LMFDB - Embedded newform 637.2.g.d.263.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([4, 2]))

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

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

chi := DirichletCharacter("637.263");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			263.2
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	637.263
Dual form			637.2.g.d.373.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 1.50000i) q^{2} +0.732051 q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 - 1.50000i) q^{5} +(0.633975 - 1.09808i) q^{6} +1.73205 q^{8} -2.46410 q^{9} +O(q^{10})$	\(q+(0.866025 - 1.50000i) q^{2} +0.732051 q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 - 1.50000i) q^{5} +(0.633975 - 1.09808i) q^{6} +1.73205 q^{8} -2.46410 q^{9} -3.00000 q^{10} +4.73205 q^{11} +(-0.366025 - 0.633975i) q^{12} +(1.59808 - 3.23205i) q^{13} +(-0.633975 - 1.09808i) q^{15} +(2.50000 - 4.33013i) q^{16} +(-2.13397 - 3.69615i) q^{17} +(-2.13397 + 3.69615i) q^{18} -2.00000 q^{19} +(-0.866025 + 1.50000i) q^{20} +(4.09808 - 7.09808i) q^{22} +(-0.633975 + 1.09808i) q^{23} +1.26795 q^{24} +(1.00000 - 1.73205i) q^{25} +(-3.46410 - 5.19615i) q^{26} -4.00000 q^{27} +(1.50000 + 2.59808i) q^{29} -2.19615 q^{30} +(-3.09808 + 5.36603i) q^{31} +(-2.59808 - 4.50000i) q^{32} +3.46410 q^{33} -7.39230 q^{34} +(1.23205 + 2.13397i) q^{36} +(3.50000 - 6.06218i) q^{37} +(-1.73205 + 3.00000i) q^{38} +(1.16987 - 2.36603i) q^{39} +(-1.50000 - 2.59808i) q^{40} +(2.59808 + 4.50000i) q^{41} +(-5.09808 + 8.83013i) q^{43} +(-2.36603 - 4.09808i) q^{44} +(2.13397 + 3.69615i) q^{45} +(1.09808 + 1.90192i) q^{46} +(-0.464102 - 0.803848i) q^{47} +(1.83013 - 3.16987i) q^{48} +(-1.73205 - 3.00000i) q^{50} +(-1.56218 - 2.70577i) q^{51} +(-3.59808 + 0.232051i) q^{52} +(-1.96410 + 3.40192i) q^{53} +(-3.46410 + 6.00000i) q^{54} +(-4.09808 - 7.09808i) q^{55} -1.46410 q^{57} +5.19615 q^{58} +(5.36603 + 9.29423i) q^{59} +(-0.633975 + 1.09808i) q^{60} +15.1962 q^{61} +(5.36603 + 9.29423i) q^{62} +1.00000 q^{64} +(-6.23205 + 0.401924i) q^{65} +(3.00000 - 5.19615i) q^{66} +4.19615 q^{67} +(-2.13397 + 3.69615i) q^{68} +(-0.464102 + 0.803848i) q^{69} +(-3.00000 + 5.19615i) q^{71} -4.26795 q^{72} +(3.59808 - 6.23205i) q^{73} +(-6.06218 - 10.5000i) q^{74} +(0.732051 - 1.26795i) q^{75} +(1.00000 + 1.73205i) q^{76} +(-2.53590 - 3.80385i) q^{78} +(-2.90192 - 5.02628i) q^{79} -8.66025 q^{80} +4.46410 q^{81} +9.00000 q^{82} -8.19615 q^{83} +(-3.69615 + 6.40192i) q^{85} +(8.83013 + 15.2942i) q^{86} +(1.09808 + 1.90192i) q^{87} +8.19615 q^{88} +(-0.464102 + 0.803848i) q^{89} +7.39230 q^{90} +1.26795 q^{92} +(-2.26795 + 3.92820i) q^{93} -1.60770 q^{94} +(1.73205 + 3.00000i) q^{95} +(-1.90192 - 3.29423i) q^{96} +(-7.19615 + 12.4641i) q^{97} -11.6603 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{3} - 2 q^{4} + 6 q^{6} + 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^3 - 2 * q^4 + 6 * q^6 + 4 * q^9	$ 4 q - 4 q^{3} - 2 q^{4} + 6 q^{6} + 4 q^{9} - 12 q^{10} + 12 q^{11} + 2 q^{12} - 4 q^{13} - 6 q^{15} + 10 q^{16} - 12 q^{17} - 12 q^{18} - 8 q^{19} + 6 q^{22} - 6 q^{23} + 12 q^{24} + 4 q^{25} - 16 q^{27} + 6 q^{29} + 12 q^{30} - 2 q^{31} + 12 q^{34} - 2 q^{36} + 14 q^{37} + 22 q^{39} - 6 q^{40} - 10 q^{43} - 6 q^{44} + 12 q^{45} - 6 q^{46} + 12 q^{47} - 10 q^{48} + 18 q^{51} - 4 q^{52} + 6 q^{53} - 6 q^{55} + 8 q^{57} + 18 q^{59} - 6 q^{60} + 40 q^{61} + 18 q^{62} + 4 q^{64} - 18 q^{65} + 12 q^{66} - 4 q^{67} - 12 q^{68} + 12 q^{69} - 12 q^{71} - 24 q^{72} + 4 q^{73} - 4 q^{75} + 4 q^{76} - 24 q^{78} - 22 q^{79} + 4 q^{81} + 36 q^{82} - 12 q^{83} + 6 q^{85} + 18 q^{86} - 6 q^{87} + 12 q^{88} + 12 q^{89} - 12 q^{90} + 12 q^{92} - 16 q^{93} - 48 q^{94} - 18 q^{96} - 8 q^{97} - 12 q^{99}+O(q^{100}) $ 4 * q - 4 * q^3 - 2 * q^4 + 6 * q^6 + 4 * q^9 - 12 * q^10 + 12 * q^11 + 2 * q^12 - 4 * q^13 - 6 * q^15 + 10 * q^16 - 12 * q^17 - 12 * q^18 - 8 * q^19 + 6 * q^22 - 6 * q^23 + 12 * q^24 + 4 * q^25 - 16 * q^27 + 6 * q^29 + 12 * q^30 - 2 * q^31 + 12 * q^34 - 2 * q^36 + 14 * q^37 + 22 * q^39 - 6 * q^40 - 10 * q^43 - 6 * q^44 + 12 * q^45 - 6 * q^46 + 12 * q^47 - 10 * q^48 + 18 * q^51 - 4 * q^52 + 6 * q^53 - 6 * q^55 + 8 * q^57 + 18 * q^59 - 6 * q^60 + 40 * q^61 + 18 * q^62 + 4 * q^64 - 18 * q^65 + 12 * q^66 - 4 * q^67 - 12 * q^68 + 12 * q^69 - 12 * q^71 - 24 * q^72 + 4 * q^73 - 4 * q^75 + 4 * q^76 - 24 * q^78 - 22 * q^79 + 4 * q^81 + 36 * q^82 - 12 * q^83 + 6 * q^85 + 18 * q^86 - 6 * q^87 + 12 * q^88 + 12 * q^89 - 12 * q^90 + 12 * q^92 - 16 * q^93 - 48 * q^94 - 18 * q^96 - 8 * q^97 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.866025	−	1.50000i	0.612372	−	1.06066i	−0.378467	−	0.925615i	$-0.623549\pi$
$2$	0.866025	−	1.50000i	0.612372	−	1.06066i	0.990839	−	0.135045i	$-0.0431180\pi$
$3$	0.732051			0.422650			0.211325	−	0.977416i	$-0.432222\pi$
$3$	0.732051			0.422650			0.211325	+	0.977416i	$0.432222\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.866025	−	1.50000i	−0.387298	−	0.670820i	0.604787	−	0.796387i	$-0.293258\pi$
$5$	−0.866025	−	1.50000i	−0.387298	−	0.670820i	−0.992085	+	0.125567i	$0.959925\pi$
$6$	0.633975	−	1.09808i	0.258819	−	0.448288i
$7$		0			0
$7$		0			0
$8$	1.73205			0.612372
$9$	−2.46410			−0.821367
$10$	−3.00000			−0.948683
$11$	4.73205			1.42677			0.713384	−	0.700774i	$-0.247162\pi$
$11$	4.73205			1.42677			0.713384	+	0.700774i	$0.247162\pi$
$12$	−0.366025	−	0.633975i	−0.105662	−	0.183013i
$13$	1.59808	−	3.23205i	0.443227	−	0.896410i
$13$	1.59808	−	3.23205i	0.443227	−	0.896410i
$14$		0			0
$15$	−0.633975	−	1.09808i	−0.163692	−	0.283522i
$16$	2.50000	−	4.33013i	0.625000	−	1.08253i
$17$	−2.13397	−	3.69615i	−0.517565	−	0.896449i	−0.999792	−	0.0204023i	$-0.993505\pi$
$17$	−2.13397	−	3.69615i	−0.517565	−	0.896449i	0.482227	−	0.876046i	$-0.339828\pi$
$18$	−2.13397	+	3.69615i	−0.502983	+	0.871191i
$19$	−2.00000			−0.458831			−0.229416	−	0.973329i	$-0.573682\pi$
$19$	−2.00000			−0.458831			−0.229416	+	0.973329i	$0.573682\pi$
$20$	−0.866025	+	1.50000i	−0.193649	+	0.335410i
$21$		0			0
$22$	4.09808	−	7.09808i	0.873713	−	1.51331i
$23$	−0.633975	+	1.09808i	−0.132193	+	0.228965i	−0.924522	−	0.381130i	$-0.875535\pi$
$23$	−0.633975	+	1.09808i	−0.132193	+	0.228965i	0.792329	+	0.610094i	$0.208868\pi$
$24$	1.26795			0.258819
$25$	1.00000	−	1.73205i	0.200000	−	0.346410i
$26$	−3.46410	−	5.19615i	−0.679366	−	1.01905i
$27$	−4.00000			−0.769800
$28$		0			0
$29$	1.50000	+	2.59808i	0.278543	+	0.482451i	0.971023	−	0.238987i	$-0.0768152\pi$
$29$	1.50000	+	2.59808i	0.278543	+	0.482451i	−0.692480	+	0.721437i	$0.743482\pi$
$30$	−2.19615			−0.400961
$31$	−3.09808	+	5.36603i	−0.556431	+	0.963767i	0.441360	+	0.897330i	$0.354496\pi$
$31$	−3.09808	+	5.36603i	−0.556431	+	0.963767i	−0.997791	+	0.0664364i	$0.978837\pi$
$32$	−2.59808	−	4.50000i	−0.459279	−	0.795495i
$33$	3.46410			0.603023
$34$	−7.39230			−1.26777
$35$		0			0
$36$	1.23205	+	2.13397i	0.205342	+	0.355662i
$37$	3.50000	−	6.06218i	0.575396	−	0.996616i	−0.420602	−	0.907245i	$-0.638181\pi$
$37$	3.50000	−	6.06218i	0.575396	−	0.996616i	0.995998	−	0.0893706i	$-0.0284856\pi$
$38$	−1.73205	+	3.00000i	−0.280976	+	0.486664i
$39$	1.16987	−	2.36603i	0.187330	−	0.378867i
$40$	−1.50000	−	2.59808i	−0.237171	−	0.410792i
$41$	2.59808	+	4.50000i	0.405751	+	0.702782i	0.994409	−	0.105601i	$-0.0336766\pi$
$41$	2.59808	+	4.50000i	0.405751	+	0.702782i	−0.588657	+	0.808383i	$0.700343\pi$
$42$		0			0
$43$	−5.09808	+	8.83013i	−0.777449	+	1.34658i	0.155958	+	0.987764i	$0.450153\pi$
$43$	−5.09808	+	8.83013i	−0.777449	+	1.34658i	−0.933408	+	0.358818i	$0.883180\pi$
$44$	−2.36603	−	4.09808i	−0.356692	−	0.617808i
$45$	2.13397	+	3.69615i	0.318114	+	0.550990i
$46$	1.09808	+	1.90192i	0.161903	+	0.280423i
$47$	−0.464102	−	0.803848i	−0.0676962	−	0.117253i	0.830191	−	0.557480i	$-0.188232\pi$
$47$	−0.464102	−	0.803848i	−0.0676962	−	0.117253i	−0.897887	+	0.440226i	$0.854898\pi$
$48$	1.83013	−	3.16987i	0.264156	−	0.457532i
$49$		0			0
$50$	−1.73205	−	3.00000i	−0.244949	−	0.424264i
$51$	−1.56218	−	2.70577i	−0.218749	−	0.378884i
$52$	−3.59808	+	0.232051i	−0.498963	+	0.0321797i
$53$	−1.96410	+	3.40192i	−0.269790	+	0.467290i	−0.968808	−	0.247814i	$-0.920288\pi$
$53$	−1.96410	+	3.40192i	−0.269790	+	0.467290i	0.699017	+	0.715105i	$0.253621\pi$
$54$	−3.46410	+	6.00000i	−0.471405	+	0.816497i
$55$	−4.09808	−	7.09808i	−0.552584	−	0.957104i
$56$		0			0
$57$	−1.46410			−0.193925
$58$	5.19615			0.682288
$59$	5.36603	+	9.29423i	0.698597	+	1.21001i	0.968953	+	0.247245i	$0.0795253\pi$
$59$	5.36603	+	9.29423i	0.698597	+	1.21001i	−0.270356	+	0.962760i	$0.587141\pi$
$60$	−0.633975	+	1.09808i	−0.0818458	+	0.141761i
$61$	15.1962			1.94567			0.972834	−	0.231504i	$-0.0743646\pi$
$61$	15.1962			1.94567			0.972834	+	0.231504i	$0.0743646\pi$
$62$	5.36603	+	9.29423i	0.681486	+	1.18037i
$63$		0			0
$64$	1.00000			0.125000
$65$	−6.23205	+	0.401924i	−0.772991	+	0.0498525i
$66$	3.00000	−	5.19615i	0.369274	−	0.639602i
$67$	4.19615			0.512642			0.256321	−	0.966592i	$-0.417490\pi$
$67$	4.19615			0.512642			0.256321	+	0.966592i	$0.417490\pi$
$68$	−2.13397	+	3.69615i	−0.258782	+	0.448224i
$69$	−0.464102	+	0.803848i	−0.0558713	+	0.0967719i
$70$		0			0
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	−0.987294	−	0.158901i	$-0.949205\pi$
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	0.631260	+	0.775571i	$0.282538\pi$
$72$	−4.26795			−0.502983
$73$	3.59808	−	6.23205i	0.421123	−	0.729406i	−0.574927	−	0.818205i	$-0.694969\pi$
$73$	3.59808	−	6.23205i	0.421123	−	0.729406i	0.996050	+	0.0887986i	$0.0283027\pi$
$74$	−6.06218	−	10.5000i	−0.704714	−	1.22060i
$75$	0.732051	−	1.26795i	0.0845299	−	0.146410i
$76$	1.00000	+	1.73205i	0.114708	+	0.198680i
$77$		0			0
$78$	−2.53590	−	3.80385i	−0.287134	−	0.430701i
$79$	−2.90192	−	5.02628i	−0.326492	−	0.565501i	0.655321	−	0.755350i	$-0.272533\pi$
$79$	−2.90192	−	5.02628i	−0.326492	−	0.565501i	−0.981813	+	0.189850i	$0.939200\pi$
$80$	−8.66025			−0.968246
$81$	4.46410			0.496011
$82$	9.00000			0.993884
$83$	−8.19615			−0.899645			−0.449822	−	0.893118i	$-0.648513\pi$
$83$	−8.19615			−0.899645			−0.449822	+	0.893118i	$0.648513\pi$
$84$		0			0
$85$	−3.69615	+	6.40192i	−0.400904	+	0.694386i
$86$	8.83013	+	15.2942i	0.952177	+	1.64922i
$87$	1.09808	+	1.90192i	0.117726	+	0.203908i
$88$	8.19615			0.873713
$89$	−0.464102	+	0.803848i	−0.0491947	+	0.0852077i	−0.889574	−	0.456791i	$-0.848999\pi$
$89$	−0.464102	+	0.803848i	−0.0491947	+	0.0852077i	0.840379	+	0.541998i	$0.182332\pi$
$90$	7.39230			0.779217
$91$		0			0
$92$	1.26795			0.132193
$93$	−2.26795	+	3.92820i	−0.235175	+	0.407336i
$94$	−1.60770			−0.165821
$95$	1.73205	+	3.00000i	0.177705	+	0.307794i
$96$	−1.90192	−	3.29423i	−0.194114	−	0.336216i
$97$	−7.19615	+	12.4641i	−0.730659	+	1.26554i	0.225944	+	0.974140i	$0.427454\pi$
$97$	−7.19615	+	12.4641i	−0.730659	+	1.26554i	−0.956602	+	0.291397i	$0.905880\pi$
$98$		0			0
$99$	−11.6603			−1.17190
$100$	−2.00000			−0.200000
$101$	4.26795			0.424677			0.212338	−	0.977196i	$-0.431892\pi$
$101$	4.26795			0.424677			0.212338	+	0.977196i	$0.431892\pi$
$102$	−5.41154			−0.535823
$103$	3.19615	+	5.53590i	0.314926	+	0.545468i	0.979422	−	0.201824i	$-0.0646869\pi$
$103$	3.19615	+	5.53590i	0.314926	+	0.545468i	−0.664496	+	0.747292i	$0.731354\pi$
$104$	2.76795	−	5.59808i	0.271420	−	0.548937i
$105$		0			0
$106$	3.40192	+	5.89230i	0.330424	+	0.572311i
$107$	−9.92820	+	17.1962i	−0.959796	+	1.66241i	−0.236805	+	0.971557i	$0.576100\pi$
$107$	−9.92820	+	17.1962i	−0.959796	+	1.66241i	−0.722991	+	0.690858i	$0.757233\pi$
$108$	2.00000	+	3.46410i	0.192450	+	0.333333i
$109$	−6.19615	+	10.7321i	−0.593484	+	1.02794i	0.400275	+	0.916395i	$0.368915\pi$
$109$	−6.19615	+	10.7321i	−0.593484	+	1.02794i	−0.993759	+	0.111549i	$0.964419\pi$
$110$	−14.1962			−1.35355
$111$	2.56218	−	4.43782i	0.243191	−	0.421219i
$112$		0			0
$113$	3.69615	−	6.40192i	0.347705	−	0.602242i	−0.638137	−	0.769923i	$-0.720294\pi$
$113$	3.69615	−	6.40192i	0.347705	−	0.602242i	0.985841	+	0.167681i	$0.0536278\pi$
$114$	−1.26795	+	2.19615i	−0.118754	+	0.205689i
$115$	2.19615			0.204792
$116$	1.50000	−	2.59808i	0.139272	−	0.241225i
$117$	−3.93782	+	7.96410i	−0.364052	+	0.736281i
$118$	18.5885			1.71121
$119$		0			0
$120$	−1.09808	−	1.90192i	−0.100240	−	0.173621i
$121$	11.3923			1.03566
$122$	13.1603	−	22.7942i	1.19147	−	2.06369i
$123$	1.90192	+	3.29423i	0.171491	+	0.297031i
$124$	6.19615			0.556431
$125$	−12.1244			−1.08444
$126$		0			0
$127$	1.19615	+	2.07180i	0.106141	+	0.183842i	0.914204	−	0.405254i	$-0.132817\pi$
$127$	1.19615	+	2.07180i	0.106141	+	0.183842i	−0.808063	+	0.589097i	$0.799484\pi$
$128$	6.06218	−	10.5000i	0.535826	−	0.928078i
$129$	−3.73205	+	6.46410i	−0.328589	+	0.569132i
$130$	−4.79423	+	9.69615i	−0.420482	+	0.850409i
$131$	1.73205	+	3.00000i	0.151330	+	0.262111i	0.931717	−	0.363186i	$-0.118311\pi$
$131$	1.73205	+	3.00000i	0.151330	+	0.262111i	−0.780387	+	0.625297i	$0.784978\pi$
$132$	−1.73205	−	3.00000i	−0.150756	−	0.261116i
$133$		0			0
$134$	3.63397	−	6.29423i	0.313928	−	0.543739i
$135$	3.46410	+	6.00000i	0.298142	+	0.516398i
$136$	−3.69615	−	6.40192i	−0.316942	−	0.548960i
$137$	−10.9641	−	18.9904i	−0.936726	−	1.62246i	−0.771526	−	0.636198i	$-0.780506\pi$
$137$	−10.9641	−	18.9904i	−0.936726	−	1.62246i	−0.165200	−	0.986260i	$-0.552827\pi$
$138$	0.803848	+	1.39230i	0.0684280	+	0.118521i
$139$	10.2942	−	17.8301i	0.873145	−	1.51233i	0.0144194	−	0.999896i	$-0.495410\pi$
$139$	10.2942	−	17.8301i	0.873145	−	1.51233i	0.858726	−	0.512436i	$-0.171257\pi$
$140$		0			0
$141$	−0.339746	−	0.588457i	−0.0286118	−	0.0495570i
$142$	5.19615	+	9.00000i	0.436051	+	0.755263i
$143$	7.56218	−	15.2942i	0.632381	−	1.27897i
$144$	−6.16025	+	10.6699i	−0.513355	+	0.889156i
$145$	2.59808	−	4.50000i	0.215758	−	0.373705i
$146$	−6.23205	−	10.7942i	−0.515768	−	0.893337i
$147$		0			0
$148$	−7.00000			−0.575396
$149$	0.464102			0.0380207			0.0190103	−	0.999819i	$-0.493948\pi$
$149$	0.464102			0.0380207			0.0190103	+	0.999819i	$0.493948\pi$
$150$	−1.26795	−	2.19615i	−0.103528	−	0.179315i
$151$	−1.00000	+	1.73205i	−0.0813788	+	0.140952i	−0.903842	−	0.427865i	$-0.859266\pi$
$151$	−1.00000	+	1.73205i	−0.0813788	+	0.140952i	0.822464	+	0.568818i	$0.192599\pi$
$152$	−3.46410			−0.280976
$153$	5.25833	+	9.10770i	0.425111	+	0.736314i
$154$		0			0
$155$	10.7321			0.862019
$156$	−2.63397	+	0.169873i	−0.210887	+	0.0136007i
$157$	−4.59808	+	7.96410i	−0.366966	+	0.635605i	−0.989090	−	0.147315i	$-0.952937\pi$
$157$	−4.59808	+	7.96410i	−0.366966	+	0.635605i	0.622123	+	0.782919i	$0.286270\pi$
$158$	−10.0526			−0.799739
$159$	−1.43782	+	2.49038i	−0.114027	+	0.197500i
$160$	−4.50000	+	7.79423i	−0.355756	+	0.616188i
$161$		0			0
$162$	3.86603	−	6.69615i	0.303744	−	0.526099i
$163$	5.80385			0.454592			0.227296	−	0.973826i	$-0.427011\pi$
$163$	5.80385			0.454592			0.227296	+	0.973826i	$0.427011\pi$
$164$	2.59808	−	4.50000i	0.202876	−	0.351391i
$165$	−3.00000	−	5.19615i	−0.233550	−	0.404520i
$166$	−7.09808	+	12.2942i	−0.550918	+	0.954217i
$167$	12.2942	+	21.2942i	0.951356	+	1.64780i	0.742495	+	0.669852i	$0.233642\pi$
$167$	12.2942	+	21.2942i	0.951356	+	1.64780i	0.208861	+	0.977945i	$0.433024\pi$
$168$		0			0
$169$	−7.89230	−	10.3301i	−0.607100	−	0.794625i
$170$	6.40192	+	11.0885i	0.491005	+	0.850446i
$171$	4.92820			0.376869
$172$	10.1962			0.777449
$173$	−15.4641			−1.17571			−0.587857	−	0.808965i	$-0.700028\pi$
$173$	−15.4641			−1.17571			−0.587857	+	0.808965i	$0.700028\pi$
$174$	3.80385			0.288369
$175$		0			0
$176$	11.8301	−	20.4904i	0.891729	−	1.54452i
$177$	3.92820	+	6.80385i	0.295262	+	0.511409i
$178$	0.803848	+	1.39230i	0.0602509	+	0.104358i
$179$	6.92820			0.517838			0.258919	−	0.965899i	$-0.416634\pi$
$179$	6.92820			0.517838			0.258919	+	0.965899i	$0.416634\pi$
$180$	2.13397	−	3.69615i	0.159057	−	0.275495i
$181$	25.5885			1.90198			0.950988	−	0.309229i	$-0.100071\pi$
$181$	25.5885			1.90198			0.950988	+	0.309229i	$0.100071\pi$
$182$		0			0
$183$	11.1244			0.822336
$184$	−1.09808	+	1.90192i	−0.0809513	+	0.140212i
$185$	−12.1244			−0.891400
$186$	3.92820	+	6.80385i	0.288030	+	0.498882i
$187$	−10.0981	−	17.4904i	−0.738444	−	1.27902i
$188$	−0.464102	+	0.803848i	−0.0338481	+	0.0586266i
$189$		0			0
$190$	6.00000			0.435286
$191$	1.26795			0.0917456			0.0458728	−	0.998947i	$-0.485393\pi$
$191$	1.26795			0.0917456			0.0458728	+	0.998947i	$0.485393\pi$
$192$	0.732051			0.0528312
$193$	5.00000			0.359908			0.179954	−	0.983675i	$-0.442405\pi$
$193$	5.00000			0.359908			0.179954	+	0.983675i	$0.442405\pi$
$194$	12.4641	+	21.5885i	0.894870	+	1.54996i
$195$	−4.56218	+	0.294229i	−0.326704	+	0.0210702i
$196$		0			0
$197$	−6.00000	−	10.3923i	−0.427482	−	0.740421i	0.569166	−	0.822222i	$-0.307266\pi$
$197$	−6.00000	−	10.3923i	−0.427482	−	0.740421i	−0.996649	+	0.0818013i	$0.973933\pi$
$198$	−10.0981	+	17.4904i	−0.717639	+	1.24299i
$199$	1.00000	+	1.73205i	0.0708881	+	0.122782i	0.899291	−	0.437351i	$-0.144083\pi$
$199$	1.00000	+	1.73205i	0.0708881	+	0.122782i	−0.828403	+	0.560133i	$0.810750\pi$
$200$	1.73205	−	3.00000i	0.122474	−	0.212132i
$201$	3.07180			0.216668
$202$	3.69615	−	6.40192i	0.260060	−	0.450438i
$203$		0			0
$204$	−1.56218	+	2.70577i	−0.109374	+	0.189442i
$205$	4.50000	−	7.79423i	0.314294	−	0.544373i
$206$	11.0718			0.771409
$207$	1.56218	−	2.70577i	0.108579	−	0.188064i
$208$	−10.0000	−	15.0000i	−0.693375	−	1.04006i
$209$	−9.46410			−0.654646
$210$		0			0
$211$	6.09808	+	10.5622i	0.419809	+	0.727130i	0.995920	−	0.0902411i	$-0.0287638\pi$
$211$	6.09808	+	10.5622i	0.419809	+	0.727130i	−0.576111	+	0.817371i	$0.695430\pi$
$212$	3.92820			0.269790
$213$	−2.19615	+	3.80385i	−0.150478	+	0.260635i
$214$	17.1962	+	29.7846i	1.17550	+	2.03603i
$215$	17.6603			1.20442
$216$	−6.92820			−0.471405
$217$		0			0
$218$	10.7321	+	18.5885i	0.726866	+	1.25897i
$219$	2.63397	−	4.56218i	0.177988	−	0.308283i
$220$	−4.09808	+	7.09808i	−0.276292	+	0.478552i
$221$	−15.3564	+	0.990381i	−1.03298	+	0.0666202i
$222$	−4.43782	−	7.68653i	−0.297847	−	0.515886i
$223$	−5.00000	−	8.66025i	−0.334825	−	0.579934i	0.648626	−	0.761107i	$-0.275344\pi$
$223$	−5.00000	−	8.66025i	−0.334825	−	0.579934i	−0.983451	+	0.181173i	$0.942010\pi$
$224$		0			0
$225$	−2.46410	+	4.26795i	−0.164273	+	0.284530i
$226$	−6.40192	−	11.0885i	−0.425850	−	0.737593i
$227$	−5.83013	−	10.0981i	−0.386959	−	0.670233i	0.605080	−	0.796165i	$-0.293141\pi$
$227$	−5.83013	−	10.0981i	−0.386959	−	0.670233i	−0.992039	+	0.125932i	$0.959808\pi$
$228$	0.732051	+	1.26795i	0.0484812	+	0.0839720i
$229$	3.19615	+	5.53590i	0.211208	+	0.365822i	0.952093	−	0.305809i	$-0.0989270\pi$
$229$	3.19615	+	5.53590i	0.211208	+	0.365822i	−0.740885	+	0.671632i	$0.765594\pi$
$230$	1.90192	−	3.29423i	0.125409	−	0.217215i
$231$		0			0
$232$	2.59808	+	4.50000i	0.170572	+	0.295439i
$233$	−12.9282	−	22.3923i	−0.846955	−	1.46697i	−0.883913	−	0.467652i	$-0.845100\pi$
$233$	−12.9282	−	22.3923i	−0.846955	−	1.46697i	0.0369580	−	0.999317i	$-0.488233\pi$
$234$	8.53590	+	12.8038i	0.558009	+	0.837014i
$235$	−0.803848	+	1.39230i	−0.0524372	+	0.0908240i
$236$	5.36603	−	9.29423i	0.349299	−	0.605003i
$237$	−2.12436	−	3.67949i	−0.137992	−	0.239009i
$238$		0			0
$239$	−26.1962			−1.69449			−0.847244	−	0.531204i	$-0.821740\pi$
$239$	−26.1962			−1.69449			−0.847244	+	0.531204i	$0.821740\pi$
$240$	−6.33975			−0.409229
$241$	−5.40192	−	9.35641i	−0.347969	−	0.602699i	0.637920	−	0.770103i	$-0.279795\pi$
$241$	−5.40192	−	9.35641i	−0.347969	−	0.602699i	−0.985888	+	0.167404i	$0.946462\pi$
$242$	9.86603	−	17.0885i	0.634212	−	1.09849i
$243$	15.2679			0.979439
$244$	−7.59808	−	13.1603i	−0.486417	−	0.842499i
$245$		0			0
$246$	6.58846			0.420065
$247$	−3.19615	+	6.46410i	−0.203366	+	0.411301i
$248$	−5.36603	+	9.29423i	−0.340743	+	0.590184i
$249$	−6.00000			−0.380235
$250$	−10.5000	+	18.1865i	−0.664078	+	1.15022i
$251$	−11.1962	+	19.3923i	−0.706695	+	1.22403i	0.259382	+	0.965775i	$0.416481\pi$
$251$	−11.1962	+	19.3923i	−0.706695	+	1.22403i	−0.966076	+	0.258256i	$0.916852\pi$
$252$		0			0
$253$	−3.00000	+	5.19615i	−0.188608	+	0.326679i
$254$	4.14359			0.259992
$255$	−2.70577	+	4.68653i	−0.169442	+	0.293482i
$256$	−9.50000	−	16.4545i	−0.593750	−	1.02841i
$257$	−9.06218	+	15.6962i	−0.565283	+	0.979099i	0.431740	+	0.901998i	$0.357900\pi$
$257$	−9.06218	+	15.6962i	−0.565283	+	0.979099i	−0.997023	+	0.0771011i	$0.975434\pi$
$258$	6.46410	+	11.1962i	0.402437	+	0.697042i
$259$		0			0
$260$	3.46410	+	5.19615i	0.214834	+	0.322252i
$261$	−3.69615	−	6.40192i	−0.228786	−	0.396269i
$262$	6.00000			0.370681
$263$	4.73205			0.291791			0.145895	−	0.989300i	$-0.453394\pi$
$263$	4.73205			0.291791			0.145895	+	0.989300i	$0.453394\pi$
$264$	6.00000			0.369274
$265$	6.80385			0.417957
$266$		0			0
$267$	−0.339746	+	0.588457i	−0.0207921	+	0.0360130i
$268$	−2.09808	−	3.63397i	−0.128160	−	0.221980i
$269$	9.46410	+	16.3923i	0.577036	+	0.999456i	0.995817	+	0.0913690i	$0.0291243\pi$
$269$	9.46410	+	16.3923i	0.577036	+	0.999456i	−0.418781	+	0.908087i	$0.637542\pi$
$270$	12.0000			0.730297
$271$	8.09808	−	14.0263i	0.491923	−	0.852036i	−0.508034	−	0.861337i	$-0.669627\pi$
$271$	8.09808	−	14.0263i	0.491923	−	0.852036i	0.999957	+	0.00930143i	$0.00296078\pi$
$272$	−21.3397			−1.29391
$273$		0			0
$274$	−37.9808			−2.29450
$275$	4.73205	−	8.19615i	0.285353	−	0.494247i
$276$	0.928203			0.0558713
$277$	−8.50000	−	14.7224i	−0.510716	−	0.884585i	−0.999923	−	0.0124177i	$-0.996047\pi$
$277$	−8.50000	−	14.7224i	−0.510716	−	0.884585i	0.489207	−	0.872167i	$-0.337286\pi$
$278$	−17.8301	−	30.8827i	−1.06938	−	1.85222i
$279$	7.63397	−	13.2224i	0.457034	−	0.791606i
$280$		0			0
$281$	−7.39230			−0.440988			−0.220494	−	0.975388i	$-0.570767\pi$
$281$	−7.39230			−0.440988			−0.220494	+	0.975388i	$0.570767\pi$
$282$	−1.17691			−0.0700842
$283$	0.196152			0.0116601			0.00583003	−	0.999983i	$-0.498144\pi$
$283$	0.196152			0.0116601			0.00583003	+	0.999983i	$0.498144\pi$
$284$	6.00000			0.356034
$285$	1.26795	+	2.19615i	0.0751068	+	0.130089i
$286$	−16.3923	−	24.5885i	−0.969297	−	1.45395i
$287$		0			0
$288$	6.40192	+	11.0885i	0.377237	+	0.653394i
$289$	−0.607695	+	1.05256i	−0.0357468	+	0.0619152i
$290$	−4.50000	−	7.79423i	−0.264249	−	0.457693i
$291$	−5.26795	+	9.12436i	−0.308813	+	0.534879i
$292$	−7.19615			−0.421123
$293$	−5.59808	+	9.69615i	−0.327043	+	0.566455i	−0.981924	−	0.189277i	$-0.939386\pi$
$293$	−5.59808	+	9.69615i	−0.327043	+	0.566455i	0.654881	+	0.755732i	$0.272719\pi$
$294$		0			0
$295$	9.29423	−	16.0981i	0.541131	−	0.937266i
$296$	6.06218	−	10.5000i	0.352357	−	0.610300i
$297$	−18.9282			−1.09833
$298$	0.401924	−	0.696152i	0.0232828	−	0.0403270i
$299$	2.53590	+	3.80385i	0.146655	+	0.219982i
$300$	−1.46410			−0.0845299
$301$		0			0
$302$	1.73205	+	3.00000i	0.0996683	+	0.172631i
$303$	3.12436			0.179490
$304$	−5.00000	+	8.66025i	−0.286770	+	0.496700i
$305$	−13.1603	−	22.7942i	−0.753554	−	1.30519i
$306$	18.2154			1.04130
$307$	−26.5885			−1.51748			−0.758742	−	0.651392i	$-0.774186\pi$
$307$	−26.5885			−1.51748			−0.758742	+	0.651392i	$0.774186\pi$
$308$		0			0
$309$	2.33975	+	4.05256i	0.133103	+	0.230542i
$310$	9.29423	−	16.0981i	0.527877	−	0.914309i
$311$	2.36603	−	4.09808i	0.134165	−	0.232381i	−0.791113	−	0.611670i	$-0.790498\pi$
$311$	2.36603	−	4.09808i	0.134165	−	0.232381i	0.925278	+	0.379289i	$0.123831\pi$
$312$	2.02628	−	4.09808i	0.114715	−	0.232008i
$313$	−6.39230	−	11.0718i	−0.361314	−	0.625815i	0.626863	−	0.779129i	$-0.284339\pi$
$313$	−6.39230	−	11.0718i	−0.361314	−	0.625815i	−0.988177	+	0.153315i	$0.951005\pi$
$314$	7.96410	+	13.7942i	0.449440	+	0.778453i
$315$		0			0
$316$	−2.90192	+	5.02628i	−0.163246	+	0.282750i
$317$	−0.232051	−	0.401924i	−0.0130333	−	0.0225743i	0.859435	−	0.511245i	$-0.170815\pi$
$317$	−0.232051	−	0.401924i	−0.0130333	−	0.0225743i	−0.872468	+	0.488670i	$0.837482\pi$
$318$	2.49038	+	4.31347i	0.139654	+	0.241887i
$319$	7.09808	+	12.2942i	0.397416	+	0.688345i
$320$	−0.866025	−	1.50000i	−0.0484123	−	0.0838525i
$321$	−7.26795	+	12.5885i	−0.405657	+	0.702619i
$322$		0			0
$323$	4.26795	+	7.39230i	0.237475	+	0.411319i
$324$	−2.23205	−	3.86603i	−0.124003	−	0.214779i
$325$	−4.00000	−	6.00000i	−0.221880	−	0.332820i
$326$	5.02628	−	8.70577i	0.278380	−	0.482168i
$327$	−4.53590	+	7.85641i	−0.250836	+	0.434460i
$328$	4.50000	+	7.79423i	0.248471	+	0.430364i
$329$		0			0
$330$	−10.3923			−0.572078
$331$	−26.9808			−1.48300			−0.741498	−	0.670955i	$-0.765885\pi$
$331$	−26.9808			−1.48300			−0.741498	+	0.670955i	$0.765885\pi$
$332$	4.09808	+	7.09808i	0.224911	+	0.389558i
$333$	−8.62436	+	14.9378i	−0.472612	+	0.818588i
$334$	42.5885			2.33034
$335$	−3.63397	−	6.29423i	−0.198545	−	0.343890i
$336$		0			0
$337$	11.0000			0.599208			0.299604	−	0.954064i	$-0.403145\pi$
$337$	11.0000			0.599208			0.299604	+	0.954064i	$0.403145\pi$
$338$	−22.3301	+	2.89230i	−1.21460	+	0.157321i
$339$	2.70577	−	4.68653i	0.146957	−	0.254538i
$340$	7.39230			0.400904
$341$	−14.6603	+	25.3923i	−0.793897	+	1.37507i
$342$	4.26795	−	7.39230i	0.230784	−	0.399730i
$343$		0			0
$344$	−8.83013	+	15.2942i	−0.476089	+	0.824610i
$345$	1.60770			0.0865554
$346$	−13.3923	+	23.1962i	−0.719975	+	1.24703i
$347$	−5.36603	−	9.29423i	−0.288063	−	0.498940i	0.685284	−	0.728276i	$-0.259678\pi$
$347$	−5.36603	−	9.29423i	−0.288063	−	0.498940i	−0.973347	+	0.229336i	$0.926345\pi$
$348$	1.09808	−	1.90192i	0.0588631	−	0.101954i
$349$	8.39230	+	14.5359i	0.449230	+	0.778089i	0.998336	−	0.0576637i	$-0.0183651\pi$
$349$	8.39230	+	14.5359i	0.449230	+	0.778089i	−0.549106	+	0.835753i	$0.685032\pi$
$350$		0			0
$351$	−6.39230	+	12.9282i	−0.341196	+	0.690056i
$352$	−12.2942	−	21.2942i	−0.655285	−	1.13499i
$353$	−3.33975			−0.177757			−0.0888784	−	0.996042i	$-0.528328\pi$
$353$	−3.33975			−0.177757			−0.0888784	+	0.996042i	$0.528328\pi$
$354$	13.6077			0.723241
$355$	10.3923			0.551566
$356$	0.928203			0.0491947
$357$		0			0
$358$	6.00000	−	10.3923i	0.317110	−	0.549250i
$359$	−2.53590	−	4.39230i	−0.133840	−	0.231817i	0.791314	−	0.611410i	$-0.209397\pi$
$359$	−2.53590	−	4.39230i	−0.133840	−	0.231817i	−0.925154	+	0.379593i	$0.876064\pi$
$360$	3.69615	+	6.40192i	0.194804	+	0.337411i
$361$	−15.0000			−0.789474
$362$	22.1603	−	38.3827i	1.16472	−	2.01735i
$363$	8.33975			0.437723
$364$		0			0
$365$	−12.4641			−0.652401
$366$	9.63397	−	16.6865i	0.503576	−	0.872219i
$367$	6.19615			0.323437			0.161718	−	0.986837i	$-0.448296\pi$
$367$	6.19615			0.323437			0.161718	+	0.986837i	$0.448296\pi$
$368$	3.16987	+	5.49038i	0.165241	+	0.286206i
$369$	−6.40192	−	11.0885i	−0.333271	−	0.577242i
$370$	−10.5000	+	18.1865i	−0.545869	+	0.945473i
$371$		0			0
$372$	4.53590			0.235175
$373$	9.39230			0.486315			0.243158	−	0.969987i	$-0.421817\pi$
$373$	9.39230			0.486315			0.243158	+	0.969987i	$0.421817\pi$
$374$	−34.9808			−1.80881
$375$	−8.87564			−0.458336
$376$	−0.803848	−	1.39230i	−0.0414553	−	0.0718026i
$377$	10.7942	−	0.696152i	0.555931	−	0.0358537i
$378$		0			0
$379$	2.29423	+	3.97372i	0.117847	+	0.204116i	0.918914	−	0.394458i	$-0.129068\pi$
$379$	2.29423	+	3.97372i	0.117847	+	0.204116i	−0.801067	+	0.598574i	$0.795734\pi$
$380$	1.73205	−	3.00000i	0.0888523	−	0.153897i
$381$	0.875644	+	1.51666i	0.0448606	+	0.0777009i
$382$	1.09808	−	1.90192i	0.0561825	−	0.0973109i
$383$	−5.66025			−0.289225			−0.144613	−	0.989488i	$-0.546194\pi$
$383$	−5.66025			−0.289225			−0.144613	+	0.989488i	$0.546194\pi$
$384$	4.43782	−	7.68653i	0.226467	−	0.392252i
$385$		0			0
$386$	4.33013	−	7.50000i	0.220398	−	0.381740i
$387$	12.5622	−	21.7583i	0.638571	−	1.10604i
$388$	14.3923			0.730659
$389$	15.2321	−	26.3827i	0.772296	−	1.33766i	−0.164006	−	0.986459i	$-0.552442\pi$
$389$	15.2321	−	26.3827i	0.772296	−	1.33766i	0.936302	−	0.351196i	$-0.114225\pi$
$390$	−3.50962	+	7.09808i	−0.177716	+	0.359425i
$391$	5.41154			0.273673
$392$		0			0
$393$	1.26795	+	2.19615i	0.0639596	+	0.110781i
$394$	−20.7846			−1.04711
$395$	−5.02628	+	8.70577i	−0.252900	+	0.438035i
$396$	5.83013	+	10.0981i	0.292975	+	0.507447i
$397$	−22.7846			−1.14353			−0.571763	−	0.820419i	$-0.693740\pi$
$397$	−22.7846			−1.14353			−0.571763	+	0.820419i	$0.693740\pi$
$398$	3.46410			0.173640
$399$		0			0
$400$	−5.00000	−	8.66025i	−0.250000	−	0.433013i
$401$	−8.42820	+	14.5981i	−0.420884	+	0.728993i	−0.996026	−	0.0890606i	$-0.971614\pi$
$401$	−8.42820	+	14.5981i	−0.420884	+	0.728993i	0.575142	+	0.818054i	$0.304947\pi$
$402$	2.66025	−	4.60770i	0.132681	−	0.229811i
$403$	12.3923	+	18.5885i	0.617305	+	0.925957i
$404$	−2.13397	−	3.69615i	−0.106169	−	0.183890i
$405$	−3.86603	−	6.69615i	−0.192104	−	0.332734i
$406$		0			0
$407$	16.5622	−	28.6865i	0.820957	−	1.42194i
$408$	−2.70577	−	4.68653i	−0.133956	−	0.232018i
$409$	−13.5981	−	23.5526i	−0.672382	−	1.16460i	−0.977227	−	0.212197i	$-0.931938\pi$
$409$	−13.5981	−	23.5526i	−0.672382	−	1.16460i	0.304845	−	0.952402i	$-0.401395\pi$
$410$	−7.79423	−	13.5000i	−0.384930	−	0.666717i
$411$	−8.02628	−	13.9019i	−0.395907	−	0.685731i
$412$	3.19615	−	5.53590i	0.157463	−	0.272734i
$413$		0			0
$414$	−2.70577	−	4.68653i	−0.132981	−	0.230331i
$415$	7.09808	+	12.2942i	0.348431	+	0.603500i
$416$	−18.6962	+	1.20577i	−0.916654	+	0.0591178i
$417$	7.53590	−	13.0526i	0.369035	−	0.639187i
$418$	−8.19615	+	14.1962i	−0.400887	+	0.694357i
$419$	−10.9019	−	18.8827i	−0.532594	−	0.922480i	−0.999276	−	0.0380543i	$-0.987884\pi$
$419$	−10.9019	−	18.8827i	−0.532594	−	0.922480i	0.466682	−	0.884425i	$-0.345449\pi$
$420$		0			0
$421$	30.1769			1.47073			0.735366	−	0.677670i	$-0.237010\pi$
$421$	30.1769			1.47073			0.735366	+	0.677670i	$0.237010\pi$
$422$	21.1244			1.02832
$423$	1.14359	+	1.98076i	0.0556034	+	0.0963079i
$424$	−3.40192	+	5.89230i	−0.165212	+	0.286156i
$425$	−8.53590			−0.414052
$426$	3.80385	+	6.58846i	0.184297	+	0.319212i
$427$		0			0
$428$	19.8564			0.959796
$429$	5.53590	−	11.1962i	0.267276	−	0.540555i
$430$	15.2942	−	26.4904i	0.737553	−	1.27748i
$431$	35.3205			1.70133			0.850665	−	0.525709i	$-0.176200\pi$
$431$	35.3205			1.70133			0.850665	+	0.525709i	$0.176200\pi$
$432$	−10.0000	+	17.3205i	−0.481125	+	0.833333i
$433$	8.79423	−	15.2321i	0.422624	−	0.732006i	−0.573572	−	0.819155i	$-0.694443\pi$
$433$	8.79423	−	15.2321i	0.422624	−	0.732006i	0.996195	+	0.0871498i	$0.0277759\pi$
$434$		0			0
$435$	1.90192	−	3.29423i	0.0911903	−	0.157946i
$436$	12.3923			0.593484
$437$	1.26795	−	2.19615i	0.0606542	−	0.105056i
$438$	−4.56218	−	7.90192i	−0.217989	−	0.377569i
$439$	−8.29423	+	14.3660i	−0.395862	+	0.685653i	−0.993211	−	0.116329i	$-0.962887\pi$
$439$	−8.29423	+	14.3660i	−0.395862	+	0.685653i	0.597349	+	0.801982i	$0.296221\pi$
$440$	−7.09808	−	12.2942i	−0.338388	−	0.586104i
$441$		0			0
$442$	−11.8135	+	23.8923i	−0.561909	+	1.13644i
$443$	5.66025	+	9.80385i	0.268927	+	0.465795i	0.968585	−	0.248683i	$-0.0799977\pi$
$443$	5.66025	+	9.80385i	0.268927	+	0.465795i	−0.699658	+	0.714478i	$0.746664\pi$
$444$	−5.12436			−0.243191
$445$	1.60770			0.0762121
$446$	−17.3205			−0.820150
$447$	0.339746			0.0160694
$448$		0			0
$449$	6.00000	−	10.3923i	0.283158	−	0.490443i	−0.689003	−	0.724758i	$-0.741951\pi$
$449$	6.00000	−	10.3923i	0.283158	−	0.490443i	0.972161	+	0.234315i	$0.0752847\pi$
$450$	4.26795	+	7.39230i	0.201193	+	0.348477i
$451$	12.2942	+	21.2942i	0.578913	+	1.00271i
$452$	−7.39230			−0.347705
$453$	−0.732051	+	1.26795i	−0.0343947	+	0.0595734i
$454$	−20.1962			−0.947852
$455$		0			0
$456$	−2.53590			−0.118754
$457$	−5.50000	+	9.52628i	−0.257279	+	0.445621i	−0.965512	−	0.260358i	$-0.916159\pi$
$457$	−5.50000	+	9.52628i	−0.257279	+	0.445621i	0.708233	+	0.705979i	$0.249493\pi$
$458$	11.0718			0.517351
$459$	8.53590	+	14.7846i	0.398422	+	0.690086i
$460$	−1.09808	−	1.90192i	−0.0511981	−	0.0886777i
$461$	7.79423	−	13.5000i	0.363013	−	0.628758i	−0.625442	−	0.780271i	$-0.715081\pi$
$461$	7.79423	−	13.5000i	0.363013	−	0.628758i	0.988455	+	0.151513i	$0.0484146\pi$
$462$		0			0
$463$	26.5885			1.23567			0.617835	−	0.786308i	$-0.288010\pi$
$463$	26.5885			1.23567			0.617835	+	0.786308i	$0.288010\pi$
$464$	15.0000			0.696358
$465$	7.85641			0.364332
$466$	−44.7846			−2.07461
$467$	−9.75833	−	16.9019i	−0.451562	−	0.782128i	0.546922	−	0.837184i	$-0.315800\pi$
$467$	−9.75833	−	16.9019i	−0.451562	−	0.782128i	−0.998483	+	0.0550561i	$0.982466\pi$
$468$	8.86603	−	0.571797i	0.409832	−	0.0264313i
$469$		0			0
$470$	1.39230	+	2.41154i	0.0642222	+	0.111236i
$471$	−3.36603	+	5.83013i	−0.155098	+	0.268638i
$472$	9.29423	+	16.0981i	0.427802	+	0.740974i
$473$	−24.1244	+	41.7846i	−1.10924	+	1.92126i
$474$	−7.35898			−0.338009
$475$	−2.00000	+	3.46410i	−0.0917663	+	0.158944i
$476$		0			0
$477$	4.83975	−	8.38269i	0.221597	−	0.383817i
$478$	−22.6865	+	39.2942i	−1.03766	+	1.79728i
$479$	−4.73205			−0.216213			−0.108106	−	0.994139i	$-0.534479\pi$
$479$	−4.73205			−0.216213			−0.108106	+	0.994139i	$0.534479\pi$
$480$	−3.29423	+	5.70577i	−0.150360	+	0.260432i
$481$	−14.0000	−	21.0000i	−0.638345	−	0.957518i
$482$	−18.7128			−0.852345
$483$		0			0
$484$	−5.69615	−	9.86603i	−0.258916	−	0.448456i
$485$	24.9282			1.13193
$486$	13.2224	−	22.9019i	0.599782	−	1.03885i
$487$	0.392305	+	0.679492i	0.0177770	+	0.0307907i	0.874777	−	0.484526i	$-0.161008\pi$
$487$	0.392305	+	0.679492i	0.0177770	+	0.0307907i	−0.857000	+	0.515316i	$0.827674\pi$
$488$	26.3205			1.19147
$489$	4.24871			0.192133
$490$		0			0
$491$	−14.1962	−	24.5885i	−0.640663	−	1.10966i	−0.985285	−	0.170920i	$-0.945326\pi$
$491$	−14.1962	−	24.5885i	−0.640663	−	1.10966i	0.344622	−	0.938742i	$-0.388007\pi$
$492$	1.90192	−	3.29423i	0.0857453	−	0.148515i
$493$	6.40192	−	11.0885i	0.288328	−	0.499399i
$494$	6.92820	+	10.3923i	0.311715	+	0.467572i
$495$	10.0981	+	17.4904i	0.453875	+	0.786134i
$496$	15.4904	+	26.8301i	0.695539	+	1.20471i
$497$		0			0
$498$	−5.19615	+	9.00000i	−0.232845	+	0.403300i
$499$	−6.49038	−	11.2417i	−0.290549	−	0.503246i	0.683390	−	0.730053i	$-0.260505\pi$
$499$	−6.49038	−	11.2417i	−0.290549	−	0.503246i	−0.973940	+	0.226807i	$0.927171\pi$
$500$	6.06218	+	10.5000i	0.271109	+	0.469574i
$501$	9.00000	+	15.5885i	0.402090	+	0.696441i
$502$	19.3923	+	33.5885i	0.865521	+	1.49913i
$503$	6.29423	−	10.9019i	0.280646	−	0.486093i	−0.690898	−	0.722952i	$-0.742785\pi$
$503$	6.29423	−	10.9019i	0.280646	−	0.486093i	0.971544	+	0.236859i	$0.0761181\pi$
$504$		0			0
$505$	−3.69615	−	6.40192i	−0.164477	−	0.284882i
$506$	5.19615	+	9.00000i	0.230997	+	0.400099i
$507$	−5.77757	−	7.56218i	−0.256591	−	0.335848i
$508$	1.19615	−	2.07180i	0.0530707	−	0.0919211i
$509$	5.13397	−	8.89230i	0.227559	−	0.394144i	−0.729525	−	0.683954i	$-0.760259\pi$
$509$	5.13397	−	8.89230i	0.227559	−	0.394144i	0.957084	+	0.289810i	$0.0935921\pi$
$510$	4.68653	+	8.11731i	0.207523	+	0.359441i
$511$		0			0
$512$	−8.66025			−0.382733
$513$	8.00000			0.353209
$514$	15.6962	+	27.1865i	0.692328	+	1.19915i
$515$	5.53590	−	9.58846i	0.243941	−	0.422518i
$516$	7.46410			0.328589
$517$	−2.19615	−	3.80385i	−0.0965867	−	0.167293i
$518$		0			0
$519$	−11.3205			−0.496915
$520$	−10.7942	+	0.696152i	−0.473358	+	0.0305283i
$521$	0.0621778	−	0.107695i	0.00272406	−	0.00471821i	−0.864660	−	0.502357i	$-0.832466\pi$
$521$	0.0621778	−	0.107695i	0.00272406	−	0.00471821i	0.867384	+	0.497639i	$0.165800\pi$
$522$	−12.8038			−0.560409
$523$	16.5885	−	28.7321i	0.725363	−	1.25636i	−0.233462	−	0.972366i	$-0.575005\pi$
$523$	16.5885	−	28.7321i	0.725363	−	1.25636i	0.958825	−	0.283999i	$-0.0916612\pi$
$524$	1.73205	−	3.00000i	0.0756650	−	0.131056i
$525$		0			0
$526$	4.09808	−	7.09808i	0.178685	−	0.309491i
$527$	26.4449			1.15196
$528$	8.66025	−	15.0000i	0.376889	−	0.652791i
$529$	10.6962	+	18.5263i	0.465050	+	0.805490i
$530$	5.89230	−	10.2058i	0.255945	−	0.443310i
$531$	−13.2224	−	22.9019i	−0.573805	−	0.993859i
$532$		0			0
$533$	18.6962	−	1.20577i	0.809820	−	0.0522278i
$534$	0.588457	+	1.01924i	0.0254650	+	0.0441067i
$535$	34.3923			1.48691
$536$	7.26795			0.313928
$537$	5.07180			0.218864
$538$	32.7846			1.41344
$539$		0			0
$540$	3.46410	−	6.00000i	0.149071	−	0.258199i
$541$	17.6962	+	30.6506i	0.760817	+	1.31777i	0.942430	+	0.334404i	$0.108535\pi$
$541$	17.6962	+	30.6506i	0.760817	+	1.31777i	−0.181613	+	0.983370i	$0.558132\pi$
$542$	−14.0263	−	24.2942i	−0.602480	−	1.04353i
$543$	18.7321			0.803869
$544$	−11.0885	+	19.2058i	−0.475414	+	0.823441i
$545$	21.4641			0.919421
$546$		0			0
$547$	28.1962			1.20558			0.602790	−	0.797900i	$-0.294056\pi$
$547$	28.1962			1.20558			0.602790	+	0.797900i	$0.294056\pi$
$548$	−10.9641	+	18.9904i	−0.468363	+	0.811229i
$549$	−37.4449			−1.59811
$550$	−8.19615	−	14.1962i	−0.349485	−	0.605326i
$551$	−3.00000	−	5.19615i	−0.127804	−	0.221364i
$552$	−0.803848	+	1.39230i	−0.0342140	+	0.0592604i
$553$		0			0
$554$	−29.4449			−1.25099
$555$	−8.87564			−0.376750
$556$	−20.5885			−0.873145
$557$	−25.6410			−1.08644			−0.543222	−	0.839589i	$-0.682796\pi$
$557$	−25.6410			−1.08644			−0.543222	+	0.839589i	$0.682796\pi$
$558$	−13.2224	−	22.9019i	−0.559750	−	0.969516i
$559$	20.3923	+	30.5885i	0.862503	+	1.29375i
$560$		0			0
$561$	−7.39230	−	12.8038i	−0.312103	−	0.540579i
$562$	−6.40192	+	11.0885i	−0.270049	+	0.467738i
$563$	−5.02628	−	8.70577i	−0.211832	−	0.366905i	0.740456	−	0.672105i	$-0.234610\pi$
$563$	−5.02628	−	8.70577i	−0.211832	−	0.366905i	−0.952288	+	0.305201i	$0.901276\pi$
$564$	−0.339746	+	0.588457i	−0.0143059	+	0.0247785i
$565$	−12.8038			−0.538662
$566$	0.169873	−	0.294229i	0.00714029	−	0.0123674i
$567$		0			0
$568$	−5.19615	+	9.00000i	−0.218026	+	0.377632i
$569$	−14.5359	+	25.1769i	−0.609377	+	1.05547i	0.381967	+	0.924176i	$0.375247\pi$
$569$	−14.5359	+	25.1769i	−0.609377	+	1.05547i	−0.991343	+	0.131295i	$0.958086\pi$
$570$	4.39230			0.183973
$571$	12.3923	−	21.4641i	0.518602	−	0.898245i	−0.481165	−	0.876630i	$-0.659786\pi$
$571$	12.3923	−	21.4641i	0.518602	−	0.898245i	0.999766	−	0.0216144i	$-0.00688062\pi$
$572$	−17.0263	+	1.09808i	−0.711905	+	0.0459129i
$573$	0.928203			0.0387762
$574$		0			0
$575$	1.26795	+	2.19615i	0.0528771	+	0.0915859i
$576$	−2.46410			−0.102671
$577$	16.4019	−	28.4090i	0.682821	−	1.18268i	−0.291295	−	0.956633i	$-0.594086\pi$
$577$	16.4019	−	28.4090i	0.682821	−	1.18268i	0.974116	−	0.226048i	$-0.0725805\pi$
$578$	1.05256	+	1.82309i	0.0437807	+	0.0758304i
$579$	3.66025			0.152115
$580$	−5.19615			−0.215758
$581$		0			0
$582$	9.12436	+	15.8038i	0.378217	+	0.655091i
$583$	−9.29423	+	16.0981i	−0.384928	+	0.666714i
$584$	6.23205	−	10.7942i	0.257884	−	0.446668i
$585$	15.3564	−	0.990381i	0.634909	−	0.0409472i
$586$	9.69615	+	16.7942i	0.400544	+	0.693763i
$587$	−2.19615	−	3.80385i	−0.0906449	−	0.157002i	0.817138	−	0.576442i	$-0.195559\pi$
$587$	−2.19615	−	3.80385i	−0.0906449	−	0.157002i	−0.907783	+	0.419441i	$0.862226\pi$
$588$		0			0
$589$	6.19615	−	10.7321i	0.255308	−	0.442206i
$590$	−16.0981	−	27.8827i	−0.662747	−	1.14791i
$591$	−4.39230	−	7.60770i	−0.180675	−	0.312939i
$592$	−17.5000	−	30.3109i	−0.719246	−	1.24577i
$593$	20.7224	+	35.8923i	0.850968	+	1.47392i	0.880335	+	0.474352i	$0.157317\pi$
$593$	20.7224	+	35.8923i	0.850968	+	1.47392i	−0.0293672	+	0.999569i	$0.509349\pi$
$594$	−16.3923	+	28.3923i	−0.672584	+	1.16495i
$595$		0			0
$596$	−0.232051	−	0.401924i	−0.00950517	−	0.0164634i
$597$	0.732051	+	1.26795i	0.0299608	+	0.0518937i
$598$	7.90192	−	0.509619i	0.323134	−	0.0208399i
$599$	−8.07180	+	13.9808i	−0.329805	+	0.571238i	−0.982473	−	0.186405i	$-0.940316\pi$
$599$	−8.07180	+	13.9808i	−0.329805	+	0.571238i	0.652668	+	0.757644i	$0.273650\pi$
$600$	1.26795	−	2.19615i	0.0517638	−	0.0896575i
$601$	10.9904	+	19.0359i	0.448307	+	0.776490i	0.998276	−	0.0586946i	$-0.0186938\pi$
$601$	10.9904	+	19.0359i	0.448307	+	0.776490i	−0.549969	+	0.835185i	$0.685360\pi$
$602$		0			0
$603$	−10.3397			−0.421067
$604$	2.00000			0.0813788
$605$	−9.86603	−	17.0885i	−0.401111	−	0.694745i
$606$	2.70577	−	4.68653i	0.109914	−	0.190377i
$607$	−6.39230			−0.259456			−0.129728	−	0.991550i	$-0.541410\pi$
$607$	−6.39230			−0.259456			−0.129728	+	0.991550i	$0.541410\pi$
$608$	5.19615	+	9.00000i	0.210732	+	0.364998i
$609$		0			0
$610$	−45.5885			−1.84582
$611$	−3.33975	+	0.215390i	−0.135112	+	0.00871376i
$612$	5.25833	−	9.10770i	0.212555	−	0.368157i
$613$	−17.3923			−0.702469			−0.351234	−	0.936288i	$-0.614238\pi$
$613$	−17.3923			−0.702469			−0.351234	+	0.936288i	$0.614238\pi$
$614$	−23.0263	+	39.8827i	−0.929265	+	1.60953i
$615$	3.29423	−	5.70577i	0.132836	−	0.230079i
$616$		0			0
$617$	−14.3038	+	24.7750i	−0.575851	+	0.997404i	0.420097	+	0.907479i	$0.361996\pi$
$617$	−14.3038	+	24.7750i	−0.575851	+	0.997404i	−0.995949	+	0.0899245i	$0.971337\pi$
$618$	8.10512			0.326036
$619$	−18.6865	+	32.3660i	−0.751075	+	1.30090i	0.196227	+	0.980559i	$0.437131\pi$
$619$	−18.6865	+	32.3660i	−0.751075	+	1.30090i	−0.947302	+	0.320342i	$0.896202\pi$
$620$	−5.36603	−	9.29423i	−0.215505	−	0.373265i
$621$	2.53590	−	4.39230i	0.101762	−	0.176257i
$622$	−4.09808	−	7.09808i	−0.164318	−	0.284607i
$623$		0			0
$624$	−7.32051	−	10.9808i	−0.293055	−	0.439582i
$625$	5.50000	+	9.52628i	0.220000	+	0.381051i
$626$	−22.1436			−0.885036
$627$	−6.92820			−0.276686
$628$	9.19615			0.366966
$629$	−29.8756			−1.19122
$630$		0			0
$631$	−14.3923	+	24.9282i	−0.572949	+	0.992376i	0.423313	+	0.905984i	$0.360867\pi$
$631$	−14.3923	+	24.9282i	−0.572949	+	0.992376i	−0.996261	+	0.0863924i	$0.972466\pi$
$632$	−5.02628	−	8.70577i	−0.199935	−	0.346297i
$633$	4.46410	+	7.73205i	0.177432	+	0.307321i
$634$	−0.803848			−0.0319249
$635$	2.07180	−	3.58846i	0.0822167	−	0.142404i
$636$	2.87564			0.114027
$637$		0			0
$638$	24.5885			0.973466
$639$	7.39230	−	12.8038i	0.292435	−	0.506512i
$640$	−21.0000			−0.830098
$641$	−0.571797	−	0.990381i	−0.0225846	−	0.0391177i	0.854512	−	0.519431i	$-0.173856\pi$
$641$	−0.571797	−	0.990381i	−0.0225846	−	0.0391177i	−0.877097	+	0.480314i	$0.840523\pi$
$642$	12.5885	+	21.8038i	0.496827	+	0.860529i
$643$	20.3923	−	35.3205i	0.804194	−	1.39290i	−0.112640	−	0.993636i	$-0.535931\pi$
$643$	20.3923	−	35.3205i	0.804194	−	1.39290i	0.916834	−	0.399269i	$-0.130736\pi$
$644$		0			0
$645$	12.9282			0.509048
$646$	14.7846			0.581693
$647$	45.0333			1.77044			0.885221	−	0.465170i	$-0.154007\pi$
$647$	45.0333			1.77044			0.885221	+	0.465170i	$0.154007\pi$
$648$	7.73205			0.303744
$649$	25.3923	+	43.9808i	0.996735	+	1.72640i
$650$	−12.4641	+	0.803848i	−0.488882	+	0.0315295i
$651$		0			0
$652$	−2.90192	−	5.02628i	−0.113648	−	0.196844i
$653$	5.07180	−	8.78461i	0.198475	−	0.343768i	−0.749559	−	0.661937i	$-0.769735\pi$
$653$	5.07180	−	8.78461i	0.198475	−	0.343768i	0.948034	+	0.318169i	$0.103068\pi$
$654$	7.85641	+	13.6077i	0.307210	+	0.532103i
$655$	3.00000	−	5.19615i	0.117220	−	0.203030i
$656$	25.9808			1.01438
$657$	−8.86603	+	15.3564i	−0.345897	+	0.599110i
$658$		0			0
$659$	−3.80385	+	6.58846i	−0.148177	+	0.256650i	−0.930554	−	0.366156i	$-0.880674\pi$
$659$	−3.80385	+	6.58846i	−0.148177	+	0.256650i	0.782377	+	0.622805i	$0.214007\pi$
$660$	−3.00000	+	5.19615i	−0.116775	+	0.202260i
$661$	22.8038			0.886967			0.443483	−	0.896283i	$-0.353742\pi$
$661$	22.8038			0.886967			0.443483	+	0.896283i	$0.353742\pi$
$662$	−23.3660	+	40.4711i	−0.908146	+	1.57296i
$663$	−11.2417	+	0.725009i	−0.436590	+	0.0281570i
$664$	−14.1962			−0.550918
$665$		0			0
$666$	14.9378	+	25.8731i	0.578829	+	1.00256i
$667$	−3.80385			−0.147286
$668$	12.2942	−	21.2942i	0.475678	−	0.823898i
$669$	−3.66025	−	6.33975i	−0.141514	−	0.245109i
$670$	−12.5885			−0.486335
$671$	71.9090			2.77601
$672$		0			0
$673$	−9.08846	−	15.7417i	−0.350334	−	0.606797i	0.635974	−	0.771711i	$-0.280599\pi$
$673$	−9.08846	−	15.7417i	−0.350334	−	0.606797i	−0.986308	+	0.164914i	$0.947265\pi$
$674$	9.52628	−	16.5000i	0.366939	−	0.635556i
$675$	−4.00000	+	6.92820i	−0.153960	+	0.266667i
$676$	−5.00000	+	12.0000i	−0.192308	+	0.461538i
$677$	−18.4641	−	31.9808i	−0.709633	−	1.22912i	−0.964993	−	0.262275i	$-0.915527\pi$
$677$	−18.4641	−	31.9808i	−0.709633	−	1.22912i	0.255360	−	0.966846i	$-0.417806\pi$
$678$	−4.68653	−	8.11731i	−0.179985	−	0.311744i
$679$		0			0
$680$	−6.40192	+	11.0885i	−0.245503	+	0.425223i
$681$	−4.26795	−	7.39230i	−0.163548	−	0.283274i
$682$	25.3923	+	43.9808i	0.972322	+	1.68411i
$683$	−4.26795	−	7.39230i	−0.163309	−	0.282859i	0.772745	−	0.634717i	$-0.218883\pi$
$683$	−4.26795	−	7.39230i	−0.163309	−	0.282859i	−0.936053	+	0.351858i	$0.885550\pi$
$684$	−2.46410	−	4.26795i	−0.0942173	−	0.163189i
$685$	−18.9904	+	32.8923i	−0.725585	+	1.25675i
$686$		0			0
$687$	2.33975	+	4.05256i	0.0892669	+	0.154615i
$688$	25.4904	+	44.1506i	0.971812	+	1.68323i
$689$	7.85641	+	11.7846i	0.299305	+	0.448958i
$690$	1.39230	−	2.41154i	0.0530041	−	0.0918059i
$691$	−10.1962	+	17.6603i	−0.387880	+	0.671828i	−0.992164	−	0.124941i	$-0.960126\pi$
$691$	−10.1962	+	17.6603i	−0.387880	+	0.671828i	0.604284	+	0.796769i	$0.293459\pi$
$692$	7.73205	+	13.3923i	0.293928	+	0.509099i
$693$		0			0
$694$	−18.5885			−0.705608
$695$	−35.6603			−1.35267
$696$	1.90192	+	3.29423i	0.0720922	+	0.124867i
$697$	11.0885	−	19.2058i	0.420005	−	0.727470i
$698$	29.0718			1.10038
$699$	−9.46410	−	16.3923i	−0.357965	−	0.620014i
$700$		0			0
$701$	−20.7846			−0.785024			−0.392512	−	0.919747i	$-0.628394\pi$
$701$	−20.7846			−0.785024			−0.392512	+	0.919747i	$0.628394\pi$
$702$	13.8564	+	20.7846i	0.522976	+	0.784465i
$703$	−7.00000	+	12.1244i	−0.264010	+	0.457279i
$704$	4.73205			0.178346
$705$	−0.588457	+	1.01924i	−0.0221626	+	0.0383867i
$706$	−2.89230	+	5.00962i	−0.108853	+	0.188539i
$707$		0			0
$708$	3.92820	−	6.80385i	0.147631	−	0.255704i
$709$	−32.1769			−1.20843			−0.604215	−	0.796822i	$-0.706513\pi$
$709$	−32.1769			−1.20843			−0.604215	+	0.796822i	$0.706513\pi$
$710$	9.00000	−	15.5885i	0.337764	−	0.585024i
$711$	7.15064	+	12.3853i	0.268170	+	0.464484i
$712$	−0.803848	+	1.39230i	−0.0301255	+	0.0521788i
$713$	−3.92820	−	6.80385i	−0.147112	−	0.254806i
$714$		0			0
$715$	−29.4904	+	1.90192i	−1.10288	+	0.0711279i
$716$	−3.46410	−	6.00000i	−0.129460	−	0.224231i
$717$	−19.1769			−0.716175
$718$	−8.78461			−0.327839
$719$	10.7321			0.400238			0.200119	−	0.979772i	$-0.435867\pi$
$719$	10.7321			0.400238			0.200119	+	0.979772i	$0.435867\pi$
$720$	21.3397			0.795285
$721$		0			0
$722$	−12.9904	+	22.5000i	−0.483452	+	0.837363i
$723$	−3.95448	−	6.84936i	−0.147069	−	0.254731i
$724$	−12.7942	−	22.1603i	−0.475494	−	0.823579i
$725$	6.00000			0.222834
$726$	7.22243	−	12.5096i	0.268050	−	0.464276i
$727$	−21.1769			−0.785408			−0.392704	−	0.919665i	$-0.628460\pi$
$727$	−21.1769			−0.785408			−0.392704	+	0.919665i	$0.628460\pi$
$728$		0			0
$729$	−2.21539			−0.0820515
$730$	−10.7942	+	18.6962i	−0.399512	+	0.691976i
$731$	43.5167			1.60952
$732$	−5.56218	−	9.63397i	−0.205584	−	0.356082i
$733$	−3.79423	−	6.57180i	−0.140143	−	0.242735i	0.787407	−	0.616433i	$-0.211423\pi$
$733$	−3.79423	−	6.57180i	−0.140143	−	0.242735i	−0.927550	+	0.373698i	$0.878090\pi$
$734$	5.36603	−	9.29423i	0.198064	−	0.343056i
$735$		0			0
$736$	6.58846			0.242854
$737$	19.8564			0.731420
$738$	−22.1769			−0.816344
$739$	−0.784610			−0.0288623			−0.0144312	−	0.999896i	$-0.504594\pi$
$739$	−0.784610			−0.0288623			−0.0144312	+	0.999896i	$0.504594\pi$
$740$	6.06218	+	10.5000i	0.222850	+	0.385988i
$741$	−2.33975	+	4.73205i	−0.0859527	+	0.173836i
$742$		0			0
$743$	14.1962	+	24.5885i	0.520806	+	0.902063i	0.999707	+	0.0241941i	$0.00770196\pi$
$743$	14.1962	+	24.5885i	0.520806	+	0.902063i	−0.478901	+	0.877869i	$0.658965\pi$
$744$	−3.92820	+	6.80385i	−0.144015	+	0.249441i
$745$	−0.401924	−	0.696152i	−0.0147253	−	0.0255051i
$746$	8.13397	−	14.0885i	0.297806	−	0.515815i
$747$	20.1962			0.738939
$748$	−10.0981	+	17.4904i	−0.369222	+	0.639512i
$749$		0			0
$750$	−7.68653	+	13.3135i	−0.280673	+	0.486139i
$751$	−23.0981	+	40.0070i	−0.842861	+	1.45988i	0.0446053	+	0.999005i	$0.485797\pi$
$751$	−23.0981	+	40.0070i	−0.842861	+	1.45988i	−0.887466	+	0.460873i	$0.847536\pi$
$752$	−4.64102			−0.169240
$753$	−8.19615	+	14.1962i	−0.298684	+	0.517337i
$754$	8.30385	−	16.7942i	0.302408	−	0.611610i
$755$	3.46410			0.126072
$756$		0			0
$757$	8.00000	+	13.8564i	0.290765	+	0.503620i	0.973991	−	0.226587i	$-0.0727569\pi$
$757$	8.00000	+	13.8564i	0.290765	+	0.503620i	−0.683226	+	0.730207i	$0.739424\pi$
$758$	7.94744			0.288664
$759$	−2.19615	+	3.80385i	−0.0797153	+	0.138071i
$760$	3.00000	+	5.19615i	0.108821	+	0.188484i
$761$	−6.67949			−0.242131			−0.121066	−	0.992644i	$-0.538631\pi$
$761$	−6.67949			−0.242131			−0.121066	+	0.992644i	$0.538631\pi$
$762$	3.03332			0.109886
$763$		0			0
$764$	−0.633975	−	1.09808i	−0.0229364	−	0.0397270i
$765$	9.10770	−	15.7750i	0.329289	−	0.570346i
$766$	−4.90192	+	8.49038i	−0.177114	+	0.306770i
$767$	38.6147	−	2.49038i	1.39430	−	0.0899224i
$768$	−6.95448	−	12.0455i	−0.250948	−	0.434655i
$769$	−23.5885	−	40.8564i	−0.850622	−	1.47332i	−0.880648	−	0.473771i	$-0.842893\pi$
$769$	−23.5885	−	40.8564i	−0.850622	−	1.47332i	0.0300268	−	0.999549i	$-0.490441\pi$
$770$		0			0
$771$	−6.63397	+	11.4904i	−0.238917	+	0.413816i
$772$	−2.50000	−	4.33013i	−0.0899770	−	0.155845i
$773$	0.464102	+	0.803848i	0.0166926	+	0.0289124i	0.874251	−	0.485474i	$-0.161353\pi$
$773$	0.464102	+	0.803848i	0.0166926	+	0.0289124i	−0.857558	+	0.514387i	$0.828020\pi$
$774$	−21.7583	−	37.6865i	−0.782087	−	1.35461i
$775$	6.19615	+	10.7321i	0.222572	+	0.385507i
$776$	−12.4641	+	21.5885i	−0.447435	+	0.774980i
$777$		0			0
$778$	−26.3827	−	45.6962i	−0.945865	−	1.63829i
$779$	−5.19615	−	9.00000i	−0.186171	−	0.322458i
$780$	2.53590	+	3.80385i	0.0907997	+	0.136200i
$781$	−14.1962	+	24.5885i	−0.507978	+	0.879844i
$782$	4.68653	−	8.11731i	0.167590	−	0.290275i
$783$	−6.00000	−	10.3923i	−0.214423	−	0.371391i
$784$		0			0
$785$	15.9282			0.568502
$786$	4.39230			0.156668
$787$	−19.4904	−	33.7583i	−0.694757	−	1.20335i	−0.970263	−	0.242055i	$-0.922179\pi$
$787$	−19.4904	−	33.7583i	−0.694757	−	1.20335i	0.275505	−	0.961300i	$-0.411155\pi$
$788$	−6.00000	+	10.3923i	−0.213741	+	0.370211i
$789$	3.46410			0.123325
$790$	8.70577	+	15.0788i	0.309737	+	0.536481i
$791$		0			0
$792$	−20.1962			−0.717639
$793$	24.2846	−	49.1147i	0.862372	−	1.74412i
$794$	−19.7321	+	34.1769i	−0.700264	+	1.21289i
$795$	4.98076			0.176649
$796$	1.00000	−	1.73205i	0.0354441	−	0.0613909i
$797$	−6.80385	+	11.7846i	−0.241005	+	0.417432i	−0.961001	−	0.276546i	$-0.910810\pi$
$797$	−6.80385	+	11.7846i	−0.241005	+	0.417432i	0.719996	+	0.693978i	$0.244144\pi$
$798$		0			0
$799$	−1.98076	+	3.43078i	−0.0700743	+	0.121372i
$800$	−10.3923			−0.367423
$801$	1.14359	−	1.98076i	0.0404069	−	0.0699868i
$802$	14.5981	+	25.2846i	0.515476	+	0.892831i
$803$	17.0263	−	29.4904i	0.600844	−	1.04069i
$804$	−1.53590	−	2.66025i	−0.0541670	−	0.0938199i
$805$		0			0
$806$	38.6147	−	2.49038i	1.36015	−	0.0877199i
$807$	6.92820	+	12.0000i	0.243884	+	0.422420i
$808$	7.39230			0.260060
$809$	15.9282			0.560006			0.280003	−	0.959999i	$-0.409665\pi$
$809$	15.9282			0.560006			0.280003	+	0.959999i	$0.409665\pi$
$810$	−13.3923			−0.470558
$811$	−14.5885			−0.512270			−0.256135	−	0.966641i	$-0.582449\pi$
$811$	−14.5885			−0.512270			−0.256135	+	0.966641i	$0.582449\pi$
$812$		0			0
$813$	5.92820	−	10.2679i	0.207911	−	0.360113i
$814$	−28.6865	−	49.6865i	−1.00546	−	1.74151i
$815$	−5.02628	−	8.70577i	−0.176063	−	0.304950i
$816$	−15.6218			−0.546872
$817$	10.1962	−	17.6603i	0.356718	−	0.617854i
$818$	−47.1051			−1.64699
$819$		0			0
$820$	−9.00000			−0.314294
$821$	−15.9282	+	27.5885i	−0.555898	+	0.962844i	0.441935	+	0.897047i	$0.354292\pi$
$821$	−15.9282	+	27.5885i	−0.555898	+	0.962844i	−0.997833	+	0.0657967i	$0.979041\pi$
$822$	−27.8038			−0.969771
$823$	−10.5885	−	18.3397i	−0.369090	−	0.639283i	0.620333	−	0.784338i	$-0.286997\pi$
$823$	−10.5885	−	18.3397i	−0.369090	−	0.639283i	−0.989424	+	0.145055i	$0.953664\pi$
$824$	5.53590	+	9.58846i	0.192852	+	0.334030i
$825$	3.46410	−	6.00000i	0.120605	−	0.208893i
$826$		0			0
$827$	34.9808			1.21640			0.608200	−	0.793784i	$-0.291892\pi$
$827$	34.9808			1.21640			0.608200	+	0.793784i	$0.291892\pi$
$828$	−3.12436			−0.108579
$829$	31.5885			1.09711			0.548556	−	0.836114i	$-0.315178\pi$
$829$	31.5885			1.09711			0.548556	+	0.836114i	$0.315178\pi$
$830$	24.5885			0.853478
$831$	−6.22243	−	10.7776i	−0.215854	−	0.373870i
$832$	1.59808	−	3.23205i	0.0554033	−	0.112051i
$833$		0			0
$834$	−13.0526	−	22.6077i	−0.451973	−	0.782840i
$835$	21.2942	−	36.8827i	0.736917	−	1.27638i
$836$	4.73205	+	8.19615i	0.163661	+	0.283470i
$837$	12.3923	−	21.4641i	0.428341	−	0.741908i
$838$	−37.7654			−1.30458
$839$	−9.00000	+	15.5885i	−0.310715	+	0.538173i	−0.978517	−	0.206165i	$-0.933902\pi$
$839$	−9.00000	+	15.5885i	−0.310715	+	0.538173i	0.667803	+	0.744338i	$0.267235\pi$
$840$		0			0
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$	26.1340	−	45.2654i	0.900636	−	1.55995i
$843$	−5.41154			−0.186383
$844$	6.09808	−	10.5622i	0.209904	−	0.363565i
$845$	−8.66025	+	20.7846i	−0.297922	+	0.715012i
$846$	3.96152			0.136200
$847$		0			0
$848$	9.82051	+	17.0096i	0.337238	+	0.584113i
$849$	0.143594			0.00492812
$850$	−7.39230	+	12.8038i	−0.253554	+	0.439168i
$851$	4.43782	+	7.68653i	0.152127	+	0.263491i
$852$	4.39230			0.150478
$853$	25.5885			0.876132			0.438066	−	0.898943i	$-0.355664\pi$
$853$	25.5885			0.876132			0.438066	+	0.898943i	$0.355664\pi$
$854$		0			0
$855$	−4.26795	−	7.39230i	−0.145961	−	0.252811i
$856$	−17.1962	+	29.7846i	−0.587752	+	1.01802i
$857$	−2.93782	+	5.08846i	−0.100354	+	0.173818i	−0.911831	−	0.410567i	$-0.865331\pi$
$857$	−2.93782	+	5.08846i	−0.100354	+	0.173818i	0.811476	+	0.584385i	$0.198664\pi$
$858$	−12.0000	−	18.0000i	−0.409673	−	0.614510i
$859$	−9.09808	−	15.7583i	−0.310422	−	0.537667i	0.668031	−	0.744133i	$-0.267137\pi$
$859$	−9.09808	−	15.7583i	−0.310422	−	0.537667i	−0.978454	+	0.206466i	$0.933804\pi$
$860$	−8.83013	−	15.2942i	−0.301105	−	0.521529i
$861$		0			0
$862$	30.5885	−	52.9808i	1.04185	−	1.80453i
$863$	18.7583	+	32.4904i	0.638541	+	1.10599i	0.985753	+	0.168199i	$0.0537951\pi$
$863$	18.7583	+	32.4904i	0.638541	+	1.10599i	−0.347212	+	0.937787i	$0.612872\pi$
$864$	10.3923	+	18.0000i	0.353553	+	0.612372i
$865$	13.3923	+	23.1962i	0.455352	+	0.788693i
$866$	−15.2321	−	26.3827i	−0.517606	−	0.896520i
$867$	−0.444864	+	0.770527i	−0.0151084	+	0.0261685i
$868$		0			0
$869$	−13.7321	−	23.7846i	−0.465828	−	0.806838i
$870$	−3.29423	−	5.70577i	−0.111685	−	0.193444i
$871$	6.70577	−	13.5622i	0.227216	−	0.459537i
$872$	−10.7321	+	18.5885i	−0.363433	+	0.629485i
$873$	17.7321	−	30.7128i	0.600139	−	1.03947i
$874$	−2.19615	−	3.80385i	−0.0742860	−	0.128667i
$875$		0			0
$876$	−5.26795			−0.177988
$877$	−21.7846			−0.735614			−0.367807	−	0.929902i	$-0.619891\pi$
$877$	−21.7846			−0.735614			−0.367807	+	0.929902i	$0.619891\pi$
$878$	14.3660	+	24.8827i	0.484830	+	0.839750i
$879$	−4.09808	+	7.09808i	−0.138225	+	0.239412i
$880$	−40.9808			−1.38146
$881$	−19.7942	−	34.2846i	−0.666885	−	1.15508i	−0.978771	−	0.204958i	$-0.934294\pi$
$881$	−19.7942	−	34.2846i	−0.666885	−	1.15508i	0.311886	−	0.950119i	$-0.399039\pi$
$882$		0			0
$883$	45.7654			1.54013			0.770064	−	0.637967i	$-0.220224\pi$
$883$	45.7654			1.54013			0.770064	+	0.637967i	$0.220224\pi$
$884$	8.53590	+	12.8038i	0.287093	+	0.430640i
$885$	6.80385	−	11.7846i	0.228709	−	0.396135i
$886$	19.6077			0.658733
$887$	−11.6603	+	20.1962i	−0.391513	+	0.678120i	−0.992649	−	0.121026i	$-0.961382\pi$
$887$	−11.6603	+	20.1962i	−0.391513	+	0.678120i	0.601136	+	0.799147i	$0.294715\pi$
$888$	4.43782	−	7.68653i	0.148924	−	0.257943i
$889$		0			0
$890$	1.39230	−	2.41154i	0.0466702	−	0.0808351i
$891$	21.1244			0.707693
$892$	−5.00000	+	8.66025i	−0.167412	+	0.289967i
$893$	0.928203	+	1.60770i	0.0310611	+	0.0537995i
$894$	0.294229	−	0.509619i	0.00984048	−	0.0170442i
$895$	−6.00000	−	10.3923i	−0.200558	−	0.347376i
$896$		0			0
$897$	1.85641	+	2.78461i	0.0619836	+	0.0929754i
$898$	−10.3923	−	18.0000i	−0.346796	−	0.600668i
$899$	−18.5885			−0.619960
$900$	4.92820			0.164273
$901$	16.7654			0.558536
$902$	42.5885			1.41804
$903$		0			0
$904$	6.40192	−	11.0885i	0.212925	−	0.368797i
$905$	−22.1603	−	38.3827i	−0.736632	−	1.27588i
$906$	1.26795	+	2.19615i	0.0421248	+	0.0729623i
$907$	14.5885			0.484402			0.242201	−	0.970226i	$-0.422131\pi$
$907$	14.5885			0.484402			0.242201	+	0.970226i	$0.422131\pi$
$908$	−5.83013	+	10.0981i	−0.193480	+	0.335116i
$909$	−10.5167			−0.348816
$910$		0			0
$911$	12.0000			0.397578			0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000			0.397578			0.198789	+	0.980042i	$0.436299\pi$
$912$	−3.66025	+	6.33975i	−0.121203	+	0.209930i
$913$	−38.7846			−1.28358
$914$	9.52628	+	16.5000i	0.315101	+	0.545771i
$915$	−9.63397	−	16.6865i	−0.318489	−	0.551640i
$916$	3.19615	−	5.53590i	0.105604	−	0.182911i
$917$		0			0
$918$	29.5692			0.975930
$919$	43.5692			1.43722			0.718608	−	0.695415i	$-0.244780\pi$
$919$	43.5692			1.43722			0.718608	+	0.695415i	$0.244780\pi$
$920$	3.80385			0.125409
$921$	−19.4641			−0.641364
$922$	−13.5000	−	23.3827i	−0.444599	−	0.770068i
$923$	12.0000	+	18.0000i	0.394985	+	0.592477i
$924$		0			0
$925$	−7.00000	−	12.1244i	−0.230159	−	0.398646i
$926$	23.0263	−	39.8827i	0.756690	−	1.31063i
$927$	−7.87564	−	13.6410i	−0.258670	−	0.448030i
$928$	7.79423	−	13.5000i	0.255858	−	0.443159i
$929$	−7.48334			−0.245520			−0.122760	−	0.992436i	$-0.539175\pi$
$929$	−7.48334			−0.245520			−0.122760	+	0.992436i	$0.539175\pi$
$930$	6.80385	−	11.7846i	0.223107	−	0.386433i
$931$		0			0
$932$	−12.9282	+	22.3923i	−0.423477	+	0.733484i
$933$	1.73205	−	3.00000i	0.0567048	−	0.0982156i
$934$	−33.8038			−1.10610
$935$	−17.4904	+	30.2942i	−0.571997	+	0.990727i
$936$	−6.82051	+	13.7942i	−0.222935	+	0.450878i
$937$	40.8038			1.33300			0.666502	−	0.745503i	$-0.267791\pi$
$937$	40.8038			1.33300			0.666502	+	0.745503i	$0.267791\pi$
$938$		0			0
$939$	−4.67949	−	8.10512i	−0.152709	−	0.264501i
$940$	1.60770			0.0524372
$941$	−27.9282	+	48.3731i	−0.910433	+	1.57692i	−0.0969804	+	0.995286i	$0.530918\pi$
$941$	−27.9282	+	48.3731i	−0.910433	+	1.57692i	−0.813453	+	0.581631i	$0.802415\pi$
$942$	5.83013	+	10.0981i	0.189956	+	0.329013i
$943$	−6.58846			−0.214550
$944$	53.6603			1.74649
$945$		0			0
$946$	41.7846	+	72.3731i	1.35853	+	2.35305i
$947$	5.36603	−	9.29423i	0.174372	−	0.302022i	−0.765572	−	0.643351i	$-0.777544\pi$
$947$	5.36603	−	9.29423i	0.174372	−	0.302022i	0.939944	+	0.341329i	$0.110877\pi$
$948$	−2.12436	+	3.67949i	−0.0689959	+	0.119504i
$949$	−14.3923	−	21.5885i	−0.467194	−	0.700791i
$950$	3.46410	+	6.00000i	0.112390	+	0.194666i
$951$	−0.169873	−	0.294229i	−0.00550851	−	0.00954102i
$952$		0			0
$953$	−18.5885	+	32.1962i	−0.602139	+	1.04294i	0.390357	+	0.920663i	$0.372351\pi$
$953$	−18.5885	+	32.1962i	−0.602139	+	1.04294i	−0.992497	+	0.122272i	$0.960982\pi$
$954$	−8.38269	−	14.5192i	−0.271399	−	0.470078i
$955$	−1.09808	−	1.90192i	−0.0355329	−	0.0615448i
$956$	13.0981	+	22.6865i	0.423622	+	0.733735i
$957$	5.19615	+	9.00000i	0.167968	+	0.290929i
$958$	−4.09808	+	7.09808i	−0.132403	+	0.229328i
$959$		0			0
$960$	−0.633975	−	1.09808i	−0.0204614	−	0.0354403i
$961$	−3.69615	−	6.40192i	−0.119231	−	0.206514i
$962$	−43.6244	+	2.81347i	−1.40651	+	0.0907098i
$963$	24.4641	−	42.3731i	0.788345	−	1.36545i
$964$	−5.40192	+	9.35641i	−0.173984	+	0.301350i
$965$	−4.33013	−	7.50000i	−0.139392	−	0.241434i
$966$		0			0
$967$	3.01924			0.0970921			0.0485461	−	0.998821i	$-0.484541\pi$
$967$	3.01924			0.0970921			0.0485461	+	0.998821i	$0.484541\pi$
$968$	19.7321			0.634212
$969$	3.12436	+	5.41154i	0.100369	+	0.173844i
$970$	21.5885	−	37.3923i	0.693164	−	1.20059i
$971$	−16.6410			−0.534036			−0.267018	−	0.963692i	$-0.586038\pi$
$971$	−16.6410			−0.534036			−0.267018	+	0.963692i	$0.586038\pi$
$972$	−7.63397	−	13.2224i	−0.244860	−	0.424110i
$973$		0			0
$974$	1.35898			0.0435447
$975$	−2.92820	−	4.39230i	−0.0937776	−	0.140666i
$976$	37.9904	−	65.8013i	1.21604	−	2.10625i
$977$	−37.6410			−1.20424			−0.602121	−	0.798405i	$-0.705678\pi$
$977$	−37.6410			−1.20424			−0.602121	+	0.798405i	$0.705678\pi$
$978$	3.67949	−	6.37307i	0.117657	−	0.203788i
$979$	−2.19615	+	3.80385i	−0.0701893	+	0.121571i
$980$		0			0
$981$	15.2679	−	26.4449i	0.487468	−	0.844320i
$982$	−49.1769			−1.56930
$983$	8.66025	−	15.0000i	0.276219	−	0.478426i	−0.694223	−	0.719760i	$-0.744252\pi$
$983$	8.66025	−	15.0000i	0.276219	−	0.478426i	0.970442	+	0.241334i	$0.0775851\pi$
$984$	3.29423	+	5.70577i	0.105016	+	0.181893i
$985$	−10.3923	+	18.0000i	−0.331126	+	0.573528i
$986$	−11.0885	−	19.2058i	−0.353128	−	0.611636i
$987$		0			0
$988$	7.19615	−	0.464102i	0.228940	−	0.0147650i
$989$	−6.46410	−	11.1962i	−0.205546	−	0.356017i
$990$	34.9808			1.11176
$991$	−32.9808			−1.04767			−0.523834	−	0.851820i	$-0.675499\pi$
$991$	−32.9808			−1.04767			−0.523834	+	0.851820i	$0.675499\pi$
$992$	32.1962			1.02223
$993$	−19.7513			−0.626788
$994$		0			0
$995$	1.73205	−	3.00000i	0.0549097	−	0.0951064i
$996$	3.00000	+	5.19615i	0.0950586	+	0.164646i
$997$	−7.59808	−	13.1603i	−0.240633	−	0.416789i	0.720261	−	0.693703i	$-0.244022\pi$
$997$	−7.59808	−	13.1603i	−0.240633	−	0.416789i	−0.960895	+	0.276913i	$0.910689\pi$
$998$	−22.4833			−0.711698
$999$	−14.0000	+	24.2487i	−0.442940	+	0.767195i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.g.d.263.2		4
7.2	even	3		637.2.h.e.471.1		4
7.3	odd	6		91.2.f.b.29.2	yes	4
7.4	even	3		637.2.f.d.393.2		4
7.5	odd	6		637.2.h.d.471.1		4
7.6	odd	2		637.2.g.e.263.2		4
13.9	even	3		637.2.h.e.165.1		4
21.17	even	6		819.2.o.b.757.1		4
28.3	even	6		1456.2.s.o.1121.1		4
91.3	odd	6		1183.2.a.f.1.1		2
91.9	even	3	inner	637.2.g.d.373.2		4
91.10	odd	6		1183.2.a.e.1.2		2
91.24	even	12		1183.2.c.e.337.1		4
91.48	odd	6		637.2.h.d.165.1		4
91.61	odd	6		637.2.g.e.373.2		4
91.74	even	3		637.2.f.d.295.2		4
91.80	even	12		1183.2.c.e.337.3		4
91.81	even	3		8281.2.a.r.1.1		2
91.87	odd	6		91.2.f.b.22.2	✓	4
91.88	even	6		8281.2.a.t.1.2		2
273.269	even	6		819.2.o.b.568.1		4
364.87	even	6		1456.2.s.o.113.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.f.b.22.2	✓	4	91.87	odd	6
91.2.f.b.29.2	yes	4	7.3	odd	6
637.2.f.d.295.2		4	91.74	even	3
637.2.f.d.393.2		4	7.4	even	3
637.2.g.d.263.2		4	1.1	even	1	trivial
637.2.g.d.373.2		4	91.9	even	3	inner
637.2.g.e.263.2		4	7.6	odd	2
637.2.g.e.373.2		4	91.61	odd	6
637.2.h.d.165.1		4	91.48	odd	6
637.2.h.d.471.1		4	7.5	odd	6
637.2.h.e.165.1		4	13.9	even	3
637.2.h.e.471.1		4	7.2	even	3
819.2.o.b.568.1		4	273.269	even	6
819.2.o.b.757.1		4	21.17	even	6
1183.2.a.e.1.2		2	91.10	odd	6
1183.2.a.f.1.1		2	91.3	odd	6
1183.2.c.e.337.1		4	91.24	even	12
1183.2.c.e.337.3		4	91.80	even	12
1456.2.s.o.113.1		4	364.87	even	6
1456.2.s.o.1121.1		4	28.3	even	6
8281.2.a.r.1.1		2	91.81	even	3
8281.2.a.t.1.2		2	91.88	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.866025 - 1.50000i) q^{2} +0.732051 q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 - 1.50000i) q^{5} +(0.633975 - 1.09808i) q^{6} +1.73205 q^{8} -2.46410 q^{9} +O(q^{10})\)	\(q+(0.866025 - 1.50000i) q^{2} +0.732051 q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 - 1.50000i) q^{5} +(0.633975 - 1.09808i) q^{6} +1.73205 q^{8} -2.46410 q^{9} -3.00000 q^{10} +4.73205 q^{11} +(-0.366025 - 0.633975i) q^{12} +(1.59808 - 3.23205i) q^{13} +(-0.633975 - 1.09808i) q^{15} +(2.50000 - 4.33013i) q^{16} +(-2.13397 - 3.69615i) q^{17} +(-2.13397 + 3.69615i) q^{18} -2.00000 q^{19} +(-0.866025 + 1.50000i) q^{20} +(4.09808 - 7.09808i) q^{22} +(-0.633975 + 1.09808i) q^{23} +1.26795 q^{24} +(1.00000 - 1.73205i) q^{25} +(-3.46410 - 5.19615i) q^{26} -4.00000 q^{27} +(1.50000 + 2.59808i) q^{29} -2.19615 q^{30} +(-3.09808 + 5.36603i) q^{31} +(-2.59808 - 4.50000i) q^{32} +3.46410 q^{33} -7.39230 q^{34} +(1.23205 + 2.13397i) q^{36} +(3.50000 - 6.06218i) q^{37} +(-1.73205 + 3.00000i) q^{38} +(1.16987 - 2.36603i) q^{39} +(-1.50000 - 2.59808i) q^{40} +(2.59808 + 4.50000i) q^{41} +(-5.09808 + 8.83013i) q^{43} +(-2.36603 - 4.09808i) q^{44} +(2.13397 + 3.69615i) q^{45} +(1.09808 + 1.90192i) q^{46} +(-0.464102 - 0.803848i) q^{47} +(1.83013 - 3.16987i) q^{48} +(-1.73205 - 3.00000i) q^{50} +(-1.56218 - 2.70577i) q^{51} +(-3.59808 + 0.232051i) q^{52} +(-1.96410 + 3.40192i) q^{53} +(-3.46410 + 6.00000i) q^{54} +(-4.09808 - 7.09808i) q^{55} -1.46410 q^{57} +5.19615 q^{58} +(5.36603 + 9.29423i) q^{59} +(-0.633975 + 1.09808i) q^{60} +15.1962 q^{61} +(5.36603 + 9.29423i) q^{62} +1.00000 q^{64} +(-6.23205 + 0.401924i) q^{65} +(3.00000 - 5.19615i) q^{66} +4.19615 q^{67} +(-2.13397 + 3.69615i) q^{68} +(-0.464102 + 0.803848i) q^{69} +(-3.00000 + 5.19615i) q^{71} -4.26795 q^{72} +(3.59808 - 6.23205i) q^{73} +(-6.06218 - 10.5000i) q^{74} +(0.732051 - 1.26795i) q^{75} +(1.00000 + 1.73205i) q^{76} +(-2.53590 - 3.80385i) q^{78} +(-2.90192 - 5.02628i) q^{79} -8.66025 q^{80} +4.46410 q^{81} +9.00000 q^{82} -8.19615 q^{83} +(-3.69615 + 6.40192i) q^{85} +(8.83013 + 15.2942i) q^{86} +(1.09808 + 1.90192i) q^{87} +8.19615 q^{88} +(-0.464102 + 0.803848i) q^{89} +7.39230 q^{90} +1.26795 q^{92} +(-2.26795 + 3.92820i) q^{93} -1.60770 q^{94} +(1.73205 + 3.00000i) q^{95} +(-1.90192 - 3.29423i) q^{96} +(-7.19615 + 12.4641i) q^{97} -11.6603 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} - 2 q^{4} + 6 q^{6} + 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^3 - 2 * q^4 + 6 * q^6 + 4 * q^9	\( 4 q - 4 q^{3} - 2 q^{4} + 6 q^{6} + 4 q^{9} - 12 q^{10} + 12 q^{11} + 2 q^{12} - 4 q^{13} - 6 q^{15} + 10 q^{16} - 12 q^{17} - 12 q^{18} - 8 q^{19} + 6 q^{22} - 6 q^{23} + 12 q^{24} + 4 q^{25} - 16 q^{27} + 6 q^{29} + 12 q^{30} - 2 q^{31} + 12 q^{34} - 2 q^{36} + 14 q^{37} + 22 q^{39} - 6 q^{40} - 10 q^{43} - 6 q^{44} + 12 q^{45} - 6 q^{46} + 12 q^{47} - 10 q^{48} + 18 q^{51} - 4 q^{52} + 6 q^{53} - 6 q^{55} + 8 q^{57} + 18 q^{59} - 6 q^{60} + 40 q^{61} + 18 q^{62} + 4 q^{64} - 18 q^{65} + 12 q^{66} - 4 q^{67} - 12 q^{68} + 12 q^{69} - 12 q^{71} - 24 q^{72} + 4 q^{73} - 4 q^{75} + 4 q^{76} - 24 q^{78} - 22 q^{79} + 4 q^{81} + 36 q^{82} - 12 q^{83} + 6 q^{85} + 18 q^{86} - 6 q^{87} + 12 q^{88} + 12 q^{89} - 12 q^{90} + 12 q^{92} - 16 q^{93} - 48 q^{94} - 18 q^{96} - 8 q^{97} - 12 q^{99}+O(q^{100}) \) 4 * q - 4 * q^3 - 2 * q^4 + 6 * q^6 + 4 * q^9 - 12 * q^10 + 12 * q^11 + 2 * q^12 - 4 * q^13 - 6 * q^15 + 10 * q^16 - 12 * q^17 - 12 * q^18 - 8 * q^19 + 6 * q^22 - 6 * q^23 + 12 * q^24 + 4 * q^25 - 16 * q^27 + 6 * q^29 + 12 * q^30 - 2 * q^31 + 12 * q^34 - 2 * q^36 + 14 * q^37 + 22 * q^39 - 6 * q^40 - 10 * q^43 - 6 * q^44 + 12 * q^45 - 6 * q^46 + 12 * q^47 - 10 * q^48 + 18 * q^51 - 4 * q^52 + 6 * q^53 - 6 * q^55 + 8 * q^57 + 18 * q^59 - 6 * q^60 + 40 * q^61 + 18 * q^62 + 4 * q^64 - 18 * q^65 + 12 * q^66 - 4 * q^67 - 12 * q^68 + 12 * q^69 - 12 * q^71 - 24 * q^72 + 4 * q^73 - 4 * q^75 + 4 * q^76 - 24 * q^78 - 22 * q^79 + 4 * q^81 + 36 * q^82 - 12 * q^83 + 6 * q^85 + 18 * q^86 - 6 * q^87 + 12 * q^88 + 12 * q^89 - 12 * q^90 + 12 * q^92 - 16 * q^93 - 48 * q^94 - 18 * q^96 - 8 * q^97 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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