LMFDB - Embedded newform 240.2.bl.a.109.3

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			109.3
Character	$\chi$	$=$	240.109
Dual form			240.2.bl.a.229.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36038 + 0.386472i) q^{2} +(0.707107 - 0.707107i) q^{3} +(1.70128 - 1.05150i) q^{4} +(-1.98421 + 1.03097i) q^{5} +(-0.688658 + 1.23521i) q^{6} -3.91927 q^{7} +(-1.90801 + 2.08794i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(-1.36038 + 0.386472i) q^{2} +(0.707107 - 0.707107i) q^{3} +(1.70128 - 1.05150i) q^{4} +(-1.98421 + 1.03097i) q^{5} +(-0.688658 + 1.23521i) q^{6} -3.91927 q^{7} +(-1.90801 + 2.08794i) q^{8} -1.00000i q^{9} +(2.30085 - 2.16936i) q^{10} +(-2.93423 + 2.93423i) q^{11} +(0.459462 - 1.94651i) q^{12} +(-0.732828 + 0.732828i) q^{13} +(5.33170 - 1.51469i) q^{14} +(-0.674045 + 2.13206i) q^{15} +(1.78869 - 3.57779i) q^{16} +2.89302i q^{17} +(0.386472 + 1.36038i) q^{18} +(1.67534 + 1.67534i) q^{19} +(-2.29163 + 3.84037i) q^{20} +(-2.77134 + 2.77134i) q^{21} +(2.85767 - 5.12567i) q^{22} -1.73133 q^{23} +(0.127228 + 2.82556i) q^{24} +(2.87420 - 4.09133i) q^{25} +(0.713708 - 1.28014i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(-6.66776 + 4.12111i) q^{28} +(-4.99003 - 4.99003i) q^{29} +(0.0929773 - 3.16091i) q^{30} -10.8149 q^{31} +(-1.05059 + 5.55844i) q^{32} +4.14963i q^{33} +(-1.11807 - 3.93561i) q^{34} +(7.77666 - 4.04065i) q^{35} +(-1.05150 - 1.70128i) q^{36} +(6.41524 + 6.41524i) q^{37} +(-2.92658 - 1.63163i) q^{38} +1.03637i q^{39} +(1.63330 - 6.11002i) q^{40} +0.00577512i q^{41} +(2.69904 - 4.84113i) q^{42} +(-2.23930 - 2.23930i) q^{43} +(-1.90660 + 8.07728i) q^{44} +(1.03097 + 1.98421i) q^{45} +(2.35527 - 0.669110i) q^{46} -11.6451i q^{47} +(-1.26508 - 3.79468i) q^{48} +8.36066 q^{49} +(-2.32883 + 6.67657i) q^{50} +(2.04567 + 2.04567i) q^{51} +(-0.476175 + 2.01731i) q^{52} +(5.55765 + 5.55765i) q^{53} +(1.23521 + 0.688658i) q^{54} +(2.79703 - 8.84724i) q^{55} +(7.47801 - 8.18319i) q^{56} +2.36929 q^{57} +(8.71685 + 4.85983i) q^{58} +(3.83290 - 3.83290i) q^{59} +(1.09512 + 4.33598i) q^{60} +(9.30595 + 9.30595i) q^{61} +(14.7123 - 4.17964i) q^{62} +3.91927i q^{63} +(-0.718981 - 7.96763i) q^{64} +(0.698563 - 2.20961i) q^{65} +(-1.60372 - 5.64508i) q^{66} +(-3.85243 + 3.85243i) q^{67} +(3.04201 + 4.92182i) q^{68} +(-1.22423 + 1.22423i) q^{69} +(-9.01763 + 8.50229i) q^{70} +1.15355i q^{71} +(2.08794 + 1.90801i) q^{72} -7.98713 q^{73} +(-11.2065 - 6.24786i) q^{74} +(-0.860637 - 4.92537i) q^{75} +(4.61185 + 1.08860i) q^{76} +(11.5000 - 11.5000i) q^{77} +(-0.400530 - 1.40987i) q^{78} +0.843960 q^{79} +(0.139442 + 8.94318i) q^{80} -1.00000 q^{81} +(-0.00223193 - 0.00785637i) q^{82} +(-5.20069 + 5.20069i) q^{83} +(-1.80076 + 7.62889i) q^{84} +(-2.98261 - 5.74036i) q^{85} +(3.91173 + 2.18088i) q^{86} -7.05696 q^{87} +(-0.527948 - 11.7250i) q^{88} -5.40896i q^{89} +(-2.16936 - 2.30085i) q^{90} +(2.87215 - 2.87215i) q^{91} +(-2.94547 + 1.82049i) q^{92} +(-7.64726 + 7.64726i) q^{93} +(4.50051 + 15.8418i) q^{94} +(-5.05147 - 1.59701i) q^{95} +(3.18753 + 4.67329i) q^{96} -2.24154i q^{97} +(-11.3737 + 3.23117i) q^{98} +(2.93423 + 2.93423i) 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 $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.36038	+	0.386472i	−0.961935	+	0.273277i
$2$	−1.36038	+	0.386472i	−0.961935	+	0.273277i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$	1.70128	−	1.05150i	0.850639	−	0.525750i
$5$	−1.98421	+	1.03097i	−0.887367	+	0.461064i
$5$	−1.98421	+	1.03097i	−0.887367	+	0.461064i
$6$	−0.688658	+	1.23521i	−0.281143	+	0.504273i
$7$	−3.91927			−1.48134			−0.740672	−	0.671867i	$-0.765493\pi$
$7$	−3.91927			−1.48134			−0.740672	+	0.671867i	$0.765493\pi$
$8$	−1.90801	+	2.08794i	−0.674584	+	0.738198i
$9$		−	1.00000i		−	0.333333i
$10$	2.30085	−	2.16936i	0.727591	−	0.686011i
$11$	−2.93423	+	2.93423i	−0.884703	+	0.884703i	−0.994008	−	0.109305i	$-0.965138\pi$
$11$	−2.93423	+	2.93423i	−0.884703	+	0.884703i	0.109305	+	0.994008i	$0.465138\pi$
$12$	0.459462	−	1.94651i	0.132635	−	0.561909i
$13$	−0.732828	+	0.732828i	−0.203250	+	0.203250i	−0.801391	−	0.598141i	$-0.795906\pi$
$13$	−0.732828	+	0.732828i	−0.203250	+	0.203250i	0.598141	+	0.801391i	$0.295906\pi$
$14$	5.33170	−	1.51469i	1.42496	−	0.404818i
$15$	−0.674045	+	2.13206i	−0.174038	+	0.550495i
$16$	1.78869	−	3.57779i	0.447173	−	0.894447i
$17$			2.89302i			0.701659i	0.936439	+	0.350830i	$0.114100\pi$
$17$			2.89302i			0.701659i	−0.936439	+	0.350830i	$0.885900\pi$
$18$	0.386472	+	1.36038i	0.0910924	+	0.320645i
$19$	1.67534	+	1.67534i	0.384350	+	0.384350i	0.872667	−	0.488316i	$-0.162389\pi$
$19$	1.67534	+	1.67534i	0.384350	+	0.384350i	−0.488316	+	0.872667i	$0.662389\pi$
$20$	−2.29163	+	3.84037i	−0.512425	+	0.858732i
$21$	−2.77134	+	2.77134i	−0.604756	+	0.604756i
$22$	2.85767	−	5.12567i	0.609258	−	1.09280i
$23$	−1.73133			−0.361006			−0.180503	−	0.983574i	$-0.557773\pi$
$23$	−1.73133			−0.361006			−0.180503	+	0.983574i	$0.557773\pi$
$24$	0.127228	+	2.82556i	0.0259703	+	0.576766i
$25$	2.87420	−	4.09133i	0.574841	−	0.818265i
$26$	0.713708	−	1.28014i	0.139970	−	0.251057i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	−6.66776	+	4.12111i	−1.26009	+	0.778817i
$29$	−4.99003	−	4.99003i	−0.926625	−	0.926625i	0.0708617	−	0.997486i	$-0.477425\pi$
$29$	−4.99003	−	4.99003i	−0.926625	−	0.926625i	−0.997486	+	0.0708617i	$0.977425\pi$
$30$	0.0929773	−	3.16091i	0.0169753	−	0.577101i
$31$	−10.8149			−1.94241			−0.971203	−	0.238254i	$-0.923425\pi$
$31$	−10.8149			−1.94241			−0.971203	+	0.238254i	$0.923425\pi$
$32$	−1.05059	+	5.55844i	−0.185720	+	0.982603i
$33$			4.14963i			0.722357i
$34$	−1.11807	−	3.93561i	−0.191748	−	0.674951i
$35$	7.77666	−	4.04065i	1.31450	−	0.682994i
$36$	−1.05150	−	1.70128i	−0.175250	−	0.283546i
$37$	6.41524	+	6.41524i	1.05466	+	1.05466i	0.998417	+	0.0562413i	$0.0179116\pi$
$37$	6.41524	+	6.41524i	1.05466	+	1.05466i	0.0562413	+	0.998417i	$0.482088\pi$
$38$	−2.92658	−	1.63163i	−0.474754	−	0.264686i
$39$			1.03637i			0.165953i
$40$	1.63330	−	6.11002i	0.258247	−	0.966079i
$41$			0.00577512i			0.000901923i	1.00000		0.000450961i	$0.000143545\pi$
$41$			0.00577512i			0.000901923i	−1.00000		0.000450961i	$0.999856\pi$
$42$	2.69904	−	4.84113i	0.416470	−	0.747002i
$43$	−2.23930	−	2.23930i	−0.341490	−	0.341490i	0.515437	−	0.856927i	$-0.327630\pi$
$43$	−2.23930	−	2.23930i	−0.341490	−	0.341490i	−0.856927	+	0.515437i	$0.827630\pi$
$44$	−1.90660	+	8.07728i	−0.287430	+	1.21770i
$45$	1.03097	+	1.98421i	0.153688	+	0.295789i
$46$	2.35527	−	0.669110i	0.347265	−	0.0986549i
$47$		−	11.6451i		−	1.69861i	−0.527900	−	0.849307i	$-0.677020\pi$
$47$		−	11.6451i		−	1.69861i	0.527900	−	0.849307i	$-0.322980\pi$
$48$	−1.26508	−	3.79468i	−0.182599	−	0.547714i
$49$	8.36066			1.19438
$50$	−2.32883	+	6.67657i	−0.329346	+	0.944209i
$51$	2.04567	+	2.04567i	0.286451	+	0.286451i
$52$	−0.476175	+	2.01731i	−0.0660336	+	0.279751i
$53$	5.55765	+	5.55765i	0.763402	+	0.763402i	0.976936	−	0.213533i	$-0.0684972\pi$
$53$	5.55765	+	5.55765i	0.763402	+	0.763402i	−0.213533	+	0.976936i	$0.568497\pi$
$54$	1.23521	+	0.688658i	0.168091	+	0.0937145i
$55$	2.79703	−	8.84724i	0.377152	−	1.19296i
$56$	7.47801	−	8.18319i	0.999291	−	1.09353i
$57$	2.36929			0.313821
$58$	8.71685	+	4.85983i	1.14458	+	0.638127i
$59$	3.83290	−	3.83290i	0.499001	−	0.499001i	−0.412126	−	0.911127i	$-0.635214\pi$
$59$	3.83290	−	3.83290i	0.499001	−	0.499001i	0.911127	+	0.412126i	$0.135214\pi$
$60$	1.09512	+	4.33598i	0.141379	+	0.559772i
$61$	9.30595	+	9.30595i	1.19150	+	1.19150i	0.976645	+	0.214859i	$0.0689293\pi$
$61$	9.30595	+	9.30595i	1.19150	+	1.19150i	0.214859	+	0.976645i	$0.431071\pi$
$62$	14.7123	−	4.17964i	1.86847	−	0.530815i
$63$			3.91927i			0.493781i
$64$	−0.718981	−	7.96763i	−0.0898726	−	0.995953i
$65$	0.698563	−	2.20961i	0.0866461	−	0.274068i
$66$	−1.60372	−	5.64508i	−0.197404	−	0.694861i
$67$	−3.85243	+	3.85243i	−0.470649	+	0.470649i	−0.902124	−	0.431476i	$-0.857993\pi$
$67$	−3.85243	+	3.85243i	−0.470649	+	0.470649i	0.431476	+	0.902124i	$0.357993\pi$
$68$	3.04201	+	4.92182i	0.368898	+	0.596859i
$69$	−1.22423	+	1.22423i	−0.147380	+	0.147380i
$70$	−9.01763	+	8.50229i	−1.07781	+	1.01622i
$71$			1.15355i			0.136901i	0.997655	+	0.0684504i	$0.0218055\pi$
$71$			1.15355i			0.136901i	−0.997655	+	0.0684504i	$0.978195\pi$
$72$	2.08794	+	1.90801i	0.246066	+	0.224861i
$73$	−7.98713			−0.934823			−0.467411	−	0.884040i	$-0.654813\pi$
$73$	−7.98713			−0.934823			−0.467411	+	0.884040i	$0.654813\pi$
$74$	−11.2065	−	6.24786i	−1.30273	−	0.726299i
$75$	−0.860637	−	4.92537i	−0.0993778	−	0.568733i
$76$	4.61185	+	1.08860i	0.529016	+	0.124871i
$77$	11.5000	−	11.5000i	1.31055	−	1.31055i
$78$	−0.400530	−	1.40987i	−0.0453511	−	0.159636i
$79$	0.843960			0.0949529			0.0474765	−	0.998872i	$-0.484882\pi$
$79$	0.843960			0.0949529			0.0474765	+	0.998872i	$0.484882\pi$
$80$	0.139442	+	8.94318i	0.0155901	+	0.999878i
$81$	−1.00000			−0.111111
$82$	−0.00223193	−	0.00785637i	−0.000246475	−	0.000867591i
$83$	−5.20069	+	5.20069i	−0.570850	+	0.570850i	−0.932366	−	0.361516i	$-0.882259\pi$
$83$	−5.20069	+	5.20069i	−0.570850	+	0.570850i	0.361516	+	0.932366i	$0.382259\pi$
$84$	−1.80076	+	7.62889i	−0.196479	+	0.832380i
$85$	−2.98261	−	5.74036i	−0.323510	−	0.622629i
$86$	3.91173	+	2.18088i	0.421813	+	0.235170i
$87$	−7.05696			−0.756586
$88$	−0.527948	−	11.7250i	−0.0562794	−	1.24989i
$89$		−	5.40896i		−	0.573349i	−0.958028	−	0.286674i	$-0.907450\pi$
$89$		−	5.40896i		−	0.573349i	0.958028	−	0.286674i	$-0.0925498\pi$
$90$	−2.16936	−	2.30085i	−0.228670	−	0.242530i
$91$	2.87215	−	2.87215i	0.301083	−	0.301083i
$92$	−2.94547	+	1.82049i	−0.307086	+	0.189799i
$93$	−7.64726	+	7.64726i	−0.792984	+	0.792984i
$94$	4.50051	+	15.8418i	0.464193	+	1.63396i
$95$	−5.05147	−	1.59701i	−0.518270	−	0.163850i
$96$	3.18753	+	4.67329i	0.325326	+	0.476966i
$97$		−	2.24154i		−	0.227594i	−0.993504	−	0.113797i	$-0.963699\pi$
$97$		−	2.24154i		−	0.227594i	0.993504	−	0.113797i	$-0.0363013\pi$
$98$	−11.3737	+	3.23117i	−1.14892	+	0.326397i
$99$	2.93423	+	2.93423i	0.294901	+	0.294901i
$100$	0.587786	−	9.98271i	0.0587786	−	0.998271i
$101$	−7.50655	+	7.50655i	−0.746930	+	0.746930i	−0.973901	−	0.226972i	$-0.927118\pi$
$101$	−7.50655	+	7.50655i	−0.746930	+	0.746930i	0.226972	+	0.973901i	$0.427118\pi$
$102$	−3.57349	−	1.99230i	−0.353828	−	0.197267i
$103$	3.91110			0.385372			0.192686	−	0.981260i	$-0.438280\pi$
$103$	3.91110			0.385372			0.192686	+	0.981260i	$0.438280\pi$
$104$	−0.131856	−	2.92834i	−0.0129295	−	0.287148i
$105$	2.64176	−	8.35610i	0.257810	−	0.815472i
$106$	−9.70841	−	5.41265i	−0.942964	−	0.525723i
$107$	−2.60233	−	2.60233i	−0.251577	−	0.251577i	0.570040	−	0.821617i	$-0.306928\pi$
$107$	−2.60233	−	2.60233i	−0.251577	−	0.251577i	−0.821617	+	0.570040i	$0.806928\pi$
$108$	−1.94651	−	0.459462i	−0.187303	−	0.0442118i
$109$	−2.06635	−	2.06635i	−0.197920	−	0.197920i	0.601188	−	0.799108i	$-0.294694\pi$
$109$	−2.06635	−	2.06635i	−0.197920	−	0.197920i	−0.799108	+	0.601188i	$0.794694\pi$
$110$	−0.385821	+	13.1166i	−0.0367866	+	1.25062i
$111$	9.07252			0.861125
$112$	−7.01037	+	14.0223i	−0.662418	+	1.32498i
$113$		−	8.13610i		−	0.765380i	−0.923877	−	0.382690i	$-0.874998\pi$
$113$		−	8.13610i		−	0.765380i	0.923877	−	0.382690i	$-0.125002\pi$
$114$	−3.22315	+	0.915667i	−0.301875	+	0.0857601i
$115$	3.43532	−	1.78495i	0.320345	−	0.166447i
$116$	−13.7364	−	3.24241i	−1.27540	−	0.301050i
$117$	0.732828	+	0.732828i	0.0677500	+	0.0677500i
$118$	−3.73290	+	6.69551i	−0.343641	+	0.616372i
$119$		−	11.3385i		−	1.03940i
$120$	−3.16552	−	5.47535i	−0.288971	−	0.499829i
$121$		−	6.21941i		−	0.565401i
$122$	−16.2561	−	9.06315i	−1.47176	−	0.820539i
$123$	0.00408363	+	0.00408363i	0.000368208	+	0.000368208i
$124$	−18.3991	+	11.3718i	−1.65229	+	1.02122i
$125$	−1.48500	+	11.0813i	−0.132822	+	0.991140i
$126$	−1.51469	−	5.33170i	−0.134939	−	0.474986i
$127$			16.0862i			1.42742i	0.700442	+	0.713709i	$0.252986\pi$
$127$			16.0862i			1.42742i	−0.700442	+	0.713709i	$0.747014\pi$
$128$	4.05736	+	10.5611i	0.358623	+	0.933482i
$129$	−3.16685			−0.278826
$130$	−0.0963593	+	3.27589i	−0.00845127	+	0.287314i
$131$	13.0407	+	13.0407i	1.13937	+	1.13937i	0.988563	+	0.150808i	$0.0481875\pi$
$131$	13.0407	+	13.0407i	1.13937	+	1.13937i	0.150808	+	0.988563i	$0.451813\pi$
$132$	4.36333	+	7.05967i	0.379780	+	0.614465i
$133$	−6.56612	−	6.56612i	−0.569355	−	0.569355i
$134$	3.75191	−	6.72963i	0.324116	−	0.581351i
$135$	2.13206	+	0.674045i	0.183498	+	0.0580125i
$136$	−6.04044	−	5.51991i	−0.517964	−	0.473328i
$137$	−6.51614			−0.556711			−0.278356	−	0.960478i	$-0.589789\pi$
$137$	−6.51614			−0.556711			−0.278356	+	0.960478i	$0.589789\pi$
$138$	1.19229	−	2.13856i	0.101495	−	0.182046i
$139$	−15.0953	+	15.0953i	−1.28036	+	1.28036i	−0.339902	+	0.940461i	$0.610394\pi$
$139$	−15.0953	+	15.0953i	−1.28036	+	1.28036i	−0.940461	+	0.339902i	$0.889606\pi$
$140$	8.98152	−	15.0514i	0.759077	−	1.27208i
$141$	−8.23434	−	8.23434i	−0.693456	−	0.693456i
$142$	−0.445814	−	1.56926i	−0.0374119	−	0.131690i
$143$		−	4.30057i		−	0.359632i
$144$	−3.57779	−	1.78869i	−0.298149	−	0.149058i
$145$	15.0458	+	4.75671i	1.24949	+	0.395023i
$146$	10.8655	−	3.08681i	0.899239	−	0.255466i
$147$	5.91188	−	5.91188i	0.487604	−	0.487604i
$148$	17.6597	+	4.16848i	1.45162	+	0.342647i
$149$	4.27402	−	4.27402i	0.350141	−	0.350141i	−0.510021	−	0.860162i	$-0.670362\pi$
$149$	4.27402	−	4.27402i	0.350141	−	0.350141i	0.860162	+	0.510021i	$0.170362\pi$
$150$	3.07432	+	6.36778i	0.251017	+	0.519927i
$151$			8.39998i			0.683581i	0.939776	+	0.341790i	$0.111033\pi$
$151$			8.39998i			0.683581i	−0.939776	+	0.341790i	$0.888967\pi$
$152$	−6.69459	+	0.301440i	−0.543003	+	0.0244500i
$153$	2.89302			0.233886
$154$	−11.2000	+	20.0889i	−0.902521	+	1.61881i
$155$	21.4590	−	11.1498i	1.72363	−	0.895573i
$156$	1.08975	+	1.76316i	0.0872497	+	0.141166i
$157$	−5.68893	+	5.68893i	−0.454026	+	0.454026i	−0.896689	−	0.442662i	$-0.854034\pi$
$157$	−5.68893	+	5.68893i	−0.454026	+	0.454026i	0.442662	+	0.896689i	$0.354034\pi$
$158$	−1.14811	+	0.326167i	−0.0913386	+	0.0259485i
$159$	7.85971			0.623315
$160$	−3.64599	−	12.1123i	−0.288241	−	0.957558i
$161$	6.78553			0.534775
$162$	1.36038	−	0.386472i	0.106882	−	0.0303641i
$163$	5.63869	−	5.63869i	0.441656	−	0.441656i	−0.450912	−	0.892568i	$-0.648901\pi$
$163$	5.63869	−	5.63869i	0.441656	−	0.441656i	0.892568	+	0.450912i	$0.148901\pi$
$164$	0.00607254	+	0.00982509i	0.000474186	+	0.000767211i
$165$	−4.27814	−	8.23374i	−0.333053	−	0.640996i
$166$	5.06500	−	9.08485i	0.393120	−	0.705121i
$167$	−6.45583			−0.499567			−0.249783	−	0.968302i	$-0.580359\pi$
$167$	−6.45583			−0.499567			−0.249783	+	0.968302i	$0.580359\pi$
$168$	−0.498640	−	11.0741i	−0.0384709	−	0.854389i
$169$			11.9259i			0.917379i
$170$	6.27598	+	6.65638i	0.481346	+	0.510521i
$171$	1.67534	−	1.67534i	0.128117	−	0.128117i
$172$	−6.16430	−	1.45505i	−0.470023	−	0.110946i
$173$	7.33664	−	7.33664i	0.557795	−	0.557795i	−0.370884	−	0.928679i	$-0.620945\pi$
$173$	7.33664	−	7.33664i	0.557795	−	0.557795i	0.928679	+	0.370884i	$0.120945\pi$
$174$	9.60016	−	2.72732i	0.727787	−	0.206758i
$175$	−11.2648	+	16.0350i	−0.851537	+	1.21213i
$176$	5.24962	+	15.7465i	0.395705	+	1.18694i
$177$		−	5.42054i		−	0.407432i
$178$	2.09042	+	7.35826i	0.156683	+	0.551525i
$179$	−1.04377	−	1.04377i	−0.0780153	−	0.0780153i	0.667022	−	0.745038i	$-0.267569\pi$
$179$	−1.04377	−	1.04377i	−0.0780153	−	0.0780153i	−0.745038	+	0.667022i	$0.767569\pi$
$180$	3.84037	+	2.29163i	0.286244	+	0.170808i
$181$	−12.1024	+	12.1024i	−0.899567	+	0.899567i	−0.995398	−	0.0958310i	$-0.969449\pi$
$181$	−12.1024	+	12.1024i	−0.899567	+	0.899567i	0.0958310	+	0.995398i	$0.469449\pi$
$182$	−2.79721	+	5.01723i	−0.207343	+	0.371901i
$183$	13.1606			0.972859
$184$	3.30339	−	3.61490i	0.243529	−	0.266494i
$185$	−19.3431	−	6.11528i	−1.42213	−	0.449604i
$186$	7.44774	−	13.3586i	0.546095	−	0.979504i
$187$	−8.48877	−	8.48877i	−0.620761	−	0.620761i
$188$	−12.2448	−	19.8116i	−0.893046	−	1.44491i
$189$	2.77134	+	2.77134i	0.201585	+	0.201585i
$190$	7.48913	+	0.220291i	0.543318	+	0.0159816i
$191$	−21.2273			−1.53596			−0.767978	−	0.640477i	$-0.778737\pi$
$191$	−21.2273			−1.53596			−0.767978	+	0.640477i	$0.778737\pi$
$192$	−6.14236	−	5.12557i	−0.443287	−	0.369906i
$193$		−	19.2782i		−	1.38767i	−0.720132	−	0.693837i	$-0.755919\pi$
$193$		−	19.2782i		−	1.38767i	0.720132	−	0.693837i	$-0.244081\pi$
$194$	0.866292	+	3.04935i	0.0621961	+	0.218930i
$195$	−1.06847	−	2.05639i	−0.0765148	−	0.147261i
$196$	14.2238	−	8.79124i	1.01599	−	0.627946i
$197$	9.48350	+	9.48350i	0.675672	+	0.675672i	0.959018	−	0.283346i	$-0.0914445\pi$
$197$	9.48350	+	9.48350i	0.675672	+	0.675672i	−0.283346	+	0.959018i	$0.591444\pi$
$198$	−5.12567	−	2.85767i	−0.364266	−	0.203086i
$199$		−	8.65421i		−	0.613481i	−0.951793	−	0.306740i	$-0.900762\pi$
$199$		−	8.65421i		−	0.613481i	0.951793	−	0.306740i	$-0.0992383\pi$
$200$	3.05843	+	13.8075i	0.216264	+	0.976335i
$201$			5.44815i			0.384283i
$202$	7.31070	−	13.1129i	0.514379	−	0.922617i
$203$	19.5572	+	19.5572i	1.37265	+	1.37265i
$204$	5.63128	+	1.32923i	0.394268	+	0.0930648i
$205$	−0.00595398	−	0.0114591i	−0.000415844	−	0.000800336i
$206$	−5.32059	+	1.51153i	−0.370703	+	0.105313i
$207$			1.73133i			0.120335i
$208$	1.31110	+	3.93271i	0.0909083	+	0.272684i
$209$	−9.83169			−0.680072
$210$	−0.364403	+	12.3885i	−0.0251462	+	0.854885i
$211$	−0.875946	−	0.875946i	−0.0603026	−	0.0603026i	0.676312	−	0.736615i	$-0.263577\pi$
$211$	−0.875946	−	0.875946i	−0.0603026	−	0.0603026i	−0.736615	+	0.676312i	$0.763577\pi$
$212$	15.2990	+	3.61124i	1.05074	+	0.248021i
$213$	0.815681	+	0.815681i	0.0558895	+	0.0558895i
$214$	4.54589	+	2.53443i	0.310751	+	0.173250i
$215$	6.75190	+	2.13460i	0.460476	+	0.145578i
$216$	2.82556	−	0.127228i	0.192255	−	0.00865675i
$217$	42.3863			2.87737
$218$	3.60961	+	2.01243i	0.244473	+	0.136299i
$219$	−5.64775	+	5.64775i	−0.381640	+	0.381640i
$220$	−4.54434	−	17.9927i	−0.306379	−	1.21307i
$221$	−2.12008	−	2.12008i	−0.142612	−	0.142612i
$222$	−12.3421	+	3.50628i	−0.828347	+	0.235326i
$223$		−	10.4375i		−	0.698946i	−0.936946	−	0.349473i	$-0.886361\pi$
$223$		−	10.4375i		−	0.698946i	0.936946	−	0.349473i	$-0.113639\pi$
$224$	4.11754	−	21.7850i	0.275115	−	1.45557i
$225$	−4.09133	−	2.87420i	−0.272755	−	0.191614i
$226$	3.14438	+	11.0682i	0.209161	+	0.736246i
$227$	−13.7218	+	13.7218i	−0.910747	+	0.910747i	−0.996331	−	0.0855842i	$-0.972724\pi$
$227$	−13.7218	+	13.7218i	−0.910747	+	0.910747i	0.0855842	+	0.996331i	$0.472724\pi$
$228$	4.03083	−	2.49131i	0.266948	−	0.164991i
$229$	8.43878	−	8.43878i	0.557651	−	0.557651i	−0.370987	−	0.928638i	$-0.620981\pi$
$229$	8.43878	−	8.43878i	0.557651	−	0.557651i	0.928638	+	0.370987i	$0.120981\pi$
$230$	−3.98352	+	3.75586i	−0.262665	+	0.247654i
$231$		−	16.2635i		−	1.07006i
$232$	19.9399	−	0.897842i	1.30912	−	0.0589462i
$233$	−28.6100			−1.87431			−0.937153	−	0.348919i	$-0.886549\pi$
$233$	−28.6100			−1.87431			−0.937153	+	0.348919i	$0.886549\pi$
$234$	−1.28014	−	0.713708i	−0.0836856	−	0.0466565i
$235$	12.0058	+	23.1064i	0.783169	+	1.50729i
$236$	2.49053	−	10.5511i	0.162120	−	0.686819i
$237$	0.596770	−	0.596770i	0.0387644	−	0.0387644i
$238$	4.38202	+	15.4247i	0.284044	+	0.999835i
$239$	21.4924			1.39023			0.695115	−	0.718899i	$-0.255354\pi$
$239$	21.4924			1.39023			0.695115	+	0.718899i	$0.255354\pi$
$240$	6.42239	+	6.22519i	0.414563	+	0.401834i
$241$	−19.5943			−1.26218			−0.631091	−	0.775709i	$-0.717393\pi$
$241$	−19.5943			−1.26218			−0.631091	+	0.775709i	$0.717393\pi$
$242$	2.40363	+	8.46077i	0.154511	+	0.543879i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	25.6172	+	6.04680i	1.63997	+	0.387106i
$245$	−16.5893	+	8.61959i	−1.05985	+	0.550685i
$246$	−0.00713350	−	0.00397708i	−0.000454816	−	0.000253570i
$247$	−2.45548			−0.156238
$248$	20.6349	−	22.5808i	1.31032	−	1.43388i
$249$			7.35489i			0.466097i
$250$	−2.26245	−	15.6487i	−0.143090	−	0.989710i
$251$	−9.58072	+	9.58072i	−0.604730	+	0.604730i	−0.941564	−	0.336834i	$-0.890644\pi$
$251$	−9.58072	+	9.58072i	−0.604730	+	0.604730i	0.336834	+	0.941564i	$0.390644\pi$
$252$	4.12111	+	6.66776i	0.259606	+	0.420030i
$253$	5.08011	−	5.08011i	0.319384	−	0.319384i
$254$	−6.21687	−	21.8834i	−0.390081	−	1.37308i
$255$	−6.16807	−	1.95002i	−0.386260	−	0.122115i
$256$	−9.60115	−	12.7991i	−0.600072	−	0.799946i
$257$			13.2730i			0.827946i	0.910289	+	0.413973i	$0.135859\pi$
$257$			13.2730i			0.827946i	−0.910289	+	0.413973i	$0.864141\pi$
$258$	4.30813	−	1.22390i	0.268212	−	0.0761967i
$259$	−25.1430	−	25.1430i	−1.56231	−	1.56231i
$260$	−1.13496	−	4.49370i	−0.0703869	−	0.278687i
$261$	−4.99003	+	4.99003i	−0.308875	+	0.308875i
$262$	−22.7802	−	12.7005i	−1.40737	−	0.784637i
$263$	13.0606			0.805349			0.402675	−	0.915343i	$-0.368081\pi$
$263$	13.0606			0.805349			0.402675	+	0.915343i	$0.368081\pi$
$264$	−8.66417	−	7.91754i	−0.533243	−	0.487291i
$265$	−16.7573	−	5.29780i	−1.02940	−	0.325441i
$266$	11.4701	+	6.39481i	0.703274	+	0.392091i
$267$	−3.82471	−	3.82471i	−0.234069	−	0.234069i
$268$	−2.50322	+	10.6049i	−0.152908	+	0.647796i
$269$	−12.4067	−	12.4067i	−0.756451	−	0.756451i	0.219224	−	0.975675i	$-0.429647\pi$
$269$	−12.4067	−	12.4067i	−0.756451	−	0.756451i	−0.975675	+	0.219224i	$0.929647\pi$
$270$	−3.16091	−	0.0929773i	−0.192367	−	0.00565842i
$271$	2.11193			0.128291			0.0641453	−	0.997941i	$-0.479568\pi$
$271$	2.11193			0.128291			0.0641453	+	0.997941i	$0.479568\pi$
$272$	10.3506	+	5.17472i	0.627597	+	0.313763i
$273$		−	4.06183i		−	0.245833i
$274$	8.86444	−	2.51831i	0.535520	−	0.152137i
$275$	3.57132	+	20.4385i	0.215359	+	1.23249i
$276$	−0.795479	+	3.37004i	−0.0478822	+	0.202853i
$277$	−13.2116	−	13.2116i	−0.793808	−	0.793808i	0.188303	−	0.982111i	$-0.439701\pi$
$277$	−13.2116	−	13.2116i	−0.793808	−	0.793808i	−0.982111	+	0.188303i	$0.939701\pi$
$278$	14.7014	−	26.3692i	0.881732	−	1.58152i
$279$			10.8149i			0.647469i
$280$	−6.40134	+	23.9468i	−0.382553	+	1.43110i
$281$			3.78786i			0.225965i	0.993597	+	0.112982i	$0.0360404\pi$
$281$			3.78786i			0.225965i	−0.993597	+	0.112982i	$0.963960\pi$
$282$	14.3842	+	8.01950i	0.856566	+	0.477554i
$283$	−3.16274	−	3.16274i	−0.188005	−	0.188005i	0.606828	−	0.794833i	$-0.292442\pi$
$283$	−3.16274	−	3.16274i	−0.188005	−	0.188005i	−0.794833	+	0.606828i	$0.792442\pi$
$284$	1.21295	+	1.96250i	0.0719756	+	0.116453i
$285$	−4.70118	+	2.44267i	−0.278474	+	0.144691i
$286$	1.66205	+	5.85042i	0.0982792	+	0.345942i
$287$		−	0.0226343i		−	0.00133606i
$288$	5.55844	+	1.05059i	0.327534	+	0.0619066i
$289$	8.63046			0.507674
$290$	−22.3064	−	0.656137i	−1.30988	−	0.0385297i
$291$	−1.58501	−	1.58501i	−0.0929147	−	0.0929147i
$292$	−13.5883	+	8.39847i	−0.795197	+	0.491483i
$293$	8.51339	+	8.51339i	0.497357	+	0.497357i	0.910614	−	0.413257i	$-0.135609\pi$
$293$	8.51339	+	8.51339i	0.497357	+	0.497357i	−0.413257	+	0.910614i	$0.635609\pi$
$294$	−5.75764	+	10.3272i	−0.335792	+	0.602294i
$295$	−3.65368	+	11.5569i	−0.212726	+	0.672868i
$296$	−25.6350	+	1.15428i	−1.49000	+	0.0670909i
$297$	4.14963			0.240786
$298$	−4.16251	+	7.46609i	−0.241128	+	0.432499i
$299$	1.26876	−	1.26876i	0.0733745	−	0.0733745i
$300$	−6.64321	−	7.47447i	−0.383546	−	0.431539i
$301$	8.77642	+	8.77642i	0.505864	+	0.505864i
$302$	−3.24636	−	11.4272i	−0.186807	−	0.657560i
$303$			10.6159i			0.609866i
$304$	8.99071	−	2.99735i	0.515652	−	0.171910i
$305$	−28.0591	−	8.87083i	−1.60666	−	0.507942i
$306$	−3.93561	+	1.11807i	−0.224984	+	0.0639159i
$307$	7.12093	−	7.12093i	0.406413	−	0.406413i	−0.474073	−	0.880486i	$-0.657217\pi$
$307$	7.12093	−	7.12093i	0.406413	−	0.406413i	0.880486	+	0.474073i	$0.157217\pi$
$308$	7.47246	−	31.6570i	0.425783	−	1.80383i
$309$	2.76557	−	2.76557i	0.157328	−	0.157328i
$310$	−24.8833	+	23.4613i	−1.41328	+	1.33251i
$311$			21.2980i			1.20770i	0.797099	+	0.603849i	$0.206367\pi$
$311$			21.2980i			1.20770i	−0.797099	+	0.603849i	$0.793633\pi$
$312$	−2.16389	−	1.97742i	−0.122506	−	0.111949i
$313$	7.49789			0.423806			0.211903	−	0.977291i	$-0.432034\pi$
$313$	7.49789			0.423806			0.211903	+	0.977291i	$0.432034\pi$
$314$	5.54051	−	9.93774i	0.312669	−	0.560819i
$315$	−4.04065	−	7.77666i	−0.227665	−	0.438165i
$316$	1.43581	−	0.887425i	0.0807707	−	0.0499215i
$317$	2.35354	−	2.35354i	0.132188	−	0.132188i	−0.637917	−	0.770105i	$-0.720204\pi$
$317$	2.35354	−	2.35354i	0.132188	−	0.132188i	0.770105	+	0.637917i	$0.220204\pi$
$318$	−10.6922	+	3.03756i	−0.599589	+	0.170338i
$319$	29.2838			1.63958
$320$	9.64099	+	15.0682i	0.538948	+	0.842339i
$321$	−3.68025			−0.205412
$322$	−9.23091	+	2.62242i	−0.514419	+	0.146142i
$323$	−4.84680	+	4.84680i	−0.269683	+	0.269683i
$324$	−1.70128	+	1.05150i	−0.0945154	+	0.0584167i
$325$	0.891943	+	5.10453i	0.0494761	+	0.283149i
$326$	−5.49157	+	9.84997i	−0.304150	+	0.545539i
$327$	−2.92226			−0.161601
$328$	−0.0120581	−	0.0110190i	−0.000665797	−	0.000608423i
$329$			45.6403i			2.51623i
$330$	9.00202	+	9.54765i	0.495545	+	0.525581i
$331$	22.6845	−	22.6845i	1.24685	−	1.24685i	0.289753	−	0.957102i	$-0.406427\pi$
$331$	22.6845	−	22.6845i	1.24685	−	1.24685i	0.957102	−	0.289753i	$-0.0935730\pi$
$332$	−3.37929	+	14.3163i	−0.185463	+	0.785712i
$333$	6.41524	−	6.41524i	0.351553	−	0.351553i
$334$	8.78239	−	2.49500i	0.480551	−	0.136520i
$335$	3.67230	−	11.6158i	0.200639	−	0.634637i
$336$	4.95819	+	14.8724i	0.270492	+	0.811353i
$337$		−	8.90357i		−	0.485008i	−0.970150	−	0.242504i	$-0.922031\pi$
$337$		−	8.90357i		−	0.485008i	0.970150	−	0.242504i	$-0.0779688\pi$
$338$	−4.60904	−	16.2238i	−0.250699	−	0.882459i
$339$	−5.75309	−	5.75309i	−0.312465	−	0.312465i
$340$	−11.1102	−	6.62973i	−0.602538	−	0.359548i
$341$	31.7333	−	31.7333i	1.71845	−	1.71845i
$342$	−1.63163	+	2.92658i	−0.0882286	+	0.158251i
$343$	−5.33279			−0.287944
$344$	8.94814	−	0.402911i	0.482451	−	0.0217235i
$345$	1.16699	−	3.69129i	0.0628287	−	0.198732i
$346$	−7.14523	+	12.8160i	−0.384130	+	0.688995i
$347$	8.87783	+	8.87783i	0.476587	+	0.476587i	0.904038	−	0.427451i	$-0.140588\pi$
$347$	8.87783	+	8.87783i	0.476587	+	0.476587i	−0.427451	+	0.904038i	$0.640588\pi$
$348$	−12.0059	+	7.42040i	−0.643581	+	0.397775i
$349$	−8.23040	−	8.23040i	−0.440563	−	0.440563i	0.451638	−	0.892201i	$-0.350840\pi$
$349$	−8.23040	−	8.23040i	−0.440563	−	0.440563i	−0.892201	+	0.451638i	$0.850840\pi$
$350$	9.12730	−	26.1673i	0.487875	−	1.39870i
$351$	1.03637			0.0553176
$352$	−13.2271	−	19.3924i	−0.705005	−	1.03362i
$353$			34.7125i			1.84756i	0.382922	+	0.923781i	$0.374918\pi$
$353$			34.7125i			1.84756i	−0.382922	+	0.923781i	$0.625082\pi$
$354$	2.09489	+	7.37400i	0.111342	+	0.391924i
$355$	−1.18927	−	2.28888i	−0.0631200	−	0.121481i
$356$	−5.68753	−	9.20215i	−0.301438	−	0.487713i
$357$	−8.01753	−	8.01753i	−0.424333	−	0.424333i
$358$	1.82332	+	1.01654i	0.0963655	+	0.0537259i
$359$			2.81082i			0.148350i	0.997245	+	0.0741748i	$0.0236323\pi$
$359$			2.81082i			0.148350i	−0.997245	+	0.0741748i	$0.976368\pi$
$360$	−6.11002	−	1.63330i	−0.322026	−	0.0860825i
$361$		−	13.3864i		−	0.704550i
$362$	11.7867	−	21.1412i	0.619494	−	1.11116i
$363$	−4.39778	−	4.39778i	−0.230824	−	0.230824i
$364$	1.86626	−	7.90639i	0.0978185	−	0.414407i
$365$	15.8482	−	8.23449i	0.829531	−	0.431013i
$366$	−17.9034	+	5.08621i	−0.935828	+	0.265860i
$367$			18.2835i			0.954392i	0.878797	+	0.477196i	$0.158347\pi$
$367$			18.2835i			0.954392i	−0.878797	+	0.477196i	$0.841653\pi$
$368$	−3.09681	+	6.19432i	−0.161433	+	0.322901i
$369$	0.00577512			0.000300641
$370$	28.6774	+	0.843538i	1.49087	+	0.0438534i
$371$	−21.7819	−	21.7819i	−1.13086	−	1.13086i
$372$	−4.96902	+	21.0512i	−0.257632	+	1.09145i
$373$	−23.4176	−	23.4176i	−1.21252	−	1.21252i	−0.970195	−	0.242324i	$-0.922090\pi$
$373$	−23.4176	−	23.4176i	−1.21252	−	1.21252i	−0.242324	−	0.970195i	$-0.577910\pi$
$374$	14.8287	+	8.26730i	0.766771	+	0.427492i
$375$	6.78560	+	8.88570i	0.350407	+	0.458856i
$376$	24.3143	+	22.2190i	1.25391	+	1.14586i
$377$	7.31366			0.376673
$378$	−4.84113	−	2.69904i	−0.249001	−	0.138823i
$379$	−6.20944	+	6.20944i	−0.318957	+	0.318957i	−0.848367	−	0.529409i	$-0.822414\pi$
$379$	−6.20944	+	6.20944i	−0.318957	+	0.318957i	0.529409	+	0.848367i	$0.322414\pi$
$380$	−10.2732	+	2.59466i	−0.527005	+	0.133103i
$381$	11.3746	+	11.3746i	0.582741	+	0.582741i
$382$	28.8773	−	8.20378i	1.47749	−	0.419742i
$383$		−	14.4005i		−	0.735832i	−0.929859	−	0.367916i	$-0.880071\pi$
$383$		−	14.4005i		−	0.735832i	0.929859	−	0.367916i	$-0.119929\pi$
$384$	10.3368	+	4.59888i	0.527500	+	0.234685i
$385$	−10.9623	+	34.6747i	−0.558692	+	1.76719i
$386$	7.45049	+	26.2257i	0.379220	+	1.33485i
$387$	−2.23930	+	2.23930i	−0.113830	+	0.113830i
$388$	−2.35698	−	3.81348i	−0.119657	−	0.193600i
$389$	15.4753	−	15.4753i	0.784630	−	0.784630i	−0.195978	−	0.980608i	$-0.562788\pi$
$389$	15.4753	−	15.4753i	0.784630	−	0.784630i	0.980608	+	0.195978i	$0.0627882\pi$
$390$	2.24827	+	2.38454i	0.113845	+	0.120746i
$391$		−	5.00875i		−	0.253304i
$392$	−15.9522	+	17.4566i	−0.805710	+	0.881689i
$393$	18.4423			0.930292
$394$	−16.5663	−	9.23607i	−0.834598	−	0.465307i
$395$	−1.67460	+	0.870098i	−0.0842581	+	0.0437794i
$396$	8.07728	+	1.90660i	0.405899	+	0.0958101i
$397$	−15.0440	+	15.0440i	−0.755036	+	0.755036i	−0.975414	−	0.220378i	$-0.929271\pi$
$397$	−15.0440	+	15.0440i	−0.755036	+	0.755036i	0.220378	+	0.975414i	$0.429271\pi$
$398$	3.34461	+	11.7730i	0.167650	+	0.590129i
$399$	−9.28590			−0.464876
$400$	−9.49684	−	17.6014i	−0.474842	−	0.880071i
$401$	28.7953			1.43797			0.718985	−	0.695026i	$-0.244607\pi$
$401$	28.7953			1.43797			0.718985	+	0.695026i	$0.244607\pi$
$402$	−2.10556	−	7.41157i	−0.105016	−	0.369655i
$403$	7.92543	−	7.92543i	0.394794	−	0.394794i
$404$	−4.87759	+	20.6639i	−0.242669	+	1.02807i
$405$	1.98421	−	1.03097i	0.0985963	−	0.0512293i
$406$	−34.1637	−	19.0470i	−1.69551	−	0.945286i
$407$	−37.6476			−1.86612
$408$	−8.17440	+	0.368072i	−0.404693	+	0.0182223i
$409$			23.3562i			1.15489i	0.816430	+	0.577444i	$0.195950\pi$
$409$			23.3562i			1.15489i	−0.816430	+	0.577444i	$0.804050\pi$
$410$	0.0125283	+	0.0132877i	0.000618729	+	0.000656231i
$411$	−4.60760	+	4.60760i	−0.227276	+	0.227276i
$412$	6.65387	−	4.11252i	0.327813	−	0.202610i
$413$	−15.0222	+	15.0222i	−0.739192	+	0.739192i
$414$	−0.669110	−	2.35527i	−0.0328850	−	0.115755i
$415$	4.95752	−	15.6810i	0.243355	−	0.769751i
$416$	−3.30348	−	4.84328i	−0.161966	−	0.237461i
$417$			21.3479i			1.04541i
$418$	13.3749	−	3.79968i	0.654185	−	0.185848i
$419$	−22.4332	−	22.4332i	−1.09594	−	1.09594i	−0.994881	−	0.101055i	$-0.967778\pi$
$419$	−22.4332	−	22.4332i	−1.09594	−	1.09594i	−0.101055	−	0.994881i	$-0.532222\pi$
$420$	−4.29207	−	16.9939i	−0.209432	−	0.829216i
$421$	14.7632	−	14.7632i	0.719513	−	0.719513i	−0.248993	−	0.968505i	$-0.580100\pi$
$421$	14.7632	−	14.7632i	0.719513	−	0.719513i	0.968505	+	0.248993i	$0.0800995\pi$
$422$	1.53015	+	0.853092i	0.0744865	+	0.0415279i
$423$	−11.6451			−0.566205
$424$	−22.2081	+	0.999973i	−1.07852	+	0.0485630i
$425$	11.8363	+	8.31511i	0.574144	+	0.403342i
$426$	−1.42488	−	0.794399i	−0.0690354	−	0.0384888i
$427$	−36.4725	−	36.4725i	−1.76503	−	1.76503i
$428$	−7.16364	−	1.69094i	−0.346268	−	0.0817345i
$429$	−3.04096	−	3.04096i	−0.146819	−	0.146819i
$430$	−10.0101	−	0.294445i	−0.482731	−	0.0141994i
$431$	5.92220			0.285262			0.142631	−	0.989776i	$-0.454444\pi$
$431$	5.92220			0.285262			0.142631	+	0.989776i	$0.454444\pi$
$432$	−3.79468	+	1.26508i	−0.182571	+	0.0608662i
$433$			5.27026i			0.253272i	0.991949	+	0.126636i	$0.0404181\pi$
$433$			5.27026i			0.253272i	−0.991949	+	0.126636i	$0.959582\pi$
$434$	−57.6616	+	16.3811i	−2.76784	+	0.786320i
$435$	14.0025	−	7.27551i	0.671369	−	0.348834i
$436$	−5.68819	−	1.34267i	−0.272415	−	0.0643020i
$437$	−2.90057	−	2.90057i	−0.138753	−	0.138753i
$438$	5.50040	−	9.86580i	0.262819	−	0.471406i
$439$			17.8427i			0.851587i	0.904820	+	0.425793i	$0.140005\pi$
$439$			17.8427i			0.851587i	−0.904820	+	0.425793i	$0.859995\pi$
$440$	13.1357	+	22.7207i	0.626221	+	1.08317i
$441$		−	8.36066i		−	0.398127i
$442$	3.70348	+	2.06477i	0.176156	+	0.0982110i
$443$	−5.89855	−	5.89855i	−0.280248	−	0.280248i	0.552960	−	0.833208i	$-0.313498\pi$
$443$	−5.89855	−	5.89855i	−0.280248	−	0.280248i	−0.833208	+	0.552960i	$0.813498\pi$
$444$	15.4349	−	9.53975i	0.732507	−	0.452737i
$445$	5.57648	+	10.7325i	0.264350	+	0.508771i
$446$	4.03380	+	14.1990i	0.191006	+	0.672341i
$447$		−	6.04438i		−	0.285889i
$448$	2.81788	+	31.2273i	0.133132	+	1.47535i
$449$	8.12803			0.383586			0.191793	−	0.981435i	$-0.438570\pi$
$449$	8.12803			0.383586			0.191793	+	0.981435i	$0.438570\pi$
$450$	6.67657	+	2.32883i	0.314736	+	0.109782i
$451$	−0.0169455	−	0.0169455i	−0.000797934	−	0.000797934i
$452$	−8.55511	−	13.8418i	−0.402399	−	0.651062i
$453$	5.93968	+	5.93968i	0.279071	+	0.279071i
$454$	13.3638	−	23.9700i	0.627193	−	1.12497i
$455$	−2.73786	+	8.66005i	−0.128353	+	0.405990i
$456$	−4.52064	+	4.94694i	−0.211698	+	0.231662i
$457$	−6.35488			−0.297269			−0.148634	−	0.988892i	$-0.547488\pi$
$457$	−6.35488			−0.297269			−0.148634	+	0.988892i	$0.547488\pi$
$458$	−8.21861	+	14.7413i	−0.384030	+	0.688817i
$459$	2.04567	−	2.04567i	0.0954838	−	0.0954838i
$460$	3.96756	−	6.64893i	0.184989	−	0.310008i
$461$	2.13085	+	2.13085i	0.0992438	+	0.0992438i	0.754985	−	0.655742i	$-0.227644\pi$
$461$	2.13085	+	2.13085i	0.0992438	+	0.0992438i	−0.655742	+	0.754985i	$0.727644\pi$
$462$	6.28540	+	22.1246i	0.292423	+	1.02933i
$463$		−	18.4540i		−	0.857630i	−0.903392	−	0.428815i	$-0.858931\pi$
$463$		−	18.4540i		−	0.857630i	0.903392	−	0.428815i	$-0.141069\pi$
$464$	−26.7789	+	8.92763i	−1.24318	+	0.414455i
$465$	7.28970	−	23.0579i	0.338052	−	1.06928i
$466$	38.9206	−	11.0570i	1.80296	−	0.512205i
$467$	−5.63243	+	5.63243i	−0.260638	+	0.260638i	−0.825313	−	0.564675i	$-0.809001\pi$
$467$	−5.63243	+	5.63243i	−0.260638	+	0.260638i	0.564675	+	0.825313i	$0.309001\pi$
$468$	2.01731	+	0.476175i	0.0932503	+	0.0220112i
$469$	15.0987	−	15.0987i	0.697193	−	0.697193i
$470$	−25.2624	−	26.7936i	−1.16527	−	1.23590i
$471$			8.04537i			0.370711i
$472$	0.689643	+	15.3161i	0.0317434	+	0.704979i
$473$	13.1412			0.604235
$474$	−0.581200	+	1.04247i	−0.0266954	+	0.0478822i
$475$	11.6697	−	2.03910i	0.535441	−	0.0935604i
$476$	−11.9224	−	19.2899i	−0.546464	−	0.884153i
$477$	5.55765	−	5.55765i	0.254467	−	0.254467i
$478$	−29.2379	+	8.30623i	−1.33731	+	0.379918i
$479$	21.4860			0.981720			0.490860	−	0.871239i	$-0.336683\pi$
$479$	21.4860			0.981720			0.490860	+	0.871239i	$0.336683\pi$
$480$	−11.1428	−	5.98655i	−0.508595	−	0.273248i
$481$	−9.40253			−0.428718
$482$	26.6558	−	7.57267i	1.21414	−	0.344926i
$483$	4.79810	−	4.79810i	0.218321	−	0.218321i
$484$	−6.53971	−	10.5809i	−0.297259	−	0.480952i
$485$	2.31096	+	4.44769i	0.104935	+	0.201959i
$486$	0.688658	−	1.23521i	0.0312382	−	0.0560304i
$487$	36.3297			1.64626			0.823128	−	0.567856i	$-0.192227\pi$
$487$	36.3297			1.64626			0.823128	+	0.567856i	$0.192227\pi$
$488$	−37.1861	+	1.67439i	−1.68334	+	0.0757962i
$489$		−	7.97431i		−	0.360611i
$490$	19.2366	−	18.1373i	0.869021	−	0.819358i
$491$	1.63599	−	1.63599i	0.0738313	−	0.0738313i	−0.669227	−	0.743058i	$-0.733375\pi$
$491$	1.63599	−	1.63599i	0.0738313	−	0.0738313i	0.743058	+	0.669227i	$0.233375\pi$
$492$	0.0112413	+	0.00265345i	0.000506798	+	0.000119627i
$493$	14.4362	−	14.4362i	0.650175	−	0.650175i
$494$	3.34039	−	0.948974i	0.150291	−	0.0426964i
$495$	−8.84724	−	2.79703i	−0.397654	−	0.125717i
$496$	−19.3445	+	38.6933i	−0.868592	+	1.73738i
$497$		−	4.52106i		−	0.202797i
$498$	−2.84246	−	10.0055i	−0.127374	−	0.448355i
$499$	18.7955	+	18.7955i	0.841402	+	0.841402i	0.989041	−	0.147639i	$-0.0471674\pi$
$499$	18.7955	+	18.7955i	0.841402	+	0.841402i	−0.147639	+	0.989041i	$0.547167\pi$
$500$	9.12558	+	20.4138i	0.408108	+	0.912933i
$501$	−4.56496	+	4.56496i	−0.203947	+	0.203947i
$502$	9.33076	−	16.7361i	0.416452	−	0.746970i
$503$	13.8118			0.615838			0.307919	−	0.951413i	$-0.400367\pi$
$503$	13.8118			0.615838			0.307919	+	0.951413i	$0.400367\pi$
$504$	−8.18319	−	7.47801i	−0.364508	−	0.333097i
$505$	7.15557	−	22.6336i	0.318419	−	1.00718i
$506$	−4.94757	+	8.87421i	−0.219946	+	0.394507i
$507$	8.43290	+	8.43290i	0.374518	+	0.374518i
$508$	16.9146	+	27.3671i	0.750465	+	1.21422i
$509$	−5.40184	−	5.40184i	−0.239432	−	0.239432i	0.577183	−	0.816615i	$-0.304152\pi$
$509$	−5.40184	−	5.40184i	−0.239432	−	0.239432i	−0.816615	+	0.577183i	$0.804152\pi$
$510$	9.14456	+	0.268985i	0.404928	+	0.0119108i
$511$	31.3037			1.38479
$512$	18.0077	+	13.7011i	0.795837	+	0.605510i
$513$		−	2.36929i		−	0.104607i
$514$	−5.12964	−	18.0563i	−0.226259	−	0.796431i
$515$	−7.76046	+	4.03223i	−0.341967	+	0.177681i
$516$	−5.38769	+	3.32994i	−0.237180	+	0.146593i
$517$	34.1694	+	34.1694i	1.50277	+	1.50277i
$518$	43.9212	+	24.4870i	1.92979	+	1.07590i
$519$		−	10.3756i		−	0.455437i
$520$	3.28066	+	5.67452i	0.143867	+	0.248844i
$521$		−	33.6969i		−	1.47629i	−0.674642	−	0.738145i	$-0.735702\pi$
$521$		−	33.6969i		−	1.47629i	0.674642	−	0.738145i	$-0.264298\pi$
$522$	4.85983	−	8.71685i	0.212709	−	0.381526i
$523$	−4.31481	−	4.31481i	−0.188673	−	0.188673i	0.606449	−	0.795122i	$-0.292593\pi$
$523$	−4.31481	−	4.31481i	−0.188673	−	0.188673i	−0.795122	+	0.606449i	$0.792593\pi$
$524$	35.8981	+	8.47355i	1.56822	+	0.370169i
$525$	3.37307	+	19.3039i	0.147213	+	0.842489i
$526$	−17.7674	+	5.04755i	−0.774694	+	0.220084i
$527$		−	31.2876i		−	1.36291i
$528$	14.8465	+	7.42241i	0.646111	+	0.323019i
$529$	−20.0025			−0.869674
$530$	24.8438	+	0.730774i	1.07915	+	0.0317428i
$531$	−3.83290	−	3.83290i	−0.166334	−	0.166334i
$532$	−18.0751	−	4.26652i	−0.783654	−	0.184977i
$533$	−0.00423217	−	0.00423217i	−0.000183316	−	0.000183316i
$534$	6.68122	+	3.72493i	0.289125	+	0.161193i
$535$	7.84650	+	2.48065i	0.339234	+	0.107248i
$536$	−0.693156	−	15.3941i	−0.0299398	−	0.664924i
$537$	−1.47612			−0.0636993
$538$	21.6727	+	12.0830i	0.934377	+	0.520936i
$539$	−24.5321	+	24.5321i	−1.05667	+	1.05667i
$540$	4.33598	−	1.09512i	0.186591	−	0.0471265i
$541$	−22.8010	−	22.8010i	−0.980290	−	0.980290i	0.0195198	−	0.999809i	$-0.493786\pi$
$541$	−22.8010	−	22.8010i	−0.980290	−	0.980290i	−0.999809	+	0.0195198i	$0.993786\pi$
$542$	−2.87303	+	0.816203i	−0.123407	+	0.0350589i
$543$			17.1154i			0.734493i
$544$	−16.0807	−	3.03937i	−0.689452	−	0.130312i
$545$	6.23041	+	1.96973i	0.266882	+	0.0843740i
$546$	1.56979	+	5.52564i	0.0671806	+	0.236476i
$547$	−5.56014	+	5.56014i	−0.237735	+	0.237735i	−0.815911	−	0.578177i	$-0.803764\pi$
$547$	−5.56014	+	5.56014i	−0.237735	+	0.237735i	0.578177	+	0.815911i	$0.303764\pi$
$548$	−11.0858	+	6.85172i	−0.473560	+	0.292691i
$549$	9.30595	−	9.30595i	0.397168	−	0.397168i
$550$	−12.7573	−	26.4239i	−0.543972	−	1.12672i
$551$		−	16.7200i		−	0.712297i
$552$	−0.220273	−	4.89197i	−0.00937543	−	0.208216i
$553$	−3.30771			−0.140658
$554$	23.0787	+	12.8669i	0.980521	+	0.546662i
$555$	−18.0018	+	9.35349i	−0.764134	+	0.397034i
$556$	−9.80856	+	41.5539i	−0.415976	+	1.76228i
$557$	12.2628	−	12.2628i	0.519591	−	0.519591i	−0.397857	−	0.917447i	$-0.630246\pi$
$557$	12.2628	−	12.2628i	0.519591	−	0.519591i	0.917447	+	0.397857i	$0.130246\pi$
$558$	−4.17964	−	14.7123i	−0.176938	−	0.622823i
$559$	3.28204			0.138816
$560$	−0.546512	−	35.0507i	−0.0230943	−	1.48116i
$561$	−12.0049			−0.506849
$562$	−1.46390	−	5.15294i	−0.0617510	−	0.217363i
$563$	0.327630	−	0.327630i	0.0138079	−	0.0138079i	−0.700169	−	0.713977i	$-0.746892\pi$
$563$	0.327630	−	0.327630i	0.0138079	−	0.0138079i	0.713977	+	0.700169i	$0.246892\pi$
$564$	−22.6673	−	5.35049i	−0.954465	−	0.225296i
$565$	8.38807	+	16.1438i	0.352889	+	0.679173i
$566$	5.52484	+	3.08022i	0.232226	+	0.129471i
$567$	3.91927			0.164594
$568$	−2.40853	−	2.20098i	−0.101060	−	0.0923511i
$569$			35.6010i			1.49247i	0.665681	+	0.746237i	$0.268141\pi$
$569$			35.6010i			1.49247i	−0.665681	+	0.746237i	$0.731859\pi$
$570$	5.45138	−	5.13984i	0.228333	−	0.215284i
$571$	3.57427	−	3.57427i	0.149579	−	0.149579i	−0.628351	−	0.777930i	$-0.716270\pi$
$571$	3.57427	−	3.57427i	0.149579	−	0.149579i	0.777930	+	0.628351i	$0.216270\pi$
$572$	−4.52205	−	7.31646i	−0.189076	−	0.305917i
$573$	−15.0100	+	15.0100i	−0.627051	+	0.627051i
$574$	0.00874752	+	0.0307912i	0.000365114	+	0.00128520i
$575$	−4.97618	+	7.08342i	−0.207521	+	0.295399i
$576$	−7.96763	+	0.718981i	−0.331984	+	0.0299575i
$577$		−	8.80260i		−	0.366457i	−0.983070	−	0.183229i	$-0.941345\pi$
$577$		−	8.80260i		−	0.366457i	0.983070	−	0.183229i	$-0.0586548\pi$
$578$	−11.7407	+	3.33543i	−0.488350	+	0.138736i
$579$	−13.6317	−	13.6317i	−0.566515	−	0.566515i
$580$	30.5988	−	7.72822i	1.27055	−	0.320897i
$581$	20.3829	−	20.3829i	0.845625	−	0.845625i
$582$	2.76877	+	1.54365i	0.114769	+	0.0639864i
$583$	−32.6149			−1.35077
$584$	15.2395	−	16.6766i	0.630616	−	0.690084i
$585$	−2.20961	−	0.698563i	−0.0913561	−	0.0288820i
$586$	−14.8716	−	8.29127i	−0.614342	−	0.342509i
$587$	17.9887	+	17.9887i	0.742475	+	0.742475i	0.973054	−	0.230579i	$-0.0740619\pi$
$587$	17.9887	+	17.9887i	0.742475	+	0.742475i	−0.230579	+	0.973054i	$0.574062\pi$
$588$	3.84141	−	16.2741i	0.158417	−	0.671132i
$589$	−18.1186	−	18.1186i	−0.746564	−	0.746564i
$590$	0.503987	−	17.1338i	0.0207488	−	0.705389i
$591$	13.4117			0.551684
$592$	34.4273	−	11.4775i	1.41495	−	0.471721i
$593$		−	25.4791i		−	1.04630i	−0.852240	−	0.523150i	$-0.824757\pi$
$593$		−	25.4791i		−	1.04630i	0.852240	−	0.523150i	$-0.175243\pi$
$594$	−5.64508	+	1.60372i	−0.231620	+	0.0658013i
$595$	11.6897	+	22.4980i	0.479229	+	0.922328i
$596$	2.77716	−	11.7654i	0.113757	−	0.481931i
$597$	−6.11945	−	6.11945i	−0.250452	−	0.250452i
$598$	−1.23566	+	2.21635i	−0.0505299	+	0.0906331i
$599$			14.6977i			0.600532i	0.953856	+	0.300266i	$0.0970754\pi$
$599$			14.6977i			0.600532i	−0.953856	+	0.300266i	$0.902925\pi$
$600$	11.9260	+	7.60071i	0.486876	+	0.310298i
$601$			12.2790i			0.500869i	0.968134	+	0.250434i	$0.0805735\pi$
$601$			12.2790i			0.500869i	−0.968134	+	0.250434i	$0.919427\pi$
$602$	−15.3311	−	8.54744i	−0.624850	−	0.348368i
$603$	3.85243	+	3.85243i	0.156883	+	0.156883i
$604$	8.83258	+	14.2907i	0.359393	+	0.581480i
$605$	6.41202	+	12.3406i	0.260686	+	0.501718i
$606$	−4.10274	−	14.4416i	−0.166662	−	0.586651i
$607$		−	26.2195i		−	1.06421i	−0.846677	−	0.532107i	$-0.821400\pi$
$607$		−	26.2195i		−	1.06421i	0.846677	−	0.532107i	$-0.178600\pi$
$608$	−11.0724	+	7.55220i	−0.449045	+	0.306282i
$609$	27.6581			1.12076
$610$	41.5995	+	1.22364i	1.68431	+	0.0495436i
$611$	8.53386	+	8.53386i	0.345243	+	0.345243i
$612$	4.92182	−	3.04201i	0.198953	−	0.122966i
$613$	23.4055	+	23.4055i	0.945340	+	0.945340i	0.998582	−	0.0532416i	$-0.0169553\pi$
$613$	23.4055	+	23.4055i	0.945340	+	0.945340i	−0.0532416	+	0.998582i	$0.516955\pi$
$614$	−6.93514	+	12.4392i	−0.279880	+	0.502007i
$615$	−0.0123129	−	0.00389269i	−0.000496503	−	0.000156968i
$616$	2.06917	+	45.9536i	0.0833692	+	1.85152i
$617$	−27.5735			−1.11007			−0.555033	−	0.831828i	$-0.687294\pi$
$617$	−27.5735			−1.11007			−0.555033	+	0.831828i	$0.687294\pi$
$618$	−2.69341	+	4.83104i	−0.108345	+	0.194333i
$619$	−12.2452	+	12.2452i	−0.492176	+	0.492176i	−0.908991	−	0.416815i	$-0.863146\pi$
$619$	−12.2452	+	12.2452i	−0.492176	+	0.492176i	0.416815	+	0.908991i	$0.363146\pi$
$620$	24.7837	−	41.5330i	0.995337	−	1.66801i
$621$	1.22423	+	1.22423i	0.0491268	+	0.0491268i
$622$	−8.23108	−	28.9734i	−0.330036	−	1.16173i
$623$			21.1992i			0.849327i
$624$	3.70793	+	1.85376i	0.148436	+	0.0742097i
$625$	−8.47792	−	23.5186i	−0.339117	−	0.940744i
$626$	−10.2000	+	2.89773i	−0.407673	+	0.115816i
$627$	−6.95205	+	6.95205i	−0.277638	+	0.277638i
$628$	−3.69654	+	15.6604i	−0.147508	+	0.624917i
$629$	−18.5594	+	18.5594i	−0.740011	+	0.740011i
$630$	8.50229	+	9.01763i	0.338739	+	0.359271i
$631$		−	25.5846i		−	1.01851i	−0.860617	−	0.509253i	$-0.829922\pi$
$631$		−	25.5846i		−	1.01851i	0.860617	−	0.509253i	$-0.170078\pi$
$632$	−1.61029	+	1.76214i	−0.0640537	+	0.0700941i
$633$	−1.23877			−0.0492369
$634$	−2.29214	+	4.11130i	−0.0910324	+	0.163281i
$635$	−16.5844	−	31.9184i	−0.658131	−	1.26664i
$636$	13.3716	−	8.26449i	0.530216	−	0.327708i
$637$	−6.12692	+	6.12692i	−0.242758	+	0.242758i
$638$	−39.8371	+	11.3174i	−1.57717	+	0.448059i
$639$	1.15355			0.0456336
$640$	−18.9389	−	16.7726i	−0.748625	−	0.662994i
$641$	−3.52020			−0.139040			−0.0695198	−	0.997581i	$-0.522147\pi$
$641$	−3.52020			−0.139040			−0.0695198	+	0.997581i	$0.522147\pi$
$642$	5.00655	−	1.42232i	0.197593	−	0.0561343i
$643$	−19.0869	+	19.0869i	−0.752715	+	0.752715i	−0.974985	−	0.222270i	$-0.928653\pi$
$643$	−19.0869	+	19.0869i	−0.752715	+	0.752715i	0.222270	+	0.974985i	$0.428653\pi$
$644$	11.5441	−	7.13499i	0.454900	−	0.281158i
$645$	6.28370	−	3.26493i	0.247421	−	0.128556i
$646$	4.72034	−	8.46665i	0.185719	−	0.333116i
$647$	5.02456			0.197536			0.0987678	−	0.995111i	$-0.468510\pi$
$647$	5.02456			0.197536			0.0987678	+	0.995111i	$0.468510\pi$
$648$	1.90801	−	2.08794i	0.0749538	−	0.0820220i
$649$			22.4932i			0.882935i
$650$	−3.18614	−	6.59940i	−0.124971	−	0.258850i
$651$	29.9717	−	29.9717i	1.17468	−	1.17468i
$652$	3.66389	−	15.5221i	0.143489	−	0.607891i
$653$	−6.07220	+	6.07220i	−0.237623	+	0.237623i	−0.815865	−	0.578242i	$-0.803739\pi$
$653$	−6.07220	+	6.07220i	−0.237623	+	0.237623i	0.578242	+	0.815865i	$0.303739\pi$
$654$	3.97538	−	1.12937i	0.155450	−	0.0441619i
$655$	−39.3201	−	12.4310i	−1.53636	−	0.485718i
$656$	0.0206622	+	0.0103299i	0.000806722	+	0.000403316i
$657$			7.98713i			0.311608i
$658$	−17.6387	−	62.0882i	−0.687629	−	2.42045i
$659$	−5.88182	−	5.88182i	−0.229123	−	0.229123i	0.583203	−	0.812326i	$-0.301799\pi$
$659$	−5.88182	−	5.88182i	−0.229123	−	0.229123i	−0.812326	+	0.583203i	$0.801799\pi$
$660$	−15.9361	−	9.50942i	−0.620312	−	0.370154i
$661$	−24.0275	+	24.0275i	−0.934562	+	0.934562i	−0.997987	−	0.0634242i	$-0.979798\pi$
$661$	−24.0275	+	24.0275i	−0.934562	+	0.934562i	0.0634242	+	0.997987i	$0.479798\pi$
$662$	−22.0927	+	39.6266i	−0.858656	+	1.54013i
$663$	−2.99825			−0.116442
$664$	−0.935746	−	20.7817i	−0.0363140	−	0.806486i
$665$	19.7981	+	6.25911i	0.767736	+	0.242718i
$666$	−6.24786	+	11.2065i	−0.242100	+	0.434243i
$667$	8.63936	+	8.63936i	0.334517	+	0.334517i
$668$	−10.9832	+	6.78831i	−0.424951	+	0.262647i
$669$	−7.38042	−	7.38042i	−0.285344	−	0.285344i
$670$	−0.506554	+	17.2211i	−0.0195699	+	0.665310i
$671$	−54.6116			−2.10826
$672$	−12.4928	−	18.3159i	−0.481920	−	0.706550i
$673$			36.5327i			1.40823i	0.710084	+	0.704117i	$0.248657\pi$
$673$			36.5327i			1.40823i	−0.710084	+	0.704117i	$0.751343\pi$
$674$	3.44098	+	12.1123i	0.132542	+	0.466546i
$675$	−4.92537	+	0.860637i	−0.189578	+	0.0331259i
$676$	12.5401	+	20.2893i	0.482312	+	0.780358i
$677$	20.5460	+	20.5460i	0.789645	+	0.789645i	0.981436	−	0.191791i	$-0.0614294\pi$
$677$	20.5460	+	20.5460i	0.789645	+	0.789645i	−0.191791	+	0.981436i	$0.561429\pi$
$678$	10.0498	+	5.60299i	0.385961	+	0.215182i
$679$			8.78518i			0.337144i
$680$	17.6764	+	4.72516i	0.677858	+	0.181202i
$681$			19.4055i			0.743622i
$682$	−30.9053	+	55.4334i	−1.18343	+	2.12265i
$683$	−18.2074	−	18.2074i	−0.696688	−	0.696688i	0.267007	−	0.963695i	$-0.413965\pi$
$683$	−18.2074	−	18.2074i	−0.696688	−	0.696688i	−0.963695	+	0.267007i	$0.913965\pi$
$684$	1.08860	−	4.61185i	0.0416237	−	0.176339i
$685$	12.9294	−	6.71794i	0.494007	−	0.256679i
$686$	7.25464	−	2.06098i	0.276983	−	0.0786885i
$687$		−	11.9342i		−	0.455320i
$688$	−12.0172	+	4.00632i	−0.458150	+	0.152740i
$689$	−8.14561			−0.310323
$690$	−0.160974	+	5.47257i	−0.00612818	+	0.208337i
$691$	11.5350	+	11.5350i	0.438811	+	0.438811i	0.891612	−	0.452801i	$-0.149575\pi$
$691$	11.5350	+	11.5350i	0.438811	+	0.438811i	−0.452801	+	0.891612i	$0.649575\pi$
$692$	4.76719	−	20.1962i	0.181221	−	0.767743i
$693$	−11.5000	−	11.5000i	−0.436850	−	0.436850i
$694$	−15.5083	−	8.64620i	−0.588686	−	0.328205i
$695$	14.3894	−	45.5149i	0.545823	−	1.72648i
$696$	13.4648	−	14.7345i	0.510381	−	0.558510i
$697$	−0.0167075			−0.000632842
$698$	14.3773	+	8.01567i	0.544189	+	0.303397i
$699$	−20.2304	+	20.2304i	−0.765182	+	0.765182i
$700$	−2.30369	+	39.1249i	−0.0870713	+	1.47878i
$701$	16.5440	+	16.5440i	0.624859	+	0.624859i	0.946770	−	0.321911i	$-0.104325\pi$
$701$	16.5440	+	16.5440i	0.624859	+	0.624859i	−0.321911	+	0.946770i	$0.604325\pi$
$702$	−1.40987	+	0.400530i	−0.0532120	+	0.0151170i
$703$			21.4955i			0.810717i
$704$	25.4885	+	21.2692i	0.960634	+	0.801613i
$705$	24.8280	+	7.84932i	0.935078	+	0.295623i
$706$	−13.4154	−	47.2223i	−0.504897	−	1.77723i
$707$	29.4202	−	29.4202i	1.10646	−	1.10646i
$708$	−5.69970	−	9.22184i	−0.214208	−	0.346578i
$709$	−8.47518	+	8.47518i	−0.318292	+	0.318292i	−0.848111	−	0.529819i	$-0.822260\pi$
$709$	−8.47518	+	8.47518i	−0.318292	+	0.318292i	0.529819	+	0.848111i	$0.322260\pi$
$710$	2.50245	+	2.65413i	0.0939154	+	0.0996078i
$711$		−	0.843960i		−	0.0316510i
$712$	11.2936	+	10.3204i	0.423245	+	0.386772i
$713$	18.7240			0.701221
$714$	14.0055	+	7.80835i	0.524141	+	0.292220i
$715$	4.43376	+	8.53325i	0.165813	+	0.319125i
$716$	−2.87328	−	0.678221i	−0.107379	−	0.0253463i
$717$	15.1974	−	15.1974i	0.567559	−	0.567559i
$718$	−1.08631	−	3.82380i	−0.0405406	−	0.142703i
$719$	−11.5303			−0.430008			−0.215004	−	0.976613i	$-0.568976\pi$
$719$	−11.5303			−0.430008			−0.215004	+	0.976613i	$0.568976\pi$
$720$	8.94318	−	0.139442i	0.333293	−	0.00519671i
$721$	−15.3287			−0.570869
$722$	5.17349	+	18.2107i	0.192537	+	0.677731i
$723$	−13.8553	+	13.8553i	−0.515284	+	0.515284i
$724$	−7.86389	+	33.3153i	−0.292259	+	1.23815i
$725$	−34.7582	+	6.07348i	−1.29089	+	0.225564i
$726$	7.68229	+	4.28304i	0.285116	+	0.158959i
$727$	32.2855			1.19740			0.598702	−	0.800972i	$-0.295684\pi$
$727$	32.2855			1.19740			0.598702	+	0.800972i	$0.295684\pi$
$728$	0.516778	+	11.4770i	0.0191531	+	0.425365i
$729$			1.00000i			0.0370370i
$730$	−18.3772	+	17.3269i	−0.680169	+	0.641298i
$731$	6.47833	−	6.47833i	0.239610	−	0.239610i
$732$	22.3898	−	13.8384i	0.827552	−	0.511481i
$733$	−33.6309	+	33.6309i	−1.24219	+	1.24219i	−0.283094	+	0.959092i	$0.591361\pi$
$733$	−33.6309	+	33.6309i	−1.24219	+	1.24219i	−0.959092	+	0.283094i	$0.908639\pi$
$734$	−7.06607	−	24.8726i	−0.260814	−	0.918063i
$735$	−5.63546	+	17.8254i	−0.207867	+	0.657500i
$736$	1.81891	−	9.62347i	0.0670461	−	0.354726i
$737$		−	22.6078i		−	0.832769i
$738$	−0.00785637	+	0.00223193i	−0.000289197	+	8.21583e-5i
$739$	−11.6806	−	11.6806i	−0.429676	−	0.429676i	0.458842	−	0.888518i	$-0.348264\pi$
$739$	−11.6806	−	11.6806i	−0.429676	−	0.429676i	−0.888518	+	0.458842i	$0.848264\pi$
$740$	−39.3382	+	9.93550i	−1.44610	+	0.365236i
$741$	−1.73628	+	1.73628i	−0.0637840	+	0.0637840i
$742$	38.0499	+	21.2136i	1.39685	+	0.778777i
$743$	−11.7641			−0.431582			−0.215791	−	0.976440i	$-0.569233\pi$
$743$	−11.7641			−0.431582			−0.215791	+	0.976440i	$0.569233\pi$
$744$	−1.37595	−	30.5581i	−0.0504448	−	1.12031i
$745$	−4.07418	+	12.8870i	−0.149266	+	0.472142i
$746$	40.9072	+	22.8067i	1.49772	+	0.835011i
$747$	5.20069	+	5.20069i	0.190283	+	0.190283i
$748$	−23.3677	−	5.51582i	−0.854408	−	0.201678i
$749$	10.1992	+	10.1992i	0.372672	+	0.372672i
$750$	−12.6651	−	9.46550i	−0.462463	−	0.345631i
$751$	9.89062			0.360914			0.180457	−	0.983583i	$-0.442242\pi$
$751$	9.89062			0.360914			0.180457	+	0.983583i	$0.442242\pi$
$752$	−41.6637	−	20.8295i	−1.51932	−	0.759575i
$753$			13.5492i			0.493760i
$754$	−9.94937	+	2.82653i	−0.362335	+	0.102936i
$755$	−8.66012	−	16.6673i	−0.315174	−	0.606587i
$756$	7.62889	+	1.80076i	0.277460	+	0.0654928i
$757$	−19.7078	−	19.7078i	−0.716291	−	0.716291i	0.251553	−	0.967844i	$-0.419059\pi$
$757$	−19.7078	−	19.7078i	−0.716291	−	0.716291i	−0.967844	+	0.251553i	$0.919059\pi$
$758$	6.04743	−	10.8470i	0.219653	−	0.393980i
$759$		−	7.18436i		−	0.260776i
$760$	12.9727	−	7.50004i	0.470570	−	0.272055i
$761$		−	48.2102i		−	1.74762i	−0.486270	−	0.873808i	$-0.661643\pi$
$761$		−	48.2102i		−	1.74762i	0.486270	−	0.873808i	$-0.338357\pi$
$762$	−19.8699	−	11.0779i	−0.719809	−	0.401309i
$763$	8.09857	+	8.09857i	0.293188	+	0.293188i
$764$	−36.1136	+	22.3205i	−1.30654	+	0.807529i
$765$	−5.74036	+	2.98261i	−0.207543	+	0.107837i
$766$	5.56540	+	19.5902i	0.201086	+	0.707823i
$767$			5.61771i			0.202844i
$768$	−15.8394	−	2.26132i	−0.571555	−	0.0815984i
$769$	−30.7814			−1.11000			−0.555002	−	0.831849i	$-0.687283\pi$
$769$	−30.7814			−1.11000			−0.555002	+	0.831849i	$0.687283\pi$
$770$	1.51214	−	51.4075i	0.0544936	−	1.85260i
$771$	9.38542	+	9.38542i	0.338008	+	0.338008i
$772$	−20.2710	−	32.7975i	−0.729570	−	1.18041i
$773$	−31.7802	−	31.7802i	−1.14306	−	1.14306i	−0.987888	−	0.155167i	$-0.950408\pi$
$773$	−31.7802	−	31.7802i	−1.14306	−	1.14306i	−0.155167	−	0.987888i	$-0.549592\pi$
$774$	2.18088	−	3.91173i	0.0783900	−	0.140604i
$775$	−31.0841	+	44.2471i	−1.11657	+	1.58940i
$776$	4.68019	+	4.27688i	0.168009	+	0.153531i
$777$	−35.5576			−1.27562
$778$	−15.0716	+	27.0331i	−0.540342	+	0.969185i
$779$	−0.00967532	+	0.00967532i	−0.000346654	+	0.000346654i
$780$	−3.98006	−	2.37499i	−0.142509	−	0.0850383i
$781$	−3.38477	−	3.38477i	−0.121117	−	0.121117i
$782$	1.93575	+	6.81382i	0.0692221	+	0.243662i
$783$			7.05696i			0.252195i
$784$	14.9547	−	29.9127i	0.534095	−	1.06831i
$785$	5.42294	−	17.1532i	0.193553	−	0.612223i
$786$	−25.0886	+	7.12745i	−0.894881	+	0.254228i
$787$	−21.8749	+	21.8749i	−0.779754	+	0.779754i	−0.979789	−	0.200035i	$-0.935895\pi$
$787$	−21.8749	+	21.8749i	−0.779754	+	0.779754i	0.200035	+	0.979789i	$0.435895\pi$
$788$	26.1060	+	6.16217i	0.929987	+	0.219518i
$789$	9.23522	−	9.23522i	0.328782	−	0.328782i
$790$	1.94182	−	1.83085i	0.0690870	−	0.0651387i
$791$			31.8876i			1.13379i
$792$	−11.7250	+	0.527948i	−0.416631	+	0.0187598i
$793$	−13.6393			−0.484346
$794$	14.6515	−	26.2797i	0.519962	−	0.932630i
$795$	−15.5953	+	8.10312i	−0.553110	+	0.287388i
$796$	−9.09990	−	14.7232i	−0.322538	−	0.521850i
$797$	16.0370	−	16.0370i	0.568058	−	0.568058i	−0.363526	−	0.931584i	$-0.618427\pi$
$797$	16.0370	−	16.0370i	0.568058	−	0.568058i	0.931584	+	0.363526i	$0.118427\pi$
$798$	12.6324	−	3.58874i	0.447181	−	0.127040i
$799$	33.6895			1.19185
$800$	19.7218	+	20.2744i	0.697271	+	0.716808i
$801$	−5.40896			−0.191116
$802$	−39.1726	+	11.1286i	−1.38323	+	0.392964i
$803$	23.4361	−	23.4361i	0.827041	−	0.827041i
$804$	5.72873	+	9.26882i	0.202037	+	0.326886i
$805$	−13.4639	+	6.99568i	−0.474542	+	0.246565i
$806$	−7.71865	+	13.8446i	−0.271878	+	0.487654i
$807$	−17.5457			−0.617639
$808$	−1.35063	−	29.9958i	−0.0475151	−	1.05525i
$809$		−	37.0836i		−	1.30379i	−0.758309	−	0.651895i	$-0.773974\pi$
$809$		−	37.0836i		−	1.30379i	0.758309	−	0.651895i	$-0.226026\pi$
$810$	−2.30085	+	2.16936i	−0.0808435	+	0.0762234i
$811$	−11.8858	+	11.8858i	−0.417369	+	0.417369i	−0.884296	−	0.466927i	$-0.845361\pi$
$811$	−11.8858	+	11.8858i	−0.417369	+	0.417369i	0.466927	+	0.884296i	$0.345361\pi$
$812$	53.8368	+	12.7079i	1.88930	+	0.445959i
$813$	1.49336	−	1.49336i	0.0523744	−	0.0523744i
$814$	51.2151	−	14.5497i	1.79509	−	0.509968i
$815$	−5.37504	+	17.0017i	−0.188279	+	0.595543i
$816$	10.9781	−	3.65990i	0.384309	−	0.128122i
$817$		−	7.50320i		−	0.262504i
$818$	−9.02651	−	31.7733i	−0.315605	−	1.11093i
$819$	−2.87215	−	2.87215i	−0.100361	−	0.100361i
$820$	−0.0221786	−	0.0132345i	−0.000774510	−	0.000462167i
$821$	−18.0568	+	18.0568i	−0.630186	+	0.630186i	−0.948115	−	0.317928i	$-0.897013\pi$
$821$	−18.0568	+	18.0568i	−0.630186	+	0.630186i	0.317928	+	0.948115i	$0.397013\pi$
$822$	4.48739	−	8.04881i	0.156516	−	0.280735i
$823$	−9.66750			−0.336988			−0.168494	−	0.985703i	$-0.553890\pi$
$823$	−9.66750			−0.336988			−0.168494	+	0.985703i	$0.553890\pi$
$824$	−7.46243	+	8.16614i	−0.259966	+	0.284481i
$825$	16.9775	+	11.9269i	0.591080	+	0.415240i
$826$	14.6302	−	26.2415i	0.509050	−	0.913059i
$827$	15.9204	+	15.9204i	0.553607	+	0.553607i	0.927480	−	0.373873i	$-0.121970\pi$
$827$	15.9204	+	15.9204i	0.553607	+	0.553607i	−0.373873	+	0.927480i	$0.621970\pi$
$828$	1.82049	+	2.94547i	0.0632664	+	0.102362i
$829$	6.21199	+	6.21199i	0.215751	+	0.215751i	0.806705	−	0.590954i	$-0.201249\pi$
$829$	6.21199	+	6.21199i	0.215751	+	0.215751i	−0.590954	+	0.806705i	$0.701249\pi$
$830$	−0.683837	+	23.2481i	−0.0237363	+	0.806955i
$831$	−18.6840			−0.648141
$832$	6.36579	+	5.31201i	0.220694	+	0.184161i
$833$			24.1875i			0.838048i
$834$	−8.25038	−	29.0413i	−0.285687	−	1.00562i
$835$	12.8097	−	6.65576i	0.443299	−	0.230332i
$836$	−16.7264	+	10.3380i	−0.578496	+	0.357548i
$837$	7.64726	+	7.64726i	0.264328	+	0.264328i
$838$	39.1876	+	21.8479i	1.35371	+	0.754725i
$839$		−	11.4138i		−	0.394047i	−0.980399	−	0.197023i	$-0.936873\pi$
$839$		−	11.4138i		−	0.394047i	0.980399	−	0.197023i	$-0.0631275\pi$
$840$	12.4065	+	21.4594i	0.428065	+	0.740419i
$841$			20.8007i			0.717266i
$842$	−14.3780	+	25.7891i	−0.495498	+	0.888751i
$843$	2.67842	+	2.67842i	0.0922497	+	0.0922497i
$844$	−2.41128	−	0.569170i	−0.0829998	−	0.0195916i
$845$	−12.2953	−	23.6636i	−0.422970	−	0.814052i
$846$	15.8418	−	4.50051i	0.544652	−	0.154731i
$847$			24.3755i			0.837553i
$848$	29.8251	−	9.94317i	1.02420	−	0.341450i
$849$	−4.47278			−0.153506
$850$	−19.3154	−	6.73734i	−0.662513	−	0.231089i
$851$	−11.1069	−	11.1069i	−0.380739	−	0.380739i
$852$	2.24539	+	0.530011i	0.0769257	+	0.0181579i
$853$	−12.1530	−	12.1530i	−0.416110	−	0.416110i	0.467751	−	0.883861i	$-0.345065\pi$
$853$	−12.1530	−	12.1530i	−0.416110	−	0.416110i	−0.883861	+	0.467751i	$0.845065\pi$
$854$	63.7121	+	35.5209i	2.18018	+	1.21550i
$855$	−1.59701	+	5.05147i	−0.0546166	+	0.172757i
$856$	10.3988	−	0.468230i	0.355423	−	0.0160038i
$857$	−23.6445			−0.807681			−0.403840	−	0.914829i	$-0.632325\pi$
$857$	−23.6445			−0.807681			−0.403840	+	0.914829i	$0.632325\pi$
$858$	5.31212	+	2.96162i	0.181353	+	0.101108i
$859$	18.9186	−	18.9186i	0.645494	−	0.645494i	−0.306407	−	0.951901i	$-0.599127\pi$
$859$	18.9186	−	18.9186i	0.645494	−	0.645494i	0.951901	+	0.306407i	$0.0991268\pi$
$860$	13.7314	−	3.46808i	0.468237	−	0.118261i
$861$	−0.0160048	−	0.0160048i	−0.000545443	−	0.000545443i
$862$	−8.05645	+	2.28877i	−0.274404	+	0.0779557i
$863$			32.1371i			1.09396i	0.837146	+	0.546980i	$0.184223\pi$
$863$			32.1371i			1.09396i	−0.837146	+	0.546980i	$0.815777\pi$
$864$	4.67329	−	3.18753i	0.158989	−	0.108442i
$865$	−6.99361	+	22.1213i	−0.237790	+	0.752148i
$866$	−2.03681	−	7.16956i	−0.0692136	−	0.243632i
$867$	6.10266	−	6.10266i	0.207257	−	0.207257i
$868$	72.1109	−	44.5692i	2.44760	−	1.51278i
$869$	−2.47637	+	2.47637i	−0.0840052	+	0.0840052i
$870$	−16.2370	+	15.3091i	−0.550485	+	0.519026i
$871$		−	5.64633i		−	0.191319i
$872$	8.25702	−	0.371792i	0.279618	−	0.0125905i
$873$	−2.24154			−0.0758645
$874$	5.06687	+	2.82489i	0.171389	+	0.0955533i
$875$	5.82010	−	43.4305i	0.196755	−	1.46822i
$876$	−3.66978	+	15.5470i	−0.123990	+	0.525285i
$877$	−33.5598	+	33.5598i	−1.13323	+	1.13323i	−0.143597	+	0.989636i	$0.545867\pi$
$877$	−33.5598	+	33.5598i	−1.13323	+	1.13323i	−0.989636	+	0.143597i	$0.954133\pi$
$878$	−6.89572	−	24.2729i	−0.232719	−	0.819171i
$879$	12.0397			0.406091
$880$	−26.6505	−	25.8322i	−0.898389	−	0.870803i
$881$	3.11390			0.104910			0.0524550	−	0.998623i	$-0.483295\pi$
$881$	3.11390			0.104910			0.0524550	+	0.998623i	$0.483295\pi$
$882$	3.23117	+	11.3737i	0.108799	+	0.382972i
$883$	36.1043	−	36.1043i	1.21501	−	1.21501i	0.245647	−	0.969359i	$-0.421000\pi$
$883$	36.1043	−	36.1043i	1.21501	−	1.21501i	0.969359	−	0.245647i	$-0.0790004\pi$
$884$	−5.83612	−	1.37758i	−0.196290	−	0.0463331i
$885$	5.58841	+	10.7555i	0.187852	+	0.361542i
$886$	10.3039	+	5.74465i	0.346166	+	0.192995i
$887$	38.4317			1.29041			0.645206	−	0.764009i	$-0.276772\pi$
$887$	38.4317			1.29041			0.645206	+	0.764009i	$0.276772\pi$
$888$	−17.3105	+	18.9429i	−0.580901	+	0.635681i
$889$		−	63.0461i		−	2.11450i
$890$	−11.7340	−	12.4452i	−0.393324	−	0.417164i
$891$	2.93423	−	2.93423i	0.0983004	−	0.0983004i
$892$	−10.9750	−	17.7571i	−0.367471	−	0.594551i
$893$	19.5096	−	19.5096i	0.652863	−	0.652863i
$894$	2.33599	+	8.22266i	0.0781271	+	0.275007i
$895$	3.14717	+	0.994971i	0.105198	+	0.0332582i
$896$	−15.9019	−	41.3920i	−0.531244	−	1.38281i
$897$		−	1.79430i		−	0.0599100i
$898$	−11.0572	+	3.14126i	−0.368985	+	0.104825i
$899$	53.9664	+	53.9664i	1.79988	+	1.79988i
$900$	−9.98271	−	0.587786i	−0.332757	−	0.0195929i
$901$	−16.0784	+	16.0784i	−0.535649	+	0.535649i
$902$	0.0296014	+	0.0165034i	0.000985618	+	0.000549504i
$903$	12.4117			0.413037
$904$	16.9877	+	15.5238i	0.565002	+	0.516313i
$905$	11.5366	−	36.4910i	0.383488	−	1.21300i
$906$	−10.3758	−	5.78471i	−0.344712	−	0.192184i
$907$	37.6279	+	37.6279i	1.24941	+	1.24941i	0.955979	+	0.293436i	$0.0947987\pi$
$907$	37.6279	+	37.6279i	1.24941	+	1.24941i	0.293436	+	0.955979i	$0.405201\pi$
$908$	−8.91611	+	37.7730i	−0.295891	+	1.25354i
$909$	7.50655	+	7.50655i	0.248977	+	0.248977i
$910$	0.377658	−	12.8391i	0.0125192	−	0.425612i
$911$	−11.8631			−0.393042			−0.196521	−	0.980500i	$-0.562964\pi$
$911$	−11.8631			−0.393042			−0.196521	+	0.980500i	$0.562964\pi$
$912$	4.23794	−	8.47684i	0.140332	−	0.280696i
$913$		−	30.5200i		−	1.01007i
$914$	8.64506	−	2.45599i	0.285953	−	0.0812368i
$915$	−26.1134	+	13.5682i	−0.863283	+	0.448550i
$916$	5.48333	−	23.2301i	0.181174	−	0.767544i
$917$	−51.1100	−	51.1100i	−1.68780	−	1.68780i
$918$	−1.99230	+	3.57349i	−0.0657556	+	0.117943i
$919$		−	46.4906i		−	1.53358i	−0.641895	−	0.766792i	$-0.721852\pi$
$919$		−	46.4906i		−	1.53358i	0.641895	−	0.766792i	$-0.278148\pi$
$920$	−2.82778	+	10.5784i	−0.0932290	+	0.348761i
$921$		−	10.0705i		−	0.331835i
$922$	−3.72229	−	2.07526i	−0.122587	−	0.0683450i
$923$	−0.845351	−	0.845351i	−0.0278251	−	0.0278251i
$924$	−17.1011	−	27.6687i	−0.562584	−	0.910235i
$925$	44.6855	−	7.80814i	1.46925	−	0.256730i
$926$	7.13196	+	25.1045i	0.234371	+	0.824985i
$927$		−	3.91110i		−	0.128457i
$928$	32.9792	−	22.4943i	1.08260	−	0.738411i
$929$	3.18351			0.104448			0.0522238	−	0.998635i	$-0.483369\pi$
$929$	3.18351			0.104448			0.0522238	+	0.998635i	$0.483369\pi$
$930$	−1.00554	+	34.1848i	−0.0329728	+	1.12096i
$931$	14.0070	+	14.0070i	0.459060	+	0.459060i
$932$	−48.6736	+	30.0835i	−1.59436	+	0.985417i
$933$	15.0599	+	15.0599i	0.493040	+	0.493040i
$934$	5.48548	−	9.83903i	0.179490	−	0.321943i
$935$	25.5952	+	8.09187i	0.837053	+	0.264632i
$936$	−2.92834	+	0.131856i	−0.0957159	+	0.00430984i
$937$	−27.2455			−0.890072			−0.445036	−	0.895513i	$-0.646809\pi$
$937$	−27.2455			−0.890072			−0.445036	+	0.895513i	$0.646809\pi$
$938$	−14.7048	+	26.3752i	−0.480127	+	0.861181i
$939$	5.30181	−	5.30181i	0.173018	−	0.173018i
$940$	44.7215	+	26.6863i	1.45865	+	0.870412i
$941$	4.15297	+	4.15297i	0.135383	+	0.135383i	0.771551	−	0.636168i	$-0.219481\pi$
$941$	4.15297	+	4.15297i	0.135383	+	0.135383i	−0.636168	+	0.771551i	$0.719481\pi$
$942$	−3.10931	−	10.9448i	−0.101307	−	0.356600i
$943$		−	0.00999862i		−	0.000325600i
$944$	−6.85742	−	20.5692i	−0.223190	−	0.669470i
$945$	−8.35610	−	2.64176i	−0.271824	−	0.0859365i
$946$	−17.8771	+	5.07873i	−0.581235	+	0.165124i
$947$	18.3519	−	18.3519i	0.596358	−	0.596358i	−0.342984	−	0.939341i	$-0.611438\pi$
$947$	18.3519	−	18.3519i	0.596358	−	0.596358i	0.939341	+	0.342984i	$0.111438\pi$
$948$	0.387768	−	1.64278i	0.0125941	−	0.0533549i
$949$	5.85319	−	5.85319i	0.190003	−	0.190003i
$950$	−15.0871	+	7.28396i	−0.489491	+	0.236323i
$951$		−	3.32841i		−	0.107931i
$952$	23.6741	+	21.6340i	0.767282	+	0.701162i
$953$	52.0669			1.68661			0.843307	−	0.537433i	$-0.180606\pi$
$953$	52.0669			1.68661			0.843307	+	0.537433i	$0.180606\pi$
$954$	−5.41265	+	9.70841i	−0.175241	+	0.314321i
$955$	42.1195	−	21.8847i	1.36296	−	0.708173i
$956$	36.5646	−	22.5993i	1.18258	−	0.730913i
$957$	20.7067	−	20.7067i	0.669354	−	0.669354i
$958$	−29.2291	+	8.30374i	−0.944351	+	0.268282i
$959$	25.5385			0.824681
$960$	17.4721	+	3.83763i	0.563908	+	0.123859i
$961$	85.9611			2.77294
$962$	12.7910	−	3.63382i	0.412399	−	0.117159i
$963$	−2.60233	+	2.60233i	−0.0838589	+	0.0838589i
$964$	−33.3354	+	20.6035i	−1.07366	+	0.663593i
$965$	19.8752	+	38.2520i	0.639806	+	1.23138i
$966$	−4.67291	+	8.38157i	−0.150348	+	0.269673i
$967$	32.8074			1.05502			0.527508	−	0.849550i	$-0.323127\pi$
$967$	32.8074			1.05502			0.527508	+	0.849550i	$0.323127\pi$
$968$	12.9857	+	11.8667i	0.417378	+	0.381410i
$969$			6.85441i			0.220195i
$970$	−4.86269	−	5.15743i	−0.156132	−	0.165595i
$971$	−25.4682	+	25.4682i	−0.817314	+	0.817314i	−0.985718	−	0.168404i	$-0.946139\pi$
$971$	−25.4682	+	25.4682i	−0.817314	+	0.817314i	0.168404	+	0.985718i	$0.446139\pi$
$972$	−0.459462	+	1.94651i	−0.0147373	+	0.0624343i
$973$	59.1623	−	59.1623i	1.89666	−	1.89666i
$974$	−49.4223	+	14.0404i	−1.58359	+	0.449884i
$975$	4.24015	+	2.97875i	0.135793	+	0.0953964i
$976$	49.9402	−	16.6492i	1.59855	−	0.532929i
$977$			2.69863i			0.0863367i	0.999068	+	0.0431684i	$0.0137452\pi$
$977$			2.69863i			0.0863367i	−0.999068	+	0.0431684i	$0.986255\pi$
$978$	3.08185	+	10.8481i	0.0985467	+	0.346884i
$979$	15.8711	+	15.8711i	0.507244	+	0.507244i
$980$	−19.1596	+	32.1080i	−0.612030	+	1.02565i
$981$	−2.06635	+	2.06635i	−0.0659734	+	0.0659734i
$982$	−1.59331	+	2.85784i	−0.0508445	+	0.0911973i
$983$	−25.2037			−0.803875			−0.401937	−	0.915667i	$-0.631663\pi$
$983$	−25.2037			−0.803875			−0.401937	+	0.915667i	$0.631663\pi$
$984$	−0.0163180		0.000734756i	−0.000520198		2.34232e-5i
$985$	−28.5945	−	9.04009i	−0.911097	−	0.288041i
$986$	−14.0596	+	25.2180i	−0.447748	+	0.803104i
$987$	32.2726	+	32.2726i	1.02725	+	1.02725i
$988$	−4.17745	+	2.58194i	−0.132902	+	0.0821423i
$989$	3.87696	+	3.87696i	0.123280	+	0.123280i
$990$	13.1166	+	0.385821i	0.416873	+	0.0122622i
$991$	−9.06410			−0.287931			−0.143965	−	0.989583i	$-0.545985\pi$
$991$	−9.06410			−0.287931			−0.143965	+	0.989583i	$0.545985\pi$
$992$	11.3620	−	60.1137i	0.360743	−	1.90861i
$993$		−	32.0808i		−	1.01805i
$994$	1.74726	+	6.15037i	0.0554199	+	0.195078i
$995$	8.92223	+	17.1718i	0.282854	+	0.544382i
$996$	7.73366	+	12.5127i	0.245051	+	0.396480i
$997$	−25.5035	−	25.5035i	−0.807703	−	0.807703i	0.176583	−	0.984286i	$-0.443496\pi$
$997$	−25.5035	−	25.5035i	−0.807703	−	0.807703i	−0.984286	+	0.176583i	$0.943496\pi$
$998$	−32.8330	−	18.3051i	−1.03931	−	0.579438i
$999$		−	9.07252i		−	0.287042i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.bl.a.109.3	✓	48
3.2	odd	2		720.2.bm.h.109.22		48
4.3	odd	2		960.2.bl.a.529.2		48
5.4	even	2	inner	240.2.bl.a.109.22	yes	48
8.3	odd	2		1920.2.bl.b.289.23		48
8.5	even	2		1920.2.bl.a.289.2		48
15.14	odd	2		720.2.bm.h.109.3		48
16.3	odd	4		1920.2.bl.b.1249.2		48
16.5	even	4	inner	240.2.bl.a.229.22	yes	48
16.11	odd	4		960.2.bl.a.49.17		48
16.13	even	4		1920.2.bl.a.1249.23		48
20.19	odd	2		960.2.bl.a.529.17		48
40.19	odd	2		1920.2.bl.b.289.2		48
40.29	even	2		1920.2.bl.a.289.23		48
48.5	odd	4		720.2.bm.h.469.3		48
80.19	odd	4		1920.2.bl.b.1249.23		48
80.29	even	4		1920.2.bl.a.1249.2		48
80.59	odd	4		960.2.bl.a.49.2		48
80.69	even	4	inner	240.2.bl.a.229.3	yes	48
240.149	odd	4		720.2.bm.h.469.22		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bl.a.109.3	✓	48	1.1	even	1	trivial
240.2.bl.a.109.22	yes	48	5.4	even	2	inner
240.2.bl.a.229.3	yes	48	80.69	even	4	inner
240.2.bl.a.229.22	yes	48	16.5	even	4	inner
720.2.bm.h.109.3		48	15.14	odd	2
720.2.bm.h.109.22		48	3.2	odd	2
720.2.bm.h.469.3		48	48.5	odd	4
720.2.bm.h.469.22		48	240.149	odd	4
960.2.bl.a.49.2		48	80.59	odd	4
960.2.bl.a.49.17		48	16.11	odd	4
960.2.bl.a.529.2		48	4.3	odd	2
960.2.bl.a.529.17		48	20.19	odd	2
1920.2.bl.a.289.2		48	8.5	even	2
1920.2.bl.a.289.23		48	40.29	even	2
1920.2.bl.a.1249.2		48	80.29	even	4
1920.2.bl.a.1249.23		48	16.13	even	4
1920.2.bl.b.289.2		48	40.19	odd	2
1920.2.bl.b.289.23		48	8.3	odd	2
1920.2.bl.b.1249.2		48	16.3	odd	4
1920.2.bl.b.1249.23		48	80.19	odd	4

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)

\(f(q)\)	\(=\)	\(q+(-1.36038 + 0.386472i) q^{2} +(0.707107 - 0.707107i) q^{3} +(1.70128 - 1.05150i) q^{4} +(-1.98421 + 1.03097i) q^{5} +(-0.688658 + 1.23521i) q^{6} -3.91927 q^{7} +(-1.90801 + 2.08794i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(-1.36038 + 0.386472i) q^{2} +(0.707107 - 0.707107i) q^{3} +(1.70128 - 1.05150i) q^{4} +(-1.98421 + 1.03097i) q^{5} +(-0.688658 + 1.23521i) q^{6} -3.91927 q^{7} +(-1.90801 + 2.08794i) q^{8} -1.00000i q^{9} +(2.30085 - 2.16936i) q^{10} +(-2.93423 + 2.93423i) q^{11} +(0.459462 - 1.94651i) q^{12} +(-0.732828 + 0.732828i) q^{13} +(5.33170 - 1.51469i) q^{14} +(-0.674045 + 2.13206i) q^{15} +(1.78869 - 3.57779i) q^{16} +2.89302i q^{17} +(0.386472 + 1.36038i) q^{18} +(1.67534 + 1.67534i) q^{19} +(-2.29163 + 3.84037i) q^{20} +(-2.77134 + 2.77134i) q^{21} +(2.85767 - 5.12567i) q^{22} -1.73133 q^{23} +(0.127228 + 2.82556i) q^{24} +(2.87420 - 4.09133i) q^{25} +(0.713708 - 1.28014i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(-6.66776 + 4.12111i) q^{28} +(-4.99003 - 4.99003i) q^{29} +(0.0929773 - 3.16091i) q^{30} -10.8149 q^{31} +(-1.05059 + 5.55844i) q^{32} +4.14963i q^{33} +(-1.11807 - 3.93561i) q^{34} +(7.77666 - 4.04065i) q^{35} +(-1.05150 - 1.70128i) q^{36} +(6.41524 + 6.41524i) q^{37} +(-2.92658 - 1.63163i) q^{38} +1.03637i q^{39} +(1.63330 - 6.11002i) q^{40} +0.00577512i q^{41} +(2.69904 - 4.84113i) q^{42} +(-2.23930 - 2.23930i) q^{43} +(-1.90660 + 8.07728i) q^{44} +(1.03097 + 1.98421i) q^{45} +(2.35527 - 0.669110i) q^{46} -11.6451i q^{47} +(-1.26508 - 3.79468i) q^{48} +8.36066 q^{49} +(-2.32883 + 6.67657i) q^{50} +(2.04567 + 2.04567i) q^{51} +(-0.476175 + 2.01731i) q^{52} +(5.55765 + 5.55765i) q^{53} +(1.23521 + 0.688658i) q^{54} +(2.79703 - 8.84724i) q^{55} +(7.47801 - 8.18319i) q^{56} +2.36929 q^{57} +(8.71685 + 4.85983i) q^{58} +(3.83290 - 3.83290i) q^{59} +(1.09512 + 4.33598i) q^{60} +(9.30595 + 9.30595i) q^{61} +(14.7123 - 4.17964i) q^{62} +3.91927i q^{63} +(-0.718981 - 7.96763i) q^{64} +(0.698563 - 2.20961i) q^{65} +(-1.60372 - 5.64508i) q^{66} +(-3.85243 + 3.85243i) q^{67} +(3.04201 + 4.92182i) q^{68} +(-1.22423 + 1.22423i) q^{69} +(-9.01763 + 8.50229i) q^{70} +1.15355i q^{71} +(2.08794 + 1.90801i) q^{72} -7.98713 q^{73} +(-11.2065 - 6.24786i) q^{74} +(-0.860637 - 4.92537i) q^{75} +(4.61185 + 1.08860i) q^{76} +(11.5000 - 11.5000i) q^{77} +(-0.400530 - 1.40987i) q^{78} +0.843960 q^{79} +(0.139442 + 8.94318i) q^{80} -1.00000 q^{81} +(-0.00223193 - 0.00785637i) q^{82} +(-5.20069 + 5.20069i) q^{83} +(-1.80076 + 7.62889i) q^{84} +(-2.98261 - 5.74036i) q^{85} +(3.91173 + 2.18088i) q^{86} -7.05696 q^{87} +(-0.527948 - 11.7250i) q^{88} -5.40896i q^{89} +(-2.16936 - 2.30085i) q^{90} +(2.87215 - 2.87215i) q^{91} +(-2.94547 + 1.82049i) q^{92} +(-7.64726 + 7.64726i) q^{93} +(4.50051 + 15.8418i) q^{94} +(-5.05147 - 1.59701i) q^{95} +(3.18753 + 4.67329i) q^{96} -2.24154i q^{97} +(-11.3737 + 3.23117i) q^{98} +(2.93423 + 2.93423i) 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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