LMFDB - Embedded newform 637.2.r.e.324.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(116,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 3]))

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

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

chi := DirichletCharacter("637.116");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.r (of order $6$, degree $2$, 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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.89539436150784.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{11} + 2x^{10} - 8x^{9} + 4x^{8} + 16x^{7} - 8x^{6} + 20x^{5} + 20x^{4} - 24x^{3} + 8x^{2} - 8x + 4 $ x^12 - 2x^11 + 2x^10 - 8x^9 + 4x^8 + 16x^7 - 8x^6 + 20x^5 + 20x^4 - 24x^3 + 8x^2 - 8*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			324.2
Root			$0.312819 + 1.16746i$ of defining polynomial
Character	$\chi$	$=$	637.324
Dual form			637.2.r.e.116.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.01332 - 0.585043i) q^{2} +(-0.269594 - 0.466951i) q^{3} +(-0.315449 - 0.546373i) q^{4} +(0.399074 + 0.230406i) q^{5} +0.630898i q^{6} +3.07838i q^{8} +(1.35464 - 2.34630i) q^{9} +O(q^{10})$	\(q+(-1.01332 - 0.585043i) q^{2} +(-0.269594 - 0.466951i) q^{3} +(-0.315449 - 0.546373i) q^{4} +(0.399074 + 0.230406i) q^{5} +0.630898i q^{6} +3.07838i q^{8} +(1.35464 - 2.34630i) q^{9} +(-0.269594 - 0.466951i) q^{10} +(0.718726 - 0.414957i) q^{11} +(-0.170086 + 0.294598i) q^{12} +(-2.87936 - 2.17009i) q^{13} -0.248464i q^{15} +(1.17009 - 2.02665i) q^{16} +(-1.43968 - 2.49360i) q^{17} +(-2.74538 + 1.58504i) q^{18} +(3.74716 + 2.16342i) q^{19} -0.290725i q^{20} -0.971071 q^{22} +(2.52472 - 4.37295i) q^{23} +(1.43745 - 0.829914i) q^{24} +(-2.39383 - 4.14623i) q^{25} +(1.64813 + 3.88355i) q^{26} -3.07838 q^{27} +0.261795 q^{29} +(-0.145362 + 0.251775i) q^{30} +(-5.88983 + 3.40049i) q^{31} +(2.96055 - 1.70928i) q^{32} +(-0.387529 - 0.223740i) q^{33} +3.36910i q^{34} -1.70928 q^{36} +(-8.23613 - 4.75513i) q^{37} +(-2.53139 - 4.38450i) q^{38} +(-0.237065 + 1.92956i) q^{39} +(-0.709275 + 1.22850i) q^{40} +6.68035i q^{41} +0.418551 q^{43} +(-0.453443 - 0.261795i) q^{44} +(1.08120 - 0.624232i) q^{45} +(-5.11673 + 2.95415i) q^{46} +(-8.00940 - 4.62423i) q^{47} -1.26180 q^{48} +5.60197i q^{50} +(-0.776260 + 1.34452i) q^{51} +(-0.277386 + 2.25776i) q^{52} +(-0.815449 - 1.41240i) q^{53} +(3.11940 + 1.80098i) q^{54} +0.382433 q^{55} -2.33299i q^{57} +(-0.265284 - 0.153162i) q^{58} +(-2.41418 + 1.39383i) q^{59} +(-0.135754 + 0.0783777i) q^{60} +(-3.63090 + 6.28890i) q^{61} +7.95774 q^{62} -8.68035 q^{64} +(-0.649079 - 1.52945i) q^{65} +(0.261795 + 0.453443i) q^{66} +(4.39800 - 2.53919i) q^{67} +(-0.908291 + 1.57321i) q^{68} -2.72261 q^{69} -12.7721i q^{71} +(7.22280 + 4.17009i) q^{72} +(0.306143 - 0.176752i) q^{73} +(5.56391 + 9.63698i) q^{74} +(-1.29072 + 2.23560i) q^{75} -2.72979i q^{76} +(1.36910 - 1.81658i) q^{78} +(-1.40829 + 2.43923i) q^{79} +(0.933903 - 0.539189i) q^{80} +(-3.23400 - 5.60145i) q^{81} +(3.90829 - 6.76936i) q^{82} -10.3763i q^{83} -1.32684i q^{85} +(-0.424128 - 0.244870i) q^{86} +(-0.0705785 - 0.122246i) q^{87} +(1.27739 + 2.21251i) q^{88} +(-4.70415 - 2.71594i) q^{89} -1.46081 q^{90} -3.18568 q^{92} +(3.17573 + 1.83351i) q^{93} +(5.41075 + 9.37170i) q^{94} +(0.996928 + 1.72673i) q^{95} +(-1.59630 - 0.921622i) q^{96} +12.6092i q^{97} -2.24846i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{4} + 2 q^{9}+O(q^{10}) $ 12 * q + 4 * q^4 + 2 * q^9	$ 12 q + 4 q^{4} + 2 q^{9} + 20 q^{12} + 16 q^{13} - 8 q^{16} + 8 q^{17} + 48 q^{22} - 6 q^{23} - 8 q^{25} - 12 q^{26} - 24 q^{27} - 28 q^{29} - 16 q^{30} + 8 q^{36} + 4 q^{38} + 8 q^{39} + 20 q^{40} - 52 q^{43} + 16 q^{48} - 8 q^{51} + 20 q^{52} - 2 q^{53} + 24 q^{55} - 28 q^{61} + 32 q^{62} - 16 q^{64} + 6 q^{65} - 28 q^{66} - 20 q^{68} - 8 q^{69} + 24 q^{74} - 44 q^{75} + 32 q^{78} - 26 q^{79} + 26 q^{81} + 56 q^{82} + 40 q^{87} + 40 q^{88} - 24 q^{90} - 72 q^{92} - 20 q^{94} - 58 q^{95}+O(q^{100}) $ 12 * q + 4 * q^4 + 2 * q^9 + 20 * q^12 + 16 * q^13 - 8 * q^16 + 8 * q^17 + 48 * q^22 - 6 * q^23 - 8 * q^25 - 12 * q^26 - 24 * q^27 - 28 * q^29 - 16 * q^30 + 8 * q^36 + 4 * q^38 + 8 * q^39 + 20 * q^40 - 52 * q^43 + 16 * q^48 - 8 * q^51 + 20 * q^52 - 2 * q^53 + 24 * q^55 - 28 * q^61 + 32 * q^62 - 16 * q^64 + 6 * q^65 - 28 * q^66 - 20 * q^68 - 8 * q^69 + 24 * q^74 - 44 * q^75 + 32 * q^78 - 26 * q^79 + 26 * q^81 + 56 * q^82 + 40 * q^87 + 40 * q^88 - 24 * q^90 - 72 * q^92 - 20 * q^94 - 58 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.01332	−	0.585043i	−0.716529	−	0.413688i	0.0969450	−	0.995290i	$-0.469093\pi$
$2$	−1.01332	−	0.585043i	−0.716529	−	0.413688i	−0.813474	+	0.581602i	$0.802426\pi$
$3$	−0.269594	−	0.466951i	−0.155650	−	0.269594i	0.777645	−	0.628703i	$-0.216414\pi$
$3$	−0.269594	−	0.466951i	−0.155650	−	0.269594i	−0.933296	+	0.359109i	$0.883081\pi$
$4$	−0.315449	−	0.546373i	−0.157724	−	0.273187i
$5$	0.399074	+	0.230406i	0.178471	+	0.103041i	0.586574	−	0.809895i	$-0.300476\pi$
$5$	0.399074	+	0.230406i	0.178471	+	0.103041i	−0.408103	+	0.912936i	$0.633810\pi$
$6$			0.630898i			0.257563i
$7$		0			0
$7$		0			0
$8$			3.07838i			1.08837i
$9$	1.35464	−	2.34630i	0.451546	−	0.782100i
$10$	−0.269594	−	0.466951i	−0.0852532	−	0.147663i
$11$	0.718726	−	0.414957i	0.216704	−	0.125114i	−0.387719	−	0.921778i	$-0.626737\pi$
$11$	0.718726	−	0.414957i	0.216704	−	0.125114i	0.604423	+	0.796663i	$0.293404\pi$
$12$	−0.170086	+	0.294598i	−0.0490997	+	0.0850432i
$13$	−2.87936	−	2.17009i	−0.798591	−	0.601874i
$13$	−2.87936	−	2.17009i	−0.798591	−	0.601874i
$14$		0			0
$15$		−	0.248464i		−	0.0641532i
$16$	1.17009	−	2.02665i	0.292522	−	0.506662i
$17$	−1.43968	−	2.49360i	−0.349174	−	0.604787i	0.636929	−	0.770922i	$-0.280204\pi$
$17$	−1.43968	−	2.49360i	−0.349174	−	0.604787i	−0.986103	+	0.166135i	$0.946871\pi$
$18$	−2.74538	+	1.58504i	−0.647091	+	0.373598i
$19$	3.74716	+	2.16342i	0.859656	+	0.496323i	0.863897	−	0.503668i	$-0.168017\pi$
$19$	3.74716	+	2.16342i	0.859656	+	0.496323i	−0.00424086	+	0.999991i	$0.501350\pi$
$20$		−	0.290725i		−	0.0650080i
$21$		0			0
$22$	−0.971071			−0.207033
$23$	2.52472	−	4.37295i	0.526441	−	0.911823i	−0.473084	−	0.881017i	$-0.656859\pi$
$23$	2.52472	−	4.37295i	0.526441	−	0.911823i	0.999525	−	0.0308059i	$-0.00980737\pi$
$24$	1.43745	−	0.829914i	0.293419	−	0.169405i
$25$	−2.39383	−	4.14623i	−0.478765	−	0.829246i
$26$	1.64813	+	3.88355i	0.323226	+	0.761627i
$27$	−3.07838			−0.592434
$28$		0			0
$29$	0.261795			0.0486142			0.0243071	−	0.999705i	$-0.492262\pi$
$29$	0.261795			0.0486142			0.0243071	+	0.999705i	$0.492262\pi$
$30$	−0.145362	+	0.251775i	−0.0265394	+	0.0459676i
$31$	−5.88983	+	3.40049i	−1.05784	+	0.610746i	−0.924835	−	0.380368i	$-0.875797\pi$
$31$	−5.88983	+	3.40049i	−1.05784	+	0.610746i	−0.133009	+	0.991115i	$0.542464\pi$
$32$	2.96055	−	1.70928i	0.523357	−	0.302160i
$33$	−0.387529	−	0.223740i	−0.0674602	−	0.0389481i
$34$			3.36910i			0.577796i
$35$		0			0
$36$	−1.70928			−0.284879
$37$	−8.23613	−	4.75513i	−1.35401	−	0.781739i	−0.365202	−	0.930928i	$-0.619000\pi$
$37$	−8.23613	−	4.75513i	−1.35401	−	0.781739i	−0.988809	+	0.149190i	$0.952333\pi$
$38$	−2.53139	−	4.38450i	−0.410646	−	0.711259i
$39$	−0.237065	+	1.92956i	−0.0379607	+	0.308978i
$40$	−0.709275	+	1.22850i	−0.112146	+	0.194243i
$41$			6.68035i			1.04329i	0.853161	+	0.521647i	$0.174682\pi$
$41$			6.68035i			1.04329i	−0.853161	+	0.521647i	$0.825318\pi$
$42$		0			0
$43$	0.418551			0.0638284			0.0319142	−	0.999491i	$-0.489840\pi$
$43$	0.418551			0.0638284			0.0319142	+	0.999491i	$0.489840\pi$
$44$	−0.453443	−	0.261795i	−0.0683590	−	0.0394671i
$45$	1.08120	−	0.624232i	0.161176	−	0.0930550i
$46$	−5.11673	+	2.95415i	−0.754421	+	0.435565i
$47$	−8.00940	−	4.62423i	−1.16829	−	0.674514i	−0.215015	−	0.976611i	$-0.568980\pi$
$47$	−8.00940	−	4.62423i	−1.16829	−	0.674514i	−0.953277	+	0.302097i	$0.902313\pi$
$48$	−1.26180			−0.182124
$49$		0			0
$50$			5.60197i			0.792238i
$51$	−0.776260	+	1.34452i	−0.108698	+	0.188271i
$52$	−0.277386	+	2.25776i	−0.0384665	+	0.313095i
$53$	−0.815449	−	1.41240i	−0.112011	−	0.194008i	0.804570	−	0.593857i	$-0.202396\pi$
$53$	−0.815449	−	1.41240i	−0.112011	−	0.194008i	−0.916581	+	0.399850i	$0.869062\pi$
$54$	3.11940	+	1.80098i	0.424496	+	0.245083i
$55$	0.382433			0.0515673
$56$		0			0
$57$		−	2.33299i		−	0.309011i
$58$	−0.265284	−	0.153162i	−0.0348334	−	0.0201111i
$59$	−2.41418	+	1.39383i	−0.314299	+	0.181461i	−0.648849	−	0.760917i	$-0.724749\pi$
$59$	−2.41418	+	1.39383i	−0.314299	+	0.181461i	0.334549	+	0.942378i	$0.391416\pi$
$60$	−0.135754	+	0.0783777i	−0.0175258	+	0.0101185i
$61$	−3.63090	+	6.28890i	−0.464889	+	0.805211i	−0.999197	−	0.0400790i	$-0.987239\pi$
$61$	−3.63090	+	6.28890i	−0.464889	+	0.805211i	0.534308	+	0.845290i	$0.320572\pi$
$62$	7.95774			1.01063
$63$		0			0
$64$	−8.68035			−1.08504
$65$	−0.649079	−	1.52945i	−0.0805083	−	0.189704i
$66$	0.261795	+	0.453443i	0.0322248	+	0.0558149i
$67$	4.39800	−	2.53919i	0.537302	−	0.310211i	−0.206683	−	0.978408i	$-0.566267\pi$
$67$	4.39800	−	2.53919i	0.537302	−	0.310211i	0.743985	+	0.668197i	$0.232934\pi$
$68$	−0.908291	+	1.57321i	−0.110146	+	0.190779i
$69$	−2.72261			−0.327763
$70$		0			0
$71$		−	12.7721i		−	1.51576i	−0.652392	−	0.757882i	$-0.726234\pi$
$71$		−	12.7721i		−	1.51576i	0.652392	−	0.757882i	$-0.273766\pi$
$72$	7.22280	+	4.17009i	0.851215	+	0.491449i
$73$	0.306143	−	0.176752i	0.0358314	−	0.0206873i	−0.481977	−	0.876184i	$-0.660081\pi$
$73$	0.306143	−	0.176752i	0.0358314	−	0.0206873i	0.517809	+	0.855496i	$0.326748\pi$
$74$	5.56391	+	9.63698i	0.646792	+	1.12028i
$75$	−1.29072	+	2.23560i	−0.149040	+	0.258145i
$76$		−	2.72979i		−	0.313129i
$77$		0			0
$78$	1.36910	−	1.81658i	0.155020	−	0.205687i
$79$	−1.40829	+	2.43923i	−0.158445	+	0.274435i	−0.934308	−	0.356466i	$-0.883981\pi$
$79$	−1.40829	+	2.43923i	−0.158445	+	0.274435i	0.775863	+	0.630901i	$0.217315\pi$
$80$	0.933903	−	0.539189i	0.104413	−	0.0602831i
$81$	−3.23400	−	5.60145i	−0.359333	−	0.622383i
$82$	3.90829	−	6.76936i	0.431599	−	0.747551i
$83$		−	10.3763i		−	1.13895i	−0.822010	−	0.569473i	$-0.807147\pi$
$83$		−	10.3763i		−	1.13895i	0.822010	−	0.569473i	$-0.192853\pi$
$84$		0			0
$85$		−	1.32684i		−	0.143916i
$86$	−0.424128	−	0.244870i	−0.0457349	−	0.0264050i
$87$	−0.0705785	−	0.122246i	−0.00756681	−	0.0131061i
$88$	1.27739	+	2.21251i	0.136171	+	0.235854i
$89$	−4.70415	−	2.71594i	−0.498639	−	0.287889i	0.229513	−	0.973306i	$-0.426287\pi$
$89$	−4.70415	−	2.71594i	−0.498639	−	0.287889i	−0.728151	+	0.685417i	$0.759620\pi$
$90$	−1.46081			−0.153983
$91$		0			0
$92$	−3.18568			−0.332131
$93$	3.17573	+	1.83351i	0.329308	+	0.190126i
$94$	5.41075	+	9.37170i	0.558076	+	0.966617i
$95$	0.996928	+	1.72673i	0.102283	+	0.177159i
$96$	−1.59630	−	0.921622i	−0.162921	−	0.0940627i
$97$			12.6092i			1.28027i	0.768264	+	0.640133i	$0.221121\pi$
$97$			12.6092i			1.28027i	−0.768264	+	0.640133i	$0.778879\pi$
$98$		0			0
$99$		−	2.24846i		−	0.225979i
$100$	−1.51026	+	2.61585i	−0.151026	+	0.261585i
$101$	1.82211	+	3.15599i	0.181307	+	0.314033i	0.942326	−	0.334697i	$-0.108634\pi$
$101$	1.82211	+	3.15599i	0.181307	+	0.314033i	−0.761019	+	0.648730i	$0.775301\pi$
$102$	1.57321	−	0.908291i	0.155771	−	0.0899342i
$103$	8.97107	−	15.5384i	0.883946	−	1.53104i	0.0370287	−	0.999314i	$-0.488211\pi$
$103$	8.97107	−	15.5384i	0.883946	−	1.53104i	0.846917	−	0.531725i	$-0.178456\pi$
$104$	6.68035	−	8.86376i	0.655062	−	0.869164i
$105$		0			0
$106$			1.90829i			0.185350i
$107$	−1.47220	+	2.54993i	−0.142323	+	0.246511i	−0.928371	−	0.371654i	$-0.878791\pi$
$107$	−1.47220	+	2.54993i	−0.142323	+	0.246511i	0.786048	+	0.618166i	$0.212124\pi$
$108$	0.971071	+	1.68194i	0.0934413	+	0.161845i
$109$	−7.30222	+	4.21594i	−0.699426	+	0.403814i	−0.807134	−	0.590369i	$-0.798982\pi$
$109$	−7.30222	+	4.21594i	−0.699426	+	0.403814i	0.107707	+	0.994183i	$0.465649\pi$
$110$	−0.387529	−	0.223740i	−0.0369495	−	0.0213328i
$111$			5.12783i			0.486712i
$112$		0			0
$113$	12.8082			1.20489			0.602446	−	0.798160i	$-0.294193\pi$
$113$	12.8082			1.20489			0.602446	+	0.798160i	$0.294193\pi$
$114$	−1.36490	+	2.36407i	−0.127834	+	0.221416i
$115$	2.01510	−	1.16342i	0.187909	−	0.108490i
$116$	−0.0825830	−	0.143038i	−0.00766764	−	0.0132807i
$117$	−8.99217	+	3.81617i	−0.831326	+	0.352805i
$118$	3.26180			0.300273
$119$		0			0
$120$	0.764867			0.0698225
$121$	−5.15562	+	8.92980i	−0.468693	+	0.811800i
$122$	7.35856	−	4.24846i	0.666212	−	0.384638i
$123$	3.11940	−	1.80098i	0.281266	−	0.162389i
$124$	3.71588	+	2.14536i	0.333696	+	0.192659i
$125$		−	4.51026i		−	0.403410i
$126$		0			0
$127$	13.4680			1.19509			0.597546	−	0.801835i	$-0.296143\pi$
$127$	13.4680			1.19509			0.597546	+	0.801835i	$0.296143\pi$
$128$	2.87490	+	1.65983i	0.254108	+	0.146709i
$129$	−0.112839	−	0.195443i	−0.00993492	−	0.0172078i
$130$	−0.237065	+	1.92956i	−0.0207919	+	0.169234i
$131$	7.21953	−	12.5046i	0.630774	−	1.09253i	−0.356620	−	0.934249i	$-0.616071\pi$
$131$	7.21953	−	12.5046i	0.630774	−	1.09253i	0.987394	−	0.158283i	$-0.0505957\pi$
$132$			0.282314i			0.0245723i
$133$		0			0
$134$	−5.94214			−0.513323
$135$	−1.22850	−	0.709275i	−0.105733	−	0.0610447i
$136$	7.67624	−	4.43188i	0.658233	−	0.380031i
$137$	14.2304	−	8.21594i	1.21579	−	0.701935i	0.251773	−	0.967786i	$-0.418986\pi$
$137$	14.2304	−	8.21594i	1.21579	−	0.701935i	0.964014	+	0.265851i	$0.0856529\pi$
$138$	2.75888	+	1.59284i	0.234852	+	0.135592i
$139$	13.2195			1.12127			0.560633	−	0.828064i	$-0.310558\pi$
$139$	13.2195			1.12127			0.560633	+	0.828064i	$0.310558\pi$
$140$		0			0
$141$			4.98667i			0.419953i
$142$	−7.47220	+	12.9422i	−0.627053	+	1.08609i
$143$	−2.96996	−	0.364887i	−0.248361	−	0.0305134i
$144$	−3.17009	−	5.49075i	−0.264174	−	0.457563i
$145$	0.104476	+	0.0603191i	0.00867624	+	0.00500923i
$146$	−0.413630			−0.0342323
$147$		0			0
$148$			6.00000i			0.493197i
$149$	17.7571	+	10.2521i	1.45472	+	0.839881i	0.998744	−	0.0501120i	$-0.0159578\pi$
$149$	17.7571	+	10.2521i	1.45472	+	0.839881i	0.455974	+	0.889993i	$0.349291\pi$
$150$	2.61585	−	1.51026i	0.213583	−	0.123312i
$151$	−1.38112	+	0.797390i	−0.112394	+	0.0648907i	−0.555143	−	0.831755i	$-0.687337\pi$
$151$	−1.38112	+	0.797390i	−0.112394	+	0.0648907i	0.442749	+	0.896645i	$0.354003\pi$
$152$	−6.65983	+	11.5352i	−0.540183	+	0.935625i
$153$	−7.80098			−0.630672
$154$		0			0
$155$	−3.13397			−0.251726
$156$	1.12904	−	0.479153i	0.0903959	−	0.0383630i
$157$	4.14896	+	7.18620i	0.331123	+	0.573521i	0.982732	−	0.185033i	$-0.0592392\pi$
$157$	4.14896	+	7.18620i	0.331123	+	0.573521i	−0.651610	+	0.758555i	$0.725906\pi$
$158$	2.85411	−	1.64782i	0.227061	−	0.131094i
$159$	−0.439681	+	0.761550i	−0.0348690	+	0.0603948i
$160$	1.57531			0.124539
$161$		0			0
$162$			7.56812i			0.594608i
$163$	−0.344706	−	0.199016i	−0.0269994	−	0.0155881i	0.486440	−	0.873714i	$-0.338295\pi$
$163$	−0.344706	−	0.199016i	−0.0269994	−	0.0155881i	−0.513439	+	0.858126i	$0.671629\pi$
$164$	3.64996	−	2.10731i	0.285014	−	0.164553i
$165$	−0.103102	−	0.178578i	−0.00802647	−	0.0139023i
$166$	−6.07058	+	10.5146i	−0.471168	+	0.816087i
$167$		−	23.8710i		−	1.84719i	−0.383370	−	0.923595i	$-0.625237\pi$
$167$		−	23.8710i		−	1.84719i	0.383370	−	0.923595i	$-0.374763\pi$
$168$		0			0
$169$	3.58145	+	12.4969i	0.275496	+	0.961302i
$170$	−0.776260	+	1.34452i	−0.0595364	+	0.103120i
$171$	10.1521	−	5.86130i	0.776349	−	0.448225i
$172$	−0.132031	−	0.228685i	−0.0100673	−	0.0174371i
$173$	12.9499	−	22.4300i	0.984566	−	1.70532i	0.340715	−	0.940167i	$-0.389331\pi$
$173$	12.9499	−	22.4300i	0.984566	−	1.70532i	0.643850	−	0.765151i	$-0.277336\pi$
$174$			0.165166i			0.0125212i
$175$		0			0
$176$		−	1.94214i		−	0.146394i
$177$	1.30170	+	0.751536i	0.0978416	+	0.0564889i
$178$	3.17789	+	5.50426i	0.238193	+	0.412562i
$179$	10.3371	+	17.9044i	0.772631	+	1.33824i	0.936116	+	0.351691i	$0.114393\pi$
$179$	10.3371	+	17.9044i	0.772631	+	1.33824i	−0.163485	+	0.986546i	$0.552274\pi$
$180$	−0.682128	−	0.393827i	−0.0508428	−	0.0293541i
$181$	−15.7165			−1.16820			−0.584098	−	0.811683i	$-0.698552\pi$
$181$	−15.7165			−1.16820			−0.584098	+	0.811683i	$0.698552\pi$
$182$		0			0
$183$	3.91548			0.289441
$184$	13.4616	+	7.77205i	0.992402	+	0.572963i
$185$	−2.19122	−	3.79530i	−0.161101	−	0.279036i
$186$	−2.14536	−	3.71588i	−0.157306	−	0.272461i
$187$	−2.06947	−	1.19481i	−0.151335	−	0.0873732i
$188$			5.83483i			0.425549i
$189$		0			0
$190$		−	2.33299i		−	0.169253i
$191$	8.39383	−	14.5385i	0.607356	−	1.05197i	−0.384318	−	0.923201i	$-0.625564\pi$
$191$	8.39383	−	14.5385i	0.607356	−	1.05197i	0.991674	−	0.128771i	$-0.0411032\pi$
$192$	2.34017	+	4.05330i	0.168887	+	0.292522i
$193$	−17.3330	+	10.0072i	−1.24765	+	0.720333i	−0.970641	−	0.240533i	$-0.922678\pi$
$193$	−17.3330	+	10.0072i	−1.24765	+	0.720333i	−0.277013	+	0.960866i	$0.589344\pi$
$194$	7.37690	−	12.7772i	0.529631	−	0.917347i
$195$	−0.539189	+	0.715418i	−0.0386121	+	0.0512322i
$196$		0			0
$197$		−	17.5174i		−	1.24807i	−0.781398	−	0.624033i	$-0.785493\pi$
$197$		−	17.5174i		−	1.24807i	0.781398	−	0.624033i	$-0.214507\pi$
$198$	−1.31545	+	2.27842i	−0.0934849	+	0.161921i
$199$	−8.14896	−	14.1144i	−0.577664	−	1.00054i	−0.995747	−	0.0921346i	$-0.970631\pi$
$199$	−8.14896	−	14.1144i	−0.577664	−	1.00054i	0.418082	−	0.908409i	$-0.362702\pi$
$200$	12.7637	−	7.36910i	0.902527	−	0.521074i
$201$	−2.37135	−	1.36910i	−0.167262	−	0.0965690i
$202$		−	4.26406i		−	0.300018i
$203$		0			0
$204$	0.979481			0.0685774
$205$	−1.53919	+	2.66595i	−0.107502	+	0.186198i
$206$	−18.1812	+	10.4969i	−1.26675	+	0.731356i
$207$	−6.84017	−	11.8475i	−0.475425	−	0.823460i
$208$	−7.76711	+	3.29627i	−0.538552	+	0.228555i
$209$	3.59090			0.248388
$210$		0			0
$211$	2.70928			0.186514			0.0932571	−	0.995642i	$-0.470272\pi$
$211$	2.70928			0.186514			0.0932571	+	0.995642i	$0.470272\pi$
$212$	−0.514465	+	0.891079i	−0.0353336	+	0.0611996i
$213$	−5.96393	+	3.44327i	−0.408642	+	0.235929i
$214$	2.98364	−	1.72261i	0.203958	−	0.117755i
$215$	0.167033	+	0.0964364i	0.0113915	+	0.00657691i
$216$		−	9.47641i		−	0.644788i
$217$		0			0
$218$	9.86603			0.668212
$219$	−0.165069	−	0.0953027i	−0.0111543	−	0.00643996i
$220$	−0.120638	−	0.208951i	−0.00813342	−	0.0140875i
$221$	−1.26597	+	10.3042i	−0.0851581	+	0.693136i
$222$	3.00000	−	5.19615i	0.201347	−	0.348743i
$223$			19.7948i			1.32556i	0.748814	+	0.662780i	$0.230624\pi$
$223$			19.7948i			1.32556i	−0.748814	+	0.662780i	$0.769376\pi$
$224$		0			0
$225$	−12.9711			−0.864738
$226$	−12.9788	−	7.49333i	−0.863339	−	0.498449i
$227$	−11.4851	+	6.63090i	−0.762290	+	0.440108i	−0.830117	−	0.557589i	$-0.811727\pi$
$227$	−11.4851	+	6.63090i	−0.762290	+	0.440108i	0.0678276	+	0.997697i	$0.478393\pi$
$228$	−1.27468	+	0.735937i	−0.0844178	+	0.0487386i
$229$	24.0826	+	13.9041i	1.59142	+	0.918808i	0.993063	+	0.117579i	$0.0375134\pi$
$229$	24.0826	+	13.9041i	1.59142	+	0.918808i	0.598358	+	0.801229i	$0.295820\pi$
$230$	−2.72261			−0.179523
$231$		0			0
$232$			0.805905i			0.0529102i
$233$	−6.68342	+	11.5760i	−0.437845	+	0.758370i	−0.997523	−	0.0703401i	$-0.977592\pi$
$233$	−6.68342	+	11.5760i	−0.437845	+	0.758370i	0.559678	+	0.828710i	$0.310925\pi$
$234$	11.3446	+	1.39379i	0.741620	+	0.0911148i
$235$	−2.13090	−	3.69082i	−0.139004	−	0.240763i
$236$	1.52310	+	0.879362i	0.0991453	+	0.0572416i
$237$	1.51867			0.0986482
$238$		0			0
$239$			8.70701i			0.563210i	0.959530	+	0.281605i	$0.0908667\pi$
$239$			8.70701i			0.563210i	−0.959530	+	0.281605i	$0.909133\pi$
$240$	−0.503550	−	0.290725i	−0.0325040	−	0.0187662i
$241$	14.6627	−	8.46554i	0.944510	−	0.545313i	0.0531390	−	0.998587i	$-0.483077\pi$
$241$	14.6627	−	8.46554i	0.944510	−	0.545313i	0.891371	+	0.453274i	$0.149744\pi$
$242$	10.4486	−	6.03252i	0.671664	−	0.387785i
$243$	−6.36130	+	11.0181i	−0.408078	+	0.706811i
$244$	4.58145			0.293297
$245$		0			0
$246$	−4.21461			−0.268714
$247$	−6.09460	−	14.3609i	−0.387790	−	0.913764i
$248$	−10.4680	−	18.1311i	−0.664719	−	1.15133i
$249$	−4.84522	+	2.79739i	−0.307053	+	0.177277i
$250$	−2.63870	+	4.57036i	−0.166886	+	0.289055i
$251$	8.82150			0.556808			0.278404	−	0.960464i	$-0.410195\pi$
$251$	8.82150			0.556808			0.278404	+	0.960464i	$0.410195\pi$
$252$		0			0
$253$		−	4.19061i		−	0.263461i
$254$	−13.6475	−	7.87936i	−0.856317	−	0.494395i
$255$	−0.619571	+	0.357709i	−0.0387990	+	0.0224006i
$256$	6.73820	+	11.6709i	0.421138	+	0.729432i
$257$	−6.82211	+	11.8162i	−0.425552	+	0.737077i	−0.996472	−	0.0839284i	$-0.973253\pi$
$257$	−6.82211	+	11.8162i	−0.425552	+	0.737077i	0.570920	+	0.821006i	$0.306587\pi$
$258$			0.264063i			0.0164398i
$259$		0			0
$260$	−0.630898	+	0.837101i	−0.0391266	+	0.0519148i
$261$	0.354638	−	0.614250i	0.0219515	−	0.0380212i
$262$	−14.6315	+	8.44748i	−0.903935	+	0.521887i
$263$	6.08864	+	10.5458i	0.375441	+	0.650284i	0.990393	−	0.138281i	$-0.0441578\pi$
$263$	6.08864	+	10.5458i	0.375441	+	0.650284i	−0.614952	+	0.788565i	$0.710824\pi$
$264$	0.688756	−	1.19296i	0.0423900	−	0.0734217i
$265$		−	0.751536i		−	0.0461665i
$266$		0			0
$267$			2.92881i			0.179240i
$268$	−2.77469	−	1.60197i	−0.169491	−	0.0978558i
$269$	5.52359	+	9.56714i	0.336779	+	0.583319i	0.983825	−	0.179132i	$-0.0573291\pi$
$269$	5.52359	+	9.56714i	0.336779	+	0.583319i	−0.647046	+	0.762451i	$0.723996\pi$
$270$	0.829914	+	1.43745i	0.0505069	+	0.0874806i
$271$	−9.47085	−	5.46800i	−0.575313	−	0.332157i	0.183955	−	0.982935i	$-0.441110\pi$
$271$	−9.47085	−	5.46800i	−0.575313	−	0.332157i	−0.759269	+	0.650777i	$0.774443\pi$
$272$	−6.73820			−0.408564
$273$		0			0
$274$	−19.2267			−1.16153
$275$	−3.44101	−	1.98667i	−0.207501	−	0.119801i
$276$	0.858843	+	1.48756i	0.0516963	+	0.0895406i
$277$	−13.0597	−	22.6201i	−0.784682	−	1.35911i	−0.929189	−	0.369605i	$-0.879493\pi$
$277$	−13.0597	−	22.6201i	−0.784682	−	1.35911i	0.144507	−	0.989504i	$-0.453840\pi$
$278$	−13.3957	−	7.73400i	−0.803420	−	0.463854i
$279$			18.4257i			1.10312i
$280$		0			0
$281$		−	4.80325i		−	0.286538i	−0.989684	−	0.143269i	$-0.954239\pi$
$281$		−	4.80325i		−	0.286538i	0.989684	−	0.143269i	$-0.0457614\pi$
$282$	2.91742	−	5.05311i	0.173730	−	0.300909i
$283$	0.489741	+	0.848255i	0.0291121	+	0.0504236i	0.880214	−	0.474576i	$-0.157399\pi$
$283$	0.489741	+	0.848255i	0.0291121	+	0.0504236i	−0.851102	+	0.525000i	$0.824065\pi$
$284$	−6.97831	+	4.02893i	−0.414087	+	0.239073i
$285$	0.537533	−	0.931034i	0.0318407	−	0.0551497i
$286$	2.79606	+	2.10731i	0.165335	+	0.124608i
$287$		0			0
$288$		−	9.26180i		−	0.545757i
$289$	4.35464	−	7.54245i	0.256155	−	0.443674i
$290$	−0.0705785	−	0.122246i	−0.00414451	−	0.00717851i
$291$	5.88786	−	3.39936i	0.345153	−	0.199274i
$292$	−0.193145	−	0.111512i	−0.0113030	−	0.00652577i
$293$			24.3268i			1.42119i	0.703602	+	0.710595i	$0.251574\pi$
$293$			24.3268i			1.42119i	−0.703602	+	0.710595i	$0.748426\pi$
$294$		0			0
$295$	−1.28458			−0.0747912
$296$	14.6381	−	25.3539i	0.850821	−	1.47367i
$297$	−2.21251	+	1.27739i	−0.128383	+	0.0741219i
$298$	−11.9958	−	20.7773i	−0.694898	−	1.20360i
$299$	−16.7593	+	7.11244i	−0.969214	+	0.411323i
$300$	1.62863			0.0940290
$301$		0			0
$302$	1.86603			0.107378
$303$	0.982464	−	1.70168i	0.0564411	−	0.0977588i
$304$	8.76899	−	5.06278i	0.502936	−	0.290370i
$305$	−2.89799	+	1.67316i	−0.165939	+	0.0958047i
$306$	7.90493	+	4.56391i	0.451895	+	0.260902i
$307$		−	6.21953i		−	0.354968i	−0.984124	−	0.177484i	$-0.943204\pi$
$307$		−	6.21953i		−	0.354968i	0.984124	−	0.177484i	$-0.0567957\pi$
$308$		0			0
$309$	−9.67420			−0.550346
$310$	3.17573	+	1.83351i	0.180369	+	0.104136i
$311$	−12.5542	−	21.7445i	−0.711882	−	1.23302i	−0.964150	−	0.265358i	$-0.914510\pi$
$311$	−12.5542	−	21.7445i	−0.711882	−	1.23302i	0.252268	−	0.967657i	$-0.418824\pi$
$312$	−5.93993	−	0.729775i	−0.336282	−	0.0413154i
$313$	−1.12003	+	1.93994i	−0.0633077	+	0.109652i	−0.895942	−	0.444171i	$-0.853498\pi$
$313$	−1.12003	+	1.93994i	−0.0633077	+	0.109652i	0.832634	+	0.553823i	$0.186832\pi$
$314$		−	9.70928i		−	0.547926i
$315$		0			0
$316$	1.77698			0.0999627
$317$	−2.50711	−	1.44748i	−0.140813	−	0.0812986i	0.427938	−	0.903808i	$-0.359240\pi$
$317$	−2.50711	−	1.44748i	−0.140813	−	0.0812986i	−0.568752	+	0.822509i	$0.692573\pi$
$318$	0.891079	−	0.514465i	0.0499692	−	0.0288497i
$319$	0.188159	−	0.108634i	0.0105349	−	0.00608232i
$320$	−3.46410	−	2.00000i	−0.193649	−	0.111803i
$321$	1.58759			0.0886108
$322$		0			0
$323$		−	12.4585i		−	0.693212i
$324$	−2.04032	+	3.53394i	−0.113351	+	0.196330i
$325$	−2.10498	+	17.1333i	−0.116763	+	0.950385i
$326$	0.232866	+	0.403335i	0.0128972	+	0.0223387i
$327$	3.93728	+	2.27319i	0.217732	+	0.125708i
$328$	−20.5646			−1.13549
$329$		0			0
$330$			0.241276i			0.0132818i
$331$	−3.68550	−	2.12783i	−0.202574	−	0.116956i	0.395282	−	0.918560i	$-0.370647\pi$
$331$	−3.68550	−	2.12783i	−0.202574	−	0.116956i	−0.597855	+	0.801604i	$0.703980\pi$
$332$	−5.66933	+	3.27319i	−0.311145	+	0.179640i
$333$	−22.3139	+	12.8830i	−1.22280	+	0.705982i
$334$	−13.9655	+	24.1890i	−0.764160	+	1.32356i
$335$	2.34017			0.127857
$336$		0			0
$337$	−15.5464			−0.846865			−0.423433	−	0.905928i	$-0.639175\pi$
$337$	−15.5464			−0.846865			−0.423433	+	0.905928i	$0.639175\pi$
$338$	3.68207	−	14.7587i	0.200278	−	0.802770i
$339$	−3.45301	−	5.98079i	−0.187542	−	0.324832i
$340$	−0.724951	+	0.418551i	−0.0393160	+	0.0226991i
$341$	−2.82211	+	4.88805i	−0.152826	+	0.264702i
$342$	−13.7165			−0.741701
$343$		0			0
$344$			1.28846i			0.0694690i
$345$	−1.08652	−	0.627304i	−0.0584964	−	0.0337729i
$346$	−26.2450	+	15.1526i	−1.41094	+	0.814606i
$347$	10.1906	+	17.6506i	0.547060	+	0.947536i	0.998474	+	0.0552216i	$0.0175865\pi$
$347$	10.1906	+	17.6506i	0.547060	+	0.947536i	−0.451414	+	0.892315i	$0.649080\pi$
$348$	−0.0445278	+	0.0771245i	−0.00238694	+	0.00413431i
$349$		−	7.16394i		−	0.383477i	−0.981446	−	0.191739i	$-0.938587\pi$
$349$		−	7.16394i		−	0.383477i	0.981446	−	0.191739i	$-0.0614126\pi$
$350$		0			0
$351$	8.86376	+	6.68035i	0.473113	+	0.356570i
$352$	1.41855	−	2.45700i	0.0756090	−	0.130959i
$353$	4.66223	−	2.69174i	0.248145	−	0.143267i	−0.370769	−	0.928725i	$-0.620906\pi$
$353$	4.66223	−	2.69174i	0.248145	−	0.143267i	0.618915	+	0.785458i	$0.287573\pi$
$354$	−0.879362	−	1.52310i	−0.0467376	−	0.0809518i
$355$	2.94275	−	5.09700i	0.156185	−	0.270521i
$356$			3.42696i			0.181629i
$357$		0			0
$358$		−	24.1906i		−	1.27851i
$359$	−13.5911	−	7.84684i	−0.717312	−	0.414140i	0.0964505	−	0.995338i	$-0.469251\pi$
$359$	−13.5911	−	7.84684i	−0.717312	−	0.414140i	−0.813763	+	0.581197i	$0.802584\pi$
$360$	1.92162	+	3.32835i	0.101278	+	0.175419i
$361$	−0.139219	−	0.241135i	−0.00732733	−	0.0126913i
$362$	15.9259	+	9.19481i	0.837046	+	0.483269i
$363$	5.55971			0.291809
$364$		0			0
$365$	0.162899			0.00852650
$366$	−3.96765	−	2.29072i	−0.207392	−	0.119738i
$367$	−0.162287	−	0.281090i	−0.00847133	−	0.0146728i	0.861759	−	0.507318i	$-0.169363\pi$
$367$	−0.162287	−	0.281090i	−0.00847133	−	0.0146728i	−0.870230	+	0.492646i	$0.836030\pi$
$368$	−5.90829	−	10.2335i	−0.307991	−	0.533456i
$369$	15.6741	+	9.04945i	0.815961	+	0.471095i
$370$			5.12783i			0.266583i
$371$		0			0
$372$		−	2.31351i		−	0.119950i
$373$	12.6556	−	21.9202i	0.655283	−	1.13498i	−0.326539	−	0.945184i	$-0.605883\pi$
$373$	12.6556	−	21.9202i	0.655283	−	1.13498i	0.981823	−	0.189800i	$-0.0607841\pi$
$374$	1.39803	+	2.42146i	0.0722905	+	0.125211i
$375$	−2.10607	+	1.21594i	−0.108757	+	0.0627909i
$376$	14.2351	−	24.6560i	0.734121	−	1.27153i
$377$	−0.753803	−	0.568118i	−0.0388228	−	0.0292596i
$378$		0			0
$379$			16.7187i			0.858784i	0.903118	+	0.429392i	$0.141272\pi$
$379$			16.7187i			0.858784i	−0.903118	+	0.429392i	$0.858728\pi$
$380$	0.628960	−	1.08939i	0.0322650	−	0.0558845i
$381$	−3.63090	−	6.28890i	−0.186017	−	0.322190i
$382$	−17.0113	+	9.82150i	−0.870376	+	0.502512i
$383$	11.3994	+	6.58145i	0.582482	+	0.336296i	0.762119	−	0.647437i	$-0.224159\pi$
$383$	11.3994	+	6.58145i	0.582482	+	0.336296i	−0.179637	+	0.983733i	$0.557492\pi$
$384$		−	1.78992i		−	0.0913415i
$385$		0			0
$386$	23.4186			1.19197
$387$	0.566985	−	0.982046i	0.0288214	−	0.0499202i
$388$	6.88931	−	3.97754i	0.349752	−	0.201929i
$389$	−5.03806	−	8.72617i	−0.255440	−	0.442434i	0.709575	−	0.704630i	$-0.248887\pi$
$389$	−5.03806	−	8.72617i	−0.255440	−	0.442434i	−0.965015	+	0.262195i	$0.915554\pi$
$390$	0.964924	−	0.409502i	0.0488608	−	0.0207360i
$391$	−14.5392			−0.735278
$392$		0			0
$393$	−7.78539			−0.392721
$394$	−10.2485	+	17.7509i	−0.516310	+	0.894275i
$395$	−1.12403	+	0.648956i	−0.0565558	+	0.0326525i
$396$	−1.22850	+	0.709275i	−0.0617345	+	0.0356424i
$397$	−6.98986	−	4.03559i	−0.350811	−	0.202541i	0.314232	−	0.949346i	$-0.398253\pi$
$397$	−6.98986	−	4.03559i	−0.350811	−	0.202541i	−0.665042	+	0.746806i	$0.731587\pi$
$398$			19.0700i			0.955891i
$399$		0			0
$400$	−11.2039			−0.560197
$401$	−11.1173	−	6.41855i	−0.555169	−	0.320527i	0.196035	−	0.980597i	$-0.437193\pi$
$401$	−11.1173	−	6.41855i	−0.555169	−	0.320527i	−0.751204	+	0.660070i	$0.770527\pi$
$402$	1.60197	+	2.77469i	0.0798989	+	0.138389i
$403$	24.3383	+	2.99018i	1.21238	+	0.148952i
$404$	1.14957	−	1.99111i	0.0571931	−	0.0990614i
$405$		−	2.98053i		−	0.148104i
$406$		0			0
$407$	−7.89269			−0.391226
$408$	−4.13895	−	2.38962i	−0.204908	−	0.118304i
$409$	16.2393	−	9.37577i	0.802982	−	0.463602i	−0.0415308	−	0.999137i	$-0.513223\pi$
$409$	16.2393	−	9.37577i	0.802982	−	0.463602i	0.844513	+	0.535535i	$0.179890\pi$
$410$	3.11940	−	1.80098i	0.154056	−	0.0889443i
$411$	−7.67289	−	4.42994i	−0.378476	−	0.218513i
$412$	−11.3197			−0.557679
$413$		0			0
$414$			16.0072i			0.786710i
$415$	2.39076	−	4.14091i	0.117358	−	0.203269i
$416$	−12.2338	−	1.50303i	−0.599810	−	0.0736922i
$417$	−3.56391	−	6.17288i	−0.174526	−	0.302287i
$418$	−3.63875	−	2.10083i	−0.177977	−	0.102755i
$419$	23.6319			1.15450			0.577248	−	0.816569i	$-0.304127\pi$
$419$	23.6319			1.15450			0.577248	+	0.816569i	$0.304127\pi$
$420$		0			0
$421$			19.4524i			0.948052i	0.880511	+	0.474026i	$0.157200\pi$
$421$			19.4524i			0.948052i	−0.880511	+	0.474026i	$0.842800\pi$
$422$	−2.74538	−	1.58504i	−0.133643	−	0.0771587i
$423$	−21.6997	+	12.5283i	−1.05507	+	0.609148i
$424$	4.34790	−	2.51026i	0.211153	−	0.121909i
$425$	−6.89269	+	11.9385i	−0.334345	+	0.579102i
$426$	8.05786			0.390405
$427$		0			0
$428$	1.85762			0.0897915
$429$	0.630301	+	1.48520i	0.0304312	+	0.0717062i
$430$	−0.112839	−	0.195443i	−0.00544158	−	0.00942509i
$431$	15.6741	−	9.04945i	0.754995	−	0.435897i	−0.0725009	−	0.997368i	$-0.523098\pi$
$431$	15.6741	−	9.04945i	0.754995	−	0.435897i	0.827496	+	0.561472i	$0.189765\pi$
$432$	−3.60197	+	6.23879i	−0.173300	+	0.300164i
$433$	−20.5380			−0.986992			−0.493496	−	0.869748i	$-0.664281\pi$
$433$	−20.5380			−0.986992			−0.493496	+	0.869748i	$0.664281\pi$
$434$		0			0
$435$		−	0.0650468i		−	0.00311875i
$436$	4.60696	+	2.65983i	0.220633	+	0.127383i
$437$	18.9211	−	10.9241i	0.905117	−	0.522570i
$438$	0.111512	+	0.193145i	0.00532827	+	0.00922883i
$439$	−13.4813	+	23.3503i	−0.643429	+	1.11445i	0.341233	+	0.939979i	$0.389155\pi$
$439$	−13.4813	+	23.3503i	−0.643429	+	1.11445i	−0.984662	+	0.174473i	$0.944178\pi$
$440$			1.17727i			0.0561244i
$441$		0			0
$442$	7.31124	−	9.70086i	0.347760	−	0.461423i
$443$	−13.2051	+	22.8719i	−0.627392	+	1.08667i	0.360681	+	0.932689i	$0.382544\pi$
$443$	−13.2051	+	22.8719i	−0.627392	+	1.08667i	−0.988073	+	0.153985i	$0.950789\pi$
$444$	2.80171	−	1.61757i	0.132963	−	0.0767663i
$445$	−1.25154	−	2.16772i	−0.0593285	−	0.102760i
$446$	11.5808	−	20.0586i	0.548369	−	0.949802i
$447$		−	11.0556i		−	0.522912i
$448$		0			0
$449$			31.4329i			1.48341i	0.670725	+	0.741706i	$0.265983\pi$
$449$			31.4329i			1.48341i	−0.670725	+	0.741706i	$0.734017\pi$
$450$	13.1439	+	7.58864i	0.619610	+	0.357732i
$451$	2.77205	+	4.80134i	0.130531	+	0.226086i
$452$	−4.04032	−	6.99804i	−0.190041	−	0.329160i
$453$	0.744685	+	0.429944i	0.0349883	+	0.0202005i
$454$	15.5174			0.728270
$455$		0			0
$456$	7.18181			0.336319
$457$	15.6448	+	9.03252i	0.731832	+	0.422524i	0.819092	−	0.573662i	$-0.194478\pi$
$457$	15.6448	+	9.03252i	0.731832	+	0.422524i	−0.0872598	+	0.996186i	$0.527811\pi$
$458$	−16.2690	−	28.1787i	−0.760200	−	1.31670i
$459$	4.43188	+	7.67624i	0.206863	+	0.358296i
$460$	−1.27132	−	0.734000i	−0.0592758	−	0.0342229i
$461$		−	23.0784i		−	1.07487i	−0.843306	−	0.537434i	$-0.819394\pi$
$461$		−	23.0784i		−	1.07487i	0.843306	−	0.537434i	$-0.180606\pi$
$462$		0			0
$463$			4.54760i			0.211345i	0.994401	+	0.105672i	$0.0336995\pi$
$463$			4.54760i			0.211345i	−0.994401	+	0.105672i	$0.966301\pi$
$464$	0.306323	−	0.530567i	0.0142207	−	0.0246310i
$465$	0.844901	+	1.46341i	0.0391813	+	0.0678641i
$466$	13.5449	−	7.82018i	0.627457	−	0.362263i
$467$	18.9077	−	32.7491i	0.874943	−	1.51545i	0.0181197	−	0.999836i	$-0.494232\pi$
$467$	18.9077	−	32.7491i	0.874943	−	1.51545i	0.856823	−	0.515610i	$-0.172435\pi$
$468$	4.92162	+	3.70928i	0.227502	+	0.171461i
$469$		0			0
$470$			4.98667i			0.230018i
$471$	2.23707	−	3.87472i	0.103079	−	0.178538i
$472$	−4.29072	−	7.43175i	−0.197497	−	0.342074i
$473$	0.300823	−	0.173680i	0.0138319	−	0.00798584i
$474$	−1.53891	−	0.888488i	−0.0706843	−	0.0408096i
$475$		−	20.7154i		−	0.950489i
$476$		0			0
$477$	−4.41855			−0.202312
$478$	5.09398	−	8.82303i	0.232993	−	0.403556i
$479$	8.00212	−	4.62003i	0.365626	−	0.211094i	−0.305920	−	0.952057i	$-0.598964\pi$
$479$	8.00212	−	4.62003i	0.365626	−	0.211094i	0.671546	+	0.740963i	$0.265631\pi$
$480$	−0.424694	−	0.735591i	−0.0193845	−	0.0335750i
$481$	13.3957	+	31.5648i	0.610793	+	1.43923i
$482$	−19.8108			−0.902358
$483$		0			0
$484$	6.50534			0.295697
$485$	−2.90522	+	5.03199i	−0.131919	+	0.228491i
$486$	12.8921	−	7.44327i	0.584799	−	0.337634i
$487$	11.8298	−	6.82991i	0.536057	−	0.309493i	−0.207422	−	0.978252i	$-0.566507\pi$
$487$	11.8298	−	6.82991i	0.536057	−	0.309493i	0.743480	+	0.668759i	$0.233174\pi$
$488$	−19.3596	−	11.1773i	−0.876368	−	0.505971i
$489$			0.214614i			0.00970519i
$490$		0			0
$491$	29.6514			1.33815			0.669075	−	0.743195i	$-0.266691\pi$
$491$	29.6514			1.33815			0.669075	+	0.743195i	$0.266691\pi$
$492$	−1.96802	−	1.13624i	−0.0887252	−	0.0512255i
$493$	−0.376902	−	0.652813i	−0.0169748	−	0.0294012i
$494$	−2.22595	+	18.1179i	−0.100150	+	0.815162i
$495$	0.518059	−	0.897304i	0.0232850	−	0.0403308i
$496$			15.9155i			0.714626i
$497$		0			0
$498$	6.54638			0.293350
$499$	30.7652	+	17.7623i	1.37724	+	0.795151i	0.991827	−	0.127593i	$-0.0407251\pi$
$499$	30.7652	+	17.7623i	1.37724	+	0.795151i	0.385415	+	0.922744i	$0.374058\pi$
$500$	−2.46429	+	1.42276i	−0.110206	+	0.0636276i
$501$	−11.1466	+	6.43548i	−0.497992	+	0.287516i
$502$	−8.93905	−	5.16096i	−0.398969	−	0.230345i
$503$	34.4124			1.53437			0.767187	−	0.641424i	$-0.221656\pi$
$503$	34.4124			1.53437			0.767187	+	0.641424i	$0.221656\pi$
$504$		0			0
$505$			1.67930i			0.0747279i
$506$	−2.45169	+	4.24644i	−0.108991	+	0.188777i
$507$	4.86992	−	5.04146i	0.216281	−	0.223899i
$508$	−4.24846	−	7.35856i	−0.188495	−	0.326483i
$509$	9.62879	+	5.55919i	0.426789	+	0.246407i	0.697978	−	0.716120i	$-0.254083\pi$
$509$	9.62879	+	5.55919i	0.426789	+	0.246407i	−0.271189	+	0.962526i	$0.587417\pi$
$510$	0.837101			0.0370675
$511$		0			0
$512$		−	22.4079i		−	0.990297i
$513$	−11.5352	−	6.65983i	−0.509290	−	0.294039i
$514$	13.8260	−	7.98246i	0.609840	−	0.352091i
$515$	7.16024	−	4.13397i	0.315518	−	0.182164i
$516$	−0.0711898	+	0.123304i	−0.00313396	+	0.00542817i
$517$	−7.67543			−0.337565
$518$		0			0
$519$	−13.9649			−0.612992
$520$	4.70821	−	1.99811i	0.206469	−	0.0876229i
$521$	8.94441	+	15.4922i	0.391862	+	0.678724i	0.992695	−	0.120650i	$-0.0384979\pi$
$521$	8.94441	+	15.4922i	0.391862	+	0.678724i	−0.600833	+	0.799374i	$0.705165\pi$
$522$	−0.718726	+	0.414957i	−0.0314578	+	0.0181622i
$523$	11.9939	−	20.7740i	0.524455	−	0.908382i	−0.475140	−	0.879910i	$-0.657603\pi$
$523$	11.9939	−	20.7740i	0.524455	−	0.908382i	0.999595	−	0.0284720i	$-0.00906413\pi$
$524$	−9.10957			−0.397954
$525$		0			0
$526$		−	14.2485i		−	0.621263i
$527$	16.9589	+	9.79125i	0.738743	+	0.426513i
$528$	−0.906885	+	0.523590i	−0.0394671	+	0.0227863i
$529$	−1.24846	−	2.16240i	−0.0542811	−	0.0940175i
$530$	−0.439681	+	0.761550i	−0.0190985	+	0.0330796i
$531$			7.55252i			0.327751i
$532$		0			0
$533$	14.4969	−	19.2351i	0.627932	−	0.833166i
$534$	1.71348	−	2.96784i	0.0741496	−	0.128431i
$535$	−1.17504	+	0.678408i	−0.0508013	+	0.0293301i
$536$	7.81658	+	13.5387i	0.337625	+	0.584784i
$537$	5.57365	−	9.65385i	0.240521	−	0.416594i
$538$		−	12.9262i		−	0.557286i
$539$		0			0
$540$			0.894960i			0.0385130i
$541$	16.8107	+	9.70568i	0.722750	+	0.417280i	0.815764	−	0.578385i	$-0.196317\pi$
$541$	16.8107	+	9.70568i	0.722750	+	0.417280i	−0.0930141	+	0.995665i	$0.529650\pi$
$542$	6.39803	+	11.0817i	0.274819	+	0.476000i
$543$	4.23707	+	7.33882i	0.181830	+	0.314939i
$544$	−8.52450	−	4.92162i	−0.365485	−	0.211013i
$545$	−3.88550			−0.166437
$546$		0			0
$547$	−1.81432			−0.0775745			−0.0387873	−	0.999247i	$-0.512349\pi$
$547$	−1.81432			−0.0775745			−0.0387873	+	0.999247i	$0.512349\pi$
$548$	−8.97794	−	5.18342i	−0.383519	−	0.221425i
$549$	9.83710	+	17.0384i	0.419837	+	0.727179i
$550$	2.32457	+	4.02628i	0.0991202	+	0.171681i
$551$	0.980987	+	0.566373i	0.0417915	+	0.0241283i
$552$		−	8.38121i		−	0.356728i
$553$		0			0
$554$			30.5620i			1.29845i
$555$	−1.18148	+	2.04638i	−0.0501510	+	0.0868641i
$556$	−4.17009	−	7.22280i	−0.176851	−	0.306315i
$557$	20.2811	−	11.7093i	0.859336	−	0.496138i	−0.00445382	−	0.999990i	$-0.501418\pi$
$557$	20.2811	−	11.7093i	0.859336	−	0.496138i	0.863790	+	0.503852i	$0.168084\pi$
$558$	10.7799	−	18.6713i	0.456348	−	0.790417i
$559$	−1.20516	−	0.908291i	−0.0509728	−	0.0384166i
$560$		0			0
$561$			1.28846i			0.0543987i
$562$	−2.81011	+	4.86725i	−0.118537	+	0.205313i
$563$	13.3474	+	23.1183i	0.562524	+	0.974320i	0.997275	+	0.0737698i	$0.0235030\pi$
$563$	13.3474	+	23.1183i	0.562524	+	0.974320i	−0.434751	+	0.900551i	$0.643164\pi$
$564$	2.72458	−	1.57304i	0.114726	−	0.0662369i
$565$	5.11141	+	2.95107i	0.215039	+	0.124153i
$566$		−	1.14608i		−	0.0481732i
$567$		0			0
$568$	39.3172			1.64971
$569$	−13.2948	+	23.0273i	−0.557349	+	0.965356i	0.440368	+	0.897817i	$0.354848\pi$
$569$	−13.2948	+	23.0273i	−0.557349	+	0.965356i	−0.997717	+	0.0675389i	$0.978485\pi$
$570$	−1.08939	+	0.628960i	−0.0456295	+	0.0263442i
$571$	−1.71655	−	2.97316i	−0.0718355	−	0.124423i	0.827870	−	0.560920i	$-0.189552\pi$
$571$	−1.71655	−	2.97316i	−0.0718355	−	0.124423i	−0.899706	+	0.436497i	$0.856219\pi$
$572$	0.737507	+	1.73781i	0.0308367	+	0.0726616i
$573$	−9.05172			−0.378141
$574$		0			0
$575$	−24.1750			−1.00817
$576$	−11.7587	+	20.3667i	−0.489947	+	0.848613i
$577$	−26.3841	+	15.2329i	−1.09838	+	0.634153i	−0.935796	−	0.352542i	$-0.885318\pi$
$577$	−26.3841	+	15.2329i	−1.09838	+	0.634153i	−0.162588	+	0.986694i	$0.551984\pi$
$578$	−8.82532	+	5.09530i	−0.367085	+	0.211937i
$579$	9.34574	+	5.39576i	0.388396	+	0.224240i
$580$		−	0.0761103i		−	0.00316031i
$581$		0			0
$582$	−7.95509			−0.329749
$583$	−1.17217	−	0.676752i	−0.0485463	−	0.0280282i
$584$	0.544109	+	0.942425i	0.0225154	+	0.0389978i
$585$	−4.46781	−	0.548911i	−0.184721	−	0.0226947i
$586$	14.2323	−	24.6510i	0.587929	−	1.01832i
$587$		−	26.2606i		−	1.08389i	−0.840414	−	0.541945i	$-0.817688\pi$
$587$		−	26.2606i		−	1.08389i	0.840414	−	0.541945i	$-0.182312\pi$
$588$		0			0
$589$	−29.4268			−1.21251
$590$	1.30170	+	0.751536i	0.0535901	+	0.0309402i
$591$	−8.17979	+	4.72261i	−0.336472	+	0.194262i
$592$	−19.2740	+	11.1278i	−0.792155	+	0.457351i
$593$	−35.3702	−	20.4210i	−1.45248	−	0.838590i	−0.453859	−	0.891073i	$-0.649953\pi$
$593$	−35.3702	−	20.4210i	−1.45248	−	0.838590i	−0.998622	+	0.0524829i	$0.983286\pi$
$594$	2.98932			0.122653
$595$		0			0
$596$		−	12.9360i		−	0.529879i
$597$	−4.39383	+	7.61033i	−0.179827	+	0.311470i
$598$	21.1437	+	2.59769i	0.864629	+	0.106228i
$599$	13.6773	+	23.6897i	0.558838	+	0.967936i	0.997594	+	0.0693298i	$0.0220861\pi$
$599$	13.6773	+	23.6897i	0.558838	+	0.967936i	−0.438756	+	0.898606i	$0.644581\pi$
$600$	−6.88202	−	3.97334i	−0.280957	−	0.162211i
$601$	25.4908			1.03979			0.519895	−	0.854230i	$-0.325971\pi$
$601$	25.4908			1.03979			0.519895	+	0.854230i	$0.325971\pi$
$602$		0			0
$603$		−	13.7587i		−	0.560299i
$604$	0.871345	+	0.503072i	0.0354545	+	0.0204697i
$605$	−4.11495	+	2.37577i	−0.167297	+	0.0965887i
$606$	−1.99111	+	1.14957i	−0.0808833	+	0.0466980i
$607$	−9.96554	+	17.2608i	−0.404489	+	0.700595i	−0.994262	−	0.106974i	$-0.965884\pi$
$607$	−9.96554	+	17.2608i	−0.404489	+	0.700595i	0.589773	+	0.807569i	$0.299217\pi$
$608$	14.7915			0.599876
$609$		0			0
$610$	3.91548			0.158533
$611$	13.0270	+	30.6959i	0.527016	+	1.24182i
$612$	2.46081	+	4.26225i	0.0994724	+	0.172291i
$613$	−19.6773	+	11.3607i	−0.794758	+	0.458854i	−0.841635	−	0.540047i	$-0.818407\pi$
$613$	−19.6773	+	11.3607i	−0.794758	+	0.458854i	0.0468766	+	0.998901i	$0.485073\pi$
$614$	−3.63870	+	6.30241i	−0.146846	+	0.254344i
$615$	1.65983			0.0669307
$616$		0			0
$617$			14.3545i			0.577892i	0.957345	+	0.288946i	$0.0933049\pi$
$617$			14.3545i			0.577892i	−0.957345	+	0.288946i	$0.906695\pi$
$618$	9.80311	+	5.65983i	0.394339	+	0.227672i
$619$	24.2341	−	13.9916i	0.974052	−	0.562369i	0.0735832	−	0.997289i	$-0.476557\pi$
$619$	24.2341	−	13.9916i	0.974052	−	0.562369i	0.900469	+	0.434920i	$0.143223\pi$
$620$	0.988607	+	1.71232i	0.0397034	+	0.0687683i
$621$	−7.77205	+	13.4616i	−0.311882	+	0.540195i
$622$			29.3789i			1.17799i
$623$		0			0
$624$	3.63317	+	2.73820i	0.145443	+	0.109616i
$625$	−10.9299	+	18.9312i	−0.437198	+	0.757249i
$626$	2.26990	−	1.31053i	0.0907235	−	0.0523792i
$627$	−0.968088	−	1.67678i	−0.0386617	−	0.0669640i
$628$	2.61757	−	4.53376i	0.104452	−	0.180917i
$629$			27.3835i			1.09185i
$630$		0			0
$631$		−	21.4186i		−	0.852659i	−0.904568	−	0.426330i	$-0.859806\pi$
$631$		−	21.4186i		−	0.852659i	0.904568	−	0.426330i	$-0.140194\pi$
$632$	−7.50888	−	4.33525i	−0.298687	−	0.172447i
$633$	−0.730406	−	1.26510i	−0.0290310	−	0.0502832i
$634$	1.69368	+	2.93353i	0.0672645	+	0.116506i
$635$	5.37473	+	3.10310i	0.213290	+	0.123143i
$636$	0.554787			0.0219987
$637$		0			0
$638$	−0.254222			−0.0100647
$639$	−29.9671	−	17.3015i	−1.18548	−	0.684437i
$640$	0.764867	+	1.32479i	0.0302340	+	0.0523668i
$641$	−18.9680	−	32.8535i	−0.749191	−	1.29764i	−0.948211	−	0.317641i	$-0.897109\pi$
$641$	−18.9680	−	32.8535i	−0.749191	−	1.29764i	0.199020	−	0.979995i	$-0.436224\pi$
$642$	−1.60875	−	0.928810i	−0.0634922	−	0.0366572i
$643$		−	36.2122i		−	1.42807i	−0.700111	−	0.714034i	$-0.746866\pi$
$643$		−	36.2122i		−	1.42807i	0.700111	−	0.714034i	$-0.253134\pi$
$644$		0			0
$645$		−	0.103995i		−	0.00409479i
$646$	−7.28879	+	12.6245i	−0.286773	+	0.496706i
$647$	21.3974	+	37.0614i	0.841219	+	1.45703i	0.888864	+	0.458170i	$0.151495\pi$
$647$	21.3974	+	37.0614i	0.841219	+	1.45703i	−0.0476450	+	0.998864i	$0.515172\pi$
$648$	17.2434	−	9.95547i	0.677384	−	0.391088i
$649$	−1.15676	+	2.00356i	−0.0454066	+	0.0786466i
$650$	12.1568	−	16.1301i	0.476827	−	0.632674i
$651$		0			0
$652$			0.251117i			0.00983451i
$653$	−2.77432	+	4.80527i	−0.108568	+	0.188045i	−0.915190	−	0.403022i	$-0.867960\pi$
$653$	−2.77432	+	4.80527i	−0.108568	+	0.188045i	0.806623	+	0.591067i	$0.201293\pi$
$654$	−2.65983	−	4.60696i	−0.104007	−	0.180146i
$655$	5.76226	−	3.32684i	0.225150	−	0.129990i
$656$	13.5387	+	7.81658i	0.528598	+	0.305186i
$657$		−	0.957740i		−	0.0373650i
$658$		0			0
$659$	−23.1529			−0.901908			−0.450954	−	0.892547i	$-0.648916\pi$
$659$	−23.1529			−0.901908			−0.450954	+	0.892547i	$0.648916\pi$
$660$	−0.0650468	+	0.112664i	−0.00253194	+	0.00438545i
$661$	40.9235	−	23.6272i	1.59174	−	0.918992i	0.598733	−	0.800949i	$-0.295671\pi$
$661$	40.9235	−	23.6272i	1.59174	−	0.918992i	0.993008	−	0.118043i	$-0.0376621\pi$
$662$	2.48974	+	4.31236i	0.0967665	+	0.167605i
$663$	5.15286	−	2.18681i	0.200121	−	0.0849288i
$664$	31.9421			1.23960
$665$		0			0
$666$	30.1483			1.16822
$667$	0.660961	−	1.14482i	0.0255925	−	0.0443275i
$668$	−13.0425	+	7.53006i	−0.504628	+	0.291347i
$669$	9.24323	−	5.33658i	0.357364	−	0.206324i
$670$	−2.37135	−	1.36910i	−0.0916134	−	0.0528930i
$671$			6.02666i			0.232657i
$672$		0			0
$673$	3.42082			0.131863			0.0659314	−	0.997824i	$-0.478998\pi$
$673$	3.42082			0.131863			0.0659314	+	0.997824i	$0.478998\pi$
$674$	15.7535	+	9.09530i	0.606803	+	0.350338i
$675$	7.36910	+	12.7637i	0.283637	+	0.491273i
$676$	5.69822	−	5.89895i	0.219162	−	0.226883i
$677$	−5.34797	+	9.26296i	−0.205539	+	0.356004i	−0.950304	−	0.311322i	$-0.899228\pi$
$677$	−5.34797	+	9.26296i	−0.205539	+	0.356004i	0.744765	+	0.667327i	$0.232561\pi$
$678$			8.08065i			0.310335i
$679$		0			0
$680$	4.08452			0.156634
$681$	6.19261	+	3.57531i	0.237301	+	0.137006i
$682$	5.71944	−	3.30212i	0.219009	−	0.126445i
$683$	5.71215	−	3.29791i	0.218569	−	0.126191i	−0.386718	−	0.922198i	$-0.626391\pi$
$683$	5.71215	−	3.29791i	0.218569	−	0.126191i	0.605288	+	0.796007i	$0.293058\pi$
$684$	−6.40492	−	3.69788i	−0.244898	−	0.141392i
$685$	7.57199			0.289311
$686$		0			0
$687$		−	14.9939i		−	0.572051i
$688$	0.489741	−	0.848255i	0.0186712	−	0.0323394i
$689$	−0.717055	+	5.83640i	−0.0273176	+	0.222349i
$690$	0.734000	+	1.27132i	0.0279429	+	0.0483985i
$691$	−42.8448	−	24.7365i	−1.62989	−	0.941019i	−0.984123	−	0.177487i	$-0.943203\pi$
$691$	−42.8448	−	24.7365i	−1.62989	−	0.941019i	−0.645770	−	0.763532i	$-0.723464\pi$
$692$	−16.3402			−0.621160
$693$		0			0
$694$		−	23.8478i		−	0.905249i
$695$	5.27557	+	3.04585i	0.200114	+	0.115536i
$696$	0.376318	−	0.217267i	0.0142643	−	0.00823550i
$697$	16.6581	−	9.61757i	0.630971	−	0.364291i
$698$	−4.19122	+	7.25940i	−0.158640	+	0.274772i
$699$	7.20725			0.272603
$700$		0			0
$701$	−20.8166			−0.786231			−0.393116	−	0.919489i	$-0.628603\pi$
$701$	−20.8166			−0.786231			−0.393116	+	0.919489i	$0.628603\pi$
$702$	−5.07358	−	11.9550i	−0.191490	−	0.451214i
$703$	−20.5747	−	35.6364i	−0.775989	−	1.34405i
$704$	−6.23879	+	3.60197i	−0.235133	+	0.135754i
$705$	−1.14896	+	1.99005i	−0.0432722	+	0.0749496i
$706$	−6.29914			−0.237071
$707$		0			0
$708$		−	0.948284i		−	0.0356387i
$709$	−5.15620	−	2.97693i	−0.193645	−	0.111801i	0.400043	−	0.916496i	$-0.368995\pi$
$709$	−5.15620	−	2.97693i	−0.193645	−	0.111801i	−0.593688	+	0.804695i	$0.702329\pi$
$710$	−5.96393	+	3.44327i	−0.223822	+	0.129224i
$711$	3.81545	+	6.60855i	0.143091	+	0.247840i
$712$	8.36069	−	14.4811i	0.313330	−	0.542704i
$713$			34.3412i			1.28609i
$714$		0			0
$715$	−1.10116	−	0.829914i	−0.0411812	−	0.0310370i
$716$	6.52165	−	11.2958i	0.243726	−	0.422145i
$717$	4.06575	−	2.34736i	0.151838	−	0.0876638i
$718$	9.18148	+	15.9028i	0.342650	+	0.593487i
$719$	−0.844901	+	1.46341i	−0.0315095	+	0.0545760i	−0.881350	−	0.472464i	$-0.843365\pi$
$719$	−0.844901	+	1.46341i	−0.0315095	+	0.0545760i	0.849841	+	0.527040i	$0.176698\pi$
$720$		−	2.92162i		−	0.108882i
$721$		0			0
$722$			0.325797i			0.0121249i
$723$	−7.90599	−	4.56452i	−0.294027	−	0.169756i
$724$	4.95774	+	8.58706i	0.184253	+	0.319135i
$725$	−0.626692	−	1.08546i	−0.0232748	−	0.0403131i
$726$	−5.63379	−	3.25267i	−0.209090	−	0.120718i
$727$	−14.0722			−0.521910			−0.260955	−	0.965351i	$-0.584037\pi$
$727$	−14.0722			−0.521910			−0.260955	+	0.965351i	$0.584037\pi$
$728$		0			0
$729$	−12.5441			−0.464597
$730$	−0.165069	−	0.0953027i	−0.00610948	−	0.00352731i
$731$	−0.602579	−	1.04370i	−0.0222872	−	0.0386026i
$732$	−1.23513	−	2.13931i	−0.0456518	−	0.0790713i
$733$	−9.46659	−	5.46554i	−0.349657	−	0.201874i	0.314877	−	0.949132i	$-0.398037\pi$
$733$	−9.46659	−	5.46554i	−0.349657	−	0.201874i	−0.664534	+	0.747258i	$0.731370\pi$
$734$			0.379780i			0.0140179i
$735$		0			0
$736$		−	17.2618i		−	0.636278i
$737$	2.10731	−	3.64996i	0.0776237	−	0.134448i
$738$	−10.5886	−	18.3401i	−0.389773	−	0.675107i
$739$	−2.74538	+	1.58504i	−0.100990	+	0.0583068i	−0.549644	−	0.835399i	$-0.685237\pi$
$739$	−2.74538	+	1.58504i	−0.100990	+	0.0583068i	0.448654	+	0.893705i	$0.351903\pi$
$740$	−1.38243	+	2.39444i	−0.0508193	+	0.0880215i
$741$	−5.06278	+	6.71751i	−0.185986	+	0.246774i
$742$		0			0
$743$		−	9.73206i		−	0.357035i	−0.983937	−	0.178517i	$-0.942870\pi$
$743$		−	9.73206i		−	0.357035i	0.983937	−	0.178517i	$-0.0571301\pi$
$744$	−5.64423	+	9.77609i	−0.206927	+	0.358409i
$745$	4.72426	+	8.18266i	0.173084	+	0.299790i
$746$	−25.6485	+	14.8082i	−0.939059	+	0.542166i
$747$	−24.3459	−	14.0561i	−0.890770	−	0.514286i
$748$			1.50761i			0.0551235i
$749$		0			0
$750$	2.84551			0.103903
$751$	3.88962	−	6.73702i	0.141934	−	0.245837i	−0.786291	−	0.617857i	$-0.788001\pi$
$751$	3.88962	−	6.73702i	0.141934	−	0.245837i	0.928225	+	0.372019i	$0.121334\pi$
$752$	−18.7434	+	10.8215i	−0.683501	+	0.394620i
$753$	−2.37823	−	4.11921i	−0.0866675	−	0.150112i
$754$	0.431474	+	1.01670i	0.0157133	+	0.0370259i
$755$	−0.734892			−0.0267455
$756$		0			0
$757$	10.8576			0.394627			0.197313	−	0.980340i	$-0.436778\pi$
$757$	10.8576			0.394627			0.197313	+	0.980340i	$0.436778\pi$
$758$	9.78118	−	16.9415i	0.355268	−	0.615343i
$759$	−1.95681	+	1.12976i	−0.0710276	+	0.0410078i
$760$	−5.31553	+	3.06892i	−0.192815	+	0.111322i
$761$	−1.57747	−	0.910752i	−0.0571832	−	0.0330147i	0.471136	−	0.882061i	$-0.343844\pi$
$761$	−1.57747	−	0.910752i	−0.0571832	−	0.0330147i	−0.528319	+	0.849046i	$0.677177\pi$
$762$			8.49693i			0.307811i
$763$		0			0
$764$	−10.5913			−0.383179
$765$	−3.11317	−	1.79739i	−0.112557	−	0.0649848i
$766$	−7.70086	−	13.3383i	−0.278244	−	0.481932i
$767$	9.97602	+	1.22564i	0.360213	+	0.0442555i
$768$	3.63317	−	6.29283i	0.131101	−	0.227073i
$769$		−	39.7948i		−	1.43504i	−0.696539	−	0.717519i	$-0.745277\pi$
$769$		−	39.7948i		−	1.43504i	0.696539	−	0.717519i	$-0.254723\pi$
$770$		0			0
$771$	7.35682			0.264949
$772$	10.9353	+	6.31351i	0.393571	+	0.227228i
$773$	−15.8600	+	9.15676i	−0.570443	+	0.329346i	−0.757326	−	0.653037i	$-0.773495\pi$
$773$	−15.8600	+	9.15676i	−0.570443	+	0.329346i	0.186883	+	0.982382i	$0.440161\pi$
$774$	−1.14908	+	0.663421i	−0.0413028	+	0.0238462i
$775$	28.1984	+	16.2804i	1.01292	+	0.584808i
$776$	−38.8157			−1.39340
$777$		0			0
$778$			11.7899i			0.422689i
$779$	−14.4524	+	25.0323i	−0.517811	+	0.896875i
$780$	0.560972	+	0.0689205i	0.0200860	+	0.00246775i
$781$	−5.29985	−	9.17961i	−0.189644	−	0.328472i
$782$	14.7329	+	8.50605i	0.526848	+	0.304176i
$783$	−0.805905			−0.0288007
$784$		0			0
$785$			3.82377i			0.136476i
$786$	7.88912	+	4.55479i	0.281396	+	0.162464i
$787$	−22.7423	+	13.1303i	−0.810676	+	0.468044i	−0.847191	−	0.531289i	$-0.821708\pi$
$787$	−22.7423	+	13.1303i	−0.810676	+	0.468044i	0.0365144	+	0.999333i	$0.488375\pi$
$788$	−9.57107	+	5.52586i	−0.340955	+	0.196851i
$789$	3.28293	−	5.68619i	0.116875	−	0.202434i
$790$	1.51867			0.0540319
$791$		0			0
$792$	6.92162			0.245949
$793$	24.1021	−	10.2287i	0.855891	−	0.363230i
$794$	4.72200	+	8.17874i	0.167577	+	0.290252i
$795$	−0.350931	+	0.202610i	−0.0124462	+	0.00718583i
$796$	−5.14116	+	8.90475i	−0.182223	+	0.315620i
$797$	44.0677			1.56096			0.780479	−	0.625182i	$-0.214975\pi$
$797$	44.0677			1.56096			0.780479	+	0.625182i	$0.214975\pi$
$798$		0			0
$799$			26.6297i			0.942090i
$800$	−14.1741	−	8.18342i	−0.501130	−	0.289327i
$801$	−12.7448	+	7.35823i	−0.450316	+	0.259990i
$802$	7.51026	+	13.0082i	0.265196	+	0.459334i
$803$	0.146689	−	0.254073i	0.00517654	−	0.00896603i
$804$			1.72753i			0.0609252i
$805$		0			0
$806$	−22.9132	−	17.2690i	−0.807083	−	0.608274i
$807$	2.97826	−	5.15850i	0.104840	−	0.181588i
$808$	−9.71534	+	5.60916i	−0.341785	+	0.197329i
$809$	4.03919	+	6.99608i	0.142010	+	0.245969i	0.928254	−	0.371948i	$-0.121310\pi$
$809$	4.03919	+	6.99608i	0.142010	+	0.245969i	−0.786243	+	0.617917i	$0.787977\pi$
$810$	−1.74374	+	3.02024i	−0.0612687	+	0.106120i
$811$			38.0098i			1.33471i	0.744742	+	0.667353i	$0.232573\pi$
$811$			38.0098i			1.33471i	−0.744742	+	0.667353i	$0.767427\pi$
$812$		0			0
$813$			5.89657i			0.206802i
$814$	7.99786	+	4.61757i	0.280325	+	0.161846i
$815$	−0.0917087	−	0.158844i	−0.00321242	−	0.00556407i
$816$	1.81658	+	3.14641i	0.0635931	+	0.110146i
$817$	1.56837	+	0.905501i	0.0548705	+	0.0316795i
$818$	−21.9409			−0.767146
$819$		0			0
$820$	1.94214			0.0678225
$821$	−11.9115	−	6.87709i	−0.415713	−	0.240012i	0.277528	−	0.960717i	$-0.410485\pi$
$821$	−11.9115	−	6.87709i	−0.415713	−	0.240012i	−0.693242	+	0.720705i	$0.743818\pi$
$822$	5.18342	+	8.97794i	0.180792	+	0.313142i
$823$	4.95968	+	8.59041i	0.172883	+	0.299443i	0.939427	−	0.342750i	$-0.111358\pi$
$823$	4.95968	+	8.59041i	0.172883	+	0.299443i	−0.766543	+	0.642193i	$0.778025\pi$
$824$	47.8329	+	27.6163i	1.66634	+	0.962061i
$825$			2.14238i			0.0745881i
$826$		0			0
$827$			3.77101i			0.131131i	0.997848	+	0.0655654i	$0.0208851\pi$
$827$			3.77101i			0.131131i	−0.997848	+	0.0655654i	$0.979115\pi$
$828$	−4.31545	+	7.47458i	−0.149972	+	0.259759i
$829$	−5.75933	−	9.97546i	−0.200030	−	0.346462i	0.748508	−	0.663126i	$-0.230771\pi$
$829$	−5.75933	−	9.97546i	−0.200030	−	0.346462i	−0.948538	+	0.316664i	$0.897437\pi$
$830$	−4.84522	+	2.79739i	−0.168180	+	0.0970988i
$831$	−7.04165	+	12.1965i	−0.244272	+	0.423092i
$832$	24.9939	+	18.8371i	0.866506	+	0.653059i
$833$		0			0
$834$			8.34017i			0.288797i
$835$	5.50000	−	9.52628i	0.190335	−	0.329670i
$836$	−1.13275	−	1.96197i	−0.0391769	−	0.0678563i
$837$	18.1311	−	10.4680i	0.626703	−	0.361827i
$838$	−23.9468	−	13.8257i	−0.827229	−	0.477601i
$839$		−	43.6475i		−	1.50688i	−0.657516	−	0.753440i	$-0.728393\pi$
$839$		−	43.6475i		−	1.50688i	0.657516	−	0.753440i	$-0.271607\pi$
$840$		0			0
$841$	−28.9315			−0.997637
$842$	11.3805	−	19.7116i	0.392198	−	0.679306i
$843$	−2.24288	+	1.29493i	−0.0772490	+	0.0445998i
$844$	−0.854638	−	1.48028i	−0.0294178	−	0.0509532i
$845$	−1.45010	+	5.81239i	−0.0498849	+	0.199952i
$846$	29.3184			1.00799
$847$		0			0
$848$	−3.81658			−0.131062
$849$	0.264063	−	0.457370i	0.00906261	−	0.0156969i
$850$	13.9691	−	8.06505i	0.479135	−	0.276629i
$851$	−41.5879	+	24.0108i	−1.42561	+	0.823079i
$852$	3.76263	+	2.17235i	0.128905	+	0.0744236i
$853$		−	10.0940i		−	0.345611i	−0.984956	−	0.172806i	$-0.944717\pi$
$853$		−	10.0940i		−	0.345611i	0.984956	−	0.172806i	$-0.0552832\pi$
$854$		0			0
$855$	5.40191			0.184741
$856$	−7.84966	−	4.53200i	−0.268296	−	0.154901i
$857$	−12.0133	−	20.8077i	−0.410368	−	0.710777i	0.584562	−	0.811349i	$-0.301266\pi$
$857$	−12.0133	−	20.8077i	−0.410368	−	0.710777i	−0.994930	+	0.100571i	$0.967933\pi$
$858$	0.230207	−	1.87374i	0.00785912	−	0.0639686i
$859$	0.829914	−	1.43745i	0.0283163	−	0.0490452i	−0.851520	−	0.524322i	$-0.824319\pi$
$859$	0.829914	−	1.43745i	0.0283163	−	0.0490452i	0.879836	+	0.475277i	$0.157652\pi$
$860$		−	0.121683i		−	0.00414936i
$861$		0			0
$862$	−21.1773			−0.721301
$863$	−24.7917	−	14.3135i	−0.843920	−	0.487238i	0.0146746	−	0.999892i	$-0.495329\pi$
$863$	−24.7917	−	14.3135i	−0.843920	−	0.487238i	−0.858595	+	0.512655i	$0.828662\pi$
$864$	−9.11370	+	5.26180i	−0.310054	+	0.179010i
$865$	10.3360	−	5.96748i	0.351434	−	0.202900i
$866$	20.8116	+	12.0156i	0.707208	+	0.408307i
$867$	−4.69594			−0.159483
$868$		0			0
$869$			2.33752i			0.0792949i
$870$	−0.0380552	+	0.0659135i	−0.00129019	+	0.00223468i
$871$	−18.1737	−	2.23281i	−0.615792	−	0.0756557i
$872$	−12.9783	−	22.4790i	−0.439499	−	0.761235i
$873$	29.5849	+	17.0808i	1.00130	+	0.578099i
$874$	−25.5642			−0.864723
$875$		0			0
$876$			0.120252i			0.00406296i
$877$	−35.3846	−	20.4293i	−1.19485	−	0.689850i	−0.235451	−	0.971886i	$-0.575657\pi$
$877$	−35.3846	−	20.4293i	−1.19485	−	0.689850i	−0.959404	+	0.282037i	$0.908990\pi$
$878$	27.3219	−	15.7743i	0.922070	−	0.532358i
$879$	11.3594	−	6.55838i	0.383145	−	0.221209i
$880$	0.447480	−	0.775058i	0.0150846	−	0.0261272i
$881$	−48.5835			−1.63682			−0.818411	−	0.574634i	$-0.805144\pi$
$881$	−48.5835			−1.63682			−0.818411	+	0.574634i	$0.805144\pi$
$882$		0			0
$883$	49.2456			1.65725			0.828624	−	0.559806i	$-0.189124\pi$
$883$	49.2456			1.65725			0.828624	+	0.559806i	$0.189124\pi$
$884$	6.02929	−	2.55876i	0.202787	−	0.0860604i
$885$	0.346316	+	0.599837i	0.0116413	+	0.0201633i
$886$	26.7620	−	15.4511i	0.899088	−	0.519089i
$887$	6.58864	−	11.4119i	0.221225	−	0.383173i	−0.733955	−	0.679198i	$-0.762328\pi$
$887$	6.58864	−	11.4119i	0.221225	−	0.383173i	0.955180	+	0.296025i	$0.0956612\pi$
$888$	−15.7854			−0.529723
$889$		0			0
$890$			2.92881i			0.0981739i
$891$	−4.64872	−	2.68394i	−0.155738	−	0.0899154i
$892$	10.8154	−	6.24426i	0.362125	−	0.209073i
$893$	−20.0083	−	34.6554i	−0.669553	−	1.15970i
$894$	−6.46800	+	11.2029i	−0.216322	+	0.374681i
$895$			9.52690i			0.318449i
$896$		0			0
$897$	7.83937	+	5.90829i	0.261749	+	0.197272i
$898$	18.3896	−	31.8518i	0.613670	−	1.06291i
$899$	−1.54193	+	0.890233i	−0.0514262	+	0.0296909i
$900$	4.09171	+	7.08705i	0.136390	+	0.236235i
$901$	−2.34797	+	4.06681i	−0.0782223	+	0.135485i
$902$		−	6.48709i		−	0.215996i
$903$		0			0
$904$			39.4284i			1.31137i
$905$	−6.27203	−	3.62116i	−0.208489	−	0.120371i
$906$	−0.503072	−	0.871345i	−0.0167134	−	0.0289485i
$907$	7.65255	+	13.2546i	0.254099	+	0.440112i	0.964650	−	0.263533i	$-0.0848878\pi$
$907$	7.65255	+	13.2546i	0.254099	+	0.440112i	−0.710552	+	0.703645i	$0.751555\pi$
$908$	7.24589	+	4.18342i	0.240463	+	0.138832i
$909$	9.87322			0.327474
$910$		0			0
$911$	−5.07223			−0.168051			−0.0840253	−	0.996464i	$-0.526778\pi$
$911$	−5.07223			−0.168051			−0.0840253	+	0.996464i	$0.526778\pi$
$912$	−4.72814	−	2.72979i	−0.156564	−	0.0903925i
$913$	−4.30571	−	7.45771i	−0.142498	−	0.246814i
$914$	−10.5688	−	18.3058i	−0.349586	−	0.605501i
$915$	1.56257	+	0.902148i	0.0516569	+	0.0298241i
$916$		−	17.5441i		−	0.579674i
$917$		0			0
$918$		−	10.3714i		−	0.342306i
$919$	23.1845	−	40.1567i	0.764785	−	1.32465i	−0.175575	−	0.984466i	$-0.556179\pi$
$919$	23.1845	−	40.1567i	0.764785	−	1.32465i	0.940360	−	0.340180i	$-0.110488\pi$
$920$	3.58145	+	6.20325i	0.118077	+	0.204515i
$921$	−2.90422	+	1.67675i	−0.0956973	+	0.0552509i
$922$	−13.5018	+	23.3859i	−0.444660	+	0.770173i
$923$	−27.7165	+	36.7754i	−0.912299	+	1.21048i
$924$		0			0
$925$			45.5318i			1.49708i
$926$	2.66054	−	4.60819i	0.0874308	−	0.151435i
$927$	−24.3051	−	42.0977i	−0.798284	−	1.38267i
$928$	0.775058	−	0.447480i	0.0254425	−	0.0146893i
$929$	−20.3123	−	11.7273i	−0.666426	−	0.384761i	0.128295	−	0.991736i	$-0.459050\pi$
$929$	−20.3123	−	11.7273i	−0.666426	−	0.384761i	−0.794721	+	0.606975i	$0.792383\pi$
$930$		−	1.97721i		−	0.0648354i
$931$		0			0
$932$	8.43310			0.276236
$933$	−6.76907	+	11.7244i	−0.221609	+	0.383839i
$934$	−38.3192	+	22.1236i	−1.25384	+	0.723907i
$935$	−0.550582	−	0.953636i	−0.0180060	−	0.0311872i
$936$	−11.7476	−	27.6813i	−0.383983	−	0.904791i
$937$	−18.0156			−0.588544			−0.294272	−	0.955722i	$-0.595077\pi$
$937$	−18.0156			−0.588544			−0.294272	+	0.955722i	$0.595077\pi$
$938$		0			0
$939$	1.20781			0.0394155
$940$	−1.34438	+	2.32853i	−0.0438488	+	0.0759483i
$941$	27.5227	−	15.8902i	0.897214	−	0.518007i	0.0209188	−	0.999781i	$-0.493341\pi$
$941$	27.5227	−	15.8902i	0.897214	−	0.518007i	0.876295	+	0.481774i	$0.160008\pi$
$942$	−4.53376	+	2.61757i	−0.147718	+	0.0852849i
$943$	29.2128	+	16.8660i	0.951300	+	0.549234i
$944$			6.52359i			0.212325i
$945$		0			0
$946$	−0.406442			−0.0132146
$947$	40.1673	+	23.1906i	1.30526	+	0.753593i	0.981301	−	0.192477i	$-0.0616521\pi$
$947$	40.1673	+	23.1906i	1.30526	+	0.753593i	0.323961	+	0.946071i	$0.394985\pi$
$948$	−0.479063	−	0.829761i	−0.0155592	−	0.0269494i
$949$	−1.26506	−	0.155425i	−0.0410657	−	0.00504530i
$950$	−12.1194	+	20.9914i	−0.393206	+	0.681052i
$951$			1.56093i			0.0506166i
$952$		0			0
$953$	27.2511			0.882750			0.441375	−	0.897323i	$-0.354491\pi$
$953$	27.2511			0.882750			0.441375	+	0.897323i	$0.354491\pi$
$954$	4.47743	+	2.58504i	0.144962	+	0.0836939i
$955$	6.69952	−	3.86797i	0.216791	−	0.125165i
$956$	4.75728	−	2.74662i	0.153861	−	0.0888319i
$957$	−0.101453	−	0.0585741i	−0.00327952	−	0.00189343i
$958$	−10.8117			−0.349309
$959$		0			0
$960$			2.15676i			0.0696090i
$961$	7.62669	−	13.2098i	0.246022	−	0.426123i
$962$	4.89256	−	39.8225i	0.157743	−	1.28393i
$963$	3.98861	+	6.90847i	0.128531	+	0.222622i
$964$	−9.25069	−	5.34089i	−0.297945	−	0.172018i
$965$	−9.22285			−0.296894
$966$		0			0
$967$			9.77045i			0.314196i	0.987583	+	0.157098i	$0.0502139\pi$
$967$			9.77045i			0.314196i	−0.987583	+	0.157098i	$0.949786\pi$
$968$	−27.4893	−	15.8710i	−0.883539	−	0.510112i
$969$	−5.81753	+	3.35875i	−0.186886	+	0.107899i
$970$	5.88786	−	3.39936i	0.189048	−	0.109147i
$971$	6.99281	−	12.1119i	0.224410	−	0.388690i	−0.731732	−	0.681592i	$-0.761288\pi$
$971$	6.99281	−	12.1119i	0.224410	−	0.388690i	0.956142	+	0.292903i	$0.0946212\pi$
$972$	8.02666			0.257455
$973$		0			0
$974$	−15.9832			−0.512134
$975$	8.56791	−	3.63612i	0.274393	−	0.116449i
$976$	8.49693	+	14.7171i	0.271980	+	0.471083i
$977$	−47.4109	+	27.3727i	−1.51681	+	0.875730i	−0.517004	+	0.855983i	$0.672953\pi$
$977$	−47.4109	+	27.3727i	−1.51681	+	0.875730i	−0.999805	+	0.0197472i	$0.993714\pi$
$978$	0.125559	−	0.217474i	0.00401492	−	0.00695405i
$979$	−4.50799			−0.144076
$980$		0			0
$981$			22.8443i			0.729362i
$982$	−30.0465	−	17.3474i	−0.958823	−	0.553577i
$983$	−0.0346349	+	0.0199965i	−0.00110468	+	0.000637789i	−0.500552	−	0.865706i	$-0.666870\pi$
$983$	−0.0346349	+	0.0199965i	−0.00110468	+	0.000637789i	0.499448	+	0.866344i	$0.333536\pi$
$984$	5.54411	+	9.60268i	0.176740	+	0.306122i
$985$	4.03612	−	6.99076i	0.128601	−	0.222744i
$986$			0.882015i			0.0280891i
$987$		0			0
$988$	−5.92389	+	7.86007i	−0.188464	+	0.250062i
$989$	1.05673	−	1.83030i	0.0336019	−	0.0582002i
$990$	−1.04992	+	0.606173i	−0.0333688	+	0.0192655i
$991$	−26.9741	−	46.7204i	−0.856859	−	1.48412i	−0.874910	−	0.484286i	$-0.839079\pi$
$991$	−26.9741	−	46.7204i	−0.856859	−	1.48412i	0.0180505	−	0.999837i	$-0.494254\pi$
$992$	−11.6248	+	20.1347i	−0.369086	+	0.639276i
$993$			2.29460i			0.0728169i
$994$		0			0
$995$		−	7.51026i		−	0.238091i
$996$	3.05684	+	1.76487i	0.0968596	+	0.0559219i
$997$	−21.0277	−	36.4211i	−0.665954	−	1.15347i	−0.979026	−	0.203737i	$-0.934691\pi$
$997$	−21.0277	−	36.4211i	−0.665954	−	1.15347i	0.313072	−	0.949730i	$-0.398642\pi$
$998$	−20.7834	−	35.9980i	−0.657889	−	1.13950i
$999$	25.3539	+	14.6381i	0.802162	+	0.463129i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.r.e.324.2		12
7.2	even	3		91.2.c.a.64.5	yes	6
7.3	odd	6		637.2.r.d.116.5		12
7.4	even	3	inner	637.2.r.e.116.5		12
7.5	odd	6		637.2.c.d.246.5		6
7.6	odd	2		637.2.r.d.324.2		12
13.12	even	2	inner	637.2.r.e.324.5		12
21.2	odd	6		819.2.c.b.64.2		6
28.23	odd	6		1456.2.k.c.337.3		6
91.5	even	12		8281.2.a.be.1.3		3
91.12	odd	6		637.2.c.d.246.2		6
91.25	even	6	inner	637.2.r.e.116.2		12
91.38	odd	6		637.2.r.d.116.2		12
91.44	odd	12		1183.2.a.h.1.3		3
91.47	even	12		8281.2.a.bi.1.1		3
91.51	even	6		91.2.c.a.64.2	✓	6
91.86	odd	12		1183.2.a.j.1.1		3
91.90	odd	2		637.2.r.d.324.5		12
273.233	odd	6		819.2.c.b.64.5		6
364.51	odd	6		1456.2.k.c.337.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.c.a.64.2	✓	6	91.51	even	6
91.2.c.a.64.5	yes	6	7.2	even	3
637.2.c.d.246.2		6	91.12	odd	6
637.2.c.d.246.5		6	7.5	odd	6
637.2.r.d.116.2		12	91.38	odd	6
637.2.r.d.116.5		12	7.3	odd	6
637.2.r.d.324.2		12	7.6	odd	2
637.2.r.d.324.5		12	91.90	odd	2
637.2.r.e.116.2		12	91.25	even	6	inner
637.2.r.e.116.5		12	7.4	even	3	inner
637.2.r.e.324.2		12	1.1	even	1	trivial
637.2.r.e.324.5		12	13.12	even	2	inner
819.2.c.b.64.2		6	21.2	odd	6
819.2.c.b.64.5		6	273.233	odd	6
1183.2.a.h.1.3		3	91.44	odd	12
1183.2.a.j.1.1		3	91.86	odd	12
1456.2.k.c.337.3		6	28.23	odd	6
1456.2.k.c.337.4		6	364.51	odd	6
8281.2.a.be.1.3		3	91.5	even	12
8281.2.a.bi.1.1		3	91.47	even	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.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.01332 - 0.585043i) q^{2} +(-0.269594 - 0.466951i) q^{3} +(-0.315449 - 0.546373i) q^{4} +(0.399074 + 0.230406i) q^{5} +0.630898i q^{6} +3.07838i q^{8} +(1.35464 - 2.34630i) q^{9} +O(q^{10})\)	\(q+(-1.01332 - 0.585043i) q^{2} +(-0.269594 - 0.466951i) q^{3} +(-0.315449 - 0.546373i) q^{4} +(0.399074 + 0.230406i) q^{5} +0.630898i q^{6} +3.07838i q^{8} +(1.35464 - 2.34630i) q^{9} +(-0.269594 - 0.466951i) q^{10} +(0.718726 - 0.414957i) q^{11} +(-0.170086 + 0.294598i) q^{12} +(-2.87936 - 2.17009i) q^{13} -0.248464i q^{15} +(1.17009 - 2.02665i) q^{16} +(-1.43968 - 2.49360i) q^{17} +(-2.74538 + 1.58504i) q^{18} +(3.74716 + 2.16342i) q^{19} -0.290725i q^{20} -0.971071 q^{22} +(2.52472 - 4.37295i) q^{23} +(1.43745 - 0.829914i) q^{24} +(-2.39383 - 4.14623i) q^{25} +(1.64813 + 3.88355i) q^{26} -3.07838 q^{27} +0.261795 q^{29} +(-0.145362 + 0.251775i) q^{30} +(-5.88983 + 3.40049i) q^{31} +(2.96055 - 1.70928i) q^{32} +(-0.387529 - 0.223740i) q^{33} +3.36910i q^{34} -1.70928 q^{36} +(-8.23613 - 4.75513i) q^{37} +(-2.53139 - 4.38450i) q^{38} +(-0.237065 + 1.92956i) q^{39} +(-0.709275 + 1.22850i) q^{40} +6.68035i q^{41} +0.418551 q^{43} +(-0.453443 - 0.261795i) q^{44} +(1.08120 - 0.624232i) q^{45} +(-5.11673 + 2.95415i) q^{46} +(-8.00940 - 4.62423i) q^{47} -1.26180 q^{48} +5.60197i q^{50} +(-0.776260 + 1.34452i) q^{51} +(-0.277386 + 2.25776i) q^{52} +(-0.815449 - 1.41240i) q^{53} +(3.11940 + 1.80098i) q^{54} +0.382433 q^{55} -2.33299i q^{57} +(-0.265284 - 0.153162i) q^{58} +(-2.41418 + 1.39383i) q^{59} +(-0.135754 + 0.0783777i) q^{60} +(-3.63090 + 6.28890i) q^{61} +7.95774 q^{62} -8.68035 q^{64} +(-0.649079 - 1.52945i) q^{65} +(0.261795 + 0.453443i) q^{66} +(4.39800 - 2.53919i) q^{67} +(-0.908291 + 1.57321i) q^{68} -2.72261 q^{69} -12.7721i q^{71} +(7.22280 + 4.17009i) q^{72} +(0.306143 - 0.176752i) q^{73} +(5.56391 + 9.63698i) q^{74} +(-1.29072 + 2.23560i) q^{75} -2.72979i q^{76} +(1.36910 - 1.81658i) q^{78} +(-1.40829 + 2.43923i) q^{79} +(0.933903 - 0.539189i) q^{80} +(-3.23400 - 5.60145i) q^{81} +(3.90829 - 6.76936i) q^{82} -10.3763i q^{83} -1.32684i q^{85} +(-0.424128 - 0.244870i) q^{86} +(-0.0705785 - 0.122246i) q^{87} +(1.27739 + 2.21251i) q^{88} +(-4.70415 - 2.71594i) q^{89} -1.46081 q^{90} -3.18568 q^{92} +(3.17573 + 1.83351i) q^{93} +(5.41075 + 9.37170i) q^{94} +(0.996928 + 1.72673i) q^{95} +(-1.59630 - 0.921622i) q^{96} +12.6092i q^{97} -2.24846i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{4} + 2 q^{9}+O(q^{10}) \) 12 * q + 4 * q^4 + 2 * q^9	\( 12 q + 4 q^{4} + 2 q^{9} + 20 q^{12} + 16 q^{13} - 8 q^{16} + 8 q^{17} + 48 q^{22} - 6 q^{23} - 8 q^{25} - 12 q^{26} - 24 q^{27} - 28 q^{29} - 16 q^{30} + 8 q^{36} + 4 q^{38} + 8 q^{39} + 20 q^{40} - 52 q^{43} + 16 q^{48} - 8 q^{51} + 20 q^{52} - 2 q^{53} + 24 q^{55} - 28 q^{61} + 32 q^{62} - 16 q^{64} + 6 q^{65} - 28 q^{66} - 20 q^{68} - 8 q^{69} + 24 q^{74} - 44 q^{75} + 32 q^{78} - 26 q^{79} + 26 q^{81} + 56 q^{82} + 40 q^{87} + 40 q^{88} - 24 q^{90} - 72 q^{92} - 20 q^{94} - 58 q^{95}+O(q^{100}) \) 12 * q + 4 * q^4 + 2 * q^9 + 20 * q^12 + 16 * q^13 - 8 * q^16 + 8 * q^17 + 48 * q^22 - 6 * q^23 - 8 * q^25 - 12 * q^26 - 24 * q^27 - 28 * q^29 - 16 * q^30 + 8 * q^36 + 4 * q^38 + 8 * q^39 + 20 * q^40 - 52 * q^43 + 16 * q^48 - 8 * q^51 + 20 * q^52 - 2 * q^53 + 24 * q^55 - 28 * q^61 + 32 * q^62 - 16 * q^64 + 6 * q^65 - 28 * q^66 - 20 * q^68 - 8 * q^69 + 24 * q^74 - 44 * q^75 + 32 * q^78 - 26 * q^79 + 26 * q^81 + 56 * q^82 + 40 * q^87 + 40 * q^88 - 24 * q^90 - 72 * q^92 - 20 * q^94 - 58 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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