LMFDB - Embedded newform 637.2.g.j.263.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(263,637)]

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, 2]))

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

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

chi := DirichletCharacter("637.263");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.g (of order $3$, 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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 7x^{6} + 38x^{4} - 16x^{3} + 15x^{2} + 3x + 1 $ x^8 - x^7 + 7x^6 + 38x^4 - 16x^3 + 15x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			263.3
Root			$0.355143 - 0.615126i$ of defining polynomial
Character	$\chi$	$=$	637.263
Dual form			637.2.g.j.373.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.355143 - 0.615126i) q^{2} -2.40788 q^{3} +(0.747746 + 1.29513i) q^{4} +(-0.644857 - 1.11692i) q^{5} +(-0.855143 + 1.48115i) q^{6} +2.48280 q^{8} +2.79790 q^{9} +O(q^{10})$	\(q+(0.355143 - 0.615126i) q^{2} -2.40788 q^{3} +(0.747746 + 1.29513i) q^{4} +(-0.644857 - 1.11692i) q^{5} +(-0.855143 + 1.48115i) q^{6} +2.48280 q^{8} +2.79790 q^{9} -0.916066 q^{10} -2.40788 q^{11} +(-1.80049 - 3.11853i) q^{12} +(-1.25409 - 3.38042i) q^{13} +(1.55274 + 2.68942i) q^{15} +(-0.613742 + 1.06303i) q^{16} +(1.95169 + 3.38042i) q^{17} +(0.993655 - 1.72106i) q^{18} +5.89068 q^{19} +(0.964379 - 1.67035i) q^{20} +(-0.855143 + 1.48115i) q^{22} +(3.16197 - 5.47670i) q^{23} -5.97829 q^{24} +(1.66832 - 2.88961i) q^{25} +(-2.52477 - 0.429109i) q^{26} +0.486640 q^{27} +(-2.80683 - 4.86157i) q^{29} +2.20578 q^{30} +(1.10289 - 1.91026i) q^{31} +(2.91873 + 5.05540i) q^{32} +5.79790 q^{33} +2.77252 q^{34} +(2.09212 + 3.62365i) q^{36} +(2.55908 - 4.43246i) q^{37} +(2.09204 - 3.62351i) q^{38} +(3.01971 + 8.13966i) q^{39} +(-1.60105 - 2.77310i) q^{40} +(-3.89260 - 6.74219i) q^{41} +(-0.144857 + 0.250899i) q^{43} +(-1.80049 - 3.11853i) q^{44} +(-1.80424 - 3.12504i) q^{45} +(-2.24591 - 3.89003i) q^{46} +(0.638511 + 1.10593i) q^{47} +(1.47782 - 2.55966i) q^{48} +(-1.18499 - 2.05245i) q^{50} +(-4.69943 - 8.13966i) q^{51} +(3.44036 - 4.15192i) q^{52} +(6.81126 - 11.7974i) q^{53} +(0.172827 - 0.299345i) q^{54} +(1.55274 + 2.68942i) q^{55} -14.1841 q^{57} -3.98731 q^{58} +(-2.01528 - 3.49057i) q^{59} +(-2.32211 + 4.02201i) q^{60} +4.60097 q^{61} +(-0.783368 - 1.35683i) q^{62} +1.69131 q^{64} +(-2.96697 + 3.58061i) q^{65} +(2.05908 - 3.56644i) q^{66} +7.57559 q^{67} +(-2.91873 + 5.05540i) q^{68} +(-7.61366 + 13.1872i) q^{69} +(-3.61366 + 6.25905i) q^{71} +6.94662 q^{72} +(-7.50626 + 13.0012i) q^{73} +(-1.81768 - 3.14832i) q^{74} +(-4.01712 + 6.95785i) q^{75} +(4.40474 + 7.62923i) q^{76} +(6.07935 + 1.03324i) q^{78} +(4.65379 + 8.06060i) q^{79} +1.58310 q^{80} -9.56546 q^{81} -5.52973 q^{82} +1.36463 q^{83} +(2.51712 - 4.35978i) q^{85} +(0.102890 + 0.178210i) q^{86} +(6.75852 + 11.7061i) q^{87} -5.97829 q^{88} +(-0.449849 + 0.779162i) q^{89} -2.56306 q^{90} +9.45742 q^{92} +(-2.65563 + 4.59968i) q^{93} +0.907052 q^{94} +(-3.79865 - 6.57945i) q^{95} +(-7.02797 - 12.1728i) q^{96} +(7.83288 - 13.5669i) q^{97} -6.73701 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} - 2 q^{3} - 5 q^{4} - 7 q^{5} - 5 q^{6} - 12 q^{8} + 14 q^{9}+O(q^{10}) $ 8 * q + q^2 - 2 * q^3 - 5 * q^4 - 7 * q^5 - 5 * q^6 - 12 * q^8 + 14 * q^9	$ 8 q + q^{2} - 2 q^{3} - 5 q^{4} - 7 q^{5} - 5 q^{6} - 12 q^{8} + 14 q^{9} + 22 q^{10} - 2 q^{11} + 12 q^{12} - 4 q^{13} - 3 q^{15} - 19 q^{16} - 4 q^{17} + 3 q^{18} - 2 q^{19} - 2 q^{20} - 5 q^{22} + 2 q^{23} + 6 q^{24} - 5 q^{25} - 3 q^{26} + 52 q^{27} - q^{29} - 8 q^{30} - 4 q^{31} + 33 q^{32} + 38 q^{33} - 6 q^{34} + 34 q^{36} + 10 q^{37} - 23 q^{38} - 19 q^{39} - 17 q^{40} - 22 q^{41} - 3 q^{43} + 12 q^{44} - 11 q^{45} - 24 q^{46} + 2 q^{47} + 11 q^{48} - 43 q^{50} - 7 q^{51} + 34 q^{52} - 2 q^{53} + 5 q^{54} - 3 q^{55} - 34 q^{57} - 22 q^{58} - 8 q^{59} + 11 q^{60} - 16 q^{61} - 5 q^{62} + 28 q^{64} + 4 q^{65} + 6 q^{66} - 12 q^{67} - 33 q^{68} - 18 q^{69} + 14 q^{71} + 10 q^{72} - 8 q^{73} - 20 q^{74} - 7 q^{75} + 32 q^{76} - q^{78} + 26 q^{79} - 14 q^{80} + 48 q^{81} + 28 q^{82} - 5 q^{85} - 12 q^{86} + 13 q^{87} + 6 q^{88} - q^{89} - 52 q^{90} + 24 q^{92} + 7 q^{93} - 66 q^{94} - 21 q^{95} - 58 q^{96} + 3 q^{97} + 46 q^{99}+O(q^{100}) $ 8 * q + q^2 - 2 * q^3 - 5 * q^4 - 7 * q^5 - 5 * q^6 - 12 * q^8 + 14 * q^9 + 22 * q^10 - 2 * q^11 + 12 * q^12 - 4 * q^13 - 3 * q^15 - 19 * q^16 - 4 * q^17 + 3 * q^18 - 2 * q^19 - 2 * q^20 - 5 * q^22 + 2 * q^23 + 6 * q^24 - 5 * q^25 - 3 * q^26 + 52 * q^27 - q^29 - 8 * q^30 - 4 * q^31 + 33 * q^32 + 38 * q^33 - 6 * q^34 + 34 * q^36 + 10 * q^37 - 23 * q^38 - 19 * q^39 - 17 * q^40 - 22 * q^41 - 3 * q^43 + 12 * q^44 - 11 * q^45 - 24 * q^46 + 2 * q^47 + 11 * q^48 - 43 * q^50 - 7 * q^51 + 34 * q^52 - 2 * q^53 + 5 * q^54 - 3 * q^55 - 34 * q^57 - 22 * q^58 - 8 * q^59 + 11 * q^60 - 16 * q^61 - 5 * q^62 + 28 * q^64 + 4 * q^65 + 6 * q^66 - 12 * q^67 - 33 * q^68 - 18 * q^69 + 14 * q^71 + 10 * q^72 - 8 * q^73 - 20 * q^74 - 7 * q^75 + 32 * q^76 - q^78 + 26 * q^79 - 14 * q^80 + 48 * q^81 + 28 * q^82 - 5 * q^85 - 12 * q^86 + 13 * q^87 + 6 * q^88 - q^89 - 52 * q^90 + 24 * q^92 + 7 * q^93 - 66 * q^94 - 21 * q^95 - 58 * q^96 + 3 * q^97 + 46 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.355143	−	0.615126i	0.251124	−	0.434960i	−0.712711	−	0.701457i	$-0.752533\pi$
$2$	0.355143	−	0.615126i	0.251124	−	0.434960i	0.963836	+	0.266497i	$0.0858664\pi$
$3$	−2.40788			−1.39019			−0.695096	−	0.718917i	$-0.744638\pi$
$3$	−2.40788			−1.39019			−0.695096	+	0.718917i	$0.744638\pi$
$4$	0.747746	+	1.29513i	0.373873	+	0.647567i
$5$	−0.644857	−	1.11692i	−0.288389	−	0.499504i	0.685037	−	0.728509i	$-0.259786\pi$
$5$	−0.644857	−	1.11692i	−0.288389	−	0.499504i	−0.973425	+	0.229005i	$0.926453\pi$
$6$	−0.855143	+	1.48115i	−0.349111	+	0.604678i
$7$		0			0
$7$		0			0
$8$	2.48280			0.877803
$9$	2.79790			0.932632
$10$	−0.916066			−0.289686
$11$	−2.40788			−0.726004			−0.363002	−	0.931788i	$-0.618248\pi$
$11$	−2.40788			−0.726004			−0.363002	+	0.931788i	$0.618248\pi$
$12$	−1.80049	−	3.11853i	−0.519755	−	0.900243i
$13$	−1.25409	−	3.38042i	−0.347823	−	0.937560i
$13$	−1.25409	−	3.38042i	−0.347823	−	0.937560i
$14$		0			0
$15$	1.55274	+	2.68942i	0.400915	+	0.694406i
$16$	−0.613742	+	1.06303i	−0.153436	+	0.265758i
$17$	1.95169	+	3.38042i	0.473354	+	0.819873i	0.999535	−	0.0304998i	$-0.00970990\pi$
$17$	1.95169	+	3.38042i	0.473354	+	0.819873i	−0.526181	+	0.850373i	$0.676377\pi$
$18$	0.993655	−	1.72106i	0.234207	−	0.405658i
$19$	5.89068			1.35142			0.675708	−	0.737170i	$-0.263838\pi$
$19$	5.89068			1.35142			0.675708	+	0.737170i	$0.263838\pi$
$20$	0.964379	−	1.67035i	0.215642	−	0.373502i
$21$		0			0
$22$	−0.855143	+	1.48115i	−0.182317	+	0.315783i
$23$	3.16197	−	5.47670i	0.659317	−	1.14197i	−0.321475	−	0.946918i	$-0.604179\pi$
$23$	3.16197	−	5.47670i	0.659317	−	1.14197i	0.980793	−	0.195053i	$-0.0624879\pi$
$24$	−5.97829			−1.22031
$25$	1.66832	−	2.88961i	0.333664	−	0.577923i
$26$	−2.52477	−	0.429109i	−0.495148	−	0.0841553i
$27$	0.486640			0.0936539
$28$		0			0
$29$	−2.80683	−	4.86157i	−0.521215	−	0.902772i	−0.999696	−	0.0246732i	$-0.992145\pi$
$29$	−2.80683	−	4.86157i	−0.521215	−	0.902772i	0.478480	−	0.878098i	$-0.341188\pi$
$30$	2.20578			0.402718
$31$	1.10289	−	1.91026i	0.198085	−	0.343093i	−0.749823	−	0.661639i	$-0.769861\pi$
$31$	1.10289	−	1.91026i	0.198085	−	0.343093i	0.947907	+	0.318546i	$0.103195\pi$
$32$	2.91873	+	5.05540i	0.515964	+	0.893676i
$33$	5.79790			1.00928
$34$	2.77252			0.475482
$35$		0			0
$36$	2.09212	+	3.62365i	0.348686	+	0.603942i
$37$	2.55908	−	4.43246i	0.420711	−	0.728693i	−0.575298	−	0.817944i	$-0.695114\pi$
$37$	2.55908	−	4.43246i	0.420711	−	0.728693i	0.996009	+	0.0892511i	$0.0284473\pi$
$38$	2.09204	−	3.62351i	0.339373	−	0.587812i
$39$	3.01971	+	8.13966i	0.483540	+	1.30339i
$40$	−1.60105	−	2.77310i	−0.253148	−	0.438466i
$41$	−3.89260	−	6.74219i	−0.607922	−	1.05295i	−0.991582	−	0.129478i	$-0.958670\pi$
$41$	−3.89260	−	6.74219i	−0.607922	−	1.05295i	0.383660	−	0.923474i	$-0.374664\pi$
$42$		0			0
$43$	−0.144857	+	0.250899i	−0.0220904	+	0.0382618i	−0.876859	−	0.480747i	$-0.840366\pi$
$43$	−0.144857	+	0.250899i	−0.0220904	+	0.0382618i	0.854769	+	0.519009i	$0.173699\pi$
$44$	−1.80049	−	3.11853i	−0.271433	−	0.470136i
$45$	−1.80424	−	3.12504i	−0.268961	−	0.465853i
$46$	−2.24591	−	3.89003i	−0.331141	−	0.573553i
$47$	0.638511	+	1.10593i	0.0931364	+	0.161317i	0.908829	−	0.417168i	$-0.136977\pi$
$47$	0.638511	+	1.10593i	0.0931364	+	0.161317i	−0.815693	+	0.578485i	$0.803644\pi$
$48$	1.47782	−	2.55966i	0.213305	−	0.369455i
$49$		0			0
$50$	−1.18499	−	2.05245i	−0.167582	−	0.290261i
$51$	−4.69943	−	8.13966i	−0.658052	−	1.13978i
$52$	3.44036	−	4.15192i	0.477092	−	0.575767i
$53$	6.81126	−	11.7974i	0.935598	−	1.62050i	0.162034	−	0.986785i	$-0.448194\pi$
$53$	6.81126	−	11.7974i	0.935598	−	1.62050i	0.773564	−	0.633718i	$-0.218472\pi$
$54$	0.172827	−	0.299345i	0.0235188	−	0.0407357i
$55$	1.55274	+	2.68942i	0.209371	+	0.362642i
$56$		0			0
$57$	−14.1841			−1.87873
$58$	−3.98731			−0.523559
$59$	−2.01528	−	3.49057i	−0.262367	−	0.454433i	0.704503	−	0.709701i	$-0.251170\pi$
$59$	−2.01528	−	3.49057i	−0.262367	−	0.454433i	−0.966870	+	0.255268i	$0.917836\pi$
$60$	−2.32211	+	4.02201i	−0.299783	+	0.519240i
$61$	4.60097			0.589094			0.294547	−	0.955637i	$-0.404831\pi$
$61$	4.60097			0.589094			0.294547	+	0.955637i	$0.404831\pi$
$62$	−0.783368	−	1.35683i	−0.0994878	−	0.172318i
$63$		0			0
$64$	1.69131			0.211413
$65$	−2.96697	+	3.58061i	−0.368007	+	0.444120i
$66$	2.05908	−	3.56644i	0.253456	−	0.438998i
$67$	7.57559			0.925505			0.462753	−	0.886487i	$-0.346862\pi$
$67$	7.57559			0.925505			0.462753	+	0.886487i	$0.346862\pi$
$68$	−2.91873	+	5.05540i	−0.353949	+	0.613057i
$69$	−7.61366	+	13.1872i	−0.916577	+	1.58756i
$70$		0			0
$71$	−3.61366	+	6.25905i	−0.428863	+	0.742812i	−0.996772	−	0.0802788i	$-0.974419\pi$
$71$	−3.61366	+	6.25905i	−0.428863	+	0.742812i	0.567910	+	0.823091i	$0.307752\pi$
$72$	6.94662			0.818668
$73$	−7.50626	+	13.0012i	−0.878542	+	1.52168i	−0.0256006	+	0.999672i	$0.508150\pi$
$73$	−7.50626	+	13.0012i	−0.878542	+	1.52168i	−0.852941	+	0.522007i	$0.825184\pi$
$74$	−1.81768	−	3.14832i	−0.211301	−	0.365985i
$75$	−4.01712	+	6.95785i	−0.463857	+	0.803424i
$76$	4.40474	+	7.62923i	0.505258	+	0.875133i
$77$		0			0
$78$	6.07935	+	1.03324i	0.688350	+	0.116992i
$79$	4.65379	+	8.06060i	0.523592	+	0.906889i	0.999623	+	0.0274598i	$0.00874182\pi$
$79$	4.65379	+	8.06060i	0.523592	+	0.906889i	−0.476031	+	0.879429i	$0.657925\pi$
$80$	1.58310			0.176996
$81$	−9.56546			−1.06283
$82$	−5.52973			−0.610656
$83$	1.36463			0.149788			0.0748940	−	0.997192i	$-0.476138\pi$
$83$	1.36463			0.149788			0.0748940	+	0.997192i	$0.476138\pi$
$84$		0			0
$85$	2.51712	−	4.35978i	0.273020	−	0.472884i
$86$	0.102890	+	0.178210i	0.0110949	+	0.0192169i
$87$	6.75852	+	11.7061i	0.724589	+	1.25503i
$88$	−5.97829			−0.637288
$89$	−0.449849	+	0.779162i	−0.0476839	+	0.0825910i	−0.888882	−	0.458136i	$-0.848517\pi$
$89$	−0.449849	+	0.779162i	−0.0476839	+	0.0825910i	0.841198	+	0.540727i	$0.181851\pi$
$90$	−2.56306			−0.270170
$91$		0			0
$92$	9.45742			0.986004
$93$	−2.65563	+	4.59968i	−0.275376	+	0.476965i
$94$	0.907052			0.0935553
$95$	−3.79865	−	6.57945i	−0.389733	−	0.675037i
$96$	−7.02797	−	12.1728i	−0.717289	−	1.24238i
$97$	7.83288	−	13.5669i	0.795309	−	1.37752i	−0.127334	−	0.991860i	$-0.540642\pi$
$97$	7.83288	−	13.5669i	0.795309	−	1.37752i	0.922643	−	0.385655i	$-0.126025\pi$
$98$		0			0
$99$	−6.73701			−0.677095
$100$	4.98992			0.498992
$101$	−0.684905			−0.0681506			−0.0340753	−	0.999419i	$-0.510849\pi$
$101$	−0.684905			−0.0681506			−0.0340753	+	0.999419i	$0.510849\pi$
$102$	−6.67589			−0.661012
$103$	8.96246	+	15.5234i	0.883097	+	1.52957i	0.847879	+	0.530190i	$0.177879\pi$
$103$	8.96246	+	15.5234i	0.883097	+	1.52957i	0.0352185	+	0.999380i	$0.488787\pi$
$104$	−3.11366	−	8.39292i	−0.305320	−	0.822993i
$105$		0			0
$106$	−4.83795	−	8.37957i	−0.469903	−	0.813895i
$107$	−4.24775	+	7.35731i	−0.410645	+	0.711258i	−0.994960	−	0.100268i	$-0.968030\pi$
$107$	−4.24775	+	7.35731i	−0.410645	+	0.711258i	0.584315	+	0.811527i	$0.301363\pi$
$108$	0.363883	+	0.630264i	0.0350147	+	0.0606472i
$109$	−6.04639	+	10.4727i	−0.579139	+	1.00310i	0.416439	+	0.909164i	$0.363278\pi$
$109$	−6.04639	+	10.4727i	−0.579139	+	1.00310i	−0.995578	+	0.0939352i	$0.970055\pi$
$110$	2.20578			0.210313
$111$	−6.16197	+	10.6729i	−0.584869	+	1.01302i
$112$		0			0
$113$	7.12635	−	12.3432i	0.670391	−	1.16115i	−0.307402	−	0.951580i	$-0.599460\pi$
$113$	7.12635	−	12.3432i	0.670391	−	1.16115i	0.977793	−	0.209571i	$-0.0672069\pi$
$114$	−5.03738	+	8.72500i	−0.471794	+	0.817171i
$115$	−8.15608			−0.760558
$116$	4.19760	−	7.27045i	0.389737	−	0.675044i
$117$	−3.50882	−	9.45807i	−0.324391	−	0.874399i
$118$	−2.86285			−0.263547
$119$		0			0
$120$	3.85514	+	6.67730i	0.351925	+	0.609552i
$121$	−5.20210			−0.472918
$122$	1.63400	−	2.83018i	0.147936	−	0.256232i
$123$	9.37293	+	16.2344i	0.845129	+	1.46381i
$124$	3.29873			0.296234
$125$	−10.7519			−0.961677
$126$		0			0
$127$	4.41231	+	7.64234i	0.391529	+	0.678148i	0.992651	−	0.121009i	$-0.0386129\pi$
$127$	4.41231	+	7.64234i	0.391529	+	0.678148i	−0.601122	+	0.799157i	$0.705280\pi$
$128$	−5.23681	+	9.07043i	−0.462873	+	0.801720i
$129$	0.348798	−	0.604136i	0.0307099	−	0.0531912i
$130$	1.14883	+	3.09669i	0.100759	+	0.271598i
$131$	−9.71471	−	16.8264i	−0.848778	−	1.47013i	−0.882299	−	0.470689i	$-0.844005\pi$
$131$	−9.71471	−	16.8264i	−0.848778	−	1.47013i	0.0335206	−	0.999438i	$-0.489328\pi$
$132$	4.33536	+	7.50906i	0.377344	+	0.653580i
$133$		0			0
$134$	2.69042	−	4.65994i	0.232417	−	0.402558i
$135$	−0.313813	−	0.543540i	−0.0270087	−	0.0467805i
$136$	4.84565	+	8.39292i	0.415511	+	0.719687i
$137$	−5.11809	−	8.86479i	−0.437268	−	0.757370i	0.560210	−	0.828351i	$-0.310720\pi$
$137$	−5.11809	−	8.86479i	−0.437268	−	0.757370i	−0.997478	+	0.0709806i	$0.977387\pi$
$138$	5.40788	+	9.36673i	0.460350	+	0.797349i
$139$	4.07361	−	7.05571i	0.345519	−	0.598457i	−0.639929	−	0.768434i	$-0.721036\pi$
$139$	4.07361	−	7.05571i	0.345519	−	0.598457i	0.985448	+	0.169977i	$0.0543694\pi$
$140$		0			0
$141$	−1.53746	−	2.66296i	−0.129477	−	0.224262i
$142$	2.56674	+	4.44572i	0.215396	+	0.373076i
$143$	3.01971	+	8.13966i	0.252520	+	0.680672i
$144$	−1.71719	+	2.97426i	−0.143099	+	0.247855i
$145$	−3.62001	+	6.27004i	−0.300625	+	0.520698i
$146$	5.33160	+	9.23460i	0.441246	+	0.764261i
$147$		0			0
$148$	7.65419			0.629170
$149$	−9.78888			−0.801937			−0.400968	−	0.916092i	$-0.631326\pi$
$149$	−9.78888			−0.801937			−0.400968	+	0.916092i	$0.631326\pi$
$150$	2.85330	+	4.94207i	0.232971	+	0.403518i
$151$	−7.37034	+	12.7658i	−0.599790	+	1.03887i	0.393062	+	0.919512i	$0.371416\pi$
$151$	−7.37034	+	12.7658i	−0.599790	+	1.03887i	−0.992852	+	0.119355i	$0.961917\pi$
$152$	14.6254			1.18628
$153$	5.46062	+	9.45807i	0.441465	+	0.764640i
$154$		0			0
$155$	−2.84482			−0.228502
$156$	−8.28398	+	9.99733i	−0.663249	+	0.800427i
$157$	10.2922	−	17.8266i	0.821409	−	1.42272i	−0.0832247	−	0.996531i	$-0.526522\pi$
$157$	10.2922	−	17.8266i	0.821409	−	1.42272i	0.904633	−	0.426191i	$-0.140145\pi$
$158$	6.61105			0.525947
$159$	−16.4007	+	28.4069i	−1.30066	+	2.25281i
$160$	3.76433	−	6.52001i	0.297597	−	0.515452i
$161$		0			0
$162$	−3.39711	+	5.88397i	−0.266902	+	0.462288i
$163$	−3.98086			−0.311805			−0.155902	−	0.987772i	$-0.549829\pi$
$163$	−3.98086			−0.311805			−0.155902	+	0.987772i	$0.549829\pi$
$164$	5.82136	−	10.0829i	0.454572	−	0.787342i
$165$	−3.73881	−	6.47581i	−0.291066	−	0.504141i
$166$	0.484640	−	0.839422i	0.0376154	−	0.0651518i
$167$	4.33923	+	7.51576i	0.335780	+	0.581587i	0.983634	−	0.180177i	$-0.0576670\pi$
$167$	4.33923	+	7.51576i	0.335780	+	0.581587i	−0.647855	+	0.761764i	$0.724334\pi$
$168$		0			0
$169$	−9.85451	+	8.47872i	−0.758039	+	0.652209i
$170$	−1.78787	−	3.09669i	−0.137124	−	0.237505i
$171$	16.4815			1.26037
$172$	−0.433264			−0.0330361
$173$	−0.933934			−0.0710057			−0.0355028	−	0.999370i	$-0.511303\pi$
$173$	−0.933934			−0.0710057			−0.0355028	+	0.999370i	$0.511303\pi$
$174$	9.60097			0.727848
$175$		0			0
$176$	1.47782	−	2.55966i	0.111395	−	0.192942i
$177$	4.85256	+	8.40487i	0.364740	+	0.631749i
$178$	0.319522	+	0.553428i	0.0239492	+	0.0414812i
$179$	13.5461			1.01248			0.506241	−	0.862392i	$-0.331034\pi$
$179$	13.5461			1.01248			0.506241	+	0.862392i	$0.331034\pi$
$180$	2.69823	−	4.67348i	0.201114	−	0.348340i
$181$	8.86269			0.658759			0.329379	−	0.944198i	$-0.393161\pi$
$181$	8.86269			0.658759			0.329379	+	0.944198i	$0.393161\pi$
$182$		0			0
$183$	−11.0786			−0.818953
$184$	7.85056	−	13.5976i	0.578751	−	1.00243i
$185$	−6.60097			−0.485313
$186$	1.88626	+	3.26709i	0.138307	+	0.239555i
$187$	−4.69943	−	8.13966i	−0.343657	−	0.595231i
$188$	−0.954889	+	1.65392i	−0.0696424	+	0.120624i
$189$		0			0
$190$	−5.39626			−0.391486
$191$	−15.3735			−1.11239			−0.556193	−	0.831053i	$-0.687739\pi$
$191$	−15.3735			−1.11239			−0.556193	+	0.831053i	$0.687739\pi$
$192$	−4.07247			−0.293905
$193$	−24.4953			−1.76321			−0.881606	−	0.471986i	$-0.843537\pi$
$193$	−24.4953			−1.76321			−0.881606	+	0.471986i	$0.843537\pi$
$194$	−5.56359	−	9.63642i	−0.399443	−	0.691855i
$195$	7.14411	−	8.62170i	0.511600	−	0.617413i
$196$		0			0
$197$	3.35706	+	5.81460i	0.239181	+	0.414273i	0.960479	−	0.278351i	$-0.0897878\pi$
$197$	3.35706	+	5.81460i	0.239181	+	0.414273i	−0.721299	+	0.692624i	$0.756454\pi$
$198$	−2.39260	+	4.14411i	−0.170035	+	0.294509i
$199$	−2.43641	−	4.21998i	−0.172712	−	0.299147i	0.766655	−	0.642059i	$-0.221920\pi$
$199$	−2.43641	−	4.21998i	−0.172712	−	0.299147i	−0.939367	+	0.342913i	$0.888586\pi$
$200$	4.14211	−	7.17434i	0.292891	−	0.507302i
$201$	−18.2411			−1.28663
$202$	−0.243239	+	0.421303i	−0.0171143	+	0.0296428i
$203$		0			0
$204$	7.02797	−	12.1728i	0.492056	−	0.852267i
$205$	−5.02034	+	8.69549i	−0.350636	+	0.607319i
$206$	12.7318			0.887069
$207$	8.84688	−	15.3232i	0.614901	−	1.06504i
$208$	4.36319	+	0.741567i	0.302533	+	0.0514184i
$209$	−14.1841			−0.981133
$210$		0			0
$211$	−1.84373	−	3.19344i	−0.126928	−	0.219846i	0.795557	−	0.605879i	$-0.207178\pi$
$211$	−1.84373	−	3.19344i	−0.126928	−	0.219846i	−0.922485	+	0.386033i	$0.873845\pi$
$212$	20.3724			1.39918
$213$	8.70127	−	15.0710i	0.596201	−	1.03265i
$214$	3.01712	+	5.22580i	0.206246	+	0.357228i
$215$	0.373647			0.0254825
$216$	1.20823			0.0822096
$217$		0			0
$218$	4.29467	+	7.43859i	0.290872	+	0.503805i
$219$	18.0742	−	31.3054i	1.22134	−	2.11543i
$220$	−2.32211	+	4.02201i	−0.156557	+	0.271164i
$221$	8.97966	−	10.8369i	0.604037	−	0.728968i
$222$	4.37677	+	7.58078i	0.293749	+	0.508789i
$223$	4.40713	+	7.63338i	0.295123	+	0.511169i	0.975014	−	0.222145i	$-0.0713059\pi$
$223$	4.40713	+	7.63338i	0.295123	+	0.511169i	−0.679890	+	0.733314i	$0.737973\pi$
$224$		0			0
$225$	4.66779	−	8.08484i	0.311186	−	0.538990i
$226$	−5.06175	−	8.76721i	−0.336703	−	0.583186i
$227$	−6.72557	−	11.6490i	−0.446391	−	0.773173i	0.551757	−	0.834005i	$-0.313958\pi$
$227$	−6.72557	−	11.6490i	−0.446391	−	0.773173i	−0.998148	+	0.0608325i	$0.980624\pi$
$228$	−10.6061	−	18.3703i	−0.702406	−	1.21660i
$229$	3.40788	+	5.90263i	0.225199	+	0.390056i	0.956379	−	0.292128i	$-0.0943634\pi$
$229$	3.40788	+	5.90263i	0.225199	+	0.390056i	−0.731180	+	0.682185i	$0.761030\pi$
$230$	−2.89658	+	5.01702i	−0.190995	+	0.330812i
$231$		0			0
$232$	−6.96881	−	12.0703i	−0.457524	−	0.792456i
$233$	12.5336	+	21.7089i	0.821105	+	1.42220i	0.904860	+	0.425709i	$0.139975\pi$
$233$	12.5336	+	21.7089i	0.821105	+	1.42220i	−0.0837552	+	0.996486i	$0.526691\pi$
$234$	−7.06404	−	1.20060i	−0.461791	−	0.0784859i
$235$	0.823496	−	1.42634i	0.0537190	−	0.0930440i
$236$	3.01384	−	5.22012i	0.196184	−	0.339801i
$237$	−11.2058	−	19.4090i	−0.727894	−	1.26075i
$238$		0			0
$239$	−2.78521			−0.180160			−0.0900800	−	0.995935i	$-0.528712\pi$
$239$	−2.78521			−0.180160			−0.0900800	+	0.995935i	$0.528712\pi$
$240$	−3.81193			−0.246059
$241$	3.48915	+	6.04338i	0.224756	+	0.389288i	0.956246	−	0.292563i	$-0.0945082\pi$
$241$	3.48915	+	6.04338i	0.224756	+	0.389288i	−0.731490	+	0.681852i	$0.761175\pi$
$242$	−1.84749	+	3.19995i	−0.118761	+	0.205701i
$243$	21.5726			1.38388
$244$	3.44036	+	5.95888i	0.220246	+	0.381478i
$245$		0			0
$246$	13.3149			0.848929
$247$	−7.38746	−	19.9130i	−0.470053	−	1.26703i
$248$	2.73826	−	4.74280i	0.173879	−	0.301168i
$249$	−3.28588			−0.208234
$250$	−3.81846	+	6.61376i	−0.241500	+	0.418291i
$251$	−0.391515	+	0.678123i	−0.0247122	+	0.0428028i	−0.878117	−	0.478446i	$-0.841200\pi$
$251$	−0.391515	+	0.678123i	−0.0247122	+	0.0428028i	0.853405	+	0.521249i	$0.174534\pi$
$252$		0			0
$253$	−7.61366	+	13.1872i	−0.478667	+	0.829075i
$254$	6.26801			0.393290
$255$	−6.06092	+	10.4978i	−0.379550	+	0.657399i
$256$	5.41095	+	9.37203i	0.338184	+	0.585752i
$257$	1.62902	−	2.82155i	0.101616	−	0.176003i	−0.810735	−	0.585414i	$-0.800932\pi$
$257$	1.62902	−	2.82155i	0.101616	−	0.176003i	0.912350	+	0.409410i	$0.134266\pi$
$258$	−0.247746	−	0.429109i	−0.0154240	−	0.0267152i
$259$		0			0
$260$	−6.85592	−	1.16523i	−0.425186	−	0.0722645i
$261$	−7.85322	−	13.6022i	−0.486102	−	0.841954i
$262$	−13.8005			−0.852595
$263$	29.5829			1.82416			0.912081	−	0.410010i	$-0.134475\pi$
$263$	29.5829			1.82416			0.912081	+	0.410010i	$0.134475\pi$
$264$	14.3950			0.885953
$265$	−17.5691			−1.07926
$266$		0			0
$267$	1.08318	−	1.87613i	0.0662898	−	0.114817i
$268$	5.66462	+	9.81141i	0.346022	+	0.599327i
$269$	0.618249	+	1.07084i	0.0376953	+	0.0652902i	0.884258	−	0.467000i	$-0.154665\pi$
$269$	0.618249	+	1.07084i	0.0376953	+	0.0652902i	−0.846562	+	0.532290i	$0.821332\pi$
$270$	−0.445794			−0.0271302
$271$	12.6036	−	21.8300i	0.765612	−	1.32608i	−0.174311	−	0.984691i	$-0.555770\pi$
$271$	12.6036	−	21.8300i	0.765612	−	1.32608i	0.939923	−	0.341388i	$-0.110897\pi$
$272$	−4.79133			−0.290517
$273$		0			0
$274$	−7.27062			−0.439234
$275$	−4.01712	+	6.95785i	−0.242241	+	0.419574i
$276$	−22.7724			−1.37073
$277$	−4.76801	−	8.25843i	−0.286482	−	0.496201i	0.686486	−	0.727143i	$-0.259152\pi$
$277$	−4.76801	−	8.25843i	−0.286482	−	0.496201i	−0.972967	+	0.230942i	$0.925819\pi$
$278$	−2.89343	−	5.01157i	−0.173537	−	0.300574i
$279$	3.08577	−	5.34471i	0.184740	−	0.319980i
$280$		0			0
$281$	9.56546			0.570628			0.285314	−	0.958434i	$-0.407902\pi$
$281$	9.56546			0.570628			0.285314	+	0.958434i	$0.407902\pi$
$282$	−2.18407			−0.130060
$283$	−11.4320			−0.679564			−0.339782	−	0.940504i	$-0.610353\pi$
$283$	−11.4320			−0.679564			−0.339782	+	0.940504i	$0.610353\pi$
$284$	−10.8084			−0.641361
$285$	9.14670	+	15.8425i	0.541803	+	0.938431i
$286$	6.07935	+	1.03324i	0.359479	+	0.0610971i
$287$		0			0
$288$	8.16632	+	14.1445i	0.481205	+	0.833472i
$289$	0.881831	−	1.52738i	0.0518724	−	0.0898457i
$290$	2.57124	+	4.45352i	0.150989	+	0.261520i
$291$	−18.8607	+	32.6676i	−1.10563	+	1.91501i
$292$	−22.4511			−1.31385
$293$	−4.67781	+	8.10220i	−0.273281	+	0.473336i	−0.969700	−	0.244299i	$-0.921442\pi$
$293$	−4.67781	+	8.10220i	−0.273281	+	0.473336i	0.696419	+	0.717635i	$0.254775\pi$
$294$		0			0
$295$	−2.59913	+	4.50183i	−0.151327	+	0.262107i
$296$	6.35370	−	11.0049i	0.369301	−	0.639649i
$297$	−1.17177			−0.0679931
$298$	−3.47646	+	6.02140i	−0.201386	+	0.348810i
$299$	−22.4790	−	3.82052i	−1.29999	−	0.220947i
$300$	−12.0151			−0.693695
$301$		0			0
$302$	5.23506	+	9.06738i	0.301244	+	0.521769i
$303$	1.64917			0.0947423
$304$	−3.61536	+	6.26199i	−0.207355	+	0.359150i
$305$	−2.96697	−	5.13894i	−0.169888	−	0.294255i
$306$	7.75721			0.443450
$307$	−8.11449			−0.463119			−0.231559	−	0.972821i	$-0.574383\pi$
$307$	−8.11449			−0.463119			−0.231559	+	0.972821i	$0.574383\pi$
$308$		0			0
$309$	−21.5805	−	37.3786i	−1.22767	−	2.12639i
$310$	−1.01032	+	1.74993i	−0.0573823	+	0.0993891i
$311$	−4.32008	+	7.48259i	−0.244969	+	0.424299i	−0.962123	−	0.272616i	$-0.912111\pi$
$311$	−4.32008	+	7.48259i	−0.244969	+	0.424299i	0.717154	+	0.696915i	$0.245444\pi$
$312$	7.49733	+	20.2092i	0.424453	+	1.14412i
$313$	−2.61366	−	4.52700i	−0.147733	−	0.255881i	0.782656	−	0.622454i	$-0.213864\pi$
$313$	−2.61366	−	4.52700i	−0.147733	−	0.255881i	−0.930389	+	0.366573i	$0.880531\pi$
$314$	−7.31043	−	12.6620i	−0.412551	−	0.714560i
$315$		0			0
$316$	−6.95971	+	12.0546i	−0.391514	+	0.678123i
$317$	−5.59646	−	9.69336i	−0.314329	−	0.544433i	0.664966	−	0.746874i	$-0.268446\pi$
$317$	−5.59646	−	9.69336i	−0.314329	−	0.544433i	−0.979295	+	0.202440i	$0.935113\pi$
$318$	11.6492	+	20.1770i	0.653255	+	1.13147i
$319$	6.75852	+	11.7061i	0.378404	+	0.655416i
$320$	−1.09065	−	1.88906i	−0.0609692	−	0.105602i
$321$	10.2281	−	17.7155i	0.570875	−	0.988785i
$322$		0			0
$323$	11.4968	+	19.9130i	0.639698	+	1.10799i
$324$	−7.15254	−	12.3886i	−0.397363	−	0.688254i
$325$	−11.8603	−	2.01578i	−0.657893	−	0.111815i
$326$	−1.41378	+	2.44873i	−0.0783018	+	0.135623i
$327$	14.5590	−	25.2169i	0.805115	−	1.39450i
$328$	−9.66456	−	16.7395i	−0.533636	−	0.924285i
$329$		0			0
$330$	−5.31126			−0.292375
$331$	20.0468			1.10187			0.550935	−	0.834548i	$-0.314271\pi$
$331$	20.0468			1.10187			0.550935	+	0.834548i	$0.314271\pi$
$332$	1.02040	+	1.76738i	0.0560017	+	0.0969978i
$333$	7.16006	−	12.4016i	0.392369	−	0.679602i
$334$	6.16419			0.337290
$335$	−4.88517	−	8.46136i	−0.266905	−	0.462294i
$336$		0			0
$337$	18.5866			1.01248			0.506239	−	0.862393i	$-0.331035\pi$
$337$	18.5866			1.01248			0.506239	+	0.862393i	$0.331035\pi$
$338$	1.71572	+	9.07293i	0.0933229	+	0.493502i
$339$	−17.1594	+	29.7210i	−0.931972	+	1.61422i
$340$	7.52866			0.408299
$341$	−2.65563	+	4.59968i	−0.143810	+	0.249087i
$342$	5.85330	−	10.1382i	0.316510	−	0.548212i
$343$		0			0
$344$	−0.359650	+	0.622933i	−0.0193911	+	0.0335863i
$345$	19.6389			1.05732
$346$	−0.331680	+	0.574487i	−0.0178312	+	0.0308846i
$347$	−11.1708	−	19.3484i	−0.599681	−	1.03868i	−0.992868	−	0.119220i	$-0.961961\pi$
$347$	−11.1708	−	19.3484i	−0.599681	−	1.03868i	0.393186	−	0.919459i	$-0.371373\pi$
$348$	−10.1073	+	17.5064i	−0.541809	+	0.938441i
$349$	4.39316	+	7.60917i	0.235160	+	0.407310i	0.959319	−	0.282323i	$-0.0911051\pi$
$349$	4.39316	+	7.60917i	0.235160	+	0.407310i	−0.724159	+	0.689633i	$0.757772\pi$
$350$		0			0
$351$	−0.610291	−	1.64505i	−0.0325749	−	0.0878061i
$352$	−7.02797	−	12.1728i	−0.374592	−	0.648812i
$353$	−7.71898			−0.410840			−0.205420	−	0.978674i	$-0.565856\pi$
$353$	−7.71898			−0.410840			−0.205420	+	0.978674i	$0.565856\pi$
$354$	6.89341			0.366381
$355$	9.32118			0.494717
$356$	−1.34549			−0.0713110
$357$		0			0
$358$	4.81081	−	8.33256i	0.254259	−	0.440389i
$359$	5.29782	+	9.17609i	0.279608	+	0.484295i	0.971287	−	0.237909i	$-0.0764621\pi$
$359$	5.29782	+	9.17609i	0.279608	+	0.484295i	−0.691679	+	0.722205i	$0.743129\pi$
$360$	−4.47958	−	7.75886i	−0.236094	−	0.408928i
$361$	15.7002			0.826324
$362$	3.14753	−	5.45167i	0.165430	−	0.286534i
$363$	12.5261			0.657447
$364$		0			0
$365$	19.3619			1.01345
$366$	−3.93449	+	6.81474i	−0.205659	+	0.356212i
$367$	−5.82067			−0.303836			−0.151918	−	0.988393i	$-0.548545\pi$
$367$	−5.82067			−0.303836			−0.151918	+	0.988393i	$0.548545\pi$
$368$	3.88128	+	6.72257i	0.202325	+	0.350438i
$369$	−10.8911	−	18.8639i	−0.566968	−	0.982018i
$370$	−2.34429	+	4.06043i	−0.121874	+	0.211092i
$371$		0			0
$372$	−7.94295			−0.411823
$373$	26.0569			1.34917			0.674587	−	0.738195i	$-0.264322\pi$
$373$	26.0569			1.34917			0.674587	+	0.738195i	$0.264322\pi$
$374$	−6.67589			−0.345202
$375$	25.8893			1.33692
$376$	1.58530	+	2.74581i	0.0817554	+	0.141605i
$377$	−12.9141	+	15.5851i	−0.665112	+	0.802675i
$378$		0			0
$379$	−7.82662	−	13.5561i	−0.402026	−	0.696330i	0.591944	−	0.805979i	$-0.298361\pi$
$379$	−7.82662	−	13.5561i	−0.402026	−	0.696330i	−0.993970	+	0.109649i	$0.965027\pi$
$380$	5.68085	−	9.83952i	0.291421	−	0.504757i
$381$	−10.6243	−	18.4019i	−0.544300	−	0.942756i
$382$	−5.45979	+	9.45664i	−0.279347	+	0.483844i
$383$	12.5588			0.641724			0.320862	−	0.947126i	$-0.396027\pi$
$383$	12.5588			0.641724			0.320862	+	0.947126i	$0.396027\pi$
$384$	12.6096	−	21.8405i	0.643482	−	1.11454i
$385$		0			0
$386$	−8.69935	+	15.0677i	−0.442785	+	0.766927i
$387$	−0.405294	+	0.701990i	−0.0206023	+	0.0356842i
$388$	23.4280			1.18938
$389$	0.251504	−	0.435617i	0.0127517	−	0.0220867i	−0.859579	−	0.511003i	$-0.829274\pi$
$389$	0.251504	−	0.435617i	0.0127517	−	0.0220867i	0.872331	+	0.488916i	$0.162608\pi$
$390$	−2.76625	−	7.45647i	−0.140075	−	0.377573i
$391$	24.6847			1.24836
$392$		0			0
$393$	23.3919	+	40.5159i	1.17996	+	2.04376i
$394$	4.76895			0.240256
$395$	6.00206	−	10.3959i	0.301996	−	0.523073i
$396$	−5.03757	−	8.72533i	−0.253148	−	0.438464i
$397$	2.35044			0.117965			0.0589827	−	0.998259i	$-0.481214\pi$
$397$	2.35044			0.117965			0.0589827	+	0.998259i	$0.481214\pi$
$398$	−3.46110			−0.173489
$399$		0			0
$400$	2.04784	+	3.54696i	0.102392	+	0.177348i
$401$	17.3023	−	29.9685i	0.864037	−	1.49656i	−0.00396357	−	0.999992i	$-0.501262\pi$
$401$	17.3023	−	29.9685i	0.864037	−	1.49656i	0.868000	−	0.496564i	$-0.165405\pi$
$402$	−6.47821	+	11.2206i	−0.323104	+	0.559632i
$403$	−7.84061	−	1.33259i	−0.390569	−	0.0663810i
$404$	−0.512135	−	0.887044i	−0.0254797	−	0.0441321i
$405$	6.16835	+	10.6839i	0.306508	+	0.530887i
$406$		0			0
$407$	−6.16197	+	10.6729i	−0.305438	+	0.529034i
$408$	−11.6678	−	20.2092i	−0.577640	−	1.00050i
$409$	−4.01205	−	6.94908i	−0.198383	−	0.343610i	0.749621	−	0.661867i	$-0.230236\pi$
$409$	−4.01205	−	6.94908i	−0.198383	−	0.343610i	−0.948004	+	0.318257i	$0.896902\pi$
$410$	3.56588	+	6.17629i	0.176106	+	0.305025i
$411$	12.3238	+	21.3454i	0.607886	+	1.05289i
$412$	−13.4033	+	23.2152i	−0.660333	+	1.14373i
$413$		0			0
$414$	−6.28382	−	10.8839i	−0.308833	−	0.534914i
$415$	−0.879993	−	1.52419i	−0.0431971	−	0.0748196i
$416$	13.4290	−	16.2065i	0.658412	−	0.794588i
$417$	−9.80878	+	16.9893i	−0.480338	+	0.831970i
$418$	−5.03738	+	8.72500i	−0.246386	+	0.426754i
$419$	−5.83472	−	10.1060i	−0.285045	−	0.493712i	0.687575	−	0.726113i	$-0.258675\pi$
$419$	−5.83472	−	10.1060i	−0.285045	−	0.493712i	−0.972620	+	0.232401i	$0.925342\pi$
$420$		0			0
$421$	−18.3381			−0.893746			−0.446873	−	0.894597i	$-0.647462\pi$
$421$	−18.3381			−0.893746			−0.446873	+	0.894597i	$0.647462\pi$
$422$	−2.61916			−0.127499
$423$	1.78649	+	3.09429i	0.0868621	+	0.150449i
$424$	16.9110	−	29.2907i	0.821271	−	1.42248i
$425$	13.0242			0.631764
$426$	−6.18040	−	10.7048i	−0.299441	−	0.518647i
$427$		0			0
$428$	−12.7049			−0.614117
$429$	−7.27110	−	19.5993i	−0.351052	−	0.946265i
$430$	0.132698	−	0.229840i	0.00639928	−	0.0110839i
$431$	−31.2435			−1.50495			−0.752474	−	0.658622i	$-0.771140\pi$
$431$	−31.2435			−1.50495			−0.752474	+	0.658622i	$0.771140\pi$
$432$	−0.298671	+	0.517314i	−0.0143698	+	0.0248893i
$433$	−15.2756	+	26.4582i	−0.734100	+	1.27150i	0.221017	+	0.975270i	$0.429062\pi$
$433$	−15.2756	+	26.4582i	−0.734100	+	1.27150i	−0.955117	+	0.296229i	$0.904271\pi$
$434$		0			0
$435$	8.71655	−	15.0975i	0.417927	−	0.723870i
$436$	−18.0847			−0.866099
$437$	18.6262	−	32.2615i	0.891012	−	1.54328i
$438$	−12.8379	−	22.2358i	−0.613417	−	1.06247i
$439$	−6.07361	+	10.5198i	−0.289878	+	0.502083i	−0.973780	−	0.227490i	$-0.926948\pi$
$439$	−6.07361	+	10.5198i	−0.289878	+	0.502083i	0.683903	+	0.729573i	$0.260281\pi$
$440$	3.85514	+	6.67730i	0.183787	+	0.318328i
$441$		0			0
$442$	−3.47699	−	9.37227i	−0.165384	−	0.445794i
$443$	4.23266	+	7.33118i	0.201100	+	0.348315i	0.948883	−	0.315628i	$-0.102215\pi$
$443$	4.23266	+	7.33118i	0.201100	+	0.348315i	−0.747783	+	0.663943i	$0.768882\pi$
$444$	−18.4304			−0.874667
$445$	1.16035			0.0550060
$446$	6.26065			0.296451
$447$	23.5705			1.11485
$448$		0			0
$449$	11.6632	−	20.2013i	0.550420	−	0.953356i	−0.447824	−	0.894122i	$-0.647801\pi$
$449$	11.6632	−	20.2013i	0.550420	−	0.953356i	0.998244	−	0.0592342i	$-0.0188659\pi$
$450$	−3.31547	−	5.74256i	−0.156293	−	0.270707i
$451$	9.37293	+	16.2344i	0.441354	+	0.764448i
$452$	21.3148			1.00256
$453$	17.7469	−	30.7386i	0.833823	−	1.44422i
$454$	−9.55416			−0.448399
$455$		0			0
$456$	−35.2162			−1.64915
$457$	−7.74332	+	13.4118i	−0.362217	+	0.627379i	−0.988325	−	0.152358i	$-0.951313\pi$
$457$	−7.74332	+	13.4118i	−0.362217	+	0.627379i	0.626108	+	0.779736i	$0.284647\pi$
$458$	4.84115			0.226212
$459$	0.949769	+	1.64505i	0.0443314	+	0.0767842i
$460$	−6.09868	−	10.5632i	−0.284352	−	0.492513i
$461$	−4.64102	+	8.03848i	−0.216154	+	0.374389i	−0.953629	−	0.300985i	$-0.902685\pi$
$461$	−4.64102	+	8.03848i	−0.216154	+	0.374389i	0.737475	+	0.675374i	$0.236018\pi$
$462$		0			0
$463$	28.8283			1.33976			0.669882	−	0.742467i	$-0.266345\pi$
$463$	28.8283			1.33976			0.669882	+	0.742467i	$0.266345\pi$
$464$	6.89068			0.319892
$465$	6.85000			0.317661
$466$	17.8049			0.824797
$467$	−1.43696	−	2.48890i	−0.0664948	−	0.115172i	0.830861	−	0.556480i	$-0.187848\pi$
$467$	−1.43696	−	2.48890i	−0.0664948	−	0.115172i	−0.897356	+	0.441307i	$0.854515\pi$
$468$	9.62577	−	11.6166i	0.444951	−	0.536979i
$469$		0			0
$470$	−0.584919	−	1.01311i	−0.0269803	−	0.0467312i
$471$	−24.7825	+	42.9245i	−1.14192	+	1.97786i
$472$	−5.00354	−	8.66638i	−0.230307	−	0.398903i
$473$	0.348798	−	0.604136i	0.0160377	−	0.0277782i
$474$	−15.9186			−0.731167
$475$	9.82754	−	17.0218i	0.450919	−	0.781014i
$476$		0			0
$477$	19.0572	−	33.0080i	0.872569	−	1.51133i
$478$	−0.989147	+	1.71325i	−0.0452425	+	0.0783624i
$479$	22.6082			1.03299			0.516497	−	0.856289i	$-0.327236\pi$
$479$	22.6082			1.03299			0.516497	+	0.856289i	$0.327236\pi$
$480$	−9.06407	+	15.6994i	−0.413716	+	0.716577i
$481$	−18.1929	−	3.09207i	−0.829526	−	0.140986i
$482$	4.95659			0.225766
$483$		0			0
$484$	−3.88985	−	6.73742i	−0.176812	−	0.306247i
$485$	−20.2043			−0.917432
$486$	7.66136	−	13.2699i	0.347526	−	0.601933i
$487$	−1.43401	−	2.48379i	−0.0649814	−	0.112551i	0.831704	−	0.555219i	$-0.187365\pi$
$487$	−1.43401	−	2.48379i	−0.0649814	−	0.112551i	−0.896686	+	0.442668i	$0.854032\pi$
$488$	11.4233			0.517108
$489$	9.58544			0.433469
$490$		0			0
$491$	11.3600	+	19.6762i	0.512672	+	0.887973i	0.999892	+	0.0146943i	$0.00467751\pi$
$491$	11.3600	+	19.6762i	0.512672	+	0.887973i	−0.487220	+	0.873279i	$0.661989\pi$
$492$	−14.0172	+	24.2784i	−0.631942	+	1.09456i
$493$	10.9561	−	18.9765i	0.493439	−	0.854661i
$494$	−14.8726	−	2.52775i	−0.669151	−	0.113729i
$495$	4.34440	+	7.52473i	0.195266	+	0.338211i
$496$	1.35378	+	2.34482i	0.0607865	+	0.105285i
$497$		0			0
$498$	−1.16696	+	2.02123i	−0.0522926	+	0.0905734i
$499$	9.00755	+	15.6015i	0.403233	+	0.698420i	0.994114	−	0.108338i	$-0.0345530\pi$
$499$	9.00755	+	15.6015i	0.403233	+	0.698420i	−0.590881	+	0.806759i	$0.701220\pi$
$500$	−8.03968	−	13.9251i	−0.359545	−	0.622751i
$501$	−10.4483	−	18.0971i	−0.466798	−	0.808518i
$502$	0.278088	+	0.481662i	0.0124117	+	0.0214976i
$503$	−15.5748	+	26.9764i	−0.694447	+	1.20282i	0.275920	+	0.961181i	$0.411017\pi$
$503$	−15.5748	+	26.9764i	−0.694447	+	1.20282i	−0.970367	+	0.241636i	$0.922316\pi$
$504$		0			0
$505$	0.441665	+	0.764987i	0.0196539	+	0.0340415i
$506$	5.40788	+	9.36673i	0.240410	+	0.416402i
$507$	23.7285	−	20.4158i	1.05382	−	0.906696i
$508$	−6.59858	+	11.4291i	−0.292764	+	0.507083i
$509$	−19.7509	+	34.2096i	−0.875444	+	1.51631i	−0.0191556	+	0.999817i	$0.506098\pi$
$509$	−19.7509	+	34.2096i	−0.875444	+	1.51631i	−0.856289	+	0.516497i	$0.827236\pi$
$510$	4.30499	+	7.45647i	0.190628	+	0.330178i
$511$		0			0
$512$	−13.2606			−0.586042
$513$	2.86664			0.126565
$514$	−1.15707	−	2.00411i	−0.0510363	−	0.0883974i
$515$	11.5590	−	20.0208i	0.509351	−	0.882221i
$516$	1.04325			0.0459265
$517$	−1.53746	−	2.66296i	−0.0676174	−	0.117117i
$518$		0			0
$519$	2.24880			0.0987115
$520$	−7.36639	+	8.88995i	−0.323038	+	0.389850i
$521$	−8.88359	+	15.3868i	−0.389197	+	0.674109i	−0.992342	−	0.123523i	$-0.960581\pi$
$521$	−8.88359	+	15.3868i	−0.389197	+	0.674109i	0.603145	+	0.797632i	$0.293914\pi$
$522$	−11.1561			−0.488288
$523$	−0.894522	+	1.54936i	−0.0391147	+	0.0677487i	−0.884920	−	0.465743i	$-0.845787\pi$
$523$	−0.894522	+	1.54936i	−0.0391147	+	0.0677487i	0.845805	+	0.533492i	$0.179120\pi$
$524$	14.5283	−	25.1637i	0.634671	−	1.09928i
$525$		0			0
$526$	10.5062	−	18.1972i	0.458091	−	0.793438i
$527$	8.60999			0.375057
$528$	−3.55842	+	6.16336i	−0.154860	+	0.268226i
$529$	−8.49616	−	14.7158i	−0.369398	−	0.639817i
$530$	−6.23956	+	10.8072i	−0.271029	+	0.469436i
$531$	−5.63854	−	9.76624i	−0.244692	−	0.423819i
$532$		0			0
$533$	−17.9098	+	21.6140i	−0.775758	+	0.936205i
$534$	−0.769371	−	1.33259i	−0.0332939	−	0.0576668i
$535$	10.9568			0.473702
$536$	18.8087			0.812412
$537$	−32.6174			−1.40754
$538$	0.878269			0.0378649
$539$		0			0
$540$	0.469305	−	0.812860i	0.0201957	−	0.0349799i
$541$	−7.70135	−	13.3391i	−0.331107	−	0.573494i	0.651622	−	0.758544i	$-0.274089\pi$
$541$	−7.70135	−	13.3391i	−0.331107	−	0.573494i	−0.982729	+	0.185050i	$0.940755\pi$
$542$	−8.95214	−	15.5056i	−0.384527	−	0.666021i
$543$	−21.3403			−0.915801
$544$	−11.3929	+	19.7331i	−0.488467	+	0.846050i
$545$	15.5962			0.668069
$546$		0			0
$547$	−3.96944			−0.169721			−0.0848605	−	0.996393i	$-0.527044\pi$
$547$	−3.96944			−0.169721			−0.0848605	+	0.996393i	$0.527044\pi$
$548$	7.65406	−	13.2572i	0.326965	−	0.566321i
$549$	12.8730			0.549408
$550$	2.85330	+	4.94207i	0.121665	+	0.210731i
$551$	−16.5342	−	28.6380i	−0.704379	−	1.22002i
$552$	−18.9032	+	32.7413i	−0.804574	+	1.39356i
$553$		0			0
$554$	−6.77331			−0.287770
$555$	15.8944			0.674678
$556$	12.1841			0.516722
$557$	18.6901			0.791924			0.395962	−	0.918267i	$-0.370411\pi$
$557$	18.6901			0.791924			0.395962	+	0.918267i	$0.370411\pi$
$558$	−2.19178	−	3.79628i	−0.0927856	−	0.160709i
$559$	1.02981	+	0.175026i	0.0435563	+	0.00740282i
$560$		0			0
$561$	11.3157	+	19.5993i	0.477749	+	0.827485i
$562$	3.39711	−	5.88397i	0.143298	−	0.248200i
$563$	18.1530	+	31.4418i	0.765056	+	1.32512i	0.940217	+	0.340576i	$0.110622\pi$
$563$	18.1530	+	31.4418i	0.765056	+	1.32512i	−0.175161	+	0.984540i	$0.556045\pi$
$564$	2.29926	−	3.98244i	0.0968163	−	0.167691i
$565$	−18.3819			−0.773333
$566$	−4.06001	+	7.03215i	−0.170655	+	0.295583i
$567$		0			0
$568$	−8.97201	+	15.5400i	−0.376457	+	0.652043i
$569$	−5.48798	+	9.50546i	−0.230068	+	0.398489i	−0.957828	−	0.287343i	$-0.907228\pi$
$569$	−5.48798	+	9.50546i	−0.230068	+	0.398489i	0.727760	+	0.685832i	$0.240562\pi$
$570$	12.9936			0.544240
$571$	−15.6682	+	27.1380i	−0.655692	+	1.13569i	0.326028	+	0.945360i	$0.394290\pi$
$571$	−15.6682	+	27.1380i	−0.655692	+	1.13569i	−0.981720	+	0.190332i	$0.939044\pi$
$572$	−8.28398	+	9.99733i	−0.346371	+	0.418009i
$573$	37.0175			1.54643
$574$		0			0
$575$	−10.5504	−	18.2738i	−0.439981	−	0.762069i
$576$	4.73210			0.197171
$577$	−21.3938	+	37.0552i	−0.890636	+	1.54263i	−0.0515210	+	0.998672i	$0.516407\pi$
$577$	−21.3938	+	37.0552i	−0.890636	+	1.54263i	−0.839115	+	0.543954i	$0.816926\pi$
$578$	−0.626353	−	1.08487i	−0.0260528	−	0.0451248i
$579$	58.9819			2.45120
$580$	−10.8274			−0.449583
$581$		0			0
$582$	13.3965	+	23.2034i	0.555302	+	0.961811i
$583$	−16.4007	+	28.4069i	−0.679248	+	1.17649i
$584$	−18.6366	+	32.2795i	−0.771187	+	1.33573i
$585$	−8.30127	+	10.0182i	−0.343215	+	0.414201i
$586$	3.32259	+	5.75489i	0.137255	+	0.237732i
$587$	−19.3943	−	33.5919i	−0.800488	−	1.38649i	−0.919296	−	0.393568i	$-0.871241\pi$
$587$	−19.3943	−	33.5919i	−0.800488	−	1.38649i	0.118808	−	0.992917i	$-0.462093\pi$
$588$		0			0
$589$	6.49678	−	11.2527i	0.267695	−	0.463661i
$590$	1.84613	+	3.19759i	0.0760039	+	0.131643i
$591$	−8.08341	−	14.0009i	−0.332507	−	0.575919i
$592$	3.14124	+	5.44078i	0.129104	+	0.223615i
$593$	−14.9782	−	25.9430i	−0.615081	−	1.06535i	−0.990370	−	0.138443i	$-0.955790\pi$
$593$	−14.9782	−	25.9430i	−0.615081	−	1.06535i	0.375290	−	0.926908i	$-0.377543\pi$
$594$	−0.416147	+	0.720787i	−0.0170747	+	0.0295743i
$595$		0			0
$596$	−7.31960	−	12.6779i	−0.299823	−	0.519308i
$597$	5.86658	+	10.1612i	0.240103	+	0.415871i
$598$	−10.3334	+	12.4706i	−0.422562	+	0.509959i
$599$	−20.6269	+	35.7269i	−0.842794	+	1.45976i	0.0447293	+	0.998999i	$0.485757\pi$
$599$	−20.6269	+	35.7269i	−0.842794	+	1.45976i	−0.887523	+	0.460763i	$0.847576\pi$
$600$	−9.97371	+	17.2750i	−0.407175	+	0.705248i
$601$	3.30544	+	5.72520i	0.134832	+	0.233536i	0.925533	−	0.378666i	$-0.123617\pi$
$601$	3.30544	+	5.72520i	0.134832	+	0.233536i	−0.790701	+	0.612202i	$0.790284\pi$
$602$		0			0
$603$	21.1957			0.863156
$604$	−22.0446			−0.896982
$605$	3.35461	+	5.81036i	0.136384	+	0.236225i
$606$	0.585692	−	1.01445i	0.0237921	−	0.0412091i
$607$	20.8832			0.847622			0.423811	−	0.905751i	$-0.360692\pi$
$607$	20.8832			0.847622			0.423811	+	0.905751i	$0.360692\pi$
$608$	17.1933	+	29.7797i	0.697282	+	1.20773i
$609$		0			0
$610$	−4.21479			−0.170652
$611$	2.93777	−	3.54538i	0.118850	−	0.143431i
$612$	−8.16632	+	14.1445i	−0.330104	+	0.571757i
$613$	−4.29655			−0.173536			−0.0867680	−	0.996229i	$-0.527654\pi$
$613$	−4.29655			−0.173536			−0.0867680	+	0.996229i	$0.527654\pi$
$614$	−2.88181	+	4.99144i	−0.116300	+	0.201438i
$615$	12.0884	−	20.9377i	0.487451	−	0.844290i
$616$		0			0
$617$	15.3690	−	26.6199i	0.618732	−	1.07167i	−0.370986	−	0.928639i	$-0.620980\pi$
$617$	15.3690	−	26.6199i	0.618732	−	1.07167i	0.989717	−	0.143036i	$-0.0456866\pi$
$618$	−30.6568			−1.23320
$619$	−10.3208	+	17.8762i	−0.414829	+	0.718505i	−0.995410	−	0.0956971i	$-0.969492\pi$
$619$	−10.3208	+	17.8762i	−0.414829	+	0.718505i	0.580581	+	0.814202i	$0.302825\pi$
$620$	−2.12721	−	3.68443i	−0.0854307	−	0.147970i
$621$	1.53874	−	2.66518i	0.0617476	−	0.106950i
$622$	3.06849	+	5.31479i	0.123035	+	0.213104i
$623$		0			0
$624$	−10.5060	−	1.78561i	−0.420578	−	0.0714815i
$625$	−1.40818	−	2.43904i	−0.0563272	−	0.0975616i
$626$	−3.71290			−0.148397
$627$	34.1536			1.36396
$628$	30.7839			1.22841
$629$	19.9781			0.796580
$630$		0			0
$631$	−14.6683	+	25.4063i	−0.583937	+	1.01141i	0.411070	+	0.911604i	$0.365155\pi$
$631$	−14.6683	+	25.4063i	−0.583937	+	1.01141i	−0.995007	+	0.0998043i	$0.968178\pi$
$632$	11.5544	+	20.0129i	0.459611	+	0.796069i
$633$	4.43950	+	7.68943i	0.176454	+	0.305628i
$634$	−7.95019			−0.315742
$635$	5.69061	−	9.85643i	0.225825	−	0.391141i
$636$	−49.0543			−1.94513
$637$		0			0
$638$	9.60097			0.380106
$639$	−10.1107	+	17.5122i	−0.399971	+	0.692771i
$640$	13.5080			0.533950
$641$	2.00840	+	3.47865i	0.0793271	+	0.137399i	0.902960	−	0.429725i	$-0.141390\pi$
$641$	2.00840	+	3.47865i	0.0793271	+	0.137399i	−0.823633	+	0.567124i	$0.808056\pi$
$642$	−7.26486	−	12.5831i	−0.286721	−	0.496616i
$643$	−3.43641	+	5.95203i	−0.135519	+	0.234725i	−0.925795	−	0.378025i	$-0.876603\pi$
$643$	−3.43641	+	5.95203i	−0.135519	+	0.234725i	0.790277	+	0.612750i	$0.209937\pi$
$644$		0			0
$645$	−0.899698			−0.0354256
$646$	16.3320			0.642574
$647$	33.7431			1.32658			0.663289	−	0.748363i	$-0.269160\pi$
$647$	33.7431			1.32658			0.663289	+	0.748363i	$0.269160\pi$
$648$	−23.7491			−0.932955
$649$	4.85256	+	8.40487i	0.190479	+	0.329920i
$650$	−5.45208	+	6.57972i	−0.213848	+	0.258078i
$651$		0			0
$652$	−2.97667	−	5.15575i	−0.116576	−	0.201915i
$653$	−16.2001	+	28.0594i	−0.633958	+	1.09805i	0.352777	+	0.935708i	$0.385238\pi$
$653$	−16.2001	+	28.0594i	−0.633958	+	1.09805i	−0.986735	+	0.162340i	$0.948096\pi$
$654$	−10.3411	−	17.9113i	−0.404368	−	0.700385i
$655$	−12.5292	+	21.7012i	−0.489556	+	0.847936i
$656$	9.55622			0.373108
$657$	−21.0018	+	36.3761i	−0.819357	+	1.41917i
$658$		0			0
$659$	−2.00518	+	3.47307i	−0.0781106	+	0.135291i	−0.902435	−	0.430827i	$-0.858222\pi$
$659$	−2.00518	+	3.47307i	−0.0781106	+	0.135291i	0.824324	+	0.566118i	$0.191555\pi$
$660$	5.59137	−	9.68453i	0.217644	−	0.376970i
$661$	1.81794			0.0707097			0.0353549	−	0.999375i	$-0.488744\pi$
$661$	1.81794			0.0707097			0.0353549	+	0.999375i	$0.488744\pi$
$662$	7.11947	−	12.3313i	0.276706	−	0.479269i
$663$	−21.6220	+	26.0940i	−0.839727	+	1.01341i
$664$	3.38811			0.131484
$665$		0			0
$666$	−5.08569	−	8.80868i	−0.197067	−	0.341329i
$667$	−35.5005			−1.37459
$668$	−6.48928	+	11.2398i	−0.251078	+	0.434880i
$669$	−10.6119	−	18.3803i	−0.410278	−	0.710622i
$670$	−6.93974			−0.268106
$671$	−11.0786			−0.427684
$672$		0			0
$673$	11.4871	+	19.8963i	0.442797	+	0.766947i	0.997896	−	0.0648375i	$-0.0206529\pi$
$673$	11.4871	+	19.8963i	0.442797	+	0.766947i	−0.555099	+	0.831784i	$0.687320\pi$
$674$	6.60091	−	11.4331i	0.254258	−	0.440387i
$675$	0.811871	−	1.40620i	0.0312489	−	0.0541247i
$676$	−18.3498	−	6.42298i	−0.705760	−	0.247038i
$677$	19.0138	+	32.9329i	0.730760	+	1.26571i	0.956559	+	0.291540i	$0.0941676\pi$
$677$	19.0138	+	32.9329i	0.730760	+	1.26571i	−0.225799	+	0.974174i	$0.572499\pi$
$678$	12.1881	+	21.1104i	0.468081	+	0.810741i
$679$		0			0
$680$	6.24950	−	10.8245i	0.239658	−	0.415099i
$681$	16.1944	+	28.0495i	0.620570	+	1.07486i
$682$	1.88626	+	3.26709i	0.0722285	+	0.125103i
$683$	20.3893	+	35.3153i	0.780176	+	1.35130i	0.931839	+	0.362872i	$0.118204\pi$
$683$	20.3893	+	35.3153i	0.780176	+	1.35130i	−0.151663	+	0.988432i	$0.548463\pi$
$684$	12.3240	+	21.3458i	0.471220	+	0.816177i
$685$	−6.60087	+	11.4330i	−0.252206	+	0.436834i
$686$		0			0
$687$	−8.20578	−	14.2128i	−0.313070	−	0.542253i
$688$	−0.177809	−	0.307975i	−0.00677892	−	0.0117414i
$689$	−48.4223	−	8.22985i	−1.84474	−	0.313532i
$690$	6.97462	−	12.0804i	0.265519	−	0.459893i
$691$	−1.56434	+	2.70952i	−0.0595104	+	0.103075i	−0.894246	−	0.447576i	$-0.852287\pi$
$691$	−1.56434	+	2.70952i	−0.0595104	+	0.103075i	0.834735	+	0.550651i	$0.185621\pi$
$692$	−0.698346	−	1.20957i	−0.0265471	−	0.0459809i
$693$		0			0
$694$	−15.8690			−0.602378
$695$	−10.5076			−0.398576
$696$	16.7801	+	29.0639i	0.636047	+	1.10167i
$697$	15.1943	−	26.3173i	0.575525	−	0.996838i
$698$	6.24080			0.236218
$699$	−30.1795	−	52.2724i	−1.14149	−	1.97712i
$700$		0			0
$701$	9.61382			0.363109			0.181555	−	0.983381i	$-0.441887\pi$
$701$	9.61382			0.363109			0.181555	+	0.983381i	$0.441887\pi$
$702$	−1.22865	−	0.208822i	−0.0463725	−	0.00788147i
$703$	15.0748	−	26.1102i	0.568555	−	0.984767i
$704$	−4.07247			−0.153487
$705$	−1.98288	+	3.43445i	−0.0746797	+	0.129349i
$706$	−2.74134	+	4.74815i	−0.103172	+	0.178699i
$707$		0			0
$708$	−7.25696	+	12.5694i	−0.272733	+	0.472388i
$709$	28.1294			1.05642			0.528211	−	0.849113i	$-0.322863\pi$
$709$	28.1294			1.05642			0.528211	+	0.849113i	$0.322863\pi$
$710$	3.31035	−	5.73370i	0.124235	−	0.215182i
$711$	13.0208	+	22.5527i	0.488319	+	0.845794i
$712$	−1.11689	+	1.93450i	−0.0418571	+	0.0724986i
$713$	−6.97462	−	12.0804i	−0.261201	−	0.452414i
$714$		0			0
$715$	7.14411	−	8.62170i	0.267174	−	0.322433i
$716$	10.1290	+	17.5440i	0.378540	+	0.655651i
$717$	6.70645			0.250457
$718$	7.52594			0.280865
$719$	−24.9044			−0.928779			−0.464389	−	0.885631i	$-0.653726\pi$
$719$	−24.9044			−0.928779			−0.464389	+	0.885631i	$0.653726\pi$
$720$	4.42936			0.165073
$721$		0			0
$722$	5.57581	−	9.65758i	0.207510	−	0.359418i
$723$	−8.40146	−	14.5517i	−0.312454	−	0.541185i
$724$	6.62705	+	11.4784i	0.246292	+	0.426591i
$725$	−18.7308			−0.695643
$726$	4.44854	−	7.70510i	0.165101	−	0.285963i
$727$	24.2120			0.897974			0.448987	−	0.893538i	$-0.351785\pi$
$727$	24.2120			0.897974			0.448987	+	0.893538i	$0.351785\pi$
$728$		0			0
$729$	−23.2479			−0.861032
$730$	6.87624	−	11.9100i	0.254501	−	0.440808i
$731$	−1.13086			−0.0418264
$732$	−8.28398	−	14.3483i	−0.306185	−	0.530328i
$733$	−6.19943	−	10.7377i	−0.228981	−	0.396607i	0.728525	−	0.685019i	$-0.240206\pi$
$733$	−6.19943	−	10.7377i	−0.228981	−	0.396607i	−0.957506	+	0.288412i	$0.906873\pi$
$734$	−2.06717	+	3.58045i	−0.0763007	+	0.132157i
$735$		0			0
$736$	36.9159			1.36074
$737$	−18.2411			−0.671921
$738$	−15.4716			−0.569518
$739$	−10.9604			−0.403184			−0.201592	−	0.979470i	$-0.564612\pi$
$739$	−10.9604			−0.403184			−0.201592	+	0.979470i	$0.564612\pi$
$740$	−4.93585	−	8.54915i	−0.181446	−	0.314273i
$741$	17.7881	+	47.9482i	0.653463	+	1.76142i
$742$		0			0
$743$	−20.3462	−	35.2407i	−0.746431	−	1.29286i	−0.949523	−	0.313697i	$-0.898432\pi$
$743$	−20.3462	−	35.2407i	−0.746431	−	1.29286i	0.203092	−	0.979160i	$-0.434901\pi$
$744$	−6.59340	+	11.4201i	−0.241726	+	0.418681i
$745$	6.31243	+	10.9334i	0.231269	+	0.400570i
$746$	9.25393	−	16.0283i	0.338810	−	0.586837i
$747$	3.81810			0.139697
$748$	7.02797	−	12.1728i	0.256968	−	0.445082i
$749$		0			0
$750$	9.19439	−	15.9252i	0.335732	−	0.581505i
$751$	−4.70236	+	8.14473i	−0.171592	+	0.297205i	−0.938976	−	0.343981i	$-0.888224\pi$
$751$	−4.70236	+	8.14473i	−0.171592	+	0.297205i	0.767385	+	0.641187i	$0.221558\pi$
$752$	−1.56753			−0.0571618
$753$	0.942721	−	1.63284i	0.0343547	−	0.0595040i
$754$	5.00045	+	13.4788i	0.182106	+	0.490868i
$755$	19.0113			0.691890
$756$		0			0
$757$	14.7904	+	25.6177i	0.537566	+	0.931091i	0.999034	+	0.0439345i	$0.0139893\pi$
$757$	14.7904	+	25.6177i	0.537566	+	0.931091i	−0.461469	+	0.887156i	$0.652677\pi$
$758$	−11.1183			−0.403834
$759$	18.3328	−	31.7533i	0.665439	−	1.15257i
$760$	−9.43129	−	16.3355i	−0.342109	−	0.592550i
$761$	−16.9417			−0.614137			−0.307068	−	0.951687i	$-0.599348\pi$
$761$	−16.9417			−0.614137			−0.307068	+	0.951687i	$0.599348\pi$
$762$	−15.0926			−0.546748
$763$		0			0
$764$	−11.4955	−	19.9107i	−0.415891	−	0.720345i
$765$	7.04264	−	12.1982i	0.254627	−	0.441027i
$766$	4.46017	−	7.72524i	0.161152	−	0.279124i
$767$	−9.27224	+	11.1900i	−0.334801	+	0.404047i
$768$	−13.0289	−	22.5668i	−0.470141	−	0.814308i
$769$	3.68287	+	6.37892i	0.132808	+	0.230030i	0.924758	−	0.380556i	$-0.124267\pi$
$769$	3.68287	+	6.37892i	0.132808	+	0.230030i	−0.791950	+	0.610586i	$0.790934\pi$
$770$		0			0
$771$	−3.92249	+	6.79396i	−0.141265	+	0.244678i
$772$	−18.3163	−	31.7248i	−0.659218	−	1.14180i
$773$	−22.3867	−	38.7749i	−0.805194	−	1.39464i	−0.916160	−	0.400813i	$-0.868728\pi$
$773$	−22.3867	−	38.7749i	−0.805194	−	1.39464i	0.110966	−	0.993824i	$-0.464606\pi$
$774$	0.287875	+	0.498614i	0.0103475	+	0.0179223i
$775$	−3.67995	−	6.37385i	−0.132188	−	0.228956i
$776$	19.4475	−	33.6840i	0.698124	−	1.20919i
$777$		0			0
$778$	−0.178640	−	0.309413i	−0.00640454	−	0.0110930i
$779$	−22.9301	−	39.7161i	−0.821556	−	1.42298i
$780$	16.5082	+	2.80574i	0.591090	+	0.100462i
$781$	8.70127	−	15.0710i	0.311356	−	0.539284i
$782$	8.76662	−	15.1842i	0.313494	−	0.542987i
$783$	−1.36592	−	2.36583i	−0.0488138	−	0.0845480i
$784$		0			0
$785$	−26.5480			−0.947540
$786$	33.2299			1.18527
$787$	−9.38412	−	16.2538i	−0.334508	−	0.579385i	0.648882	−	0.760889i	$-0.275237\pi$
$787$	−9.38412	−	16.2538i	−0.334508	−	0.579385i	−0.983390	+	0.181504i	$0.941903\pi$
$788$	−5.02046	+	8.69570i	−0.178847	+	0.309771i
$789$	−71.2322			−2.53594
$790$	−4.26318	−	7.38404i	−0.151677	−	0.262713i
$791$		0			0
$792$	−16.7267			−0.594356
$793$	−5.77004	−	15.5532i	−0.204900	−	0.552311i
$794$	0.834744	−	1.44582i	0.0296240	−	0.0513102i
$795$	42.3044			1.50038
$796$	3.64363	−	6.31095i	0.129145	−	0.223686i
$797$	3.60849	−	6.25008i	0.127819	−	0.221389i	−0.795012	−	0.606593i	$-0.792536\pi$
$797$	3.60849	−	6.25008i	0.127819	−	0.221389i	0.922831	+	0.385204i	$0.125869\pi$
$798$		0			0
$799$	−2.49235	+	4.31687i	−0.0881730	+	0.152720i
$800$	19.4775			0.688635
$801$	−1.25863	+	2.18001i	−0.0444716	+	0.0770270i
$802$	−12.2896	−	21.2862i	−0.433961	−	0.751643i
$803$	18.0742	−	31.3054i	0.637825	−	1.10474i
$804$	−13.6397	−	23.6247i	−0.481036	−	0.833180i
$805$		0			0
$806$	−3.60425	+	4.34971i	−0.126954	+	0.153212i
$807$	−1.48867	−	2.57846i	−0.0524037	−	0.0907659i
$808$	−1.70048			−0.0598228
$809$	14.8318			0.521459			0.260729	−	0.965412i	$-0.416037\pi$
$809$	14.8318			0.521459			0.260729	+	0.965412i	$0.416037\pi$
$810$	8.76260			0.307886
$811$	−18.5831			−0.652541			−0.326271	−	0.945276i	$-0.605792\pi$
$811$	−18.5831			−0.652541			−0.326271	+	0.945276i	$0.605792\pi$
$812$		0			0
$813$	−30.3479	+	52.5641i	−1.06435	+	1.84350i
$814$	4.37677	+	7.58078i	0.153406	+	0.265706i
$815$	2.56708	+	4.44632i	0.0899210	+	0.155748i
$816$	11.5370			0.403875
$817$	−0.853305	+	1.47797i	−0.0298534	+	0.0517075i
$818$	−5.69942			−0.199275
$819$		0			0
$820$	−15.0158			−0.524374
$821$	13.3118	−	23.0567i	0.464585	−	0.804684i	−0.534598	−	0.845106i	$-0.679537\pi$
$821$	13.3118	−	23.0567i	0.464585	−	0.804684i	0.999183	+	0.0404222i	$0.0128703\pi$
$822$	17.5068			0.610620
$823$	−3.37568	−	5.84685i	−0.117669	−	0.203808i	0.801175	−	0.598431i	$-0.204209\pi$
$823$	−3.37568	−	5.84685i	−0.117669	−	0.203808i	−0.918843	+	0.394622i	$0.870875\pi$
$824$	22.2520	+	38.5416i	0.775186	+	1.34266i
$825$	9.67275	−	16.7537i	0.336762	−	0.583289i
$826$		0			0
$827$	−21.7430			−0.756079			−0.378039	−	0.925789i	$-0.623402\pi$
$827$	−21.7430			−0.756079			−0.378039	+	0.925789i	$0.623402\pi$
$828$	26.4609			0.919579
$829$	14.6216			0.507828			0.253914	−	0.967227i	$-0.418282\pi$
$829$	14.6216			0.507828			0.253914	+	0.967227i	$0.418282\pi$
$830$	−1.25009			−0.0433914
$831$	11.4808	+	19.8853i	0.398265	+	0.689815i
$832$	−2.12105	−	5.71733i	−0.0735343	−	0.198213i
$833$		0			0
$834$	6.96705	+	12.0673i	0.241249	+	0.417856i
$835$	5.59636	−	9.69318i	0.193670	−	0.335446i
$836$	−10.6061	−	18.3703i	−0.366819	−	0.635350i
$837$	0.536710	−	0.929609i	0.0185514	−	0.0321320i
$838$	−8.28865			−0.286327
$839$	−5.37343	+	9.30705i	−0.185511	+	0.321315i	−0.943749	−	0.330663i	$-0.892727\pi$
$839$	−5.37343	+	9.30705i	−0.185511	+	0.321315i	0.758237	+	0.651979i	$0.226061\pi$
$840$		0			0
$841$	−1.25660	+	2.17649i	−0.0433310	+	0.0750515i
$842$	−6.51267	+	11.2803i	−0.224441	+	0.388744i
$843$	−23.0325			−0.793282
$844$	2.75729	−	4.77577i	0.0949099	−	0.164389i
$845$	15.8248	+	5.53918i	0.544391	+	0.190554i
$846$	2.53784			0.0872527
$847$		0			0
$848$	8.36071	+	14.4812i	0.287108	+	0.497286i
$849$	27.5270			0.944724
$850$	4.62544	−	8.01150i	0.158651	−	0.274792i
$851$	−16.1835	−	28.0307i	−0.554764	−	0.960879i
$852$	26.0254			0.891615
$853$	31.7709			1.08782			0.543908	−	0.839145i	$-0.316944\pi$
$853$	31.7709			1.08782			0.543908	+	0.839145i	$0.316944\pi$
$854$		0			0
$855$	−10.6282	−	18.4086i	−0.363478	−	0.629562i
$856$	−10.5463	+	18.2667i	−0.360466	+	0.624345i
$857$	−0.324052	+	0.561275i	−0.0110694	+	0.0191728i	−0.871507	−	0.490383i	$-0.836857\pi$
$857$	−0.324052	+	0.561275i	−0.0110694	+	0.0191728i	0.860438	+	0.509556i	$0.170190\pi$
$858$	−14.6384	−	2.48793i	−0.499745	−	0.0849366i
$859$	−21.5951	−	37.4038i	−0.736815	−	1.27620i	−0.953923	−	0.300053i	$-0.902996\pi$
$859$	−21.5951	−	37.4038i	−0.736815	−	1.27620i	0.217108	−	0.976148i	$-0.430338\pi$
$860$	0.279393	+	0.483923i	0.00952723	+	0.0165017i
$861$		0			0
$862$	−11.0959	+	19.2187i	−0.377929	+	0.654592i
$863$	−10.8047	−	18.7143i	−0.367796	−	0.637042i	0.621425	−	0.783474i	$-0.286554\pi$
$863$	−10.8047	−	18.7143i	−0.367796	−	0.637042i	−0.989221	+	0.146432i	$0.953221\pi$
$864$	1.42037	+	2.46016i	0.0483220	+	0.0836962i
$865$	0.602253	+	1.04313i	0.0204772	+	0.0354676i
$866$	10.8501	+	18.7929i	0.368701	+	0.638608i
$867$	−2.12335	+	3.67774i	−0.0721126	+	0.124903i
$868$		0			0
$869$	−11.2058	−	19.4090i	−0.380130	−	0.658405i
$870$	−6.19125	−	10.7236i	−0.209903	−	0.363563i
$871$	−9.50048	−	25.6087i	−0.321912	−	0.867717i
$872$	−15.0120	+	26.0015i	−0.508370	+	0.880523i
$873$	21.9156	−	37.9589i	0.741731	−	1.28472i
$874$	−13.2299	−	22.9149i	−0.447509	−	0.775109i
$875$		0			0
$876$	54.0597			1.82651
$877$	−0.880766			−0.0297413			−0.0148707	−	0.999889i	$-0.504734\pi$
$877$	−0.880766			−0.0297413			−0.0148707	+	0.999889i	$0.504734\pi$
$878$	4.31401	+	7.47208i	0.145591	+	0.252170i
$879$	11.2636	−	19.5092i	0.379912	−	0.658027i
$880$	−3.81193			−0.128500
$881$	−0.0700176	−	0.121274i	−0.00235895	−	0.00408583i	0.864844	−	0.502042i	$-0.167418\pi$
$881$	−0.0700176	−	0.121274i	−0.00235895	−	0.00408583i	−0.867202	+	0.497956i	$0.834084\pi$
$882$		0			0
$883$	−18.8253			−0.633522			−0.316761	−	0.948505i	$-0.602595\pi$
$883$	−18.8253			−0.633522			−0.316761	+	0.948505i	$0.602595\pi$
$884$	20.7497	+	3.52662i	0.697889	+	0.118613i
$885$	6.25841	−	10.8399i	0.210374	−	0.364378i
$886$	6.01281			0.202004
$887$	−16.6505	+	28.8395i	−0.559069	+	0.968337i	0.438505	+	0.898729i	$0.355508\pi$
$887$	−16.6505	+	28.8395i	−0.559069	+	0.968337i	−0.997574	+	0.0696078i	$0.977825\pi$
$888$	−15.2990	+	26.4986i	−0.513400	+	0.889234i
$889$		0			0
$890$	0.412092	−	0.713764i	0.0138133	−	0.0239254i
$891$	23.0325			0.771618
$892$	−6.59084	+	11.4157i	−0.220677	+	0.382225i
$893$	3.76127	+	6.51471i	0.125866	+	0.218006i
$894$	8.37090	−	14.4988i	0.279965	−	0.484913i
$895$	−8.73529	−	15.1300i	−0.291989	−	0.505739i
$896$		0			0
$897$	54.1267	+	9.19937i	1.80724	+	0.307158i
$898$	−8.28421	−	14.3487i	−0.276448	−	0.478822i
$899$	−12.3825			−0.412980
$900$	13.9613			0.465376
$901$	53.1738			1.77148
$902$	13.3149			0.443339
$903$		0			0
$904$	17.6933	−	30.6457i	0.588471	−	1.01926i
$905$	−5.71517	−	9.89896i	−0.189979	−	0.329052i
$906$	−12.6054	−	21.8332i	−0.418786	−	0.725359i
$907$	11.5870			0.384740			0.192370	−	0.981322i	$-0.438383\pi$
$907$	11.5870			0.384740			0.192370	+	0.981322i	$0.438383\pi$
$908$	10.0580	−	17.4210i	0.333788	−	0.578137i
$909$	−1.91629			−0.0635594
$910$		0			0
$911$	52.5489			1.74102			0.870512	−	0.492147i	$-0.163788\pi$
$911$	52.5489			1.74102			0.870512	+	0.492147i	$0.163788\pi$
$912$	8.70537	−	15.0781i	0.288264	−	0.499287i
$913$	−3.28588			−0.108747
$914$	5.49998	+	9.52624i	0.181923	+	0.315100i
$915$	7.14411	+	12.3740i	0.236177	+	0.409070i
$916$	−5.09646	+	8.82733i	−0.168392	+	0.291663i
$917$		0			0
$918$	1.34922			0.0445308
$919$	−20.0534			−0.661502			−0.330751	−	0.943718i	$-0.607302\pi$
$919$	−20.0534			−0.661502			−0.330751	+	0.943718i	$0.607302\pi$
$920$	−20.2499			−0.667621
$921$	19.5387			0.643823
$922$	3.29645	+	5.70963i	0.108563	+	0.188036i
$923$	25.6901	+	4.36628i	0.845599	+	0.143718i
$924$		0			0
$925$	−8.53874	−	14.7895i	−0.280752	−	0.486277i
$926$	10.2382	−	17.7330i	0.336447	−	0.582744i
$927$	25.0760	+	43.4330i	0.823605	+	1.42653i
$928$	16.3848	−	28.3793i	0.537857	−	0.931596i
$929$	15.9085			0.521941			0.260971	−	0.965347i	$-0.415957\pi$
$929$	15.9085			0.521941			0.260971	+	0.965347i	$0.415957\pi$
$930$	2.43273	−	4.21361i	0.0797724	−	0.138170i
$931$		0			0
$932$	−18.7439	+	32.4655i	−0.613978	+	1.06344i
$933$	10.4022	−	18.0172i	0.340554	−	0.589857i
$934$	−2.04131			−0.0667938
$935$	−6.06092	+	10.4978i	−0.198213	+	0.343316i
$936$	−8.71171	−	23.4825i	−0.284751	−	0.767550i
$937$	−26.1978			−0.855846			−0.427923	−	0.903815i	$-0.640755\pi$
$937$	−26.1978			−0.855846			−0.427923	+	0.903815i	$0.640755\pi$
$938$		0			0
$939$	6.29339	+	10.9005i	0.205377	+	0.355723i
$940$	2.46307			0.0803364
$941$	−18.1529	+	31.4418i	−0.591769	+	1.02497i	0.402225	+	0.915541i	$0.368237\pi$
$941$	−18.1529	+	31.4418i	−0.591769	+	1.02497i	−0.993994	+	0.109433i	$0.965097\pi$
$942$	17.6026	+	30.4887i	0.573525	+	0.993375i
$943$	−49.2332			−1.60325
$944$	4.94745			0.161026
$945$		0			0
$946$	−0.247746	−	0.429109i	−0.00805493	−	0.0139516i
$947$	0.459419	−	0.795738i	0.0149291	−	0.0258580i	−0.858464	−	0.512873i	$-0.828581\pi$
$947$	0.459419	−	0.795738i	0.0149291	−	0.0258580i	0.873393	+	0.487015i	$0.161914\pi$
$948$	16.7582	−	29.0260i	0.544280	−	0.942720i
$949$	53.3632	+	9.06960i	1.73224	+	0.294412i
$950$	−6.98037	−	12.0904i	−0.226473	−	0.392263i
$951$	13.4756	+	23.3405i	0.436977	+	0.756867i
$952$		0			0
$953$	9.17943	−	15.8992i	0.297351	−	0.515027i	−0.678178	−	0.734898i	$-0.737230\pi$
$953$	9.17943	−	15.8992i	0.297351	−	0.515027i	0.975529	+	0.219871i	$0.0705635\pi$
$954$	−13.5361	−	23.4452i	−0.438247	−	0.759065i
$955$	9.91370	+	17.1710i	0.320800	+	0.555641i
$956$	−2.08263	−	3.60722i	−0.0673570	−	0.116666i
$957$	−16.2737	−	28.1869i	−0.526055	−	0.911153i
$958$	8.02914	−	13.9069i	0.259410	−	0.449311i
$959$		0			0
$960$	2.62616	+	4.54864i	0.0847589	+	0.146807i
$961$	13.0673	+	22.6332i	0.421525	+	0.730102i
$962$	−8.36311	+	10.0928i	−0.269637	+	0.325406i
$963$	−11.8848	+	20.5850i	−0.382981	+	0.663343i
$964$	−5.21800	+	9.03783i	−0.168060	+	0.291089i
$965$	15.7960	+	27.3594i	0.508491	+	0.880731i
$966$		0			0
$967$	12.5923			0.404940			0.202470	−	0.979288i	$-0.435103\pi$
$967$	12.5923			0.404940			0.202470	+	0.979288i	$0.435103\pi$
$968$	−12.9158			−0.415129
$969$	−27.6829	−	47.9482i	−0.889302	−	1.54032i
$970$	−7.17544	+	12.4282i	−0.230389	+	0.399046i
$971$	21.3308			0.684537			0.342269	−	0.939602i	$-0.388805\pi$
$971$	21.3308			0.684537			0.342269	+	0.939602i	$0.388805\pi$
$972$	16.1308	+	27.9394i	0.517397	+	0.896157i
$973$		0			0
$974$	−2.03712			−0.0652736
$975$	28.5583	+	4.85377i	0.914598	+	0.155445i
$976$	−2.82381	+	4.89098i	−0.0903880	+	0.156557i
$977$	−42.4279			−1.35739			−0.678695	−	0.734420i	$-0.737454\pi$
$977$	−42.4279			−1.35739			−0.678695	+	0.734420i	$0.737454\pi$
$978$	3.40421	−	5.89626i	0.108854	−	0.188542i
$979$	1.08318	−	1.87613i	0.0346187	−	0.0599614i
$980$		0			0
$981$	−16.9172	+	29.3014i	−0.540124	+	0.935523i
$982$	16.1378			0.514977
$983$	1.04879	−	1.81655i	0.0334511	−	0.0579391i	−0.848815	−	0.528690i	$-0.822684\pi$
$983$	1.04879	−	1.81655i	0.0334511	−	0.0579391i	0.882266	+	0.470751i	$0.156017\pi$
$984$	23.2711	+	40.3068i	0.741856	+	1.28493i
$985$	4.32965	−	7.49917i	0.137954	−	0.238943i
$986$	−7.78198	−	13.4788i	−0.247829	−	0.429252i
$987$		0			0
$988$	20.2661	−	24.4576i	0.644750	−	0.778101i
$989$	0.916066	+	1.58667i	0.0291292	+	0.0504533i
$990$	6.17154			0.196145
$991$	−27.6349			−0.877851			−0.438926	−	0.898523i	$-0.644641\pi$
$991$	−27.6349			−0.877851			−0.438926	+	0.898523i	$0.644641\pi$
$992$	12.8762			0.408819
$993$	−48.2703			−1.53181
$994$		0			0
$995$	−3.14227	+	5.44257i	−0.0996166	+	0.172541i
$996$	−2.45700	−	4.25565i	−0.0778531	−	0.134845i
$997$	−1.01392	−	1.75615i	−0.0321110	−	0.0556180i	0.849523	−	0.527551i	$-0.176890\pi$
$997$	−1.01392	−	1.75615i	−0.0321110	−	0.0556180i	−0.881634	+	0.471933i	$0.843556\pi$
$998$	12.7959			0.405047
$999$	1.24535	−	2.15701i	0.0394012	−	0.0682449i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.g.j.263.3		8
7.2	even	3		637.2.h.i.471.2		8
7.3	odd	6		91.2.f.c.29.3	yes	8
7.4	even	3		637.2.f.i.393.3		8
7.5	odd	6		637.2.h.h.471.2		8
7.6	odd	2		637.2.g.k.263.3		8
13.9	even	3		637.2.h.i.165.2		8
21.17	even	6		819.2.o.h.757.2		8
28.3	even	6		1456.2.s.q.1121.4		8
91.3	odd	6		1183.2.a.k.1.2		4
91.9	even	3	inner	637.2.g.j.373.3		8
91.10	odd	6		1183.2.a.l.1.3		4
91.24	even	12		1183.2.c.g.337.3		8
91.48	odd	6		637.2.h.h.165.2		8
91.61	odd	6		637.2.g.k.373.3		8
91.74	even	3		637.2.f.i.295.3		8
91.80	even	12		1183.2.c.g.337.6		8
91.81	even	3		8281.2.a.bp.1.2		4
91.87	odd	6		91.2.f.c.22.3	✓	8
91.88	even	6		8281.2.a.bt.1.3		4
273.269	even	6		819.2.o.h.568.2		8
364.87	even	6		1456.2.s.q.113.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.f.c.22.3	✓	8	91.87	odd	6
91.2.f.c.29.3	yes	8	7.3	odd	6
637.2.f.i.295.3		8	91.74	even	3
637.2.f.i.393.3		8	7.4	even	3
637.2.g.j.263.3		8	1.1	even	1	trivial
637.2.g.j.373.3		8	91.9	even	3	inner
637.2.g.k.263.3		8	7.6	odd	2
637.2.g.k.373.3		8	91.61	odd	6
637.2.h.h.165.2		8	91.48	odd	6
637.2.h.h.471.2		8	7.5	odd	6
637.2.h.i.165.2		8	13.9	even	3
637.2.h.i.471.2		8	7.2	even	3
819.2.o.h.568.2		8	273.269	even	6
819.2.o.h.757.2		8	21.17	even	6
1183.2.a.k.1.2		4	91.3	odd	6
1183.2.a.l.1.3		4	91.10	odd	6
1183.2.c.g.337.3		8	91.24	even	12
1183.2.c.g.337.6		8	91.80	even	12
1456.2.s.q.113.4		8	364.87	even	6
1456.2.s.q.1121.4		8	28.3	even	6
8281.2.a.bp.1.2		4	91.81	even	3
8281.2.a.bt.1.3		4	91.88	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.355143 - 0.615126i) q^{2} -2.40788 q^{3} +(0.747746 + 1.29513i) q^{4} +(-0.644857 - 1.11692i) q^{5} +(-0.855143 + 1.48115i) q^{6} +2.48280 q^{8} +2.79790 q^{9} +O(q^{10})\)	\(q+(0.355143 - 0.615126i) q^{2} -2.40788 q^{3} +(0.747746 + 1.29513i) q^{4} +(-0.644857 - 1.11692i) q^{5} +(-0.855143 + 1.48115i) q^{6} +2.48280 q^{8} +2.79790 q^{9} -0.916066 q^{10} -2.40788 q^{11} +(-1.80049 - 3.11853i) q^{12} +(-1.25409 - 3.38042i) q^{13} +(1.55274 + 2.68942i) q^{15} +(-0.613742 + 1.06303i) q^{16} +(1.95169 + 3.38042i) q^{17} +(0.993655 - 1.72106i) q^{18} +5.89068 q^{19} +(0.964379 - 1.67035i) q^{20} +(-0.855143 + 1.48115i) q^{22} +(3.16197 - 5.47670i) q^{23} -5.97829 q^{24} +(1.66832 - 2.88961i) q^{25} +(-2.52477 - 0.429109i) q^{26} +0.486640 q^{27} +(-2.80683 - 4.86157i) q^{29} +2.20578 q^{30} +(1.10289 - 1.91026i) q^{31} +(2.91873 + 5.05540i) q^{32} +5.79790 q^{33} +2.77252 q^{34} +(2.09212 + 3.62365i) q^{36} +(2.55908 - 4.43246i) q^{37} +(2.09204 - 3.62351i) q^{38} +(3.01971 + 8.13966i) q^{39} +(-1.60105 - 2.77310i) q^{40} +(-3.89260 - 6.74219i) q^{41} +(-0.144857 + 0.250899i) q^{43} +(-1.80049 - 3.11853i) q^{44} +(-1.80424 - 3.12504i) q^{45} +(-2.24591 - 3.89003i) q^{46} +(0.638511 + 1.10593i) q^{47} +(1.47782 - 2.55966i) q^{48} +(-1.18499 - 2.05245i) q^{50} +(-4.69943 - 8.13966i) q^{51} +(3.44036 - 4.15192i) q^{52} +(6.81126 - 11.7974i) q^{53} +(0.172827 - 0.299345i) q^{54} +(1.55274 + 2.68942i) q^{55} -14.1841 q^{57} -3.98731 q^{58} +(-2.01528 - 3.49057i) q^{59} +(-2.32211 + 4.02201i) q^{60} +4.60097 q^{61} +(-0.783368 - 1.35683i) q^{62} +1.69131 q^{64} +(-2.96697 + 3.58061i) q^{65} +(2.05908 - 3.56644i) q^{66} +7.57559 q^{67} +(-2.91873 + 5.05540i) q^{68} +(-7.61366 + 13.1872i) q^{69} +(-3.61366 + 6.25905i) q^{71} +6.94662 q^{72} +(-7.50626 + 13.0012i) q^{73} +(-1.81768 - 3.14832i) q^{74} +(-4.01712 + 6.95785i) q^{75} +(4.40474 + 7.62923i) q^{76} +(6.07935 + 1.03324i) q^{78} +(4.65379 + 8.06060i) q^{79} +1.58310 q^{80} -9.56546 q^{81} -5.52973 q^{82} +1.36463 q^{83} +(2.51712 - 4.35978i) q^{85} +(0.102890 + 0.178210i) q^{86} +(6.75852 + 11.7061i) q^{87} -5.97829 q^{88} +(-0.449849 + 0.779162i) q^{89} -2.56306 q^{90} +9.45742 q^{92} +(-2.65563 + 4.59968i) q^{93} +0.907052 q^{94} +(-3.79865 - 6.57945i) q^{95} +(-7.02797 - 12.1728i) q^{96} +(7.83288 - 13.5669i) q^{97} -6.73701 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} - 2 q^{3} - 5 q^{4} - 7 q^{5} - 5 q^{6} - 12 q^{8} + 14 q^{9}+O(q^{10}) \) 8 * q + q^2 - 2 * q^3 - 5 * q^4 - 7 * q^5 - 5 * q^6 - 12 * q^8 + 14 * q^9	\( 8 q + q^{2} - 2 q^{3} - 5 q^{4} - 7 q^{5} - 5 q^{6} - 12 q^{8} + 14 q^{9} + 22 q^{10} - 2 q^{11} + 12 q^{12} - 4 q^{13} - 3 q^{15} - 19 q^{16} - 4 q^{17} + 3 q^{18} - 2 q^{19} - 2 q^{20} - 5 q^{22} + 2 q^{23} + 6 q^{24} - 5 q^{25} - 3 q^{26} + 52 q^{27} - q^{29} - 8 q^{30} - 4 q^{31} + 33 q^{32} + 38 q^{33} - 6 q^{34} + 34 q^{36} + 10 q^{37} - 23 q^{38} - 19 q^{39} - 17 q^{40} - 22 q^{41} - 3 q^{43} + 12 q^{44} - 11 q^{45} - 24 q^{46} + 2 q^{47} + 11 q^{48} - 43 q^{50} - 7 q^{51} + 34 q^{52} - 2 q^{53} + 5 q^{54} - 3 q^{55} - 34 q^{57} - 22 q^{58} - 8 q^{59} + 11 q^{60} - 16 q^{61} - 5 q^{62} + 28 q^{64} + 4 q^{65} + 6 q^{66} - 12 q^{67} - 33 q^{68} - 18 q^{69} + 14 q^{71} + 10 q^{72} - 8 q^{73} - 20 q^{74} - 7 q^{75} + 32 q^{76} - q^{78} + 26 q^{79} - 14 q^{80} + 48 q^{81} + 28 q^{82} - 5 q^{85} - 12 q^{86} + 13 q^{87} + 6 q^{88} - q^{89} - 52 q^{90} + 24 q^{92} + 7 q^{93} - 66 q^{94} - 21 q^{95} - 58 q^{96} + 3 q^{97} + 46 q^{99}+O(q^{100}) \) 8 * q + q^2 - 2 * q^3 - 5 * q^4 - 7 * q^5 - 5 * q^6 - 12 * q^8 + 14 * q^9 + 22 * q^10 - 2 * q^11 + 12 * q^12 - 4 * q^13 - 3 * q^15 - 19 * q^16 - 4 * q^17 + 3 * q^18 - 2 * q^19 - 2 * q^20 - 5 * q^22 + 2 * q^23 + 6 * q^24 - 5 * q^25 - 3 * q^26 + 52 * q^27 - q^29 - 8 * q^30 - 4 * q^31 + 33 * q^32 + 38 * q^33 - 6 * q^34 + 34 * q^36 + 10 * q^37 - 23 * q^38 - 19 * q^39 - 17 * q^40 - 22 * q^41 - 3 * q^43 + 12 * q^44 - 11 * q^45 - 24 * q^46 + 2 * q^47 + 11 * q^48 - 43 * q^50 - 7 * q^51 + 34 * q^52 - 2 * q^53 + 5 * q^54 - 3 * q^55 - 34 * q^57 - 22 * q^58 - 8 * q^59 + 11 * q^60 - 16 * q^61 - 5 * q^62 + 28 * q^64 + 4 * q^65 + 6 * q^66 - 12 * q^67 - 33 * q^68 - 18 * q^69 + 14 * q^71 + 10 * q^72 - 8 * q^73 - 20 * q^74 - 7 * q^75 + 32 * q^76 - q^78 + 26 * q^79 - 14 * q^80 + 48 * q^81 + 28 * q^82 - 5 * q^85 - 12 * q^86 + 13 * q^87 + 6 * q^88 - q^89 - 52 * q^90 + 24 * q^92 + 7 * q^93 - 66 * q^94 - 21 * q^95 - 58 * q^96 + 3 * q^97 + 46 * q^99

Introduction

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