LMFDB - Embedded newform 152.2.o.c.27.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [152,2,Mod(27,152)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(152, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("152.27"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 152 = 2^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	152.o (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [28,-3,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$1.21372611072$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			27.10
Character	$\chi$	$=$	152.27
Dual form			152.2.o.c.107.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.540330 - 1.30692i) q^{2} +(2.07624 + 1.19872i) q^{3} +(-1.41609 - 1.41234i) q^{4} +(-0.418341 - 0.241529i) q^{5} +(2.68848 - 2.06578i) q^{6} -1.56686i q^{7} +(-2.61097 + 1.08759i) q^{8} +(1.37385 + 2.37958i) q^{9} +(-0.541701 + 0.416233i) q^{10} +1.24363 q^{11} +(-1.24714 - 4.62984i) q^{12} +(1.80015 + 3.11796i) q^{13} +(-2.04776 - 0.846621i) q^{14} +(-0.579050 - 1.00294i) q^{15} +(0.0106066 + 3.99999i) q^{16} +(-1.35570 + 2.34815i) q^{17} +(3.85225 - 0.509757i) q^{18} +(-4.25703 + 0.936862i) q^{19} +(0.251286 + 0.932864i) q^{20} +(1.87822 - 3.25318i) q^{21} +(0.671968 - 1.62532i) q^{22} +(-5.52533 + 3.19005i) q^{23} +(-6.72471 - 0.871723i) q^{24} +(-2.38333 - 4.12804i) q^{25} +(5.04760 - 0.667934i) q^{26} -0.604878i q^{27} +(-2.21293 + 2.21881i) q^{28} +(-0.695157 - 1.20405i) q^{29} +(-1.62365 + 0.214852i) q^{30} -4.86016 q^{31} +(5.23340 + 2.14745i) q^{32} +(2.58207 + 1.49076i) q^{33} +(2.33632 + 3.04058i) q^{34} +(-0.378442 + 0.655481i) q^{35} +(1.41527 - 5.31003i) q^{36} +10.9720 q^{37} +(-1.07579 + 6.06982i) q^{38} +8.63150i q^{39} +(1.35496 + 0.175643i) q^{40} +(1.10008 + 0.635132i) q^{41} +(-3.23679 - 4.21248i) q^{42} +(4.78175 - 8.28223i) q^{43} +(-1.76108 - 1.75642i) q^{44} -1.32730i q^{45} +(1.18364 + 8.94485i) q^{46} +(-7.26763 + 4.19597i) q^{47} +(-4.77283 + 8.31765i) q^{48} +4.54495 q^{49} +(-6.68281 + 0.884316i) q^{50} +(-5.62954 + 3.25022i) q^{51} +(1.85443 - 6.95772i) q^{52} +(1.50024 + 2.59849i) q^{53} +(-0.790529 - 0.326834i) q^{54} +(-0.520259 - 0.300372i) q^{55} +(1.70410 + 4.09102i) q^{56} +(-9.96165 - 3.15782i) q^{57} +(-1.94921 + 0.257933i) q^{58} +(4.43723 + 2.56184i) q^{59} +(-0.596510 + 2.23807i) q^{60} +(9.42313 - 5.44044i) q^{61} +(-2.62609 + 6.35185i) q^{62} +(3.72846 - 2.15263i) q^{63} +(5.63431 - 5.67931i) q^{64} -1.73916i q^{65} +(3.34347 - 2.56906i) q^{66} +(-3.22460 + 1.86172i) q^{67} +(5.23618 - 1.41047i) q^{68} -15.2959 q^{69} +(0.652179 + 0.848770i) q^{70} +(6.62670 - 11.4778i) q^{71} +(-6.17507 - 4.71882i) q^{72} +(-0.494526 + 0.856544i) q^{73} +(5.92851 - 14.3396i) q^{74} -11.4277i q^{75} +(7.35149 + 4.68568i) q^{76} -1.94859i q^{77} +(11.2807 + 4.66386i) q^{78} +(5.81311 - 10.0686i) q^{79} +(0.961676 - 1.67592i) q^{80} +(4.84663 - 8.39460i) q^{81} +(1.42447 - 1.09454i) q^{82} -12.1949 q^{83} +(-7.25431 + 1.95410i) q^{84} +(1.13429 - 0.654884i) q^{85} +(-8.24050 - 10.7245i) q^{86} -3.33319i q^{87} +(-3.24707 + 1.35255i) q^{88} +(-11.1625 + 6.44469i) q^{89} +(-1.73467 - 0.717179i) q^{90} +(4.88540 - 2.82059i) q^{91} +(12.3298 + 3.28624i) q^{92} +(-10.0909 - 5.82596i) q^{93} +(1.55688 + 11.7654i) q^{94} +(2.00717 + 0.636268i) q^{95} +(8.29161 + 10.7320i) q^{96} +(2.42717 + 1.40133i) q^{97} +(2.45577 - 5.93989i) q^{98} +(1.70855 + 2.95930i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 3 q^{2} - 6 q^{3} + q^{4} - 3 q^{6} + 8 q^{9} + 6 q^{10} - 16 q^{11} + 13 q^{16} - 22 q^{17} + 4 q^{19} - 40 q^{20} - 21 q^{22} - 11 q^{24} + 16 q^{25} + 36 q^{26} - 10 q^{28} + 4 q^{30} - 3 q^{32}+ \cdots - 28 q^{99}+O(q^{100}) $ 28 * q - 3 * q^2 - 6 * q^3 + q^4 - 3 * q^6 + 8 * q^9 + 6 * q^10 - 16 * q^11 + 13 * q^16 - 22 * q^17 + 4 * q^19 - 40 * q^20 - 21 * q^22 - 11 * q^24 + 16 * q^25 + 36 * q^26 - 10 * q^28 + 4 * q^30 - 3 * q^32 + 36 * q^33 - 12 * q^34 - 28 * q^35 - 8 * q^36 + 38 * q^38 - 48 * q^40 + 6 * q^41 + 14 * q^42 + 30 * q^43 + 5 * q^44 - 15 * q^48 - 68 * q^49 - 42 * q^51 + 36 * q^52 + 23 * q^54 - 26 * q^57 + 20 * q^58 - 18 * q^59 - 42 * q^60 + 22 * q^62 + 70 * q^64 - 27 * q^66 + 78 * q^67 + 4 * q^68 + 18 * q^70 - 24 * q^72 + 14 * q^73 + 4 * q^74 + 47 * q^76 - 30 * q^78 - 20 * q^80 + 6 * q^81 + 23 * q^82 - 32 * q^83 + 42 * q^86 - 18 * q^89 - 96 * q^90 - 12 * q^91 + 46 * q^92 + 50 * q^96 + 30 * q^97 + 15 * q^98 - 28 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/152\mathbb{Z}\right)^\times$.

$n$	$39$	$77$	$97$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.540330	−	1.30692i	0.382071	−	0.924133i
$2$	0.540330	−	1.30692i	0.382071	−	0.924133i
$3$	2.07624	+	1.19872i	1.19872	+	0.692080i	0.960269	−	0.279075i	$-0.0900278\pi$
$3$	2.07624	+	1.19872i	1.19872	+	0.692080i	0.238449	+	0.971155i	$0.423361\pi$
$4$	−1.41609	−	1.41234i	−0.708044	−	0.706169i
$5$	−0.418341	−	0.241529i	−0.187088	−	0.108015i	0.403531	−	0.914966i	$-0.367783\pi$
$5$	−0.418341	−	0.241529i	−0.187088	−	0.108015i	−0.590618	+	0.806951i	$0.701116\pi$
$6$	2.68848	−	2.06578i	1.09757	−	0.843351i
$7$		−	1.56686i		−	0.592217i	−0.955154	−	0.296109i	$-0.904311\pi$
$7$		−	1.56686i		−	0.592217i	0.955154	−	0.296109i	$-0.0956891\pi$
$8$	−2.61097	+	1.08759i	−0.923117	+	0.384520i
$9$	1.37385	+	2.37958i	0.457950	+	0.793192i
$10$	−0.541701	+	0.416233i	−0.171301	+	0.131624i
$11$	1.24363			0.374967			0.187484	−	0.982268i	$-0.439967\pi$
$11$	1.24363			0.374967			0.187484	+	0.982268i	$0.439967\pi$
$12$	−1.24714	−	4.62984i	−0.360019	−	1.33652i
$13$	1.80015	+	3.11796i	0.499273	+	0.864766i	1.00000		0.000839577i	$-0.000267246\pi$
$13$	1.80015	+	3.11796i	0.499273	+	0.864766i	−0.500727	+	0.865605i	$0.666934\pi$
$14$	−2.04776	−	0.846621i	−0.547288	−	0.226269i
$15$	−0.579050	−	1.00294i	−0.149510	−	0.258959i
$16$	0.0106066	+	3.99999i	0.00265164	+	0.999996i
$17$	−1.35570	+	2.34815i	−0.328807	+	0.569510i	−0.982275	−	0.187444i	$-0.939980\pi$
$17$	−1.35570	+	2.34815i	−0.328807	+	0.569510i	0.653469	+	0.756954i	$0.273313\pi$
$18$	3.85225	−	0.509757i	0.907984	−	0.120151i
$19$	−4.25703	+	0.936862i	−0.976629	+	0.214931i
$19$	−4.25703	+	0.936862i	−0.976629	+	0.214931i
$20$	0.251286	+	0.932864i	0.0561893	+	0.208595i
$21$	1.87822	−	3.25318i	0.409862	−	0.709901i
$22$	0.671968	−	1.62532i	0.143264	−	0.346520i
$23$	−5.52533	+	3.19005i	−1.15211	+	0.665171i	−0.949401	−	0.314068i	$-0.898308\pi$
$23$	−5.52533	+	3.19005i	−1.15211	+	0.665171i	−0.202710	+	0.979239i	$0.564975\pi$
$24$	−6.72471	−	0.871723i	−1.37268	−	0.177940i
$25$	−2.38333	−	4.12804i	−0.476665	−	0.825609i
$26$	5.04760	−	0.667934i	0.989916	−	0.130993i
$27$		−	0.604878i		−	0.116409i
$28$	−2.21293	+	2.21881i	−0.418205	+	0.419316i
$29$	−0.695157	−	1.20405i	−0.129087	−	0.223586i	0.794236	−	0.607610i	$-0.207871\pi$
$29$	−0.695157	−	1.20405i	−0.129087	−	0.223586i	−0.923323	+	0.384024i	$0.874538\pi$
$30$	−1.62365	+	0.214852i	−0.296436	+	0.0392265i
$31$	−4.86016			−0.872910			−0.436455	−	0.899726i	$-0.643766\pi$
$31$	−4.86016			−0.872910			−0.436455	+	0.899726i	$0.643766\pi$
$32$	5.23340	+	2.14745i	0.925143	+	0.379619i
$33$	2.58207	+	1.49076i	0.449480	+	0.259507i
$34$	2.33632	+	3.04058i	0.400675	+	0.521454i
$35$	−0.378442	+	0.655481i	−0.0639684	+	0.110797i
$36$	1.41527	−	5.31003i	0.235879	−	0.885004i
$37$	10.9720			1.80379			0.901894	−	0.431957i	$-0.142177\pi$
$37$	10.9720			1.80379			0.901894	+	0.431957i	$0.142177\pi$
$38$	−1.07579	+	6.06982i	−0.174517	+	0.984654i
$39$			8.63150i			1.38215i
$40$	1.35496	+	0.175643i	0.214238	+	0.0277716i
$41$	1.10008	+	0.635132i	0.171804	+	0.0991909i	0.583436	−	0.812159i	$-0.301708\pi$
$41$	1.10008	+	0.635132i	0.171804	+	0.0991909i	−0.411632	+	0.911350i	$0.635041\pi$
$42$	−3.23679	−	4.21248i	−0.499447	−	0.649999i
$43$	4.78175	−	8.28223i	0.729210	−	1.26303i	−0.228008	−	0.973659i	$-0.573221\pi$
$43$	4.78175	−	8.28223i	0.729210	−	1.26303i	0.957218	−	0.289369i	$-0.0934455\pi$
$44$	−1.76108	−	1.75642i	−0.265493	−	0.264790i
$45$		−	1.32730i		−	0.197862i
$46$	1.18364	+	8.94485i	0.174519	+	1.31885i
$47$	−7.26763	+	4.19597i	−1.06009	+	0.612045i	−0.925458	−	0.378850i	$-0.876320\pi$
$47$	−7.26763	+	4.19597i	−1.06009	+	0.612045i	−0.134635	+	0.990895i	$0.542986\pi$
$48$	−4.77283	+	8.31765i	−0.688899	+	1.20055i
$49$	4.54495			0.649279
$50$	−6.68281	+	0.884316i	−0.945092	+	0.125061i
$51$	−5.62954	+	3.25022i	−0.788293	+	0.455121i
$52$	1.85443	−	6.95772i	0.257164	−	0.964863i
$53$	1.50024	+	2.59849i	0.206074	+	0.356930i	0.950474	−	0.310803i	$-0.100598\pi$
$53$	1.50024	+	2.59849i	0.206074	+	0.356930i	−0.744400	+	0.667733i	$0.767265\pi$
$54$	−0.790529	−	0.326834i	−0.107577	−	0.0444765i
$55$	−0.520259	−	0.300372i	−0.0701517	−	0.0405021i
$56$	1.70410	+	4.09102i	0.227719	+	0.546686i
$57$	−9.96165	−	3.15782i	−1.31945	−	0.418264i
$58$	−1.94921	+	0.257933i	−0.255944	+	0.0338682i
$59$	4.43723	+	2.56184i	0.577678	+	0.333523i	0.760210	−	0.649677i	$-0.225096\pi$
$59$	4.43723	+	2.56184i	0.577678	+	0.333523i	−0.182532	+	0.983200i	$0.558429\pi$
$60$	−0.596510	+	2.23807i	−0.0770092	+	0.288934i
$61$	9.42313	−	5.44044i	1.20651	−	0.696578i	0.244513	−	0.969646i	$-0.421372\pi$
$61$	9.42313	−	5.44044i	1.20651	−	0.696578i	0.961995	+	0.273068i	$0.0880385\pi$
$62$	−2.62609	+	6.35185i	−0.333514	+	0.806685i
$63$	3.72846	−	2.15263i	0.469742	−	0.271206i
$64$	5.63431	−	5.67931i	0.704289	−	0.709914i
$65$		−	1.73916i		−	0.215716i
$66$	3.34347	−	2.56906i	0.411553	−	0.316229i
$67$	−3.22460	+	1.86172i	−0.393947	+	0.227446i	−0.683869	−	0.729605i	$-0.739704\pi$
$67$	−3.22460	+	1.86172i	−0.393947	+	0.227446i	0.289922	+	0.957050i	$0.406371\pi$
$68$	5.23618	−	1.41047i	0.634980	−	0.171045i
$69$	−15.2959			−1.84141
$70$	0.652179	+	0.848770i	0.0779503	+	0.101447i
$71$	6.62670	−	11.4778i	0.786444	−	1.36216i	−0.141688	−	0.989911i	$-0.545253\pi$
$71$	6.62670	−	11.4778i	0.786444	−	1.36216i	0.928132	−	0.372250i	$-0.121414\pi$
$72$	−6.17507	−	4.71882i	−0.727739	−	0.556118i
$73$	−0.494526	+	0.856544i	−0.0578799	+	0.100251i	−0.893514	−	0.449036i	$-0.851767\pi$
$73$	−0.494526	+	0.856544i	−0.0578799	+	0.100251i	0.835634	+	0.549287i	$0.185101\pi$
$74$	5.92851	−	14.3396i	0.689175	−	1.66694i
$75$		−	11.4277i		−	1.31956i
$76$	7.35149	+	4.68568i	0.843274	+	0.537484i
$77$		−	1.94859i		−	0.222062i
$78$	11.2807	+	4.66386i	1.27729	+	0.528078i
$79$	5.81311	−	10.0686i	0.654026	−	1.13281i	−0.328111	−	0.944639i	$-0.606412\pi$
$79$	5.81311	−	10.0686i	0.654026	−	1.13281i	0.982137	−	0.188168i	$-0.0602548\pi$
$80$	0.961676	−	1.67592i	0.107519	−	0.187373i
$81$	4.84663	−	8.39460i	0.538514	−	0.932733i
$82$	1.42447	−	1.09454i	0.157307	−	0.120871i
$83$	−12.1949			−1.33856			−0.669280	−	0.743010i	$-0.733397\pi$
$83$	−12.1949			−1.33856			−0.669280	+	0.743010i	$0.733397\pi$
$84$	−7.25431	+	1.95410i	−0.791510	+	0.213210i
$85$	1.13429	−	0.654884i	0.123031	−	0.0710322i
$86$	−8.24050	−	10.7245i	−0.888596	−	1.15645i
$87$		−	3.33319i		−	0.357355i
$88$	−3.24707	+	1.35255i	−0.346139	+	0.144182i
$89$	−11.1625	+	6.44469i	−1.18323	+	0.683136i	−0.956759	−	0.290883i	$-0.906051\pi$
$89$	−11.1625	+	6.44469i	−1.18323	+	0.683136i	−0.226467	+	0.974019i	$0.572718\pi$
$90$	−1.73467	−	0.717179i	−0.182851	−	0.0755973i
$91$	4.88540	−	2.82059i	0.512129	−	0.295678i
$92$	12.3298	+	3.28624i	1.28547	+	0.342614i
$93$	−10.0909	−	5.82596i	−1.04637	−	0.604124i
$94$	1.55688	+	11.7654i	0.160580	+	1.21351i
$95$	2.00717	+	0.636268i	0.205931	+	0.0652798i
$96$	8.29161	+	10.7320i	0.846258	+	1.09533i
$97$	2.42717	+	1.40133i	0.246442	+	0.142283i	0.618134	−	0.786073i	$-0.287889\pi$
$97$	2.42717	+	1.40133i	0.246442	+	0.142283i	−0.371692	+	0.928356i	$0.621222\pi$
$98$	2.45577	−	5.93989i	0.248070	−	0.600020i
$99$	1.70855	+	2.95930i	0.171716	+	0.297421i
$100$	−2.45519	+	9.21173i	−0.245519	+	0.921173i
$101$	−0.655955	+	0.378716i	−0.0652700	+	0.0376837i	−0.532280	−	0.846568i	$-0.678665\pi$
$101$	−0.655955	+	0.378716i	−0.0652700	+	0.0376837i	0.467010	+	0.884252i	$0.345331\pi$
$102$	1.20597	+	9.11355i	0.119409	+	0.902376i
$103$	4.06152			0.400193			0.200097	−	0.979776i	$-0.435874\pi$
$103$	4.06152			0.400193			0.200097	+	0.979776i	$0.435874\pi$
$104$	−8.09119	−	6.18306i	−0.793407	−	0.606299i
$105$	−1.57147	+	0.907291i	−0.153360	+	0.0885425i
$106$	4.20665	−	0.556653i	0.408586	−	0.0540670i
$107$			4.15320i			0.401505i	0.979642	+	0.200753i	$0.0643388\pi$
$107$			4.15320i			0.401505i	−0.979642	+	0.200753i	$0.935661\pi$
$108$	−0.854292	+	0.856561i	−0.0822043	+	0.0824226i
$109$	−9.07011	+	15.7099i	−0.868759	+	1.50473i	−0.00549325	+	0.999985i	$0.501749\pi$
$109$	−9.07011	+	15.7099i	−0.868759	+	1.50473i	−0.863266	+	0.504750i	$0.831585\pi$
$110$	−0.673674	+	0.517638i	−0.0642323	+	0.0493548i
$111$	22.7805	+	13.1523i	2.16223	+	1.24837i
$112$	6.26742	−	0.0166190i	0.592215	−	0.00157035i
$113$		−	7.00334i		−	0.658819i	−0.944187	−	0.329409i	$-0.893150\pi$
$113$		−	7.00334i		−	0.658819i	0.944187	−	0.329409i	$-0.106850\pi$
$114$	−9.50960	+	11.3128i	−0.890656	+	1.05954i
$115$	3.08196			0.287394
$116$	−0.716118	+	2.68683i	−0.0664898	+	0.249466i
$117$	−4.94628	+	8.56720i	−0.457284	+	0.792038i
$118$	5.74569	−	4.41488i	0.528934	−	0.406422i
$119$	3.67922	+	2.12420i	0.337274	+	0.194725i
$120$	2.60267	+	1.98889i	0.237590	+	0.181560i
$121$	−9.45340			−0.859400
$122$	−2.01864	−	15.2549i	−0.182759	−	1.38112i
$123$	1.52269	+	2.63737i	0.137296	+	0.237804i
$124$	6.88241	+	6.86418i	0.618059	+	0.616422i
$125$			4.71786i			0.421978i
$126$	−0.798717	−	6.03594i	−0.0711554	−	0.537724i
$127$	−7.61514	−	13.1898i	−0.675734	−	1.17041i	−0.976254	−	0.216630i	$-0.930493\pi$
$127$	−7.61514	−	13.1898i	−0.675734	−	1.17041i	0.300520	−	0.953776i	$-0.402840\pi$
$128$	−4.37803	−	10.4323i	−0.386966	−	0.922094i
$129$	19.8561	−	11.4639i	1.74823	−	1.00934i
$130$	−2.27294	−	0.939719i	−0.199350	−	0.0824188i
$131$	−4.14342	+	7.17662i	−0.362012	+	0.627024i	−0.988292	−	0.152575i	$-0.951244\pi$
$131$	−4.14342	+	7.17662i	−0.362012	+	0.627024i	0.626279	+	0.779599i	$0.284577\pi$
$132$	−1.55098	−	5.75779i	−0.134995	−	0.501151i
$133$	1.46793	+	6.67017i	0.127286	+	0.578377i
$134$	0.690778	+	5.22024i	0.0596742	+	0.450960i
$135$	−0.146096	+	0.253045i	−0.0125739	+	0.0217787i
$136$	0.985886	−	7.60539i	0.0845390	−	0.652157i
$137$	8.90976	+	15.4322i	0.761212	+	1.31846i	0.942226	+	0.334978i	$0.108729\pi$
$137$	8.90976	+	15.4322i	0.761212	+	1.31846i	−0.181013	+	0.983481i	$0.557938\pi$
$138$	−8.26482	+	19.9905i	−0.703548	+	1.70171i
$139$	4.16150	+	7.20793i	0.352974	+	0.611368i	0.986769	−	0.162132i	$-0.0518372\pi$
$139$	4.16150	+	7.20793i	0.352974	+	0.611368i	−0.633795	+	0.773501i	$0.718504\pi$
$140$	1.46167	−	0.393730i	0.123533	−	0.0332763i
$141$	−20.1191			−1.69434
$142$	−11.4200	−	14.8624i	−0.958341	−	1.24722i
$143$	2.23872	+	3.87757i	0.187211	+	0.324259i
$144$	−9.50370	+	5.52062i	−0.791975	+	0.460051i
$145$			0.671602i			0.0557735i
$146$	0.852229	+	1.10912i	0.0705310	+	0.0917917i
$147$	9.43641	+	5.44811i	0.778302	+	0.449353i
$148$	−15.5373	−	15.4962i	−1.27716	−	1.27378i
$149$	−16.0928	−	9.29117i	−1.31837	−	0.761162i	−0.334905	−	0.942252i	$-0.608704\pi$
$149$	−16.0928	−	9.29117i	−1.31837	−	0.761162i	−0.983467	+	0.181090i	$0.942037\pi$
$150$	−14.9352	−	6.17475i	−1.21945	−	0.504167i
$151$	−4.56745			−0.371694			−0.185847	−	0.982579i	$-0.559503\pi$
$151$	−4.56745			−0.371694			−0.185847	+	0.982579i	$0.559503\pi$
$152$	10.0960	−	7.07601i	0.818897	−	0.573940i
$153$	−7.45013			−0.602308
$154$	−2.54665	−	1.05288i	−0.205215	−	0.0848435i
$155$	2.03320	+	1.17387i	0.163311	+	0.0942875i
$156$	12.1906	−	12.2230i	0.976029	−	0.978620i
$157$	16.0994	+	9.29499i	1.28487	+	0.741821i	0.977735	−	0.209844i	$-0.0672957\pi$
$157$	16.0994	+	9.29499i	1.28487	+	0.741821i	0.307137	+	0.951665i	$0.400629\pi$
$158$	−10.0179	−	13.0377i	−0.796980	−	1.03722i
$159$			7.19346i			0.570479i
$160$	−1.67067	−	2.16238i	−0.132078	−	0.170951i
$161$	4.99836	+	8.65741i	0.393926	+	0.682300i
$162$	−8.35231	−	10.8700i	−0.656219	−	0.854029i
$163$	13.2618			1.03874			0.519370	−	0.854549i	$-0.326167\pi$
$163$	13.2618			1.03874			0.519370	+	0.854549i	$0.326167\pi$
$164$	−0.660790	−	2.45309i	−0.0515990	−	0.191554i
$165$	−0.720122	−	1.24729i	−0.0560614	−	0.0971012i
$166$	−6.58925	+	15.9377i	−0.511425	+	1.23701i
$167$	−5.01139	−	8.67998i	−0.387793	−	0.671677i	0.604359	−	0.796712i	$-0.293429\pi$
$167$	−5.01139	−	8.67998i	−0.387793	−	0.671677i	−0.992152	+	0.125035i	$0.960096\pi$
$168$	−1.36587	+	10.5367i	−0.105379	+	0.812922i
$169$	0.0188953	−	0.0327276i	0.00145348	−	0.00251751i
$170$	−0.242990	−	1.83629i	−0.0186365	−	0.140837i
$171$	−8.07785	−	8.84281i	−0.617729	−	0.676227i
$172$	−18.4687	+	4.97492i	−1.40822	+	0.379334i
$173$	7.75097	−	13.4251i	0.589296	−	1.02069i	−0.405029	−	0.914304i	$-0.632739\pi$
$173$	7.75097	−	13.4251i	0.589296	−	1.02069i	0.994325	−	0.106386i	$-0.0339280\pi$
$174$	−4.35621	−	1.80102i	−0.330244	−	0.136535i
$175$	−6.46807	+	3.73434i	−0.488940	+	0.282290i
$176$	0.0131906	+	4.97449i	0.000994279	+	0.374966i
$177$	6.14184	+	10.6380i	0.461649	+	0.799599i
$178$	2.39126	+	18.0708i	0.179232	+	1.35446i
$179$			2.86093i			0.213836i	0.994268	+	0.106918i	$0.0340982\pi$
$179$			2.86093i			0.213836i	−0.994268	+	0.106918i	$0.965902\pi$
$180$	−1.87459	+	1.87957i	−0.139724	+	0.140095i
$181$	−0.305140	−	0.528519i	−0.0226809	−	0.0392845i	0.854462	−	0.519514i	$-0.173887\pi$
$181$	−0.305140	−	0.528519i	−0.0226809	−	0.0392845i	−0.877143	+	0.480229i	$0.840554\pi$
$182$	−1.04656	−	7.90888i	−0.0775761	−	0.586245i
$183$	26.0862			1.92835
$184$	10.9570	−	14.3384i	0.807761	−	1.05704i
$185$	−4.59004	−	2.65006i	−0.337466	−	0.194836i
$186$	−13.0665	+	10.0400i	−0.958079	+	0.736170i
$187$	−1.68599	+	2.92022i	−0.123292	+	0.213548i
$188$	16.2177	+	4.32249i	1.18280	+	0.315250i
$189$	−0.947760			−0.0689394
$190$	1.91609	−	2.27942i	0.139007	−	0.165366i
$191$			21.9035i			1.58488i	0.609947	+	0.792442i	$0.291191\pi$
$191$			21.9035i			1.58488i	−0.609947	+	0.792442i	$0.708809\pi$
$192$	18.5061	−	5.03766i	1.33556	−	0.363562i
$193$	4.60435	+	2.65832i	0.331428	+	0.191350i	0.656475	−	0.754348i	$-0.272047\pi$
$193$	4.60435	+	2.65832i	0.331428	+	0.191350i	−0.325047	+	0.945698i	$0.605380\pi$
$194$	3.14290	−	2.41494i	0.225647	−	0.173383i
$195$	2.08476	−	3.61091i	0.149293	−	0.258583i
$196$	−6.43605	−	6.41900i	−0.459718	−	0.458500i
$197$		−	0.913518i		−	0.0650855i	−0.999470	−	0.0325427i	$-0.989639\pi$
$197$		−	0.913518i		−	0.0650855i	0.999470	−	0.0325427i	$-0.0103605\pi$
$198$	4.79076	−	0.633946i	0.340464	−	0.0450526i
$199$	−17.3763	+	10.0322i	−1.23177	+	0.711164i	−0.967399	−	0.253257i	$-0.918498\pi$
$199$	−17.3763	+	10.0322i	−1.23177	+	0.711164i	−0.264373	+	0.964421i	$0.585165\pi$
$200$	10.7124	+	8.18612i	0.757481	+	0.578846i
$201$	−8.92672			−0.629642
$202$	0.140520	+	1.06191i	0.00988694	+	0.0747160i
$203$	−1.88657	+	1.08921i	−0.132411	+	0.0764478i
$204$	12.5623	+	3.34822i	0.879538	+	0.234422i
$205$	−0.306806	−	0.531403i	−0.0214282	−	0.0371148i
$206$	2.19456	−	5.30808i	0.152902	−	0.369832i
$207$	−15.1819	−	8.76529i	−1.05522	−	0.609230i
$208$	−12.4527	+	7.23366i	−0.863439	+	0.501564i
$209$	−5.29415	+	1.16511i	−0.366204	+	0.0805921i
$210$	0.336644	+	2.54403i	0.0232306	+	0.175555i
$211$	−21.5716	−	12.4544i	−1.48505	−	0.857394i	−0.485194	−	0.874406i	$-0.661251\pi$
$211$	−21.5716	−	12.4544i	−1.48505	−	0.857394i	−0.999855	+	0.0170124i	$0.994585\pi$
$212$	1.54548	−	5.79854i	0.106144	−	0.398245i
$213$	27.5172	−	15.8871i	1.88545	−	1.08856i
$214$	5.42791	+	2.24410i	0.371044	+	0.153404i
$215$	−4.00080	+	2.30986i	−0.272852	+	0.157531i
$216$	0.657858	+	1.57932i	0.0447616	+	0.107459i
$217$			7.61519i			0.516953i
$218$	15.6307	+	20.3424i	1.05865	+	1.37776i
$219$	−2.05351	+	1.18559i	−0.138763	+	0.0801151i
$220$	0.312506	+	1.16013i	0.0210692	+	0.0782162i
$221$	−9.76191			−0.656657
$222$	29.4981	−	22.6658i	1.97978	−	1.52123i
$223$	1.75003	−	3.03114i	0.117191	−	0.202980i	−0.801463	−	0.598045i	$-0.795944\pi$
$223$	1.75003	−	3.03114i	0.117191	−	0.202980i	0.918653	+	0.395065i	$0.129278\pi$
$224$	3.36475	−	8.20000i	0.224817	−	0.547886i
$225$	6.54866	−	11.3426i	0.436578	−	0.756175i
$226$	−9.15281	−	3.78411i	−0.608836	−	0.251715i
$227$			5.29383i			0.351364i	0.984447	+	0.175682i	$0.0562130\pi$
$227$			5.29383i			0.351364i	−0.984447	+	0.175682i	$0.943787\pi$
$228$	9.64665	+	18.5410i	0.638865	+	1.22791i
$229$			1.20868i			0.0798721i	0.999202	+	0.0399360i	$0.0127154\pi$
$229$			1.20868i			0.0798721i	−0.999202	+	0.0399360i	$0.987285\pi$
$230$	1.66527	−	4.02788i	0.109805	−	0.265590i
$231$	2.33581	−	4.04573i	0.153685	−	0.266190i
$232$	3.12454	+	2.38768i	0.205136	+	0.156759i
$233$	5.58944	−	9.68119i	0.366176	−	0.634236i	−0.622788	−	0.782391i	$-0.714000\pi$
$233$	5.58944	−	9.68119i	0.366176	−	0.634236i	0.988964	+	0.148155i	$0.0473334\pi$
$234$	8.52404	+	11.0935i	0.557234	+	0.725206i
$235$	4.05380			0.264440
$236$	−2.66533	−	9.89465i	−0.173498	−	0.644087i
$237$	24.1388	−	13.9366i	1.56799	−	0.905277i
$238$	4.76415	−	3.66068i	0.308814	−	0.237287i
$239$		−	20.3237i		−	1.31463i	−0.753615	−	0.657317i	$-0.771691\pi$
$239$		−	20.3237i		−	1.31463i	0.753615	−	0.657317i	$-0.228309\pi$
$240$	4.00562	−	2.32683i	0.258562	−	0.150196i
$241$	5.48096	−	3.16443i	0.353060	−	0.203839i	−0.312972	−	0.949762i	$-0.601325\pi$
$241$	5.48096	−	3.16443i	0.353060	−	0.203839i	0.666032	+	0.745923i	$0.267991\pi$
$242$	−5.10795	+	12.3548i	−0.328352	+	0.794200i
$243$	18.5540	−	10.7122i	1.19024	−	0.687185i
$244$	−21.0277	−	5.60449i	−1.34616	−	0.358791i
$245$	−1.90134	−	1.09774i	−0.121472	−	0.0701319i
$246$	4.26959	−	0.564982i	0.272219	−	0.0360219i
$247$	−10.5844	−	11.5867i	−0.673469	−	0.737246i
$248$	12.6897	−	5.28584i	0.805798	−	0.335651i
$249$	−25.3195	−	14.6182i	−1.60456	−	0.926391i
$250$	6.16587	+	2.54920i	0.389964	+	0.161226i
$251$	12.1536	+	21.0507i	0.767131	+	1.32871i	0.939113	+	0.343609i	$0.111650\pi$
$251$	12.1536	+	21.0507i	0.767131	+	1.32871i	−0.171982	+	0.985100i	$0.555017\pi$
$252$	−8.32007	−	2.21754i	−0.524115	−	0.139692i
$253$	−6.87144	+	3.96723i	−0.432004	+	0.249417i
$254$	−21.3527	+	2.82554i	−1.33979	+	0.177290i
$255$	3.14009			0.196640
$256$	−15.9998	+	0.0848522i	−0.999986	+	0.00530326i
$257$	7.08286	−	4.08929i	0.441817	−	0.255083i	−0.262551	−	0.964918i	$-0.584564\pi$
$257$	7.08286	−	4.08929i	0.441817	−	0.255083i	0.704368	+	0.709835i	$0.251231\pi$
$258$	−4.25361	−	32.1447i	−0.264818	−	2.00124i
$259$		−	17.1916i		−	1.06823i
$260$	−2.45628	+	2.46280i	−0.152332	+	0.152736i
$261$	1.91008	−	3.30836i	0.118231	−	0.204782i
$262$	7.14046	+	9.29287i	0.441139	+	0.574115i
$263$	19.0322	+	10.9882i	1.17358	+	0.677564i	0.954520	−	0.298148i	$-0.0963689\pi$
$263$	19.0322	+	10.9882i	1.17358	+	0.677564i	0.219056	+	0.975712i	$0.429702\pi$
$264$	−8.36302	−	1.08410i	−0.514708	−	0.0667215i
$265$		−	1.44941i		−	0.0890364i
$266$	9.51055	+	1.68562i	0.583129	+	0.103352i
$267$	−30.9015			−1.89114
$268$	7.19569	+	1.91786i	0.439547	+	0.117152i
$269$	1.94226	−	3.36410i	0.118422	−	0.205113i	−0.800721	−	0.599038i	$-0.795550\pi$
$269$	1.94226	−	3.36410i	0.118422	−	0.205113i	0.919142	+	0.393925i	$0.128883\pi$
$270$	0.251770	+	0.327664i	0.0153223	+	0.0199410i
$271$	−1.81233	−	1.04635i	−0.110091	−	0.0635611i	0.443943	−	0.896055i	$-0.353579\pi$
$271$	−1.81233	−	1.04635i	−0.110091	−	0.0635611i	−0.554035	+	0.832494i	$0.686912\pi$
$272$	−9.40695	−	5.39789i	−0.570380	−	0.327295i
$273$	13.5244			0.818531
$274$	24.9828	−	3.30590i	1.50927	−	0.199717i
$275$	−2.96397	−	5.13374i	−0.178734	−	0.309576i
$276$	21.6603	+	21.6029i	1.30380	+	1.30034i
$277$			27.8262i			1.67191i	0.548797	+	0.835956i	$0.315086\pi$
$277$			27.8262i			1.67191i	−0.548797	+	0.835956i	$0.684914\pi$
$278$	11.6688	−	1.54409i	0.699847	−	0.0926086i
$279$	−6.67712	−	11.5651i	−0.399749	−	0.692385i
$280$	0.275208	−	2.12303i	0.0164468	−	0.126875i
$281$	−20.0761	+	11.5910i	−1.19764	+	0.691458i	−0.960029	−	0.279902i	$-0.909698\pi$
$281$	−20.0761	+	11.5910i	−1.19764	+	0.691458i	−0.237612	+	0.971360i	$0.576365\pi$
$282$	−10.8710	+	26.2941i	−0.647357	+	1.56579i
$283$	1.40718	−	2.43730i	0.0836480	−	0.144883i	−0.821166	−	0.570689i	$-0.806676\pi$
$283$	1.40718	−	2.43730i	0.0836480	−	0.144883i	0.904814	+	0.425806i	$0.140010\pi$
$284$	−25.5945	+	6.89440i	−1.51875	+	0.409108i
$285$	3.40466	+	3.72707i	0.201674	+	0.220773i
$286$	6.27733	−	0.830660i	0.371186	−	0.0491179i
$287$	0.995162	−	1.72367i	0.0587426	−	0.101745i
$288$	2.07988	+	15.4035i	0.122558	+	0.907662i
$289$	4.82413	+	8.35564i	0.283772	+	0.491508i
$290$	0.877731	+	0.362887i	0.0515422	+	0.0213094i
$291$	3.35959	+	5.81899i	0.196943	+	0.341115i
$292$	1.91002	−	0.514504i	0.111776	−	0.0301091i
$293$	−8.65633			−0.505708			−0.252854	−	0.967504i	$-0.581369\pi$
$293$	−8.65633			−0.505708			−0.252854	+	0.967504i	$0.581369\pi$
$294$	12.2190	−	9.38887i	0.712628	−	0.547570i
$295$	−1.23752	−	2.14344i	−0.0720510	−	0.124796i
$296$	−28.6476	+	11.9330i	−1.66511	+	0.693593i
$297$		−	0.752242i		−	0.0436495i
$298$	−20.8382	+	16.0117i	−1.20713	+	0.927533i
$299$	−19.8929	−	11.4852i	−1.15043	−	0.664204i
$300$	−16.1398	+	16.1827i	−0.931834	+	0.934308i
$301$	−12.9771	−	7.49233i	−0.747987	−	0.431851i
$302$	−2.46793	+	5.96930i	−0.142013	+	0.343495i
$303$	−1.81589			−0.104320
$304$	−3.79259	−	17.0181i	−0.217520	−	0.976056i
$305$	−5.25610			−0.300964
$306$	−4.02553	+	9.73674i	−0.230124	+	0.556612i
$307$	8.98393	+	5.18688i	0.512740	+	0.296031i	0.733959	−	0.679194i	$-0.237670\pi$
$307$	8.98393	+	5.18688i	0.512740	+	0.296031i	−0.221219	+	0.975224i	$0.571004\pi$
$308$	−2.75206	+	2.75937i	−0.156813	+	0.157230i
$309$	8.43268	+	4.86861i	0.479719	+	0.276966i
$310$	2.63275	−	2.02296i	0.149530	−	0.114896i
$311$			20.7808i			1.17837i	0.807997	+	0.589186i	$0.200551\pi$
$311$			20.7808i			1.17837i	−0.807997	+	0.589186i	$0.799449\pi$
$312$	−9.38751	−	22.5366i	−0.531463	−	1.27588i
$313$	−11.9901	−	20.7674i	−0.677720	−	1.17384i	−0.975666	−	0.219262i	$-0.929635\pi$
$313$	−11.9901	−	20.7674i	−0.677720	−	1.17384i	0.297946	−	0.954583i	$-0.403698\pi$
$314$	20.8468	−	16.0183i	1.17645	−	0.903964i
$315$	−2.07969			−0.117177
$316$	−22.4521	+	6.04795i	−1.26303	+	0.340224i
$317$	9.45498	+	16.3765i	0.531045	+	0.919797i	0.999344	+	0.0362265i	$0.0115338\pi$
$317$	9.45498	+	16.3765i	0.531045	+	0.919797i	−0.468299	+	0.883570i	$0.655133\pi$
$318$	9.40129	+	3.88684i	0.527198	+	0.217963i
$319$	−0.864515	−	1.49738i	−0.0484035	−	0.0838374i
$320$	−3.72878	+	1.01504i	−0.208445	+	0.0567423i
$321$	−4.97852	+	8.62305i	−0.277874	+	0.481292i
$322$	14.0153	−	1.85461i	0.781043	−	0.103353i
$323$	3.57138	−	11.2662i	0.198717	−	0.626871i
$324$	−18.7193	+	5.04242i	−1.03996	+	0.280134i
$325$	8.58071	−	14.8622i	0.475972	−	0.824408i
$326$	7.16572	−	17.3321i	0.396873	−	0.959935i
$327$	−37.6635	+	21.7450i	−2.08279	+	1.20250i
$328$	−3.56304	−	0.461876i	−0.196736	−	0.0255028i
$329$	6.57450	+	11.3874i	0.362464	+	0.627806i
$330$	−2.01921	+	0.267196i	−0.111154	+	0.0147087i
$331$			15.9594i			0.877208i	0.898680	+	0.438604i	$0.144527\pi$
$331$			15.9594i			0.877208i	−0.898680	+	0.438604i	$0.855473\pi$
$332$	17.2690	+	17.2233i	0.947759	+	0.945250i
$333$	15.0739	+	26.1087i	0.826044	+	1.43075i
$334$	−14.0519	+	1.85944i	−0.768883	+	0.101744i
$335$	1.79864			0.0982702
$336$	13.0326	+	7.47836i	0.710986	+	0.407978i
$337$	−21.3485	−	12.3256i	−1.16293	−	0.671418i	−0.210925	−	0.977502i	$-0.567648\pi$
$337$	−21.3485	−	12.3256i	−1.16293	−	0.671418i	−0.952004	+	0.306085i	$0.900981\pi$
$338$	−0.0325627	−	0.0423784i	−0.00177118	−	0.00230508i
$339$	8.39503	−	14.5406i	0.455955	−	0.789738i
$340$	−2.53118	−	0.674631i	−0.137272	−	0.0365870i
$341$	−6.04422			−0.327313
$342$	−15.9216	+	5.77908i	−0.860940	+	0.312497i
$343$		−	18.0893i		−	0.976731i
$344$	−3.47735	+	26.8252i	−0.187486	+	1.44632i
$345$	6.39889	+	3.69440i	0.344504	+	0.198900i
$346$	−13.3574	−	17.3839i	−0.718101	−	0.934563i
$347$	4.57443	−	7.92314i	0.245568	−	0.425336i	−0.716723	−	0.697358i	$-0.754359\pi$
$347$	4.57443	−	7.92314i	0.245568	−	0.425336i	0.962291	+	0.272022i	$0.0876922\pi$
$348$	−4.70758	+	4.72008i	−0.252353	+	0.253023i
$349$		−	17.8070i		−	0.953189i	−0.879123	−	0.476595i	$-0.841871\pi$
$349$		−	17.8070i		−	0.953189i	0.879123	−	0.476595i	$-0.158129\pi$
$350$	1.38560	+	10.4710i	0.0740634	+	0.559700i
$351$	1.88599	−	1.08887i	0.100666	−	0.0581198i
$352$	6.50839	+	2.67062i	0.346898	+	0.142345i
$353$	23.3856			1.24469			0.622344	−	0.782744i	$-0.286181\pi$
$353$	23.3856			1.24469			0.622344	+	0.782744i	$0.286181\pi$
$354$	17.2216	−	2.27888i	0.915319	−	0.121121i
$355$	−5.54443	+	3.20108i	−0.294268	+	0.169896i
$356$	24.9092	+	6.63902i	1.32018	+	0.351867i
$357$	5.09263	+	8.82070i	0.269531	+	0.466841i
$358$	3.73901	+	1.54584i	0.197613	+	0.0817004i
$359$	11.4051	+	6.58476i	0.601940	+	0.347530i	0.769805	−	0.638280i	$-0.220354\pi$
$359$	11.4051	+	6.58476i	0.601940	+	0.347530i	−0.167864	+	0.985810i	$0.553687\pi$
$360$	1.44355	+	3.46553i	0.0760818	+	0.182650i
$361$	17.2446	−	7.97650i	0.907609	−	0.419816i
$362$	−0.855609	+	0.113220i	−0.0449698	+	0.00595072i
$363$	−19.6275	−	11.3320i	−1.03018	−	0.594773i
$364$	−10.9018	−	2.90564i	−0.571408	−	0.152297i
$365$	0.413761	−	0.238885i	0.0216572	−	0.0125038i
$366$	14.0952	−	34.0927i	0.736766	−	1.78205i
$367$	−13.2710	+	7.66199i	−0.692738	+	0.399953i	−0.804637	−	0.593767i	$-0.797640\pi$
$367$	−13.2710	+	7.66199i	−0.692738	+	0.399953i	0.111899	+	0.993720i	$0.464307\pi$
$368$	−12.8188	−	22.0674i	−0.668224	−	1.15034i
$369$			3.49030i			0.181698i
$370$	−5.94356	+	4.56691i	−0.308991	+	0.237423i
$371$	4.07147	−	2.35067i	0.211380	−	0.122041i
$372$	6.06131	+	22.5018i	0.314265	+	1.16666i
$373$	−8.33115			−0.431370			−0.215685	−	0.976463i	$-0.569199\pi$
$373$	−8.33115			−0.431370			−0.215685	+	0.976463i	$0.569199\pi$
$374$	2.90551	+	3.78134i	0.150240	+	0.195528i
$375$	−5.65539	+	9.79541i	−0.292043	+	0.505833i
$376$	14.4121	−	18.8597i	0.743246	−	0.972616i
$377$	2.50278	−	4.33494i	0.128900	−	0.223261i
$378$	−0.512103	+	1.23865i	−0.0263397	+	0.0637092i
$379$			10.4481i			0.536682i	0.963324	+	0.268341i	$0.0864754\pi$
$379$			10.4481i			0.536682i	−0.963324	+	0.268341i	$0.913525\pi$
$380$	−1.94370	−	3.73581i	−0.0997096	−	0.191643i
$381$		−	36.5136i		−	1.87065i
$382$	28.6262	+	11.8351i	1.46464	+	0.605538i
$383$	4.22512	−	7.31812i	0.215893	−	0.373938i	−0.737655	−	0.675178i	$-0.764067\pi$
$383$	4.22512	−	7.31812i	0.215893	−	0.373938i	0.953549	+	0.301239i	$0.0974003\pi$
$384$	3.41555	−	26.9080i	0.174299	−	1.37314i
$385$	−0.470640	+	0.815173i	−0.0239861	+	0.0415451i
$386$	5.96208	−	4.58115i	0.303462	−	0.233174i
$387$	26.2776			1.33577
$388$	−1.45794	−	5.41239i	−0.0740156	−	0.274772i
$389$	5.29150	−	3.05505i	0.268290	−	0.154897i	−0.359820	−	0.933022i	$-0.617162\pi$
$389$	5.29150	−	3.05505i	0.268290	−	0.154897i	0.628110	+	0.778124i	$0.283829\pi$
$390$	−3.59272	−	4.67570i	−0.181924	−	0.236763i
$391$		−	17.2991i		−	0.874851i
$392$	−11.8667	+	4.94303i	−0.599360	+	0.249661i
$393$	−17.2055	+	9.93359i	−0.867902	+	0.501083i
$394$	−1.19390	−	0.493601i	−0.0601476	−	0.0248673i
$395$	−4.86372	+	2.80807i	−0.244720	+	0.141289i
$396$	1.76007	−	6.60368i	0.0884469	−	0.331848i
$397$	19.5160	+	11.2676i	0.979481	+	0.565504i	0.902113	−	0.431499i	$-0.142015\pi$
$397$	19.5160	+	11.2676i	0.979481	+	0.565504i	0.0773678	+	0.997003i	$0.475348\pi$
$398$	3.72238	+	28.1301i	0.186586	+	1.41004i
$399$	−4.94787	+	15.6085i	−0.247703	+	0.781403i
$400$	16.4868	−	9.57706i	0.824342	−	0.478853i
$401$	−1.59335	−	0.919919i	−0.0795679	−	0.0459386i	0.459688	−	0.888080i	$-0.347961\pi$
$401$	−1.59335	−	0.919919i	−0.0795679	−	0.0459386i	−0.539256	+	0.842142i	$0.681295\pi$
$402$	−4.82337	+	11.6665i	−0.240568	+	0.581873i
$403$	−8.74903	−	15.1538i	−0.435820	−	0.754863i
$404$	1.46376	+	0.390135i	0.0728250	+	0.0194100i
$405$	−4.05508	+	2.34120i	−0.201499	+	0.116335i
$406$	0.404145	+	3.05414i	0.0200574	+	0.151574i
$407$	13.6451			0.676361
$408$	11.1637	−	14.6088i	0.552683	−	0.723244i
$409$	−31.6805	+	18.2907i	−1.56650	+	0.904418i	−0.569925	+	0.821696i	$0.693028\pi$
$409$	−31.6805	+	18.2907i	−1.56650	+	0.904418i	−0.996573	+	0.0827216i	$0.973639\pi$
$410$	−0.860278	+	0.113838i	−0.0424861	+	0.00562206i
$411$			42.7212i			2.10728i
$412$	−5.75146	−	5.73623i	−0.283354	−	0.282604i
$413$	4.01404	−	6.95252i	0.197518	−	0.342111i
$414$	−19.6588	+	15.1054i	−0.966177	+	0.742392i
$415$	5.10161	+	2.94542i	0.250428	+	0.144585i
$416$	2.72526	+	20.1833i	0.133617	+	0.989565i
$417$			19.9539i			0.977144i
$418$	−1.33788	+	7.54858i	−0.0654381	+	0.369213i
$419$	4.03779			0.197259			0.0986294	−	0.995124i	$-0.468554\pi$
$419$	4.03779			0.197259			0.0986294	+	0.995124i	$0.468554\pi$
$420$	3.50674	+	0.934648i	0.171112	+	0.0456062i
$421$	−3.23520	+	5.60354i	−0.157674	+	0.273100i	−0.934030	−	0.357196i	$-0.883733\pi$
$421$	−3.23520	+	5.60354i	−0.157674	+	0.273100i	0.776355	+	0.630295i	$0.217066\pi$
$422$	−27.9327	+	21.4629i	−1.35974	+	1.04480i
$423$	−19.9693	−	11.5293i	−0.970939	−	0.560572i
$424$	−6.74317	−	5.15294i	−0.327477	−	0.250249i
$425$	12.9244			0.626923
$426$	−5.89479	−	44.5471i	−0.285603	−	2.15832i
$427$	−8.52441	−	14.7647i	−0.412525	−	0.714515i
$428$	5.86573	−	5.88130i	0.283531	−	0.284283i
$429$			10.7344i			0.518260i
$430$	0.857058	+	6.47682i	0.0413310	+	0.312340i
$431$	3.17434	+	5.49811i	0.152902	+	0.264835i	0.932293	−	0.361703i	$-0.117805\pi$
$431$	3.17434	+	5.49811i	0.152902	+	0.264835i	−0.779391	+	0.626538i	$0.784471\pi$
$432$	2.41951	−	0.00641568i	0.116409	−	0.000308675i
$433$	20.1286	−	11.6213i	0.967320	−	0.558482i	0.0689019	−	0.997623i	$-0.478050\pi$
$433$	20.1286	−	11.6213i	0.967320	−	0.558482i	0.898418	+	0.439141i	$0.144717\pi$
$434$	9.95245	+	4.11471i	0.477733	+	0.197513i
$435$	−0.805062	+	1.39441i	−0.0385997	+	0.0668567i
$436$	35.0317	−	9.43652i	1.67772	−	0.451927i
$437$	20.5328	−	18.7566i	0.982219	−	0.897250i
$438$	0.439906	+	3.32439i	0.0210195	+	0.158845i
$439$	−5.22682	+	9.05312i	−0.249462	+	0.432082i	−0.963377	−	0.268151i	$-0.913587\pi$
$439$	−5.22682	+	9.05312i	−0.249462	+	0.432082i	0.713914	+	0.700233i	$0.246921\pi$
$440$	1.68506	+	0.218434i	0.0803321	+	0.0104134i
$441$	6.24408	+	10.8151i	0.297337	+	0.515003i
$442$	−5.27465	+	12.7580i	−0.250890	+	0.606838i
$443$	7.15226	+	12.3881i	0.339814	+	0.588575i	0.984398	−	0.175959i	$-0.0563026\pi$
$443$	7.15226	+	12.3881i	0.339814	+	0.588575i	−0.644584	+	0.764534i	$0.722969\pi$
$444$	−13.6837	−	50.7987i	−0.649398	−	2.41080i
$445$	6.22632			0.295156
$446$	−3.01587	−	3.92497i	−0.142806	−	0.185853i
$447$	−22.2750	−	38.5814i	−1.05357	−	1.82484i
$448$	−8.89868	−	8.82817i	−0.420423	−	0.417092i
$449$		−	35.1956i		−	1.66098i	−0.557030	−	0.830492i	$-0.688059\pi$
$449$		−	35.1956i		−	1.66098i	0.557030	−	0.830492i	$-0.311941\pi$
$450$	−11.2855	−	14.6873i	−0.532002	−	0.692368i
$451$	1.36809	+	0.789866i	0.0644208	+	0.0371933i
$452$	−9.89108	+	9.91734i	−0.465237	+	0.466472i
$453$	−9.48312	−	5.47508i	−0.445556	−	0.257242i
$454$	6.91862	+	2.86041i	0.324707	+	0.134246i
$455$	−2.72502			−0.127751
$456$	29.4440	−	2.58918i	1.37884	−	0.121249i
$457$	5.76335			0.269598			0.134799	−	0.990873i	$-0.456961\pi$
$457$	5.76335			0.269598			0.134799	+	0.990873i	$0.456961\pi$
$458$	1.57966	+	0.653088i	0.0738124	+	0.0305168i
$459$	1.42035	+	0.820037i	0.0662960	+	0.0382760i
$460$	−4.36432	−	4.35277i	−0.203488	−	0.202949i
$461$	−23.7050	−	13.6861i	−1.10405	−	0.637424i	−0.166769	−	0.985996i	$-0.553333\pi$
$461$	−23.7050	−	13.6861i	−1.10405	−	0.637424i	−0.937282	+	0.348572i	$0.886667\pi$
$462$	−4.02535	−	5.23875i	−0.187276	−	0.243729i
$463$			9.63243i			0.447657i	0.974629	+	0.223828i	$0.0718555\pi$
$463$			9.63243i			0.447657i	−0.974629	+	0.223828i	$0.928144\pi$
$464$	4.80880	−	2.79339i	0.223243	−	0.129680i
$465$	2.81428	+	4.87447i	0.130509	+	0.226048i
$466$	−9.63242	−	12.5360i	−0.446213	−	0.580719i
$467$	14.1545			0.654992			0.327496	−	0.944853i	$-0.393795\pi$
$467$	14.1545			0.654992			0.327496	+	0.944853i	$0.393795\pi$
$468$	19.1041	−	5.14610i	0.883089	−	0.237878i
$469$	2.91706	+	5.05249i	0.134697	+	0.233302i
$470$	2.19039	−	5.29799i	0.101035	−	0.244378i
$471$	22.2841	+	38.5973i	1.02680	+	1.77847i
$472$	−14.3717	−	1.86300i	−0.661511	−	0.0857515i
$473$	5.94671	−	10.3000i	0.273430	−	0.473594i
$474$	−5.17106	−	39.0779i	−0.237515	−	1.79491i
$475$	14.0133	+	15.3404i	0.642974	+	0.703864i
$476$	−2.21001	−	8.20435i	−0.101296	−	0.376046i
$477$	−4.12221	+	7.13987i	−0.188743	+	0.326912i
$478$	−26.5615	−	10.9815i	−1.21490	−	0.502283i
$479$	−20.5947	+	11.8903i	−0.940995	+	0.543284i	−0.890272	−	0.455429i	$-0.849486\pi$
$479$	−20.5947	+	11.8903i	−0.940995	+	0.543284i	−0.0507227	+	0.998713i	$0.516152\pi$
$480$	−0.876628	−	6.49229i	−0.0400124	−	0.296331i
$481$	19.7513	+	34.2103i	0.900582	+	1.55985i
$482$	−1.17414	−	8.87302i	−0.0534806	−	0.404155i
$483$			23.9665i			1.09051i
$484$	13.3868	+	13.3514i	0.608492	+	0.606881i
$485$	−0.676923	−	1.17246i	−0.0307375	−	0.0532389i
$486$	−3.97467	−	30.0367i	−0.180295	−	1.36249i
$487$	7.31176			0.331327			0.165664	−	0.986182i	$-0.447023\pi$
$487$	7.31176			0.331327			0.165664	+	0.986182i	$0.447023\pi$
$488$	−18.6865	+	24.4533i	−0.845899	+	1.10695i
$489$	27.5346	+	15.8971i	1.24516	+	0.718892i
$490$	−2.46201	+	1.89176i	−0.111222	+	0.0854609i
$491$	7.42662	−	12.8633i	0.335159	−	0.580512i	−0.648357	−	0.761337i	$-0.724543\pi$
$491$	7.42662	−	12.8633i	0.335159	−	0.580512i	0.983515	+	0.180825i	$0.0578768\pi$
$492$	1.56860	−	5.88530i	0.0707180	−	0.265330i
$493$	3.76971			0.169779
$494$	−20.8620	+	7.57232i	−0.938627	+	0.340695i
$495$		−	1.65066i		−	0.0741917i
$496$	−0.0515496	−	19.4406i	−0.00231464	−	0.872907i
$497$	−17.9841	−	10.3831i	−0.806696	−	0.465746i
$498$	−32.7857	+	25.1919i	−1.46916	+	1.12888i
$499$	−1.07280	+	1.85814i	−0.0480251	+	0.0831819i	−0.889039	−	0.457832i	$-0.848626\pi$
$499$	−1.07280	+	1.85814i	−0.0480251	+	0.0831819i	0.841014	+	0.541014i	$0.181959\pi$
$500$	6.66321	−	6.68090i	0.297988	−	0.298779i
$501$		−	24.0290i		−	1.07353i
$502$	34.0786	−	4.50952i	1.52100	−	0.201270i
$503$	17.1288	−	9.88932i	0.763736	−	0.440943i	−0.0668997	−	0.997760i	$-0.521311\pi$
$503$	17.1288	−	9.88932i	0.763736	−	0.440943i	0.830635	+	0.556817i	$0.187977\pi$
$504$	−7.39372	+	9.67547i	−0.329343	+	0.430980i
$505$	0.365884			0.0162816
$506$	1.47201	+	11.1240i	0.0654389	+	0.494524i
$507$	0.0784624	−	0.0453003i	0.00348464	−	0.00201186i
$508$	−7.84475	+	29.4331i	−0.348055	+	1.30588i
$509$	−7.29492	−	12.6352i	−0.323342	−	0.560044i	0.657834	−	0.753163i	$-0.271473\pi$
$509$	−7.29492	−	12.6352i	−0.323342	−	0.560044i	−0.981175	+	0.193119i	$0.938140\pi$
$510$	1.69668	−	4.10385i	0.0751303	−	0.181721i
$511$	1.34208	+	0.774853i	0.0593703	+	0.0342775i
$512$	−8.53426	+	20.9563i	−0.377165	+	0.926146i
$513$	0.566688	+	2.57498i	0.0250199	+	0.113688i
$514$	−1.51730	−	11.4663i	−0.0669253	−	0.505757i
$515$	−1.69910	−	0.980974i	−0.0748712	−	0.0432269i
$516$	−44.3089	−	11.8096i	−1.95059	−	0.519889i
$517$	−9.03822	+	5.21822i	−0.397500	+	0.229497i
$518$	−22.4681	−	9.28914i	−0.987191	−	0.408141i
$519$	32.1858	−	18.5825i	1.41280	−	0.815679i
$520$	1.89148	+	4.54088i	0.0829471	+	0.199131i
$521$			27.1524i			1.18957i	0.803885	+	0.594784i	$0.202763\pi$
$521$			27.1524i			1.18957i	−0.803885	+	0.594784i	$0.797237\pi$
$522$	−3.29169	−	4.28393i	−0.144073	−	0.187502i
$523$	1.66719	−	0.962550i	0.0729009	−	0.0420894i	−0.463106	−	0.886303i	$-0.653265\pi$
$523$	1.66719	−	0.962550i	0.0729009	−	0.0420894i	0.536007	+	0.844213i	$0.319932\pi$
$524$	16.0033	−	4.31081i	0.699105	−	0.188319i
$525$	−17.9057			−0.781468
$526$	24.6444	−	18.9363i	1.07455	−	0.825662i
$527$	6.58894	−	11.4124i	0.287019	−	0.497131i
$528$	−5.93562	+	10.3440i	−0.258315	+	0.450166i
$529$	8.85283	−	15.3336i	0.384906	−	0.666676i
$530$	−1.89426	−	0.783158i	−0.0822814	−	0.0340182i
$531$			14.0783i			0.610947i
$532$	7.34180	−	11.5188i	0.318308	−	0.499401i
$533$			4.57334i			0.198093i
$534$	−16.6970	+	40.3858i	−0.722549	+	1.74766i
$535$	1.00312	−	1.73745i	0.0433686	−	0.0751167i
$536$	6.39454	−	8.36793i	0.276202	−	0.361439i
$537$	−3.42944	+	5.93997i	−0.147991	+	0.256329i
$538$	−3.34715	−	4.35611i	−0.144306	−	0.187805i
$539$	5.65222			0.243458
$540$	0.564270	−	0.151998i	0.0242823	−	0.00654094i
$541$	−30.5146	+	17.6176i	−1.31193	+	0.757441i	−0.982415	−	0.186711i	$-0.940217\pi$
$541$	−30.5146	+	17.6176i	−1.31193	+	0.757441i	−0.329511	+	0.944152i	$0.606884\pi$
$542$	−2.34675	+	1.80320i	−0.100802	+	0.0774540i
$543$		−	1.46311i		−	0.0627880i
$544$	−12.1375	+	9.37750i	−0.520390	+	0.402057i
$545$	7.58879	−	4.38139i	0.325068	−	0.187678i
$546$	7.30761	−	17.6753i	0.312737	−	0.756432i
$547$	−7.93165	+	4.57934i	−0.339133	+	0.195798i	−0.659888	−	0.751364i	$-0.729396\pi$
$547$	−7.93165	+	4.57934i	−0.339133	+	0.195798i	0.320756	+	0.947162i	$0.396063\pi$
$548$	9.17842	−	34.4369i	0.392083	−	1.47107i
$549$	25.8919	+	14.9487i	1.10504	+	0.637995i
$550$	−8.31092	+	1.09976i	−0.354379	+	0.0468939i
$551$	4.08733	+	4.47439i	0.174126	+	0.190616i
$552$	39.9370	−	16.6356i	1.69983	−	0.708058i
$553$	−15.7761	−	9.10833i	−0.670868	−	0.387326i
$554$	36.3666	+	15.0353i	1.54507	+	0.638789i
$555$	−6.35335	−	11.0043i	−0.269685	−	0.467108i
$556$	4.28698	−	16.0845i	0.181808	−	0.682135i
$557$	−26.0361	+	15.0319i	−1.10318	+	0.636924i	−0.937056	−	0.349180i	$-0.886460\pi$
$557$	−26.0361	+	15.0319i	−1.10318	+	0.636924i	−0.166129	+	0.986104i	$0.553127\pi$
$558$	−18.7225	+	2.47750i	−0.792589	+	0.104881i
$559$	34.4315			1.45630
$560$	−2.62593	−	1.50681i	−0.110966	−	0.0636744i
$561$	−7.00104	+	4.04205i	−0.295584	+	0.170656i
$562$	4.30074	+	32.5009i	0.181416	+	1.37097i
$563$		−	35.3632i		−	1.49038i	−0.666851	−	0.745191i	$-0.732358\pi$
$563$		−	35.3632i		−	1.49038i	0.666851	−	0.745191i	$-0.267642\pi$
$564$	28.4905	+	28.4150i	1.19966	+	1.19649i
$565$	−1.69151	+	2.92978i	−0.0711624	+	0.123257i
$566$	−2.42502	−	3.15602i	−0.101931	−	0.132657i
$567$	−13.1532	−	7.59398i	−0.552381	−	0.318917i
$568$	−4.81902	+	37.1752i	−0.202201	+	1.55984i
$569$		−	24.5320i		−	1.02844i	−0.857660	−	0.514218i	$-0.828082\pi$
$569$		−	24.5320i		−	1.02844i	0.857660	−	0.514218i	$-0.171918\pi$
$570$	6.71063	−	2.43577i	0.281077	−	0.102023i
$571$	16.3080			0.682467			0.341233	−	0.939979i	$-0.389155\pi$
$571$	16.3080			0.682467			0.341233	+	0.939979i	$0.389155\pi$
$572$	2.30622	−	8.65280i	0.0964279	−	0.361792i
$573$	−26.2562	+	45.4770i	−1.09687	+	1.89983i
$574$	−1.71499	−	2.23195i	−0.0715822	−	0.0931598i
$575$	26.3373	+	15.2059i	1.09834	+	0.634128i
$576$	21.2550	+	5.60476i	0.885627	+	0.233531i
$577$	−13.0747			−0.544305			−0.272153	−	0.962254i	$-0.587736\pi$
$577$	−13.0747			−0.544305			−0.272153	+	0.962254i	$0.587736\pi$
$578$	13.5268	−	1.78996i	0.562640	−	0.0744524i
$579$	6.37315	+	11.0386i	0.264859	+	0.458750i
$580$	0.948529	−	0.951047i	0.0393855	−	0.0394901i
$581$			19.1076i			0.792719i
$582$	9.42025	−	1.24655i	0.390482	−	0.0516713i
$583$	1.86574	+	3.23155i	0.0772710	+	0.133837i
$584$	0.359626	−	2.77425i	0.0148814	−	0.114799i
$585$	4.13846	−	2.38934i	0.171104	−	0.0987870i
$586$	−4.67728	+	11.3131i	−0.193216	+	0.467342i
$587$	8.90580	−	15.4253i	0.367582	−	0.636671i	−0.621605	−	0.783331i	$-0.713519\pi$
$587$	8.90580	−	15.4253i	0.367582	−	0.636671i	0.989187	+	0.146660i	$0.0468524\pi$
$588$	−5.66821	−	21.0424i	−0.233753	−	0.867774i
$589$	20.6898	−	4.55330i	0.852510	−	0.187615i
$590$	−3.46998	+	0.459171i	−0.142857	+	0.0189038i
$591$	1.09505	−	1.89668i	0.0450443	−	0.0780191i
$592$	0.116375	+	43.8879i	0.00478300	+	1.80378i
$593$	−14.1110	−	24.4410i	−0.579471	−	1.00367i	−0.995540	−	0.0943399i	$-0.969926\pi$
$593$	−14.1110	−	24.4410i	−0.579471	−	1.00367i	0.416069	−	0.909333i	$-0.363407\pi$
$594$	−0.983122	−	0.406459i	−0.0403380	−	0.0166772i
$595$	−1.02611	−	1.77728i	−0.0420665	−	0.0728613i
$596$	9.66651	+	35.8855i	0.395956	+	1.46993i
$597$	−48.1031			−1.96873
$598$	−25.7589	+	19.7927i	−1.05336	+	0.809382i
$599$	−18.3746	−	31.8258i	−0.750766	−	1.30037i	−0.947452	−	0.319899i	$-0.896351\pi$
$599$	−18.3746	−	31.8258i	−0.750766	−	1.30037i	0.196685	−	0.980467i	$-0.436982\pi$
$600$	12.4287	+	29.8375i	0.507398	+	1.21811i
$601$			13.0119i			0.530767i	0.964143	+	0.265384i	$0.0854986\pi$
$601$			13.0119i			0.530767i	−0.964143	+	0.265384i	$0.914501\pi$
$602$	−16.8038	+	12.9117i	−0.684872	+	0.526242i
$603$	−8.86022	−	5.11545i	−0.360816	−	0.208317i
$604$	6.46791	+	6.45078i	0.263175	+	0.262479i
$605$	3.95474	+	2.28327i	0.160783	+	0.0928281i
$606$	−0.981182	+	2.37323i	−0.0398578	+	0.0964059i
$607$	28.9061			1.17326			0.586631	−	0.809854i	$-0.300454\pi$
$607$	28.9061			1.17326			0.586631	+	0.809854i	$0.300454\pi$
$608$	−24.2906	−	4.23878i	−0.985113	−	0.171905i
$609$	−5.22264			−0.211632
$610$	−2.84003	+	6.86931i	−0.114989	+	0.278130i
$611$	−26.1657	−	15.1068i	−1.05855	−	0.611155i
$612$	10.5500	+	10.5221i	0.426460	+	0.425331i
$613$	−25.3842	−	14.6556i	−1.02526	−	0.591934i	−0.109636	−	0.993972i	$-0.534969\pi$
$613$	−25.3842	−	14.6556i	−1.02526	−	0.591934i	−0.915623	+	0.402038i	$0.868302\pi$
$614$	11.6331	−	8.93867i	0.469475	−	0.360735i
$615$		−	1.47109i		−	0.0593202i
$616$	2.11926	+	5.08770i	0.0853873	+	0.204989i
$617$	−2.44550	−	4.23572i	−0.0984519	−	0.170524i	0.812592	−	0.582833i	$-0.198056\pi$
$617$	−2.44550	−	4.23572i	−0.0984519	−	0.170524i	−0.911044	+	0.412309i	$0.864722\pi$
$618$	10.9193	−	8.39020i	0.439240	−	0.337503i
$619$	−31.8807			−1.28139			−0.640696	−	0.767795i	$-0.721354\pi$
$619$	−31.8807			−1.28139			−0.640696	+	0.767795i	$0.721354\pi$
$620$	−1.22129	−	4.53387i	−0.0490482	−	0.182085i
$621$	1.92959	+	3.34215i	0.0774319	+	0.134116i
$622$	27.1589	+	11.2285i	1.08897	+	0.450222i
$623$	10.0979	+	17.4901i	0.404565	+	0.700727i
$624$	−34.5259	+	0.0915506i	−1.38214	+	0.00366496i
$625$	−10.7771	+	18.6665i	−0.431085	+	0.746662i
$626$	−33.6200	+	4.44883i	−1.34373	+	0.177811i
$627$	−12.3886	−	3.92715i	−0.494751	−	0.156835i
$628$	−9.67049	−	35.9003i	−0.385894	−	1.43258i
$629$	−14.8748	+	25.7639i	−0.593098	+	1.02728i
$630$	−1.12372	+	2.71799i	−0.0447700	+	0.108287i
$631$	7.83877	−	4.52572i	0.312057	−	0.180166i	−0.335790	−	0.941937i	$-0.609003\pi$
$631$	7.83877	−	4.52572i	0.312057	−	0.180166i	0.647846	+	0.761771i	$0.275670\pi$
$632$	−4.22737	+	32.6111i	−0.168156	+	1.29720i
$633$	−29.8585	−	51.7165i	−1.18677	−	2.05555i
$634$	26.5116	−	3.50820i	1.05291	−	0.139329i
$635$			7.35711i			0.291958i
$636$	10.1596	−	10.1866i	0.402854	−	0.403924i
$637$	8.18161	+	14.1710i	0.324167	+	0.561474i
$638$	−2.42409	+	0.320772i	−0.0959705	+	0.0126995i
$639$	36.4163			1.44061
$640$	−0.688198	+	5.42168i	−0.0272034	+	0.214311i
$641$	−33.2407	−	19.1916i	−1.31293	−	0.758021i	−0.330350	−	0.943859i	$-0.607167\pi$
$641$	−33.2407	−	19.1916i	−1.31293	−	0.758021i	−0.982580	+	0.185838i	$0.940500\pi$
$642$	8.57961	+	11.1658i	0.338610	+	0.440680i
$643$	−14.9780	+	25.9427i	−0.590677	+	1.02308i	0.403465	+	0.914995i	$0.367806\pi$
$643$	−14.9780	+	25.9427i	−0.590677	+	1.02308i	−0.994141	+	0.108087i	$0.965528\pi$
$644$	5.14907	−	19.3190i	0.202902	−	0.761276i
$645$	−11.0755			−0.436097
$646$	−12.7944	−	10.7550i	−0.503388	−	0.423150i
$647$		−	14.7012i		−	0.577963i	−0.957335	−	0.288982i	$-0.906683\pi$
$647$		−	14.7012i		−	0.577963i	0.957335	−	0.288982i	$-0.0933167\pi$
$648$	−3.52453	+	27.1892i	−0.138456	+	1.06809i
$649$	5.51826	+	3.18597i	0.216610	+	0.125060i
$650$	−14.7873	−	19.2448i	−0.580007	−	0.754844i
$651$	−9.12846	+	15.8110i	−0.357773	+	0.619680i
$652$	−18.7798	−	18.7301i	−0.735474	−	0.733526i
$653$		−	12.1042i		−	0.473673i	−0.971550	−	0.236836i	$-0.923889\pi$
$653$		−	12.1042i		−	0.473673i	0.971550	−	0.236836i	$-0.0761105\pi$
$654$	8.06833	+	60.9726i	0.315496	+	2.38422i
$655$	3.46672	−	2.00151i	0.135456	−	0.0782056i
$656$	−2.52885	+	4.40704i	−0.0987350	+	0.172066i
$657$	−2.71762			−0.106024
$658$	18.4348	−	2.43942i	0.718663	−	0.0950985i
$659$	−8.35717	+	4.82502i	−0.325549	+	0.187956i	−0.653863	−	0.756613i	$-0.726853\pi$
$659$	−8.35717	+	4.82502i	−0.325549	+	0.187956i	0.328314	+	0.944569i	$0.393520\pi$
$660$	−0.741836	+	2.78332i	−0.0288759	+	0.108341i
$661$	−18.5479	−	32.1258i	−0.721428	−	1.24955i	−0.960427	−	0.278530i	$-0.910153\pi$
$661$	−18.5479	−	32.1258i	−0.721428	−	1.24955i	0.238999	−	0.971020i	$-0.423181\pi$
$662$	20.8577	+	8.62334i	0.810657	+	0.335156i
$663$	−20.2681	−	11.7018i	−0.787146	−	0.454459i
$664$	31.8404	−	13.2630i	1.23565	−	0.514703i
$665$	0.996943	−	3.14495i	0.0386598	−	0.121956i
$666$	42.2669	−	5.59306i	1.63781	−	0.216727i
$667$	7.68194	+	4.43517i	0.297446	+	0.171730i
$668$	−5.16250	+	19.3694i	−0.199743	+	0.749424i
$669$	7.26697	−	4.19559i	0.280957	−	0.162211i
$670$	0.971859	−	2.35068i	0.0375462	−	0.0908147i
$671$	11.7188	−	6.76588i	0.452401	−	0.261194i
$672$	16.8155	−	12.9918i	0.648673	−	0.501169i
$673$		−	10.8787i		−	0.419342i	−0.977772	−	0.209671i	$-0.932761\pi$
$673$		−	10.8787i		−	0.419342i	0.977772	−	0.209671i	$-0.0672392\pi$
$674$	−27.6438	+	21.2410i	−1.06480	+	0.818172i
$675$	−2.49697	+	1.44162i	−0.0961082	+	0.0554881i
$676$	−0.0729798	+	0.0196586i	−0.00280692	+	0.000756101i
$677$	37.4698			1.44008			0.720040	−	0.693932i	$-0.244123\pi$
$677$	37.4698			1.44008			0.720040	+	0.693932i	$0.244123\pi$
$678$	−14.4674	−	18.8284i	−0.555616	−	0.723099i
$679$	2.19568	−	3.80304i	0.0842626	−	0.145947i
$680$	−2.24936	+	2.94352i	−0.0862590	+	0.112879i
$681$	−6.34580	+	10.9913i	−0.243172	+	0.421186i
$682$	−3.26587	+	7.89932i	−0.125057	+	0.302480i
$683$		−	51.9840i		−	1.98911i	−0.104201	−	0.994556i	$-0.533229\pi$
$683$		−	51.9840i		−	1.98911i	0.104201	−	0.994556i	$-0.466771\pi$
$684$	−1.05010	+	23.9308i	−0.0401515	+	0.915019i
$685$		−	8.60787i		−	0.328890i
$686$	−23.6413	−	9.77420i	−0.902630	−	0.373181i
$687$	−1.44887	+	2.50952i	−0.0552779	+	0.0957441i
$688$	33.1795	+	19.0391i	1.26496	+	0.725858i
$689$	−5.40133	+	9.35537i	−0.205774	+	0.356411i
$690$	8.28580	−	6.36665i	0.315435	−	0.242374i
$691$	−7.12137			−0.270910			−0.135455	−	0.990784i	$-0.543250\pi$
$691$	−7.12137			−0.270910			−0.135455	+	0.990784i	$0.543250\pi$
$692$	−29.9368	+	8.06410i	−1.13803	+	0.306551i
$693$	4.63681	−	2.67706i	0.176138	−	0.101693i
$694$	−7.88322	−	10.2595i	−0.299243	−	0.389446i
$695$		−	4.02049i		−	0.152506i
$696$	3.62513	+	8.70285i	0.137410	+	0.329881i
$697$	−2.98277	+	1.72210i	−0.112980	+	0.0652293i
$698$	−23.2724	−	9.62168i	−0.880874	−	0.364186i
$699$	23.2100	−	13.4003i	0.877884	−	0.506847i
$700$	14.4335	+	3.84694i	0.545535	+	0.145401i
$701$	6.27811	+	3.62467i	0.237121	+	0.136902i	0.613853	−	0.789421i	$-0.289619\pi$
$701$	6.27811	+	3.62467i	0.237121	+	0.136902i	−0.376732	+	0.926322i	$0.622952\pi$
$702$	−0.404019	−	3.05319i	−0.0152487	−	0.115235i
$703$	−46.7082	+	10.2793i	−1.76163	+	0.387690i
$704$	7.00697	−	7.06293i	0.264085	−	0.266194i
$705$	8.41665	+	4.85936i	0.316990	+	0.183014i
$706$	12.6359	−	30.5631i	0.475559	−	1.15026i
$707$	0.593395	+	1.02779i	0.0223169	+	0.0386540i
$708$	6.32703	−	23.7387i	0.237784	−	0.892153i
$709$	16.8968	−	9.75535i	0.634571	−	0.366370i	−0.147949	−	0.988995i	$-0.547267\pi$
$709$	16.8968	−	9.75535i	0.634571	−	0.366370i	0.782520	+	0.622625i	$0.213934\pi$
$710$	1.18774	+	8.97578i	0.0445750	+	0.336855i
$711$	31.9454			1.19804
$712$	22.1359	−	28.9671i	0.829576	−	1.08559i
$713$	26.8540	−	15.5041i	1.00569	−	0.580635i
$714$	14.2797	−	1.88958i	0.534403	−	0.0707159i
$715$		−	2.16286i		−	0.0808864i
$716$	4.04059	−	4.05132i	0.151004	−	0.151405i
$717$	24.3624	−	42.1970i	0.909831	−	1.57587i
$718$	14.7683	−	11.3477i	0.551148	−	0.423492i
$719$	−37.0563	−	21.3944i	−1.38197	−	0.797878i	−0.389573	−	0.920995i	$-0.627378\pi$
$719$	−37.0563	−	21.3944i	−1.38197	−	0.797878i	−0.992392	+	0.123117i	$0.960711\pi$
$720$	5.30917	−	0.0140781i	0.197861	−	0.000524659i
$721$		−	6.36383i		−	0.237001i
$722$	−1.10690	−	26.8472i	−0.0411945	−	0.999151i
$723$	15.1731			0.564292
$724$	−0.314341	+	1.17939i	−0.0116824	+	0.0438317i
$725$	−3.31357	+	5.73928i	−0.123063	+	0.213151i
$726$	−25.4153	+	19.5286i	−0.943251	+	0.724776i
$727$	21.7487	+	12.5566i	0.806614	+	0.465699i	0.845779	−	0.533534i	$-0.179136\pi$
$727$	21.7487	+	12.5566i	0.806614	+	0.465699i	−0.0391646	+	0.999233i	$0.512470\pi$
$728$	−9.68799	+	12.6778i	−0.359061	+	0.469869i
$729$	22.2837			0.825320
$730$	−0.0886365	−	0.669829i	−0.00328058	−	0.0247915i
$731$	12.9653	+	22.4565i	0.479538	+	0.830585i
$732$	−36.9404	−	36.8426i	−1.36536	−	1.36174i
$733$		−	0.990917i		−	0.0366004i	−0.999833	−	0.0183002i	$-0.994175\pi$
$733$		−	0.990917i		−	0.0366004i	0.999833	−	0.0183002i	$-0.00582545\pi$
$734$	2.84293	+	21.4841i	0.104934	+	0.792993i
$735$	−2.63176	−	4.55833i	−0.0970738	−	0.168137i
$736$	−35.7667	+	4.82944i	−1.31838	+	0.178015i
$737$	−4.01019	+	2.31529i	−0.147717	+	0.0852846i
$738$	4.56155	+	1.88591i	0.167913	+	0.0694214i
$739$	−8.15940	+	14.1325i	−0.300149	+	0.519872i	−0.976169	−	0.217010i	$-0.930370\pi$
$739$	−8.15940	+	14.1325i	−0.300149	+	0.519872i	0.676021	+	0.736882i	$0.263703\pi$
$740$	2.75712	+	10.2354i	0.101354	+	0.376261i
$741$	−8.08653	−	36.7446i	−0.297066	−	1.34984i
$742$	−0.872198	−	6.59123i	−0.0320194	−	0.241972i
$743$	−21.4854	+	37.2138i	−0.788223	+	1.36524i	0.138832	+	0.990316i	$0.455665\pi$
$743$	−21.4854	+	37.2138i	−0.788223	+	1.36524i	−0.927055	+	0.374926i	$0.877668\pi$
$744$	32.6831	+	4.23671i	1.19822	+	0.155325i
$745$	4.48817	+	7.77374i	0.164434	+	0.284808i
$746$	−4.50157	+	10.8882i	−0.164814	+	0.398644i
$747$	−16.7539	−	29.0186i	−0.612993	−	1.06174i
$748$	6.51184	−	1.75410i	0.238097	−	0.0641362i
$749$	6.50749			0.237778
$750$	9.74606	+	12.6839i	0.355876	+	0.463151i
$751$	−10.3838	−	17.9853i	−0.378910	−	0.656292i	0.611994	−	0.790863i	$-0.290368\pi$
$751$	−10.3838	−	17.9853i	−0.378910	−	0.656292i	−0.990904	+	0.134571i	$0.957034\pi$
$752$	−16.8609	−	29.0259i	−0.614854	−	1.05847i
$753$			58.2751i			2.12366i
$754$	−4.31310	−	5.61323i	−0.157074	−	0.204422i
$755$	1.91075	+	1.10317i	0.0695393	+	0.0401485i
$756$	1.34211	+	1.33856i	0.0488121	+	0.0486828i
$757$	10.7348	+	6.19774i	0.390163	+	0.225261i	0.682231	−	0.731137i	$-0.261010\pi$
$757$	10.7348	+	6.19774i	0.390163	+	0.225261i	−0.292068	+	0.956398i	$0.594343\pi$
$758$	13.6548	+	5.64541i	0.495965	+	0.205051i
$759$	−19.0223			−0.690467
$760$	−5.93265	+	0.521692i	−0.215200	+	0.0189238i
$761$	46.1918			1.67445			0.837226	−	0.546858i	$-0.184176\pi$
$761$	46.1918			1.67445			0.837226	+	0.546858i	$0.184176\pi$
$762$	−47.7204	−	19.7294i	−1.72873	−	0.714720i
$763$	24.6152	+	14.2116i	0.891130	+	0.514494i
$764$	30.9352	−	31.0173i	1.11920	−	1.12217i
$765$	3.11669	+	1.79942i	0.112684	+	0.0650583i
$766$	−7.28125	−	9.47610i	−0.263082	−	0.342385i
$767$			18.4468i			0.666075i
$768$	−33.3211	−	19.0030i	−1.20237	−	0.685713i
$769$	7.84569	+	13.5891i	0.282923	+	0.490037i	0.972103	−	0.234553i	$-0.0753627\pi$
$769$	7.84569	+	13.5891i	0.282923	+	0.490037i	−0.689181	+	0.724590i	$0.742029\pi$
$770$	0.811066	+	1.05555i	0.0292288	+	0.0380395i
$771$	19.6076			0.706151
$772$	−2.76571	−	10.2673i	−0.0995401	−	0.369528i
$773$	2.97659	+	5.15560i	0.107060	+	0.185434i	0.914578	−	0.404409i	$-0.132523\pi$
$773$	2.97659	+	5.15560i	0.107060	+	0.185434i	−0.807518	+	0.589843i	$0.799190\pi$
$774$	14.1986	−	34.3428i	0.510357	−	1.23443i
$775$	11.5833	+	20.0629i	0.416086	+	0.720682i
$776$	−7.86133	−	1.01906i	−0.282205	−	0.0365822i
$777$	20.6079	−	35.6939i	0.739304	−	1.28051i
$778$	−1.13355	−	8.56632i	−0.0406399	−	0.307117i
$779$	−5.27810	−	1.67315i	−0.189108	−	0.0599468i
$780$	−8.05202	+	2.16898i	−0.288309	+	0.0776619i
$781$	8.24113	−	14.2741i	0.294891	−	0.510766i
$782$	−22.6085	−	9.34720i	−0.808479	−	0.334255i
$783$	−0.728302	+	0.420485i	−0.0260274	+	0.0150269i
$784$	0.0482063	+	18.1797i	0.00172165	+	0.649276i
$785$	−4.49002	−	7.77694i	−0.160256	−	0.277571i
$786$	3.68579	+	27.8536i	0.131468	+	0.993506i
$787$		−	5.02671i		−	0.179183i	−0.995979	−	0.0895915i	$-0.971444\pi$
$787$		−	5.02671i		−	0.179183i	0.995979	−	0.0895915i	$-0.0285561\pi$
$788$	−1.29020	+	1.29362i	−0.0459613	+	0.0460833i
$789$	26.3436	+	45.6285i	0.937857	+	1.62442i
$790$	1.04191	+	7.87379i	0.0370697	+	0.280137i
$791$	−10.9733			−0.390164
$792$	−7.67948	−	5.86844i	−0.272878	−	0.208526i
$793$	33.9261	+	19.5873i	1.20475	+	0.695564i
$794$	25.2709	−	19.4177i	0.896832	−	0.689108i
$795$	1.73743	−	3.00932i	0.0616203	−	0.106729i
$796$	38.7752	+	10.3347i	1.37435	+	0.366304i
$797$	−23.2783			−0.824558			−0.412279	−	0.911058i	$-0.635267\pi$
$797$	−23.2783			−0.824558			−0.412279	+	0.911058i	$0.635267\pi$
$798$	17.7256	+	14.9002i	0.627480	+	0.527462i
$799$		−	22.7540i		−	0.804978i
$800$	−3.60813	−	26.7218i	−0.127567	−	0.944757i
$801$	−30.6713	−	17.7081i	−1.08372	−	0.625684i
$802$	−2.06320	+	1.58532i	−0.0728540	+	0.0559796i
$803$	−0.615005	+	1.06522i	−0.0217031	+	0.0375908i
$804$	12.6410	+	12.6075i	0.445814	+	0.444634i
$805$		−	4.82900i		−	0.170200i
$806$	−24.5321	+	3.24626i	−0.864108	+	0.114345i
$807$	8.06521	−	4.65645i	0.283909	−	0.163915i
$808$	1.30079	−	1.70222i	0.0457617	−	0.0598840i
$809$	−38.1510			−1.34132			−0.670659	−	0.741766i	$-0.733989\pi$
$809$	−38.1510			−1.34132			−0.670659	+	0.741766i	$0.733989\pi$
$810$	0.868686	+	6.56469i	0.0305225	+	0.230660i
$811$	43.8993	−	25.3453i	1.54151	−	0.889993i	0.542770	−	0.839881i	$-0.317375\pi$
$811$	43.8993	−	25.3453i	1.54151	−	0.889993i	0.998744	−	0.0501122i	$-0.0159579\pi$
$812$	4.20989	+	1.12206i	0.147738	+	0.0393764i
$813$	−2.50855	−	4.34494i	−0.0879788	−	0.152384i
$814$	7.37284	−	17.8330i	0.258418	−	0.625048i
$815$	−5.54793	−	3.20310i	−0.194336	−	0.112200i
$816$	−13.0605	−	22.4836i	−0.457210	−	0.787083i
$817$	−12.5967	+	39.7375i	−0.440704	+	1.39024i
$818$	6.78664	+	51.2869i	0.237289	+	1.79320i
$819$	13.4236	+	7.75012i	0.469059	+	0.270811i
$820$	−0.316057	+	1.18583i	−0.0110372	+	0.0414108i
$821$	17.8048	−	10.2796i	0.621391	−	0.358760i	−0.156019	−	0.987754i	$-0.549866\pi$
$821$	17.8048	−	10.2796i	0.621391	−	0.358760i	0.777410	+	0.628994i	$0.216533\pi$
$822$	55.8332	+	23.0835i	1.94741	+	0.805130i
$823$	−16.8787	+	9.74491i	−0.588354	+	0.339686i	−0.764446	−	0.644687i	$-0.776988\pi$
$823$	−16.8787	+	9.74491i	−0.588354	+	0.339686i	0.176093	+	0.984374i	$0.443654\pi$
$824$	−10.6045	+	4.41725i	−0.369425	+	0.153882i
$825$		−	14.2118i		−	0.494793i
$826$	−6.91749	−	9.00269i	−0.240690	−	0.313244i
$827$	12.7206	−	7.34424i	0.442338	−	0.255384i	−0.262251	−	0.965000i	$-0.584465\pi$
$827$	12.7206	−	7.34424i	0.442338	−	0.255384i	0.704589	+	0.709616i	$0.251131\pi$
$828$	9.11939	+	33.8544i	0.316921	+	1.17652i
$829$	35.2405			1.22395			0.611976	−	0.790876i	$-0.290375\pi$
$829$	35.2405			1.22395			0.611976	+	0.790876i	$0.290375\pi$
$830$	6.60598	−	5.07591i	0.229297	−	0.176187i
$831$	−33.3557	+	57.7738i	−1.15710	+	2.00415i
$832$	27.8505	+	7.34391i	0.965541	+	0.254604i
$833$	−6.16161	+	10.6722i	−0.213487	+	0.369771i
$834$	26.0781	+	10.7817i	0.903011	+	0.373338i
$835$			4.84158i			0.167550i
$836$	9.14250	+	5.82723i	0.316200	+	0.201539i
$837$			2.93981i			0.101615i
$838$	2.18174	−	5.27707i	0.0753669	−	0.182293i
$839$	−3.11351	+	5.39276i	−0.107490	+	0.186179i	−0.914753	−	0.404014i	$-0.867615\pi$
$839$	−3.11351	+	5.39276i	−0.107490	+	0.186179i	0.807263	+	0.590192i	$0.200948\pi$
$840$	3.11631	−	4.07802i	0.107523	−	0.140705i
$841$	13.5335	−	23.4407i	0.466673	−	0.808301i
$842$	5.57531	+	7.25592i	0.192138	+	0.250055i
$843$	−55.5771			−1.91418
$844$	12.9575	+	48.1028i	0.446015	+	1.65577i
$845$	−0.0158093	+	0.00912753i	−0.000543858	+	0.000313997i
$846$	−25.8578	+	19.8687i	−0.889010	+	0.683098i
$847$			14.8121i			0.508951i
$848$	−10.3780	+	6.02850i	−0.356383	+	0.207020i
$849$	5.84328	−	3.37362i	0.200541	−	0.115782i
$850$	6.98341	−	16.8911i	0.239529	−	0.579361i
$851$	−60.6240	+	35.0013i	−2.07816	+	1.19983i
$852$	−61.4047	−	16.3661i	−2.10369	−	0.560694i
$853$	28.3047	+	16.3417i	0.969134	+	0.559530i	0.898972	−	0.438006i	$-0.144315\pi$
$853$	28.3047	+	16.3417i	0.969134	+	0.559530i	0.0701616	+	0.997536i	$0.477649\pi$
$854$	−23.9023	+	3.16292i	−0.817921	+	0.108233i
$855$	1.24350	+	5.65034i	0.0425266	+	0.193238i
$856$	−4.51697	−	10.8439i	−0.154387	−	0.370636i
$857$	45.5110	+	26.2758i	1.55463	+	0.897564i	0.997755	+	0.0669647i	$0.0213315\pi$
$857$	45.5110	+	26.2758i	1.55463	+	0.897564i	0.556871	+	0.830599i	$0.312002\pi$
$858$	14.0290	+	5.80009i	0.478941	+	0.198012i
$859$	12.3600	+	21.4082i	0.421718	+	0.730437i	0.996108	−	0.0881450i	$-0.0280939\pi$
$859$	12.3600	+	21.4082i	0.421718	+	0.730437i	−0.574390	+	0.818582i	$0.694761\pi$
$860$	8.92779	+	2.37951i	0.304435	+	0.0811407i
$861$	4.13239	−	2.38584i	0.140832	−	0.0813091i
$862$	8.90079	−	1.17781i	0.303162	−	0.0401165i
$863$	−25.0075			−0.851266			−0.425633	−	0.904896i	$-0.639949\pi$
$863$	−25.0075			−0.851266			−0.425633	+	0.904896i	$0.639949\pi$
$864$	1.29895	−	3.16557i	0.0441910	−	0.107695i
$865$	−6.48509	+	3.74417i	−0.220500	+	0.127306i
$866$	−4.31199	−	32.5859i	−0.146527	−	1.10731i
$867$			23.1311i			0.785572i
$868$	10.7552	−	10.7838i	0.365056	−	0.366025i
$869$	7.22934	−	12.5216i	0.245238	−	0.424765i
$870$	1.38738	+	1.80559i	0.0470367	+	0.0612153i
$871$	−11.6095	−	6.70277i	−0.393374	−	0.227115i
$872$	6.59590	−	50.8826i	0.223365	−	1.72310i
$873$			7.70085i			0.260634i
$874$	−13.4189	−	36.9696i	−0.453901	−	1.25051i
$875$	7.39223			0.249903
$876$	4.58241	+	1.22134i	0.154825	+	0.0412654i
$877$	1.76754	−	3.06146i	0.0596855	−	0.103378i	−0.834639	−	0.550798i	$-0.814324\pi$
$877$	1.76754	−	3.06146i	0.0596855	−	0.103378i	0.894324	+	0.447419i	$0.147657\pi$
$878$	9.00751	+	11.7227i	0.303989	+	0.395622i
$879$	−17.9726	−	10.3765i	−0.606202	−	0.349991i
$880$	1.19596	−	2.08422i	0.0403160	−	0.0702589i
$881$	−5.22599			−0.176068			−0.0880341	−	0.996117i	$-0.528058\pi$
$881$	−5.22599			−0.176068			−0.0880341	+	0.996117i	$0.528058\pi$
$882$	17.5083	−	2.31682i	0.589535	−	0.0780113i
$883$	−2.22587	−	3.85532i	−0.0749066	−	0.129742i	0.826139	−	0.563466i	$-0.190533\pi$
$883$	−2.22587	−	3.85532i	−0.0749066	−	0.129742i	−0.901046	+	0.433724i	$0.857199\pi$
$884$	13.8237	+	13.7871i	0.464942	+	0.463711i
$885$		−	5.93373i		−	0.199460i
$886$	20.0548	−	2.65379i	0.673755	−	0.0891559i
$887$	−23.1207	−	40.0463i	−0.776318	−	1.34462i	−0.934051	−	0.357141i	$-0.883752\pi$
$887$	−23.1207	−	40.0463i	−0.776318	−	1.34462i	0.157732	−	0.987482i	$-0.449582\pi$
$888$	−73.7836	−	9.56455i	−2.47601	−	0.320965i
$889$	−20.6666	+	11.9318i	−0.693134	+	0.400181i
$890$	3.36427	−	8.13731i	0.112770	−	0.272763i
$891$	6.02739	−	10.4397i	0.201925	−	0.349744i
$892$	−6.75919	+	1.82073i	−0.226314	+	0.0609625i
$893$	27.0075	−	24.6711i	0.903771	−	0.825588i
$894$	−62.4587	+	8.26497i	−2.08893	+	0.276422i
$895$	0.690997	−	1.19684i	0.0230975	−	0.0400060i
$896$	−16.3460	+	6.85975i	−0.546080	+	0.229168i
$897$	−27.5349	−	47.6919i	−0.919364	−	1.59239i
$898$	−45.9979	−	19.0173i	−1.53497	−	0.634614i
$899$	3.37857	+	5.85186i	0.112682	+	0.195170i
$900$	−25.2931	+	6.81322i	−0.843103	+	0.227107i
$901$	−8.13553			−0.271034
$902$	1.77151	−	1.36120i	0.0589849	−	0.0453229i
$903$	−17.9624	−	31.1118i	−0.597751	−	1.03533i
$904$	7.61674	+	18.2855i	0.253329	+	0.608167i
$905$			0.294801i			0.00979952i
$906$	−12.2795	+	9.43535i	−0.407960	+	0.313468i
$907$	1.48781	+	0.858985i	0.0494018	+	0.0285221i	0.524497	−	0.851412i	$-0.324253\pi$
$907$	1.48781	+	0.858985i	0.0494018	+	0.0285221i	−0.475096	+	0.879934i	$0.657587\pi$
$908$	7.47667	−	7.49652i	0.248122	−	0.248781i
$909$	−1.80237	−	1.04060i	−0.0597807	−	0.0345144i
$910$	−1.47241	+	3.56138i	−0.0488098	+	0.118059i
$911$	−0.307661			−0.0101933			−0.00509664	−	0.999987i	$-0.501622\pi$
$911$	−0.307661			−0.0101933			−0.00509664	+	0.999987i	$0.501622\pi$
$912$	12.5256	−	39.8799i	0.414764	−	1.32056i
$913$	−15.1659			−0.501916
$914$	3.11411	−	7.53225i	0.103006	−	0.249145i
$915$	−10.9129	−	6.30058i	−0.360770	−	0.208291i
$916$	1.70707	−	1.71160i	0.0564032	−	0.0565529i
$917$	11.2448	+	6.49216i	0.371334	+	0.214390i
$918$	1.83918	−	1.41319i	0.0607019	−	0.0466422i
$919$			28.6229i			0.944183i	0.881550	+	0.472091i	$0.156501\pi$
$919$			28.6229i			0.944183i	−0.881550	+	0.472091i	$0.843499\pi$
$920$	−8.04690	+	3.35190i	−0.265298	+	0.110509i
$921$	12.4352	+	21.5384i	0.409754	+	0.709714i
$922$	−30.6951	+	23.5855i	−1.01089	+	0.776749i
$923$	47.7163			1.57060
$924$	−9.02165	+	2.43017i	−0.296790	+	0.0799466i
$925$	−26.1499	−	45.2930i	−0.859803	−	1.48922i
$926$	12.5888	+	5.20469i	0.413694	+	0.171037i
$927$	5.57991	+	9.66469i	0.183268	+	0.317430i
$928$	−1.05240	−	7.79407i	−0.0345468	−	0.255853i
$929$	−30.2173	+	52.3378i	−0.991396	+	1.71715i	−0.382337	+	0.924023i	$0.624881\pi$
$929$	−30.2173	+	52.3378i	−0.991396	+	1.71715i	−0.609059	+	0.793125i	$0.708453\pi$
$930$	7.89119	−	1.04422i	0.258762	−	0.0342412i
$931$	−19.3480	+	4.25799i	−0.634105	+	0.139550i
$932$	−21.5882	+	5.81524i	−0.707146	+	0.190485i
$933$	−24.9103	+	43.1460i	−0.815528	+	1.41254i
$934$	7.64810	−	18.4988i	0.250253	−	0.605300i
$935$	1.41064	−	0.814431i	0.0461327	−	0.0266347i
$936$	3.59699	−	27.7482i	0.117571	−	0.906978i
$937$	−10.5175	−	18.2168i	−0.343592	−	0.595118i	0.641505	−	0.767119i	$-0.278310\pi$
$937$	−10.5175	−	18.2168i	−0.343592	−	0.595118i	−0.985097	+	0.172000i	$0.944977\pi$
$938$	8.17938	−	1.08235i	0.267066	−	0.0353401i
$939$		−	57.4909i		−	1.87614i
$940$	−5.74053	−	5.72533i	−0.187235	−	0.186740i
$941$	17.6157	+	30.5113i	0.574256	+	0.994641i	0.996122	+	0.0879826i	$0.0280420\pi$
$941$	17.6157	+	30.5113i	0.574256	+	0.994641i	−0.421866	+	0.906658i	$0.638625\pi$
$942$	62.4844	−	8.26837i	2.03585	−	0.269398i
$943$	−8.10441			−0.263916
$944$	−10.2002	+	17.7760i	−0.331990	+	0.578561i
$945$	0.396486	+	0.228912i	0.0128977	+	0.00744649i
$946$	−10.2481	−	13.3373i	−0.333195	−	0.433632i
$947$	−8.10653	+	14.0409i	−0.263427	+	0.456268i	−0.967150	−	0.254205i	$-0.918186\pi$
$947$	−8.10653	+	14.0409i	−0.263427	+	0.456268i	0.703724	+	0.710474i	$0.251519\pi$
$948$	−53.8658	−	14.3568i	−1.74948	−	0.466287i
$949$	−3.56089			−0.115591
$950$	27.6204	−	10.0254i	0.896125	−	0.325268i
$951$			45.3354i			1.47010i
$952$	−11.9166	−	1.54474i	−0.386219	−	0.0500655i
$953$	32.1131	+	18.5405i	1.04024	+	0.600585i	0.919902	−	0.392148i	$-0.128268\pi$
$953$	32.1131	+	18.5405i	1.04024	+	0.600585i	0.120341	+	0.992733i	$0.461601\pi$
$954$	7.10390	+	9.24529i	0.229997	+	0.299327i
$955$	5.29034	−	9.16314i	0.171191	−	0.296512i
$956$	−28.7040	+	28.7802i	−0.928353	+	0.930818i
$957$		−	4.14524i		−	0.133996i
$958$	4.41182	+	33.3403i	0.142540	+	1.07718i
$959$	24.1800	−	13.9603i	0.780814	−	0.450803i
$960$	−8.95858	−	2.36229i	−0.289137	−	0.0762427i
$961$	−7.37886			−0.238028
$962$	55.3824	−	7.32858i	1.78560	−	0.236283i
$963$	−9.88286	+	5.70587i	−0.318471	+	0.183869i
$964$	−12.2308	−	3.25985i	−0.393926	−	0.104993i
$965$	−1.28412	−	2.22417i	−0.0413374	−	0.0715985i
$966$	31.3223	+	12.9498i	1.00778	+	0.416653i
$967$	0.859439	+	0.496197i	0.0276377	+	0.0159566i	0.513755	−	0.857937i	$-0.328254\pi$
$967$	0.859439	+	0.496197i	0.0276377	+	0.0159566i	−0.486117	+	0.873893i	$0.661587\pi$
$968$	24.6825	−	10.2814i	0.793326	−	0.330456i
$969$	20.9201	−	19.1104i	0.672050	−	0.613913i
$970$	−1.89808	+	0.251167i	−0.0609437	+	0.00806450i
$971$	31.4894	+	18.1804i	1.01054	+	0.583437i	0.911351	−	0.411631i	$-0.135041\pi$
$971$	31.4894	+	18.1804i	1.01054	+	0.583437i	0.0991922	+	0.995068i	$0.468374\pi$
$972$	−41.4033	−	11.0352i	−1.32801	−	0.353953i
$973$	11.2938	−	6.52049i	0.362063	−	0.209037i
$974$	3.95076	−	9.55590i	0.126591	−	0.306191i
$975$	35.6312	−	20.5717i	1.14111	−	0.658822i
$976$	21.8616	+	37.6347i	0.699774	+	1.20466i
$977$		−	39.6271i		−	1.26778i	−0.773421	−	0.633892i	$-0.781456\pi$
$977$		−	39.6271i		−	1.26778i	0.773421	−	0.633892i	$-0.218544\pi$
$978$	35.6540	−	27.3959i	1.14009	−	0.876023i
$979$	−13.8820	+	8.01478i	−0.443671	+	0.256154i
$980$	1.14208	+	4.23982i	0.0364825	+	0.135436i
$981$	−49.8438			−1.59139
$982$	−12.7985	−	16.6564i	−0.408416	−	0.531528i
$983$	−21.5716	+	37.3631i	−0.688027	+	1.19170i	0.284448	+	0.958691i	$0.408190\pi$
$983$	−21.5716	+	37.3631i	−0.688027	+	1.19170i	−0.972475	+	0.233007i	$0.925144\pi$
$984$	−6.84406	−	5.23004i	−0.218181	−	0.166728i
$985$	−0.220641	+	0.382162i	−0.00703021	+	0.0121767i
$986$	2.03689	−	4.92671i	0.0648677	−	0.156899i
$987$			31.5239i			1.00342i
$988$	−1.37594	+	31.3566i	−0.0437746	+	0.997585i
$989$			61.0161i			1.94020i
$990$	−2.15728	−	0.891902i	−0.0685630	−	0.0283465i
$991$	−4.38682	+	7.59820i	−0.139352	+	0.241365i	−0.927252	−	0.374439i	$-0.877835\pi$
$991$	−4.38682	+	7.59820i	−0.139352	+	0.241365i	0.787899	+	0.615804i	$0.211169\pi$
$992$	−25.4351	−	10.4369i	−0.807567	−	0.331373i
$993$	−19.1308	+	33.1356i	−0.607098	+	1.05153i
$994$	−23.2872	+	17.8935i	−0.738626	+	0.567546i
$995$	9.69227			0.307266
$996$	15.2088	+	56.4603i	0.481908	+	1.78901i
$997$	−15.8403	+	9.14540i	−0.501667	+	0.289638i	−0.729402	−	0.684085i	$-0.760202\pi$
$997$	−15.8403	+	9.14540i	−0.501667	+	0.289638i	0.227734	+	0.973723i	$0.426868\pi$
$998$	1.84878	+	2.40608i	0.0585222	+	0.0761630i
$999$		−	6.63673i		−	0.209977i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.2.o.c.27.10	yes	28
4.3	odd	2		608.2.s.c.559.1		28
8.3	odd	2	inner	152.2.o.c.27.4	✓	28
8.5	even	2		608.2.s.c.559.2		28
19.12	odd	6	inner	152.2.o.c.107.4	yes	28
76.31	even	6		608.2.s.c.335.2		28
152.69	odd	6		608.2.s.c.335.1		28
152.107	even	6	inner	152.2.o.c.107.10	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.o.c.27.4	✓	28	8.3	odd	2	inner
152.2.o.c.27.10	yes	28	1.1	even	1	trivial
152.2.o.c.107.4	yes	28	19.12	odd	6	inner
152.2.o.c.107.10	yes	28	152.107	even	6	inner
608.2.s.c.335.1		28	152.69	odd	6
608.2.s.c.335.2		28	76.31	even	6
608.2.s.c.559.1		28	4.3	odd	2
608.2.s.c.559.2		28	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	152.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.540330 - 1.30692i) q^{2} +(2.07624 + 1.19872i) q^{3} +(-1.41609 - 1.41234i) q^{4} +(-0.418341 - 0.241529i) q^{5} +(2.68848 - 2.06578i) q^{6} -1.56686i q^{7} +(-2.61097 + 1.08759i) q^{8} +(1.37385 + 2.37958i) q^{9} +(-0.541701 + 0.416233i) q^{10} +1.24363 q^{11} +(-1.24714 - 4.62984i) q^{12} +(1.80015 + 3.11796i) q^{13} +(-2.04776 - 0.846621i) q^{14} +(-0.579050 - 1.00294i) q^{15} +(0.0106066 + 3.99999i) q^{16} +(-1.35570 + 2.34815i) q^{17} +(3.85225 - 0.509757i) q^{18} +(-4.25703 + 0.936862i) q^{19} +(0.251286 + 0.932864i) q^{20} +(1.87822 - 3.25318i) q^{21} +(0.671968 - 1.62532i) q^{22} +(-5.52533 + 3.19005i) q^{23} +(-6.72471 - 0.871723i) q^{24} +(-2.38333 - 4.12804i) q^{25} +(5.04760 - 0.667934i) q^{26} -0.604878i q^{27} +(-2.21293 + 2.21881i) q^{28} +(-0.695157 - 1.20405i) q^{29} +(-1.62365 + 0.214852i) q^{30} -4.86016 q^{31} +(5.23340 + 2.14745i) q^{32} +(2.58207 + 1.49076i) q^{33} +(2.33632 + 3.04058i) q^{34} +(-0.378442 + 0.655481i) q^{35} +(1.41527 - 5.31003i) q^{36} +10.9720 q^{37} +(-1.07579 + 6.06982i) q^{38} +8.63150i q^{39} +(1.35496 + 0.175643i) q^{40} +(1.10008 + 0.635132i) q^{41} +(-3.23679 - 4.21248i) q^{42} +(4.78175 - 8.28223i) q^{43} +(-1.76108 - 1.75642i) q^{44} -1.32730i q^{45} +(1.18364 + 8.94485i) q^{46} +(-7.26763 + 4.19597i) q^{47} +(-4.77283 + 8.31765i) q^{48} +4.54495 q^{49} +(-6.68281 + 0.884316i) q^{50} +(-5.62954 + 3.25022i) q^{51} +(1.85443 - 6.95772i) q^{52} +(1.50024 + 2.59849i) q^{53} +(-0.790529 - 0.326834i) q^{54} +(-0.520259 - 0.300372i) q^{55} +(1.70410 + 4.09102i) q^{56} +(-9.96165 - 3.15782i) q^{57} +(-1.94921 + 0.257933i) q^{58} +(4.43723 + 2.56184i) q^{59} +(-0.596510 + 2.23807i) q^{60} +(9.42313 - 5.44044i) q^{61} +(-2.62609 + 6.35185i) q^{62} +(3.72846 - 2.15263i) q^{63} +(5.63431 - 5.67931i) q^{64} -1.73916i q^{65} +(3.34347 - 2.56906i) q^{66} +(-3.22460 + 1.86172i) q^{67} +(5.23618 - 1.41047i) q^{68} -15.2959 q^{69} +(0.652179 + 0.848770i) q^{70} +(6.62670 - 11.4778i) q^{71} +(-6.17507 - 4.71882i) q^{72} +(-0.494526 + 0.856544i) q^{73} +(5.92851 - 14.3396i) q^{74} -11.4277i q^{75} +(7.35149 + 4.68568i) q^{76} -1.94859i q^{77} +(11.2807 + 4.66386i) q^{78} +(5.81311 - 10.0686i) q^{79} +(0.961676 - 1.67592i) q^{80} +(4.84663 - 8.39460i) q^{81} +(1.42447 - 1.09454i) q^{82} -12.1949 q^{83} +(-7.25431 + 1.95410i) q^{84} +(1.13429 - 0.654884i) q^{85} +(-8.24050 - 10.7245i) q^{86} -3.33319i q^{87} +(-3.24707 + 1.35255i) q^{88} +(-11.1625 + 6.44469i) q^{89} +(-1.73467 - 0.717179i) q^{90} +(4.88540 - 2.82059i) q^{91} +(12.3298 + 3.28624i) q^{92} +(-10.0909 - 5.82596i) q^{93} +(1.55688 + 11.7654i) q^{94} +(2.00717 + 0.636268i) q^{95} +(8.29161 + 10.7320i) q^{96} +(2.42717 + 1.40133i) q^{97} +(2.45577 - 5.93989i) q^{98} +(1.70855 + 2.95930i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 3 q^{2} - 6 q^{3} + q^{4} - 3 q^{6} + 8 q^{9} + 6 q^{10} - 16 q^{11} + 13 q^{16} - 22 q^{17} + 4 q^{19} - 40 q^{20} - 21 q^{22} - 11 q^{24} + 16 q^{25} + 36 q^{26} - 10 q^{28} + 4 q^{30} - 3 q^{32}+ \cdots - 28 q^{99}+O(q^{100}) \) 28 * q - 3 * q^2 - 6 * q^3 + q^4 - 3 * q^6 + 8 * q^9 + 6 * q^10 - 16 * q^11 + 13 * q^16 - 22 * q^17 + 4 * q^19 - 40 * q^20 - 21 * q^22 - 11 * q^24 + 16 * q^25 + 36 * q^26 - 10 * q^28 + 4 * q^30 - 3 * q^32 + 36 * q^33 - 12 * q^34 - 28 * q^35 - 8 * q^36 + 38 * q^38 - 48 * q^40 + 6 * q^41 + 14 * q^42 + 30 * q^43 + 5 * q^44 - 15 * q^48 - 68 * q^49 - 42 * q^51 + 36 * q^52 + 23 * q^54 - 26 * q^57 + 20 * q^58 - 18 * q^59 - 42 * q^60 + 22 * q^62 + 70 * q^64 - 27 * q^66 + 78 * q^67 + 4 * q^68 + 18 * q^70 - 24 * q^72 + 14 * q^73 + 4 * q^74 + 47 * q^76 - 30 * q^78 - 20 * q^80 + 6 * q^81 + 23 * q^82 - 32 * q^83 + 42 * q^86 - 18 * q^89 - 96 * q^90 - 12 * q^91 + 46 * q^92 + 50 * q^96 + 30 * q^97 + 15 * q^98 - 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more