LMFDB - Embedded newform 975.2.bc.j.751.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(751,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("975.751");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.bc (of order $6$, degree $2$, 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:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.191102976.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 6x^{6} + 6x^{4} + 36x^{2} + 36 $ x^8 - 6x^6 + 6x^4 + 36*x^2 + 36
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			751.3
Root			$2.10121 - 0.563016i$ of defining polynomial
Character	$\chi$	$=$	975.751
Dual form			975.2.bc.j.901.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.975173 - 0.563016i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.366025 + 0.633975i) q^{4} +(-0.975173 - 0.563016i) q^{6} +(-2.47517 - 1.42904i) q^{7} +3.07638i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.975173 - 0.563016i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.366025 + 0.633975i) q^{4} +(-0.975173 - 0.563016i) q^{6} +(-2.47517 - 1.42904i) q^{7} +3.07638i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-2.66422 + 1.53819i) q^{11} +0.732051 q^{12} +(3.55507 - 0.601205i) q^{13} -3.21829 q^{14} +(1.00000 + 1.73205i) q^{16} +(0.975173 - 1.68905i) q^{17} +1.12603i q^{18} +(6.42652 + 3.71035i) q^{19} +2.85808i q^{21} +(-1.73205 + 3.00000i) q^{22} +(4.39627 + 7.61457i) q^{23} +(2.66422 - 1.53819i) q^{24} +(3.12832 - 2.58784i) q^{26} +1.00000 q^{27} +(1.81195 - 1.04613i) q^{28} +(3.34120 + 5.78712i) q^{29} +3.15276i q^{31} +(-3.37810 - 1.95035i) q^{32} +(2.66422 + 1.53819i) q^{33} -2.19615i q^{34} +(-0.366025 - 0.633975i) q^{36} +(-7.14650 + 4.12603i) q^{37} +8.35596 q^{38} +(-2.29820 - 2.77818i) q^{39} +(2.87710 - 1.66109i) q^{41} +(1.60915 + 2.78712i) q^{42} +(-4.77337 + 8.26772i) q^{43} -2.25207i q^{44} +(8.57425 + 4.95035i) q^{46} -1.79759i q^{47} +(1.00000 - 1.73205i) q^{48} +(0.584320 + 1.01207i) q^{49} -1.95035 q^{51} +(-0.920099 + 2.47388i) q^{52} -10.6569 q^{53} +(0.975173 - 0.563016i) q^{54} +(4.39627 - 7.61457i) q^{56} -7.42071i q^{57} +(6.51649 + 3.76230i) q^{58} +(4.17256 + 2.40903i) q^{59} +(3.13397 - 5.42820i) q^{61} +(1.77505 + 3.07448i) q^{62} +(2.47517 - 1.42904i) q^{63} -8.39230 q^{64} +3.46410 q^{66} +(5.09097 - 2.93927i) q^{67} +(0.713876 + 1.23647i) q^{68} +(4.39627 - 7.61457i) q^{69} +(8.91942 + 5.14963i) q^{71} +(-2.66422 - 1.53819i) q^{72} -11.1101i q^{73} +(-4.64605 + 8.04719i) q^{74} +(-4.70454 + 2.71617i) q^{76} +8.79254 q^{77} +(-3.80530 - 1.41529i) q^{78} -11.0968 q^{79} +(-0.500000 - 0.866025i) q^{81} +(1.87044 - 3.23970i) q^{82} +6.97707i q^{83} +(-1.81195 - 1.04613i) q^{84} +10.7499i q^{86} +(3.34120 - 5.78712i) q^{87} +(-4.73205 - 8.19615i) q^{88} +(0.0805845 - 0.0465255i) q^{89} +(-9.65857 - 3.59226i) q^{91} -6.43659 q^{92} +(2.73037 - 1.57638i) q^{93} +(-1.01207 - 1.75296i) q^{94} +3.90069i q^{96} +(-4.15483 - 2.39879i) q^{97} +(1.13963 + 0.657963i) q^{98} -3.07638i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} + 4 q^{4} - 12 q^{7} - 4 q^{9}+O(q^{10}) $ 8 * q - 4 * q^3 + 4 * q^4 - 12 * q^7 - 4 * q^9	$ 8 q - 4 q^{3} + 4 q^{4} - 12 q^{7} - 4 q^{9} - 8 q^{12} + 8 q^{13} - 24 q^{14} + 8 q^{16} - 12 q^{19} - 24 q^{26} + 8 q^{27} - 12 q^{28} + 12 q^{29} + 4 q^{36} - 4 q^{39} + 36 q^{41} + 12 q^{42} - 16 q^{43} + 8 q^{48} - 4 q^{49} - 20 q^{52} + 36 q^{58} + 36 q^{59} + 32 q^{61} + 12 q^{63} + 16 q^{64} + 48 q^{67} + 36 q^{71} - 24 q^{74} - 48 q^{76} + 12 q^{78} - 16 q^{79} - 4 q^{81} + 12 q^{82} + 12 q^{84} + 12 q^{87} - 24 q^{88} + 36 q^{89} - 48 q^{92} + 12 q^{94} + 72 q^{98}+O(q^{100}) $ 8 * q - 4 * q^3 + 4 * q^4 - 12 * q^7 - 4 * q^9 - 8 * q^12 + 8 * q^13 - 24 * q^14 + 8 * q^16 - 12 * q^19 - 24 * q^26 + 8 * q^27 - 12 * q^28 + 12 * q^29 + 4 * q^36 - 4 * q^39 + 36 * q^41 + 12 * q^42 - 16 * q^43 + 8 * q^48 - 4 * q^49 - 20 * q^52 + 36 * q^58 + 36 * q^59 + 32 * q^61 + 12 * q^63 + 16 * q^64 + 48 * q^67 + 36 * q^71 - 24 * q^74 - 48 * q^76 + 12 * q^78 - 16 * q^79 - 4 * q^81 + 12 * q^82 + 12 * q^84 + 12 * q^87 - 24 * q^88 + 36 * q^89 - 48 * q^92 + 12 * q^94 + 72 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

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 $

$2$	0.975173	−	0.563016i	0.689551	−	0.398113i	−0.113893	−	0.993493i	$-0.536332\pi$
$2$	0.975173	−	0.563016i	0.689551	−	0.398113i	0.803444	+	0.595380i	$0.202999\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−0.366025	+	0.633975i	−0.183013	+	0.316987i
$5$		0			0
$5$		0			0
$6$	−0.975173	−	0.563016i	−0.398113	−	0.229850i
$7$	−2.47517	−	1.42904i	−0.935527	−	0.540127i	−0.0469719	−	0.998896i	$-0.514957\pi$
$7$	−2.47517	−	1.42904i	−0.935527	−	0.540127i	−0.888555	+	0.458769i	$0.848290\pi$
$8$			3.07638i			1.08766i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	−2.66422	+	1.53819i	−0.803293	+	0.463781i	−0.844621	−	0.535364i	$-0.820174\pi$
$11$	−2.66422	+	1.53819i	−0.803293	+	0.463781i	0.0413283	+	0.999146i	$0.486841\pi$
$12$	0.732051			0.211325
$13$	3.55507	−	0.601205i	0.986000	−	0.166744i
$13$	3.55507	−	0.601205i	0.986000	−	0.166744i
$14$	−3.21829			−0.860125
$15$		0			0
$16$	1.00000	+	1.73205i	0.250000	+	0.433013i
$17$	0.975173	−	1.68905i	0.236514	−	0.409654i	−0.723198	−	0.690641i	$-0.757328\pi$
$17$	0.975173	−	1.68905i	0.236514	−	0.409654i	0.959712	+	0.280987i	$0.0906617\pi$
$18$			1.12603i			0.265408i
$19$	6.42652	+	3.71035i	1.47434	+	0.851213i	0.999582	−	0.0289008i	$-0.00920068\pi$
$19$	6.42652	+	3.71035i	1.47434	+	0.851213i	0.474762	+	0.880114i	$0.342534\pi$
$20$		0			0
$21$			2.85808i			0.623685i
$22$	−1.73205	+	3.00000i	−0.369274	+	0.639602i
$23$	4.39627	+	7.61457i	0.916686	+	1.58775i	0.804414	+	0.594070i	$0.202480\pi$
$23$	4.39627	+	7.61457i	0.916686	+	1.58775i	0.112272	+	0.993677i	$0.464187\pi$
$24$	2.66422	−	1.53819i	0.543832	−	0.313982i
$25$		0			0
$26$	3.12832	−	2.58784i	0.613515	−	0.507518i
$27$	1.00000			0.192450
$28$	1.81195	−	1.04613i	0.342427	−	0.197700i
$29$	3.34120	+	5.78712i	0.620445	+	1.07464i	0.989403	+	0.145196i	$0.0463813\pi$
$29$	3.34120	+	5.78712i	0.620445	+	1.07464i	−0.368958	+	0.929446i	$0.620285\pi$
$30$		0			0
$31$			3.15276i			0.566252i	0.959083	+	0.283126i	$0.0913714\pi$
$31$			3.15276i			0.566252i	−0.959083	+	0.283126i	$0.908629\pi$
$32$	−3.37810	−	1.95035i	−0.597169	−	0.344776i
$33$	2.66422	+	1.53819i	0.463781	+	0.267764i
$34$		−	2.19615i		−	0.376637i
$35$		0			0
$36$	−0.366025	−	0.633975i	−0.0610042	−	0.105662i
$37$	−7.14650	+	4.12603i	−1.17488	+	0.678316i	−0.954824	−	0.297172i	$-0.903956\pi$
$37$	−7.14650	+	4.12603i	−1.17488	+	0.678316i	−0.220053	+	0.975488i	$0.570623\pi$
$38$	8.35596			1.35551
$39$	−2.29820	−	2.77818i	−0.368006	−	0.444865i
$40$		0			0
$41$	2.87710	−	1.66109i	0.449327	−	0.259419i	−0.258219	−	0.966086i	$-0.583136\pi$
$41$	2.87710	−	1.66109i	0.449327	−	0.259419i	0.707546	+	0.706667i	$0.249802\pi$
$42$	1.60915	+	2.78712i	0.248297	+	0.430063i
$43$	−4.77337	+	8.26772i	−0.727932	+	1.26082i	0.229824	+	0.973232i	$0.426185\pi$
$43$	−4.77337	+	8.26772i	−0.727932	+	1.26082i	−0.957756	+	0.287583i	$0.907148\pi$
$44$		−	2.25207i		−	0.339512i
$45$		0			0
$46$	8.57425	+	4.95035i	1.26420	+	0.729889i
$47$		−	1.79759i		−	0.262205i	−0.991369	−	0.131103i	$-0.958148\pi$
$47$		−	1.79759i		−	0.262205i	0.991369	−	0.131103i	$-0.0418518\pi$
$48$	1.00000	−	1.73205i	0.144338	−	0.250000i
$49$	0.584320	+	1.01207i	0.0834743	+	0.144582i
$50$		0			0
$51$	−1.95035			−0.273103
$52$	−0.920099	+	2.47388i	−0.127595	+	0.343066i
$53$	−10.6569			−1.46384			−0.731918	−	0.681393i	$-0.761375\pi$
$53$	−10.6569			−1.46384			−0.731918	+	0.681393i	$0.761375\pi$
$54$	0.975173	−	0.563016i	0.132704	−	0.0766168i
$55$		0			0
$56$	4.39627	−	7.61457i	0.587477	−	1.01754i
$57$		−	7.42071i		−	0.982896i
$58$	6.51649	+	3.76230i	0.855657	+	0.494014i
$59$	4.17256	+	2.40903i	0.543221	+	0.313629i	0.746383	−	0.665516i	$-0.231789\pi$
$59$	4.17256	+	2.40903i	0.543221	+	0.313629i	−0.203162	+	0.979145i	$0.565122\pi$
$60$		0			0
$61$	3.13397	−	5.42820i	0.401264	−	0.695010i	−0.592614	−	0.805486i	$-0.701904\pi$
$61$	3.13397	−	5.42820i	0.401264	−	0.695010i	0.993879	+	0.110476i	$0.0352375\pi$
$62$	1.77505	+	3.07448i	0.225432	+	0.390460i
$63$	2.47517	−	1.42904i	0.311842	−	0.180042i
$64$	−8.39230			−1.04904
$65$		0			0
$66$	3.46410			0.426401
$67$	5.09097	−	2.93927i	0.621961	−	0.359090i	−0.155671	−	0.987809i	$-0.549754\pi$
$67$	5.09097	−	2.93927i	0.621961	−	0.359090i	0.777632	+	0.628719i	$0.216421\pi$
$68$	0.713876	+	1.23647i	0.0865702	+	0.149944i
$69$	4.39627	−	7.61457i	0.529249	−	0.916686i
$70$		0			0
$71$	8.91942	+	5.14963i	1.05854	+	0.611148i	0.925028	−	0.379899i	$-0.124041\pi$
$71$	8.91942	+	5.14963i	1.05854	+	0.611148i	0.133512	+	0.991047i	$0.457375\pi$
$72$	−2.66422	−	1.53819i	−0.313982	−	0.181277i
$73$		−	11.1101i		−	1.30034i	−0.759787	−	0.650172i	$-0.774697\pi$
$73$		−	11.1101i		−	1.30034i	0.759787	−	0.650172i	$-0.225303\pi$
$74$	−4.64605	+	8.04719i	−0.540092	+	0.935467i
$75$		0			0
$76$	−4.70454	+	2.71617i	−0.539648	+	0.311566i
$77$	8.79254			1.00200
$78$	−3.80530	−	1.41529i	−0.430865	−	0.160250i
$79$	−11.0968			−1.24849			−0.624246	−	0.781228i	$-0.714594\pi$
$79$	−11.0968			−1.24849			−0.624246	+	0.781228i	$0.714594\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	1.87044	−	3.23970i	0.206556	−	0.357765i
$83$			6.97707i			0.765833i	0.923783	+	0.382916i	$0.125080\pi$
$83$			6.97707i			0.765833i	−0.923783	+	0.382916i	$0.874920\pi$
$84$	−1.81195	−	1.04613i	−0.197700	−	0.114142i
$85$		0			0
$86$			10.7499i			1.15920i
$87$	3.34120	−	5.78712i	0.358214	−	0.620445i
$88$	−4.73205	−	8.19615i	−0.504438	−	0.873713i
$89$	0.0805845	−	0.0465255i	0.00854194	−	0.00493169i	−0.495723	−	0.868481i	$-0.665097\pi$
$89$	0.0805845	−	0.0465255i	0.00854194	−	0.00493169i	0.504265	+	0.863549i	$0.331764\pi$
$90$		0			0
$91$	−9.65857	−	3.59226i	−1.01249	−	0.376571i
$92$	−6.43659			−0.671061
$93$	2.73037	−	1.57638i	0.283126	−	0.163463i
$94$	−1.01207	−	1.75296i	−0.104387	−	0.180804i
$95$		0			0
$96$			3.90069i			0.398113i
$97$	−4.15483	−	2.39879i	−0.421860	−	0.243561i	0.274013	−	0.961726i	$-0.411649\pi$
$97$	−4.15483	−	2.39879i	−0.421860	−	0.243561i	−0.695873	+	0.718165i	$0.744982\pi$
$98$	1.13963	+	0.657963i	0.115120	+	0.0664643i
$99$		−	3.07638i		−	0.309188i
$100$		0			0
$101$	1.39627	+	2.41841i	0.138934	+	0.240641i	0.927093	−	0.374830i	$-0.122299\pi$
$101$	1.39627	+	2.41841i	0.138934	+	0.240641i	−0.788159	+	0.615471i	$0.788966\pi$
$102$	−1.90192	+	1.09808i	−0.188319	+	0.108726i
$103$	8.35395			0.823139			0.411570	−	0.911378i	$-0.364981\pi$
$103$	8.35395			0.823139			0.411570	+	0.911378i	$0.364981\pi$
$104$	1.84953	+	10.9368i	0.181362	+	1.07244i
$105$		0			0
$106$	−10.3923	+	6.00000i	−1.00939	+	0.582772i
$107$	3.17529	+	5.49977i	0.306967	+	0.531683i	0.977697	−	0.210019i	$-0.0673525\pi$
$107$	3.17529	+	5.49977i	0.306967	+	0.531683i	−0.670730	+	0.741701i	$0.734019\pi$
$108$	−0.366025	+	0.633975i	−0.0352208	+	0.0610042i
$109$		−	11.7996i		−	1.13020i	−0.825024	−	0.565098i	$-0.808838\pi$
$109$		−	11.7996i		−	1.13020i	0.825024	−	0.565098i	$-0.191162\pi$
$110$		0			0
$111$	7.14650	+	4.12603i	0.678316	+	0.391626i
$112$		−	5.71617i		−	0.540127i
$113$	1.73205	−	3.00000i	0.162938	−	0.282216i	−0.772983	−	0.634426i	$-0.781236\pi$
$113$	1.73205	−	3.00000i	0.162938	−	0.282216i	0.935921	+	0.352210i	$0.114570\pi$
$114$	−4.17798	−	7.23647i	−0.391303	−	0.677757i
$115$		0			0
$116$	−4.89185			−0.454197
$117$	−1.25688	+	3.37939i	−0.116198	+	0.312424i
$118$	5.42529			0.499438
$119$	−4.82744	+	2.78712i	−0.442531	+	0.255495i
$120$		0			0
$121$	−0.767949	+	1.33013i	−0.0698136	+	0.120921i
$122$		−	7.05791i		−	0.638994i
$123$	−2.87710	−	1.66109i	−0.259419	−	0.149776i
$124$	−1.99877	−	1.15399i	−0.179495	−	0.103631i
$125$		0			0
$126$	1.60915	−	2.78712i	0.143354	−	0.248297i
$127$	7.48601	+	12.9662i	0.664276	+	1.15056i	0.979481	+	0.201536i	$0.0645934\pi$
$127$	7.48601	+	12.9662i	0.664276	+	1.15056i	−0.315205	+	0.949024i	$0.602073\pi$
$128$	−1.42775	+	0.824313i	−0.126197	+	0.0728597i
$129$	9.54674			0.840543
$130$		0			0
$131$	−10.5831			−0.924649			−0.462324	−	0.886711i	$-0.652984\pi$
$131$	−10.5831			−0.924649			−0.462324	+	0.886711i	$0.652984\pi$
$132$	−1.95035	+	1.12603i	−0.169756	+	0.0980085i
$133$	−10.6045	−	18.3675i	−0.919526	−	1.59267i
$134$	3.30972	−	5.73260i	0.285916	−	0.495221i
$135$		0			0
$136$	5.19615	+	3.00000i	0.445566	+	0.257248i
$137$	−7.54009	−	4.35327i	−0.644193	−	0.371925i	0.142035	−	0.989862i	$-0.454635\pi$
$137$	−7.54009	−	4.35327i	−0.644193	−	0.371925i	−0.786228	+	0.617937i	$0.787969\pi$
$138$		−	9.90069i		−	0.842803i
$139$	5.82844	−	10.0952i	0.494362	−	0.856260i	−0.505617	−	0.862758i	$-0.668735\pi$
$139$	5.82844	−	10.0952i	0.494362	−	0.856260i	0.999979	+	0.00649792i	$0.00206837\pi$
$140$		0			0
$141$	−1.55676	+	0.898795i	−0.131103	+	0.0756922i
$142$	11.5973			0.973223
$143$	−8.54674	+	7.07012i	−0.714714	+	0.591233i
$144$	−2.00000			−0.166667
$145$		0			0
$146$	−6.25519	−	10.8343i	−0.517684	−	0.896654i
$147$	0.584320	−	1.01207i	0.0481939	−	0.0834743i
$148$		−	6.04093i		−	0.496561i
$149$	5.91003	+	3.41216i	0.484168	+	0.279535i	0.722152	−	0.691734i	$-0.243153\pi$
$149$	5.91003	+	3.41216i	0.484168	+	0.279535i	−0.237984	+	0.971269i	$0.576486\pi$
$150$		0			0
$151$		−	12.6810i		−	1.03197i	−0.856598	−	0.515984i	$-0.827426\pi$
$151$		−	12.6810i		−	1.03197i	0.856598	−	0.515984i	$-0.172574\pi$
$152$	−11.4144	+	19.7704i	−0.925834	+	1.60359i
$153$	0.975173	+	1.68905i	0.0788380	+	0.136551i
$154$	8.57425	−	4.95035i	0.690933	−	0.398910i
$155$		0			0
$156$	2.60249	−	0.440113i	0.208366	−	0.0352372i
$157$	−7.98333			−0.637139			−0.318569	−	0.947900i	$-0.603202\pi$
$157$	−7.98333			−0.637139			−0.318569	+	0.947900i	$0.603202\pi$
$158$	−10.8213	+	6.24770i	−0.860900	+	0.497041i
$159$	5.32844	+	9.22913i	0.422573	+	0.731918i
$160$		0			0
$161$		−	25.1298i		−	1.98051i
$162$	−0.975173	−	0.563016i	−0.0766168	−	0.0442347i
$163$	10.6713	+	6.16109i	0.835843	+	0.482574i	0.855849	−	0.517226i	$-0.173035\pi$
$163$	10.6713	+	6.16109i	0.835843	+	0.482574i	−0.0200063	+	0.999800i	$0.506369\pi$
$164$			2.43201i			0.189908i
$165$		0			0
$166$	3.92820	+	6.80385i	0.304888	+	0.528081i
$167$	19.0020	−	10.9708i	1.47042	−	0.848947i	0.470970	−	0.882149i	$-0.343904\pi$
$167$	19.0020	−	10.9708i	1.47042	−	0.848947i	0.999449	+	0.0332022i	$0.0105705\pi$
$168$	−8.79254			−0.678360
$169$	12.2771	−	4.27466i	0.944393	−	0.328820i
$170$		0			0
$171$	−6.42652	+	3.71035i	−0.491448	+	0.283738i
$172$	−3.49435	−	6.05239i	−0.266442	−	0.461490i
$173$	−7.52528	+	13.0342i	−0.572136	+	0.990969i	0.424210	+	0.905564i	$0.360552\pi$
$173$	−7.52528	+	13.0342i	−0.572136	+	0.990969i	−0.996346	+	0.0854053i	$0.972781\pi$
$174$		−	7.52460i		−	0.570438i
$175$		0			0
$176$	−5.32844	−	3.07638i	−0.401647	−	0.231891i
$177$		−	4.81805i		−	0.362147i
$178$	0.0523892	−	0.0907407i	0.00392673	−	0.00680130i
$179$	−0.240387	−	0.416363i	−0.0179674	−	0.0311204i	0.856902	−	0.515480i	$-0.172386\pi$
$179$	−0.240387	−	0.416363i	−0.0179674	−	0.0311204i	−0.874869	+	0.484359i	$0.839053\pi$
$180$		0			0
$181$	−1.85887			−0.138169			−0.0690844	−	0.997611i	$-0.522008\pi$
$181$	−1.85887			−0.138169			−0.0690844	+	0.997611i	$0.522008\pi$
$182$	−11.4413	+	1.93486i	−0.848084	+	0.143421i
$183$	−6.26795			−0.463340
$184$	−23.4253	+	13.5246i	−1.72694	+	0.997046i
$185$		0			0
$186$	1.77505	−	3.07448i	0.130153	−	0.225432i
$187$			6.00000i			0.438763i
$188$	1.13963	+	0.657963i	0.0831158	+	0.0479869i
$189$	−2.47517	−	1.42904i	−0.180042	−	0.103947i
$190$		0			0
$191$	−4.35937	+	7.55066i	−0.315433	+	0.546346i	−0.979529	−	0.201301i	$-0.935483\pi$
$191$	−4.35937	+	7.55066i	−0.315433	+	0.546346i	0.664096	+	0.747647i	$0.268816\pi$
$192$	4.19615	+	7.26795i	0.302831	+	0.524519i
$193$	−5.58869	+	3.22663i	−0.402283	+	0.232258i	−0.687468	−	0.726214i	$-0.741278\pi$
$193$	−5.58869	+	3.22663i	−0.402283	+	0.232258i	0.285186	+	0.958472i	$0.407945\pi$
$194$	−5.40224			−0.387858
$195$		0			0
$196$	−0.855504			−0.0611074
$197$	−10.0399	+	5.79651i	−0.715310	+	0.412984i	−0.813024	−	0.582230i	$-0.802180\pi$
$197$	−10.0399	+	5.79651i	−0.715310	+	0.412984i	0.0977141	+	0.995215i	$0.468847\pi$
$198$	−1.73205	−	3.00000i	−0.123091	−	0.213201i
$199$	0.400691	−	0.694017i	0.0284042	−	0.0491976i	−0.851474	−	0.524397i	$-0.824291\pi$
$199$	0.400691	−	0.694017i	0.0284042	−	0.0491976i	0.879878	+	0.475199i	$0.157624\pi$
$200$		0			0
$201$	−5.09097	−	2.93927i	−0.359090	−	0.207320i
$202$	2.72321	+	1.57225i	0.191605	+	0.110623i
$203$		−	19.0988i		−	1.34048i
$204$	0.713876	−	1.23647i	0.0499813	−	0.0865702i
$205$		0			0
$206$	8.14655	−	4.70341i	0.567597	−	0.327702i
$207$	−8.79254			−0.611124
$208$	4.59639	+	5.55636i	0.318702	+	0.385265i
$209$	−22.8289			−1.57911
$210$		0			0
$211$	4.14605	+	7.18116i	0.285426	+	0.494372i	0.972712	−	0.232015i	$-0.0745317\pi$
$211$	4.14605	+	7.18116i	0.285426	+	0.494372i	−0.687287	+	0.726386i	$0.741198\pi$
$212$	3.90069	−	6.75620i	0.267901	−	0.464017i
$213$		−	10.2993i		−	0.705693i
$214$	6.19292	+	3.57548i	0.423339	+	0.244415i
$215$		0			0
$216$			3.07638i			0.209321i
$217$	4.50542	−	7.80362i	0.305848	−	0.529744i
$218$	−6.64336	−	11.5066i	−0.449945	−	0.779328i
$219$	−9.62167	+	5.55507i	−0.650172	+	0.375377i
$220$		0			0
$221$	2.45135	−	6.59097i	0.164895	−	0.443357i
$222$	9.29209			0.623644
$223$	−11.0517	+	6.38068i	−0.740074	+	0.427282i	−0.822096	−	0.569349i	$-0.807195\pi$
$223$	−11.0517	+	6.38068i	−0.740074	+	0.427282i	0.0820224	+	0.996630i	$0.473862\pi$
$224$	5.57425	+	9.65488i	0.372445	+	0.645094i
$225$		0			0
$226$		−	3.90069i		−	0.259470i
$227$	14.8189	+	8.55568i	0.983563	+	0.567860i	0.903344	−	0.428917i	$-0.141105\pi$
$227$	14.8189	+	8.55568i	0.983563	+	0.567860i	0.0802192	+	0.996777i	$0.474438\pi$
$228$	4.70454	+	2.71617i	0.311566	+	0.179883i
$229$		−	6.39993i		−	0.422919i	−0.977387	−	0.211460i	$-0.932178\pi$
$229$		−	6.39993i		−	0.422919i	0.977387	−	0.211460i	$-0.0678217\pi$
$230$		0			0
$231$	−4.39627	−	7.61457i	−0.289253	−	0.501002i
$232$	−17.8034	+	10.2788i	−1.16885	+	0.674836i
$233$	0.671557			0.0439952			0.0219976	−	0.999758i	$-0.492997\pi$
$233$	0.671557			0.0439952			0.0219976	+	0.999758i	$0.492997\pi$
$234$	0.676977	+	4.00313i	0.0442553	+	0.261693i
$235$		0			0
$236$	−3.05452	+	1.76353i	−0.198833	+	0.114796i
$237$	5.54842	+	9.61015i	0.360409	+	0.624246i
$238$	−3.13839	+	5.43586i	−0.203432	+	0.352354i
$239$		−	7.12983i		−	0.461190i	−0.973050	−	0.230595i	$-0.925933\pi$
$239$		−	7.12983i		−	0.461190i	0.973050	−	0.230595i	$-0.0740673\pi$
$240$		0			0
$241$	−23.3292	−	13.4691i	−1.50277	−	0.867623i	−0.999995	−	0.00320355i	$-0.998980\pi$
$241$	−23.3292	−	13.4691i	−1.50277	−	0.867623i	−0.502772	−	0.864419i	$-0.667686\pi$
$242$			1.72947i			0.111175i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	2.29423	+	3.97372i	0.146873	+	0.254391i
$245$		0			0
$246$	−3.74089			−0.238510
$247$	25.0774	+	9.32692i	1.59564	+	0.593458i
$248$	−9.69907			−0.615892
$249$	6.04232	−	3.48853i	0.382916	−	0.221077i
$250$		0			0
$251$	−5.82402	+	10.0875i	−0.367609	+	0.636718i	−0.989191	−	0.146631i	$-0.953157\pi$
$251$	−5.82402	+	10.0875i	−0.367609	+	0.636718i	0.621582	+	0.783349i	$0.286490\pi$
$252$			2.09226i			0.131800i
$253$	−23.4253	−	13.5246i	−1.47274	−	0.850284i
$254$	14.6003	+	8.42949i	0.916105	+	0.528913i
$255$		0			0
$256$	7.46410	−	12.9282i	0.466506	−	0.808013i
$257$	3.63939	+	6.30362i	0.227019	+	0.393209i	0.956923	−	0.290341i	$-0.0937687\pi$
$257$	3.63939	+	6.30362i	0.227019	+	0.393209i	−0.729904	+	0.683550i	$0.760435\pi$
$258$	9.30972	−	5.37497i	0.579598	−	0.334631i
$259$	23.5851			1.46551
$260$		0			0
$261$	−6.68240			−0.413630
$262$	−10.3203	+	5.95845i	−0.637593	+	0.368114i
$263$	11.9639	+	20.7220i	0.737724	+	1.27778i	0.953518	+	0.301336i	$0.0974327\pi$
$263$	11.9639	+	20.7220i	0.737724	+	1.27778i	−0.215794	+	0.976439i	$0.569234\pi$
$264$	−4.73205	+	8.19615i	−0.291238	+	0.504438i
$265$		0			0
$266$	−20.6824	−	11.9410i	−1.26812	−	0.732150i
$267$	−0.0805845	−	0.0465255i	−0.00493169	−	0.00284731i
$268$			4.30340i			0.262872i
$269$	−2.19073	+	3.79446i	−0.133571	+	0.231352i	−0.925051	−	0.379843i	$-0.875978\pi$
$269$	−2.19073	+	3.79446i	−0.133571	+	0.231352i	0.791479	+	0.611196i	$0.209311\pi$
$270$		0			0
$271$	−2.15488	+	1.24412i	−0.130900	+	0.0755751i	−0.564020	−	0.825761i	$-0.690746\pi$
$271$	−2.15488	+	1.24412i	−0.130900	+	0.0755751i	0.433120	+	0.901336i	$0.357413\pi$
$272$	3.90069			0.236514
$273$	1.71829	+	10.1607i	0.103996	+	0.614953i
$274$	−9.80385			−0.592272
$275$		0			0
$276$	3.21829	+	5.57425i	0.193719	+	0.335530i
$277$	10.8530	−	18.7980i	0.652096	−	1.12946i	−0.330518	−	0.943800i	$-0.607223\pi$
$277$	10.8530	−	18.7980i	0.652096	−	1.12946i	0.982613	−	0.185663i	$-0.0594434\pi$
$278$		−	13.1260i		−	0.787247i
$279$	−2.73037	−	1.57638i	−0.163463	−	0.0943753i
$280$		0			0
$281$			29.7270i			1.77336i	0.462379	+	0.886682i	$0.346996\pi$
$281$			29.7270i			1.77336i	−0.462379	+	0.886682i	$0.653004\pi$
$282$	−1.01207	+	1.75296i	−0.0602680	+	0.104387i
$283$	−13.9998	−	24.2483i	−0.832200	−	1.44141i	−0.896290	−	0.443468i	$-0.853748\pi$
$283$	−13.9998	−	24.2483i	−0.832200	−	1.44141i	0.0640902	−	0.997944i	$-0.479585\pi$
$284$	−6.52947	+	3.76979i	−0.387452	+	0.223696i
$285$		0			0
$286$	−4.35395	+	11.7065i	−0.257455	+	0.692222i
$287$	−9.49508			−0.560477
$288$	3.37810	−	1.95035i	0.199056	−	0.114925i
$289$	6.59808	+	11.4282i	0.388122	+	0.672247i
$290$		0			0
$291$			4.79759i			0.281240i
$292$	7.04355	+	4.06660i	0.412193	+	0.237980i
$293$	14.6866	+	8.47930i	0.857999	+	0.495366i	0.863342	−	0.504620i	$-0.168367\pi$
$293$	14.6866	+	8.47930i	0.857999	+	0.495366i	−0.00534246	+	0.999986i	$0.501701\pi$
$294$		−	1.31593i		−	0.0767464i
$295$		0			0
$296$	−12.6932	−	21.9853i	−0.737779	−	1.27787i
$297$	−2.66422	+	1.53819i	−0.154594	+	0.0892548i
$298$	7.68440			0.445145
$299$	20.2070	+	24.4273i	1.16860	+	1.41267i
$300$		0			0
$301$	23.6298	−	13.6427i	1.36200	−	0.786351i
$302$	−7.13963	−	12.3662i	−0.410839	−	0.711595i
$303$	1.39627	−	2.41841i	0.0802137	−	0.138934i
$304$			14.8414i			0.851213i
$305$		0			0
$306$	1.90192	+	1.09808i	0.108726	+	0.0627728i
$307$		−	15.6072i		−	0.890752i	−0.895344	−	0.445376i	$-0.853070\pi$
$307$		−	15.6072i		−	0.890752i	0.895344	−	0.445376i	$-0.146930\pi$
$308$	−3.21829	+	5.57425i	−0.183379	+	0.317622i
$309$	−4.17698	−	7.23474i	−0.237620	−	0.411570i
$310$		0			0
$311$	24.9941			1.41728			0.708642	−	0.705568i	$-0.249308\pi$
$311$	24.9941			1.41728			0.708642	+	0.705568i	$0.249308\pi$
$312$	8.54674	−	7.07012i	0.483864	−	0.400267i
$313$	−1.16117			−0.0656331			−0.0328166	−	0.999461i	$-0.510448\pi$
$313$	−1.16117			−0.0656331			−0.0328166	+	0.999461i	$0.510448\pi$
$314$	−7.78512	+	4.49474i	−0.439340	+	0.253653i
$315$		0			0
$316$	4.06173	−	7.03512i	0.228490	−	0.395756i
$317$			8.62570i			0.484467i	0.970218	+	0.242234i	$0.0778801\pi$
$317$			8.62570i			0.484467i	−0.970218	+	0.242234i	$0.922120\pi$
$318$	10.3923	+	6.00000i	0.582772	+	0.336463i
$319$	−17.8034	−	10.2788i	−0.996798	−	0.575502i
$320$		0			0
$321$	3.17529	−	5.49977i	0.177228	−	0.306967i
$322$	−14.1485	−	24.5059i	−0.788465	−	1.36566i
$323$	12.5339	−	7.23647i	0.697407	−	0.402648i
$324$	0.732051			0.0406695
$325$		0			0
$326$	13.8752			0.768475
$327$	−10.2187	+	5.89980i	−0.565098	+	0.326259i
$328$	5.11015	+	8.85104i	0.282161	+	0.488717i
$329$	−2.56883	+	4.44934i	−0.141624	+	0.245300i
$330$		0			0
$331$	−22.1899	−	12.8113i	−1.21967	−	0.704174i	−0.254819	−	0.966989i	$-0.582016\pi$
$331$	−22.1899	−	12.8113i	−1.21967	−	0.704174i	−0.964846	+	0.262815i	$0.915349\pi$
$332$	−4.42328	−	2.55378i	−0.242759	−	0.140157i
$333$		−	8.25207i		−	0.452210i
$334$	12.3535	−	21.3969i	0.675953	−	1.17078i
$335$		0			0
$336$	−4.95035	+	2.85808i	−0.270063	+	0.155921i
$337$	20.1770			1.09911			0.549556	−	0.835457i	$-0.314797\pi$
$337$	20.1770			1.09911			0.549556	+	0.835457i	$0.314797\pi$
$338$	9.56560	−	11.0807i	0.520300	−	0.602713i
$339$	−3.46410			−0.188144
$340$		0			0
$341$	−4.84953	−	8.39964i	−0.262617	−	0.454866i
$342$	−4.17798	+	7.23647i	−0.225919	+	0.391303i
$343$			16.6665i			0.899907i
$344$	−25.4346	−	14.6847i	−1.37134	−	0.791745i
$345$		0			0
$346$			16.9474i			0.911099i
$347$	12.0968	−	20.9523i	0.649393	−	1.12478i	−0.333876	−	0.942617i	$-0.608357\pi$
$347$	12.0968	−	20.9523i	0.649393	−	1.12478i	0.983268	−	0.182164i	$-0.0583101\pi$
$348$	2.44593	+	4.23647i	0.131115	+	0.227099i
$349$	22.2362	−	12.8381i	1.19028	−	0.687206i	0.231907	−	0.972738i	$-0.425504\pi$
$349$	22.2362	−	12.8381i	1.19028	−	0.687206i	0.958369	+	0.285532i	$0.0921703\pi$
$350$		0			0
$351$	3.55507	−	0.601205i	0.189756	−	0.0320900i
$352$	12.0000			0.639602
$353$	6.79405	−	3.92254i	0.361611	−	0.208776i	−0.308176	−	0.951329i	$-0.599719\pi$
$353$	6.79405	−	3.92254i	0.361611	−	0.208776i	0.669787	+	0.742553i	$0.266385\pi$
$354$	−2.71264	−	4.69844i	−0.144175	−	0.249719i
$355$		0			0
$356$			0.0681180i			0.00361025i
$357$	4.82744	+	2.78712i	0.255495	+	0.147510i
$358$	−0.468838	−	0.270684i	−0.0247789	−	0.0143061i
$359$		−	19.7145i		−	1.04049i	−0.854017	−	0.520245i	$-0.825840\pi$
$359$		−	19.7145i		−	1.04049i	0.854017	−	0.520245i	$-0.174160\pi$
$360$		0			0
$361$	18.0334	+	31.2348i	0.949128	+	1.64394i
$362$	−1.81272	+	1.04658i	−0.0952745	+	0.0550068i
$363$	1.53590			0.0806138
$364$	5.81268	−	4.80843i	0.304667	−	0.252030i
$365$		0			0
$366$	−6.11233	+	3.52896i	−0.319497	+	0.184462i
$367$	−5.58806	−	9.67880i	−0.291694	−	0.505229i	0.682516	−	0.730870i	$-0.260886\pi$
$367$	−5.58806	−	9.67880i	−0.291694	−	0.505229i	−0.974210	+	0.225641i	$0.927552\pi$
$368$	−8.79254	+	15.2291i	−0.458343	+	0.793873i
$369$			3.32218i			0.172946i
$370$		0			0
$371$	26.3776	+	15.2291i	1.36946	+	0.790657i
$372$			2.30798i			0.119663i
$373$	−4.37586	+	7.57922i	−0.226574	+	0.392437i	−0.956790	−	0.290778i	$-0.906086\pi$
$373$	−4.37586	+	7.57922i	−0.226574	+	0.392437i	0.730217	+	0.683216i	$0.239419\pi$
$374$	3.37810	+	5.85104i	0.174677	+	0.302550i
$375$		0			0
$376$	5.53006			0.285191
$377$	15.3575	+	18.5649i	0.790949	+	0.956142i
$378$	−3.21829			−0.165531
$379$	−16.2550	+	9.38481i	−0.834961	+	0.482065i	−0.855548	−	0.517723i	$-0.826780\pi$
$379$	−16.2550	+	9.38481i	−0.834961	+	0.482065i	0.0205870	+	0.999788i	$0.493446\pi$
$380$		0			0
$381$	7.48601	−	12.9662i	0.383520	−	0.664276i
$382$			9.81759i			0.502312i
$383$	−5.26083	−	3.03734i	−0.268816	−	0.155201i	0.359533	−	0.933132i	$-0.382936\pi$
$383$	−5.26083	−	3.03734i	−0.268816	−	0.155201i	−0.628349	+	0.777931i	$0.716269\pi$
$384$	1.42775	+	0.824313i	0.0728597	+	0.0420655i
$385$		0			0
$386$	−3.63329	+	6.29305i	−0.184930	+	0.320308i
$387$	−4.77337	−	8.26772i	−0.242644	−	0.420272i
$388$	3.04155	−	1.75604i	0.154411	−	0.0891494i
$389$	9.66572			0.490072			0.245036	−	0.969514i	$-0.421200\pi$
$389$	9.66572			0.490072			0.245036	+	0.969514i	$0.421200\pi$
$390$		0			0
$391$	17.1485			0.867237
$392$	−3.11352	+	1.79759i	−0.157256	+	0.0907920i
$393$	5.29154	+	9.16522i	0.266923	+	0.462324i
$394$	−6.52706	+	11.3052i	−0.328829	+	0.569548i
$395$		0			0
$396$	1.95035	+	1.12603i	0.0980085	+	0.0565853i
$397$	−21.0718	−	12.1658i	−1.05757	−	0.610585i	−0.132807	−	0.991142i	$-0.542399\pi$
$397$	−21.0718	−	12.1658i	−1.05757	−	0.610585i	−0.924758	+	0.380556i	$0.875732\pi$
$398$		−	0.902382i		−	0.0452323i
$399$	−10.6045	+	18.3675i	−0.530889	+	0.919526i
$400$		0			0
$401$	−7.70454	+	4.44822i	−0.384746	+	0.222133i	−0.679881	−	0.733322i	$-0.737969\pi$
$401$	−7.70454	+	4.44822i	−0.384746	+	0.222133i	0.295135	+	0.955456i	$0.404635\pi$
$402$	−6.61944			−0.330148
$403$	1.89545	+	11.2083i	0.0944193	+	0.558324i
$404$	−2.04428			−0.101707
$405$		0			0
$406$	−10.7530	−	18.6247i	−0.533660	−	0.924327i
$407$	12.6932	−	21.9853i	0.629180	−	1.08977i
$408$		−	6.00000i		−	0.297044i
$409$	24.4988	+	14.1444i	1.21139	+	0.699394i	0.963061	−	0.269283i	$-0.0867866\pi$
$409$	24.4988	+	14.1444i	1.21139	+	0.699394i	0.248325	+	0.968677i	$0.420120\pi$
$410$		0			0
$411$			8.70654i			0.429462i
$412$	−3.05776	+	5.29619i	−0.150645	+	0.260925i
$413$	−6.88520	−	11.9255i	−0.338799	−	0.586816i
$414$	−8.57425	+	4.95035i	−0.421401	+	0.243296i
$415$		0			0
$416$	−13.1819	−	4.90269i	−0.646298	−	0.240374i
$417$	−11.6569			−0.570840
$418$	−22.2621	+	12.8530i	−1.08888	+	0.628663i
$419$	−14.4474	−	25.0236i	−0.705801	−	1.22248i	−0.966402	−	0.257036i	$-0.917254\pi$
$419$	−14.4474	−	25.0236i	−0.705801	−	1.22248i	0.260601	−	0.965447i	$-0.416079\pi$
$420$		0			0
$421$		−	12.0134i		−	0.585498i	−0.956189	−	0.292749i	$-0.905430\pi$
$421$		−	12.0134i		−	0.585498i	0.956189	−	0.292749i	$-0.0945701\pi$
$422$	8.08622	+	4.66858i	0.393631	+	0.227263i
$423$	1.55676	+	0.898795i	0.0756922	+	0.0437009i
$424$		−	32.7846i		−	1.59216i
$425$		0			0
$426$	−5.79865	−	10.0436i	−0.280945	−	0.486612i
$427$	−15.5143	+	8.95716i	−0.750788	+	0.433467i
$428$	−4.64895			−0.224716
$429$	10.3963	+	3.86663i	0.501937	+	0.186683i
$430$		0			0
$431$	19.9384	−	11.5115i	0.960401	−	0.554488i	0.0641046	−	0.997943i	$-0.479581\pi$
$431$	19.9384	−	11.5115i	0.960401	−	0.554488i	0.896296	+	0.443455i	$0.146248\pi$
$432$	1.00000	+	1.73205i	0.0481125	+	0.0833333i
$433$	13.4397	−	23.2783i	0.645872	−	1.11868i	−0.338227	−	0.941064i	$-0.609827\pi$
$433$	13.4397	−	23.2783i	0.645872	−	1.11868i	0.984099	−	0.177619i	$-0.0568394\pi$
$434$		−	10.1465i		−	0.487047i
$435$		0			0
$436$	7.48064	+	4.31895i	0.358258	+	0.206840i
$437$			65.2469i			3.12118i
$438$	−6.25519	+	10.8343i	−0.298885	+	0.517684i
$439$	−15.8272	−	27.4135i	−0.755392	−	1.30838i	−0.945179	−	0.326551i	$-0.894113\pi$
$439$	−15.8272	−	27.4135i	−0.755392	−	1.30838i	0.189788	−	0.981825i	$-0.439220\pi$
$440$		0			0
$441$	−1.16864			−0.0556495
$442$	−1.32034	−	7.80748i	−0.0628021	−	0.371364i
$443$	9.89932			0.470331			0.235166	−	0.971955i	$-0.424437\pi$
$443$	9.89932			0.470331			0.235166	+	0.971955i	$0.424437\pi$
$444$	−5.23160	+	3.02047i	−0.248281	+	0.143345i
$445$		0			0
$446$	−7.18485	+	12.4445i	−0.340212	+	0.589265i
$447$		−	6.82431i		−	0.322779i
$448$	20.7724	+	11.9930i	0.981404	+	0.566614i
$449$	−12.9975	−	7.50413i	−0.613392	−	0.354142i	0.160900	−	0.986971i	$-0.448560\pi$
$449$	−12.9975	−	7.50413i	−0.613392	−	0.354142i	−0.774292	+	0.632829i	$0.781894\pi$
$450$		0			0
$451$	−5.11015	+	8.85104i	−0.240627	+	0.416779i
$452$	1.26795	+	2.19615i	0.0596393	+	0.103298i
$453$	−10.9821	+	6.34052i	−0.515984	+	0.297903i
$454$	19.2679			0.904290
$455$		0			0
$456$	22.8289			1.06906
$457$	11.2847	−	6.51520i	0.527874	−	0.304768i	−0.212276	−	0.977210i	$-0.568088\pi$
$457$	11.2847	−	6.51520i	0.527874	−	0.304768i	0.740150	+	0.672441i	$0.234754\pi$
$458$	−3.60326	−	6.24104i	−0.168369	−	0.291624i
$459$	0.975173	−	1.68905i	0.0455172	−	0.0788380i
$460$		0			0
$461$	24.8693	+	14.3583i	1.15828	+	0.668732i	0.950891	−	0.309526i	$-0.100170\pi$
$461$	24.8693	+	14.3583i	1.15828	+	0.668732i	0.207388	+	0.978259i	$0.433504\pi$
$462$	−8.57425	−	4.95035i	−0.398910	−	0.230311i
$463$		−	0.460309i		−	0.0213924i	−0.999943	−	0.0106962i	$-0.996595\pi$
$463$		−	0.460309i		−	0.0213924i	0.999943	−	0.0106962i	$-0.00340477\pi$
$464$	−6.68240	+	11.5742i	−0.310222	+	0.537321i
$465$		0			0
$466$	0.654884	−	0.378098i	0.0303369	−	0.0175150i
$467$	−34.0634			−1.57627			−0.788133	−	0.615505i	$-0.788952\pi$
$467$	−34.0634			−1.57627			−0.788133	+	0.615505i	$0.788952\pi$
$468$	−1.68240	−	2.03377i	−0.0777688	−	0.0940111i
$469$	−16.8014			−0.775816
$470$		0			0
$471$	3.99166	+	6.91376i	0.183926	+	0.318569i
$472$	−7.41108	+	12.8364i	−0.341123	+	0.590842i
$473$		−	29.3694i		−	1.35041i
$474$	10.8213	+	6.24770i	0.497041	+	0.286967i
$475$		0			0
$476$		−	4.08063i		−	0.187036i
$477$	5.32844	−	9.22913i	0.243973	−	0.422573i
$478$	−4.01421	−	6.95281i	−0.183606	−	0.318014i
$479$	26.7871	−	15.4656i	1.22393	−	0.706639i	0.258180	−	0.966097i	$-0.416877\pi$
$479$	26.7871	−	15.4656i	1.22393	−	0.706639i	0.965755	+	0.259458i	$0.0835438\pi$
$480$		0			0
$481$	−22.9257	+	18.9649i	−1.04532	+	0.864723i
$482$	−30.3333			−1.38165
$483$	−21.7631	+	12.5649i	−0.990254	+	0.571723i
$484$	−0.562178	−	0.973721i	−0.0255535	−	0.0442600i
$485$		0			0
$486$			1.12603i			0.0510779i
$487$	−14.3223	−	8.26901i	−0.649007	−	0.374704i	0.139069	−	0.990283i	$-0.455589\pi$
$487$	−14.3223	−	8.26901i	−0.649007	−	0.374704i	−0.788076	+	0.615578i	$0.788922\pi$
$488$	16.6992	+	9.64129i	0.755937	+	0.436441i
$489$		−	12.3222i		−	0.557228i
$490$		0			0
$491$	9.34120	+	16.1794i	0.421562	+	0.730167i	0.996093	−	0.0883160i	$-0.0281485\pi$
$491$	9.34120	+	16.1794i	0.421562	+	0.730167i	−0.574530	+	0.818483i	$0.694815\pi$
$492$	2.10618	−	1.21600i	0.0949540	−	0.0548217i
$493$	13.0330			0.586976
$494$	29.7060	−	5.02364i	1.33654	−	0.226024i
$495$		0			0
$496$	−5.46073	+	3.15276i	−0.245194	+	0.141563i
$497$	−14.7181	−	25.4924i	−0.660195	−	1.14349i
$498$	3.92820	−	6.80385i	0.176027	−	0.304888i
$499$		−	10.9966i		−	0.492277i	−0.969235	−	0.246138i	$-0.920838\pi$
$499$		−	10.9966i		−	0.492277i	0.969235	−	0.246138i	$-0.0791618\pi$
$500$		0			0
$501$	−19.0020	−	10.9708i	−0.848947	−	0.490140i
$502$			13.1161i			0.585399i
$503$	−7.99663	+	13.8506i	−0.356552	+	0.617567i	−0.987382	−	0.158354i	$-0.949381\pi$
$503$	−7.99663	+	13.8506i	−0.356552	+	0.617567i	0.630830	+	0.775921i	$0.282714\pi$
$504$	4.39627	+	7.61457i	0.195826	+	0.339180i
$505$		0			0
$506$	−30.4583			−1.35404
$507$	−9.84052	−	8.49496i	−0.437033	−	0.377274i
$508$	−10.9603			−0.486284
$509$	1.23647	−	0.713876i	0.0548055	−	0.0316420i	−0.472347	−	0.881413i	$-0.656593\pi$
$509$	1.23647	−	0.713876i	0.0548055	−	0.0316420i	0.527152	+	0.849771i	$0.323260\pi$
$510$		0			0
$511$	−15.8769	+	27.4995i	−0.702351	+	1.21651i
$512$		−	20.1069i		−	0.888608i
$513$	6.42652	+	3.71035i	0.283738	+	0.163816i
$514$	7.09808	+	4.09808i	0.313083	+	0.180758i
$515$		0			0
$516$	−3.49435	+	6.05239i	−0.153830	+	0.266442i
$517$	2.76503	+	4.78918i	0.121606	+	0.210628i
$518$	22.9995	−	13.2788i	1.01054	−	0.583436i
$519$	15.0506			0.660646
$520$		0			0
$521$	11.8172			0.517719			0.258859	−	0.965915i	$-0.416653\pi$
$521$	11.8172			0.517719			0.258859	+	0.965915i	$0.416653\pi$
$522$	−6.51649	+	3.76230i	−0.285219	+	0.164671i
$523$	14.3063	+	24.7792i	0.625571	+	1.08352i	0.988430	+	0.151677i	$0.0484672\pi$
$523$	14.3063	+	24.7792i	0.625571	+	1.08352i	−0.362859	+	0.931844i	$0.618199\pi$
$524$	3.87368	−	6.70941i	0.169222	−	0.293102i
$525$		0			0
$526$	23.3337	+	13.4717i	1.01740	+	0.587394i
$527$	5.32516	+	3.07448i	0.231968	+	0.133927i
$528$			6.15276i			0.267764i
$529$	−27.1544	+	47.0328i	−1.18063	+	2.04491i
$530$		0			0
$531$	−4.17256	+	2.40903i	−0.181074	+	0.104543i
$532$	15.5261			0.673140
$533$	9.22963	−	7.63503i	0.399780	−	0.330710i
$534$	−0.104778			−0.00453420
$535$		0			0
$536$	9.04232	+	15.6618i	0.390569	+	0.676485i
$537$	−0.240387	+	0.416363i	−0.0103735	+	0.0179674i
$538$			4.93367i			0.212706i
$539$	−3.11352	−	1.79759i	−0.134109	−	0.0774277i
$540$		0			0
$541$		−	33.9315i		−	1.45883i	−0.684072	−	0.729415i	$-0.739792\pi$
$541$		−	33.9315i		−	1.45883i	0.684072	−	0.729415i	$-0.260208\pi$
$542$	−1.40092	+	2.42647i	−0.0601748	+	0.104226i
$543$	0.929436	+	1.60983i	0.0398859	+	0.0690844i
$544$	−6.58846	+	3.80385i	−0.282478	+	0.163089i
$545$		0			0
$546$	7.39627	+	8.94101i	0.316531	+	0.382640i
$547$	0.0276116			0.00118059			0.000590294	−	1.00000i	$-0.499812\pi$
$547$	0.0276116			0.00118059			0.000590294		1.00000i	$0.499812\pi$
$548$	5.51973	−	3.18682i	0.235791	−	0.136134i
$549$	3.13397	+	5.42820i	0.133755	+	0.231670i
$550$		0			0
$551$			49.5881i			2.11252i
$552$	23.4253	+	13.5246i	0.997046	+	0.575645i
$553$	27.4666	+	15.8579i	1.16800	+	0.674344i
$554$		−	24.4417i		−	1.03843i
$555$		0			0
$556$	4.26672	+	7.39017i	0.180949	+	0.313413i
$557$	34.9572	−	20.1826i	1.48118	−	0.855162i	0.481412	−	0.876494i	$-0.340124\pi$
$557$	34.9572	−	20.1826i	1.48118	−	0.855162i	0.999772	+	0.0213318i	$0.00679062\pi$
$558$	−3.55011			−0.150288
$559$	−11.9991	+	32.2621i	−0.507507	+	1.36454i
$560$		0			0
$561$	5.19615	−	3.00000i	0.219382	−	0.126660i
$562$	16.7368	+	28.9890i	0.705999	+	1.22283i
$563$	−7.06049	+	12.2291i	−0.297564	+	0.515397i	−0.975578	−	0.219653i	$-0.929508\pi$
$563$	−7.06049	+	12.2291i	−0.297564	+	0.515397i	0.678014	+	0.735049i	$0.262841\pi$
$564$		−	1.31593i		−	0.0554105i
$565$		0			0
$566$	−27.3044	−	15.7642i	−1.14769	−	0.662618i
$567$			2.85808i			0.120028i
$568$	−15.8422	+	27.4395i	−0.664724	+	1.15134i
$569$	−15.5158	−	26.8742i	−0.650456	−	1.12662i	−0.983012	−	0.183540i	$-0.941244\pi$
$569$	−15.5158	−	26.8742i	−0.650456	−	1.12662i	0.332556	−	0.943084i	$-0.392089\pi$
$570$		0			0
$571$	29.6336			1.24013			0.620065	−	0.784551i	$-0.287106\pi$
$571$	29.6336			1.24013			0.620065	+	0.784551i	$0.287106\pi$
$572$	−1.35395	−	8.00626i	−0.0566116	−	0.334758i
$573$	8.71875			0.364231
$574$	−9.25934	+	5.34589i	−0.386478	+	0.223133i
$575$		0			0
$576$	4.19615	−	7.26795i	0.174840	−	0.302831i
$577$		−	17.7788i		−	0.740140i	−0.929004	−	0.370070i	$-0.879334\pi$
$577$		−	17.7788i		−	0.740140i	0.929004	−	0.370070i	$-0.120666\pi$
$578$	12.8685	+	7.42965i	0.535260	+	0.309033i
$579$	5.58869	+	3.22663i	0.232258	+	0.134094i
$580$		0			0
$581$	9.97052	−	17.2695i	0.413647	−	0.716458i
$582$	2.70112	+	4.67848i	0.111965	+	0.193929i
$583$	28.3923	−	16.3923i	1.17589	−	0.678900i
$584$	34.1790			1.41434
$585$		0			0
$586$	19.0959			0.788846
$587$	−4.81687	+	2.78102i	−0.198814	+	0.114785i	−0.596102	−	0.802909i	$-0.703285\pi$
$587$	−4.81687	+	2.78102i	−0.198814	+	0.114785i	0.397288	+	0.917694i	$0.369951\pi$
$588$	0.427752	+	0.740888i	0.0176402	+	0.0305537i
$589$	−11.6978	+	20.2612i	−0.482001	+	0.834850i
$590$		0			0
$591$	10.0399	+	5.79651i	0.412984	+	0.238437i
$592$	−14.2930	−	8.25207i	−0.587439	−	0.339158i
$593$		−	33.4290i		−	1.37276i	−0.727241	−	0.686382i	$-0.759198\pi$
$593$		−	33.4290i		−	1.37276i	0.727241	−	0.686382i	$-0.240802\pi$
$594$	−1.73205	+	3.00000i	−0.0710669	+	0.123091i
$595$		0			0
$596$	−4.32644	+	2.49787i	−0.177218	+	0.102317i
$597$	−0.801382			−0.0327984
$598$	33.4583	+	12.4440i	1.36821	+	0.508871i
$599$	−8.14349			−0.332734			−0.166367	−	0.986064i	$-0.553204\pi$
$599$	−8.14349			−0.332734			−0.166367	+	0.986064i	$0.553204\pi$
$600$		0			0
$601$	−11.5588	−	20.0204i	−0.471494	−	0.816651i	0.527974	−	0.849260i	$-0.322952\pi$
$601$	−11.5588	−	20.0204i	−0.471494	−	0.816651i	−0.999468	+	0.0326092i	$0.989618\pi$
$602$	15.3621	−	26.6080i	0.626113	−	1.08446i
$603$			5.87855i			0.239393i
$604$	8.03945	+	4.64158i	0.327121	+	0.188863i
$605$		0			0
$606$		−	3.14450i		−	0.127736i
$607$	3.48351	−	6.03361i	0.141391	−	0.244897i	−0.786629	−	0.617425i	$-0.788176\pi$
$607$	3.48351	−	6.03361i	0.141391	−	0.244897i	0.928021	+	0.372528i	$0.121509\pi$
$608$	−14.4729	−	25.0679i	−0.586955	−	1.01664i
$609$	−16.5401	+	9.54942i	−0.670238	+	0.386962i
$610$		0			0
$611$	−1.08072	−	6.39056i	−0.0437213	−	0.258535i
$612$	−1.42775			−0.0577135
$613$	29.7784	−	17.1926i	1.20274	−	0.694401i	0.241574	−	0.970382i	$-0.422336\pi$
$613$	29.7784	−	17.1926i	1.20274	−	0.694401i	0.961163	+	0.275982i	$0.0890029\pi$
$614$	−8.78712	−	15.2197i	−0.354620	−	0.614219i
$615$		0			0
$616$			27.0492i			1.08984i
$617$	−13.5177	−	7.80446i	−0.544203	−	0.314196i	0.202578	−	0.979266i	$-0.435068\pi$
$617$	−13.5177	−	7.80446i	−0.544203	−	0.314196i	−0.746781	+	0.665070i	$0.768402\pi$
$618$	−8.14655	−	4.70341i	−0.327702	−	0.189199i
$619$			16.0626i			0.645610i	0.946465	+	0.322805i	$0.104626\pi$
$619$			16.0626i			0.645610i	−0.946465	+	0.322805i	$0.895374\pi$
$620$		0			0
$621$	4.39627	+	7.61457i	0.176416	+	0.305562i
$622$	24.3735	−	14.0721i	0.977290	−	0.564238i
$623$	−0.265947			−0.0106550
$624$	2.51376	−	6.75877i	0.100631	−	0.270568i
$625$		0			0
$626$	−1.13234	+	0.653757i	−0.0452574	+	0.0261294i
$627$	11.4144	+	19.7704i	0.455849	+	0.789554i
$628$	2.92210	−	5.06123i	0.116605	−	0.201965i
$629$			16.0944i			0.641725i
$630$		0			0
$631$	−31.7588	−	18.3359i	−1.26430	−	0.729942i	−0.290394	−	0.956907i	$-0.593786\pi$
$631$	−31.7588	−	18.3359i	−1.26430	−	0.729942i	−0.973903	+	0.226965i	$0.927120\pi$
$632$		−	34.1381i		−	1.35794i
$633$	4.14605	−	7.18116i	0.164791	−	0.285426i
$634$	4.85641	+	8.41154i	0.192873	+	0.334065i
$635$		0			0
$636$	−7.80138			−0.309345
$637$	2.68576	+	3.24670i	0.106414	+	0.128639i
$638$	−23.1485			−0.916458
$639$	−8.91942	+	5.14963i	−0.352847	+	0.203716i
$640$		0			0
$641$	13.3211	−	23.0728i	0.526152	−	0.911322i	−0.473384	−	0.880856i	$-0.656968\pi$
$641$	13.3211	−	23.0728i	0.526152	−	0.911322i	0.999536	−	0.0304659i	$-0.00969909\pi$
$642$		−	7.15097i		−	0.282226i
$643$	1.78484	+	1.03048i	0.0703873	+	0.0406381i	0.534781	−	0.844991i	$-0.320394\pi$
$643$	1.78484	+	1.03048i	0.0703873	+	0.0406381i	−0.464393	+	0.885629i	$0.653728\pi$
$644$	15.9317	+	9.19815i	0.627796	+	0.362458i
$645$		0			0
$646$	8.14850	−	14.1136i	0.320598	−	0.555293i
$647$	7.76353	+	13.4468i	0.305216	+	0.528649i	0.977309	−	0.211817i	$-0.0679380\pi$
$647$	7.76353	+	13.4468i	0.305216	+	0.528649i	−0.672093	+	0.740466i	$0.734605\pi$
$648$	2.66422	−	1.53819i	0.104661	−	0.0604258i
$649$	−14.8222			−0.581821
$650$		0			0
$651$	−9.01084			−0.353163
$652$	−7.81195	+	4.51023i	−0.305940	+	0.176634i
$653$	20.4368	+	35.3976i	0.799754	+	1.38521i	0.919776	+	0.392444i	$0.128370\pi$
$653$	20.4368	+	35.3976i	0.799754	+	1.38521i	−0.120022	+	0.992771i	$0.538297\pi$
$654$	−6.64336	+	11.5066i	−0.259776	+	0.449945i
$655$		0			0
$656$	5.75419	+	3.32218i	0.224663	+	0.129710i
$657$	9.62167	+	5.55507i	0.375377	+	0.216724i
$658$			5.78517i			0.225530i
$659$	−0.917364	+	1.58892i	−0.0357354	+	0.0618956i	−0.883340	−	0.468733i	$-0.844711\pi$
$659$	−0.917364	+	1.58892i	−0.0357354	+	0.0618956i	0.847605	+	0.530628i	$0.178044\pi$
$660$		0			0
$661$	15.0413	−	8.68408i	0.585038	−	0.337772i	−0.178095	−	0.984013i	$-0.556994\pi$
$661$	15.0413	−	8.68408i	0.585038	−	0.337772i	0.763133	+	0.646242i	$0.223660\pi$
$662$	−28.8519			−1.12136
$663$	−6.93362	+	1.17256i	−0.269280	+	0.0455384i
$664$	−21.4641			−0.832969
$665$		0			0
$666$	−4.64605	−	8.04719i	−0.180031	−	0.311822i
$667$	−29.3776	+	50.8836i	−1.13751	+	1.97022i
$668$			16.0624i			0.621472i
$669$	11.0517	+	6.38068i	0.427282	+	0.246691i
$670$		0			0
$671$			19.2826i			0.744396i
$672$	5.57425	−	9.65488i	0.215031	−	0.372445i
$673$	4.75396	+	8.23410i	0.183252	+	0.317401i	0.942986	−	0.332832i	$-0.108004\pi$
$673$	4.75396	+	8.23410i	0.183252	+	0.317401i	−0.759734	+	0.650234i	$0.774671\pi$
$674$	19.6761	−	11.3600i	0.757894	−	0.437570i
$675$		0			0
$676$	−1.78371	+	9.34801i	−0.0686041	+	0.359539i
$677$	−20.7375			−0.797008			−0.398504	−	0.917167i	$-0.630470\pi$
$677$	−20.7375			−0.797008			−0.398504	+	0.917167i	$0.630470\pi$
$678$	−3.37810	+	1.95035i	−0.129735	+	0.0749026i
$679$	6.85596	+	11.8749i	0.263107	+	0.455715i
$680$		0			0
$681$		−	17.1114i		−	0.655709i
$682$	−9.45827	−	5.46073i	−0.362176	−	0.209102i
$683$	−14.4521	−	8.34393i	−0.552995	−	0.319272i	0.197334	−	0.980336i	$-0.436772\pi$
$683$	−14.4521	−	8.34393i	−0.552995	−	0.319272i	−0.750329	+	0.661065i	$0.770105\pi$
$684$		−	5.43233i		−	0.207710i
$685$		0			0
$686$	9.38352	+	16.2527i	0.358264	+	0.620532i
$687$	−5.54250	+	3.19996i	−0.211460	+	0.122086i
$688$	−19.0935			−0.727932
$689$	−37.8860	+	6.40698i	−1.44334	+	0.244086i
$690$		0			0
$691$	19.6119	−	11.3229i	0.746073	−	0.430745i	−0.0782005	−	0.996938i	$-0.524917\pi$
$691$	19.6119	−	11.3229i	0.746073	−	0.430745i	0.824273	+	0.566192i	$0.191584\pi$
$692$	−5.50889	−	9.54167i	−0.209416	−	0.362720i
$693$	−4.39627	+	7.61457i	−0.167001	+	0.289253i
$694$		−	27.2429i		−	1.03413i
$695$		0			0
$696$	17.8034	+	10.2788i	0.674836	+	0.389616i
$697$		−	6.47941i		−	0.245425i
$698$	14.4561	−	25.0387i	0.547171	−	0.947728i
$699$	−0.335778	−	0.581585i	−0.0127003	−	0.0219976i
$700$		0			0
$701$	−9.33818			−0.352698			−0.176349	−	0.984328i	$-0.556429\pi$
$701$	−9.33818			−0.352698			−0.176349	+	0.984328i	$0.556429\pi$
$702$	3.12832	−	2.58784i	0.118071	−	0.0976719i
$703$	−61.2361			−2.30956
$704$	22.3590	−	12.9090i	0.842685	−	0.486524i
$705$		0			0
$706$	4.41691	−	7.65032i	0.166233	−	0.287923i
$707$		−	7.98133i		−	0.300169i
$708$	3.05452	+	1.76353i	0.114796	+	0.0662775i
$709$	24.6318	+	14.2212i	0.925068	+	0.534088i	0.885248	−	0.465119i	$-0.153988\pi$
$709$	24.6318	+	14.2212i	0.925068	+	0.534088i	0.0398194	+	0.999207i	$0.487322\pi$
$710$		0			0
$711$	5.54842	−	9.61015i	0.208082	−	0.360409i
$712$	0.143130	+	0.247908i	0.00536402	+	0.00929075i
$713$	−24.0069	+	13.8604i	−0.899064	+	0.519075i
$714$	6.27679			0.234903
$715$		0			0
$716$	0.351951			0.0131530
$717$	−6.17461	+	3.56491i	−0.230595	+	0.133134i
$718$	−11.0996	−	19.2250i	−0.414233	−	0.717472i
$719$	15.9484	−	27.6235i	0.594776	−	1.03018i	−0.398802	−	0.917037i	$-0.630574\pi$
$719$	15.9484	−	27.6235i	0.594776	−	1.03018i	0.993578	−	0.113145i	$-0.0360926\pi$
$720$		0			0
$721$	−20.6775	−	11.9381i	−0.770070	−	0.444600i
$722$	35.1714	+	20.3062i	1.30894	+	0.755720i
$723$			26.9383i			1.00184i
$724$	0.680394	−	1.17848i	0.0252867	−	0.0437978i
$725$		0			0
$726$	1.49777	−	0.864736i	0.0555873	−	0.0320934i
$727$	−4.68029			−0.173583			−0.0867913	−	0.996227i	$-0.527661\pi$
$727$	−4.68029			−0.173583			−0.0867913	+	0.996227i	$0.527661\pi$
$728$	11.0512	−	29.7134i	0.409583	−	1.10125i
$729$	1.00000			0.0370370
$730$		0			0
$731$	9.30972	+	16.1249i	0.344332	+	0.596401i
$732$	2.29423	−	3.97372i	0.0847971	−	0.146873i
$733$			14.1306i			0.521926i	0.965349	+	0.260963i	$0.0840401\pi$
$733$			14.1306i			0.521926i	−0.965349	+	0.260963i	$0.915960\pi$
$734$	−10.8986	−	6.29233i	−0.402276	−	0.232254i
$735$		0			0
$736$		−	34.2970i		−	1.26420i
$737$	−9.04232	+	15.6618i	−0.333078	+	0.576908i
$738$	1.87044	+	3.23970i	0.0688520	+	0.119255i
$739$	−10.2955	+	5.94409i	−0.378725	+	0.218657i	−0.677263	−	0.735741i	$-0.736834\pi$
$739$	−10.2955	+	5.94409i	−0.378725	+	0.218657i	0.298539	+	0.954398i	$0.403501\pi$
$740$		0			0
$741$	−4.46137	−	26.3812i	−0.163892	−	0.969136i
$742$	34.2970			1.25908
$743$	−20.7932	+	12.0050i	−0.762830	+	0.440420i	−0.830311	−	0.557301i	$-0.811837\pi$
$743$	−20.7932	+	12.0050i	−0.762830	+	0.440420i	0.0674812	+	0.997721i	$0.478504\pi$
$744$	4.84953	+	8.39964i	0.177793	+	0.307946i
$745$		0			0
$746$			9.85473i			0.360807i
$747$	−6.04232	−	3.48853i	−0.221077	−	0.127639i
$748$	−3.80385	−	2.19615i	−0.139082	−	0.0802993i
$749$		−	18.1505i		−	0.663205i
$750$		0			0
$751$	7.93491	+	13.7437i	0.289549	+	0.501513i	0.973702	−	0.227825i	$-0.0731614\pi$
$751$	7.93491	+	13.7437i	0.289549	+	0.501513i	−0.684153	+	0.729338i	$0.739828\pi$
$752$	3.11352	−	1.79759i	0.113538	−	0.0655513i
$753$	11.6480			0.424478
$754$	25.4285	+	9.45750i	0.926052	+	0.344422i
$755$		0			0
$756$	1.81195	−	1.04613i	0.0659001	−	0.0380474i
$757$	18.0819	+	31.3188i	0.657198	+	1.13830i	0.981338	+	0.192291i	$0.0615918\pi$
$757$	18.0819	+	31.3188i	0.657198	+	1.13830i	−0.324140	+	0.946009i	$0.605075\pi$
$758$	−10.5676	+	18.3036i	−0.383832	+	0.664817i
$759$			27.0492i			0.981823i
$760$		0			0
$761$	−12.6597	−	7.30905i	−0.458912	−	0.264953i	0.252675	−	0.967551i	$-0.418690\pi$
$761$	−12.6597	−	7.30905i	−0.458912	−	0.264953i	−0.711587	+	0.702598i	$0.752023\pi$
$762$		−	16.8590i		−	0.610737i
$763$	−16.8621	+	29.2060i	−0.610449	+	1.05733i
$764$	−3.19128	−	5.52746i	−0.115457	−	0.199977i
$765$		0			0
$766$	−6.84029			−0.247150
$767$	16.2821	+	6.05571i	0.587912	+	0.218659i
$768$	−14.9282			−0.538675
$769$	−15.8994	+	9.17950i	−0.573346	+	0.331021i	−0.758484	−	0.651691i	$-0.774060\pi$
$769$	−15.8994	+	9.17950i	−0.573346	+	0.331021i	0.185139	+	0.982712i	$0.440727\pi$
$770$		0			0
$771$	3.63939	−	6.30362i	0.131070	−	0.227019i
$772$		−	4.72412i		−	0.170025i
$773$	7.38753	+	4.26519i	0.265711	+	0.153408i	0.626937	−	0.779070i	$-0.284308\pi$
$773$	7.38753	+	4.26519i	0.265711	+	0.153408i	−0.361226	+	0.932478i	$0.617642\pi$
$774$	−9.30972	−	5.37497i	−0.334631	−	0.193199i
$775$		0			0
$776$	7.37960	−	12.7818i	0.264912	−	0.458841i
$777$	−11.7925	−	20.4253i	−0.423055	−	0.732753i
$778$	9.42575	−	5.44196i	0.337930	−	0.195104i
$779$	24.6530			0.883284
$780$		0			0
$781$	−31.6844			−1.13376
$782$	16.7227	−	9.65488i	0.598004	−	0.345258i
$783$	3.34120	+	5.78712i	0.119405	+	0.206815i
$784$	−1.16864	+	2.02414i	−0.0417371	+	0.0722909i
$785$		0			0
$786$	10.3203	+	5.95845i	0.368114	+	0.212531i
$787$	2.96679	+	1.71288i	0.105755	+	0.0610574i	0.551944	−	0.833881i	$-0.313886\pi$
$787$	2.96679	+	1.71288i	0.105755	+	0.0610574i	−0.446190	+	0.894938i	$0.647219\pi$
$788$		−	8.48668i		−	0.302326i
$789$	11.9639	−	20.7220i	0.425925	−	0.737724i
$790$		0			0
$791$	−8.57425	+	4.95035i	−0.304865	+	0.176014i
$792$	9.46410			0.336292
$793$	7.87805	−	21.1818i	0.279758	−	0.752189i
$794$	−27.3982			−0.972327
$795$		0			0
$796$	0.293326	+	0.508056i	0.0103967	+	0.0180076i
$797$	−14.0505	+	24.3361i	−0.497693	+	0.862030i	−0.999996	−	0.00266150i	$-0.999153\pi$
$797$	−14.0505	+	24.3361i	−0.497693	+	0.862030i	0.502303	+	0.864692i	$0.332486\pi$
$798$			23.8820i			0.845414i
$799$	−3.03622	−	1.75296i	−0.107414	−	0.0620153i
$800$		0			0
$801$			0.0930509i			0.00328779i
$802$	−5.00884	+	8.67556i	−0.176868	+	0.306345i
$803$	17.0895	+	29.5999i	0.603076	+	1.04456i
$804$	3.72685	−	2.15170i	0.131436	−	0.0758845i
$805$		0			0
$806$	8.15884	+	9.86284i	0.287383	+	0.347404i
$807$	4.38147			0.154235
$808$	−7.43996	+	4.29546i	−0.261737	+	0.151114i
$809$	−18.0846	−	31.3235i	−0.635822	−	1.10128i	−0.986340	−	0.164720i	$-0.947328\pi$
$809$	−18.0846	−	31.3235i	−0.635822	−	1.10128i	0.350518	−	0.936556i	$-0.386005\pi$
$810$		0			0
$811$			13.9825i			0.490993i	0.969397	+	0.245497i	$0.0789510\pi$
$811$			13.9825i			0.490993i	−0.969397	+	0.245497i	$0.921049\pi$
$812$	12.1082	+	6.99066i	0.424914	+	0.245324i
$813$	2.15488	+	1.24412i	0.0755751	+	0.0436333i
$814$		−	28.5860i		−	1.00194i
$815$		0			0
$816$	−1.95035	−	3.37810i	−0.0682757	−	0.118257i
$817$	−61.3523	+	35.4218i	−2.14645	+	1.23925i
$818$	31.8540			1.11375
$819$	7.94028	−	6.56844i	0.277456	−	0.229520i
$820$		0			0
$821$	3.67156	−	2.11977i	0.128138	−	0.0739806i	−0.434561	−	0.900643i	$-0.643096\pi$
$821$	3.67156	−	2.11977i	0.128138	−	0.0739806i	0.562699	+	0.826662i	$0.309763\pi$
$822$	4.90192	+	8.49038i	0.170974	+	0.296136i
$823$	−16.8201	+	29.1332i	−0.586310	+	1.01552i	0.408400	+	0.912803i	$0.366087\pi$
$823$	−16.8201	+	29.1332i	−0.586310	+	1.01552i	−0.994711	+	0.102716i	$0.967247\pi$
$824$			25.6999i			0.895299i
$825$		0			0
$826$	−13.4285	−	7.75296i	−0.467238	−	0.269760i
$827$		−	6.94609i		−	0.241539i	−0.992681	−	0.120770i	$-0.961464\pi$
$827$		−	6.94609i		−	0.241539i	0.992681	−	0.120770i	$-0.0385362\pi$
$828$	3.21829	−	5.57425i	0.111843	−	0.193719i
$829$	6.68271	+	11.5748i	0.232100	+	0.402009i	0.958426	−	0.285341i	$-0.0921069\pi$
$829$	6.68271	+	11.5748i	0.232100	+	0.402009i	−0.726326	+	0.687351i	$0.758774\pi$
$830$		0			0
$831$	−21.7061			−0.752975
$832$	−29.8353	+	5.04550i	−1.03435	+	0.174921i
$833$	2.27925			0.0789714
$834$	−11.3675	+	6.56302i	−0.393624	+	0.227259i
$835$		0			0
$836$	8.35596	−	14.4729i	0.288997	−	0.500557i
$837$			3.15276i			0.108975i
$838$	−28.1774	−	16.2682i	−0.973371	−	0.561976i
$839$	17.3830	+	10.0361i	0.600127	+	0.346483i	0.769091	−	0.639139i	$-0.220709\pi$
$839$	17.3830	+	10.0361i	0.600127	+	0.346483i	−0.168965	+	0.985622i	$0.554042\pi$
$840$		0			0
$841$	−7.82721	+	13.5571i	−0.269904	+	0.467487i
$842$	−6.76375	−	11.7152i	−0.233094	−	0.403731i
$843$	25.7443	−	14.8635i	0.886682	−	0.511926i
$844$	−6.07023			−0.208946
$845$		0			0
$846$	2.02414			0.0695915
$847$	3.80161	−	2.19486i	0.130625	−	0.0754164i
$848$	−10.6569	−	18.4583i	−0.365959	−	0.633860i
$849$	−13.9998	+	24.2483i	−0.480471	+	0.832200i
$850$		0			0
$851$	−62.8359	−	36.2783i	−2.15399	−	1.24360i
$852$	6.52947	+	3.76979i	0.223696	+	0.129151i
$853$		−	54.6353i		−	1.87068i	−0.353755	−	0.935338i	$-0.615095\pi$
$853$		−	54.6353i		−	1.87068i	0.353755	−	0.935338i	$-0.384905\pi$
$854$	−10.0861	+	17.4696i	−0.345138	+	0.597796i
$855$		0			0
$856$	−16.9194	+	9.76840i	−0.578292	+	0.333877i
$857$	−3.66436			−0.125172			−0.0625860	−	0.998040i	$-0.519935\pi$
$857$	−3.66436			−0.125172			−0.0625860	+	0.998040i	$0.519935\pi$
$858$	12.3151	−	2.08264i	0.420432	−	0.0711000i
$859$	28.1460			0.960330			0.480165	−	0.877178i	$-0.340577\pi$
$859$	28.1460			0.960330			0.480165	+	0.877178i	$0.340577\pi$
$860$		0			0
$861$	4.74754	+	8.22298i	0.161796	+	0.280238i
$862$	12.9623	−	22.4513i	0.441497	−	0.764696i
$863$		−	50.4623i		−	1.71776i	−0.512180	−	0.858878i	$-0.671162\pi$
$863$		−	50.4623i		−	1.71776i	0.512180	−	0.858878i	$-0.328838\pi$
$864$	−3.37810	−	1.95035i	−0.114925	−	0.0663521i
$865$		0			0
$866$		−	30.2671i		−	1.02852i
$867$	6.59808	−	11.4282i	0.224082	−	0.388122i
$868$	3.29820	+	5.71264i	0.111948	+	0.193900i
$869$	29.5644	−	17.0690i	1.00291	−	0.579028i
$870$		0			0
$871$	16.3317	−	13.5101i	0.553378	−	0.457771i
$872$	36.3000			1.22927
$873$	4.15483	−	2.39879i	0.140620	−	0.0811869i
$874$	36.7351	+	63.6270i	1.24258	+	2.15221i
$875$		0			0
$876$		−	8.13319i		−	0.274795i
$877$	20.0993	+	11.6043i	0.678705	+	0.391851i	0.799367	−	0.600843i	$-0.205168\pi$
$877$	20.0993	+	11.6043i	0.678705	+	0.391851i	−0.120662	+	0.992694i	$0.538502\pi$
$878$	−30.8685	−	17.8220i	−1.04176	−	0.601462i
$879$		−	16.9586i		−	0.572000i
$880$		0			0
$881$	−8.55758	−	14.8222i	−0.288312	−	0.499371i	0.685095	−	0.728454i	$-0.259761\pi$
$881$	−8.55758	−	14.8222i	−0.288312	−	0.499371i	−0.973407	+	0.229083i	$0.926427\pi$
$882$	−1.13963	+	0.657963i	−0.0383732	+	0.0221548i
$883$	−21.3589			−0.718783			−0.359391	−	0.933187i	$-0.617016\pi$
$883$	−21.3589			−0.718783			−0.359391	+	0.933187i	$0.617016\pi$
$884$	3.28125	+	3.96655i	0.110361	+	0.133410i
$885$		0			0
$886$	9.65355	−	5.57348i	0.324317	−	0.187245i
$887$	17.1600	+	29.7220i	0.576177	+	0.997968i	0.995913	+	0.0903216i	$0.0287895\pi$
$887$	17.1600	+	29.7220i	0.576177	+	0.997968i	−0.419735	+	0.907646i	$0.637877\pi$
$888$	−12.6932	+	21.9853i	−0.425957	+	0.737779i
$889$		−	42.7913i		−	1.43517i
$890$		0			0
$891$	2.66422	+	1.53819i	0.0892548	+	0.0515313i
$892$		−	9.34196i		−	0.312792i
$893$	6.66969	−	11.5522i	0.223193	−	0.386581i
$894$	−3.84220	−	6.65488i	−0.128502	−	0.222573i
$895$		0			0
$896$	4.71191			0.157414
$897$	11.0512	−	29.7134i	0.368987	−	0.992102i
$898$	−16.8998			−0.563953
$899$	−18.2454	+	10.5340i	−0.608518	+	0.351328i
$900$		0			0
$901$	−10.3923	+	18.0000i	−0.346218	+	0.599667i
$902$			11.5084i			0.383187i
$903$	−23.6298	−	13.6427i	−0.786351	−	0.454000i
$904$	9.22913	+	5.32844i	0.306956	+	0.177221i
$905$		0			0
$906$	−7.13963	+	12.3662i	−0.237198	+	0.410839i
$907$	−29.4542	−	51.0161i	−0.978010	−	1.69396i	−0.669623	−	0.742701i	$-0.733544\pi$
$907$	−29.4542	−	51.0161i	−0.978010	−	1.69396i	−0.308387	−	0.951261i	$-0.599789\pi$
$908$	−10.8482	+	6.26319i	−0.360009	+	0.207851i
$909$	−2.79254			−0.0926229
$910$		0			0
$911$	−55.5007			−1.83882			−0.919410	−	0.393299i	$-0.871334\pi$
$911$	−55.5007			−1.83882			−0.919410	+	0.393299i	$0.871334\pi$
$912$	12.8530	−	7.42071i	0.425607	−	0.245724i
$913$	−10.7321	−	18.5885i	−0.355179	−	0.615188i
$914$	7.33633	−	12.7069i	0.242664	−	0.420307i
$915$		0			0
$916$	4.05739	+	2.34254i	0.134060	+	0.0773996i
$917$	26.1950	+	15.1237i	0.865034	+	0.499428i
$918$		−	2.19615i		−	0.0724838i
$919$	−27.3656	+	47.3985i	−0.902707	+	1.56353i	−0.0787401	+	0.996895i	$0.525090\pi$
$919$	−27.3656	+	47.3985i	−0.902707	+	1.56353i	−0.823967	+	0.566638i	$0.808244\pi$
$920$		0			0
$921$	−13.5163	+	7.80362i	−0.445376	+	0.257138i
$922$	32.3358			1.06492
$923$	34.8052	+	12.9449i	1.14563	+	0.426087i
$924$	6.43659			0.211748
$925$		0			0
$926$	−0.259162	−	0.448881i	−0.00851658	−	0.0147511i
$927$	−4.17698	+	7.23474i	−0.137190	+	0.237620i
$928$		−	26.0660i		−	0.855657i
$929$	14.8799	+	8.59092i	0.488194	+	0.281859i	0.723825	−	0.689984i	$-0.242382\pi$
$929$	14.8799	+	8.59092i	0.488194	+	0.281859i	−0.235631	+	0.971843i	$0.575716\pi$
$930$		0			0
$931$			8.67213i			0.284218i
$932$	−0.245807	+	0.425750i	−0.00805167	+	0.0139459i
$933$	−12.4970	−	21.6455i	−0.409135	−	0.708642i
$934$	−33.2177	+	19.1782i	−1.08692	+	0.627531i
$935$		0			0
$936$	−10.3963	−	3.86663i	−0.339813	−	0.126385i
$937$	−39.6401			−1.29499			−0.647493	−	0.762071i	$-0.724183\pi$
$937$	−39.6401			−1.29499			−0.647493	+	0.762071i	$0.724183\pi$
$938$	−16.3842	+	9.45945i	−0.534965	+	0.308862i
$939$	0.580584	+	1.00560i	0.0189467	+	0.0328166i
$940$		0			0
$941$		−	33.3796i		−	1.08815i	−0.839038	−	0.544073i	$-0.816882\pi$
$941$		−	33.3796i		−	1.08815i	0.839038	−	0.544073i	$-0.183118\pi$
$942$	7.78512	+	4.49474i	0.253653	+	0.146447i
$943$	25.2970	+	14.6052i	0.823784	+	0.475612i
$944$			9.63611i			0.313629i
$945$		0			0
$946$	−16.5354	−	28.6402i	−0.537613	−	0.931174i
$947$	17.8054	−	10.2800i	0.578599	−	0.334054i	−0.181978	−	0.983303i	$-0.558250\pi$
$947$	17.8054	−	10.2800i	0.578599	−	0.334054i	0.760576	+	0.649249i	$0.224916\pi$
$948$	−8.12345			−0.263837
$949$	−6.67948	−	39.4974i	−0.216825	−	1.28214i
$950$		0			0
$951$	7.47007	−	4.31285i	0.242234	−	0.139854i
$952$	−8.57425	−	14.8510i	−0.277893	−	0.481325i
$953$	27.4376	−	47.5234i	0.888792	−	1.53943i	0.0474871	−	0.998872i	$-0.484879\pi$
$953$	27.4376	−	47.5234i	0.888792	−	1.53943i	0.841305	−	0.540561i	$-0.181788\pi$
$954$		−	12.0000i		−	0.388514i
$955$		0			0
$956$	4.52013	+	2.60970i	0.146191	+	0.0844036i
$957$			20.5576i			0.664532i
$958$	17.4147	−	30.1632i	0.562644	−	0.974528i
$959$	12.4420	+	21.5502i	0.401773	+	0.695892i
$960$		0			0
$961$	21.0601			0.679359
$962$	−11.6790	+	31.4016i	−0.376547	+	1.01243i
$963$	−6.35059			−0.204645
$964$	17.0782	−	9.86009i	0.550051	−	0.317572i
$965$		0			0
$966$	−14.1485	+	24.5059i	−0.455221	+	0.788465i
$967$			10.9215i			0.351211i	0.984461	+	0.175605i	$0.0561883\pi$
$967$			10.9215i			0.351211i	−0.984461	+	0.175605i	$0.943812\pi$
$968$	−4.09197	−	2.36250i	−0.131521	−	0.0759337i
$969$	−12.5339	−	7.23647i	−0.402648	−	0.232469i
$970$		0			0
$971$	−15.7356	+	27.2548i	−0.504978	+	0.874648i	0.495005	+	0.868890i	$0.335166\pi$
$971$	−15.7356	+	27.2548i	−0.504978	+	0.874648i	−0.999983	+	0.00575765i	$0.998167\pi$
$972$	−0.366025	−	0.633975i	−0.0117403	−	0.0203347i
$973$	−28.8528	+	16.6582i	−0.924979	+	0.534037i
$974$	−18.6223			−0.596698
$975$		0			0
$976$	12.5359			0.401264
$977$	27.3260	−	15.7767i	0.874235	−	0.504740i	0.00548205	−	0.999985i	$-0.498255\pi$
$977$	27.3260	−	15.7767i	0.874235	−	0.504740i	0.868753	+	0.495245i	$0.164922\pi$
$978$	−6.93759	−	12.0163i	−0.221840	−	0.384238i
$979$	−0.143130	+	0.247908i	−0.00457445	+	0.00792318i
$980$		0			0
$981$	10.2187	+	5.89980i	0.326259	+	0.188366i
$982$	18.2186	+	10.5185i	0.581378	+	0.335659i
$983$		−	43.6214i		−	1.39131i	−0.718377	−	0.695654i	$-0.755115\pi$
$983$		−	43.6214i		−	1.39131i	0.718377	−	0.695654i	$-0.244885\pi$
$984$	5.11015	−	8.85104i	0.162906	−	0.282161i
$985$		0			0
$986$	12.7094	−	7.33778i	0.404750	−	0.233683i
$987$	5.13766			0.163534
$988$	−15.0920	+	12.4846i	−0.480141	+	0.397187i
$989$	−83.9401			−2.66914
$990$		0			0
$991$	−8.99740	−	15.5840i	−0.285812	−	0.495041i	0.686994	−	0.726663i	$-0.258930\pi$
$991$	−8.99740	−	15.5840i	−0.285812	−	0.495041i	−0.972806	+	0.231623i	$0.925597\pi$
$992$	6.14896	−	10.6503i	0.195230	−	0.338148i
$993$			25.6227i			0.813110i
$994$	−28.7053	−	16.5730i	−0.910477	−	0.525664i
$995$		0			0
$996$			5.10757i			0.161840i
$997$	−12.1045	+	20.9657i	−0.383355	+	0.663990i	−0.991539	−	0.129806i	$-0.958565\pi$
$997$	−12.1045	+	20.9657i	−0.383355	+	0.663990i	0.608185	+	0.793796i	$0.291898\pi$
$998$	−6.19128	−	10.7236i	−0.195982	−	0.339450i
$999$	−7.14650	+	4.12603i	−0.226105	+	0.130542i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.bc.j.751.3		8
5.2	odd	4		975.2.w.i.49.3		8
5.3	odd	4		975.2.w.h.49.2		8
5.4	even	2		195.2.bb.b.166.2	yes	8
13.4	even	6	inner	975.2.bc.j.901.3		8
15.14	odd	2		585.2.bu.d.361.3		8
65.4	even	6		195.2.bb.b.121.2	✓	8
65.17	odd	12		975.2.w.h.199.2		8
65.24	odd	12		2535.2.a.bj.1.3		4
65.43	odd	12		975.2.w.i.199.3		8
65.54	odd	12		2535.2.a.bk.1.2		4
195.89	even	12		7605.2.a.ci.1.2		4
195.119	even	12		7605.2.a.ch.1.3		4
195.134	odd	6		585.2.bu.d.316.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bb.b.121.2	✓	8	65.4	even	6
195.2.bb.b.166.2	yes	8	5.4	even	2
585.2.bu.d.316.3		8	195.134	odd	6
585.2.bu.d.361.3		8	15.14	odd	2
975.2.w.h.49.2		8	5.3	odd	4
975.2.w.h.199.2		8	65.17	odd	12
975.2.w.i.49.3		8	5.2	odd	4
975.2.w.i.199.3		8	65.43	odd	12
975.2.bc.j.751.3		8	1.1	even	1	trivial
975.2.bc.j.901.3		8	13.4	even	6	inner
2535.2.a.bj.1.3		4	65.24	odd	12
2535.2.a.bk.1.2		4	65.54	odd	12
7605.2.a.ch.1.3		4	195.119	even	12
7605.2.a.ci.1.2		4	195.89	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.bc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.975173 - 0.563016i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.366025 + 0.633975i) q^{4} +(-0.975173 - 0.563016i) q^{6} +(-2.47517 - 1.42904i) q^{7} +3.07638i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.975173 - 0.563016i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.366025 + 0.633975i) q^{4} +(-0.975173 - 0.563016i) q^{6} +(-2.47517 - 1.42904i) q^{7} +3.07638i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-2.66422 + 1.53819i) q^{11} +0.732051 q^{12} +(3.55507 - 0.601205i) q^{13} -3.21829 q^{14} +(1.00000 + 1.73205i) q^{16} +(0.975173 - 1.68905i) q^{17} +1.12603i q^{18} +(6.42652 + 3.71035i) q^{19} +2.85808i q^{21} +(-1.73205 + 3.00000i) q^{22} +(4.39627 + 7.61457i) q^{23} +(2.66422 - 1.53819i) q^{24} +(3.12832 - 2.58784i) q^{26} +1.00000 q^{27} +(1.81195 - 1.04613i) q^{28} +(3.34120 + 5.78712i) q^{29} +3.15276i q^{31} +(-3.37810 - 1.95035i) q^{32} +(2.66422 + 1.53819i) q^{33} -2.19615i q^{34} +(-0.366025 - 0.633975i) q^{36} +(-7.14650 + 4.12603i) q^{37} +8.35596 q^{38} +(-2.29820 - 2.77818i) q^{39} +(2.87710 - 1.66109i) q^{41} +(1.60915 + 2.78712i) q^{42} +(-4.77337 + 8.26772i) q^{43} -2.25207i q^{44} +(8.57425 + 4.95035i) q^{46} -1.79759i q^{47} +(1.00000 - 1.73205i) q^{48} +(0.584320 + 1.01207i) q^{49} -1.95035 q^{51} +(-0.920099 + 2.47388i) q^{52} -10.6569 q^{53} +(0.975173 - 0.563016i) q^{54} +(4.39627 - 7.61457i) q^{56} -7.42071i q^{57} +(6.51649 + 3.76230i) q^{58} +(4.17256 + 2.40903i) q^{59} +(3.13397 - 5.42820i) q^{61} +(1.77505 + 3.07448i) q^{62} +(2.47517 - 1.42904i) q^{63} -8.39230 q^{64} +3.46410 q^{66} +(5.09097 - 2.93927i) q^{67} +(0.713876 + 1.23647i) q^{68} +(4.39627 - 7.61457i) q^{69} +(8.91942 + 5.14963i) q^{71} +(-2.66422 - 1.53819i) q^{72} -11.1101i q^{73} +(-4.64605 + 8.04719i) q^{74} +(-4.70454 + 2.71617i) q^{76} +8.79254 q^{77} +(-3.80530 - 1.41529i) q^{78} -11.0968 q^{79} +(-0.500000 - 0.866025i) q^{81} +(1.87044 - 3.23970i) q^{82} +6.97707i q^{83} +(-1.81195 - 1.04613i) q^{84} +10.7499i q^{86} +(3.34120 - 5.78712i) q^{87} +(-4.73205 - 8.19615i) q^{88} +(0.0805845 - 0.0465255i) q^{89} +(-9.65857 - 3.59226i) q^{91} -6.43659 q^{92} +(2.73037 - 1.57638i) q^{93} +(-1.01207 - 1.75296i) q^{94} +3.90069i q^{96} +(-4.15483 - 2.39879i) q^{97} +(1.13963 + 0.657963i) q^{98} -3.07638i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} + 4 q^{4} - 12 q^{7} - 4 q^{9}+O(q^{10}) \) 8 * q - 4 * q^3 + 4 * q^4 - 12 * q^7 - 4 * q^9	\( 8 q - 4 q^{3} + 4 q^{4} - 12 q^{7} - 4 q^{9} - 8 q^{12} + 8 q^{13} - 24 q^{14} + 8 q^{16} - 12 q^{19} - 24 q^{26} + 8 q^{27} - 12 q^{28} + 12 q^{29} + 4 q^{36} - 4 q^{39} + 36 q^{41} + 12 q^{42} - 16 q^{43} + 8 q^{48} - 4 q^{49} - 20 q^{52} + 36 q^{58} + 36 q^{59} + 32 q^{61} + 12 q^{63} + 16 q^{64} + 48 q^{67} + 36 q^{71} - 24 q^{74} - 48 q^{76} + 12 q^{78} - 16 q^{79} - 4 q^{81} + 12 q^{82} + 12 q^{84} + 12 q^{87} - 24 q^{88} + 36 q^{89} - 48 q^{92} + 12 q^{94} + 72 q^{98}+O(q^{100}) \) 8 * q - 4 * q^3 + 4 * q^4 - 12 * q^7 - 4 * q^9 - 8 * q^12 + 8 * q^13 - 24 * q^14 + 8 * q^16 - 12 * q^19 - 24 * q^26 + 8 * q^27 - 12 * q^28 + 12 * q^29 + 4 * q^36 - 4 * q^39 + 36 * q^41 + 12 * q^42 - 16 * q^43 + 8 * q^48 - 4 * q^49 - 20 * q^52 + 36 * q^58 + 36 * q^59 + 32 * q^61 + 12 * q^63 + 16 * q^64 + 48 * q^67 + 36 * q^71 - 24 * q^74 - 48 * q^76 + 12 * q^78 - 16 * q^79 - 4 * q^81 + 12 * q^82 + 12 * q^84 + 12 * q^87 - 24 * q^88 + 36 * q^89 - 48 * q^92 + 12 * q^94 + 72 * q^98

Introduction

L-functions

Modular forms

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