LMFDB - Embedded newform 357.2.bh.a.100.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [357,2,Mod(25,357)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(357, base_ring=CyclotomicField(24)) chi = DirichletCharacter(H, H._module([0, 16, 15])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("357.25"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 357 = 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	357.bh (of order $24$, degree $8$, 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:	$2.85065935216$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$24$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			100.11
Character	$\chi$	$=$	357.100
Dual form			357.2.bh.a.25.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.610148 + 0.163489i) q^{2} +(0.608761 - 0.793353i) q^{3} +(-1.38650 + 0.800496i) q^{4} +(-0.0694837 + 0.527781i) q^{5} +(-0.241730 + 0.583588i) q^{6} +(-2.47899 + 0.924458i) q^{7} +(1.60842 - 1.60842i) q^{8} +(-0.258819 - 0.965926i) q^{9} +(-0.0438909 - 0.333384i) q^{10} +(-2.95403 + 0.388906i) q^{11} +(-0.208971 + 1.58729i) q^{12} -7.01782i q^{13} +(1.36141 - 0.969342i) q^{14} +(0.376418 + 0.376418i) q^{15} +(0.882578 - 1.52867i) q^{16} +(-3.98218 + 1.06875i) q^{17} +(0.315836 + 0.547043i) q^{18} +(-3.45468 + 0.925679i) q^{19} +(-0.326147 - 0.787390i) q^{20} +(-0.775690 + 2.52949i) q^{21} +(1.73881 - 0.720241i) q^{22} +(-3.61497 - 4.71112i) q^{23} +(-0.296901 - 2.25518i) q^{24} +(4.55590 + 1.22075i) q^{25} +(1.14733 + 4.28191i) q^{26} +(-0.923880 - 0.382683i) q^{27} +(2.69709 - 3.26618i) q^{28} +(-6.59890 + 2.73335i) q^{29} +(-0.291211 - 0.168131i) q^{30} +(-2.37564 + 3.09599i) q^{31} +(-1.46602 + 5.47128i) q^{32} +(-1.48976 + 2.58034i) q^{33} +(2.25499 - 1.30314i) q^{34} +(-0.315662 - 1.37260i) q^{35} +(1.13207 + 1.13207i) q^{36} +(6.56759 + 0.864639i) q^{37} +(1.95653 - 1.12960i) q^{38} +(-5.56761 - 4.27218i) q^{39} +(0.737133 + 0.960650i) q^{40} +(-6.09363 - 2.52406i) q^{41} +(0.0597432 - 1.67018i) q^{42} +(0.374756 - 0.374756i) q^{43} +(3.78445 - 2.90391i) q^{44} +(0.527781 - 0.0694837i) q^{45} +(2.97588 + 2.28347i) q^{46} +(-0.462686 - 0.267132i) q^{47} +(-0.675496 - 1.63079i) q^{48} +(5.29075 - 4.58344i) q^{49} -2.97935 q^{50} +(-1.57630 + 3.80989i) q^{51} +(5.61774 + 9.73020i) q^{52} +(-0.445072 + 1.66103i) q^{53} +(0.626267 + 0.0824497i) q^{54} -1.58611i q^{55} +(-2.50033 + 5.47415i) q^{56} +(-1.36869 + 3.30430i) q^{57} +(3.57943 - 2.74659i) q^{58} +(1.39119 + 0.372768i) q^{59} +(-0.823224 - 0.220582i) q^{60} +(6.43920 - 4.94097i) q^{61} +(0.943331 - 2.27740i) q^{62} +(1.53457 + 2.15525i) q^{63} -0.0476554i q^{64} +(3.70387 + 0.487624i) q^{65} +(0.487118 - 1.81795i) q^{66} +(-2.02119 - 3.50081i) q^{67} +(4.66576 - 4.66954i) q^{68} -5.93824 q^{69} +(0.417005 + 0.785880i) q^{70} +(3.65271 + 8.81842i) q^{71} +(-1.96990 - 1.13732i) q^{72} +(-11.0176 - 8.45411i) q^{73} +(-4.14856 + 0.546168i) q^{74} +(3.74195 - 2.87130i) q^{75} +(4.04891 - 4.04891i) q^{76} +(6.96348 - 3.69497i) q^{77} +(4.09552 + 1.69642i) q^{78} +(-1.55803 - 2.03047i) q^{79} +(0.745478 + 0.572026i) q^{80} +(-0.866025 + 0.500000i) q^{81} +(4.13067 + 0.543813i) q^{82} +(6.29877 + 6.29877i) q^{83} +(-0.949350 - 4.12807i) q^{84} +(-0.287370 - 2.17598i) q^{85} +(-0.167388 + 0.289925i) q^{86} +(-1.84864 + 6.89922i) q^{87} +(-4.12579 + 5.37684i) q^{88} +(10.9606 + 6.32813i) q^{89} +(-0.310665 + 0.128682i) q^{90} +(6.48768 + 17.3971i) q^{91} +(8.78339 + 3.63820i) q^{92} +(1.01002 + 3.76944i) q^{93} +(0.325980 + 0.0873461i) q^{94} +(-0.248512 - 1.88764i) q^{95} +(3.44820 + 4.49378i) q^{96} +(5.00008 - 2.07110i) q^{97} +(-2.47880 + 3.66155i) q^{98} +(1.14021 + 2.75272i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 8 q^{5} + 8 q^{11} - 80 q^{14} + 96 q^{16} - 16 q^{17} + 16 q^{22} + 8 q^{25} - 64 q^{26} - 88 q^{28} - 40 q^{32} - 32 q^{33} - 32 q^{35} + 32 q^{37} - 64 q^{40} - 64 q^{41} - 56 q^{42} - 32 q^{43}+ \cdots - 16 q^{99}+O(q^{100}) $ 192 * q - 8 * q^5 + 8 * q^11 - 80 * q^14 + 96 * q^16 - 16 * q^17 + 16 * q^22 + 8 * q^25 - 64 * q^26 - 88 * q^28 - 40 * q^32 - 32 * q^33 - 32 * q^35 + 32 * q^37 - 64 * q^40 - 64 * q^41 - 56 * q^42 - 32 * q^43 + 32 * q^44 + 56 * q^49 + 64 * q^50 + 96 * q^52 + 64 * q^53 - 152 * q^56 - 32 * q^58 - 16 * q^59 + 40 * q^61 - 112 * q^62 + 32 * q^65 - 16 * q^67 + 48 * q^68 - 128 * q^69 - 120 * q^70 + 96 * q^71 + 8 * q^73 - 64 * q^74 - 112 * q^76 + 32 * q^77 - 16 * q^78 + 16 * q^79 + 192 * q^80 - 8 * q^82 - 16 * q^83 + 48 * q^84 - 64 * q^86 + 24 * q^87 - 136 * q^88 - 160 * q^92 + 48 * q^93 - 64 * q^94 - 104 * q^95 - 48 * q^96 - 96 * q^97 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/357\mathbb{Z}\right)^\times$.

$n$	$52$	$190$	$239$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{8}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.610148	+	0.163489i	−0.431440	+	0.115604i	−0.468002	−	0.883727i	$-0.655026\pi$
$2$	−0.610148	+	0.163489i	−0.431440	+	0.115604i	0.0365623	+	0.999331i	$0.488359\pi$
$3$	0.608761	−	0.793353i	0.351469	−	0.458043i
$3$	0.608761	−	0.793353i	0.351469	−	0.458043i
$4$	−1.38650	+	0.800496i	−0.693250	+	0.400248i
$5$	−0.0694837	+	0.527781i	−0.0310741	+	0.236031i	−0.999933	−	0.0115827i	$-0.996313\pi$
$5$	−0.0694837	+	0.527781i	−0.0310741	+	0.236031i	0.968859	+	0.247614i	$0.0796464\pi$
$6$	−0.241730	+	0.583588i	−0.0986859	+	0.238249i
$7$	−2.47899	+	0.924458i	−0.936969	+	0.349412i
$7$	−2.47899	+	0.924458i	−0.936969	+	0.349412i
$8$	1.60842	−	1.60842i	0.568661	−	0.568661i
$9$	−0.258819	−	0.965926i	−0.0862730	−	0.321975i
$10$	−0.0438909	−	0.333384i	−0.0138795	−	0.105425i
$11$	−2.95403	+	0.388906i	−0.890675	+	0.117260i	−0.561955	−	0.827168i	$-0.689951\pi$
$11$	−2.95403	+	0.388906i	−0.890675	+	0.117260i	−0.328720	+	0.944427i	$0.606617\pi$
$12$	−0.208971	+	1.58729i	−0.0603248	+	0.458212i
$13$		−	7.01782i		−	1.94639i	−0.229974	−	0.973197i	$-0.573864\pi$
$13$		−	7.01782i		−	1.94639i	0.229974	−	0.973197i	$-0.426136\pi$
$14$	1.36141	−	0.969342i	0.363852	−	0.259068i
$15$	0.376418	+	0.376418i	0.0971907	+	0.0971907i
$16$	0.882578	−	1.52867i	0.220644	−	0.382167i
$17$	−3.98218	+	1.06875i	−0.965821	+	0.259210i
$17$	−3.98218	+	1.06875i	−0.965821	+	0.259210i
$18$	0.315836	+	0.547043i	0.0744432	+	0.128939i
$19$	−3.45468	+	0.925679i	−0.792558	+	0.212365i	−0.632314	−	0.774712i	$-0.717895\pi$
$19$	−3.45468	+	0.925679i	−0.792558	+	0.212365i	−0.160244	+	0.987077i	$0.551228\pi$
$20$	−0.326147	−	0.787390i	−0.0729288	−	0.176066i
$21$	−0.775690	+	2.52949i	−0.169269	+	0.551979i
$22$	1.73881	−	0.720241i	0.370717	−	0.153556i
$23$	−3.61497	−	4.71112i	−0.753774	−	0.982337i	−0.999914	−	0.0131029i	$-0.995829\pi$
$23$	−3.61497	−	4.71112i	−0.753774	−	0.982337i	0.246140	−	0.969234i	$-0.420838\pi$
$24$	−0.296901	−	2.25518i	−0.0606046	−	0.460337i
$25$	4.55590	+	1.22075i	0.911181	+	0.244150i
$26$	1.14733	+	4.28191i	0.225011	+	0.839751i
$27$	−0.923880	−	0.382683i	−0.177801	−	0.0736475i
$28$	2.69709	−	3.26618i	0.509702	−	0.617250i
$29$	−6.59890	+	2.73335i	−1.22539	+	0.507571i	−0.899118	−	0.437706i	$-0.855791\pi$
$29$	−6.59890	+	2.73335i	−1.22539	+	0.507571i	−0.326267	+	0.945278i	$0.605791\pi$
$30$	−0.291211	−	0.168131i	−0.0531675	−	0.0306963i
$31$	−2.37564	+	3.09599i	−0.426677	+	0.556057i	−0.956380	−	0.292127i	$-0.905637\pi$
$31$	−2.37564	+	3.09599i	−0.426677	+	0.556057i	0.529702	+	0.848184i	$0.322304\pi$
$32$	−1.46602	+	5.47128i	−0.259159	+	0.967195i
$33$	−1.48976	+	2.58034i	−0.259334	+	0.449180i
$34$	2.25499	−	1.30314i	0.386728	−	0.223486i
$35$	−0.315662	−	1.37260i	−0.0533567	−	0.232011i
$36$	1.13207	+	1.13207i	0.188679	+	0.188679i
$37$	6.56759	+	0.864639i	1.07970	+	0.142146i	0.649332	−	0.760505i	$-0.275049\pi$
$37$	6.56759	+	0.864639i	1.07970	+	0.142146i	0.430373	+	0.902651i	$0.358382\pi$
$38$	1.95653	−	1.12960i	0.317391	−	0.183246i
$39$	−5.56761	−	4.27218i	−0.891532	−	0.684096i
$40$	0.737133	+	0.960650i	0.116551	+	0.151892i
$41$	−6.09363	−	2.52406i	−0.951665	−	0.394192i	−0.147808	−	0.989016i	$-0.547222\pi$
$41$	−6.09363	−	2.52406i	−0.951665	−	0.394192i	−0.803856	+	0.594824i	$0.797222\pi$
$42$	0.0597432	−	1.67018i	0.00921857	−	0.257714i
$43$	0.374756	−	0.374756i	0.0571498	−	0.0571498i	−0.677954	−	0.735104i	$-0.737133\pi$
$43$	0.374756	−	0.374756i	0.0571498	−	0.0571498i	0.735104	+	0.677954i	$0.237133\pi$
$44$	3.78445	−	2.90391i	0.570527	−	0.437781i
$45$	0.527781	−	0.0694837i	0.0786770	−	0.0103580i
$46$	2.97588	+	2.28347i	0.438770	+	0.336680i
$47$	−0.462686	−	0.267132i	−0.0674897	−	0.0389652i	0.465875	−	0.884850i	$-0.345739\pi$
$47$	−0.462686	−	0.267132i	−0.0674897	−	0.0389652i	−0.533365	+	0.845885i	$0.679073\pi$
$48$	−0.675496	−	1.63079i	−0.0974994	−	0.235384i
$49$	5.29075	−	4.58344i	0.755822	−	0.654777i
$50$	−2.97935			−0.421344
$51$	−1.57630	+	3.80989i	−0.220726	+	0.533492i
$52$	5.61774	+	9.73020i	0.779040	+	1.34934i
$53$	−0.445072	+	1.66103i	−0.0611354	+	0.228160i	−0.989733	−	0.142927i	$-0.954348\pi$
$53$	−0.445072	+	1.66103i	−0.0611354	+	0.228160i	0.928598	+	0.371088i	$0.121015\pi$
$54$	0.626267	+	0.0824497i	0.0852242	+	0.0112200i
$55$		−	1.58611i		−	0.213870i
$56$	−2.50033	+	5.47415i	−0.334121	+	0.731515i
$57$	−1.36869	+	3.30430i	−0.181287	+	0.437665i
$58$	3.57943	−	2.74659i	0.470002	−	0.360646i
$59$	1.39119	+	0.372768i	0.181117	+	0.0485302i	0.348238	−	0.937406i	$-0.386780\pi$
$59$	1.39119	+	0.372768i	0.181117	+	0.0485302i	−0.167120	+	0.985936i	$0.553447\pi$
$60$	−0.823224	−	0.220582i	−0.106278	−	0.0284770i
$61$	6.43920	−	4.94097i	0.824455	−	0.632626i	−0.107904	−	0.994161i	$-0.534414\pi$
$61$	6.43920	−	4.94097i	0.824455	−	0.632626i	0.932359	+	0.361535i	$0.117747\pi$
$62$	0.943331	−	2.27740i	0.119803	−	0.289231i
$63$	1.53457	+	2.15525i	0.193337	+	0.271536i
$64$		−	0.0476554i		−	0.00595693i
$65$	3.70387	+	0.487624i	0.459409	+	0.0604824i
$66$	0.487118	−	1.81795i	0.0599601	−	0.223774i
$67$	−2.02119	−	3.50081i	−0.246928	−	0.427692i	0.715744	−	0.698363i	$-0.246088\pi$
$67$	−2.02119	−	3.50081i	−0.246928	−	0.427692i	−0.962672	+	0.270671i	$0.912754\pi$
$68$	4.66576	−	4.66954i	0.565806	−	0.566265i
$69$	−5.93824			−0.714880
$70$	0.417005	+	0.785880i	0.0498416	+	0.0939306i
$71$	3.65271	+	8.81842i	0.433497	+	1.04655i	0.978151	+	0.207893i	$0.0666607\pi$
$71$	3.65271	+	8.81842i	0.433497	+	1.04655i	−0.544655	+	0.838660i	$0.683339\pi$
$72$	−1.96990	−	1.13732i	−0.232155	−	0.134035i
$73$	−11.0176	−	8.45411i	−1.28951	−	0.989478i	−0.999473	−	0.0324641i	$-0.989665\pi$
$73$	−11.0176	−	8.45411i	−1.28951	−	0.989478i	−0.290041	−	0.957014i	$-0.593669\pi$
$74$	−4.14856	+	0.546168i	−0.482260	+	0.0634907i
$75$	3.74195	−	2.87130i	0.432083	−	0.331549i
$76$	4.04891	−	4.04891i	0.464442	−	0.464442i
$77$	6.96348	−	3.69497i	0.793563	−	0.421081i
$78$	4.09552	+	1.69642i	0.463726	+	0.192082i
$79$	−1.55803	−	2.03047i	−0.175292	−	0.228445i	0.697442	−	0.716642i	$-0.254322\pi$
$79$	−1.55803	−	2.03047i	−0.175292	−	0.228445i	−0.872734	+	0.488196i	$0.837655\pi$
$80$	0.745478	+	0.572026i	0.0833470	+	0.0639544i
$81$	−0.866025	+	0.500000i	−0.0962250	+	0.0555556i
$82$	4.13067	+	0.543813i	0.456156	+	0.0600541i
$83$	6.29877	+	6.29877i	0.691380	+	0.691380i	0.962535	−	0.271156i	$-0.0874058\pi$
$83$	6.29877	+	6.29877i	0.691380	+	0.691380i	−0.271156	+	0.962535i	$0.587406\pi$
$84$	−0.949350	−	4.12807i	−0.103583	−	0.450409i
$85$	−0.287370	−	2.17598i	−0.0311697	−	0.236018i
$86$	−0.167388	+	0.289925i	−0.0180499	+	0.0312634i
$87$	−1.84864	+	6.89922i	−0.198195	+	0.739674i
$88$	−4.12579	+	5.37684i	−0.439811	+	0.573173i
$89$	10.9606	+	6.32813i	1.16182	+	0.670780i	0.951741	−	0.306903i	$-0.0992928\pi$
$89$	10.9606	+	6.32813i	1.16182	+	0.670780i	0.210084	+	0.977683i	$0.432626\pi$
$90$	−0.310665	+	0.128682i	−0.0327469	+	0.0135642i
$91$	6.48768	+	17.3971i	0.680094	+	1.82371i
$92$	8.78339	+	3.63820i	0.915732	+	0.379308i
$93$	1.01002	+	3.76944i	0.104734	+	0.390873i
$94$	0.325980	+	0.0873461i	0.0336223	+	0.00900906i
$95$	−0.248512	−	1.88764i	−0.0254968	−	0.193667i
$96$	3.44820	+	4.49378i	0.351930	+	0.458644i
$97$	5.00008	−	2.07110i	0.507681	−	0.210288i	−0.114115	−	0.993468i	$-0.536403\pi$
$97$	5.00008	−	2.07110i	0.507681	−	0.210288i	0.621796	+	0.783179i	$0.286403\pi$
$98$	−2.47880	+	3.66155i	−0.250397	+	0.369873i
$99$	1.14021	+	2.75272i	0.114596	+	0.276659i
$100$	−7.29396	+	1.95441i	−0.729396	+	0.195441i
$101$	−6.24674	−	10.8197i	−0.621574	−	1.07660i	−0.989193	−	0.146621i	$-0.953160\pi$
$101$	−6.24674	−	10.8197i	−0.621574	−	1.07660i	0.367619	−	0.929977i	$-0.380173\pi$
$102$	0.338902	−	2.58230i	0.0335563	−	0.255686i
$103$	−0.549070	+	0.951017i	−0.0541015	+	0.0937065i	−0.891808	−	0.452414i	$-0.850563\pi$
$103$	−0.549070	+	0.951017i	−0.0541015	+	0.0937065i	0.837706	+	0.546121i	$0.183896\pi$
$104$	−11.2876	−	11.2876i	−1.10684	−	1.10684i
$105$	−1.28112	−	0.585153i	−0.125024	−	0.0571051i
$106$		−	1.08624i		−	0.105505i
$107$	−2.10395	+	15.9811i	−0.203396	+	1.54495i	0.519790	+	0.854294i	$0.326010\pi$
$107$	−2.10395	+	15.9811i	−0.203396	+	1.54495i	−0.723186	+	0.690653i	$0.757323\pi$
$108$	1.58729	−	0.208971i	0.152737	−	0.0201083i
$109$	1.87992	+	14.2794i	0.180064	+	1.36772i	0.807875	+	0.589353i	$0.200617\pi$
$109$	1.87992	+	14.2794i	0.180064	+	1.36772i	−0.627812	+	0.778365i	$0.716049\pi$
$110$	0.259310	+	0.967759i	0.0247243	+	0.0922722i
$111$	4.68406	−	4.68406i	0.444591	−	0.444591i
$112$	−0.774708	+	4.60546i	−0.0732030	+	0.435175i
$113$	0.700799	−	1.69188i	0.0659257	−	0.159159i	−0.887483	−	0.460840i	$-0.847548\pi$
$113$	0.700799	−	1.69188i	0.0659257	−	0.159159i	0.953409	+	0.301682i	$0.0975480\pi$
$114$	0.294885	−	2.23988i	0.0276185	−	0.209784i
$115$	2.73762	−	1.58057i	0.255285	−	0.147389i
$116$	6.96133	−	9.07218i	0.646343	−	0.842331i
$117$	−6.77870	+	1.81635i	−0.626691	+	0.167921i
$118$	−0.909773			−0.0837514
$119$	8.88376	−	6.33078i	0.814373	−	0.580342i
$120$	1.21087			0.110537
$121$	−2.05012	+	0.549328i	−0.186374	+	0.0499389i
$122$	−3.12107	+	4.06746i	−0.282568	+	0.368250i
$123$	−5.71204	+	3.29785i	−0.515037	+	0.297357i
$124$	0.815493	−	6.19428i	0.0732334	−	0.556263i
$125$	−1.97943	+	4.77877i	−0.177046	+	0.427426i
$126$	−1.28867	−	1.06414i	−0.114804	−	0.0948009i
$127$	2.97026	−	2.97026i	0.263568	−	0.263568i	−0.562934	−	0.826502i	$-0.690327\pi$
$127$	2.97026	−	2.97026i	0.263568	−	0.263568i	0.826502	+	0.562934i	$0.190327\pi$
$128$	−2.92426	−	10.9135i	−0.258470	−	0.964625i
$129$	−0.0691770	−	0.525451i	−0.00609069	−	0.0462634i
$130$	−2.33963	+	0.308018i	−0.205199	+	0.0270150i
$131$	−0.286347	+	2.17502i	−0.0250182	+	0.190032i	−0.999390	−	0.0349093i	$-0.988886\pi$
$131$	−0.286347	+	2.17502i	−0.0250182	+	0.190032i	0.974372	+	0.224942i	$0.0722191\pi$
$132$		−	4.77019i		−	0.415192i
$133$	7.70836	−	5.48845i	0.668400	−	0.475909i
$134$	1.80557	+	1.80557i	0.155977	+	0.155977i
$135$	0.266168	−	0.461016i	0.0229081	−	0.0396779i
$136$	−4.68601	+	8.12400i	−0.401822	+	0.696627i
$137$	−9.57730	−	16.5884i	−0.818244	−	1.41724i	−0.906975	−	0.421185i	$-0.861614\pi$
$137$	−9.57730	−	16.5884i	−0.818244	−	1.41724i	0.0887309	−	0.996056i	$-0.471719\pi$
$138$	3.62320	−	0.970835i	0.308428	−	0.0826429i
$139$	−1.59479	−	3.85017i	−0.135269	−	0.326568i	0.841702	−	0.539943i	$-0.181554\pi$
$139$	−1.59479	−	3.85017i	−0.135269	−	0.326568i	−0.976970	+	0.213375i	$0.931554\pi$
$140$	1.53642	+	1.65042i	0.129852	+	0.139486i
$141$	−0.493596	+	0.204454i	−0.0415682	+	0.0172181i
$142$	−3.67040	−	4.78336i	−0.308013	−	0.401411i
$143$	2.72927	+	20.7309i	0.228233	+	1.73360i
$144$	−1.70501	−	0.456856i	−0.142084	−	0.0380713i
$145$	−0.984097	−	3.67270i	−0.0817248	−	0.305001i
$146$	8.10452	+	3.35700i	0.670735	+	0.277827i
$147$	−0.415479	−	6.98766i	−0.0342681	−	0.576332i
$148$	−9.79810	+	4.05850i	−0.805398	+	0.333607i
$149$	−13.4251	−	7.75096i	−1.09982	−	0.634983i	−0.163649	−	0.986519i	$-0.552326\pi$
$149$	−13.4251	−	7.75096i	−1.09982	−	0.634983i	−0.936175	+	0.351535i	$0.885660\pi$
$150$	−1.81372	+	2.36368i	−0.148089	+	0.192994i
$151$	−2.50239	+	9.33906i	−0.203642	+	0.760002i	0.786217	+	0.617950i	$0.212037\pi$
$151$	−2.50239	+	9.33906i	−0.203642	+	0.760002i	−0.989859	+	0.142052i	$0.954630\pi$
$152$	−4.06769	+	7.04544i	−0.329933	+	0.571461i
$153$	2.06300	+	3.56988i	0.166784	+	0.288608i
$154$	−3.64467	+	3.39293i	−0.293696	+	0.273410i
$155$	−1.46894	−	1.46894i	−0.117988	−	0.117988i
$156$	11.1394	+	1.46652i	0.891862	+	0.117416i
$157$	13.8480	−	7.99516i	1.10519	−	0.638084i	0.167613	−	0.985853i	$-0.446394\pi$
$157$	13.8480	−	7.99516i	1.10519	−	0.638084i	0.937580	+	0.347769i	$0.113061\pi$
$158$	1.28259	+	0.984164i	0.102037	+	0.0782959i
$159$	1.04684	+	1.36427i	0.0830201	+	0.108194i
$160$	−2.78577	−	1.15391i	−0.220235	−	0.0912242i
$161$	13.3167	+	8.33692i	1.04950	+	0.657042i
$162$	0.446659	−	0.446659i	0.0350929	−	0.0350929i
$163$	0.131553	−	0.100944i	0.0103040	−	0.00790655i	−0.603597	−	0.797290i	$-0.706266\pi$
$163$	0.131553	−	0.100944i	0.0103040	−	0.00790655i	0.613901	+	0.789383i	$0.289600\pi$
$164$	10.4693	−	1.37831i	0.817516	−	0.107628i
$165$	−1.25834	−	0.965560i	−0.0979618	−	0.0751687i
$166$	−4.87296	−	2.81340i	−0.378215	−	0.218362i
$167$	−9.16771	−	22.1328i	−0.709418	−	1.71269i	−0.701450	−	0.712719i	$-0.747463\pi$
$167$	−9.16771	−	22.1328i	−0.709418	−	1.71269i	−0.00796876	−	0.999968i	$-0.502537\pi$
$168$	2.82083	+	5.31610i	0.217632	+	0.410146i
$169$	−36.2498			−2.78845
$170$	0.531087	+	1.28069i	0.0407325	+	0.0982243i
$171$	1.78827	+	3.09738i	0.136753	+	0.236863i
$172$	−0.219609	+	0.819590i	−0.0167450	+	0.0624932i
$173$	9.83094	+	1.29427i	0.747433	+	0.0984014i	0.494615	−	0.869112i	$-0.335309\pi$
$173$	9.83094	+	1.29427i	0.747433	+	0.0984014i	0.252818	+	0.967514i	$0.418643\pi$
$174$		−	4.51178i		−	0.342037i
$175$	−12.4226	+	1.18552i	−0.939057	+	0.0896166i
$176$	−2.01266	+	4.85898i	−0.151710	+	0.366259i
$177$	1.14264	−	0.876777i	0.0858859	−	0.0659026i
$178$	−7.72218	−	2.06915i	−0.578802	−	0.155090i
$179$	−19.7319	−	5.28715i	−1.47483	−	0.395180i	−0.570248	−	0.821473i	$-0.693153\pi$
$179$	−19.7319	−	5.28715i	−1.47483	−	0.395180i	−0.904585	+	0.426293i	$0.859819\pi$
$180$	−0.676147	+	0.518826i	−0.0503970	+	0.0386710i
$181$	6.94727	−	16.7722i	0.516387	−	1.24667i	−0.423722	−	0.905792i	$-0.639277\pi$
$181$	6.94727	−	16.7722i	0.516387	−	1.24667i	0.940108	−	0.340875i	$-0.110723\pi$
$182$	−6.80267	−	9.55413i	−0.504247	−	0.708199i
$183$		−	8.11643i		−	0.599984i
$184$	−13.3918	−	1.76307i	−0.987258	−	0.129975i
$185$	−0.912681	+	3.40617i	−0.0671016	+	0.250427i
$186$	−1.23252	−	2.13479i	−0.0903729	−	0.156530i
$187$	11.3479	−	4.70582i	0.829837	−	0.344124i
$188$	0.855352			0.0623830
$189$	2.64406	+	0.0945795i	0.192327	+	0.00687965i
$190$	0.460236	+	1.11111i	0.0333890	+	0.0806082i
$191$	−19.8286	−	11.4480i	−1.43474	−	0.828350i	−0.437266	−	0.899332i	$-0.644053\pi$
$191$	−19.8286	−	11.4480i	−1.43474	−	0.828350i	−0.997478	+	0.0709821i	$0.977387\pi$
$192$	−0.0378076	−	0.0290108i	−0.00272853	−	0.00209367i
$193$	−8.24659	+	1.08568i	−0.593602	+	0.0781493i	−0.421341	−	0.906902i	$-0.638441\pi$
$193$	−8.24659	+	1.08568i	−0.593602	+	0.0781493i	−0.172261	+	0.985051i	$0.555107\pi$
$194$	−2.71219	+	2.08113i	−0.194724	+	0.149417i
$195$	2.64163	−	2.64163i	0.189171	−	0.189171i
$196$	−3.66660	+	10.5902i	−0.261900	+	0.756440i
$197$	1.07464	+	0.445132i	0.0765652	+	0.0317143i	0.420637	−	0.907229i	$-0.361806\pi$
$197$	1.07464	+	0.445132i	0.0765652	+	0.0317143i	−0.344072	+	0.938943i	$0.611806\pi$
$198$	−1.14574	−	1.49315i	−0.0814240	−	0.106114i
$199$	−15.5529	−	11.9341i	−1.10251	−	0.845989i	−0.113460	−	0.993543i	$-0.536193\pi$
$199$	−15.5529	−	11.9341i	−1.10251	−	0.845989i	−0.989054	+	0.147553i	$0.952860\pi$
$200$	9.29126	−	5.36431i	0.656991	−	0.379314i
$201$	−4.00780	−	0.527637i	−0.282689	−	0.0372167i
$202$	5.58033	+	5.58033i	0.392630	+	0.392630i
$203$	13.8317	−	12.8764i	0.970796	−	0.903743i
$204$	−0.864263	−	6.54423i	−0.0605105	−	0.458188i
$205$	1.75556	−	3.04072i	0.122614	−	0.212373i
$206$	0.179533	−	0.670027i	0.0125087	−	0.0466830i
$207$	−3.61497	+	4.71112i	−0.251258	+	0.327446i
$208$	−10.7279	−	6.19377i	−0.743848	−	0.429461i
$209$	9.84524	−	4.07803i	0.681010	−	0.282083i
$210$	0.877337	+	0.147581i	0.0605420	+	0.0101841i
$211$	−10.5047	−	4.35120i	−0.723176	−	0.299549i	−0.00943133	−	0.999956i	$-0.503002\pi$
$211$	−10.5047	−	4.35120i	−0.723176	−	0.299549i	−0.713744	+	0.700406i	$0.753002\pi$
$212$	−0.712557	−	2.65930i	−0.0489386	−	0.182641i
$213$	9.21975	+	2.47042i	0.631727	+	0.169271i
$214$	−1.32900	−	10.0948i	−0.0908487	−	0.690065i
$215$	0.171750	+	0.223829i	0.0117132	+	0.0152650i
$216$	−2.10150	+	0.870468i	−0.142989	+	0.0592279i
$217$	3.02706	−	9.87111i	0.205490	−	0.670094i
$218$	−3.48155	−	8.40520i	−0.235800	−	0.569272i
$219$	−13.4142	+	3.59432i	−0.906447	+	0.242882i
$220$	1.26967	+	2.19913i	0.0856012	+	0.148266i
$221$	7.50031	+	27.9462i	0.504526	+	1.87987i
$222$	−2.09218	+	3.62376i	−0.140418	+	0.243211i
$223$	18.1222	+	18.1222i	1.21356	+	1.21356i	0.969849	+	0.243706i	$0.0783633\pi$
$223$	18.1222	+	18.1222i	1.21356	+	1.21356i	0.243706	+	0.969849i	$0.421637\pi$
$224$	−1.42371	−	14.9185i	−0.0951257	−	0.996785i
$225$		−	4.71662i		−	0.314441i
$226$	−0.150988	+	1.14687i	−0.0100436	+	0.0762886i
$227$	−4.33359	+	0.570528i	−0.287630	+	0.0378672i	−0.272961	−	0.962025i	$-0.588003\pi$
$227$	−4.33359	+	0.570528i	−0.287630	+	0.0378672i	−0.0146695	+	0.999892i	$0.504670\pi$
$228$	−0.747396	−	5.67704i	−0.0494975	−	0.375971i
$229$	−1.09126	−	4.07265i	−0.0721126	−	0.269128i	0.920450	−	0.390859i	$-0.127822\pi$
$229$	−1.09126	−	4.07265i	−0.0721126	−	0.269128i	−0.992563	+	0.121731i	$0.961155\pi$
$230$	−1.41195	+	1.41195i	−0.0931012	+	0.0931012i
$231$	1.30768	−	7.77386i	0.0860391	−	0.511482i
$232$	−6.21741	+	15.0101i	−0.408193	+	0.985464i
$233$	−2.55097	+	19.3766i	−0.167120	+	1.26940i	0.678095	+	0.734974i	$0.262806\pi$
$233$	−2.55097	+	19.3766i	−0.167120	+	1.26940i	−0.845215	+	0.534427i	$0.820528\pi$
$234$	3.83905	−	2.21648i	0.250967	−	0.144896i
$235$	0.173136	−	0.225636i	0.0112942	−	0.0147189i
$236$	−2.22728	+	0.596798i	−0.144984	+	0.0388482i
$237$	−2.55935			−0.166247
$238$	−4.38540	+	5.31511i	−0.284263	+	0.344527i
$239$	24.1067			1.55933			0.779667	−	0.626194i	$-0.215388\pi$
$239$	24.1067			1.55933			0.779667	+	0.626194i	$0.215388\pi$
$240$	0.907637	−	0.243201i	0.0585877	−	0.0156985i
$241$	−6.47604	+	8.43974i	−0.417159	+	0.543652i	−0.953912	−	0.300088i	$-0.902984\pi$
$241$	−6.47604	+	8.43974i	−0.417159	+	0.543652i	0.536753	+	0.843739i	$0.319651\pi$
$242$	1.16107	−	0.670342i	0.0746362	−	0.0430912i
$243$	−0.130526	+	0.991445i	−0.00837326	+	0.0636012i
$244$	−4.97272	+	12.0052i	−0.318346	+	0.768554i
$245$	2.05143	+	3.11084i	0.131061	+	0.198744i
$246$	2.94603	−	2.94603i	0.187832	−	0.187832i
$247$	6.49625	+	24.2443i	0.413347	+	1.54263i
$248$	1.15863	+	8.80066i	0.0735730	+	0.558842i
$249$	8.83160	−	1.16270i	0.559680	−	0.0736832i
$250$	0.426471	−	3.23937i	0.0269724	−	0.204876i
$251$			6.09820i			0.384915i	0.981305	+	0.192457i	$0.0616457\pi$
$251$			6.09820i			0.384915i	−0.981305	+	0.192457i	$0.938354\pi$
$252$	−3.85294	−	1.75984i	−0.242713	−	0.110859i
$253$	12.5109	+	12.5109i	0.786555	+	0.786555i
$254$	−1.32669	+	2.29790i	−0.0832442	+	0.144183i
$255$	−1.90126	−	1.09667i	−0.119062	−	0.0686760i
$256$	3.61611	+	6.26329i	0.226007	+	0.391456i
$257$	−3.21204	+	0.860662i	−0.200361	+	0.0536866i	−0.357604	−	0.933873i	$-0.616406\pi$
$257$	−3.21204	+	0.860662i	−0.200361	+	0.0536866i	0.157243	+	0.987560i	$0.449740\pi$
$258$	0.128113	+	0.309293i	0.00797600	+	0.0192558i
$259$	−17.0803	+	3.92803i	−1.06132	+	0.244076i
$260$	−5.52576	+	2.28884i	−0.342693	+	0.141948i
$261$	4.34814	+	5.66660i	0.269143	+	0.350754i
$262$	−0.180877	−	1.37390i	−0.0111746	−	0.0848796i
$263$	0.268846	+	0.0720370i	0.0165777	+	0.00444199i	0.267098	−	0.963669i	$-0.413935\pi$
$263$	0.268846	+	0.0720370i	0.0165777	+	0.00444199i	−0.250521	+	0.968111i	$0.580602\pi$
$264$	1.75411	+	6.54642i	0.107958	+	0.402904i
$265$	−0.845737	−	0.350316i	−0.0519532	−	0.0215197i
$266$	−3.80594	+	4.60900i	−0.233357	+	0.282596i
$267$	11.6929	−	4.84334i	0.715591	−	0.296407i
$268$	5.60476	+	3.23591i	0.342365	+	0.197665i
$269$	18.4082	−	23.9900i	1.12237	−	1.46270i	0.253715	−	0.967279i	$-0.418348\pi$
$269$	18.4082	−	23.9900i	1.12237	−	1.46270i	0.868654	−	0.495420i	$-0.164986\pi$
$270$	−0.0870308	+	0.324803i	−0.00529652	+	0.0197669i
$271$	6.71294	−	11.6272i	0.407782	−	0.706300i	−0.586859	−	0.809689i	$-0.699636\pi$
$271$	6.71294	−	11.6272i	0.407782	−	0.706300i	0.994641	+	0.103390i	$0.0329689\pi$
$272$	−1.88082	+	7.03070i	−0.114041	+	0.426299i
$273$	17.7515	+	5.44365i	1.07437	+	0.329465i
$274$	8.55558	+	8.55558i	0.516861	+	0.516861i
$275$	−13.9330	−	1.83432i	−0.840195	−	0.110614i
$276$	8.23337	−	4.75354i	0.495590	−	0.286129i
$277$	11.3002	+	8.67095i	0.678963	+	0.520987i	0.889694	−	0.456557i	$-0.150918\pi$
$277$	11.3002	+	8.67095i	0.678963	+	0.520987i	−0.210731	+	0.977544i	$0.567584\pi$
$278$	1.60252	+	2.08844i	0.0961128	+	0.125257i
$279$	3.60536	+	1.49339i	0.215847	+	0.0894069i
$280$	−2.71542	−	1.69999i	−0.162278	−	0.101594i
$281$	6.65457	−	6.65457i	0.396978	−	0.396978i	−0.480187	−	0.877166i	$-0.659431\pi$
$281$	6.65457	−	6.65457i	0.396978	−	0.396978i	0.877166	+	0.480187i	$0.159431\pi$
$282$	0.267740	−	0.205444i	0.0159437	−	0.0122340i
$283$	0.386282	−	0.0508550i	0.0229621	−	0.00302302i	−0.119036	−	0.992890i	$-0.537981\pi$
$283$	0.386282	−	0.0508550i	0.0229621	−	0.00302302i	0.141998	+	0.989867i	$0.454647\pi$
$284$	−12.1236	−	9.30275i	−0.719402	−	0.552017i
$285$	−1.64885	−	0.951962i	−0.0976692	−	0.0563894i
$286$	−5.05452	−	12.2027i	−0.298880	−	0.721560i
$287$	17.4394	+	0.623818i	1.02942	+	0.0368228i
$288$	5.66428			0.333771
$289$	14.7155	−	8.51193i	0.865620	−	0.500702i
$290$	1.20089	+	2.08000i	0.0705186	+	0.122142i
$291$	1.40074	−	5.22764i	0.0821129	−	0.306450i
$292$	22.0434	+	2.90207i	1.28999	+	0.169831i
$293$			8.32965i			0.486623i	0.969948	+	0.243312i	$0.0782338\pi$
$293$			8.32965i			0.486623i	−0.969948	+	0.243312i	$0.921766\pi$
$294$	1.39591	+	4.19558i	0.0814109	+	0.244691i
$295$	−0.293405	+	0.708341i	−0.0170827	+	0.0412412i
$296$	11.9541	−	9.17271i	0.694819	−	0.533153i
$297$	2.87800	+	0.771157i	0.166998	+	0.0447471i
$298$	9.45846	+	2.53439i	0.547914	+	0.146813i
$299$	−33.0618	+	25.3692i	−1.91201	+	1.46714i
$300$	−2.88974	+	6.97646i	−0.166839	+	0.402786i
$301$	−0.582570	+	1.27546i	−0.0335788	+	0.0735164i
$302$		−	6.10732i		−	0.351437i
$303$	−12.3866	−	1.63073i	−0.711591	−	0.0936828i
$304$	−1.63397	+	6.09805i	−0.0937145	+	0.349747i
$305$	2.16033	+	3.74180i	0.123700	+	0.214255i
$306$	−1.84237	−	1.84088i	−0.105321	−	0.105236i
$307$	−18.0680			−1.03119			−0.515597	−	0.856831i	$-0.672430\pi$
$307$	−18.0680			−1.03119			−0.515597	+	0.856831i	$0.672430\pi$
$308$	−6.69705	+	10.6973i	−0.381600	+	0.609536i
$309$	0.420240	+	1.01455i	0.0239066	+	0.0577157i
$310$	1.13642	+	0.656115i	0.0645446	+	0.0372648i
$311$	−22.2091	−	17.0417i	−1.25936	−	0.966344i	−1.00000		0.000564839i	$-0.999820\pi$
$311$	−22.2091	−	17.0417i	−1.25936	−	0.966344i	−0.259365	−	0.965779i	$-0.583513\pi$
$312$	−15.8265	+	2.08359i	−0.895998	+	0.117960i
$313$	0.526387	−	0.403911i	0.0297532	−	0.0228304i	−0.593778	−	0.804629i	$-0.702364\pi$
$313$	0.526387	−	0.403911i	0.0297532	−	0.0228304i	0.623531	+	0.781799i	$0.285698\pi$
$314$	−7.14223	+	7.14223i	−0.403059	+	0.403059i
$315$	−1.24413	+	0.660161i	−0.0700987	+	0.0371958i
$316$	3.78559	+	1.56804i	0.212956	+	0.0882093i
$317$	1.29105	+	1.68253i	0.0725126	+	0.0945003i	0.828201	−	0.560431i	$-0.189364\pi$
$317$	1.29105	+	1.68253i	0.0725126	+	0.0945003i	−0.755689	+	0.654931i	$0.772698\pi$
$318$	−0.861772	−	0.661261i	−0.0483258	−	0.0370817i
$319$	18.4304	−	10.6408i	1.03190	−	0.595769i
$320$	0.0251516	+	0.00331128i	0.00140602	+	0.000185106i
$321$	11.3978	+	11.3978i	0.636164	+	0.636164i
$322$	−9.48815	−	2.90963i	−0.528754	−	0.162147i
$323$	12.7678	−	7.37842i	0.710422	−	0.410546i
$324$	0.800496	−	1.38650i	0.0444720	−	0.0770277i
$325$	8.56701	−	31.9725i	0.475212	−	1.77352i
$326$	−0.0637635	+	0.0830982i	−0.00353153	+	0.00460238i
$327$	12.4730	+	7.20131i	0.689760	+	0.398233i
$328$	−13.8608	+	5.74134i	−0.765336	+	0.317013i
$329$	1.39395	+	0.234483i	0.0768507	+	0.0129275i
$330$	0.925633	+	0.383410i	0.0509544	+	0.0211060i
$331$	1.64938	+	6.15556i	0.0906580	+	0.338340i	0.996325	−	0.0856486i	$-0.0272962\pi$
$331$	1.64938	+	6.15556i	0.0906580	+	0.338340i	−0.905667	+	0.423989i	$0.860630\pi$
$332$	−13.7754	−	3.69110i	−0.756022	−	0.202575i
$333$	−0.864639	−	6.56759i	−0.0473819	−	0.359902i
$334$	9.21211	+	12.0055i	0.504064	+	0.656910i
$335$	1.98810	−	0.823498i	0.108622	−	0.0449925i
$336$	3.18214	+	3.41824i	0.173600	+	0.186480i
$337$	−0.867625	−	2.09463i	−0.0472625	−	0.114102i	0.898485	−	0.439004i	$-0.144669\pi$
$337$	−0.867625	−	2.09463i	−0.0472625	−	0.114102i	−0.945748	+	0.324902i	$0.894669\pi$
$338$	22.1177	−	5.92643i	1.20305	−	0.322355i
$339$	−0.915639	−	1.58593i	−0.0497307	−	0.0861360i
$340$	2.14030	+	2.78696i	0.116074	+	0.151144i
$341$	5.81367	−	10.0696i	0.314828	−	0.545298i
$342$	−1.59750	−	1.59750i	−0.0863828	−	0.0863828i
$343$	−8.87852	+	16.2534i	−0.479395	+	0.877599i
$344$		−	1.20553i		−	0.0649977i
$345$	0.412611	−	3.13409i	0.0222142	−	0.168734i
$346$	−6.20992	+	0.817552i	−0.333848	+	0.0439519i
$347$	2.65274	+	20.1496i	0.142407	+	1.08169i	0.902138	+	0.431448i	$0.141997\pi$
$347$	2.65274	+	20.1496i	0.142407	+	1.08169i	−0.759731	+	0.650237i	$0.774670\pi$
$348$	−2.95966	−	11.0456i	−0.158654	−	0.592106i
$349$	17.7162	−	17.7162i	0.948327	−	0.948327i	−0.0504018	−	0.998729i	$-0.516050\pi$
$349$	17.7162	−	17.7162i	0.948327	−	0.948327i	0.998729	+	0.0504018i	$0.0160502\pi$
$350$	7.38578	−	2.75429i	0.394786	−	0.147223i
$351$	−2.68560	+	6.48362i	−0.143347	+	0.346070i
$352$	2.20287	−	16.7325i	0.117414	−	0.891844i
$353$	3.15963	−	1.82421i	0.168170	−	0.0970929i	−0.413553	−	0.910480i	$-0.635712\pi$
$353$	3.15963	−	1.82421i	0.168170	−	0.0970929i	0.581723	+	0.813387i	$0.302379\pi$
$354$	−0.553835	+	0.721772i	−0.0294360	+	0.0383617i
$355$	−4.90800	+	1.31509i	−0.260490	+	0.0697980i
$356$	−20.2625			−1.07391
$357$	0.385544	−	10.9019i	0.0204051	−	0.576990i
$358$	12.9038			0.681986
$359$	29.0448	−	7.78253i	1.53292	−	0.410746i	0.608953	−	0.793206i	$-0.291590\pi$
$359$	29.0448	−	7.78253i	1.53292	−	0.410746i	0.923972	+	0.382460i	$0.124923\pi$
$360$	0.737133	−	0.960650i	0.0388503	−	0.0506307i
$361$	−5.37654	+	3.10415i	−0.282976	+	0.163376i
$362$	−1.49680	+	11.3693i	−0.0786700	+	0.597558i
$363$	−0.812222	+	1.96088i	−0.0426306	+	0.102919i
$364$	−22.9215	−	18.9277i	−1.20141	−	0.992081i
$365$	5.22746	−	5.22746i	0.273618	−	0.273618i
$366$	1.32694	+	4.95222i	0.0693605	+	0.258857i
$367$	−0.335073	−	2.54513i	−0.0174907	−	0.132855i	0.980472	−	0.196660i	$-0.0630096\pi$
$367$	−0.335073	−	2.54513i	−0.0174907	−	0.132855i	−0.997962	+	0.0638055i	$0.979676\pi$
$368$	−10.3922	+	1.36816i	−0.541733	+	0.0713205i
$369$	−0.860911	+	6.53927i	−0.0448172	+	0.340421i
$370$		−	2.22748i		−	0.115801i
$371$	−0.432226	−	4.52913i	−0.0224401	−	0.235141i
$372$	−4.41781	−	4.41781i	−0.229053	−	0.229053i
$373$	1.76286	−	3.05337i	0.0912776	−	0.158098i	−0.816771	−	0.576961i	$-0.804238\pi$
$373$	1.76286	−	3.05337i	0.0912776	−	0.158098i	0.908049	+	0.418864i	$0.137572\pi$
$374$	−6.15452	+	4.72649i	−0.318243	+	0.244401i
$375$	2.58625	+	4.47952i	0.133553	+	0.231321i
$376$	−1.17385	+	0.314532i	−0.0605367	+	0.0162208i
$377$	19.1822	+	46.3099i	0.987933	+	2.38508i
$378$	−1.62873	+	0.374566i	−0.0837728	+	0.0192656i
$379$	−25.3901	+	10.5169i	−1.30420	+	0.540218i	−0.923187	−	0.384351i	$-0.874425\pi$
$379$	−25.3901	+	10.5169i	−1.30420	+	0.540218i	−0.381014	+	0.924569i	$0.624425\pi$
$380$	1.85561	+	2.41827i	0.0951906	+	0.124055i
$381$	−0.548286	−	4.16465i	−0.0280896	−	0.213361i
$382$	13.9700	+	3.74324i	0.714766	+	0.191521i
$383$	−4.55464	−	16.9982i	−0.232731	−	0.868566i	−0.979158	−	0.203098i	$-0.934899\pi$
$383$	−4.55464	−	16.9982i	−0.232731	−	0.868566i	0.746427	−	0.665467i	$-0.231768\pi$
$384$	−10.4384	−	4.32374i	−0.532683	−	0.220645i
$385$	1.46629	+	3.93194i	0.0747290	+	0.200390i
$386$	4.85414	−	2.01065i	0.247069	−	0.102339i
$387$	−0.458981	−	0.264993i	−0.0233313	−	0.0134703i
$388$	−5.27470	+	6.87412i	−0.267782	+	0.348981i
$389$	10.0582	−	37.5378i	0.509972	−	1.90324i	0.0893584	−	0.996000i	$-0.471518\pi$
$389$	10.0582	−	37.5378i	0.509972	−	1.90324i	0.420613	−	0.907240i	$-0.361815\pi$
$390$	−1.17991	+	2.04366i	−0.0597471	+	0.103485i
$391$	19.4305	+	14.8970i	0.982642	+	0.753376i
$392$	1.13766	−	15.8818i	0.0574604	−	0.802152i
$393$	1.55124	+	1.55124i	0.0782498	+	0.0782498i
$394$	−0.728465	−	0.0959043i	−0.0366996	−	0.00483159i
$395$	1.17990	−	0.681216i	0.0593672	−	0.0342757i
$396$	−3.78445	−	2.90391i	−0.190176	−	0.145927i
$397$	−7.93507	−	10.3412i	−0.398250	−	0.519009i	0.550586	−	0.834778i	$-0.314404\pi$
$397$	−7.93507	−	10.3412i	−0.398250	−	0.519009i	−0.948836	+	0.315769i	$0.897738\pi$
$398$	11.4407	+	4.73887i	0.573468	+	0.237538i
$399$	0.338268	−	9.45661i	0.0169346	−	0.473423i
$400$	5.88706	−	5.88706i	0.294353	−	0.294353i
$401$	2.87850	−	2.20875i	0.143745	−	0.110300i	−0.534385	−	0.845241i	$-0.679457\pi$
$401$	2.87850	−	2.20875i	0.143745	−	0.110300i	0.678131	+	0.734941i	$0.262790\pi$
$402$	2.53161	−	0.333293i	0.126265	−	0.0166232i
$403$	21.7271	+	16.6718i	1.08231	+	0.830482i
$404$	17.3222	+	10.0010i	0.861812	+	0.497567i
$405$	−0.203716	−	0.491814i	−0.0101227	−	0.0244384i
$406$	−6.33425	+	10.1178i	−0.314364	+	0.502138i
$407$	−19.7371			−0.978334
$408$	3.59254	+	8.66324i	0.177857	+	0.428894i
$409$	−11.6761	−	20.2236i	−0.577345	−	0.999991i	−0.995782	−	0.0917455i	$-0.970755\pi$
$409$	−11.6761	−	20.2236i	−0.577345	−	0.999991i	0.418437	−	0.908246i	$-0.362578\pi$
$410$	−0.574028	+	2.14230i	−0.0283492	+	0.105801i
$411$	−18.9907	−	2.50018i	−0.936744	−	0.123325i
$412$		−	1.75811i		−	0.0866160i
$413$	−3.79334	+	0.362008i	−0.186658	+	0.0178133i
$414$	1.43545	−	3.46549i	0.0705486	−	0.170319i
$415$	−3.76203	+	2.88671i	−0.184671	+	0.141703i
$416$	38.3965	+	10.2883i	1.88254	+	0.504425i
$417$	−4.02540	−	1.07860i	−0.197125	−	0.0528194i
$418$	−5.34034	+	4.09779i	−0.261205	+	0.200429i
$419$	−0.713835	+	1.72335i	−0.0348731	+	0.0841911i	−0.940357	−	0.340190i	$-0.889508\pi$
$419$	−0.713835	+	1.72335i	−0.0348731	+	0.0841911i	0.905483	+	0.424382i	$0.139508\pi$
$420$	2.24468	−	0.214216i	0.109529	−	0.0104526i
$421$			30.6590i			1.49423i	0.664695	+	0.747115i	$0.268562\pi$
$421$			30.6590i			1.49423i	−0.664695	+	0.747115i	$0.731438\pi$
$422$	7.12081	+	0.937472i	0.346636	+	0.0456354i
$423$	−0.138278	+	0.516059i	−0.00672329	+	0.0250917i
$424$	1.95577	+	3.38749i	0.0949806	+	0.164511i
$425$	−19.4471	+	0.00788022i	−0.943324	+	0.000382247i
$426$	−6.02930			−0.292120
$427$	−11.3950	+	18.2014i	−0.551441	+	0.880826i
$428$	−9.87565	−	23.8419i	−0.477357	−	1.15244i
$429$	18.1084	+	10.4549i	0.874281	+	0.504767i
$430$	−0.141386	−	0.108489i	−0.00681825	−	0.00523183i
$431$	13.2044	−	1.73839i	0.636034	−	0.0837355i	0.194388	−	0.980925i	$-0.437728\pi$
$431$	13.2044	−	1.73839i	0.636034	−	0.0837355i	0.441646	+	0.897189i	$0.354395\pi$
$432$	−1.40039	+	1.07456i	−0.0673764	+	0.0516997i
$433$	6.52785	−	6.52785i	0.313708	−	0.313708i	−0.532636	−	0.846344i	$-0.678799\pi$
$433$	6.52785	−	6.52785i	0.313708	−	0.313708i	0.846344	+	0.532636i	$0.178799\pi$
$434$	−0.233143	+	6.51772i	−0.0111912	+	0.312861i
$435$	−3.51283	−	1.45506i	−0.168427	−	0.0697648i
$436$	−14.0371	−	18.2935i	−0.672255	−	0.876100i
$437$	16.8496	+	12.9291i	0.806024	+	0.618484i
$438$	7.59701	−	4.38613i	0.362999	−	0.209578i
$439$	−16.0424	−	2.11202i	−0.765661	−	0.100801i	−0.262427	−	0.964952i	$-0.584523\pi$
$439$	−16.0424	−	2.11202i	−0.765661	−	0.100801i	−0.503233	+	0.864151i	$0.667856\pi$
$440$	−2.55112	−	2.55112i	−0.121620	−	0.121620i
$441$	−5.79661	−	3.92420i	−0.276029	−	0.186866i
$442$	−9.14519	−	15.8251i	−0.434992	−	0.752724i
$443$	−10.8564	+	18.8039i	−0.515805	+	0.893400i	0.484027	+	0.875053i	$0.339174\pi$
$443$	−10.8564	+	18.8039i	−0.515805	+	0.893400i	−0.999832	+	0.0183467i	$0.994160\pi$
$444$	−2.74487	+	10.2440i	−0.130266	+	0.486159i
$445$	−4.10145	+	5.34511i	−0.194427	+	0.253383i
$446$	−14.0200	−	8.09447i	−0.663868	−	0.383284i
$447$	−14.3219	+	5.93233i	−0.677403	+	0.280589i
$448$	0.0440554	+	0.118137i	0.00208142	+	0.00558146i
$449$	−14.8882	−	6.16691i	−0.702619	−	0.291034i	0.00262747	−	0.999997i	$-0.499164\pi$
$449$	−14.8882	−	6.16691i	−0.702619	−	0.291034i	−0.705246	+	0.708962i	$0.749164\pi$
$450$	0.771113	+	2.87783i	0.0363506	+	0.135662i
$451$	18.9824	+	5.08632i	0.893846	+	0.239505i
$452$	0.382684	+	2.90678i	0.0180000	+	0.136723i
$453$	5.88581	+	7.67054i	0.276540	+	0.360394i
$454$	2.55085	−	1.05660i	0.119718	−	0.0495886i
$455$	−9.63265	+	2.21526i	−0.451585	+	0.103853i
$456$	3.11327	+	7.51611i	0.145792	+	0.351974i
$457$	−3.23245	+	0.866134i	−0.151208	+	0.0405160i	−0.333629	−	0.942704i	$-0.608273\pi$
$457$	−3.23245	+	0.866134i	−0.151208	+	0.0405160i	0.182421	+	0.983220i	$0.441607\pi$
$458$	1.33166	+	2.30651i	0.0622245	+	0.107776i
$459$	4.08805	+	0.536517i	0.190814	+	0.0250425i
$460$	−2.53048	+	4.38291i	−0.117984	+	0.204354i
$461$	−5.50483	−	5.50483i	−0.256386	−	0.256386i	0.567197	−	0.823582i	$-0.308028\pi$
$461$	−5.50483	−	5.50483i	−0.256386	−	0.256386i	−0.823582	+	0.567197i	$0.808028\pi$
$462$	0.473058	+	4.95699i	0.0220087	+	0.230620i
$463$		−	15.8081i		−	0.734663i	−0.930090	−	0.367332i	$-0.880271\pi$
$463$		−	15.8081i		−	0.734663i	0.930090	−	0.367332i	$-0.119729\pi$
$464$	−1.64565	+	12.4999i	−0.0763973	+	0.580295i
$465$	−2.05962	+	0.271154i	−0.0955126	+	0.0125745i
$466$	−1.61138	−	12.2396i	−0.0746456	−	0.566990i
$467$	3.88156	+	14.4862i	0.179617	+	0.670341i	0.995719	+	0.0924324i	$0.0294642\pi$
$467$	3.88156	+	14.4862i	0.179617	+	0.670341i	−0.816102	+	0.577908i	$0.803869\pi$
$468$	7.94468	−	7.94468i	0.367243	−	0.367243i
$469$	8.24686	+	6.80995i	0.380805	+	0.314454i
$470$	−0.0687499	+	0.165977i	−0.00317120	+	0.00765595i
$471$	2.08716	−	15.8535i	0.0961711	−	0.730492i
$472$	2.83717	−	1.63804i	0.130591	−	0.0753970i
$473$	−0.961298	+	1.25279i	−0.0442005	+	0.0576032i
$474$	1.56158	−	0.418424i	0.0717257	−	0.0192189i
$475$	−16.8692			−0.774013
$476$	−7.24956	+	15.8890i	−0.332283	+	0.728273i
$477$	1.71963			0.0787364
$478$	−14.7087	+	3.94118i	−0.672759	+	0.180265i
$479$	−18.3275	+	23.8849i	−0.837406	+	1.09133i	0.157196	+	0.987567i	$0.449755\pi$
$479$	−18.3275	+	23.8849i	−0.837406	+	1.09133i	−0.994602	+	0.103761i	$0.966912\pi$
$480$	−2.61133	+	1.50765i	−0.119190	+	0.0688145i
$481$	6.06789	−	46.0902i	0.276672	−	2.10153i
$482$	2.57154	−	6.20825i	0.117130	−	0.282778i
$483$	14.7208	−	5.48965i	0.669821	−	0.249788i
$484$	2.40275	−	2.40275i	0.109216	−	0.109216i
$485$	0.745664	+	2.78286i	0.0338589	+	0.126363i
$486$	−0.0824497	−	0.626267i	−0.00373999	−	0.0284081i
$487$	36.4582	−	4.79981i	1.65208	−	0.217500i	0.753855	−	0.657041i	$-0.228192\pi$
$487$	36.4582	−	4.79981i	1.65208	−	0.217500i	0.898223	+	0.439541i	$0.144859\pi$
$488$	2.40977	−	18.3040i	0.109085	−	0.828585i
$489$		−	0.165819i		−	0.00749858i
$490$	−1.76026	−	1.56268i	−0.0795205	−	0.0705948i
$491$	−6.58579	−	6.58579i	−0.297212	−	0.297212i	0.542709	−	0.839921i	$-0.317399\pi$
$491$	−6.58579	−	6.58579i	−0.297212	−	0.297212i	−0.839921	+	0.542709i	$0.817399\pi$
$492$	5.27982	−	9.14492i	0.238033	−	0.412285i
$493$	23.3567	−	17.9373i	1.05193	−	0.807855i
$494$	−7.92735	−	13.7306i	−0.356668	−	0.617767i
$495$	−1.53206	+	0.410514i	−0.0688610	+	0.0184512i
$496$	2.63606	+	6.36402i	0.118363	+	0.285753i
$497$	−17.2073	−	18.4840i	−0.771852	−	0.829119i
$498$	−5.19849	+	2.15329i	−0.232950	+	0.0964910i
$499$	−6.01167	−	7.83457i	−0.269120	−	0.350723i	0.639170	−	0.769065i	$-0.279278\pi$
$499$	−6.01167	−	7.83457i	−0.269120	−	0.350723i	−0.908290	+	0.418342i	$0.862611\pi$
$500$	−1.08090	−	8.21028i	−0.0483395	−	0.367175i
$501$	−23.1401	−	6.20036i	−1.03382	−	0.277012i
$502$	−0.996986	−	3.72080i	−0.0444976	−	0.166067i
$503$	−2.30269	−	0.953804i	−0.102672	−	0.0425280i	0.330756	−	0.943716i	$-0.392696\pi$
$503$	−2.30269	−	0.953804i	−0.102672	−	0.0425280i	−0.433428	+	0.901188i	$0.642696\pi$
$504$	5.93476	+	0.998317i	0.264355	+	0.0444686i
$505$	6.14447	−	2.54512i	0.273425	−	0.113256i
$506$	−9.67891	−	5.58812i	−0.430280	−	0.248422i
$507$	−22.0675	+	28.7589i	−0.980052	+	1.27723i
$508$	−1.74058	+	6.49595i	−0.0772259	+	0.288211i
$509$	−8.77257	+	15.1945i	−0.388837	+	0.673486i	−0.992293	−	0.123910i	$-0.960456\pi$
$509$	−8.77257	+	15.1945i	−0.388837	+	0.673486i	0.603456	+	0.797396i	$0.293790\pi$
$510$	1.33934	+	0.358294i	0.0593071	+	0.0158655i
$511$	35.1280	+	10.7723i	1.55397	+	0.476539i
$512$	12.7481	+	12.7481i	0.563392	+	0.563392i
$513$	3.54595	+	0.466833i	0.156558	+	0.0206112i
$514$	1.81911	−	1.05026i	0.0802374	−	0.0463251i
$515$	−0.463777	−	0.355869i	−0.0204365	−	0.0156815i
$516$	0.516535	+	0.673162i	0.0227392	+	0.0296343i
$517$	1.47068	+	0.609175i	0.0646804	+	0.0267915i
$518$	9.77931	−	5.18911i	0.429678	−	0.227996i
$519$	7.01151	−	7.01151i	0.307771	−	0.307771i
$520$	6.74167	−	5.17307i	0.295642	−	0.226854i
$521$	−18.8034	+	2.47551i	−0.823791	+	0.108454i	−0.530624	−	0.847607i	$-0.678042\pi$
$521$	−18.8034	+	2.47551i	−0.823791	+	0.108454i	−0.293167	+	0.956061i	$0.594709\pi$
$522$	−3.57943	−	2.74659i	−0.156667	−	0.120215i
$523$	−20.5178	−	11.8459i	−0.897179	−	0.517987i	−0.0208952	−	0.999782i	$-0.506652\pi$
$523$	−20.5178	−	11.8459i	−0.897179	−	0.517987i	−0.876284	+	0.481795i	$0.839985\pi$
$524$	−1.34407	−	3.24488i	−0.0587161	−	0.141753i
$525$	−6.62184	+	10.5772i	−0.289001	+	0.461626i
$526$	−0.175813			−0.00766581
$527$	6.15138	−	14.8678i	0.267958	−	0.647651i
$528$	2.62966	+	4.55471i	0.114441	+	0.198218i
$529$	−3.17382	+	11.8449i	−0.137992	+	0.514994i
$530$	0.573297	+	0.0754760i	0.0249024	+	0.00327847i
$531$		−	1.44026i		−	0.0625021i
$532$	−6.29415	+	13.7802i	−0.272886	+	0.597449i
$533$	−17.7134	+	42.7640i	−0.767254	+	1.85231i
$534$	−6.34254	+	4.86680i	−0.274468	+	0.210607i
$535$	−8.28831	−	2.22085i	−0.358335	−	0.0960156i
$536$	−8.88167	−	2.37984i	−0.383630	−	0.102793i
$537$	−16.2066	+	12.4358i	−0.699367	+	0.536643i
$538$	−7.30963	+	17.6470i	−0.315140	+	0.760816i
$539$	−13.8465	+	15.5972i	−0.596413	+	0.671821i
$540$			0.852264i			0.0366756i
$541$	−0.141229	−	0.0185931i	−0.00607190	−	0.000799381i	0.127490	−	0.991840i	$-0.459308\pi$
$541$	−0.141229	−	0.0185931i	−0.00607190	−	0.000799381i	−0.133562	+	0.991041i	$0.542641\pi$
$542$	−2.19498	+	8.19177i	−0.0942824	+	0.351867i
$543$	−9.07705	−	15.7219i	−0.389533	−	0.674692i
$544$	−0.00946352	−	23.3544i	−0.000405745	−	1.00131i
$545$	−7.66702			−0.328419
$546$	−11.7210	−	0.419267i	−0.501613	−	0.0179430i
$547$	−8.56929	−	20.6881i	−0.366396	−	0.884559i	−0.994335	−	0.106296i	$-0.966101\pi$
$547$	−8.56929	−	20.6881i	−0.366396	−	0.884559i	0.627938	−	0.778263i	$-0.283899\pi$
$548$	26.5578	+	15.3332i	1.13449	+	0.655001i
$549$	−6.43920	−	4.94097i	−0.274818	−	0.210875i
$550$	8.80111	−	1.15869i	0.375281	−	0.0494066i
$551$	20.2669	−	15.5513i	0.863399	−	0.662509i
$552$	−9.55116	+	9.55116i	−0.406524	+	0.406524i
$553$	5.73942	+	3.59317i	0.244065	+	0.152797i
$554$	−8.31239	−	3.44311i	−0.353160	−	0.146284i
$555$	2.14669	+	2.79762i	0.0911220	+	0.118753i
$556$	5.29323	+	4.06164i	0.224483	+	0.172252i
$557$	14.9065	−	8.60627i	0.631609	−	0.364660i	−0.149766	−	0.988721i	$-0.547852\pi$
$557$	14.9065	−	8.60627i	0.631609	−	0.364660i	0.781375	+	0.624062i	$0.214519\pi$
$558$	−2.44395	−	0.321753i	−0.103461	−	0.0136209i
$559$	−2.62997	−	2.62997i	−0.111236	−	0.111236i
$560$	−2.37684	−	0.728881i	−0.100440	−	0.0308008i
$561$	3.17475	−	11.8676i	0.134038	−	0.501050i
$562$	−2.97232	+	5.14822i	−0.125380	+	0.217164i
$563$	9.16144	−	34.1909i	0.386109	−	1.44098i	−0.450304	−	0.892876i	$-0.648684\pi$
$563$	9.16144	−	34.1909i	0.386109	−	1.44098i	0.836412	−	0.548101i	$-0.184649\pi$
$564$	0.520705	−	0.678596i	0.0219256	−	0.0285741i
$565$	0.844248	+	0.487427i	0.0355178	+	0.0205062i
$566$	−0.227375	+	0.0941818i	−0.00955728	+	0.00395876i
$567$	1.68464	−	2.04010i	0.0707481	−	0.0856760i
$568$	20.0588	+	8.30861i	0.841647	+	0.348621i
$569$	2.99096	+	11.1624i	0.125388	+	0.467953i	0.999853	−	0.0171346i	$-0.00545437\pi$
$569$	2.99096	+	11.1624i	0.125388	+	0.467953i	−0.874466	+	0.485088i	$0.838788\pi$
$570$	1.16167	+	0.311270i	0.0486572	+	0.0130377i
$571$	−0.162567	−	1.23482i	−0.00680321	−	0.0516755i	0.987707	−	0.156320i	$-0.0499630\pi$
$571$	−0.162567	−	1.23482i	−0.00680321	−	0.0516755i	−0.994510	+	0.104644i	$0.966630\pi$
$572$	−20.3791	−	26.5586i	−0.852093	−	1.11047i
$573$	−21.1532	+	8.76194i	−0.883687	+	0.366035i
$574$	−10.7426	+	2.47052i	−0.448388	+	0.103118i
$575$	−10.7184	−	25.8764i	−0.446986	−	1.07912i
$576$	−0.0460316	+	0.0123341i	−0.00191798	+	0.000513922i
$577$	20.7735	+	35.9808i	0.864813	+	1.49790i	0.867233	+	0.497903i	$0.165896\pi$
$577$	20.7735	+	35.9808i	0.864813	+	1.49790i	−0.00241960	+	0.999997i	$0.500770\pi$
$578$	−7.58705	+	7.59936i	−0.315580	+	0.316092i
$579$	−4.15887	+	7.20338i	−0.172837	+	0.299362i
$580$	4.30443	+	4.30443i	0.178732	+	0.178732i
$581$	−21.4375	−	9.79162i	−0.889378	−	0.406225i
$582$			3.41864i			0.141707i
$583$	0.668773	−	5.07984i	0.0276978	−	0.210385i
$584$	−31.3186	+	4.12317i	−1.29597	+	0.170618i
$585$	−0.487624	−	3.70387i	−0.0201608	−	0.153136i
$586$	−1.36180	−	5.08232i	−0.0562556	−	0.209949i
$587$	−0.505213	+	0.505213i	−0.0208524	+	0.0208524i	−0.717456	−	0.696604i	$-0.754694\pi$
$587$	−0.505213	+	0.505213i	−0.0208524	+	0.0208524i	0.696604	+	0.717456i	$0.254694\pi$
$588$	6.16965	+	9.35579i	0.254432	+	0.385826i
$589$	5.34118	−	12.8948i	0.220080	−	0.531319i
$590$	0.0632144	−	0.480161i	0.00260250	−	0.0197679i
$591$	1.00735	−	0.581593i	0.0414368	−	0.0239235i
$592$	7.11816	−	9.27656i	0.292554	−	0.381264i
$593$	15.5884	−	4.17690i	0.640140	−	0.171525i	0.0758730	−	0.997117i	$-0.475826\pi$
$593$	15.5884	−	4.17690i	0.640140	−	0.171525i	0.564267	+	0.825593i	$0.309159\pi$
$594$	−1.88208			−0.0772227
$595$	2.72399	+	5.12857i	0.111673	+	0.210251i
$596$	24.8184			1.01660
$597$	−18.9360	+	5.07388i	−0.774998	+	0.207660i
$598$	16.0250	−	20.8842i	0.655312	−	0.854019i
$599$	14.9092	−	8.60785i	0.609175	−	0.351707i	−0.163468	−	0.986549i	$-0.552268\pi$
$599$	14.9092	−	8.60785i	0.609175	−	0.351707i	0.772642	+	0.634841i	$0.218935\pi$
$600$	1.40037	−	10.6368i	0.0571697	−	0.434247i
$601$	3.39755	−	8.20241i	0.138589	−	0.334583i	−0.839313	−	0.543649i	$-0.817042\pi$
$601$	3.39755	−	8.20241i	0.138589	−	0.334583i	0.977902	+	0.209066i	$0.0670423\pi$
$602$	0.146930	−	0.873464i	0.00598842	−	0.0355997i
$603$	−2.85840	+	2.85840i	−0.116403	+	0.116403i
$604$	−4.00631	−	14.9518i	−0.163014	−	0.608378i
$605$	−0.147475	−	1.12018i	−0.00599571	−	0.0455419i
$606$	7.82426	−	1.03008i	0.317839	−	0.0418443i
$607$	1.57079	−	11.9313i	0.0637563	−	0.484277i	−0.929544	−	0.368712i	$-0.879799\pi$
$607$	1.57079	−	11.9313i	0.0637563	−	0.484277i	0.993300	−	0.115565i	$-0.0368679\pi$
$608$		−	20.2586i		−	0.821594i
$609$	−1.79528	−	18.8121i	−0.0727485	−	0.762304i
$610$	−1.92986	−	1.92986i	−0.0781379	−	0.0781379i
$611$	−1.87468	+	3.24705i	−0.0758416	+	0.131362i
$612$	−5.71802	−	3.29821i	−0.231137	−	0.133322i
$613$	3.48231	+	6.03154i	0.140649	+	0.243612i	0.927741	−	0.373224i	$-0.121748\pi$
$613$	3.48231	+	6.03154i	0.140649	+	0.243612i	−0.787092	+	0.616836i	$0.788414\pi$
$614$	11.0241	−	2.95391i	0.444898	−	0.119210i
$615$	−1.34365	−	3.24385i	−0.0541811	−	0.130805i
$616$	5.25712	−	17.1432i	0.211816	−	0.690720i
$617$	34.0031	−	14.0846i	1.36891	−	0.567023i	0.427421	−	0.904053i	$-0.359422\pi$
$617$	34.0031	−	14.0846i	1.36891	−	0.567023i	0.941494	+	0.337030i	$0.109422\pi$
$618$	−0.422276	−	0.550320i	−0.0169864	−	0.0221371i
$619$	−2.29893	−	17.4621i	−0.0924016	−	0.701860i	−0.973461	−	0.228854i	$-0.926502\pi$
$619$	−2.29893	−	17.4621i	−0.0924016	−	0.701860i	0.881059	−	0.473006i	$-0.156831\pi$
$620$	3.21256	+	0.860803i	0.129020	+	0.0345707i
$621$	1.53693	+	5.73590i	0.0616749	+	0.230174i
$622$	16.3370	+	6.76699i	0.655053	+	0.271332i
$623$	−33.0214	−	5.55470i	−1.32297	−	0.222544i
$624$	−11.4446	+	4.74051i	−0.458151	+	0.189772i
$625$	18.0390	+	10.4148i	0.721558	+	0.416592i
$626$	−0.255139	+	0.332504i	−0.0101974	+	0.0132895i
$627$	2.75808	−	10.2933i	0.110147	−	0.411075i
$628$	−12.8002	+	22.1706i	−0.510783	+	0.884702i
$629$	−27.0774	+	3.57597i	−1.07965	+	0.142583i
$630$	0.651173	−	0.606196i	0.0259434	−	0.0241514i
$631$	−5.45452	−	5.45452i	−0.217141	−	0.217141i	0.590151	−	0.807293i	$-0.299068\pi$
$631$	−5.45452	−	5.45452i	−0.217141	−	0.217141i	−0.807293	+	0.590151i	$0.799068\pi$
$632$	−5.77180	−	0.759872i	−0.229590	−	0.0302261i
$633$	−9.84692	+	5.68512i	−0.391380	+	0.225963i
$634$	−1.06281	−	0.815520i	−0.0422094	−	0.0323884i
$635$	1.36126	+	1.77403i	0.0540201	+	0.0704004i
$636$	−2.54354	−	1.05357i	−0.100858	−	0.0417767i
$637$	−32.1658	−	37.1296i	−1.27445	−	1.47113i
$638$	−9.50559	+	9.50559i	−0.376330	+	0.376330i
$639$	7.57255	−	5.81062i	0.299565	−	0.229865i
$640$	5.96312	−	0.785059i	0.235713	−	0.0310322i
$641$	10.0941	+	7.74548i	0.398693	+	0.305928i	0.788577	−	0.614936i	$-0.210818\pi$
$641$	10.0941	+	7.74548i	0.398693	+	0.305928i	−0.389884	+	0.920864i	$0.627485\pi$
$642$	−8.81777	−	5.09094i	−0.348010	−	0.200923i
$643$	10.6612	+	25.7385i	0.420438	+	1.01503i	0.982219	+	0.187740i	$0.0601163\pi$
$643$	10.6612	+	25.7385i	0.420438	+	1.01503i	−0.561781	+	0.827286i	$0.689884\pi$
$644$	−25.1373	−	0.899174i	−0.990547	−	0.0354324i
$645$	0.282130			0.0111089
$646$	−6.58399	+	6.58932i	−0.259043	+	0.259253i
$647$	−11.1927	−	19.3863i	−0.440030	−	0.762154i	0.557661	−	0.830069i	$-0.311699\pi$
$647$	−11.1927	−	19.3863i	−0.440030	−	0.762154i	−0.997691	+	0.0679147i	$0.978365\pi$
$648$	−0.588721	+	2.19714i	−0.0231271	+	0.0863117i
$649$	−4.25459	−	0.560127i	−0.167007	−	0.0219869i
$650$			20.9086i			0.820102i
$651$	−5.98852	−	8.41068i	−0.234708	−	0.329641i
$652$	−0.101593	+	0.245266i	−0.00397867	+	0.00960537i
$653$	−27.9243	+	21.4270i	−1.09276	+	0.838505i	−0.987762	−	0.155967i	$-0.950151\pi$
$653$	−27.9243	+	21.4270i	−1.09276	+	0.838505i	−0.104999	+	0.994472i	$0.533484\pi$
$654$	−8.78773	−	2.35466i	−0.343627	−	0.0920746i
$655$	−1.12804	−	0.302257i	−0.0440761	−	0.0118101i
$656$	−9.23656	+	7.08746i	−0.360627	+	0.276719i
$657$	−5.31447	+	12.8303i	−0.207337	+	0.500557i
$658$	−0.888848	+	0.0848250i	−0.0346509	+	0.00330682i
$659$			16.9137i			0.658864i	0.944179	+	0.329432i	$0.106857\pi$
$659$			16.9137i			0.658864i	−0.944179	+	0.329432i	$0.893143\pi$
$660$	2.51762	+	0.331451i	0.0979981	+	0.0129017i
$661$	−8.38062	+	31.2769i	−0.325968	+	1.21653i	0.587366	+	0.809321i	$0.300165\pi$
$661$	−8.38062	+	31.2769i	−0.325968	+	1.21653i	−0.913335	+	0.407209i	$0.866502\pi$
$662$	−2.01273	−	3.48615i	−0.0782269	−	0.135493i
$663$	26.7371	+	11.0622i	1.03838	+	0.429620i
$664$	20.2621			0.786321
$665$	2.36110	+	4.44969i	0.0915594	+	0.172551i
$666$	1.60128	+	3.86584i	0.0620485	+	0.149798i
$667$	36.7320	+	21.2072i	1.42227	+	0.821147i
$668$	30.4282	+	23.3484i	1.17730	+	0.903377i
$669$	25.4095	−	3.34522i	0.982387	−	0.129334i
$670$	−1.07840	+	0.827487i	−0.0416623	+	0.0319686i
$671$	−17.1000	+	17.1000i	−0.660140	+	0.660140i
$672$	−12.7023	−	7.95231i	−0.490004	−	0.306767i
$673$	−23.4908	−	9.73019i	−0.905502	−	0.375071i	−0.119169	−	0.992874i	$-0.538023\pi$
$673$	−23.4908	−	9.73019i	−0.905502	−	0.375071i	−0.786333	+	0.617803i	$0.788023\pi$
$674$	0.871828	+	1.13619i	0.0335816	+	0.0437643i
$675$	−3.74195	−	2.87130i	−0.144028	−	0.110516i
$676$	50.2604	−	29.0178i	1.93309	−	1.11607i
$677$	19.4771	+	2.56421i	0.748565	+	0.0985505i	0.495150	−	0.868807i	$-0.335113\pi$
$677$	19.4771	+	2.56421i	0.748565	+	0.0985505i	0.253415	+	0.967358i	$0.418446\pi$
$678$	0.817957	+	0.817957i	0.0314134	+	0.0314134i
$679$	−10.4805	+	9.75660i	−0.402204	+	0.374424i
$680$	−3.96209	−	3.03767i	−0.151939	−	0.116489i
$681$	−2.18549	+	3.78538i	−0.0837482	+	0.145056i
$682$	−1.90094	+	7.09439i	−0.0727906	+	0.271658i
$683$	−3.71024	+	4.83527i	−0.141968	+	0.185017i	−0.858926	−	0.512100i	$-0.828868\pi$
$683$	−3.71024	+	4.83527i	−0.141968	+	0.185017i	0.716957	+	0.697117i	$0.245534\pi$
$684$	−4.95888	−	2.86301i	−0.189608	−	0.109470i
$685$	9.42050	−	3.90210i	0.359939	−	0.149091i
$686$	2.75997	−	11.3685i	0.105376	−	0.434051i
$687$	−3.89537	−	1.61351i	−0.148617	−	0.0615594i
$688$	−0.242127	−	0.903630i	−0.00923101	−	0.0344506i
$689$	11.6568	+	3.12344i	0.444090	+	0.118994i
$690$	0.260635	+	1.97972i	0.00992219	+	0.0753665i
$691$	16.2521	+	21.1801i	0.618259	+	0.805731i	0.992583	−	0.121567i	$-0.0387919\pi$
$691$	16.2521	+	21.1801i	0.618259	+	0.805731i	−0.374324	+	0.927298i	$0.622125\pi$
$692$	−14.6666	+	6.07512i	−0.557542	+	0.230942i
$693$	−5.37135	−	5.76988i	−0.204041	−	0.219180i
$694$	−4.91279	−	11.8605i	−0.186487	−	0.450219i
$695$	2.14286	−	0.574178i	0.0812834	−	0.0217798i
$696$	8.12343	+	14.0702i	0.307918	+	0.533329i
$697$	26.9635	+	3.53870i	1.02132	+	0.134038i
$698$	−7.91311	+	13.7059i	−0.299516	+	0.518776i
$699$	13.8195	+	13.8195i	0.522703	+	0.522703i
$700$	16.2749	−	11.5879i	0.615132	−	0.437982i
$701$		−	7.46326i		−	0.281883i	−0.990018	−	0.140942i	$-0.954987\pi$
$701$		−	7.46326i		−	0.281883i	0.990018	−	0.140942i	$-0.0450130\pi$
$702$	0.578617	−	4.39503i	0.0218385	−	0.165880i
$703$	−23.4893	+	3.09243i	−0.885916	+	0.116633i
$704$	0.0185335	+	0.140776i	0.000698507	+	0.00530568i
$705$	−0.0736101	−	0.274717i	−0.00277232	−	0.0103464i
$706$	−1.62960	+	1.62960i	−0.0613308	+	0.0613308i
$707$	25.4879	+	21.0470i	0.958572	+	0.791553i
$708$	−0.882410	+	2.13033i	−0.0331630	+	0.0800626i
$709$	−1.73719	+	13.1953i	−0.0652416	+	0.495559i	0.927363	+	0.374164i	$0.122070\pi$
$709$	−1.73719	+	13.1953i	−0.0652416	+	0.495559i	−0.992604	+	0.121395i	$0.961263\pi$
$710$	2.77960	−	1.60480i	0.104317	−	0.0602272i
$711$	−1.55803	+	2.03047i	−0.0584308	+	0.0761485i
$712$	27.8075	−	7.45100i	1.04213	−	0.279238i
$713$	23.1735			0.867854
$714$	1.54710	+	6.71480i	0.0578987	+	0.251295i
$715$	−11.1310			−0.416276
$716$	31.5906	−	8.46468i	1.18060	−	0.316340i
$717$	14.6752	−	19.1252i	0.548057	−	0.714242i
$718$	−16.4493	+	9.49698i	−0.613881	+	0.354424i
$719$	−0.497758	+	3.78085i	−0.0185632	+	0.141002i	−0.998217	−	0.0596948i	$-0.980987\pi$
$719$	−0.497758	+	3.78085i	−0.0185632	+	0.141002i	0.979653	+	0.200697i	$0.0643206\pi$
$720$	0.359590	−	0.868128i	0.0134011	−	0.0323532i
$721$	0.481962	−	2.86515i	0.0179492	−	0.106704i
$722$	2.77299	−	2.77299i	0.103200	−	0.103200i
$723$	2.75333	+	10.2756i	0.102398	+	0.382153i
$724$	3.79369	+	28.8159i	0.140991	+	1.07093i
$725$	−33.4007	+	4.39729i	−1.24047	+	0.163311i
$726$	0.174994	−	1.32921i	0.00649465	−	0.0493318i
$727$		−	6.45965i		−	0.239575i	−0.992800	−	0.119788i	$-0.961779\pi$
$727$		−	6.45965i		−	0.239575i	0.992800	−	0.119788i	$-0.0382214\pi$
$728$	38.4166	+	17.5469i	1.42382	+	0.650330i
$729$	0.707107	+	0.707107i	0.0261891	+	0.0261891i
$730$	−2.33489	+	4.04416i	−0.0864183	+	0.149681i
$731$	−1.09183	+	1.89287i	−0.0403827	+	0.0700103i
$732$	6.49717	+	11.2534i	0.240142	+	0.415939i
$733$	−9.70662	+	2.60088i	−0.358522	+	0.0960657i	−0.433584	−	0.901113i	$-0.642751\pi$
$733$	−9.70662	+	2.60088i	−0.358522	+	0.0960657i	0.0750619	+	0.997179i	$0.476085\pi$
$734$	0.620544	+	1.49813i	0.0229047	+	0.0552968i
$735$	3.71682	+	0.266246i	0.137097	+	0.00982065i
$736$	31.0755	−	12.8719i	1.14546	−	0.474464i
$737$	7.33216	+	9.55545i	0.270083	+	0.351980i
$738$	−0.543813	−	4.13067i	−0.0200180	−	0.152052i
$739$	−45.8281	−	12.2796i	−1.68581	−	0.451713i	−0.716510	−	0.697577i	$-0.754262\pi$
$739$	−45.8281	−	12.2796i	−1.68581	−	0.451713i	−0.969304	+	0.245864i	$0.920928\pi$
$740$	−1.46119	−	5.45325i	−0.0537146	−	0.200465i
$741$	23.1890	+	9.60520i	0.851869	+	0.352856i
$742$	1.00418	+	2.69277i	0.0368647	+	0.0988549i
$743$	−9.49146	+	3.93149i	−0.348208	+	0.144232i	−0.549931	−	0.835210i	$-0.685346\pi$
$743$	−9.49146	+	3.93149i	−0.348208	+	0.144232i	0.201723	+	0.979443i	$0.435346\pi$
$744$	7.68736	+	4.43830i	0.281832	+	0.162716i
$745$	5.02363	−	6.54693i	0.184052	−	0.239861i
$746$	−0.576416	+	2.15121i	−0.0211041	+	0.0787616i
$747$	4.45390	−	7.71439i	0.162960	−	0.282255i
$748$	−11.9668	+	15.6085i	−0.437549	+	0.570704i
$749$	−9.55816	−	41.5618i	−0.349248	−	1.51864i
$750$	−2.31034	−	2.31034i	−0.0843618	−	0.0843618i
$751$	0.915291	+	0.120500i	0.0333994	+	0.00439712i	0.147207	−	0.989106i	$-0.452972\pi$
$751$	0.915291	+	0.120500i	0.0333994	+	0.00439712i	−0.113808	+	0.993503i	$0.536305\pi$
$752$	−0.816713	+	0.471530i	−0.0297825	+	0.0171949i
$753$	4.83803	+	3.71235i	0.176307	+	0.135285i
$754$	−19.2751	−	25.1198i	−0.701958	−	0.914810i
$755$	−4.75511	−	1.96963i	−0.173056	−	0.0716821i
$756$	−3.74170	+	1.98542i	−0.136084	+	0.0722092i
$757$	−31.5133	+	31.5133i	−1.14537	+	1.14537i	−0.157919	+	0.987452i	$0.550479\pi$
$757$	−31.5133	+	31.5133i	−1.14537	+	1.14537i	−0.987452	+	0.157919i	$0.949521\pi$
$758$	13.7723	−	10.5679i	0.500233	−	0.383842i
$759$	17.5418	−	2.30942i	0.636726	−	0.0838265i
$760$	−3.43581	−	2.63639i	−0.124630	−	0.0956320i
$761$	−36.8073	−	21.2507i	−1.33426	−	0.770338i	−0.348314	−	0.937378i	$-0.613246\pi$
$761$	−36.8073	−	21.2507i	−1.33426	−	0.770338i	−0.985950	+	0.167040i	$0.946579\pi$
$762$	1.01541	+	2.45141i	0.0367844	+	0.0888053i
$763$	−17.8610	−	33.6606i	−0.646612	−	1.21859i
$764$	36.6564			1.32618
$765$	−2.02746	+	0.840764i	−0.0733030	+	0.0303979i
$766$	5.55801	+	9.62676i	0.200819	+	0.347829i
$767$	2.61602	−	9.76311i	0.0944589	−	0.352525i
$768$	7.17036	+	0.943995i	0.258738	+	0.0340635i
$769$		−	9.73505i		−	0.351055i	−0.984475	−	0.175527i	$-0.943837\pi$
$769$		−	9.73505i		−	0.351055i	0.984475	−	0.175527i	$-0.0561631\pi$
$770$	−1.53748	−	2.15934i	−0.0554069	−	0.0778172i
$771$	−1.27255	+	3.07222i	−0.0458299	+	0.110643i
$772$	10.5648	−	8.10666i	0.380236	−	0.291765i
$773$	38.1316	+	10.2173i	1.37150	+	0.367492i	0.868026	−	0.496518i	$-0.165388\pi$
$773$	38.1316	+	10.2173i	1.37150	+	0.367492i	0.503474	+	0.864011i	$0.332055\pi$
$774$	0.323369	+	0.0866466i	0.0116233	+	0.00311445i
$775$	−14.6026	+	11.2050i	−0.524542	+	0.402495i
$776$	4.71102	−	11.3734i	0.169116	−	0.408281i
$777$	−7.28151	+	15.9419i	−0.261223	+	0.571914i
$778$			24.5480i			0.880088i
$779$	23.3880	+	3.07909i	0.837962	+	0.110320i
$780$	−1.54801	+	5.77724i	−0.0554275	+	0.206858i
$781$	−14.2198	−	24.6293i	−0.508823	−	0.881307i
$782$	−14.2910	−	5.91273i	−0.511044	−	0.211439i
$783$	7.14260			0.255256
$784$	−2.33706	−	12.1331i	−0.0834665	−	0.433323i
$785$	3.25748	+	7.86426i	0.116265	+	0.280688i
$786$	−1.20010	−	0.692876i	−0.0428060	−	0.0247141i
$787$	9.12124	+	6.99897i	0.325137	+	0.249486i	0.758412	−	0.651775i	$-0.225975\pi$
$787$	9.12124	+	6.99897i	0.325137	+	0.249486i	−0.433275	+	0.901262i	$0.642642\pi$
$788$	−1.84632	+	0.243072i	−0.0657724	+	0.00865910i
$789$	0.220814	−	0.169436i	0.00786118	−	0.00603209i
$790$	−0.608542	+	0.608542i	−0.0216510	+	0.0216510i
$791$	−0.173201	+	4.84201i	−0.00615833	+	0.172162i
$792$	6.26146	+	2.59358i	0.222491	+	0.0921589i
$793$	−34.6749	−	45.1891i	−1.23134	−	1.60471i
$794$	6.53223	+	5.01236i	0.231820	+	0.177882i
$795$	−0.792776	+	0.457709i	−0.0281169	+	0.0162333i
$796$	31.1173	+	4.09667i	1.10292	+	0.145203i
$797$	−1.35887	−	1.35887i	−0.0481338	−	0.0481338i	0.682630	−	0.730764i	$-0.260836\pi$
$797$	−1.35887	−	1.35887i	−0.0481338	−	0.0481338i	−0.730764	+	0.682630i	$0.760836\pi$
$798$	1.33965	+	5.82523i	0.0474233	+	0.206211i
$799$	2.12800	+	0.569271i	0.0752832	+	0.0201394i
$800$	−13.3581	+	23.1370i	−0.472281	+	0.818015i
$801$	3.27568	−	12.2250i	0.115740	−	0.431949i
$802$	−1.39520	+	1.81827i	−0.0492664	+	0.0642052i
$803$	35.8342	+	20.6889i	1.26456	+	0.730096i
$804$	5.97919	−	2.47666i	0.210870	−	0.0873451i
$805$	−5.32537	+	6.44903i	−0.187694	+	0.227298i
$806$	−15.9824	−	6.62013i	−0.562956	−	0.233184i
$807$	−7.82637	−	29.2084i	−0.275501	−	1.02819i
$808$	−27.4499	−	7.35517i	−0.965683	−	0.258754i
$809$	−4.90253	−	37.2384i	−0.172364	−	1.30923i	−0.830790	−	0.556586i	$-0.812111\pi$
$809$	−4.90253	−	37.2384i	−0.172364	−	1.30923i	0.658426	−	0.752645i	$-0.271223\pi$
$810$	0.204703	+	0.266774i	0.00719252	+	0.00937348i
$811$	−27.8998	+	11.5565i	−0.979696	+	0.405803i	−0.814313	−	0.580426i	$-0.802886\pi$
$811$	−27.8998	+	11.5565i	−0.979696	+	0.405803i	−0.165383	+	0.986229i	$0.552886\pi$
$812$	−8.87020	+	28.9253i	−0.311283	+	1.01508i
$813$	−5.13786	−	12.4039i	−0.180193	−	0.435024i
$814$	12.0426	−	3.22680i	0.422092	−	0.113099i
$815$	0.0441356	+	0.0764451i	0.00154600	+	0.00267775i
$816$	4.43286	+	5.77217i	0.155181	+	0.202066i
$817$	−0.947760	+	1.64157i	−0.0331579	+	0.0574312i
$818$	10.4305	+	10.4305i	0.364692	+	0.364692i
$819$	15.1252	−	10.7693i	0.528516	−	0.376310i
$820$			5.62127i			0.196303i
$821$	−3.74974	+	28.4821i	−0.130867	+	0.994033i	0.792435	+	0.609957i	$0.208813\pi$
$821$	−3.74974	+	28.4821i	−0.130867	+	0.994033i	−0.923302	+	0.384076i	$0.874520\pi$
$822$	11.9959	−	1.57929i	0.418405	−	0.0550841i
$823$	4.71579	+	35.8200i	0.164382	+	1.24861i	0.852391	+	0.522905i	$0.175152\pi$
$823$	4.71579	+	35.8200i	0.164382	+	1.24861i	−0.688009	+	0.725702i	$0.741515\pi$
$824$	0.646498	+	2.41276i	0.0225218	+	0.0840526i
$825$	−9.93717	+	9.93717i	−0.345968	+	0.345968i
$826$	2.25532	−	0.841047i	0.0784725	−	0.0292638i
$827$	−10.2394	+	24.7200i	−0.356058	+	0.859600i	0.639788	+	0.768551i	$0.279022\pi$
$827$	−10.2394	+	24.7200i	−0.356058	+	0.859600i	−0.995846	+	0.0910489i	$0.970978\pi$
$828$	1.24092	−	9.42574i	0.0431250	−	0.327567i
$829$	−21.4971	+	12.4113i	−0.746624	+	0.431064i	−0.824473	−	0.565902i	$-0.808528\pi$
$829$	−21.4971	+	12.4113i	−0.746624	+	0.431064i	0.0778487	+	0.996965i	$0.475195\pi$
$830$	1.82345	−	2.37637i	0.0632930	−	0.0824850i
$831$	13.7583	−	3.68651i	0.477268	−	0.127884i
$832$	−0.334437			−0.0115945
$833$	−16.1702	+	23.9066i	−0.560264	+	0.828314i
$834$	2.63243			0.0911535
$835$	12.3183	−	3.30067i	0.426292	−	0.114225i
$836$	−10.3860	+	13.5353i	−0.359206	+	0.468127i
$837$	3.37959	−	1.95121i	0.116816	−	0.0674436i
$838$	0.153797	−	1.16820i	0.00531282	−	0.0403549i
$839$	13.4785	−	32.5400i	0.465330	−	1.12341i	−0.500849	−	0.865535i	$-0.666979\pi$
$839$	13.4785	−	32.5400i	0.465330	−	1.12341i	0.966179	−	0.257872i	$-0.0830213\pi$
$840$	−3.00174	+	1.11940i	−0.103570	+	0.0386230i
$841$	15.5682	−	15.5682i	0.536834	−	0.536834i
$842$	−5.01240	−	18.7065i	−0.172739	−	0.644670i
$843$	−1.22838	−	9.33047i	−0.0423077	−	0.321359i
$844$	18.0479	−	2.37605i	0.621235	−	0.0817871i
$845$	2.51877	−	19.1320i	0.0866484	−	0.658160i
$846$		−	0.337479i		−	0.0116028i
$847$	4.57439	−	3.25703i	0.157178	−	0.111913i
$848$	2.14636	+	2.14636i	0.0737063	+	0.0737063i
$849$	0.194808	−	0.337417i	0.00668578	−	0.0115801i
$850$	11.8643	−	3.18419i	0.406943	−	0.109217i
$851$	−19.6682	−	34.0664i	−0.674218	−	1.16778i
$852$	−14.7607	+	3.95513i	−0.505695	+	0.135500i
$853$	15.2282	+	36.7640i	0.521402	+	1.25878i	0.937033	+	0.349242i	$0.113561\pi$
$853$	15.2282	+	36.7640i	0.521402	+	1.25878i	−0.415631	+	0.909534i	$0.636439\pi$
$854$	3.97690	−	12.9685i	0.136087	−	0.443772i
$855$	−1.75900	+	0.728600i	−0.0601564	+	0.0249176i
$856$	22.3202	+	29.0882i	0.762887	+	0.994214i
$857$	−0.784930	−	5.96214i	−0.0268127	−	0.203663i	0.972795	−	0.231667i	$-0.0744180\pi$
$857$	−0.784930	−	5.96214i	−0.0268127	−	0.203663i	−0.999608	+	0.0280045i	$0.991085\pi$
$858$	−12.7580	−	3.41851i	−0.435552	−	0.116706i
$859$	11.5053	+	42.9385i	0.392557	+	1.46504i	0.825901	+	0.563815i	$0.190667\pi$
$859$	11.5053	+	42.9385i	0.392557	+	1.46504i	−0.433344	+	0.901229i	$0.642666\pi$
$860$	−0.417305	−	0.172853i	−0.0142300	−	0.00589425i
$861$	11.1113	−	13.4559i	0.378674	−	0.458574i
$862$	−7.77243	+	3.21945i	−0.264730	+	0.109655i
$863$	−30.8392	−	17.8050i	−1.04978	−	0.606089i	−0.127191	−	0.991878i	$-0.540596\pi$
$863$	−30.8392	−	17.8050i	−1.04978	−	0.606089i	−0.922587	+	0.385789i	$0.873929\pi$
$864$	3.44820	−	4.49378i	0.117310	−	0.152881i
$865$	−1.36618	+	5.09866i	−0.0464515	+	0.173359i
$866$	−2.91572	+	5.05018i	−0.0990803	+	0.171612i
$867$	2.20529	−	16.8564i	0.0748954	−	0.572472i
$868$	3.70476	+	16.1094i	0.125748	+	0.546790i
$869$	5.39214	+	5.39214i	0.182916	+	0.182916i
$870$	2.38123	+	0.313495i	0.0807313	+	0.0106285i
$871$	−24.5681	+	14.1844i	−0.832457	+	0.480619i
$872$	25.9909	+	19.9435i	0.880163	+	0.675373i
$873$	−3.29465	−	4.29367i	−0.111507	−	0.145319i
$874$	−12.3945	−	5.13396i	−0.419250	−	0.173659i
$875$	0.489213	−	13.6764i	0.0165384	−	0.462347i
$876$	15.7215	−	15.7215i	0.531181	−	0.531181i
$877$	14.9272	−	11.4541i	0.504057	−	0.386776i	−0.325199	−	0.945646i	$-0.605431\pi$
$877$	14.9272	−	11.4541i	0.504057	−	0.386776i	0.829256	+	0.558869i	$0.188765\pi$
$878$	10.1335	−	1.33410i	0.341989	−	0.0450237i
$879$	6.60836	+	5.07077i	0.222894	+	0.171033i
$880$	−2.42463	−	1.39986i	−0.0817343	−	0.0471893i
$881$	11.8582	+	28.6281i	0.399511	+	0.964506i	0.987782	+	0.155842i	$0.0498089\pi$
$881$	11.8582	+	28.6281i	0.399511	+	0.964506i	−0.588271	+	0.808664i	$0.700191\pi$
$882$	4.17835	+	1.44666i	0.140692	+	0.0487116i
$883$	48.2187			1.62269			0.811344	−	0.584569i	$-0.198736\pi$
$883$	48.2187			1.62269			0.811344	+	0.584569i	$0.198736\pi$
$884$	−32.7700	−	32.7435i	−1.10217	−	1.10128i
$885$	0.383352	+	0.663984i	0.0128862	+	0.0223196i
$886$	3.54980	−	13.2481i	0.119258	−	0.445077i
$887$	5.62295	+	0.740275i	0.188800	+	0.0248560i	0.224333	−	0.974512i	$-0.427980\pi$
$887$	5.62295	+	0.740275i	0.188800	+	0.0248560i	−0.0355331	+	0.999368i	$0.511313\pi$
$888$		−	15.0678i		−	0.505643i
$889$	−4.61736	+	10.1091i	−0.154861	+	0.339049i
$890$	1.62863	−	3.93185i	0.0545917	−	0.131796i
$891$	2.36381	−	1.81382i	0.0791908	−	0.0607652i
$892$	−39.6333	−	10.6197i	−1.32702	−	0.355574i
$893$	1.84571	+	0.494557i	0.0617644	+	0.0165497i
$894$	7.76861	−	5.96106i	0.259821	−	0.199368i
$895$	4.16151	−	10.0468i	0.139104	−	0.335826i
$896$	17.3383	+	24.3510i	0.579230	+	0.813511i
$897$			41.6735i			1.39144i
$898$	10.0922	+	1.32867i	0.336782	+	0.0443382i
$899$	7.21416	−	26.9236i	0.240606	−	0.897953i
$900$	3.77563	+	6.53959i	0.125854	+	0.217986i
$901$	−0.00287304	−	7.09021i	−9.57149e−5	−	0.236209i
$902$	−12.4136			−0.413328
$903$	0.657247	+	1.23864i	0.0218718	+	0.0412192i
$904$	−1.59407	−	3.84842i	−0.0530179	−	0.127997i
$905$	8.36933	+	4.83203i	0.278206	+	0.160622i
$906$	−4.84526	−	3.71790i	−0.160973	−	0.123519i
$907$	56.4832	−	7.43616i	1.87549	−	0.246914i	0.895374	−	0.445315i	$-0.146908\pi$
$907$	56.4832	−	7.43616i	1.87549	−	0.246914i	0.980121	+	0.198402i	$0.0635751\pi$
$908$	5.55181	−	4.26005i	0.184243	−	0.141375i
$909$	−8.83422	+	8.83422i	−0.293013	+	0.293013i
$910$	5.51517	−	2.92646i	0.182826	−	0.0970114i
$911$	32.2556	+	13.3607i	1.06868	+	0.442660i	0.846523	−	0.532352i	$-0.178692\pi$
$911$	32.2556	+	13.3607i	1.06868	+	0.442660i	0.222153	+	0.975012i	$0.428692\pi$
$912$	3.84321	+	5.00857i	0.127261	+	0.165850i
$913$	−21.0564	−	16.1571i	−0.696865	−	0.534724i
$914$	1.83067	−	1.05694i	0.0605532	−	0.0349604i
$915$	4.28370	+	0.563960i	0.141615	+	0.0186439i
$916$	4.77317	+	4.77317i	0.157710	+	0.157710i
$917$	−1.30086	−	5.65656i	−0.0429583	−	0.186796i
$918$	−2.58203	+	0.340995i	−0.0852196	+	0.0112545i
$919$	−23.1775	+	40.1446i	−0.764555	+	1.32425i	0.175926	+	0.984403i	$0.443708\pi$
$919$	−23.1775	+	40.1446i	−0.764555	+	1.32425i	−0.940481	+	0.339845i	$0.889625\pi$
$920$	1.86103	−	6.94545i	0.0613562	−	0.228985i
$921$	−10.9991	+	14.3343i	−0.362432	+	0.472331i
$922$	4.25874	+	2.45878i	0.140254	+	0.0809757i
$923$	61.8861	−	25.6341i	2.03701	−	0.843755i
$924$	4.40984	+	11.8252i	0.145073	+	0.389022i
$925$	28.8658	+	11.9566i	0.949101	+	0.393131i
$926$	2.58444	+	9.64526i	0.0849299	+	0.316963i
$927$	1.06072	+	0.284219i	0.0348387	+	0.00933499i
$928$	−5.28079	−	40.1116i	−0.173350	−	1.31673i
$929$	2.11323	+	2.75402i	0.0693329	+	0.0903564i	0.826732	−	0.562595i	$-0.190197\pi$
$929$	2.11323	+	2.75402i	0.0693329	+	0.0903564i	−0.757399	+	0.652952i	$0.773530\pi$
$930$	1.21234	−	0.502169i	0.0397543	−	0.0164668i
$931$	−14.0351	+	20.7319i	−0.459981	+	0.679459i
$932$	−11.9739	−	28.9076i	−0.392219	−	0.946901i
$933$	−27.0401	+	7.24538i	−0.885254	+	0.237203i
$934$	−4.73665	−	8.20412i	−0.154988	−	0.268447i
$935$	1.69515	+	6.31616i	0.0554375	+	0.206561i
$936$	−7.98152	+	13.8244i	−0.260884	+	0.451865i
$937$	−23.6146	−	23.6146i	−0.771457	−	0.771457i	0.206904	−	0.978361i	$-0.433661\pi$
$937$	−23.6146	−	23.6146i	−0.771457	−	0.771457i	−0.978361	+	0.206904i	$0.933661\pi$
$938$	−6.14515	−	2.80681i	−0.200646	−	0.0916456i
$939$		−	0.663497i		−	0.0216524i
$940$	−0.0594330	+	0.451439i	−0.00193849	+	0.0147243i
$941$	−24.3192	+	3.20168i	−0.792783	+	0.104372i	−0.516031	−	0.856570i	$-0.672591\pi$
$941$	−24.3192	+	3.20168i	−0.792783	+	0.104372i	−0.276751	+	0.960942i	$0.589258\pi$
$942$	1.31840	+	10.0142i	0.0429557	+	0.326281i
$943$	10.1371	+	37.8322i	0.330110	+	1.23199i
$944$	1.79767	−	1.79767i	0.0585092	−	0.0585092i
$945$	−0.233636	+	1.38891i	−0.00760019	+	0.0451814i
$946$	0.381717	−	0.921547i	0.0124107	−	0.0299621i
$947$	−1.34601	+	10.2240i	−0.0437394	+	0.332234i	0.955560	+	0.294798i	$0.0952524\pi$
$947$	−1.34601	+	10.2240i	−0.0437394	+	0.332234i	−0.999299	+	0.0374360i	$0.988081\pi$
$948$	3.54853	−	2.04875i	0.115251	−	0.0665402i
$949$	−59.3294	+	77.3196i	−1.92591	+	2.50990i
$950$	10.2927	−	2.75793i	0.333940	−	0.0894789i
$951$	2.12078			0.0687711
$952$	4.10625	−	24.4713i	0.133084	−	0.793120i
$953$	−7.58653			−0.245752			−0.122876	−	0.992422i	$-0.539212\pi$
$953$	−7.58653			−0.245752			−0.122876	+	0.992422i	$0.539212\pi$
$954$	−1.04923	+	0.281140i	−0.0339700	+	0.00910223i
$955$	7.41981	−	9.66969i	0.240100	−	0.312904i
$956$	−33.4240	+	19.2973i	−1.08101	+	0.624120i
$957$	2.77780	−	21.0995i	0.0897935	−	0.682049i
$958$	7.27759	−	17.5697i	0.235128	−	0.567650i
$959$	39.0773	+	32.2685i	1.26187	+	1.04201i
$960$	0.0179384	−	0.0179384i	0.000578958	−	0.000578958i
$961$	4.08188	+	15.2338i	0.131673	+	0.491412i
$962$	3.83291	+	29.1138i	0.123578	+	0.938668i
$963$	15.9811	−	2.10395i	0.514982	−	0.0677987i
$964$	2.22305	−	16.8857i	0.0715996	−	0.543853i
$965$		−	4.42783i		−	0.142537i
$966$	−8.08438	+	5.75619i	−0.260111	+	0.185202i
$967$	−15.6694	−	15.6694i	−0.503895	−	0.503895i	0.408751	−	0.912646i	$-0.365965\pi$
$967$	−15.6694	−	15.6694i	−0.503895	−	0.503895i	−0.912646	+	0.408751i	$0.865965\pi$
$968$	−2.41390	+	4.18099i	−0.0775856	+	0.134382i
$969$	1.91888	−	14.6211i	0.0616433	−	0.469698i
$970$	−0.909931	−	1.57605i	−0.0292161	−	0.0506038i
$971$	−22.4222	+	6.00801i	−0.719562	+	0.192806i	−0.599976	−	0.800018i	$-0.704823\pi$
$971$	−22.4222	+	6.00801i	−0.719562	+	0.192806i	−0.119586	+	0.992824i	$0.538157\pi$
$972$	−0.612673	−	1.47912i	−0.0196515	−	0.0474429i
$973$	7.51280	+	8.07021i	0.240849	+	0.258719i
$974$	−21.4602	+	8.88909i	−0.687628	+	0.284825i
$975$	−20.1502	−	26.2603i	−0.645324	−	0.841003i
$976$	−1.87002	−	14.2042i	−0.0598578	−	0.454665i
$977$	−2.08002	−	0.557340i	−0.0665458	−	0.0178309i	0.225393	−	0.974268i	$-0.427634\pi$
$977$	−2.08002	−	0.557340i	−0.0665458	−	0.0178309i	−0.291938	+	0.956437i	$0.594300\pi$
$978$	0.0271095	+	0.101174i	0.000866865	+	0.00323518i
$979$	−34.8391	−	14.4308i	−1.11346	−	0.461212i
$980$	−5.33452	−	2.67101i	−0.170405	−	0.0853222i
$981$	13.3063	−	5.51164i	0.424837	−	0.175973i
$982$	5.09500	+	2.94160i	0.162588	+	0.0938703i
$983$	12.1023	−	15.7720i	0.386004	−	0.503050i	−0.559424	−	0.828882i	$-0.688978\pi$
$983$	12.1023	−	15.7720i	0.386004	−	0.503050i	0.945428	+	0.325832i	$0.105644\pi$
$984$	−3.88302	+	14.4916i	−0.123786	+	0.461977i
$985$	−0.309603	+	0.536247i	−0.00986476	+	0.0170863i
$986$	−11.3185	+	14.7630i	−0.360455	+	0.470149i
$987$	1.03461	−	0.963147i	0.0329319	−	0.0306573i
$988$	−28.4145	−	28.4145i	−0.903987	−	0.903987i
$989$	−3.12026	−	0.410790i	−0.0992184	−	0.0130623i
$990$	0.867669	−	0.500949i	0.0275763	−	0.0159212i
$991$	−48.3468	−	37.0978i	−1.53579	−	1.17845i	−0.920876	−	0.389855i	$-0.872525\pi$
$991$	−48.3468	−	37.0978i	−1.53579	−	1.17845i	−0.614912	−	0.788596i	$-0.710808\pi$
$992$	−13.4563	−	17.5366i	−0.427238	−	0.556787i
$993$	5.88761	+	2.43873i	0.186838	+	0.0773907i
$994$	13.5209	+	8.46476i	0.428857	+	0.268486i
$995$	7.37929	−	7.37929i	0.233939	−	0.233939i
$996$	−11.3143	+	8.68174i	−0.358506	+	0.275091i
$997$	−3.44020	+	0.452911i	−0.108952	+	0.0143438i	−0.184805	−	0.982775i	$-0.559165\pi$
$997$	−3.44020	+	0.452911i	−0.108952	+	0.0143438i	0.0758529	+	0.997119i	$0.475832\pi$
$998$	4.94887	+	3.79740i	0.156654	+	0.120205i
$999$	−5.73678	−	3.31213i	−0.181504	−	0.104791i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.bh.a.100.11	yes	192
7.4	even	3	inner	357.2.bh.a.151.14	yes	192
17.8	even	8	inner	357.2.bh.a.331.14	yes	192
119.25	even	24	inner	357.2.bh.a.25.11	✓	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.bh.a.25.11	✓	192	119.25	even	24	inner
357.2.bh.a.100.11	yes	192	1.1	even	1	trivial
357.2.bh.a.151.14	yes	192	7.4	even	3	inner
357.2.bh.a.331.14	yes	192	17.8	even	8	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:	\( N \)	\(=\)	\( 357 = 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	357.bh (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.610148 + 0.163489i) q^{2} +(0.608761 - 0.793353i) q^{3} +(-1.38650 + 0.800496i) q^{4} +(-0.0694837 + 0.527781i) q^{5} +(-0.241730 + 0.583588i) q^{6} +(-2.47899 + 0.924458i) q^{7} +(1.60842 - 1.60842i) q^{8} +(-0.258819 - 0.965926i) q^{9} +(-0.0438909 - 0.333384i) q^{10} +(-2.95403 + 0.388906i) q^{11} +(-0.208971 + 1.58729i) q^{12} -7.01782i q^{13} +(1.36141 - 0.969342i) q^{14} +(0.376418 + 0.376418i) q^{15} +(0.882578 - 1.52867i) q^{16} +(-3.98218 + 1.06875i) q^{17} +(0.315836 + 0.547043i) q^{18} +(-3.45468 + 0.925679i) q^{19} +(-0.326147 - 0.787390i) q^{20} +(-0.775690 + 2.52949i) q^{21} +(1.73881 - 0.720241i) q^{22} +(-3.61497 - 4.71112i) q^{23} +(-0.296901 - 2.25518i) q^{24} +(4.55590 + 1.22075i) q^{25} +(1.14733 + 4.28191i) q^{26} +(-0.923880 - 0.382683i) q^{27} +(2.69709 - 3.26618i) q^{28} +(-6.59890 + 2.73335i) q^{29} +(-0.291211 - 0.168131i) q^{30} +(-2.37564 + 3.09599i) q^{31} +(-1.46602 + 5.47128i) q^{32} +(-1.48976 + 2.58034i) q^{33} +(2.25499 - 1.30314i) q^{34} +(-0.315662 - 1.37260i) q^{35} +(1.13207 + 1.13207i) q^{36} +(6.56759 + 0.864639i) q^{37} +(1.95653 - 1.12960i) q^{38} +(-5.56761 - 4.27218i) q^{39} +(0.737133 + 0.960650i) q^{40} +(-6.09363 - 2.52406i) q^{41} +(0.0597432 - 1.67018i) q^{42} +(0.374756 - 0.374756i) q^{43} +(3.78445 - 2.90391i) q^{44} +(0.527781 - 0.0694837i) q^{45} +(2.97588 + 2.28347i) q^{46} +(-0.462686 - 0.267132i) q^{47} +(-0.675496 - 1.63079i) q^{48} +(5.29075 - 4.58344i) q^{49} -2.97935 q^{50} +(-1.57630 + 3.80989i) q^{51} +(5.61774 + 9.73020i) q^{52} +(-0.445072 + 1.66103i) q^{53} +(0.626267 + 0.0824497i) q^{54} -1.58611i q^{55} +(-2.50033 + 5.47415i) q^{56} +(-1.36869 + 3.30430i) q^{57} +(3.57943 - 2.74659i) q^{58} +(1.39119 + 0.372768i) q^{59} +(-0.823224 - 0.220582i) q^{60} +(6.43920 - 4.94097i) q^{61} +(0.943331 - 2.27740i) q^{62} +(1.53457 + 2.15525i) q^{63} -0.0476554i q^{64} +(3.70387 + 0.487624i) q^{65} +(0.487118 - 1.81795i) q^{66} +(-2.02119 - 3.50081i) q^{67} +(4.66576 - 4.66954i) q^{68} -5.93824 q^{69} +(0.417005 + 0.785880i) q^{70} +(3.65271 + 8.81842i) q^{71} +(-1.96990 - 1.13732i) q^{72} +(-11.0176 - 8.45411i) q^{73} +(-4.14856 + 0.546168i) q^{74} +(3.74195 - 2.87130i) q^{75} +(4.04891 - 4.04891i) q^{76} +(6.96348 - 3.69497i) q^{77} +(4.09552 + 1.69642i) q^{78} +(-1.55803 - 2.03047i) q^{79} +(0.745478 + 0.572026i) q^{80} +(-0.866025 + 0.500000i) q^{81} +(4.13067 + 0.543813i) q^{82} +(6.29877 + 6.29877i) q^{83} +(-0.949350 - 4.12807i) q^{84} +(-0.287370 - 2.17598i) q^{85} +(-0.167388 + 0.289925i) q^{86} +(-1.84864 + 6.89922i) q^{87} +(-4.12579 + 5.37684i) q^{88} +(10.9606 + 6.32813i) q^{89} +(-0.310665 + 0.128682i) q^{90} +(6.48768 + 17.3971i) q^{91} +(8.78339 + 3.63820i) q^{92} +(1.01002 + 3.76944i) q^{93} +(0.325980 + 0.0873461i) q^{94} +(-0.248512 - 1.88764i) q^{95} +(3.44820 + 4.49378i) q^{96} +(5.00008 - 2.07110i) q^{97} +(-2.47880 + 3.66155i) q^{98} +(1.14021 + 2.75272i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 8 q^{5} + 8 q^{11} - 80 q^{14} + 96 q^{16} - 16 q^{17} + 16 q^{22} + 8 q^{25} - 64 q^{26} - 88 q^{28} - 40 q^{32} - 32 q^{33} - 32 q^{35} + 32 q^{37} - 64 q^{40} - 64 q^{41} - 56 q^{42} - 32 q^{43}+ \cdots - 16 q^{99}+O(q^{100}) \) 192 * q - 8 * q^5 + 8 * q^11 - 80 * q^14 + 96 * q^16 - 16 * q^17 + 16 * q^22 + 8 * q^25 - 64 * q^26 - 88 * q^28 - 40 * q^32 - 32 * q^33 - 32 * q^35 + 32 * q^37 - 64 * q^40 - 64 * q^41 - 56 * q^42 - 32 * q^43 + 32 * q^44 + 56 * q^49 + 64 * q^50 + 96 * q^52 + 64 * q^53 - 152 * q^56 - 32 * q^58 - 16 * q^59 + 40 * q^61 - 112 * q^62 + 32 * q^65 - 16 * q^67 + 48 * q^68 - 128 * q^69 - 120 * q^70 + 96 * q^71 + 8 * q^73 - 64 * q^74 - 112 * q^76 + 32 * q^77 - 16 * q^78 + 16 * q^79 + 192 * q^80 - 8 * q^82 - 16 * q^83 + 48 * q^84 - 64 * q^86 + 24 * q^87 - 136 * q^88 - 160 * q^92 + 48 * q^93 - 64 * q^94 - 104 * q^95 - 48 * q^96 - 96 * q^97 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

Properties

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