LMFDB - Embedded newform 1050.2.s.e.101.3

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			101.3
Root			$1.26217 + 1.18614i$ of defining polynomial
Character	$\chi$	$=$	1050.101
Dual form			1050.2.s.e.551.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 - 0.500000i) q^{2} +(-1.65831 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.18614 + 1.26217i) q^{6} +(-0.866025 - 2.50000i) q^{7} -1.00000i q^{8} +(2.50000 - 1.65831i) q^{9} +(-3.68614 - 2.12819i) q^{11} +(-0.396143 + 1.68614i) q^{12} +2.00000i q^{13} +(-2.00000 - 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.31662 + 5.74456i) q^{17} +(1.33591 - 2.68614i) q^{18} +(3.00000 - 1.73205i) q^{19} +(2.68614 + 3.71277i) q^{21} -4.25639 q^{22} +(-3.78651 + 2.18614i) 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} +(-2.05842 - 1.18843i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(7.17687 + 1.68614i) q^{33} +6.63325i q^{34} +(-0.186141 - 2.99422i) q^{36} +(-5.84096 - 10.1168i) q^{37} +(1.73205 - 3.00000i) q^{38} +(-1.00000 - 3.31662i) q^{39} -1.62772 q^{41} +(4.18265 + 1.87228i) q^{42} -11.0371 q^{43} +(-3.68614 + 2.12819i) q^{44} +(-2.18614 + 3.78651i) q^{46} +(-0.939764 - 1.62772i) q^{47} +(1.26217 + 1.18614i) q^{48} +(-5.50000 + 4.33013i) q^{49} +(2.62772 - 11.1846i) q^{51} +(1.73205 + 1.00000i) q^{52} +(1.18843 + 0.686141i) q^{53} +(-0.872281 + 5.12241i) q^{54} +(-2.50000 + 0.866025i) q^{56} +(-4.10891 + 4.37228i) q^{57} +(1.65831 + 2.87228i) q^{58} +(2.05842 - 3.56529i) q^{59} +(-2.44158 + 1.40965i) q^{61} -2.37686 q^{62} +(-6.31084 - 4.81386i) q^{63} -1.00000 q^{64} +(7.05842 - 2.12819i) q^{66} +(-3.78651 + 6.55842i) q^{67} +(3.31662 + 5.74456i) q^{68} +(5.18614 - 5.51856i) q^{69} +1.87953i q^{71} +(-1.65831 - 2.50000i) q^{72} +(-1.73205 - 1.00000i) q^{73} +(-10.1168 - 5.84096i) q^{74} -3.46410i q^{76} +(-2.12819 + 11.0584i) q^{77} +(-2.52434 - 2.37228i) q^{78} +(-4.05842 - 7.02939i) q^{79} +(3.50000 - 8.29156i) q^{81} +(-1.40965 + 0.813859i) q^{82} -1.43710 q^{83} +(4.55842 - 0.469882i) q^{84} +(-9.55842 + 5.51856i) q^{86} +(-1.65831 - 5.50000i) q^{87} +(-2.12819 + 3.68614i) q^{88} +(2.18614 + 3.78651i) q^{89} +(5.00000 - 1.73205i) q^{91} +4.37228i q^{92} +(4.00772 + 0.941578i) q^{93} +(-1.62772 - 0.939764i) q^{94} +(1.68614 + 0.396143i) q^{96} +2.11684i q^{97} +(-2.59808 + 6.50000i) q^{98} +(-12.7446 + 0.792287i) 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
$6$	−1.18614	+	1.26217i	−0.484240	+	0.515278i
$7$	−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
$11$	−3.68614	−	2.12819i	−1.11141	−	0.641675i	−0.172218	−	0.985059i	$-0.555093\pi$
$11$	−3.68614	−	2.12819i	−1.11141	−	0.641675i	−0.939195	+	0.343384i	$0.888427\pi$
$12$	−0.396143	+	1.68614i	−0.114357	+	0.486747i
$13$			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	$0.464180\pi$
$17$	−3.31662	+	5.74456i	−0.804400	+	1.39326i	−0.916696	+	0.399586i	$0.869154\pi$
$18$	1.33591	−	2.68614i	0.314876	−	0.633129i
$19$	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
$21$	2.68614	+	3.71277i	0.586164	+	0.810192i
$22$	−4.25639			−0.907465
$23$	−3.78651	+	2.18614i	−0.789541	+	0.455842i	−0.839801	−	0.542894i	$-0.817328\pi$
$23$	−3.78651	+	2.18614i	−0.789541	+	0.455842i	0.0502598	+	0.998736i	$0.483995\pi$
$24$	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	$0.0996399\pi$
$29$			3.31662i			0.615882i	−0.951405	+	0.307941i	$0.900360\pi$
$30$		0			0
$31$	−2.05842	−	1.18843i	−0.369704	−	0.213448i	0.303625	−	0.952791i	$-0.401803\pi$
$31$	−2.05842	−	1.18843i	−0.369704	−	0.213448i	−0.673329	+	0.739343i	$0.735136\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	7.17687	+	1.68614i	1.24933	+	0.293519i
$34$			6.63325i			1.13759i
$35$		0			0
$36$	−0.186141	−	2.99422i	−0.0310234	−	0.499037i
$37$	−5.84096	−	10.1168i	−0.960248	−	1.66320i	−0.721873	−	0.692026i	$-0.756718\pi$
$37$	−5.84096	−	10.1168i	−0.960248	−	1.66320i	−0.238376	−	0.971173i	$-0.576615\pi$
$38$	1.73205	−	3.00000i	0.280976	−	0.486664i
$39$	−1.00000	−	3.31662i	−0.160128	−	0.531085i
$40$		0			0
$41$	−1.62772			−0.254207			−0.127103	−	0.991889i	$-0.540568\pi$
$41$	−1.62772			−0.254207			−0.127103	+	0.991889i	$0.540568\pi$
$42$	4.18265	+	1.87228i	0.645397	+	0.288899i
$43$	−11.0371			−1.68314			−0.841572	−	0.540145i	$-0.818369\pi$
$43$	−11.0371			−1.68314			−0.841572	+	0.540145i	$0.818369\pi$
$44$	−3.68614	+	2.12819i	−0.555707	+	0.320837i
$45$		0			0
$46$	−2.18614	+	3.78651i	−0.322329	+	0.558290i
$47$	−0.939764	−	1.62772i	−0.137079	−	0.237427i	0.789311	−	0.613994i	$-0.210438\pi$
$47$	−0.939764	−	1.62772i	−0.137079	−	0.237427i	−0.926390	+	0.376566i	$0.877105\pi$
$48$	1.26217	+	1.18614i	0.182178	+	0.171205i
$49$	−5.50000	+	4.33013i	−0.785714	+	0.618590i
$50$		0			0
$51$	2.62772	−	11.1846i	0.367954	−	1.56616i
$52$	1.73205	+	1.00000i	0.240192	+	0.138675i
$53$	1.18843	+	0.686141i	0.163243	+	0.0942487i	0.579396	−	0.815046i	$-0.303288\pi$
$53$	1.18843	+	0.686141i	0.163243	+	0.0942487i	−0.416153	+	0.909295i	$0.636622\pi$
$54$	−0.872281	+	5.12241i	−0.118702	+	0.697072i
$55$		0			0
$56$	−2.50000	+	0.866025i	−0.334077	+	0.115728i
$57$	−4.10891	+	4.37228i	−0.544239	+	0.579123i
$58$	1.65831	+	2.87228i	0.217747	+	0.377149i
$59$	2.05842	−	3.56529i	0.267984	−	0.464161i	−0.700357	−	0.713792i	$-0.746976\pi$
$59$	2.05842	−	3.56529i	0.267984	−	0.464161i	0.968341	+	0.249631i	$0.0803093\pi$
$60$		0			0
$61$	−2.44158	+	1.40965i	−0.312612	+	0.180487i	−0.648095	−	0.761560i	$-0.724434\pi$
$61$	−2.44158	+	1.40965i	−0.312612	+	0.180487i	0.335483	+	0.942046i	$0.391101\pi$
$62$	−2.37686			−0.301862
$63$	−6.31084	−	4.81386i	−0.795092	−	0.606489i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	7.05842	−	2.12819i	0.868832	−	0.261963i
$67$	−3.78651	+	6.55842i	−0.462595	+	0.801239i	−0.999089	−	0.0426654i	$-0.986415\pi$
$67$	−3.78651	+	6.55842i	−0.462595	+	0.801239i	0.536494	+	0.843904i	$0.319748\pi$
$68$	3.31662	+	5.74456i	0.402200	+	0.696631i
$69$	5.18614	−	5.51856i	0.624338	−	0.664356i
$70$		0			0
$71$			1.87953i			0.223059i	0.993761	+	0.111529i	$0.0355749\pi$
$71$			1.87953i			0.223059i	−0.993761	+	0.111529i	$0.964425\pi$
$72$	−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	$0.704008\pi$
$74$	−10.1168	−	5.84096i	−1.17606	−	0.678998i
$75$		0			0
$76$		−	3.46410i		−	0.397360i
$77$	−2.12819	+	11.0584i	−0.242530	+	1.26022i
$78$	−2.52434	−	2.37228i	−0.285825	−	0.268608i
$79$	−4.05842	−	7.02939i	−0.456608	−	0.790869i	0.542171	−	0.840268i	$-0.317603\pi$
$79$	−4.05842	−	7.02939i	−0.456608	−	0.790869i	−0.998779	+	0.0493997i	$0.984269\pi$
$80$		0			0
$81$	3.50000	−	8.29156i	0.388889	−	0.921285i
$82$	−1.40965	+	0.813859i	−0.155669	+	0.0898757i
$83$	−1.43710			−0.157742			−0.0788710	−	0.996885i	$-0.525132\pi$
$83$	−1.43710			−0.157742			−0.0788710	+	0.996885i	$0.525132\pi$
$84$	4.55842	−	0.469882i	0.497365	−	0.0512683i
$85$		0			0
$86$	−9.55842	+	5.51856i	−1.03071	+	0.595081i
$87$	−1.65831	−	5.50000i	−0.177790	−	0.589662i
$88$	−2.12819	+	3.68614i	−0.226866	+	0.392944i
$89$	2.18614	+	3.78651i	0.231730	+	0.401369i	0.958317	−	0.285706i	$-0.0922279\pi$
$89$	2.18614	+	3.78651i	0.231730	+	0.401369i	−0.726587	+	0.687074i	$0.758895\pi$
$90$		0			0
$91$	5.00000	−	1.73205i	0.524142	−	0.181568i
$92$			4.37228i			0.455842i
$93$	4.00772	+	0.941578i	0.415581	+	0.0976371i
$94$	−1.62772	−	0.939764i	−0.167886	−	0.0969292i
$95$		0			0
$96$	1.68614	+	0.396143i	0.172091	+	0.0404312i
$97$			2.11684i			0.214933i	0.994209	+	0.107466i	$0.0342738\pi$
$97$			2.11684i			0.214933i	−0.994209	+	0.107466i	$0.965726\pi$
$98$	−2.59808	+	6.50000i	−0.262445	+	0.656599i
$99$	−12.7446	+	0.792287i	−1.28088	+	0.0796278i
$100$		0			0
$101$	−8.18614	+	14.1788i	−0.814551	+	1.41084i	0.0950981	+	0.995468i	$0.469684\pi$
$101$	−8.18614	+	14.1788i	−0.814551	+	1.41084i	−0.909650	+	0.415377i	$0.863650\pi$
$102$	−3.31662	−	11.0000i	−0.328395	−	1.08916i
$103$	13.0916	−	7.55842i	1.28995	−	0.744753i	0.311306	−	0.950310i	$-0.399234\pi$
$103$	13.0916	−	7.55842i	1.28995	−	0.744753i	0.978645	+	0.205556i	$0.0659004\pi$
$104$	2.00000			0.196116
$105$		0			0
$106$	1.37228			0.133288
$107$	15.3672	−	8.87228i	1.48561	−	0.857716i	0.485742	−	0.874102i	$-0.338550\pi$
$107$	15.3672	−	8.87228i	1.48561	−	0.857716i	0.999866	+	0.0163866i	$0.00521626\pi$
$108$	1.80579	+	4.87228i	0.173762	+	0.468835i
$109$	4.55842	−	7.89542i	0.436618	−	0.756244i	−0.560808	−	0.827946i	$-0.689510\pi$
$109$	4.55842	−	7.89542i	0.436618	−	0.756244i	0.997426	+	0.0717016i	$0.0228429\pi$
$110$		0			0
$111$	14.7446	+	13.8564i	1.39949	+	1.31519i
$112$	−1.73205	+	2.00000i	−0.163663	+	0.188982i
$113$			3.25544i			0.306246i	0.988207	+	0.153123i	$0.0489330\pi$
$113$			3.25544i			0.306246i	−0.988207	+	0.153123i	$0.951067\pi$
$114$	−1.37228	+	5.84096i	−0.128526	+	0.547056i
$115$		0			0
$116$	2.87228	+	1.65831i	0.266685	+	0.153970i
$117$	3.31662	+	5.00000i	0.306622	+	0.462250i
$118$		−	4.11684i		−	0.378986i
$119$	17.2337	+	3.31662i	1.57981	+	0.304034i
$120$		0			0
$121$	3.55842	+	6.16337i	0.323493	+	0.560306i
$122$	−1.40965	+	2.44158i	−0.127623	+	0.221050i
$123$	2.69927	−	0.813859i	0.243385	−	0.0733832i
$124$	−2.05842	+	1.18843i	−0.184852	+	0.106724i
$125$		0			0
$126$	−7.87228	−	1.01350i	−0.701319	−	0.0902900i
$127$	2.37686			0.210912			0.105456	−	0.994424i	$-0.466370\pi$
$127$	2.37686			0.210912			0.105456	+	0.994424i	$0.466370\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	18.3030	−	5.51856i	1.61149	−	0.485882i
$130$		0			0
$131$	−2.31386	−	4.00772i	−0.202163	−	0.350156i	0.747062	−	0.664754i	$-0.231464\pi$
$131$	−2.31386	−	4.00772i	−0.202163	−	0.350156i	−0.949225	+	0.314598i	$0.898130\pi$
$132$	5.04868	−	5.37228i	0.439431	−	0.467597i
$133$	−6.92820	−	6.00000i	−0.600751	−	0.520266i
$134$			7.57301i			0.654209i
$135$		0			0
$136$	5.74456	+	3.31662i	0.492592	+	0.284398i
$137$	−2.37686	−	1.37228i	−0.203069	−	0.117242i	0.395017	−	0.918674i	$-0.370739\pi$
$137$	−2.37686	−	1.37228i	−0.203069	−	0.117242i	−0.598086	+	0.801432i	$0.704072\pi$
$138$	1.73205	−	7.37228i	0.147442	−	0.627570i
$139$		−	11.6819i		−	0.990848i	−0.868651	−	0.495424i	$-0.835013\pi$
$139$		−	11.6819i		−	0.990848i	0.868651	−	0.495424i	$-0.164987\pi$
$140$		0			0
$141$	2.37228	+	2.22938i	0.199782	+	0.187748i
$142$	0.939764	+	1.62772i	0.0788632	+	0.136595i
$143$	4.25639	−	7.37228i	0.355937	−	0.616501i
$144$	−2.68614	−	1.33591i	−0.223845	−	0.111326i
$145$		0			0
$146$	−2.00000			−0.165521
$147$	6.95565	−	9.93070i	0.573693	−	0.819071i
$148$	−11.6819			−0.960248
$149$	−12.3030	+	7.10313i	−1.00790	+	0.581911i	−0.910576	−	0.413342i	$-0.864362\pi$
$149$	−12.3030	+	7.10313i	−1.00790	+	0.581911i	−0.0973237	+	0.995253i	$0.531028\pi$
$150$		0			0
$151$	4.05842	−	7.02939i	0.330270	−	0.572044i	−0.652295	−	0.757965i	$-0.726194\pi$
$151$	4.05842	−	7.02939i	0.330270	−	0.572044i	0.982565	+	0.185921i	$0.0595270\pi$
$152$	−1.73205	−	3.00000i	−0.140488	−	0.243332i
$153$	1.23472	+	19.8614i	0.0998210	+	1.60570i
$154$	3.68614	+	10.6410i	0.297038	+	0.857474i
$155$		0			0
$156$	−3.37228	−	0.792287i	−0.269999	−	0.0634337i
$157$	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	$0.563241\pi$
$158$	−7.02939	−	4.05842i	−0.559228	−	0.322871i
$159$	−2.31386	−	0.543620i	−0.183501	−	0.0431119i
$160$		0			0
$161$	8.74456	+	7.57301i	0.689168	+	0.596837i
$162$	−1.11469	−	8.93070i	−0.0875785	−	0.701662i
$163$	−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	$0.876650\pi$
$164$	−0.813859	+	1.40965i	−0.0635517	+	0.110075i
$165$		0			0
$166$	−1.24456	+	0.718549i	−0.0965968	+	0.0557702i
$167$	−11.3321			−0.876902			−0.438451	−	0.898755i	$-0.644473\pi$
$167$	−11.3321			−0.876902			−0.438451	+	0.898755i	$0.644473\pi$
$168$	3.71277	−	2.68614i	0.286446	−	0.207240i
$169$	9.00000			0.692308
$170$		0			0
$171$	4.62772	−	9.30506i	0.353890	−	0.711576i
$172$	−5.51856	+	9.55842i	−0.420786	+	0.728823i
$173$	−1.87953	−	3.25544i	−0.142898	−	0.247506i	0.785689	−	0.618622i	$-0.212309\pi$
$173$	−1.87953	−	3.25544i	−0.142898	−	0.247506i	−0.928587	+	0.371116i	$0.878975\pi$
$174$	−4.18614	−	3.93398i	−0.317351	−	0.298235i
$175$		0			0
$176$			4.25639i			0.320837i
$177$	−1.63086	+	6.94158i	−0.122583	+	0.521761i
$178$	3.78651	+	2.18614i	0.283811	+	0.163858i
$179$	−2.48913	−	1.43710i	−0.186046	−	0.107414i	0.404084	−	0.914722i	$-0.367590\pi$
$179$	−2.48913	−	1.43710i	−0.186046	−	0.107414i	−0.590130	+	0.807308i	$0.700924\pi$
$180$		0			0
$181$		−	17.9653i		−	1.33535i	−0.744452	−	0.667676i	$-0.767289\pi$
$181$		−	17.9653i		−	1.33535i	0.744452	−	0.667676i	$-0.232711\pi$
$182$	3.46410	−	4.00000i	0.256776	−	0.296500i
$183$	3.34408	−	3.55842i	0.247201	−	0.263046i
$184$	2.18614	+	3.78651i	0.161164	+	0.279145i
$185$		0			0
$186$	3.94158	−	1.18843i	0.289011	−	0.0871400i
$187$	24.4511	−	14.1168i	1.78804	−	1.03233i
$188$	−1.87953			−0.137079
$189$	12.8723	+	4.82746i	0.936321	+	0.351146i
$190$		0			0
$191$	−3.25544	+	1.87953i	−0.235555	+	0.135998i	−0.613132	−	0.789980i	$-0.710091\pi$
$191$	−3.25544	+	1.87953i	−0.235555	+	0.135998i	0.377577	+	0.925978i	$0.376757\pi$
$192$	1.65831	−	0.500000i	0.119678	−	0.0360844i
$193$	4.00772	−	6.94158i	0.288482	−	0.499666i	−0.684966	−	0.728575i	$-0.740183\pi$
$193$	4.00772	−	6.94158i	0.288482	−	0.499666i	0.973448	+	0.228910i	$0.0735161\pi$
$194$	1.05842	+	1.83324i	0.0759903	+	0.131619i
$195$		0			0
$196$	1.00000	+	6.92820i	0.0714286	+	0.494872i
$197$		−	20.2337i		−	1.44159i	−0.693148	−	0.720795i	$-0.743777\pi$
$197$		−	20.2337i		−	1.44159i	0.693148	−	0.720795i	$-0.256223\pi$
$198$	−10.6410	+	7.05842i	−0.756221	+	0.501620i
$199$	16.1168	+	9.30506i	1.14249	+	0.659619i	0.947047	−	0.321096i	$-0.104051\pi$
$199$	16.1168	+	9.30506i	1.14249	+	0.659619i	0.195446	+	0.980714i	$0.437385\pi$
$200$		0			0
$201$	3.00000	−	12.7692i	0.211604	−	0.900668i
$202$			16.3723i			1.15195i
$203$	8.29156	−	2.87228i	0.581954	−	0.201595i
$204$	−8.37228	−	7.86797i	−0.586177	−	0.550868i
$205$		0			0
$206$	7.55842	−	13.0916i	0.526620	−	0.912133i
$207$	−5.84096	+	11.7446i	−0.405975	+	0.816304i
$208$	1.73205	−	1.00000i	0.120096	−	0.0693375i
$209$	−14.7446			−1.01990
$210$		0			0
$211$	−18.2337			−1.25526			−0.627629	−	0.778512i	$-0.715975\pi$
$211$	−18.2337			−1.25526			−0.627629	+	0.778512i	$0.715975\pi$
$212$	1.18843	−	0.686141i	0.0816217	−	0.0471243i
$213$	−0.939764	−	3.11684i	−0.0643916	−	0.213563i
$214$	8.87228	−	15.3672i	0.606497	−	1.05048i
$215$		0			0
$216$	4.00000	+	3.31662i	0.272166	+	0.225668i
$217$	−1.18843	+	6.17527i	−0.0806759	+	0.419204i
$218$		−	9.11684i		−	0.617471i
$219$	3.37228	+	0.792287i	0.227878	+	0.0535378i
$220$		0			0
$221$	−11.4891	−	6.63325i	−0.772842	−	0.446201i
$222$	19.6974	+	4.62772i	1.32200	+	0.310592i
$223$			18.1168i			1.21319i	0.795010	+	0.606597i	$0.207466\pi$
$223$			18.1168i			1.21319i	−0.795010	+	0.606597i	$0.792534\pi$
$224$	−0.500000	+	2.59808i	−0.0334077	+	0.173591i
$225$		0			0
$226$	1.62772	+	2.81929i	0.108274	+	0.187536i
$227$	7.82168	−	13.5475i	0.519143	−	0.899182i	−0.480609	−	0.876935i	$-0.659584\pi$
$227$	7.82168	−	13.5475i	0.519143	−	0.899182i	0.999752	−	0.0222475i	$-0.00708218\pi$
$228$	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	−	19.4024i	−0.131590	−	1.27659i
$232$	3.31662			0.217747
$233$	20.3422	−	11.7446i	1.33266	−	0.769412i	0.346954	−	0.937882i	$-0.387216\pi$
$233$	20.3422	−	11.7446i	1.33266	−	0.769412i	0.985707	+	0.168470i	$0.0538827\pi$
$234$	5.37228	+	2.67181i	0.351197	+	0.174662i
$235$		0			0
$236$	−2.05842	−	3.56529i	−0.133992	−	0.232081i
$237$	10.2448	+	9.62772i	0.665473	+	0.625388i
$238$	16.5831	−	5.74456i	1.07492	−	0.372365i
$239$			2.87419i			0.185916i	0.995670	+	0.0929581i	$0.0296323\pi$
$239$			2.87419i			0.185916i	−0.995670	+	0.0929581i	$0.970368\pi$
$240$		0			0
$241$	9.17527	+	5.29734i	0.591031	+	0.341232i	0.765505	−	0.643430i	$-0.222489\pi$
$241$	9.17527	+	5.29734i	0.591031	+	0.341232i	−0.174474	+	0.984662i	$0.555823\pi$
$242$	6.16337	+	3.55842i	0.396196	+	0.228744i
$243$	−1.65831	+	15.5000i	−0.106381	+	0.994325i
$244$			2.81929i			0.180487i
$245$		0			0
$246$	1.93070	−	2.05446i	0.123097	−	0.130987i
$247$	3.46410	+	6.00000i	0.220416	+	0.381771i
$248$	−1.18843	+	2.05842i	−0.0754654	+	0.130710i
$249$	2.38316	−	0.718549i	0.151026	−	0.0455362i
$250$		0			0
$251$	−16.1168			−1.01729			−0.508643	−	0.860977i	$-0.669853\pi$
$251$	−16.1168			−1.01729			−0.508643	+	0.860977i	$0.669853\pi$
$252$	−7.32435	+	3.05842i	−0.461390	+	0.192662i
$253$	18.6101			1.17001
$254$	2.05842	−	1.18843i	0.129157	−	0.0745688i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	4.25639	+	7.37228i	0.265506	+	0.459870i	0.967696	−	0.252119i	$-0.0811276\pi$
$257$	4.25639	+	7.37228i	0.265506	+	0.459870i	−0.702190	+	0.711990i	$0.747794\pi$
$258$	13.0916	−	13.9307i	0.815046	−	0.867288i
$259$	−20.2337	+	23.3639i	−1.25726	+	1.45176i
$260$		0			0
$261$	5.50000	+	8.29156i	0.340441	+	0.513235i
$262$	−4.00772	−	2.31386i	−0.247598	−	0.142951i
$263$	1.40965	+	0.813859i	0.0869225	+	0.0501847i	0.542831	−	0.839842i	$-0.317352\pi$
$263$	1.40965	+	0.813859i	0.0869225	+	0.0501847i	−0.455909	+	0.890027i	$0.650686\pi$
$264$	1.68614	−	7.17687i	0.103775	−	0.441706i
$265$		0			0
$266$	−9.00000	−	1.73205i	−0.551825	−	0.106199i
$267$	−5.51856	−	5.18614i	−0.337730	−	0.317387i
$268$	3.78651	+	6.55842i	0.231298	+	0.400619i
$269$	9.98913	−	17.3017i	0.609048	−	1.05490i	−0.382350	−	0.924018i	$-0.624885\pi$
$269$	9.98913	−	17.3017i	0.609048	−	1.05490i	0.991398	−	0.130884i	$-0.0417815\pi$
$270$		0			0
$271$	−18.1753	+	10.4935i	−1.10407	+	0.637434i	−0.937287	−	0.348559i	$-0.886671\pi$
$271$	−18.1753	+	10.4935i	−1.10407	+	0.637434i	−0.166782	+	0.985994i	$0.553338\pi$
$272$	6.63325			0.402200
$273$	−7.42554	+	5.37228i	−0.449414	+	0.325145i
$274$	−2.74456			−0.165805
$275$		0			0
$276$	−2.18614	−	7.25061i	−0.131590	−	0.436435i
$277$	14.5012	−	25.1168i	0.871294	−	1.50912i	0.0106345	−	0.999943i	$-0.496615\pi$
$277$	14.5012	−	25.1168i	0.871294	−	1.50912i	0.860659	−	0.509181i	$-0.170052\pi$
$278$	−5.84096	−	10.1168i	−0.350318	−	0.606768i
$279$	−7.11684	+	0.442430i	−0.426074	+	0.0264876i
$280$		0			0
$281$			21.7793i			1.29924i	0.760258	+	0.649621i	$0.225073\pi$
$281$			21.7793i			1.29924i	−0.760258	+	0.649621i	$0.774927\pi$
$282$	3.16915	+	0.744563i	0.188720	+	0.0443381i
$283$	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	$0.508916\pi$
$284$	1.62772	+	0.939764i	0.0965873	+	0.0557647i
$285$		0			0
$286$		−	8.51278i		−	0.503371i
$287$	1.40965	+	4.06930i	0.0832088	+	0.240203i
$288$	−2.99422	+	0.186141i	−0.176436	+	0.0109684i
$289$	−13.5000	−	23.3827i	−0.794118	−	1.37545i
$290$		0			0
$291$	−1.05842	−	3.51039i	−0.0620458	−	0.205783i
$292$	−1.73205	+	1.00000i	−0.101361	+	0.0585206i
$293$	−25.0410			−1.46291			−0.731455	−	0.681889i	$-0.761159\pi$
$293$	−25.0410			−1.46291			−0.731455	+	0.681889i	$0.761159\pi$
$294$	1.05842	−	12.0781i	0.0617284	−	0.704407i
$295$		0			0
$296$	−10.1168	+	5.84096i	−0.588030	+	0.339499i
$297$	20.7383	−	7.68614i	1.20336	−	0.445995i
$298$	−7.10313	+	12.3030i	−0.411473	+	0.712693i
$299$	−4.37228	−	7.57301i	−0.252856	−	0.437959i
$300$		0			0
$301$	9.55842	+	27.5928i	0.550938	+	1.59042i
$302$		−	8.11684i		−	0.467072i
$303$	6.48577	−	27.6060i	0.372598	−	1.58592i
$304$	−3.00000	−	1.73205i	−0.172062	−	0.0993399i
$305$		0			0
$306$	11.0000	+	16.5831i	0.628828	+	0.947994i
$307$		−	6.88316i		−	0.392842i	−0.980520	−	0.196421i	$-0.937068\pi$
$307$		−	6.88316i		−	0.392842i	0.980520	−	0.196421i	$-0.0629320\pi$
$308$	8.51278	+	7.37228i	0.485060	+	0.420075i
$309$	−17.9307	+	19.0800i	−1.02004	+	1.08542i
$310$		0			0
$311$	7.11684	−	12.3267i	0.403559	−	0.698985i	−0.590593	−	0.806969i	$-0.701106\pi$
$311$	7.11684	−	12.3267i	0.403559	−	0.698985i	0.994153	+	0.107984i	$0.0344396\pi$
$312$	−3.31662	+	1.00000i	−0.187767	+	0.0566139i
$313$	−12.2255	+	7.05842i	−0.691029	+	0.398966i	−0.803997	−	0.594633i	$-0.797297\pi$
$313$	−12.2255	+	7.05842i	−0.691029	+	0.398966i	0.112969	+	0.993599i	$0.463964\pi$
$314$	8.00000			0.451466
$315$		0			0
$316$	−8.11684			−0.456608
$317$	13.9576	−	8.05842i	0.783937	−	0.452606i	−0.0538869	−	0.998547i	$-0.517161\pi$
$317$	13.9576	−	8.05842i	0.783937	−	0.452606i	0.837824	+	0.545941i	$0.183828\pi$
$318$	−2.27567	+	0.686141i	−0.127613	+	0.0384769i
$319$	7.05842	−	12.2255i	0.395196	−	0.684499i
$320$		0			0
$321$	−21.0475	+	22.3966i	−1.17476	+	1.25006i
$322$	11.3595	+	2.18614i	0.633041	+	0.121829i
$323$			22.9783i			1.27854i
$324$	−5.43070	−	7.17687i	−0.301706	−	0.398715i
$325$		0			0
$326$	−3.00000	−	1.73205i	−0.166155	−	0.0959294i
$327$	−3.61158	+	15.3723i	−0.199721	+	0.850089i
$328$			1.62772i			0.0898757i
$329$	−3.25544	+	3.75906i	−0.179478	+	0.207243i
$330$		0			0
$331$	−5.11684	−	8.86263i	−0.281247	−	0.487134i	0.690445	−	0.723385i	$-0.257415\pi$
$331$	−5.11684	−	8.86263i	−0.281247	−	0.487134i	−0.971692	+	0.236250i	$0.924081\pi$
$332$	−0.718549	+	1.24456i	−0.0394355	+	0.0683042i
$333$	−31.3793	−	15.6060i	−1.71957	−	0.855202i
$334$	−9.81386	+	5.66603i	−0.536990	+	0.310032i
$335$		0			0
$336$	1.87228	−	4.18265i	0.102141	−	0.228182i
$337$	9.30506			0.506879			0.253440	−	0.967351i	$-0.418438\pi$
$337$	9.30506			0.506879			0.253440	+	0.967351i	$0.418438\pi$
$338$	7.79423	−	4.50000i	0.423950	−	0.244768i
$339$	−1.62772	−	5.39853i	−0.0884055	−	0.293208i
$340$		0			0
$341$	5.05842	+	8.76144i	0.273929	+	0.474459i
$342$	−0.644810	−	10.3723i	−0.0348673	−	0.560869i
$343$	15.5885	+	10.0000i	0.841698	+	0.539949i
$344$			11.0371i			0.595081i
$345$		0			0
$346$	−3.25544	−	1.87953i	−0.175013	−	0.101044i
$347$	−16.5557	−	9.55842i	−0.888755	−	0.513123i	−0.0152200	−	0.999884i	$-0.504845\pi$
$347$	−16.5557	−	9.55842i	−0.888755	−	0.513123i	−0.873535	+	0.486761i	$0.838178\pi$
$348$	−5.59230	−	1.31386i	−0.299779	−	0.0704303i
$349$			24.0087i			1.28515i	0.766221	+	0.642577i	$0.222135\pi$
$349$			24.0087i			1.28515i	−0.766221	+	0.642577i	$0.777865\pi$
$350$		0			0
$351$	−8.00000	−	6.63325i	−0.427008	−	0.354057i
$352$	2.12819	+	3.68614i	0.113433	+	0.196472i
$353$	−9.45254	+	16.3723i	−0.503108	+	0.871409i	0.496886	+	0.867816i	$0.334477\pi$
$353$	−9.45254	+	16.3723i	−0.503108	+	0.871409i	−0.999994	+	0.00359253i	$0.998856\pi$
$354$	2.05842	+	6.82701i	0.109404	+	0.362852i
$355$		0			0
$356$	4.37228			0.231730
$357$	−30.2372	+	3.11684i	−1.60032	+	0.164961i
$358$	−2.87419			−0.151906
$359$	12.2554	−	7.07568i	0.646817	−	0.373440i	−0.140419	−	0.990092i	$-0.544845\pi$
$359$	12.2554	−	7.07568i	0.646817	−	0.373440i	0.787236	+	0.616652i	$0.211511\pi$
$360$		0			0
$361$	−3.50000	+	6.06218i	−0.184211	+	0.319062i
$362$	−8.98266	−	15.5584i	−0.472118	−	0.817733i
$363$	−8.98266	−	8.44158i	−0.471467	−	0.443068i
$364$	1.00000	−	5.19615i	0.0524142	−	0.272352i
$365$		0			0
$366$	1.11684	−	4.75372i	0.0583784	−	0.248481i
$367$	−18.3889	−	10.6168i	−0.959893	−	0.554195i	−0.0637532	−	0.997966i	$-0.520307\pi$
$367$	−18.3889	−	10.6168i	−0.959893	−	0.554195i	−0.896140	+	0.443771i	$0.853640\pi$
$368$	3.78651	+	2.18614i	0.197385	+	0.113960i
$369$	−4.06930	+	2.69927i	−0.211839	+	0.140518i
$370$		0			0
$371$	0.686141	−	3.56529i	0.0356226	−	0.185101i
$372$	2.81929	−	3.00000i	0.146173	−	0.155543i
$373$	−8.21782	−	14.2337i	−0.425503	−	0.736992i	0.570964	−	0.820975i	$-0.306569\pi$
$373$	−8.21782	−	14.2337i	−0.425503	−	0.736992i	−0.996467	+	0.0839823i	$0.973236\pi$
$374$	14.1168	−	24.4511i	0.729965	−	1.26434i
$375$		0			0
$376$	−1.62772	+	0.939764i	−0.0839432	+	0.0484646i
$377$	−6.63325			−0.341630
$378$	13.5615	−	2.25544i	0.697526	−	0.116007i
$379$	−22.2337			−1.14207			−0.571034	−	0.820926i	$-0.693458\pi$
$379$	−22.2337			−1.14207			−0.571034	+	0.820926i	$0.693458\pi$
$380$		0			0
$381$	−3.94158	+	1.18843i	−0.201933	+	0.0608851i
$382$	−1.87953	+	3.25544i	−0.0961650	+	0.166563i
$383$	−10.4198	−	18.0475i	−0.532425	−	0.922187i	−0.999283	−	0.0378546i	$-0.987948\pi$
$383$	−10.4198	−	18.0475i	−0.532425	−	0.922187i	0.466859	−	0.884332i	$-0.345386\pi$
$384$	1.18614	−	1.26217i	0.0605300	−	0.0644098i
$385$		0			0
$386$		−	8.01544i		−	0.407975i
$387$	−27.5928	+	18.3030i	−1.40262	+	0.930393i
$388$	1.83324	+	1.05842i	0.0930687	+	0.0537332i
$389$	−29.4891	−	17.0256i	−1.49516	−	0.863230i	−0.495173	−	0.868794i	$-0.664896\pi$
$389$	−29.4891	−	17.0256i	−1.49516	−	0.863230i	−0.999985	+	0.00556424i	$0.998229\pi$
$390$		0			0
$391$		−	29.0024i		−	1.46672i
$392$	4.33013	+	5.50000i	0.218704	+	0.277792i
$393$	5.84096	+	5.48913i	0.294638	+	0.276890i
$394$	−10.1168	−	17.5229i	−0.509679	−	0.882790i
$395$		0			0
$396$	−5.68614	+	11.4333i	−0.285739	+	0.574543i
$397$	−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	$0.397673\pi$
$398$	18.6101			0.932841
$399$	14.4891	+	6.48577i	0.725364	+	0.324695i
$400$		0			0
$401$	17.1861	−	9.92242i	0.858235	−	0.495502i	−0.00518590	−	0.999987i	$-0.501651\pi$
$401$	17.1861	−	9.92242i	0.858235	−	0.495502i	0.863421	+	0.504484i	$0.168317\pi$
$402$	−3.78651	−	12.5584i	−0.188854	−	0.626357i
$403$	2.37686	−	4.11684i	0.118400	−	0.205075i
$404$	8.18614	+	14.1788i	0.407276	+	0.705422i
$405$		0			0
$406$	5.74456	−	6.63325i	0.285098	−	0.329203i
$407$			49.7228i			2.46467i
$408$	−11.1846	−	2.62772i	−0.553720	−	0.130091i
$409$	30.7337	+	17.7441i	1.51968	+	0.877389i	0.999731	+	0.0231940i	$0.00738354\pi$
$409$	30.7337	+	17.7441i	1.51968	+	0.877389i	0.519952	+	0.854195i	$0.325950\pi$
$410$		0			0
$411$	4.62772	+	1.08724i	0.228269	+	0.0536296i
$412$		−	15.1168i		−	0.744753i
$413$	−10.6959	−	2.05842i	−0.526310	−	0.101288i
$414$	0.813859	+	13.0916i	0.0399990	+	0.643416i
$415$		0			0
$416$	1.00000	−	1.73205i	0.0490290	−	0.0849208i
$417$	5.84096	+	19.3723i	0.286033	+	0.948665i
$418$	−12.7692	+	7.37228i	−0.624560	+	0.360590i
$419$	−29.4891			−1.44064			−0.720319	−	0.693643i	$-0.756005\pi$
$419$	−29.4891			−1.44064			−0.720319	+	0.693643i	$0.756005\pi$
$420$		0			0
$421$	15.1168			0.736750			0.368375	−	0.929677i	$-0.379914\pi$
$421$	15.1168			0.736750			0.368375	+	0.929677i	$0.379914\pi$
$422$	−15.7908	+	9.11684i	−0.768686	+	0.443801i
$423$	−5.04868	−	2.51087i	−0.245475	−	0.122083i
$424$	0.686141	−	1.18843i	0.0333219	−	0.0577153i
$425$		0			0
$426$	−2.37228	−	2.22938i	−0.114937	−	0.108014i
$427$	5.63858	+	4.88316i	0.272870	+	0.236312i
$428$		−	17.7446i		−	0.857716i
$429$	−3.37228	+	14.3537i	−0.162815	+	0.693005i
$430$		0			0
$431$	3.25544	+	1.87953i	0.156809	+	0.0905337i	0.576351	−	0.817202i	$-0.304476\pi$
$431$	3.25544	+	1.87953i	0.156809	+	0.0905337i	−0.419542	+	0.907736i	$0.637809\pi$
$432$	5.12241	+	0.872281i	0.246452	+	0.0419677i
$433$		−	34.0000i		−	1.63394i	−0.576683	−	0.816968i	$-0.695653\pi$
$433$		−	34.0000i		−	1.63394i	0.576683	−	0.816968i	$-0.304347\pi$
$434$	2.05842	+	5.94215i	0.0988074	+	0.285232i
$435$		0			0
$436$	−4.55842	−	7.89542i	−0.218309	−	0.378122i
$437$	−7.57301	+	13.1168i	−0.362266	+	0.627464i
$438$	3.31662	−	1.00000i	0.158474	−	0.0477818i
$439$	11.0584	−	6.38458i	0.527790	−	0.304720i	−0.212326	−	0.977199i	$-0.568104\pi$
$439$	11.0584	−	6.38458i	0.527790	−	0.304720i	0.740116	+	0.672479i	$0.234771\pi$
$440$		0			0
$441$	−6.56930	+	19.9460i	−0.312824	+	0.949811i
$442$	−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	$0.401918\pi$
$444$	19.3723	−	5.84096i	0.919368	−	0.277200i
$445$		0			0
$446$	9.05842	+	15.6896i	0.428929	+	0.742926i
$447$	16.8506	−	17.9307i	0.797007	−	0.848093i
$448$	0.866025	+	2.50000i	0.0409159	+	0.118114i
$449$			35.9855i			1.69826i	0.528182	+	0.849131i	$0.322874\pi$
$449$			35.9855i			1.69826i	−0.528182	+	0.849131i	$0.677126\pi$
$450$		0			0
$451$	6.00000	+	3.46410i	0.282529	+	0.163118i
$452$	2.81929	+	1.62772i	0.132608	+	0.0765614i
$453$	−3.21543	+	13.6861i	−0.151074	+	0.643031i
$454$		−	15.6434i		−	0.734179i
$455$		0			0
$456$	4.37228	+	4.10891i	0.204751	+	0.192417i
$457$	−6.38458	−	11.0584i	−0.298658	−	0.517291i	0.677171	−	0.735826i	$-0.263206\pi$
$457$	−6.38458	−	11.0584i	−0.298658	−	0.517291i	−0.975829	+	0.218534i	$0.929872\pi$
$458$	−6.92820	+	12.0000i	−0.323734	+	0.560723i
$459$	−11.9783	−	32.3191i	−0.559097	−	1.50852i
$460$		0			0
$461$	0.510875			0.0237938			0.0118969	−	0.999929i	$-0.496213\pi$
$461$	0.510875			0.0237938			0.0118969	+	0.999929i	$0.496213\pi$
$462$	−11.4333	−	15.8030i	−0.531923	−	0.735221i
$463$	36.5754			1.69981			0.849903	−	0.526940i	$-0.176661\pi$
$463$	36.5754			1.69981			0.849903	+	0.526940i	$0.176661\pi$
$464$	2.87228	−	1.65831i	0.133342	−	0.0769852i
$465$		0			0
$466$	11.7446	−	20.3422i	0.544056	−	0.942333i
$467$	0.0274514	+	0.0475473i	0.00127030	+	0.00220023i	0.866660	−	0.498899i	$-0.166262\pi$
$467$	0.0274514	+	0.0475473i	0.00127030	+	0.00220023i	−0.865390	+	0.501100i	$0.832929\pi$
$468$	5.98844	−	0.372281i	0.276816	−	0.0172087i
$469$	19.6753	+	3.78651i	0.908519	+	0.174845i
$470$		0			0
$471$	−13.4891	−	3.16915i	−0.621546	−	0.146027i
$472$	−3.56529	−	2.05842i	−0.164106	−	0.0947466i
$473$	40.6844	+	23.4891i	1.87067	+	1.08003i
$474$	13.6861	+	3.21543i	0.628625	+	0.147690i
$475$		0			0
$476$	11.4891	−	13.2665i	0.526603	−	0.608069i
$477$	4.10891	−	0.255437i	0.188134	−	0.0116957i
$478$	1.43710	+	2.48913i	0.0657313	+	0.113850i
$479$	−4.37228	+	7.57301i	−0.199775	+	0.346020i	−0.948455	−	0.316911i	$-0.897354\pi$
$479$	−4.37228	+	7.57301i	−0.199775	+	0.346020i	0.748681	+	0.662931i	$0.230688\pi$
$480$		0			0
$481$	20.2337	−	11.6819i	0.922577	−	0.532650i
$482$	10.5947			0.482575
$483$	−18.2877	−	8.18614i	−0.832120	−	0.372482i
$484$	7.11684			0.323493
$485$		0			0
$486$	6.31386	+	14.2525i	0.286402	+	0.646509i
$487$	2.27567	−	3.94158i	0.103121	−	0.178610i	−0.809848	−	0.586639i	$-0.800451\pi$
$487$	2.27567	−	3.94158i	0.103121	−	0.178610i	0.912969	+	0.408029i	$0.133784\pi$
$488$	1.40965	+	2.44158i	0.0638117	+	0.110525i
$489$	4.37228	+	4.10891i	0.197721	+	0.185811i
$490$		0			0
$491$		−	26.9205i		−	1.21491i	−0.794355	−	0.607453i	$-0.792191\pi$
$491$		−	26.9205i		−	1.21491i	0.794355	−	0.607453i	$-0.207809\pi$
$492$	0.644810	−	2.74456i	0.0290703	−	0.123734i
$493$	−19.0526	−	11.0000i	−0.858084	−	0.495415i
$494$	6.00000	+	3.46410i	0.269953	+	0.155857i
$495$		0			0
$496$			2.37686i			0.106724i
$497$	4.69882	−	1.62772i	0.210771	−	0.0730132i
$498$	1.70460	−	1.81386i	0.0763849	−	0.0812810i
$499$	14.1168	+	24.4511i	0.631957	+	1.09458i	0.987151	+	0.159789i	$0.0510813\pi$
$499$	14.1168	+	24.4511i	0.631957	+	1.09458i	−0.355195	+	0.934792i	$0.615585\pi$
$500$		0			0
$501$	18.7921	−	5.66603i	0.839570	−	0.253140i
$502$	−13.9576	+	8.05842i	−0.622958	+	0.359665i
$503$	−9.45254			−0.421468			−0.210734	−	0.977543i	$-0.567585\pi$
$503$	−9.45254			−0.421468			−0.210734	+	0.977543i	$0.567585\pi$
$504$	−4.81386	+	6.31084i	−0.214426	+	0.281107i
$505$		0			0
$506$	16.1168	−	9.30506i	0.716481	−	0.413661i
$507$	−14.9248	+	4.50000i	−0.662834	+	0.199852i
$508$	1.18843	−	2.05842i	0.0527281	−	0.0913277i
$509$	−0.127719	−	0.221215i	−0.00566103	−	0.00980519i	0.863181	−	0.504895i	$-0.168469\pi$
$509$	−0.127719	−	0.221215i	−0.00566103	−	0.00980519i	−0.868842	+	0.495089i	$0.835135\pi$
$510$		0			0
$511$	−1.00000	+	5.19615i	−0.0442374	+	0.229864i
$512$			1.00000i			0.0441942i
$513$	−3.02167	+	17.7446i	−0.133410	+	0.783442i
$514$	7.37228	+	4.25639i	0.325177	+	0.187741i
$515$		0			0
$516$	4.37228	−	18.6101i	0.192479	−	0.819265i
$517$			8.00000i			0.351840i
$518$	−5.84096	+	30.3505i	−0.256637	+	1.33353i
$519$	4.74456	+	4.45877i	0.208263	+	0.195718i
$520$		0			0
$521$	1.62772	−	2.81929i	0.0713116	−	0.123515i	−0.828165	−	0.560485i	$-0.810615\pi$
$521$	1.62772	−	2.81929i	0.0713116	−	0.123515i	0.899476	+	0.436969i	$0.143948\pi$
$522$	8.90892	+	4.43070i	0.389933	+	0.193927i
$523$	−20.9870	+	12.1168i	−0.917697	+	0.529833i	−0.882900	−	0.469562i	$-0.844412\pi$
$523$	−20.9870	+	12.1168i	−0.917697	+	0.529833i	−0.0347974	+	0.999394i	$0.511079\pi$
$524$	−4.62772			−0.202163
$525$		0			0
$526$	1.62772			0.0709719
$527$	13.6540	−	7.88316i	0.594779	−	0.343396i
$528$	−2.12819	−	7.05842i	−0.0926178	−	0.307178i
$529$	−1.94158	+	3.36291i	−0.0844164	+	0.146214i
$530$		0			0
$531$	−0.766312	−	12.3267i	−0.0332551	−	0.534935i
$532$	−8.66025	+	3.00000i	−0.375470	+	0.130066i
$533$		−	3.25544i		−	0.141009i
$534$	−7.37228	−	1.73205i	−0.319030	−	0.0749532i
$535$		0			0
$536$	6.55842	+	3.78651i	0.283281	+	0.163552i
$537$	4.84630	+	1.13859i	0.209133	+	0.0491339i
$538$		−	19.9783i		−	0.861324i
$539$	29.4891	−	4.25639i	1.27019	−	0.183336i
$540$		0			0
$541$	6.67527	+	11.5619i	0.286992	+	0.497085i	0.973090	−	0.230424i	$-0.0740113\pi$
$541$	6.67527	+	11.5619i	0.286992	+	0.497085i	−0.686098	+	0.727509i	$0.740678\pi$
$542$	−10.4935	+	18.1753i	−0.450734	+	0.780695i
$543$	8.98266	+	29.7921i	0.385483	+	1.27850i
$544$	5.74456	−	3.31662i	0.246296	−	0.142199i
$545$		0			0
$546$	−3.74456	+	8.36530i	−0.160252	+	0.358002i
$547$	0.644810			0.0275701			0.0137850	−	0.999905i	$-0.495612\pi$
$547$	0.644810			0.0275701			0.0137850	+	0.999905i	$0.495612\pi$
$548$	−2.37686	+	1.37228i	−0.101534	+	0.0586210i
$549$	−3.76631	+	7.57301i	−0.160742	+	0.323208i
$550$		0			0
$551$	5.74456	+	9.94987i	0.244727	+	0.423879i
$552$	−5.51856	−	5.18614i	−0.234885	−	0.220737i
$553$	−14.0588	+	16.2337i	−0.597840	+	0.690327i
$554$		−	29.0024i		−	1.23220i
$555$		0			0
$556$	−10.1168	−	5.84096i	−0.429050	−	0.247712i
$557$	0.746000	+	0.430703i	0.0316090	+	0.0182495i	0.515721	−	0.856756i	$-0.327524\pi$
$557$	0.746000	+	0.430703i	0.0316090	+	0.0182495i	−0.484112	+	0.875006i	$0.660857\pi$
$558$	−5.94215	+	3.94158i	−0.251551	+	0.166860i
$559$		−	22.0742i		−	0.933640i
$560$		0			0
$561$	−33.4891	+	35.6357i	−1.41391	+	1.50454i
$562$	10.8896	+	18.8614i	0.459352	+	0.795620i
$563$	5.91470	−	10.2446i	0.249275	−	0.431757i	−0.714050	−	0.700095i	$-0.753141\pi$
$563$	5.91470	−	10.2446i	0.249275	−	0.431757i	0.963325	+	0.268338i	$0.0864744\pi$
$564$	3.11684	−	0.939764i	0.131243	−	0.0395712i
$565$		0			0
$566$	16.0000			0.672530
$567$	−23.7600	−	1.56930i	−0.997826	−	0.0659043i
$568$	1.87953			0.0788632
$569$	−18.8614	+	10.8896i	−0.790711	+	0.456517i	−0.840213	−	0.542257i	$-0.817570\pi$
$569$	−18.8614	+	10.8896i	−0.790711	+	0.456517i	0.0495016	+	0.998774i	$0.484237\pi$
$570$		0			0
$571$	−17.1168	+	29.6472i	−0.716318	+	1.24070i	0.246132	+	0.969236i	$0.420840\pi$
$571$	−17.1168	+	29.6472i	−0.716318	+	1.24070i	−0.962449	+	0.271462i	$0.912493\pi$
$572$	−4.25639	−	7.37228i	−0.177969	−	0.308251i
$573$	4.45877	−	4.74456i	0.186268	−	0.198207i
$574$	3.25544	+	2.81929i	0.135879	+	0.117675i
$575$		0			0
$576$	−2.50000	+	1.65831i	−0.104167	+	0.0690963i
$577$	−15.4873	−	8.94158i	−0.644743	−	0.372243i	0.141696	−	0.989910i	$-0.454744\pi$
$577$	−15.4873	−	8.94158i	−0.644743	−	0.372243i	−0.786439	+	0.617667i	$0.788078\pi$
$578$	−23.3827	−	13.5000i	−0.972592	−	0.561526i
$579$	−3.17527	+	13.5152i	−0.131960	+	0.561671i
$580$		0			0
$581$	1.24456	+	3.59274i	0.0516332	+	0.149052i
$582$	−2.67181	−	2.51087i	−0.110750	−	0.104079i
$583$	−2.92048	−	5.05842i	−0.120954	−	0.209498i
$584$	−1.00000	+	1.73205i	−0.0413803	+	0.0716728i
$585$		0			0
$586$	−21.6861	+	12.5205i	−0.895846	+	0.517217i
$587$	−36.4280			−1.50354			−0.751772	−	0.659424i	$-0.770800\pi$
$587$	−36.4280			−1.50354			−0.751772	+	0.659424i	$0.770800\pi$
$588$	−5.12241	−	10.9891i	−0.211245	−	0.453184i
$589$	−8.23369			−0.339263
$590$		0			0
$591$	10.1168	+	33.5538i	0.416151	+	1.38022i
$592$	−5.84096	+	10.1168i	−0.240062	+	0.415800i
$593$	−7.07568	−	12.2554i	−0.290563	−	0.503270i	0.683380	−	0.730063i	$-0.260509\pi$
$593$	−7.07568	−	12.2554i	−0.290563	−	0.503270i	−0.973943	+	0.226793i	$0.927176\pi$
$594$	14.1168	−	17.0256i	0.579221	−	0.698567i
$595$		0			0
$596$			14.2063i			0.581911i
$597$	−31.3793	−	7.37228i	−1.28427	−	0.301727i
$598$	−7.57301	−	4.37228i	−0.309684	−	0.178796i
$599$	−7.37228	−	4.25639i	−0.301223	−	0.173911i	0.341769	−	0.939784i	$-0.388974\pi$
$599$	−7.37228	−	4.25639i	−0.301223	−	0.173911i	−0.642992	+	0.765873i	$0.722307\pi$
$600$		0			0
$601$			10.5947i			0.432166i	0.976375	+	0.216083i	$0.0693282\pi$
$601$			10.5947i			0.432166i	−0.976375	+	0.216083i	$0.930672\pi$
$602$	22.0742	+	19.1168i	0.899678	+	0.779144i
$603$	1.40965	+	22.6753i	0.0574052	+	0.923408i
$604$	−4.05842	−	7.02939i	−0.165135	−	0.286022i
$605$		0			0
$606$	−8.18614	−	27.1504i	−0.332539	−	1.10291i
$607$	−23.7874	+	13.7337i	−0.965503	+	0.557433i	−0.897862	−	0.440277i	$-0.854880\pi$
$607$	−23.7874	+	13.7337i	−0.965503	+	0.557433i	−0.0676404	+	0.997710i	$0.521547\pi$
$608$	−3.46410			−0.140488
$609$	−12.3139	+	8.90892i	−0.498983	+	0.361008i
$610$		0			0
$611$	3.25544	−	1.87953i	0.131701	−	0.0760375i
$612$	17.8178	+	8.86141i	0.720244	+	0.358201i
$613$	6.48577	−	11.2337i	0.261958	−	0.453724i	−0.704804	−	0.709402i	$-0.748965\pi$
$613$	6.48577	−	11.2337i	0.261958	−	0.453724i	0.966762	+	0.255677i	$0.0822985\pi$
$614$	−3.44158	−	5.96099i	−0.138891	−	0.240566i
$615$		0			0
$616$	11.0584	+	2.12819i	0.445557	+	0.0857474i
$617$		−	1.02175i		−	0.0411341i	−0.999788	−	0.0205670i	$-0.993453\pi$
$617$		−	1.02175i		−	0.0411341i	0.999788	−	0.0205670i	$-0.00654715\pi$
$618$	−5.98844	+	25.4891i	−0.240890	+	1.02532i
$619$	−20.2337	−	11.6819i	−0.813261	−	0.469536i	0.0348263	−	0.999393i	$-0.488912\pi$
$619$	−20.2337	−	11.6819i	−0.813261	−	0.469536i	−0.848087	+	0.529857i	$0.822246\pi$
$620$		0			0
$621$	3.81386	−	22.3966i	0.153045	−	0.898746i
$622$		−	14.2337i		−	0.570719i
$623$	7.57301	−	8.74456i	0.303406	−	0.350344i
$624$	−2.37228	+	2.52434i	−0.0949673	+	0.101054i
$625$		0			0
$626$	−7.05842	+	12.2255i	−0.282111	+	0.488631i
$627$	24.4511	−	7.37228i	0.976483	−	0.294421i
$628$	6.92820	−	4.00000i	0.276465	−	0.159617i
$629$	77.4891			3.08969
$630$		0			0
$631$	30.1168			1.19893			0.599466	−	0.800400i	$-0.295380\pi$
$631$	30.1168			1.19893			0.599466	+	0.800400i	$0.295380\pi$
$632$	−7.02939	+	4.05842i	−0.279614	+	0.161435i
$633$	30.2372	−	9.11684i	1.20182	−	0.362362i
$634$	8.05842	−	13.9576i	0.320041	−	0.554327i
$635$		0			0
$636$	−1.62772	+	1.73205i	−0.0645432	+	0.0686803i
$637$	−8.66025	−	11.0000i	−0.343132	−	0.435836i
$638$		−	14.1168i		−	0.558891i
$639$	3.11684	+	4.69882i	0.123300	+	0.185882i
$640$		0			0
$641$	−12.3030	−	7.10313i	−0.485939	−	0.280557i	0.236949	−	0.971522i	$-0.423852\pi$
$641$	−12.3030	−	7.10313i	−0.485939	−	0.280557i	−0.722888	+	0.690965i	$0.757186\pi$
$642$	−7.02939	+	29.9198i	−0.277428	+	1.18084i
$643$			16.2337i			0.640194i	0.947385	+	0.320097i	$0.103716\pi$
$643$			16.2337i			0.640194i	−0.947385	+	0.320097i	$0.896284\pi$
$644$	10.9307	−	3.78651i	0.430730	−	0.149209i
$645$		0			0
$646$	11.4891	+	19.8997i	0.452034	+	0.782945i
$647$	−12.7417	+	22.0693i	−0.500928	+	0.867634i	0.499071	+	0.866561i	$0.333675\pi$
$647$	−12.7417	+	22.0693i	−0.500928	+	0.867634i	−0.999999	+	0.00107245i	$0.999659\pi$
$648$	−8.29156	−	3.50000i	−0.325723	−	0.137493i
$649$	−15.1753	+	8.76144i	−0.595681	+	0.343917i
$650$		0			0
$651$	−1.11684	−	10.8347i	−0.0437726	−	0.424647i
$652$	−3.46410			−0.135665
$653$	9.20387	−	5.31386i	0.360175	−	0.207947i	−0.308982	−	0.951068i	$-0.599988\pi$
$653$	9.20387	−	5.31386i	0.360175	−	0.207947i	0.669158	+	0.743120i	$0.266655\pi$
$654$	4.55842	+	15.1186i	0.178248	+	0.591183i
$655$		0			0
$656$	0.813859	+	1.40965i	0.0317759	+	0.0550374i
$657$	−5.98844	+	0.372281i	−0.233631	+	0.0145241i
$658$	−0.939764	+	4.88316i	−0.0366358	+	0.190365i
$659$		−	36.9253i		−	1.43841i	−0.694800	−	0.719203i	$-0.744507\pi$
$659$		−	36.9253i		−	1.43841i	0.694800	−	0.719203i	$-0.255493\pi$
$660$		0			0
$661$	2.44158	+	1.40965i	0.0949664	+	0.0548289i	0.546731	−	0.837308i	$-0.315872\pi$
$661$	2.44158	+	1.40965i	0.0949664	+	0.0548289i	−0.451765	+	0.892137i	$0.649205\pi$
$662$	−8.86263	−	5.11684i	−0.344456	−	0.198872i
$663$	22.3692	+	5.25544i	0.868747	+	0.204104i
$664$			1.43710i			0.0557702i
$665$		0			0
$666$	−34.9783	+	2.17448i	−1.35538	+	0.0842594i
$667$	−7.25061	−	12.5584i	−0.280745	−	0.486264i
$668$	−5.66603	+	9.81386i	−0.219225	+	0.379710i
$669$	−9.05842	−	30.0434i	−0.350219	−	1.16154i
$670$		0			0
$671$	12.0000			0.463255
$672$	−0.469882	−	4.55842i	−0.0181261	−	0.175845i
$673$	−17.1181			−0.659855			−0.329928	−	0.944006i	$-0.607024\pi$
$673$	−17.1181			−0.659855			−0.329928	+	0.944006i	$0.607024\pi$
$674$	8.05842	−	4.65253i	0.310399	−	0.179209i
$675$		0			0
$676$	4.50000	−	7.79423i	0.173077	−	0.299778i
$677$	−22.4704	−	38.9198i	−0.863607	−	1.49581i	−0.868424	−	0.495822i	$-0.834867\pi$
$677$	−22.4704	−	38.9198i	−0.863607	−	1.49581i	0.00481749	−	0.999988i	$-0.498467\pi$
$678$	−4.10891	−	3.86141i	−0.157802	−	0.148296i
$679$	5.29211	−	1.83324i	0.203093	−	0.0703533i
$680$		0			0
$681$	−6.19702	+	26.3769i	−0.237470	+	1.01077i
$682$	8.76144	+	5.05842i	0.335493	+	0.193697i
$683$	−12.1055	−	6.98913i	−0.463205	−	0.267431i	0.250186	−	0.968198i	$-0.419508\pi$
$683$	−12.1055	−	6.98913i	−0.463205	−	0.267431i	−0.713391	+	0.700766i	$0.752842\pi$
$684$	−5.74456	−	8.66025i	−0.219649	−	0.331133i
$685$		0			0
$686$	18.5000	+	0.866025i	0.706333	+	0.0330650i
$687$	16.4356	−	17.4891i	0.627059	−	0.667252i
$688$	5.51856	+	9.55842i	0.210393	+	0.364411i
$689$	−1.37228	+	2.37686i	−0.0522798	+	0.0905512i
$690$		0			0
$691$	−26.2337	+	15.1460i	−0.997977	+	0.576182i	−0.907649	−	0.419730i	$-0.862125\pi$
$691$	−26.2337	+	15.1460i	−0.997977	+	0.576182i	−0.0903276	+	0.995912i	$0.528791\pi$
$692$	−3.75906			−0.142898
$693$	13.0178	+	31.1753i	0.494507	+	1.18425i
$694$	−19.1168			−0.725665
$695$		0			0
$696$	−5.50000	+	1.65831i	−0.208477	+	0.0628582i
$697$	5.39853	−	9.35053i	0.204484	−	0.354177i
$698$	12.0043	+	20.7921i	0.454371	+	0.786993i
$699$	−27.8614	+	29.6472i	−1.05382	+	1.12136i
$700$		0			0
$701$			12.7143i			0.480211i	0.970747	+	0.240106i	$0.0771821\pi$
$701$			12.7143i			0.480211i	−0.970747	+	0.240106i	$0.922818\pi$
$702$	−10.2448	−	1.74456i	−0.386666	−	0.0658443i
$703$	−35.0458	−	20.2337i	−1.32178	−	0.763128i
$704$	3.68614	+	2.12819i	0.138927	+	0.0802093i
$705$		0			0
$706$			18.9051i			0.711502i
$707$	42.5364	+	8.18614i	1.59975	+	0.307872i
$708$	5.19615	+	4.88316i	0.195283	+	0.183520i
$709$	−2.55842	−	4.43132i	−0.0960836	−	0.166422i	0.813977	−	0.580897i	$-0.197298\pi$
$709$	−2.55842	−	4.43132i	−0.0960836	−	0.166422i	−0.910060	+	0.414476i	$0.863965\pi$
$710$		0			0
$711$	−21.8030	−	10.8434i	−0.817676	−	0.406657i
$712$	3.78651	−	2.18614i	0.141905	−	0.0819291i
$713$	10.3923			0.389195
$714$	−24.6277	+	17.8178i	−0.921669	+	0.666816i
$715$		0			0
$716$	−2.48913	+	1.43710i	−0.0930230	+	0.0537068i
$717$	−1.43710	−	4.76631i	−0.0536694	−	0.178001i
$718$	7.07568	−	12.2554i	0.264062	−	0.457369i
$719$	16.6277	+	28.8001i	0.620109	+	1.07406i	0.989465	+	0.144773i	$0.0462451\pi$
$719$	16.6277	+	28.8001i	0.620109	+	1.07406i	−0.369356	+	0.929288i	$0.620422\pi$
$720$		0			0
$721$	−30.2337	−	26.1831i	−1.12596	−	0.975111i
$722$			7.00000i			0.260513i
$723$	−17.8641	−	4.19702i	−0.664374	−	0.156089i
$724$	−15.5584	−	8.98266i	−0.578224	−	0.333838i
$725$		0			0
$726$	−12.0000	−	2.81929i	−0.445362	−	0.104634i
$727$			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
$731$	36.6060	−	63.4034i	1.35392	−	2.34506i
$732$	−1.40965	−	4.67527i	−0.0521020	−	0.172803i
$733$	31.5817	−	18.2337i	1.16650	−	0.673477i	0.213644	−	0.976912i	$-0.431467\pi$
$733$	31.5817	−	18.2337i	1.16650	−	0.673477i	0.952852	+	0.303435i	$0.0981335\pi$
$734$	−21.2337			−0.783750
$735$		0			0
$736$	4.37228			0.161164
$737$	27.9152	−	16.1168i	1.02827	−	0.593672i
$738$	−2.17448	+	4.37228i	−0.0800438	+	0.160946i
$739$	−18.1168	+	31.3793i	−0.666439	+	1.15431i	0.312454	+	0.949933i	$0.398849\pi$
$739$	−18.1168	+	31.3793i	−0.666439	+	1.15431i	−0.978893	+	0.204373i	$0.934484\pi$
$740$		0			0
$741$	−8.74456	−	8.21782i	−0.321240	−	0.301889i
$742$	−1.18843	−	3.43070i	−0.0436287	−	0.125945i
$743$			18.6060i			0.682587i	0.939957	+	0.341293i	$0.110865\pi$
$743$			18.6060i			0.682587i	−0.939957	+	0.341293i	$0.889135\pi$
$744$	0.941578	−	4.00772i	0.0345199	−	0.146930i
$745$		0			0
$746$	−14.2337	−	8.21782i	−0.521132	−	0.300876i
$747$	−3.59274	+	2.38316i	−0.131452	+	0.0871951i
$748$		−	28.2337i		−	1.03233i
$749$	−35.4891	−	30.7345i	−1.29674	−	1.12301i
$750$		0			0
$751$	−21.0584	−	36.4743i	−0.768433	−	1.33096i	−0.938412	−	0.345517i	$-0.887704\pi$
$751$	−21.0584	−	36.4743i	−0.768433	−	1.33096i	0.169980	−	0.985448i	$-0.445630\pi$
$752$	−0.939764	+	1.62772i	−0.0342697	+	0.0593568i
$753$	26.7268	−	8.05842i	0.973977	−	0.293665i
$754$	−5.74456	+	3.31662i	−0.209205	+	0.120784i
$755$		0			0
$756$	10.6168	−	8.73399i	0.386131	−	0.317652i
$757$	5.63858			0.204938			0.102469	−	0.994736i	$-0.467326\pi$
$757$	5.63858			0.204938			0.102469	+	0.994736i	$0.467326\pi$
$758$	−19.2549	+	11.1168i	−0.699371	+	0.403782i
$759$	−30.8614	+	9.30506i	−1.12020	+	0.337752i
$760$		0			0
$761$	−26.4891	−	45.8805i	−0.960230	−	1.66317i	−0.721918	−	0.691979i	$-0.756739\pi$
$761$	−26.4891	−	45.8805i	−0.960230	−	1.66317i	−0.238312	−	0.971189i	$-0.576594\pi$
$762$	−2.81929	+	3.00000i	−0.102132	+	0.108679i
$763$	−23.6863	−	4.55842i	−0.857500	−	0.165026i
$764$			3.75906i			0.135998i
$765$		0			0
$766$	−18.0475	−	10.4198i	−0.652084	−	0.376481i
$767$	7.13058	+	4.11684i	0.257470	+	0.148651i
$768$	0.396143	−	1.68614i	0.0142946	−	0.0608434i
$769$		−	40.4820i		−	1.45982i	−0.683545	−	0.729909i	$-0.739563\pi$
$769$		−	40.4820i		−	1.45982i	0.683545	−	0.729909i	$-0.260437\pi$
$770$		0			0
$771$	−10.7446	−	10.0974i	−0.386956	−	0.363647i
$772$	−4.00772	−	6.94158i	−0.144241	−	0.249833i
$773$	0.939764	−	1.62772i	0.0338010	−	0.0585450i	−0.848630	−	0.528987i	$-0.822572\pi$
$773$	0.939764	−	1.62772i	0.0338010	−	0.0585450i	0.882431	+	0.470442i	$0.155905\pi$
$774$	−14.7446	+	29.6472i	−0.529982	+	1.06565i
$775$		0			0
$776$	2.11684			0.0759903
$777$	21.8719	−	48.8614i	0.784648	−	1.75289i
$778$	−34.0511			−1.22079
$779$	−4.88316	+	2.81929i	−0.174957	+	0.101012i
$780$		0			0
$781$	4.00000	−	6.92820i	0.143131	−	0.247911i
$782$	−14.5012	−	25.1168i	−0.518562	−	0.898177i
$783$	−13.2665	−	11.0000i	−0.474106	−	0.393108i
$784$	6.50000	+	2.59808i	0.232143	+	0.0927884i
$785$		0			0
$786$	7.80298	+	1.83324i	0.278323	+	0.0653895i
$787$	23.4839	+	13.5584i	0.837110	+	0.483306i	0.856281	−	0.516511i	$-0.172769\pi$
$787$	23.4839	+	13.5584i	0.837110	+	0.483306i	−0.0191710	+	0.999816i	$0.506103\pi$
$788$	−17.5229	−	10.1168i	−0.624227	−	0.360398i
$789$	−2.74456	−	0.644810i	−0.0977090	−	0.0229558i
$790$		0			0
$791$	8.13859	−	2.81929i	0.289375	−	0.100242i
$792$	0.792287	+	12.7446i	0.0281527	+	0.452858i
$793$	−2.81929	−	4.88316i	−0.100116	−	0.173406i
$794$	−4.00000	+	6.92820i	−0.141955	+	0.245873i
$795$		0			0
$796$	16.1168	−	9.30506i	0.571246	−	0.329809i
$797$	4.25639			0.150769			0.0753845	−	0.997155i	$-0.475982\pi$
$797$	4.25639			0.150769			0.0753845	+	0.997155i	$0.475982\pi$
$798$	15.7908	−	1.62772i	0.558990	−	0.0576206i
$799$	12.4674			0.441064
$800$		0			0
$801$	11.7446	+	5.84096i	0.414974	+	0.206380i
$802$	9.92242	−	17.1861i	0.350373	−	0.606864i
$803$	4.25639	+	7.37228i	0.150205	+	0.260162i
$804$	−9.55842	−	8.98266i	−0.337100	−	0.316794i
$805$		0			0
$806$		−	4.75372i		−	0.167443i
$807$	−7.91425	+	33.6861i	−0.278595	+	1.18581i
$808$	14.1788	+	8.18614i	0.498809	+	0.287987i
$809$	22.0693	+	12.7417i	0.775915	+	0.447975i	0.834981	−	0.550279i	$-0.185479\pi$
$809$	22.0693	+	12.7417i	0.775915	+	0.447975i	−0.0590655	+	0.998254i	$0.518812\pi$
$810$		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
$813$	24.8935	−	26.4891i	0.873054	−	0.929014i
$814$	24.8614	+	43.0612i	0.871392	+	1.50929i
$815$		0			0
$816$	−11.0000	+	3.31662i	−0.385077	+	0.116105i
$817$	−33.1113	+	19.1168i	−1.15842	+	0.668814i
$818$	35.4882			1.24082
$819$	9.62772	−	12.6217i	0.336420	−	0.441038i
$820$		0			0
$821$	−18.4307	+	10.6410i	−0.643236	+	0.371372i	−0.785860	−	0.618404i	$-0.787779\pi$
$821$	−18.4307	+	10.6410i	−0.643236	+	0.371372i	0.142624	+	0.989777i	$0.454446\pi$
$822$	4.55134	−	1.37228i	0.158746	−	0.0478638i
$823$	−21.7518	+	37.6753i	−0.758221	+	1.31328i	0.185536	+	0.982637i	$0.440598\pi$
$823$	−21.7518	+	37.6753i	−0.758221	+	1.31328i	−0.943757	+	0.330640i	$0.892735\pi$
$824$	−7.55842	−	13.0916i	−0.263310	−	0.456066i
$825$		0			0
$826$	−10.2921	+	3.56529i	−0.358108	+	0.124052i
$827$			33.0000i			1.14752i	0.819023	+	0.573761i	$0.194516\pi$
$827$			33.0000i			1.14752i	−0.819023	+	0.573761i	$0.805484\pi$
$828$	7.25061	+	10.9307i	0.251976	+	0.379868i
$829$	16.1168	+	9.30506i	0.559761	+	0.323178i	0.753050	−	0.657964i	$-0.228582\pi$
$829$	16.1168	+	9.30506i	0.559761	+	0.323178i	−0.193288	+	0.981142i	$0.561915\pi$
$830$		0			0
$831$	−11.4891	+	48.9022i	−0.398553	+	1.69640i
$832$		−	2.00000i		−	0.0693375i
$833$	−6.63325	−	45.9565i	−0.229828	−	1.59230i
$834$	14.7446	+	13.8564i	0.510562	+	0.479808i
$835$		0			0
$836$	−7.37228	+	12.7692i	−0.254976	+	0.441631i
$837$	11.5807	−	4.29211i	0.400289	−	0.148357i
$838$	−25.5383	+	14.7446i	−0.882207	+	0.509342i
$839$	1.72281			0.0594781			0.0297391	−	0.999558i	$-0.490532\pi$
$839$	1.72281			0.0594781			0.0297391	+	0.999558i	$0.490532\pi$
$840$		0			0
$841$	18.0000			0.620690
$842$	13.0916	−	7.55842i	0.451165	−	0.260480i
$843$	−10.8896	−	36.1168i	−0.375059	−	1.24393i
$844$	−9.11684	+	15.7908i	−0.313815	+	0.543543i
$845$		0			0
$846$	−5.62772	+	0.349857i	−0.193485	+	0.0120283i
$847$	12.3267	−	14.2337i	0.423552	−	0.489075i
$848$		−	1.37228i		−	0.0471243i
$849$	−26.9783	−	6.33830i	−0.925891	−	0.217530i
$850$		0			0
$851$	44.2337	+	25.5383i	1.51631	+	0.875443i
$852$	−3.16915	−	0.744563i	−0.108573	−	0.0255083i
$853$			30.4674i			1.04318i	0.853195	+	0.521592i	$0.174661\pi$
$853$			30.4674i			1.04318i	−0.853195	+	0.521592i	$0.825339\pi$
$854$	7.32473	+	1.40965i	0.250647	+	0.0482371i
$855$		0			0
$856$	−8.87228	−	15.3672i	−0.303248	−	0.525242i
$857$	−18.9051	+	32.7446i	−0.645785	+	1.11853i	0.338334	+	0.941026i	$0.390137\pi$
$857$	−18.9051	+	32.7446i	−0.645785	+	1.11853i	−0.984120	+	0.177507i	$0.943197\pi$
$858$	4.25639	+	14.1168i	0.145311	+	0.481941i
$859$	−28.4674	+	16.4356i	−0.971294	+	0.560777i	−0.899631	−	0.436652i	$-0.856164\pi$
$859$	−28.4674	+	16.4356i	−0.971294	+	0.560777i	−0.0716637	+	0.997429i	$0.522831\pi$
$860$		0			0
$861$	−4.37228	−	6.04334i	−0.149007	−	0.205957i
$862$	3.75906			0.128034
$863$	−6.60580	+	3.81386i	−0.224864	+	0.129825i	−0.608200	−	0.793783i	$-0.708108\pi$
$863$	−6.60580	+	3.81386i	−0.224864	+	0.129825i	0.383336	+	0.923609i	$0.374775\pi$
$864$	4.87228	−	1.80579i	0.165758	−	0.0614342i
$865$		0			0
$866$	−17.0000	−	29.4449i	−0.577684	−	1.00058i
$867$	34.0786	+	32.0258i	1.15737	+	1.08765i
$868$	4.75372	+	4.11684i	0.161352	+	0.139735i
$869$			34.5484i			1.17198i
$870$		0			0
$871$	−13.1168	−	7.57301i	−0.444447	−	0.256602i
$872$	−7.89542	−	4.55842i	−0.267373	−	0.154368i
$873$	3.51039	+	5.29211i	0.118809	+	0.179111i
$874$			15.1460i			0.512322i
$875$		0			0
$876$	2.37228	−	2.52434i	0.0801520	−	0.0852895i
$877$	15.7908	+	27.3505i	0.533219	+	0.923562i	0.999247	+	0.0387922i	$0.0123510\pi$
$877$	15.7908	+	27.3505i	0.533219	+	0.923562i	−0.466029	+	0.884770i	$0.654316\pi$
$878$	6.38458	−	11.0584i	0.215469	−	0.373204i
$879$	41.5258	−	12.5205i	1.40063	−	0.422306i
$880$		0			0
$881$	51.3505			1.73004			0.865022	−	0.501734i	$-0.167305\pi$
$881$	51.3505			1.73004			0.865022	+	0.501734i	$0.167305\pi$
$882$	4.28384	+	20.5584i	0.144244	+	0.692238i
$883$	54.9455			1.84906			0.924532	−	0.381104i	$-0.124456\pi$
$883$	54.9455			1.84906			0.924532	+	0.381104i	$0.124456\pi$
$884$	−11.4891	+	6.63325i	−0.386421	+	0.223100i
$885$		0			0
$886$	−4.50000	+	7.79423i	−0.151180	+	0.261852i
$887$	−27.4453	−	47.5367i	−0.921523	−	1.59613i	−0.797059	−	0.603901i	$-0.793612\pi$
$887$	−27.4453	−	47.5367i	−0.921523	−	1.59613i	−0.124464	−	0.992224i	$-0.539721\pi$
$888$	13.8564	−	14.7446i	0.464991	−	0.494795i
$889$	−2.05842	−	5.94215i	−0.0690373	−	0.199293i
$890$		0			0
$891$	−30.5475	+	23.1152i	−1.02338	+	0.774388i
$892$	15.6896	+	9.05842i	0.525328	+	0.303298i
$893$	−5.63858	−	3.25544i	−0.188688	−	0.108939i
$894$	5.62772	−	23.9538i	0.188219	−	0.801133i
$895$		0			0
$896$	2.00000	+	1.73205i	0.0668153	+	0.0578638i
$897$	11.0371	+	10.3723i	0.368519	+	0.346320i
$898$	17.9928	+	31.1644i	0.600427	+	1.03997i
$899$	3.94158	−	6.82701i	0.131459	−	0.227694i
$900$		0			0
$901$	−7.88316	+	4.55134i	−0.262626	+	0.151627i
$902$	6.92820			0.230684
$903$	−29.6472	−	40.9783i	−0.986598	−	1.36367i
$904$	3.25544			0.108274
$905$		0			0
$906$	4.05842	+	13.4603i	0.134832	+	0.447187i
$907$	−22.3966	+	38.7921i	−0.743668	+	1.28807i	0.207146	+	0.978310i	$0.433582\pi$
$907$	−22.3966	+	38.7921i	−0.743668	+	1.28807i	−0.950814	+	0.309761i	$0.899751\pi$
$908$	−7.82168	−	13.5475i	−0.259572	−	0.449591i
$909$	3.04755	+	49.0222i	0.101081	+	1.62596i
$910$		0			0
$911$		−	24.5437i		−	0.813168i	−0.913613	−	0.406584i	$-0.866720\pi$
$911$		−	24.5437i		−	0.813168i	0.913613	−	0.406584i	$-0.133280\pi$
$912$	5.84096	+	1.37228i	0.193414	+	0.0454408i
$913$	5.29734	+	3.05842i	0.175316	+	0.101219i
$914$	−11.0584	−	6.38458i	−0.365780	−	0.211183i
$915$		0			0
$916$			13.8564i			0.457829i
$917$	−8.01544	+	9.25544i	−0.264693	+	0.305641i
$918$	−26.5330	−	22.0000i	−0.875719	−	0.726108i
$919$	−9.11684	−	15.7908i	−0.300737	−	0.520892i	0.675566	−	0.737299i	$-0.263899\pi$
$919$	−9.11684	−	15.7908i	−0.300737	−	0.520892i	−0.976303	+	0.216408i	$0.930566\pi$
$920$		0			0
$921$	3.44158	+	11.4144i	0.113404	+	0.376118i
$922$	0.442430	−	0.255437i	0.0145707	−	0.00841238i
$923$	−3.75906			−0.123731
$924$	−17.8030	−	7.96916i	−0.585675	−	0.262166i
$925$		0			0
$926$	31.6753	−	18.2877i	1.04091	−	0.600972i
$927$	20.1947	−	40.6060i	0.663281	−	1.33368i
$928$	1.65831	−	2.87228i	0.0544368	−	0.0942873i
$929$	−8.44158	−	14.6212i	−0.276959	−	0.479707i	0.693668	−	0.720295i	$-0.255993\pi$
$929$	−8.44158	−	14.6212i	−0.276959	−	0.479707i	−0.970628	+	0.240587i	$0.922660\pi$
$930$		0			0
$931$	−9.00000	+	22.5167i	−0.294963	+	0.737954i
$932$		−	23.4891i		−	0.769412i
$933$	−5.63858	+	24.0000i	−0.184599	+	0.785725i
$934$	0.0475473	+	0.0274514i	0.00155579	+	0.000898238i
$935$		0			0
$936$	5.00000	−	3.31662i	0.163430	−	0.108407i
$937$		−	50.3505i		−	1.64488i	−0.568852	−	0.822440i	$-0.692612\pi$
$937$		−	50.3505i		−	1.64488i	0.568852	−	0.822440i	$-0.307388\pi$
$938$	18.9325	−	6.55842i	0.618169	−	0.214140i
$939$	16.7446	−	17.8178i	0.546438	−	0.581463i
$940$		0			0
$941$	−12.1753	+	21.0882i	−0.396902	+	0.687455i	−0.993342	−	0.115203i	$-0.963248\pi$
$941$	−12.1753	+	21.0882i	−0.396902	+	0.687455i	0.596440	+	0.802658i	$0.296582\pi$
$942$	−13.2665	+	4.00000i	−0.432246	+	0.130327i
$943$	6.16337	−	3.55842i	0.200707	−	0.115878i
$944$	−4.11684			−0.133992
$945$		0			0
$946$	46.9783			1.52739
$947$	37.3403	−	21.5584i	1.21340	−	0.700555i	0.249899	−	0.968272i	$-0.419603\pi$
$947$	37.3403	−	21.5584i	1.21340	−	0.700555i	0.963497	+	0.267717i	$0.0862694\pi$
$948$	13.4603	−	4.05842i	0.437169	−	0.131811i
$949$	2.00000	−	3.46410i	0.0649227	−	0.112449i
$950$		0			0
$951$	−19.1168	+	20.3422i	−0.619906	+	0.659640i
$952$	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	$0.716520\pi$
$954$	3.43070	−	2.27567i	0.111073	−	0.0736776i
$955$		0			0
$956$	2.48913	+	1.43710i	0.0805041	+	0.0464790i
$957$	−5.59230	+	23.8030i	−0.180773	+	0.769441i
$958$			8.74456i			0.282524i
$959$	−1.37228	+	7.13058i	−0.0443133	+	0.230259i
$960$		0			0
$961$	−12.6753	−	21.9542i	−0.408880	−	0.708200i
$962$	11.6819	−	20.2337i	0.376640	−	0.652360i
$963$	23.7051	−	47.6644i	0.763886	−	1.53596i
$964$	9.17527	−	5.29734i	0.295515	−	0.170616i
$965$		0			0
$966$	−19.9307	+	2.05446i	−0.641260	+	0.0661010i
$967$	51.9239			1.66976			0.834879	−	0.550433i	$-0.185537\pi$
$967$	51.9239			1.66976			0.834879	+	0.550433i	$0.185537\pi$
$968$	6.16337	−	3.55842i	0.198098	−	0.114372i
$969$	−11.4891	−	38.1051i	−0.369084	−	1.22411i
$970$		0			0
$971$	14.3139	+	24.7923i	0.459354	+	0.795624i	0.998927	−	0.0463149i	$-0.0147478\pi$
$971$	14.3139	+	24.7923i	0.459354	+	0.795624i	−0.539573	+	0.841939i	$0.681414\pi$
$972$	12.5942	+	9.18614i	0.403960	+	0.294646i
$973$	−29.2048	+	10.1168i	−0.936263	+	0.324331i
$974$		−	4.55134i		−	0.145834i
$975$		0			0
$976$	2.44158	+	1.40965i	0.0781530	+	0.0451217i
$977$	35.0458	+	20.2337i	1.12121	+	0.647333i	0.941710	−	0.336424i	$-0.109218\pi$
$977$	35.0458	+	20.2337i	1.12121	+	0.647333i	0.179503	+	0.983757i	$0.442551\pi$
$978$	5.84096	+	1.37228i	0.186773	+	0.0438807i
$979$		−	18.6101i		−	0.594782i
$980$		0			0
$981$	−1.69702	−	27.2978i	−0.0541815	−	0.871553i
$982$	−13.4603	−	23.3139i	−0.429534	−	0.743975i
$983$	−10.8622	+	18.8139i	−0.346450	+	0.600069i	−0.985616	−	0.169000i	$-0.945946\pi$
$983$	−10.8622	+	18.8139i	−0.346450	+	0.600069i	0.639166	+	0.769069i	$0.279280\pi$
$984$	−0.813859	−	2.69927i	−0.0259449	−	0.0860495i
$985$		0			0
$986$	−22.0000			−0.700623
$987$	3.51900	−	7.86141i	0.112011	−	0.250231i
$988$	6.92820			0.220416
$989$	41.7921	−	24.1287i	1.32891	−	0.767248i
$990$		0			0
$991$	14.1753	−	24.5523i	0.450292	−	0.779929i	−0.548112	−	0.836405i	$-0.684653\pi$
$991$	14.1753	−	24.5523i	0.450292	−	0.779929i	0.998404	+	0.0564762i	$0.0179865\pi$
$992$	1.18843	+	2.05842i	0.0377327	+	0.0653550i
$993$	12.9166	+	12.1386i	0.409897	+	0.385207i
$994$	3.25544	−	3.75906i	0.103256	−	0.119230i
$995$		0			0
$996$	0.569297	−	2.42315i	0.0180389	−	0.0767804i
$997$	26.3855	+	15.2337i	0.835638	+	0.482456i	0.855779	−	0.517341i	$-0.173078\pi$
$997$	26.3855	+	15.2337i	0.835638	+	0.482456i	−0.0201413	+	0.999797i	$0.506412\pi$
$998$	24.4511	+	14.1168i	0.773986	+	0.446861i
$999$	59.8397	+	10.1899i	1.89324	+	0.322395i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.t.a.59.1	✓	4	5.3	odd	4
210.2.t.a.89.2	yes	4	105.47	odd	12
210.2.t.b.59.1	yes	4	15.2	even	4
210.2.t.b.89.1	yes	4	35.33	even	12
210.2.t.c.59.2	yes	4	15.8	even	4
210.2.t.c.89.2	yes	4	35.12	even	12
210.2.t.d.59.2	yes	4	5.2	odd	4
210.2.t.d.89.1	yes	4	105.68	odd	12
1050.2.s.d.101.1		8	3.2	odd	2
1050.2.s.d.101.4		8	15.14	odd	2
1050.2.s.d.551.1		8	7.5	odd	6
1050.2.s.d.551.4		8	35.19	odd	6
1050.2.s.e.101.2		8	5.4	even	2	inner
1050.2.s.e.101.3		8	1.1	even	1	trivial
1050.2.s.e.551.2		8	105.89	even	6	inner
1050.2.s.e.551.3		8	21.5	even	6	inner
1470.2.d.a.1469.3		4	35.32	odd	12
1470.2.d.a.1469.4		4	105.38	odd	12
1470.2.d.b.1469.1		4	105.53	even	12
1470.2.d.b.1469.2		4	35.17	even	12
1470.2.d.c.1469.3		4	35.3	even	12
1470.2.d.c.1469.4		4	105.32	even	12
1470.2.d.d.1469.1		4	105.17	odd	12
1470.2.d.d.1469.2		4	35.18	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} +(-1.18614 + 1.26217i) q^{6} +(-0.866025 - 2.50000i) q^{7} -1.00000i q^{8} +(2.50000 - 1.65831i) q^{9} +(-3.68614 - 2.12819i) q^{11} +(-0.396143 + 1.68614i) q^{12} +2.00000i q^{13} +(-2.00000 - 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.31662 + 5.74456i) q^{17} +(1.33591 - 2.68614i) q^{18} +(3.00000 - 1.73205i) q^{19} +(2.68614 + 3.71277i) q^{21} -4.25639 q^{22} +(-3.78651 + 2.18614i) 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} +(-2.05842 - 1.18843i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(7.17687 + 1.68614i) q^{33} +6.63325i q^{34} +(-0.186141 - 2.99422i) q^{36} +(-5.84096 - 10.1168i) q^{37} +(1.73205 - 3.00000i) q^{38} +(-1.00000 - 3.31662i) q^{39} -1.62772 q^{41} +(4.18265 + 1.87228i) q^{42} -11.0371 q^{43} +(-3.68614 + 2.12819i) q^{44} +(-2.18614 + 3.78651i) q^{46} +(-0.939764 - 1.62772i) q^{47} +(1.26217 + 1.18614i) q^{48} +(-5.50000 + 4.33013i) q^{49} +(2.62772 - 11.1846i) q^{51} +(1.73205 + 1.00000i) q^{52} +(1.18843 + 0.686141i) q^{53} +(-0.872281 + 5.12241i) q^{54} +(-2.50000 + 0.866025i) q^{56} +(-4.10891 + 4.37228i) q^{57} +(1.65831 + 2.87228i) q^{58} +(2.05842 - 3.56529i) q^{59} +(-2.44158 + 1.40965i) q^{61} -2.37686 q^{62} +(-6.31084 - 4.81386i) q^{63} -1.00000 q^{64} +(7.05842 - 2.12819i) q^{66} +(-3.78651 + 6.55842i) q^{67} +(3.31662 + 5.74456i) q^{68} +(5.18614 - 5.51856i) q^{69} +1.87953i q^{71} +(-1.65831 - 2.50000i) q^{72} +(-1.73205 - 1.00000i) q^{73} +(-10.1168 - 5.84096i) q^{74} -3.46410i q^{76} +(-2.12819 + 11.0584i) q^{77} +(-2.52434 - 2.37228i) q^{78} +(-4.05842 - 7.02939i) q^{79} +(3.50000 - 8.29156i) q^{81} +(-1.40965 + 0.813859i) q^{82} -1.43710 q^{83} +(4.55842 - 0.469882i) q^{84} +(-9.55842 + 5.51856i) q^{86} +(-1.65831 - 5.50000i) q^{87} +(-2.12819 + 3.68614i) q^{88} +(2.18614 + 3.78651i) q^{89} +(5.00000 - 1.73205i) q^{91} +4.37228i q^{92} +(4.00772 + 0.941578i) q^{93} +(-1.62772 - 0.939764i) q^{94} +(1.68614 + 0.396143i) q^{96} +2.11684i q^{97} +(-2.59808 + 6.50000i) q^{98} +(-12.7446 + 0.792287i) 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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