LMFDB - Embedded newform 1110.2.ba.b.619.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(529,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("1110.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.ba (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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			619.16
Character	$\chi$	$=$	1110.619
Dual form			1110.2.ba.b.529.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.64331 + 1.51642i) q^{5} -1.00000i q^{6} +(0.916644 - 0.529225i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.64331 + 1.51642i) q^{5} -1.00000i q^{6} +(0.916644 - 0.529225i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(2.13491 - 0.664945i) q^{10} -0.825600 q^{11} +(-0.866025 - 0.500000i) q^{12} +(-1.81865 - 3.14999i) q^{13} -1.05845i q^{14} +(2.18136 + 0.491597i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.742138 - 1.28542i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(4.75785 - 2.74695i) q^{19} +(0.491597 - 2.18136i) q^{20} +(0.529225 - 0.916644i) q^{21} +(-0.412800 + 0.714991i) q^{22} +2.23982 q^{23} +(-0.866025 + 0.500000i) q^{24} +(0.400968 + 4.98390i) q^{25} -3.63729 q^{26} -1.00000i q^{27} +(-0.916644 - 0.529225i) q^{28} -2.02537i q^{29} +(1.51642 - 1.64331i) q^{30} -6.27676i q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.714991 + 0.412800i) q^{33} +(-0.742138 - 1.28542i) q^{34} +(2.30886 + 0.520331i) q^{35} -1.00000 q^{36} +(5.95462 - 1.24197i) q^{37} -5.49389i q^{38} +(-3.14999 - 1.81865i) q^{39} +(-1.64331 - 1.51642i) q^{40} +(-1.42858 - 2.47438i) q^{41} +(-0.529225 - 0.916644i) q^{42} +10.6694 q^{43} +(0.412800 + 0.714991i) q^{44} +(2.13491 - 0.664945i) q^{45} +(1.11991 - 1.93975i) q^{46} +11.7632i q^{47} +1.00000i q^{48} +(-2.93984 + 5.09196i) q^{49} +(4.51666 + 2.14470i) q^{50} -1.48428i q^{51} +(-1.81865 + 3.14999i) q^{52} +(8.00978 + 4.62445i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(-1.35672 - 1.25195i) q^{55} +(-0.916644 + 0.529225i) q^{56} +(2.74695 - 4.75785i) q^{57} +(-1.75402 - 1.01268i) q^{58} +(-6.33426 - 3.65709i) q^{59} +(-0.664945 - 2.13491i) q^{60} +(-5.60990 + 3.23888i) q^{61} +(-5.43583 - 3.13838i) q^{62} -1.05845i q^{63} +1.00000 q^{64} +(1.78808 - 7.93425i) q^{65} +0.825600i q^{66} +(-11.2463 + 6.49307i) q^{67} -1.48428 q^{68} +(1.93975 - 1.11991i) q^{69} +(1.60505 - 1.73937i) q^{70} +(-0.701131 - 1.21439i) q^{71} +(-0.500000 + 0.866025i) q^{72} -8.82512i q^{73} +(1.90173 - 5.77784i) q^{74} +(2.83920 + 4.11570i) q^{75} +(-4.75785 - 2.74695i) q^{76} +(-0.756782 + 0.436928i) q^{77} +(-3.14999 + 1.81865i) q^{78} +(-3.10453 + 1.79240i) q^{79} +(-2.13491 + 0.664945i) q^{80} +(-0.500000 - 0.866025i) q^{81} -2.85716 q^{82} +(13.4101 + 7.74230i) q^{83} -1.05845 q^{84} +(3.16880 - 0.986962i) q^{85} +(5.33471 - 9.23999i) q^{86} +(-1.01268 - 1.75402i) q^{87} +0.825600 q^{88} +(-2.86558 - 1.65444i) q^{89} +(0.491597 - 2.18136i) q^{90} +(-3.33410 - 1.92495i) q^{91} +(-1.11991 - 1.93975i) q^{92} +(-3.13838 - 5.43583i) q^{93} +(10.1872 + 5.88160i) q^{94} +(11.9842 + 2.70078i) q^{95} +(0.866025 + 0.500000i) q^{96} -5.18358 q^{97} +(2.93984 + 5.09196i) q^{98} +(-0.412800 + 0.714991i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 18 q^{2} - 18 q^{4} + 4 q^{5} - 36 q^{8} + 18 q^{9}+O(q^{10}) $ 36 * q + 18 * q^2 - 18 * q^4 + 4 * q^5 - 36 * q^8 + 18 * q^9	$ 36 q + 18 q^{2} - 18 q^{4} + 4 q^{5} - 36 q^{8} + 18 q^{9} + 2 q^{10} + 4 q^{11} + 14 q^{13} + 2 q^{15} - 18 q^{16} - 18 q^{18} + 6 q^{19} - 2 q^{20} + 2 q^{22} + 20 q^{23} - 2 q^{25} + 28 q^{26} - 2 q^{30} + 18 q^{32} + 6 q^{33} - 20 q^{35} - 36 q^{36} - 20 q^{37} + 6 q^{39} - 4 q^{40} + 10 q^{41} - 2 q^{44} + 2 q^{45} + 10 q^{46} + 10 q^{49} - 4 q^{50} + 14 q^{52} + 12 q^{53} + 40 q^{55} - 8 q^{57} - 30 q^{58} + 18 q^{59} - 4 q^{60} - 6 q^{61} + 12 q^{62} + 36 q^{64} - 32 q^{65} - 36 q^{67} + 12 q^{69} - 40 q^{70} - 24 q^{71} - 18 q^{72} - 34 q^{74} + 8 q^{75} - 6 q^{76} + 24 q^{77} + 6 q^{78} - 2 q^{80} - 18 q^{81} + 20 q^{82} - 36 q^{83} + 26 q^{85} + 10 q^{87} - 4 q^{88} - 2 q^{90} - 36 q^{91} - 10 q^{92} - 12 q^{93} + 12 q^{94} + 18 q^{95} - 52 q^{97} - 10 q^{98} + 2 q^{99}+O(q^{100}) $ 36 * q + 18 * q^2 - 18 * q^4 + 4 * q^5 - 36 * q^8 + 18 * q^9 + 2 * q^10 + 4 * q^11 + 14 * q^13 + 2 * q^15 - 18 * q^16 - 18 * q^18 + 6 * q^19 - 2 * q^20 + 2 * q^22 + 20 * q^23 - 2 * q^25 + 28 * q^26 - 2 * q^30 + 18 * q^32 + 6 * q^33 - 20 * q^35 - 36 * q^36 - 20 * q^37 + 6 * q^39 - 4 * q^40 + 10 * q^41 - 2 * q^44 + 2 * q^45 + 10 * q^46 + 10 * q^49 - 4 * q^50 + 14 * q^52 + 12 * q^53 + 40 * q^55 - 8 * q^57 - 30 * q^58 + 18 * q^59 - 4 * q^60 - 6 * q^61 + 12 * q^62 + 36 * q^64 - 32 * q^65 - 36 * q^67 + 12 * q^69 - 40 * q^70 - 24 * q^71 - 18 * q^72 - 34 * q^74 + 8 * q^75 - 6 * q^76 + 24 * q^77 + 6 * q^78 - 2 * q^80 - 18 * q^81 + 20 * q^82 - 36 * q^83 + 26 * q^85 + 10 * q^87 - 4 * q^88 - 2 * q^90 - 36 * q^91 - 10 * q^92 - 12 * q^93 + 12 * q^94 + 18 * q^95 - 52 * q^97 - 10 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.64331	+	1.51642i	0.734913	+	0.678162i
$5$	1.64331	+	1.51642i	0.734913	+	0.678162i
$6$		−	1.00000i		−	0.408248i
$7$	0.916644	−	0.529225i	0.346459	−	0.200028i	−0.316666	−	0.948537i	$-0.602563\pi$
$7$	0.916644	−	0.529225i	0.346459	−	0.200028i	0.663125	+	0.748509i	$0.269230\pi$
$8$	−1.00000			−0.353553
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	2.13491	−	0.664945i	0.675118	−	0.210274i
$11$	−0.825600			−0.248928			−0.124464	−	0.992224i	$-0.539721\pi$
$11$	−0.825600			−0.248928			−0.124464	+	0.992224i	$0.539721\pi$
$12$	−0.866025	−	0.500000i	−0.250000	−	0.144338i
$13$	−1.81865	−	3.14999i	−0.504402	−	0.873649i	−0.999987	−	0.00509014i	$-0.998380\pi$
$13$	−1.81865	−	3.14999i	−0.504402	−	0.873649i	0.495585	−	0.868559i	$-0.334954\pi$
$14$		−	1.05845i		−	0.282883i
$15$	2.18136	+	0.491597i	0.563225	+	0.126930i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.742138	−	1.28542i	0.179995	−	0.311760i	−0.761884	−	0.647714i	$-0.775725\pi$
$17$	0.742138	−	1.28542i	0.179995	−	0.311760i	0.941879	+	0.335954i	$0.109059\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	4.75785	−	2.74695i	1.09153	−	0.630193i	0.157543	−	0.987512i	$-0.449643\pi$
$19$	4.75785	−	2.74695i	1.09153	−	0.630193i	0.933982	+	0.357319i	$0.116309\pi$
$20$	0.491597	−	2.18136i	0.109924	−	0.487767i
$21$	0.529225	−	0.916644i	0.115486	−	0.200028i
$22$	−0.412800	+	0.714991i	−0.0880093	+	0.152437i
$23$	2.23982			0.467036			0.233518	−	0.972353i	$-0.424976\pi$
$23$	2.23982			0.467036			0.233518	+	0.972353i	$0.424976\pi$
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$	0.400968	+	4.98390i	0.0801936	+	0.996779i
$26$	−3.63729			−0.713332
$27$		−	1.00000i		−	0.192450i
$28$	−0.916644	−	0.529225i	−0.173229	−	0.100014i
$29$		−	2.02537i		−	0.376101i	−0.982159	−	0.188050i	$-0.939783\pi$
$29$		−	2.02537i		−	0.376101i	0.982159	−	0.188050i	$-0.0602168\pi$
$30$	1.51642	−	1.64331i	0.276858	−	0.300027i
$31$		−	6.27676i		−	1.12734i	−0.826000	−	0.563669i	$-0.809389\pi$
$31$		−	6.27676i		−	1.12734i	0.826000	−	0.563669i	$-0.190611\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−0.714991	+	0.412800i	−0.124464	+	0.0718593i
$34$	−0.742138	−	1.28542i	−0.127276	−	0.220448i
$35$	2.30886	+	0.520331i	0.390269	+	0.0879519i
$36$	−1.00000			−0.166667
$37$	5.95462	−	1.24197i	0.978934	−	0.204179i
$37$	5.95462	−	1.24197i	0.978934	−	0.204179i
$38$		−	5.49389i		−	0.891227i
$39$	−3.14999	−	1.81865i	−0.504402	−	0.291216i
$40$	−1.64331	−	1.51642i	−0.259831	−	0.239766i
$41$	−1.42858	−	2.47438i	−0.223107	−	0.386433i	0.732643	−	0.680613i	$-0.238287\pi$
$41$	−1.42858	−	2.47438i	−0.223107	−	0.386433i	−0.955750	+	0.294181i	$0.904953\pi$
$42$	−0.529225	−	0.916644i	−0.0816612	−	0.141441i
$43$	10.6694			1.62707			0.813536	−	0.581515i	$-0.197540\pi$
$43$	10.6694			1.62707			0.813536	+	0.581515i	$0.197540\pi$
$44$	0.412800	+	0.714991i	0.0622319	+	0.107789i
$45$	2.13491	−	0.664945i	0.318254	−	0.0991241i
$46$	1.11991	−	1.93975i	0.165122	−	0.286000i
$47$			11.7632i			1.71584i	0.513783	+	0.857920i	$0.328244\pi$
$47$			11.7632i			1.71584i	−0.513783	+	0.857920i	$0.671756\pi$
$48$			1.00000i			0.144338i
$49$	−2.93984	+	5.09196i	−0.419977	+	0.727422i
$50$	4.51666	+	2.14470i	0.638753	+	0.303306i
$51$		−	1.48428i		−	0.207840i
$52$	−1.81865	+	3.14999i	−0.252201	+	0.436825i
$53$	8.00978	+	4.62445i	1.10023	+	0.635217i	0.936281	−	0.351252i	$-0.114244\pi$
$53$	8.00978	+	4.62445i	1.10023	+	0.635217i	0.163947	+	0.986469i	$0.447577\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$	−1.35672	−	1.25195i	−0.182940	−	0.168813i
$56$	−0.916644	+	0.529225i	−0.122492	+	0.0707206i
$57$	2.74695	−	4.75785i	0.363842	−	0.630193i
$58$	−1.75402	−	1.01268i	−0.230314	−	0.132972i
$59$	−6.33426	−	3.65709i	−0.824651	−	0.476112i	0.0273670	−	0.999625i	$-0.491288\pi$
$59$	−6.33426	−	3.65709i	−0.824651	−	0.476112i	−0.852018	+	0.523513i	$0.824621\pi$
$60$	−0.664945	−	2.13491i	−0.0858440	−	0.275616i
$61$	−5.60990	+	3.23888i	−0.718274	+	0.414696i	−0.814117	−	0.580701i	$-0.802779\pi$
$61$	−5.60990	+	3.23888i	−0.718274	+	0.414696i	0.0958432	+	0.995396i	$0.469445\pi$
$62$	−5.43583	−	3.13838i	−0.690351	−	0.398574i
$63$		−	1.05845i		−	0.133352i
$64$	1.00000			0.125000
$65$	1.78808	−	7.93425i	0.221784	−	0.984122i
$66$			0.825600i			0.101624i
$67$	−11.2463	+	6.49307i	−1.37396	+	0.793255i	−0.991424	−	0.130686i	$-0.958282\pi$
$67$	−11.2463	+	6.49307i	−1.37396	+	0.793255i	−0.382535	+	0.923941i	$0.624949\pi$
$68$	−1.48428			−0.179995
$69$	1.93975	−	1.11991i	0.233518	−	0.134822i
$70$	1.60505	−	1.73937i	0.191840	−	0.207894i
$71$	−0.701131	−	1.21439i	−0.0832089	−	0.144122i	0.821418	−	0.570327i	$-0.193184\pi$
$71$	−0.701131	−	1.21439i	−0.0832089	−	0.144122i	−0.904627	+	0.426205i	$0.859850\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$		−	8.82512i		−	1.03290i	−0.856317	−	0.516451i	$-0.827253\pi$
$73$		−	8.82512i		−	1.03290i	0.856317	−	0.516451i	$-0.172747\pi$
$74$	1.90173	−	5.77784i	0.221072	−	0.671660i
$75$	2.83920	+	4.11570i	0.327842	+	0.475240i
$76$	−4.75785	−	2.74695i	−0.545763	−	0.315096i
$77$	−0.756782	+	0.436928i	−0.0862433	+	0.0497926i
$78$	−3.14999	+	1.81865i	−0.356666	+	0.205921i
$79$	−3.10453	+	1.79240i	−0.349287	+	0.201661i	−0.664371	−	0.747403i	$-0.731300\pi$
$79$	−3.10453	+	1.79240i	−0.349287	+	0.201661i	0.315084	+	0.949064i	$0.397967\pi$
$80$	−2.13491	+	0.664945i	−0.238690	+	0.0743431i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−2.85716			−0.315521
$83$	13.4101	+	7.74230i	1.47195	+	0.849828i	0.999503	−	0.0315331i	$-0.0100390\pi$
$83$	13.4101	+	7.74230i	1.47195	+	0.849828i	0.472443	+	0.881361i	$0.343372\pi$
$84$	−1.05845			−0.115486
$85$	3.16880	−	0.986962i	0.343705	−	0.107051i
$86$	5.33471	−	9.23999i	0.575257	−	0.996374i
$87$	−1.01268	−	1.75402i	−0.108571	−	0.188050i
$88$	0.825600			0.0880093
$89$	−2.86558	−	1.65444i	−0.303751	−	0.175371i	0.340376	−	0.940289i	$-0.389446\pi$
$89$	−2.86558	−	1.65444i	−0.303751	−	0.175371i	−0.644127	+	0.764919i	$0.722779\pi$
$90$	0.491597	−	2.18136i	0.0518189	−	0.229936i
$91$	−3.33410	−	1.92495i	−0.349509	−	0.201789i
$92$	−1.11991	−	1.93975i	−0.116759	−	0.202232i
$93$	−3.13838	−	5.43583i	−0.325435	−	0.563669i
$94$	10.1872	+	5.88160i	1.05073	+	0.606641i
$95$	11.9842	+	2.70078i	1.22955	+	0.277094i
$96$	0.866025	+	0.500000i	0.0883883	+	0.0510310i
$97$	−5.18358			−0.526313			−0.263157	−	0.964753i	$-0.584764\pi$
$97$	−5.18358			−0.526313			−0.263157	+	0.964753i	$0.584764\pi$
$98$	2.93984	+	5.09196i	0.296969	+	0.514365i
$99$	−0.412800	+	0.714991i	−0.0414880	+	0.0718593i
$100$	4.11570	−	2.83920i	0.411570	−	0.283920i
$101$	−10.5205			−1.04682			−0.523412	−	0.852080i	$-0.675341\pi$
$101$	−10.5205			−1.04682			−0.523412	+	0.852080i	$0.675341\pi$
$102$	−1.28542	−	0.742138i	−0.127276	−	0.0734826i
$103$	−16.1758			−1.59385			−0.796923	−	0.604081i	$-0.793540\pi$
$103$	−16.1758			−1.59385			−0.796923	+	0.604081i	$0.793540\pi$
$104$	1.81865	+	3.14999i	0.178333	+	0.308882i
$105$	2.25970	−	0.703810i	0.220524	−	0.0686849i
$106$	8.00978	−	4.62445i	0.777979	−	0.449166i
$107$	−12.2112	+	7.05015i	−1.18050	+	0.681563i	−0.956131	−	0.292940i	$-0.905366\pi$
$107$	−12.2112	+	7.05015i	−1.18050	+	0.681563i	−0.224372	+	0.974504i	$0.572033\pi$
$108$	−0.866025	+	0.500000i	−0.0833333	+	0.0481125i
$109$	−4.54656	−	2.62496i	−0.435481	−	0.251425i	0.266198	−	0.963918i	$-0.414233\pi$
$109$	−4.54656	−	2.62496i	−0.435481	−	0.251425i	−0.701679	+	0.712493i	$0.747566\pi$
$110$	−1.76258	+	0.548978i	−0.168056	+	0.0523430i
$111$	4.53587	−	4.05289i	0.430525	−	0.384683i
$112$			1.05845i			0.100014i
$113$	1.67721	−	2.90502i	0.157779	−	0.273281i	−0.776288	−	0.630378i	$-0.782900\pi$
$113$	1.67721	−	2.90502i	0.157779	−	0.273281i	0.934067	+	0.357097i	$0.116233\pi$
$114$	−2.74695	−	4.75785i	−0.257275	−	0.445613i
$115$	3.68074	+	3.39651i	0.343231	+	0.316726i
$116$	−1.75402	+	1.01268i	−0.162856	+	0.0940252i
$117$	−3.63729			−0.336268
$118$	−6.33426	+	3.65709i	−0.583116	+	0.336662i
$119$		−	1.57103i		−	0.144016i
$120$	−2.18136	−	0.491597i	−0.199130	−	0.0448765i
$121$	−10.3184			−0.938035
$122$			6.47775i			0.586468i
$123$	−2.47438	−	1.42858i	−0.223107	−	0.128811i
$124$	−5.43583	+	3.13838i	−0.488152	+	0.281835i
$125$	−6.89874	+	8.79815i	−0.617042	+	0.786930i
$126$	−0.916644	−	0.529225i	−0.0816612	−	0.0471471i
$127$	5.43873	+	3.14005i	0.482609	+	0.278634i	0.721503	−	0.692411i	$-0.243452\pi$
$127$	5.43873	+	3.14005i	0.482609	+	0.278634i	−0.238894	+	0.971046i	$0.576785\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	9.23999	−	5.33471i	0.813536	−	0.469695i
$130$	−5.97722	−	5.51565i	−0.524237	−	0.483754i
$131$	11.2829	+	6.51420i	0.985794	+	0.569148i	0.904014	−	0.427502i	$-0.140606\pi$
$131$	11.2829	+	6.51420i	0.985794	+	0.569148i	0.0817796	+	0.996650i	$0.473940\pi$
$132$	0.714991	+	0.412800i	0.0622319	+	0.0359296i
$133$	2.90750	−	5.03594i	0.252113	−	0.436672i
$134$			12.9861i			1.12183i
$135$	1.51642	−	1.64331i	0.130512	−	0.141434i
$136$	−0.742138	+	1.28542i	−0.0636378	+	0.110224i
$137$			7.15737i			0.611496i	0.952113	+	0.305748i	$0.0989064\pi$
$137$			7.15737i			0.611496i	−0.952113	+	0.305748i	$0.901094\pi$
$138$		−	2.23982i		−	0.190667i
$139$	−5.76530	+	9.98579i	−0.489006	+	0.846983i	−0.999920	−	0.0126486i	$-0.995974\pi$
$139$	−5.76530	+	9.98579i	−0.489006	+	0.846983i	0.510914	+	0.859632i	$0.329307\pi$
$140$	−0.703810	−	2.25970i	−0.0594828	−	0.190979i
$141$	5.88160	+	10.1872i	0.495320	+	0.857920i
$142$	−1.40226			−0.117675
$143$	1.50147	+	2.60063i	0.125560	+	0.217476i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	3.07130	−	3.32831i	0.255057	−	0.276401i
$146$	−7.64277	−	4.41256i	−0.632520	−	0.365186i
$147$			5.87968i			0.484948i
$148$	−4.05289	−	4.53587i	−0.333145	−	0.372846i
$149$	−3.03860			−0.248932			−0.124466	−	0.992224i	$-0.539722\pi$
$149$	−3.03860			−0.248932			−0.124466	+	0.992224i	$0.539722\pi$
$150$	4.98390	−	0.400968i	0.406933	−	0.0327389i
$151$	−4.20011	−	7.27481i	−0.341800	−	0.592015i	0.642967	−	0.765894i	$-0.277703\pi$
$151$	−4.20011	−	7.27481i	−0.341800	−	0.592015i	−0.984767	+	0.173879i	$0.944370\pi$
$152$	−4.75785	+	2.74695i	−0.385913	+	0.222807i
$153$	−0.742138	−	1.28542i	−0.0599983	−	0.103920i
$154$			0.873856i			0.0704173i
$155$	9.51817	−	10.3147i	0.764518	−	0.828496i
$156$			3.63729i			0.291216i
$157$	−12.7985	−	7.38920i	−1.02143	−	0.589722i	−0.106911	−	0.994269i	$-0.534096\pi$
$157$	−12.7985	−	7.38920i	−1.02143	−	0.589722i	−0.914517	+	0.404546i	$0.867429\pi$
$158$			3.58480i			0.285191i
$159$	9.24890			0.733485
$160$	−0.491597	+	2.18136i	−0.0388641	+	0.172452i
$161$	2.05312	−	1.18537i	0.161809	−	0.0934203i
$162$	−1.00000			−0.0785674
$163$	−1.76345	+	3.05439i	−0.138124	+	0.239238i	−0.926787	−	0.375588i	$-0.877441\pi$
$163$	−1.76345	+	3.05439i	−0.138124	+	0.239238i	0.788662	+	0.614827i	$0.210774\pi$
$164$	−1.42858	+	2.47438i	−0.111554	+	0.193216i
$165$	−1.80093	−	0.405862i	−0.140202	−	0.0315963i
$166$	13.4101	−	7.74230i	1.04082	−	0.600919i
$167$	10.7385	+	18.5996i	0.830969	+	1.43928i	0.897270	+	0.441482i	$0.145547\pi$
$167$	10.7385	+	18.5996i	0.830969	+	1.43928i	−0.0663009	+	0.997800i	$0.521120\pi$
$168$	−0.529225	+	0.916644i	−0.0408306	+	0.0707206i
$169$	−0.114948	+	0.199096i	−0.00884218	+	0.0153151i
$170$	0.729666	−	3.23774i	0.0559628	−	0.248323i
$171$		−	5.49389i		−	0.420128i
$172$	−5.33471	−	9.23999i	−0.406768	−	0.704543i
$173$	2.69931	+	1.55845i	0.205225	+	0.118487i	0.599090	−	0.800681i	$-0.295529\pi$
$173$	2.69931	+	1.55845i	0.205225	+	0.118487i	−0.393865	+	0.919168i	$0.628862\pi$
$174$	−2.02537			−0.153543
$175$	3.00515	+	4.35626i	0.227168	+	0.329302i
$176$	0.412800	−	0.714991i	0.0311160	−	0.0538944i
$177$	−7.31417			−0.549767
$178$	−2.86558	+	1.65444i	−0.214784	+	0.124006i
$179$		−	10.0254i		−	0.749333i	−0.927160	−	0.374666i	$-0.877757\pi$
$179$		−	10.0254i		−	0.749333i	0.927160	−	0.374666i	$-0.122243\pi$
$180$	−1.64331	−	1.51642i	−0.122485	−	0.113027i
$181$	0.887705	+	1.53755i	0.0659826	+	0.114285i	0.897129	−	0.441768i	$-0.145648\pi$
$181$	0.887705	+	1.53755i	0.0659826	+	0.114285i	−0.831147	+	0.556053i	$0.812315\pi$
$182$	−3.33410	+	1.92495i	−0.247140	+	0.142686i
$183$	−3.23888	+	5.60990i	−0.239425	+	0.414696i
$184$	−2.23982			−0.165122
$185$	11.6687	+	6.98873i	0.857897	+	0.513822i
$186$	−6.27676			−0.460234
$187$	−0.612709	+	1.06124i	−0.0448058	+	0.0776058i
$188$	10.1872	−	5.88160i	0.742981	−	0.428960i
$189$	−0.529225	−	0.916644i	−0.0384954	−	0.0666761i
$190$	8.33102	−	9.02819i	0.604396	−	0.654974i
$191$			19.2656i			1.39401i	0.717066	+	0.697006i	$0.245485\pi$
$191$			19.2656i			1.39401i	−0.717066	+	0.697006i	$0.754515\pi$
$192$	0.866025	−	0.500000i	0.0625000	−	0.0360844i
$193$	18.5203			1.33312			0.666561	−	0.745451i	$-0.267766\pi$
$193$	18.5203			1.33312			0.666561	+	0.745451i	$0.267766\pi$
$194$	−2.59179	+	4.48912i	−0.186080	+	0.322300i
$195$	−2.41860	−	7.76530i	−0.173199	−	0.556085i
$196$	5.87968			0.419977
$197$	4.21694	+	2.43465i	0.300444	+	0.173462i	0.642642	−	0.766166i	$-0.277838\pi$
$197$	4.21694	+	2.43465i	0.300444	+	0.173462i	−0.342198	+	0.939628i	$0.611171\pi$
$198$	0.412800	+	0.714991i	0.0293364	+	0.0508122i
$199$			17.8813i			1.26757i	0.773509	+	0.633785i	$0.218500\pi$
$199$			17.8813i			1.26757i	−0.773509	+	0.633785i	$0.781500\pi$
$200$	−0.400968	−	4.98390i	−0.0283527	−	0.352415i
$201$	−6.49307	+	11.2463i	−0.457986	+	0.793255i
$202$	−5.26023	+	9.11098i	−0.370108	+	0.641046i
$203$	−1.07187	−	1.85654i	−0.0752308	−	0.130304i
$204$	−1.28542	+	0.742138i	−0.0899975	+	0.0519601i
$205$	1.40457	−	6.23251i	0.0980997	−	0.435297i
$206$	−8.08789	+	14.0086i	−0.563510	+	0.976028i
$207$	1.11991	−	1.93975i	0.0778393	−	0.134822i
$208$	3.63729			0.252201
$209$	−3.92808	+	2.26788i	−0.271711	+	0.156872i
$210$	0.520331	−	2.30886i	0.0359062	−	0.159326i
$211$	−0.395745			−0.0272442			−0.0136221	−	0.999907i	$-0.504336\pi$
$211$	−0.395745			−0.0272442			−0.0136221	+	0.999907i	$0.504336\pi$
$212$		−	9.24890i		−	0.635217i
$213$	−1.21439	−	0.701131i	−0.0832089	−	0.0480407i
$214$			14.1003i			0.963876i
$215$	17.5332	+	16.1793i	1.19576	+	1.10342i
$216$			1.00000i			0.0680414i
$217$	−3.32182	−	5.75355i	−0.225500	−	0.390577i
$218$	−4.54656	+	2.62496i	−0.307932	+	0.177785i
$219$	−4.41256	−	7.64277i	−0.298173	−	0.516451i
$220$	−0.405862	+	1.80093i	−0.0273632	+	0.121419i
$221$	−5.39875			−0.363159
$222$	−1.24197	−	5.95462i	−0.0833557	−	0.399648i
$223$		−	25.5883i		−	1.71352i	−0.515713	−	0.856761i	$-0.672473\pi$
$223$		−	25.5883i		−	1.71352i	0.515713	−	0.856761i	$-0.327527\pi$
$224$	0.916644	+	0.529225i	0.0612459	+	0.0353603i
$225$	4.51666	+	2.14470i	0.301111	+	0.142980i
$226$	−1.67721	−	2.90502i	−0.111567	−	0.193239i
$227$	11.6633	+	20.2013i	0.774117	+	1.34081i	0.935289	+	0.353884i	$0.115139\pi$
$227$	11.6633	+	20.2013i	0.774117	+	1.34081i	−0.161172	+	0.986926i	$0.551527\pi$
$228$	−5.49389			−0.363842
$229$	−11.6531	−	20.1837i	−0.770055	−	1.33377i	−0.937532	−	0.347899i	$-0.886895\pi$
$229$	−11.6531	−	20.1837i	−0.770055	−	1.33377i	0.167477	−	0.985876i	$-0.446438\pi$
$230$	4.78183	−	1.48936i	0.315304	−	0.0982055i
$231$	−0.436928	+	0.756782i	−0.0287478	+	0.0497926i
$232$			2.02537i			0.132972i
$233$		−	0.508726i		−	0.0333277i	−0.999861	−	0.0166639i	$-0.994695\pi$
$233$		−	0.508726i		−	0.0333277i	0.999861	−	0.0166639i	$-0.00530452\pi$
$234$	−1.81865	+	3.14999i	−0.118889	+	0.205921i
$235$	−17.8379	+	19.3307i	−1.16362	+	1.26099i
$236$			7.31417i			0.476112i
$237$	−1.79240	+	3.10453i	−0.116429	+	0.201661i
$238$	−1.36055	−	0.785516i	−0.0881916	−	0.0509174i
$239$	5.12135	+	2.95681i	0.331273	+	0.191260i	0.656406	−	0.754408i	$-0.272076\pi$
$239$	5.12135	+	2.95681i	0.331273	+	0.191260i	−0.325133	+	0.945668i	$0.605409\pi$
$240$	−1.51642	+	1.64331i	−0.0978842	+	0.106076i
$241$	1.48624	−	0.858078i	0.0957368	−	0.0552737i	−0.451367	−	0.892338i	$-0.649064\pi$
$241$	1.48624	−	0.858078i	0.0957368	−	0.0552737i	0.547104	+	0.837065i	$0.315730\pi$
$242$	−5.15919	+	8.93598i	−0.331645	+	0.574427i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	5.60990	+	3.23888i	0.359137	+	0.207348i
$245$	−12.5526	+	3.90966i	−0.801957	+	0.249779i
$246$	−2.47438	+	1.42858i	−0.157761	+	0.0910831i
$247$	−17.3057	−	9.99145i	−1.10113	−	0.635740i
$248$			6.27676i			0.398574i
$249$	15.4846			0.981297
$250$	4.17005	+	10.3736i	0.263737	+	0.656081i
$251$			16.7132i			1.05493i	0.849576	+	0.527465i	$0.176858\pi$
$251$			16.7132i			1.05493i	−0.849576	+	0.527465i	$0.823142\pi$
$252$	−0.916644	+	0.529225i	−0.0577432	+	0.0333380i
$253$	−1.84920			−0.116258
$254$	5.43873	−	3.14005i	0.341256	−	0.197024i
$255$	2.25078	−	2.43913i	0.140949	−	0.152744i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	1.47817	−	2.56026i	0.0922055	−	0.159705i	−0.816233	−	0.577722i	$-0.803942\pi$
$257$	1.47817	−	2.56026i	0.0922055	−	0.159705i	0.908439	+	0.418018i	$0.137275\pi$
$258$		−	10.6694i		−	0.664249i
$259$	4.80099	−	4.28978i	0.298319	−	0.266554i
$260$	−7.76530	+	2.41860i	−0.481583	+	0.149995i
$261$	−1.75402	−	1.01268i	−0.108571	−	0.0626835i
$262$	11.2829	−	6.51420i	0.697062	−	0.402449i
$263$	15.9056	−	9.18313i	0.980784	−	0.566256i	0.0782774	−	0.996932i	$-0.475058\pi$
$263$	15.9056	−	9.18313i	0.980784	−	0.566256i	0.902507	+	0.430676i	$0.141725\pi$
$264$	0.714991	−	0.412800i	0.0440046	−	0.0254061i
$265$	6.15001	+	19.7456i	0.377792	+	1.21296i
$266$	−2.90750	−	5.03594i	−0.178271	−	0.308774i
$267$	−3.30888			−0.202500
$268$	11.2463	+	6.49307i	0.686979	+	0.396628i
$269$	23.1442			1.41113			0.705563	−	0.708648i	$-0.250694\pi$
$269$	23.1442			1.41113			0.705563	+	0.708648i	$0.250694\pi$
$270$	−0.664945	−	2.13491i	−0.0404672	−	0.129927i
$271$	8.12733	−	14.0769i	0.493700	−	0.855113i	−0.506274	−	0.862373i	$-0.668977\pi$
$271$	8.12733	−	14.0769i	0.493700	−	0.855113i	0.999974	+	0.00725939i	$0.00231076\pi$
$272$	0.742138	+	1.28542i	0.0449987	+	0.0779401i
$273$	−3.84989			−0.233006
$274$	6.19847	+	3.57869i	0.374463	+	0.216196i
$275$	−0.331039	−	4.11471i	−0.0199624	−	0.248126i
$276$	−1.93975	−	1.11991i	−0.116759	−	0.0674108i
$277$	2.33406	+	4.04271i	0.140240	+	0.242903i	0.927587	−	0.373607i	$-0.121879\pi$
$277$	2.33406	+	4.04271i	0.140240	+	0.242903i	−0.787347	+	0.616510i	$0.788546\pi$
$278$	5.76530	+	9.98579i	0.345779	+	0.598908i
$279$	−5.43583	−	3.13838i	−0.325435	−	0.187890i
$280$	−2.30886	−	0.520331i	−0.137981	−	0.0310957i
$281$	12.2372	+	7.06515i	0.730010	+	0.421471i	0.818426	−	0.574612i	$-0.194847\pi$
$281$	12.2372	+	7.06515i	0.730010	+	0.421471i	−0.0884158	+	0.996084i	$0.528180\pi$
$282$	11.7632			0.700489
$283$	5.01437	+	8.68515i	0.298073	+	0.516278i	0.975695	−	0.219132i	$-0.0703226\pi$
$283$	5.01437	+	8.68515i	0.298073	+	0.516278i	−0.677622	+	0.735411i	$0.736989\pi$
$284$	−0.701131	+	1.21439i	−0.0416045	+	0.0720611i
$285$	11.7290	−	3.65313i	0.694765	−	0.216393i
$286$	3.00295			0.177568
$287$	−2.61900	−	1.51208i	−0.154595	−	0.0892554i
$288$	1.00000			0.0589256
$289$	7.39846	+	12.8145i	0.435204	+	0.753795i
$290$	−1.34676	−	4.32398i	−0.0790842	−	0.253913i
$291$	−4.48912	+	2.59179i	−0.263157	+	0.151934i
$292$	−7.64277	+	4.41256i	−0.447260	+	0.258225i
$293$	0.821707	−	0.474413i	0.0480046	−	0.0277155i	−0.475806	−	0.879550i	$-0.657843\pi$
$293$	0.821707	−	0.474413i	0.0480046	−	0.0277155i	0.523810	+	0.851835i	$0.324510\pi$
$294$	5.09196	+	2.93984i	0.296969	+	0.171455i
$295$	−4.86352	−	15.6151i	−0.283165	−	0.909147i
$296$	−5.95462	+	1.24197i	−0.346105	+	0.0721881i
$297$			0.825600i			0.0479062i
$298$	−1.51930	+	2.63151i	−0.0880107	+	0.152439i
$299$	−4.07345	−	7.05542i	−0.235574	−	0.408026i
$300$	2.14470	−	4.51666i	0.123824	−	0.260770i
$301$	9.78007	−	5.64652i	0.563714	−	0.325460i
$302$	−8.40022			−0.483379
$303$	−9.11098	+	5.26023i	−0.523412	+	0.302192i
$304$			5.49389i			0.315096i
$305$	−14.1303	−	3.18444i	−0.809099	−	0.182341i
$306$	−1.48428			−0.0848504
$307$			12.8973i			0.736088i	0.929808	+	0.368044i	$0.119972\pi$
$307$			12.8973i			0.736088i	−0.929808	+	0.368044i	$0.880028\pi$
$308$	0.756782	+	0.436928i	0.0431216	+	0.0248963i
$309$	−14.0086	+	8.08789i	−0.796923	+	0.460104i
$310$	−4.17370	−	13.4003i	−0.237050	−	0.761087i
$311$	−22.1356	−	12.7800i	−1.25520	−	0.724688i	−0.283060	−	0.959102i	$-0.591349\pi$
$311$	−22.1356	−	12.7800i	−1.25520	−	0.724688i	−0.972137	+	0.234414i	$0.924683\pi$
$312$	3.14999	+	1.81865i	0.178333	+	0.102961i
$313$	−2.35334	+	4.07611i	−0.133019	+	0.230395i	−0.924839	−	0.380359i	$-0.875800\pi$
$313$	−2.35334	+	4.07611i	−0.133019	+	0.230395i	0.791820	+	0.610754i	$0.209134\pi$
$314$	−12.7985	+	7.38920i	−0.722259	+	0.416997i
$315$	1.60505	−	1.73937i	0.0904343	−	0.0980022i
$316$	3.10453	+	1.79240i	0.174643	+	0.100830i
$317$	−21.7227	−	12.5416i	−1.22007	−	0.704407i	−0.255137	−	0.966905i	$-0.582120\pi$
$317$	−21.7227	−	12.5416i	−1.22007	−	0.704407i	−0.964933	+	0.262498i	$0.915454\pi$
$318$	4.62445	−	8.00978i	0.259326	−	0.449166i
$319$			1.67214i			0.0936219i
$320$	1.64331	+	1.51642i	0.0918641	+	0.0847702i
$321$	−7.05015	+	12.2112i	−0.393501	+	0.681563i
$322$		−	2.37074i		−	0.132116i
$323$		−	8.15446i		−	0.453726i
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	14.9700	−	10.3270i	0.830386	−	0.572838i
$326$	1.76345	+	3.05439i	0.0976686	+	0.169167i
$327$	−5.24991			−0.290321
$328$	1.42858	+	2.47438i	0.0788803	+	0.136625i
$329$	6.22538	+	10.7827i	0.343216	+	0.594468i
$330$	−1.25195	+	1.35672i	−0.0689177	+	0.0746850i
$331$	7.92971	+	4.57822i	0.435856	+	0.251642i	0.701838	−	0.712336i	$-0.252363\pi$
$331$	7.92971	+	4.57822i	0.435856	+	0.251642i	−0.265982	+	0.963978i	$0.585696\pi$
$332$		−	15.4846i		−	0.849828i
$333$	1.90173	−	5.77784i	0.104214	−	0.316624i
$334$	21.4770			1.17517
$335$	−28.3275	−	6.38395i	−1.54770	−	0.348793i
$336$	0.529225	+	0.916644i	0.0288716	+	0.0500070i
$337$	−8.94213	+	5.16274i	−0.487109	+	0.281232i	−0.723374	−	0.690456i	$-0.757410\pi$
$337$	−8.94213	+	5.16274i	−0.487109	+	0.281232i	0.236266	+	0.971689i	$0.424076\pi$
$338$	0.114948	+	0.199096i	0.00625236	+	0.0108294i
$339$		−	3.35443i		−	0.182188i
$340$	−2.43913	−	2.25078i	−0.132281	−	0.122066i
$341$			5.18209i			0.280626i
$342$	−4.75785	−	2.74695i	−0.257275	−	0.148538i
$343$			13.6325i			0.736086i
$344$	−10.6694			−0.575257
$345$	4.88587	+	1.10109i	0.263046	+	0.0592808i
$346$	2.69931	−	1.55845i	0.145116	−	0.0837827i
$347$	−25.3284			−1.35970			−0.679850	−	0.733351i	$-0.737955\pi$
$347$	−25.3284			−1.35970			−0.679850	+	0.733351i	$0.737955\pi$
$348$	−1.01268	+	1.75402i	−0.0542855	+	0.0940252i
$349$	11.2916	−	19.5576i	0.604426	−	1.04690i	−0.387716	−	0.921779i	$-0.626736\pi$
$349$	11.2916	−	19.5576i	0.604426	−	1.04690i	0.992142	−	0.125117i	$-0.0399308\pi$
$350$	5.27520	−	0.424404i	0.281971	−	0.0226854i
$351$	−3.14999	+	1.81865i	−0.168134	+	0.0970722i
$352$	−0.412800	−	0.714991i	−0.0220023	−	0.0381091i
$353$	11.5240	−	19.9601i	0.613360	−	1.06237i	−0.377310	−	0.926087i	$-0.623151\pi$
$353$	11.5240	−	19.9601i	0.613360	−	1.06237i	0.990670	−	0.136283i	$-0.0435156\pi$
$354$	−3.65709	+	6.33426i	−0.194372	+	0.336662i
$355$	0.689348	−	3.05884i	0.0365868	−	0.162346i
$356$			3.30888i			0.175371i
$357$	−0.785516	−	1.36055i	−0.0415739	−	0.0720081i
$358$	−8.68224	−	5.01269i	−0.458871	−	0.264929i
$359$	−15.2488			−0.804799			−0.402400	−	0.915464i	$-0.631824\pi$
$359$	−15.2488			−0.804799			−0.402400	+	0.915464i	$0.631824\pi$
$360$	−2.13491	+	0.664945i	−0.112520	+	0.0350457i
$361$	5.59142	−	9.68463i	0.294285	−	0.509717i
$362$	1.77541			0.0933135
$363$	−8.93598	+	5.15919i	−0.469017	+	0.270787i
$364$			3.84989i			0.201789i
$365$	13.3825	−	14.5024i	0.700474	−	0.759093i
$366$	3.23888	+	5.60990i	0.169299	+	0.293234i
$367$	−5.59808	+	3.23205i	−0.292217	+	0.168712i	−0.638941	−	0.769255i	$-0.720627\pi$
$367$	−5.59808	+	3.23205i	−0.292217	+	0.168712i	0.346724	+	0.937967i	$0.387294\pi$
$368$	−1.11991	+	1.93975i	−0.0583795	+	0.101116i
$369$	−2.85716			−0.148738
$370$	11.8867	−	6.61099i	0.617963	−	0.343689i
$371$	9.78949			0.508245
$372$	−3.13838	+	5.43583i	−0.162717	+	0.281835i
$373$	−22.1461	+	12.7860i	−1.14668	+	0.662036i	−0.948076	−	0.318044i	$-0.896974\pi$
$373$	−22.1461	+	12.7860i	−1.14668	+	0.662036i	−0.198604	+	0.980080i	$0.563641\pi$
$374$	0.612709	+	1.06124i	0.0316824	+	0.0548756i
$375$	−1.57541	+	11.0688i	−0.0813540	+	0.571590i
$376$		−	11.7632i		−	0.606641i
$377$	−6.37988	+	3.68342i	−0.328580	+	0.189706i
$378$	−1.05845			−0.0544408
$379$	0.395361	−	0.684786i	0.0203084	−	0.0351751i	−0.855693	−	0.517484i	$-0.826869\pi$
$379$	0.395361	−	0.684786i	0.0203084	−	0.0351751i	0.876001	+	0.482309i	$0.160202\pi$
$380$	−3.65313	−	11.7290i	−0.187402	−	0.601684i
$381$	6.28010			0.321739
$382$	16.6845	+	9.63281i	0.853654	+	0.492857i
$383$	7.08892	+	12.2784i	0.362227	+	0.627396i	0.988327	−	0.152347i	$-0.0486831\pi$
$383$	7.08892	+	12.2784i	0.362227	+	0.627396i	−0.626100	+	0.779743i	$0.715350\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	−1.90619	−	0.429585i	−0.0971487	−	0.0218937i
$386$	9.26016	−	16.0391i	0.471330	−	0.816367i
$387$	5.33471	−	9.23999i	0.271179	−	0.469695i
$388$	2.59179	+	4.48912i	0.131578	+	0.227900i
$389$	14.9727	−	8.64452i	0.759149	−	0.438295i	−0.0698414	−	0.997558i	$-0.522249\pi$
$389$	14.9727	−	8.64452i	0.759149	−	0.438295i	0.828990	+	0.559264i	$0.188916\pi$
$390$	−7.93425	−	1.78808i	−0.401766	−	0.0905430i
$391$	1.66226	−	2.87912i	0.0840641	−	0.145603i
$392$	2.93984	−	5.09196i	0.148484	−	0.257183i
$393$	13.0284			0.657196
$394$	4.21694	−	2.43465i	0.212446	−	0.122656i
$395$	−7.81974	−	1.76228i	−0.393454	−	0.0886697i
$396$	0.825600			0.0414880
$397$			5.32580i			0.267294i	0.991029	+	0.133647i	$0.0426689\pi$
$397$			5.32580i			0.267294i	−0.991029	+	0.133647i	$0.957331\pi$
$398$	15.4856	+	8.94064i	0.776225	+	0.448154i
$399$		−	5.81501i		−	0.291115i
$400$	−4.51666	−	2.14470i	−0.225833	−	0.107235i
$401$			29.8380i			1.49004i	0.667043	+	0.745019i	$0.267560\pi$
$401$			29.8380i			1.49004i	−0.667043	+	0.745019i	$0.732440\pi$
$402$	6.49307	+	11.2463i	0.323845	+	0.560916i
$403$	−19.7717	+	11.4152i	−0.984899	+	0.568632i
$404$	5.26023	+	9.11098i	0.261706	+	0.453288i
$405$	0.491597	−	2.18136i	0.0244276	−	0.108393i
$406$	−2.14375			−0.106392
$407$	−4.91613	+	1.02537i	−0.243684	+	0.0508258i
$408$			1.48428i			0.0734826i
$409$	−6.17878	−	3.56732i	−0.305521	−	0.176393i	0.339399	−	0.940642i	$-0.389776\pi$
$409$	−6.17878	−	3.56732i	−0.305521	−	0.176393i	−0.644921	+	0.764250i	$0.723110\pi$
$410$	−4.69522	−	4.33265i	−0.231880	−	0.213974i
$411$	3.57869	+	6.19847i	0.176524	+	0.305748i
$412$	8.08789	+	14.0086i	0.398462	+	0.690156i
$413$	−7.74169			−0.380943
$414$	−1.11991	−	1.93975i	−0.0550407	−	0.0953333i
$415$	10.2964	+	33.0583i	0.505431	+	1.62277i
$416$	1.81865	−	3.14999i	0.0891665	−	0.154441i
$417$			11.5306i			0.564655i
$418$			4.53576i			0.221851i
$419$	3.74432	−	6.48535i	0.182922	−	0.316830i	−0.759952	−	0.649979i	$-0.774778\pi$
$419$	3.74432	−	6.48535i	0.182922	−	0.316830i	0.942874	+	0.333149i	$0.108111\pi$
$420$	−1.73937	−	1.60505i	−0.0848724	−	0.0783184i
$421$		−	11.6772i		−	0.569114i	−0.958659	−	0.284557i	$-0.908153\pi$
$421$		−	11.6772i		−	0.569114i	0.958659	−	0.284557i	$-0.0918465\pi$
$422$	−0.197873	+	0.342726i	−0.00963229	+	0.0166836i
$423$	10.1872	+	5.88160i	0.495320	+	0.285973i
$424$	−8.00978	−	4.62445i	−0.388989	−	0.224583i
$425$	6.70398	+	3.18333i	0.325191	+	0.154414i
$426$	−1.21439	+	0.701131i	−0.0588376	+	0.0339699i
$427$	−3.42819	+	5.93779i	−0.165902	+	0.287350i
$428$	12.2112	+	7.05015i	0.590251	+	0.340782i
$429$	2.60063	+	1.50147i	0.125560	+	0.0724919i
$430$	22.7783	−	7.09458i	1.09847	−	0.342131i
$431$	−12.6642	+	7.31168i	−0.610013	+	0.352191i	−0.772971	−	0.634442i	$-0.781230\pi$
$431$	−12.6642	+	7.31168i	−0.610013	+	0.352191i	0.162957	+	0.986633i	$0.447897\pi$
$432$	0.866025	+	0.500000i	0.0416667	+	0.0240563i
$433$		−	39.9241i		−	1.91863i	−0.282341	−	0.959314i	$-0.591111\pi$
$433$		−	39.9241i		−	1.91863i	0.282341	−	0.959314i	$-0.408889\pi$
$434$	−6.64363			−0.318905
$435$	0.995663	−	4.41805i	0.0477384	−	0.211829i
$436$			5.24991i			0.251425i
$437$	10.6568	−	6.15268i	0.509782	−	0.294323i
$438$	−8.82512			−0.421680
$439$	1.05841	−	0.611072i	0.0505151	−	0.0291649i	−0.474530	−	0.880239i	$-0.657382\pi$
$439$	1.05841	−	0.611072i	0.0505151	−	0.0291649i	0.525045	+	0.851075i	$0.324049\pi$
$440$	1.35672	+	1.25195i	0.0646791	+	0.0596845i
$441$	2.93984	+	5.09196i	0.139992	+	0.242474i
$442$	−2.69937	+	4.67545i	−0.128396	+	0.222389i
$443$		−	7.35235i		−	0.349321i	−0.984629	−	0.174660i	$-0.944117\pi$
$443$		−	7.35235i		−	0.349321i	0.984629	−	0.174660i	$-0.0558828\pi$
$444$	−5.77784	−	1.90173i	−0.274204	−	0.0902522i
$445$	−2.20022	−	7.06418i	−0.104301	−	0.334874i
$446$	−22.1602	−	12.7942i	−1.04931	−	0.605822i
$447$	−2.63151	+	1.51930i	−0.124466	+	0.0718605i
$448$	0.916644	−	0.529225i	0.0433074	−	0.0250035i
$449$	10.2005	−	5.88927i	0.481392	−	0.277932i	−0.239604	−	0.970871i	$-0.577018\pi$
$449$	10.2005	−	5.88927i	0.481392	−	0.277932i	0.720997	+	0.692939i	$0.243684\pi$
$450$	4.11570	−	2.83920i	0.194016	−	0.133841i
$451$	1.17944	+	2.04285i	0.0555375	+	0.0961939i
$452$	−3.35443			−0.157779
$453$	−7.27481	−	4.20011i	−0.341800	−	0.197338i
$454$	23.3265			1.09477
$455$	−2.55996	−	8.21918i	−0.120013	−	0.385321i
$456$	−2.74695	+	4.75785i	−0.128638	+	0.222807i
$457$	−7.85584	−	13.6067i	−0.367481	−	0.636496i	0.621690	−	0.783263i	$-0.286446\pi$
$457$	−7.85584	−	13.6067i	−0.367481	−	0.636496i	−0.989171	+	0.146768i	$0.953113\pi$
$458$	−23.3061			−1.08902
$459$	−1.28542	−	0.742138i	−0.0599983	−	0.0346401i
$460$	1.10109	−	4.88587i	0.0513386	−	0.227805i
$461$	−21.3746	−	12.3407i	−0.995517	−	0.574762i	−0.0885978	−	0.996067i	$-0.528239\pi$
$461$	−21.3746	−	12.3407i	−0.995517	−	0.574762i	−0.906919	+	0.421306i	$0.861572\pi$
$462$	0.436928	+	0.756782i	0.0203277	+	0.0352087i
$463$	18.6610	+	32.3218i	0.867249	+	1.50212i	0.864796	+	0.502123i	$0.167448\pi$
$463$	18.6610	+	32.3218i	0.867249	+	1.50212i	0.00245324	+	0.999997i	$0.499219\pi$
$464$	1.75402	+	1.01268i	0.0814282	+	0.0470126i
$465$	3.08563	−	13.6919i	0.143093	−	0.634945i
$466$	−0.440570	−	0.254363i	−0.0204090	−	0.0117831i
$467$	−9.17134			−0.424399			−0.212200	−	0.977226i	$-0.568063\pi$
$467$	−9.17134			−0.424399			−0.212200	+	0.977226i	$0.568063\pi$
$468$	1.81865	+	3.14999i	0.0840670	+	0.145608i
$469$	−6.87259	+	11.9037i	−0.317347	+	0.549661i
$470$	7.82188	+	25.1134i	0.360797	+	1.15840i
$471$	−14.7784			−0.680953
$472$	6.33426	+	3.65709i	0.291558	+	0.168331i
$473$	−8.80868			−0.405023
$474$	1.79240	+	3.10453i	0.0823276	+	0.142596i
$475$	15.5982	+	22.6112i	0.715696	+	1.03747i
$476$	−1.36055	+	0.785516i	−0.0623609	+	0.0360041i
$477$	8.00978	−	4.62445i	0.366743	−	0.211739i
$478$	5.12135	−	2.95681i	0.234245	−	0.135242i
$479$	−3.81113	−	2.20036i	−0.174135	−	0.100537i	0.410399	−	0.911906i	$-0.365389\pi$
$479$	−3.81113	−	2.20036i	−0.174135	−	0.100537i	−0.584534	+	0.811369i	$0.698723\pi$
$480$	0.664945	+	2.13491i	0.0303504	+	0.0974449i
$481$	−14.7415	−	16.4983i	−0.672157	−	0.752257i
$482$		−	1.71616i		−	0.0781688i
$483$	1.18537	−	2.05312i	0.0539362	−	0.0934203i
$484$	5.15919	+	8.93598i	0.234509	+	0.406181i
$485$	−8.51826	−	7.86047i	−0.386794	−	0.356926i
$486$	−0.866025	+	0.500000i	−0.0392837	+	0.0226805i
$487$	−21.3719			−0.968451			−0.484226	−	0.874943i	$-0.660899\pi$
$487$	−21.3719			−0.968451			−0.484226	+	0.874943i	$0.660899\pi$
$488$	5.60990	−	3.23888i	0.253948	−	0.146617i
$489$			3.52691i			0.159492i
$490$	−2.89043	+	12.8257i	−0.130577	+	0.579406i
$491$	17.2381			0.777944			0.388972	−	0.921250i	$-0.372830\pi$
$491$	17.2381			0.777944			0.388972	+	0.921250i	$0.372830\pi$
$492$			2.85716i			0.128811i
$493$	−2.60345	−	1.50310i	−0.117253	−	0.0676963i
$494$	−17.3057	+	9.99145i	−0.778620	+	0.449536i
$495$	−1.76258	+	0.548978i	−0.0792222	+	0.0246747i
$496$	5.43583	+	3.13838i	0.244076	+	0.140917i
$497$	−1.28538	−	0.742112i	−0.0576570	−	0.0332883i
$498$	7.74230	−	13.4101i	0.346941	−	0.600919i
$499$	27.1360	−	15.6670i	1.21478	−	0.701351i	0.250979	−	0.967992i	$-0.419247\pi$
$499$	27.1360	−	15.6670i	1.21478	−	0.701351i	0.963796	+	0.266642i	$0.0859140\pi$
$500$	11.0688	+	1.57541i	0.495011	+	0.0704546i
$501$	18.5996	+	10.7385i	0.830969	+	0.479760i
$502$	14.4741	+	8.35662i	0.646011	+	0.372974i
$503$	7.38550	−	12.7921i	0.329303	−	0.570370i	−0.653070	−	0.757297i	$-0.726519\pi$
$503$	7.38550	−	12.7921i	0.329303	−	0.570370i	0.982374	+	0.186927i	$0.0598528\pi$
$504$			1.05845i			0.0471471i
$505$	−17.2884	−	15.9534i	−0.769324	−	0.709916i
$506$	−0.924600	+	1.60145i	−0.0411035	+	0.0711933i
$507$			0.229897i			0.0102101i
$508$		−	6.28010i		−	0.278634i
$509$	10.6815	−	18.5009i	0.473449	−	0.820039i	−0.526089	−	0.850430i	$-0.676342\pi$
$509$	10.6815	−	18.5009i	0.473449	−	0.820039i	0.999538	+	0.0303912i	$0.00967531\pi$
$510$	−0.986962	−	3.16880i	−0.0437034	−	0.140317i
$511$	−4.67047	−	8.08949i	−0.206609	−	0.357858i
$512$	−1.00000			−0.0441942
$513$	−2.74695	−	4.75785i	−0.121281	−	0.210064i
$514$	−1.47817	−	2.56026i	−0.0651991	−	0.112928i
$515$	−26.5819	−	24.5292i	−1.17134	−	1.08089i
$516$	−9.23999	−	5.33471i	−0.406768	−	0.234848i
$517$		−	9.71171i		−	0.427120i
$518$	−1.31456	−	6.30267i	−0.0577586	−	0.276923i
$519$	3.11690			0.136817
$520$	−1.78808	+	7.93425i	−0.0784126	+	0.347940i
$521$	16.6844	+	28.8982i	0.730957	+	1.26606i	0.956474	+	0.291816i	$0.0942595\pi$
$521$	16.6844	+	28.8982i	0.730957	+	1.26606i	−0.225517	+	0.974239i	$0.572407\pi$
$522$	−1.75402	+	1.01268i	−0.0767713	+	0.0443239i
$523$	6.52639	+	11.3040i	0.285379	+	0.494291i	0.972701	−	0.232062i	$-0.0745472\pi$
$523$	6.52639	+	11.3040i	0.285379	+	0.494291i	−0.687322	+	0.726353i	$0.741214\pi$
$524$		−	13.0284i		−	0.569148i
$525$	4.78066	+	2.27006i	0.208645	+	0.0990734i
$526$		−	18.3663i		−	0.800807i
$527$	−8.06828	−	4.65822i	−0.351460	−	0.202915i
$528$		−	0.825600i		−	0.0359296i
$529$	−17.9832			−0.781878
$530$	20.1752	+	4.54673i	0.876354	+	0.197497i
$531$	−6.33426	+	3.65709i	−0.274884	+	0.158704i
$532$	−5.81501			−0.252113
$533$	−5.19617	+	9.00003i	−0.225071	+	0.389835i
$534$	−1.65444	+	2.86558i	−0.0715947	+	0.124006i
$535$	−30.7578	−	6.93166i	−1.32978	−	0.299682i
$536$	11.2463	−	6.49307i	0.485768	−	0.280458i
$537$	−5.01269	−	8.68224i	−0.216314	−	0.374666i
$538$	11.5721	−	20.0434i	0.498908	−	0.864134i
$539$	2.42713	−	4.20392i	0.104544	−	0.181076i
$540$	−2.18136	−	0.491597i	−0.0938708	−	0.0211550i
$541$		−	21.6228i		−	0.929635i	−0.885406	−	0.464818i	$-0.846120\pi$
$541$		−	21.6228i		−	0.929635i	0.885406	−	0.464818i	$-0.153880\pi$
$542$	−8.12733	−	14.0769i	−0.349099	−	0.604657i
$543$	1.53755	+	0.887705i	0.0659826	+	0.0380951i
$544$	1.48428			0.0636378
$545$	−3.49090	−	11.2081i	−0.149534	−	0.480102i
$546$	−1.92495	+	3.33410i	−0.0823801	+	0.142686i
$547$	19.0025			0.812488			0.406244	−	0.913765i	$-0.366838\pi$
$547$	19.0025			0.812488			0.406244	+	0.913765i	$0.366838\pi$
$548$	6.19847	−	3.57869i	0.264785	−	0.152874i
$549$			6.47775i			0.276464i
$550$	−3.72896	−	1.77066i	−0.159003	−	0.0755014i
$551$	−5.56357	−	9.63638i	−0.237016	−	0.410524i
$552$	−1.93975	+	1.11991i	−0.0825610	+	0.0476666i
$553$	−1.89716	+	3.28599i	−0.0806757	+	0.139734i
$554$	4.66812			0.198329
$555$	13.5997	+	0.218086i	0.577276	+	0.00925722i
$556$	11.5306			0.489006
$557$	−18.9136	+	32.7593i	−0.801395	+	1.38806i	0.117304	+	0.993096i	$0.462575\pi$
$557$	−18.9136	+	32.7593i	−0.801395	+	1.38806i	−0.918698	+	0.394960i	$0.870758\pi$
$558$	−5.43583	+	3.13838i	−0.230117	+	0.132858i
$559$	−19.4039	−	33.6086i	−0.820698	−	1.42149i
$560$	−1.60505	+	1.73937i	−0.0678257	+	0.0735016i
$561$			1.22542i			0.0517372i
$562$	12.2372	−	7.06515i	0.516195	−	0.298025i
$563$	−2.80373			−0.118163			−0.0590815	−	0.998253i	$-0.518817\pi$
$563$	−2.80373			−0.118163			−0.0590815	+	0.998253i	$0.518817\pi$
$564$	5.88160	−	10.1872i	0.247660	−	0.428960i
$565$	7.16141	−	2.23051i	0.301283	−	0.0938383i
$566$	10.0287			0.421539
$567$	−0.916644	−	0.529225i	−0.0384954	−	0.0222254i
$568$	0.701131	+	1.21439i	0.0294188	+	0.0509549i
$569$		−	39.6236i		−	1.66111i	−0.556937	−	0.830555i	$-0.688024\pi$
$569$		−	39.6236i		−	1.66111i	0.556937	−	0.830555i	$-0.311976\pi$
$570$	2.70078	−	11.9842i	0.113123	−	0.501961i
$571$	−3.77916	+	6.54570i	−0.158153	+	0.273929i	−0.934203	−	0.356743i	$-0.883887\pi$
$571$	−3.77916	+	6.54570i	−0.158153	+	0.273929i	0.776050	+	0.630672i	$0.217221\pi$
$572$	1.50147	−	2.60063i	0.0627798	−	0.108738i
$573$	9.63281	+	16.6845i	0.402416	+	0.697006i
$574$	−2.61900	+	1.51208i	−0.109315	+	0.0631131i
$575$	0.898098	+	11.1631i	0.0374533	+	0.465532i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	14.7782	−	25.5966i	0.615224	−	1.06560i	−0.375121	−	0.926976i	$-0.622399\pi$
$577$	14.7782	−	25.5966i	0.615224	−	1.06560i	0.990345	−	0.138624i	$-0.0442680\pi$
$578$	14.7969			0.615471
$579$	16.0391	−	9.26016i	0.666561	−	0.384839i
$580$	−4.41805	−	0.995663i	−0.183450	−	0.0413427i
$581$	16.3897			0.679958
$582$			5.18358i			0.214867i
$583$	−6.61288	−	3.81795i	−0.273877	−	0.158123i
$584$			8.82512i			0.365186i
$585$	−5.97722	−	5.51565i	−0.247128	−	0.228044i
$586$		−	0.948825i		−	0.0391956i
$587$	−16.1870	−	28.0366i	−0.668108	−	1.15720i	−0.978433	−	0.206566i	$-0.933771\pi$
$587$	−16.1870	−	28.0366i	−0.668108	−	1.15720i	0.310325	−	0.950631i	$-0.399562\pi$
$588$	5.09196	−	2.93984i	0.209989	−	0.121237i
$589$	−17.2419	−	29.8639i	−0.710441	−	1.23052i
$590$	−15.9549	−	3.59563i	−0.656851	−	0.148030i
$591$	4.86930			0.200296
$592$	−1.90173	+	5.77784i	−0.0781607	+	0.237468i
$593$		−	8.03864i		−	0.330107i	−0.986285	−	0.165054i	$-0.947220\pi$
$593$		−	8.03864i		−	0.330107i	0.986285	−	0.165054i	$-0.0527797\pi$
$594$	0.714991	+	0.412800i	0.0293364	+	0.0169374i
$595$	2.38234	−	2.58170i	0.0976663	−	0.105839i
$596$	1.51930	+	2.63151i	0.0622330	+	0.107791i
$597$	8.94064	+	15.4856i	0.365916	+	0.633785i
$598$	−8.14690			−0.333151
$599$	−1.25133	−	2.16737i	−0.0511279	−	0.0885562i	0.839329	−	0.543624i	$-0.182948\pi$
$599$	−1.25133	−	2.16737i	−0.0511279	−	0.0885562i	−0.890457	+	0.455068i	$0.849615\pi$
$600$	−2.83920	−	4.11570i	−0.115910	−	0.168023i
$601$	8.38293	−	14.5197i	0.341947	−	0.592269i	−0.642847	−	0.765994i	$-0.722247\pi$
$601$	8.38293	−	14.5197i	0.341947	−	0.592269i	0.984794	+	0.173725i	$0.0555804\pi$
$602$		−	11.2930i		−	0.460270i
$603$			12.9861i			0.528837i
$604$	−4.20011	+	7.27481i	−0.170900	+	0.296008i
$605$	−16.9564	−	15.6470i	−0.689374	−	0.636139i
$606$			10.5205i			0.427364i
$607$	5.24017	−	9.07623i	0.212692	−	0.368393i	−0.739864	−	0.672756i	$-0.765110\pi$
$607$	5.24017	−	9.07623i	0.212692	−	0.368393i	0.952556	+	0.304363i	$0.0984436\pi$
$608$	4.75785	+	2.74695i	0.192956	+	0.111403i
$609$	−1.85654	−	1.07187i	−0.0752308	−	0.0434345i
$610$	−9.82296	+	10.6450i	−0.397720	+	0.431003i
$611$	37.0540	−	21.3931i	1.49904	−	0.865473i
$612$	−0.742138	+	1.28542i	−0.0299992	+	0.0519601i
$613$	−5.61834	−	3.24375i	−0.226923	−	0.131014i	0.382229	−	0.924068i	$-0.375157\pi$
$613$	−5.61834	−	3.24375i	−0.226923	−	0.131014i	−0.609152	+	0.793054i	$0.708490\pi$
$614$	11.1694	+	6.44866i	0.450760	+	0.260247i
$615$	−1.89986	−	6.09979i	−0.0766096	−	0.245967i
$616$	0.756782	−	0.436928i	0.0304916	−	0.0176043i
$617$	20.5224	+	11.8486i	0.826200	+	0.477007i	0.852550	−	0.522646i	$-0.175055\pi$
$617$	20.5224	+	11.8486i	0.826200	+	0.477007i	−0.0263501	+	0.999653i	$0.508388\pi$
$618$			16.1758i			0.650685i
$619$	−31.0146			−1.24658			−0.623291	−	0.781990i	$-0.714205\pi$
$619$	−31.0146			−1.24658			−0.623291	+	0.781990i	$0.714205\pi$
$620$	−13.6919	−	3.08563i	−0.549879	−	0.123922i
$621$		−	2.23982i		−	0.0898811i
$622$	−22.1356	+	12.7800i	−0.887558	+	0.512432i
$623$	−3.50229			−0.140316
$624$	3.14999	−	1.81865i	0.126100	−	0.0728041i
$625$	−24.6784	+	3.99676i	−0.987138	+	0.159871i
$626$	2.35334	+	4.07611i	0.0940585	+	0.162914i
$627$	−2.26788	+	3.92808i	−0.0905703	+	0.156872i
$628$			14.7784i			0.589722i
$629$	2.82270	−	8.57591i	0.112548	−	0.341944i
$630$	−0.703810	−	2.25970i	−0.0280405	−	0.0900285i
$631$	9.21344	+	5.31938i	0.366781	+	0.211761i	0.672051	−	0.740504i	$-0.265413\pi$
$631$	9.21344	+	5.31938i	0.366781	+	0.211761i	−0.305270	+	0.952266i	$0.598747\pi$
$632$	3.10453	−	1.79240i	0.123491	−	0.0712978i
$633$	−0.342726	+	0.197873i	−0.0136221	+	0.00786473i
$634$	−21.7227	+	12.5416i	−0.862719	+	0.498091i
$635$	4.17592	+	13.4075i	0.165716	+	0.532059i
$636$	−4.62445	−	8.00978i	−0.183371	−	0.317609i
$637$	21.3861			0.847349
$638$	1.44812	+	0.836071i	0.0573315	+	0.0331004i
$639$	−1.40226			−0.0554726
$640$	2.13491	−	0.664945i	0.0843898	−	0.0262842i
$641$	4.38870	−	7.60145i	0.173343	−	0.300239i	−0.766243	−	0.642550i	$-0.777876\pi$
$641$	4.38870	−	7.60145i	0.173343	−	0.300239i	0.939587	+	0.342311i	$0.111210\pi$
$642$	7.05015	+	12.2112i	0.278247	+	0.481938i
$643$	−26.7207			−1.05376			−0.526882	−	0.849939i	$-0.676639\pi$
$643$	−26.7207			−1.05376			−0.526882	+	0.849939i	$0.676639\pi$
$644$	−2.05312	−	1.18537i	−0.0809044	−	0.0467102i
$645$	23.2739	+	5.24506i	0.916407	+	0.206524i
$646$	−7.06197	−	4.07723i	−0.277849	−	0.160416i
$647$	9.72305	+	16.8408i	0.382252	+	0.662081i	0.991384	−	0.130989i	$-0.0418151\pi$
$647$	9.72305	+	16.8408i	0.382252	+	0.662081i	−0.609131	+	0.793069i	$0.708482\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	5.22957	+	3.01929i	0.205278	+	0.118518i
$650$	−1.45844	−	18.1279i	−0.0572046	−	0.711034i
$651$	−5.75355	−	3.32182i	−0.225500	−	0.130192i
$652$	3.52691			0.138124
$653$	−12.7773	−	22.1309i	−0.500014	−	0.866049i	−1.00000		1.60106e-5i	$-0.999995\pi$
$653$	−12.7773	−	22.1309i	−0.500014	−	0.866049i	0.499986	−	0.866033i	$-0.333338\pi$
$654$	−2.62496	+	4.54656i	−0.102644	+	0.177785i
$655$	8.66317	+	27.8145i	0.338498	+	1.08680i
$656$	2.85716			0.111554
$657$	−7.64277	−	4.41256i	−0.298173	−	0.172150i
$658$	12.4508			0.485381
$659$	1.11439	+	1.93019i	0.0434106	+	0.0751893i	0.886914	−	0.461934i	$-0.152844\pi$
$659$	1.11439	+	1.93019i	0.0434106	+	0.0751893i	−0.843504	+	0.537123i	$0.819511\pi$
$660$	0.548978	+	1.76258i	0.0213690	+	0.0686085i
$661$	10.9781	−	6.33818i	0.426997	−	0.246527i	−0.271070	−	0.962560i	$-0.587377\pi$
$661$	10.9781	−	6.33818i	0.426997	−	0.246527i	0.698066	+	0.716033i	$0.254044\pi$
$662$	7.92971	−	4.57822i	0.308197	−	0.177938i
$663$	−4.67545	+	2.69937i	−0.181580	+	0.104835i
$664$	−13.4101	−	7.74230i	−0.520411	−	0.300460i
$665$	12.4145	−	3.86666i	0.481415	−	0.149943i
$666$	−4.05289	−	4.53587i	−0.157046	−	0.175761i
$667$		−	4.53646i		−	0.175653i
$668$	10.7385	−	18.5996i	0.415485	−	0.719641i
$669$	−12.7942	−	22.1602i	−0.494651	−	0.856761i
$670$	−19.6924	+	21.3403i	−0.760784	+	0.824449i
$671$	4.63153	−	2.67402i	0.178798	−	0.103229i
$672$	1.05845			0.0408306
$673$	34.8308	−	20.1096i	1.34263	−	0.775168i	0.355438	−	0.934700i	$-0.384332\pi$
$673$	34.8308	−	20.1096i	1.34263	−	0.775168i	0.987193	+	0.159532i	$0.0509985\pi$
$674$			10.3255i			0.397723i
$675$	4.98390	−	0.400968i	0.191830	−	0.0154333i
$676$	0.229897			0.00884218
$677$		−	29.7892i		−	1.14489i	−0.819942	−	0.572446i	$-0.805995\pi$
$677$		−	29.7892i		−	1.14489i	0.819942	−	0.572446i	$-0.194005\pi$
$678$	−2.90502	−	1.67721i	−0.111567	−	0.0644130i
$679$	−4.75150	+	2.74328i	−0.182346	+	0.105277i
$680$	−3.16880	+	0.986962i	−0.121518	+	0.0378483i
$681$	20.2013	+	11.6633i	0.774117	+	0.446937i
$682$	4.48782	+	2.59105i	0.171848	+	0.0992163i
$683$	10.7369	−	18.5968i	0.410835	−	0.711587i	−0.584146	−	0.811649i	$-0.698571\pi$
$683$	10.7369	−	18.5968i	0.410835	−	0.711587i	0.994981	+	0.100061i	$0.0319038\pi$
$684$	−4.75785	+	2.74695i	−0.181921	+	0.105032i
$685$	−10.8536	+	11.7618i	−0.414693	+	0.449396i
$686$	11.8061	+	6.81625i	0.450759	+	0.260246i
$687$	−20.1837	−	11.6531i	−0.770055	−	0.444592i
$688$	−5.33471	+	9.23999i	−0.203384	+	0.352271i
$689$		−	33.6410i		−	1.28162i
$690$	3.39651	−	3.68074i	0.129303	−	0.140123i
$691$	7.87430	−	13.6387i	0.299553	−	0.518840i	−0.676481	−	0.736460i	$-0.736496\pi$
$691$	7.87430	−	13.6387i	0.299553	−	0.518840i	0.976034	+	0.217620i	$0.0698293\pi$
$692$		−	3.11690i		−	0.118487i
$693$			0.873856i			0.0331950i
$694$	−12.6642	+	21.9350i	−0.480727	+	0.832643i
$695$	−24.6168	+	7.66721i	−0.933768	+	0.290834i
$696$	1.01268	+	1.75402i	0.0383856	+	0.0664859i
$697$	−4.24082			−0.160633
$698$	−11.2916	−	19.5576i	−0.427394	−	0.740268i
$699$	−0.254363	−	0.440570i	−0.00962089	−	0.0166639i
$700$	2.27006	−	4.78066i	0.0858001	−	0.180692i
$701$	−32.3179	−	18.6588i	−1.22063	−	0.704732i	−0.255579	−	0.966788i	$-0.582266\pi$
$701$	−32.3179	−	18.6588i	−1.22063	−	0.704732i	−0.965053	+	0.262056i	$0.915600\pi$
$702$			3.63729i			0.137281i
$703$	24.9196	−	22.2661i	0.939859	−	0.839783i
$704$	−0.825600			−0.0311160
$705$	−5.78276	+	25.6598i	−0.217791	+	0.966404i
$706$	−11.5240	−	19.9601i	−0.433711	−	0.751209i
$707$	−9.64351	+	5.56768i	−0.362682	+	0.209394i
$708$	3.65709	+	6.33426i	0.137442	+	0.238056i
$709$			27.0809i			1.01705i	0.861048	+	0.508523i	$0.169808\pi$
$709$			27.0809i			1.01705i	−0.861048	+	0.508523i	$0.830192\pi$
$710$	−2.30436	−	2.12641i	−0.0864810	−	0.0798028i
$711$			3.58480i			0.134440i
$712$	2.86558	+	1.65444i	0.107392	+	0.0620028i
$713$		−	14.0588i		−	0.526508i
$714$	−1.57103			−0.0587944
$715$	−1.47624	+	6.55051i	−0.0552083	+	0.244975i
$716$	−8.68224	+	5.01269i	−0.324471	+	0.187333i
$717$	5.91363			0.220849
$718$	−7.62438	+	13.2058i	−0.284539	+	0.492837i
$719$	−0.353769	+	0.612746i	−0.0131934	+	0.0228516i	−0.872547	−	0.488531i	$-0.837533\pi$
$719$	−0.353769	+	0.612746i	−0.0131934	+	0.0228516i	0.859353	+	0.511382i	$0.170866\pi$
$720$	−0.491597	+	2.18136i	−0.0183207	+	0.0812945i
$721$	−14.8274	+	8.56062i	−0.552202	+	0.318814i
$722$	−5.59142	−	9.68463i	−0.208091	−	0.360425i
$723$	0.858078	−	1.48624i	0.0319123	−	0.0552737i
$724$	0.887705	−	1.53755i	0.0329913	−	0.0571426i
$725$	10.0942	−	0.812106i	0.374890	−	0.0301609i
$726$			10.3184i			0.382951i
$727$	25.3278	+	43.8690i	0.939356	+	1.62701i	0.766676	+	0.642034i	$0.221909\pi$
$727$	25.3278	+	43.8690i	0.939356	+	1.62701i	0.172680	+	0.984978i	$0.444757\pi$
$728$	3.33410	+	1.92495i	0.123570	+	0.0713432i
$729$	−1.00000			−0.0370370
$730$	−5.86821	−	18.8408i	−0.217192	−	0.697331i
$731$	7.91819	−	13.7147i	0.292865	−	0.507257i
$732$	6.47775			0.239425
$733$	−29.3112	+	16.9228i	−1.08263	+	0.625058i	−0.931605	−	0.363471i	$-0.881592\pi$
$733$	−29.3112	+	16.9228i	−1.08263	+	0.625058i	−0.151027	+	0.988530i	$0.548258\pi$
$734$			6.46411i			0.238595i
$735$	−8.91604	+	9.66217i	−0.328873	+	0.356395i
$736$	1.11991	+	1.93975i	0.0412805	+	0.0715000i
$737$	9.28497	−	5.36068i	0.342016	−	0.197463i
$738$	−1.42858	+	2.47438i	−0.0525868	+	0.0910831i
$739$	−13.7161			−0.504555			−0.252277	−	0.967655i	$-0.581180\pi$
$739$	−13.7161			−0.504555			−0.252277	+	0.967655i	$0.581180\pi$
$740$	0.218086	−	13.5997i	0.00801698	−	0.499936i
$741$	−19.9829			−0.734090
$742$	4.89475	−	8.47795i	0.179692	−	0.311235i
$743$	−13.8765	+	8.01159i	−0.509079	+	0.293917i	−0.732455	−	0.680816i	$-0.761625\pi$
$743$	−13.8765	+	8.01159i	−0.509079	+	0.293917i	0.223376	+	0.974732i	$0.428292\pi$
$744$	3.13838	+	5.43583i	0.115059	+	0.199287i
$745$	−4.99338	−	4.60778i	−0.182943	−	0.168816i
$746$			25.5721i			0.936260i
$747$	13.4101	−	7.74230i	0.490649	−	0.283276i
$748$	1.22542			0.0448058
$749$	−7.46223	+	12.9250i	−0.272664	+	0.472268i
$750$	8.79815	+	6.89874i	0.321263	+	0.251906i
$751$	33.4440			1.22039			0.610195	−	0.792251i	$-0.291091\pi$
$751$	33.4440			1.22039			0.610195	+	0.792251i	$0.291091\pi$
$752$	−10.1872	−	5.88160i	−0.371490	−	0.214480i
$753$	8.35662	+	14.4741i	0.304532	+	0.527465i
$754$			7.36685i			0.268285i
$755$	4.12952	−	18.3239i	0.150289	−	0.666875i
$756$	−0.529225	+	0.916644i	−0.0192477	+	0.0333380i
$757$	−25.2767	+	43.7805i	−0.918697	+	1.59123i	−0.117301	+	0.993096i	$0.537424\pi$
$757$	−25.2767	+	43.7805i	−0.918697	+	1.59123i	−0.801396	+	0.598134i	$0.795909\pi$
$758$	−0.395361	−	0.684786i	−0.0143602	−	0.0248726i
$759$	−1.60145	+	0.924600i	−0.0581291	+	0.0335608i
$760$	−11.9842	−	2.70078i	−0.434711	−	0.0979676i
$761$	−19.6784	+	34.0840i	−0.713341	+	1.23554i	0.250255	+	0.968180i	$0.419485\pi$
$761$	−19.6784	+	34.0840i	−0.713341	+	1.23554i	−0.963596	+	0.267362i	$0.913848\pi$
$762$	3.14005	−	5.43873i	0.113752	−	0.197024i
$763$	−5.55677			−0.201169
$764$	16.6845	−	9.63281i	0.603625	−	0.348503i
$765$	0.729666	−	3.23774i	0.0263811	−	0.117061i
$766$	14.1778			0.512267
$767$			26.6038i			0.960607i
$768$	−0.866025	−	0.500000i	−0.0312500	−	0.0180422i
$769$		−	4.77703i		−	0.172264i	−0.996284	−	0.0861320i	$-0.972549\pi$
$769$		−	4.77703i		−	0.172264i	0.996284	−	0.0861320i	$-0.0274507\pi$
$770$	−1.32513	+	1.43602i	−0.0477543	+	0.0517506i
$771$		−	2.95633i		−	0.106470i
$772$	−9.26016	−	16.0391i	−0.333280	−	0.577259i
$773$	−11.8192	+	6.82383i	−0.425108	+	0.245436i	−0.697260	−	0.716818i	$-0.745598\pi$
$773$	−11.8192	+	6.82383i	−0.425108	+	0.245436i	0.272153	+	0.962254i	$0.412264\pi$
$774$	−5.33471	−	9.23999i	−0.191752	−	0.332125i
$775$	31.2827	−	2.51678i	1.12371	−	0.0904053i
$776$	5.18358			0.186080
$777$	2.01289	−	6.11555i	0.0722119	−	0.219394i
$778$		−	17.2890i		−	0.619842i
$779$	−13.5940	−	7.84848i	−0.487054	−	0.281201i
$780$	−5.51565	+	5.97722i	−0.197492	+	0.214019i
$781$	0.578854	+	1.00260i	0.0207130	+	0.0358760i
$782$	−1.66226	−	2.87912i	−0.0594423	−	0.102957i
$783$	−2.02537			−0.0723806
$784$	−2.93984	−	5.09196i	−0.104994	−	0.181856i
$785$	−9.82682	−	31.5506i	−0.350734	−	1.12609i
$786$	6.51420	−	11.2829i	0.232354	−	0.402449i
$787$		−	21.9350i		−	0.781897i	−0.920413	−	0.390949i	$-0.872147\pi$
$787$		−	21.9350i		−	0.781897i	0.920413	−	0.390949i	$-0.127853\pi$
$788$		−	4.86930i		−	0.173462i
$789$	9.18313	−	15.9056i	0.326928	−	0.566256i
$790$	−5.43605	+	5.89095i	−0.193406	+	0.209591i
$791$		−	3.55049i		−	0.126241i
$792$	0.412800	−	0.714991i	0.0146682	−	0.0254061i
$793$	20.4048	+	11.7807i	0.724597	+	0.418346i
$794$	4.61228	+	2.66290i	0.163684	+	0.0945028i
$795$	15.1989	+	14.0252i	0.539048	+	0.497422i
$796$	15.4856	−	8.94064i	0.548874	−	0.316893i
$797$	23.6068	−	40.8882i	0.836196	−	1.44833i	−0.0568572	−	0.998382i	$-0.518108\pi$
$797$	23.6068	−	40.8882i	0.836196	−	1.44833i	0.893053	−	0.449951i	$-0.148559\pi$
$798$	−5.03594	−	2.90750i	−0.178271	−	0.102925i
$799$	15.1207	+	8.72993i	0.534931	+	0.308843i
$800$	−4.11570	+	2.83920i	−0.145512	+	0.100381i
$801$	−2.86558	+	1.65444i	−0.101250	+	0.0584568i
$802$	25.8405	+	14.9190i	0.912459	+	0.526808i
$803$			7.28602i			0.257118i
$804$	12.9861			0.457986
$805$	5.17144	+	1.16545i	0.182269	+	0.0410767i
$806$			22.8304i			0.804167i
$807$	20.0434	−	11.5721i	0.705563	−	0.407357i
$808$	10.5205			0.370108
$809$	−1.01187	+	0.584203i	−0.0355754	+	0.0205395i	−0.517682	−	0.855573i	$-0.673205\pi$
$809$	−1.01187	+	0.584203i	−0.0355754	+	0.0205395i	0.482107	+	0.876112i	$0.339872\pi$
$810$	−1.64331	−	1.51642i	−0.0577402	−	0.0532814i
$811$	8.38136	+	14.5169i	0.294309	+	0.509759i	0.974824	−	0.222976i	$-0.0715770\pi$
$811$	8.38136	+	14.5169i	0.294309	+	0.509759i	−0.680515	+	0.732735i	$0.738244\pi$
$812$	−1.07187	+	1.85654i	−0.0376154	+	0.0651518i
$813$		−	16.2547i		−	0.570076i
$814$	−1.57007	+	4.77018i	−0.0550309	+	0.167195i
$815$	−7.52963	+	2.34520i	−0.263752	+	0.0821487i
$816$	1.28542	+	0.742138i	0.0449987	+	0.0259800i
$817$	50.7635	−	29.3083i	1.77599	−	1.02537i
$818$	−6.17878	+	3.56732i	−0.216036	+	0.124729i
$819$	−3.33410	+	1.92495i	−0.116503	+	0.0672630i
$820$	−6.09979	+	1.89986i	−0.213014	+	0.0663459i
$821$	6.82793	+	11.8263i	0.238296	+	0.412741i	0.960226	−	0.279226i	$-0.0900777\pi$
$821$	6.82793	+	11.8263i	0.238296	+	0.412741i	−0.721929	+	0.691967i	$0.756744\pi$
$822$	7.15737			0.249642
$823$	−44.2226	−	25.5319i	−1.54150	−	0.889987i	−0.998744	−	0.0500971i	$-0.984047\pi$
$823$	−44.2226	−	25.5319i	−1.54150	−	0.889987i	−0.542758	−	0.839889i	$-0.682620\pi$
$824$	16.1758			0.563510
$825$	−2.34404	−	3.39792i	−0.0816090	−	0.118300i
$826$	−3.87084	+	6.70450i	−0.134684	+	0.233279i
$827$	0.503911	+	0.872799i	0.0175227	+	0.0303502i	0.874654	−	0.484748i	$-0.161089\pi$
$827$	0.503911	+	0.872799i	0.0175227	+	0.0303502i	−0.857131	+	0.515098i	$0.827755\pi$
$828$	−2.23982			−0.0778393
$829$	−44.8670	−	25.9040i	−1.55830	−	0.899682i	−0.997420	−	0.0717819i	$-0.977131\pi$
$829$	−44.8670	−	25.9040i	−1.55830	−	0.899682i	−0.560875	−	0.827900i	$-0.689535\pi$
$830$	33.7775	+	7.61219i	1.17243	+	0.264223i
$831$	4.04271	+	2.33406i	0.140240	+	0.0809676i
$832$	−1.81865	−	3.14999i	−0.0630502	−	0.109206i
$833$	4.36354	+	7.55787i	0.151188	+	0.261865i
$834$	9.98579	+	5.76530i	0.345779	+	0.199636i
$835$	−10.5580	+	46.8490i	−0.365375	+	1.62128i
$836$	3.92808	+	2.26788i	0.135856	+	0.0784362i
$837$	−6.27676			−0.216956
$838$	−3.74432	−	6.48535i	−0.129345	−	0.224033i
$839$	−5.30628	+	9.19075i	−0.183193	+	0.317300i	−0.942966	−	0.332889i	$-0.891977\pi$
$839$	−5.30628	+	9.19075i	−0.183193	+	0.317300i	0.759773	+	0.650188i	$0.225310\pi$
$840$	−2.25970	+	0.703810i	−0.0779669	+	0.0242838i
$841$	24.8979			0.858548
$842$	−10.1128	−	5.83862i	−0.348510	−	0.201212i
$843$	14.1303			0.486673
$844$	0.197873	+	0.342726i	0.00681106	+	0.0117971i
$845$	−0.490809	+	0.152869i	−0.0168843	+	0.00525884i
$846$	10.1872	−	5.88160i	0.350244	−	0.202214i
$847$	−9.45829	+	5.46075i	−0.324991	+	0.187633i
$848$	−8.00978	+	4.62445i	−0.275057	+	0.158804i
$849$	8.68515	+	5.01437i	0.298073	+	0.172093i
$850$	6.10883	−	4.21415i	0.209531	−	0.144544i
$851$	13.3373	−	2.78180i	0.457197	−	0.0953588i
$852$			1.40226i			0.0480407i
$853$	−8.25535	+	14.2987i	−0.282658	+	0.489578i	−0.972038	−	0.234822i	$-0.924549\pi$
$853$	−8.25535	+	14.2987i	−0.282658	+	0.489578i	0.689381	+	0.724399i	$0.257883\pi$
$854$	3.42819	+	5.93779i	0.117310	+	0.203187i
$855$	8.33102	−	9.02819i	0.284915	−	0.308758i
$856$	12.2112	−	7.05015i	0.417371	−	0.240969i
$857$	18.5888			0.634983			0.317491	−	0.948261i	$-0.397160\pi$
$857$	18.5888			0.634983			0.317491	+	0.948261i	$0.397160\pi$
$858$	2.60063	−	1.50147i	0.0887840	−	0.0512595i
$859$			55.7543i			1.90231i	0.308709	+	0.951156i	$0.400103\pi$
$859$			55.7543i			1.90231i	−0.308709	+	0.951156i	$0.599897\pi$
$860$	5.24506	−	23.2739i	0.178855	−	0.793632i
$861$	−3.02416			−0.103063
$862$			14.6234i			0.498074i
$863$	6.09879	+	3.52114i	0.207605	+	0.119861i	0.600198	−	0.799851i	$-0.295088\pi$
$863$	6.09879	+	3.52114i	0.207605	+	0.119861i	−0.392593	+	0.919712i	$0.628422\pi$
$864$	0.866025	−	0.500000i	0.0294628	−	0.0170103i
$865$	2.07256	+	6.65430i	0.0704693	+	0.226253i
$866$	−34.5753	−	19.9620i	−1.17492	−	0.678338i
$867$	12.8145	+	7.39846i	0.435204	+	0.251265i
$868$	−3.32182	+	5.75355i	−0.112750	+	0.195288i
$869$	2.56310	−	1.47981i	0.0869471	−	0.0501990i
$870$	−3.32831	−	3.07130i	−0.112840	−	0.104127i
$871$	40.9062	+	23.6172i	1.38605	+	0.800239i
$872$	4.54656	+	2.62496i	0.153966	+	0.0888923i
$873$	−2.59179	+	4.48912i	−0.0877189	+	0.151934i
$874$		−	12.3054i		−	0.416235i
$875$	−1.66750	+	11.7158i	−0.0563716	+	0.396065i
$876$	−4.41256	+	7.64277i	−0.149087	+	0.258225i
$877$		−	3.30067i		−	0.111456i	−0.998446	−	0.0557279i	$-0.982252\pi$
$877$		−	3.30067i		−	0.111456i	0.998446	−	0.0557279i	$-0.0177479\pi$
$878$		−	1.22214i		−	0.0412454i
$879$	0.474413	−	0.821707i	0.0160015	−	0.0277155i
$880$	1.76258	−	0.548978i	0.0594167	−	0.0185061i
$881$	6.08870	+	10.5459i	0.205133	+	0.355301i	0.950175	−	0.311716i	$-0.100904\pi$
$881$	6.08870	+	10.5459i	0.205133	+	0.355301i	−0.745042	+	0.667018i	$0.767571\pi$
$882$	5.87968			0.197979
$883$	17.4587	+	30.2394i	0.587532	+	1.01764i	0.994555	+	0.104217i	$0.0332337\pi$
$883$	17.4587	+	30.2394i	0.587532	+	1.01764i	−0.407023	+	0.913418i	$0.633433\pi$
$884$	2.69937	+	4.67545i	0.0907898	+	0.157253i
$885$	−12.0195	−	11.0913i	−0.404031	−	0.372831i
$886$	−6.36732	−	3.67618i	−0.213914	−	0.123504i
$887$		−	5.64373i		−	0.189498i	−0.995501	−	0.0947490i	$-0.969795\pi$
$887$		−	5.64373i		−	0.189498i	0.995501	−	0.0947490i	$-0.0302048\pi$
$888$	−4.53587	+	4.05289i	−0.152214	+	0.136006i
$889$	6.64717			0.222939
$890$	−7.21787	−	1.62664i	−0.241943	−	0.0545250i
$891$	0.412800	+	0.714991i	0.0138293	+	0.0239531i
$892$	−22.1602	+	12.7942i	−0.741977	+	0.428381i
$893$	32.3129	+	55.9676i	1.08131	+	1.87288i
$894$			3.03860i			0.101626i
$895$	15.2027	−	16.4749i	0.508169	−	0.550694i
$896$		−	1.05845i		−	0.0353603i
$897$	−7.05542	−	4.07345i	−0.235574	−	0.136009i
$898$		−	11.7785i		−	0.393055i
$899$	−12.7127			−0.423993
$900$	−0.400968	−	4.98390i	−0.0133656	−	0.166130i
$901$	11.8887	−	6.86396i	0.396071	−	0.228672i
$902$	2.35888			0.0785420
$903$	5.64652	−	9.78007i	0.187905	−	0.325460i
$904$	−1.67721	+	2.90502i	−0.0557833	+	0.0966196i
$905$	−0.872786	+	3.87281i	−0.0290124	+	0.128737i
$906$	−7.27481	+	4.20011i	−0.241689	+	0.139539i
$907$	−1.71682	−	2.97363i	−0.0570062	−	0.0987377i	0.836114	−	0.548556i	$-0.184822\pi$
$907$	−1.71682	−	2.97363i	−0.0570062	−	0.0987377i	−0.893120	+	0.449818i	$0.851489\pi$
$908$	11.6633	−	20.2013i	0.387059	−	0.670405i
$909$	−5.26023	+	9.11098i	−0.174471	+	0.302192i
$910$	−8.39800	−	1.89259i	−0.278391	−	0.0627389i
$911$		−	21.1245i		−	0.699887i	−0.936771	−	0.349944i	$-0.886201\pi$
$911$		−	21.1245i		−	0.699887i	0.936771	−	0.349944i	$-0.113799\pi$
$912$	2.74695	+	4.75785i	0.0909605	+	0.157548i
$913$	−11.0713	−	6.39205i	−0.366408	−	0.211546i
$914$	−15.7117			−0.519696
$915$	−13.8294	+	4.30735i	−0.457187	+	0.142396i
$916$	−11.6531	+	20.1837i	−0.385028	+	0.666887i
$917$	13.7899			0.455383
$918$	−1.28542	+	0.742138i	−0.0424252	+	0.0244942i
$919$			43.4122i			1.43204i	0.698081	+	0.716019i	$0.254038\pi$
$919$			43.4122i			1.43204i	−0.698081	+	0.716019i	$0.745962\pi$
$920$	−3.68074	−	3.39651i	−0.121350	−	0.111979i
$921$	6.44866	+	11.1694i	0.212490	+	0.368044i
$922$	−21.3746	+	12.3407i	−0.703936	+	0.406418i
$923$	−2.55022	+	4.41711i	−0.0839415	+	0.145391i
$924$	0.873856			0.0287478
$925$	8.57747	+	29.1792i	0.282025	+	0.959407i
$926$	37.3220			1.22648
$927$	−8.08789	+	14.0086i	−0.265641	+	0.460104i
$928$	1.75402	−	1.01268i	0.0575785	−	0.0332429i
$929$	22.4240	+	38.8395i	0.735707	+	1.27428i	0.954412	+	0.298491i	$0.0964834\pi$
$929$	22.4240	+	38.8395i	0.735707	+	1.27428i	−0.218705	+	0.975791i	$0.570183\pi$
$930$	−10.3147	−	9.51817i	−0.338232	−	0.312113i
$931$			32.3023i			1.05867i
$932$	−0.440570	+	0.254363i	−0.0144313	+	0.00833194i
$933$	−25.5600			−0.836798
$934$	−4.58567	+	7.94262i	−0.150048	+	0.259890i
$935$	−2.61616	+	0.814836i	−0.0855576	+	0.0266480i
$936$	3.63729			0.118889
$937$	39.4709	+	22.7885i	1.28946	+	0.744469i	0.978558	−	0.205974i	$-0.0660361\pi$
$937$	39.4709	+	22.7885i	1.28946	+	0.744469i	0.310900	+	0.950443i	$0.399369\pi$
$938$	6.87259	+	11.9037i	0.224398	+	0.388669i
$939$			4.70669i			0.153597i
$940$	25.6598	+	5.78276i	0.836930	+	0.188613i
$941$	−25.2217	+	43.6853i	−0.822205	+	1.42410i	0.0818313	+	0.996646i	$0.473923\pi$
$941$	−25.2217	+	43.6853i	−0.822205	+	1.42410i	−0.904037	+	0.427455i	$0.859410\pi$
$942$	−7.38920	+	12.7985i	−0.240753	+	0.416997i
$943$	−3.19977	−	5.54217i	−0.104199	−	0.180478i
$944$	6.33426	−	3.65709i	0.206163	−	0.119028i
$945$	0.520331	−	2.30886i	0.0169264	−	0.0751072i
$946$	−4.40434	+	7.62854i	−0.143197	+	0.248025i
$947$	25.3654	−	43.9341i	0.824264	−	1.42767i	−0.0782163	−	0.996936i	$-0.524922\pi$
$947$	25.3654	−	43.9341i	0.824264	−	1.42767i	0.902480	−	0.430731i	$-0.141744\pi$
$948$	3.58480			0.116429
$949$	−27.7990	+	16.0498i	−0.902394	+	0.520997i
$950$	27.3810	−	2.20287i	0.888357	−	0.0714707i
$951$	−25.0832			−0.813379
$952$			1.57103i			0.0509174i
$953$	−50.0894	−	28.9192i	−1.62256	−	0.936783i	−0.986233	−	0.165360i	$-0.947121\pi$
$953$	−50.0894	−	28.9192i	−1.62256	−	0.936783i	−0.636323	−	0.771423i	$-0.719545\pi$
$954$		−	9.24890i		−	0.299444i
$955$	−29.2147	+	31.6595i	−0.945365	+	1.02448i
$956$		−	5.91363i		−	0.191260i
$957$	0.836071	+	1.44812i	0.0270263	+	0.0468110i
$958$	−3.81113	+	2.20036i	−0.123132	+	0.0710903i
$959$	3.78786	+	6.56076i	0.122316	+	0.211858i
$960$	2.18136	+	0.491597i	0.0704031	+	0.0158662i
$961$	−8.39768			−0.270893
$962$	−21.6587	+	4.51741i	−0.698304	+	0.145647i
$963$			14.1003i			0.454376i
$964$	−1.48624	−	0.858078i	−0.0478684	−	0.0276368i
$965$	30.4347	+	28.0845i	0.979728	+	0.904072i
$966$	−1.18537	−	2.05312i	−0.0381387	−	0.0660581i
$967$	−13.0477	−	22.5993i	−0.419586	−	0.726744i	0.576312	−	0.817230i	$-0.304491\pi$
$967$	−13.0477	−	22.5993i	−0.419586	−	0.726744i	−0.995898	+	0.0904856i	$0.971158\pi$
$968$	10.3184			0.331645
$969$	−4.07723	−	7.06197i	−0.130979	−	0.226863i
$970$	−11.0665	+	3.44680i	−0.355324	+	0.110670i
$971$	2.69897	−	4.67476i	0.0866142	−	0.150020i	−0.819464	−	0.573131i	$-0.805729\pi$
$971$	2.69897	−	4.67476i	0.0866142	−	0.150020i	0.906078	+	0.423111i	$0.139062\pi$
$972$			1.00000i			0.0320750i
$973$			12.2046i			0.391260i
$974$	−10.6859	+	18.5086i	−0.342399	+	0.593053i
$975$	7.80090	−	16.4284i	0.249829	−	0.526131i
$976$		−	6.47775i		−	0.207348i
$977$	7.00738	−	12.1371i	0.224186	−	0.388302i	−0.731889	−	0.681424i	$-0.761361\pi$
$977$	7.00738	−	12.1371i	0.224186	−	0.388302i	0.956075	+	0.293122i	$0.0946944\pi$
$978$	3.05439	+	1.76345i	0.0976686	+	0.0563890i
$979$	2.36582	+	1.36591i	0.0756120	+	0.0436546i
$980$	9.66217	+	8.91604i	0.308647	+	0.284813i
$981$	−4.54656	+	2.62496i	−0.145160	+	0.0838084i
$982$	8.61904	−	14.9286i	0.275045	−	0.476391i
$983$	−51.5289	−	29.7502i	−1.64352	−	0.948885i	−0.979570	−	0.201104i	$-0.935547\pi$
$983$	−51.5289	−	29.7502i	−1.64352	−	0.948885i	−0.663946	−	0.747780i	$-0.731120\pi$
$984$	2.47438	+	1.42858i	0.0788803	+	0.0455415i
$985$	3.23781	+	10.3955i	0.103165	+	0.331229i
$986$	−2.60345	+	1.50310i	−0.0829107	+	0.0478685i
$987$	10.7827	+	6.22538i	0.343216	+	0.198156i
$988$			19.9829i			0.635740i
$989$	23.8976			0.759901
$990$	−0.405862	+	1.80093i	−0.0128992	+	0.0572373i
$991$		−	56.8156i		−	1.80481i	−0.430893	−	0.902403i	$-0.641801\pi$
$991$		−	56.8156i		−	1.80481i	0.430893	−	0.902403i	$-0.358199\pi$
$992$	5.43583	−	3.13838i	0.172588	−	0.0996436i
$993$	9.15644			0.290571
$994$	−1.28538	+	0.742112i	−0.0407696	+	0.0235384i
$995$	−27.1155	+	29.3846i	−0.859618	+	0.931554i
$996$	−7.74230	−	13.4101i	−0.245324	−	0.424914i
$997$	19.9693	−	34.5879i	0.632435	−	1.09541i	−0.354618	−	0.935011i	$-0.615389\pi$
$997$	19.9693	−	34.5879i	0.632435	−	1.09541i	0.987052	−	0.160398i	$-0.0512777\pi$
$998$		−	31.3340i		−	0.991860i
$999$	−1.24197	−	5.95462i	−0.0392942	−	0.188396i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.ba.b.619.16	yes	36
5.4	even	2		1110.2.ba.a.619.3	yes	36
37.11	even	6		1110.2.ba.a.529.3	✓	36
185.159	even	6	inner	1110.2.ba.b.529.16	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.ba.a.529.3	✓	36	37.11	even	6
1110.2.ba.a.619.3	yes	36	5.4	even	2
1110.2.ba.b.529.16	yes	36	185.159	even	6	inner
1110.2.ba.b.619.16	yes	36	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.64331 + 1.51642i) q^{5} -1.00000i q^{6} +(0.916644 - 0.529225i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.64331 + 1.51642i) q^{5} -1.00000i q^{6} +(0.916644 - 0.529225i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(2.13491 - 0.664945i) q^{10} -0.825600 q^{11} +(-0.866025 - 0.500000i) q^{12} +(-1.81865 - 3.14999i) q^{13} -1.05845i q^{14} +(2.18136 + 0.491597i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.742138 - 1.28542i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(4.75785 - 2.74695i) q^{19} +(0.491597 - 2.18136i) q^{20} +(0.529225 - 0.916644i) q^{21} +(-0.412800 + 0.714991i) q^{22} +2.23982 q^{23} +(-0.866025 + 0.500000i) q^{24} +(0.400968 + 4.98390i) q^{25} -3.63729 q^{26} -1.00000i q^{27} +(-0.916644 - 0.529225i) q^{28} -2.02537i q^{29} +(1.51642 - 1.64331i) q^{30} -6.27676i q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.714991 + 0.412800i) q^{33} +(-0.742138 - 1.28542i) q^{34} +(2.30886 + 0.520331i) q^{35} -1.00000 q^{36} +(5.95462 - 1.24197i) q^{37} -5.49389i q^{38} +(-3.14999 - 1.81865i) q^{39} +(-1.64331 - 1.51642i) q^{40} +(-1.42858 - 2.47438i) q^{41} +(-0.529225 - 0.916644i) q^{42} +10.6694 q^{43} +(0.412800 + 0.714991i) q^{44} +(2.13491 - 0.664945i) q^{45} +(1.11991 - 1.93975i) q^{46} +11.7632i q^{47} +1.00000i q^{48} +(-2.93984 + 5.09196i) q^{49} +(4.51666 + 2.14470i) q^{50} -1.48428i q^{51} +(-1.81865 + 3.14999i) q^{52} +(8.00978 + 4.62445i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(-1.35672 - 1.25195i) q^{55} +(-0.916644 + 0.529225i) q^{56} +(2.74695 - 4.75785i) q^{57} +(-1.75402 - 1.01268i) q^{58} +(-6.33426 - 3.65709i) q^{59} +(-0.664945 - 2.13491i) q^{60} +(-5.60990 + 3.23888i) q^{61} +(-5.43583 - 3.13838i) q^{62} -1.05845i q^{63} +1.00000 q^{64} +(1.78808 - 7.93425i) q^{65} +0.825600i q^{66} +(-11.2463 + 6.49307i) q^{67} -1.48428 q^{68} +(1.93975 - 1.11991i) q^{69} +(1.60505 - 1.73937i) q^{70} +(-0.701131 - 1.21439i) q^{71} +(-0.500000 + 0.866025i) q^{72} -8.82512i q^{73} +(1.90173 - 5.77784i) q^{74} +(2.83920 + 4.11570i) q^{75} +(-4.75785 - 2.74695i) q^{76} +(-0.756782 + 0.436928i) q^{77} +(-3.14999 + 1.81865i) q^{78} +(-3.10453 + 1.79240i) q^{79} +(-2.13491 + 0.664945i) q^{80} +(-0.500000 - 0.866025i) q^{81} -2.85716 q^{82} +(13.4101 + 7.74230i) q^{83} -1.05845 q^{84} +(3.16880 - 0.986962i) q^{85} +(5.33471 - 9.23999i) q^{86} +(-1.01268 - 1.75402i) q^{87} +0.825600 q^{88} +(-2.86558 - 1.65444i) q^{89} +(0.491597 - 2.18136i) q^{90} +(-3.33410 - 1.92495i) q^{91} +(-1.11991 - 1.93975i) q^{92} +(-3.13838 - 5.43583i) q^{93} +(10.1872 + 5.88160i) q^{94} +(11.9842 + 2.70078i) q^{95} +(0.866025 + 0.500000i) q^{96} -5.18358 q^{97} +(2.93984 + 5.09196i) q^{98} +(-0.412800 + 0.714991i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 18 q^{2} - 18 q^{4} + 4 q^{5} - 36 q^{8} + 18 q^{9}+O(q^{10}) \) 36 * q + 18 * q^2 - 18 * q^4 + 4 * q^5 - 36 * q^8 + 18 * q^9	\( 36 q + 18 q^{2} - 18 q^{4} + 4 q^{5} - 36 q^{8} + 18 q^{9} + 2 q^{10} + 4 q^{11} + 14 q^{13} + 2 q^{15} - 18 q^{16} - 18 q^{18} + 6 q^{19} - 2 q^{20} + 2 q^{22} + 20 q^{23} - 2 q^{25} + 28 q^{26} - 2 q^{30} + 18 q^{32} + 6 q^{33} - 20 q^{35} - 36 q^{36} - 20 q^{37} + 6 q^{39} - 4 q^{40} + 10 q^{41} - 2 q^{44} + 2 q^{45} + 10 q^{46} + 10 q^{49} - 4 q^{50} + 14 q^{52} + 12 q^{53} + 40 q^{55} - 8 q^{57} - 30 q^{58} + 18 q^{59} - 4 q^{60} - 6 q^{61} + 12 q^{62} + 36 q^{64} - 32 q^{65} - 36 q^{67} + 12 q^{69} - 40 q^{70} - 24 q^{71} - 18 q^{72} - 34 q^{74} + 8 q^{75} - 6 q^{76} + 24 q^{77} + 6 q^{78} - 2 q^{80} - 18 q^{81} + 20 q^{82} - 36 q^{83} + 26 q^{85} + 10 q^{87} - 4 q^{88} - 2 q^{90} - 36 q^{91} - 10 q^{92} - 12 q^{93} + 12 q^{94} + 18 q^{95} - 52 q^{97} - 10 q^{98} + 2 q^{99}+O(q^{100}) \) 36 * q + 18 * q^2 - 18 * q^4 + 4 * q^5 - 36 * q^8 + 18 * q^9 + 2 * q^10 + 4 * q^11 + 14 * q^13 + 2 * q^15 - 18 * q^16 - 18 * q^18 + 6 * q^19 - 2 * q^20 + 2 * q^22 + 20 * q^23 - 2 * q^25 + 28 * q^26 - 2 * q^30 + 18 * q^32 + 6 * q^33 - 20 * q^35 - 36 * q^36 - 20 * q^37 + 6 * q^39 - 4 * q^40 + 10 * q^41 - 2 * q^44 + 2 * q^45 + 10 * q^46 + 10 * q^49 - 4 * q^50 + 14 * q^52 + 12 * q^53 + 40 * q^55 - 8 * q^57 - 30 * q^58 + 18 * q^59 - 4 * q^60 - 6 * q^61 + 12 * q^62 + 36 * q^64 - 32 * q^65 - 36 * q^67 + 12 * q^69 - 40 * q^70 - 24 * q^71 - 18 * q^72 - 34 * q^74 + 8 * q^75 - 6 * q^76 + 24 * q^77 + 6 * q^78 - 2 * q^80 - 18 * q^81 + 20 * q^82 - 36 * q^83 + 26 * q^85 + 10 * q^87 - 4 * q^88 - 2 * q^90 - 36 * q^91 - 10 * q^92 - 12 * q^93 + 12 * q^94 + 18 * q^95 - 52 * q^97 - 10 * q^98 + 2 * q^99

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