LMFDB - Embedded newform 546.2.bb.a.269.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(269,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 4]))

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

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

chi := DirichletCharacter("546.269");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bb (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			269.18
Character	$\chi$	$=$	546.269
Dual form			546.2.bb.a.341.37

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(1.63815 + 0.562548i) q^{3} -1.00000 q^{4} +(0.604752 + 1.04746i) q^{5} +(0.562548 - 1.63815i) q^{6} +(0.374319 - 2.61914i) q^{7} +1.00000i q^{8} +(2.36708 + 1.84308i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(1.63815 + 0.562548i) q^{3} -1.00000 q^{4} +(0.604752 + 1.04746i) q^{5} +(0.562548 - 1.63815i) q^{6} +(0.374319 - 2.61914i) q^{7} +1.00000i q^{8} +(2.36708 + 1.84308i) q^{9} +(1.04746 - 0.604752i) q^{10} +(1.03855 - 0.599608i) q^{11} +(-1.63815 - 0.562548i) q^{12} +(1.92468 + 3.04887i) q^{13} +(-2.61914 - 0.374319i) q^{14} +(0.401428 + 2.05610i) q^{15} +1.00000 q^{16} +5.23850 q^{17} +(1.84308 - 2.36708i) q^{18} +(-6.37226 - 3.67902i) q^{19} +(-0.604752 - 1.04746i) q^{20} +(2.08658 - 4.07997i) q^{21} +(-0.599608 - 1.03855i) q^{22} +3.62026i q^{23} +(-0.562548 + 1.63815i) q^{24} +(1.76855 - 3.06322i) q^{25} +(3.04887 - 1.92468i) q^{26} +(2.84082 + 4.35083i) q^{27} +(-0.374319 + 2.61914i) q^{28} +(-1.43268 - 0.827158i) q^{29} +(2.05610 - 0.401428i) q^{30} +(-3.45662 - 1.99568i) q^{31} -1.00000i q^{32} +(2.03861 - 0.398014i) q^{33} -5.23850i q^{34} +(2.96981 - 1.19184i) q^{35} +(-2.36708 - 1.84308i) q^{36} +9.00405 q^{37} +(-3.67902 + 6.37226i) q^{38} +(1.43778 + 6.07724i) q^{39} +(-1.04746 + 0.604752i) q^{40} +(-0.0914442 + 0.158386i) q^{41} +(-4.07997 - 2.08658i) q^{42} +(0.527263 + 0.913245i) q^{43} +(-1.03855 + 0.599608i) q^{44} +(-0.499054 + 3.59403i) q^{45} +3.62026 q^{46} +(3.56307 + 6.17142i) q^{47} +(1.63815 + 0.562548i) q^{48} +(-6.71977 - 1.96079i) q^{49} +(-3.06322 - 1.76855i) q^{50} +(8.58145 + 2.94690i) q^{51} +(-1.92468 - 3.04887i) q^{52} +(-1.91564 - 1.10599i) q^{53} +(4.35083 - 2.84082i) q^{54} +(1.25613 + 0.725228i) q^{55} +(2.61914 + 0.374319i) q^{56} +(-8.36910 - 9.61150i) q^{57} +(-0.827158 + 1.43268i) q^{58} -11.2653 q^{59} +(-0.401428 - 2.05610i) q^{60} +(-5.72549 - 3.30561i) q^{61} +(-1.99568 + 3.45662i) q^{62} +(5.71331 - 5.50981i) q^{63} -1.00000 q^{64} +(-2.02962 + 3.85983i) q^{65} +(-0.398014 - 2.03861i) q^{66} +(-5.37236 - 9.30520i) q^{67} -5.23850 q^{68} +(-2.03657 + 5.93053i) q^{69} +(-1.19184 - 2.96981i) q^{70} +(-6.08827 + 3.51507i) q^{71} +(-1.84308 + 2.36708i) q^{72} +(5.40931 + 3.12307i) q^{73} -9.00405i q^{74} +(4.62036 - 4.02312i) q^{75} +(6.37226 + 3.67902i) q^{76} +(-1.18171 - 2.94455i) q^{77} +(6.07724 - 1.43778i) q^{78} +(2.23131 + 3.86475i) q^{79} +(0.604752 + 1.04746i) q^{80} +(2.20614 + 8.72542i) q^{81} +(0.158386 + 0.0914442i) q^{82} -16.6675 q^{83} +(-2.08658 + 4.07997i) q^{84} +(3.16799 + 5.48712i) q^{85} +(0.913245 - 0.527263i) q^{86} +(-1.88163 - 2.16096i) q^{87} +(0.599608 + 1.03855i) q^{88} -7.19208 q^{89} +(3.59403 + 0.499054i) q^{90} +(8.70586 - 3.89974i) q^{91} -3.62026i q^{92} +(-4.53980 - 5.21374i) q^{93} +(6.17142 - 3.56307i) q^{94} -8.89958i q^{95} +(0.562548 - 1.63815i) q^{96} +(-11.8894 + 6.86436i) q^{97} +(-1.96079 + 6.71977i) q^{98} +(3.56346 + 0.494809i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9}+O(q^{10}) $ 76 * q - 76 * q^4 + 10 * q^7 + 4 * q^9	$ 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9} - 2 q^{13} + 12 q^{15} + 76 q^{16} + 18 q^{19} - 8 q^{21} - 42 q^{25} - 10 q^{28} - 10 q^{30} + 12 q^{31} + 72 q^{33} - 4 q^{36} + 12 q^{37} - 42 q^{39} + 2 q^{42} - 2 q^{43} + 8 q^{46} - 10 q^{49} + 10 q^{51} + 2 q^{52} - 24 q^{55} + 8 q^{57} - 8 q^{58} - 12 q^{60} + 78 q^{61} + 2 q^{63} - 76 q^{64} - 24 q^{66} - 48 q^{67} + 30 q^{69} - 54 q^{73} - 18 q^{76} - 12 q^{78} - 60 q^{79} - 4 q^{81} - 24 q^{82} + 8 q^{84} + 8 q^{85} - 8 q^{91} - 32 q^{93} - 24 q^{94} + 66 q^{97}+O(q^{100}) $ 76 * q - 76 * q^4 + 10 * q^7 + 4 * q^9 - 2 * q^13 + 12 * q^15 + 76 * q^16 + 18 * q^19 - 8 * q^21 - 42 * q^25 - 10 * q^28 - 10 * q^30 + 12 * q^31 + 72 * q^33 - 4 * q^36 + 12 * q^37 - 42 * q^39 + 2 * q^42 - 2 * q^43 + 8 * q^46 - 10 * q^49 + 10 * q^51 + 2 * q^52 - 24 * q^55 + 8 * q^57 - 8 * q^58 - 12 * q^60 + 78 * q^61 + 2 * q^63 - 76 * q^64 - 24 * q^66 - 48 * q^67 + 30 * q^69 - 54 * q^73 - 18 * q^76 - 12 * q^78 - 60 * q^79 - 4 * q^81 - 24 * q^82 + 8 * q^84 + 8 * q^85 - 8 * q^91 - 32 * q^93 - 24 * q^94 + 66 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	1.63815	+	0.562548i	0.945787	+	0.324787i
$3$	1.63815	+	0.562548i	0.945787	+	0.324787i
$4$	−1.00000			−0.500000
$5$	0.604752	+	1.04746i	0.270453	+	0.468439i	0.968978	−	0.247147i	$-0.0794932\pi$
$5$	0.604752	+	1.04746i	0.270453	+	0.468439i	−0.698525	+	0.715586i	$0.746160\pi$
$6$	0.562548	−	1.63815i	0.229659	−	0.668773i
$7$	0.374319	−	2.61914i	0.141479	−	0.989941i
$7$	0.374319	−	2.61914i	0.141479	−	0.989941i
$8$			1.00000i			0.353553i
$9$	2.36708	+	1.84308i	0.789027	+	0.614359i
$10$	1.04746	−	0.604752i	0.331236	−	0.191239i
$11$	1.03855	−	0.599608i	0.313135	−	0.180789i	−0.335193	−	0.942149i	$-0.608802\pi$
$11$	1.03855	−	0.599608i	0.313135	−	0.180789i	0.648328	+	0.761361i	$0.275468\pi$
$12$	−1.63815	−	0.562548i	−0.472894	−	0.162393i
$13$	1.92468	+	3.04887i	0.533809	+	0.845605i
$13$	1.92468	+	3.04887i	0.533809	+	0.845605i
$14$	−2.61914	−	0.374319i	−0.699994	−	0.100041i
$15$	0.401428	+	2.05610i	0.103648	+	0.530883i
$16$	1.00000			0.250000
$17$	5.23850			1.27052			0.635261	−	0.772298i	$-0.280893\pi$
$17$	5.23850			1.27052			0.635261	+	0.772298i	$0.280893\pi$
$18$	1.84308	−	2.36708i	0.434417	−	0.557926i
$19$	−6.37226	−	3.67902i	−1.46190	−	0.844026i	−0.462797	−	0.886464i	$-0.653154\pi$
$19$	−6.37226	−	3.67902i	−1.46190	−	0.844026i	−0.999099	+	0.0424381i	$0.986487\pi$
$20$	−0.604752	−	1.04746i	−0.135227	−	0.234219i
$21$	2.08658	−	4.07997i	0.455329	−	0.890323i
$22$	−0.599608	−	1.03855i	−0.127837	−	0.221420i
$23$			3.62026i			0.754876i	0.926035	+	0.377438i	$0.123195\pi$
$23$			3.62026i			0.754876i	−0.926035	+	0.377438i	$0.876805\pi$
$24$	−0.562548	+	1.63815i	−0.114830	+	0.334386i
$25$	1.76855	−	3.06322i	0.353710	−	0.612644i
$26$	3.04887	−	1.92468i	0.597933	−	0.377460i
$27$	2.84082	+	4.35083i	0.546716	+	0.837318i
$28$	−0.374319	+	2.61914i	−0.0707397	+	0.494971i
$29$	−1.43268	−	0.827158i	−0.266042	−	0.153599i	0.361046	−	0.932548i	$-0.382420\pi$
$29$	−1.43268	−	0.827158i	−0.266042	−	0.153599i	−0.627088	+	0.778949i	$0.715753\pi$
$30$	2.05610	−	0.401428i	0.375391	−	0.0732905i
$31$	−3.45662	−	1.99568i	−0.620827	−	0.358435i	0.156364	−	0.987700i	$-0.450023\pi$
$31$	−3.45662	−	1.99568i	−0.620827	−	0.358435i	−0.777191	+	0.629265i	$0.783356\pi$
$32$		−	1.00000i		−	0.176777i
$33$	2.03861	−	0.398014i	0.354877	−	0.0692853i
$34$		−	5.23850i		−	0.898395i
$35$	2.96981	−	1.19184i	0.501990	−	0.201458i
$36$	−2.36708	−	1.84308i	−0.394513	−	0.307179i
$37$	9.00405			1.48026			0.740128	−	0.672466i	$-0.234765\pi$
$37$	9.00405			1.48026			0.740128	+	0.672466i	$0.234765\pi$
$38$	−3.67902	+	6.37226i	−0.596817	+	1.03372i
$39$	1.43778	+	6.07724i	0.230228	+	0.973137i
$40$	−1.04746	+	0.604752i	−0.165618	+	0.0956196i
$41$	−0.0914442	+	0.158386i	−0.0142812	+	0.0247357i	−0.873078	−	0.487581i	$-0.837879\pi$
$41$	−0.0914442	+	0.158386i	−0.0142812	+	0.0247357i	0.858796	+	0.512317i	$0.171213\pi$
$42$	−4.07997	−	2.08658i	−0.629553	−	0.321966i
$43$	0.527263	+	0.913245i	0.0804068	+	0.139269i	0.903425	−	0.428747i	$-0.141045\pi$
$43$	0.527263	+	0.913245i	0.0804068	+	0.139269i	−0.823018	+	0.568015i	$0.807711\pi$
$44$	−1.03855	+	0.599608i	−0.156567	+	0.0903943i
$45$	−0.499054	+	3.59403i	−0.0743945	+	0.535766i
$46$	3.62026			0.533778
$47$	3.56307	+	6.17142i	0.519728	+	0.900195i	0.999737	+	0.0229314i	$0.00729993\pi$
$47$	3.56307	+	6.17142i	0.519728	+	0.900195i	−0.480009	+	0.877263i	$0.659367\pi$
$48$	1.63815	+	0.562548i	0.236447	+	0.0811967i
$49$	−6.71977	−	1.96079i	−0.959967	−	0.280112i
$50$	−3.06322	−	1.76855i	−0.433205	−	0.250111i
$51$	8.58145	+	2.94690i	1.20164	+	0.412649i
$52$	−1.92468	−	3.04887i	−0.266905	−	0.422803i
$53$	−1.91564	−	1.10599i	−0.263133	−	0.151920i	0.362630	−	0.931933i	$-0.381879\pi$
$53$	−1.91564	−	1.10599i	−0.263133	−	0.151920i	−0.625763	+	0.780013i	$0.715212\pi$
$54$	4.35083	−	2.84082i	0.592073	−	0.386586i
$55$	1.25613	+	0.725228i	0.169377	+	0.0977897i
$56$	2.61914	+	0.374319i	0.349997	+	0.0500205i
$57$	−8.36910	−	9.61150i	−1.10851	−	1.27307i
$58$	−0.827158	+	1.43268i	−0.108611	+	0.188120i
$59$	−11.2653			−1.46662			−0.733308	−	0.679897i	$-0.762025\pi$
$59$	−11.2653			−1.46662			−0.733308	+	0.679897i	$0.762025\pi$
$60$	−0.401428	−	2.05610i	−0.0518242	−	0.265441i
$61$	−5.72549	−	3.30561i	−0.733074	−	0.423241i	0.0864717	−	0.996254i	$-0.472441\pi$
$61$	−5.72549	−	3.30561i	−0.733074	−	0.423241i	−0.819546	+	0.573014i	$0.805774\pi$
$62$	−1.99568	+	3.45662i	−0.253452	+	0.438991i
$63$	5.71331	−	5.50981i	0.719810	−	0.694171i
$64$	−1.00000			−0.125000
$65$	−2.02962	+	3.85983i	−0.251744	+	0.478753i
$66$	−0.398014	−	2.03861i	−0.0489921	−	0.250936i
$67$	−5.37236	−	9.30520i	−0.656338	−	1.13681i	−0.981557	−	0.191172i	$-0.938771\pi$
$67$	−5.37236	−	9.30520i	−0.656338	−	1.13681i	0.325219	−	0.945639i	$-0.394562\pi$
$68$	−5.23850			−0.635261
$69$	−2.03657	+	5.93053i	−0.245174	+	0.713952i
$70$	−1.19184	−	2.96981i	−0.142453	−	0.354961i
$71$	−6.08827	+	3.51507i	−0.722545	+	0.417162i	−0.815689	−	0.578491i	$-0.803642\pi$
$71$	−6.08827	+	3.51507i	−0.722545	+	0.417162i	0.0931436	+	0.995653i	$0.470308\pi$
$72$	−1.84308	+	2.36708i	−0.217209	+	0.278963i
$73$	5.40931	+	3.12307i	0.633112	+	0.365527i	0.781956	−	0.623333i	$-0.214222\pi$
$73$	5.40931	+	3.12307i	0.633112	+	0.365527i	−0.148845	+	0.988861i	$0.547555\pi$
$74$		−	9.00405i		−	1.04670i
$75$	4.62036	−	4.02312i	0.533513	−	0.464550i
$76$	6.37226	+	3.67902i	0.730948	+	0.422013i
$77$	−1.18171	−	2.94455i	−0.134668	−	0.335563i
$78$	6.07724	−	1.43778i	0.688112	−	0.162796i
$79$	2.23131	+	3.86475i	0.251042	+	0.434818i	0.963813	−	0.266579i	$-0.0858934\pi$
$79$	2.23131	+	3.86475i	0.251042	+	0.434818i	−0.712771	+	0.701397i	$0.752560\pi$
$80$	0.604752	+	1.04746i	0.0676133	+	0.117110i
$81$	2.20614	+	8.72542i	0.245127	+	0.969491i
$82$	0.158386	+	0.0914442i	0.0174908	+	0.0100983i
$83$	−16.6675			−1.82949			−0.914747	−	0.404027i	$-0.867610\pi$
$83$	−16.6675			−1.82949			−0.914747	+	0.404027i	$0.867610\pi$
$84$	−2.08658	+	4.07997i	−0.227665	+	0.445162i
$85$	3.16799	+	5.48712i	0.343617	+	0.595161i
$86$	0.913245	−	0.527263i	0.0984778	−	0.0568562i
$87$	−1.88163	−	2.16096i	−0.201732	−	0.231679i
$88$	0.599608	+	1.03855i	0.0639184	+	0.110710i
$89$	−7.19208			−0.762359			−0.381179	−	0.924501i	$-0.624482\pi$
$89$	−7.19208			−0.762359			−0.381179	+	0.924501i	$0.624482\pi$
$90$	3.59403	+	0.499054i	0.378844	+	0.0526049i
$91$	8.70586	−	3.89974i	0.912622	−	0.408804i
$92$		−	3.62026i		−	0.377438i
$93$	−4.53980	−	5.21374i	−0.470755	−	0.540639i
$94$	6.17142	−	3.56307i	0.636534	−	0.367503i
$95$		−	8.89958i		−	0.913078i
$96$	0.562548	−	1.63815i	0.0574148	−	0.167193i
$97$	−11.8894	+	6.86436i	−1.20719	+	0.696970i	−0.962144	−	0.272541i	$-0.912136\pi$
$97$	−11.8894	+	6.86436i	−1.20719	+	0.696970i	−0.245044	+	0.969512i	$0.578802\pi$
$98$	−1.96079	+	6.71977i	−0.198069	+	0.678799i
$99$	3.56346	+	0.494809i	0.358141	+	0.0497302i
$100$	−1.76855	+	3.06322i	−0.176855	+	0.306322i
$101$	1.62511	+	2.81477i	0.161704	+	0.280080i	0.935480	−	0.353380i	$-0.114968\pi$
$101$	1.62511	+	2.81477i	0.161704	+	0.280080i	−0.773776	+	0.633460i	$0.781634\pi$
$102$	2.94690	−	8.58145i	0.291787	−	0.849690i
$103$	−0.504870	+	0.291487i	−0.0497463	+	0.0287210i	−0.524667	−	0.851308i	$-0.675810\pi$
$103$	−0.504870	+	0.291487i	−0.0497463	+	0.0287210i	0.474921	+	0.880029i	$0.342477\pi$
$104$	−3.04887	+	1.92468i	−0.298967	+	0.188730i
$105$	5.53547	−	0.281759i	0.540207	−	0.0274968i
$106$	−1.10599	+	1.91564i	−0.107424	+	0.186063i
$107$		−	9.48742i		−	0.917183i	−0.888647	−	0.458592i	$-0.848354\pi$
$107$		−	9.48742i		−	0.917183i	0.888647	−	0.458592i	$-0.151646\pi$
$108$	−2.84082	−	4.35083i	−0.273358	−	0.418659i
$109$	6.23249	−	10.7950i	0.596964	−	1.03397i	−0.396302	−	0.918120i	$-0.629707\pi$
$109$	6.23249	−	10.7950i	0.596964	−	1.03397i	0.993266	−	0.115852i	$-0.0369599\pi$
$110$	0.725228	−	1.25613i	0.0691477	−	0.119767i
$111$	14.7500	+	5.06521i	1.40001	+	0.480768i
$112$	0.374319	−	2.61914i	0.0353698	−	0.247485i
$113$	−9.73622	+	5.62121i	−0.915907	+	0.528799i	−0.882327	−	0.470637i	$-0.844024\pi$
$113$	−9.73622	+	5.62121i	−0.915907	+	0.528799i	−0.0335797	+	0.999436i	$0.510691\pi$
$114$	−9.61150	+	8.36910i	−0.900199	+	0.783838i
$115$	−3.79208	+	2.18936i	−0.353613	+	0.204159i
$116$	1.43268	+	0.827158i	0.133021	+	0.0767997i
$117$	−1.06344	+	10.7643i	−0.0983151	+	0.995155i
$118$			11.2653i			1.03705i
$119$	1.96087	−	13.7203i	0.179753	−	1.25774i
$120$	−2.05610	+	0.401428i	−0.187695	+	0.0366452i
$121$	−4.78094	+	8.28083i	−0.434631	+	0.752803i
$122$	−3.30561	+	5.72549i	−0.299276	+	0.518362i
$123$	−0.238899	+	0.208018i	−0.0215408	+	0.0187564i
$124$	3.45662	+	1.99568i	0.310413	+	0.179217i
$125$	10.3257			0.923554
$126$	−5.50981	−	5.71331i	−0.490853	−	0.508983i
$127$	−5.39553	+	9.34534i	−0.478776	+	0.829265i	−0.999704	−	0.0243362i	$-0.992253\pi$
$127$	−5.39553	+	9.34534i	−0.478776	+	0.829265i	0.520928	+	0.853601i	$0.325586\pi$
$128$			1.00000i			0.0883883i
$129$	0.349992	+	1.79264i	0.0308151	+	0.157834i
$130$	3.85983	+	2.02962i	0.338530	+	0.178010i
$131$	9.42418	+	16.3232i	0.823394	+	1.42616i	0.903140	+	0.429346i	$0.141256\pi$
$131$	9.42418	+	16.3232i	0.823394	+	1.42616i	−0.0797457	+	0.996815i	$0.525411\pi$
$132$	−2.03861	+	0.398014i	−0.177438	+	0.0346427i
$133$	−12.0211	+	15.3127i	−1.04236	+	1.32778i
$134$	−9.30520	+	5.37236i	−0.803846	+	0.464101i
$135$	−2.83934	+	5.60682i	−0.244371	+	0.482558i
$136$			5.23850i			0.449197i
$137$		−	10.6870i		−	0.913054i	−0.889709	−	0.456527i	$-0.849093\pi$
$137$		−	10.6870i		−	0.913054i	0.889709	−	0.456527i	$-0.150907\pi$
$138$	5.93053	+	2.03657i	0.504841	+	0.173364i
$139$	2.36204	−	1.36372i	0.200345	−	0.115669i	−0.396471	−	0.918047i	$-0.629765\pi$
$139$	2.36204	−	1.36372i	0.200345	−	0.115669i	0.596817	+	0.802378i	$0.296432\pi$
$140$	−2.96981	+	1.19184i	−0.250995	+	0.100729i
$141$	2.36513	+	12.1141i	0.199180	+	1.02019i
$142$	3.51507	+	6.08827i	0.294978	+	0.510917i
$143$	3.82700	+	2.01236i	0.320030	+	0.168282i
$144$	2.36708	+	1.84308i	0.197257	+	0.153590i
$145$		−	2.00090i		−	0.166166i
$146$	3.12307	−	5.40931i	0.258467	−	0.447678i
$147$	−9.90497	−	6.99226i	−0.816948	−	0.576712i
$148$	−9.00405			−0.740128
$149$	−1.31022	−	0.756457i	−0.107338	−	0.0619714i	0.445370	−	0.895347i	$-0.353072\pi$
$149$	−1.31022	−	0.756457i	−0.107338	−	0.0619714i	−0.552708	+	0.833375i	$0.686405\pi$
$150$	−4.02312	−	4.62036i	−0.328487	−	0.377251i
$151$	1.52530	−	2.64189i	0.124127	−	0.214994i	−0.797264	−	0.603630i	$-0.793720\pi$
$151$	1.52530	−	2.64189i	0.124127	−	0.214994i	0.921391	+	0.388636i	$0.127054\pi$
$152$	3.67902	−	6.37226i	0.298408	−	0.516858i
$153$	12.3999	+	9.65495i	1.00248	+	0.780556i
$154$	−2.94455	+	1.18171i	−0.237279	+	0.0952246i
$155$		−	4.82756i		−	0.387759i
$156$	−1.43778	−	6.07724i	−0.115114	−	0.486568i
$157$	2.30973	+	1.33352i	0.184336	+	0.106427i	0.589328	−	0.807894i	$-0.299392\pi$
$157$	2.30973	+	1.33352i	0.184336	+	0.106427i	−0.404992	+	0.914320i	$0.632726\pi$
$158$	3.86475	−	2.23131i	0.307463	−	0.177514i
$159$	−2.51593	−	2.88942i	−0.199526	−	0.229146i
$160$	1.04746	−	0.604752i	0.0828090	−	0.0478098i
$161$	9.48196	+	1.35513i	0.747283	+	0.106799i
$162$	8.72542	−	2.20614i	0.685534	−	0.173331i
$163$	8.95954	−	15.5184i	0.701766	−	1.21549i	−0.266081	−	0.963951i	$-0.585729\pi$
$163$	8.95954	−	15.5184i	0.701766	−	1.21549i	0.967846	−	0.251543i	$-0.0809379\pi$
$164$	0.0914442	−	0.158386i	0.00714059	−	0.0123679i
$165$	1.64976	+	1.89467i	0.128433	+	0.147500i
$166$			16.6675i			1.29365i
$167$	−9.94539	+	17.2259i	−0.769597	+	1.33298i	0.168184	+	0.985756i	$0.446210\pi$
$167$	−9.94539	+	17.2259i	−0.769597	+	1.33298i	−0.937782	+	0.347226i	$0.887124\pi$
$168$	4.07997	+	2.08658i	0.314777	+	0.160983i
$169$	−5.59124	+	11.7362i	−0.430096	+	0.902783i
$170$	5.48712	−	3.16799i	0.420843	−	0.242974i
$171$	−8.30292	−	20.4531i	−0.634940	−	1.56409i
$172$	−0.527263	−	0.913245i	−0.0402034	−	0.0696343i
$173$	8.77428	−	15.1975i	0.667096	−	1.15544i	−0.311616	−	0.950208i	$-0.600870\pi$
$173$	8.77428	−	15.1975i	0.667096	−	1.15544i	0.978712	−	0.205237i	$-0.0657964\pi$
$174$	−2.16096	+	1.88163i	−0.163822	+	0.142646i
$175$	−7.36099	−	5.77870i	−0.556439	−	0.436829i
$176$	1.03855	−	0.599608i	0.0782837	−	0.0451971i
$177$	−18.4542	−	6.33726i	−1.38711	−	0.476338i
$178$			7.19208i			0.539069i
$179$	−19.9172	+	11.4992i	−1.48868	+	0.859490i	−0.999916	−	0.0129254i	$-0.995886\pi$
$179$	−19.9172	+	11.4992i	−1.48868	+	0.859490i	−0.488764	+	0.872416i	$0.662552\pi$
$180$	0.499054	−	3.59403i	0.0371973	−	0.267883i
$181$			7.49251i			0.556914i	0.960449	+	0.278457i	$0.0898230\pi$
$181$			7.49251i			0.556914i	−0.960449	+	0.278457i	$0.910177\pi$
$182$	−3.89974	−	8.70586i	−0.289068	−	0.645321i
$183$	−7.51966	−	8.63596i	−0.555869	−	0.638388i
$184$	−3.62026			−0.266889
$185$	5.44521	+	9.43139i	0.400340	+	0.693409i
$186$	−5.21374	+	4.53980i	−0.382290	+	0.332874i
$187$	5.44045	−	3.14104i	0.397845	−	0.229696i
$188$	−3.56307	−	6.17142i	−0.259864	−	0.450097i
$189$	12.4588	−	5.81190i	0.906245	−	0.422753i
$190$	−8.89958			−0.645644
$191$	−17.8434	−	10.3019i	−1.29110	−	0.745419i	−0.312254	−	0.949999i	$-0.601084\pi$
$191$	−17.8434	−	10.3019i	−1.29110	−	0.745419i	−0.978850	+	0.204579i	$0.934417\pi$
$192$	−1.63815	−	0.562548i	−0.118223	−	0.0405984i
$193$	−3.99673	−	6.92254i	−0.287691	−	0.498295i	0.685567	−	0.728009i	$-0.259554\pi$
$193$	−3.99673	−	6.92254i	−0.287691	−	0.498295i	−0.973258	+	0.229714i	$0.926221\pi$
$194$	6.86436	+	11.8894i	0.492833	+	0.853611i
$195$	−5.49617	+	5.18123i	−0.393589	+	0.371036i
$196$	6.71977	+	1.96079i	0.479984	+	0.140056i
$197$	12.3941	+	7.15573i	0.883042	+	0.509825i	0.871660	−	0.490111i	$-0.163044\pi$
$197$	12.3941	+	7.15573i	0.883042	+	0.509825i	0.0113819	+	0.999935i	$0.496377\pi$
$198$	0.494809	−	3.56346i	0.0351645	−	0.253244i
$199$			3.28144i			0.232615i	0.993213	+	0.116308i	$0.0371058\pi$
$199$			3.28144i			0.232615i	−0.993213	+	0.116308i	$0.962894\pi$
$200$	3.06322	+	1.76855i	0.216602	+	0.125055i
$201$	−3.56612	−	18.2655i	−0.251535	−	1.28835i
$202$	2.81477	−	1.62511i	0.198046	−	0.114342i
$203$	−2.70272	+	3.44277i	−0.189694	+	0.241635i
$204$	−8.58145	−	2.94690i	−0.600822	−	0.206324i
$205$	−0.221204			−0.0154496
$206$	0.291487	+	0.504870i	0.0203088	+	0.0351760i
$207$	−6.67241	+	8.56945i	−0.463765	+	0.595618i
$208$	1.92468	+	3.04887i	0.133452	+	0.211401i
$209$	−8.82389			−0.610361
$210$	−0.281759	−	5.53547i	−0.0194432	−	0.381984i
$211$	5.52912	−	9.57673i	0.380641	−	0.659289i	−0.610513	−	0.792006i	$-0.709037\pi$
$211$	5.52912	−	9.57673i	0.380641	−	0.659289i	0.991154	+	0.132717i	$0.0423702\pi$
$212$	1.91564	+	1.10599i	0.131567	+	0.0759600i
$213$	−11.9509	+	2.33327i	−0.818863	+	0.159873i
$214$	−9.48742			−0.648546
$215$	−0.637726	+	1.10457i	−0.0434925	+	0.0753313i
$216$	−4.35083	+	2.84082i	−0.296037	+	0.193293i
$217$	−6.52084	+	8.30634i	−0.442663	+	0.563871i
$218$	−10.7950	−	6.23249i	−0.731129	−	0.422117i
$219$	7.10439	+	8.15905i	0.480070	+	0.551337i
$220$	−1.25613	−	0.725228i	−0.0846883	−	0.0488948i
$221$	10.0824	+	15.9715i	0.678216	+	1.07436i
$222$	5.06521	−	14.7500i	0.339954	−	0.989955i
$223$	10.5899	+	6.11409i	0.709153	+	0.409429i	0.810747	−	0.585396i	$-0.199061\pi$
$223$	10.5899	+	6.11409i	0.709153	+	0.409429i	−0.101595	+	0.994826i	$0.532394\pi$
$224$	−2.61914	−	0.374319i	−0.174999	−	0.0250102i
$225$	9.83205	−	3.99131i	0.655470	−	0.266088i
$226$	5.62121	+	9.73622i	0.373917	+	0.647644i
$227$	29.0111			1.92553			0.962766	−	0.270335i	$-0.0871344\pi$
$227$	29.0111			1.92553			0.962766	+	0.270335i	$0.0871344\pi$
$228$	8.36910	+	9.61150i	0.554257	+	0.636537i
$229$	24.0075	−	13.8607i	1.58646	−	0.915943i	0.592576	−	0.805515i	$-0.298111\pi$
$229$	24.0075	−	13.8607i	1.58646	−	0.915943i	0.993884	−	0.110428i	$-0.0352222\pi$
$230$	2.18936	+	3.79208i	0.144362	+	0.250042i
$231$	−0.279362	−	5.48839i	−0.0183807	−	0.361110i
$232$	0.827158	−	1.43268i	0.0543056	−	0.0940601i
$233$	−3.05589	+	1.76432i	−0.200198	+	0.115584i	−0.596748	−	0.802429i	$-0.703541\pi$
$233$	−3.05589	+	1.76432i	−0.200198	+	0.115584i	0.396550	+	0.918013i	$0.370207\pi$
$234$	10.7643	+	1.06344i	0.703681	+	0.0695193i
$235$	−4.30955	+	7.46436i	−0.281124	+	0.486921i
$236$	11.2653			0.733308
$237$	1.48112	+	7.58626i	0.0962093	+	0.492780i
$238$	−13.7203	−	1.96087i	−0.889358	−	0.127104i
$239$		−	7.54413i		−	0.487989i	−0.969777	−	0.243994i	$-0.921542\pi$
$239$		−	7.54413i		−	0.487989i	0.969777	−	0.243994i	$-0.0784579\pi$
$240$	0.401428	+	2.05610i	0.0259121	+	0.132721i
$241$		−	12.3343i		−	0.794524i	−0.917705	−	0.397262i	$-0.869960\pi$
$241$		−	12.3343i		−	0.794524i	0.917705	−	0.397262i	$-0.130040\pi$
$242$	8.28083	+	4.78094i	0.532312	+	0.307331i
$243$	−1.29447	+	15.5346i	−0.0830404	+	0.996546i
$244$	5.72549	+	3.30561i	0.366537	+	0.211620i
$245$	−2.00995	−	8.22448i	−0.128411	−	0.525443i
$246$	0.208018	+	0.238899i	0.0132628	+	0.0152316i
$247$	−1.04766	−	26.5091i	−0.0666607	−	1.68674i
$248$	1.99568	−	3.45662i	0.126726	−	0.219495i
$249$	−27.3039	−	9.37625i	−1.73031	−	0.594196i
$250$		−	10.3257i		−	0.653052i
$251$	−5.07909	−	8.79724i	−0.320589	−	0.555277i	0.660020	−	0.751248i	$-0.270548\pi$
$251$	−5.07909	−	8.79724i	−0.320589	−	0.555277i	−0.980610	+	0.195971i	$0.937214\pi$
$252$	−5.71331	+	5.50981i	−0.359905	+	0.347086i
$253$	2.17074	+	3.75983i	0.136473	+	0.236378i
$254$	9.34534	+	5.39553i	0.586379	+	0.338546i
$255$	2.10288	+	10.7709i	0.131687	+	0.674498i
$256$	1.00000			0.0625000
$257$	−13.6772			−0.853162			−0.426581	−	0.904449i	$-0.640282\pi$
$257$	−13.6772			−0.853162			−0.426581	+	0.904449i	$0.640282\pi$
$258$	1.79264	−	0.349992i	0.111605	−	0.0217895i
$259$	3.37039	−	23.5829i	0.209426	−	1.46537i
$260$	2.02962	−	3.85983i	0.125872	−	0.239377i
$261$	−1.86675	−	4.59849i	−0.115549	−	0.284639i
$262$	16.3232	−	9.42418i	1.00845	−	0.582228i
$263$	18.6245	−	10.7529i	1.14844	−	0.663051i	0.199932	−	0.979810i	$-0.435928\pi$
$263$	18.6245	−	10.7529i	1.14844	−	0.663051i	0.948506	+	0.316758i	$0.102594\pi$
$264$	0.398014	+	2.03861i	0.0244961	+	0.125468i
$265$		−	2.67541i		−	0.164349i
$266$	15.3127	+	12.0211i	0.938882	+	0.737063i
$267$	−11.7817	−	4.04589i	−0.721029	−	0.247604i
$268$	5.37236	+	9.30520i	0.328169	+	0.568405i
$269$	28.1567			1.71675			0.858373	−	0.513026i	$-0.171475\pi$
$269$	28.1567			1.71675			0.858373	+	0.513026i	$0.171475\pi$
$270$	5.60682	+	2.83934i	0.341220	+	0.172797i
$271$		−	3.01820i		−	0.183342i	−0.995789	−	0.0916712i	$-0.970779\pi$
$271$		−	3.01820i		−	0.183342i	0.995789	−	0.0916712i	$-0.0292209\pi$
$272$	5.23850			0.317630
$273$	16.4553	−	1.49091i	0.995921	−	0.0902338i
$274$	−10.6870			−0.645627
$275$		−	4.24175i		−	0.255787i
$276$	2.03657	−	5.93053i	0.122587	−	0.356976i
$277$	−11.3331			−0.680942			−0.340471	−	0.940255i	$-0.610586\pi$
$277$	−11.3331			−0.680942			−0.340471	+	0.940255i	$0.610586\pi$
$278$	−1.36372	−	2.36204i	−0.0817906	−	0.141665i
$279$	−4.50390	−	11.0947i	−0.269642	−	0.664225i
$280$	1.19184	+	2.96981i	0.0712263	+	0.177480i
$281$		−	8.18525i		−	0.488291i	−0.969739	−	0.244146i	$-0.921493\pi$
$281$		−	8.18525i		−	0.488291i	0.969739	−	0.244146i	$-0.0785075\pi$
$282$	12.1141	−	2.36513i	0.721386	−	0.140842i
$283$	11.2614	−	6.50177i	0.669420	−	0.386490i	−0.126437	−	0.991975i	$-0.540354\pi$
$283$	11.2614	−	6.50177i	0.669420	−	0.386490i	0.795857	+	0.605485i	$0.207021\pi$
$284$	6.08827	−	3.51507i	0.361273	−	0.208581i
$285$	5.00644	−	14.5789i	0.296556	−	0.863578i
$286$	2.01236	−	3.82700i	0.118993	−	0.226295i
$287$	0.380605	+	0.298792i	0.0224664	+	0.0176371i
$288$	1.84308	−	2.36708i	0.108604	−	0.139482i
$289$	10.4418			0.614225
$290$	−2.00090			−0.117497
$291$	−23.3382	+	4.55650i	−1.36811	+	0.267107i
$292$	−5.40931	−	3.12307i	−0.316556	−	0.182764i
$293$	9.77684	+	16.9340i	0.571169	+	0.989294i	0.996446	+	0.0842309i	$0.0268433\pi$
$293$	9.77684	+	16.9340i	0.571169	+	0.989294i	−0.425277	+	0.905063i	$0.639823\pi$
$294$	−6.99226	+	9.90497i	−0.407797	+	0.577669i
$295$	−6.81270	−	11.7999i	−0.396651	−	0.687019i
$296$			9.00405i			0.523350i
$297$	5.55913	+	2.81519i	0.322573	+	0.163354i
$298$	−0.756457	+	1.31022i	−0.0438204	+	0.0758991i
$299$	−11.0377	+	6.96783i	−0.638327	+	0.402960i
$300$	−4.62036	+	4.02312i	−0.266757	+	0.232275i
$301$	2.58928	−	1.03913i	0.149244	−	0.0598944i
$302$	−2.64189	−	1.52530i	−0.152024	−	0.0877710i
$303$	1.07873	+	5.52522i	0.0619715	+	0.317415i
$304$	−6.37226	−	3.67902i	−0.365474	−	0.211007i
$305$		−	7.99630i		−	0.457867i
$306$	9.65495	−	12.3999i	0.551937	−	0.708857i
$307$		−	27.7274i		−	1.58248i	−0.611503	−	0.791242i	$-0.709435\pi$
$307$		−	27.7274i		−	1.58248i	0.611503	−	0.791242i	$-0.290565\pi$
$308$	1.18171	+	2.94455i	0.0673340	+	0.167782i
$309$	−0.991029	+	0.193486i	−0.0563776	+	0.0110070i
$310$	−4.82756			−0.274187
$311$	3.82623	−	6.62722i	0.216965	−	0.375795i	−0.736913	−	0.675987i	$-0.763717\pi$
$311$	3.82623	−	6.62722i	0.216965	−	0.375795i	0.953879	+	0.300192i	$0.0970508\pi$
$312$	−6.07724	+	1.43778i	−0.344056	+	0.0813980i
$313$	3.76450	−	2.17344i	0.212782	−	0.122850i	−0.389821	−	0.920890i	$-0.627463\pi$
$313$	3.76450	−	2.17344i	0.212782	−	0.122850i	0.602604	+	0.798041i	$0.294130\pi$
$314$	1.33352	−	2.30973i	0.0752550	−	0.130345i
$315$	9.22645	+	2.65240i	0.519851	+	0.149446i
$316$	−2.23131	−	3.86475i	−0.125521	−	0.217409i
$317$	−13.4867	+	7.78654i	−0.757488	+	0.437336i	−0.828393	−	0.560147i	$-0.810745\pi$
$317$	−13.4867	+	7.78654i	−0.757488	+	0.437336i	0.0709052	+	0.997483i	$0.477411\pi$
$318$	−2.88942	+	2.51593i	−0.162031	+	0.141086i
$319$	−1.98388			−0.111076
$320$	−0.604752	−	1.04746i	−0.0338066	−	0.0585548i
$321$	5.33712	−	15.5418i	0.297889	−	0.867460i
$322$	1.35513	−	9.48196i	0.0755186	−	0.528409i
$323$	−33.3810	−	19.2726i	−1.85737	−	1.07235i
$324$	−2.20614	−	8.72542i	−0.122563	−	0.484746i
$325$	12.7433	−	0.503620i	0.706869	−	0.0279358i
$326$	−15.5184	−	8.95954i	−0.859484	−	0.496223i
$327$	16.2825	−	14.1778i	0.900422	−	0.784032i
$328$	−0.158386	−	0.0914442i	−0.00874540	−	0.00504916i
$329$	17.4975	−	7.02210i	0.964671	−	0.387141i
$330$	1.89467	−	1.64976i	0.104298	−	0.0908162i
$331$	7.84608	−	13.5898i	0.431260	−	0.746964i	−0.565722	−	0.824596i	$-0.691403\pi$
$331$	7.84608	−	13.5898i	0.431260	−	0.746964i	0.996982	+	0.0776319i	$0.0247359\pi$
$332$	16.6675			0.914747
$333$	21.3133	+	16.5952i	1.16796	+	0.909409i
$334$	17.2259	+	9.94539i	0.942560	+	0.544187i
$335$	6.49788	−	11.2547i	0.355017	−	0.614908i
$336$	2.08658	−	4.07997i	0.113832	−	0.222581i
$337$	0.251195			0.0136835			0.00684174	−	0.999977i	$-0.497822\pi$
$337$	0.251195			0.0136835			0.00684174	+	0.999977i	$0.497822\pi$
$338$	11.7362	+	5.59124i	0.638364	+	0.304124i
$339$	−19.1116	+	3.73131i	−1.03800	+	0.202657i
$340$	−3.16799	−	5.48712i	−0.171808	−	0.297581i
$341$	−4.78650			−0.259203
$342$	−20.4531	+	8.30292i	−1.10598	+	0.448971i
$343$	−7.65091	+	16.8660i	−0.413110	+	0.910681i
$344$	−0.913245	+	0.527263i	−0.0492389	+	0.0284281i
$345$	−7.44362	+	1.45327i	−0.400751	+	0.0782417i
$346$	−15.1975	−	8.77428i	−0.817023	−	0.471708i
$347$		−	21.2631i		−	1.14146i	−0.821137	−	0.570731i	$-0.806660\pi$
$347$		−	21.2631i		−	1.14146i	0.821137	−	0.570731i	$-0.193340\pi$
$348$	1.88163	+	2.16096i	0.100866	+	0.115840i
$349$	3.33934	+	1.92797i	0.178751	+	0.103202i	0.586706	−	0.809800i	$-0.300425\pi$
$349$	3.33934	+	1.92797i	0.178751	+	0.103202i	−0.407955	+	0.913002i	$0.633758\pi$
$350$	−5.77870	+	7.36099i	−0.308885	+	0.393462i
$351$	−7.79748	+	17.0352i	−0.416199	+	0.909274i
$352$	−0.599608	−	1.03855i	−0.0319592	−	0.0553550i
$353$	4.35693	+	7.54643i	0.231896	+	0.401656i	0.958366	−	0.285542i	$-0.0921737\pi$
$353$	4.35693	+	7.54643i	0.231896	+	0.401656i	−0.726470	+	0.687198i	$0.758840\pi$
$354$	−6.33726	+	18.4542i	−0.336822	+	0.980832i
$355$	−7.36379	−	4.25148i	−0.390829	−	0.225645i
$356$	7.19208			0.381179
$357$	10.9305	−	21.3729i	0.578506	−	1.13117i
$358$	11.4992	+	19.9172i	0.607751	+	1.05266i
$359$	17.7662	−	10.2573i	0.937663	−	0.541360i	0.0484360	−	0.998826i	$-0.484576\pi$
$359$	17.7662	−	10.2573i	0.937663	−	0.541360i	0.889227	+	0.457466i	$0.151243\pi$
$360$	−3.59403	−	0.499054i	−0.189422	−	0.0263024i
$361$	17.5704	+	30.4329i	0.924760	+	1.60173i
$362$	7.49251			0.393798
$363$	−12.4903	+	10.8758i	−0.655569	+	0.570829i
$364$	−8.70586	+	3.89974i	−0.456311	+	0.204402i
$365$			7.55472i			0.395432i
$366$	−8.63596	+	7.51966i	−0.451409	+	0.393059i
$367$	−20.6758	+	11.9372i	−1.07927	+	0.623114i	−0.930698	−	0.365788i	$-0.880800\pi$
$367$	−20.6758	+	11.9372i	−1.07927	+	0.623114i	−0.148567	+	0.988902i	$0.547466\pi$
$368$			3.62026i			0.188719i
$369$	−0.508373	+	0.206374i	−0.0264648	+	0.0107434i
$370$	9.43139	−	5.44521i	0.490314	−	0.283083i
$371$	−3.61381	+	4.60333i	−0.187620	+	0.238993i
$372$	4.53980	+	5.21374i	0.235378	+	0.270320i
$373$	−1.53051	+	2.65092i	−0.0792467	+	0.137259i	−0.902925	−	0.429798i	$-0.858585\pi$
$373$	−1.53051	+	2.65092i	−0.0792467	+	0.137259i	0.823678	+	0.567057i	$0.191918\pi$
$374$	−3.14104	−	5.44045i	−0.162419	−	0.281319i
$375$	16.9150	+	5.80867i	0.873486	+	0.299958i
$376$	−6.17142	+	3.56307i	−0.318267	+	0.183751i
$377$	−0.235545	−	5.96007i	−0.0121312	−	0.306959i
$378$	−5.81190	−	12.4588i	−0.298932	−	0.640812i
$379$	8.74613	−	15.1487i	0.449259	−	0.778139i	−0.549079	−	0.835770i	$-0.685021\pi$
$379$	8.74613	−	15.1487i	0.449259	−	0.778139i	0.998338	+	0.0576314i	$0.0183548\pi$
$380$			8.89958i			0.456539i
$381$	−14.0959	+	12.2738i	−0.722155	+	0.628808i
$382$	−10.3019	+	17.8434i	−0.527091	+	0.912948i
$383$	−14.2376	+	24.6602i	−0.727506	+	1.26008i	0.230428	+	0.973089i	$0.425987\pi$
$383$	−14.2376	+	24.6602i	−0.727506	+	1.26008i	−0.957934	+	0.286988i	$0.907346\pi$
$384$	−0.562548	+	1.63815i	−0.0287074	+	0.0835966i
$385$	2.36967	−	3.01851i	0.120769	−	0.153838i
$386$	−6.92254	+	3.99673i	−0.352348	+	0.203428i
$387$	−0.435108	+	3.13351i	−0.0221178	+	0.159285i
$388$	11.8894	−	6.86436i	0.603594	−	0.348485i
$389$	31.0564	+	17.9304i	1.57462	+	0.909107i	0.995591	+	0.0938003i	$0.0299015\pi$
$389$	31.0564	+	17.9304i	1.57462	+	0.909107i	0.579029	+	0.815307i	$0.303432\pi$
$390$	5.18123	+	5.49617i	0.262362	+	0.278309i
$391$			18.9647i			0.959087i
$392$	1.96079	−	6.71977i	0.0990347	−	0.339400i
$393$	6.25568	+	32.0414i	0.315557	+	1.61627i
$394$	7.15573	−	12.3941i	0.360500	−	0.624405i
$395$	−2.69878	+	4.67442i	−0.135790	+	0.235196i
$396$	−3.56346	−	0.494809i	−0.179070	−	0.0248651i
$397$	−28.8039	−	16.6300i	−1.44563	−	0.834633i	−0.447411	−	0.894329i	$-0.647654\pi$
$397$	−28.8039	−	16.6300i	−1.44563	−	0.834633i	−0.998217	+	0.0596954i	$0.980987\pi$
$398$	3.28144			0.164484
$399$	−28.3066	+	18.3221i	−1.41710	+	0.917250i
$400$	1.76855	−	3.06322i	0.0884276	−	0.153161i
$401$		−	6.24114i		−	0.311668i	−0.987783	−	0.155834i	$-0.950194\pi$
$401$		−	6.24114i		−	0.311668i	0.987783	−	0.155834i	$-0.0498065\pi$
$402$	−18.2655	+	3.56612i	−0.911002	+	0.177862i
$403$	−0.568298	−	14.3798i	−0.0283090	−	0.716310i
$404$	−1.62511	−	2.81477i	−0.0808521	−	0.140040i
$405$	−7.80537	+	7.58756i	−0.387852	+	0.377029i
$406$	3.44277	+	2.70272i	0.170862	+	0.134134i
$407$	9.35117	−	5.39890i	0.463520	−	0.267614i
$408$	−2.94690	+	8.58145i	−0.145893	+	0.424845i
$409$			30.9890i			1.53231i	0.642657	+	0.766154i	$0.277832\pi$
$409$			30.9890i			1.53231i	−0.642657	+	0.766154i	$0.722168\pi$
$410$			0.221204i			0.0109245i
$411$	6.01196	−	17.5070i	0.296548	−	0.863555i
$412$	0.504870	−	0.291487i	0.0248732	−	0.0143605i
$413$	−4.21681	+	29.5053i	−0.207496	+	1.45186i
$414$	8.56945	+	6.67241i	0.421165	+	0.327931i
$415$	−10.0797	−	17.4585i	−0.494792	−	0.857006i
$416$	3.04887	−	1.92468i	0.149483	−	0.0943650i
$417$	4.63653	−	0.905226i	0.227052	−	0.0443291i
$418$			8.82389i			0.431590i
$419$	−12.6145	+	21.8489i	−0.616258	+	1.06739i	0.373904	+	0.927467i	$0.378019\pi$
$419$	−12.6145	+	21.8489i	−0.616258	+	1.06739i	−0.990162	+	0.139923i	$0.955314\pi$
$420$	−5.53547	+	0.281759i	−0.270103	+	0.0137484i
$421$	−8.22465			−0.400845			−0.200422	−	0.979710i	$-0.564231\pi$
$421$	−8.22465			−0.400845			−0.200422	+	0.979710i	$0.564231\pi$
$422$	−9.57673	−	5.52912i	−0.466188	−	0.269154i
$423$	−2.94032	+	21.1753i	−0.142963	+	1.02958i
$424$	1.10599	−	1.91564i	0.0537118	−	0.0930316i
$425$	9.26455	−	16.0467i	0.449396	−	0.778378i
$426$	2.33327	+	11.9509i	0.113047	+	0.579023i
$427$	−10.8010	+	13.7585i	−0.522698	+	0.665820i
$428$			9.48742i			0.458592i
$429$	5.13716	+	5.44942i	0.248025	+	0.263100i
$430$	1.10457	+	0.637726i	0.0532673	+	0.0307539i
$431$	17.2811	−	9.97727i	0.832403	−	0.480588i	−0.0222715	−	0.999752i	$-0.507090\pi$
$431$	17.2811	−	9.97727i	0.832403	−	0.480588i	0.854675	+	0.519164i	$0.173757\pi$
$432$	2.84082	+	4.35083i	0.136679	+	0.209330i
$433$	−19.2106	+	11.0912i	−0.923202	+	0.533011i	−0.884655	−	0.466246i	$-0.845606\pi$
$433$	−19.2106	+	11.0912i	−0.923202	+	0.533011i	−0.0385467	+	0.999257i	$0.512273\pi$
$434$	8.30634	+	6.52084i	0.398717	+	0.313010i
$435$	1.12560	−	3.27778i	0.0539685	−	0.157157i
$436$	−6.23249	+	10.7950i	−0.298482	+	0.516986i
$437$	13.3190	−	23.0692i	0.637135	−	1.10355i
$438$	8.15905	−	7.10439i	0.389854	−	0.339461i
$439$			27.3281i			1.30430i	0.758090	+	0.652150i	$0.226133\pi$
$439$			27.3281i			1.30430i	−0.758090	+	0.652150i	$0.773867\pi$
$440$	−0.725228	+	1.25613i	−0.0345739	+	0.0598837i
$441$	−12.2924	−	17.0264i	−0.585350	−	0.810780i
$442$	15.9715	−	10.0824i	0.759687	−	0.479571i
$443$	19.5551	−	11.2902i	0.929093	−	0.536412i	0.0425684	−	0.999094i	$-0.486446\pi$
$443$	19.5551	−	11.2902i	0.929093	−	0.536412i	0.886525	+	0.462681i	$0.153113\pi$
$444$	−14.7500	−	5.06521i	−0.700004	−	0.240384i
$445$	−4.34942	−	7.53342i	−0.206182	−	0.357118i
$446$	6.11409	−	10.5899i	0.289510	−	0.501447i
$447$	−1.72080	−	1.97625i	−0.0813910	−	0.0934736i
$448$	−0.374319	+	2.61914i	−0.0176849	+	0.123743i
$449$	−7.97653	+	4.60525i	−0.376436	+	0.217335i	−0.676266	−	0.736657i	$-0.736403\pi$
$449$	−7.97653	+	4.60525i	−0.376436	+	0.217335i	0.299831	+	0.953992i	$0.403070\pi$
$450$	−3.99131	−	9.83205i	−0.188152	−	0.463487i
$451$			0.219323i			0.0103275i
$452$	9.73622	−	5.62121i	0.457953	−	0.264399i
$453$	3.98486	−	3.46977i	0.187225	−	0.163024i
$454$		−	29.0111i		−	1.36156i
$455$	9.34971	+	6.76067i	0.438321	+	0.316945i
$456$	9.61150	−	8.36910i	0.450100	−	0.391919i
$457$	−6.64919			−0.311036			−0.155518	−	0.987833i	$-0.549705\pi$
$457$	−6.64919			−0.311036			−0.155518	+	0.987833i	$0.549705\pi$
$458$	−13.8607	−	24.0075i	−0.647669	−	1.12180i
$459$	14.8816	+	22.7918i	0.694614	+	1.06383i
$460$	3.79208	−	2.18936i	0.176807	−	0.102079i
$461$	−11.8184	−	20.4701i	−0.550439	−	0.953388i	−0.998243	−	0.0592563i	$-0.981127\pi$
$461$	−11.8184	−	20.4701i	−0.550439	−	0.953388i	0.447804	−	0.894132i	$-0.352206\pi$
$462$	−5.48839	+	0.279362i	−0.255343	+	0.0129971i
$463$	8.09426			0.376172			0.188086	−	0.982153i	$-0.439772\pi$
$463$	8.09426			0.376172			0.188086	+	0.982153i	$0.439772\pi$
$464$	−1.43268	−	0.827158i	−0.0665105	−	0.0383999i
$465$	2.71573	−	7.90828i	0.125939	−	0.366738i
$466$	1.76432	+	3.05589i	0.0817306	+	0.141561i
$467$	1.92869	+	3.34059i	0.0892492	+	0.154584i	0.907194	−	0.420713i	$-0.138220\pi$
$467$	1.92869	+	3.34059i	0.0892492	+	0.154584i	−0.817945	+	0.575297i	$0.804887\pi$
$468$	1.06344	−	10.7643i	0.0491576	−	0.497578i
$469$	−26.3826	+	10.5878i	−1.21823	+	0.488901i
$470$	7.46436	+	4.30955i	0.344305	+	0.198785i
$471$	3.03351	+	3.48384i	0.139777	+	0.160527i
$472$		−	11.2653i		−	0.518527i
$473$	1.09518	+	0.632301i	0.0503564	+	0.0290733i
$474$	7.58626	−	1.48112i	0.348448	−	0.0680303i
$475$	−22.5393	+	13.0131i	−1.03418	+	0.597081i
$476$	−1.96087	+	13.7203i	−0.0898763	+	0.628871i
$477$	−2.49604	−	6.14864i	−0.114286	−	0.281527i
$478$	−7.54413			−0.345060
$479$	4.11487	+	7.12716i	0.188013	+	0.325648i	0.944588	−	0.328259i	$-0.106462\pi$
$479$	4.11487	+	7.12716i	0.188013	+	0.325648i	−0.756575	+	0.653907i	$0.773129\pi$
$480$	2.05610	−	0.401428i	0.0938477	−	0.0183226i
$481$	17.3299	+	27.4522i	0.790175	+	1.25171i
$482$	−12.3343			−0.561813
$483$	14.7706	+	7.55397i	0.672084	+	0.343717i
$484$	4.78094	−	8.28083i	0.217315	−	0.376401i
$485$	−14.3803	−	8.30247i	−0.652976	−	0.376996i
$486$	15.5346	+	1.29447i	0.704665	+	0.0587184i
$487$	−23.0181			−1.04305			−0.521525	−	0.853236i	$-0.674637\pi$
$487$	−23.0181			−1.04305			−0.521525	+	0.853236i	$0.674637\pi$
$488$	3.30561	−	5.72549i	0.149638	−	0.259181i
$489$	23.4069	−	20.3813i	1.05850	−	0.921674i
$490$	−8.22448	+	2.00995i	−0.371544	+	0.0908001i
$491$	−25.3393	−	14.6297i	−1.14355	−	0.660228i	−0.196241	−	0.980556i	$-0.562873\pi$
$491$	−25.3393	−	14.6297i	−1.14355	−	0.660228i	−0.947307	+	0.320328i	$0.896207\pi$
$492$	0.238899	−	0.208018i	0.0107704	−	0.00937820i
$493$	−7.50509	−	4.33306i	−0.338012	−	0.195151i
$494$	−26.5091	+	1.04766i	−1.19270	+	0.0471362i
$495$	1.63671	+	4.03182i	0.0735648	+	0.181217i
$496$	−3.45662	−	1.99568i	−0.155207	−	0.0896086i
$497$	6.92749	+	17.2618i	0.310740	+	0.774297i
$498$	−9.37625	+	27.3039i	−0.420160	+	1.22352i
$499$	15.3836	+	26.6451i	0.688663	+	1.19280i	0.972270	+	0.233859i	$0.0751355\pi$
$499$	15.3836	+	26.6451i	0.688663	+	1.19280i	−0.283607	+	0.958941i	$0.591531\pi$
$500$	−10.3257			−0.461777
$501$	−25.9824	+	22.6239i	−1.16081	+	1.01076i
$502$	−8.79724	+	5.07909i	−0.392640	+	0.226691i
$503$	10.0612	+	17.4265i	0.448606	+	0.777008i	0.998296	−	0.0583607i	$-0.0185873\pi$
$503$	10.0612	+	17.4265i	0.448606	+	0.777008i	−0.549690	+	0.835369i	$0.685254\pi$
$504$	5.50981	+	5.71331i	0.245427	+	0.254491i
$505$	−1.96557	+	3.40447i	−0.0874668	+	0.151497i
$506$	3.75983	−	2.17074i	0.167145	−	0.0965010i
$507$	−15.7615	+	16.0803i	−0.699991	+	0.714151i
$508$	5.39553	−	9.34534i	0.239388	−	0.414632i
$509$	−10.6843			−0.473574			−0.236787	−	0.971562i	$-0.576094\pi$
$509$	−10.6843			−0.473574			−0.236787	+	0.971562i	$0.576094\pi$
$510$	10.7709	−	2.10288i	0.476942	−	0.0931171i
$511$	10.2045	−	12.9987i	0.451423	−	0.575029i
$512$		−	1.00000i		−	0.0441942i
$513$	−2.09560	−	38.1761i	−0.0925232	−	1.68551i
$514$			13.6772i			0.603277i
$515$	−0.610642	−	0.352554i	−0.0269081	−	0.0155354i
$516$	−0.349992	−	1.79264i	−0.0154075	−	0.0789168i
$517$	7.40087	+	4.27289i	0.325490	+	0.187922i
$518$	−23.5829	−	3.37039i	−1.03617	−	0.148086i
$519$	22.9229	−	19.9599i	1.00620	−	0.876141i
$520$	−3.85983	−	2.02962i	−0.169265	−	0.0890048i
$521$	−9.16008	+	15.8657i	−0.401310	+	0.695090i	−0.993884	−	0.110426i	$-0.964778\pi$
$521$	−9.16008	+	15.8657i	−0.401310	+	0.695090i	0.592574	+	0.805516i	$0.298112\pi$
$522$	−4.59849	+	1.86675i	−0.201270	+	0.0817056i
$523$			1.45926i			0.0638091i	0.999491	+	0.0319045i	$0.0101573\pi$
$523$			1.45926i			0.0638091i	−0.999491	+	0.0319045i	$0.989843\pi$
$524$	−9.42418	−	16.3232i	−0.411697	−	0.713081i
$525$	−8.80763	−	13.6073i	−0.384397	−	0.593871i
$526$	−10.7529	−	18.6245i	−0.468848	−	0.812069i
$527$	−18.1075	−	10.4544i	−0.788774	−	0.455399i
$528$	2.03861	−	0.398014i	0.0887192	−	0.0173213i
$529$	9.89372			0.430162
$530$	−2.67541			−0.116212
$531$	−26.6658	−	20.7628i	−1.15720	−	0.901028i
$532$	12.0211	−	15.3127i	0.521182	−	0.663890i
$533$	−0.658899	+	0.0260400i	−0.0285401	+	0.00112792i
$534$	−4.04589	+	11.7817i	−0.175083	+	0.509845i
$535$	9.93769	−	5.73753i	0.429644	−	0.248055i
$536$	9.30520	−	5.37236i	0.401923	−	0.232050i
$537$	−39.0962	+	7.63306i	−1.68713	+	0.329391i
$538$		−	28.1567i		−	1.21392i
$539$	−8.15453	+	1.99285i	−0.351240	+	0.0858381i
$540$	2.83934	−	5.60682i	0.122186	−	0.241279i
$541$	16.5670	+	28.6949i	0.712270	+	1.23369i	0.964003	+	0.265892i	$0.0856663\pi$
$541$	16.5670	+	28.6949i	0.712270	+	1.23369i	−0.251733	+	0.967797i	$0.581000\pi$
$542$	−3.01820			−0.129643
$543$	−4.21490	+	12.2739i	−0.180878	+	0.526722i
$544$		−	5.23850i		−	0.224599i
$545$	15.0764			0.645803
$546$	−1.49091	−	16.4553i	−0.0638049	−	0.704222i
$547$	29.1612			1.24684			0.623421	−	0.781886i	$-0.285742\pi$
$547$	29.1612			1.24684			0.623421	+	0.781886i	$0.285742\pi$
$548$			10.6870i			0.456527i
$549$	−7.46020	−	18.3772i	−0.318394	−	0.784319i
$550$	−4.24175			−0.180869
$551$	6.08627	+	10.5417i	0.259284	+	0.449093i
$552$	−5.93053	−	2.03657i	−0.252420	−	0.0866821i
$553$	10.9575	−	4.39747i	0.465961	−	0.186999i
$554$			11.3331i			0.481499i
$555$	3.61448	+	18.5132i	0.153426	+	0.785843i
$556$	−2.36204	+	1.36372i	−0.100173	+	0.0578347i
$557$	−6.20283	+	3.58121i	−0.262822	+	0.151741i	−0.625621	−	0.780127i	$-0.715155\pi$
$557$	−6.20283	+	3.58121i	−0.262822	+	0.151741i	0.362799	+	0.931867i	$0.381821\pi$
$558$	−11.0947	+	4.50390i	−0.469678	+	0.190665i
$559$	−1.76956	+	3.36526i	−0.0748444	+	0.142335i
$560$	2.96981	−	1.19184i	0.125498	−	0.0503646i
$561$	10.6793	−	2.08499i	0.450879	−	0.0880285i
$562$	−8.18525			−0.345274
$563$	39.3675			1.65914			0.829571	−	0.558401i	$-0.188585\pi$
$563$	39.3675			1.65914			0.829571	+	0.558401i	$0.188585\pi$
$564$	−2.36513	−	12.1141i	−0.0995901	−	0.510097i
$565$	−11.7760	−	6.79887i	−0.495420	−	0.286031i
$566$	−6.50177	−	11.2614i	−0.273290	−	0.473351i
$567$	23.6789	−	2.51210i	0.994420	−	0.105498i
$568$	−3.51507	−	6.08827i	−0.147489	−	0.255458i
$569$		−	32.9720i		−	1.38226i	−0.722731	−	0.691129i	$-0.757114\pi$
$569$		−	32.9720i		−	1.38226i	0.722731	−	0.691129i	$-0.242886\pi$
$570$	−14.5789	−	5.00644i	−0.610642	−	0.209697i
$571$	17.1019	−	29.6214i	0.715693	−	1.23962i	−0.246999	−	0.969016i	$-0.579444\pi$
$571$	17.1019	−	29.6214i	0.715693	−	1.23962i	0.962692	−	0.270600i	$-0.0872222\pi$
$572$	−3.82700	−	2.01236i	−0.160015	−	0.0841410i
$573$	−23.4349	−	26.9138i	−0.979007	−	1.12434i
$574$	0.298792	−	0.380605i	0.0124713	−	0.0158862i
$575$	11.0897	+	6.40261i	0.462470	+	0.267007i
$576$	−2.36708	−	1.84308i	−0.0986284	−	0.0767948i
$577$	30.4639	+	17.5883i	1.26823	+	0.732212i	0.974653	−	0.223723i	$-0.0718212\pi$
$577$	30.4639	+	17.5883i	1.26823	+	0.732212i	0.293576	+	0.955936i	$0.405155\pi$
$578$		−	10.4418i		−	0.434323i
$579$	−2.65299	−	13.5885i	−0.110255	−	0.564719i
$580$			2.00090i			0.0830829i
$581$	−6.23896	+	43.6544i	−0.258836	+	1.81109i
$582$	4.55650	+	23.3382i	0.188873	+	0.967400i
$583$	−2.65265			−0.109862
$584$	−3.12307	+	5.40931i	−0.129233	+	0.223839i
$585$	−11.9182	+	5.39579i	−0.492759	+	0.223088i
$586$	16.9340	−	9.77684i	0.699537	−	0.403878i
$587$	14.3923	−	24.9281i	0.594032	−	1.02889i	−0.399650	−	0.916668i	$-0.630868\pi$
$587$	14.3923	−	24.9281i	0.594032	−	1.02889i	0.993683	−	0.112226i	$-0.0357982\pi$
$588$	9.90497	+	6.99226i	0.408474	+	0.288356i
$589$	14.6843	+	25.4340i	0.605056	+	1.04799i
$590$	−11.7999	+	6.81270i	−0.485796	+	0.280474i
$591$	16.2780	+	18.6944i	0.669586	+	0.768986i
$592$	9.00405			0.370064
$593$	−12.0411	−	20.8558i	−0.494469	−	0.856445i	0.505511	−	0.862820i	$-0.331304\pi$
$593$	−12.0411	−	20.8558i	−0.494469	−	0.856445i	−0.999980	+	0.00637535i	$0.997971\pi$
$594$	2.81519	−	5.55913i	0.115508	−	0.228094i
$595$	15.5574	−	6.24347i	0.637789	−	0.255957i
$596$	1.31022	+	0.756457i	0.0536688	+	0.0309857i
$597$	−1.84597	+	5.37550i	−0.0755504	+	0.220005i
$598$	6.96783	+	11.0377i	0.284936	+	0.451365i
$599$	0.694359	+	0.400888i	0.0283707	+	0.0163798i	0.514118	−	0.857719i	$-0.328119\pi$
$599$	0.694359	+	0.400888i	0.0283707	+	0.0163798i	−0.485748	+	0.874099i	$0.661453\pi$
$600$	4.02312	+	4.62036i	0.164243	+	0.188625i
$601$	12.0618	+	6.96387i	0.492010	+	0.284062i	0.725408	−	0.688319i	$-0.241651\pi$
$601$	12.0618	+	6.96387i	0.492010	+	0.284062i	−0.233398	+	0.972381i	$0.574984\pi$
$602$	−1.03913	−	2.58928i	−0.0423517	−	0.105531i
$603$	4.43338	−	31.9278i	0.180541	−	1.30020i
$604$	−1.52530	+	2.64189i	−0.0620635	+	0.107497i
$605$	−11.5651			−0.470189
$606$	5.52522	−	1.07873i	0.224447	−	0.0438204i
$607$	−4.89134	−	2.82402i	−0.198533	−	0.114623i	0.397438	−	0.917629i	$-0.369899\pi$
$607$	−4.89134	−	2.82402i	−0.198533	−	0.114623i	−0.595971	+	0.803006i	$0.703233\pi$
$608$	−3.67902	+	6.37226i	−0.149204	+	0.258429i
$609$	−6.36419	+	4.11936i	−0.257890	+	0.166925i
$610$	−7.99630			−0.323761
$611$	−11.9581	+	22.7413i	−0.483774	+	0.920016i
$612$	−12.3999	−	9.65495i	−0.501238	−	0.390278i
$613$	−7.92336	−	13.7237i	−0.320022	−	0.554294i	0.660471	−	0.750852i	$-0.270357\pi$
$613$	−7.92336	−	13.7237i	−0.320022	−	0.554294i	−0.980492	+	0.196558i	$0.937023\pi$
$614$	−27.7274			−1.11899
$615$	−0.362366	−	0.124438i	−0.0146120	−	0.00501782i
$616$	2.94455	−	1.18171i	0.118639	−	0.0476123i
$617$	−8.95185	+	5.16835i	−0.360388	+	0.208070i	−0.669251	−	0.743036i	$-0.733385\pi$
$617$	−8.95185	+	5.16835i	−0.360388	+	0.208070i	0.308863	+	0.951107i	$0.400052\pi$
$618$	0.193486	+	0.991029i	0.00778316	+	0.0398650i
$619$	−5.47367	−	3.16022i	−0.220005	−	0.127020i	0.385947	−	0.922521i	$-0.373875\pi$
$619$	−5.47367	−	3.16022i	−0.220005	−	0.127020i	−0.605953	+	0.795501i	$0.707208\pi$
$620$			4.82756i			0.193880i
$621$	−15.7511	+	10.2845i	−0.632072	+	0.412703i
$622$	−6.62722	−	3.82623i	−0.265727	−	0.153418i
$623$	−2.69213	+	18.8371i	−0.107858	+	0.754691i
$624$	1.43778	+	6.07724i	0.0575571	+	0.243284i
$625$	−2.59830	−	4.50039i	−0.103932	−	0.180016i
$626$	−2.17344	−	3.76450i	−0.0868680	−	0.150460i
$627$	−14.4549	−	4.96386i	−0.577272	−	0.198237i
$628$	−2.30973	−	1.33352i	−0.0921681	−	0.0532133i
$629$	47.1677			1.88070
$630$	2.65240	−	9.22645i	0.105674	−	0.367590i
$631$	3.51416	+	6.08670i	0.139897	+	0.242308i	0.927457	−	0.373929i	$-0.121990\pi$
$631$	3.51416	+	6.08670i	0.139897	+	0.242308i	−0.787561	+	0.616237i	$0.788656\pi$
$632$	−3.86475	+	2.23131i	−0.153731	+	0.0887568i
$633$	14.4449	−	12.5777i	0.574134	−	0.499920i
$634$	7.78654	+	13.4867i	0.309243	+	0.535625i
$635$	−13.0518			−0.517946
$636$	2.51593	+	2.88942i	0.0997631	+	0.114573i
$637$	−6.95519	−	24.2616i	−0.275575	−	0.961280i
$638$			1.98388i			0.0785427i
$639$	−20.8900	−	2.90071i	−0.826394	−	0.114750i
$640$	−1.04746	+	0.604752i	−0.0414045	+	0.0239049i
$641$		−	47.4186i		−	1.87292i	−0.350772	−	0.936461i	$-0.614081\pi$
$641$		−	47.4186i		−	1.87292i	0.350772	−	0.936461i	$-0.385919\pi$
$642$	−15.5418	−	5.33712i	−0.613387	−	0.210639i
$643$	−16.3622	+	9.44671i	−0.645261	+	0.372542i	−0.786638	−	0.617414i	$-0.788180\pi$
$643$	−16.3622	+	9.44671i	−0.645261	+	0.372542i	0.141377	+	0.989956i	$0.454847\pi$
$644$	−9.48196	−	1.35513i	−0.373642	−	0.0533997i
$645$	−1.66607	+	1.45071i	−0.0656013	+	0.0571215i
$646$	−19.2726	+	33.3810i	−0.758268	+	1.31336i
$647$	10.7234	+	18.5736i	0.421582	+	0.730202i	0.996094	−	0.0882941i	$-0.0281415\pi$
$647$	10.7234	+	18.5736i	0.421582	+	0.730202i	−0.574512	+	0.818496i	$0.694808\pi$
$648$	−8.72542	+	2.20614i	−0.342767	+	0.0866654i
$649$	−11.6996	+	6.75475i	−0.459249	+	0.265147i
$650$	−0.503620	−	12.7433i	−0.0197536	−	0.499832i
$651$	−15.3548	+	9.93876i	−0.601803	+	0.389531i
$652$	−8.95954	+	15.5184i	−0.350883	+	0.607747i
$653$			1.56420i			0.0612119i	0.999532	+	0.0306060i	$0.00974370\pi$
$653$			1.56420i			0.0612119i	−0.999532	+	0.0306060i	$0.990256\pi$
$654$	−14.1778	−	16.2825i	−0.554394	−	0.636694i
$655$	−11.3986	+	19.7429i	−0.445379	+	0.771419i
$656$	−0.0914442	+	0.158386i	−0.00357030	+	0.00618393i
$657$	7.04822	+	17.3623i	0.274977	+	0.677368i
$658$	−7.02210	−	17.4975i	−0.273750	−	0.682125i
$659$	5.73747	−	3.31253i	0.223500	−	0.129038i	−0.384070	−	0.923304i	$-0.625478\pi$
$659$	5.73747	−	3.31253i	0.223500	−	0.129038i	0.607570	+	0.794266i	$0.292144\pi$
$660$	−1.64976	−	1.89467i	−0.0642167	−	0.0737498i
$661$	−20.5608	+	11.8708i	−0.799721	+	0.461719i	−0.843374	−	0.537327i	$-0.819434\pi$
$661$	−20.5608	+	11.8708i	−0.799721	+	0.461719i	0.0436524	+	0.999047i	$0.486101\pi$
$662$	−13.5898	−	7.84608i	−0.528183	−	0.304947i
$663$	7.53178	+	31.8356i	0.292510	+	1.23639i
$664$		−	16.6675i		−	0.646824i
$665$	−23.3092	−	3.33128i	−0.903894	−	0.129182i
$666$	16.5952	−	21.3133i	0.643049	−	0.825874i
$667$	2.99453	−	5.18667i	0.115949	−	0.200829i
$668$	9.94539	−	17.2259i	0.384799	−	0.666491i
$669$	13.9084	+	15.9731i	0.537730	+	0.617557i
$670$	−11.2547	−	6.49788i	−0.434806	−	0.251035i
$671$	−7.92829			−0.306068
$672$	−4.07997	−	2.08658i	−0.157388	−	0.0804916i
$673$	9.99916	−	17.3191i	0.385439	−	0.667601i	−0.606391	−	0.795167i	$-0.707383\pi$
$673$	9.99916	−	17.3191i	0.385439	−	0.667601i	0.991830	+	0.127566i	$0.0407166\pi$
$674$		−	0.251195i		−	0.00967568i
$675$	18.3517	−	1.00738i	0.706357	−	0.0387741i
$676$	5.59124	−	11.7362i	0.215048	−	0.451392i
$677$	−8.62455	−	14.9382i	−0.331469	−	0.574120i	0.651332	−	0.758793i	$-0.274211\pi$
$677$	−8.62455	−	14.9382i	−0.331469	−	0.574120i	−0.982800	+	0.184673i	$0.940877\pi$
$678$	3.73131	+	19.1116i	0.143300	+	0.733977i
$679$	13.5283	+	33.7095i	0.519168	+	1.29365i
$680$	−5.48712	+	3.16799i	−0.210421	+	0.121487i
$681$	47.5245	+	16.3201i	1.82114	+	0.625388i
$682$			4.78650i			0.183285i
$683$			9.86796i			0.377587i	0.982017	+	0.188794i	$0.0604577\pi$
$683$			9.86796i			0.377587i	−0.982017	+	0.188794i	$0.939542\pi$
$684$	8.30292	+	20.4531i	0.317470	+	0.782044i
$685$	11.1942	−	6.46300i	0.427710	−	0.246938i
$686$	16.8660	+	7.65091i	0.643949	+	0.292113i
$687$	47.1252	−	9.20062i	1.79794	−	0.351026i
$688$	0.527263	+	0.913245i	0.0201017	+	0.0348172i
$689$	−0.314948	−	7.96922i	−0.0119986	−	0.303603i
$690$	1.45327	+	7.44362i	0.0553252	+	0.283374i
$691$			47.7591i			1.81684i	0.418058	+	0.908420i	$0.362711\pi$
$691$			47.7591i			1.81684i	−0.418058	+	0.908420i	$0.637289\pi$
$692$	−8.77428	+	15.1975i	−0.333548	+	0.577722i
$693$	2.62984	−	9.14797i	0.0998995	−	0.347503i
$694$	−21.2631			−0.807136
$695$	2.85689	+	1.64943i	0.108368	+	0.0625663i
$696$	2.16096	−	1.88163i	0.0819110	−	0.0713231i
$697$	−0.479030	+	0.829704i	−0.0181445	+	0.0314273i
$698$	1.92797	−	3.33934i	0.0729747	−	0.126396i
$699$	−5.99853	+	1.17114i	−0.226885	+	0.0442966i
$700$	7.36099	+	5.77870i	0.278219	+	0.218414i
$701$			27.3612i			1.03342i	0.856161	+	0.516709i	$0.172843\pi$
$701$			27.3612i			1.03342i	−0.856161	+	0.516709i	$0.827157\pi$
$702$	17.0352	+	7.79748i	0.642954	+	0.294297i
$703$	−57.3761	−	33.1261i	−2.16398	−	1.24938i
$704$	−1.03855	+	0.599608i	−0.0391419	+	0.0225986i
$705$	−11.2587	+	9.80342i	−0.424029	+	0.369218i
$706$	7.54643	−	4.35693i	0.284014	−	0.163975i
$707$	7.98058	−	3.20276i	0.300140	−	0.120452i
$708$	18.4542	+	6.33726i	0.693553	+	0.238169i
$709$	−5.83287	+	10.1028i	−0.219058	+	0.379419i	−0.954520	−	0.298146i	$-0.903632\pi$
$709$	−5.83287	+	10.1028i	−0.219058	+	0.379419i	0.735462	+	0.677566i	$0.236965\pi$
$710$	−4.25148	+	7.36379i	−0.159555	+	0.276358i
$711$	−1.84133	+	13.2606i	−0.0690551	+	0.497313i
$712$		−	7.19208i		−	0.269535i
$713$	7.22488	−	12.5139i	0.270574	−	0.468647i
$714$	−21.3729	−	10.9305i	−0.799861	−	0.409065i
$715$	0.206519	+	5.22561i	0.00772337	+	0.195427i
$716$	19.9172	−	11.4992i	0.744340	−	0.429745i
$717$	4.24393	−	12.3584i	0.158492	−	0.461534i
$718$	−10.2573	−	17.7662i	−0.382799	−	0.663028i
$719$	6.78169	−	11.7462i	0.252914	−	0.438061i	−0.711413	−	0.702775i	$-0.751944\pi$
$719$	6.78169	−	11.7462i	0.252914	−	0.438061i	0.964327	+	0.264714i	$0.0852776\pi$
$720$	−0.499054	+	3.59403i	−0.0185986	+	0.133941i
$721$	0.574462	+	1.43143i	0.0213941	+	0.0533094i
$722$	30.4329	−	17.5704i	1.13260	−	0.653904i
$723$	6.93865	−	20.2055i	0.258051	−	0.751451i
$724$		−	7.49251i		−	0.278457i
$725$	−5.06754	+	2.92574i	−0.188204	+	0.108659i
$726$	10.8758	+	12.4903i	0.403637	+	0.463557i
$727$		−	22.4921i		−	0.834186i	−0.908864	−	0.417093i	$-0.863049\pi$
$727$		−	22.4921i		−	0.834186i	0.908864	−	0.417093i	$-0.136951\pi$
$728$	3.89974	+	8.70586i	0.144534	+	0.322661i
$729$	−10.8595	+	24.7199i	−0.402204	+	0.915550i
$730$	7.55472			0.279613
$731$	2.76206	+	4.78403i	0.102159	+	0.176944i
$732$	7.51966	+	8.63596i	0.277935	+	0.319194i
$733$	−5.25647	+	3.03483i	−0.194152	+	0.112094i	−0.593925	−	0.804520i	$-0.702422\pi$
$733$	−5.25647	+	3.03483i	−0.194152	+	0.112094i	0.399773	+	0.916614i	$0.369089\pi$
$734$	11.9372	+	20.6758i	0.440608	+	0.763156i
$735$	1.33407	−	14.6036i	0.0492078	−	0.538663i
$736$	3.62026			0.133445
$737$	−11.1589	−	6.44261i	−0.411045	−	0.237317i
$738$	0.206374	+	0.508373i	0.00759672	+	0.0187135i
$739$	20.7997	+	36.0261i	0.765129	+	1.32524i	0.940178	+	0.340683i	$0.110658\pi$
$739$	20.7997	+	36.0261i	0.765129	+	1.32524i	−0.175049	+	0.984560i	$0.556008\pi$
$740$	−5.44521	−	9.43139i	−0.200170	−	0.346705i
$741$	13.1964	−	44.0153i	0.484783	−	1.61694i
$742$	4.60333	+	3.61381i	0.168993	+	0.132667i
$743$	47.1331	+	27.2123i	1.72914	+	0.998322i	0.893523	+	0.449017i	$0.148226\pi$
$743$	47.1331	+	27.2123i	1.72914	+	0.998322i	0.835622	+	0.549305i	$0.185107\pi$
$744$	5.21374	−	4.53980i	0.191145	−	0.166437i
$745$		−	1.82987i		−	0.0670414i
$746$	2.65092	+	1.53051i	0.0970570	+	0.0560359i
$747$	−39.4533	−	30.7194i	−1.44352	−	1.12397i
$748$	−5.44045	+	3.14104i	−0.198922	+	0.114848i
$749$	−24.8489	−	3.55132i	−0.907957	−	0.129762i
$750$	5.80867	−	16.9150i	0.212103	−	0.617648i
$751$	−5.85081			−0.213499			−0.106749	−	0.994286i	$-0.534044\pi$
$751$	−5.85081			−0.213499			−0.106749	+	0.994286i	$0.534044\pi$
$752$	3.56307	+	6.17142i	0.129932	+	0.225049i
$753$	−3.37145	−	17.2684i	−0.122863	−	0.629297i
$754$	−5.96007	+	0.235545i	−0.217053	+	0.00857805i
$755$	3.68970			0.134282
$756$	−12.4588	+	5.81190i	−0.453122	+	0.211377i
$757$	1.38330	−	2.39594i	0.0502768	−	0.0870820i	−0.839792	−	0.542909i	$-0.817323\pi$
$757$	1.38330	−	2.39594i	0.0502768	−	0.0870820i	0.890069	+	0.455827i	$0.150656\pi$
$758$	−15.1487	−	8.74613i	−0.550227	−	0.317674i
$759$	1.44091	+	7.38031i	0.0523019	+	0.267888i
$760$	8.89958			0.322822
$761$	−25.3626	+	43.9293i	−0.919393	+	1.59243i	−0.119053	+	0.992888i	$0.537986\pi$
$761$	−25.3626	+	43.9293i	−0.919393	+	1.59243i	−0.800339	+	0.599547i	$0.795347\pi$
$762$	12.2738	+	14.0959i	0.444634	+	0.510641i
$763$	−25.9406	−	20.3645i	−0.939114	−	0.737245i
$764$	17.8434	+	10.3019i	0.645552	+	0.372710i
$765$	−2.61429	+	18.8273i	−0.0945199	+	0.680702i
$766$	24.6602	+	14.2376i	0.891009	+	0.514425i
$767$	−21.6820	−	34.3464i	−0.782893	−	1.24018i
$768$	1.63815	+	0.562548i	0.0591117	+	0.0202992i
$769$	6.29042	+	3.63178i	0.226838	+	0.130965i	0.609113	−	0.793084i	$-0.291526\pi$
$769$	6.29042	+	3.63178i	0.226838	+	0.130965i	−0.382274	+	0.924049i	$0.624859\pi$
$770$	−3.01851	−	2.36967i	−0.108780	−	0.0853968i
$771$	−22.4054	−	7.69409i	−0.806910	−	0.277096i
$772$	3.99673	+	6.92254i	0.143845	+	0.249148i
$773$	−40.0086			−1.43901			−0.719504	−	0.694488i	$-0.755631\pi$
$773$	−40.0086			−1.43901			−0.719504	+	0.694488i	$0.755631\pi$
$774$	3.13351	+	0.435108i	0.112632	+	0.0156396i
$775$	−12.2264	+	7.05892i	−0.439186	+	0.253564i
$776$	−6.86436	−	11.8894i	−0.246416	−	0.426806i
$777$	18.7877	−	36.7363i	0.674004	−	1.31791i
$778$	17.9304	−	31.0564i	0.642836	−	1.11342i
$779$	1.16541	−	0.672851i	0.0417552	−	0.0241074i
$780$	5.49617	−	5.18123i	0.196794	−	0.185518i
$781$	−4.21532	+	7.30115i	−0.150836	+	0.261256i
$782$	18.9647			0.678177
$783$	−0.471157	−	8.58316i	−0.0168378	−	0.306737i
$784$	−6.71977	−	1.96079i	−0.239992	−	0.0700281i
$785$			3.22580i			0.115134i
$786$	32.0414	−	6.25568i	1.14288	−	0.223133i
$787$			4.27842i			0.152509i	0.997088	+	0.0762545i	$0.0242962\pi$
$787$			4.27842i			0.152509i	−0.997088	+	0.0762545i	$0.975704\pi$
$788$	−12.3941	−	7.15573i	−0.441521	−	0.254912i
$789$	36.5588	−	7.13767i	1.30153	−	0.254108i
$790$	4.67442	+	2.69878i	0.166308	+	0.0960182i
$791$	11.0783	+	27.6046i	0.393898	+	0.981508i
$792$	−0.494809	+	3.56346i	−0.0175823	+	0.126622i
$793$	−0.941321	−	23.8185i	−0.0334273	−	0.845821i
$794$	−16.6300	+	28.8039i	−0.590175	+	1.02221i
$795$	1.50504	−	4.38272i	0.0533784	−	0.155439i
$796$		−	3.28144i		−	0.116308i
$797$	−20.0925	−	34.8013i	−0.711714	−	1.23273i	−0.964213	−	0.265128i	$-0.914586\pi$
$797$	−20.0925	−	34.8013i	−0.711714	−	1.23273i	0.252499	−	0.967597i	$-0.418748\pi$
$798$	18.3221	+	28.3066i	0.648594	+	1.00204i
$799$	18.6651	+	32.3290i	0.660325	+	1.14372i
$800$	−3.06322	−	1.76855i	−0.108301	−	0.0625277i
$801$	−17.0242	−	13.2556i	−0.601522	−	0.468362i
$802$	−6.24114			−0.220382
$803$	7.49046			0.264333
$804$	3.56612	+	18.2655i	0.125767	+	0.644175i
$805$	4.31478	+	10.7515i	0.152076	+	0.378940i
$806$	−14.3798	+	0.568298i	−0.506508	+	0.0200175i
$807$	46.1250	+	15.8395i	1.62368	+	0.557577i
$808$	−2.81477	+	1.62511i	−0.0990232	+	0.0571711i
$809$	−8.44667	+	4.87669i	−0.296969	+	0.171455i	−0.641080	−	0.767474i	$-0.721514\pi$
$809$	−8.44667	+	4.87669i	−0.296969	+	0.171455i	0.344111	+	0.938929i	$0.388180\pi$
$810$	7.58756	+	7.80537i	0.266600	+	0.274253i
$811$		−	31.7759i		−	1.11580i	−0.829907	−	0.557902i	$-0.811607\pi$
$811$		−	31.7759i		−	1.11580i	0.829907	−	0.557902i	$-0.188393\pi$
$812$	2.70272	−	3.44277i	0.0948469	−	0.120817i
$813$	1.69788	−	4.94426i	0.0595472	−	0.173403i
$814$	−5.39890	−	9.35117i	−0.189231	−	0.327758i
$815$	21.6732			0.759179
$816$	8.58145	+	2.94690i	0.300411	+	0.103162i
$817$		−	7.75925i		−	0.271462i
$818$	30.9890			1.08350
$819$	27.7950	+	6.81456i	0.971236	+	0.238120i
$820$	0.221204			0.00772478
$821$			21.6303i			0.754901i	0.926030	+	0.377451i	$0.123199\pi$
$821$			21.6303i			0.754901i	−0.926030	+	0.377451i	$0.876801\pi$
$822$	−17.5070	−	6.01196i	−0.610626	−	0.209691i
$823$	48.7594			1.69964			0.849822	−	0.527069i	$-0.176709\pi$
$823$	48.7594			1.69964			0.849822	+	0.527069i	$0.176709\pi$
$824$	−0.291487	−	0.504870i	−0.0101544	−	0.0175880i
$825$	2.38619	−	6.94863i	0.0830763	−	0.241920i
$826$	29.5053	+	4.21681i	1.02662	+	0.146722i
$827$		−	12.1112i		−	0.421149i	−0.977578	−	0.210575i	$-0.932467\pi$
$827$		−	12.1112i		−	0.421149i	0.977578	−	0.210575i	$-0.0675335\pi$
$828$	6.67241	−	8.56945i	0.231882	−	0.297809i
$829$	20.3522	−	11.7504i	0.706862	−	0.408107i	−0.103036	−	0.994678i	$-0.532856\pi$
$829$	20.3522	−	11.7504i	0.706862	−	0.408107i	0.809898	+	0.586571i	$0.199522\pi$
$830$	−17.4585	+	10.0797i	−0.605994	+	0.349871i
$831$	−18.5654	−	6.37542i	−0.644026	−	0.221161i
$832$	−1.92468	−	3.04887i	−0.0667261	−	0.105701i
$833$	−35.2015	−	10.2716i	−1.21966	−	0.355889i
$834$	−0.905226	−	4.63653i	−0.0313454	−	0.160550i
$835$	−24.0580			−0.832560
$836$	8.82389			0.305181
$837$	−1.13676	−	20.7085i	−0.0392920	−	0.715792i
$838$	21.8489	+	12.6145i	0.754759	+	0.435760i
$839$	8.86105	+	15.3478i	0.305917	+	0.529864i	0.977465	−	0.211097i	$-0.0677036\pi$
$839$	8.86105	+	15.3478i	0.305917	+	0.529864i	−0.671548	+	0.740961i	$0.734370\pi$
$840$	0.281759	+	5.53547i	0.00972160	+	0.190992i
$841$	−13.1316	−	22.7446i	−0.452814	−	0.784298i
$842$			8.22465i			0.283440i
$843$	4.60459	−	13.4087i	0.158591	−	0.461819i
$844$	−5.52912	+	9.57673i	−0.190320	+	0.329644i
$845$	−15.6745	+	1.24087i	−0.539219	+	0.0426871i
$846$	21.1753	+	2.94032i	0.728021	+	0.101090i
$847$	19.8990	+	15.6216i	0.683739	+	0.536765i
$848$	−1.91564	−	1.10599i	−0.0657833	−	0.0379800i
$849$	22.1054	−	4.31581i	0.758656	−	0.148118i
$850$	−16.0467	−	9.26455i	−0.550396	−	0.317771i
$851$			32.5970i			1.11741i
$852$	11.9509	−	2.33327i	0.409431	−	0.0799364i
$853$			31.2313i			1.06934i	0.845061	+	0.534669i	$0.179564\pi$
$853$			31.2313i			1.06934i	−0.845061	+	0.534669i	$0.820436\pi$
$854$	13.7585	+	10.8010i	0.470806	+	0.369603i
$855$	16.4026	−	21.0660i	0.560957	−	0.720443i
$856$	9.48742			0.324273
$857$	8.47281	−	14.6753i	0.289426	−	0.501300i	−0.684247	−	0.729250i	$-0.739869\pi$
$857$	8.47281	−	14.6753i	0.289426	−	0.501300i	0.973673	+	0.227950i	$0.0732024\pi$
$858$	5.44942	−	5.13716i	0.186040	−	0.175380i
$859$	18.2086	−	10.5127i	0.621269	−	0.358690i	−0.156094	−	0.987742i	$-0.549890\pi$
$859$	18.2086	−	10.5127i	0.621269	−	0.358690i	0.777363	+	0.629052i	$0.216557\pi$
$860$	0.637726	−	1.10457i	0.0217463	−	0.0376656i
$861$	0.455405	+	0.703575i	0.0155202	+	0.0239778i
$862$	−9.97727	−	17.2811i	−0.339827	−	0.588598i
$863$	−17.7086	+	10.2241i	−0.602809	+	0.348032i	−0.770146	−	0.637868i	$-0.779817\pi$
$863$	−17.7086	+	10.2241i	−0.602809	+	0.348032i	0.167337	+	0.985900i	$0.446483\pi$
$864$	4.35083	−	2.84082i	0.148018	−	0.0966466i
$865$	21.2250			0.721673
$866$	11.0912	+	19.2106i	0.376896	+	0.652802i
$867$	17.1053	+	5.87403i	0.580927	+	0.199492i
$868$	6.52084	−	8.30634i	0.221332	−	0.281936i
$869$	4.63466	+	2.67582i	0.157220	+	0.0907711i
$870$	−3.27778	−	1.12560i	−0.111127	−	0.0381615i
$871$	18.0303	−	34.2891i	0.610934	−	1.16184i
$872$	10.7950	+	6.23249i	0.365564	+	0.211059i
$873$	−40.7948	−	5.66462i	−1.38069	−	0.191718i
$874$	−23.0692	−	13.3190i	−0.780328	−	0.450523i
$875$	3.86509	−	27.0443i	0.130664	−	0.914265i
$876$	−7.10439	−	8.15905i	−0.240035	−	0.275669i
$877$	20.6041	−	35.6874i	0.695752	−	1.20508i	−0.274174	−	0.961680i	$-0.588405\pi$
$877$	20.6041	−	35.6874i	0.695752	−	1.20508i	0.969926	−	0.243398i	$-0.0782621\pi$
$878$	27.3281			0.922279
$879$	6.48978	+	33.2404i	0.218895	+	1.12117i
$880$	1.25613	+	0.725228i	0.0423442	+	0.0244474i
$881$	9.30917	−	16.1240i	0.313634	−	0.543230i	−0.665512	−	0.746387i	$-0.731787\pi$
$881$	9.30917	−	16.1240i	0.313634	−	0.543230i	0.979146	+	0.203157i	$0.0651202\pi$
$882$	−17.0264	+	12.2924i	−0.573308	+	0.413905i
$883$	28.5626			0.961209			0.480604	−	0.876938i	$-0.340417\pi$
$883$	28.5626			0.961209			0.480604	+	0.876938i	$0.340417\pi$
$884$	−10.0824	−	15.9715i	−0.339108	−	0.537180i
$885$	−4.52221	−	23.1626i	−0.152012	−	0.778601i
$886$	−11.2902	−	19.5551i	−0.379301	−	0.656968i
$887$	44.4177			1.49140			0.745701	−	0.666281i	$-0.232115\pi$
$887$	44.4177			1.49140			0.745701	+	0.666281i	$0.232115\pi$
$888$	−5.06521	+	14.7500i	−0.169977	+	0.494978i
$889$	22.4571	+	17.6298i	0.753186	+	0.591284i
$890$	−7.53342	+	4.34942i	−0.252521	+	0.145793i
$891$	7.52302	+	7.73898i	0.252031	+	0.259265i
$892$	−10.5899	−	6.11409i	−0.354576	−	0.204715i
$893$		−	52.4345i		−	1.75466i
$894$	−1.97625	+	1.72080i	−0.0660958	+	0.0575521i
$895$	−24.0899	−	13.9083i	−0.805237	−	0.464904i
$896$	2.61914	+	0.374319i	0.0874993	+	0.0125051i
$897$	−22.0012	+	5.20512i	−0.734598	+	0.173794i
$898$	4.60525	+	7.97653i	0.153679	+	0.266180i
$899$	3.30149	+	5.71834i	0.110111	+	0.190717i
$900$	−9.83205	+	3.99131i	−0.327735	+	0.133044i
$901$	−10.0351	−	5.79374i	−0.334316	−	0.193018i
$902$	0.219323			0.00730264
$903$	4.82619	−	0.245656i	0.160606	−	0.00817492i
$904$	−5.62121	−	9.73622i	−0.186959	−	0.323822i
$905$	−7.84811	+	4.53111i	−0.260880	+	0.150619i
$906$	−3.46977	−	3.98486i	−0.115275	−	0.132388i
$907$	−7.99385	−	13.8457i	−0.265431	−	0.459741i	0.702245	−	0.711935i	$-0.252181\pi$
$907$	−7.99385	−	13.8457i	−0.265431	−	0.459741i	−0.967677	+	0.252195i	$0.918848\pi$
$908$	−29.0111			−0.962766
$909$	−1.34107	+	9.65798i	−0.0444806	+	0.320335i
$910$	6.76067	−	9.34971i	0.224114	−	0.309940i
$911$			23.0432i			0.763457i	0.924275	+	0.381728i	$0.124671\pi$
$911$			23.0432i			0.763457i	−0.924275	+	0.381728i	$0.875329\pi$
$912$	−8.36910	−	9.61150i	−0.277128	−	0.318268i
$913$	−17.3100	+	9.99395i	−0.572879	+	0.330752i
$914$			6.64919i			0.219936i
$915$	4.49830	−	13.0992i	0.148709	−	0.433045i
$916$	−24.0075	+	13.8607i	−0.793230	+	0.457971i
$917$	46.2803	−	18.5732i	1.52831	−	0.613340i
$918$	22.7918	−	14.8816i	0.752242	−	0.491166i
$919$	−7.60114	+	13.1656i	−0.250738	+	0.434291i	−0.963729	−	0.266882i	$-0.914007\pi$
$919$	−7.60114	+	13.1656i	−0.250738	+	0.434291i	0.712991	+	0.701173i	$0.247340\pi$
$920$	−2.18936	−	3.79208i	−0.0721810	−	0.125021i
$921$	15.5980	−	45.4216i	0.513970	−	1.49669i
$922$	−20.4701	+	11.8184i	−0.674147	+	0.389219i
$923$	−22.4349	−	11.7970i	−0.738455	−	0.388303i
$924$	0.279362	+	5.48839i	0.00919034	+	0.180555i
$925$	15.9241	−	27.5814i	0.523582	−	0.906871i
$926$		−	8.09426i		−	0.265994i
$927$	−1.73230	−	0.240541i	−0.0568962	−	0.00790040i
$928$	−0.827158	+	1.43268i	−0.0271528	+	0.0470300i
$929$	−7.29018	+	12.6270i	−0.239183	+	0.414277i	−0.960480	−	0.278349i	$-0.910213\pi$
$929$	−7.29018	+	12.6270i	−0.239183	+	0.414277i	0.721297	+	0.692626i	$0.243546\pi$
$930$	−7.90828	−	2.71573i	−0.259323	−	0.0890524i
$931$	35.6063	+	37.2168i	1.16695	+	1.21973i
$932$	3.05589	−	1.76432i	0.100099	−	0.0577922i
$933$	9.99606	−	8.70395i	0.327256	−	0.284955i
$934$	3.34059	−	1.92869i	0.109307	−	0.0631087i
$935$	6.58024	+	3.79910i	0.215197	+	0.124244i
$936$	−10.7643	−	1.06344i	−0.351841	−	0.0347596i
$937$			32.9784i			1.07736i	0.842511	+	0.538678i	$0.181076\pi$
$937$			32.9784i			1.07736i	−0.842511	+	0.538678i	$0.818924\pi$
$938$	10.5878	+	26.3826i	0.345705	+	0.861421i
$939$	7.38949	−	1.44271i	0.241147	−	0.0470810i
$940$	4.30955	−	7.46436i	0.140562	−	0.243460i
$941$	−6.25946	+	10.8417i	−0.204053	+	0.353430i	−0.949830	−	0.312765i	$-0.898745\pi$
$941$	−6.25946	+	10.8417i	−0.204053	+	0.353430i	0.745778	+	0.666195i	$0.232078\pi$
$942$	3.48384	−	3.03351i	0.113510	−	0.0988372i
$943$	−0.573398	−	0.331052i	−0.0186724	−	0.0107805i
$944$	−11.2653			−0.366654
$945$	13.6222	+	9.53535i	0.443131	+	0.310185i
$946$	0.632301	−	1.09518i	0.0205579	−	0.0356073i
$947$		−	5.42144i		−	0.176173i	−0.996113	−	0.0880866i	$-0.971925\pi$
$947$		−	5.42144i		−	0.176173i	0.996113	−	0.0880866i	$-0.0280752\pi$
$948$	−1.48112	−	7.58626i	−0.0481047	−	0.246390i
$949$	0.889338	+	22.5032i	0.0288691	+	0.730484i
$950$	13.0131	+	22.5393i	0.422200	+	0.731272i
$951$	−26.4735	+	5.16863i	−0.858463	+	0.167604i
$952$	13.7203	+	1.96087i	0.444679	+	0.0635521i
$953$	−40.2976	+	23.2658i	−1.30537	+	0.753654i	−0.981319	−	0.192386i	$-0.938377\pi$
$953$	−40.2976	+	23.2658i	−1.30537	+	0.753654i	−0.324048	+	0.946040i	$0.605044\pi$
$954$	−6.14864	+	2.49604i	−0.199070	+	0.0808122i
$955$		−	24.9204i		−	0.806404i
$956$			7.54413i			0.243994i
$957$	−3.24990	−	1.11603i	−0.105054	−	0.0360761i
$958$	7.12716	−	4.11487i	0.230268	−	0.132945i
$959$	−27.9908	−	4.00036i	−0.903870	−	0.129178i
$960$	−0.401428	−	2.05610i	−0.0129560	−	0.0663604i
$961$	−7.53453	−	13.0502i	−0.243049	−	0.420974i
$962$	27.4522	−	17.3299i	0.885094	−	0.558738i
$963$	17.4860	−	22.4575i	0.563479	−	0.723682i
$964$			12.3343i			0.397262i
$965$	4.83406	−	8.37283i	0.155614	−	0.269531i
$966$	7.55397	−	14.7706i	0.243045	−	0.475235i
$967$	−27.2924			−0.877664			−0.438832	−	0.898569i	$-0.644608\pi$
$967$	−27.2924			−0.877664			−0.438832	+	0.898569i	$0.644608\pi$
$968$	−8.28083	−	4.78094i	−0.266156	−	0.153665i
$969$	−43.8415	−	50.3498i	−1.40839	−	1.61747i
$970$	−8.30247	+	14.3803i	−0.266576	+	0.461724i
$971$	−15.6819	+	27.1619i	−0.503257	+	0.871667i	0.496736	+	0.867902i	$0.334532\pi$
$971$	−15.6819	+	27.1619i	−0.503257	+	0.871667i	−0.999993	+	0.00376493i	$0.998802\pi$
$972$	1.29447	−	15.5346i	0.0415202	−	0.498273i
$973$	−2.68762	−	6.69697i	−0.0861612	−	0.214695i
$974$			23.0181i			0.737548i
$975$	21.1587	+	6.34368i	0.677620	+	0.203160i
$976$	−5.72549	−	3.30561i	−0.183269	−	0.105810i
$977$	−43.5100	+	25.1205i	−1.39201	+	0.803677i	−0.993538	−	0.113504i	$-0.963793\pi$
$977$	−43.5100	+	25.1205i	−1.39201	+	0.803677i	−0.398472	+	0.917181i	$0.630459\pi$
$978$	−20.3813	−	23.4069i	−0.651722	−	0.748471i
$979$	−7.46934	+	4.31243i	−0.238721	+	0.137826i
$980$	2.00995	+	8.22448i	0.0642053	+	0.262721i
$981$	34.6488	−	14.0657i	1.10625	−	0.449082i
$982$	−14.6297	+	25.3393i	−0.466851	+	0.808610i
$983$	−18.7346	+	32.4492i	−0.597540	+	1.03497i	0.395643	+	0.918404i	$0.370522\pi$
$983$	−18.7346	+	32.4492i	−0.597540	+	1.03497i	−0.993183	+	0.116565i	$0.962812\pi$
$984$	−0.208018	−	0.238899i	−0.00663139	−	0.00761582i
$985$			17.3098i			0.551535i
$986$	−4.33306	+	7.50509i	−0.137993	+	0.239011i
$987$	32.6139	−	1.66007i	1.03811	−	0.0528405i
$988$	1.04766	+	26.5091i	0.0333304	+	0.843368i
$989$	−3.30619	+	1.90883i	−0.105131	+	0.0606972i
$990$	4.03182	−	1.63671i	0.128140	−	0.0520182i
$991$	−12.2319	−	21.1862i	−0.388559	−	0.673003i	0.603697	−	0.797214i	$-0.293694\pi$
$991$	−12.2319	−	21.1862i	−0.388559	−	0.673003i	−0.992256	+	0.124210i	$0.960360\pi$
$992$	−1.99568	+	3.45662i	−0.0633629	+	0.109748i
$993$	20.4980	−	17.8484i	0.650484	−	0.566401i
$994$	17.2618	−	6.92749i	0.547511	−	0.219727i
$995$	−3.43718	+	1.98446i	−0.108966	+	0.0629115i
$996$	27.3039	+	9.37625i	0.865156	+	0.297098i
$997$			8.01278i			0.253767i	0.991918	+	0.126884i	$0.0404975\pi$
$997$			8.01278i			0.253767i	−0.991918	+	0.126884i	$0.959503\pi$
$998$	26.6451	−	15.3836i	0.843437	−	0.486958i
$999$	25.5789	+	39.1751i	0.809280	+	1.23945i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bb.a.269.18	yes	76
3.2	odd	2	inner	546.2.bb.a.269.31	yes	76
7.5	odd	6		546.2.u.a.425.16	yes	76
13.3	even	3		546.2.u.a.185.23	yes	76
21.5	even	6		546.2.u.a.425.23	yes	76
39.29	odd	6		546.2.u.a.185.16	✓	76
91.68	odd	6	inner	546.2.bb.a.341.12	yes	76
273.68	even	6	inner	546.2.bb.a.341.37	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.u.a.185.16	✓	76	39.29	odd	6
546.2.u.a.185.23	yes	76	13.3	even	3
546.2.u.a.425.16	yes	76	7.5	odd	6
546.2.u.a.425.23	yes	76	21.5	even	6
546.2.bb.a.269.18	yes	76	1.1	even	1	trivial
546.2.bb.a.269.31	yes	76	3.2	odd	2	inner
546.2.bb.a.341.12	yes	76	91.68	odd	6	inner
546.2.bb.a.341.37	yes	76	273.68	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(1.63815 + 0.562548i) q^{3} -1.00000 q^{4} +(0.604752 + 1.04746i) q^{5} +(0.562548 - 1.63815i) q^{6} +(0.374319 - 2.61914i) q^{7} +1.00000i q^{8} +(2.36708 + 1.84308i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(1.63815 + 0.562548i) q^{3} -1.00000 q^{4} +(0.604752 + 1.04746i) q^{5} +(0.562548 - 1.63815i) q^{6} +(0.374319 - 2.61914i) q^{7} +1.00000i q^{8} +(2.36708 + 1.84308i) q^{9} +(1.04746 - 0.604752i) q^{10} +(1.03855 - 0.599608i) q^{11} +(-1.63815 - 0.562548i) q^{12} +(1.92468 + 3.04887i) q^{13} +(-2.61914 - 0.374319i) q^{14} +(0.401428 + 2.05610i) q^{15} +1.00000 q^{16} +5.23850 q^{17} +(1.84308 - 2.36708i) q^{18} +(-6.37226 - 3.67902i) q^{19} +(-0.604752 - 1.04746i) q^{20} +(2.08658 - 4.07997i) q^{21} +(-0.599608 - 1.03855i) q^{22} +3.62026i q^{23} +(-0.562548 + 1.63815i) q^{24} +(1.76855 - 3.06322i) q^{25} +(3.04887 - 1.92468i) q^{26} +(2.84082 + 4.35083i) q^{27} +(-0.374319 + 2.61914i) q^{28} +(-1.43268 - 0.827158i) q^{29} +(2.05610 - 0.401428i) q^{30} +(-3.45662 - 1.99568i) q^{31} -1.00000i q^{32} +(2.03861 - 0.398014i) q^{33} -5.23850i q^{34} +(2.96981 - 1.19184i) q^{35} +(-2.36708 - 1.84308i) q^{36} +9.00405 q^{37} +(-3.67902 + 6.37226i) q^{38} +(1.43778 + 6.07724i) q^{39} +(-1.04746 + 0.604752i) q^{40} +(-0.0914442 + 0.158386i) q^{41} +(-4.07997 - 2.08658i) q^{42} +(0.527263 + 0.913245i) q^{43} +(-1.03855 + 0.599608i) q^{44} +(-0.499054 + 3.59403i) q^{45} +3.62026 q^{46} +(3.56307 + 6.17142i) q^{47} +(1.63815 + 0.562548i) q^{48} +(-6.71977 - 1.96079i) q^{49} +(-3.06322 - 1.76855i) q^{50} +(8.58145 + 2.94690i) q^{51} +(-1.92468 - 3.04887i) q^{52} +(-1.91564 - 1.10599i) q^{53} +(4.35083 - 2.84082i) q^{54} +(1.25613 + 0.725228i) q^{55} +(2.61914 + 0.374319i) q^{56} +(-8.36910 - 9.61150i) q^{57} +(-0.827158 + 1.43268i) q^{58} -11.2653 q^{59} +(-0.401428 - 2.05610i) q^{60} +(-5.72549 - 3.30561i) q^{61} +(-1.99568 + 3.45662i) q^{62} +(5.71331 - 5.50981i) q^{63} -1.00000 q^{64} +(-2.02962 + 3.85983i) q^{65} +(-0.398014 - 2.03861i) q^{66} +(-5.37236 - 9.30520i) q^{67} -5.23850 q^{68} +(-2.03657 + 5.93053i) q^{69} +(-1.19184 - 2.96981i) q^{70} +(-6.08827 + 3.51507i) q^{71} +(-1.84308 + 2.36708i) q^{72} +(5.40931 + 3.12307i) q^{73} -9.00405i q^{74} +(4.62036 - 4.02312i) q^{75} +(6.37226 + 3.67902i) q^{76} +(-1.18171 - 2.94455i) q^{77} +(6.07724 - 1.43778i) q^{78} +(2.23131 + 3.86475i) q^{79} +(0.604752 + 1.04746i) q^{80} +(2.20614 + 8.72542i) q^{81} +(0.158386 + 0.0914442i) q^{82} -16.6675 q^{83} +(-2.08658 + 4.07997i) q^{84} +(3.16799 + 5.48712i) q^{85} +(0.913245 - 0.527263i) q^{86} +(-1.88163 - 2.16096i) q^{87} +(0.599608 + 1.03855i) q^{88} -7.19208 q^{89} +(3.59403 + 0.499054i) q^{90} +(8.70586 - 3.89974i) q^{91} -3.62026i q^{92} +(-4.53980 - 5.21374i) q^{93} +(6.17142 - 3.56307i) q^{94} -8.89958i q^{95} +(0.562548 - 1.63815i) q^{96} +(-11.8894 + 6.86436i) q^{97} +(-1.96079 + 6.71977i) q^{98} +(3.56346 + 0.494809i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9}+O(q^{10}) \) 76 * q - 76 * q^4 + 10 * q^7 + 4 * q^9	\( 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9} - 2 q^{13} + 12 q^{15} + 76 q^{16} + 18 q^{19} - 8 q^{21} - 42 q^{25} - 10 q^{28} - 10 q^{30} + 12 q^{31} + 72 q^{33} - 4 q^{36} + 12 q^{37} - 42 q^{39} + 2 q^{42} - 2 q^{43} + 8 q^{46} - 10 q^{49} + 10 q^{51} + 2 q^{52} - 24 q^{55} + 8 q^{57} - 8 q^{58} - 12 q^{60} + 78 q^{61} + 2 q^{63} - 76 q^{64} - 24 q^{66} - 48 q^{67} + 30 q^{69} - 54 q^{73} - 18 q^{76} - 12 q^{78} - 60 q^{79} - 4 q^{81} - 24 q^{82} + 8 q^{84} + 8 q^{85} - 8 q^{91} - 32 q^{93} - 24 q^{94} + 66 q^{97}+O(q^{100}) \) 76 * q - 76 * q^4 + 10 * q^7 + 4 * q^9 - 2 * q^13 + 12 * q^15 + 76 * q^16 + 18 * q^19 - 8 * q^21 - 42 * q^25 - 10 * q^28 - 10 * q^30 + 12 * q^31 + 72 * q^33 - 4 * q^36 + 12 * q^37 - 42 * q^39 + 2 * q^42 - 2 * q^43 + 8 * q^46 - 10 * q^49 + 10 * q^51 + 2 * q^52 - 24 * q^55 + 8 * q^57 - 8 * q^58 - 12 * q^60 + 78 * q^61 + 2 * q^63 - 76 * q^64 - 24 * q^66 - 48 * q^67 + 30 * q^69 - 54 * q^73 - 18 * q^76 - 12 * q^78 - 60 * q^79 - 4 * q^81 - 24 * q^82 + 8 * q^84 + 8 * q^85 - 8 * q^91 - 32 * q^93 - 24 * q^94 + 66 * q^97

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