LMFDB - Embedded newform 240.2.bl.a.229.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(109,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0, 2]))

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

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

chi := DirichletCharacter("240.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.bl (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.91640964851$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			229.4
Character	$\chi$	$=$	240.229
Dual form			240.2.bl.a.109.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22294 + 0.710230i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(0.991146 - 1.73713i) q^{4} +(-2.15195 + 0.607542i) q^{5} +(1.36696 + 0.362538i) q^{6} +2.25286 q^{7} +(0.0216568 + 2.82834i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(-1.22294 + 0.710230i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(0.991146 - 1.73713i) q^{4} +(-2.15195 + 0.607542i) q^{5} +(1.36696 + 0.362538i) q^{6} +2.25286 q^{7} +(0.0216568 + 2.82834i) q^{8} +1.00000i q^{9} +(2.20020 - 2.27137i) q^{10} +(-1.66088 - 1.66088i) q^{11} +(-1.92918 + 0.527493i) q^{12} +(-4.76925 - 4.76925i) q^{13} +(-2.75511 + 1.60005i) q^{14} +(1.95126 + 1.09206i) q^{15} +(-2.03526 - 3.44350i) q^{16} -6.99777i q^{17} +(-0.710230 - 1.22294i) q^{18} +(-2.66634 + 2.66634i) q^{19} +(-1.07751 + 4.34039i) q^{20} +(-1.59301 - 1.59301i) q^{21} +(3.21076 + 0.851543i) q^{22} -4.41825 q^{23} +(1.98463 - 2.01526i) q^{24} +(4.26178 - 2.61480i) q^{25} +(9.21975 + 2.44522i) q^{26} +(0.707107 - 0.707107i) q^{27} +(2.23291 - 3.91352i) q^{28} +(2.59286 - 2.59286i) q^{29} +(-3.16188 + 0.0503198i) q^{30} -3.93331 q^{31} +(4.93467 + 2.76568i) q^{32} +2.34884i q^{33} +(4.97003 + 8.55783i) q^{34} +(-4.84805 + 1.36871i) q^{35} +(1.73713 + 0.991146i) q^{36} +(-2.01181 + 2.01181i) q^{37} +(1.36705 - 5.15448i) q^{38} +6.74474i q^{39} +(-1.76494 - 6.07330i) q^{40} -4.50104i q^{41} +(3.07956 + 0.816748i) q^{42} +(7.14876 - 7.14876i) q^{43} +(-4.53135 + 1.23900i) q^{44} +(-0.607542 - 2.15195i) q^{45} +(5.40324 - 3.13798i) q^{46} +10.1154i q^{47} +(-0.995778 + 3.87407i) q^{48} -1.92461 q^{49} +(-3.35478 + 6.22459i) q^{50} +(-4.94817 + 4.94817i) q^{51} +(-13.0118 + 3.55780i) q^{52} +(0.649299 - 0.649299i) q^{53} +(-0.362538 + 1.36696i) q^{54} +(4.58319 + 2.56508i) q^{55} +(0.0487897 + 6.37187i) q^{56} +3.77078 q^{57} +(-1.32937 + 5.01242i) q^{58} +(5.64696 + 5.64696i) q^{59} +(3.83104 - 2.30720i) q^{60} +(-5.00520 + 5.00520i) q^{61} +(4.81018 - 2.79355i) q^{62} +2.25286i q^{63} +(-7.99906 + 0.122506i) q^{64} +(13.1607 + 7.36567i) q^{65} +(-1.66822 - 2.87248i) q^{66} +(4.95274 + 4.95274i) q^{67} +(-12.1561 - 6.93581i) q^{68} +(3.12417 + 3.12417i) q^{69} +(4.95676 - 5.11708i) q^{70} -2.33178i q^{71} +(-2.82834 + 0.0216568i) q^{72} -2.18275 q^{73} +(1.03146 - 3.88915i) q^{74} +(-4.86248 - 1.16459i) q^{75} +(1.98906 + 7.27452i) q^{76} +(-3.74174 - 3.74174i) q^{77} +(-4.79032 - 8.24838i) q^{78} +6.38450 q^{79} +(6.47186 + 6.17374i) q^{80} -1.00000 q^{81} +(3.19678 + 5.50449i) q^{82} +(-5.25073 - 5.25073i) q^{83} +(-4.34619 + 1.18837i) q^{84} +(4.25144 + 15.0589i) q^{85} +(-3.66521 + 13.8197i) q^{86} -3.66685 q^{87} +(4.66157 - 4.73351i) q^{88} -15.7100i q^{89} +(2.27137 + 2.20020i) q^{90} +(-10.7445 - 10.7445i) q^{91} +(-4.37913 + 7.67509i) q^{92} +(2.78127 + 2.78127i) q^{93} +(-7.18424 - 12.3705i) q^{94} +(4.11792 - 7.35775i) q^{95} +(-1.53371 - 5.44497i) q^{96} +4.61603i q^{97} +(2.35368 - 1.36692i) q^{98} +(1.66088 - 1.66088i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q + 12 q^{10} - 16 q^{14} - 4 q^{16} + 8 q^{19} - 4 q^{24} - 40 q^{26} - 8 q^{30} - 48 q^{31} - 28 q^{34} + 24 q^{35} - 4 q^{36} - 16 q^{40} - 40 q^{44} - 4 q^{46} + 48 q^{49} - 32 q^{50} + 8 q^{51} - 4 q^{54} + 48 q^{56} - 32 q^{59} - 24 q^{60} + 16 q^{61} + 48 q^{64} + 16 q^{65} + 24 q^{66} - 16 q^{69} + 40 q^{74} - 16 q^{75} + 60 q^{76} - 96 q^{79} + 72 q^{80} - 48 q^{81} + 16 q^{86} + 8 q^{90} - 32 q^{91} + 44 q^{94} - 48 q^{95} - 40 q^{96}+O(q^{100}) $ 48 * q + 12 * q^10 - 16 * q^14 - 4 * q^16 + 8 * q^19 - 4 * q^24 - 40 * q^26 - 8 * q^30 - 48 * q^31 - 28 * q^34 + 24 * q^35 - 4 * q^36 - 16 * q^40 - 40 * q^44 - 4 * q^46 + 48 * q^49 - 32 * q^50 + 8 * q^51 - 4 * q^54 + 48 * q^56 - 32 * q^59 - 24 * q^60 + 16 * q^61 + 48 * q^64 + 16 * q^65 + 24 * q^66 - 16 * q^69 + 40 * q^74 - 16 * q^75 + 60 * q^76 - 96 * q^79 + 72 * q^80 - 48 * q^81 + 16 * q^86 + 8 * q^90 - 32 * q^91 + 44 * q^94 - 48 * q^95 - 40 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.22294	+	0.710230i	−0.864746	+	0.502209i
$2$	−1.22294	+	0.710230i	−0.864746	+	0.502209i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$	0.991146	−	1.73713i	0.495573	−	0.868566i
$5$	−2.15195	+	0.607542i	−0.962382	+	0.271701i
$5$	−2.15195	+	0.607542i	−0.962382	+	0.271701i
$6$	1.36696	+	0.362538i	0.558057	+	0.148005i
$7$	2.25286			0.851502			0.425751	−	0.904840i	$-0.360010\pi$
$7$	2.25286			0.851502			0.425751	+	0.904840i	$0.360010\pi$
$8$	0.0216568	+	2.82834i	0.00765682	+	0.999971i
$9$			1.00000i			0.333333i
$10$	2.20020	−	2.27137i	0.695765	−	0.718269i
$11$	−1.66088	−	1.66088i	−0.500775	−	0.500775i	0.410904	−	0.911679i	$-0.365213\pi$
$11$	−1.66088	−	1.66088i	−0.500775	−	0.500775i	−0.911679	+	0.410904i	$0.865213\pi$
$12$	−1.92918	+	0.527493i	−0.556907	+	0.152274i
$13$	−4.76925	−	4.76925i	−1.32275	−	1.32275i	−0.911540	−	0.411212i	$-0.865106\pi$
$13$	−4.76925	−	4.76925i	−1.32275	−	1.32275i	−0.411212	−	0.911540i	$-0.634894\pi$
$14$	−2.75511	+	1.60005i	−0.736333	+	0.427632i
$15$	1.95126	+	1.09206i	0.503812	+	0.281969i
$16$	−2.03526	−	3.44350i	−0.508815	−	0.860876i
$17$		−	6.99777i		−	1.69721i	−0.529028	−	0.848604i	$-0.677443\pi$
$17$		−	6.99777i		−	1.69721i	0.529028	−	0.848604i	$-0.322557\pi$
$18$	−0.710230	−	1.22294i	−0.167403	−	0.288249i
$19$	−2.66634	+	2.66634i	−0.611701	+	0.611701i	−0.943389	−	0.331688i	$-0.892382\pi$
$19$	−2.66634	+	2.66634i	−0.611701	+	0.611701i	0.331688	+	0.943389i	$0.392382\pi$
$20$	−1.07751	+	4.34039i	−0.240940	+	0.970540i
$21$	−1.59301	−	1.59301i	−0.347624	−	0.347624i
$22$	3.21076	+	0.851543i	0.684536	+	0.181550i
$23$	−4.41825			−0.921269			−0.460634	−	0.887590i	$-0.652378\pi$
$23$	−4.41825			−0.921269			−0.460634	+	0.887590i	$0.652378\pi$
$24$	1.98463	−	2.01526i	0.405110	−	0.411362i
$25$	4.26178	−	2.61480i	0.852357	−	0.522960i
$26$	9.21975	+	2.44522i	1.80814	+	0.479547i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	2.23291	−	3.91352i	0.421981	−	0.739586i
$29$	2.59286	−	2.59286i	0.481481	−	0.481481i	−0.424123	−	0.905604i	$-0.639418\pi$
$29$	2.59286	−	2.59286i	0.481481	−	0.481481i	0.905604	+	0.424123i	$0.139418\pi$
$30$	−3.16188	+	0.0503198i	−0.577277	+	0.00918710i
$31$	−3.93331			−0.706443			−0.353221	−	0.935540i	$-0.614914\pi$
$31$	−3.93331			−0.706443			−0.353221	+	0.935540i	$0.614914\pi$
$32$	4.93467	+	2.76568i	0.872335	+	0.488908i
$33$			2.34884i			0.408881i
$34$	4.97003	+	8.55783i	0.852353	+	1.46766i
$35$	−4.84805	+	1.36871i	−0.819470	+	0.231354i
$36$	1.73713	+	0.991146i	0.289522	+	0.165191i
$37$	−2.01181	+	2.01181i	−0.330739	+	0.330739i	−0.852867	−	0.522128i	$-0.825138\pi$
$37$	−2.01181	+	2.01181i	−0.330739	+	0.330739i	0.522128	+	0.852867i	$0.325138\pi$
$38$	1.36705	−	5.15448i	0.221765	−	0.836167i
$39$			6.74474i			1.08002i
$40$	−1.76494	−	6.07330i	−0.279062	−	0.960273i
$41$		−	4.50104i		−	0.702945i	−0.936198	−	0.351472i	$-0.885681\pi$
$41$		−	4.50104i		−	0.702945i	0.936198	−	0.351472i	$-0.114319\pi$
$42$	3.07956	+	0.816748i	0.475187	+	0.126027i
$43$	7.14876	−	7.14876i	1.09017	−	1.09017i	0.0946658	−	0.995509i	$-0.469822\pi$
$43$	7.14876	−	7.14876i	1.09017	−	1.09017i	0.995509	−	0.0946658i	$-0.0301783\pi$
$44$	−4.53135	+	1.23900i	−0.683126	+	0.186786i
$45$	−0.607542	−	2.15195i	−0.0905671	−	0.320794i
$46$	5.40324	−	3.13798i	0.796664	−	0.462669i
$47$			10.1154i			1.47548i	0.675086	+	0.737739i	$0.264107\pi$
$47$			10.1154i			1.47548i	−0.675086	+	0.737739i	$0.735893\pi$
$48$	−0.995778	+	3.87407i	−0.143728	+	0.559174i
$49$	−1.92461			−0.274945
$50$	−3.35478	+	6.22459i	−0.474437	+	0.880289i
$51$	−4.94817	+	4.94817i	−0.692883	+	0.692883i
$52$	−13.0118	+	3.55780i	−1.80442	+	0.493378i
$53$	0.649299	−	0.649299i	0.0891881	−	0.0891881i	−0.661105	−	0.750293i	$-0.729912\pi$
$53$	0.649299	−	0.649299i	0.0891881	−	0.0891881i	0.750293	+	0.661105i	$0.229912\pi$
$54$	−0.362538	+	1.36696i	−0.0493351	+	0.186019i
$55$	4.58319	+	2.56508i	0.617997	+	0.345875i
$56$	0.0487897	+	6.37187i	0.00651980	+	0.851477i
$57$	3.77078			0.499452
$58$	−1.32937	+	5.01242i	−0.174555	+	0.658163i
$59$	5.64696	+	5.64696i	0.735172	+	0.735172i	0.971639	−	0.236468i	$-0.0759897\pi$
$59$	5.64696	+	5.64696i	0.735172	+	0.735172i	−0.236468	+	0.971639i	$0.575990\pi$
$60$	3.83104	−	2.30720i	0.494585	−	0.297858i
$61$	−5.00520	+	5.00520i	−0.640851	+	0.640851i	−0.950765	−	0.309914i	$-0.899700\pi$
$61$	−5.00520	+	5.00520i	−0.640851	+	0.640851i	0.309914	+	0.950765i	$0.399700\pi$
$62$	4.81018	−	2.79355i	0.610894	−	0.354782i
$63$			2.25286i			0.283834i
$64$	−7.99906	+	0.122506i	−0.999883	+	0.0153132i
$65$	13.1607	+	7.36567i	1.63239	+	0.913599i
$66$	−1.66822	−	2.87248i	−0.205343	−	0.353578i
$67$	4.95274	+	4.95274i	0.605074	+	0.605074i	0.941655	−	0.336581i	$-0.109271\pi$
$67$	4.95274	+	4.95274i	0.605074	+	0.605074i	−0.336581	+	0.941655i	$0.609271\pi$
$68$	−12.1561	−	6.93581i	−1.47414	−	0.841091i
$69$	3.12417	+	3.12417i	0.376106	+	0.376106i
$70$	4.95676	−	5.11708i	0.592446	−	0.611607i
$71$		−	2.33178i		−	0.276732i	−0.990381	−	0.138366i	$-0.955815\pi$
$71$		−	2.33178i		−	0.276732i	0.990381	−	0.138366i	$-0.0441850\pi$
$72$	−2.82834	+	0.0216568i	−0.333324	+	0.00255227i
$73$	−2.18275			−0.255472			−0.127736	−	0.991808i	$-0.540771\pi$
$73$	−2.18275			−0.255472			−0.127736	+	0.991808i	$0.540771\pi$
$74$	1.03146	−	3.88915i	0.119905	−	0.452105i
$75$	−4.86248	−	1.16459i	−0.561471	−	0.134476i
$76$	1.98906	+	7.27452i	0.228160	+	0.834445i
$77$	−3.74174	−	3.74174i	−0.426410	−	0.426410i
$78$	−4.79032	−	8.24838i	−0.542397	−	0.933945i
$79$	6.38450			0.718312			0.359156	−	0.933278i	$-0.383065\pi$
$79$	6.38450			0.718312			0.359156	+	0.933278i	$0.383065\pi$
$80$	6.47186	+	6.17374i	0.723575	+	0.690245i
$81$	−1.00000			−0.111111
$82$	3.19678	+	5.50449i	0.353025	+	0.607869i
$83$	−5.25073	−	5.25073i	−0.576342	−	0.576342i	0.357551	−	0.933894i	$-0.383612\pi$
$83$	−5.25073	−	5.25073i	−0.576342	−	0.576342i	−0.933894	+	0.357551i	$0.883612\pi$
$84$	−4.34619	+	1.18837i	−0.474208	+	0.129662i
$85$	4.25144	+	15.0589i	0.461134	+	1.63336i
$86$	−3.66521	+	13.8197i	−0.395230	+	1.49022i
$87$	−3.66685			−0.393128
$88$	4.66157	−	4.73351i	0.496926	−	0.504594i
$89$		−	15.7100i		−	1.66525i	−0.553833	−	0.832627i	$-0.686836\pi$
$89$		−	15.7100i		−	1.66525i	0.553833	−	0.832627i	$-0.313164\pi$
$90$	2.27137	+	2.20020i	0.239423	+	0.231922i
$91$	−10.7445	−	10.7445i	−1.12633	−	1.12633i
$92$	−4.37913	+	7.67509i	−0.456556	+	0.800183i
$93$	2.78127	+	2.78127i	0.288404	+	0.288404i
$94$	−7.18424	−	12.3705i	−0.740998	−	1.27591i
$95$	4.11792	−	7.35775i	0.422490	−	0.754889i
$96$	−1.53371	−	5.44497i	−0.156534	−	0.555725i
$97$			4.61603i			0.468687i	0.972154	+	0.234343i	$0.0752940\pi$
$97$			4.61603i			0.468687i	−0.972154	+	0.234343i	$0.924706\pi$
$98$	2.35368	−	1.36692i	0.237757	−	0.138080i
$99$	1.66088	−	1.66088i	0.166925	−	0.166925i
$100$	−0.318210	−	9.99494i	−0.0318210	−	0.999494i
$101$	−1.13980	−	1.13980i	−0.113415	−	0.113415i	0.648122	−	0.761537i	$-0.275555\pi$
$101$	−1.13980	−	1.13980i	−0.113415	−	0.113415i	−0.761537	+	0.648122i	$0.775555\pi$
$102$	2.53696	−	9.56564i	0.251196	−	0.947140i
$103$	4.11257			0.405224			0.202612	−	0.979259i	$-0.435057\pi$
$103$	4.11257			0.405224			0.202612	+	0.979259i	$0.435057\pi$
$104$	13.3858	−	13.5924i	1.31258	−	1.33284i
$105$	4.39591	+	2.46026i	0.428997	+	0.240097i
$106$	−0.332899	+	1.25520i	−0.0323340	+	0.121916i
$107$	4.98634	−	4.98634i	0.482048	−	0.482048i	−0.423737	−	0.905785i	$-0.639282\pi$
$107$	4.98634	−	4.98634i	0.482048	−	0.482048i	0.905785	+	0.423737i	$0.139282\pi$
$108$	−0.527493	−	1.92918i	−0.0507580	−	0.185636i
$109$	3.62560	−	3.62560i	0.347269	−	0.347269i	−0.511822	−	0.859091i	$-0.671029\pi$
$109$	3.62560	−	3.62560i	0.347269	−	0.347269i	0.859091	+	0.511822i	$0.171029\pi$
$110$	−7.42675	+	0.118193i	−0.708113	+	0.0112693i
$111$	2.84512			0.270047
$112$	−4.58516	−	7.75774i	−0.433257	−	0.733037i
$113$		−	0.639228i		−	0.0601335i	−0.999548	−	0.0300668i	$-0.990428\pi$
$113$		−	0.639228i		−	0.0601335i	0.999548	−	0.0300668i	$-0.00957199\pi$
$114$	−4.61142	+	2.67812i	−0.431899	+	0.250829i
$115$	9.50786	−	2.68427i	0.886612	−	0.250310i
$116$	−1.93424	−	7.07403i	−0.179589	−	0.656807i
$117$	4.76925	−	4.76925i	0.440917	−	0.440917i
$118$	−10.9165	−	2.89523i	−1.00495	−	0.266527i
$119$		−	15.7650i		−	1.44518i
$120$	−3.04647	+	5.54248i	−0.278103	+	0.505956i
$121$		−	5.48295i		−	0.498450i
$122$	2.56620	−	9.67589i	0.232333	−	0.876014i
$123$	−3.18272	+	3.18272i	−0.286976	+	0.286976i
$124$	−3.89848	+	6.83268i	−0.350094	+	0.613593i
$125$	−7.58255	+	8.21614i	−0.678204	+	0.734874i
$126$	−1.60005	−	2.75511i	−0.142544	−	0.245444i
$127$			17.5549i			1.55774i	0.627184	+	0.778871i	$0.284207\pi$
$127$			17.5549i			1.55774i	−0.627184	+	0.778871i	$0.715793\pi$
$128$	9.69533	−	5.83099i	0.856955	−	0.515392i
$129$	−10.1099			−0.890124
$130$	−21.3260	+	0.339394i	−1.87042	+	0.0297668i
$131$	0.826200	−	0.826200i	0.0721855	−	0.0721855i	−0.670092	−	0.742278i	$-0.733745\pi$
$131$	0.826200	−	0.826200i	0.0721855	−	0.0721855i	0.742278	+	0.670092i	$0.233745\pi$
$132$	4.08025	+	2.32804i	0.355140	+	0.202630i
$133$	−6.00690	+	6.00690i	−0.520864	+	0.520864i
$134$	−9.57448	−	2.53930i	−0.827109	−	0.219362i
$135$	−1.09206	+	1.95126i	−0.0939897	+	0.167937i
$136$	19.7921	−	0.151549i	1.69716	−	0.0129952i
$137$	8.92457			0.762477			0.381239	−	0.924477i	$-0.375498\pi$
$137$	8.92457			0.762477			0.381239	+	0.924477i	$0.375498\pi$
$138$	−6.03955	−	1.60178i	−0.514121	−	0.136353i
$139$	4.83668	+	4.83668i	0.410242	+	0.410242i	0.881823	−	0.471581i	$-0.156317\pi$
$139$	4.83668	+	4.83668i	0.410242	+	0.410242i	−0.471581	+	0.881823i	$0.656317\pi$
$140$	−2.42749	+	9.77829i	−0.205161	+	0.826417i
$141$	7.15265	−	7.15265i	0.602361	−	0.602361i
$142$	1.65610	+	2.85162i	0.138977	+	0.239303i
$143$			15.8423i			1.32480i
$144$	3.44350	−	2.03526i	0.286959	−	0.169605i
$145$	−4.00443	+	7.15497i	−0.332550	+	0.594188i
$146$	2.66936	−	1.55026i	0.220918	−	0.128300i
$147$	1.36091	+	1.36091i	0.112246	+	0.112246i
$148$	1.50078	+	5.48876i	0.123363	+	0.451174i
$149$	−1.49085	−	1.49085i	−0.122135	−	0.122135i	0.643397	−	0.765533i	$-0.277524\pi$
$149$	−1.49085	−	1.49085i	−0.122135	−	0.122135i	−0.765533	+	0.643397i	$0.777524\pi$
$150$	6.77363	−	2.02926i	0.553065	−	0.165688i
$151$			9.61540i			0.782490i	0.920287	+	0.391245i	$0.127956\pi$
$151$			9.61540i			0.782490i	−0.920287	+	0.391245i	$0.872044\pi$
$152$	−7.59908	−	7.48359i	−0.616366	−	0.606999i
$153$	6.99777			0.565736
$154$	7.23340	+	1.91841i	0.582884	+	0.154590i
$155$	8.46429	−	2.38965i	0.679868	−	0.191941i
$156$	11.7165	+	6.68502i	0.938071	+	0.535230i
$157$	−16.0158	−	16.0158i	−1.27820	−	1.27820i	−0.941676	−	0.336521i	$-0.890750\pi$
$157$	−16.0158	−	16.0158i	−1.27820	−	1.27820i	−0.336521	−	0.941676i	$-0.609250\pi$
$158$	−7.80783	+	4.53446i	−0.621158	+	0.360743i
$159$	−0.918248			−0.0728218
$160$	−12.2994	−	2.95358i	−0.972356	−	0.233501i
$161$	−9.95371			−0.784462
$162$	1.22294	−	0.710230i	0.0960829	−	0.0558010i
$163$	−13.3477	−	13.3477i	−1.04547	−	1.04547i	−0.998916	−	0.0465557i	$-0.985176\pi$
$163$	−13.3477	−	13.3477i	−1.04547	−	1.04547i	−0.0465557	−	0.998916i	$-0.514824\pi$
$164$	−7.81891	−	4.46119i	−0.610554	−	0.348360i
$165$	−1.42702	−	5.05459i	−0.111093	−	0.393499i
$166$	10.1505	+	2.69208i	0.787834	+	0.208946i
$167$	−12.8029			−0.990720			−0.495360	−	0.868688i	$-0.664964\pi$
$167$	−12.8029			−0.990720			−0.495360	+	0.868688i	$0.664964\pi$
$168$	4.47109	−	4.54009i	0.344952	−	0.350276i
$169$			32.4915i			2.49934i
$170$	−15.8945	−	15.3965i	−1.21905	−	1.18086i
$171$	−2.66634	−	2.66634i	−0.203900	−	0.203900i
$172$	−5.33288	−	19.5038i	−0.406628	−	1.48715i
$173$	12.8300	+	12.8300i	0.975450	+	0.975450i	0.999706	−	0.0242559i	$-0.00772166\pi$
$173$	12.8300	+	12.8300i	0.975450	+	0.975450i	−0.0242559	+	0.999706i	$0.507722\pi$
$174$	4.48433	−	2.60431i	0.339956	−	0.197432i
$175$	9.60121	−	5.89079i	0.725784	−	0.445302i
$176$	−2.33892	+	9.09958i	−0.176303	+	0.685906i
$177$		−	7.98601i		−	0.600265i
$178$	11.1577	+	19.2123i	0.836306	+	1.44002i
$179$	4.61252	−	4.61252i	0.344756	−	0.344756i	−0.513396	−	0.858152i	$-0.671613\pi$
$179$	4.61252	−	4.61252i	0.344756	−	0.344756i	0.858152	+	0.513396i	$0.171613\pi$
$180$	−4.34039	−	1.07751i	−0.323513	−	0.0803132i
$181$	−4.12071	−	4.12071i	−0.306290	−	0.306290i	0.537179	−	0.843468i	$-0.319490\pi$
$181$	−4.12071	−	4.12071i	−0.306290	−	0.306290i	−0.843468	+	0.537179i	$0.819490\pi$
$182$	20.7708	+	5.50875i	1.53964	+	0.408335i
$183$	7.07843			0.523252
$184$	−0.0956850	−	12.4963i	−0.00705399	−	0.921242i
$185$	3.10705	−	5.55156i	0.228435	−	0.408159i
$186$	−5.37666	−	1.42597i	−0.394236	−	0.104557i
$187$	−11.6225	+	11.6225i	−0.849919	+	0.849919i
$188$	17.5717	+	10.0258i	1.28155	+	0.731207i
$189$	1.59301	−	1.59301i	0.115875	−	0.115875i
$190$	0.189745	+	11.9227i	0.0137655	+	0.864966i
$191$	−0.953399			−0.0689855			−0.0344928	−	0.999405i	$-0.510982\pi$
$191$	−0.953399			−0.0689855			−0.0344928	+	0.999405i	$0.510982\pi$
$192$	5.74282	+	5.56957i	0.414452	+	0.401949i
$193$		−	4.82186i		−	0.347085i	−0.984826	−	0.173543i	$-0.944479\pi$
$193$		−	4.82186i		−	0.347085i	0.984826	−	0.173543i	$-0.0555214\pi$
$194$	−3.27844	−	5.64511i	−0.235379	−	0.405295i
$195$	−4.09771	−	14.5143i	−0.293443	−	1.03939i
$196$	−1.90757	+	3.34331i	−0.136255	+	0.238808i
$197$	−2.47660	+	2.47660i	−0.176451	+	0.176451i	−0.789807	−	0.613356i	$-0.789819\pi$
$197$	−2.47660	+	2.47660i	−0.176451	+	0.176451i	0.613356	+	0.789807i	$0.289819\pi$
$198$	−0.851543	+	3.21076i	−0.0605166	+	0.228179i
$199$		−	17.4435i		−	1.23654i	−0.785966	−	0.618270i	$-0.787834\pi$
$199$		−	17.4435i		−	1.23654i	0.785966	−	0.618270i	$-0.212166\pi$
$200$	7.48786	+	11.9972i	0.529472	+	0.848328i
$201$		−	7.00424i		−	0.494041i
$202$	2.20343	+	0.584384i	0.155033	+	0.0411171i
$203$	5.84135	−	5.84135i	0.409982	−	0.409982i
$204$	3.69127	+	13.5000i	0.258441	+	0.945188i
$205$	2.73457	+	9.68602i	0.190991	+	0.676501i
$206$	−5.02941	+	2.92087i	−0.350416	+	0.203507i
$207$		−	4.41825i		−	0.307090i
$208$	−6.71626	+	26.1296i	−0.465689	+	1.81176i
$209$	8.85695			0.612648
$210$	−7.12327	+	0.113364i	−0.491553	+	0.00782283i
$211$	5.41135	−	5.41135i	0.372533	−	0.372533i	−0.495866	−	0.868399i	$-0.665149\pi$
$211$	5.41135	−	5.41135i	0.372533	−	0.372533i	0.868399	+	0.495866i	$0.165149\pi$
$212$	−0.484369	−	1.77147i	−0.0332666	−	0.121665i
$213$	−1.64882	+	1.64882i	−0.112975	+	0.112975i
$214$	−2.55653	+	9.63943i	−0.174761	+	0.658938i
$215$	−11.0406	+	19.7269i	−0.752963	+	1.34537i
$216$	2.01526	+	1.98463i	0.137121	+	0.135037i
$217$	−8.86120			−0.601538
$218$	−1.85886	+	7.00888i	−0.125898	+	0.474701i
$219$	1.54344	+	1.54344i	0.104296	+	0.104296i
$220$	8.99849	−	5.41924i	0.606678	−	0.365365i
$221$	−33.3741	+	33.3741i	−2.24499	+	2.24499i
$222$	−3.47940	+	2.02069i	−0.233522	+	0.135620i
$223$		−	18.2634i		−	1.22301i	−0.791241	−	0.611505i	$-0.790564\pi$
$223$		−	18.2634i		−	1.22301i	0.791241	−	0.611505i	$-0.209436\pi$
$224$	11.1171	+	6.23070i	0.742795	+	0.416306i
$225$	2.61480	+	4.26178i	0.174320	+	0.284119i
$226$	0.453999	+	0.781735i	0.0301996	+	0.0520002i
$227$	2.23773	+	2.23773i	0.148523	+	0.148523i	0.777458	−	0.628935i	$-0.216509\pi$
$227$	2.23773	+	2.23773i	0.148523	+	0.148523i	−0.628935	+	0.777458i	$0.716509\pi$
$228$	3.73739	−	6.55034i	0.247515	−	0.433807i
$229$	6.40974	+	6.40974i	0.423568	+	0.423568i	0.886430	−	0.462862i	$-0.153178\pi$
$229$	6.40974	+	6.40974i	0.423568	+	0.423568i	−0.462862	+	0.886430i	$0.653178\pi$
$230$	−9.72105	+	10.0355i	−0.640987	+	0.661719i
$231$			5.29162i			0.348163i
$232$	7.38964	+	7.27734i	0.485154	+	0.477781i
$233$	2.67972			0.175555			0.0877773	−	0.996140i	$-0.472024\pi$
$233$	2.67972			0.175555			0.0877773	+	0.996140i	$0.472024\pi$
$234$	−2.44522	+	9.21975i	−0.159849	+	0.602714i
$235$	−6.14551	−	21.7678i	−0.400889	−	1.41997i
$236$	15.4065	−	4.21256i	1.00288	−	0.274214i
$237$	−4.51452	−	4.51452i	−0.293250	−	0.293250i
$238$	11.1968	+	19.2796i	0.725780	+	1.24971i
$239$	−26.0323			−1.68389			−0.841946	−	0.539562i	$-0.818590\pi$
$239$	−26.0323			−1.68389			−0.841946	+	0.539562i	$0.818590\pi$
$240$	−0.210798	−	8.94179i	−0.0136069	−	0.577190i
$241$	5.87408			0.378383			0.189191	−	0.981940i	$-0.439413\pi$
$241$	5.87408			0.378383			0.189191	+	0.981940i	$0.439413\pi$
$242$	3.89415	+	6.70529i	0.250326	+	0.431033i
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	3.73382	+	13.6556i	0.239033	+	0.874209i
$245$	4.14167	−	1.16928i	0.264602	−	0.0747028i
$246$	1.63180	−	6.15272i	0.104040	−	0.392283i
$247$	25.4329			1.61826
$248$	−0.0851827	−	11.1247i	−0.00540911	−	0.706422i
$249$			7.42565i			0.470582i
$250$	3.43762	−	15.4332i	0.217414	−	0.976079i
$251$	8.44080	+	8.44080i	0.532779	+	0.532779i	0.921398	−	0.388620i	$-0.127048\pi$
$251$	8.44080	+	8.44080i	0.532779	+	0.532779i	−0.388620	+	0.921398i	$0.627048\pi$
$252$	3.91352	+	2.23291i	0.246529	+	0.140660i
$253$	7.33819	+	7.33819i	0.461348	+	0.461348i
$254$	−12.4680	−	21.4685i	−0.782311	−	1.34705i
$255$	7.64200	−	13.6544i	0.478561	−	0.855075i
$256$	−7.71543	+	14.0169i	−0.482214	+	0.876053i
$257$		−	22.2011i		−	1.38487i	−0.721480	−	0.692435i	$-0.756538\pi$
$257$		−	22.2011i		−	1.38487i	0.721480	−	0.692435i	$-0.243462\pi$
$258$	12.3637	−	7.18033i	0.769732	−	0.447028i
$259$	−4.53232	+	4.53232i	−0.281625	+	0.281625i
$260$	25.8393	−	15.5615i	1.60249	−	0.965080i
$261$	2.59286	+	2.59286i	0.160494	+	0.160494i
$262$	−0.423598	+	1.59718i	−0.0261700	+	0.0986743i
$263$	−0.464456			−0.0286396			−0.0143198	−	0.999897i	$-0.504558\pi$
$263$	−0.464456			−0.0286396			−0.0143198	+	0.999897i	$0.504558\pi$
$264$	−6.64333	+	0.0508683i	−0.408869	+	0.00313073i
$265$	−1.00278	+	1.79174i	−0.0616005	+	0.110065i
$266$	3.07977	−	11.6123i	0.188833	−	0.711998i
$267$	−11.1086	+	11.1086i	−0.679837	+	0.679837i
$268$	13.5125	−	3.69468i	0.825405	−	0.225689i
$269$	4.74205	−	4.74205i	0.289128	−	0.289128i	−0.547608	−	0.836735i	$-0.684461\pi$
$269$	4.74205	−	4.74205i	0.289128	−	0.289128i	0.836735	+	0.547608i	$0.184461\pi$
$270$	−0.0503198	−	3.16188i	−0.00306237	−	0.192426i
$271$	12.0417			0.731482			0.365741	−	0.930717i	$-0.380816\pi$
$271$	12.0417			0.731482			0.365741	+	0.930717i	$0.380816\pi$
$272$	−24.0968	+	14.2423i	−1.46109	+	0.863566i
$273$			15.1950i			0.919641i
$274$	−10.9142	+	6.33850i	−0.659349	+	0.382923i
$275$	−11.4212	−	2.73544i	−0.688724	−	0.164953i
$276$	8.52362	−	2.33059i	0.513061	−	0.140285i
$277$	17.9760	−	17.9760i	1.08007	−	1.08007i	0.0835733	−	0.996502i	$-0.473367\pi$
$277$	17.9760	−	17.9760i	1.08007	−	1.08007i	0.996502	−	0.0835733i	$-0.0266333\pi$
$278$	−9.35010	−	2.47979i	−0.560782	−	0.148728i
$279$		−	3.93331i		−	0.235481i
$280$	−3.97617	−	13.6823i	−0.237622	−	0.817674i
$281$			9.58712i			0.571919i	0.958242	+	0.285960i	$0.0923123\pi$
$281$			9.58712i			0.571919i	−0.958242	+	0.285960i	$0.907688\pi$
$282$	−3.66720	+	13.8273i	−0.218379	+	0.823401i
$283$	5.09022	−	5.09022i	0.302582	−	0.302582i	−0.539441	−	0.842023i	$-0.681364\pi$
$283$	5.09022	−	5.09022i	0.302582	−	0.302582i	0.842023	+	0.539441i	$0.181364\pi$
$284$	−4.05062	−	2.31114i	−0.240360	−	0.137141i
$285$	−8.11453	+	2.29091i	−0.480663	+	0.135702i
$286$	−11.2517	−	19.3741i	−0.665327	−	1.14562i
$287$		−	10.1402i		−	0.598559i
$288$	−2.76568	+	4.93467i	−0.162969	+	0.290778i
$289$	−31.9688			−1.88052
$290$	−0.184515	−	11.5941i	−0.0108351	−	0.680831i
$291$	3.26403	−	3.26403i	0.191341	−	0.191341i
$292$	−2.16342	+	3.79173i	−0.126605	+	0.221894i
$293$	4.25071	−	4.25071i	0.248329	−	0.248329i	−0.571955	−	0.820285i	$-0.693815\pi$
$293$	4.25071	−	4.25071i	0.248329	−	0.248329i	0.820285	+	0.571955i	$0.193815\pi$
$294$	−2.63086	−	0.697744i	−0.153435	−	0.0406933i
$295$	−15.5827	−	8.72121i	−0.907263	−	0.507769i
$296$	−5.73365	−	5.64651i	−0.333261	−	0.328197i
$297$	−2.34884			−0.136294
$298$	2.88206	+	0.764368i	0.166953	+	0.0442787i
$299$	21.0717	+	21.0717i	1.21861	+	1.21861i
$300$	−6.84248	+	7.29250i	−0.395051	+	0.421032i
$301$	16.1052	−	16.1052i	0.928286	−	0.928286i
$302$	−6.82915	−	11.7590i	−0.392973	−	0.676655i
$303$			1.61193i			0.0926028i
$304$	14.6083	+	3.75485i	0.837841	+	0.215356i
$305$	7.73008	−	13.8118i	0.442623	−	0.790863i
$306$	−8.55783	+	4.97003i	−0.489218	+	0.284118i
$307$	−0.153856	−	0.153856i	−0.00878103	−	0.00878103i	0.702703	−	0.711484i	$-0.251976\pi$
$307$	−0.153856	−	0.153856i	−0.00878103	−	0.00878103i	−0.711484	+	0.702703i	$0.751976\pi$
$308$	−10.2085	+	2.79129i	−0.581683	+	0.159048i
$309$	−2.90803	−	2.90803i	−0.165432	−	0.165432i
$310$	−8.65408	+	8.93398i	−0.491519	+	0.507416i
$311$		−	34.8210i		−	1.97452i	−0.159115	−	0.987260i	$-0.550864\pi$
$311$		−	34.8210i		−	1.97452i	0.159115	−	0.987260i	$-0.449136\pi$
$312$	−19.0764	+	0.146069i	−1.07999	+	0.00826954i
$313$	−17.3412			−0.980182			−0.490091	−	0.871671i	$-0.663036\pi$
$313$	−17.3412			−0.980182			−0.490091	+	0.871671i	$0.663036\pi$
$314$	30.9611	+	8.21137i	1.74724	+	0.463395i
$315$	−1.36871	−	4.84805i	−0.0771180	−	0.273157i
$316$	6.32797	−	11.0907i	0.355976	−	0.623902i
$317$	10.1485	+	10.1485i	0.569999	+	0.569999i	0.932128	−	0.362129i	$-0.117950\pi$
$317$	10.1485	+	10.1485i	0.569999	+	0.569999i	−0.362129	+	0.932128i	$0.617950\pi$
$318$	1.12296	−	0.652167i	0.0629724	−	0.0365717i
$319$	−8.61285			−0.482227
$320$	17.1392	−	5.12339i	0.958108	−	0.286406i
$321$	−7.05175			−0.393591
$322$	12.1727	−	7.06943i	0.678361	−	0.393964i
$323$	18.6584	+	18.6584i	1.03818	+	1.03818i
$324$	−0.991146	+	1.73713i	−0.0550636	+	0.0965074i
$325$	−32.7962	−	7.85487i	−1.81920	−	0.435710i
$326$	25.8033	+	6.84343i	1.42911	+	0.379023i
$327$	−5.12737			−0.283544
$328$	12.7305	−	0.0974780i	0.702924	−	0.00538232i
$329$			22.7885i			1.25637i
$330$	5.33508	+	5.16793i	0.293686	+	0.284485i
$331$	−9.12552	−	9.12552i	−0.501584	−	0.501584i	0.410346	−	0.911930i	$-0.365408\pi$
$331$	−9.12552	−	9.12552i	−0.501584	−	0.501584i	−0.911930	+	0.410346i	$0.865408\pi$
$332$	−14.3255	+	3.91698i	−0.786211	+	0.214972i
$333$	−2.01181	−	2.01181i	−0.110246	−	0.110246i
$334$	15.6572	−	9.09303i	0.856722	−	0.497548i
$335$	−13.6671	−	7.64906i	−0.746711	−	0.417913i
$336$	−2.24335	+	8.72775i	−0.122385	+	0.476138i
$337$			4.62620i			0.252005i	0.992030	+	0.126002i	$0.0402147\pi$
$337$			4.62620i			0.252005i	−0.992030	+	0.126002i	$0.959785\pi$
$338$	−23.0764	−	39.7350i	−1.25519	−	2.16130i
$339$	−0.452002	+	0.452002i	−0.0245494	+	0.0245494i
$340$	30.3730	+	7.54020i	1.64721	+	0.408925i
$341$	6.53276	+	6.53276i	0.353769	+	0.353769i
$342$	5.15448	+	1.36705i	0.278722	+	0.0739215i
$343$	−20.1059			−1.08562
$344$	20.3740	+	20.0643i	1.09849	+	1.08180i
$345$	−8.62114	−	4.82500i	−0.464146	−	0.259769i
$346$	−24.8026	−	6.57804i	−1.33340	−	0.353637i
$347$	−16.1909	+	16.1909i	−0.869173	+	0.869173i	−0.992381	−	0.123208i	$-0.960682\pi$
$347$	−16.1909	+	16.1909i	−0.869173	+	0.869173i	0.123208	+	0.992381i	$0.460682\pi$
$348$	−3.63438	+	6.36981i	−0.194823	+	0.341458i
$349$	21.6447	−	21.6447i	1.15862	−	1.15862i	0.173842	−	0.984774i	$-0.444382\pi$
$349$	21.6447	−	21.6447i	1.15862	−	1.15862i	0.984774	−	0.173842i	$-0.0556182\pi$
$350$	−7.55785	+	14.0231i	−0.403984	+	0.749568i
$351$	−6.74474			−0.360007
$352$	−3.60244	−	12.7894i	−0.192011	−	0.681676i
$353$			26.1933i			1.39413i	0.717009	+	0.697064i	$0.245511\pi$
$353$			26.1933i			1.39413i	−0.717009	+	0.697064i	$0.754489\pi$
$354$	5.67191	+	9.76638i	0.301458	+	0.519077i
$355$	1.41666	+	5.01788i	0.0751883	+	0.266322i
$356$	−27.2903	−	15.5709i	−1.44638	−	0.825255i
$357$	−11.1475	+	11.1475i	−0.589991	+	0.589991i
$358$	−2.36487	+	8.91677i	−0.124987	+	0.471266i
$359$		−	5.73157i		−	0.302501i	−0.988495	−	0.151250i	$-0.951670\pi$
$359$		−	5.73157i		−	0.302501i	0.988495	−	0.151250i	$-0.0483300\pi$
$360$	6.07330	−	1.76494i	0.320091	−	0.0930207i
$361$			4.78125i			0.251645i
$362$	7.96601	+	2.11271i	0.418684	+	0.111042i
$363$	−3.87703	+	3.87703i	−0.203491	+	0.203491i
$364$	−29.3139	+	8.01523i	−1.53646	+	0.420112i
$365$	4.69717	−	1.32611i	0.245861	−	0.0694119i
$366$	−8.65646	+	5.02731i	−0.452481	+	0.262782i
$367$		−	20.9879i		−	1.09556i	−0.836623	−	0.547778i	$-0.815474\pi$
$367$		−	20.9879i		−	1.09556i	0.836623	−	0.547778i	$-0.184526\pi$
$368$	8.99229	+	15.2143i	0.468756	+	0.793098i
$369$	4.50104			0.234315
$370$	0.143166	+	8.99593i	0.00744285	+	0.467676i
$371$	1.46278	−	1.46278i	0.0759438	−	0.0759438i
$372$	7.58808	−	2.07479i	0.393423	−	0.107573i
$373$	12.9141	−	12.9141i	0.668667	−	0.668667i	−0.288740	−	0.957407i	$-0.593236\pi$
$373$	12.9141	−	12.9141i	0.668667	−	0.668667i	0.957407	+	0.288740i	$0.0932365\pi$
$374$	5.95891	−	22.4682i	0.308128	−	1.16180i
$375$	11.1714	−	0.448018i	0.576887	−	0.0231356i
$376$	−28.6097	+	0.219066i	−1.47543	+	0.0112975i
$377$	−24.7320			−1.27376
$378$	−0.816748	+	3.07956i	−0.0420090	+	0.158396i
$379$	8.07361	+	8.07361i	0.414713	+	0.414713i	0.883377	−	0.468663i	$-0.155264\pi$
$379$	8.07361	+	8.07361i	0.414713	+	0.414713i	−0.468663	+	0.883377i	$0.655264\pi$
$380$	−8.69993	−	14.4460i	−0.446297	−	0.741063i
$381$	12.4132	−	12.4132i	0.635945	−	0.635945i
$382$	1.16595	−	0.677133i	0.0596550	−	0.0346451i
$383$		−	9.23276i		−	0.471772i	−0.971781	−	0.235886i	$-0.924201\pi$
$383$		−	9.23276i		−	0.471772i	0.971781	−	0.235886i	$-0.0757992\pi$
$384$	−10.9788	−	2.73250i	−0.560258	−	0.139442i
$385$	10.3253	+	5.77877i	0.526226	+	0.294513i
$386$	3.42463	+	5.89683i	0.174309	+	0.300141i
$387$	7.14876	+	7.14876i	0.363392	+	0.363392i
$388$	8.01866	+	4.57516i	0.407086	+	0.232268i
$389$	−6.32362	−	6.32362i	−0.320620	−	0.320620i	0.528385	−	0.849005i	$-0.322798\pi$
$389$	−6.32362	−	6.32362i	−0.320620	−	0.320620i	−0.849005	+	0.528385i	$0.822798\pi$
$390$	15.3198	+	14.8398i	0.775747	+	0.751442i
$391$			30.9179i			1.56359i
$392$	−0.0416809	−	5.44347i	−0.00210520	−	0.274937i
$393$	−1.16842			−0.0589392
$394$	1.26977	−	4.78769i	0.0639700	−	0.241200i
$395$	−13.7391	+	3.87885i	−0.691290	+	0.195166i
$396$	−1.23900	−	4.53135i	−0.0622619	−	0.227709i
$397$	1.07806	+	1.07806i	0.0541061	+	0.0541061i	0.733642	−	0.679536i	$-0.237819\pi$
$397$	1.07806	+	1.07806i	0.0541061	+	0.0541061i	−0.679536	+	0.733642i	$0.737819\pi$
$398$	12.3889	+	21.3323i	0.621001	+	1.06929i
$399$	8.49504			0.425284
$400$	−17.6779	−	9.35366i	−0.883896	−	0.467683i
$401$	37.0966			1.85252			0.926258	−	0.376891i	$-0.123007\pi$
$401$	37.0966			1.85252			0.926258	+	0.376891i	$0.123007\pi$
$402$	4.97462	+	8.56573i	0.248112	+	0.427220i
$403$	18.7589	+	18.7589i	0.934449	+	0.934449i
$404$	−3.10970	+	0.850280i	−0.154714	+	0.0423030i
$405$	2.15195	−	0.607542i	0.106931	−	0.0301890i
$406$	−2.99489	+	11.2923i	−0.148634	+	0.560427i
$407$	6.68274			0.331251
$408$	−14.1023	−	13.8880i	−0.698168	−	0.687557i
$409$		−	17.3422i		−	0.857518i	−0.903419	−	0.428759i	$-0.858951\pi$
$409$		−	17.3422i		−	0.857518i	0.903419	−	0.428759i	$-0.141049\pi$
$410$	−10.2235	−	9.90321i	−0.504903	−	0.489085i
$411$	−6.31062	−	6.31062i	−0.311280	−	0.311280i
$412$	4.07616	−	7.14408i	0.200818	−	0.351964i
$413$	12.7218	+	12.7218i	0.626000	+	0.626000i
$414$	3.13798	+	5.40324i	0.154223	+	0.265555i
$415$	14.4894	+	8.10927i	0.711254	+	0.398068i
$416$	−10.3445	−	36.7249i	−0.507180	−	1.80059i
$417$		−	6.84010i		−	0.334961i
$418$	−10.8315	+	6.29048i	−0.529785	+	0.307677i
$419$	−20.4718	+	20.4718i	−1.00011	+	1.00011i	−0.000110566		1.00000i	$0.500035\pi$
$419$	−20.4718	+	20.4718i	−1.00011	+	1.00011i	−1.00000		0.000110566i	$0.999965\pi$
$420$	8.63079	−	5.19780i	0.421140	−	0.253627i
$421$	−10.6143	−	10.6143i	−0.517308	−	0.517308i	0.399448	−	0.916756i	$-0.369202\pi$
$421$	−10.6143	−	10.6143i	−0.517308	−	0.517308i	−0.916756	+	0.399448i	$0.869202\pi$
$422$	−2.77443	+	10.4610i	−0.135057	+	0.509236i
$423$	−10.1154			−0.491826
$424$	1.85050	+	1.82238i	0.0898684	+	0.0885026i
$425$	−18.2978	−	29.8230i	−0.887573	−	1.44663i
$426$	0.845359	−	3.18744i	0.0409578	−	0.154432i
$427$	−11.2760	+	11.2760i	−0.545685	+	0.545685i
$428$	−3.71975	−	13.6041i	−0.179801	−	0.657581i
$429$	11.2022	−	11.2022i	0.540848	−	0.540848i
$430$	−0.508727	−	31.9662i	−0.0245330	−	1.54155i
$431$	17.9747			0.865812			0.432906	−	0.901439i	$-0.357488\pi$
$431$	17.9747			0.865812			0.432906	+	0.901439i	$0.357488\pi$
$432$	−3.87407	−	0.995778i	−0.186391	−	0.0479094i
$433$		−	23.1120i		−	1.11069i	−0.831619	−	0.555347i	$-0.812586\pi$
$433$		−	23.1120i		−	1.11069i	0.831619	−	0.555347i	$-0.187414\pi$
$434$	10.8367	−	6.29349i	0.520177	−	0.302097i
$435$	7.89089	−	2.22777i	0.378339	−	0.106813i
$436$	−2.70465	−	9.89164i	−0.129529	−	0.473724i
$437$	11.7806	−	11.7806i	0.563541	−	0.563541i
$438$	−2.98372	−	0.791329i	−0.142568	−	0.0378112i
$439$		−	2.65049i		−	0.126501i	−0.997998	−	0.0632505i	$-0.979853\pi$
$439$		−	2.65049i		−	0.126501i	0.997998	−	0.0632505i	$-0.0201467\pi$
$440$	−7.15567	+	13.0184i	−0.341133	+	0.620628i
$441$		−	1.92461i		−	0.0916482i
$442$	17.1111	−	64.5177i	0.813892	−	3.06880i
$443$	0.977227	−	0.977227i	0.0464294	−	0.0464294i	−0.683511	−	0.729940i	$-0.739548\pi$
$443$	0.977227	−	0.977227i	0.0464294	−	0.0464294i	0.729940	+	0.683511i	$0.239548\pi$
$444$	2.81993	−	4.94236i	0.133828	−	0.234554i
$445$	9.54448	+	33.8071i	0.452452	+	1.60261i
$446$	12.9712	+	22.3350i	0.614206	+	1.05759i
$447$			2.10838i			0.0997231i
$448$	−18.0208	+	0.275988i	−0.851402	+	0.0130392i
$449$	−19.6612			−0.927867			−0.463934	−	0.885870i	$-0.653562\pi$
$449$	−19.6612			−0.927867			−0.463934	+	0.885870i	$0.653562\pi$
$450$	−6.22459	−	3.35478i	−0.293430	−	0.158146i
$451$	−7.47570	+	7.47570i	−0.352017	+	0.352017i
$452$	−1.11042	−	0.633568i	−0.0522299	−	0.0298005i
$453$	6.79911	−	6.79911i	0.319450	−	0.319450i
$454$	−4.32590	−	1.14730i	−0.203024	−	0.0538452i
$455$	29.6493	+	16.5938i	1.38998	+	0.777931i
$456$	0.0816628	+	10.6651i	0.00382421	+	0.499437i
$457$	25.9752			1.21507			0.607535	−	0.794293i	$-0.292159\pi$
$457$	25.9752			1.21507			0.607535	+	0.794293i	$0.292159\pi$
$458$	−12.3911	−	3.28631i	−0.578998	−	0.153559i
$459$	−4.94817	−	4.94817i	−0.230961	−	0.230961i
$460$	4.76073	−	19.1769i	0.221970	−	0.894128i
$461$	−1.94218	+	1.94218i	−0.0904565	+	0.0904565i	−0.750887	−	0.660431i	$-0.770374\pi$
$461$	−1.94218	+	1.94218i	−0.0904565	+	0.0904565i	0.660431	+	0.750887i	$0.270374\pi$
$462$	−3.75827	−	6.47131i	−0.174850	−	0.301072i
$463$		−	12.7805i		−	0.593960i	−0.954884	−	0.296980i	$-0.904021\pi$
$463$		−	12.7805i		−	0.593960i	0.954884	−	0.296980i	$-0.0959795\pi$
$464$	−14.2056	−	3.65137i	−0.659481	−	0.169511i
$465$	−7.67489	−	4.29541i	−0.355915	−	0.199195i
$466$	−3.27713	+	1.90322i	−0.151810	+	0.0881650i
$467$	28.2154	+	28.2154i	1.30565	+	1.30565i	0.924522	+	0.381129i	$0.124465\pi$
$467$	28.2154	+	28.2154i	1.30565	+	1.30565i	0.381129	+	0.924522i	$0.375535\pi$
$468$	−3.55780	−	13.0118i	−0.164459	−	0.601472i
$469$	11.1578	+	11.1578i	0.515222	+	0.515222i
$470$	22.9757	+	22.2559i	1.05979	+	1.02659i
$471$			22.6497i			1.04364i
$472$	−15.8493	+	16.0938i	−0.729521	+	0.740779i
$473$	−23.7465			−1.09186
$474$	8.72732	+	2.31462i	0.400859	+	0.106314i
$475$	−4.39142	+	18.3353i	−0.201492	+	0.841283i
$476$	−27.3859	−	15.6254i	−1.25523	−	0.716190i
$477$	0.649299	+	0.649299i	0.0297294	+	0.0297294i
$478$	31.8359	−	18.4890i	1.45614	−	0.845665i
$479$	−22.6500			−1.03490			−0.517452	−	0.855712i	$-0.673119\pi$
$479$	−22.6500			−1.03490			−0.517452	+	0.855712i	$0.673119\pi$
$480$	6.60852	+	10.7855i	0.301636	+	0.492289i
$481$	19.1896			0.874970
$482$	−7.18363	+	4.17195i	−0.327205	+	0.190027i
$483$	7.03833	+	7.03833i	0.320255	+	0.320255i
$484$	−9.52461	−	5.43440i	−0.432937	−	0.247018i
$485$	−2.80443	−	9.93347i	−0.127343	−	0.451056i
$486$	−1.36696	−	0.362538i	−0.0620063	−	0.0164450i
$487$	20.1202			0.911733			0.455866	−	0.890048i	$-0.349329\pi$
$487$	20.1202			0.911733			0.455866	+	0.890048i	$0.349329\pi$
$488$	−14.2648	−	14.0480i	−0.645739	−	0.635925i
$489$			18.8765i			0.853624i
$490$	−4.23454	+	4.37150i	−0.191297	+	0.197484i
$491$	20.4434	+	20.4434i	0.922596	+	0.922596i	0.997212	−	0.0746163i	$-0.0237732\pi$
$491$	20.4434	+	20.4434i	0.922596	+	0.922596i	−0.0746163	+	0.997212i	$0.523773\pi$
$492$	2.37427	+	8.68334i	0.107040	+	0.391475i
$493$	−18.1442	−	18.1442i	−0.817174	−	0.817174i
$494$	−31.1028	+	18.0632i	−1.39938	+	0.812702i
$495$	−2.56508	+	4.58319i	−0.115292	+	0.205999i
$496$	8.00531	+	13.5444i	0.359449	+	0.608160i
$497$		−	5.25319i		−	0.235638i
$498$	−5.27392	−	9.08110i	−0.236330	−	0.406934i
$499$	26.7236	−	26.7236i	1.19631	−	1.19631i	0.221052	−	0.975262i	$-0.429051\pi$
$499$	26.7236	−	26.7236i	1.19631	−	1.19631i	0.975262	−	0.221052i	$-0.0709489\pi$
$500$	6.75712	+	21.3153i	0.302188	+	0.953248i
$501$	9.05304	+	9.05304i	0.404460	+	0.404460i
$502$	−16.3175	−	4.32765i	−0.728284	−	0.193152i
$503$	17.4692			0.778911			0.389456	−	0.921045i	$-0.372663\pi$
$503$	17.4692			0.778911			0.389456	+	0.921045i	$0.372663\pi$
$504$	−6.37187	+	0.0487897i	−0.283826	+	0.00217327i
$505$	3.14528	+	1.76032i	0.139963	+	0.0783334i
$506$	−14.1859	−	3.76233i	−0.630642	−	0.167256i
$507$	22.9749	−	22.9749i	1.02035	−	1.02035i
$508$	30.4951	+	17.3994i	1.35300	+	0.771974i
$509$	22.1370	−	22.1370i	0.981205	−	0.981205i	−0.0186215	−	0.999827i	$-0.505928\pi$
$509$	22.1370	−	22.1370i	0.981205	−	0.981205i	0.999827	+	0.0186215i	$0.00592774\pi$
$510$	0.352127	+	22.1261i	0.0155924	+	0.979760i
$511$	−4.91744			−0.217535
$512$	−0.519722	−	22.6214i	−0.0229687	−	0.999736i
$513$			3.77078i			0.166484i
$514$	15.7679	+	27.1506i	0.695494	+	1.19756i
$515$	−8.85005	+	2.49856i	−0.389980	+	0.110100i
$516$	−10.0203	+	17.5622i	−0.441121	+	0.773132i
$517$	16.8004	−	16.8004i	0.738882	−	0.738882i
$518$	2.32375	−	8.76173i	0.102100	−	0.384968i
$519$		−	18.1444i		−	0.796451i
$520$	−20.5476	+	37.3825i	−0.901073	+	1.63933i
$521$			20.7634i			0.909663i	0.890577	+	0.454832i	$0.150301\pi$
$521$			20.7634i			0.909663i	−0.890577	+	0.454832i	$0.849699\pi$
$522$	−5.01242	−	1.32937i	−0.219388	−	0.0581850i
$523$	−25.9884	+	25.9884i	−1.13640	+	1.13640i	−0.147304	+	0.989091i	$0.547059\pi$
$523$	−25.9884	+	25.9884i	−1.13640	+	1.13640i	−0.989091	+	0.147304i	$0.952941\pi$
$524$	−0.616335	−	2.25410i	−0.0269247	−	0.0984710i
$525$	−10.9545	−	2.62367i	−0.478094	−	0.114506i
$526$	0.568000	−	0.329871i	0.0247660	−	0.0143830i
$527$			27.5244i			1.19898i
$528$	8.08824	−	4.78050i	0.351996	−	0.208045i
$529$	−3.47907			−0.151264
$530$	−0.0462060	−	2.90339i	−0.00200706	−	0.126115i
$531$	−5.64696	+	5.64696i	−0.245057	+	0.245057i
$532$	4.48107	+	16.3885i	0.194279	+	0.710531i
$533$	−21.4666	+	21.4666i	−0.929821	+	0.929821i
$534$	5.69546	−	21.4748i	0.246467	−	0.929307i
$535$	−7.70095	+	13.7598i	−0.332941	+	0.594887i
$536$	−13.9008	+	14.1153i	−0.600423	+	0.609689i
$537$	−6.52309			−0.281492
$538$	−2.43127	+	9.16716i	−0.104820	+	0.395224i
$539$	3.19655	+	3.19655i	0.137685	+	0.137685i
$540$	2.30720	+	3.83104i	0.0992860	+	0.164862i
$541$	4.86704	−	4.86704i	0.209250	−	0.209250i	−0.594698	−	0.803949i	$-0.702729\pi$
$541$	4.86704	−	4.86704i	0.209250	−	0.209250i	0.803949	+	0.594698i	$0.202729\pi$
$542$	−14.7262	+	8.55239i	−0.632546	+	0.367356i
$543$			5.82756i			0.250085i
$544$	19.3536	−	34.5317i	0.829779	−	1.48054i
$545$	−5.59940	+	10.0048i	−0.239852	+	0.428559i
$546$	−10.7919	−	18.5825i	−0.461852	−	0.795256i
$547$	−16.2487	−	16.2487i	−0.694742	−	0.694742i	0.268529	−	0.963272i	$-0.413462\pi$
$547$	−16.2487	−	16.2487i	−0.694742	−	0.694742i	−0.963272	+	0.268529i	$0.913462\pi$
$548$	8.84555	−	15.5032i	0.377863	−	0.662262i
$549$	−5.00520	−	5.00520i	−0.213617	−	0.213617i
$550$	15.9102	−	4.76641i	0.678413	−	0.203240i
$551$			13.8269i			0.589045i
$552$	−8.76858	+	8.90390i	−0.373216	+	0.378975i
$553$	14.3834			0.611644
$554$	−9.21641	+	34.7507i	−0.391568	+	1.47641i
$555$	−6.12256	+	1.72853i	−0.259888	+	0.0733721i
$556$	13.1958	−	3.60810i	0.559627	−	0.153018i
$557$	−0.616853	−	0.616853i	−0.0261369	−	0.0261369i	0.693918	−	0.720054i	$-0.255883\pi$
$557$	−0.616853	−	0.616853i	−0.0261369	−	0.0261369i	−0.720054	+	0.693918i	$0.755883\pi$
$558$	2.79355	+	4.81018i	0.118261	+	0.203631i
$559$	−68.1884			−2.88406
$560$	14.5802	+	13.9086i	0.616126	+	0.587745i
$561$	16.4367			0.693956
$562$	−6.80906	−	11.7244i	−0.287223	−	0.494565i
$563$	−17.4063	−	17.4063i	−0.733587	−	0.733587i	0.237742	−	0.971328i	$-0.423593\pi$
$563$	−17.4063	−	17.4063i	−0.733587	−	0.733587i	−0.971328	+	0.237742i	$0.923593\pi$
$564$	−5.33578	−	19.5144i	−0.224677	−	0.821705i
$565$	0.388358	+	1.37559i	0.0163383	+	0.0578714i
$566$	−2.60979	+	9.84024i	−0.109697	+	0.413616i
$567$	−2.25286			−0.0946113
$568$	6.59509	−	0.0504989i	0.276724	−	0.00211889i
$569$			1.57959i			0.0662197i	0.999452	+	0.0331098i	$0.0105411\pi$
$569$			1.57959i			0.0662197i	−0.999452	+	0.0331098i	$0.989459\pi$
$570$	8.29647	−	8.56481i	0.347501	−	0.358741i
$571$	24.6949	+	24.6949i	1.03345	+	1.03345i	0.999421	+	0.0340299i	$0.0108341\pi$
$571$	24.6949	+	24.6949i	1.03345	+	1.03345i	0.0340299	+	0.999421i	$0.489166\pi$
$572$	27.5202	+	15.7020i	1.15068	+	0.656535i
$573$	0.674155	+	0.674155i	0.0281632	+	0.0281632i
$574$	7.20190	+	12.4008i	0.300601	+	0.517601i
$575$	−18.8296	+	11.5528i	−0.785250	+	0.481787i
$576$	−0.122506	−	7.99906i	−0.00510440	−	0.333294i
$577$			33.6673i			1.40159i	0.713363	+	0.700795i	$0.247171\pi$
$577$			33.6673i			1.40159i	−0.713363	+	0.700795i	$0.752829\pi$
$578$	39.0958	−	22.7052i	1.62617	−	0.944413i
$579$	−3.40957	+	3.40957i	−0.141697	+	0.141697i
$580$	8.46016	+	14.0478i	0.351289	+	0.583305i
$581$	−11.8292	−	11.8292i	−0.490757	−	0.490757i
$582$	−1.67348	+	6.30991i	−0.0693682	+	0.261554i
$583$	−2.15682			−0.0893263
$584$	−0.0472713	−	6.17357i	−0.00195610	−	0.255464i
$585$	−7.36567	+	13.1607i	−0.304533	+	0.544128i
$586$	−2.17937	+	8.21734i	−0.0900288	+	0.339455i
$587$	30.6327	−	30.6327i	1.26435	−	1.26435i	0.315385	−	0.948964i	$-0.397866\pi$
$587$	30.6327	−	30.6327i	1.26435	−	1.26435i	0.948964	−	0.315385i	$-0.102134\pi$
$588$	3.71293	−	1.01522i	0.153119	−	0.0418669i
$589$	10.4875	−	10.4875i	0.432132	−	0.432132i
$590$	25.2508	−	0.401854i	1.03956	−	0.0165441i
$591$	3.50245			0.144071
$592$	11.0222	+	2.83311i	0.453010	+	0.116440i
$593$		−	25.1477i		−	1.03269i	−0.856380	−	0.516347i	$-0.827292\pi$
$593$		−	25.1477i		−	1.03269i	0.856380	−	0.516347i	$-0.172708\pi$
$594$	2.87248	−	1.66822i	0.117859	−	0.0684478i
$595$	9.57791	+	33.9255i	0.392656	+	1.39081i
$596$	−4.06746	+	1.11216i	−0.166610	+	0.0455557i
$597$	−12.3344	+	12.3344i	−0.504815	+	0.504815i
$598$	−40.7352	−	10.8036i	−1.66578	−	0.441792i
$599$		−	18.0767i		−	0.738594i	−0.929311	−	0.369297i	$-0.879598\pi$
$599$		−	18.0767i		−	0.738594i	0.929311	−	0.369297i	$-0.120402\pi$
$600$	3.18856	−	13.7780i	0.130173	−	0.562484i
$601$		−	26.5291i		−	1.08214i	−0.840977	−	0.541072i	$-0.818019\pi$
$601$		−	26.5291i		−	1.08214i	0.840977	−	0.541072i	$-0.181981\pi$
$602$	−8.25721	+	31.1340i	−0.336539	+	1.26893i
$603$	−4.95274	+	4.95274i	−0.201691	+	0.201691i
$604$	16.7032	+	9.53026i	0.679645	+	0.387781i
$605$	3.33112	+	11.7990i	0.135429	+	0.479699i
$606$	−1.14484	−	1.97128i	−0.0465059	−	0.0800779i
$607$			28.3496i			1.15068i	0.817916	+	0.575338i	$0.195129\pi$
$607$			28.3496i			1.15068i	−0.817916	+	0.575338i	$0.804871\pi$
$608$	−20.5318	+	5.78328i	−0.832673	+	0.234543i
$609$	−8.26091			−0.334749
$610$	0.356185	+	22.3811i	0.0144215	+	0.906185i
$611$	48.2427	−	48.2427i	1.95169	−	1.95169i
$612$	6.93581	−	12.1561i	0.280364	−	0.491380i
$613$	−3.24941	+	3.24941i	−0.131243	+	0.131243i	−0.769677	−	0.638434i	$-0.779583\pi$
$613$	−3.24941	+	3.24941i	−0.131243	+	0.131243i	0.638434	+	0.769677i	$0.279583\pi$
$614$	0.297430	+	0.0788829i	0.0120033	+	0.00318346i
$615$	4.91542	−	8.78269i	0.198209	−	0.354152i
$616$	10.5019	−	10.6640i	0.423133	−	0.429663i
$617$	−18.4370			−0.742245			−0.371123	−	0.928584i	$-0.621027\pi$
$617$	−18.4370			−0.742245			−0.371123	+	0.928584i	$0.621027\pi$
$618$	5.62170	+	1.49096i	0.226138	+	0.0599753i
$619$	9.47769	+	9.47769i	0.380941	+	0.380941i	0.871441	−	0.490500i	$-0.163186\pi$
$619$	9.47769	+	9.47769i	0.380941	+	0.380941i	−0.490500	+	0.871441i	$0.663186\pi$
$620$	4.23820	−	17.0721i	0.170210	−	0.685631i
$621$	−3.12417	+	3.12417i	−0.125369	+	0.125369i
$622$	24.7310	+	42.5839i	0.991621	+	1.70746i
$623$		−	35.3924i		−	1.41797i
$624$	23.2255	−	13.7273i	0.929765	−	0.549532i
$625$	11.3256	−	22.2874i	0.453025	−	0.891498i
$626$	21.2072	−	12.3162i	0.847609	−	0.492256i
$627$	−6.26281	−	6.26281i	−0.250113	−	0.250113i
$628$	−43.6955	+	11.9476i	−1.74364	+	0.476759i
$629$	14.0782	+	14.0782i	0.561333	+	0.561333i
$630$	5.11708	+	4.95676i	0.203869	+	0.197482i
$631$			10.6343i			0.423346i	0.977341	+	0.211673i	$0.0678912\pi$
$631$			10.6343i			0.423346i	−0.977341	+	0.211673i	$0.932109\pi$
$632$	0.138268	+	18.0576i	0.00549999	+	0.718291i
$633$	−7.65281			−0.304172
$634$	−19.6188	−	5.20322i	−0.779163	−	0.206646i
$635$	−10.6653	−	37.7772i	−0.423240	−	1.49914i
$636$	−0.910117	+	1.59512i	−0.0360885	+	0.0632505i
$637$	9.17895	+	9.17895i	0.363683	+	0.363683i
$638$	10.5330	−	6.11711i	0.417004	−	0.242179i
$639$	2.33178			0.0922439
$640$	−17.3213	+	18.4383i	−0.684685	+	0.728839i
$641$	−21.4256			−0.846261			−0.423130	−	0.906069i	$-0.639069\pi$
$641$	−21.4256			−0.846261			−0.423130	+	0.906069i	$0.639069\pi$
$642$	8.62385	−	5.00837i	0.340356	−	0.197665i
$643$	−28.7046	−	28.7046i	−1.13200	−	1.13200i	−0.989845	−	0.142152i	$-0.954598\pi$
$643$	−28.7046	−	28.7046i	−1.13200	−	1.13200i	−0.142152	−	0.989845i	$-0.545402\pi$
$644$	−9.86557	+	17.2909i	−0.388758	+	0.681357i
$645$	21.7559	−	6.14217i	0.856639	−	0.241848i
$646$	−36.0699	−	9.56629i	−1.41915	−	0.376381i
$647$	−36.8695			−1.44949			−0.724746	−	0.689017i	$-0.758043\pi$
$647$	−36.8695			−1.44949			−0.724746	+	0.689017i	$0.758043\pi$
$648$	−0.0216568	−	2.82834i	−0.000850758	−	0.111108i
$649$		−	18.7579i		−	0.736311i
$650$	45.6864	−	13.6868i	1.79197	−	0.536841i
$651$	6.26582	+	6.26582i	0.245577	+	0.245577i
$652$	−36.4162	+	9.95720i	−1.42617	+	0.389954i
$653$	−27.8096	−	27.8096i	−1.08828	−	1.08828i	−0.995706	−	0.0925688i	$-0.970492\pi$
$653$	−27.8096	−	27.8096i	−1.08828	−	1.08828i	−0.0925688	−	0.995706i	$-0.529508\pi$
$654$	6.27044	−	3.64161i	0.245194	−	0.142398i
$655$	−1.27599	+	2.27989i	−0.0498571	+	0.0890829i
$656$	−15.4994	+	9.16079i	−0.605148	+	0.357669i
$657$		−	2.18275i		−	0.0851572i
$658$	−16.1851	−	27.8689i	−0.630961	−	1.08644i
$659$	−11.6956	+	11.6956i	−0.455596	+	0.455596i	−0.897207	−	0.441611i	$-0.854407\pi$
$659$	−11.6956	+	11.6956i	−0.455596	+	0.455596i	0.441611	+	0.897207i	$0.354407\pi$
$660$	−10.1949	−	2.53091i	−0.396835	−	0.0985156i
$661$	29.7275	+	29.7275i	1.15627	+	1.15627i	0.985272	+	0.170994i	$0.0546979\pi$
$661$	29.7275	+	29.7275i	1.15627	+	1.15627i	0.170994	+	0.985272i	$0.445302\pi$
$662$	17.6411	+	4.67871i	0.685643	+	0.181843i
$663$	47.1981			1.83302
$664$	14.7372	−	14.9646i	0.571913	−	0.580739i
$665$	9.27711	−	16.5760i	0.359751	−	0.642790i
$666$	3.88915	+	1.03146i	0.150702	+	0.0399684i
$667$	−11.4559	+	11.4559i	−0.443574	+	0.443574i
$668$	−12.6896	+	22.2404i	−0.490974	+	0.860506i
$669$	−12.9142	+	12.9142i	−0.499292	+	0.499292i
$670$	22.1465	−	0.352452i	0.855595	−	0.0136164i
$671$	16.6261			0.641843
$672$	−3.45524	−	12.2668i	−0.133289	−	0.473201i
$673$		−	19.4197i		−	0.748575i	−0.927313	−	0.374287i	$-0.877887\pi$
$673$		−	19.4197i		−	0.748575i	0.927313	−	0.374287i	$-0.122113\pi$
$674$	−3.28567	−	5.65754i	−0.126559	−	0.217920i
$675$	1.16459	−	4.86248i	0.0448252	−	0.187157i
$676$	56.4420	+	32.2038i	2.17085	+	1.23861i
$677$	−22.0550	+	22.0550i	−0.847643	+	0.847643i	−0.989839	−	0.142196i	$-0.954584\pi$
$677$	−22.0550	+	22.0550i	−0.847643	+	0.847643i	0.142196	+	0.989839i	$0.454584\pi$
$678$	0.231744	−	0.873796i	0.00890008	−	0.0335579i
$679$			10.3993i			0.399088i
$680$	−42.4996	+	12.3507i	−1.62978	+	0.473627i
$681$		−	3.16462i		−	0.121269i
$682$	−12.6289	−	3.34938i	−0.483586	−	0.128254i
$683$	−9.95729	+	9.95729i	−0.381005	+	0.381005i	−0.871464	−	0.490459i	$-0.836829\pi$
$683$	−9.95729	+	9.95729i	−0.381005	+	0.381005i	0.490459	+	0.871464i	$0.336829\pi$
$684$	−7.27452	+	1.98906i	−0.278148	+	0.0760535i
$685$	−19.2052	+	5.42205i	−0.733794	+	0.207166i
$686$	24.5883	−	14.2798i	0.938784	−	0.545207i
$687$		−	9.06474i		−	0.345842i
$688$	−39.1663	−	10.0672i	−1.49320	−	0.383808i
$689$	−6.19334			−0.235947
$690$	13.9700	−	0.222325i	0.531827	−	0.00846379i
$691$	−30.1664	+	30.1664i	−1.14758	+	1.14758i	−0.160556	+	0.987027i	$0.551329\pi$
$691$	−30.1664	+	30.1664i	−1.14758	+	1.14758i	−0.987027	+	0.160556i	$0.948671\pi$
$692$	35.0039	−	9.57105i	1.33065	−	0.363837i
$693$	3.74174	−	3.74174i	0.142137	−	0.142137i
$694$	8.30117	−	31.2997i	0.315108	−	1.18812i
$695$	−13.3468	−	7.46981i	−0.506272	−	0.283346i
$696$	−0.0794121	−	10.3711i	−0.00301011	−	0.393116i
$697$	−31.4973			−1.19304
$698$	−11.0974	+	41.8429i	−0.420042	+	1.58378i
$699$	−1.89485	−	1.89485i	−0.0716698	−	0.0716698i
$700$	−0.716884	−	22.5172i	−0.0270957	−	0.851071i
$701$	−2.10793	+	2.10793i	−0.0796155	+	0.0796155i	−0.745793	−	0.666178i	$-0.767929\pi$
$701$	−2.10793	+	2.10793i	−0.0796155	+	0.0796155i	0.666178	+	0.745793i	$0.267929\pi$
$702$	8.24838	−	4.79032i	0.311315	−	0.180799i
$703$		−	10.7283i		−	0.404626i
$704$	13.4890	+	13.0820i	0.508384	+	0.493047i
$705$	−11.0466	+	19.7377i	−0.416039	+	0.743364i
$706$	−18.6033	−	32.0327i	−0.700143	−	1.20557i
$707$	−2.56782	−	2.56782i	−0.0965729	−	0.0965729i
$708$	−13.8728	−	7.91530i	−0.521370	−	0.297475i
$709$	−29.5759	−	29.5759i	−1.11075	−	1.11075i	−0.993050	−	0.117697i	$-0.962449\pi$
$709$	−29.5759	−	29.5759i	−1.11075	−	1.11075i	−0.117697	−	0.993050i	$-0.537551\pi$
$710$	−5.29633	−	5.13040i	−0.198768	−	0.192540i
$711$			6.38450i			0.239437i
$712$	44.4332	−	0.340227i	1.66521	−	0.0127506i
$713$	17.3783			0.650824
$714$	5.71541	−	21.5501i	0.213894	−	0.806491i
$715$	−9.62488	−	34.0919i	−0.359950	−	1.27496i
$716$	−3.44088	−	12.5842i	−0.128592	−	0.470295i
$717$	18.4076	+	18.4076i	0.687446	+	0.687446i
$718$	4.07074	+	7.00935i	0.151919	+	0.261587i
$719$	15.2528			0.568833			0.284417	−	0.958701i	$-0.408200\pi$
$719$	15.2528			0.568833			0.284417	+	0.958701i	$0.408200\pi$
$720$	−6.17374	+	6.47186i	−0.230082	+	0.241192i
$721$	9.26506			0.345049
$722$	−3.39579	−	5.84716i	−0.126378	−	0.217609i
$723$	−4.15360	−	4.15360i	−0.154474	−	0.154474i
$724$	−11.2424	+	3.07399i	−0.417822	+	0.114244i
$725$	4.27039	−	17.8300i	0.158598	−	0.662190i
$726$	1.98777	−	7.49494i	0.0737732	−	0.278163i
$727$	−22.5396			−0.835947			−0.417973	−	0.908459i	$-0.637260\pi$
$727$	−22.5396			−0.835947			−0.417973	+	0.908459i	$0.637260\pi$
$728$	30.1563	−	30.6217i	1.11767	−	1.13492i
$729$		−	1.00000i		−	0.0370370i
$730$	−4.80249	+	4.95783i	−0.177748	+	0.183497i
$731$	−50.0254	−	50.0254i	−1.85025	−	1.85025i
$732$	7.01575	−	12.2962i	0.259310	−	0.454479i
$733$	8.88368	+	8.88368i	0.328126	+	0.328126i	0.851874	−	0.523747i	$-0.175466\pi$
$733$	8.88368	+	8.88368i	0.328126	+	0.328126i	−0.523747	+	0.851874i	$0.675466\pi$
$734$	14.9062	+	25.6668i	0.550198	+	0.947379i
$735$	−3.75541	−	2.10180i	−0.138520	−	0.0775259i
$736$	−21.8026	−	12.2195i	−0.803655	−	0.450415i
$737$		−	16.4518i		−	0.606011i
$738$	−5.50449	+	3.19678i	−0.202623	+	0.117675i
$739$	−3.00557	+	3.00557i	−0.110562	+	0.110562i	−0.760223	−	0.649662i	$-0.774911\pi$
$739$	−3.00557	+	3.00557i	−0.110562	+	0.110562i	0.649662	+	0.760223i	$0.274911\pi$
$740$	−6.56426	−	10.8998i	−0.241307	−	0.400683i
$741$	−17.9838	−	17.9838i	−0.660650	−	0.660650i
$742$	−0.749976	+	2.82780i	−0.0275325	+	0.103812i
$743$	14.5808			0.534919			0.267459	−	0.963569i	$-0.413816\pi$
$743$	14.5808			0.534919			0.267459	+	0.963569i	$0.413816\pi$
$744$	−7.80615	+	7.92662i	−0.286187	+	0.290604i
$745$	4.11399	+	2.30248i	0.150725	+	0.0843565i
$746$	−6.62114	+	24.9651i	−0.242417	+	0.914038i
$747$	5.25073	−	5.25073i	0.192114	−	0.192114i
$748$	8.67021	+	31.7093i	0.317014	+	1.15941i
$749$	11.2335	−	11.2335i	0.410465	−	0.410465i
$750$	−13.3437	+	8.48214i	−0.487242	+	0.309724i
$751$	−1.92675			−0.0703083			−0.0351541	−	0.999382i	$-0.511192\pi$
$751$	−1.92675			−0.0703083			−0.0351541	+	0.999382i	$0.511192\pi$
$752$	34.8323	−	20.5874i	1.27020	−	0.750746i
$753$		−	11.9371i		−	0.435012i
$754$	30.2456	−	17.5654i	1.10148	−	0.639694i
$755$	−5.84176	−	20.6919i	−0.212603	−	0.753054i
$756$	−1.18837	−	4.34619i	−0.0432205	−	0.158069i
$757$	0.389306	−	0.389306i	0.0141496	−	0.0141496i	−0.699997	−	0.714146i	$-0.746815\pi$
$757$	0.389306	−	0.389306i	0.0141496	−	0.0141496i	0.714146	+	0.699997i	$0.246815\pi$
$758$	−15.6076	−	4.13938i	−0.566894	−	0.150349i
$759$		−	10.3778i		−	0.376689i
$760$	20.8994	+	11.4876i	0.758102	+	0.416697i
$761$		−	18.0200i		−	0.653223i	−0.945159	−	0.326612i	$-0.894093\pi$
$761$		−	18.0200i		−	0.653223i	0.945159	−	0.326612i	$-0.105907\pi$
$762$	−6.36430	+	23.9967i	−0.230554	+	0.869309i
$763$	8.16797	−	8.16797i	0.295700	−	0.295700i
$764$	−0.944957	+	1.65618i	−0.0341873	+	0.0599185i
$765$	−15.0589	+	4.25144i	−0.544454	+	0.153711i
$766$	6.55738	+	11.2911i	0.236928	+	0.407963i
$767$		−	53.8635i		−	1.94490i
$768$	15.3670	−	4.45578i	0.554510	−	0.160784i
$769$	−34.9422			−1.26005			−0.630024	−	0.776576i	$-0.716955\pi$
$769$	−34.9422			−1.26005			−0.630024	+	0.776576i	$0.716955\pi$
$770$	−16.7314	+	0.266273i	−0.602959	+	0.00959582i
$771$	−15.6986	+	15.6986i	−0.565371	+	0.565371i
$772$	−8.37621	−	4.77917i	−0.301466	−	0.172006i
$773$	9.83112	−	9.83112i	0.353601	−	0.353601i	−0.507847	−	0.861447i	$-0.669558\pi$
$773$	9.83112	−	9.83112i	0.353601	−	0.353601i	0.861447	+	0.507847i	$0.169558\pi$
$774$	−13.8197	−	3.66521i	−0.496740	−	0.131743i
$775$	−16.7629	+	10.2848i	−0.602142	+	0.369442i
$776$	−13.0557	+	0.0999682i	−0.468673	+	0.00358865i
$777$	6.40967			0.229946
$778$	12.2246	+	3.24216i	0.438274	+	0.116237i
$779$	12.0013	+	12.0013i	0.429992	+	0.429992i
$780$	−29.2748	−	7.26755i	−1.04820	−	0.260220i
$781$	−3.87282	+	3.87282i	−0.138580	+	0.138580i
$782$	−21.9588	−	37.8106i	−0.785246	−	1.35210i
$783$		−	3.66685i		−	0.131043i
$784$	3.91709	+	6.62741i	0.139896	+	0.236693i
$785$	44.1954	+	24.7349i	1.57740	+	0.882826i
$786$	1.42891	−	0.829850i	0.0509675	−	0.0295998i
$787$	−34.3615	−	34.3615i	−1.22486	−	1.22486i	−0.965885	−	0.258970i	$-0.916617\pi$
$787$	−34.3615	−	34.3615i	−1.22486	−	1.22486i	−0.258970	−	0.965885i	$-0.583383\pi$
$788$	1.84751	+	6.75686i	0.0658150	+	0.240703i
$789$	0.328420	+	0.328420i	0.0116921	+	0.0116921i
$790$	14.0472	−	14.5015i	0.499777	−	0.515941i
$791$		−	1.44009i		−	0.0512038i
$792$	4.73351	+	4.66157i	0.168198	+	0.165642i
$793$	47.7421			1.69537
$794$	−2.08406	−	0.552725i	−0.0739606	−	0.0196155i
$795$	1.97602	−	0.557874i	0.0700823	−	0.0197858i
$796$	−30.3017	−	17.2891i	−1.07402	−	0.612795i
$797$	3.63103	+	3.63103i	0.128618	+	0.128618i	0.768485	−	0.639868i	$-0.221011\pi$
$797$	3.63103	+	3.63103i	0.128618	+	0.128618i	−0.639868	+	0.768485i	$0.721011\pi$
$798$	−10.3889	+	6.03344i	−0.367763	+	0.213581i
$799$	70.7850			2.50419
$800$	28.2622	−	1.11647i	0.999221	−	0.0394730i
$801$	15.7100			0.555085
$802$	−45.3668	+	26.3471i	−1.60196	+	0.930349i
$803$	3.62529	+	3.62529i	0.127934	+	0.127934i
$804$	−12.1673	−	6.94222i	−0.429107	−	0.244833i
$805$	21.4199	−	6.04730i	0.754952	−	0.213139i
$806$	−36.2641	−	9.61781i	−1.27735	−	0.338773i
$807$	−6.70626			−0.236072
$808$	3.19908	−	3.24844i	0.112543	−	0.114280i
$809$			15.9241i			0.559860i	0.960020	+	0.279930i	$0.0903113\pi$
$809$			15.9241i			0.559860i	−0.960020	+	0.279930i	$0.909689\pi$
$810$	−2.20020	+	2.27137i	−0.0773073	+	0.0798077i
$811$	11.6448	+	11.6448i	0.408906	+	0.408906i	0.881357	−	0.472451i	$-0.156631\pi$
$811$	11.6448	+	11.6448i	0.408906	+	0.408906i	−0.472451	+	0.881357i	$0.656631\pi$
$812$	−4.35757	−	15.9368i	−0.152921	−	0.559273i
$813$	−8.51477	−	8.51477i	−0.298626	−	0.298626i
$814$	−8.17256	+	4.74628i	−0.286448	+	0.166357i
$815$	36.8328	+	20.6143i	1.29020	+	0.722087i
$816$	27.1099	+	6.96822i	0.949035	+	0.243937i
$817$			38.1220i			1.33372i
$818$	12.3170	+	21.2084i	0.430653	+	0.741536i
$819$	10.7445	−	10.7445i	0.375442	−	0.375442i
$820$	19.5363	+	4.84994i	0.682236	+	0.169367i
$821$	24.3703	+	24.3703i	0.850530	+	0.850530i	0.990198	−	0.139669i	$-0.0446037\pi$
$821$	24.3703	+	24.3703i	0.850530	+	0.850530i	−0.139669	+	0.990198i	$0.544604\pi$
$822$	12.1995	+	3.23549i	0.425506	+	0.112851i
$823$	−51.2425			−1.78620			−0.893101	−	0.449856i	$-0.851475\pi$
$823$	−51.2425			−1.78620			−0.893101	+	0.449856i	$0.851475\pi$
$824$	0.0890650	+	11.6318i	0.00310273	+	0.405212i
$825$	6.14176	+	10.0103i	0.213828	+	0.348512i
$826$	−24.5934	−	6.52255i	−0.855714	−	0.226949i
$827$	9.55201	−	9.55201i	0.332156	−	0.332156i	−0.521249	−	0.853405i	$-0.674534\pi$
$827$	9.55201	−	9.55201i	0.332156	−	0.332156i	0.853405	+	0.521249i	$0.174534\pi$
$828$	−7.67509	−	4.37913i	−0.266728	−	0.152185i
$829$	−33.3127	+	33.3127i	−1.15700	+	1.15700i	−0.171879	+	0.985118i	$0.554984\pi$
$829$	−33.3127	+	33.3127i	−1.15700	+	1.15700i	−0.985118	+	0.171879i	$0.945016\pi$
$830$	−23.4790	+	0.373657i	−0.814968	+	0.0129698i
$831$	−25.4219			−0.881877
$832$	38.7338	+	37.5653i	1.34285	+	1.30234i
$833$			13.4680i			0.466638i
$834$	4.85804	+	8.36500i	0.168220	+	0.289656i
$835$	27.5513	−	7.77832i	0.953451	−	0.269180i
$836$	8.77853	−	15.3857i	0.303612	−	0.532126i
$837$	−2.78127	+	2.78127i	−0.0961347	+	0.0961347i
$838$	10.4960	−	39.5753i	0.362578	−	1.36711i
$839$			9.50181i			0.328039i	0.986457	+	0.164019i	$0.0524460\pi$
$839$			9.50181i			0.328039i	−0.986457	+	0.164019i	$0.947554\pi$
$840$	−6.86327	+	12.4864i	−0.236805	+	0.430823i
$841$			15.5542i			0.536352i
$842$	20.5192	+	5.44200i	0.707137	+	0.187544i
$843$	6.77911	−	6.77911i	0.233485	−	0.233485i
$844$	−4.03680	−	14.7637i	−0.138952	−	0.508187i
$845$	−19.7399	−	69.9200i	−0.679075	−	2.40532i
$846$	12.3705	−	7.18424i	0.425305	−	0.246999i
$847$		−	12.3523i		−	0.424431i
$848$	−3.55736	−	0.914370i	−0.122160	−	0.0313996i
$849$	−7.19866			−0.247057
$850$	43.5582	+	23.4760i	1.49403	+	0.805219i
$851$	8.88866	−	8.88866i	0.304699	−	0.304699i
$852$	1.23000	+	4.49844i	0.0421391	+	0.154114i
$853$	−14.2909	+	14.2909i	−0.489310	+	0.489310i	−0.908089	−	0.418778i	$-0.862458\pi$
$853$	−14.2909	+	14.2909i	−0.489310	+	0.489310i	0.418778	+	0.908089i	$0.362458\pi$
$854$	5.78129	−	21.7984i	0.197832	−	0.745928i
$855$	7.35775	+	4.11792i	0.251630	+	0.140830i
$856$	14.2111	+	13.9951i	0.485725	+	0.478343i
$857$	24.4246			0.834327			0.417164	−	0.908831i	$-0.363024\pi$
$857$	24.4246			0.834327			0.417164	+	0.908831i	$0.363024\pi$
$858$	−5.74344	+	21.6557i	−0.196078	+	0.739314i
$859$	21.3398	+	21.3398i	0.728105	+	0.728105i	0.970242	−	0.242137i	$-0.0778485\pi$
$859$	21.3398	+	21.3398i	0.728105	+	0.728105i	−0.242137	+	0.970242i	$0.577848\pi$
$860$	23.3255	+	38.7313i	0.795392	+	1.32072i
$861$	−7.17022	+	7.17022i	−0.244361	+	0.244361i
$862$	−21.9819	+	12.7662i	−0.748708	+	0.434818i
$863$			54.8339i			1.86657i	0.359138	+	0.933284i	$0.383071\pi$
$863$			54.8339i			1.86657i	−0.359138	+	0.933284i	$0.616929\pi$
$864$	5.44497	−	1.53371i	0.185242	−	0.0521779i
$865$	−35.4044	−	19.8148i	−1.20379	−	0.673724i
$866$	16.4149	+	28.2645i	0.557800	+	0.960468i
$867$	22.6054	+	22.6054i	0.767718	+	0.767718i
$868$	−8.78274	+	15.3931i	−0.298106	+	0.522475i
$869$	−10.6039	−	10.6039i	−0.359712	−	0.359712i
$870$	−8.06782	+	8.32876i	−0.273525	+	0.282372i
$871$		−	47.2417i		−	1.60072i
$872$	10.3330	+	10.1759i	0.349918	+	0.344600i
$873$	−4.61603			−0.156229
$874$	−6.03996	+	22.7738i	−0.204305	+	0.770335i
$875$	−17.0824	+	18.5098i	−0.577492	+	0.625747i
$876$	4.21093	−	1.15138i	0.142274	−	0.0389017i
$877$	8.43052	+	8.43052i	0.284678	+	0.284678i	0.834972	−	0.550293i	$-0.185484\pi$
$877$	8.43052	+	8.43052i	0.284678	+	0.284678i	−0.550293	+	0.834972i	$0.685484\pi$
$878$	1.88246	+	3.24138i	0.0635299	+	0.109391i
$879$	−6.01142			−0.202760
$880$	−0.495130	−	21.0028i	−0.0166908	−	0.708005i
$881$	−33.7215			−1.13611			−0.568053	−	0.822992i	$-0.692303\pi$
$881$	−33.7215			−1.13611			−0.568053	+	0.822992i	$0.692303\pi$
$882$	1.36692	+	2.35368i	0.0460265	+	0.0792524i
$883$	33.5737	+	33.5737i	1.12984	+	1.12984i	0.990202	+	0.139642i	$0.0445953\pi$
$883$	33.5737	+	33.5737i	1.12984	+	1.12984i	0.139642	+	0.990202i	$0.455405\pi$
$884$	24.8967	+	91.0539i	0.837365	+	3.06247i
$885$	4.85184	+	17.1855i	0.163093	+	0.577684i
$886$	−0.501030	+	1.88914i	−0.0168324	+	0.0634670i
$887$	−7.09705			−0.238295			−0.119148	−	0.992877i	$-0.538016\pi$
$887$	−7.09705			−0.238295			−0.119148	+	0.992877i	$0.538016\pi$
$888$	0.0616161	+	8.04698i	0.00206770	+	0.270039i
$889$			39.5487i			1.32642i
$890$	−35.6831	−	34.5652i	−1.19610	−	1.15863i
$891$	1.66088	+	1.66088i	0.0556416	+	0.0556416i
$892$	−31.7260	−	18.1017i	−1.06227	−	0.606091i
$893$	−26.9710	−	26.9710i	−0.902551	−	0.902551i
$894$	−1.49744	−	2.57842i	−0.0500818	−	0.0862352i
$895$	−7.12362	+	12.7282i	−0.238116	+	0.425457i
$896$	21.8423	−	13.1364i	0.729698	−	0.438857i
$897$		−	29.7999i		−	0.994991i
$898$	24.0443	−	13.9640i	0.802370	−	0.465983i
$899$	−10.1985	+	10.1985i	−0.340139	+	0.340139i
$900$	9.99494	−	0.318210i	0.333165	−	0.0106070i
$901$	−4.54365	−	4.54365i	−0.151371	−	0.151371i
$902$	3.83283	−	14.4518i	0.127619	−	0.481191i
$903$	−22.7761			−0.757942
$904$	1.80796	−	0.0138436i	0.0601317	−	0.000460431i
$905$	11.3711	+	6.36405i	0.377987	+	0.211548i
$906$	−3.48594	+	13.1438i	−0.115813	+	0.436674i
$907$	4.37877	−	4.37877i	0.145395	−	0.145395i	−0.630662	−	0.776057i	$-0.717217\pi$
$907$	4.37877	−	4.37877i	0.145395	−	0.145395i	0.776057	+	0.630662i	$0.217217\pi$
$908$	6.10514	−	1.66932i	0.202606	−	0.0553982i
$909$	1.13980	−	1.13980i	0.0378049	−	0.0378049i
$910$	−48.0446	+	0.764608i	−1.59266	+	0.0253465i
$911$	26.7307			0.885627			0.442814	−	0.896614i	$-0.353980\pi$
$911$	26.7307			0.885627			0.442814	+	0.896614i	$0.353980\pi$
$912$	−7.67451	−	12.9847i	−0.254129	−	0.429966i
$913$			17.4417i			0.577235i
$914$	−31.7660	+	18.4484i	−1.05073	+	0.610218i
$915$	−15.2324	+	4.30044i	−0.503568	+	0.142168i
$916$	17.4876	−	4.78159i	0.577805	−	0.157988i
$917$	1.86132	−	1.86132i	0.0614661	−	0.0614661i
$918$	9.56564	+	2.53696i	0.315713	+	0.0837320i
$919$		−	24.5598i		−	0.810154i	−0.914282	−	0.405077i	$-0.867245\pi$
$919$		−	24.5598i		−	0.810154i	0.914282	−	0.405077i	$-0.132755\pi$
$920$	7.79796	+	26.8334i	0.257091	+	0.884670i
$921$			0.217585i			0.00716968i
$922$	0.995768	−	3.75456i	0.0327939	−	0.123650i
$923$	−11.1209	+	11.1209i	−0.366047	+	0.366047i
$924$	9.19224	+	5.24476i	0.302402	+	0.172540i
$925$	−3.31341	+	13.8344i	−0.108944	+	0.454871i
$926$	9.07710	+	15.6297i	0.298292	+	0.513625i
$927$			4.11257i			0.135075i
$928$	19.9659	−	5.62389i	0.655413	−	0.184613i
$929$	6.25552			0.205237			0.102619	−	0.994721i	$-0.467278\pi$
$929$	6.25552			0.205237			0.102619	+	0.994721i	$0.467278\pi$
$930$	12.4366	−	0.197923i	0.407813	−	0.00649016i
$931$	5.13167	−	5.13167i	0.168184	−	0.168184i
$932$	2.65600	−	4.65504i	0.0870001	−	0.152481i
$933$	−24.6222	+	24.6222i	−0.806095	+	0.806095i
$934$	−54.5450	−	14.4662i	−1.78477	−	0.473348i
$935$	17.9498	−	32.0721i	0.587023	−	1.04887i
$936$	13.5924	+	13.3858i	0.444280	+	0.437528i
$937$	33.0332			1.07915			0.539574	−	0.841938i	$-0.318585\pi$
$937$	33.0332			1.07915			0.539574	+	0.841938i	$0.318585\pi$
$938$	−21.5700	−	5.72069i	−0.704285	−	0.186787i
$939$	12.2621	+	12.2621i	0.400158	+	0.400158i
$940$	−43.9046	−	10.8995i	−1.43201	−	0.355501i
$941$	−24.4774	+	24.4774i	−0.797941	+	0.797941i	−0.982771	−	0.184830i	$-0.940827\pi$
$941$	−24.4774	+	24.4774i	−0.797941	+	0.797941i	0.184830	+	0.982771i	$0.440827\pi$
$942$	−16.0865	−	27.6991i	−0.524127	−	0.902487i
$943$			19.8867i			0.647601i
$944$	7.95229	−	30.9384i	0.258825	−	1.00696i
$945$	−2.46026	+	4.39591i	−0.0800324	+	0.142999i
$946$	29.0404	−	16.8655i	0.944185	−	0.548344i
$947$	−34.7666	−	34.7666i	−1.12976	−	1.12976i	−0.990216	−	0.139546i	$-0.955436\pi$
$947$	−34.7666	−	34.7666i	−1.12976	−	1.12976i	−0.139546	−	0.990216i	$-0.544564\pi$
$948$	−12.3169	+	3.36778i	−0.400033	+	0.109380i
$949$	10.4101	+	10.4101i	0.337925	+	0.337925i
$950$	−7.65189	−	25.5419i	−0.248260	−	0.828687i
$951$		−	14.3522i		−	0.465402i
$952$	44.5889	−	0.341419i	1.44513	−	0.0110655i
$953$	16.9913			0.550403			0.275201	−	0.961387i	$-0.411255\pi$
$953$	16.9913			0.550403			0.275201	+	0.961387i	$0.411255\pi$
$954$	−1.25520	−	0.332899i	−0.0406387	−	0.0107780i
$955$	2.05167	−	0.579230i	0.0663904	−	0.0187434i
$956$	−25.8018	+	45.2216i	−0.834491	+	1.46257i
$957$	6.09021	+	6.09021i	0.196868	+	0.196868i
$958$	27.6995	−	16.0867i	0.894929	−	0.519738i
$959$	20.1058			0.649251
$960$	−15.7420	−	8.49643i	−0.508071	−	0.274221i
$961$	−15.5291			−0.500938
$962$	−23.4677	+	13.6290i	−0.756628	+	0.439418i
$963$	4.98634	+	4.98634i	0.160683	+	0.160683i
$964$	5.82207	−	10.2041i	0.187516	−	0.328651i
$965$	2.92948	+	10.3764i	0.0943034	+	0.334028i
$966$	−13.6063	−	3.60859i	−0.437775	−	0.116105i
$967$	57.8174			1.85928			0.929641	−	0.368467i	$-0.120117\pi$
$967$	57.8174			1.85928			0.929641	+	0.368467i	$0.120117\pi$
$968$	15.5077	−	0.118743i	0.498435	−	0.00381654i
$969$		−	26.3870i		−	0.847674i
$970$	10.4847	+	10.1562i	0.336643	+	0.326096i
$971$	−39.9663	−	39.9663i	−1.28258	−	1.28258i	−0.939196	−	0.343383i	$-0.888427\pi$
$971$	−39.9663	−	39.9663i	−1.28258	−	1.28258i	−0.343383	−	0.939196i	$-0.611573\pi$
$972$	1.92918	−	0.527493i	0.0618786	−	0.0169193i
$973$	10.8964	+	10.8964i	0.349322	+	0.349322i
$974$	−24.6057	+	14.2900i	−0.788418	+	0.457880i
$975$	17.6362	+	28.7446i	0.564809	+	0.920564i
$976$	27.4223	+	7.04854i	0.877767	+	0.225618i
$977$			55.3797i			1.77175i	0.463921	+	0.885877i	$0.346442\pi$
$977$			55.3797i			1.77175i	−0.463921	+	0.885877i	$0.653558\pi$
$978$	−13.4066	−	23.0847i	−0.428697	−	0.738168i
$979$	−26.0924	+	26.0924i	−0.833917	+	0.833917i
$980$	2.07380	−	8.35356i	0.0662450	−	0.266845i
$981$	3.62560	+	3.62560i	0.115756	+	0.115756i
$982$	−39.5204	−	10.4814i	−1.26115	−	0.334476i
$983$	−3.19883			−0.102027			−0.0510134	−	0.998698i	$-0.516245\pi$
$983$	−3.19883			−0.102027			−0.0510134	+	0.998698i	$0.516245\pi$
$984$	−9.07075	−	8.93289i	−0.289165	−	0.284770i
$985$	3.82489	−	6.83417i	0.121871	−	0.217755i
$986$	35.0758	+	9.30264i	1.11704	+	0.296257i
$987$	16.1139	−	16.1139i	0.512912	−	0.512912i
$988$	25.2077	−	44.1803i	0.801964	−	1.40556i
$989$	−31.5850	+	31.5850i	−1.00434	+	1.00434i
$990$	−0.118193	−	7.42675i	−0.00375643	−	0.236038i
$991$	10.5891			0.336373			0.168186	−	0.985755i	$-0.446209\pi$
$991$	10.5891			0.336373			0.168186	+	0.985755i	$0.446209\pi$
$992$	−19.4096	−	10.8783i	−0.616255	−	0.345385i
$993$			12.9054i			0.409541i
$994$	3.73097	+	6.42431i	0.118339	+	0.203767i
$995$	10.5977	+	37.5376i	0.335969	+	1.19002i
$996$	12.8993	+	7.35990i	0.408731	+	0.233207i
$997$	−18.1735	+	18.1735i	−0.575559	+	0.575559i	−0.933677	−	0.358117i	$-0.883419\pi$
$997$	−18.1735	+	18.1735i	−0.575559	+	0.575559i	0.358117	+	0.933677i	$0.383419\pi$
$998$	−13.7014	+	51.6612i	−0.433709	+	1.63531i
$999$			2.84512i			0.0900157i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.bl.a.229.4	yes	48
3.2	odd	2		720.2.bm.h.469.21		48
4.3	odd	2		960.2.bl.a.49.14		48
5.4	even	2	inner	240.2.bl.a.229.21	yes	48
8.3	odd	2		1920.2.bl.b.1249.9		48
8.5	even	2		1920.2.bl.a.1249.16		48
15.14	odd	2		720.2.bm.h.469.4		48
16.3	odd	4		960.2.bl.a.529.8		48
16.5	even	4		1920.2.bl.a.289.9		48
16.11	odd	4		1920.2.bl.b.289.16		48
16.13	even	4	inner	240.2.bl.a.109.21	yes	48
20.19	odd	2		960.2.bl.a.49.8		48
40.19	odd	2		1920.2.bl.b.1249.16		48
40.29	even	2		1920.2.bl.a.1249.9		48
48.29	odd	4		720.2.bm.h.109.4		48
80.19	odd	4		960.2.bl.a.529.14		48
80.29	even	4	inner	240.2.bl.a.109.4	✓	48
80.59	odd	4		1920.2.bl.b.289.9		48
80.69	even	4		1920.2.bl.a.289.16		48
240.29	odd	4		720.2.bm.h.109.21		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bl.a.109.4	✓	48	80.29	even	4	inner
240.2.bl.a.109.21	yes	48	16.13	even	4	inner
240.2.bl.a.229.4	yes	48	1.1	even	1	trivial
240.2.bl.a.229.21	yes	48	5.4	even	2	inner
720.2.bm.h.109.4		48	48.29	odd	4
720.2.bm.h.109.21		48	240.29	odd	4
720.2.bm.h.469.4		48	15.14	odd	2
720.2.bm.h.469.21		48	3.2	odd	2
960.2.bl.a.49.8		48	20.19	odd	2
960.2.bl.a.49.14		48	4.3	odd	2
960.2.bl.a.529.8		48	16.3	odd	4
960.2.bl.a.529.14		48	80.19	odd	4
1920.2.bl.a.289.9		48	16.5	even	4
1920.2.bl.a.289.16		48	80.69	even	4
1920.2.bl.a.1249.9		48	40.29	even	2
1920.2.bl.a.1249.16		48	8.5	even	2
1920.2.bl.b.289.9		48	80.59	odd	4
1920.2.bl.b.289.16		48	16.11	odd	4
1920.2.bl.b.1249.9		48	8.3	odd	2
1920.2.bl.b.1249.16		48	40.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	240.bl (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22294 + 0.710230i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(0.991146 - 1.73713i) q^{4} +(-2.15195 + 0.607542i) q^{5} +(1.36696 + 0.362538i) q^{6} +2.25286 q^{7} +(0.0216568 + 2.82834i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(-1.22294 + 0.710230i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(0.991146 - 1.73713i) q^{4} +(-2.15195 + 0.607542i) q^{5} +(1.36696 + 0.362538i) q^{6} +2.25286 q^{7} +(0.0216568 + 2.82834i) q^{8} +1.00000i q^{9} +(2.20020 - 2.27137i) q^{10} +(-1.66088 - 1.66088i) q^{11} +(-1.92918 + 0.527493i) q^{12} +(-4.76925 - 4.76925i) q^{13} +(-2.75511 + 1.60005i) q^{14} +(1.95126 + 1.09206i) q^{15} +(-2.03526 - 3.44350i) q^{16} -6.99777i q^{17} +(-0.710230 - 1.22294i) q^{18} +(-2.66634 + 2.66634i) q^{19} +(-1.07751 + 4.34039i) q^{20} +(-1.59301 - 1.59301i) q^{21} +(3.21076 + 0.851543i) q^{22} -4.41825 q^{23} +(1.98463 - 2.01526i) q^{24} +(4.26178 - 2.61480i) q^{25} +(9.21975 + 2.44522i) q^{26} +(0.707107 - 0.707107i) q^{27} +(2.23291 - 3.91352i) q^{28} +(2.59286 - 2.59286i) q^{29} +(-3.16188 + 0.0503198i) q^{30} -3.93331 q^{31} +(4.93467 + 2.76568i) q^{32} +2.34884i q^{33} +(4.97003 + 8.55783i) q^{34} +(-4.84805 + 1.36871i) q^{35} +(1.73713 + 0.991146i) q^{36} +(-2.01181 + 2.01181i) q^{37} +(1.36705 - 5.15448i) q^{38} +6.74474i q^{39} +(-1.76494 - 6.07330i) q^{40} -4.50104i q^{41} +(3.07956 + 0.816748i) q^{42} +(7.14876 - 7.14876i) q^{43} +(-4.53135 + 1.23900i) q^{44} +(-0.607542 - 2.15195i) q^{45} +(5.40324 - 3.13798i) q^{46} +10.1154i q^{47} +(-0.995778 + 3.87407i) q^{48} -1.92461 q^{49} +(-3.35478 + 6.22459i) q^{50} +(-4.94817 + 4.94817i) q^{51} +(-13.0118 + 3.55780i) q^{52} +(0.649299 - 0.649299i) q^{53} +(-0.362538 + 1.36696i) q^{54} +(4.58319 + 2.56508i) q^{55} +(0.0487897 + 6.37187i) q^{56} +3.77078 q^{57} +(-1.32937 + 5.01242i) q^{58} +(5.64696 + 5.64696i) q^{59} +(3.83104 - 2.30720i) q^{60} +(-5.00520 + 5.00520i) q^{61} +(4.81018 - 2.79355i) q^{62} +2.25286i q^{63} +(-7.99906 + 0.122506i) q^{64} +(13.1607 + 7.36567i) q^{65} +(-1.66822 - 2.87248i) q^{66} +(4.95274 + 4.95274i) q^{67} +(-12.1561 - 6.93581i) q^{68} +(3.12417 + 3.12417i) q^{69} +(4.95676 - 5.11708i) q^{70} -2.33178i q^{71} +(-2.82834 + 0.0216568i) q^{72} -2.18275 q^{73} +(1.03146 - 3.88915i) q^{74} +(-4.86248 - 1.16459i) q^{75} +(1.98906 + 7.27452i) q^{76} +(-3.74174 - 3.74174i) q^{77} +(-4.79032 - 8.24838i) q^{78} +6.38450 q^{79} +(6.47186 + 6.17374i) q^{80} -1.00000 q^{81} +(3.19678 + 5.50449i) q^{82} +(-5.25073 - 5.25073i) q^{83} +(-4.34619 + 1.18837i) q^{84} +(4.25144 + 15.0589i) q^{85} +(-3.66521 + 13.8197i) q^{86} -3.66685 q^{87} +(4.66157 - 4.73351i) q^{88} -15.7100i q^{89} +(2.27137 + 2.20020i) q^{90} +(-10.7445 - 10.7445i) q^{91} +(-4.37913 + 7.67509i) q^{92} +(2.78127 + 2.78127i) q^{93} +(-7.18424 - 12.3705i) q^{94} +(4.11792 - 7.35775i) q^{95} +(-1.53371 - 5.44497i) q^{96} +4.61603i q^{97} +(2.35368 - 1.36692i) q^{98} +(1.66088 - 1.66088i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q + 12 q^{10} - 16 q^{14} - 4 q^{16} + 8 q^{19} - 4 q^{24} - 40 q^{26} - 8 q^{30} - 48 q^{31} - 28 q^{34} + 24 q^{35} - 4 q^{36} - 16 q^{40} - 40 q^{44} - 4 q^{46} + 48 q^{49} - 32 q^{50} + 8 q^{51} - 4 q^{54} + 48 q^{56} - 32 q^{59} - 24 q^{60} + 16 q^{61} + 48 q^{64} + 16 q^{65} + 24 q^{66} - 16 q^{69} + 40 q^{74} - 16 q^{75} + 60 q^{76} - 96 q^{79} + 72 q^{80} - 48 q^{81} + 16 q^{86} + 8 q^{90} - 32 q^{91} + 44 q^{94} - 48 q^{95} - 40 q^{96}+O(q^{100}) \) 48 * q + 12 * q^10 - 16 * q^14 - 4 * q^16 + 8 * q^19 - 4 * q^24 - 40 * q^26 - 8 * q^30 - 48 * q^31 - 28 * q^34 + 24 * q^35 - 4 * q^36 - 16 * q^40 - 40 * q^44 - 4 * q^46 + 48 * q^49 - 32 * q^50 + 8 * q^51 - 4 * q^54 + 48 * q^56 - 32 * q^59 - 24 * q^60 + 16 * q^61 + 48 * q^64 + 16 * q^65 + 24 * q^66 - 16 * q^69 + 40 * q^74 - 16 * q^75 + 60 * q^76 - 96 * q^79 + 72 * q^80 - 48 * q^81 + 16 * q^86 + 8 * q^90 - 32 * q^91 + 44 * q^94 - 48 * q^95 - 40 * q^96

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