LMFDB - Embedded newform 540.2.be.a.11.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [540,2,Mod(11,540)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(540, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 13, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("540.11"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 540 = 2^{2} \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	540.be (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$4.31192170915$
Analytic rank:	$0$
Dimension:	$432$
Relative dimension:	$72$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			11.17
Character	$\chi$	$=$	540.11
Dual form			540.2.be.a.491.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.11807 + 0.865978i) q^{2} +(1.71259 - 0.258927i) q^{3} +(0.500164 - 1.93645i) q^{4} +(0.342020 - 0.939693i) q^{5} +(-1.69057 + 1.77256i) q^{6} +(-1.15631 - 0.203889i) q^{7} +(1.11770 + 2.59822i) q^{8} +(2.86591 - 0.886872i) q^{9} +(0.431350 + 1.34682i) q^{10} +(2.85119 - 1.03775i) q^{11} +(0.355176 - 3.44585i) q^{12} +(-4.28879 + 3.59872i) q^{13} +(1.46940 - 0.773380i) q^{14} +(0.342427 - 1.69786i) q^{15} +(-3.49967 - 1.93709i) q^{16} +(4.31642 - 2.49209i) q^{17} +(-2.43628 + 3.47340i) q^{18} +(6.90180 + 3.98476i) q^{19} +(-1.64860 - 1.13231i) q^{20} +(-2.03308 - 0.0497770i) q^{21} +(-2.28917 + 3.62934i) q^{22} +(-1.20858 - 6.85418i) q^{23} +(2.58691 + 4.16027i) q^{24} +(-0.766044 - 0.642788i) q^{25} +(1.67876 - 7.73762i) q^{26} +(4.67849 - 2.26091i) q^{27} +(-0.973169 + 2.13717i) q^{28} +(1.09882 - 1.30952i) q^{29} +(1.08746 + 2.19487i) q^{30} +(5.55873 - 0.980155i) q^{31} +(5.59035 - 0.864839i) q^{32} +(4.61421 - 2.51549i) q^{33} +(-2.66797 + 6.52426i) q^{34} +(-0.587076 + 1.01685i) q^{35} +(-0.283954 - 5.99328i) q^{36} +(-4.91372 - 8.51081i) q^{37} +(-11.1674 + 1.52157i) q^{38} +(-6.41312 + 7.27361i) q^{39} +(2.82380 - 0.161654i) q^{40} +(-3.87603 - 4.61927i) q^{41} +(2.31624 - 1.70495i) q^{42} +(1.49409 + 4.10499i) q^{43} +(-0.583483 - 6.04023i) q^{44} +(0.146813 - 2.99641i) q^{45} +(7.28684 + 6.61686i) q^{46} +(0.473716 - 2.68657i) q^{47} +(-6.49506 - 2.41127i) q^{48} +(-5.28236 - 1.92262i) q^{49} +(1.41313 + 0.0553044i) q^{50} +(6.74698 - 5.38556i) q^{51} +(4.82364 + 10.1050i) q^{52} +9.27592i q^{53} +(-3.27299 + 6.57933i) q^{54} -3.03417i q^{55} +(-0.762667 - 3.23225i) q^{56} +(12.8517 + 5.03718i) q^{57} +(-0.0945406 + 2.41569i) q^{58} +(2.33098 + 0.848408i) q^{59} +(-3.11656 - 1.51230i) q^{60} +(-1.25627 + 7.12463i) q^{61} +(-5.36626 + 5.90962i) q^{62} +(-3.49472 + 0.441173i) q^{63} +(-5.50148 + 5.80807i) q^{64} +(1.91484 + 5.26098i) q^{65} +(-2.98066 + 6.80830i) q^{66} +(-1.90954 - 2.27570i) q^{67} +(-2.66688 - 9.60499i) q^{68} +(-3.84453 - 11.4254i) q^{69} +(-0.224173 - 1.64530i) q^{70} +(6.41995 + 11.1197i) q^{71} +(5.50753 + 6.45501i) q^{72} +(-8.11069 + 14.0481i) q^{73} +(12.8641 + 5.26051i) q^{74} +(-1.47835 - 0.902480i) q^{75} +(11.1683 - 11.3720i) q^{76} +(-3.50846 + 0.618636i) q^{77} +(0.871535 - 13.6860i) q^{78} +(1.49431 - 1.78084i) q^{79} +(-3.01722 + 2.62609i) q^{80} +(7.42692 - 5.08340i) q^{81} +(8.33386 + 1.80812i) q^{82} +(6.69262 + 5.61578i) q^{83} +(-1.11327 + 3.91206i) q^{84} +(-0.865493 - 4.90845i) q^{85} +(-5.22533 - 3.29581i) q^{86} +(1.54275 - 2.52718i) q^{87} +(5.88308 + 6.24812i) q^{88} +(0.487273 + 0.281327i) q^{89} +(2.43067 + 3.47733i) q^{90} +(5.69293 - 3.28681i) q^{91} +(-13.8773 - 1.08787i) q^{92} +(9.26603 - 3.11791i) q^{93} +(1.79687 + 3.41401i) q^{94} +(6.10500 - 5.12270i) q^{95} +(9.35004 - 2.92861i) q^{96} +(-11.9520 + 4.35018i) q^{97} +(7.57100 - 2.42478i) q^{98} +(7.25091 - 5.50274i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 432 q + 18 q^{12} + 30 q^{14} + 30 q^{24} + 12 q^{29} - 24 q^{30} + 60 q^{33} - 60 q^{36} - 60 q^{38} + 60 q^{41} - 60 q^{42} - 72 q^{44} + 12 q^{45} - 150 q^{48} + 54 q^{52} - 84 q^{54} - 84 q^{56} - 12 q^{57}+ \cdots + 36 q^{97}+O(q^{100}) $ 432 * q + 18 * q^12 + 30 * q^14 + 30 * q^24 + 12 * q^29 - 24 * q^30 + 60 * q^33 - 60 * q^36 - 60 * q^38 + 60 * q^41 - 60 * q^42 - 72 * q^44 + 12 * q^45 - 150 * q^48 + 54 * q^52 - 84 * q^54 - 84 * q^56 - 12 * q^57 + 54 * q^58 - 198 * q^62 - 48 * q^66 - 138 * q^68 - 48 * q^69 - 84 * q^72 - 84 * q^74 - 48 * q^77 - 78 * q^78 - 66 * q^84 + 54 * q^86 - 36 * q^89 + 120 * q^92 - 54 * q^94 + 210 * q^96 + 36 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/540\mathbb{Z}\right)^\times$.

$n$	$217$	$271$	$461$
$\chi(n)$	$1$	$-1$	$e\left(\frac{13}{18}\right)$

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 $

$2$	−1.11807	+	0.865978i	−0.790595	+	0.612339i
$2$	−1.11807	+	0.865978i	−0.790595	+	0.612339i
$3$	1.71259	−	0.258927i	0.988763	−	0.149492i
$3$	1.71259	−	0.258927i	0.988763	−	0.149492i
$4$	0.500164	−	1.93645i	0.250082	−	0.968225i
$5$	0.342020	−	0.939693i	0.152956	−	0.420243i
$5$	0.342020	−	0.939693i	0.152956	−	0.420243i
$6$	−1.69057	+	1.77256i	−0.690172	+	0.723646i
$7$	−1.15631	−	0.203889i	−0.437046	−	0.0770630i	−0.0492036	−	0.998789i	$-0.515668\pi$
$7$	−1.15631	−	0.203889i	−0.437046	−	0.0770630i	−0.387842	+	0.921726i	$0.626779\pi$
$8$	1.11770	+	2.59822i	0.395168	+	0.918609i
$9$	2.86591	−	0.886872i	0.955304	−	0.295624i
$10$	0.431350	+	1.34682i	0.136405	+	0.425903i
$11$	2.85119	−	1.03775i	0.859666	−	0.312893i	0.125691	−	0.992069i	$-0.459885\pi$
$11$	2.85119	−	1.03775i	0.859666	−	0.312893i	0.733975	+	0.679176i	$0.237663\pi$
$12$	0.355176	−	3.44585i	0.102530	−	0.994730i
$13$	−4.28879	+	3.59872i	−1.18950	+	0.998105i	−0.189627	+	0.981856i	$0.560728\pi$
$13$	−4.28879	+	3.59872i	−1.18950	+	0.998105i	−0.999868	+	0.0162490i	$0.994828\pi$
$14$	1.46940	−	0.773380i	0.392715	−	0.206694i
$15$	0.342427	−	1.69786i	0.0884144	−	0.438387i
$16$	−3.49967	−	1.93709i	−0.874918	−	0.484271i
$17$	4.31642	−	2.49209i	1.04689	−	0.604420i	0.125110	−	0.992143i	$-0.460072\pi$
$17$	4.31642	−	2.49209i	1.04689	−	0.604420i	0.921776	+	0.387723i	$0.126738\pi$
$18$	−2.43628	+	3.47340i	−0.574237	+	0.818689i
$19$	6.90180	+	3.98476i	1.58338	+	0.914166i	0.994361	+	0.106048i	$0.0338196\pi$
$19$	6.90180	+	3.98476i	1.58338	+	0.914166i	0.589021	+	0.808118i	$0.299514\pi$
$20$	−1.64860	−	1.13231i	−0.368638	−	0.253191i
$21$	−2.03308	−	0.0497770i	−0.443655	−	0.0108622i
$22$	−2.28917	+	3.62934i	−0.488052	+	0.773779i
$23$	−1.20858	−	6.85418i	−0.252006	−	1.42920i	−0.803643	−	0.595111i	$-0.797108\pi$
$23$	−1.20858	−	6.85418i	−0.252006	−	1.42920i	0.551638	−	0.834084i	$-0.314003\pi$
$24$	2.58691	+	4.16027i	0.528052	+	0.849212i
$25$	−0.766044	−	0.642788i	−0.153209	−	0.128558i
$26$	1.67876	−	7.73762i	0.329231	−	1.51747i
$27$	4.67849	−	2.26091i	0.900376	−	0.435112i
$28$	−0.973169	+	2.13717i	−0.183912	+	0.403886i
$29$	1.09882	−	1.30952i	0.204045	−	0.243172i	−0.654311	−	0.756225i	$-0.727041\pi$
$29$	1.09882	−	1.30952i	0.204045	−	0.243172i	0.858357	+	0.513054i	$0.171486\pi$
$30$	1.08746	+	2.19487i	0.198541	+	0.400726i
$31$	5.55873	−	0.980155i	0.998378	−	0.176041i	0.349502	−	0.936936i	$-0.386351\pi$
$31$	5.55873	−	0.980155i	0.998378	−	0.176041i	0.648876	+	0.760895i	$0.275240\pi$
$32$	5.59035	−	0.864839i	0.988244	−	0.152883i
$33$	4.61421	−	2.51549i	0.803231	−	0.437890i
$34$	−2.66797	+	6.52426i	−0.457554	+	1.11890i
$35$	−0.587076	+	1.01685i	−0.0992340	+	0.171878i
$36$	−0.283954	−	5.99328i	−0.0473257	−	0.998880i
$37$	−4.91372	−	8.51081i	−0.807810	−	1.39917i	−0.914377	−	0.404863i	$-0.867319\pi$
$37$	−4.91372	−	8.51081i	−0.807810	−	1.39917i	0.106567	−	0.994305i	$-0.466014\pi$
$38$	−11.1674	+	1.52157i	−1.81159	+	0.246831i
$39$	−6.41312	+	7.27361i	−1.02692	+	1.16471i
$40$	2.82380	−	0.161654i	0.446483	−	0.0255598i
$41$	−3.87603	−	4.61927i	−0.605334	−	0.721409i	0.373141	−	0.927775i	$-0.378281\pi$
$41$	−3.87603	−	4.61927i	−0.605334	−	0.721409i	−0.978475	+	0.206366i	$0.933836\pi$
$42$	2.31624	−	1.70495i	0.357403	−	0.263080i
$43$	1.49409	+	4.10499i	0.227847	+	0.626005i	0.999955	−	0.00948681i	$-0.00301979\pi$
$43$	1.49409	+	4.10499i	0.227847	+	0.626005i	−0.772108	+	0.635491i	$0.780798\pi$
$44$	−0.583483	−	6.04023i	−0.0879634	−	0.910599i
$45$	0.146813	−	2.99641i	0.0218856	−	0.446678i
$46$	7.28684	+	6.61686i	1.07439	+	0.975602i
$47$	0.473716	−	2.68657i	0.0690985	−	0.391877i	−0.930570	−	0.366115i	$-0.880688\pi$
$47$	0.473716	−	2.68657i	0.0690985	−	0.391877i	0.999668	−	0.0257621i	$-0.00820124\pi$
$48$	−6.49506	−	2.41127i	−0.937481	−	0.348037i
$49$	−5.28236	−	1.92262i	−0.754622	−	0.274660i
$50$	1.41313	+	0.0553044i	0.199847	+	0.00782123i
$51$	6.74698	−	5.38556i	0.944767	−	0.754129i
$52$	4.82364	+	10.1050i	0.668918	+	1.40131i
$53$			9.27592i			1.27415i	0.770804	+	0.637073i	$0.219855\pi$
$53$			9.27592i			1.27415i	−0.770804	+	0.637073i	$0.780145\pi$
$54$	−3.27299	+	6.57933i	−0.445397	+	0.895333i
$55$		−	3.03417i		−	0.409128i
$56$	−0.762667	−	3.23225i	−0.101916	−	0.431927i
$57$	12.8517	+	5.03718i	1.70225	+	0.667191i
$58$	−0.0945406	+	2.41569i	−0.0124138	+	0.317196i
$59$	2.33098	+	0.848408i	0.303468	+	0.110453i	0.489266	−	0.872135i	$-0.337265\pi$
$59$	2.33098	+	0.848408i	0.303468	+	0.110453i	−0.185798	+	0.982588i	$0.559487\pi$
$60$	−3.11656	−	1.51230i	−0.402346	−	0.195238i
$61$	−1.25627	+	7.12463i	−0.160848	+	0.912216i	0.792394	+	0.610009i	$0.208834\pi$
$61$	−1.25627	+	7.12463i	−0.160848	+	0.912216i	−0.953242	+	0.302207i	$0.902277\pi$
$62$	−5.36626	+	5.90962i	−0.681516	+	0.750523i
$63$	−3.49472	+	0.441173i	−0.440293	+	0.0555826i
$64$	−5.50148	+	5.80807i	−0.687685	+	0.726009i
$65$	1.91484	+	5.26098i	0.237506	+	0.652544i
$66$	−2.98066	+	6.80830i	−0.366894	+	0.838044i
$67$	−1.90954	−	2.27570i	−0.233288	−	0.278021i	0.636682	−	0.771126i	$-0.280306\pi$
$67$	−1.90954	−	2.27570i	−0.233288	−	0.278021i	−0.869970	+	0.493105i	$0.835862\pi$
$68$	−2.66688	−	9.60499i	−0.323407	−	1.16478i
$69$	−3.84453	−	11.4254i	−0.462827	−	1.37546i
$70$	−0.224173	−	1.64530i	−0.0267938	−	0.196651i
$71$	6.41995	+	11.1197i	0.761908	+	1.31966i	0.941866	+	0.335989i	$0.109070\pi$
$71$	6.41995	+	11.1197i	0.761908	+	1.31966i	−0.179958	+	0.983674i	$0.557596\pi$
$72$	5.50753	+	6.45501i	0.649068	+	0.760730i
$73$	−8.11069	+	14.0481i	−0.949284	+	1.64421i	−0.202347	+	0.979314i	$0.564857\pi$
$73$	−8.11069	+	14.0481i	−0.949284	+	1.64421i	−0.746937	+	0.664895i	$0.768476\pi$
$74$	12.8641	+	5.26051i	1.49542	+	0.611522i
$75$	−1.47835	−	0.902480i	−0.170706	−	0.104209i
$76$	11.1683	−	11.3720i	1.28109	−	1.30445i
$77$	−3.50846	+	0.618636i	−0.399826	+	0.0705001i
$78$	0.871535	−	13.6860i	0.0986819	−	1.54964i
$79$	1.49431	−	1.78084i	0.168122	−	0.200361i	−0.675404	−	0.737448i	$-0.736031\pi$
$79$	1.49431	−	1.78084i	0.168122	−	0.200361i	0.843527	+	0.537087i	$0.180475\pi$
$80$	−3.01722	+	2.62609i	−0.337336	+	0.293606i
$81$	7.42692	−	5.08340i	0.825213	−	0.564822i
$82$	8.33386	+	1.80812i	0.920321	+	0.199673i
$83$	6.69262	+	5.61578i	0.734611	+	0.616411i	0.931384	−	0.364037i	$-0.118602\pi$
$83$	6.69262	+	5.61578i	0.734611	+	0.616411i	−0.196774	+	0.980449i	$0.563046\pi$
$84$	−1.11327	+	3.91206i	−0.121467	+	0.426841i
$85$	−0.865493	−	4.90845i	−0.0938759	−	0.532397i
$86$	−5.22533	−	3.29581i	−0.563462	−	0.355397i
$87$	1.54275	−	2.52718i	0.165400	−	0.270942i
$88$	5.88308	+	6.24812i	0.627139	+	0.666052i
$89$	0.487273	+	0.281327i	0.0516509	+	0.0298207i	0.525603	−	0.850730i	$-0.323840\pi$
$89$	0.487273	+	0.281327i	0.0516509	+	0.0298207i	−0.473952	+	0.880551i	$0.657173\pi$
$90$	2.43067	+	3.47733i	0.256215	+	0.366543i
$91$	5.69293	−	3.28681i	0.596781	−	0.344552i
$92$	−13.8773	−	1.08787i	−1.44680	−	0.113418i
$93$	9.26603	−	3.11791i	0.960842	−	0.323312i
$94$	1.79687	+	3.41401i	0.185333	+	0.352128i
$95$	6.10500	−	5.12270i	0.626360	−	0.525578i
$96$	9.35004	−	2.92861i	0.954284	−	0.298900i
$97$	−11.9520	+	4.35018i	−1.21354	+	0.441694i	−0.867931	−	0.496684i	$-0.834551\pi$
$97$	−11.9520	+	4.35018i	−1.21354	+	0.441694i	−0.345612	+	0.938378i	$0.612329\pi$
$98$	7.57100	−	2.42478i	0.764786	−	0.244940i
$99$	7.25091	−	5.50274i	0.728744	−	0.553046i
$100$	−1.62787	+	1.16191i	−0.162787	+	0.116191i
$101$	−7.80207	−	1.37571i	−0.776335	−	0.136889i	−0.228577	−	0.973526i	$-0.573407\pi$
$101$	−7.80207	−	1.37571i	−0.776335	−	0.136889i	−0.547758	+	0.836637i	$0.684518\pi$
$102$	−2.87983	+	11.8642i	−0.285146	+	1.17473i
$103$	−3.88248	+	10.6670i	−0.382552	+	1.05105i	0.587726	+	0.809060i	$0.300023\pi$
$103$	−3.88248	+	10.6670i	−0.382552	+	1.05105i	−0.970278	+	0.241993i	$0.922199\pi$
$104$	−14.1438	−	7.12091i	−1.38692	−	0.698262i
$105$	−0.742130	+	1.89345i	−0.0724245	+	0.184782i
$106$	−8.03274	−	10.3711i	−0.780209	−	1.00733i
$107$	−16.9271			−1.63640			−0.818201	−	0.574932i	$-0.805028\pi$
$107$	−16.9271			−1.63640			−0.818201	+	0.574932i	$0.805028\pi$
$108$	−2.03812	−	10.1905i	−0.196118	−	0.980580i
$109$	2.74833			0.263243			0.131621	−	0.991300i	$-0.457982\pi$
$109$	2.74833			0.263243			0.131621	+	0.991300i	$0.457982\pi$
$110$	2.62753	+	3.39242i	0.250525	+	0.323455i
$111$	−10.6189	−	13.3032i	−1.00790	−	1.26268i
$112$	3.65177	+	2.95343i	0.345060	+	0.279073i
$113$	0.190608	−	0.523692i	0.0179309	−	0.0492648i	−0.930404	−	0.366535i	$-0.880544\pi$
$113$	0.190608	−	0.523692i	0.0179309	−	0.0492648i	0.948335	+	0.317270i	$0.102766\pi$
$114$	−18.7312	+	5.49737i	−1.75434	+	0.514876i
$115$	−6.85418	−	1.20858i	−0.639155	−	0.112700i
$116$	−1.98623	−	2.78278i	−0.184417	−	0.258375i
$117$	−9.09969	+	14.1172i	−0.841266	+	1.30514i
$118$	−3.34091	+	1.07000i	−0.307555	+	0.0985014i
$119$	−5.49925	+	2.00156i	−0.504116	+	0.183483i
$120$	4.79415	−	1.00801i	0.437644	−	0.0920181i
$121$	−1.37412	+	1.15303i	−0.124920	+	0.104821i
$122$	−4.76518	−	9.05374i	−0.431419	−	0.819687i
$123$	−7.83409	−	6.90729i	−0.706376	−	0.622810i
$124$	0.882261	−	11.2544i	0.0792294	−	1.01068i
$125$	−0.866025	+	0.500000i	−0.0774597	+	0.0447214i
$126$	3.52530	−	3.51961i	0.314059	−	0.313552i
$127$	2.52649	+	1.45867i	0.224189	+	0.129436i	0.607889	−	0.794022i	$-0.292017\pi$
$127$	2.52649	+	1.45867i	0.224189	+	0.129436i	−0.383699	+	0.923458i	$0.625350\pi$
$128$	1.12138	−	11.2580i	0.0991169	−	0.995076i
$129$	3.62166	+	6.64329i	0.318869	+	0.584909i
$130$	−6.69681	−	4.22394i	−0.587349	−	0.370464i
$131$	−2.23398	−	12.6695i	−0.195184	−	1.10694i	−0.912157	−	0.409841i	$-0.865584\pi$
$131$	−2.23398	−	12.6695i	−0.195184	−	1.10694i	0.716973	−	0.697101i	$-0.245527\pi$
$132$	−2.56325	−	10.1933i	−0.223102	−	0.887217i
$133$	−7.16820	−	6.01483i	−0.621562	−	0.521552i
$134$	4.10571	+	0.890776i	0.354679	+	0.0769513i
$135$	−0.524421	−	5.16962i	−0.0451350	−	0.444930i
$136$	11.2995	+	8.42960i	0.968921	+	0.722832i
$137$	−2.50055	+	2.98004i	−0.213636	+	0.254602i	−0.862211	−	0.506549i	$-0.830921\pi$
$137$	−2.50055	+	2.98004i	−0.213636	+	0.254602i	0.648575	+	0.761151i	$0.275365\pi$
$138$	14.1926	+	9.44518i	1.20816	+	0.804027i
$139$	−15.6275	+	2.75554i	−1.32550	+	0.233722i	−0.791194	−	0.611566i	$-0.790540\pi$
$139$	−15.6275	+	2.75554i	−1.32550	+	0.233722i	−0.534311	+	0.845288i	$0.679429\pi$
$140$	1.67544	+	1.64543i	0.141600	+	0.139064i
$141$	0.115652	−	4.72365i	0.00973963	−	0.397803i
$142$	−16.8074	−	6.87305i	−1.41044	−	0.576774i
$143$	−8.49358	+	14.7113i	−0.710269	+	1.23022i
$144$	−11.7477	−	2.44776i	−0.978975	−	0.203980i
$145$	−0.854729	−	1.48043i	−0.0709814	−	0.122943i
$146$	−3.09704	−	22.7305i	−0.256313	−	1.88119i
$147$	−9.54432	−	1.92491i	−0.787202	−	0.158764i
$148$	−18.9384	+	5.25836i	−1.55673	+	0.432235i
$149$	3.81097	+	4.54174i	0.312207	+	0.372074i	0.899215	−	0.437508i	$-0.144139\pi$
$149$	3.81097	+	4.54174i	0.312207	+	0.372074i	−0.587008	+	0.809581i	$0.699694\pi$
$150$	2.43443	−	0.271185i	0.198771	−	0.0221422i
$151$	−3.00545	−	8.25740i	−0.244580	−	0.671977i	−0.999863	−	0.0165783i	$-0.994723\pi$
$151$	−3.00545	−	8.25740i	−0.244580	−	0.671977i	0.755283	−	0.655399i	$-0.227500\pi$
$152$	−2.63910	+	22.3862i	−0.214060	+	1.81576i
$153$	10.1603	−	10.9702i	0.821414	−	0.886890i
$154$	3.38698	−	3.72993i	0.272931	−	0.300566i
$155$	0.980155	−	5.55873i	0.0787279	−	0.446488i
$156$	10.8774	+	16.0567i	0.870886	+	1.28556i
$157$	11.0640	+	4.02696i	0.883001	+	0.321386i	0.743420	−	0.668825i	$-0.233202\pi$
$157$	11.0640	+	4.02696i	0.883001	+	0.321386i	0.139581	+	0.990211i	$0.455425\pi$
$158$	−0.128568	+	3.28514i	−0.0102283	+	0.261352i
$159$	2.40179	+	15.8858i	0.190474	+	1.25983i
$160$	1.09933	−	5.54901i	0.0869097	−	0.438687i
$161$			8.17200i			0.644044i
$162$	−3.90171	+	12.1151i	−0.306547	+	0.951855i
$163$		−	2.43330i		−	0.190590i	−0.995449	−	0.0952952i	$-0.969620\pi$
$163$		−	2.43330i		−	0.190590i	0.995449	−	0.0952952i	$-0.0303795\pi$
$164$	−10.8836	+	5.19534i	−0.849869	+	0.405688i
$165$	−0.785631	−	5.19629i	−0.0611613	−	0.404531i
$166$	−12.3460	−	0.483172i	−0.958232	−	0.0375015i
$167$	4.57229	+	1.66418i	0.353814	+	0.128778i	0.512812	−	0.858501i	$-0.328604\pi$
$167$	4.57229	+	1.66418i	0.353814	+	0.128778i	−0.158997	+	0.987279i	$0.550826\pi$
$168$	−2.14305	−	5.33803i	−0.165340	−	0.411838i
$169$	3.18548	−	18.0658i	0.245037	−	1.38968i
$170$	5.21830	+	4.73850i	0.400225	+	0.363427i
$171$	23.3139	+	5.29895i	1.78286	+	0.405221i
$172$	8.69639	−	0.840067i	0.663094	−	0.0640545i
$173$	1.81851	+	4.99632i	0.138259	+	0.379863i	0.989427	−	0.145030i	$-0.0463277\pi$
$173$	1.81851	+	4.99632i	0.138259	+	0.379863i	−0.851169	+	0.524893i	$0.824106\pi$
$174$	0.463579	+	4.16156i	0.0351438	+	0.315487i
$175$	0.754731	+	0.899453i	0.0570523	+	0.0679922i
$176$	−11.9884	−	1.89122i	−0.903662	−	0.142556i
$177$	4.21169	+	0.849418i	0.316570	+	0.0638462i
$178$	−0.788430	+	0.107424i	−0.0590953	+	0.00805177i
$179$	−1.80938	−	3.13394i	−0.135239	−	0.234242i	0.790449	−	0.612527i	$-0.209847\pi$
$179$	−1.80938	−	3.13394i	−0.135239	−	0.234242i	−0.925689	+	0.378286i	$0.876514\pi$
$180$	−5.72896	−	1.78299i	−0.427011	−	0.132896i
$181$	11.3921	−	19.7317i	0.846769	−	1.46665i	−0.0373061	−	0.999304i	$-0.511878\pi$
$181$	11.3921	−	19.7317i	0.846769	−	1.46665i	0.884076	−	0.467344i	$-0.154789\pi$
$182$	−3.51879	+	8.60484i	−0.260830	+	0.637833i
$183$	−0.306701	+	12.5268i	−0.0226720	+	0.926011i
$184$	16.4578	−	10.8011i	1.21329	−	0.796266i
$185$	−9.67813	+	1.70652i	−0.711551	+	0.125466i
$186$	−7.66003	+	11.5102i	−0.561661	+	0.843970i
$187$	9.72078	−	11.5848i	0.710854	−	0.847163i
$188$	−4.96548	−	2.26106i	−0.362145	−	0.164904i
$189$	−5.87078	+	1.66043i	−0.427037	+	0.120778i
$190$	−2.38967	+	11.0143i	−0.173365	+	0.799064i
$191$	−7.41382	−	6.22093i	−0.536445	−	0.450131i	0.333875	−	0.942617i	$-0.391644\pi$
$191$	−7.41382	−	6.22093i	−0.536445	−	0.450131i	−0.870320	+	0.492486i	$0.836088\pi$
$192$	−7.91790	+	11.3713i	−0.571425	+	0.820654i
$193$	−0.762647	−	4.32519i	−0.0548965	−	0.311334i	0.944979	−	0.327132i	$-0.106082\pi$
$193$	−0.762647	−	4.32519i	−0.0548965	−	0.311334i	−0.999875	+	0.0157983i	$0.994971\pi$
$194$	9.59604	−	15.2140i	0.688955	−	1.09230i
$195$	4.64154	+	8.51408i	0.332388	+	0.609706i
$196$	−6.36510	+	9.26739i	−0.454650	+	0.661956i
$197$	−0.748537	−	0.432168i	−0.0533310	−	0.0307907i	0.473097	−	0.881010i	$-0.343136\pi$
$197$	−0.748537	−	0.432168i	−0.0533310	−	0.0307907i	−0.526428	+	0.850219i	$0.676469\pi$
$198$	−3.34179	+	12.4316i	−0.237490	+	0.883474i
$199$	−19.0045	+	10.9722i	−1.34719	+	0.777801i	−0.987851	−	0.155406i	$-0.950331\pi$
$199$	−19.0045	+	10.9722i	−1.34719	+	0.777801i	−0.359340	+	0.933207i	$0.616998\pi$
$200$	0.813892	−	2.70880i	0.0575509	−	0.191541i
$201$	−3.85950	−	3.40291i	−0.272228	−	0.240023i
$202$	9.91460	−	5.21827i	0.697589	−	0.367156i
$203$	−1.53758	+	1.29018i	−0.107917	+	0.0905529i
$204$	−7.05426	−	15.7589i	−0.493897	−	1.10334i
$205$	−5.66637	+	2.06239i	−0.395757	+	0.144044i
$206$	−4.89652	−	15.2886i	−0.341157	−	1.06521i
$207$	−9.54245	−	18.5716i	−0.663246	−	1.29082i
$208$	21.9804	−	4.28659i	1.52406	−	0.297221i
$209$	23.8135	+	4.19897i	1.64722	+	0.290449i
$210$	−0.809930	−	2.75968i	−0.0558905	−	0.190436i
$211$	−3.96775	+	10.9013i	−0.273151	+	0.750477i	0.724945	+	0.688806i	$0.241865\pi$
$211$	−3.96775	+	10.9013i	−0.273151	+	0.750477i	−0.998097	+	0.0616704i	$0.980357\pi$
$212$	17.9623	+	4.63949i	1.23366	+	0.318641i
$213$	13.8739	+	17.3811i	0.950625	+	1.19094i
$214$	18.9257	−	14.6585i	1.29373	−	1.00203i
$215$	4.36844			0.297925
$216$	11.1035	+	9.62872i	0.755498	+	0.655151i
$217$	−6.62749			−0.449903
$218$	−3.07283	+	2.38000i	−0.208118	+	0.161194i
$219$	−10.2528	+	26.1587i	−0.692821	+	1.76764i
$220$	−5.87552	−	1.51759i	−0.396128	−	0.102316i
$221$	−9.54389	+	26.2216i	−0.641992	+	1.76386i
$222$	23.3929	+	5.67824i	1.57003	+	0.381098i
$223$	15.9401	+	2.81066i	1.06743	+	0.188216i	0.679649	−	0.733538i	$-0.262132\pi$
$223$	15.9401	+	2.81066i	1.06743	+	0.188216i	0.387777	+	0.921753i	$0.373243\pi$
$224$	−6.64054	−	0.139788i	−0.443690	−	0.00934000i
$225$	−2.76549	−	1.16279i	−0.184366	−	0.0775194i
$226$	0.240392	+	0.750588i	0.0159907	+	0.0499283i
$227$	8.08343	−	2.94213i	0.536516	−	0.195276i	−0.0595295	−	0.998227i	$-0.518960\pi$
$227$	8.08343	−	2.94213i	0.536516	−	0.195276i	0.596045	+	0.802951i	$0.296738\pi$
$228$	16.1822	−	22.3672i	1.07169	−	1.48131i
$229$	−7.28113	+	6.10959i	−0.481151	+	0.403733i	−0.850842	−	0.525421i	$-0.823908\pi$
$229$	−7.28113	+	6.10959i	−0.481151	+	0.403733i	0.369692	+	0.929155i	$0.379463\pi$
$230$	8.71006	−	4.58429i	0.574324	−	0.302279i
$231$	−5.84836	+	1.96790i	−0.384794	+	0.129479i
$232$	4.63057	+	1.39131i	0.304012	+	0.0913443i
$233$	6.29764	−	3.63594i	0.412572	−	0.238199i	−0.279322	−	0.960197i	$-0.590110\pi$
$233$	6.29764	−	3.63594i	0.412572	−	0.238199i	0.691894	+	0.721999i	$0.256776\pi$
$234$	−2.05111	−	23.6642i	−0.134085	−	1.54698i
$235$	−2.36253	−	1.36401i	−0.154115	−	0.0889782i
$236$	2.80877	−	4.08949i	0.182836	−	0.266203i
$237$	2.09802	−	3.43677i	0.136281	−	0.223242i
$238$	4.41524	−	7.00012i	0.286198	−	0.453750i
$239$	−0.375127	−	2.12745i	−0.0242649	−	0.137613i	0.970269	−	0.242030i	$-0.0778134\pi$
$239$	−0.375127	−	2.12745i	−0.0242649	−	0.137613i	−0.994534	+	0.104417i	$0.966702\pi$
$240$	−4.48729	+	5.27866i	−0.289653	+	0.340736i
$241$	7.15121	+	6.00057i	0.460650	+	0.386531i	0.843370	−	0.537333i	$-0.180568\pi$
$241$	7.15121	+	6.00057i	0.460650	+	0.386531i	−0.382720	+	0.923864i	$0.625013\pi$
$242$	0.537872	−	2.47912i	0.0345757	−	0.159364i
$243$	11.4030	−	10.6288i	0.731504	−	0.681837i
$244$	13.1682	+	5.99618i	0.843005	+	0.383866i
$245$	−3.61334	+	4.30622i	−0.230848	+	0.275114i
$246$	14.7406	+	0.938693i	0.939828	+	0.0598489i
$247$	−43.9404	+	7.74787i	−2.79586	+	0.492985i
$248$	8.75967	+	13.3473i	0.556240	+	0.847553i
$249$	12.9158	+	7.88460i	0.818504	+	0.499667i
$250$	0.535289	−	1.30899i	0.0338546	−	0.0827881i
$251$	−14.1125	+	24.4435i	−0.890770	+	1.54286i	−0.0518165	+	0.998657i	$0.516501\pi$
$251$	−14.1125	+	24.4435i	−0.890770	+	1.54286i	−0.838954	+	0.544203i	$0.816832\pi$
$252$	−0.893625	+	6.98801i	−0.0562931	+	0.440203i
$253$	−10.5588	−	18.2884i	−0.663826	−	1.14978i
$254$	−4.08797	+	0.556988i	−0.256502	+	0.0349485i
$255$	−2.75317	−	8.18206i	−0.172410	−	0.512380i
$256$	8.49540	+	13.5583i	0.530962	+	0.847395i
$257$	−1.42825	−	1.70213i	−0.0890920	−	0.106176i	0.719657	−	0.694330i	$-0.244299\pi$
$257$	−1.42825	−	1.70213i	−0.0890920	−	0.106176i	−0.808749	+	0.588154i	$0.799855\pi$
$258$	−9.80221	−	4.29139i	−0.610259	−	0.267170i
$259$	3.94654	+	10.8430i	0.245226	+	0.673753i
$260$	11.1453	−	1.07663i	0.691205	−	0.0667701i
$261$	1.98774	−	4.72748i	0.123038	−	0.292624i
$262$	13.4693	+	12.2309i	0.832135	+	0.755625i
$263$	1.05908	−	6.00633i	0.0653055	−	0.370366i	−0.934587	−	0.355733i	$-0.884231\pi$
$263$	1.05908	−	6.00633i	0.0653055	−	0.370366i	0.999893	−	0.0146324i	$-0.00465781\pi$
$264$	11.6931	+	9.17717i	0.719661	+	0.564815i
$265$	8.71651	+	3.17255i	0.535451	+	0.194888i
$266$	13.2233	+	0.517507i	0.810771	+	0.0317304i
$267$	0.907342	+	0.355629i	0.0555284	+	0.0217642i
$268$	−5.36187	+	2.55950i	−0.327528	+	0.156347i
$269$			11.8116i			0.720168i	0.932920	+	0.360084i	$0.117252\pi$
$269$			11.8116i			0.720168i	−0.932920	+	0.360084i	$0.882748\pi$
$270$	5.06312	+	5.32587i	0.308132	+	0.324122i
$271$		−	0.670335i		−	0.0407200i	−0.999793	−	0.0203600i	$-0.993519\pi$
$271$		−	0.670335i		−	0.0407200i	0.999793	−	0.0203600i	$-0.00648123\pi$
$272$	−19.9334	+	0.360206i	−1.20864	+	0.0218407i
$273$	8.89859	−	7.10301i	0.538567	−	0.429894i
$274$	0.215143	−	5.49731i	0.0129973	−	0.332105i
$275$	−2.85119	−	1.03775i	−0.171933	−	0.0625786i
$276$	−24.0477	+	1.73013i	−1.44750	+	0.104142i
$277$	1.24793	−	7.07738i	0.0749810	−	0.425238i	−0.924091	−	0.382172i	$-0.875176\pi$
$277$	1.24793	−	7.07738i	0.0749810	−	0.425238i	0.999072	−	0.0430664i	$-0.0137127\pi$
$278$	15.0864	−	16.6139i	0.904821	−	0.996438i
$279$	15.0616	−	7.73892i	0.901713	−	0.463317i
$280$	−3.29816	−	0.388821i	−0.197103	−	0.0232365i
$281$	−8.61420	−	23.6673i	−0.513880	−	1.41187i	−0.877162	−	0.480195i	$-0.840566\pi$
$281$	−8.61420	−	23.6673i	−0.513880	−	1.41187i	0.363282	−	0.931679i	$-0.381656\pi$
$282$	3.96127	+	5.38153i	0.235890	+	0.320465i
$283$	−0.706919	−	0.842473i	−0.0420220	−	0.0500798i	0.744624	−	0.667484i	$-0.232629\pi$
$283$	−0.706919	−	0.842473i	−0.0420220	−	0.0500798i	−0.786646	+	0.617404i	$0.788184\pi$
$284$	24.7437	−	6.87024i	1.46827	−	0.407674i
$285$	9.12894	−	10.3538i	0.540752	−	0.613308i
$286$	−3.24325	−	23.8035i	−0.191777	−	1.40753i
$287$	3.54009	+	6.13161i	0.208965	+	0.361937i
$288$	15.2545	−	7.43648i	0.898878	−	0.438199i
$289$	3.92100	−	6.79138i	0.230647	−	0.399493i
$290$	2.23767	+	0.915053i	0.131401	+	0.0537338i
$291$	−19.3425	+	10.5448i	−1.13388	+	0.618145i
$292$	23.1468	+	22.7323i	1.35456	+	1.33031i
$293$	11.3344	−	1.99857i	0.662165	−	0.116758i	0.167542	−	0.985865i	$-0.446417\pi$
$293$	11.3344	−	1.99857i	0.662165	−	0.116758i	0.494623	+	0.869107i	$0.335306\pi$
$294$	12.3382	−	6.11298i	0.719576	−	0.356516i
$295$	1.59449	−	1.90023i	0.0928346	−	0.110636i
$296$	16.6209	−	22.2795i	0.966068	−	1.29497i
$297$	10.9930	−	11.3014i	0.637880	−	0.655773i
$298$	−8.19398	−	1.77777i	−0.474664	−	0.102983i
$299$	29.8496	+	25.0468i	1.72625	+	1.44849i
$300$	−2.48703	+	2.41137i	−0.143589	+	0.139220i
$301$	−0.890678	−	5.05128i	−0.0513378	−	0.291151i
$302$	10.5110	+	6.62970i	0.604841	+	0.381497i
$303$	−13.7179	−	0.335863i	−0.788075	−	0.0192949i
$304$	−16.4352	−	27.3147i	−0.942624	−	1.56661i
$305$	6.26530	+	3.61727i	0.358750	+	0.207124i
$306$	−1.86000	+	21.0641i	−0.106329	+	1.20415i
$307$	20.0571	−	11.5800i	1.14472	−	0.660903i	0.197123	−	0.980379i	$-0.436840\pi$
$307$	20.0571	−	11.5800i	1.14472	−	0.660903i	0.947595	+	0.319475i	$0.103507\pi$
$308$	−0.556849	+	7.10337i	−0.0317294	+	0.404752i
$309$	−3.88710	+	19.2735i	−0.221130	+	1.09643i
$310$	3.71786	+	7.06385i	0.211160	+	0.401200i
$311$	−1.44219	+	1.21014i	−0.0817793	+	0.0686210i	−0.682761	−	0.730642i	$-0.739221\pi$
$311$	−1.44219	+	1.21014i	−0.0817793	+	0.0686210i	0.600982	+	0.799263i	$0.294776\pi$
$312$	−26.0664	−	8.53294i	−1.47572	−	0.483083i
$313$	−4.86174	+	1.76953i	−0.274802	+	0.100020i	−0.475745	−	0.879583i	$-0.657822\pi$
$313$	−4.86174	+	1.76953i	−0.274802	+	0.100020i	0.200943	+	0.979603i	$0.435599\pi$
$314$	−15.8576	+	5.07873i	−0.894894	+	0.286609i
$315$	−0.780698	+	3.43485i	−0.0439873	+	0.193532i
$316$	−2.70112	−	3.78436i	−0.151950	−	0.212887i
$317$	1.61998	+	0.285646i	0.0909872	+	0.0160435i	0.218956	−	0.975735i	$-0.429735\pi$
$317$	1.61998	+	0.285646i	0.0909872	+	0.0160435i	−0.127969	+	0.991778i	$0.540846\pi$
$318$	−16.4421	−	15.6816i	−0.922030	−	0.879379i
$319$	1.77399	−	4.87399i	0.0993242	−	0.272891i
$320$	3.57619	+	7.15618i	0.199915	+	0.400043i
$321$	−28.9891	+	4.38288i	−1.61801	+	0.244629i
$322$	−7.07677	−	9.13688i	−0.394373	−	0.509178i
$323$	39.7215			2.21016
$324$	−6.12906	−	16.9244i	−0.340503	−	0.940243i
$325$	5.59861			0.310555
$326$	2.10718	+	2.72060i	0.116706	+	0.150680i
$327$	4.70676	−	0.711619i	0.260285	−	0.0393526i
$328$	7.66962	−	15.2337i	0.423484	−	0.841142i
$329$	−1.09553	+	3.00994i	−0.0603984	+	0.165943i
$330$	5.37826	+	5.12948i	0.296064	+	0.282369i
$331$	25.2796	+	4.45747i	1.38949	+	0.245005i	0.817818	−	0.575477i	$-0.195184\pi$
$331$	25.2796	+	4.45747i	1.38949	+	0.245005i	0.571672	+	0.820482i	$0.306295\pi$
$332$	14.2221	−	10.1511i	0.780538	−	0.557114i
$333$	−21.6303	−	20.0334i	−1.18533	−	1.09782i
$334$	−6.55328	+	2.09883i	−0.358580	+	0.114843i
$335$	−2.79156	+	1.01605i	−0.152519	+	0.0555125i
$336$	7.01870	+	4.11246i	0.382901	+	0.224353i
$337$	−18.1521	+	15.2315i	−0.988810	+	0.829710i	−0.985395	−	0.170284i	$-0.945531\pi$
$337$	−18.1521	+	15.2315i	−0.988810	+	0.829710i	−0.00341493	+	0.999994i	$0.501087\pi$
$338$	12.0830	+	22.9574i	0.657227	+	1.24872i
$339$	0.190835	−	0.946223i	0.0103648	−	0.0513918i
$340$	−9.93786	−	0.779051i	−0.538956	−	0.0422500i
$341$	14.8319	−	8.56317i	0.803190	−	0.463722i
$342$	−30.6554	+	14.2647i	−1.65765	+	0.771349i
$343$	12.8340	+	7.40970i	0.692970	+	0.400086i
$344$	−8.99570	+	8.47014i	−0.485016	+	0.456679i
$345$	−12.0513	−	0.295059i	−0.648821	−	0.0158854i
$346$	−6.35992	−	4.01145i	−0.341912	−	0.215657i
$347$	−3.42568	−	19.4280i	−0.183900	−	1.04295i	−0.927360	−	0.374170i	$-0.877928\pi$
$347$	−3.42568	−	19.4280i	−0.183900	−	1.04295i	0.743460	−	0.668781i	$-0.233183\pi$
$348$	−4.12213	−	4.25147i	−0.220969	−	0.227903i
$349$	−5.19327	−	4.35767i	−0.277989	−	0.233261i	0.493123	−	0.869959i	$-0.335855\pi$
$349$	−5.19327	−	4.35767i	−0.277989	−	0.233261i	−0.771113	+	0.636699i	$0.780300\pi$
$350$	−1.62275	−	0.352072i	−0.0867396	−	0.0188190i
$351$	−11.9287	+	26.5331i	−0.636706	+	1.41623i
$352$	15.0417	−	8.26720i	0.801724	−	0.440643i
$353$	−12.6406	+	15.0645i	−0.672792	+	0.801802i	−0.989161	−	0.146834i	$-0.953092\pi$
$353$	−12.6406	+	15.0645i	−0.672792	+	0.801802i	0.316369	+	0.948636i	$0.397536\pi$
$354$	−5.44454	+	2.69752i	−0.289374	+	0.143372i
$355$	12.6448	−	2.22963i	0.671118	−	0.118336i
$356$	0.788493	−	0.802870i	0.0417901	−	0.0425520i
$357$	−8.89969	+	4.85176i	−0.471022	+	0.256782i
$358$	4.73694	+	1.93708i	0.250355	+	0.102378i
$359$	−4.81727	+	8.34375i	−0.254246	+	0.440366i	−0.964690	−	0.263387i	$-0.915160\pi$
$359$	−4.81727	+	8.34375i	−0.254246	+	0.440366i	0.710445	+	0.703753i	$0.248494\pi$
$360$	7.94941	−	2.96764i	0.418971	−	0.156408i
$361$	22.2566	+	38.5495i	1.17140	+	2.02892i
$362$	4.35005	+	31.9268i	0.228633	+	1.67803i
$363$	−2.05476	+	2.33046i	−0.107847	+	0.122317i
$364$	−3.51735	−	12.6680i	−0.184359	−	0.663984i
$365$	10.4269	+	12.4263i	0.545769	+	0.650422i
$366$	−10.5051	−	14.2715i	−0.549108	−	0.745983i
$367$	0.684345	+	1.88022i	0.0357225	+	0.0981468i	0.956272	−	0.292480i	$-0.0944805\pi$
$367$	0.684345	+	1.88022i	0.0357225	+	0.0981468i	−0.920549	+	0.390627i	$0.872258\pi$
$368$	−9.04751	+	26.3285i	−0.471634	+	1.37247i
$369$	−15.2051	−	9.80089i	−0.791544	−	0.510214i
$370$	9.34303	−	10.2891i	0.485721	−	0.534903i
$371$	1.89126	−	10.7259i	0.0981894	−	0.556860i
$372$	−1.40313	−	19.5027i	−0.0727491	−	1.01117i
$373$	−10.5447	−	3.83797i	−0.545986	−	0.198723i	0.0542761	−	0.998526i	$-0.482715\pi$
$373$	−10.5447	−	3.83797i	−0.545986	−	0.198723i	−0.600262	+	0.799803i	$0.704937\pi$
$374$	−0.836361	+	21.3706i	−0.0432472	+	1.10505i
$375$	−1.35368	+	1.08053i	−0.0699038	+	0.0557984i
$376$	7.50978	−	1.77198i	0.387287	−	0.0913827i
$377$			9.57059i			0.492911i
$378$	5.12606	−	6.94044i	0.263656	−	0.356978i
$379$		−	3.38300i		−	0.173773i	−0.996218	−	0.0868866i	$-0.972308\pi$
$379$		−	3.38300i		−	0.173773i	0.996218	−	0.0868866i	$-0.0276918\pi$
$380$	−6.86635	−	14.3842i	−0.352236	−	0.737895i
$381$	4.70452	+	1.84392i	0.241020	+	0.0944669i
$382$	13.6764	+	0.535239i	0.699744	+	0.0273852i
$383$	−35.8386	−	13.0442i	−1.83127	−	0.666527i	−0.992531	−	0.121991i	$-0.961072\pi$
$383$	−35.8386	−	13.0442i	−1.83127	−	0.666527i	−0.838738	−	0.544536i	$-0.816706\pi$
$384$	−0.994544	−	19.5707i	−0.0507526	−	0.998711i
$385$	−0.618636	+	3.50846i	−0.0315286	+	0.178808i
$386$	4.59821	+	4.17543i	0.234043	+	0.212524i
$387$	7.92254	+	10.4395i	0.402725	+	0.530668i
$388$	2.44593	+	25.3203i	0.124173	+	1.28544i
$389$	−1.45869	−	4.00772i	−0.0739586	−	0.203200i	0.897205	−	0.441615i	$-0.145594\pi$
$389$	−1.45869	−	4.00772i	−0.0739586	−	0.203200i	−0.971163	+	0.238415i	$0.923372\pi$
$390$	−12.5626	−	5.49987i	−0.636131	−	0.278497i
$391$	−22.2979	−	26.5737i	−1.12766	−	1.34389i
$392$	−0.908718	−	15.8736i	−0.0458972	−	0.801740i
$393$	−7.10638	−	21.1192i	−0.358469	−	1.06532i
$394$	1.21116	−	0.165022i	0.0610176	−	0.00831369i
$395$	−1.16236	−	2.01327i	−0.0584848	−	0.101299i
$396$	−7.02912	−	16.7933i	−0.353227	−	0.843895i
$397$	−0.350354	+	0.606831i	−0.0175838	+	0.0304560i	−0.874683	−	0.484695i	$-0.838931\pi$
$397$	−0.350354	+	0.606831i	−0.0175838	+	0.0304560i	0.857100	+	0.515151i	$0.172264\pi$
$398$	11.7466	−	28.7252i	0.588805	−	1.43986i
$399$	−13.8336	−	8.44489i	−0.692545	−	0.422773i
$400$	1.43577	+	3.73344i	0.0717884	+	0.186672i
$401$	−13.4606	+	2.37347i	−0.672192	+	0.118526i	−0.499319	−	0.866418i	$-0.666416\pi$
$401$	−13.4606	+	2.37347i	−0.672192	+	0.118526i	−0.172874	+	0.984944i	$0.555305\pi$
$402$	7.26204	+	0.462451i	0.362197	+	0.0230650i
$403$	−20.3129	+	24.2080i	−1.01186	+	1.20589i
$404$	−6.56632	+	14.4202i	−0.326687	+	0.717433i
$405$	−2.23667	−	8.71764i	−0.111141	−	0.433183i
$406$	0.601852	−	2.77402i	0.0298694	−	0.137672i
$407$	−22.8420	−	19.1667i	−1.13224	−	0.950060i
$408$	21.5340	+	11.5107i	1.06609	+	0.569864i
$409$	−1.14340	−	6.48456i	−0.0565376	−	0.320641i	0.943402	−	0.331652i	$-0.107606\pi$
$409$	−1.14340	−	6.48456i	−0.0565376	−	0.320641i	−0.999939	+	0.0110114i	$0.996495\pi$
$410$	4.54942	−	7.21285i	0.224680	−	0.356217i
$411$	−3.51080	+	5.75104i	−0.173175	+	0.283678i
$412$	18.7143	+	12.8535i	0.921987	+	0.633246i
$413$	−2.52237	−	1.45629i	−0.124118	−	0.0716593i
$414$	26.7518	+	12.5008i	1.31478	+	0.614383i
$415$	7.56611	−	4.36830i	0.371406	−	0.214431i
$416$	−20.8635	+	23.8272i	−1.02292	+	1.16823i
$417$	−26.0499	+	8.76549i	−1.27567	+	0.429248i
$418$	−30.2614	+	15.9272i	−1.48013	+	0.779027i
$419$	11.0137	−	9.24160i	0.538055	−	0.451482i	−0.332817	−	0.942991i	$-0.607999\pi$
$419$	11.0137	−	9.24160i	0.538055	−	0.451482i	0.870872	+	0.491510i	$0.163555\pi$
$420$	3.29538	+	2.38413i	0.160798	+	0.116334i
$421$	31.2521	−	11.3748i	1.52314	−	0.554376i	0.561206	−	0.827676i	$-0.310337\pi$
$421$	31.2521	−	11.3748i	1.52314	−	0.554376i	0.961929	+	0.273300i	$0.0881152\pi$
$422$	−5.00406	−	15.6244i	−0.243594	−	0.760585i
$423$	−1.02502	−	8.11962i	−0.0498382	−	0.394789i
$424$	−24.1009	+	10.3677i	−1.17044	+	0.503501i
$425$	−4.90845	−	0.865493i	−0.238095	−	0.0419826i
$426$	−30.5637	−	7.41882i	−1.48082	−	0.359443i
$427$	2.90527	−	7.98218i	0.140596	−	0.386285i
$428$	−8.46632	+	32.7784i	−0.409235	+	1.58440i
$429$	−10.7368	+	27.3936i	−0.518380	+	1.32258i
$430$	−4.88422	+	3.78297i	−0.235538	+	0.182431i
$431$	−9.73700			−0.469015			−0.234507	−	0.972114i	$-0.575348\pi$
$431$	−9.73700			−0.469015			−0.234507	+	0.972114i	$0.575348\pi$
$432$	−20.7528	−	1.15020i	−0.998468	−	0.0553392i
$433$	−7.52188			−0.361479			−0.180739	−	0.983531i	$-0.557849\pi$
$433$	−7.52188			−0.361479			−0.180739	+	0.983531i	$0.557849\pi$
$434$	7.41000	−	5.73926i	0.355691	−	0.275493i
$435$	−1.84712	−	2.31406i	−0.0885628	−	0.110951i
$436$	1.37462	−	5.32201i	0.0658323	−	0.254878i
$437$	18.9709	−	52.1221i	0.907500	−	2.49334i
$438$	−11.1895	−	38.1260i	−0.534655	−	1.82173i
$439$	16.3092	+	2.87576i	0.778397	+	0.137252i	0.548711	−	0.836012i	$-0.315119\pi$
$439$	16.3092	+	2.87576i	0.778397	+	0.137252i	0.229686	+	0.973265i	$0.426230\pi$
$440$	7.88345	−	3.39131i	0.375829	−	0.161674i
$441$	−16.8439	−	0.825291i	−0.802090	−	0.0392996i
$442$	−12.0366	−	37.5824i	−0.572523	−	1.78761i
$443$	11.0132	−	4.00846i	0.523251	−	0.190448i	−0.0668713	−	0.997762i	$-0.521302\pi$
$443$	11.0132	−	4.00846i	0.523251	−	0.190448i	0.590122	+	0.807314i	$0.299079\pi$
$444$	−31.0722	+	13.9091i	−1.47462	+	0.660096i
$445$	0.431019	−	0.361668i	0.0204322	−	0.0171447i
$446$	−20.2561	+	10.6612i	−0.959154	+	0.504823i
$447$	7.70260	+	6.79136i	0.364320	+	0.321220i
$448$	7.54564	−	5.59427i	0.356498	−	0.264304i
$449$	11.8755	−	6.85630i	0.560438	−	0.323569i	−0.192883	−	0.981222i	$-0.561784\pi$
$449$	11.8755	−	6.85630i	0.560438	−	0.323569i	0.753321	+	0.657653i	$0.228451\pi$
$450$	4.09896	−	1.09477i	0.193227	−	0.0516079i
$451$	−15.8449	−	9.14808i	−0.746109	−	0.430766i
$452$	−0.918768	−	0.631036i	−0.0432152	−	0.0296814i
$453$	−7.28516	−	13.3633i	−0.342287	−	0.627864i
$454$	−6.49003	+	10.2896i	−0.304592	+	0.482914i
$455$	−1.14150	−	6.47376i	−0.0535143	−	0.303494i
$456$	1.27669	+	39.0216i	0.0597866	+	1.82735i
$457$	−1.16899	−	0.980898i	−0.0546830	−	0.0458845i	0.615037	−	0.788499i	$-0.289141\pi$
$457$	−1.16899	−	0.980898i	−0.0546830	−	0.0458845i	−0.669720	+	0.742614i	$0.733586\pi$
$458$	2.85005	−	13.1363i	0.133174	−	0.613817i
$459$	14.5600	−	21.4183i	0.679601	−	0.999718i
$460$	−5.76856	+	12.6683i	−0.268961	+	0.590662i
$461$	−25.3705	+	30.2354i	−1.18162	+	1.40820i	−0.289040	+	0.957317i	$0.593336\pi$
$461$	−25.3705	+	30.2354i	−1.18162	+	1.40820i	−0.892582	+	0.450886i	$0.851108\pi$
$462$	4.83472	−	7.26481i	0.224932	−	0.337989i
$463$	−35.3028	+	6.22484i	−1.64066	+	0.289293i	−0.916409	−	0.400243i	$-0.868926\pi$
$463$	−35.3028	+	6.22484i	−1.64066	+	0.289293i	−0.724252	+	0.689536i	$0.757815\pi$
$464$	−6.38216	+	2.45439i	−0.296284	+	0.113942i
$465$	0.239292	−	9.77361i	0.0110969	−	0.453240i
$466$	−3.89256	+	9.51886i	−0.180319	+	0.440953i
$467$	−6.56355	+	11.3684i	−0.303725	+	0.526067i	−0.976977	−	0.213346i	$-0.931564\pi$
$467$	−6.56355	+	11.3684i	−0.303725	+	0.526067i	0.673252	+	0.739413i	$0.264897\pi$
$468$	22.7859	+	24.6820i	1.05328	+	1.14093i
$469$	1.74404	+	3.02076i	0.0805322	+	0.139486i
$470$	3.82268	−	0.520843i	0.176327	−	0.0240247i
$471$	19.9907	+	4.03175i	0.921123	+	0.185773i
$472$	0.400996	+	7.00467i	0.0184574	+	0.322416i
$473$	8.51989	+	10.1536i	0.391745	+	0.466863i
$474$	0.630431	+	5.65939i	0.0289566	+	0.259944i
$475$	−2.72573	−	7.48889i	−0.125065	−	0.343614i
$476$	1.12540	+	11.6501i	0.0515825	+	0.533983i
$477$	8.22655	+	26.5840i	0.376668	+	1.21720i
$478$	2.26174	+	2.05379i	0.103450	+	0.0939380i
$479$	−0.258483	+	1.46593i	−0.0118104	+	0.0669800i	−0.990143	−	0.140058i	$-0.955271\pi$
$479$	−0.258483	+	1.46593i	−0.0118104	+	0.0669800i	0.978333	+	0.207038i	$0.0663823\pi$
$480$	0.445911	−	9.78781i	0.0203529	−	0.446750i
$481$	51.7019	+	18.8180i	2.35740	+	0.858025i
$482$	−13.1919	−	0.516280i	−0.600875	−	0.0235159i
$483$	2.11596	+	13.9953i	0.0962793	+	0.636807i
$484$	1.54549	+	3.23762i	0.0702495	+	0.147165i
$485$			12.7191i			0.577543i
$486$	−3.54508	+	21.7585i	−0.160808	+	0.986986i
$487$		−	30.9109i		−	1.40071i	−0.713797	−	0.700353i	$-0.753026\pi$
$487$		−	30.9109i		−	1.40071i	0.713797	−	0.700353i	$-0.246974\pi$
$488$	−19.9155	+	4.69917i	−0.901532	+	0.212722i
$489$	−0.630047	−	4.16723i	−0.0284917	−	0.188449i
$490$	0.310886	−	7.94373i	0.0140444	−	0.358861i
$491$	8.07835	+	2.94028i	0.364571	+	0.132693i	0.517809	−	0.855496i	$-0.326748\pi$
$491$	8.07835	+	2.94028i	0.364571	+	0.132693i	−0.153238	+	0.988189i	$0.548970\pi$
$492$	−17.2940	+	11.7155i	−0.779672	+	0.528177i
$493$	1.47952	−	8.39080i	0.0666344	−	0.377902i
$494$	42.4190	−	46.7141i	1.90852	−	2.10176i
$495$	−2.69092	−	8.69568i	−0.120948	−	0.390842i
$496$	−21.3524	−	7.33752i	−0.958750	−	0.329465i
$497$	−5.15629	−	14.1668i	−0.231291	−	0.635468i
$498$	−21.2686	+	2.36923i	−0.953071	+	0.106168i
$499$	14.0974	+	16.8007i	0.631087	+	0.752101i	0.982934	−	0.183957i	$-0.0588907\pi$
$499$	14.0974	+	16.8007i	0.631087	+	0.752101i	−0.351847	+	0.936058i	$0.614446\pi$
$500$	0.535070	+	1.92710i	0.0239290	+	0.0861824i
$501$	8.26135	+	1.66616i	0.369090	+	0.0744385i
$502$	−5.38880	−	39.5506i	−0.240514	−	1.76523i
$503$	6.53892	+	11.3257i	0.291556	+	0.504990i	0.974178	−	0.225782i	$-0.0724937\pi$
$503$	6.53892	+	11.3257i	0.291556	+	0.504990i	−0.682622	+	0.730772i	$0.739160\pi$
$504$	−5.05232	−	8.58695i	−0.225048	−	0.382493i
$505$	−3.96121	+	6.86102i	−0.176272	+	0.305311i
$506$	27.6428	+	11.3040i	1.22887	+	0.502525i
$507$	0.777696	−	31.7640i	0.0345387	−	1.41069i
$508$	4.08829	−	4.16284i	0.181389	−	0.184696i
$509$	−5.46154	+	0.963016i	−0.242078	+	0.0426849i	−0.293371	−	0.955999i	$-0.594777\pi$
$509$	−5.46154	+	0.963016i	−0.242078	+	0.0426849i	0.0512924	+	0.998684i	$0.483666\pi$
$510$	10.1637	+	6.76394i	0.450057	+	0.299512i
$511$	12.2428	−	14.5904i	0.541588	−	0.645440i
$512$	−21.2397	−	7.80234i	−0.938670	−	0.344818i
$513$	41.2992	+	3.03831i	1.82340	+	0.134145i
$514$	3.07089	+	0.666261i	0.135451	+	0.0293875i
$515$	8.69584	+	7.29668i	0.383185	+	0.321530i
$516$	14.6758	−	3.69042i	0.646067	−	0.162462i
$517$	−1.43734	−	8.15153i	−0.0632139	−	0.358504i
$518$	−13.8023	−	8.70565i	−0.606440	−	0.382504i
$519$	4.40804	+	8.08577i	0.193492	+	0.354926i
$520$	−11.5289	+	10.8554i	−0.505578	+	0.476040i
$521$	−15.4724	−	8.93299i	−0.677858	−	0.391362i	0.121189	−	0.992629i	$-0.461329\pi$
$521$	−15.4724	−	8.93299i	−0.677858	−	0.391362i	−0.799048	+	0.601268i	$0.794662\pi$
$522$	1.87146	+	7.00700i	0.0819116	+	0.306688i
$523$	25.0331	−	14.4529i	1.09462	−	0.631981i	0.159819	−	0.987146i	$-0.448909\pi$
$523$	25.0331	−	14.4529i	1.09462	−	0.631981i	0.934803	+	0.355166i	$0.115576\pi$
$524$	−25.6513	−	2.01086i	−1.12058	−	0.0878448i
$525$	1.52544	+	1.34497i	0.0665755	+	0.0586994i
$526$	4.01722	+	7.63263i	0.175159	+	0.332799i
$527$	21.5512	−	18.0836i	0.938785	−	0.787734i
$528$	−21.0209	−	0.134750i	−0.914819	−	0.00586423i
$529$	−23.9062	+	8.70114i	−1.03940	+	0.378310i
$530$	−12.4930	+	4.00117i	−0.542663	+	0.173800i
$531$	7.43282	+	0.364182i	0.322557	+	0.0158041i
$532$	−15.2327	+	10.8725i	−0.660421	+	0.471381i
$533$	33.2469	+	5.86233i	1.44008	+	0.253926i
$534$	−1.32244	+	0.388119i	−0.0572276	+	0.0167956i
$535$	−5.78940	+	15.9062i	−0.250298	+	0.687687i
$536$	3.77847	−	7.50497i	0.163205	−	0.324165i
$537$	−3.91019	−	4.89865i	−0.168737	−	0.211392i
$538$	−10.2286	−	13.2062i	−0.440987	−	0.569361i
$539$	−17.0562			−0.734663
$540$	−10.2730	−	1.57015i	−0.442080	−	0.0675683i
$541$	−1.03091			−0.0443222			−0.0221611	−	0.999754i	$-0.507055\pi$
$541$	−1.03091			−0.0443222			−0.0221611	+	0.999754i	$0.507055\pi$
$542$	0.580496	+	0.749482i	0.0249344	+	0.0321930i
$543$	14.4009	−	36.7420i	0.618002	−	1.57675i
$544$	21.9751	−	17.6647i	0.942174	−	0.757366i
$545$	0.939986	−	2.58259i	0.0402646	−	0.110626i
$546$	−3.79820	+	15.6476i	−0.162548	+	0.669658i
$547$	12.5955	+	2.22093i	0.538545	+	0.0949600i	0.436303	−	0.899800i	$-0.356287\pi$
$547$	12.5955	+	2.22093i	0.538545	+	0.0949600i	0.102241	+	0.994760i	$0.467399\pi$
$548$	4.52001	+	6.33270i	0.193085	+	0.270519i
$549$	2.71829	+	21.5327i	0.116014	+	0.918995i
$550$	4.08650	−	1.30879i	0.174249	−	0.0558071i
$551$	12.8019	−	4.65953i	0.545381	−	0.198503i
$552$	25.3888	−	22.7592i	1.08062	−	0.968695i
$553$	−2.09098	+	1.75454i	−0.0889176	+	0.0746107i
$554$	4.73357	+	8.99369i	0.201110	+	0.382105i
$555$	−16.1328	+	5.42849i	−0.684799	+	0.230427i
$556$	−2.48033	+	31.6400i	−0.105190	+	1.34184i
$557$	28.9194	−	16.6966i	1.22535	−	0.707458i	0.259298	−	0.965797i	$-0.416509\pi$
$557$	28.9194	−	16.6966i	1.22535	−	0.707458i	0.966054	+	0.258340i	$0.0831754\pi$
$558$	−10.1382	+	21.6957i	−0.429183	+	0.918450i
$559$	−21.1805	−	12.2286i	−0.895841	−	0.517214i
$560$	4.02429	−	2.42141i	0.170057	−	0.102323i
$561$	13.6481	−	22.3569i	0.576222	−	0.943910i
$562$	30.1267	+	19.0020i	1.27082	+	0.801552i
$563$	2.10526	+	11.9395i	0.0887262	+	0.503191i	0.996490	+	0.0837099i	$0.0266769\pi$
$563$	2.10526	+	11.9395i	0.0887262	+	0.503191i	−0.907764	+	0.419481i	$0.862212\pi$
$564$	−9.08927	−	2.58656i	−0.382727	−	0.108914i
$565$	−0.426918	−	0.358227i	−0.0179606	−	0.0150707i
$566$	1.51995	+	0.329768i	0.0638882	+	0.0138612i
$567$	−9.62430	+	4.36373i	−0.404183	+	0.183260i
$568$	−21.7158	+	29.1089i	−0.911173	+	1.22138i
$569$	2.11615	−	2.52193i	0.0887136	−	0.105725i	−0.719862	−	0.694118i	$-0.755795\pi$
$569$	2.11615	−	2.52193i	0.0887136	−	0.105725i	0.808575	+	0.588393i	$0.200239\pi$
$570$	−1.24061	+	19.4818i	−0.0519635	+	0.816002i
$571$	−33.5971	+	5.92407i	−1.40599	+	0.247915i	−0.824604	−	0.565711i	$-0.808602\pi$
$571$	−33.5971	+	5.92407i	−1.40599	+	0.247915i	−0.581390	+	0.813625i	$0.697491\pi$
$572$	24.2395	+	23.8055i	1.01351	+	0.995357i
$573$	−14.3076	−	8.73425i	−0.597708	−	0.364879i
$574$	−9.26790	−	3.78994i	−0.386835	−	0.158189i
$575$	−3.47996	+	6.02746i	−0.145124	+	0.251363i
$576$	−10.6157	+	21.5245i	−0.442323	+	0.896856i
$577$	−10.8649	−	18.8186i	−0.452312	−	0.783428i	0.546217	−	0.837644i	$-0.316067\pi$
$577$	−10.8649	−	18.8186i	−0.452312	−	0.783428i	−0.998529	+	0.0542160i	$0.982734\pi$
$578$	1.49722	+	10.9887i	0.0622763	+	0.457071i
$579$	−2.42601	−	7.20979i	−0.100821	−	0.299629i
$580$	−3.29429	+	0.914679i	−0.136788	+	0.0379800i
$581$	−6.59378	−	7.85816i	−0.273556	−	0.326011i
$582$	12.4947	−	28.5400i	0.517924	−	1.18302i
$583$	9.62607	+	26.4474i	0.398671	+	1.09534i
$584$	−45.5654	−	5.37171i	−1.88551	−	0.222283i
$585$	10.1536	+	13.3793i	0.419799	+	0.553165i
$586$	−10.9420	+	12.0499i	−0.452010	+	0.497778i
$587$	7.17040	−	40.6654i	0.295954	−	1.67844i	−0.367344	−	0.930085i	$-0.619733\pi$
$587$	7.17040	−	40.6654i	0.295954	−	1.67844i	0.663298	−	0.748355i	$-0.269156\pi$
$588$	−8.50122	+	17.5193i	−0.350584	+	0.722484i
$589$	42.2709	+	15.3854i	1.74174	+	0.633943i
$590$	−0.137187	+	3.50539i	−0.00564790	+	0.144314i
$591$	−1.39383	−	0.546309i	−0.0573347	−	0.0224721i
$592$	0.710228	+	39.3033i	0.0291902	+	1.61536i
$593$		−	15.5861i		−	0.640045i	−0.947410	−	0.320022i	$-0.896310\pi$
$593$		−	15.5861i		−	0.640045i	0.947410	−	0.320022i	$-0.103690\pi$
$594$	−2.50423	+	22.1555i	−0.102750	+	0.909049i
$595$			5.85218i			0.239916i
$596$	10.7010	−	5.10813i	0.438328	−	0.209237i
$597$	−29.7058	+	23.7117i	−1.21578	+	0.970455i
$598$	−55.0639	−	2.15499i	−2.25173	−	0.0881239i
$599$	−4.77060	−	1.73635i	−0.194921	−	0.0709455i	0.242715	−	0.970098i	$-0.421962\pi$
$599$	−4.77060	−	1.73635i	−0.194921	−	0.0709455i	−0.437636	+	0.899152i	$0.644184\pi$
$600$	0.692481	−	4.84979i	0.0282704	−	0.197992i
$601$	4.61643	−	26.1811i	0.188308	−	1.06795i	−0.733323	−	0.679881i	$-0.762031\pi$
$601$	4.61643	−	26.1811i	0.188308	−	1.06795i	0.921631	−	0.388068i	$-0.126857\pi$
$602$	5.37014	+	4.87639i	0.218871	+	0.198747i
$603$	−7.49084	−	4.82845i	−0.305050	−	0.196630i
$604$	−17.4932	+	1.68984i	−0.711790	+	0.0687586i
$605$	0.613512	+	1.68561i	0.0249428	+	0.0685298i
$606$	15.6285	−	11.5039i	0.634863	−	0.467314i
$607$	28.1110	+	33.5014i	1.14099	+	1.35978i	0.923445	+	0.383732i	$0.125361\pi$
$607$	28.1110	+	33.5014i	1.14099	+	1.35978i	0.217548	+	0.976050i	$0.430194\pi$
$608$	42.0297	+	16.3073i	1.70453	+	0.661346i
$609$	−2.29917	+	2.60767i	−0.0931672	+	0.105668i
$610$	−10.1375	+	1.38124i	−0.410456	+	0.0559250i
$611$	7.63656	+	13.2269i	0.308942	+	0.535104i
$612$	−16.1614	−	25.1619i	−0.653287	−	1.01711i
$613$	−6.03227	+	10.4482i	−0.243641	+	0.421998i	−0.961749	−	0.273934i	$-0.911675\pi$
$613$	−6.03227	+	10.4482i	−0.243641	+	0.421998i	0.718108	+	0.695932i	$0.245008\pi$
$614$	−12.3972	+	30.3162i	−0.500312	+	1.22346i
$615$	−9.17015	+	4.99920i	−0.369776	+	0.201587i
$616$	−5.52877	−	8.42429i	−0.222760	−	0.339424i
$617$	24.7488	−	4.36389i	0.996351	−	0.175683i	0.348384	−	0.937352i	$-0.386731\pi$
$617$	24.7488	−	4.36389i	0.996351	−	0.175683i	0.647967	+	0.761669i	$0.275620\pi$
$618$	−12.3444	−	24.9153i	−0.496564	−	1.00224i
$619$	26.8388	−	31.9852i	1.07874	−	1.28559i	0.122675	−	0.992447i	$-0.460853\pi$
$619$	26.8388	−	31.9852i	1.07874	−	1.28559i	0.956067	−	0.293148i	$-0.0947029\pi$
$620$	−10.2740	−	4.67830i	−0.412612	−	0.187885i
$621$	−21.1510	−	29.3347i	−0.848760	−	1.17716i
$622$	0.564517	−	2.60194i	0.0226351	−	0.104328i
$623$	−0.506082	−	0.424653i	−0.0202757	−	0.0170134i
$624$	36.5334	−	13.0325i	1.46251	−	0.521717i
$625$	0.173648	+	0.984808i	0.00694593	+	0.0393923i
$626$	3.90340	−	6.18862i	0.156011	−	0.247347i
$627$	41.8700	+	1.02512i	1.67213	+	0.0409395i
$628$	13.3318	−	19.4107i	0.531997	−	0.774570i
$629$	−42.4194	−	24.4908i	−1.69137	−	0.976513i
$630$	−2.10163	−	4.51648i	−0.0837310	−	0.179941i
$631$	9.21688	−	5.32137i	0.366918	−	0.211840i	−0.305193	−	0.952290i	$-0.598721\pi$
$631$	9.21688	−	5.32137i	0.366918	−	0.211840i	0.672111	+	0.740450i	$0.265388\pi$
$632$	6.29721	+	1.89208i	0.250490	+	0.0752628i
$633$	−3.97247	+	19.6968i	−0.157892	+	0.782878i
$634$	−2.05862	+	1.08349i	−0.0817581	+	0.0430311i
$635$	2.23481	−	1.87523i	0.0886857	−	0.0744161i
$636$	31.9634	+	3.29458i	1.26743	+	0.130639i
$637$	29.5739	−	10.7640i	1.17176	−	0.426486i
$638$	2.23732	+	6.98570i	0.0885765	+	0.276567i
$639$	28.2607	+	26.1744i	1.11798	+	1.03544i
$640$	−10.1955	−	4.90421i	−0.403013	−	0.193856i
$641$	−14.0779	−	2.48232i	−0.556045	−	0.0980457i	−0.111438	−	0.993771i	$-0.535546\pi$
$641$	−14.0779	−	2.48232i	−0.556045	−	0.0980457i	−0.444607	+	0.895726i	$0.646657\pi$
$642$	28.6164	−	30.0043i	1.12940	−	1.18418i
$643$	2.79875	−	7.68950i	0.110372	−	0.303244i	−0.872194	−	0.489161i	$-0.837303\pi$
$643$	2.79875	−	7.68950i	0.110372	−	0.303244i	0.982566	+	0.185917i	$0.0595254\pi$
$644$	15.8247	+	4.08734i	0.623579	+	0.161064i
$645$	7.48133	−	1.13111i	0.294577	−	0.0445373i
$646$	−44.4114	+	34.3979i	−1.74734	+	1.35337i
$647$	−4.68724			−0.184275			−0.0921373	−	0.995746i	$-0.529370\pi$
$647$	−4.68724			−0.184275			−0.0921373	+	0.995746i	$0.529370\pi$
$648$	21.5089	+	13.6150i	0.844948	+	0.534849i
$649$	7.52651			0.295441
$650$	−6.25965	+	4.84828i	−0.245524	+	0.190165i
$651$	−11.3501	+	1.71604i	−0.444847	+	0.0672568i
$652$	−4.71195	−	1.21705i	−0.184534	−	0.0476633i
$653$	−13.6916	+	37.6172i	−0.535792	+	1.47208i	0.316287	+	0.948664i	$0.397564\pi$
$653$	−13.6916	+	37.6172i	−0.535792	+	1.47208i	−0.852079	+	0.523413i	$0.824658\pi$
$654$	−4.64625	+	4.87159i	−0.181683	+	0.190494i
$655$	−12.6695	−	2.23398i	−0.495040	−	0.0872888i
$656$	4.61690	+	23.6741i	0.180260	+	0.924319i
$657$	−10.7856	+	47.4538i	−0.420788	+	1.85135i
$658$	−1.38166	−	4.31403i	−0.0538628	−	0.168178i
$659$	−28.5553	+	10.3933i	−1.11236	+	0.404865i	−0.831857	−	0.554989i	$-0.812722\pi$
$659$	−28.5553	+	10.3933i	−1.11236	+	0.404865i	−0.280499	+	0.959854i	$0.590500\pi$
$660$	−10.4553	−	1.07766i	−0.406972	−	0.0419480i
$661$	12.5749	−	10.5516i	0.489107	−	0.410409i	−0.364599	−	0.931165i	$-0.618794\pi$
$661$	12.5749	−	10.5516i	0.489107	−	0.410409i	0.853706	+	0.520755i	$0.174350\pi$
$662$	−32.1244	+	16.9078i	−1.24855	+	0.657139i
$663$	−9.55525	+	47.3780i	−0.371095	+	1.84001i
$664$	−7.11065	+	23.6657i	−0.275947	+	0.918406i
$665$	−8.10376	+	4.67871i	−0.314251	+	0.181433i
$666$	41.5327	+	3.66741i	1.60936	+	0.142109i
$667$	−10.3037	−	5.94884i	−0.398961	−	0.230340i
$668$	5.50949	−	8.02164i	0.213169	−	0.310367i
$669$	28.0265	+	0.686188i	1.08357	+	0.0265296i
$670$	2.24129	−	3.55344i	0.0865887	−	0.137281i
$671$	3.81173	+	21.6174i	0.147150	+	0.834530i
$672$	−11.4087	+	1.48002i	−0.440100	+	0.0570929i
$673$	20.0439	+	16.8188i	0.772634	+	0.648317i	0.941382	−	0.337342i	$-0.109528\pi$
$673$	20.0439	+	16.8188i	0.772634	+	0.648317i	−0.168748	+	0.985659i	$0.553972\pi$
$674$	7.10527	−	32.7492i	0.273685	−	1.26145i
$675$	−5.03722	−	1.27532i	−0.193883	−	0.0490871i
$676$	−33.3902	−	15.2044i	−1.28424	−	0.584784i
$677$	24.0741	−	28.6903i	0.925241	−	1.10266i	−0.0692248	−	0.997601i	$-0.522053\pi$
$677$	24.0741	−	28.6903i	0.925241	−	1.10266i	0.994466	−	0.105058i	$-0.0335030\pi$
$678$	0.606040	+	1.22320i	0.0232748	+	0.0469768i
$679$	14.7072	−	2.59328i	0.564412	−	0.0995211i
$680$	11.7859	−	7.73494i	0.451968	−	0.296621i
$681$	13.0818	−	7.13167i	0.501295	−	0.273286i
$682$	−9.16754	+	22.4183i	−0.351043	+	0.858441i
$683$	25.6637	−	44.4508i	0.981994	−	1.70086i	0.327394	−	0.944888i	$-0.393829\pi$
$683$	25.6637	−	44.4508i	0.981994	−	1.70086i	0.654600	−	0.755976i	$-0.272837\pi$
$684$	21.9220	−	42.4959i	0.838207	−	1.62487i
$685$	1.94508	+	3.36898i	0.0743178	+	0.128722i
$686$	−20.7659	+	2.82937i	−0.792847	+	0.108026i
$687$	−10.8876	+	12.3485i	−0.415389	+	0.471125i
$688$	2.72288	−	17.2603i	0.103809	−	0.658042i
$689$	−33.3814	−	39.7824i	−1.27173	−	1.51559i
$690$	13.7297	−	10.1063i	0.522682	−	0.384739i
$691$	13.3964	+	36.8063i	0.509623	+	1.40018i	0.881627	+	0.471946i	$0.156448\pi$
$691$	13.3964	+	36.8063i	0.509623	+	1.40018i	−0.372004	+	0.928231i	$0.621329\pi$
$692$	10.5847	−	1.02247i	0.402369	−	0.0388686i
$693$	−9.50629	+	4.88451i	−0.361114	+	0.185547i
$694$	20.6544	+	18.7553i	0.784030	+	0.711943i
$695$	−2.75554	+	15.6275i	−0.104524	+	0.592784i
$696$	8.29051	+	1.18377i	0.314251	+	0.0448705i
$697$	−28.2422	−	10.2793i	−1.06975	−	0.389357i
$698$	9.58009	+	0.374927i	0.362612	+	0.0141912i
$699$	9.84381	−	7.85750i	0.372327	−	0.297198i
$700$	2.11923	−	1.01162i	0.0800995	−	0.0382358i
$701$			7.79342i			0.294353i	0.989110	+	0.147177i	$0.0470186\pi$
$701$			7.79342i			0.294353i	−0.989110	+	0.147177i	$0.952981\pi$
$702$	−9.64001	−	39.9959i	−0.363839	−	1.50955i
$703$		−	78.3199i		−	2.95389i
$704$	−9.65845	+	22.2691i	−0.364016	+	0.839297i
$705$	−4.39923	−	1.72426i	−0.165684	−	0.0649394i
$706$	1.08758	−	27.7897i	0.0409316	−	1.04588i
$707$	8.74115	+	3.18152i	0.328745	+	0.119653i
$708$	3.75139	−	7.73087i	0.140986	−	0.290544i
$709$	−2.00005	+	11.3428i	−0.0751133	+	0.425989i	0.923942	+	0.382533i	$0.124948\pi$
$709$	−2.00005	+	11.3428i	−0.0751133	+	0.425989i	−0.999055	+	0.0434563i	$0.986163\pi$
$710$	−12.2070	+	13.4430i	−0.458121	+	0.504508i
$711$	2.70317	−	6.42900i	0.101377	−	0.241106i
$712$	−0.186323	+	1.58048i	−0.00698276	+	0.0592311i
$713$	−13.4363	−	36.9160i	−0.503194	−	1.38251i
$714$	5.74897	−	13.1315i	0.215150	−	0.491436i
$715$	10.9191	+	13.0129i	0.408353	+	0.486656i
$716$	−6.97370	+	1.93629i	−0.260619	+	0.0723625i
$717$	−1.19329	−	3.54631i	−0.0445643	−	0.132439i
$718$	−1.83946	−	13.5006i	−0.0686480	−	0.503836i
$719$	−7.66981	−	13.2845i	−0.286036	−	0.495428i	0.686824	−	0.726824i	$-0.259004\pi$
$719$	−7.66981	−	13.2845i	−0.286036	−	0.495428i	−0.972860	+	0.231395i	$0.925671\pi$
$720$	−6.31809	+	10.2020i	−0.235461	+	0.380208i
$721$	6.66426	−	11.5428i	0.248190	−	0.429878i
$722$	−58.2674	−	23.8274i	−2.16849	−	0.886763i
$723$	13.8008	+	8.42487i	0.513256	+	0.313324i
$724$	−32.5116	−	31.9294i	−1.20828	−	1.18665i
$725$	−1.68349	+	0.296844i	−0.0625232	+	0.0110245i
$726$	0.279239	−	4.38499i	0.0103635	−	0.162742i
$727$	−9.49776	+	11.3190i	−0.352252	+	0.419798i	−0.912853	−	0.408288i	$-0.866126\pi$
$727$	−9.49776	+	11.3190i	−0.352252	+	0.419798i	0.560601	+	0.828086i	$0.310570\pi$
$728$	14.9029	+	11.1178i	0.552337	+	0.412053i
$729$	16.7766	−	21.1553i	0.621355	−	0.783529i
$730$	−22.4189	−	4.86401i	−0.829761	−	0.180025i
$731$	16.6791	+	13.9954i	0.616900	+	0.517640i
$732$	24.1042	+	6.85939i	0.890917	+	0.253530i
$733$	3.24395	+	18.3973i	0.119818	+	0.679521i	0.984251	+	0.176774i	$0.0565662\pi$
$733$	3.24395	+	18.3973i	0.119818	+	0.679521i	−0.864434	+	0.502747i	$0.832323\pi$
$734$	−2.39338	−	1.50959i	−0.0883411	−	0.0557201i
$735$	−5.07317	+	8.31037i	−0.187127	+	0.306533i
$736$	−12.6841	−	37.2721i	−0.467543	−	1.37387i
$737$	−7.80607	−	4.50684i	−0.287540	−	0.166012i
$738$	25.4877	−	2.20916i	0.938214	−	0.0813203i
$739$	−19.7389	+	11.3963i	−0.726107	+	0.419218i	−0.816996	−	0.576643i	$-0.804362\pi$
$739$	−19.7389	+	11.3963i	−0.726107	+	0.419218i	0.0908895	+	0.995861i	$0.471029\pi$
$740$	−1.53608	+	19.5948i	−0.0564673	+	0.720317i
$741$	−73.2456	+	24.6463i	−2.69074	+	0.905404i
$742$	7.17381	+	13.6301i	0.263359	+	0.500376i
$743$	−21.1827	+	17.7744i	−0.777119	+	0.652081i	−0.942521	−	0.334146i	$-0.891552\pi$
$743$	−21.1827	+	17.7744i	−0.777119	+	0.652081i	0.165402	+	0.986226i	$0.447108\pi$
$744$	18.4577	+	20.5903i	0.676691	+	0.754876i
$745$	5.57126	−	2.02777i	0.204115	−	0.0742919i
$746$	15.1134	−	4.84039i	0.553340	−	0.177219i
$747$	24.1609	+	10.1588i	0.884003	+	0.371692i
$748$	−17.5713	−	24.6181i	−0.642472	−	0.900127i
$749$	19.5730	+	3.45125i	0.715182	+	0.126106i
$750$	0.577794	−	2.38037i	0.0210981	−	0.0869188i
$751$	8.29466	−	22.7894i	0.302676	−	0.831597i	−0.691356	−	0.722514i	$-0.742986\pi$
$751$	8.29466	−	22.7894i	0.302676	−	0.831597i	0.994033	−	0.109083i	$-0.0347913\pi$
$752$	−6.86198	+	8.48450i	−0.250230	+	0.309398i
$753$	−17.8397	+	45.5157i	−0.650116	+	1.65869i
$754$	−8.28792	−	10.7006i	−0.301828	−	0.389693i
$755$	−8.78734			−0.319804
$756$	0.278975	+	12.1990i	0.0101462	+	0.443672i
$757$	−31.2490			−1.13576			−0.567882	−	0.823110i	$-0.692237\pi$
$757$	−31.2490			−1.13576			−0.567882	+	0.823110i	$0.692237\pi$
$758$	2.92961	+	3.78244i	0.106408	+	0.137384i
$759$	−22.8182	−	28.5865i	−0.828249	−	1.03762i
$760$	20.1335	+	10.1365i	0.730318	+	0.367688i
$761$	7.08591	−	19.4684i	0.256864	−	0.705728i	−0.742492	−	0.669854i	$-0.766356\pi$
$761$	7.08591	−	19.4684i	0.256864	−	0.705728i	0.999356	−	0.0358734i	$-0.0114213\pi$
$762$	−6.85678	+	2.01238i	−0.248395	+	0.0729007i
$763$	−3.17794	−	0.560356i	−0.115049	−	0.0202863i
$764$	−15.7547	+	11.2450i	−0.569983	+	0.406830i
$765$	−6.83360	−	13.2996i	−0.247069	−	0.480849i
$766$	51.3661	−	16.4511i	1.85593	−	0.594404i
$767$	−13.0503	+	4.74991i	−0.471218	+	0.171509i
$768$	18.0597	+	21.0201i	0.651674	+	0.758499i
$769$	−34.8781	+	29.2662i	−1.25774	+	1.05537i	−0.261816	+	0.965118i	$0.584321\pi$
$769$	−34.8781	+	29.2662i	−1.25774	+	1.05537i	−0.995919	+	0.0902479i	$0.971234\pi$
$770$	−2.34657	−	4.45843i	−0.0845645	−	0.160671i
$771$	−2.88673	−	2.54523i	−0.103963	−	0.0916640i
$772$	−8.75695	−	0.686477i	−0.315170	−	0.0247068i
$773$	20.8651	−	12.0465i	0.750465	−	0.433281i	−0.0753966	−	0.997154i	$-0.524022\pi$
$773$	20.8651	−	12.0465i	0.750465	−	0.433281i	0.825862	+	0.563872i	$0.190689\pi$
$774$	−17.8983	−	4.81132i	−0.643341	−	0.172939i
$775$	−4.88827	−	2.82224i	−0.175592	−	0.101378i
$776$	−24.6615	−	26.1917i	−0.885297	−	0.940229i
$777$	9.56635	+	17.5478i	0.343191	+	0.629522i
$778$	5.10152	+	3.21772i	0.182898	+	0.115361i
$779$	−8.34490	−	47.3263i	−0.298987	−	1.69564i
$780$	18.8086	−	4.72967i	0.673456	−	0.169349i
$781$	29.8439	+	25.0420i	1.06790	+	0.896074i
$782$	47.9429	+	10.4017i	1.71443	+	0.371964i
$783$	2.18011	−	8.61091i	0.0779106	−	0.307729i
$784$	14.7622	+	16.9609i	0.527222	+	0.605747i
$785$	7.56820	−	9.01943i	0.270121	−	0.321917i
$786$	26.2342	+	17.4588i	0.935744	+	0.622736i
$787$	20.2913	−	3.57790i	0.723307	−	0.127539i	0.200138	−	0.979768i	$-0.435861\pi$
$787$	20.2913	−	3.57790i	0.723307	−	0.127539i	0.523169	+	0.852229i	$0.324750\pi$
$788$	−1.21126	+	1.23335i	−0.0431494	+	0.0439362i
$789$	0.258560	−	10.5606i	0.00920499	−	0.375967i
$790$	3.04305	+	1.24440i	0.108267	+	0.0442738i
$791$	−0.327178	+	0.566690i	−0.0116331	+	0.0201492i
$792$	22.4017	+	12.6890i	0.796009	+	0.450885i
$793$	−20.2517	−	35.0770i	−0.719159	−	1.24562i
$794$	−0.133782	−	0.981879i	−0.00474774	−	0.0348456i
$795$	15.7493	+	3.17633i	0.558569	+	0.112653i
$796$	11.7418	+	42.2891i	0.416177	+	1.49890i
$797$	−13.5810	−	16.1852i	−0.481062	−	0.573308i	0.469859	−	0.882742i	$-0.344305\pi$
$797$	−13.5810	−	16.1852i	−0.481062	−	0.573308i	−0.950921	+	0.309434i	$0.899860\pi$
$798$	22.7800	−	2.53759i	0.806403	−	0.0898297i
$799$	−4.65042	−	12.7769i	−0.164520	−	0.452015i
$800$	−4.83837	−	2.93091i	−0.171062	−	0.103623i
$801$	1.64598	+	0.374111i	0.0581580	+	0.0132186i
$802$	12.9946	−	14.3103i	0.458854	−	0.505315i
$803$	−8.54670	+	48.4707i	−0.301606	+	1.71050i
$804$	−8.51994	+	5.77171i	−0.300475	+	0.203553i
$805$	7.67917	+	2.79499i	0.270655	+	0.0985104i
$806$	1.74769	−	44.6568i	0.0615598	−	1.57297i
$807$	3.05835	+	20.2284i	0.107659	+	0.712075i
$808$	−5.14599	−	21.8091i	−0.181035	−	0.767242i
$809$		−	24.8874i		−	0.874996i	−0.899219	−	0.437498i	$-0.855865\pi$
$809$		−	24.8874i		−	0.874996i	0.899219	−	0.437498i	$-0.144135\pi$
$810$	10.0500	+	7.81003i	0.353123	+	0.274417i
$811$			40.3830i			1.41804i	0.705188	+	0.709020i	$0.250862\pi$
$811$			40.3830i			1.41804i	−0.705188	+	0.709020i	$0.749138\pi$
$812$	1.72933	+	3.62274i	0.0606875	+	0.127133i
$813$	−0.173568	−	1.14801i	−0.00608730	−	0.0402624i
$814$	42.1370	+	1.64908i	1.47690	+	0.0578001i
$815$	−2.28655	−	0.832236i	−0.0800944	−	0.0291520i
$816$	−34.0445	+	5.77820i	−1.19180	+	0.202277i
$817$	−6.04544	+	34.2854i	−0.211503	+	1.19949i
$818$	6.89389	+	6.26003i	0.241039	+	0.218877i
$819$	13.4005	−	14.4686i	0.468250	−	0.505574i
$820$	1.15960	+	12.0042i	0.0404949	+	0.419204i
$821$	8.86004	+	24.3428i	0.309217	+	0.849568i	0.992810	+	0.119704i	$0.0381945\pi$
$821$	8.86004	+	24.3428i	0.309217	+	0.849568i	−0.683592	+	0.729864i	$0.739583\pi$
$822$	−1.05495	−	9.47034i	−0.0367957	−	0.330316i
$823$	17.9572	+	21.4006i	0.625950	+	0.745978i	0.982081	−	0.188458i	$-0.0603490\pi$
$823$	17.9572	+	21.4006i	0.625950	+	0.745978i	−0.356132	+	0.934436i	$0.615905\pi$
$824$	−32.0547	+	1.83504i	−1.11668	+	0.0639266i
$825$	−5.15162	−	1.03898i	−0.179356	−	0.0361728i
$826$	4.08130	−	0.556080i	0.142007	−	0.0193485i
$827$	8.11061	+	14.0480i	0.282034	+	0.488497i	0.971886	−	0.235454i	$-0.0756577\pi$
$827$	8.11061	+	14.0480i	0.282034	+	0.488497i	−0.689852	+	0.723951i	$0.742324\pi$
$828$	−40.7358	+	9.18961i	−1.41567	+	0.319361i
$829$	−15.6570	+	27.1187i	−0.543789	+	0.941871i	0.454893	+	0.890546i	$0.349678\pi$
$829$	−15.6570	+	27.1187i	−0.543789	+	0.941871i	−0.998682	+	0.0513246i	$0.983656\pi$
$830$	−4.67660	+	11.4362i	−0.162327	+	0.396955i
$831$	0.304667	−	12.4438i	0.0105688	−	0.431669i
$832$	2.69304	−	44.7079i	0.0933645	−	1.54997i
$833$	−27.5922	+	4.86525i	−0.956014	+	0.168571i
$834$	21.5349	−	32.3591i	0.745694	−	1.12050i
$835$	3.12763	−	3.72736i	0.108236	−	0.128991i
$836$	20.0418	−	44.0135i	0.693159	−	1.52224i
$837$	23.7904	−	17.1534i	0.822318	−	0.592909i
$838$	−4.31109	+	19.8704i	−0.148924	+	0.686411i
$839$	20.5964	+	17.2824i	0.711066	+	0.596655i	0.924898	−	0.380215i	$-0.124150\pi$
$839$	20.5964	+	17.2824i	0.711066	+	0.596655i	−0.213832	+	0.976870i	$0.568595\pi$
$840$	−5.74907	+	0.188096i	−0.198362	+	0.00648992i
$841$	4.52835	+	25.6816i	0.156150	+	0.885572i
$842$	−25.0917	+	39.7815i	−0.864718	+	1.37096i
$843$	−20.8807	−	38.3019i	−0.719169	−	1.31919i
$844$	19.1253	+	13.1358i	0.658320	+	0.452153i
$845$	−15.8868	−	9.17224i	−0.546522	−	0.315535i
$846$	8.17745	+	8.19066i	0.281147	+	0.281601i
$847$	1.82401	−	1.05309i	0.0626736	−	0.0361846i
$848$	17.9683	−	32.4627i	0.617032	−	1.11477i
$849$	−1.42880	−	1.25977i	−0.0490363	−	0.0432351i
$850$	6.23750	−	3.28293i	0.213944	−	0.112604i
$851$	−52.3960	+	43.9655i	−1.79611	+	1.50712i
$852$	40.5969	−	18.1727i	1.39083	−	0.622587i
$853$	23.2693	−	8.46932i	0.796724	−	0.289984i	0.0885960	−	0.996068i	$-0.471762\pi$
$853$	23.2693	−	8.46932i	0.796724	−	0.289984i	0.708128	+	0.706084i	$0.249540\pi$
$854$	3.66409	+	11.4405i	0.125382	+	0.391487i
$855$	12.9532	−	20.0956i	0.442991	−	0.687254i
$856$	−18.9194	−	43.9802i	−0.646653	−	1.50321i
$857$	−51.7986	−	9.13349i	−1.76941	−	0.311994i	−0.808423	−	0.588602i	$-0.799679\pi$
$857$	−51.7986	−	9.13349i	−1.76941	−	0.311994i	−0.960983	+	0.276607i	$0.910790\pi$
$858$	−11.7177	−	39.9259i	−0.400037	−	1.36305i
$859$	8.98827	−	24.6951i	0.306676	−	0.842585i	−0.686623	−	0.727013i	$-0.740908\pi$
$859$	8.98827	−	24.6951i	0.306676	−	0.842585i	0.993299	−	0.115572i	$-0.0368699\pi$
$860$	2.18494	−	8.45925i	0.0745057	−	0.288458i
$861$	7.65035	+	9.58429i	0.260723	+	0.326632i
$862$	10.8867	−	8.43202i	0.370801	−	0.287196i
$863$	3.54545			0.120689			0.0603443	−	0.998178i	$-0.480780\pi$
$863$	3.54545			0.120689			0.0603443	+	0.998178i	$0.480780\pi$
$864$	24.1991	−	16.6854i	0.823270	−	0.567650i
$865$	5.31697			0.180782
$866$	8.41000	−	6.51378i	0.285783	−	0.221347i
$867$	4.95659	−	12.6461i	0.168335	−	0.429484i
$868$	−3.31483	+	12.8338i	−0.112513	+	0.435607i
$869$	2.41248	−	6.62824i	0.0818378	−	0.224848i
$870$	4.06914	+	0.987715i	0.137957	+	0.0334867i
$871$	16.3792	+	2.88810i	0.554989	+	0.0978596i
$872$	3.07182	+	7.14077i	0.104025	+	0.241817i
$873$	−30.3954	+	23.0671i	−1.02873	+	0.780704i
$874$	23.9258	+	74.7045i	0.809301	+	2.52692i
$875$	1.10334	−	0.401584i	0.0372998	−	0.0135760i
$876$	45.5269	+	32.9377i	1.53821	+	1.11286i
$877$	28.1647	−	23.6330i	0.951055	−	0.798030i	−0.0284196	−	0.999596i	$-0.509047\pi$
$877$	28.1647	−	23.6330i	0.951055	−	0.798030i	0.979475	+	0.201566i	$0.0646030\pi$
$878$	−20.7252	+	10.9081i	−0.699442	+	0.368132i
$879$	18.8937	−	6.35752i	0.637270	−	0.214434i
$880$	−5.87746	+	10.6186i	−0.198129	+	0.357953i
$881$	−30.8554	+	17.8144i	−1.03955	+	0.600182i	−0.919705	−	0.392611i	$-0.871572\pi$
$881$	−30.8554	+	17.8144i	−1.03955	+	0.600182i	−0.119841	+	0.992793i	$0.538239\pi$
$882$	19.5473	−	13.6637i	0.658193	−	0.460081i
$883$	−28.3376	−	16.3607i	−0.953637	−	0.550582i	−0.0594280	−	0.998233i	$-0.518928\pi$
$883$	−28.3376	−	16.3607i	−0.953637	−	0.550582i	−0.894209	+	0.447650i	$0.852261\pi$
$884$	46.0033	+	31.5964i	1.54726	+	1.06270i
$885$	2.23867	−	3.66717i	0.0752522	−	0.123271i
$886$	−8.84225	+	14.0189i	−0.297061	+	0.470974i
$887$	5.90617	+	33.4955i	0.198310	+	1.12467i	0.907626	+	0.419780i	$0.137893\pi$
$887$	5.90617	+	33.4955i	0.198310	+	1.12467i	−0.709316	+	0.704890i	$0.750996\pi$
$888$	22.6959	−	42.4591i	0.761625	−	1.42484i
$889$	−2.62401	−	2.20180i	−0.0880063	−	0.0738461i
$890$	−0.168713	+	0.777623i	−0.00565528	+	0.0260660i
$891$	15.9003	−	22.2010i	0.532679	−	0.743761i
$892$	13.4154	−	29.4613i	0.449179	−	0.986438i
$893$	13.9748	−	16.6546i	0.467650	−	0.557324i
$894$	−14.4932	−	0.922937i	−0.484726	−	0.0308676i
$895$	−3.56378	+	0.628391i	−0.119124	+	0.0210048i
$896$	−3.59205	+	12.7891i	−0.120002	+	0.427255i
$897$	57.6053	+	35.1659i	1.92339	+	1.17416i
$898$	−7.34020	+	17.9497i	−0.244946	+	0.598990i
$899$	4.82450	−	8.35629i	0.160906	−	0.278698i
$900$	−3.63488	+	4.77364i	−0.121163	+	0.159121i
$901$	23.1164	+	40.0388i	0.770119	+	1.33389i
$902$	25.6378	−	3.49317i	0.853645	−	0.116310i
$903$	−2.83328	−	8.42015i	−0.0942856	−	0.280205i
$904$	1.57371	−	0.0900902i	0.0523408	−	0.00299636i
$905$	−14.6454	−	17.4537i	−0.486830	−	0.580182i
$906$	19.7177	+	8.63235i	0.655075	+	0.286791i
$907$	8.63317	+	23.7195i	0.286660	+	0.787591i	0.996528	+	0.0832570i	$0.0265322\pi$
$907$	8.63317	+	23.7195i	0.286660	+	0.787591i	−0.709868	+	0.704334i	$0.751246\pi$
$908$	−1.65424	−	17.1247i	−0.0548978	−	0.568303i
$909$	−23.5801	+	2.97675i	−0.782103	+	0.0987327i
$910$	6.88241	+	6.24961i	0.228150	+	0.207172i
$911$	9.08545	−	51.5262i	0.301014	−	1.70714i	−0.340681	−	0.940179i	$-0.610658\pi$
$911$	9.08545	−	51.5262i	0.301014	−	1.70714i	0.641696	−	0.766959i	$-0.278231\pi$
$912$	−35.2193	−	42.5233i	−1.16623	−	1.40809i
$913$	24.9097	+	9.06639i	0.824391	+	0.300054i
$914$	2.15645	+	0.0843949i	0.0713290	+	0.00279154i
$915$	11.6665	+	4.57264i	0.385682	+	0.151167i
$916$	8.18916	+	17.1553i	0.270577	+	0.566828i
$917$			15.1054i			0.498826i
$918$	2.26866	+	36.5557i	0.0748770	+	1.20652i
$919$			30.8422i			1.01739i	0.860947	+	0.508695i	$0.169872\pi$
$919$			30.8422i			1.01739i	−0.860947	+	0.508695i	$0.830128\pi$
$920$	−4.52079	−	19.1595i	−0.149046	−	0.631670i
$921$	31.3511	−	25.0250i	1.03306	−	0.824603i
$922$	2.18284	−	55.7756i	0.0718879	−	1.83687i
$923$	−67.5504	−	24.5863i	−2.22345	−	0.809269i
$924$	0.885605	+	12.3093i	0.0291343	+	0.404947i
$925$	−1.70652	+	9.67813i	−0.0561099	+	0.318215i
$926$	34.0805	−	37.5313i	1.11995	−	1.23335i
$927$	−1.66657	+	34.0140i	−0.0547372	+	1.11717i
$928$	5.01026	−	8.27098i	0.164470	−	0.271508i
$929$	−14.1109	−	38.7694i	−0.462964	−	1.27198i	−0.923246	−	0.384209i	$-0.874474\pi$
$929$	−14.1109	−	38.7694i	−0.462964	−	1.27198i	0.460283	−	0.887772i	$-0.347748\pi$
$930$	8.19618	+	11.1348i	0.268763	+	0.365125i
$931$	−28.7966	−	34.3184i	−0.943770	−	1.12474i
$932$	−3.89096	−	14.0136i	−0.127453	−	0.459032i
$933$	−2.15654	+	2.44590i	−0.0706021	+	0.0800753i
$934$	−2.50627	−	18.3946i	−0.0820078	−	0.601889i
$935$	−7.56143	−	13.0968i	−0.247285	−	0.428310i
$936$	−46.8504	−	7.86412i	−1.53135	−	0.257047i
$937$	−12.2017	+	21.1339i	−0.398612	+	0.690416i	−0.993555	−	0.113352i	$-0.963841\pi$
$937$	−12.2017	+	21.1339i	−0.398612	+	0.690416i	0.594943	+	0.803768i	$0.297175\pi$
$938$	−4.56587	−	1.86713i	−0.149081	−	0.0609639i
$939$	−7.86798	+	4.28931i	−0.256762	+	0.139976i
$940$	−3.82299	+	3.89270i	−0.124692	+	0.126966i
$941$	22.4628	−	3.96080i	0.732266	−	0.129118i	0.204932	−	0.978776i	$-0.434303\pi$
$941$	22.4628	−	3.96080i	0.732266	−	0.129118i	0.527334	+	0.849658i	$0.323192\pi$
$942$	−25.8424	+	12.8037i	−0.841992	+	0.417168i
$943$	−26.9768	+	32.1497i	−0.878486	+	1.04694i
$944$	−6.51423	−	7.48446i	−0.212020	−	0.243599i
$945$	−0.447635	+	6.08463i	−0.0145616	+	0.197933i
$946$	−18.3186	−	3.97442i	−0.595590	−	0.129219i
$947$	4.51614	+	3.78949i	0.146755	+	0.123142i	0.713209	−	0.700951i	$-0.247241\pi$
$947$	4.51614	+	3.78949i	0.146755	+	0.123142i	−0.566455	+	0.824093i	$0.691685\pi$
$948$	−5.60577	−	5.78166i	−0.182067	−	0.187780i
$949$	−15.7702	−	89.4375i	−0.511924	−	2.90326i
$950$	9.53278	+	6.01269i	0.309284	+	0.195077i
$951$	2.84832	+	0.0697369i	0.0923631	+	0.00226137i
$952$	−11.3470	−	12.0511i	−0.367759	−	0.390579i
$953$	−30.5741	−	17.6519i	−0.990391	−	0.571803i	−0.0850000	−	0.996381i	$-0.527089\pi$
$953$	−30.5741	−	17.6519i	−0.990391	−	0.571803i	−0.905391	+	0.424578i	$0.860422\pi$
$954$	−32.2190	−	22.5988i	−1.04313	−	0.731662i
$955$	−8.38144	+	4.83903i	−0.271217	+	0.156587i
$956$	−4.30732	−	0.337661i	−0.139309	−	0.0109207i
$957$	1.77610	−	8.80647i	0.0574131	−	0.284673i
$958$	−0.980460	−	1.86285i	−0.0316772	−	0.0601860i
$959$	3.49902	−	2.93603i	0.112989	−	0.0948092i
$960$	7.97747	+	11.3296i	0.257472	+	0.365662i
$961$	0.808335	−	0.294210i	0.0260753	−	0.00949064i
$962$	−74.1023	+	23.7329i	−2.38915	+	0.765179i
$963$	−48.5115	+	15.0121i	−1.56326	+	0.483760i
$964$	15.1966	−	10.8467i	0.489449	−	0.349348i
$965$	−4.32519	−	0.762647i	−0.139233	−	0.0245505i
$966$	−14.4854	−	13.8153i	−0.466060	−	0.444501i
$967$	−9.42821	+	25.9038i	−0.303191	+	0.833010i	0.690750	+	0.723094i	$0.257281\pi$
$967$	−9.42821	+	25.9038i	−0.303191	+	0.833010i	−0.993941	+	0.109916i	$0.964942\pi$
$968$	−4.53167	−	2.28153i	−0.145654	−	0.0733312i
$969$	68.0265	−	10.2850i	2.18532	−	0.330401i
$970$	−11.0144	−	14.2208i	−0.353652	−	0.456603i
$971$	−2.82903			−0.0907879			−0.0453939	−	0.998969i	$-0.514454\pi$
$971$	−2.82903			−0.0907879			−0.0453939	+	0.998969i	$0.514454\pi$
$972$	−14.8787	−	27.3975i	−0.477236	−	0.878775i
$973$	18.6321			0.597317
$974$	26.7681	+	34.5606i	0.857707	+	1.10739i
$975$	9.58812	−	1.44963i	0.307065	−	0.0464255i
$976$	18.1975	−	22.5004i	0.582489	−	0.720220i
$977$	−8.65912	+	23.7907i	−0.277030	+	0.761133i	0.720666	+	0.693283i	$0.243836\pi$
$977$	−8.65912	+	23.7907i	−0.277030	+	0.761133i	−0.997696	+	0.0678504i	$0.978386\pi$
$978$	4.31317	+	4.11366i	0.137920	+	0.131540i
$979$	1.68126	+	0.296451i	0.0537332	+	0.00947461i
$980$	6.53150	+	9.15087i	0.208641	+	0.292314i
$981$	7.87649	−	2.43742i	0.251477	−	0.0778208i
$982$	−11.5784	+	3.70823i	−0.369481	+	0.118334i
$983$	54.7300	−	19.9201i	1.74562	−	0.635352i	0.746081	−	0.665856i	$-0.231933\pi$
$983$	54.7300	−	19.9201i	1.74562	−	0.635352i	0.999535	+	0.0305036i	$0.00971109\pi$
$984$	9.19047	−	28.0750i	0.292982	−	0.894998i
$985$	−0.662119	+	0.555584i	−0.0210969	+	0.0177024i
$986$	5.61203	+	10.6627i	0.178724	+	0.339571i
$987$	−1.09683	+	5.43845i	−0.0349126	+	0.173108i
$988$	−6.97405	+	88.9635i	−0.221874	+	2.83031i
$989$	26.3306	−	15.2020i	0.837264	−	0.483395i
$990$	10.5389	+	7.39210i	0.334948	+	0.234936i
$991$	−0.591603	−	0.341562i	−0.0187929	−	0.0108501i	0.490574	−	0.871399i	$-0.336787\pi$
$991$	−0.591603	−	0.341562i	−0.0187929	−	0.0108501i	−0.509367	+	0.860549i	$0.670120\pi$
$992$	30.2276	−	10.2868i	0.959727	−	0.326607i
$993$	44.4476	+	1.08823i	1.41050	+	0.0345341i
$994$	18.0332	+	11.3743i	0.571980	+	0.360769i
$995$	3.81062	+	21.6111i	0.120805	+	0.685117i
$996$	21.7281	−	21.0671i	0.688483	−	0.667538i
$997$	−33.3998	−	28.0258i	−1.05778	−	0.887586i	−0.0638932	−	0.997957i	$-0.520352\pi$
$997$	−33.3998	−	28.0258i	−1.05778	−	0.887586i	−0.993890	+	0.110371i	$0.964796\pi$
$998$	−30.3109	−	6.57626i	−0.959475	−	0.208168i
$999$	−42.2310	−	28.7083i	−1.33613	−	0.908290i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	540.2.be.a.11.17	✓	432
4.3	odd	2	inner	540.2.be.a.11.25	yes	432
27.5	odd	18	inner	540.2.be.a.491.25	yes	432
108.59	even	18	inner	540.2.be.a.491.17	yes	432

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
540.2.be.a.11.17	✓	432	1.1	even	1	trivial
540.2.be.a.11.25	yes	432	4.3	odd	2	inner
540.2.be.a.491.17	yes	432	108.59	even	18	inner
540.2.be.a.491.25	yes	432	27.5	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 540 = 2^{2} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	540.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.11807 + 0.865978i) q^{2} +(1.71259 - 0.258927i) q^{3} +(0.500164 - 1.93645i) q^{4} +(0.342020 - 0.939693i) q^{5} +(-1.69057 + 1.77256i) q^{6} +(-1.15631 - 0.203889i) q^{7} +(1.11770 + 2.59822i) q^{8} +(2.86591 - 0.886872i) q^{9} +(0.431350 + 1.34682i) q^{10} +(2.85119 - 1.03775i) q^{11} +(0.355176 - 3.44585i) q^{12} +(-4.28879 + 3.59872i) q^{13} +(1.46940 - 0.773380i) q^{14} +(0.342427 - 1.69786i) q^{15} +(-3.49967 - 1.93709i) q^{16} +(4.31642 - 2.49209i) q^{17} +(-2.43628 + 3.47340i) q^{18} +(6.90180 + 3.98476i) q^{19} +(-1.64860 - 1.13231i) q^{20} +(-2.03308 - 0.0497770i) q^{21} +(-2.28917 + 3.62934i) q^{22} +(-1.20858 - 6.85418i) q^{23} +(2.58691 + 4.16027i) q^{24} +(-0.766044 - 0.642788i) q^{25} +(1.67876 - 7.73762i) q^{26} +(4.67849 - 2.26091i) q^{27} +(-0.973169 + 2.13717i) q^{28} +(1.09882 - 1.30952i) q^{29} +(1.08746 + 2.19487i) q^{30} +(5.55873 - 0.980155i) q^{31} +(5.59035 - 0.864839i) q^{32} +(4.61421 - 2.51549i) q^{33} +(-2.66797 + 6.52426i) q^{34} +(-0.587076 + 1.01685i) q^{35} +(-0.283954 - 5.99328i) q^{36} +(-4.91372 - 8.51081i) q^{37} +(-11.1674 + 1.52157i) q^{38} +(-6.41312 + 7.27361i) q^{39} +(2.82380 - 0.161654i) q^{40} +(-3.87603 - 4.61927i) q^{41} +(2.31624 - 1.70495i) q^{42} +(1.49409 + 4.10499i) q^{43} +(-0.583483 - 6.04023i) q^{44} +(0.146813 - 2.99641i) q^{45} +(7.28684 + 6.61686i) q^{46} +(0.473716 - 2.68657i) q^{47} +(-6.49506 - 2.41127i) q^{48} +(-5.28236 - 1.92262i) q^{49} +(1.41313 + 0.0553044i) q^{50} +(6.74698 - 5.38556i) q^{51} +(4.82364 + 10.1050i) q^{52} +9.27592i q^{53} +(-3.27299 + 6.57933i) q^{54} -3.03417i q^{55} +(-0.762667 - 3.23225i) q^{56} +(12.8517 + 5.03718i) q^{57} +(-0.0945406 + 2.41569i) q^{58} +(2.33098 + 0.848408i) q^{59} +(-3.11656 - 1.51230i) q^{60} +(-1.25627 + 7.12463i) q^{61} +(-5.36626 + 5.90962i) q^{62} +(-3.49472 + 0.441173i) q^{63} +(-5.50148 + 5.80807i) q^{64} +(1.91484 + 5.26098i) q^{65} +(-2.98066 + 6.80830i) q^{66} +(-1.90954 - 2.27570i) q^{67} +(-2.66688 - 9.60499i) q^{68} +(-3.84453 - 11.4254i) q^{69} +(-0.224173 - 1.64530i) q^{70} +(6.41995 + 11.1197i) q^{71} +(5.50753 + 6.45501i) q^{72} +(-8.11069 + 14.0481i) q^{73} +(12.8641 + 5.26051i) q^{74} +(-1.47835 - 0.902480i) q^{75} +(11.1683 - 11.3720i) q^{76} +(-3.50846 + 0.618636i) q^{77} +(0.871535 - 13.6860i) q^{78} +(1.49431 - 1.78084i) q^{79} +(-3.01722 + 2.62609i) q^{80} +(7.42692 - 5.08340i) q^{81} +(8.33386 + 1.80812i) q^{82} +(6.69262 + 5.61578i) q^{83} +(-1.11327 + 3.91206i) q^{84} +(-0.865493 - 4.90845i) q^{85} +(-5.22533 - 3.29581i) q^{86} +(1.54275 - 2.52718i) q^{87} +(5.88308 + 6.24812i) q^{88} +(0.487273 + 0.281327i) q^{89} +(2.43067 + 3.47733i) q^{90} +(5.69293 - 3.28681i) q^{91} +(-13.8773 - 1.08787i) q^{92} +(9.26603 - 3.11791i) q^{93} +(1.79687 + 3.41401i) q^{94} +(6.10500 - 5.12270i) q^{95} +(9.35004 - 2.92861i) q^{96} +(-11.9520 + 4.35018i) q^{97} +(7.57100 - 2.42478i) q^{98} +(7.25091 - 5.50274i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 432 q + 18 q^{12} + 30 q^{14} + 30 q^{24} + 12 q^{29} - 24 q^{30} + 60 q^{33} - 60 q^{36} - 60 q^{38} + 60 q^{41} - 60 q^{42} - 72 q^{44} + 12 q^{45} - 150 q^{48} + 54 q^{52} - 84 q^{54} - 84 q^{56} - 12 q^{57}+ \cdots + 36 q^{97}+O(q^{100}) \) 432 * q + 18 * q^12 + 30 * q^14 + 30 * q^24 + 12 * q^29 - 24 * q^30 + 60 * q^33 - 60 * q^36 - 60 * q^38 + 60 * q^41 - 60 * q^42 - 72 * q^44 + 12 * q^45 - 150 * q^48 + 54 * q^52 - 84 * q^54 - 84 * q^56 - 12 * q^57 + 54 * q^58 - 198 * q^62 - 48 * q^66 - 138 * q^68 - 48 * q^69 - 84 * q^72 - 84 * q^74 - 48 * q^77 - 78 * q^78 - 66 * q^84 + 54 * q^86 - 36 * q^89 + 120 * q^92 - 54 * q^94 + 210 * q^96 + 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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