LMFDB - Embedded newform 637.2.bb.b.362.3

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			362.3
Character	$\chi$	$=$	637.362
Dual form			637.2.bb.b.227.3

$q$-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 $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$

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	0.272011	−	0.962294i	$-0.412311\pi$
$2$	−0.976208	−	0.976208i	−0.690284	−	0.690284i	−0.962294	+	0.272011i	$0.912311\pi$
$3$	−0.928437	−	0.536034i	−0.536034	−	0.309479i	0.207436	−	0.978249i	$-0.433488\pi$
$3$	−0.928437	−	0.536034i	−0.536034	−	0.309479i	−0.743470	+	0.668769i	$0.766821\pi$
$4$		−	0.0940343i		−	0.0470171i
$5$	0.742756	+	2.77200i	0.332171	+	1.23968i	0.906904	+	0.421337i	$0.138439\pi$
$5$	0.742756	+	2.77200i	0.332171	+	1.23968i	−0.574734	+	0.818341i	$0.694894\pi$
$6$	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	0.887554	−	0.460703i	$-0.152403\pi$
$11$	−0.369611	−	1.37941i	−0.111442	−	0.415906i	−0.998996	+	0.0447966i	$0.985736\pi$
$12$	−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	$-0.329977\pi$
$17$	4.19818			1.01821			0.509105	+	0.860705i	$0.329977\pi$
$18$	−0.661277	+	2.46792i	−0.155864	+	0.581694i
$19$	5.95551	+	1.59577i	1.36629	+	0.366096i	0.866121	−	0.499834i	$-0.166606\pi$
$19$	5.95551	+	1.59577i	1.36629	+	0.366096i	0.500166	+	0.865929i	$0.333272\pi$
$20$	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	$0.303706\pi$
$23$			7.82493i			1.63161i	−0.578327	+	0.815805i	$0.696294\pi$
$24$	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	0.904101	−	0.427319i	$-0.140542\pi$
$29$	0.441485	+	0.764674i	0.0819817	+	0.141996i	−0.822119	+	0.569315i	$0.807208\pi$
$30$	−3.67841	+	2.12373i	−0.671583	+	0.387738i
$31$	−0.886225	−	0.237463i	−0.159171	−	0.0426497i	0.178354	−	0.983966i	$-0.442923\pi$
$31$	−0.886225	−	0.237463i	−0.159171	−	0.0426497i	−0.337524	+	0.941317i	$0.609590\pi$
$32$	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	−0.126279	−	0.991995i	$-0.540303\pi$
$37$	5.26594	−	5.26594i	0.865716	−	0.865716i	0.991995	+	0.126279i	$0.0403034\pi$
$38$	−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	$-0.0387317\pi$
$41$	11.4714	+	3.07376i	1.79154	+	0.480041i	0.798933	+	0.601421i	$0.205398\pi$
$42$		0			0
$43$	0.809734	+	0.467500i	0.123483	+	0.0712931i	0.560469	−	0.828175i	$-0.310621\pi$
$43$	0.809734	+	0.467500i	0.123483	+	0.0712931i	−0.436986	+	0.899468i	$0.643954\pi$
$44$	−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	$-0.510155\pi$
$47$	3.01803	−	0.808679i	0.440225	−	0.117958i	0.472122	+	0.881533i	$0.343488\pi$
$48$	−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	0.766201	−	0.642601i	$-0.222145\pi$
$53$	−1.26243	−	2.18659i	−0.173408	−	0.300351i	−0.939609	+	0.342249i	$0.888811\pi$
$54$	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	$-0.125580\pi$
$59$	4.13872	+	4.13872i	0.538815	+	0.538815i	−0.384366	+	0.923181i	$0.625580\pi$
$60$	−0.279449	−	0.0748780i	−0.0360767	−	0.00966671i
$61$	−0.0739657	+	0.0427041i	−0.00947033	+	0.00546770i	−0.504728	−	0.863279i	$-0.668407\pi$
$61$	−0.0739657	+	0.0427041i	−0.00947033	+	0.00546770i	0.495257	+	0.868746i	$0.335074\pi$
$62$	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	−0.319102	−	0.947720i	$-0.603381\pi$
$67$	−0.995278	+	0.266684i	−0.121593	+	0.0325806i	0.197510	+	0.980301i	$0.436715\pi$
$68$		−	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	−0.0888143	−	0.996048i	$-0.528308\pi$
$71$	2.79996	−	0.750247i	0.332294	−	0.0890380i	0.421109	+	0.907010i	$0.361641\pi$
$72$	5.16791	+	1.38474i	0.609044	+	0.163193i
$73$	−0.737278	+	2.75156i	−0.0862919	+	0.322046i	−0.995556	−	0.0941746i	$-0.969979\pi$
$73$	−0.737278	+	2.75156i	−0.0862919	+	0.322046i	0.909264	+	0.416220i	$0.136645\pi$
$74$	−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	0.468849	+	0.883279i	$0.344669\pi$
$79$	−4.71534	+	8.16721i	−0.530517	+	0.918883i	−0.999366	+	0.0356045i	$0.988664\pi$
$80$	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	$-0.788148\pi$
$83$	−1.54040	+	1.54040i	−0.169081	+	0.169081i	0.617494	+	0.786575i	$0.288148\pi$
$84$		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	$-0.334061\pi$
$89$	−3.48251	−	3.48251i	−0.369146	−	0.369146i	−0.867166	+	0.498020i	$0.834061\pi$
$90$	−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	0.975158	+	0.221509i	$0.0710981\pi$
$97$	2.37752	+	8.87303i	0.241401	+	0.900920i	−0.733758	+	0.679411i	$0.762235\pi$
$98$		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	$-0.938988\pi$
$101$	−3.27488	+	5.67227i	−0.325863	+	0.564412i	0.655824	+	0.754914i	$0.272322\pi$
$102$	1.60819	+	6.00184i	0.159234	+	0.594271i
$103$	−4.92770	+	8.53503i	−0.485541	+	0.840982i	−0.999862	−	0.0166161i	$-0.994711\pi$
$103$	−4.92770	+	8.53503i	−0.485541	+	0.840982i	0.514321	+	0.857598i	$0.328044\pi$
$104$	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	−0.387252	−	0.921974i	$-0.626576\pi$
$109$	4.27118	−	15.9403i	0.409105	−	1.52680i	0.796357	−	0.604827i	$-0.206758\pi$
$110$	−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	−0.880779	−	0.473528i	$-0.842980\pi$
$113$	−0.322118	+	0.557925i	−0.0303023	+	0.0524851i	0.850477	+	0.526013i	$0.176314\pi$
$114$			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	−0.971841	−	0.235640i	$-0.924282\pi$
$127$	−14.1284	+	8.15702i	−1.25369	+	0.723819i	−0.281850	+	0.959458i	$0.590948\pi$
$128$	−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	$-0.366108\pi$
$131$	−2.03759	−	1.17640i	−0.178025	−	0.102783i	−0.586364	+	0.810047i	$0.699441\pi$
$132$	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	−0.319933	−	0.947440i	$-0.603660\pi$
$137$	7.34478	−	7.34478i	0.627507	−	0.627507i	0.947440	+	0.319933i	$0.103660\pi$
$138$	−11.1867	+	2.99748i	−0.952278	+	0.255162i
$139$	−5.33208	−	3.07848i	−0.452261	−	0.261113i	0.256524	−	0.966538i	$-0.417423\pi$
$139$	−5.33208	−	3.07848i	−0.452261	−	0.261113i	−0.708784	+	0.705425i	$0.750756\pi$
$140$		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	−0.810113	−	0.586274i	$-0.800594\pi$
$149$	2.25336	−	8.40965i	0.184602	−	0.688945i	0.994715	−	0.102672i	$-0.0327391\pi$
$150$	−3.38635	−	3.38635i	−0.276494	−	0.276494i
$151$	−13.0482	−	3.49627i	−1.06185	−	0.284522i	−0.314710	−	0.949188i	$-0.601907\pi$
$151$	−13.0482	−	3.49627i	−1.06185	−	0.284522i	−0.747141	+	0.664665i	$0.768574\pi$
$152$	−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	$-0.753869\pi$
$157$	−5.87142	+	3.38986i	−0.468590	+	0.270541i	0.247059	+	0.969000i	$0.420536\pi$
$158$	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	0.647200	−	0.762320i	$-0.275940\pi$
$163$	10.5525	+	2.82752i	0.826532	+	0.221469i	0.179332	+	0.983789i	$0.442606\pi$
$164$	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	0.502962	+	0.864308i	$0.332244\pi$
$167$	−4.71387	+	17.5924i	−0.364770	+	1.36134i	−0.867732	+	0.497032i	$0.834423\pi$
$168$		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	0.939679	+	0.342058i	$0.111124\pi$
$173$	10.0761	+	17.4523i	0.766070	+	1.32687i	−0.173608	+	0.984815i	$0.555543\pi$
$174$	−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	0.928216	−	0.372043i	$-0.121343\pi$
$179$	14.3173	+	8.26609i	1.07012	+	0.617837i	0.141909	+	0.989880i	$0.454676\pi$
$180$	−0.353143	−	0.353143i	−0.0263217	−	0.0263217i
$181$	−13.6897			−1.01755			−0.508774	−	0.860900i	$-0.669901\pi$
$181$	−13.6897			−1.01755			−0.508774	+	0.860900i	$0.669901\pi$
$182$		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	0.974942	−	0.222458i	$-0.0714081\pi$
$191$	4.07445	+	7.05715i	0.294817	+	0.510638i	−0.680126	+	0.733096i	$0.738075\pi$
$192$	−4.47049	+	7.74311i	−0.322629	+	0.558811i
$193$	6.93304	+	25.8745i	0.499051	+	1.86249i	0.506040	+	0.862510i	$0.331109\pi$
$193$	6.93304	+	25.8745i	0.499051	+	1.86249i	−0.00698876	+	0.999976i	$0.502225\pi$
$194$	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	−0.558617	−	0.829426i	$-0.688668\pi$
$197$	4.77033	−	17.8031i	0.339872	−	1.26842i	0.898490	−	0.438995i	$-0.144665\pi$
$198$	3.64868			0.259300
$199$	−12.7116			−0.901099			−0.450550	−	0.892751i	$-0.648772\pi$
$199$	−12.7116			−0.901099			−0.450550	+	0.892751i	$0.648772\pi$
$200$	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	0.777486	−	0.628900i	$-0.216495\pi$
$211$	−2.26459	−	3.92239i	−0.155901	−	0.270028i	−0.933387	+	0.358872i	$0.883161\pi$
$212$	−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	$-0.701039\pi$
$223$	−22.4788	−	6.02318i	−1.50529	−	0.403342i	−0.914868	+	0.403752i	$0.867706\pi$
$224$		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	$-0.862434\pi$
$227$	−7.37068	+	7.37068i	−0.489210	+	0.489210i	0.418847	+	0.908057i	$0.362434\pi$
$228$	−0.439510	+	0.439510i	−0.0291072	+	0.0291072i
$229$	1.86301	−	0.499191i	0.123111	−	0.0329875i	−0.196738	−	0.980456i	$-0.563035\pi$
$229$	1.86301	−	0.499191i	0.123111	−	0.0329875i	0.319848	+	0.947469i	$0.396368\pi$
$230$	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	0.235945	−	0.971766i	$-0.424182\pi$
$233$	−7.44377	−	4.29766i	−0.487657	−	0.281549i	−0.723602	+	0.690217i	$0.757515\pi$
$234$	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	0.466960	−	0.884278i	$-0.345349\pi$
$239$	−6.45158	−	6.45158i	−0.417318	−	0.417318i	−0.884278	+	0.466960i	$0.845349\pi$
$240$	3.02834	−	11.3019i	0.195479	−	0.729536i
$241$	−3.08557	−	3.08557i	−0.198759	−	0.198759i	0.600709	−	0.799468i	$-0.294885\pi$
$241$	−3.08557	−	3.08557i	−0.198759	−	0.198759i	−0.799468	+	0.600709i	$0.794885\pi$
$242$	−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	$-0.879292\pi$
$251$	−2.27953	+	3.94826i	−0.143883	+	0.249212i	0.785073	+	0.619403i	$0.212625\pi$
$252$		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	$-0.586781\pi$
$257$	−8.63332			−0.538532			−0.269266	+	0.963066i	$0.586781\pi$
$258$	−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	−0.591311	−	0.806444i	$-0.701389\pi$
$263$	6.53143	−	11.3128i	0.402745	−	0.697575i	0.994056	+	0.108868i	$0.0347227\pi$
$264$	−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	$-0.294755\pi$
$271$	−3.26259	−	3.26259i	−0.198188	−	0.198188i	−0.799223	+	0.601035i	$0.794755\pi$
$272$	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	$0.0160000\pi$
$277$			1.67246i			0.100489i	−0.998737	+	0.0502443i	$0.984000\pi$
$278$	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	−0.987619	−	0.156870i	$-0.949860\pi$
$281$	−13.9259	+	13.9259i	−0.830749	+	0.830749i	0.156870	+	0.987619i	$0.449860\pi$
$282$	2.31222	+	4.00489i	0.137691	+	0.238488i
$283$	16.4969	−	28.5736i	0.980642	−	1.69852i	0.320744	−	0.947166i	$-0.396067\pi$
$283$	16.4969	−	28.5736i	0.980642	−	1.69852i	0.659897	−	0.751356i	$-0.270600\pi$
$284$	−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	$-0.361659\pi$
$293$	21.2120	−	5.68375i	1.23922	−	0.332048i	0.818163	+	0.574986i	$0.194993\pi$
$294$		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	$-0.0622399\pi$
$307$	13.7833	+	13.7833i	0.786656	+	0.786656i	−0.194289	+	0.980944i	$0.562240\pi$
$308$		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	0.955920	+	0.293627i	$0.0948622\pi$
$311$	12.9133	+	22.3666i	0.732248	+	1.26829i	−0.223672	+	0.974664i	$0.571804\pi$
$312$	−10.1163	+	4.74693i	−0.572724	+	0.268742i
$313$	24.8257	+	14.3331i	1.40323	+	0.810155i	0.994723	−	0.102600i	$-0.0327162\pi$
$313$	24.8257	+	14.3331i	1.40323	+	0.810155i	0.408507	+	0.912755i	$0.366050\pi$
$314$	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	−0.580599	−	0.814190i	$-0.697181\pi$
$317$	−12.0415	+	3.22651i	−0.676317	+	0.181219i	−0.0957183	+	0.995408i	$0.530515\pi$
$318$	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	−0.335395	−	0.942078i	$-0.608870\pi$
$331$	7.75229	−	28.9319i	0.426104	−	1.59024i	0.761499	−	0.648166i	$-0.224464\pi$
$332$	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	$-0.880704\pi$
$337$		−	13.4402i		−	0.732137i	0.930588	−	0.366068i	$-0.119296\pi$
$338$	−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	−0.629504	−	0.776998i	$-0.716742\pi$
$349$	5.68220	−	21.2063i	0.304161	−	1.13515i	0.933665	−	0.358148i	$-0.116592\pi$
$350$		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	−0.998722	−	0.0505316i	$-0.983908\pi$
$353$	−2.98864	−	11.1538i	−0.159069	−	0.593655i	0.839653	−	0.543123i	$-0.182758\pi$
$354$	−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	0.959563	−	0.281494i	$-0.0908300\pi$
$359$	−0.230969	−	0.861987i	−0.0121901	−	0.0454939i	−0.971753	+	0.236000i	$0.924163\pi$
$360$			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	$-0.456634\pi$
$367$	−12.5341	−	7.23654i	−0.654273	−	0.377744i	−0.790091	+	0.612989i	$0.789967\pi$
$368$			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	−0.998802	−	0.0489327i	$-0.984418\pi$
$373$	−10.4635	−	18.1233i	−0.541778	−	0.938387i	0.457024	−	0.889454i	$-0.348915\pi$
$374$	−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	0.665355	+	0.746527i	$0.268280\pi$
$379$	−5.53128	+	20.6430i	−0.284123	+	1.06036i	−0.949478	+	0.313834i	$0.898387\pi$
$380$	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	$-0.568089\pi$
$383$	−17.3144	−	4.63937i	−0.884723	−	0.237061i	−0.672444	+	0.740148i	$0.734755\pi$
$384$	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	−0.602921	−	0.797801i	$-0.705997\pi$
$389$	−4.21022	+	2.43077i	−0.213467	+	0.123245i	0.389455	+	0.921046i	$0.372663\pi$
$390$	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	−0.714455	−	0.699682i	$-0.753325\pi$
$397$	5.06335	−	18.8967i	0.254122	−	0.948397i	0.968577	−	0.248715i	$-0.0800082\pi$
$398$	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	−0.778885	−	0.627167i	$-0.784214\pi$
$401$	−3.03815	+	3.03815i	−0.151718	+	0.151718i	0.627167	+	0.778885i	$0.284214\pi$
$402$	−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	0.0625056	−	0.998045i	$-0.480091\pi$
$409$	21.4483	−	21.4483i	1.06055	−	1.06055i	0.998045	−	0.0625056i	$-0.0199091\pi$
$410$	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	$-0.604573\pi$
$419$	6.87240	−	3.96778i	0.335739	−	0.193839i	0.658386	+	0.752680i	$0.271239\pi$
$420$		0			0
$421$	−5.98090	−	5.98090i	−0.291491	−	0.291491i	0.546178	−	0.837669i	$-0.316082\pi$
$421$	−5.98090	−	5.98090i	−0.291491	−	0.291491i	−0.837669	+	0.546178i	$0.816082\pi$
$422$	−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	−0.272253	−	0.962226i	$-0.587769\pi$
$431$	−0.558842	+	0.149741i	−0.0269185	+	0.00721278i	0.245335	+	0.969438i	$0.421102\pi$
$432$			19.7770i			0.951521i
$433$	−4.11334	+	7.12452i	−0.197675	+	0.342382i	−0.947774	−	0.318943i	$-0.896672\pi$
$433$	−4.11334	+	7.12452i	−0.197675	+	0.342382i	0.750099	+	0.661325i	$0.230006\pi$
$434$		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	$-0.401803\pi$
$439$	12.7234			0.607253			0.303626	+	0.952791i	$0.401803\pi$
$440$	−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	−0.838313	−	0.545189i	$-0.816458\pi$
$443$	1.11534	−	1.93182i	0.0529912	−	0.0917834i	0.891304	+	0.453406i	$0.149791\pi$
$444$	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	0.617184	+	0.786819i	$0.288273\pi$
$449$	10.0883	+	37.6500i	0.476096	+	1.77682i	−0.141088	+	0.989997i	$0.545060\pi$
$450$	−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	0.976628	−	0.214937i	$-0.0689545\pi$
$457$	16.2831	+	16.2831i	0.761691	+	0.761691i	−0.214937	+	0.976628i	$0.568954\pi$
$458$	−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	−0.868822	−	0.495125i	$-0.835122\pi$
$461$	−7.81461	−	29.1645i	−0.363962	−	1.35833i	0.504859	−	0.863202i	$-0.331544\pi$
$462$		0			0
$463$	2.19856	−	2.19856i	0.102176	−	0.102176i	−0.654171	−	0.756347i	$-0.726982\pi$
$463$	2.19856	−	2.19856i	0.102176	−	0.102176i	0.756347	+	0.654171i	$0.226982\pi$
$464$	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	$-0.996280\pi$
$467$	−10.5856	+	18.3348i	−0.489844	+	0.848434i	0.510088	+	0.860122i	$0.329613\pi$
$468$	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	$-0.398485\pi$
$479$	23.1962	−	6.21539i	1.05986	−	0.283988i	0.746320	+	0.665587i	$0.231819\pi$
$480$	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	−0.995326	−	0.0965685i	$-0.969213\pi$
$487$	−24.0960	−	24.0960i	−1.09189	−	1.09189i	−0.0965685	−	0.995326i	$-0.530787\pi$
$488$	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	−0.196924	−	0.980419i	$-0.563095\pi$
$491$	12.2688	−	7.08337i	0.553681	−	0.319668i	0.750605	+	0.660751i	$0.229762\pi$
$492$	−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	0.451972	−	0.892032i	$-0.350721\pi$
$499$	28.8032	−	7.71779i	1.28941	−	0.345496i	0.837436	+	0.546536i	$0.184054\pi$
$500$	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	$-0.431703\pi$
$503$	−11.8147	−	6.82122i	−0.526791	−	0.304143i	−0.739709	+	0.672927i	$0.765037\pi$
$504$		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	$-0.731156\pi$
$509$	1.88773	−	1.88773i	0.0836722	−	0.0836722i	0.747704	+	0.664032i	$0.231156\pi$
$510$	−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	$-0.777282\pi$
$521$	−13.4638	+	7.77333i	−0.589860	+	0.340556i	0.175182	+	0.984536i	$0.443948\pi$
$522$	−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	0.935382	−	0.353638i	$-0.115055\pi$
$541$	−1.19789	−	4.47060i	−0.0515014	−	0.192206i	−0.986884	+	0.161432i	$0.948389\pi$
$542$			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	0.972965	−	0.230951i	$-0.0741837\pi$
$557$	0.351113	+	1.31037i	0.0148771	+	0.0555222i	−0.958088	+	0.286473i	$0.907517\pi$
$558$	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	$-0.743000\pi$
$563$	−32.8100			−1.38278			−0.691388	+	0.722484i	$0.743000\pi$
$564$	−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	$-0.784584\pi$
$569$		−	29.8773i		−	1.25252i	0.779613	−	0.626261i	$-0.215416\pi$
$570$	−25.2958	+	6.77799i	−1.05952	+	0.283899i
$571$	0.640877	−	0.370010i	0.0268198	−	0.0154844i	−0.486530	−	0.873664i	$-0.661738\pi$
$571$	0.640877	−	0.370010i	0.0268198	−	0.0154844i	0.513350	+	0.858179i	$0.328404\pi$
$572$	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	$-0.165365\pi$
$577$	32.9470	+	8.82812i	1.37160	+	0.367519i	0.503538	+	0.863973i	$0.332031\pi$
$578$	−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	$-0.499014\pi$
$587$	−11.9740	−	3.20842i	−0.494219	−	0.132426i	−0.497316	+	0.867569i	$0.665681\pi$
$588$		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	$-0.738839\pi$
$593$	−22.0792	+	5.91611i	−0.906685	+	0.242945i	−0.224800	+	0.974405i	$0.572173\pi$
$594$	−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	0.839425	−	0.543476i	$-0.182892\pi$
$599$	−1.24701	−	2.15989i	−0.0509516	−	0.0882508i	−0.890376	+	0.455225i	$0.849559\pi$
$600$	−7.09113	+	7.09113i	−0.289494	+	0.289494i
$601$	18.5873	−	10.7314i	0.758193	−	0.437743i	−0.0704537	−	0.997515i	$-0.522445\pi$
$601$	18.5873	−	10.7314i	0.758193	−	0.437743i	0.828647	+	0.559772i	$0.189111\pi$
$602$		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	$-0.561129\pi$
$607$	13.8907	−	8.01981i	0.563807	−	0.325514i	0.754672	+	0.656102i	$0.227796\pi$
$608$	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	−0.121431	−	0.992600i	$-0.538748\pi$
$613$	6.67764	−	1.78927i	0.269707	−	0.0722679i	0.391138	+	0.920332i	$0.372082\pi$
$614$		−	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	0.327751	−	0.944764i	$-0.393709\pi$
$617$	26.9254	−	7.21463i	1.08397	−	0.290450i	0.756223	+	0.654314i	$0.227043\pi$
$618$	−14.0896	−	3.77529i	−0.566766	−	0.151864i
$619$	−3.58815	+	13.3912i	−0.144220	+	0.538237i	0.855569	+	0.517689i	$0.173208\pi$
$619$	−3.58815	+	13.3912i	−0.144220	+	0.538237i	−0.999789	+	0.0205475i	$0.993459\pi$
$620$	−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	0.961302	+	0.275496i	$0.0888419\pi$
$631$	6.69536	+	24.9874i	0.266538	+	0.994733i	−0.694764	+	0.719237i	$0.744491\pi$
$632$	−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	$0.0798847\pi$
$641$			12.5749i			0.496678i	−0.968673	+	0.248339i	$0.920115\pi$
$642$	4.05806	+	15.1449i	0.160159	+	0.597720i
$643$	6.40174	+	23.8916i	0.252460	+	0.942193i	0.969486	+	0.245147i	$0.0788361\pi$
$643$	6.40174	+	23.8916i	0.252460	+	0.942193i	−0.717026	+	0.697046i	$0.754497\pi$
$644$		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	0.294205	+	0.955742i	$0.404945\pi$
$647$	−17.3117	+	29.9848i	−0.680595	+	1.17883i	−0.974800	+	0.223083i	$0.928388\pi$
$648$	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	−0.821192	−	0.570652i	$-0.806691\pi$
$659$	2.14617	−	3.71728i	0.0836031	−	0.144805i	0.904795	+	0.425847i	$0.140024\pi$
$660$			0.413149i			0.0160818i
$661$	−14.6944	+	3.93734i	−0.571544	+	0.153145i	−0.533005	−	0.846112i	$-0.678937\pi$
$661$	−14.6944	+	3.93734i	−0.571544	+	0.153145i	−0.0385395	+	0.999257i	$0.512271\pi$
$662$	−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	0.101526	−	0.994833i	$-0.467627\pi$
$673$	26.3013	−	15.1851i	1.01384	−	0.585341i	0.912314	+	0.409492i	$0.134294\pi$
$674$	−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	$-0.582261\pi$
$677$	−31.7593	−	18.3363i	−1.22061	−	0.704720i	−0.965048	+	0.262073i	$0.915594\pi$
$678$	−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	−0.456557	−	0.889694i	$-0.650918\pi$
$683$	11.3197	−	11.3197i	0.433137	−	0.433137i	0.889694	+	0.456557i	$0.150918\pi$
$684$	−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	$-0.638340\pi$
$691$	12.7750	−	12.7750i	0.485982	−	0.485982i	0.907036	+	0.421054i	$0.138340\pi$
$692$	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	$0.251645\pi$
$701$			37.6363i			1.42150i	−0.703444	+	0.710751i	$0.748355\pi$
$702$	−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	0.461798	−	0.886985i	$-0.347204\pi$
$709$	11.1364	+	2.98398i	0.418235	+	0.112066i	−0.0435634	+	0.999051i	$0.513871\pi$
$710$	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	−0.870622	−	0.491953i	$-0.836283\pi$
$719$	−23.0965	−	40.0043i	−0.861355	−	1.49191i	0.00926691	−	0.999957i	$-0.497050\pi$
$720$	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	$-0.519343\pi$
$727$	−3.27502			−0.121464			−0.0607318	+	0.998154i	$0.519343\pi$
$728$		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	0.916676	+	0.399630i	$0.130861\pi$
$733$	8.73478	+	32.5986i	0.322626	+	1.20406i	−0.594050	+	0.804428i	$0.702472\pi$
$734$	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	0.955121	−	0.296215i	$-0.0957244\pi$
$739$	−0.547643	−	2.04383i	−0.0201454	−	0.0751836i	−0.975267	+	0.221031i	$0.929058\pi$
$740$	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	0.702053	+	0.712125i	$0.252267\pi$
$743$	−7.14174	+	26.6533i	−0.262005	+	0.977816i	−0.964058	+	0.265692i	$0.914400\pi$
$744$	−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	$-0.956101\pi$
$751$		−	7.53493i		−	0.274954i	0.990505	−	0.137477i	$-0.0438993\pi$
$752$	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	−0.939297	−	0.343104i	$-0.888522\pi$
$757$	−21.0971	−	36.5412i	−0.766786	−	1.32811i	0.172512	−	0.985007i	$-0.444812\pi$
$758$	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	$-0.906824\pi$
$761$	0.441464	−	1.64757i	0.0160031	−	0.0597243i	0.973466	+	0.228833i	$0.0734910\pi$
$762$	−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	$-0.437454\pi$
$769$	−3.49612	−	0.936782i	−0.126073	−	0.0337812i	−0.321304	+	0.946976i	$0.604121\pi$
$770$		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	$-0.590407\pi$
$773$	18.8981	−	18.8981i	0.679717	−	0.679717i	0.959936	+	0.280219i	$0.0904072\pi$
$774$	−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	−0.993218	−	0.116263i	$-0.962908\pi$
$787$	−31.1249	−	31.1249i	−1.10948	−	1.10948i	−0.116263	−	0.993218i	$-0.537092\pi$
$788$	−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	$-0.912483\pi$
$797$	−6.94770	+	12.0338i	−0.246100	+	0.426258i	0.716340	+	0.697751i	$0.245816\pi$
$798$		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	−0.151010	−	0.988532i	$-0.548253\pi$
$809$	22.2022	−	38.4554i	0.780589	−	1.35202i	0.931599	−	0.363488i	$-0.118414\pi$
$810$	−0.0455546	−	0.0789029i	−0.00160063	−	0.00277237i
$811$	9.49597	−	9.49597i	0.333449	−	0.333449i	−0.520446	−	0.853895i	$-0.674234\pi$
$811$	9.49597	−	9.49597i	0.333449	−	0.333449i	0.853895	+	0.520446i	$0.174234\pi$
$812$		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	0.946786	+	0.321864i	$0.104309\pi$
$821$	36.3507	+	36.3507i	1.26865	+	1.26865i	0.321864	+	0.946786i	$0.395691\pi$
$822$	13.3139	+	7.68676i	0.464374	+	0.268107i
$823$		−	25.9783i		−	0.905548i	−0.891625	−	0.452774i	$-0.850435\pi$
$823$		−	25.9783i		−	0.905548i	0.891625	−	0.452774i	$-0.149565\pi$
$824$	−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	−0.725272	−	0.688463i	$-0.758286\pi$
$827$	−1.05853	+	1.05853i	−0.0368089	+	0.0368089i	0.688463	+	0.725272i	$0.258286\pi$
$828$	−0.680873	−	1.17931i	−0.0236620	−	0.0409837i
$829$	7.34482	−	12.7216i	0.255096	−	0.441839i	−0.709826	−	0.704378i	$-0.751226\pi$
$829$	7.34482	−	12.7216i	0.255096	−	0.441839i	0.964922	+	0.262538i	$0.0845596\pi$
$830$	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	$-0.691820\pi$
$839$	−18.7042	+	5.01177i	−0.645740	+	0.173025i	−0.0789379	+	0.996880i	$0.525153\pi$
$840$		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	$-0.383210\pi$
$853$	−16.7852	−	16.7852i	−0.574713	−	0.574713i	−0.933442	+	0.358728i	$0.883210\pi$
$854$		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	−0.858343	−	0.513076i	$-0.828506\pi$
$857$	−25.5716	−	44.2913i	−0.873508	−	1.51296i	−0.0151651	−	0.999885i	$-0.504827\pi$
$858$	−5.82608	+	4.91254i	−0.198899	+	0.167712i
$859$	13.0666	+	7.54398i	0.445825	+	0.257397i	0.706065	−	0.708147i	$-0.250468\pi$
$859$	13.0666	+	7.54398i	0.445825	+	0.257397i	−0.260240	+	0.965544i	$0.583802\pi$
$860$	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	−0.0351791	−	0.999381i	$-0.511200\pi$
$863$	12.7509	−	3.41659i	0.434045	−	0.116302i	0.469225	+	0.883079i	$0.344533\pi$
$864$	−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	−0.557083	−	0.830457i	$-0.688079\pi$
$877$	10.0864	−	37.6430i	0.340594	−	1.27111i	0.897676	−	0.440655i	$-0.145254\pi$
$878$	−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	$-0.00293878\pi$
$881$	14.6029	+	25.2929i	0.491983	+	0.852140i	−0.507974	+	0.861372i	$0.669605\pi$
$882$		0			0
$883$		−	2.58799i		−	0.0870929i	−0.999051	−	0.0435464i	$-0.986134\pi$
$883$		−	2.58799i		−	0.0870929i	0.999051	−	0.0435464i	$-0.0138656\pi$
$884$	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	0.999966	−	0.00829638i	$-0.00264085\pi$
$907$	44.9567	+	25.9558i	1.49276	+	0.861847i	0.492798	+	0.870144i	$0.335974\pi$
$908$	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	0.837966	−	0.545722i	$-0.183745\pi$
$919$	−1.62567	−	2.81574i	−0.0536259	−	0.0928828i	−0.891592	+	0.452839i	$0.850411\pi$
$920$	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	$-0.169085\pi$
$929$	41.3182	+	11.0712i	1.35561	+	0.363234i	0.493405	+	0.869799i	$0.335752\pi$
$930$	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	$-0.357260\pi$
$941$	10.9959	+	2.94635i	0.358457	+	0.0960482i	−0.0750961	+	0.997176i	$0.523926\pi$
$942$	−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	−0.972338	−	0.233577i	$-0.924957\pi$
$947$	−22.7342	+	22.7342i	−0.738761	+	0.738761i	0.233577	+	0.972338i	$0.424957\pi$
$948$	−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	0.923068	−	0.384638i	$-0.125674\pi$
$953$	32.4604	+	18.7410i	1.05150	+	0.607081i	0.128428	+	0.991719i	$0.459007\pi$
$954$	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	0.860459	−	0.509520i	$-0.170177\pi$
$967$	10.9130	+	10.9130i	0.350939	+	0.350939i	−0.509520	+	0.860459i	$0.670177\pi$
$968$	−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	$-0.657547\pi$
$971$	1.54608	−	0.892628i	0.0496160	−	0.0286458i	0.524603	+	0.851347i	$0.324214\pi$
$972$	−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	−0.223559	−	0.974690i	$-0.571768\pi$
$977$	2.19357	−	0.587766i	0.0701786	−	0.0188043i	0.293737	+	0.955886i	$0.405101\pi$
$978$			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	−0.528609	−	0.848865i	$-0.677286\pi$
$983$	11.0868	−	41.3763i	0.353613	−	1.31970i	0.882221	−	0.470835i	$-0.156047\pi$
$984$	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	0.0358964	+	0.999356i	$0.488571\pi$
$991$	−26.6800	+	46.2112i	−0.847519	+	1.46795i	−0.883415	+	0.468591i	$0.844762\pi$
$992$	−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.362.3		32
7.2	even	3		91.2.bc.a.76.4	yes	32
7.3	odd	6		637.2.x.b.570.5		32
7.4	even	3		637.2.x.b.570.6		32
7.5	odd	6		91.2.bc.a.76.3	yes	32
7.6	odd	2	inner	637.2.bb.b.362.4		32
13.6	odd	12		637.2.x.b.19.6		32
21.2	odd	6		819.2.fm.g.622.5		32
21.5	even	6		819.2.fm.g.622.6		32
91.6	even	12		637.2.x.b.19.5		32
91.19	even	12		91.2.bc.a.6.4	yes	32
91.32	odd	12	inner	637.2.bb.b.227.4		32
91.45	even	12	inner	637.2.bb.b.227.3		32
91.58	odd	12		91.2.bc.a.6.3	✓	32
273.110	odd	12		819.2.fm.g.370.5		32
273.149	even	12		819.2.fm.g.370.6		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.bc.a.6.3	✓	32	91.58	odd	12
91.2.bc.a.6.4	yes	32	91.19	even	12
91.2.bc.a.76.3	yes	32	7.5	odd	6
91.2.bc.a.76.4	yes	32	7.2	even	3
637.2.x.b.19.5		32	91.6	even	12
637.2.x.b.19.6		32	13.6	odd	12
637.2.x.b.570.5		32	7.3	odd	6
637.2.x.b.570.6		32	7.4	even	3
637.2.bb.b.227.3		32	91.45	even	12	inner
637.2.bb.b.227.4		32	91.32	odd	12	inner
637.2.bb.b.362.3		32	1.1	even	1	trivial
637.2.bb.b.362.4		32	7.6	odd	2	inner
819.2.fm.g.370.5		32	273.110	odd	12
819.2.fm.g.370.6		32	273.149	even	12
819.2.fm.g.622.5		32	21.2	odd	6
819.2.fm.g.622.6		32	21.5	even	6

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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