LMFDB - Embedded newform 637.2.h.i.471.1

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:	$8$
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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			471.1
Root			$1.37054 - 2.37385i$ of defining polynomial
Character	$\chi$	$=$	637.471
Dual form			637.2.h.i.165.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.74108 q^{2} +(0.682410 - 1.18197i) q^{3} +5.51353 q^{4} +(0.370541 - 0.641796i) q^{5} +(-1.87054 + 3.23987i) q^{6} -9.63087 q^{8} +(0.568634 + 0.984903i) q^{9} +O(q^{10})$	\(q-2.74108 q^{2} +(0.682410 - 1.18197i) q^{3} +5.51353 q^{4} +(0.370541 - 0.641796i) q^{5} +(-1.87054 + 3.23987i) q^{6} -9.63087 q^{8} +(0.568634 + 0.984903i) q^{9} +(-1.01568 + 1.75921i) q^{10} +(0.682410 - 1.18197i) q^{11} +(3.76249 - 6.51682i) q^{12} +(-0.301907 + 3.59289i) q^{13} +(-0.505722 - 0.875935i) q^{15} +15.3720 q^{16} +4.14871 q^{17} +(-1.55867 - 2.69970i) q^{18} +(3.63303 + 6.29259i) q^{19} +(2.04299 - 3.53856i) q^{20} +(-1.87054 + 3.23987i) q^{22} -2.33345 q^{23} +(-6.57220 + 11.3834i) q^{24} +(2.22540 + 3.85450i) q^{25} +(0.827552 - 9.84840i) q^{26} +5.64662 q^{27} +(0.203815 + 0.353017i) q^{29} +(1.38622 + 2.40101i) q^{30} +(-1.38622 - 2.40101i) q^{31} -22.8740 q^{32} +(-0.931366 - 1.61317i) q^{33} -11.3720 q^{34} +(3.13518 + 5.43029i) q^{36} -6.10590 q^{37} +(-9.95843 - 17.2485i) q^{38} +(4.04066 + 2.80867i) q^{39} +(-3.56863 + 6.18106i) q^{40} +(0.627306 + 1.08653i) q^{41} +(0.870541 - 1.50782i) q^{43} +(3.76249 - 6.51682i) q^{44} +0.842809 q^{45} +6.39619 q^{46} +(-2.92921 + 5.07355i) q^{47} +(10.4900 - 18.1692i) q^{48} +(-6.10000 - 10.5655i) q^{50} +(2.83112 - 4.90364i) q^{51} +(-1.66457 + 19.8095i) q^{52} +(-2.28389 - 3.95582i) q^{53} -15.4779 q^{54} +(-0.505722 - 0.875935i) q^{55} +9.91685 q^{57} +(-0.558672 - 0.967649i) q^{58} +10.9843 q^{59} +(-2.78831 - 4.82950i) q^{60} +(3.26249 + 5.65079i) q^{61} +(3.79975 + 6.58137i) q^{62} +31.9557 q^{64} +(2.19403 + 1.52508i) q^{65} +(2.55295 + 4.42184i) q^{66} +(6.87983 - 11.9162i) q^{67} +22.8740 q^{68} +(-1.59237 + 2.75807i) q^{69} +(2.40763 - 4.17014i) q^{71} +(-5.47644 - 9.48548i) q^{72} +(3.03494 + 5.25666i) q^{73} +16.7368 q^{74} +6.07453 q^{75} +(20.0308 + 34.6944i) q^{76} +(-11.0758 - 7.69879i) q^{78} +(4.56291 - 7.90320i) q^{79} +(5.69594 - 9.86566i) q^{80} +(2.14741 - 3.71942i) q^{81} +(-1.71950 - 2.97826i) q^{82} -11.7368 q^{83} +(1.53727 - 2.66263i) q^{85} +(-2.38622 + 4.13306i) q^{86} +0.556340 q^{87} +(-6.57220 + 11.3834i) q^{88} +1.76101 q^{89} -2.31021 q^{90} -12.8656 q^{92} -3.78389 q^{93} +(8.02921 - 13.9070i) q^{94} +5.38474 q^{95} +(-15.6095 + 27.0364i) q^{96} +(4.76691 - 8.25652i) q^{97} +1.55217 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + q^{3} + 10 q^{4} - 7 q^{5} - 5 q^{6} - 12 q^{8} - 7 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 + q^3 + 10 * q^4 - 7 * q^5 - 5 * q^6 - 12 * q^8 - 7 * q^9	$ 8 q - 2 q^{2} + q^{3} + 10 q^{4} - 7 q^{5} - 5 q^{6} - 12 q^{8} - 7 q^{9} - 11 q^{10} + q^{11} + 12 q^{12} - 4 q^{13} - 3 q^{15} + 38 q^{16} + 8 q^{17} + 3 q^{18} + q^{19} - 2 q^{20} - 5 q^{22} - 4 q^{23} - 3 q^{24} - 5 q^{25} + 15 q^{26} + 52 q^{27} - q^{29} + 4 q^{30} - 4 q^{31} - 66 q^{32} - 19 q^{33} - 6 q^{34} + 34 q^{36} - 20 q^{37} - 23 q^{38} - q^{39} - 17 q^{40} - 22 q^{41} - 3 q^{43} + 12 q^{44} + 22 q^{45} + 48 q^{46} + 2 q^{47} + 11 q^{48} - 43 q^{50} - 7 q^{51} + 31 q^{52} - 2 q^{53} - 10 q^{54} - 3 q^{55} - 34 q^{57} + 11 q^{58} + 16 q^{59} + 11 q^{60} + 8 q^{61} - 5 q^{62} + 28 q^{64} - 11 q^{65} + 6 q^{66} + 6 q^{67} + 66 q^{68} - 18 q^{69} + 14 q^{71} - 5 q^{72} - 8 q^{73} + 40 q^{74} + 14 q^{75} + 32 q^{76} - q^{78} + 26 q^{79} + 7 q^{80} - 24 q^{81} - 14 q^{82} - 5 q^{85} - 12 q^{86} - 26 q^{87} - 3 q^{88} + 2 q^{89} - 52 q^{90} + 24 q^{92} - 14 q^{93} + 33 q^{94} + 42 q^{95} - 58 q^{96} + 3 q^{97} + 46 q^{99}+O(q^{100}) $ 8 * q - 2 * q^2 + q^3 + 10 * q^4 - 7 * q^5 - 5 * q^6 - 12 * q^8 - 7 * q^9 - 11 * q^10 + q^11 + 12 * q^12 - 4 * q^13 - 3 * q^15 + 38 * q^16 + 8 * q^17 + 3 * q^18 + q^19 - 2 * q^20 - 5 * q^22 - 4 * q^23 - 3 * q^24 - 5 * q^25 + 15 * q^26 + 52 * q^27 - q^29 + 4 * q^30 - 4 * q^31 - 66 * q^32 - 19 * q^33 - 6 * q^34 + 34 * q^36 - 20 * q^37 - 23 * q^38 - q^39 - 17 * q^40 - 22 * q^41 - 3 * q^43 + 12 * q^44 + 22 * q^45 + 48 * q^46 + 2 * q^47 + 11 * q^48 - 43 * q^50 - 7 * q^51 + 31 * q^52 - 2 * q^53 - 10 * q^54 - 3 * q^55 - 34 * q^57 + 11 * q^58 + 16 * q^59 + 11 * q^60 + 8 * q^61 - 5 * q^62 + 28 * q^64 - 11 * q^65 + 6 * q^66 + 6 * q^67 + 66 * q^68 - 18 * q^69 + 14 * q^71 - 5 * q^72 - 8 * q^73 + 40 * q^74 + 14 * q^75 + 32 * q^76 - q^78 + 26 * q^79 + 7 * q^80 - 24 * q^81 - 14 * q^82 - 5 * q^85 - 12 * q^86 - 26 * q^87 - 3 * q^88 + 2 * q^89 - 52 * q^90 + 24 * q^92 - 14 * q^93 + 33 * q^94 + 42 * 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 $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.74108			−1.93824			−0.969119	−	0.246594i	$-0.920689\pi$
$2$	−2.74108			−1.93824			−0.969119	+	0.246594i	$0.920689\pi$
$3$	0.682410	−	1.18197i	0.393989	−	0.682410i	−0.598982	−	0.800762i	$-0.704428\pi$
$3$	0.682410	−	1.18197i	0.393989	−	0.682410i	0.992972	+	0.118353i	$0.0377613\pi$
$4$	5.51353			2.75677
$5$	0.370541	−	0.641796i	0.165711	−	0.287020i	−0.771197	−	0.636597i	$-0.780341\pi$
$5$	0.370541	−	0.641796i	0.165711	−	0.287020i	0.936908	+	0.349577i	$0.113675\pi$
$6$	−1.87054	+	3.23987i	−0.763645	+	1.32267i
$7$		0			0
$7$		0			0
$8$	−9.63087			−3.40503
$9$	0.568634	+	0.984903i	0.189545	+	0.328301i
$10$	−1.01568	+	1.75921i	−0.321187	+	0.556313i
$11$	0.682410	−	1.18197i	0.205754	−	0.356377i	−0.744619	−	0.667490i	$-0.767369\pi$
$11$	0.682410	−	1.18197i	0.205754	−	0.356377i	0.950373	+	0.311113i	$0.100702\pi$
$12$	3.76249	−	6.51682i	1.08614	−	1.88124i
$13$	−0.301907	+	3.59289i	−0.0837339	+	0.996488i
$13$	−0.301907	+	3.59289i	−0.0837339	+	0.996488i
$14$		0			0
$15$	−0.505722	−	0.875935i	−0.130577	−	0.226166i
$16$	15.3720			3.84299
$17$	4.14871			1.00621			0.503105	−	0.864225i	$-0.332191\pi$
$17$	4.14871			1.00621			0.503105	+	0.864225i	$0.332191\pi$
$18$	−1.55867	−	2.69970i	−0.367383	−	0.636325i
$19$	3.63303	+	6.29259i	0.833474	+	1.44362i	0.895267	+	0.445530i	$0.146985\pi$
$19$	3.63303	+	6.29259i	0.833474	+	1.44362i	−0.0617933	+	0.998089i	$0.519682\pi$
$20$	2.04299	−	3.53856i	0.456826	−	0.791246i
$21$		0			0
$22$	−1.87054	+	3.23987i	−0.398801	+	0.690743i
$23$	−2.33345			−0.486559			−0.243279	−	0.969956i	$-0.578223\pi$
$23$	−2.33345			−0.486559			−0.243279	+	0.969956i	$0.578223\pi$
$24$	−6.57220	+	11.3834i	−1.34155	+	2.32362i
$25$	2.22540	+	3.85450i	0.445080	+	0.770901i
$26$	0.827552	−	9.84840i	0.162296	−	1.93143i
$27$	5.64662			1.08669
$28$		0			0
$29$	0.203815	+	0.353017i	0.0378474	+	0.0655536i	0.884329	−	0.466865i	$-0.154617\pi$
$29$	0.203815	+	0.353017i	0.0378474	+	0.0655536i	−0.846481	+	0.532419i	$0.821283\pi$
$30$	1.38622	+	2.40101i	0.253089	+	0.438363i
$31$	−1.38622	−	2.40101i	−0.248973	−	0.431234i	0.714268	−	0.699872i	$-0.246760\pi$
$31$	−1.38622	−	2.40101i	−0.248973	−	0.431234i	−0.963241	+	0.268638i	$0.913426\pi$
$32$	−22.8740			−4.04360
$33$	−0.931366	−	1.61317i	−0.162130	−	0.280817i
$34$	−11.3720			−1.95027
$35$		0			0
$36$	3.13518	+	5.43029i	0.522530	+	0.905049i
$37$	−6.10590			−1.00380			−0.501902	−	0.864924i	$-0.667366\pi$
$37$	−6.10590			−1.00380			−0.501902	+	0.864924i	$0.667366\pi$
$38$	−9.95843	−	17.2485i	−1.61547	−	2.79808i
$39$	4.04066	+	2.80867i	0.647023	+	0.449747i
$40$	−3.56863	+	6.18106i	−0.564251	+	0.977311i
$41$	0.627306	+	1.08653i	0.0979688	+	0.169687i	0.910844	−	0.412751i	$-0.135432\pi$
$41$	0.627306	+	1.08653i	0.0979688	+	0.169687i	−0.812875	+	0.582438i	$0.802099\pi$
$42$		0			0
$43$	0.870541	−	1.50782i	0.132756	−	0.229941i	−0.791982	−	0.610545i	$-0.790951\pi$
$43$	0.870541	−	1.50782i	0.132756	−	0.229941i	0.924738	+	0.380604i	$0.124284\pi$
$44$	3.76249	−	6.51682i	0.567216	−	0.982447i
$45$	0.842809			0.125639
$46$	6.39619			0.943066
$47$	−2.92921	+	5.07355i	−0.427270	+	0.740053i	−0.996629	−	0.0820357i	$-0.973858\pi$
$47$	−2.92921	+	5.07355i	−0.427270	+	0.740053i	0.569360	+	0.822089i	$0.307191\pi$
$48$	10.4900	−	18.1692i	1.51410	−	2.62249i
$49$		0			0
$50$	−6.10000	−	10.5655i	−0.862670	−	1.49419i
$51$	2.83112	−	4.90364i	0.396436	−	0.686648i
$52$	−1.66457	+	19.8095i	−0.230835	+	2.74708i
$53$	−2.28389	−	3.95582i	−0.313717	−	0.543373i	0.665447	−	0.746445i	$-0.268241\pi$
$53$	−2.28389	−	3.95582i	−0.313717	−	0.543373i	−0.979164	+	0.203072i	$0.934908\pi$
$54$	−15.4779			−2.10627
$55$	−0.505722	−	0.875935i	−0.0681915	−	0.118111i
$56$		0			0
$57$	9.91685			1.31352
$58$	−0.558672	−	0.967649i	−0.0733573	−	0.127059i
$59$	10.9843			1.43003			0.715014	−	0.699110i	$-0.246420\pi$
$59$	10.9843			1.43003			0.715014	+	0.699110i	$0.246420\pi$
$60$	−2.78831	−	4.82950i	−0.359969	−	0.623485i
$61$	3.26249	+	5.65079i	0.417719	+	0.723510i	0.995710	−	0.0925333i	$-0.0294965\pi$
$61$	3.26249	+	5.65079i	0.417719	+	0.723510i	−0.577991	+	0.816043i	$0.696163\pi$
$62$	3.79975	+	6.58137i	0.482569	+	0.835834i
$63$		0			0
$64$	31.9557			3.99446
$65$	2.19403	+	1.52508i	0.272136	+	0.189162i
$66$	2.55295	+	4.42184i	0.314247	+	0.544291i
$67$	6.87983	−	11.9162i	0.840505	−	1.45580i	−0.0489630	−	0.998801i	$-0.515592\pi$
$67$	6.87983	−	11.9162i	0.840505	−	1.45580i	0.889468	−	0.456997i	$-0.151075\pi$
$68$	22.8740			2.77389
$69$	−1.59237	+	2.75807i	−0.191699	+	0.332032i
$70$		0			0
$71$	2.40763	−	4.17014i	0.285733	−	0.494904i	−0.687054	−	0.726607i	$-0.741096\pi$
$71$	2.40763	−	4.17014i	0.285733	−	0.494904i	0.972787	+	0.231703i	$0.0744296\pi$
$72$	−5.47644	−	9.48548i	−0.645405	−	1.11787i
$73$	3.03494	+	5.25666i	0.355212	+	0.615246i	0.987154	−	0.159770i	$-0.0510752\pi$
$73$	3.03494	+	5.25666i	0.355212	+	0.615246i	−0.631942	+	0.775016i	$0.717742\pi$
$74$	16.7368			1.94561
$75$	6.07453			0.701427
$76$	20.0308	+	34.6944i	2.29769	+	3.97972i
$77$		0			0
$78$	−11.0758	−	7.69879i	−1.25408	−	0.871716i
$79$	4.56291	−	7.90320i	0.513368	−	0.889179i	−0.486512	−	0.873674i	$-0.661731\pi$
$79$	4.56291	−	7.90320i	0.513368	−	0.889179i	0.999880	−	0.0155052i	$-0.00493564\pi$
$80$	5.69594	−	9.86566i	0.636825	−	1.10301i
$81$	2.14741	−	3.71942i	0.238601	−	0.413269i
$82$	−1.71950	−	2.97826i	−0.189887	−	0.328894i
$83$	−11.7368			−1.28828			−0.644139	−	0.764908i	$-0.722784\pi$
$83$	−11.7368			−1.28828			−0.644139	+	0.764908i	$0.722784\pi$
$84$		0			0
$85$	1.53727	−	2.66263i	0.166740	−	0.288802i
$86$	−2.38622	+	4.13306i	−0.257313	+	0.445679i
$87$	0.556340			0.0596459
$88$	−6.57220	+	11.3834i	−0.700599	+	1.21347i
$89$	1.76101			0.186666			0.0933331	−	0.995635i	$-0.470248\pi$
$89$	1.76101			0.186666			0.0933331	+	0.995635i	$0.470248\pi$
$90$	−2.31021			−0.243517
$91$		0			0
$92$	−12.8656			−1.34133
$93$	−3.78389			−0.392371
$94$	8.02921	−	13.9070i	0.828150	−	1.43440i
$95$	5.38474			0.552463
$96$	−15.6095	+	27.0364i	−1.59313	+	2.75939i
$97$	4.76691	−	8.25652i	0.484006	−	0.838323i	−0.515825	−	0.856694i	$-0.672515\pi$
$97$	4.76691	−	8.25652i	0.484006	−	0.838323i	0.999831	+	0.0183708i	$0.00584795\pi$
$98$		0			0
$99$	1.55217			0.155998
$100$	12.2698	+	21.2519i	1.22698	+	2.12519i
$101$	−3.74680	+	6.48965i	−0.372821	+	0.645745i	−0.989998	−	0.141079i	$-0.954943\pi$
$101$	−3.74680	+	6.48965i	−0.372821	+	0.645745i	0.617177	+	0.786824i	$0.288276\pi$
$102$	−7.76033	+	13.4413i	−0.768388	+	1.33089i
$103$	1.40424	−	2.43221i	0.138364	−	0.239653i	−0.788514	−	0.615017i	$-0.789149\pi$
$103$	1.40424	−	2.43221i	0.138364	−	0.239653i	0.926877	+	0.375364i	$0.122482\pi$
$104$	2.90763	−	34.6027i	0.285116	−	3.39307i
$105$		0			0
$106$	6.26033	+	10.8432i	0.608057	+	1.05319i
$107$	1.48647			0.143702			0.0718512	−	0.997415i	$-0.477109\pi$
$107$	1.48647			0.143702			0.0718512	+	0.997415i	$0.477109\pi$
$108$	31.1328			2.99576
$109$	−1.43561	−	2.48654i	−0.137506	−	0.238168i	0.789046	−	0.614334i	$-0.210575\pi$
$109$	−1.43561	−	2.48654i	−0.137506	−	0.238168i	−0.926552	+	0.376167i	$0.877242\pi$
$110$	1.38622	+	2.40101i	0.132171	+	0.228927i
$111$	−4.16673	+	7.21698i	−0.395488	+	0.685006i
$112$		0			0
$113$	6.20972	−	10.7555i	0.584161	−	1.01180i	−0.410819	−	0.911717i	$-0.634757\pi$
$113$	6.20972	−	10.7555i	0.584161	−	1.01180i	0.994979	−	0.100079i	$-0.0319096\pi$
$114$	−27.1829			−2.54591
$115$	−0.864640	+	1.49760i	−0.0806281	+	0.139652i
$116$	1.12374	+	1.94637i	0.104336	+	0.180716i
$117$	−3.71032	+	1.74569i	−0.343019	+	0.161389i
$118$	−30.1087			−2.77173
$119$		0			0
$120$	4.87054	+	8.43602i	0.444618	+	0.770100i
$121$	4.56863	+	7.91311i	0.415330	+	0.719373i
$122$	−8.94274	−	15.4893i	−0.809638	−	1.40233i
$123$	1.71232			0.154395
$124$	−7.64299	−	13.2380i	−0.686361	−	1.18881i
$125$	7.00382			0.626440
$126$		0			0
$127$	−2.71526	−	4.70296i	−0.240940	−	0.417321i	0.720042	−	0.693930i	$-0.244122\pi$
$127$	−2.71526	−	4.70296i	−0.240940	−	0.417321i	−0.960982	+	0.276610i	$0.910789\pi$
$128$	−41.8452			−3.69862
$129$	−1.18813	−	2.05790i	−0.104609	−	0.181188i
$130$	−6.01402	−	4.18036i	−0.527465	−	0.366642i
$131$	−5.66100	+	9.80515i	−0.494604	+	0.856680i	−0.999981	−	0.00621925i	$-0.998020\pi$
$131$	−5.66100	+	9.80515i	−0.494604	+	0.856680i	0.505376	+	0.862899i	$0.331354\pi$
$132$	−5.13512	−	8.89428i	−0.446954	−	0.774148i
$133$		0			0
$134$	−18.8582	+	32.6633i	−1.62910	+	2.82168i
$135$	2.09231	−	3.62398i	0.180077	−	0.311902i
$136$	−39.9557			−3.42617
$137$	−13.9754			−1.19400			−0.597000	−	0.802241i	$-0.703641\pi$
$137$	−13.9754			−1.19400			−0.597000	+	0.802241i	$0.703641\pi$
$138$	4.36482	−	7.56009i	0.371558	−	0.643558i
$139$	5.21544	−	9.03340i	0.442368	−	0.766203i	−0.555497	−	0.831518i	$-0.687472\pi$
$139$	5.21544	−	9.03340i	0.442368	−	0.766203i	0.997865	+	0.0653153i	$0.0208053\pi$
$140$		0			0
$141$	3.99785	+	6.92447i	0.336679	+	0.583146i
$142$	−6.59951	+	11.4307i	−0.553818	+	0.959242i
$143$	4.04066	+	2.80867i	0.337897	+	0.234873i
$144$	8.74102	+	15.1399i	0.728418	+	1.26166i
$145$	0.302087			0.0250869
$146$	−8.31901	−	14.4089i	−0.688486	−	1.19249i
$147$		0			0
$148$	−33.6651			−2.76725
$149$	−4.08216	−	7.07052i	−0.334424	−	0.579239i	0.648950	−	0.760831i	$-0.275208\pi$
$149$	−4.08216	−	7.07052i	−0.334424	−	0.579239i	−0.983374	+	0.181592i	$0.941875\pi$
$150$	−16.6508			−1.35953
$151$	1.23094	+	2.13205i	0.100173	+	0.173504i	0.911756	−	0.410733i	$-0.134727\pi$
$151$	1.23094	+	2.13205i	0.100173	+	0.173504i	−0.811583	+	0.584237i	$0.801394\pi$
$152$	−34.9892	−	60.6031i	−2.83800	−	4.91556i
$153$	2.35910	+	4.08608i	0.190722	+	0.330340i
$154$		0			0
$155$	−2.05461			−0.165030
$156$	22.2783	+	15.4857i	1.78369	+	1.23985i
$157$	−6.45991	−	11.1889i	−0.515557	−	0.892971i	−0.999837	−	0.0180576i	$-0.994252\pi$
$157$	−6.45991	−	11.1889i	−0.515557	−	0.892971i	0.484280	−	0.874913i	$-0.339082\pi$
$158$	−12.5073	+	21.6633i	−0.995029	+	1.72344i
$159$	−6.23420			−0.494404
$160$	−8.47577	+	14.6805i	−0.670069	+	1.16059i
$161$		0			0
$162$	−5.88622	+	10.1952i	−0.462465	+	0.801014i
$163$	3.01371	+	5.21990i	0.236052	+	0.408854i	0.959578	−	0.281443i	$-0.0908131\pi$
$163$	3.01371	+	5.21990i	0.236052	+	0.408854i	−0.723526	+	0.690297i	$0.757480\pi$
$164$	3.45867	+	5.99060i	0.270077	+	0.467787i
$165$	−1.38044			−0.107467
$166$	32.1715			2.49699
$167$	3.82558	+	6.62610i	0.296032	+	0.512743i	0.975224	−	0.221218i	$-0.0710031\pi$
$167$	3.82558	+	6.62610i	0.296032	+	0.512743i	−0.679192	+	0.733960i	$0.737670\pi$
$168$		0			0
$169$	−12.8177	−	2.16944i	−0.985977	−	0.166880i
$170$	−4.21378	+	7.29847i	−0.323182	+	0.559767i
$171$	−4.13173	+	7.15636i	−0.315961	+	0.547260i
$172$	4.79975	−	8.31342i	0.365978	−	0.633892i
$173$	−0.0822298	−	0.142426i	−0.00625182	−	0.0108285i	0.862883	−	0.505404i	$-0.168657\pi$
$173$	−0.0822298	−	0.142426i	−0.00625182	−	0.0108285i	−0.869134	+	0.494576i	$0.835323\pi$
$174$	−1.52497			−0.115608
$175$		0			0
$176$	10.4900	−	18.1692i	0.790711	−	1.36955i
$177$	7.49576	−	12.9830i	0.563416	−	0.975865i
$178$	−4.82706			−0.361803
$179$	−0.384316	+	0.665655i	−0.0287252	+	0.0497534i	−0.880031	−	0.474917i	$-0.842478\pi$
$179$	−0.384316	+	0.665655i	−0.0287252	+	0.0497534i	0.851305	+	0.524670i	$0.175811\pi$
$180$	4.64685			0.346356
$181$	9.92152			0.737461			0.368730	−	0.929536i	$-0.379793\pi$
$181$	9.92152			0.737461			0.368730	+	0.929536i	$0.379793\pi$
$182$		0			0
$183$	8.90541			0.658307
$184$	22.4732			1.65675
$185$	−2.26249	+	3.91874i	−0.166341	+	0.288112i
$186$	10.3720			0.760509
$187$	2.83112	−	4.90364i	0.207032	−	0.358590i
$188$	−16.1503	+	27.9732i	−1.17788	+	2.04015i
$189$		0			0
$190$	−14.7600			−1.07080
$191$	−4.94847	−	8.57099i	−0.358058	−	0.620175i	0.629578	−	0.776937i	$-0.283228\pi$
$191$	−4.94847	−	8.57099i	−0.358058	−	0.620175i	−0.987636	+	0.156762i	$0.949894\pi$
$192$	21.8069	−	37.7706i	1.57378	−	2.72586i
$193$	−4.35037	+	7.53507i	−0.313147	+	0.542386i	−0.979042	−	0.203659i	$-0.934716\pi$
$193$	−4.35037	+	7.53507i	−0.313147	+	0.542386i	0.665895	+	0.746045i	$0.268050\pi$
$194$	−13.0665	+	22.6318i	−0.938119	+	1.62487i
$195$	3.29982	−	1.55255i	0.236305	−	0.111180i
$196$		0			0
$197$	13.0093	+	22.5328i	0.926874	+	1.60539i	0.788520	+	0.615009i	$0.210848\pi$
$197$	13.0093	+	22.5328i	0.926874	+	1.60539i	0.138354	+	0.990383i	$0.455819\pi$
$198$	−4.25461			−0.302362
$199$	−10.1330			−0.718307			−0.359153	−	0.933279i	$-0.616934\pi$
$199$	−10.1330			−0.718307			−0.359153	+	0.933279i	$0.616934\pi$
$200$	−21.4325	−	37.1222i	−1.51551	−	2.62494i
$201$	−9.38973	−	16.2635i	−0.662300	−	1.14714i
$202$	10.2703	−	17.7887i	0.722615	−	1.25161i
$203$		0			0
$204$	15.6095	−	27.0364i	1.09288	−	1.89293i
$205$	0.929771			0.0649380
$206$	−3.84914	+	6.66690i	−0.268182	+	0.464505i
$207$	−1.32688	−	2.29822i	−0.0922246	−	0.159738i
$208$	−4.64090	+	55.2297i	−0.321789	+	3.82949i
$209$	9.91685			0.685963
$210$		0			0
$211$	−8.33911	−	14.4438i	−0.574088	−	0.994349i	−0.996140	−	0.0877779i	$-0.972023\pi$
$211$	−8.33911	−	14.4438i	−0.574088	−	0.994349i	0.422052	−	0.906572i	$-0.361310\pi$
$212$	−12.5923	−	21.8105i	−0.864843	−	1.49795i
$213$	−3.28598	−	5.69148i	−0.225152	−	0.389974i
$214$	−4.07453			−0.278529
$215$	−0.645142	−	1.11742i	−0.0439983	−	0.0762074i
$216$	−54.3819			−3.70022
$217$		0			0
$218$	3.93511	+	6.81582i	0.266520	+	0.461625i
$219$	8.28428			0.559800
$220$	−2.78831	−	4.82950i	−0.187988	−	0.325605i
$221$	−1.25253	+	14.9059i	−0.0842540	+	1.00268i
$222$	11.4213	−	19.7823i	0.766550	−	1.32770i
$223$	0.535180	+	0.926959i	0.0358383	+	0.0620738i	0.883388	−	0.468642i	$-0.155257\pi$
$223$	0.535180	+	0.926959i	0.0358383	+	0.0620738i	−0.847550	+	0.530716i	$0.821923\pi$
$224$		0			0
$225$	−2.53087	+	4.38360i	−0.168725	+	0.292240i
$226$	−17.0213	+	29.4818i	−1.13224	+	1.96110i
$227$	24.4664			1.62389			0.811947	−	0.583732i	$-0.198408\pi$
$227$	24.4664			1.62389			0.811947	+	0.583732i	$0.198408\pi$
$228$	54.6769			3.62106
$229$	2.36482	−	4.09599i	0.156272	−	0.270670i	−0.777250	−	0.629192i	$-0.783386\pi$
$229$	2.36482	−	4.09599i	0.156272	−	0.270670i	0.933521	+	0.358522i	$0.116719\pi$
$230$	2.37005	−	4.10505i	0.156276	−	0.270679i
$231$		0			0
$232$	−1.96291	−	3.39986i	−0.128871	−	0.223212i
$233$	−10.2753	+	17.7974i	−0.673160	+	1.16595i	0.303843	+	0.952722i	$0.401730\pi$
$233$	−10.2753	+	17.7974i	−0.673160	+	1.16595i	−0.977003	+	0.213226i	$0.931603\pi$
$234$	10.1703	−	4.78508i	0.664853	−	0.312810i
$235$	2.17079	+	3.75991i	0.141607	+	0.245270i
$236$	60.5620			3.94225
$237$	−6.22755	−	10.7864i	−0.404523	−	0.700654i
$238$		0			0
$239$	6.25461			0.404577			0.202289	−	0.979326i	$-0.435162\pi$
$239$	6.25461			0.404577			0.202289	+	0.979326i	$0.435162\pi$
$240$	−7.77393	−	13.4648i	−0.501805	−	0.869152i
$241$	12.1444			0.782290			0.391145	−	0.920329i	$-0.372079\pi$
$241$	12.1444			0.782290			0.391145	+	0.920329i	$0.372079\pi$
$242$	−12.5230	−	21.6905i	−0.805009	−	1.39432i
$243$	5.53911	+	9.59402i	0.355334	+	0.615457i
$244$	17.9878	+	31.1558i	1.15155	+	1.99455i
$245$		0			0
$246$	−4.69361			−0.299254
$247$	−23.7054	+	11.1533i	−1.50834	+	0.709667i
$248$	13.3506	+	23.1238i	0.847761	+	1.46836i
$249$	−8.00929	+	13.8725i	−0.507568	+	0.879134i
$250$	−19.1980			−1.21419
$251$	−3.15719	+	5.46842i	−0.199280	+	0.345163i	−0.948295	−	0.317390i	$-0.897194\pi$
$251$	−3.15719	+	5.46842i	−0.199280	+	0.345163i	0.749015	+	0.662553i	$0.230527\pi$
$252$		0			0
$253$	−1.59237	+	2.75807i	−0.100112	+	0.173398i
$254$	7.44274	+	12.8912i	0.466999	+	0.808866i
$255$	−2.09809	−	3.63400i	−0.131388	−	0.227570i
$256$	50.7896			3.17435
$257$	−24.3562			−1.51930			−0.759649	−	0.650333i	$-0.774629\pi$
$257$	−24.3562			−1.51930			−0.759649	+	0.650333i	$0.774629\pi$
$258$	3.25677	+	5.64088i	0.202757	+	0.351186i
$259$		0			0
$260$	12.0969	+	8.40855i	0.750216	+	0.521476i
$261$	−0.231792	+	0.401475i	−0.0143475	+	0.0248507i
$262$	15.5173	−	26.8767i	0.958661	−	1.66045i
$263$	4.78955	−	8.29574i	0.295336	−	0.511537i	−0.679727	−	0.733465i	$-0.737902\pi$
$263$	4.78955	−	8.29574i	0.295336	−	0.511537i	0.975063	+	0.221928i	$0.0712350\pi$
$264$	8.96987	+	15.5363i	0.552057	+	0.956191i
$265$	−3.38510			−0.207945
$266$		0			0
$267$	1.20173	−	2.08145i	0.0735445	−	0.127383i
$268$	37.9322	−	65.7004i	2.31708	−	4.01329i
$269$	−29.3990			−1.79249			−0.896245	−	0.443560i	$-0.853715\pi$
$269$	−29.3990			−1.79249			−0.896245	+	0.443560i	$0.853715\pi$
$270$	−5.73518	+	9.93362i	−0.349032	+	0.604541i
$271$	0.300385			0.0182471			0.00912354	−	0.999958i	$-0.497096\pi$
$271$	0.300385			0.0182471			0.00912354	+	0.999958i	$0.497096\pi$
$272$	63.7738			3.86686
$273$		0			0
$274$	38.3078			2.31426
$275$	6.07453			0.366308
$276$	−8.77959	+	15.2067i	−0.528469	+	0.915335i
$277$	−32.7710			−1.96902			−0.984509	−	0.175337i	$-0.943899\pi$
$277$	−32.7710			−1.96902			−0.984509	+	0.175337i	$0.943899\pi$
$278$	−14.2959	+	24.7613i	−0.857414	+	1.48508i
$279$	1.57651	−	2.73059i	0.0943831	−	0.163476i
$280$		0			0
$281$	4.29482			0.256207			0.128104	−	0.991761i	$-0.459111\pi$
$281$	4.29482			0.256207			0.128104	+	0.991761i	$0.459111\pi$
$282$	−10.9584	−	18.9806i	−0.652565	−	1.13028i
$283$	−10.5501	+	18.2734i	−0.627140	+	1.08624i	0.360983	+	0.932572i	$0.382441\pi$
$283$	−10.5501	+	18.2734i	−0.627140	+	1.08624i	−0.988123	+	0.153666i	$0.950892\pi$
$284$	13.2745	−	22.9922i	0.787699	−	1.36433i
$285$	3.67460	−	6.36460i	0.217665	−	0.377006i
$286$	−11.0758	−	7.69879i	−0.654924	−	0.455239i
$287$		0			0
$288$	−13.0070	−	22.5287i	−0.766442	−	1.32752i
$289$	0.211803			0.0124590
$290$	−0.828044			−0.0486244
$291$	−6.50597	−	11.2687i	−0.381387	−	0.660581i
$292$	16.7332	+	28.9828i	0.979237	+	1.69609i
$293$	8.88192	−	15.3839i	0.518887	−	0.898739i	−0.480872	−	0.876791i	$-0.659680\pi$
$293$	8.88192	−	15.3839i	0.518887	−	0.898739i	0.999759	−	0.0219482i	$-0.00698688\pi$
$294$		0			0
$295$	4.07012	−	7.04965i	0.236971	−	0.410446i
$296$	58.8052			3.41798
$297$	3.85331	−	6.67413i	0.223592	−	0.387272i
$298$	11.1895	+	19.3809i	0.648193	+	1.12270i
$299$	0.704486	−	8.38384i	0.0407415	−	0.484850i
$300$	33.4921			1.93367
$301$		0			0
$302$	−3.37411	−	5.84413i	−0.194158	−	0.336292i
$303$	5.11371	+	8.85721i	0.293775	+	0.508833i
$304$	55.8467	+	96.7294i	3.20303	+	5.54781i
$305$	4.83554			0.276882
$306$	−6.46648	−	11.2003i	−0.369664	−	0.640277i
$307$	−18.0156			−1.02821			−0.514103	−	0.857729i	$-0.671875\pi$
$307$	−18.0156			−1.02821			−0.514103	+	0.857729i	$0.671875\pi$
$308$		0			0
$309$	−1.91653	−	3.31953i	−0.109028	−	0.188842i
$310$	5.63186			0.319868
$311$	8.62724	+	14.9428i	0.489206	+	0.847330i	0.999923	−	0.0124194i	$-0.00395331\pi$
$311$	8.62724	+	14.9428i	0.489206	+	0.847330i	−0.510717	+	0.859749i	$0.670620\pi$
$312$	−38.9151	−	27.0499i	−2.20313	−	1.53140i
$313$	3.40763	−	5.90219i	0.192611	−	0.333611i	−0.753504	−	0.657443i	$-0.771638\pi$
$313$	3.40763	−	5.90219i	0.192611	−	0.333611i	0.946115	+	0.323832i	$0.104971\pi$
$314$	17.7071	+	30.6697i	0.999272	+	1.73079i
$315$		0			0
$316$	25.1578	−	43.5745i	1.41523	−	2.45126i
$317$	12.5385	−	21.7173i	0.704233	−	1.21977i	−0.262735	−	0.964868i	$-0.584625\pi$
$317$	12.5385	−	21.7173i	0.704233	−	1.21977i	0.966968	−	0.254899i	$-0.0820421\pi$
$318$	17.0885			0.958273
$319$	0.556340			0.0311491
$320$	11.8409	−	20.5090i	0.661927	−	1.14649i
$321$	1.01438	−	1.75696i	0.0566172	−	0.0980639i
$322$		0			0
$323$	15.0724	+	26.1061i	0.838650	+	1.45258i
$324$	11.8398	−	20.5071i	0.657767	−	1.13929i
$325$	−14.5207	+	6.83191i	−0.805462	+	0.378966i
$326$	−8.26083	−	14.3082i	−0.457525	−	0.792456i
$327$	−3.91869			−0.216704
$328$	−6.04151	−	10.4642i	−0.333586	−	0.577789i
$329$		0			0
$330$	3.78389			0.208296
$331$	1.49767	+	2.59404i	0.0823193	+	0.142581i	0.904246	−	0.427012i	$-0.140434\pi$
$331$	1.49767	+	2.59404i	0.0823193	+	0.142581i	−0.821926	+	0.569594i	$0.807101\pi$
$332$	−64.7111			−3.55148
$333$	−3.47202	−	6.01372i	−0.190266	−	0.329550i
$334$	−10.4862	−	18.1627i	−0.573781	−	0.993817i
$335$	−5.09852	−	8.83089i	−0.278562	−	0.482483i
$336$		0			0
$337$	−29.4888			−1.60636			−0.803179	−	0.595738i	$-0.796860\pi$
$337$	−29.4888			−1.60636			−0.803179	+	0.595738i	$0.796860\pi$
$338$	35.1344	+	5.94660i	1.91106	+	0.323453i
$339$	−8.47514	−	14.6794i	−0.460306	−	0.797274i
$340$	8.47577	−	14.6805i	0.459663	−	0.796160i
$341$	−3.78389			−0.204909
$342$	11.3254	−	19.6162i	0.612407	−	1.06072i
$343$		0			0
$344$	−8.38407	+	14.5216i	−0.452039	+	0.782954i
$345$	1.18008	+	2.04395i	0.0635332	+	0.110043i
$346$	0.225399	+	0.390402i	0.0121175	+	0.0209881i
$347$	−5.98686			−0.321391			−0.160696	−	0.987004i	$-0.551374\pi$
$347$	−5.98686			−0.321391			−0.160696	+	0.987004i	$0.551374\pi$
$348$	3.06740			0.164430
$349$	−15.1681	−	26.2719i	−0.811929	−	1.40630i	−0.911513	−	0.411272i	$-0.865085\pi$
$349$	−15.1681	−	26.2719i	−0.811929	−	1.40630i	0.0995840	−	0.995029i	$-0.468249\pi$
$350$		0			0
$351$	−1.70476	+	20.2877i	−0.0909931	+	1.08288i
$352$	−15.6095	+	27.0364i	−0.831988	+	1.44104i
$353$	−14.3031	+	24.7738i	−0.761280	+	1.31857i	0.180912	+	0.983499i	$0.442095\pi$
$353$	−14.3031	+	24.7738i	−0.761280	+	1.31857i	−0.942191	+	0.335075i	$0.891238\pi$
$354$	−20.5465	+	35.5876i	−1.09203	+	1.89146i
$355$	−1.78425	−	3.09041i	−0.0946982	−	0.164022i
$356$	9.70936			0.514595
$357$		0			0
$358$	1.05344	−	1.82462i	0.0556762	−	0.0964340i
$359$	−11.7309	+	20.3185i	−0.619132	+	1.07237i	0.370513	+	0.928827i	$0.379182\pi$
$359$	−11.7309	+	20.3185i	−0.619132	+	1.07237i	−0.989644	+	0.143540i	$0.954151\pi$
$360$	−8.11699			−0.427803
$361$	−16.8978	+	29.2678i	−0.889357	+	1.54041i
$362$	−27.1957			−1.42937
$363$	12.4707			0.654543
$364$		0			0
$365$	4.49827			0.235450
$366$	−24.4105			−1.27596
$367$	18.2598	−	31.6270i	0.953156	−	1.65091i	0.214623	−	0.976697i	$-0.431148\pi$
$367$	18.2598	−	31.6270i	0.953156	−	1.65091i	0.738533	−	0.674218i	$-0.235519\pi$
$368$	−35.8697			−1.86984
$369$	−0.713415	+	1.23567i	−0.0371389	+	0.0643265i
$370$	6.20166	−	10.7416i	0.322409	−	0.558429i
$371$		0			0
$372$	−20.8626			−1.08168
$373$	6.52491	+	11.3015i	0.337847	+	0.585168i	0.984028	−	0.178017i	$-0.0569680\pi$
$373$	6.52491	+	11.3015i	0.337847	+	0.585168i	−0.646181	+	0.763185i	$0.723635\pi$
$374$	−7.76033	+	13.4413i	−0.401277	+	0.695033i
$375$	4.77947	−	8.27829i	0.246811	−	0.427489i
$376$	28.2109	−	48.8627i	1.45487	−	2.51990i
$377$	−1.32988	+	0.625705i	−0.0684925	+	0.0322254i
$378$		0			0
$379$	−15.3018	−	26.5036i	−0.786003	−	1.36140i	−0.928398	−	0.371587i	$-0.878814\pi$
$379$	−15.3018	−	26.5036i	−0.786003	−	1.36140i	0.142395	−	0.989810i	$-0.454520\pi$
$380$	29.6889			1.52301
$381$	−7.41167			−0.379711
$382$	13.5641	+	23.4938i	0.694002	+	1.20205i
$383$	−2.44299	−	4.23138i	−0.124831	−	0.216213i	0.796836	−	0.604196i	$-0.206505\pi$
$383$	−2.44299	−	4.23138i	−0.124831	−	0.216213i	−0.921667	+	0.387982i	$0.873172\pi$
$384$	−28.5555	+	49.4596i	−1.45722	+	2.52398i
$385$		0			0
$386$	11.9247	−	20.6542i	0.606953	−	1.05127i
$387$	1.98008			0.100653
$388$	26.2825	−	45.5226i	1.33429	−	2.31106i
$389$	0.927126	+	1.60583i	0.0470072	+	0.0814188i	0.888572	−	0.458738i	$-0.151698\pi$
$389$	0.927126	+	1.60583i	0.0470072	+	0.0814188i	−0.841564	+	0.540157i	$0.818365\pi$
$390$	−9.04508	+	4.25567i	−0.458015	+	0.215494i
$391$	−9.68082			−0.489580
$392$		0			0
$393$	7.72625	+	13.3823i	0.389738	+	0.675046i
$394$	−35.6595	−	61.7641i	−1.79650	−	3.11163i
$395$	−3.38149	−	5.85692i	−0.170141	−	0.294693i
$396$	8.55791			0.430051
$397$	10.7567	+	18.6312i	0.539863	+	0.935071i	0.998911	+	0.0466590i	$0.0148574\pi$
$397$	10.7567	+	18.6312i	0.539863	+	0.935071i	−0.459048	+	0.888412i	$0.651809\pi$
$398$	27.7753			1.39225
$399$		0			0
$400$	34.2087	+	59.2513i	1.71044	+	2.96256i
$401$	−14.5653			−0.727357			−0.363678	−	0.931525i	$-0.618479\pi$
$401$	−14.5653			−0.727357			−0.363678	+	0.931525i	$0.618479\pi$
$402$	25.7380	+	44.5795i	1.28370	+	2.22343i
$403$	9.04508	−	4.25567i	0.450567	−	0.211990i
$404$	−20.6581	+	35.7809i	−1.02778	+	1.78017i
$405$	−1.59141	−	2.75640i	−0.0790776	−	0.136966i
$406$		0			0
$407$	−4.16673	+	7.21698i	−0.206537	+	0.357733i
$408$	−27.2662	+	47.2264i	−1.34988	+	2.33805i
$409$	22.1290			1.09421			0.547105	−	0.837064i	$-0.315730\pi$
$409$	22.1290			1.09421			0.547105	+	0.837064i	$0.315730\pi$
$410$	−2.54858			−0.125865
$411$	−9.53696	+	16.5185i	−0.470423	+	0.814797i
$412$	7.74232	−	13.4101i	0.381437	−	0.660668i
$413$		0			0
$414$	3.63709	+	6.29962i	0.178753	+	0.309610i
$415$	−4.34896	+	7.53261i	−0.213482	+	0.369761i
$416$	6.90584	−	82.1839i	0.338586	−	4.02940i
$417$	−7.11813	−	12.3290i	−0.348576	−	0.603752i
$418$	−27.1829			−1.32956
$419$	1.68795	+	2.92362i	0.0824618	+	0.142828i	0.904307	−	0.426883i	$-0.140388\pi$
$419$	1.68795	+	2.92362i	0.0824618	+	0.142828i	−0.821845	+	0.569711i	$0.807055\pi$
$420$		0			0
$421$	−25.1101			−1.22379			−0.611895	−	0.790939i	$-0.709593\pi$
$421$	−25.1101			−1.22379			−0.611895	+	0.790939i	$0.709593\pi$
$422$	22.8582	+	39.5915i	1.11272	+	1.92729i
$423$	−6.66260			−0.323947
$424$	21.9959	+	38.0980i	1.06821	+	1.85020i
$425$	9.23254	+	15.9912i	0.447844	+	0.775688i
$426$	9.00714	+	15.6008i	0.436397	+	0.755862i
$427$		0			0
$428$	8.19570			0.396154
$429$	6.07714	−	2.85927i	0.293407	−	0.138047i
$430$	1.76839	+	3.06294i	0.0852792	+	0.147708i
$431$	−5.39742	+	9.34861i	−0.259985	+	0.450307i	−0.966238	−	0.257653i	$-0.917051\pi$
$431$	−5.39742	+	9.34861i	−0.259985	+	0.450307i	0.706253	+	0.707960i	$0.250384\pi$
$432$	86.7997			4.17615
$433$	−7.25910	+	12.5731i	−0.348850	+	0.604226i	−0.986045	−	0.166476i	$-0.946761\pi$
$433$	−7.25910	+	12.5731i	−0.348850	+	0.604226i	0.637195	+	0.770702i	$0.280094\pi$
$434$		0			0
$435$	0.206147	−	0.357057i	0.00988398	−	0.0171196i
$436$	−7.91526	−	13.7096i	−0.379072	−	0.656572i
$437$	−8.47750	−	14.6835i	−0.405534	−	0.702405i
$438$	−22.7079			−1.08502
$439$	14.4309			0.688748			0.344374	−	0.938833i	$-0.388091\pi$
$439$	14.4309			0.688748			0.344374	+	0.938833i	$0.388091\pi$
$440$	4.87054	+	8.43602i	0.232194	+	0.402172i
$441$		0			0
$442$	3.43327	−	40.8582i	0.163304	−	1.94343i
$443$	15.1215	−	26.1912i	0.718445	−	1.24438i	−0.243171	−	0.969984i	$-0.578187\pi$
$443$	15.1215	−	26.1912i	0.718445	−	1.24438i	0.961616	−	0.274400i	$-0.0884792\pi$
$444$	−22.9734	+	39.7910i	−1.09027	+	1.88840i
$445$	0.652525	−	1.13021i	0.0309326	−	0.0535769i
$446$	−1.46697	−	2.54087i	−0.0694632	−	0.120314i
$447$	−11.1428			−0.527038
$448$		0			0
$449$	−15.6380	+	27.0858i	−0.738003	+	1.27826i	0.215390	+	0.976528i	$0.430898\pi$
$449$	−15.6380	+	27.0858i	−0.738003	+	1.27826i	−0.953393	+	0.301731i	$0.902435\pi$
$450$	6.93733	−	12.0158i	0.327029	−	0.566431i
$451$	1.71232			0.0806300
$452$	34.2375	−	59.3010i	1.61039	−	2.78928i
$453$	3.36002			0.157868
$454$	−67.0645			−3.14749
$455$		0			0
$456$	−95.5080			−4.47257
$457$	20.6466			0.965808			0.482904	−	0.875673i	$-0.339582\pi$
$457$	20.6466			0.965808			0.482904	+	0.875673i	$0.339582\pi$
$458$	−6.48216	+	11.2274i	−0.302892	+	0.524624i
$459$	23.4262			1.09344
$460$	−4.76722	+	8.25707i	−0.222273	+	0.384988i
$461$	13.6480	−	23.6391i	0.635653	−	1.10098i	−0.350724	−	0.936479i	$-0.614064\pi$
$461$	13.6480	−	23.6391i	0.635653	−	1.10098i	0.986376	−	0.164504i	$-0.0526022\pi$
$462$		0			0
$463$	5.65977			0.263032			0.131516	−	0.991314i	$-0.458016\pi$
$463$	5.65977			0.263032			0.131516	+	0.991314i	$0.458016\pi$
$464$	3.13303	+	5.42656i	0.145447	+	0.251922i
$465$	−1.40209	+	2.42849i	−0.0650202	+	0.112618i
$466$	28.1656	−	48.7842i	1.30474	−	2.25988i
$467$	21.1073	−	36.5588i	0.976727	−	1.69174i	0.302614	−	0.953113i	$-0.402141\pi$
$467$	21.1073	−	36.5588i	0.976727	−	1.69174i	0.674114	−	0.738628i	$-0.264526\pi$
$468$	−20.4570	+	9.62491i	−0.945624	+	0.444912i
$469$		0			0
$470$	−5.95031	−	10.3062i	−0.274467	−	0.475391i
$471$	−17.6332			−0.812496
$472$	−105.788			−4.86929
$473$	−1.18813	−	2.05790i	−0.0546303	−	0.0946225i
$474$	17.0702	+	29.5665i	0.784062	+	1.35803i
$475$	−16.1699	+	28.0070i	−0.741925	+	1.28505i
$476$		0			0
$477$	2.59740	−	4.49882i	0.118927	−	0.205987i
$478$	−17.1444			−0.784167
$479$	16.2658	−	28.1732i	0.743204	−	1.28727i	−0.207825	−	0.978166i	$-0.566639\pi$
$479$	16.2658	−	28.1732i	0.743204	−	1.28727i	0.951029	−	0.309101i	$-0.100028\pi$
$480$	11.5679	+	20.0362i	0.528000	+	0.914523i
$481$	1.84341	−	21.9378i	0.0840525	−	1.00028i
$482$	−33.2888			−1.51626
$483$		0			0
$484$	25.1893	+	43.6292i	1.14497	+	1.98314i
$485$	−3.53267	−	6.11876i	−0.160410	−	0.277839i
$486$	−15.1832	−	26.2980i	−0.688722	−	1.19290i
$487$	26.8583			1.21707			0.608533	−	0.793529i	$-0.291758\pi$
$487$	26.8583			1.21707			0.608533	+	0.793529i	$0.291758\pi$
$488$	−31.4206	−	54.4221i	−1.42234	−	2.46357i
$489$	8.22634			0.372008
$490$		0			0
$491$	−21.8439	−	37.8348i	−0.985802	−	1.70746i	−0.638317	−	0.769774i	$-0.720369\pi$
$491$	−21.8439	−	37.8348i	−0.985802	−	1.70746i	−0.347485	−	0.937685i	$-0.612964\pi$
$492$	9.44093			0.425630
$493$	0.845567	+	1.46457i	0.0380824	+	0.0659607i
$494$	64.9785	−	30.5721i	2.92352	−	1.37550i
$495$	0.575141	−	0.996173i	0.0258507	−	0.0447747i
$496$	−21.3090	−	36.9082i	−0.956801	−	1.65723i
$497$		0			0
$498$	21.9541	−	38.0257i	0.983788	−	1.70397i
$499$	9.05098	−	15.6768i	0.405177	−	0.701788i	−0.589165	−	0.808013i	$-0.700543\pi$
$499$	9.05098	−	15.6768i	0.405177	−	0.701788i	0.994342	+	0.106225i	$0.0338764\pi$
$500$	38.6158			1.72695
$501$	10.4424			0.466534
$502$	8.65412	−	14.9894i	0.386252	−	0.669009i
$503$	−14.2077	+	24.6085i	−0.633492	+	1.09724i	0.353341	+	0.935495i	$0.385046\pi$
$503$	−14.2077	+	24.6085i	−0.633492	+	1.09724i	−0.986833	+	0.161745i	$0.948288\pi$
$504$		0			0
$505$	2.77669	+	4.80937i	0.123561	+	0.214014i
$506$	4.36482	−	7.56009i	0.194040	−	0.336087i
$507$	−11.3111	+	13.6697i	−0.502345	+	0.607092i
$508$	−14.9707	−	25.9299i	−0.664215	−	1.15045i
$509$	−17.4791			−0.774748			−0.387374	−	0.921923i	$-0.626618\pi$
$509$	−17.4791			−0.774748			−0.387374	+	0.921923i	$0.626618\pi$
$510$	5.75104	+	9.96110i	0.254660	+	0.441085i
$511$		0			0
$512$	−55.5280			−2.45402
$513$	20.5143	+	35.5319i	0.905730	+	1.56877i
$514$	66.7624			2.94476
$515$	−1.04066	−	1.80247i	−0.0458568	−	0.0794263i
$516$	−6.55080	−	11.3463i	−0.288383	−	0.499494i
$517$	3.99785	+	6.92447i	0.175825	+	0.304538i
$518$		0			0
$519$	−0.224458			−0.00985260
$520$	−21.1305	−	14.6878i	−0.926632	−	0.644103i
$521$	9.65437	+	16.7219i	0.422966	+	0.732598i	0.996228	−	0.0867740i	$-0.0276558\pi$
$521$	9.65437	+	16.7219i	0.422966	+	0.732598i	−0.573263	+	0.819372i	$0.694322\pi$
$522$	0.635360	−	1.10048i	0.0278090	−	0.0481665i
$523$	10.0229			0.438270			0.219135	−	0.975695i	$-0.429676\pi$
$523$	10.0229			0.438270			0.219135	+	0.975695i	$0.429676\pi$
$524$	−31.2121	+	54.0610i	−1.36351	+	2.36167i
$525$		0			0
$526$	−13.1285	+	22.7393i	−0.572432	+	0.991481i
$527$	−5.75104	−	9.96110i	−0.250519	−	0.433912i
$528$	−14.3169	−	24.7976i	−0.623064	−	1.07918i
$529$	−17.5550			−0.763261
$530$	9.27884			0.403047
$531$	6.24602	+	10.8184i	0.271054	+	0.469479i
$532$		0			0
$533$	−4.09316	+	1.92581i	−0.177294	+	0.0834162i
$534$	−3.29403	+	5.70543i	−0.142547	+	0.246898i
$535$	0.550798	−	0.954010i	0.0238131	−	0.0412454i
$536$	−66.2588	+	114.764i	−2.86194	+	4.95703i
$537$	0.524522	+	0.908500i	0.0226348	+	0.0392046i
$538$	80.5851			3.47427
$539$		0			0
$540$	11.5360	−	19.9809i	0.496430	−	0.859842i
$541$	−8.80763	+	15.2553i	−0.378670	+	0.655875i	−0.990869	−	0.134829i	$-0.956952\pi$
$541$	−8.80763	+	15.2553i	−0.378670	+	0.655875i	0.612199	+	0.790703i	$0.290285\pi$
$542$	−0.823379			−0.0353672
$543$	6.77054	−	11.7269i	0.290552	−	0.503250i
$544$	−94.8978			−4.06871
$545$	−2.12780			−0.0911451
$546$		0			0
$547$	2.98425			0.127597			0.0637987	−	0.997963i	$-0.479678\pi$
$547$	2.98425			0.127597			0.0637987	+	0.997963i	$0.479678\pi$
$548$	−77.0539			−3.29158
$549$	−3.71032	+	6.42647i	−0.158353	+	0.274275i
$550$	−16.6508			−0.709992
$551$	−1.48093	+	2.56504i	−0.0630896	+	0.109274i
$552$	15.3359	−	26.5626i	0.652740	−	1.13058i
$553$		0			0
$554$	89.8279			3.81642
$555$	3.08789	+	5.34838i	0.131073	+	0.227026i
$556$	28.7555	−	49.8059i	1.21950	−	2.11224i
$557$	−3.62798	+	6.28384i	−0.153722	+	0.266255i	−0.932593	−	0.360930i	$-0.882459\pi$
$557$	−3.62798	+	6.28384i	−0.153722	+	0.266255i	0.778871	+	0.627184i	$0.215793\pi$
$558$	−4.32134	+	7.48478i	−0.182937	+	0.316856i
$559$	5.15461	+	3.58298i	0.218017	+	0.151544i
$560$		0			0
$561$	−3.86397	−	6.69259i	−0.163137	−	0.282561i
$562$	−11.7724			−0.496591
$563$	−4.27933			−0.180352			−0.0901762	−	0.995926i	$-0.528743\pi$
$563$	−4.27933			−0.180352			−0.0901762	+	0.995926i	$0.528743\pi$
$564$	22.0423	+	38.1783i	0.928146	+	1.60760i
$565$	−4.60191	−	7.97074i	−0.193604	−	0.335332i
$566$	28.9188	−	50.0888i	1.21555	−	2.10539i
$567$		0			0
$568$	−23.1876	+	40.1621i	−0.972929	+	1.68516i
$569$	−19.7626			−0.828492			−0.414246	−	0.910165i	$-0.635955\pi$
$569$	−19.7626			−0.828492			−0.414246	+	0.910165i	$0.635955\pi$
$570$	−10.0724	+	17.4459i	−0.421886	+	0.730727i
$571$	9.96182	+	17.2544i	0.416889	+	0.722073i	0.995625	−	0.0934422i	$-0.0297870\pi$
$571$	9.96182	+	17.2544i	0.416889	+	0.722073i	−0.578736	+	0.815515i	$0.696454\pi$
$572$	22.2783	+	15.4857i	0.931502	+	0.647488i
$573$	−13.5075			−0.564285
$574$		0			0
$575$	−5.19286	−	8.99430i	−0.216557	−	0.375088i
$576$	18.1711	+	31.4733i	0.757129	+	1.31139i
$577$	−14.3650	−	24.8809i	−0.598023	−	1.03581i	−0.993113	−	0.117163i	$-0.962620\pi$
$577$	−14.3650	−	24.8809i	−0.598023	−	1.03581i	0.395090	−	0.918642i	$-0.370713\pi$
$578$	−0.580569			−0.0241485
$579$	5.93747	+	10.2840i	0.246753	+	0.427389i
$580$	1.66556			0.0691587
$581$		0			0
$582$	17.8334	+	30.8883i	0.739218	+	1.28036i
$583$	−6.23420			−0.258194
$584$	−29.2291	−	50.6263i	−1.20951	−	2.09493i
$585$	−0.254450	+	3.02812i	−0.0105202	+	0.125197i
$586$	−24.3461	+	42.1686i	−1.00573	+	1.74197i
$587$	15.7694	+	27.3134i	0.650872	+	1.12734i	0.982912	+	0.184078i	$0.0589299\pi$
$587$	15.7694	+	27.3134i	0.650872	+	1.12734i	−0.332040	+	0.943265i	$0.607737\pi$
$588$		0			0
$589$	10.0724	−	17.4459i	0.415025	−	0.718845i
$590$	−11.1565	+	19.3237i	−0.459307	+	0.795542i
$591$	35.5107			1.46071
$592$	−93.8597			−3.85761
$593$	−5.55903	+	9.62852i	−0.228282	+	0.395396i	−0.957299	−	0.289099i	$-0.906644\pi$
$593$	−5.55903	+	9.62852i	−0.228282	+	0.395396i	0.729017	+	0.684496i	$0.239977\pi$
$594$	−10.5622	+	18.2943i	−0.433374	+	0.750626i
$595$		0			0
$596$	−22.5071	−	38.9835i	−0.921928	−	1.59683i
$597$	−6.91483	+	11.9768i	−0.283005	+	0.490179i
$598$	−1.93105	+	22.9808i	−0.0789667	+	0.939754i
$599$	3.64786	+	6.31828i	0.149048	+	0.258158i	0.930876	−	0.365336i	$-0.119046\pi$
$599$	3.64786	+	6.31828i	0.149048	+	0.258158i	−0.781828	+	0.623494i	$0.785713\pi$
$600$	−58.5031			−2.38838
$601$	−0.586291	−	1.01548i	−0.0239153	−	0.0414225i	0.853820	−	0.520568i	$-0.174280\pi$
$601$	−0.586291	−	1.01548i	−0.0239153	−	0.0414225i	−0.877735	+	0.479146i	$0.840947\pi$
$602$		0			0
$603$	15.6484			0.637253
$604$	6.78683	+	11.7551i	0.276152	+	0.478310i
$605$	6.77146			0.275299
$606$	−14.0171	−	24.2783i	−0.569406	−	0.986240i
$607$	0.316919	+	0.548920i	0.0128633	+	0.0222800i	0.872385	−	0.488819i	$-0.162572\pi$
$607$	0.316919	+	0.548920i	0.0128633	+	0.0222800i	−0.859522	+	0.511099i	$0.829239\pi$
$608$	−83.1020	−	143.937i	−3.37023	−	5.83741i
$609$		0			0
$610$	−13.2546			−0.536664
$611$	−17.3443	−	12.0561i	−0.701677	−	0.487737i
$612$	13.0070	+	22.5287i	0.525775	+	0.910669i
$613$	15.4275	−	26.7212i	0.623110	−	1.07926i	−0.365793	−	0.930696i	$-0.619202\pi$
$613$	15.4275	−	26.7212i	0.623110	−	1.07926i	0.988903	−	0.148562i	$-0.0474646\pi$
$614$	49.3823			1.99291
$615$	0.634485	−	1.09896i	0.0255849	−	0.0443143i
$616$		0			0
$617$	−16.9105	+	29.2898i	−0.680790	+	1.17916i	0.293951	+	0.955821i	$0.405030\pi$
$617$	−16.9105	+	29.2898i	−0.680790	+	1.17916i	−0.974740	+	0.223341i	$0.928304\pi$
$618$	5.25338	+	9.09911i	0.211322	+	0.366020i
$619$	−0.202399	−	0.350565i	−0.00813509	−	0.0140904i	0.861929	−	0.507029i	$-0.169256\pi$
$619$	−0.202399	−	0.350565i	−0.00813509	−	0.0140904i	−0.870064	+	0.492938i	$0.835923\pi$
$620$	−11.3282			−0.454950
$621$	−13.1761			−0.528740
$622$	−23.6480	−	40.9595i	−0.948197	−	1.64233i
$623$		0			0
$624$	62.1128	+	43.1747i	2.48650	+	1.72837i
$625$	−8.53179	+	14.7775i	−0.341272	+	0.591100i
$626$	−9.34059	+	16.1784i	−0.373325	+	0.646618i
$627$	6.76736	−	11.7214i	0.270262	−	0.468108i
$628$	−35.6169	−	61.6903i	−1.42127	−	2.46171i
$629$	−25.3316			−1.01004
$630$		0			0
$631$	−15.2254	+	26.3712i	−0.606114	+	1.04982i	0.385761	+	0.922599i	$0.373939\pi$
$631$	−15.2254	+	26.3712i	−0.606114	+	1.04982i	−0.991874	+	0.127221i	$0.959394\pi$
$632$	−43.9448	+	76.1147i	−1.74803	+	3.02768i
$633$	−22.7628			−0.904738
$634$	−34.3691	+	59.5290i	−1.36497	+	2.36420i
$635$	−4.02446			−0.159706
$636$	−34.3724			−1.36296
$637$		0			0
$638$	−1.52497			−0.0603743
$639$	5.47624			0.216637
$640$	−15.5053	+	26.8560i	−0.612903	+	1.06158i
$641$	9.64564			0.380980			0.190490	−	0.981689i	$-0.438992\pi$
$641$	9.64564			0.380980			0.190490	+	0.981689i	$0.438992\pi$
$642$	−2.78050	+	4.81597i	−0.109738	+	0.190071i
$643$	4.06648	−	7.04335i	0.160366	−	0.277763i	−0.774634	−	0.632410i	$-0.782066\pi$
$643$	4.06648	−	7.04335i	0.160366	−	0.277763i	0.935000	+	0.354647i	$0.115399\pi$
$644$		0			0
$645$	−1.76101			−0.0693395
$646$	−41.3146	−	71.5590i	−1.62550	−	2.81545i
$647$	−5.76136	+	9.97898i	−0.226503	+	0.392314i	−0.956769	−	0.290848i	$-0.906063\pi$
$647$	−5.76136	+	9.97898i	−0.226503	+	0.392314i	0.730267	+	0.683162i	$0.239396\pi$
$648$	−20.6814	+	35.8213i	−0.812443	+	1.40719i
$649$	7.49576	−	12.9830i	0.294234	−	0.509629i
$650$	39.8023	−	18.7268i	1.56118	−	0.734526i
$651$		0			0
$652$	16.6162	+	28.7801i	0.650740	+	1.12711i
$653$	42.4039			1.65939			0.829697	−	0.558215i	$-0.188513\pi$
$653$	42.4039			1.65939			0.829697	+	0.558215i	$0.188513\pi$
$654$	10.7414			0.420024
$655$	4.19527	+	7.26642i	0.163923	+	0.283922i
$656$	9.64292	+	16.7020i	0.376493	+	0.652105i
$657$	−3.45153	+	5.97823i	−0.134657	+	0.233233i
$658$		0			0
$659$	1.25044	−	2.16582i	0.0487101	−	0.0843684i	−0.840642	−	0.541591i	$-0.817822\pi$
$659$	1.25044	−	2.16582i	0.0487101	−	0.0843684i	0.889352	+	0.457222i	$0.151156\pi$
$660$	−7.61108			−0.296261
$661$	7.41968	−	12.8513i	0.288592	−	0.499856i	−0.684882	−	0.728654i	$-0.740146\pi$
$661$	7.41968	−	12.8513i	0.288592	−	0.499856i	0.973474	+	0.228798i	$0.0734795\pi$
$662$	−4.10523	−	7.11047i	−0.159554	−	0.276356i
$663$	16.7635	+	11.6523i	0.651041	+	0.452540i
$664$	113.035			4.38663
$665$		0			0
$666$	9.51710	+	16.4841i	0.368780	+	0.638746i
$667$	−0.475592	−	0.823749i	−0.0184150	−	0.0318957i
$668$	21.0924	+	36.5332i	0.816091	+	1.41351i
$669$	1.46085			0.0564797
$670$	13.9755	+	24.2062i	0.539919	+	0.935167i
$671$	8.90541			0.343790
$672$		0			0
$673$	−19.8046	−	34.3025i	−0.763410	−	1.32226i	−0.941083	−	0.338175i	$-0.890190\pi$
$673$	−19.8046	−	34.3025i	−0.763410	−	1.32226i	0.177674	−	0.984089i	$-0.443143\pi$
$674$	80.8313			3.11350
$675$	12.5660	+	21.7649i	0.483665	+	0.837733i
$676$	−70.6708	−	11.9613i	−2.71811	−	0.460048i
$677$	8.51604	−	14.7502i	0.327298	−	0.566897i	−0.654677	−	0.755909i	$-0.727195\pi$
$677$	8.51604	−	14.7502i	0.327298	−	0.566897i	0.981975	+	0.189012i	$0.0605285\pi$
$678$	23.2311	+	40.2374i	0.892183	+	1.54531i
$679$		0			0
$680$	−14.8052	+	25.6434i	−0.567755	+	0.983380i
$681$	16.6961	−	28.9185i	0.639797	−	1.10816i
$682$	10.3720			0.397163
$683$	32.8912			1.25854			0.629272	−	0.777185i	$-0.283353\pi$
$683$	32.8912			1.25854			0.629272	+	0.777185i	$0.283353\pi$
$684$	−22.7804	+	39.4568i	−0.871030	+	1.50867i
$685$	−5.17846	+	8.96936i	−0.197859	+	0.342702i
$686$		0			0
$687$	−3.22755	−	5.59028i	−0.123139	−	0.213283i
$688$	13.3819	−	23.1782i	0.510181	−	0.883659i
$689$	14.9023	−	7.01148i	0.567734	−	0.267116i
$690$	−3.23469	−	5.60265i	−0.123143	−	0.213289i
$691$	23.7922			0.905099			0.452550	−	0.891739i	$-0.350514\pi$
$691$	23.7922			0.905099			0.452550	+	0.891739i	$0.350514\pi$
$692$	−0.453377	−	0.785272i	−0.0172348	−	0.0298515i
$693$		0			0
$694$	16.4105			0.622933
$695$	−3.86507	−	6.69449i	−0.146610	−	0.253937i
$696$	−5.35804			−0.203096
$697$	2.60251	+	4.50768i	0.0985772	+	0.170741i
$698$	41.5769	+	72.0134i	1.57371	+	2.72575i
$699$	14.0240	+	24.2903i	0.530436	+	0.918742i
$700$		0			0
$701$	29.7796			1.12476			0.562380	−	0.826879i	$-0.309886\pi$
$701$	29.7796			1.12476			0.562380	+	0.826879i	$0.309886\pi$
$702$	4.67287	−	55.6102i	0.176366	−	2.09887i
$703$	−22.1829	−	38.4219i	−0.836644	−	1.44911i
$704$	21.8069	−	37.7706i	0.821878	−	1.42353i
$705$	5.92547			0.223166
$706$	39.2061	−	67.9069i	1.47554	−	2.55571i
$707$		0			0
$708$	41.3281	−	71.5824i	1.55321	−	2.69023i
$709$	−5.96518	−	10.3320i	−0.224027	−	0.388026i	0.732000	−	0.681305i	$-0.238587\pi$
$709$	−5.96518	−	10.3320i	−0.224027	−	0.388026i	−0.956027	+	0.293278i	$0.905254\pi$
$710$	4.89078	+	8.47107i	0.183548	+	0.317914i
$711$	10.3785			0.389224
$712$	−16.9600			−0.635604
$713$	3.23469	+	5.60265i	0.121140	+	0.209821i
$714$		0			0
$715$	3.29982	−	1.55255i	0.123406	−	0.0580621i
$716$	−2.11894	+	3.67011i	−0.0791885	+	0.137159i
$717$	4.26821	−	7.39275i	0.159399	−	0.276087i
$718$	32.1553	−	55.6946i	1.20002	−	2.07850i
$719$	16.1819	+	28.0279i	0.603484	+	1.04526i	0.992289	+	0.123945i	$0.0395545\pi$
$719$	16.1819	+	28.0279i	0.603484	+	1.04526i	−0.388805	+	0.921320i	$0.627112\pi$
$720$	12.9556			0.482827
$721$		0			0
$722$	46.3182	−	80.2255i	1.72379	−	2.98568i
$723$	8.28746	−	14.3543i	0.308214	−	0.533842i
$724$	54.7026			2.03301
$725$	−0.907137	+	1.57121i	−0.0336902	+	0.0583532i
$726$	−34.1833			−1.26866
$727$	31.4897			1.16789			0.583943	−	0.811794i	$-0.301509\pi$
$727$	31.4897			1.16789			0.583943	+	0.811794i	$0.301509\pi$
$728$		0			0
$729$	28.0042			1.03719
$730$	−12.3301			−0.456359
$731$	3.61162	−	6.25551i	0.133581	−	0.231369i
$732$	49.1003			1.81480
$733$	1.33112	−	2.30557i	0.0491661	−	0.0851581i	−0.840395	−	0.541974i	$-0.817677\pi$
$733$	1.33112	−	2.30557i	0.0491661	−	0.0851581i	0.889561	+	0.456816i	$0.151010\pi$
$734$	−50.0517	+	86.6921i	−1.84744	+	3.19986i
$735$		0			0
$736$	53.3755			1.96745
$737$	−9.38973	−	16.2635i	−0.345875	−	0.599073i
$738$	1.95553	−	3.38708i	0.0719840	−	0.124680i
$739$	17.7914	−	30.8156i	0.654467	−	1.13357i	−0.327560	−	0.944830i	$-0.606226\pi$
$739$	17.7914	−	30.8156i	0.654467	−	1.13357i	0.982027	−	0.188739i	$-0.0604402\pi$
$740$	−12.4743	+	21.6061i	−0.458564	+	0.794256i
$741$	−2.99397	+	35.6302i	−0.109986	+	1.30891i
$742$		0			0
$743$	−12.1203	−	20.9929i	−0.444650	−	0.770156i	0.553378	−	0.832930i	$-0.313339\pi$
$743$	−12.1203	−	20.9929i	−0.444650	−	0.770156i	−0.998028	+	0.0627740i	$0.980005\pi$
$744$	36.4422			1.33604
$745$	−6.05044			−0.221671
$746$	−17.8853	−	30.9783i	−0.654828	−	1.13419i
$747$	−6.67393	−	11.5596i	−0.244186	−	0.422943i
$748$	15.6095	−	27.0364i	0.570739	−	0.988549i
$749$		0			0
$750$	−13.1009	+	22.6915i	−0.478378	+	0.828575i
$751$	−29.1410			−1.06337			−0.531684	−	0.846943i	$-0.678441\pi$
$751$	−29.1410			−1.06337			−0.531684	+	0.846943i	$0.678441\pi$
$752$	−45.0277	+	77.9903i	−1.64199	+	2.84401i
$753$	4.30900	+	7.46340i	0.157029	+	0.271981i
$754$	3.64532	−	1.71511i	0.132755	−	0.0624605i
$755$	1.82446			0.0663988
$756$		0			0
$757$	2.49495	+	4.32138i	0.0906805	+	0.157063i	0.907798	−	0.419408i	$-0.137762\pi$
$757$	2.49495	+	4.32138i	0.0906805	+	0.157063i	−0.817117	+	0.576472i	$0.804429\pi$
$758$	41.9436	+	72.6485i	1.52346	+	2.63871i
$759$	2.17330	+	3.76426i	0.0788858	+	0.136634i
$760$	−51.8598			−1.88115
$761$	−5.91858	−	10.2513i	−0.214548	−	0.371609i	0.738584	−	0.674161i	$-0.235495\pi$
$761$	−5.91858	−	10.2513i	−0.214548	−	0.371609i	−0.953133	+	0.302552i	$0.902161\pi$
$762$	20.3160			0.735971
$763$		0			0
$764$	−27.2835	−	47.2564i	−0.987083	−	1.70968i
$765$	3.49657			0.126419
$766$	6.69643	+	11.5986i	0.241952	+	0.419073i
$767$	−3.31622	+	39.4652i	−0.119742	+	1.42501i
$768$	34.6593	−	60.0316i	1.25066	−	2.16621i
$769$	−17.9092	−	31.0196i	−0.645821	−	1.11859i	−0.984111	−	0.177553i	$-0.943182\pi$
$769$	−17.9092	−	31.0196i	−0.645821	−	1.11859i	0.338291	−	0.941042i	$-0.390151\pi$
$770$		0			0
$771$	−16.6209	+	28.7883i	−0.598588	+	1.03678i
$772$	−23.9859	+	41.5448i	−0.863272	+	1.49523i
$773$	19.9534			0.717673			0.358837	−	0.933400i	$-0.383174\pi$
$773$	19.9534			0.717673			0.358837	+	0.933400i	$0.383174\pi$
$774$	−5.42755			−0.195089
$775$	6.16980	−	10.6864i	0.221626	−	0.383867i
$776$	−45.9095	+	79.5176i	−1.64805	+	2.85451i
$777$		0			0
$778$	−2.54133	−	4.40171i	−0.0911110	−	0.157809i
$779$	−4.55804	+	7.89476i	−0.163309	+	0.282859i
$780$	18.1937	−	8.56003i	0.651437	−	0.306498i
$781$	−3.28598	−	5.69148i	−0.117582	−	0.203657i
$782$	26.5359			0.948923
$783$	1.15086	+	1.99335i	0.0411285	+	0.0712367i
$784$		0			0
$785$	−9.57464			−0.341734
$786$	−21.1783	−	36.6819i	−0.755404	−	1.30840i
$787$	−2.79619			−0.0996733			−0.0498367	−	0.998757i	$-0.515870\pi$
$787$	−2.79619			−0.0996733			−0.0498367	+	0.998757i	$0.515870\pi$
$788$	71.7271	+	124.235i	2.55517	+	4.42569i
$789$	−6.53687	−	11.3222i	−0.232719	−	0.403081i
$790$	9.26895	+	16.0543i	0.329774	+	0.571186i
$791$		0			0
$792$	−14.9487			−0.531179
$793$	−21.2876	+	10.0157i	−0.755946	+	0.355669i
$794$	−29.4850	−	51.0695i	−1.04638	−	1.81239i
$795$	−2.31003	+	4.00108i	−0.0819282	+	0.141904i
$796$	−55.8684			−1.98020
$797$	0.842809	−	1.45979i	0.0298538	−	0.0517083i	−0.850712	−	0.525631i	$-0.823829\pi$
$797$	0.842809	−	1.45979i	0.0298538	−	0.0517083i	0.880566	+	0.473923i	$0.157162\pi$
$798$		0			0
$799$	−12.1525	+	21.0487i	−0.429923	+	0.744649i
$800$	−50.9039	−	88.1681i	−1.79972	−	3.11721i
$801$	1.00137	+	1.73442i	0.0353816	+	0.0612827i
$802$	39.9247			1.40979
$803$	8.28428			0.292346
$804$	−51.7705	−	89.6692i	−1.82581	−	3.16239i
$805$		0			0
$806$	−24.7933	+	11.6651i	−0.873307	+	0.410887i
$807$	−20.0622	+	34.7487i	−0.706222	+	1.22321i
$808$	36.0850	−	62.5010i	1.26947	−	2.19878i
$809$	21.7186	−	37.6177i	0.763585	−	1.32257i	−0.177407	−	0.984138i	$-0.556771\pi$
$809$	21.7186	−	37.6177i	0.763585	−	1.32257i	0.940992	−	0.338430i	$-0.109896\pi$
$810$	4.36217	+	7.55551i	0.153271	+	0.265473i
$811$	−5.60812			−0.196928			−0.0984639	−	0.995141i	$-0.531393\pi$
$811$	−5.60812			−0.196928			−0.0984639	+	0.995141i	$0.531393\pi$
$812$		0			0
$813$	0.204986	−	0.355045i	0.00718916	−	0.0124520i
$814$	11.4213	−	19.7823i	0.400318	−	0.693371i
$815$	4.46681			0.156466
$816$	43.5199	−	75.3786i	1.52350	−	2.63878i
$817$	12.6508			0.442595
$818$	−60.6574			−2.12084
$819$		0			0
$820$	5.12632			0.179019
$821$	−23.9448			−0.835678			−0.417839	−	0.908521i	$-0.637212\pi$
$821$	−23.9448			−0.835678			−0.417839	+	0.908521i	$0.637212\pi$
$822$	26.1416	−	45.2785i	0.911792	−	1.57927i
$823$	35.4117			1.23437			0.617187	−	0.786817i	$-0.288272\pi$
$823$	35.4117			1.23437			0.617187	+	0.786817i	$0.288272\pi$
$824$	−13.5241	+	23.4244i	−0.471133	+	0.816026i
$825$	4.14532	−	7.17991i	0.144322	−	0.249972i
$826$		0			0
$827$	−16.1563			−0.561811			−0.280905	−	0.959735i	$-0.590635\pi$
$827$	−16.1563			−0.561811			−0.280905	+	0.959735i	$0.590635\pi$
$828$	−7.31580	−	12.6713i	−0.254242	−	0.440359i
$829$	−26.3505	+	45.6404i	−0.915190	+	1.58516i	−0.108568	+	0.994089i	$0.534626\pi$
$829$	−26.3505	+	45.6404i	−0.915190	+	1.58516i	−0.806623	+	0.591067i	$0.798707\pi$
$830$	11.9208	−	20.6475i	0.413779	−	0.716686i
$831$	−22.3632	+	38.7343i	−0.775772	+	1.34368i
$832$	−9.64766	+	114.813i	−0.334472	+	3.98044i
$833$		0			0
$834$	19.5114	+	33.7947i	0.675624	+	1.17021i
$835$	5.67013			0.196223
$836$	54.6769			1.89104
$837$	−7.82749	−	13.5576i	−0.270558	−	0.468619i
$838$	−4.62681	−	8.01388i	−0.159831	−	0.276835i
$839$	−11.2169	+	19.4283i	−0.387251	+	0.670738i	−0.992079	−	0.125618i	$-0.959909\pi$
$839$	−11.2169	+	19.4283i	−0.387251	+	0.670738i	0.604828	+	0.796356i	$0.293242\pi$
$840$		0			0
$841$	14.4169	−	24.9708i	0.497135	−	0.861063i
$842$	68.8288			2.37200
$843$	2.93083	−	5.07634i	0.100943	−	0.174838i
$844$	−45.9779	−	79.6361i	−1.58263	−	2.74119i
$845$	−6.14182	+	7.42248i	−0.211285	+	0.255341i
$846$	18.2627			0.627886
$847$		0			0
$848$	−35.1079	−	60.8086i	−1.20561	−	2.08818i
$849$	14.3990	+	24.9398i	0.494173	+	0.855933i
$850$	−25.3071	−	43.8333i	−0.868028	−	1.50347i
$851$	14.2478			0.488409
$852$	−18.1173	−	31.3802i	−0.620690	−	1.07507i
$853$	−30.8521			−1.05635			−0.528177	−	0.849134i	$-0.677124\pi$
$853$	−30.8521			−1.05635			−0.528177	+	0.849134i	$0.677124\pi$
$854$		0			0
$855$	3.06195	+	5.30345i	0.104716	+	0.181374i
$856$	−14.3160			−0.489311
$857$	13.3700	+	23.1575i	0.456710	+	0.791045i	0.998785	−	0.0492854i	$-0.0156944\pi$
$857$	13.3700	+	23.1575i	0.456710	+	0.791045i	−0.542075	+	0.840330i	$0.682361\pi$
$858$	−16.6579	+	7.83748i	−0.568693	+	0.267567i
$859$	−2.57902	+	4.46699i	−0.0879950	+	0.152412i	−0.906664	−	0.421855i	$-0.861379\pi$
$859$	−2.57902	+	4.46699i	−0.0879950	+	0.152412i	0.818669	+	0.574266i	$0.194713\pi$
$860$	−3.55701	−	6.16092i	−0.121293	−	0.210086i
$861$		0			0
$862$	14.7948	−	25.6253i	0.503912	−	0.872801i
$863$	−4.08407	+	7.07382i	−0.139023	+	0.240796i	−0.927127	−	0.374747i	$-0.877730\pi$
$863$	−4.08407	+	7.07382i	−0.139023	+	0.240796i	0.788104	+	0.615542i	$0.211063\pi$
$864$	−129.161			−4.39415
$865$	−0.121878			−0.00414398
$866$	19.8978	−	34.4640i	0.676154	−	1.17113i
$867$	0.144536	−	0.250344i	0.00490871	−	0.00850214i
$868$		0			0
$869$	−6.22755	−	10.7864i	−0.211255	−	0.365905i
$870$	−0.565065	+	0.978722i	−0.0191575	+	0.0331818i
$871$	40.7366	+	28.3161i	1.38031	+	0.959453i
$872$	13.8261	+	23.9476i	0.468212	+	0.810968i
$873$	10.8425			0.366963
$874$	23.2375	+	40.2486i	0.786021	+	1.36143i
$875$		0			0
$876$	45.6756			1.54324
$877$	−7.80922	−	13.5260i	−0.263699	−	0.456740i	0.703523	−	0.710672i	$-0.251609\pi$
$877$	−7.80922	−	13.5260i	−0.263699	−	0.456740i	−0.967222	+	0.253933i	$0.918276\pi$
$878$	−39.5562			−1.33496
$879$	−12.1222	−	20.9963i	−0.408872	−	0.708187i
$880$	−7.77393	−	13.4648i	−0.262059	−	0.453900i
$881$	−23.2188	−	40.2161i	−0.782260	−	1.35491i	−0.930622	−	0.365981i	$-0.880734\pi$
$881$	−23.2188	−	40.2161i	−0.782260	−	1.35491i	0.148362	−	0.988933i	$-0.452600\pi$
$882$		0			0
$883$	15.6588			0.526960			0.263480	−	0.964665i	$-0.415130\pi$
$883$	15.6588			0.526960			0.263480	+	0.964665i	$0.415130\pi$
$884$	−6.90584	+	82.1839i	−0.232268	+	2.76414i
$885$	−5.55497	−	9.62149i	−0.186728	−	0.323423i
$886$	−41.4493	+	71.7923i	−1.39252	+	2.41191i
$887$	−31.5107			−1.05803			−0.529013	−	0.848614i	$-0.677438\pi$
$887$	−31.5107			−1.05803			−0.529013	+	0.848614i	$0.677438\pi$
$888$	40.1292	−	69.5059i	1.34665	−	2.33246i
$889$		0			0
$890$	−1.78862	+	3.09799i	−0.0599548	+	0.103845i
$891$	−2.93083	−	5.07634i	−0.0981864	−	0.170064i
$892$	2.95073	+	5.11082i	0.0987978	+	0.171123i
$893$	−42.5677			−1.42447
$894$	30.5434			1.02152
$895$	0.284810	+	0.493305i	0.00952015	+	0.0164894i
$896$		0			0
$897$	−9.42868	−	6.55389i	−0.314815	−	0.218828i
$898$	42.8651	−	74.2445i	1.43043	−	2.47757i
$899$	0.565065	−	0.978722i	0.0188460	−	0.0326422i
$900$	−13.9541	+	24.1691i	−0.465135	+	0.805638i
$901$	−9.47521	−	16.4115i	−0.315665	−	0.546748i
$902$	−4.69361			−0.156280
$903$		0			0
$904$	−59.8050	+	103.585i	−1.98908	+	3.44520i
$905$	3.67633	−	6.36759i	0.122205	−	0.211666i
$906$	−9.21010			−0.305985
$907$	0.373996	−	0.647780i	0.0124183	−	0.0215092i	−0.859749	−	0.510716i	$-0.829380\pi$
$907$	0.373996	−	0.647780i	0.0124183	−	0.0215092i	0.872168	+	0.489207i	$0.162714\pi$
$908$	134.896			4.47669
$909$	−8.52224			−0.282665
$910$		0			0
$911$	24.9000			0.824973			0.412486	−	0.910964i	$-0.364660\pi$
$911$	24.9000			0.824973			0.412486	+	0.910964i	$0.364660\pi$
$912$	152.441			5.04784
$913$	−8.00929	+	13.8725i	−0.265069	+	0.459113i
$914$	−56.5941			−1.87197
$915$	3.29982	−	5.71546i	0.109089	−	0.188947i
$916$	13.0385	−	22.5834i	0.430804	−	0.746175i
$917$		0			0
$918$	−64.2132			−2.11935
$919$	−0.293247	−	0.507919i	−0.00967334	−	0.0167547i	0.861148	−	0.508354i	$-0.169746\pi$
$919$	−0.293247	−	0.507919i	−0.00967334	−	0.0167547i	−0.870822	+	0.491599i	$0.836412\pi$
$920$	8.32724	−	14.4232i	0.274541	−	0.475519i
$921$	−12.2940	+	21.2939i	−0.405102	+	0.701658i
$922$	−37.4104	+	64.7967i	−1.23205	+	2.13397i
$923$	14.2560	+	9.90934i	0.469240	+	0.326170i
$924$		0			0
$925$	−13.5881	−	23.5352i	−0.446773	−	0.773833i
$926$	−15.5139			−0.509818
$927$	3.19399			0.104905
$928$	−4.66206	−	8.07493i	−0.153040	−	0.265073i
$929$	−25.0975	−	43.4701i	−0.823421	−	1.42621i	−0.903120	−	0.429388i	$-0.858729\pi$
$929$	−25.0975	−	43.4701i	−0.823421	−	1.42621i	0.0796986	−	0.996819i	$-0.474604\pi$
$930$	3.84324	−	6.65668i	0.126025	−	0.218281i
$931$		0			0
$932$	−56.6534	+	98.1266i	−1.85574	+	3.21424i
$933$	23.5493			0.770968
$934$	−57.8567	+	100.211i	−1.89313	+	3.27900i
$935$	−2.09809	−	3.63400i	−0.0686150	−	0.118845i
$936$	35.7336	−	16.8125i	1.16799	−	0.549534i
$937$	−22.7130			−0.742003			−0.371001	−	0.928632i	$-0.620985\pi$
$937$	−22.7130			−0.742003			−0.371001	+	0.928632i	$0.620985\pi$
$938$		0			0
$939$	−4.65080	−	8.05542i	−0.151773	−	0.262879i
$940$	11.9687	+	20.7304i	0.390376	+	0.676151i
$941$	−24.9367	−	43.1916i	−0.812914	−	1.40801i	−0.910816	−	0.412812i	$-0.864547\pi$
$941$	−24.9367	−	43.1916i	−0.812914	−	1.40801i	0.0979030	−	0.995196i	$-0.468787\pi$
$942$	48.3341			1.57481
$943$	−1.46379	−	2.53536i	−0.0476675	−	0.0825626i
$944$	168.849			5.49558
$945$		0			0
$946$	3.25677	+	5.64088i	0.105887	+	0.183401i
$947$	0.266414			0.00865731			0.00432865	−	0.999991i	$-0.498622\pi$
$947$	0.266414			0.00865731			0.00432865	+	0.999991i	$0.498622\pi$
$948$	−34.3358	−	59.4713i	−1.11517	−	1.93154i
$949$	−19.8029	+	9.31716i	−0.642828	+	0.302448i
$950$	44.3229	−	76.7696i	1.43803	−	2.49073i
$951$	−17.1128	−	29.6402i	−0.554920	−	0.961150i
$952$		0			0
$953$	−3.91014	+	6.77257i	−0.126662	+	0.219385i	−0.922381	−	0.386281i	$-0.873760\pi$
$953$	−3.91014	+	6.77257i	−0.126662	+	0.219385i	0.795719	+	0.605665i	$0.207093\pi$
$954$	−7.11968	+	12.3316i	−0.230508	+	0.399252i
$955$	−7.33444			−0.237337
$956$	34.4850			1.11532
$957$	0.379652	−	0.657576i	0.0122724	−	0.0212564i
$958$	−44.5859	+	77.2251i	−1.44051	+	2.49503i
$959$		0			0
$960$	−16.1607	−	27.9911i	−0.521584	−	0.903410i
$961$	11.6568	−	20.1901i	0.376025	−	0.651294i
$962$	−5.05295	+	60.1334i	−0.162914	+	1.93878i
$963$	0.845257	+	1.46403i	0.0272380	+	0.0471776i
$964$	66.9585			2.15659
$965$	3.22398	+	5.58410i	0.103784	+	0.179759i
$966$		0			0
$967$	39.8224			1.28060			0.640301	−	0.768124i	$-0.278810\pi$
$967$	39.8224			1.28060			0.640301	+	0.768124i	$0.278810\pi$
$968$	−43.9999	−	76.2101i	−1.41421	−	2.44949i
$969$	41.1422			1.32168
$970$	9.68333	+	16.7720i	0.310913	+	0.538517i
$971$	−22.9648	−	39.7761i	−0.736974	−	1.27648i	−0.953852	−	0.300278i	$-0.902921\pi$
$971$	−22.9648	−	39.7761i	−0.736974	−	1.27648i	0.216878	−	0.976199i	$-0.430413\pi$
$972$	30.5401	+	52.8969i	0.979573	+	1.69667i
$973$		0			0
$974$	−73.6208			−2.35896
$975$	−1.83394	+	21.8251i	−0.0587332	+	0.698964i
$976$	50.1508	+	86.8637i	1.60529	+	2.78044i
$977$	14.3314	−	24.8227i	0.458501	−	0.794147i	−0.540381	−	0.841420i	$-0.681720\pi$
$977$	14.3314	−	24.8227i	0.458501	−	0.794147i	0.998882	+	0.0472734i	$0.0150532\pi$
$978$	−22.5491			−0.721040
$979$	1.20173	−	2.08145i	0.0384074	−	0.0665235i
$980$		0			0
$981$	1.63267	−	2.82787i	0.0521271	−	0.0902868i
$982$	59.8760	+	103.708i	1.91072	+	3.30946i
$983$	−23.0600	−	39.9411i	−0.735500	−	1.27392i	−0.954503	−	0.298200i	$-0.903614\pi$
$983$	−23.0600	−	39.9411i	−0.735500	−	1.27392i	0.219003	−	0.975724i	$-0.429720\pi$
$984$	−16.4911			−0.525718
$985$	19.2819			0.614372
$986$	−2.31777	−	4.01449i	−0.0738128	−	0.127848i
$987$		0			0
$988$	−130.700	+	61.4940i	−4.15814	+	1.95638i
$989$	−2.03137	+	3.51843i	−0.0645937	+	0.111880i
$990$	−1.57651	+	2.73059i	−0.0501047	+	0.0867839i
$991$	−18.9124	+	32.7573i	−0.600773	+	1.04057i	0.391931	+	0.919995i	$0.371807\pi$
$991$	−18.9124	+	32.7573i	−0.600773	+	1.04057i	−0.992704	+	0.120575i	$0.961526\pi$
$992$	31.7086	+	54.9208i	1.00675	+	1.74374i
$993$	4.08809			0.129732
$994$		0			0
$995$	−3.75468	+	6.50329i	−0.119031	+	0.206168i
$996$	−44.1595	+	76.4864i	−1.39925	+	2.42357i
$997$	−38.3748			−1.21534			−0.607671	−	0.794189i	$-0.707896\pi$
$997$	−38.3748			−1.21534			−0.607671	+	0.794189i	$0.707896\pi$
$998$	−24.8095	+	42.9713i	−0.785330	+	1.36023i
$999$	−34.4777			−1.09083

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.h.i.471.1		8
7.2	even	3		637.2.f.i.393.4		8
7.3	odd	6		637.2.g.k.263.4		8
7.4	even	3		637.2.g.j.263.4		8
7.5	odd	6		91.2.f.c.29.4	yes	8
7.6	odd	2		637.2.h.h.471.1		8
13.9	even	3		637.2.g.j.373.4		8
21.5	even	6		819.2.o.h.757.1		8
28.19	even	6		1456.2.s.q.1121.3		8
91.9	even	3		637.2.f.i.295.4		8
91.16	even	3		8281.2.a.bp.1.1		4
91.23	even	6		8281.2.a.bt.1.4		4
91.48	odd	6		637.2.g.k.373.4		8
91.54	even	12		1183.2.c.g.337.8		8
91.61	odd	6		91.2.f.c.22.4	✓	8
91.68	odd	6		1183.2.a.k.1.1		4
91.74	even	3	inner	637.2.h.i.165.1		8
91.75	odd	6		1183.2.a.l.1.4		4
91.87	odd	6		637.2.h.h.165.1		8
91.89	even	12		1183.2.c.g.337.1		8
273.152	even	6		819.2.o.h.568.1		8
364.243	even	6		1456.2.s.q.113.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.f.c.22.4	✓	8	91.61	odd	6
91.2.f.c.29.4	yes	8	7.5	odd	6
637.2.f.i.295.4		8	91.9	even	3
637.2.f.i.393.4		8	7.2	even	3
637.2.g.j.263.4		8	7.4	even	3
637.2.g.j.373.4		8	13.9	even	3
637.2.g.k.263.4		8	7.3	odd	6
637.2.g.k.373.4		8	91.48	odd	6
637.2.h.h.165.1		8	91.87	odd	6
637.2.h.h.471.1		8	7.6	odd	2
637.2.h.i.165.1		8	91.74	even	3	inner
637.2.h.i.471.1		8	1.1	even	1	trivial
819.2.o.h.568.1		8	273.152	even	6
819.2.o.h.757.1		8	21.5	even	6
1183.2.a.k.1.1		4	91.68	odd	6
1183.2.a.l.1.4		4	91.75	odd	6
1183.2.c.g.337.1		8	91.89	even	12
1183.2.c.g.337.8		8	91.54	even	12
1456.2.s.q.113.3		8	364.243	even	6
1456.2.s.q.1121.3		8	28.19	even	6
8281.2.a.bp.1.1		4	91.16	even	3
8281.2.a.bt.1.4		4	91.23	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)

\(f(q)\)	\(=\)	\(q-2.74108 q^{2} +(0.682410 - 1.18197i) q^{3} +5.51353 q^{4} +(0.370541 - 0.641796i) q^{5} +(-1.87054 + 3.23987i) q^{6} -9.63087 q^{8} +(0.568634 + 0.984903i) q^{9} +O(q^{10})\)	\(q-2.74108 q^{2} +(0.682410 - 1.18197i) q^{3} +5.51353 q^{4} +(0.370541 - 0.641796i) q^{5} +(-1.87054 + 3.23987i) q^{6} -9.63087 q^{8} +(0.568634 + 0.984903i) q^{9} +(-1.01568 + 1.75921i) q^{10} +(0.682410 - 1.18197i) q^{11} +(3.76249 - 6.51682i) q^{12} +(-0.301907 + 3.59289i) q^{13} +(-0.505722 - 0.875935i) q^{15} +15.3720 q^{16} +4.14871 q^{17} +(-1.55867 - 2.69970i) q^{18} +(3.63303 + 6.29259i) q^{19} +(2.04299 - 3.53856i) q^{20} +(-1.87054 + 3.23987i) q^{22} -2.33345 q^{23} +(-6.57220 + 11.3834i) q^{24} +(2.22540 + 3.85450i) q^{25} +(0.827552 - 9.84840i) q^{26} +5.64662 q^{27} +(0.203815 + 0.353017i) q^{29} +(1.38622 + 2.40101i) q^{30} +(-1.38622 - 2.40101i) q^{31} -22.8740 q^{32} +(-0.931366 - 1.61317i) q^{33} -11.3720 q^{34} +(3.13518 + 5.43029i) q^{36} -6.10590 q^{37} +(-9.95843 - 17.2485i) q^{38} +(4.04066 + 2.80867i) q^{39} +(-3.56863 + 6.18106i) q^{40} +(0.627306 + 1.08653i) q^{41} +(0.870541 - 1.50782i) q^{43} +(3.76249 - 6.51682i) q^{44} +0.842809 q^{45} +6.39619 q^{46} +(-2.92921 + 5.07355i) q^{47} +(10.4900 - 18.1692i) q^{48} +(-6.10000 - 10.5655i) q^{50} +(2.83112 - 4.90364i) q^{51} +(-1.66457 + 19.8095i) q^{52} +(-2.28389 - 3.95582i) q^{53} -15.4779 q^{54} +(-0.505722 - 0.875935i) q^{55} +9.91685 q^{57} +(-0.558672 - 0.967649i) q^{58} +10.9843 q^{59} +(-2.78831 - 4.82950i) q^{60} +(3.26249 + 5.65079i) q^{61} +(3.79975 + 6.58137i) q^{62} +31.9557 q^{64} +(2.19403 + 1.52508i) q^{65} +(2.55295 + 4.42184i) q^{66} +(6.87983 - 11.9162i) q^{67} +22.8740 q^{68} +(-1.59237 + 2.75807i) q^{69} +(2.40763 - 4.17014i) q^{71} +(-5.47644 - 9.48548i) q^{72} +(3.03494 + 5.25666i) q^{73} +16.7368 q^{74} +6.07453 q^{75} +(20.0308 + 34.6944i) q^{76} +(-11.0758 - 7.69879i) q^{78} +(4.56291 - 7.90320i) q^{79} +(5.69594 - 9.86566i) q^{80} +(2.14741 - 3.71942i) q^{81} +(-1.71950 - 2.97826i) q^{82} -11.7368 q^{83} +(1.53727 - 2.66263i) q^{85} +(-2.38622 + 4.13306i) q^{86} +0.556340 q^{87} +(-6.57220 + 11.3834i) q^{88} +1.76101 q^{89} -2.31021 q^{90} -12.8656 q^{92} -3.78389 q^{93} +(8.02921 - 13.9070i) q^{94} +5.38474 q^{95} +(-15.6095 + 27.0364i) q^{96} +(4.76691 - 8.25652i) q^{97} +1.55217 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + q^{3} + 10 q^{4} - 7 q^{5} - 5 q^{6} - 12 q^{8} - 7 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 + q^3 + 10 * q^4 - 7 * q^5 - 5 * q^6 - 12 * q^8 - 7 * q^9	\( 8 q - 2 q^{2} + q^{3} + 10 q^{4} - 7 q^{5} - 5 q^{6} - 12 q^{8} - 7 q^{9} - 11 q^{10} + q^{11} + 12 q^{12} - 4 q^{13} - 3 q^{15} + 38 q^{16} + 8 q^{17} + 3 q^{18} + q^{19} - 2 q^{20} - 5 q^{22} - 4 q^{23} - 3 q^{24} - 5 q^{25} + 15 q^{26} + 52 q^{27} - q^{29} + 4 q^{30} - 4 q^{31} - 66 q^{32} - 19 q^{33} - 6 q^{34} + 34 q^{36} - 20 q^{37} - 23 q^{38} - q^{39} - 17 q^{40} - 22 q^{41} - 3 q^{43} + 12 q^{44} + 22 q^{45} + 48 q^{46} + 2 q^{47} + 11 q^{48} - 43 q^{50} - 7 q^{51} + 31 q^{52} - 2 q^{53} - 10 q^{54} - 3 q^{55} - 34 q^{57} + 11 q^{58} + 16 q^{59} + 11 q^{60} + 8 q^{61} - 5 q^{62} + 28 q^{64} - 11 q^{65} + 6 q^{66} + 6 q^{67} + 66 q^{68} - 18 q^{69} + 14 q^{71} - 5 q^{72} - 8 q^{73} + 40 q^{74} + 14 q^{75} + 32 q^{76} - q^{78} + 26 q^{79} + 7 q^{80} - 24 q^{81} - 14 q^{82} - 5 q^{85} - 12 q^{86} - 26 q^{87} - 3 q^{88} + 2 q^{89} - 52 q^{90} + 24 q^{92} - 14 q^{93} + 33 q^{94} + 42 q^{95} - 58 q^{96} + 3 q^{97} + 46 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + q^3 + 10 * q^4 - 7 * q^5 - 5 * q^6 - 12 * q^8 - 7 * q^9 - 11 * q^10 + q^11 + 12 * q^12 - 4 * q^13 - 3 * q^15 + 38 * q^16 + 8 * q^17 + 3 * q^18 + q^19 - 2 * q^20 - 5 * q^22 - 4 * q^23 - 3 * q^24 - 5 * q^25 + 15 * q^26 + 52 * q^27 - q^29 + 4 * q^30 - 4 * q^31 - 66 * q^32 - 19 * q^33 - 6 * q^34 + 34 * q^36 - 20 * q^37 - 23 * q^38 - q^39 - 17 * q^40 - 22 * q^41 - 3 * q^43 + 12 * q^44 + 22 * q^45 + 48 * q^46 + 2 * q^47 + 11 * q^48 - 43 * q^50 - 7 * q^51 + 31 * q^52 - 2 * q^53 - 10 * q^54 - 3 * q^55 - 34 * q^57 + 11 * q^58 + 16 * q^59 + 11 * q^60 + 8 * q^61 - 5 * q^62 + 28 * q^64 - 11 * q^65 + 6 * q^66 + 6 * q^67 + 66 * q^68 - 18 * q^69 + 14 * q^71 - 5 * q^72 - 8 * q^73 + 40 * q^74 + 14 * q^75 + 32 * q^76 - q^78 + 26 * q^79 + 7 * q^80 - 24 * q^81 - 14 * q^82 - 5 * q^85 - 12 * q^86 - 26 * q^87 - 3 * q^88 + 2 * q^89 - 52 * q^90 + 24 * q^92 - 14 * q^93 + 33 * q^94 + 42 * q^95 - 58 * q^96 + 3 * q^97 + 46 * q^99

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