LMFDB - Embedded newform 637.2.bb.b.227.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(227,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 5]))

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

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

chi := DirichletCharacter("637.227");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bb (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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			227.4
Character	$\chi$	$=$	637.227
Dual form			637.2.bb.b.362.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.976208 + 0.976208i) q^{2} +(0.928437 - 0.536034i) q^{3} +0.0940343i q^{4} +(-0.742756 + 2.77200i) q^{5} +(-0.383068 + 1.42963i) q^{6} +(-2.04421 - 2.04421i) q^{8} +(-0.925336 + 1.60273i) q^{9} +O(q^{10})$	\(q+(-0.976208 + 0.976208i) q^{2} +(0.928437 - 0.536034i) q^{3} +0.0940343i q^{4} +(-0.742756 + 2.77200i) q^{5} +(-0.383068 + 1.42963i) q^{6} +(-2.04421 - 2.04421i) q^{8} +(-0.925336 + 1.60273i) q^{9} +(-1.98097 - 3.43114i) q^{10} +(-0.369611 + 1.37941i) q^{11} +(0.0504055 + 0.0873049i) q^{12} +(3.54926 + 0.634621i) q^{13} +(0.796284 + 2.97177i) q^{15} +3.80309 q^{16} -4.19818 q^{17} +(-0.661277 - 2.46792i) q^{18} +(-5.95551 + 1.59577i) q^{19} +(-0.260663 - 0.0698445i) q^{20} +(-0.985770 - 1.70740i) q^{22} -7.82493i q^{23} +(-2.99369 - 0.802157i) q^{24} +(-2.80219 - 1.61784i) q^{25} +(-4.08434 + 2.84530i) q^{26} +5.20025i q^{27} +(0.441485 - 0.764674i) q^{29} +(-3.67841 - 2.12373i) q^{30} +(0.886225 - 0.237463i) q^{31} +(0.375820 - 0.375820i) q^{32} +(0.396247 + 1.47882i) q^{33} +(4.09830 - 4.09830i) q^{34} +(-0.150711 - 0.0870133i) q^{36} +(5.26594 + 5.26594i) q^{37} +(4.25601 - 7.37163i) q^{38} +(3.63544 - 1.31332i) q^{39} +(7.18492 - 4.14822i) q^{40} +(-11.4714 + 3.07376i) q^{41} +(0.809734 - 0.467500i) q^{43} +(-0.129711 - 0.0347561i) q^{44} +(-3.75547 - 3.75547i) q^{45} +(7.63876 + 7.63876i) q^{46} +(-3.01803 - 0.808679i) q^{47} +(3.53093 - 2.03858i) q^{48} +(4.31487 - 1.15617i) q^{50} +(-3.89775 + 2.25037i) q^{51} +(-0.0596761 + 0.333752i) q^{52} +(-1.26243 + 2.18659i) q^{53} +(-5.07652 - 5.07652i) q^{54} +(-3.54919 - 2.04912i) q^{55} +(-4.67393 + 4.67393i) q^{57} +(0.315500 + 1.17746i) q^{58} +(-4.13872 + 4.13872i) q^{59} +(-0.279449 + 0.0748780i) q^{60} +(0.0739657 + 0.0427041i) q^{61} +(-0.633327 + 1.09695i) q^{62} +8.33994i q^{64} +(-4.39541 + 9.36720i) q^{65} +(-1.83045 - 1.05681i) q^{66} +(-0.995278 - 0.266684i) q^{67} -0.394773i q^{68} +(-4.19442 - 7.26495i) q^{69} +(2.79996 + 0.750247i) q^{71} +(5.16791 - 1.38474i) q^{72} +(0.737278 + 2.75156i) q^{73} -10.2813 q^{74} -3.46888 q^{75} +(-0.150057 - 0.560022i) q^{76} +(-2.26688 + 4.83102i) q^{78} +(-4.71534 - 8.16721i) q^{79} +(-2.82477 + 10.5422i) q^{80} +(0.0114981 + 0.0199152i) q^{81} +(8.19789 - 14.1992i) q^{82} +(1.54040 + 1.54040i) q^{83} +(3.11823 - 11.6374i) q^{85} +(-0.334092 + 1.24685i) q^{86} -0.946603i q^{87} +(3.57536 - 2.06424i) q^{88} +(3.48251 - 3.48251i) q^{89} +7.33225 q^{90} +0.735811 q^{92} +(0.695516 - 0.695516i) q^{93} +(3.73567 - 2.15679i) q^{94} -17.6940i q^{95} +(0.147473 - 0.550378i) q^{96} +(-2.37752 + 8.87303i) q^{97} +(-1.86880 - 1.86880i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{2} - 16 q^{8} + 8 q^{9}+O(q^{10}) $ 32 * q + 4 * q^2 - 16 * q^8 + 8 * q^9	$ 32 q + 4 q^{2} - 16 q^{8} + 8 q^{9} - 16 q^{11} - 8 q^{15} - 24 q^{16} + 68 q^{18} + 4 q^{22} + 4 q^{29} - 12 q^{30} - 68 q^{32} - 8 q^{37} - 48 q^{43} + 60 q^{44} + 24 q^{46} - 44 q^{50} - 12 q^{51} - 36 q^{53} - 92 q^{57} - 28 q^{58} - 104 q^{60} - 32 q^{65} - 8 q^{67} + 84 q^{71} + 124 q^{72} + 48 q^{74} + 148 q^{78} + 40 q^{79} + 28 q^{81} + 36 q^{85} - 60 q^{86} + 228 q^{88} + 24 q^{92} - 84 q^{93} - 60 q^{99}+O(q^{100}) $ 32 * q + 4 * q^2 - 16 * q^8 + 8 * q^9 - 16 * q^11 - 8 * q^15 - 24 * q^16 + 68 * q^18 + 4 * q^22 + 4 * q^29 - 12 * q^30 - 68 * q^32 - 8 * q^37 - 48 * q^43 + 60 * q^44 + 24 * q^46 - 44 * q^50 - 12 * q^51 - 36 * q^53 - 92 * q^57 - 28 * q^58 - 104 * q^60 - 32 * q^65 - 8 * q^67 + 84 * q^71 + 124 * q^72 + 48 * q^74 + 148 * q^78 + 40 * q^79 + 28 * q^81 + 36 * q^85 - 60 * q^86 + 228 * q^88 + 24 * q^92 - 84 * q^93 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.976208	+	0.976208i	−0.690284	+	0.690284i	−0.962294	−	0.272011i	$-0.912311\pi$
$2$	−0.976208	+	0.976208i	−0.690284	+	0.690284i	0.272011	+	0.962294i	$0.412311\pi$
$3$	0.928437	−	0.536034i	0.536034	−	0.309479i	−0.207436	−	0.978249i	$-0.566512\pi$
$3$	0.928437	−	0.536034i	0.536034	−	0.309479i	0.743470	+	0.668769i	$0.233179\pi$
$4$			0.0940343i			0.0470171i
$5$	−0.742756	+	2.77200i	−0.332171	+	1.23968i	0.574734	+	0.818341i	$0.305106\pi$
$5$	−0.742756	+	2.77200i	−0.332171	+	1.23968i	−0.906904	+	0.421337i	$0.861561\pi$
$6$	−0.383068	+	1.42963i	−0.156387	+	0.583644i
$7$		0			0
$7$		0			0
$8$	−2.04421	−	2.04421i	−0.722739	−	0.722739i
$9$	−0.925336	+	1.60273i	−0.308445	+	0.534243i
$10$	−1.98097	−	3.43114i	−0.626437	−	1.08502i
$11$	−0.369611	+	1.37941i	−0.111442	+	0.415906i	−0.998996	−	0.0447966i	$-0.985736\pi$
$11$	−0.369611	+	1.37941i	−0.111442	+	0.415906i	0.887554	+	0.460703i	$0.152403\pi$
$12$	0.0504055	+	0.0873049i	0.0145508	+	0.0252028i
$13$	3.54926	+	0.634621i	0.984388	+	0.176012i
$13$	3.54926	+	0.634621i	0.984388	+	0.176012i
$14$		0			0
$15$	0.796284	+	2.97177i	0.205600	+	0.767309i
$16$	3.80309			0.950772
$17$	−4.19818			−1.01821			−0.509105	−	0.860705i	$-0.670023\pi$
$17$	−4.19818			−1.01821			−0.509105	+	0.860705i	$0.670023\pi$
$18$	−0.661277	−	2.46792i	−0.155864	−	0.581694i
$19$	−5.95551	+	1.59577i	−1.36629	+	0.366096i	−0.866121	−	0.499834i	$-0.833394\pi$
$19$	−5.95551	+	1.59577i	−1.36629	+	0.366096i	−0.500166	+	0.865929i	$0.666728\pi$
$20$	−0.260663	−	0.0698445i	−0.0582861	−	0.0156177i
$21$		0			0
$22$	−0.985770	−	1.70740i	−0.210167	−	0.364020i
$23$		−	7.82493i		−	1.63161i	−0.578327	−	0.815805i	$-0.696294\pi$
$23$		−	7.82493i		−	1.63161i	0.578327	−	0.815805i	$-0.303706\pi$
$24$	−2.99369	−	0.802157i	−0.611085	−	0.163740i
$25$	−2.80219	−	1.61784i	−0.560438	−	0.323569i
$26$	−4.08434	+	2.84530i	−0.801005	+	0.558009i
$27$			5.20025i			1.00079i
$28$		0			0
$29$	0.441485	−	0.764674i	0.0819817	−	0.141996i	−0.822119	−	0.569315i	$-0.807208\pi$
$29$	0.441485	−	0.764674i	0.0819817	−	0.141996i	0.904101	+	0.427319i	$0.140542\pi$
$30$	−3.67841	−	2.12373i	−0.671583	−	0.387738i
$31$	0.886225	−	0.237463i	0.159171	−	0.0426497i	−0.178354	−	0.983966i	$-0.557077\pi$
$31$	0.886225	−	0.237463i	0.159171	−	0.0426497i	0.337524	+	0.941317i	$0.390410\pi$
$32$	0.375820	−	0.375820i	0.0664363	−	0.0664363i
$33$	0.396247	+	1.47882i	0.0689778	+	0.257429i
$34$	4.09830	−	4.09830i	0.702853	−	0.702853i
$35$		0			0
$36$	−0.150711	−	0.0870133i	−0.0251186	−	0.0145022i
$37$	5.26594	+	5.26594i	0.865716	+	0.865716i	0.991995	−	0.126279i	$-0.0403034\pi$
$37$	5.26594	+	5.26594i	0.865716	+	0.865716i	−0.126279	+	0.991995i	$0.540303\pi$
$38$	4.25601	−	7.37163i	0.690416	−	1.19584i
$39$	3.63544	−	1.31332i	0.582137	−	0.210299i
$40$	7.18492	−	4.14822i	1.13604	−	0.655890i
$41$	−11.4714	+	3.07376i	−1.79154	+	0.480041i	−0.992606	−	0.121379i	$-0.961268\pi$
$41$	−11.4714	+	3.07376i	−1.79154	+	0.480041i	−0.798933	+	0.601421i	$0.794602\pi$
$42$		0			0
$43$	0.809734	−	0.467500i	0.123483	−	0.0712931i	−0.436986	−	0.899468i	$-0.643954\pi$
$43$	0.809734	−	0.467500i	0.123483	−	0.0712931i	0.560469	+	0.828175i	$0.310621\pi$
$44$	−0.129711	−	0.0347561i	−0.0195547	−	0.00523967i
$45$	−3.75547	−	3.75547i	−0.559833	−	0.559833i
$46$	7.63876	+	7.63876i	1.12627	+	1.12627i
$47$	−3.01803	−	0.808679i	−0.440225	−	0.117958i	0.0318968	−	0.999491i	$-0.489845\pi$
$47$	−3.01803	−	0.808679i	−0.440225	−	0.117958i	−0.472122	+	0.881533i	$0.656512\pi$
$48$	3.53093	−	2.03858i	0.509646	−	0.294244i
$49$		0			0
$50$	4.31487	−	1.15617i	0.610215	−	0.163507i
$51$	−3.89775	+	2.25037i	−0.545794	+	0.315114i
$52$	−0.0596761	+	0.333752i	−0.00827559	+	0.0462831i
$53$	−1.26243	+	2.18659i	−0.173408	+	0.300351i	−0.939609	−	0.342249i	$-0.888811\pi$
$53$	−1.26243	+	2.18659i	−0.173408	+	0.300351i	0.766201	+	0.642601i	$0.222145\pi$
$54$	−5.07652	−	5.07652i	−0.690827	−	0.690827i
$55$	−3.54919	−	2.04912i	−0.478572	−	0.276304i
$56$		0			0
$57$	−4.67393	+	4.67393i	−0.619077	+	0.619077i
$58$	0.315500	+	1.17746i	0.0414272	+	0.154608i
$59$	−4.13872	+	4.13872i	−0.538815	+	0.538815i	−0.923181	−	0.384366i	$-0.874420\pi$
$59$	−4.13872	+	4.13872i	−0.538815	+	0.538815i	0.384366	+	0.923181i	$0.374420\pi$
$60$	−0.279449	+	0.0748780i	−0.0360767	+	0.00966671i
$61$	0.0739657	+	0.0427041i	0.00947033	+	0.00546770i	0.504728	−	0.863279i	$-0.331593\pi$
$61$	0.0739657	+	0.0427041i	0.00947033	+	0.00546770i	−0.495257	+	0.868746i	$0.664926\pi$
$62$	−0.633327	+	1.09695i	−0.0804326	+	0.139313i
$63$		0			0
$64$			8.33994i			1.04249i
$65$	−4.39541	+	9.36720i	−0.545183	+	1.16186i
$66$	−1.83045	−	1.05681i	−0.225313	−	0.130085i
$67$	−0.995278	−	0.266684i	−0.121593	−	0.0325806i	0.197510	−	0.980301i	$-0.436715\pi$
$67$	−0.995278	−	0.266684i	−0.121593	−	0.0325806i	−0.319102	+	0.947720i	$0.603381\pi$
$68$		−	0.394773i		−	0.0478733i
$69$	−4.19442	−	7.26495i	−0.504949	−	0.874598i
$70$		0			0
$71$	2.79996	+	0.750247i	0.332294	+	0.0890380i	0.421109	−	0.907010i	$-0.361641\pi$
$71$	2.79996	+	0.750247i	0.332294	+	0.0890380i	−0.0888143	+	0.996048i	$0.528308\pi$
$72$	5.16791	−	1.38474i	0.609044	−	0.163193i
$73$	0.737278	+	2.75156i	0.0862919	+	0.322046i	0.995556	−	0.0941746i	$-0.0300212\pi$
$73$	0.737278	+	2.75156i	0.0862919	+	0.322046i	−0.909264	+	0.416220i	$0.863355\pi$
$74$	−10.2813			−1.19518
$75$	−3.46888			−0.400551
$76$	−0.150057	−	0.560022i	−0.0172128	−	0.0642389i
$77$		0			0
$78$	−2.26688	+	4.83102i	−0.256674	+	0.547006i
$79$	−4.71534	−	8.16721i	−0.530517	−	0.918883i	−0.999366	−	0.0356045i	$-0.988664\pi$
$79$	−4.71534	−	8.16721i	−0.530517	−	0.918883i	0.468849	−	0.883279i	$-0.344669\pi$
$80$	−2.82477	+	10.5422i	−0.315819	+	1.17865i
$81$	0.0114981	+	0.0199152i	0.00127756	+	0.00221280i
$82$	8.19789	−	14.1992i	0.905305	−	1.56803i
$83$	1.54040	+	1.54040i	0.169081	+	0.169081i	0.786575	−	0.617494i	$-0.211852\pi$
$83$	1.54040	+	1.54040i	0.169081	+	0.169081i	−0.617494	+	0.786575i	$0.711852\pi$
$84$		0			0
$85$	3.11823	−	11.6374i	0.338219	−	1.26225i
$86$	−0.334092	+	1.24685i	−0.0360260	+	0.134451i
$87$		−	0.946603i		−	0.101486i
$88$	3.57536	−	2.06424i	0.381135	−	0.220048i
$89$	3.48251	−	3.48251i	0.369146	−	0.369146i	−0.498020	−	0.867166i	$-0.665939\pi$
$89$	3.48251	−	3.48251i	0.369146	−	0.369146i	0.867166	+	0.498020i	$0.165939\pi$
$90$	7.33225			0.772887
$91$		0			0
$92$	0.735811			0.0767136
$93$	0.695516	−	0.695516i	0.0721217	−	0.0721217i
$94$	3.73567	−	2.15679i	0.385305	−	0.222456i
$95$		−	17.6940i		−	1.81536i
$96$	0.147473	−	0.550378i	0.0150514	−	0.0561727i
$97$	−2.37752	+	8.87303i	−0.241401	+	0.900920i	0.733758	+	0.679411i	$0.237765\pi$
$97$	−2.37752	+	8.87303i	−0.241401	+	0.900920i	−0.975158	+	0.221509i	$0.928902\pi$
$98$		0			0
$99$	−1.86880	−	1.86880i	−0.187821	−	0.187821i
$100$	0.152133	−	0.263502i	0.0152133	−	0.0263502i
$101$	3.27488	+	5.67227i	0.325863	+	0.564412i	0.981687	−	0.190503i	$-0.0610118\pi$
$101$	3.27488	+	5.67227i	0.325863	+	0.564412i	−0.655824	+	0.754914i	$0.727678\pi$
$102$	1.60819	−	6.00184i	0.159234	−	0.594271i
$103$	4.92770	+	8.53503i	0.485541	+	0.840982i	0.999862	−	0.0166161i	$-0.00528932\pi$
$103$	4.92770	+	8.53503i	0.485541	+	0.840982i	−0.514321	+	0.857598i	$0.671956\pi$
$104$	−5.95815	−	8.55275i	−0.584245	−	0.838666i
$105$		0			0
$106$	−0.902174	−	3.36696i	−0.0876269	−	0.327028i
$107$	10.5936			1.02412			0.512059	−	0.858950i	$-0.328883\pi$
$107$	10.5936			1.02412			0.512059	+	0.858950i	$0.328883\pi$
$108$	−0.489001			−0.0470542
$109$	4.27118	+	15.9403i	0.409105	+	1.52680i	0.796357	+	0.604827i	$0.206758\pi$
$109$	4.27118	+	15.9403i	0.409105	+	1.52680i	−0.387252	+	0.921974i	$0.626576\pi$
$110$	5.46512	−	1.46437i	0.521078	−	0.139623i
$111$	7.71182	+	2.06638i	0.731974	+	0.196132i
$112$		0			0
$113$	−0.322118	−	0.557925i	−0.0303023	−	0.0524851i	0.850477	−	0.526013i	$-0.176314\pi$
$113$	−0.322118	−	0.557925i	−0.0303023	−	0.0524851i	−0.880779	+	0.473528i	$0.842980\pi$
$114$		−	9.12546i		−	0.854677i
$115$	21.6907	+	5.81201i	2.02267	+	0.541973i
$116$	0.0719056	+	0.0415147i	0.00667627	+	0.00385454i
$117$	−4.30139	+	5.10127i	−0.397663	+	0.471612i
$118$		−	8.08051i		−	0.743871i
$119$		0			0
$120$	4.44717	−	7.70272i	0.405969	−	0.703159i
$121$	7.76013	+	4.48031i	0.705467	+	0.407301i
$122$	−0.113894	+	0.0305178i	−0.0103115	+	0.00276295i
$123$	−9.00288	+	9.00288i	−0.811762	+	0.811762i
$124$	0.0223297	+	0.0833356i	0.00200527	+	0.00748376i
$125$	−3.58022	+	3.58022i	−0.320225	+	0.320225i
$126$		0			0
$127$	−14.1284	−	8.15702i	−1.25369	−	0.723819i	−0.281850	−	0.959458i	$-0.590948\pi$
$127$	−14.1284	−	8.15702i	−1.25369	−	0.723819i	−0.971841	+	0.235640i	$0.924282\pi$
$128$	−7.38987	−	7.38987i	−0.653179	−	0.653179i
$129$	0.501191	−	0.868089i	0.0441274	−	0.0764310i
$130$	−4.85350	−	13.4352i	−0.425680	−	1.17834i
$131$	2.03759	−	1.17640i	0.178025	−	0.102783i	−0.408340	−	0.912830i	$-0.633892\pi$
$131$	2.03759	−	1.17640i	0.178025	−	0.102783i	0.586364	+	0.810047i	$0.300559\pi$
$132$	−0.139059	+	0.0372608i	−0.0121036	+	0.00324314i
$133$		0			0
$134$	1.23194	−	0.711259i	0.106423	−	0.0614435i
$135$	−14.4151	−	3.86251i	−1.24065	−	0.332432i
$136$	8.58199	+	8.58199i	0.735899	+	0.735899i
$137$	7.34478	+	7.34478i	0.627507	+	0.627507i	0.947440	−	0.319933i	$-0.103660\pi$
$137$	7.34478	+	7.34478i	0.627507	+	0.627507i	−0.319933	+	0.947440i	$0.603660\pi$
$138$	11.1867	+	2.99748i	0.952278	+	0.255162i
$139$	5.33208	−	3.07848i	0.452261	−	0.261113i	−0.256524	−	0.966538i	$-0.582577\pi$
$139$	5.33208	−	3.07848i	0.452261	−	0.261113i	0.708784	+	0.705425i	$0.249244\pi$
$140$		0			0
$141$	−3.23553	+	0.866959i	−0.272481	+	0.0730111i
$142$	−3.46574	+	2.00095i	−0.290839	+	0.167916i
$143$	−2.18724	+	4.66131i	−0.182907	+	0.389798i
$144$	−3.51914	+	6.09532i	−0.293261	+	0.507943i
$145$	1.79176	+	1.79176i	0.148798	+	0.148798i
$146$	−3.40583	−	1.96636i	−0.281869	−	0.162737i
$147$		0			0
$148$	−0.495179	+	0.495179i	−0.0407035	+	0.0407035i
$149$	2.25336	+	8.40965i	0.184602	+	0.688945i	0.994715	+	0.102672i	$0.0327391\pi$
$149$	2.25336	+	8.40965i	0.184602	+	0.688945i	−0.810113	+	0.586274i	$0.800594\pi$
$150$	3.38635	−	3.38635i	0.276494	−	0.276494i
$151$	−13.0482	+	3.49627i	−1.06185	+	0.284522i	−0.747141	−	0.664665i	$-0.768574\pi$
$151$	−13.0482	+	3.49627i	−1.06185	+	0.284522i	−0.314710	+	0.949188i	$0.601907\pi$
$152$	15.4364	+	8.91223i	1.25206	+	0.722877i
$153$	3.88473	−	6.72855i	0.314062	−	0.543971i
$154$		0			0
$155$			2.63300i			0.211487i
$156$	0.123497	+	0.341856i	0.00988766	+	0.0273704i
$157$	5.87142	+	3.38986i	0.468590	+	0.270541i	0.715649	−	0.698460i	$-0.246131\pi$
$157$	5.87142	+	3.38986i	0.468590	+	0.270541i	−0.247059	+	0.969000i	$0.579464\pi$
$158$	12.5761	+	3.36974i	1.00050	+	0.268082i
$159$			2.70681i			0.214664i
$160$	0.762632	+	1.32092i	0.0602914	+	0.104428i
$161$		0			0
$162$	−0.0306659	−	0.00821691i	−0.00240934	−	0.000645582i
$163$	10.5525	−	2.82752i	0.826532	−	0.221469i	0.179332	−	0.983789i	$-0.442606\pi$
$163$	10.5525	−	2.82752i	0.826532	−	0.221469i	0.647200	+	0.762320i	$0.275940\pi$
$164$	−0.289039	−	1.07871i	−0.0225702	−	0.0842330i
$165$	−4.39360			−0.342041
$166$	−3.00751			−0.233428
$167$	4.71387	+	17.5924i	0.364770	+	1.36134i	0.867732	+	0.497032i	$0.165577\pi$
$167$	4.71387	+	17.5924i	0.364770	+	1.36134i	−0.502962	+	0.864308i	$0.667756\pi$
$168$		0			0
$169$	12.1945	+	4.50487i	0.938039	+	0.346529i
$170$	8.31647	+	14.4045i	0.637844	+	1.10478i
$171$	2.95325	−	11.0217i	0.225841	−	0.842850i
$172$	0.0439610	+	0.0761428i	0.00335200	+	0.00580583i
$173$	−10.0761	+	17.4523i	−0.766070	+	1.32687i	0.173608	+	0.984815i	$0.444457\pi$
$173$	−10.0761	+	17.4523i	−0.766070	+	1.32687i	−0.939679	+	0.342058i	$0.888876\pi$
$174$	0.924081	+	0.924081i	0.0700544	+	0.0700544i
$175$		0			0
$176$	−1.40566	+	5.24600i	−0.105956	+	0.395432i
$177$	−1.62405	+	6.06103i	−0.122071	+	0.455575i
$178$			6.79932i			0.509630i
$179$	14.3173	−	8.26609i	1.07012	−	0.617837i	0.141909	−	0.989880i	$-0.454676\pi$
$179$	14.3173	−	8.26609i	1.07012	−	0.617837i	0.928216	+	0.372043i	$0.121343\pi$
$180$	0.353143	−	0.353143i	0.0263217	−	0.0263217i
$181$	13.6897			1.01755			0.508774	−	0.860900i	$-0.330099\pi$
$181$	13.6897			1.01755			0.508774	+	0.860900i	$0.330099\pi$
$182$		0			0
$183$	0.0915633			0.00676855
$184$	−15.9958	+	15.9958i	−1.17923	+	1.17923i
$185$	−18.5085	+	10.6859i	−1.36077	+	0.785643i
$186$			1.35794i			0.0995688i
$187$	1.55169	−	5.79100i	0.113471	−	0.423480i
$188$	0.0760436	−	0.283799i	0.00554605	−	0.0206981i
$189$		0			0
$190$	17.2730	+	17.2730i	1.25311	+	1.25311i
$191$	4.07445	−	7.05715i	0.294817	−	0.510638i	−0.680126	−	0.733096i	$-0.738075\pi$
$191$	4.07445	−	7.05715i	0.294817	−	0.510638i	0.974942	+	0.222458i	$0.0714081\pi$
$192$	4.47049	+	7.74311i	0.322629	+	0.558811i
$193$	6.93304	−	25.8745i	0.499051	−	1.86249i	−0.00698876	−	0.999976i	$-0.502225\pi$
$193$	6.93304	−	25.8745i	0.499051	−	1.86249i	0.506040	−	0.862510i	$-0.331109\pi$
$194$	−6.34097	−	10.9829i	−0.455255	−	0.788525i
$195$	0.940271	+	11.0529i	0.0673342	+	0.791517i
$196$		0			0
$197$	4.77033	+	17.8031i	0.339872	+	1.26842i	0.898490	+	0.438995i	$0.144665\pi$
$197$	4.77033	+	17.8031i	0.339872	+	1.26842i	−0.558617	+	0.829426i	$0.688668\pi$
$198$	3.64868			0.259300
$199$	12.7116			0.901099			0.450550	−	0.892751i	$-0.351228\pi$
$199$	12.7116			0.901099			0.450550	+	0.892751i	$0.351228\pi$
$200$	2.42105	+	9.03550i	0.171194	+	0.638906i
$201$	−1.06700	+	0.285903i	−0.0752607	+	0.0201660i
$202$	−8.73428	−	2.34034i	−0.614542	−	0.164666i
$203$		0			0
$204$	−0.211612	−	0.366522i	−0.0148158	−	0.0256617i
$205$		−	34.0819i		−	2.38039i
$206$	−13.1424	−	3.52150i	−0.915677	−	0.245355i
$207$	12.5412	+	7.24069i	0.871676	+	0.503262i
$208$	13.4982	+	2.41352i	0.935929	+	0.167348i
$209$		−	8.80488i		−	0.609046i
$210$		0			0
$211$	−2.26459	+	3.92239i	−0.155901	+	0.270028i	−0.933387	−	0.358872i	$-0.883161\pi$
$211$	−2.26459	+	3.92239i	−0.155901	+	0.270028i	0.777486	+	0.628900i	$0.216495\pi$
$212$	−0.205614	−	0.118712i	−0.0141217	−	0.00815314i
$213$	3.00175	−	0.804316i	0.205676	−	0.0551108i
$214$	−10.3415	+	10.3415i	−0.706932	+	0.706932i
$215$	0.694477	+	2.59182i	0.0473629	+	0.176761i
$216$	10.6304	−	10.6304i	0.723308	−	0.723308i
$217$		0			0
$218$	−19.7306	−	11.3915i	−1.33632	−	0.771527i
$219$	2.15945	+	2.15945i	0.145922	+	0.145922i
$220$	0.192688	−	0.333745i	0.0129910	−	0.0225011i
$221$	−14.9005	−	2.66426i	−1.00231	−	0.179217i
$222$	−9.54556	+	5.51113i	−0.640656	+	0.369883i
$223$	22.4788	−	6.02318i	1.50529	−	0.403342i	0.590423	−	0.807094i	$-0.298961\pi$
$223$	22.4788	−	6.02318i	1.50529	−	0.403342i	0.914868	+	0.403752i	$0.132294\pi$
$224$		0			0
$225$	5.18593	−	2.99410i	0.345729	−	0.199607i
$226$	0.859105	+	0.230197i	0.0571468	+	0.0153124i
$227$	7.37068	+	7.37068i	0.489210	+	0.489210i	0.908057	−	0.418847i	$-0.137566\pi$
$227$	7.37068	+	7.37068i	0.489210	+	0.489210i	−0.418847	+	0.908057i	$0.637566\pi$
$228$	−0.439510	−	0.439510i	−0.0291072	−	0.0291072i
$229$	−1.86301	−	0.499191i	−0.123111	−	0.0329875i	0.196738	−	0.980456i	$-0.436965\pi$
$229$	−1.86301	−	0.499191i	−0.123111	−	0.0329875i	−0.319848	+	0.947469i	$0.603632\pi$
$230$	−26.8484	+	15.5009i	−1.77033	+	1.02210i
$231$		0			0
$232$	−2.46565	+	0.660668i	−0.161878	+	0.0433750i
$233$	−7.44377	+	4.29766i	−0.487657	+	0.281549i	−0.723602	−	0.690217i	$-0.757515\pi$
$233$	−7.44377	+	4.29766i	−0.487657	+	0.281549i	0.235945	+	0.971766i	$0.424182\pi$
$234$	−0.780851	−	9.17895i	−0.0510458	−	0.600047i
$235$	4.48332	−	7.76535i	0.292460	−	0.506555i
$236$	−0.389182	−	0.389182i	−0.0253336	−	0.0253336i
$237$	−8.75580	−	5.05516i	−0.568750	−	0.328368i
$238$		0			0
$239$	−6.45158	+	6.45158i	−0.417318	+	0.417318i	−0.884278	−	0.466960i	$-0.845349\pi$
$239$	−6.45158	+	6.45158i	−0.417318	+	0.417318i	0.466960	+	0.884278i	$0.345349\pi$
$240$	3.02834	+	11.3019i	0.195479	+	0.729536i
$241$	3.08557	−	3.08557i	0.198759	−	0.198759i	−0.600709	−	0.799468i	$-0.705115\pi$
$241$	3.08557	−	3.08557i	0.198759	−	0.198759i	0.799468	+	0.600709i	$0.205115\pi$
$242$	−11.9492	+	3.20179i	−0.768125	+	0.205819i
$243$	−13.4893	−	7.78804i	−0.865338	−	0.499603i
$244$	−0.00401565	+	0.00695531i	−0.000257076	+	0.000445268i
$245$		0			0
$246$		−	17.5774i		−	1.12069i
$247$	−22.1504	+	1.88433i	−1.40939	+	0.119897i
$248$	−2.29706	−	1.32621i	−0.145863	−	0.0842143i
$249$	2.25588	+	0.604460i	0.142960	+	0.0383061i
$250$		−	6.99009i		−	0.442092i
$251$	2.27953	+	3.94826i	0.143883	+	0.249212i	0.928956	−	0.370191i	$-0.120708\pi$
$251$	2.27953	+	3.94826i	0.143883	+	0.249212i	−0.785073	+	0.619403i	$0.787375\pi$
$252$		0			0
$253$	10.7937	+	2.89218i	0.678597	+	0.181830i
$254$	21.7552	−	5.82929i	1.36504	−	0.365762i
$255$	−3.34295	−	12.4761i	−0.209344	−	0.781281i
$256$	−2.25176			−0.140735
$257$	8.63332			0.538532			0.269266	−	0.963066i	$-0.413219\pi$
$257$	8.63332			0.538532			0.269266	+	0.963066i	$0.413219\pi$
$258$	0.358169	+	1.33670i	0.0222986	+	0.0832195i
$259$		0			0
$260$	−0.880838	−	0.413319i	−0.0546272	−	0.0256330i
$261$	0.817044	+	1.41516i	0.0505737	+	0.0875963i
$262$	−0.840697	+	3.13752i	−0.0519384	+	0.193837i
$263$	6.53143	+	11.3128i	0.402745	+	0.697575i	0.994056	−	0.108868i	$-0.0347227\pi$
$263$	6.53143	+	11.3128i	0.402745	+	0.697575i	−0.591311	+	0.806444i	$0.701389\pi$
$264$	2.21300	−	3.83303i	0.136201	−	0.235907i
$265$	−5.12356	−	5.12356i	−0.314738	−	0.314738i
$266$		0			0
$267$	1.36655	−	5.10004i	0.0836316	−	0.312117i
$268$	0.0250774	−	0.0935902i	0.00153185	−	0.00571693i
$269$		−	12.5580i		−	0.765676i	−0.923815	−	0.382838i	$-0.874947\pi$
$269$		−	12.5580i		−	0.765676i	0.923815	−	0.382838i	$-0.125053\pi$
$270$	17.8428	−	10.3015i	1.08588	−	0.626931i
$271$	3.26259	−	3.26259i	0.198188	−	0.198188i	−0.601035	−	0.799223i	$-0.705245\pi$
$271$	3.26259	−	3.26259i	0.198188	−	0.198188i	0.799223	+	0.601035i	$0.205245\pi$
$272$	−15.9661			−0.968085
$273$		0			0
$274$	−14.3401			−0.866315
$275$	3.26738	−	3.26738i	0.197031	−	0.197031i
$276$	0.683155	−	0.394420i	0.0411211	−	0.0237413i
$277$		−	1.67246i		−	0.100489i	−0.998737	−	0.0502443i	$-0.984000\pi$
$277$		−	1.67246i		−	0.100489i	0.998737	−	0.0502443i	$-0.0160000\pi$
$278$	−2.19998	+	8.21045i	−0.131946	+	0.492430i
$279$	−0.439467	+	1.64011i	−0.0263102	+	0.0981910i
$280$		0			0
$281$	−13.9259	−	13.9259i	−0.830749	−	0.830749i	0.156870	−	0.987619i	$-0.449860\pi$
$281$	−13.9259	−	13.9259i	−0.830749	−	0.830749i	−0.987619	+	0.156870i	$0.949860\pi$
$282$	2.31222	−	4.00489i	0.137691	−	0.238488i
$283$	−16.4969	−	28.5736i	−0.980642	−	1.69852i	−0.659897	−	0.751356i	$-0.729400\pi$
$283$	−16.4969	−	28.5736i	−0.980642	−	1.69852i	−0.320744	−	0.947166i	$-0.603933\pi$
$284$	−0.0705490	+	0.263292i	−0.00418631	+	0.0156235i
$285$	−9.48456	−	16.4277i	−0.561817	−	0.973095i
$286$	−2.41520	−	6.68561i	−0.142814	−	0.395329i
$287$		0			0
$288$	0.254578	+	0.950098i	0.0150012	+	0.0559851i
$289$	0.624747			0.0367498
$290$	−3.49827			−0.205425
$291$	2.54886	+	9.51249i	0.149417	+	0.557632i
$292$	−0.258741	+	0.0693294i	−0.0151417	+	0.00405720i
$293$	−21.2120	−	5.68375i	−1.23922	−	0.332048i	−0.421057	−	0.907034i	$-0.638341\pi$
$293$	−21.2120	−	5.68375i	−1.23922	−	0.332048i	−0.818163	+	0.574986i	$0.805007\pi$
$294$		0			0
$295$	−8.39849	−	14.5466i	−0.488979	−	0.846936i
$296$		−	21.5294i		−	1.25137i
$297$	−7.17325	−	1.92207i	−0.416234	−	0.111530i
$298$	−10.4093	−	6.00982i	−0.602996	−	0.348140i
$299$	4.96586	−	27.7727i	0.287183	−	1.60614i
$300$		−	0.326193i		−	0.0188328i
$301$		0			0
$302$	9.32472	−	16.1509i	0.536578	−	0.929380i
$303$	6.08105	+	3.51090i	0.349347	+	0.201696i
$304$	−22.6493	+	6.06887i	−1.29903	+	0.348074i
$305$	−0.173314	+	0.173314i	−0.00992395	+	0.00992395i
$306$	2.77616	+	10.3608i	0.158703	+	0.592286i
$307$	−13.7833	+	13.7833i	−0.786656	+	0.786656i	−0.980944	−	0.194289i	$-0.937760\pi$
$307$	−13.7833	+	13.7833i	−0.786656	+	0.786656i	0.194289	+	0.980944i	$0.437760\pi$
$308$		0			0
$309$	9.15013	+	5.28283i	0.520533	+	0.300530i
$310$	−2.57035	−	2.57035i	−0.145986	−	0.145986i
$311$	−12.9133	+	22.3666i	−0.732248	+	1.26829i	0.223672	+	0.974664i	$0.428196\pi$
$311$	−12.9133	+	22.3666i	−0.732248	+	1.26829i	−0.955920	+	0.293627i	$0.905138\pi$
$312$	−10.1163	−	4.74693i	−0.572724	−	0.268742i
$313$	−24.8257	+	14.3331i	−1.40323	+	0.810155i	−0.994723	−	0.102600i	$-0.967284\pi$
$313$	−24.8257	+	14.3331i	−1.40323	+	0.810155i	−0.408507	+	0.912755i	$0.633950\pi$
$314$	−9.04094	+	2.42251i	−0.510210	+	0.136710i
$315$		0			0
$316$	0.767998	−	0.443404i	0.0432033	−	0.0249434i
$317$	−12.0415	−	3.22651i	−0.676317	−	0.181219i	−0.0957183	−	0.995408i	$-0.530515\pi$
$317$	−12.0415	−	3.22651i	−0.676317	−	0.181219i	−0.580599	+	0.814190i	$0.697181\pi$
$318$	−2.64242	−	2.64242i	−0.148179	−	0.148179i
$319$	0.891618	+	0.891618i	0.0499210	+	0.0499210i
$320$	−23.1183	−	6.19454i	−1.29235	−	0.346285i
$321$	9.83546	−	5.67851i	0.548962	−	0.316943i
$322$		0			0
$323$	25.0023	−	6.69935i	1.39117	−	0.372762i
$324$	−0.00187272	+	0.00108121i	−0.000104040	+	6.00674e-5i
$325$	−8.91898	−	7.52048i	−0.494736	−	0.417161i
$326$	−7.54114	+	13.0616i	−0.417665	+	0.723418i
$327$	12.5100	+	12.5100i	0.691807	+	0.691807i
$328$	29.7335	+	17.1667i	1.64176	+	0.947870i
$329$		0			0
$330$	4.28907	−	4.28907i	0.236105	−	0.236105i
$331$	7.75229	+	28.9319i	0.426104	+	1.59024i	0.761499	+	0.648166i	$0.224464\pi$
$331$	7.75229	+	28.9319i	0.426104	+	1.59024i	−0.335395	+	0.942078i	$0.608870\pi$
$332$	−0.144851	+	0.144851i	−0.00794971	+	0.00794971i
$333$	−13.3126	+	3.56711i	−0.729529	+	0.195477i
$334$	−21.7756	−	12.5721i	−1.19151	−	0.687916i
$335$	1.47850	−	2.56083i	0.0807789	−	0.139913i
$336$		0			0
$337$			13.4402i			0.732137i	0.930588	+	0.366068i	$0.119296\pi$
$337$			13.4402i			0.732137i	−0.930588	+	0.366068i	$0.880704\pi$
$338$	−16.3021	+	7.50669i	−0.886716	+	0.408310i
$339$	−0.598133	−	0.345332i	−0.0324861	−	0.0187559i
$340$	1.09431	+	0.293220i	0.0593474	+	0.0159021i
$341$			1.31023i			0.0709531i
$342$	7.87648	+	13.6425i	0.425911	+	0.737700i
$343$		0			0
$344$	−2.61094	−	0.699599i	−0.140772	−	0.0377199i
$345$	23.2539	−	6.23087i	1.25195	−	0.335459i
$346$	−7.20071	−	26.8734i	−0.387113	−	1.44472i
$347$	−14.4987			−0.778332			−0.389166	−	0.921168i	$-0.627237\pi$
$347$	−14.4987			−0.778332			−0.389166	+	0.921168i	$0.627237\pi$
$348$	0.0890131			0.00477160
$349$	−5.68220	−	21.2063i	−0.304161	−	1.13515i	−0.933665	−	0.358148i	$-0.883408\pi$
$349$	−5.68220	−	21.2063i	−0.304161	−	1.13515i	0.629504	−	0.776998i	$-0.283258\pi$
$350$		0			0
$351$	−3.30019	+	18.4570i	−0.176151	+	0.985163i
$352$	0.379501	+	0.657316i	0.0202275	+	0.0350351i
$353$	2.98864	−	11.1538i	0.159069	−	0.593655i	−0.839653	−	0.543123i	$-0.817242\pi$
$353$	2.98864	−	11.1538i	0.159069	−	0.593655i	0.998722	−	0.0505316i	$-0.0160916\pi$
$354$	−4.33142	−	7.50224i	−0.230212	−	0.398740i
$355$	−4.15938	+	7.20425i	−0.220757	+	0.382362i
$356$	0.327476	+	0.327476i	0.0173562	+	0.0173562i
$357$		0			0
$358$	−5.90723	+	22.0461i	−0.312207	+	1.16517i
$359$	−0.230969	+	0.861987i	−0.0121901	+	0.0454939i	−0.971753	−	0.236000i	$-0.924163\pi$
$359$	−0.230969	+	0.861987i	−0.0121901	+	0.0454939i	0.959563	+	0.281494i	$0.0908300\pi$
$360$			15.3540i			0.809225i
$361$	16.4671	−	9.50729i	0.866690	−	0.500384i
$362$	−13.3640	+	13.3640i	−0.702396	+	0.702396i
$363$	9.60639			0.504205
$364$		0			0
$365$	−8.17495			−0.427897
$366$	−0.0893849	+	0.0893849i	−0.00467222	+	0.00467222i
$367$	12.5341	−	7.23654i	0.654273	−	0.377744i	−0.135819	−	0.990734i	$-0.543366\pi$
$367$	12.5341	−	7.23654i	0.654273	−	0.377744i	0.790091	+	0.612989i	$0.210033\pi$
$368$		−	29.7589i		−	1.55129i
$369$	5.68853	−	21.2299i	0.296133	−	1.10518i
$370$	7.63651	−	28.4998i	0.397003	−	1.48164i
$371$		0			0
$372$	0.0654024	+	0.0654024i	0.00339096	+	0.00339096i
$373$	−10.4635	+	18.1233i	−0.541778	+	0.938387i	0.457024	+	0.889454i	$0.348915\pi$
$373$	−10.4635	+	18.1233i	−0.541778	+	0.938387i	−0.998802	+	0.0489327i	$0.984418\pi$
$374$	4.13844	+	7.16800i	0.213994	+	0.370648i
$375$	−1.40489	+	5.24313i	−0.0725483	+	0.270754i
$376$	4.51639	+	7.82262i	0.232915	+	0.403421i
$377$	2.05222	−	2.43385i	0.105695	−	0.125350i
$378$		0			0
$379$	−5.53128	−	20.6430i	−0.284123	−	1.06036i	−0.949478	−	0.313834i	$-0.898387\pi$
$379$	−5.53128	−	20.6430i	−0.284123	−	1.06036i	0.665355	−	0.746527i	$-0.268280\pi$
$380$	1.66384			0.0853532
$381$	−17.4898			−0.896027
$382$	2.91174	+	10.8668i	0.148978	+	0.555992i
$383$	17.3144	−	4.63937i	0.884723	−	0.237061i	0.212279	−	0.977209i	$-0.431911\pi$
$383$	17.3144	−	4.63937i	0.884723	−	0.237061i	0.672444	+	0.740148i	$0.265245\pi$
$384$	−10.8223	−	2.89981i	−0.552271	−	0.147981i
$385$		0			0
$386$	18.4908	+	32.0270i	0.941156	+	1.63013i
$387$			1.73038i			0.0879601i
$388$	−0.834369	−	0.223569i	−0.0423587	−	0.0113500i
$389$	−4.21022	−	2.43077i	−0.213467	−	0.123245i	0.389455	−	0.921046i	$-0.372663\pi$
$389$	−4.21022	−	2.43077i	−0.213467	−	0.123245i	−0.602921	+	0.797801i	$0.705997\pi$
$390$	−11.7079	−	9.87207i	−0.592851	−	0.499892i
$391$			32.8505i			1.66132i
$392$		0			0
$393$	1.26118	−	2.18443i	0.0636182	−	0.110190i
$394$	−22.0364	−	12.7227i	−1.11018	−	0.640962i
$395$	26.1419	−	7.00470i	1.31534	−	0.352445i
$396$	0.175731	−	0.175731i	0.00883083	−	0.00883083i
$397$	−5.06335	−	18.8967i	−0.254122	−	0.948397i	−0.968577	−	0.248715i	$-0.919992\pi$
$397$	−5.06335	−	18.8967i	−0.254122	−	0.948397i	0.714455	−	0.699682i	$-0.246675\pi$
$398$	−12.4091	+	12.4091i	−0.622014	+	0.622014i
$399$		0			0
$400$	−10.6570	−	6.15281i	−0.532849	−	0.307640i
$401$	−3.03815	−	3.03815i	−0.151718	−	0.151718i	0.627167	−	0.778885i	$-0.284214\pi$
$401$	−3.03815	−	3.03815i	−0.151718	−	0.151718i	−0.778885	+	0.627167i	$0.784214\pi$
$402$	0.762518	−	1.32072i	0.0380309	−	0.0658715i
$403$	3.29615	−	0.280402i	0.164193	−	0.0139678i
$404$	−0.533387	+	0.307951i	−0.0265370	+	0.0153212i
$405$	−0.0637454	+	0.0170805i	−0.00316753	+	0.000848738i
$406$		0			0
$407$	−9.21022	+	5.31752i	−0.456534	+	0.263580i
$408$	12.5681	+	3.36760i	0.622212	+	0.166721i
$409$	−21.4483	−	21.4483i	−1.06055	−	1.06055i	−0.998045	−	0.0625056i	$-0.980091\pi$
$409$	−21.4483	−	21.4483i	−1.06055	−	1.06055i	−0.0625056	−	0.998045i	$-0.519909\pi$
$410$	33.2711	+	33.2711i	1.64314	+	1.64314i
$411$	10.7562	+	2.88212i	0.530565	+	0.142164i
$412$	−0.802586	+	0.463373i	−0.0395406	+	0.0228288i
$413$		0			0
$414$	−19.3113	+	5.17444i	−0.949098	+	0.254310i
$415$	−5.41415	+	3.12586i	−0.265770	+	0.153442i
$416$	1.57239	−	1.09538i	0.0770927	−	0.0537055i
$417$	3.30033	−	5.71634i	0.161618	−	0.279930i
$418$	8.59540	+	8.59540i	0.420415	+	0.420415i
$419$	−6.87240	−	3.96778i	−0.335739	−	0.193839i	0.322647	−	0.946519i	$-0.395427\pi$
$419$	−6.87240	−	3.96778i	−0.335739	−	0.193839i	−0.658386	+	0.752680i	$0.728761\pi$
$420$		0			0
$421$	−5.98090	+	5.98090i	−0.291491	+	0.291491i	−0.837669	−	0.546178i	$-0.816082\pi$
$421$	−5.98090	+	5.98090i	−0.291491	+	0.291491i	0.546178	+	0.837669i	$0.316082\pi$
$422$	−1.61835	−	6.03978i	−0.0787802	−	0.294012i
$423$	4.08879	−	4.08879i	0.198804	−	0.198804i
$424$	7.05053	−	1.88918i	0.342404	−	0.0917469i
$425$	11.7641	+	6.79201i	0.570643	+	0.329461i
$426$	−2.14515	+	3.71551i	−0.103933	+	0.180017i
$427$		0			0
$428$			0.996159i			0.0481511i
$429$	0.467898	+	5.50017i	0.0225903	+	0.265551i
$430$	−3.20811	−	1.85221i	−0.154709	−	0.0893213i
$431$	−0.558842	−	0.149741i	−0.0269185	−	0.00721278i	0.245335	−	0.969438i	$-0.421102\pi$
$431$	−0.558842	−	0.149741i	−0.0269185	−	0.00721278i	−0.272253	+	0.962226i	$0.587769\pi$
$432$			19.7770i			0.951521i
$433$	4.11334	+	7.12452i	0.197675	+	0.342382i	0.947774	−	0.318943i	$-0.103328\pi$
$433$	4.11334	+	7.12452i	0.197675	+	0.342382i	−0.750099	+	0.661325i	$0.769994\pi$
$434$		0			0
$435$	2.62399	+	0.703095i	0.125810	+	0.0337108i
$436$	−1.49893	+	0.401638i	−0.0717858	+	0.0192350i
$437$	12.4868	+	46.6014i	0.597325	+	2.22925i
$438$	−4.21614			−0.201455
$439$	−12.7234			−0.607253			−0.303626	−	0.952791i	$-0.598197\pi$
$439$	−12.7234			−0.607253			−0.303626	+	0.952791i	$0.598197\pi$
$440$	3.06645	+	11.4441i	0.146187	+	0.545578i
$441$		0			0
$442$	17.1468	−	11.9451i	0.815591	−	0.568169i
$443$	1.11534	+	1.93182i	0.0529912	+	0.0917834i	0.891304	−	0.453406i	$-0.149791\pi$
$443$	1.11534	+	1.93182i	0.0529912	+	0.0917834i	−0.838313	+	0.545189i	$0.816458\pi$
$444$	−0.194310	+	0.725176i	−0.00922156	+	0.0344153i
$445$	7.06688	+	12.2402i	0.335002	+	0.580241i
$446$	−16.0641	+	27.8239i	−0.760658	+	1.31750i
$447$	6.59996	+	6.59996i	0.312167	+	0.312167i
$448$		0			0
$449$	10.0883	−	37.6500i	0.476096	−	1.77682i	−0.141088	−	0.989997i	$-0.545060\pi$
$449$	10.0883	−	37.6500i	0.476096	−	1.77682i	0.617184	−	0.786819i	$-0.288273\pi$
$450$	−2.13969	+	7.98542i	−0.100866	+	0.376436i
$451$		−	16.9599i		−	0.798609i
$452$	0.0524641	−	0.0302901i	0.00246770	−	0.00142473i
$453$	−10.2404	+	10.2404i	−0.481134	+	0.481134i
$454$	−14.3906			−0.675387
$455$		0			0
$456$	19.1090			0.894862
$457$	16.2831	−	16.2831i	0.761691	−	0.761691i	−0.214937	−	0.976628i	$-0.568954\pi$
$457$	16.2831	−	16.2831i	0.761691	−	0.761691i	0.976628	+	0.214937i	$0.0689545\pi$
$458$	2.30600	−	1.33137i	0.107752	−	0.0622107i
$459$		−	21.8316i		−	1.01901i
$460$	−0.546528	+	2.03967i	−0.0254820	+	0.0951002i
$461$	7.81461	−	29.1645i	0.363962	−	1.35833i	−0.504859	−	0.863202i	$-0.668456\pi$
$461$	7.81461	−	29.1645i	0.363962	−	1.35833i	0.868822	−	0.495125i	$-0.164878\pi$
$462$		0			0
$463$	2.19856	+	2.19856i	0.102176	+	0.102176i	0.756347	−	0.654171i	$-0.226982\pi$
$463$	2.19856	+	2.19856i	0.102176	+	0.102176i	−0.654171	+	0.756347i	$0.726982\pi$
$464$	1.67901	−	2.90812i	0.0779459	−	0.135006i
$465$	1.41137	+	2.44457i	0.0654509	+	0.113364i
$466$	3.07126	−	11.4621i	0.142273	−	0.530971i
$467$	10.5856	+	18.3348i	0.489844	+	0.848434i	0.999932	−	0.0116879i	$-0.00372046\pi$
$467$	10.5856	+	18.3348i	0.489844	+	0.848434i	−0.510088	+	0.860122i	$0.670387\pi$
$468$	−0.479694	−	0.404478i	−0.0221739	−	0.0186970i
$469$		0			0
$470$	3.20394	+	11.9573i	0.147787	+	0.551547i
$471$	7.26832			0.334907
$472$	16.9209			0.778845
$473$	0.345586	+	1.28974i	0.0158901	+	0.0593025i
$474$	13.4824	−	3.61259i	0.619266	−	0.165932i
$475$	19.2702	+	5.16343i	0.884176	+	0.236914i
$476$		0			0
$477$	−2.33634	−	4.04666i	−0.106974	−	0.185284i
$478$		−	12.5962i		−	0.576135i
$479$	−23.1962	−	6.21539i	−1.05986	−	0.283988i	−0.313539	−	0.949575i	$-0.601515\pi$
$479$	−23.1962	−	6.21539i	−1.05986	−	0.283988i	−0.746320	+	0.665587i	$0.768181\pi$
$480$	1.41611	+	0.817593i	0.0646364	+	0.0373179i
$481$	15.3483	+	22.0321i	0.699824	+	1.00458i
$482$			6.02432i			0.274400i
$483$		0			0
$484$	−0.421303	+	0.729719i	−0.0191501	+	0.0331690i
$485$	−22.8302	−	13.1810i	−1.03666	−	0.598518i
$486$	20.7711	−	5.56560i	0.942196	−	0.252461i
$487$	−24.0960	+	24.0960i	−1.09189	+	1.09189i	−0.0965685	+	0.995326i	$0.530787\pi$
$487$	−24.0960	+	24.0960i	−1.09189	+	1.09189i	−0.995326	+	0.0965685i	$0.969213\pi$
$488$	−0.0639053	−	0.238498i	−0.00289286	−	0.0107963i
$489$	8.28165	−	8.28165i	0.374509	−	0.374509i
$490$		0			0
$491$	12.2688	+	7.08337i	0.553681	+	0.319668i	0.750605	−	0.660751i	$-0.229762\pi$
$491$	12.2688	+	7.08337i	0.553681	+	0.319668i	−0.196924	+	0.980419i	$0.563095\pi$
$492$	−0.846579	−	0.846579i	−0.0381667	−	0.0381667i
$493$	−1.85343	+	3.21024i	−0.0834745	+	0.144582i
$494$	19.7839	−	23.4629i	0.890119	−	1.05564i
$495$	6.56838	−	3.79226i	0.295227	−	0.170449i
$496$	3.37039	−	0.903094i	0.151335	−	0.0405501i
$497$		0			0
$498$	−2.79228	+	1.61213i	−0.125125	+	0.0722411i
$499$	28.8032	+	7.71779i	1.28941	+	0.345496i	0.837436	−	0.546536i	$-0.184054\pi$
$499$	28.8032	+	7.71779i	1.28941	+	0.345496i	0.451972	+	0.892032i	$0.350721\pi$
$500$	−0.336664	−	0.336664i	−0.0150561	−	0.0150561i
$501$	13.8066	+	13.8066i	0.616835	+	0.616835i
$502$	−6.07962	−	1.62903i	−0.271347	−	0.0727072i
$503$	11.8147	−	6.82122i	0.526791	−	0.304143i	−0.212918	−	0.977070i	$-0.568297\pi$
$503$	11.8147	−	6.82122i	0.526791	−	0.304143i	0.739709	+	0.672927i	$0.234963\pi$
$504$		0			0
$505$	−18.1560	+	4.86488i	−0.807930	+	0.216484i
$506$	−13.3603	+	7.71358i	−0.593938	+	0.342910i
$507$	13.7366	−	2.35418i	0.610064	−	0.104553i
$508$	0.767040	−	1.32855i	0.0340319	−	0.0589450i
$509$	−1.88773	−	1.88773i	−0.0836722	−	0.0836722i	0.664032	−	0.747704i	$-0.268844\pi$
$509$	−1.88773	−	1.88773i	−0.0836722	−	0.0836722i	−0.747704	+	0.664032i	$0.768844\pi$
$510$	15.4426	+	8.91581i	0.683812	+	0.394799i
$511$		0			0
$512$	16.9779	−	16.9779i	0.750326	−	0.750326i
$513$	−8.29842	−	30.9701i	−0.366384	−	1.36736i
$514$	−8.42792	+	8.42792i	−0.371740	+	0.371740i
$515$	−27.3192	+	7.32016i	−1.20383	+	0.322565i
$516$	0.0816301	+	0.0471292i	0.00359357	+	0.00207475i
$517$	2.23099	−	3.86419i	0.0981190	−	0.169947i
$518$		0			0
$519$			21.6045i			0.948331i
$520$	28.1337	−	10.1634i	1.23374	−	0.445695i
$521$	13.4638	+	7.77333i	0.589860	+	0.340556i	0.765042	−	0.643980i	$-0.222718\pi$
$521$	13.4638	+	7.77333i	0.589860	+	0.340556i	−0.175182	+	0.984536i	$0.556052\pi$
$522$	−2.17910	−	0.583887i	−0.0953765	−	0.0255561i
$523$			0.118473i			0.00518048i	0.999997	+	0.00259024i	$0.000824501\pi$
$523$			0.118473i			0.00518048i	−0.999997	+	0.00259024i	$0.999175\pi$
$524$	0.110622	+	0.191603i	0.00483255	+	0.00837022i
$525$		0			0
$526$	−17.4197	−	4.66758i	−0.759533	−	0.203516i
$527$	−3.72054	+	0.996915i	−0.162069	+	0.0434263i
$528$	1.50696	+	5.62407i	0.0655822	+	0.244756i
$529$	−38.2295			−1.66215
$530$	10.0033			0.434516
$531$	−2.80354	−	10.4630i	−0.121663	−	0.454053i
$532$		0			0
$533$	−42.6658	+	3.62957i	−1.84806	+	0.157214i
$534$	3.64466	+	6.31274i	0.157720	+	0.273179i
$535$	−7.86844	+	29.3654i	−0.340182	+	1.26958i
$536$	1.48940	+	2.57972i	0.0643324	+	0.111427i
$537$	8.86181	−	15.3491i	0.382415	−	0.662362i
$538$	12.2592	+	12.2592i	0.528534	+	0.528534i
$539$		0			0
$540$	0.363209	−	1.35551i	0.0156300	−	0.0583320i
$541$	−1.19789	+	4.47060i	−0.0515014	+	0.192206i	−0.986884	−	0.161432i	$-0.948389\pi$
$541$	−1.19789	+	4.47060i	−0.0515014	+	0.192206i	0.935382	+	0.353638i	$0.115055\pi$
$542$			6.36993i			0.273612i
$543$	12.7100	−	7.33814i	0.545440	−	0.314910i
$544$	−1.57776	+	1.57776i	−0.0676460	+	0.0676460i
$545$	−47.3589			−2.02863
$546$		0			0
$547$	29.4860			1.26073			0.630365	−	0.776299i	$-0.282905\pi$
$547$	29.4860			1.26073			0.630365	+	0.776299i	$0.282905\pi$
$548$	−0.690661	+	0.690661i	−0.0295036	+	0.0295036i
$549$	−0.136886	+	0.0790313i	−0.00584216	+	0.00337297i
$550$			6.37929i			0.272014i
$551$	−1.40902	+	5.25853i	−0.0600263	+	0.224021i
$552$	−6.27682	+	23.4254i	−0.267159	+	0.997052i
$553$		0			0
$554$	1.63267	+	1.63267i	0.0693657	+	0.0693657i
$555$	−11.4560	+	19.8424i	−0.486280	+	0.842262i
$556$	0.289482	+	0.501398i	0.0122768	+	0.0212640i
$557$	0.351113	−	1.31037i	0.0148771	−	0.0555222i	−0.958088	−	0.286473i	$-0.907517\pi$
$557$	0.351113	−	1.31037i	0.0148771	−	0.0555222i	0.972965	+	0.230951i	$0.0741837\pi$
$558$	−1.17208	−	2.03010i	−0.0496181	−	0.0859411i
$559$	3.17064	−	1.14541i	0.134104	−	0.0484455i
$560$		0			0
$561$	−1.66352	−	6.20834i	−0.0702338	−	0.262116i
$562$	27.1892			1.14691
$563$	32.8100			1.38278			0.691388	−	0.722484i	$-0.257000\pi$
$563$	32.8100			1.38278			0.691388	+	0.722484i	$0.257000\pi$
$564$	−0.0815238	−	0.304251i	−0.00343277	−	0.0128113i
$565$	1.78582	−	0.478510i	0.0751302	−	0.0201311i
$566$	43.9982	+	11.7893i	1.84938	+	0.495541i
$567$		0			0
$568$	−4.19005	−	7.25739i	−0.175811	−	0.304513i
$569$			29.8773i			1.25252i	0.779613	+	0.626261i	$0.215416\pi$
$569$			29.8773i			1.25252i	−0.779613	+	0.626261i	$0.784584\pi$
$570$	25.2958	+	6.77799i	1.05952	+	0.283899i
$571$	0.640877	+	0.370010i	0.0268198	+	0.0154844i	0.513350	−	0.858179i	$-0.328404\pi$
$571$	0.640877	+	0.370010i	0.0268198	+	0.0154844i	−0.486530	+	0.873664i	$0.661738\pi$
$572$	−0.438323	−	0.205676i	−0.0183272	−	0.00859974i
$573$		−	8.73616i		−	0.364958i
$574$		0			0
$575$	−12.6595	+	21.9269i	−0.527938	+	0.914416i
$576$	−13.3667	−	7.71724i	−0.556944	−	0.321552i
$577$	−32.9470	+	8.82812i	−1.37160	+	0.367519i	−0.868063	−	0.496454i	$-0.834635\pi$
$577$	−32.9470	+	8.82812i	−1.37160	+	0.367519i	−0.503538	+	0.863973i	$0.667969\pi$
$578$	−0.609883	+	0.609883i	−0.0253678	+	0.0253678i
$579$	−7.43269	−	27.7392i	−0.308892	−	1.15280i
$580$	−0.168487	+	0.168487i	−0.00699605	+	0.00699605i
$581$		0			0
$582$	−11.7744	−	6.79795i	−0.488064	−	0.281784i
$583$	−2.54959	−	2.54959i	−0.105593	−	0.105593i
$584$	4.11762	−	7.13193i	0.170388	−	0.295121i
$585$	−10.9458	−	15.7125i	−0.452555	−	0.649630i
$586$	26.2559	−	15.1588i	1.08462	−	0.626206i
$587$	11.9740	−	3.20842i	0.494219	−	0.132426i	−0.00309648	−	0.999995i	$-0.500986\pi$
$587$	11.9740	−	3.20842i	0.494219	−	0.132426i	0.497316	+	0.867569i	$0.334319\pi$
$588$		0			0
$589$	−4.89899	+	2.82843i	−0.201859	+	0.116543i
$590$	22.3992	+	6.00184i	0.922160	+	0.247092i
$591$	13.9720	+	13.9720i	0.574733	+	0.574733i
$592$	20.0269	+	20.0269i	0.823099	+	0.823099i
$593$	22.0792	+	5.91611i	0.906685	+	0.242945i	0.681885	−	0.731460i	$-0.261161\pi$
$593$	22.0792	+	5.91611i	0.906685	+	0.242945i	0.224800	+	0.974405i	$0.427827\pi$
$594$	8.87892	−	5.12625i	0.364307	−	0.210333i
$595$		0			0
$596$	−0.790795	+	0.211893i	−0.0323922	+	0.00867948i
$597$	11.8019	−	6.81383i	0.483019	−	0.278871i
$598$	22.2642	+	31.9597i	0.910452	+	1.30693i
$599$	−1.24701	+	2.15989i	−0.0509516	+	0.0882508i	−0.890376	−	0.455225i	$-0.849559\pi$
$599$	−1.24701	+	2.15989i	−0.0509516	+	0.0882508i	0.839425	+	0.543476i	$0.182892\pi$
$600$	7.09113	+	7.09113i	0.289494	+	0.289494i
$601$	−18.5873	−	10.7314i	−0.758193	−	0.437743i	0.0704537	−	0.997515i	$-0.477555\pi$
$601$	−18.5873	−	10.7314i	−0.758193	−	0.437743i	−0.828647	+	0.559772i	$0.810889\pi$
$602$		0			0
$603$	1.34839	−	1.34839i	0.0549106	−	0.0549106i
$604$	−0.328769	−	1.22698i	−0.0133774	−	0.0499252i
$605$	−18.1833	+	18.1833i	−0.739258	+	0.739258i
$606$	−9.36374	+	2.50901i	−0.380376	+	0.101921i
$607$	−13.8907	−	8.01981i	−0.563807	−	0.325514i	0.190865	−	0.981616i	$-0.438871\pi$
$607$	−13.8907	−	8.01981i	−0.563807	−	0.325514i	−0.754672	+	0.656102i	$0.772204\pi$
$608$	−1.63848	+	2.83793i	−0.0664490	+	0.115093i
$609$		0			0
$610$		−	0.338382i		−	0.0137007i
$611$	−10.1986	−	4.78552i	−0.412590	−	0.193601i
$612$	0.632715	+	0.365298i	0.0255760	+	0.0147663i
$613$	6.67764	+	1.78927i	0.269707	+	0.0722679i	0.391138	−	0.920332i	$-0.372082\pi$
$613$	6.67764	+	1.78927i	0.269707	+	0.0722679i	−0.121431	+	0.992600i	$0.538748\pi$
$614$		−	26.9108i		−	1.08603i
$615$	−18.2691	−	31.6429i	−0.736680	−	1.27597i
$616$		0			0
$617$	26.9254	+	7.21463i	1.08397	+	0.290450i	0.756223	−	0.654314i	$-0.227043\pi$
$617$	26.9254	+	7.21463i	1.08397	+	0.290450i	0.327751	+	0.944764i	$0.393709\pi$
$618$	−14.0896	+	3.77529i	−0.566766	+	0.151864i
$619$	3.58815	+	13.3912i	0.144220	+	0.538237i	0.999789	+	0.0205475i	$0.00654094\pi$
$619$	3.58815	+	13.3912i	0.144220	+	0.538237i	−0.855569	+	0.517689i	$0.826792\pi$
$620$	−0.247592			−0.00994354
$621$	40.6915			1.63290
$622$	−9.22831	−	34.4405i	−0.370022	−	1.38094i
$623$		0			0
$624$	13.8259	−	4.99466i	0.553480	−	0.199947i
$625$	−15.3544	−	26.5946i	−0.614175	−	1.06378i
$626$	10.2429	−	38.2271i	0.409390	−	1.52786i
$627$	−4.71971	−	8.17478i	−0.188487	−	0.326469i
$628$	−0.318763	+	0.552115i	−0.0127200	+	0.0220318i
$629$	−22.1074	−	22.1074i	−0.881480	−	0.881480i
$630$		0			0
$631$	6.69536	−	24.9874i	0.266538	−	0.994733i	−0.694764	−	0.719237i	$-0.744491\pi$
$631$	6.69536	−	24.9874i	0.266538	−	0.994733i	0.961302	−	0.275496i	$-0.0888419\pi$
$632$	−7.05636	+	26.3347i	−0.280687	+	1.04754i
$633$			4.85559i			0.192992i
$634$	14.9047	−	8.60525i	0.591943	−	0.341758i
$635$	33.1052	−	33.1052i	1.31374	−	1.31374i
$636$	−0.254533			−0.0100929
$637$		0			0
$638$	−1.74081			−0.0689193
$639$	−3.79335	+	3.79335i	−0.150063	+	0.150063i
$640$	25.9736	−	14.9959i	1.02670	−	0.592764i
$641$		−	12.5749i		−	0.496678i	−0.968673	−	0.248339i	$-0.920115\pi$
$641$		−	12.5749i		−	0.496678i	0.968673	−	0.248339i	$-0.0798847\pi$
$642$	−4.05806	+	15.1449i	−0.160159	+	0.597720i
$643$	−6.40174	+	23.8916i	−0.252460	+	0.942193i	0.717026	+	0.697046i	$0.245503\pi$
$643$	−6.40174	+	23.8916i	−0.252460	+	0.942193i	−0.969486	+	0.245147i	$0.921164\pi$
$644$		0			0
$645$	2.03408	+	2.03408i	0.0800919	+	0.0800919i
$646$	−17.8675	+	30.9474i	−0.702988	+	1.21761i
$647$	17.3117	+	29.9848i	0.680595	+	1.17883i	0.974800	+	0.223083i	$0.0716120\pi$
$647$	17.3117	+	29.9848i	0.680595	+	1.17883i	−0.294205	+	0.955742i	$0.595055\pi$
$648$	0.0172065	−	0.0642155i	0.000675935	−	0.00252262i
$649$	−4.17926	−	7.23869i	−0.164050	−	0.284143i
$650$	16.0483	−	1.36523i	0.629468	−	0.0535487i
$651$		0			0
$652$	0.265884	+	0.992293i	0.0104128	+	0.0388612i
$653$	−27.4003			−1.07225			−0.536127	−	0.844137i	$-0.680113\pi$
$653$	−27.4003			−1.07225			−0.536127	+	0.844137i	$0.680113\pi$
$654$	−24.4248			−0.955086
$655$	1.74756	+	6.52198i	0.0682828	+	0.254835i
$656$	−43.6269	+	11.6898i	−1.70335	+	0.456410i
$657$	−5.09224	−	1.36446i	−0.198667	−	0.0532327i
$658$		0			0
$659$	2.14617	+	3.71728i	0.0836031	+	0.144805i	0.904795	−	0.425847i	$-0.140024\pi$
$659$	2.14617	+	3.71728i	0.0836031	+	0.144805i	−0.821192	+	0.570652i	$0.806691\pi$
$660$		−	0.413149i		−	0.0160818i
$661$	14.6944	+	3.93734i	0.571544	+	0.153145i	0.533005	−	0.846112i	$-0.321063\pi$
$661$	14.6944	+	3.93734i	0.571544	+	0.153145i	0.0385395	+	0.999257i	$0.487729\pi$
$662$	−35.8115	−	20.6758i	−1.39185	−	0.803586i
$663$	−15.2623	+	5.51355i	−0.592737	+	0.214128i
$664$		−	6.29783i		−	0.244403i
$665$		0			0
$666$	9.51367	−	16.4782i	0.368647	−	0.638516i
$667$	−5.98352	−	3.45459i	−0.231683	−	0.133762i
$668$	−1.65429	+	0.443265i	−0.0640063	+	0.0171504i
$669$	17.6415	−	17.6415i	0.682061	−	0.682061i
$670$	1.05658	+	3.94323i	0.0408194	+	0.152340i
$671$	−0.0862447	+	0.0862447i	−0.00332944	+	0.00332944i
$672$		0			0
$673$	26.3013	+	15.1851i	1.01384	+	0.585341i	0.912314	−	0.409492i	$-0.134294\pi$
$673$	26.3013	+	15.1851i	1.01384	+	0.585341i	0.101526	+	0.994833i	$0.467627\pi$
$674$	−13.1205	−	13.1205i	−0.505382	−	0.505382i
$675$	8.41319	−	14.5721i	0.323824	−	0.560879i
$676$	−0.423612	+	1.14670i	−0.0162928	+	0.0441039i
$677$	31.7593	−	18.3363i	1.22061	−	0.704720i	0.255562	−	0.966793i	$-0.417739\pi$
$677$	31.7593	−	18.3363i	1.22061	−	0.704720i	0.965048	+	0.262073i	$0.0844060\pi$
$678$	0.921018	−	0.246786i	0.0353715	−	0.00947776i
$679$		0			0
$680$	−30.1636	+	17.4150i	−1.15672	+	0.667834i
$681$	10.7942	+	2.89228i	0.413633	+	0.110833i
$682$	−1.27906	−	1.27906i	−0.0489778	−	0.0489778i
$683$	11.3197	+	11.3197i	0.433137	+	0.433137i	0.889694	−	0.456557i	$-0.150918\pi$
$683$	11.3197	+	11.3197i	0.433137	+	0.433137i	−0.456557	+	0.889694i	$0.650918\pi$
$684$	1.03642	+	0.277707i	0.0396284	+	0.0106184i
$685$	−25.8151	+	14.9044i	−0.986346	+	0.569467i
$686$		0			0
$687$	−1.99727	+	0.535166i	−0.0762005	+	0.0204179i
$688$	3.07949	−	1.77794i	0.117404	−	0.0677835i
$689$	−5.86834	+	6.95961i	−0.223566	+	0.265140i
$690$	−16.6180	+	28.7833i	−0.632638	+	1.09576i
$691$	−12.7750	−	12.7750i	−0.485982	−	0.485982i	0.421054	−	0.907036i	$-0.361660\pi$
$691$	−12.7750	−	12.7750i	−0.485982	−	0.485982i	−0.907036	+	0.421054i	$0.861660\pi$
$692$	−1.64111	−	0.947497i	−0.0623858	−	0.0360184i
$693$		0			0
$694$	14.1538	−	14.1538i	0.537270	−	0.537270i
$695$	4.57311	+	17.0671i	0.173468	+	0.647391i
$696$	−1.93506	+	1.93506i	−0.0733482	+	0.0733482i
$697$	48.1592	−	12.9042i	1.82416	−	0.488783i
$698$	26.2487	+	15.1547i	0.993530	+	0.573615i
$699$	−4.60738	+	7.98022i	−0.174267	+	0.301840i
$700$		0			0
$701$		−	37.6363i		−	1.42150i	−0.703444	−	0.710751i	$-0.748355\pi$
$701$		−	37.6363i		−	1.42150i	0.703444	−	0.710751i	$-0.251645\pi$
$702$	−14.7962	−	21.2396i	−0.558448	−	0.801636i
$703$	−39.7646	−	22.9581i	−1.49975	−	0.865882i
$704$	−11.5042	−	3.08253i	−0.433579	−	0.116177i
$705$		−	9.61285i		−	0.362041i
$706$	7.97086	+	13.8059i	0.299987	+	0.519593i
$707$		0			0
$708$	−0.569945	−	0.152716i	−0.0214198	−	0.00573943i
$709$	11.1364	−	2.98398i	0.418235	−	0.112066i	−0.0435634	−	0.999051i	$-0.513871\pi$
$709$	11.1364	−	2.98398i	0.418235	−	0.112066i	0.461798	+	0.886985i	$0.347204\pi$
$710$	−2.97243	−	11.0933i	−0.111553	−	0.416323i
$711$	17.4531			0.654542
$712$	−14.2380			−0.533592
$713$	−1.85813	−	6.93465i	−0.0695876	−	0.259705i
$714$		0			0
$715$	−11.2966	−	9.52526i	−0.422468	−	0.356225i
$716$	0.777296	+	1.34632i	0.0290489	+	0.0503142i
$717$	−2.53162	+	9.44815i	−0.0945452	+	0.352848i
$718$	−0.616005	−	1.06695i	−0.0229891	−	0.0398183i
$719$	23.0965	−	40.0043i	0.861355	−	1.49191i	−0.00926691	−	0.999957i	$-0.502950\pi$
$719$	23.0965	−	40.0043i	0.861355	−	1.49191i	0.870622	−	0.491953i	$-0.163717\pi$
$720$	−14.2824	−	14.2824i	−0.532273	−	0.532273i
$721$		0			0
$722$	−6.79424	+	25.3564i	−0.252855	+	0.943669i
$723$	1.21079	−	4.51873i	0.0450298	−	0.168053i
$724$			1.28730i			0.0478422i
$725$	−2.47425	+	1.42851i	−0.0918913	+	0.0530534i
$726$	−9.37784	+	9.37784i	−0.348044	+	0.348044i
$727$	3.27502			0.121464			0.0607318	−	0.998154i	$-0.480657\pi$
$727$	3.27502			0.121464			0.0607318	+	0.998154i	$0.480657\pi$
$728$		0			0
$729$	−16.7676			−0.621022
$730$	7.98046	−	7.98046i	0.295370	−	0.295370i
$731$	−3.39941	+	1.96265i	−0.125732	+	0.0725913i
$732$			0.00861009i			0.000318238i
$733$	−8.73478	+	32.5986i	−0.322626	+	1.20406i	0.594050	+	0.804428i	$0.297528\pi$
$733$	−8.73478	+	32.5986i	−0.322626	+	1.20406i	−0.916676	+	0.399630i	$0.869139\pi$
$734$	−5.17148	+	19.3002i	−0.190883	+	0.712384i
$735$		0			0
$736$	−2.94077	−	2.94077i	−0.108398	−	0.108398i
$737$	0.735730	−	1.27432i	0.0271010	−	0.0469403i
$738$	15.1716	+	26.2780i	0.558474	+	0.967306i
$739$	−0.547643	+	2.04383i	−0.0201454	+	0.0751836i	−0.975267	−	0.221031i	$-0.929058\pi$
$739$	−0.547643	+	2.04383i	−0.0201454	+	0.0751836i	0.955121	+	0.296215i	$0.0957244\pi$
$740$	−1.00484	−	1.74044i	−0.0369387	−	0.0639797i
$741$	−19.5552	+	13.6228i	−0.718377	+	0.500447i
$742$		0			0
$743$	−7.14174	−	26.6533i	−0.262005	−	0.977816i	−0.964058	−	0.265692i	$-0.914400\pi$
$743$	−7.14174	−	26.6533i	−0.262005	−	0.977816i	0.702053	−	0.712125i	$-0.252267\pi$
$744$	−2.84357			−0.104250
$745$	−24.9853			−0.915390
$746$	−7.47755	−	27.9066i	−0.273773	−	1.02173i
$747$	−3.89424	+	1.04346i	−0.142483	+	0.0381781i
$748$	0.544552	+	0.145912i	0.0199108	+	0.00533508i
$749$		0			0
$750$	−3.74692	−	6.48986i	−0.136818	−	0.236976i
$751$			7.53493i			0.274954i	0.990505	+	0.137477i	$0.0438993\pi$
$751$			7.53493i			0.274954i	−0.990505	+	0.137477i	$0.956101\pi$
$752$	−11.4778	−	3.07548i	−0.418554	−	0.112151i
$753$	4.23280	+	2.44381i	0.154252	+	0.0890574i
$754$	0.372550	+	4.37934i	0.0135675	+	0.159486i
$755$		−	38.7667i		−	1.41086i
$756$		0			0
$757$	−21.0971	+	36.5412i	−0.766786	+	1.32811i	0.172512	+	0.985007i	$0.444812\pi$
$757$	−21.0971	+	36.5412i	−0.766786	+	1.32811i	−0.939297	+	0.343104i	$0.888522\pi$
$758$	25.5516	+	14.7522i	0.928075	+	0.535824i
$759$	11.5716	−	3.10061i	0.420023	−	0.112545i
$760$	−36.1702	+	36.1702i	−1.31203	+	1.31203i
$761$	−0.441464	−	1.64757i	−0.0160031	−	0.0597243i	0.957463	−	0.288557i	$-0.0931756\pi$
$761$	−0.441464	−	1.64757i	−0.0160031	−	0.0597243i	−0.973466	+	0.228833i	$0.926509\pi$
$762$	17.0736	−	17.0736i	0.618513	−	0.618513i
$763$		0			0
$764$	0.663614	+	0.383138i	0.0240087	+	0.0138614i
$765$	15.7662	+	15.7662i	0.570027	+	0.570027i
$766$	−12.3734	+	21.4314i	−0.447070	+	0.774349i
$767$	−17.3159	+	12.0629i	−0.625241	+	0.435565i
$768$	−2.09061	+	1.20702i	−0.0754385	+	0.0435545i
$769$	3.49612	−	0.936782i	0.126073	−	0.0337812i	−0.195231	−	0.980757i	$-0.562546\pi$
$769$	3.49612	−	0.936782i	0.126073	−	0.0337812i	0.321304	+	0.946976i	$0.395879\pi$
$770$		0			0
$771$	8.01550	−	4.62775i	0.288671	−	0.166664i
$772$	2.43309	+	0.651944i	0.0875688	+	0.0234640i
$773$	−18.8981	−	18.8981i	−0.679717	−	0.679717i	0.280219	−	0.959936i	$-0.409593\pi$
$773$	−18.8981	−	18.8981i	−0.679717	−	0.679717i	−0.959936	+	0.280219i	$0.909593\pi$
$774$	−1.68921	−	1.68921i	−0.0607174	−	0.0607174i
$775$	−2.86755	−	0.768358i	−0.103005	−	0.0276002i
$776$	22.9985	−	13.2782i	0.825600	−	0.476660i
$777$		0			0
$778$	6.48299	−	1.73711i	0.232426	−	0.0622785i
$779$	63.4133	−	36.6117i	2.27202	−	1.31175i
$780$	−1.03936	+	0.0884177i	−0.0372149	+	0.00316586i
$781$	−2.06979	+	3.58498i	−0.0740629	+	0.128281i
$782$	−32.0689	−	32.0689i	−1.14678	−	1.14678i
$783$	3.97649	+	2.29583i	0.142108	+	0.0820463i
$784$		0			0
$785$	−13.7577	+	13.7577i	−0.491035	+	0.491035i
$786$	0.901283	+	3.36364i	0.0321477	+	0.119977i
$787$	31.1249	−	31.1249i	1.10948	−	1.10948i	0.116263	−	0.993218i	$-0.462908\pi$
$787$	31.1249	−	31.1249i	1.10948	−	1.10948i	0.993218	−	0.116263i	$-0.0370915\pi$
$788$	−1.67410	+	0.448575i	−0.0596375	+	0.0159798i
$789$	12.1280	+	7.00213i	0.431770	+	0.249283i
$790$	−18.6819	+	32.3580i	−0.664672	+	1.15124i
$791$		0			0
$792$			7.64045i			0.271492i
$793$	0.235423	+	0.198508i	0.00836010	+	0.00704923i
$794$	23.3900	+	13.5042i	0.830079	+	0.479246i
$795$	−7.50330	−	2.01050i	−0.266115	−	0.0713052i
$796$			1.19532i			0.0423671i
$797$	6.94770	+	12.0338i	0.246100	+	0.426258i	0.962440	−	0.271493i	$-0.0875175\pi$
$797$	6.94770	+	12.0338i	0.246100	+	0.426258i	−0.716340	+	0.697751i	$0.754184\pi$
$798$		0			0
$799$	12.6703	+	3.39499i	0.448241	+	0.120106i
$800$	−1.66114	+	0.445101i	−0.0587301	+	0.0157367i
$801$	2.35903	+	8.80402i	0.0833522	+	0.311075i
$802$	5.93174			0.209457
$803$	−4.06802			−0.143557
$804$	−0.0268847	−	0.100335i	−0.000948150	−	0.00353854i
$805$		0			0
$806$	−2.94399	+	3.49146i	−0.103698	+	0.122981i
$807$	−6.73152	−	11.6593i	−0.236961	−	0.410428i
$808$	4.90076	−	18.2899i	0.172408	−	0.643436i
$809$	22.2022	+	38.4554i	0.780589	+	1.35202i	0.931599	+	0.363488i	$0.118414\pi$
$809$	22.2022	+	38.4554i	0.780589	+	1.35202i	−0.151010	+	0.988532i	$0.548253\pi$
$810$	0.0455546	−	0.0789029i	0.00160063	−	0.00277237i
$811$	−9.49597	−	9.49597i	−0.333449	−	0.333449i	0.520446	−	0.853895i	$-0.325766\pi$
$811$	−9.49597	−	9.49597i	−0.333449	−	0.333449i	−0.853895	+	0.520446i	$0.825766\pi$
$812$		0			0
$813$	1.28025	−	4.77796i	0.0449004	−	0.167570i
$814$	3.80008	−	14.1821i	0.133193	−	0.497083i
$815$			31.3516i			1.09820i
$816$	−14.8235	+	8.55835i	−0.518926	+	0.299602i
$817$	−4.07635	+	4.07635i	−0.142614	+	0.142614i
$818$	41.8760			1.46416
$819$		0			0
$820$	3.20487			0.111919
$821$	36.3507	−	36.3507i	1.26865	−	1.26865i	0.321864	−	0.946786i	$-0.395691\pi$
$821$	36.3507	−	36.3507i	1.26865	−	1.26865i	0.946786	−	0.321864i	$-0.104309\pi$
$822$	−13.3139	+	7.68676i	−0.464374	+	0.268107i
$823$			25.9783i			0.905548i	0.891625	+	0.452774i	$0.149565\pi$
$823$			25.9783i			0.905548i	−0.891625	+	0.452774i	$0.850435\pi$
$824$	7.37415	−	27.5207i	0.256891	−	0.958729i
$825$	1.28213	−	4.78499i	0.0446382	−	0.166592i
$826$		0			0
$827$	−1.05853	−	1.05853i	−0.0368089	−	0.0368089i	0.688463	−	0.725272i	$-0.258286\pi$
$827$	−1.05853	−	1.05853i	−0.0368089	−	0.0368089i	−0.725272	+	0.688463i	$0.758286\pi$
$828$	−0.680873	+	1.17931i	−0.0236620	+	0.0409837i
$829$	−7.34482	−	12.7216i	−0.255096	−	0.441839i	0.709826	−	0.704378i	$-0.248774\pi$
$829$	−7.34482	−	12.7216i	−0.255096	−	0.441839i	−0.964922	+	0.262538i	$0.915440\pi$
$830$	2.23385	−	8.33682i	0.0775379	−	0.289375i
$831$	−0.896497	−	1.55278i	−0.0310991	−	0.0538653i
$832$	−5.29270	+	29.6006i	−0.183491	+	1.02622i
$833$		0			0
$834$	2.35853	+	8.80215i	0.0816692	+	0.304794i
$835$	−52.2674			−1.80879
$836$	0.827960			0.0286356
$837$	1.23487	+	4.60859i	0.0426833	+	0.159296i
$838$	10.5823	−	2.83551i	0.365559	−	0.0979511i
$839$	18.7042	+	5.01177i	0.645740	+	0.173025i	0.566802	−	0.823854i	$-0.308180\pi$
$839$	18.7042	+	5.01177i	0.645740	+	0.173025i	0.0789379	+	0.996880i	$0.474847\pi$
$840$		0			0
$841$	14.1102	+	24.4396i	0.486558	+	0.842743i
$842$		−	11.6772i		−	0.402423i
$843$	−20.3941	−	5.46457i	−0.702409	−	0.188210i
$844$	−0.368839	−	0.212949i	−0.0126960	−	0.00733001i
$845$	−21.5451	+	30.4572i	−0.741173	+	1.04776i
$846$			7.98302i			0.274462i
$847$		0			0
$848$	−4.80113	+	8.31579i	−0.164871	+	0.285566i
$849$	−30.6328	−	17.6858i	−1.05131	−	0.606976i
$850$	−18.1146	+	4.85380i	−0.621327	+	0.166484i
$851$	41.2056	−	41.2056i	1.41251	−	1.41251i
$852$	0.0756332	+	0.282267i	0.00259115	+	0.00967031i
$853$	16.7852	−	16.7852i	0.574713	−	0.574713i	−0.358728	−	0.933442i	$-0.616790\pi$
$853$	16.7852	−	16.7852i	0.574713	−	0.574713i	0.933442	+	0.358728i	$0.116790\pi$
$854$		0			0
$855$	28.3586	+	16.3729i	0.969845	+	0.559940i
$856$	−21.6555	−	21.6555i	−0.740170	−	0.740170i
$857$	25.5716	−	44.2913i	0.873508	−	1.51296i	0.0151651	−	0.999885i	$-0.495173\pi$
$857$	25.5716	−	44.2913i	0.873508	−	1.51296i	0.858343	−	0.513076i	$-0.171494\pi$
$858$	−5.82608	−	4.91254i	−0.198899	−	0.167712i
$859$	−13.0666	+	7.54398i	−0.445825	+	0.257397i	−0.706065	−	0.708147i	$-0.749532\pi$
$859$	−13.0666	+	7.54398i	−0.445825	+	0.257397i	0.260240	+	0.965544i	$0.416198\pi$
$860$	−0.243720	+	0.0653047i	−0.00831079	+	0.00222687i
$861$		0			0
$862$	0.691725	−	0.399367i	0.0235602	−	0.0136025i
$863$	12.7509	+	3.41659i	0.434045	+	0.116302i	0.469225	−	0.883079i	$-0.344533\pi$
$863$	12.7509	+	3.41659i	0.434045	+	0.116302i	−0.0351791	+	0.999381i	$0.511200\pi$
$864$	1.95436	+	1.95436i	0.0664886	+	0.0664886i
$865$	−40.8937	−	40.8937i	−1.39043	−	1.39043i
$866$	−10.9705	−	2.93953i	−0.372793	−	0.0998895i
$867$	0.580039	−	0.334885i	0.0196991	−	0.0113733i
$868$		0			0
$869$	13.0087	−	3.48568i	0.441291	−	0.118244i
$870$	−3.24792	+	1.87519i	−0.110115	+	0.0635749i
$871$	−3.36326	−	1.57815i	−0.113960	−	0.0534737i
$872$	23.8541	−	41.3165i	0.807802	−	1.39915i
$873$	−12.0211	−	12.0211i	−0.406851	−	0.406851i
$874$	−57.6824	−	33.3030i	−1.95114	−	1.12649i
$875$		0			0
$876$	−0.203062	+	0.203062i	−0.00686083	+	0.00686083i
$877$	10.0864	+	37.6430i	0.340594	+	1.27111i	0.897676	+	0.440655i	$0.145254\pi$
$877$	10.0864	+	37.6430i	0.340594	+	1.27111i	−0.557083	+	0.830457i	$0.688079\pi$
$878$	12.4206	−	12.4206i	0.419177	−	0.419177i
$879$	−22.7407	+	6.09336i	−0.767025	+	0.205524i
$880$	−13.4979	−	7.79300i	−0.455013	−	0.262702i
$881$	−14.6029	+	25.2929i	−0.491983	+	0.852140i	−0.999957	−	0.00923231i	$-0.997061\pi$
$881$	−14.6029	+	25.2929i	−0.491983	+	0.852140i	0.507974	+	0.861372i	$0.330395\pi$
$882$		0			0
$883$			2.58799i			0.0870929i	0.999051	+	0.0435464i	$0.0138656\pi$
$883$			2.58799i			0.0870929i	−0.999051	+	0.0435464i	$0.986134\pi$
$884$	0.250531	−	1.40115i	0.00842628	−	0.0471259i
$885$	−15.5949	−	9.00374i	−0.524218	−	0.302657i
$886$	−2.97466	−	0.797057i	−0.0999355	−	0.0267776i
$887$			37.7267i			1.26674i	0.773849	+	0.633370i	$0.218329\pi$
$887$			37.7267i			1.26674i	−0.773849	+	0.633370i	$0.781671\pi$
$888$	−11.5405	−	19.9887i	−0.387274	−	0.670778i
$889$		0			0
$890$	−18.8477	−	5.05023i	−0.631777	−	0.169284i
$891$	−0.0317210	+	0.00849962i	−0.00106269	+	0.000284748i
$892$	0.566385	+	2.11378i	0.0189640	+	0.0707745i
$893$	19.2644			0.644658
$894$	−12.8859			−0.430968
$895$	12.2794	+	45.8273i	0.410454	+	1.53184i
$896$		0			0
$897$	−10.2766	−	28.4471i	−0.343126	−	0.949821i
$898$	26.9060	+	46.6026i	0.897865	+	1.55515i
$899$	0.209673	−	0.782510i	0.00699298	−	0.0260982i
$900$	0.281548	+	0.487656i	0.00938494	+	0.0162552i
$901$	5.29990	−	9.17970i	0.176565	−	0.305820i
$902$	16.5564	+	16.5564i	0.551267	+	0.551267i
$903$		0			0
$904$	−0.482039	+	1.79900i	−0.0160324	+	0.0598337i
$905$	−10.1681	+	37.9479i	−0.337999	+	1.26143i
$906$		−	19.9935i		−	0.664238i
$907$	44.9567	−	25.9558i	1.49276	−	0.861847i	0.492798	−	0.870144i	$-0.335974\pi$
$907$	44.9567	−	25.9558i	1.49276	−	0.861847i	0.999966	+	0.00829638i	$0.00264085\pi$
$908$	−0.693097	+	0.693097i	−0.0230012	+	0.0230012i
$909$	−12.1215			−0.402044
$910$		0			0
$911$	15.0311			0.498003			0.249002	−	0.968503i	$-0.419898\pi$
$911$	15.0311			0.498003			0.249002	+	0.968503i	$0.419898\pi$
$912$	−17.7754	+	17.7754i	−0.588601	+	0.588601i
$913$	−2.69419	+	1.55549i	−0.0891647	+	0.0514792i
$914$			31.7914i			1.05157i
$915$	−0.0680092	+	0.253814i	−0.00224831	+	0.00839082i
$916$	0.0469410	−	0.175186i	0.00155098	−	0.00578832i
$917$		0			0
$918$	21.3122	+	21.3122i	0.703407	+	0.703407i
$919$	−1.62567	+	2.81574i	−0.0536259	+	0.0928828i	−0.891592	−	0.452839i	$-0.850411\pi$
$919$	−1.62567	+	2.81574i	−0.0536259	+	0.0928828i	0.837966	+	0.545722i	$0.183745\pi$
$920$	−32.4595	−	56.2215i	−1.07016	−	1.85357i
$921$	−5.40863	+	20.1853i	−0.178220	+	0.665127i
$922$	20.8420	+	36.0993i	0.686393	+	1.18887i
$923$	9.46167	+	4.43974i	0.311435	+	0.146136i
$924$		0			0
$925$	−6.23669	−	23.2757i	−0.205061	−	0.765299i
$926$	−4.29251			−0.141061
$927$	−18.2391			−0.599051
$928$	−0.121461	−	0.453299i	−0.00398716	−	0.0148803i
$929$	−41.3182	+	11.0712i	−1.35561	+	0.363234i	−0.862201	−	0.506566i	$-0.830915\pi$
$929$	−41.3182	+	11.0712i	−1.35561	+	0.363234i	−0.493405	+	0.869799i	$0.664248\pi$
$930$	−3.76421	−	1.00862i	−0.123433	−	0.0330738i
$931$		0			0
$932$	−0.404128	−	0.699969i	−0.0132376	−	0.0229283i
$933$			27.6879i			0.906462i
$934$	−28.2324	−	7.56484i	−0.923791	−	0.247529i
$935$	14.9001	+	8.60260i	0.487287	+	0.281335i
$936$	19.2210	−	1.63513i	0.628259	−	0.0534459i
$937$		−	14.9401i		−	0.488071i	−0.969766	−	0.244035i	$-0.921529\pi$
$937$		−	14.9401i		−	0.488071i	0.969766	−	0.244035i	$-0.0784713\pi$
$938$		0			0
$939$	−15.3661	+	26.6148i	−0.501452	+	0.868541i
$940$	0.730209	+	0.421586i	0.0238168	+	0.0137506i
$941$	−10.9959	+	2.94635i	−0.358457	+	0.0960482i	−0.433553	−	0.901128i	$-0.642740\pi$
$941$	−10.9959	+	2.94635i	−0.358457	+	0.0960482i	0.0750961	+	0.997176i	$0.476074\pi$
$942$	−7.09540	+	7.09540i	−0.231181	+	0.231181i
$943$	24.0520	+	89.7632i	0.783240	+	2.92309i
$944$	−15.7399	+	15.7399i	−0.512291	+	0.512291i
$945$		0			0
$946$	−1.59642	−	0.921695i	−0.0519042	−	0.0299669i
$947$	−22.7342	−	22.7342i	−0.738761	−	0.738761i	0.233577	−	0.972338i	$-0.424957\pi$
$947$	−22.7342	−	22.7342i	−0.738761	−	0.738761i	−0.972338	+	0.233577i	$0.924957\pi$
$948$	0.475359	−	0.823345i	0.0154389	−	0.0267410i
$949$	0.870595	+	10.2339i	0.0282607	+	0.332206i
$950$	−23.8523	+	13.7711i	−0.773871	+	0.446794i
$951$	−12.9093	+	3.45903i	−0.418612	+	0.112167i
$952$		0			0
$953$	32.4604	−	18.7410i	1.05150	−	0.607081i	0.128428	−	0.991719i	$-0.459007\pi$
$953$	32.4604	−	18.7410i	1.05150	−	0.607081i	0.923068	+	0.384638i	$0.125674\pi$
$954$	6.23114	+	1.66963i	0.201741	+	0.0540562i
$955$	16.5361	+	16.5361i	0.535096	+	0.535096i
$956$	−0.606670	−	0.606670i	−0.0196211	−	0.0196211i
$957$	1.30575	+	0.349874i	0.0422089	+	0.0113098i
$958$	28.7118	−	16.5768i	0.927636	−	0.535571i
$959$		0			0
$960$	−24.7844	+	6.64096i	−0.799913	+	0.214336i
$961$	−26.1178	+	15.0791i	−0.842509	+	0.486423i
$962$	−36.4911	−	6.52474i	−1.17652	−	0.210366i
$963$	−9.80261	+	16.9786i	−0.315885	+	0.547128i
$964$	0.290150	+	0.290150i	0.00934509	+	0.00934509i
$965$	66.5746	+	38.4368i	2.14311	+	1.23733i
$966$		0			0
$967$	10.9130	−	10.9130i	0.350939	−	0.350939i	−0.509520	−	0.860459i	$-0.670177\pi$
$967$	10.9130	−	10.9130i	0.350939	−	0.350939i	0.860459	+	0.509520i	$0.170177\pi$
$968$	−6.70465	−	25.0221i	−0.215496	−	0.804240i
$969$	19.6220	−	19.6220i	0.630350	−	0.630350i
$970$	35.1544	−	9.41959i	1.12874	−	0.302445i
$971$	−1.54608	−	0.892628i	−0.0496160	−	0.0286458i	0.474987	−	0.879993i	$-0.342453\pi$
$971$	−1.54608	−	0.892628i	−0.0496160	−	0.0286458i	−0.524603	+	0.851347i	$0.675786\pi$
$972$	0.732343	−	1.26846i	0.0234899	−	0.0406857i
$973$		0			0
$974$		−	47.0455i		−	1.50743i
$975$	−12.3119	−	2.20142i	−0.394298	−	0.0705019i
$976$	0.281298	+	0.162407i	0.00900413	+	0.00519854i
$977$	2.19357	+	0.587766i	0.0701786	+	0.0188043i	0.293737	−	0.955886i	$-0.405101\pi$
$977$	2.19357	+	0.587766i	0.0701786	+	0.0188043i	−0.223559	+	0.974690i	$0.571768\pi$
$978$			16.1692i			0.517035i
$979$	3.51662	+	6.09097i	0.112392	+	0.194668i
$980$		0			0
$981$	−29.5002	−	7.90456i	−0.941869	−	0.252373i
$982$	−18.8917	+	5.06202i	−0.602858	+	0.161535i
$983$	−11.0868	−	41.3763i	−0.353613	−	1.31970i	−0.882221	−	0.470835i	$-0.843953\pi$
$983$	−11.0868	−	41.3763i	−0.353613	−	1.31970i	0.528609	−	0.848865i	$-0.322714\pi$
$984$	36.8076			1.17338
$985$	−52.8935			−1.68533
$986$	−1.32453	−	4.94320i	−0.0421815	−	0.157424i
$987$		0			0
$988$	−0.177191	−	2.08289i	−0.00563721	−	0.0662657i
$989$	−3.65815	−	6.33611i	−0.116323	−	0.201477i
$990$	−2.71008	+	10.1141i	−0.0861319	+	0.321448i
$991$	−26.6800	−	46.2112i	−0.847519	−	1.46795i	−0.883415	−	0.468591i	$-0.844762\pi$
$991$	−26.6800	−	46.2112i	−0.847519	−	1.46795i	0.0358964	−	0.999356i	$-0.488571\pi$
$992$	0.243818	−	0.422305i	0.00774123	−	0.0134082i
$993$	22.7060	+	22.7060i	0.720553	+	0.720553i
$994$		0			0
$995$	−9.44159	+	35.2365i	−0.299319	+	1.11707i
$996$	−0.0568400	+	0.212130i	−0.00180104	+	0.00672158i
$997$		−	47.0248i		−	1.48929i	−0.667460	−	0.744645i	$-0.732619\pi$
$997$		−	47.0248i		−	1.48929i	0.667460	−	0.744645i	$-0.267381\pi$
$998$	−35.6521	+	20.5837i	−1.12855	+	0.651567i
$999$	−27.3842	+	27.3842i	−0.866398	+	0.866398i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bb.b.227.4		32
7.2	even	3		637.2.x.b.19.6		32
7.3	odd	6		91.2.bc.a.6.4	yes	32
7.4	even	3		91.2.bc.a.6.3	✓	32
7.5	odd	6		637.2.x.b.19.5		32
7.6	odd	2	inner	637.2.bb.b.227.3		32
13.11	odd	12		637.2.x.b.570.6		32
21.11	odd	6		819.2.fm.g.370.6		32
21.17	even	6		819.2.fm.g.370.5		32
91.11	odd	12		91.2.bc.a.76.4	yes	32
91.24	even	12		91.2.bc.a.76.3	yes	32
91.37	odd	12	inner	637.2.bb.b.362.3		32
91.76	even	12		637.2.x.b.570.5		32
91.89	even	12	inner	637.2.bb.b.362.4		32
273.11	even	12		819.2.fm.g.622.5		32
273.206	odd	12		819.2.fm.g.622.6		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.bc.a.6.3	✓	32	7.4	even	3
91.2.bc.a.6.4	yes	32	7.3	odd	6
91.2.bc.a.76.3	yes	32	91.24	even	12
91.2.bc.a.76.4	yes	32	91.11	odd	12
637.2.x.b.19.5		32	7.5	odd	6
637.2.x.b.19.6		32	7.2	even	3
637.2.x.b.570.5		32	91.76	even	12
637.2.x.b.570.6		32	13.11	odd	12
637.2.bb.b.227.3		32	7.6	odd	2	inner
637.2.bb.b.227.4		32	1.1	even	1	trivial
637.2.bb.b.362.3		32	91.37	odd	12	inner
637.2.bb.b.362.4		32	91.89	even	12	inner
819.2.fm.g.370.5		32	21.17	even	6
819.2.fm.g.370.6		32	21.11	odd	6
819.2.fm.g.622.5		32	273.11	even	12
819.2.fm.g.622.6		32	273.206	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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bb (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.976208 + 0.976208i) q^{2} +(0.928437 - 0.536034i) q^{3} +0.0940343i q^{4} +(-0.742756 + 2.77200i) q^{5} +(-0.383068 + 1.42963i) q^{6} +(-2.04421 - 2.04421i) q^{8} +(-0.925336 + 1.60273i) q^{9} +O(q^{10})\)	\(q+(-0.976208 + 0.976208i) q^{2} +(0.928437 - 0.536034i) q^{3} +0.0940343i q^{4} +(-0.742756 + 2.77200i) q^{5} +(-0.383068 + 1.42963i) q^{6} +(-2.04421 - 2.04421i) q^{8} +(-0.925336 + 1.60273i) q^{9} +(-1.98097 - 3.43114i) q^{10} +(-0.369611 + 1.37941i) q^{11} +(0.0504055 + 0.0873049i) q^{12} +(3.54926 + 0.634621i) q^{13} +(0.796284 + 2.97177i) q^{15} +3.80309 q^{16} -4.19818 q^{17} +(-0.661277 - 2.46792i) q^{18} +(-5.95551 + 1.59577i) q^{19} +(-0.260663 - 0.0698445i) q^{20} +(-0.985770 - 1.70740i) q^{22} -7.82493i q^{23} +(-2.99369 - 0.802157i) q^{24} +(-2.80219 - 1.61784i) q^{25} +(-4.08434 + 2.84530i) q^{26} +5.20025i q^{27} +(0.441485 - 0.764674i) q^{29} +(-3.67841 - 2.12373i) q^{30} +(0.886225 - 0.237463i) q^{31} +(0.375820 - 0.375820i) q^{32} +(0.396247 + 1.47882i) q^{33} +(4.09830 - 4.09830i) q^{34} +(-0.150711 - 0.0870133i) q^{36} +(5.26594 + 5.26594i) q^{37} +(4.25601 - 7.37163i) q^{38} +(3.63544 - 1.31332i) q^{39} +(7.18492 - 4.14822i) q^{40} +(-11.4714 + 3.07376i) q^{41} +(0.809734 - 0.467500i) q^{43} +(-0.129711 - 0.0347561i) q^{44} +(-3.75547 - 3.75547i) q^{45} +(7.63876 + 7.63876i) q^{46} +(-3.01803 - 0.808679i) q^{47} +(3.53093 - 2.03858i) q^{48} +(4.31487 - 1.15617i) q^{50} +(-3.89775 + 2.25037i) q^{51} +(-0.0596761 + 0.333752i) q^{52} +(-1.26243 + 2.18659i) q^{53} +(-5.07652 - 5.07652i) q^{54} +(-3.54919 - 2.04912i) q^{55} +(-4.67393 + 4.67393i) q^{57} +(0.315500 + 1.17746i) q^{58} +(-4.13872 + 4.13872i) q^{59} +(-0.279449 + 0.0748780i) q^{60} +(0.0739657 + 0.0427041i) q^{61} +(-0.633327 + 1.09695i) q^{62} +8.33994i q^{64} +(-4.39541 + 9.36720i) q^{65} +(-1.83045 - 1.05681i) q^{66} +(-0.995278 - 0.266684i) q^{67} -0.394773i q^{68} +(-4.19442 - 7.26495i) q^{69} +(2.79996 + 0.750247i) q^{71} +(5.16791 - 1.38474i) q^{72} +(0.737278 + 2.75156i) q^{73} -10.2813 q^{74} -3.46888 q^{75} +(-0.150057 - 0.560022i) q^{76} +(-2.26688 + 4.83102i) q^{78} +(-4.71534 - 8.16721i) q^{79} +(-2.82477 + 10.5422i) q^{80} +(0.0114981 + 0.0199152i) q^{81} +(8.19789 - 14.1992i) q^{82} +(1.54040 + 1.54040i) q^{83} +(3.11823 - 11.6374i) q^{85} +(-0.334092 + 1.24685i) q^{86} -0.946603i q^{87} +(3.57536 - 2.06424i) q^{88} +(3.48251 - 3.48251i) q^{89} +7.33225 q^{90} +0.735811 q^{92} +(0.695516 - 0.695516i) q^{93} +(3.73567 - 2.15679i) q^{94} -17.6940i q^{95} +(0.147473 - 0.550378i) q^{96} +(-2.37752 + 8.87303i) q^{97} +(-1.86880 - 1.86880i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{2} - 16 q^{8} + 8 q^{9}+O(q^{10}) \) 32 * q + 4 * q^2 - 16 * q^8 + 8 * q^9	\( 32 q + 4 q^{2} - 16 q^{8} + 8 q^{9} - 16 q^{11} - 8 q^{15} - 24 q^{16} + 68 q^{18} + 4 q^{22} + 4 q^{29} - 12 q^{30} - 68 q^{32} - 8 q^{37} - 48 q^{43} + 60 q^{44} + 24 q^{46} - 44 q^{50} - 12 q^{51} - 36 q^{53} - 92 q^{57} - 28 q^{58} - 104 q^{60} - 32 q^{65} - 8 q^{67} + 84 q^{71} + 124 q^{72} + 48 q^{74} + 148 q^{78} + 40 q^{79} + 28 q^{81} + 36 q^{85} - 60 q^{86} + 228 q^{88} + 24 q^{92} - 84 q^{93} - 60 q^{99}+O(q^{100}) \) 32 * q + 4 * q^2 - 16 * q^8 + 8 * q^9 - 16 * q^11 - 8 * q^15 - 24 * q^16 + 68 * q^18 + 4 * q^22 + 4 * q^29 - 12 * q^30 - 68 * q^32 - 8 * q^37 - 48 * q^43 + 60 * q^44 + 24 * q^46 - 44 * q^50 - 12 * q^51 - 36 * q^53 - 92 * q^57 - 28 * q^58 - 104 * q^60 - 32 * q^65 - 8 * q^67 + 84 * q^71 + 124 * q^72 + 48 * q^74 + 148 * q^78 + 40 * q^79 + 28 * q^81 + 36 * q^85 - 60 * q^86 + 228 * q^88 + 24 * q^92 - 84 * q^93 - 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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