LMFDB - Embedded newform 230.2.l.a.7.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,2,Mod(7,230)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([11, 38]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("230.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.l (of order $44$, degree $20$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			7.8
Character	$\chi$	$=$	230.7
Dual form			230.2.l.a.33.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.997452 - 0.0713392i) q^{2} +(-0.372248 + 1.71120i) q^{3} +(0.989821 - 0.142315i) q^{4} +(-2.13965 + 0.649526i) q^{5} +(-0.249224 + 1.73339i) q^{6} +(-1.73066 + 3.16947i) q^{7} +(0.977147 - 0.212565i) q^{8} +(-0.0607343 - 0.0277364i) q^{9} +(-2.08786 + 0.800513i) q^{10} +(-1.69797 + 1.47130i) q^{11} +(-0.124931 + 1.74676i) q^{12} +(4.63061 - 2.52851i) q^{13} +(-1.50014 + 3.28486i) q^{14} +(-0.314986 - 3.90316i) q^{15} +(0.959493 - 0.281733i) q^{16} +(1.55083 + 2.07167i) q^{17} +(-0.0625582 - 0.0233330i) q^{18} +(-0.731070 - 5.08470i) q^{19} +(-2.02544 + 0.947420i) q^{20} +(-4.77935 - 4.14133i) q^{21} +(-1.58869 + 1.58869i) q^{22} +(4.14027 + 2.42036i) q^{23} +1.75122i q^{24} +(4.15623 - 2.77952i) q^{25} +(4.43844 - 2.85241i) q^{26} +(-3.07833 + 4.11217i) q^{27} +(-1.26198 + 3.38351i) q^{28} +(4.62333 + 0.664735i) q^{29} +(-0.592631 - 3.87074i) q^{30} +(-7.65941 - 4.92241i) q^{31} +(0.936950 - 0.349464i) q^{32} +(-1.88562 - 3.45326i) q^{33} +(1.69467 + 1.95575i) q^{34} +(1.64436 - 7.90568i) q^{35} +(-0.0640634 - 0.0188107i) q^{36} +(-1.06956 - 2.86759i) q^{37} +(-1.09195 - 5.01960i) q^{38} +(2.60304 + 8.86513i) q^{39} +(-1.95269 + 1.08950i) q^{40} +(1.83808 + 4.02483i) q^{41} +(-5.06262 - 3.78983i) q^{42} +(11.7859 + 2.56386i) q^{43} +(-1.47130 + 1.69797i) q^{44} +(0.147966 + 0.0198978i) q^{45} +(4.30239 + 2.11883i) q^{46} +(-0.0966659 - 0.0966659i) q^{47} +(0.124931 + 1.74676i) q^{48} +(-3.26586 - 5.08178i) q^{49} +(3.94735 - 3.06894i) q^{50} +(-4.12232 + 1.88260i) q^{51} +(4.22364 - 3.16178i) q^{52} +(-7.42874 - 4.05640i) q^{53} +(-2.77713 + 4.32129i) q^{54} +(2.67742 - 4.25095i) q^{55} +(-1.01739 + 3.46492i) q^{56} +(8.97308 + 0.641767i) q^{57} +(4.65898 + 0.333216i) q^{58} +(1.72602 - 5.87829i) q^{59} +(-0.867257 - 3.81860i) q^{60} +(6.06094 - 9.43101i) q^{61} +(-7.99106 - 4.36345i) q^{62} +(0.193020 - 0.144493i) q^{63} +(0.909632 - 0.415415i) q^{64} +(-8.26558 + 8.41783i) q^{65} +(-2.12717 - 3.30994i) q^{66} +(0.697475 + 9.75197i) q^{67} +(1.82987 + 1.82987i) q^{68} +(-5.68292 + 6.18385i) q^{69} +(1.07619 - 8.00284i) q^{70} +(-3.94966 + 4.55815i) q^{71} +(-0.0652421 - 0.0141926i) q^{72} +(-5.36891 - 4.01911i) q^{73} +(-1.27140 - 2.78398i) q^{74} +(3.20916 + 8.14681i) q^{75} +(-1.44726 - 4.92891i) q^{76} +(-1.72463 - 7.92800i) q^{77} +(3.22884 + 8.65685i) q^{78} +(-2.52895 - 0.742567i) q^{79} +(-1.86999 + 1.22603i) q^{80} +(-6.02200 - 6.94976i) q^{81} +(2.12053 + 3.88345i) q^{82} +(-4.32977 + 1.61492i) q^{83} +(-5.32008 - 3.41901i) q^{84} +(-4.66384 - 3.42534i) q^{85} +(11.9387 + 1.71653i) q^{86} +(-2.85852 + 7.66399i) q^{87} +(-1.34642 + 1.79861i) q^{88} +(-11.8000 + 7.58338i) q^{89} +(0.149008 + 0.00929133i) q^{90} +19.0526i q^{91} +(4.44258 + 1.80650i) q^{92} +(11.2744 - 11.2744i) q^{93} +(-0.103316 - 0.0895236i) q^{94} +(4.86689 + 10.4047i) q^{95} +(0.249224 + 1.73339i) q^{96} +(7.86547 + 2.93367i) q^{97} +(-3.62007 - 4.83585i) q^{98} +(0.143934 - 0.0422628i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) $ 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{19}{22}\right)$

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 $

$2$	0.997452	−	0.0713392i	0.705305	−	0.0504444i
$2$	0.997452	−	0.0713392i	0.705305	−	0.0504444i
$3$	−0.372248	+	1.71120i	−0.214918	+	0.987961i	0.735630	+	0.677383i	$0.236886\pi$
$3$	−0.372248	+	1.71120i	−0.214918	+	0.987961i	−0.950548	+	0.310578i	$0.899478\pi$
$4$	0.989821	−	0.142315i	0.494911	−	0.0711574i
$5$	−2.13965	+	0.649526i	−0.956882	+	0.290477i
$5$	−2.13965	+	0.649526i	−0.956882	+	0.290477i
$6$	−0.249224	+	1.73339i	−0.101745	+	0.707655i
$7$	−1.73066	+	3.16947i	−0.654129	+	1.19795i	0.314458	+	0.949271i	$0.398177\pi$
$7$	−1.73066	+	3.16947i	−0.654129	+	1.19795i	−0.968587	+	0.248676i	$0.920005\pi$
$8$	0.977147	−	0.212565i	0.345474	−	0.0751532i
$9$	−0.0607343	−	0.0277364i	−0.0202448	−	0.00924547i
$10$	−2.08786	+	0.800513i	−0.660241	+	0.253144i
$11$	−1.69797	+	1.47130i	−0.511958	+	0.443614i	−0.872132	−	0.489271i	$-0.837263\pi$
$11$	−1.69797	+	1.47130i	−0.511958	+	0.443614i	0.360174	+	0.932885i	$0.382717\pi$
$12$	−0.124931	+	1.74676i	−0.0360643	+	0.504245i
$13$	4.63061	−	2.52851i	1.28430	−	0.701282i	0.315454	−	0.948941i	$-0.397843\pi$
$13$	4.63061	−	2.52851i	1.28430	−	0.701282i	0.968847	+	0.247659i	$0.0796613\pi$
$14$	−1.50014	+	3.28486i	−0.400930	+	0.877915i
$15$	−0.314986	−	3.90316i	−0.0813290	−	1.00779i
$16$	0.959493	−	0.281733i	0.239873	−	0.0704331i
$17$	1.55083	+	2.07167i	0.376131	+	0.502453i	0.948165	−	0.317777i	$-0.102936\pi$
$17$	1.55083	+	2.07167i	0.376131	+	0.502453i	−0.572034	+	0.820230i	$0.693845\pi$
$18$	−0.0625582	−	0.0233330i	−0.0147451	−	0.00549964i
$19$	−0.731070	−	5.08470i	−0.167719	−	1.16651i	−0.883584	−	0.468273i	$-0.844877\pi$
$19$	−0.731070	−	5.08470i	−0.167719	−	1.16651i	0.715865	−	0.698239i	$-0.246033\pi$
$20$	−2.02544	+	0.947420i	−0.452902	+	0.211849i
$21$	−4.77935	−	4.14133i	−1.04294	−	0.903713i
$22$	−1.58869	+	1.58869i	−0.338709	+	0.338709i
$23$	4.14027	+	2.42036i	0.863307	+	0.504680i
$23$	4.14027	+	2.42036i	0.863307	+	0.504680i
$24$			1.75122i			0.357466i
$25$	4.15623	−	2.77952i	0.831246	−	0.555904i
$26$	4.43844	−	2.85241i	0.870449	−	0.559403i
$27$	−3.07833	+	4.11217i	−0.592425	+	0.791387i
$28$	−1.26198	+	3.38351i	−0.238492	+	0.639423i
$29$	4.62333	+	0.664735i	0.858531	+	0.123438i	0.557501	−	0.830176i	$-0.311760\pi$
$29$	4.62333	+	0.664735i	0.858531	+	0.123438i	0.301031	+	0.953615i	$0.402669\pi$
$30$	−0.592631	−	3.87074i	−0.108199	−	0.706697i
$31$	−7.65941	−	4.92241i	−1.37567	−	0.884090i	−0.376566	−	0.926390i	$-0.622895\pi$
$31$	−7.65941	−	4.92241i	−1.37567	−	0.884090i	−0.999105	+	0.0422994i	$0.986532\pi$
$32$	0.936950	−	0.349464i	0.165631	−	0.0617771i
$33$	−1.88562	−	3.45326i	−0.328245	−	0.601135i
$34$	1.69467	+	1.95575i	0.290633	+	0.335409i
$35$	1.64436	−	7.90568i	0.277948	−	1.33630i
$36$	−0.0640634	−	0.0188107i	−0.0106772	−	0.00313512i
$37$	−1.06956	−	2.86759i	−0.175834	−	0.471429i	0.818898	−	0.573939i	$-0.194585\pi$
$37$	−1.06956	−	2.86759i	−0.175834	−	0.471429i	−0.994732	+	0.102510i	$0.967313\pi$
$38$	−1.09195	−	5.01960i	−0.177137	−	0.814286i
$39$	2.60304	+	8.86513i	0.416820	+	1.41956i
$40$	−1.95269	+	1.08950i	−0.308747	+	0.172265i
$41$	1.83808	+	4.02483i	0.287060	+	0.628574i	0.997142	−	0.0755450i	$-0.0240696\pi$
$41$	1.83808	+	4.02483i	0.287060	+	0.628574i	−0.710082	+	0.704119i	$0.751342\pi$
$42$	−5.06262	−	3.78983i	−0.781179	−	0.584783i
$43$	11.7859	+	2.56386i	1.79733	+	0.390985i	0.982131	−	0.188200i	$-0.0602653\pi$
$43$	11.7859	+	2.56386i	1.79733	+	0.390985i	0.815197	+	0.579184i	$0.196629\pi$
$44$	−1.47130	+	1.69797i	−0.221807	+	0.255979i
$45$	0.147966	+	0.0198978i	0.0220574	+	0.00296619i
$46$	4.30239	+	2.11883i	0.634353	+	0.312404i
$47$	−0.0966659	−	0.0966659i	−0.0141002	−	0.0141002i	0.700022	−	0.714122i	$-0.253174\pi$
$47$	−0.0966659	−	0.0966659i	−0.0141002	−	0.0141002i	−0.714122	+	0.700022i	$0.753174\pi$
$48$	0.124931	+	1.74676i	0.0180322	+	0.252123i
$49$	−3.26586	−	5.08178i	−0.466552	−	0.725969i
$50$	3.94735	−	3.06894i	0.558240	−	0.434014i
$51$	−4.12232	+	1.88260i	−0.577241	+	0.263617i
$52$	4.22364	−	3.16178i	0.585713	−	0.438459i
$53$	−7.42874	−	4.05640i	−1.02042	−	0.557189i	−0.120253	−	0.992743i	$-0.538371\pi$
$53$	−7.42874	−	4.05640i	−1.02042	−	0.557189i	−0.900163	+	0.435554i	$0.856552\pi$
$54$	−2.77713	+	4.32129i	−0.377919	+	0.588054i
$55$	2.67742	−	4.25095i	0.361024	−	0.573199i
$56$	−1.01739	+	3.46492i	−0.135955	+	0.463019i
$57$	8.97308	+	0.641767i	1.18851	+	0.0850041i
$58$	4.65898	+	0.333216i	0.611753	+	0.0437535i
$59$	1.72602	−	5.87829i	0.224709	−	0.765288i	−0.767538	−	0.641004i	$-0.778518\pi$
$59$	1.72602	−	5.87829i	0.224709	−	0.765288i	0.992247	−	0.124284i	$-0.0396635\pi$
$60$	−0.867257	−	3.81860i	−0.111962	−	0.492979i
$61$	6.06094	−	9.43101i	0.776024	−	1.20752i	−0.197806	−	0.980241i	$-0.563382\pi$
$61$	6.06094	−	9.43101i	0.776024	−	1.20752i	0.973830	−	0.227276i	$-0.0729820\pi$
$62$	−7.99106	−	4.36345i	−1.01487	−	0.554158i
$63$	0.193020	−	0.144493i	0.0243183	−	0.0182044i
$64$	0.909632	−	0.415415i	0.113704	−	0.0519269i
$65$	−8.26558	+	8.41783i	−1.02522	+	1.04410i
$66$	−2.12717	−	3.30994i	−0.261837	−	0.407426i
$67$	0.697475	+	9.75197i	0.0852101	+	1.19139i	0.842640	+	0.538477i	$0.181000\pi$
$67$	0.697475	+	9.75197i	0.0852101	+	1.19139i	−0.757430	+	0.652916i	$0.773545\pi$
$68$	1.82987	+	1.82987i	0.221905	+	0.221905i
$69$	−5.68292	+	6.18385i	−0.684143	+	0.744449i
$70$	1.07619	−	8.00284i	0.128629	−	0.956522i
$71$	−3.94966	+	4.55815i	−0.468739	+	0.540953i	−0.940060	−	0.341008i	$-0.889232\pi$
$71$	−3.94966	+	4.55815i	−0.468739	+	0.540953i	0.471322	+	0.881961i	$0.343777\pi$
$72$	−0.0652421	−	0.0141926i	−0.00768886	−	0.00167261i
$73$	−5.36891	−	4.01911i	−0.628383	−	0.470402i	0.237002	−	0.971509i	$-0.423835\pi$
$73$	−5.36891	−	4.01911i	−0.628383	−	0.470402i	−0.865385	+	0.501108i	$0.832926\pi$
$74$	−1.27140	−	2.78398i	−0.147798	−	0.323632i
$75$	3.20916	+	8.14681i	0.370562	+	0.940712i
$76$	−1.44726	−	4.92891i	−0.166012	−	0.565384i
$77$	−1.72463	−	7.92800i	−0.196540	−	0.903480i
$78$	3.22884	+	8.65685i	0.365594	+	0.980195i
$79$	−2.52895	−	0.742567i	−0.284529	−	0.0835454i	0.136354	−	0.990660i	$-0.456462\pi$
$79$	−2.52895	−	0.742567i	−0.284529	−	0.0835454i	−0.420883	+	0.907115i	$0.638280\pi$
$80$	−1.86999	+	1.22603i	−0.209071	+	0.137074i
$81$	−6.02200	−	6.94976i	−0.669111	−	0.772195i
$82$	2.12053	+	3.88345i	0.234173	+	0.428856i
$83$	−4.32977	+	1.61492i	−0.475254	+	0.177261i	−0.575666	−	0.817685i	$-0.695257\pi$
$83$	−4.32977	+	1.61492i	−0.475254	+	0.177261i	0.100411	+	0.994946i	$0.467984\pi$
$84$	−5.32008	−	3.41901i	−0.580468	−	0.373044i
$85$	−4.66384	−	3.42534i	−0.505864	−	0.371530i
$86$	11.9387	+	1.71653i	1.28739	+	0.185098i
$87$	−2.85852	+	7.66399i	−0.306466	+	0.821666i
$88$	−1.34642	+	1.79861i	−0.143529	+	0.191732i
$89$	−11.8000	+	7.58338i	−1.25079	+	0.803836i	−0.986996	−	0.160742i	$-0.948611\pi$
$89$	−11.8000	+	7.58338i	−1.25079	+	0.803836i	−0.263797	+	0.964578i	$0.584975\pi$
$90$	0.149008	+	0.00929133i	0.0157069	+	0.000979393i
$91$			19.0526i			1.99725i
$92$	4.44258	+	1.80650i	0.463171	+	0.188341i
$93$	11.2744	−	11.2744i	1.16910	−	1.16910i
$94$	−0.103316	−	0.0895236i	−0.0106562	−	0.00923365i
$95$	4.86689	+	10.4047i	0.499332	+	1.06750i
$96$	0.249224	+	1.73339i	0.0254364	+	0.176914i
$97$	7.86547	+	2.93367i	0.798618	+	0.297869i	0.715448	−	0.698666i	$-0.246223\pi$
$97$	7.86547	+	2.93367i	0.798618	+	0.297869i	0.0831701	+	0.996535i	$0.473496\pi$
$98$	−3.62007	−	4.83585i	−0.365683	−	0.488495i
$99$	0.143934	−	0.0422628i	0.0144659	−	0.00424757i
$100$	3.71836	−	3.34272i	0.371836	−	0.334272i
$101$	0.715713	−	1.56719i	0.0712161	−	0.155942i	−0.870676	−	0.491857i	$-0.836318\pi$
$101$	0.715713	−	1.56719i	0.0712161	−	0.155942i	0.941892	+	0.335915i	$0.109046\pi$
$102$	−3.97752	+	2.17189i	−0.393833	+	0.215049i
$103$	0.0714432	−	0.998906i	0.00703950	−	0.0984251i	−0.992718	−	0.120465i	$-0.961561\pi$
$103$	0.0714432	−	0.998906i	0.00703950	−	0.0984251i	0.999757	+	0.0220397i	$0.00701603\pi$
$104$	3.98732	−	3.45503i	0.390989	−	0.338794i
$105$	12.9161	+	5.75670i	1.26048	+	0.561797i
$106$	−7.69919	−	3.51610i	−0.747812	−	0.341514i
$107$	8.29577	−	1.80463i	0.801982	−	0.174460i	0.207149	−	0.978310i	$-0.433582\pi$
$107$	8.29577	−	1.80463i	0.801982	−	0.174460i	0.594833	+	0.803849i	$0.297218\pi$
$108$	−2.46177	+	4.50840i	−0.236884	+	0.433821i
$109$	1.34854	−	9.37933i	0.129167	−	0.898377i	−0.817446	−	0.576005i	$-0.804611\pi$
$109$	1.34854	−	9.37933i	0.129167	−	0.898377i	0.946613	−	0.322372i	$-0.104480\pi$
$110$	2.36734	−	4.43113i	0.225717	−	0.422492i
$111$	5.30516	−	0.762767i	0.503543	−	0.0723986i
$112$	−0.767615	+	3.52867i	−0.0725328	+	0.333428i
$113$	9.31592	−	0.666288i	0.876368	−	0.0626791i	0.374097	−	0.927389i	$-0.377953\pi$
$113$	9.31592	−	0.666288i	0.876368	−	0.0626791i	0.502271	+	0.864710i	$0.332498\pi$
$114$	8.99600			0.842552
$115$	−10.4308	−	2.48951i	−0.972680	−	0.232148i
$116$	4.67088			0.433680
$117$	−0.351369	+	0.0251304i	−0.0324841	+	0.00232331i
$118$	1.30227	−	5.98644i	0.119884	−	0.551097i
$119$	−9.25004	+	1.32996i	−0.847950	+	0.121917i
$120$	−1.13746	−	3.74700i	−0.103836	−	0.342053i
$121$	−0.847080	+	5.89157i	−0.0770073	+	0.535597i
$122$	5.37270	−	9.83936i	0.486421	−	0.890814i
$123$	−7.57151	+	1.64708i	−0.682700	+	0.148512i
$124$	−8.28198	−	3.78226i	−0.743744	−	0.339657i
$125$	−7.08752	+	8.64680i	−0.633927	+	0.773393i
$126$	0.182220	−	0.157895i	0.0162335	−	0.0140664i
$127$	0.0889953	−	1.24432i	0.00789705	−	0.110415i	−0.991975	−	0.126437i	$-0.959646\pi$
$127$	0.0889953	−	1.24432i	0.00789705	−	0.110415i	0.999872	+	0.0160222i	$0.00510025\pi$
$128$	0.877679	−	0.479249i	0.0775766	−	0.0423600i
$129$	−8.77454	+	19.2136i	−0.772555	+	1.69166i
$130$	−7.64400	+	8.98605i	−0.670423	+	0.788128i
$131$	10.0529	−	2.95181i	0.878330	−	0.257901i	0.188675	−	0.982040i	$-0.439581\pi$
$131$	10.0529	−	2.95181i	0.878330	−	0.257901i	0.689654	+	0.724139i	$0.257762\pi$
$132$	−2.35788	−	3.14976i	−0.205227	−	0.274151i
$133$	17.3811	+	6.48280i	1.50713	+	0.562130i
$134$	1.39140	+	9.67737i	0.120198	+	0.835997i
$135$	3.91560	−	10.7981i	0.337001	−	0.929349i
$136$	1.95575	+	1.69467i	0.167704	+	0.145317i
$137$	−1.44533	+	1.44533i	−0.123483	+	0.123483i	−0.766148	−	0.642665i	$-0.777829\pi$
$137$	−1.44533	+	1.44533i	−0.123483	+	0.123483i	0.642665	+	0.766148i	$0.277829\pi$
$138$	−5.22729	+	6.57351i	−0.444977	+	0.559575i
$139$			0.981060i			0.0832124i	0.999134	+	0.0416062i	$0.0132475\pi$
$139$			0.981060i			0.0832124i	−0.999134	+	0.0416062i	$0.986753\pi$
$140$	0.502529	−	8.05922i	0.0424714	−	0.681129i
$141$	0.201398	−	0.129431i	0.0169608	−	0.0109000i
$142$	−3.61442	+	4.82830i	−0.303316	+	0.405182i
$143$	−4.14246	+	11.1064i	−0.346410	+	0.928761i
$144$	−0.0660884	−	0.00950207i	−0.00550736	−	0.000791839i
$145$	−10.3241	+	1.58067i	−0.857369	+	0.131268i
$146$	−5.64195	−	3.62586i	−0.466931	−	0.300078i
$147$	9.91165	−	3.69685i	0.817499	−	0.304911i
$148$	−1.46677	−	2.68619i	−0.120568	−	0.220804i
$149$	−0.791383	−	0.913305i	−0.0648326	−	0.0748208i	0.722407	−	0.691468i	$-0.243036\pi$
$149$	−0.791383	−	0.913305i	−0.0648326	−	0.0748208i	−0.787239	+	0.616648i	$0.788490\pi$
$150$	3.78217	+	7.89711i	0.308813	+	0.644796i
$151$	−1.00248	−	0.294354i	−0.0815804	−	0.0239542i	0.240688	−	0.970603i	$-0.422627\pi$
$151$	−1.00248	−	0.294354i	−0.0815804	−	0.0239542i	−0.322268	+	0.946648i	$0.604445\pi$
$152$	−1.79519	−	4.81310i	−0.145610	−	0.390394i
$153$	−0.0367279	−	0.168836i	−0.00296928	−	0.0136495i
$154$	−2.28581	−	7.78477i	−0.184196	−	0.627314i
$155$	19.5857	+	5.55725i	1.57316	+	0.446369i
$156$	3.83818	+	8.40445i	0.307301	+	0.672894i
$157$	−13.7776	−	10.3138i	−1.09957	−	0.823128i	−0.114184	−	0.993460i	$-0.536425\pi$
$157$	−13.7776	−	10.3138i	−1.09957	−	0.823128i	−0.985387	+	0.170331i	$0.945516\pi$
$158$	−2.57548	−	0.560262i	−0.204894	−	0.0445721i
$159$	9.70664	−	11.2021i	0.769786	−	0.888381i
$160$	−1.77776	+	1.35631i	−0.140544	+	0.107225i
$161$	−14.8367	+	8.93365i	−1.16929	+	0.704070i
$162$	−6.50245	−	6.50245i	−0.510880	−	0.510880i
$163$	−1.01007	−	14.1227i	−0.0791151	−	1.10617i	−0.869621	−	0.493719i	$-0.835637\pi$
$163$	−1.01007	−	14.1227i	−0.0791151	−	1.10617i	0.790506	−	0.612454i	$-0.209818\pi$
$164$	2.39216	+	3.72228i	0.186797	+	0.290661i
$165$	6.27756	+	6.16401i	0.488707	+	0.479868i
$166$	−4.20354	+	1.91969i	−0.326258	+	0.148997i
$167$	−15.2459	+	11.4129i	−1.17976	+	0.883158i	−0.995024	−	0.0996307i	$-0.968234\pi$
$167$	−15.2459	+	11.4129i	−1.17976	+	0.883158i	−0.184736	+	0.982788i	$0.559143\pi$
$168$	−5.55044	−	3.03077i	−0.428225	−	0.233829i
$169$	8.02092	−	12.4808i	0.616994	−	0.960061i
$170$	−4.89632	−	3.08390i	−0.375530	−	0.236524i
$171$	−0.0966305	+	0.329093i	−0.00738952	+	0.0251664i
$172$	12.0308	+	0.860458i	0.917338	+	0.0656093i
$173$	−17.7495	−	1.26947i	−1.34947	−	0.0965160i	−0.622195	−	0.782862i	$-0.713759\pi$
$173$	−17.7495	−	1.26947i	−1.34947	−	0.0965160i	−0.727275	+	0.686346i	$0.759214\pi$
$174$	−2.30450	+	7.84839i	−0.174703	+	0.594985i
$175$	1.61658	+	17.9835i	0.122202	+	1.35942i
$176$	−1.21468	+	1.89008i	−0.0915599	+	0.142470i
$177$	9.41641	+	5.14175i	0.707781	+	0.386477i
$178$	−11.2289	+	8.40585i	−0.841642	+	0.630045i
$179$	13.3136	−	6.08011i	0.995104	−	0.454449i	0.149789	−	0.988718i	$-0.452140\pi$
$179$	13.3136	−	6.08011i	0.995104	−	0.454449i	0.845314	+	0.534269i	$0.179413\pi$
$180$	0.149291	−	0.00136247i	0.0111275	−	0.000101552i
$181$	−5.27923	−	8.21464i	−0.392402	−	0.610589i	0.587701	−	0.809078i	$-0.300033\pi$
$181$	−5.27923	−	8.21464i	−0.392402	−	0.610589i	−0.980103	+	0.198489i	$0.936397\pi$
$182$	1.35920	+	19.0040i	0.100750	+	1.40867i
$183$	13.8822	+	13.8822i	1.02620	+	1.02620i
$184$	4.56014	+	1.48497i	0.336178	+	0.109473i
$185$	4.15106	+	5.44095i	0.305192	+	0.400026i
$186$	10.4414	−	12.0500i	0.765599	−	0.883549i
$187$	−5.68131	−	1.23589i	−0.415459	−	0.0903775i
$188$	−0.109439	−	0.0819250i	−0.00798166	−	0.00597500i
$189$	−7.70584	−	16.8734i	−0.560517	−	1.22736i
$190$	5.59675	+	10.0309i	0.406031	+	0.727721i
$191$	−3.00785	−	10.2438i	−0.217641	−	0.741216i	−0.993849	−	0.110740i	$-0.964678\pi$
$191$	−3.00785	−	10.2438i	−0.217641	−	0.741216i	0.776209	−	0.630476i	$-0.217140\pi$
$192$	0.372248	+	1.71120i	0.0268647	+	0.123495i
$193$	6.45659	+	17.3108i	0.464756	+	1.24606i	0.932170	+	0.362020i	$0.117913\pi$
$193$	6.45659	+	17.3108i	0.464756	+	1.24606i	−0.467414	+	0.884038i	$0.654814\pi$
$194$	8.05472	+	2.36508i	0.578295	+	0.169803i
$195$	−11.3277	−	17.2776i	−0.811196	−	1.23727i
$196$	−3.95583	−	4.56528i	−0.282560	−	0.326091i
$197$	−8.11322	−	14.8582i	−0.578043	−	1.05861i	−0.989135	−	0.147012i	$-0.953034\pi$
$197$	−8.11322	−	14.8582i	−0.578043	−	1.05861i	0.411092	−	0.911594i	$-0.365148\pi$
$198$	0.140552	−	0.0524232i	0.00998860	−	0.00372556i
$199$	−1.13079	−	0.726716i	−0.0801597	−	0.0515155i	0.499947	−	0.866056i	$-0.333353\pi$
$199$	−1.13079	−	0.726716i	−0.0801597	−	0.0515155i	−0.580107	+	0.814540i	$0.696989\pi$
$200$	3.47042	−	3.59947i	0.245396	−	0.254521i
$201$	−16.9472	−	2.43664i	−1.19536	−	0.171867i
$202$	0.602088	−	1.61426i	0.0423627	−	0.113579i
$203$	−10.1083	+	13.5031i	−0.709462	+	0.947731i
$204$	−3.81244	+	2.45011i	−0.266924	+	0.171542i
$205$	−6.54709	−	7.41787i	−0.457269	−	0.518086i
$206$		−	1.00146i		−	0.0697749i
$207$	−0.184324	−	0.261835i	−0.0128114	−	0.0181988i
$208$	3.73068	−	3.73068i	0.258676	−	0.258676i
$209$	8.72247	+	7.55807i	0.603346	+	0.522802i
$210$	13.2938	+	4.82061i	0.917362	+	0.332654i
$211$	−2.98777	−	20.7804i	−0.205686	−	1.43058i	−0.787026	−	0.616919i	$-0.788380\pi$
$211$	−2.98777	−	20.7804i	−0.205686	−	1.43058i	0.581340	−	0.813661i	$-0.302529\pi$
$212$	−7.93041	−	2.95789i	−0.544663	−	0.203149i
$213$	−6.32965	−	8.45542i	−0.433700	−	0.579356i
$214$	8.14589	−	2.39185i	0.556841	−	0.163503i
$215$	−26.8830	+	2.16946i	−1.83340	+	0.147956i
$216$	−2.13388	+	4.67254i	−0.145192	+	0.317926i
$217$	28.8573	−	15.7573i	1.95896	−	1.06967i
$218$	0.675994	−	9.45164i	0.0457841	−	0.640146i
$219$	8.87606	−	7.69115i	0.599789	−	0.519720i
$220$	2.04520	−	4.58872i	0.137887	−	0.309372i
$221$	12.4195	+	5.67180i	0.835427	+	0.381527i
$222$	5.23723	−	1.13929i	0.351500	−	0.0764641i
$223$	9.74246	−	17.8420i	0.652403	−	1.19479i	−0.316792	−	0.948495i	$-0.602606\pi$
$223$	9.74246	−	17.8420i	0.652403	−	1.19479i	0.969196	−	0.246293i	$-0.0792124\pi$
$224$	−0.513927	+	3.57444i	−0.0343382	+	0.238827i
$225$	−0.329520	+	0.0535333i	−0.0219680	+	0.00356889i
$226$	9.24465	−	1.32918i	0.614945	−	0.0884158i
$227$	4.16615	−	19.1515i	0.276517	−	1.27113i	−0.603951	−	0.797022i	$-0.706408\pi$
$227$	4.16615	−	19.1515i	0.276517	−	1.27113i	0.880468	−	0.474106i	$-0.157229\pi$
$228$	8.97308	−	0.641767i	0.594257	−	0.0425021i
$229$	7.56270			0.499757			0.249879	−	0.968277i	$-0.419609\pi$
$229$	7.56270			0.499757			0.249879	+	0.968277i	$0.419609\pi$
$230$	−10.5819	−	1.73904i	−0.697747	−	0.114669i
$231$	14.2084			0.934842
$232$	4.65898	−	0.333216i	0.305877	−	0.0218767i
$233$	1.29200	−	5.93922i	0.0846416	−	0.389091i	−0.915264	−	0.402855i	$-0.868018\pi$
$233$	1.29200	−	5.93922i	0.0846416	−	0.389091i	0.999905	+	0.0137643i	$0.00438145\pi$
$234$	−0.348681	+	0.0501327i	−0.0227940	+	0.00327728i
$235$	0.269619	+	0.144044i	0.0175880	+	0.00939643i
$236$	0.871885	−	6.06409i	0.0567549	−	0.394739i
$237$	2.21208	−	4.05112i	0.143690	−	0.263148i
$238$	−9.13159	+	1.98646i	−0.591913	+	0.128763i
$239$	−8.43984	−	3.85434i	−0.545928	−	0.249317i	0.123306	−	0.992369i	$-0.460650\pi$
$239$	−8.43984	−	3.85434i	−0.545928	−	0.249317i	−0.669234	+	0.743052i	$0.733378\pi$
$240$	−1.40187	−	3.65631i	−0.0904905	−	0.236014i
$241$	19.1531	−	16.5963i	1.23376	−	1.06906i	0.238568	−	0.971126i	$-0.423322\pi$
$241$	19.1531	−	16.5963i	1.23376	−	1.06906i	0.995193	−	0.0979345i	$-0.0312236\pi$
$242$	−0.424622	+	5.93699i	−0.0272957	+	0.381644i
$243$	0.608885	−	0.332477i	0.0390600	−	0.0213284i
$244$	4.65708	−	10.1976i	0.298139	−	0.652833i
$245$	10.2886	+	8.75199i	0.657312	+	0.559144i
$246$	−7.43472	+	2.18303i	−0.474020	+	0.139185i
$247$	−16.2420	−	21.6968i	−1.03345	−	1.38053i
$248$	−8.53070	−	3.18179i	−0.541700	−	0.202044i
$249$	−1.15170	−	8.01025i	−0.0729861	−	0.507629i
$250$	−6.45261	+	9.13038i	−0.408099	+	0.577456i
$251$	5.67899	+	4.92088i	0.358455	+	0.310603i	0.815407	−	0.578888i	$-0.196513\pi$
$251$	5.67899	+	4.92088i	0.358455	+	0.310603i	−0.456952	+	0.889491i	$0.651059\pi$
$252$	0.170492	−	0.170492i	0.0107400	−	0.0107400i
$253$	−10.5912	+	1.98189i	−0.665860	+	0.124600i
$254$		−	1.24749i		−	0.0782748i
$255$	7.59754	−	6.70567i	0.475777	−	0.419926i
$256$	0.841254	−	0.540641i	0.0525783	−	0.0337901i
$257$	−16.1033	+	21.5115i	−1.00450	+	1.34185i	−0.0655286	+	0.997851i	$0.520873\pi$
$257$	−16.1033	+	21.5115i	−1.00450	+	1.34185i	−0.938969	+	0.344001i	$0.888218\pi$
$258$	−7.38150	+	19.7906i	−0.459552	+	1.23211i
$259$	10.9398	+	1.57290i	0.679765	+	0.0977355i
$260$	−6.98346	+	9.50847i	−0.433096	+	0.589690i
$261$	−0.262357	−	0.168607i	−0.0162395	−	0.0104365i
$262$	9.81675	−	3.66146i	0.606481	−	0.226206i
$263$	−7.56732	−	13.8585i	−0.466621	−	0.854553i	−0.999963	−	0.00865277i	$-0.997246\pi$
$263$	−7.56732	−	13.8585i	−0.466621	−	0.854553i	0.533341	−	0.845900i	$-0.320936\pi$
$264$	−2.57657	−	2.97352i	−0.158577	−	0.183008i
$265$	18.5297	+	3.85412i	1.13827	+	0.236757i
$266$	17.7992	+	5.22633i	1.09134	+	0.320447i
$267$	−8.58414	−	23.0150i	−0.525341	−	1.40849i
$268$	2.07823	+	9.55345i	0.126948	+	0.583570i
$269$	3.66513	+	12.4823i	0.223467	+	0.761058i	0.992542	+	0.121900i	$0.0388987\pi$
$269$	3.66513	+	12.4823i	0.223467	+	0.761058i	−0.769076	+	0.639158i	$0.779283\pi$
$270$	3.13529	−	11.0499i	0.190808	−	0.672475i
$271$	6.25153	+	13.6889i	0.379753	+	0.831544i	0.998928	+	0.0462905i	$0.0147400\pi$
$271$	6.25153	+	13.6889i	0.379753	+	0.831544i	−0.619175	+	0.785253i	$0.712533\pi$
$272$	2.07167	+	1.55083i	0.125613	+	0.0940328i
$273$	−32.6027	−	7.09229i	−1.97321	−	0.429245i
$274$	−1.33854	+	1.54476i	−0.0808643	+	0.0933224i
$275$	−2.96765	+	10.8346i	−0.178956	+	0.653353i
$276$	−4.74502	+	6.92968i	−0.285617	+	0.417117i
$277$	15.8497	+	15.8497i	0.952318	+	0.952318i	0.998914	−	0.0465955i	$-0.0148372\pi$
$277$	15.8497	+	15.8497i	0.952318	+	0.952318i	−0.0465955	+	0.998914i	$0.514837\pi$
$278$	0.0699880	+	0.978560i	0.00419760	+	0.0586901i
$279$	0.328659	+	0.511403i	0.0196763	+	0.0306169i
$280$	−0.0736902	−	8.07454i	−0.00440383	−	0.482546i
$281$	13.7320	−	6.27120i	0.819183	−	0.374108i	0.0386733	−	0.999252i	$-0.487687\pi$
$281$	13.7320	−	6.27120i	0.819183	−	0.374108i	0.780510	+	0.625143i	$0.214960\pi$
$282$	0.191652	−	0.143469i	0.0114127	−	0.00854343i
$283$	−19.2809	−	10.5282i	−1.14613	−	0.625835i	−0.210074	−	0.977685i	$-0.567371\pi$
$283$	−19.2809	−	10.5282i	−1.14613	−	0.625835i	−0.936056	+	0.351851i	$0.885552\pi$
$284$	−3.26077	+	5.07385i	−0.193491	+	0.301078i
$285$	−19.6161	+	4.45509i	−1.16196	+	0.263897i
$286$	−3.33959	+	11.3736i	−0.197474	+	0.672535i
$287$	−15.9377	−	1.13989i	−0.940772	−	0.0672853i
$288$	−0.0665978	−	0.00476317i	−0.00392432	−	0.000280673i
$289$	2.90273	−	9.88578i	0.170749	−	0.581517i
$290$	−10.1850	+	2.31316i	−0.598085	+	0.135833i
$291$	−7.94800	+	12.3673i	−0.465920	+	0.724986i
$292$	−5.88624	−	3.21413i	−0.344466	−	0.188093i
$293$	5.93715	−	4.44449i	0.346852	−	0.259650i	−0.411620	−	0.911355i	$-0.635037\pi$
$293$	5.93715	−	4.44449i	0.346852	−	0.259650i	0.758472	+	0.651705i	$0.225946\pi$
$294$	9.62267	−	4.39452i	0.561205	−	0.256294i
$295$	0.125017	+	13.6986i	0.00727875	+	0.797563i
$296$	−1.65466	−	2.57471i	−0.0961754	−	0.149652i
$297$	−0.823319	−	11.5115i	−0.0477738	−	0.667965i
$298$	−0.854521	−	0.854521i	−0.0495011	−	0.0495011i
$299$	25.2919	+	0.739034i	1.46267	+	0.0427394i
$300$	4.33591	+	7.60717i	0.250334	+	0.439200i
$301$	−28.5234	+	32.9178i	−1.64406	+	1.89735i
$302$	−1.02092	−	0.222088i	−0.0587475	−	0.0127797i
$303$	2.41536	+	1.80811i	0.138759	+	0.103873i
$304$	−2.13398	−	4.67277i	−0.122392	−	0.268002i
$305$	−6.84262	+	24.1158i	−0.391808	+	1.38087i
$306$	−0.0486789	−	0.165785i	−0.00278279	−	0.00947731i
$307$	7.24723	+	33.3150i	0.413621	+	1.90139i	0.432640	+	0.901567i	$0.357582\pi$
$307$	7.24723	+	33.3150i	0.413621	+	1.90139i	−0.0190191	+	0.999819i	$0.506054\pi$
$308$	−2.83535	−	7.60186i	−0.161559	−	0.433156i
$309$	1.68273	+	0.494095i	0.0957272	+	0.0281081i
$310$	19.9323	+	4.14586i	1.13208	+	0.235469i
$311$	0.898739	+	1.03720i	0.0509628	+	0.0588142i	0.780659	−	0.624958i	$-0.214884\pi$
$311$	0.898739	+	1.03720i	0.0509628	+	0.0588142i	−0.729696	+	0.683772i	$0.760338\pi$
$312$	4.42797	+	8.10922i	0.250684	+	0.459094i
$313$	−13.4885	+	5.03096i	−0.762417	+	0.284367i	−0.700441	−	0.713711i	$-0.747013\pi$
$313$	−13.4885	+	5.03096i	−0.762417	+	0.284367i	−0.0619766	+	0.998078i	$0.519740\pi$
$314$	−14.4783	−	9.30461i	−0.817055	−	0.525089i
$315$	−0.319144	+	0.434537i	−0.0179817	+	0.0244834i
$316$	−2.60889	−	0.375102i	−0.146762	−	0.0211011i
$317$	−3.78770	+	10.1552i	−0.212738	+	0.570374i	−0.998862	−	0.0476956i	$-0.984812\pi$
$317$	−3.78770	+	10.1552i	−0.212738	+	0.570374i	0.786123	+	0.618070i	$0.212085\pi$
$318$	8.88276	−	11.8660i	0.498120	−	0.665411i
$319$	−8.82832	+	5.67362i	−0.494291	+	0.317662i
$320$	−1.67647	+	1.47967i	−0.0937177	+	0.0827163i
$321$			14.8675i			0.829821i
$322$	−14.1615	+	9.96933i	−0.789192	+	0.555569i
$323$	9.40004	−	9.40004i	0.523032	−	0.523032i
$324$	−6.94976	−	6.02200i	−0.386098	−	0.334555i
$325$	12.2179	−	23.3800i	0.677725	−	1.29689i
$326$	−2.01500	−	14.0146i	−0.111601	−	0.776199i
$327$	15.5479	+	5.79907i	0.859801	+	0.320689i
$328$	2.65161	+	3.54214i	0.146411	+	0.195582i
$329$	0.473676	−	0.139084i	0.0261146	−	0.00766794i
$330$	6.70130	+	5.70047i	0.368894	+	0.313801i
$331$	−5.79727	+	12.6943i	−0.318647	+	0.697739i	−0.999395	−	0.0347781i	$-0.988928\pi$
$331$	−5.79727	+	12.6943i	−0.318647	+	0.697739i	0.680748	+	0.732518i	$0.261655\pi$
$332$	−4.05588	+	2.21468i	−0.222595	+	0.121546i
$333$	−0.0145780	+	0.203827i	−0.000798869	+	0.0111696i
$334$	−14.3928	+	12.4715i	−0.787541	+	0.682408i
$335$	−7.82652	−	20.4128i	−0.427608	−	1.11527i
$336$	−5.75251	−	2.62708i	−0.313825	−	0.143319i
$337$	−3.74255	+	0.814141i	−0.203870	+	0.0443491i	−0.313340	−	0.949641i	$-0.601448\pi$
$337$	−3.74255	+	0.814141i	−0.203870	+	0.0443491i	0.109471	+	0.993990i	$0.465084\pi$
$338$	7.11011	−	13.0212i	0.386739	−	0.708260i
$339$	−2.32769	+	16.1894i	−0.126423	+	0.879288i
$340$	−5.10384	−	2.72674i	−0.276795	−	0.147878i
$341$	20.2478	−	2.91120i	1.09648	−	0.157650i
$342$	−0.0729070	+	0.335148i	−0.00394236	+	0.0181227i
$343$	−3.45530	+	0.247128i	−0.186568	+	0.0133436i
$344$	12.0615			0.650313
$345$	8.14291	−	16.9225i	0.438399	−	0.911077i
$346$	−17.7949			−0.956657
$347$	−26.3354	+	1.88355i	−1.41376	+	0.101114i	−0.757212	−	0.653169i	$-0.773439\pi$
$347$	−26.3354	+	1.88355i	−1.41376	+	0.101114i	−0.656549	+	0.754284i	$0.727984\pi$
$348$	−1.73873	+	7.99279i	−0.0932055	+	0.428459i
$349$	19.2657	−	2.76999i	1.03127	−	0.148274i	0.394156	−	0.919044i	$-0.371037\pi$
$349$	19.2657	−	2.76999i	1.03127	−	0.148274i	0.637114	+	0.770769i	$0.280128\pi$
$350$	2.89539	+	17.8223i	0.154765	+	0.952643i
$351$	−3.85691	+	26.8254i	−0.205867	+	1.43184i
$352$	−1.07675	+	1.97192i	−0.0573909	+	0.105104i
$353$	27.8819	−	6.06534i	1.48400	−	0.322825i	0.603691	−	0.797218i	$-0.293696\pi$
$353$	27.8819	−	6.06534i	1.48400	−	0.322825i	0.880313	+	0.474393i	$0.157332\pi$
$354$	9.75922	+	4.45689i	0.518697	+	0.236881i
$355$	5.49026	−	12.3183i	0.291393	−	0.653786i
$356$	−10.6006	+	9.18550i	−0.561832	+	0.486830i
$357$	1.16750	−	16.3237i	0.0617904	−	0.863943i
$358$	12.8459	−	7.01440i	0.678927	−	0.370722i
$359$	9.62341	−	21.0723i	0.507904	−	1.11216i	−0.465915	−	0.884830i	$-0.654275\pi$
$359$	9.62341	−	21.0723i	0.507904	−	1.11216i	0.973819	−	0.227325i	$-0.0729981\pi$
$360$	0.148814	−	0.0120093i	0.00784318	−	0.000632947i
$361$	−7.08939	+	2.08163i	−0.373126	+	0.109560i
$362$	−5.85180	−	7.81709i	−0.307564	−	0.410857i
$363$	−9.76632	−	3.64265i	−0.512599	−	0.191190i
$364$	2.71147	+	18.8587i	0.142119	+	0.988462i
$365$	14.0981	+	5.11226i	0.737929	+	0.267588i
$366$	14.8371	+	12.8564i	0.775549	+	0.672017i
$367$	−6.71663	+	6.71663i	−0.350605	+	0.350605i	−0.860335	−	0.509729i	$-0.829746\pi$
$367$	−6.71663	+	6.71663i	−0.350605	+	0.350605i	0.509729	+	0.860335i	$0.329746\pi$
$368$	4.65446	+	1.15587i	0.242630	+	0.0602537i
$369$		−	0.295427i		−	0.0153793i
$370$	4.52863	+	5.13095i	0.235432	+	0.266746i
$371$	25.7133	−	16.5249i	1.33497	−	0.857931i
$372$	9.55514	−	12.7642i	0.495411	−	0.661792i
$373$	−13.2311	+	35.4739i	−0.685079	+	1.83677i	−0.156946	+	0.987607i	$0.550165\pi$
$373$	−13.2311	+	35.4739i	−0.685079	+	1.83677i	−0.528133	+	0.849162i	$0.677108\pi$
$374$	−5.75500	−	0.827445i	−0.297584	−	0.0427861i
$375$	−12.1581	−	15.3469i	−0.627840	−	0.792511i
$376$	−0.115005	−	0.0739090i	−0.00593091	−	0.00381157i
$377$	23.0897	−	8.61200i	1.18918	−	0.443541i
$378$	−8.88994	−	16.2807i	−0.457249	−	0.837390i
$379$	9.95211	+	11.4854i	0.511206	+	0.589963i	0.951407	−	0.307936i	$-0.0996384\pi$
$379$	9.95211	+	11.4854i	0.511206	+	0.589963i	−0.440201	+	0.897899i	$0.645093\pi$
$380$	6.29808	+	9.60612i	0.323085	+	0.492784i
$381$	2.09614	+	0.615483i	0.107389	+	0.0315322i
$382$	−3.73097	−	10.0031i	−0.190893	−	0.511805i
$383$	1.68130	+	7.72883i	0.0859106	+	0.394925i	0.999943	−	0.0107175i	$-0.00341155\pi$
$383$	1.68130	+	7.72883i	0.0859106	+	0.394925i	−0.914032	+	0.405642i	$0.867048\pi$
$384$	0.493375	+	1.68028i	0.0251775	+	0.0857465i
$385$	8.83956	+	15.8430i	0.450506	+	0.807433i
$386$	7.67508	+	16.8061i	0.390651	+	0.855407i
$387$	−0.644694	−	0.482612i	−0.0327716	−	0.0245325i
$388$	8.20292	+	1.78444i	0.416440	+	0.0905910i
$389$	−12.4039	+	14.3148i	−0.628901	+	0.725790i	−0.977372	−	0.211529i	$-0.932156\pi$
$389$	−12.4039	+	14.3148i	−0.628901	+	0.725790i	0.348471	+	0.937320i	$0.386701\pi$
$390$	−12.5314	−	16.4254i	−0.634554	−	0.831734i
$391$	1.40669	+	12.3308i	0.0711392	+	0.623597i
$392$	−4.27144	−	4.27144i	−0.215740	−	0.215740i
$393$	1.30894	+	18.3014i	0.0660273	+	0.923183i
$394$	−9.15252	−	14.2416i	−0.461097	−	0.717481i
$395$	5.89340	−	0.0537846i	0.296529	−	0.00270619i
$396$	0.136454	−	0.0623165i	0.00685708	−	0.00313152i
$397$	−4.05543	+	3.03585i	−0.203536	+	0.152365i	−0.696184	−	0.717864i	$-0.745120\pi$
$397$	−4.05543	+	3.03585i	−0.203536	+	0.152365i	0.492648	+	0.870229i	$0.336029\pi$
$398$	−1.17975	−	0.644195i	−0.0591357	−	0.0322906i
$399$	−17.5634	+	27.3292i	−0.879271	+	1.36817i
$400$	3.20479	−	3.83788i	0.160240	−	0.191894i
$401$	1.13945	−	3.88061i	0.0569014	−	0.193788i	−0.926137	−	0.377186i	$-0.876892\pi$
$401$	1.13945	−	3.88061i	0.0569014	−	0.193788i	0.983039	+	0.183398i	$0.0587098\pi$
$402$	−17.0778	−	1.22143i	−0.851765	−	0.0609194i
$403$	−47.9141	−	3.42689i	−2.38677	−	0.170705i
$404$	0.485394	−	1.65310i	0.0241492	−	0.0822447i
$405$	17.3990	+	10.9586i	0.864565	+	0.544538i
$406$	−9.11923	+	14.1898i	−0.452580	+	0.704228i
$407$	6.03517	+	3.29545i	0.299152	+	0.163350i
$408$	−3.62794	+	2.71584i	−0.179610	+	0.134454i
$409$	−22.5328	+	10.2904i	−1.11417	+	0.508826i	−0.885483	−	0.464672i	$-0.846172\pi$
$409$	−22.5328	+	10.2904i	−1.11417	+	0.508826i	−0.228692	+	0.973499i	$0.573445\pi$
$410$	−7.05959	−	6.93190i	−0.348648	−	0.342342i
$411$	−1.93523	−	3.01128i	−0.0954578	−	0.148535i
$412$	−0.0714432	−	0.998906i	−0.00351975	−	0.0492126i
$413$	15.6439	+	15.6439i	0.769786	+	0.769786i
$414$	−0.202534	−	0.248018i	−0.00995400	−	0.0121894i
$415$	8.21528	−	6.26768i	0.403272	−	0.307668i
$416$	3.45503	−	3.98732i	0.169397	−	0.195494i
$417$	−1.67879	−	0.365198i	−0.0822106	−	0.0178838i
$418$	9.23944	+	6.91656i	0.451916	+	0.338300i
$419$	−10.5036	−	22.9997i	−0.513135	−	1.12361i	−0.971974	−	0.235089i	$-0.924462\pi$
$419$	−10.5036	−	22.9997i	−0.513135	−	1.12361i	0.458839	−	0.888520i	$-0.348266\pi$
$420$	13.6039	+	3.85996i	0.663801	+	0.188347i
$421$	−5.68010	−	19.3446i	−0.276831	−	0.942800i	−0.974124	−	0.226014i	$-0.927431\pi$
$421$	−5.68010	−	19.3446i	−0.276831	−	0.942800i	0.697293	−	0.716786i	$-0.254388\pi$
$422$	−4.46261	−	20.5143i	−0.217236	−	0.998620i
$423$	0.00318977	+	0.00855210i	0.000155092	+	0.000415817i
$424$	−8.12122	−	2.38460i	−0.394401	−	0.115807i
$425$	12.2038	+	4.29976i	0.591973	+	0.208569i
$426$	−6.91672	−	7.98232i	−0.335116	−	0.386745i
$427$	19.4019	+	35.5319i	0.938922	+	1.71951i
$428$	7.95450	−	2.96688i	0.384495	−	0.143409i
$429$	−17.4632	−	11.2229i	−0.843130	−	0.541847i
$430$	−26.6597	+	4.08174i	−1.28564	+	0.196839i
$431$	0.926902	+	0.133268i	0.0446473	+	0.00641931i	0.164602	−	0.986360i	$-0.447366\pi$
$431$	0.926902	+	0.133268i	0.0446473	+	0.00641931i	−0.119955	+	0.992779i	$0.538275\pi$
$432$	−1.79510	+	4.81286i	−0.0863670	+	0.231559i
$433$	9.00313	−	12.0268i	0.432663	−	0.577970i	−0.530230	−	0.847854i	$-0.677894\pi$
$433$	9.00313	−	12.0268i	0.432663	−	0.577970i	0.962893	+	0.269884i	$0.0869854\pi$
$434$	27.6596	−	17.7758i	1.32770	−	0.853264i
$435$	1.13828	−	18.2550i	0.0545763	−	0.875259i
$436$		−	9.47578i		−	0.453807i
$437$	9.27997	−	22.8215i	0.443921	−	1.09170i
$438$	8.30477	−	8.30477i	0.396817	−	0.396817i
$439$	6.21461	+	5.38499i	0.296607	+	0.257012i	0.790432	−	0.612550i	$-0.209856\pi$
$439$	6.21461	+	5.38499i	0.296607	+	0.257012i	−0.493825	+	0.869561i	$0.664402\pi$
$440$	1.71263	−	4.72293i	0.0816465	−	0.225157i
$441$	0.0573994	+	0.399222i	0.00273331	+	0.0190106i
$442$	12.7925	+	4.77135i	0.608477	+	0.226950i
$443$	3.27264	+	4.37174i	0.155488	+	0.207708i	0.871520	−	0.490360i	$-0.163135\pi$
$443$	3.27264	+	4.37174i	0.155488	+	0.207708i	−0.716032	+	0.698067i	$0.754044\pi$
$444$	5.14261	−	1.51001i	0.244057	−	0.0716617i
$445$	20.3222	−	23.8902i	0.963366	−	1.13250i
$446$	8.44480	−	18.4915i	0.399873	−	0.875600i
$447$	1.85744	−	1.01424i	0.0878537	−	0.0479718i
$448$	−0.257620	+	3.60199i	−0.0121714	+	0.170178i
$449$	−23.4308	+	20.3029i	−1.10577	+	0.958155i	−0.999346	−	0.0361661i	$-0.988485\pi$
$449$	−23.4308	+	20.3029i	−1.10577	+	0.958155i	−0.106424	+	0.994321i	$0.533940\pi$
$450$	−0.324861	+	0.0769046i	−0.0153141	+	0.00362532i
$451$	−9.04276	−	4.12969i	−0.425807	−	0.194459i
$452$	9.12628	−	1.98530i	0.429264	−	0.0933806i
$453$	0.876868	−	1.60586i	0.0411989	−	0.0754501i
$454$	2.78928	−	19.3999i	0.130908	−	0.910482i
$455$	−12.3752	−	40.7659i	−0.580156	−	1.91114i
$456$	8.90443	−	1.28026i	0.416988	−	0.0599539i
$457$	−5.28520	+	24.2957i	−0.247231	+	1.13650i	0.671310	+	0.741177i	$0.265732\pi$
$457$	−5.28520	+	24.2957i	−0.247231	+	1.13650i	−0.918541	+	0.395326i	$0.870632\pi$
$458$	7.54343	−	0.539517i	0.352481	−	0.0252100i
$459$	−13.2930			−0.620464
$460$	−10.6790	−	0.979707i	−0.497909	−	0.0456791i
$461$	22.2564			1.03658			0.518292	−	0.855204i	$-0.326568\pi$
$461$	22.2564			1.03658			0.518292	+	0.855204i	$0.326568\pi$
$462$	14.1722	−	1.01361i	0.659349	−	0.0471576i
$463$	−0.112399	+	0.516689i	−0.00522361	+	0.0240126i	−0.979685	−	0.200543i	$-0.935729\pi$
$463$	−0.112399	+	0.516689i	−0.00522361	+	0.0240126i	0.974461	+	0.224556i	$0.0720930\pi$
$464$	4.62333	−	0.664735i	0.214633	−	0.0308595i
$465$	−16.8003	+	31.4464i	−0.779096	+	1.45829i
$466$	0.865007	−	6.01625i	0.0400707	−	0.278698i
$467$	−15.8677	+	29.0595i	−0.734268	+	1.34471i	0.197010	+	0.980402i	$0.436877\pi$
$467$	−15.8677	+	29.0595i	−0.734268	+	1.34471i	−0.931278	+	0.364310i	$0.881305\pi$
$468$	−0.344216	+	0.0748796i	−0.0159114	+	0.00346131i
$469$	−32.1157	−	14.6667i	−1.48296	−	0.677247i
$470$	0.279208	+	0.124443i	0.0128789	+	0.00574013i
$471$	22.7776	−	19.7369i	1.04954	−	0.909428i
$472$	0.437056	−	6.11084i	0.0201171	−	0.281274i
$473$	−23.7843	+	12.9872i	−1.09360	+	0.597152i
$474$	1.91744	−	4.19861i	0.0880709	−	0.192848i
$475$	−17.1715	−	19.1012i	−0.787885	−	0.876422i
$476$	−8.96662	+	2.63284i	−0.410984	+	0.120676i
$477$	0.338669	+	0.452409i	0.0155066	+	0.0207144i
$478$	−8.69330	−	3.24243i	−0.397622	−	0.148305i
$479$	2.24546	+	15.6175i	0.102598	+	0.713583i	0.974579	+	0.224044i	$0.0719259\pi$
$479$	2.24546	+	15.6175i	0.102598	+	0.713583i	−0.871981	+	0.489539i	$0.837165\pi$
$480$	−1.65914	−	3.54698i	−0.0757290	−	0.161897i
$481$	−12.2034	−	10.5743i	−0.556429	−	0.482148i
$482$	17.9204	−	17.9204i	0.816250	−	0.816250i
$483$	−9.76433	−	28.7140i	−0.444292	−	1.30653i
$484$			5.95216i			0.270553i
$485$	−18.7349	−	1.16820i	−0.850707	−	0.0530454i
$486$	0.583615	−	0.375067i	0.0264733	−	0.0170134i
$487$	11.6038	−	15.5009i	0.525820	−	0.702414i	−0.456479	−	0.889734i	$-0.650889\pi$
$487$	11.6038	−	15.5009i	0.525820	−	0.702414i	0.982299	+	0.187321i	$0.0599804\pi$
$488$	3.91773	−	10.5038i	0.177347	−	0.475486i
$489$	24.5427	+	3.52871i	1.10986	+	0.159574i
$490$	10.8867	+	7.99571i	0.491812	+	0.361209i
$491$	−29.0161	−	18.6475i	−1.30948	−	0.841550i	−0.315267	−	0.949003i	$-0.602094\pi$
$491$	−29.0161	−	18.6475i	−1.30948	−	0.841550i	−0.994210	+	0.107453i	$0.965730\pi$
$492$	−7.26004	+	2.70786i	−0.327308	+	0.122080i
$493$	5.79289	+	10.6089i	0.260899	+	0.477800i
$494$	−17.7485	−	20.4828i	−0.798541	−	0.921566i
$495$	−0.280518	+	0.183917i	−0.0126083	+	0.00826643i
$496$	−8.73596	−	2.56511i	−0.392256	−	0.115177i
$497$	−7.61140	−	20.4069i	−0.341418	−	0.915377i
$498$	−1.72021	−	7.90768i	−0.0770845	−	0.354352i
$499$	5.43053	+	18.4947i	0.243104	+	0.827935i	0.987149	+	0.159806i	$0.0510867\pi$
$499$	5.43053	+	18.4947i	0.243104	+	0.827935i	−0.744045	+	0.668130i	$0.767095\pi$
$500$	−5.78481	+	9.56744i	−0.258705	+	0.427869i
$501$	−13.8545	−	30.3371i	−0.618974	−	1.35536i
$502$	6.01558	+	4.50320i	0.268488	+	0.200988i
$503$	21.1684	+	4.60490i	0.943852	+	0.205322i	0.658057	−	0.752968i	$-0.271379\pi$
$503$	21.1684	+	4.60490i	0.943852	+	0.205322i	0.285795	+	0.958291i	$0.407742\pi$
$504$	0.157895	−	0.182220i	0.00703320	−	0.00811674i
$505$	−0.513445	+	3.81813i	−0.0228480	+	0.169904i
$506$	−10.4228	+	2.73241i	−0.463349	+	0.121470i
$507$	18.3713	+	18.3713i	0.815899	+	0.815899i
$508$	−0.0889953	−	1.24432i	−0.00394853	−	0.0552076i
$509$	−16.1664	−	25.1554i	−0.716563	−	1.11499i	−0.988285	−	0.152619i	$-0.951229\pi$
$509$	−16.1664	−	25.1554i	−0.716563	−	1.11499i	0.271722	−	0.962376i	$-0.412407\pi$
$510$	7.09981	−	7.23059i	0.314385	−	0.320176i
$511$	22.0302	−	10.0609i	0.974559	−	0.445066i
$512$	0.800541	−	0.599278i	0.0353793	−	0.0264846i
$513$	23.1596	+	12.6461i	1.02252	+	0.558339i
$514$	−14.5277	+	22.6055i	−0.640789	+	0.997086i
$515$	0.495952	+	2.18372i	0.0218543	+	0.0962260i
$516$	−5.95085	+	20.2667i	−0.261972	+	0.892193i
$517$	0.306361	+	0.0219114i	0.0134737	+	0.000963661i
$518$	11.0241	+	0.788461i	0.484372	+	0.0346430i
$519$	8.77954	−	29.9004i	0.385379	−	1.31248i
$520$	−6.28734	+	9.98244i	−0.275718	+	0.437759i
$521$	7.21703	−	11.2299i	0.316184	−	0.491991i	−0.646392	−	0.763006i	$-0.723723\pi$
$521$	7.21703	−	11.2299i	0.316184	−	0.491991i	0.962575	+	0.271014i	$0.0873591\pi$
$522$	−0.273717	−	0.149461i	−0.0119803	−	0.00654173i
$523$	−8.98694	+	6.72754i	−0.392971	+	0.294175i	−0.777432	−	0.628967i	$-0.783478\pi$
$523$	−8.98694	+	6.72754i	−0.392971	+	0.294175i	0.384461	+	0.923141i	$0.374387\pi$
$524$	9.53053	−	4.35245i	0.416343	−	0.190138i
$525$	−31.3750	−	3.92802i	−1.36932	−	0.171433i
$526$	−8.53670	−	13.2834i	−0.372218	−	0.579182i
$527$	−1.68086	−	23.5016i	−0.0732196	−	1.02374i
$528$	−2.78214	−	2.78214i	−0.121077	−	0.121077i
$529$	11.2837	+	20.0419i	0.490597	+	0.871386i
$530$	18.7574	+	2.52241i	0.814769	+	0.109567i
$531$	−0.267871	+	0.309140i	−0.0116246	+	0.0134155i
$532$	18.1267	+	3.94323i	0.785894	+	0.170961i
$533$	18.6883	+	13.9899i	0.809479	+	0.605968i
$534$	−10.2041	−	22.3439i	−0.441576	−	0.966917i
$535$	−16.5779	+	9.24961i	−0.716725	+	0.399895i
$536$	2.75447	+	9.38085i	0.118975	+	0.405191i
$537$	5.44831	+	25.0455i	0.235112	+	1.08079i
$538$	4.54626	+	12.1890i	0.196003	+	0.525505i
$539$	13.0222	+	3.82366i	0.560905	+	0.164697i
$540$	2.33902	−	11.2454i	0.100655	−	0.483925i
$541$	13.6111	+	15.7080i	0.585187	+	0.675341i	0.968712	−	0.248189i	$-0.0798354\pi$
$541$	13.6111	+	15.7080i	0.585187	+	0.675341i	−0.383525	+	0.923531i	$0.625290\pi$
$542$	7.21216	+	13.2081i	0.309789	+	0.567336i
$543$	16.0221	−	5.97592i	0.687572	−	0.256451i
$544$	2.17702	+	1.39909i	0.0933390	+	0.0599854i
$545$	3.20671	+	20.9444i	0.137360	+	0.897161i
$546$	−33.0256	−	4.74837i	−1.41337	−	0.203211i
$547$	4.22819	−	11.3362i	0.180784	−	0.484701i	−0.814672	−	0.579922i	$-0.803083\pi$
$547$	4.22819	−	11.3362i	0.180784	−	0.484701i	0.995456	+	0.0952208i	$0.0303557\pi$
$548$	−1.22493	+	1.63631i	−0.0523264	+	0.0698999i
$549$	−0.629689	+	0.404677i	−0.0268745	+	0.0172712i
$550$	−2.18716	+	11.0187i	−0.0932607	+	0.469840i
$551$		−	23.9943i		−	1.02219i
$552$	−4.23858	+	7.25053i	−0.180406	+	0.308603i
$553$	6.73031	−	6.73031i	0.286202	−	0.286202i
$554$	16.9401	+	14.6786i	0.719714	+	0.623636i
$555$	−10.8558	+	5.07790i	−0.460802	+	0.215545i
$556$	0.139619	+	0.971074i	0.00592118	+	0.0411827i
$557$	−31.9438	−	11.9144i	−1.35350	−	0.504830i	−0.435066	−	0.900399i	$-0.643275\pi$
$557$	−31.9438	−	11.9144i	−1.35350	−	0.504830i	−0.918437	+	0.395568i	$0.870548\pi$
$558$	0.364305	+	0.486654i	0.0154223	+	0.0206017i
$559$	61.0585	−	17.9284i	2.58250	−	0.758291i
$560$	−0.649534	−	8.04871i	−0.0274478	−	0.340120i
$561$	4.22972	−	9.26179i	0.178579	−	0.391033i
$562$	13.2496	−	7.23485i	0.558902	−	0.305184i
$563$	−1.21035	+	16.9230i	−0.0510104	+	0.713218i	0.906021	+	0.423233i	$0.139105\pi$
$563$	−1.21035	+	16.9230i	−0.0510104	+	0.713218i	−0.957031	+	0.289985i	$0.906350\pi$
$564$	0.180928	−	0.156775i	0.00761846	−	0.00660143i
$565$	−19.5001	+	7.47656i	−0.820374	+	0.314541i
$566$	−19.9828	−	9.12586i	−0.839942	−	0.383588i
$567$	32.4491	−	7.05887i	1.36273	−	0.296445i
$568$	−2.89049	+	5.29354i	−0.121282	+	0.222112i
$569$	−4.65508	+	32.3768i	−0.195151	+	1.35731i	0.622963	+	0.782251i	$0.285929\pi$
$569$	−4.65508	+	32.3768i	−0.195151	+	1.35731i	−0.818114	+	0.575056i	$0.804980\pi$
$570$	−19.2483	+	5.84314i	−0.806223	+	0.244742i
$571$	−18.4786	+	2.65682i	−0.773305	+	0.111184i	−0.517660	−	0.855586i	$-0.673197\pi$
$571$	−18.4786	+	2.65682i	−0.773305	+	0.111184i	−0.255645	+	0.966771i	$0.582288\pi$
$572$	−2.51970	+	11.5829i	−0.105354	+	0.484304i
$573$	18.6488	−	1.33379i	0.779067	−	0.0557200i
$574$	−15.9784			−0.666925
$575$	23.9354	−	1.44842i	0.998174	−	0.0604032i
$576$	−0.0667680			−0.00278200
$577$	−28.0869	+	2.00881i	−1.16927	+	0.0836280i	−0.642437	−	0.766339i	$-0.722076\pi$
$577$	−28.0869	+	2.00881i	−1.16927	+	0.0836280i	−0.526836	+	0.849967i	$0.676622\pi$
$578$	2.19009	−	10.0677i	0.0910957	−	0.418760i
$579$	−32.0257	+	4.60460i	−1.33094	+	0.191360i
$580$	−9.99405	+	3.03386i	−0.414981	+	0.125974i
$581$	2.37493	−	16.5180i	0.0985285	−	0.685281i
$582$	−7.04547	+	12.9028i	−0.292044	+	0.534839i
$583$	18.5820	−	4.04226i	0.769587	−	0.167413i
$584$	−6.10053	−	2.78602i	−0.252442	−	0.115286i
$585$	0.735484	−	0.281994i	0.0304085	−	0.0116590i
$586$	5.60495	−	4.85672i	0.231538	−	0.200629i
$587$	1.60069	−	22.3805i	0.0660675	−	0.923744i	−0.851039	−	0.525102i	$-0.824027\pi$
$587$	1.60069	−	22.3805i	0.0660675	−	0.923744i	0.917107	−	0.398642i	$-0.130518\pi$
$588$	9.28465	−	5.06980i	0.382892	−	0.209075i
$589$	−19.4294	+	42.5445i	−0.800575	+	1.75301i
$590$	1.10194	+	13.6548i	0.0453663	+	0.562158i
$591$	28.4455	−	8.35236i	1.17009	−	0.343570i
$592$	−1.83413	−	2.45011i	−0.0753821	−	0.100699i
$593$	31.1925	+	11.6342i	1.28092	+	0.477760i	0.895533	−	0.444994i	$-0.146794\pi$
$593$	31.1925	+	11.6342i	1.28092	+	0.477760i	0.385390	+	0.922754i	$0.374067\pi$
$594$	−1.64244	−	11.4234i	−0.0673902	−	0.468709i
$595$	18.9280	−	8.85379i	0.775974	−	0.362970i
$596$	−0.913305	−	0.791383i	−0.0374104	−	0.0324163i
$597$	1.66449	−	1.66449i	0.0681231	−	0.0681231i
$598$	25.2802	−	1.06715i	1.03378	−	0.0436391i
$599$			22.5496i			0.921351i	0.887569	+	0.460676i	$0.152393\pi$
$599$			22.5496i			0.921351i	−0.887569	+	0.460676i	$0.847607\pi$
$600$	4.86755	+	7.27847i	0.198717	+	0.297142i
$601$	−31.3782	+	20.1656i	−1.27994	+	0.822570i	−0.990881	−	0.134740i	$-0.956980\pi$
$601$	−31.3782	+	20.1656i	−1.27994	+	0.822570i	−0.289063	+	0.957310i	$0.593344\pi$
$602$	−26.1024	+	34.8687i	−1.06385	+	1.42114i
$603$	0.228124	−	0.611624i	0.00928993	−	0.0249073i
$604$	−1.03416	−	0.148690i	−0.0420795	−	0.00605013i
$605$	−2.01427	−	13.1561i	−0.0818919	−	0.534872i
$606$	2.53819	+	1.63120i	0.103107	+	0.0662628i
$607$	−4.54501	+	1.69520i	−0.184476	+	0.0688062i	−0.440005	−	0.897995i	$-0.645023\pi$
$607$	−4.54501	+	1.69520i	−0.184476	+	0.0688062i	0.255528	+	0.966802i	$0.417751\pi$
$608$	−2.46190	−	4.50863i	−0.0998431	−	0.182849i
$609$	−19.3437	−	22.3238i	−0.783845	−	0.904605i
$610$	−5.10479	+	24.5425i	−0.206687	+	0.993698i
$611$	−0.692043	−	0.203202i	−0.0279971	−	0.00822068i
$612$	−0.0603819	−	0.161890i	−0.00244079	−	0.00654402i
$613$	8.84262	+	40.6489i	0.357150	+	1.64179i	0.708618	+	0.705592i	$0.249319\pi$
$613$	8.84262	+	40.6489i	0.357150	+	1.64179i	−0.351468	+	0.936200i	$0.614317\pi$
$614$	9.60543	+	32.7131i	0.387643	+	1.32019i
$615$	15.1306	−	8.44208i	0.610124	−	0.340418i
$616$	−3.37044	−	7.38022i	−0.135799	−	0.297358i
$617$	18.6181	+	13.9373i	0.749535	+	0.561095i	0.904321	−	0.426853i	$-0.140378\pi$
$617$	18.6181	+	13.9373i	0.749535	+	0.561095i	−0.154786	+	0.987948i	$0.549469\pi$
$618$	1.71369	+	0.372791i	0.0689348	+	0.0149959i
$619$	6.07425	−	7.01005i	0.244145	−	0.281758i	−0.620431	−	0.784261i	$-0.713042\pi$
$619$	6.07425	−	7.01005i	0.244145	−	0.281758i	0.864575	+	0.502504i	$0.167588\pi$
$620$	20.1772	+	2.71335i	0.810338	+	0.108971i
$621$	−22.6980	+	9.57483i	−0.910841	+	0.384225i
$622$	0.970442	+	0.970442i	0.0389112	+	0.0389112i
$623$	−3.61354	−	50.5239i	−0.144773	−	2.02420i
$624$	4.99519	+	7.77267i	0.199968	+	0.311156i
$625$	9.54851	−	23.1047i	0.381940	−	0.924187i
$626$	−13.0953	+	5.98041i	−0.523392	+	0.239025i
$627$	−16.1803	+	12.1124i	−0.646178	+	0.483723i
$628$	−15.1051	−	8.24803i	−0.602761	−	0.329132i
$629$	4.28199	−	6.66291i	0.170734	−	0.265668i
$630$	−0.287332	+	0.456197i	−0.0114476	+	0.0181753i
$631$	8.81062	−	30.0062i	0.350745	−	1.19453i	−0.575562	−	0.817758i	$-0.695217\pi$
$631$	8.81062	−	30.0062i	0.350745	−	1.19453i	0.926307	−	0.376770i	$-0.122965\pi$
$632$	−2.62900	−	0.188030i	−0.104576	−	0.00747943i
$633$	36.6715	+	2.62280i	1.45756	+	0.104247i
$634$	−3.05359	+	10.3996i	−0.121273	+	0.413019i
$635$	0.617797	+	2.72021i	0.0245165	+	0.107948i
$636$	8.01362	−	12.4694i	0.317761	−	0.494445i
$637$	−27.9723	−	15.2740i	−1.10830	−	0.605179i
$638$	−8.40108	+	6.28897i	−0.332602	+	0.248983i
$639$	0.366307	−	0.167287i	0.0144909	−	0.00661776i
$640$	−1.56664	+	1.59550i	−0.0619270	+	0.0630678i
$641$	−2.82868	−	4.40151i	−0.111726	−	0.173849i	0.780888	−	0.624672i	$-0.214767\pi$
$641$	−2.82868	−	4.40151i	−0.111726	−	0.173849i	−0.892614	+	0.450822i	$0.851131\pi$
$642$	1.06063	+	14.8296i	0.0418599	+	0.585277i
$643$	−14.7979	−	14.7979i	−0.583571	−	0.583571i	0.352312	−	0.935883i	$-0.385396\pi$
$643$	−14.7979	−	14.7979i	−0.583571	−	0.583571i	−0.935883	+	0.352312i	$0.885396\pi$
$644$	−13.4143	+	10.9542i	−0.528596	+	0.431656i
$645$	6.29475	−	46.8096i	0.247856	−	1.84313i
$646$	8.70550	−	10.0467i	0.342513	−	0.395281i
$647$	−28.4425	−	6.18729i	−1.11819	−	0.243247i	−0.384763	−	0.923015i	$-0.625717\pi$
$647$	−28.4425	−	6.18729i	−1.11819	−	0.243247i	−0.733427	+	0.679768i	$0.762081\pi$
$648$	−7.36165	−	5.51087i	−0.289193	−	0.216487i
$649$	5.71800	+	12.5207i	0.224451	+	0.491480i
$650$	10.5188	−	24.1920i	0.412582	−	0.948888i
$651$	16.2217	+	55.2461i	0.635780	+	2.16527i
$652$	−3.00966	−	13.8352i	−0.117867	−	0.541828i
$653$	−8.54423	−	22.9080i	−0.334361	−	0.896458i	−0.989960	−	0.141348i	$-0.954856\pi$
$653$	−8.54423	−	22.9080i	−0.334361	−	0.896458i	0.655599	−	0.755110i	$-0.272416\pi$
$654$	15.9220	+	4.67512i	0.622599	+	0.182812i
$655$	−19.5925	+	12.8455i	−0.765544	+	0.501915i
$656$	2.89755	+	3.34395i	0.113130	+	0.130559i
$657$	0.214601	+	0.393012i	0.00837238	+	0.0153329i
$658$	0.462547	−	0.172521i	0.0180319	−	0.00672557i
$659$	−18.1011	−	11.6329i	−0.705119	−	0.453152i	0.138313	−	0.990389i	$-0.455832\pi$
$659$	−18.1011	−	11.6329i	−0.705119	−	0.453152i	−0.843432	+	0.537236i	$0.819468\pi$
$660$	7.09089	+	5.20788i	0.276013	+	0.202717i
$661$	19.0591	+	2.74028i	0.741312	+	0.106585i	0.502616	−	0.864510i	$-0.332371\pi$
$661$	19.0591	+	2.74028i	0.741312	+	0.106585i	0.238696	+	0.971094i	$0.423280\pi$
$662$	−4.87690	+	13.0755i	−0.189546	+	0.508193i
$663$	−14.3287	+	19.1409i	−0.556481	+	0.743372i
$664$	−3.88755	+	2.49838i	−0.150866	+	0.0969558i
$665$	−41.4002	−	2.58149i	−1.60543	−	0.100106i
$666$			0.204347i			0.00791830i
$667$	17.5330	+	13.9423i	0.678879	+	0.539848i
$668$	−13.4665	+	13.4665i	−0.521033	+	0.521033i
$669$	26.9046	+	23.3129i	1.04019	+	0.901330i
$670$	−9.26281	−	19.8025i	−0.357854	−	0.765036i
$671$	3.58455	+	24.9311i	0.138380	+	0.962454i
$672$	−5.92526	−	2.21001i	−0.228572	−	0.0852529i
$673$	8.28196	+	11.0634i	0.319246	+	0.426463i	0.931244	−	0.364397i	$-0.118725\pi$
$673$	8.28196	+	11.0634i	0.319246	+	0.426463i	−0.611998	+	0.790859i	$0.709634\pi$
$674$	−3.67493	+	1.07906i	−0.141553	+	0.0415637i
$675$	−1.36439	+	25.6474i	−0.0525154	+	0.987169i
$676$	6.16307	−	13.4952i	0.237041	−	0.519048i
$677$	−17.0941	+	9.33407i	−0.656979	+	0.358737i	−0.772906	−	0.634520i	$-0.781198\pi$
$677$	−17.0941	+	9.33407i	−0.656979	+	0.358737i	0.115928	+	0.993258i	$0.463016\pi$
$678$	−1.16682	+	16.3142i	−0.0448113	+	0.626544i
$679$	−22.9106	+	19.8522i	−0.879230	+	0.761857i
$680$	−5.28536	−	2.35569i	−0.202684	−	0.0903366i
$681$	31.2211	+	14.2582i	1.19640	+	0.546376i
$682$	19.9886	−	4.34824i	0.765401	−	0.166503i
$683$	15.2367	−	27.9039i	0.583016	−	1.06771i	−0.405140	−	0.914255i	$-0.632777\pi$
$683$	15.2367	−	27.9039i	0.583016	−	1.06771i	0.988155	−	0.153458i	$-0.0490411\pi$
$684$	−0.0488121	+	0.339495i	−0.00186638	+	0.0129809i
$685$	2.15373	−	4.03130i	0.0822898	−	0.154028i
$686$	−3.42886	+	0.492996i	−0.130915	+	0.0188227i
$687$	−2.81520	+	12.9413i	−0.107407	+	0.493740i
$688$	12.0308	−	0.860458i	0.458669	−	0.0328047i
$689$	−44.6563			−1.70127
$690$	6.91492	−	17.4603i	0.263247	−	0.664702i
$691$	−46.4204			−1.76591			−0.882957	−	0.469454i	$-0.844451\pi$
$691$	−46.4204			−1.76591			−0.882957	+	0.469454i	$0.844451\pi$
$692$	−17.7495	+	1.26947i	−0.674735	+	0.0482580i
$693$	−0.115150	+	0.529336i	−0.00437419	+	0.0201078i
$694$	−26.1340	+	3.75750i	−0.992032	+	0.142633i
$695$	−0.637224	−	2.09913i	−0.0241713	−	0.0796245i
$696$	−1.16410	+	8.09647i	−0.0441250	+	0.306896i
$697$	−5.48756	+	10.0497i	−0.207856	+	0.380660i
$698$	19.0190	−	4.13733i	0.719880	−	0.156600i
$699$	9.68223	+	4.42173i	0.366216	+	0.167245i
$700$	4.15944	+	17.5704i	0.157212	+	0.664097i
$701$	−1.89054	+	1.63816i	−0.0714048	+	0.0618726i	−0.689832	−	0.723969i	$-0.742316\pi$
$701$	−1.89054	+	1.63816i	−0.0714048	+	0.0618726i	0.618427	+	0.785842i	$0.287770\pi$
$702$	−1.93338	+	27.0322i	−0.0729709	+	1.02027i
$703$	−13.7989	+	7.53479i	−0.520437	+	0.284180i
$704$	−0.933330	+	2.04371i	−0.0351762	+	0.0770251i
$705$	−0.346854	+	0.407751i	−0.0130633	+	0.0153568i
$706$	27.3782	−	8.03896i	1.03039	−	0.302550i
$707$	3.72852	+	4.98071i	0.140225	+	0.187319i
$708$	10.0523	+	3.74932i	0.377789	+	0.140908i
$709$	−7.00962	−	48.7530i	−0.263252	−	1.83096i	−0.507985	−	0.861366i	$-0.669609\pi$
$709$	−7.00962	−	48.7530i	−0.263252	−	1.83096i	0.244733	−	0.969591i	$-0.421300\pi$
$710$	4.59750	−	12.6786i	0.172541	−	0.475818i
$711$	0.132998	+	0.115243i	0.00498781	+	0.00432196i
$712$	−9.91833	+	9.91833i	−0.371705	+	0.371705i
$713$	−19.7981	−	38.9186i	−0.741444	−	1.45751i
$714$		−	16.3654i		−	0.612461i
$715$	1.64955	−	26.4544i	0.0616897	−	0.989339i
$716$	12.3128	−	7.91294i	0.460150	−	0.295721i
$717$	9.73726	−	13.0075i	0.363645	−	0.485773i
$718$	8.09561	−	21.7052i	0.302125	−	0.810030i
$719$	18.4498	+	2.65268i	0.688062	+	0.0989284i	0.477473	−	0.878646i	$-0.341553\pi$
$719$	18.4498	+	2.65268i	0.688062	+	0.0989284i	0.210589	+	0.977575i	$0.432462\pi$
$720$	0.147578	−	0.0225950i	0.00549991	−	0.000842066i
$721$	3.04236	+	1.95520i	0.113303	+	0.0728156i
$722$	−6.92282	+	2.58208i	−0.257641	+	0.0960951i
$723$	21.2698	+	38.9527i	0.791032	+	1.44867i
$724$	−6.39456	−	7.37971i	−0.237652	−	0.274265i
$725$	21.0633	−	10.0879i	0.782271	−	0.374654i
$726$	−10.0013	−	2.93665i	−0.371183	−	0.108989i
$727$	3.54473	+	9.50379i	0.131467	+	0.352476i	0.985959	−	0.166988i	$-0.0534042\pi$
$727$	3.54473	+	9.50379i	0.131467	+	0.352476i	−0.854492	+	0.519464i	$0.826131\pi$
$728$	4.04992	+	18.6172i	0.150100	+	0.689998i
$729$	−7.43003	−	25.3044i	−0.275186	−	0.937199i
$730$	14.4269	+	4.09349i	0.533963	+	0.151507i
$731$	12.9664	+	28.3925i	0.479580	+	1.05013i
$732$	15.7165	+	11.7652i	0.580898	+	0.434855i
$733$	−8.70986	−	1.89471i	−0.321706	−	0.0699829i	0.0488125	−	0.998808i	$-0.484456\pi$
$733$	−8.70986	−	1.89471i	−0.321706	−	0.0699829i	−0.370518	+	0.928825i	$0.620820\pi$
$734$	−6.22036	+	7.17868i	−0.229598	+	0.264970i
$735$	−18.8063	+	14.3479i	−0.693680	+	0.529229i
$736$	4.72506	+	0.820876i	0.174168	+	0.0302579i
$737$	−15.5324	−	15.5324i	−0.572143	−	0.572143i
$738$	−0.0210755	−	0.294674i	−0.000775801	−	0.0108471i
$739$	9.42070	+	14.6589i	0.346546	+	0.539236i	0.970150	−	0.242504i	$-0.0779688\pi$
$739$	9.42070	+	14.6589i	0.346546	+	0.539236i	−0.623604	+	0.781740i	$0.714332\pi$
$740$	4.88313	+	4.79481i	0.179508	+	0.176261i
$741$	43.1736	−	19.7167i	1.58602	−	0.724311i
$742$	24.4689	−	18.3172i	0.898281	−	0.672444i
$743$	−18.4305	−	10.0638i	−0.676150	−	0.369206i	0.104194	−	0.994557i	$-0.466774\pi$
$743$	−18.4305	−	10.0638i	−0.676150	−	0.369206i	−0.780343	+	0.625351i	$0.784956\pi$
$744$	8.62021	−	13.4133i	0.316032	−	0.491756i
$745$	2.28650	+	1.44013i	0.0837709	+	0.0527623i
$746$	−10.6667	+	36.3274i	−0.390535	+	1.33004i
$747$	0.307758	+	0.0220113i	0.0112603	+	0.000805351i
$748$	−5.79937	−	0.414779i	−0.212046	−	0.0151658i
$749$	−8.63743	+	29.4164i	−0.315605	+	1.07485i
$750$	−13.2219	−	14.4405i	−0.482796	−	0.527291i
$751$	−9.31921	+	14.5010i	−0.340063	+	0.529148i	−0.968598	−	0.248633i	$-0.920019\pi$
$751$	−9.31921	+	14.5010i	−0.340063	+	0.529148i	0.628535	+	0.777781i	$0.283655\pi$
$752$	−0.119984	−	0.0655163i	−0.00437537	−	0.00238914i
$753$	−10.5346	+	7.88610i	−0.383902	+	0.287385i
$754$	22.4165	−	10.2373i	0.816359	−	0.372819i
$755$	2.33614	−	0.0213202i	0.0850210	−	0.000775922i
$756$	−10.0287	−	15.6050i	−0.364742	−	0.567550i
$757$	1.08705	+	15.1989i	0.0395095	+	0.552415i	0.978201	+	0.207658i	$0.0665842\pi$
$757$	1.08705	+	15.1989i	0.0395095	+	0.552415i	−0.938692	+	0.344757i	$0.887961\pi$
$758$	10.7461	+	10.7461i	0.390316	+	0.390316i
$759$	0.551131	−	18.8613i	0.0200048	−	0.684622i
$760$	6.96733	+	9.13234i	0.252732	+	0.331265i
$761$	13.9410	−	16.0888i	0.505360	−	0.583217i	−0.444544	−	0.895757i	$-0.646634\pi$
$761$	13.9410	−	16.0888i	0.505360	−	0.583217i	0.949905	+	0.312540i	$0.101180\pi$
$762$	2.13471	+	0.464378i	0.0773324	+	0.0168226i
$763$	27.3936	+	20.5066i	0.991716	+	0.742389i
$764$	−4.43508	−	9.71148i	−0.160456	−	0.351349i
$765$	0.188248	+	0.337394i	0.00680613	+	0.0121985i
$766$	2.22839	+	7.58919i	0.0805149	+	0.274209i
$767$	−6.87075	−	31.5843i	−0.248089	−	1.14044i
$768$	0.611988	+	1.64080i	0.0220832	+	0.0592074i
$769$	−17.6534	−	5.18351i	−0.636599	−	0.186922i	−0.0525208	−	0.998620i	$-0.516726\pi$
$769$	−17.6534	−	5.18351i	−0.636599	−	0.186922i	−0.584078	+	0.811698i	$0.698544\pi$
$770$	9.94726	+	15.1720i	0.358474	+	0.546761i
$771$	−30.8160	−	35.5636i	−1.10981	−	1.28079i
$772$	8.85446	+	16.2157i	0.318679	+	0.583617i
$773$	1.79980	−	0.671292i	0.0647344	−	0.0241447i	−0.316888	−	0.948463i	$-0.602638\pi$
$773$	1.79980	−	0.671292i	0.0647344	−	0.0241447i	0.381623	+	0.924318i	$0.375365\pi$
$774$	−0.677480	−	0.435390i	−0.0243515	−	0.0156498i
$775$	−45.5162	+	0.830853i	−1.63499	+	0.0298451i
$776$	8.30932	+	1.19470i	0.298287	+	0.0428872i
$777$	−6.76387	+	18.1346i	−0.242652	+	0.650576i
$778$	−11.3511	+	15.1632i	−0.406955	+	0.543628i
$779$	19.1213	−	12.2885i	0.685093	−	0.440282i
$780$	−13.6713	−	15.4896i	−0.489511	−	0.554617i
$781$		−	13.5508i		−	0.484884i
$782$	2.28277	+	12.1991i	0.0816318	+	0.436237i
$783$	−16.9656	+	16.9656i	−0.606302	+	0.606302i
$784$	−4.56528	−	3.95583i	−0.163046	−	0.141280i
$785$	36.1783	+	13.1190i	1.29126	+	0.468237i
$786$	2.61121	+	18.1614i	0.0931388	+	0.647795i
$787$	34.3212	+	12.8011i	1.22342	+	0.456311i	0.876417	−	0.481554i	$-0.159927\pi$
$787$	34.3212	+	12.8011i	1.22342	+	0.456311i	0.347001	+	0.937865i	$0.387200\pi$
$788$	−10.1452	−	13.5524i	−0.361407	−	0.482784i
$789$	26.5316	−	7.79038i	0.944550	−	0.277345i
$790$	5.87455	−	0.474078i	0.209007	−	0.0168669i
$791$	−14.0109	+	30.6796i	−0.498171	+	1.09084i
$792$	0.131661	−	0.0718923i	0.00467837	−	0.00255458i
$793$	4.21951	−	58.9965i	0.149839	−	2.09503i
$794$	−3.82852	+	3.31743i	−0.135869	+	0.117731i
$795$	−13.4928	+	30.2732i	−0.478540	+	1.07368i
$796$	−1.22270	−	0.558391i	−0.0433376	−	0.0197916i
$797$	25.7106	−	5.59300i	0.910716	−	0.198114i	0.267284	−	0.963618i	$-0.413874\pi$
$797$	25.7106	−	5.59300i	0.910716	−	0.198114i	0.643431	+	0.765504i	$0.277510\pi$
$798$	−15.5690	+	28.5125i	−0.551138	+	1.00933i
$799$	0.0503471	−	0.350172i	0.00178115	−	0.0123882i
$800$	2.92284	−	4.05673i	0.103338	−	0.143427i
$801$	0.926998	−	0.133282i	0.0327539	−	0.00470929i
$802$	0.859707	−	3.95201i	0.0303573	−	0.139550i
$803$	15.0296	−	1.07494i	0.530383	−	0.0379337i
$804$	−17.1215			−0.603827
$805$	25.9427	−	28.7517i	0.914359	−	1.01337i
$806$	−48.0365			−1.69201
$807$	−22.7240	+	1.62525i	−0.799922	+	0.0572115i
$808$	0.366226	−	1.68351i	0.0128838	−	0.0592258i
$809$	−5.17281	+	0.743738i	−0.181866	+	0.0261484i	−0.232646	−	0.972561i	$-0.574738\pi$
$809$	−5.17281	+	0.743738i	−0.181866	+	0.0261484i	0.0507798	+	0.998710i	$0.483829\pi$
$810$	18.1365	+	9.68947i	0.637251	+	0.340453i
$811$	0.393712	−	2.73833i	0.0138251	−	0.0961556i	−0.981741	−	0.190225i	$-0.939078\pi$
$811$	0.393712	−	2.73833i	0.0138251	−	0.0961556i	0.995566	+	0.0940690i	$0.0299874\pi$
$812$	−8.08370	+	14.8042i	−0.283682	+	0.519526i
$813$	−25.7516	+	5.60192i	−0.903148	+	0.196468i
$814$	6.25489	+	2.85651i	0.219234	+	0.100121i
$815$	11.3343	+	29.5616i	0.397022	+	1.03550i
$816$	−3.42495	+	2.96774i	−0.119897	+	0.103892i
$817$	4.42017	−	61.8020i	0.154642	−	2.16218i
$818$	−21.7413	+	11.8716i	−0.760166	+	0.415082i
$819$	0.528450	−	1.15714i	0.0184655	−	0.0404339i
$820$	−7.53612	−	6.41062i	−0.263173	−	0.223868i
$821$	−17.7675	+	5.21702i	−0.620092	+	0.182075i	−0.576664	−	0.816981i	$-0.695646\pi$
$821$	−17.7675	+	5.21702i	−0.620092	+	0.182075i	−0.0434274	+	0.999057i	$0.513828\pi$
$822$	−2.14512	−	2.86555i	−0.0748197	−	0.0999474i
$823$	−14.6973	−	5.48181i	−0.512316	−	0.191084i	0.0799922	−	0.996795i	$-0.474510\pi$
$823$	−14.6973	−	5.48181i	−0.512316	−	0.191084i	−0.592308	+	0.805712i	$0.701783\pi$
$824$	−0.142522	−	0.991264i	−0.00496500	−	0.0345323i
$825$	−17.4355	−	9.11141i	−0.607026	−	0.317219i
$826$	16.7201	+	14.4880i	0.581765	+	0.504103i
$827$	6.52483	−	6.52483i	0.226891	−	0.226891i	−0.584502	−	0.811392i	$-0.698710\pi$
$827$	6.52483	−	6.52483i	0.226891	−	0.226891i	0.811392	+	0.584502i	$0.198710\pi$
$828$	−0.219711	−	0.232938i	−0.00763550	−	0.00809515i
$829$			22.8591i			0.793928i	0.917834	+	0.396964i	$0.129936\pi$
$829$			22.8591i			0.793928i	−0.917834	+	0.396964i	$0.870064\pi$
$830$	7.74722	−	6.83778i	0.268910	−	0.237343i
$831$	−33.0221	+	21.2220i	−1.14552	+	0.736183i
$832$	3.16178	−	4.22364i	0.109615	−	0.146428i
$833$	5.46296	−	14.6468i	0.189280	−	0.507480i
$834$	−1.70056	−	0.244504i	−0.0588857	−	0.00846649i
$835$	25.2079	−	34.3223i	0.872354	−	1.18777i
$836$	9.70932	+	6.23980i	0.335804	+	0.215808i
$837$	43.8199	−	16.3440i	1.51464	−	0.564931i
$838$	−12.1176	−	22.1918i	−0.418597	−	0.766602i
$839$	22.2510	+	25.6791i	0.768191	+	0.886540i	0.996198	−	0.0871196i	$-0.0277662\pi$
$839$	22.2510	+	25.6791i	0.768191	+	0.886540i	−0.228007	+	0.973660i	$0.573221\pi$
$840$	13.8446	+	2.87964i	0.477683	+	0.0993569i
$841$	−6.89196	−	2.02366i	−0.237654	−	0.0697814i
$842$	−7.04565	−	18.8901i	−0.242809	−	0.650997i
$843$	5.61955	+	25.8326i	0.193547	+	0.889723i
$844$	−5.91471	−	20.1437i	−0.203593	−	0.693373i
$845$	−9.05538	+	31.9144i	−0.311514	+	1.09789i
$846$	0.00379174	+	0.00830276i	0.000130363	+	0.000285455i
$847$	−17.2072	−	12.8811i	−0.591245	−	0.442600i
$848$	−8.27064	−	1.79917i	−0.284015	−	0.0617837i
$849$	25.1931	−	29.0743i	0.864624	−	0.997829i
$850$	12.4795	+	3.41819i	0.428043	+	0.117243i
$851$	2.51234	−	14.4613i	0.0861220	−	0.495728i
$852$	−7.46855	−	7.46855i	−0.255868	−	0.255868i
$853$	1.17899	+	16.4844i	0.0403678	+	0.564416i	0.976881	+	0.213784i	$0.0685787\pi$
$853$	1.17899	+	16.4844i	0.0403678	+	0.564416i	−0.936513	+	0.350632i	$0.885967\pi$
$854$	21.8872	+	34.0572i	0.748966	+	1.16541i
$855$	−0.00699899	−	0.766909i	−0.000239361	−	0.0262277i
$856$	7.72258	−	3.52678i	0.263952	−	0.120543i
$857$	27.8196	−	20.8255i	0.950300	−	0.711385i	−0.00715352	−	0.999974i	$-0.502277\pi$
$857$	27.8196	−	20.8255i	0.950300	−	0.711385i	0.957453	+	0.288589i	$0.0931861\pi$
$858$	−18.2193	−	9.94850i	−0.621997	−	0.339636i
$859$	0.693862	−	1.07967i	0.0236743	−	0.0368379i	−0.829215	−	0.558930i	$-0.811212\pi$
$859$	0.693862	−	1.07967i	0.0236743	−	0.0368379i	0.852889	+	0.522092i	$0.174848\pi$
$860$	−26.3006	+	5.97322i	−0.896842	+	0.203685i
$861$	7.88335	−	26.8482i	0.268664	−	0.914985i
$862$	0.934047	+	0.0668044i	0.0318138	+	0.00227537i
$863$	6.24941	+	0.446967i	0.212733	+	0.0152149i	0.177299	−	0.984157i	$-0.443264\pi$
$863$	6.24941	+	0.446967i	0.212733	+	0.0152149i	0.0354339	+	0.999372i	$0.488719\pi$
$864$	−1.44718	+	4.92866i	−0.0492342	+	0.167676i
$865$	38.8024	−	8.81255i	1.31932	−	0.299636i
$866$	8.12221	−	12.6384i	0.276004	−	0.429471i
$867$	15.8360	+	8.64711i	0.537819	+	0.293671i
$868$	26.3211	−	19.7037i	0.893395	−	0.668787i
$869$	5.38663	−	2.45999i	0.182729	−	0.0834496i
$870$	−0.166916	−	18.2897i	−0.00565898	−	0.620078i
$871$	27.8877	+	43.3941i	0.944938	+	1.47035i
$872$	−0.675994	−	9.45164i	−0.0228921	−	0.320073i
$873$	−0.396334	−	0.396334i	−0.0134139	−	0.0134139i
$874$	7.62826	−	23.4254i	0.258030	−	0.792376i
$875$	−15.1397	−	37.4284i	−0.511814	−	1.26531i
$876$	7.69115	−	8.87606i	0.259860	−	0.299894i
$877$	−35.0531	−	7.62532i	−1.18366	−	0.257489i	−0.422687	−	0.906276i	$-0.638913\pi$
$877$	−35.0531	−	7.62532i	−1.18366	−	0.257489i	−0.760970	+	0.648787i	$0.775277\pi$
$878$	6.58294	+	4.92793i	0.222163	+	0.166309i
$879$	5.39531	+	11.8141i	0.181979	+	0.398479i
$880$	1.37134	−	4.83308i	0.0462278	−	0.162923i
$881$	4.38210	+	14.9240i	0.147637	+	0.502804i	0.999790	−	0.0204879i	$-0.00652194\pi$
$881$	4.38210	+	14.9240i	0.147637	+	0.502804i	−0.852154	+	0.523292i	$0.824704\pi$
$882$	0.0857333	+	0.394110i	0.00288679	+	0.0132704i
$883$	1.93254	+	5.18134i	0.0650352	+	0.174366i	0.965402	−	0.260765i	$-0.0839748\pi$
$883$	1.93254	+	5.18134i	0.0650352	+	0.174366i	−0.900367	+	0.435131i	$0.856702\pi$
$884$	13.1003	+	3.84659i	0.440610	+	0.129375i
$885$	−23.4875	−	4.88535i	−0.789525	−	0.164219i
$886$	3.57618	+	4.12713i	0.120144	+	0.138654i
$887$	3.00649	+	5.50598i	0.100948	+	0.184873i	0.923272	−	0.384147i	$-0.125505\pi$
$887$	3.00649	+	5.50598i	0.100948	+	0.184873i	−0.822324	+	0.569020i	$0.807323\pi$
$888$	5.02178	−	1.87303i	0.168520	−	0.0628547i
$889$	3.78980	+	2.43556i	0.127106	+	0.0816860i
$890$	18.5661	−	25.2791i	0.622338	−	0.847357i
$891$	20.4504	+	2.94032i	0.685114	+	0.0985045i
$892$	7.10412	−	19.0469i	0.237863	−	0.637737i
$893$	−0.420848	+	0.562187i	−0.0140831	+	0.0188129i
$894$	1.78035	−	1.14416i	0.0595438	−	0.0382665i
$895$	−24.5373	+	21.6568i	−0.820190	+	0.723909i
$896$			3.61119i			0.120642i
$897$	−10.6795	+	43.0044i	−0.356578	+	1.43587i
$898$	−21.9227	+	21.9227i	−0.731571	+	0.731571i
$899$	−32.1399	−	27.8494i	−1.07193	−	0.928830i
$900$	−0.318547	+	0.0998840i	−0.0106182	+	0.00332947i
$901$	−3.11721	−	21.6806i	−0.103849	−	0.722287i
$902$	−9.31433	−	3.47406i	−0.310133	−	0.115674i
$903$	−45.7110	−	61.0628i	−1.52117	−	2.03204i
$904$	8.96139	−	2.63130i	0.298051	−	0.0875158i
$905$	16.6313	+	14.1475i	0.552844	+	0.470278i
$906$	0.760073	−	1.66433i	0.0252517	−	0.0552936i
$907$	−36.5326	+	19.9483i	−1.21304	+	0.662372i	−0.952925	−	0.303205i	$-0.901943\pi$
$907$	−36.5326	+	19.9483i	−1.21304	+	0.662372i	−0.260118	+	0.965577i	$0.583762\pi$
$908$	1.39820	−	19.5494i	0.0464010	−	0.648771i
$909$	−0.0869367	+	0.0753311i	−0.00288351	+	0.00249857i
$910$	−15.2518	−	39.7792i	−0.505593	−	1.31867i
$911$	37.0109	+	16.9023i	1.22623	+	0.559999i	0.919985	−	0.391954i	$-0.128201\pi$
$911$	37.0109	+	16.9023i	1.22623	+	0.559999i	0.306242	+	0.951954i	$0.400928\pi$
$912$	8.79041	−	1.91224i	0.291080	−	0.0633205i
$913$	4.97580	−	9.11250i	0.164675	−	0.301580i
$914$	−3.53850	+	24.6108i	−0.117043	+	0.814053i
$915$	−38.7198	−	20.6862i	−1.28004	−	0.683864i
$916$	7.48572	−	1.07628i	0.247335	−	0.0355614i
$917$	−8.04257	+	36.9711i	−0.265589	+	1.22089i
$918$	−13.2591	+	0.948311i	−0.437616	+	0.0312989i
$919$	24.2774			0.800837			0.400419	−	0.916332i	$-0.368865\pi$
$919$	24.2774			0.800837			0.400419	+	0.916332i	$0.368865\pi$
$920$	−10.7216	−	0.215382i	−0.353482	−	0.00710095i
$921$	−59.7063			−1.96739
$922$	22.1997	−	1.58775i	0.731108	−	0.0522899i
$923$	−6.76404	+	31.0938i	−0.222641	+	1.02346i
$924$	14.0638	−	2.02206i	0.462663	−	0.0665210i
$925$	−12.4159	−	8.94552i	−0.408231	−	0.294127i
$926$	−0.0752522	+	0.523391i	−0.00247294	+	0.0171997i
$927$	−0.0320451	+	0.0586863i	−0.00105250	+	0.00192751i
$928$	4.56413	−	0.992866i	0.149825	−	0.0325924i
$929$	−31.2902	−	14.2897i	−1.02660	−	0.468831i	−0.170342	−	0.985385i	$-0.554487\pi$
$929$	−31.2902	−	14.2897i	−1.02660	−	0.468831i	−0.856255	+	0.516554i	$0.827215\pi$
$930$	−14.5141	+	32.5648i	−0.475938	+	1.06784i
$931$	−23.4518	+	20.3211i	−0.768601	+	0.665997i
$932$	0.433608	−	6.06263i	0.0142033	−	0.198588i
$933$	−2.10941	+	1.15182i	−0.0690589	+	0.0377090i
$934$	−13.7542	+	30.1174i	−0.450050	+	0.985472i
$935$	12.9588	−	1.04578i	0.423798	−	0.0342006i
$936$	−0.337997	+	0.0992449i	−0.0110478	+	0.00324392i
$937$	−5.71997	−	7.64098i	−0.186863	−	0.249620i	0.697320	−	0.716760i	$-0.254375\pi$
$937$	−5.71997	−	7.64098i	−0.186863	−	0.249620i	−0.884184	+	0.467140i	$0.845285\pi$
$938$	−33.0802	−	12.3383i	−1.08011	−	0.402858i
$939$	−3.58789	−	24.9543i	−0.117086	−	0.814354i
$940$	0.287374	+	0.104208i	0.00937311	+	0.00339888i
$941$	26.9422	+	23.3455i	0.878291	+	0.761043i	0.972105	−	0.234547i	$-0.0753605\pi$
$941$	26.9422	+	23.3455i	0.878291	+	0.761043i	−0.0938143	+	0.995590i	$0.529906\pi$
$942$	21.3115	−	21.3115i	0.694367	−	0.694367i
$943$	−2.13138	+	21.1127i	−0.0694074	+	0.687525i
$944$		−	6.12645i		−	0.199399i
$945$	27.4476	+	31.0982i	0.892869	+	1.01162i
$946$	−22.7972	+	14.6509i	−0.741201	+	0.476341i
$947$	24.8821	−	33.2386i	0.808559	−	1.08011i	−0.186659	−	0.982425i	$-0.559766\pi$
$947$	24.8821	−	33.2386i	0.808559	−	1.08011i	0.995218	−	0.0976833i	$-0.0311432\pi$
$948$	1.61303	−	4.32470i	0.0523887	−	0.140460i
$949$	−35.0237	−	5.03565i	−1.13692	−	0.163464i
$950$	−18.4905	−	17.8275i	−0.599910	−	0.578401i
$951$	−15.9676	−	10.2618i	−0.517786	−	0.332761i
$952$	−8.75595	+	3.26580i	−0.283782	+	0.105845i
$953$	−15.8473	−	29.0222i	−0.513345	−	0.940121i	−0.997863	−	0.0653399i	$-0.979187\pi$
$953$	−15.8473	−	29.0222i	−0.513345	−	0.940121i	0.484518	−	0.874781i	$-0.338995\pi$
$954$	0.370081	+	0.427096i	0.0119818	+	0.0138277i
$955$	13.0894	+	19.9645i	0.423562	+	0.646036i
$956$	−8.90246	−	2.61400i	−0.287926	−	0.0845428i
$957$	−6.42236	−	17.2190i	−0.207605	−	0.556611i
$958$	3.35388	+	15.4175i	0.108359	+	0.498118i
$959$	−2.07956	−	7.08232i	−0.0671524	−	0.228700i
$960$	−1.90795	−	3.41959i	−0.0615788	−	0.110367i
$961$	21.5587	+	47.2069i	0.695441	+	1.52280i
$962$	−12.9267	−	9.67681i	−0.416774	−	0.311993i
$963$	−0.553891	−	0.120492i	−0.0178489	−	0.00388279i
$964$	16.5963	−	19.1531i	0.534530	−	0.616881i
$965$	−25.0587	−	32.8454i	−0.806668	−	1.05733i
$966$	−11.7879	−	27.9443i	−0.379269	−	0.899092i
$967$	4.45222	+	4.45222i	0.143174	+	0.143174i	0.775061	−	0.631887i	$-0.217719\pi$
$967$	4.45222	+	4.45222i	0.143174	+	0.143174i	−0.631887	+	0.775061i	$0.717719\pi$
$968$	0.424622	+	5.93699i	0.0136479	+	0.190822i
$969$	12.5862	+	19.5845i	0.404326	+	0.629144i
$970$	−18.7705	+	0.171304i	−0.602684	+	0.00550024i
$971$	14.2439	−	6.50495i	0.457107	−	0.208754i	−0.173535	−	0.984828i	$-0.555519\pi$
$971$	14.2439	−	6.50495i	0.457107	−	0.208754i	0.630642	+	0.776074i	$0.282792\pi$
$972$	0.555372	−	0.415746i	0.0178136	−	0.0133351i
$973$	−3.10944	−	1.69788i	−0.0996841	−	0.0544316i
$974$	10.4685	−	16.2892i	0.335431	−	0.521941i
$975$	35.4597	+	29.6103i	1.13562	+	0.948290i
$976$	3.15841	−	10.7566i	0.101098	−	0.344309i
$977$	32.0489	+	2.29218i	1.02533	+	0.0733334i	0.573862	−	0.818952i	$-0.305445\pi$
$977$	32.0489	+	2.29218i	1.02533	+	0.0733334i	0.451472	+	0.892285i	$0.350899\pi$
$978$	24.7319	+	1.76886i	0.790839	+	0.0565619i
$979$	8.87858	−	30.2377i	0.283761	−	0.966400i
$980$	11.4294	+	7.19869i	0.365098	+	0.229954i
$981$	−0.342052	+	0.532243i	−0.0109209	+	0.0169932i
$982$	−30.2724	−	16.5300i	−0.966032	−	0.527494i
$983$	15.7938	−	11.8231i	0.503745	−	0.377099i	−0.316971	−	0.948435i	$-0.602666\pi$
$983$	15.7938	−	11.8231i	0.503745	−	0.377099i	0.820716	+	0.571336i	$0.193575\pi$
$984$	−7.04837	+	3.21888i	−0.224694	+	0.102614i
$985$	27.0103	+	26.5217i	0.860619	+	0.845053i
$986$	6.53496	+	10.1686i	0.208116	+	0.323834i
$987$	0.0616748	+	0.862327i	0.00196313	+	0.0274482i
$988$	−19.1645	−	19.1645i	−0.609703	−	0.609703i
$989$	42.5912	+	39.1411i	1.35432	+	1.24461i
$990$	−0.266682	+	0.203460i	−0.00847573	+	0.00646638i
$991$	−21.5167	+	24.8316i	−0.683500	+	0.788801i	−0.986425	−	0.164213i	$-0.947492\pi$
$991$	−21.5167	+	24.8316i	−0.683500	+	0.788801i	0.302925	+	0.953015i	$0.402037\pi$
$992$	−8.89669	−	1.93536i	−0.282470	−	0.0614476i
$993$	−19.5644	−	14.6457i	−0.620856	−	0.464767i
$994$	−9.04782	−	19.8120i	−0.286979	−	0.628397i
$995$	2.89152	+	0.820441i	0.0916675	+	0.0260097i
$996$	−2.27996	−	7.76482i	−0.0722432	−	0.246038i
$997$	−7.72996	−	35.5341i	−0.244810	−	1.12538i	−0.921279	−	0.388903i	$-0.872854\pi$
$997$	−7.72996	−	35.5341i	−0.244810	−	1.12538i	0.676468	−	0.736472i	$-0.263510\pi$
$998$	6.73608	+	18.0601i	0.213227	+	0.571684i
$999$	15.0845	+	4.42920i	0.477251	+	0.140134i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.l.a.7.8	✓	240
5.3	odd	4	inner	230.2.l.a.53.2	yes	240
23.10	odd	22	inner	230.2.l.a.217.2	yes	240
115.33	even	44	inner	230.2.l.a.33.8	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.7.8	✓	240	1.1	even	1	trivial
230.2.l.a.33.8	yes	240	115.33	even	44	inner
230.2.l.a.53.2	yes	240	5.3	odd	4	inner
230.2.l.a.217.2	yes	240	23.10	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.997452 - 0.0713392i) q^{2} +(-0.372248 + 1.71120i) q^{3} +(0.989821 - 0.142315i) q^{4} +(-2.13965 + 0.649526i) q^{5} +(-0.249224 + 1.73339i) q^{6} +(-1.73066 + 3.16947i) q^{7} +(0.977147 - 0.212565i) q^{8} +(-0.0607343 - 0.0277364i) q^{9} +(-2.08786 + 0.800513i) q^{10} +(-1.69797 + 1.47130i) q^{11} +(-0.124931 + 1.74676i) q^{12} +(4.63061 - 2.52851i) q^{13} +(-1.50014 + 3.28486i) q^{14} +(-0.314986 - 3.90316i) q^{15} +(0.959493 - 0.281733i) q^{16} +(1.55083 + 2.07167i) q^{17} +(-0.0625582 - 0.0233330i) q^{18} +(-0.731070 - 5.08470i) q^{19} +(-2.02544 + 0.947420i) q^{20} +(-4.77935 - 4.14133i) q^{21} +(-1.58869 + 1.58869i) q^{22} +(4.14027 + 2.42036i) q^{23} +1.75122i q^{24} +(4.15623 - 2.77952i) q^{25} +(4.43844 - 2.85241i) q^{26} +(-3.07833 + 4.11217i) q^{27} +(-1.26198 + 3.38351i) q^{28} +(4.62333 + 0.664735i) q^{29} +(-0.592631 - 3.87074i) q^{30} +(-7.65941 - 4.92241i) q^{31} +(0.936950 - 0.349464i) q^{32} +(-1.88562 - 3.45326i) q^{33} +(1.69467 + 1.95575i) q^{34} +(1.64436 - 7.90568i) q^{35} +(-0.0640634 - 0.0188107i) q^{36} +(-1.06956 - 2.86759i) q^{37} +(-1.09195 - 5.01960i) q^{38} +(2.60304 + 8.86513i) q^{39} +(-1.95269 + 1.08950i) q^{40} +(1.83808 + 4.02483i) q^{41} +(-5.06262 - 3.78983i) q^{42} +(11.7859 + 2.56386i) q^{43} +(-1.47130 + 1.69797i) q^{44} +(0.147966 + 0.0198978i) q^{45} +(4.30239 + 2.11883i) q^{46} +(-0.0966659 - 0.0966659i) q^{47} +(0.124931 + 1.74676i) q^{48} +(-3.26586 - 5.08178i) q^{49} +(3.94735 - 3.06894i) q^{50} +(-4.12232 + 1.88260i) q^{51} +(4.22364 - 3.16178i) q^{52} +(-7.42874 - 4.05640i) q^{53} +(-2.77713 + 4.32129i) q^{54} +(2.67742 - 4.25095i) q^{55} +(-1.01739 + 3.46492i) q^{56} +(8.97308 + 0.641767i) q^{57} +(4.65898 + 0.333216i) q^{58} +(1.72602 - 5.87829i) q^{59} +(-0.867257 - 3.81860i) q^{60} +(6.06094 - 9.43101i) q^{61} +(-7.99106 - 4.36345i) q^{62} +(0.193020 - 0.144493i) q^{63} +(0.909632 - 0.415415i) q^{64} +(-8.26558 + 8.41783i) q^{65} +(-2.12717 - 3.30994i) q^{66} +(0.697475 + 9.75197i) q^{67} +(1.82987 + 1.82987i) q^{68} +(-5.68292 + 6.18385i) q^{69} +(1.07619 - 8.00284i) q^{70} +(-3.94966 + 4.55815i) q^{71} +(-0.0652421 - 0.0141926i) q^{72} +(-5.36891 - 4.01911i) q^{73} +(-1.27140 - 2.78398i) q^{74} +(3.20916 + 8.14681i) q^{75} +(-1.44726 - 4.92891i) q^{76} +(-1.72463 - 7.92800i) q^{77} +(3.22884 + 8.65685i) q^{78} +(-2.52895 - 0.742567i) q^{79} +(-1.86999 + 1.22603i) q^{80} +(-6.02200 - 6.94976i) q^{81} +(2.12053 + 3.88345i) q^{82} +(-4.32977 + 1.61492i) q^{83} +(-5.32008 - 3.41901i) q^{84} +(-4.66384 - 3.42534i) q^{85} +(11.9387 + 1.71653i) q^{86} +(-2.85852 + 7.66399i) q^{87} +(-1.34642 + 1.79861i) q^{88} +(-11.8000 + 7.58338i) q^{89} +(0.149008 + 0.00929133i) q^{90} +19.0526i q^{91} +(4.44258 + 1.80650i) q^{92} +(11.2744 - 11.2744i) q^{93} +(-0.103316 - 0.0895236i) q^{94} +(4.86689 + 10.4047i) q^{95} +(0.249224 + 1.73339i) q^{96} +(7.86547 + 2.93367i) q^{97} +(-3.62007 - 4.83585i) q^{98} +(0.143934 - 0.0422628i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) \) 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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