LMFDB - Embedded newform 637.2.h.l.165.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(165,637)]

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, 4]))

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

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

chi := DirichletCharacter("637.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.h (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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1 $ x^12 - x^11 + 7x^10 - 2x^9 + 33x^8 - 11x^7 + 55x^6 + 17x^5 + 47x^4 + x^3 + 8x^2 + 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			165.2
Root			$1.16700 - 2.02131i$ of defining polynomial
Character	$\chi$	$=$	637.165
Dual form			637.2.h.l.471.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.90556 q^{2} +(0.214224 + 0.371047i) q^{3} +1.63116 q^{4} +(-0.736565 - 1.27577i) q^{5} +(-0.408216 - 0.707051i) q^{6} +0.702849 q^{8} +(1.40822 - 2.43910i) q^{9} +O(q^{10})$	\(q-1.90556 q^{2} +(0.214224 + 0.371047i) q^{3} +1.63116 q^{4} +(-0.736565 - 1.27577i) q^{5} +(-0.408216 - 0.707051i) q^{6} +0.702849 q^{8} +(1.40822 - 2.43910i) q^{9} +(1.40357 + 2.43105i) q^{10} +(2.19681 + 3.80498i) q^{11} +(0.349433 + 0.605236i) q^{12} +(-2.69752 + 2.39236i) q^{13} +(0.315580 - 0.546600i) q^{15} -4.60164 q^{16} +1.20271 q^{17} +(-2.68344 + 4.64786i) q^{18} +(1.62105 - 2.80773i) q^{19} +(-1.20145 - 2.08098i) q^{20} +(-4.18615 - 7.25062i) q^{22} -4.43710 q^{23} +(0.150567 + 0.260790i) q^{24} +(1.41494 - 2.45075i) q^{25} +(5.14029 - 4.55878i) q^{26} +2.49204 q^{27} +(-0.0837807 + 0.145112i) q^{29} +(-0.601356 + 1.04158i) q^{30} +(2.62272 - 4.54268i) q^{31} +7.36300 q^{32} +(-0.941217 + 1.63024i) q^{33} -2.29184 q^{34} +(2.29702 - 3.97856i) q^{36} +7.05055 q^{37} +(-3.08900 + 5.35031i) q^{38} +(-1.46555 - 0.488407i) q^{39} +(-0.517694 - 0.896672i) q^{40} +(2.58195 - 4.47206i) q^{41} +(-0.0113752 - 0.0197024i) q^{43} +(3.58334 + 6.20653i) q^{44} -4.14897 q^{45} +8.45516 q^{46} +(5.84178 + 10.1183i) q^{47} +(-0.985780 - 1.70742i) q^{48} +(-2.69626 + 4.67006i) q^{50} +(0.257649 + 0.446262i) q^{51} +(-4.40009 + 3.90231i) q^{52} +(0.0708929 - 0.122790i) q^{53} -4.74873 q^{54} +(3.23618 - 5.60523i) q^{55} +1.38907 q^{57} +(0.159649 - 0.276520i) q^{58} +5.34354 q^{59} +(0.514760 - 0.891591i) q^{60} +(5.77287 - 9.99891i) q^{61} +(-4.99774 + 8.65635i) q^{62} -4.82736 q^{64} +(5.03899 + 1.67929i) q^{65} +(1.79355 - 3.10651i) q^{66} +(-2.06773 - 3.58141i) q^{67} +1.96181 q^{68} +(-0.950533 - 1.64637i) q^{69} +(4.98486 + 8.63403i) q^{71} +(0.989763 - 1.71432i) q^{72} +(7.62080 - 13.1996i) q^{73} -13.4352 q^{74} +1.21246 q^{75} +(2.64418 - 4.57986i) q^{76} +(2.79269 + 0.930689i) q^{78} +(-0.387251 - 0.670738i) q^{79} +(3.38941 + 5.87062i) q^{80} +(-3.69080 - 6.39265i) q^{81} +(-4.92006 + 8.52179i) q^{82} +16.0186 q^{83} +(-0.885875 - 1.53438i) q^{85} +(0.0216761 + 0.0375441i) q^{86} -0.0717913 q^{87} +(1.54402 + 2.67433i) q^{88} -6.55760 q^{89} +7.90611 q^{90} -7.23762 q^{92} +2.24739 q^{93} +(-11.1319 - 19.2809i) q^{94} -4.77602 q^{95} +(1.57733 + 2.73202i) q^{96} +(1.74583 + 3.02387i) q^{97} +12.3743 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} - q^{3} + 8 q^{4} - q^{5} + 9 q^{6} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 12 * q - 4 * q^2 - q^3 + 8 * q^4 - q^5 + 9 * q^6 - 6 * q^8 + 3 * q^9	$ 12 q - 4 q^{2} - q^{3} + 8 q^{4} - q^{5} + 9 q^{6} - 6 q^{8} + 3 q^{9} - 4 q^{10} + 4 q^{11} - 5 q^{12} + 2 q^{13} - 2 q^{15} - 16 q^{16} + 10 q^{17} + 3 q^{18} + q^{19} + q^{20} - 5 q^{22} + 2 q^{23} + 11 q^{24} + 7 q^{25} + 16 q^{26} + 8 q^{27} + 3 q^{29} - 5 q^{30} - 16 q^{31} - 16 q^{32} - 16 q^{33} - 32 q^{34} - 21 q^{36} + 26 q^{37} + 17 q^{38} - 20 q^{39} + 5 q^{40} + 8 q^{41} - 11 q^{43} + 21 q^{44} - 14 q^{45} - 32 q^{46} + q^{47} - 21 q^{48} + 6 q^{50} - 20 q^{51} - 41 q^{52} - 2 q^{53} - 36 q^{54} - 9 q^{55} + 42 q^{57} - 8 q^{58} + 26 q^{59} + 20 q^{60} + 5 q^{61} - 5 q^{62} - 30 q^{64} - 5 q^{65} - 18 q^{66} - 11 q^{67} + 58 q^{68} - 23 q^{69} + 6 q^{71} + 25 q^{72} + 30 q^{73} + 6 q^{74} - 6 q^{75} + 9 q^{76} + 16 q^{78} + 7 q^{79} + 7 q^{80} - 6 q^{81} - q^{82} + 54 q^{83} - q^{85} - 7 q^{86} + 32 q^{87} + 8 q^{89} + 16 q^{90} + 54 q^{92} + 14 q^{93} - 45 q^{94} + 12 q^{95} - 19 q^{96} + 35 q^{97} - 20 q^{99}+O(q^{100}) $ 12 * q - 4 * q^2 - q^3 + 8 * q^4 - q^5 + 9 * q^6 - 6 * q^8 + 3 * q^9 - 4 * q^10 + 4 * q^11 - 5 * q^12 + 2 * q^13 - 2 * q^15 - 16 * q^16 + 10 * q^17 + 3 * q^18 + q^19 + q^20 - 5 * q^22 + 2 * q^23 + 11 * q^24 + 7 * q^25 + 16 * q^26 + 8 * q^27 + 3 * q^29 - 5 * q^30 - 16 * q^31 - 16 * q^32 - 16 * q^33 - 32 * q^34 - 21 * q^36 + 26 * q^37 + 17 * q^38 - 20 * q^39 + 5 * q^40 + 8 * q^41 - 11 * q^43 + 21 * q^44 - 14 * q^45 - 32 * q^46 + q^47 - 21 * q^48 + 6 * q^50 - 20 * q^51 - 41 * q^52 - 2 * q^53 - 36 * q^54 - 9 * q^55 + 42 * q^57 - 8 * q^58 + 26 * q^59 + 20 * q^60 + 5 * q^61 - 5 * q^62 - 30 * q^64 - 5 * q^65 - 18 * q^66 - 11 * q^67 + 58 * q^68 - 23 * q^69 + 6 * q^71 + 25 * q^72 + 30 * q^73 + 6 * q^74 - 6 * q^75 + 9 * q^76 + 16 * q^78 + 7 * q^79 + 7 * q^80 - 6 * q^81 - q^82 + 54 * q^83 - q^85 - 7 * q^86 + 32 * q^87 + 8 * q^89 + 16 * q^90 + 54 * q^92 + 14 * q^93 - 45 * q^94 + 12 * q^95 - 19 * q^96 + 35 * q^97 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.90556			−1.34743			−0.673717	−	0.738989i	$-0.735303\pi$
$2$	−1.90556			−1.34743			−0.673717	+	0.738989i	$0.735303\pi$
$3$	0.214224	+	0.371047i	0.123682	+	0.214224i	0.921217	−	0.389049i	$-0.127196\pi$
$3$	0.214224	+	0.371047i	0.123682	+	0.214224i	−0.797535	+	0.603273i	$0.793863\pi$
$4$	1.63116			0.815580
$5$	−0.736565	−	1.27577i	−0.329402	−	0.570541i	0.652991	−	0.757365i	$-0.273514\pi$
$5$	−0.736565	−	1.27577i	−0.329402	−	0.570541i	−0.982393	+	0.186825i	$0.940180\pi$
$6$	−0.408216	−	0.707051i	−0.166654	−	0.288653i
$7$		0			0
$7$		0			0
$8$	0.702849			0.248495
$9$	1.40822	−	2.43910i	0.469405	−	0.813034i
$10$	1.40357	+	2.43105i	0.443847	+	0.768766i
$11$	2.19681	+	3.80498i	0.662362	+	1.14725i	0.979993	+	0.199031i	$0.0637794\pi$
$11$	2.19681	+	3.80498i	0.662362	+	1.14725i	−0.317631	+	0.948214i	$0.602887\pi$
$12$	0.349433	+	0.605236i	0.100873	+	0.174717i
$13$	−2.69752	+	2.39236i	−0.748158	+	0.663520i
$13$	−2.69752	+	2.39236i	−0.748158	+	0.663520i
$14$		0			0
$15$	0.315580	−	0.546600i	0.0814823	−	0.141131i
$16$	−4.60164			−1.15041
$17$	1.20271			0.291700			0.145850	−	0.989307i	$-0.453408\pi$
$17$	1.20271			0.291700			0.145850	+	0.989307i	$0.453408\pi$
$18$	−2.68344	+	4.64786i	−0.632493	+	1.09551i
$19$	1.62105	−	2.80773i	0.371893	−	0.644138i	−0.617963	−	0.786207i	$-0.712042\pi$
$19$	1.62105	−	2.80773i	0.371893	−	0.644138i	0.989857	+	0.142068i	$0.0453753\pi$
$20$	−1.20145	−	2.08098i	−0.268653	−	0.465321i
$21$		0			0
$22$	−4.18615	−	7.25062i	−0.892490	−	1.54584i
$23$	−4.43710			−0.925200			−0.462600	−	0.886567i	$-0.653083\pi$
$23$	−4.43710			−0.925200			−0.462600	+	0.886567i	$0.653083\pi$
$24$	0.150567	+	0.260790i	0.0307343	+	0.0532334i
$25$	1.41494	−	2.45075i	0.282989	−	0.490151i
$26$	5.14029	−	4.55878i	1.00809	−	0.894050i
$27$	2.49204			0.479593
$28$		0			0
$29$	−0.0837807	+	0.145112i	−0.0155577	+	0.0269467i	−0.873699	−	0.486466i	$-0.838286\pi$
$29$	−0.0837807	+	0.145112i	−0.0155577	+	0.0269467i	0.858142	+	0.513413i	$0.171619\pi$
$30$	−0.601356	+	1.04158i	−0.109792	+	0.190165i
$31$	2.62272	−	4.54268i	0.471054	−	0.815889i	−0.528398	−	0.848997i	$-0.677207\pi$
$31$	2.62272	−	4.54268i	0.471054	−	0.815889i	0.999452	+	0.0331076i	$0.0105404\pi$
$32$	7.36300			1.30161
$33$	−0.941217	+	1.63024i	−0.163845	+	0.283788i
$34$	−2.29184			−0.393047
$35$		0			0
$36$	2.29702	−	3.97856i	0.382837	−	0.663094i
$37$	7.05055			1.15910			0.579552	−	0.814936i	$-0.303228\pi$
$37$	7.05055			1.15910			0.579552	+	0.814936i	$0.303228\pi$
$38$	−3.08900	+	5.35031i	−0.501102	+	0.867934i
$39$	−1.46555	−	0.488407i	−0.234676	−	0.0782077i
$40$	−0.517694	−	0.896672i	−0.0818546	−	0.141776i
$41$	2.58195	−	4.47206i	0.403233	−	0.698419i	−0.590881	−	0.806758i	$-0.701220\pi$
$41$	2.58195	−	4.47206i	0.403233	−	0.698419i	0.994114	+	0.108339i	$0.0345533\pi$
$42$		0			0
$43$	−0.0113752	−	0.0197024i	−0.00173470	−	0.00300459i	0.865157	−	0.501502i	$-0.167219\pi$
$43$	−0.0113752	−	0.0197024i	−0.00173470	−	0.00300459i	−0.866891	+	0.498497i	$0.833886\pi$
$44$	3.58334	+	6.20653i	0.540209	+	0.935670i
$45$	−4.14897			−0.618492
$46$	8.45516			1.24665
$47$	5.84178	+	10.1183i	0.852111	+	1.47590i	0.879300	+	0.476269i	$0.158011\pi$
$47$	5.84178	+	10.1183i	0.852111	+	1.47590i	−0.0271891	+	0.999630i	$0.508656\pi$
$48$	−0.985780	−	1.70742i	−0.142285	−	0.246445i
$49$		0			0
$50$	−2.69626	+	4.67006i	−0.381309	+	0.660446i
$51$	0.257649	+	0.446262i	0.0360781	+	0.0624892i
$52$	−4.40009	+	3.90231i	−0.610183	+	0.541154i
$53$	0.0708929	−	0.122790i	0.00973788	−	0.0168665i	−0.861115	−	0.508410i	$-0.830234\pi$
$53$	0.0708929	−	0.122790i	0.00973788	−	0.0168665i	0.870853	+	0.491543i	$0.163567\pi$
$54$	−4.74873			−0.646220
$55$	3.23618	−	5.60523i	0.436367	−	0.755809i
$56$		0			0
$57$	1.38907			0.183986
$58$	0.159649	−	0.276520i	0.0209630	−	0.0363089i
$59$	5.34354			0.695670			0.347835	−	0.937556i	$-0.386917\pi$
$59$	5.34354			0.695670			0.347835	+	0.937556i	$0.386917\pi$
$60$	0.514760	−	0.891591i	0.0664553	−	0.115104i
$61$	5.77287	−	9.99891i	0.739141	−	1.28023i	−0.213742	−	0.976890i	$-0.568565\pi$
$61$	5.77287	−	9.99891i	0.739141	−	1.28023i	0.952883	−	0.303339i	$-0.0981016\pi$
$62$	−4.99774	+	8.65635i	−0.634714	+	1.09936i
$63$		0			0
$64$	−4.82736			−0.603420
$65$	5.03899	+	1.67929i	0.625010	+	0.208290i
$66$	1.79355	−	3.10651i	0.220770	−	0.382385i
$67$	−2.06773	−	3.58141i	−0.252613	−	0.437539i	0.711631	−	0.702553i	$-0.247957\pi$
$67$	−2.06773	−	3.58141i	−0.252613	−	0.437539i	−0.964245	+	0.265014i	$0.914623\pi$
$68$	1.96181			0.237905
$69$	−0.950533	−	1.64637i	−0.114431	−	0.198200i
$70$		0			0
$71$	4.98486	+	8.63403i	0.591594	+	1.02467i	0.994018	+	0.109217i	$0.0348344\pi$
$71$	4.98486	+	8.63403i	0.591594	+	1.02467i	−0.402424	+	0.915453i	$0.631832\pi$
$72$	0.989763	−	1.71432i	0.116645	−	0.202035i
$73$	7.62080	−	13.1996i	0.891947	−	1.54490i	0.0544080	−	0.998519i	$-0.482673\pi$
$73$	7.62080	−	13.1996i	0.891947	−	1.54490i	0.837539	−	0.546378i	$-0.183994\pi$
$74$	−13.4352			−1.56182
$75$	1.21246			0.140003
$76$	2.64418	−	4.57986i	0.303309	−	0.525346i
$77$		0			0
$78$	2.79269	+	0.930689i	0.316210	+	0.105380i
$79$	−0.387251	−	0.670738i	−0.0435691	−	0.0754639i	0.843418	−	0.537257i	$-0.180540\pi$
$79$	−0.387251	−	0.670738i	−0.0435691	−	0.0754639i	−0.886988	+	0.461793i	$0.847206\pi$
$80$	3.38941	+	5.87062i	0.378947	+	0.656356i
$81$	−3.69080	−	6.39265i	−0.410088	−	0.710294i
$82$	−4.92006	+	8.52179i	−0.543329	+	0.941074i
$83$	16.0186			1.75827			0.879136	−	0.476571i	$-0.158121\pi$
$83$	16.0186			1.75827			0.879136	+	0.476571i	$0.158121\pi$
$84$		0			0
$85$	−0.885875	−	1.53438i	−0.0960866	−	0.166427i
$86$	0.0216761	+	0.0375441i	0.00233740	+	0.00404849i
$87$	−0.0717913			−0.00769683
$88$	1.54402	+	2.67433i	0.164593	+	0.285084i
$89$	−6.55760			−0.695104			−0.347552	−	0.937661i	$-0.612987\pi$
$89$	−6.55760			−0.695104			−0.347552	+	0.937661i	$0.612987\pi$
$90$	7.90611			0.833378
$91$		0			0
$92$	−7.23762			−0.754574
$93$	2.24739			0.233044
$94$	−11.1319	−	19.2809i	−1.14816	−	1.98868i
$95$	−4.77602			−0.490010
$96$	1.57733	+	2.73202i	0.160986	+	0.278835i
$97$	1.74583	+	3.02387i	0.177262	+	0.307027i	0.940942	−	0.338568i	$-0.109943\pi$
$97$	1.74583	+	3.02387i	0.177262	+	0.307027i	−0.763680	+	0.645595i	$0.776609\pi$
$98$		0			0
$99$	12.3743			1.24367
$100$	2.30800	−	3.99757i	0.230800	−	0.399757i
$101$	1.28890	+	2.23244i	0.128250	+	0.222136i	0.922999	−	0.384803i	$-0.125731\pi$
$101$	1.28890	+	2.23244i	0.128250	+	0.222136i	−0.794749	+	0.606939i	$0.792397\pi$
$102$	−0.490966	−	0.850379i	−0.0486129	−	0.0842000i
$103$	−8.43173	−	14.6042i	−0.830803	−	1.43899i	−0.897402	−	0.441213i	$-0.854548\pi$
$103$	−8.43173	−	14.6042i	−0.830803	−	1.43899i	0.0665997	−	0.997780i	$-0.478785\pi$
$104$	−1.89595	+	1.68146i	−0.185913	+	0.164881i
$105$		0			0
$106$	−0.135091	+	0.233984i	−0.0131212	+	0.0227265i
$107$	8.68265			0.839383			0.419692	−	0.907667i	$-0.362138\pi$
$107$	8.68265			0.839383			0.419692	+	0.907667i	$0.362138\pi$
$108$	4.06491			0.391146
$109$	6.02026	−	10.4274i	0.576637	−	0.998764i	−0.419225	−	0.907882i	$-0.637698\pi$
$109$	6.02026	−	10.4274i	0.576637	−	0.998764i	0.995862	−	0.0908816i	$-0.0289685\pi$
$110$	−6.16674	+	10.6811i	−0.587976	+	1.01840i
$111$	1.51040	+	2.61608i	0.143360	+	0.248307i
$112$		0			0
$113$	−4.68616	−	8.11667i	−0.440837	−	0.763552i	0.556915	−	0.830570i	$-0.311985\pi$
$113$	−4.68616	−	8.11667i	−0.440837	−	0.763552i	−0.997752	+	0.0670176i	$0.978652\pi$
$114$	−2.64695			−0.247910
$115$	3.26821	+	5.66071i	0.304763	+	0.527864i
$116$	−0.136660	+	0.236701i	−0.0126885	+	0.0219772i
$117$	2.03651	+	9.94849i	0.188275	+	0.919738i
$118$	−10.1824			−0.937369
$119$		0			0
$120$	0.221805	−	0.384177i	0.0202479	−	0.0350704i
$121$	−4.15192	+	7.19134i	−0.377448	+	0.653758i
$122$	−11.0006	+	19.0535i	−0.995944	+	1.72503i
$123$	2.21246			0.199491
$124$	4.27807	−	7.40983i	0.384182	−	0.665423i
$125$	−11.5344			−1.03167
$126$		0			0
$127$	−7.94269	+	13.7571i	−0.704800	+	1.22075i	0.261964	+	0.965078i	$0.415630\pi$
$127$	−7.94269	+	13.7571i	−0.704800	+	1.22075i	−0.966764	+	0.255672i	$0.917703\pi$
$128$	−5.52717			−0.488537
$129$	0.00487367	−	0.00844145i	0.000429103	−	0.000743228i
$130$	−9.60210	−	3.19998i	−0.842160	−	0.280657i
$131$	0.928725	+	1.60860i	0.0811430	+	0.140544i	0.903741	−	0.428079i	$-0.140810\pi$
$131$	0.928725	+	1.60860i	0.0811430	+	0.140544i	−0.822598	+	0.568623i	$0.807476\pi$
$132$	−1.53527	+	2.65917i	−0.133628	+	0.231451i
$133$		0			0
$134$	3.94018	+	6.82459i	0.340380	+	0.589555i
$135$	−1.83555	−	3.17926i	−0.157979	−	0.273627i
$136$	0.845324			0.0724859
$137$	−12.8002			−1.09360			−0.546798	−	0.837264i	$-0.684153\pi$
$137$	−12.8002			−1.09360			−0.546798	+	0.837264i	$0.684153\pi$
$138$	1.81130	+	3.13726i	0.154188	+	0.267061i
$139$	−0.169365	−	0.293348i	−0.0143653	−	0.0248815i	0.858753	−	0.512389i	$-0.171239\pi$
$139$	−0.169365	−	0.293348i	−0.0143653	−	0.0248815i	−0.873119	+	0.487508i	$0.837906\pi$
$140$		0			0
$141$	−2.50290	+	4.33514i	−0.210782	+	0.365085i
$142$	−9.49894	−	16.4527i	−0.797134	−	1.38068i
$143$	−15.0288	−	5.00848i	−1.25677	−	0.418830i
$144$	−6.48010	+	11.2239i	−0.540009	+	0.935322i
$145$	0.246840			0.0204989
$146$	−14.5219	+	25.1526i	−1.20184	+	2.08165i
$147$		0			0
$148$	11.5006			0.945341
$149$	−1.96158	+	3.39756i	−0.160699	+	0.278339i	−0.935120	−	0.354332i	$-0.884708\pi$
$149$	−1.96158	+	3.39756i	−0.160699	+	0.278339i	0.774421	+	0.632671i	$0.218041\pi$
$150$	−2.31041			−0.188644
$151$	1.05939	−	1.83492i	0.0862122	−	0.149324i	−0.819695	−	0.572800i	$-0.805857\pi$
$151$	1.05939	−	1.83492i	0.0862122	−	0.149324i	0.905907	+	0.423476i	$0.139190\pi$
$152$	1.13935	−	1.97341i	0.0924135	−	0.160065i
$153$	1.69368	−	2.93354i	0.136926	−	0.237162i
$154$		0			0
$155$	−7.72721			−0.620664
$156$	−2.39054	−	0.796669i	−0.191397	−	0.0637846i
$157$	−11.0564	+	19.1502i	−0.882397	+	1.52836i	−0.0337285	+	0.999431i	$0.510738\pi$
$157$	−11.0564	+	19.1502i	−0.882397	+	1.52836i	−0.848668	+	0.528925i	$0.822595\pi$
$158$	0.737929	+	1.27813i	0.0587065	+	0.101683i
$159$	0.0607478			0.00481761
$160$	−5.42333	−	9.39348i	−0.428752	−	0.742620i
$161$		0			0
$162$	7.03303	+	12.1816i	0.552567	+	0.957074i
$163$	−1.92607	+	3.33605i	−0.150861	+	0.261299i	−0.931544	−	0.363628i	$-0.881538\pi$
$163$	−1.92607	+	3.33605i	−0.150861	+	0.261299i	0.780683	+	0.624927i	$0.214871\pi$
$164$	4.21157	−	7.29465i	0.328868	−	0.569616i
$165$	2.77307			0.215883
$166$	−30.5244			−2.36916
$167$	1.06947	−	1.85238i	0.0827582	−	0.143341i	−0.821676	−	0.569956i	$-0.806960\pi$
$167$	1.06947	−	1.85238i	0.0827582	−	0.143341i	0.904434	+	0.426614i	$0.140294\pi$
$168$		0			0
$169$	1.55326	−	12.9069i	0.119482	−	0.992836i
$170$	1.68809	+	2.92385i	0.129470	+	0.224249i
$171$	−4.56557	−	7.90779i	−0.349138	−	0.604724i
$172$	−0.0185547	−	0.0321378i	−0.00141479	−	0.00245048i
$173$	−8.30664	+	14.3875i	−0.631542	+	1.09386i	0.355695	+	0.934602i	$0.384244\pi$
$173$	−8.30664	+	14.3875i	−0.631542	+	1.09386i	−0.987237	+	0.159260i	$0.949089\pi$
$174$	0.136803			0.0103710
$175$		0			0
$176$	−10.1089	−	17.5091i	−0.761988	−	1.31980i
$177$	1.14471	+	1.98270i	0.0860419	+	0.149029i
$178$	12.4959			0.936607
$179$	0.269748	+	0.467217i	0.0201619	+	0.0349214i	0.875930	−	0.482438i	$-0.160248\pi$
$179$	0.269748	+	0.467217i	0.0201619	+	0.0349214i	−0.855768	+	0.517359i	$0.826915\pi$
$180$	−6.76763			−0.504430
$181$	−2.77164			−0.206014			−0.103007	−	0.994681i	$-0.532846\pi$
$181$	−2.77164			−0.206014			−0.103007	+	0.994681i	$0.532846\pi$
$182$		0			0
$183$	4.94675			0.365674
$184$	−3.11861			−0.229907
$185$	−5.19319	−	8.99486i	−0.381811	−	0.661316i
$186$	−4.28254			−0.314011
$187$	2.64213	+	4.57629i	0.193211	+	0.334652i
$188$	9.52887	+	16.5045i	0.694964	+	1.20371i
$189$		0			0
$190$	9.10100			0.660256
$191$	10.1204	−	17.5290i	0.732284	−	1.26835i	−0.223621	−	0.974676i	$-0.571788\pi$
$191$	10.1204	−	17.5290i	0.732284	−	1.26835i	0.955905	−	0.293677i	$-0.0948790\pi$
$192$	−1.03414	−	1.79118i	−0.0746323	−	0.129267i
$193$	8.18856	+	14.1830i	0.589425	+	1.02091i	0.994308	+	0.106546i	$0.0339791\pi$
$193$	8.18856	+	14.1830i	0.589425	+	1.02091i	−0.404882	+	0.914369i	$0.632688\pi$
$194$	−3.32678	−	5.76216i	−0.238849	−	0.413699i
$195$	0.456378	+	2.22944i	0.0326819	+	0.159654i
$196$		0			0
$197$	−9.86676	+	17.0897i	−0.702977	+	1.21759i	0.264439	+	0.964402i	$0.414813\pi$
$197$	−9.86676	+	17.0897i	−0.702977	+	1.21759i	−0.967417	+	0.253190i	$0.918520\pi$
$198$	−23.5800			−1.67576
$199$	14.1175			1.00076			0.500380	−	0.865806i	$-0.333194\pi$
$199$	14.1175			1.00076			0.500380	+	0.865806i	$0.333194\pi$
$200$	0.994491	−	1.72251i	0.0703212	−	0.121800i
$201$	0.885913	−	1.53445i	0.0624875	−	0.108232i
$202$	−2.45607	−	4.25404i	−0.172809	−	0.299313i
$203$		0			0
$204$	0.420267	+	0.727924i	0.0294246	+	0.0509649i
$205$	−7.60709			−0.531302
$206$	16.0672	+	27.8291i	1.11945	+	1.93895i
$207$	−6.24840	+	10.8225i	−0.434294	+	0.752219i
$208$	12.4130	−	11.0088i	0.860688	−	0.763320i
$209$	14.2445			0.985313
$210$		0			0
$211$	2.31317	−	4.00652i	0.159245	−	0.275820i	−0.775352	−	0.631530i	$-0.782427\pi$
$211$	2.31317	−	4.00652i	0.159245	−	0.275820i	0.934597	+	0.355709i	$0.115761\pi$
$212$	0.115638	−	0.200290i	0.00794202	−	0.0137560i
$213$	−2.13575	+	3.69923i	−0.146339	+	0.253467i
$214$	−16.5453			−1.13101
$215$	−0.0167571	+	0.0290242i	−0.00114283	+	0.00197943i
$216$	1.75152			0.119176
$217$		0			0
$218$	−11.4720	+	19.8700i	−0.776980	+	1.34577i
$219$	6.53022			0.441272
$220$	5.27873	−	9.14303i	0.355892	−	0.616423i
$221$	−3.24434	+	2.87731i	−0.218238	+	0.193549i
$222$	−2.87815	−	4.98510i	−0.193169	−	0.334578i
$223$	−10.6761	+	18.4916i	−0.714926	+	1.23829i	0.248061	+	0.968744i	$0.420207\pi$
$223$	−10.6761	+	18.4916i	−0.714926	+	1.23829i	−0.962988	+	0.269545i	$0.913127\pi$
$224$		0			0
$225$	−3.98509	−	6.90239i	−0.265673	−	0.460159i
$226$	8.92976	+	15.4668i	0.593999	+	1.02884i
$227$	10.4490			0.693526			0.346763	−	0.937953i	$-0.387281\pi$
$227$	10.4490			0.693526			0.346763	+	0.937953i	$0.387281\pi$
$228$	2.26579			0.150056
$229$	7.22901	+	12.5210i	0.477706	+	0.827412i	0.999673	−	0.0255538i	$-0.00813493\pi$
$229$	7.22901	+	12.5210i	0.477706	+	0.827412i	−0.521967	+	0.852966i	$0.674802\pi$
$230$	−6.22778	−	10.7868i	−0.410648	−	0.711262i
$231$		0			0
$232$	−0.0588852	+	0.101992i	−0.00386600	+	0.00669611i
$233$	4.64413	+	8.04388i	0.304247	+	0.526972i	0.977093	−	0.212811i	$-0.0682617\pi$
$233$	4.64413	+	8.04388i	0.304247	+	0.526972i	−0.672846	+	0.739783i	$0.734928\pi$
$234$	−3.88068	−	18.9574i	−0.253688	−	1.23929i
$235$	8.60570	−	14.9055i	0.561374	−	0.972328i
$236$	8.71616			0.567374
$237$	0.165917	−	0.287376i	0.0107774	−	0.0186671i
$238$		0			0
$239$	19.6332			1.26997			0.634983	−	0.772526i	$-0.281007\pi$
$239$	19.6332			1.26997			0.634983	+	0.772526i	$0.281007\pi$
$240$	−1.45218	+	2.51525i	−0.0937380	+	0.162359i
$241$	−7.31105			−0.470946			−0.235473	−	0.971881i	$-0.575664\pi$
$241$	−7.31105			−0.470946			−0.235473	+	0.971881i	$0.575664\pi$
$242$	7.91174	−	13.7035i	0.508586	−	0.880897i
$243$	5.31937	−	9.21341i	0.341238	−	0.591041i
$244$	9.41648	−	16.3098i	0.602828	−	1.04413i
$245$		0			0
$246$	−4.21597			−0.268801
$247$	2.34429	+	11.4520i	0.149164	+	0.728676i
$248$	1.84337	−	3.19282i	0.117054	−	0.202744i
$249$	3.43157	+	5.94365i	0.217467	+	0.376664i
$250$	21.9796			1.39011
$251$	−5.93191	−	10.2744i	−0.374419	−	0.648512i	0.615821	−	0.787886i	$-0.288824\pi$
$251$	−5.93191	−	10.2744i	−0.374419	−	0.648512i	−0.990240	+	0.139374i	$0.955491\pi$
$252$		0			0
$253$	−9.74746	−	16.8831i	−0.612817	−	1.06143i
$254$	15.1353	−	26.2151i	0.949672	−	1.64488i
$255$	0.379551	−	0.657402i	0.0237684	−	0.0411681i
$256$	20.1871			1.26169
$257$	15.1722			0.946413			0.473206	−	0.880952i	$-0.343096\pi$
$257$	15.1722			0.946413			0.473206	+	0.880952i	$0.343096\pi$
$258$	−0.00928708	+	0.0160857i	−0.000578188	+	0.00100145i
$259$		0			0
$260$	8.21940	+	2.73919i	0.509745	+	0.169877i
$261$	0.235963	+	0.408699i	0.0146057	+	0.0252979i
$262$	−1.76974	−	3.06528i	−0.109335	−	0.189374i
$263$	−8.59820	−	14.8925i	−0.530187	−	0.918312i	−0.999380	−	0.0352156i	$-0.988788\pi$
$263$	−8.59820	−	14.8925i	−0.530187	−	0.918312i	0.469192	−	0.883096i	$-0.344545\pi$
$264$	−0.661533	+	1.14581i	−0.0407145	+	0.0705196i
$265$	−0.208869			−0.0128307
$266$		0			0
$267$	−1.40479	−	2.43317i	−0.0859719	−	0.148908i
$268$	−3.37279	−	5.84185i	−0.206026	−	0.356848i
$269$	−18.9220			−1.15370			−0.576849	−	0.816851i	$-0.695718\pi$
$269$	−18.9220			−1.15370			−0.576849	+	0.816851i	$0.695718\pi$
$270$	3.49774	+	6.05827i	0.212866	+	0.368695i
$271$	−32.1334			−1.95196			−0.975982	−	0.217853i	$-0.930095\pi$
$271$	−32.1334			−1.95196			−0.975982	+	0.217853i	$0.930095\pi$
$272$	−5.53444			−0.335575
$273$		0			0
$274$	24.3916			1.47355
$275$	12.4334			0.749764
$276$	−1.55047	−	2.68549i	−0.0933273	−	0.161648i
$277$	18.4054			1.10587			0.552936	−	0.833224i	$-0.313507\pi$
$277$	18.4054			1.10587			0.552936	+	0.833224i	$0.313507\pi$
$278$	0.322734	+	0.558992i	0.0193563	+	0.0335261i
$279$	−7.38671	−	12.7942i	−0.442231	−	0.765966i
$280$		0			0
$281$	−14.2252			−0.848603			−0.424302	−	0.905521i	$-0.639480\pi$
$281$	−14.2252			−0.848603			−0.424302	+	0.905521i	$0.639480\pi$
$282$	4.76942	−	8.26087i	0.284015	−	0.491928i
$283$	−5.71446	−	9.89773i	−0.339689	−	0.588359i	0.644685	−	0.764448i	$-0.276989\pi$
$283$	−5.71446	−	9.89773i	−0.339689	−	0.588359i	−0.984374	+	0.176089i	$0.943655\pi$
$284$	8.13109	+	14.0835i	0.482492	+	0.835700i
$285$	−1.02314	−	1.77213i	−0.0606055	−	0.104972i
$286$	28.6383	+	9.54396i	1.69342	+	0.564346i
$287$		0			0
$288$	10.3687	−	17.9591i	0.610981	−	1.05825i
$289$	−15.5535			−0.914911
$290$	−0.470368			−0.0276210
$291$	−0.747997	+	1.29557i	−0.0438483	+	0.0759476i
$292$	12.4307	−	21.5307i	0.727453	−	1.25999i
$293$	−6.60231	−	11.4355i	−0.385711	−	0.668071i	0.606156	−	0.795345i	$-0.292711\pi$
$293$	−6.60231	−	11.4355i	−0.385711	−	0.668071i	−0.991868	+	0.127274i	$0.959377\pi$
$294$		0			0
$295$	−3.93586	−	6.81712i	−0.229155	−	0.396908i
$296$	4.95547			0.288031
$297$	5.47452	+	9.48215i	0.317664	+	0.550210i
$298$	3.73791	−	6.47425i	0.216531	−	0.375043i
$299$	11.9692	−	10.6151i	0.692196	−	0.613889i
$300$	1.97771			0.114183
$301$		0			0
$302$	−2.01874	+	3.49656i	−0.116165	+	0.201204i
$303$	−0.552225	+	0.956482i	−0.0317245	+	0.0549484i
$304$	−7.45947	+	12.9202i	−0.427830	+	0.741023i
$305$	−17.0084			−0.973898
$306$	−3.22740	+	5.59003i	−0.184498	+	0.319561i
$307$	6.65903			0.380051			0.190026	−	0.981779i	$-0.439143\pi$
$307$	6.65903			0.380051			0.190026	+	0.981779i	$0.439143\pi$
$308$		0			0
$309$	3.61255	−	6.25713i	0.205511	−	0.355955i
$310$	14.7247			0.836304
$311$	−1.02298	+	1.77186i	−0.0580081	+	0.100473i	−0.893571	−	0.448922i	$-0.851808\pi$
$311$	−1.02298	+	1.77186i	−0.0580081	+	0.100473i	0.835563	+	0.549395i	$0.185142\pi$
$312$	−1.03006	−	0.343276i	−0.0583156	−	0.0194342i
$313$	4.70883	+	8.15594i	0.266159	+	0.461001i	0.967867	−	0.251464i	$-0.0809120\pi$
$313$	4.70883	+	8.15594i	0.266159	+	0.461001i	−0.701708	+	0.712465i	$0.747579\pi$
$314$	21.0686	−	36.4919i	1.18897	−	2.05936i
$315$		0			0
$316$	−0.631667	−	1.09408i	−0.0355341	−	0.0615468i
$317$	16.6856	+	28.9004i	0.937159	+	1.62321i	0.770738	+	0.637153i	$0.219888\pi$
$317$	16.6856	+	28.9004i	0.937159	+	1.62321i	0.166421	+	0.986055i	$0.446779\pi$
$318$	−0.115758			−0.00649141
$319$	−0.736200			−0.0412193
$320$	3.55567	+	6.15860i	0.198768	+	0.344276i
$321$	1.86003	+	3.22167i	0.103817	+	0.179816i
$322$		0			0
$323$	1.94965	−	3.37689i	0.108481	−	0.187895i
$324$	−6.02027	−	10.4274i	−0.334460	−	0.579301i
$325$	2.04624	+	9.99602i	0.113505	+	0.554479i
$326$	3.67024	−	6.35704i	0.203276	−	0.352084i
$327$	5.15873			0.285279
$328$	1.81472	−	3.14318i	0.100201	−	0.173553i
$329$		0			0
$330$	−5.28425			−0.290888
$331$	−9.53298	+	16.5116i	−0.523980	+	0.907560i	0.475631	+	0.879645i	$0.342220\pi$
$331$	−9.53298	+	16.5116i	−0.523980	+	0.907560i	−0.999610	+	0.0279144i	$0.991113\pi$
$332$	26.1289			1.43401
$333$	9.92870	−	17.1970i	0.544089	−	0.942390i
$334$	−2.03794	+	3.52982i	−0.111511	+	0.193143i
$335$	−3.04603	+	5.27588i	−0.166423	+	0.288252i
$336$		0			0
$337$	−31.2849			−1.70420			−0.852098	−	0.523382i	$-0.824670\pi$
$337$	−31.2849			−1.70420			−0.852098	+	0.523382i	$0.824670\pi$
$338$	−2.95983	+	24.5948i	−0.160994	+	1.33778i
$339$	2.00777	−	3.47757i	0.109047	−	0.188876i
$340$	−1.44500	−	2.50282i	−0.0783663	−	0.135734i
$341$	23.0464			1.24803
$342$	8.69996	+	15.0688i	0.470440	+	0.814826i
$343$		0			0
$344$	−0.00799504	−	0.0138478i	−0.000431064	−	0.000746624i
$345$	−1.40026	+	2.42532i	−0.0753874	+	0.130575i
$346$	15.8288	−	27.4163i	0.850961	−	1.47391i
$347$	11.6752			0.626757			0.313378	−	0.949628i	$-0.398539\pi$
$347$	11.6752			0.626757			0.313378	+	0.949628i	$0.398539\pi$
$348$	−0.117103			−0.00627738
$349$	11.9952	−	20.7763i	0.642089	−	1.11213i	−0.342877	−	0.939380i	$-0.611401\pi$
$349$	11.9952	−	20.7763i	0.642089	−	1.11213i	0.984966	−	0.172750i	$-0.0552652\pi$
$350$		0			0
$351$	−6.72233	+	5.96184i	−0.358811	+	0.318219i
$352$	16.1751	+	28.0161i	0.862135	+	1.49326i
$353$	6.39668	+	11.0794i	0.340461	+	0.589696i	0.984518	−	0.175282i	$-0.0560836\pi$
$353$	6.39668	+	11.0794i	0.340461	+	0.589696i	−0.644057	+	0.764977i	$0.722750\pi$
$354$	−2.18132	−	3.77816i	−0.115936	−	0.200807i
$355$	7.34334	−	12.7190i	0.389744	−	0.675057i
$356$	−10.6965			−0.566912
$357$		0			0
$358$	−0.514021	−	0.890310i	−0.0271668	−	0.0470544i
$359$	−6.16986	−	10.6865i	−0.325633	−	0.564012i	0.656008	−	0.754754i	$-0.272244\pi$
$359$	−6.16986	−	10.6865i	−0.325633	−	0.564012i	−0.981640	+	0.190742i	$0.938911\pi$
$360$	−2.91610			−0.153692
$361$	4.24442	+	7.35155i	0.223390	+	0.386924i
$362$	5.28152			0.277591
$363$	−3.55776			−0.186734
$364$		0			0
$365$	−22.4528			−1.17524
$366$	−9.42633			−0.492722
$367$	1.01538	+	1.75870i	0.0530026	+	0.0918032i	0.891309	−	0.453396i	$-0.149788\pi$
$367$	1.01538	+	1.75870i	0.0530026	+	0.0918032i	−0.838307	+	0.545199i	$0.816454\pi$
$368$	20.4179			1.06436
$369$	−7.27188	−	12.5953i	−0.378559	−	0.655684i
$370$	9.89593	+	17.1403i	0.514465	+	0.891079i
$371$		0			0
$372$	3.66586			0.190066
$373$	1.93700	−	3.35498i	0.100294	−	0.173714i	−0.811512	−	0.584336i	$-0.801355\pi$
$373$	1.93700	−	3.35498i	0.100294	−	0.173714i	0.911806	+	0.410622i	$0.134688\pi$
$374$	−5.03473	−	8.72040i	−0.260340	−	0.450921i
$375$	−2.47095	−	4.27981i	−0.127599	−	0.221009i
$376$	4.10588	+	7.11160i	0.211745	+	0.366753i
$377$	−0.121160	−	0.591877i	−0.00624007	−	0.0304832i
$378$		0			0
$379$	7.28396	−	12.6162i	0.374152	−	0.648050i	−0.616048	−	0.787709i	$-0.711267\pi$
$379$	7.28396	−	12.6162i	0.374152	−	0.648050i	0.990200	+	0.139659i	$0.0446006\pi$
$380$	−7.79045			−0.399642
$381$	−6.80606			−0.348685
$382$	−19.2850	+	33.4025i	−0.986705	+	1.70902i
$383$	−13.3909	+	23.1937i	−0.684243	+	1.18514i	0.289430	+	0.957199i	$0.406534\pi$
$383$	−13.3909	+	23.1937i	−0.684243	+	1.18514i	−0.973674	+	0.227945i	$0.926799\pi$
$384$	−1.18405	−	2.05084i	−0.0604234	−	0.104656i
$385$		0			0
$386$	−15.6038	−	27.0266i	−0.794212	−	1.37562i
$387$	−0.0640749			−0.00325711
$388$	2.84773	+	4.93241i	0.144571	+	0.250405i
$389$	−6.00738	+	10.4051i	−0.304586	+	0.527559i	−0.977169	−	0.212463i	$-0.931852\pi$
$389$	−6.00738	+	10.4051i	−0.304586	+	0.527559i	0.672583	+	0.740022i	$0.265185\pi$
$390$	−0.869656	−	4.24834i	−0.0440368	−	0.215123i
$391$	−5.33655			−0.269881
$392$		0			0
$393$	−0.397910	+	0.689200i	−0.0200719	+	0.0347655i
$394$	18.8017	−	32.5655i	0.947216	−	1.64063i
$395$	−0.570470	+	0.988084i	−0.0287035	+	0.0497159i
$396$	20.1845			1.01431
$397$	−0.828825	+	1.43557i	−0.0415975	+	0.0720491i	−0.886075	−	0.463543i	$-0.846578\pi$
$397$	−0.828825	+	1.43557i	−0.0415975	+	0.0720491i	0.844477	+	0.535592i	$0.179911\pi$
$398$	−26.9017			−1.34846
$399$		0			0
$400$	−6.51106	+	11.2775i	−0.325553	+	0.563874i
$401$	−20.4828			−1.02286			−0.511430	−	0.859325i	$-0.670884\pi$
$401$	−20.4828			−1.02286			−0.511430	+	0.859325i	$0.670884\pi$
$402$	−1.68816	+	2.92398i	−0.0841978	+	0.145835i
$403$	3.79287	+	18.5285i	0.188936	+	0.922968i
$404$	2.10240	+	3.64146i	0.104598	+	0.181169i
$405$	−5.43702	+	9.41720i	−0.270168	+	0.467944i
$406$		0			0
$407$	15.4887	+	26.8272i	0.767746	+	1.32978i
$408$	0.181089	+	0.313655i	0.00896522	+	0.0155282i
$409$	−14.8659			−0.735070			−0.367535	−	0.930010i	$-0.619798\pi$
$409$	−14.8659			−0.735070			−0.367535	+	0.930010i	$0.619798\pi$
$410$	14.4958			0.715895
$411$	−2.74211	−	4.74948i	−0.135258	−	0.234274i
$412$	−13.7535	−	23.8217i	−0.677586	−	1.17361i
$413$		0			0
$414$	11.9067	−	20.6230i	0.585182	−	1.01357i
$415$	−11.7988	−	20.4360i	−0.579178	−	1.00317i
$416$	−19.8619	+	17.6149i	−0.973808	+	0.863643i
$417$	0.0725639	−	0.125684i	0.00355347	−	0.00615479i
$418$	−27.1438			−1.32764
$419$	−11.8087	+	20.4533i	−0.576895	+	0.999211i	0.418938	+	0.908015i	$0.362402\pi$
$419$	−11.8087	+	20.4533i	−0.576895	+	0.999211i	−0.995833	+	0.0911962i	$0.970931\pi$
$420$		0			0
$421$	26.0822			1.27117			0.635585	−	0.772031i	$-0.280759\pi$
$421$	26.0822			1.27117			0.635585	+	0.772031i	$0.280759\pi$
$422$	−4.40788	+	7.63467i	−0.214572	+	0.371650i
$423$	32.9059			1.59994
$424$	0.0498269	−	0.0863028i	0.00241981	−	0.00419123i
$425$	1.70177	−	2.94755i	0.0825479	−	0.142977i
$426$	4.06980	−	7.04910i	0.197182	−	0.341530i
$427$		0			0
$428$	14.1628			0.684584
$429$	−1.36115	−	6.64932i	−0.0657169	−	0.321032i
$430$	0.0319317	−	0.0553074i	0.00153988	−	0.00266716i
$431$	6.65859	+	11.5330i	0.320733	+	0.555526i	0.980640	−	0.195822i	$-0.0627374\pi$
$431$	6.65859	+	11.5330i	0.320733	+	0.555526i	−0.659906	+	0.751348i	$0.729404\pi$
$432$	−11.4675			−0.551728
$433$	10.2110	+	17.6860i	0.490711	+	0.849937i	0.999943	−	0.0106929i	$-0.00340371\pi$
$433$	10.2110	+	17.6860i	0.490711	+	0.849937i	−0.509232	+	0.860629i	$0.670070\pi$
$434$		0			0
$435$	0.0528790	+	0.0915890i	0.00253535	+	0.00439136i
$436$	9.82001	−	17.0087i	0.470293	−	0.814571i
$437$	−7.19275	+	12.4582i	−0.344076	+	0.595957i
$438$	−12.4437			−0.594585
$439$	9.77074			0.466332			0.233166	−	0.972437i	$-0.425091\pi$
$439$	9.77074			0.466332			0.233166	+	0.972437i	$0.425091\pi$
$440$	2.27455	−	3.93963i	0.108435	−	0.187814i
$441$		0			0
$442$	6.18229	−	5.48290i	0.294061	−	0.260795i
$443$	−10.5819	−	18.3285i	−0.502763	−	0.870811i	−0.999995	−	0.00319331i	$-0.998984\pi$
$443$	−10.5819	−	18.3285i	−0.502763	−	0.870811i	0.497232	−	0.867618i	$-0.334350\pi$
$444$	2.46370	+	4.26725i	0.116922	+	0.202514i
$445$	4.83010	+	8.36597i	0.228968	+	0.396585i
$446$	20.3440	−	35.2368i	0.963317	−	1.66851i
$447$	−1.68087			−0.0795023
$448$		0			0
$449$	9.07320	+	15.7152i	0.428191	+	0.741648i	0.996712	−	0.0810200i	$-0.0258178\pi$
$449$	9.07320	+	15.7152i	0.428191	+	0.741648i	−0.568522	+	0.822668i	$0.692484\pi$
$450$	7.59384	+	13.1529i	0.357977	+	0.620034i
$451$	22.6882			1.06834
$452$	−7.64387	−	13.2396i	−0.359538	−	0.622737i
$453$	0.907789			0.0426517
$454$	−19.9112			−0.934480
$455$		0			0
$456$	0.976304			0.0457196
$457$	−18.0198			−0.842932			−0.421466	−	0.906844i	$-0.638484\pi$
$457$	−18.0198			−0.842932			−0.421466	+	0.906844i	$0.638484\pi$
$458$	−13.7753	−	23.8595i	−0.643678	−	1.11488i
$459$	2.99720			0.139897
$460$	5.33098	+	9.23352i	0.248558	+	0.430515i
$461$	−14.8873	−	25.7855i	−0.693370	−	1.20095i	−0.970727	−	0.240185i	$-0.922792\pi$
$461$	−14.8873	−	25.7855i	−0.693370	−	1.20095i	0.277357	−	0.960767i	$-0.410542\pi$
$462$		0			0
$463$	17.7067			0.822900			0.411450	−	0.911432i	$-0.365023\pi$
$463$	17.7067			0.822900			0.411450	+	0.911432i	$0.365023\pi$
$464$	0.385529	−	0.667755i	0.0178977	−	0.0309997i
$465$	−1.65535	−	2.86715i	−0.0767651	−	0.132961i
$466$	−8.84968	−	15.3281i	−0.409953	−	0.710060i
$467$	−2.91461	−	5.04825i	−0.134872	−	0.233605i	0.790677	−	0.612234i	$-0.209729\pi$
$467$	−2.91461	−	5.04825i	−0.134872	−	0.233605i	−0.925549	+	0.378629i	$0.876396\pi$
$468$	3.32186	+	16.2276i	0.153553	+	0.750120i
$469$		0			0
$470$	−16.3987	+	28.4033i	−0.756414	+	1.31015i
$471$	−9.47418			−0.436547
$472$	3.75570			0.172870
$473$	0.0499782	−	0.0865648i	0.00229800	−	0.00398025i
$474$	−0.316164	+	0.547612i	−0.0145219	+	0.0251527i
$475$	−4.58738	−	7.94557i	−0.210483	−	0.364568i
$476$		0			0
$477$	−0.199665	−	0.345830i	−0.00914203	−	0.0158345i
$478$	−37.4122			−1.71120
$479$	7.24565	+	12.5498i	0.331062	+	0.573417i	0.982720	−	0.185096i	$-0.0592596\pi$
$479$	7.24565	+	12.5498i	0.331062	+	0.573417i	−0.651658	+	0.758513i	$0.725926\pi$
$480$	2.32361	−	4.02461i	0.106058	−	0.183698i
$481$	−19.0190	+	16.8674i	−0.867193	+	0.769088i
$482$	13.9316			0.634569
$483$		0			0
$484$	−6.77245	+	11.7302i	−0.307839	+	0.533192i
$485$	2.57183	−	4.45455i	0.116781	−	0.202271i
$486$	−10.1364	+	17.5567i	−0.459795	+	0.796389i
$487$	−17.9601			−0.813851			−0.406926	−	0.913461i	$-0.633399\pi$
$487$	−17.9601			−0.813851			−0.406926	+	0.913461i	$0.633399\pi$
$488$	4.05746	−	7.02772i	0.183672	−	0.318130i
$489$	−1.65044			−0.0746354
$490$		0			0
$491$	18.1505	−	31.4375i	0.819119	−	1.41876i	−0.0872134	−	0.996190i	$-0.527796\pi$
$491$	18.1505	−	31.4375i	0.819119	−	1.41876i	0.906332	−	0.422566i	$-0.138870\pi$
$492$	3.60887			0.162701
$493$	−0.100764	+	0.174528i	−0.00453818	+	0.00786036i
$494$	−4.46719	−	21.8226i	−0.200988	−	0.981844i
$495$	−9.11449	−	15.7868i	−0.409666	−	0.709562i
$496$	−12.0688	+	20.9038i	−0.541905	+	0.938607i
$497$		0			0
$498$	−6.53906	−	11.3260i	−0.293022	−	0.507530i
$499$	−11.8538	−	20.5314i	−0.530649	−	0.919112i	−0.999360	−	0.0357602i	$-0.988615\pi$
$499$	−11.8538	−	20.5314i	−0.530649	−	0.919112i	0.468711	−	0.883352i	$-0.344719\pi$
$500$	−18.8145			−0.841410
$501$	0.916426			0.0409429
$502$	11.3036	+	19.5784i	0.504505	+	0.873828i
$503$	13.8876	+	24.0540i	0.619217	+	1.07252i	0.989629	+	0.143648i	$0.0458834\pi$
$503$	13.8876	+	24.0540i	0.619217	+	1.07252i	−0.370411	+	0.928868i	$0.620783\pi$
$504$		0			0
$505$	1.89871	−	3.28867i	0.0844916	−	0.146344i
$506$	18.5744	+	32.1717i	0.825731	+	1.43021i
$507$	5.12180	−	2.18863i	0.227467	−	0.0972003i
$508$	−12.9558	+	22.4401i	−0.574820	+	0.995618i
$509$	−8.70416			−0.385805			−0.192902	−	0.981218i	$-0.561790\pi$
$509$	−8.70416			−0.385805			−0.192902	+	0.981218i	$0.561790\pi$
$510$	−0.723257	+	1.25272i	−0.0320264	+	0.0554713i
$511$		0			0
$512$	−27.4134			−1.21151
$513$	4.03971	−	6.99698i	0.178357	−	0.308924i
$514$	−28.9114			−1.27523
$515$	−12.4210	+	21.5139i	−0.547336	+	0.948014i
$516$	0.00794974	−	0.0137693i	0.000349968	−	0.000606162i
$517$	−25.6665	+	44.4557i	−1.12881	+	1.95516i
$518$		0			0
$519$	−7.11792			−0.312442
$520$	3.54165	+	1.18028i	0.155312	+	0.0517589i
$521$	−4.28573	+	7.42310i	−0.187761	+	0.325212i	−0.944504	−	0.328501i	$-0.893456\pi$
$521$	−4.28573	+	7.42310i	−0.187761	+	0.325212i	0.756742	+	0.653713i	$0.226790\pi$
$522$	−0.449641	−	0.778801i	−0.0196803	−	0.0340872i
$523$	−29.9493			−1.30959			−0.654796	−	0.755806i	$-0.727245\pi$
$523$	−29.9493			−1.30959			−0.654796	+	0.755806i	$0.727245\pi$
$524$	1.51490	+	2.62388i	0.0661786	+	0.114625i
$525$		0			0
$526$	16.3844	+	28.3786i	0.714393	+	1.23736i
$527$	3.15437	−	5.46353i	0.137407	−	0.237995i
$528$	4.33114	−	7.50175i	0.188489	−	0.326472i
$529$	−3.31212			−0.144005
$530$	0.398012			0.0172885
$531$	7.52486	−	13.0334i	0.326551	−	0.565603i
$532$		0			0
$533$	3.73391	+	18.2404i	0.161734	+	0.790081i
$534$	2.67692	+	4.63656i	0.115842	+	0.200643i
$535$	−6.39534	−	11.0770i	−0.276494	−	0.478902i
$536$	−1.45330	−	2.51719i	−0.0627730	−	0.108726i
$537$	−0.115573	+	0.200178i	−0.00498734	+	0.00863832i
$538$	36.0571			1.55453
$539$		0			0
$540$	−2.99407	−	5.18588i	−0.128844	−	0.223165i
$541$	−5.24095	−	9.07760i	−0.225326	−	0.390276i	0.731091	−	0.682280i	$-0.239011\pi$
$541$	−5.24095	−	9.07760i	−0.225326	−	0.390276i	−0.956417	+	0.292003i	$0.905678\pi$
$542$	61.2321			2.63014
$543$	−0.593751	−	1.02841i	−0.0254803	−	0.0441331i
$544$	8.85557			0.379679
$545$	−17.7373			−0.759781
$546$		0			0
$547$	15.2216			0.650829			0.325415	−	0.945571i	$-0.394496\pi$
$547$	15.2216			0.650829			0.325415	+	0.945571i	$0.394496\pi$
$548$	−20.8792			−0.891915
$549$	−16.2589	−	28.1613i	−0.693914	−	1.20189i
$550$	−23.6927			−1.01026
$551$	0.271625	+	0.470468i	0.0115716	+	0.0200426i
$552$	−0.668081	−	1.15715i	−0.0284354	−	0.0492516i
$553$		0			0
$554$	−35.0726			−1.49009
$555$	2.22501	−	3.85383i	0.0944464	−	0.163586i
$556$	−0.276261	−	0.478497i	−0.0117161	−	0.0202928i
$557$	−5.92986	−	10.2708i	−0.251256	−	0.435189i	0.712616	−	0.701555i	$-0.247510\pi$
$557$	−5.92986	−	10.2708i	−0.251256	−	0.435189i	−0.963872	+	0.266366i	$0.914177\pi$
$558$	14.0758	+	24.3800i	0.595877	+	1.03209i
$559$	0.0778200	+	0.0259342i	0.00329144	+	0.00109690i
$560$		0			0
$561$	−1.13201	+	1.96070i	−0.0477936	+	0.0827809i
$562$	27.1069			1.14344
$563$	−7.69349			−0.324242			−0.162121	−	0.986771i	$-0.551834\pi$
$563$	−7.69349			−0.324242			−0.162121	+	0.986771i	$0.551834\pi$
$564$	−4.08262	+	7.07131i	−0.171909	+	0.297756i
$565$	−6.90332	+	11.9569i	−0.290425	+	0.503031i
$566$	10.8892	+	18.8607i	0.457709	+	0.792775i
$567$		0			0
$568$	3.50360	+	6.06841i	0.147008	+	0.254625i
$569$	37.4196			1.56871			0.784355	−	0.620312i	$-0.212994\pi$
$569$	37.4196			1.56871			0.784355	+	0.620312i	$0.212994\pi$
$570$	1.94965	+	3.37689i	0.0816619	+	0.141443i
$571$	−7.08285	+	12.2679i	−0.296408	+	0.513394i	−0.975311	−	0.220834i	$-0.929122\pi$
$571$	−7.08285	+	12.2679i	−0.296408	+	0.513394i	0.678903	+	0.734228i	$0.262456\pi$
$572$	−24.5144	−	8.16963i	−1.02500	−	0.341589i
$573$	8.67209			0.362282
$574$		0			0
$575$	−6.27825	+	10.8742i	−0.261821	+	0.453488i
$576$	−6.79797	+	11.7744i	−0.283249	+	0.490601i
$577$	−7.48776	+	12.9692i	−0.311720	+	0.539914i	−0.978735	−	0.205130i	$-0.934238\pi$
$577$	−7.48776	+	12.9692i	−0.311720	+	0.539914i	0.667015	+	0.745044i	$0.267572\pi$
$578$	29.6381			1.23278
$579$	−3.50837	+	6.07667i	−0.145803	+	0.252538i
$580$	0.402635			0.0167185
$581$		0			0
$582$	1.42535	−	2.46878i	0.0590828	−	0.102334i
$583$	0.622952			0.0258000
$584$	5.35627	−	9.27732i	0.221644	−	0.383898i
$585$	11.1919	−	9.92582i	0.462730	−	0.410382i
$586$	12.5811	+	21.7911i	0.519720	+	0.900182i
$587$	−6.58821	+	11.4111i	−0.271925	+	0.470987i	−0.969355	−	0.245666i	$-0.920993\pi$
$587$	−6.58821	+	11.4111i	−0.271925	+	0.470987i	0.697430	+	0.716653i	$0.254327\pi$
$588$		0			0
$589$	−8.50309	−	14.7278i	−0.350364	−	0.606848i
$590$	7.50003	+	12.9904i	0.308771	+	0.534807i
$591$	−8.45478			−0.347783
$592$	−32.4441			−1.33344
$593$	−22.0663	−	38.2200i	−0.906156	−	1.56951i	−0.819357	−	0.573283i	$-0.805670\pi$
$593$	−22.0663	−	38.2200i	−0.906156	−	1.56951i	−0.0867989	−	0.996226i	$-0.527664\pi$
$594$	−10.4320	−	18.0688i	−0.428032	−	0.741372i
$595$		0			0
$596$	−3.19965	+	5.54195i	−0.131063	+	0.227007i
$597$	3.02429	+	5.23823i	0.123776	+	0.214387i
$598$	−22.8080	+	20.2278i	−0.932689	+	0.827175i
$599$	3.01349	−	5.21952i	0.123128	−	0.213264i	−0.797872	−	0.602827i	$-0.794041\pi$
$599$	3.01349	−	5.21952i	0.123128	−	0.213264i	0.921000	+	0.389564i	$0.127374\pi$
$600$	0.852175			0.0347899
$601$	1.86260	−	3.22612i	0.0759770	−	0.131596i	−0.825534	−	0.564353i	$-0.809126\pi$
$601$	1.86260	−	3.22612i	0.0759770	−	0.131596i	0.901511	+	0.432757i	$0.142459\pi$
$602$		0			0
$603$	−11.6472			−0.474312
$604$	1.72804	−	2.99305i	0.0703129	−	0.121786i
$605$	12.2326			0.497328
$606$	1.05230	−	1.82263i	0.0427467	−	0.0740394i
$607$	−3.00825	+	5.21045i	−0.122101	+	0.211486i	−0.920596	−	0.390516i	$-0.872297\pi$
$607$	−3.00825	+	5.21045i	−0.122101	+	0.211486i	0.798495	+	0.602002i	$0.205630\pi$
$608$	11.9358	−	20.6733i	0.484059	−	0.838415i
$609$		0			0
$610$	32.4105			1.31226
$611$	−39.9648	−	13.3186i	−1.61680	−	0.538813i
$612$	2.76266	−	4.78506i	0.111674	−	0.193425i
$613$	−4.90413	−	8.49420i	−0.198076	−	0.343077i	0.749829	−	0.661632i	$-0.230136\pi$
$613$	−4.90413	−	8.49420i	−0.198076	−	0.343077i	−0.947904	+	0.318555i	$0.896803\pi$
$614$	−12.6892			−0.512094
$615$	−1.62962	−	2.82258i	−0.0657126	−	0.113818i
$616$		0			0
$617$	−16.8838	−	29.2436i	−0.679716	−	1.17730i	−0.975066	−	0.221914i	$-0.928770\pi$
$617$	−16.8838	−	29.2436i	−0.679716	−	1.17730i	0.295350	−	0.955389i	$-0.404564\pi$
$618$	−6.88394	+	11.9233i	−0.276913	+	0.479627i
$619$	2.04671	−	3.54501i	0.0822644	−	0.142486i	−0.821958	−	0.569548i	$-0.807118\pi$
$619$	2.04671	−	3.54501i	0.0822644	−	0.142486i	0.904222	+	0.427062i	$0.140451\pi$
$620$	−12.6043			−0.506201
$621$	−11.0574			−0.443719
$622$	1.94936	−	3.37639i	0.0781621	−	0.135381i
$623$		0			0
$624$	6.74393	+	2.24747i	0.269973	+	0.0899709i
$625$	1.42115	+	2.46150i	0.0568459	+	0.0984599i
$626$	−8.97297	−	15.5416i	−0.358632	−	0.621169i
$627$	3.05151	+	5.28537i	0.121866	+	0.211077i
$628$	−18.0347	+	31.2371i	−0.719665	+	1.24650i
$629$	8.47978			0.338111
$630$		0			0
$631$	13.3868	+	23.1866i	0.532921	+	0.923046i	0.999261	+	0.0384402i	$0.0122389\pi$
$631$	13.3868	+	23.1866i	0.532921	+	0.923046i	−0.466340	+	0.884605i	$0.654428\pi$
$632$	−0.272179	−	0.471427i	−0.0108267	−	0.0187524i
$633$	1.98214			0.0787831
$634$	−31.7955	−	55.0714i	−1.26276	−	2.18717i
$635$	23.4012			0.928650
$636$	0.0990892			0.00392914
$637$		0			0
$638$	1.40287			0.0555403
$639$	28.0790			1.11079
$640$	4.07112	+	7.05139i	0.160925	+	0.278731i
$641$	−18.5722			−0.733558			−0.366779	−	0.930308i	$-0.619539\pi$
$641$	−18.5722			−0.733558			−0.366779	+	0.930308i	$0.619539\pi$
$642$	−3.54440	−	6.13908i	−0.139886	−	0.242290i
$643$	−1.96695	−	3.40686i	−0.0775690	−	0.134353i	0.824632	−	0.565670i	$-0.191382\pi$
$643$	−1.96695	−	3.40686i	−0.0775690	−	0.134353i	−0.902201	+	0.431317i	$0.858049\pi$
$644$		0			0
$645$	−0.0143591			−0.000565389
$646$	−3.71518	+	6.43487i	−0.146172	+	0.253177i
$647$	−0.0985378	−	0.170672i	−0.00387392	−	0.00670983i	0.864082	−	0.503351i	$-0.167900\pi$
$647$	−0.0985378	−	0.170672i	−0.00387392	−	0.00670983i	−0.867956	+	0.496641i	$0.834566\pi$
$648$	−2.59407	−	4.49306i	−0.101905	−	0.176504i
$649$	11.7387	+	20.3321i	0.460785	+	0.798104i
$650$	−3.89922	−	19.0480i	−0.152940	−	0.747125i
$651$		0			0
$652$	−3.14172	+	5.44163i	−0.123039	+	0.213110i
$653$	−14.4673			−0.566148			−0.283074	−	0.959098i	$-0.591354\pi$
$653$	−14.4673			−0.566148			−0.283074	+	0.959098i	$0.591354\pi$
$654$	−9.83028			−0.384394
$655$	1.36813	−	2.36967i	0.0534573	−	0.0925908i
$656$	−11.8812	+	20.5788i	−0.463883	+	0.803468i
$657$	−21.4635	−	37.1758i	−0.837369	−	1.45037i
$658$		0			0
$659$	11.7066	+	20.2764i	0.456024	+	0.789857i	0.998746	−	0.0500552i	$-0.0159397\pi$
$659$	11.7066	+	20.2764i	0.456024	+	0.789857i	−0.542722	+	0.839912i	$0.682606\pi$
$660$	4.52332			0.176070
$661$	−2.02409	−	3.50582i	−0.0787278	−	0.136361i	0.823973	−	0.566628i	$-0.191752\pi$
$661$	−2.02409	−	3.50582i	−0.0787278	−	0.136361i	−0.902701	+	0.430268i	$0.858419\pi$
$662$	18.1657	−	31.4638i	0.706028	−	1.22288i
$663$	−1.76263	−	0.587412i	−0.0684550	−	0.0228132i
$664$	11.2587			0.436921
$665$		0			0
$666$	−18.9197	+	32.7699i	−0.733125	+	1.26981i
$667$	0.371744	−	0.643879i	0.0143940	−	0.0249311i
$668$	1.74448	−	3.02153i	0.0674959	−	0.116906i
$669$	−9.14832			−0.353695
$670$	5.80440	−	10.0535i	0.224243	−	0.388401i
$671$	50.7276			1.95832
$672$		0			0
$673$	−3.64704	+	6.31685i	−0.140583	+	0.243497i	−0.927716	−	0.373286i	$-0.878231\pi$
$673$	−3.64704	+	6.31685i	−0.140583	+	0.243497i	0.787133	+	0.616783i	$0.211564\pi$
$674$	59.6152			2.29629
$675$	3.52609	−	6.10737i	0.135719	−	0.235073i
$676$	2.53362	−	21.0532i	0.0974468	−	0.809737i
$677$	−7.87553	−	13.6408i	−0.302681	−	0.524259i	0.674061	−	0.738676i	$-0.264548\pi$
$677$	−7.87553	−	13.6408i	−0.302681	−	0.524259i	−0.976742	+	0.214416i	$0.931215\pi$
$678$	−3.82593	+	6.62671i	−0.146934	+	0.254497i
$679$		0			0
$680$	−0.622636	−	1.07844i	−0.0238770	−	0.0413562i
$681$	2.23843	+	3.87707i	0.0857767	+	0.148570i
$682$	−43.9163			−1.68164
$683$	41.4854			1.58739			0.793697	−	0.608314i	$-0.208154\pi$
$683$	41.4854			1.58739			0.793697	+	0.608314i	$0.208154\pi$
$684$	−7.44717	−	12.8989i	−0.284750	−	0.493201i
$685$	9.42819	+	16.3301i	0.360233	+	0.623941i
$686$		0			0
$687$	−3.09725	+	5.36460i	−0.118168	+	0.204672i
$688$	0.0523445	+	0.0906634i	0.00199562	+	0.00345651i
$689$	0.102522	+	0.500830i	0.00390579	+	0.0190801i
$690$	2.66828	−	4.62159i	0.101580	−	0.175941i
$691$	46.8216			1.78118			0.890589	−	0.454809i	$-0.150292\pi$
$691$	46.8216			1.78118			0.890589	+	0.454809i	$0.150292\pi$
$692$	−13.5494	+	23.4683i	−0.515073	+	0.892132i
$693$		0			0
$694$	−22.2478			−0.844514
$695$	−0.249496	+	0.432140i	−0.00946392	+	0.0163920i
$696$	−0.0504584			−0.00191262
$697$	3.10534	−	5.37860i	0.117623	−	0.203729i
$698$	−22.8576	+	39.5905i	−0.865172	+	1.49852i
$699$	−1.98977	+	3.44638i	−0.0752600	+	0.130354i
$700$		0			0
$701$	29.8626			1.12790			0.563948	−	0.825810i	$-0.309282\pi$
$701$	29.8626			1.12790			0.563948	+	0.825810i	$0.309282\pi$
$702$	12.8098	−	11.3606i	0.483475	−	0.428780i
$703$	11.4293	−	19.7961i	0.431063	−	0.746623i
$704$	−10.6048	−	18.3680i	−0.399683	−	0.692271i
$705$	7.37418			0.277728
$706$	−12.1893	−	21.1124i	−0.458749	−	0.794576i
$707$		0			0
$708$	1.86721	+	3.23410i	0.0701740	+	0.121545i
$709$	−13.4666	+	23.3249i	−0.505750	+	0.875984i	0.494228	+	0.869332i	$0.335451\pi$
$709$	−13.4666	+	23.3249i	−0.505750	+	0.875984i	−0.999978	+	0.00665185i	$0.997883\pi$
$710$	−13.9932	+	24.2369i	−0.525155	+	0.909595i
$711$	−2.18133			−0.0818063
$712$	−4.60900			−0.172729
$713$	−11.6373	+	20.1563i	−0.435819	+	0.754861i
$714$		0			0
$715$	4.68004	+	22.8623i	0.175023	+	0.855003i
$716$	0.440002	+	0.762105i	0.0164436	+	0.0284812i
$717$	4.20590	+	7.28483i	0.157072	+	0.272057i
$718$	11.7570	+	20.3638i	0.438769	+	0.759969i
$719$	−7.24938	+	12.5563i	−0.270356	+	0.468271i	−0.968953	−	0.247245i	$-0.920475\pi$
$719$	−7.24938	+	12.5563i	−0.270356	+	0.468271i	0.698597	+	0.715516i	$0.253808\pi$
$720$	19.0921			0.711519
$721$		0			0
$722$	−8.08799	−	14.0088i	−0.301004	−	0.521354i
$723$	−1.56620	−	2.71274i	−0.0582476	−	0.100888i
$724$	−4.52098			−0.168021
$725$	0.237090	+	0.410652i	0.00880530	+	0.0152512i
$726$	6.77953			0.251612
$727$	6.26424			0.232328			0.116164	−	0.993230i	$-0.462940\pi$
$727$	6.26424			0.232328			0.116164	+	0.993230i	$0.462940\pi$
$728$		0			0
$729$	−17.5866			−0.651357
$730$	42.7852			1.58355
$731$	−0.0136811	−	0.0236963i	−0.000506013	−	0.000876440i
$732$	8.06893			0.298236
$733$	−5.99189	−	10.3783i	−0.221316	−	0.383330i	0.733892	−	0.679266i	$-0.237702\pi$
$733$	−5.99189	−	10.3783i	−0.221316	−	0.383330i	−0.955208	+	0.295936i	$0.904368\pi$
$734$	−1.93487	−	3.35130i	−0.0714175	−	0.123699i
$735$		0			0
$736$	−32.6704			−1.20425
$737$	9.08480	−	15.7353i	0.334643	−	0.579619i
$738$	13.8570	+	24.0010i	0.510084	+	0.883491i
$739$	−6.76269	−	11.7133i	−0.248770	−	0.430882i	0.714415	−	0.699722i	$-0.246693\pi$
$739$	−6.76269	−	11.7133i	−0.248770	−	0.430882i	−0.963185	+	0.268840i	$0.913360\pi$
$740$	−8.47091	−	14.6721i	−0.311397	−	0.539355i
$741$	−3.74704	+	3.32314i	−0.137651	+	0.122079i
$742$		0			0
$743$	19.2299	−	33.3072i	0.705477	−	1.22192i	−0.261043	−	0.965327i	$-0.584066\pi$
$743$	19.2299	−	33.3072i	0.705477	−	1.22192i	0.966519	−	0.256594i	$-0.0826003\pi$
$744$	1.57958			0.0579101
$745$	5.77932			0.211738
$746$	−3.69107	+	6.39312i	−0.135140	+	0.234069i
$747$	22.5577	−	39.0710i	0.825342	−	1.42953i
$748$	4.30973	+	7.46466i	0.157579	+	0.272935i
$749$		0			0
$750$	4.70855	+	8.15544i	0.171932	+	0.297795i
$751$	11.7115			0.427357			0.213679	−	0.976904i	$-0.431455\pi$
$751$	11.7115			0.427357			0.213679	+	0.976904i	$0.431455\pi$
$752$	−26.8817	−	46.5605i	−0.980276	−	1.69789i
$753$	2.54151	−	4.40203i	0.0926178	−	0.160419i
$754$	0.230878	+	1.12786i	0.00840809	+	0.0410742i
$755$	−3.12125			−0.113594
$756$		0			0
$757$	−4.65791	+	8.06773i	−0.169295	+	0.293227i	−0.938172	−	0.346169i	$-0.887482\pi$
$757$	−4.65791	+	8.06773i	−0.169295	+	0.293227i	0.768877	+	0.639396i	$0.220816\pi$
$758$	−13.8800	+	24.0409i	−0.504145	+	0.873205i
$759$	4.17627	−	7.23352i	0.151589	−	0.262560i
$760$	−3.35682			−0.121765
$761$	−21.9691	+	38.0515i	−0.796378	+	1.37937i	0.125582	+	0.992083i	$0.459920\pi$
$761$	−21.9691	+	38.0515i	−0.796378	+	1.37937i	−0.921960	+	0.387284i	$0.873413\pi$
$762$	12.9693			0.469830
$763$		0			0
$764$	16.5079	−	28.5926i	0.597236	−	1.03444i
$765$	−4.99002			−0.180414
$766$	25.5172	−	44.1971i	0.921973	−	1.59690i
$767$	−14.4143	+	12.7837i	−0.520471	+	0.461591i
$768$	4.32455	+	7.49035i	0.156049	+	0.270285i
$769$	12.6771	−	21.9573i	0.457147	−	0.791802i	−0.541662	−	0.840597i	$-0.682205\pi$
$769$	12.6771	−	21.9573i	0.457147	−	0.791802i	0.998809	+	0.0487946i	$0.0155380\pi$
$770$		0			0
$771$	3.25024	+	5.62957i	0.117054	+	0.202744i
$772$	13.3568	+	23.1347i	0.480723	+	0.832637i
$773$	23.1084			0.831152			0.415576	−	0.909559i	$-0.363580\pi$
$773$	23.1084			0.831152			0.415576	+	0.909559i	$0.363580\pi$
$774$	0.122099			0.00438874
$775$	−7.42200	−	12.8553i	−0.266606	−	0.461775i
$776$	1.22705	+	2.12532i	0.0440487	+	0.0762946i
$777$		0			0
$778$	11.4474	−	19.8275i	0.410410	−	0.710851i
$779$	−8.37091	−	14.4988i	−0.299919	−	0.519475i
$780$	0.744426	+	3.63658i	0.0266547	+	0.130210i
$781$	−21.9015	+	37.9346i	−0.783699	+	1.35741i
$782$	10.1691			0.363647
$783$	−0.208785	+	0.361626i	−0.00746135	+	0.0129234i
$784$		0			0
$785$	32.5750			1.16265
$786$	0.758241	−	1.31331i	0.0270456	−	0.0468443i
$787$	24.6692			0.879364			0.439682	−	0.898154i	$-0.355091\pi$
$787$	24.6692			0.879364			0.439682	+	0.898154i	$0.355091\pi$
$788$	−16.0943	+	27.8761i	−0.573334	+	0.993044i
$789$	3.68388	−	6.38066i	0.131149	−	0.227158i
$790$	1.08707	−	1.88285i	0.0386761	−	0.0669889i
$791$		0			0
$792$	8.69727			0.309044
$793$	8.34850	+	40.7831i	0.296464	+	1.44825i
$794$	1.57938	−	2.73556i	0.0560500	−	0.0970814i
$795$	−0.0447447	−	0.0775000i	−0.00158693	−	0.00274864i
$796$	23.0278			0.816199
$797$	5.65686	+	9.79797i	0.200376	+	0.347062i	0.948650	−	0.316329i	$-0.102450\pi$
$797$	5.65686	+	9.79797i	0.200376	+	0.347062i	−0.748273	+	0.663390i	$0.769117\pi$
$798$		0			0
$799$	7.02597	+	12.1693i	0.248561	+	0.430520i
$800$	10.4182	−	18.0449i	0.368340	−	0.637984i
$801$	−9.23451	+	15.9946i	−0.326285	+	0.565143i
$802$	39.0311			1.37824
$803$	66.9657			2.36317
$804$	1.44507	−	2.50293i	0.0509635	−	0.0882714i
$805$		0			0
$806$	−7.22754	−	35.3071i	−0.254579	−	1.24364i
$807$	−4.05355	−	7.02096i	−0.142692	−	0.247149i
$808$	0.905900	+	1.56906i	0.0318694	+	0.0551995i
$809$	−8.18540	−	14.1775i	−0.287783	−	0.498455i	0.685497	−	0.728075i	$-0.259585\pi$
$809$	−8.18540	−	14.1775i	−0.287783	−	0.498455i	−0.973280	+	0.229620i	$0.926252\pi$
$810$	10.3606	−	17.9450i	0.364033	−	0.630524i
$811$	29.0412			1.01978			0.509888	−	0.860241i	$-0.329687\pi$
$811$	29.0412			1.01978			0.509888	+	0.860241i	$0.329687\pi$
$812$		0			0
$813$	−6.88373	−	11.9230i	−0.241423	−	0.418157i
$814$	−29.5146	−	51.1209i	−1.03449	−	1.79179i
$815$	5.67470			0.198776
$816$	−1.18561	−	2.05354i	−0.0415046	−	0.0718881i
$817$	−0.0737588			−0.00258050
$818$	28.3278			0.990458
$819$		0			0
$820$	−12.4084			−0.433319
$821$	−13.7518			−0.479940			−0.239970	−	0.970780i	$-0.577138\pi$
$821$	−13.7518			−0.479940			−0.239970	+	0.970780i	$0.577138\pi$
$822$	5.22526	+	9.05041i	0.182252	+	0.315669i
$823$	−29.1153			−1.01490			−0.507448	−	0.861682i	$-0.669411\pi$
$823$	−29.1153			−1.01490			−0.507448	+	0.861682i	$0.669411\pi$
$824$	−5.92623	−	10.2645i	−0.206450	−	0.357582i
$825$	2.66354	+	4.61338i	0.0927325	+	0.160617i
$826$		0			0
$827$	−22.9118			−0.796722			−0.398361	−	0.917229i	$-0.630421\pi$
$827$	−22.9118			−0.796722			−0.398361	+	0.917229i	$0.630421\pi$
$828$	−10.1921	+	17.6533i	−0.354201	+	0.613494i
$829$	−11.6914	−	20.2502i	−0.406061	−	0.703317i	0.588384	−	0.808582i	$-0.299764\pi$
$829$	−11.6914	−	20.2502i	−0.406061	−	0.703317i	−0.994444	+	0.105264i	$0.966431\pi$
$830$	22.4832	+	38.9421i	0.780404	+	1.35170i
$831$	3.94287	+	6.82925i	0.136777	+	0.236904i
$832$	13.0219	−	11.5488i	0.451454	−	0.400382i
$833$		0			0
$834$	−0.138275	+	0.239499i	−0.00478806	+	0.00829317i
$835$	−3.15094			−0.109043
$836$	23.2350			0.803601
$837$	6.53591	−	11.3205i	0.225914	−	0.391295i
$838$	22.5023	−	38.9751i	0.777328	−	1.34637i
$839$	0.367168	+	0.635954i	0.0126761	+	0.0219556i	0.872294	−	0.488982i	$-0.162632\pi$
$839$	0.367168	+	0.635954i	0.0126761	+	0.0219556i	−0.859618	+	0.510938i	$0.829298\pi$
$840$		0			0
$841$	14.4860	+	25.0904i	0.499516	+	0.865187i
$842$	−49.7013			−1.71282
$843$	−3.04737	−	5.27820i	−0.104957	−	0.181791i
$844$	3.77314	−	6.53528i	0.129877	−	0.224954i
$845$	−17.6103	+	7.52515i	−0.605811	+	0.258873i
$846$	−62.7042			−2.15582
$847$		0			0
$848$	−0.326223	+	0.565035i	−0.0112026	+	0.0194034i
$849$	2.44834	−	4.24066i	0.0840270	−	0.145539i
$850$	−3.24282	+	5.61674i	−0.111228	+	0.192652i
$851$	−31.2840			−1.07240
$852$	−3.48375	+	6.03403i	−0.119351	+	0.206722i
$853$	−54.3567			−1.86114			−0.930569	−	0.366118i	$-0.880687\pi$
$853$	−54.3567			−1.86114			−0.930569	+	0.366118i	$0.880687\pi$
$854$		0			0
$855$	−6.72567	+	11.6492i	−0.230013	+	0.398395i
$856$	6.10259			0.208582
$857$	−10.5106	+	18.2048i	−0.359034	+	0.621864i	−0.987800	−	0.155730i	$-0.950227\pi$
$857$	−10.5106	+	18.2048i	−0.359034	+	0.621864i	0.628766	+	0.777595i	$0.283560\pi$
$858$	2.59375	+	12.6707i	0.0885493	+	0.432570i
$859$	−25.6814	−	44.4816i	−0.876240	−	1.51769i	−0.855436	−	0.517908i	$-0.826711\pi$
$859$	−25.6814	−	44.4816i	−0.876240	−	1.51769i	−0.0208035	−	0.999784i	$-0.506622\pi$
$860$	−0.0273336	+	0.0473431i	−0.000932066	+	0.00161439i
$861$		0			0
$862$	−12.6884	−	21.9769i	−0.432167	−	0.748535i
$863$	−3.55660	−	6.16021i	−0.121068	−	0.209696i	0.799121	−	0.601170i	$-0.205299\pi$
$863$	−3.55660	−	6.16021i	−0.121068	−	0.209696i	−0.920189	+	0.391474i	$0.871965\pi$
$864$	18.3489			0.624241
$865$	24.4735			0.832124
$866$	−19.4577	−	33.7018i	−0.661201	−	1.14523i
$867$	−3.33193	−	5.77107i	−0.113158	−	0.195996i
$868$		0			0
$869$	1.70143	−	2.94696i	0.0577171	−	0.0999689i
$870$	−0.100764	−	0.174528i	−0.00341622	−	0.00591707i
$871$	14.1458	+	4.71419i	0.479311	+	0.159734i
$872$	4.23133	−	7.32888i	0.143291	−	0.248187i
$873$	9.83403			0.332831
$874$	13.7062	−	23.7399i	0.463620	−	0.803013i
$875$		0			0
$876$	10.6518			0.359892
$877$	−0.256238	+	0.443818i	−0.00865255	+	0.0149867i	−0.870319	−	0.492488i	$-0.836088\pi$
$877$	−0.256238	+	0.443818i	−0.00865255	+	0.0149867i	0.861667	+	0.507475i	$0.169421\pi$
$878$	−18.6187			−0.628352
$879$	2.82874	−	4.89953i	0.0954112	−	0.165257i
$880$	−14.8917	+	25.7933i	−0.502000	+	0.869490i
$881$	−18.5464	+	32.1232i	−0.624843	+	1.08226i	0.363729	+	0.931505i	$0.381503\pi$
$881$	−18.5464	+	32.1232i	−0.624843	+	1.08226i	−0.988571	+	0.150754i	$0.951830\pi$
$882$		0			0
$883$	−15.5667			−0.523860			−0.261930	−	0.965087i	$-0.584359\pi$
$883$	−15.5667			−0.523860			−0.261930	+	0.965087i	$0.584359\pi$
$884$	−5.29204	+	4.69336i	−0.177990	+	0.157855i
$885$	1.68631	−	2.92078i	0.0566847	−	0.0981809i
$886$	20.1645	+	34.9260i	0.677440	+	1.17336i
$887$	−27.5799			−0.926043			−0.463022	−	0.886347i	$-0.653235\pi$
$887$	−27.5799			−0.926043			−0.463022	+	0.886347i	$0.653235\pi$
$888$	1.06158	+	1.83871i	0.0356243	+	0.0617030i
$889$		0			0
$890$	−9.20404	−	15.9419i	−0.308520	−	0.534372i
$891$	16.2159	−	28.0868i	0.543254	−	0.940944i
$892$	−17.4145	+	30.1627i	−0.583079	+	1.00992i
$893$	37.8792			1.26758
$894$	3.20300			0.107124
$895$	0.397374	−	0.688272i	0.0132827	−	0.0230064i
$896$		0			0
$897$	6.50279	+	2.16711i	0.217122	+	0.0723577i
$898$	−17.2895	−	29.9463i	−0.576959	−	0.999323i
$899$	0.439466	+	0.761178i	0.0146570	+	0.0253867i
$900$	−6.50032	−	11.2589i	−0.216677	−	0.375296i
$901$	0.0852637	−	0.147681i	0.00284054	−	0.00491997i
$902$	−43.2337			−1.43952
$903$		0			0
$904$	−3.29366	−	5.70479i	−0.109546	−	0.189738i
$905$	2.04149	+	3.53597i	0.0678615	+	0.117539i
$906$	−1.72985			−0.0574703
$907$	22.5236	+	39.0119i	0.747882	+	1.29537i	0.948836	+	0.315769i	$0.102263\pi$
$907$	22.5236	+	39.0119i	0.747882	+	1.29537i	−0.200954	+	0.979601i	$0.564404\pi$
$908$	17.0440			0.565625
$909$	7.26019			0.240805
$910$		0			0
$911$	35.4678			1.17510			0.587550	−	0.809188i	$-0.300093\pi$
$911$	35.4678			1.17510			0.587550	+	0.809188i	$0.300093\pi$
$912$	−6.39198			−0.211660
$913$	35.1898	+	60.9505i	1.16461	+	2.01717i
$914$	34.3379			1.13580
$915$	−3.64360	−	6.31090i	−0.120454	−	0.208632i
$916$	11.7917	+	20.4238i	0.389608	+	0.674820i
$917$		0			0
$918$	−5.71135			−0.188503
$919$	−8.68622	+	15.0450i	−0.286532	+	0.496288i	−0.972980	−	0.230891i	$-0.925836\pi$
$919$	−8.68622	+	15.0450i	−0.286532	+	0.496288i	0.686447	+	0.727179i	$0.259169\pi$
$920$	2.29706	+	3.97862i	0.0757318	+	0.131171i
$921$	1.42652	+	2.47081i	0.0470056	+	0.0814160i
$922$	28.3686	+	49.1359i	0.934271	+	1.61820i
$923$	−34.1024	−	11.3649i	−1.12250	−	0.374081i
$924$		0			0
$925$	9.97613	−	17.2792i	0.328013	−	0.568136i
$926$	−33.7412			−1.10880
$927$	−47.4948			−1.55993
$928$	−0.616877	+	1.06846i	−0.0202500	+	0.0350740i
$929$	5.38001	−	9.31845i	0.176512	−	0.305729i	−0.764171	−	0.645013i	$-0.776852\pi$
$929$	5.38001	−	9.31845i	0.176512	−	0.305729i	0.940684	+	0.339285i	$0.110185\pi$
$930$	3.15437	+	5.46353i	0.103436	+	0.179156i
$931$		0			0
$932$	7.57532	+	13.1208i	0.248138	+	0.429788i
$933$	−0.876590			−0.0286983
$934$	5.55396	+	9.61975i	0.181731	+	0.314768i
$935$	3.89219	−	6.74148i	0.127288	−	0.220470i
$936$	1.43136	+	6.99228i	0.0467853	+	0.228550i
$937$	10.9816			0.358755			0.179377	−	0.983780i	$-0.442592\pi$
$937$	10.9816			0.358755			0.179377	+	0.983780i	$0.442592\pi$
$938$		0			0
$939$	−2.01749	+	3.49439i	−0.0658383	+	0.114035i
$940$	14.0373	−	24.3132i	0.457845	−	0.793011i
$941$	4.08897	−	7.08231i	0.133297	−	0.230877i	−0.791649	−	0.610976i	$-0.790777\pi$
$941$	4.08897	−	7.08231i	0.133297	−	0.230877i	0.924946	+	0.380100i	$0.124110\pi$
$942$	18.0536			0.588219
$943$	−11.4564	+	19.8430i	−0.373071	+	0.646177i
$944$	−24.5890			−0.800305
$945$		0			0
$946$	−0.0952365	+	0.164954i	−0.00309640	+	0.00536313i
$947$	−4.59378			−0.149278			−0.0746389	−	0.997211i	$-0.523780\pi$
$947$	−4.59378			−0.149278			−0.0746389	+	0.997211i	$0.523780\pi$
$948$	0.270636	−	0.468756i	0.00878986	−	0.0152245i
$949$	11.0209	+	53.8379i	0.357753	+	1.74765i
$950$	8.74153	+	15.1408i	0.283613	+	0.491231i
$951$	−7.14892	+	12.3823i	−0.231820	+	0.401524i
$952$		0			0
$953$	−10.5714	−	18.3102i	−0.342442	−	0.593126i	0.642444	−	0.766333i	$-0.277921\pi$
$953$	−10.5714	−	18.3102i	−0.342442	−	0.593126i	−0.984886	+	0.173206i	$0.944587\pi$
$954$	0.380474	+	0.659000i	0.0123183	+	0.0213359i
$955$	−29.8172			−0.964863
$956$	32.0249			1.03576
$957$	−0.157712	−	0.273165i	−0.00509809	−	0.00883016i
$958$	−13.8070	−	23.9145i	−0.446085	−	0.772641i
$959$		0			0
$960$	−1.52342	+	2.63864i	−0.0491681	+	0.0851616i
$961$	1.74271	+	3.01846i	0.0562164	+	0.0973697i
$962$	36.2419	−	32.1419i	1.16849	−	1.03630i
$963$	12.2270	−	21.1779i	0.394011	−	0.682447i
$964$	−11.9255			−0.384094
$965$	12.0628	−	20.8934i	0.388316	−	0.672582i
$966$		0			0
$967$	−32.0750			−1.03146			−0.515731	−	0.856750i	$-0.672480\pi$
$967$	−32.0750			−1.03146			−0.515731	+	0.856750i	$0.672480\pi$
$968$	−2.91817	+	5.05442i	−0.0937936	+	0.162455i
$969$	1.67065			0.0536689
$970$	−4.90079	+	8.48841i	−0.157355	+	0.272546i
$971$	−26.0417	+	45.1056i	−0.835719	+	1.44751i	0.0577245	+	0.998333i	$0.481616\pi$
$971$	−26.0417	+	45.1056i	−0.835719	+	1.44751i	−0.893444	+	0.449175i	$0.851718\pi$
$972$	8.67673	−	15.0285i	0.278306	−	0.482041i
$973$		0			0
$974$	34.2241			1.09661
$975$	−3.27064	+	2.90063i	−0.104744	+	0.0928946i
$976$	−26.5647	+	46.0114i	−0.850315	+	1.47279i
$977$	−9.62898	−	16.6779i	−0.308058	−	0.533573i	0.669879	−	0.742470i	$-0.266346\pi$
$977$	−9.62898	−	16.6779i	−0.308058	−	0.533573i	−0.977938	+	0.208897i	$0.933013\pi$
$978$	3.14501			0.100566
$979$	−14.4058	−	24.9515i	−0.460410	−	0.797454i
$980$		0			0
$981$	−16.9557	−	29.3681i	−0.541353	−	0.937650i
$982$	−34.5868	+	59.9061i	−1.10371	+	1.91168i
$983$	−8.03657	+	13.9197i	−0.256327	+	0.443971i	−0.965255	−	0.261310i	$-0.915846\pi$
$983$	−8.03657	+	13.9197i	−0.256327	+	0.443971i	0.708928	+	0.705280i	$0.249179\pi$
$984$	1.55502			0.0495723
$985$	29.0700			0.926248
$986$	0.192012	−	0.332574i	0.00611490	−	0.0105913i
$987$		0			0
$988$	3.82391	+	18.6801i	0.121655	+	0.594294i
$989$	0.0504729	+	0.0874216i	0.00160494	+	0.00277985i
$990$	17.3682	+	30.0826i	0.551998	+	0.956088i
$991$	−10.7132	−	18.5559i	−0.340317	−	0.589447i	0.644174	−	0.764879i	$-0.277201\pi$
$991$	−10.7132	−	18.5559i	−0.340317	−	0.589447i	−0.984492	+	0.175432i	$0.943868\pi$
$992$	19.3111	−	33.4478i	0.613127	−	1.06197i
$993$	−8.16876			−0.259228
$994$		0			0
$995$	−10.3984	−	18.0106i	−0.329652	−	0.570974i
$996$	5.59743	+	9.69504i	0.177362	+	0.307199i
$997$	16.9537			0.536931			0.268465	−	0.963289i	$-0.413484\pi$
$997$	16.9537			0.536931			0.268465	+	0.963289i	$0.413484\pi$
$998$	22.5881	+	39.1238i	0.715015	+	1.23844i
$999$	17.5702			0.555897

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.h.l.165.2		12
7.2	even	3		637.2.g.l.373.5		12
7.3	odd	6		637.2.f.k.295.5		12
7.4	even	3		637.2.f.j.295.5		12
7.5	odd	6		91.2.g.b.9.5	✓	12
7.6	odd	2		91.2.h.b.74.2	yes	12
13.3	even	3		637.2.g.l.263.5		12
21.5	even	6		819.2.n.d.100.2		12
21.20	even	2		819.2.s.d.802.5		12
91.3	odd	6		637.2.f.k.393.5		12
91.4	even	6		8281.2.a.cf.1.5		6
91.16	even	3	inner	637.2.h.l.471.2		12
91.17	odd	6		8281.2.a.ce.1.5		6
91.48	odd	6		1183.2.e.h.508.5		12
91.55	odd	6		91.2.g.b.81.5	yes	12
91.61	odd	6		1183.2.e.h.170.5		12
91.68	odd	6		91.2.h.b.16.2	yes	12
91.69	odd	6		1183.2.e.g.508.2		12
91.74	even	3		8281.2.a.ca.1.2		6
91.81	even	3		637.2.f.j.393.5		12
91.82	odd	6		1183.2.e.g.170.2		12
91.87	odd	6		8281.2.a.bz.1.2		6
273.68	even	6		819.2.s.d.289.5		12
273.146	even	6		819.2.n.d.172.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.g.b.9.5	✓	12	7.5	odd	6
91.2.g.b.81.5	yes	12	91.55	odd	6
91.2.h.b.16.2	yes	12	91.68	odd	6
91.2.h.b.74.2	yes	12	7.6	odd	2
637.2.f.j.295.5		12	7.4	even	3
637.2.f.j.393.5		12	91.81	even	3
637.2.f.k.295.5		12	7.3	odd	6
637.2.f.k.393.5		12	91.3	odd	6
637.2.g.l.263.5		12	13.3	even	3
637.2.g.l.373.5		12	7.2	even	3
637.2.h.l.165.2		12	1.1	even	1	trivial
637.2.h.l.471.2		12	91.16	even	3	inner
819.2.n.d.100.2		12	21.5	even	6
819.2.n.d.172.2		12	273.146	even	6
819.2.s.d.289.5		12	273.68	even	6
819.2.s.d.802.5		12	21.20	even	2
1183.2.e.g.170.2		12	91.82	odd	6
1183.2.e.g.508.2		12	91.69	odd	6
1183.2.e.h.170.5		12	91.61	odd	6
1183.2.e.h.508.5		12	91.48	odd	6
8281.2.a.bz.1.2		6	91.87	odd	6
8281.2.a.ca.1.2		6	91.74	even	3
8281.2.a.ce.1.5		6	91.17	odd	6
8281.2.a.cf.1.5		6	91.4	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.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.90556 q^{2} +(0.214224 + 0.371047i) q^{3} +1.63116 q^{4} +(-0.736565 - 1.27577i) q^{5} +(-0.408216 - 0.707051i) q^{6} +0.702849 q^{8} +(1.40822 - 2.43910i) q^{9} +O(q^{10})\)	\(q-1.90556 q^{2} +(0.214224 + 0.371047i) q^{3} +1.63116 q^{4} +(-0.736565 - 1.27577i) q^{5} +(-0.408216 - 0.707051i) q^{6} +0.702849 q^{8} +(1.40822 - 2.43910i) q^{9} +(1.40357 + 2.43105i) q^{10} +(2.19681 + 3.80498i) q^{11} +(0.349433 + 0.605236i) q^{12} +(-2.69752 + 2.39236i) q^{13} +(0.315580 - 0.546600i) q^{15} -4.60164 q^{16} +1.20271 q^{17} +(-2.68344 + 4.64786i) q^{18} +(1.62105 - 2.80773i) q^{19} +(-1.20145 - 2.08098i) q^{20} +(-4.18615 - 7.25062i) q^{22} -4.43710 q^{23} +(0.150567 + 0.260790i) q^{24} +(1.41494 - 2.45075i) q^{25} +(5.14029 - 4.55878i) q^{26} +2.49204 q^{27} +(-0.0837807 + 0.145112i) q^{29} +(-0.601356 + 1.04158i) q^{30} +(2.62272 - 4.54268i) q^{31} +7.36300 q^{32} +(-0.941217 + 1.63024i) q^{33} -2.29184 q^{34} +(2.29702 - 3.97856i) q^{36} +7.05055 q^{37} +(-3.08900 + 5.35031i) q^{38} +(-1.46555 - 0.488407i) q^{39} +(-0.517694 - 0.896672i) q^{40} +(2.58195 - 4.47206i) q^{41} +(-0.0113752 - 0.0197024i) q^{43} +(3.58334 + 6.20653i) q^{44} -4.14897 q^{45} +8.45516 q^{46} +(5.84178 + 10.1183i) q^{47} +(-0.985780 - 1.70742i) q^{48} +(-2.69626 + 4.67006i) q^{50} +(0.257649 + 0.446262i) q^{51} +(-4.40009 + 3.90231i) q^{52} +(0.0708929 - 0.122790i) q^{53} -4.74873 q^{54} +(3.23618 - 5.60523i) q^{55} +1.38907 q^{57} +(0.159649 - 0.276520i) q^{58} +5.34354 q^{59} +(0.514760 - 0.891591i) q^{60} +(5.77287 - 9.99891i) q^{61} +(-4.99774 + 8.65635i) q^{62} -4.82736 q^{64} +(5.03899 + 1.67929i) q^{65} +(1.79355 - 3.10651i) q^{66} +(-2.06773 - 3.58141i) q^{67} +1.96181 q^{68} +(-0.950533 - 1.64637i) q^{69} +(4.98486 + 8.63403i) q^{71} +(0.989763 - 1.71432i) q^{72} +(7.62080 - 13.1996i) q^{73} -13.4352 q^{74} +1.21246 q^{75} +(2.64418 - 4.57986i) q^{76} +(2.79269 + 0.930689i) q^{78} +(-0.387251 - 0.670738i) q^{79} +(3.38941 + 5.87062i) q^{80} +(-3.69080 - 6.39265i) q^{81} +(-4.92006 + 8.52179i) q^{82} +16.0186 q^{83} +(-0.885875 - 1.53438i) q^{85} +(0.0216761 + 0.0375441i) q^{86} -0.0717913 q^{87} +(1.54402 + 2.67433i) q^{88} -6.55760 q^{89} +7.90611 q^{90} -7.23762 q^{92} +2.24739 q^{93} +(-11.1319 - 19.2809i) q^{94} -4.77602 q^{95} +(1.57733 + 2.73202i) q^{96} +(1.74583 + 3.02387i) q^{97} +12.3743 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} - q^{3} + 8 q^{4} - q^{5} + 9 q^{6} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 12 * q - 4 * q^2 - q^3 + 8 * q^4 - q^5 + 9 * q^6 - 6 * q^8 + 3 * q^9	\( 12 q - 4 q^{2} - q^{3} + 8 q^{4} - q^{5} + 9 q^{6} - 6 q^{8} + 3 q^{9} - 4 q^{10} + 4 q^{11} - 5 q^{12} + 2 q^{13} - 2 q^{15} - 16 q^{16} + 10 q^{17} + 3 q^{18} + q^{19} + q^{20} - 5 q^{22} + 2 q^{23} + 11 q^{24} + 7 q^{25} + 16 q^{26} + 8 q^{27} + 3 q^{29} - 5 q^{30} - 16 q^{31} - 16 q^{32} - 16 q^{33} - 32 q^{34} - 21 q^{36} + 26 q^{37} + 17 q^{38} - 20 q^{39} + 5 q^{40} + 8 q^{41} - 11 q^{43} + 21 q^{44} - 14 q^{45} - 32 q^{46} + q^{47} - 21 q^{48} + 6 q^{50} - 20 q^{51} - 41 q^{52} - 2 q^{53} - 36 q^{54} - 9 q^{55} + 42 q^{57} - 8 q^{58} + 26 q^{59} + 20 q^{60} + 5 q^{61} - 5 q^{62} - 30 q^{64} - 5 q^{65} - 18 q^{66} - 11 q^{67} + 58 q^{68} - 23 q^{69} + 6 q^{71} + 25 q^{72} + 30 q^{73} + 6 q^{74} - 6 q^{75} + 9 q^{76} + 16 q^{78} + 7 q^{79} + 7 q^{80} - 6 q^{81} - q^{82} + 54 q^{83} - q^{85} - 7 q^{86} + 32 q^{87} + 8 q^{89} + 16 q^{90} + 54 q^{92} + 14 q^{93} - 45 q^{94} + 12 q^{95} - 19 q^{96} + 35 q^{97} - 20 q^{99}+O(q^{100}) \) 12 * q - 4 * q^2 - q^3 + 8 * q^4 - q^5 + 9 * q^6 - 6 * q^8 + 3 * q^9 - 4 * q^10 + 4 * q^11 - 5 * q^12 + 2 * q^13 - 2 * q^15 - 16 * q^16 + 10 * q^17 + 3 * q^18 + q^19 + q^20 - 5 * q^22 + 2 * q^23 + 11 * q^24 + 7 * q^25 + 16 * q^26 + 8 * q^27 + 3 * q^29 - 5 * q^30 - 16 * q^31 - 16 * q^32 - 16 * q^33 - 32 * q^34 - 21 * q^36 + 26 * q^37 + 17 * q^38 - 20 * q^39 + 5 * q^40 + 8 * q^41 - 11 * q^43 + 21 * q^44 - 14 * q^45 - 32 * q^46 + q^47 - 21 * q^48 + 6 * q^50 - 20 * q^51 - 41 * q^52 - 2 * q^53 - 36 * q^54 - 9 * q^55 + 42 * q^57 - 8 * q^58 + 26 * q^59 + 20 * q^60 + 5 * q^61 - 5 * q^62 - 30 * q^64 - 5 * q^65 - 18 * q^66 - 11 * q^67 + 58 * q^68 - 23 * q^69 + 6 * q^71 + 25 * q^72 + 30 * q^73 + 6 * q^74 - 6 * q^75 + 9 * q^76 + 16 * q^78 + 7 * q^79 + 7 * q^80 - 6 * q^81 - q^82 + 54 * q^83 - q^85 - 7 * q^86 + 32 * q^87 + 8 * q^89 + 16 * q^90 + 54 * q^92 + 14 * q^93 - 45 * q^94 + 12 * q^95 - 19 * q^96 + 35 * q^97 - 20 * q^99

Introduction

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