LMFDB - Embedded newform 261.2.e.a.175.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [261,2,Mod(88,261)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(261, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("261.88"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	261.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [22] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$2.08409549276$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			175.7
Character	$\chi$	$=$	261.175
Dual form			261.2.e.a.88.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.100158 + 0.173479i) q^{2} +(1.19785 + 1.25106i) q^{3} +(0.979937 - 1.69730i) q^{4} +(0.556635 - 0.964120i) q^{5} +(-0.0970582 + 0.333105i) q^{6} +(0.359329 + 0.622375i) q^{7} +0.793225 q^{8} +(-0.130309 + 2.99717i) q^{9} +0.223006 q^{10} +(-0.874706 - 1.51504i) q^{11} +(3.29724 - 0.807151i) q^{12} +(0.587818 - 1.01813i) q^{13} +(-0.0719792 + 0.124672i) q^{14} +(1.87294 - 0.458487i) q^{15} +(-1.88043 - 3.25699i) q^{16} -4.38083 q^{17} +(-0.532996 + 0.277584i) q^{18} +4.97408 q^{19} +(-1.09093 - 1.88955i) q^{20} +(-0.348208 + 1.19505i) q^{21} +(0.175218 - 0.303486i) q^{22} +(-3.61871 + 6.26778i) q^{23} +(0.950165 + 0.992374i) q^{24} +(1.88032 + 3.25680i) q^{25} +0.235498 q^{26} +(-3.90573 + 3.42714i) q^{27} +1.40848 q^{28} +(0.500000 + 0.866025i) q^{29} +(0.267127 + 0.278994i) q^{30} +(-0.127529 + 0.220886i) q^{31} +(1.16990 - 2.02633i) q^{32} +(0.847635 - 2.90910i) q^{33} +(-0.438775 - 0.759981i) q^{34} +0.800059 q^{35} +(4.95940 + 3.15821i) q^{36} -6.12592 q^{37} +(0.498193 + 0.862896i) q^{38} +(1.97786 - 0.484172i) q^{39} +(0.441537 - 0.764764i) q^{40} +(-2.52182 + 4.36792i) q^{41} +(-0.242192 + 0.0592876i) q^{42} +(-3.94035 - 6.82488i) q^{43} -3.42863 q^{44} +(2.81709 + 1.79396i) q^{45} -1.44977 q^{46} +(-2.05254 - 3.55510i) q^{47} +(1.82223 - 6.25392i) q^{48} +(3.24177 - 5.61490i) q^{49} +(-0.376657 + 0.652389i) q^{50} +(-5.24758 - 5.48069i) q^{51} +(-1.15205 - 1.99541i) q^{52} -7.37363 q^{53} +(-0.985725 - 0.334306i) q^{54} -1.94757 q^{55} +(0.285029 + 0.493684i) q^{56} +(5.95820 + 6.22288i) q^{57} +(-0.100158 + 0.173479i) q^{58} +(1.94345 - 3.36616i) q^{59} +(1.05717 - 3.62823i) q^{60} +(2.59104 + 4.48781i) q^{61} -0.0510920 q^{62} +(-1.91219 + 0.995867i) q^{63} -7.05300 q^{64} +(-0.654399 - 1.13345i) q^{65} +(0.589564 - 0.144323i) q^{66} +(3.74658 - 6.48926i) q^{67} +(-4.29294 + 7.43559i) q^{68} +(-12.1761 + 2.98064i) q^{69} +(0.0801323 + 0.138793i) q^{70} +5.68338 q^{71} +(-0.103364 + 2.37743i) q^{72} -10.1960 q^{73} +(-0.613559 - 1.06272i) q^{74} +(-1.82212 + 6.25355i) q^{75} +(4.87428 - 8.44250i) q^{76} +(0.628614 - 1.08879i) q^{77} +(0.282092 + 0.294623i) q^{78} +(6.19034 + 10.7220i) q^{79} -4.18684 q^{80} +(-8.96604 - 0.781116i) q^{81} -1.01032 q^{82} +(-5.47200 - 9.47778i) q^{83} +(1.68714 + 1.76209i) q^{84} +(-2.43852 + 4.22364i) q^{85} +(0.789314 - 1.36713i) q^{86} +(-0.484526 + 1.66290i) q^{87} +(-0.693839 - 1.20176i) q^{88} -0.231289 q^{89} +(-0.0290596 + 0.668385i) q^{90} +0.844879 q^{91} +(7.09221 + 12.2841i) q^{92} +(-0.429102 + 0.105042i) q^{93} +(0.411156 - 0.712142i) q^{94} +(2.76874 - 4.79560i) q^{95} +(3.93644 - 0.963623i) q^{96} +(5.16660 + 8.94881i) q^{97} +1.29875 q^{98} +(4.65480 - 2.42422i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - q^{2} - 2 q^{3} - 5 q^{4} + q^{5} - q^{6} + 7 q^{7} + 6 q^{8} - 2 q^{9} - 20 q^{10} - 3 q^{11} + 10 q^{12} + 7 q^{13} + 10 q^{14} - 8 q^{15} + 7 q^{16} + 2 q^{17} + 2 q^{18} - 56 q^{19} + 4 q^{20}+ \cdots - 40 q^{99}+O(q^{100}) $ 22 * q - q^2 - 2 * q^3 - 5 * q^4 + q^5 - q^6 + 7 * q^7 + 6 * q^8 - 2 * q^9 - 20 * q^10 - 3 * q^11 + 10 * q^12 + 7 * q^13 + 10 * q^14 - 8 * q^15 + 7 * q^16 + 2 * q^17 + 2 * q^18 - 56 * q^19 + 4 * q^20 + 16 * q^21 + 13 * q^22 - 4 * q^23 - 33 * q^24 + 4 * q^25 - 12 * q^26 + 13 * q^27 - 32 * q^28 + 11 * q^29 + 46 * q^30 + 27 * q^31 - 7 * q^32 - 10 * q^33 + 19 * q^34 - 22 * q^35 + 19 * q^36 - 28 * q^37 + 5 * q^38 + 17 * q^39 + 24 * q^40 + 9 * q^41 - 50 * q^42 + 25 * q^43 + 46 * q^44 - 56 * q^45 - 20 * q^46 - 6 * q^47 + 33 * q^48 + 12 * q^49 - 41 * q^50 - 15 * q^51 + 20 * q^52 - 12 * q^53 + 5 * q^54 - 70 * q^55 + 10 * q^56 + 25 * q^57 + q^58 - 48 * q^60 + 25 * q^61 - 12 * q^62 - 11 * q^63 - 50 * q^64 - 5 * q^65 + 29 * q^66 + 29 * q^67 + 50 * q^68 + 20 * q^69 + 7 * q^70 - 2 * q^71 + 30 * q^72 - 26 * q^73 - 14 * q^74 + 46 * q^75 + 38 * q^76 - 9 * q^77 - 39 * q^78 + 27 * q^79 - 74 * q^80 - 38 * q^81 - 34 * q^82 + 12 * q^83 + 60 * q^84 + 7 * q^85 - q^86 - q^87 - 5 * q^88 + 46 * q^89 - 35 * q^90 - 86 * q^91 - 19 * q^92 + 78 * q^93 - 10 * q^94 - 8 * q^95 - 75 * q^96 + 36 * q^97 + 86 * q^98 - 40 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.100158	+	0.173479i	0.0708224	+	0.122668i	0.899262	−	0.437411i	$-0.144104\pi$
$2$	0.100158	+	0.173479i	0.0708224	+	0.122668i	−0.828440	+	0.560078i	$0.810771\pi$
$3$	1.19785	+	1.25106i	0.691579	+	0.722301i
$3$	1.19785	+	1.25106i	0.691579	+	0.722301i
$4$	0.979937	−	1.69730i	0.489968	−	0.848650i
$5$	0.556635	−	0.964120i	0.248935	−	0.431167i	−0.714296	−	0.699844i	$-0.753253\pi$
$5$	0.556635	−	0.964120i	0.248935	−	0.431167i	0.963230	+	0.268676i	$0.0865862\pi$
$6$	−0.0970582	+	0.333105i	−0.0396238	+	0.135990i
$7$	0.359329	+	0.622375i	0.135813	+	0.235236i	0.925908	−	0.377749i	$-0.123302\pi$
$7$	0.359329	+	0.622375i	0.135813	+	0.235236i	−0.790094	+	0.612985i	$0.789969\pi$
$8$	0.793225			0.280448
$9$	−0.130309	+	2.99717i	−0.0434363	+	0.999056i
$10$	0.223006			0.0705205
$11$	−0.874706	−	1.51504i	−0.263734	−	0.456800i	0.703497	−	0.710698i	$-0.251621\pi$
$11$	−0.874706	−	1.51504i	−0.263734	−	0.456800i	−0.967231	+	0.253898i	$0.918287\pi$
$12$	3.29724	−	0.807151i	0.951832	−	0.233004i
$13$	0.587818	−	1.01813i	0.163031	−	0.282379i	−0.772923	−	0.634500i	$-0.781206\pi$
$13$	0.587818	−	1.01813i	0.163031	−	0.282379i	0.935954	+	0.352121i	$0.114540\pi$
$14$	−0.0719792	+	0.124672i	−0.0192373	+	0.0333199i
$15$	1.87294	−	0.458487i	0.483590	−	0.118381i
$16$	−1.88043	−	3.25699i	−0.470106	−	0.814248i
$17$	−4.38083			−1.06251			−0.531254	−	0.847213i	$-0.678279\pi$
$17$	−4.38083			−1.06251			−0.531254	+	0.847213i	$0.678279\pi$
$18$	−0.532996	+	0.277584i	−0.125628	+	0.0654273i
$19$	4.97408			1.14113			0.570566	−	0.821252i	$-0.306724\pi$
$19$	4.97408			1.14113			0.570566	+	0.821252i	$0.306724\pi$
$20$	−1.09093	−	1.88955i	−0.243940	−	0.422517i
$21$	−0.348208	+	1.19505i	−0.0759852	+	0.260782i
$22$	0.175218	−	0.303486i	0.0373565	−	0.0647034i
$23$	−3.61871	+	6.26778i	−0.754553	+	1.30692i	0.191044	+	0.981581i	$0.438813\pi$
$23$	−3.61871	+	6.26778i	−0.754553	+	1.30692i	−0.945596	+	0.325342i	$0.894521\pi$
$24$	0.950165	+	0.992374i	0.193952	+	0.202567i
$25$	1.88032	+	3.25680i	0.376063	+	0.651360i
$26$	0.235498			0.0461850
$27$	−3.90573	+	3.42714i	−0.751659	+	0.659552i
$28$	1.40848			0.266177
$29$	0.500000	+	0.866025i	0.0928477	+	0.160817i
$29$	0.500000	+	0.866025i	0.0928477	+	0.160817i
$30$	0.267127	+	0.278994i	0.0487705	+	0.0509370i
$31$	−0.127529	+	0.220886i	−0.0229048	+	0.0396723i	−0.877251	−	0.480033i	$-0.840625\pi$
$31$	−0.127529	+	0.220886i	−0.0229048	+	0.0396723i	0.854346	+	0.519705i	$0.173958\pi$
$32$	1.16990	−	2.02633i	0.206812	−	0.358209i
$33$	0.847635	−	2.90910i	0.147554	−	0.506409i
$34$	−0.438775	−	0.759981i	−0.0752493	−	0.130336i
$35$	0.800059			0.135235
$36$	4.95940	+	3.15821i	0.826567	+	0.526368i
$37$	−6.12592			−1.00709			−0.503547	−	0.863968i	$-0.667972\pi$
$37$	−6.12592			−1.00709			−0.503547	+	0.863968i	$0.667972\pi$
$38$	0.498193	+	0.862896i	0.0808176	+	0.139980i
$39$	1.97786	−	0.484172i	0.316711	−	0.0775295i
$40$	0.441537	−	0.764764i	0.0698131	−	0.120920i
$41$	−2.52182	+	4.36792i	−0.393842	+	0.682155i	−0.992953	−	0.118512i	$-0.962188\pi$
$41$	−2.52182	+	4.36792i	−0.393842	+	0.682155i	0.599111	+	0.800666i	$0.295521\pi$
$42$	−0.242192	+	0.0592876i	−0.0373711	+	0.00914827i
$43$	−3.94035	−	6.82488i	−0.600898	−	1.04079i	−0.992685	−	0.120730i	$-0.961477\pi$
$43$	−3.94035	−	6.82488i	−0.600898	−	1.04079i	0.391788	−	0.920056i	$-0.371857\pi$
$44$	−3.42863			−0.516885
$45$	2.81709	+	1.79396i	0.419948	+	0.267428i
$46$	−1.44977			−0.213757
$47$	−2.05254	−	3.55510i	−0.299393	−	0.518564i	0.676604	−	0.736347i	$-0.263451\pi$
$47$	−2.05254	−	3.55510i	−0.299393	−	0.518564i	−0.975997	+	0.217783i	$0.930118\pi$
$48$	1.82223	−	6.25392i	0.263016	−	0.902675i
$49$	3.24177	−	5.61490i	0.463109	−	0.802129i
$50$	−0.376657	+	0.652389i	−0.0532674	+	0.0922618i
$51$	−5.24758	−	5.48069i	−0.734808	−	0.767450i
$52$	−1.15205	−	1.99541i	−0.159760	−	0.276713i
$53$	−7.37363			−1.01285			−0.506423	−	0.862285i	$-0.669033\pi$
$53$	−7.37363			−1.01285			−0.506423	+	0.862285i	$0.669033\pi$
$54$	−0.985725	−	0.334306i	−0.134140	−	0.0454933i
$55$	−1.94757			−0.262610
$56$	0.285029	+	0.493684i	0.0380885	+	0.0659713i
$57$	5.95820	+	6.22288i	0.789183	+	0.824240i
$58$	−0.100158	+	0.173479i	−0.0131514	+	0.0227789i
$59$	1.94345	−	3.36616i	0.253016	−	0.438236i	−0.711339	−	0.702849i	$-0.751911\pi$
$59$	1.94345	−	3.36616i	0.253016	−	0.438236i	0.964355	+	0.264613i	$0.0852442\pi$
$60$	1.05717	−	3.62823i	0.136480	−	0.468402i
$61$	2.59104	+	4.48781i	0.331748	+	0.574605i	0.982855	−	0.184381i	$-0.0590282\pi$
$61$	2.59104	+	4.48781i	0.331748	+	0.574605i	−0.651106	+	0.758987i	$0.725695\pi$
$62$	−0.0510920			−0.00648870
$63$	−1.91219	+	0.995867i	−0.240913	+	0.125467i
$64$	−7.05300			−0.881625
$65$	−0.654399	−	1.13345i	−0.0811683	−	0.140588i
$66$	0.589564	−	0.144323i	0.0725703	−	0.0177649i
$67$	3.74658	−	6.48926i	0.457717	−	0.792790i	−0.541122	−	0.840944i	$-0.682000\pi$
$67$	3.74658	−	6.48926i	0.457717	−	0.792790i	0.998840	+	0.0481539i	$0.0153338\pi$
$68$	−4.29294	+	7.43559i	−0.520595	+	0.901697i
$69$	−12.1761	+	2.98064i	−1.46582	+	0.358827i
$70$	0.0801323	+	0.138793i	0.00957764	+	0.0165890i
$71$	5.68338			0.674494			0.337247	−	0.941416i	$-0.390504\pi$
$71$	5.68338			0.674494			0.337247	+	0.941416i	$0.390504\pi$
$72$	−0.103364	+	2.37743i	−0.0121816	+	0.280183i
$73$	−10.1960			−1.19335			−0.596675	−	0.802483i	$-0.703512\pi$
$73$	−10.1960			−1.19335			−0.596675	+	0.802483i	$0.703512\pi$
$74$	−0.613559	−	1.06272i	−0.0713248	−	0.123538i
$75$	−1.82212	+	6.25355i	−0.210401	+	0.722098i
$76$	4.87428	−	8.44250i	0.559118	−	0.968421i
$77$	0.628614	−	1.08879i	0.0716372	−	0.124079i
$78$	0.282092	+	0.294623i	0.0319406	+	0.0333595i
$79$	6.19034	+	10.7220i	0.696467	+	1.20632i	0.969684	+	0.244364i	$0.0785791\pi$
$79$	6.19034	+	10.7220i	0.696467	+	1.20632i	−0.273216	+	0.961953i	$0.588088\pi$
$80$	−4.18684			−0.468103
$81$	−8.96604	−	0.781116i	−0.996227	−	0.0867906i
$82$	−1.01032			−0.111571
$83$	−5.47200	−	9.47778i	−0.600630	−	1.04032i	−0.992726	−	0.120397i	$-0.961583\pi$
$83$	−5.47200	−	9.47778i	−0.600630	−	1.04032i	0.392096	−	0.919924i	$-0.371750\pi$
$84$	1.68714	+	1.76209i	0.184083	+	0.192260i
$85$	−2.43852	+	4.22364i	−0.264495	+	0.458119i
$86$	0.789314	−	1.36713i	0.0851140	−	0.147422i
$87$	−0.484526	+	1.66290i	−0.0519466	+	0.178282i
$88$	−0.693839	−	1.20176i	−0.0739635	−	0.128109i
$89$	−0.231289			−0.0245166			−0.0122583	−	0.999925i	$-0.503902\pi$
$89$	−0.231289			−0.0245166			−0.0122583	+	0.999925i	$0.503902\pi$
$90$	−0.0290596	+	0.668385i	−0.00306315	+	0.0704540i
$91$	0.844879			0.0885674
$92$	7.09221	+	12.2841i	0.739414	+	1.28070i
$93$	−0.429102	+	0.105042i	−0.0444959	+	0.0108924i
$94$	0.411156	−	0.712142i	0.0424075	−	0.0734519i
$95$	2.76874	−	4.79560i	0.284067	−	0.492019i
$96$	3.93644	−	0.963623i	0.401761	−	0.0983493i
$97$	5.16660	+	8.94881i	0.524588	+	0.908614i	0.999590	+	0.0286289i	$0.00911410\pi$
$97$	5.16660	+	8.94881i	0.524588	+	0.908614i	−0.475002	+	0.879985i	$0.657553\pi$
$98$	1.29875			0.131194
$99$	4.65480	−	2.42422i	0.467825	−	0.243643i
$100$	7.37036			0.737036
$101$	1.78745	+	3.09596i	0.177858	+	0.308060i	0.941147	−	0.337998i	$-0.109750\pi$
$101$	1.78745	+	3.09596i	0.177858	+	0.308060i	−0.763288	+	0.646058i	$0.776416\pi$
$102$	0.425195	−	1.45928i	0.0421006	−	0.144490i
$103$	0.309953	−	0.536855i	0.0305406	−	0.0528979i	−0.850351	−	0.526216i	$-0.823610\pi$
$103$	0.309953	−	0.536855i	0.0305406	−	0.0528979i	0.880892	+	0.473318i	$0.156944\pi$
$104$	0.466272	−	0.807607i	0.0457217	−	0.0791924i
$105$	0.958351	+	1.00092i	0.0935255	+	0.0976801i
$106$	−0.738528	−	1.27917i	−0.0717322	−	0.124244i
$107$	4.75430			0.459615			0.229808	−	0.973236i	$-0.426190\pi$
$107$	4.75430			0.459615			0.229808	+	0.973236i	$0.426190\pi$
$108$	1.98951	+	9.98758i	0.191440	+	0.961055i
$109$	−2.64202			−0.253060			−0.126530	−	0.991963i	$-0.540384\pi$
$109$	−2.64202			−0.253060			−0.126530	+	0.991963i	$0.540384\pi$
$110$	−0.195064	−	0.337861i	−0.0185987	−	0.0322138i
$111$	−7.33794	−	7.66390i	−0.696486	−	0.727425i
$112$	1.35138	−	2.34066i	0.127694	−	0.221172i
$113$	0.730644	−	1.26551i	0.0687332	−	0.119049i	−0.829611	−	0.558342i	$-0.811438\pi$
$113$	0.730644	−	1.26551i	0.0687332	−	0.119049i	0.898344	+	0.439293i	$0.144771\pi$
$114$	−0.482775	+	1.65689i	−0.0452160	+	0.155182i
$115$	4.02860	+	6.97773i	0.375668	+	0.650677i
$116$	1.95987			0.181970
$117$	2.97491	+	1.89446i	0.275031	+	0.175143i
$118$	0.778608			0.0716767
$119$	−1.57416	−	2.72652i	−0.144303	−	0.249940i
$120$	1.48566	−	0.363683i	0.135622	−	0.0331996i
$121$	3.96978	−	6.87586i	0.360889	−	0.625078i
$122$	−0.519026	+	0.898979i	−0.0469904	+	0.0813898i
$123$	−8.48530	+	2.07716i	−0.765094	+	0.187292i
$124$	0.249940	+	0.432909i	0.0224453	+	0.0388764i
$125$	9.75294			0.872330
$126$	−0.364282	−	0.231980i	−0.0324529	−	0.0206664i
$127$	1.85264			0.164395			0.0821976	−	0.996616i	$-0.473806\pi$
$127$	1.85264			0.164395			0.0821976	+	0.996616i	$0.473806\pi$
$128$	−3.04622	−	5.27621i	−0.269251	−	0.466356i
$129$	3.81840	−	13.1048i	0.336191	−	1.15381i
$130$	0.131087	−	0.227049i	0.0114971	−	0.0199135i
$131$	5.59673	−	9.69381i	0.488988	−	0.846952i	−0.510932	−	0.859621i	$-0.670699\pi$
$131$	5.59673	−	9.69381i	0.488988	−	0.846952i	0.999920	+	0.0126690i	$0.00403279\pi$
$132$	−4.10698	−	4.28942i	−0.357467	−	0.373346i
$133$	1.78733	+	3.09574i	0.154981	+	0.268435i
$134$	1.50100			0.129667
$135$	1.13010	+	5.67325i	0.0972637	+	0.488276i
$136$	−3.47499			−0.297978
$137$	10.1097	+	17.5106i	0.863733	+	1.49603i	0.868300	+	0.496040i	$0.165213\pi$
$137$	10.1097	+	17.5106i	0.863733	+	1.49603i	−0.00456701	+	0.999990i	$0.501454\pi$
$138$	−1.73661	−	1.81375i	−0.147830	−	0.154397i
$139$	4.12472	−	7.14423i	0.349854	−	0.605965i	−0.636369	−	0.771385i	$-0.719564\pi$
$139$	4.12472	−	7.14423i	0.349854	−	0.605965i	0.986223	+	0.165419i	$0.0528978\pi$
$140$	0.784007	−	1.35794i	0.0662607	−	0.114767i
$141$	1.98901	−	6.82632i	0.167505	−	0.574880i
$142$	0.569236	+	0.985946i	0.0477692	+	0.0827387i
$143$	−2.05667			−0.171987
$144$	10.0068	−	5.21154i	0.833899	−	0.434295i
$145$	1.11327			0.0924520
$146$	−1.02121	−	1.76879i	−0.0845159	−	0.146386i
$147$	10.9077	−	2.67017i	0.899655	−	0.220232i
$148$	−6.00301	+	10.3975i	−0.493445	+	0.854671i
$149$	11.4249	−	19.7884i	0.935961	−	1.62113i	0.163050	−	0.986618i	$-0.447867\pi$
$149$	11.4249	−	19.7884i	0.935961	−	1.62113i	0.772911	−	0.634514i	$-0.218800\pi$
$150$	−1.26736	+	0.310244i	−0.103479	+	0.0253313i
$151$	9.04588	+	15.6679i	0.736143	+	1.27504i	0.954220	+	0.299106i	$0.0966883\pi$
$151$	9.04588	+	15.6679i	0.736143	+	1.27504i	−0.218077	+	0.975932i	$0.569978\pi$
$152$	3.94556			0.320028
$153$	0.570861	−	13.1301i	0.0461514	−	1.06150i
$154$	0.251843			0.0202941
$155$	0.141974	+	0.245906i	0.0114036	+	0.0197516i
$156$	1.11639	−	3.83148i	0.0893831	−	0.306764i
$157$	−9.44065	+	16.3517i	−0.753446	+	1.30501i	0.192697	+	0.981258i	$0.438277\pi$
$157$	−9.44065	+	16.3517i	−0.753446	+	1.30501i	−0.946143	+	0.323749i	$0.895057\pi$
$158$	−1.24002	+	2.14778i	−0.0986509	+	0.170868i
$159$	−8.83251	−	9.22487i	−0.700464	−	0.731580i
$160$	−1.30242	−	2.25586i	−0.102965	−	0.178341i
$161$	−5.20122			−0.409914
$162$	−0.762513	−	1.63365i	−0.0599087	−	0.128352i
$163$	−9.58127			−0.750463			−0.375231	−	0.926931i	$-0.622437\pi$
$163$	−9.58127			−0.750463			−0.375231	+	0.926931i	$0.622437\pi$
$164$	4.94245	+	8.56057i	0.385940	+	0.668468i
$165$	−2.33289	−	2.43653i	−0.181616	−	0.189683i
$166$	1.09613	−	1.89855i	0.0850761	−	0.147356i
$167$	−0.395980	+	0.685857i	−0.0306418	+	0.0530732i	−0.880940	−	0.473229i	$-0.843088\pi$
$167$	−0.395980	+	0.685857i	−0.0306418	+	0.0530732i	0.850298	+	0.526302i	$0.176422\pi$
$168$	−0.276207	+	0.947948i	−0.0213099	+	0.0731358i
$169$	5.80894	+	10.0614i	0.446842	+	0.773952i
$170$	−0.976949			−0.0749286
$171$	−0.648167	+	14.9081i	−0.0495665	+	1.14005i
$172$	−15.4452			−1.17768
$173$	7.76382	+	13.4473i	0.590272	+	1.02238i	0.994196	+	0.107588i	$0.0343129\pi$
$173$	7.76382	+	13.4473i	0.590272	+	1.02238i	−0.403924	+	0.914793i	$0.632354\pi$
$174$	−0.337007	+	0.0824977i	−0.0255484	+	0.00625414i
$175$	−1.35130	+	2.34052i	−0.102149	+	0.176927i
$176$	−3.28964	+	5.69782i	−0.247966	+	0.429490i
$177$	6.53923	−	1.60077i	0.491519	−	0.120322i
$178$	−0.0231654	−	0.0401237i	−0.00173632	−	0.00300739i
$179$	17.8289			1.33260			0.666298	−	0.745686i	$-0.267878\pi$
$179$	17.8289			1.33260			0.666298	+	0.745686i	$0.267878\pi$
$180$	5.80547	−	3.02349i	0.432714	−	0.225357i
$181$	−4.10193			−0.304894			−0.152447	−	0.988312i	$-0.548715\pi$
$181$	−4.10193			−0.304894			−0.152447	+	0.988312i	$0.548715\pi$
$182$	0.0846213	+	0.146568i	0.00627255	+	0.0108644i
$183$	−2.51085	+	8.61727i	−0.185607	+	0.637007i
$184$	−2.87045	+	4.97177i	−0.211612	+	0.366523i
$185$	−3.40990	+	5.90612i	−0.250701	+	0.434226i
$186$	−0.0612006	−	0.0639193i	−0.00448745	−	0.00468679i
$187$	3.83194	+	6.63711i	0.280219	+	0.485354i
$188$	−8.04542			−0.586773
$189$	−3.53641	−	1.19936i	−0.257236	−	0.0872409i
$190$	1.10925			0.0804732
$191$	−7.35271	−	12.7353i	−0.532024	−	0.921492i	−0.999301	−	0.0373811i	$-0.988098\pi$
$191$	−7.35271	−	12.7353i	−0.532024	−	0.921492i	0.467278	−	0.884111i	$-0.345235\pi$
$192$	−8.44844	−	8.82374i	−0.609714	−	0.636798i
$193$	0.367922	−	0.637259i	0.0264836	−	0.0458709i	−0.852480	−	0.522760i	$-0.824902\pi$
$193$	0.367922	−	0.637259i	0.0264836	−	0.0458709i	0.878963	+	0.476889i	$0.158236\pi$
$194$	−1.03495	+	1.79259i	−0.0743052	+	0.128700i
$195$	0.634147	−	2.17640i	0.0454122	−	0.155855i
$196$	−6.35345	−	11.0045i	−0.453818	−	0.786036i
$197$	21.7386			1.54881			0.774406	−	0.632689i	$-0.218049\pi$
$197$	21.7386			1.54881			0.774406	+	0.632689i	$0.218049\pi$
$198$	0.886765	+	0.564703i	0.0630197	+	0.0401317i
$199$	−15.8209			−1.12151			−0.560756	−	0.827981i	$-0.689489\pi$
$199$	−15.8209			−1.12151			−0.560756	+	0.827981i	$0.689489\pi$
$200$	1.49151	+	2.58338i	0.105466	+	0.182672i
$201$	12.6063	−	3.08597i	0.889180	−	0.217667i
$202$	−0.358055	+	0.620170i	−0.0251927	+	0.0436350i
$203$	−0.359329	+	0.622375i	−0.0252199	+	0.0436822i
$204$	−14.4447	+	3.53599i	−1.01133	+	0.247569i
$205$	2.80746	+	4.86267i	0.196082	+	0.339624i
$206$	0.124177			0.00865183
$207$	−18.3141	−	11.6626i	−1.27291	−	0.810608i
$208$	−4.42139			−0.306568
$209$	−4.35086	−	7.53590i	−0.300955	−	0.521269i
$210$	−0.0776523	+	0.266504i	−0.00535852	+	0.0183905i
$211$	8.88504	−	15.3893i	0.611671	−	1.05945i	−0.379288	−	0.925279i	$-0.623831\pi$
$211$	8.88504	−	15.3893i	0.611671	−	1.05945i	0.990959	−	0.134167i	$-0.0428357\pi$
$212$	−7.22570	+	12.5153i	−0.496263	+	0.859552i
$213$	6.80784	+	7.11026i	0.466466	+	0.487187i
$214$	0.476181	+	0.824769i	0.0325510	+	0.0563801i
$215$	−8.77334			−0.598337
$216$	−3.09813	+	2.71849i	−0.210801	+	0.184970i
$217$	−0.183299			−0.0124431
$218$	−0.264619	−	0.458334i	−0.0179223	−	0.0310423i
$219$	−12.2133	−	12.7558i	−0.825297	−	0.861958i
$220$	−1.90849	+	3.30561i	−0.128671	+	0.222864i
$221$	−2.57513	+	4.46026i	−0.173222	+	0.300029i
$222$	0.594571	−	2.04058i	0.0399050	−	0.136954i
$223$	−10.4315	−	18.0679i	−0.698546	−	1.20992i	−0.968971	−	0.247175i	$-0.920498\pi$
$223$	−10.4315	−	18.0679i	−0.698546	−	1.20992i	0.270425	−	0.962741i	$-0.412836\pi$
$224$	1.68152			0.112351
$225$	−10.0062	+	5.21123i	−0.667081	+	0.347416i
$226$	0.292719			0.0194714
$227$	0.797071	+	1.38057i	0.0529035	+	0.0916315i	0.891264	−	0.453484i	$-0.149819\pi$
$227$	0.797071	+	1.38057i	0.0529035	+	0.0916315i	−0.838361	+	0.545116i	$0.816486\pi$
$228$	16.4007	−	4.01483i	1.08617	−	0.265889i
$229$	−9.93007	+	17.1994i	−0.656197	+	1.13657i	0.325395	+	0.945578i	$0.394503\pi$
$229$	−9.93007	+	17.1994i	−0.656197	+	1.13657i	−0.981592	+	0.190989i	$0.938831\pi$
$230$	−0.806992	+	1.39775i	−0.0532114	+	0.0921649i
$231$	2.11513	−	0.517774i	0.139165	−	0.0340671i
$232$	0.396613	+	0.686953i	0.0260389	+	0.0451007i
$233$	27.3329			1.79064			0.895319	−	0.445426i	$-0.146948\pi$
$233$	27.3329			1.79064			0.895319	+	0.445426i	$0.146948\pi$
$234$	−0.0306876	+	0.705829i	−0.00200611	+	0.0461415i
$235$	−4.57005			−0.298117
$236$	−3.80892	−	6.59724i	−0.247939	−	0.429444i
$237$	−5.99875	+	20.5878i	−0.389661	+	1.33732i
$238$	0.315329	−	0.546165i	0.0204397	−	0.0354026i
$239$	5.81904	−	10.0789i	0.376402	−	0.651948i	−0.614134	−	0.789202i	$-0.710494\pi$
$239$	5.81904	−	10.0789i	0.376402	−	0.651948i	0.990536	+	0.137254i	$0.0438278\pi$
$240$	−5.01521	−	5.23799i	−0.323730	−	0.338111i
$241$	6.11725	+	10.5954i	0.394047	+	0.682509i	0.992979	−	0.118291i	$-0.0377415\pi$
$241$	6.11725	+	10.5954i	0.394047	+	0.682509i	−0.598932	+	0.800800i	$0.704408\pi$
$242$	1.59042			0.102236
$243$	−9.76275	−	12.1527i	−0.626281	−	0.779598i
$244$	10.1562			0.650185
$245$	−3.60896	−	6.25090i	−0.230568	−	0.399355i
$246$	−1.21021	−	1.26397i	−0.0771604	−	0.0805880i
$247$	2.92385	−	5.06426i	0.186040	−	0.322231i
$248$	−0.101159	+	0.175213i	−0.00642360	+	0.0111260i
$249$	5.30265	−	18.1988i	0.336042	−	1.15330i
$250$	0.976835	+	1.69193i	0.0617804	+	0.107007i
$251$	−13.9999			−0.883666			−0.441833	−	0.897097i	$-0.645672\pi$
$251$	−13.9999			−0.883666			−0.441833	+	0.897097i	$0.645672\pi$
$252$	−0.183537	+	4.22144i	−0.0115618	+	0.265926i
$253$	12.6612			0.796004
$254$	0.185557	+	0.321394i	0.0116429	+	0.0201660i
$255$	−8.20502	+	2.00855i	−0.513818	+	0.125780i
$256$	−6.44280	+	11.1592i	−0.402675	+	0.697453i
$257$	3.34923	−	5.80104i	0.208919	−	0.361859i	−0.742455	−	0.669896i	$-0.766339\pi$
$257$	3.34923	−	5.80104i	0.208919	−	0.361859i	0.951374	+	0.308037i	$0.0996720\pi$
$258$	2.65585	−	0.650140i	0.165346	−	0.0404759i
$259$	−2.20122	−	3.81262i	−0.136777	−	0.236905i
$260$	−2.56508			−0.159080
$261$	−2.66078	+	1.38573i	−0.164698	+	0.0857747i
$262$	2.24223			0.138525
$263$	−10.9025	−	18.8837i	−0.672279	−	1.16442i	−0.977256	−	0.212061i	$-0.931982\pi$
$263$	−10.9025	−	18.8837i	−0.672279	−	1.16442i	0.304978	−	0.952360i	$-0.401351\pi$
$264$	0.672366	−	2.30757i	0.0413813	−	0.142021i
$265$	−4.10442	+	7.10907i	−0.252133	+	0.436706i
$266$	−0.358030	+	0.620126i	−0.0219522	+	0.0380224i
$267$	−0.277049	−	0.289356i	−0.0169551	−	0.0177083i
$268$	−7.34282	−	12.7181i	−0.448534	−	0.776884i
$269$	−28.6547			−1.74711			−0.873553	−	0.486729i	$-0.838190\pi$
$269$	−28.6547			−1.74711			−0.873553	+	0.486729i	$0.838190\pi$
$270$	−0.871000	+	0.764270i	−0.0530074	+	0.0465120i
$271$	−2.06951			−0.125714			−0.0628570	−	0.998023i	$-0.520021\pi$
$271$	−2.06951			−0.125714			−0.0628570	+	0.998023i	$0.520021\pi$
$272$	8.23783	+	14.2683i	0.499492	+	0.865145i
$273$	1.01204	+	1.05700i	0.0612514	+	0.0639723i
$274$	−2.02514	+	3.50765i	−0.122343	+	0.211905i
$275$	3.28945	−	5.69749i	0.198361	−	0.343572i
$276$	−6.87271	+	23.5873i	−0.413689	+	1.41979i
$277$	−1.69727	−	2.93975i	−0.101979	−	0.176633i	0.810521	−	0.585710i	$-0.199184\pi$
$277$	−1.69727	−	2.93975i	−0.101979	−	0.176633i	−0.912500	+	0.409077i	$0.865851\pi$
$278$	1.65249			0.0991100
$279$	−0.645415	−	0.411008i	−0.0386400	−	0.0246064i
$280$	0.634627			0.0379262
$281$	−7.69685	−	13.3313i	−0.459155	−	0.795281i	0.539761	−	0.841818i	$-0.318515\pi$
$281$	−7.69685	−	13.3313i	−0.459155	−	0.795281i	−0.998917	+	0.0465377i	$0.985181\pi$
$282$	1.38344	−	0.338659i	0.0823825	−	0.0201669i
$283$	12.2698	−	21.2520i	0.729366	−	1.26330i	−0.227786	−	0.973711i	$-0.573149\pi$
$283$	12.2698	−	21.2520i	0.729366	−	1.26330i	0.957152	−	0.289587i	$-0.0935179\pi$
$284$	5.56936	−	9.64641i	0.330481	−	0.572409i
$285$	9.31614	−	2.28055i	0.551840	−	0.135088i
$286$	−0.205992	−	0.356789i	−0.0121806	−	0.0210973i
$287$	−3.62465			−0.213956
$288$	5.92082	+	3.77045i	0.348887	+	0.222176i
$289$	2.19168			0.128922
$290$	0.111503	+	0.193128i	0.00654767	+	0.0113409i
$291$	−5.00670	+	17.1831i	−0.293498	+	1.00729i
$292$	−9.99143	+	17.3057i	−0.584704	+	1.01274i
$293$	4.51809	−	7.82556i	0.263949	−	0.457174i	−0.703338	−	0.710855i	$-0.748308\pi$
$293$	4.51809	−	7.82556i	0.263949	−	0.457174i	0.967288	+	0.253681i	$0.0816415\pi$
$294$	1.55571	+	1.62482i	0.0907310	+	0.0947615i
$295$	−2.16358	−	3.74744i	−0.125969	−	0.218184i
$296$	−4.85924			−0.282437
$297$	8.60860	+	2.91959i	0.499522	+	0.169412i
$298$	4.57716			0.265148
$299$	4.25428	+	7.36863i	0.246031	+	0.426139i
$300$	8.82859	+	9.22078i	0.509719	+	0.532362i
$301$	2.83176	−	4.90475i	0.163220	−	0.282705i
$302$	−1.81203	+	3.13853i	−0.104271	+	0.180602i
$303$	−1.73213	+	5.94471i	−0.0995085	+	0.341515i
$304$	−9.35338	−	16.2005i	−0.536453	−	0.929164i
$305$	5.76905			0.330335
$306$	2.33497	−	1.21605i	0.133481	−	0.0695170i
$307$	16.6320			0.949239			0.474620	−	0.880191i	$-0.342586\pi$
$307$	16.6320			0.949239			0.474620	+	0.880191i	$0.342586\pi$
$308$	−1.23200	−	2.13389i	−0.0701999	−	0.121590i
$309$	1.04292	−	0.255301i	0.0593294	−	0.0145236i
$310$	−0.0284396	+	0.0492588i	−0.00161526	+	0.00279771i
$311$	−8.61447	+	14.9207i	−0.488482	+	0.846076i	−0.999912	−	0.0132492i	$-0.995783\pi$
$311$	−8.61447	+	14.9207i	−0.488482	+	0.846076i	0.511430	+	0.859325i	$0.329116\pi$
$312$	1.56889	−	0.384057i	0.0888209	−	0.0217430i
$313$	−16.4733	−	28.5326i	−0.931127	−	1.61276i	−0.781399	−	0.624032i	$-0.785494\pi$
$313$	−16.4733	−	28.5326i	−0.931127	−	1.61276i	−0.149728	−	0.988727i	$-0.547840\pi$
$314$	−3.78223			−0.213443
$315$	−0.104255	+	2.39791i	−0.00587409	+	0.135107i
$316$	24.2645			1.36499
$317$	7.63755	+	13.2286i	0.428968	+	0.742994i	0.996782	−	0.0801629i	$-0.0255441\pi$
$317$	7.63755	+	13.2286i	0.428968	+	0.742994i	−0.567814	+	0.823157i	$0.692211\pi$
$318$	0.715672	−	2.45620i	0.0401329	−	0.137737i
$319$	0.874706	−	1.51504i	0.0489741	−	0.0848257i
$320$	−3.92595	+	6.79994i	−0.219467	+	0.380128i
$321$	5.69494	+	5.94792i	0.317860	+	0.331980i
$322$	−0.520943	−	0.902300i	−0.0290310	−	0.0502832i
$323$	−21.7906			−1.21246
$324$	−10.1119	+	14.4526i	−0.561774	+	0.802923i
$325$	4.42113			0.245240
$326$	−0.959640	−	1.66214i	−0.0531495	−	0.0920577i
$327$	−3.16474	−	3.30533i	−0.175011	−	0.182785i
$328$	−2.00037	+	3.46475i	−0.110452	+	0.191309i
$329$	1.47507	−	2.55490i	0.0813232	−	0.140856i
$330$	0.189027	−	0.648745i	0.0104056	−	0.0357122i
$331$	15.7537	+	27.2862i	0.865902	+	1.49979i	0.866149	+	0.499785i	$0.166588\pi$
$331$	15.7537	+	27.2862i	0.865902	+	1.49979i	−0.000247710		1.00000i	$0.500079\pi$
$332$	−21.4489			−1.17716
$333$	0.798262	−	18.3604i	0.0437445	−	1.00614i
$334$	−0.158642			−0.00868051
$335$	−4.17095	−	7.22430i	−0.227883	−	0.394706i
$336$	4.54706	−	1.11310i	0.248063	−	0.0607246i
$337$	0.0185574	−	0.0321424i	0.00101089	−	0.00175091i	−0.865520	−	0.500875i	$-0.833012\pi$
$337$	0.0185574	−	0.0321424i	0.00101089	−	0.00175091i	0.866530	+	0.499124i	$0.166345\pi$
$338$	−1.16362	+	2.01545i	−0.0632927	+	0.109626i
$339$	2.45844	−	0.601814i	0.133524	−	0.0326861i
$340$	4.77920	+	8.27781i	0.259188	+	0.448927i
$341$	0.446201			0.0241631
$342$	−2.65116	+	1.38073i	−0.143359	+	0.0746611i
$343$	9.69004			0.523213
$344$	−3.12559	−	5.41367i	−0.168520	−	0.291886i
$345$	−3.90392	+	13.3983i	−0.210180	+	0.721340i
$346$	−1.55522	+	2.69371i	−0.0836089	+	0.144815i
$347$	−7.82100	+	13.5464i	−0.419853	+	0.727207i	−0.995924	−	0.0901924i	$-0.971252\pi$
$347$	−7.82100	+	13.5464i	−0.419853	+	0.727207i	0.576071	+	0.817400i	$0.304585\pi$
$348$	2.34764	+	2.45192i	0.125846	+	0.131437i
$349$	−6.60224	−	11.4354i	−0.353410	−	0.612124i	0.633434	−	0.773796i	$-0.281645\pi$
$349$	−6.60224	−	11.4354i	−0.353410	−	0.612124i	−0.986845	+	0.161672i	$0.948311\pi$
$350$	−0.541375			−0.0289377
$351$	1.19341	+	5.99107i	0.0636996	+	0.319780i
$352$	−4.09329			−0.218173
$353$	17.4198	+	30.1719i	0.927161	+	1.60589i	0.788048	+	0.615614i	$0.211092\pi$
$353$	17.4198	+	30.1719i	0.927161	+	1.60589i	0.139114	+	0.990276i	$0.455575\pi$
$354$	0.932656	+	0.974087i	0.0495701	+	0.0517721i
$355$	3.16357	−	5.47946i	0.167905	−	0.290820i
$356$	−0.226648	+	0.392566i	−0.0120123	+	0.0208060i
$357$	1.52544	−	5.23533i	0.0807348	−	0.277083i
$358$	1.78571	+	3.09294i	0.0943776	+	0.163467i
$359$	−11.2109			−0.591688			−0.295844	−	0.955236i	$-0.595601\pi$
$359$	−11.2109			−0.591688			−0.295844	+	0.955236i	$0.595601\pi$
$360$	2.23459	+	1.42302i	0.117773	+	0.0749995i
$361$	5.74144			0.302181
$362$	−0.410841	−	0.711598i	−0.0215933	−	0.0374007i
$363$	13.3573	−	3.26981i	0.701077	−	0.171621i
$364$	0.827928	−	1.43401i	0.0433952	−	0.0751627i
$365$	−5.67544	+	9.83015i	−0.297066	+	0.514534i
$366$	−1.74639	+	0.427509i	−0.0912855	+	0.0223463i
$367$	1.19502	+	2.06984i	0.0623797	+	0.108045i	0.895529	−	0.445004i	$-0.146798\pi$
$367$	1.19502	+	2.06984i	0.0623797	+	0.108045i	−0.833149	+	0.553049i	$0.813464\pi$
$368$	27.2188			1.41888
$369$	−12.7628	−	8.12750i	−0.664404	−	0.423101i
$370$	−1.36611			−0.0710209
$371$	−2.64956	−	4.58917i	−0.137558	−	0.238258i
$372$	−0.242205	+	0.831251i	−0.0125577	+	0.0430983i
$373$	−4.74900	+	8.22550i	−0.245894	+	0.425900i	−0.962382	−	0.271698i	$-0.912415\pi$
$373$	−4.74900	+	8.22550i	−0.245894	+	0.425900i	0.716489	+	0.697599i	$0.245748\pi$
$374$	−0.767598	+	1.32952i	−0.0396916	+	0.0687478i
$375$	11.6826	+	12.2015i	0.603285	+	0.630084i
$376$	−1.62812	−	2.81999i	−0.0839641	−	0.145430i
$377$	1.17564			0.0605483
$378$	−0.146135	−	0.733617i	−0.00751638	−	0.0377332i
$379$	18.4353			0.946959			0.473480	−	0.880805i	$-0.342998\pi$
$379$	18.4353			0.946959			0.473480	+	0.880805i	$0.342998\pi$
$380$	−5.42639	−	9.39878i	−0.278368	−	0.482147i
$381$	2.21919	+	2.31777i	0.113692	+	0.118743i
$382$	1.47286	−	2.55108i	0.0753583	−	0.130524i
$383$	10.5510	−	18.2749i	0.539133	−	0.933806i	−0.459818	−	0.888013i	$-0.652085\pi$
$383$	10.5510	−	18.2749i	0.539133	−	0.933806i	0.998951	−	0.0457926i	$-0.0145813\pi$
$384$	2.95195	−	10.1311i	0.150641	−	0.517002i
$385$	−0.699817	−	1.21212i	−0.0356660	−	0.0617752i
$386$	0.147401			0.00750252
$387$	20.9688	−	10.9205i	1.06590	−	0.555123i
$388$	20.2518			1.02813
$389$	1.55415	+	2.69186i	0.0787983	+	0.136483i	0.902732	−	0.430204i	$-0.141558\pi$
$389$	1.55415	+	2.69186i	0.0787983	+	0.136483i	−0.823933	+	0.566687i	$0.808225\pi$
$390$	0.441074	−	0.107973i	0.0223346	−	0.00546742i
$391$	15.8529	−	27.4581i	0.801718	−	1.38862i
$392$	2.57145	−	4.45388i	0.129878	−	0.224955i
$393$	18.8316	−	4.60989i	0.949928	−	0.232538i
$394$	2.17729	+	3.77118i	0.109691	+	0.189990i
$395$	13.7830			0.693499
$396$	0.446781	−	10.2762i	0.0224516	−	0.516397i
$397$	−28.1778			−1.41420			−0.707102	−	0.707111i	$-0.749998\pi$
$397$	−28.1778			−1.41420			−0.707102	+	0.707111i	$0.749998\pi$
$398$	−1.58459	−	2.74458i	−0.0794281	−	0.137574i
$399$	−1.73201	+	5.94429i	−0.0867091	+	0.297587i
$400$	7.07159	−	12.2483i	0.353579	−	0.612417i
$401$	−3.24353	+	5.61796i	−0.161974	+	0.280547i	−0.935577	−	0.353124i	$-0.885119\pi$
$401$	−3.24353	+	5.61796i	−0.161974	+	0.280547i	0.773603	+	0.633671i	$0.218453\pi$
$402$	1.79797	+	1.87784i	0.0896747	+	0.0936582i
$403$	0.149927	+	0.259682i	0.00746841	+	0.0129357i
$404$	7.00637			0.348580
$405$	−5.74390	+	8.20954i	−0.285417	+	0.407935i
$406$	−0.143958			−0.00714454
$407$	5.35838	+	9.28099i	0.265605	+	0.460041i
$408$	−4.16251	−	4.34742i	−0.206075	−	0.215229i
$409$	7.85167	−	13.5995i	0.388240	−	0.672452i	−0.603973	−	0.797005i	$-0.706416\pi$
$409$	7.85167	−	13.5995i	0.388240	−	0.672452i	0.992213	+	0.124553i	$0.0397497\pi$
$410$	−0.562380	+	0.974070i	−0.0277740	+	0.0481059i
$411$	−9.79685	+	33.6229i	−0.483243	+	1.65850i
$412$	−0.607469	−	1.05217i	−0.0299279	−	0.0518366i
$413$	2.79335			0.137452
$414$	0.188918	−	4.34520i	0.00928481	−	0.213555i
$415$	−12.1836			−0.598070
$416$	−1.37538	−	2.38223i	−0.0674336	−	0.116798i
$417$	13.8787	−	3.39744i	0.679641	−	0.166373i
$418$	0.871545	−	1.50956i	0.0426287	−	0.0738350i
$419$	−1.87618	+	3.24963i	−0.0916572	+	0.158755i	−0.908209	−	0.418518i	$-0.862550\pi$
$419$	−1.87618	+	3.24963i	−0.0916572	+	0.158755i	0.816551	+	0.577273i	$0.195883\pi$
$420$	2.63799	−	0.645768i	0.128721	−	0.0315103i
$421$	−18.6578	−	32.3163i	−0.909328	−	1.57500i	−0.815000	−	0.579461i	$-0.803263\pi$
$421$	−18.6578	−	32.3163i	−0.909328	−	1.57500i	−0.0943281	−	0.995541i	$-0.530070\pi$
$422$	3.55963			0.173280
$423$	10.9227	−	5.68854i	0.531079	−	0.276586i
$424$	−5.84896			−0.284050
$425$	−8.23735	−	14.2675i	−0.399570	−	0.692075i
$426$	−0.551619	+	1.89316i	−0.0267260	+	0.0917241i
$427$	−1.86207	+	3.22520i	−0.0901118	+	0.156078i
$428$	4.65891	−	8.06947i	0.225197	−	0.390053i
$429$	−2.46358	−	2.57302i	−0.118943	−	0.124227i
$430$	−0.878720	−	1.52199i	−0.0423756	−	0.0733967i
$431$	−22.0148			−1.06041			−0.530207	−	0.847868i	$-0.677886\pi$
$431$	−22.0148			−1.06041			−0.530207	+	0.847868i	$0.677886\pi$
$432$	18.5066	+	6.27647i	0.890399	+	0.301977i
$433$	21.0621			1.01218			0.506090	−	0.862481i	$-0.331090\pi$
$433$	21.0621			1.01218			0.506090	+	0.862481i	$0.331090\pi$
$434$	−0.0183588	−	0.0317984i	−0.000881252	−	0.00152637i
$435$	1.33353	+	1.39277i	0.0639379	+	0.0667781i
$436$	−2.58901	+	4.48430i	−0.123991	+	0.214759i
$437$	−17.9997	+	31.1764i	−0.861044	+	1.49137i
$438$	0.989604	−	3.39634i	0.0472851	−	0.162283i
$439$	−19.3519	−	33.5185i	−0.923618	−	1.59975i	−0.793769	−	0.608219i	$-0.791884\pi$
$439$	−19.3519	−	33.5185i	−0.923618	−	1.59975i	−0.129849	−	0.991534i	$-0.541449\pi$
$440$	−1.54486			−0.0736483
$441$	16.4064	+	10.4478i	0.781256	+	0.497514i
$442$	−1.03168			−0.0490720
$443$	−5.63422	−	9.75876i	−0.267690	−	0.463653i	0.700575	−	0.713579i	$-0.252927\pi$
$443$	−5.63422	−	9.75876i	−0.267690	−	0.463653i	−0.968265	+	0.249926i	$0.919594\pi$
$444$	−20.1987	+	4.94454i	−0.958586	+	0.234658i
$445$	−0.128743	+	0.222990i	−0.00610302	+	0.0105707i
$446$	2.08960	−	3.61929i	0.0989453	−	0.171378i
$447$	38.4418	−	9.41039i	1.81824	−	0.445096i
$448$	−2.53435	−	4.38961i	−0.119737	−	0.207390i
$449$	12.8135			0.604708			0.302354	−	0.953196i	$-0.402228\pi$
$449$	12.8135			0.604708			0.302354	+	0.953196i	$0.402228\pi$
$450$	−1.90624	−	1.21392i	−0.0898609	−	0.0572246i
$451$	8.82341			0.415478
$452$	−1.43197	−	2.48024i	−0.0673542	−	0.116661i
$453$	−8.76592	+	30.0848i	−0.411859	+	1.41351i
$454$	−0.159666	+	0.276550i	−0.00749349	+	0.0129791i
$455$	0.470289	−	0.814564i	0.0220475	−	0.0381874i
$456$	4.72620	+	4.93614i	0.221324	+	0.231156i
$457$	10.9867	+	19.0295i	0.513936	+	0.890163i	0.999869	+	0.0161675i	$0.00514649\pi$
$457$	10.9867	+	19.0295i	0.513936	+	0.890163i	−0.485933	+	0.873996i	$0.661520\pi$
$458$	−3.97830			−0.185894
$459$	17.1104	−	15.0137i	0.798643	−	0.700779i
$460$	15.7911			0.736263
$461$	15.7697	+	27.3140i	0.734469	+	1.27214i	0.954956	+	0.296748i	$0.0959022\pi$
$461$	15.7697	+	27.3140i	0.734469	+	1.27214i	−0.220486	+	0.975390i	$0.570764\pi$
$462$	0.301670	+	0.315071i	0.0140350	+	0.0146584i
$463$	−11.1352	+	19.2868i	−0.517498	+	0.896332i	0.482296	+	0.876008i	$0.339803\pi$
$463$	−11.1352	+	19.2868i	−0.517498	+	0.896332i	−0.999793	+	0.0203236i	$0.993530\pi$
$464$	1.88043	−	3.25699i	0.0872966	−	0.151202i
$465$	−0.137580	+	0.472176i	−0.00638011	+	0.0218967i
$466$	2.73761	+	4.74167i	0.126817	+	0.219654i
$467$	−0.900593			−0.0416745			−0.0208372	−	0.999783i	$-0.506633\pi$
$467$	−0.900593			−0.0416745			−0.0208372	+	0.999783i	$0.506633\pi$
$468$	6.13069	−	3.19286i	0.283391	−	0.147590i
$469$	5.38501			0.248657
$470$	−0.457727	−	0.792806i	−0.0211134	−	0.0365694i
$471$	−31.7655	+	7.77604i	−1.46368	+	0.358301i
$472$	1.54160	−	2.67012i	0.0709577	−	0.122902i
$473$	−6.89330	+	11.9395i	−0.316954	+	0.548981i
$474$	−4.17237	+	1.02138i	−0.191643	+	0.0469134i
$475$	9.35283	+	16.1996i	0.429137	+	0.743288i
$476$	−6.17030			−0.282815
$477$	0.960851	−	22.1000i	0.0439943	−	1.01189i
$478$	2.33129			0.106631
$479$	0.962817	+	1.66765i	0.0439922	+	0.0761968i	0.887183	−	0.461418i	$-0.152659\pi$
$479$	0.962817	+	1.66765i	0.0439922	+	0.0761968i	−0.843191	+	0.537614i	$0.819326\pi$
$480$	1.26211	−	4.33158i	0.0576072	−	0.197709i
$481$	−3.60092	+	6.23698i	−0.164188	+	0.284382i
$482$	−1.22538	+	2.12242i	−0.0558146	+	0.0966738i
$483$	−6.23028	−	6.50704i	−0.283488	−	0.296081i
$484$	−7.78026	−	13.4758i	−0.353648	−	0.612537i
$485$	11.5036			0.522353
$486$	1.13042	−	2.91082i	0.0512769	−	0.132037i
$487$	0.168069			0.00761594			0.00380797	−	0.999993i	$-0.498788\pi$
$487$	0.168069			0.00761594			0.00380797	+	0.999993i	$0.498788\pi$
$488$	2.05528	+	3.55984i	0.0930380	+	0.161147i
$489$	−11.4769	−	11.9868i	−0.519004	−	0.542060i
$490$	0.722932	−	1.25215i	0.0326587	−	0.0565666i
$491$	21.5347	−	37.2992i	0.971847	−	1.68329i	0.281875	−	0.959451i	$-0.409044\pi$
$491$	21.5347	−	37.2992i	0.971847	−	1.68329i	0.689972	−	0.723837i	$-0.257623\pi$
$492$	−4.78949	+	16.4376i	−0.215927	+	0.741064i
$493$	−2.19042	−	3.79391i	−0.0986513	−	0.170869i
$494$	1.17139			0.0527032
$495$	0.253785	−	5.83719i	0.0114068	−	0.262362i
$496$	0.959233			0.0430708
$497$	2.04220	+	3.53720i	0.0916053	+	0.158665i
$498$	3.68820	−	0.902855i	0.165272	−	0.0404579i
$499$	−16.5651	+	28.6916i	−0.741555	+	1.28441i	0.210232	+	0.977652i	$0.432578\pi$
$499$	−16.5651	+	28.6916i	−0.741555	+	1.28441i	−0.951787	+	0.306760i	$0.900755\pi$
$500$	9.55727	−	16.5537i	0.427414	−	0.740303i
$501$	−1.33237	+	0.326159i	−0.0595261	+	0.0145717i
$502$	−1.40220	−	2.42868i	−0.0625833	−	0.108397i
$503$	−28.6639			−1.27806			−0.639030	−	0.769182i	$-0.720664\pi$
$503$	−28.6639			−1.27806			−0.639030	+	0.769182i	$0.720664\pi$
$504$	−1.51680	+	0.789947i	−0.0675635	+	0.0351870i
$505$	3.97983			0.177100
$506$	1.26812	+	2.19645i	0.0563749	+	0.0976442i
$507$	−5.62916	+	19.3194i	−0.250000	+	0.858003i
$508$	1.81547	−	3.14449i	0.0805485	−	0.139514i
$509$	−15.1739	+	26.2820i	−0.672572	+	1.16493i	0.304601	+	0.952480i	$0.401477\pi$
$509$	−15.1739	+	26.2820i	−0.672572	+	1.16493i	−0.977172	+	0.212448i	$0.931856\pi$
$510$	−1.17024	−	1.22222i	−0.0518191	−	0.0541210i
$511$	−3.66371	−	6.34573i	−0.162073	−	0.280719i
$512$	−14.7661			−0.652575
$513$	−19.4274	+	17.0468i	−0.857741	+	0.752636i
$514$	1.34181			0.0591847
$515$	−0.345062	−	0.597664i	−0.0152052	−	0.0263362i
$516$	−18.5010	−	19.3229i	−0.814461	−	0.850641i
$517$	−3.59073	+	6.21933i	−0.157920	+	0.273526i
$518$	0.440939	−	0.763729i	0.0193737	−	0.0335563i
$519$	−7.52354	+	25.8209i	−0.330247	+	1.13341i
$520$	−0.519086	−	0.899084i	−0.0227634	−	0.0394274i
$521$	−31.0573			−1.36065			−0.680323	−	0.732913i	$-0.738160\pi$
$521$	−31.0573			−1.36065			−0.680323	+	0.732913i	$0.738160\pi$
$522$	−0.506893	−	0.322796i	−0.0221861	−	0.0141284i
$523$	−10.3024			−0.450491			−0.225245	−	0.974302i	$-0.572318\pi$
$523$	−10.3024			−0.450491			−0.225245	+	0.974302i	$0.572318\pi$
$524$	−10.9689	−	18.9986i	−0.479177	−	0.829960i
$525$	−4.54680	+	1.11304i	−0.198439	+	0.0485769i
$526$	2.18395	−	3.78271i	0.0952247	−	0.164934i
$527$	0.558682	−	0.967665i	0.0243366	−	0.0421521i
$528$	−11.0688	+	2.70960i	−0.481709	+	0.117920i
$529$	−14.6901	−	25.4440i	−0.638699	−	1.10626i
$530$	−1.64436			−0.0714265
$531$	9.83569	+	6.26349i	0.426833	+	0.271812i
$532$	7.00587			0.303743
$533$	2.96474	+	5.13508i	0.128417	+	0.222425i
$534$	0.0224485	−	0.0770435i	0.000971440	−	0.00333400i
$535$	2.64641	−	4.58371i	0.114414	−	0.198171i
$536$	2.97188	−	5.14745i	0.128366	−	0.222336i
$537$	21.3564	+	22.3051i	0.921595	+	0.962535i
$538$	−2.86999	−	4.97097i	−0.123734	−	0.214314i
$539$	−11.3424			−0.488551
$540$	10.7366	+	3.64131i	0.462032	+	0.156697i
$541$	−10.3441			−0.444728			−0.222364	−	0.974964i	$-0.571377\pi$
$541$	−10.3441			−0.444728			−0.222364	+	0.974964i	$0.571377\pi$
$542$	−0.207278	−	0.359016i	−0.00890335	−	0.0154211i
$543$	−4.91350	−	5.13177i	−0.210859	−	0.220225i
$544$	−5.12515	+	8.87703i	−0.219739	+	0.380599i
$545$	−1.47064	+	2.54722i	−0.0629953	+	0.109111i
$546$	−0.0820024	+	0.281434i	−0.00350938	+	0.0120442i
$547$	4.78485	+	8.28761i	0.204585	+	0.354352i	0.950001	−	0.312248i	$-0.101082\pi$
$547$	4.78485	+	8.28761i	0.204585	+	0.354352i	−0.745415	+	0.666601i	$0.767749\pi$
$548$	39.6276			1.69281
$549$	−13.7884	+	7.18098i	−0.588473	+	0.306477i
$550$	1.31786			0.0561936
$551$	2.48704	+	4.30768i	0.105951	+	0.183513i
$552$	−9.65835	+	2.36432i	−0.411087	+	0.100632i
$553$	−4.44873	+	7.70542i	−0.189179	+	0.327668i
$554$	0.339990	−	0.588879i	0.0144448	−	0.0250191i
$555$	−11.4735	+	2.80865i	−0.487021	+	0.119221i
$556$	−8.08393	−	14.0018i	−0.342835	−	0.593808i
$557$	15.0530			0.637815			0.318908	−	0.947786i	$-0.396684\pi$
$557$	15.0530			0.637815			0.318908	+	0.947786i	$0.396684\pi$
$558$	0.00665775	−	0.153131i	0.000281845	−	0.00648257i
$559$	−9.26483			−0.391860
$560$	−1.50445	−	2.60579i	−0.0635747	−	0.110115i
$561$	−3.71335	+	12.7443i	−0.156778	+	0.538063i
$562$	1.54180	−	2.67048i	0.0650369	−	0.112647i
$563$	−17.4383	+	30.2040i	−0.734936	+	1.27295i	0.219815	+	0.975542i	$0.429455\pi$
$563$	−17.4383	+	30.2040i	−0.734936	+	1.27295i	−0.954751	+	0.297406i	$0.903879\pi$
$564$	−9.63721	−	10.0653i	−0.405800	−	0.423826i
$565$	−0.813403	−	1.40886i	−0.0342201	−	0.0592710i
$566$	4.91568			0.206622
$567$	−2.73561	−	5.86092i	−0.114885	−	0.246135i
$568$	4.50820			0.189160
$569$	−4.47272	−	7.74698i	−0.187506	−	0.324770i	0.756912	−	0.653517i	$-0.226707\pi$
$569$	−4.47272	−	7.74698i	−0.187506	−	0.324770i	−0.944418	+	0.328747i	$0.893374\pi$
$570$	1.32871	+	1.38774i	0.0556536	+	0.0581258i
$571$	5.75861	−	9.97421i	0.240991	−	0.417408i	−0.720006	−	0.693968i	$-0.755861\pi$
$571$	5.75861	−	9.97421i	0.240991	−	0.417408i	0.960997	+	0.276560i	$0.0891944\pi$
$572$	−2.01541	+	3.49079i	−0.0842684	+	0.145957i
$573$	7.12516	−	24.4536i	0.297658	−	1.02157i
$574$	−0.363037	−	0.628799i	−0.0151529	−	0.0262456i
$575$	−27.2172			−1.13504
$576$	0.919069	−	21.1390i	0.0382946	−	0.880793i
$577$	−39.3542			−1.63834			−0.819169	−	0.573552i	$-0.805565\pi$
$577$	−39.3542			−1.63834			−0.819169	+	0.573552i	$0.805565\pi$
$578$	0.219514	+	0.380209i	0.00913058	+	0.0158146i
$579$	1.23796	−	0.303048i	0.0514481	−	0.0125943i
$580$	1.09093	−	1.88955i	0.0452985	−	0.0784594i
$581$	3.93249	−	6.81128i	0.163147	−	0.282579i
$582$	−3.48235	+	0.852465i	−0.144348	+	0.0353358i
$583$	6.44976	+	11.1713i	0.267122	+	0.462669i
$584$	−8.08772			−0.334672
$585$	3.48242	−	1.81365i	0.143981	−	0.0749851i
$586$	1.81009			0.0747741
$587$	−3.38263	−	5.85889i	−0.139616	−	0.241822i	0.787735	−	0.616014i	$-0.211254\pi$
$587$	−3.38263	−	5.85889i	−0.139616	−	0.241822i	−0.927351	+	0.374192i	$0.877920\pi$
$588$	6.15682	−	21.1303i	0.253903	−	0.871399i
$589$	−0.634338	+	1.09870i	−0.0261374	+	0.0452713i
$590$	0.433400	−	0.750671i	0.0178428	−	0.0309047i
$591$	26.0396	+	27.1963i	1.07113	+	1.11871i
$592$	11.5193	+	19.9521i	0.473442	+	0.820025i
$593$	−41.8168			−1.71721			−0.858606	−	0.512636i	$-0.828669\pi$
$593$	−41.8168			−1.71721			−0.858606	+	0.512636i	$0.828669\pi$
$594$	0.355734	+	1.78583i	0.0145959	+	0.0732734i
$595$	−3.50492			−0.143688
$596$	−22.3913	−	38.7828i	−0.917183	−	1.58861i
$597$	−18.9510	−	19.7929i	−0.775614	−	0.810069i
$598$	−0.852200	+	1.47605i	−0.0348490	+	0.0603603i
$599$	−1.33709	+	2.31591i	−0.0546321	+	0.0946256i	−0.892048	−	0.451940i	$-0.850732\pi$
$599$	−1.33709	+	2.31591i	−0.0546321	+	0.0946256i	0.837416	+	0.546566i	$0.184065\pi$
$600$	−1.44535	+	4.96048i	−0.0590063	+	0.202511i
$601$	3.65206	+	6.32555i	0.148971	+	0.258025i	0.930847	−	0.365409i	$-0.119071\pi$
$601$	3.65206	+	6.32555i	0.148971	+	0.258025i	−0.781877	+	0.623433i	$0.785737\pi$
$602$	1.13449			0.0462385
$603$	18.9612	+	12.0747i	0.772160	+	0.491721i
$604$	35.4576			1.44275
$605$	−4.41943	−	7.65468i	−0.179675	−	0.311207i
$606$	−1.20477	+	0.294922i	−0.0489403	+	0.0119804i
$607$	10.2311	−	17.7207i	0.415266	−	0.719262i	−0.580190	−	0.814481i	$-0.697022\pi$
$607$	10.2311	−	17.7207i	0.415266	−	0.719262i	0.995456	+	0.0952189i	$0.0303551\pi$
$608$	5.81920	−	10.0791i	0.236000	−	0.408763i
$609$	−1.20905	+	0.295970i	−0.0489932	+	0.0119933i
$610$	0.577816	+	1.00081i	0.0233951	+	0.0405215i
$611$	−4.82607			−0.195242
$612$	−21.7263	−	13.8356i	−0.878233	−	0.559270i
$613$	−10.5862			−0.427571			−0.213786	−	0.976881i	$-0.568579\pi$
$613$	−10.5862			−0.427571			−0.213786	+	0.976881i	$0.568579\pi$
$614$	1.66583	+	2.88530i	0.0672274	+	0.116441i
$615$	−2.72058	+	9.33706i	−0.109704	+	0.376507i
$616$	0.498633	−	0.863657i	0.0200905	−	0.0347977i
$617$	6.36377	−	11.0224i	0.256196	−	0.443744i	−0.709024	−	0.705185i	$-0.750864\pi$
$617$	6.36377	−	11.0224i	0.256196	−	0.443744i	0.965220	+	0.261440i	$0.0841975\pi$
$618$	0.148746	+	0.155353i	0.00598343	+	0.00624922i
$619$	8.31609	+	14.4039i	0.334252	+	0.578941i	0.983341	−	0.181771i	$-0.0581831\pi$
$619$	8.31609	+	14.4039i	0.334252	+	0.578941i	−0.649089	+	0.760712i	$0.724850\pi$
$620$	0.556501			0.0223496
$621$	−7.34684	−	36.8821i	−0.294819	−	1.48003i
$622$	−3.45123			−0.138382
$623$	−0.0831087	−	0.143948i	−0.00332968	−	0.00576717i
$624$	−5.29616	−	5.53143i	−0.212016	−	0.221434i
$625$	−3.97275	+	6.88101i	−0.158910	+	0.275240i
$626$	3.29987	−	5.71554i	0.131889	−	0.228439i
$627$	4.21620	−	14.4701i	0.168379	−	0.577879i
$628$	18.5025	+	32.0472i	0.738330	+	1.27882i
$629$	26.8366			1.07005
$630$	−0.426428	+	0.222084i	−0.0169893	+	0.00884803i
$631$	32.1616			1.28033			0.640166	−	0.768237i	$-0.278866\pi$
$631$	32.1616			1.28033			0.640166	+	0.768237i	$0.278866\pi$
$632$	4.91033	+	8.50494i	0.195323	+	0.338309i
$633$	29.8959	−	7.31839i	1.18826	−	0.290880i
$634$	−1.52992	+	2.64990i	−0.0607610	+	0.105241i
$635$	1.03124	−	1.78617i	0.0409237	−	0.0708819i
$636$	−24.3127	+	5.95164i	−0.964060	+	0.235998i
$637$	−3.81114	−	6.60108i	−0.151003	−	0.261544i
$638$	0.350435			0.0138739
$639$	−0.740596	+	17.0341i	−0.0292975	+	0.673857i
$640$	−6.78253			−0.268103
$641$	−3.36868	−	5.83472i	−0.133055	−	0.230458i	0.791798	−	0.610783i	$-0.209145\pi$
$641$	−3.36868	−	5.83472i	−0.133055	−	0.230458i	−0.924853	+	0.380326i	$0.875812\pi$
$642$	−0.461444	+	1.58368i	−0.0182117	+	0.0625029i
$643$	−6.34818	+	10.9954i	−0.250348	+	0.433615i	−0.963622	−	0.267271i	$-0.913878\pi$
$643$	−6.34818	+	10.9954i	−0.250348	+	0.433615i	0.713274	+	0.700885i	$0.247212\pi$
$644$	−5.09687	+	8.82803i	−0.200845	+	0.347873i
$645$	−10.5091	−	10.9760i	−0.413797	−	0.432179i
$646$	−2.18250	−	3.78020i	−0.0858693	−	0.148730i
$647$	24.8669			0.977617			0.488809	−	0.872391i	$-0.337432\pi$
$647$	24.8669			0.977617			0.488809	+	0.872391i	$0.337432\pi$
$648$	−7.11209	−	0.619601i	−0.279389	−	0.0243402i
$649$	−6.79980			−0.266915
$650$	0.442811	+	0.766972i	0.0173685	+	0.0300831i
$651$	−0.219565	−	0.229318i	−0.00860541	−	0.00898768i
$652$	−9.38904	+	16.2623i	−0.367703	+	0.636880i
$653$	6.65645	−	11.5293i	0.260487	−	0.451177i	−0.705884	−	0.708327i	$-0.749450\pi$
$653$	6.65645	−	11.5293i	0.260487	−	0.451177i	0.966371	+	0.257150i	$0.0827835\pi$
$654$	0.256430	−	0.880070i	0.0100272	−	0.0344135i
$655$	−6.23066	−	10.7918i	−0.243452	−	0.421671i
$656$	18.9684			0.740591
$657$	1.32863	−	30.5591i	0.0518348	−	1.19222i
$658$	0.590960			0.0230380
$659$	−15.6719	−	27.1445i	−0.610489	−	1.05740i	−0.991158	−	0.132687i	$-0.957639\pi$
$659$	−15.6719	−	27.1445i	−0.610489	−	1.05740i	0.380669	−	0.924712i	$-0.375694\pi$
$660$	−6.42160	+	1.57198i	−0.249961	+	0.0611893i
$661$	−11.1857	+	19.3743i	−0.435075	+	0.753572i	−0.997302	−	0.0734109i	$-0.976612\pi$
$661$	−11.1857	+	19.3743i	−0.435075	+	0.753572i	0.562227	+	0.826983i	$0.309945\pi$
$662$	−3.15572	+	5.46586i	−0.122650	+	0.212437i
$663$	−8.66467	+	2.12107i	−0.336508	+	0.0823757i
$664$	−4.34053	−	7.51802i	−0.168445	−	0.291756i
$665$	3.97955			0.154321
$666$	3.26509	−	1.70046i	0.126520	−	0.0658915i
$667$	−7.23741			−0.280234
$668$	0.776071	+	1.34419i	0.0300271	+	0.0520084i
$669$	10.1087	−	34.6931i	0.390824	−	1.34131i
$670$	0.835508	−	1.44714i	0.0322785	−	0.0559080i
$671$	4.53279	−	7.85103i	0.174987	−	0.303086i
$672$	2.01421	+	2.10369i	0.0776998	+	0.0811514i
$673$	−18.7805	−	32.5288i	−0.723937	−	1.25389i	−0.959410	−	0.282014i	$-0.908997\pi$
$673$	−18.7805	−	32.5288i	−0.723937	−	1.25389i	0.235474	−	0.971881i	$-0.424336\pi$
$674$	0.00743469			0.000286373
$675$	−18.5055	−	6.27610i	−0.712277	−	0.241567i
$676$	22.7696			0.875753
$677$	24.1974	+	41.9111i	0.929980	+	1.61077i	0.783349	+	0.621582i	$0.213510\pi$
$677$	24.1974	+	41.9111i	0.929980	+	1.61077i	0.146631	+	0.989191i	$0.453157\pi$
$678$	0.350634	+	0.366210i	0.0134660	+	0.0140642i
$679$	−3.71301	+	6.43112i	−0.142492	+	0.246804i
$680$	−1.93430	+	3.35030i	−0.0741769	+	0.128478i
$681$	−0.772403	+	2.65090i	−0.0295985	+	0.101583i
$682$	0.0446905	+	0.0774063i	0.00171129	+	0.00296404i
$683$	41.0436			1.57049			0.785244	−	0.619186i	$-0.212537\pi$
$683$	41.0436			1.57049			0.785244	+	0.619186i	$0.212537\pi$
$684$	24.6684	+	15.7092i	0.943221	+	0.600655i
$685$	22.5097			0.860052
$686$	0.970534	+	1.68101i	0.0370552	+	0.0641814i
$687$	−33.4122	+	8.17916i	−1.27476	+	0.312054i
$688$	−14.8191	+	25.6674i	−0.564972	+	0.978560i
$689$	−4.33435	+	7.50732i	−0.165126	+	0.286006i
$690$	−2.71533	+	0.664700i	−0.103371	+	0.0253047i
$691$	21.1108	+	36.5650i	0.803094	+	1.39100i	0.917570	+	0.397574i	$0.130148\pi$
$691$	21.1108	+	36.5650i	0.803094	+	1.39100i	−0.114476	+	0.993426i	$0.536519\pi$
$692$	30.4322			1.15686
$693$	3.18138	+	2.02594i	0.120851	+	0.0769591i
$694$	−3.13334			−0.118940
$695$	−4.59193	−	7.95345i	−0.174182	−	0.301691i
$696$	−0.384338	+	1.31905i	−0.0145683	+	0.0499986i
$697$	11.0477	−	19.1351i	0.418460	−	0.724794i
$698$	1.32253	−	2.29070i	0.0500587	−	0.0867042i
$699$	32.7407	+	34.1951i	1.23837	+	1.29338i
$700$	2.64838	+	4.58713i	0.100099	+	0.173377i
$701$	38.2085			1.44312			0.721558	−	0.692354i	$-0.243426\pi$
$701$	38.2085			1.44312			0.721558	+	0.692354i	$0.243426\pi$
$702$	−0.919794	+	0.807085i	−0.0347154	+	0.0304615i
$703$	−30.4708			−1.14923
$704$	6.16930	+	10.6855i	0.232514	+	0.402727i
$705$	−5.47424	−	5.71741i	−0.206172	−	0.215330i
$706$	−3.48946	+	6.04392i	−0.131327	+	0.227466i
$707$	−1.28457	+	2.22493i	−0.0483111	+	0.0836773i
$708$	3.69104	−	12.6677i	0.138718	−	0.476081i
$709$	4.07026	+	7.04989i	0.152862	+	0.264764i	0.932278	−	0.361742i	$-0.117818\pi$
$709$	4.07026	+	7.04989i	0.152862	+	0.264764i	−0.779417	+	0.626506i	$0.784484\pi$
$710$	1.26743			0.0475656
$711$	−32.9422	+	17.1563i	−1.23543	+	0.643412i
$712$	−0.183464			−0.00687561
$713$	−0.922978	−	1.59864i	−0.0345658	−	0.0598697i
$714$	1.06100	−	0.259729i	0.0397070	−	0.00972011i
$715$	−1.14481	+	1.98288i	−0.0428136	+	0.0741554i
$716$	17.4712	−	30.2610i	0.652930	−	1.13091i
$717$	19.5796	−	4.79300i	0.731214	−	0.178998i
$718$	−1.12286	−	1.94485i	−0.0419048	−	0.0725812i
$719$	15.6490			0.583610			0.291805	−	0.956478i	$-0.405744\pi$
$719$	15.6490			0.583610			0.291805	+	0.956478i	$0.405744\pi$
$720$	0.545583	−	12.5487i	0.0203327	−	0.467661i
$721$	0.445500			0.0165913
$722$	0.575051	+	0.996017i	0.0214012	+	0.0370679i
$723$	−5.92793	+	20.3447i	−0.220462	+	0.756629i
$724$	−4.01964	+	6.96221i	−0.149389	+	0.258749i
$725$	−1.88032	+	3.25680i	−0.0698332	+	0.120955i
$726$	1.90508	+	1.98971i	0.0707043	+	0.0738451i
$727$	10.6561	+	18.4569i	0.395213	+	0.684529i	0.993128	−	0.117030i	$-0.0373375\pi$
$727$	10.6561	+	18.4569i	0.395213	+	0.684529i	−0.597915	+	0.801559i	$0.704004\pi$
$728$	0.670179			0.0248385
$729$	3.50949	−	26.7709i	0.129981	−	0.991516i
$730$	−2.27376			−0.0841557
$731$	17.2620	+	29.8987i	0.638458	+	1.10584i
$732$	12.1656	+	12.7060i	0.449654	+	0.469629i
$733$	−15.9259	+	27.5844i	−0.588236	+	1.01885i	0.406228	+	0.913772i	$0.366844\pi$
$733$	−15.9259	+	27.5844i	−0.588236	+	1.01885i	−0.994464	+	0.105083i	$0.966489\pi$
$734$	−0.239382	+	0.414622i	−0.00883576	+	0.0153040i
$735$	3.49727	−	12.0027i	0.128999	−	0.442725i
$736$	8.46708	+	14.6654i	0.312101	+	0.540575i
$737$	−13.1086			−0.482862
$738$	0.131654	−	3.02810i	0.00484625	−	0.111466i
$739$	−29.5769			−1.08800			−0.544001	−	0.839084i	$-0.683091\pi$
$739$	−29.5769			−1.08800			−0.544001	+	0.839084i	$0.683091\pi$
$740$	6.68297	+	11.5752i	0.245671	+	0.425514i
$741$	9.83803	−	2.40831i	0.361409	−	0.0884714i
$742$	0.530748	−	0.919283i	0.0194844	−	0.0337480i
$743$	−2.55972	+	4.43357i	−0.0939070	+	0.162652i	−0.909152	−	0.416465i	$-0.863269\pi$
$743$	−2.55972	+	4.43357i	−0.0939070	+	0.162652i	0.815245	+	0.579116i	$0.196602\pi$
$744$	−0.340375	+	0.0833223i	−0.0124788	+	0.00305474i
$745$	−12.7189	−	22.0299i	−0.465986	−	0.807112i
$746$	−1.90260			−0.0696591
$747$	29.1196	−	15.1655i	1.06543	−	0.554875i
$748$	15.0202			0.549194
$749$	1.70836	+	2.95896i	0.0624219	+	0.108118i
$750$	−0.946603	+	3.24876i	−0.0345650	+	0.118628i
$751$	9.09635	−	15.7553i	0.331930	−	0.574920i	−0.650960	−	0.759112i	$-0.725633\pi$
$751$	9.09635	−	15.7553i	0.331930	−	0.574920i	0.982890	+	0.184192i	$0.0589667\pi$
$752$	−7.71928	+	13.3702i	−0.281493	+	0.487561i
$753$	−16.7698	−	17.5147i	−0.611125	−	0.638273i
$754$	0.117749	+	0.203948i	0.00428817	+	0.00742733i
$755$	20.1410			0.733006
$756$	−5.50113	+	4.82704i	−0.200074	+	0.175558i
$757$	−40.1892			−1.46070			−0.730351	−	0.683072i	$-0.760643\pi$
$757$	−40.1892			−1.46070			−0.730351	+	0.683072i	$0.760643\pi$
$758$	1.84644	+	3.19814i	0.0670659	+	0.116162i
$759$	15.1662	+	15.8400i	0.550500	+	0.574954i
$760$	2.19624	−	3.80400i	0.0796659	−	0.137985i
$761$	−7.84047	+	13.5801i	−0.284217	+	0.492278i	−0.972419	−	0.233241i	$-0.925067\pi$
$761$	−7.84047	+	13.5801i	−0.284217	+	0.492278i	0.688202	+	0.725519i	$0.258400\pi$
$762$	−0.179814	+	0.617124i	−0.00651397	+	0.0223561i
$763$	−0.949353	−	1.64433i	−0.0343689	−	0.0595287i
$764$	−28.8208			−1.04270
$765$	−12.3412	−	7.85904i	−0.446198	−	0.284144i
$766$	4.22708			0.152731
$767$	−2.28479	−	3.95737i	−0.0824990	−	0.142892i
$768$	−21.6784	+	5.30678i	−0.782252	+	0.191492i
$769$	0.543526	−	0.941414i	0.0196000	−	0.0339483i	−0.856059	−	0.516878i	$-0.827094\pi$
$769$	0.543526	−	0.941414i	0.0196000	−	0.0339483i	0.875659	+	0.482930i	$0.160427\pi$
$770$	0.140184	−	0.242806i	0.00505189	−	0.00875014i
$771$	11.2693	−	2.75868i	0.405855	−	0.0993516i
$772$	−0.721080	−	1.24895i	−0.0259522	−	0.0449506i
$773$	−8.23186			−0.296080			−0.148040	−	0.988981i	$-0.547296\pi$
$773$	−8.23186			−0.296080			−0.148040	+	0.988981i	$0.547296\pi$
$774$	3.99467	+	2.54386i	0.143586	+	0.0914371i
$775$	−0.959177			−0.0344546
$776$	4.09828	+	7.09842i	0.147120	+	0.254819i
$777$	2.13309	−	7.32081i	0.0765243	−	0.262633i
$778$	−0.311320	+	0.539222i	−0.0111614	+	0.0193321i
$779$	−12.5437	+	21.7264i	−0.449426	+	0.778428i
$780$	−3.07258	−	3.20907i	−0.110016	−	0.114903i
$781$	−4.97129	−	8.61053i	−0.177887	−	0.308109i
$782$	6.35119			0.227118
$783$	−4.92085	−	1.66890i	−0.175857	−	0.0596415i
$784$	−24.3836			−0.870843
$785$	10.5100	+	18.2038i	0.375118	+	0.649723i
$786$	2.68585	+	2.80516i	0.0958011	+	0.100057i
$787$	12.5101	−	21.6681i	0.445935	−	0.772383i	−0.552181	−	0.833724i	$-0.686204\pi$
$787$	12.5101	−	21.6681i	0.445935	−	0.772383i	0.998117	+	0.0613412i	$0.0195378\pi$
$788$	21.3025	−	36.8970i	0.758869	−	1.31440i
$789$	10.5651	−	36.2596i	0.376128	−	1.29088i
$790$	1.38048	+	2.39106i	0.0491152	+	0.0850701i
$791$	1.05016			0.0373396
$792$	3.69231	−	1.92295i	0.131200	−	0.0683291i
$793$	6.09223			0.216342
$794$	−2.82223	−	4.88825i	−0.100157	−	0.173477i
$795$	−13.8104	+	3.38071i	−0.489803	+	0.119902i
$796$	−15.5035	+	26.8528i	−0.549505	+	0.951771i
$797$	20.4442	−	35.4105i	0.724172	−	1.25430i	−0.235142	−	0.971961i	$-0.575555\pi$
$797$	20.4442	−	35.4105i	0.724172	−	1.25430i	0.959314	−	0.282342i	$-0.0911113\pi$
$798$	−1.20468	+	0.294901i	−0.0426453	+	0.0104394i
$799$	8.99181	+	15.5743i	0.318108	+	0.550978i
$800$	8.79916			0.311097
$801$	0.0301390	−	0.693211i	0.00106491	−	0.0244934i
$802$	−1.29946			−0.0458855
$803$	8.91850	+	15.4473i	0.314727	+	0.545123i
$804$	7.11557	−	24.4207i	0.250947	−	0.861253i
$805$	−2.89518	+	5.01460i	−0.102042	+	0.176741i
$806$	−0.0300328	+	0.0520183i	−0.00105786	+	0.00183227i
$807$	−34.3240	−	35.8488i	−1.20826	−	1.26194i
$808$	1.41785	+	2.45579i	0.0498799	+	0.0863946i
$809$	31.2887			1.10005			0.550026	−	0.835148i	$-0.314618\pi$
$809$	31.2887			1.10005			0.550026	+	0.835148i	$0.314618\pi$
$810$	−1.99948	−	0.174193i	−0.0702544	−	0.00612052i
$811$	36.1607			1.26977			0.634886	−	0.772606i	$-0.281047\pi$
$811$	36.1607			1.26977			0.634886	+	0.772606i	$0.281047\pi$
$812$	0.704239	+	1.21978i	0.0247139	+	0.0428058i
$813$	−2.47897	−	2.58909i	−0.0869411	−	0.0908032i
$814$	−1.07337	+	1.85913i	−0.0376215	+	0.0651624i
$815$	−5.33327	+	9.23749i	−0.186816	+	0.323575i
$816$	−7.98288	+	27.3974i	−0.279457	+	0.959099i
$817$	−19.5996	−	33.9475i	−0.685703	−	1.18767i
$818$	3.14563			0.109984
$819$	−0.110095	+	2.53224i	−0.00384704	+	0.0884838i
$820$	11.0046			0.384296
$821$	−23.4565	−	40.6279i	−0.818639	−	1.41792i	−0.906685	−	0.421808i	$-0.861396\pi$
$821$	−23.4565	−	40.6279i	−0.818639	−	1.41792i	0.0880458	−	0.996116i	$-0.471938\pi$
$822$	−6.81409	+	1.66806i	−0.237669	+	0.0581803i
$823$	−17.2807	+	29.9311i	−0.602369	+	1.04333i	0.390093	+	0.920776i	$0.372443\pi$
$823$	−17.2807	+	29.9311i	−0.602369	+	1.04333i	−0.992461	+	0.122557i	$0.960890\pi$
$824$	0.245863	−	0.425847i	0.00856504	−	0.0148351i
$825$	11.0682	−	2.70944i	0.385344	−	0.0943306i
$826$	0.279776	+	0.484587i	0.00973466	+	0.0168609i
$827$	55.9915			1.94701			0.973507	−	0.228657i	$-0.0734333\pi$
$827$	55.9915			1.94701			0.973507	+	0.228657i	$0.0734333\pi$
$828$	−37.7416	+	19.6558i	−1.31161	+	0.683087i
$829$	−2.90297			−0.100824			−0.0504121	−	0.998729i	$-0.516053\pi$
$829$	−2.90297			−0.100824			−0.0504121	+	0.998729i	$0.516053\pi$
$830$	−1.22029	−	2.11360i	−0.0423568	−	0.0733641i
$831$	1.64474	−	5.64477i	0.0570554	−	0.195815i
$832$	−4.14588	+	7.18087i	−0.143733	+	0.248952i
$833$	−14.2016	+	24.5979i	−0.492057	+	0.852268i
$834$	1.97944	+	2.06737i	0.0685424	+	0.0715872i
$835$	0.440832	+	0.763544i	0.0152556	+	0.0264235i
$836$	−17.0543			−0.589834
$837$	−0.258914	−	1.29978i	−0.00894937	−	0.0449270i
$838$	−0.751656			−0.0259655
$839$	24.9166	+	43.1567i	0.860215	+	1.48994i	0.871721	+	0.490003i	$0.163004\pi$
$839$	24.9166	+	43.1567i	0.860215	+	1.48994i	−0.0115057	+	0.999934i	$0.503662\pi$
$840$	0.760188	+	0.793958i	0.0262290	+	0.0273941i
$841$	−0.500000	+	0.866025i	−0.0172414	+	0.0298629i
$842$	3.73746	−	6.47348i	0.128801	−	0.223091i
$843$	7.45864	−	25.5982i	0.256889	−	0.881648i
$844$	−17.4135	−	30.1611i	−0.599399	−	1.03819i
$845$	12.9338			0.444937
$846$	2.08083	+	1.32510i	0.0715405	+	0.0455579i
$847$	5.70582			0.196054
$848$	13.8656	+	24.0159i	0.476146	+	0.824709i
$849$	41.2849	−	10.1064i	1.41690	−	0.346850i
$850$	1.65007	−	2.85801i	0.0565970	−	0.0980288i
$851$	22.1679	−	38.3959i	0.759906	−	1.31620i
$852$	18.7395	−	4.58735i	0.642005	−	0.157160i
$853$	21.5576	+	37.3388i	0.738118	+	1.27846i	0.953342	+	0.301893i	$0.0976184\pi$
$853$	21.5576	+	37.3388i	0.738118	+	1.27846i	−0.215224	+	0.976565i	$0.569048\pi$
$854$	−0.746004			−0.0255277
$855$	14.0124	+	8.92330i	0.479215	+	0.305170i
$856$	3.77123			0.128898
$857$	−11.3711	−	19.6953i	−0.388429	−	0.672779i	0.603809	−	0.797129i	$-0.293649\pi$
$857$	−11.3711	−	19.6953i	−0.388429	−	0.672779i	−0.992238	+	0.124350i	$0.960316\pi$
$858$	0.199617	−	0.685088i	0.00681480	−	0.0233885i
$859$	6.11742	−	10.5957i	0.208724	−	0.361520i	−0.742589	−	0.669747i	$-0.766402\pi$
$859$	6.11742	−	10.5957i	0.208724	−	0.361520i	0.951313	+	0.308227i	$0.0997358\pi$
$860$	−8.59732	+	14.8910i	−0.293166	+	0.507779i
$861$	−4.34179	−	4.53466i	−0.147968	−	0.154541i
$862$	−2.20495	−	3.81909i	−0.0751010	−	0.130079i
$863$	−19.8296			−0.675007			−0.337504	−	0.941324i	$-0.609582\pi$
$863$	−19.8296			−0.675007			−0.337504	+	0.941324i	$0.609582\pi$
$864$	2.37519	+	11.9237i	0.0808055	+	0.405654i
$865$	17.2864			0.587756
$866$	2.10954	+	3.65382i	0.0716850	+	0.124162i
$867$	2.62530	+	2.74192i	0.0891600	+	0.0931207i
$868$	−0.179621	+	0.311113i	−0.00609674	+	0.0105599i
$869$	10.8294	−	18.7572i	0.367364	−	0.636293i
$870$	−0.108052	+	0.370836i	−0.00366330	+	0.0125725i
$871$	−4.40461	−	7.62901i	−0.149245	−	0.258499i
$872$	−2.09572			−0.0709699
$873$	−27.4943	+	14.3191i	−0.930542	+	0.484626i
$874$	−7.21126			−0.243925
$875$	3.50451	+	6.06999i	0.118474	+	0.205203i
$876$	−33.6187	+	8.22970i	−1.13587	+	0.278056i
$877$	−1.07965	+	1.87001i	−0.0364572	+	0.0631458i	−0.883678	−	0.468095i	$-0.844941\pi$
$877$	−1.07965	+	1.87001i	−0.0364572	+	0.0631458i	0.847221	+	0.531241i	$0.178274\pi$
$878$	3.87650	−	6.71430i	0.130826	−	0.226597i
$879$	15.2022	−	3.72144i	0.512759	−	0.125521i
$880$	3.66226	+	6.34321i	0.123455	+	0.213830i
$881$	−46.3330			−1.56100			−0.780499	−	0.625158i	$-0.785035\pi$
$881$	−46.3330			−1.56100			−0.780499	+	0.625158i	$0.785035\pi$
$882$	−0.169239	+	3.89259i	−0.00569858	+	0.131070i
$883$	48.5475			1.63375			0.816876	−	0.576813i	$-0.195704\pi$
$883$	48.5475			1.63375			0.816876	+	0.576813i	$0.195704\pi$
$884$	5.04693	+	8.74154i	0.169747	+	0.294010i
$885$	2.09662	−	7.19565i	0.0704773	−	0.241879i
$886$	1.12862	−	1.95483i	0.0379169	−	0.0656739i
$887$	−22.0866	+	38.2551i	−0.741594	+	1.28448i	0.210175	+	0.977664i	$0.432597\pi$
$887$	−22.0866	+	38.2551i	−0.741594	+	1.28448i	−0.951769	+	0.306815i	$0.900737\pi$
$888$	−5.82064	−	6.07920i	−0.195328	−	0.204005i
$889$	0.665707	+	1.15304i	0.0223271	+	0.0386717i
$890$	−0.0515787			−0.00172892
$891$	6.65923	+	14.2671i	0.223093	+	0.477966i
$892$	−40.8889			−1.36906
$893$	−10.2095	−	17.6833i	−0.341647	−	0.591750i
$894$	5.48275	+	5.72631i	0.183371	+	0.191516i
$895$	9.92419	−	17.1892i	0.331729	−	0.574572i
$896$	2.18919	−	3.79179i	0.0731357	−	0.126675i
$897$	−4.12262	+	14.1489i	−0.137650	+	0.472417i
$898$	1.28338	+	2.22287i	0.0428269	+	0.0741783i
$899$	−0.255057			−0.00850664
$900$	−0.960424	+	22.0902i	−0.0320141	+	0.736341i
$901$	32.3026			1.07616
$902$	0.883734	+	1.53067i	0.0294251	+	0.0509658i
$903$	9.52817	−	2.33245i	0.317078	−	0.0776192i
$904$	0.579565	−	1.00384i	0.0192761	−	0.0333871i
$905$	−2.28328	+	3.95475i	−0.0758987	+	0.131460i
$906$	−6.09704	+	1.49253i	−0.202561	+	0.0495859i
$907$	12.0599	+	20.8883i	0.400441	+	0.693584i	0.993779	−	0.111369i	$-0.0355235\pi$
$907$	12.0599	+	20.8883i	0.400441	+	0.693584i	−0.593338	+	0.804953i	$0.702190\pi$
$908$	3.12432			0.103684
$909$	−9.51204	+	4.95387i	−0.315494	+	0.164309i
$910$	0.188413			0.00624582
$911$	−13.1960	−	22.8562i	−0.437203	−	0.757258i	0.560269	−	0.828311i	$-0.310698\pi$
$911$	−13.1960	−	22.8562i	−0.437203	−	0.757258i	−0.997473	+	0.0710522i	$0.977364\pi$
$912$	9.06391	−	31.1075i	0.300136	−	1.03007i
$913$	−9.57279	+	16.5806i	−0.316813	+	0.548736i
$914$	−2.20081	+	3.81191i	−0.0727963	+	0.126087i
$915$	6.91045	+	7.21743i	0.228453	+	0.238601i
$916$	19.4617	+	33.7086i	0.643032	+	1.11376i
$917$	8.04425			0.265645
$918$	4.31829	+	1.46454i	0.142525	+	0.0483370i
$919$	−0.199873			−0.00659321			−0.00329660	−	0.999995i	$-0.501049\pi$
$919$	−0.199873			−0.00659321			−0.00329660	+	0.999995i	$0.501049\pi$
$920$	3.19558	+	5.53491i	0.105355	+	0.182481i
$921$	19.9227	+	20.8077i	0.656474	+	0.685636i
$922$	−3.15893	+	5.47142i	−0.104034	+	0.180192i
$923$	3.34079	−	5.78642i	0.109964	−	0.190462i
$924$	1.19387	−	4.09740i	0.0392756	−	0.134794i
$925$	−11.5187	−	19.9509i	−0.378731	−	0.655982i
$926$	−4.46112			−0.146602
$927$	1.56866	+	0.998940i	0.0515214	+	0.0328095i
$928$	2.33981			0.0768080
$929$	2.55131	+	4.41900i	0.0837058	+	0.144983i	0.904839	−	0.425754i	$-0.139991\pi$
$929$	2.55131	+	4.41900i	0.0837058	+	0.144983i	−0.821133	+	0.570737i	$0.806658\pi$
$930$	−0.0956922	+	0.0234250i	−0.00313787	+	0.000768137i
$931$	16.1248	−	27.9290i	0.528469	−	0.915335i
$932$	26.7845	−	46.3921i	0.877356	−	1.51963i
$933$	−28.9856	+	7.09554i	−0.948945	+	0.232297i
$934$	−0.0902015	−	0.156234i	−0.00295148	−	0.00511212i
$935$	8.53196			0.279025
$936$	2.35977	+	1.50273i	0.0771316	+	0.0491184i
$937$	−12.5457			−0.409852			−0.204926	−	0.978778i	$-0.565695\pi$
$937$	−12.5457			−0.409852			−0.204926	+	0.978778i	$0.565695\pi$
$938$	0.539352	+	0.934184i	0.0176105	+	0.0305022i
$939$	15.9635	−	54.7869i	0.520949	−	1.78790i
$940$	−4.47836	+	7.75675i	−0.146068	+	0.252997i
$941$	−7.69552	+	13.3290i	−0.250867	+	0.434514i	−0.963765	−	0.266754i	$-0.914049\pi$
$941$	−7.69552	+	13.3290i	−0.250867	+	0.434514i	0.712898	+	0.701268i	$0.247382\pi$
$942$	−4.53054	−	4.73180i	−0.147613	−	0.154170i
$943$	−18.2515	−	31.6124i	−0.594349	−	1.02944i
$944$	−14.6181			−0.475777
$945$	−3.12482	+	2.74191i	−0.101650	+	0.0891943i
$946$	−2.76167			−0.0897897
$947$	−9.18962	−	15.9169i	−0.298623	−	0.517230i	0.677198	−	0.735800i	$-0.263194\pi$
$947$	−9.18962	−	15.9169i	−0.298623	−	0.517230i	−0.975821	+	0.218571i	$0.929861\pi$
$948$	29.0653	+	30.3564i	0.943997	+	0.985931i
$949$	−5.99339	+	10.3808i	−0.194554	+	0.336977i
$950$	−1.87352	+	3.24503i	−0.0607851	+	0.105283i
$951$	−7.40118	+	25.4010i	−0.240000	+	0.823683i
$952$	−1.24866	−	2.16275i	−0.0404694	−	0.0700950i
$953$	−34.7398			−1.12533			−0.562666	−	0.826684i	$-0.690224\pi$
$953$	−34.7398			−1.12533			−0.562666	+	0.826684i	$0.690224\pi$
$954$	3.93012	−	2.04681i	0.127242	−	0.0662678i
$955$	−16.3711			−0.529756
$956$	−11.4046	−	19.7533i	−0.368850	−	0.638867i
$957$	2.94317	−	0.720475i	0.0951392	−	0.0232896i
$958$	−0.192867	+	0.334056i	−0.00623127	+	0.0107929i
$959$	−7.26543	+	12.5841i	−0.234613	+	0.406362i
$960$	−13.2098	+	3.23371i	−0.426346	+	0.104367i
$961$	15.4675	+	26.7904i	0.498951	+	0.864208i
$962$	−1.44264			−0.0465127
$963$	−0.619528	+	14.2494i	−0.0199640	+	0.459182i
$964$	23.9781			0.772282
$965$	−0.409596	−	0.709441i	−0.0131854	−	0.0228377i
$966$	0.504821	−	1.73255i	0.0162423	−	0.0557440i
$967$	7.42914	−	12.8676i	0.238905	−	0.413796i	−0.721495	−	0.692419i	$-0.756545\pi$
$967$	7.42914	−	12.8676i	0.238905	−	0.413796i	0.960400	+	0.278624i	$0.0898782\pi$
$968$	3.14893	−	5.45411i	0.101210	−	0.175302i
$969$	−26.1019	−	27.2614i	−0.838513	−	0.875761i
$970$	1.15218	+	1.99563i	0.0369943	+	0.0640759i
$971$	−43.2023			−1.38643			−0.693214	−	0.720732i	$-0.743806\pi$
$971$	−43.2023			−1.38643			−0.693214	+	0.720732i	$0.743806\pi$
$972$	−30.1937	+	4.66142i	−0.968463	+	0.149515i
$973$	5.92852			0.190060
$974$	0.0168335	+	0.0291564i	0.000539379	+	0.000934232i
$975$	5.29585	+	5.53111i	0.169603	+	0.177137i
$976$	9.74451	−	16.8780i	0.311914	−	0.540251i
$977$	−3.57799	+	6.19726i	−0.114470	+	0.198268i	−0.917568	−	0.397579i	$-0.869850\pi$
$977$	−3.57799	+	6.19726i	−0.114470	+	0.198268i	0.803098	+	0.595847i	$0.203184\pi$
$978$	0.929940	−	3.19157i	0.0297362	−	0.102055i
$979$	0.202310	+	0.350411i	0.00646585	+	0.0111992i
$980$	−14.1462			−0.451884
$981$	0.344279	−	7.91858i	0.0109920	−	0.252821i
$982$	8.62748			0.275314
$983$	−25.9422	−	44.9332i	−0.827428	−	1.43315i	−0.900050	−	0.435787i	$-0.856470\pi$
$983$	−25.9422	−	44.9332i	−0.827428	−	1.43315i	0.0726221	−	0.997360i	$-0.476863\pi$
$984$	−6.73076	+	1.64766i	−0.214569	+	0.0525254i
$985$	12.1005	−	20.9586i	0.385553	−	0.667797i
$986$	0.438775	−	0.759981i	0.0139734	−	0.0242027i
$987$	4.96325	−	1.21498i	0.157982	−	0.0386732i
$988$	−5.73038	−	9.92530i	−0.182308	−	0.315766i
$989$	57.0359			1.81364
$990$	1.03805	−	0.540614i	0.0329913	−	0.0171818i
$991$	−23.6947			−0.752687			−0.376344	−	0.926480i	$-0.622819\pi$
$991$	−23.6947			−0.752687			−0.376344	+	0.926480i	$0.622819\pi$
$992$	0.298393	+	0.516832i	0.00947398	+	0.0164094i
$993$	−15.2661	+	52.3936i	−0.484456	+	1.66266i
$994$	−0.409086	+	0.708557i	−0.0129754	+	0.0224741i
$995$	−8.80644	+	15.2532i	−0.279183	+	0.483559i
$996$	−25.6925	−	26.8338i	−0.814099	−	0.850263i
$997$	−5.22186	−	9.04452i	−0.165378	−	0.286443i	0.771412	−	0.636337i	$-0.219551\pi$
$997$	−5.22186	−	9.04452i	−0.165378	−	0.286443i	−0.936789	+	0.349894i	$0.886218\pi$
$998$	−6.63650			−0.210075
$999$	23.9262	−	20.9944i	0.756992	−	0.664232i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.2.e.a.175.7	yes	22
3.2	odd	2		783.2.e.a.523.5		22
9.2	odd	6		783.2.e.a.262.5		22
9.4	even	3		2349.2.a.f.1.5		11
9.5	odd	6		2349.2.a.e.1.7		11
9.7	even	3	inner	261.2.e.a.88.7	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
261.2.e.a.88.7	✓	22	9.7	even	3	inner
261.2.e.a.175.7	yes	22	1.1	even	1	trivial
783.2.e.a.262.5		22	9.2	odd	6
783.2.e.a.523.5		22	3.2	odd	2
2349.2.a.e.1.7		11	9.5	odd	6
2349.2.a.f.1.5		11	9.4	even	3

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:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	261.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.100158 + 0.173479i) q^{2} +(1.19785 + 1.25106i) q^{3} +(0.979937 - 1.69730i) q^{4} +(0.556635 - 0.964120i) q^{5} +(-0.0970582 + 0.333105i) q^{6} +(0.359329 + 0.622375i) q^{7} +0.793225 q^{8} +(-0.130309 + 2.99717i) q^{9} +0.223006 q^{10} +(-0.874706 - 1.51504i) q^{11} +(3.29724 - 0.807151i) q^{12} +(0.587818 - 1.01813i) q^{13} +(-0.0719792 + 0.124672i) q^{14} +(1.87294 - 0.458487i) q^{15} +(-1.88043 - 3.25699i) q^{16} -4.38083 q^{17} +(-0.532996 + 0.277584i) q^{18} +4.97408 q^{19} +(-1.09093 - 1.88955i) q^{20} +(-0.348208 + 1.19505i) q^{21} +(0.175218 - 0.303486i) q^{22} +(-3.61871 + 6.26778i) q^{23} +(0.950165 + 0.992374i) q^{24} +(1.88032 + 3.25680i) q^{25} +0.235498 q^{26} +(-3.90573 + 3.42714i) q^{27} +1.40848 q^{28} +(0.500000 + 0.866025i) q^{29} +(0.267127 + 0.278994i) q^{30} +(-0.127529 + 0.220886i) q^{31} +(1.16990 - 2.02633i) q^{32} +(0.847635 - 2.90910i) q^{33} +(-0.438775 - 0.759981i) q^{34} +0.800059 q^{35} +(4.95940 + 3.15821i) q^{36} -6.12592 q^{37} +(0.498193 + 0.862896i) q^{38} +(1.97786 - 0.484172i) q^{39} +(0.441537 - 0.764764i) q^{40} +(-2.52182 + 4.36792i) q^{41} +(-0.242192 + 0.0592876i) q^{42} +(-3.94035 - 6.82488i) q^{43} -3.42863 q^{44} +(2.81709 + 1.79396i) q^{45} -1.44977 q^{46} +(-2.05254 - 3.55510i) q^{47} +(1.82223 - 6.25392i) q^{48} +(3.24177 - 5.61490i) q^{49} +(-0.376657 + 0.652389i) q^{50} +(-5.24758 - 5.48069i) q^{51} +(-1.15205 - 1.99541i) q^{52} -7.37363 q^{53} +(-0.985725 - 0.334306i) q^{54} -1.94757 q^{55} +(0.285029 + 0.493684i) q^{56} +(5.95820 + 6.22288i) q^{57} +(-0.100158 + 0.173479i) q^{58} +(1.94345 - 3.36616i) q^{59} +(1.05717 - 3.62823i) q^{60} +(2.59104 + 4.48781i) q^{61} -0.0510920 q^{62} +(-1.91219 + 0.995867i) q^{63} -7.05300 q^{64} +(-0.654399 - 1.13345i) q^{65} +(0.589564 - 0.144323i) q^{66} +(3.74658 - 6.48926i) q^{67} +(-4.29294 + 7.43559i) q^{68} +(-12.1761 + 2.98064i) q^{69} +(0.0801323 + 0.138793i) q^{70} +5.68338 q^{71} +(-0.103364 + 2.37743i) q^{72} -10.1960 q^{73} +(-0.613559 - 1.06272i) q^{74} +(-1.82212 + 6.25355i) q^{75} +(4.87428 - 8.44250i) q^{76} +(0.628614 - 1.08879i) q^{77} +(0.282092 + 0.294623i) q^{78} +(6.19034 + 10.7220i) q^{79} -4.18684 q^{80} +(-8.96604 - 0.781116i) q^{81} -1.01032 q^{82} +(-5.47200 - 9.47778i) q^{83} +(1.68714 + 1.76209i) q^{84} +(-2.43852 + 4.22364i) q^{85} +(0.789314 - 1.36713i) q^{86} +(-0.484526 + 1.66290i) q^{87} +(-0.693839 - 1.20176i) q^{88} -0.231289 q^{89} +(-0.0290596 + 0.668385i) q^{90} +0.844879 q^{91} +(7.09221 + 12.2841i) q^{92} +(-0.429102 + 0.105042i) q^{93} +(0.411156 - 0.712142i) q^{94} +(2.76874 - 4.79560i) q^{95} +(3.93644 - 0.963623i) q^{96} +(5.16660 + 8.94881i) q^{97} +1.29875 q^{98} +(4.65480 - 2.42422i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - q^{2} - 2 q^{3} - 5 q^{4} + q^{5} - q^{6} + 7 q^{7} + 6 q^{8} - 2 q^{9} - 20 q^{10} - 3 q^{11} + 10 q^{12} + 7 q^{13} + 10 q^{14} - 8 q^{15} + 7 q^{16} + 2 q^{17} + 2 q^{18} - 56 q^{19} + 4 q^{20}+ \cdots - 40 q^{99}+O(q^{100}) \) 22 * q - q^2 - 2 * q^3 - 5 * q^4 + q^5 - q^6 + 7 * q^7 + 6 * q^8 - 2 * q^9 - 20 * q^10 - 3 * q^11 + 10 * q^12 + 7 * q^13 + 10 * q^14 - 8 * q^15 + 7 * q^16 + 2 * q^17 + 2 * q^18 - 56 * q^19 + 4 * q^20 + 16 * q^21 + 13 * q^22 - 4 * q^23 - 33 * q^24 + 4 * q^25 - 12 * q^26 + 13 * q^27 - 32 * q^28 + 11 * q^29 + 46 * q^30 + 27 * q^31 - 7 * q^32 - 10 * q^33 + 19 * q^34 - 22 * q^35 + 19 * q^36 - 28 * q^37 + 5 * q^38 + 17 * q^39 + 24 * q^40 + 9 * q^41 - 50 * q^42 + 25 * q^43 + 46 * q^44 - 56 * q^45 - 20 * q^46 - 6 * q^47 + 33 * q^48 + 12 * q^49 - 41 * q^50 - 15 * q^51 + 20 * q^52 - 12 * q^53 + 5 * q^54 - 70 * q^55 + 10 * q^56 + 25 * q^57 + q^58 - 48 * q^60 + 25 * q^61 - 12 * q^62 - 11 * q^63 - 50 * q^64 - 5 * q^65 + 29 * q^66 + 29 * q^67 + 50 * q^68 + 20 * q^69 + 7 * q^70 - 2 * q^71 + 30 * q^72 - 26 * q^73 - 14 * q^74 + 46 * q^75 + 38 * q^76 - 9 * q^77 - 39 * q^78 + 27 * q^79 - 74 * q^80 - 38 * q^81 - 34 * q^82 + 12 * q^83 + 60 * q^84 + 7 * q^85 - q^86 - q^87 - 5 * q^88 + 46 * q^89 - 35 * q^90 - 86 * q^91 - 19 * q^92 + 78 * q^93 - 10 * q^94 - 8 * q^95 - 75 * q^96 + 36 * q^97 + 86 * q^98 - 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more