LMFDB - Embedded newform 273.2.u.c.62.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(62,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 5]))

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

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

chi := DirichletCharacter("273.62");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.u (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			62.12
Character	$\chi$	$=$	273.62
Dual form			273.2.u.c.251.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.584057 - 1.01162i) q^{2} +(0.340045 + 1.69834i) q^{3} +(0.317754 - 0.550366i) q^{4} -3.55045i q^{5} +(1.51947 - 1.33593i) q^{6} +(-2.64534 - 0.0464413i) q^{7} -3.07858 q^{8} +(-2.76874 + 1.15503i) q^{9} +O(q^{10})$	\(q+(-0.584057 - 1.01162i) q^{2} +(0.340045 + 1.69834i) q^{3} +(0.317754 - 0.550366i) q^{4} -3.55045i q^{5} +(1.51947 - 1.33593i) q^{6} +(-2.64534 - 0.0464413i) q^{7} -3.07858 q^{8} +(-2.76874 + 1.15503i) q^{9} +(-3.59170 + 2.07367i) q^{10} +(-2.54090 - 4.40096i) q^{11} +(1.04276 + 0.352506i) q^{12} +(3.23163 + 1.59893i) q^{13} +(1.49805 + 2.70320i) q^{14} +(6.02988 - 1.20731i) q^{15} +(1.16256 + 2.01361i) q^{16} +(-1.08363 + 1.87690i) q^{17} +(2.78555 + 2.12630i) q^{18} +(1.43850 - 2.49155i) q^{19} +(-1.95405 - 1.12817i) q^{20} +(-0.820663 - 4.50849i) q^{21} +(-2.96806 + 5.14083i) q^{22} +(2.33890 - 1.35037i) q^{23} +(-1.04685 - 5.22848i) q^{24} -7.60570 q^{25} +(-0.269957 - 4.20304i) q^{26} +(-2.90313 - 4.30951i) q^{27} +(-0.866128 + 1.44115i) q^{28} +(6.51871 - 3.76358i) q^{29} +(-4.74314 - 5.39479i) q^{30} -3.58776 q^{31} +(-1.72058 + 2.98012i) q^{32} +(6.61033 - 5.81184i) q^{33} +2.53160 q^{34} +(-0.164887 + 9.39216i) q^{35} +(-0.244091 + 1.89083i) q^{36} +(2.53568 - 1.46398i) q^{37} -3.36066 q^{38} +(-1.61662 + 6.03212i) q^{39} +10.9303i q^{40} +(5.45458 - 3.14920i) q^{41} +(-4.08155 + 3.46342i) q^{42} +(4.48749 - 7.77256i) q^{43} -3.22952 q^{44} +(4.10086 + 9.83027i) q^{45} +(-2.73210 - 1.57738i) q^{46} +10.3146i q^{47} +(-3.02448 + 2.65914i) q^{48} +(6.99569 + 0.245706i) q^{49} +(4.44217 + 7.69406i) q^{50} +(-3.55610 - 1.20214i) q^{51} +(1.90686 - 1.27051i) q^{52} -1.79048i q^{53} +(-2.66398 + 5.45385i) q^{54} +(-15.6254 + 9.02133i) q^{55} +(8.14389 + 0.142973i) q^{56} +(4.72066 + 1.59582i) q^{57} +(-7.61460 - 4.39629i) q^{58} +(-4.23466 - 2.44488i) q^{59} +(1.25156 - 3.70227i) q^{60} +(0.145945 + 0.0842615i) q^{61} +(2.09546 + 3.62944i) q^{62} +(7.37791 - 2.92686i) q^{63} +8.66989 q^{64} +(5.67691 - 11.4737i) q^{65} +(-9.74017 - 3.29267i) q^{66} +(3.78238 - 2.18376i) q^{67} +(0.688654 + 1.19278i) q^{68} +(3.08871 + 3.51307i) q^{69} +(9.59758 - 5.31876i) q^{70} +(-5.26351 + 9.11667i) q^{71} +(8.52377 - 3.55584i) q^{72} +10.7603 q^{73} +(-2.96197 - 1.71009i) q^{74} +(-2.58628 - 12.9171i) q^{75} +(-0.914176 - 1.58340i) q^{76} +(6.51716 + 11.7601i) q^{77} +(7.04640 - 1.88770i) q^{78} -4.68895 q^{79} +(7.14922 - 4.12760i) q^{80} +(6.33183 - 6.39593i) q^{81} +(-6.37157 - 3.67863i) q^{82} +0.468856i q^{83} +(-2.74209 - 0.980927i) q^{84} +(6.66384 + 3.84737i) q^{85} -10.4838 q^{86} +(8.60850 + 9.79122i) q^{87} +(7.82234 + 13.5487i) q^{88} +(-5.64141 + 3.25707i) q^{89} +(7.54933 - 9.88995i) q^{90} +(-8.47452 - 4.37979i) q^{91} -1.71634i q^{92} +(-1.22000 - 6.09325i) q^{93} +(10.4344 - 6.02431i) q^{94} +(-8.84612 - 5.10731i) q^{95} +(-5.64635 - 1.90875i) q^{96} +(-4.02073 + 6.96410i) q^{97} +(-3.83732 - 7.22046i) q^{98} +(12.1183 + 9.25031i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 40 q^{4} - 6 q^{9}+O(q^{10}) $ 64 * q - 40 * q^4 - 6 * q^9	$ 64 q - 40 q^{4} - 6 q^{9} + 18 q^{15} - 32 q^{16} + 24 q^{22} - 80 q^{25} + 12 q^{28} + 20 q^{30} + 50 q^{36} - 36 q^{37} - 60 q^{39} + 48 q^{43} - 84 q^{46} - 16 q^{49} + 52 q^{51} - 48 q^{58} - 36 q^{63} + 176 q^{64} + 60 q^{67} - 66 q^{72} + 166 q^{78} - 104 q^{79} - 30 q^{81} + 60 q^{84} + 132 q^{85} - 8 q^{91} - 162 q^{93}+O(q^{100}) $ 64 * q - 40 * q^4 - 6 * q^9 + 18 * q^15 - 32 * q^16 + 24 * q^22 - 80 * q^25 + 12 * q^28 + 20 * q^30 + 50 * q^36 - 36 * q^37 - 60 * q^39 + 48 * q^43 - 84 * q^46 - 16 * q^49 + 52 * q^51 - 48 * q^58 - 36 * q^63 + 176 * q^64 + 60 * q^67 - 66 * q^72 + 166 * q^78 - 104 * q^79 - 30 * q^81 + 60 * q^84 + 132 * q^85 - 8 * q^91 - 162 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−0.584057	−	1.01162i	−0.412991	−	0.715321i	0.582224	−	0.813028i	$-0.302183\pi$
$2$	−0.584057	−	1.01162i	−0.412991	−	0.715321i	−0.995215	+	0.0977069i	$0.968849\pi$
$3$	0.340045	+	1.69834i	0.196325	+	0.980539i
$3$	0.340045	+	1.69834i	0.196325	+	0.980539i
$4$	0.317754	−	0.550366i	0.158877	−	0.275183i
$5$		−	3.55045i		−	1.58781i	−0.608042	−	0.793905i	$-0.708045\pi$
$5$		−	3.55045i		−	1.58781i	0.608042	−	0.793905i	$-0.291955\pi$
$6$	1.51947	−	1.33593i	0.620320	−	0.545389i
$7$	−2.64534	−	0.0464413i	−0.999846	−	0.0175531i
$7$	−2.64534	−	0.0464413i	−0.999846	−	0.0175531i
$8$	−3.07858			−1.08844
$9$	−2.76874	+	1.15503i	−0.922913	+	0.385009i
$10$	−3.59170	+	2.07367i	−1.13579	+	0.655751i
$11$	−2.54090	−	4.40096i	−0.766109	−	1.32694i	−0.939658	−	0.342115i	$-0.888857\pi$
$11$	−2.54090	−	4.40096i	−0.766109	−	1.32694i	0.173549	−	0.984825i	$-0.444477\pi$
$12$	1.04276	+	0.352506i	0.301019	+	0.101760i
$13$	3.23163	+	1.59893i	0.896293	+	0.443462i
$13$	3.23163	+	1.59893i	0.896293	+	0.443462i
$14$	1.49805	+	2.70320i	0.400371	+	0.722460i
$15$	6.02988	−	1.20731i	1.55691	−	0.311727i
$16$	1.16256	+	2.01361i	0.290639	+	0.503402i
$17$	−1.08363	+	1.87690i	−0.262818	+	0.455215i	−0.966990	−	0.254815i	$-0.917985\pi$
$17$	−1.08363	+	1.87690i	−0.262818	+	0.455215i	0.704171	+	0.710030i	$0.251319\pi$
$18$	2.78555	+	2.12630i	0.656560	+	0.501174i
$19$	1.43850	−	2.49155i	0.330014	−	0.571600i	−0.652501	−	0.757788i	$-0.726280\pi$
$19$	1.43850	−	2.49155i	0.330014	−	0.571600i	0.982514	+	0.186188i	$0.0596133\pi$
$20$	−1.95405	−	1.12817i	−0.436938	−	0.252266i
$21$	−0.820663	−	4.50849i	−0.179083	−	0.983834i
$22$	−2.96806	+	5.14083i	−0.632792	+	1.09603i
$23$	2.33890	−	1.35037i	0.487695	−	0.281571i	−0.235923	−	0.971772i	$-0.575811\pi$
$23$	2.33890	−	1.35037i	0.487695	−	0.281571i	0.723618	+	0.690201i	$0.242478\pi$
$24$	−1.04685	−	5.22848i	−0.213688	−	1.06726i
$25$	−7.60570			−1.52114
$26$	−0.269957	−	4.20304i	−0.0529429	−	0.824283i
$27$	−2.90313	−	4.30951i	−0.558707	−	0.829365i
$28$	−0.866128	+	1.44115i	−0.163683	+	0.272352i
$29$	6.51871	−	3.76358i	1.21049	−	0.698879i	0.247627	−	0.968856i	$-0.420349\pi$
$29$	6.51871	−	3.76358i	1.21049	−	0.698879i	0.962867	+	0.269977i	$0.0870160\pi$
$30$	−4.74314	−	5.39479i	−0.865974	−	0.984950i
$31$	−3.58776			−0.644381			−0.322190	−	0.946675i	$-0.604419\pi$
$31$	−3.58776			−0.644381			−0.322190	+	0.946675i	$0.604419\pi$
$32$	−1.72058	+	2.98012i	−0.304158	+	0.526817i
$33$	6.61033	−	5.81184i	1.15071	−	1.01171i
$34$	2.53160			0.434167
$35$	−0.164887	+	9.39216i	−0.0278711	+	1.58757i
$36$	−0.244091	+	1.89083i	−0.0406818	+	0.315139i
$37$	2.53568	−	1.46398i	0.416863	−	0.240676i	−0.276871	−	0.960907i	$-0.589297\pi$
$37$	2.53568	−	1.46398i	0.416863	−	0.240676i	0.693734	+	0.720231i	$0.255964\pi$
$38$	−3.36066			−0.545171
$39$	−1.61662	+	6.03212i	−0.258867	+	0.965913i
$40$			10.9303i			1.72824i
$41$	5.45458	−	3.14920i	0.851862	−	0.491823i	−0.00941653	−	0.999956i	$-0.502997\pi$
$41$	5.45458	−	3.14920i	0.851862	−	0.491823i	0.861279	+	0.508133i	$0.169664\pi$
$42$	−4.08155	+	3.46342i	−0.629798	+	0.534417i
$43$	4.48749	−	7.77256i	0.684336	−	1.18530i	−0.289309	−	0.957236i	$-0.593426\pi$
$43$	4.48749	−	7.77256i	0.684336	−	1.18530i	0.973645	−	0.228069i	$-0.0732411\pi$
$44$	−3.22952			−0.486869
$45$	4.10086	+	9.83027i	0.611321	+	1.46541i
$46$	−2.73210	−	1.57738i	−0.402827	−	0.232572i
$47$			10.3146i			1.50454i	0.658857	+	0.752269i	$0.271040\pi$
$47$			10.3146i			1.50454i	−0.658857	+	0.752269i	$0.728960\pi$
$48$	−3.02448	+	2.65914i	−0.436545	+	0.383813i
$49$	6.99569	+	0.245706i	0.999384	+	0.0351009i
$50$	4.44217	+	7.69406i	0.628217	+	1.08810i
$51$	−3.55610	−	1.20214i	−0.497954	−	0.168334i
$52$	1.90686	−	1.27051i	0.264434	−	0.176189i
$53$		−	1.79048i		−	0.245942i	−0.992410	−	0.122971i	$-0.960758\pi$
$53$		−	1.79048i		−	0.245942i	0.992410	−	0.122971i	$-0.0392422\pi$
$54$	−2.66398	+	5.45385i	−0.362522	+	0.742175i
$55$	−15.6254	+	9.02133i	−2.10693	+	1.21644i
$56$	8.14389	+	0.142973i	1.08827	+	0.0191056i
$57$	4.72066	+	1.59582i	0.625266	+	0.211372i
$58$	−7.61460	−	4.39629i	−0.999846	−	0.577261i
$59$	−4.23466	−	2.44488i	−0.551305	−	0.318296i	0.198343	−	0.980133i	$-0.436444\pi$
$59$	−4.23466	−	2.44488i	−0.551305	−	0.318296i	−0.749648	+	0.661836i	$0.769777\pi$
$60$	1.25156	−	3.70227i	0.161575	−	0.477961i
$61$	0.145945	+	0.0842615i	0.0186864	+	0.0107886i	0.509314	−	0.860581i	$-0.329899\pi$
$61$	0.145945	+	0.0842615i	0.0186864	+	0.0107886i	−0.490628	+	0.871369i	$0.663232\pi$
$62$	2.09546	+	3.62944i	0.266123	+	0.460939i
$63$	7.37791	−	2.92686i	0.929529	−	0.368749i
$64$	8.66989			1.08374
$65$	5.67691	−	11.4737i	0.704134	−	1.42314i
$66$	−9.74017	−	3.29267i	−1.19893	−	0.405300i
$67$	3.78238	−	2.18376i	0.462091	−	0.266788i	−0.250832	−	0.968031i	$-0.580704\pi$
$67$	3.78238	−	2.18376i	0.462091	−	0.266788i	0.712923	+	0.701242i	$0.247371\pi$
$68$	0.688654	+	1.19278i	0.0835116	+	0.144646i
$69$	3.08871	+	3.51307i	0.371838	+	0.422924i
$70$	9.59758	−	5.31876i	1.14713	−	0.635713i
$71$	−5.26351	+	9.11667i	−0.624664	+	1.08195i	0.363942	+	0.931422i	$0.381431\pi$
$71$	−5.26351	+	9.11667i	−0.624664	+	1.08195i	−0.988606	+	0.150528i	$0.951903\pi$
$72$	8.52377	−	3.55584i	1.00454	−	0.419059i
$73$	10.7603			1.25940			0.629700	−	0.776838i	$-0.283178\pi$
$73$	10.7603			1.25940			0.629700	+	0.776838i	$0.283178\pi$
$74$	−2.96197	−	1.71009i	−0.344322	−	0.198794i
$75$	−2.58628	−	12.9171i	−0.298638	−	1.49154i
$76$	−0.914176	−	1.58340i	−0.104863	−	0.181628i
$77$	6.51716	+	11.7601i	0.742699	+	1.34018i
$78$	7.04640	−	1.88770i	0.797848	−	0.213740i
$79$	−4.68895			−0.527548			−0.263774	−	0.964584i	$-0.584967\pi$
$79$	−4.68895			−0.527548			−0.263774	+	0.964584i	$0.584967\pi$
$80$	7.14922	−	4.12760i	0.799307	−	0.461480i
$81$	6.33183	−	6.39593i	0.703537	−	0.710659i
$82$	−6.37157	−	3.67863i	−0.703623	−	0.406237i
$83$			0.468856i			0.0514637i	0.999669	+	0.0257318i	$0.00819160\pi$
$83$			0.468856i			0.0514637i	−0.999669	+	0.0257318i	$0.991808\pi$
$84$	−2.74209	−	0.980927i	−0.299187	−	0.107028i
$85$	6.66384	+	3.84737i	0.722795	+	0.417306i
$86$	−10.4838			−1.13050
$87$	8.60850	+	9.79122i	0.922928	+	1.04973i
$88$	7.82234	+	13.5487i	0.833865	+	1.44430i
$89$	−5.64141	+	3.25707i	−0.597989	+	0.345249i	−0.768250	−	0.640150i	$-0.778872\pi$
$89$	−5.64141	+	3.25707i	−0.597989	+	0.345249i	0.170261	+	0.985399i	$0.445539\pi$
$90$	7.54933	−	9.88995i	0.795769	−	1.04249i
$91$	−8.47452	−	4.37979i	−0.888371	−	0.459127i
$92$		−	1.71634i		−	0.178940i
$93$	−1.22000	−	6.09325i	−0.126508	−	0.631840i
$94$	10.4344	−	6.02431i	1.07623	−	0.621360i
$95$	−8.84612	−	5.10731i	−0.907593	−	0.523999i
$96$	−5.64635	−	1.90875i	−0.576278	−	0.194811i
$97$	−4.02073	+	6.96410i	−0.408243	+	0.707098i	−0.994693	−	0.102888i	$-0.967192\pi$
$97$	−4.02073	+	6.96410i	−0.408243	+	0.707098i	0.586450	+	0.809985i	$0.300525\pi$
$98$	−3.83732	−	7.22046i	−0.387628	−	0.729377i
$99$	12.1183	+	9.25031i	1.21794	+	0.929692i
$100$	−2.41674	+	4.18592i	−0.241674	+	0.418592i
$101$	−1.05407	−	1.82570i	−0.104883	−	0.181663i	0.808807	−	0.588074i	$-0.200114\pi$
$101$	−1.05407	−	1.82570i	−0.104883	−	0.181663i	−0.913691	+	0.406411i	$0.866780\pi$
$102$	0.860859	+	4.29953i	0.0852378	+	0.425717i
$103$			6.48373i			0.638860i	0.947610	+	0.319430i	$0.103492\pi$
$103$			6.48373i			0.638860i	−0.947610	+	0.319430i	$0.896508\pi$
$104$	−9.94882	−	4.92241i	−0.975562	−	0.482682i
$105$	−16.0072	+	2.91372i	−1.56214	+	0.284350i
$106$	−1.81128	+	1.04575i	−0.175927	+	0.101572i
$107$	−1.45422	+	0.839596i	−0.140585	+	0.0811668i	−0.568643	−	0.822585i	$-0.692531\pi$
$107$	−1.45422	+	0.839596i	−0.140585	+	0.0811668i	0.428058	+	0.903751i	$0.359198\pi$
$108$	−3.29429	+	0.228419i	−0.316993	+	0.0219796i
$109$		−	10.6995i		−	1.02483i	−0.858738	−	0.512415i	$-0.828751\pi$
$109$		−	10.6995i		−	1.02483i	0.858738	−	0.512415i	$-0.171249\pi$
$110$	18.2523	+	10.5380i	1.74029	+	1.00475i
$111$	3.34858	+	3.80864i	0.317833	+	0.361500i
$112$	−2.98185	−	5.38067i	−0.281758	−	0.508426i
$113$	3.60061	+	2.07881i	0.338717	+	0.195558i	0.659704	−	0.751525i	$-0.270681\pi$
$113$	3.60061	+	2.07881i	0.338717	+	0.195558i	−0.320988	+	0.947083i	$0.604015\pi$
$114$	−1.14277	−	5.70755i	−0.107031	−	0.534561i
$115$	−4.79441	−	8.30415i	−0.447081	−	0.774366i
$116$		−	4.78357i		−	0.444143i
$117$	−10.7943	−	0.694390i	−0.997937	−	0.0641964i
$118$			5.71180i			0.525814i
$119$	2.95373	−	4.91472i	0.270768	−	0.450531i
$120$	−18.5635	+	3.71680i	−1.69460	+	0.339296i
$121$	−7.41232	+	12.8385i	−0.673847	+	1.16714i
$122$		−	0.196854i		−	0.0178223i
$123$	7.20323	+	8.19288i	0.649493	+	0.738727i
$124$	−1.14002	+	1.97458i	−0.102377	+	0.177323i
$125$			9.25143i			0.827473i
$126$	−7.26998	−	5.75416i	−0.647661	−	0.512622i
$127$	−11.1004	−	19.2265i	−0.985001	−	1.70607i	−0.641931	−	0.766763i	$-0.721866\pi$
$127$	−11.1004	−	19.2265i	−0.985001	−	1.70607i	−0.343071	−	0.939310i	$-0.611467\pi$
$128$	−1.62256	−	2.81036i	−0.143415	−	0.248403i
$129$	14.7264	+	4.97828i	1.29659	+	0.438313i
$130$	−14.9227	+	0.958469i	−1.30881	+	0.0840633i
$131$	4.74553			0.414619			0.207310	−	0.978275i	$-0.433529\pi$
$131$	4.74553			0.414619			0.207310	+	0.978275i	$0.433529\pi$
$132$	−1.09818	−	5.48483i	−0.0955845	−	0.477394i
$133$	−3.92103	+	6.52420i	−0.339996	+	0.565720i
$134$	−4.41825	−	2.55088i	−0.381679	−	0.220362i
$135$	−15.3007	+	10.3074i	−1.31687	+	0.887120i
$136$	3.33603	−	5.77818i	0.286062	−	0.495475i
$137$	−3.97315	+	6.88169i	−0.339449	+	0.587943i	−0.984329	−	0.176341i	$-0.943574\pi$
$137$	−3.97315	+	6.88169i	−0.339449	+	0.587943i	0.644880	+	0.764284i	$0.276907\pi$
$138$	1.74990	−	5.17643i	0.148961	−	0.440647i
$139$	1.09322	+	0.631171i	0.0927257	+	0.0535352i	0.545646	−	0.838016i	$-0.316284\pi$
$139$	1.09322	+	0.631171i	0.0927257	+	0.0535352i	−0.452920	+	0.891551i	$0.649618\pi$
$140$	5.11673	+	3.07515i	0.432443	+	0.259897i
$141$	−17.5177	+	3.50742i	−1.47526	+	0.295378i
$142$	12.2968			1.03192
$143$	−1.17443	−	18.2850i	−0.0982106	−	1.52907i
$144$	−5.54459	−	4.23237i	−0.462049	−	0.352698i
$145$	−13.3624	−	23.1444i	−1.10969	−	1.92203i
$146$	−6.28464	−	10.8853i	−0.520121	−	0.900876i
$147$	1.96155	+	11.9646i	0.161786	+	0.986826i
$148$		−	1.86074i		−	0.152952i
$149$	4.39027	−	7.60417i	0.359665	−	0.622958i	−0.628240	−	0.778020i	$-0.716224\pi$
$149$	4.39027	−	7.60417i	0.359665	−	0.622958i	0.987905	+	0.155062i	$0.0495576\pi$
$150$	−11.5566	+	10.1607i	−0.943594	+	0.829614i
$151$			15.1199i			1.23044i	0.788354	+	0.615222i	$0.210933\pi$
$151$			15.1199i			1.23044i	−0.788354	+	0.615222i	$0.789067\pi$
$152$	−4.42852	+	7.67042i	−0.359200	+	0.622153i
$153$	0.832416	−	6.44826i	0.0672969	−	0.521311i
$154$	8.09028	−	13.4614i	0.651934	−	1.08475i
$155$			12.7382i			1.02315i
$156$	2.80619	+	2.80647i	0.224675	+	0.224697i
$157$		−	5.64339i		−	0.450391i	−0.974314	−	0.225196i	$-0.927698\pi$
$157$		−	5.64339i		−	0.450391i	0.974314	−	0.225196i	$-0.0723021\pi$
$158$	2.73862	+	4.74342i	0.217873	+	0.377367i
$159$	3.04086	−	0.608845i	0.241156	−	0.0482846i
$160$	10.5808	+	6.10882i	0.836485	+	0.482945i
$161$	−6.24991	+	3.46356i	−0.492562	+	0.272967i
$162$	−10.1684	−	2.66980i	−0.798904	−	0.209759i
$163$	6.08960	+	3.51583i	0.476974	+	0.275381i	0.719155	−	0.694850i	$-0.244529\pi$
$163$	6.08960	+	3.51583i	0.476974	+	0.275381i	−0.242181	+	0.970231i	$0.577863\pi$
$164$		−	4.00269i		−	0.312557i
$165$	−20.6347	−	23.4696i	−1.60641	−	1.82711i
$166$	0.474303	−	0.273839i	0.0368130	−	0.0212540i
$167$	6.76367	−	3.90501i	0.523388	−	0.302178i	−0.214931	−	0.976629i	$-0.568953\pi$
$167$	6.76367	−	3.90501i	0.523388	−	0.302178i	0.738320	+	0.674451i	$0.235619\pi$
$168$	2.52647	+	13.8797i	0.194922	+	1.07085i
$169$	7.88687	+	10.3343i	0.606682	+	0.794944i
$170$		−	8.98834i		−	0.689374i
$171$	−1.10502	+	8.55995i	−0.0845027	+	0.654596i
$172$	−2.85184	−	4.93952i	−0.217450	−	0.376635i
$173$	−0.714366	+	1.23732i	−0.0543122	+	0.0940715i	−0.891903	−	0.452226i	$-0.850630\pi$
$173$	−0.714366	+	1.23732i	−0.0543122	+	0.0940715i	0.837591	+	0.546298i	$0.183963\pi$
$174$	4.87710	−	14.4271i	0.369732	−	1.09372i
$175$	20.1197	+	0.353218i	1.52091	+	0.0267008i
$176$	5.90788	−	10.2327i	0.445323	−	0.771322i
$177$	2.71227	−	8.02327i	0.203867	−	0.603066i
$178$	6.58982	+	3.80463i	0.493928	+	0.285169i
$179$	8.02921	−	4.63566i	0.600131	−	0.346486i	−0.168962	−	0.985623i	$-0.554042\pi$
$179$	8.02921	−	4.63566i	0.600131	−	0.346486i	0.769093	+	0.639137i	$0.220708\pi$
$180$	6.71331	+	0.866632i	0.500381	+	0.0645949i
$181$		−	18.8579i		−	1.40169i	−0.713312	−	0.700847i	$-0.752806\pi$
$181$		−	18.8579i		−	1.40169i	0.713312	−	0.700847i	$-0.247194\pi$
$182$	0.518935	+	11.1310i	0.0384660	+	0.825086i
$183$	−0.0934770	+	0.276518i	−0.00691002	+	0.0204408i
$184$	−7.20048	+	4.15720i	−0.530827	+	0.306473i
$185$	−5.19778	−	9.00281i	−0.382148	−	0.661900i
$186$	−5.45148	+	4.79298i	−0.399722	+	0.351438i
$187$	11.0136			0.805391
$188$	5.67680	+	3.27750i	0.414023	+	0.239036i
$189$	7.47963	+	11.5350i	0.544063	+	0.839044i
$190$			11.9318i			0.865627i
$191$	−12.6936	−	7.32866i	−0.918477	−	0.530283i	−0.0353282	−	0.999376i	$-0.511248\pi$
$191$	−12.6936	−	7.32866i	−0.918477	−	0.530283i	−0.883149	+	0.469093i	$0.844581\pi$
$192$	2.94815	+	14.7244i	0.212765	+	1.06265i
$193$	17.8122	−	10.2839i	1.28215	−	0.740248i	0.304907	−	0.952382i	$-0.401375\pi$
$193$	17.8122	−	10.2839i	1.28215	−	0.740248i	0.977241	+	0.212134i	$0.0680414\pi$
$194$	9.39334			0.674403
$195$	21.4168	+	5.73975i	1.53369	+	0.411032i
$196$	2.35814	−	3.77211i	0.168438	−	0.269437i
$197$	1.25664	+	2.17657i	0.0895322	+	0.155074i	0.907314	−	0.420455i	$-0.138129\pi$
$197$	1.25664	+	2.17657i	0.0895322	+	0.155074i	−0.817781	+	0.575529i	$0.804796\pi$
$198$	2.27999	−	17.6618i	0.162032	−	1.25517i
$199$	−8.53047	−	4.92507i	−0.604709	−	0.349129i	0.166183	−	0.986095i	$-0.446856\pi$
$199$	−8.53047	−	4.92507i	−0.604709	−	0.349129i	−0.770892	+	0.636966i	$0.780189\pi$
$200$	23.4147			1.65567
$201$	4.99494	+	5.68120i	0.352316	+	0.400721i
$202$	−1.23127	+	2.13262i	−0.0866318	+	0.150051i
$203$	−17.4190	+	9.65322i	−1.22257	+	0.677523i
$204$	−1.79158	+	1.57517i	−0.125436	+	0.110284i
$205$	−11.1811	−	19.3662i	−0.780921	−	1.35260i
$206$	6.55905	−	3.78687i	0.456990	−	0.263844i
$207$	−4.91610	+	6.44030i	−0.341692	+	0.447632i
$208$	0.537345	+	8.36608i	0.0372582	+	0.580083i
$209$	−14.6203			−1.01131
$210$	12.2967	+	14.4914i	0.848552	+	0.999999i
$211$	−4.82479	−	8.35678i	−0.332152	−	0.575304i	0.650782	−	0.759265i	$-0.274441\pi$
$211$	−4.82479	−	8.35678i	−0.332152	−	0.575304i	−0.982934	+	0.183961i	$0.941108\pi$
$212$	−0.985422	−	0.568933i	−0.0676790	−	0.0390745i
$213$	−17.2731	−	5.83917i	−1.18353	−	0.400093i
$214$	1.69870	+	0.980745i	0.116121	+	0.0670423i
$215$	−27.5961	−	15.9326i	−1.88204	−	1.08660i
$216$	8.93749	+	13.2671i	0.608119	+	0.902715i
$217$	9.49086	+	0.166620i	0.644281	+	0.0113109i
$218$	−10.8238	+	6.24915i	−0.733083	+	0.423246i
$219$	3.65899	+	18.2747i	0.247252	+	1.23489i
$220$			11.4663i			0.773055i
$221$	−6.50291	+	4.33280i	−0.437433	+	0.291456i
$222$	1.89712	−	5.61194i	0.127326	−	0.376649i
$223$	5.03517	+	8.72117i	0.337180	+	0.584013i	0.983901	−	0.178714i	$-0.0571935\pi$
$223$	5.03517	+	8.72117i	0.337180	+	0.584013i	−0.646721	+	0.762727i	$0.723860\pi$
$224$	4.68992	−	7.80355i	0.313358	−	0.521397i
$225$	21.0582	−	8.78479i	1.40388	−	0.585652i
$226$		−	4.85658i		−	0.323055i
$227$	−8.91928	−	5.14955i	−0.591993	−	0.341787i	0.173892	−	0.984765i	$-0.444366\pi$
$227$	−8.91928	−	5.14955i	−0.591993	−	0.341787i	−0.765885	+	0.642977i	$0.777699\pi$
$228$	2.37829	−	2.09101i	0.157506	−	0.138481i
$229$	−15.5100			−1.02493			−0.512464	−	0.858709i	$-0.671267\pi$
$229$	−15.5100			−1.02493			−0.512464	+	0.858709i	$0.671267\pi$
$230$	−5.60042	+	9.70020i	−0.369280	+	0.639613i
$231$	−17.7565	+	15.0673i	−1.16829	+	0.991357i
$232$	−20.0683	+	11.5865i	−1.31755	+	0.760688i
$233$		−	2.29887i		−	0.150604i	−0.997161	−	0.0753020i	$-0.976008\pi$
$233$		−	2.29887i		−	0.150604i	0.997161	−	0.0753020i	$-0.0239921\pi$
$234$	5.60206	+	11.3253i	0.366218	+	0.740358i
$235$	36.6214			2.38892
$236$	−2.69116	+	1.55374i	−0.175179	+	0.101140i
$237$	−1.59445	−	7.96345i	−0.103571	−	0.517282i
$238$	−6.69696	−	0.117571i	−0.434100	−	0.00762099i
$239$	24.3089			1.57241			0.786205	−	0.617965i	$-0.212043\pi$
$239$	24.3089			1.57241			0.786205	+	0.617965i	$0.212043\pi$
$240$	9.44114	+	10.7383i	0.609423	+	0.693151i
$241$	6.90894	−	11.9666i	0.445044	−	0.770839i	−0.553011	−	0.833174i	$-0.686521\pi$
$241$	6.90894	−	11.9666i	0.445044	−	0.770839i	0.998055	+	0.0623347i	$0.0198546\pi$
$242$	17.3169			1.11317
$243$	13.0156	+	8.57872i	0.834951	+	0.550325i
$244$	0.0927493	−	0.0535488i	0.00593767	−	0.00342811i
$245$	0.872368	−	24.8378i	0.0557335	−	1.58683i
$246$	4.08095	−	12.0720i	0.260192	−	0.769684i
$247$	8.63249	−	5.75172i	0.549272	−	0.365973i
$248$	11.0452			0.701370
$249$	−0.796279	+	0.159432i	−0.0504621	+	0.0101036i
$250$	9.35890	−	5.40336i	0.591909	−	0.341739i
$251$	4.27689	−	7.40779i	0.269955	−	0.467576i	−0.698895	−	0.715224i	$-0.746324\pi$
$251$	4.27689	−	7.40779i	0.269955	−	0.467576i	0.968850	+	0.247649i	$0.0796578\pi$
$252$	0.733516	−	4.99057i	0.0462072	−	0.314376i
$253$	−11.8858	−	6.86228i	−0.747255	−	0.431428i
$254$	−12.9665	+	22.4587i	−0.813593	+	1.40918i
$255$	−4.26815	+	12.6258i	−0.267282	+	0.790656i
$256$	6.77455	−	11.7339i	0.423409	−	0.733367i
$257$	−0.974388	−	1.68769i	−0.0607806	−	0.105275i	0.834034	−	0.551713i	$-0.186026\pi$
$257$	−0.974388	−	1.68769i	−0.0607806	−	0.105275i	−0.894815	+	0.446438i	$0.852692\pi$
$258$	−3.56497	−	17.8051i	−0.221945	−	1.10850i
$259$	−6.77574	+	3.75496i	−0.421024	+	0.233322i
$260$	−4.51090	−	6.77021i	−0.279754	−	0.419870i
$261$	−13.7016	+	17.9496i	−0.848106	+	1.11105i
$262$	−2.77166	−	4.80066i	−0.171234	−	0.296586i
$263$	−6.70957	+	3.87377i	−0.413730	+	0.238867i	−0.692391	−	0.721523i	$-0.743443\pi$
$263$	−6.70957	+	3.87377i	−0.413730	+	0.238867i	0.278661	+	0.960389i	$0.410109\pi$
$264$	−20.3504	+	17.8922i	−1.25248	+	1.10119i
$265$	−6.35703			−0.390509
$266$	8.89009	+	0.156073i	0.545087	+	0.00956946i
$267$	−7.44996	−	8.47351i	−0.455930	−	0.518570i
$268$		−	2.77559i		−	0.169546i
$269$	−14.1755	+	24.5528i	−0.864298	+	1.49701i	0.00344363	+	0.999994i	$0.498904\pi$
$269$	−14.1755	+	24.5528i	−0.864298	+	1.49701i	−0.867742	+	0.497015i	$0.834429\pi$
$270$	19.3636	+	9.45833i	1.17843	+	0.575616i
$271$	13.4325	+	23.2658i	0.815969	+	1.41330i	0.908630	+	0.417601i	$0.137129\pi$
$271$	13.4325	+	23.2658i	0.815969	+	1.41330i	−0.0926617	+	0.995698i	$0.529538\pi$
$272$	−5.03912			−0.305541
$273$	4.55667	−	15.8820i	0.275782	−	0.961220i
$274$	9.28218			0.560757
$275$	19.3253	+	33.4724i	1.16536	+	2.01846i
$276$	2.91493	−	0.583631i	0.175458	−	0.0351305i
$277$	−6.79226	+	11.7645i	−0.408108	+	0.706863i	−0.994678	−	0.103035i	$-0.967145\pi$
$277$	−6.79226	+	11.7645i	−0.408108	+	0.706863i	0.586570	+	0.809898i	$0.300478\pi$
$278$		−	1.47456i		−	0.0884382i
$279$	9.93357	−	4.14396i	0.594707	−	0.248092i
$280$	0.507618	−	28.9145i	0.0303360	−	1.72797i
$281$	−13.4869			−0.804561			−0.402281	−	0.915516i	$-0.631782\pi$
$281$	−13.4869			−0.804561			−0.402281	+	0.915516i	$0.631782\pi$
$282$	13.7795	+	15.6727i	0.820558	+	0.933294i
$283$	9.37572	−	5.41308i	0.557329	−	0.321774i	−0.194744	−	0.980854i	$-0.562388\pi$
$283$	9.37572	−	5.41308i	0.557329	−	0.321774i	0.752073	+	0.659080i	$0.229054\pi$
$284$	3.34500	+	5.79371i	0.198489	+	0.343794i
$285$	5.66589	−	16.7605i	0.335618	−	0.992804i
$286$	−17.8115	+	11.8676i	−1.05321	+	0.701743i
$287$	−14.5755	+	8.07741i	−0.860364	+	0.476794i
$288$	1.32170	−	10.2385i	0.0778821	−	0.603309i
$289$	6.15150	+	10.6547i	0.361853	+	0.626748i
$290$	−15.6088	+	27.0353i	−0.916581	+	1.58757i
$291$	−13.1947	−	4.46047i	−0.773485	−	0.261477i
$292$	3.41913	−	5.92211i	0.200090	−	0.346565i
$293$	23.5405	+	13.5911i	1.37525	+	0.794000i	0.991583	−	0.129471i	$-0.0413281\pi$
$293$	23.5405	+	13.5911i	1.37525	+	0.794000i	0.383666	+	0.923472i	$0.374661\pi$
$294$	10.9580	−	8.97237i	0.639081	−	0.523279i
$295$	−8.68042	+	15.0349i	−0.505394	+	0.875368i
$296$	−7.80629	+	4.50696i	−0.453731	+	0.261962i
$297$	−11.5894	+	23.7266i	−0.672487	+	1.37676i
$298$	−10.2567			−0.594154
$299$	9.71760	−	0.624152i	0.561983	−	0.0360956i
$300$	−7.93093	−	2.68106i	−0.457893	−	0.154791i
$301$	−12.2319	+	20.3527i	−0.705036	+	1.17311i
$302$	15.2956	−	8.83091i	0.880162	−	0.508162i
$303$	2.74223	−	2.41098i	0.157537	−	0.138507i
$304$	6.68933			0.383660
$305$	0.299166	−	0.518171i	0.0171302	−	0.0296704i
$306$	−7.00935	+	2.92407i	−0.400698	+	0.167158i
$307$	−34.4944			−1.96870			−0.984350	−	0.176225i	$-0.943611\pi$
$307$	−34.4944			−1.96870			−0.984350	+	0.176225i	$0.943611\pi$
$308$	8.54319	+	0.149983i	0.486794	+	0.00854607i
$309$	−11.0116	+	2.20476i	−0.626428	+	0.125424i
$310$	12.8861	−	7.43982i	0.731884	−	0.422553i
$311$	16.5987			0.941228			0.470614	−	0.882339i	$-0.344032\pi$
$311$	16.5987			0.941228			0.470614	+	0.882339i	$0.344032\pi$
$312$	4.97690	−	18.5704i	0.281762	−	1.05134i
$313$			2.40647i			0.136022i	0.997685	+	0.0680109i	$0.0216653\pi$
$313$			2.40647i			0.136022i	−0.997685	+	0.0680109i	$0.978335\pi$
$314$	−5.70895	+	3.29606i	−0.322175	+	0.186008i
$315$	−10.3917	−	26.1949i	−0.585504	−	1.47592i
$316$	−1.48993	+	2.58064i	−0.0838153	+	0.145172i
$317$	14.4082			0.809247			0.404624	−	0.914483i	$-0.367403\pi$
$317$	14.4082			0.809247			0.404624	+	0.914483i	$0.367403\pi$
$318$	−2.39195	−	2.72058i	−0.134134	−	0.152563i
$319$	−33.1267	−	19.1257i	−1.85474	−	1.07084i
$320$		−	30.7820i		−	1.72077i
$321$	−1.92042	−	2.18427i	−0.107188	−	0.121914i
$322$	7.15410	+	4.29960i	0.398682	+	0.239607i
$323$	3.11759	+	5.39982i	0.173467	+	0.300454i
$324$	−1.50814	−	5.51716i	−0.0837855	−	0.306509i
$325$	−24.5788	−	12.1610i	−1.36339	−	0.674569i
$326$		−	8.21379i		−	0.454919i
$327$	18.1715	−	3.63833i	1.00489	−	0.201200i
$328$	−16.7923	+	9.69506i	−0.927202	+	0.535320i
$329$	0.479022	−	27.2856i	0.0264094	−	1.50431i
$330$	−11.6905	+	34.5820i	−0.643539	+	1.90368i
$331$	3.78126	+	2.18311i	0.207837	+	0.119995i	0.600306	−	0.799771i	$-0.295046\pi$
$331$	3.78126	+	2.18311i	0.207837	+	0.119995i	−0.392469	+	0.919765i	$0.628379\pi$
$332$	0.258043	+	0.148981i	0.0141619	+	0.00817639i
$333$	−5.32971	+	6.98214i	−0.292066	+	0.382619i
$334$	−7.90074	−	4.56150i	−0.432309	−	0.249594i
$335$	−7.75332	−	13.4291i	−0.423609	−	0.733712i
$336$	8.12427	−	6.89387i	0.443215	−	0.376092i
$337$	8.68524			0.473115			0.236558	−	0.971617i	$-0.423981\pi$
$337$	8.68524			0.473115			0.236558	+	0.971617i	$0.423981\pi$
$338$	5.84794	−	14.0143i	0.318086	−	0.762278i
$339$	−2.30617	+	6.82196i	−0.125254	+	0.370518i
$340$	4.23492	−	2.44503i	0.229671	−	0.132601i
$341$	9.11613	+	15.7896i	0.493666	+	0.855055i
$342$	9.30478	−	3.88165i	0.503145	−	0.209895i
$343$	−18.4946	−	0.974866i	−0.998614	−	0.0526378i
$344$	−13.8151	+	23.9284i	−0.744859	+	1.29013i
$345$	12.4730	−	10.9663i	0.671523	−	0.590407i
$346$	1.66892			0.0897218
$347$	14.4709	+	8.35477i	0.776838	+	0.448508i	0.835309	−	0.549781i	$-0.185289\pi$
$347$	14.4709	+	8.35477i	0.776838	+	0.448508i	−0.0584704	+	0.998289i	$0.518622\pi$
$348$	8.12414	−	1.62663i	0.435499	−	0.0871964i
$349$	16.6660	+	28.8664i	0.892111	+	1.54518i	0.837340	+	0.546683i	$0.184110\pi$
$349$	16.6660	+	28.8664i	0.892111	+	1.54518i	0.0547712	+	0.998499i	$0.482557\pi$
$350$	−11.3937	−	20.5597i	−0.609021	−	1.09896i
$351$	−2.49125	−	18.5686i	−0.132973	−	0.991120i
$352$	17.4872			0.932072
$353$	10.3711	−	5.98773i	0.551996	−	0.318695i	−0.197931	−	0.980216i	$-0.563422\pi$
$353$	10.3711	−	5.98773i	0.551996	−	0.318695i	0.749927	+	0.661521i	$0.230089\pi$
$354$	−9.70059	+	1.94227i	−0.515581	+	0.103230i
$355$	32.3683	+	18.6878i	1.71793	+	0.991847i
$356$			4.13979i			0.219408i
$357$	9.35128	+	3.34523i	0.494922	+	0.177048i
$358$	−9.37903	−	5.41499i	−0.495697	−	0.286191i
$359$	5.50745			0.290672			0.145336	−	0.989382i	$-0.453574\pi$
$359$	5.50745			0.290672			0.145336	+	0.989382i	$0.453574\pi$
$360$	−12.6248	−	30.2632i	−0.665386	−	1.59501i
$361$	5.36146	+	9.28632i	0.282182	+	0.488754i
$362$	−19.0769	+	11.0141i	−1.00266	+	0.578887i
$363$	−24.3247	−	8.22299i	−1.27672	−	0.431595i
$364$	−5.10330	+	3.27239i	−0.267486	+	0.171520i
$365$		−	38.2040i		−	1.99969i
$366$	0.334326	−	0.0669393i	0.0174755	−	0.00349897i
$367$	8.24711	−	4.76147i	0.430496	−	0.248547i	−0.269062	−	0.963123i	$-0.586714\pi$
$367$	8.24711	−	4.76147i	0.430496	−	0.248547i	0.699558	+	0.714576i	$0.253380\pi$
$368$	5.43821	+	3.13975i	0.283486	+	0.163671i
$369$	−11.4649	+	15.0195i	−0.596839	+	0.781884i
$370$	−6.07160	+	10.5163i	−0.315647	+	0.546717i
$371$	−0.0831523	+	4.73645i	−0.00431705	+	0.245904i
$372$	−3.74118	−	1.26471i	−0.193971	−	0.0655720i
$373$	−7.40112	+	12.8191i	−0.383216	+	0.663749i	−0.991520	−	0.129955i	$-0.958517\pi$
$373$	−7.40112	+	12.8191i	−0.383216	+	0.663749i	0.608304	+	0.793704i	$0.291850\pi$
$374$	−6.43255	−	11.1415i	−0.332619	−	0.576113i
$375$	−15.7121	+	3.14590i	−0.811369	+	0.162454i
$376$		−	31.7542i		−	1.63760i
$377$	27.0837	−	1.73956i	1.39488	−	0.0895920i
$378$	7.30042	−	14.3036i	0.375493	−	0.735697i
$379$	9.74185	−	5.62446i	0.500405	−	0.288909i	−0.228476	−	0.973550i	$-0.573374\pi$
$379$	9.74185	−	5.62446i	0.500405	−	0.288909i	0.728881	+	0.684641i	$0.240041\pi$
$380$	−5.62178	+	3.24574i	−0.288391	+	0.166503i
$381$	28.8785	−	25.3902i	1.47949	−	1.30078i
$382$			17.1214i			0.876008i
$383$	10.2167	+	5.89859i	0.522047	+	0.301404i	0.737772	−	0.675050i	$-0.235878\pi$
$383$	10.2167	+	5.89859i	0.522047	+	0.301404i	−0.215725	+	0.976454i	$0.569211\pi$
$384$	4.22121	−	3.71131i	0.215413	−	0.189392i
$385$	41.7535	−	23.1389i	2.12796	−	1.17927i
$386$	−20.8066	−	12.0127i	−1.05903	−	0.611431i
$387$	−3.44718	+	26.7034i	−0.175230	+	1.35741i
$388$	2.55520	+	4.42574i	0.129721	+	0.224683i
$389$			15.3002i			0.775749i	0.921712	+	0.387874i	$0.126791\pi$
$389$			15.3002i			0.775749i	−0.921712	+	0.387874i	$0.873209\pi$
$390$	−6.70219	−	25.0179i	−0.339379	−	1.26683i
$391$			5.85317i			0.296008i
$392$	−21.5368	−	0.756425i	−1.08777	−	0.0382052i
$393$	1.61370	+	8.05955i	0.0814002	+	0.406550i
$394$	1.46791	−	2.54249i	0.0739520	−	0.128089i
$395$			16.6479i			0.837647i
$396$	8.94170	−	3.73018i	0.449337	−	0.187449i
$397$	−10.7610	+	18.6387i	−0.540081	+	0.935449i	0.458817	+	0.888531i	$0.348273\pi$
$397$	−10.7610	+	18.6387i	−0.540081	+	0.935449i	−0.998899	+	0.0469179i	$0.985060\pi$
$398$			11.5061i			0.576748i
$399$	−12.4136	−	4.44073i	−0.621460	−	0.222315i
$400$	−8.84206	−	15.3149i	−0.442103	−	0.765745i
$401$	−6.81360	−	11.8015i	−0.340255	−	0.589339i	0.644225	−	0.764836i	$-0.277180\pi$
$401$	−6.81360	−	11.8015i	−0.340255	−	0.589339i	−0.984480	+	0.175497i	$0.943847\pi$
$402$	2.82986	−	8.37111i	0.141141	−	0.417513i
$403$	−11.5943	−	5.73656i	−0.577554	−	0.285758i
$404$	−1.33973			−0.0666543
$405$	−22.7084	−	22.4809i	−1.12839	−	1.11708i
$406$	19.9391	+	11.9833i	0.989559	+	0.594723i
$407$	−12.8858	−	7.43963i	−0.638726	−	0.368769i
$408$	10.9477	+	3.70089i	0.541993	+	0.183221i
$409$	12.5613	−	21.7568i	0.621117	−	1.07581i	−0.368161	−	0.929762i	$-0.620012\pi$
$409$	12.5613	−	21.7568i	0.621117	−	1.07581i	0.989278	−	0.146045i	$-0.0466543\pi$
$410$	−13.0608	+	22.6220i	−0.645027	+	1.11722i
$411$	−13.0385	−	4.40768i	−0.643143	−	0.217415i
$412$	3.56842	+	2.06023i	0.175804	+	0.101500i
$413$	11.0886	+	6.66421i	0.545633	+	0.327924i
$414$	9.38640	+	1.21170i	0.461316	+	0.0595520i
$415$	1.66465			0.0817145
$416$	−10.3253	+	6.87959i	−0.506238	+	0.337300i
$417$	−0.700201	+	2.07129i	−0.0342890	+	0.101431i
$418$	8.53908	+	14.7901i	0.417660	+	0.723409i
$419$	3.24454	+	5.61971i	0.158506	+	0.274541i	0.934330	−	0.356408i	$-0.115999\pi$
$419$	3.24454	+	5.61971i	0.158506	+	0.274541i	−0.775824	+	0.630949i	$0.782666\pi$
$420$	−3.48273	+	9.73566i	−0.169940	+	0.475051i
$421$		−	21.8360i		−	1.06422i	−0.846674	−	0.532111i	$-0.821399\pi$
$421$		−	21.8360i		−	1.06422i	0.846674	−	0.532111i	$-0.178601\pi$
$422$	−5.63590	+	9.76167i	−0.274352	+	0.475191i
$423$	−11.9136	−	28.5584i	−0.579260	−	1.38856i
$424$			5.51214i			0.267693i
$425$	8.24176	−	14.2751i	0.399784	−	0.692446i
$426$	4.18145	+	20.8841i	0.202592	+	1.01184i
$427$	−0.382162	−	0.229678i	−0.0184941	−	0.0111149i
$428$			1.06714i			0.0515822i
$429$	30.6548	−	8.21230i	1.48003	−	0.396494i
$430$			37.2222i			1.79502i
$431$	−13.6869	−	23.7064i	−0.659275	−	1.14190i	−0.980804	−	0.194998i	$-0.937530\pi$
$431$	−13.6869	−	23.7064i	−0.659275	−	1.14190i	0.321529	−	0.946900i	$-0.395803\pi$
$432$	5.30261	−	10.8558i	0.255122	−	0.522300i
$433$	−15.4442	−	8.91673i	−0.742203	−	0.428511i	0.0806671	−	0.996741i	$-0.474295\pi$
$433$	−15.4442	−	8.91673i	−0.742203	−	0.428511i	−0.822870	+	0.568230i	$0.807628\pi$
$434$	−5.37465	−	9.69843i	−0.257991	−	0.465539i
$435$	34.7632	−	30.5641i	1.66677	−	1.46543i
$436$	−5.88867	−	3.39982i	−0.282016	−	0.162822i
$437$		−	7.76998i		−	0.371689i
$438$	16.3500	−	14.3750i	0.781231	−	0.686863i
$439$	−29.6011	+	17.0902i	−1.41278	+	0.815671i	−0.995650	−	0.0931745i	$-0.970299\pi$
$439$	−29.6011	+	17.0902i	−1.41278	+	0.815671i	−0.417133	+	0.908845i	$0.636965\pi$
$440$	48.1040	−	27.7729i	2.29327	−	1.32402i
$441$	−19.6530	+	7.39990i	−0.935858	+	0.352376i
$442$	8.18121	+	4.04785i	0.389140	+	0.192536i
$443$			29.5103i			1.40208i	0.713123	+	0.701039i	$0.247280\pi$
$443$			29.5103i			1.40208i	−0.713123	+	0.701039i	$0.752720\pi$
$444$	3.16017	−	0.632734i	0.149975	−	0.0300282i
$445$	11.5641	+	20.0296i	0.548190	+	0.949493i
$446$	5.88166	−	10.1873i	0.278505	−	0.482384i
$447$	14.4074	+	4.87043i	0.681446	+	0.230363i
$448$	−22.9348	−	0.402640i	−1.08357	−	0.0190230i
$449$	−1.47702	+	2.55828i	−0.0697051	+	0.120733i	−0.898771	−	0.438417i	$-0.855539\pi$
$449$	−1.47702	+	2.55828i	−0.0697051	+	0.120733i	0.829066	+	0.559150i	$0.188872\pi$
$450$	−21.1860	−	16.1720i	−0.998720	−	0.762357i
$451$	−27.7191	−	16.0036i	−1.30524	−	0.753580i
$452$	2.28822	−	1.32110i	0.107629	−	0.0621394i
$453$	−25.6788	+	5.14146i	−1.20650	+	0.241567i
$454$			12.0305i			0.564620i
$455$	−15.5502	+	30.0884i	−0.729006	+	1.41056i
$456$	−14.5329	−	4.91286i	−0.680565	−	0.230066i
$457$	3.49027	−	2.01511i	0.163268	−	0.0942627i	−0.416140	−	0.909301i	$-0.636617\pi$
$457$	3.49027	−	2.01511i	0.163268	−	0.0942627i	0.579408	+	0.815038i	$0.303284\pi$
$458$	9.05871	+	15.6901i	0.423286	+	0.733152i
$459$	11.2344	−	0.778971i	0.524378	−	0.0363592i
$460$	−6.09377			−0.284123
$461$	−32.8020	−	18.9383i	−1.52774	−	0.882043i	−0.999456	−	0.0329769i	$-0.989501\pi$
$461$	−32.8020	−	18.9383i	−1.52774	−	0.882043i	−0.528287	−	0.849066i	$-0.677165\pi$
$462$	25.6132	+	9.16259i	1.19163	+	0.426282i
$463$			27.4672i			1.27651i	0.769825	+	0.638255i	$0.220343\pi$
$463$			27.4672i			1.27651i	−0.769825	+	0.638255i	$0.779657\pi$
$464$	15.1567	+	8.75075i	0.703634	+	0.406243i
$465$	−21.6338	+	4.33155i	−1.00324	+	0.200871i
$466$	−2.32558	+	1.34267i	−0.107730	+	0.0621981i
$467$	23.9875			1.11001			0.555005	−	0.831847i	$-0.312716\pi$
$467$	23.9875			1.11001			0.555005	+	0.831847i	$0.312716\pi$
$468$	−3.81211	+	5.72019i	−0.176215	+	0.264416i
$469$	−10.1071	+	5.60113i	−0.466702	+	0.258636i
$470$	−21.3890	−	37.0469i	−0.986602	−	1.70884i
$471$	9.58441	−	1.91901i	0.441626	−	0.0884231i
$472$	13.0367	+	7.52675i	0.600063	+	0.346447i
$473$	−45.6090			−2.09710
$474$	−7.12471	+	6.26409i	−0.327249	+	0.287719i
$475$	−10.9408	+	18.9500i	−0.501997	+	0.869485i
$476$	−1.76633	−	3.18731i	−0.0809597	−	0.146090i
$477$	2.06806	+	4.95738i	0.0946898	+	0.226983i
$478$	−14.1978	−	24.5913i	−0.649391	−	1.12478i
$479$	10.7451	−	6.20368i	0.490956	−	0.283453i	−0.234015	−	0.972233i	$-0.575187\pi$
$479$	10.7451	−	6.20368i	0.490956	−	0.283453i	0.724971	+	0.688780i	$0.241853\pi$
$480$	−6.77693	+	20.0471i	−0.309323	+	0.915020i
$481$	10.5352	−	0.676664i	0.480363	−	0.0308532i
$482$	−16.1409			−0.735197
$483$	−8.00756	−	9.43672i	−0.364357	−	0.429386i
$484$	4.71059	+	8.15897i	0.214118	+	0.370862i
$485$	24.7257	+	14.2754i	1.12274	+	0.648212i
$486$	1.07652	−	18.1773i	0.0488320	−	0.824537i
$487$	−27.6788	−	15.9804i	−1.25425	−	0.724140i	−0.282297	−	0.959327i	$-0.591096\pi$
$487$	−27.6788	−	15.9804i	−1.25425	−	0.724140i	−0.971950	+	0.235187i	$0.924430\pi$
$488$	−0.449303	−	0.259405i	−0.0203390	−	0.0117427i
$489$	−3.90035	+	11.5378i	−0.176380	+	0.521756i
$490$	−25.6359	+	13.6242i	−1.15811	+	0.615480i
$491$	25.3216	−	14.6195i	1.14275	−	0.659767i	0.195640	−	0.980676i	$-0.437322\pi$
$491$	25.3216	−	14.6195i	1.14275	−	0.659767i	0.947110	+	0.320909i	$0.103988\pi$
$492$	6.79794	−	1.36109i	0.306475	−	0.0613628i
$493$			16.3133i			0.734713i
$494$	−10.8604	−	5.37344i	−0.488633	−	0.241763i
$495$	32.8428	−	43.0255i	1.47617	−	1.93385i
$496$	−4.17097	−	7.22434i	−0.187282	−	0.324382i
$497$	14.3472	−	23.8723i	0.643559	−	1.07082i
$498$	0.626357	+	0.712412i	0.0280677	+	0.0319239i
$499$		−	14.0573i		−	0.629292i	−0.949209	−	0.314646i	$-0.898114\pi$
$499$		−	14.0573i		−	0.629292i	0.949209	−	0.314646i	$-0.101886\pi$
$500$	5.09167	+	2.93968i	0.227706	+	0.131466i
$501$	8.93199	+	10.1592i	0.399052	+	0.453878i
$502$	−9.99180			−0.445956
$503$	−9.67979	+	16.7659i	−0.431600	+	0.747554i	−0.997011	−	0.0772557i	$-0.975384\pi$
$503$	−9.67979	+	16.7659i	−0.431600	+	0.747554i	0.565411	+	0.824809i	$0.308718\pi$
$504$	−22.7134	+	9.01055i	−1.01174	+	0.401362i
$505$	−6.48204	+	3.74241i	−0.288447	+	0.166535i
$506$			16.0319i			0.712703i
$507$	−14.8693	+	16.9087i	−0.660367	+	0.750943i
$508$	−14.1088			−0.625976
$509$	−28.3202	+	16.3507i	−1.25527	+	0.724732i	−0.972152	−	0.234352i	$-0.924703\pi$
$509$	−28.3202	+	16.3507i	−1.25527	+	0.724732i	−0.283121	+	0.959084i	$0.591370\pi$
$510$	15.2653	−	3.05644i	0.675958	−	0.135341i
$511$	−28.4647	−	0.499723i	−1.25921	−	0.0221064i
$512$	−22.3171			−0.986288
$513$	−14.9135	+	1.03407i	−0.658446	+	0.0456553i
$514$	−1.13820	+	1.97141i	−0.0502037	+	0.0869554i
$515$	23.0202			1.01439
$516$	7.41926	−	6.52306i	0.326615	−	0.287162i
$517$	45.3941	−	26.2083i	1.99643	−	1.15264i
$518$	7.75600	+	4.66134i	0.340779	+	0.204807i
$519$	−2.34431	−	0.792495i	−0.102904	−	0.0347866i
$520$	−17.4768	+	35.3228i	−0.766408	+	1.54901i
$521$	13.9767			0.612330			0.306165	−	0.951978i	$-0.400954\pi$
$521$	13.9767			0.612330			0.306165	+	0.951978i	$0.400954\pi$
$522$	26.1607	+	3.37712i	1.14502	+	0.147813i
$523$	−9.57398	+	5.52754i	−0.418641	+	0.241702i	−0.694496	−	0.719497i	$-0.744372\pi$
$523$	−9.57398	+	5.52754i	−0.418641	+	0.241702i	0.275855	+	0.961199i	$0.411039\pi$
$524$	1.50791	−	2.61178i	0.0658735	−	0.114096i
$525$	6.24172	+	34.2903i	0.272411	+	1.49655i
$526$	7.83754	+	4.52501i	0.341733	+	0.197300i
$527$	3.88780	−	6.73386i	0.169355	−	0.293332i
$528$	19.3876	+	6.55401i	0.843739	+	0.285227i
$529$	−7.85303	+	13.6018i	−0.341436	+	0.591385i
$530$	3.71287	+	6.43088i	0.161277	+	0.279339i
$531$	14.5486	+	1.87810i	0.631353	+	0.0815024i
$532$	2.34477	+	4.23109i	0.101659	+	0.183441i
$533$	22.6625	−	1.45559i	0.981623	−	0.0630487i
$534$	−4.22074	+	12.4855i	−0.182649	+	0.540301i
$535$	2.98095	+	5.16315i	0.128878	+	0.223222i
$536$	−11.6443	+	6.72286i	−0.502958	+	0.290383i
$537$	10.6032	+	12.0600i	0.457564	+	0.520428i
$538$	33.1173			1.42779
$539$	−16.6940	−	31.4121i	−0.719060	−	1.35301i
$540$	0.810990	+	11.6962i	0.0348995	+	0.503324i
$541$		−	20.4903i		−	0.880947i	−0.897766	−	0.440473i	$-0.854811\pi$
$541$		−	20.4903i		−	0.880947i	0.897766	−	0.440473i	$-0.145189\pi$
$542$	15.6907	−	27.1772i	0.673975	−	1.16736i
$543$	32.0271	−	6.41252i	1.37441	−	0.275187i
$544$	−3.72893	−	6.45869i	−0.159877	−	0.276914i
$545$	−37.9882			−1.62724
$546$	−18.7278	+	4.66637i	−0.801477	+	0.199702i
$547$	26.2483			1.12230			0.561148	−	0.827715i	$-0.310360\pi$
$547$	26.2483			1.12230			0.561148	+	0.827715i	$0.310360\pi$
$548$	2.52497	+	4.37337i	0.107861	+	0.186821i
$549$	−0.501408	−	0.0647276i	−0.0213996	−	0.00276251i
$550$	22.5742	−	39.0996i	0.962566	−	1.66721i
$551$		−	21.6556i		−	0.922558i
$552$	−9.50884	−	10.8153i	−0.404723	−	0.460328i
$553$	12.4039	+	0.217761i	0.527467	+	0.00926013i
$554$	15.8683			0.674179
$555$	13.5224	−	11.8890i	0.573993	−	0.504659i
$556$	0.694750	−	0.401114i	0.0294640	−	0.0170110i
$557$	19.9909	+	34.6252i	0.847041	+	1.46712i	0.883837	+	0.467795i	$0.154952\pi$
$557$	19.9909	+	34.6252i	0.847041	+	1.46712i	−0.0367957	+	0.999323i	$0.511715\pi$
$558$	−9.99387	−	7.62866i	−0.423074	−	0.322947i
$559$	26.9297	−	17.9429i	1.13900	−	0.758903i
$560$	−19.1038	+	10.5869i	−0.807284	+	0.447378i
$561$	3.74510	+	18.7048i	0.158118	+	0.789717i
$562$	7.87713	+	13.6436i	0.332277	+	0.575520i
$563$	−21.4554	+	37.1618i	−0.904237	+	1.56618i	−0.0822995	+	0.996608i	$0.526226\pi$
$563$	−21.4554	+	37.1618i	−0.904237	+	1.56618i	−0.821938	+	0.569577i	$0.807107\pi$
$564$	−3.63595	+	10.7556i	−0.153101	+	0.452895i
$565$	7.38072	−	12.7838i	0.310509	−	0.537818i
$566$	−10.9519	−	6.32309i	−0.460344	−	0.265780i
$567$	−17.0469	+	16.6254i	−0.715903	+	0.698200i
$568$	16.2041	−	28.0663i	0.679909	−	1.17764i
$569$	23.9412	−	13.8224i	1.00367	−	0.579467i	0.0943349	−	0.995541i	$-0.469928\pi$
$569$	23.9412	−	13.8224i	1.00367	−	0.579467i	0.909331	+	0.416074i	$0.136594\pi$
$570$	−20.2644	+	4.05737i	−0.848781	+	0.169944i
$571$	11.8871			0.497458			0.248729	−	0.968573i	$-0.419987\pi$
$571$	11.8871			0.497458			0.248729	+	0.968573i	$0.419987\pi$
$572$	−10.4366	−	5.16376i	−0.436377	−	0.215908i
$573$	8.13018	−	24.0502i	0.339643	−	1.00471i
$574$	16.6842	+	10.0271i	0.696384	+	0.418525i
$575$	−17.7890	+	10.2705i	−0.741852	+	0.428309i
$576$	−24.0047	+	10.0139i	−1.00019	+	0.417248i
$577$	26.4428			1.10083			0.550414	−	0.834892i	$-0.314470\pi$
$577$	26.4428			1.10083			0.550414	+	0.834892i	$0.314470\pi$
$578$	7.18566	−	12.4459i	0.298884	−	0.517682i
$579$	23.5224	+	26.7542i	0.977559	+	1.11187i
$580$	−16.9838			−0.705215
$581$	0.0217743	−	1.24029i	0.000903349	−	0.0514557i
$582$	3.19416	+	15.9531i	0.132402	+	0.661278i
$583$	−7.87985	+	4.54944i	−0.326350	+	0.188418i
$584$	−33.1265			−1.37078
$585$	−2.46540	+	38.3248i	−0.101932	+	1.58453i
$586$		−	31.7519i		−	1.31166i
$587$	7.27507	−	4.20026i	0.300274	−	0.173363i	−0.342292	−	0.939594i	$-0.611203\pi$
$587$	7.27507	−	4.20026i	0.300274	−	0.173363i	0.642566	+	0.766230i	$0.277870\pi$
$588$	7.20822	+	2.72223i	0.297262	+	0.112263i
$589$	−5.16098	+	8.93908i	−0.212654	+	0.368328i
$590$	20.2795			0.834892
$591$	−3.26925	+	2.87435i	−0.134479	+	0.118235i
$592$	5.89575	+	3.40391i	0.242314	+	0.139900i
$593$		−	23.8760i		−	0.980468i	−0.871591	−	0.490234i	$-0.836911\pi$
$593$		−	23.8760i		−	0.980468i	0.871591	−	0.490234i	$-0.163089\pi$
$594$	30.7711	−	2.13360i	1.26255	−	0.0875428i
$595$	−17.4495	−	10.4871i	−0.715358	−	0.429929i
$596$	−2.79005	−	4.83251i	−0.114285	−	0.197947i
$597$	5.46371	−	16.1624i	0.223615	−	0.661483i
$598$	−6.30704	−	9.46595i	−0.257914	−	0.387091i
$599$		−	38.5869i		−	1.57662i	−0.615279	−	0.788310i	$-0.710956\pi$
$599$		−	38.5869i		−	1.57662i	0.615279	−	0.788310i	$-0.289044\pi$
$600$	7.96206	+	39.7663i	0.325050	+	1.62345i
$601$	−2.90334	+	1.67625i	−0.118430	+	0.0683755i	−0.558045	−	0.829811i	$-0.688448\pi$
$601$	−2.90334	+	1.67625i	−0.118430	+	0.0683755i	0.439615	+	0.898186i	$0.355115\pi$
$602$	27.7333	+	0.486881i	1.13032	+	0.0198438i
$603$	−7.95011	+	10.4150i	−0.323754	+	0.424131i
$604$	8.32150	+	4.80442i	0.338597	+	0.195489i
$605$	45.5825	+	26.3171i	1.85319	+	1.06994i
$606$	−4.04061	−	1.36593i	−0.164139	−	0.0554872i
$607$	−13.3140	−	7.68682i	−0.540397	−	0.311998i	0.204843	−	0.978795i	$-0.434332\pi$
$607$	−13.3140	−	7.68682i	−0.540397	−	0.311998i	−0.745240	+	0.666797i	$0.767665\pi$
$608$	4.95008	+	8.57380i	0.200752	+	0.347713i
$609$	−22.3177	−	26.3009i	−0.904360	−	1.06577i
$610$	−0.698921			−0.0282985
$611$	−16.4923	+	33.3329i	−0.667205	+	1.34851i
$612$	−3.28440	−	2.50709i	−0.132764	−	0.101343i
$613$	−22.6306	+	13.0658i	−0.914043	+	0.527723i	−0.881730	−	0.471755i	$-0.843621\pi$
$613$	−22.6306	+	13.0658i	−0.914043	+	0.527723i	−0.0323129	+	0.999478i	$0.510287\pi$
$614$	20.1467	+	34.8951i	0.813055	+	1.40825i
$615$	29.0884	−	25.5747i	1.17296	−	1.03127i
$616$	−20.0636	−	36.2042i	−0.808384	−	1.45871i
$617$	4.95040	−	8.57435i	0.199296	−	0.345190i	−0.749005	−	0.662565i	$-0.769468\pi$
$617$	4.95040	−	8.57435i	0.199296	−	0.345190i	0.948300	+	0.317375i	$0.102801\pi$
$618$	8.66177	+	9.85181i	0.348428	+	0.396298i
$619$	5.81010			0.233528			0.116764	−	0.993160i	$-0.462748\pi$
$619$	5.81010			0.233528			0.116764	+	0.993160i	$0.462748\pi$
$620$	7.01065	+	4.04760i	0.281555	+	0.162556i
$621$	−12.6095	−	6.15923i	−0.506003	−	0.247161i
$622$	−9.69462	−	16.7916i	−0.388719	−	0.673281i
$623$	15.0747	−	8.35408i	0.603957	−	0.334699i
$624$	−14.0258	+	3.75744i	−0.561479	+	0.150418i
$625$	−5.18178			−0.207271
$626$	2.43443	−	1.40552i	0.0972993	−	0.0561758i
$627$	−4.97155	−	24.8303i	−0.198545	−	0.991625i
$628$	−3.10593	−	1.79321i	−0.123940	−	0.0715568i
$629$			6.34562i			0.253017i
$630$	−20.4299	+	25.8117i	−0.813946	+	1.02836i
$631$	30.6338	+	17.6864i	1.21951	+	0.704086i	0.964814	−	0.262934i	$-0.0846901\pi$
$631$	30.6338	+	17.6864i	1.21951	+	0.704086i	0.254700	+	0.967020i	$0.418023\pi$
$632$	14.4353			0.574205
$633$	12.5520	−	11.0358i	0.498898	−	0.438635i
$634$	−8.41524	−	14.5756i	−0.334212	−	0.578872i
$635$	−68.2626	+	39.4114i	−2.70892	+	1.56400i
$636$	0.631157	−	1.86705i	0.0250270	−	0.0740332i
$637$	22.2146	+	11.9796i	0.880175	+	0.474650i
$638$			44.6821i			1.76898i
$639$	4.04330	−	31.3212i	0.159950	−	1.23905i
$640$	−9.97803	+	5.76082i	−0.394416	+	0.227716i
$641$	−1.24524	−	0.718939i	−0.0491840	−	0.0283964i	0.475206	−	0.879874i	$-0.342373\pi$
$641$	−1.24524	−	0.718939i	−0.0491840	−	0.0283964i	−0.524390	+	0.851478i	$0.675707\pi$
$642$	−1.08801	+	3.21847i	−0.0429402	+	0.127023i
$643$	−15.9331	+	27.5969i	−0.628339	+	1.08831i	0.359546	+	0.933127i	$0.382931\pi$
$643$	−15.9331	+	27.5969i	−0.628339	+	1.08831i	−0.987885	+	0.155187i	$0.950402\pi$
$644$	−0.0797088	+	4.54030i	−0.00314097	+	0.178913i
$645$	17.6751	−	52.2855i	0.695958	−	2.05874i
$646$	3.64170	−	6.30761i	0.143281	−	0.248170i
$647$	−4.68755	−	8.11907i	−0.184287	−	0.319194i	0.759049	−	0.651033i	$-0.225664\pi$
$647$	−4.68755	−	8.11907i	−0.184287	−	0.319194i	−0.943336	+	0.331839i	$0.892331\pi$
$648$	−19.4930	+	19.6904i	−0.765758	+	0.773510i
$649$			24.8487i			0.975399i
$650$	2.05321	+	31.9671i	0.0805337	+	1.25385i
$651$	2.94434	+	16.1754i	0.115398	+	0.633963i
$652$	3.86999	−	2.23434i	0.151560	−	0.0875034i
$653$	0.786151	−	0.453885i	0.0307645	−	0.0177619i	−0.484539	−	0.874770i	$-0.661013\pi$
$653$	0.786151	−	0.453885i	0.0307645	−	0.0177619i	0.515303	+	0.857008i	$0.327679\pi$
$654$	−14.2938	−	16.2576i	−0.558931	−	0.635723i
$655$		−	16.8488i		−	0.658337i
$656$	12.6825	+	7.32226i	0.495169	+	0.285886i
$657$	−29.7925	+	12.4284i	−1.16232	+	0.484880i
$658$	−27.8824	+	15.4518i	−1.08697	+	0.602373i
$659$	23.6999	+	13.6832i	0.923218	+	0.533020i	0.884660	−	0.466236i	$-0.154390\pi$
$659$	23.6999	+	13.6832i	0.923218	+	0.533020i	0.0385576	+	0.999256i	$0.487724\pi$
$660$	−19.4736	+	3.89904i	−0.758010	+	0.151770i
$661$	16.8620	+	29.2058i	0.655854	+	1.13597i	0.981679	+	0.190543i	$0.0610247\pi$
$661$	16.8620	+	29.2058i	0.655854	+	1.13597i	−0.325825	+	0.945430i	$0.605642\pi$
$662$		−	5.10025i		−	0.198227i
$663$	−9.56987	−	9.57082i	−0.371663	−	0.371700i
$664$		−	1.44341i		−	0.0560151i
$665$	23.1638	+	13.9214i	0.898255	+	0.539849i
$666$	10.1761	+	1.31365i	0.394316	+	0.0509029i
$667$	10.1644	−	17.6053i	0.393567	−	0.681679i
$668$		−	4.96333i		−	0.192037i
$669$	−13.0994	+	11.5170i	−0.506451	+	0.445275i
$670$	−9.05676	+	15.6868i	−0.349893	+	0.606033i
$671$		−	0.856399i		−	0.0330609i
$672$	14.8479	+	5.31153i	0.572770	+	0.204897i
$673$	6.43713	+	11.1494i	0.248133	+	0.429779i	0.963008	−	0.269473i	$-0.0868496\pi$
$673$	6.43713	+	11.1494i	0.248133	+	0.429779i	−0.714875	+	0.699253i	$0.753516\pi$
$674$	−5.07268	−	8.78613i	−0.195392	−	0.338429i
$675$	22.0803	+	32.7768i	0.849872	+	1.26158i
$676$	8.19372	−	1.05691i	0.315143	−	0.0406504i
$677$	−10.4739			−0.402543			−0.201271	−	0.979536i	$-0.564507\pi$
$677$	−10.4739			−0.402543			−0.201271	+	0.979536i	$0.564507\pi$
$678$	8.24815	−	1.65146i	0.316768	−	0.0634238i
$679$	10.9596	−	18.2357i	0.420592	−	0.699823i
$680$	−20.5151	−	11.8444i	−0.786719	−	0.454213i
$681$	5.71274	−	16.8991i	0.218913	−	0.647574i
$682$	10.6487	−	18.4441i	0.407759	−	0.706260i
$683$	13.4691	−	23.3292i	0.515382	−	0.892668i	−0.484458	−	0.874814i	$-0.660983\pi$
$683$	13.4691	−	23.3292i	0.515382	−	0.892668i	0.999841	−	0.0178539i	$-0.00568339\pi$
$684$	4.35998	+	3.32812i	0.166708	+	0.127254i
$685$	24.4331	+	14.1065i	0.933541	+	0.538980i
$686$	9.81571	+	19.2788i	0.374765	+	0.736069i
$687$	−5.27409	−	26.3412i	−0.201219	−	1.00498i
$688$	20.8679			0.795579
$689$	2.86285	−	5.78618i	0.109066	−	0.220436i
$690$	−18.3787	−	6.21292i	−0.699664	−	0.236522i
$691$	1.32650	+	2.29757i	0.0504625	+	0.0874036i	0.890153	−	0.455661i	$-0.150597\pi$
$691$	1.32650	+	2.29757i	0.0504625	+	0.0874036i	−0.839691	+	0.543065i	$0.817264\pi$
$692$	0.453985	+	0.786325i	0.0172579	+	0.0298916i
$693$	−31.6275	−	25.0331i	−1.20143	−	0.950927i
$694$		−	19.5187i		−	0.740918i
$695$	2.24094	−	3.88142i	0.0850037	−	0.147231i
$696$	−26.5019	−	30.1430i	−1.00455	−	1.14257i
$697$			13.6503i			0.517041i
$698$	19.4678	−	33.7192i	0.736868	−	1.27629i
$699$	3.90427	−	0.781719i	0.147673	−	0.0295673i
$700$	6.58751	−	10.9610i	0.248985	−	0.414285i
$701$		−	10.5490i		−	0.398429i	−0.979956	−	0.199215i	$-0.936161\pi$
$701$		−	10.5490i		−	0.398429i	0.979956	−	0.199215i	$-0.0638391\pi$
$702$	−17.3293	+	13.3653i	−0.654052	+	0.504442i
$703$		−	8.42370i		−	0.317706i
$704$	−22.0293	−	38.1559i	−0.830260	−	1.43805i
$705$	12.4529	+	62.1958i	0.469005	+	2.34243i
$706$	−12.1146	−	6.99436i	−0.455939	−	0.263236i
$707$	2.70358	+	4.87854i	0.101679	+	0.183477i
$708$	−3.55390	−	4.04217i	−0.133564	−	0.151914i
$709$	22.0271	+	12.7174i	0.827245	+	0.477610i	0.852909	−	0.522060i	$-0.174836\pi$
$709$	22.0271	+	12.7174i	0.827245	+	0.477610i	−0.0256633	+	0.999671i	$0.508170\pi$
$710$		−	43.6591i		−	1.63850i
$711$	12.9825	−	5.41586i	0.486881	−	0.203111i
$712$	17.3675	−	10.0271i	0.650875	−	0.375783i
$713$	−8.39141	+	4.84478i	−0.314261	+	0.181439i
$714$	−2.07759	−	11.4137i	−0.0777520	−	0.427148i
$715$	−64.9200	+	4.16975i	−2.42787	+	0.155940i
$716$		−	5.89200i		−	0.220194i
$717$	8.26611	+	41.2848i	0.308704	+	1.54181i
$718$	−3.21667	−	5.57143i	−0.120045	−	0.207924i
$719$	1.57349	−	2.72536i	0.0586811	−	0.101639i	−0.835192	−	0.549958i	$-0.814644\pi$
$719$	1.57349	−	2.72536i	0.0586811	−	0.101639i	0.893874	+	0.448319i	$0.147977\pi$
$720$	−15.0268	+	19.6858i	−0.560017	+	0.733646i
$721$	0.301112	−	17.1517i	0.0112140	−	0.638762i
$722$	6.26280	−	10.8475i	0.233077	−	0.403702i
$723$	22.6728	+	7.66456i	0.843211	+	0.285048i
$724$	−10.3787	−	5.99216i	−0.385722	−	0.222697i
$725$	−49.5794	+	28.6247i	−1.84133	+	1.06309i
$726$	5.88852	+	29.4100i	0.218543	+	1.09151i
$727$		−	23.8257i		−	0.883647i	−0.897102	−	0.441824i	$-0.854332\pi$
$727$		−	23.8257i		−	0.883647i	0.897102	−	0.441824i	$-0.145668\pi$
$728$	26.0894	+	13.4835i	0.966939	+	0.499732i
$729$	−10.1437	+	25.0221i	−0.375693	+	0.926744i
$730$	−38.6478	+	22.3133i	−1.43042	+	0.825853i
$731$	9.72554	+	16.8451i	0.359712	+	0.623040i
$732$	0.122483	+	0.139311i	0.00452711	+	0.00514909i
$733$	23.3759			0.863407			0.431704	−	0.902016i	$-0.357913\pi$
$733$	23.3759			0.863407			0.431704	+	0.902016i	$0.357913\pi$
$734$	−9.63357	−	5.56195i	−0.355582	−	0.205295i
$735$	42.4798	−	6.96440i	1.56689	−	0.256886i
$736$			9.29362i			0.342567i
$737$	−19.2213	−	11.0974i	−0.708024	−	0.408778i
$738$	21.8901	+	2.82583i	0.805787	+	0.104020i
$739$	−8.74351	+	5.04807i	−0.321635	+	0.185696i	−0.652121	−	0.758115i	$-0.726121\pi$
$739$	−8.74351	+	5.04807i	−0.321635	+	0.185696i	0.330486	+	0.943811i	$0.392787\pi$
$740$	−6.60646			−0.242858
$741$	12.7038	+	12.7051i	0.466686	+	0.466733i
$742$	4.84004	−	2.68224i	0.177683	−	0.0984680i
$743$	5.58427	+	9.67223i	0.204867	+	0.354840i	0.950090	−	0.311975i	$-0.100991\pi$
$743$	5.58427	+	9.67223i	0.204867	+	0.354840i	−0.745223	+	0.666815i	$0.767657\pi$
$744$	3.75586	+	18.7585i	0.137697	+	0.687721i
$745$	−26.9982	−	15.5874i	−0.989139	−	0.571080i
$746$	17.2907			0.633058
$747$	−0.541541	−	1.29814i	−0.0198140	−	0.0474965i
$748$	3.49960	−	6.06148i	0.127958	−	0.221630i
$749$	3.88591	−	2.15348i	0.141988	−	0.0786866i
$750$	12.3592	+	14.0572i	0.451295	+	0.513298i
$751$	19.1851	+	33.2296i	0.700074	+	1.21256i	0.968440	+	0.249247i	$0.0801832\pi$
$751$	19.1851	+	33.2296i	0.700074	+	1.21256i	−0.268366	+	0.963317i	$0.586483\pi$
$752$	−20.7695	+	11.9913i	−0.757387	+	0.437278i
$753$	14.0353	+	4.74465i	0.511475	+	0.172905i
$754$	−17.5782	−	26.3824i	−0.640161	−	0.960789i
$755$	53.6826			1.95371
$756$	8.72513	−	0.451256i	0.317330	−	0.0164120i
$757$	−0.537117	−	0.930315i	−0.0195219	−	0.0338129i	0.856099	−	0.516811i	$-0.172881\pi$
$757$	−0.537117	−	0.930315i	−0.0195219	−	0.0338129i	−0.875621	+	0.482998i	$0.839548\pi$
$758$	−11.3796	−	6.57001i	−0.413326	−	0.238634i
$759$	7.61279	−	22.5197i	0.276327	−	0.817412i
$760$	27.2335	+	15.7232i	0.987861	+	0.570342i
$761$	−19.3646	−	11.1801i	−0.701965	−	0.405280i	0.106114	−	0.994354i	$-0.466159\pi$
$761$	−19.3646	−	11.1801i	−0.701965	−	0.405280i	−0.808079	+	0.589074i	$0.799492\pi$
$762$	−42.5518	−	14.3847i	−1.54149	−	0.521101i
$763$	−0.496900	+	28.3040i	−0.0179890	+	1.02467i
$764$	−8.06689	+	4.65742i	−0.291850	+	0.168500i
$765$	−22.8942	−	2.95545i	−0.827743	−	0.106855i
$766$		−	13.7805i		−	0.497908i
$767$	−9.77566	−	14.6718i	−0.352979	−	0.529770i
$768$	22.2318	+	7.51547i	0.802220	+	0.271191i
$769$	−27.4733	−	47.5851i	−0.990711	−	1.71596i	−0.613121	−	0.789989i	$-0.710086\pi$
$769$	−27.4733	−	47.5851i	−0.990711	−	1.71596i	−0.377590	−	0.925973i	$-0.623247\pi$
$770$	−47.7941	−	28.7242i	−1.72238	−	1.03515i
$771$	2.53494	−	2.22873i	0.0912936	−	0.0802659i
$772$		−	13.0709i		−	0.470433i
$773$	−32.8675	−	18.9761i	−1.18216	−	0.682521i	−0.225648	−	0.974209i	$-0.572450\pi$
$773$	−32.8675	−	18.9761i	−1.18216	−	0.682521i	−0.956514	+	0.291687i	$0.905783\pi$
$774$	29.0269	−	12.1091i	1.04335	−	0.435252i
$775$	27.2874			0.980194
$776$	12.3781	−	21.4395i	0.444348	−	0.769634i
$777$	−8.68126	−	10.2307i	−0.311439	−	0.367023i
$778$	15.4779	−	8.93617i	0.554910	−	0.320377i
$779$		−	18.1205i		−	0.649233i
$780$	9.96422	−	9.96323i	0.356776	−	0.356741i
$781$	53.4961			1.91424
$782$	5.92117	−	3.41859i	0.211741	−	0.122249i
$783$	−35.1438	−	17.1663i	−1.25594	−	0.613473i
$784$	7.63813	+	14.3722i	0.272790	+	0.513293i
$785$	−20.0366			−0.715136
$786$	7.21068	−	6.33968i	0.257197	−	0.226129i
$787$	11.9389	−	20.6788i	0.425576	−	0.737120i	−0.570898	−	0.821021i	$-0.693405\pi$
$787$	11.9389	−	20.6788i	0.425576	−	0.737120i	0.996474	+	0.0839014i	$0.0267381\pi$
$788$	1.59722			0.0568985
$789$	−8.86055	−	10.0779i	−0.315444	−	0.358782i
$790$	16.8413	−	9.72333i	0.599186	−	0.345940i
$791$	−9.42831	−	5.66639i	−0.335232	−	0.201474i
$792$	−37.3071	−	28.4778i	−1.32565	−	1.01191i
$793$	0.336913	+	0.505658i	0.0119641	+	0.0179564i
$794$	25.1403			0.892195
$795$	−2.16167	−	10.7964i	−0.0766667	−	0.382909i
$796$	−5.42118	+	3.12992i	−0.192149	+	0.110937i
$797$	6.27271	−	10.8646i	0.222191	−	0.384845i	−0.733282	−	0.679924i	$-0.762013\pi$
$797$	6.27271	−	10.8646i	0.222191	−	0.384845i	0.955473	+	0.295079i	$0.0953459\pi$
$798$	2.75797	+	15.1515i	0.0976309	+	0.536357i
$799$	−19.3594	−	11.1772i	−0.684888	−	0.395420i
$800$	13.0862	−	22.6659i	0.462667	−	0.801362i
$801$	11.8576	−	15.5340i	0.418968	−	0.548866i
$802$	−7.95907	+	13.7855i	−0.281045	+	0.486783i
$803$	−27.3409	−	47.3558i	−0.964838	−	1.67115i
$804$	4.71390	−	0.943825i	0.166246	−	0.0332861i
$805$	12.2972	+	22.1900i	0.433419	+	0.782095i
$806$	0.968541	+	15.0795i	0.0341154	+	0.531152i
$807$	−46.5194	−	15.7259i	−1.63756	−	0.553578i
$808$	3.24502	+	5.62054i	0.114159	+	0.197730i
$809$	−16.5215	+	9.53870i	−0.580866	+	0.335363i	−0.761477	−	0.648192i	$-0.775526\pi$
$809$	−16.5215	+	9.53870i	−0.580866	+	0.335363i	0.180612	+	0.983554i	$0.442192\pi$
$810$	−9.47898	+	36.1024i	−0.333057	+	1.26851i
$811$	10.1759			0.357324			0.178662	−	0.983910i	$-0.442823\pi$
$811$	10.1759			0.357324			0.178662	+	0.983910i	$0.442823\pi$
$812$	−0.222155	+	12.6542i	−0.00779611	+	0.444075i
$813$	−34.9457	+	30.7245i	−1.22560	+	1.07755i
$814$			17.3807i			0.609192i
$815$	12.4828	−	21.6208i	0.437253	−	0.757344i
$816$	−1.71353	−	8.55815i	−0.0599854	−	0.299595i
$817$	−12.9105	−	22.3616i	−0.451680	−	0.782333i
$818$	−29.3461			−1.02606
$819$	28.5225	+	2.33820i	0.996657	+	0.0817035i
$820$	−14.2113			−0.496282
$821$	−6.84141	−	11.8497i	−0.238767	−	0.413556i	0.721594	−	0.692317i	$-0.243410\pi$
$821$	−6.84141	−	11.8497i	−0.238767	−	0.413556i	−0.960361	+	0.278760i	$0.910077\pi$
$822$	3.15636	+	15.7643i	0.110091	+	0.549844i
$823$	−6.07866	+	10.5285i	−0.211889	+	0.367002i	−0.952306	−	0.305146i	$-0.901295\pi$
$823$	−6.07866	+	10.5285i	−0.211889	+	0.367002i	0.740417	+	0.672148i	$0.234628\pi$
$824$		−	19.9606i		−	0.695362i
$825$	−50.2762	+	44.2031i	−1.75039	+	1.53896i
$826$	0.265263	−	15.1097i	0.00922968	−	0.525733i
$827$	−1.41387			−0.0491652			−0.0245826	−	0.999698i	$-0.507826\pi$
$827$	−1.41387			−0.0491652			−0.0245826	+	0.999698i	$0.507826\pi$
$828$	1.98241	+	4.75208i	0.0688936	+	0.165146i
$829$	−29.3186	+	16.9271i	−1.01828	+	0.587903i	−0.913605	−	0.406604i	$-0.866713\pi$
$829$	−29.3186	+	16.9271i	−1.01828	+	0.587903i	−0.104673	+	0.994507i	$0.533380\pi$
$830$	−0.972252	−	1.68399i	−0.0337474	−	0.0584521i
$831$	−22.2899	−	7.53512i	−0.773228	−	0.261390i
$832$	28.0179	+	13.8625i	0.971345	+	0.480596i
$833$	−8.04189	+	12.8639i	−0.278635	+	0.445709i
$834$	2.50431	−	0.501417i	0.0867171	−	0.0173626i
$835$	−13.8645	−	24.0141i	−0.479802	−	0.831042i
$836$	−4.64565	+	8.04651i	−0.160673	+	0.278294i
$837$	10.4157	+	15.4615i	0.360020	+	0.534427i
$838$	3.79000	−	6.56447i	0.130923	−	0.226766i
$839$	41.7382	+	24.0976i	1.44096	+	0.831940i	0.997914	−	0.0645579i	$-0.0205637\pi$
$839$	41.7382	+	24.0976i	1.44096	+	0.831940i	0.443048	+	0.896498i	$0.353897\pi$
$840$	49.2793	−	8.97012i	1.70030	−	0.309498i
$841$	13.8290	−	23.9526i	0.476863	−	0.825951i
$842$	−22.0897	+	12.7535i	−0.761261	+	0.439514i
$843$	−4.58615	−	22.9054i	−0.157956	−	0.788904i
$844$	−6.13238			−0.211085
$845$	36.6913	−	28.0020i	1.26222	−	0.963297i
$846$	−21.9319	+	28.7318i	−0.754035	+	0.987818i
$847$	20.2044	−	33.6180i	0.694230	−	1.15513i
$848$	3.60533	−	2.08154i	0.123808	−	0.0714804i
$849$	12.3814	+	14.0825i	0.424930	+	0.483310i
$850$	−19.2546			−0.660429
$851$	3.95380	−	6.84819i	0.135535	−	0.234753i
$852$	−8.70226	+	7.65108i	−0.298135	+	0.262122i
$853$	−20.7351			−0.709956			−0.354978	−	0.934875i	$-0.615512\pi$
$853$	−20.7351			−0.709956			−0.354978	+	0.934875i	$0.615512\pi$
$854$	−0.00914216	+	0.520747i	−0.000312838	+	0.0178196i
$855$	30.3917	+	3.92331i	1.03937	+	0.134174i
$856$	4.47694	−	2.58476i	0.153019	−	0.0883453i
$857$	10.5052			0.358851			0.179426	−	0.983772i	$-0.442576\pi$
$857$	10.5052			0.358851			0.179426	+	0.983772i	$0.442576\pi$
$858$	−26.2119	−	26.2145i	−0.894859	−	0.894948i
$859$			12.9974i			0.443464i	0.975108	+	0.221732i	$0.0711711\pi$
$859$			12.9974i			0.443464i	−0.975108	+	0.221732i	$0.928829\pi$
$860$	−17.5375	+	10.1253i	−0.598025	+	0.345270i
$861$	−18.6745	−	22.0075i	−0.636426	−	0.750014i
$862$	−15.9879	+	27.6918i	−0.544549	+	0.943187i
$863$	−54.6116			−1.85900			−0.929500	−	0.368822i	$-0.879761\pi$
$863$	−54.6116			−1.85900			−0.929500	+	0.368822i	$0.879761\pi$
$864$	17.8379	−	1.23684i	0.606858	−	0.0420783i
$865$	4.39304	+	2.53632i	0.149368	+	0.0862375i
$866$			20.8315i			0.707884i
$867$	−16.0036	+	14.0704i	−0.543510	+	0.477857i
$868$	3.10746	−	5.17050i	0.105474	−	0.175498i
$869$	11.9141	+	20.6359i	0.404160	+	0.700025i
$870$	−51.2228	−	17.3159i	−1.73662	−	0.587065i
$871$	15.7149	−	1.00935i	0.532479	−	0.0342006i
$872$			32.9394i			1.11547i
$873$	3.08862	−	23.9258i	0.104534	−	0.809767i
$874$	−7.86024	+	4.53811i	−0.265877	+	0.153504i
$875$	0.429648	−	24.4732i	0.0145248	−	0.827345i
$876$	11.2204	+	3.79308i	0.379104	+	0.128156i
$877$	−25.9547	−	14.9849i	−0.876427	−	0.506005i	−0.00694821	−	0.999976i	$-0.502212\pi$
$877$	−25.9547	−	14.9849i	−0.876427	−	0.506005i	−0.869479	+	0.493971i	$0.835545\pi$
$878$	34.5775	+	19.9633i	1.16693	+	0.673729i
$879$	−15.0775	+	44.6014i	−0.508552	+	1.50437i
$880$	−36.3308	−	20.9756i	−1.22471	−	0.707088i
$881$	24.5095	+	42.4518i	0.825747	+	1.43024i	0.901347	+	0.433098i	$0.142580\pi$
$881$	24.5095	+	42.4518i	0.825747	+	1.43024i	−0.0755992	+	0.997138i	$0.524087\pi$
$882$	18.9644	+	15.5594i	0.638563	+	0.523911i
$883$	−23.5583			−0.792800			−0.396400	−	0.918078i	$-0.629741\pi$
$883$	−23.5583			−0.792800			−0.396400	+	0.918078i	$0.629741\pi$
$884$	0.318303	+	4.95575i	0.0107057	+	0.166680i
$885$	−28.4862	−	9.62979i	−0.957554	−	0.323702i
$886$	29.8531	−	17.2357i	1.00294	−	0.579045i
$887$	23.4791	+	40.6669i	0.788350	+	1.36546i	0.926977	+	0.375117i	$0.122398\pi$
$887$	23.4791	+	40.6669i	0.788350	+	1.36546i	−0.138627	+	0.990345i	$0.544269\pi$
$888$	−10.3089	−	11.7252i	−0.345943	−	0.393471i
$889$	28.4715	+	51.3761i	0.954903	+	1.72310i
$890$	13.5082	−	23.3968i	0.452795	−	0.784264i
$891$	−44.2368	−	11.6147i	−1.48199	−	0.389109i
$892$	6.39978			0.214281
$893$	25.6993	+	14.8375i	0.859994	+	0.496518i
$894$	−3.48773	−	17.4194i	−0.116647	−	0.582591i
$895$	−16.4587	−	28.5073i	−0.550154	−	0.952894i
$896$	4.16171	+	7.50971i	0.139033	+	0.250882i
$897$	4.36444	+	16.2916i	0.145725	+	0.543960i
$898$	3.45067			0.115150
$899$	−23.3876	+	13.5028i	−0.780018	+	0.450344i
$900$	1.85648	−	14.3811i	0.0618827	−	0.479371i
$901$	3.36056	+	1.94022i	0.111956	+	0.0646381i
$902$			37.3881i			1.24489i
$903$	−38.7253	−	13.8532i	−1.28870	−	0.461005i
$904$	−11.0848	−	6.39978i	−0.368673	−	0.212854i
$905$	−66.9539			−2.22562
$906$	20.1991	+	22.9742i	0.671070	+	0.763268i
$907$	−20.1500	−	34.9009i	−0.669071	−	1.15887i	−0.978164	−	0.207834i	$-0.933359\pi$
$907$	−20.1500	−	34.9009i	−0.669071	−	1.15887i	0.309093	−	0.951032i	$-0.399975\pi$
$908$	−5.66827	+	3.27258i	−0.188108	+	0.108604i
$909$	5.02716	+	3.83740i	0.166740	+	0.127279i
$910$	39.5201	−	1.84245i	1.31008	−	0.0610767i
$911$			11.3974i			0.377612i	0.982014	+	0.188806i	$0.0604617\pi$
$911$			11.3974i			0.377612i	−0.982014	+	0.188806i	$0.939538\pi$
$912$	2.27467	+	11.3608i	0.0753220	+	0.376193i
$913$	2.06342	−	1.19132i	0.0682892	−	0.0394268i
$914$	−4.07703	−	2.35387i	−0.134856	−	0.0778593i
$915$	0.981763	+	0.331886i	0.0324561	+	0.0109718i
$916$	−4.92835	+	8.53616i	−0.162837	+	0.282043i
$917$	−12.5536	−	0.220389i	−0.414555	−	0.00727787i
$918$	−7.34957	−	10.9100i	−0.242572	−	0.360083i
$919$	10.8590	−	18.8083i	0.358205	−	0.620430i	−0.629456	−	0.777036i	$-0.716722\pi$
$919$	10.8590	−	18.8083i	0.358205	−	0.620430i	0.987661	+	0.156606i	$0.0500554\pi$
$920$	14.7599	+	25.5650i	0.486621	+	0.842852i
$921$	−11.7296	−	58.5833i	−0.386505	−	1.93039i
$922$			44.2441i			1.45710i
$923$	−31.5866	+	21.0457i	−1.03969	+	0.692729i
$924$	2.65035	+	14.5603i	0.0871900	+	0.478998i
$925$	−19.2856	+	11.1346i	−0.634108	+	0.366102i
$926$	27.7863	−	16.0424i	0.913115	−	0.527187i
$927$	−7.48887	−	17.9517i	−0.245967	−	0.589613i
$928$			25.9021i			0.850277i
$929$	13.4799	+	7.78265i	0.442263	+	0.255340i	0.704557	−	0.709647i	$-0.251146\pi$
$929$	13.4799	+	7.78265i	0.442263	+	0.255340i	−0.262294	+	0.964988i	$0.584479\pi$
$930$	17.0172	+	19.3552i	0.558017	+	0.634683i
$931$	10.6755	−	17.0766i	0.349874	−	0.559664i
$932$	−1.26522	−	0.730475i	−0.0414437	−	0.0239275i
$933$	5.64432	+	28.1904i	0.184787	+	0.922911i
$934$	−14.0101	−	24.2662i	−0.458424	−	0.794014i
$935$		−	39.1031i		−	1.27881i
$936$	33.2312	+	2.13773i	1.08620	+	0.0698740i
$937$			25.7421i			0.840957i	0.907302	+	0.420479i	$0.138138\pi$
$937$			25.7421i			0.840957i	−0.907302	+	0.420479i	$0.861862\pi$
$938$	11.5693	+	6.95314i	0.377752	+	0.227028i
$939$	−4.08701	+	0.818309i	−0.133375	+	0.0267045i
$940$	11.6366	−	20.1552i	0.379544	−	0.657390i
$941$			52.3679i			1.70714i	0.520975	+	0.853572i	$0.325569\pi$
$941$			52.3679i			1.70714i	−0.520975	+	0.853572i	$0.674431\pi$
$942$	−7.53914	−	8.57494i	−0.245639	−	0.279387i
$943$	8.50515	−	14.7313i	0.276966	−	0.479719i
$944$		−	11.3692i		−	0.370037i
$945$	40.9543	−	26.5561i	1.33224	−	0.863869i
$946$	26.6383	+	46.1389i	0.866085	+	1.50010i
$947$	−22.3864	−	38.7745i	−0.727462	−	1.26000i	−0.957953	−	0.286926i	$-0.907367\pi$
$947$	−22.3864	−	38.7745i	−0.727462	−	1.26000i	0.230491	−	0.973074i	$-0.425967\pi$
$948$	−4.88946	−	1.65288i	−0.158802	−	0.0536832i
$949$	34.7734	+	17.2050i	1.12879	+	0.558496i
$950$	25.5602			0.829281
$951$	4.89945	+	24.4701i	0.158876	+	0.793498i
$952$	−9.09330	+	15.1303i	−0.294715	+	0.490377i
$953$	27.2295	+	15.7209i	0.882048	+	0.509251i	0.871333	−	0.490692i	$-0.163256\pi$
$953$	27.2295	+	15.7209i	0.882048	+	0.509251i	0.0107152	+	0.999943i	$0.496589\pi$
$954$	3.80711	−	4.98748i	0.123260	−	0.161476i
$955$	−26.0200	+	45.0680i	−0.841989	+	1.45837i
$956$	7.72424	−	13.3788i	0.249820	−	0.432701i
$957$	21.2175	−	62.7642i	0.685863	−	2.02888i
$958$	−12.5515	−	7.24661i	−0.405520	−	0.234127i
$959$	10.8299	−	18.0199i	0.349717	−	0.581894i
$960$	52.2784	−	10.4673i	1.68728	−	0.337830i
$961$	−18.1280			−0.584774
$962$	−6.83767	−	10.2623i	−0.220455	−	0.330871i
$963$	3.05661	−	4.00429i	0.0984979	−	0.129036i
$964$	−4.39069	−	7.60490i	−0.141415	−	0.244937i
$965$	−36.5123	−	63.2412i	−1.17537	−	2.03581i
$966$	−4.86948	+	13.6122i	−0.156673	+	0.437964i
$967$		−	15.6510i		−	0.503302i	−0.967818	−	0.251651i	$-0.919026\pi$
$967$		−	15.6510i		−	0.503302i	0.967818	−	0.251651i	$-0.0809735\pi$
$968$	22.8194	−	39.5243i	0.733443	−	1.27036i
$969$	−8.11063	+	7.13092i	−0.260551	+	0.229078i
$970$		−	33.3506i		−	1.07082i
$971$	15.8546	−	27.4610i	0.508800	−	0.881267i	−0.491148	−	0.871076i	$-0.663423\pi$
$971$	15.8546	−	27.4610i	0.508800	−	0.881267i	0.999948	−	0.0101910i	$-0.00324396\pi$
$972$	8.85719	−	4.43742i	0.284094	−	0.142330i
$973$	−2.86263	−	1.72043i	−0.0917717	−	0.0551546i
$974$			37.3338i			1.19625i
$975$	12.2956	−	45.8786i	0.393773	−	1.46929i
$976$			0.391835i			0.0125423i
$977$	15.0361	+	26.0433i	0.481047	+	0.833198i	0.999763	−	0.0217482i	$-0.00692321\pi$
$977$	15.0361	+	26.0433i	0.481047	+	0.833198i	−0.518716	+	0.854946i	$0.673590\pi$
$978$	13.9498	−	2.79306i	0.446066	−	0.0893121i
$979$	28.6685	+	16.5518i	0.916249	+	0.528997i
$980$	−13.3927	−	8.37245i	−0.427814	−	0.267448i
$981$	12.3583	+	29.6242i	0.394569	+	0.945829i
$982$	−29.5786	−	17.0772i	−0.943891	−	0.544955i
$983$		−	2.46092i		−	0.0784910i	−0.999230	−	0.0392455i	$-0.987505\pi$
$983$		−	2.46092i		−	0.0784910i	0.999230	−	0.0392455i	$-0.0124954\pi$
$984$	−22.1757	−	25.2224i	−0.706935	−	0.804061i
$985$	7.72782	−	4.46166i	0.246229	−	0.142160i
$986$	16.5028	−	9.52789i	0.525556	−	0.303430i
$987$	46.5032	−	8.46480i	1.48021	−	0.269437i
$988$	−0.422541	−	6.57866i	−0.0134428	−	0.209295i
$989$		−	24.2390i		−	0.770755i
$990$	−62.7074	−	8.09499i	−1.99297	−	0.257276i
$991$	13.9551	+	24.1710i	0.443299	+	0.767817i	0.997932	−	0.0642786i	$-0.0204746\pi$
$991$	13.9551	+	24.1710i	0.443299	+	0.767817i	−0.554633	+	0.832095i	$0.687141\pi$
$992$	6.17301	−	10.6920i	0.195993	−	0.339470i
$993$	−2.42187	+	7.16423i	−0.0768558	+	0.227350i
$994$	−32.5292	−	0.571077i	−1.03176	−	0.0181135i
$995$	−17.4862	+	30.2870i	−0.554350	+	0.960163i
$996$	−0.165275	+	0.488905i	−0.00523693	+	0.0154915i
$997$	−21.3078	−	12.3020i	−0.674823	−	0.389609i	0.123078	−	0.992397i	$-0.460723\pi$
$997$	−21.3078	−	12.3020i	−0.674823	−	0.389609i	−0.797902	+	0.602788i	$0.794057\pi$
$998$	−14.2206	+	8.21029i	−0.450146	+	0.259892i
$999$	−13.6704	−	6.67743i	−0.432513	−	0.211265i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.u.c.62.12	yes	64
3.2	odd	2	inner	273.2.u.c.62.21	yes	64
7.6	odd	2	inner	273.2.u.c.62.11	✓	64
13.4	even	6	inner	273.2.u.c.251.22	yes	64
21.20	even	2	inner	273.2.u.c.62.22	yes	64
39.17	odd	6	inner	273.2.u.c.251.11	yes	64
91.69	odd	6	inner	273.2.u.c.251.21	yes	64
273.251	even	6	inner	273.2.u.c.251.12	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.u.c.62.11	✓	64	7.6	odd	2	inner
273.2.u.c.62.12	yes	64	1.1	even	1	trivial
273.2.u.c.62.21	yes	64	3.2	odd	2	inner
273.2.u.c.62.22	yes	64	21.20	even	2	inner
273.2.u.c.251.11	yes	64	39.17	odd	6	inner
273.2.u.c.251.12	yes	64	273.251	even	6	inner
273.2.u.c.251.21	yes	64	91.69	odd	6	inner
273.2.u.c.251.22	yes	64	13.4	even	6	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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.u (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.584057 - 1.01162i) q^{2} +(0.340045 + 1.69834i) q^{3} +(0.317754 - 0.550366i) q^{4} -3.55045i q^{5} +(1.51947 - 1.33593i) q^{6} +(-2.64534 - 0.0464413i) q^{7} -3.07858 q^{8} +(-2.76874 + 1.15503i) q^{9} +O(q^{10})\)	\(q+(-0.584057 - 1.01162i) q^{2} +(0.340045 + 1.69834i) q^{3} +(0.317754 - 0.550366i) q^{4} -3.55045i q^{5} +(1.51947 - 1.33593i) q^{6} +(-2.64534 - 0.0464413i) q^{7} -3.07858 q^{8} +(-2.76874 + 1.15503i) q^{9} +(-3.59170 + 2.07367i) q^{10} +(-2.54090 - 4.40096i) q^{11} +(1.04276 + 0.352506i) q^{12} +(3.23163 + 1.59893i) q^{13} +(1.49805 + 2.70320i) q^{14} +(6.02988 - 1.20731i) q^{15} +(1.16256 + 2.01361i) q^{16} +(-1.08363 + 1.87690i) q^{17} +(2.78555 + 2.12630i) q^{18} +(1.43850 - 2.49155i) q^{19} +(-1.95405 - 1.12817i) q^{20} +(-0.820663 - 4.50849i) q^{21} +(-2.96806 + 5.14083i) q^{22} +(2.33890 - 1.35037i) q^{23} +(-1.04685 - 5.22848i) q^{24} -7.60570 q^{25} +(-0.269957 - 4.20304i) q^{26} +(-2.90313 - 4.30951i) q^{27} +(-0.866128 + 1.44115i) q^{28} +(6.51871 - 3.76358i) q^{29} +(-4.74314 - 5.39479i) q^{30} -3.58776 q^{31} +(-1.72058 + 2.98012i) q^{32} +(6.61033 - 5.81184i) q^{33} +2.53160 q^{34} +(-0.164887 + 9.39216i) q^{35} +(-0.244091 + 1.89083i) q^{36} +(2.53568 - 1.46398i) q^{37} -3.36066 q^{38} +(-1.61662 + 6.03212i) q^{39} +10.9303i q^{40} +(5.45458 - 3.14920i) q^{41} +(-4.08155 + 3.46342i) q^{42} +(4.48749 - 7.77256i) q^{43} -3.22952 q^{44} +(4.10086 + 9.83027i) q^{45} +(-2.73210 - 1.57738i) q^{46} +10.3146i q^{47} +(-3.02448 + 2.65914i) q^{48} +(6.99569 + 0.245706i) q^{49} +(4.44217 + 7.69406i) q^{50} +(-3.55610 - 1.20214i) q^{51} +(1.90686 - 1.27051i) q^{52} -1.79048i q^{53} +(-2.66398 + 5.45385i) q^{54} +(-15.6254 + 9.02133i) q^{55} +(8.14389 + 0.142973i) q^{56} +(4.72066 + 1.59582i) q^{57} +(-7.61460 - 4.39629i) q^{58} +(-4.23466 - 2.44488i) q^{59} +(1.25156 - 3.70227i) q^{60} +(0.145945 + 0.0842615i) q^{61} +(2.09546 + 3.62944i) q^{62} +(7.37791 - 2.92686i) q^{63} +8.66989 q^{64} +(5.67691 - 11.4737i) q^{65} +(-9.74017 - 3.29267i) q^{66} +(3.78238 - 2.18376i) q^{67} +(0.688654 + 1.19278i) q^{68} +(3.08871 + 3.51307i) q^{69} +(9.59758 - 5.31876i) q^{70} +(-5.26351 + 9.11667i) q^{71} +(8.52377 - 3.55584i) q^{72} +10.7603 q^{73} +(-2.96197 - 1.71009i) q^{74} +(-2.58628 - 12.9171i) q^{75} +(-0.914176 - 1.58340i) q^{76} +(6.51716 + 11.7601i) q^{77} +(7.04640 - 1.88770i) q^{78} -4.68895 q^{79} +(7.14922 - 4.12760i) q^{80} +(6.33183 - 6.39593i) q^{81} +(-6.37157 - 3.67863i) q^{82} +0.468856i q^{83} +(-2.74209 - 0.980927i) q^{84} +(6.66384 + 3.84737i) q^{85} -10.4838 q^{86} +(8.60850 + 9.79122i) q^{87} +(7.82234 + 13.5487i) q^{88} +(-5.64141 + 3.25707i) q^{89} +(7.54933 - 9.88995i) q^{90} +(-8.47452 - 4.37979i) q^{91} -1.71634i q^{92} +(-1.22000 - 6.09325i) q^{93} +(10.4344 - 6.02431i) q^{94} +(-8.84612 - 5.10731i) q^{95} +(-5.64635 - 1.90875i) q^{96} +(-4.02073 + 6.96410i) q^{97} +(-3.83732 - 7.22046i) q^{98} +(12.1183 + 9.25031i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 40 q^{4} - 6 q^{9}+O(q^{10}) \) 64 * q - 40 * q^4 - 6 * q^9	\( 64 q - 40 q^{4} - 6 q^{9} + 18 q^{15} - 32 q^{16} + 24 q^{22} - 80 q^{25} + 12 q^{28} + 20 q^{30} + 50 q^{36} - 36 q^{37} - 60 q^{39} + 48 q^{43} - 84 q^{46} - 16 q^{49} + 52 q^{51} - 48 q^{58} - 36 q^{63} + 176 q^{64} + 60 q^{67} - 66 q^{72} + 166 q^{78} - 104 q^{79} - 30 q^{81} + 60 q^{84} + 132 q^{85} - 8 q^{91} - 162 q^{93}+O(q^{100}) \) 64 * q - 40 * q^4 - 6 * q^9 + 18 * q^15 - 32 * q^16 + 24 * q^22 - 80 * q^25 + 12 * q^28 + 20 * q^30 + 50 * q^36 - 36 * q^37 - 60 * q^39 + 48 * q^43 - 84 * q^46 - 16 * q^49 + 52 * q^51 - 48 * q^58 - 36 * q^63 + 176 * q^64 + 60 * q^67 - 66 * q^72 + 166 * q^78 - 104 * q^79 - 30 * q^81 + 60 * q^84 + 132 * q^85 - 8 * q^91 - 162 * q^93

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