LMFDB - Embedded newform 1050.2.s.e.101.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1050,2,Mod(101,1050)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1050, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1050.101"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1050.s (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,4,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$8.38429221223$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.303595776.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 5x^{6} + 16x^{4} + 45x^{2} + 81 $ x^8 + 5x^6 + 16x^4 + 45*x^2 + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.4
Root			$-0.396143 - 1.68614i$ of defining polynomial
Character	$\chi$	$=$	1050.101
Dual form			1050.2.s.e.551.4

$q$-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 - 0.500000i) q^{2} +(1.65831 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.68614 - 0.396143i) q^{6} +(-0.866025 - 2.50000i) q^{7} -1.00000i q^{8} +(2.50000 + 1.65831i) q^{9} +(-0.813859 - 0.469882i) q^{11} +(1.26217 - 1.18614i) q^{12} +2.00000i q^{13} +(-2.00000 - 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(3.31662 - 5.74456i) q^{17} +(2.99422 + 0.186141i) q^{18} +(3.00000 - 1.73205i) q^{19} +(-0.186141 - 4.57879i) q^{21} -0.939764 q^{22} +(1.18843 - 0.686141i) q^{23} +(0.500000 - 1.65831i) q^{24} +(1.00000 + 1.73205i) q^{26} +(3.31662 + 4.00000i) q^{27} +(-2.59808 - 0.500000i) q^{28} -3.31662i q^{29} +(6.55842 + 3.78651i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-1.11469 - 1.18614i) q^{33} -6.63325i q^{34} +(2.68614 - 1.33591i) q^{36} +(4.10891 + 7.11684i) q^{37} +(1.73205 - 3.00000i) q^{38} +(-1.00000 + 3.31662i) q^{39} -7.37228 q^{41} +(-2.45060 - 3.87228i) q^{42} -1.08724 q^{43} +(-0.813859 + 0.469882i) q^{44} +(0.686141 - 1.18843i) q^{46} +(-4.25639 - 7.37228i) q^{47} +(-0.396143 - 1.68614i) q^{48} +(-5.50000 + 4.33013i) q^{49} +(8.37228 - 7.86797i) q^{51} +(1.73205 + 1.00000i) q^{52} +(-3.78651 - 2.18614i) q^{53} +(4.87228 + 1.80579i) q^{54} +(-2.50000 + 0.866025i) q^{56} +(5.84096 - 1.37228i) q^{57} +(-1.65831 - 2.87228i) q^{58} +(-6.55842 + 11.3595i) q^{59} +(-11.0584 + 6.38458i) q^{61} +7.57301 q^{62} +(1.98072 - 7.68614i) q^{63} -1.00000 q^{64} +(-1.55842 - 0.469882i) q^{66} +(1.18843 - 2.05842i) q^{67} +(-3.31662 - 5.74456i) q^{68} +(2.31386 - 0.543620i) q^{69} +8.51278i q^{71} +(1.65831 - 2.50000i) q^{72} +(-1.73205 - 1.00000i) q^{73} +(7.11684 + 4.10891i) q^{74} -3.46410i q^{76} +(-0.469882 + 2.44158i) q^{77} +(0.792287 + 3.37228i) q^{78} +(4.55842 + 7.89542i) q^{79} +(3.50000 + 8.29156i) q^{81} +(-6.38458 + 3.68614i) q^{82} +11.8294 q^{83} +(-4.05842 - 2.12819i) q^{84} +(-0.941578 + 0.543620i) q^{86} +(1.65831 - 5.50000i) q^{87} +(-0.469882 + 0.813859i) q^{88} +(-0.686141 - 1.18843i) q^{89} +(5.00000 - 1.73205i) q^{91} -1.37228i q^{92} +(8.98266 + 9.55842i) q^{93} +(-7.37228 - 4.25639i) q^{94} +(-1.18614 - 1.26217i) q^{96} -15.1168i q^{97} +(-2.59808 + 6.50000i) q^{98} +(-1.25544 - 2.52434i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} + 2 q^{6} + 20 q^{9} - 18 q^{11} - 16 q^{14} - 4 q^{16} + 24 q^{19} + 10 q^{21} + 4 q^{24} + 8 q^{26} + 18 q^{31} + 10 q^{36} - 8 q^{39} - 36 q^{41} - 18 q^{44} - 6 q^{46} - 44 q^{49} + 44 q^{51}+ \cdots - 56 q^{99}+O(q^{100}) $ 8 * q + 4 * q^4 + 2 * q^6 + 20 * q^9 - 18 * q^11 - 16 * q^14 - 4 * q^16 + 24 * q^19 + 10 * q^21 + 4 * q^24 + 8 * q^26 + 18 * q^31 + 10 * q^36 - 8 * q^39 - 36 * q^41 - 18 * q^44 - 6 * q^46 - 44 * q^49 + 44 * q^51 + 16 * q^54 - 20 * q^56 - 18 * q^59 - 54 * q^61 - 8 * q^64 + 22 * q^66 + 30 * q^69 - 12 * q^74 + 2 * q^79 + 28 * q^81 + 2 * q^84 - 42 * q^86 + 6 * q^89 + 40 * q^91 - 36 * q^94 + 2 * q^96 - 56 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	1.65831	+	0.500000i	0.957427	+	0.288675i
$3$	1.65831	+	0.500000i	0.957427	+	0.288675i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	1.68614	−	0.396143i	0.688364	−	0.161725i
$7$	−0.866025	−	2.50000i	−0.327327	−	0.944911i
$7$	−0.866025	−	2.50000i	−0.327327	−	0.944911i
$8$		−	1.00000i		−	0.353553i
$9$	2.50000	+	1.65831i	0.833333	+	0.552771i
$10$		0			0
$11$	−0.813859	−	0.469882i	−0.245388	−	0.141675i	0.372263	−	0.928127i	$-0.378582\pi$
$11$	−0.813859	−	0.469882i	−0.245388	−	0.141675i	−0.617651	+	0.786453i	$0.711915\pi$
$12$	1.26217	−	1.18614i	0.364357	−	0.342409i
$13$			2.00000i			0.554700i	0.960769	+	0.277350i	$0.0894562\pi$
$13$			2.00000i			0.554700i	−0.960769	+	0.277350i	$0.910544\pi$
$14$	−2.00000	−	1.73205i	−0.534522	−	0.462910i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.31662	−	5.74456i	0.804400	−	1.39326i	−0.112296	−	0.993675i	$-0.535820\pi$
$17$	3.31662	−	5.74456i	0.804400	−	1.39326i	0.916696	−	0.399586i	$-0.130846\pi$
$18$	2.99422	+	0.186141i	0.705744	+	0.0438738i
$19$	3.00000	−	1.73205i	0.688247	−	0.397360i	−0.114708	−	0.993399i	$-0.536593\pi$
$19$	3.00000	−	1.73205i	0.688247	−	0.397360i	0.802955	+	0.596040i	$0.203260\pi$
$20$		0			0
$21$	−0.186141	−	4.57879i	−0.0406192	−	0.999175i
$22$	−0.939764			−0.200358
$23$	1.18843	−	0.686141i	0.247805	−	0.143070i	−0.370954	−	0.928651i	$-0.620969\pi$
$23$	1.18843	−	0.686141i	0.247805	−	0.143070i	0.618759	+	0.785581i	$0.287636\pi$
$24$	0.500000	−	1.65831i	0.102062	−	0.338502i
$25$		0			0
$26$	1.00000	+	1.73205i	0.196116	+	0.339683i
$27$	3.31662	+	4.00000i	0.638285	+	0.769800i
$28$	−2.59808	−	0.500000i	−0.490990	−	0.0944911i
$29$		−	3.31662i		−	0.615882i	−0.951405	−	0.307941i	$-0.900360\pi$
$29$		−	3.31662i		−	0.615882i	0.951405	−	0.307941i	$-0.0996399\pi$
$30$		0			0
$31$	6.55842	+	3.78651i	1.17793	+	0.680077i	0.955534	−	0.294880i	$-0.0952798\pi$
$31$	6.55842	+	3.78651i	1.17793	+	0.680077i	0.222393	+	0.974957i	$0.428613\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−1.11469	−	1.18614i	−0.194043	−	0.206481i
$34$		−	6.63325i		−	1.13759i
$35$		0			0
$36$	2.68614	−	1.33591i	0.447690	−	0.222651i
$37$	4.10891	+	7.11684i	0.675501	+	1.17000i	0.976322	+	0.216321i	$0.0694059\pi$
$37$	4.10891	+	7.11684i	0.675501	+	1.17000i	−0.300821	+	0.953681i	$0.597261\pi$
$38$	1.73205	−	3.00000i	0.280976	−	0.486664i
$39$	−1.00000	+	3.31662i	−0.160128	+	0.531085i
$40$		0			0
$41$	−7.37228			−1.15136			−0.575678	−	0.817676i	$-0.695262\pi$
$41$	−7.37228			−1.15136			−0.575678	+	0.817676i	$0.695262\pi$
$42$	−2.45060	−	3.87228i	−0.378136	−	0.597506i
$43$	−1.08724			−0.165803			−0.0829013	−	0.996558i	$-0.526419\pi$
$43$	−1.08724			−0.165803			−0.0829013	+	0.996558i	$0.526419\pi$
$44$	−0.813859	+	0.469882i	−0.122694	+	0.0708374i
$45$		0			0
$46$	0.686141	−	1.18843i	0.101166	−	0.175225i
$47$	−4.25639	−	7.37228i	−0.620858	−	1.07536i	−0.989326	−	0.145717i	$-0.953451\pi$
$47$	−4.25639	−	7.37228i	−0.620858	−	1.07536i	0.368468	−	0.929640i	$-0.379882\pi$
$48$	−0.396143	−	1.68614i	−0.0571784	−	0.243373i
$49$	−5.50000	+	4.33013i	−0.785714	+	0.618590i
$50$		0			0
$51$	8.37228	−	7.86797i	1.17235	−	1.10174i
$52$	1.73205	+	1.00000i	0.240192	+	0.138675i
$53$	−3.78651	−	2.18614i	−0.520117	−	0.300290i	0.216866	−	0.976201i	$-0.430417\pi$
$53$	−3.78651	−	2.18614i	−0.520117	−	0.300290i	−0.736982	+	0.675912i	$0.763750\pi$
$54$	4.87228	+	1.80579i	0.663034	+	0.245737i
$55$		0			0
$56$	−2.50000	+	0.866025i	−0.334077	+	0.115728i
$57$	5.84096	−	1.37228i	0.773654	−	0.181763i
$58$	−1.65831	−	2.87228i	−0.217747	−	0.377149i
$59$	−6.55842	+	11.3595i	−0.853834	+	1.47888i	0.0238889	+	0.999715i	$0.492395\pi$
$59$	−6.55842	+	11.3595i	−0.853834	+	1.47888i	−0.877723	+	0.479169i	$0.840938\pi$
$60$		0			0
$61$	−11.0584	+	6.38458i	−1.41589	+	0.817462i	−0.995934	−	0.0900844i	$-0.971286\pi$
$61$	−11.0584	+	6.38458i	−1.41589	+	0.817462i	−0.419952	+	0.907546i	$0.637953\pi$
$62$	7.57301			0.961774
$63$	1.98072	−	7.68614i	0.249547	−	0.968363i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−1.55842	−	0.469882i	−0.191828	−	0.0578385i
$67$	1.18843	−	2.05842i	0.145190	−	0.251476i	−0.784254	−	0.620440i	$-0.786954\pi$
$67$	1.18843	−	2.05842i	0.145190	−	0.251476i	0.929444	+	0.368964i	$0.120287\pi$
$68$	−3.31662	−	5.74456i	−0.402200	−	0.696631i
$69$	2.31386	−	0.543620i	0.278556	−	0.0654442i
$70$		0			0
$71$			8.51278i			1.01028i	0.863037	+	0.505140i	$0.168559\pi$
$71$			8.51278i			1.01028i	−0.863037	+	0.505140i	$0.831441\pi$
$72$	1.65831	−	2.50000i	0.195434	−	0.294628i
$73$	−1.73205	−	1.00000i	−0.202721	−	0.117041i	0.395203	−	0.918594i	$-0.370674\pi$
$73$	−1.73205	−	1.00000i	−0.202721	−	0.117041i	−0.597924	+	0.801553i	$0.704008\pi$
$74$	7.11684	+	4.10891i	0.827316	+	0.477651i
$75$		0			0
$76$		−	3.46410i		−	0.397360i
$77$	−0.469882	+	2.44158i	−0.0535480	+	0.278244i
$78$	0.792287	+	3.37228i	0.0897088	+	0.381836i
$79$	4.55842	+	7.89542i	0.512863	+	0.888304i	0.999889	+	0.0149166i	$0.00474828\pi$
$79$	4.55842	+	7.89542i	0.512863	+	0.888304i	−0.487026	+	0.873387i	$0.661918\pi$
$80$		0			0
$81$	3.50000	+	8.29156i	0.388889	+	0.921285i
$82$	−6.38458	+	3.68614i	−0.705059	+	0.407066i
$83$	11.8294			1.29845			0.649223	−	0.760598i	$-0.275094\pi$
$83$	11.8294			1.29845			0.649223	+	0.760598i	$0.275094\pi$
$84$	−4.05842	−	2.12819i	−0.442810	−	0.232205i
$85$		0			0
$86$	−0.941578	+	0.543620i	−0.101533	+	0.0586201i
$87$	1.65831	−	5.50000i	0.177790	−	0.589662i
$88$	−0.469882	+	0.813859i	−0.0500896	+	0.0867577i
$89$	−0.686141	−	1.18843i	−0.0727308	−	0.125973i	0.827366	−	0.561662i	$-0.189838\pi$
$89$	−0.686141	−	1.18843i	−0.0727308	−	0.125973i	−0.900097	+	0.435689i	$0.856505\pi$
$90$		0			0
$91$	5.00000	−	1.73205i	0.524142	−	0.181568i
$92$		−	1.37228i		−	0.143070i
$93$	8.98266	+	9.55842i	0.931458	+	0.991162i
$94$	−7.37228	−	4.25639i	−0.760393	−	0.439013i
$95$		0			0
$96$	−1.18614	−	1.26217i	−0.121060	−	0.128820i
$97$		−	15.1168i		−	1.53488i	−0.641119	−	0.767441i	$-0.721530\pi$
$97$		−	15.1168i		−	1.53488i	0.641119	−	0.767441i	$-0.278470\pi$
$98$	−2.59808	+	6.50000i	−0.262445	+	0.656599i
$99$	−1.25544	−	2.52434i	−0.126176	−	0.253705i
$100$		0			0
$101$	−5.31386	+	9.20387i	−0.528749	+	0.915820i	0.470689	+	0.882299i	$0.344005\pi$
$101$	−5.31386	+	9.20387i	−0.528749	+	0.915820i	−0.999438	+	0.0335207i	$0.989328\pi$
$102$	3.31662	−	11.0000i	0.328395	−	1.08916i
$103$	−1.83324	+	1.05842i	−0.180635	+	0.104289i	−0.587591	−	0.809158i	$-0.699923\pi$
$103$	−1.83324	+	1.05842i	−0.180635	+	0.104289i	0.406956	+	0.913448i	$0.366590\pi$
$104$	2.00000			0.196116
$105$		0			0
$106$	−4.37228			−0.424674
$107$	5.41737	−	3.12772i	0.523717	−	0.302368i	−0.214737	−	0.976672i	$-0.568890\pi$
$107$	5.41737	−	3.12772i	0.523717	−	0.302368i	0.738454	+	0.674304i	$0.235556\pi$
$108$	5.12241	−	0.872281i	0.492905	−	0.0839353i
$109$	−4.05842	+	7.02939i	−0.388726	+	0.673294i	−0.992278	−	0.124030i	$-0.960418\pi$
$109$	−4.05842	+	7.02939i	−0.388726	+	0.673294i	0.603552	+	0.797324i	$0.293752\pi$
$110$		0			0
$111$	3.25544	+	13.8564i	0.308992	+	1.31519i
$112$	−1.73205	+	2.00000i	−0.163663	+	0.188982i
$113$			14.7446i			1.38705i	0.720432	+	0.693526i	$0.243944\pi$
$113$			14.7446i			1.38705i	−0.720432	+	0.693526i	$0.756056\pi$
$114$	4.37228	−	4.10891i	0.409502	−	0.384835i
$115$		0			0
$116$	−2.87228	−	1.65831i	−0.266685	−	0.153970i
$117$	−3.31662	+	5.00000i	−0.306622	+	0.462250i
$118$			13.1168i			1.20750i
$119$	−17.2337	−	3.31662i	−1.57981	−	0.304034i
$120$		0			0
$121$	−5.05842	−	8.76144i	−0.459857	−	0.796495i
$122$	−6.38458	+	11.0584i	−0.578033	+	1.00118i
$123$	−12.2255	−	3.68614i	−1.10234	−	0.332368i
$124$	6.55842	−	3.78651i	0.588964	−	0.340038i
$125$		0			0
$126$	−2.12772	−	7.64675i	−0.189552	−	0.681227i
$127$	−7.57301			−0.671996			−0.335998	−	0.941863i	$-0.609074\pi$
$127$	−7.57301			−0.671996			−0.335998	+	0.941863i	$0.609074\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−1.80298	−	0.543620i	−0.158744	−	0.0478631i
$130$		0			0
$131$	−5.18614	−	8.98266i	−0.453115	−	0.784819i	0.545462	−	0.838135i	$-0.316354\pi$
$131$	−5.18614	−	8.98266i	−0.453115	−	0.784819i	−0.998578	+	0.0533167i	$0.983021\pi$
$132$	−1.58457	+	0.372281i	−0.137919	+	0.0324029i
$133$	−6.92820	−	6.00000i	−0.600751	−	0.520266i
$134$		−	2.37686i		−	0.205330i
$135$		0			0
$136$	−5.74456	−	3.31662i	−0.492592	−	0.284398i
$137$	7.57301	+	4.37228i	0.647006	+	0.373549i	0.787308	−	0.616560i	$-0.211474\pi$
$137$	7.57301	+	4.37228i	0.647006	+	0.373549i	−0.140302	+	0.990109i	$0.544807\pi$
$138$	1.73205	−	1.62772i	0.147442	−	0.138561i
$139$			8.21782i			0.697027i	0.937304	+	0.348513i	$0.113313\pi$
$139$			8.21782i			0.697027i	−0.937304	+	0.348513i	$0.886687\pi$
$140$		0			0
$141$	−3.37228	−	14.3537i	−0.283997	−	1.20880i
$142$	4.25639	+	7.37228i	0.357188	+	0.618668i
$143$	0.939764	−	1.62772i	0.0785870	−	0.136117i
$144$	0.186141	−	2.99422i	0.0155117	−	0.249518i
$145$		0			0
$146$	−2.00000			−0.165521
$147$	−11.2858	+	4.43070i	−0.930836	+	0.365438i
$148$	8.21782			0.675501
$149$	7.80298	−	4.50506i	0.639245	−	0.369069i	−0.145078	−	0.989420i	$-0.546343\pi$
$149$	7.80298	−	4.50506i	0.639245	−	0.369069i	0.784324	+	0.620352i	$0.213010\pi$
$150$		0			0
$151$	−4.55842	+	7.89542i	−0.370959	+	0.642520i	−0.989713	−	0.143065i	$-0.954304\pi$
$151$	−4.55842	+	7.89542i	−0.370959	+	0.642520i	0.618754	+	0.785585i	$0.287638\pi$
$152$	−1.73205	−	3.00000i	−0.140488	−	0.243332i
$153$	17.8178	−	8.86141i	1.44049	−	0.716402i
$154$	0.813859	+	2.34941i	0.0655827	+	0.189321i
$155$		0			0
$156$	2.37228	+	2.52434i	0.189935	+	0.202109i
$157$	6.92820	+	4.00000i	0.552931	+	0.319235i	0.750303	−	0.661094i	$-0.229907\pi$
$157$	6.92820	+	4.00000i	0.552931	+	0.319235i	−0.197372	+	0.980329i	$0.563241\pi$
$158$	7.89542	+	4.55842i	0.628126	+	0.362649i
$159$	−5.18614	−	5.51856i	−0.411288	−	0.437650i
$160$		0			0
$161$	−2.74456	−	2.37686i	−0.216302	−	0.187323i
$162$	7.17687	+	5.43070i	0.563868	+	0.426676i
$163$	−1.73205	−	3.00000i	−0.135665	−	0.234978i	0.790186	−	0.612866i	$-0.209984\pi$
$163$	−1.73205	−	3.00000i	−0.135665	−	0.234978i	−0.925851	+	0.377888i	$0.876650\pi$
$164$	−3.68614	+	6.38458i	−0.287839	+	0.498552i
$165$		0			0
$166$	10.2446	−	5.91470i	0.795132	−	0.459070i
$167$	−14.6487			−1.13355			−0.566775	−	0.823873i	$-0.691809\pi$
$167$	−14.6487			−1.13355			−0.566775	+	0.823873i	$0.691809\pi$
$168$	−4.57879	+	0.186141i	−0.353262	+	0.0143611i
$169$	9.00000			0.692308
$170$		0			0
$171$	10.3723	+	0.644810i	0.793188	+	0.0493099i
$172$	−0.543620	+	0.941578i	−0.0414507	+	0.0717947i
$173$	−8.51278	−	14.7446i	−0.647214	−	1.12101i	−0.983785	−	0.179350i	$-0.942600\pi$
$173$	−8.51278	−	14.7446i	−0.647214	−	1.12101i	0.336571	−	0.941658i	$-0.390733\pi$
$174$	−1.31386	−	5.59230i	−0.0996034	−	0.423951i
$175$		0			0
$176$			0.939764i			0.0708374i
$177$	−16.5557	+	15.5584i	−1.24440	+	1.16944i
$178$	−1.18843	−	0.686141i	−0.0890766	−	0.0514284i
$179$	20.4891	+	11.8294i	1.53143	+	0.884171i	0.999296	+	0.0375102i	$0.0119427\pi$
$179$	20.4891	+	11.8294i	1.53143	+	0.884171i	0.532133	+	0.846661i	$0.321391\pi$
$180$		0			0
$181$		−	8.01544i		−	0.595783i	−0.954600	−	0.297892i	$-0.903717\pi$
$181$		−	8.01544i		−	0.595783i	0.954600	−	0.297892i	$-0.0962834\pi$
$182$	3.46410	−	4.00000i	0.256776	−	0.296500i
$183$	−21.5306	+	5.05842i	−1.59159	+	0.373929i
$184$	−0.686141	−	1.18843i	−0.0505830	−	0.0876123i
$185$		0			0
$186$	12.5584	+	3.78651i	0.920828	+	0.277640i
$187$	−5.39853	+	3.11684i	−0.394780	+	0.227926i
$188$	−8.51278			−0.620858
$189$	7.12772	−	11.7557i	0.518465	−	0.855099i
$190$		0			0
$191$	−14.7446	+	8.51278i	−1.06688	+	0.615963i	−0.927327	−	0.374252i	$-0.877900\pi$
$191$	−14.7446	+	8.51278i	−1.06688	+	0.615963i	−0.139552	+	0.990215i	$0.544566\pi$
$192$	−1.65831	−	0.500000i	−0.119678	−	0.0360844i
$193$	8.98266	−	15.5584i	0.646586	−	1.11992i	−0.337347	−	0.941380i	$-0.609530\pi$
$193$	8.98266	−	15.5584i	0.646586	−	1.11992i	0.983933	−	0.178539i	$-0.0571372\pi$
$194$	−7.55842	−	13.0916i	−0.542663	−	0.939920i
$195$		0			0
$196$	1.00000	+	6.92820i	0.0714286	+	0.494872i
$197$			14.2337i			1.01411i	0.861914	+	0.507054i	$0.169266\pi$
$197$			14.2337i			1.01411i	−0.861914	+	0.507054i	$0.830734\pi$
$198$	−2.34941	−	1.55842i	−0.166965	−	0.110752i
$199$	−1.11684	−	0.644810i	−0.0791710	−	0.0457094i	0.459892	−	0.887975i	$-0.347888\pi$
$199$	−1.11684	−	0.644810i	−0.0791710	−	0.0457094i	−0.539063	+	0.842266i	$0.681221\pi$
$200$		0			0
$201$	3.00000	−	2.81929i	0.211604	−	0.198857i
$202$			10.6277i			0.747764i
$203$	−8.29156	+	2.87228i	−0.581954	+	0.201595i
$204$	−2.62772	−	11.1846i	−0.183977	−	0.783078i
$205$		0			0
$206$	−1.05842	+	1.83324i	−0.0737438	+	0.127728i
$207$	4.10891	+	0.255437i	0.285589	+	0.0177541i
$208$	1.73205	−	1.00000i	0.120096	−	0.0693375i
$209$	−3.25544			−0.225183
$210$		0			0
$211$	16.2337			1.11757			0.558787	−	0.829311i	$-0.311267\pi$
$211$	16.2337			1.11757			0.558787	+	0.829311i	$0.311267\pi$
$212$	−3.78651	+	2.18614i	−0.260058	+	0.150145i
$213$	−4.25639	+	14.1168i	−0.291643	+	0.967270i
$214$	3.12772	−	5.41737i	0.213806	−	0.370324i
$215$		0			0
$216$	4.00000	−	3.31662i	0.272166	−	0.225668i
$217$	3.78651	−	19.6753i	0.257045	−	1.33564i
$218$			8.11684i			0.549742i
$219$	−2.37228	−	2.52434i	−0.160304	−	0.170579i
$220$		0			0
$221$	11.4891	+	6.63325i	0.772842	+	0.446201i
$222$	9.74749	+	10.3723i	0.654209	+	0.696142i
$223$			0.883156i			0.0591405i	0.999563	+	0.0295703i	$0.00941388\pi$
$223$			0.883156i			0.0591405i	−0.999563	+	0.0295703i	$0.990586\pi$
$224$	−0.500000	+	2.59808i	−0.0334077	+	0.173591i
$225$		0			0
$226$	7.37228	+	12.7692i	0.490397	+	0.849392i
$227$	−10.4198	+	18.0475i	−0.691584	+	1.19786i	0.279735	+	0.960077i	$0.409753\pi$
$227$	−10.4198	+	18.0475i	−0.691584	+	1.19786i	−0.971319	+	0.237781i	$0.923580\pi$
$228$	1.73205	−	5.74456i	0.114708	−	0.380443i
$229$	−12.0000	+	6.92820i	−0.792982	+	0.457829i	−0.841011	−	0.541017i	$-0.818039\pi$
$229$	−12.0000	+	6.92820i	−0.792982	+	0.457829i	0.0480291	+	0.998846i	$0.484706\pi$
$230$		0			0
$231$	−2.00000	+	3.81396i	−0.131590	+	0.250940i
$232$	−3.31662			−0.217747
$233$	0.442430	−	0.255437i	0.0289846	−	0.0167343i	−0.485438	−	0.874271i	$-0.661340\pi$
$233$	0.442430	−	0.255437i	0.0289846	−	0.0167343i	0.514422	+	0.857537i	$0.328006\pi$
$234$	−0.372281	+	5.98844i	−0.0243368	+	0.391477i
$235$		0			0
$236$	6.55842	+	11.3595i	0.426917	+	0.739442i
$237$	3.61158	+	15.3723i	0.234597	+	0.998537i
$238$	−16.5831	+	5.74456i	−1.07492	+	0.372365i
$239$		−	23.6588i		−	1.53036i	−0.643816	−	0.765180i	$-0.722650\pi$
$239$		−	23.6588i		−	1.53036i	0.643816	−	0.765180i	$-0.277350\pi$
$240$		0			0
$241$	−16.6753	−	9.62747i	−1.07415	−	0.620160i	−0.144836	−	0.989456i	$-0.546266\pi$
$241$	−16.6753	−	9.62747i	−1.07415	−	0.620160i	−0.929312	+	0.369296i	$0.879599\pi$
$242$	−8.76144	−	5.05842i	−0.563207	−	0.325168i
$243$	1.65831	+	15.5000i	0.106381	+	0.994325i
$244$			12.7692i			0.817462i
$245$		0			0
$246$	−12.4307	+	2.92048i	−0.792553	+	0.186203i
$247$	3.46410	+	6.00000i	0.220416	+	0.381771i
$248$	3.78651	−	6.55842i	0.240443	−	0.416460i
$249$	19.6168	+	5.91470i	1.24317	+	0.374829i
$250$		0			0
$251$	1.11684			0.0704946			0.0352473	−	0.999379i	$-0.488778\pi$
$251$	1.11684			0.0704946			0.0352473	+	0.999379i	$0.488778\pi$
$252$	−5.66603	−	5.55842i	−0.356927	−	0.350148i
$253$	−1.28962			−0.0810777
$254$	−6.55842	+	3.78651i	−0.411512	+	0.237587i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	0.939764	+	1.62772i	0.0586209	+	0.101534i	0.893847	−	0.448373i	$-0.147996\pi$
$257$	0.939764	+	1.62772i	0.0586209	+	0.101534i	−0.835226	+	0.549907i	$0.814663\pi$
$258$	−1.83324	+	0.430703i	−0.114133	+	0.0268144i
$259$	14.2337	−	16.4356i	0.884438	−	1.02126i
$260$		0			0
$261$	5.50000	−	8.29156i	0.340441	−	0.513235i
$262$	−8.98266	−	5.18614i	−0.554951	−	0.320401i
$263$	6.38458	+	3.68614i	0.393690	+	0.227297i	0.683758	−	0.729709i	$-0.260344\pi$
$263$	6.38458	+	3.68614i	0.393690	+	0.227297i	−0.290068	+	0.957006i	$0.593678\pi$
$264$	−1.18614	+	1.11469i	−0.0730019	+	0.0686046i
$265$		0			0
$266$	−9.00000	−	1.73205i	−0.551825	−	0.106199i
$267$	−0.543620	−	2.31386i	−0.0332690	−	0.141606i
$268$	−1.18843	−	2.05842i	−0.0725949	−	0.125738i
$269$	−12.9891	+	22.4978i	−0.791961	+	1.37172i	0.132790	+	0.991144i	$0.457606\pi$
$269$	−12.9891	+	22.4978i	−0.791961	+	1.37172i	−0.924751	+	0.380572i	$0.875727\pi$
$270$		0			0
$271$	7.67527	−	4.43132i	0.466239	−	0.269183i	−0.248425	−	0.968651i	$-0.579913\pi$
$271$	7.67527	−	4.43132i	0.466239	−	0.269183i	0.714664	+	0.699468i	$0.246580\pi$
$272$	−6.63325			−0.402200
$273$	9.15759	−	0.372281i	0.554242	−	0.0225315i
$274$	8.74456			0.528278
$275$		0			0
$276$	0.686141	−	2.27567i	0.0413008	−	0.136979i
$277$	4.55134	−	7.88316i	0.273464	−	0.473653i	−0.696283	−	0.717768i	$-0.745164\pi$
$277$	4.55134	−	7.88316i	0.273464	−	0.473653i	0.969746	+	0.244115i	$0.0784973\pi$
$278$	4.10891	+	7.11684i	0.246436	+	0.426840i
$279$	10.1168	+	20.3422i	0.605680	+	1.21785i
$280$		0			0
$281$		−	11.3870i		−	0.679290i	−0.940554	−	0.339645i	$-0.889693\pi$
$281$		−	11.3870i		−	0.679290i	0.940554	−	0.339645i	$-0.110307\pi$
$282$	−10.0974	−	10.7446i	−0.601289	−	0.639829i
$283$	13.8564	+	8.00000i	0.823678	+	0.475551i	0.851683	−	0.524057i	$-0.175582\pi$
$283$	13.8564	+	8.00000i	0.823678	+	0.475551i	−0.0280052	+	0.999608i	$0.508916\pi$
$284$	7.37228	+	4.25639i	0.437464	+	0.252570i
$285$		0			0
$286$		−	1.87953i		−	0.111139i
$287$	6.38458	+	18.4307i	0.376870	+	1.08793i
$288$	−1.33591	−	2.68614i	−0.0787191	−	0.158282i
$289$	−13.5000	−	23.3827i	−0.794118	−	1.37545i
$290$		0			0
$291$	7.55842	−	25.0684i	0.443083	−	1.46954i
$292$	−1.73205	+	1.00000i	−0.101361	+	0.0585206i
$293$	−21.7244			−1.26915			−0.634576	−	0.772861i	$-0.718825\pi$
$293$	−21.7244			−1.26915			−0.634576	+	0.772861i	$0.718825\pi$
$294$	−7.55842	+	9.47999i	−0.440816	+	0.552884i
$295$		0			0
$296$	7.11684	−	4.10891i	0.413658	−	0.238826i
$297$	−0.819738	−	4.81386i	−0.0475660	−	0.279328i
$298$	4.50506	−	7.80298i	0.260971	−	0.452015i
$299$	1.37228	+	2.37686i	0.0793611	+	0.137457i
$300$		0			0
$301$	0.941578	+	2.71810i	0.0542717	+	0.156669i
$302$			9.11684i			0.524615i
$303$	−13.4140	+	12.6060i	−0.770613	+	0.724194i
$304$	−3.00000	−	1.73205i	−0.172062	−	0.0993399i
$305$		0			0
$306$	11.0000	−	16.5831i	0.628828	−	0.947994i
$307$		−	24.1168i		−	1.37642i	−0.725511	−	0.688210i	$-0.758397\pi$
$307$		−	24.1168i		−	1.37642i	0.725511	−	0.688210i	$-0.241603\pi$
$308$	1.87953	+	1.62772i	0.107096	+	0.0927479i
$309$	−3.56930	+	0.838574i	−0.203050	+	0.0477048i
$310$		0			0
$311$	−10.1168	+	17.5229i	−0.573674	+	0.993632i	0.422511	+	0.906358i	$0.361149\pi$
$311$	−10.1168	+	17.5229i	−0.573674	+	0.993632i	−0.996184	+	0.0872739i	$0.972184\pi$
$312$	3.31662	+	1.00000i	0.187767	+	0.0566139i
$313$	2.69927	−	1.55842i	0.152572	−	0.0880872i	−0.421771	−	0.906703i	$-0.638591\pi$
$313$	2.69927	−	1.55842i	0.152572	−	0.0880872i	0.574342	+	0.818615i	$0.305258\pi$
$314$	8.00000			0.451466
$315$		0			0
$316$	9.11684			0.512863
$317$	−0.967215	+	0.558422i	−0.0543242	+	0.0313641i	−0.526916	−	0.849917i	$-0.676652\pi$
$317$	−0.967215	+	0.558422i	−0.0543242	+	0.0313641i	0.472592	+	0.881281i	$0.343318\pi$
$318$	−7.25061	−	2.18614i	−0.406594	−	0.122593i
$319$	−1.55842	+	2.69927i	−0.0872549	+	0.151130i
$320$		0			0
$321$	10.5475	−	2.47805i	0.588707	−	0.138311i
$322$	−3.56529	−	0.686141i	−0.198686	−	0.0382371i
$323$		−	22.9783i		−	1.27854i
$324$	8.93070	+	1.11469i	0.496150	+	0.0619273i
$325$		0			0
$326$	−3.00000	−	1.73205i	−0.166155	−	0.0959294i
$327$	−10.2448	+	9.62772i	−0.566540	+	0.532414i
$328$			7.37228i			0.407066i
$329$	−14.7446	+	17.0256i	−0.812894	+	0.938649i
$330$		0			0
$331$	12.1168	+	20.9870i	0.666002	+	1.15355i	0.979013	+	0.203800i	$0.0653291\pi$
$331$	12.1168	+	20.9870i	0.666002	+	1.15355i	−0.313011	+	0.949750i	$0.601338\pi$
$332$	5.91470	−	10.2446i	0.324611	−	0.562243i
$333$	−1.52967	+	24.6060i	−0.0838255	+	1.34840i
$334$	−12.6861	+	7.32435i	−0.694155	+	0.400770i
$335$		0			0
$336$	−3.87228	+	2.45060i	−0.211250	+	0.133691i
$337$	−0.644810			−0.0351250			−0.0175625	−	0.999846i	$-0.505591\pi$
$337$	−0.644810			−0.0351250			−0.0175625	+	0.999846i	$0.505591\pi$
$338$	7.79423	−	4.50000i	0.423950	−	0.244768i
$339$	−7.37228	+	24.4511i	−0.400407	+	1.32800i
$340$		0			0
$341$	−3.55842	−	6.16337i	−0.192699	−	0.333765i
$342$	9.30506	−	4.62772i	0.503160	−	0.250238i
$343$	15.5885	+	10.0000i	0.841698	+	0.539949i
$344$			1.08724i			0.0586201i
$345$		0			0
$346$	−14.7446	−	8.51278i	−0.792673	−	0.457650i
$347$	−1.63086	−	0.941578i	−0.0875492	−	0.0505466i	0.455586	−	0.890192i	$-0.349430\pi$
$347$	−1.63086	−	0.941578i	−0.0875492	−	0.0505466i	−0.543135	+	0.839645i	$0.682763\pi$
$348$	−3.93398	−	4.18614i	−0.210884	−	0.224401i
$349$		−	25.7407i		−	1.37787i	−0.724824	−	0.688934i	$-0.758079\pi$
$349$		−	25.7407i		−	1.37787i	0.724824	−	0.688934i	$-0.241921\pi$
$350$		0			0
$351$	−8.00000	+	6.63325i	−0.427008	+	0.354057i
$352$	0.469882	+	0.813859i	0.0250448	+	0.0433788i
$353$	−6.13592	+	10.6277i	−0.326582	+	0.565656i	−0.981831	−	0.189756i	$-0.939230\pi$
$353$	−6.13592	+	10.6277i	−0.326582	+	0.565656i	0.655249	+	0.755413i	$0.272564\pi$
$354$	−6.55842	+	21.7518i	−0.348576	+	1.15610i
$355$		0			0
$356$	−1.37228			−0.0727308
$357$	−26.9205	−	14.1168i	−1.42479	−	0.747143i
$358$	23.6588			1.25041
$359$	23.7446	−	13.7089i	1.25319	−	0.723530i	0.281448	−	0.959576i	$-0.409185\pi$
$359$	23.7446	−	13.7089i	1.25319	−	0.723530i	0.971742	+	0.236047i	$0.0758518\pi$
$360$		0			0
$361$	−3.50000	+	6.06218i	−0.184211	+	0.319062i
$362$	−4.00772	−	6.94158i	−0.210641	−	0.364841i
$363$	−4.00772	−	17.0584i	−0.210351	−	0.895335i
$364$	1.00000	−	5.19615i	0.0524142	−	0.272352i
$365$		0			0
$366$	−16.1168	+	15.1460i	−0.842441	+	0.791696i
$367$	11.4607	+	6.61684i	0.598244	+	0.345396i	0.768351	−	0.640029i	$-0.221078\pi$
$367$	11.4607	+	6.61684i	0.598244	+	0.345396i	−0.170106	+	0.985426i	$0.554411\pi$
$368$	−1.18843	−	0.686141i	−0.0619512	−	0.0357676i
$369$	−18.4307	−	12.2255i	−0.959464	−	0.636436i
$370$		0			0
$371$	−2.18614	+	11.3595i	−0.113499	+	0.589757i
$372$	12.7692	−	3.00000i	0.662050	−	0.155543i
$373$	11.6819	+	20.2337i	0.604867	+	1.04766i	0.992072	+	0.125667i	$0.0401071\pi$
$373$	11.6819	+	20.2337i	0.604867	+	1.04766i	−0.387205	+	0.921994i	$0.626560\pi$
$374$	−3.11684	+	5.39853i	−0.161168	+	0.279151i
$375$		0			0
$376$	−7.37228	+	4.25639i	−0.380196	+	0.219506i
$377$	6.63325			0.341630
$378$	0.294954	−	13.7446i	0.0151708	−	0.706944i
$379$	12.2337			0.628402			0.314201	−	0.949356i	$-0.398263\pi$
$379$	12.2337			0.628402			0.314201	+	0.949356i	$0.398263\pi$
$380$		0			0
$381$	−12.5584	−	3.78651i	−0.643387	−	0.193989i
$382$	−8.51278	+	14.7446i	−0.435552	+	0.754397i
$383$	7.82168	+	13.5475i	0.399669	+	0.692247i	0.993685	−	0.112206i	$-0.0357917\pi$
$383$	7.82168	+	13.5475i	0.399669	+	0.692247i	−0.594016	+	0.804453i	$0.702458\pi$
$384$	−1.68614	+	0.396143i	−0.0860455	+	0.0202156i
$385$		0			0
$386$		−	17.9653i		−	0.914411i
$387$	−2.71810	−	1.80298i	−0.138169	−	0.0916509i
$388$	−13.0916	−	7.55842i	−0.664624	−	0.383721i
$389$	−6.51087	−	3.75906i	−0.330114	−	0.190592i	0.325777	−	0.945446i	$-0.394374\pi$
$389$	−6.51087	−	3.75906i	−0.330114	−	0.190592i	−0.655892	+	0.754855i	$0.727707\pi$
$390$		0			0
$391$		−	9.10268i		−	0.460343i
$392$	4.33013	+	5.50000i	0.218704	+	0.277792i
$393$	−4.10891	−	17.4891i	−0.207267	−	0.882210i
$394$	7.11684	+	12.3267i	0.358541	+	0.621012i
$395$		0			0
$396$	−2.81386	−	0.174928i	−0.141402	−	0.00879048i
$397$	−6.92820	+	4.00000i	−0.347717	+	0.200754i	−0.663679	−	0.748017i	$-0.731006\pi$
$397$	−6.92820	+	4.00000i	−0.347717	+	0.200754i	0.315963	+	0.948772i	$0.397673\pi$
$398$	−1.28962			−0.0646428
$399$	−8.48913	−	13.4140i	−0.424988	−	0.671539i
$400$		0			0
$401$	14.3139	−	8.26411i	0.714800	−	0.412690i	−0.0980358	−	0.995183i	$-0.531256\pi$
$401$	14.3139	−	8.26411i	0.714800	−	0.412690i	0.812836	+	0.582493i	$0.197923\pi$
$402$	1.18843	−	3.94158i	0.0592735	−	0.196588i
$403$	−7.57301	+	13.1168i	−0.377239	+	0.653397i
$404$	5.31386	+	9.20387i	0.264374	+	0.457910i
$405$		0			0
$406$	−5.74456	+	6.63325i	−0.285098	+	0.329203i
$407$		−	7.72281i		−	0.382806i
$408$	−7.86797	−	8.37228i	−0.389522	−	0.414490i
$409$	−3.73369	−	2.15565i	−0.184619	−	0.106590i	0.404842	−	0.914387i	$-0.367327\pi$
$409$	−3.73369	−	2.15565i	−0.184619	−	0.106590i	−0.589461	+	0.807797i	$0.700660\pi$
$410$		0			0
$411$	10.3723	+	11.0371i	0.511627	+	0.544421i
$412$			2.11684i			0.104289i
$413$	34.0786	+	6.55842i	1.67690	+	0.322719i
$414$	3.68614	−	1.83324i	0.181164	−	0.0900989i
$415$		0			0
$416$	1.00000	−	1.73205i	0.0490290	−	0.0849208i
$417$	−4.10891	+	13.6277i	−0.201214	+	0.667352i
$418$	−2.81929	+	1.62772i	−0.137896	+	0.0796143i
$419$	−6.51087			−0.318077			−0.159039	−	0.987272i	$-0.550839\pi$
$419$	−6.51087			−0.318077			−0.159039	+	0.987272i	$0.550839\pi$
$420$		0			0
$421$	−2.11684			−0.103169			−0.0515843	−	0.998669i	$-0.516427\pi$
$421$	−2.11684			−0.103169			−0.0515843	+	0.998669i	$0.516427\pi$
$422$	14.0588	−	8.11684i	0.684371	−	0.395122i
$423$	1.58457	−	25.4891i	0.0770446	−	1.23932i
$424$	−2.18614	+	3.78651i	−0.106168	+	0.183889i
$425$		0			0
$426$	3.37228	+	14.3537i	0.163388	+	0.695441i
$427$	25.5383	+	22.1168i	1.23589	+	1.07031i
$428$		−	6.25544i		−	0.302368i
$429$	2.37228	−	2.22938i	0.114535	−	0.107636i
$430$		0			0
$431$	14.7446	+	8.51278i	0.710221	+	0.410046i	0.811143	−	0.584848i	$-0.198846\pi$
$431$	14.7446	+	8.51278i	0.710221	+	0.410046i	−0.100922	+	0.994894i	$0.532179\pi$
$432$	1.80579	−	4.87228i	0.0868811	−	0.234418i
$433$		−	34.0000i		−	1.63394i	−0.576683	−	0.816968i	$-0.695653\pi$
$433$		−	34.0000i		−	1.63394i	0.576683	−	0.816968i	$-0.304347\pi$
$434$	−6.55842	−	18.9325i	−0.314814	−	0.908791i
$435$		0			0
$436$	4.05842	+	7.02939i	0.194363	+	0.336647i
$437$	2.37686	−	4.11684i	0.113701	−	0.196935i
$438$	−3.31662	−	1.00000i	−0.158474	−	0.0477818i
$439$	2.44158	−	1.40965i	0.116530	−	0.0672787i	−0.440602	−	0.897703i	$-0.645235\pi$
$439$	2.44158	−	1.40965i	0.116530	−	0.0672787i	0.557132	+	0.830424i	$0.311902\pi$
$440$		0			0
$441$	−20.9307	+	1.70460i	−0.996700	+	0.0811714i
$442$	13.2665			0.631023
$443$	−7.79423	+	4.50000i	−0.370315	+	0.213801i	−0.673596	−	0.739100i	$-0.735251\pi$
$443$	−7.79423	+	4.50000i	−0.370315	+	0.213801i	0.303281	+	0.952901i	$0.401918\pi$
$444$	13.6277	+	4.10891i	0.646743	+	0.195000i
$445$		0			0
$446$	0.441578	+	0.764836i	0.0209093	+	0.0362160i
$447$	15.1923	−	3.56930i	0.718572	−	0.168822i
$448$	0.866025	+	2.50000i	0.0409159	+	0.118114i
$449$		−	20.3971i		−	0.962598i	−0.876557	−	0.481299i	$-0.840165\pi$
$449$		−	20.3971i		−	0.962598i	0.876557	−	0.481299i	$-0.159835\pi$
$450$		0			0
$451$	6.00000	+	3.46410i	0.282529	+	0.163118i
$452$	12.7692	+	7.37228i	0.600611	+	0.346763i
$453$	−11.5070	+	10.8139i	−0.540646	+	0.508079i
$454$			20.8395i			0.978047i
$455$		0			0
$456$	−1.37228	−	5.84096i	−0.0642630	−	0.273528i
$457$	−1.40965	−	2.44158i	−0.0659404	−	0.114212i	0.831170	−	0.556018i	$-0.187671\pi$
$457$	−1.40965	−	2.44158i	−0.0659404	−	0.114212i	−0.897111	+	0.441806i	$0.854338\pi$
$458$	−6.92820	+	12.0000i	−0.323734	+	0.560723i
$459$	33.9783	−	5.78606i	1.58597	−	0.270070i
$460$		0			0
$461$	23.4891			1.09400			0.546999	−	0.837133i	$-0.315770\pi$
$461$	23.4891			1.09400			0.546999	+	0.837133i	$0.315770\pi$
$462$	0.174928	+	4.30298i	0.00813840	+	0.200193i
$463$	6.72582			0.312576			0.156288	−	0.987712i	$-0.450047\pi$
$463$	6.72582			0.312576			0.156288	+	0.987712i	$0.450047\pi$
$464$	−2.87228	+	1.65831i	−0.133342	+	0.0769852i
$465$		0			0
$466$	0.255437	−	0.442430i	0.0118329	−	0.0204952i
$467$	−18.2140	−	31.5475i	−0.842843	−	1.45985i	−0.887482	−	0.460843i	$-0.847547\pi$
$467$	−18.2140	−	31.5475i	−0.842843	−	1.45985i	0.0446389	−	0.999003i	$-0.485786\pi$
$468$	2.67181	+	5.37228i	0.123505	+	0.248334i
$469$	−6.17527	−	1.18843i	−0.285147	−	0.0548766i
$470$		0			0
$471$	9.48913	+	10.0974i	0.437236	+	0.465261i
$472$	11.3595	+	6.55842i	0.522864	+	0.301876i
$473$	0.884861	+	0.510875i	0.0406859	+	0.0234900i
$474$	10.8139	+	11.5070i	0.496697	+	0.528534i
$475$		0			0
$476$	−11.4891	+	13.2665i	−0.526603	+	0.608069i
$477$	−5.84096	−	11.7446i	−0.267439	−	0.537747i
$478$	−11.8294	−	20.4891i	−0.541064	−	0.937151i
$479$	1.37228	−	2.37686i	0.0627011	−	0.108602i	−0.832971	−	0.553317i	$-0.813362\pi$
$479$	1.37228	−	2.37686i	0.0627011	−	0.108602i	0.895672	+	0.444715i	$0.146695\pi$
$480$		0			0
$481$	−14.2337	+	8.21782i	−0.649000	+	0.374701i
$482$	−19.2549			−0.877038
$483$	−3.36291	−	5.31386i	−0.153018	−	0.241789i
$484$	−10.1168			−0.459857
$485$		0			0
$486$	9.18614	+	12.5942i	0.416692	+	0.571286i
$487$	7.25061	−	12.5584i	0.328556	−	0.569076i	−0.653669	−	0.756780i	$-0.726771\pi$
$487$	7.25061	−	12.5584i	0.328556	−	0.569076i	0.982226	+	0.187704i	$0.0601046\pi$
$488$	6.38458	+	11.0584i	0.289016	+	0.500591i
$489$	−1.37228	−	5.84096i	−0.0620567	−	0.264137i
$490$		0			0
$491$		−	30.2372i		−	1.36458i	−0.731080	−	0.682292i	$-0.760983\pi$
$491$		−	30.2372i		−	1.36458i	0.731080	−	0.682292i	$-0.239017\pi$
$492$	−9.30506	+	8.74456i	−0.419505	+	0.394235i
$493$	−19.0526	−	11.0000i	−0.858084	−	0.495415i
$494$	6.00000	+	3.46410i	0.269953	+	0.155857i
$495$		0			0
$496$		−	7.57301i		−	0.340038i
$497$	21.2819	−	7.37228i	0.954626	−	0.330692i
$498$	19.9460	−	4.68614i	0.893803	−	0.209991i
$499$	−3.11684	−	5.39853i	−0.139529	−	0.241671i	0.787789	−	0.615945i	$-0.211226\pi$
$499$	−3.11684	−	5.39853i	−0.139529	−	0.241671i	−0.927318	+	0.374273i	$0.877892\pi$
$500$		0			0
$501$	−24.2921	−	7.32435i	−1.08529	−	0.327228i
$502$	0.967215	−	0.558422i	0.0431689	−	0.0249236i
$503$	−6.13592			−0.273587			−0.136793	−	0.990600i	$-0.543680\pi$
$503$	−6.13592			−0.273587			−0.136793	+	0.990600i	$0.543680\pi$
$504$	−7.68614	−	1.98072i	−0.342368	−	0.0882282i
$505$		0			0
$506$	−1.11684	+	0.644810i	−0.0496498	+	0.0286653i
$507$	14.9248	+	4.50000i	0.662834	+	0.199852i
$508$	−3.78651	+	6.55842i	−0.167999	+	0.290983i
$509$	−5.87228	−	10.1711i	−0.260284	−	0.450826i	0.706033	−	0.708179i	$-0.250483\pi$
$509$	−5.87228	−	10.1711i	−0.260284	−	0.450826i	−0.966317	+	0.257353i	$0.917150\pi$
$510$		0			0
$511$	−1.00000	+	5.19615i	−0.0442374	+	0.229864i
$512$			1.00000i			0.0441942i
$513$	16.8781	+	6.25544i	0.745185	+	0.276184i
$514$	1.62772	+	0.939764i	0.0717956	+	0.0414512i
$515$		0			0
$516$	−1.37228	+	1.28962i	−0.0604113	+	0.0567724i
$517$			8.00000i			0.351840i
$518$	4.10891	−	21.3505i	0.180535	−	0.938089i
$519$	−6.74456	−	28.7075i	−0.296053	−	1.26012i
$520$		0			0
$521$	7.37228	−	12.7692i	0.322986	−	0.559427i	−0.658117	−	0.752916i	$-0.728647\pi$
$521$	7.37228	−	12.7692i	0.322986	−	0.559427i	0.981103	+	0.193488i	$0.0619802\pi$
$522$	0.617359	−	9.93070i	0.0270211	−	0.434655i
$523$	8.86263	−	5.11684i	0.387536	−	0.223744i	−0.293556	−	0.955942i	$-0.594839\pi$
$523$	8.86263	−	5.11684i	0.387536	−	0.223744i	0.681092	+	0.732198i	$0.261505\pi$
$524$	−10.3723			−0.453115
$525$		0			0
$526$	7.37228			0.321447
$527$	43.5036	−	25.1168i	1.89505	−	1.09411i
$528$	−0.469882	+	1.55842i	−0.0204490	+	0.0678216i
$529$	−10.5584	+	18.2877i	−0.459062	+	0.795118i
$530$		0			0
$531$	−35.2337	+	17.5229i	−1.52901	+	0.760429i
$532$	−8.66025	+	3.00000i	−0.375470	+	0.130066i
$533$		−	14.7446i		−	0.638658i
$534$	−1.62772	−	1.73205i	−0.0704383	−	0.0749532i
$535$		0			0
$536$	−2.05842	−	1.18843i	−0.0889103	−	0.0513324i
$537$	28.0627	+	29.8614i	1.21099	+	1.28861i
$538$			25.9783i			1.12000i
$539$	6.51087	−	0.939764i	0.280443	−	0.0404785i
$540$		0			0
$541$	−19.1753	−	33.2125i	−0.824409	−	1.42792i	−0.902370	−	0.430962i	$-0.858174\pi$
$541$	−19.1753	−	33.2125i	−0.824409	−	1.42792i	0.0779610	−	0.996956i	$-0.475159\pi$
$542$	4.43132	−	7.67527i	0.190341	−	0.329681i
$543$	4.00772	−	13.2921i	0.171988	−	0.570419i
$544$	−5.74456	+	3.31662i	−0.246296	+	0.142199i
$545$		0			0
$546$	7.74456	−	4.90120i	0.331437	−	0.209752i
$547$	−9.30506			−0.397856			−0.198928	−	0.980014i	$-0.563746\pi$
$547$	−9.30506			−0.397856			−0.198928	+	0.980014i	$0.563746\pi$
$548$	7.57301	−	4.37228i	0.323503	−	0.186775i
$549$	−38.2337	−	2.37686i	−1.63177	−	0.101442i
$550$		0			0
$551$	−5.74456	−	9.94987i	−0.244727	−	0.423879i
$552$	−0.543620	−	2.31386i	−0.0231380	−	0.0984844i
$553$	15.7908	−	18.2337i	0.671495	−	0.775375i
$554$		−	9.10268i		−	0.386736i
$555$		0			0
$556$	7.11684	+	4.10891i	0.301821	+	0.174257i
$557$	−24.1287	−	13.9307i	−1.02237	−	0.590263i	−0.107577	−	0.994197i	$-0.534309\pi$
$557$	−24.1287	−	13.9307i	−1.02237	−	0.590263i	−0.914788	+	0.403934i	$0.867643\pi$
$558$	18.9325	+	12.5584i	0.801478	+	0.531640i
$559$		−	2.17448i		−	0.0919708i
$560$		0			0
$561$	−10.5109	+	2.46943i	−0.443769	+	0.104260i
$562$	−5.69349	−	9.86141i	−0.240165	−	0.415978i
$563$	−0.718549	+	1.24456i	−0.0302832	+	0.0524521i	−0.880770	−	0.473545i	$-0.842974\pi$
$563$	−0.718549	+	1.24456i	−0.0302832	+	0.0524521i	0.850487	+	0.525997i	$0.176308\pi$
$564$	−14.1168	−	4.25639i	−0.594426	−	0.179226i
$565$		0			0
$566$	16.0000			0.672530
$567$	17.6978	−	15.9307i	0.743238	−	0.669027i
$568$	8.51278			0.357188
$569$	9.86141	−	5.69349i	0.413412	−	0.238683i	−0.278843	−	0.960337i	$-0.589951\pi$
$569$	9.86141	−	5.69349i	0.413412	−	0.238683i	0.692255	+	0.721653i	$0.256618\pi$
$570$		0			0
$571$	0.116844	−	0.202380i	0.00488977	−	0.00846933i	−0.863570	−	0.504229i	$-0.831777\pi$
$571$	0.116844	−	0.202380i	0.00488977	−	0.00846933i	0.868460	+	0.495759i	$0.165110\pi$
$572$	−0.939764	−	1.62772i	−0.0392935	−	0.0680583i
$573$	−28.7075	+	6.74456i	−1.19927	+	0.281758i
$574$	14.7446	+	12.7692i	0.615426	+	0.532975i
$575$		0			0
$576$	−2.50000	−	1.65831i	−0.104167	−	0.0690963i
$577$	−30.4121	−	17.5584i	−1.26607	−	0.730967i	−0.291829	−	0.956470i	$-0.594264\pi$
$577$	−30.4121	−	17.5584i	−1.26607	−	0.730967i	−0.974242	+	0.225504i	$0.927597\pi$
$578$	−23.3827	−	13.5000i	−0.972592	−	0.561526i
$579$	22.6753	−	21.3094i	0.942352	−	0.885588i
$580$		0			0
$581$	−10.2446	−	29.5735i	−0.425016	−	1.22692i
$582$	−5.98844	−	25.4891i	−0.248229	−	1.05656i
$583$	2.05446	+	3.55842i	0.0850869	+	0.147375i
$584$	−1.00000	+	1.73205i	−0.0413803	+	0.0716728i
$585$		0			0
$586$	−18.8139	+	10.8622i	−0.777193	+	0.448713i
$587$	0.0549029			0.00226608			0.00113304	−	0.999999i	$-0.499639\pi$
$587$	0.0549029			0.00226608			0.00113304	+	0.999999i	$0.499639\pi$
$588$	−1.80579	+	11.9891i	−0.0744695	+	0.494423i
$589$	26.2337			1.08094
$590$		0			0
$591$	−7.11684	+	23.6039i	−0.292748	+	0.970935i
$592$	4.10891	−	7.11684i	0.168875	−	0.292500i
$593$	−13.7089	−	23.7446i	−0.562958	−	0.975072i	−0.997236	−	0.0742935i	$-0.976330\pi$
$593$	−13.7089	−	23.7446i	−0.562958	−	0.975072i	0.434278	−	0.900779i	$-0.357003\pi$
$594$	−3.11684	−	3.75906i	−0.127886	−	0.154236i
$595$		0			0
$596$		−	9.01011i		−	0.369069i
$597$	−1.52967	−	1.62772i	−0.0626053	−	0.0666181i
$598$	2.37686	+	1.37228i	0.0971971	+	0.0561168i
$599$	−1.62772	−	0.939764i	−0.0665068	−	0.0383977i	0.466378	−	0.884586i	$-0.345559\pi$
$599$	−1.62772	−	0.939764i	−0.0665068	−	0.0383977i	−0.532885	+	0.846188i	$0.678892\pi$
$600$		0			0
$601$		−	19.2549i		−	0.785425i	−0.919661	−	0.392713i	$-0.871537\pi$
$601$		−	19.2549i		−	0.785425i	0.919661	−	0.392713i	$-0.128463\pi$
$602$	2.17448	+	1.88316i	0.0886252	+	0.0767517i
$603$	6.38458	−	3.17527i	0.260000	−	0.129307i
$604$	4.55842	+	7.89542i	0.185480	+	0.321260i
$605$		0			0
$606$	−5.31386	+	17.6241i	−0.215861	+	0.715929i
$607$	35.9118	−	20.7337i	1.45762	−	0.841554i	0.458721	−	0.888580i	$-0.348308\pi$
$607$	35.9118	−	20.7337i	1.45762	−	0.841554i	0.998894	+	0.0470257i	$0.0149743\pi$
$608$	−3.46410			−0.140488
$609$	−15.1861	+	0.617359i	−0.615373	+	0.0250166i
$610$		0			0
$611$	14.7446	−	8.51278i	0.596501	−	0.344390i
$612$	1.23472	−	19.8614i	0.0499105	−	0.802850i
$613$	−13.4140	+	23.2337i	−0.541785	+	0.938400i	0.457016	+	0.889458i	$0.348918\pi$
$613$	−13.4140	+	23.2337i	−0.541785	+	0.938400i	−0.998802	+	0.0489415i	$0.984415\pi$
$614$	−12.0584	−	20.8858i	−0.486638	−	0.842882i
$615$		0			0
$616$	2.44158	+	0.469882i	0.0983740	+	0.0189321i
$617$		−	46.9783i		−	1.89127i	−0.325225	−	0.945637i	$-0.605440\pi$
$617$		−	46.9783i		−	1.89127i	0.325225	−	0.945637i	$-0.394560\pi$
$618$	−2.67181	+	2.51087i	−0.107476	+	0.101002i
$619$	14.2337	+	8.21782i	0.572100	+	0.330302i	0.757988	−	0.652269i	$-0.226183\pi$
$619$	14.2337	+	8.21782i	0.572100	+	0.330302i	−0.185888	+	0.982571i	$0.559516\pi$
$620$		0			0
$621$	6.68614	+	2.47805i	0.268306	+	0.0994408i
$622$			20.2337i			0.811297i
$623$	−2.37686	+	2.74456i	−0.0952269	+	0.109959i
$624$	3.37228	−	0.792287i	0.134999	−	0.0317169i
$625$		0			0
$626$	1.55842	−	2.69927i	0.0622871	−	0.107884i
$627$	−5.39853	−	1.62772i	−0.215597	−	0.0650048i
$628$	6.92820	−	4.00000i	0.276465	−	0.159617i
$629$	54.5109			2.17349
$630$		0			0
$631$	12.8832			0.512870			0.256435	−	0.966561i	$-0.417452\pi$
$631$	12.8832			0.512870			0.256435	+	0.966561i	$0.417452\pi$
$632$	7.89542	−	4.55842i	0.314063	−	0.181324i
$633$	26.9205	+	8.11684i	1.06999	+	0.322616i
$634$	−0.558422	+	0.967215i	−0.0221778	+	0.0384130i
$635$		0			0
$636$	−7.37228	+	1.73205i	−0.292330	+	0.0686803i
$637$	−8.66025	−	11.0000i	−0.343132	−	0.435836i
$638$			3.11684i			0.123397i
$639$	−14.1168	+	21.2819i	−0.558454	+	0.841901i
$640$		0			0
$641$	7.80298	+	4.50506i	0.308199	+	0.177939i	0.646120	−	0.763235i	$-0.276390\pi$
$641$	7.80298	+	4.50506i	0.308199	+	0.177939i	−0.337921	+	0.941174i	$0.609724\pi$
$642$	7.89542	−	7.41983i	0.311607	−	0.292837i
$643$		−	18.2337i		−	0.719066i	−0.933132	−	0.359533i	$-0.882936\pi$
$643$		−	18.2337i		−	0.719066i	0.933132	−	0.359533i	$-0.117064\pi$
$644$	−3.43070	+	1.18843i	−0.135189	+	0.0468307i
$645$		0			0
$646$	−11.4891	−	19.8997i	−0.452034	−	0.782945i
$647$	−21.0333	+	36.4307i	−0.826903	+	1.43224i	0.0735524	+	0.997291i	$0.476566\pi$
$647$	−21.0333	+	36.4307i	−0.826903	+	1.43224i	−0.900456	+	0.434947i	$0.856767\pi$
$648$	8.29156	−	3.50000i	0.325723	−	0.137493i
$649$	10.6753	−	6.16337i	0.419041	−	0.241933i
$650$		0			0
$651$	16.1168	−	30.7345i	0.631669	−	1.20458i
$652$	−3.46410			−0.135665
$653$	14.1788	−	8.18614i	0.554860	−	0.320348i	−0.196220	−	0.980560i	$-0.562867\pi$
$653$	14.1788	−	8.18614i	0.554860	−	0.320348i	0.751080	+	0.660211i	$0.229533\pi$
$654$	−4.05842	+	13.4603i	−0.158697	+	0.526338i
$655$		0			0
$656$	3.68614	+	6.38458i	0.143920	+	0.249276i
$657$	−2.67181	−	5.37228i	−0.104237	−	0.209593i
$658$	−4.25639	+	22.1168i	−0.165931	+	0.862204i
$659$			16.1407i			0.628752i	0.949299	+	0.314376i	$0.101795\pi$
$659$			16.1407i			0.628752i	−0.949299	+	0.314376i	$0.898205\pi$
$660$		0			0
$661$	11.0584	+	6.38458i	0.430123	+	0.248331i	0.699399	−	0.714732i	$-0.253451\pi$
$661$	11.0584	+	6.38458i	0.430123	+	0.248331i	−0.269276	+	0.963063i	$0.586784\pi$
$662$	20.9870	+	12.1168i	0.815683	+	0.470935i
$663$	15.7359	+	16.7446i	0.611133	+	0.650305i
$664$		−	11.8294i		−	0.459070i
$665$		0			0
$666$	10.9783	+	22.0742i	0.425399	+	0.855359i
$667$	−2.27567	−	3.94158i	−0.0881143	−	0.152619i
$668$	−7.32435	+	12.6861i	−0.283387	+	0.490842i
$669$	−0.441578	+	1.46455i	−0.0170724	+	0.0566227i
$670$		0			0
$671$	12.0000			0.463255
$672$	−2.12819	+	4.05842i	−0.0820969	+	0.156557i
$673$	−46.9678			−1.81047			−0.905237	−	0.424907i	$-0.860307\pi$
$673$	−46.9678			−1.81047			−0.905237	+	0.424907i	$0.860307\pi$
$674$	−0.558422	+	0.322405i	−0.0215096	+	0.0124186i
$675$		0			0
$676$	4.50000	−	7.79423i	0.173077	−	0.299778i
$677$	−0.912312	−	1.58017i	−0.0350630	−	0.0607309i	0.847961	−	0.530058i	$-0.177830\pi$
$677$	−0.912312	−	1.58017i	−0.0350630	−	0.0607309i	−0.883024	+	0.469327i	$0.844497\pi$
$678$	5.84096	+	24.8614i	0.224321	+	0.954797i
$679$	−37.7921	+	13.0916i	−1.45033	+	0.502408i
$680$		0			0
$681$	−26.3030	+	24.7186i	−1.00793	+	0.947219i
$682$	−6.16337	−	3.55842i	−0.236008	−	0.136259i
$683$	27.6940	+	15.9891i	1.05968	+	0.611807i	0.925344	−	0.379129i	$-0.123776\pi$
$683$	27.6940	+	15.9891i	1.05968	+	0.611807i	0.134337	+	0.990936i	$0.457110\pi$
$684$	5.74456	−	8.66025i	0.219649	−	0.331133i
$685$		0			0
$686$	18.5000	+	0.866025i	0.706333	+	0.0330650i
$687$	−23.3639	+	5.48913i	−0.891386	+	0.209423i
$688$	0.543620	+	0.941578i	0.0207253	+	0.0358973i
$689$	4.37228	−	7.57301i	0.166571	−	0.288509i
$690$		0			0
$691$	8.23369	−	4.75372i	0.313224	−	0.180840i	−0.335144	−	0.942167i	$-0.608785\pi$
$691$	8.23369	−	4.75372i	0.313224	−	0.180840i	0.648368	+	0.761327i	$0.275452\pi$
$692$	−17.0256			−0.647214
$693$	−5.22360	+	5.32473i	−0.198428	+	0.202270i
$694$	−1.88316			−0.0714836
$695$		0			0
$696$	−5.50000	−	1.65831i	−0.208477	−	0.0628582i
$697$	−24.4511	+	42.3505i	−0.926151	+	1.60414i
$698$	−12.8704	−	22.2921i	−0.487150	−	0.843769i
$699$	0.861407	−	0.202380i	0.0325814	−	0.00765470i
$700$		0			0
$701$			39.2473i			1.48235i	0.671313	+	0.741174i	$0.265731\pi$
$701$			39.2473i			1.48235i	−0.671313	+	0.741174i	$0.734269\pi$
$702$	−3.61158	+	9.74456i	−0.136310	+	0.367785i
$703$	24.6535	+	14.2337i	0.929823	+	0.536834i
$704$	0.813859	+	0.469882i	0.0306735	+	0.0177093i
$705$		0			0
$706$			12.2718i			0.461857i
$707$	27.6116	+	5.31386i	1.03844	+	0.199848i
$708$	5.19615	+	22.1168i	0.195283	+	0.831202i
$709$	6.05842	+	10.4935i	0.227529	+	0.394091i	0.957075	−	0.289840i	$-0.0936021\pi$
$709$	6.05842	+	10.4935i	0.227529	+	0.394091i	−0.729546	+	0.683931i	$0.760269\pi$
$710$		0			0
$711$	−1.69702	+	27.2978i	−0.0636430	+	1.02375i
$712$	−1.18843	+	0.686141i	−0.0445383	+	0.0257142i
$713$	10.3923			0.389195
$714$	−30.3723	+	1.23472i	−1.13665	+	0.0462081i
$715$		0			0
$716$	20.4891	−	11.8294i	0.765715	−	0.442086i
$717$	11.8294	−	39.2337i	0.441777	−	1.46521i
$718$	13.7089	−	23.7446i	0.511613	−	0.886139i
$719$	22.3723	+	38.7499i	0.834345	+	1.44513i	0.894562	+	0.446943i	$0.147487\pi$
$719$	22.3723	+	38.7499i	0.834345	+	1.44513i	−0.0602171	+	0.998185i	$0.519179\pi$
$720$		0			0
$721$	4.23369	+	3.66648i	0.157671	+	0.136547i
$722$			7.00000i			0.260513i
$723$	−22.8391	−	24.3030i	−0.849394	−	0.903838i
$724$	−6.94158	−	4.00772i	−0.257982	−	0.148946i
$725$		0			0
$726$	−12.0000	−	12.7692i	−0.445362	−	0.473908i
$727$			19.0000i			0.704671i	0.935874	+	0.352335i	$0.114612\pi$
$727$			19.0000i			0.704671i	−0.935874	+	0.352335i	$0.885388\pi$
$728$	−1.73205	−	5.00000i	−0.0641941	−	0.185312i
$729$	−5.00000	+	26.5330i	−0.185185	+	0.982704i
$730$		0			0
$731$	−3.60597	+	6.24572i	−0.133372	+	0.231006i
$732$	−6.38458	+	21.1753i	−0.235981	+	0.782660i
$733$	−28.1176	+	16.2337i	−1.03855	+	0.599605i	−0.919421	−	0.393274i	$-0.871342\pi$
$733$	−28.1176	+	16.2337i	−1.03855	+	0.599605i	−0.119125	+	0.992879i	$0.538009\pi$
$734$	13.2337			0.488464
$735$		0			0
$736$	−1.37228			−0.0505830
$737$	−1.93443	+	1.11684i	−0.0712557	+	0.0411395i
$738$	−22.0742	−	1.37228i	−0.812564	−	0.0505144i
$739$	−0.883156	+	1.52967i	−0.0324874	+	0.0562699i	−0.881812	−	0.471601i	$-0.843676\pi$
$739$	−0.883156	+	1.52967i	−0.0324874	+	0.0562699i	0.849325	+	0.527871i	$0.177010\pi$
$740$		0			0
$741$	2.74456	+	11.6819i	0.100824	+	0.429146i
$742$	3.78651	+	10.9307i	0.139007	+	0.401279i
$743$		−	21.6060i		−	0.792646i	−0.918111	−	0.396323i	$-0.870286\pi$
$743$		−	21.6060i		−	0.792646i	0.918111	−	0.396323i	$-0.129714\pi$
$744$	9.55842	−	8.98266i	0.350429	−	0.329320i
$745$		0			0
$746$	20.2337	+	11.6819i	0.740808	+	0.427706i
$747$	29.5735	+	19.6168i	1.08204	+	0.717743i
$748$			6.23369i			0.227926i
$749$	−12.5109	−	10.8347i	−0.457137	−	0.395893i
$750$		0			0
$751$	−12.4416	−	21.5494i	−0.454000	−	0.786350i	0.544630	−	0.838676i	$-0.316670\pi$
$751$	−12.4416	−	21.5494i	−0.454000	−	0.786350i	−0.998630	+	0.0523257i	$0.983337\pi$
$752$	−4.25639	+	7.37228i	−0.155215	+	0.268839i
$753$	1.85208	+	0.558422i	0.0674934	+	0.0203500i
$754$	5.74456	−	3.31662i	0.209205	−	0.120784i
$755$		0			0
$756$	−6.61684	−	12.0506i	−0.240652	−	0.438277i
$757$	25.5383			0.928206			0.464103	−	0.885781i	$-0.346377\pi$
$757$	25.5383			0.928206			0.464103	+	0.885781i	$0.346377\pi$
$758$	10.5947	−	6.11684i	0.384816	−	0.222174i
$759$	−2.13859	−	0.644810i	−0.0776260	−	0.0234051i
$760$		0			0
$761$	−3.51087	−	6.08101i	−0.127269	−	0.220437i	0.795349	−	0.606152i	$-0.207288\pi$
$761$	−3.51087	−	6.08101i	−0.127269	−	0.220437i	−0.922618	+	0.385716i	$0.873955\pi$
$762$	−12.7692	+	3.00000i	−0.462578	+	0.108679i
$763$	21.0882	+	4.05842i	0.763443	+	0.146925i
$764$			17.0256i			0.615963i
$765$		0			0
$766$	13.5475	+	7.82168i	0.489493	+	0.282609i
$767$	−22.7190	−	13.1168i	−0.820337	−	0.473622i
$768$	−1.26217	+	1.18614i	−0.0455446	+	0.0428012i
$769$		−	30.5321i		−	1.10102i	−0.834830	−	0.550508i	$-0.814434\pi$
$769$		−	30.5321i		−	1.10102i	0.834830	−	0.550508i	$-0.185566\pi$
$770$		0			0
$771$	0.744563	+	3.16915i	0.0268148	+	0.114134i
$772$	−8.98266	−	15.5584i	−0.323293	−	0.559960i
$773$	4.25639	−	7.37228i	0.153092	−	0.265163i	−0.779271	−	0.626687i	$-0.784410\pi$
$773$	4.25639	−	7.37228i	0.153092	−	0.265163i	0.932363	+	0.361525i	$0.117744\pi$
$774$	−3.25544	−	0.202380i	−0.117014	−	0.00727439i
$775$		0			0
$776$	−15.1168			−0.542663
$777$	31.8217	−	20.1386i	1.14160	−	0.722468i
$778$	−7.51811			−0.269537
$779$	−22.1168	+	12.7692i	−0.792418	+	0.457503i
$780$		0			0
$781$	4.00000	−	6.92820i	0.143131	−	0.247911i
$782$	−4.55134	−	7.88316i	−0.162756	−	0.281901i
$783$	13.2665	−	11.0000i	0.474106	−	0.393108i
$784$	6.50000	+	2.59808i	0.232143	+	0.0927884i
$785$		0			0
$786$	−12.3030	−	13.0916i	−0.438833	−	0.466961i
$787$	8.55906	+	4.94158i	0.305098	+	0.176148i	0.644731	−	0.764410i	$-0.276970\pi$
$787$	8.55906	+	4.94158i	0.305098	+	0.176148i	−0.339633	+	0.940558i	$0.610303\pi$
$788$	12.3267	+	7.11684i	0.439122	+	0.253527i
$789$	8.74456	+	9.30506i	0.311315	+	0.331269i
$790$		0			0
$791$	36.8614	−	12.7692i	1.31064	−	0.454019i
$792$	−2.52434	+	1.25544i	−0.0896984	+	0.0446100i
$793$	−12.7692	−	22.1168i	−0.453446	−	0.785392i
$794$	−4.00000	+	6.92820i	−0.141955	+	0.245873i
$795$		0			0
$796$	−1.11684	+	0.644810i	−0.0395855	+	0.0228547i
$797$	0.939764			0.0332881			0.0166441	−	0.999861i	$-0.494702\pi$
$797$	0.939764			0.0332881			0.0166441	+	0.999861i	$0.494702\pi$
$798$	−14.0588	−	7.37228i	−0.497676	−	0.260976i
$799$	−56.4674			−1.99767
$800$		0			0
$801$	0.255437	−	4.10891i	0.00902544	−	0.145181i
$802$	8.26411	−	14.3139i	0.291816	−	0.505440i
$803$	0.939764	+	1.62772i	0.0331635	+	0.0574409i
$804$	−0.941578	−	4.00772i	−0.0332069	−	0.141341i
$805$		0			0
$806$			15.1460i			0.533496i
$807$	−32.7889	+	30.8139i	−1.15423	+	1.08470i
$808$	9.20387	+	5.31386i	0.323791	+	0.186941i
$809$	36.4307	+	21.0333i	1.28084	+	0.739491i	0.977001	−	0.213234i	$-0.0683998\pi$
$809$	36.4307	+	21.0333i	1.28084	+	0.739491i	0.303834	+	0.952725i	$0.401733\pi$
$810$		0			0
$811$			10.3923i			0.364923i	0.983213	+	0.182462i	$0.0584065\pi$
$811$			10.3923i			0.364923i	−0.983213	+	0.182462i	$0.941593\pi$
$812$	−1.65831	+	8.61684i	−0.0581954	+	0.302392i
$813$	14.9436	−	3.51087i	0.524097	−	0.123132i
$814$	−3.86141	−	6.68815i	−0.135342	−	0.234420i
$815$		0			0
$816$	−11.0000	−	3.31662i	−0.385077	−	0.116105i
$817$	−3.26172	+	1.88316i	−0.114113	+	0.0658833i
$818$	−4.31129			−0.150741
$819$	15.3723	+	3.96143i	0.537151	+	0.138424i
$820$		0			0
$821$	−4.06930	+	2.34941i	−0.142019	+	0.0819950i	−0.569326	−	0.822112i	$-0.692796\pi$
$821$	−4.06930	+	2.34941i	−0.142019	+	0.0819950i	0.427307	+	0.904107i	$0.359462\pi$
$822$	14.5012	+	4.37228i	0.505788	+	0.152501i
$823$	−6.82701	+	11.8247i	−0.237975	+	0.412184i	−0.960133	−	0.279544i	$-0.909817\pi$
$823$	−6.82701	+	11.8247i	−0.237975	+	0.412184i	0.722158	+	0.691728i	$0.243150\pi$
$824$	1.05842	+	1.83324i	0.0368719	+	0.0638640i
$825$		0			0
$826$	32.7921	−	11.3595i	1.14098	−	0.395248i
$827$			33.0000i			1.14752i	0.819023	+	0.573761i	$0.194516\pi$
$827$			33.0000i			1.14752i	−0.819023	+	0.573761i	$0.805484\pi$
$828$	2.27567	−	3.43070i	0.0790850	−	0.119225i
$829$	−1.11684	−	0.644810i	−0.0387896	−	0.0223952i	0.480480	−	0.877006i	$-0.340463\pi$
$829$	−1.11684	−	0.644810i	−0.0387896	−	0.0223952i	−0.519269	+	0.854611i	$0.673796\pi$
$830$		0			0
$831$	11.4891	−	10.7971i	0.398553	−	0.374546i
$832$		−	2.00000i		−	0.0693375i
$833$	6.63325	+	45.9565i	0.229828	+	1.59230i
$834$	3.25544	+	13.8564i	0.112727	+	0.479808i
$835$		0			0
$836$	−1.62772	+	2.81929i	−0.0562958	+	0.0975072i
$837$	6.60580	+	38.7921i	0.228330	+	1.34085i
$838$	−5.63858	+	3.25544i	−0.194782	+	0.112457i
$839$	−55.7228			−1.92377			−0.961883	−	0.273463i	$-0.911831\pi$
$839$	−55.7228			−1.92377			−0.961883	+	0.273463i	$0.911831\pi$
$840$		0			0
$841$	18.0000			0.620690
$842$	−1.83324	+	1.05842i	−0.0631776	+	0.0364756i
$843$	5.69349	−	18.8832i	0.196094	−	0.650370i
$844$	8.11684	−	14.0588i	0.279393	−	0.483923i
$845$		0			0
$846$	−11.3723	−	22.8665i	−0.390987	−	0.786167i
$847$	−17.5229	+	20.2337i	−0.602094	+	0.695238i
$848$			4.37228i			0.150145i
$849$	18.9783	+	20.1947i	0.651332	+	0.693080i
$850$		0			0
$851$	9.76631	+	5.63858i	0.334785	+	0.193288i
$852$	10.0974	+	10.7446i	0.345930	+	0.368103i
$853$		−	38.4674i		−	1.31710i	−0.752538	−	0.658549i	$-0.771171\pi$
$853$		−	38.4674i		−	1.31710i	0.752538	−	0.658549i	$-0.228829\pi$
$854$	33.1753	+	6.38458i	1.13523	+	0.218476i
$855$		0			0
$856$	−3.12772	−	5.41737i	−0.106903	−	0.185162i
$857$	−12.2718	+	21.2554i	−0.419198	+	0.726072i	−0.995859	−	0.0909115i	$-0.971022\pi$
$857$	−12.2718	+	21.2554i	−0.419198	+	0.726072i	0.576661	+	0.816983i	$0.304355\pi$
$858$	0.939764	−	3.11684i	0.0320830	−	0.106407i
$859$	40.4674	−	23.3639i	1.38073	−	0.797164i	0.388483	−	0.921456i	$-0.372999\pi$
$859$	40.4674	−	23.3639i	1.38073	−	0.797164i	0.992246	+	0.124291i	$0.0396658\pi$
$860$		0			0
$861$	1.37228	+	33.7562i	0.0467672	+	1.15041i
$862$	17.0256			0.579893
$863$	−11.5807	+	6.68614i	−0.394213	+	0.227599i	−0.683984	−	0.729497i	$-0.739754\pi$
$863$	−11.5807	+	6.68614i	−0.394213	+	0.227599i	0.289771	+	0.957096i	$0.406421\pi$
$864$	−0.872281	−	5.12241i	−0.0296756	−	0.174268i
$865$		0			0
$866$	−17.0000	−	29.4449i	−0.577684	−	1.00058i
$867$	−10.6959	−	45.5258i	−0.363251	−	1.54614i
$868$	−15.1460	−	13.1168i	−0.514090	−	0.445215i
$869$		−	8.56768i		−	0.290639i
$870$		0			0
$871$	4.11684	+	2.37686i	0.139494	+	0.0805369i
$872$	7.02939	+	4.05842i	0.238045	+	0.137436i
$873$	25.0684	−	37.7921i	0.848438	−	1.27907i
$874$		−	4.75372i		−	0.160797i
$875$		0			0
$876$	−3.37228	+	0.792287i	−0.113939	+	0.0267689i
$877$	−14.0588	−	24.3505i	−0.474731	−	0.822259i	0.524850	−	0.851195i	$-0.324121\pi$
$877$	−14.0588	−	24.3505i	−0.474731	−	0.822259i	−0.999581	+	0.0289358i	$0.990788\pi$
$878$	1.40965	−	2.44158i	0.0475732	−	0.0823993i
$879$	−36.0258	−	10.8622i	−1.21512	−	0.366372i
$880$		0			0
$881$	−0.350532			−0.0118097			−0.00590486	−	0.999983i	$-0.501880\pi$
$881$	−0.350532			−0.0118097			−0.00590486	+	0.999983i	$0.501880\pi$
$882$	−17.2742	+	11.9416i	−0.581653	+	0.402094i
$883$	−44.5532			−1.49934			−0.749668	−	0.661815i	$-0.769787\pi$
$883$	−44.5532			−1.49934			−0.749668	+	0.661815i	$0.769787\pi$
$884$	11.4891	−	6.63325i	0.386421	−	0.223100i
$885$		0			0
$886$	−4.50000	+	7.79423i	−0.151180	+	0.261852i
$887$	4.06262	+	7.03667i	0.136410	+	0.236268i	0.926135	−	0.377192i	$-0.123110\pi$
$887$	4.06262	+	7.03667i	0.136410	+	0.236268i	−0.789725	+	0.613460i	$0.789777\pi$
$888$	13.8564	−	3.25544i	0.464991	−	0.109245i
$889$	6.55842	+	18.9325i	0.219962	+	0.634977i
$890$		0			0
$891$	1.04755	−	8.39275i	0.0350942	−	0.281168i
$892$	0.764836	+	0.441578i	0.0256086	+	0.0147851i
$893$	−25.5383	−	14.7446i	−0.854608	−	0.493408i
$894$	11.3723	−	10.6873i	0.380346	−	0.357435i
$895$		0			0
$896$	2.00000	+	1.73205i	0.0668153	+	0.0578638i
$897$	1.08724	+	4.62772i	0.0363019	+	0.154515i
$898$	−10.1985	−	17.6644i	−0.340330	−	0.589468i
$899$	12.5584	−	21.7518i	0.418847	−	0.725464i
$900$		0			0
$901$	−25.1168	+	14.5012i	−0.836763	+	0.483106i
$902$	6.92820			0.230684
$903$	0.202380	+	4.97825i	0.00673477	+	0.165666i
$904$	14.7446			0.490397
$905$		0			0
$906$	−4.55842	+	15.1186i	−0.151443	+	0.502281i
$907$	2.47805	−	4.29211i	0.0822823	−	0.142517i	−0.821948	−	0.569563i	$-0.807112\pi$
$907$	2.47805	−	4.29211i	0.0822823	−	0.142517i	0.904230	+	0.427046i	$0.140446\pi$
$908$	10.4198	+	18.0475i	0.345792	+	0.598929i
$909$	−28.5475	+	14.1976i	−0.946862	+	0.470906i
$910$		0			0
$911$		−	37.8102i		−	1.25271i	−0.779539	−	0.626353i	$-0.784547\pi$
$911$		−	37.8102i		−	1.25271i	0.779539	−	0.626353i	$-0.215453\pi$
$912$	−4.10891	−	4.37228i	−0.136060	−	0.144781i
$913$	−9.62747	−	5.55842i	−0.318623	−	0.183957i
$914$	−2.44158	−	1.40965i	−0.0807602	−	0.0466269i
$915$		0			0
$916$			13.8564i			0.457829i
$917$	−17.9653	+	20.7446i	−0.593267	+	0.685046i
$918$	26.5330	−	22.0000i	0.875719	−	0.726108i
$919$	8.11684	+	14.0588i	0.267750	+	0.463757i	0.968280	−	0.249866i	$-0.0803865\pi$
$919$	8.11684	+	14.0588i	0.267750	+	0.463757i	−0.700530	+	0.713622i	$0.747053\pi$
$920$		0			0
$921$	12.0584	−	39.9933i	0.397339	−	1.31782i
$922$	20.3422	−	11.7446i	0.669934	−	0.386787i
$923$	−17.0256			−0.560403
$924$	2.30298	+	3.63903i	0.0757626	+	0.119715i
$925$		0			0
$926$	5.82473	−	3.36291i	0.191413	−	0.110512i
$927$	−6.33830	−	0.394031i	−0.208177	−	0.0129417i
$928$	−1.65831	+	2.87228i	−0.0544368	+	0.0942873i
$929$	−17.0584	−	29.5461i	−0.559669	−	0.969375i	−0.997524	−	0.0703291i	$-0.977595\pi$
$929$	−17.0584	−	29.5461i	−0.559669	−	0.969375i	0.437855	−	0.899046i	$-0.355738\pi$
$930$		0			0
$931$	−9.00000	+	22.5167i	−0.294963	+	0.737954i
$932$		−	0.510875i		−	0.0167343i
$933$	−25.5383	+	24.0000i	−0.836087	+	0.785725i
$934$	−31.5475	−	18.2140i	−1.03227	−	0.595980i
$935$		0			0
$936$	5.00000	+	3.31662i	0.163430	+	0.108407i
$937$			1.35053i			0.0441200i	0.999757	+	0.0220600i	$0.00702248\pi$
$937$			1.35053i			0.0441200i	−0.999757	+	0.0220600i	$0.992978\pi$
$938$	−5.94215	+	2.05842i	−0.194018	+	0.0672099i
$939$	5.25544	−	1.23472i	0.171505	−	0.0402935i
$940$		0			0
$941$	13.6753	−	23.6863i	0.445801	−	0.772150i	−0.552307	−	0.833641i	$-0.686252\pi$
$941$	13.6753	−	23.6863i	0.445801	−	0.772150i	0.998108	+	0.0614911i	$0.0195856\pi$
$942$	13.2665	+	4.00000i	0.432246	+	0.130327i
$943$	−8.76144	+	5.05842i	−0.285312	+	0.164725i
$944$	13.1168			0.426917
$945$		0			0
$946$	1.02175			0.0332199
$947$	22.4155	−	12.9416i	0.728405	−	0.420545i	−0.0894334	−	0.995993i	$-0.528506\pi$
$947$	22.4155	−	12.9416i	0.728405	−	0.420545i	0.817838	+	0.575448i	$0.195172\pi$
$948$	15.1186	+	4.55842i	0.491029	+	0.148051i
$949$	2.00000	−	3.46410i	0.0649227	−	0.112449i
$950$		0			0
$951$	−1.88316	+	0.442430i	−0.0610655	+	0.0143468i
$952$	−3.31662	+	17.2337i	−0.107492	+	0.558547i
$953$			48.0000i			1.55487i	0.628962	+	0.777436i	$0.283480\pi$
$953$			48.0000i			1.55487i	−0.628962	+	0.777436i	$0.716520\pi$
$954$	−10.9307	−	7.25061i	−0.353895	−	0.234747i
$955$		0			0
$956$	−20.4891	−	11.8294i	−0.662666	−	0.382590i
$957$	−3.93398	+	3.69702i	−0.127168	+	0.119508i
$958$		−	2.74456i		−	0.0886728i
$959$	4.37228	−	22.7190i	0.141188	−	0.733636i
$960$		0			0
$961$	13.1753	+	22.8202i	0.425009	+	0.736136i
$962$	−8.21782	+	14.2337i	−0.264953	+	0.458913i
$963$	18.7302	+	1.16439i	0.603571	+	0.0375220i
$964$	−16.6753	+	9.62747i	−0.537074	+	0.310080i
$965$		0			0
$966$	−5.56930	−	2.92048i	−0.179189	−	0.0939649i
$967$	−27.6751			−0.889973			−0.444986	−	0.895537i	$-0.646791\pi$
$967$	−27.6751			−0.889973			−0.444986	+	0.895537i	$0.646791\pi$
$968$	−8.76144	+	5.05842i	−0.281603	+	0.162584i
$969$	11.4891	−	38.1051i	0.369084	−	1.22411i
$970$		0			0
$971$	17.1861	+	29.7673i	0.551530	+	0.955277i	0.998165	+	0.0605609i	$0.0192889\pi$
$971$	17.1861	+	29.7673i	0.551530	+	0.955277i	−0.446635	+	0.894716i	$0.647378\pi$
$972$	14.2525	+	6.31386i	0.457151	+	0.202517i
$973$	20.5446	−	7.11684i	0.658628	−	0.228156i
$974$		−	14.5012i		−	0.464649i
$975$		0			0
$976$	11.0584	+	6.38458i	0.353971	+	0.204366i
$977$	−24.6535	−	14.2337i	−0.788734	−	0.455376i	0.0507824	−	0.998710i	$-0.483829\pi$
$977$	−24.6535	−	14.2337i	−0.788734	−	0.455376i	−0.839517	+	0.543334i	$0.817162\pi$
$978$	−4.10891	−	4.37228i	−0.131389	−	0.139810i
$979$			1.28962i			0.0412164i
$980$		0			0
$981$	−21.8030	+	10.8434i	−0.696116	+	0.346202i
$982$	−15.1186	−	26.1861i	−0.482453	−	0.835633i
$983$	−12.5205	+	21.6861i	−0.399342	+	0.691680i	−0.993645	−	0.112561i	$-0.964095\pi$
$983$	−12.5205	+	21.6861i	−0.399342	+	0.691680i	0.594303	+	0.804241i	$0.297428\pi$
$984$	−3.68614	+	12.2255i	−0.117510	+	0.389736i
$985$		0			0
$986$	−22.0000			−0.700623
$987$	−32.9639	+	20.8614i	−1.04925	+	0.664026i
$988$	6.92820			0.220416
$989$	−1.29211	+	0.746000i	−0.0410867	+	0.0237214i
$990$		0			0
$991$	−11.6753	+	20.2222i	−0.370877	+	0.642378i	−0.989701	−	0.143152i	$-0.954276\pi$
$991$	−11.6753	+	20.2222i	−0.370877	+	0.642378i	0.618824	+	0.785530i	$0.287610\pi$
$992$	−3.78651	−	6.55842i	−0.120222	−	0.208230i
$993$	9.60002	+	40.8614i	0.304647	+	1.29670i
$994$	14.7446	−	17.0256i	0.467669	−	0.540018i
$995$		0			0
$996$	14.9307	−	14.0313i	0.473097	−	0.444600i
$997$	−33.3137	−	19.2337i	−1.05506	−	0.609137i	−0.130996	−	0.991383i	$-0.541817\pi$
$997$	−33.3137	−	19.2337i	−1.05506	−	0.609137i	−0.924061	+	0.382246i	$0.875151\pi$
$998$	−5.39853	−	3.11684i	−0.170888	−	0.0986620i
$999$	−14.8397	+	40.0395i	−0.469506	+	1.26680i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.s.e.101.4		8
3.2	odd	2		1050.2.s.d.101.2		8
5.2	odd	4		210.2.t.d.59.1	yes	4
5.3	odd	4		210.2.t.a.59.2	✓	4
5.4	even	2	inner	1050.2.s.e.101.1		8
7.5	odd	6		1050.2.s.d.551.2		8
15.2	even	4		210.2.t.b.59.2	yes	4
15.8	even	4		210.2.t.c.59.1	yes	4
15.14	odd	2		1050.2.s.d.101.3		8
21.5	even	6	inner	1050.2.s.e.551.4		8
35.3	even	12		1470.2.d.c.1469.2		4
35.12	even	12		210.2.t.c.89.1	yes	4
35.17	even	12		1470.2.d.b.1469.3		4
35.18	odd	12		1470.2.d.d.1469.3		4
35.19	odd	6		1050.2.s.d.551.3		8
35.32	odd	12		1470.2.d.a.1469.2		4
35.33	even	12		210.2.t.b.89.2	yes	4
105.17	odd	12		1470.2.d.d.1469.4		4
105.32	even	12		1470.2.d.c.1469.1		4
105.38	odd	12		1470.2.d.a.1469.1		4
105.47	odd	12		210.2.t.a.89.1	yes	4
105.53	even	12		1470.2.d.b.1469.4		4
105.68	odd	12		210.2.t.d.89.2	yes	4
105.89	even	6	inner	1050.2.s.e.551.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.t.a.59.2	✓	4	5.3	odd	4
210.2.t.a.89.1	yes	4	105.47	odd	12
210.2.t.b.59.2	yes	4	15.2	even	4
210.2.t.b.89.2	yes	4	35.33	even	12
210.2.t.c.59.1	yes	4	15.8	even	4
210.2.t.c.89.1	yes	4	35.12	even	12
210.2.t.d.59.1	yes	4	5.2	odd	4
210.2.t.d.89.2	yes	4	105.68	odd	12
1050.2.s.d.101.2		8	3.2	odd	2
1050.2.s.d.101.3		8	15.14	odd	2
1050.2.s.d.551.2		8	7.5	odd	6
1050.2.s.d.551.3		8	35.19	odd	6
1050.2.s.e.101.1		8	5.4	even	2	inner
1050.2.s.e.101.4		8	1.1	even	1	trivial
1050.2.s.e.551.1		8	105.89	even	6	inner
1050.2.s.e.551.4		8	21.5	even	6	inner
1470.2.d.a.1469.1		4	105.38	odd	12
1470.2.d.a.1469.2		4	35.32	odd	12
1470.2.d.b.1469.3		4	35.17	even	12
1470.2.d.b.1469.4		4	105.53	even	12
1470.2.d.c.1469.1		4	105.32	even	12
1470.2.d.c.1469.2		4	35.3	even	12
1470.2.d.d.1469.3		4	35.18	odd	12
1470.2.d.d.1469.4		4	105.17	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(1.65831 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.68614 - 0.396143i) q^{6} +(-0.866025 - 2.50000i) q^{7} -1.00000i q^{8} +(2.50000 + 1.65831i) q^{9} +(-0.813859 - 0.469882i) q^{11} +(1.26217 - 1.18614i) q^{12} +2.00000i q^{13} +(-2.00000 - 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(3.31662 - 5.74456i) q^{17} +(2.99422 + 0.186141i) q^{18} +(3.00000 - 1.73205i) q^{19} +(-0.186141 - 4.57879i) q^{21} -0.939764 q^{22} +(1.18843 - 0.686141i) q^{23} +(0.500000 - 1.65831i) q^{24} +(1.00000 + 1.73205i) q^{26} +(3.31662 + 4.00000i) q^{27} +(-2.59808 - 0.500000i) q^{28} -3.31662i q^{29} +(6.55842 + 3.78651i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-1.11469 - 1.18614i) q^{33} -6.63325i q^{34} +(2.68614 - 1.33591i) q^{36} +(4.10891 + 7.11684i) q^{37} +(1.73205 - 3.00000i) q^{38} +(-1.00000 + 3.31662i) q^{39} -7.37228 q^{41} +(-2.45060 - 3.87228i) q^{42} -1.08724 q^{43} +(-0.813859 + 0.469882i) q^{44} +(0.686141 - 1.18843i) q^{46} +(-4.25639 - 7.37228i) q^{47} +(-0.396143 - 1.68614i) q^{48} +(-5.50000 + 4.33013i) q^{49} +(8.37228 - 7.86797i) q^{51} +(1.73205 + 1.00000i) q^{52} +(-3.78651 - 2.18614i) q^{53} +(4.87228 + 1.80579i) q^{54} +(-2.50000 + 0.866025i) q^{56} +(5.84096 - 1.37228i) q^{57} +(-1.65831 - 2.87228i) q^{58} +(-6.55842 + 11.3595i) q^{59} +(-11.0584 + 6.38458i) q^{61} +7.57301 q^{62} +(1.98072 - 7.68614i) q^{63} -1.00000 q^{64} +(-1.55842 - 0.469882i) q^{66} +(1.18843 - 2.05842i) q^{67} +(-3.31662 - 5.74456i) q^{68} +(2.31386 - 0.543620i) q^{69} +8.51278i q^{71} +(1.65831 - 2.50000i) q^{72} +(-1.73205 - 1.00000i) q^{73} +(7.11684 + 4.10891i) q^{74} -3.46410i q^{76} +(-0.469882 + 2.44158i) q^{77} +(0.792287 + 3.37228i) q^{78} +(4.55842 + 7.89542i) q^{79} +(3.50000 + 8.29156i) q^{81} +(-6.38458 + 3.68614i) q^{82} +11.8294 q^{83} +(-4.05842 - 2.12819i) q^{84} +(-0.941578 + 0.543620i) q^{86} +(1.65831 - 5.50000i) q^{87} +(-0.469882 + 0.813859i) q^{88} +(-0.686141 - 1.18843i) q^{89} +(5.00000 - 1.73205i) q^{91} -1.37228i q^{92} +(8.98266 + 9.55842i) q^{93} +(-7.37228 - 4.25639i) q^{94} +(-1.18614 - 1.26217i) q^{96} -15.1168i q^{97} +(-2.59808 + 6.50000i) q^{98} +(-1.25544 - 2.52434i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} + 2 q^{6} + 20 q^{9} - 18 q^{11} - 16 q^{14} - 4 q^{16} + 24 q^{19} + 10 q^{21} + 4 q^{24} + 8 q^{26} + 18 q^{31} + 10 q^{36} - 8 q^{39} - 36 q^{41} - 18 q^{44} - 6 q^{46} - 44 q^{49} + 44 q^{51}+ \cdots - 56 q^{99}+O(q^{100}) \) 8 * q + 4 * q^4 + 2 * q^6 + 20 * q^9 - 18 * q^11 - 16 * q^14 - 4 * q^16 + 24 * q^19 + 10 * q^21 + 4 * q^24 + 8 * q^26 + 18 * q^31 + 10 * q^36 - 8 * q^39 - 36 * q^41 - 18 * q^44 - 6 * q^46 - 44 * q^49 + 44 * q^51 + 16 * q^54 - 20 * q^56 - 18 * q^59 - 54 * q^61 - 8 * q^64 + 22 * q^66 + 30 * q^69 - 12 * q^74 + 2 * q^79 + 28 * q^81 + 2 * q^84 - 42 * q^86 + 6 * q^89 + 40 * q^91 - 36 * q^94 + 2 * q^96 - 56 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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