LMFDB - Embedded newform 240.2.bl.a.109.2

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			109.2
Character	$\chi$	$=$	240.109
Dual form			240.2.bl.a.229.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39033 - 0.258835i) q^{2} +(0.707107 - 0.707107i) q^{3} +(1.86601 + 0.719729i) q^{4} +(0.404088 - 2.19925i) q^{5} +(-1.16613 + 0.800085i) q^{6} +1.81567 q^{7} +(-2.40807 - 1.48364i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(-1.39033 - 0.258835i) q^{2} +(0.707107 - 0.707107i) q^{3} +(1.86601 + 0.719729i) q^{4} +(0.404088 - 2.19925i) q^{5} +(-1.16613 + 0.800085i) q^{6} +1.81567 q^{7} +(-2.40807 - 1.48364i) q^{8} -1.00000i q^{9} +(-1.13106 + 2.95308i) q^{10} +(-0.331965 + 0.331965i) q^{11} +(1.82839 - 0.810543i) q^{12} +(-0.0310184 + 0.0310184i) q^{13} +(-2.52438 - 0.469959i) q^{14} +(-1.26937 - 1.84084i) q^{15} +(2.96398 + 2.68604i) q^{16} -1.00474i q^{17} +(-0.258835 + 1.39033i) q^{18} +(-2.08203 - 2.08203i) q^{19} +(2.33690 - 3.81299i) q^{20} +(1.28388 - 1.28388i) q^{21} +(0.547464 - 0.375616i) q^{22} +6.22794 q^{23} +(-2.75186 + 0.653667i) q^{24} +(-4.67343 - 1.77739i) q^{25} +(0.0511543 - 0.0350971i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(3.38806 + 1.30679i) q^{28} +(-6.28959 - 6.28959i) q^{29} +(1.28837 + 2.88792i) q^{30} +7.11301 q^{31} +(-3.42566 - 4.50165i) q^{32} +0.469470i q^{33} +(-0.260063 + 1.39692i) q^{34} +(0.733693 - 3.99313i) q^{35} +(0.719729 - 1.86601i) q^{36} +(-0.0723513 - 0.0723513i) q^{37} +(2.35580 + 3.43360i) q^{38} +0.0438667i q^{39} +(-4.23598 + 4.69643i) q^{40} +3.06050i q^{41} +(-2.11732 + 1.45269i) q^{42} +(3.78495 + 3.78495i) q^{43} +(-0.858375 + 0.380525i) q^{44} +(-2.19925 - 0.404088i) q^{45} +(-8.65886 - 1.61201i) q^{46} +10.0476i q^{47} +(3.99517 - 0.196534i) q^{48} -3.70333 q^{49} +(6.03753 + 3.68079i) q^{50} +(-0.710461 - 0.710461i) q^{51} +(-0.0802055 + 0.0355558i) q^{52} +(7.04636 + 7.04636i) q^{53} +(0.800085 + 1.16613i) q^{54} +(0.595932 + 0.864219i) q^{55} +(-4.37227 - 2.69382i) q^{56} -2.94443 q^{57} +(7.11661 + 10.3725i) q^{58} +(-6.68042 + 6.68042i) q^{59} +(-1.04376 - 4.34863i) q^{60} +(2.89442 + 2.89442i) q^{61} +(-9.88940 - 1.84109i) q^{62} -1.81567i q^{63} +(3.59760 + 7.14544i) q^{64} +(0.0556832 + 0.0807515i) q^{65} +(0.121515 - 0.652716i) q^{66} +(-0.150837 + 0.150837i) q^{67} +(0.723143 - 1.87486i) q^{68} +(4.40382 - 4.40382i) q^{69} +(-2.05363 + 5.36184i) q^{70} +14.5503i q^{71} +(-1.48364 + 2.40807i) q^{72} -15.0323 q^{73} +(0.0818648 + 0.119319i) q^{74} +(-4.56141 + 2.04781i) q^{75} +(-2.38659 - 5.38358i) q^{76} +(-0.602741 + 0.602741i) q^{77} +(0.0113542 - 0.0609889i) q^{78} +15.5985 q^{79} +(7.10499 - 5.43315i) q^{80} -1.00000 q^{81} +(0.792162 - 4.25508i) q^{82} +(5.48985 - 5.48985i) q^{83} +(3.31977 - 1.47168i) q^{84} +(-2.20969 - 0.406005i) q^{85} +(-4.28263 - 6.24198i) q^{86} -8.89482 q^{87} +(1.29191 - 0.306877i) q^{88} +14.3520i q^{89} +(2.95308 + 1.13106i) q^{90} +(-0.0563193 + 0.0563193i) q^{91} +(11.6214 + 4.48242i) q^{92} +(5.02966 - 5.02966i) q^{93} +(2.60066 - 13.9694i) q^{94} +(-5.42023 + 3.73758i) q^{95} +(-5.60545 - 0.760842i) q^{96} -13.5585i q^{97} +(5.14883 + 0.958550i) q^{98} +(0.331965 + 0.331965i) 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 $

$2$	−1.39033	−	0.258835i	−0.983108	−	0.183024i
$2$	−1.39033	−	0.258835i	−0.983108	−	0.183024i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$	1.86601	+	0.719729i	0.933005	+	0.359864i
$5$	0.404088	−	2.19925i	0.180714	−	0.983536i
$5$	0.404088	−	2.19925i	0.180714	−	0.983536i
$6$	−1.16613	+	0.800085i	−0.476071	+	0.326633i
$7$	1.81567			0.686260			0.343130	−	0.939288i	$-0.388513\pi$
$7$	1.81567			0.686260			0.343130	+	0.939288i	$0.388513\pi$
$8$	−2.40807	−	1.48364i	−0.851381	−	0.524548i
$9$		−	1.00000i		−	0.333333i
$10$	−1.13106	+	2.95308i	−0.357672	+	0.933847i
$11$	−0.331965	+	0.331965i	−0.100091	+	0.100091i	−0.755379	−	0.655288i	$-0.772547\pi$
$11$	−0.331965	+	0.331965i	−0.100091	+	0.100091i	0.655288	+	0.755379i	$0.272547\pi$
$12$	1.82839	−	0.810543i	0.527812	−	0.233984i
$13$	−0.0310184	+	0.0310184i	−0.00860296	+	0.00860296i	−0.711395	−	0.702792i	$-0.751936\pi$
$13$	−0.0310184	+	0.0310184i	−0.00860296	+	0.00860296i	0.702792	+	0.711395i	$0.251936\pi$
$14$	−2.52438	−	0.469959i	−0.674668	−	0.125602i
$15$	−1.26937	−	1.84084i	−0.327751	−	0.475303i
$16$	2.96398	+	2.68604i	0.740995	+	0.671510i
$17$		−	1.00474i		−	0.243686i	−0.992549	−	0.121843i	$-0.961120\pi$
$17$		−	1.00474i		−	0.243686i	0.992549	−	0.121843i	$-0.0388805\pi$
$18$	−0.258835	+	1.39033i	−0.0610079	+	0.327703i
$19$	−2.08203	−	2.08203i	−0.477650	−	0.477650i	0.426729	−	0.904379i	$-0.359666\pi$
$19$	−2.08203	−	2.08203i	−0.477650	−	0.477650i	−0.904379	+	0.426729i	$0.859666\pi$
$20$	2.33690	−	3.81299i	0.522546	−	0.852611i
$21$	1.28388	−	1.28388i	0.280165	−	0.280165i
$22$	0.547464	−	0.375616i	0.116720	−	0.0800815i
$23$	6.22794			1.29861			0.649307	−	0.760526i	$-0.275059\pi$
$23$	6.22794			1.29861			0.649307	+	0.760526i	$0.275059\pi$
$24$	−2.75186	+	0.653667i	−0.561721	+	0.133429i
$25$	−4.67343	−	1.77739i	−0.934685	−	0.355477i
$26$	0.0511543	−	0.0350971i	0.0100322	−	0.00688310i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	3.38806	+	1.30679i	0.640284	+	0.246961i
$29$	−6.28959	−	6.28959i	−1.16795	−	1.16795i	−0.982690	−	0.185258i	$-0.940688\pi$
$29$	−6.28959	−	6.28959i	−1.16795	−	1.16795i	−0.185258	−	0.982690i	$-0.559312\pi$
$30$	1.28837	+	2.88792i	0.235223	+	0.527260i
$31$	7.11301			1.27753			0.638767	−	0.769400i	$-0.279445\pi$
$31$	7.11301			1.27753			0.638767	+	0.769400i	$0.279445\pi$
$32$	−3.42566	−	4.50165i	−0.605576	−	0.795787i
$33$			0.469470i			0.0817242i
$34$	−0.260063	+	1.39692i	−0.0446004	+	0.239570i
$35$	0.733693	−	3.99313i	0.124017	−	0.674961i
$36$	0.719729	−	1.86601i	0.119955	−	0.311002i
$37$	−0.0723513	−	0.0723513i	−0.0118945	−	0.0118945i	0.701135	−	0.713029i	$-0.252677\pi$
$37$	−0.0723513	−	0.0723513i	−0.0118945	−	0.0118945i	−0.713029	+	0.701135i	$0.752677\pi$
$38$	2.35580	+	3.43360i	0.382161	+	0.557003i
$39$			0.0438667i			0.00702429i
$40$	−4.23598	+	4.69643i	−0.669768	+	0.742571i
$41$			3.06050i			0.477969i	0.971023	+	0.238985i	$0.0768145\pi$
$41$			3.06050i			0.477969i	−0.971023	+	0.238985i	$0.923185\pi$
$42$	−2.11732	+	1.45269i	−0.326709	+	0.224155i
$43$	3.78495	+	3.78495i	0.577199	+	0.577199i	0.934131	−	0.356932i	$-0.116177\pi$
$43$	3.78495	+	3.78495i	0.577199	+	0.577199i	−0.356932	+	0.934131i	$0.616177\pi$
$44$	−0.858375	+	0.380525i	−0.129405	+	0.0573663i
$45$	−2.19925	−	0.404088i	−0.327845	−	0.0602379i
$46$	−8.65886	−	1.61201i	−1.27668	−	0.237677i
$47$			10.0476i			1.46559i	0.680450	+	0.732795i	$0.261785\pi$
$47$			10.0476i			1.46559i	−0.680450	+	0.732795i	$0.738215\pi$
$48$	3.99517	−	0.196534i	0.576653	−	0.0283672i
$49$	−3.70333			−0.529047
$50$	6.03753	+	3.68079i	0.853836	+	0.520542i
$51$	−0.710461	−	0.710461i	−0.0994845	−	0.0994845i
$52$	−0.0802055	+	0.0355558i	−0.0111225	+	0.00493070i
$53$	7.04636	+	7.04636i	0.967892	+	0.967892i	0.999500	−	0.0316087i	$-0.0100630\pi$
$53$	7.04636	+	7.04636i	0.967892	+	0.967892i	−0.0316087	+	0.999500i	$0.510063\pi$
$54$	0.800085	+	1.16613i	0.108878	+	0.158690i
$55$	0.595932	+	0.864219i	0.0803555	+	0.116531i
$56$	−4.37227	−	2.69382i	−0.584269	−	0.359976i
$57$	−2.94443			−0.390000
$58$	7.11661	+	10.3725i	0.934457	+	1.36198i
$59$	−6.68042	+	6.68042i	−0.869717	+	0.869717i	−0.992441	−	0.122724i	$-0.960837\pi$
$59$	−6.68042	+	6.68042i	−0.869717	+	0.869717i	0.122724	+	0.992441i	$0.460837\pi$
$60$	−1.04376	−	4.34863i	−0.134748	−	0.561406i
$61$	2.89442	+	2.89442i	0.370592	+	0.370592i	0.867693	−	0.497101i	$-0.165602\pi$
$61$	2.89442	+	2.89442i	0.370592	+	0.370592i	−0.497101	+	0.867693i	$0.665602\pi$
$62$	−9.88940	−	1.84109i	−1.25596	−	0.233819i
$63$		−	1.81567i		−	0.228753i
$64$	3.59760	+	7.14544i	0.449699	+	0.893180i
$65$	0.0556832	+	0.0807515i	0.00690665	+	0.0100160i
$66$	0.121515	−	0.652716i	0.0149575	−	0.0803437i
$67$	−0.150837	+	0.150837i	−0.0184276	+	0.0184276i	−0.716261	−	0.697833i	$-0.754148\pi$
$67$	−0.150837	+	0.150837i	−0.0184276	+	0.0184276i	0.697833	+	0.716261i	$0.254148\pi$
$68$	0.723143	−	1.87486i	0.0876940	−	0.227360i
$69$	4.40382	−	4.40382i	0.530157	−	0.530157i
$70$	−2.05363	+	5.36184i	−0.245456	+	0.640862i
$71$			14.5503i			1.72680i	0.504520	+	0.863400i	$0.331669\pi$
$71$			14.5503i			1.72680i	−0.504520	+	0.863400i	$0.668331\pi$
$72$	−1.48364	+	2.40807i	−0.174849	+	0.283794i
$73$	−15.0323			−1.75939			−0.879697	−	0.475534i	$-0.842255\pi$
$73$	−15.0323			−1.75939			−0.879697	+	0.475534i	$0.842255\pi$
$74$	0.0818648	+	0.119319i	0.00951659	+	0.0138705i
$75$	−4.56141	+	2.04781i	−0.526706	+	0.236461i
$76$	−2.38659	−	5.38358i	−0.273760	−	0.617539i
$77$	−0.602741	+	0.602741i	−0.0686887	+	0.0686887i
$78$	0.0113542	−	0.0609889i	0.00128561	−	0.00690564i
$79$	15.5985			1.75497			0.877487	−	0.479601i	$-0.159219\pi$
$79$	15.5985			1.75497			0.877487	+	0.479601i	$0.159219\pi$
$80$	7.10499	−	5.43315i	0.794362	−	0.607444i
$81$	−1.00000			−0.111111
$82$	0.792162	−	4.25508i	0.0874797	−	0.469895i
$83$	5.48985	−	5.48985i	0.602590	−	0.602590i	−0.338409	−	0.940999i	$-0.609889\pi$
$83$	5.48985	−	5.48985i	0.602590	−	0.602590i	0.940999	+	0.338409i	$0.109889\pi$
$84$	3.31977	−	1.47168i	0.362216	−	0.160574i
$85$	−2.20969	−	0.406005i	−0.239674	−	0.0440375i
$86$	−4.28263	−	6.24198i	−0.461808	−	0.673090i
$87$	−8.89482			−0.953625
$88$	1.29191	−	0.306877i	0.137718	−	0.0327132i
$89$			14.3520i			1.52131i	0.649157	+	0.760655i	$0.275122\pi$
$89$			14.3520i			1.52131i	−0.649157	+	0.760655i	$0.724878\pi$
$90$	2.95308	+	1.13106i	0.311282	+	0.119224i
$91$	−0.0563193	+	0.0563193i	−0.00590387	+	0.00590387i
$92$	11.6214	+	4.48242i	1.21161	+	0.467325i
$93$	5.02966	−	5.02966i	0.521551	−	0.521551i
$94$	2.60066	−	13.9694i	0.268238	−	1.44083i
$95$	−5.42023	+	3.73758i	−0.556104	+	0.383468i
$96$	−5.60545	−	0.760842i	−0.572104	−	0.0776532i
$97$		−	13.5585i		−	1.37666i	−0.725399	−	0.688329i	$-0.758345\pi$
$97$		−	13.5585i		−	1.37666i	0.725399	−	0.688329i	$-0.241655\pi$
$98$	5.14883	+	0.958550i	0.520111	+	0.0968281i
$99$	0.331965	+	0.331965i	0.0333638	+	0.0333638i
$100$	−7.44142	−	6.68022i	−0.744142	−	0.668022i
$101$	10.5132	−	10.5132i	1.04610	−	1.04610i	0.0472186	−	0.998885i	$-0.484964\pi$
$101$	10.5132	−	10.5132i	1.04610	−	1.04610i	0.998885	−	0.0472186i	$-0.0150357\pi$
$102$	0.803880	+	1.17166i	0.0795960	+	0.116012i
$103$	−6.14387			−0.605373			−0.302687	−	0.953090i	$-0.597884\pi$
$103$	−6.14387			−0.605373			−0.302687	+	0.953090i	$0.597884\pi$
$104$	0.120715	−	0.0286742i	0.0118371	−	0.00281174i
$105$	−2.30477	−	3.34237i	−0.224922	−	0.326181i
$106$	−7.97289	−	11.6206i	−0.774395	−	1.12869i
$107$	−6.91512	−	6.91512i	−0.668510	−	0.668510i	0.288861	−	0.957371i	$-0.406723\pi$
$107$	−6.91512	−	6.91512i	−0.668510	−	0.668510i	−0.957371	+	0.288861i	$0.906723\pi$
$108$	−0.810543	−	1.82839i	−0.0779945	−	0.175937i
$109$	−6.15941	−	6.15941i	−0.589964	−	0.589964i	0.347657	−	0.937622i	$-0.386977\pi$
$109$	−6.15941	−	6.15941i	−0.589964	−	0.589964i	−0.937622	+	0.347657i	$0.886977\pi$
$110$	−0.604850	−	1.35579i	−0.0576702	−	0.129270i
$111$	−0.102320			−0.00971180
$112$	5.38162	+	4.87697i	0.508516	+	0.460831i
$113$			2.13102i			0.200470i	0.994964	+	0.100235i	$0.0319594\pi$
$113$			2.13102i			0.200470i	−0.994964	+	0.100235i	$0.968041\pi$
$114$	4.09372	+	0.762121i	0.383412	+	0.0713792i
$115$	2.51664	−	13.6968i	0.234678	−	1.27723i
$116$	−7.20964	−	16.2632i	−0.669398	−	1.51000i
$117$	0.0310184	+	0.0310184i	0.00286765	+	0.00286765i
$118$	11.0171	−	7.55884i	1.01421	−	0.695847i
$119$		−	1.82429i		−	0.167232i
$120$	0.325585	+	6.31617i	0.0297217	+	0.576585i
$121$			10.7796i			0.979963i
$122$	−3.27501	−	4.77336i	−0.296505	−	0.432159i
$123$	2.16410	+	2.16410i	0.195130	+	0.195130i
$124$	13.2729	+	5.11944i	1.19195	+	0.459739i
$125$	−5.79740	+	9.55982i	−0.518535	+	0.855056i
$126$	−0.469959	+	2.52438i	−0.0418673	+	0.224889i
$127$			10.5491i			0.936077i	0.883708	+	0.468039i	$0.155039\pi$
$127$			10.5491i			0.936077i	−0.883708	+	0.468039i	$0.844961\pi$
$128$	−3.15234	−	10.8657i	−0.278630	−	0.960398i
$129$	5.35272			0.471281
$130$	−0.0565164	−	0.126684i	−0.00495682	−	0.0111109i
$131$	5.82338	+	5.82338i	0.508791	+	0.508791i	0.914155	−	0.405364i	$-0.132855\pi$
$131$	5.82338	+	5.82338i	0.508791	+	0.508791i	−0.405364	+	0.914155i	$0.632855\pi$
$132$	−0.337891	+	0.876035i	−0.0294096	+	0.0762490i
$133$	−3.78028	−	3.78028i	−0.327792	−	0.327792i
$134$	0.248754	−	0.170670i	0.0214890	−	0.0147437i
$135$	−1.84084	+	1.26937i	−0.158434	+	0.109250i
$136$	−1.49068	+	2.41949i	−0.127825	+	0.207470i
$137$	15.6554			1.33753			0.668764	−	0.743475i	$-0.266824\pi$
$137$	15.6554			1.33753			0.668764	+	0.743475i	$0.266824\pi$
$138$	−7.26260	+	4.98288i	−0.618233	+	0.424171i
$139$	−1.14177	+	1.14177i	−0.0968440	+	0.0968440i	−0.753869	−	0.657025i	$-0.771815\pi$
$139$	−1.14177	+	1.14177i	−0.0968440	+	0.0968440i	0.657025	+	0.753869i	$0.271815\pi$
$140$	4.24304	−	6.92315i	0.358603	−	0.585113i
$141$	7.10471	+	7.10471i	0.598325	+	0.598325i
$142$	3.76611	−	20.2296i	0.316045	−	1.69763i
$143$		−	0.0205941i		−	0.00172216i
$144$	2.68604	−	2.96398i	0.223837	−	0.246998i
$145$	−16.3740	+	11.2908i	−1.35978	+	0.937654i
$146$	20.8997	+	3.89087i	1.72968	+	0.322011i
$147$	−2.61865	+	2.61865i	−0.215983	+	0.215983i
$148$	−0.0829349	−	0.187081i	−0.00681720	−	0.0153780i
$149$	−1.81817	+	1.81817i	−0.148951	+	0.148951i	−0.777649	−	0.628698i	$-0.783588\pi$
$149$	−1.81817	+	1.81817i	−0.148951	+	0.148951i	0.628698	+	0.777649i	$0.283588\pi$
$150$	6.87189	−	1.66647i	0.561087	−	0.136067i
$151$		−	11.2409i		−	0.914774i	−0.889268	−	0.457387i	$-0.848785\pi$
$151$		−	11.2409i		−	0.914774i	0.889268	−	0.457387i	$-0.151215\pi$
$152$	1.92468	+	8.10266i	0.156112	+	0.657212i
$153$	−1.00474			−0.0812287
$154$	0.994016	−	0.681995i	0.0801001	−	0.0549567i
$155$	2.87429	−	15.6433i	0.230868	−	1.25650i
$156$	−0.0315721	+	0.0818556i	−0.00252779	+	0.00655369i
$157$	14.8194	−	14.8194i	1.18272	−	1.18272i	0.203681	−	0.979037i	$-0.434709\pi$
$157$	14.8194	−	14.8194i	1.18272	−	1.18272i	0.979037	−	0.203681i	$-0.0652907\pi$
$158$	−21.6871	−	4.03744i	−1.72533	−	0.321202i
$159$	9.96505			0.790280
$160$	−11.2845	+	5.71482i	−0.892121	+	0.451796i
$161$	11.3079			0.891187
$162$	1.39033	+	0.258835i	0.109234	+	0.0203360i
$163$	−6.87622	+	6.87622i	−0.538587	+	0.538587i	−0.923114	−	0.384527i	$-0.874365\pi$
$163$	−6.87622	+	6.87622i	−0.538587	+	0.538587i	0.384527	+	0.923114i	$0.374365\pi$
$164$	−2.20273	+	5.71091i	−0.172004	+	0.445947i
$165$	1.03248	+	0.189707i	0.0803787	+	0.0147687i
$166$	−9.05365	+	6.21172i	−0.702699	+	0.482123i
$167$	−12.8174			−0.991838			−0.495919	−	0.868369i	$-0.665169\pi$
$167$	−12.8174			−0.991838			−0.495919	+	0.868369i	$0.665169\pi$
$168$	−4.99648	+	1.18685i	−0.385486	+	0.0915671i
$169$			12.9981i			0.999852i
$170$	2.96709	+	1.13642i	0.227566	+	0.0871597i
$171$	−2.08203	+	2.08203i	−0.159217	+	0.159217i
$172$	4.33861	+	9.78688i	0.330816	+	0.746243i
$173$	−5.88931	+	5.88931i	−0.447756	+	0.447756i	−0.894608	−	0.446852i	$-0.852545\pi$
$173$	−5.88931	+	5.88931i	−0.447756	+	0.447756i	0.446852	+	0.894608i	$0.352545\pi$
$174$	12.3667	+	2.30229i	0.937517	+	0.174536i
$175$	−8.48542	−	3.22715i	−0.641437	−	0.243950i
$176$	−1.87561	+	0.0922665i	−0.141379	+	0.00695485i
$177$			9.44755i			0.710121i
$178$	3.71479	−	19.9540i	0.278436	−	1.49561i
$179$	−10.1383	−	10.1383i	−0.757769	−	0.757769i	0.218147	−	0.975916i	$-0.429999\pi$
$179$	−10.1383	−	10.1383i	−0.757769	−	0.757769i	−0.975916	+	0.218147i	$0.929999\pi$
$180$	−3.81299	−	2.33690i	−0.284204	−	0.174182i
$181$	−10.8678	+	10.8678i	−0.807798	+	0.807798i	−0.984300	−	0.176503i	$-0.943522\pi$
$181$	−10.8678	+	10.8678i	−0.807798	+	0.807798i	0.176503	+	0.984300i	$0.443522\pi$
$182$	0.0928796	−	0.0637248i	0.00688469	−	0.00472360i
$183$	4.09332			0.302587
$184$	−14.9973	−	9.24005i	−1.10562	−	0.681185i
$185$	−0.188355	+	0.129882i	−0.0138481	+	0.00954915i
$186$	−8.29471	+	5.69101i	−0.608198	+	0.417285i
$187$	0.333540	+	0.333540i	0.0243909	+	0.0243909i
$188$	−7.23153	+	18.7489i	−0.527414	+	1.36740i
$189$	−1.28388	−	1.28388i	−0.0933882	−	0.0933882i
$190$	8.50330	−	3.79351i	0.616894	−	0.275210i
$191$	−1.57307			−0.113823			−0.0569116	−	0.998379i	$-0.518125\pi$
$191$	−1.57307			−0.113823			−0.0569116	+	0.998379i	$0.518125\pi$
$192$	7.59647	+	2.50870i	0.548228	+	0.181050i
$193$			3.91815i			0.282034i	0.990007	+	0.141017i	$0.0450373\pi$
$193$			3.91815i			0.282034i	−0.990007	+	0.141017i	$0.954963\pi$
$194$	−3.50941	+	18.8507i	−0.251961	+	1.35340i
$195$	0.0964739	+	0.0177260i	0.00690864	+	0.00126939i
$196$	−6.91045	−	2.66539i	−0.493603	−	0.190385i
$197$	−2.72966	−	2.72966i	−0.194480	−	0.194480i	0.603149	−	0.797629i	$-0.293913\pi$
$197$	−2.72966	−	2.72966i	−0.194480	−	0.194480i	−0.797629	+	0.603149i	$0.793913\pi$
$198$	−0.375616	−	0.547464i	−0.0266938	−	0.0389066i
$199$		−	19.6851i		−	1.39544i	−0.716371	−	0.697719i	$-0.754198\pi$
$199$		−	19.6851i		−	1.39544i	0.716371	−	0.697719i	$-0.245802\pi$
$200$	8.61692	+	11.2138i	0.609308	+	0.792933i
$201$			0.213315i			0.0150461i
$202$	−17.3380	+	11.8956i	−1.21989	+	0.836971i
$203$	−11.4198	−	11.4198i	−0.801516	−	0.801516i
$204$	−0.814388	−	1.83707i	−0.0570186	−	0.128620i
$205$	6.73080	+	1.23671i	0.470100	+	0.0863756i
$206$	8.54198	+	1.59025i	0.595148	+	0.110798i
$207$		−	6.22794i		−	0.432872i
$208$	−0.175255	+	0.00862127i	−0.0121517	+	0.000597778i
$209$	1.38232			0.0956172
$210$	2.33926	+	5.24353i	0.161424	+	0.361838i
$211$	1.93798	+	1.93798i	0.133416	+	0.133416i	0.770661	−	0.637245i	$-0.219926\pi$
$211$	1.93798	+	1.93798i	0.133416	+	0.133416i	−0.637245	+	0.770661i	$0.719926\pi$
$212$	8.07710	+	18.2200i	0.554738	+	1.25136i
$213$	10.2886	+	10.2886i	0.704963	+	0.704963i
$214$	7.82439	+	11.4041i	0.534864	+	0.779571i
$215$	9.85351	−	6.79460i	0.672004	−	0.463388i
$216$	0.653667	+	2.75186i	0.0444764	+	0.187240i
$217$	12.9149			0.876721
$218$	6.96931	+	10.1578i	0.472021	+	0.687976i
$219$	−10.6294	+	10.6294i	−0.718270	+	0.718270i
$220$	0.490012	+	2.04155i	0.0330366	+	0.137641i
$221$	0.0311656	+	0.0311656i	0.00209642	+	0.00209642i
$222$	0.142258	+	0.0264840i	0.00954775	+	0.00177749i
$223$		−	9.22040i		−	0.617443i	−0.951152	−	0.308722i	$-0.900099\pi$
$223$		−	9.22040i		−	0.617443i	0.951152	−	0.308722i	$-0.0999012\pi$
$224$	−6.21988	−	8.17353i	−0.415583	−	0.546117i
$225$	−1.77739	+	4.67343i	−0.118492	+	0.311562i
$226$	0.551582	−	2.96281i	0.0366907	−	0.197083i
$227$	−11.0458	+	11.0458i	−0.733132	+	0.733132i	−0.971239	−	0.238107i	$-0.923473\pi$
$227$	−11.0458	+	11.0458i	−0.733132	+	0.733132i	0.238107	+	0.971239i	$0.423473\pi$
$228$	−5.49434	−	2.11919i	−0.363871	−	0.140347i
$229$	5.23103	−	5.23103i	0.345676	−	0.345676i	−0.512820	−	0.858496i	$-0.671399\pi$
$229$	5.23103	−	5.23103i	0.345676	−	0.345676i	0.858496	+	0.512820i	$0.171399\pi$
$230$	−7.04415	+	18.3916i	−0.464478	+	1.21271i
$231$			0.852404i			0.0560841i
$232$	5.81425	+	24.4773i	0.381724	+	1.60701i
$233$	14.5509			0.953262			0.476631	−	0.879103i	$-0.341858\pi$
$233$	14.5509			0.953262			0.476631	+	0.879103i	$0.341858\pi$
$234$	−0.0350971	−	0.0511543i	−0.00229437	−	0.00334406i
$235$	22.0972	+	4.06011i	1.44146	+	0.264852i
$236$	−17.2738	+	7.65764i	−1.12443	+	0.498470i
$237$	11.0298	−	11.0298i	0.716465	−	0.716465i
$238$	−0.472189	+	2.53635i	−0.0306075	+	0.164407i
$239$	−8.23404			−0.532616			−0.266308	−	0.963888i	$-0.585804\pi$
$239$	−8.23404			−0.532616			−0.266308	+	0.963888i	$0.585804\pi$
$240$	1.18217	−	8.86580i	0.0763090	−	0.572285i
$241$	−6.81789			−0.439179			−0.219589	−	0.975592i	$-0.570472\pi$
$241$	−6.81789			−0.439179			−0.219589	+	0.975592i	$0.570472\pi$
$242$	2.79013	−	14.9871i	0.179357	−	0.963410i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	3.31781	+	7.48421i	0.212401	+	0.479127i
$245$	−1.49647	+	8.14456i	−0.0956061	+	0.520337i
$246$	−2.44866	−	3.56894i	−0.156121	−	0.227547i
$247$	0.129162			0.00821841
$248$	−17.1286	−	10.5532i	−1.08767	−	0.670128i
$249$		−	7.76382i		−	0.492012i
$250$	10.5347	−	11.7907i	0.666272	−	0.745709i
$251$	12.1421	−	12.1421i	0.766403	−	0.766403i	−0.211068	−	0.977471i	$-0.567694\pi$
$251$	12.1421	−	12.1421i	0.766403	−	0.766403i	0.977471	+	0.211068i	$0.0676942\pi$
$252$	1.30679	−	3.38806i	0.0823202	−	0.213428i
$253$	−2.06746	+	2.06746i	−0.129980	+	0.129980i
$254$	2.73046	−	14.6666i	0.171324	−	0.920266i
$255$	−1.84957	+	1.27539i	−0.115825	+	0.0798683i
$256$	1.57037	+	15.9227i	0.0981481	+	0.995172i
$257$		−	13.9667i		−	0.871217i	−0.900136	−	0.435609i	$-0.856533\pi$
$257$		−	13.9667i		−	0.871217i	0.900136	−	0.435609i	$-0.143467\pi$
$258$	−7.44203	−	1.38547i	−0.463320	−	0.0862556i
$259$	−0.131366	−	0.131366i	−0.00816271	−	0.00816271i
$260$	0.0457861	+	0.190760i	0.00283953	+	0.0118304i
$261$	−6.28959	+	6.28959i	−0.389316	+	0.389316i
$262$	−6.58910	−	9.60368i	−0.407076	−	0.593317i
$263$	3.31340			0.204313			0.102157	−	0.994768i	$-0.467426\pi$
$263$	3.31340			0.204313			0.102157	+	0.994768i	$0.467426\pi$
$264$	0.696526	−	1.13052i	0.0428682	−	0.0695784i
$265$	18.3441	−	12.6494i	1.12687	−	0.777045i
$266$	4.27736	+	6.23429i	0.262262	+	0.382249i
$267$	10.1484	+	10.1484i	0.621072	+	0.621072i
$268$	−0.390024	+	0.172901i	−0.0238245	+	0.0105616i
$269$	−14.5006	−	14.5006i	−0.884120	−	0.884120i	0.109831	−	0.993950i	$-0.464969\pi$
$269$	−14.5006	−	14.5006i	−0.884120	−	0.884120i	−0.993950	+	0.109831i	$0.964969\pi$
$270$	2.88792	−	1.28837i	0.175753	−	0.0784076i
$271$	−7.51560			−0.456540			−0.228270	−	0.973598i	$-0.573307\pi$
$271$	−7.51560			−0.456540			−0.228270	+	0.973598i	$0.573307\pi$
$272$	2.69878	−	2.97804i	0.163638	−	0.180570i
$273$			0.0796476i			0.00482049i
$274$	−21.7661	−	4.05215i	−1.31494	−	0.244799i
$275$	2.14144	−	0.961384i	0.129134	−	0.0579737i
$276$	11.3871	−	5.04801i	0.685424	−	0.303854i
$277$	11.7421	+	11.7421i	0.705512	+	0.705512i	0.965588	−	0.260076i	$-0.0837477\pi$
$277$	11.7421	+	11.7421i	0.705512	+	0.705512i	−0.260076	+	0.965588i	$0.583748\pi$
$278$	1.88297	−	1.29191i	0.112933	−	0.0774834i
$279$		−	7.11301i		−	0.425845i
$280$	−7.69116	+	8.52718i	−0.459635	+	0.509597i
$281$		−	32.4999i		−	1.93878i	−0.245523	−	0.969391i	$-0.578960\pi$
$281$		−	32.4999i		−	1.93878i	0.245523	−	0.969391i	$-0.421040\pi$
$282$	−8.03891	−	11.7168i	−0.478710	−	0.697726i
$283$	−3.88285	−	3.88285i	−0.230811	−	0.230811i	0.582220	−	0.813031i	$-0.302184\pi$
$283$	−3.88285	−	3.88285i	−0.230811	−	0.230811i	−0.813031	+	0.582220i	$0.802184\pi$
$284$	−10.4723	+	27.1509i	−0.621414	+	1.61111i
$285$	−1.18981	+	6.47555i	−0.0704783	+	0.383579i
$286$	−0.00533046	+	0.0286325i	−0.000315197	+	0.00169307i
$287$			5.55686i			0.328011i
$288$	−4.50165	+	3.42566i	−0.265262	+	0.201859i
$289$	15.9905			0.940617
$290$	25.6876	−	11.4598i	1.50843	−	0.672943i
$291$	−9.58731	−	9.58731i	−0.562018	−	0.562018i
$292$	−28.0504	−	10.8192i	−1.64152	−	0.633143i
$293$	−10.6693	−	10.6693i	−0.623305	−	0.623305i	0.323070	−	0.946375i	$-0.395285\pi$
$293$	−10.6693	−	10.6693i	−0.623305	−	0.623305i	−0.946375	+	0.323070i	$0.895285\pi$
$294$	4.31857	−	2.96298i	0.251864	−	0.172804i
$295$	11.9925	+	17.3914i	0.698228	+	1.01257i
$296$	0.0668833	+	0.281570i	0.00388751	+	0.0163660i
$297$	0.469470			0.0272414
$298$	2.99846	−	2.05725i	0.173696	−	0.119173i
$299$	−0.193181	+	0.193181i	−0.0111719	+	0.0111719i
$300$	−9.98550	+	0.538253i	−0.576513	+	0.0310760i
$301$	6.87223	+	6.87223i	0.396109	+	0.396109i
$302$	−2.90954	+	15.6286i	−0.167425	+	0.899322i
$303$		−	14.8679i		−	0.854140i
$304$	−0.578680	−	11.7635i	−0.0331896	−	0.674683i
$305$	7.53516	−	5.19596i	0.431462	−	0.297520i
$306$	1.39692	+	0.260063i	0.0798567	+	0.0148668i
$307$	−16.3961	+	16.3961i	−0.935778	+	0.935778i	−0.998059	−	0.0622811i	$-0.980162\pi$
$307$	−16.3961	+	16.3961i	−0.935778	+	0.935778i	0.0622811	+	0.998059i	$0.480162\pi$
$308$	−1.55853	+	0.690910i	−0.0888054	+	0.0393682i
$309$	−4.34437	+	4.34437i	−0.247143	+	0.247143i
$310$	−8.04522	+	21.0053i	−0.456938	+	1.19302i
$311$			10.1406i			0.575023i	0.957777	+	0.287512i	$0.0928280\pi$
$311$			10.1406i			0.575023i	−0.957777	+	0.287512i	$0.907172\pi$
$312$	0.0650826	−	0.105634i	0.00368457	−	0.00598035i
$313$	−23.3811			−1.32158			−0.660790	−	0.750571i	$-0.729779\pi$
$313$	−23.3811			−1.32158			−0.660790	+	0.750571i	$0.729779\pi$
$314$	−24.4396	+	16.7680i	−1.37921	+	0.946275i
$315$	−3.99313	−	0.733693i	−0.224987	−	0.0413389i
$316$	29.1070	+	11.2267i	1.63740	+	0.631552i
$317$	10.8253	−	10.8253i	0.608009	−	0.608009i	−0.334416	−	0.942425i	$-0.608539\pi$
$317$	10.8253	−	10.8253i	0.608009	−	0.608009i	0.942425	+	0.334416i	$0.108539\pi$
$318$	−13.8547	−	2.57930i	−0.776931	−	0.144640i
$319$	4.17585			0.233803
$320$	17.1684	−	5.02463i	0.959741	−	0.280886i
$321$	−9.77945			−0.545836
$322$	−15.7217	−	2.92688i	−0.876134	−	0.163108i
$323$	−2.09191	+	2.09191i	−0.116397	+	0.116397i
$324$	−1.86601	−	0.719729i	−0.103667	−	0.0399849i
$325$	0.200094	−	0.0898306i	0.0110992	−	0.00498290i
$326$	11.3400	−	7.78038i	0.628064	−	0.430915i
$327$	−8.71072			−0.481704
$328$	4.54069	−	7.36989i	0.250718	−	0.406934i
$329$			18.2431i			1.00578i
$330$	−1.38638	−	0.530997i	−0.0763179	−	0.0292304i
$331$	12.1611	−	12.1611i	0.668432	−	0.668432i	−0.288921	−	0.957353i	$-0.593296\pi$
$331$	12.1611	−	12.1611i	0.668432	−	0.668432i	0.957353	+	0.288921i	$0.0932964\pi$
$332$	14.1953	−	6.29291i	0.779069	−	0.345368i
$333$	−0.0723513	+	0.0723513i	−0.00396483	+	0.00396483i
$334$	17.8203	+	3.31758i	0.975085	+	0.181530i
$335$	0.270776	+	0.392679i	0.0147941	+	0.0214543i
$336$	7.25392	−	0.356841i	0.395734	−	0.0194673i
$337$		−	1.91202i		−	0.104154i	−0.998643	−	0.0520772i	$-0.983416\pi$
$337$		−	1.91202i		−	0.104154i	0.998643	−	0.0520772i	$-0.0165842\pi$
$338$	3.36435	−	18.0716i	0.182997	−	0.982963i
$339$	1.50686	+	1.50686i	0.0818414	+	0.0818414i
$340$	−3.83108	−	2.34798i	−0.207770	−	0.127337i
$341$	−2.36127	+	2.36127i	−0.127870	+	0.127870i
$342$	3.43360	−	2.35580i	0.185668	−	0.127387i
$343$	−19.4338			−1.04932
$344$	−3.49890	−	14.7299i	−0.188648	−	0.794185i
$345$	−7.90557	−	11.4646i	−0.425622	−	0.617235i
$346$	9.71241	−	6.66370i	0.522143	−	0.358243i
$347$	0.274551	+	0.274551i	0.0147386	+	0.0147386i	0.714438	−	0.699699i	$-0.246683\pi$
$347$	0.274551	+	0.274551i	0.0147386	+	0.0147386i	−0.699699	+	0.714438i	$0.746683\pi$
$348$	−16.5978	−	6.40186i	−0.889737	−	0.343176i
$349$	−1.33045	−	1.33045i	−0.0712172	−	0.0712172i	0.670601	−	0.741818i	$-0.266036\pi$
$349$	−1.33045	−	1.33045i	−0.0712172	−	0.0712172i	−0.741818	+	0.670601i	$0.766036\pi$
$350$	10.9622	+	6.68311i	0.585954	+	0.357227i
$351$	0.0438667			0.00234143
$352$	2.63159	+	0.357192i	0.140264	+	0.0190384i
$353$		−	27.5571i		−	1.46672i	−0.679841	−	0.733359i	$-0.737951\pi$
$353$		−	27.5571i		−	1.46672i	0.679841	−	0.733359i	$-0.262049\pi$
$354$	2.44535	−	13.1352i	0.129969	−	0.698126i
$355$	31.9997	+	5.87960i	1.69837	+	0.312057i
$356$	−10.3295	+	26.7810i	−0.547465	+	1.41939i
$357$	−1.28997	−	1.28997i	−0.0682722	−	0.0682722i
$358$	11.4714	+	16.7196i	0.606280	+	0.883659i
$359$		−	9.65759i		−	0.509708i	−0.966980	−	0.254854i	$-0.917973\pi$
$359$		−	9.65759i		−	0.509708i	0.966980	−	0.254854i	$-0.0820274\pi$
$360$	4.69643	+	4.23598i	0.247524	+	0.223256i
$361$		−	10.3303i		−	0.543701i
$362$	17.9227	−	12.2968i	0.941999	−	0.646307i
$363$	7.62233	+	7.62233i	0.400068	+	0.400068i
$364$	−0.145627	+	0.0645578i	−0.00763293	+	0.00338375i
$365$	−6.07437	+	33.0598i	−0.317947	+	1.73043i
$366$	−5.69105	−	1.05949i	−0.297476	−	0.0553806i
$367$		−	5.40212i		−	0.281988i	−0.990010	−	0.140994i	$-0.954970\pi$
$367$		−	5.40212i		−	0.281988i	0.990010	−	0.140994i	$-0.0450299\pi$
$368$	18.4595	+	16.7285i	0.962267	+	0.872033i
$369$	3.06050			0.159323
$370$	0.295493	−	0.131826i	0.0153619	−	0.00685331i
$371$	12.7939	+	12.7939i	0.664225	+	0.664225i
$372$	13.0054	−	5.76540i	0.674298	−	0.298922i
$373$	−6.54862	−	6.54862i	−0.339075	−	0.339075i	0.516944	−	0.856019i	$-0.327069\pi$
$373$	−6.54862	−	6.54862i	−0.339075	−	0.339075i	−0.856019	+	0.516944i	$0.827069\pi$
$374$	−0.377398	−	0.550061i	−0.0195148	−	0.0284430i
$375$	2.66044	+	10.8592i	0.137384	+	0.560766i
$376$	14.9070	−	24.1953i	0.768772	−	1.24778i
$377$	0.390186			0.0200956
$378$	1.45269	+	2.11732i	0.0747185	+	0.108903i
$379$	−24.8255	+	24.8255i	−1.27520	+	1.27520i	−0.331877	+	0.943323i	$0.607682\pi$
$379$	−24.8255	+	24.8255i	−1.27520	+	1.27520i	−0.943323	+	0.331877i	$0.892318\pi$
$380$	−12.8042	+	3.07327i	−0.656844	+	0.157655i
$381$	7.45931	+	7.45931i	0.382152	+	0.382152i
$382$	2.18708	+	0.407164i	0.111901	+	0.0208323i
$383$		−	0.293274i		−	0.0149856i	−0.999972	−	0.00749279i	$-0.997615\pi$
$383$		−	0.293274i		−	0.0149856i	0.999972	−	0.00749279i	$-0.00238505\pi$
$384$	−9.91223	−	5.45415i	−0.505831	−	0.278331i
$385$	1.08202	+	1.56914i	0.0551448	+	0.0799707i
$386$	1.01415	−	5.44750i	0.0516190	−	0.277270i
$387$	3.78495	−	3.78495i	0.192400	−	0.192400i
$388$	9.75844	−	25.3003i	0.495410	−	1.28443i
$389$	−0.442101	+	0.442101i	−0.0224154	+	0.0224154i	−0.718226	−	0.695810i	$-0.755045\pi$
$389$	−0.442101	+	0.442101i	−0.0224154	+	0.0224154i	0.695810	+	0.718226i	$0.255045\pi$
$390$	−0.129542	−	0.0496157i	−0.00655961	−	0.00251239i
$391$		−	6.25748i		−	0.316454i
$392$	8.91787	+	5.49442i	0.450421	+	0.277510i
$393$	8.23550			0.415426
$394$	3.08859	+	4.50165i	0.155601	+	0.226790i
$395$	6.30319	−	34.3051i	0.317148	−	1.72608i
$396$	0.380525	+	0.858375i	0.0191221	+	0.0431350i
$397$	−24.4503	+	24.4503i	−1.22712	+	1.22712i	−0.262078	+	0.965047i	$0.584408\pi$
$397$	−24.4503	+	24.4503i	−1.22712	+	1.22712i	−0.965047	+	0.262078i	$0.915592\pi$
$398$	−5.09518	+	27.3687i	−0.255398	+	1.37187i
$399$	−5.34613			−0.267641
$400$	−9.07782	−	17.8211i	−0.453891	−	0.891057i
$401$	−17.3106			−0.864451			−0.432226	−	0.901765i	$-0.642272\pi$
$401$	−17.3106			−0.864451			−0.432226	+	0.901765i	$0.642272\pi$
$402$	0.0552133	−	0.296577i	0.00275379	−	0.0147919i
$403$	−0.220634	+	0.220634i	−0.0109906	+	0.0109906i
$404$	27.1844	−	12.0511i	1.35247	−	0.599564i
$405$	−0.404088	+	2.19925i	−0.0200793	+	0.109282i
$406$	12.9214	+	18.8332i	0.641281	+	0.934674i
$407$	0.0480362			0.00238107
$408$	0.656768	+	2.76491i	0.0325149	+	0.136884i
$409$		−	7.62314i		−	0.376940i	−0.982079	−	0.188470i	$-0.939647\pi$
$409$		−	7.62314i		−	0.376940i	0.982079	−	0.188470i	$-0.0603528\pi$
$410$	−9.03790	−	3.46160i	−0.446350	−	0.170956i
$411$	11.0700	−	11.0700i	0.546044	−	0.546044i
$412$	−11.4645	−	4.42192i	−0.564816	−	0.217852i
$413$	−12.1295	+	12.1295i	−0.596852	+	0.596852i
$414$	−1.61201	+	8.65886i	−0.0792258	+	0.425560i
$415$	−9.85519	−	14.2920i	−0.483772	−	0.701565i
$416$	0.245893	+	0.0333756i	0.0120559	+	0.00163637i
$417$			1.61471i			0.0790728i
$418$	−1.92188	−	0.357793i	−0.0940021	−	0.0175002i
$419$	3.21455	+	3.21455i	0.157041	+	0.157041i	0.781254	−	0.624213i	$-0.214580\pi$
$419$	3.21455	+	3.21455i	0.157041	+	0.157041i	−0.624213	+	0.781254i	$0.714580\pi$
$420$	−1.89512	−	7.89569i	−0.0924724	−	0.385270i
$421$	−8.12907	+	8.12907i	−0.396187	+	0.396187i	−0.876886	−	0.480699i	$-0.840383\pi$
$421$	−8.12907	+	8.12907i	−0.396187	+	0.396187i	0.480699	+	0.876886i	$0.340383\pi$
$422$	−2.19280	−	3.19603i	−0.106744	−	0.155580i
$423$	10.0476			0.488530
$424$	−6.51383	−	27.4224i	−0.316339	−	1.33175i
$425$	−1.78582	+	4.69560i	−0.0866249	+	0.227770i
$426$	−11.6415	−	16.9675i	−0.564030	−	0.822080i
$427$	5.25532	+	5.25532i	0.254323	+	0.254323i
$428$	−7.92666	−	17.8807i	−0.383150	−	0.864295i
$429$	−0.0145622	−	0.0145622i	−0.000703070	−	0.000703070i
$430$	−15.4583	+	6.89628i	−0.745464	+	0.332568i
$431$	−34.3410			−1.65415			−0.827074	−	0.562093i	$-0.809996\pi$
$431$	−34.3410			−1.65415			−0.827074	+	0.562093i	$0.809996\pi$
$432$	−0.196534	−	3.99517i	−0.00945572	−	0.192218i
$433$			31.2038i			1.49956i	0.661687	+	0.749780i	$0.269841\pi$
$433$			31.2038i			1.49956i	−0.661687	+	0.749780i	$0.730159\pi$
$434$	−17.9559	−	3.34283i	−0.861912	−	0.160461i
$435$	−3.59430	+	19.5620i	−0.172333	+	0.937925i
$436$	−7.06041	−	15.9266i	−0.338132	−	0.762747i
$437$	−12.9667	−	12.9667i	−0.620283	−	0.620283i
$438$	17.5296	−	12.0271i	0.837598	−	0.574677i
$439$			25.1727i			1.20143i	0.799464	+	0.600714i	$0.205117\pi$
$439$			25.1727i			1.20143i	−0.799464	+	0.600714i	$0.794883\pi$
$440$	−0.152852	−	2.96525i	−0.00728694	−	0.141363i
$441$			3.70333i			0.176349i
$442$	−0.0352636	−	0.0513970i	−0.00167732	−	0.00244471i
$443$	4.89367	+	4.89367i	0.232505	+	0.232505i	0.813738	−	0.581232i	$-0.197429\pi$
$443$	4.89367	+	4.89367i	0.232505	+	0.232505i	−0.581232	+	0.813738i	$0.697429\pi$
$444$	−0.190930	−	0.0736428i	−0.00906115	−	0.00349493i
$445$	31.5637	+	5.79948i	1.49626	+	0.274922i
$446$	−2.38656	+	12.8194i	−0.113007	+	0.607014i
$447$			2.57129i			0.121618i
$448$	6.53206	+	12.9738i	0.308611	+	0.612954i
$449$	36.7865			1.73606			0.868031	−	0.496511i	$-0.165386\pi$
$449$	36.7865			1.73606			0.868031	+	0.496511i	$0.165386\pi$
$450$	3.68079	−	6.03753i	0.173514	−	0.284612i
$451$	−1.01598	−	1.01598i	−0.0478405	−	0.0478405i
$452$	−1.53376	+	3.97651i	−0.0721419	+	0.187039i
$453$	−7.94854	−	7.94854i	−0.373455	−	0.373455i
$454$	18.2162	−	12.4982i	0.854929	−	0.586568i
$455$	0.101102	+	0.146618i	0.00473976	+	0.00687358i
$456$	7.09040	+	4.36849i	0.332038	+	0.204573i
$457$	3.78613			0.177108			0.0885539	−	0.996071i	$-0.471775\pi$
$457$	3.78613			0.177108			0.0885539	+	0.996071i	$0.471775\pi$
$458$	−8.62680	+	5.91886i	−0.403104	+	0.276570i
$459$	−0.710461	+	0.710461i	−0.0331615	+	0.0331615i
$460$	14.5541	−	23.7471i	0.678586	−	1.10721i
$461$	−24.6710	−	24.6710i	−1.14904	−	1.14904i	−0.986741	−	0.162303i	$-0.948108\pi$
$461$	−24.6710	−	24.6710i	−1.14904	−	1.14904i	−0.162303	−	0.986741i	$-0.551892\pi$
$462$	0.220632	−	1.18512i	0.0102647	−	0.0551367i
$463$		−	3.86935i		−	0.179824i	−0.995950	−	0.0899120i	$-0.971341\pi$
$463$		−	3.86935i		−	0.179824i	0.995950	−	0.0899120i	$-0.0286586\pi$
$464$	−1.74813	−	35.5363i	−0.0811550	−	1.64973i
$465$	−9.02906	−	13.0939i	−0.418713	−	0.607216i
$466$	−20.2305	−	3.76628i	−0.937160	−	0.174470i
$467$	12.5440	−	12.5440i	0.580469	−	0.580469i	−0.354563	−	0.935032i	$-0.615370\pi$
$467$	12.5440	−	12.5440i	0.580469	−	0.580469i	0.935032	+	0.354563i	$0.115370\pi$
$468$	0.0355558	+	0.0802055i	0.00164357	+	0.00370750i
$469$	−0.273870	+	0.273870i	−0.0126461	+	0.0126461i
$470$	−29.6714	−	11.3644i	−1.36864	−	0.524200i
$471$		−	20.9578i		−	0.965686i
$472$	25.9983	−	6.17555i	1.19667	−	0.284253i
$473$	−2.51294			−0.115545
$474$	−18.1900	+	12.4802i	−0.835493	+	0.573233i
$475$	6.02964	+	13.4308i	0.276659	+	0.616246i
$476$	1.31299	−	3.40414i	0.0601809	−	0.156028i
$477$	7.04636	−	7.04636i	0.322631	−	0.322631i
$478$	11.4480	+	2.13126i	0.523619	+	0.0974814i
$479$	26.9702			1.23230			0.616150	−	0.787629i	$-0.288692\pi$
$479$	26.9702			1.23230			0.616150	+	0.787629i	$0.288692\pi$
$480$	−3.93838	+	12.0204i	−0.179762	+	0.548652i
$481$	0.00448844			0.000204655
$482$	9.47908	+	1.76471i	0.431760	+	0.0803801i
$483$	7.99589	−	7.99589i	0.363826	−	0.363826i
$484$	−7.75839	+	20.1148i	−0.352654	+	0.914310i
$485$	−29.8186	−	5.47883i	−1.35399	−	0.248781i
$486$	1.16613	−	0.800085i	0.0528968	−	0.0362926i
$487$	25.1835			1.14117			0.570586	−	0.821238i	$-0.306716\pi$
$487$	25.1835			1.14117			0.570586	+	0.821238i	$0.306716\pi$
$488$	−2.67567	−	11.2642i	−0.121122	−	0.509908i
$489$			9.72445i			0.439755i
$490$	4.18868	−	10.9362i	0.189225	−	0.494049i
$491$	−17.0641	+	17.0641i	−0.770094	+	0.770094i	−0.978123	−	0.208029i	$-0.933295\pi$
$491$	−17.0641	+	17.0641i	−0.770094	+	0.770094i	0.208029	+	0.978123i	$0.433295\pi$
$492$	2.48066	+	5.59579i	0.111837	+	0.252278i
$493$	−6.31943	+	6.31943i	−0.284613	+	0.284613i
$494$	−0.179578	−	0.0334317i	−0.00807959	−	0.00150416i
$495$	0.864219	−	0.595932i	0.0388437	−	0.0267852i
$496$	21.0828	+	19.1058i	0.946647	+	0.857878i
$497$			26.4186i			1.18503i
$498$	−2.00955	+	10.7942i	−0.0900499	+	0.483702i
$499$	11.2471	+	11.2471i	0.503488	+	0.503488i	0.912520	−	0.409032i	$-0.134133\pi$
$499$	11.2471	+	11.2471i	0.503488	+	0.503488i	−0.409032	+	0.912520i	$0.634133\pi$
$500$	−17.6985	+	13.6662i	−0.791500	+	0.611169i
$501$	−9.06325	+	9.06325i	−0.404916	+	0.404916i
$502$	−20.0243	+	13.7387i	−0.893728	+	0.613188i
$503$	37.0584			1.65235			0.826176	−	0.563412i	$-0.190512\pi$
$503$	37.0584			1.65235			0.826176	+	0.563412i	$0.190512\pi$
$504$	−2.69382	+	4.37227i	−0.119992	+	0.194756i
$505$	−18.8729	−	27.3695i	−0.839834	−	1.21793i
$506$	3.40957	−	2.33931i	0.151574	−	0.103995i
$507$	9.19103	+	9.19103i	0.408188	+	0.408188i
$508$	−7.59246	+	19.6846i	−0.336861	+	0.873365i
$509$	6.60068	+	6.60068i	0.292570	+	0.292570i	0.838095	−	0.545525i	$-0.183670\pi$
$509$	6.60068	+	6.60068i	0.292570	+	0.292570i	−0.545525	+	0.838095i	$0.683670\pi$
$510$	2.90163	−	1.29448i	0.128486	−	0.0573206i
$511$	−27.2937			−1.20740
$512$	1.93803	−	22.5443i	0.0856498	−	0.996325i
$513$			2.94443i			0.130000i
$514$	−3.61506	+	19.4182i	−0.159453	+	0.856501i
$515$	−2.48267	+	13.5119i	−0.109399	+	0.595406i
$516$	9.98823	+	3.85251i	0.439707	+	0.169597i
$517$	−3.33545	−	3.33545i	−0.146693	−	0.146693i
$518$	0.148640	+	0.216644i	0.00653086	+	0.00951879i
$519$			8.32874i			0.365591i
$520$	−0.0142823	−	0.277069i	−0.000626321	−	0.0121503i
$521$		−	11.8337i		−	0.518442i	−0.965818	−	0.259221i	$-0.916534\pi$
$521$		−	11.8337i		−	0.518442i	0.965818	−	0.259221i	$-0.0834657\pi$
$522$	10.3725	−	7.11661i	0.453994	−	0.311486i
$523$	8.02817	+	8.02817i	0.351047	+	0.351047i	0.860499	−	0.509452i	$-0.170152\pi$
$523$	8.02817	+	8.02817i	0.351047	+	0.351047i	−0.509452	+	0.860499i	$0.670152\pi$
$524$	6.67522	+	15.0577i	0.291608	+	0.657800i
$525$	−8.28204	+	3.71815i	−0.361458	+	0.162274i
$526$	−4.60671	−	0.857623i	−0.200862	−	0.0373941i
$527$		−	7.14676i		−	0.311318i
$528$	−1.26101	+	1.39150i	−0.0548786	+	0.0605572i
$529$	15.7872			0.686400
$530$	−28.7783	+	12.8387i	−1.25005	+	0.557676i
$531$	6.68042	+	6.68042i	0.289906	+	0.289906i
$532$	−4.33327	−	9.77482i	−0.187871	−	0.423792i
$533$	−0.0949317	−	0.0949317i	−0.00411195	−	0.00411195i
$534$	−11.4828	−	16.7363i	−0.496910	−	0.724252i
$535$	−18.0024	+	12.4138i	−0.778312	+	0.536694i
$536$	0.587013	−	0.139437i	0.0253551	−	0.00602276i
$537$	−14.3377			−0.618716
$538$	16.4073	+	23.9139i	0.707371	+	1.03100i
$539$	1.22938	−	1.22938i	0.0529530	−	0.0529530i
$540$	−4.34863	+	1.04376i	−0.187135	+	0.0449161i
$541$	10.9990	+	10.9990i	0.472882	+	0.472882i	0.902846	−	0.429964i	$-0.141474\pi$
$541$	10.9990	+	10.9990i	0.472882	+	0.472882i	−0.429964	+	0.902846i	$0.641474\pi$
$542$	10.4491	+	1.94530i	0.448829	+	0.0835577i
$543$			15.3694i			0.659564i
$544$	−4.52301	+	3.44191i	−0.193922	+	0.147571i
$545$	−16.0350	+	11.0571i	−0.686866	+	0.473636i
$546$	0.0206155	−	0.110736i	0.000882264	−	0.00473906i
$547$	−21.3064	+	21.3064i	−0.910997	+	0.910997i	−0.996351	−	0.0853539i	$-0.972798\pi$
$547$	−21.3064	+	21.3064i	−0.910997	+	0.910997i	0.0853539	+	0.996351i	$0.472798\pi$
$548$	29.2131	+	11.2676i	1.24792	+	0.481329i
$549$	2.89442	−	2.89442i	0.123531	−	0.123531i
$550$	−3.22614	+	0.782357i	−0.137563	+	0.0333598i
$551$			26.1902i			1.11574i
$552$	−17.1384	+	4.07100i	−0.729458	+	0.173273i
$553$	28.3219			1.20437
$554$	−13.2860	−	19.3645i	−0.564469	−	0.822720i
$555$	−0.0413464	+	0.225028i	−0.00175506	+	0.00955190i
$556$	−2.95233	+	1.30879i	−0.125207	+	0.0555052i
$557$	−18.9715	+	18.9715i	−0.803846	+	0.803846i	−0.983694	−	0.179848i	$-0.942439\pi$
$557$	−18.9715	+	18.9715i	−0.803846	+	0.803846i	0.179848	+	0.983694i	$0.442439\pi$
$558$	−1.84109	+	9.88940i	−0.0779397	+	0.418652i
$559$	−0.234806			−0.00993124
$560$	12.9004	−	9.86482i	0.545139	−	0.416865i
$561$	0.471697			0.0199151
$562$	−8.41210	+	45.1854i	−0.354843	+	1.90603i
$563$	−0.478449	+	0.478449i	−0.0201642	+	0.0201642i	−0.717117	−	0.696953i	$-0.754539\pi$
$563$	−0.478449	+	0.478449i	−0.0201642	+	0.0201642i	0.696953	+	0.717117i	$0.254539\pi$
$564$	8.14399	+	18.3709i	0.342924	+	0.773555i
$565$	4.68666	+	0.861121i	0.197169	+	0.0362276i
$566$	4.39341	+	6.40344i	0.184669	+	0.269157i
$567$	−1.81567			−0.0762511
$568$	21.5874	−	35.0381i	0.905789	−	1.47016i
$569$			11.7904i			0.494278i	0.968980	+	0.247139i	$0.0794904\pi$
$569$			11.7904i			0.494278i	−0.968980	+	0.247139i	$0.920510\pi$
$570$	3.33032	−	8.69516i	0.139492	−	0.364200i
$571$	−6.72738	+	6.72738i	−0.281532	+	0.281532i	−0.833720	−	0.552188i	$-0.813793\pi$
$571$	−6.72738	+	6.72738i	−0.281532	+	0.281532i	0.552188	+	0.833720i	$0.313793\pi$
$572$	0.0148221	−	0.0384287i	0.000619745	−	0.00160679i
$573$	−1.11233	+	1.11233i	−0.0464681	+	0.0464681i
$574$	1.43831	−	7.72585i	0.0600338	−	0.322471i
$575$	−29.1058	−	11.0694i	−1.21380	−	0.461628i
$576$	7.14544	−	3.59760i	0.297727	−	0.149900i
$577$		−	27.7420i		−	1.15491i	−0.816421	−	0.577457i	$-0.804045\pi$
$577$		−	27.7420i		−	1.15491i	0.816421	−	0.577457i	$-0.195955\pi$
$578$	−22.2320	−	4.13889i	−0.924729	−	0.172155i
$579$	2.77055	+	2.77055i	0.115140	+	0.115140i
$580$	−38.6803	+	9.28403i	−1.60611	+	0.385498i
$581$	9.96778	−	9.96778i	0.413533	−	0.413533i
$582$	10.8480	+	15.8110i	0.449662	+	0.655387i
$583$	−4.67829			−0.193755
$584$	36.1988	+	22.3026i	1.49792	+	0.922886i
$585$	0.0807515	−	0.0556832i	0.00333866	−	0.00230222i
$586$	12.0722	+	17.5953i	0.498697	+	0.726856i
$587$	9.78016	+	9.78016i	0.403670	+	0.403670i	0.879524	−	0.475854i	$-0.157861\pi$
$587$	9.78016	+	9.78016i	0.403670	+	0.403670i	−0.475854	+	0.879524i	$0.657861\pi$
$588$	−6.77114	+	3.00171i	−0.279237	+	0.123788i
$589$	−14.8095	−	14.8095i	−0.610214	−	0.610214i
$590$	−12.1719	−	27.2838i	−0.501110	−	1.12326i
$591$	−3.86032			−0.158792
$592$	−0.0201093	−	0.408786i	−0.000826489	−	0.0168010i
$593$			12.8018i			0.525707i	0.964836	+	0.262854i	$0.0846637\pi$
$593$			12.8018i			0.525707i	−0.964836	+	0.262854i	$0.915336\pi$
$594$	−0.652716	−	0.121515i	−0.0267812	−	0.00498582i
$595$	−4.01207	−	0.737174i	−0.164479	−	0.0302212i
$596$	−4.70132	+	2.08414i	−0.192574	+	0.0853696i
$597$	−13.9195	−	13.9195i	−0.569685	−	0.569685i
$598$	0.318586	−	0.218582i	0.0130279	−	0.00893849i
$599$		−	35.6315i		−	1.45586i	−0.685650	−	0.727932i	$-0.740482\pi$
$599$		−	35.6315i		−	1.45586i	0.685650	−	0.727932i	$-0.259518\pi$
$600$	14.0224	+	1.83625i	0.572463	+	0.0749645i
$601$		−	43.3118i		−	1.76672i	−0.468692	−	0.883362i	$-0.655275\pi$
$601$		−	43.3118i		−	1.76672i	0.468692	−	0.883362i	$-0.344725\pi$
$602$	−7.77586	−	11.3334i	−0.316921	−	0.461915i
$603$	0.150837	+	0.150837i	0.00614254	+	0.00614254i
$604$	8.09042	−	20.9757i	0.329195	−	0.853488i
$605$	23.7071	+	4.35591i	0.963829	+	0.177093i
$606$	−3.84833	+	20.6712i	−0.156328	+	0.839712i
$607$		−	18.4382i		−	0.748385i	−0.927351	−	0.374192i	$-0.877920\pi$
$607$		−	18.4382i		−	0.748385i	0.927351	−	0.374192i	$-0.122080\pi$
$608$	−2.24025	+	16.5049i	−0.0908541	+	0.669361i
$609$	−16.1501			−0.654435
$610$	−11.8212	+	5.27371i	−0.478627	+	0.213526i
$611$	−0.311660	−	0.311660i	−0.0126084	−	0.0126084i
$612$	−1.87486	−	0.723143i	−0.0757868	−	0.0292313i
$613$	−9.81446	−	9.81446i	−0.396402	−	0.396402i	0.480560	−	0.876962i	$-0.340434\pi$
$613$	−9.81446	−	9.81446i	−0.396402	−	0.396402i	−0.876962	+	0.480560i	$0.840434\pi$
$614$	27.0399	−	18.5521i	1.09124	−	0.748701i
$615$	5.63388	−	3.88491i	0.227180	−	0.156655i
$616$	2.34569	−	0.557188i	0.0945107	−	0.0224497i
$617$	−9.02339			−0.363268			−0.181634	−	0.983366i	$-0.558139\pi$
$617$	−9.02339			−0.363268			−0.181634	+	0.983366i	$0.558139\pi$
$618$	7.16456	−	4.91562i	0.288201	−	0.197735i
$619$	−15.6705	+	15.6705i	−0.629850	+	0.629850i	−0.948030	−	0.318181i	$-0.896928\pi$
$619$	−15.6705	+	15.6705i	−0.629850	+	0.629850i	0.318181	+	0.948030i	$0.396928\pi$
$620$	16.6224	−	27.1219i	0.667571	−	1.08924i
$621$	−4.40382	−	4.40382i	−0.176719	−	0.176719i
$622$	2.62475	−	14.0988i	0.105243	−	0.565310i
$623$			26.0586i			1.04401i
$624$	−0.117828	+	0.130020i	−0.00471688	+	0.00520496i
$625$	18.6818	+	16.6130i	0.747272	+	0.664518i
$626$	32.5074	+	6.05185i	1.29926	+	0.241881i
$627$	0.977449	−	0.977449i	0.0390356	−	0.0390356i
$628$	38.3191	−	16.9872i	1.52910	−	0.677864i
$629$	−0.0726945	+	0.0726945i	−0.00289852	+	0.00289852i
$630$	5.36184	+	2.05363i	0.213621	+	0.0818186i
$631$			7.32472i			0.291593i	0.989315	+	0.145796i	$0.0465744\pi$
$631$			7.32472i			0.291593i	−0.989315	+	0.145796i	$0.953426\pi$
$632$	−37.5624	−	23.1427i	−1.49415	−	0.920567i
$633$	2.74071			0.108933
$634$	−17.8526	+	12.2487i	−0.709019	+	0.486459i
$635$	23.2000	+	4.26275i	0.920666	+	0.169162i
$636$	18.5949	+	7.17214i	0.737335	+	0.284394i
$637$	0.114871	−	0.114871i	0.00455137	−	0.00455137i
$638$	−5.80579	−	1.08085i	−0.229853	−	0.0427914i
$639$	14.5503			0.575600
$640$	−25.1702	+	2.54211i	−0.994939	+	0.100486i
$641$	−22.8353			−0.901939			−0.450970	−	0.892539i	$-0.648922\pi$
$641$	−22.8353			−0.901939			−0.450970	+	0.892539i	$0.648922\pi$
$642$	13.5966	+	2.53126i	0.536616	+	0.0999009i
$643$	15.9787	−	15.9787i	0.630138	−	0.630138i	−0.317965	−	0.948102i	$-0.602999\pi$
$643$	15.9787	−	15.9787i	0.630138	−	0.630138i	0.948102	+	0.317965i	$0.102999\pi$
$644$	21.1006	+	8.13862i	0.831482	+	0.320707i
$645$	2.16297	−	11.7720i	0.0851670	−	0.463522i
$646$	3.44989	−	2.36697i	0.135734	−	0.0931273i
$647$	−7.57070			−0.297635			−0.148817	−	0.988865i	$-0.547547\pi$
$647$	−7.57070			−0.297635			−0.148817	+	0.988865i	$0.547547\pi$
$648$	2.40807	+	1.48364i	0.0945979	+	0.0582831i
$649$		−	4.43534i		−	0.174102i
$650$	−0.301447	+	0.0731025i	−0.0118237	+	0.00286732i
$651$	9.13222	−	9.13222i	0.357920	−	0.357920i
$652$	−17.7801	+	7.88208i	−0.696323	+	0.308686i
$653$	8.64398	−	8.64398i	0.338265	−	0.338265i	−0.517449	−	0.855714i	$-0.673118\pi$
$653$	8.64398	−	8.64398i	0.338265	−	0.338265i	0.855714	+	0.517449i	$0.173118\pi$
$654$	12.1107	+	2.25464i	0.473567	+	0.0881632i
$655$	15.1602	−	10.4539i	0.592359	−	0.408468i
$656$	−8.22062	+	9.07125i	−0.320961	+	0.354173i
$657$			15.0323i			0.586465i
$658$	4.72195	−	25.3639i	0.184081	−	0.988787i
$659$	22.8915	+	22.8915i	0.891728	+	0.891728i	0.994686	−	0.102958i	$-0.0328308\pi$
$659$	22.8915	+	22.8915i	0.891728	+	0.891728i	−0.102958	+	0.994686i	$0.532831\pi$
$660$	1.79008	+	1.09710i	0.0696789	+	0.0427047i
$661$	16.8355	−	16.8355i	0.654824	−	0.654824i	−0.299326	−	0.954151i	$-0.596762\pi$
$661$	16.8355	−	16.8355i	0.654824	−	0.654824i	0.954151	+	0.299326i	$0.0967619\pi$
$662$	−20.0555	+	13.7601i	−0.779480	+	0.534802i
$663$	0.0440748			0.00171172
$664$	−21.3649	+	5.07495i	−0.829120	+	0.196946i
$665$	−9.84137	+	6.78623i	−0.381632	+	0.263159i
$666$	0.119319	−	0.0818648i	0.00462351	−	0.00317220i
$667$	−39.1712	−	39.1712i	−1.51671	−	1.51671i
$668$	−23.9173	−	9.22503i	−0.925390	−	0.356927i
$669$	−6.51980	−	6.51980i	−0.252070	−	0.252070i
$670$	−0.274828	−	0.616038i	−0.0106175	−	0.0237996i
$671$	−1.92169			−0.0741861
$672$	−10.1777	−	1.38144i	−0.392612	−	0.0532903i
$673$		−	5.34019i		−	0.205849i	−0.994689	−	0.102925i	$-0.967180\pi$
$673$		−	5.34019i		−	0.205849i	0.994689	−	0.102925i	$-0.0328200\pi$
$674$	−0.494897	+	2.65833i	−0.0190627	+	0.102395i
$675$	2.04781	+	4.56141i	0.0788202	+	0.175569i
$676$	−9.35509	+	24.2545i	−0.359811	+	0.932867i
$677$	−0.117760	−	0.117760i	−0.00452590	−	0.00452590i	0.704840	−	0.709366i	$-0.251019\pi$
$677$	−0.117760	−	0.117760i	−0.00452590	−	0.00452590i	−0.709366	+	0.704840i	$0.751019\pi$
$678$	−1.70500	−	2.48505i	−0.0654801	−	0.0954379i
$679$		−	24.6178i		−	0.944745i
$680$	4.71871	+	4.25608i	0.180954	+	0.163213i
$681$			15.6211i			0.598600i
$682$	3.89412	−	2.67176i	0.149113	−	0.102307i
$683$	11.0216	+	11.0216i	0.421729	+	0.421729i	0.885799	−	0.464070i	$-0.153611\pi$
$683$	11.0216	+	11.0216i	0.421729	+	0.421729i	−0.464070	+	0.885799i	$0.653611\pi$
$684$	−5.38358	+	2.38659i	−0.205846	+	0.0912535i
$685$	6.32615	−	34.4301i	0.241710	−	1.31551i
$686$	27.0192	+	5.03013i	1.03160	+	0.192051i
$687$		−	7.39779i		−	0.282243i
$688$	1.05199	+	21.3850i	0.0401067	+	0.815297i
$689$	−0.437134			−0.0166535
$690$	8.02387	+	17.9858i	0.305464	+	0.684708i
$691$	−33.0825	−	33.0825i	−1.25852	−	1.25852i	−0.951801	−	0.306716i	$-0.900770\pi$
$691$	−33.0825	−	33.0825i	−1.25852	−	1.25852i	−0.306716	−	0.951801i	$-0.599230\pi$
$692$	−15.2282	+	6.75080i	−0.578890	+	0.256627i
$693$	0.602741	+	0.602741i	0.0228962	+	0.0228962i
$694$	−0.310651	−	0.452778i	−0.0117922	−	0.0171872i
$695$	2.04967	+	2.97243i	0.0777485	+	0.112751i
$696$	21.4194	+	13.1968i	0.811899	+	0.500222i
$697$	3.07501			0.116474
$698$	1.50539	+	2.19412i	0.0569798	+	0.0830486i
$699$	10.2890	−	10.2890i	0.389168	−	0.389168i
$700$	−13.5112	−	12.1291i	−0.510675	−	0.458437i
$701$	3.90473	+	3.90473i	0.147480	+	0.147480i	0.776991	−	0.629511i	$-0.216745\pi$
$701$	3.90473	+	3.90473i	0.147480	+	0.147480i	−0.629511	+	0.776991i	$0.716745\pi$
$702$	−0.0609889	−	0.0113542i	−0.00230188	−	0.000428537i
$703$			0.301275i			0.0113628i
$704$	−3.56631	−	1.17776i	−0.134411	−	0.0443885i
$705$	18.4960	−	12.7541i	0.696599	−	0.480348i
$706$	−7.13274	+	38.3134i	−0.268444	+	1.44194i
$707$	19.0886	−	19.0886i	0.717899	−	0.717899i
$708$	−6.79967	+	17.6292i	−0.255547	+	0.662546i
$709$	7.84907	−	7.84907i	0.294778	−	0.294778i	−0.544186	−	0.838964i	$-0.683162\pi$
$709$	7.84907	−	7.84907i	0.294778	−	0.294778i	0.838964	+	0.544186i	$0.183162\pi$
$710$	−42.9682	−	16.4572i	−1.61257	−	0.617627i
$711$		−	15.5985i		−	0.584991i
$712$	21.2933	−	34.5606i	0.797999	−	1.29521i
$713$	44.2994			1.65903
$714$	1.45958	+	2.12736i	0.0546236	+	0.0796145i
$715$	−0.0452916	−	0.00832183i	−0.00169381	−	0.000311219i
$716$	−11.6213	−	26.2149i	−0.434308	−	0.979697i
$717$	−5.82235	+	5.82235i	−0.217440	+	0.217440i
$718$	−2.49972	+	13.4272i	−0.0932886	+	0.501098i
$719$	24.3830			0.909331			0.454665	−	0.890662i	$-0.349759\pi$
$719$	24.3830			0.909331			0.454665	+	0.890662i	$0.349759\pi$
$720$	−5.43315	−	7.10499i	−0.202481	−	0.264787i
$721$	−11.1553			−0.415444
$722$	−2.67384	+	14.3625i	−0.0995102	+	0.534517i
$723$	−4.82097	+	4.82097i	−0.179294	+	0.179294i
$724$	−28.1013	+	12.4576i	−1.04438	+	0.462981i
$725$	18.2149	+	40.5730i	0.676485	+	1.50684i
$726$	−8.62459	−	12.5704i	−0.320089	−	0.466533i
$727$	25.7991			0.956834			0.478417	−	0.878133i	$-0.341211\pi$
$727$	25.7991			0.956834			0.478417	+	0.878133i	$0.341211\pi$
$728$	0.219179	−	0.0520630i	0.00812330	−	0.00192958i
$729$			1.00000i			0.0370370i
$730$	17.0024	−	44.3916i	0.629286	−	1.64301i
$731$	3.80290	−	3.80290i	0.140655	−	0.140655i
$732$	7.63818	+	2.94608i	0.282315	+	0.108890i
$733$	15.0948	−	15.0948i	0.557537	−	0.557537i	−0.371068	−	0.928606i	$-0.621008\pi$
$733$	15.0948	−	15.0948i	0.557537	−	0.557537i	0.928606	+	0.371068i	$0.121008\pi$
$734$	−1.39826	+	7.51070i	−0.0516105	+	0.277225i
$735$	4.70090	+	6.81724i	0.173395	+	0.251458i
$736$	−21.3348	−	28.0360i	−0.786410	−	1.03342i
$737$		−	0.100145i		−	0.00368889i
$738$	−4.25508	−	0.792162i	−0.156632	−	0.0291599i
$739$	−17.9291	−	17.9291i	−0.659531	−	0.659531i	0.295738	−	0.955269i	$-0.404434\pi$
$739$	−17.9291	−	17.9291i	−0.659531	−	0.659531i	−0.955269	+	0.295738i	$0.904434\pi$
$740$	−0.444952	+	0.106797i	−0.0163568	+	0.00392595i
$741$	0.0913316	−	0.0913316i	0.00335515	−	0.00335515i
$742$	−14.4762	−	21.0992i	−0.531437	−	0.774575i
$743$	−8.25344			−0.302789			−0.151395	−	0.988473i	$-0.548376\pi$
$743$	−8.25344			−0.302789			−0.151395	+	0.988473i	$0.548376\pi$
$744$	−19.5740	+	4.64954i	−0.717618	+	0.170460i
$745$	3.26392	+	4.73333i	0.119581	+	0.173416i
$746$	7.40970	+	10.7997i	0.271289	+	0.395406i
$747$	−5.48985	−	5.48985i	−0.200863	−	0.200863i
$748$	0.382331	+	0.862447i	0.0139794	+	0.0315342i
$749$	−12.5556	−	12.5556i	−0.458772	−	0.458772i
$750$	−0.888138	−	15.7864i	−0.0324302	−	0.576439i
$751$	6.07037			0.221511			0.110755	−	0.993848i	$-0.464673\pi$
$751$	6.07037			0.221511			0.110755	+	0.993848i	$0.464673\pi$
$752$	−26.9882	+	29.7808i	−0.984159	+	1.08600i
$753$		−	17.1715i		−	0.625766i
$754$	−0.542486	−	0.100994i	−0.0197562	−	0.00367797i
$755$	−24.7216	−	4.54233i	−0.899713	−	0.165312i
$756$	−1.47168	−	3.31977i	−0.0535245	−	0.120739i
$757$	21.4003	+	21.4003i	0.777806	+	0.777806i	0.979457	−	0.201651i	$-0.0646308\pi$
$757$	21.4003	+	21.4003i	0.777806	+	0.777806i	−0.201651	+	0.979457i	$0.564631\pi$
$758$	40.9412	−	28.0898i	1.48705	−	1.02027i
$759$			2.92383i			0.106128i
$760$	18.5975	−	0.958662i	0.674603	−	0.0347743i
$761$		−	20.8862i		−	0.757125i	−0.925576	−	0.378563i	$-0.876418\pi$
$761$		−	20.8862i		−	0.757125i	0.925576	−	0.378563i	$-0.123582\pi$
$762$	−8.44014	−	12.3016i	−0.305754	−	0.445640i
$763$	−11.1835	−	11.1835i	−0.404869	−	0.404869i
$764$	−2.93536	−	1.13218i	−0.106198	−	0.0409609i
$765$	−0.406005	+	2.20969i	−0.0146792	+	0.0798914i
$766$	−0.0759093	+	0.407746i	−0.00274272	+	0.0147324i
$767$		−	0.414432i		−	0.0149643i
$768$	12.3695	+	10.1487i	0.446346	+	0.366208i
$769$	−8.06017			−0.290657			−0.145329	−	0.989383i	$-0.546424\pi$
$769$	−8.06017			−0.290657			−0.145329	+	0.989383i	$0.546424\pi$
$770$	−1.09821	−	2.46168i	−0.0395767	−	0.0887127i
$771$	−9.87593	−	9.87593i	−0.355673	−	0.355673i
$772$	−2.82000	+	7.31130i	−0.101494	+	0.263139i
$773$	11.9200	+	11.9200i	0.428731	+	0.428731i	0.888196	−	0.459465i	$-0.151959\pi$
$773$	11.9200	+	11.9200i	0.428731	+	0.428731i	−0.459465	+	0.888196i	$0.651959\pi$
$774$	−6.24198	+	4.28263i	−0.224363	+	0.153936i
$775$	−33.2421	−	12.6426i	−1.19409	−	0.454134i
$776$	−20.1160	+	32.6498i	−0.722123	+	1.17206i
$777$	−0.185780			−0.00666482
$778$	0.729095	−	0.500233i	0.0261393	−	0.0179342i
$779$	6.37204	−	6.37204i	0.228302	−	0.228302i
$780$	0.167263	+	0.102512i	0.00598898	+	0.00367052i
$781$	−4.83018	−	4.83018i	−0.172838	−	0.172838i
$782$	−1.61965	+	8.69994i	−0.0579187	+	0.311109i
$783$			8.89482i			0.317875i
$784$	−10.9766	−	9.94729i	−0.392021	−	0.355260i
$785$	−26.6033	−	38.5800i	−0.949512	−	1.37698i
$786$	−11.4500	−	2.13163i	−0.408409	−	0.0760328i
$787$	38.1416	−	38.1416i	1.35960	−	1.35960i	0.485194	−	0.874407i	$-0.338749\pi$
$787$	38.1416	−	38.1416i	1.35960	−	1.35960i	0.874407	−	0.485194i	$-0.161251\pi$
$788$	−3.12896	−	7.05819i	−0.111464	−	0.251437i
$789$	2.34293	−	2.34293i	0.0834105	−	0.0834105i
$790$	−17.6428	+	46.0638i	−0.627704	+	1.63888i
$791$			3.86924i			0.137574i
$792$	−0.306877	−	1.29191i	−0.0109044	−	0.0459062i
$793$	−0.179561			−0.00637638
$794$	40.3224	−	27.6653i	1.43099	−	0.981804i
$795$	4.02676	−	21.9157i	0.142815	−	0.777269i
$796$	14.1679	−	36.7325i	0.502168	−	1.30195i
$797$	22.2285	−	22.2285i	0.787373	−	0.787373i	−0.193690	−	0.981063i	$-0.562046\pi$
$797$	22.2285	−	22.2285i	0.787373	−	0.787373i	0.981063	+	0.193690i	$0.0620456\pi$
$798$	7.43286	+	1.38376i	0.263120	+	0.0489847i
$799$	10.0952			0.357144
$800$	8.00839	+	27.1268i	0.283139	+	0.959079i
$801$	14.3520			0.507103
$802$	24.0674	+	4.48059i	0.849849	+	0.158215i
$803$	4.99019	−	4.99019i	0.176100	−	0.176100i
$804$	−0.153529	+	0.398048i	−0.00541455	+	0.0140381i
$805$	4.56939	−	24.8689i	0.161050	−	0.876515i
$806$	0.363861	−	0.249646i	0.0128165	−	0.00879340i
$807$	−20.5070			−0.721881
$808$	−40.9144	+	9.71867i	−1.43936	+	0.341901i
$809$			41.1080i			1.44528i	0.691225	+	0.722639i	$0.257071\pi$
$809$			41.1080i			1.44528i	−0.691225	+	0.722639i	$0.742929\pi$
$810$	1.13106	−	2.95308i	0.0397413	−	0.103761i
$811$	10.2679	−	10.2679i	0.360555	−	0.360555i	−0.503462	−	0.864017i	$-0.667941\pi$
$811$	10.2679	−	10.2679i	0.360555	−	0.360555i	0.864017	+	0.503462i	$0.167941\pi$
$812$	−13.0903	−	29.5287i	−0.459381	−	1.03626i
$813$	−5.31433	+	5.31433i	−0.186382	+	0.186382i
$814$	−0.0667860	−	0.0124334i	−0.00234085	−	0.000435792i
$815$	12.3439	+	17.9011i	0.432390	+	0.627050i
$816$	−0.197466	−	4.01412i	−0.00691269	−	0.140522i
$817$		−	15.7607i		−	0.551398i
$818$	−1.97313	+	10.5986i	−0.0689890	+	0.370573i
$819$	0.0563193	+	0.0563193i	0.00196796	+	0.00196796i
$820$	11.6696	+	7.15207i	0.407522	+	0.249761i
$821$	−6.82793	+	6.82793i	−0.238296	+	0.238296i	−0.816144	−	0.577848i	$-0.803893\pi$
$821$	−6.82793	+	6.82793i	−0.238296	+	0.238296i	0.577848	+	0.816144i	$0.303893\pi$
$822$	−18.2562	+	12.5256i	−0.636759	+	0.436881i
$823$	−40.4181			−1.40889			−0.704444	−	0.709760i	$-0.748803\pi$
$823$	−40.4181			−1.40889			−0.704444	+	0.709760i	$0.748803\pi$
$824$	14.7949	+	9.11532i	0.515403	+	0.317547i
$825$	0.834428	−	2.19403i	0.0290511	−	0.0763864i
$826$	20.0034	−	13.7244i	0.696009	−	0.477532i
$827$	23.8197	+	23.8197i	0.828291	+	0.828291i	0.987280	−	0.158989i	$-0.0508236\pi$
$827$	23.8197	+	23.8197i	0.828291	+	0.828291i	−0.158989	+	0.987280i	$0.550824\pi$
$828$	4.48242	−	11.6214i	0.155775	−	0.403871i
$829$	−13.6687	−	13.6687i	−0.474734	−	0.474734i	0.428709	−	0.903443i	$-0.358969\pi$
$829$	−13.6687	−	13.6687i	−0.474734	−	0.474734i	−0.903443	+	0.428709i	$0.858969\pi$
$830$	10.0027	+	22.4213i	0.347198	+	0.778256i
$831$	16.6058			0.576048
$832$	−0.333232	−	0.110048i	−0.0115527	−	0.00381525i
$833$			3.72090i			0.128921i
$834$	0.417943	−	2.24498i	0.0144722	−	0.0777371i
$835$	−5.17935	+	28.1886i	−0.179239	+	0.975508i
$836$	2.57943	+	0.994897i	0.0892113	+	0.0344092i
$837$	−5.02966	−	5.02966i	−0.173850	−	0.173850i
$838$	−3.63723	−	5.30130i	−0.125646	−	0.183130i
$839$			0.00707031i			0.000244094i	1.00000		0.000122047i	$3.88488e-5\pi$
$839$			0.00707031i			0.000244094i	−1.00000		0.000122047i	$0.999961\pi$
$840$	0.591156	+	11.4681i	0.0203968	+	0.395687i
$841$			50.1179i			1.72820i
$842$	13.4061	−	9.19797i	0.462006	−	0.316983i
$843$	−22.9809	−	22.9809i	−0.791504	−	0.791504i
$844$	2.22146	+	5.01110i	0.0764659	+	0.172489i
$845$	28.5861	+	5.25237i	0.983390	+	0.180687i
$846$	−13.9694	−	2.60066i	−0.480278	−	0.0894126i
$847$			19.5722i			0.672510i
$848$	1.95847	+	39.8121i	0.0672540	+	1.36715i
$849$	−5.49118			−0.188457
$850$	3.69825	−	6.06618i	0.126849	−	0.208068i
$851$	−0.450599	−	0.450599i	−0.0154463	−	0.0154463i
$852$	11.7936	+	26.6036i	0.404043	+	0.911425i
$853$	24.8778	+	24.8778i	0.851800	+	0.851800i	0.990355	−	0.138555i	$-0.0442457\pi$
$853$	24.8778	+	24.8778i	0.851800	+	0.851800i	−0.138555	+	0.990355i	$0.544246\pi$
$854$	−5.94634	−	8.66686i	−0.203480	−	0.296574i
$855$	3.73758	+	5.42023i	0.127823	+	0.185368i
$856$	6.39250	+	26.9117i	0.218491	+	0.919822i
$857$	−17.0079			−0.580979			−0.290490	−	0.956878i	$-0.593818\pi$
$857$	−17.0079			−0.580979			−0.290490	+	0.956878i	$0.593818\pi$
$858$	0.0164770	+	0.0240154i	0.000562516	+	0.000819873i
$859$	−10.6241	+	10.6241i	−0.362490	+	0.362490i	−0.864729	−	0.502239i	$-0.832510\pi$
$859$	−10.6241	+	10.6241i	−0.362490	+	0.362490i	0.502239	+	0.864729i	$0.332510\pi$
$860$	23.2770	−	5.58694i	0.793739	−	0.190513i
$861$	3.92929	+	3.92929i	0.133910	+	0.133910i
$862$	47.7452	+	8.88864i	1.62621	+	0.302748i
$863$			8.48545i			0.288848i	0.989516	+	0.144424i	$0.0461329\pi$
$863$			8.48545i			0.288848i	−0.989516	+	0.144424i	$0.953867\pi$
$864$	−0.760842	+	5.60545i	−0.0258844	+	0.190701i
$865$	10.5723	+	15.3319i	0.359468	+	0.521300i
$866$	8.07663	−	43.3835i	0.274455	−	1.47423i
$867$	11.3070	−	11.3070i	0.384005	−	0.384005i
$868$	24.0993	+	9.29523i	0.817985	+	0.315501i
$869$	−5.17817	+	5.17817i	−0.175658	+	0.175658i
$870$	10.0606	−	26.2672i	0.341085	−	0.890540i
$871$		−	0.00935742i		−	0.000317064i
$872$	5.69391	+	23.9707i	0.192820	+	0.811749i
$873$	−13.5585			−0.458886
$874$	14.6717	+	21.3842i	0.496279	+	0.723332i
$875$	−10.5262	+	17.3575i	−0.355850	+	0.586791i
$876$	−27.4849	+	12.1843i	−0.928629	+	0.411669i
$877$	−37.8615	+	37.8615i	−1.27849	+	1.27849i	−0.336982	+	0.941511i	$0.609406\pi$
$877$	−37.8615	+	37.8615i	−1.27849	+	1.27849i	−0.941511	+	0.336982i	$0.890594\pi$
$878$	6.51557	−	34.9983i	0.219890	−	1.18113i
$879$	−15.0886			−0.508926
$880$	−0.554995	+	4.16223i	−0.0187089	+	0.140309i
$881$	13.4706			0.453836			0.226918	−	0.973914i	$-0.427135\pi$
$881$	13.4706			0.453836			0.226918	+	0.973914i	$0.427135\pi$
$882$	0.958550	−	5.14883i	0.0322760	−	0.173370i
$883$	−9.55258	+	9.55258i	−0.321470	+	0.321470i	−0.849331	−	0.527861i	$-0.822994\pi$
$883$	−9.55258	+	9.55258i	−0.321470	+	0.321470i	0.527861	+	0.849331i	$0.322994\pi$
$884$	0.0357245	+	0.0805860i	0.00120154	+	0.00271040i
$885$	20.7775	+	3.81764i	0.698429	+	0.128329i
$886$	−5.53714	−	8.07045i	−0.186024	−	0.271132i
$887$	0.288617			0.00969081			0.00484540	−	0.999988i	$-0.498458\pi$
$887$	0.288617			0.00969081			0.00484540	+	0.999988i	$0.498458\pi$
$888$	0.246394	+	0.151807i	0.00826844	+	0.00509430i
$889$			19.1536i			0.642393i
$890$	−42.3827	−	16.2329i	−1.42067	−	0.544129i
$891$	0.331965	−	0.331965i	0.0111213	−	0.0111213i
$892$	6.63618	−	17.2053i	0.222196	−	0.576078i
$893$	20.9193	−	20.9193i	0.700039	−	0.700039i
$894$	0.665538	−	3.57493i	0.0222589	−	0.119563i
$895$	−26.3934	+	18.1998i	−0.882233	+	0.608354i
$896$	−5.72362	−	19.7285i	−0.191213	−	0.659083i
$897$			0.273199i			0.00912184i
$898$	−51.1452	−	9.52161i	−1.70674	−	0.317740i
$899$	−44.7379	−	44.7379i	−1.49209	−	1.49209i
$900$	−6.68022	+	7.44142i	−0.222674	+	0.248047i
$901$	7.07979	−	7.07979i	0.235862	−	0.235862i
$902$	1.14957	+	1.67551i	0.0382765	+	0.0557884i
$903$	9.71880			0.323421
$904$	3.16168	−	5.13165i	0.105156	−	0.170676i
$905$	19.5095	+	28.2926i	0.648518	+	0.940478i
$906$	8.99370	+	13.1084i	0.298796	+	0.435498i
$907$	−38.0634	−	38.0634i	−1.26387	−	1.26387i	−0.949200	−	0.314672i	$-0.898105\pi$
$907$	−38.0634	−	38.0634i	−1.26387	−	1.26387i	−0.314672	−	0.949200i	$-0.601895\pi$
$908$	−28.5614	+	12.6615i	−0.947844	+	0.420188i
$909$	−10.5132	−	10.5132i	−0.348701	−	0.348701i
$910$	−0.102615	−	0.230016i	−0.00340167	−	0.00762496i
$911$	27.9067			0.924591			0.462295	−	0.886726i	$-0.347026\pi$
$911$	27.9067			0.924591			0.462295	+	0.886726i	$0.347026\pi$
$912$	−8.72724	−	7.90887i	−0.288988	−	0.261889i
$913$			3.64488i			0.120628i
$914$	−5.26395	−	0.979982i	−0.174116	−	0.0324149i
$915$	1.65407	−	9.00226i	0.0546817	−	0.297605i
$916$	13.5261	−	5.99623i	0.446914	−	0.198121i
$917$	10.5734	+	10.5734i	0.349163	+	0.349163i
$918$	1.17166	−	0.803880i	0.0386707	−	0.0265320i
$919$			27.9263i			0.921202i	0.887607	+	0.460601i	$0.152366\pi$
$919$			27.9263i			0.921202i	−0.887607	+	0.460601i	$0.847634\pi$
$920$	−26.3814	+	29.2491i	−0.869770	+	0.964313i
$921$			23.1877i			0.764059i
$922$	27.9150	+	40.6865i	0.919332	+	1.33994i
$923$	−0.451327	−	0.451327i	−0.0148556	−	0.0148556i
$924$	−0.613499	+	1.59059i	−0.0201827	+	0.0523267i
$925$	0.209532	+	0.466724i	0.00688938	+	0.0153458i
$926$	−1.00152	+	5.37966i	−0.0329121	+	0.176787i
$927$			6.14387i			0.201791i
$928$	−6.76756	+	49.8595i	−0.222156	+	1.63672i
$929$	−24.8391			−0.814943			−0.407472	−	0.913218i	$-0.633589\pi$
$929$	−24.8391			−0.814943			−0.407472	+	0.913218i	$0.633589\pi$
$930$	9.16418	+	20.5418i	0.300505	+	0.673594i
$931$	7.71043	+	7.71043i	0.252699	+	0.252699i
$932$	27.1521	+	10.4727i	0.889398	+	0.343045i
$933$	7.17052	+	7.17052i	0.234752	+	0.234752i
$934$	−20.6871	+	14.1935i	−0.676904	+	0.464425i
$935$	0.868319	−	0.598759i	0.0283971	−	0.0195815i
$936$	−0.0286742	−	0.120715i	−0.000937245	−	0.00394569i
$937$	−14.2052			−0.464062			−0.232031	−	0.972708i	$-0.574537\pi$
$937$	−14.2052			−0.464062			−0.232031	+	0.972708i	$0.574537\pi$
$938$	0.451655	−	0.309881i	0.0147471	−	0.0101180i
$939$	−16.5330	+	16.5330i	−0.539533	+	0.539533i
$940$	38.3113	+	23.4802i	1.24958	+	0.765839i
$941$	0.916857	+	0.916857i	0.0298887	+	0.0298887i	0.721893	−	0.692005i	$-0.243272\pi$
$941$	0.916857	+	0.916857i	0.0298887	+	0.0298887i	−0.692005	+	0.721893i	$0.743272\pi$
$942$	−5.42461	+	29.1382i	−0.176743	+	0.949374i
$943$			19.0606i			0.620698i
$944$	−37.7445	+	1.85676i	−1.22848	+	0.0604324i
$945$	−3.34237	+	2.30477i	−0.108727	+	0.0749741i
$946$	3.49381	+	0.650436i	0.113593	+	0.0211475i
$947$	−20.1404	+	20.1404i	−0.654474	+	0.654474i	−0.954067	−	0.299593i	$-0.903149\pi$
$947$	−20.1404	+	20.1404i	−0.654474	+	0.654474i	0.299593	+	0.954067i	$0.403149\pi$
$948$	28.5203	−	12.6433i	0.926295	−	0.410635i
$949$	0.466277	−	0.466277i	0.0151360	−	0.0151360i
$950$	−4.90681	−	20.2338i	−0.159198	−	0.656472i
$951$		−	15.3093i		−	0.496437i
$952$	−2.70660	+	4.39301i	−0.0877212	+	0.142378i
$953$	−49.1705			−1.59279			−0.796394	−	0.604777i	$-0.793262\pi$
$953$	−49.1705			−1.59279			−0.796394	+	0.604777i	$0.793262\pi$
$954$	−11.6206	+	7.97289i	−0.376230	+	0.258132i
$955$	−0.635658	+	3.45957i	−0.0205694	+	0.111949i
$956$	−15.3648	−	5.92628i	−0.496933	−	0.191669i
$957$	2.95277	−	2.95277i	0.0954496	−	0.0954496i
$958$	−37.4973	−	6.98082i	−1.21148	−	0.225540i
$959$	28.4250			0.917892
$960$	8.58692	−	15.6928i	0.277142	−	0.506484i
$961$	19.5949			0.632095
$962$	−0.00624040	−	0.00116176i	−0.000201198	−	3.74568e-5i
$963$	−6.91512	+	6.91512i	−0.222837	+	0.222837i
$964$	−12.7222	−	4.90703i	−0.409756	−	0.158045i
$965$	8.61700	+	1.58328i	0.277391	+	0.0509675i
$966$	−13.1865	+	9.04728i	−0.424269	+	0.291091i
$967$	52.7223			1.69543			0.847717	−	0.530449i	$-0.177977\pi$
$967$	52.7223			1.69543			0.847717	+	0.530449i	$0.177977\pi$
$968$	15.9931	−	25.9580i	0.514038	−	0.834322i
$969$			2.95840i			0.0950375i
$970$	40.0394	+	15.3354i	1.28559	+	0.492391i
$971$	−36.7211	+	36.7211i	−1.17843	+	1.17843i	−0.198292	+	0.980143i	$0.563539\pi$
$971$	−36.7211	+	36.7211i	−1.17843	+	1.17843i	−0.980143	+	0.198292i	$0.936461\pi$
$972$	−1.82839	+	0.810543i	−0.0586457	+	0.0259982i
$973$	−2.07309	+	2.07309i	−0.0664602	+	0.0664602i
$974$	−35.0132	−	6.51835i	−1.12190	−	0.208862i
$975$	0.0779680	−	0.205008i	0.00249697	−	0.00656550i
$976$	0.804476	+	16.3535i	0.0257506	+	0.523464i
$977$			44.2340i			1.41517i	0.706628	+	0.707585i	$0.250215\pi$
$977$			44.2340i			1.41517i	−0.706628	+	0.707585i	$0.749785\pi$
$978$	2.51702	−	13.5201i	0.0804855	−	0.432326i
$979$	−4.76436	−	4.76436i	−0.152270	−	0.152270i
$980$	−8.65430	+	14.1208i	−0.276452	+	0.451071i
$981$	−6.15941	+	6.15941i	−0.196655	+	0.196655i
$982$	28.1415	−	19.3079i	0.898031	−	0.616140i
$983$	−55.1017			−1.75747			−0.878736	−	0.477308i	$-0.841612\pi$
$983$	−55.1017			−1.75747			−0.878736	+	0.477308i	$0.841612\pi$
$984$	−2.00054	−	8.42205i	−0.0637750	−	0.268485i
$985$	−7.10624	+	4.90019i	−0.226424	+	0.156133i
$986$	10.4217	−	7.15038i	0.331896	−	0.227714i
$987$	12.8998	+	12.8998i	0.410606	+	0.410606i
$988$	0.241018	+	0.0929619i	0.00766781	+	0.00295751i
$989$	23.5724	+	23.5724i	0.749559	+	0.749559i
$990$	−1.35579	+	0.604850i	−0.0430899	+	0.0192234i
$991$	−0.865019			−0.0274782			−0.0137391	−	0.999906i	$-0.504373\pi$
$991$	−0.865019			−0.0274782			−0.0137391	+	0.999906i	$0.504373\pi$
$992$	−24.3667	−	32.0203i	−0.773645	−	1.01665i
$993$		−	17.1983i		−	0.545773i
$994$	6.83804	−	36.7304i	0.216889	−	1.16502i
$995$	−43.2925	−	7.95451i	−1.37246	−	0.252175i
$996$	5.58785	−	14.4874i	0.177058	−	0.459050i
$997$	41.8219	+	41.8219i	1.32451	+	1.32451i	0.910080	+	0.414433i	$0.136020\pi$
$997$	41.8219	+	41.8219i	1.32451	+	1.32451i	0.414433	+	0.910080i	$0.363980\pi$
$998$	−12.7260	−	18.5482i	−0.402833	−	0.587134i
$999$			0.102320i			0.00323727i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.bl.a.109.2	✓	48
3.2	odd	2		720.2.bm.h.109.23		48
4.3	odd	2		960.2.bl.a.529.7		48
5.4	even	2	inner	240.2.bl.a.109.23	yes	48
8.3	odd	2		1920.2.bl.b.289.21		48
8.5	even	2		1920.2.bl.a.289.4		48
15.14	odd	2		720.2.bm.h.109.2		48
16.3	odd	4		1920.2.bl.b.1249.4		48
16.5	even	4	inner	240.2.bl.a.229.23	yes	48
16.11	odd	4		960.2.bl.a.49.24		48
16.13	even	4		1920.2.bl.a.1249.21		48
20.19	odd	2		960.2.bl.a.529.24		48
40.19	odd	2		1920.2.bl.b.289.4		48
40.29	even	2		1920.2.bl.a.289.21		48
48.5	odd	4		720.2.bm.h.469.2		48
80.19	odd	4		1920.2.bl.b.1249.21		48
80.29	even	4		1920.2.bl.a.1249.4		48
80.59	odd	4		960.2.bl.a.49.7		48
80.69	even	4	inner	240.2.bl.a.229.2	yes	48
240.149	odd	4		720.2.bm.h.469.23		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bl.a.109.2	✓	48	1.1	even	1	trivial
240.2.bl.a.109.23	yes	48	5.4	even	2	inner
240.2.bl.a.229.2	yes	48	80.69	even	4	inner
240.2.bl.a.229.23	yes	48	16.5	even	4	inner
720.2.bm.h.109.2		48	15.14	odd	2
720.2.bm.h.109.23		48	3.2	odd	2
720.2.bm.h.469.2		48	48.5	odd	4
720.2.bm.h.469.23		48	240.149	odd	4
960.2.bl.a.49.7		48	80.59	odd	4
960.2.bl.a.49.24		48	16.11	odd	4
960.2.bl.a.529.7		48	4.3	odd	2
960.2.bl.a.529.24		48	20.19	odd	2
1920.2.bl.a.289.4		48	8.5	even	2
1920.2.bl.a.289.21		48	40.29	even	2
1920.2.bl.a.1249.4		48	80.29	even	4
1920.2.bl.a.1249.21		48	16.13	even	4
1920.2.bl.b.289.4		48	40.19	odd	2
1920.2.bl.b.289.21		48	8.3	odd	2
1920.2.bl.b.1249.4		48	16.3	odd	4
1920.2.bl.b.1249.21		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)

\(f(q)\)	\(=\)	\(q+(-1.39033 - 0.258835i) q^{2} +(0.707107 - 0.707107i) q^{3} +(1.86601 + 0.719729i) q^{4} +(0.404088 - 2.19925i) q^{5} +(-1.16613 + 0.800085i) q^{6} +1.81567 q^{7} +(-2.40807 - 1.48364i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(-1.39033 - 0.258835i) q^{2} +(0.707107 - 0.707107i) q^{3} +(1.86601 + 0.719729i) q^{4} +(0.404088 - 2.19925i) q^{5} +(-1.16613 + 0.800085i) q^{6} +1.81567 q^{7} +(-2.40807 - 1.48364i) q^{8} -1.00000i q^{9} +(-1.13106 + 2.95308i) q^{10} +(-0.331965 + 0.331965i) q^{11} +(1.82839 - 0.810543i) q^{12} +(-0.0310184 + 0.0310184i) q^{13} +(-2.52438 - 0.469959i) q^{14} +(-1.26937 - 1.84084i) q^{15} +(2.96398 + 2.68604i) q^{16} -1.00474i q^{17} +(-0.258835 + 1.39033i) q^{18} +(-2.08203 - 2.08203i) q^{19} +(2.33690 - 3.81299i) q^{20} +(1.28388 - 1.28388i) q^{21} +(0.547464 - 0.375616i) q^{22} +6.22794 q^{23} +(-2.75186 + 0.653667i) q^{24} +(-4.67343 - 1.77739i) q^{25} +(0.0511543 - 0.0350971i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(3.38806 + 1.30679i) q^{28} +(-6.28959 - 6.28959i) q^{29} +(1.28837 + 2.88792i) q^{30} +7.11301 q^{31} +(-3.42566 - 4.50165i) q^{32} +0.469470i q^{33} +(-0.260063 + 1.39692i) q^{34} +(0.733693 - 3.99313i) q^{35} +(0.719729 - 1.86601i) q^{36} +(-0.0723513 - 0.0723513i) q^{37} +(2.35580 + 3.43360i) q^{38} +0.0438667i q^{39} +(-4.23598 + 4.69643i) q^{40} +3.06050i q^{41} +(-2.11732 + 1.45269i) q^{42} +(3.78495 + 3.78495i) q^{43} +(-0.858375 + 0.380525i) q^{44} +(-2.19925 - 0.404088i) q^{45} +(-8.65886 - 1.61201i) q^{46} +10.0476i q^{47} +(3.99517 - 0.196534i) q^{48} -3.70333 q^{49} +(6.03753 + 3.68079i) q^{50} +(-0.710461 - 0.710461i) q^{51} +(-0.0802055 + 0.0355558i) q^{52} +(7.04636 + 7.04636i) q^{53} +(0.800085 + 1.16613i) q^{54} +(0.595932 + 0.864219i) q^{55} +(-4.37227 - 2.69382i) q^{56} -2.94443 q^{57} +(7.11661 + 10.3725i) q^{58} +(-6.68042 + 6.68042i) q^{59} +(-1.04376 - 4.34863i) q^{60} +(2.89442 + 2.89442i) q^{61} +(-9.88940 - 1.84109i) q^{62} -1.81567i q^{63} +(3.59760 + 7.14544i) q^{64} +(0.0556832 + 0.0807515i) q^{65} +(0.121515 - 0.652716i) q^{66} +(-0.150837 + 0.150837i) q^{67} +(0.723143 - 1.87486i) q^{68} +(4.40382 - 4.40382i) q^{69} +(-2.05363 + 5.36184i) q^{70} +14.5503i q^{71} +(-1.48364 + 2.40807i) q^{72} -15.0323 q^{73} +(0.0818648 + 0.119319i) q^{74} +(-4.56141 + 2.04781i) q^{75} +(-2.38659 - 5.38358i) q^{76} +(-0.602741 + 0.602741i) q^{77} +(0.0113542 - 0.0609889i) q^{78} +15.5985 q^{79} +(7.10499 - 5.43315i) q^{80} -1.00000 q^{81} +(0.792162 - 4.25508i) q^{82} +(5.48985 - 5.48985i) q^{83} +(3.31977 - 1.47168i) q^{84} +(-2.20969 - 0.406005i) q^{85} +(-4.28263 - 6.24198i) q^{86} -8.89482 q^{87} +(1.29191 - 0.306877i) q^{88} +14.3520i q^{89} +(2.95308 + 1.13106i) q^{90} +(-0.0563193 + 0.0563193i) q^{91} +(11.6214 + 4.48242i) q^{92} +(5.02966 - 5.02966i) q^{93} +(2.60066 - 13.9694i) q^{94} +(-5.42023 + 3.73758i) q^{95} +(-5.60545 - 0.760842i) q^{96} -13.5585i q^{97} +(5.14883 + 0.958550i) q^{98} +(0.331965 + 0.331965i) 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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