\pi$
$272$	6.73205	−	6.73205i	0.408191	−	0.408191i
$273$		0			0
$274$			7.07180i			0.427223i
$275$	13.5622	+	1.63397i	0.817830	+	0.0985324i
$276$	−0.107695	−	0.0621778i	−0.00648249	−	0.00374267i
$277$	5.19615	−	1.39230i	0.312207	−	0.0836555i	−0.0993135	−	0.995056i	$-0.531665\pi$
$277$	5.19615	−	1.39230i	0.312207	−	0.0836555i	0.411520	+	0.911401i	$0.364998\pi$
$278$	0.758330	−	2.83013i	0.0454816	−	0.169740i
$279$	−20.3923			−1.22086
$280$		0			0
$281$	−0.928203			−0.0553720			−0.0276860	−	0.999617i	$-0.508814\pi$
$281$	−0.928203			−0.0553720			−0.0276860	+	0.999617i	$0.508814\pi$
$282$	0.633975	−	2.36603i	0.0377526	−	0.140895i
$283$	1.90192	−	0.509619i	0.113058	−	0.0302937i	−0.201847	−	0.979417i	$-0.564694\pi$
$283$	1.90192	−	0.509619i	0.113058	−	0.0302937i	0.314904	+	0.949123i	$0.398028\pi$
$284$	1.90192	+	1.09808i	0.112858	+	0.0651588i
$285$	0.169873	+	0.830127i	0.0100624	+	0.0491725i
$286$		−	4.00000i		−	0.236525i
$287$		0			0
$288$	9.92820	−	9.92820i	0.585025	−	0.585025i
$289$	1.79423	−	1.03590i	0.105543	−	0.0609352i
$290$	2.30385	+	2.59808i	0.135287	+	0.152564i
$291$	−2.16987	+	3.75833i	−0.127200	+	0.220317i
$292$	22.3923	+	6.00000i	1.31041	+	0.351123i
$293$	−2.39230	−	2.39230i	−0.139760	−	0.139760i	0.633765	−	0.773525i	$-0.281508\pi$
$293$	−2.39230	−	2.39230i	−0.139760	−	0.139760i	−0.773525	+	0.633765i	$0.781508\pi$
$294$		0			0
$295$	−16.3923	+	8.19615i	−0.954397	+	0.477198i
$296$	4.73205	+	8.19615i	0.275045	+	0.476392i
$297$	2.09808	+	7.83013i	0.121743	+	0.454350i
$298$	−0.107695	−	0.401924i	−0.00623861	−	0.0232828i
$299$	0.196152	+	0.339746i	0.0113438	+	0.0196480i
$300$	0.633975	+	4.43782i	0.0366025	+	0.256218i
$301$		0			0
$302$	−5.07180	−	5.07180i	−0.291849	−	0.291849i
$303$	−4.13397	−	1.10770i	−0.237491	−	0.0636354i
$304$	−0.901924	+	1.56218i	−0.0517289	+	0.0895970i
$305$	−3.42820	−	0.205771i	−0.196298	−	0.0117824i
$306$	−4.73205	+	2.73205i	−0.270513	+	0.156181i
$307$	6.29423	−	6.29423i	0.359231	−	0.359231i	−0.504299	−	0.863529i	$-0.668249\pi$
$307$	6.29423	−	6.29423i	0.359231	−	0.359231i	0.863529	+	0.504299i	$0.168249\pi$
$308$		0			0
$309$			2.46410i			0.140178i
$310$	−8.46410	+	1.73205i	−0.480729	+	0.0983739i
$311$	13.2224	+	7.63397i	0.749775	+	0.432883i	0.825613	−	0.564237i	$-0.190830\pi$
$311$	13.2224	+	7.63397i	0.749775	+	0.432883i	−0.0758374	+	0.997120i	$0.524163\pi$
$312$	2.73205	−	0.732051i	0.154672	−	0.0414442i
$313$	1.39230	−	5.19615i	0.0786977	−	0.293704i	−0.915349	−	0.402662i	$-0.868085\pi$
$313$	1.39230	−	5.19615i	0.0786977	−	0.293704i	0.994046	+	0.108958i	$0.0347515\pi$
$314$	−2.48334			−0.140143
$315$		0			0
$316$	−5.66025			−0.318414
$317$	−2.46410	+	9.19615i	−0.138398	+	0.516507i	0.861563	+	0.507651i	$0.169486\pi$
$317$	−2.46410	+	9.19615i	−0.138398	+	0.516507i	−0.999961	+	0.00885679i	$0.997181\pi$
$318$	1.83013	−	0.490381i	0.102628	−	0.0274992i
$319$	−7.09808	−	4.09808i	−0.397416	−	0.229448i
$320$	−2.79423	+	4.23205i	−0.156202	+	0.236579i
$321$			6.80385i			0.379754i
$322$		0			0
$323$	2.00000	−	2.00000i	0.111283	−	0.111283i
$324$	9.99038	−	5.76795i	0.555021	−	0.320442i
$325$	5.26795	−	13.1244i	0.292213	−	0.728008i
$326$	−3.63397	+	6.29423i	−0.201267	+	0.348605i
$327$	5.06218	+	1.35641i	0.279939	+	0.0750094i
$328$	8.83013	+	8.83013i	0.487562	+	0.487562i
$329$		0			0
$330$	0.732051	+	1.46410i	0.0402981	+	0.0805961i
$331$	0.928203	+	1.60770i	0.0510187	+	0.0883669i	0.890407	−	0.455165i	$-0.150420\pi$
$331$	0.928203	+	1.60770i	0.0510187	+	0.0883669i	−0.839388	+	0.543532i	$0.817087\pi$
$332$	−1.33013	−	4.96410i	−0.0730002	−	0.272440i
$333$	3.46410	+	12.9282i	0.189832	+	0.708461i
$334$	4.30385	+	7.45448i	0.235496	+	0.407891i
$335$	−23.4904	−	7.83013i	−1.28342	−	0.427806i
$336$		0			0
$337$	9.53590	+	9.53590i	0.519453	+	0.519453i	0.917406	−	0.397953i	$-0.130279\pi$
$337$	9.53590	+	9.53590i	0.519453	+	0.519453i	−0.397953	+	0.917406i	$0.630279\pi$
$338$	2.50000	+	0.669873i	0.135982	+	0.0364363i
$339$	−2.83013	+	4.90192i	−0.153711	+	0.266236i
$340$	11.1962	−	9.92820i	0.607197	−	0.538432i
$341$	17.6603	−	10.1962i	0.956356	−	0.552153i
$342$	0.732051	−	0.732051i	0.0395848	−	0.0395848i
$343$		0			0
$344$			7.73205i			0.416884i
$345$	−0.133975	−	0.0884573i	−0.00721295	−	0.00476238i
$346$	−9.24871	−	5.33975i	−0.497214	−	0.287067i
$347$	29.0885	−	7.79423i	1.56155	−	0.418416i	0.628396	−	0.777893i	$-0.283712\pi$
$347$	29.0885	−	7.79423i	1.56155	−	0.418416i	0.933154	+	0.359477i	$0.117045\pi$
$348$	0.696152	−	2.59808i	0.0373177	−	0.139272i
$349$	6.26795			0.335516			0.167758	−	0.985828i	$-0.446347\pi$
$349$	6.26795			0.335516			0.167758	+	0.985828i	$0.446347\pi$
$350$		0			0
$351$	8.39230			0.447948
$352$	−3.63397	+	13.5622i	−0.193691	+	0.722867i
$353$	−13.5622	+	3.63397i	−0.721842	+	0.193417i	−0.600993	−	0.799254i	$-0.705228\pi$
$353$	−13.5622	+	3.63397i	−0.721842	+	0.193417i	−0.120849	+	0.992671i	$0.538562\pi$
$354$	−1.90192	−	1.09808i	−0.101086	−	0.0583621i
$355$	2.36603	+	1.56218i	0.125576	+	0.0829118i
$356$		−	1.14359i		−	0.0606103i
$357$		0			0
$358$	2.87564	−	2.87564i	0.151983	−	0.151983i
$359$	−29.6603	+	17.1244i	−1.56541	+	0.903789i	−0.568715	+	0.822535i	$0.692559\pi$
$359$	−29.6603	+	17.1244i	−1.56541	+	0.903789i	−0.996693	+	0.0812542i	$0.974107\pi$
$360$	8.83013	−	7.83013i	0.465389	−	0.412684i
$361$	9.23205	−	15.9904i	0.485897	−	0.841599i
$362$	0.598076	+	0.160254i	0.0314342	+	0.00842277i
$363$	1.29423	+	1.29423i	0.0679294	+	0.0679294i
$364$		0			0
$365$	28.3923	+	9.46410i	1.48612	+	0.495374i
$366$	−0.205771	−	0.356406i	−0.0107558	−	0.0186297i
$367$	−0.133975	−	0.500000i	−0.00699342	−	0.0260998i	0.962341	−	0.271845i	$-0.0876339\pi$
$367$	−0.133975	−	0.500000i	−0.00699342	−	0.0260998i	−0.969334	+	0.245746i	$0.920967\pi$
$368$	−0.0884573	−	0.330127i	−0.00461115	−	0.0172091i
$369$	8.83013	+	15.2942i	0.459678	+	0.796186i
$370$	2.53590	+	5.07180i	0.131835	+	0.263670i
$371$		0			0
$372$	4.73205	+	4.73205i	0.245345	+	0.245345i
$373$	−7.73205	−	2.07180i	−0.400350	−	0.107274i	0.0530251	−	0.998593i	$-0.483114\pi$
$373$	−7.73205	−	2.07180i	−0.400350	−	0.107274i	−0.453376	+	0.891320i	$0.649780\pi$
$374$	2.73205	−	4.73205i	0.141271	−	0.244689i
$375$	0.473721	+	5.76795i	0.0244628	+	0.297856i
$376$	15.2942	−	8.83013i	0.788740	−	0.455379i
$377$	−6.00000	+	6.00000i	−0.309016	+	0.309016i
$378$		0			0
$379$			2.33975i			0.120185i	0.998193	+	0.0600923i	$0.0191395\pi$
$379$			2.33975i			0.120185i	−0.998193	+	0.0600923i	$0.980860\pi$
$380$	−1.56218	+	2.36603i	−0.0801380	+	0.121375i
$381$	0.294229	+	0.169873i	0.0150738	+	0.00870286i
$382$	6.63397	−	1.77757i	0.339424	−	0.0909483i
$383$	−8.18653	+	30.5526i	−0.418312	+	1.56116i	0.359795	+	0.933031i	$0.382847\pi$
$383$	−8.18653	+	30.5526i	−0.418312	+	1.56116i	−0.778107	+	0.628131i	$0.783820\pi$
$384$	−5.92820			−0.302522
$385$		0			0
$386$	−4.19615			−0.213579
$387$	−2.83013	+	10.5622i	−0.143863	+	0.536906i
$388$	−14.0263	+	3.75833i	−0.712076	+	0.190800i
$389$	4.26795	+	2.46410i	0.216394	+	0.124935i	0.604279	−	0.796773i	$-0.293461\pi$
$389$	4.26795	+	2.46410i	0.216394	+	0.124935i	−0.387886	+	0.921707i	$0.626794\pi$
$390$	1.66025	−	0.339746i	0.0840702	−	0.0172037i
$391$			0.535898i			0.0271015i
$392$		0			0
$393$	5.66025	−	5.66025i	0.285522	−	0.285522i
$394$	6.41858	−	3.70577i	0.323364	−	0.186694i
$395$	−7.29423	−	0.437822i	−0.367012	−	0.0220292i
$396$	−6.46410	+	11.1962i	−0.324833	+	0.562628i
$397$	3.63397	+	0.973721i	0.182384	+	0.0488696i	0.348855	−	0.937177i	$-0.386571\pi$
$397$	3.63397	+	0.973721i	0.182384	+	0.0488696i	−0.166471	+	0.986046i	$0.553237\pi$
$398$	−4.05256	−	4.05256i	−0.203136	−	0.203136i
$399$		0			0
$400$	−7.39230	+	9.85641i	−0.369615	+	0.492820i
$401$	−5.50000	−	9.52628i	−0.274657	−	0.475720i	0.695392	−	0.718631i	$-0.255231\pi$
$401$	−5.50000	−	9.52628i	−0.274657	−	0.475720i	−0.970049	+	0.242911i	$0.921898\pi$
$402$	−0.767949	−	2.86603i	−0.0383018	−	0.142944i
$403$	−5.46410	−	20.3923i	−0.272186	−	1.01581i
$404$	−7.16025	−	12.4019i	−0.356236	−	0.617019i
$405$	13.3205	−	6.66025i	0.661901	−	0.330951i
$406$		0			0
$407$	−9.46410	−	9.46410i	−0.469118	−	0.469118i
$408$	3.73205	+	1.00000i	0.184764	+	0.0495074i
$409$	−10.4282	+	18.0622i	−0.515641	+	0.893117i	0.484194	+	0.874961i	$0.339113\pi$
$409$	−10.4282	+	18.0622i	−0.515641	+	0.893117i	−0.999835	+	0.0181564i	$0.994220\pi$
$410$	4.96410	+	5.59808i	0.245160	+	0.276469i
$411$	6.12436	−	3.53590i	0.302092	−	0.174413i
$412$	−5.83013	+	5.83013i	−0.287230	+	0.287230i
$413$		0			0
$414$			0.196152i			0.00964037i
$415$	−1.33013	−	6.50000i	−0.0652934	−	0.319072i
$416$	12.5885	+	7.26795i	0.617200	+	0.356341i
$417$	−2.83013	+	0.758330i	−0.138592	+	0.0371356i
$418$	−0.267949	+	1.00000i	−0.0131058	+	0.0489116i
$419$	23.8564			1.16546			0.582731	−	0.812665i	$-0.301984\pi$
$419$	23.8564			1.16546			0.582731	+	0.812665i	$0.301984\pi$
$420$		0			0
$421$	−17.3397			−0.845088			−0.422544	−	0.906343i	$-0.638863\pi$
$421$	−17.3397			−0.845088			−0.422544	+	0.906343i	$0.638863\pi$
$422$	0.0262794	−	0.0980762i	0.00127926	−	0.00477428i
$423$	24.1244	−	6.46410i	1.17297	−	0.314295i
$424$	11.8301	+	6.83013i	0.574522	+	0.331700i
$425$	15.1962	−	11.9282i	0.737122	−	0.578603i
$426$			0.339746i			0.0164607i
$427$		0			0
$428$	−16.0981	+	16.0981i	−0.778130	+	0.778130i
$429$	−3.46410	+	2.00000i	−0.167248	+	0.0965609i
$430$	−0.277568	+	4.62436i	−0.0133855	+	0.223006i
$431$	−3.09808	+	5.36603i	−0.149229	+	0.258472i	−0.930943	−	0.365165i	$-0.881013\pi$
$431$	−3.09808	+	5.36603i	−0.149229	+	0.258472i	0.781714	+	0.623637i	$0.214346\pi$
$432$	−7.06218	−	1.89230i	−0.339779	−	0.0910436i
$433$	−17.5359	−	17.5359i	−0.842721	−	0.842721i	0.146491	−	0.989212i	$-0.453202\pi$
$433$	−17.5359	−	17.5359i	−0.842721	−	0.842721i	−0.989212	+	0.146491i	$0.953202\pi$
$434$		0			0
$435$	1.09808	−	3.29423i	0.0526487	−	0.157946i
$436$	8.76795	+	15.1865i	0.419909	+	0.727303i
$437$	−0.0262794	−	0.0980762i	−0.00125712	−	0.00469162i
$438$	0.928203	+	3.46410i	0.0443513	+	0.165521i
$439$	1.66025	+	2.87564i	0.0792396	+	0.137247i	0.902922	−	0.429804i	$-0.141417\pi$
$439$	1.66025	+	2.87564i	0.0792396	+	0.137247i	−0.823682	+	0.567051i	$0.808084\pi$
$440$	−3.73205	+	11.1962i	−0.177919	+	0.533756i
$441$		0			0
$442$	−4.00000	−	4.00000i	−0.190261	−	0.190261i
$443$	13.0622	+	3.50000i	0.620603	+	0.166290i	0.555402	−	0.831582i	$-0.312564\pi$
$443$	13.0622	+	3.50000i	0.620603	+	0.166290i	0.0652010	+	0.997872i	$0.479231\pi$
$444$	2.19615	−	3.80385i	0.104225	−	0.180523i
$445$	0.0884573	−	1.47372i	0.00419328	−	0.0698611i
$446$	−11.4904	+	6.63397i	−0.544085	+	0.314128i
$447$	−0.294229	+	0.294229i	−0.0139165	+	0.0139165i
$448$		0			0
$449$		−	33.0526i		−	1.55985i	−0.625875	−	0.779923i	$-0.715258\pi$
$449$		−	33.0526i		−	1.55985i	0.625875	−	0.779923i	$-0.284742\pi$
$450$	5.56218	−	4.36603i	0.262204	−	0.205816i
$451$	−15.2942	−	8.83013i	−0.720177	−	0.415794i
$452$	−18.2942	+	4.90192i	−0.860488	+	0.230567i
$453$	−1.85641	+	6.92820i	−0.0872216	+	0.325515i
$454$	−10.1962			−0.478529
$455$		0			0
$456$	−0.732051			−0.0342814
$457$	3.14359	−	11.7321i	0.147051	−	0.548802i	−0.852604	−	0.522557i	$-0.824978\pi$
$457$	3.14359	−	11.7321i	0.147051	−	0.548802i	0.999656	−	0.0262453i	$-0.00835510\pi$
$458$	9.19615	−	2.46410i	0.429708	−	0.115140i
$459$	9.92820	+	5.73205i	0.463409	+	0.267549i
$460$	−0.107695	−	0.526279i	−0.00502131	−	0.0245379i
$461$		−	5.60770i		−	0.261176i	−0.991437	−	0.130588i	$-0.958313\pi$
$461$		−	5.60770i		−	0.261176i	0.991437	−	0.130588i	$-0.0416866\pi$
$462$		0			0
$463$	−4.75833	+	4.75833i	−0.221138	+	0.221138i	−0.808978	−	0.587839i	$-0.799979\pi$
$463$	−4.75833	+	4.75833i	−0.221138	+	0.221138i	0.587839	+	0.808978i	$0.299979\pi$
$464$	6.40192	−	3.69615i	0.297202	−	0.171590i
$465$	5.73205	+	6.46410i	0.265817	+	0.299766i
$466$	−1.73205	+	3.00000i	−0.0802357	+	0.138972i
$467$	−13.5981	−	3.64359i	−0.629244	−	0.168605i	−0.0699173	−	0.997553i	$-0.522274\pi$
$467$	−13.5981	−	3.64359i	−0.629244	−	0.168605i	−0.559327	+	0.828947i	$0.688940\pi$
$468$	9.46410	+	9.46410i	0.437478	+	0.437478i
$469$		0			0
$470$	9.46410	−	4.73205i	0.436546	−	0.218273i
$471$	1.24167	+	2.15064i	0.0572131	+	0.0990960i
$472$	−4.09808	−	15.2942i	−0.188629	−	0.703974i
$473$	−2.83013	−	10.5622i	−0.130129	−	0.485649i
$474$	−0.437822	−	0.758330i	−0.0201098	−	0.0348313i
$475$	−2.19615	+	2.92820i	−0.100766	+	0.134355i
$476$		0			0
$477$	13.6603	+	13.6603i	0.625460	+	0.625460i
$478$	−1.19615	−	0.320508i	−0.0547107	−	0.0146597i
$479$	6.53590	−	11.3205i	0.298633	−	0.517247i	−0.677191	−	0.735808i	$-0.736803\pi$
$479$	6.53590	−	11.3205i	0.298633	−	0.517247i	0.975823	+	0.218560i	$0.0701361\pi$
$480$	−5.93782	−	0.356406i	−0.271023	−	0.0162677i
$481$	−12.0000	+	6.92820i	−0.547153	+	0.315899i
$482$	9.07180	−	9.07180i	0.413209	−	0.413209i
$483$		0			0
$484$			6.12436i			0.278380i
$485$	−18.3660	+	3.75833i	−0.833958	+	0.170657i
$486$	5.53590	+	3.19615i	0.251113	+	0.144980i
$487$	−27.2224	+	7.29423i	−1.23357	+	0.330533i	−0.815967	−	0.578098i	$-0.803795\pi$
$487$	−27.2224	+	7.29423i	−1.23357	+	0.330533i	−0.417599	+	0.908631i	$0.637128\pi$
$488$	0.767949	−	2.86603i	0.0347634	−	0.129739i
$489$	7.26795			0.328668
$490$		0			0
$491$	37.7128			1.70196			0.850978	−	0.525202i	$-0.176010\pi$
$491$	37.7128			1.70196			0.850978	+	0.525202i	$0.176010\pi$
$492$	1.50000	−	5.59808i	0.0676252	−	0.252381i
$493$	−11.1962	+	3.00000i	−0.504249	+	0.135113i
$494$	0.928203	+	0.535898i	0.0417618	+	0.0241112i
$495$	−9.19615	+	13.9282i	−0.413336	+	0.626026i
$496$			18.3923i			0.825839i
$497$		0			0
$498$	0.562178	−	0.562178i	0.0251918	−	0.0251918i
$499$	9.97372	−	5.75833i	0.446485	−	0.257778i	−0.259860	−	0.965646i	$-0.583676\pi$
$499$	9.97372	−	5.75833i	0.446485	−	0.257778i	0.706345	+	0.707868i	$0.250343\pi$
$500$	−12.5263	+	14.7679i	−0.560192	+	0.660443i
$501$	4.30385	−	7.45448i	0.192282	−	0.333042i
$502$	−10.9282	−	2.92820i	−0.487750	−	0.130692i
$503$	−17.6340	−	17.6340i	−0.786260	−	0.786260i	0.194619	−	0.980879i	$-0.437653\pi$
$503$	−17.6340	−	17.6340i	−0.786260	−	0.786260i	−0.980879	+	0.194619i	$0.937653\pi$
$504$		0			0
$505$	−8.26795	−	16.5359i	−0.367919	−	0.735838i
$506$	−0.0980762	−	0.169873i	−0.00436002	−	0.00755178i
$507$	−0.669873	−	2.50000i	−0.0297501	−	0.111029i
$508$	0.294229	+	1.09808i	0.0130543	+	0.0487193i
$509$	−19.4545	−	33.6962i	−0.862305	−	1.49356i	−0.869699	−	0.493583i	$-0.835687\pi$
$509$	−19.4545	−	33.6962i	−0.862305	−	1.49356i	0.00739389	−	0.999973i	$-0.497646\pi$
$510$	2.19615	+	0.732051i	0.0972473	+	0.0324158i
$511$		0			0
$512$	−15.6865	−	15.6865i	−0.693253	−	0.693253i
$513$	−2.09808	−	0.562178i	−0.0926323	−	0.0248208i
$514$	−0.732051	+	1.26795i	−0.0322894	+	0.0559268i
$515$	−7.96410	+	7.06218i	−0.350940	+	0.311197i
$516$	3.10770	−	1.79423i	0.136809	−	0.0789865i
$517$	−17.6603	+	17.6603i	−0.776697	+	0.776697i
$518$		0			0
$519$			10.6795i			0.468778i
$520$	10.1962	+	6.73205i	0.447131	+	0.295220i
$521$	20.6603	+	11.9282i	0.905142	+	0.522584i	0.878865	−	0.477071i	$-0.158301\pi$
$521$	20.6603	+	11.9282i	0.905142	+	0.522584i	0.0262772	+	0.999655i	$0.491635\pi$
$522$	−4.09808	+	1.09808i	−0.179368	+	0.0480615i
$523$	11.4904	−	42.8827i	0.502439	−	1.87513i	0.0188717	−	0.999822i	$-0.493993\pi$
$523$	11.4904	−	42.8827i	0.502439	−	1.87513i	0.483568	−	0.875307i	$-0.339341\pi$
$524$	26.7846			1.17009
$525$		0			0
$526$	−8.12436			−0.354239
$527$	7.46410	−	27.8564i	0.325141	−	1.21344i
$528$	3.36603	−	0.901924i	0.146487	−	0.0392512i
$529$	−19.9019	−	11.4904i	−0.865301	−	0.499582i
$530$	6.83013	+	4.50962i	0.296682	+	0.195885i
$531$		−	22.3923i		−	0.971743i
$532$		0			0
$533$	−12.9282	+	12.9282i	−0.559983	+	0.559983i
$534$	0.153212	−	0.0884573i	0.00663015	−	0.00382792i
$535$	−21.9904	+	19.5000i	−0.950727	+	0.843059i
$536$	10.6962	−	18.5263i	0.462003	−	0.800213i
$537$	−3.92820	−	1.05256i	−0.169514	−	0.0454213i
$538$	8.36603	+	8.36603i	0.360685	+	0.360685i
$539$		0			0
$540$	−10.9019	−	3.63397i	−0.469144	−	0.156381i
$541$	−18.3564	−	31.7942i	−0.789204	−	1.36694i	−0.926455	−	0.376404i	$-0.877160\pi$
$541$	−18.3564	−	31.7942i	−0.789204	−	1.36694i	0.137252	−	0.990536i	$-0.456173\pi$
$542$	−2.84936	−	10.6340i	−0.122391	−	0.456768i
$543$	−0.160254	−	0.598076i	−0.00687716	−	0.0256659i
$544$	9.92820	+	17.1962i	0.425668	+	0.737279i
$545$	10.1244	+	20.2487i	0.433680	+	0.867359i
$546$		0			0
$547$	−16.7583	−	16.7583i	−0.716534	−	0.716534i	0.251359	−	0.967894i	$-0.419122\pi$
$547$	−16.7583	−	16.7583i	−0.716534	−	0.716534i	−0.967894	+	0.251359i	$0.919122\pi$
$548$	22.8564	+	6.12436i	0.976377	+	0.261620i
$549$	2.09808	−	3.63397i	0.0895437	−	0.155094i
$550$	−2.63397	+	6.56218i	−0.112313	+	0.279812i
$551$	1.90192	−	1.09808i	0.0810247	−	0.0467796i
$552$	0.0980762	−	0.0980762i	0.00417440	−	0.00417440i
$553$		0			0
$554$			2.78461i			0.118307i
$555$	3.12436	−	4.73205i	0.132622	−	0.200864i
$556$	−8.49038	−	4.90192i	−0.360072	−	0.207888i
$557$	−31.2224	+	8.36603i	−1.32294	+	0.354480i	−0.850077	−	0.526658i	$-0.823445\pi$
$557$	−31.2224	+	8.36603i	−1.32294	+	0.354480i	−0.472860	+	0.881138i	$0.656778\pi$
$558$	2.73205	−	10.1962i	0.115657	−	0.431638i
$559$	−11.3205			−0.478806
$560$		0			0
$561$	−5.46410			−0.230695
$562$	0.124356	−	0.464102i	0.00524563	−	0.0195769i
$563$	23.7224	−	6.35641i	0.999781	−	0.267891i	0.278427	−	0.960457i	$-0.410187\pi$
$563$	23.7224	−	6.35641i	0.999781	−	0.267891i	0.721354	+	0.692567i	$0.243520\pi$
$564$	−7.09808	−	4.09808i	−0.298883	−	0.172560i
$565$	−23.9545	+	4.90192i	−1.00777	+	0.206225i
$566$			1.01924i			0.0428418i
$567$		0			0
$568$	−1.73205	+	1.73205i	−0.0726752	+	0.0726752i
$569$	25.0526	−	14.4641i	1.05026	−	0.606367i	0.127536	−	0.991834i	$-0.459293\pi$
$569$	25.0526	−	14.4641i	1.05026	−	0.606367i	0.922722	+	0.385467i	$0.125960\pi$
$570$	−0.437822	−	0.0262794i	−0.0183384	−	0.00110072i
$571$	9.02628	−	15.6340i	0.377738	−	0.654261i	−0.612995	−	0.790087i	$-0.710035\pi$
$571$	9.02628	−	15.6340i	0.377738	−	0.654261i	0.990733	+	0.135826i	$0.0433687\pi$
$572$	−12.9282	−	3.46410i	−0.540555	−	0.144841i
$573$	−4.85641	−	4.85641i	−0.202879	−	0.202879i
$574$		0			0
$575$	−0.0980762	−	0.686533i	−0.00409006	−	0.0286304i
$576$	−3.09808	−	5.36603i	−0.129087	−	0.223584i
$577$	−1.50962	−	5.63397i	−0.0628463	−	0.234545i	0.927357	−	0.374177i	$-0.122075\pi$
$577$	−1.50962	−	5.63397i	−0.0628463	−	0.234545i	−0.990204	+	0.139632i	$0.955408\pi$
$578$	0.277568	+	1.03590i	0.0115453	+	0.0430877i
$579$	2.09808	+	3.63397i	0.0871931	+	0.151023i
$580$	10.3923	−	5.19615i	0.431517	−	0.215758i
$581$		0			0
$582$	−1.58846	−	1.58846i	−0.0658437	−	0.0658437i
$583$	−18.6603	−	5.00000i	−0.772829	−	0.207079i
$584$	−12.9282	+	22.3923i	−0.534973	+	0.926600i
$585$	11.4641	+	12.9282i	0.473982	+	0.534515i
$586$	1.51666	−	0.875644i	0.0626527	−	0.0361725i
$587$	15.7846	−	15.7846i	0.651501	−	0.651501i	−0.301854	−	0.953354i	$-0.597605\pi$
$587$	15.7846	−	15.7846i	0.651501	−	0.651501i	0.953354	+	0.301854i	$0.0976054\pi$
$588$		0			0
$589$			5.46410i			0.225144i
$590$	−1.90192	−	9.29423i	−0.0783010	−	0.382637i
$591$	−6.41858	−	3.70577i	−0.264025	−	0.152435i
$592$	11.6603	−	3.12436i	0.479233	−	0.128410i
$593$	−5.56218	+	20.7583i	−0.228411	+	0.852442i	0.752598	+	0.658481i	$0.228801\pi$
$593$	−5.56218	+	20.7583i	−0.228411	+	0.852442i	−0.981009	+	0.193962i	$0.937866\pi$
$594$	−4.19615			−0.172170
$595$		0			0
$596$	−1.39230			−0.0570310
$597$	−1.48334	+	5.53590i	−0.0607090	+	0.226569i
$598$	−0.196152	+	0.0525589i	−0.00802127	+	0.00214929i
$599$	15.3397	+	8.85641i	0.626765	+	0.361863i	0.779498	−	0.626405i	$-0.215474\pi$
$599$	15.3397	+	8.85641i	0.626765	+	0.361863i	−0.152733	+	0.988267i	$0.548807\pi$
$600$	−4.96410	−	0.598076i	−0.202659	−	0.0244164i
$601$		−	41.1769i		−	1.67964i	−0.542864	−	0.839821i	$-0.682660\pi$
$601$		−	41.1769i		−	1.67964i	0.542864	−	0.839821i	$-0.317340\pi$
$602$		0			0
$603$	21.3923	−	21.3923i	0.871162	−	0.871162i
$604$	−20.7846	+	12.0000i	−0.845714	+	0.488273i
$605$	−0.473721	+	7.89230i	−0.0192595	+	0.320868i
$606$	1.10770	−	1.91858i	0.0449970	−	0.0779372i
$607$	−12.6962	−	3.40192i	−0.515321	−	0.138080i	−0.00821951	−	0.999966i	$-0.502616\pi$
$607$	−12.6962	−	3.40192i	−0.515321	−	0.138080i	−0.507101	+	0.861886i	$0.669283\pi$
$608$	−2.66025	−	2.66025i	−0.107888	−	0.107888i
$609$		0			0
$610$	0.562178	−	1.68653i	0.0227619	−	0.0682857i
$611$	12.9282	+	22.3923i	0.523019	+	0.905896i
$612$	4.73205	+	17.6603i	0.191282	+	0.713873i
$613$	−6.53590	−	24.3923i	−0.263982	−	0.985196i	−0.962870	−	0.269965i	$-0.912988\pi$
$613$	−6.53590	−	24.3923i	−0.263982	−	0.985196i	0.698888	−	0.715231i	$-0.253679\pi$
$614$	2.30385	+	3.99038i	0.0929757	+	0.161039i
$615$	2.36603	−	7.09808i	0.0954074	−	0.286222i
$616$		0			0
$617$	33.9090	+	33.9090i	1.36512	+	1.36512i	0.867249	+	0.497874i	$0.165886\pi$
$617$	33.9090	+	33.9090i	1.36512	+	1.36512i	0.497874	+	0.867249i	$0.334114\pi$
$618$	−1.23205	−	0.330127i	−0.0495604	−	0.0132797i
$619$	5.09808	−	8.83013i	0.204909	−	0.354913i	−0.745195	−	0.666847i	$-0.767643\pi$
$619$	5.09808	−	8.83013i	0.204909	−	0.354913i	0.950104	+	0.311934i	$0.100977\pi$
$620$	−1.73205	+	28.8564i	−0.0695608	+	1.15890i
$621$	0.356406	−	0.205771i	0.0143021	−	0.00825732i
$622$	−5.58846	+	5.58846i	−0.224077	+	0.224077i
$623$		0			0
$624$		−	3.60770i		−	0.144423i
$625$	−17.2846	+	18.0622i	−0.691384	+	0.722487i
$626$	2.41154	+	1.39230i	0.0963846	+	0.0556477i
$627$	1.00000	−	0.267949i	0.0399362	−	0.0107009i
$628$	−2.15064	+	8.02628i	−0.0858197	+	0.320283i
$629$	−18.9282			−0.754717
$630$		0			0
$631$	−4.58846			−0.182664			−0.0913318	−	0.995821i	$-0.529112\pi$
$631$	−4.58846			−0.182664			−0.0913318	+	0.995821i	$0.529112\pi$
$632$	1.63397	−	6.09808i	0.0649960	−	0.242568i
$633$	−0.0980762	+	0.0262794i	−0.00389818	+	0.00104451i
$634$	−4.26795	−	2.46410i	−0.169502	−	0.0978620i
$635$	0.294229	+	1.43782i	0.0116761	+	0.0570582i
$636$		−	6.33975i		−	0.251387i
$637$		0			0
$638$	3.00000	−	3.00000i	0.118771	−	0.118771i
$639$	−3.00000	+	1.73205i	−0.118678	+	0.0685189i
$640$	−16.9904	−	19.1603i	−0.671604	−	0.757376i
$641$	−5.33013	+	9.23205i	−0.210527	+	0.364644i	−0.951880	−	0.306472i	$-0.900851\pi$
$641$	−5.33013	+	9.23205i	−0.210527	+	0.364644i	0.741352	+	0.671116i	$0.234185\pi$
$642$	−3.40192	−	0.911543i	−0.134263	−	0.0359757i
$643$	17.5359	+	17.5359i	0.691548	+	0.691548i	0.962573	−	0.271024i	$-0.0873623\pi$
$643$	17.5359	+	17.5359i	0.691548	+	0.691548i	−0.271024	+	0.962573i	$0.587362\pi$
$644$		0			0
$645$	4.14359	−	2.07180i	0.163154	−	0.0815769i
$646$	0.732051	+	1.26795i	0.0288022	+	0.0498868i
$647$	−10.5981	−	39.5526i	−0.416653	−	1.55497i	−0.781501	−	0.623904i	$-0.785546\pi$
$647$	−10.5981	−	39.5526i	−0.416653	−	1.55497i	0.364847	−	0.931067i	$-0.381121\pi$
$648$	3.33013	+	12.4282i	0.130820	+	0.488226i
$649$	11.1962	+	19.3923i	0.439487	+	0.761215i
$650$	5.85641	+	4.39230i	0.229707	+	0.172280i
$651$		0			0
$652$	17.1962	+	17.1962i	0.673453	+	0.673453i
$653$	19.6603	+	5.26795i	0.769365	+	0.206151i	0.622091	−	0.782945i	$-0.286283\pi$
$653$	19.6603	+	5.26795i	0.769365	+	0.206151i	0.147274	+	0.989096i	$0.452950\pi$
$654$	−1.35641	+	2.34936i	−0.0530397	+	0.0918674i
$655$	34.5167	+	2.07180i	1.34868	+	0.0809518i
$656$	13.7942	−	7.96410i	0.538574	−	0.310946i
$657$	−25.8564	+	25.8564i	−1.00875	+	1.00875i
$658$		0			0
$659$		−	27.6603i		−	1.07749i	−0.842469	−	0.538745i	$-0.818899\pi$
$659$		−	27.6603i		−	1.07749i	0.842469	−	0.538745i	$-0.181101\pi$
$660$	5.36603	−	1.09808i	0.208872	−	0.0427426i
$661$	41.7224	+	24.0885i	1.62281	+	0.936932i	0.986163	+	0.165781i	$0.0530145\pi$
$661$	41.7224	+	24.0885i	1.62281	+	0.936932i	0.636652	+	0.771151i	$0.280319\pi$
$662$	−0.928203	+	0.248711i	−0.0360756	+	0.00966644i
$663$	−1.46410	+	5.46410i	−0.0568610	+	0.212208i
$664$	5.73205			0.222447
$665$		0			0
$666$	−6.92820			−0.268462
$667$	−0.107695	+	0.401924i	−0.00416997	+	0.0155626i
$668$	27.8205	−	7.45448i	1.07641	−	0.288423i
$669$	11.4904	+	6.63397i	0.444244	+	0.256484i
$670$	7.06218	−	10.6962i	0.272836	−	0.413228i
$671$			4.19615i			0.161991i
$672$		0			0
$673$	4.39230	−	4.39230i	0.169311	−	0.169311i	−0.617366	−	0.786676i	$-0.711800\pi$
$673$	4.39230	−	4.39230i	0.169311	−	0.169311i	0.786676	+	0.617366i	$0.211800\pi$
$674$	−6.04552	+	3.49038i	−0.232865	+	0.134444i
$675$	−13.7679	−	5.52628i	−0.529929	−	0.212707i
$676$	4.33013	−	7.50000i	0.166543	−	0.288462i
$677$	25.8564	+	6.92820i	0.993742	+	0.266272i	0.718822	−	0.695194i	$-0.244682\pi$
$677$	25.8564	+	6.92820i	0.993742	+	0.266272i	0.274921	+	0.961467i	$0.411348\pi$
$678$	−2.07180	−	2.07180i	−0.0795669	−	0.0795669i
$679$		0			0
$680$	7.46410	+	14.9282i	0.286235	+	0.572470i
$681$	5.09808	+	8.83013i	0.195359	+	0.338371i
$682$	2.73205	+	10.1962i	0.104616	+	0.390431i
$683$	−4.57180	−	17.0622i	−0.174935	−	0.652866i	−0.996563	−	0.0828417i	$-0.973600\pi$
$683$	−4.57180	−	17.0622i	−0.174935	−	0.652866i	0.821628	−	0.570024i	$-0.193066\pi$
$684$	−1.73205	−	3.00000i	−0.0662266	−	0.114708i
$685$	28.9808	+	9.66025i	1.10730	+	0.369099i
$686$		0			0
$687$	−6.73205	−	6.73205i	−0.256844	−	0.256844i
$688$	9.52628	+	2.55256i	0.363186	+	0.0973154i
$689$	−10.0000	+	17.3205i	−0.380970	+	0.659859i
$690$	0.0621778	−	0.0551363i	0.00236707	−	0.00209900i
$691$	44.0263	−	25.4186i	1.67484	−	0.966969i	0.709971	−	0.704231i	$-0.248708\pi$
$691$	44.0263	−	25.4186i	1.67484	−	0.966969i	0.964867	−	0.262738i	$-0.0846255\pi$
$692$	−25.2679	+	25.2679i	−0.960543	+	0.960543i
$693$		0			0
$694$			15.5885i			0.591730i
$695$	−10.5622	−	6.97372i	−0.400646	−	0.264528i
$696$	2.59808	+	1.50000i	0.0984798	+	0.0568574i
$697$	−24.1244	+	6.46410i	−0.913775	+	0.244845i
$698$	−0.839746	+	3.13397i	−0.0317849	+	0.118623i
$699$	3.46410			0.131024
$700$		0			0
$701$	−20.2679			−0.765510			−0.382755	−	0.923850i	$-0.625025\pi$
$701$	−20.2679			−0.765510			−0.382755	+	0.923850i	$0.625025\pi$
$702$	−1.12436	+	4.19615i	−0.0424361	+	0.158374i
$703$	3.46410	−	0.928203i	0.130651	−	0.0350078i
$704$	5.36603	+	3.09808i	0.202240	+	0.116763i
$705$	−8.83013	−	5.83013i	−0.332562	−	0.219575i
$706$		−	7.26795i		−	0.273533i
$707$		0			0
$708$	−5.19615	+	5.19615i	−0.195283	+	0.195283i
$709$	−18.9904	+	10.9641i	−0.713199	+	0.411765i	−0.812244	−	0.583317i	$-0.801754\pi$
$709$	−18.9904	+	10.9641i	−0.713199	+	0.411765i	0.0990456	+	0.995083i	$0.468421\pi$
$710$	−1.09808	+	0.973721i	−0.0412101	+	0.0365431i
$711$	4.46410	−	7.73205i	0.167417	−	0.289975i
$712$	1.23205	+	0.330127i	0.0461731	+	0.0123720i
$713$	−0.732051	−	0.732051i	−0.0274155	−	0.0274155i
$714$		0			0
$715$	−16.3923	−	5.46410i	−0.613037	−	0.204346i
$716$	−6.80385	−	11.7846i	−0.254272	−	0.440412i
$717$	0.320508	+	1.19615i	0.0119696	+	0.0446711i
$718$	−4.58846	−	17.1244i	−0.171240	−	0.639075i
$719$	19.2942	+	33.4186i	0.719553	+	1.24630i	0.961177	+	0.275933i	$0.0889867\pi$
$719$	19.2942	+	33.4186i	0.719553	+	1.24630i	−0.241624	+	0.970370i	$0.577680\pi$
$720$	−6.73205	−	13.4641i	−0.250889	−	0.501777i
$721$		0			0
$722$	6.75833	+	6.75833i	0.251519	+	0.251519i
$723$	−12.3923	−	3.32051i	−0.460875	−	0.123491i
$724$	1.03590	−	1.79423i	0.0384989	−	0.0666820i
$725$	13.7942	−	5.89230i	0.512305	−	0.218835i
$726$	−0.820508	+	0.473721i	−0.0304519	+	0.0175814i
$727$	−10.0981	+	10.0981i	−0.374517	+	0.374517i	−0.869119	−	0.494602i	$-0.835314\pi$
$727$	−10.0981	+	10.0981i	−0.374517	+	0.374517i	0.494602	+	0.869119i	$0.335314\pi$
$728$		0			0
$729$			13.5885i			0.503276i
$730$	−8.53590	+	12.9282i	−0.315928	+	0.478494i
$731$	−13.3923	−	7.73205i	−0.495332	−	0.285980i
$732$	−1.33013	+	0.356406i	−0.0491629	+	0.0131732i
$733$	1.16987	−	4.36603i	0.0432102	−	0.161263i	−0.940949	−	0.338547i	$-0.890065\pi$
$733$	1.16987	−	4.36603i	0.0432102	−	0.161263i	0.984160	+	0.177284i	$0.0567312\pi$
$734$	0.267949			0.00989019
$735$		0			0
$736$	0.712813			0.0262746
$737$	−7.83013	+	29.2224i	−0.288426	+	1.07642i
$738$	−8.83013	+	2.36603i	−0.325041	+	0.0870946i
$739$	19.5622	+	11.2942i	0.719606	+	0.415465i	0.814608	−	0.580012i	$-0.196952\pi$
$739$	19.5622	+	11.2942i	0.719606	+	0.415465i	−0.0950014	+	0.995477i	$0.530286\pi$
$740$	18.5885	−	3.80385i	0.683325	−	0.139832i
$741$		−	1.07180i		−	0.0393734i
$742$		0			0
$743$	−6.16987	+	6.16987i	−0.226351	+	0.226351i	−0.811166	−	0.584816i	$-0.801167\pi$
$743$	−6.16987	+	6.16987i	−0.226351	+	0.226351i	0.584816	+	0.811166i	$0.301167\pi$
$744$	−6.46410	+	3.73205i	−0.236985	+	0.136824i
$745$	−1.79423	−	0.107695i	−0.0657355	−	0.00394565i
$746$	2.07180	−	3.58846i	0.0758539	−	0.131383i
$747$	7.83013	+	2.09808i	0.286489	+	0.0767646i
$748$	−12.9282	−	12.9282i	−0.472702	−	0.472702i
$749$		0			0
$750$	−2.94744	−	0.535898i	−0.107625	−	0.0195682i
$751$	3.19615	+	5.53590i	0.116629	+	0.202008i	0.918430	−	0.395584i	$-0.129458\pi$
$751$	3.19615	+	5.53590i	0.116629	+	0.202008i	−0.801801	+	0.597592i	$0.796124\pi$
$752$	−5.83013	−	21.7583i	−0.212603	−	0.793445i
$753$	2.92820	+	10.9282i	0.106710	+	0.398246i
$754$	−2.19615	−	3.80385i	−0.0799792	−	0.138528i
$755$	−27.7128	+	13.8564i	−1.00857	+	0.504286i
$756$		0			0
$757$	12.7321	+	12.7321i	0.462754	+	0.462754i	0.899557	−	0.436803i	$-0.143889\pi$
$757$	12.7321	+	12.7321i	0.462754	+	0.462754i	−0.436803	+	0.899557i	$0.643889\pi$
$758$	−1.16987	−	0.313467i	−0.0424917	−	0.0113856i
$759$	−0.0980762	+	0.169873i	−0.00355994	+	0.00616600i
$760$	−2.09808	−	2.36603i	−0.0761052	−	0.0858248i
$761$	−24.9282	+	14.3923i	−0.903647	+	0.521721i	−0.878382	−	0.477960i	$-0.841376\pi$
$761$	−24.9282	+	14.3923i	−0.903647	+	0.521721i	−0.0252651	+	0.999681i	$0.508043\pi$
$762$	−0.124356	+	0.124356i	−0.00450493	+	0.00450493i
$763$		0			0
$764$		−	22.9808i		−	0.831415i
$765$	4.73205	+	23.1244i	0.171088	+	0.836063i
$766$	−14.1795	−	8.18653i	−0.512326	−	0.295791i
$767$	22.3923	−	6.00000i	0.808539	−	0.216647i
$768$	0.186533	−	0.696152i	0.00673095	−	0.0251202i
$769$	15.1769			0.547294			0.273647	−	0.961830i	$-0.411770\pi$
$769$	15.1769			0.547294			0.273647	+	0.961830i	$0.411770\pi$
$770$		0			0
$771$	1.46410			0.0527283
$772$	−3.63397	+	13.5622i	−0.130790	+	0.488113i
$773$	−15.1962	+	4.07180i	−0.546568	+	0.146452i	−0.521528	−	0.853234i	$-0.674638\pi$
$773$	−15.1962	+	4.07180i	−0.546568	+	0.146452i	−0.0250395	+	0.999686i	$0.507971\pi$
$774$	−4.90192	−	2.83013i	−0.176196	−	0.101727i
$775$	−4.46410	+	37.0526i	−0.160355	+	1.33097i
$776$		−	16.1962i		−	0.581408i
$777$		0			0
$778$	−1.80385	+	1.80385i	−0.0646711	+	0.0646711i
$779$	4.09808	−	2.36603i	0.146829	−	0.0847717i
$780$	0.339746	−	5.66025i	0.0121649	−	0.202670i
$781$	1.73205	−	3.00000i	0.0619777	−	0.107348i
$782$	−0.267949	−	0.0717968i	−0.00958184	−	0.00256745i
$783$	6.29423	+	6.29423i	0.224937	+	0.224937i
$784$		0			0
$785$	−3.39230	+	10.1769i	−0.121077	+	0.363230i
$786$	2.07180	+	3.58846i	0.0738985	+	0.127996i
$787$	−8.35641	−	31.1865i	−0.297874	−	1.11168i	−0.938908	−	0.344168i	$-0.888161\pi$
$787$	−8.35641	−	31.1865i	−0.297874	−	1.11168i	0.641034	−	0.767512i	$-0.278506\pi$
$788$	−6.41858	−	23.9545i	−0.228653	−	0.853343i
$789$	4.06218	+	7.03590i	0.144617	+	0.250485i
$790$	1.19615	−	3.58846i	0.0425572	−	0.127672i
$791$		0			0
$792$	−10.1962	−	10.1962i	−0.362305	−	0.362305i
$793$	4.19615	+	1.12436i	0.149010	+	0.0399270i
$794$	−0.973721	+	1.68653i	−0.0345560	+	0.0598528i
$795$	0.490381	−	8.16987i	0.0173920	−	0.289756i
$796$	−16.6077	+	9.58846i	−0.588644	+	0.339854i
$797$	22.5359	−	22.5359i	0.798262	−	0.798262i	−0.184559	−	0.982821i	$-0.559086\pi$
$797$	22.5359	−	22.5359i	0.798262	−	0.798262i	0.982821	+	0.184559i	$0.0590857\pi$
$798$		0			0
$799$			35.3205i			1.24955i
$800$	−15.8660	−	20.2128i	−0.560949	−	0.714631i
$801$	1.56218	+	0.901924i	0.0551968	+	0.0318679i
$802$	5.50000	−	1.47372i	0.194212	−	0.0520389i
$803$	9.46410	−	35.3205i	0.333981	−	1.24643i
$804$	−9.92820			−0.350141
$805$		0			0
$806$	10.9282			0.384930
$807$	3.06218	−	11.4282i	0.107794	−	0.402292i
$808$	15.4282	−	4.13397i	0.542762	−	0.145433i
$809$	3.99038	+	2.30385i	0.140294	+	0.0809990i	0.568504	−	0.822680i	$-0.307522\pi$
$809$	3.99038	+	2.30385i	0.140294	+	0.0809990i	−0.428210	+	0.903679i	$0.640856\pi$
$810$	1.54552	+	7.55256i	0.0543039	+	0.265370i
$811$			42.9282i			1.50741i	0.657211	+	0.753707i	$0.271736\pi$
$811$			42.9282i			1.50741i	−0.657211	+	0.753707i	$0.728264\pi$
$812$		0			0
$813$	−7.78461	+	7.78461i	−0.273018	+	0.273018i
$814$	6.00000	−	3.46410i	0.210300	−	0.121417i
$815$	20.8301	+	23.4904i	0.729648	+	0.822832i
$816$	2.46410	−	4.26795i	0.0862608	−	0.149408i
$817$	2.83013	+	0.758330i	0.0990136	+	0.0265306i
$818$	−7.63397	−	7.63397i	−0.266916	−	0.266916i
$819$		0			0
$820$	22.3923	−	11.1962i	0.781973	−	0.390987i
$821$	24.6603	+	42.7128i	0.860649	+	1.49069i	0.871304	+	0.490744i	$0.163275\pi$
$821$	24.6603	+	42.7128i	0.860649	+	1.49069i	−0.0106549	+	0.999943i	$0.503392\pi$
$822$	0.947441	+	3.53590i	0.0330458	+	0.123329i
$823$	14.3038	+	53.3827i	0.498601	+	1.86080i	0.508849	+	0.860856i	$0.330071\pi$
$823$	14.3038	+	53.3827i	0.498601	+	1.86080i	−0.0102479	+	0.999947i	$0.503262\pi$
$824$	−4.59808	−	7.96410i	−0.160182	−	0.277443i
$825$	7.00000	−	1.00000i	0.243709	−	0.0348155i
$826$		0			0
$827$	−33.2224	−	33.2224i	−1.15526	−	1.15526i	−0.985483	−	0.169774i	$-0.945696\pi$
$827$	−33.2224	−	33.2224i	−1.15526	−	1.15526i	−0.169774	−	0.985483i	$-0.554304\pi$
$828$	0.633975	+	0.169873i	0.0220321	+	0.00590349i
$829$	−7.26795	+	12.5885i	−0.252426	+	0.437215i	−0.964193	−	0.265200i	$-0.914562\pi$
$829$	−7.26795	+	12.5885i	−0.252426	+	0.437215i	0.711767	+	0.702416i	$0.247895\pi$
$830$	3.42820	+	0.205771i	0.118995	+	0.00714243i
$831$	2.41154	−	1.39230i	0.0836555	−	0.0482985i
$832$	4.53590	−	4.53590i	0.157254	−	0.157254i
$833$		0			0
$834$		−	1.51666i		−	0.0525177i
$835$	36.4282	−	7.45448i	1.26065	−	0.257973i
$836$	3.00000	+	1.73205i	0.103757	+	0.0599042i
$837$	−21.3923	+	5.73205i	−0.739426	+	0.198129i
$838$	−3.19615	+	11.9282i	−0.110409	+	0.412053i
$839$	6.87564			0.237374			0.118687	−	0.992932i	$-0.462132\pi$
$839$	6.87564			0.237374			0.118687	+	0.992932i	$0.462132\pi$
$840$		0			0
$841$	20.0000			0.689655
$842$	2.32309	−	8.66987i	0.0800588	−	0.298784i
$843$	−0.464102	+	0.124356i	−0.0159845	+	0.00428304i
$844$	−0.294229	−	0.169873i	−0.0101278	−	0.00584727i
$845$	6.16025	−	9.33013i	0.211919	−	0.320966i
$846$			12.9282i			0.444481i
$847$		0			0
$848$	12.3205	−	12.3205i	0.423088	−	0.423088i
$849$	0.882686	−	0.509619i	0.0302937	−	0.0174901i
$850$	3.92820	+	9.19615i	0.134736	+	0.315425i
$851$	−0.339746	+	0.588457i	−0.0116463	+	0.0201721i
$852$	1.09808	+	0.294229i	0.0376195	+	0.0100801i
$853$	−18.1244	−	18.1244i	−0.620566	−	0.620566i	0.325110	−	0.945676i	$-0.394599\pi$
$853$	−18.1244	−	18.1244i	−0.620566	−	0.620566i	−0.945676	+	0.325110i	$0.894599\pi$
$854$		0			0
$855$	−2.00000	−	4.00000i	−0.0683986	−	0.136797i
$856$	−12.6962	−	21.9904i	−0.433946	−	0.751616i
$857$	2.97372	+	11.0981i	0.101580	+	0.379103i	0.997935	−	0.0642351i	$-0.0204608\pi$
$857$	2.97372	+	11.0981i	0.101580	+	0.379103i	−0.896354	+	0.443338i	$0.853794\pi$
$858$	−0.535898	−	2.00000i	−0.0182953	−	0.0682789i
$859$	−17.4641	−	30.2487i	−0.595867	−	1.03207i	−0.993424	−	0.114495i	$-0.963475\pi$
$859$	−17.4641	−	30.2487i	−0.595867	−	1.03207i	0.397556	−	0.917578i	$-0.369858\pi$
$860$	14.7058	+	4.90192i	0.501463	+	0.167154i
$861$		0			0
$862$	−2.26795	−	2.26795i	−0.0772467	−	0.0772467i
$863$	−49.9449	−	13.3827i	−1.70014	−	0.455552i	−0.727167	−	0.686460i	$-0.759164\pi$
$863$	−49.9449	−	13.3827i	−1.70014	−	0.455552i	−0.972976	+	0.230908i	$0.925830\pi$
$864$	7.62436	−	13.2058i	0.259386	−	0.449269i
$865$	−34.5167	+	30.6077i	−1.17360	+	1.04069i
$866$	11.1173	−	6.41858i	0.377782	−	0.218112i
$867$	0.758330	−	0.758330i	0.0257542	−	0.0257542i
$868$		0			0
$869$			8.92820i			0.302869i
$870$	1.50000	+	0.990381i	0.0508548	+	0.0335771i
$871$	27.1244	+	15.6603i	0.919074	+	0.530627i
$872$	−18.8923	+	5.06218i	−0.639774	+	0.171427i
$873$	5.92820	−	22.1244i	0.200639	−	0.748796i
$874$	0.0525589			0.00177783
$875$		0			0
$876$	12.0000			0.405442
$877$	10.4904	−	39.1506i	0.354235	−	1.32202i	−0.527209	−	0.849735i	$-0.676762\pi$
$877$	10.4904	−	39.1506i	0.354235	−	1.32202i	0.881444	−	0.472288i	$-0.156572\pi$
$878$	−1.66025	+	0.444864i	−0.0560309	+	0.0150134i
$879$	−1.51666	−	0.875644i	−0.0511557	−	0.0295348i
$880$	12.5622	+	8.29423i	0.423471	+	0.279598i
$881$			25.1436i			0.847109i	0.905871	+	0.423555i	$0.139218\pi$
$881$			25.1436i			0.847109i	−0.905871	+	0.423555i	$0.860782\pi$
$882$		0			0
$883$	8.07180	−	8.07180i	0.271638	−	0.271638i	−0.558122	−	0.829759i	$-0.688478\pi$
$883$	8.07180	−	8.07180i	0.271638	−	0.271638i	0.829759	+	0.558122i	$0.188478\pi$
$884$	−16.3923	+	9.46410i	−0.551333	+	0.318312i
$885$	−7.09808	+	6.29423i	−0.238599	+	0.211578i
$886$	−3.50000	+	6.06218i	−0.117585	+	0.203663i
$887$	−10.8923	−	2.91858i	−0.365728	−	0.0979965i	0.0712748	−	0.997457i	$-0.477293\pi$
$887$	−10.8923	−	2.91858i	−0.365728	−	0.0979965i	−0.437003	+	0.899460i	$0.643960\pi$
$888$	3.46410	+	3.46410i	0.116248	+	0.116248i
$889$		0			0
$890$	0.725009	+	0.241670i	0.0243024	+	0.00810079i
$891$	−9.09808	−	15.7583i	−0.304797	−	0.527924i
$892$	11.4904	+	42.8827i	0.384726	+	1.43582i
$893$	−1.73205	−	6.46410i	−0.0579609	−	0.216313i
$894$	−0.107695	−	0.186533i	−0.00360186	−	0.00623861i
$895$	−7.85641	−	15.7128i	−0.262611	−	0.525221i
$896$		0			0
$897$	0.143594	+	0.143594i	0.00479445	+	0.00479445i
$898$	16.5263	+	4.42820i	0.551489	+	0.147771i
$899$	11.1962	−	19.3923i	0.373413	−	0.646770i
$900$	−9.29423	−	21.7583i	−0.309808	−	0.725278i
$901$	−23.6603	+	13.6603i	−0.788237	+	0.455089i
$902$	6.46410	−	6.46410i	0.215231	−	0.215231i
$903$		0			0
$904$		−	21.1244i		−	0.702586i
$905$	1.47372	−	2.23205i	0.0489881	−	0.0741959i
$906$	−3.21539	−	1.85641i	−0.106824	−	0.0616750i
$907$	32.4545	−	8.69615i	1.07763	−	0.288751i	0.324007	−	0.946055i	$-0.394970\pi$
$907$	32.4545	−	8.69615i	1.07763	−	0.288751i	0.753626	+	0.657304i	$0.228303\pi$
$908$	−8.83013	+	32.9545i	−0.293038	+	1.09363i
$909$	22.5885			0.749212
$910$		0			0
$911$	−7.51666			−0.249038			−0.124519	−	0.992217i	$-0.539739\pi$
$911$	−7.51666			−0.249038			−0.124519	+	0.992217i	$0.539739\pi$
$912$	−0.241670	+	0.901924i	−0.00800249	+	0.0298657i
$913$	−7.83013	+	2.09808i	−0.259139	+	0.0694362i
$914$	5.44486	+	3.14359i	0.180100	+	0.103981i
$915$	−1.74167	+	0.356406i	−0.0575778	+	0.0117824i
$916$		−	31.8564i		−	1.05257i
$917$		0			0
$918$	−4.19615	+	4.19615i	−0.138494	+	0.138494i
$919$	48.6673	−	28.0981i	1.60539	−	0.926870i	0.615002	−	0.788526i	$-0.289155\pi$
$919$	48.6673	−	28.0981i	1.60539	−	0.926870i	0.990384	−	0.138344i	$-0.0441780\pi$
$920$	0.598076	+	0.0358984i	0.0197180	+	0.00118353i
$921$	2.30385	−	3.99038i	0.0759144	−	0.131488i
$922$	2.80385	+	0.751289i	0.0923398	+	0.0247424i
$923$	−2.53590	−	2.53590i	−0.0834701	−	0.0834701i
$924$		0			0
$925$	24.2487	−	3.46410i	0.797293	−	0.113899i
$926$	−1.74167	−	3.01666i	−0.0572348	−	0.0991336i
$927$	−3.36603	−	12.5622i	−0.110555	−	0.412596i
$928$	3.99038	+	14.8923i	0.130991	+	0.488864i
$929$	−18.1603	−	31.4545i	−0.595819	−	1.03199i	−0.993431	−	0.114435i	$-0.963494\pi$
$929$	−18.1603	−	31.4545i	−0.595819	−	1.03199i	0.397612	−	0.917554i	$-0.369839\pi$
$930$	−4.00000	+	2.00000i	−0.131165	+	0.0655826i
$931$		0			0
$932$	8.19615	+	8.19615i	0.268474	+	0.268474i
$933$	7.63397	+	2.04552i	0.249925	+	0.0669672i
$934$	3.64359	−	6.31089i	0.119222	−	0.206499i
$935$	−15.6603	−	17.6603i	−0.512145	−	0.577552i
$936$	−12.9282	+	7.46410i	−0.422572	+	0.243972i
$937$	17.0718	−	17.0718i	0.557711	−	0.557711i	−0.370944	−	0.928655i	$-0.620966\pi$
$937$	17.0718	−	17.0718i	0.557711	−	0.557711i	0.928655	+	0.370944i	$0.120966\pi$
$938$		0			0
$939$		−	2.78461i		−	0.0908723i
$940$	−7.09808	−	34.6865i	−0.231514	−	1.13135i
$941$	−35.1962	−	20.3205i	−1.14736	−	0.662430i	−0.199119	−	0.979975i	$-0.563808\pi$
$941$	−35.1962	−	20.3205i	−1.14736	−	0.662430i	−0.948243	+	0.317546i	$0.897141\pi$
$942$	−1.24167	+	0.332704i	−0.0404558	+	0.0108401i
$943$	−0.232051	+	0.866025i	−0.00755661	+	0.0282017i
$944$	−20.1962			−0.657329
$945$		0			0
$946$	5.66025			0.184031
$947$	0.349365	−	1.30385i	0.0113528	−	0.0423694i	−0.960017	−	0.279941i	$-0.909685\pi$
$947$	0.349365	−	1.30385i	0.0113528	−	0.0423694i	0.971370	+	0.237572i	$0.0763516\pi$
$948$	−2.83013	+	0.758330i	−0.0919183	+	0.0246294i
$949$	−32.7846	−	18.9282i	−1.06423	−	0.614435i
$950$	−1.16987	−	1.49038i	−0.0379557	−	0.0483543i
$951$			4.92820i			0.159808i
$952$		0			0
$953$	−37.8564	+	37.8564i	−1.22629	+	1.22629i	−0.260932	+	0.965357i	$0.584030\pi$
$953$	−37.8564	+	37.8564i	−1.22629	+	1.22629i	−0.965357	+	0.260932i	$0.915970\pi$
$954$	−8.66025	+	5.00000i	−0.280386	+	0.161881i
$955$	1.77757	−	29.6147i	0.0575208	−	0.958310i
$956$	−2.07180	+	3.58846i	−0.0670067	+	0.116059i
$957$	−4.09808	−	1.09808i	−0.132472	−	0.0354958i
$958$	4.78461	+	4.78461i	0.154584	+	0.154584i
$959$		0			0
$960$	−0.830127	+	2.49038i	−0.0267922	+	0.0803767i
$961$	12.3564	+	21.4019i	0.398594	+	0.690385i
$962$	−1.85641	−	6.92820i	−0.0598529	−	0.223374i
$963$	−9.29423	−	34.6865i	−0.299502	−	1.11776i
$964$	−21.4641	−	37.1769i	−0.691312	−	1.19739i
$965$	−5.73205	+	17.1962i	−0.184521	+	0.553564i
$966$		0			0
$967$	−13.5622	−	13.5622i	−0.436130	−	0.436130i	0.454577	−	0.890707i	$-0.349790\pi$
$967$	−13.5622	−	13.5622i	−0.436130	−	0.436130i	−0.890707	+	0.454577i	$0.849790\pi$
$968$	−6.59808	−	1.76795i	−0.212070	−	0.0568240i
$969$	0.732051	−	1.26795i	0.0235169	−	0.0407324i
$970$	0.581416	−	9.68653i	0.0186681	−	0.311016i
$971$	−29.0718	+	16.7846i	−0.932958	+	0.538644i	−0.887746	−	0.460334i	$-0.847730\pi$
$971$	−29.0718	+	16.7846i	−0.932958	+	0.538644i	−0.0452124	+	0.998977i	$0.514396\pi$
$972$	15.1244	−	15.1244i	0.485114	−	0.485114i
$973$		0			0
$974$		−	14.5885i		−	0.467444i
$975$	0.875644	−	7.26795i	0.0280431	−	0.232761i
$976$	−3.27757	−	1.89230i	−0.104912	−	0.0605712i
$977$	0.562178	−	0.150635i	0.0179857	−	0.00481924i	−0.249815	−	0.968294i	$-0.580370\pi$
$977$	0.562178	−	0.150635i	0.0179857	−	0.00481924i	0.267801	+	0.963474i	$0.413703\pi$
$978$	−0.973721	+	3.63397i	−0.0311362	+	0.116202i
$979$	−1.80385			−0.0576512
$980$		0			0
$981$	−27.6603			−0.883124
$982$	−5.05256	+	18.8564i	−0.161234	+	0.601732i
$983$	−54.1147	+	14.5000i	−1.72599	+	0.462478i	−0.979253	−	0.202639i	$-0.935048\pi$
$983$	−54.1147	+	14.5000i	−1.72599	+	0.462478i	−0.746739	+	0.665118i	$0.768381\pi$
$984$	5.59808	+	3.23205i	0.178460	+	0.103034i
$985$	−6.41858	−	31.3660i	−0.204513	−	0.999405i
$986$		−	6.00000i		−	0.191079i
$987$		0			0
$988$	2.53590	−	2.53590i	0.0806777	−	0.0806777i
$989$	−0.480762	+	0.277568i	−0.0152873	+	0.00882615i
$990$	−5.73205	−	6.46410i	−0.182177	−	0.205443i
$991$	−15.8564	+	27.4641i	−0.503695	+	0.872426i	0.496296	+	0.868154i	$0.334693\pi$
$991$	−15.8564	+	27.4641i	−0.503695	+	0.872426i	−0.999991	+	0.00427229i	$0.998640\pi$
$992$	−37.0526	−	9.92820i	−1.17642	−	0.315221i
$993$	0.679492	+	0.679492i	0.0215630	+	0.0215630i
$994$		0			0
$995$	−22.1436	+	11.0718i	−0.701999	+	0.351000i
$996$	−1.33013	−	2.30385i	−0.0421467	−	0.0730002i
$997$	10.6865	+	39.8827i	0.338446	+	1.26310i	0.900085	+	0.435715i	$0.143504\pi$
$997$	10.6865	+	39.8827i	0.338446	+	1.26310i	−0.561639	+	0.827382i	$0.689829\pi$
$998$	1.54294	+	5.75833i	0.0488409	+	0.182277i
$999$	7.26795	+	12.5885i	0.229948	+	0.398281i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.2.l.a.227.1		4
5.3	odd	4		245.2.l.b.178.1		4
7.2	even	3		35.2.k.b.12.1	yes	4
7.3	odd	6		245.2.f.a.97.1		4
7.4	even	3		245.2.f.b.97.1		4
7.5	odd	6		245.2.l.b.117.1		4
7.6	odd	2		35.2.k.a.17.1	✓	4
21.2	odd	6		315.2.bz.a.82.1		4
21.20	even	2		315.2.bz.b.262.1		4
28.23	odd	6		560.2.ci.b.257.1		4
28.27	even	2		560.2.ci.a.17.1		4
35.2	odd	12		175.2.o.b.68.1		4
35.3	even	12		245.2.f.b.48.1		4
35.9	even	6		175.2.o.a.82.1		4
35.13	even	4		35.2.k.b.3.1	yes	4
35.18	odd	12		245.2.f.a.48.1		4
35.23	odd	12		35.2.k.a.33.1	yes	4
35.27	even	4		175.2.o.a.143.1		4
35.33	even	12	inner	245.2.l.a.68.1		4
35.34	odd	2		175.2.o.b.157.1		4
105.23	even	12		315.2.bz.b.208.1		4
105.83	odd	4		315.2.bz.a.73.1		4
140.23	even	12		560.2.ci.a.33.1		4
140.83	odd	4		560.2.ci.b.353.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.2.k.a.17.1	✓	4	7.6	odd	2
35.2.k.a.33.1	yes	4	35.23	odd	12
35.2.k.b.3.1	yes	4	35.13	even	4
35.2.k.b.12.1	yes	4	7.2	even	3
175.2.o.a.82.1		4	35.9	even	6
175.2.o.a.143.1		4	35.27	even	4
175.2.o.b.68.1		4	35.2	odd	12
175.2.o.b.157.1		4	35.34	odd	2
245.2.f.a.48.1		4	35.18	odd	12
245.2.f.a.97.1		4	7.3	odd	6
245.2.f.b.48.1		4	35.3	even	12
245.2.f.b.97.1		4	7.4	even	3
245.2.l.a.68.1		4	35.33	even	12	inner
245.2.l.a.227.1		4	1.1	even	1	trivial
245.2.l.b.117.1		4	7.5	odd	6
245.2.l.b.178.1		4	5.3	odd	4
315.2.bz.a.73.1		4	105.83	odd	4
315.2.bz.a.82.1		4	21.2	odd	6
315.2.bz.b.208.1		4	105.23	even	12
315.2.bz.b.262.1		4	21.20	even	2
560.2.ci.a.17.1		4	28.27	even	2
560.2.ci.a.33.1		4	140.23	even	12
560.2.ci.b.257.1		4	28.23	odd	6
560.2.ci.b.353.1		4	140.83	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	245.l (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.133975 + 0.500000i) q^{2} +(0.500000 - 0.133975i) q^{3} +(1.50000 + 0.866025i) q^{4} +(1.86603 + 1.23205i) q^{5} +0.267949i q^{6} +(-1.36603 + 1.36603i) q^{8} +(-2.36603 + 1.36603i) q^{9} +O(q^{10})\)	\(q+(-0.133975 + 0.500000i) q^{2} +(0.500000 - 0.133975i) q^{3} +(1.50000 + 0.866025i) q^{4} +(1.86603 + 1.23205i) q^{5} +0.267949i q^{6} +(-1.36603 + 1.36603i) q^{8} +(-2.36603 + 1.36603i) q^{9} +(-0.866025 + 0.767949i) q^{10} +(1.36603 - 2.36603i) q^{11} +(0.866025 + 0.232051i) q^{12} +(-2.00000 - 2.00000i) q^{13} +(1.09808 + 0.366025i) q^{15} +(1.23205 + 2.13397i) q^{16} +(-1.00000 - 3.73205i) q^{17} +(-0.366025 - 1.36603i) q^{18} +(0.366025 + 0.633975i) q^{19} +(1.73205 + 3.46410i) q^{20} +(1.00000 + 1.00000i) q^{22} +(-0.133975 - 0.0358984i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(1.96410 + 4.59808i) q^{25} +(1.26795 - 0.732051i) q^{26} +(-2.09808 + 2.09808i) q^{27} -3.00000i q^{29} +(-0.330127 + 0.500000i) q^{30} +(6.46410 + 3.73205i) q^{31} +(-4.96410 + 1.33013i) q^{32} +(0.366025 - 1.36603i) q^{33} +2.00000 q^{34} -4.73205 q^{36} +(1.26795 - 4.73205i) q^{37} +(-0.366025 + 0.0980762i) q^{38} +(-1.26795 - 0.732051i) q^{39} +(-4.23205 + 0.866025i) q^{40} -6.46410i q^{41} +(2.83013 - 2.83013i) q^{43} +(4.09808 - 2.36603i) q^{44} +(-6.09808 - 0.366025i) q^{45} +(0.0358984 - 0.0621778i) q^{46} +(-8.83013 - 2.36603i) q^{47} +(0.901924 + 0.901924i) q^{48} +(-2.56218 + 0.366025i) q^{50} +(-1.00000 - 1.73205i) q^{51} +(-1.26795 - 4.73205i) q^{52} +(-1.83013 - 6.83013i) q^{53} +(-0.767949 - 1.33013i) q^{54} +(5.46410 - 2.73205i) q^{55} +(0.267949 + 0.267949i) q^{57} +(1.50000 + 0.401924i) q^{58} +(-4.09808 + 7.09808i) q^{59} +(1.33013 + 1.50000i) q^{60} +(-1.33013 + 0.767949i) q^{61} +(-2.73205 + 2.73205i) q^{62} +2.26795i q^{64} +(-1.26795 - 6.19615i) q^{65} +(0.633975 + 0.366025i) q^{66} +(-10.6962 + 2.86603i) q^{67} +(1.73205 - 6.46410i) q^{68} -0.0717968 q^{69} +1.26795 q^{71} +(1.36603 - 5.09808i) q^{72} +(12.9282 - 3.46410i) q^{73} +(2.19615 + 1.26795i) q^{74} +(1.59808 + 2.03590i) q^{75} +1.26795i q^{76} +(0.535898 - 0.535898i) q^{78} +(-2.83013 + 1.63397i) q^{79} +(-0.330127 + 5.50000i) q^{80} +(3.33013 - 5.76795i) q^{81} +(3.23205 + 0.866025i) q^{82} +(-2.09808 - 2.09808i) q^{83} +(2.73205 - 8.19615i) q^{85} +(1.03590 + 1.79423i) q^{86} +(-0.401924 - 1.50000i) q^{87} +(1.36603 + 5.09808i) q^{88} +(-0.330127 - 0.571797i) q^{89} +(1.00000 - 3.00000i) q^{90} +(-0.169873 - 0.169873i) q^{92} +(3.73205 + 1.00000i) q^{93} +(2.36603 - 4.09808i) q^{94} +(-0.0980762 + 1.63397i) q^{95} +(-2.30385 + 1.33013i) q^{96} +(-5.92820 + 5.92820i) q^{97} +7.46410i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 2 q^{3} + 6 q^{4} + 4 q^{5} - 2 q^{8} - 6 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 + 2 * q^3 + 6 * q^4 + 4 * q^5 - 2 * q^8 - 6 * q^9	\( 4 q - 4 q^{2} + 2 q^{3} + 6 q^{4} + 4 q^{5} - 2 q^{8} - 6 q^{9} + 2 q^{11} - 8 q^{13} - 6 q^{15} - 2 q^{16} - 4 q^{17} + 2 q^{18} - 2 q^{19} + 4 q^{22} - 4 q^{23} - 2 q^{24} - 6 q^{25} + 12 q^{26} + 2 q^{27} + 16 q^{30} + 12 q^{31} - 6 q^{32} - 2 q^{33} + 8 q^{34} - 12 q^{36} + 12 q^{37} + 2 q^{38} - 12 q^{39} - 10 q^{40} - 6 q^{43} + 6 q^{44} - 14 q^{45} + 14 q^{46} - 18 q^{47} + 14 q^{48} + 14 q^{50} - 4 q^{51} - 12 q^{52} + 10 q^{53} - 10 q^{54} + 8 q^{55} + 8 q^{57} + 6 q^{58} - 6 q^{59} - 12 q^{60} + 12 q^{61} - 4 q^{62} - 12 q^{65} + 6 q^{66} - 22 q^{67} - 28 q^{69} + 12 q^{71} + 2 q^{72} + 24 q^{73} - 12 q^{74} - 4 q^{75} + 16 q^{78} + 6 q^{79} + 16 q^{80} - 4 q^{81} + 6 q^{82} + 2 q^{83} + 4 q^{85} + 18 q^{86} - 12 q^{87} + 2 q^{88} + 16 q^{89} + 4 q^{90} - 18 q^{92} + 8 q^{93} + 6 q^{94} + 10 q^{95} - 30 q^{96} + 4 q^{97}+O(q^{100}) \) 4 * q - 4 * q^2 + 2 * q^3 + 6 * q^4 + 4 * q^5 - 2 * q^8 - 6 * q^9 + 2 * q^11 - 8 * q^13 - 6 * q^15 - 2 * q^16 - 4 * q^17 + 2 * q^18 - 2 * q^19 + 4 * q^22 - 4 * q^23 - 2 * q^24 - 6 * q^25 + 12 * q^26 + 2 * q^27 + 16 * q^30 + 12 * q^31 - 6 * q^32 - 2 * q^33 + 8 * q^34 - 12 * q^36 + 12 * q^37 + 2 * q^38 - 12 * q^39 - 10 * q^40 - 6 * q^43 + 6 * q^44 - 14 * q^45 + 14 * q^46 - 18 * q^47 + 14 * q^48 + 14 * q^50 - 4 * q^51 - 12 * q^52 + 10 * q^53 - 10 * q^54 + 8 * q^55 + 8 * q^57 + 6 * q^58 - 6 * q^59 - 12 * q^60 + 12 * q^61 - 4 * q^62 - 12 * q^65 + 6 * q^66 - 22 * q^67 - 28 * q^69 + 12 * q^71 + 2 * q^72 + 24 * q^73 - 12 * q^74 - 4 * q^75 + 16 * q^78 + 6 * q^79 + 16 * q^80 - 4 * q^81 + 6 * q^82 + 2 * q^83 + 4 * q^85 + 18 * q^86 - 12 * q^87 + 2 * q^88 + 16 * q^89 + 4 * q^90 - 18 * q^92 + 8 * q^93 + 6 * q^94 + 10 * q^95 - 30 * q^96 + 4 * q^97

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