LMFDB - Embedded newform 228.2.w.b.67.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [228,2,Mod(67,228)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(228, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 0, 17])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("228.67"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 228 = 2^{2} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	228.w (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [60,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$1.82058916609$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			67.6
Character	$\chi$	$=$	228.67
Dual form			228.2.w.b.211.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0625414 - 1.41283i) q^{2} +(0.766044 - 0.642788i) q^{3} +(-1.99218 - 0.176721i) q^{4} +(-3.72560 - 1.35601i) q^{5} +(-0.860240 - 1.12249i) q^{6} +(-0.752955 - 0.434719i) q^{7} +(-0.374270 + 2.80356i) q^{8} +(0.173648 - 0.984808i) q^{9} +(-2.14881 + 5.17883i) q^{10} +(1.56958 - 0.906199i) q^{11} +(-1.63969 + 1.14517i) q^{12} +(-2.72675 + 3.24962i) q^{13} +(-0.661275 + 1.03661i) q^{14} +(-3.72560 + 1.35601i) q^{15} +(3.93754 + 0.704118i) q^{16} +(-0.968005 - 5.48983i) q^{17} +(-1.38051 - 0.306927i) q^{18} +(2.07308 - 3.83437i) q^{19} +(7.18242 + 3.35980i) q^{20} +(-0.856229 + 0.150976i) q^{21} +(-1.18214 - 2.27423i) q^{22} +(-2.47491 - 6.79975i) q^{23} +(1.51538 + 2.38822i) q^{24} +(8.21110 + 6.88993i) q^{25} +(4.42062 + 4.05567i) q^{26} +(-0.500000 - 0.866025i) q^{27} +(1.42320 + 0.999100i) q^{28} +(-2.40462 - 0.423999i) q^{29} +(1.68280 + 5.34844i) q^{30} +(2.51180 - 4.35057i) q^{31} +(1.24106 - 5.51904i) q^{32} +(0.619877 - 1.70310i) q^{33} +(-7.81674 + 1.02428i) q^{34} +(2.21573 + 2.64060i) q^{35} +(-0.519974 + 1.93122i) q^{36} +3.74939i q^{37} +(-5.28765 - 3.16871i) q^{38} +4.24207i q^{39} +(5.19602 - 9.93741i) q^{40} +(-0.216824 - 0.258400i) q^{41} +(0.159754 + 1.21915i) q^{42} +(-1.75948 + 4.83414i) q^{43} +(-3.28703 + 1.52793i) q^{44} +(-1.98235 + 3.43353i) q^{45} +(-9.76167 + 3.07136i) q^{46} +(9.77372 + 1.72337i) q^{47} +(3.46893 - 1.99162i) q^{48} +(-3.12204 - 5.40753i) q^{49} +(10.2478 - 11.1700i) q^{50} +(-4.27033 - 3.58323i) q^{51} +(6.00645 - 5.99194i) q^{52} +(3.00014 + 8.24282i) q^{53} +(-1.25482 + 0.652253i) q^{54} +(-7.07645 + 1.24777i) q^{55} +(1.50057 - 1.94825i) q^{56} +(-0.876614 - 4.26984i) q^{57} +(-0.749427 + 3.37080i) q^{58} +(-0.976716 - 5.53923i) q^{59} +(7.66169 - 2.04302i) q^{60} +(4.26876 - 1.55370i) q^{61} +(-5.98952 - 3.82084i) q^{62} +(-0.558864 + 0.666028i) q^{63} +(-7.71984 - 2.09857i) q^{64} +(14.5653 - 8.40927i) q^{65} +(-2.36742 - 0.982295i) q^{66} +(-1.03153 + 5.85008i) q^{67} +(0.958271 + 11.1078i) q^{68} +(-6.26668 - 3.61807i) q^{69} +(3.86930 - 2.96530i) q^{70} +(3.33873 + 1.21520i) q^{71} +(2.69597 + 0.855416i) q^{72} +(9.37379 - 7.86555i) q^{73} +(5.29726 + 0.234492i) q^{74} +10.7188 q^{75} +(-4.80755 + 7.27238i) q^{76} -1.57577 q^{77} +(5.99333 + 0.265305i) q^{78} +(3.56820 - 2.99408i) q^{79} +(-13.7149 - 7.96259i) q^{80} +(-0.939693 - 0.342020i) q^{81} +(-0.378636 + 0.290174i) q^{82} +(-5.17652 - 2.98867i) q^{83} +(1.73244 - 0.149458i) q^{84} +(-3.83785 + 21.7655i) q^{85} +(6.71978 + 2.78819i) q^{86} +(-2.11459 + 1.22086i) q^{87} +(1.95313 + 4.73958i) q^{88} +(-6.31437 + 7.52518i) q^{89} +(4.72701 + 3.01546i) q^{90} +(3.46579 - 1.26145i) q^{91} +(3.72879 + 13.9837i) q^{92} +(-0.872339 - 4.94728i) q^{93} +(3.04609 - 13.7008i) q^{94} +(-12.9229 + 11.4742i) q^{95} +(-2.59686 - 5.02557i) q^{96} +(-4.82529 + 0.850829i) q^{97} +(-7.83518 + 4.07272i) q^{98} +(-0.619877 - 1.70310i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 3 q^{2} - 3 q^{4} + 3 q^{6} - 3 q^{8} - 6 q^{10} - 6 q^{13} - 9 q^{14} + 21 q^{16} + 18 q^{19} + 30 q^{20} - 6 q^{21} - 12 q^{22} - 18 q^{24} - 30 q^{27} - 18 q^{28} - 12 q^{31} + 33 q^{32} - 15 q^{34}+ \cdots - 105 q^{98}+O(q^{100}) $ 60 * q + 3 * q^2 - 3 * q^4 + 3 * q^6 - 3 * q^8 - 6 * q^10 - 6 * q^13 - 9 * q^14 + 21 * q^16 + 18 * q^19 + 30 * q^20 - 6 * q^21 - 12 * q^22 - 18 * q^24 - 30 * q^27 - 18 * q^28 - 12 * q^31 + 33 * q^32 - 15 * q^34 - 3 * q^36 - 84 * q^38 - 87 * q^40 - 12 * q^41 + 9 * q^42 - 18 * q^43 - 51 * q^44 - 21 * q^46 + 18 * q^48 + 30 * q^49 - 27 * q^50 - 3 * q^52 + 12 * q^53 + 3 * q^54 + 42 * q^56 - 36 * q^58 + 15 * q^60 + 105 * q^62 - 12 * q^63 + 21 * q^64 - 36 * q^65 + 24 * q^66 + 42 * q^67 - 15 * q^68 - 72 * q^69 - 96 * q^70 + 24 * q^71 + 18 * q^72 + 18 * q^73 + 69 * q^74 + 60 * q^75 + 54 * q^76 - 72 * q^77 + 57 * q^78 + 12 * q^79 - 12 * q^80 + 75 * q^82 + 39 * q^84 - 60 * q^85 + 21 * q^86 + 36 * q^88 - 12 * q^89 + 15 * q^90 - 84 * q^91 + 99 * q^92 - 12 * q^93 - 24 * q^95 + 12 * q^97 - 105 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/228\mathbb{Z}\right)^\times$.

$n$	$77$	$97$	$115$
$\chi(n)$	$1$	$e\left(\frac{17}{18}\right)$	$-1$

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 $

$2$	0.0625414	−	1.41283i	0.0442235	−	0.999022i
$2$	0.0625414	−	1.41283i	0.0442235	−	0.999022i
$3$	0.766044	−	0.642788i	0.442276	−	0.371114i
$3$	0.766044	−	0.642788i	0.442276	−	0.371114i
$4$	−1.99218	−	0.176721i	−0.996089	−	0.0883604i
$5$	−3.72560	−	1.35601i	−1.66614	−	0.606425i	−0.674828	−	0.737975i	$-0.735782\pi$
$5$	−3.72560	−	1.35601i	−1.66614	−	0.606425i	−0.991310	+	0.131550i	$0.958005\pi$
$6$	−0.860240	−	1.12249i	−0.351192	−	0.458255i
$7$	−0.752955	−	0.434719i	−0.284590	−	0.164308i	0.350909	−	0.936409i	$-0.385873\pi$
$7$	−0.752955	−	0.434719i	−0.284590	−	0.164308i	−0.635500	+	0.772101i	$0.719206\pi$
$8$	−0.374270	+	2.80356i	−0.132324	+	0.991206i
$9$	0.173648	−	0.984808i	0.0578827	−	0.328269i
$10$	−2.14881	+	5.17883i	−0.679514	+	1.63769i
$11$	1.56958	−	0.906199i	0.473247	−	0.273229i	−0.244351	−	0.969687i	$-0.578575\pi$
$11$	1.56958	−	0.906199i	0.473247	−	0.273229i	0.717598	+	0.696457i	$0.245242\pi$
$12$	−1.63969	+	1.14517i	−0.473338	+	0.330582i
$13$	−2.72675	+	3.24962i	−0.756265	+	0.901281i	−0.997606	−	0.0691592i	$-0.977968\pi$
$13$	−2.72675	+	3.24962i	−0.756265	+	0.901281i	0.241341	+	0.970440i	$0.422413\pi$
$14$	−0.661275	+	1.03661i	−0.176733	+	0.277046i
$15$	−3.72560	+	1.35601i	−0.961945	+	0.350119i
$16$	3.93754	+	0.704118i	0.984385	+	0.176030i
$17$	−0.968005	−	5.48983i	−0.234776	−	1.33148i	−0.843086	−	0.537780i	$-0.819263\pi$
$17$	−0.968005	−	5.48983i	−0.234776	−	1.33148i	0.608310	−	0.793700i	$-0.291848\pi$
$18$	−1.38051	−	0.306927i	−0.325388	−	0.0723433i
$19$	2.07308	−	3.83437i	0.475596	−	0.879664i
$19$	2.07308	−	3.83437i	0.475596	−	0.879664i
$20$	7.18242	+	3.35980i	1.60604	+	0.751273i
$21$	−0.856229	+	0.150976i	−0.186845	+	0.0329457i
$22$	−1.18214	−	2.27423i	−0.252033	−	0.484867i
$23$	−2.47491	−	6.79975i	−0.516054	−	1.41785i	−0.874834	−	0.484424i	$-0.839029\pi$
$23$	−2.47491	−	6.79975i	−0.516054	−	1.41785i	0.358780	−	0.933422i	$-0.383193\pi$
$24$	1.51538	+	2.38822i	0.309326	+	0.487494i
$25$	8.21110	+	6.88993i	1.64222	+	1.37799i
$26$	4.42062	+	4.05567i	0.866955	+	0.795383i
$27$	−0.500000	−	0.866025i	−0.0962250	−	0.166667i
$28$	1.42320	+	0.999100i	0.268959	+	0.188812i
$29$	−2.40462	−	0.423999i	−0.446527	−	0.0787347i	−0.0541365	−	0.998534i	$-0.517241\pi$
$29$	−2.40462	−	0.423999i	−0.446527	−	0.0787347i	−0.392390	+	0.919799i	$0.628352\pi$
$30$	1.68280	+	5.34844i	0.307236	+	0.976488i
$31$	2.51180	−	4.35057i	0.451133	−	0.781385i	−0.547324	−	0.836921i	$-0.684353\pi$
$31$	2.51180	−	4.35057i	0.451133	−	0.781385i	0.998457	+	0.0555360i	$0.0176868\pi$
$32$	1.24106	−	5.51904i	0.219390	−	0.975637i
$33$	0.619877	−	1.70310i	0.107907	−	0.296471i
$34$	−7.81674	+	1.02428i	−1.34056	+	0.175663i
$35$	2.21573	+	2.64060i	0.374526	+	0.446343i
$36$	−0.519974	+	1.93122i	−0.0866623	+	0.321871i
$37$			3.74939i			0.616397i	0.951322	+	0.308198i	$0.0997260\pi$
$37$			3.74939i			0.616397i	−0.951322	+	0.308198i	$0.900274\pi$
$38$	−5.28765	−	3.16871i	−0.857771	−	0.514033i
$39$			4.24207i			0.679275i
$40$	5.19602	−	9.93741i	0.821563	−	1.57124i
$41$	−0.216824	−	0.258400i	−0.0338622	−	0.0403554i	0.748848	−	0.662742i	$-0.230608\pi$
$41$	−0.216824	−	0.258400i	−0.0338622	−	0.0403554i	−0.782710	+	0.622387i	$0.786163\pi$
$42$	0.159754	+	1.21915i	0.0246506	+	0.188119i
$43$	−1.75948	+	4.83414i	−0.268319	+	0.737200i	0.730223	+	0.683209i	$0.239416\pi$
$43$	−1.75948	+	4.83414i	−0.268319	+	0.737200i	−0.998541	+	0.0539905i	$0.982806\pi$
$44$	−3.28703	+	1.52793i	−0.495539	+	0.230344i
$45$	−1.98235	+	3.43353i	−0.295511	+	0.511840i
$46$	−9.76167	+	3.07136i	−1.43928	+	0.452847i
$47$	9.77372	+	1.72337i	1.42564	+	0.251379i	0.832638	−	0.553818i	$-0.186830\pi$
$47$	9.77372	+	1.72337i	1.42564	+	0.251379i	0.593006	+	0.805198i	$0.297941\pi$
$48$	3.46893	−	1.99162i	0.500697	−	0.287465i
$49$	−3.12204	−	5.40753i	−0.446006	−	0.772504i
$50$	10.2478	−	11.1700i	1.44926	−	1.57967i
$51$	−4.27033	−	3.58323i	−0.597966	−	0.501753i
$52$	6.00645	−	5.99194i	0.832944	−	0.830932i
$53$	3.00014	+	8.24282i	0.412101	+	1.13224i	0.956071	+	0.293134i	$0.0946983\pi$
$53$	3.00014	+	8.24282i	0.412101	+	1.13224i	−0.543970	+	0.839105i	$0.683079\pi$
$54$	−1.25482	+	0.652253i	−0.170759	+	0.0887603i
$55$	−7.07645	+	1.24777i	−0.954188	+	0.168249i
$56$	1.50057	−	1.94825i	0.200522	−	0.260346i
$57$	−0.876614	−	4.26984i	−0.116110	−	0.565554i
$58$	−0.749427	+	3.37080i	−0.0984046	+	0.442608i
$59$	−0.976716	−	5.53923i	−0.127158	−	0.721146i	−0.980003	−	0.198983i	$-0.936236\pi$
$59$	−0.976716	−	5.53923i	−0.127158	−	0.721146i	0.852845	−	0.522163i	$-0.174875\pi$
$60$	7.66169	−	2.04302i	0.989119	−	0.263752i
$61$	4.26876	−	1.55370i	0.546559	−	0.198931i	−0.0539578	−	0.998543i	$-0.517184\pi$
$61$	4.26876	−	1.55370i	0.546559	−	0.198931i	0.600517	+	0.799612i	$0.294961\pi$
$62$	−5.98952	−	3.82084i	−0.760670	−	0.485247i
$63$	−0.558864	+	0.666028i	−0.0704103	+	0.0839117i
$64$	−7.71984	−	2.09857i	−0.964980	−	0.262322i
$65$	14.5653	−	8.40927i	1.80660	−	1.04304i
$66$	−2.36742	−	0.982295i	−0.291409	−	0.120912i
$67$	−1.03153	+	5.85008i	−0.126021	+	0.714701i	0.854675	+	0.519163i	$0.173756\pi$
$67$	−1.03153	+	5.85008i	−0.126021	+	0.714701i	−0.980696	+	0.195538i	$0.937355\pi$
$68$	0.958271	+	11.1078i	0.116207	+	1.34702i
$69$	−6.26668	−	3.61807i	−0.754420	−	0.435565i
$70$	3.86930	−	2.96530i	0.462469	−	0.354421i
$71$	3.33873	+	1.21520i	0.396235	+	0.144218i	0.532450	−	0.846462i	$-0.321272\pi$
$71$	3.33873	+	1.21520i	0.396235	+	0.144218i	−0.136215	+	0.990679i	$0.543494\pi$
$72$	2.69597	+	0.855416i	0.317723	+	0.100812i
$73$	9.37379	−	7.86555i	1.09712	−	0.920593i	0.0998915	−	0.994998i	$-0.468150\pi$
$73$	9.37379	−	7.86555i	1.09712	−	0.920593i	0.997228	+	0.0744057i	$0.0237060\pi$
$74$	5.29726	+	0.234492i	0.615794	+	0.0272592i
$75$	10.7188			1.23770
$76$	−4.80755	+	7.27238i	−0.551463	+	0.834199i
$77$	−1.57577			−0.179576
$78$	5.99333	+	0.265305i	0.678611	+	0.0300399i
$79$	3.56820	−	2.99408i	0.401454	−	0.336860i	−0.419601	−	0.907709i	$-0.637830\pi$
$79$	3.56820	−	2.99408i	0.401454	−	0.336860i	0.821055	+	0.570848i	$0.193386\pi$
$80$	−13.7149	−	7.96259i	−1.53337	−	0.890245i
$81$	−0.939693	−	0.342020i	−0.104410	−	0.0380022i
$82$	−0.378636	+	0.290174i	−0.0418134	+	0.0320444i
$83$	−5.17652	−	2.98867i	−0.568197	−	0.328049i	0.188232	−	0.982125i	$-0.439724\pi$
$83$	−5.17652	−	2.98867i	−0.568197	−	0.328049i	−0.756429	+	0.654076i	$0.773058\pi$
$84$	1.73244	−	0.149458i	0.189025	−	0.0163072i
$85$	−3.83785	+	21.7655i	−0.416273	+	2.36080i
$86$	6.71978	+	2.78819i	0.724612	+	0.300658i
$87$	−2.11459	+	1.22086i	−0.226708	+	0.130890i
$88$	1.95313	+	4.73958i	0.208205	+	0.505241i
$89$	−6.31437	+	7.52518i	−0.669322	+	0.797667i	−0.988692	−	0.149963i	$-0.952085\pi$
$89$	−6.31437	+	7.52518i	−0.669322	+	0.797667i	0.319369	+	0.947630i	$0.396529\pi$
$90$	4.72701	+	3.01546i	0.498271	+	0.317857i
$91$	3.46579	−	1.26145i	0.363314	−	0.132235i
$92$	3.72879	+	13.9837i	0.388754	+	1.45790i
$93$	−0.872339	−	4.94728i	−0.0904574	−	0.513009i
$94$	3.04609	−	13.7008i	0.314180	−	1.41313i
$95$	−12.9229	+	11.4742i	−1.32586	+	1.17723i
$96$	−2.59686	−	5.02557i	−0.265041	−	0.512920i
$97$	−4.82529	+	0.850829i	−0.489934	+	0.0863886i	−0.413157	−	0.910660i	$-0.635574\pi$
$97$	−4.82529	+	0.850829i	−0.489934	+	0.0863886i	−0.0767770	+	0.997048i	$0.524463\pi$
$98$	−7.83518	+	4.07272i	−0.791472	+	0.411406i
$99$	−0.619877	−	1.70310i	−0.0623000	−	0.171168i
$100$	−15.1404	−	15.1770i	−1.51404	−	1.51770i
$101$	−4.40278	−	3.69437i	−0.438093	−	0.367604i	0.396902	−	0.917861i	$-0.370085\pi$
$101$	−4.40278	−	3.69437i	−0.438093	−	0.367604i	−0.834995	+	0.550257i	$0.814530\pi$
$102$	−5.32957	+	5.80915i	−0.527706	+	0.575191i
$103$	−1.68759	−	2.92300i	−0.166283	−	0.288011i	0.770827	−	0.637045i	$-0.219843\pi$
$103$	−1.68759	−	2.92300i	−0.166283	−	0.288011i	−0.937110	+	0.349033i	$0.886510\pi$
$104$	−8.08994	−	8.86083i	−0.793283	−	0.868876i
$105$	3.39469	+	0.598576i	0.331288	+	0.0584150i
$106$	11.8333	−	3.72317i	1.14936	−	0.361627i
$107$	−8.95362	+	15.5081i	−0.865579	+	1.49923i	0.000892133		1.00000i	$0.499716\pi$
$107$	−8.95362	+	15.5081i	−0.865579	+	1.49923i	−0.866471	+	0.499227i	$0.833617\pi$
$108$	0.843044	+	1.81364i	0.0811219	+	0.174517i
$109$	6.09069	−	16.7340i	0.583383	−	1.60283i	−0.198978	−	0.980004i	$-0.563762\pi$
$109$	6.09069	−	16.7340i	0.583383	−	1.60283i	0.782360	−	0.622826i	$-0.214016\pi$
$110$	1.32031	+	10.0759i	0.125887	+	0.960695i
$111$	2.41006	+	2.87220i	0.228753	+	0.272617i
$112$	−2.65870	−	2.24189i	−0.251223	−	0.211839i
$113$			7.78251i			0.732117i	0.930592	+	0.366058i	$0.119293\pi$
$113$			7.78251i			0.732117i	−0.930592	+	0.366058i	$0.880707\pi$
$114$	−6.08739	+	0.971464i	−0.570136	+	0.0909860i
$115$			28.6891i			2.67527i
$116$	4.71550	+	1.26963i	0.437823	+	0.117882i
$117$	2.72675	+	3.24962i	0.252088	+	0.300427i
$118$	−7.88708	+	1.03350i	−0.726064	+	0.0951416i
$119$	−1.65767	+	4.55441i	−0.151958	+	0.417502i
$120$	−2.40726	−	10.9524i	−0.219752	−	0.999816i
$121$	−3.85761	+	6.68157i	−0.350691	+	0.607415i
$122$	−1.92814	−	6.12821i	−0.174566	−	0.554822i
$123$	−0.332193	−	0.0585746i	−0.0299528	−	0.00528149i
$124$	−5.77279	+	8.22321i	−0.518412	+	0.738466i
$125$	−11.3367	−	19.6358i	−1.01399	−	1.75628i
$126$	0.906033	+	0.831234i	0.0807158	+	0.0740522i
$127$	−7.07199	−	5.93410i	−0.627538	−	0.526567i	0.272625	−	0.962120i	$-0.412108\pi$
$127$	−7.07199	−	5.93410i	−0.627538	−	0.526567i	−0.900163	+	0.435554i	$0.856553\pi$
$128$	−3.44774	+	10.7756i	−0.304740	+	0.952436i
$129$	1.75948	+	4.83414i	0.154914	+	0.425622i
$130$	−10.9699	−	21.1042i	−0.962127	−	1.85096i
$131$	16.9003	−	2.97998i	1.47658	−	0.260362i	0.623372	−	0.781925i	$-0.285762\pi$
$131$	16.9003	−	2.97998i	1.47658	−	0.260362i	0.853212	+	0.521563i	$0.174651\pi$
$132$	−1.53588	+	3.28333i	−0.133681	+	0.285777i
$133$	−3.22781	+	1.98590i	−0.279886	+	0.172199i
$134$	8.20065	+	1.82324i	0.708428	+	0.157504i
$135$	0.688463	+	3.90447i	0.0592534	+	0.336043i
$136$	15.7533	−	0.659177i	1.35084	−	0.0565240i
$137$	3.76681	−	1.37101i	0.321820	−	0.117133i	−0.176058	−	0.984380i	$-0.556335\pi$
$137$	3.76681	−	1.37101i	0.321820	−	0.117133i	0.497878	+	0.867247i	$0.334113\pi$
$138$	−5.50365	+	8.62748i	−0.468501	+	0.734420i
$139$	6.29372	−	7.50056i	0.533826	−	0.636189i	−0.429965	−	0.902845i	$-0.641474\pi$
$139$	6.29372	−	7.50056i	0.533826	−	0.636189i	0.963792	+	0.266656i	$0.0859187\pi$
$140$	−3.94747	−	5.65211i	−0.333622	−	0.477691i
$141$	8.59487	−	4.96225i	0.723818	−	0.417897i
$142$	1.92568	−	4.64106i	0.161599	−	0.389469i
$143$	−1.33506	+	7.57152i	−0.111644	+	0.633163i
$144$	1.37717	−	3.75545i	0.114764	−	0.312954i
$145$	8.38370	+	4.84033i	0.696229	+	0.401968i
$146$	−10.5264	−	13.7355i	−0.871174	−	1.13676i
$147$	−5.86751	−	2.13560i	−0.483944	−	0.176141i
$148$	0.662596	−	7.46946i	0.0544650	−	0.613986i
$149$	−13.6227	+	11.4308i	−1.11601	+	0.936445i	−0.998396	−	0.0566140i	$-0.981970\pi$
$149$	−13.6227	+	11.4308i	−1.11601	+	0.936445i	−0.117616	+	0.993059i	$0.537525\pi$
$150$	0.670371	−	15.1439i	0.0547356	−	1.23649i
$151$	13.4662			1.09586			0.547930	−	0.836524i	$-0.315416\pi$
$151$	13.4662			1.09586			0.547930	+	0.836524i	$0.315416\pi$
$152$	9.97396	+	7.24707i	0.808995	+	0.587815i
$153$	−5.57452			−0.450673
$154$	−0.0985508	+	2.22629i	−0.00794145	+	0.179400i
$155$	−15.2574	+	12.8024i	−1.22550	+	1.02832i
$156$	0.749662	−	8.45096i	0.0600210	−	0.676618i
$157$	−6.47409	−	2.35638i	−0.516689	−	0.188059i	0.0704964	−	0.997512i	$-0.477542\pi$
$157$	−6.47409	−	2.35638i	−0.516689	−	0.188059i	−0.587185	+	0.809453i	$0.699764\pi$
$158$	−4.00696	−	5.22852i	−0.318777	−	0.415959i
$159$	7.59663	+	4.38592i	0.602452	+	0.347826i
$160$	−12.1075	+	18.8788i	−0.957185	+	1.49250i
$161$	−1.09249	+	6.19580i	−0.0861000	+	0.488297i
$162$	−0.541986	+	1.30624i	−0.0425824	+	0.102628i
$163$	18.2502	−	10.5368i	1.42947	−	0.825302i	0.432387	−	0.901688i	$-0.357671\pi$
$163$	18.2502	−	10.5368i	1.42947	−	0.825302i	0.997078	+	0.0763855i	$0.0243380\pi$
$164$	0.386286	+	0.553097i	0.0301639	+	0.0431896i
$165$	−4.61882	+	5.50450i	−0.359575	+	0.428525i
$166$	−4.54623	+	7.12663i	−0.352856	+	0.553134i
$167$	−0.949239	+	0.345495i	−0.0734543	+	0.0267352i	−0.378486	−	0.925607i	$-0.623555\pi$
$167$	−0.949239	+	0.345495i	−0.0734543	+	0.0267352i	0.305032	+	0.952342i	$0.401333\pi$
$168$	−0.102810	−	2.45699i	−0.00793193	−	0.189561i
$169$	−0.867403	−	4.91928i	−0.0667233	−	0.378407i
$170$	30.5110	+	6.78347i	2.34008	+	0.520269i
$171$	−3.41613	−	2.70741i	−0.261238	−	0.207041i
$172$	4.35950	−	9.31953i	0.332408	−	0.710607i
$173$	6.19095	−	1.09163i	0.470689	−	0.0829951i	0.0667276	−	0.997771i	$-0.478744\pi$
$173$	6.19095	−	1.09163i	0.470689	−	0.0829951i	0.403961	+	0.914776i	$0.367633\pi$
$174$	1.59261	+	3.06391i	0.120736	+	0.232274i
$175$	−3.18741	−	8.75734i	−0.240946	−	0.661992i
$176$	6.81837	−	2.46302i	0.513954	−	0.185657i
$177$	−4.30876	−	3.61548i	−0.323866	−	0.271756i
$178$	10.2369	+	9.39177i	0.767287	+	0.703943i
$179$	−8.11925	−	14.0630i	−0.606862	−	1.05112i	−0.991754	−	0.128154i	$-0.959095\pi$
$179$	−8.11925	−	14.0630i	−0.606862	−	1.05112i	0.384893	−	0.922961i	$-0.374238\pi$
$180$	4.55597	−	6.48988i	0.339582	−	0.483727i
$181$	0.450664	+	0.0794641i	0.0334976	+	0.00590652i	0.190372	−	0.981712i	$-0.439031\pi$
$181$	0.450664	+	0.0794641i	0.0334976	+	0.00590652i	−0.156874	+	0.987619i	$0.550142\pi$
$182$	−1.56545	−	4.97547i	−0.116039	−	0.368806i
$183$	2.27136	−	3.93411i	0.167904	−	0.290818i
$184$	19.9898	−	4.39359i	1.47366	−	0.323900i
$185$	5.08420	−	13.9687i	0.373798	−	1.02700i
$186$	−7.04423	+	0.923057i	−0.516508	+	0.0676818i
$187$	−6.49425	−	7.73954i	−0.474906	−	0.565971i
$188$	−19.1664	−	5.16048i	−1.39786	−	0.376367i
$189$			0.869438i			0.0632423i
$190$	15.4029	+	18.9754i	1.11744	+	1.37662i
$191$		−	26.2954i		−	1.90267i	−0.308156	−	0.951336i	$-0.599712\pi$
$191$		−	26.2954i		−	1.90267i	0.308156	−	0.951336i	$-0.400288\pi$
$192$	−7.26268	+	3.35462i	−0.524139	+	0.242099i
$193$	6.46443	+	7.70401i	0.465320	+	0.554547i	0.946763	−	0.321930i	$-0.104332\pi$
$193$	6.46443	+	7.70401i	0.465320	+	0.554547i	−0.481443	+	0.876477i	$0.659887\pi$
$194$	0.900297	+	6.87053i	0.0646375	+	0.493275i
$195$	5.75228	−	15.8043i	0.411929	−	1.13177i
$196$	5.26403	+	11.3245i	0.376002	+	0.808892i
$197$	0.214662	−	0.371805i	0.0152940	−	0.0264900i	−0.858277	−	0.513187i	$-0.828465\pi$
$197$	0.214662	−	0.371805i	0.0152940	−	0.0264900i	0.873571	+	0.486697i	$0.161798\pi$
$198$	−2.44496	+	0.769267i	−0.173755	+	0.0546694i
$199$	−9.85367	−	1.73747i	−0.698508	−	0.123166i	−0.186893	−	0.982380i	$-0.559842\pi$
$199$	−9.85367	−	1.73747i	−0.698508	−	0.123166i	−0.511616	+	0.859214i	$0.670953\pi$
$200$	−22.3895	+	20.4416i	−1.58318	+	1.44544i
$201$	2.97016	+	5.14447i	0.209499	+	0.362863i
$202$	−5.49487	+	5.98933i	−0.386618	+	0.421408i
$203$	1.62625	+	1.36459i	0.114140	+	0.0957752i
$204$	7.87402	+	7.89309i	0.551292	+	0.552627i
$205$	0.457405	+	1.25671i	0.0319466	+	0.0877724i
$206$	−4.23524	+	2.20147i	−0.295083	+	0.153384i
$207$	−7.12621	+	1.25654i	−0.495306	+	0.0873358i
$208$	−13.0248	+	10.8755i	−0.903108	+	0.754083i
$209$	−0.220833	−	7.89698i	−0.0152754	−	0.546245i
$210$	1.05799	−	4.75869i	0.0730086	−	0.328381i
$211$	0.797058	+	4.52034i	0.0548717	+	0.311193i	0.999874	−	0.0158706i	$-0.00505197\pi$
$211$	0.797058	+	4.52034i	0.0548717	+	0.311193i	−0.945002	+	0.327064i	$0.893941\pi$
$212$	−4.52014	−	16.9514i	−0.310444	−	1.16422i
$213$	3.33873	−	1.21520i	0.228766	−	0.0832641i
$214$	21.3504	+	13.6198i	1.45948	+	0.931033i
$215$	13.1103	−	15.6242i	0.894112	−	1.06556i
$216$	2.61509	−	1.07765i	0.177934	−	0.0733248i
$217$	−3.78255	+	2.18386i	−0.256776	+	0.148250i
$218$	−23.2614	−	9.65168i	−1.57546	−	0.653695i
$219$	2.12487	−	12.0507i	0.143585	−	0.814312i
$220$	14.3180	−	1.23522i	0.965323	−	0.0832786i
$221$	20.4793	+	11.8238i	1.37759	+	0.795352i
$222$	4.20866	−	3.22538i	0.282467	−	0.216473i
$223$	14.0876	+	5.12748i	0.943378	+	0.343361i	0.767499	−	0.641050i	$-0.221501\pi$
$223$	14.0876	+	5.12748i	0.943378	+	0.343361i	0.175879	+	0.984412i	$0.443723\pi$
$224$	−3.33369	+	3.61608i	−0.222742	+	0.241609i
$225$	8.21110	−	6.88993i	0.547407	−	0.459329i
$226$	10.9954	+	0.486729i	0.731401	+	0.0323767i
$227$	−10.1623			−0.674494			−0.337247	−	0.941416i	$-0.609496\pi$
$227$	−10.1623			−0.674494			−0.337247	+	0.941416i	$0.609496\pi$
$228$	0.991800	+	8.66120i	0.0656836	+	0.573602i
$229$	−12.3552			−0.816453			−0.408227	−	0.912881i	$-0.633853\pi$
$229$	−12.3552			−0.816453			−0.408227	+	0.912881i	$0.633853\pi$
$230$	40.5328	+	1.79426i	2.67266	+	0.118310i
$231$	−1.20711	+	1.01288i	−0.0794219	+	0.0666429i
$232$	2.08868	−	6.58279i	0.137129	−	0.432182i
$233$	7.64972	+	2.78427i	0.501150	+	0.182404i	0.580211	−	0.814466i	$-0.302970\pi$
$233$	7.64972	+	2.78427i	0.501150	+	0.182404i	−0.0790614	+	0.996870i	$0.525192\pi$
$234$	4.76169	−	3.64920i	0.311281	−	0.238556i
$235$	−34.0761	−	19.6738i	−2.22288	−	1.28338i
$236$	0.966894	+	11.2077i	0.0629394	+	0.729561i
$237$	0.808846	−	4.58719i	0.0525402	−	0.297970i
$238$	6.33093	+	2.62684i	0.410373	+	0.170273i
$239$	3.82623	−	2.20908i	0.247498	−	0.142893i	−0.371120	−	0.928585i	$-0.621026\pi$
$239$	3.82623	−	2.20908i	0.247498	−	0.142893i	0.618618	+	0.785692i	$0.287693\pi$
$240$	−15.6245	+	2.71607i	−1.00856	+	0.175321i
$241$	9.06529	−	10.8036i	0.583947	−	0.695921i	−0.390484	−	0.920610i	$-0.627692\pi$
$241$	9.06529	−	10.8036i	0.583947	−	0.695921i	0.974431	+	0.224689i	$0.0721366\pi$
$242$	9.19866	+	5.86801i	0.591312	+	0.377210i
$243$	−0.939693	+	0.342020i	−0.0602813	+	0.0219406i
$244$	−8.77871	+	2.34087i	−0.561999	+	0.149859i
$245$	4.29881	+	24.3798i	0.274641	+	1.55757i
$246$	−0.103532	+	0.465669i	−0.00660095	+	0.0296900i
$247$	6.80745	+	17.1921i	0.433148	+	1.09390i
$248$	11.2570	+	8.67026i	0.714818	+	0.550562i
$249$	−5.88652	+	1.03795i	−0.373043	+	0.0657776i
$250$	−28.4510	+	14.7888i	−1.79940	+	0.935327i
$251$	2.93162	+	8.05457i	0.185042	+	0.508400i	0.997178	−	0.0750683i	$-0.0239175\pi$
$251$	2.93162	+	8.05457i	0.185042	+	0.508400i	−0.812136	+	0.583468i	$0.801695\pi$
$252$	1.23106	−	1.22808i	0.0775493	−	0.0773620i
$253$	−10.0465	−	8.43002i	−0.631618	−	0.529991i
$254$	−8.82617	+	9.62039i	−0.553803	+	0.603637i
$255$	11.0506	+	19.1403i	0.692018	+	1.19861i
$256$	15.0084	+	5.54499i	0.938027	+	0.346562i
$257$	8.44352	+	1.48882i	0.526693	+	0.0928701i	0.430671	−	0.902509i	$-0.358277\pi$
$257$	8.44352	+	1.48882i	0.526693	+	0.0928701i	0.0960218	+	0.995379i	$0.469388\pi$
$258$	6.93986	−	2.18352i	0.432057	−	0.135940i
$259$	1.62993	−	2.82313i	0.101279	−	0.175421i
$260$	−30.5027	+	14.1788i	−1.89170	+	0.879330i
$261$	−0.835116	+	2.29446i	−0.0516924	+	0.142024i
$262$	−3.15323	−	24.0636i	−0.194807	−	1.48665i
$263$	−11.3659	−	13.5454i	−0.700853	−	0.835244i	0.291770	−	0.956489i	$-0.405756\pi$
$263$	−11.3659	−	13.5454i	−0.700853	−	0.835244i	−0.992623	+	0.121245i	$0.961311\pi$
$264$	4.54273	+	2.37528i	0.279586	+	0.146188i
$265$		−	34.7777i		−	2.13637i
$266$	2.60387	+	4.68454i	0.159653	+	0.287228i
$267$			9.82342i			0.601184i
$268$	3.08881	−	11.4721i	0.188679	−	0.700770i
$269$	3.24145	+	3.86301i	0.197635	+	0.235532i	0.855756	−	0.517380i	$-0.173093\pi$
$269$	3.24145	+	3.86301i	0.197635	+	0.235532i	−0.658121	+	0.752913i	$0.728648\pi$
$270$	5.55940	−	0.728490i	0.338335	−	0.0443345i
$271$	3.37522	−	9.27335i	0.205030	−	0.563316i	−0.793973	−	0.607953i	$-0.791991\pi$
$271$	3.37522	−	9.27335i	0.205030	−	0.563316i	0.999003	+	0.0446372i	$0.0142132\pi$
$272$	0.0539310	−	22.2980i	0.00327005	−	1.35202i
$273$	1.84411	−	3.19409i	0.111611	−	0.193315i
$274$	−1.70142	−	5.40760i	−0.102786	−	0.326685i
$275$	19.1317	+	3.37343i	1.15368	+	0.203425i
$276$	11.8450	+	8.31529i	0.712982	+	0.500522i
$277$	−9.92129	−	17.1842i	−0.596112	−	1.03250i	−0.993389	−	0.114798i	$-0.963378\pi$
$277$	−9.92129	−	17.1842i	−0.596112	−	1.03250i	0.397276	−	0.917699i	$-0.369955\pi$
$278$	−10.2034	−	9.36105i	−0.611959	−	0.561439i
$279$	−3.84830	−	3.22911i	−0.230392	−	0.193322i
$280$	−8.23235	+	5.22362i	−0.491977	+	0.312171i
$281$	10.5492	+	28.9837i	0.629312	+	1.72902i	0.682954	+	0.730461i	$0.260695\pi$
$281$	10.5492	+	28.9837i	0.629312	+	1.72902i	−0.0536421	+	0.998560i	$0.517083\pi$
$282$	−6.47328	−	12.4534i	−0.385478	−	0.741591i
$283$	1.81192	−	0.319490i	0.107707	−	0.0189917i	−0.119535	−	0.992830i	$-0.538140\pi$
$283$	1.81192	−	0.319490i	0.107707	−	0.0189917i	0.227242	+	0.973838i	$0.427029\pi$
$284$	−6.43660	−	3.01092i	−0.381942	−	0.178665i
$285$	−2.52402	+	17.0964i	−0.149510	+	1.01270i
$286$	10.6138	+	2.35975i	0.627606	+	0.139535i
$287$	0.0509270	+	0.288821i	0.00300613	+	0.0170486i
$288$	−5.21968	−	2.18058i	−0.307573	−	0.128492i
$289$	−13.2264	+	4.81402i	−0.778025	+	0.283178i
$290$	7.36290	−	11.5420i	0.432364	−	0.677771i
$291$	−3.14949	+	3.75341i	−0.184626	+	0.220029i
$292$	−20.0643	+	14.0130i	−1.17417	+	0.820050i
$293$	−4.99553	+	2.88417i	−0.291842	+	0.168495i	−0.638772	−	0.769396i	$-0.720557\pi$
$293$	−4.99553	+	2.88417i	−0.291842	+	0.168495i	0.346930	+	0.937891i	$0.387224\pi$
$294$	−3.38420	+	8.15624i	−0.197371	+	0.475681i
$295$	−3.87238	+	21.9614i	−0.225459	+	1.27864i
$296$	−10.5116	−	1.40329i	−0.610976	−	0.0815643i
$297$	−1.56958	−	0.906199i	−0.0910765	−	0.0525830i
$298$	15.2978	+	19.9614i	0.886175	+	1.15633i
$299$	28.8450	+	10.4987i	1.66815	+	0.607157i
$300$	−21.3538	−	1.89424i	−1.23286	−	0.109364i
$301$	3.42631	−	2.87501i	0.197489	−	0.165713i
$302$	0.842193	−	19.0254i	0.0484627	−	1.09479i
$303$	−5.74742			−0.330181
$304$	10.8627	−	13.6383i	0.623017	−	0.782209i
$305$	−18.0105			−1.03128
$306$	−0.348638	+	7.87585i	−0.0199303	+	0.450232i
$307$	4.54342	−	3.81238i	0.259307	−	0.217584i	−0.503861	−	0.863785i	$-0.668088\pi$
$307$	4.54342	−	3.81238i	0.259307	−	0.217584i	0.763167	+	0.646201i	$0.223643\pi$
$308$	3.13921	+	0.278471i	0.178873	+	0.0158674i
$309$	−3.17164	−	1.15438i	−0.180428	−	0.0656705i
$310$	17.1335	+	22.3567i	0.973115	+	1.26978i
$311$	−2.24925	−	1.29860i	−0.127543	−	0.0736370i	0.434871	−	0.900493i	$-0.356794\pi$
$311$	−2.24925	−	1.29860i	−0.127543	−	0.0736370i	−0.562414	+	0.826856i	$0.690127\pi$
$312$	−11.8929	−	1.58768i	−0.673302	−	0.0898847i
$313$	0.124975	−	0.708768i	0.00706400	−	0.0400619i	−0.981072	−	0.193643i	$-0.937970\pi$
$313$	0.124975	−	0.708768i	0.00706400	−	0.0400619i	0.988136	+	0.153581i	$0.0490807\pi$
$314$	−3.73406	+	8.99942i	−0.210725	+	0.507867i
$315$	2.98524	−	1.72353i	0.168199	−	0.0971099i
$316$	−7.63761	+	5.33416i	−0.429649	+	0.300070i
$317$	17.2094	−	20.5093i	0.966575	−	1.15192i	−0.0217809	−	0.999763i	$-0.506934\pi$
$317$	17.2094	−	20.5093i	0.966575	−	1.15192i	0.988356	−	0.152157i	$-0.0486219\pi$
$318$	6.67166	−	10.4584i	0.374128	−	0.586480i
$319$	−4.15848	+	1.51356i	−0.232830	+	0.0847433i
$320$	25.9154	+	18.2866i	1.44871	+	1.02225i
$321$	3.10956	+	17.6352i	0.173559	+	0.984300i
$322$	8.68528	+	1.93099i	0.484012	+	0.107610i
$323$	−23.0568	−	7.66915i	−1.28291	−	0.426723i
$324$	1.81159	+	0.847428i	0.100644	+	0.0470793i
$325$	−44.7793	+	7.89579i	−2.48391	+	0.437980i
$326$	−13.7453	−	26.4434i	−0.761279	−	1.46457i
$327$	−6.09069	−	16.7340i	−0.336816	−	0.925395i
$328$	0.805590	−	0.511166i	0.0444813	−	0.0282244i
$329$	−6.61000	−	5.54644i	−0.364421	−	0.305785i
$330$	7.48806	+	6.86987i	0.412204	+	0.378174i
$331$	−13.0538	−	22.6098i	−0.717500	−	1.24275i	−0.961987	−	0.273094i	$-0.911953\pi$
$331$	−13.0538	−	22.6098i	−0.717500	−	1.24275i	0.244488	−	0.969652i	$-0.421380\pi$
$332$	9.78439	+	6.86875i	0.536988	+	0.376972i
$333$	3.69243	+	0.651075i	0.202344	+	0.0356787i
$334$	0.428758	+	1.36272i	0.0234606	+	0.0745648i
$335$	11.7758	−	20.3963i	0.643380	−	1.11437i
$336$	−3.47774	−	0.00841143i	−0.189726	−	0.000458881i
$337$	0.864185	−	2.37433i	0.0470751	−	0.129338i	−0.913927	−	0.405878i	$-0.866966\pi$
$337$	0.864185	−	2.37433i	0.0470751	−	0.129338i	0.961002	+	0.276540i	$0.0891879\pi$
$338$	−7.00436	+	0.917833i	−0.380987	+	0.0499236i
$339$	5.00250	+	5.96175i	0.271699	+	0.323798i
$340$	11.4921	−	42.6825i	0.623246	−	2.31479i
$341$		−	9.10477i		−	0.493051i
$342$	−4.03876	+	4.65708i	−0.218391	+	0.251826i
$343$			11.5149i			0.621746i
$344$	−12.8943	−	6.74208i	−0.695212	−	0.363509i
$345$	18.4410	+	21.9771i	0.992831	+	1.18321i
$346$	−1.15510	−	8.81502i	−0.0620985	−	0.473899i
$347$	−9.50746	+	26.1215i	−0.510387	+	1.40228i	0.370448	+	0.928853i	$0.379204\pi$
$347$	−9.50746	+	26.1215i	−0.510387	+	1.40228i	−0.880835	+	0.473424i	$0.843018\pi$
$348$	4.42838	−	2.05847i	0.237386	−	0.110346i
$349$	5.59457	−	9.69009i	0.299471	−	0.518699i	−0.676544	−	0.736402i	$-0.736523\pi$
$349$	5.59457	−	9.69009i	0.299471	−	0.518699i	0.976015	+	0.217703i	$0.0698566\pi$
$350$	−12.5720	+	3.95557i	−0.672000	+	0.211434i
$351$	4.17763	+	0.736628i	0.222985	+	0.0393183i
$352$	−3.05340	−	9.78724i	−0.162747	−	0.521661i
$353$	−11.5259	−	19.9634i	−0.613460	−	1.06254i	−0.990653	−	0.136409i	$-0.956444\pi$
$353$	−11.5259	−	19.9634i	−0.613460	−	1.06254i	0.377192	−	0.926135i	$-0.376890\pi$
$354$	−5.37753	+	5.86142i	−0.285812	+	0.311531i
$355$	−10.7910	−	9.05469i	−0.572725	−	0.480573i
$356$	13.9092	−	13.8756i	0.737186	−	0.735406i
$357$	1.65767	+	4.55441i	0.0877331	+	0.241045i
$358$	−20.3764	+	10.5916i	−1.07692	+	0.559784i
$359$	35.6849	−	6.29220i	1.88337	−	0.332090i	0.890866	−	0.454266i	$-0.150098\pi$
$359$	35.6849	−	6.29220i	1.88337	−	0.332090i	0.992508	+	0.122176i	$0.0389872\pi$
$360$	−8.88416	−	6.84269i	−0.468236	−	0.360642i
$361$	−10.4047	−	15.8979i	−0.547616	−	0.836730i
$362$	0.140454	−	0.631741i	0.00738212	−	0.0332036i
$363$	1.33973	+	7.59800i	0.0703177	+	0.398792i
$364$	−7.12740	+	1.90054i	−0.373577	+	0.0996156i
$365$	−45.5887	+	16.5929i	−2.38622	+	0.868514i
$366$	−5.41618	−	3.45509i	−0.283108	−	0.180601i
$367$	−16.0860	+	19.1706i	−0.839683	+	1.00070i	0.160224	+	0.987081i	$0.448778\pi$
$367$	−16.0860	+	19.1706i	−0.839683	+	1.00070i	−0.999907	+	0.0136149i	$0.995666\pi$
$368$	−4.95721	−	28.5169i	−0.258413	−	1.48655i
$369$	−0.292126	+	0.168659i	−0.0152075	+	0.00878003i
$370$	−19.4175	−	8.05674i	−1.00947	−	0.418850i
$371$	1.32434	−	7.51070i	0.0687562	−	0.389936i
$372$	0.863567	+	10.0100i	0.0447739	+	0.518996i
$373$	−5.76111	−	3.32618i	−0.298299	−	0.172223i	0.343379	−	0.939197i	$-0.388428\pi$
$373$	−5.76111	−	3.32618i	−0.298299	−	0.172223i	−0.641678	+	0.766974i	$0.721762\pi$
$374$	−11.3408	+	8.69122i	−0.586420	+	0.449412i
$375$	−21.3061	−	7.75478i	−1.10024	−	0.400455i
$376$	−8.48958	+	26.7562i	−0.437817	+	1.37984i
$377$	7.93464	−	6.65795i	0.408655	−	0.342902i
$378$	1.22837	+	0.0543759i	0.0631804	+	0.00279679i
$379$	9.56273			0.491204			0.245602	−	0.969371i	$-0.421014\pi$
$379$	9.56273			0.491204			0.245602	+	0.969371i	$0.421014\pi$
$380$	27.7724	−	20.5749i	1.42469	−	1.05547i
$381$	−9.23183			−0.472961
$382$	−37.1510	−	1.64455i	−1.90081	−	0.0841427i
$383$	13.8759	−	11.6433i	0.709028	−	0.594945i	−0.215298	−	0.976548i	$-0.569072\pi$
$383$	13.8759	−	11.6433i	0.709028	−	0.594945i	0.924326	+	0.381603i	$0.124628\pi$
$384$	4.28529	+	10.4707i	0.218683	+	0.534332i
$385$	5.87068	+	2.13675i	0.299198	+	0.108899i
$386$	11.2888	−	8.65132i	0.574582	−	0.440341i
$387$	4.45517	+	2.57219i	0.226469	+	0.130752i
$388$	9.76320	−	0.842273i	0.495651	−	0.0427599i
$389$	−0.701692	+	3.97949i	−0.0355772	+	0.201768i	−0.997415	−	0.0718505i	$-0.977110\pi$
$389$	−0.701692	+	3.97949i	−0.0355772	+	0.201768i	0.961838	+	0.273619i	$0.0882207\pi$
$390$	−21.9690	−	9.11541i	−1.11244	−	0.461577i
$391$	−34.9337	+	20.1690i	−1.76668	+	1.01999i
$392$	16.3288	−	6.72893i	0.824729	−	0.339862i
$393$	11.0309	−	13.1461i	0.556434	−	0.663132i
$394$	−0.511872	−	0.326534i	−0.0257877	−	0.0164505i
$395$	−17.3537	+	6.31622i	−0.873158	+	0.317804i
$396$	0.933932	+	3.50242i	0.0469318	+	0.176003i
$397$	6.33251	+	35.9134i	0.317819	+	1.80244i	0.555956	+	0.831212i	$0.312352\pi$
$397$	6.33251	+	35.9134i	0.317819	+	1.80244i	−0.238136	+	0.971232i	$0.576536\pi$
$398$	−3.07101	+	13.8129i	−0.153936	+	0.692378i
$399$	−1.19613	+	3.59608i	−0.0598814	+	0.180029i
$400$	27.4802	+	32.9110i	1.37401	+	1.64555i
$401$	−17.3556	+	3.06026i	−0.866698	+	0.152822i	−0.589282	−	0.807928i	$-0.700589\pi$
$401$	−17.3556	+	3.06026i	−0.866698	+	0.152822i	−0.277416	+	0.960750i	$0.589478\pi$
$402$	7.45402	−	3.87459i	0.371773	−	0.193247i
$403$	7.28861	+	20.0253i	0.363072	+	0.997531i
$404$	8.11824	+	8.13790i	0.403898	+	0.404876i
$405$	3.03714	+	2.54846i	0.150916	+	0.126634i
$406$	2.02964	−	2.21227i	0.100729	−	0.109793i
$407$	3.39770	+	5.88499i	0.168418	+	0.291708i
$408$	11.6440	−	10.6310i	0.576466	−	0.526313i
$409$	31.6880	+	5.58745i	1.56687	+	0.276281i	0.888653	−	0.458580i	$-0.151642\pi$
$409$	31.6880	+	5.58745i	1.56687	+	0.276281i	0.678217	+	0.734862i	$0.262753\pi$
$410$	1.80412	−	0.567639i	0.0890994	−	0.0280337i
$411$	2.00428	−	3.47151i	0.0988636	−	0.171237i
$412$	2.84543	+	6.12136i	0.140184	+	0.301578i
$413$	−1.67259	+	4.59539i	−0.0823025	+	0.226124i
$414$	1.32960	+	10.1467i	0.0653462	+	0.498683i
$415$	15.2330	+	18.1540i	0.747758	+	0.891143i
$416$	14.5507	+	19.0820i	0.713406	+	0.935572i
$417$		−	9.79129i		−	0.479482i
$418$	−11.1709	−	0.181888i	−0.546386	−	0.00889644i
$419$			12.8080i			0.625711i	0.949801	+	0.312855i	$0.101285\pi$
$419$			12.8080i			0.625711i	−0.949801	+	0.312855i	$0.898715\pi$
$420$	−6.65705	−	1.79238i	−0.324831	−	0.0874593i
$421$	17.0225	+	20.2867i	0.829628	+	0.988712i	0.999994	+	0.00333104i	$0.00106030\pi$
$421$	17.0225	+	20.2867i	0.829628	+	0.988712i	−0.170367	+	0.985381i	$0.554495\pi$
$422$	6.43632	−	0.843399i	0.313315	−	0.0410560i
$423$	3.39438	−	9.32598i	0.165040	−	0.453445i
$424$	−24.2321	+	5.32602i	−1.17681	+	0.258655i
$425$	29.8762	−	51.7470i	1.44921	−	2.51010i
$426$	−1.50806	−	4.79306i	−0.0730658	−	0.232225i
$427$	−3.88961	−	0.685844i	−0.188232	−	0.0331903i
$428$	20.5778	−	29.3126i	0.994666	−	1.41688i
$429$	3.84416	+	6.65829i	0.185598	+	0.321465i
$430$	−21.2544	−	19.4997i	−1.02498	−	0.940360i
$431$	28.4206	+	23.8477i	1.36897	+	1.14870i	0.973097	+	0.230397i	$0.0740024\pi$
$431$	28.4206	+	23.8477i	1.36897	+	1.14870i	0.395873	+	0.918305i	$0.370442\pi$
$432$	−1.35899	−	3.76207i	−0.0653842	−	0.181003i
$433$	−1.92432	−	5.28704i	−0.0924771	−	0.254079i	0.884827	−	0.465920i	$-0.154276\pi$
$433$	−1.92432	−	5.28704i	−0.0924771	−	0.254079i	−0.977304	+	0.211841i	$0.932054\pi$
$434$	2.84885	+	5.48068i	0.136749	+	0.263081i
$435$	9.53359	−	1.68103i	0.457101	−	0.0805992i
$436$	−15.0910	+	32.2608i	−0.722727	+	1.54501i
$437$	−31.2034	−	4.60670i	−1.49266	−	0.220369i
$438$	−16.8927	−	3.75574i	−0.807165	−	0.179456i
$439$	−0.456897	−	2.59119i	−0.0218065	−	0.123671i	0.971961	−	0.235141i	$-0.0755552\pi$
$439$	−0.456897	−	2.59119i	−0.0218065	−	0.123671i	−0.993768	+	0.111470i	$0.964444\pi$
$440$	−0.849686	−	20.3062i	−0.0405072	−	0.968061i
$441$	−5.86751	+	2.13560i	−0.279405	+	0.101695i
$442$	17.9858	−	28.1944i	0.855495	−	1.34107i
$443$	−20.0120	+	23.8494i	−0.950801	+	1.13312i	0.0401902	+	0.999192i	$0.487204\pi$
$443$	−20.0120	+	23.8494i	−0.950801	+	1.13312i	−0.990991	+	0.133928i	$0.957241\pi$
$444$	−4.29370	−	6.14784i	−0.203770	−	0.291764i
$445$	33.7290	−	19.4735i	1.59891	−	0.923130i
$446$	8.12532	−	19.5828i	0.384745	−	0.927270i
$447$	−3.08801	+	17.5130i	−0.146058	+	0.828334i
$448$	4.90041	+	4.93610i	0.231523	+	0.233209i
$449$	28.9369	+	16.7067i	1.36562	+	0.788440i	0.990365	−	0.138482i	$-0.0442225\pi$
$449$	28.9369	+	16.7067i	1.36562	+	0.788440i	0.375253	+	0.926922i	$0.377556\pi$
$450$	−9.22077	−	12.0318i	−0.434671	−	0.567184i
$451$	−0.574485	−	0.209095i	−0.0270514	−	0.00984592i
$452$	1.37533	−	15.5041i	0.0646901	−	0.729253i
$453$	10.3157	−	8.65588i	0.484673	−	0.406689i
$454$	−0.635563	+	14.3576i	−0.0298285	+	0.673834i
$455$	−14.6227			−0.685522
$456$	12.2988	−	0.859562i	0.575945	−	0.0402527i
$457$	−3.40575			−0.159314			−0.0796571	−	0.996822i	$-0.525383\pi$
$457$	−3.40575			−0.159314			−0.0796571	+	0.996822i	$0.525383\pi$
$458$	−0.772710	+	17.4558i	−0.0361064	+	0.815654i
$459$	−4.27033	+	3.58323i	−0.199322	+	0.167251i
$460$	5.06996	−	57.1538i	0.236388	−	2.66481i
$461$	24.7986	+	9.02595i	1.15499	+	0.420380i	0.847303	−	0.531109i	$-0.178225\pi$
$461$	24.7986	+	9.02595i	1.15499	+	0.420380i	0.307682	+	0.951489i	$0.400447\pi$
$462$	1.35554	+	1.76879i	0.0630654	+	0.0822914i
$463$	11.7841	+	6.80357i	0.547655	+	0.316189i	0.748176	−	0.663501i	$-0.230930\pi$
$463$	11.7841	+	6.80357i	0.547655	+	0.316189i	−0.200521	+	0.979689i	$0.564263\pi$
$464$	−9.16974	−	3.36265i	−0.425695	−	0.156107i
$465$	−3.45856	+	19.6145i	−0.160387	+	0.909600i
$466$	4.41212	−	10.6336i	0.204388	−	0.492593i
$467$	−1.99495	+	1.15179i	−0.0923154	+	0.0532983i	−0.545447	−	0.838145i	$-0.683640\pi$
$467$	−1.99495	+	1.15179i	−0.0923154	+	0.0532983i	0.453132	+	0.891444i	$0.350307\pi$
$468$	−4.85790	−	6.95568i	−0.224556	−	0.321527i
$469$	3.31983	−	3.95642i	0.153296	−	0.182691i
$470$	−29.9269	+	46.9132i	−1.38043	+	2.16395i
$471$	−6.47409	+	2.35638i	−0.298310	+	0.108576i
$472$	15.8951	−	0.665109i	0.731631	−	0.0306141i
$473$	1.61904	+	9.18203i	0.0744435	+	0.422190i
$474$	−6.43034	−	1.42965i	−0.295355	−	0.0656661i
$475$	43.4408	−	17.2010i	1.99320	−	0.789236i
$476$	4.10723	−	8.78024i	0.188255	−	0.402442i
$477$	8.63857	−	1.52321i	0.395533	−	0.0697431i
$478$	−2.88175	−	5.54397i	−0.131808	−	0.253575i
$479$	−6.00950	−	16.5110i	−0.274581	−	0.754405i	−0.997953	−	0.0639471i	$-0.979631\pi$
$479$	−6.00950	−	16.5110i	−0.274581	−	0.754405i	0.723372	−	0.690458i	$-0.242591\pi$
$480$	2.86017	+	22.2446i	0.130548	+	1.01532i
$481$	−12.1841	−	10.2237i	−0.555547	−	0.466159i
$482$	−14.6967	−	13.4834i	−0.669416	−	0.614152i
$483$	3.14569	+	5.44849i	0.143134	+	0.247915i
$484$	8.86580	−	12.6291i	0.402991	−	0.574052i
$485$	19.1308	+	3.37328i	0.868686	+	0.153173i
$486$	0.424447	+	1.34902i	0.0192533	+	0.0611926i
$487$	−17.9591	+	31.1061i	−0.813804	+	1.40955i	0.0963787	+	0.995345i	$0.469274\pi$
$487$	−17.9591	+	31.1061i	−0.813804	+	1.40955i	−0.910183	+	0.414206i	$0.864059\pi$
$488$	2.75822	+	12.5492i	0.124859	+	0.568077i
$489$	7.20757	−	19.8026i	0.325937	−	0.895506i
$490$	34.7133	−	4.54875i	1.56819	−	0.205491i
$491$	10.2071	+	12.1643i	0.460638	+	0.548967i	0.945499	−	0.325624i	$-0.105574\pi$
$491$	10.2071	+	12.1643i	0.460638	+	0.548967i	−0.484862	+	0.874591i	$0.661130\pi$
$492$	0.651436	+	0.175396i	0.0293690	+	0.00790748i
$493$			13.6114i			0.613026i
$494$	24.7152	−	8.54255i	1.11199	−	0.384348i
$495$			7.18562i			0.322969i
$496$	12.9536	−	15.3619i	0.581635	−	0.689771i
$497$	−1.98565	−	2.36640i	−0.0890684	−	0.106148i
$498$	1.09830	+	8.38157i	0.0492160	+	0.375587i
$499$	−6.22746	+	17.1098i	−0.278779	+	0.765940i	0.718723	+	0.695297i	$0.244727\pi$
$499$	−6.22746	+	17.1098i	−0.278779	+	0.765940i	−0.997502	+	0.0706425i	$0.977495\pi$
$500$	19.1147	+	41.1214i	0.854836	+	1.83900i
$501$	−0.505079	+	0.874823i	−0.0225653	+	0.0390842i
$502$	11.5631	−	3.63814i	0.516086	−	0.162378i
$503$	−21.1417	−	3.72785i	−0.942661	−	0.166217i	−0.318862	−	0.947801i	$-0.603301\pi$
$503$	−21.1417	−	3.72785i	−0.942661	−	0.166217i	−0.623799	+	0.781585i	$0.714412\pi$
$504$	−1.65808	−	1.81608i	−0.0738568	−	0.0808947i
$505$	11.3934	+	19.7339i	0.506999	+	0.878149i
$506$	−12.5385	+	13.6668i	−0.557404	+	0.607562i
$507$	−3.82652	−	3.21083i	−0.169942	−	0.142598i
$508$	13.0400	+	13.0716i	0.578555	+	0.579956i
$509$	−5.12864	−	14.0908i	−0.227323	−	0.624564i	0.772624	−	0.634864i	$-0.218944\pi$
$509$	−5.12864	−	14.0908i	−0.227323	−	0.624564i	−0.999947	+	0.0102993i	$0.996722\pi$
$510$	27.7331	−	14.4156i	1.22804	−	0.638334i
$511$	−10.4774	+	1.84744i	−0.463491	+	0.0817259i
$512$	8.77277	−	20.8576i	0.387705	−	0.921783i
$513$	−4.35720	+	0.121846i	−0.192375	+	0.00537963i
$514$	2.63152	−	11.8362i	0.116071	−	0.522070i
$515$	2.32369	+	13.1783i	0.102394	+	0.580705i
$516$	−2.65091	−	9.94140i	−0.116700	−	0.437646i
$517$	16.9024	−	6.15197i	0.743366	−	0.270563i
$518$	−3.88666	−	2.47938i	−0.170770	−	0.108938i
$519$	4.04085	−	4.81570i	0.177374	−	0.211386i
$520$	18.1245	+	43.9819i	0.794812	+	1.92873i
$521$	22.0879	−	12.7525i	0.967691	−	0.558696i	0.0691591	−	0.997606i	$-0.477968\pi$
$521$	22.0879	−	12.7525i	0.967691	−	0.558696i	0.898531	+	0.438909i	$0.144635\pi$
$522$	3.18946	+	1.32338i	0.139599	+	0.0579226i
$523$	7.47935	−	42.4175i	0.327049	−	1.85479i	−0.167815	−	0.985818i	$-0.553671\pi$
$523$	7.47935	−	42.4175i	0.327049	−	1.85479i	0.494864	−	0.868970i	$-0.335218\pi$
$524$	−34.1950	+	2.95001i	−1.49381	+	0.128872i
$525$	−8.07081	−	4.65968i	−0.352239	−	0.203365i
$526$	−19.8482	+	15.2110i	−0.865421	+	0.663230i
$527$	−26.3153	−	9.57799i	−1.14631	−	0.417224i
$528$	3.63997	−	6.26955i	0.158409	−	0.272847i
$529$	−22.4924	+	18.8734i	−0.977931	+	0.820581i
$530$	−49.1349	−	2.17504i	−2.13428	−	0.0944779i
$531$	−5.62468			−0.244090
$532$	6.78131	−	3.38585i	0.294007	−	0.146795i
$533$	1.43093			0.0619803
$534$	13.8788	+	0.614371i	0.600595	+	0.0265864i
$535$	54.3867	−	45.6359i	2.35134	−	1.97301i
$536$	−16.0149	−	5.08145i	−0.691740	−	0.219485i
$537$	−15.2592	−	5.55390i	−0.658483	−	0.239668i
$538$	5.66051	−	4.33803i	0.244042	−	0.187026i
$539$	−9.80060	−	5.65838i	−0.422142	−	0.243724i
$540$	−0.681539	−	7.90005i	−0.0293288	−	0.339964i
$541$	0.00900876	−	0.0510912i	0.000387317	−	0.00219658i	−0.984613	−	0.174746i	$-0.944089\pi$
$541$	0.00900876	−	0.0510912i	0.000387317	−	0.00219658i	0.985001	+	0.172550i	$0.0552006\pi$
$542$	−12.8906	−	5.34858i	−0.553697	−	0.229741i
$543$	0.396307	−	0.228808i	0.0170072	−	0.00981909i
$544$	−31.4999	−	1.47074i	−1.35055	−	0.0630577i
$545$	−45.3829	+	54.0853i	−1.94399	+	2.31676i
$546$	−4.39737	−	2.80518i	−0.188190	−	0.120050i
$547$	−4.04234	+	1.47129i	−0.172838	+	0.0629079i	−0.426990	−	0.904256i	$-0.640426\pi$
$547$	−4.04234	+	1.47129i	−0.172838	+	0.0629079i	0.254152	+	0.967164i	$0.418204\pi$
$548$	−7.74643	+	2.06561i	−0.330911	+	0.0882386i
$549$	−0.788836	−	4.47371i	−0.0336667	−	0.190933i
$550$	5.96260	−	26.8188i	0.254246	−	1.14356i
$551$	−6.61073	+	8.34121i	−0.281627	+	0.355347i
$552$	12.4889	−	16.2149i	0.531563	−	0.690150i
$553$	−3.98828	+	0.703242i	−0.169599	+	0.0299049i
$554$	−24.8988	+	12.9424i	−1.05785	+	0.549869i
$555$	−5.08420	−	13.9687i	−0.215812	−	0.592940i
$556$	−13.8637	+	13.8302i	−0.587952	+	0.586532i
$557$	2.34819	+	1.97036i	0.0994959	+	0.0834870i	0.691179	−	0.722684i	$-0.257092\pi$
$557$	2.34819	+	1.97036i	0.0994959	+	0.0834870i	−0.591683	+	0.806171i	$0.701536\pi$
$558$	−4.80286	+	5.23504i	−0.203321	+	0.221617i
$559$	−10.9114	−	18.8991i	−0.461504	−	0.799349i
$560$	6.86522	+	11.9576i	0.290108	+	0.505301i
$561$	−9.94976	−	1.75441i	−0.420079	−	0.0740713i
$562$	41.6088	−	13.0915i	1.75516	−	0.552233i
$563$	4.93823	−	8.55327i	0.208122	−	0.360477i	−0.743001	−	0.669290i	$-0.766598\pi$
$563$	4.93823	−	8.55327i	0.208122	−	0.360477i	0.951123	+	0.308813i	$0.0999316\pi$
$564$	−17.9994	+	8.36679i	−0.757913	+	0.352305i
$565$	10.5531	−	28.9945i	0.443974	−	1.21981i
$566$	−0.338065	−	2.57992i	−0.0142100	−	0.108442i
$567$	0.558864	+	0.666028i	0.0234701	+	0.0279706i
$568$	−4.65647	+	8.90551i	−0.195381	+	0.373667i
$569$		−	2.42543i		−	0.101679i	−0.998707	−	0.0508397i	$-0.983810\pi$
$569$		−	2.42543i		−	0.101679i	0.998707	−	0.0508397i	$-0.0161897\pi$
$570$	23.9965	+	4.63525i	1.00510	+	0.194149i
$571$		−	22.3845i		−	0.936761i	−0.883527	−	0.468380i	$-0.844838\pi$
$571$		−	22.3845i		−	0.936761i	0.883527	−	0.468380i	$-0.155162\pi$
$572$	3.99773	−	14.8479i	0.167153	−	0.620821i
$573$	−16.9024	−	20.1435i	−0.706107	−	0.841506i
$574$	0.411240	−	0.0538879i	0.0171648	−	0.00224924i
$575$	26.5281	−	72.8854i	1.10630	−	3.03953i
$576$	−3.40723	+	7.23815i	−0.141968	+	0.301590i
$577$	−22.1664	+	38.3934i	−0.922800	+	1.59834i	−0.127738	+	0.991808i	$0.540772\pi$
$577$	−22.1664	+	38.3934i	−0.922800	+	1.59834i	−0.795062	+	0.606528i	$0.792562\pi$
$578$	5.97420	+	18.9878i	0.248494	+	0.789787i
$579$	9.90409	+	1.74636i	0.411600	+	0.0725761i
$580$	−15.8464	−	11.1244i	−0.657987	−	0.461914i
$581$	2.59846	+	4.50067i	0.107802	+	0.186719i
$582$	5.10596	+	4.68443i	0.211649	+	0.194176i
$583$	12.1786	+	10.2191i	0.504387	+	0.423231i
$584$	18.5432	+	29.2238i	0.767322	+	1.20929i
$585$	−5.75228	−	15.8043i	−0.237827	−	0.653425i
$586$	3.76241	+	7.23821i	0.155424	+	0.299008i
$587$	−13.0986	+	2.30964i	−0.540638	+	0.0953291i	−0.437298	−	0.899317i	$-0.644064\pi$
$587$	−13.0986	+	2.30964i	−0.540638	+	0.0953291i	−0.103341	+	0.994646i	$0.532953\pi$
$588$	11.3117	+	5.29141i	0.466488	+	0.218214i
$589$	−11.4745	−	18.6502i	−0.472799	−	0.768469i
$590$	30.7855	+	6.84451i	1.26742	+	0.281784i
$591$	−0.0745512	−	0.422801i	−0.00306663	−	0.0173917i
$592$	−2.64002	+	14.7634i	−0.108504	+	0.606771i
$593$	−16.1945	+	5.89431i	−0.665027	+	0.242050i	−0.652405	−	0.757870i	$-0.726240\pi$
$593$	−16.1945	+	5.89431i	−0.665027	+	0.242050i	−0.0126220	+	0.999920i	$0.504018\pi$
$594$	−1.37847	+	2.16088i	−0.0565593	+	0.0886620i
$595$	12.3516	−	14.7201i	0.506367	−	0.603464i
$596$	29.1588	−	20.3647i	1.19439	−	0.834171i
$597$	−8.66517	+	5.00284i	−0.354642	+	0.204753i
$598$	16.6369	−	40.0965i	0.680335	−	1.63967i
$599$	−0.274360	+	1.55597i	−0.0112101	+	0.0635754i	−0.989900	−	0.141770i	$-0.954721\pi$
$599$	−0.274360	+	1.55597i	−0.0112101	+	0.0635754i	0.978690	+	0.205345i	$0.0658318\pi$
$600$	−4.01174	+	30.0508i	−0.163779	+	1.22682i
$601$	−26.4523	−	15.2722i	−1.07901	−	0.622967i	−0.148382	−	0.988930i	$-0.547406\pi$
$601$	−26.4523	−	15.2722i	−1.07901	−	0.622967i	−0.930629	+	0.365963i	$0.880740\pi$
$602$	−3.84762	−	5.02060i	−0.156817	−	0.204624i
$603$	5.58208	+	2.03171i	0.227320	+	0.0827376i
$604$	−26.8270	−	2.37975i	−1.09157	−	0.0968307i
$605$	23.4321	−	19.6619i	0.952652	−	0.799370i
$606$	−0.359452	+	8.12013i	−0.0146017	+	0.329858i
$607$	−26.8285			−1.08894			−0.544468	−	0.838782i	$-0.683268\pi$
$607$	−26.8285			−1.08894			−0.544468	+	0.838782i	$0.683268\pi$
$608$	−18.5892	−	16.2001i	−0.753891	−	0.656999i
$609$	2.12292			0.0860251
$610$	−1.12640	+	25.4458i	−0.0456068	+	1.03027i
$611$	−32.2508	+	27.0616i	−1.30473	+	1.09480i
$612$	11.1054	+	0.985133i	0.448910	+	0.0398217i
$613$	18.7118	+	6.81053i	0.755762	+	0.275075i	0.691028	−	0.722828i	$-0.257158\pi$
$613$	18.7118	+	6.81053i	0.755762	+	0.275075i	0.0647337	+	0.997903i	$0.479380\pi$
$614$	−5.10209	−	6.65751i	−0.205904	−	0.268675i
$615$	1.15819	+	0.668681i	0.0467027	+	0.0269638i
$616$	0.589763	−	4.41775i	0.0237622	−	0.177996i
$617$	−0.926976	+	5.25714i	−0.0373187	+	0.211645i	−0.997765	−	0.0668205i	$-0.978715\pi$
$617$	−0.926976	+	5.25714i	−0.0373187	+	0.211645i	0.960446	+	0.278465i	$0.0898256\pi$
$618$	−1.82930	+	4.40879i	−0.0735854	+	0.177347i
$619$	12.0891	−	6.97966i	0.485903	−	0.280536i	−0.236970	−	0.971517i	$-0.576154\pi$
$619$	12.0891	−	6.97966i	0.485903	−	0.280536i	0.722873	+	0.690981i	$0.242821\pi$
$620$	32.6578	−	22.8084i	1.31157	−	0.916009i
$621$	−4.65130	+	5.54321i	−0.186650	+	0.222441i
$622$	−1.97538	+	3.09659i	−0.0792054	+	0.124162i
$623$	8.02578	−	2.92115i	0.321546	−	0.117033i
$624$	−2.98692	+	16.7033i	−0.119573	+	0.668668i
$625$	6.30330	+	35.7478i	0.252132	+	1.42991i
$626$	−0.993553	−	0.220896i	−0.0397104	−	0.00882877i
$627$	−5.24525	−	5.90749i	−0.209475	−	0.235922i
$628$	12.4811	+	5.83843i	0.498051	+	0.232979i
$629$	20.5835	−	3.62943i	0.820719	−	0.144715i
$630$	−2.24835	−	4.32543i	−0.0895766	−	0.172329i
$631$	9.49158	+	26.0779i	0.377854	+	1.03814i	0.972244	+	0.233968i	$0.0751711\pi$
$631$	9.49158	+	26.0779i	0.377854	+	1.03814i	−0.594391	+	0.804177i	$0.702607\pi$
$632$	7.05859	+	11.1242i	0.280776	+	0.442499i
$633$	3.51620	+	2.95044i	0.139756	+	0.117270i
$634$	−27.8999	−	25.5966i	−1.10805	−	1.01657i
$635$	18.3007	+	31.6978i	0.726241	+	1.25789i
$636$	−14.3587	−	10.0800i	−0.569361	−	0.399698i
$637$	26.0854	+	4.59956i	1.03354	+	0.182241i
$638$	1.87833	+	5.96989i	0.0743638	+	0.236350i
$639$	1.77650	−	3.07699i	0.0702774	−	0.121724i
$640$	27.4566	−	35.4703i	1.08532	−	1.40209i
$641$	−9.62898	+	26.4554i	−0.380322	+	1.04493i	0.590899	+	0.806746i	$0.298773\pi$
$641$	−9.62898	+	26.4554i	−0.380322	+	1.04493i	−0.971221	+	0.238180i	$0.923449\pi$
$642$	25.1100	−	3.29035i	0.991013	−	0.129860i
$643$	−3.11526	−	3.71262i	−0.122854	−	0.146411i	0.701112	−	0.713052i	$-0.252687\pi$
$643$	−3.11526	−	3.71262i	−0.122854	−	0.146411i	−0.823965	+	0.566640i	$0.808243\pi$
$644$	3.27135	−	12.1501i	0.128909	−	0.478779i
$645$		−	20.3959i		−	0.803089i
$646$	−12.2772	+	32.0956i	−0.483040	+	1.26279i
$647$			4.89679i			0.192513i	0.995357	+	0.0962564i	$0.0306869\pi$
$647$			4.89679i			0.192513i	−0.995357	+	0.0962564i	$0.969313\pi$
$648$	1.31057	−	2.50647i	0.0514841	−	0.0984635i
$649$	−6.55268	−	7.80918i	−0.257215	−	0.306537i
$650$	8.35485	+	63.7593i	0.327704	+	2.50085i
$651$	−1.49385	+	4.10431i	−0.0585484	+	0.160860i
$652$	−38.2197	+	17.7659i	−1.49680	+	0.695766i
$653$	7.99774	−	13.8525i	0.312976	−	0.542090i	−0.666029	−	0.745926i	$-0.732007\pi$
$653$	7.99774	−	13.8525i	0.312976	−	0.542090i	0.979005	+	0.203836i	$0.0653408\pi$
$654$	−24.0233	+	7.55854i	−0.939384	+	0.295562i
$655$	−67.0045	−	11.8147i	−2.61808	−	0.461639i
$656$	−0.671807	−	1.17013i	−0.0262297	−	0.0456859i
$657$	−6.11831	−	10.5972i	−0.238698	−	0.413437i
$658$	−8.24958	+	8.99192i	−0.321602	+	0.350541i
$659$	2.39630	+	2.01074i	0.0933468	+	0.0783272i	0.688267	−	0.725458i	$-0.258372\pi$
$659$	2.39630	+	2.01074i	0.0933468	+	0.0783272i	−0.594920	+	0.803785i	$0.702816\pi$
$660$	10.1743	−	10.1497i	0.396033	−	0.395076i
$661$	5.66107	+	15.5537i	0.220190	+	0.604967i	0.999772	−	0.0213324i	$-0.00679081\pi$
$661$	5.66107	+	15.5537i	0.220190	+	0.604967i	−0.779582	+	0.626300i	$0.784569\pi$
$662$	−32.7602	+	17.0287i	−1.27326	+	0.661839i
$663$	23.2883	−	4.10635i	0.904441	−	0.159477i
$664$	10.3163	−	13.3941i	0.400350	−	0.519792i
$665$	14.7184	−	3.02174i	0.570755	−	0.117178i
$666$	1.15079	−	5.17606i	0.0445922	−	0.200568i
$667$	3.06812	+	17.4002i	0.118798	+	0.673737i
$668$	1.95211	−	0.520536i	0.0755293	−	0.0201402i
$669$	14.0876	−	5.12748i	0.544659	−	0.198240i
$670$	−28.0800	−	17.9128i	−1.08482	−	0.692032i
$671$	5.29222	−	6.30702i	0.204304	−	0.243480i
$672$	−0.229387	+	4.91293i	−0.00884879	+	0.189520i
$673$	−21.8724	+	12.6280i	−0.843118	+	0.486774i	−0.858323	−	0.513110i	$-0.828493\pi$
$673$	−21.8724	+	12.6280i	−0.843118	+	0.486774i	0.0152050	+	0.999884i	$0.495160\pi$
$674$	−3.30047	−	1.36944i	−0.127130	−	0.0527489i
$675$	1.86131	−	10.5560i	0.0716417	−	0.406300i
$676$	0.858680	+	9.95337i	0.0330261	+	0.382822i
$677$	2.48216	+	1.43307i	0.0953970	+	0.0550775i	0.546940	−	0.837172i	$-0.315793\pi$
$677$	2.48216	+	1.43307i	0.0953970	+	0.0550775i	−0.451543	+	0.892250i	$0.649126\pi$
$678$	8.73580	−	6.69483i	0.335496	−	0.257113i
$679$	4.00310	+	1.45701i	0.153625	+	0.0559149i
$680$	−59.5844	−	18.9058i	−2.28496	−	0.725004i
$681$	−7.78475	+	6.53218i	−0.298312	+	0.250314i
$682$	−12.8635	−	0.569425i	−0.492569	−	0.0218044i
$683$	20.0231			0.766162			0.383081	−	0.923715i	$-0.374863\pi$
$683$	20.0231			0.766162			0.383081	+	0.923715i	$0.374863\pi$
$684$	6.32707	+	5.99734i	0.241922	+	0.229314i
$685$	−15.8927			−0.607229
$686$	16.2686	+	0.720159i	0.621138	+	0.0274958i
$687$	−9.46462	+	7.94176i	−0.361098	+	0.302997i
$688$	−10.3318	+	17.7957i	−0.393898	+	0.678456i
$689$	−34.9667	−	12.7268i	−1.33212	−	0.484853i
$690$	32.2033	−	24.6795i	1.22596	−	0.939534i
$691$	25.7562	+	14.8704i	0.979812	+	0.565695i	0.902213	−	0.431290i	$-0.141941\pi$
$691$	25.7562	+	14.8704i	0.979812	+	0.565695i	0.0775989	+	0.996985i	$0.475275\pi$
$692$	−12.5264	+	1.08065i	−0.476181	+	0.0410803i
$693$	−0.273629	+	1.55183i	−0.0103943	+	0.0589491i
$694$	36.3107	+	15.0661i	1.37833	+	0.571901i
$695$	−33.6187	+	19.4098i	−1.27523	+	0.736254i
$696$	−2.63132	−	6.38529i	−0.0997397	−	0.242034i
$697$	−1.20869	+	1.44046i	−0.0457823	+	0.0545612i
$698$	−13.3406	−	8.51022i	−0.504947	−	0.322116i
$699$	7.64972	−	2.78427i	0.289339	−	0.105311i
$700$	4.80228	+	18.0094i	0.181509	+	0.680693i
$701$	−5.98713	−	33.9547i	−0.226131	−	1.28245i	−0.860512	−	0.509431i	$-0.829856\pi$
$701$	−5.98713	−	33.9547i	−0.226131	−	1.28245i	0.634381	−	0.773021i	$-0.281255\pi$
$702$	1.30200	−	5.85620i	0.0491410	−	0.221028i
$703$	14.3765	+	7.77278i	0.542222	+	0.293156i
$704$	−14.0187	+	3.70183i	−0.528348	+	0.139518i
$705$	−38.7499	+	6.83265i	−1.45940	+	0.257332i
$706$	−28.9257	+	15.0356i	−1.08863	+	0.565871i
$707$	1.70908	+	4.69567i	0.0642767	+	0.176599i
$708$	7.94488	+	7.96411i	0.298587	+	0.299310i
$709$	4.77106	+	4.00339i	0.179181	+	0.150351i	0.727967	−	0.685612i	$-0.240465\pi$
$709$	4.77106	+	4.00339i	0.179181	+	0.150351i	−0.548786	+	0.835963i	$0.684910\pi$
$710$	−13.4676	+	14.6795i	−0.505431	+	0.550912i
$711$	−2.32898	−	4.03391i	−0.0873435	−	0.151283i
$712$	−18.7340	−	20.5191i	−0.702085	−	0.768987i
$713$	−35.7992	−	6.31237i	−1.34069	−	0.236400i
$714$	6.53828	−	2.05717i	0.244689	−	0.0769875i
$715$	15.2409	−	26.3981i	0.569979	−	0.987233i
$716$	13.6898	+	29.4508i	0.511611	+	1.10063i
$717$	1.51110	−	4.15170i	0.0564329	−	0.155048i
$718$	−6.65803	−	50.8102i	−0.248476	−	1.89622i
$719$	−8.64221	−	10.2994i	−0.322300	−	0.384102i	0.580430	−	0.814310i	$-0.302885\pi$
$719$	−8.64221	−	10.2994i	−0.322300	−	0.384102i	−0.902730	+	0.430208i	$0.858440\pi$
$720$	−10.2232	+	12.1239i	−0.380996	+	0.451829i
$721$			2.93452i			0.109287i
$722$	−23.1117	+	13.7058i	−0.860128	+	0.510077i
$723$		−	14.1031i		−	0.524500i
$724$	−0.883759	−	0.237948i	−0.0328446	−	0.00884328i
$725$	−16.8233	−	20.0492i	−0.624800	−	0.744608i
$726$	10.8185	−	1.41762i	0.401511	−	0.0526130i
$727$	−10.0181	+	27.5244i	−0.371549	+	1.02082i	0.603213	+	0.797580i	$0.293887\pi$
$727$	−10.0181	+	27.5244i	−0.371549	+	1.02082i	−0.974763	+	0.223243i	$0.928336\pi$
$728$	2.23939	+	10.1887i	0.0829973	+	0.377617i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$	20.5918	+	65.4469i	0.762137	+	2.42230i
$731$	28.2418	+	4.97979i	1.04456	+	0.184184i
$732$	−5.22020	+	7.43606i	−0.192944	+	0.274845i
$733$	−4.73688	−	8.20451i	−0.174960	−	0.303040i	0.765187	−	0.643808i	$-0.222646\pi$
$733$	−4.73688	−	8.20451i	−0.174960	−	0.303040i	−0.940148	+	0.340768i	$0.889313\pi$
$734$	26.0787	+	23.9258i	0.962583	+	0.883116i
$735$	18.9641	+	15.9128i	0.699502	+	0.586952i
$736$	−40.5996	+	5.22021i	−1.49652	+	0.192420i
$737$	3.68227	+	10.1170i	0.135638	+	0.372663i
$738$	0.220016	+	0.423272i	0.00809891	+	0.0155809i
$739$	−11.1573	+	1.96733i	−0.410428	+	0.0723694i	−0.375050	−	0.927005i	$-0.622374\pi$
$739$	−11.1573	+	1.96733i	−0.410428	+	0.0723694i	−0.0353775	+	0.999374i	$0.511263\pi$
$740$	−12.5972	+	26.9297i	−0.463082	+	0.989956i
$741$	16.2657	+	8.79414i	0.597534	+	0.323061i
$742$	−10.5285	−	2.34080i	−0.386514	−	0.0859333i
$743$	−6.98934	−	39.6385i	−0.256414	−	1.45420i	−0.792417	−	0.609980i	$-0.791178\pi$
$743$	−6.98934	−	39.6385i	−0.256414	−	1.45420i	0.536003	−	0.844216i	$-0.319934\pi$
$744$	14.1965	−	0.594032i	0.520468	−	0.0217783i
$745$	66.2528	−	24.1140i	2.42731	−	0.883470i
$746$	−5.05963	+	7.93145i	−0.185246	+	0.290391i
$747$	−3.84216	+	4.57890i	−0.140577	+	0.167533i
$748$	11.5699	+	16.5662i	0.423039	+	0.605720i
$749$	13.4834	−	7.78462i	0.492671	−	0.284444i
$750$	−12.2887	+	29.6169i	−0.448720	+	1.08146i
$751$	−5.04851	+	28.6315i	−0.184223	+	1.04478i	0.742727	+	0.669595i	$0.233532\pi$
$751$	−5.04851	+	28.6315i	−0.184223	+	1.04478i	−0.926950	+	0.375185i	$0.877579\pi$
$752$	37.2710	+	13.6677i	1.35913	+	0.498410i
$753$	7.42313	+	4.28575i	0.270514	+	0.156181i
$754$	−8.91031	−	11.6267i	−0.324494	−	0.423419i
$755$	−50.1695	−	18.2602i	−1.82585	−	0.664557i
$756$	0.153648	−	1.73207i	0.00558812	−	0.0629949i
$757$	7.23286	−	6.06909i	0.262883	−	0.220585i	−0.501813	−	0.864976i	$-0.667334\pi$
$757$	7.23286	−	6.06909i	0.262883	−	0.220585i	0.764696	+	0.644391i	$0.222889\pi$
$758$	0.598067	−	13.5105i	0.0217228	−	0.490724i
$759$	−13.1148			−0.476036
$760$	−27.3319	−	40.5244i	−0.991432	−	1.46998i
$761$	−32.6646			−1.18409			−0.592046	−	0.805904i	$-0.701680\pi$
$761$	−32.6646			−1.18409			−0.592046	+	0.805904i	$0.701680\pi$
$762$	−0.577372	+	13.0430i	−0.0209160	+	0.472498i
$763$	−11.8606	+	9.95225i	−0.429384	+	0.360296i
$764$	−4.64695	+	52.3852i	−0.168121	+	1.89523i
$765$	20.7684	+	7.55909i	0.750884	+	0.273299i
$766$	−15.5822	−	20.3325i	−0.563007	−	0.734645i
$767$	20.6636	+	11.9302i	0.746120	+	0.430773i
$768$	15.0614	−	5.39953i	0.543481	−	0.194839i
$769$	−2.26600	+	12.8511i	−0.0817140	+	0.463423i	0.916303	+	0.400485i	$0.131158\pi$
$769$	−2.26600	+	12.8511i	−0.0817140	+	0.463423i	−0.998017	+	0.0629384i	$0.979953\pi$
$770$	3.38603	−	8.16064i	0.122024	−	0.294089i
$771$	7.42511	−	4.28689i	0.267409	−	0.154389i
$772$	−11.5168	−	16.4902i	−0.414500	−	0.593494i
$773$	6.22918	−	7.42365i	0.224048	−	0.267010i	−0.642297	−	0.766456i	$-0.722018\pi$
$773$	6.22918	−	7.42365i	0.224048	−	0.267010i	0.866345	+	0.499446i	$0.166463\pi$
$774$	3.91270	−	6.13353i	0.140639	−	0.220465i
$775$	50.5998	−	18.4168i	1.81760	−	0.661551i
$776$	−0.579385	−	13.8464i	−0.0207987	−	0.497057i
$777$	−0.566070	−	3.21034i	−0.0203076	−	0.115170i
$778$	5.57846	+	1.24025i	0.199998	+	0.0444653i
$779$	−1.44029	+	0.295697i	−0.0516039	+	0.0105945i
$780$	−14.2525	+	30.4683i	−0.510321	+	1.09094i
$781$	6.34163	−	1.11820i	0.226921	−	0.0400124i
$782$	26.3106	+	50.6168i	0.940864	+	1.81005i
$783$	0.835116	+	2.29446i	0.0298446	+	0.0819974i
$784$	−8.48561	−	23.4906i	−0.303058	−	0.838952i
$785$	20.9246	+	17.5578i	0.746831	+	0.626665i
$786$	−17.8833	−	16.4069i	−0.637876	−	0.585216i
$787$	−20.9183	−	36.2315i	−0.745655	−	1.29151i	−0.949888	−	0.312590i	$-0.898803\pi$
$787$	−20.9183	−	36.2315i	−0.745655	−	1.29151i	0.204233	−	0.978922i	$-0.434530\pi$
$788$	−0.493350	+	0.702766i	−0.0175748	+	0.0250350i
$789$	−17.4136	−	3.07049i	−0.619941	−	0.109312i
$790$	7.83843	+	24.9128i	0.278879	+	0.886359i
$791$	3.38321	−	5.85988i	0.120293	−	0.208353i
$792$	5.00673	−	1.10044i	0.177906	−	0.0391025i
$793$	−6.59092	+	18.1084i	−0.234050	+	0.643048i
$794$	51.1356	−	6.70068i	1.81474	−	0.237798i
$795$	−22.3547	−	26.6412i	−0.792838	−	0.944867i
$796$	19.3232	+	5.20269i	0.684893	+	0.184405i
$797$			38.9046i			1.37807i	0.724728	+	0.689035i	$0.241965\pi$
$797$			38.9046i			1.37807i	−0.724728	+	0.689035i	$0.758035\pi$
$798$	5.00584	+	1.91483i	0.177205	+	0.0677843i
$799$		−	55.3243i		−	1.95723i
$800$	48.2163	−	36.7666i	1.70470	−	1.29989i
$801$	6.31437	+	7.52518i	0.223107	+	0.265889i
$802$	3.23819	+	24.7119i	0.114344	+	0.872608i
$803$	7.58520	−	20.8402i	0.267676	−	0.735433i
$804$	−5.00795	−	10.7736i	−0.176617	−	0.379955i
$805$	12.4717	−	21.6016i	0.439570	−	0.761357i
$806$	28.7482	−	9.04516i	1.01261	−	0.318602i
$807$	4.96620	+	0.875674i	0.174818	+	0.0308252i
$808$	12.0052	−	10.9607i	0.422341	−	0.385598i
$809$	−18.9093	−	32.7519i	−0.664816	−	1.15150i	−0.979335	−	0.202244i	$-0.935176\pi$
$809$	−18.9093	−	32.7519i	−0.664816	−	1.15150i	0.314519	−	0.949251i	$-0.398157\pi$
$810$	3.79049	−	4.13157i	0.133184	−	0.145169i
$811$	−39.0491	−	32.7661i	−1.37120	−	1.15057i	−0.972343	−	0.233558i	$-0.924963\pi$
$811$	−39.0491	−	32.7661i	−1.37120	−	1.15057i	−0.398856	−	0.917014i	$-0.630593\pi$
$812$	−2.99863	−	3.00589i	−0.105231	−	0.105486i
$813$	−3.37522	−	9.27335i	−0.118374	−	0.325230i
$814$	8.52698	−	4.43232i	0.298871	−	0.155353i
$815$	−82.2808	+	14.5083i	−2.88217	+	0.508205i
$816$	−14.2916	−	17.1159i	−0.500305	−	0.599178i
$817$	14.8883	+	16.7680i	0.520876	+	0.586640i
$818$	9.87592	−	44.4203i	0.345304	−	1.55312i
$819$	−0.640452	−	3.63219i	−0.0223792	−	0.126919i
$820$	−0.689145	−	2.58442i	−0.0240660	−	0.0902519i
$821$	14.9710	−	5.44898i	0.522490	−	0.190171i	−0.0672920	−	0.997733i	$-0.521436\pi$
$821$	14.9710	−	5.44898i	0.522490	−	0.190171i	0.589782	+	0.807563i	$0.299214\pi$
$822$	−4.77930	−	3.04881i	−0.166697	−	0.106340i
$823$	28.1354	−	33.5305i	0.980740	−	1.16880i	−0.00490878	−	0.999988i	$-0.501563\pi$
$823$	28.1354	−	33.5305i	0.980740	−	1.16880i	0.985648	−	0.168812i	$-0.0539930\pi$
$824$	8.82640	−	3.63727i	0.307482	−	0.126710i
$825$	16.8241	−	9.71340i	0.585740	−	0.338177i
$826$	6.38790	+	2.65048i	0.222263	+	0.0922220i
$827$	5.40657	−	30.6622i	0.188005	−	1.06623i	−0.734028	−	0.679119i	$-0.762362\pi$
$827$	5.40657	−	30.6622i	0.188005	−	1.06623i	0.922033	−	0.387111i	$-0.126527\pi$
$828$	14.4187	−	1.24391i	0.501085	−	0.0432287i
$829$	10.1185	+	5.84189i	0.351429	+	0.202897i	0.665314	−	0.746563i	$-0.268298\pi$
$829$	10.1185	+	5.84189i	0.351429	+	0.202897i	−0.313886	+	0.949461i	$0.601631\pi$
$830$	26.6012	−	20.3863i	0.923340	−	0.707617i
$831$	−18.6459	−	6.78656i	−0.646820	−	0.235423i
$832$	27.8696	−	19.3642i	0.966206	−	0.671334i
$833$	−26.6643	+	22.3740i	−0.923862	+	0.775212i
$834$	−13.8334	−	0.612361i	−0.479012	−	0.0212043i
$835$	4.00497			0.138598
$836$	−0.955621	+	15.7712i	−0.0330508	+	0.545458i
$837$	−5.02360			−0.173641
$838$	18.0955	+	0.801029i	0.625098	+	0.0276711i
$839$	14.7468	−	12.3740i	0.509116	−	0.427199i	−0.351702	−	0.936112i	$-0.614397\pi$
$839$	14.7468	−	12.3740i	0.509116	−	0.427199i	0.860818	+	0.508913i	$0.169952\pi$
$840$	−2.94867	+	9.29318i	−0.101739	+	0.320645i
$841$	−21.6487	−	7.87947i	−0.746506	−	0.271706i
$842$	29.7262	−	22.7812i	1.02443	−	0.785092i
$843$	26.7115	+	15.4219i	0.919993	+	0.531158i
$844$	−0.789042	−	9.14617i	−0.0271600	−	0.314824i
$845$	−3.43899	+	19.5035i	−0.118305	+	0.670940i
$846$	−12.9637	−	5.37894i	−0.445702	−	0.184932i
$847$	5.80921	−	3.35395i	0.199607	−	0.115243i
$848$	6.00926	+	34.5689i	0.206359	+	1.18710i
$849$	1.18265	−	1.40942i	0.0405883	−	0.0483713i
$850$	−71.2413	−	45.4463i	−2.44356	−	1.55879i
$851$	25.4949	−	9.27940i	0.873955	−	0.318094i
$852$	−6.86610	+	1.83087i	−0.235229	+	0.0627245i
$853$	−3.02569	−	17.1596i	−0.103598	−	0.587532i	−0.991771	−	0.128024i	$-0.959137\pi$
$853$	−3.02569	−	17.1596i	−0.103598	−	0.587532i	0.888173	−	0.459509i	$-0.151974\pi$
$854$	−1.21224	+	5.45247i	−0.0414821	+	0.186580i
$855$	9.05584	+	14.7190i	0.309703	+	0.503380i
$856$	−40.1268	−	30.9062i	−1.37151	−	1.05635i
$857$	−14.2856	+	2.51894i	−0.487987	+	0.0860453i	−0.412228	−	0.911081i	$-0.635249\pi$
$857$	−14.2856	+	2.51894i	−0.487987	+	0.0860453i	−0.0757593	+	0.997126i	$0.524138\pi$
$858$	9.64745	−	5.01473i	0.329358	−	0.171200i
$859$	8.07128	+	22.1757i	0.275389	+	0.756624i	0.997870	+	0.0652335i	$0.0207792\pi$
$859$	8.07128	+	22.1757i	0.275389	+	0.756624i	−0.722482	+	0.691390i	$0.756999\pi$
$860$	−28.8791	+	28.8093i	−0.984768	+	0.982389i
$861$	0.224663	+	0.188515i	0.00765650	+	0.00642456i
$862$	35.4702	−	38.6619i	1.20812	−	1.31683i
$863$	21.8424	+	37.8322i	0.743525	+	1.28782i	0.950881	+	0.309557i	$0.100181\pi$
$863$	21.8424	+	37.8322i	0.743525	+	1.28782i	−0.207356	+	0.978265i	$0.566486\pi$
$864$	−5.40016	+	1.68473i	−0.183717	+	0.0573157i
$865$	−24.5452	−	4.32799i	−0.834563	−	0.147156i
$866$	−7.59003	+	2.38808i	−0.257920	+	0.0811504i
$867$	−7.03763	+	12.1895i	−0.239010	+	0.413978i
$868$	7.92144	−	3.68217i	0.268871	−	0.124981i
$869$	2.88736	−	7.93296i	0.0979470	−	0.269107i
$870$	−1.77876	−	13.5745i	−0.0603058	−	0.460218i
$871$	−16.1978	−	19.3038i	−0.548841	−	0.654083i
$872$	44.6352	+	23.3386i	1.51154	+	0.790346i
$873$			4.89973i			0.165831i
$874$	−8.45999	+	43.7970i	−0.286164	+	1.48145i
$875$			19.7132i			0.666427i
$876$	−6.36272	+	23.6317i	−0.214976	+	0.798440i
$877$	17.6952	+	21.0883i	0.597524	+	0.712101i	0.977033	−	0.213087i	$-0.0683516\pi$
$877$	17.6952	+	21.0883i	0.597524	+	0.712101i	−0.379509	+	0.925188i	$0.623907\pi$
$878$	−3.68949	+	0.483461i	−0.124514	+	0.0163160i
$879$	−1.97289	+	5.42046i	−0.0665439	+	0.182828i
$880$	−28.7424	−	0.0695176i	−0.968905	−	0.00234344i
$881$	6.14389	−	10.6415i	0.206993	−	0.358522i	−0.743773	−	0.668432i	$-0.766966\pi$
$881$	6.14389	−	10.6415i	0.206993	−	0.358522i	0.950766	+	0.309910i	$0.100299\pi$
$882$	2.65028	+	8.42336i	0.0892395	+	0.283629i
$883$	37.1547	+	6.55138i	1.25036	+	0.220472i	0.759349	−	0.650684i	$-0.225518\pi$
$883$	37.1547	+	6.55138i	1.25036	+	0.220472i	0.491007	+	0.871155i	$0.336629\pi$
$884$	−38.7090	−	27.1741i	−1.30192	−	0.913965i
$885$	11.1501	+	19.3125i	0.374806	+	0.649183i
$886$	32.4436	+	29.7652i	1.08996	+	0.999981i
$887$	27.0157	+	22.6689i	0.907099	+	0.761146i	0.971565	−	0.236774i	$-0.0760900\pi$
$887$	27.0157	+	22.6689i	0.907099	+	0.761146i	−0.0644662	+	0.997920i	$0.520534\pi$
$888$	−8.95439	+	5.68177i	−0.300490	+	0.190668i
$889$	2.74523	+	7.54245i	0.0920719	+	0.252965i
$890$	−25.4032	−	48.8713i	−0.851518	−	1.63817i
$891$	−1.78486	+	0.314720i	−0.0597952	+	0.0105435i
$892$	−27.1589	−	12.7044i	−0.909348	−	0.425376i
$893$	26.8697	−	33.9033i	0.899160	−	1.13453i
$894$	24.5497	+	5.45811i	0.821065	+	0.182547i
$895$	11.1796	+	63.4027i	0.373693	+	2.11932i
$896$	7.28034	−	6.61473i	0.243219	−	0.220983i
$897$	28.8450	−	10.4987i	0.963107	−	0.350542i
$898$	25.4135	−	39.8381i	0.848061	−	1.32941i
$899$	−7.88456	+	9.39646i	−0.262965	+	0.313389i
$900$	−17.5756	+	12.2749i	−0.585852	+	0.409163i
$901$	42.3475	−	24.4494i	1.41080	−	0.814527i
$902$	−0.331345	+	0.798573i	−0.0110326	+	0.0265896i
$903$	0.776681	−	4.40477i	0.0258463	−	0.146582i
$904$	−21.8187	−	2.91276i	−0.725679	−	0.0968770i
$905$	−1.57124	−	0.907154i	−0.0522297	−	0.0301548i
$906$	−11.5841	−	15.1156i	−0.384857	−	0.502184i
$907$	38.1781	+	13.8957i	1.26768	+	0.461399i	0.886340	−	0.463035i	$-0.153240\pi$
$907$	38.1781	+	13.8957i	1.26768	+	0.461399i	0.381343	+	0.924434i	$0.375462\pi$
$908$	20.2450	+	1.79589i	0.671856	+	0.0595985i
$909$	−4.40278	+	3.69437i	−0.146031	+	0.122535i
$910$	−0.914523	+	20.6594i	−0.0303161	+	0.684851i
$911$	14.5274			0.481315			0.240658	−	0.970610i	$-0.422637\pi$
$911$	14.5274			0.481315			0.240658	+	0.970610i	$0.422637\pi$
$912$	−0.445228	−	17.4299i	−0.0147430	−	0.577162i
$913$	−10.8333			−0.358530
$914$	−0.213000	+	4.81175i	−0.00704543	+	0.159158i
$915$	−13.7969	+	11.5769i	−0.456110	+	0.382722i
$916$	24.6137	+	2.18342i	0.813260	+	0.0721421i
$917$	−14.0206	−	5.10309i	−0.463001	−	0.168519i
$918$	4.79542	+	6.25735i	0.158273	+	0.206523i
$919$	−28.3383	−	16.3611i	−0.934793	−	0.539703i	−0.0464686	−	0.998920i	$-0.514797\pi$
$919$	−28.3383	−	16.3611i	−0.934793	−	0.539703i	−0.888324	+	0.459217i	$0.848130\pi$
$920$	−80.4315	−	10.7375i	−2.65175	−	0.354004i
$921$	1.02991	−	5.84090i	0.0339367	−	0.192464i
$922$	14.3031	−	34.4717i	0.471046	−	1.13526i
$923$	−13.0528	+	7.53605i	−0.429639	+	0.248052i
$924$	2.58377	−	1.80452i	0.0849999	−	0.0593645i
$925$	−25.8331	+	30.7867i	−0.849386	+	1.01226i
$926$	10.3493	−	16.2235i	0.340098	−	0.533136i
$927$	−3.17164	+	1.15438i	−0.104170	+	0.0379149i
$928$	−5.32434	+	12.7450i	−0.174780	+	0.418374i
$929$	1.27055	+	7.20565i	0.0416854	+	0.236410i	0.998531	−	0.0541880i	$-0.0172570\pi$
$929$	1.27055	+	7.20565i	0.0416854	+	0.236410i	−0.956845	+	0.290598i	$0.906146\pi$
$930$	27.4956	+	6.11308i	0.901617	+	0.200456i
$931$	−27.2067	+	0.760815i	−0.891662	+	0.0249347i
$932$	−14.7476	−	6.89862i	−0.483072	−	0.225972i
$933$	−2.55775	+	0.451000i	−0.0837370	+	0.0147651i
$934$	1.50251	+	2.89056i	0.0491637	+	0.0945822i
$935$	13.7001	+	37.6407i	0.448040	+	1.23098i
$936$	−10.1310	+	6.42836i	−0.331143	+	0.210118i
$937$	24.5649	+	20.6124i	0.802502	+	0.673379i	0.948806	−	0.315861i	$-0.102293\pi$
$937$	24.5649	+	20.6124i	0.802502	+	0.673379i	−0.146304	+	0.989240i	$0.546738\pi$
$938$	−5.38213	−	4.93780i	−0.175733	−	0.161225i
$939$	−0.359851	−	0.623280i	−0.0117433	−	0.0203400i
$940$	64.4088	+	45.2157i	2.10078	+	1.47477i
$941$	−7.93497	−	1.39915i	−0.258673	−	0.0456110i	0.0428078	−	0.999083i	$-0.486370\pi$
$941$	−7.93497	−	1.39915i	−0.258673	−	0.0456110i	−0.301480	+	0.953472i	$0.597481\pi$
$942$	2.92426	+	9.29416i	0.0952775	+	0.302820i
$943$	−1.22044	+	2.11386i	−0.0397430	+	0.0688368i
$944$	0.0544163	−	22.4987i	0.00177110	−	0.732269i
$945$	1.17896	−	3.23918i	0.0383517	−	0.105370i
$946$	13.0739	−	1.71317i	0.425069	−	0.0557000i
$947$	−6.93009	−	8.25896i	−0.225198	−	0.268380i	0.641601	−	0.767039i	$-0.278271\pi$
$947$	−6.93009	−	8.25896i	−0.225198	−	0.268380i	−0.866798	+	0.498659i	$0.833826\pi$
$948$	−2.42202	+	8.99556i	−0.0786635	+	0.292162i
$949$			51.9086i			1.68502i
$950$	−21.5853	−	62.4502i	−0.700318	−	2.02615i
$951$		−	26.7731i		−	0.868176i
$952$	−12.1481	−	6.35194i	−0.393723	−	0.205868i
$953$	11.5566	+	13.7727i	0.374356	+	0.446140i	0.920024	−	0.391861i	$-0.128169\pi$
$953$	11.5566	+	13.7727i	0.374356	+	0.446140i	−0.545668	+	0.838001i	$0.683724\pi$
$954$	−1.61177	−	12.3001i	−0.0521830	−	0.398230i
$955$	−35.6568	+	97.9663i	−1.15383	+	3.17011i
$956$	−8.01292	+	3.72469i	−0.259156	+	0.120465i
$957$	−2.21268	+	3.83248i	−0.0715258	+	0.123886i
$958$	−23.7030	+	7.45778i	−0.765810	+	0.240950i
$959$	−3.43224	−	0.605196i	−0.110833	−	0.0195428i
$960$	31.6067	−	2.64972i	1.02010	−	0.0855193i
$961$	2.88171	+	4.99127i	0.0929585	+	0.161009i
$962$	−15.2063	+	16.5746i	−0.490271	+	0.534388i
$963$	13.7177	+	11.5106i	0.442048	+	0.370922i
$964$	−19.9689	+	19.9207i	−0.643155	+	0.641601i
$965$	−13.6372	−	37.4679i	−0.438997	−	1.20613i
$966$	7.89453	−	4.10357i	0.254002	−	0.132030i
$967$	11.7688	−	2.07515i	0.378458	−	0.0667323i	0.0188164	−	0.999823i	$-0.494010\pi$
$967$	11.7688	−	2.07515i	0.378458	−	0.0667323i	0.359641	+	0.933091i	$0.382899\pi$
$968$	−17.2884	−	13.3157i	−0.555669	−	0.427983i
$969$	−22.5921	+	8.94569i	−0.725764	+	0.287377i
$970$	5.96234	−	26.8176i	0.191439	−	0.861063i
$971$	3.64446	+	20.6687i	0.116956	+	0.663292i	0.985763	+	0.168140i	$0.0537762\pi$
$971$	3.64446	+	20.6687i	0.116956	+	0.663292i	−0.868807	+	0.495151i	$0.835113\pi$
$972$	1.93248	−	0.515301i	0.0619842	−	0.0165283i
$973$	−7.99953	+	2.91159i	−0.256453	+	0.0933413i
$974$	42.8244	+	27.3186i	1.37218	+	0.875344i
$975$	−29.2276	+	34.8321i	−0.936032	+	1.11552i
$976$	17.9024	−	3.11205i	0.573043	−	0.0996144i
$977$	28.4849	−	16.4458i	0.911314	−	0.526147i	0.0304601	−	0.999536i	$-0.490303\pi$
$977$	28.4849	−	16.4458i	0.911314	−	0.526147i	0.880854	+	0.473389i	$0.156969\pi$
$978$	−27.5270	−	11.4215i	−0.880215	−	0.365221i
$979$	−3.09162	+	17.5335i	−0.0988088	+	0.560372i
$980$	−4.25558	−	49.3285i	−0.135940	−	1.57574i
$981$	−15.4222	−	8.90400i	−0.492392	−	0.284283i
$982$	17.8244	−	13.6601i	0.568801	−	0.435910i
$983$	−27.1088	−	9.86681i	−0.864638	−	0.314703i	−0.128644	−	0.991691i	$-0.541063\pi$
$983$	−27.1088	−	9.86681i	−0.864638	−	0.314703i	−0.735994	+	0.676988i	$0.763285\pi$
$984$	0.288547	−	0.909399i	0.00919854	−	0.0289906i
$985$	−1.30391	+	1.09411i	−0.0415461	+	0.0348613i
$986$	19.2306	+	0.851276i	0.612426	+	0.0271101i
$987$	−8.62874			−0.274656
$988$	−10.5234	−	35.4526i	−0.334796	−	1.12790i
$989$	37.2255			1.18370
$990$	10.1521	+	0.449399i	0.322653	+	0.0142828i
$991$	−3.57986	+	3.00386i	−0.113718	+	0.0954207i	−0.697874	−	0.716221i	$-0.745870\pi$
$991$	−3.57986	+	3.00386i	−0.113718	+	0.0954207i	0.584156	+	0.811642i	$0.301426\pi$
$992$	−20.8936	−	19.2620i	−0.663374	−	0.611570i
$993$	−24.5331	−	8.92930i	−0.778533	−	0.283363i
$994$	−3.46751	+	2.65738i	−0.109983	+	0.0842871i
$995$	34.3548	+	19.8348i	1.08912	+	0.628804i
$996$	11.9104	−	1.02752i	0.377396	−	0.0325581i
$997$	−5.36635	+	30.4341i	−0.169954	+	0.963857i	0.773854	+	0.633364i	$0.218326\pi$
$997$	−5.36635	+	30.4341i	−0.169954	+	0.963857i	−0.943808	+	0.330494i	$0.892785\pi$
$998$	23.7838	+	9.86841i	0.752862	+	0.312379i
$999$	3.24707	−	1.87470i	0.102733	−	0.0593128i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	228.2.w.b.67.6	yes	60
3.2	odd	2		684.2.cf.b.523.5		60
4.3	odd	2		228.2.w.a.67.7	✓	60
12.11	even	2		684.2.cf.c.523.4		60
19.2	odd	18		228.2.w.a.211.7	yes	60
57.2	even	18		684.2.cf.c.667.4		60
76.59	even	18	inner	228.2.w.b.211.6	yes	60
228.59	odd	18		684.2.cf.b.667.5		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.w.a.67.7	✓	60	4.3	odd	2
228.2.w.a.211.7	yes	60	19.2	odd	18
228.2.w.b.67.6	yes	60	1.1	even	1	trivial
228.2.w.b.211.6	yes	60	76.59	even	18	inner
684.2.cf.b.523.5		60	3.2	odd	2
684.2.cf.b.667.5		60	228.59	odd	18
684.2.cf.c.523.4		60	12.11	even	2
684.2.cf.c.667.4		60	57.2	even	18

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:	\( N \)	\(=\)	\( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	228.w (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0625414 - 1.41283i) q^{2} +(0.766044 - 0.642788i) q^{3} +(-1.99218 - 0.176721i) q^{4} +(-3.72560 - 1.35601i) q^{5} +(-0.860240 - 1.12249i) q^{6} +(-0.752955 - 0.434719i) q^{7} +(-0.374270 + 2.80356i) q^{8} +(0.173648 - 0.984808i) q^{9} +(-2.14881 + 5.17883i) q^{10} +(1.56958 - 0.906199i) q^{11} +(-1.63969 + 1.14517i) q^{12} +(-2.72675 + 3.24962i) q^{13} +(-0.661275 + 1.03661i) q^{14} +(-3.72560 + 1.35601i) q^{15} +(3.93754 + 0.704118i) q^{16} +(-0.968005 - 5.48983i) q^{17} +(-1.38051 - 0.306927i) q^{18} +(2.07308 - 3.83437i) q^{19} +(7.18242 + 3.35980i) q^{20} +(-0.856229 + 0.150976i) q^{21} +(-1.18214 - 2.27423i) q^{22} +(-2.47491 - 6.79975i) q^{23} +(1.51538 + 2.38822i) q^{24} +(8.21110 + 6.88993i) q^{25} +(4.42062 + 4.05567i) q^{26} +(-0.500000 - 0.866025i) q^{27} +(1.42320 + 0.999100i) q^{28} +(-2.40462 - 0.423999i) q^{29} +(1.68280 + 5.34844i) q^{30} +(2.51180 - 4.35057i) q^{31} +(1.24106 - 5.51904i) q^{32} +(0.619877 - 1.70310i) q^{33} +(-7.81674 + 1.02428i) q^{34} +(2.21573 + 2.64060i) q^{35} +(-0.519974 + 1.93122i) q^{36} +3.74939i q^{37} +(-5.28765 - 3.16871i) q^{38} +4.24207i q^{39} +(5.19602 - 9.93741i) q^{40} +(-0.216824 - 0.258400i) q^{41} +(0.159754 + 1.21915i) q^{42} +(-1.75948 + 4.83414i) q^{43} +(-3.28703 + 1.52793i) q^{44} +(-1.98235 + 3.43353i) q^{45} +(-9.76167 + 3.07136i) q^{46} +(9.77372 + 1.72337i) q^{47} +(3.46893 - 1.99162i) q^{48} +(-3.12204 - 5.40753i) q^{49} +(10.2478 - 11.1700i) q^{50} +(-4.27033 - 3.58323i) q^{51} +(6.00645 - 5.99194i) q^{52} +(3.00014 + 8.24282i) q^{53} +(-1.25482 + 0.652253i) q^{54} +(-7.07645 + 1.24777i) q^{55} +(1.50057 - 1.94825i) q^{56} +(-0.876614 - 4.26984i) q^{57} +(-0.749427 + 3.37080i) q^{58} +(-0.976716 - 5.53923i) q^{59} +(7.66169 - 2.04302i) q^{60} +(4.26876 - 1.55370i) q^{61} +(-5.98952 - 3.82084i) q^{62} +(-0.558864 + 0.666028i) q^{63} +(-7.71984 - 2.09857i) q^{64} +(14.5653 - 8.40927i) q^{65} +(-2.36742 - 0.982295i) q^{66} +(-1.03153 + 5.85008i) q^{67} +(0.958271 + 11.1078i) q^{68} +(-6.26668 - 3.61807i) q^{69} +(3.86930 - 2.96530i) q^{70} +(3.33873 + 1.21520i) q^{71} +(2.69597 + 0.855416i) q^{72} +(9.37379 - 7.86555i) q^{73} +(5.29726 + 0.234492i) q^{74} +10.7188 q^{75} +(-4.80755 + 7.27238i) q^{76} -1.57577 q^{77} +(5.99333 + 0.265305i) q^{78} +(3.56820 - 2.99408i) q^{79} +(-13.7149 - 7.96259i) q^{80} +(-0.939693 - 0.342020i) q^{81} +(-0.378636 + 0.290174i) q^{82} +(-5.17652 - 2.98867i) q^{83} +(1.73244 - 0.149458i) q^{84} +(-3.83785 + 21.7655i) q^{85} +(6.71978 + 2.78819i) q^{86} +(-2.11459 + 1.22086i) q^{87} +(1.95313 + 4.73958i) q^{88} +(-6.31437 + 7.52518i) q^{89} +(4.72701 + 3.01546i) q^{90} +(3.46579 - 1.26145i) q^{91} +(3.72879 + 13.9837i) q^{92} +(-0.872339 - 4.94728i) q^{93} +(3.04609 - 13.7008i) q^{94} +(-12.9229 + 11.4742i) q^{95} +(-2.59686 - 5.02557i) q^{96} +(-4.82529 + 0.850829i) q^{97} +(-7.83518 + 4.07272i) q^{98} +(-0.619877 - 1.70310i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 3 q^{2} - 3 q^{4} + 3 q^{6} - 3 q^{8} - 6 q^{10} - 6 q^{13} - 9 q^{14} + 21 q^{16} + 18 q^{19} + 30 q^{20} - 6 q^{21} - 12 q^{22} - 18 q^{24} - 30 q^{27} - 18 q^{28} - 12 q^{31} + 33 q^{32} - 15 q^{34}+ \cdots - 105 q^{98}+O(q^{100}) \) 60 * q + 3 * q^2 - 3 * q^4 + 3 * q^6 - 3 * q^8 - 6 * q^10 - 6 * q^13 - 9 * q^14 + 21 * q^16 + 18 * q^19 + 30 * q^20 - 6 * q^21 - 12 * q^22 - 18 * q^24 - 30 * q^27 - 18 * q^28 - 12 * q^31 + 33 * q^32 - 15 * q^34 - 3 * q^36 - 84 * q^38 - 87 * q^40 - 12 * q^41 + 9 * q^42 - 18 * q^43 - 51 * q^44 - 21 * q^46 + 18 * q^48 + 30 * q^49 - 27 * q^50 - 3 * q^52 + 12 * q^53 + 3 * q^54 + 42 * q^56 - 36 * q^58 + 15 * q^60 + 105 * q^62 - 12 * q^63 + 21 * q^64 - 36 * q^65 + 24 * q^66 + 42 * q^67 - 15 * q^68 - 72 * q^69 - 96 * q^70 + 24 * q^71 + 18 * q^72 + 18 * q^73 + 69 * q^74 + 60 * q^75 + 54 * q^76 - 72 * q^77 + 57 * q^78 + 12 * q^79 - 12 * q^80 + 75 * q^82 + 39 * q^84 - 60 * q^85 + 21 * q^86 + 36 * q^88 - 12 * q^89 + 15 * q^90 - 84 * q^91 + 99 * q^92 - 12 * q^93 - 24 * q^95 + 12 * q^97 - 105 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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