LMFDB - Embedded newform 930.2.s.d.439.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(439,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("930.439");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.s (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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			439.13
Character	$\chi$	$=$	930.439
Dual form			930.2.s.d.769.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000 q^{4} +(2.02972 - 0.938214i) q^{5} +(0.500000 - 0.866025i) q^{6} +(2.60552 + 1.50429i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000 q^{4} +(2.02972 - 0.938214i) q^{5} +(0.500000 - 0.866025i) q^{6} +(2.60552 + 1.50429i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(0.938214 + 2.02972i) q^{10} +(0.600738 + 1.04051i) q^{11} +(0.866025 + 0.500000i) q^{12} +(-4.95075 + 2.85832i) q^{13} +(-1.50429 + 2.60552i) q^{14} +(-2.22689 - 0.202342i) q^{15} +1.00000 q^{16} +(2.42803 + 1.40182i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(2.56153 - 4.43670i) q^{19} +(-2.02972 + 0.938214i) q^{20} +(-1.50429 - 2.60552i) q^{21} +(-1.04051 + 0.600738i) q^{22} +4.06649i q^{23} +(-0.500000 + 0.866025i) q^{24} +(3.23951 - 3.80862i) q^{25} +(-2.85832 - 4.95075i) q^{26} -1.00000i q^{27} +(-2.60552 - 1.50429i) q^{28} +8.23579 q^{29} +(0.202342 - 2.22689i) q^{30} +(-5.56725 + 0.0753491i) q^{31} +1.00000i q^{32} -1.20148i q^{33} +(-1.40182 + 2.42803i) q^{34} +(6.69981 + 0.608764i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(9.68765 + 5.59317i) q^{37} +(4.43670 + 2.56153i) q^{38} +5.71664 q^{39} +(-0.938214 - 2.02972i) q^{40} +(-3.98007 - 6.89369i) q^{41} +(2.60552 - 1.50429i) q^{42} +(3.96257 + 2.28779i) q^{43} +(-0.600738 - 1.04051i) q^{44} +(1.82738 + 1.28868i) q^{45} -4.06649 q^{46} +1.45252i q^{47} +(-0.866025 - 0.500000i) q^{48} +(1.02581 + 1.77675i) q^{49} +(3.80862 + 3.23951i) q^{50} +(-1.40182 - 2.42803i) q^{51} +(4.95075 - 2.85832i) q^{52} +(-10.7937 + 6.23175i) q^{53} +1.00000 q^{54} +(2.19555 + 1.54832i) q^{55} +(1.50429 - 2.60552i) q^{56} +(-4.43670 + 2.56153i) q^{57} +8.23579i q^{58} +(-5.11629 + 8.86167i) q^{59} +(2.22689 + 0.202342i) q^{60} +15.2374 q^{61} +(-0.0753491 - 5.56725i) q^{62} +3.00859i q^{63} -1.00000 q^{64} +(-7.36692 + 10.4464i) q^{65} +1.20148 q^{66} +(-2.67343 + 1.54350i) q^{67} +(-2.42803 - 1.40182i) q^{68} +(2.03325 - 3.52169i) q^{69} +(-0.608764 + 6.69981i) q^{70} +(7.59281 + 13.1511i) q^{71} +(0.866025 - 0.500000i) q^{72} +(5.91046 - 3.41241i) q^{73} +(-5.59317 + 9.68765i) q^{74} +(-4.70981 + 1.67861i) q^{75} +(-2.56153 + 4.43670i) q^{76} +3.61475i q^{77} +5.71664i q^{78} +(6.63002 - 11.4835i) q^{79} +(2.02972 - 0.938214i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(6.89369 - 3.98007i) q^{82} +(-4.78328 + 2.76163i) q^{83} +(1.50429 + 2.60552i) q^{84} +(6.24342 + 0.567295i) q^{85} +(-2.28779 + 3.96257i) q^{86} +(-7.13241 - 4.11790i) q^{87} +(1.04051 - 0.600738i) q^{88} -3.80912 q^{89} +(-1.28868 + 1.82738i) q^{90} -17.1990 q^{91} -4.06649i q^{92} +(4.85906 + 2.71837i) q^{93} -1.45252 q^{94} +(1.03661 - 11.4085i) q^{95} +(0.500000 - 0.866025i) q^{96} -1.57099i q^{97} +(-1.77675 + 1.02581i) q^{98} +(-0.600738 + 1.04051i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 28 q^{4} + 2 q^{5} + 14 q^{6} + 14 q^{9}+O(q^{10}) $ 28 * q - 28 * q^4 + 2 * q^5 + 14 * q^6 + 14 * q^9	$ 28 q - 28 q^{4} + 2 q^{5} + 14 q^{6} + 14 q^{9} + 4 q^{10} + 2 q^{11} - 8 q^{14} - 8 q^{15} + 28 q^{16} + 4 q^{19} - 2 q^{20} - 8 q^{21} - 14 q^{24} - 14 q^{25} - 12 q^{26} + 24 q^{29} + 4 q^{30} + 10 q^{34} + 8 q^{35} - 14 q^{36} + 24 q^{39} - 4 q^{40} + 20 q^{41} - 2 q^{44} - 2 q^{45} + 12 q^{46} + 2 q^{49} - 8 q^{50} + 10 q^{51} + 28 q^{54} + 6 q^{55} + 8 q^{56} - 20 q^{59} + 8 q^{60} + 32 q^{61} - 28 q^{64} - 12 q^{65} + 4 q^{66} - 6 q^{69} - 16 q^{70} - 16 q^{71} - 6 q^{74} - 8 q^{75} - 4 q^{76} + 10 q^{79} + 2 q^{80} - 14 q^{81} + 8 q^{84} + 72 q^{85} + 18 q^{86} - 80 q^{89} - 4 q^{90} + 32 q^{91} - 12 q^{94} - 32 q^{95} + 14 q^{96} - 2 q^{99}+O(q^{100}) $ 28 * q - 28 * q^4 + 2 * q^5 + 14 * q^6 + 14 * q^9 + 4 * q^10 + 2 * q^11 - 8 * q^14 - 8 * q^15 + 28 * q^16 + 4 * q^19 - 2 * q^20 - 8 * q^21 - 14 * q^24 - 14 * q^25 - 12 * q^26 + 24 * q^29 + 4 * q^30 + 10 * q^34 + 8 * q^35 - 14 * q^36 + 24 * q^39 - 4 * q^40 + 20 * q^41 - 2 * q^44 - 2 * q^45 + 12 * q^46 + 2 * q^49 - 8 * q^50 + 10 * q^51 + 28 * q^54 + 6 * q^55 + 8 * q^56 - 20 * q^59 + 8 * q^60 + 32 * q^61 - 28 * q^64 - 12 * q^65 + 4 * q^66 - 6 * q^69 - 16 * q^70 - 16 * q^71 - 6 * q^74 - 8 * q^75 - 4 * q^76 + 10 * q^79 + 2 * q^80 - 14 * q^81 + 8 * q^84 + 72 * q^85 + 18 * q^86 - 80 * q^89 - 4 * q^90 + 32 * q^91 - 12 * q^94 - 32 * q^95 + 14 * q^96 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	−1.00000			−0.500000
$5$	2.02972	−	0.938214i	0.907717	−	0.419582i
$5$	2.02972	−	0.938214i	0.907717	−	0.419582i
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	2.60552	+	1.50429i	0.984792	+	0.568570i	0.903714	−	0.428138i	$-0.140830\pi$
$7$	2.60552	+	1.50429i	0.984792	+	0.568570i	0.0810786	+	0.996708i	$0.474164\pi$
$8$		−	1.00000i		−	0.353553i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	0.938214	+	2.02972i	0.296689	+	0.641853i
$11$	0.600738	+	1.04051i	0.181129	+	0.313725i	0.942265	−	0.334867i	$-0.108691\pi$
$11$	0.600738	+	1.04051i	0.181129	+	0.313725i	−0.761136	+	0.648592i	$0.775358\pi$
$12$	0.866025	+	0.500000i	0.250000	+	0.144338i
$13$	−4.95075	+	2.85832i	−1.37309	+	0.792755i	−0.991316	−	0.131500i	$-0.958021\pi$
$13$	−4.95075	+	2.85832i	−1.37309	+	0.792755i	−0.381776	+	0.924255i	$0.624687\pi$
$14$	−1.50429	+	2.60552i	−0.402040	+	0.696353i
$15$	−2.22689	−	0.202342i	−0.574982	−	0.0522445i
$16$	1.00000			0.250000
$17$	2.42803	+	1.40182i	0.588883	+	0.339992i	0.764656	−	0.644439i	$-0.222909\pi$
$17$	2.42803	+	1.40182i	0.588883	+	0.339992i	−0.175773	+	0.984431i	$0.556242\pi$
$18$	−0.866025	+	0.500000i	−0.204124	+	0.117851i
$19$	2.56153	−	4.43670i	0.587655	−	1.01785i	−0.406883	−	0.913480i	$-0.633384\pi$
$19$	2.56153	−	4.43670i	0.587655	−	1.01785i	0.994539	−	0.104369i	$-0.0332822\pi$
$20$	−2.02972	+	0.938214i	−0.453859	+	0.209791i
$21$	−1.50429	−	2.60552i	−0.328264	−	0.568570i
$22$	−1.04051	+	0.600738i	−0.221837	+	0.128078i
$23$			4.06649i			0.847923i	0.905680	+	0.423961i	$0.139361\pi$
$23$			4.06649i			0.847923i	−0.905680	+	0.423961i	$0.860639\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	3.23951	−	3.80862i	0.647902	−	0.761724i
$26$	−2.85832	−	4.95075i	−0.560563	−	0.970923i
$27$		−	1.00000i		−	0.192450i
$28$	−2.60552	−	1.50429i	−0.492396	−	0.284285i
$29$	8.23579			1.52935			0.764674	−	0.644417i	$-0.222900\pi$
$29$	8.23579			1.52935			0.764674	+	0.644417i	$0.222900\pi$
$30$	0.202342	−	2.22689i	0.0369424	−	0.406573i
$31$	−5.56725	+	0.0753491i	−0.999908	+	0.0135331i
$31$	−5.56725	+	0.0753491i	−0.999908	+	0.0135331i
$32$			1.00000i			0.176777i
$33$		−	1.20148i		−	0.209150i
$34$	−1.40182	+	2.42803i	−0.240411	+	0.416403i
$35$	6.69981	+	0.608764i	1.13247	+	0.102900i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	9.68765	+	5.59317i	1.59264	+	0.919511i	0.992852	+	0.119353i	$0.0380820\pi$
$37$	9.68765	+	5.59317i	1.59264	+	0.919511i	0.599789	+	0.800158i	$0.295251\pi$
$38$	4.43670	+	2.56153i	0.719728	+	0.415535i
$39$	5.71664			0.915395
$40$	−0.938214	−	2.02972i	−0.148345	−	0.320927i
$41$	−3.98007	−	6.89369i	−0.621583	−	1.07661i	−0.989191	−	0.146633i	$-0.953156\pi$
$41$	−3.98007	−	6.89369i	−0.621583	−	1.07661i	0.367608	−	0.929981i	$-0.380177\pi$
$42$	2.60552	−	1.50429i	0.402040	−	0.232118i
$43$	3.96257	+	2.28779i	0.604286	+	0.348885i	0.770726	−	0.637167i	$-0.219894\pi$
$43$	3.96257	+	2.28779i	0.604286	+	0.348885i	−0.166440	+	0.986052i	$0.553227\pi$
$44$	−0.600738	−	1.04051i	−0.0905647	−	0.156863i
$45$	1.82738	+	1.28868i	0.272409	+	0.192105i
$46$	−4.06649			−0.599572
$47$			1.45252i			0.211872i	0.994373	+	0.105936i	$0.0337839\pi$
$47$			1.45252i			0.211872i	−0.994373	+	0.105936i	$0.966216\pi$
$48$	−0.866025	−	0.500000i	−0.125000	−	0.0721688i
$49$	1.02581	+	1.77675i	0.146544	+	0.253821i
$50$	3.80862	+	3.23951i	0.538620	+	0.458136i
$51$	−1.40182	−	2.42803i	−0.196294	−	0.339992i
$52$	4.95075	−	2.85832i	0.686546	−	0.396378i
$53$	−10.7937	+	6.23175i	−1.48263	+	0.855997i	−0.999806	−	0.0197198i	$-0.993723\pi$
$53$	−10.7937	+	6.23175i	−1.48263	+	0.855997i	−0.482825	+	0.875717i	$0.660389\pi$
$54$	1.00000			0.136083
$55$	2.19555	+	1.54832i	0.296048	+	0.208775i
$56$	1.50429	−	2.60552i	0.201020	−	0.348177i
$57$	−4.43670	+	2.56153i	−0.587655	+	0.339283i
$58$			8.23579i			1.08141i
$59$	−5.11629	+	8.86167i	−0.666084	+	1.15369i	0.312906	+	0.949784i	$0.398697\pi$
$59$	−5.11629	+	8.86167i	−0.666084	+	1.15369i	−0.978990	+	0.203907i	$0.934636\pi$
$60$	2.22689	+	0.202342i	0.287491	+	0.0261222i
$61$	15.2374			1.95096			0.975478	−	0.220099i	$-0.0706381\pi$
$61$	15.2374			1.95096			0.975478	+	0.220099i	$0.0706381\pi$
$62$	−0.0753491	−	5.56725i	−0.00956934	−	0.707042i
$63$			3.00859i			0.379047i
$64$	−1.00000			−0.125000
$65$	−7.36692	+	10.4464i	−0.913754	+	1.29572i
$66$	1.20148			0.147892
$67$	−2.67343	+	1.54350i	−0.326611	+	0.188569i	−0.654335	−	0.756204i	$-0.727052\pi$
$67$	−2.67343	+	1.54350i	−0.326611	+	0.188569i	0.327725	+	0.944773i	$0.393718\pi$
$68$	−2.42803	−	1.40182i	−0.294442	−	0.169996i
$69$	2.03325	−	3.52169i	0.244774	−	0.423961i
$70$	−0.608764	+	6.69981i	−0.0727612	+	0.800781i
$71$	7.59281	+	13.1511i	0.901101	+	1.56075i	0.826067	+	0.563572i	$0.190573\pi$
$71$	7.59281	+	13.1511i	0.901101	+	1.56075i	0.0750338	+	0.997181i	$0.476094\pi$
$72$	0.866025	−	0.500000i	0.102062	−	0.0589256i
$73$	5.91046	−	3.41241i	0.691768	−	0.399392i	−0.112506	−	0.993651i	$-0.535888\pi$
$73$	5.91046	−	3.41241i	0.691768	−	0.399392i	0.804274	+	0.594259i	$0.202555\pi$
$74$	−5.59317	+	9.68765i	−0.650193	+	1.12617i
$75$	−4.70981	+	1.67861i	−0.543842	+	0.193829i
$76$	−2.56153	+	4.43670i	−0.293828	+	0.508924i
$77$			3.61475i			0.411939i
$78$			5.71664i			0.647282i
$79$	6.63002	−	11.4835i	0.745936	−	1.29200i	−0.203821	−	0.979008i	$-0.565336\pi$
$79$	6.63002	−	11.4835i	0.745936	−	1.29200i	0.949756	−	0.312990i	$-0.101331\pi$
$80$	2.02972	−	0.938214i	0.226929	−	0.104895i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	6.89369	−	3.98007i	0.761281	−	0.439526i
$83$	−4.78328	+	2.76163i	−0.525034	+	0.303128i	−0.738992	−	0.673714i	$-0.764698\pi$
$83$	−4.78328	+	2.76163i	−0.525034	+	0.303128i	0.213958	+	0.976843i	$0.431364\pi$
$84$	1.50429	+	2.60552i	0.164132	+	0.284285i
$85$	6.24342	+	0.567295i	0.677194	+	0.0615318i
$86$	−2.28779	+	3.96257i	−0.246699	+	0.427295i
$87$	−7.13241	−	4.11790i	−0.764674	−	0.441485i
$88$	1.04051	−	0.600738i	0.110919	−	0.0640389i
$89$	−3.80912			−0.403765			−0.201883	−	0.979410i	$-0.564706\pi$
$89$	−3.80912			−0.403765			−0.201883	+	0.979410i	$0.564706\pi$
$90$	−1.28868	+	1.82738i	−0.135839	+	0.192622i
$91$	−17.1990			−1.80295
$92$		−	4.06649i		−	0.423961i
$93$	4.85906	+	2.71837i	0.503861	+	0.281882i
$94$	−1.45252			−0.149816
$95$	1.03661	−	11.4085i	0.106354	−	1.17049i
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$		−	1.57099i		−	0.159509i	−0.996815	−	0.0797547i	$-0.974586\pi$
$97$		−	1.57099i		−	0.159509i	0.996815	−	0.0797547i	$-0.0254137\pi$
$98$	−1.77675	+	1.02581i	−0.179479	+	0.103622i
$99$	−0.600738	+	1.04051i	−0.0603765	+	0.104575i
$100$	−3.23951	+	3.80862i	−0.323951	+	0.380862i
$101$	−6.32627			−0.629487			−0.314744	−	0.949177i	$-0.601919\pi$
$101$	−6.32627			−0.629487			−0.314744	+	0.949177i	$0.601919\pi$
$102$	2.42803	−	1.40182i	0.240411	−	0.138801i
$103$	0.0305311	−	0.0176271i	0.00300832	−	0.00173685i	−0.498495	−	0.866893i	$-0.666114\pi$
$103$	0.0305311	−	0.0176271i	0.00300832	−	0.00173685i	0.501503	+	0.865156i	$0.332780\pi$
$104$	2.85832	+	4.95075i	0.280281	+	0.485461i
$105$	−5.49782	−	3.87711i	−0.536533	−	0.378367i
$106$	−6.23175	−	10.7937i	−0.605281	−	1.04838i
$107$	−6.25142	−	3.60926i	−0.604347	−	0.348920i	0.166402	−	0.986058i	$-0.446785\pi$
$107$	−6.25142	−	3.60926i	−0.604347	−	0.348920i	−0.770750	+	0.637138i	$0.780118\pi$
$108$			1.00000i			0.0962250i
$109$	5.56018			0.532568			0.266284	−	0.963895i	$-0.414204\pi$
$109$	5.56018			0.532568			0.266284	+	0.963895i	$0.414204\pi$
$110$	−1.54832	+	2.19555i	−0.147626	+	0.209337i
$111$	−5.59317	−	9.68765i	−0.530880	−	0.919511i
$112$	2.60552	+	1.50429i	0.246198	+	0.142143i
$113$	10.0671	−	5.81222i	0.947029	−	0.546767i	0.0548721	−	0.998493i	$-0.482525\pi$
$113$	10.0671	−	5.81222i	0.947029	−	0.546767i	0.892157	+	0.451726i	$0.149192\pi$
$114$	−2.56153	−	4.43670i	−0.239909	−	0.415535i
$115$	3.81524	+	8.25384i	0.355773	+	0.769674i
$116$	−8.23579			−0.764674
$117$	−4.95075	−	2.85832i	−0.457697	−	0.264252i
$118$	−8.86167	−	5.11629i	−0.815783	−	0.470993i
$119$	4.21751	+	7.30494i	0.386618	+	0.669643i
$120$	−0.202342	+	2.22689i	−0.0184712	+	0.203287i
$121$	4.77823	−	8.27613i	0.434384	−	0.752376i
$122$			15.2374i			1.37953i
$123$			7.96015i			0.717743i
$124$	5.56725	−	0.0753491i	0.499954	−	0.00676655i
$125$	3.00199	−	10.7698i	0.268506	−	0.963278i
$126$	−3.00859			−0.268026
$127$	2.31282	+	1.33531i	0.205229	+	0.118489i	0.599092	−	0.800680i	$-0.295528\pi$
$127$	2.31282	+	1.33531i	0.205229	+	0.118489i	−0.393863	+	0.919169i	$0.628862\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−2.28779	−	3.96257i	−0.201429	−	0.348885i
$130$	−10.4464	−	7.36692i	−0.916214	−	0.646122i
$131$	3.26073	−	5.64775i	0.284891	−	0.493446i	−0.687692	−	0.726003i	$-0.741376\pi$
$131$	3.26073	−	5.64775i	0.284891	−	0.493446i	0.972583	+	0.232557i	$0.0747092\pi$
$132$			1.20148i			0.104575i
$133$	13.3482	−	7.70659i	1.15744	−	0.668246i
$134$	−1.54350	−	2.67343i	−0.133338	−	0.230949i
$135$	−0.938214	−	2.02972i	−0.0807486	−	0.174690i
$136$	1.40182	−	2.42803i	0.120205	−	0.208202i
$137$	17.9842	−	10.3832i	1.53650	−	0.887097i	0.537457	−	0.843291i	$-0.319385\pi$
$137$	17.9842	−	10.3832i	1.53650	−	0.887097i	0.999040	−	0.0438055i	$-0.0139482\pi$
$138$	3.52169	+	2.03325i	0.299786	+	0.173082i
$139$	−19.5531			−1.65847			−0.829237	−	0.558897i	$-0.811225\pi$
$139$	−19.5531			−1.65847			−0.829237	+	0.558897i	$0.811225\pi$
$140$	−6.69981	−	0.608764i	−0.566237	−	0.0514500i
$141$	0.726261	−	1.25792i	0.0611622	−	0.105936i
$142$	−13.1511	+	7.59281i	−1.10362	+	0.637175i
$143$	−5.94822	−	3.43420i	−0.497415	−	0.287183i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	16.7163	−	7.72694i	1.38822	−	0.641687i
$146$	3.41241	+	5.91046i	0.282413	+	0.489154i
$147$		−	2.05161i		−	0.169214i
$148$	−9.68765	−	5.59317i	−0.796320	−	0.459756i
$149$	1.45123	−	2.51360i	0.118889	−	0.205922i	−0.800439	−	0.599415i	$-0.795400\pi$
$149$	1.45123	−	2.51360i	0.118889	−	0.205922i	0.919328	+	0.393493i	$0.128733\pi$
$150$	−1.67861	−	4.70981i	−0.137058	−	0.384554i
$151$	−21.3668			−1.73880			−0.869401	−	0.494107i	$-0.835495\pi$
$151$	−21.3668			−1.73880			−0.869401	+	0.494107i	$0.835495\pi$
$152$	−4.43670	−	2.56153i	−0.359864	−	0.207768i
$153$			2.80364i			0.226661i
$154$	−3.61475			−0.291285
$155$	−11.2293	+	5.37621i	−0.901956	+	0.431828i
$156$	−5.71664			−0.457697
$157$			8.81484i			0.703501i	0.936094	+	0.351750i	$0.114413\pi$
$157$			8.81484i			0.703501i	−0.936094	+	0.351750i	$0.885587\pi$
$158$	11.4835	+	6.63002i	0.913581	+	0.527456i
$159$	12.4635			0.988420
$160$	0.938214	+	2.02972i	0.0741723	+	0.160463i
$161$	−6.11721	+	10.5953i	−0.482103	+	0.835028i
$162$	−0.866025	−	0.500000i	−0.0680414	−	0.0392837i
$163$		−	17.1278i		−	1.34155i	−0.741659	−	0.670777i	$-0.765961\pi$
$163$		−	17.1278i		−	1.34155i	0.741659	−	0.670777i	$-0.234039\pi$
$164$	3.98007	+	6.89369i	0.310792	+	0.538307i
$165$	−1.12724	−	2.43866i	−0.0877557	−	0.189849i
$166$	−2.76163	−	4.78328i	−0.214344	−	0.371255i
$167$	−6.81424	−	3.93420i	−0.527301	−	0.304438i	0.212615	−	0.977136i	$-0.431802\pi$
$167$	−6.81424	−	3.93420i	−0.527301	−	0.304438i	−0.739917	+	0.672698i	$0.765135\pi$
$168$	−2.60552	+	1.50429i	−0.201020	+	0.116059i
$169$	9.83998	−	17.0433i	0.756921	−	1.31103i
$170$	−0.567295	+	6.24342i	−0.0435095	+	0.478848i
$171$	5.12306			0.391770
$172$	−3.96257	−	2.28779i	−0.302143	−	0.174442i
$173$	−17.2579	+	9.96388i	−1.31210	+	0.757540i	−0.982443	−	0.186562i	$-0.940266\pi$
$173$	−17.2579	+	9.96388i	−1.31210	+	0.757540i	−0.329654	+	0.944102i	$0.606932\pi$
$174$	4.11790	−	7.13241i	0.312177	−	0.540706i
$175$	14.1699	−	5.05024i	1.07114	−	0.381762i
$176$	0.600738	+	1.04051i	0.0452824	+	0.0784313i
$177$	8.86167	−	5.11629i	0.666084	−	0.384564i
$178$		−	3.80912i		−	0.285505i
$179$	−13.0207	+	22.5524i	−0.973210	+	1.68565i	−0.287488	+	0.957784i	$0.592820\pi$
$179$	−13.0207	+	22.5524i	−0.973210	+	1.68565i	−0.685721	+	0.727864i	$0.740513\pi$
$180$	−1.82738	−	1.28868i	−0.136205	−	0.0960526i
$181$	−1.35348	−	2.34429i	−0.100603	−	0.174250i	0.811330	−	0.584588i	$-0.198744\pi$
$181$	−1.35348	−	2.34429i	−0.100603	−	0.174250i	−0.911933	+	0.410338i	$0.865411\pi$
$182$		−	17.1990i		−	1.27488i
$183$	−13.1960	−	7.61872i	−0.975478	−	0.563192i
$184$	4.06649			0.299786
$185$	24.9108	+	2.26347i	1.83148	+	0.166413i
$186$	−2.71837	+	4.85906i	−0.199321	+	0.356283i
$187$			3.36851i			0.246330i
$188$		−	1.45252i		−	0.105936i
$189$	1.50429	−	2.60552i	0.109421	−	0.189523i
$190$	11.4085	+	1.03661i	0.827661	+	0.0752036i
$191$	−9.16606	−	15.8761i	−0.663233	−	1.14875i	−0.979761	−	0.200170i	$-0.935851\pi$
$191$	−9.16606	−	15.8761i	−0.663233	−	1.14875i	0.316528	−	0.948583i	$-0.397483\pi$
$192$	0.866025	+	0.500000i	0.0625000	+	0.0360844i
$193$	−14.4741	−	8.35661i	−1.04187	−	0.601522i	−0.121505	−	0.992591i	$-0.538772\pi$
$193$	−14.4741	−	8.35661i	−1.04187	−	0.601522i	−0.920361	+	0.391069i	$0.872105\pi$
$194$	1.57099			0.112790
$195$	11.6032	−	5.36343i	0.830920	−	0.384083i
$196$	−1.02581	−	1.77675i	−0.0732719	−	0.126911i
$197$	−0.217940	+	0.125828i	−0.0155276	+	0.00896485i	−0.507744	−	0.861508i	$-0.669520\pi$
$197$	−0.217940	+	0.125828i	−0.0155276	+	0.00896485i	0.492216	+	0.870473i	$0.336187\pi$
$198$	−1.04051	−	0.600738i	−0.0739458	−	0.0426926i
$199$	−3.51642	−	6.09062i	−0.249272	−	0.431752i	0.714052	−	0.700093i	$-0.246858\pi$
$199$	−3.51642	−	6.09062i	−0.249272	−	0.431752i	−0.963324	+	0.268341i	$0.913525\pi$
$200$	−3.80862	−	3.23951i	−0.269310	−	0.229068i
$201$	3.08701			0.217741
$202$		−	6.32627i		−	0.445115i
$203$	21.4585	+	12.3891i	1.50609	+	0.869542i
$204$	1.40182	+	2.42803i	0.0981472	+	0.169996i
$205$	−14.5462	−	10.2581i	−1.01595	−	0.716456i
$206$	0.0176271	+	0.0305311i	0.00122814	+	0.00212720i
$207$	−3.52169	+	2.03325i	−0.244774	+	0.141320i
$208$	−4.95075	+	2.85832i	−0.343273	+	0.198189i
$209$	6.15524			0.425767
$210$	3.87711	−	5.49782i	0.267546	−	0.379386i
$211$	7.39003	−	12.7999i	0.508751	−	0.881182i	−0.491198	−	0.871048i	$-0.663441\pi$
$211$	7.39003	−	12.7999i	0.508751	−	0.881182i	0.999949	−	0.0101340i	$-0.00322580\pi$
$212$	10.7937	−	6.23175i	0.741315	−	0.427999i
$213$		−	15.1856i		−	1.04050i
$214$	3.60926	−	6.25142i	0.246724	−	0.427338i
$215$	10.1893	+	0.925833i	0.694907	+	0.0631413i
$216$	−1.00000			−0.0680414
$217$	−14.6189	−	8.17847i	−0.992396	−	0.555191i
$218$			5.56018i			0.376583i
$219$	−6.82482			−0.461178
$220$	−2.19555	−	1.54832i	−0.148024	−	0.104388i
$221$	−16.0274			−1.07812
$222$	9.68765	−	5.59317i	0.650193	−	0.375389i
$223$	2.75021	+	1.58783i	0.184167	+	0.106329i	0.589249	−	0.807951i	$-0.299424\pi$
$223$	2.75021	+	1.58783i	0.184167	+	0.106329i	−0.405082	+	0.914280i	$0.632757\pi$
$224$	−1.50429	+	2.60552i	−0.100510	+	0.174088i
$225$	4.91812	+	0.901189i	0.327874	+	0.0600792i
$226$	5.81222	+	10.0671i	0.386623	+	0.669651i
$227$	−15.3879	+	8.88422i	−1.02133	+	0.589666i	−0.914490	−	0.404609i	$-0.867407\pi$
$227$	−15.3879	+	8.88422i	−1.02133	+	0.589666i	−0.106843	+	0.994276i	$0.534074\pi$
$228$	4.43670	−	2.56153i	0.293828	−	0.169641i
$229$	−2.26737	+	3.92720i	−0.149832	+	0.259516i	−0.931165	−	0.364598i	$-0.881207\pi$
$229$	−2.26737	+	3.92720i	−0.149832	+	0.259516i	0.781333	+	0.624114i	$0.214540\pi$
$230$	−8.25384	+	3.81524i	−0.544242	+	0.251570i
$231$	1.80738	−	3.13047i	0.118917	−	0.205970i
$232$		−	8.23579i		−	0.540706i
$233$		−	9.60124i		−	0.628998i	−0.949258	−	0.314499i	$-0.898163\pi$
$233$		−	9.60124i		−	0.628998i	0.949258	−	0.314499i	$-0.101837\pi$
$234$	2.85832	−	4.95075i	0.186854	−	0.323641i
$235$	1.36278	+	2.94821i	0.0888977	+	0.192320i
$236$	5.11629	−	8.86167i	0.333042	−	0.576846i
$237$	−11.4835	+	6.63002i	−0.745936	+	0.430666i
$238$	−7.30494	+	4.21751i	−0.473509	+	0.273380i
$239$	6.54694	+	11.3396i	0.423486	+	0.733500i	0.996278	−	0.0862015i	$-0.0274729\pi$
$239$	6.54694	+	11.3396i	0.423486	+	0.733500i	−0.572792	+	0.819701i	$0.694140\pi$
$240$	−2.22689	−	0.202342i	−0.143745	−	0.0130611i
$241$	9.00731	−	15.6011i	0.580212	−	1.00496i	−0.415242	−	0.909711i	$-0.636303\pi$
$241$	9.00731	−	15.6011i	0.580212	−	1.00496i	0.995454	−	0.0952456i	$-0.0303636\pi$
$242$	8.27613	+	4.77823i	0.532010	+	0.307156i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	−15.2374			−0.975478
$245$	3.74907	+	2.64387i	0.239519	+	0.168911i
$246$	−7.96015			−0.507521
$247$			29.2867i			1.86347i
$248$	0.0753491	+	5.56725i	0.00478467	+	0.353521i
$249$	5.52326			0.350022
$250$	10.7698	+	3.00199i	0.681140	+	0.189863i
$251$	−4.23792	+	7.34029i	−0.267495	+	0.463315i	−0.968214	−	0.250122i	$-0.919529\pi$
$251$	−4.23792	+	7.34029i	−0.267495	+	0.463315i	0.700719	+	0.713437i	$0.252863\pi$
$252$		−	3.00859i		−	0.189523i
$253$	−4.23123	+	2.44290i	−0.266015	+	0.153584i
$254$	−1.33531	+	2.31282i	−0.0837845	+	0.145119i
$255$	−5.12331	−	3.61300i	−0.320834	−	0.226255i
$256$	1.00000			0.0625000
$257$	−0.560415	+	0.323556i	−0.0349577	+	0.0201829i	−0.517377	−	0.855758i	$-0.673092\pi$
$257$	−0.560415	+	0.323556i	−0.0349577	+	0.0201829i	0.482419	+	0.875940i	$0.339758\pi$
$258$	3.96257	−	2.28779i	0.246699	−	0.142432i
$259$	16.8276	+	29.1462i	1.04561	+	1.81106i
$260$	7.36692	−	10.4464i	0.456877	−	0.647861i
$261$	4.11790	+	7.13241i	0.254891	+	0.441485i
$262$	5.64775	+	3.26073i	0.348919	+	0.201448i
$263$			4.27595i			0.263667i	0.991272	+	0.131833i	$0.0420864\pi$
$263$			4.27595i			0.263667i	−0.991272	+	0.131833i	$0.957914\pi$
$264$	−1.20148			−0.0739458
$265$	−16.0615	+	22.7755i	−0.986649	+	1.39909i
$266$	7.70659	+	13.3482i	0.472522	+	0.818431i
$267$	3.29879	+	1.90456i	0.201883	+	0.116557i
$268$	2.67343	−	1.54350i	0.163305	−	0.0942844i
$269$	−7.35971	−	12.7474i	−0.448729	−	0.777222i	0.549574	−	0.835445i	$-0.314790\pi$
$269$	−7.35971	−	12.7474i	−0.448729	−	0.777222i	−0.998304	+	0.0582228i	$0.981457\pi$
$270$	2.02972	−	0.938214i	0.123525	−	0.0570979i
$271$	0.474088			0.0287988			0.0143994	−	0.999896i	$-0.495416\pi$
$271$	0.474088			0.0287988			0.0143994	+	0.999896i	$0.495416\pi$
$272$	2.42803	+	1.40182i	0.147221	+	0.0849980i
$273$	14.8948	+	8.59951i	0.901474	+	0.520466i
$274$	10.3832	+	17.9842i	0.627272	+	1.08647i
$275$	5.90900	+	1.08276i	0.356326	+	0.0652927i
$276$	−2.03325	+	3.52169i	−0.122387	+	0.211981i
$277$		−	5.24986i		−	0.315434i	−0.987484	−	0.157717i	$-0.949587\pi$
$277$		−	5.24986i		−	0.315434i	0.987484	−	0.157717i	$-0.0504133\pi$
$278$		−	19.5531i		−	1.17272i
$279$	−2.84888	−	4.78371i	−0.170558	−	0.286393i
$280$	0.608764	−	6.69981i	0.0363806	−	0.400390i
$281$	2.68919			0.160423			0.0802117	−	0.996778i	$-0.474440\pi$
$281$	2.68919			0.160423			0.0802117	+	0.996778i	$0.474440\pi$
$282$	1.25792	+	0.726261i	0.0749081	+	0.0432482i
$283$		−	11.0019i		−	0.653996i	−0.945025	−	0.326998i	$-0.893963\pi$
$283$		−	11.0019i		−	0.653996i	0.945025	−	0.326998i	$-0.106037\pi$
$284$	−7.59281	−	13.1511i	−0.450550	−	0.780376i
$285$	−6.60199	+	9.36176i	−0.391068	+	0.554543i
$286$	3.43420	−	5.94822i	0.203069	−	0.351725i
$287$		−	23.9488i		−	1.41365i
$288$	−0.866025	+	0.500000i	−0.0510310	+	0.0294628i
$289$	−4.56979	−	7.91511i	−0.268811	−	0.465595i
$290$	7.72694	+	16.7163i	0.453741	+	0.981617i
$291$	−0.785493	+	1.36051i	−0.0460464	+	0.0797547i
$292$	−5.91046	+	3.41241i	−0.345884	+	0.199696i
$293$	7.86460	+	4.54063i	0.459455	+	0.265266i	0.711815	−	0.702367i	$-0.247873\pi$
$293$	7.86460	+	4.54063i	0.459455	+	0.265266i	−0.252360	+	0.967633i	$0.581207\pi$
$294$	2.05161			0.119652
$295$	−2.07048	+	22.7869i	−0.120548	+	1.32670i
$296$	5.59317	−	9.68765i	0.325096	−	0.563083i
$297$	1.04051	−	0.600738i	0.0603765	−	0.0348584i
$298$	2.51360	+	1.45123i	0.145609	+	0.0840674i
$299$	−11.6233	−	20.1322i	−0.672195	−	1.16428i
$300$	4.70981	−	1.67861i	0.271921	−	0.0969143i
$301$	6.88302	+	11.9217i	0.396731	+	0.687158i
$302$		−	21.3668i		−	1.22952i
$303$	5.47871	+	3.16313i	0.314744	+	0.181717i
$304$	2.56153	−	4.43670i	0.146914	−	0.254462i
$305$	30.9277	−	14.2960i	1.77092	−	0.818586i
$306$	−2.80364			−0.160274
$307$	4.89604	+	2.82673i	0.279432	+	0.161330i	0.633166	−	0.774016i	$-0.281755\pi$
$307$	4.89604	+	2.82673i	0.279432	+	0.161330i	−0.353734	+	0.935346i	$0.615088\pi$
$308$		−	3.61475i		−	0.205970i
$309$	−0.0352543			−0.00200555
$310$	−5.37621	−	11.2293i	−0.305348	−	0.637779i
$311$	−17.9977			−1.02056			−0.510279	−	0.860009i	$-0.670458\pi$
$311$	−17.9977			−1.02056			−0.510279	+	0.860009i	$0.670458\pi$
$312$		−	5.71664i		−	0.323641i
$313$	−27.1825	−	15.6938i	−1.53645	−	0.887067i	−0.999043	−	0.0437412i	$-0.986072\pi$
$313$	−27.1825	−	15.6938i	−1.53645	−	0.887067i	−0.537402	−	0.843326i	$-0.680594\pi$
$314$	−8.81484			−0.497450
$315$	2.82270	+	6.10659i	0.159041	+	0.344067i
$316$	−6.63002	+	11.4835i	−0.372968	+	0.645999i
$317$	−27.3591	−	15.7958i	−1.53664	−	0.887178i	−0.999032	−	0.0439818i	$-0.985996\pi$
$317$	−27.3591	−	15.7958i	−1.53664	−	0.887178i	−0.537606	−	0.843196i	$-0.680671\pi$
$318$			12.4635i			0.698919i
$319$	4.94756	+	8.56942i	0.277010	+	0.479795i
$320$	−2.02972	+	0.938214i	−0.113465	+	0.0524477i
$321$	3.60926	+	6.25142i	0.201449	+	0.348920i
$322$	−10.5953	−	6.11721i	−0.590454	−	0.340899i
$323$	12.4389	−	7.18162i	0.692121	−	0.399596i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	−5.15177	+	28.1151i	−0.285769	+	1.55954i
$326$	17.1278			0.948622
$327$	−4.81525	−	2.78009i	−0.266284	−	0.153739i
$328$	−6.89369	+	3.98007i	−0.380640	+	0.219763i
$329$	−2.18502	+	3.78457i	−0.120464	+	0.208650i
$330$	2.43866	−	1.12724i	0.134244	−	0.0620526i
$331$	−15.2495	−	26.4129i	−0.838187	−	1.45178i	−0.891409	−	0.453200i	$-0.850282\pi$
$331$	−15.2495	−	26.4129i	−0.838187	−	1.45178i	0.0532222	−	0.998583i	$-0.483051\pi$
$332$	4.78328	−	2.76163i	0.262517	−	0.151564i
$333$			11.1863i			0.613008i
$334$	3.93420	−	6.81424i	0.215270	−	0.372858i
$335$	−3.97816	+	5.64112i	−0.217350	+	0.308207i
$336$	−1.50429	−	2.60552i	−0.0820660	−	0.142143i
$337$		−	1.19605i		−	0.0651531i	−0.999469	−	0.0325766i	$-0.989629\pi$
$337$		−	1.19605i		−	0.0651531i	0.999469	−	0.0325766i	$-0.0103713\pi$
$338$	17.0433	+	9.83998i	0.927036	+	0.535224i
$339$	−11.6244			−0.631353
$340$	−6.24342	−	0.567295i	−0.338597	−	0.0307659i
$341$	−3.42286	−	5.74752i	−0.185359	−	0.311245i
$342$			5.12306i			0.277023i
$343$		−	14.8877i		−	0.803859i
$344$	2.28779	−	3.96257i	0.123349	−	0.213647i
$345$	0.822823	−	9.05565i	0.0442993	−	0.487540i
$346$	−9.96388	−	17.2579i	−0.535662	−	0.927793i
$347$	12.7730	+	7.37449i	0.685690	+	0.395883i	0.801995	−	0.597330i	$-0.203772\pi$
$347$	12.7730	+	7.37449i	0.685690	+	0.395883i	−0.116306	+	0.993213i	$0.537105\pi$
$348$	7.13241	+	4.11790i	0.382337	+	0.220742i
$349$	22.8574			1.22353			0.611764	−	0.791041i	$-0.290460\pi$
$349$	22.8574			1.22353			0.611764	+	0.791041i	$0.290460\pi$
$350$	5.05024	+	14.1699i	0.269946	+	0.757412i
$351$	2.85832	+	4.95075i	0.152566	+	0.264252i
$352$	−1.04051	+	0.600738i	−0.0554593	+	0.0320195i
$353$	−3.65756	−	2.11169i	−0.194672	−	0.112394i	0.399496	−	0.916735i	$-0.369185\pi$
$353$	−3.65756	−	2.11169i	−0.194672	−	0.112394i	−0.594168	+	0.804341i	$0.702519\pi$
$354$	5.11629	+	8.86167i	0.271928	+	0.470993i
$355$	27.7498	+	19.5694i	1.47281	+	1.03864i
$356$	3.80912			0.201883
$357$		−	8.43502i		−	0.446428i
$358$	−22.5524	−	13.0207i	−1.19193	−	0.688163i
$359$	1.53564	+	2.65981i	0.0810481	+	0.140379i	0.903700	−	0.428165i	$-0.140840\pi$
$359$	1.53564	+	2.65981i	0.0810481	+	0.140379i	−0.822652	+	0.568545i	$0.807507\pi$
$360$	1.28868	−	1.82738i	0.0679194	−	0.0963112i
$361$	−3.62288	−	6.27501i	−0.190678	−	0.330263i
$362$	2.34429	−	1.35348i	0.123213	−	0.0711372i
$363$	−8.27613	+	4.77823i	−0.434384	+	0.250792i
$364$	17.1990			0.901474
$365$	8.79501	−	12.4715i	0.460352	−	0.652788i
$366$	7.61872	−	13.1960i	0.398237	−	0.689767i
$367$	−12.3306	+	7.11907i	−0.643651	+	0.371612i	−0.786020	−	0.618201i	$-0.787862\pi$
$367$	−12.3306	+	7.11907i	−0.643651	+	0.371612i	0.142368	+	0.989814i	$0.454528\pi$
$368$			4.06649i			0.211981i
$369$	3.98007	−	6.89369i	0.207194	−	0.358871i
$370$	−2.26347	+	24.9108i	−0.117672	+	1.29505i
$371$	−37.4976			−1.94678
$372$	−4.85906	−	2.71837i	−0.251930	−	0.140941i
$373$		−	0.345652i		−	0.0178972i	−0.999960	−	0.00894859i	$-0.997152\pi$
$373$		−	0.345652i		−	0.0178972i	0.999960	−	0.00894859i	$-0.00284846\pi$
$374$	−3.36851			−0.174182
$375$	−7.98469	+	7.82590i	−0.412328	+	0.404128i
$376$	1.45252			0.0749081
$377$	−40.7734	+	23.5405i	−2.09994	+	1.21240i
$378$	2.60552	+	1.50429i	0.134013	+	0.0773726i
$379$	−9.90195	+	17.1507i	−0.508629	+	0.880971i	0.491321	+	0.870979i	$0.336514\pi$
$379$	−9.90195	+	17.1507i	−0.508629	+	0.880971i	−0.999950	+	0.00999273i	$0.996819\pi$
$380$	−1.03661	+	11.4085i	−0.0531770	+	0.585244i
$381$	−1.33531	−	2.31282i	−0.0684098	−	0.118489i
$382$	15.8761	−	9.16606i	0.812291	−	0.468977i
$383$	−10.2322	+	5.90754i	−0.522839	+	0.301861i	−0.738095	−	0.674696i	$-0.764275\pi$
$383$	−10.2322	+	5.90754i	−0.522839	+	0.301861i	0.215257	+	0.976558i	$0.430941\pi$
$384$	−0.500000	+	0.866025i	−0.0255155	+	0.0441942i
$385$	3.39141	+	7.33692i	0.172842	+	0.373924i
$386$	8.35661	−	14.4741i	0.425340	−	0.736711i
$387$			4.57558i			0.232590i
$388$			1.57099i			0.0797547i
$389$	10.2506	−	17.7545i	0.519726	−	0.900191i	−0.480011	−	0.877262i	$-0.659368\pi$
$389$	10.2506	−	17.7545i	0.519726	−	0.900191i	0.999737	−	0.0229290i	$-0.00729916\pi$
$390$	5.36343	+	11.6032i	0.271588	+	0.587549i
$391$	−5.70050	+	9.87356i	−0.288287	+	0.499327i
$392$	1.77675	−	1.02581i	0.0897393	−	0.0518110i
$393$	−5.64775	+	3.26073i	−0.284891	+	0.164482i
$394$	−0.125828	−	0.217940i	−0.00633910	−	0.0109797i
$395$	2.68306	−	29.5287i	0.135000	−	1.48575i
$396$	0.600738	−	1.04051i	0.0301882	−	0.0522876i
$397$	−17.0357	−	9.83559i	−0.854999	−	0.493634i	0.00733518	−	0.999973i	$-0.497665\pi$
$397$	−17.0357	−	9.83559i	−0.854999	−	0.493634i	−0.862335	+	0.506339i	$0.830998\pi$
$398$	6.09062	−	3.51642i	0.305295	−	0.176262i
$399$	−15.4132			−0.771625
$400$	3.23951	−	3.80862i	0.161975	−	0.190431i
$401$	32.9839			1.64714			0.823569	−	0.567216i	$-0.191980\pi$
$401$	32.9839			1.64714			0.823569	+	0.567216i	$0.191980\pi$
$402$			3.08701i			0.153966i
$403$	27.3467	−	16.2860i	1.36224	−	0.811265i
$404$	6.32627			0.314744
$405$	−0.202342	+	2.22689i	−0.0100545	+	0.110655i
$406$	−12.3891	+	21.4585i	−0.614859	+	1.06497i
$407$			13.4401i			0.666202i
$408$	−2.42803	+	1.40182i	−0.120205	+	0.0694005i
$409$	0.315914	−	0.547178i	0.0156209	−	0.0270562i	−0.858109	−	0.513467i	$-0.828361\pi$
$409$	0.315914	−	0.547178i	0.0156209	−	0.0270562i	0.873730	+	0.486411i	$0.161694\pi$
$410$	10.2581	−	14.5462i	0.506611	−	0.718385i
$411$	−20.7664			−1.02433
$412$	−0.0305311	+	0.0176271i	−0.00150416	+	0.000868427i
$413$	−26.6611	+	15.3928i	−1.31191	+	0.757431i
$414$	−2.03325	−	3.52169i	−0.0999287	−	0.173082i
$415$	−7.11772	+	10.0931i	−0.349395	+	0.495450i
$416$	−2.85832	−	4.95075i	−0.140141	−	0.242731i
$417$	16.9335	+	9.77656i	0.829237	+	0.478760i
$418$			6.15524i			0.301063i
$419$	−30.8537			−1.50730			−0.753651	−	0.657275i	$-0.771709\pi$
$419$	−30.8537			−1.50730			−0.753651	+	0.657275i	$0.771709\pi$
$420$	5.49782	+	3.87711i	0.268266	+	0.189184i
$421$	8.19317	+	14.1910i	0.399311	+	0.691626i	0.993641	−	0.112595i	$-0.0359162\pi$
$421$	8.19317	+	14.1910i	0.399311	+	0.691626i	−0.594330	+	0.804221i	$0.702583\pi$
$422$	12.7999	+	7.39003i	0.623090	+	0.359741i
$423$	−1.25792	+	0.726261i	−0.0611622	+	0.0353120i
$424$	6.23175	+	10.7937i	0.302641	+	0.524189i
$425$	13.2046	−	4.70621i	0.640518	−	0.228285i
$426$	15.1856			0.735746
$427$	39.7014	+	22.9216i	1.92129	+	1.10925i
$428$	6.25142	+	3.60926i	0.302174	+	0.174460i
$429$	3.43420	+	5.94822i	0.165805	+	0.287183i
$430$	−0.925833	+	10.1893i	−0.0446476	+	0.491373i
$431$	6.30128	−	10.9141i	0.303522	−	0.525716i	−0.673409	−	0.739270i	$-0.735171\pi$
$431$	6.30128	−	10.9141i	0.303522	−	0.525716i	0.976931	+	0.213554i	$0.0685040\pi$
$432$		−	1.00000i		−	0.0481125i
$433$			13.1515i			0.632019i	0.948756	+	0.316009i	$0.102343\pi$
$433$			13.1515i			0.632019i	−0.948756	+	0.316009i	$0.897657\pi$
$434$	8.17847	−	14.6189i	0.392579	−	0.701730i
$435$	−18.3402	−	1.66645i	−0.879347	−	0.0799000i
$436$	−5.56018			−0.266284
$437$	18.0418	+	10.4164i	0.863057	+	0.498286i
$438$		−	6.82482i		−	0.326102i
$439$	11.4774	+	19.8795i	0.547787	+	0.948796i	0.998426	+	0.0560891i	$0.0178631\pi$
$439$	11.4774	+	19.8795i	0.547787	+	0.948796i	−0.450638	+	0.892707i	$0.648804\pi$
$440$	1.54832	−	2.19555i	0.0738132	−	0.104669i
$441$	−1.02581	+	1.77675i	−0.0488479	+	0.0846071i
$442$		−	16.0274i		−	0.762347i
$443$	16.3226	−	9.42386i	0.775510	−	0.447741i	−0.0593266	−	0.998239i	$-0.518895\pi$
$443$	16.3226	−	9.42386i	0.775510	−	0.447741i	0.834837	+	0.550498i	$0.185562\pi$
$444$	5.59317	+	9.68765i	0.265440	+	0.459756i
$445$	−7.73143	+	3.57376i	−0.366505	+	0.169413i
$446$	−1.58783	+	2.75021i	−0.0751860	+	0.130226i
$447$	−2.51360	+	1.45123i	−0.118889	+	0.0686407i
$448$	−2.60552	−	1.50429i	−0.123099	−	0.0710713i
$449$	−4.98908			−0.235449			−0.117725	−	0.993046i	$-0.537560\pi$
$449$	−4.98908			−0.235449			−0.117725	+	0.993046i	$0.537560\pi$
$450$	−0.901189	+	4.91812i	−0.0424824	+	0.231842i
$451$	4.78197	−	8.28261i	0.225174	−	0.390013i
$452$	−10.0671	+	5.81222i	−0.473514	+	0.273384i
$453$	18.5042	+	10.6834i	0.869401	+	0.501949i
$454$	−8.88422	−	15.3879i	−0.416957	−	0.722191i
$455$	−34.9092	+	16.1364i	−1.63657	+	0.756484i
$456$	2.56153	+	4.43670i	0.119955	+	0.207768i
$457$			24.5919i			1.15036i	0.818027	+	0.575180i	$0.195068\pi$
$457$			24.5919i			1.15036i	−0.818027	+	0.575180i	$0.804932\pi$
$458$	−3.92720	−	2.26737i	−0.183506	−	0.105947i
$459$	1.40182	−	2.42803i	0.0654315	−	0.113331i
$460$	−3.81524	−	8.25384i	−0.177887	−	0.384837i
$461$	−21.5361			−1.00304			−0.501519	−	0.865147i	$-0.667225\pi$
$461$	−21.5361			−1.00304			−0.501519	+	0.865147i	$0.667225\pi$
$462$	3.13047	+	1.80738i	0.145642	+	0.0840867i
$463$		−	17.5396i		−	0.815134i	−0.913175	−	0.407567i	$-0.866377\pi$
$463$		−	17.5396i		−	0.815134i	0.913175	−	0.407567i	$-0.133623\pi$
$464$	8.23579			0.382337
$465$	12.4129	+	0.958695i	0.575636	+	0.0444584i
$466$	9.60124			0.444769
$467$		−	3.79669i		−	0.175690i	−0.996134	−	0.0878450i	$-0.972002\pi$
$467$		−	3.79669i		−	0.175690i	0.996134	−	0.0878450i	$-0.0279980\pi$
$468$	4.95075	+	2.85832i	0.228849	+	0.132126i
$469$	−9.28753			−0.428858
$470$	−2.94821	+	1.36278i	−0.135991	+	0.0628601i
$471$	4.40742	−	7.63388i	0.203083	−	0.351750i
$472$	8.86167	+	5.11629i	0.407892	+	0.235496i
$473$			5.49746i			0.252773i
$474$	−6.63002	−	11.4835i	−0.304527	−	0.527456i
$475$	−8.59960	−	24.1286i	−0.394577	−	1.10710i
$476$	−4.21751	−	7.30494i	−0.193309	−	0.334821i
$477$	−10.7937	−	6.23175i	−0.494210	−	0.285332i
$478$	−11.3396	+	6.54694i	−0.518663	+	0.299450i
$479$	−2.69835	+	4.67368i	−0.123291	+	0.213546i	−0.921064	−	0.389412i	$-0.872678\pi$
$479$	−2.69835	+	4.67368i	−0.123291	+	0.213546i	0.797773	+	0.602958i	$0.206011\pi$
$480$	0.202342	−	2.22689i	0.00923561	−	0.101643i
$481$	−63.9483			−2.91579
$482$	15.6011	+	9.00731i	0.710612	+	0.410272i
$483$	10.5953	−	6.11721i	0.482103	−	0.278343i
$484$	−4.77823	+	8.27613i	−0.217192	+	0.376188i
$485$	−1.47392	−	3.18866i	−0.0669273	−	0.144789i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	7.13139	−	4.11731i	0.323154	−	0.186573i	−0.329643	−	0.944106i	$-0.606929\pi$
$487$	7.13139	−	4.11731i	0.323154	−	0.186573i	0.652798	+	0.757532i	$0.273595\pi$
$488$		−	15.2374i		−	0.689767i
$489$	−8.56391	+	14.8331i	−0.387273	+	0.670777i
$490$	−2.64387	+	3.74907i	−0.119438	+	0.169366i
$491$	7.24169	+	12.5430i	0.326813	+	0.566057i	0.981878	−	0.189516i	$-0.0606920\pi$
$491$	7.24169	+	12.5430i	0.326813	+	0.566057i	−0.655065	+	0.755573i	$0.727359\pi$
$492$		−	7.96015i		−	0.358871i
$493$	19.9967	+	11.5451i	0.900607	+	0.519966i
$494$	−29.2867			−1.31767
$495$	−0.243109	+	2.67556i	−0.0109269	+	0.120258i
$496$	−5.56725	+	0.0753491i	−0.249977	+	0.00338327i
$497$			45.6873i			2.04936i
$498$			5.52326i			0.247503i
$499$	6.91092	−	11.9701i	0.309375	−	0.535854i	−0.668850	−	0.743397i	$-0.733213\pi$
$499$	6.91092	−	11.9701i	0.309375	−	0.535854i	0.978226	+	0.207543i	$0.0665467\pi$
$500$	−3.00199	+	10.7698i	−0.134253	+	0.481639i
$501$	3.93420	+	6.81424i	0.175767	+	0.304438i
$502$	−7.34029	−	4.23792i	−0.327613	−	0.189148i
$503$	16.8962	+	9.75503i	0.753365	+	0.434955i	0.826908	−	0.562337i	$-0.190098\pi$
$503$	16.8962	+	9.75503i	0.753365	+	0.434955i	−0.0735438	+	0.997292i	$0.523431\pi$
$504$	3.00859			0.134013
$505$	−12.8405	+	5.93539i	−0.571397	+	0.264121i
$506$	−2.44290	−	4.23123i	−0.108600	−	0.188101i
$507$	−17.0433	+	9.83998i	−0.756921	+	0.437009i
$508$	−2.31282	−	1.33531i	−0.102615	−	0.0592446i
$509$	−8.58869	−	14.8761i	−0.380687	−	0.659370i	0.610473	−	0.792037i	$-0.290979\pi$
$509$	−8.58869	−	14.8761i	−0.380687	−	0.659370i	−0.991161	+	0.132667i	$0.957646\pi$
$510$	3.61300	−	5.12331i	0.159986	−	0.226864i
$511$	20.5331			0.908330
$512$			1.00000i			0.0441942i
$513$	−4.43670	−	2.56153i	−0.195885	−	0.113094i
$514$	−0.323556	−	0.560415i	−0.0142714	−	0.0247189i
$515$	0.0454315	−	0.0644228i	0.00200195	−	0.00283881i
$516$	2.28779	+	3.96257i	0.100714	+	0.174442i
$517$	−1.51136	+	0.872585i	−0.0664696	+	0.0383763i
$518$	−29.1462	+	16.8276i	−1.28061	+	0.739360i
$519$	19.9278			0.874732
$520$	10.4464	+	7.36692i	0.458107	+	0.323061i
$521$	12.9271	−	22.3904i	0.566346	−	0.980939i	−0.430578	−	0.902554i	$-0.641690\pi$
$521$	12.9271	−	22.3904i	0.566346	−	0.980939i	0.996923	−	0.0783856i	$-0.0249765\pi$
$522$	−7.13241	+	4.11790i	−0.312177	+	0.180235i
$523$		−	6.67578i		−	0.291912i	−0.989291	−	0.145956i	$-0.953374\pi$
$523$		−	6.67578i		−	0.291912i	0.989291	−	0.145956i	$-0.0466257\pi$
$524$	−3.26073	+	5.64775i	−0.142446	+	0.246723i
$525$	−14.7966	−	2.71131i	−0.645776	−	0.118331i
$526$	−4.27595			−0.186440
$527$	−13.6231	−	7.62135i	−0.593430	−	0.331991i
$528$		−	1.20148i		−	0.0522876i
$529$	6.46362			0.281027
$530$	−22.7755	−	16.0615i	−0.989305	−	0.697666i
$531$	−10.2326			−0.444056
$532$	−13.3482	+	7.70659i	−0.578718	+	0.334123i
$533$	39.4087	+	22.7526i	1.70698	+	0.985527i
$534$	−1.90456	+	3.29879i	−0.0824183	+	0.142753i
$535$	−16.0749	−	1.46061i	−0.694977	−	0.0631477i
$536$	1.54350	+	2.67343i	0.0666692	+	0.115474i
$537$	22.5524	−	13.0207i	0.973210	−	0.561883i
$538$	12.7474	−	7.35971i	0.549579	−	0.317300i
$539$	−1.23248	+	2.13472i	−0.0530868	+	0.0919490i
$540$	0.938214	+	2.02972i	0.0403743	+	0.0873452i
$541$	−0.135685	+	0.235013i	−0.00583356	+	0.0101040i	−0.868927	−	0.494939i	$-0.835190\pi$
$541$	−0.135685	+	0.235013i	−0.00583356	+	0.0101040i	0.863094	+	0.505044i	$0.168524\pi$
$542$			0.474088i			0.0203638i
$543$			2.70696i			0.116167i
$544$	−1.40182	+	2.42803i	−0.0601026	+	0.104101i
$545$	11.2856	−	5.21663i	0.483421	−	0.223456i
$546$	−8.59951	+	14.8948i	−0.368025	+	0.637438i
$547$	−3.20058	+	1.84786i	−0.136847	+	0.0790086i	−0.566860	−	0.823814i	$-0.691842\pi$
$547$	−3.20058	+	1.84786i	−0.136847	+	0.0790086i	0.430014	+	0.902822i	$0.358509\pi$
$548$	−17.9842	+	10.3832i	−0.768248	+	0.443548i
$549$	7.61872	+	13.1960i	0.325159	+	0.563192i
$550$	−1.08276	+	5.90900i	−0.0461689	+	0.251961i
$551$	21.0962	−	36.5398i	0.898730	−	1.55665i
$552$	−3.52169	−	2.03325i	−0.149893	−	0.0865408i
$553$	34.5492	−	19.9470i	1.46918	−	0.848233i
$554$	5.24986			0.223045
$555$	−20.4416	−	14.4156i	−0.867700	−	0.611909i
$556$	19.5531			0.829237
$557$			29.1994i			1.23722i	0.785699	+	0.618609i	$0.212304\pi$
$557$			29.1994i			1.23722i	−0.785699	+	0.618609i	$0.787696\pi$
$558$	4.78371	−	2.84888i	0.202511	−	0.120603i
$559$	−26.1569			−1.10632
$560$	6.69981	+	0.608764i	0.283119	+	0.0257250i
$561$	1.68426	−	2.91722i	0.0711094	−	0.123165i
$562$			2.68919i			0.113436i
$563$	24.1198	−	13.9255i	1.01653	−	0.586892i	0.103431	−	0.994637i	$-0.467018\pi$
$563$	24.1198	−	13.9255i	1.01653	−	0.586892i	0.913096	+	0.407745i	$0.133685\pi$
$564$	−0.726261	+	1.25792i	−0.0305811	+	0.0529680i
$565$	14.9802	−	21.2422i	0.630221	−	0.893667i
$566$	11.0019			0.462445
$567$	−2.60552	+	1.50429i	−0.109421	+	0.0631744i
$568$	13.1511	−	7.59281i	0.551809	−	0.318587i
$569$	17.6605	+	30.5890i	0.740368	+	1.28236i	0.952328	+	0.305077i	$0.0986822\pi$
$569$	17.6605	+	30.5890i	0.740368	+	1.28236i	−0.211959	+	0.977278i	$0.567984\pi$
$570$	−9.36176	−	6.60199i	−0.392121	−	0.276527i
$571$	14.6608	+	25.3933i	0.613537	+	1.06268i	0.990639	+	0.136506i	$0.0435872\pi$
$571$	14.6608	+	25.3933i	0.613537	+	1.06268i	−0.377102	+	0.926172i	$0.623079\pi$
$572$	5.94822	+	3.43420i	0.248707	+	0.143591i
$573$			18.3321i			0.765836i
$574$	23.9488			0.999605
$575$	15.4877	+	13.1734i	0.645883	+	0.549371i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	18.2475	+	10.5352i	0.759654	+	0.438586i	0.829172	−	0.558994i	$-0.188813\pi$
$577$	18.2475	+	10.5352i	0.759654	+	0.438586i	−0.0695174	+	0.997581i	$0.522146\pi$
$578$	7.91511	−	4.56979i	0.329225	−	0.190078i
$579$	8.35661	+	14.4741i	0.347289	+	0.601522i
$580$	−16.7163	+	7.72694i	−0.694108	+	0.320844i
$581$	−16.6172			−0.689399
$582$	−1.36051	−	0.785493i	−0.0563951	−	0.0325597i
$583$	−12.9684	−	7.48731i	−0.537096	−	0.310093i
$584$	−3.41241	−	5.91046i	−0.141206	−	0.244577i
$585$	−12.7303	−	1.15672i	−0.526335	−	0.0478243i
$586$	−4.54063	+	7.86460i	−0.187572	+	0.324884i
$587$			40.9867i			1.69170i	0.533420	+	0.845851i	$0.320907\pi$
$587$			40.9867i			1.69170i	−0.533420	+	0.845851i	$0.679093\pi$
$588$			2.05161i			0.0846071i
$589$	−13.9264	+	24.8933i	−0.573827	+	1.02571i
$590$	−22.7869	−	2.07048i	−0.938121	−	0.0852403i
$591$	0.251655			0.0103517
$592$	9.68765	+	5.59317i	0.398160	+	0.229878i
$593$		−	7.86984i		−	0.323176i	−0.986858	−	0.161588i	$-0.948339\pi$
$593$		−	7.86984i		−	0.323176i	0.986858	−	0.161588i	$-0.0516615\pi$
$594$	0.600738	+	1.04051i	0.0246486	+	0.0426926i
$595$	15.4139	+	10.8700i	0.631910	+	0.445628i
$596$	−1.45123	+	2.51360i	−0.0594446	+	0.102961i
$597$			7.03284i			0.287835i
$598$	20.1322	−	11.6233i	0.823268	−	0.475314i
$599$	3.29261	+	5.70297i	0.134533	+	0.233017i	0.925419	−	0.378946i	$-0.123713\pi$
$599$	3.29261	+	5.70297i	0.134533	+	0.233017i	−0.790886	+	0.611963i	$0.790380\pi$
$600$	1.67861	+	4.70981i	0.0685288	+	0.192277i
$601$	−2.28051	+	3.94996i	−0.0930240	+	0.161122i	−0.908782	−	0.417271i	$-0.862987\pi$
$601$	−2.28051	+	3.94996i	−0.0930240	+	0.161122i	0.815758	+	0.578393i	$0.196320\pi$
$602$	−11.9217	+	6.88302i	−0.485894	+	0.280531i
$603$	−2.67343	−	1.54350i	−0.108870	−	0.0628563i
$604$	21.3668			0.869401
$605$	1.93367	−	21.2812i	0.0786150	−	0.865204i
$606$	−3.16313	+	5.47871i	−0.128494	+	0.222557i
$607$	−11.4842	+	6.63041i	−0.466129	+	0.269120i	−0.714618	−	0.699515i	$-0.753399\pi$
$607$	−11.4842	+	6.63041i	−0.466129	+	0.269120i	0.248489	+	0.968635i	$0.420066\pi$
$608$	4.43670	+	2.56153i	0.179932	+	0.103884i
$609$	−12.3891	−	21.4585i	−0.502030	−	0.869542i
$610$	14.2960	+	30.9277i	0.578827	+	1.25223i
$611$	−4.15177	−	7.19108i	−0.167963	−	0.290920i
$612$		−	2.80364i		−	0.113331i
$613$	−14.3777	−	8.30098i	−0.580711	−	0.335273i	0.180705	−	0.983537i	$-0.442162\pi$
$613$	−14.3777	−	8.30098i	−0.580711	−	0.335273i	−0.761416	+	0.648264i	$0.775495\pi$
$614$	−2.82673	+	4.89604i	−0.114078	+	0.197588i
$615$	7.46832	+	16.1569i	0.301152	+	0.651507i
$616$	3.61475			0.145642
$617$	−28.2888	−	16.3326i	−1.13886	−	0.657524i	−0.192716	−	0.981255i	$-0.561729\pi$
$617$	−28.2888	−	16.3326i	−1.13886	−	0.657524i	−0.946149	+	0.323731i	$0.895063\pi$
$618$		−	0.0352543i		−	0.00141813i
$619$	3.71218			0.149205			0.0746026	−	0.997213i	$-0.476231\pi$
$619$	3.71218			0.149205			0.0746026	+	0.997213i	$0.476231\pi$
$620$	11.2293	−	5.37621i	0.450978	−	0.215914i
$621$	4.06649			0.163183
$622$		−	17.9977i		−	0.721643i
$623$	−9.92471	−	5.73003i	−0.397625	−	0.229569i
$624$	5.71664			0.228849
$625$	−4.01115	−	24.6761i	−0.160446	−	0.987045i
$626$	15.6938	−	27.1825i	0.627251	−	1.08643i
$627$	−5.33059	−	3.07762i	−0.212883	−	0.122908i
$628$		−	8.81484i		−	0.351750i
$629$	15.6813	+	27.1607i	0.625253	+	1.08297i
$630$	−6.10659	+	2.82270i	−0.243292	+	0.112459i
$631$	0.203204	+	0.351959i	0.00808941	+	0.0140113i	0.870042	−	0.492978i	$-0.164092\pi$
$631$	0.203204	+	0.351959i	0.00808941	+	0.0140113i	−0.861952	+	0.506989i	$0.830758\pi$
$632$	−11.4835	−	6.63002i	−0.456790	−	0.263728i
$633$	−12.7999	+	7.39003i	−0.508751	+	0.293727i
$634$	15.7958	−	27.3591i	0.627330	−	1.08657i
$635$	5.94717	+	0.540377i	0.236006	+	0.0214442i
$636$	−12.4635			−0.494210
$637$	−10.1570	−	5.86416i	−0.402436	−	0.232347i
$638$	−8.56942	+	4.94756i	−0.339267	+	0.195876i
$639$	−7.59281	+	13.1511i	−0.300367	+	0.520251i
$640$	−0.938214	−	2.02972i	−0.0370862	−	0.0802316i
$641$	4.63912	+	8.03520i	0.183234	+	0.317371i	0.942980	−	0.332849i	$-0.108010\pi$
$641$	4.63912	+	8.03520i	0.183234	+	0.317371i	−0.759746	+	0.650220i	$0.774677\pi$
$642$	−6.25142	+	3.60926i	−0.246724	+	0.142446i
$643$		−	31.0306i		−	1.22373i	−0.790963	−	0.611864i	$-0.790420\pi$
$643$		−	31.0306i		−	1.22373i	0.790963	−	0.611864i	$-0.209580\pi$
$644$	6.11721	−	10.5953i	0.241052	−	0.417514i
$645$	−8.36131	−	5.89646i	−0.329226	−	0.232173i
$646$	7.18162	+	12.4389i	0.282557	+	0.489403i
$647$		−	49.5095i		−	1.94642i	−0.229921	−	0.973209i	$-0.573847\pi$
$647$		−	49.5095i		−	1.94642i	0.229921	−	0.973209i	$-0.426153\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$	−12.2942			−0.482590
$650$	−28.1151	−	5.15177i	−1.10276	−	0.202069i
$651$	8.57112	+	14.3922i	0.335929	+	0.564076i
$652$			17.1278i			0.670777i
$653$			5.17526i			0.202524i	0.994860	+	0.101262i	$0.0322880\pi$
$653$			5.17526i			0.202524i	−0.994860	+	0.101262i	$0.967712\pi$
$654$	2.78009	−	4.81525i	0.108710	−	0.188291i
$655$	1.31956	−	14.5226i	0.0515596	−	0.567445i
$656$	−3.98007	−	6.89369i	−0.155396	−	0.269153i
$657$	5.91046	+	3.41241i	0.230589	+	0.133131i
$658$	−3.78457	−	2.18502i	−0.147538	−	0.0851810i
$659$	−1.22550			−0.0477388			−0.0238694	−	0.999715i	$-0.507599\pi$
$659$	−1.22550			−0.0477388			−0.0238694	+	0.999715i	$0.507599\pi$
$660$	1.12724	+	2.43866i	0.0438778	+	0.0949247i
$661$	25.4301	+	44.0463i	0.989117	+	1.71320i	0.621976	+	0.783037i	$0.286330\pi$
$661$	25.4301	+	44.0463i	0.989117	+	1.71320i	0.367142	+	0.930165i	$0.380336\pi$
$662$	26.4129	−	15.2495i	1.02657	−	0.592688i
$663$	13.8802	+	8.01371i	0.539061	+	0.311227i
$664$	2.76163	+	4.78328i	0.107172	+	0.185627i
$665$	19.8627	−	28.1657i	0.770241	−	1.09222i
$666$	−11.1863			−0.433462
$667$			33.4908i			1.29677i
$668$	6.81424	+	3.93420i	0.263651	+	0.152219i
$669$	−1.58783	−	2.75021i	−0.0613891	−	0.106329i
$670$	−5.64112	−	3.97816i	−0.217935	−	0.153690i
$671$	9.15372	+	15.8547i	0.353375	+	0.612064i
$672$	2.60552	−	1.50429i	0.100510	−	0.0580294i
$673$	−29.2867	+	16.9087i	−1.12892	+	0.651782i	−0.943663	−	0.330908i	$-0.892645\pi$
$673$	−29.2867	+	16.9087i	−1.12892	+	0.651782i	−0.185257	+	0.982690i	$0.559312\pi$
$674$	1.19605			0.0460702
$675$	−3.80862	−	3.23951i	−0.146594	−	0.124689i
$676$	−9.83998	+	17.0433i	−0.378461	+	0.655513i
$677$	19.5034	−	11.2603i	0.749577	−	0.432769i	−0.0759640	−	0.997111i	$-0.524203\pi$
$677$	19.5034	−	11.2603i	0.749577	−	0.432769i	0.825541	+	0.564342i	$0.190870\pi$
$678$		−	11.6244i		−	0.446434i
$679$	2.36323	−	4.09323i	0.0906923	−	0.157084i
$680$	0.567295	−	6.24342i	0.0217548	−	0.239424i
$681$	17.7684			0.680888
$682$	5.74752	−	3.42286i	0.220084	−	0.131068i
$683$			2.66178i			0.101850i	0.998702	+	0.0509250i	$0.0162169\pi$
$683$			2.66178i			0.101850i	−0.998702	+	0.0509250i	$0.983783\pi$
$684$	−5.12306			−0.195885
$685$	26.7613	−	37.9480i	1.02250	−	1.44992i
$686$	14.8877			0.568414
$687$	3.92720	−	2.26737i	0.149832	−	0.0865055i
$688$	3.96257	+	2.28779i	0.151072	+	0.0872212i
$689$	35.6247	−	61.7038i	1.35719	−	2.35073i
$690$	9.05565	+	0.822823i	0.344743	+	0.0313243i
$691$	16.0361	+	27.7754i	0.610042	+	1.05662i	0.991233	+	0.132128i	$0.0421809\pi$
$691$	16.0361	+	27.7754i	0.610042	+	1.05662i	−0.381190	+	0.924497i	$0.624486\pi$
$692$	17.2579	−	9.96388i	0.656049	−	0.378770i
$693$	−3.13047	+	1.80738i	−0.118917	+	0.0686565i
$694$	−7.37449	+	12.7730i	−0.279932	+	0.484856i
$695$	−39.6873	+	18.3450i	−1.50543	+	0.695866i
$696$	−4.11790	+	7.13241i	−0.156088	+	0.270353i
$697$		−	22.3174i		−	0.845333i
$698$			22.8574i			0.865164i
$699$	−4.80062	+	8.31492i	−0.181576	+	0.314499i
$700$	−14.1699	+	5.05024i	−0.535571	+	0.190881i
$701$	−5.81376	+	10.0697i	−0.219583	+	0.380328i	−0.954680	−	0.297633i	$-0.903803\pi$
$701$	−5.81376	+	10.0697i	−0.219583	+	0.380328i	0.735098	+	0.677961i	$0.237136\pi$
$702$	−4.95075	+	2.85832i	−0.186854	+	0.107880i
$703$	49.6304	−	28.6541i	1.87185	−	1.08071i
$704$	−0.600738	−	1.04051i	−0.0226412	−	0.0392157i
$705$	0.293906	−	3.23461i	0.0110691	−	0.121823i
$706$	2.11169	−	3.65756i	0.0794746	−	0.137654i
$707$	−16.4832	−	9.51657i	−0.619914	−	0.357908i
$708$	−8.86167	+	5.11629i	−0.333042	+	0.192282i
$709$	32.5740			1.22334			0.611672	−	0.791112i	$-0.290497\pi$
$709$	32.5740			1.22334			0.611672	+	0.791112i	$0.290497\pi$
$710$	−19.5694	+	27.7498i	−0.734427	+	1.04143i
$711$	13.2600			0.497290
$712$			3.80912i			0.142753i
$713$	−0.306407	−	22.6392i	−0.0114750	−	0.847845i
$714$	8.43502			0.315673
$715$	−15.2952	−	1.38977i	−0.572009	−	0.0519744i
$716$	13.0207	−	22.5524i	0.486605	−	0.842824i
$717$		−	13.0939i		−	0.489000i
$718$	−2.65981	+	1.53564i	−0.0992632	+	0.0573096i
$719$	19.9502	−	34.5548i	0.744017	−	1.28868i	−0.206635	−	0.978418i	$-0.566251\pi$
$719$	19.9502	−	34.5548i	0.744017	−	1.28868i	0.950652	−	0.310258i	$-0.100415\pi$
$720$	1.82738	+	1.28868i	0.0681023	+	0.0480263i
$721$	0.106066			0.00395009
$722$	6.27501	−	3.62288i	0.233532	−	0.134829i
$723$	−15.6011	+	9.00731i	−0.580212	+	0.334986i
$724$	1.35348	+	2.34429i	0.0503016	+	0.0871249i
$725$	26.6799	−	31.3670i	0.990868	−	1.16494i
$726$	−4.77823	−	8.27613i	−0.177337	−	0.307156i
$727$	19.3836	+	11.1911i	0.718898	+	0.415056i	0.814347	−	0.580378i	$-0.197095\pi$
$727$	19.3836	+	11.1911i	0.718898	+	0.415056i	−0.0954490	+	0.995434i	$0.530429\pi$
$728$			17.1990i			0.637438i
$729$	−1.00000			−0.0370370
$730$	12.4715	+	8.79501i	0.461591	+	0.325518i
$731$	6.41415	+	11.1096i	0.237236	+	0.410905i
$732$	13.1960	+	7.61872i	0.487739	+	0.281596i
$733$	12.5246	−	7.23106i	0.462606	−	0.267085i	−0.250534	−	0.968108i	$-0.580606\pi$
$733$	12.5246	−	7.23106i	0.462606	−	0.267085i	0.713139	+	0.701022i	$0.247273\pi$
$734$	−7.11907	−	12.3306i	−0.262770	−	0.455130i
$735$	−1.92485	−	4.16419i	−0.0709992	−	0.153599i
$736$	−4.06649			−0.149893
$737$	−3.21206	−	1.85448i	−0.118318	−	0.0683107i
$738$	6.89369	+	3.98007i	0.253760	+	0.146509i
$739$	−11.1868	−	19.3761i	−0.411513	−	0.712761i	0.583543	−	0.812083i	$-0.301666\pi$
$739$	−11.1868	−	19.3761i	−0.411513	−	0.712761i	−0.995055	+	0.0993215i	$0.968333\pi$
$740$	−24.9108	−	2.26347i	−0.915739	−	0.0832067i
$741$	14.6433	−	25.3630i	0.537937	−	0.931734i
$742$		−	37.4976i		−	1.37658i
$743$		−	4.30333i		−	0.157874i	−0.996880	−	0.0789370i	$-0.974847\pi$
$743$		−	4.30333i		−	0.157874i	0.996880	−	0.0789370i	$-0.0251526\pi$
$744$	2.71837	−	4.85906i	0.0996604	−	0.178142i
$745$	0.587289	−	6.46346i	0.0215166	−	0.236803i
$746$	0.345652			0.0126552
$747$	−4.78328	−	2.76163i	−0.175011	−	0.101043i
$748$		−	3.36851i		−	0.123165i
$749$	−10.8588	−	18.8080i	−0.396771	−	0.687228i
$750$	−7.82590	−	7.98469i	−0.285762	−	0.291560i
$751$	20.3595	−	35.2637i	0.742929	−	1.28679i	−0.208227	−	0.978081i	$-0.566769\pi$
$751$	20.3595	−	35.2637i	0.742929	−	1.28679i	0.951156	−	0.308711i	$-0.0998974\pi$
$752$			1.45252i			0.0529680i
$753$	7.34029	−	4.23792i	0.267495	−	0.154438i
$754$	−23.5405	−	40.7734i	−0.857295	−	1.48488i
$755$	−43.3685	+	20.0466i	−1.57834	+	0.729570i
$756$	−1.50429	+	2.60552i	−0.0547107	+	0.0947617i
$757$	−19.0134	+	10.9774i	−0.691055	+	0.398981i	−0.804007	−	0.594620i	$-0.797303\pi$
$757$	−19.0134	+	10.9774i	−0.691055	+	0.398981i	0.112952	+	0.993600i	$0.463969\pi$
$758$	−17.1507	−	9.90195i	−0.622941	−	0.359655i
$759$	4.88580			0.177343
$760$	−11.4085	−	1.03661i	−0.413830	−	0.0376018i
$761$	−25.7144	+	44.5386i	−0.932146	+	1.61452i	−0.152501	+	0.988303i	$0.548733\pi$
$761$	−25.7144	+	44.5386i	−0.932146	+	1.61452i	−0.779645	+	0.626221i	$0.784601\pi$
$762$	2.31282	−	1.33531i	0.0837845	−	0.0483730i
$763$	14.4871	+	8.36414i	0.524469	+	0.302802i
$764$	9.16606	+	15.8761i	0.331617	+	0.574377i
$765$	2.63042	+	5.69061i	0.0951030	+	0.205744i
$766$	−5.90754	−	10.2322i	−0.213448	−	0.369703i
$767$		−	58.4959i		−	2.11217i
$768$	−0.866025	−	0.500000i	−0.0312500	−	0.0180422i
$769$	7.79704	−	13.5049i	0.281168	−	0.486998i	−0.690504	−	0.723328i	$-0.742611\pi$
$769$	7.79704	−	13.5049i	0.281168	−	0.486998i	0.971673	+	0.236330i	$0.0759447\pi$
$770$	−7.33692	+	3.39141i	−0.264404	+	0.122218i
$771$	0.647112			0.0233052
$772$	14.4741	+	8.35661i	0.520933	+	0.300761i
$773$		−	32.6585i		−	1.17465i	−0.809353	−	0.587323i	$-0.800182\pi$
$773$		−	32.6585i		−	1.17465i	0.809353	−	0.587323i	$-0.199818\pi$
$774$	−4.57558			−0.164466
$775$	−17.7482	+	21.4476i	−0.637534	+	0.770422i
$776$	−1.57099			−0.0563951
$777$		−	33.6551i		−	1.20737i
$778$	17.7545	+	10.2506i	0.636531	+	0.367502i
$779$	−40.7803			−1.46111
$780$	−11.6032	+	5.36343i	−0.415460	+	0.192042i
$781$	−9.12259	+	15.8008i	−0.326432	+	0.565396i
$782$	−9.87356	−	5.70050i	−0.353078	−	0.203850i
$783$		−	8.23579i		−	0.294323i
$784$	1.02581	+	1.77675i	0.0366359	+	0.0634553i
$785$	8.27020	+	17.8916i	0.295176	+	0.638580i
$786$	−3.26073	−	5.64775i	−0.116306	−	0.201448i
$787$	−34.1540	−	19.7188i	−1.21746	−	0.702900i	−0.253085	−	0.967444i	$-0.581445\pi$
$787$	−34.1540	−	19.7188i	−1.21746	−	0.702900i	−0.964374	+	0.264544i	$0.914779\pi$
$788$	0.217940	−	0.125828i	0.00776379	−	0.00448242i
$789$	2.13798	−	3.70308i	0.0761140	−	0.131833i
$790$	29.5287	+	2.68306i	1.05058	+	0.0954591i
$791$	34.9732			1.24350
$792$	1.04051	+	0.600738i	0.0369729	+	0.0213463i
$793$	−75.4369	+	43.5535i	−2.67884	+	1.54663i
$794$	9.83559	−	17.0357i	0.349052	−	0.604576i
$795$	25.2974	−	11.6934i	0.897206	−	0.414723i
$796$	3.51642	+	6.09062i	0.124636	+	0.215876i
$797$	−13.2700	+	7.66143i	−0.470047	+	0.271382i	−0.716259	−	0.697834i	$-0.754147\pi$
$797$	−13.2700	+	7.66143i	−0.470047	+	0.271382i	0.246212	+	0.969216i	$0.420814\pi$
$798$		−	15.4132i		−	0.545621i
$799$	−2.03618	+	3.52676i	−0.0720347	+	0.124768i
$800$	3.80862	+	3.23951i	0.134655	+	0.114534i
$801$	−1.90456	−	3.29879i	−0.0672942	−	0.116557i
$802$			32.9839i			1.16470i
$803$	7.10129	+	4.09993i	0.250599	+	0.144683i
$804$	−3.08701			−0.108870
$805$	−2.47554	+	27.2447i	−0.0872512	+	0.960251i
$806$	16.2860	+	27.3467i	0.573651	+	0.963248i
$807$			14.7194i			0.518148i
$808$			6.32627i			0.222557i
$809$	−4.51618	+	7.82225i	−0.158780	+	0.275016i	−0.934429	−	0.356149i	$-0.884089\pi$
$809$	−4.51618	+	7.82225i	−0.158780	+	0.275016i	0.775649	+	0.631165i	$0.217423\pi$
$810$	−2.22689	−	0.202342i	−0.0782451	−	0.00710957i
$811$	4.94419	+	8.56358i	0.173614	+	0.300708i	0.939681	−	0.342053i	$-0.111122\pi$
$811$	4.94419	+	8.56358i	0.173614	+	0.300708i	−0.766067	+	0.642761i	$0.777789\pi$
$812$	−21.4585	−	12.3891i	−0.753045	−	0.434771i
$813$	−0.410573	−	0.237044i	−0.0143994	−	0.00831350i
$814$	−13.4401			−0.471076
$815$	−16.0696	−	34.7647i	−0.562892	−	1.21775i
$816$	−1.40182	−	2.42803i	−0.0490736	−	0.0849980i
$817$	20.3005	−	11.7205i	0.710224	−	0.410048i
$818$	0.547178	+	0.315914i	0.0191316	+	0.0110457i
$819$	−8.59951	−	14.8948i	−0.300491	−	0.520466i
$820$	14.5462	+	10.2581i	0.507975	+	0.358228i
$821$	26.2119			0.914802			0.457401	−	0.889260i	$-0.348780\pi$
$821$	26.2119			0.914802			0.457401	+	0.889260i	$0.348780\pi$
$822$		−	20.7664i		−	0.724312i
$823$	−45.9214	−	26.5127i	−1.60072	−	0.924176i	−0.991343	−	0.131294i	$-0.958087\pi$
$823$	−45.9214	−	26.5127i	−1.60072	−	0.924176i	−0.609376	−	0.792882i	$-0.708580\pi$
$824$	−0.0176271	−	0.0305311i	−0.000614070	−	0.00106360i
$825$	−4.57597	−	3.89220i	−0.159315	−	0.135509i
$826$	−15.3928	−	26.6611i	−0.535585	−	0.927660i
$827$	−18.1752	+	10.4935i	−0.632015	+	0.364894i	−0.781532	−	0.623865i	$-0.785561\pi$
$827$	−18.1752	+	10.4935i	−0.632015	+	0.364894i	0.149517	+	0.988759i	$0.452228\pi$
$828$	3.52169	−	2.03325i	0.122387	−	0.0706602i
$829$	−29.7496			−1.03325			−0.516623	−	0.856213i	$-0.672811\pi$
$829$	−29.7496			−1.03325			−0.516623	+	0.856213i	$0.672811\pi$
$830$	−10.0931	−	7.11772i	−0.350336	−	0.247060i
$831$	−2.62493	+	4.54651i	−0.0910579	+	0.157717i
$832$	4.95075	−	2.85832i	0.171637	−	0.0990944i
$833$			5.75199i			0.199295i
$834$	−9.77656	+	16.9335i	−0.338535	+	0.586359i
$835$	−17.5221	−	1.59211i	−0.606377	−	0.0550972i
$836$	−6.15524			−0.212883
$837$	0.0753491	+	5.56725i	0.00260445	+	0.192432i
$838$		−	30.8537i		−	1.06582i
$839$	−6.24044			−0.215444			−0.107722	−	0.994181i	$-0.534356\pi$
$839$	−6.24044			−0.215444			−0.107722	+	0.994181i	$0.534356\pi$
$840$	−3.87711	+	5.49782i	−0.133773	+	0.189693i
$841$	38.8283			1.33891
$842$	−14.1910	+	8.19317i	−0.489054	+	0.282355i
$843$	−2.32890	−	1.34459i	−0.0802117	−	0.0463102i
$844$	−7.39003	+	12.7999i	−0.254375	+	0.440591i
$845$	3.98208	−	43.8252i	0.136988	−	1.50763i
$846$	−0.726261	−	1.25792i	−0.0249694	−	0.0432482i
$847$	24.8995	−	14.3757i	0.855556	−	0.493956i
$848$	−10.7937	+	6.23175i	−0.370658	+	0.213999i
$849$	−5.50095	+	9.52793i	−0.188792	+	0.326998i
$850$	4.70621	+	13.2046i	0.161422	+	0.452915i
$851$	−22.7446	+	39.3948i	−0.779675	+	1.35044i
$852$			15.1856i			0.520251i
$853$		−	17.0117i		−	0.582471i	−0.956651	−	0.291235i	$-0.905934\pi$
$853$		−	17.0117i		−	0.582471i	0.956651	−	0.291235i	$-0.0940663\pi$
$854$	−22.9216	+	39.7014i	−0.784361	+	1.35855i
$855$	10.3984	−	4.80653i	0.355617	−	0.164380i
$856$	−3.60926	+	6.25142i	−0.123362	+	0.213669i
$857$	33.5407	−	19.3647i	1.14573	−	0.661486i	0.197885	−	0.980225i	$-0.436593\pi$
$857$	33.5407	−	19.3647i	1.14573	−	0.661486i	0.947842	+	0.318739i	$0.103259\pi$
$858$	−5.94822	+	3.43420i	−0.203069	+	0.117242i
$859$	−2.80998	−	4.86702i	−0.0958751	−	0.166061i	0.814098	−	0.580727i	$-0.197232\pi$
$859$	−2.80998	−	4.86702i	−0.0958751	−	0.166061i	−0.909974	+	0.414666i	$0.863898\pi$
$860$	−10.1893	−	0.925833i	−0.347454	−	0.0315706i
$861$	−11.9744	+	20.7403i	−0.408087	+	0.706827i
$862$	10.9141	+	6.30128i	0.371737	+	0.214623i
$863$	−4.03169	+	2.32770i	−0.137240	+	0.0792357i	−0.567048	−	0.823685i	$-0.691915\pi$
$863$	−4.03169	+	2.32770i	−0.137240	+	0.0792357i	0.429808	+	0.902920i	$0.358581\pi$
$864$	1.00000			0.0340207
$865$	−25.6805	+	36.4155i	−0.873164	+	1.23816i
$866$	−13.1515			−0.446905
$867$			9.13958i			0.310396i
$868$	14.6189	+	8.17847i	0.496198	+	0.277595i
$869$	15.9316			0.540444
$870$	1.66645	−	18.3402i	0.0564979	−	0.621792i
$871$	8.82365	−	15.2830i	0.298978	−	0.517845i
$872$		−	5.56018i		−	0.188291i
$873$	1.36051	−	0.785493i	0.0460464	−	0.0265849i
$874$	−10.4164	+	18.0418i	−0.352342	+	0.610274i
$875$	24.0227	−	23.5449i	0.812114	−	0.795964i
$876$	6.82482			0.230589
$877$	−6.74812	+	3.89603i	−0.227868	+	0.131560i	−0.609588	−	0.792718i	$-0.708665\pi$
$877$	−6.74812	+	3.89603i	−0.227868	+	0.131560i	0.381720	+	0.924278i	$0.375332\pi$
$878$	−19.8795	+	11.4774i	−0.670900	+	0.387344i
$879$	−4.54063	−	7.86460i	−0.153152	−	0.265266i
$880$	2.19555	+	1.54832i	0.0740120	+	0.0521938i
$881$	−16.5085	−	28.5936i	−0.556186	−	0.963342i	−0.997810	−	0.0661419i	$-0.978931\pi$
$881$	−16.5085	−	28.5936i	−0.556186	−	0.963342i	0.441625	−	0.897200i	$-0.354402\pi$
$882$	−1.77675	−	1.02581i	−0.0598262	−	0.0345407i
$883$			44.9432i			1.51246i	0.654306	+	0.756230i	$0.272961\pi$
$883$			44.9432i			1.51246i	−0.654306	+	0.756230i	$0.727039\pi$
$884$	16.0274			0.539061
$885$	13.1865	−	18.6988i	0.443260	−	0.628552i
$886$	9.42386	+	16.3226i	0.316601	+	0.548368i
$887$	28.0557	+	16.1980i	0.942019	+	0.543875i	0.890593	−	0.454802i	$-0.150290\pi$
$887$	28.0557	+	16.1980i	0.942019	+	0.543875i	0.0514263	+	0.998677i	$0.483623\pi$
$888$	−9.68765	+	5.59317i	−0.325096	+	0.187694i
$889$	4.01739	+	6.95832i	0.134739	+	0.233374i
$890$	−3.57376	−	7.73143i	−0.119793	−	0.259158i
$891$	−1.20148			−0.0402510
$892$	−2.75021	−	1.58783i	−0.0920837	−	0.0531645i
$893$	6.44440	+	3.72068i	0.215654	+	0.124508i
$894$	−1.45123	−	2.51360i	−0.0485363	−	0.0840674i
$895$	−5.26925	+	57.9912i	−0.176132	+	1.93843i
$896$	1.50429	−	2.60552i	0.0502550	−	0.0870442i
$897$			23.2467i			0.776184i
$898$		−	4.98908i		−	0.166488i
$899$	−45.8508	+	0.620560i	−1.52921	+	0.0206968i
$900$	−4.91812	−	0.901189i	−0.163937	−	0.0300396i
$901$	−34.9432			−1.16413
$902$	8.28261	+	4.78197i	0.275781	+	0.159222i
$903$		−	13.7660i		−	0.458105i
$904$	−5.81222	−	10.0671i	−0.193311	−	0.334825i
$905$	−4.94663	−	3.48840i	−0.164431	−	0.115958i
$906$	−10.6834	+	18.5042i	−0.354932	+	0.614760i
$907$		−	45.2536i		−	1.50262i	−0.659948	−	0.751311i	$-0.729422\pi$
$907$		−	45.2536i		−	1.50262i	0.659948	−	0.751311i	$-0.270578\pi$
$908$	15.3879	−	8.88422i	0.510666	−	0.294833i
$909$	−3.16313	−	5.47871i	−0.104915	−	0.181717i
$910$	−16.1364	−	34.9092i	−0.534915	−	1.15723i
$911$	14.8705	−	25.7564i	0.492680	−	0.853347i	−0.507284	−	0.861779i	$-0.669351\pi$
$911$	14.8705	−	25.7564i	0.492680	−	0.853347i	0.999964	+	0.00843152i	$0.00268387\pi$
$912$	−4.43670	+	2.56153i	−0.146914	+	0.0848207i
$913$	−5.74701	−	3.31804i	−0.190198	−	0.109811i
$914$	−24.5919			−0.813428
$915$	−33.9322	−	3.08318i	−1.12176	−	0.101927i
$916$	2.26737	−	3.92720i	0.0749159	−	0.129758i
$917$	16.9917	−	9.81019i	0.561117	−	0.323961i
$918$	2.42803	+	1.40182i	0.0801368	+	0.0462670i
$919$	−9.10279	−	15.7665i	−0.300273	−	0.520089i	0.675924	−	0.736971i	$-0.263745\pi$
$919$	−9.10279	−	15.7665i	−0.300273	−	0.520089i	−0.976198	+	0.216882i	$0.930411\pi$
$920$	8.25384	−	3.81524i	0.272121	−	0.125785i
$921$	−2.82673	−	4.89604i	−0.0931440	−	0.161330i
$922$		−	21.5361i		−	0.709255i
$923$	−75.1803	−	43.4054i	−2.47459	−	1.42870i
$924$	−1.80738	+	3.13047i	−0.0594583	+	0.102985i
$925$	52.6855	−	18.7775i	1.73229	−	0.617399i
$926$	17.5396			0.576387
$927$	0.0305311	+	0.0176271i	0.00100277	+	0.000578951i
$928$			8.23579i			0.270353i
$929$	14.0921			0.462346			0.231173	−	0.972913i	$-0.425744\pi$
$929$	14.0921			0.462346			0.231173	+	0.972913i	$0.425744\pi$
$930$	−0.958695	+	12.4129i	−0.0314369	+	0.407036i
$931$	10.5105			0.344469
$932$			9.60124i			0.314499i
$933$	15.5865	+	8.99886i	0.510279	+	0.294610i
$934$	3.79669			0.124232
$935$	3.16039	+	6.83713i	0.103356	+	0.223598i
$936$	−2.85832	+	4.95075i	−0.0934271	+	0.161820i
$937$	8.35247	+	4.82230i	0.272863	+	0.157538i	0.630188	−	0.776442i	$-0.282978\pi$
$937$	8.35247	+	4.82230i	0.272863	+	0.157538i	−0.357325	+	0.933980i	$0.616311\pi$
$938$		−	9.28753i		−	0.303249i
$939$	15.6938	+	27.1825i	0.512148	+	0.887067i
$940$	−1.36278	−	2.94821i	−0.0444488	−	0.0961600i
$941$	19.6262	+	33.9935i	0.639795	+	1.10816i	0.985478	+	0.169806i	$0.0543140\pi$
$941$	19.6262	+	33.9935i	0.639795	+	1.10816i	−0.345683	+	0.938351i	$0.612353\pi$
$942$	7.63388	+	4.40742i	0.248725	+	0.143602i
$943$	28.0332	−	16.1850i	0.912885	−	0.527055i
$944$	−5.11629	+	8.86167i	−0.166521	+	0.288423i
$945$	0.608764	−	6.69981i	0.0198031	−	0.217945i
$946$	−5.49746			−0.178738
$947$	4.71490	+	2.72215i	0.153214	+	0.0884580i	0.574647	−	0.818401i	$-0.305139\pi$
$947$	4.71490	+	2.72215i	0.153214	+	0.0884580i	−0.421433	+	0.906860i	$0.638473\pi$
$948$	11.4835	−	6.63002i	0.372968	−	0.215333i
$949$	−19.5075	+	33.7880i	−0.633240	+	1.09680i
$950$	24.1286	−	8.59960i	0.782836	−	0.279008i
$951$	15.7958	+	27.3591i	0.512213	+	0.887178i
$952$	7.30494	−	4.21751i	0.236754	−	0.136690i
$953$			14.3903i			0.466146i	0.972459	+	0.233073i	$0.0748781\pi$
$953$			14.3903i			0.466146i	−0.972459	+	0.233073i	$0.925122\pi$
$954$	6.23175	−	10.7937i	0.201760	−	0.349459i
$955$	−33.4997	−	23.6243i	−1.08402	−	0.764463i
$956$	−6.54694	−	11.3396i	−0.211743	−	0.366750i
$957$		−	9.89511i		−	0.319864i
$958$	−4.67368	−	2.69835i	−0.151000	−	0.0871798i
$959$	62.4776			2.01751
$960$	2.22689	+	0.202342i	0.0718727	+	0.00653056i
$961$	30.9886	−	0.838975i	0.999634	−	0.0270637i
$962$		−	63.9483i		−	2.06177i
$963$		−	7.21852i		−	0.232613i
$964$	−9.00731	+	15.6011i	−0.290106	+	0.502478i
$965$	−37.2186	−	3.38179i	−1.19811	−	0.108864i
$966$	6.11721	+	10.5953i	0.196818	+	0.340899i
$967$	16.3034	+	9.41276i	0.524282	+	0.302694i	0.738685	−	0.674051i	$-0.235447\pi$
$967$	16.3034	+	9.41276i	0.524282	+	0.302694i	−0.214403	+	0.976745i	$0.568781\pi$
$968$	−8.27613	−	4.77823i	−0.266005	−	0.153578i
$969$	−14.3632			−0.461414
$970$	3.18866	−	1.47392i	0.102382	−	0.0473247i
$971$	−6.87588	−	11.9094i	−0.220657	−	0.382190i	0.734350	−	0.678771i	$-0.237487\pi$
$971$	−6.87588	−	11.9094i	−0.220657	−	0.382190i	−0.955008	+	0.296581i	$0.904154\pi$
$972$	−0.866025	+	0.500000i	−0.0277778	+	0.0160375i
$973$	−50.9460	−	29.4137i	−1.63325	−	0.942959i
$974$	4.11731	+	7.13139i	0.131927	+	0.228505i
$975$	18.5191	−	21.7725i	0.593086	−	0.697278i
$976$	15.2374			0.487739
$977$		−	28.3875i		−	0.908197i	−0.890951	−	0.454099i	$-0.849961\pi$
$977$		−	28.3875i		−	0.908197i	0.890951	−	0.454099i	$-0.150039\pi$
$978$	−14.8331	−	8.56391i	−0.474311	−	0.273844i
$979$	−2.28828	−	3.96342i	−0.0731338	−	0.126671i
$980$	−3.74907	−	2.64387i	−0.119760	−	0.0844554i
$981$	2.78009	+	4.81525i	0.0887614	+	0.153739i
$982$	−12.5430	+	7.24169i	−0.400262	+	0.231092i
$983$	9.65845	−	5.57631i	0.308057	−	0.177857i	−0.338000	−	0.941146i	$-0.609750\pi$
$983$	9.65845	−	5.57631i	0.308057	−	0.177857i	0.646057	+	0.763290i	$0.276417\pi$
$984$	7.96015			0.253760
$985$	−0.324303	+	0.459869i	−0.0103332	+	0.0146526i
$986$	−11.5451	+	19.9967i	−0.367671	+	0.636826i
$987$	3.78457	−	2.18502i	0.120464	−	0.0695500i
$988$		−	29.2867i		−	0.931734i
$989$	−9.30329	+	16.1138i	−0.295827	+	0.512388i
$990$	−2.67556	−	0.243109i	−0.0850349	−	0.00772652i
$991$	44.4401			1.41169			0.705843	−	0.708368i	$-0.250568\pi$
$991$	44.4401			1.41169			0.705843	+	0.708368i	$0.250568\pi$
$992$	−0.0753491	−	5.56725i	−0.00239234	−	0.176761i
$993$			30.4989i			0.967855i
$994$	−45.6873			−1.44911
$995$	−12.8516	−	9.06308i	−0.407424	−	0.287319i
$996$	−5.52326			−0.175011
$997$	−6.27533	+	3.62306i	−0.198742	+	0.114743i	−0.596068	−	0.802934i	$-0.703271\pi$
$997$	−6.27533	+	3.62306i	−0.198742	+	0.114743i	0.397327	+	0.917677i	$0.369938\pi$
$998$	11.9701	+	6.91092i	0.378906	+	0.218761i
$999$	5.59317	−	9.68765i	0.176960	−	0.306504i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.s.d.439.13	yes	28
5.4	even	2	inner	930.2.s.d.439.2	✓	28
31.25	even	3	inner	930.2.s.d.769.9	yes	28
155.149	even	6	inner	930.2.s.d.769.6	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.s.d.439.2	✓	28	5.4	even	2	inner
930.2.s.d.439.13	yes	28	1.1	even	1	trivial
930.2.s.d.769.6	yes	28	155.149	even	6	inner
930.2.s.d.769.9	yes	28	31.25	even	3	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000 q^{4} +(2.02972 - 0.938214i) q^{5} +(0.500000 - 0.866025i) q^{6} +(2.60552 + 1.50429i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000 q^{4} +(2.02972 - 0.938214i) q^{5} +(0.500000 - 0.866025i) q^{6} +(2.60552 + 1.50429i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(0.938214 + 2.02972i) q^{10} +(0.600738 + 1.04051i) q^{11} +(0.866025 + 0.500000i) q^{12} +(-4.95075 + 2.85832i) q^{13} +(-1.50429 + 2.60552i) q^{14} +(-2.22689 - 0.202342i) q^{15} +1.00000 q^{16} +(2.42803 + 1.40182i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(2.56153 - 4.43670i) q^{19} +(-2.02972 + 0.938214i) q^{20} +(-1.50429 - 2.60552i) q^{21} +(-1.04051 + 0.600738i) q^{22} +4.06649i q^{23} +(-0.500000 + 0.866025i) q^{24} +(3.23951 - 3.80862i) q^{25} +(-2.85832 - 4.95075i) q^{26} -1.00000i q^{27} +(-2.60552 - 1.50429i) q^{28} +8.23579 q^{29} +(0.202342 - 2.22689i) q^{30} +(-5.56725 + 0.0753491i) q^{31} +1.00000i q^{32} -1.20148i q^{33} +(-1.40182 + 2.42803i) q^{34} +(6.69981 + 0.608764i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(9.68765 + 5.59317i) q^{37} +(4.43670 + 2.56153i) q^{38} +5.71664 q^{39} +(-0.938214 - 2.02972i) q^{40} +(-3.98007 - 6.89369i) q^{41} +(2.60552 - 1.50429i) q^{42} +(3.96257 + 2.28779i) q^{43} +(-0.600738 - 1.04051i) q^{44} +(1.82738 + 1.28868i) q^{45} -4.06649 q^{46} +1.45252i q^{47} +(-0.866025 - 0.500000i) q^{48} +(1.02581 + 1.77675i) q^{49} +(3.80862 + 3.23951i) q^{50} +(-1.40182 - 2.42803i) q^{51} +(4.95075 - 2.85832i) q^{52} +(-10.7937 + 6.23175i) q^{53} +1.00000 q^{54} +(2.19555 + 1.54832i) q^{55} +(1.50429 - 2.60552i) q^{56} +(-4.43670 + 2.56153i) q^{57} +8.23579i q^{58} +(-5.11629 + 8.86167i) q^{59} +(2.22689 + 0.202342i) q^{60} +15.2374 q^{61} +(-0.0753491 - 5.56725i) q^{62} +3.00859i q^{63} -1.00000 q^{64} +(-7.36692 + 10.4464i) q^{65} +1.20148 q^{66} +(-2.67343 + 1.54350i) q^{67} +(-2.42803 - 1.40182i) q^{68} +(2.03325 - 3.52169i) q^{69} +(-0.608764 + 6.69981i) q^{70} +(7.59281 + 13.1511i) q^{71} +(0.866025 - 0.500000i) q^{72} +(5.91046 - 3.41241i) q^{73} +(-5.59317 + 9.68765i) q^{74} +(-4.70981 + 1.67861i) q^{75} +(-2.56153 + 4.43670i) q^{76} +3.61475i q^{77} +5.71664i q^{78} +(6.63002 - 11.4835i) q^{79} +(2.02972 - 0.938214i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(6.89369 - 3.98007i) q^{82} +(-4.78328 + 2.76163i) q^{83} +(1.50429 + 2.60552i) q^{84} +(6.24342 + 0.567295i) q^{85} +(-2.28779 + 3.96257i) q^{86} +(-7.13241 - 4.11790i) q^{87} +(1.04051 - 0.600738i) q^{88} -3.80912 q^{89} +(-1.28868 + 1.82738i) q^{90} -17.1990 q^{91} -4.06649i q^{92} +(4.85906 + 2.71837i) q^{93} -1.45252 q^{94} +(1.03661 - 11.4085i) q^{95} +(0.500000 - 0.866025i) q^{96} -1.57099i q^{97} +(-1.77675 + 1.02581i) q^{98} +(-0.600738 + 1.04051i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 28 q^{4} + 2 q^{5} + 14 q^{6} + 14 q^{9}+O(q^{10}) \) 28 * q - 28 * q^4 + 2 * q^5 + 14 * q^6 + 14 * q^9	\( 28 q - 28 q^{4} + 2 q^{5} + 14 q^{6} + 14 q^{9} + 4 q^{10} + 2 q^{11} - 8 q^{14} - 8 q^{15} + 28 q^{16} + 4 q^{19} - 2 q^{20} - 8 q^{21} - 14 q^{24} - 14 q^{25} - 12 q^{26} + 24 q^{29} + 4 q^{30} + 10 q^{34} + 8 q^{35} - 14 q^{36} + 24 q^{39} - 4 q^{40} + 20 q^{41} - 2 q^{44} - 2 q^{45} + 12 q^{46} + 2 q^{49} - 8 q^{50} + 10 q^{51} + 28 q^{54} + 6 q^{55} + 8 q^{56} - 20 q^{59} + 8 q^{60} + 32 q^{61} - 28 q^{64} - 12 q^{65} + 4 q^{66} - 6 q^{69} - 16 q^{70} - 16 q^{71} - 6 q^{74} - 8 q^{75} - 4 q^{76} + 10 q^{79} + 2 q^{80} - 14 q^{81} + 8 q^{84} + 72 q^{85} + 18 q^{86} - 80 q^{89} - 4 q^{90} + 32 q^{91} - 12 q^{94} - 32 q^{95} + 14 q^{96} - 2 q^{99}+O(q^{100}) \) 28 * q - 28 * q^4 + 2 * q^5 + 14 * q^6 + 14 * q^9 + 4 * q^10 + 2 * q^11 - 8 * q^14 - 8 * q^15 + 28 * q^16 + 4 * q^19 - 2 * q^20 - 8 * q^21 - 14 * q^24 - 14 * q^25 - 12 * q^26 + 24 * q^29 + 4 * q^30 + 10 * q^34 + 8 * q^35 - 14 * q^36 + 24 * q^39 - 4 * q^40 + 20 * q^41 - 2 * q^44 - 2 * q^45 + 12 * q^46 + 2 * q^49 - 8 * q^50 + 10 * q^51 + 28 * q^54 + 6 * q^55 + 8 * q^56 - 20 * q^59 + 8 * q^60 + 32 * q^61 - 28 * q^64 - 12 * q^65 + 4 * q^66 - 6 * q^69 - 16 * q^70 - 16 * q^71 - 6 * q^74 - 8 * q^75 - 4 * q^76 + 10 * q^79 + 2 * q^80 - 14 * q^81 + 8 * q^84 + 72 * q^85 + 18 * q^86 - 80 * q^89 - 4 * q^90 + 32 * q^91 - 12 * q^94 - 32 * q^95 + 14 * q^96 - 2 * q^99

Introduction

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