LMFDB - Embedded newform 637.2.r.d.116.5

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			116.5
Root			$-1.16746 - 0.312819i$ of defining polynomial
Character	$\chi$	$=$	637.116
Dual form			637.2.r.d.324.5

$q$-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} +(4.18732 + 0.514451i) 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} +(1.78958 - 0.759478i) 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} +(-2.09397 + 0.888655i) 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} +(1.64908 + 0.202604i) 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 $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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	$-0.530907\pi$
$2$	1.01332	−	0.585043i	0.716529	−	0.413688i	0.813474	+	0.581602i	$0.197574\pi$
$3$	0.269594	−	0.466951i	0.155650	−	0.269594i	−0.777645	−	0.628703i	$-0.783586\pi$
$3$	0.269594	−	0.466951i	0.155650	−	0.269594i	0.933296	+	0.359109i	$0.116919\pi$
$4$	−0.315449	+	0.546373i	−0.157724	+	0.273187i
$5$	0.399074	−	0.230406i	0.178471	−	0.103041i	−0.408103	−	0.912936i	$-0.633810\pi$
$5$	0.399074	−	0.230406i	0.178471	−	0.103041i	0.586574	+	0.809895i	$0.300476\pi$
$6$		−	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	$-0.373263\pi$
$11$	−0.718726	−	0.414957i	−0.216704	−	0.125114i	−0.604423	+	0.796663i	$0.706596\pi$
$12$	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	$-0.719796\pi$
$17$	1.43968	−	2.49360i	0.349174	−	0.604787i	0.986103	+	0.166135i	$0.0531289\pi$
$18$	2.74538	+	1.58504i	0.647091	+	0.373598i
$19$	3.74716	−	2.16342i	0.859656	−	0.496323i	−0.00424086	−	0.999991i	$-0.501350\pi$
$19$	3.74716	−	2.16342i	0.859656	−	0.496323i	0.863897	+	0.503668i	$0.168017\pi$
$20$			0.290725i			0.0650080i
$21$		0			0
$22$	−0.971071			−0.207033
$23$	2.52472	+	4.37295i	0.526441	+	0.911823i	0.999525	+	0.0308059i	$0.00980737\pi$
$23$	2.52472	+	4.37295i	0.526441	+	0.911823i	−0.473084	+	0.881017i	$0.656859\pi$
$24$	1.43745	+	0.829914i	0.293419	+	0.169405i
$25$	−2.39383	+	4.14623i	−0.478765	+	0.829246i
$26$	4.18732	+	0.514451i	0.821202	+	0.100892i
$27$	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	−0.133009	−	0.991115i	$-0.542464\pi$
$31$	−5.88983	−	3.40049i	−1.05784	−	0.610746i	−0.924835	+	0.380368i	$0.875797\pi$
$32$	−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	$-0.381000\pi$
$37$	8.23613	−	4.75513i	1.35401	−	0.781739i	0.988809	+	0.149190i	$0.0476665\pi$
$38$	2.53139	−	4.38450i	0.410646	−	0.711259i
$39$	1.78958	−	0.759478i	0.286563	−	0.121614i
$40$	0.709275	+	1.22850i	0.112146	+	0.194243i
$41$		−	6.68035i		−	1.04329i	−0.853161	−	0.521647i	$-0.825318\pi$
$41$		−	6.68035i		−	1.04329i	0.853161	−	0.521647i	$-0.174682\pi$
$42$		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	−0.953277	−	0.302097i	$-0.902313\pi$
$47$	−8.00940	+	4.62423i	−1.16829	+	0.674514i	−0.215015	+	0.976611i	$0.568980\pi$
$48$	1.26180			0.182124
$49$		0			0
$50$			5.60197i			0.792238i
$51$	−0.776260	−	1.34452i	−0.108698	−	0.188271i
$52$	−2.09397	+	0.888655i	−0.290381	+	0.123234i
$53$	−0.815449	+	1.41240i	−0.112011	+	0.194008i	−0.916581	−	0.399850i	$-0.869062\pi$
$53$	−0.815449	+	1.41240i	−0.112011	+	0.194008i	0.804570	+	0.593857i	$0.202396\pi$
$54$	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	0.334549	−	0.942378i	$-0.391416\pi$
$59$	−2.41418	−	1.39383i	−0.314299	−	0.181461i	−0.648849	+	0.760917i	$0.724749\pi$
$60$	0.135754	+	0.0783777i	0.0175258	+	0.0101185i
$61$	3.63090	+	6.28890i	0.464889	+	0.805211i	0.999197	−	0.0400790i	$-0.0127610\pi$
$61$	3.63090	+	6.28890i	0.464889	+	0.805211i	−0.534308	+	0.845290i	$0.679428\pi$
$62$	−7.95774			−1.01063
$63$		0			0
$64$	−8.68035			−1.08504
$65$	1.64908	+	0.202604i	0.204543	+	0.0251300i
$66$	−0.261795	+	0.453443i	−0.0322248	+	0.0558149i
$67$	−4.39800	−	2.53919i	−0.537302	−	0.310211i	0.206683	−	0.978408i	$-0.433733\pi$
$67$	−4.39800	−	2.53919i	−0.537302	−	0.310211i	−0.743985	+	0.668197i	$0.767066\pi$
$68$	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	0.517809	−	0.855496i	$-0.326748\pi$
$73$	0.306143	+	0.176752i	0.0358314	+	0.0206873i	−0.481977	+	0.876184i	$0.660081\pi$
$74$	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	0.775863	−	0.630901i	$-0.217315\pi$
$79$	−1.40829	−	2.43923i	−0.158445	−	0.274435i	−0.934308	+	0.356466i	$0.883981\pi$
$80$	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	$0.192853\pi$
$83$			10.3763i			1.13895i	−0.822010	+	0.569473i	$0.807147\pi$
$84$		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	−0.728151	−	0.685417i	$-0.759620\pi$
$89$	−4.70415	+	2.71594i	−0.498639	+	0.287889i	0.229513	+	0.973306i	$0.426287\pi$
$90$	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	$-0.778879\pi$
$97$		−	12.6092i		−	1.28027i	0.768264	−	0.640133i	$-0.221121\pi$
$98$		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	$-0.891366\pi$
$101$	−1.82211	+	3.15599i	−0.181307	+	0.314033i	0.761019	+	0.648730i	$0.224699\pi$
$102$	−1.57321	−	0.908291i	−0.155771	−	0.0899342i
$103$	−8.97107	−	15.5384i	−0.883946	−	1.53104i	−0.846917	−	0.531725i	$-0.821544\pi$
$103$	−8.97107	−	15.5384i	−0.883946	−	1.53104i	−0.0370287	−	0.999314i	$-0.511789\pi$
$104$	−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	0.786048	−	0.618166i	$-0.212124\pi$
$107$	−1.47220	−	2.54993i	−0.142323	−	0.246511i	−0.928371	+	0.371654i	$0.878791\pi$
$108$	−0.971071	+	1.68194i	−0.0934413	+	0.161845i
$109$	7.30222	+	4.21594i	0.699426	+	0.403814i	0.807134	−	0.590369i	$-0.201018\pi$
$109$	7.30222	+	4.21594i	0.699426	+	0.403814i	−0.107707	+	0.994183i	$0.534351\pi$
$110$	−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
$117$	−1.19118	+	9.69553i	−0.110125	+	0.896352i
$118$	−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
$130$	1.78958	−	0.759478i	0.156957	−	0.0666107i
$131$	−7.21953	−	12.5046i	−0.630774	−	1.09253i	−0.987394	−	0.158283i	$-0.949404\pi$
$131$	−7.21953	−	12.5046i	−0.630774	−	1.09253i	0.356620	−	0.934249i	$-0.383929\pi$
$132$		−	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	$-0.581014\pi$
$137$	−14.2304	−	8.21594i	−1.21579	−	0.701935i	−0.964014	+	0.265851i	$0.914347\pi$
$138$	2.75888	−	1.59284i	0.234852	−	0.135592i
$139$	−13.2195			−1.12127			−0.560633	−	0.828064i	$-0.689442\pi$
$139$	−13.2195			−1.12127			−0.560633	+	0.828064i	$0.689442\pi$
$140$		0			0
$141$			4.98667i			0.419953i
$142$	−7.47220	−	12.9422i	−0.627053	−	1.08609i
$143$	−1.16898	−	2.75451i	−0.0977551	−	0.230344i
$144$	−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	$-0.984042\pi$
$149$	−17.7571	+	10.2521i	−1.45472	+	0.839881i	−0.455974	+	0.889993i	$0.650709\pi$
$150$	2.61585	+	1.51026i	0.213583	+	0.123312i
$151$	1.38112	+	0.797390i	0.112394	+	0.0648907i	0.555143	−	0.831755i	$-0.312663\pi$
$151$	1.38112	+	0.797390i	0.112394	+	0.0648907i	−0.442749	+	0.896645i	$0.645997\pi$
$152$	6.65983	+	11.5352i	0.540183	+	0.935625i
$153$	7.80098			0.630672
$154$		0			0
$155$	−3.13397			−0.251726
$156$	−0.149564	+	1.21736i	−0.0119747	+	0.0974666i
$157$	−4.14896	+	7.18620i	−0.331123	+	0.573521i	−0.982732	−	0.185033i	$-0.940761\pi$
$157$	−4.14896	+	7.18620i	−0.331123	+	0.573521i	0.651610	+	0.758555i	$0.274094\pi$
$158$	−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	$-0.661705\pi$
$163$	0.344706	−	0.199016i	0.0269994	−	0.0155881i	0.513439	+	0.858126i	$0.328371\pi$
$164$	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	$0.374763\pi$
$167$			23.8710i			1.84719i	−0.383370	+	0.923595i	$0.625237\pi$
$168$		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	−0.643850	−	0.765151i	$-0.722664\pi$
$173$	−12.9499	−	22.4300i	−0.984566	−	1.70532i	−0.340715	−	0.940167i	$-0.610669\pi$
$174$		−	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	−0.163485	−	0.986546i	$-0.552274\pi$
$179$	10.3371	−	17.9044i	0.772631	−	1.33824i	0.936116	−	0.351691i	$-0.114393\pi$
$180$	−0.682128	+	0.393827i	−0.0508428	+	0.0293541i
$181$	15.7165			1.16820			0.584098	−	0.811683i	$-0.301448\pi$
$181$	15.7165			1.16820			0.584098	+	0.811683i	$0.301448\pi$
$182$		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	0.991674	+	0.128771i	$0.0411032\pi$
$191$	8.39383	+	14.5385i	0.607356	+	1.05197i	−0.384318	+	0.923201i	$0.625564\pi$
$192$	−2.34017	+	4.05330i	−0.168887	+	0.292522i
$193$	17.3330	+	10.0072i	1.24765	+	0.720333i	0.970641	−	0.240533i	$-0.0773223\pi$
$193$	17.3330	+	10.0072i	1.24765	+	0.720333i	0.277013	+	0.960866i	$0.410656\pi$
$194$	−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	−0.418082	−	0.908409i	$-0.637298\pi$
$199$	8.14896	−	14.1144i	0.577664	−	1.00054i	0.995747	−	0.0921346i	$-0.0293690\pi$
$200$	−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
$208$	−1.02890	+	8.37465i	−0.0713415	+	0.580677i
$209$	−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
$221$	9.55669	−	4.05575i	0.642853	−	0.272819i
$222$	−3.00000	−	5.19615i	−0.201347	−	0.348743i
$223$		−	19.7948i		−	1.32556i	−0.748814	−	0.662780i	$-0.769376\pi$
$223$		−	19.7948i		−	1.32556i	0.748814	−	0.662780i	$-0.230624\pi$
$224$		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	0.0678276	−	0.997697i	$-0.478393\pi$
$227$	−11.4851	−	6.63090i	−0.762290	−	0.440108i	−0.830117	+	0.557589i	$0.811727\pi$
$228$	1.27468	+	0.735937i	0.0844178	+	0.0487386i
$229$	24.0826	−	13.9041i	1.59142	−	0.918808i	0.598358	−	0.801229i	$-0.295820\pi$
$229$	24.0826	−	13.9041i	1.59142	−	0.918808i	0.993063	−	0.117579i	$-0.0375134\pi$
$230$	2.72261			0.179523
$231$		0			0
$232$			0.805905i			0.0529102i
$233$	−6.68342	−	11.5760i	−0.437845	−	0.758370i	0.559678	−	0.828710i	$-0.310925\pi$
$233$	−6.68342	−	11.5760i	−0.437845	−	0.758370i	−0.997523	+	0.0703401i	$0.977592\pi$
$234$	4.46525	+	10.5216i	0.291902	+	0.687820i
$235$	−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	0.891371	−	0.453274i	$-0.149744\pi$
$241$	14.6627	+	8.46554i	0.944510	+	0.545313i	0.0531390	+	0.998587i	$0.483077\pi$
$242$	−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
$247$	15.4842	+	1.90238i	0.985238	+	0.121045i
$248$	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	$-0.589805\pi$
$251$	−8.82150			−0.556808			−0.278404	+	0.960464i	$0.589805\pi$
$252$		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	$-0.0267467\pi$
$257$	6.82211	+	11.8162i	0.425552	+	0.737077i	−0.570920	+	0.821006i	$0.693413\pi$
$258$		−	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	−0.614952	−	0.788565i	$-0.710824\pi$
$263$	6.08864	−	10.5458i	0.375441	−	0.650284i	0.990393	+	0.138281i	$0.0441578\pi$
$264$	−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	$-0.942671\pi$
$269$	−5.52359	+	9.56714i	−0.336779	+	0.583319i	0.647046	+	0.762451i	$0.276004\pi$
$270$	0.829914	−	1.43745i	0.0505069	−	0.0874806i
$271$	−9.47085	+	5.46800i	−0.575313	+	0.332157i	−0.759269	−	0.650777i	$-0.774443\pi$
$271$	−9.47085	+	5.46800i	−0.575313	+	0.332157i	0.183955	+	0.982935i	$0.441110\pi$
$272$	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	0.144507	+	0.989504i	$0.453840\pi$
$277$	−13.0597	+	22.6201i	−0.784682	+	1.35911i	−0.929189	+	0.369605i	$0.879493\pi$
$278$	−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	$-0.842601\pi$
$283$	−0.489741	+	0.848255i	−0.0291121	+	0.0504236i	0.851102	+	0.525000i	$0.175935\pi$
$284$	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	$-0.748426\pi$
$293$		−	24.3268i		−	1.42119i	0.703602	−	0.710595i	$-0.251574\pi$
$294$		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
$299$	−2.22009	+	18.0702i	−0.128391	+	1.04503i
$300$	−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	$0.0567957\pi$
$307$			6.21953i			0.354968i	−0.984124	+	0.177484i	$0.943204\pi$
$308$		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	−0.252268	−	0.967657i	$-0.581176\pi$
$311$	12.5542	−	21.7445i	0.711882	−	1.23302i	0.964150	−	0.265358i	$-0.0854903\pi$
$312$	2.33796	+	5.50902i	0.132361	+	0.311887i
$313$	1.12003	+	1.93994i	0.0633077	+	0.109652i	0.895942	−	0.444171i	$-0.146502\pi$
$313$	1.12003	+	1.93994i	0.0633077	+	0.109652i	−0.832634	+	0.553823i	$0.813168\pi$
$314$			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	$-0.640760\pi$
$317$	2.50711	−	1.44748i	0.140813	−	0.0812986i	0.568752	+	0.822509i	$0.307427\pi$
$318$	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
$325$	−15.8904	+	6.74368i	−0.881439	+	0.374072i
$326$	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	$-0.629353\pi$
$331$	3.68550	−	2.12783i	0.202574	−	0.116956i	0.597855	+	0.801604i	$0.296020\pi$
$332$	−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	$0.639175\pi$
$338$	10.9404	+	10.5681i	0.595080	+	0.574831i
$339$	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	−0.451414	−	0.892315i	$-0.649080\pi$
$347$	10.1906	−	17.6506i	0.547060	−	0.947536i	0.998474	−	0.0552216i	$-0.0175865\pi$
$348$	0.0445278	+	0.0771245i	0.00238694	+	0.00413431i
$349$			7.16394i			0.383477i	0.981446	+	0.191739i	$0.0614126\pi$
$349$			7.16394i			0.383477i	−0.981446	+	0.191739i	$0.938587\pi$
$350$		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	0.618915	−	0.785458i	$-0.287573\pi$
$353$	4.66223	+	2.69174i	0.248145	+	0.143267i	−0.370769	+	0.928725i	$0.620906\pi$
$354$	−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	$-0.530749\pi$
$359$	13.5911	−	7.84684i	0.717312	−	0.414140i	0.813763	+	0.581197i	$0.197416\pi$
$360$	−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	$-0.830637\pi$
$367$	0.162287	−	0.281090i	0.00847133	−	0.0146728i	0.870230	+	0.492646i	$0.163970\pi$
$368$	−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	0.981823	+	0.189800i	$0.0607841\pi$
$373$	12.6556	+	21.9202i	0.655283	+	1.13498i	−0.326539	+	0.945184i	$0.605883\pi$
$374$	−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	−0.179637	−	0.983733i	$-0.557492\pi$
$383$	11.3994	−	6.58145i	0.582482	−	0.336296i	0.762119	+	0.647437i	$0.224159\pi$
$384$			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	−0.965015	−	0.262195i	$-0.915554\pi$
$389$	−5.03806	+	8.72617i	−0.255440	+	0.442434i	0.709575	+	0.704630i	$0.248887\pi$
$390$	0.127823	−	1.04040i	0.00647255	−	0.0526827i
$391$	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	−0.665042	−	0.746806i	$-0.731587\pi$
$397$	−6.98986	+	4.03559i	−0.350811	+	0.202541i	0.314232	+	0.949346i	$0.398253\pi$
$398$		−	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	$-0.562807\pi$
$401$	11.1173	−	6.41855i	0.555169	−	0.320527i	0.751204	+	0.660070i	$0.229473\pi$
$402$	−1.60197	+	2.77469i	−0.0798989	+	0.138389i
$403$	−9.57958	−	22.5727i	−0.477193	−	1.12443i
$404$	−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	0.844513	−	0.535535i	$-0.179890\pi$
$409$	16.2393	+	9.37577i	0.802982	+	0.463602i	−0.0415308	+	0.999137i	$0.513223\pi$
$410$	−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
$416$	−4.81522	−	11.3463i	−0.236086	−	0.556297i
$417$	−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	$-0.695873\pi$
$419$	−23.6319			−1.15450			−0.577248	+	0.816569i	$0.695873\pi$
$420$		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
$429$	−1.60137	−	0.196743i	−0.0773150	−	0.00949885i
$430$	0.112839	−	0.195443i	0.00544158	−	0.00942509i
$431$	−15.6741	−	9.04945i	−0.754995	−	0.435897i	0.0725009	−	0.997368i	$-0.476902\pi$
$431$	−15.6741	−	9.04945i	−0.754995	−	0.435897i	−0.827496	+	0.561472i	$0.810235\pi$
$432$	3.60197	+	6.23879i	0.173300	+	0.300164i
$433$	20.5380			0.986992			0.493496	−	0.869748i	$-0.335719\pi$
$433$	20.5380			0.986992			0.493496	+	0.869748i	$0.335719\pi$
$434$		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	0.984662	+	0.174473i	$0.0558221\pi$
$439$	13.4813	+	23.3503i	0.643429	+	1.11445i	−0.341233	+	0.939979i	$0.610845\pi$
$440$		−	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	−0.988073	−	0.153985i	$-0.950789\pi$
$443$	−13.2051	−	22.8719i	−0.627392	−	1.08667i	0.360681	−	0.932689i	$-0.382544\pi$
$444$	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	$-0.805522\pi$
$457$	−15.6448	+	9.03252i	−0.731832	+	0.422524i	0.0872598	+	0.996186i	$0.472189\pi$
$458$	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	$0.180606\pi$
$461$			23.0784i			1.07487i	−0.843306	+	0.537434i	$0.819394\pi$
$462$		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	−0.856823	−	0.515610i	$-0.827565\pi$
$467$	−18.9077	−	32.7491i	−0.874943	−	1.51545i	−0.0181197	−	0.999836i	$-0.505768\pi$
$468$	−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	0.671546	−	0.740963i	$-0.265631\pi$
$479$	8.00212	+	4.62003i	0.365626	+	0.211094i	−0.305920	+	0.952057i	$0.598964\pi$
$480$	−0.424694	+	0.735591i	−0.0193845	+	0.0335750i
$481$	34.0338	+	4.18137i	1.55181	+	0.190654i
$482$	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	$-0.433493\pi$
$487$	−11.8298	−	6.82991i	−0.536057	−	0.309493i	−0.743480	+	0.668759i	$0.766826\pi$
$488$	−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
$494$	16.8035	−	7.13121i	0.756026	−	0.320849i
$495$	−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	$-0.959275\pi$
$499$	−30.7652	+	17.7623i	−1.37724	+	0.795151i	−0.385415	+	0.922744i	$0.625942\pi$
$500$	−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	$-0.778344\pi$
$503$	−34.4124			−1.53437			−0.767187	+	0.641424i	$0.778344\pi$
$504$		0			0
$505$			1.67930i			0.0747279i
$506$	−2.45169	−	4.24644i	−0.108991	−	0.188777i
$507$	6.80100	+	1.69674i	0.302043	+	0.0753549i
$508$	−4.24846	+	7.35856i	−0.188495	+	0.326483i
$509$	9.62879	−	5.55919i	0.426789	−	0.246407i	−0.271189	−	0.962526i	$-0.587417\pi$
$509$	9.62879	−	5.55919i	0.426789	−	0.246407i	0.697978	+	0.716120i	$0.254083\pi$
$510$	−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
$520$	−0.623693	+	5.07649i	−0.0273507	+	0.222619i
$521$	−8.94441	+	15.4922i	−0.391862	+	0.678724i	−0.992695	−	0.120650i	$-0.961502\pi$
$521$	−8.94441	+	15.4922i	−0.391862	+	0.678724i	0.600833	+	0.799374i	$0.294835\pi$
$522$	0.718726	+	0.414957i	0.0314578	+	0.0181622i
$523$	−11.9939	−	20.7740i	−0.524455	−	0.908382i	−0.999595	−	0.0284720i	$-0.990936\pi$
$523$	−11.9939	−	20.7740i	−0.524455	−	0.908382i	0.475140	−	0.879910i	$-0.342397\pi$
$524$	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	$-0.803683\pi$
$541$	−16.8107	+	9.70568i	−0.722750	+	0.417280i	0.0930141	+	0.995665i	$0.470350\pi$
$542$	−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	$-0.498582\pi$
$557$	−20.2811	−	11.7093i	−0.859336	−	0.496138i	−0.863790	+	0.503852i	$0.831916\pi$
$558$	−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	0.434751	+	0.900551i	$0.356836\pi$
$563$	−13.3474	+	23.1183i	−0.562524	+	0.974320i	−0.997275	+	0.0737698i	$0.976497\pi$
$564$	−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	−0.997717	−	0.0675389i	$-0.978485\pi$
$569$	−13.2948	−	23.0273i	−0.557349	−	0.965356i	0.440368	−	0.897817i	$-0.354848\pi$
$570$	−1.08939	−	0.628960i	−0.0456295	−	0.0263442i
$571$	−1.71655	+	2.97316i	−0.0718355	+	0.124423i	−0.899706	−	0.436497i	$-0.856219\pi$
$571$	−1.71655	+	2.97316i	−0.0718355	+	0.124423i	0.827870	+	0.560920i	$0.189552\pi$
$572$	1.87374	+	0.230207i	0.0783452	+	0.00962542i
$573$	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	−0.162588	−	0.986694i	$-0.551984\pi$
$577$	−26.3841	−	15.2329i	−1.09838	−	0.634153i	−0.935796	+	0.352542i	$0.885318\pi$
$578$	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
$585$	1.75853	+	4.14369i	0.0727064	+	0.171321i
$586$	−14.2323	−	24.6510i	−0.587929	−	1.01832i
$587$			26.2606i			1.08389i	0.840414	+	0.541945i	$0.182312\pi$
$587$			26.2606i			1.08389i	−0.840414	+	0.541945i	$0.817688\pi$
$588$		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	−0.998622	−	0.0524829i	$-0.983286\pi$
$593$	−35.3702	+	20.4210i	−1.45248	+	0.838590i	−0.453859	+	0.891073i	$0.649953\pi$
$594$	−2.98932			−0.122653
$595$		0			0
$596$		−	12.9360i		−	0.529879i
$597$	−4.39383	−	7.61033i	−0.179827	−	0.311470i
$598$	8.32217	+	19.6098i	0.340319	+	0.801904i
$599$	13.6773	−	23.6897i	0.558838	−	0.967936i	−0.438756	−	0.898606i	$-0.644581\pi$
$599$	13.6773	−	23.6897i	0.558838	−	0.967936i	0.997594	−	0.0693298i	$-0.0220861\pi$
$600$	−6.88202	+	3.97334i	−0.280957	+	0.162211i
$601$	−25.4908			−1.03979			−0.519895	−	0.854230i	$-0.674029\pi$
$601$	−25.4908			−1.03979			−0.519895	+	0.854230i	$0.674029\pi$
$602$		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	$-0.0341161\pi$
$607$	9.96554	+	17.2608i	0.404489	+	0.700595i	−0.589773	+	0.807569i	$0.700783\pi$
$608$	−14.7915			−0.599876
$609$		0			0
$610$	3.91548			0.158533
$611$	−33.0970	−	4.06626i	−1.33896	−	0.164503i
$612$	−2.46081	+	4.26225i	−0.0994724	+	0.172291i
$613$	19.6773	+	11.3607i	0.794758	+	0.458854i	0.841635	−	0.540047i	$-0.181593\pi$
$613$	19.6773	+	11.3607i	0.794758	+	0.458854i	−0.0468766	+	0.998901i	$0.514927\pi$
$614$	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	0.900469	−	0.434920i	$-0.143223\pi$
$619$	24.2341	+	13.9916i	0.974052	+	0.562369i	0.0735832	+	0.997289i	$0.476557\pi$
$620$	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	0.199020	+	0.979995i	$0.436224\pi$
$641$	−18.9680	+	32.8535i	−0.749191	+	1.29764i	−0.948211	+	0.317641i	$0.897109\pi$
$642$	−1.60875	+	0.928810i	−0.0634922	+	0.0366572i
$643$			36.2122i			1.42807i	0.700111	+	0.714034i	$0.253134\pi$
$643$			36.2122i			1.42807i	−0.700111	+	0.714034i	$0.746866\pi$
$644$		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	0.0476450	+	0.998864i	$0.484828\pi$
$647$	−21.3974	+	37.0614i	−0.841219	+	1.45703i	−0.888864	+	0.458170i	$0.848505\pi$
$648$	−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	0.806623	−	0.591067i	$-0.201293\pi$
$653$	−2.77432	−	4.80527i	−0.108568	−	0.188045i	−0.915190	+	0.403022i	$0.867960\pi$
$654$	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	0.993008	+	0.118043i	$0.0376621\pi$
$661$	40.9235	+	23.6272i	1.59174	+	0.918992i	0.598733	+	0.800949i	$0.295671\pi$
$662$	2.48974	−	4.31236i	0.0967665	−	0.167605i
$663$	0.682595	−	5.55592i	0.0265098	−	0.215774i
$664$	−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
$676$	−7.95775	−	1.98533i	−0.306067	−	0.0763589i
$677$	5.34797	+	9.26296i	0.205539	+	0.356004i	0.950304	−	0.311322i	$-0.100772\pi$
$677$	5.34797	+	9.26296i	0.205539	+	0.356004i	−0.744765	+	0.667327i	$0.767439\pi$
$678$		−	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	$-0.373609\pi$
$683$	−5.71215	−	3.29791i	−0.218569	−	0.126191i	−0.605288	+	0.796007i	$0.706942\pi$
$684$	−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
$689$	−5.41300	+	2.29721i	−0.206219	+	0.0875168i
$690$	0.734000	−	1.27132i	0.0279429	−	0.0483985i
$691$	−42.8448	+	24.7365i	−1.62989	+	0.941019i	−0.645770	+	0.763532i	$0.723464\pi$
$691$	−42.8448	+	24.7365i	−1.62989	+	0.941019i	−0.984123	+	0.177487i	$0.943203\pi$
$692$	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	$0.628603\pi$
$702$	12.8902	+	1.58367i	0.486508	+	0.0597719i
$703$	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	$-0.631005\pi$
$709$	5.15620	−	2.97693i	0.193645	−	0.111801i	0.593688	+	0.804695i	$0.297671\pi$
$710$	−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	$-0.156635\pi$
$719$	0.844901	+	1.46341i	0.0315095	+	0.0545760i	−0.849841	+	0.527040i	$0.823302\pi$
$720$			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	$-0.415963\pi$
$727$	14.0722			0.521910			0.260955	+	0.965351i	$0.415963\pi$
$728$		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	−0.664534	−	0.747258i	$-0.731370\pi$
$733$	−9.46659	+	5.46554i	−0.349657	+	0.201874i	0.314877	+	0.949132i	$0.398037\pi$
$734$		−	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	$-0.314763\pi$
$739$	2.74538	+	1.58504i	0.100990	+	0.0583068i	−0.448654	+	0.893705i	$0.648097\pi$
$740$	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	0.928225	−	0.372019i	$-0.121334\pi$
$751$	3.88962	+	6.73702i	0.141934	+	0.245837i	−0.786291	+	0.617857i	$0.788001\pi$
$752$	−18.7434	−	10.8215i	−0.683501	−	0.394620i
$753$	−2.37823	+	4.11921i	−0.0866675	+	0.150112i
$754$	1.09622	+	0.134681i	0.0399220	+	0.00490478i
$755$	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	−0.528319	−	0.849046i	$-0.677177\pi$
$761$	−1.57747	+	0.910752i	−0.0571832	+	0.0330147i	0.471136	+	0.882061i	$0.343844\pi$
$762$		−	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
$767$	−3.92657	−	9.25231i	−0.141780	−	0.334081i
$768$	−3.63317	−	6.29283i	−0.131101	−	0.227073i
$769$			39.7948i			1.43504i	0.696539	+	0.717519i	$0.254723\pi$
$769$			39.7948i			1.43504i	−0.696539	+	0.717519i	$0.745277\pi$
$770$		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	0.186883	−	0.982382i	$-0.440161\pi$
$773$	−15.8600	−	9.15676i	−0.570443	−	0.329346i	−0.757326	+	0.653037i	$0.773495\pi$
$774$	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
$780$	0.220799	+	0.520276i	0.00790588	+	0.0186289i
$781$	−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	0.0365144	−	0.999333i	$-0.488375\pi$
$787$	−22.7423	−	13.1303i	−0.810676	−	0.468044i	−0.847191	+	0.531289i	$0.821708\pi$
$788$	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
$793$	−3.19279	+	25.9874i	−0.113379	+	0.922839i
$794$	−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	$-0.785025\pi$
$797$	−44.0677			−1.56096			−0.780479	+	0.625182i	$0.785025\pi$
$798$		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	−0.786243	−	0.617917i	$-0.787977\pi$
$809$	4.03919	−	6.99608i	0.142010	−	0.245969i	0.928254	+	0.371948i	$0.121310\pi$
$810$	1.74374	+	3.02024i	0.0612687	+	0.106120i
$811$		−	38.0098i		−	1.33471i	−0.744742	−	0.667353i	$-0.767427\pi$
$811$		−	38.0098i		−	1.33471i	0.744742	−	0.667353i	$-0.232573\pi$
$812$		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	$-0.589515\pi$
$821$	11.9115	−	6.87709i	0.415713	−	0.240012i	0.693242	+	0.720705i	$0.256182\pi$
$822$	−5.18342	+	8.97794i	−0.180792	+	0.313142i
$823$	4.95968	−	8.59041i	0.172883	−	0.299443i	−0.766543	−	0.642193i	$-0.778025\pi$
$823$	4.95968	−	8.59041i	0.172883	−	0.299443i	0.939427	+	0.342750i	$0.111358\pi$
$824$	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	$-0.769229\pi$
$829$	5.75933	−	9.97546i	0.200030	−	0.346462i	0.948538	+	0.316664i	$0.102563\pi$
$830$	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	$0.271607\pi$
$839$			43.6475i			1.50688i	−0.657516	+	0.753440i	$0.728393\pi$
$840$		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
$845$	4.30863	+	4.16202i	0.148221	+	0.143178i
$846$	−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	$0.0552832\pi$
$853$			10.0940i			0.345611i	−0.984956	+	0.172806i	$0.944717\pi$
$854$		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	$-0.698734\pi$
$857$	12.0133	−	20.8077i	0.410368	−	0.710777i	0.994930	+	0.100571i	$0.0320671\pi$
$858$	−1.73781	+	0.737507i	−0.0593280	+	0.0251781i
$859$	−0.829914	−	1.43745i	−0.0283163	−	0.0490452i	0.851520	−	0.524322i	$-0.175681\pi$
$859$	−0.829914	−	1.43745i	−0.0283163	−	0.0490452i	−0.879836	+	0.475277i	$0.842348\pi$
$860$			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	$-0.504671\pi$
$863$	24.7917	−	14.3135i	0.843920	−	0.487238i	0.858595	+	0.512655i	$0.171338\pi$
$864$	−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
$871$	−7.15319	−	16.8553i	−0.242376	−	0.571120i
$872$	−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	$-0.424343\pi$
$877$	35.3846	−	20.4293i	1.19485	−	0.689850i	0.959404	+	0.282037i	$0.0910100\pi$
$878$	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	$-0.194856\pi$
$881$	48.5835			1.63682			0.818411	+	0.574634i	$0.194856\pi$
$882$		0			0
$883$	49.2456			1.65725			0.828624	−	0.559806i	$-0.189124\pi$
$883$	49.2456			1.65725			0.828624	+	0.559806i	$0.189124\pi$
$884$	−0.798695	+	6.50090i	−0.0268630	+	0.218649i
$885$	−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	$-0.237672\pi$
$887$	−6.58864	−	11.4119i	−0.221225	−	0.383173i	−0.955180	+	0.296025i	$0.904339\pi$
$888$	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	−0.710552	−	0.703645i	$-0.751555\pi$
$907$	7.65255	−	13.2546i	0.254099	−	0.440112i	0.964650	+	0.263533i	$0.0848878\pi$
$908$	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	0.940360	+	0.340180i	$0.110488\pi$
$919$	23.1845	+	40.1567i	0.764785	+	1.32465i	−0.175575	+	0.984466i	$0.556179\pi$
$920$	−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	−0.794721	−	0.606975i	$-0.792383\pi$
$929$	−20.3123	+	11.7273i	−0.666426	+	0.384761i	0.128295	+	0.991736i	$0.459050\pi$
$930$			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
$936$	−29.8465	−	3.66692i	−0.975564	−	0.119857i
$937$	18.0156			0.588544			0.294272	−	0.955722i	$-0.404923\pi$
$937$	18.0156			0.588544			0.294272	+	0.955722i	$0.404923\pi$
$938$		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	0.876295	−	0.481774i	$-0.160008\pi$
$941$	27.5227	+	15.8902i	0.897214	+	0.518007i	0.0209188	+	0.999781i	$0.493341\pi$
$942$	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	$-0.938348\pi$
$947$	−40.1673	+	23.1906i	−1.30526	+	0.753593i	−0.323961	+	0.946071i	$0.605015\pi$
$948$	0.479063	−	0.829761i	0.0155592	−	0.0269494i
$949$	0.497931	+	1.17329i	0.0161635	+	0.0380866i
$950$	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
$962$	36.9336	−	15.6742i	1.19079	−	0.505356i
$963$	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	$-0.238712\pi$
$971$	−6.99281	−	12.1119i	−0.224410	−	0.388690i	−0.956142	+	0.292903i	$0.905379\pi$
$972$	−8.02666			−0.257455
$973$		0			0
$974$	−15.9832			−0.512134
$975$	−1.13498	+	9.23809i	−0.0363486	+	0.295856i
$976$	−8.49693	+	14.7171i	−0.271980	+	0.471083i
$977$	47.4109	+	27.3727i	1.51681	+	0.875730i	0.999805	+	0.0197472i	$0.00628614\pi$
$977$	47.4109	+	27.3727i	1.51681	+	0.875730i	0.517004	+	0.855983i	$0.327047\pi$
$978$	−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	0.499448	−	0.866344i	$-0.333536\pi$
$983$	−0.0346349	−	0.0199965i	−0.00110468	−	0.000637789i	−0.500552	+	0.865706i	$0.666870\pi$
$984$	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	0.0180505	+	0.999837i	$0.494254\pi$
$991$	−26.9741	+	46.7204i	−0.856859	+	1.48412i	−0.874910	+	0.484286i	$0.839079\pi$
$992$	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	−0.313072	−	0.949730i	$-0.601358\pi$
$997$	21.0277	−	36.4211i	0.665954	−	1.15347i	0.979026	−	0.203737i	$-0.0653087\pi$
$998$	−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.d.116.5		12
7.2	even	3	inner	637.2.r.d.324.2		12
7.3	odd	6		91.2.c.a.64.5	yes	6
7.4	even	3		637.2.c.d.246.5		6
7.5	odd	6		637.2.r.e.324.2		12
7.6	odd	2		637.2.r.e.116.5		12
13.12	even	2	inner	637.2.r.d.116.2		12
21.17	even	6		819.2.c.b.64.2		6
28.3	even	6		1456.2.k.c.337.3		6
91.12	odd	6		637.2.r.e.324.5		12
91.18	odd	12		8281.2.a.be.1.3		3
91.25	even	6		637.2.c.d.246.2		6
91.31	even	12		1183.2.a.h.1.3		3
91.38	odd	6		91.2.c.a.64.2	✓	6
91.51	even	6	inner	637.2.r.d.324.5		12
91.60	odd	12		8281.2.a.bi.1.1		3
91.73	even	12		1183.2.a.j.1.1		3
91.90	odd	2		637.2.r.e.116.2		12
273.38	even	6		819.2.c.b.64.5		6
364.311	even	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	91.38	odd	6
91.2.c.a.64.5	yes	6	7.3	odd	6
637.2.c.d.246.2		6	91.25	even	6
637.2.c.d.246.5		6	7.4	even	3
637.2.r.d.116.2		12	13.12	even	2	inner
637.2.r.d.116.5		12	1.1	even	1	trivial
637.2.r.d.324.2		12	7.2	even	3	inner
637.2.r.d.324.5		12	91.51	even	6	inner
637.2.r.e.116.2		12	91.90	odd	2
637.2.r.e.116.5		12	7.6	odd	2
637.2.r.e.324.2		12	7.5	odd	6
637.2.r.e.324.5		12	91.12	odd	6
819.2.c.b.64.2		6	21.17	even	6
819.2.c.b.64.5		6	273.38	even	6
1183.2.a.h.1.3		3	91.31	even	12
1183.2.a.j.1.1		3	91.73	even	12
1456.2.k.c.337.3		6	28.3	even	6
1456.2.k.c.337.4		6	364.311	even	6
8281.2.a.be.1.3		3	91.18	odd	12
8281.2.a.bi.1.1		3	91.60	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.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} +(4.18732 + 0.514451i) 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} +(1.78958 - 0.759478i) 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} +(-2.09397 + 0.888655i) 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} +(1.64908 + 0.202604i) 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

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Database

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