LMFDB - Embedded newform 357.2.bh.a.151.14

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)

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);

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")

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			151.14
Character	$\chi$	$=$	357.151
Dual form			357.2.bh.a.331.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.163489 - 0.610148i) q^{2} +(-0.991445 - 0.130526i) q^{3} +(1.38650 + 0.800496i) q^{4} +(-0.422330 - 0.324065i) q^{5} +(-0.241730 + 0.583588i) q^{6} +(-1.09922 - 2.40660i) q^{7} +(1.60842 - 1.60842i) q^{8} +(0.965926 + 0.258819i) q^{9} +(-0.266774 + 0.204703i) q^{10} +(1.81382 + 2.36381i) q^{11} +(-1.27015 - 0.974622i) q^{12} -7.01782i q^{13} +(-1.64809 + 0.277234i) q^{14} +(0.376418 + 0.376418i) q^{15} +(0.882578 + 1.52867i) q^{16} +(2.91666 + 2.91429i) q^{17} +(0.315836 - 0.547043i) q^{18} +(0.925679 - 3.45468i) q^{19} +(-0.326147 - 0.787390i) q^{20} +(0.775690 + 2.52949i) q^{21} +(1.73881 - 0.720241i) q^{22} +(5.88744 - 0.775096i) q^{23} +(-1.80460 + 1.38472i) q^{24} +(-1.22075 - 4.55590i) q^{25} +(-4.28191 - 1.14733i) q^{26} +(-0.923880 - 0.382683i) q^{27} +(0.402407 - 4.21667i) q^{28} +(-6.59890 + 2.73335i) q^{29} +(0.291211 - 0.168131i) q^{30} +(3.86903 + 0.509367i) q^{31} +(5.47128 - 1.46602i) 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} +(-4.03259 + 5.25538i) q^{37} +(-1.95653 - 1.12960i) q^{38} +(-0.916010 + 6.95778i) q^{39} +(-1.20051 + 0.158051i) q^{40} +(-6.09363 - 2.52406i) q^{41} +(1.67018 - 0.0597432i) q^{42} +(0.374756 - 0.374756i) q^{43} +(0.622635 + 4.72938i) q^{44} +(-0.324065 - 0.422330i) q^{45} +(0.489606 - 3.71893i) q^{46} +(0.462686 - 0.267132i) q^{47} +(-0.675496 - 1.63079i) q^{48} +(-4.58344 + 5.29075i) q^{49} -2.97935 q^{50} +(-2.51131 - 3.27006i) q^{51} +(5.61774 - 9.73020i) q^{52} +(1.66103 - 0.445072i) q^{53} +(-0.384537 + 0.501139i) q^{54} -1.58611i q^{55} +(-5.63881 - 2.10281i) q^{56} +(-1.36869 + 3.30430i) q^{57} +(0.588905 + 4.47318i) q^{58} +(-0.372768 - 1.39119i) q^{59} +(0.220582 + 0.823224i) q^{60} +(1.05941 + 8.04699i) q^{61} +(0.943331 - 2.27740i) q^{62} +(-0.438889 - 2.60909i) q^{63} -0.0476554i q^{64} +(-2.27423 + 2.96384i) q^{65} +(-1.81795 + 0.487118i) q^{66} +(-2.02119 + 3.50081i) q^{67} +(1.71106 + 6.37544i) q^{68} -5.93824 q^{69} +(0.785880 + 0.417005i) q^{70} +(3.65271 + 8.81842i) q^{71} +(1.96990 - 1.13732i) q^{72} +(-1.81267 + 13.7686i) q^{73} +(2.54727 + 3.31967i) q^{74} +(0.615642 + 4.67627i) q^{75} +(4.04891 - 4.04891i) q^{76} +(3.69497 - 6.96348i) q^{77} +(4.09552 + 1.69642i) q^{78} +(2.53745 - 0.334062i) q^{79} +(0.122650 - 0.931616i) q^{80} +(0.866025 + 0.500000i) q^{81} +(-2.53629 + 3.30536i) 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} +(6.89922 - 1.84864i) q^{87} +(6.71937 + 0.884622i) q^{88} +(-10.9606 + 6.32813i) q^{89} +(-0.310665 + 0.128682i) q^{90} +(-16.8891 + 7.71412i) q^{91} +(8.78339 + 3.63820i) q^{92} +(-3.76944 - 1.01002i) q^{93} +(-0.0873461 - 0.325980i) q^{94} +(-1.51048 + 1.15904i) q^{95} +(-5.61583 + 0.739337i) 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 $\left(\mathbb{Z}/357\mathbb{Z}\right)^\times$.

$n$	$52$	$190$	$239$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{8}\right)$	$1$

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 $

$2$	0.163489	−	0.610148i	0.115604	−	0.431440i	−0.883727	−	0.468002i	$-0.844974\pi$
$2$	0.163489	−	0.610148i	0.115604	−	0.431440i	0.999331	+	0.0365623i	$0.0116407\pi$
$3$	−0.991445	−	0.130526i	−0.572411	−	0.0753593i
$3$	−0.991445	−	0.130526i	−0.572411	−	0.0753593i
$4$	1.38650	+	0.800496i	0.693250	+	0.400248i
$5$	−0.422330	−	0.324065i	−0.188872	−	0.144926i	0.509997	−	0.860176i	$-0.329646\pi$
$5$	−0.422330	−	0.324065i	−0.188872	−	0.144926i	−0.698869	+	0.715250i	$0.746313\pi$
$6$	−0.241730	+	0.583588i	−0.0986859	+	0.238249i
$7$	−1.09922	−	2.40660i	−0.415465	−	0.909609i
$7$	−1.09922	−	2.40660i	−0.415465	−	0.909609i
$8$	1.60842	−	1.60842i	0.568661	−	0.568661i
$9$	0.965926	+	0.258819i	0.321975	+	0.0862730i
$10$	−0.266774	+	0.204703i	−0.0843613	+	0.0647327i
$11$	1.81382	+	2.36381i	0.546887	+	0.712717i	0.982258	−	0.187534i	$-0.0600495\pi$
$11$	1.81382	+	2.36381i	0.546887	+	0.712717i	−0.435371	+	0.900251i	$0.643383\pi$
$12$	−1.27015	−	0.974622i	−0.366661	−	0.281349i
$13$		−	7.01782i		−	1.94639i	−0.229974	−	0.973197i	$-0.573864\pi$
$13$		−	7.01782i		−	1.94639i	0.229974	−	0.973197i	$-0.426136\pi$
$14$	−1.64809	+	0.277234i	−0.440471	+	0.0740939i
$15$	0.376418	+	0.376418i	0.0971907	+	0.0971907i
$16$	0.882578	+	1.52867i	0.220644	+	0.382167i
$17$	2.91666	+	2.91429i	0.707393	+	0.706820i
$17$	2.91666	+	2.91429i	0.707393	+	0.706820i
$18$	0.315836	−	0.547043i	0.0744432	−	0.128939i
$19$	0.925679	−	3.45468i	0.212365	−	0.792558i	−0.774712	−	0.632314i	$-0.782105\pi$
$19$	0.925679	−	3.45468i	0.212365	−	0.792558i	0.987077	−	0.160244i	$-0.0512281\pi$
$20$	−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
$23$	5.88744	−	0.775096i	1.22762	−	0.161619i	0.511305	−	0.859400i	$-0.329162\pi$
$23$	5.88744	−	0.775096i	1.22762	−	0.161619i	0.716311	+	0.697781i	$0.245829\pi$
$24$	−1.80460	+	1.38472i	−0.368362	+	0.282654i
$25$	−1.22075	−	4.55590i	−0.244150	−	0.911181i
$26$	−4.28191	−	1.14733i	−0.839751	−	0.225011i
$27$	−0.923880	−	0.382683i	−0.177801	−	0.0736475i
$28$	0.402407	−	4.21667i	0.0760478	−	0.796875i
$29$	−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
$31$	3.86903	+	0.509367i	0.694898	+	0.0914851i	0.469698	−	0.882827i	$-0.344363\pi$
$31$	3.86903	+	0.509367i	0.694898	+	0.0914851i	0.225201	+	0.974312i	$0.427696\pi$
$32$	5.47128	−	1.46602i	0.967195	−	0.259159i
$33$	−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
$37$	−4.03259	+	5.25538i	−0.662954	+	0.863979i	−0.996905	−	0.0786115i	$-0.974951\pi$
$37$	−4.03259	+	5.25538i	−0.662954	+	0.863979i	0.333951	+	0.942590i	$0.391618\pi$
$38$	−1.95653	−	1.12960i	−0.317391	−	0.183246i
$39$	−0.916010	+	6.95778i	−0.146679	+	1.11414i
$40$	−1.20051	+	0.158051i	−0.189818	+	0.0249900i
$41$	−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	$0.797222\pi$
$42$	1.67018	−	0.0597432i	0.257714	−	0.00921857i
$43$	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	$0.237133\pi$
$44$	0.622635	+	4.72938i	0.0938657	+	0.712981i
$45$	−0.324065	−	0.422330i	−0.0483088	−	0.0629572i
$46$	0.489606	−	3.71893i	0.0721885	−	0.548326i
$47$	0.462686	−	0.267132i	0.0674897	−	0.0389652i	−0.465875	−	0.884850i	$-0.654261\pi$
$47$	0.462686	−	0.267132i	0.0674897	−	0.0389652i	0.533365	+	0.845885i	$0.320927\pi$
$48$	−0.675496	−	1.63079i	−0.0974994	−	0.235384i
$49$	−4.58344	+	5.29075i	−0.654777	+	0.755822i
$50$	−2.97935			−0.421344
$51$	−2.51131	−	3.27006i	−0.351654	−	0.457900i
$52$	5.61774	−	9.73020i	0.779040	−	1.34934i
$53$	1.66103	−	0.445072i	0.228160	−	0.0611354i	−0.142927	−	0.989733i	$-0.545652\pi$
$53$	1.66103	−	0.445072i	0.228160	−	0.0611354i	0.371088	+	0.928598i	$0.378985\pi$
$54$	−0.384537	+	0.501139i	−0.0523289	+	0.0681963i
$55$		−	1.58611i		−	0.213870i
$56$	−5.63881	−	2.10281i	−0.753518	−	0.281000i
$57$	−1.36869	+	3.30430i	−0.181287	+	0.437665i
$58$	0.588905	+	4.47318i	0.0773270	+	0.587357i
$59$	−0.372768	−	1.39119i	−0.0485302	−	0.181117i	0.937406	−	0.348238i	$-0.113220\pi$
$59$	−0.372768	−	1.39119i	−0.0485302	−	0.181117i	−0.985936	+	0.167120i	$0.946553\pi$
$60$	0.220582	+	0.823224i	0.0284770	+	0.106278i
$61$	1.05941	+	8.04699i	0.135643	+	1.03031i	0.914921	+	0.403633i	$0.132253\pi$
$61$	1.05941	+	8.04699i	0.135643	+	1.03031i	−0.779278	+	0.626679i	$0.784414\pi$
$62$	0.943331	−	2.27740i	0.119803	−	0.289231i
$63$	−0.438889	−	2.60909i	−0.0552949	−	0.328715i
$64$		−	0.0476554i		−	0.00595693i
$65$	−2.27423	+	2.96384i	−0.282084	+	0.367619i
$66$	−1.81795	+	0.487118i	−0.223774	+	0.0599601i
$67$	−2.02119	+	3.50081i	−0.246928	+	0.427692i	−0.962672	−	0.270671i	$-0.912754\pi$
$67$	−2.02119	+	3.50081i	−0.246928	+	0.427692i	0.715744	+	0.698363i	$0.246088\pi$
$68$	1.71106	+	6.37544i	0.207497	+	0.773135i
$69$	−5.93824			−0.714880
$70$	0.785880	+	0.417005i	0.0939306	+	0.0498416i
$71$	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
$73$	−1.81267	+	13.7686i	−0.212157	+	1.61149i	0.471622	+	0.881801i	$0.343669\pi$
$73$	−1.81267	+	13.7686i	−0.212157	+	1.61149i	−0.683778	+	0.729690i	$0.739665\pi$
$74$	2.54727	+	3.31967i	0.296115	+	0.385904i
$75$	0.615642	+	4.67627i	0.0710883	+	0.539969i
$76$	4.04891	−	4.04891i	0.464442	−	0.464442i
$77$	3.69497	−	6.96348i	0.421081	−	0.793563i
$78$	4.09552	+	1.69642i	0.463726	+	0.192082i
$79$	2.53745	−	0.334062i	0.285486	−	0.0375849i	0.0135765	−	0.999908i	$-0.495678\pi$
$79$	2.53745	−	0.334062i	0.285486	−	0.0375849i	0.271909	+	0.962323i	$0.412345\pi$
$80$	0.122650	−	0.931616i	0.0137126	−	0.104158i
$81$	0.866025	+	0.500000i	0.0962250	+	0.0555556i
$82$	−2.53629	+	3.30536i	−0.280086	+	0.365016i
$83$	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
$87$	6.89922	−	1.84864i	0.739674	−	0.198195i
$88$	6.71937	+	0.884622i	0.716287	+	0.0943010i
$89$	−10.9606	+	6.32813i	−1.16182	+	0.670780i	−0.951741	−	0.306903i	$-0.900707\pi$
$89$	−10.9606	+	6.32813i	−1.16182	+	0.670780i	−0.210084	+	0.977683i	$0.567374\pi$
$90$	−0.310665	+	0.128682i	−0.0327469	+	0.0135642i
$91$	−16.8891	+	7.71412i	−1.77046	+	0.808659i
$92$	8.78339	+	3.63820i	0.915732	+	0.379308i
$93$	−3.76944	−	1.01002i	−0.390873	−	0.104734i
$94$	−0.0873461	−	0.325980i	−0.00900906	−	0.0336223i
$95$	−1.51048	+	1.15904i	−0.154972	+	0.118915i
$96$	−5.61583	+	0.739337i	−0.573163	+	0.0754583i
$97$	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
$100$	1.95441	−	7.29396i	0.195441	−	0.729396i
$101$	−6.24674	+	10.8197i	−0.621574	+	1.07660i	0.367619	+	0.929977i	$0.380173\pi$
$101$	−6.24674	+	10.8197i	−0.621574	+	1.07660i	−0.989193	+	0.146621i	$0.953160\pi$
$102$	−2.40579	+	0.997654i	−0.238209	+	0.0987825i
$103$	−0.549070	−	0.951017i	−0.0541015	−	0.0937065i	0.837706	−	0.546121i	$-0.183896\pi$
$103$	−0.549070	−	0.951017i	−0.0541015	−	0.0937065i	−0.891808	+	0.452414i	$0.850563\pi$
$104$	−11.2876	−	11.2876i	−1.10684	−	1.10684i
$105$	0.492122	−	1.31965i	0.0480262	−	0.128785i
$106$		−	1.08624i		−	0.105505i
$107$	−12.7880	−	9.81260i	−1.23627	−	0.948620i	−0.236530	−	0.971624i	$-0.576010\pi$
$107$	−12.7880	−	9.81260i	−1.23627	−	0.948620i	−0.999735	+	0.0230044i	$0.992677\pi$
$108$	−0.974622	−	1.27015i	−0.0937830	−	0.122220i
$109$	11.4264	−	8.76776i	1.09445	−	0.839799i	0.106457	−	0.994317i	$-0.466049\pi$
$109$	11.4264	−	8.76776i	1.09445	−	0.839799i	0.987990	+	0.154518i	$0.0493825\pi$
$110$	−0.967759	−	0.259310i	−0.0922722	−	0.0247243i
$111$	4.68406	−	4.68406i	0.444591	−	0.444591i
$112$	2.70875	−	3.80435i	0.255953	−	0.359477i
$113$	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	$0.0975480\pi$
$114$	1.79235	+	1.37532i	0.167869	+	0.128810i
$115$	−2.73762	−	1.58057i	−0.255285	−	0.147389i
$116$	−11.3374	−	1.49260i	−1.05265	−	0.138584i
$117$	1.81635	−	6.77870i	0.167921	−	0.626691i
$118$	−0.909773			−0.0837514
$119$	3.80750	−	10.2227i	0.349033	−	0.937111i
$120$	1.21087			0.110537
$121$	0.549328	−	2.05012i	0.0499389	−	0.186374i
$122$	5.08306	+	0.669197i	0.460198	+	0.0605863i
$123$	5.71204	+	3.29785i	0.515037	+	0.297357i
$124$	4.95666	+	3.80338i	0.445121	+	0.341553i
$125$	−1.97943	+	4.77877i	−0.177046	+	0.427426i
$126$	−1.66369	−	0.158770i	−0.148213	−	0.0141443i
$127$	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	$0.190327\pi$
$128$	10.9135	+	2.92426i	0.964625	+	0.258470i
$129$	−0.420466	+	0.322635i	−0.0370199	+	0.0284064i
$130$	1.43657	+	1.87217i	0.125995	+	0.164200i
$131$	−1.74045	−	1.33549i	−0.152064	−	0.116683i	0.529928	−	0.848043i	$-0.322219\pi$
$131$	−1.74045	−	1.33549i	−0.152064	−	0.116683i	−0.681991	+	0.731360i	$0.738886\pi$
$132$		−	4.77019i		−	0.415192i
$133$	−9.33156	+	1.56971i	−0.809149	+	0.136111i
$134$	1.80557	+	1.80557i	0.155977	+	0.155977i
$135$	0.266168	+	0.461016i	0.0229081	+	0.0396779i
$136$	9.37859	−	0.00380033i	0.804208	−	0.000325875i
$137$	−9.57730	+	16.5884i	−0.818244	+	1.41724i	0.0887309	+	0.996056i	$0.471719\pi$
$137$	−9.57730	+	16.5884i	−0.818244	+	1.41724i	−0.906975	+	0.421185i	$0.861614\pi$
$138$	−0.970835	+	3.62320i	−0.0826429	+	0.308428i
$139$	−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
$142$	5.97771	−	0.786981i	0.501639	−	0.0660420i
$143$	16.5888	−	12.7291i	1.38723	−	1.06446i
$144$	0.456856	+	1.70501i	0.0380713	+	0.142084i
$145$	3.67270	+	0.984097i	0.305001	+	0.0817248i
$146$	8.10452	+	3.35700i	0.670735	+	0.277827i
$147$	5.23481	−	4.64723i	0.431760	−	0.383297i
$148$	−9.79810	+	4.05850i	−0.805398	+	0.333607i
$149$	13.4251	−	7.75096i	1.09982	−	0.634983i	0.163649	−	0.986519i	$-0.447674\pi$
$149$	13.4251	−	7.75096i	1.09982	−	0.634983i	0.936175	+	0.351535i	$0.114340\pi$
$150$	2.95386	+	0.388884i	0.241182	+	0.0317522i
$151$	9.33906	−	2.50239i	0.760002	−	0.203642i	0.142052	−	0.989859i	$-0.454630\pi$
$151$	9.33906	−	2.50239i	0.760002	−	0.203642i	0.617950	+	0.786217i	$0.287963\pi$
$152$	−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
$156$	−6.83972	+	8.91370i	−0.547616	+	0.713667i
$157$	−13.8480	−	7.99516i	−1.10519	−	0.638084i	−0.167613	−	0.985853i	$-0.553606\pi$
$157$	−13.8480	−	7.99516i	−1.10519	−	0.638084i	−0.937580	+	0.347769i	$0.886939\pi$
$158$	0.211017	−	1.60284i	0.0167876	−	0.127515i
$159$	−1.70492	+	0.224456i	−0.135209	+	0.0178006i
$160$	−2.78577	−	1.15391i	−0.220235	−	0.0912242i
$161$	−8.33692	−	13.3167i	−0.657042	−	1.04950i
$162$	0.446659	−	0.446659i	0.0350929	−	0.0350929i
$163$	0.0216437	+	0.164400i	0.00169526	+	0.0128768i	0.992272	−	0.124085i	$-0.0395996\pi$
$163$	0.0216437	+	0.164400i	0.00169526	+	0.0128768i	−0.990576	+	0.136962i	$0.956266\pi$
$164$	−6.42831	−	8.37753i	−0.501966	−	0.654175i
$165$	−0.207028	+	1.57254i	−0.0161171	+	0.122422i
$166$	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	$-0.502537\pi$
$168$	5.31610	+	2.82083i	0.410146	+	0.217632i
$169$	−36.2498			−2.78845
$170$	−1.37465	−	0.180410i	−0.105431	−	0.0138368i
$171$	1.78827	−	3.09738i	0.136753	−	0.236863i
$172$	0.819590	−	0.219609i	0.0624932	−	0.0167450i
$173$	−6.03634	+	7.86671i	−0.458934	+	0.598095i	−0.964301	−	0.264810i	$-0.914691\pi$
$173$	−6.03634	+	7.86671i	−0.458934	+	0.598095i	0.505366	+	0.862905i	$0.331357\pi$
$174$		−	4.51178i		−	0.342037i
$175$	−9.62236	+	7.94579i	−0.727382	+	0.600645i
$176$	−2.01266	+	4.85898i	−0.151710	+	0.366259i
$177$	0.187992	+	1.42794i	0.0141303	+	0.107331i
$178$	2.06915	+	7.72218i	0.155090	+	0.578802i
$179$	5.28715	+	19.7319i	0.395180	+	1.47483i	0.821473	+	0.570248i	$0.193153\pi$
$179$	5.28715	+	19.7319i	0.395180	+	1.47483i	−0.426293	+	0.904585i	$0.640181\pi$
$180$	−0.111243	−	0.844973i	−0.00829155	−	0.0629806i
$181$	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	$-0.110723\pi$
$182$	1.94558	+	11.5660i	0.144216	+	0.857329i
$183$		−	8.11643i		−	0.599984i
$184$	8.22277	−	10.7161i	0.606191	−	0.790003i
$185$	3.40617	−	0.912681i	0.250427	−	0.0671016i
$186$	−1.23252	+	2.13479i	−0.0903729	+	0.156530i
$187$	−1.59856	+	12.1804i	−0.116899	+	0.890722i
$188$	0.855352			0.0623830
$189$	0.0945795	+	2.64406i	0.00687965	+	0.192327i
$190$	0.460236	+	1.11111i	0.0333890	+	0.0806082i
$191$	19.8286	−	11.4480i	1.43474	−	0.828350i	0.437266	−	0.899332i	$-0.355947\pi$
$191$	19.8286	−	11.4480i	1.43474	−	0.828350i	0.997478	+	0.0709821i	$0.0226133\pi$
$192$	−0.00622028	+	0.0472477i	−0.000448910	+	0.00340981i
$193$	5.06352	+	6.59891i	0.364480	+	0.475000i	0.939210	−	0.343343i	$-0.111559\pi$
$193$	5.06352	+	6.59891i	0.364480	+	0.475000i	−0.574730	+	0.818343i	$0.694893\pi$
$194$	−0.446222	−	3.38939i	−0.0320368	−	0.243344i
$195$	2.64163	−	2.64163i	0.189171	−	0.189171i
$196$	−10.5902	+	3.66660i	−0.756440	+	0.261900i
$197$	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	$0.611806\pi$
$198$	1.86598	−	0.245661i	0.132609	−	0.0174583i
$199$	−2.55883	+	19.4363i	−0.181391	+	1.37780i	0.622312	+	0.782769i	$0.286193\pi$
$199$	−2.55883	+	19.4363i	−0.181391	+	1.37780i	−0.803703	+	0.595031i	$0.797140\pi$
$200$	−9.29126	−	5.36431i	−0.656991	−	0.379314i
$201$	2.46085	−	3.20704i	0.173575	−	0.226207i
$202$	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
$206$	−0.670027	+	0.179533i	−0.0466830	+	0.0125087i
$207$	5.88744	+	0.775096i	0.409205	+	0.0538729i
$208$	10.7279	−	6.19377i	0.743848	−	0.429461i
$209$	9.84524	−	4.07803i	0.681010	−	0.282083i
$210$	−0.724727	−	0.516015i	−0.0500109	−	0.0356084i
$211$	−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	$0.753002\pi$
$212$	2.65930	+	0.712557i	0.182641	+	0.0489386i
$213$	−2.47042	−	9.21975i	−0.169271	−	0.631727i
$214$	−8.07783	+	6.19834i	−0.552189	+	0.423710i
$215$	−0.279716	+	0.0368254i	−0.0190765	+	0.00251147i
$216$	−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
$219$	3.59432	−	13.4142i	0.242882	−	0.906447i
$220$	1.26967	−	2.19913i	0.0856012	−	0.148266i
$221$	20.4520	−	20.4686i	1.37575	−	1.37687i
$222$	−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	$0.421637\pi$
$224$	−9.54226	−	11.5557i	−0.637569	−	0.772097i
$225$		−	4.71662i		−	0.314441i
$226$	−0.917724	−	0.704194i	−0.0610461	−	0.0468423i
$227$	2.66089	+	3.46773i	0.176609	+	0.230162i	0.873267	−	0.487242i	$-0.161997\pi$
$227$	2.66089	+	3.46773i	0.176609	+	0.230162i	−0.696658	+	0.717404i	$0.745330\pi$
$228$	−4.54276	+	3.48578i	−0.300852	+	0.230852i
$229$	4.07265	+	1.09126i	0.269128	+	0.0721126i	0.390859	−	0.920450i	$-0.372178\pi$
$229$	4.07265	+	1.09126i	0.269128	+	0.0721126i	−0.121731	+	0.992563i	$0.538845\pi$
$230$	−1.41195	+	1.41195i	−0.0931012	+	0.0931012i
$231$	−4.57228	+	6.42162i	−0.300834	+	0.422512i
$232$	−6.21741	+	15.0101i	−0.408193	+	0.985464i
$233$	−15.5051	−	11.8975i	−1.01577	−	0.779430i	−0.0402197	−	0.999191i	$-0.512806\pi$
$233$	−15.5051	−	11.8975i	−1.01577	−	0.779430i	−0.975554	+	0.219760i	$0.929472\pi$
$234$	−3.83905	−	2.21648i	−0.250967	−	0.144896i
$235$	−0.281975	−	0.0371226i	−0.0183940	−	0.00242161i
$236$	0.596798	−	2.22728i	0.0388482	−	0.144984i
$237$	−2.55935			−0.166247
$238$	−5.61486	−	3.99442i	−0.363957	−	0.258920i
$239$	24.1067			1.55933			0.779667	−	0.626194i	$-0.215388\pi$
$239$	24.1067			1.55933			0.779667	+	0.626194i	$0.215388\pi$
$240$	−0.243201	+	0.907637i	−0.0156985	+	0.0585877i
$241$	10.5471	+	1.38855i	0.679395	+	0.0894441i	0.462323	−	0.886711i	$-0.347016\pi$
$241$	10.5471	+	1.38855i	0.679395	+	0.0894441i	0.217072	+	0.976156i	$0.430349\pi$
$242$	−1.16107	−	0.670342i	−0.0746362	−	0.0430912i
$243$	−0.793353	−	0.608761i	−0.0508936	−	0.0390521i
$244$	−4.97272	+	12.0052i	−0.318346	+	0.768554i
$245$	3.65027	−	0.749112i	0.233207	−	0.0478590i
$246$	2.94603	−	2.94603i	0.187832	−	0.187832i
$247$	−24.2443	−	6.49625i	−1.54263	−	0.413347i
$248$	7.04228	−	5.40373i	0.447185	−	0.343137i
$249$	−5.42273	−	7.06704i	−0.343651	−	0.447855i
$250$	2.59214	+	1.98902i	0.163941	+	0.125797i
$251$			6.09820i			0.384915i	0.981305	+	0.192457i	$0.0616457\pi$
$251$			6.09820i			0.384915i	−0.981305	+	0.192457i	$0.938354\pi$
$252$	1.48005	−	3.96884i	0.0932343	−	0.250013i
$253$	12.5109	+	12.5109i	0.786555	+	0.786555i
$254$	−1.32669	−	2.29790i	−0.0832442	−	0.144183i
$255$	0.000889391		2.19487i	5.56959e−5		0.137448i
$256$	3.61611	−	6.26329i	0.226007	−	0.391456i
$257$	0.860662	−	3.21204i	0.0536866	−	0.200361i	−0.933873	−	0.357604i	$-0.883594\pi$
$257$	0.860662	−	3.21204i	0.0536866	−	0.200361i	0.987560	+	0.157243i	$0.0502605\pi$
$258$	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
$261$	−7.08149	+	0.932296i	−0.438333	+	0.0577077i
$262$	−1.09939	+	0.843593i	−0.0679206	+	0.0521173i
$263$	−0.0720370	−	0.268846i	−0.00444199	−	0.0165777i	0.963669	−	0.267098i	$-0.0860649\pi$
$263$	−0.0720370	−	0.268846i	−0.00444199	−	0.0165777i	−0.968111	+	0.250521i	$0.919398\pi$
$264$	−6.54642	−	1.75411i	−0.402904	−	0.107958i
$265$	−0.845737	−	0.350316i	−0.0519532	−	0.0215197i
$266$	−0.567848	+	5.95026i	−0.0348170	+	0.364834i
$267$	11.6929	−	4.84334i	0.715591	−	0.296407i
$268$	−5.60476	+	3.23591i	−0.342365	+	0.197665i
$269$	−29.9801	−	3.94695i	−1.82792	−	0.240650i	−0.863373	−	0.504566i	$-0.831652\pi$
$269$	−29.9801	−	3.94695i	−1.82792	−	0.240650i	−0.964546	+	0.263916i	$0.914986\pi$
$270$	0.324803	−	0.0870308i	0.0197669	−	0.00529652i
$271$	6.71294	+	11.6272i	0.407782	+	0.706300i	0.994641	−	0.103390i	$-0.0329689\pi$
$271$	6.71294	+	11.6272i	0.407782	+	0.706300i	−0.586859	+	0.809689i	$0.699636\pi$
$272$	−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
$275$	8.55509	−	11.1492i	0.515892	−	0.672323i
$276$	−8.23337	−	4.75354i	−0.495590	−	0.286129i
$277$	1.85916	−	14.1217i	0.111706	−	0.848493i	−0.840237	−	0.542219i	$-0.817584\pi$
$277$	1.85916	−	14.1217i	0.111706	−	0.848493i	0.951943	−	0.306274i	$-0.0990823\pi$
$278$	−2.60991	+	0.343601i	−0.156532	+	0.0206078i
$279$	3.60536	+	1.49339i	0.215847	+	0.0894069i
$280$	1.69999	+	2.71542i	0.101594	+	0.162278i
$281$	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	$0.159431\pi$
$282$	0.0440499	+	0.334592i	0.00262313	+	0.0199247i
$283$	−0.237183	−	0.309103i	−0.0140991	−	0.0183742i	0.786251	−	0.617908i	$-0.212019\pi$
$283$	−0.237183	−	0.309103i	−0.0140991	−	0.0183742i	−0.800350	+	0.599533i	$0.795353\pi$
$284$	−1.99463	+	15.1507i	−0.118359	+	0.899029i
$285$	1.64885	−	0.951962i	0.0976692	−	0.0563894i
$286$	−5.05452	−	12.2027i	−0.298880	−	0.721560i
$287$	0.623818	+	17.4394i	0.0368228	+	1.02942i
$288$	5.66428			0.333771
$289$	0.0137772	+	17.0000i	0.000810425	+	1.00000i
$290$	1.20089	−	2.08000i	0.0705186	−	0.122142i
$291$	−5.22764	+	1.40074i	−0.306450	+	0.0821129i
$292$	−13.5350	+	17.6391i	−0.792073	+	1.03225i
$293$			8.32965i			0.486623i	0.969948	+	0.243312i	$0.0782338\pi$
$293$			8.32965i			0.486623i	−0.969948	+	0.243312i	$0.921766\pi$
$294$	−1.97967	−	3.95378i	−0.115457	−	0.230589i
$295$	−0.293405	+	0.708341i	−0.0170827	+	0.0412412i
$296$	1.96675	+	14.9389i	0.114315	+	0.868307i
$297$	−0.771157	−	2.87800i	−0.0447471	−	0.166998i
$298$	−2.53439	−	9.45846i	−0.146813	−	0.547914i
$299$	−5.43949	−	41.3170i	−0.314574	−	2.38942i
$300$	−2.88974	+	6.97646i	−0.166839	+	0.402786i
$301$	−1.31383	−	0.489949i	−0.0757277	−	0.0282402i
$302$		−	6.10732i		−	0.351437i
$303$	7.60555	−	9.91174i	0.436927	−	0.569415i
$304$	6.09805	−	1.63397i	0.349747	−	0.0937145i
$305$	2.16033	−	3.74180i	0.123700	−	0.214255i
$306$	2.51543	−	0.675100i	0.143798	−	0.0385929i
$307$	−18.0680			−1.03119			−0.515597	−	0.856831i	$-0.672430\pi$
$307$	−18.0680			−1.03119			−0.515597	+	0.856831i	$0.672430\pi$
$308$	10.6973	−	6.69705i	0.609536	−	0.381600i
$309$	0.420240	+	1.01455i	0.0239066	+	0.0577157i
$310$	−1.13642	+	0.656115i	−0.0645446	+	0.0372648i
$311$	−3.65395	+	27.7545i	−0.207197	+	1.57381i	0.499511	+	0.866308i	$0.333513\pi$
$311$	−3.65395	+	27.7545i	−0.207197	+	1.57381i	−0.706707	+	0.707506i	$0.749820\pi$
$312$	9.71768	+	12.6643i	0.550155	+	0.716977i
$313$	0.0866037	+	0.657820i	0.00489513	+	0.0371822i	0.993718	−	0.111912i	$-0.0356975\pi$
$313$	0.0866037	+	0.657820i	0.00489513	+	0.0371822i	−0.988823	+	0.149094i	$0.952364\pi$
$314$	−7.14223	+	7.14223i	−0.403059	+	0.403059i
$315$	−0.660161	+	1.24413i	−0.0371958	+	0.0700987i
$316$	3.78559	+	1.56804i	0.212956	+	0.0882093i
$317$	−2.10264	+	0.276818i	−0.118096	+	0.0155476i	−0.189342	−	0.981911i	$-0.560636\pi$
$317$	−2.10264	+	0.276818i	−0.118096	+	0.0155476i	0.0712465	+	0.997459i	$0.477302\pi$
$318$	−0.141783	+	1.07695i	−0.00795078	+	0.0603922i
$319$	−18.4304	−	10.6408i	−1.03190	−	0.595769i
$320$	−0.0154435	+	0.0201263i	−0.000863316	+	0.00112510i
$321$	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
$325$	−31.9725	+	8.56701i	−1.77352	+	0.475212i
$326$	0.103847	+	0.0136717i	0.00575154	+	0.000757205i
$327$	−12.4730	+	7.20131i	−0.689760	+	0.398233i
$328$	−13.8608	+	5.74134i	−0.765336	+	0.317013i
$329$	−1.15147	−	0.819864i	−0.0634827	−	0.0452006i
$330$	0.925633	+	0.383410i	0.0509544	+	0.0211060i
$331$	−6.15556	−	1.64938i	−0.338340	−	0.0906580i	0.0856486	−	0.996325i	$-0.472704\pi$
$331$	−6.15556	−	1.64938i	−0.338340	−	0.0906580i	−0.423989	+	0.905667i	$0.639370\pi$
$332$	3.69110	+	13.7754i	0.202575	+	0.756022i
$333$	−5.25538	+	4.03259i	−0.287993	+	0.220985i
$334$	−15.0031	+	1.97519i	−0.820933	+	0.108078i
$335$	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	$0.894669\pi$
$338$	−5.92643	+	22.1177i	−0.322355	+	1.20305i
$339$	−0.915639	+	1.58593i	−0.0497307	+	0.0861360i
$340$	1.34342	−	3.24703i	0.0728574	−	0.176095i
$341$	5.81367	+	10.0696i	0.314828	+	0.545298i
$342$	−1.59750	−	1.59750i	−0.0863828	−	0.0863828i
$343$	17.7709	+	5.21481i	0.959540	+	0.281573i
$344$		−	1.20553i		−	0.0649977i
$345$	2.50790	+	1.92438i	0.135021	+	0.103605i
$346$	3.81298	+	4.96918i	0.204987	+	0.267145i
$347$	16.1237	−	12.3721i	0.865564	−	0.664170i	−0.0774240	−	0.996998i	$-0.524670\pi$
$347$	16.1237	−	12.3721i	0.865564	−	0.664170i	0.942988	+	0.332828i	$0.108003\pi$
$348$	11.0456	+	2.95966i	0.592106	+	0.158654i
$349$	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	$0.0160502\pi$
$350$	3.27496	+	7.17011i	0.175054	+	0.383258i
$351$	−2.68560	+	6.48362i	−0.143347	+	0.346070i
$352$	13.3893	+	10.2740i	0.713653	+	0.547605i
$353$	−3.15963	−	1.82421i	−0.168170	−	0.0970929i	0.413553	−	0.910480i	$-0.364288\pi$
$353$	−3.15963	−	1.82421i	−0.168170	−	0.0970929i	−0.581723	+	0.813387i	$0.697621\pi$
$354$	0.901990	+	0.118749i	0.0479402	+	0.00631145i
$355$	1.31509	−	4.90800i	0.0697980	−	0.260490i
$356$	−20.2625			−1.07391
$357$	−5.10925	+	9.63824i	−0.270410	+	0.510110i
$358$	12.9038			0.681986
$359$	−7.78253	+	29.0448i	−0.410746	+	1.53292i	0.382460	+	0.923972i	$0.375077\pi$
$359$	−7.78253	+	29.0448i	−0.410746	+	1.53292i	−0.793206	+	0.608953i	$0.791590\pi$
$360$	−1.20051	−	0.158051i	−0.0632726	−	0.00833000i
$361$	5.37654	+	3.10415i	0.282976	+	0.163376i
$362$	−9.09772	−	6.98093i	−0.478166	−	0.366909i
$363$	−0.812222	+	1.96088i	−0.0426306	+	0.102919i
$364$	−29.5918	−	2.82402i	−1.55103	−	0.148019i
$365$	5.22746	−	5.22746i	0.273618	−	0.273618i
$366$	−4.95222	−	1.32694i	−0.258857	−	0.0693605i
$367$	−2.03661	+	1.56275i	−0.106310	+	0.0815747i	−0.660549	−	0.750783i	$-0.729676\pi$
$367$	−2.03661	+	1.56275i	−0.106310	+	0.0815747i	0.554238	+	0.832358i	$0.313010\pi$
$368$	6.38099	+	8.31586i	0.332632	+	0.433494i
$369$	−5.23272	−	4.01520i	−0.272404	−	0.209023i
$370$		−	2.22748i		−	0.115801i
$371$	−2.89695	−	3.50821i	−0.150402	−	0.182137i
$372$	−4.41781	−	4.41781i	−0.229053	−	0.229053i
$373$	1.76286	+	3.05337i	0.0912776	+	0.158098i	0.908049	−	0.418864i	$-0.137572\pi$
$373$	1.76286	+	3.05337i	0.0912776	+	0.158098i	−0.816771	+	0.576961i	$0.804238\pi$
$374$	7.17052	+	2.96672i	0.370779	+	0.153406i
$375$	2.58625	−	4.47952i	0.133553	−	0.231321i
$376$	0.314532	−	1.17385i	0.0162208	−	0.0605367i
$377$	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	$0.624425\pi$
$380$	−3.02209	+	0.397865i	−0.155030	+	0.0204101i
$381$	−3.33255	+	2.55715i	−0.170732	+	0.131007i
$382$	−3.74324	−	13.9700i	−0.191521	−	0.714766i
$383$	16.9982	+	4.55464i	0.868566	+	0.232731i	0.665467	−	0.746427i	$-0.268232\pi$
$383$	16.9982	+	4.55464i	0.868566	+	0.232731i	0.203098	+	0.979158i	$0.434899\pi$
$384$	−10.4384	−	4.32374i	−0.532683	−	0.220645i
$385$	−3.81712	+	1.74348i	−0.194538	+	0.0888558i
$386$	4.85414	−	2.01065i	0.247069	−	0.102339i
$387$	0.458981	−	0.264993i	0.0233313	−	0.0134703i
$388$	8.59052	+	1.13096i	0.436117	+	0.0574159i
$389$	−37.5378	+	10.0582i	−1.90324	+	0.509972i	−0.907240	+	0.420613i	$0.861815\pi$
$389$	−37.5378	+	10.0582i	−1.90324	+	0.509972i	−0.996000	+	0.0893584i	$0.971518\pi$
$390$	−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
$394$	0.447288	−	0.582917i	0.0225341	−	0.0293670i
$395$	−1.17990	−	0.681216i	−0.0593672	−	0.0342757i
$396$	−0.622635	+	4.72938i	−0.0312886	+	0.237660i
$397$	12.9233	−	1.70138i	0.648600	−	0.0853898i	0.200954	−	0.979601i	$-0.435596\pi$
$397$	12.9233	−	1.70138i	0.648600	−	0.0853898i	0.447646	+	0.894211i	$0.352262\pi$
$398$	11.4407	+	4.73887i	0.573468	+	0.237538i
$399$	9.45661	−	0.338268i	0.473423	−	0.0169346i
$400$	5.88706	−	5.88706i	0.294353	−	0.294353i
$401$	0.473584	+	3.59723i	0.0236497	+	0.179637i	0.999193	−	0.0401709i	$-0.0127902\pi$
$401$	0.473584	+	3.59723i	0.0236497	+	0.179637i	−0.975543	+	0.219808i	$0.929457\pi$
$402$	−1.55445	−	2.02580i	−0.0775288	−	0.101037i
$403$	3.57465	−	27.1522i	0.178066	−	1.35255i
$404$	−17.3222	+	10.0010i	−0.861812	+	0.497567i
$405$	−0.203716	−	0.491814i	−0.0101227	−	0.0244384i
$406$	10.1178	−	6.33425i	0.502138	−	0.314364i
$407$	−19.7371			−0.978334
$408$	−9.29885	−	1.22038i	−0.460362	−	0.0604180i
$409$	−11.6761	+	20.2236i	−0.577345	+	0.999991i	0.418437	+	0.908246i	$0.362578\pi$
$409$	−11.6761	+	20.2236i	−0.577345	+	0.999991i	−0.995782	+	0.0917455i	$0.970755\pi$
$410$	2.14230	−	0.574028i	0.105801	−	0.0283492i
$411$	11.6606	−	15.1964i	0.575174	−	0.749582i
$412$		−	1.75811i		−	0.0866160i
$413$	−2.93828	+	2.42632i	−0.144583	+	0.119391i
$414$	1.43545	−	3.46549i	0.0705486	−	0.170319i
$415$	−0.618947	−	4.70137i	−0.0303829	−	0.230781i
$416$	−10.2883	−	38.3965i	−0.504425	−	1.88254i
$417$	1.07860	+	4.02540i	0.0528194	+	0.197125i
$418$	−0.878618	−	6.67376i	−0.0429746	−	0.326424i
$419$	−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	$0.139508\pi$
$420$	1.73870	−	1.43576i	0.0848400	−	0.0700577i
$421$			30.6590i			1.49423i	0.664695	+	0.747115i	$0.268562\pi$
$421$			30.6590i			1.49423i	−0.664695	+	0.747115i	$0.731438\pi$
$422$	−4.37228	+	5.69807i	−0.212839	+	0.277378i
$423$	0.516059	−	0.138278i	0.0250917	−	0.00672329i
$424$	1.95577	−	3.38749i	0.0949806	−	0.164511i
$425$	9.71673	−	16.8456i	0.471331	−	0.817133i
$426$	−6.02930			−0.292120
$427$	18.2014	−	11.3950i	0.880826	−	0.551441i
$428$	−9.87565	−	23.8419i	−0.477357	−	1.15244i
$429$	−18.1084	+	10.4549i	−0.874281	+	0.504767i
$430$	−0.0232615	+	0.176689i	−0.00112177	+	0.00852069i
$431$	−8.10770	−	10.5662i	−0.390534	−	0.508954i	0.556166	−	0.831071i	$-0.312272\pi$
$431$	−8.10770	−	10.5662i	−0.390534	−	0.508954i	−0.946700	+	0.322118i	$0.895605\pi$
$432$	−0.230399	−	1.75005i	−0.0110851	−	0.0841995i
$433$	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	$0.178799\pi$
$434$	−6.51772	+	0.233143i	−0.312861	+	0.0111912i
$435$	−3.51283	−	1.45506i	−0.168427	−	0.0697648i
$436$	22.8612	−	3.00973i	1.09485	−	0.144140i
$437$	2.77217	−	21.0567i	0.132611	−	1.00728i
$438$	−7.59701	−	4.38613i	−0.362999	−	0.209578i
$439$	9.85025	−	12.8371i	0.470127	−	0.612681i	−0.496760	−	0.867888i	$-0.665477\pi$
$439$	9.85025	−	12.8371i	0.470127	−	0.612681i	0.966886	+	0.255207i	$0.0821437\pi$
$440$	−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	−0.999832	−	0.0183467i	$-0.994160\pi$
$443$	−10.8564	−	18.8039i	−0.515805	−	0.893400i	0.484027	−	0.875053i	$-0.339174\pi$
$444$	10.2440	−	2.74487i	0.486159	−	0.130266i
$445$	6.67973	+	0.879403i	0.316650	+	0.0416877i
$446$	14.0200	−	8.09447i	0.663868	−	0.383284i
$447$	−14.3219	+	5.93233i	−0.677403	+	0.280589i
$448$	−0.114688	+	0.0523837i	−0.00541848	+	0.00247490i
$449$	−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	$0.749164\pi$
$450$	−2.87783	−	0.771113i	−0.135662	−	0.0363506i
$451$	−5.08632	−	18.9824i	−0.239505	−	0.893846i
$452$	2.32600	−	1.78480i	0.109406	−	0.0839500i
$453$	−9.58579	+	1.26199i	−0.450380	+	0.0592936i
$454$	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
$457$	0.866134	−	3.23245i	0.0405160	−	0.151208i	−0.942704	−	0.333629i	$-0.891727\pi$
$457$	0.866134	−	3.23245i	0.0405160	−	0.151208i	0.983220	+	0.182421i	$0.0583934\pi$
$458$	1.33166	−	2.30651i	0.0622245	−	0.107776i
$459$	−1.57939	−	3.80861i	−0.0737195	−	0.177771i
$460$	−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	$0.808028\pi$
$462$	3.17062	+	3.83963i	0.147511	+	0.178636i
$463$		−	15.8081i		−	0.734663i	−0.930090	−	0.367332i	$-0.880271\pi$
$463$		−	15.8081i		−	0.734663i	0.930090	−	0.367332i	$-0.119729\pi$
$464$	−10.0024	−	7.67514i	−0.464352	−	0.356309i
$465$	1.26464	+	1.64811i	0.0586461	+	0.0764291i
$466$	−9.79413	+	7.51530i	−0.453705	+	0.348140i
$467$	−14.4862	−	3.88156i	−0.670341	−	0.179617i	−0.0924324	−	0.995719i	$-0.529464\pi$
$467$	−14.4862	−	3.88156i	−0.670341	−	0.179617i	−0.577908	+	0.816102i	$0.696131\pi$
$468$	7.94468	−	7.94468i	0.367243	−	0.367243i
$469$	10.6468	+	1.01605i	0.491622	+	0.0469168i
$470$	−0.0687499	+	0.165977i	−0.00317120	+	0.00765595i
$471$	12.6860	+	9.73429i	0.584539	+	0.448533i
$472$	−2.83717	−	1.63804i	−0.130591	−	0.0753970i
$473$	1.56559	+	0.206114i	0.0719861	+	0.00947715i
$474$	−0.418424	+	1.56158i	−0.0192189	+	0.0717257i
$475$	−16.8692			−0.774013
$476$	13.4623	−	11.1258i	0.617043	−	0.509952i
$477$	1.71963			0.0787364
$478$	3.94118	−	14.7087i	0.180265	−	0.672759i
$479$	29.8487	+	3.92965i	1.36382	+	0.179551i	0.776660	−	0.629920i	$-0.216912\pi$
$479$	29.8487	+	3.92965i	1.36382	+	0.179551i	0.587161	+	0.809470i	$0.300245\pi$
$480$	2.61133	+	1.50765i	0.119190	+	0.0688145i
$481$	36.8813	+	28.3000i	1.68164	+	1.29037i
$482$	2.57154	−	6.20825i	0.117130	−	0.282778i
$483$	6.52742	+	14.2910i	0.297008	+	0.650261i
$484$	2.40275	−	2.40275i	0.109216	−	0.109216i
$485$	−2.78286	−	0.745664i	−0.126363	−	0.0338589i
$486$	−0.501139	+	0.384537i	−0.0227321	+	0.0174430i
$487$	−22.3858	−	29.1738i	−1.01440	−	1.32199i	−0.945942	−	0.324337i	$-0.894859\pi$
$487$	−22.3858	−	29.1738i	−1.01440	−	1.32199i	−0.0684578	−	0.997654i	$-0.521808\pi$
$488$	14.6469	+	11.2389i	0.663033	+	0.508763i
$489$		−	0.165819i		−	0.00749858i
$490$	0.139709	−	2.34968i	0.00631143	−	0.106148i
$491$	−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
$493$	−27.2125	−	11.2589i	−1.22559	−	0.507075i
$494$	−7.92735	+	13.7306i	−0.356668	+	0.617767i
$495$	0.410514	−	1.53206i	0.0184512	−	0.0688610i
$496$	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
$499$	9.79077	−	1.28898i	0.438295	−	0.0577026i	0.0918499	−	0.995773i	$-0.470722\pi$
$499$	9.79077	−	1.28898i	0.438295	−	0.0577026i	0.346445	+	0.938070i	$0.387389\pi$
$500$	−6.56986	+	5.04123i	−0.293813	+	0.225451i
$501$	6.20036	+	23.1401i	0.277012	+	1.03382i
$502$	3.72080	+	0.996986i	0.166067	+	0.0444976i
$503$	−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	$0.642696\pi$
$504$	−4.90243	−	3.49059i	−0.218371	−	0.155483i
$505$	6.14447	−	2.54512i	0.273425	−	0.113256i
$506$	9.67891	−	5.58812i	0.430280	−	0.248422i
$507$	35.9397	+	4.73155i	1.59614	+	0.210136i
$508$	6.49595	−	1.74058i	0.288211	−	0.0772259i
$509$	−8.77257	−	15.1945i	−0.388837	−	0.673486i	0.603456	−	0.797396i	$-0.293790\pi$
$509$	−8.77257	−	15.1945i	−0.388837	−	0.673486i	−0.992293	+	0.123910i	$0.960456\pi$
$510$	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
$513$	−2.17727	+	2.83747i	−0.0961286	+	0.125277i
$514$	−1.81911	−	1.05026i	−0.0802374	−	0.0463251i
$515$	−0.0763028	+	0.579577i	−0.00336230	+	0.0255392i
$516$	−0.841243	+	0.110752i	−0.0370337	+	0.00487557i
$517$	1.47068	+	0.609175i	0.0646804	+	0.0267915i
$518$	5.18911	−	9.77931i	0.227996	−	0.429678i
$519$	7.01151	−	7.01151i	0.307771	−	0.307771i
$520$	1.10917	+	8.42499i	0.0486404	+	0.369460i
$521$	11.5455	+	15.0464i	0.505820	+	0.659197i	0.974557	−	0.224141i	$-0.0719575\pi$
$521$	11.5455	+	15.0464i	0.505820	+	0.659197i	−0.468737	+	0.883338i	$0.655291\pi$
$522$	−0.588905	+	4.47318i	−0.0257757	+	0.195786i
$523$	20.5178	−	11.8459i	0.897179	−	0.517987i	0.0208952	−	0.999782i	$-0.493348\pi$
$523$	20.5178	−	11.8459i	0.897179	−	0.517987i	0.876284	+	0.481795i	$0.160015\pi$
$524$	−1.34407	−	3.24488i	−0.0587161	−	0.141753i
$525$	10.5772	−	6.62184i	0.461626	−	0.289001i
$526$	−0.175813			−0.00766581
$527$	9.80018	+	12.7611i	0.426903	+	0.555884i
$528$	2.62966	−	4.55471i	0.114441	−	0.198218i
$529$	11.8449	−	3.17382i	0.514994	−	0.137992i
$530$	−0.352013	+	0.458752i	−0.0152904	+	0.0199269i
$531$		−	1.44026i		−	0.0625021i
$532$	−14.1947	−	5.29347i	−0.615420	−	0.229501i
$533$	−17.7134	+	42.7640i	−0.767254	+	1.85231i
$534$	−1.04350	−	7.92620i	−0.0451568	−	0.343000i
$535$	2.22085	+	8.28831i	0.0960156	+	0.358335i
$536$	2.37984	+	8.88167i	0.102793	+	0.383630i
$537$	−2.66639	−	20.2532i	−0.115063	−	0.873991i
$538$	−7.30963	+	17.6470i	−0.315140	+	0.760816i
$539$	−20.8199	−	1.23793i	−0.896776	−	0.0533214i
$540$			0.852264i			0.0366756i
$541$	0.0867166	−	0.113011i	0.00372824	−	0.00485873i	−0.791486	−	0.611188i	$-0.790692\pi$
$541$	0.0867166	−	0.113011i	0.00372824	−	0.00485873i	0.795214	+	0.606329i	$0.207359\pi$
$542$	8.19177	−	2.19498i	0.351867	−	0.0942824i
$543$	−9.07705	+	15.7219i	−0.389533	+	0.674692i
$544$	20.2303	+	11.6690i	0.867366	+	0.500305i
$545$	−7.66702			−0.328419
$546$	−0.419267	−	11.7210i	−0.0179430	−	0.501613i
$547$	−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
$549$	−1.05941	+	8.04699i	−0.0452144	+	0.343437i
$550$	−5.40401	−	7.04264i	−0.230428	−	0.300299i
$551$	3.33440	+	25.3273i	0.142050	+	1.07898i
$552$	−9.55116	+	9.55116i	−0.406524	+	0.406524i
$553$	−3.59317	−	5.73942i	−0.152797	−	0.244065i
$554$	−8.31239	−	3.44311i	−0.353160	−	0.146284i
$555$	−3.49616	+	0.460278i	−0.148404	+	0.0195377i
$556$	0.870867	−	6.61489i	0.0369330	−	0.280534i
$557$	−14.9065	−	8.60627i	−0.631609	−	0.364660i	0.149766	−	0.988721i	$-0.452148\pi$
$557$	−14.9065	−	8.60627i	−0.631609	−	0.364660i	−0.781375	+	0.624062i	$0.785481\pi$
$558$	1.50062	−	1.95565i	0.0635265	−	0.0827893i
$559$	−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
$563$	−34.1909	+	9.16144i	−1.44098	+	0.386109i	−0.892876	−	0.450304i	$-0.851316\pi$
$563$	−34.1909	+	9.16144i	−1.44098	+	0.386109i	−0.548101	+	0.836412i	$0.684649\pi$
$564$	−0.848034	−	0.111646i	−0.0357087	−	0.00470114i
$565$	−0.844248	+	0.487427i	−0.0355178	+	0.0205062i
$566$	−0.227375	+	0.0941818i	−0.00955728	+	0.00395876i
$567$	0.251349	−	2.63379i	0.0105557	−	0.110609i
$568$	20.0588	+	8.30861i	0.841647	+	0.348621i
$569$	−11.1624	−	2.99096i	−0.467953	−	0.125388i	0.0171346	−	0.999853i	$-0.494546\pi$
$569$	−11.1624	−	2.99096i	−0.467953	−	0.125388i	−0.485088	+	0.874466i	$0.661212\pi$
$570$	−0.311270	−	1.16167i	−0.0130377	−	0.0486572i
$571$	−0.988100	+	0.758196i	−0.0413507	+	0.0317295i	−0.629230	−	0.777219i	$-0.716630\pi$
$571$	−0.988100	+	0.758196i	−0.0413507	+	0.0317295i	0.587879	+	0.808949i	$0.299963\pi$
$572$	33.1900	−	4.36954i	1.38774	−	0.182700i
$573$	−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
$576$	0.0123341	−	0.0460316i	0.000513922	−	0.00191798i
$577$	20.7735	−	35.9808i	0.864813	−	1.49790i	−0.00241960	−	0.999997i	$-0.500770\pi$
$577$	20.7735	−	35.9808i	0.864813	−	1.49790i	0.867233	−	0.497903i	$-0.165896\pi$
$578$	10.3748	+	2.77090i	0.431533	+	0.115254i
$579$	−4.15887	−	7.20338i	−0.172837	−	0.299362i
$580$	4.30443	+	4.30443i	0.178732	+	0.178732i
$581$	8.23489	−	22.0823i	0.341641	−	0.916130i
$582$			3.41864i			0.141707i
$583$	4.06488	+	3.11909i	0.168350	+	0.129180i
$584$	19.2301	+	25.0611i	0.795746	+	1.03704i
$585$	−2.96384	+	2.27423i	−0.122540	+	0.0940279i
$586$	5.08232	+	1.36180i	0.209949	+	0.0562556i
$587$	−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	$0.254694\pi$
$588$	10.9781	−	2.25294i	0.452731	−	0.0929098i
$589$	5.34118	−	12.8948i	0.220080	−	0.531319i
$590$	0.384225	+	0.294826i	0.0158183	+	0.0121378i
$591$	−1.00735	−	0.581593i	−0.0414368	−	0.0239235i
$592$	−11.5928	−	1.52622i	−0.476462	−	0.0627274i
$593$	−4.17690	+	15.5884i	−0.171525	+	0.640140i	0.825593	+	0.564267i	$0.190841\pi$
$593$	−4.17690	+	15.5884i	−0.171525	+	0.640140i	−0.997117	+	0.0758730i	$0.975826\pi$
$594$	−1.88208			−0.0772227
$595$	−4.92083	+	3.08346i	−0.201734	+	0.126410i
$596$	24.8184			1.01660
$597$	5.07388	−	18.9360i	0.207660	−	0.774998i
$598$	−26.0988	−	3.43597i	−1.06726	−	0.140507i
$599$	−14.9092	−	8.60785i	−0.609175	−	0.351707i	0.163468	−	0.986549i	$-0.447732\pi$
$599$	−14.9092	−	8.60785i	−0.609175	−	0.351707i	−0.772642	+	0.634841i	$0.781065\pi$
$600$	8.51159	+	6.53117i	0.347484	+	0.266634i
$601$	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	$0.0670423\pi$
$602$	−0.513737	+	0.721528i	−0.0209384	+	0.0294073i
$603$	−2.85840	+	2.85840i	−0.116403	+	0.116403i
$604$	14.9518	+	4.00631i	0.608378	+	0.163014i
$605$	−0.896370	+	0.687809i	−0.0364426	+	0.0279634i
$606$	−4.80421	−	6.26096i	−0.195158	−	0.254334i
$607$	9.54743	+	7.32600i	0.387518	+	0.297353i	0.784086	−	0.620652i	$-0.213132\pi$
$607$	9.54743	+	7.32600i	0.387518	+	0.297353i	−0.396568	+	0.918005i	$0.629799\pi$
$608$		−	20.2586i		−	0.821594i
$609$	−12.0327	−	14.5716i	−0.487589	−	0.590471i
$610$	−1.92986	−	1.92986i	−0.0781379	−	0.0781379i
$611$	−1.87468	−	3.24705i	−0.0758416	−	0.131362i
$612$	0.00267483	+	6.60106i	0.000108124	+	0.266832i
$613$	3.48231	−	6.03154i	0.140649	−	0.243612i	−0.787092	−	0.616836i	$-0.788414\pi$
$613$	3.48231	−	6.03154i	0.140649	−	0.243612i	0.927741	+	0.373224i	$0.121748\pi$
$614$	−2.95391	+	11.0241i	−0.119210	+	0.444898i
$615$	−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	$0.109422\pi$
$618$	0.687729	−	0.0905412i	0.0276645	−	0.00364210i
$619$	−13.9731	+	10.7220i	−0.561628	+	0.430952i	−0.850165	−	0.526517i	$-0.823498\pi$
$619$	−13.9731	+	10.7220i	−0.561628	+	0.430952i	0.288537	+	0.957469i	$0.406831\pi$
$620$	−0.860803	−	3.21256i	−0.0345707	−	0.129020i
$621$	−5.73590	−	1.53693i	−0.230174	−	0.0616749i
$622$	16.3370	+	6.76699i	0.655053	+	0.271332i
$623$	27.2774	+	19.4219i	1.09285	+	0.778121i
$624$	−11.4446	+	4.74051i	−0.458151	+	0.189772i
$625$	−18.0390	+	10.4148i	−0.721558	+	0.416592i
$626$	0.415526	+	0.0547051i	0.0166078	+	0.00218645i
$627$	−10.2933	+	2.75808i	−0.411075	+	0.110147i
$628$	−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	$0.799068\pi$
$632$	3.54397	−	4.61859i	0.140971	−	0.183718i
$633$	9.84692	+	5.68512i	0.391380	+	0.225963i
$634$	−0.174858	+	1.32818i	−0.00694449	+	0.0527486i
$635$	−2.21699	+	0.291872i	−0.0879786	+	0.0115826i
$636$	−2.54354	−	1.05357i	−0.100858	−	0.0417767i
$637$	37.1296	+	32.1658i	1.47113	+	1.27445i
$638$	−9.50559	+	9.50559i	−0.376330	+	0.376330i
$639$	1.24587	+	9.46333i	0.0492859	+	0.374363i
$640$	−3.66144	−	4.77168i	−0.144731	−	0.188617i
$641$	1.66073	−	12.6145i	0.0655949	−	0.498243i	−0.926839	−	0.375460i	$-0.877485\pi$
$641$	1.66073	−	12.6145i	0.0655949	−	0.498243i	0.992434	−	0.122783i	$-0.0391818\pi$
$642$	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	$0.689884\pi$
$644$	−0.899174	−	25.1373i	−0.0354324	−	0.990547i
$645$	0.282130			0.0111089
$646$	−2.41453	−	8.99656i	−0.0949984	−	0.353965i
$647$	−11.1927	+	19.3863i	−0.440030	+	0.762154i	−0.997691	−	0.0679147i	$-0.978365\pi$
$647$	−11.1927	+	19.3863i	−0.440030	+	0.762154i	0.557661	+	0.830069i	$0.311699\pi$
$648$	2.19714	−	0.588721i	0.0863117	−	0.0231271i
$649$	2.61238	−	3.40452i	0.102545	−	0.133639i
$650$			20.9086i			0.820102i
$651$	1.71273	+	10.1818i	0.0671271	+	0.399055i
$652$	−0.101593	+	0.245266i	−0.00397867	+	0.00960537i
$653$	−4.59423	−	34.8966i	−0.179786	−	1.36561i	−0.808739	−	0.588168i	$-0.799849\pi$
$653$	−4.59423	−	34.8966i	−0.179786	−	1.36561i	0.628953	−	0.777443i	$-0.283484\pi$
$654$	2.35466	+	8.78773i	0.0920746	+	0.343627i
$655$	0.302257	+	1.12804i	0.0118101	+	0.0440761i
$656$	−1.51964	−	11.5428i	−0.0593320	−	0.450672i
$657$	−5.31447	+	12.8303i	−0.207337	+	0.500557i
$658$	−0.688491	+	0.568530i	−0.0268402	+	0.0221636i
$659$			16.9137i			0.658864i	0.944179	+	0.329432i	$0.106857\pi$
$659$			16.9137i			0.658864i	−0.944179	+	0.329432i	$0.893143\pi$
$660$	−1.54585	+	2.01460i	−0.0601723	+	0.0784180i
$661$	31.2769	−	8.38062i	1.21653	−	0.325968i	0.407209	−	0.913335i	$-0.366502\pi$
$661$	31.2769	−	8.38062i	1.21653	−	0.325968i	0.809321	+	0.587366i	$0.199835\pi$
$662$	−2.01273	+	3.48615i	−0.0782269	+	0.135493i
$663$	−22.9487	+	17.6239i	−0.891254	+	0.684457i
$664$	20.2621			0.786321
$665$	4.44969	+	2.36110i	0.172551	+	0.0915594i
$666$	1.60128	+	3.86584i	0.0620485	+	0.149798i
$667$	−36.7320	+	21.2072i	−1.42227	+	0.821147i
$668$	5.00619	−	38.0258i	0.193695	−	1.47126i
$669$	−15.6018	−	20.3326i	−0.603200	−	0.786105i
$670$	−0.177424	−	1.34767i	−0.00685448	−	0.0520649i
$671$	−17.1000	+	17.1000i	−0.660140	+	0.660140i
$672$	7.95231	+	12.7023i	0.306767	+	0.490004i
$673$	−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	$0.788023\pi$
$674$	−1.41988	+	0.186931i	−0.0546918	+	0.00720031i
$675$	−0.615642	+	4.67627i	−0.0236961	+	0.179990i
$676$	−50.2604	−	29.0178i	−1.93309	−	1.11607i
$677$	−11.9592	+	15.5855i	−0.459630	+	0.599001i	−0.964464	−	0.264215i	$-0.914887\pi$
$677$	−11.9592	+	15.5855i	−0.459630	+	0.599001i	0.504834	+	0.863216i	$0.331554\pi$
$678$	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
$682$	7.09439	−	1.90094i	0.271658	−	0.0727906i
$683$	6.04259	+	0.795522i	0.231213	+	0.0304398i	0.245242	−	0.969462i	$-0.421132\pi$
$683$	6.04259	+	0.795522i	0.231213	+	0.0304398i	−0.0140292	+	0.999902i	$0.504466\pi$
$684$	4.95888	−	2.86301i	0.189608	−	0.109470i
$685$	9.42050	−	3.90210i	0.359939	−	0.149091i
$686$	6.08715	−	9.99033i	0.232408	−	0.381432i
$687$	−3.89537	−	1.61351i	−0.148617	−	0.0615594i
$688$	0.903630	+	0.242127i	0.0344506	+	0.00923101i
$689$	−3.12344	−	11.6568i	−0.118994	−	0.444090i
$690$	1.58417	−	1.21557i	0.0603082	−	0.0462761i
$691$	−26.4686	+	3.48466i	−1.00691	+	0.132563i	−0.615901	−	0.787823i	$-0.711208\pi$
$691$	−26.4686	+	3.48466i	−1.00691	+	0.132563i	−0.391011	+	0.920386i	$0.627875\pi$
$692$	−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
$695$	−0.574178	+	2.14286i	−0.0217798	+	0.0812834i
$696$	8.12343	−	14.0702i	0.307918	−	0.533329i
$697$	−10.4172	−	25.1204i	−0.394578	−	0.951505i
$698$	−7.91311	−	13.7059i	−0.299516	−	0.518776i
$699$	13.8195	+	13.8195i	0.522703	+	0.522703i
$700$	−19.7020	+	3.31417i	−0.744664	+	0.125264i
$701$		−	7.46326i		−	0.281883i	−0.990018	−	0.140942i	$-0.954987\pi$
$701$		−	7.46326i		−	0.281883i	0.990018	−	0.140942i	$-0.0450130\pi$
$702$	3.51690	+	2.69861i	0.132737	+	0.101853i
$703$	14.4228	+	18.7961i	0.543965	+	0.708909i
$704$	0.112649	−	0.0864383i	0.00424560	−	0.00325777i
$705$	0.274717	+	0.0736101i	0.0103464	+	0.00277232i
$706$	−1.62960	+	1.62960i	−0.0613308	+	0.0613308i
$707$	32.9051	+	3.14022i	1.23753	+	0.118100i
$708$	−0.882410	+	2.13033i	−0.0331630	+	0.0800626i
$709$	−10.5589	−	8.10209i	−0.396546	−	0.304280i	0.391171	−	0.920318i	$-0.372070\pi$
$709$	−10.5589	−	8.10209i	−0.396546	−	0.304280i	−0.787717	+	0.616038i	$0.788737\pi$
$710$	−2.77960	−	1.60480i	−0.104317	−	0.0602272i
$711$	2.53745	+	0.334062i	0.0951619	+	0.0125283i
$712$	−7.45100	+	27.8075i	−0.279238	+	1.04213i
$713$	23.1735			0.867854
$714$	5.04544	+	4.69314i	0.188821	+	0.175636i
$715$	−11.1310			−0.416276
$716$	−8.46468	+	31.5906i	−0.316340	+	1.18060i
$717$	−23.9005	−	3.14656i	−0.892580	−	0.117510i
$718$	16.4493	+	9.49698i	0.613881	+	0.354424i
$719$	−3.02543	−	2.32150i	−0.112830	−	0.0865772i	0.550806	−	0.834634i	$-0.314321\pi$
$719$	−3.02543	−	2.32150i	−0.112830	−	0.0865772i	−0.663635	+	0.748056i	$0.730987\pi$
$720$	0.359590	−	0.868128i	0.0134011	−	0.0323532i
$721$	−1.68517	+	2.36677i	−0.0627590	+	0.0881430i
$722$	2.77299	−	2.77299i	0.103200	−	0.103200i
$723$	−10.2756	−	2.75333i	−0.382153	−	0.102398i
$724$	23.0585	−	17.6934i	0.856961	−	0.657569i
$725$	20.5085	+	26.7272i	0.761667	+	0.992624i
$726$	1.06364	+	0.816157i	0.0394752	+	0.0302904i
$727$		−	6.45965i		−	0.239575i	−0.992800	−	0.119788i	$-0.961779\pi$
$727$		−	6.45965i		−	0.239575i	0.992800	−	0.119788i	$-0.0382214\pi$
$728$	−14.7572	+	39.5722i	−0.546937	+	1.46664i
$729$	0.707107	+	0.707107i	0.0261891	+	0.0261891i
$730$	−2.33489	−	4.04416i	−0.0864183	−	0.149681i
$731$	2.18519		0.000885465i	0.0808220		3.27501e-5i
$732$	6.49717	−	11.2534i	0.240142	−	0.415939i
$733$	2.60088	−	9.70662i	0.0960657	−	0.358522i	−0.901113	−	0.433584i	$-0.857249\pi$
$733$	2.60088	−	9.70662i	0.0960657	−	0.358522i	0.997179	+	0.0750619i	$0.0239154\pi$
$734$	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
$737$	−11.9413	+	1.57211i	−0.439865	+	0.0579093i
$738$	−3.30536	+	2.53629i	−0.121672	+	0.0933621i
$739$	12.2796	+	45.8281i	0.451713	+	1.68581i	0.697577	+	0.716510i	$0.254262\pi$
$739$	12.2796	+	45.8281i	0.451713	+	1.68581i	−0.245864	+	0.969304i	$0.579072\pi$
$740$	5.45325	+	1.46119i	0.200465	+	0.0537146i
$741$	23.1890	+	9.60520i	0.851869	+	0.352856i
$742$	−2.61414	+	1.19401i	−0.0959682	+	0.0438336i
$743$	−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
$745$	−8.18162	−	1.07713i	−0.299751	−	0.0394630i
$746$	2.15121	−	0.576416i	0.0787616	−	0.0211041i
$747$	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
$751$	−0.562002	+	0.732415i	−0.0205077	+	0.0267262i	−0.803495	−	0.595312i	$-0.797028\pi$
$751$	−0.562002	+	0.732415i	−0.0205077	+	0.0267262i	0.782987	+	0.622038i	$0.213695\pi$
$752$	0.816713	+	0.471530i	0.0297825	+	0.0171949i
$753$	0.795974	−	6.04603i	0.0290069	−	0.220329i
$754$	31.3920	−	4.13283i	1.14323	−	0.150509i
$755$	−4.75511	−	1.96963i	−0.173056	−	0.0716821i
$756$	−1.98542	+	3.74170i	−0.0722092	+	0.136084i
$757$	−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	$0.949521\pi$
$758$	2.26588	+	17.2111i	0.0823006	+	0.625135i
$759$	−10.7709	−	14.0369i	−0.390959	−	0.509507i
$760$	−0.565276	+	4.29370i	−0.0205047	+	0.155749i
$761$	36.8073	−	21.2507i	1.33426	−	0.770338i	0.348314	−	0.937378i	$-0.386754\pi$
$761$	36.8073	−	21.2507i	1.33426	−	0.770338i	0.985950	+	0.167040i	$0.0534209\pi$
$762$	1.01541	+	2.45141i	0.0367844	+	0.0888053i
$763$	−33.6606	−	17.8610i	−1.21859	−	0.646612i
$764$	36.6564			1.32618
$765$	0.285607	−	2.17621i	0.0103261	−	0.0786812i
$766$	5.55801	−	9.62676i	0.200819	−	0.347829i
$767$	−9.76311	+	2.61602i	−0.352525	+	0.0944589i
$768$	−4.40270	+	5.73771i	−0.158869	+	0.207042i
$769$		−	9.73505i		−	0.351055i	−0.984475	−	0.175527i	$-0.943837\pi$
$769$		−	9.73505i		−	0.351055i	0.984475	−	0.175527i	$-0.0561631\pi$
$770$	0.439722	+	2.61405i	0.0158465	+	0.0942037i
$771$	−1.27255	+	3.07222i	−0.0458299	+	0.110643i
$772$	1.73817	+	13.2027i	0.0625581	+	0.475176i
$773$	−10.2173	−	38.1316i	−0.367492	−	1.37150i	−0.864011	−	0.503474i	$-0.832055\pi$
$773$	−10.2173	−	38.1316i	−0.367492	−	1.37150i	0.496518	−	0.868026i	$-0.334612\pi$
$774$	−0.0866466	−	0.323369i	−0.00311445	−	0.0116233i
$775$	−2.40249	−	18.2487i	−0.0863000	−	0.655514i
$776$	4.71102	−	11.3734i	0.169116	−	0.408281i
$777$	−16.4215	−	6.12385i	−0.589116	−	0.219692i
$778$			24.5480i			0.880088i
$779$	−14.3606	+	18.7151i	−0.514521	+	0.670537i
$780$	5.77724	−	1.54801i	0.206858	−	0.0554275i
$781$	−14.2198	+	24.6293i	−0.508823	+	0.881307i
$782$	12.2661	−	9.41998i	0.438633	−	0.336858i
$783$	7.14260			0.255256
$784$	−12.1331	−	2.33706i	−0.433323	−	0.0834665i
$785$	3.25748	+	7.86426i	0.116265	+	0.280688i
$786$	1.20010	−	0.692876i	0.0428060	−	0.0247141i
$787$	1.50067	−	11.3987i	0.0534931	−	0.406320i	−0.943660	−	0.330917i	$-0.892642\pi$
$787$	1.50067	−	11.3987i	0.0534931	−	0.406320i	0.997153	−	0.0754036i	$-0.0240245\pi$
$788$	1.13367	+	1.47742i	0.0403852	+	0.0526310i
$789$	0.0363293	+	0.275948i	0.00129336	+	0.00982403i
$790$	−0.608542	+	0.608542i	−0.0216510	+	0.0216510i
$791$	−4.84201	+	0.173201i	−0.172162	+	0.00615833i
$792$	6.26146	+	2.59358i	0.222491	+	0.0921589i
$793$	56.4724	−	7.43473i	2.00539	−	0.264015i
$794$	1.07471	−	8.16326i	0.0381401	−	0.289703i
$795$	0.792776	+	0.457709i	0.0281169	+	0.0162333i
$796$	−19.1065	+	24.9000i	−0.677211	+	0.882558i
$797$	−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
$801$	−12.2250	+	3.27568i	−0.431949	+	0.115740i
$802$	2.27227	+	0.299150i	0.0802365	+	0.0105633i
$803$	−35.8342	+	20.6889i	−1.26456	+	0.730096i
$804$	5.97919	−	2.47666i	0.210870	−	0.0873451i
$805$	−0.794547	+	8.32575i	−0.0280041	+	0.293444i
$806$	−15.9824	−	6.62013i	−0.562956	−	0.233184i
$807$	29.2084	+	7.82637i	1.02819	+	0.275501i
$808$	7.35517	+	27.4499i	0.258754	+	0.965683i
$809$	−29.7981	+	22.8649i	−1.04765	+	0.803887i	−0.981023	−	0.193891i	$-0.937889\pi$
$809$	−29.7981	+	22.8649i	−1.04765	+	0.803887i	−0.0666231	+	0.997778i	$0.521223\pi$
$810$	−0.333384	+	0.0438909i	−0.0117139	+	0.00154217i
$811$	−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
$814$	−3.22680	+	12.0426i	−0.113099	+	0.422092i
$815$	0.0441356	−	0.0764451i	0.00154600	−	0.00267775i
$816$	2.78242	−	6.72505i	0.0974040	−	0.235424i
$817$	−0.947760	−	1.64157i	−0.0331579	−	0.0574312i
$818$	10.4305	+	10.4305i	0.364692	+	0.364692i
$819$	−18.3102	+	3.08005i	−0.639809	+	0.107626i
$820$			5.62127i			0.196303i
$821$	−22.7914	−	17.4884i	−0.795424	−	0.610350i	0.129031	−	0.991641i	$-0.458813\pi$
$821$	−22.7914	−	17.4884i	−0.795424	−	0.610350i	−0.924455	+	0.381290i	$0.875480\pi$
$822$	−7.36566	−	9.59911i	−0.256907	−	0.334807i
$823$	28.6631	−	21.9940i	0.999134	−	0.766663i	0.0266533	−	0.999645i	$-0.491515\pi$
$823$	28.6631	−	21.9940i	0.999134	−	0.766663i	0.972481	+	0.232982i	$0.0748483\pi$
$824$	−2.41276	−	0.646498i	−0.0840526	−	0.0225218i
$825$	−9.93717	+	9.93717i	−0.345968	+	0.345968i
$826$	1.00004	+	2.18946i	0.0347958	+	0.0761810i
$827$	−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	$0.970978\pi$
$828$	7.54247	+	5.78754i	0.262119	+	0.201131i
$829$	21.4971	+	12.4113i	0.746624	+	0.431064i	0.824473	−	0.565902i	$-0.191472\pi$
$829$	21.4971	+	12.4113i	0.746624	+	0.431064i	−0.0778487	+	0.996965i	$0.524805\pi$
$830$	−2.96972	−	0.390971i	−0.103081	−	0.0135708i
$831$	−3.68651	+	13.7583i	−0.127884	+	0.477268i
$832$	−0.334437			−0.0115945
$833$	−28.7871	+	2.07383i	−0.997415	+	0.0718539i
$834$	2.63243			0.0911535
$835$	−3.30067	+	12.3183i	−0.114225	+	0.426292i
$836$	16.9149	+	2.22688i	0.585013	+	0.0770184i
$837$	−3.37959	−	1.95121i	−0.116816	−	0.0674436i
$838$	0.934794	+	0.717293i	0.0322919	+	0.0247785i
$839$	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	$-0.0830213\pi$
$840$	−1.33101	−	2.91409i	−0.0459243	−	0.100546i
$841$	15.5682	−	15.5682i	0.536834	−	0.536834i
$842$	18.7065	+	5.01240i	0.644670	+	0.172739i
$843$	−7.46624	+	5.72904i	−0.257151	+	0.197319i
$844$	−11.0817	−	14.4419i	−0.381447	−	0.497112i
$845$	15.3094	+	11.7473i	0.526659	+	0.404120i
$846$		−	0.337479i		−	0.0116028i
$847$	−5.53765	+	0.931516i	−0.190276	+	0.0320073i
$848$	2.14636	+	2.14636i	0.0737063	+	0.0737063i
$849$	0.194808	+	0.337417i	0.00668578	+	0.0115801i
$850$	−8.68975	−	8.68271i	−0.298056	−	0.297815i
$851$	−19.6682	+	34.0664i	−0.674218	+	1.16778i
$852$	3.95513	−	14.7607i	0.135500	−	0.505695i
$853$	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
$856$	−36.3512	+	4.78573i	−1.24246	+	0.163573i
$857$	−4.77090	+	3.66084i	−0.162971	+	0.125052i	−0.687027	−	0.726632i	$-0.741085\pi$
$857$	−4.77090	+	3.66084i	−0.162971	+	0.125052i	0.524057	+	0.851683i	$0.324418\pi$
$858$	3.41851	+	12.7580i	0.116706	+	0.435552i
$859$	−42.9385	−	11.5053i	−1.46504	−	0.392557i	−0.563815	−	0.825901i	$-0.690667\pi$
$859$	−42.9385	−	11.5053i	−1.46504	−	0.392557i	−0.901229	+	0.433344i	$0.857334\pi$
$860$	−0.417305	−	0.172853i	−0.0142300	−	0.00589425i
$861$	1.65782	−	17.3716i	0.0564983	−	0.592024i
$862$	−7.77243	+	3.21945i	−0.264730	+	0.109655i
$863$	30.8392	−	17.8050i	1.04978	−	0.606089i	0.127191	−	0.991878i	$-0.459404\pi$
$863$	30.8392	−	17.8050i	1.04978	−	0.606089i	0.922587	+	0.385789i	$0.126071\pi$
$864$	−5.61583	−	0.739337i	−0.191054	−	0.0251528i
$865$	5.09866	−	1.36618i	0.173359	−	0.0464515i
$866$	−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
$870$	−1.46211	+	1.90546i	−0.0495702	+	0.0646011i
$871$	24.5681	+	14.1844i	0.832457	+	0.480619i
$872$	4.27615	−	32.4805i	0.144809	−	1.09993i
$873$	5.36575	−	0.706414i	0.181603	−	0.0239085i
$874$	−12.3945	−	5.13396i	−0.419250	−	0.173659i
$875$	13.6764	−	0.489213i	0.462347	−	0.0165384i
$876$	15.7215	−	15.7215i	0.531181	−	0.531181i
$877$	2.45590	+	18.6544i	0.0829298	+	0.629914i	0.981553	+	0.191192i	$0.0612354\pi$
$877$	2.45590	+	18.6544i	0.0829298	+	0.629914i	−0.898623	+	0.438722i	$0.855431\pi$
$878$	−6.22212	−	8.10882i	−0.209986	−	0.273660i
$879$	1.08724	−	8.25839i	0.0366716	−	0.278549i
$880$	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	$0.700191\pi$
$882$	1.44666	+	4.17835i	0.0487116	+	0.140692i
$883$	48.2187			1.62269			0.811344	−	0.584569i	$-0.198736\pi$
$883$	48.2187			1.62269			0.811344	+	0.584569i	$0.198736\pi$
$884$	44.7417	−	12.0079i	1.50483	−	0.403870i
$885$	0.383352	−	0.663984i	0.0128862	−	0.0223196i
$886$	−13.2481	+	3.54980i	−0.445077	+	0.119258i
$887$	−3.45257	+	4.49948i	−0.115926	+	0.151078i	−0.847712	−	0.530457i	$-0.822020\pi$
$887$	−3.45257	+	4.49948i	−0.115926	+	0.151078i	0.731786	+	0.681535i	$0.238687\pi$
$888$		−	15.0678i		−	0.505643i
$889$	−10.4132	−	3.88326i	−0.349247	−	0.130241i
$890$	1.62863	−	3.93185i	0.0545917	−	0.131796i
$891$	0.388906	+	2.95403i	0.0130288	+	0.0989638i
$892$	10.6197	+	39.6333i	0.355574	+	1.32702i
$893$	−0.494557	−	1.84571i	−0.0165497	−	0.0617644i
$894$	1.27813	+	9.70835i	0.0427470	+	0.324696i
$895$	4.16151	−	10.0468i	0.139104	−	0.335826i
$896$	−4.95878	−	29.4788i	−0.165661	−	0.984817i
$897$			41.6735i			1.39144i
$898$	−6.19678	+	8.07580i	−0.206789	+	0.269493i
$899$	−26.9236	+	7.21416i	−0.897953	+	0.240606i
$900$	3.77563	−	6.53959i	0.125854	−	0.217986i
$901$	6.14174	+	3.54262i	0.204611	+	0.118022i
$902$	−12.4136			−0.413328
$903$	1.23864	+	0.657247i	0.0412192	+	0.0218718i
$904$	−1.59407	−	3.84842i	−0.0530179	−	0.127997i
$905$	−8.36933	+	4.83203i	−0.278206	+	0.160622i
$906$	−0.797165	+	6.05507i	−0.0264840	+	0.201166i
$907$	−34.6815	−	45.1978i	−1.15158	−	1.50077i	−0.833341	−	0.552759i	$-0.813575\pi$
$907$	−34.6815	−	45.1978i	−1.15158	−	1.50077i	−0.318239	−	0.948010i	$-0.603092\pi$
$908$	0.913410	+	6.93804i	0.0303126	+	0.230247i
$909$	−8.83422	+	8.83422i	−0.293013	+	0.293013i
$910$	2.92646	−	5.51517i	0.0970114	−	0.182826i
$911$	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	$0.428692\pi$
$912$	−6.25916	+	0.824034i	−0.207261	+	0.0272865i
$913$	−3.46430	+	26.3140i	−0.114652	+	0.870865i
$914$	−1.83067	−	1.05694i	−0.0605532	−	0.0349604i
$915$	−2.63025	+	3.42781i	−0.0869535	+	0.113320i
$916$	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	−0.940481	−	0.339845i	$-0.889625\pi$
$919$	−23.1775	−	40.1446i	−0.764555	−	1.32425i	0.175926	−	0.984403i	$-0.443708\pi$
$920$	−6.94545	+	1.86103i	−0.228985	+	0.0613562i
$921$	17.9134	+	2.35834i	0.590266	+	0.0777100i
$922$	−4.25874	+	2.45878i	−0.140254	+	0.0809757i
$923$	61.8861	−	25.6341i	2.03701	−	0.843755i
$924$	−11.4799	+	5.24348i	−0.377662	+	0.172498i
$925$	28.8658	+	11.9566i	0.949101	+	0.393131i
$926$	−9.64526	−	2.58444i	−0.316963	−	0.0849299i
$927$	−0.284219	−	1.06072i	−0.00933499	−	0.0348387i
$928$	−32.0973	+	24.6291i	−1.05364	+	0.808490i
$929$	−3.44166	+	0.453104i	−0.112917	+	0.0148659i	−0.186773	−	0.982403i	$-0.559803\pi$
$929$	−3.44166	+	0.453104i	−0.112917	+	0.0148659i	0.0738557	+	0.997269i	$0.476470\pi$
$930$	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
$933$	7.24538	−	27.0401i	0.237203	−	0.885254i
$934$	−4.73665	+	8.20412i	−0.154988	+	0.268447i
$935$	4.62238	−	4.62613i	0.151168	−	0.151291i
$936$	−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	$0.933661\pi$
$938$	2.36057	−	6.32999i	0.0770752	−	0.206682i
$939$		−	0.663497i		−	0.0216524i
$940$	−0.361241	−	0.277190i	−0.0117824	−	0.00904094i
$941$	14.9323	+	19.4602i	0.486780	+	0.634384i	0.970575	−	0.240797i	$-0.0774088\pi$
$941$	14.9323	+	19.4602i	0.486780	+	0.634384i	−0.483796	+	0.875181i	$0.660742\pi$
$942$	8.01337	−	6.14888i	0.261090	−	0.200341i
$943$	−37.8322	−	10.1371i	−1.23199	−	0.330110i
$944$	1.79767	−	1.79767i	0.0585092	−	0.0585092i
$945$	0.816904	−	1.14732i	0.0265739	−	0.0373222i
$946$	0.381717	−	0.921547i	0.0124107	−	0.0299621i
$947$	−8.18120	−	6.27766i	−0.265853	−	0.203996i	0.467229	−	0.884136i	$-0.345252\pi$
$947$	−8.18120	−	6.27766i	−0.265853	−	0.203996i	−0.733082	+	0.680140i	$0.761919\pi$
$948$	−3.54853	−	2.04875i	−0.115251	−	0.0665402i
$949$	96.6255	+	12.7210i	3.13660	+	0.412941i
$950$	−2.75793	+	10.2927i	−0.0894789	+	0.333940i
$951$	2.12078			0.0687711
$952$	−10.3183	−	22.5663i	−0.334417	−	0.731379i
$953$	−7.58653			−0.245752			−0.122876	−	0.992422i	$-0.539212\pi$
$953$	−7.58653			−0.245752			−0.122876	+	0.992422i	$0.539212\pi$
$954$	0.281140	−	1.04923i	0.00910223	−	0.0339700i
$955$	−12.0841	−	1.59090i	−0.391032	−	0.0514804i
$956$	33.4240	+	19.2973i	1.08101	+	0.624120i
$957$	16.8838	+	12.9554i	0.545775	+	0.418788i
$958$	7.27759	−	17.5697i	0.235128	−	0.567650i
$959$	50.4491	+	4.81449i	1.62909	+	0.155468i
$960$	0.0179384	−	0.0179384i	0.000578958	−	0.000578958i
$961$	−15.2338	−	4.08188i	−0.491412	−	0.131673i
$962$	23.2969	−	17.8763i	0.751121	−	0.576356i
$963$	−9.81260	−	12.7880i	−0.316207	−	0.412088i
$964$	13.5120	+	10.3681i	0.435191	+	0.333934i
$965$		−	4.42783i		−	0.142537i
$966$	9.78676	−	1.64628i	0.314884	−	0.0529682i
$967$	−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
$969$	−13.6217	+	5.64876i	−0.437592	+	0.181464i
$970$	−0.909931	+	1.57605i	−0.0292161	+	0.0506038i
$971$	6.00801	−	22.4222i	0.192806	−	0.719562i	−0.800018	−	0.599976i	$-0.795177\pi$
$971$	6.00801	−	22.4222i	0.192806	−	0.719562i	0.992824	−	0.119586i	$-0.0381567\pi$
$972$	−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
$975$	32.8172	−	4.32047i	1.05099	−	0.138366i
$976$	−11.3662	+	8.72158i	−0.363823	+	0.279171i
$977$	0.557340	+	2.08002i	0.0178309	+	0.0665458i	0.974268	−	0.225393i	$-0.0723665\pi$
$977$	0.557340	+	2.08002i	0.0178309	+	0.0665458i	−0.956437	+	0.291938i	$0.905700\pi$
$978$	−0.101174	−	0.0271095i	−0.00323518	−	0.000866865i
$979$	−34.8391	−	14.4308i	−1.11346	−	0.461212i
$980$	5.66076	+	1.88339i	0.180826	+	0.0601626i
$981$	13.3063	−	5.51164i	0.424837	−	0.175973i
$982$	−5.09500	+	2.94160i	−0.162588	+	0.0938703i
$983$	−19.7101	−	2.59489i	−0.628656	−	0.0827641i	−0.190535	−	0.981680i	$-0.561022\pi$
$983$	−19.7101	−	2.59489i	−0.628656	−	0.0827641i	−0.438121	+	0.898916i	$0.644356\pi$
$984$	14.4916	−	3.88302i	0.461977	−	0.123786i
$985$	−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
$989$	1.91588	−	2.49683i	0.0609215	−	0.0793945i
$990$	−0.867669	−	0.500949i	−0.0275763	−	0.0159212i
$991$	−7.95425	+	60.4185i	−0.252675	+	1.91926i	0.122813	+	0.992430i	$0.460808\pi$
$991$	−7.95425	+	60.4185i	−0.252675	+	1.91926i	−0.375488	+	0.926827i	$0.622525\pi$
$992$	21.9153	−	2.88520i	0.695811	−	0.0916052i
$993$	5.88761	+	2.43873i	0.186838	+	0.0773907i
$994$	−8.46476	−	13.5209i	−0.268486	−	0.428857i
$995$	7.37929	−	7.37929i	0.233939	−	0.233939i
$996$	−1.86148	−	14.1393i	−0.0589831	−	0.448021i
$997$	2.11233	+	2.75284i	0.0668982	+	0.0871834i	0.825604	−	0.564250i	$-0.190835\pi$
$997$	2.11233	+	2.75284i	0.0668982	+	0.0871834i	−0.758706	+	0.651433i	$0.774168\pi$
$998$	0.814212	−	6.18455i	0.0257734	−	0.195769i
$999$	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.151.14	yes	192
7.2	even	3	inner	357.2.bh.a.100.11	yes	192
17.8	even	8	inner	357.2.bh.a.25.11	✓	192
119.93	even	24	inner	357.2.bh.a.331.14	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.bh.a.25.11	✓	192	17.8	even	8	inner
357.2.bh.a.100.11	yes	192	7.2	even	3	inner
357.2.bh.a.151.14	yes	192	1.1	even	1	trivial
357.2.bh.a.331.14	yes	192	119.93	even	24	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+(0.163489 - 0.610148i) q^{2} +(-0.991445 - 0.130526i) q^{3} +(1.38650 + 0.800496i) q^{4} +(-0.422330 - 0.324065i) q^{5} +(-0.241730 + 0.583588i) q^{6} +(-1.09922 - 2.40660i) q^{7} +(1.60842 - 1.60842i) q^{8} +(0.965926 + 0.258819i) q^{9} +(-0.266774 + 0.204703i) q^{10} +(1.81382 + 2.36381i) q^{11} +(-1.27015 - 0.974622i) q^{12} -7.01782i q^{13} +(-1.64809 + 0.277234i) q^{14} +(0.376418 + 0.376418i) q^{15} +(0.882578 + 1.52867i) q^{16} +(2.91666 + 2.91429i) q^{17} +(0.315836 - 0.547043i) q^{18} +(0.925679 - 3.45468i) q^{19} +(-0.326147 - 0.787390i) q^{20} +(0.775690 + 2.52949i) q^{21} +(1.73881 - 0.720241i) q^{22} +(5.88744 - 0.775096i) q^{23} +(-1.80460 + 1.38472i) q^{24} +(-1.22075 - 4.55590i) q^{25} +(-4.28191 - 1.14733i) q^{26} +(-0.923880 - 0.382683i) q^{27} +(0.402407 - 4.21667i) q^{28} +(-6.59890 + 2.73335i) q^{29} +(0.291211 - 0.168131i) q^{30} +(3.86903 + 0.509367i) q^{31} +(5.47128 - 1.46602i) 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} +(-4.03259 + 5.25538i) q^{37} +(-1.95653 - 1.12960i) q^{38} +(-0.916010 + 6.95778i) q^{39} +(-1.20051 + 0.158051i) q^{40} +(-6.09363 - 2.52406i) q^{41} +(1.67018 - 0.0597432i) q^{42} +(0.374756 - 0.374756i) q^{43} +(0.622635 + 4.72938i) q^{44} +(-0.324065 - 0.422330i) q^{45} +(0.489606 - 3.71893i) q^{46} +(0.462686 - 0.267132i) q^{47} +(-0.675496 - 1.63079i) q^{48} +(-4.58344 + 5.29075i) q^{49} -2.97935 q^{50} +(-2.51131 - 3.27006i) q^{51} +(5.61774 - 9.73020i) q^{52} +(1.66103 - 0.445072i) q^{53} +(-0.384537 + 0.501139i) q^{54} -1.58611i q^{55} +(-5.63881 - 2.10281i) q^{56} +(-1.36869 + 3.30430i) q^{57} +(0.588905 + 4.47318i) q^{58} +(-0.372768 - 1.39119i) q^{59} +(0.220582 + 0.823224i) q^{60} +(1.05941 + 8.04699i) q^{61} +(0.943331 - 2.27740i) q^{62} +(-0.438889 - 2.60909i) q^{63} -0.0476554i q^{64} +(-2.27423 + 2.96384i) q^{65} +(-1.81795 + 0.487118i) q^{66} +(-2.02119 + 3.50081i) q^{67} +(1.71106 + 6.37544i) q^{68} -5.93824 q^{69} +(0.785880 + 0.417005i) q^{70} +(3.65271 + 8.81842i) q^{71} +(1.96990 - 1.13732i) q^{72} +(-1.81267 + 13.7686i) q^{73} +(2.54727 + 3.31967i) q^{74} +(0.615642 + 4.67627i) q^{75} +(4.04891 - 4.04891i) q^{76} +(3.69497 - 6.96348i) q^{77} +(4.09552 + 1.69642i) q^{78} +(2.53745 - 0.334062i) q^{79} +(0.122650 - 0.931616i) q^{80} +(0.866025 + 0.500000i) q^{81} +(-2.53629 + 3.30536i) 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} +(6.89922 - 1.84864i) q^{87} +(6.71937 + 0.884622i) q^{88} +(-10.9606 + 6.32813i) q^{89} +(-0.310665 + 0.128682i) q^{90} +(-16.8891 + 7.71412i) q^{91} +(8.78339 + 3.63820i) q^{92} +(-3.76944 - 1.01002i) q^{93} +(-0.0873461 - 0.325980i) q^{94} +(-1.51048 + 1.15904i) q^{95} +(-5.61583 + 0.739337i) 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

Fields

Representations

Groups

Database

Properties

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