LMFDB - Embedded newform 702.2.bs.a.5.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [702,2,Mod(5,702)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(702, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([10, 27]))

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

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

chi := DirichletCharacter("702.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 702 = 2 \cdot 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	702.bs (of order $36$, degree $12$, 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:	$5.60549822189$
Analytic rank:	$0$
Dimension:	$504$
Relative dimension:	$42$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			5.7
Character	$\chi$	$=$	702.5
Dual form			702.2.bs.a.281.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.996195 - 0.0871557i) q^{2} +(-1.17070 - 1.27650i) q^{3} +(0.984808 + 0.173648i) q^{4} +(-0.486588 - 0.226900i) q^{5} +(1.05499 + 1.37368i) q^{6} +(-1.73769 + 2.48168i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(-0.258919 + 2.98881i) q^{9} +(0.464961 + 0.268445i) q^{10} +(-1.96028 + 0.914095i) q^{11} +(-0.931253 - 1.46040i) q^{12} +(2.93422 - 2.09532i) q^{13} +(1.94737 - 2.32079i) q^{14} +(0.280011 + 0.886764i) q^{15} +(0.939693 + 0.342020i) q^{16} +(2.30561 - 3.99343i) q^{17} +(0.518425 - 2.95487i) q^{18} +(5.04909 + 1.35290i) q^{19} +(-0.439795 - 0.307948i) q^{20} +(5.20220 - 0.687139i) q^{21} +(2.03249 - 0.739767i) q^{22} +(0.0264197 - 0.149834i) q^{23} +(0.800427 + 1.53601i) q^{24} +(-3.02865 - 3.60941i) q^{25} +(-3.10567 + 1.83162i) q^{26} +(4.11834 - 3.16849i) q^{27} +(-2.14223 + 2.14223i) q^{28} +(-2.22789 - 2.65510i) q^{29} +(-0.201659 - 0.907794i) q^{30} +(0.799630 + 1.14199i) q^{31} +(-0.906308 - 0.422618i) q^{32} +(3.46175 + 1.43218i) q^{33} +(-2.64488 + 3.77729i) q^{34} +(1.40864 - 0.813276i) q^{35} +(-0.773986 + 2.89844i) q^{36} +(0.538267 - 0.144228i) q^{37} +(-4.91197 - 1.78781i) q^{38} +(-6.10978 - 1.29254i) q^{39} +(0.411282 + 0.345107i) q^{40} +(-0.506050 - 5.78418i) q^{41} +(-5.24229 + 0.231123i) q^{42} +(-0.344974 + 0.947809i) q^{43} +(-2.08923 + 0.559808i) q^{44} +(0.804147 - 1.39557i) q^{45} +(-0.0393781 + 0.146961i) q^{46} +(-1.43527 - 1.00499i) q^{47} +(-0.663509 - 1.59992i) q^{48} +(-0.745034 - 2.04696i) q^{49} +(2.70255 + 3.85964i) q^{50} +(-7.79680 + 1.73200i) q^{51} +(3.25349 - 1.55397i) q^{52} -14.2306i q^{53} +(-4.37882 + 2.79749i) q^{54} +1.16126 q^{55} +(2.32079 - 1.94737i) q^{56} +(-4.18400 - 8.02902i) q^{57} +(1.98801 + 2.83917i) q^{58} +(1.74096 - 3.73350i) q^{59} +(0.121772 + 0.921915i) q^{60} +(0.00851718 + 0.0483033i) q^{61} +(-0.697056 - 1.20734i) q^{62} +(-6.96735 - 5.83618i) q^{63} +(0.866025 + 0.500000i) q^{64} +(-1.90318 + 0.353787i) q^{65} +(-3.32376 - 1.72844i) q^{66} +(13.0146 - 1.13863i) q^{67} +(2.96403 - 3.53239i) q^{68} +(-0.222193 + 0.141686i) q^{69} +(-1.47416 + 0.687411i) q^{70} +(3.43297 - 0.919861i) q^{71} +(1.02366 - 2.81995i) q^{72} +(0.967827 - 3.61198i) q^{73} +(-0.548789 + 0.0967663i) q^{74} +(-1.06177 + 8.09162i) q^{75} +(4.73746 + 2.20911i) q^{76} +(1.13788 - 6.45322i) q^{77} +(5.97387 + 1.82012i) q^{78} +(2.50272 - 2.10003i) q^{79} +(-0.379639 - 0.379639i) q^{80} +(-8.86592 - 1.54771i) q^{81} +5.80627i q^{82} +(3.42590 + 0.299728i) q^{83} +(5.24248 + 0.226652i) q^{84} +(-2.02799 + 1.42001i) q^{85} +(0.426269 - 0.914136i) q^{86} +(-0.781045 + 5.95224i) q^{87} +(2.13007 - 0.375589i) q^{88} +(0.347731 + 0.0931743i) q^{89} +(-0.922719 + 1.32017i) q^{90} +(0.101164 + 10.9228i) q^{91} +(0.0520367 - 0.142970i) q^{92} +(0.521626 - 2.35766i) q^{93} +(1.34222 + 1.12626i) q^{94} +(-2.14986 - 1.80394i) q^{95} +(0.521542 + 1.65166i) q^{96} +(10.5067 - 4.89935i) q^{97} +(0.563794 + 2.10411i) q^{98} +(-2.22450 - 6.09558i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 504 q - 24 q^{11} + 24 q^{15} + 24 q^{21} - 144 q^{27} + 24 q^{39} + 48 q^{41} + 12 q^{45} + 132 q^{47} + 24 q^{50} + 72 q^{54} - 72 q^{57} + 12 q^{63} - 156 q^{65} + 96 q^{66} - 48 q^{72} + 36 q^{73} - 96 q^{74}+ \cdots - 144 q^{99}+O(q^{100}) $ 504 * q - 24 * q^11 + 24 * q^15 + 24 * q^21 - 144 * q^27 + 24 * q^39 + 48 * q^41 + 12 * q^45 + 132 * q^47 + 24 * q^50 + 72 * q^54 - 72 * q^57 + 12 * q^63 - 156 * q^65 + 96 * q^66 - 48 * q^72 + 36 * q^73 - 96 * q^74 - 24 * q^78 + 288 * q^79 + 24 * q^83 + 24 * q^84 - 144 * q^85 - 96 * q^86 - 192 * q^87 + 96 * q^92 - 60 * q^93 - 72 * q^98 - 144 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/702\mathbb{Z}\right)^\times$.

$n$	$379$	$677$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{18}\right)$

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 $

$2$	−0.996195	−	0.0871557i	−0.704416	−	0.0616284i
$2$	−0.996195	−	0.0871557i	−0.704416	−	0.0616284i
$3$	−1.17070	−	1.27650i	−0.675905	−	0.736989i
$3$	−1.17070	−	1.27650i	−0.675905	−	0.736989i
$4$	0.984808	+	0.173648i	0.492404	+	0.0868241i
$5$	−0.486588	−	0.226900i	−0.217609	−	0.101473i	0.310757	−	0.950489i	$-0.399417\pi$
$5$	−0.486588	−	0.226900i	−0.217609	−	0.101473i	−0.528366	+	0.849017i	$0.677195\pi$
$6$	1.05499	+	1.37368i	0.430698	+	0.560802i
$7$	−1.73769	+	2.48168i	−0.656786	+	0.937988i	−0.999999	−	0.00126941i	$-0.999596\pi$
$7$	−1.73769	+	2.48168i	−0.656786	+	0.937988i	0.343213	+	0.939258i	$0.388485\pi$
$8$	−0.965926	−	0.258819i	−0.341506	−	0.0915064i
$9$	−0.258919	+	2.98881i	−0.0863062	+	0.996269i
$10$	0.464961	+	0.268445i	0.147034	+	0.0848899i
$11$	−1.96028	+	0.914095i	−0.591048	+	0.275610i	−0.695044	−	0.718968i	$-0.744615\pi$
$11$	−1.96028	+	0.914095i	−0.591048	+	0.275610i	0.103996	+	0.994578i	$0.466837\pi$
$12$	−0.931253	−	1.46040i	−0.268830	−	0.421581i
$13$	2.93422	−	2.09532i	0.813805	−	0.581138i
$13$	2.93422	−	2.09532i	0.813805	−	0.581138i
$14$	1.94737	−	2.32079i	0.520458	−	0.620257i
$15$	0.280011	+	0.886764i	0.0722986	+	0.228961i
$16$	0.939693	+	0.342020i	0.234923	+	0.0855050i
$17$	2.30561	−	3.99343i	0.559192	−	0.968549i	−0.438372	−	0.898793i	$-0.644445\pi$
$17$	2.30561	−	3.99343i	0.559192	−	0.968549i	0.997564	−	0.0697552i	$-0.0222218\pi$
$18$	0.518425	−	2.95487i	0.122194	−	0.696469i
$19$	5.04909	+	1.35290i	1.15834	+	0.310377i	0.786303	−	0.617841i	$-0.211992\pi$
$19$	5.04909	+	1.35290i	1.15834	+	0.310377i	0.372038	+	0.928217i	$0.378659\pi$
$20$	−0.439795	−	0.307948i	−0.0983412	−	0.0688593i
$21$	5.20220	−	0.687139i	1.13521	−	0.149946i
$22$	2.03249	−	0.739767i	0.433329	−	0.157719i
$23$	0.0264197	−	0.149834i	0.00550889	−	0.0312425i	−0.981929	−	0.189248i	$-0.939395\pi$
$23$	0.0264197	−	0.149834i	0.00550889	−	0.0312425i	0.987438	+	0.158005i	$0.0505062\pi$
$24$	0.800427	+	1.53601i	0.163386	+	0.313536i
$25$	−3.02865	−	3.60941i	−0.605731	−	0.721882i
$26$	−3.10567	+	1.83162i	−0.609072	+	0.359210i
$27$	4.11834	−	3.16849i	0.792574	−	0.609776i
$28$	−2.14223	+	2.14223i	−0.404844	+	0.404844i
$29$	−2.22789	−	2.65510i	−0.413709	−	0.493040i	0.518440	−	0.855114i	$-0.326513\pi$
$29$	−2.22789	−	2.65510i	−0.413709	−	0.493040i	−0.932149	+	0.362075i	$0.882069\pi$
$30$	−0.201659	−	0.907794i	−0.0368178	−	0.165740i
$31$	0.799630	+	1.14199i	0.143618	+	0.205107i	0.884516	−	0.466510i	$-0.154489\pi$
$31$	0.799630	+	1.14199i	0.143618	+	0.205107i	−0.740898	+	0.671617i	$0.765600\pi$
$32$	−0.906308	−	0.422618i	−0.160214	−	0.0747091i
$33$	3.46175	+	1.43218i	0.602614	+	0.249310i
$34$	−2.64488	+	3.77729i	−0.453594	+	0.647799i
$35$	1.40864	−	0.813276i	0.238103	−	0.137469i
$36$	−0.773986	+	2.89844i	−0.128998	+	0.483073i
$37$	0.538267	−	0.144228i	0.0884905	−	0.0237110i	−0.214302	−	0.976767i	$-0.568748\pi$
$37$	0.538267	−	0.144228i	0.0884905	−	0.0237110i	0.302793	+	0.953056i	$0.402081\pi$
$38$	−4.91197	−	1.78781i	−0.796826	−	0.290021i
$39$	−6.10978	−	1.29254i	−0.978347	−	0.206971i
$40$	0.411282	+	0.345107i	0.0650295	+	0.0545662i
$41$	−0.506050	−	5.78418i	−0.0790317	−	0.903337i	−0.927435	−	0.373985i	$-0.877991\pi$
$41$	−0.506050	−	5.78418i	−0.0790317	−	0.903337i	0.848403	−	0.529351i	$-0.177565\pi$
$42$	−5.24229	+	0.231123i	−0.808903	+	0.0356630i
$43$	−0.344974	+	0.947809i	−0.0526081	+	0.144540i	−0.963213	−	0.268737i	$-0.913394\pi$
$43$	−0.344974	+	0.947809i	−0.0526081	+	0.144540i	0.910605	+	0.413277i	$0.135616\pi$
$44$	−2.08923	+	0.559808i	−0.314964	+	0.0843943i
$45$	0.804147	−	1.39557i	0.119875	−	0.208039i
$46$	−0.0393781	+	0.146961i	−0.00580598	+	0.0216682i
$47$	−1.43527	−	1.00499i	−0.209356	−	0.146593i	0.464196	−	0.885732i	$-0.346343\pi$
$47$	−1.43527	−	1.00499i	−0.209356	−	0.146593i	−0.673552	+	0.739140i	$0.735232\pi$
$48$	−0.663509	−	1.59992i	−0.0957693	−	0.230929i
$49$	−0.745034	−	2.04696i	−0.106433	−	0.292423i
$50$	2.70255	+	3.85964i	0.382198	+	0.545835i
$51$	−7.79680	+	1.73200i	−1.09177	+	0.242528i
$52$	3.25349	−	1.55397i	0.451177	−	0.215497i
$53$		−	14.2306i		−	1.95472i	−0.211586	−	0.977359i	$-0.567863\pi$
$53$		−	14.2306i		−	1.95472i	0.211586	−	0.977359i	$-0.432137\pi$
$54$	−4.37882	+	2.79749i	−0.595881	+	0.380691i
$55$	1.16126			0.156584
$56$	2.32079	−	1.94737i	0.310129	−	0.260229i
$57$	−4.18400	−	8.02902i	−0.554184	−	1.06347i
$58$	1.98801	+	2.83917i	0.261038	+	0.372801i
$59$	1.74096	−	3.73350i	0.226653	−	0.486060i	−0.759789	−	0.650170i	$-0.774698\pi$
$59$	1.74096	−	3.73350i	0.226653	−	0.486060i	0.986442	+	0.164111i	$0.0524754\pi$
$60$	0.121772	+	0.921915i	0.0157207	+	0.119019i
$61$	0.00851718	+	0.0483033i	0.00109051	+	0.00618461i	0.985348	−	0.170555i	$-0.0545561\pi$
$61$	0.00851718	+	0.0483033i	0.00109051	+	0.00618461i	−0.984258	+	0.176740i	$0.943445\pi$
$62$	−0.697056	−	1.20734i	−0.0885262	−	0.153332i
$63$	−6.96735	−	5.83618i	−0.877804	−	0.735290i
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$	−1.90318	+	0.353787i	−0.236061	+	0.0438819i
$66$	−3.32376	−	1.72844i	−0.409126	−	0.212756i
$67$	13.0146	−	1.13863i	1.58999	−	0.139106i	0.742474	−	0.669875i	$-0.233652\pi$
$67$	13.0146	−	1.13863i	1.58999	−	0.139106i	0.847516	+	0.530769i	$0.178097\pi$
$68$	2.96403	−	3.53239i	0.359442	−	0.428366i
$69$	−0.222193	+	0.141686i	−0.0267489	+	0.0170569i
$70$	−1.47416	+	0.687411i	−0.176195	+	0.0821613i
$71$	3.43297	−	0.919861i	0.407419	−	0.109167i	−0.0492886	−	0.998785i	$-0.515695\pi$
$71$	3.43297	−	0.919861i	0.407419	−	0.109167i	0.456707	+	0.889617i	$0.349029\pi$
$72$	1.02366	−	2.81995i	0.120639	−	0.332335i
$73$	0.967827	−	3.61198i	0.113276	−	0.422750i	−0.885877	−	0.463921i	$-0.846442\pi$
$73$	0.967827	−	3.61198i	0.113276	−	0.422750i	0.999152	+	0.0411708i	$0.0131088\pi$
$74$	−0.548789	+	0.0967663i	−0.0637954	+	0.0112489i
$75$	−1.06177	+	8.09162i	−0.122603	+	0.934340i
$76$	4.73746	+	2.20911i	0.543424	+	0.253403i
$77$	1.13788	−	6.45322i	0.129673	−	0.735413i
$78$	5.97387	+	1.82012i	0.676408	+	0.206088i
$79$	2.50272	−	2.10003i	0.281578	−	0.236272i	−0.491049	−	0.871132i	$-0.663386\pi$
$79$	2.50272	−	2.10003i	0.281578	−	0.236272i	0.772628	+	0.634860i	$0.218942\pi$
$80$	−0.379639	−	0.379639i	−0.0424450	−	0.0424450i
$81$	−8.86592	−	1.54771i	−0.985102	−	0.171968i
$82$			5.80627i			0.641195i
$83$	3.42590	+	0.299728i	0.376042	+	0.0328994i	0.273610	−	0.961841i	$-0.411782\pi$
$83$	3.42590	+	0.299728i	0.376042	+	0.0328994i	0.102432	+	0.994740i	$0.467338\pi$
$84$	5.24248	+	0.226652i	0.572002	+	0.0247298i
$85$	−2.02799	+	1.42001i	−0.219966	+	0.154022i
$86$	0.426269	−	0.914136i	0.0459657	−	0.0985738i
$87$	−0.781045	+	5.95224i	−0.0837368	+	0.638147i
$88$	2.13007	−	0.375589i	0.227067	−	0.0400380i
$89$	0.347731	+	0.0931743i	0.0368594	+	0.00987646i	0.277202	−	0.960812i	$-0.410593\pi$
$89$	0.347731	+	0.0931743i	0.0368594	+	0.00987646i	−0.240342	+	0.970688i	$0.577260\pi$
$90$	−0.922719	+	1.32017i	−0.0972631	+	0.139158i
$91$	0.101164	+	10.9228i	0.0106049	+	1.14502i
$92$	0.0520367	−	0.142970i	0.00542520	−	0.0149056i
$93$	0.521626	−	2.35766i	0.0540901	−	0.244478i
$94$	1.34222	+	1.12626i	0.138439	+	0.116164i
$95$	−2.14986	−	1.80394i	−0.220571	−	0.185081i
$96$	0.521542	+	1.65166i	0.0532297	+	0.168572i
$97$	10.5067	−	4.89935i	1.06679	−	0.497454i	0.191723	−	0.981449i	$-0.438593\pi$
$97$	10.5067	−	4.89935i	1.06679	−	0.497454i	0.875071	+	0.483995i	$0.160815\pi$
$98$	0.563794	+	2.10411i	0.0569518	+	0.212547i
$99$	−2.22450	−	6.09558i	−0.223571	−	0.612629i
$100$	−2.35587	−	4.08049i	−0.235587	−	0.408049i
$101$	0.288122	+	1.63402i	0.0286692	+	0.162591i	0.995781	−	0.0917599i	$-0.0292492\pi$
$101$	0.288122	+	1.63402i	0.0286692	+	0.162591i	−0.967112	+	0.254351i	$0.918138\pi$
$102$	7.91808	−	1.04587i	0.784007	−	0.103557i
$103$	−5.08878	−	13.9813i	−0.501413	−	1.37762i	−0.889896	−	0.456164i	$-0.849223\pi$
$103$	−5.08878	−	13.9813i	−0.501413	−	1.37762i	0.388483	−	0.921456i	$-0.372999\pi$
$104$	−3.37654	+	1.26450i	−0.331097	+	0.123994i
$105$	−2.68724	−	0.846024i	−0.262248	−	0.0825635i
$106$	−1.24028	+	14.1764i	−0.120466	+	1.37694i
$107$			1.16533i			0.112657i	0.998412	+	0.0563286i	$0.0179394\pi$
$107$			1.16533i			0.112657i	−0.998412	+	0.0563286i	$0.982061\pi$
$108$	4.60597	−	2.40521i	0.443210	−	0.231441i
$109$	−8.76498	+	8.76498i	−0.839533	+	0.839533i	−0.988797	−	0.149264i	$-0.952309\pi$
$109$	−8.76498	+	8.76498i	−0.839533	+	0.839533i	0.149264	+	0.988797i	$0.452309\pi$
$110$	−1.15684	−	0.101210i	−0.110300	−	0.00965004i
$111$	−0.814257	−	0.518251i	−0.0772859	−	0.0491902i
$112$	−2.48168	+	1.73769i	−0.234497	+	0.164197i
$113$	−3.92844	−	10.7933i	−0.369556	−	1.01535i	−0.975531	−	0.219863i	$-0.929439\pi$
$113$	−3.92844	−	10.7933i	−0.369556	−	1.01535i	0.605975	−	0.795484i	$-0.292783\pi$
$114$	3.46830	+	8.36313i	0.324836	+	0.783279i
$115$	−0.0468528	+	0.0669127i	−0.00436905	+	0.00623964i
$116$	−1.73299	−	3.00163i	−0.160904	−	0.278695i
$117$	5.50279	+	9.31232i	0.508733	+	0.860924i
$118$	−2.05973	+	3.56755i	−0.189613	+	0.328420i
$119$	5.90399	+	12.6611i	0.541218	+	1.16064i
$120$	−0.0409588	−	0.929020i	−0.00373901	−	0.0848075i
$121$	−4.06352	+	4.84272i	−0.369411	+	0.440247i
$122$	−0.00427486	−	0.0488618i	−0.000387027	−	0.00442374i
$123$	−6.79108	+	7.41751i	−0.612331	+	0.668815i
$124$	0.589177	+	1.26349i	0.0529097	+	0.113465i
$125$	1.34952	+	5.03648i	0.120705	+	0.450477i
$126$	6.43218	+	6.42122i	0.573024	+	0.572048i
$127$	14.5022	−	8.37283i	1.28686	−	0.742968i	0.308766	−	0.951138i	$-0.400084\pi$
$127$	14.5022	−	8.37283i	1.28686	−	0.742968i	0.978093	+	0.208170i	$0.0667506\pi$
$128$	−0.819152	−	0.573576i	−0.0724035	−	0.0506975i
$129$	1.61374	−	0.669240i	0.142082	−	0.0589233i
$130$	1.92678	−	0.186568i	0.168989	−	0.0163631i
$131$	14.2924	+	2.52013i	1.24873	+	0.220185i	0.758653	−	0.651495i	$-0.225858\pi$
$131$	14.2924	+	2.52013i	1.24873	+	0.220185i	0.490077	+	0.871679i	$0.336969\pi$
$132$	3.16046	+	2.01154i	0.275083	+	0.175082i
$133$	−12.1312	+	10.1793i	−1.05191	+	0.882659i
$134$	−13.0643			−1.12859
$135$	−2.72286	+	0.607300i	−0.234347	+	0.0522680i
$136$	−3.26062	+	3.26062i	−0.279596	+	0.279596i
$137$	−1.41932	+	16.2229i	−0.121260	+	1.38601i	0.655013	+	0.755617i	$0.272663\pi$
$137$	−1.41932	+	16.2229i	−0.121260	+	1.38601i	−0.776274	+	0.630396i	$0.782893\pi$
$138$	0.233696	−	0.121781i	0.0198935	−	0.0103667i
$139$	−1.01927	+	5.78058i	−0.0864536	+	0.490302i	0.910580	+	0.413333i	$0.135635\pi$
$139$	−1.01927	+	5.78058i	−0.0864536	+	0.490302i	−0.997033	+	0.0769694i	$0.975476\pi$
$140$	1.52846	−	0.556314i	0.129178	−	0.0470171i
$141$	0.397404	+	3.00867i	0.0334674	+	0.253376i
$142$	−3.50008	+	0.617158i	−0.293720	+	0.0517908i
$143$	−3.83657	+	6.78958i	−0.320830	+	0.567773i
$144$	−1.26554	+	2.72000i	−0.105461	+	0.226667i
$145$	0.481625	+	1.79745i	0.0399968	+	0.149270i
$146$	−1.27895	+	3.51388i	−0.105847	+	0.290811i
$147$	−1.74074	+	3.34742i	−0.143574	+	0.276091i
$148$	0.555134	−	0.0485680i	0.0456318	−	0.00399226i
$149$	−1.45523	−	16.6333i	−0.119217	−	1.36266i	−0.786380	−	0.617743i	$-0.788047\pi$
$149$	−1.45523	−	16.6333i	−0.119217	−	1.36266i	0.667163	−	0.744912i	$-0.267509\pi$
$150$	1.76296	−	7.96829i	0.143945	−	0.650608i
$151$	0.345882	+	0.741747i	0.0281475	+	0.0603625i	0.919879	−	0.392203i	$-0.128287\pi$
$151$	0.345882	+	0.741747i	0.0281475	+	0.0603625i	−0.891731	+	0.452565i	$0.850509\pi$
$152$	−4.52689	−	2.61360i	−0.367180	−	0.211991i
$153$	11.3386	+	7.92498i	0.916673	+	0.640697i
$154$	−1.69598	+	6.32949i	−0.136666	+	0.510045i
$155$	−0.129973	−	0.737115i	−0.0104397	−	0.0592065i
$156$	−5.79251	−	2.33385i	−0.463772	−	0.186858i
$157$	14.1781	−	5.16041i	1.13154	−	0.411845i	0.292686	−	0.956209i	$-0.405451\pi$
$157$	14.1781	−	5.16041i	1.13154	−	0.411845i	0.838849	+	0.544363i	$0.183229\pi$
$158$	−2.67623	+	1.87392i	−0.212909	+	0.149081i
$159$	−18.1654	+	16.6597i	−1.44061	+	1.32120i
$160$	0.345107	+	0.411282i	0.0272831	+	0.0325147i
$161$	0.325930	+	0.325930i	0.0256869	+	0.0256869i
$162$	8.69729	+	2.31454i	0.683324	+	0.181848i
$163$	−7.28466	−	7.28466i	−0.570578	−	0.570578i	0.361712	−	0.932290i	$-0.382192\pi$
$163$	−7.28466	−	7.28466i	−0.570578	−	0.570578i	−0.932290	+	0.361712i	$0.882192\pi$
$164$	0.506050	−	5.78418i	0.0395159	−	0.451668i
$165$	−1.35949	−	1.48235i	−0.105836	−	0.115401i
$166$	−3.38674	−	0.597175i	−0.262862	−	0.0463497i
$167$	−5.46449	+	11.7186i	−0.422855	+	0.906815i	0.573312	+	0.819337i	$0.305658\pi$
$167$	−5.46449	+	11.7186i	−0.422855	+	0.906815i	−0.996166	+	0.0874775i	$0.972119\pi$
$168$	−5.20278	−	0.682702i	−0.401403	−	0.0526716i
$169$	4.21924	−	12.2963i	0.324557	−	0.945866i
$170$	2.14404	−	1.23786i	0.164440	−	0.0949395i
$171$	−5.35086	+	14.7405i	−0.409191	+	1.12723i
$172$	−0.504319	+	0.873506i	−0.0384539	+	0.0666042i
$173$	16.9644	+	6.17453i	1.28978	+	0.469441i	0.893654	−	0.448756i	$-0.148133\pi$
$173$	16.9644	+	6.17453i	1.28978	+	0.469441i	0.396124	+	0.918197i	$0.370355\pi$
$174$	1.29684	−	5.86152i	0.0983136	−	0.444360i
$175$	14.2203	−	1.24411i	1.07495	−	0.0940461i
$176$	−2.15470	+	0.188512i	−0.162417	+	0.0142096i
$177$	−6.80396	+	2.14847i	−0.511417	+	0.161489i
$178$	−0.338287	−	0.123127i	−0.0253557	−	0.00922872i
$179$	−11.5461	+	19.9985i	−0.862999	+	1.49476i	0.00602048	+	0.999982i	$0.498084\pi$
$179$	−11.5461	+	19.9985i	−0.862999	+	1.49476i	−0.869020	+	0.494777i	$0.835250\pi$
$180$	1.03427	−	1.23473i	0.0770898	−	0.0920313i
$181$	11.2743	−	6.50921i	0.838011	−	0.483826i	−0.0185765	−	0.999827i	$-0.505913\pi$
$181$	11.2743	−	6.50921i	0.838011	−	0.483826i	0.856588	+	0.516001i	$0.172580\pi$
$182$	0.851208	−	10.8901i	0.0630957	−	0.807226i
$183$	0.0516883	−	0.0674210i	0.00382091	−	0.00498390i
$184$	−0.0642993	+	0.137890i	−0.00474021	+	0.0101654i
$185$	−0.294640	−	0.0519529i	−0.0216623	−	0.00381966i
$186$	−0.725124	+	2.30322i	−0.0531687	+	0.168881i
$187$	−0.869270	+	9.93580i	−0.0635673	+	0.726577i
$188$	−1.23895	−	1.23895i	−0.0903599	−	0.0903599i
$189$	0.706780	+	15.7263i	0.0514107	+	1.14392i
$190$	1.98445	+	1.98445i	0.143967	+	0.143967i
$191$	5.69225	+	6.78376i	0.411877	+	0.490856i	0.931603	−	0.363477i	$-0.118411\pi$
$191$	5.69225	+	6.78376i	0.411877	+	0.490856i	−0.519726	+	0.854333i	$0.673966\pi$
$192$	−0.375605	−	1.69083i	−0.0271070	−	0.122025i
$193$	14.8123	−	10.3717i	1.06621	−	0.746570i	0.0976204	−	0.995224i	$-0.468877\pi$
$193$	14.8123	−	10.3717i	1.06621	−	0.746570i	0.968593	+	0.248653i	$0.0799880\pi$
$194$	−10.8937	+	3.96499i	−0.782124	+	0.284670i
$195$	2.67967	+	2.01524i	0.191895	+	0.144314i
$196$	−0.378264	−	2.14524i	−0.0270188	−	0.153231i
$197$	−4.37026	+	16.3100i	−0.311368	+	1.16204i	0.615955	+	0.787781i	$0.288770\pi$
$197$	−4.37026	+	16.3100i	−0.311368	+	1.16204i	−0.927323	+	0.374261i	$0.877896\pi$
$198$	1.68477	+	6.26627i	0.119731	+	0.445324i
$199$	−18.2873	−	10.5582i	−1.29635	−	0.748449i	−0.316579	−	0.948566i	$-0.602534\pi$
$199$	−18.2873	−	10.5582i	−1.29635	−	0.748449i	−0.979772	+	0.200117i	$0.935868\pi$
$200$	1.99127	+	4.27029i	0.140804	+	0.301955i
$201$	−16.6897	−	15.2802i	−1.17720	−	1.07778i
$202$	−0.144611	−	1.65291i	−0.0101748	−	0.116299i
$203$	10.4605	−	0.915176i	0.734184	−	0.0642328i
$204$	−7.97911	+	0.351784i	−0.558649	+	0.0246298i
$205$	−1.06619	+	2.92934i	−0.0744660	+	0.204594i
$206$	3.85087	+	14.3716i	0.268303	+	1.00132i
$207$	0.440983	+	0.117758i	0.0306505	+	0.00818476i
$208$	3.47390	−	0.965400i	0.240872	−	0.0669384i
$209$	−11.1343	+	1.96328i	−0.770178	+	0.135803i
$210$	2.60328	+	1.07701i	0.179643	+	0.0743210i
$211$	−2.37265	+	0.863574i	−0.163340	+	0.0594509i	−0.422396	−	0.906411i	$-0.638811\pi$
$211$	−2.37265	+	0.863574i	−0.163340	+	0.0594509i	0.259056	+	0.965862i	$0.416589\pi$
$212$	2.47111	−	14.0144i	0.169717	−	0.962511i
$213$	−5.19319	−	3.30531i	−0.355831	−	0.226476i
$214$	0.101566	−	1.16090i	0.00694288	−	0.0793575i
$215$	0.382918	−	0.382918i	0.0261148	−	0.0261148i
$216$	−4.79807	+	1.99462i	−0.326467	+	0.135717i
$217$	−4.22357			−0.286715
$218$	9.49555	−	7.96771i	0.643120	−	0.539641i
$219$	−5.74374	+	2.99311i	−0.388126	+	0.202256i
$220$	1.14362	+	0.201651i	0.0771027	+	0.0135953i
$221$	−1.60238	−	16.5486i	−0.107788	−	1.11318i
$222$	0.765990	+	0.587246i	0.0514099	+	0.0394134i
$223$	−22.0012	−	15.4054i	−1.47331	−	1.03162i	−0.987511	−	0.157552i	$-0.949640\pi$
$223$	−22.0012	−	15.4054i	−1.47331	−	1.03162i	−0.485799	−	0.874071i	$-0.661471\pi$
$224$	2.62369	−	1.51479i	0.175303	−	0.101211i
$225$	11.5720	−	8.11751i	0.771466	−	0.541168i
$226$	2.97279	+	11.0946i	0.197747	+	0.738002i
$227$	5.06585	+	10.8637i	0.336232	+	0.721052i	0.999630	−	0.0272151i	$-0.00866389\pi$
$227$	5.06585	+	10.8637i	0.336232	+	0.721052i	−0.663397	+	0.748267i	$0.730886\pi$
$228$	−2.72621	−	8.63359i	−0.180547	−	0.571773i
$229$	2.16586	+	24.7559i	0.143124	+	1.63592i	0.640199	+	0.768209i	$0.278852\pi$
$229$	2.16586	+	24.7559i	0.143124	+	1.63592i	−0.497075	+	0.867707i	$0.665593\pi$
$230$	0.0525063	−	0.0625746i	0.00346217	−	0.00412605i
$231$	−9.56967	+	6.10229i	−0.629638	+	0.401501i
$232$	1.46479	+	3.14125i	0.0961681	+	0.206233i
$233$	6.74798	−	11.6879i	0.442075	−	0.765697i	−0.555768	−	0.831337i	$-0.687576\pi$
$233$	6.74798	−	11.6879i	0.442075	−	0.765697i	0.997843	+	0.0656407i	$0.0209091\pi$
$234$	−4.67023	−	9.75648i	−0.305303	−	0.637801i
$235$	0.470355	+	0.814678i	0.0306826	+	0.0531438i
$236$	2.36282	−	3.37446i	0.153807	−	0.219659i
$237$	−5.61064	−	0.736221i	−0.364450	−	0.0478227i
$238$	−4.77803	−	13.1275i	−0.309714	−	0.850931i
$239$	14.8452	−	10.3947i	0.960258	−	0.672380i	0.0154070	−	0.999881i	$-0.495096\pi$
$239$	14.8452	−	10.3947i	0.960258	−	0.672380i	0.944851	+	0.327502i	$0.106207\pi$
$240$	−0.0401665	+	0.929055i	−0.00259274	+	0.0599702i
$241$	−8.82031	−	0.771677i	−0.568166	−	0.0497081i	−0.200546	−	0.979684i	$-0.564272\pi$
$241$	−8.82031	−	0.771677i	−0.568166	−	0.0497081i	−0.367620	+	0.929976i	$0.619827\pi$
$242$	4.47013	−	4.47013i	0.287351	−	0.287351i
$243$	8.40368	+	13.1293i	0.539096	+	0.842244i
$244$			0.0490485i			0.00314001i
$245$	−0.101931	+	1.16508i	−0.00651214	+	0.0744341i
$246$	7.41172	−	6.79741i	0.472554	−	0.433387i
$247$	17.6499	−	6.60978i	1.12304	−	0.420570i
$248$	−0.476814	−	1.31004i	−0.0302777	−	0.0831874i
$249$	−3.62811	−	4.72407i	−0.229922	−	0.299376i
$250$	−0.905428	−	5.13494i	−0.0572643	−	0.324762i
$251$	5.53923	+	9.59422i	0.349633	+	0.605582i	0.986184	−	0.165652i	$-0.0529730\pi$
$251$	5.53923	+	9.59422i	0.349633	+	0.605582i	−0.636551	+	0.771234i	$0.719640\pi$
$252$	−5.84806	−	6.95739i	−0.368393	−	0.438274i
$253$	0.0851721	+	0.317867i	0.00535473	+	0.0199841i
$254$	−15.1767	+	7.07702i	−0.952272	+	0.444052i
$255$	4.18682	+	0.926323i	0.262189	+	0.0580086i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−5.89033	−	4.94258i	−0.367429	−	0.308310i	0.440315	−	0.897844i	$-0.354867\pi$
$257$	−5.89033	−	4.94258i	−0.367429	−	0.308310i	−0.807744	+	0.589534i	$0.799311\pi$
$258$	−1.66593	+	0.526047i	−0.103716	+	0.0327502i
$259$	−0.577414	+	1.58643i	−0.0358788	+	0.0985761i
$260$	−1.93570	+	0.0179279i	−0.120047	+	0.00111184i
$261$	8.51242	−	5.97128i	0.526906	−	0.369613i
$262$	−14.0183	−	3.75620i	−0.866056	−	0.232059i
$263$	−22.8325	+	4.02598i	−1.40791	+	0.248253i	−0.825390	−	0.564563i	$-0.809045\pi$
$263$	−22.8325	+	4.02598i	−1.40791	+	0.248253i	−0.582521	+	0.812816i	$0.697934\pi$
$264$	−2.97312	−	2.27934i	−0.182983	−	0.140284i
$265$	−3.22891	+	6.92443i	−0.198351	+	0.425364i
$266$	12.9723	−	9.08328i	0.795381	−	0.556932i
$267$	−0.288152	−	0.552959i	−0.0176346	−	0.0338405i
$268$	13.0146	+	1.13863i	0.794995	+	0.0695530i
$269$		−	11.9160i		−	0.726533i	−0.931685	−	0.363266i	$-0.881662\pi$
$269$		−	11.9160i		−	0.726533i	0.931685	−	0.363266i	$-0.118338\pi$
$270$	2.76543	−	0.367675i	0.168299	−	0.0223760i
$271$	7.55992	+	7.55992i	0.459233	+	0.459233i	0.898404	−	0.439171i	$-0.144728\pi$
$271$	7.55992	+	7.55992i	0.459233	+	0.459233i	−0.439171	+	0.898404i	$0.644728\pi$
$272$	3.53239	−	2.96403i	0.214183	−	0.179721i
$273$	13.8246	−	12.9165i	0.836702	−	0.781742i
$274$	2.82783	−	16.0374i	0.170836	−	0.968857i
$275$	9.23636	+	4.30699i	0.556974	+	0.259721i
$276$	−0.243421	+	0.100950i	−0.0146522	+	0.00607646i
$277$	−19.2668	+	3.39726i	−1.15763	+	0.204121i	−0.719305	−	0.694695i	$-0.755539\pi$
$277$	−19.2668	+	3.39726i	−1.15763	+	0.204121i	−0.438326	+	0.898816i	$0.644428\pi$
$278$	1.51920	−	5.66975i	0.0911158	−	0.340049i
$279$	−3.62022	+	2.09426i	−0.216737	+	0.125380i
$280$	−1.57113	+	0.420983i	−0.0938929	+	0.0251585i
$281$	23.3842	−	10.9042i	1.39498	−	0.650492i	0.427638	−	0.903950i	$-0.359346\pi$
$281$	23.3842	−	10.9042i	1.39498	−	0.650492i	0.967346	+	0.253458i	$0.0815679\pi$
$282$	−0.133669	−	3.03186i	−0.00795987	−	0.180544i
$283$	−5.94779	+	7.08829i	−0.353559	+	0.421355i	−0.913284	−	0.407323i	$-0.866462\pi$
$283$	−5.94779	+	7.08829i	−0.353559	+	0.421355i	0.559725	+	0.828678i	$0.310907\pi$
$284$	3.54055	−	0.309758i	0.210093	−	0.0183807i
$285$	0.214100	+	4.85618i	0.0126822	+	0.287655i
$286$	4.41372	−	6.42937i	0.260989	−	0.380176i
$287$	15.2339	+	8.79527i	0.899226	+	0.519168i
$288$	1.49778	−	2.59935i	0.0882578	−	0.153168i
$289$	−2.13165	−	3.69212i	−0.125391	−	0.217184i
$290$	−0.323134	−	1.83259i	−0.0189751	−	0.107613i
$291$	−18.5542	−	7.67615i	−1.08767	−	0.449984i
$292$	1.58034	−	3.38904i	0.0924823	−	0.198329i
$293$	0.373192	+	0.532973i	0.0218021	+	0.0311366i	0.829905	−	0.557905i	$-0.188394\pi$
$293$	0.373192	+	0.532973i	0.0218021	+	0.0311366i	−0.808103	+	0.589041i	$0.799506\pi$
$294$	2.02587	−	3.18297i	0.118151	−	0.185634i
$295$	−1.69426	+	1.42165i	−0.0986436	+	0.0827718i
$296$	−0.557255			−0.0323898
$297$	−5.17681	+	9.97569i	−0.300389	+	0.578848i
$298$			16.6969i			0.967224i
$299$	−0.236429	−	0.495002i	−0.0136730	−	0.0286267i
$300$	−2.45074	+	7.78432i	−0.141493	+	0.449428i
$301$	−1.75270	−	2.50312i	−0.101024	−	0.144277i
$302$	−0.279919	−	0.769070i	−0.0161075	−	0.0442550i
$303$	1.74853	−	2.28074i	0.100450	−	0.131025i
$304$	4.28188	+	2.99820i	0.245582	+	0.171959i
$305$	0.00681566	−	0.0254364i	0.000390264	−	0.00145648i
$306$	−10.6048	−	8.88305i	−0.606234	−	0.507810i
$307$	15.3718	−	4.11887i	0.877317	−	0.235076i	0.208068	−	0.978114i	$-0.433283\pi$
$307$	15.3718	−	4.11887i	0.877317	−	0.235076i	0.669249	+	0.743038i	$0.266616\pi$
$308$	2.24118	−	6.15759i	0.127703	−	0.350861i
$309$	−11.8897	+	22.8638i	−0.676384	+	1.30068i
$310$	0.0652349	+	0.745638i	0.00370509	+	0.0423494i
$311$	−18.2459	−	15.3101i	−1.03463	−	0.868157i	−0.0432348	−	0.999065i	$-0.513766\pi$
$311$	−18.2459	−	15.3101i	−1.03463	−	0.868157i	−0.991395	+	0.130908i	$0.958211\pi$
$312$	5.56706	+	2.82982i	0.315173	+	0.160207i
$313$	9.52742	+	3.46770i	0.538521	+	0.196006i	0.596939	−	0.802286i	$-0.296383\pi$
$313$	9.52742	+	3.46770i	0.538521	+	0.196006i	−0.0584178	+	0.998292i	$0.518606\pi$
$314$	−14.5739	+	3.90507i	−0.822453	+	0.220376i
$315$	2.06600	+	4.42071i	0.116406	+	0.249079i
$316$	2.82937	−	1.63354i	0.159164	−	0.0918936i
$317$	−5.41289	+	7.73041i	−0.304018	+	0.434183i	−0.941871	−	0.335975i	$-0.890934\pi$
$317$	−5.41289	+	7.73041i	−0.304018	+	0.434183i	0.637852	+	0.770159i	$0.279823\pi$
$318$	19.5482	−	15.0131i	1.09621	−	0.841894i
$319$	6.79432	+	3.16824i	0.380409	+	0.177387i
$320$	−0.307948	−	0.439795i	−0.0172148	−	0.0245853i
$321$	1.48755	−	1.36426i	0.0830271	−	0.0761455i
$322$	−0.296284	−	0.353097i	−0.0165112	−	0.0196773i
$323$	17.0439	−	17.0439i	0.948350	−	0.948350i
$324$	−8.46247	−	3.06375i	−0.470137	−	0.170208i
$325$	−16.4496	−	4.24477i	−0.912460	−	0.235458i
$326$	6.62204	+	7.89184i	0.366761	+	0.437088i
$327$	21.4497	+	0.927351i	1.18617	+	0.0512826i
$328$	−1.00825	+	5.71806i	−0.0556712	+	0.315727i
$329$	4.98812	−	1.81553i	0.275004	−	0.100093i
$330$	1.22512	+	1.59520i	0.0674406	+	0.0878127i
$331$	−29.1929	−	20.4411i	−1.60459	−	1.12355i	−0.918059	−	0.396444i	$-0.870244\pi$
$331$	−29.1929	−	20.4411i	−1.60459	−	1.12355i	−0.686530	−	0.727101i	$-0.740867\pi$
$332$	3.32181	+	0.890076i	0.182308	+	0.0488493i
$333$	0.291703	+	1.64612i	0.0159852	+	0.0902067i
$334$	6.46504	−	11.1978i	0.353751	−	0.612715i
$335$	−6.59112	−	2.39897i	−0.360112	−	0.131070i
$336$	5.12348	+	1.13356i	0.279509	+	0.0618406i
$337$	17.4591	−	20.8069i	0.951058	−	1.13343i	−0.0398932	−	0.999204i	$-0.512702\pi$
$337$	17.4591	−	20.8069i	0.951058	−	1.13343i	0.990951	−	0.134223i	$-0.0428538\pi$
$338$	−5.27487	+	11.8817i	−0.286915	+	0.646281i
$339$	−9.17864	+	17.6504i	−0.498515	+	0.958637i
$340$	−2.24376	+	1.04628i	−0.121685	+	0.0567427i
$341$	−2.61139	−	1.50769i	−0.141415	−	0.0816458i
$342$	6.61522	−	14.2180i	0.357710	−	0.768822i
$343$	−14.1099	−	3.78073i	−0.761861	−	0.204140i
$344$	0.578531	−	0.826227i	0.0311923	−	0.0445472i
$345$	0.140265	−	0.0185271i	0.00755161	−	0.000997464i
$346$	−16.3617	−	7.62958i	−0.879609	−	0.410169i
$347$	−20.1314	−	3.54971i	−1.08071	−	0.190558i	−0.395180	−	0.918604i	$-0.629318\pi$
$347$	−20.1314	−	3.54971i	−1.08071	−	0.190558i	−0.685529	+	0.728045i	$0.740429\pi$
$348$	−1.80277	+	5.72618i	−0.0966389	+	0.306956i
$349$	−3.45518	−	0.302289i	−0.184952	−	0.0161812i	−0.00569638	−	0.999984i	$-0.501813\pi$
$349$	−3.45518	−	0.302289i	−0.184952	−	0.0161812i	−0.179255	+	0.983803i	$0.557369\pi$
$350$	−14.2746			−0.763010
$351$	5.44507	−	17.9263i	0.290637	−	0.956834i
$352$	2.16293			0.115285
$353$	23.1244	+	2.02312i	1.23079	+	0.107680i	0.683931	−	0.729546i	$-0.260269\pi$
$353$	23.1244	+	2.02312i	1.23079	+	0.107680i	0.546856	+	0.837226i	$0.315824\pi$
$354$	6.96532	−	1.54729i	0.370202	−	0.0822375i
$355$	−1.87916	−	0.331347i	−0.0997355	−	0.0175861i
$356$	0.326269	+	0.152142i	0.0172922	+	0.00806349i
$357$	9.25018	−	22.3589i	0.489571	−	1.18336i
$358$	13.2452	−	18.9161i	0.700030	−	0.999747i
$359$	−21.7439	−	5.82626i	−1.14760	−	0.307498i	−0.365596	−	0.930774i	$-0.619135\pi$
$359$	−21.7439	−	5.82626i	−1.14760	−	0.307498i	−0.782002	+	0.623275i	$0.785802\pi$
$360$	−1.13795	+	1.13989i	−0.0599750	+	0.0600774i
$361$	7.20852	+	4.16184i	0.379396	+	0.219044i
$362$	−11.7987	+	5.50182i	−0.620126	+	0.289169i
$363$	10.9389	−	0.482276i	0.574144	−	0.0253129i
$364$	−1.79710	+	10.7744i	−0.0941937	+	0.564735i
$365$	−1.29049	+	1.53795i	−0.0675474	+	0.0804999i
$366$	−0.0573677	+	0.0626595i	−0.00299866	+	0.00327526i
$367$	−19.1805	−	6.98115i	−1.00122	−	0.364413i	−0.211163	−	0.977451i	$-0.567725\pi$
$367$	−19.1805	−	6.98115i	−1.00122	−	0.364413i	−0.790053	+	0.613038i	$0.789947\pi$
$368$	0.0760726	−	0.131762i	0.00396556	−	0.00686855i
$369$	17.4188	−	0.0148544i	0.906787	−	0.000773292i
$370$	0.288991	+	0.0774348i	0.0150239	+	0.00402564i
$371$	35.3158	+	24.7284i	1.83350	+	1.28383i
$372$	0.923104	−	2.23126i	0.0478607	−	0.115685i
$373$	14.7819	−	5.38017i	0.765378	−	0.278575i	0.0703160	−	0.997525i	$-0.477599\pi$
$373$	14.7819	−	5.38017i	0.765378	−	0.278575i	0.695062	+	0.718950i	$0.255377\pi$
$374$	1.73192	−	9.82223i	0.0895556	−	0.507895i
$375$	4.84920	−	7.61888i	0.250411	−	0.393437i
$376$	1.12626	+	1.34222i	0.0580822	+	0.0692197i
$377$	−12.1004	−	3.12248i	−0.623203	−	0.160816i
$378$	0.666544	−	15.7280i	0.0342833	−	0.808962i
$379$	3.11555	−	3.11555i	0.160035	−	0.160035i	−0.622547	−	0.782582i	$-0.713902\pi$
$379$	3.11555	−	3.11555i	0.160035	−	0.160035i	0.782582	+	0.622547i	$0.213902\pi$
$380$	−1.80394	−	2.14986i	−0.0925404	−	0.110285i
$381$	−27.6656	−	8.70997i	−1.41735	−	0.446226i
$382$	−5.07935	−	7.25406i	−0.259882	−	0.371150i
$383$	−0.110927	−	0.0517260i	−0.00566809	−	0.00264307i	0.419782	−	0.907625i	$-0.362106\pi$
$383$	−0.110927	−	0.0517260i	−0.00566809	−	0.00264307i	−0.425450	+	0.904982i	$0.639884\pi$
$384$	0.226810	+	1.71714i	0.0115744	+	0.0876272i
$385$	−2.01791	+	2.88188i	−0.102842	+	0.146874i
$386$	−15.6599	+	9.04124i	−0.797067	+	0.460187i
$387$	−2.74350	−	1.27647i	−0.139460	−	0.0648864i
$388$	11.1978	−	3.00045i	0.568484	−	0.152325i
$389$	11.0990	+	4.03971i	0.562742	+	0.204821i	0.607699	−	0.794168i	$-0.292093\pi$
$389$	11.0990	+	4.03971i	0.562742	+	0.204821i	−0.0449569	+	0.998989i	$0.514315\pi$
$390$	−2.49383	−	2.24112i	−0.126280	−	0.113484i
$391$	−0.537437	−	0.450963i	−0.0271793	−	0.0228062i
$392$	0.189854	+	2.17004i	0.00958909	+	0.109604i
$393$	−13.5151	−	21.1946i	−0.681748	−	1.06912i
$394$	5.77515	−	15.8671i	0.290948	−	0.799372i
$395$	−1.69429	+	0.453985i	−0.0852492	+	0.0228425i
$396$	−1.13222	−	6.38926i	−0.0568961	−	0.321072i
$397$	−4.58056	+	17.0949i	−0.229892	+	0.857968i	0.750494	+	0.660878i	$0.229816\pi$
$397$	−4.58056	+	17.0949i	−0.229892	+	0.857968i	−0.980385	+	0.197090i	$0.936851\pi$
$398$	17.2975	+	12.1118i	0.867045	+	0.607111i
$399$	27.1960	+	3.56862i	1.36150	+	0.178655i
$400$	−1.61151	−	4.42759i	−0.0805756	−	0.221380i
$401$	14.9486	+	21.3488i	0.746496	+	1.06611i	0.995232	+	0.0975352i	$0.0310958\pi$
$401$	14.9486	+	21.3488i	0.746496	+	1.06611i	−0.248736	+	0.968571i	$0.580015\pi$
$402$	15.2944	+	16.6767i	0.762817	+	0.831757i
$403$	4.73912	+	1.67536i	0.236073	+	0.0834556i
$404$			1.65923i			0.0825497i
$405$	3.96288	+	2.76478i	0.196917	+	0.137383i
$406$	−10.5005			−0.521130
$407$	−0.923317	+	0.774755i	−0.0457671	+	0.0384032i
$408$	7.97940	+	0.344979i	0.395039	+	0.0170790i
$409$	−8.19567	−	11.7046i	−0.405250	−	0.578757i	0.563711	−	0.825972i	$-0.309373\pi$
$409$	−8.19567	−	11.7046i	−0.405250	−	0.578757i	−0.968961	+	0.247215i	$0.920484\pi$
$410$	1.31744	−	2.82526i	0.0650638	−	0.139530i
$411$	22.3701	−	17.1804i	1.10344	−	0.847445i
$412$	−2.58364	−	14.6526i	−0.127287	−	0.721880i
$413$	6.24010	+	10.8082i	0.307055	+	0.531836i
$414$	−0.429042	−	0.155744i	−0.0210863	−	0.00765441i
$415$	−1.59900	−	0.923182i	−0.0784917	−	0.0453172i
$416$	−3.54482	+	0.658955i	−0.173799	+	0.0323079i
$417$	8.57219	−	5.46623i	0.419782	−	0.267682i
$418$	11.2631	−	0.985391i	0.550895	−	0.0481971i
$419$	−6.12293	+	7.29703i	−0.299125	+	0.356483i	−0.894582	−	0.446904i	$-0.852527\pi$
$419$	−6.12293	+	7.29703i	−0.299125	+	0.356483i	0.595457	+	0.803387i	$0.296971\pi$
$420$	−2.49950	−	1.29981i	−0.121963	−	0.0634240i
$421$	5.69500	−	2.65562i	0.277557	−	0.129427i	−0.278856	−	0.960333i	$-0.589955\pi$
$421$	5.69500	−	2.65562i	0.277557	−	0.129427i	0.556413	+	0.830906i	$0.312177\pi$
$422$	2.43889	−	0.653498i	0.118723	−	0.0318118i
$423$	3.37533	−	4.02954i	0.164114	−	0.195923i
$424$	−3.68314	+	13.7457i	−0.178869	+	0.667549i
$425$	−21.3968	+	3.77283i	−1.03790	+	0.183009i
$426$	4.88535	+	3.74535i	0.236696	+	0.181463i
$427$	−0.134674	−	0.0627994i	−0.00651732	−	0.00303908i
$428$	−0.202358	+	1.14763i	−0.00978136	+	0.0554728i
$429$	13.1584	−	3.05118i	0.635293	−	0.147312i
$430$	−0.414835	+	0.348088i	−0.0200051	+	0.0167863i
$431$	14.5166	+	14.5166i	0.699242	+	0.699242i	0.964247	−	0.265005i	$-0.0853735\pi$
$431$	14.5166	+	14.5166i	0.699242	+	0.699242i	−0.265005	+	0.964247i	$0.585374\pi$
$432$	4.95366	−	1.56885i	0.238333	−	0.0754814i
$433$		−	20.8066i		−	0.999901i	−0.866054	−	0.499951i	$-0.833352\pi$
$433$		−	20.8066i		−	0.999901i	0.866054	−	0.499951i	$-0.166648\pi$
$434$	4.20750	+	0.368108i	0.201966	+	0.0176698i
$435$	1.73061	−	2.71907i	0.0829764	−	0.130370i
$436$	−10.1538	+	7.10980i	−0.486281	+	0.340498i
$437$	0.336106	−	0.720781i	0.0160781	−	0.0344796i
$438$	5.98275	−	2.48113i	0.285867	−	0.118553i
$439$	−36.6203	+	6.45714i	−1.74779	+	0.308183i	−0.953955	−	0.299950i	$-0.903030\pi$
$439$	−36.6203	+	6.45714i	−1.74779	+	0.308183i	−0.793836	+	0.608132i	$0.791919\pi$
$440$	−1.12169	−	0.300556i	−0.0534745	−	0.0143284i
$441$	6.31088	−	1.69676i	0.300518	−	0.0807983i
$442$	0.153978	+	16.6253i	0.00732400	+	0.790783i
$443$	−6.51774	+	17.9073i	−0.309667	+	0.850804i	0.683054	+	0.730368i	$0.260651\pi$
$443$	−6.51774	+	17.9073i	−0.309667	+	0.850804i	−0.992721	+	0.120436i	$0.961571\pi$
$444$	−0.711893	−	0.651772i	−0.0337850	−	0.0309317i
$445$	−0.148061	−	0.124238i	−0.00701875	−	0.00588943i
$446$	20.5748	+	17.2643i	0.974245	+	0.817489i
$447$	−19.5289	+	21.3303i	−0.923683	+	1.00889i
$448$	−2.74573	+	1.28035i	−0.129723	+	0.0604911i
$449$	6.29231	+	23.4832i	0.296953	+	1.10824i	0.939654	+	0.342126i	$0.111147\pi$
$449$	6.29231	+	23.4832i	0.296953	+	1.10824i	−0.642702	+	0.766117i	$0.722186\pi$
$450$	−12.2354	+	7.07806i	−0.576785	+	0.333663i
$451$	6.27929	+	10.8760i	0.295680	+	0.512133i
$452$	−1.99452	−	11.3115i	−0.0938143	−	0.532047i
$453$	0.541917	−	1.30988i	0.0254615	−	0.0615437i
$454$	−4.09973	−	11.2639i	−0.192410	−	0.528642i
$455$	2.42916	−	5.33787i	0.113881	−	0.250243i
$456$	1.96337	+	8.83834i	0.0919431	+	0.413893i
$457$	2.96202	−	33.8560i	0.138557	−	1.58372i	−0.535175	−	0.844741i	$-0.679754\pi$
$457$	2.96202	−	33.8560i	0.138557	−	1.58372i	0.673732	−	0.738976i	$-0.264690\pi$
$458$		−	24.8505i		−	1.16119i
$459$	−3.15787	−	23.7516i	−0.147397	−	1.10863i
$460$	−0.0577603	+	0.0577603i	−0.00269309	+	0.00269309i
$461$	−20.5142	−	1.79476i	−0.955441	−	0.0835902i	−0.401240	−	0.915973i	$-0.631421\pi$
$461$	−20.5142	−	1.79476i	−0.955441	−	0.0835902i	−0.554201	+	0.832383i	$0.686976\pi$
$462$	10.0651	−	5.24502i	0.468271	−	0.244020i
$463$	4.32331	−	3.02721i	0.200921	−	0.140686i	−0.468786	−	0.883312i	$-0.655308\pi$
$463$	4.32331	−	3.02721i	0.200921	−	0.140686i	0.669707	+	0.742625i	$0.266420\pi$
$464$	−1.18544	−	3.25696i	−0.0550325	−	0.151201i
$465$	−0.788770	+	1.02885i	−0.0365783	+	0.0477119i
$466$	−7.74097	+	11.0553i	−0.358594	+	0.512125i
$467$	−12.2534	−	21.2236i	−0.567021	−	0.982110i	−0.996858	−	0.0792033i	$-0.974762\pi$
$467$	−12.2534	−	21.2236i	−0.567021	−	0.982110i	0.429837	−	0.902906i	$-0.358571\pi$
$468$	3.80213	+	10.1264i	0.175753	+	0.468093i
$469$	−19.7897	+	34.2768i	−0.913804	+	1.58275i
$470$	−0.397561	−	0.852573i	−0.0183381	−	0.0393262i
$471$	−23.1856	−	12.0571i	−1.06834	−	0.555561i
$472$	−2.64794	+	3.15569i	−0.121881	+	0.145252i
$473$	−0.190140	−	2.17331i	−0.00874266	−	0.0999291i
$474$	5.52512	+	1.22242i	0.253777	+	0.0561476i
$475$	−10.4088	−	22.3217i	−0.477588	−	1.02419i
$476$	3.61571	+	13.4940i	0.165726	+	0.618497i
$477$	42.5324	+	3.68456i	1.94742	+	0.168704i
$478$	−15.6947	+	9.06133i	−0.717858	+	0.414456i
$479$	21.9454	+	15.3663i	1.00271	+	0.702106i	0.954954	−	0.296753i	$-0.0959037\pi$
$479$	21.9454	+	15.3663i	1.00271	+	0.702106i	0.0477574	+	0.998859i	$0.484793\pi$
$480$	0.120986	−	0.922019i	0.00552224	−	0.0420842i
$481$	1.27719	−	1.55104i	0.0582347	−	0.0707213i
$482$	8.71949	+	1.53748i	0.397162	+	0.0700304i
$483$	0.0344840	−	0.797618i	0.00156908	−	0.0362929i
$484$	−4.84272	+	4.06352i	−0.220123	+	0.184706i
$485$	−6.22410			−0.282622
$486$	−7.22741	−	13.8118i	−0.327842	−	0.626514i
$487$	−3.00972	+	3.00972i	−0.136383	+	0.136383i	−0.772003	−	0.635619i	$-0.780745\pi$
$487$	−3.00972	+	3.00972i	−0.136383	+	0.136383i	0.635619	+	0.772003i	$0.280745\pi$
$488$	0.00427486	−	0.0488618i	0.000193514	−	0.00221187i
$489$	−0.770730	+	17.8270i	−0.0348536	+	0.806167i
$490$	0.203086	−	1.15176i	0.00917451	−	0.0520312i
$491$	−1.76599	+	0.642768i	−0.0796981	+	0.0290077i	−0.381562	−	0.924343i	$-0.624614\pi$
$491$	−1.76599	+	0.642768i	−0.0796981	+	0.0290077i	0.301863	+	0.953351i	$0.402391\pi$
$492$	−7.97595	+	6.12557i	−0.359584	+	0.276162i
$493$	−15.7396	+	2.77531i	−0.708876	+	0.124994i
$494$	−18.1588	+	5.04634i	−0.817003	+	0.227046i
$495$	−0.300672	+	3.47078i	−0.0135142	+	0.156000i
$496$	0.360823	+	1.34661i	0.0162014	+	0.0604645i
$497$	−3.68264	+	10.1180i	−0.165189	+	0.453854i
$498$	3.20257	+	5.02230i	0.143511	+	0.225055i
$499$	−18.4463	+	1.61385i	−0.825771	+	0.0722456i	−0.492203	−	0.870480i	$-0.663808\pi$
$499$	−18.4463	+	1.61385i	−0.825771	+	0.0722456i	−0.333568	+	0.942726i	$0.608253\pi$
$500$	0.454443	+	5.19431i	0.0203233	+	0.232297i
$501$	21.3561	−	6.74358i	0.954122	−	0.301281i
$502$	−4.68196	−	10.0405i	−0.208966	−	0.448129i
$503$	−34.8832	−	20.1399i	−1.55537	−	0.897992i	−0.997690	−	0.0679337i	$-0.978359\pi$
$503$	−34.8832	−	20.1399i	−1.55537	−	0.897992i	−0.557677	−	0.830058i	$-0.688307\pi$
$504$	5.21943	+	7.44060i	0.232492	+	0.331431i
$505$	0.230562	−	0.860471i	0.0102599	−	0.0382904i
$506$	−0.0571441	−	0.324080i	−0.00254037	−	0.0144071i
$507$	−20.6357	+	9.00938i	−0.916463	+	0.400121i
$508$	15.7358	−	5.72735i	0.698162	−	0.254110i
$509$	−16.9881	+	11.8952i	−0.752985	+	0.527246i	−0.885897	−	0.463882i	$-0.846456\pi$
$509$	−16.9881	+	11.8952i	−0.752985	+	0.527246i	0.132912	+	0.991128i	$0.457567\pi$
$510$	−4.09016	−	1.28770i	−0.181115	−	0.0570205i
$511$	7.28201	+	8.67836i	0.322137	+	0.383908i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	25.0805	−	10.4263i	1.10733	−	0.460332i
$514$	5.43715	+	5.43715i	0.239822	+	0.239822i
$515$	−0.696217	+	7.95779i	−0.0306790	+	0.350662i
$516$	1.70544	−	0.378850i	0.0750777	−	0.0166779i
$517$	3.73219	+	0.658086i	0.164142	+	0.0289426i
$518$	0.713484	−	1.53007i	0.0313487	−	0.0672274i
$519$	−11.9784	−	28.8836i	−0.525794	−	1.26785i
$520$	1.92990	+	0.150848i	0.0846318	+	0.00661513i
$521$	−33.3817	+	19.2729i	−1.46248	+	0.844362i	−0.999126	−	0.0418113i	$-0.986687\pi$
$521$	−33.3817	+	19.2729i	−1.46248	+	0.844362i	−0.463353	+	0.886174i	$0.653354\pi$
$522$	−9.00046	+	5.20666i	−0.393939	+	0.227889i
$523$	5.27353	−	9.13402i	0.230595	−	0.399403i	−0.727388	−	0.686226i	$-0.759266\pi$
$523$	5.27353	−	9.13402i	0.230595	−	0.399403i	0.957983	+	0.286824i	$0.0925993\pi$
$524$	13.6376	+	4.96369i	0.595762	+	0.216840i
$525$	−18.2358	−	16.6957i	−0.795876	−	0.728662i
$526$	23.0965	−	2.02068i	1.00705	−	0.0881059i
$527$	6.40409	−	0.560285i	0.278966	−	0.0244064i
$528$	2.76315	+	2.52979i	0.120251	+	0.110095i
$529$	21.5912	+	7.85855i	0.938747	+	0.341676i
$530$	3.82013	−	6.61666i	0.165936	−	0.287409i
$531$	10.7079	+	6.17006i	0.464684	+	0.267758i
$532$	−13.7146	+	7.91811i	−0.594602	+	0.343294i
$533$	−13.6046	−	15.9117i	−0.589280	−	0.689211i
$534$	0.238862	+	0.575969i	0.0103366	+	0.0249246i
$535$	0.264414	−	0.567039i	0.0114316	−	0.0245152i
$536$	−12.8659	−	2.26860i	−0.555721	−	0.0979886i
$537$	39.0452	−	8.67359i	1.68493	−	0.374293i
$538$	−1.03855	+	11.8707i	−0.0447751	+	0.511781i
$539$	3.33160	+	3.33160i	0.143502	+	0.143502i
$540$	−2.78695	+	0.125253i	−0.119931	+	0.00539003i
$541$	−10.8259	−	10.8259i	−0.465444	−	0.465444i	0.434991	−	0.900435i	$-0.356752\pi$
$541$	−10.8259	−	10.8259i	−0.465444	−	0.465444i	−0.900435	+	0.434991i	$0.856752\pi$
$542$	−6.87226	−	8.19004i	−0.295189	−	0.351793i
$543$	−21.5078	−	6.77132i	−0.922990	−	0.290585i
$544$	−3.77729	+	2.64488i	−0.161950	+	0.113398i
$545$	6.25371	−	2.27617i	0.267880	−	0.0975002i
$546$	−14.8977	+	11.6625i	−0.637564	+	0.499107i
$547$	−6.67655	−	37.8646i	−0.285469	−	1.61897i	−0.703607	−	0.710590i	$-0.748428\pi$
$547$	−6.67655	−	37.8646i	−0.285469	−	1.61897i	0.418138	−	0.908383i	$-0.362683\pi$
$548$	−4.21483	+	15.7299i	−0.180048	+	0.671950i
$549$	−0.146575	+	0.0129496i	−0.00625565	+	0.000552674i
$550$	−8.82584	−	5.09560i	−0.376335	−	0.217277i
$551$	−7.65675	−	16.4200i	−0.326189	−	0.699514i
$552$	0.251293	−	0.0793501i	0.0106957	−	0.00337736i
$553$	0.862654	+	9.86018i	0.0366838	+	0.419298i
$554$	19.4896	−	1.70512i	0.828033	−	0.0724435i
$555$	0.278617	+	0.436930i	0.0118266	+	0.0185466i
$556$	−2.00757	+	5.51577i	−0.0851401	+	0.233921i
$557$	−3.79363	−	14.1580i	−0.160741	−	0.599895i	−0.998545	−	0.0539233i	$-0.982827\pi$
$557$	−3.79363	−	14.1580i	−0.160741	−	0.599895i	0.837804	−	0.545972i	$-0.183839\pi$
$558$	3.78898	−	1.77076i	0.160400	−	0.0749624i
$559$	0.973738	+	3.50391i	0.0411847	+	0.148200i
$560$	1.60184	−	0.282448i	0.0676901	−	0.0119356i
$561$	13.7007	−	10.5222i	0.578445	−	0.444249i
$562$	−24.2456	+	8.82467i	−1.02274	+	0.372246i
$563$	−0.934245	+	5.29836i	−0.0393737	+	0.223299i	−0.998145	−	0.0608789i	$-0.980610\pi$
$563$	−0.934245	+	5.29836i	−0.0393737	+	0.223299i	0.958771	+	0.284178i	$0.0917208\pi$
$564$	−0.131083	+	3.03197i	−0.00551960	+	0.127669i
$565$	−0.537465	+	6.14325i	−0.0226113	+	0.258449i
$566$	6.54294	−	6.54294i	0.275020	−	0.275020i
$567$	19.2472	−	19.3130i	0.808306	−	0.811068i
$568$	−3.55407			−0.149126
$569$	15.4247	−	12.9428i	0.646635	−	0.542591i	−0.259413	−	0.965767i	$-0.583529\pi$
$569$	15.4247	−	12.9428i	0.646635	−	0.542591i	0.906048	+	0.423175i	$0.139085\pi$
$570$	0.209959	−	4.85636i	0.00879420	−	0.203411i
$571$	15.6587	+	2.76105i	0.655296	+	0.115546i	0.491404	−	0.870932i	$-0.336484\pi$
$571$	15.6587	+	2.76105i	0.655296	+	0.115546i	0.163892	+	0.986478i	$0.447595\pi$
$572$	−4.95728	+	6.02022i	−0.207274	+	0.251718i
$573$	1.99557	−	15.2079i	0.0833659	−	0.635320i
$574$	−14.4093	−	10.0895i	−0.601434	−	0.421128i
$575$	−0.620827	+	0.358435i	−0.0258903	+	0.0149478i
$576$	−1.71863	+	2.45892i	−0.0716097	+	0.102455i
$577$	11.3507	+	42.3614i	0.472536	+	1.76353i	0.630610	+	0.776100i	$0.282805\pi$
$577$	11.3507	+	42.3614i	0.472536	+	1.76353i	−0.158074	+	0.987427i	$0.550528\pi$
$578$	1.80175	+	3.86386i	0.0749427	+	0.160715i
$579$	−30.5803	−	6.76580i	−1.27087	−	0.281177i
$580$	0.162184	+	1.85378i	0.00673434	+	0.0769738i
$581$	−6.69700	+	7.98118i	−0.277838	+	0.331115i
$582$	17.8146	+	9.26405i	0.738439	+	0.384007i
$583$	13.0081	+	27.8959i	0.538740	+	1.15533i
$584$	−1.86970	+	3.23841i	−0.0773687	+	0.134006i
$585$	−0.564632	−	5.77985i	−0.0233446	−	0.238967i
$586$	−0.325320	−	0.563470i	−0.0134388	−	0.0232767i
$587$	8.47492	−	12.1034i	0.349797	−	0.499562i	−0.605242	−	0.796042i	$-0.706924\pi$
$587$	8.47492	−	12.1034i	0.349797	−	0.499562i	0.955039	+	0.296479i	$0.0958125\pi$
$588$	−2.29557	+	2.99429i	−0.0946677	+	0.123482i
$589$	2.49241	+	6.84783i	0.102698	+	0.282160i
$590$	1.81172	−	1.26858i	0.0745872	−	0.0522265i
$591$	25.9361	−	13.5155i	1.06687	−	0.555955i
$592$	0.555134	+	0.0485680i	0.0228159	+	0.00199613i
$593$	−8.18657	+	8.18657i	−0.336182	+	0.336182i	−0.854928	−	0.518746i	$-0.826399\pi$
$593$	−8.18657	+	8.18657i	−0.336182	+	0.336182i	0.518746	+	0.854928i	$0.326399\pi$
$594$	6.02654	−	9.48654i	0.247272	−	0.389237i
$595$		−	7.50038i		−	0.307486i
$596$	1.45523	−	16.6333i	0.0596085	−	0.681328i
$597$	7.93141	+	35.7042i	0.324611	+	1.46128i
$598$	0.192387	+	0.513725i	0.00786729	+	0.0210078i
$599$	15.1438	+	41.6073i	0.618759	+	1.70003i	0.710004	+	0.704198i	$0.248693\pi$
$599$	15.1438	+	41.6073i	0.618759	+	1.70003i	−0.0912448	+	0.995828i	$0.529085\pi$
$600$	3.11986	−	7.54110i	0.127368	−	0.307864i
$601$	1.21172	+	6.87201i	0.0494272	+	0.280315i	0.999497	−	0.0317229i	$-0.0100994\pi$
$601$	1.21172	+	6.87201i	0.0494272	+	0.280315i	−0.950070	+	0.312038i	$0.898988\pi$
$602$	1.52787	+	2.64635i	0.0622714	+	0.107857i
$603$	0.0334231	+	39.1930i	0.00136109	+	1.59606i
$604$	0.211825	+	0.790540i	0.00861902	+	0.0321666i
$605$	3.07608	−	1.43440i	0.125060	−	0.0583165i
$606$	−1.94065	+	2.11967i	−0.0788336	+	0.0861055i
$607$	−21.7060	−	18.2135i	−0.881021	−	0.739265i	0.0853676	−	0.996350i	$-0.472794\pi$
$607$	−21.7060	−	18.2135i	−0.881021	−	0.739265i	−0.966389	+	0.257085i	$0.917238\pi$
$608$	−4.00427	−	3.35998i	−0.162395	−	0.136265i
$609$	−13.4144	−	12.2815i	−0.543577	−	0.497670i
$610$	−0.00900665	+	0.0247456i	−0.000364669	+	0.00100192i
$611$	−6.31717	+	0.0585078i	−0.255565	+	0.00236697i
$612$	9.79020	+	9.77352i	0.395745	+	0.395071i
$613$	−32.0957	−	8.60001i	−1.29633	−	0.347351i	−0.456270	−	0.889841i	$-0.650815\pi$
$613$	−32.0957	−	8.60001i	−1.29633	−	0.347351i	−0.840062	+	0.542490i	$0.817482\pi$
$614$	−15.6723	+	2.76345i	−0.632484	+	0.111524i
$615$	4.98750	−	2.06838i	0.201115	−	0.0834052i
$616$	−2.76932	+	5.93883i	−0.111579	+	0.239282i
$617$	−14.0092	+	9.80931i	−0.563987	+	0.394908i	−0.820512	−	0.571630i	$-0.806311\pi$
$617$	−14.0092	+	9.80931i	−0.563987	+	0.394908i	0.256525	+	0.966538i	$0.417423\pi$
$618$	13.8372	−	21.7405i	0.556614	−	0.874532i
$619$	−13.7299	−	1.20121i	−0.551853	−	0.0482809i	−0.192181	−	0.981360i	$-0.561556\pi$
$619$	−13.7299	−	1.20121i	−0.551853	−	0.0482809i	−0.359672	+	0.933079i	$0.617112\pi$
$620$		−	0.748486i		−	0.0300599i
$621$	−0.365941	−	0.700776i	−0.0146847	−	0.0281212i
$622$	16.8421	+	16.8421i	0.675306	+	0.675306i
$623$	−0.835479	+	0.701050i	−0.0334728	+	0.0280870i
$624$	−5.29924	−	3.30425i	−0.212139	−	0.132276i
$625$	−3.60482	+	20.4439i	−0.144193	+	0.817757i
$626$	−9.18893	−	4.28487i	−0.367264	−	0.171258i
$627$	15.5411	+	11.9146i	0.620652	+	0.475823i
$628$	14.8588	−	2.62001i	0.592930	−	0.104550i
$629$	0.665067	−	2.48206i	0.0265180	−	0.0989663i
$630$	−1.67285	−	4.58395i	−0.0666480	−	0.182629i
$631$	16.6470	−	4.46055i	0.662706	−	0.177572i	0.0882390	−	0.996099i	$-0.471876\pi$
$631$	16.6470	−	4.46055i	0.662706	−	0.177572i	0.574467	+	0.818528i	$0.305209\pi$
$632$	−2.96097	+	1.38072i	−0.117781	+	0.0549223i
$633$	3.88002	+	2.01771i	0.154217	+	0.0801967i
$634$	6.06605	−	7.22923i	0.240913	−	0.287109i
$635$	−8.95638	+	0.783582i	−0.355423	+	0.0310955i
$636$	−20.7823	+	13.2523i	−0.824073	+	0.525486i
$637$	−6.47514	−	4.44514i	−0.256554	−	0.176123i
$638$	−6.49233	−	3.74835i	−0.257034	−	0.148399i
$639$	1.86043	+	10.4986i	0.0735974	+	0.415320i
$640$	0.268445	+	0.464961i	0.0106112	+	0.0183792i
$641$	4.78814	+	27.1549i	0.189120	+	1.07255i	0.920546	+	0.390633i	$0.127744\pi$
$641$	4.78814	+	27.1549i	0.189120	+	1.07255i	−0.731426	+	0.681921i	$0.761145\pi$
$642$	−1.60080	+	1.22942i	−0.0631784	+	0.0485213i
$643$	−15.9209	+	34.1424i	−0.627858	+	1.34645i	0.292837	+	0.956162i	$0.405401\pi$
$643$	−15.9209	+	34.1424i	−0.627858	+	1.34645i	−0.920695	+	0.390283i	$0.872377\pi$
$644$	0.264382	+	0.377576i	0.0104181	+	0.0148786i
$645$	−0.937079	−	0.0405134i	−0.0368975	−	0.00159522i
$646$	−18.4646	+	15.4936i	−0.726478	+	0.609588i
$647$	31.6114			1.24277			0.621386	−	0.783505i	$-0.286570\pi$
$647$	31.6114			1.24277			0.621386	+	0.783505i	$0.286570\pi$
$648$	8.16325	+	3.78965i	0.320683	+	0.148871i
$649$			8.91011i			0.349752i
$650$	16.0170	+	5.66230i	0.628240	+	0.222094i
$651$	4.94454	+	5.39140i	0.193792	+	0.211306i
$652$	−5.90902	−	8.43895i	−0.231415	−	0.330495i
$653$	12.4996	+	34.3423i	0.489146	+	1.34392i	0.901455	+	0.432873i	$0.142500\pi$
$653$	12.4996	+	34.3423i	0.489146	+	1.34392i	−0.412309	+	0.911044i	$0.635278\pi$
$654$	−21.2873	−	2.79329i	−0.832397	−	0.109226i
$655$	−6.38268	−	4.46920i	−0.249392	−	0.174626i
$656$	1.50277	−	5.60843i	0.0586734	−	0.218972i
$657$	10.5449	+	3.82786i	0.411396	+	0.149339i
$658$	−5.12738	+	1.37388i	−0.199886	+	0.0535593i
$659$	−7.19202	+	19.7599i	−0.280161	+	0.769737i	0.717182	+	0.696886i	$0.245432\pi$
$659$	−7.19202	+	19.7599i	−0.280161	+	0.769737i	−0.997343	+	0.0728504i	$0.976790\pi$
$660$	−1.08143	−	1.69590i	−0.0420945	−	0.0660130i
$661$	−1.29542	−	14.8067i	−0.0503859	−	0.575913i	−0.978862	−	0.204521i	$-0.934436\pi$
$661$	−1.29542	−	14.8067i	−0.0503859	−	0.575913i	0.928476	−	0.371392i	$-0.121119\pi$
$662$	27.3003	+	22.9077i	1.06106	+	0.890332i
$663$	−19.2484	+	21.4189i	−0.747545	+	0.831840i
$664$	−3.23159	−	1.17620i	−0.125410	−	0.0456456i
$665$	8.21261	−	2.20056i	0.318472	−	0.0853342i
$666$	−0.147124	−	1.66528i	−0.00570094	−	0.0645282i
$667$	−0.456684	+	0.263666i	−0.0176829	+	0.0102092i
$668$	−7.41639	+	10.5917i	−0.286949	+	0.409805i
$669$	6.09178	+	46.1197i	0.235522	+	1.78309i
$670$	6.35696	+	2.96430i	0.245591	+	0.114521i
$671$	−0.0608499	−	0.0869027i	−0.00234909	−	0.00335484i
$672$	−5.00519	−	1.57578i	−0.193079	−	0.0607872i
$673$	27.6840	+	32.9925i	1.06714	+	1.27177i	0.960742	+	0.277444i	$0.0894873\pi$
$673$	27.6840	+	32.9925i	1.06714	+	1.27177i	0.106398	+	0.994324i	$0.466068\pi$
$674$	−19.2061	+	19.2061i	−0.739792	+	0.739792i
$675$	−23.9094	−	5.26850i	−0.920272	−	0.202785i
$676$	6.29036	−	11.3768i	0.241937	−	0.437569i
$677$	−20.2310	−	24.1104i	−0.777541	−	0.926637i	0.221279	−	0.975211i	$-0.428977\pi$
$677$	−20.2310	−	24.1104i	−0.777541	−	0.926637i	−0.998820	+	0.0485736i	$0.984532\pi$
$678$	10.6820	−	16.7832i	0.410241	−	0.644556i
$679$	−6.09878	+	34.5879i	−0.234050	+	1.32736i
$680$	2.32641	−	0.846746i	0.0892139	−	0.0324712i
$681$	7.93701	−	19.1848i	0.304147	−	0.735162i
$682$	2.47005	+	1.72955i	0.0945830	+	0.0662278i
$683$	20.3296	+	5.44731i	0.777892	+	0.208436i	0.625855	−	0.779939i	$-0.284750\pi$
$683$	20.3296	+	5.44731i	0.777892	+	0.208436i	0.152037	+	0.988375i	$0.451417\pi$
$684$	−7.82922	+	13.5874i	−0.299358	+	0.519526i
$685$	4.37159	−	7.57182i	0.167030	−	0.289304i
$686$	13.7267	+	4.99610i	0.524086	+	0.190752i
$687$	29.0654	−	31.7465i	1.10891	−	1.21120i
$688$	−0.648340	+	0.772661i	−0.0247177	+	0.0294574i
$689$	−29.8176	−	41.7555i	−1.13596	−	1.59076i
$690$	−0.141346	+	0.00623168i	−0.00538095	+	0.000237236i
$691$	45.8284	−	21.3701i	1.74340	−	0.812959i	0.756023	−	0.654545i	$-0.227140\pi$
$691$	45.8284	−	21.3701i	1.74340	−	0.812959i	0.987373	−	0.158413i	$-0.0506379\pi$
$692$	15.6345	+	9.02656i	0.594333	+	0.343138i
$693$	18.9928	+	5.07175i	0.721477	+	0.192660i
$694$	19.7454	+	5.29076i	0.749525	+	0.200835i
$695$	1.80758	−	2.58149i	0.0685654	−	0.0979215i
$696$	2.29498	−	5.54727i	0.0869912	−	0.210269i
$697$	−24.2654	−	11.3152i	−0.919119	−	0.428592i
$698$	3.41569	+	0.602278i	0.129286	+	0.0227965i
$699$	−22.8194	+	5.06916i	−0.863111	+	0.191733i
$700$	14.2203	+	1.24411i	0.537476	+	0.0470231i
$701$	34.3612			1.29780			0.648901	−	0.760872i	$-0.275229\pi$
$701$	34.3612			1.29780			0.648901	+	0.760872i	$0.275229\pi$
$702$	−6.98673	+	17.3835i	−0.263697	+	0.656097i
$703$	2.91289			0.109862
$704$	−2.15470	−	0.188512i	−0.0812084	−	0.00710482i
$705$	0.489294	−	1.55415i	0.0184279	−	0.0585328i
$706$	−22.8601	−	4.03085i	−0.860350	−	0.151703i
$707$	−4.55579	−	2.12440i	−0.171338	−	0.0798963i
$708$	−7.07367	+	0.934335i	−0.265845	+	0.0351144i
$709$	−17.1077	+	24.4324i	−0.642495	+	0.917578i	−0.999866	−	0.0163849i	$-0.994784\pi$
$709$	−17.1077	+	24.4324i	−0.642495	+	0.917578i	0.357371	+	0.933962i	$0.383673\pi$
$710$	1.84313	+	0.493865i	0.0691715	+	0.0185344i
$711$	5.62859	+	8.02389i	0.211089	+	0.300919i
$712$	−0.311767	−	0.179999i	−0.0116840	−	0.00674574i
$713$	0.192235	−	0.0896404i	0.00719924	−	0.00335706i
$714$	−11.1637	+	21.4676i	−0.417790	+	0.803404i
$715$	3.40739	−	2.43321i	0.127429	−	0.0909971i
$716$	−14.8434	+	17.6897i	−0.554725	+	0.661096i
$717$	−30.6482	−	6.78084i	−1.14458	−	0.253235i
$718$	21.1534	+	7.69919i	0.789436	+	0.287331i
$719$	18.4025	−	31.8741i	0.686299	−	1.18870i	−0.286728	−	0.958012i	$-0.592568\pi$
$719$	18.4025	−	31.8741i	0.686299	−	1.18870i	0.973027	−	0.230692i	$-0.0740990\pi$
$720$	1.23296	−	1.03637i	0.0459498	−	0.0386233i
$721$	43.5400	+	11.6665i	1.62151	+	0.434483i
$722$	−6.81836	−	4.77427i	−0.253753	−	0.177680i
$723$	9.34090	+	12.1626i	0.347392	+	0.452330i
$724$	12.2333	−	4.45256i	0.454648	−	0.165478i
$725$	−2.83582	+	16.0827i	−0.105320	+	0.597298i
$726$	−10.9393	−	0.472948i	−0.405996	−	0.0175527i
$727$	13.3884	+	15.9557i	0.496549	+	0.591764i	0.954870	−	0.297023i	$-0.0959937\pi$
$727$	13.3884	+	15.9557i	0.496549	+	0.591764i	−0.458322	+	0.888786i	$0.651549\pi$
$728$	2.72932	−	10.5768i	0.101155	−	0.392003i
$729$	6.92137	−	26.0978i	0.256347	−	0.966585i
$730$	1.41962	−	1.41962i	0.0525426	−	0.0525426i
$731$	2.98963	+	3.56290i	0.110576	+	0.131779i
$732$	0.0626105	−	0.0574211i	0.00231415	−	0.00212235i
$733$	10.4062	+	14.8616i	0.384363	+	0.548927i	0.963984	−	0.265959i	$-0.0856885\pi$
$733$	10.4062	+	14.8616i	0.384363	+	0.548927i	−0.579622	+	0.814886i	$0.696800\pi$
$734$	18.4991	+	8.62628i	0.682815	+	0.318402i
$735$	1.60655	−	1.23384i	0.0592587	−	0.0455109i
$736$	−0.0872669	+	0.124630i	−0.00321670	+	0.00459392i
$737$	−24.4715	+	14.1287i	−0.901421	+	0.520436i
$738$	−17.3538	−	1.50335i	−0.638803	−	0.0553391i
$739$	32.9302	−	8.82362i	1.21136	−	0.324582i	0.404063	−	0.914731i	$-0.367598\pi$
$739$	32.9302	−	8.82362i	1.21136	−	0.324582i	0.807294	+	0.590149i	$0.200931\pi$
$740$	−0.281142	−	0.102327i	−0.0103350	−	0.00376163i
$741$	−29.1001	−	14.7921i	−1.06902	−	0.543400i
$742$	−33.0262	−	27.7122i	−1.21243	−	1.01735i
$743$	−0.568469	−	6.49763i	−0.0208551	−	0.238375i	−0.999467	−	0.0326578i	$-0.989603\pi$
$743$	−0.568469	−	6.49763i	−0.0208551	−	0.238375i	0.978611	−	0.205717i	$-0.0659527\pi$
$744$	−1.11406	+	2.14232i	−0.0408434	+	0.0785411i
$745$	−3.06600	+	8.42378i	−0.112330	+	0.308623i
$746$	−15.1946	+	4.07137i	−0.556312	+	0.149063i
$747$	−1.78286	+	10.1618i	−0.0652314	+	0.371799i
$748$	−2.58140	+	9.63390i	−0.0943852	+	0.352250i
$749$	−2.89199	−	2.02500i	−0.105671	−	0.0739917i
$750$	−5.49477	+	7.16725i	−0.200641	+	0.261711i
$751$	9.37178	+	25.7487i	0.341981	+	0.939585i	0.984819	+	0.173583i	$0.0555345\pi$
$751$	9.37178	+	25.7487i	0.341981	+	0.939585i	−0.642838	+	0.766002i	$0.722243\pi$
$752$	−1.00499	−	1.43527i	−0.0366481	−	0.0523390i
$753$	5.76227	−	18.3028i	0.209989	−	0.666991i
$754$	11.7822	+	4.16521i	0.429083	+	0.151688i
$755$		−	0.439406i		−	0.0159916i
$756$	−2.03480	+	15.6101i	−0.0740048	+	0.567733i
$757$	39.3010			1.42842			0.714209	−	0.699933i	$-0.246787\pi$
$757$	39.3010			1.42842			0.714209	+	0.699933i	$0.246787\pi$
$758$	−3.37523	+	2.83216i	−0.122594	+	0.102869i
$759$	0.306047	−	0.480849i	0.0111088	−	0.0174537i
$760$	1.60971	+	2.29890i	0.0583902	+	0.0833899i
$761$	18.2874	−	39.2176i	0.662919	−	1.42164i	−0.230797	−	0.973002i	$-0.574133\pi$
$761$	18.2874	−	39.2176i	0.662919	−	1.42164i	0.893716	−	0.448633i	$-0.148089\pi$
$762$	26.8012	+	11.0880i	0.970906	+	0.401678i
$763$	−6.52106	−	36.9828i	−0.236078	−	1.33887i
$764$	4.42779	+	7.66915i	0.160192	+	0.277460i
$765$	−3.71906	−	6.42894i	−0.134463	−	0.232439i
$766$	0.105996	+	0.0611970i	0.00382980	+	0.00221114i
$767$	−2.71454	−	14.6027i	−0.0980163	−	0.527275i
$768$	−0.0762888	−	1.73037i	−0.00275284	−	0.0624393i
$769$	−36.2448	+	3.17101i	−1.30702	+	0.114350i	−0.719292	−	0.694707i	$-0.755534\pi$
$769$	−36.2448	+	3.17101i	−1.30702	+	0.114350i	−0.587730	+	0.809057i	$0.699978\pi$
$770$	2.26141	−	2.69504i	0.0814955	−	0.0971225i
$771$	0.586606	+	13.3053i	0.0211261	+	0.479179i
$772$	16.3883	−	7.64199i	0.589828	−	0.275041i
$773$	−18.7801	+	5.03212i	−0.675475	+	0.180993i	−0.580220	−	0.814460i	$-0.697033\pi$
$773$	−18.7801	+	5.03212i	−0.675475	+	0.180993i	−0.0952550	+	0.995453i	$0.530367\pi$
$774$	2.62181	+	1.51072i	0.0942389	+	0.0543017i
$775$	1.70011	−	6.34488i	0.0610696	−	0.227915i
$776$	−11.4167	+	2.01308i	−0.409837	+	0.0722653i
$777$	2.70106	−	1.12017i	0.0969001	−	0.0401858i
$778$	−10.7047	−	4.99168i	−0.383781	−	0.178960i
$779$	5.27032	−	29.8895i	0.188829	−	1.07090i
$780$	2.28902	+	2.44994i	0.0819599	+	0.0877221i
$781$	−5.88875	+	4.94125i	−0.210716	+	0.176812i
$782$	0.496088	+	0.496088i	0.0177401	+	0.0177401i
$783$	−17.5879	−	3.87554i	−0.628539	−	0.138500i
$784$		−	2.17833i		−	0.0777976i
$785$	−8.06979	−	0.706016i	−0.288023	−	0.0251988i
$786$	11.6165	+	22.2918i	0.414346	+	0.795123i
$787$	−43.1306	+	30.2003i	−1.53744	+	1.07653i	−0.570570	+	0.821249i	$0.693278\pi$
$787$	−43.1306	+	30.2003i	−1.53744	+	1.07653i	−0.966868	+	0.255277i	$0.917833\pi$
$788$	−7.13608	+	15.3034i	−0.254212	+	0.545160i
$789$	31.8692	+	24.4325i	1.13457	+	0.869820i
$790$	1.72741	−	0.304590i	0.0614586	−	0.0108368i
$791$	33.6119	+	9.00629i	1.19510	+	0.320227i
$792$	0.571049	+	6.46362i	0.0202913	+	0.229675i
$793$	0.126202	+	0.123886i	0.00448158	+	0.00439932i
$794$	6.05305	−	16.6306i	0.214815	−	0.590198i
$795$	12.6191	−	3.98472i	0.447555	−	0.141323i
$796$	−16.1761	−	13.5733i	−0.573345	−	0.481094i
$797$	−25.2066	−	21.1508i	−0.892863	−	0.749201i	0.0759197	−	0.997114i	$-0.475811\pi$
$797$	−25.2066	−	21.1508i	−0.892863	−	0.749201i	−0.968782	+	0.247913i	$0.920255\pi$
$798$	−26.7815	−	5.92533i	−0.948054	−	0.209755i
$799$	−7.32252	+	3.41455i	−0.259052	+	0.120798i
$800$	1.21949	+	4.55120i	0.0431155	+	0.160909i
$801$	−0.368514	+	1.01518i	−0.0130208	+	0.0358695i
$802$	−13.0310	−	22.5704i	−0.460141	−	0.796988i
$803$	1.40448	+	7.96519i	0.0495630	+	0.281086i
$804$	−13.7828	−	17.9462i	−0.486081	−	0.632914i
$805$	−0.0846404	−	0.232548i	−0.00298318	−	0.00819623i
$806$	−4.57507	−	2.08203i	−0.161150	−	0.0733363i
$807$	−15.2108	+	13.9501i	−0.535447	+	0.491067i
$808$	0.144611	−	1.65291i	0.00508741	−	0.0581493i
$809$		−	53.2304i		−	1.87148i	−0.352688	−	0.935741i	$-0.614732\pi$
$809$		−	53.2304i		−	1.87148i	0.352688	−	0.935741i	$-0.385268\pi$
$810$	−3.70683	−	3.09964i	−0.130245	−	0.108910i
$811$	6.73144	−	6.73144i	0.236373	−	0.236373i	−0.578974	−	0.815346i	$-0.696547\pi$
$811$	6.73144	−	6.73144i	0.236373	−	0.236373i	0.815346	+	0.578974i	$0.196547\pi$
$812$	10.4605	+	0.915176i	0.367092	+	0.0321164i
$813$	0.799853	−	18.5007i	0.0280521	−	0.648847i
$814$	0.987328	−	0.691335i	0.0346058	−	0.0242313i
$815$	1.89174	+	5.19752i	0.0662648	+	0.182061i
$816$	−7.91897	−	1.03912i	−0.277219	−	0.0363764i
$817$	−3.02410	+	4.31886i	−0.105800	+	0.151098i
$818$	7.14436	+	12.3744i	0.249797	+	0.432661i
$819$	−32.6724	−	2.52576i	−1.14167	−	0.0882573i
$820$	−1.55867	+	2.69969i	−0.0544310	+	0.0942773i
$821$	−17.9578	−	38.5106i	−0.626732	−	1.34403i	−0.921469	−	0.388452i	$-0.873010\pi$
$821$	−17.9578	−	38.5106i	−0.626732	−	1.34403i	0.294737	−	0.955578i	$-0.404768\pi$
$822$	−23.7824	+	15.1653i	−0.829506	+	0.528951i
$823$	6.16638	−	7.34881i	0.214947	−	0.256163i	−0.647788	−	0.761821i	$-0.724306\pi$
$823$	6.16638	−	7.34881i	0.214947	−	0.256163i	0.862734	+	0.505658i	$0.168750\pi$
$824$	1.29676	+	14.8220i	0.0451746	+	0.516349i
$825$	−5.31514	−	16.8324i	−0.185049	−	0.586030i
$826$	−5.27436	−	11.3109i	−0.183519	−	0.393557i
$827$	2.26985	+	8.47121i	0.0789305	+	0.294573i	0.994096	−	0.108506i	$-0.0346067\pi$
$827$	2.26985	+	8.47121i	0.0789305	+	0.294573i	−0.915165	+	0.403079i	$0.867940\pi$
$828$	0.413835	+	0.192545i	0.0143818	+	0.00669140i
$829$	−19.3714	+	11.1841i	−0.672798	+	0.388440i	−0.797136	−	0.603800i	$-0.793653\pi$
$829$	−19.3714	+	11.1841i	−0.672798	+	0.388440i	0.124338	+	0.992240i	$0.460319\pi$
$830$	1.51245	+	1.05903i	0.0524980	+	0.0367595i
$831$	26.8923	+	20.6170i	0.932883	+	0.715194i
$832$	3.58877	−	0.347496i	0.124418	−	0.0120473i
$833$	−9.89216	−	1.74425i	−0.342743	−	0.0604348i
$834$	−9.01598	+	4.69831i	−0.312198	+	0.162689i
$835$	5.31791	−	4.46226i	0.184034	−	0.154423i
$836$	−11.3061			−0.391030
$837$	6.91152	+	2.16948i	0.238897	+	0.0749882i
$838$	6.73561	−	6.73561i	0.232678	−	0.232678i
$839$	−1.58757	+	18.1461i	−0.0548092	+	0.626472i	0.918263	+	0.395971i	$0.129592\pi$
$839$	−1.58757	+	18.1461i	−0.0548092	+	0.626472i	−0.973072	+	0.230501i	$0.925964\pi$
$840$	2.37671	+	1.51271i	0.0820042	+	0.0521933i
$841$	2.94975	−	16.7289i	0.101716	−	0.576858i
$842$	−5.90478	+	2.14916i	−0.203492	+	0.0740651i
$843$	−41.2952	−	17.0844i	−1.42228	−	0.588418i
$844$	−2.48656	+	0.438448i	−0.0855910	+	0.0150920i
$845$	−4.84305	+	5.02587i	−0.166606	+	0.172895i
$846$	−3.71369	+	3.72002i	−0.127679	+	0.127897i
$847$	−4.95694	−	18.4995i	−0.170322	−	0.635652i
$848$	4.86714	−	13.3724i	0.167138	−	0.459209i
$849$	16.0113	−	0.705909i	0.549507	−	0.0242267i
$850$	21.6442	−	1.89362i	0.742390	−	0.0649507i
$851$	−0.00738938	−	0.0844610i	−0.000253305	−	0.00289528i
$852$	−4.54033	−	4.15688i	−0.155549	−	0.142413i
$853$	15.1452	+	32.4789i	0.518561	+	1.11206i	0.974980	+	0.222293i	$0.0713540\pi$
$853$	15.1452	+	32.4789i	0.518561	+	1.11206i	−0.456419	+	0.889765i	$0.650868\pi$
$854$	0.128688	+	0.0742981i	0.00440361	+	0.00254243i
$855$	5.94828	−	5.95843i	0.203427	−	0.203774i
$856$	0.301611	−	1.12563i	0.0103088	−	0.0384731i
$857$	−3.03194	−	17.1950i	−0.103569	−	0.587370i	−0.991782	−	0.127938i	$-0.959164\pi$
$857$	−3.03194	−	17.1950i	−0.103569	−	0.587370i	0.888213	−	0.459432i	$-0.151947\pi$
$858$	−13.3742	+	1.89274i	−0.456589	+	0.0646170i
$859$	20.5423	−	7.47677i	0.700893	−	0.255104i	0.0331006	−	0.999452i	$-0.489462\pi$
$859$	20.5423	−	7.47677i	0.700893	−	0.255104i	0.667792	+	0.744348i	$0.267240\pi$
$860$	0.443594	−	0.310608i	0.0151264	−	0.0105916i
$861$	−6.60710	−	29.7427i	−0.225169	−	1.01363i
$862$	−13.1962	−	15.7266i	−0.449464	−	0.535651i
$863$	−36.9718	−	36.9718i	−1.25854	−	1.25854i	−0.951792	−	0.306743i	$-0.900761\pi$
$863$	−36.9718	−	36.9718i	−1.25854	−	1.25854i	−0.306743	−	0.951792i	$-0.599239\pi$
$864$	−5.07154	+	1.13114i	−0.172537	+	0.0384822i
$865$	−6.85367	−	6.85367i	−0.233032	−	0.233032i
$866$	−1.81341	+	20.7274i	−0.0616223	+	0.704346i
$867$	−2.21748	+	7.04342i	−0.0753096	+	0.239207i
$868$	−4.15940	−	0.733415i	−0.141179	−	0.0248937i
$869$	−2.98642	+	6.40439i	−0.101307	+	0.217254i
$870$	−1.96101	+	2.55789i	−0.0664844	+	0.0867207i
$871$	35.8019	−	30.6109i	1.21310	−	1.03721i
$872$	10.7349	−	6.19778i	0.363528	−	0.209883i
$873$	11.9228	+	32.6710i	0.403527	+	1.10575i
$874$	−0.397647	+	0.688745i	−0.0134506	+	0.0232971i
$875$	−14.8440	−	5.40278i	−0.501819	−	0.182647i
$876$	−6.17623	+	1.95025i	−0.208675	+	0.0658929i
$877$	6.10097	−	0.533765i	0.206015	−	0.0180240i	0.0163189	−	0.999867i	$-0.494805\pi$
$877$	6.10097	−	0.533765i	0.206015	−	0.0180240i	0.189696	+	0.981843i	$0.439250\pi$
$878$	37.0437	−	3.24090i	1.25016	−	0.109375i
$879$	0.243445	−	1.10033i	0.00821121	−	0.0371133i
$880$	1.09123	+	0.397174i	0.0367853	+	0.0133887i
$881$	20.4094	−	35.3501i	0.687610	−	1.19098i	−0.284999	−	0.958528i	$-0.591993\pi$
$881$	20.4094	−	35.3501i	0.687610	−	1.19098i	0.972609	−	0.232448i	$-0.0746734\pi$
$882$	−6.43475	+	1.14028i	−0.216669	+	0.0383952i
$883$	35.7439	−	20.6367i	1.20288	−	0.694481i	0.241683	−	0.970355i	$-0.422301\pi$
$883$	35.7439	−	20.6367i	1.20288	−	0.694481i	0.961194	+	0.275874i	$0.0889673\pi$
$884$	1.29559	−	16.5754i	0.0435755	−	0.557491i
$885$	3.79821	+	0.498397i	0.127676	+	0.0167534i
$886$	8.05367	−	17.2711i	0.270568	−	0.580235i
$887$	−1.26198	−	0.222521i	−0.0423731	−	0.00747152i	0.152421	−	0.988316i	$-0.451293\pi$
$887$	−1.26198	−	0.222521i	−0.0423731	−	0.00747152i	−0.194795	+	0.980844i	$0.562404\pi$
$888$	0.652379	+	0.711337i	0.0218924	+	0.0238709i
$889$	−4.42161	+	50.5392i	−0.148296	+	1.69503i
$890$	0.136669	+	0.136669i	0.00458117	+	0.00458117i
$891$	18.7945	−	5.07034i	0.629639	−	0.169863i
$892$	−18.9918	−	18.9918i	−0.635894	−	0.635894i
$893$	−5.88717	−	7.01606i	−0.197007	−	0.234783i
$894$	21.3136	−	19.5470i	0.712833	−	0.653751i
$895$	10.1559	−	7.11123i	0.339474	−	0.237702i
$896$	2.84687	−	1.03618i	0.0951073	−	0.0346162i
$897$	−0.355084	+	0.881302i	−0.0118559	+	0.0294258i
$898$	−4.22167	−	23.9423i	−0.140879	−	0.798964i
$899$	1.25061	−	4.66733i	0.0417101	−	0.155664i
$900$	12.8058	−	5.98474i	0.426859	−	0.199491i
$901$	−56.8287	−	32.8101i	−1.89324	−	1.09306i
$902$	−5.30748	−	11.3819i	−0.176720	−	0.378977i
$903$	−1.14335	+	5.16773i	−0.0380482	+	0.171971i
$904$	1.00107	+	11.4423i	0.0332951	+	0.380564i
$905$	−6.96288	+	0.609173i	−0.231454	+	0.0202496i
$906$	−0.654019	+	1.25767i	−0.0217283	+	0.0417832i
$907$	9.12402	−	25.0680i	0.302958	−	0.832370i	−0.691024	−	0.722831i	$-0.742840\pi$
$907$	9.12402	−	25.0680i	0.302958	−	0.832370i	0.993982	−	0.109539i	$-0.0349375\pi$
$908$	3.10242	+	11.5784i	0.102957	+	0.384242i
$909$	−4.95837	+	0.438062i	−0.164459	+	0.0145296i
$910$	−2.88515	+	5.10585i	−0.0956416	+	0.169257i
$911$	52.9349	−	9.33385i	1.75381	−	0.309244i	0.797876	−	0.602822i	$-0.205957\pi$
$911$	52.9349	−	9.33385i	1.75381	−	0.309244i	0.955935	+	0.293578i	$0.0948459\pi$
$912$	−1.18558	−	8.97582i	−0.0392586	−	0.297219i
$913$	−6.98972	+	2.54405i	−0.231326	+	0.0841958i
$914$	−5.90149	+	33.4690i	−0.195204	+	1.10706i
$915$	−0.0404487	+	0.0210782i	−0.00133719	+	0.000696824i
$916$	−2.16586	+	24.7559i	−0.0715621	+	0.817958i
$917$	−31.0899	+	31.0899i	−1.02668	+	1.02668i
$918$	1.07577	+	23.9364i	0.0355055	+	0.790019i
$919$	36.6851			1.21013			0.605064	−	0.796176i	$-0.293147\pi$
$919$	36.6851			1.21013			0.605064	+	0.796176i	$0.293147\pi$
$920$	0.0625746	−	0.0525063i	0.00206302	−	0.00173108i
$921$	−23.2536	−	14.8002i	−0.766231	−	0.487684i
$922$	20.2797	+	3.57586i	0.667876	+	0.117765i
$923$	8.14566	−	9.89225i	0.268118	−	0.325608i
$924$	−10.4839	+	4.34783i	−0.344896	+	0.143033i
$925$	−2.15080	−	1.50601i	−0.0707179	−	0.0495172i
$926$	−4.57069	+	2.63889i	−0.150202	+	0.0867194i
$927$	43.1050	−	11.5894i	1.41576	−	0.380645i
$928$	0.897063	+	3.34789i	0.0294475	+	0.109900i
$929$	−4.98869	−	10.6983i	−0.163673	−	0.350999i	0.807317	−	0.590118i	$-0.200919\pi$
$929$	−4.98869	−	10.6983i	−0.163673	−	0.350999i	−0.970990	+	0.239120i	$0.923141\pi$
$930$	0.875438	−	0.956192i	0.0287068	−	0.0313548i
$931$	−0.992407	−	11.3433i	−0.0325248	−	0.371761i
$932$	8.67504	−	10.3385i	0.284160	−	0.338649i
$933$	1.81707	+	41.2145i	0.0594882	+	1.34930i
$934$	10.3571	+	22.2108i	0.338893	+	0.726758i
$935$	2.67741	−	4.63741i	0.0875606	−	0.151659i
$936$	−2.90509	−	10.4192i	−0.0949557	−	0.340563i
$937$	−1.72562	−	2.98886i	−0.0563735	−	0.0976417i	0.836461	−	0.548026i	$-0.184620\pi$
$937$	−1.72562	−	2.98886i	−0.0563735	−	0.0976417i	−0.892835	+	0.450384i	$0.851287\pi$
$938$	22.7018	−	32.4216i	0.741241	−	1.05860i
$939$	−6.72723	−	16.2214i	−0.219535	−	0.529366i
$940$	0.321742	+	0.883978i	0.0104941	+	0.0288322i
$941$	24.1605	−	16.9174i	0.787610	−	0.551490i	−0.109141	−	0.994026i	$-0.534810\pi$
$941$	24.1605	−	16.9174i	0.787610	−	0.551490i	0.896751	+	0.442536i	$0.145921\pi$
$942$	22.0465	+	14.0320i	0.718314	+	0.457186i
$943$	−0.880034	−	0.0769930i	−0.0286579	−	0.00250724i
$944$	2.91290	−	2.91290i	0.0948067	−	0.0948067i
$945$	3.22438	−	7.81259i	0.104889	−	0.254144i
$946$			2.18162i			0.0709304i
$947$	−3.55745	+	40.6618i	−0.115602	+	1.32133i	0.687803	+	0.725898i	$0.258575\pi$
$947$	−3.55745	+	40.6618i	−0.115602	+	1.32133i	−0.803404	+	0.595434i	$0.796980\pi$
$948$	−5.39756	−	1.69931i	−0.175305	−	0.0551911i
$949$	−4.72846	−	12.6262i	−0.153492	−	0.409865i
$950$	8.42371	+	23.1439i	0.273301	+	0.750889i
$951$	16.2048	−	2.14043i	0.525476	−	0.0694081i
$952$	−2.42587	−	13.7578i	−0.0786229	−	0.445892i
$953$	3.75763	+	6.50840i	0.121722	+	0.210828i	0.920447	−	0.390868i	$-0.127825\pi$
$953$	3.75763	+	6.50840i	0.121722	+	0.210828i	−0.798725	+	0.601696i	$0.794492\pi$
$954$	−42.0494	−	7.37748i	−1.36140	−	0.238855i
$955$	−1.23055	−	4.59247i	−0.0398196	−	0.148609i
$956$	16.4247	−	7.65897i	0.531213	−	0.247709i
$957$	−3.90984	−	12.3820i	−0.126387	−	0.400254i
$958$	−20.5226	−	17.2205i	−0.663057	−	0.556371i
$959$	−37.7937	−	31.7127i	−1.22042	−	1.02406i
$960$	−0.200885	+	0.907965i	−0.00648353	+	0.0293045i
$961$	9.93789	−	27.3041i	0.320577	−	0.880778i
$962$	−1.40751	+	1.43382i	−0.0453799	+	0.0462283i
$963$	−3.48296	−	0.301727i	−0.112237	−	0.00972301i
$964$	−8.55231	−	2.29158i	−0.275451	−	0.0738070i
$965$	−9.56083	+	1.68583i	−0.307774	+	0.0542689i
$966$	−0.103870	+	0.791578i	−0.00334196	+	0.0254686i
$967$	−9.67494	+	20.7480i	−0.311125	+	0.667210i	−0.998238	−	0.0593408i	$-0.981100\pi$
$967$	−9.67494	+	20.7480i	−0.311125	+	0.667210i	0.687113	+	0.726551i	$0.258878\pi$
$968$	5.17845	−	3.62599i	0.166442	−	0.116544i
$969$	−41.7100	−	1.80328i	−1.33992	−	0.0579297i
$970$	6.20042	+	0.542466i	0.199083	+	0.0174175i
$971$			20.6367i			0.662263i	0.943585	+	0.331131i	$0.107430\pi$
$971$			20.6367i			0.662263i	−0.943585	+	0.331131i	$0.892570\pi$
$972$	5.99613	+	14.3891i	0.192326	+	0.461531i
$973$	−12.5744	−	12.5744i	−0.403116	−	0.403116i
$974$	3.26058	−	2.73595i	0.104476	−	0.0876655i
$975$	13.8391	+	25.9673i	0.443206	+	0.831620i
$976$	−0.00851718	+	0.0483033i	−0.000272628	+	0.00154615i
$977$	−23.3145	−	10.8717i	−0.745897	−	0.347817i	0.0122294	−	0.999925i	$-0.496107\pi$
$977$	−23.3145	−	10.8717i	−0.745897	−	0.347817i	−0.758126	+	0.652108i	$0.773885\pi$
$978$	2.32153	−	17.6920i	0.0742342	−	0.565729i
$979$	−0.766822	+	0.135211i	−0.0245077	+	0.00432138i
$980$	−0.302696	+	1.12968i	−0.00966927	+	0.0360862i
$981$	−23.9274	−	28.4662i	−0.763944	−	0.908857i
$982$	1.81529	−	0.486406i	0.0579283	−	0.0155218i
$983$	−22.7732	+	10.6193i	−0.726352	+	0.338703i	−0.750379	−	0.661008i	$-0.770129\pi$
$983$	−22.7732	+	10.6193i	−0.726352	+	0.338703i	0.0240270	+	0.999711i	$0.492351\pi$
$984$	8.47948	−	5.40711i	0.270316	−	0.172372i
$985$	5.82727	−	6.94467i	0.185672	−	0.221276i
$986$	15.9216	−	1.39296i	0.507047	−	0.0443608i
$987$	−8.15713	−	4.24191i	−0.259644	−	0.135022i
$988$	18.5295	−	3.44450i	0.589503	−	0.109584i
$989$	0.132900	+	0.0767296i	0.00422596	+	0.00243986i
$990$	0.602026	−	3.43137i	0.0191336	−	0.109056i
$991$	−0.954928	−	1.65398i	−0.0303343	−	0.0525405i	0.850460	−	0.526040i	$-0.176324\pi$
$991$	−0.954928	−	1.65398i	−0.0303343	−	0.0525405i	−0.880794	+	0.473500i	$0.842991\pi$
$992$	−0.242085	−	1.37293i	−0.00768621	−	0.0435906i
$993$	8.08306	+	61.1953i	0.256508	+	1.94197i
$994$	4.55047	−	9.75852i	0.144332	−	0.309521i
$995$	6.50273	+	9.28687i	0.206151	+	0.294413i
$996$	−2.75266	−	5.28231i	−0.0872214	−	0.167376i
$997$	−34.3262	+	28.8031i	−1.08712	+	0.912203i	−0.996493	−	0.0836819i	$-0.973332\pi$
$997$	−34.3262	+	28.8031i	−1.08712	+	0.912203i	−0.0906285	+	0.995885i	$0.528888\pi$
$998$	18.5168			0.586139
$999$	1.75978	−	2.29947i	0.0556769	−	0.0727521i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	702.2.bs.a.5.7	✓	504
13.8	odd	4	inner	702.2.bs.a.437.28	yes	504
27.11	odd	18	inner	702.2.bs.a.551.28	yes	504
351.281	even	36	inner	702.2.bs.a.281.7	yes	504

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
702.2.bs.a.5.7	✓	504	1.1	even	1	trivial
702.2.bs.a.281.7	yes	504	351.281	even	36	inner
702.2.bs.a.437.28	yes	504	13.8	odd	4	inner
702.2.bs.a.551.28	yes	504	27.11	odd	18	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:	\( N \)	\(=\)	\( 702 = 2 \cdot 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	702.bs (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.996195 - 0.0871557i) q^{2} +(-1.17070 - 1.27650i) q^{3} +(0.984808 + 0.173648i) q^{4} +(-0.486588 - 0.226900i) q^{5} +(1.05499 + 1.37368i) q^{6} +(-1.73769 + 2.48168i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(-0.258919 + 2.98881i) q^{9} +(0.464961 + 0.268445i) q^{10} +(-1.96028 + 0.914095i) q^{11} +(-0.931253 - 1.46040i) q^{12} +(2.93422 - 2.09532i) q^{13} +(1.94737 - 2.32079i) q^{14} +(0.280011 + 0.886764i) q^{15} +(0.939693 + 0.342020i) q^{16} +(2.30561 - 3.99343i) q^{17} +(0.518425 - 2.95487i) q^{18} +(5.04909 + 1.35290i) q^{19} +(-0.439795 - 0.307948i) q^{20} +(5.20220 - 0.687139i) q^{21} +(2.03249 - 0.739767i) q^{22} +(0.0264197 - 0.149834i) q^{23} +(0.800427 + 1.53601i) q^{24} +(-3.02865 - 3.60941i) q^{25} +(-3.10567 + 1.83162i) q^{26} +(4.11834 - 3.16849i) q^{27} +(-2.14223 + 2.14223i) q^{28} +(-2.22789 - 2.65510i) q^{29} +(-0.201659 - 0.907794i) q^{30} +(0.799630 + 1.14199i) q^{31} +(-0.906308 - 0.422618i) q^{32} +(3.46175 + 1.43218i) q^{33} +(-2.64488 + 3.77729i) q^{34} +(1.40864 - 0.813276i) q^{35} +(-0.773986 + 2.89844i) q^{36} +(0.538267 - 0.144228i) q^{37} +(-4.91197 - 1.78781i) q^{38} +(-6.10978 - 1.29254i) q^{39} +(0.411282 + 0.345107i) q^{40} +(-0.506050 - 5.78418i) q^{41} +(-5.24229 + 0.231123i) q^{42} +(-0.344974 + 0.947809i) q^{43} +(-2.08923 + 0.559808i) q^{44} +(0.804147 - 1.39557i) q^{45} +(-0.0393781 + 0.146961i) q^{46} +(-1.43527 - 1.00499i) q^{47} +(-0.663509 - 1.59992i) q^{48} +(-0.745034 - 2.04696i) q^{49} +(2.70255 + 3.85964i) q^{50} +(-7.79680 + 1.73200i) q^{51} +(3.25349 - 1.55397i) q^{52} -14.2306i q^{53} +(-4.37882 + 2.79749i) q^{54} +1.16126 q^{55} +(2.32079 - 1.94737i) q^{56} +(-4.18400 - 8.02902i) q^{57} +(1.98801 + 2.83917i) q^{58} +(1.74096 - 3.73350i) q^{59} +(0.121772 + 0.921915i) q^{60} +(0.00851718 + 0.0483033i) q^{61} +(-0.697056 - 1.20734i) q^{62} +(-6.96735 - 5.83618i) q^{63} +(0.866025 + 0.500000i) q^{64} +(-1.90318 + 0.353787i) q^{65} +(-3.32376 - 1.72844i) q^{66} +(13.0146 - 1.13863i) q^{67} +(2.96403 - 3.53239i) q^{68} +(-0.222193 + 0.141686i) q^{69} +(-1.47416 + 0.687411i) q^{70} +(3.43297 - 0.919861i) q^{71} +(1.02366 - 2.81995i) q^{72} +(0.967827 - 3.61198i) q^{73} +(-0.548789 + 0.0967663i) q^{74} +(-1.06177 + 8.09162i) q^{75} +(4.73746 + 2.20911i) q^{76} +(1.13788 - 6.45322i) q^{77} +(5.97387 + 1.82012i) q^{78} +(2.50272 - 2.10003i) q^{79} +(-0.379639 - 0.379639i) q^{80} +(-8.86592 - 1.54771i) q^{81} +5.80627i q^{82} +(3.42590 + 0.299728i) q^{83} +(5.24248 + 0.226652i) q^{84} +(-2.02799 + 1.42001i) q^{85} +(0.426269 - 0.914136i) q^{86} +(-0.781045 + 5.95224i) q^{87} +(2.13007 - 0.375589i) q^{88} +(0.347731 + 0.0931743i) q^{89} +(-0.922719 + 1.32017i) q^{90} +(0.101164 + 10.9228i) q^{91} +(0.0520367 - 0.142970i) q^{92} +(0.521626 - 2.35766i) q^{93} +(1.34222 + 1.12626i) q^{94} +(-2.14986 - 1.80394i) q^{95} +(0.521542 + 1.65166i) q^{96} +(10.5067 - 4.89935i) q^{97} +(0.563794 + 2.10411i) q^{98} +(-2.22450 - 6.09558i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 504 q - 24 q^{11} + 24 q^{15} + 24 q^{21} - 144 q^{27} + 24 q^{39} + 48 q^{41} + 12 q^{45} + 132 q^{47} + 24 q^{50} + 72 q^{54} - 72 q^{57} + 12 q^{63} - 156 q^{65} + 96 q^{66} - 48 q^{72} + 36 q^{73} - 96 q^{74}+ \cdots - 144 q^{99}+O(q^{100}) \) 504 * q - 24 * q^11 + 24 * q^15 + 24 * q^21 - 144 * q^27 + 24 * q^39 + 48 * q^41 + 12 * q^45 + 132 * q^47 + 24 * q^50 + 72 * q^54 - 72 * q^57 + 12 * q^63 - 156 * q^65 + 96 * q^66 - 48 * q^72 + 36 * q^73 - 96 * q^74 - 24 * q^78 + 288 * q^79 + 24 * q^83 + 24 * q^84 - 144 * q^85 - 96 * q^86 - 192 * q^87 + 96 * q^92 - 60 * q^93 - 72 * q^98 - 144 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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