LMFDB - Embedded newform 1110.2.ba.a.529.3

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			529.3
Character	$\chi$	$=$	1110.529
Dual form			1110.2.ba.a.619.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.491597 + 2.18136i) q^{5} +1.00000i q^{6} +(-0.916644 - 0.529225i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.491597 + 2.18136i) 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} +(1.51642 - 1.64331i) 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} +(-1.64331 - 1.51642i) q^{20} +(0.529225 + 0.916644i) q^{21} +(0.412800 + 0.714991i) q^{22} -2.23982 q^{23} +(-0.866025 - 0.500000i) q^{24} +(-4.51666 - 2.14470i) q^{25} -3.63729 q^{26} -1.00000i q^{27} +(0.916644 - 0.529225i) q^{28} +2.02537i q^{29} +(-2.18136 - 0.491597i) q^{30} +6.27676i q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.714991 + 0.412800i) q^{33} +(-0.742138 + 1.28542i) q^{34} +(1.60505 - 1.73937i) q^{35} -1.00000 q^{36} +(-5.95462 - 1.24197i) q^{37} -5.49389i q^{38} +(-3.14999 + 1.81865i) q^{39} +(-0.491597 + 2.18136i) 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} +(0.400968 + 4.98390i) q^{50} +1.48428i q^{51} +(1.81865 + 3.14999i) q^{52} +(-8.00978 + 4.62445i) q^{53} +(-0.866025 + 0.500000i) q^{54} +(0.405862 - 1.80093i) 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} +(5.97722 + 5.51565i) q^{65} -0.825600i q^{66} +(11.2463 + 6.49307i) q^{67} +1.48428 q^{68} +(1.93975 + 1.11991i) q^{69} +(-2.30886 - 0.520331i) 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} +(1.64331 + 1.51642i) 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} +(-8.33102 + 9.02819i) 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} + 2 q^{5} + 36 q^{8} + 18 q^{9}+O(q^{10}) $ 36 * q - 18 * q^2 - 18 * q^4 + 2 * q^5 + 36 * q^8 + 18 * q^9	$ 36 q - 18 q^{2} - 18 q^{4} + 2 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} - 4 q^{20} - 2 q^{22} - 20 q^{23} + 4 q^{25} + 28 q^{26} - 2 q^{30} - 18 q^{32} - 6 q^{33} - 40 q^{35} - 36 q^{36} + 20 q^{37} + 6 q^{39} + 2 q^{40} + 10 q^{41} - 2 q^{44} - 2 q^{45} + 10 q^{46} + 10 q^{49} - 2 q^{50} - 14 q^{52} - 12 q^{53} + 56 q^{55} + 8 q^{57} + 30 q^{58} + 18 q^{59} + 4 q^{60} - 6 q^{61} - 12 q^{62} + 36 q^{64} + 40 q^{65} + 36 q^{67} + 12 q^{69} + 20 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} + 4 q^{90} - 36 q^{91} + 10 q^{92} + 12 q^{93} + 12 q^{94} - 30 q^{95} + 52 q^{97} + 10 q^{98} + 2 q^{99}+O(q^{100}) $ 36 * q - 18 * q^2 - 18 * q^4 + 2 * 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 - 4 * q^20 - 2 * q^22 - 20 * q^23 + 4 * q^25 + 28 * q^26 - 2 * q^30 - 18 * q^32 - 6 * q^33 - 40 * q^35 - 36 * q^36 + 20 * q^37 + 6 * q^39 + 2 * q^40 + 10 * q^41 - 2 * q^44 - 2 * q^45 + 10 * q^46 + 10 * q^49 - 2 * q^50 - 14 * q^52 - 12 * q^53 + 56 * q^55 + 8 * q^57 + 30 * q^58 + 18 * q^59 + 4 * q^60 - 6 * q^61 - 12 * q^62 + 36 * q^64 + 40 * q^65 + 36 * q^67 + 12 * q^69 + 20 * 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 + 4 * q^90 - 36 * q^91 + 10 * q^92 + 12 * q^93 + 12 * q^94 - 30 * 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 $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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
$5$	−0.491597	+	2.18136i	−0.219849	+	0.975534i
$5$	−0.491597	+	2.18136i	−0.219849	+	0.975534i
$6$			1.00000i			0.408248i
$7$	−0.916644	−	0.529225i	−0.346459	−	0.200028i	0.316666	−	0.948537i	$-0.397437\pi$
$7$	−0.916644	−	0.529225i	−0.346459	−	0.200028i	−0.663125	+	0.748509i	$0.730770\pi$
$8$	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	−0.495585	−	0.868559i	$-0.665046\pi$
$13$	1.81865	−	3.14999i	0.504402	−	0.873649i	0.999987	−	0.00509014i	$-0.00162025\pi$
$14$			1.05845i			0.282883i
$15$	1.51642	−	1.64331i	0.391537	−	0.424302i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.742138	−	1.28542i	−0.179995	−	0.311760i	0.761884	−	0.647714i	$-0.224275\pi$
$17$	−0.742138	−	1.28542i	−0.179995	−	0.311760i	−0.941879	+	0.335954i	$0.890941\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	4.75785	+	2.74695i	1.09153	+	0.630193i	0.933982	−	0.357319i	$-0.116309\pi$
$19$	4.75785	+	2.74695i	1.09153	+	0.630193i	0.157543	+	0.987512i	$0.449643\pi$
$20$	−1.64331	−	1.51642i	−0.367456	−	0.339081i
$21$	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	$-0.575024\pi$
$23$	−2.23982			−0.467036			−0.233518	+	0.972353i	$0.575024\pi$
$24$	−0.866025	−	0.500000i	−0.176777	−	0.102062i
$25$	−4.51666	−	2.14470i	−0.903333	−	0.428940i
$26$	−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	$0.0602168\pi$
$29$			2.02537i			0.376101i	−0.982159	+	0.188050i	$0.939783\pi$
$30$	−2.18136	−	0.491597i	−0.398260	−	0.0897529i
$31$			6.27676i			1.12734i	0.826000	+	0.563669i	$0.190611\pi$
$31$			6.27676i			1.12734i	−0.826000	+	0.563669i	$0.809389\pi$
$32$	−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
$35$	1.60505	−	1.73937i	0.271303	−	0.294007i
$36$	−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
$40$	−0.491597	+	2.18136i	−0.0777283	+	0.344903i
$41$	−1.42858	+	2.47438i	−0.223107	+	0.386433i	−0.955750	−	0.294181i	$-0.904953\pi$
$41$	−1.42858	+	2.47438i	−0.223107	+	0.386433i	0.732643	+	0.680613i	$0.238287\pi$
$42$	0.529225	−	0.916644i	0.0816612	−	0.141441i
$43$	−10.6694			−1.62707			−0.813536	−	0.581515i	$-0.802460\pi$
$43$	−10.6694			−1.62707			−0.813536	+	0.581515i	$0.802460\pi$
$44$	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
$50$	0.400968	+	4.98390i	0.0567054	+	0.704829i
$51$			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	$-0.885756\pi$
$53$	−8.00978	+	4.62445i	−1.10023	+	0.635217i	−0.163947	+	0.986469i	$0.552423\pi$
$54$	−0.866025	+	0.500000i	−0.117851	+	0.0680414i
$55$	0.405862	−	1.80093i	0.0547265	−	0.242837i
$56$	−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	−0.852018	−	0.523513i	$-0.824621\pi$
$59$	−6.33426	+	3.65709i	−0.824651	+	0.476112i	0.0273670	+	0.999625i	$0.491288\pi$
$60$	0.664945	+	2.13491i	0.0858440	+	0.275616i
$61$	−5.60990	−	3.23888i	−0.718274	−	0.414696i	0.0958432	−	0.995396i	$-0.469445\pi$
$61$	−5.60990	−	3.23888i	−0.718274	−	0.414696i	−0.814117	+	0.580701i	$0.802779\pi$
$62$	5.43583	−	3.13838i	0.690351	−	0.398574i
$63$		−	1.05845i		−	0.133352i
$64$	1.00000			0.125000
$65$	5.97722	+	5.51565i	0.741383	+	0.684132i
$66$		−	0.825600i		−	0.101624i
$67$	11.2463	+	6.49307i	1.37396	+	0.793255i	0.991424	−	0.130686i	$-0.0417179\pi$
$67$	11.2463	+	6.49307i	1.37396	+	0.793255i	0.382535	+	0.923941i	$0.375051\pi$
$68$	1.48428			0.179995
$69$	1.93975	+	1.11991i	0.233518	+	0.134822i
$70$	−2.30886	−	0.520331i	−0.275962	−	0.0621914i
$71$	−0.701131	+	1.21439i	−0.0832089	+	0.144122i	−0.904627	−	0.426205i	$-0.859850\pi$
$71$	−0.701131	+	1.21439i	−0.0832089	+	0.144122i	0.821418	+	0.570327i	$0.193184\pi$
$72$	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	0.315084	−	0.949064i	$-0.397967\pi$
$79$	−3.10453	−	1.79240i	−0.349287	−	0.201661i	−0.664371	+	0.747403i	$0.731300\pi$
$80$	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	$-0.989961\pi$
$83$	−13.4101	+	7.74230i	−1.47195	+	0.849828i	−0.472443	+	0.881361i	$0.656628\pi$
$84$	−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	−0.644127	−	0.764919i	$-0.722779\pi$
$89$	−2.86558	+	1.65444i	−0.303751	+	0.175371i	0.340376	+	0.940289i	$0.389446\pi$
$90$	1.64331	+	1.51642i	0.173221	+	0.159844i
$91$	−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
$95$	−8.33102	+	9.02819i	−0.854745	+	0.926273i
$96$	0.866025	−	0.500000i	0.0883883	−	0.0510310i
$97$	5.18358			0.526313			0.263157	−	0.964753i	$-0.415236\pi$
$97$	5.18358			0.526313			0.263157	+	0.964753i	$0.415236\pi$
$98$	−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	$-0.206460\pi$
$103$	16.1758			1.59385			0.796923	+	0.604081i	$0.206460\pi$
$104$	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	$-0.0946337\pi$
$107$	12.2112	+	7.05015i	1.18050	+	0.681563i	0.224372	+	0.974504i	$0.427967\pi$
$108$	0.866025	+	0.500000i	0.0833333	+	0.0481125i
$109$	−4.54656	+	2.62496i	−0.435481	+	0.251425i	−0.701679	−	0.712493i	$-0.747566\pi$
$109$	−4.54656	+	2.62496i	−0.435481	+	0.251425i	0.266198	+	0.963918i	$0.414233\pi$
$110$	−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	$-0.217100\pi$
$113$	−1.67721	−	2.90502i	−0.157779	−	0.273281i	−0.934067	+	0.357097i	$0.883767\pi$
$114$	−2.74695	+	4.75785i	−0.257275	+	0.445613i
$115$	1.10109	−	4.88587i	0.102677	−	0.455609i
$116$	−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
$120$	1.51642	−	1.64331i	0.138429	−	0.150013i
$121$	−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	$-0.756548\pi$
$127$	−5.43873	+	3.14005i	−0.482609	+	0.278634i	0.238894	+	0.971046i	$0.423215\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	9.23999	+	5.33471i	0.813536	+	0.469695i
$130$	1.78808	−	7.93425i	0.156825	−	0.695879i
$131$	11.2829	−	6.51420i	0.985794	−	0.569148i	0.0817796	−	0.996650i	$-0.473940\pi$
$131$	11.2829	−	6.51420i	0.985794	−	0.569148i	0.904014	+	0.427502i	$0.140606\pi$
$132$	−0.714991	+	0.412800i	−0.0622319	+	0.0359296i
$133$	−2.90750	−	5.03594i	−0.252113	−	0.436672i
$134$		−	12.9861i		−	1.12183i
$135$	2.18136	+	0.491597i	0.187742	+	0.0423099i
$136$	−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	0.510914	−	0.859632i	$-0.329307\pi$
$139$	−5.76530	−	9.98579i	−0.489006	−	0.846983i	−0.999920	+	0.0126486i	$0.995974\pi$
$140$	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
$145$	−4.41805	−	0.995663i	−0.366899	−	0.0826853i
$146$	−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	$0.539722\pi$
$150$	2.14470	−	4.51666i	0.175114	−	0.368784i
$151$	−4.20011	+	7.27481i	−0.341800	+	0.592015i	−0.984767	−	0.173879i	$-0.944370\pi$
$151$	−4.20011	+	7.27481i	−0.341800	+	0.592015i	0.642967	+	0.765894i	$0.277703\pi$
$152$	4.75785	+	2.74695i	0.385913	+	0.222807i
$153$	0.742138	−	1.28542i	0.0599983	−	0.103920i
$154$		−	0.873856i		−	0.0704173i
$155$	−13.6919	−	3.08563i	−1.09976	−	0.247844i
$156$		−	3.63729i		−	0.291216i
$157$	12.7985	−	7.38920i	1.02143	−	0.589722i	0.106911	−	0.994269i	$-0.465904\pi$
$157$	12.7985	−	7.38920i	1.02143	−	0.589722i	0.914517	+	0.404546i	$0.132571\pi$
$158$			3.58480i			0.285191i
$159$	9.24890			0.733485
$160$	−1.64331	−	1.51642i	−0.129915	−	0.119883i
$161$	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	$-0.122559\pi$
$163$	1.76345	+	3.05439i	0.138124	+	0.239238i	−0.788662	+	0.614827i	$0.789226\pi$
$164$	−1.42858	−	2.47438i	−0.111554	−	0.193216i
$165$	−1.25195	+	1.35672i	−0.0974644	+	0.105621i
$166$	13.4101	+	7.74230i	1.04082	+	0.600919i
$167$	−10.7385	+	18.5996i	−0.830969	+	1.43928i	0.0663009	+	0.997800i	$0.478880\pi$
$167$	−10.7385	+	18.5996i	−0.830969	+	1.43928i	−0.897270	+	0.441482i	$0.854453\pi$
$168$	0.529225	+	0.916644i	0.0408306	+	0.0707206i
$169$	−0.114948	−	0.199096i	−0.00884218	−	0.0153151i
$170$	−2.43913	−	2.25078i	−0.187073	−	0.172627i
$171$			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	$-0.704471\pi$
$173$	−2.69931	+	1.55845i	−0.205225	+	0.118487i	0.393865	+	0.919168i	$0.371138\pi$
$174$	−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	$0.122243\pi$
$179$			10.0254i			0.749333i	−0.927160	+	0.374666i	$0.877757\pi$
$180$	0.491597	−	2.18136i	0.0366415	−	0.162589i
$181$	0.887705	−	1.53755i	0.0659826	−	0.114285i	−0.831147	−	0.556053i	$-0.812315\pi$
$181$	0.887705	−	1.53755i	0.0659826	−	0.114285i	0.897129	+	0.441768i	$0.145648\pi$
$182$	3.33410	+	1.92495i	0.247140	+	0.142686i
$183$	3.23888	+	5.60990i	0.239425	+	0.414696i
$184$	−2.23982			−0.165122
$185$	5.63646	−	12.3786i	0.414401	−	0.910094i
$186$	−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
$190$	11.9842	+	2.70078i	0.869422	+	0.195935i
$191$		−	19.2656i		−	1.39401i	−0.717066	−	0.697006i	$-0.754515\pi$
$191$		−	19.2656i		−	1.39401i	0.717066	−	0.697006i	$-0.245485\pi$
$192$	−0.866025	−	0.500000i	−0.0625000	−	0.0360844i
$193$	−18.5203			−1.33312			−0.666561	−	0.745451i	$-0.732234\pi$
$193$	−18.5203			−1.33312			−0.666561	+	0.745451i	$0.732234\pi$
$194$	−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	$-0.722162\pi$
$197$	−4.21694	+	2.43465i	−0.300444	+	0.173462i	0.342198	+	0.939628i	$0.388829\pi$
$198$	−0.412800	+	0.714991i	−0.0293364	+	0.0508122i
$199$		−	17.8813i		−	1.26757i	−0.773509	−	0.633785i	$-0.781500\pi$
$199$		−	17.8813i		−	1.26757i	0.773509	−	0.633785i	$-0.218500\pi$
$200$	−4.51666	−	2.14470i	−0.319376	−	0.151653i
$201$	−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
$205$	−4.69522	−	4.33265i	−0.327928	−	0.302605i
$206$	−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
$210$	1.73937	+	1.60505i	0.120028	+	0.110759i
$211$	−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
$215$	5.24506	−	23.2739i	0.357710	−	1.58726i
$216$		−	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
$220$	1.35672	+	1.25195i	0.0914701	+	0.0844066i
$221$	−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
$225$	−0.400968	−	4.98390i	−0.0267312	−	0.332260i
$226$	−1.67721	+	2.90502i	−0.111567	+	0.193239i
$227$	−11.6633	+	20.2013i	−0.774117	+	1.34081i	0.161172	+	0.986926i	$0.448473\pi$
$227$	−11.6633	+	20.2013i	−0.774117	+	1.34081i	−0.935289	+	0.353884i	$0.884861\pi$
$228$	5.49389			0.363842
$229$	−11.6531	+	20.1837i	−0.770055	+	1.33377i	0.167477	+	0.985876i	$0.446438\pi$
$229$	−11.6531	+	20.1837i	−0.770055	+	1.33377i	−0.937532	+	0.347899i	$0.886895\pi$
$230$	−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
$235$	−25.6598	−	5.78276i	−1.67386	−	0.377226i
$236$		−	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	−0.325133	−	0.945668i	$-0.605409\pi$
$239$	5.12135	−	2.95681i	0.331273	−	0.191260i	0.656406	+	0.754408i	$0.272076\pi$
$240$	−2.18136	−	0.491597i	−0.140806	−	0.0317324i
$241$	1.48624	+	0.858078i	0.0957368	+	0.0552737i	0.547104	−	0.837065i	$-0.315730\pi$
$241$	1.48624	+	0.858078i	0.0957368	+	0.0552737i	−0.451367	+	0.892338i	$0.649064\pi$
$242$	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
$250$	−11.0688	−	1.57541i	−0.700052	−	0.0996379i
$251$		−	16.7132i		−	1.05493i	−0.849576	−	0.527465i	$-0.823142\pi$
$251$		−	16.7132i		−	1.05493i	0.849576	−	0.527465i	$-0.176858\pi$
$252$	0.916644	+	0.529225i	0.0577432	+	0.0333380i
$253$	1.84920			0.116258
$254$	5.43873	+	3.14005i	0.341256	+	0.197024i
$255$	−3.23774	−	0.729666i	−0.202755	−	0.0456934i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−1.47817	−	2.56026i	−0.0922055	−	0.159705i	0.816233	−	0.577722i	$-0.196058\pi$
$257$	−1.47817	−	2.56026i	−0.0922055	−	0.159705i	−0.908439	+	0.418018i	$0.862725\pi$
$258$		−	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	$-0.524942\pi$
$263$	−15.9056	−	9.18313i	−0.980784	−	0.566256i	−0.902507	+	0.430676i	$0.858275\pi$
$264$	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	0.999974	−	0.00725939i	$-0.00231076\pi$
$271$	8.12733	+	14.0769i	0.493700	+	0.855113i	−0.506274	+	0.862373i	$0.668977\pi$
$272$	−0.742138	+	1.28542i	−0.0449987	+	0.0779401i
$273$	3.84989			0.233006
$274$	6.19847	−	3.57869i	0.374463	−	0.216196i
$275$	3.72896	+	1.77066i	0.224865	+	0.106775i
$276$	−1.93975	+	1.11991i	−0.116759	+	0.0674108i
$277$	−2.33406	+	4.04271i	−0.140240	+	0.242903i	−0.927587	−	0.373607i	$-0.878121\pi$
$277$	−2.33406	+	4.04271i	−0.140240	+	0.242903i	0.787347	+	0.616510i	$0.211454\pi$
$278$	−5.76530	+	9.98579i	−0.345779	+	0.598908i
$279$	−5.43583	+	3.13838i	−0.325435	+	0.187890i
$280$	1.60505	−	1.73937i	0.0959201	−	0.103947i
$281$	12.2372	−	7.06515i	0.730010	−	0.421471i	−0.0884158	−	0.996084i	$-0.528180\pi$
$281$	12.2372	−	7.06515i	0.730010	−	0.421471i	0.818426	+	0.574612i	$0.194847\pi$
$282$	−11.7632			−0.700489
$283$	−5.01437	+	8.68515i	−0.298073	+	0.516278i	−0.975695	−	0.219132i	$-0.929677\pi$
$283$	−5.01437	+	8.68515i	−0.298073	+	0.516278i	0.677622	+	0.735411i	$0.263011\pi$
$284$	−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	$-0.342157\pi$
$293$	−0.821707	−	0.474413i	−0.0480046	−	0.0277155i	−0.523810	+	0.851835i	$0.675490\pi$
$294$	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
$300$	−4.98390	+	0.400968i	−0.287745	+	0.0231499i
$301$	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
$305$	9.82296	−	10.6450i	0.562461	−	0.609530i
$306$	−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	−0.972137	−	0.234414i	$-0.924683\pi$
$311$	−22.1356	+	12.7800i	−1.25520	+	0.724688i	−0.283060	+	0.959102i	$0.591349\pi$
$312$	−3.14999	+	1.81865i	−0.178333	+	0.102961i
$313$	2.35334	+	4.07611i	0.133019	+	0.230395i	0.924839	−	0.380359i	$-0.124200\pi$
$313$	2.35334	+	4.07611i	0.133019	+	0.230395i	−0.791820	+	0.610754i	$0.790866\pi$
$314$	−12.7985	−	7.38920i	−0.722259	−	0.416997i
$315$	2.30886	+	0.520331i	0.130090	+	0.0293173i
$316$	3.10453	−	1.79240i	0.174643	−	0.100830i
$317$	21.7227	−	12.5416i	1.22007	−	0.704407i	0.255137	−	0.966905i	$-0.417880\pi$
$317$	21.7227	−	12.5416i	1.22007	−	0.704407i	0.964933	+	0.262498i	$0.0845462\pi$
$318$	−4.62445	−	8.00978i	−0.259326	−	0.449166i
$319$		−	1.67214i		−	0.0936219i
$320$	−0.491597	+	2.18136i	−0.0274811	+	0.121942i
$321$	−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
$330$	1.80093	+	0.405862i	0.0991380	+	0.0223420i
$331$	7.92971	−	4.57822i	0.435856	−	0.251642i	−0.265982	−	0.963978i	$-0.585696\pi$
$331$	7.92971	−	4.57822i	0.435856	−	0.251642i	0.701838	+	0.712336i	$0.252363\pi$
$332$		−	15.4846i		−	0.849828i
$333$	−1.90173	−	5.77784i	−0.104214	−	0.316624i
$334$	21.4770			1.17517
$335$	−19.6924	+	21.3403i	−1.07591	+	1.16595i
$336$	0.529225	−	0.916644i	0.0288716	−	0.0500070i
$337$	8.94213	+	5.16274i	0.487109	+	0.281232i	0.723374	−	0.690456i	$-0.242590\pi$
$337$	8.94213	+	5.16274i	0.487109	+	0.281232i	−0.236266	+	0.971689i	$0.575924\pi$
$338$	−0.114948	+	0.199096i	−0.00625236	+	0.0108294i
$339$			3.35443i			0.182188i
$340$	−0.729666	+	3.23774i	−0.0395717	+	0.175591i
$341$		−	5.18209i		−	0.280626i
$342$	4.75785	−	2.74695i	0.257275	−	0.148538i
$343$			13.6325i			0.736086i
$344$	−10.6694			−0.575257
$345$	−3.39651	+	3.68074i	−0.182862	+	0.198164i
$346$	2.69931	+	1.55845i	0.145116	+	0.0837827i
$347$	25.3284			1.35970			0.679850	−	0.733351i	$-0.262045\pi$
$347$	25.3284			1.35970			0.679850	+	0.733351i	$0.262045\pi$
$348$	1.01268	+	1.75402i	0.0542855	+	0.0940252i
$349$	11.2916	+	19.5576i	0.604426	+	1.04690i	0.992142	+	0.125117i	$0.0399308\pi$
$349$	11.2916	+	19.5576i	0.604426	+	1.04690i	−0.387716	+	0.921779i	$0.626736\pi$
$350$	2.27006	−	4.78066i	0.121340	−	0.255537i
$351$	−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	−0.990670	−	0.136283i	$-0.956484\pi$
$353$	−11.5240	−	19.9601i	−0.613360	−	1.06237i	0.377310	−	0.926087i	$-0.376849\pi$
$354$	−3.65709	−	6.33426i	−0.194372	−	0.336662i
$355$	−2.30436	−	2.12641i	−0.122303	−	0.112858i
$356$		−	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
$365$	19.2508	+	4.33840i	1.00763	+	0.227082i
$366$	3.23888	−	5.60990i	0.169299	−	0.293234i
$367$	5.59808	+	3.23205i	0.292217	+	0.168712i	0.638941	−	0.769255i	$-0.279373\pi$
$367$	5.59808	+	3.23205i	0.292217	+	0.168712i	−0.346724	+	0.937967i	$0.612706\pi$
$368$	1.11991	+	1.93975i	0.0583795	+	0.101116i
$369$	−2.85716			−0.148738
$370$	−13.5384	+	1.30799i	−0.703830	+	0.0679993i
$371$	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	$-0.103026\pi$
$373$	22.1461	+	12.7860i	1.14668	+	0.662036i	0.198604	+	0.980080i	$0.436359\pi$
$374$	0.612709	−	1.06124i	0.0316824	−	0.0548756i
$375$	−10.3736	+	4.17005i	−0.535688	+	0.215340i
$376$			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	0.876001	−	0.482309i	$-0.160202\pi$
$379$	0.395361	+	0.684786i	0.0203084	+	0.0351751i	−0.855693	+	0.517484i	$0.826869\pi$
$380$	−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	$-0.951317\pi$
$383$	−7.08892	+	12.2784i	−0.362227	+	0.627396i	0.626100	+	0.779743i	$0.284650\pi$
$384$			1.00000i			0.0510310i
$385$	−1.32513	+	1.43602i	−0.0675348	+	0.0731864i
$386$	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	0.828990	−	0.559264i	$-0.188916\pi$
$389$	14.9727	+	8.64452i	0.759149	+	0.438295i	−0.0698414	+	0.997558i	$0.522249\pi$
$390$	−5.51565	+	5.97722i	−0.279296	+	0.302668i
$391$	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
$395$	5.43605	−	5.89095i	0.273517	−	0.296406i
$396$	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
$400$	0.400968	+	4.98390i	0.0200484	+	0.249195i
$401$		−	29.8380i		−	1.49004i	−0.667043	−	0.745019i	$-0.732440\pi$
$401$		−	29.8380i		−	1.49004i	0.667043	−	0.745019i	$-0.267560\pi$
$402$	−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
$405$	−1.64331	−	1.51642i	−0.0816570	−	0.0753513i
$406$	−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	−0.644921	−	0.764250i	$-0.723110\pi$
$409$	−6.17878	+	3.56732i	−0.305521	+	0.176393i	0.339399	+	0.940642i	$0.389776\pi$
$410$	−1.40457	+	6.23251i	−0.0693669	+	0.307801i
$411$	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	0.942874	−	0.333149i	$-0.108111\pi$
$419$	3.74432	+	6.48535i	0.182922	+	0.316830i	−0.759952	+	0.649979i	$0.774778\pi$
$420$	0.520331	−	2.30886i	0.0253895	−	0.112661i
$421$			11.6772i			0.569114i	0.958659	+	0.284557i	$0.0918465\pi$
$421$			11.6772i			0.569114i	−0.958659	+	0.284557i	$0.908153\pi$
$422$	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
$425$	0.595147	+	7.39748i	0.0288689	+	0.358831i
$426$	−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	0.162957	−	0.986633i	$-0.447897\pi$
$431$	−12.6642	−	7.31168i	−0.610013	−	0.352191i	−0.772971	+	0.634442i	$0.781230\pi$
$432$	−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
$435$	3.32831	+	3.07130i	0.159580	+	0.147257i
$436$		−	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	0.525045	−	0.851075i	$-0.324049\pi$
$439$	1.05841	+	0.611072i	0.0505151	+	0.0291649i	−0.474530	+	0.880239i	$0.657382\pi$
$440$	0.405862	−	1.80093i	0.0193487	−	0.0858560i
$441$	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	0.720997	−	0.692939i	$-0.243684\pi$
$449$	10.2005	+	5.88927i	0.481392	+	0.277932i	−0.239604	+	0.970871i	$0.577018\pi$
$450$	−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	$-0.713554\pi$
$457$	7.85584	−	13.6067i	0.367481	−	0.636496i	0.989171	+	0.146768i	$0.0468870\pi$
$458$	23.3061			1.08902
$459$	−1.28542	+	0.742138i	−0.0599983	+	0.0346401i
$460$	3.68074	+	3.39651i	0.171615	+	0.158363i
$461$	−21.3746	+	12.3407i	−0.995517	+	0.574762i	−0.906919	−	0.421306i	$-0.861572\pi$
$461$	−21.3746	+	12.3407i	−0.995517	+	0.574762i	−0.0885978	+	0.996067i	$0.528239\pi$
$462$	−0.436928	+	0.756782i	−0.0203277	+	0.0352087i
$463$	−18.6610	+	32.3218i	−0.867249	+	1.50212i	−0.00245324	+	0.999997i	$0.500781\pi$
$463$	−18.6610	+	32.3218i	−0.867249	+	1.50212i	−0.864796	+	0.502123i	$0.832552\pi$
$464$	1.75402	−	1.01268i	0.0814282	−	0.0470126i
$465$	10.3147	+	9.51817i	0.478332	+	0.441395i
$466$	−0.440570	+	0.254363i	−0.0204090	+	0.0117831i
$467$	9.17134			0.424399			0.212200	−	0.977226i	$-0.431937\pi$
$467$	9.17134			0.424399			0.212200	+	0.977226i	$0.431937\pi$
$468$	−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	−0.584534	−	0.811369i	$-0.698723\pi$
$479$	−3.81113	+	2.20036i	−0.174135	+	0.100537i	0.410399	+	0.911906i	$0.365389\pi$
$480$	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
$485$	−2.54823	+	11.3073i	−0.115709	+	0.513437i
$486$	−0.866025	−	0.500000i	−0.0392837	−	0.0226805i
$487$	21.3719			0.968451			0.484226	−	0.874943i	$-0.339101\pi$
$487$	21.3719			0.968451			0.484226	+	0.874943i	$0.339101\pi$
$488$	−5.60990	−	3.23888i	−0.253948	−	0.146617i
$489$		−	3.52691i		−	0.159492i
$490$	−9.66217	−	8.91604i	−0.436492	−	0.402786i
$491$	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	0.963796	−	0.266642i	$-0.0859140\pi$
$499$	27.1360	+	15.6670i	1.21478	+	0.701351i	0.250979	+	0.967992i	$0.419247\pi$
$500$	4.17005	+	10.3736i	0.186490	+	0.463920i
$501$	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	$-0.273481\pi$
$503$	−7.38550	−	12.7921i	−0.329303	−	0.570370i	−0.982374	+	0.186927i	$0.940147\pi$
$504$		−	1.05845i		−	0.0471471i
$505$	5.17182	−	22.9489i	0.230143	−	1.02121i
$506$	−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	0.999538	−	0.0303912i	$-0.00967531\pi$
$509$	10.6815	+	18.5009i	0.473449	+	0.820039i	−0.526089	+	0.850430i	$0.676342\pi$
$510$	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
$515$	−7.95196	+	35.2852i	−0.350405	+	1.55485i
$516$	−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
$520$	5.97722	+	5.51565i	0.262118	+	0.241877i
$521$	16.6844	−	28.8982i	0.730957	−	1.26606i	−0.225517	−	0.974239i	$-0.572407\pi$
$521$	16.6844	−	28.8982i	0.730957	−	1.26606i	0.956474	−	0.291816i	$-0.0942595\pi$
$522$	1.75402	+	1.01268i	0.0767713	+	0.0443239i
$523$	−6.52639	+	11.3040i	−0.285379	+	0.494291i	−0.972701	−	0.232062i	$-0.925453\pi$
$523$	−6.52639	+	11.3040i	−0.285379	+	0.494291i	0.687322	+	0.726353i	$0.258786\pi$
$524$			13.0284i			0.569148i
$525$	−0.424404	−	5.27520i	−0.0185225	−	0.230229i
$526$			18.3663i			0.800807i
$527$	8.06828	−	4.65822i	0.351460	−	0.202915i
$528$		−	0.825600i		−	0.0359296i
$529$	−17.9832			−0.781878
$530$	−14.0252	+	15.1989i	−0.609215	+	0.660196i
$531$	−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
$535$	−21.3819	+	23.1712i	−0.924420	+	1.00178i
$536$	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
$540$	−1.51642	+	1.64331i	−0.0652561	+	0.0707170i
$541$			21.6228i			0.929635i	0.885406	+	0.464818i	$0.153880\pi$
$541$			21.6228i			0.929635i	−0.885406	+	0.464818i	$0.846120\pi$
$542$	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	$-0.633162\pi$
$547$	−19.0025			−0.812488			−0.406244	+	0.913765i	$0.633162\pi$
$548$	−6.19847	−	3.57869i	−0.264785	−	0.152874i
$549$		−	6.47775i		−	0.276464i
$550$	−0.331039	−	4.11471i	−0.0141156	−	0.175452i
$551$	−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
$555$	−11.0706	+	7.90197i	−0.469922	+	0.335420i
$556$	11.5306			0.489006
$557$	18.9136	+	32.7593i	0.801395	+	1.38806i	0.918698	+	0.394960i	$0.129242\pi$
$557$	18.9136	+	32.7593i	0.801395	+	1.38806i	−0.117304	+	0.993096i	$0.537425\pi$
$558$	5.43583	+	3.13838i	0.230117	+	0.132858i
$559$	−19.4039	+	33.6086i	−0.820698	+	1.42149i
$560$	−2.30886	−	0.520331i	−0.0975671	−	0.0219880i
$561$		−	1.22542i		−	0.0517372i
$562$	−12.2372	−	7.06515i	−0.516195	−	0.298025i
$563$	2.80373			0.118163			0.0590815	−	0.998253i	$-0.481183\pi$
$563$	2.80373			0.118163			0.0590815	+	0.998253i	$0.481183\pi$
$564$	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	$0.311976\pi$
$569$			39.6236i			1.66111i	−0.556937	+	0.830555i	$0.688024\pi$
$570$	−9.02819	−	8.33102i	−0.378149	−	0.348948i
$571$	−3.77916	−	6.54570i	−0.158153	−	0.273929i	0.776050	−	0.630672i	$-0.217221\pi$
$571$	−3.77916	−	6.54570i	−0.158153	−	0.273929i	−0.934203	+	0.356743i	$0.883887\pi$
$572$	−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
$575$	10.1165	+	4.80375i	0.421889	+	0.200330i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	−14.7782	−	25.5966i	−0.615224	−	1.06560i	−0.990345	−	0.138624i	$-0.955732\pi$
$577$	−14.7782	−	25.5966i	−0.615224	−	1.06560i	0.375121	−	0.926976i	$-0.377601\pi$
$578$	−14.7969			−0.615471
$579$	16.0391	+	9.26016i	0.666561	+	0.384839i
$580$	3.07130	−	3.32831i	0.127529	−	0.138201i
$581$	16.3897			0.679958
$582$			5.18358i			0.214867i
$583$	6.61288	−	3.81795i	0.273877	−	0.158123i
$584$		−	8.82512i		−	0.365186i
$585$	−1.78808	+	7.93425i	−0.0739281	+	0.328041i
$586$			0.948825i			0.0391956i
$587$	16.1870	−	28.0366i	0.668108	−	1.15720i	−0.310325	−	0.950631i	$-0.600438\pi$
$587$	16.1870	−	28.0366i	0.668108	−	1.15720i	0.978433	−	0.206566i	$-0.0662288\pi$
$588$	−5.09196	−	2.93984i	−0.209989	−	0.121237i
$589$	−17.2419	+	29.8639i	−0.710441	+	1.23052i
$590$	−11.0913	+	12.0195i	−0.456623	+	0.494835i
$591$	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
$595$	−3.42699	−	0.772315i	−0.140493	−	0.0316618i
$596$	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	−0.890457	−	0.455068i	$-0.849615\pi$
$599$	−1.25133	+	2.16737i	−0.0511279	+	0.0885562i	0.839329	+	0.543624i	$0.182948\pi$
$600$	2.83920	+	4.11570i	0.115910	+	0.168023i
$601$	8.38293	+	14.5197i	0.341947	+	0.592269i	0.984794	−	0.173725i	$-0.0555804\pi$
$601$	8.38293	+	14.5197i	0.341947	+	0.592269i	−0.642847	+	0.765994i	$0.722247\pi$
$602$		−	11.2930i		−	0.460270i
$603$			12.9861i			0.528837i
$604$	−4.20011	−	7.27481i	−0.170900	−	0.296008i
$605$	5.07249	−	22.5081i	0.206226	−	0.915085i
$606$		−	10.5205i		−	0.427364i
$607$	−5.24017	−	9.07623i	−0.212692	−	0.368393i	0.739864	−	0.672756i	$-0.234890\pi$
$607$	−5.24017	−	9.07623i	−0.212692	−	0.368393i	−0.952556	+	0.304363i	$0.901556\pi$
$608$	−4.75785	+	2.74695i	−0.192956	+	0.111403i
$609$	−1.85654	+	1.07187i	−0.0752308	+	0.0434345i
$610$	−14.1303	−	3.18444i	−0.572120	−	0.128934i
$611$	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	$-0.624843\pi$
$613$	5.61834	−	3.24375i	0.226923	−	0.131014i	0.609152	+	0.793054i	$0.291510\pi$
$614$	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	$-0.824945\pi$
$617$	−20.5224	+	11.8486i	−0.826200	+	0.477007i	0.0263501	+	0.999653i	$0.491612\pi$
$618$			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	$0.714205\pi$
$620$	9.51817	−	10.3147i	0.382259	−	0.414248i
$621$			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
$625$	15.8005	+	19.3738i	0.632021	+	0.774951i
$626$	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	−0.305270	−	0.952266i	$-0.598747\pi$
$631$	9.21344	−	5.31938i	0.366781	−	0.211761i	0.672051	+	0.740504i	$0.265413\pi$
$632$	−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	0.939587	−	0.342311i	$-0.111210\pi$
$641$	4.38870	+	7.60145i	0.173343	+	0.300239i	−0.766243	+	0.642550i	$0.777876\pi$
$642$	−7.05015	+	12.2112i	−0.278247	+	0.481938i
$643$	26.7207			1.05376			0.526882	−	0.849939i	$-0.323361\pi$
$643$	26.7207			1.05376			0.526882	+	0.849939i	$0.323361\pi$
$644$	−2.05312	+	1.18537i	−0.0809044	+	0.0467102i
$645$	−16.1793	+	17.5332i	−0.637059	+	0.690370i
$646$	−7.06197	+	4.07723i	−0.277849	+	0.160416i
$647$	−9.72305	+	16.8408i	−0.382252	+	0.662081i	−0.991384	−	0.130989i	$-0.958185\pi$
$647$	−9.72305	+	16.8408i	−0.382252	+	0.662081i	0.609131	+	0.793069i	$0.291518\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	5.22957	−	3.01929i	0.205278	−	0.118518i
$650$	16.4284	+	7.80090i	0.644376	+	0.305977i
$651$	−5.75355	+	3.32182i	−0.225500	+	0.130192i
$652$	−3.52691			−0.138124
$653$	12.7773	−	22.1309i	0.500014	−	0.866049i	−0.499986	−	0.866033i	$-0.666662\pi$
$653$	12.7773	−	22.1309i	0.500014	−	0.866049i	1.00000		1.60106e-5i	$-5.09633e-6\pi$
$654$	−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	−0.843504	−	0.537123i	$-0.819511\pi$
$659$	1.11439	−	1.93019i	0.0434106	−	0.0751893i	0.886914	+	0.461934i	$0.152844\pi$
$660$	−0.548978	−	1.76258i	−0.0213690	−	0.0686085i
$661$	10.9781	+	6.33818i	0.426997	+	0.246527i	0.698066	−	0.716033i	$-0.254044\pi$
$661$	10.9781	+	6.33818i	0.426997	+	0.246527i	−0.271070	+	0.962560i	$0.587377\pi$
$662$	−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
$670$	28.3275	+	6.38395i	1.09439	+	0.246634i
$671$	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	$-0.615668\pi$
$673$	−34.8308	−	20.1096i	−1.34263	−	0.775168i	−0.987193	+	0.159532i	$0.949002\pi$
$674$		−	10.3255i		−	0.397723i
$675$	−2.14470	+	4.51666i	−0.0825495	+	0.173847i
$676$	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	$-0.301429\pi$
$683$	−10.7369	−	18.5968i	−0.410835	−	0.711587i	−0.994981	+	0.100061i	$0.968096\pi$
$684$	−4.75785	−	2.74695i	−0.181921	−	0.105032i
$685$	−15.6128	−	3.51854i	−0.596535	−	0.134437i
$686$	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
$690$	4.88587	+	1.10109i	0.186002	+	0.0419178i
$691$	7.87430	+	13.6387i	0.299553	+	0.518840i	0.976034	−	0.217620i	$-0.0698293\pi$
$691$	7.87430	+	13.6387i	0.299553	+	0.518840i	−0.676481	+	0.736460i	$0.736496\pi$
$692$		−	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
$700$	−5.27520	+	0.424404i	−0.199384	+	0.0160410i
$701$	−32.3179	+	18.6588i	−1.22063	+	0.704732i	−0.965053	−	0.262056i	$-0.915600\pi$
$701$	−32.3179	+	18.6588i	−1.22063	+	0.704732i	−0.255579	+	0.966788i	$0.582266\pi$
$702$			3.63729i			0.137281i
$703$	−24.9196	−	22.2661i	−0.939859	−	0.839783i
$704$	−0.825600			−0.0311160
$705$	19.3307	+	17.8379i	0.728035	+	0.671815i
$706$	−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	$-0.830192\pi$
$709$		−	27.0809i		−	1.01705i	0.861048	−	0.508523i	$-0.169808\pi$
$710$	−0.689348	+	3.05884i	−0.0258708	+	0.114796i
$711$		−	3.58480i		−	0.134440i
$712$	−2.86558	+	1.65444i	−0.107392	+	0.0620028i
$713$		−	14.0588i		−	0.526508i
$714$	−1.57103			−0.0587944
$715$	−4.93479	−	4.55372i	−0.184551	−	0.170299i
$716$	−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	0.859353	−	0.511382i	$-0.170866\pi$
$719$	−0.353769	−	0.612746i	−0.0131934	−	0.0228516i	−0.872547	+	0.488531i	$0.837533\pi$
$720$	1.64331	+	1.51642i	0.0612427	+	0.0565135i
$721$	−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
$725$	4.34380	−	9.14790i	0.161325	−	0.339744i
$726$		−	10.3184i		−	0.382951i
$727$	−25.3278	+	43.8690i	−0.939356	+	1.62701i	−0.172680	+	0.984978i	$0.555243\pi$
$727$	−25.3278	+	43.8690i	−0.939356	+	1.62701i	−0.766676	+	0.642034i	$0.778091\pi$
$728$	−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	$-0.118408\pi$
$733$	29.3112	+	16.9228i	1.08263	+	0.625058i	0.151027	+	0.988530i	$0.451742\pi$
$734$		−	6.46411i		−	0.238595i
$735$	−12.8257	−	2.89043i	−0.473083	−	0.106615i
$736$	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	$0.581180\pi$
$740$	7.90197	+	11.0706i	0.290482	+	0.406964i
$741$	−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	$-0.238375\pi$
$743$	13.8765	+	8.01159i	0.509079	+	0.293917i	−0.223376	+	0.974732i	$0.571708\pi$
$744$	3.13838	−	5.43583i	0.115059	−	0.199287i
$745$	1.49377	−	6.62829i	0.0547274	−	0.242842i
$746$		−	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
$755$	−13.8042	−	12.7382i	−0.502387	−	0.463592i
$756$	−0.529225	−	0.916644i	−0.0192477	−	0.0333380i
$757$	25.2767	+	43.7805i	0.918697	+	1.59123i	0.801396	+	0.598134i	$0.204091\pi$
$757$	25.2767	+	43.7805i	0.918697	+	1.59123i	0.117301	+	0.993096i	$0.462576\pi$
$758$	0.395361	−	0.684786i	0.0143602	−	0.0248726i
$759$	−1.60145	−	0.924600i	−0.0581291	−	0.0335608i
$760$	−8.33102	+	9.02819i	−0.302198	+	0.327487i
$761$	−19.6784	−	34.0840i	−0.713341	−	1.23554i	−0.963596	−	0.267362i	$-0.913848\pi$
$761$	−19.6784	−	34.0840i	−0.713341	−	1.23554i	0.250255	−	0.968180i	$-0.419485\pi$
$762$	−3.14005	−	5.43873i	−0.113752	−	0.197024i
$763$	5.55677			0.201169
$764$	16.6845	+	9.63281i	0.603625	+	0.348503i
$765$	2.43913	+	2.25078i	0.0881871	+	0.0813771i
$766$	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	$0.0274507\pi$
$769$			4.77703i			0.172264i	−0.996284	+	0.0861320i	$0.972549\pi$
$770$	1.90619	+	0.429585i	0.0686945	+	0.0154812i
$771$			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	$-0.254402\pi$
$773$	11.8192	+	6.82383i	0.425108	+	0.245436i	−0.272153	+	0.962254i	$0.587736\pi$
$774$	−5.33471	+	9.23999i	−0.191752	+	0.332125i
$775$	13.4618	−	28.3500i	0.483561	−	1.01836i
$776$	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
$780$	7.93425	+	1.78808i	0.284092	+	0.0640236i
$781$	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
$790$	−7.81974	−	1.76228i	−0.278214	−	0.0626990i
$791$			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
$795$	−4.54673	+	20.1752i	−0.161256	+	0.715540i
$796$	15.4856	+	8.94064i	0.548874	+	0.316893i
$797$	−23.6068	−	40.8882i	−0.836196	−	1.44833i	−0.893053	−	0.449951i	$-0.851441\pi$
$797$	−23.6068	−	40.8882i	−0.836196	−	1.44833i	0.0568572	−	0.998382i	$-0.481892\pi$
$798$	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
$805$	−3.59503	+	3.89588i	−0.126708	+	0.137312i
$806$		−	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	0.482107	−	0.876112i	$-0.339872\pi$
$809$	−1.01187	−	0.584203i	−0.0355754	−	0.0205395i	−0.517682	+	0.855573i	$0.673205\pi$
$810$	−0.491597	+	2.18136i	−0.0172730	+	0.0766452i
$811$	8.38136	−	14.5169i	0.294309	−	0.509759i	−0.680515	−	0.732735i	$-0.738244\pi$
$811$	8.38136	−	14.5169i	0.294309	−	0.509759i	0.974824	+	0.222976i	$0.0715770\pi$
$812$	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	−0.721929	−	0.691967i	$-0.756744\pi$
$821$	6.82793	−	11.8263i	0.238296	−	0.412741i	0.960226	+	0.279226i	$0.0900777\pi$
$822$	−7.15737			−0.249642
$823$	44.2226	−	25.5319i	1.54150	−	0.889987i	0.542758	−	0.839889i	$-0.317380\pi$
$823$	44.2226	−	25.5319i	1.54150	−	0.889987i	0.998744	−	0.0500971i	$-0.0159531\pi$
$824$	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	$-0.838911\pi$
$827$	−0.503911	+	0.872799i	−0.0175227	+	0.0303502i	0.857131	+	0.515098i	$0.172245\pi$
$828$	2.23982			0.0778393
$829$	−44.8670	+	25.9040i	−1.55830	+	0.899682i	−0.560875	+	0.827900i	$0.689535\pi$
$829$	−44.8670	+	25.9040i	−1.55830	+	0.899682i	−0.997420	+	0.0717819i	$0.977131\pi$
$830$	−23.4811	+	25.4461i	−0.815041	+	0.883246i
$831$	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
$835$	−35.2934	−	32.5680i	−1.22138	−	1.12706i
$836$	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	0.759773	−	0.650188i	$-0.225310\pi$
$839$	−5.30628	−	9.19075i	−0.183193	−	0.317300i	−0.942966	+	0.332889i	$0.891977\pi$
$840$	−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	$-0.0754506\pi$
$853$	8.25535	+	14.2987i	0.282658	+	0.489578i	−0.689381	+	0.724399i	$0.742117\pi$
$854$	3.42819	−	5.93779i	0.117310	−	0.203187i
$855$	−11.9842	−	2.70078i	−0.409850	−	0.0923647i
$856$	12.2112	+	7.05015i	0.417371	+	0.240969i
$857$	−18.5888			−0.634983			−0.317491	−	0.948261i	$-0.602840\pi$
$857$	−18.5888			−0.634983			−0.317491	+	0.948261i	$0.602840\pi$
$858$	−2.60063	−	1.50147i	−0.0887840	−	0.0512595i
$859$		−	55.7543i		−	1.90231i	−0.308709	−	0.951156i	$-0.599897\pi$
$859$		−	55.7543i		−	1.90231i	0.308709	−	0.951156i	$-0.400103\pi$
$860$	17.5332	+	16.1793i	0.597878	+	0.551709i
$861$	−3.02416			−0.103063
$862$			14.6234i			0.498074i
$863$	−6.09879	+	3.52114i	−0.207605	+	0.119861i	−0.600198	−	0.799851i	$-0.704912\pi$
$863$	−6.09879	+	3.52114i	−0.207605	+	0.119861i	0.392593	+	0.919712i	$0.371578\pi$
$864$	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
$870$	0.995663	−	4.41805i	0.0337561	−	0.149786i
$871$	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
$875$	−10.9799	+	4.41378i	−0.371188	+	0.149213i
$876$	−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	−0.745042	−	0.667018i	$-0.767571\pi$
$881$	6.08870	−	10.5459i	0.205133	−	0.355301i	0.950175	+	0.311716i	$0.100904\pi$
$882$	−5.87968			−0.197979
$883$	−17.4587	+	30.2394i	−0.587532	+	1.01764i	0.407023	+	0.913418i	$0.366567\pi$
$883$	−17.4587	+	30.2394i	−0.587532	+	1.01764i	−0.994555	+	0.104217i	$0.966766\pi$
$884$	2.69937	−	4.67545i	0.0907898	−	0.157253i
$885$	−3.59563	+	15.9549i	−0.120866	+	0.536316i
$886$	−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
$890$	−5.01764	+	5.43754i	−0.168192	+	0.182267i
$891$	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
$895$	−21.8690	−	4.92845i	−0.731000	−	0.164740i
$896$			1.05845i			0.0353603i
$897$	7.05542	−	4.07345i	0.235574	−	0.136009i
$898$		−	11.7785i		−	0.393055i
$899$	−12.7127			−0.423993
$900$	4.51666	+	2.14470i	0.150555	+	0.0714900i
$901$	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
$905$	2.91756	+	2.69226i	0.0969829	+	0.0894938i
$906$	−7.27481	−	4.20011i	−0.241689	−	0.139539i
$907$	1.71682	−	2.97363i	0.0570062	−	0.0987377i	−0.836114	−	0.548556i	$-0.815178\pi$
$907$	1.71682	−	2.97363i	0.0570062	−	0.0987377i	0.893120	+	0.449818i	$0.148511\pi$
$908$	−11.6633	−	20.2013i	−0.387059	−	0.670405i
$909$	−5.26023	−	9.11098i	−0.174471	−	0.302192i
$910$	−5.83803	+	6.32658i	−0.193529	+	0.209724i
$911$			21.1245i			0.699887i	0.936771	+	0.349944i	$0.113799\pi$
$911$			21.1245i			0.699887i	−0.936771	+	0.349944i	$0.886201\pi$
$912$	−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	$-0.745962\pi$
$919$		−	43.4122i		−	1.43204i	0.698081	−	0.716019i	$-0.254038\pi$
$920$	1.10109	−	4.88587i	0.0363019	−	0.161082i
$921$	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
$925$	24.2314	+	18.3804i	0.796723	+	0.604345i
$926$	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	−0.218705	−	0.975791i	$-0.570183\pi$
$929$	22.4240	−	38.8395i	0.735707	−	1.27428i	0.954412	−	0.298491i	$-0.0964834\pi$
$930$	3.08563	−	13.6919i	0.101182	−	0.448974i
$931$		−	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	$-0.933964\pi$
$937$	−39.4709	+	22.7885i	−1.28946	+	0.744469i	−0.310900	+	0.950443i	$0.600631\pi$
$938$	−6.87259	+	11.9037i	−0.224398	+	0.388669i
$939$		−	4.70669i		−	0.153597i
$940$	17.8379	−	19.3307i	0.581809	−	0.630497i
$941$	−25.2217	−	43.6853i	−0.822205	−	1.42410i	−0.904037	−	0.427455i	$-0.859410\pi$
$941$	−25.2217	−	43.6853i	−0.822205	−	1.42410i	0.0818313	−	0.996646i	$-0.473923\pi$
$942$	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
$945$	−1.73937	−	1.60505i	−0.0565816	−	0.0522123i
$946$	−4.40434	−	7.62854i	−0.143197	−	0.248025i
$947$	−25.3654	−	43.9341i	−0.824264	−	1.42767i	−0.902480	−	0.430731i	$-0.858256\pi$
$947$	−25.3654	−	43.9341i	−0.824264	−	1.42767i	0.0782163	−	0.996936i	$-0.475078\pi$
$948$	−3.58480			−0.116429
$949$	−27.7990	−	16.0498i	−0.902394	−	0.520997i
$950$	−11.7827	+	24.8141i	−0.382283	+	0.805075i
$951$	−25.0832			−0.813379
$952$			1.57103i			0.0509174i
$953$	50.0894	−	28.9192i	1.62256	−	0.936783i	0.636323	−	0.771423i	$-0.280455\pi$
$953$	50.0894	−	28.9192i	1.62256	−	0.936783i	0.986233	−	0.165360i	$-0.0528787\pi$
$954$			9.24890i			0.299444i
$955$	42.0253	+	9.47092i	1.35991	+	0.306472i
$956$			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
$960$	1.51642	−	1.64331i	0.0489421	−	0.0530378i
$961$	−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
$965$	9.10453	−	40.3995i	0.293085	−	1.30051i
$966$	−1.18537	+	2.05312i	−0.0381387	+	0.0660581i
$967$	13.0477	−	22.5993i	0.419586	−	0.726744i	−0.576312	−	0.817230i	$-0.695509\pi$
$967$	13.0477	−	22.5993i	0.419586	−	0.726744i	0.995898	+	0.0904856i	$0.0288419\pi$
$968$	−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	0.906078	−	0.423111i	$-0.139062\pi$
$971$	2.69897	+	4.67476i	0.0866142	+	0.150020i	−0.819464	+	0.573131i	$0.805729\pi$
$972$			1.00000i			0.0320750i
$973$			12.2046i			0.391260i
$974$	−10.6859	−	18.5086i	−0.342399	−	0.593053i
$975$	18.1279	−	1.45844i	0.580557	−	0.0467074i
$976$			6.47775i			0.207348i
$977$	−7.00738	−	12.1371i	−0.224186	−	0.388302i	0.731889	−	0.681424i	$-0.238639\pi$
$977$	−7.00738	−	12.1371i	−0.224186	−	0.388302i	−0.956075	+	0.293122i	$0.905306\pi$
$978$	−3.05439	+	1.76345i	−0.0976686	+	0.0563890i
$979$	2.36582	−	1.36591i	0.0756120	−	0.0436546i
$980$	−2.89043	+	12.8257i	−0.0923316	+	0.409702i
$981$	−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	0.663946	−	0.747780i	$-0.268880\pi$
$983$	51.5289	−	29.7502i	1.64352	−	0.948885i	0.979570	−	0.201104i	$-0.0644531\pi$
$984$	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
$990$	−1.35672	−	1.25195i	−0.0431194	−	0.0397897i
$991$			56.8156i			1.80481i	0.430893	+	0.902403i	$0.358199\pi$
$991$			56.8156i			1.80481i	−0.430893	+	0.902403i	$0.641801\pi$
$992$	−5.43583	−	3.13838i	−0.172588	−	0.0996436i
$993$	−9.15644			−0.290571
$994$	−1.28538	−	0.742112i	−0.0407696	−	0.0235384i
$995$	39.0055	+	8.79039i	1.23656	+	0.278674i
$996$	−7.74230	+	13.4101i	−0.245324	+	0.424914i
$997$	−19.9693	−	34.5879i	−0.632435	−	1.09541i	−0.987052	−	0.160398i	$-0.948722\pi$
$997$	−19.9693	−	34.5879i	−0.632435	−	1.09541i	0.354618	−	0.935011i	$-0.384611\pi$
$998$		−	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.a.529.3	✓	36
5.4	even	2		1110.2.ba.b.529.16	yes	36
37.27	even	6		1110.2.ba.b.619.16	yes	36
185.64	even	6	inner	1110.2.ba.a.619.3	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.ba.a.529.3	✓	36	1.1	even	1	trivial
1110.2.ba.a.619.3	yes	36	185.64	even	6	inner
1110.2.ba.b.529.16	yes	36	5.4	even	2
1110.2.ba.b.619.16	yes	36	37.27	even	6

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)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.491597 + 2.18136i) q^{5} +1.00000i q^{6} +(-0.916644 - 0.529225i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.491597 + 2.18136i) 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} +(1.51642 - 1.64331i) 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} +(-1.64331 - 1.51642i) q^{20} +(0.529225 + 0.916644i) q^{21} +(0.412800 + 0.714991i) q^{22} -2.23982 q^{23} +(-0.866025 - 0.500000i) q^{24} +(-4.51666 - 2.14470i) q^{25} -3.63729 q^{26} -1.00000i q^{27} +(0.916644 - 0.529225i) q^{28} +2.02537i q^{29} +(-2.18136 - 0.491597i) q^{30} +6.27676i q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.714991 + 0.412800i) q^{33} +(-0.742138 + 1.28542i) q^{34} +(1.60505 - 1.73937i) q^{35} -1.00000 q^{36} +(-5.95462 - 1.24197i) q^{37} -5.49389i q^{38} +(-3.14999 + 1.81865i) q^{39} +(-0.491597 + 2.18136i) 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} +(0.400968 + 4.98390i) q^{50} +1.48428i q^{51} +(1.81865 + 3.14999i) q^{52} +(-8.00978 + 4.62445i) q^{53} +(-0.866025 + 0.500000i) q^{54} +(0.405862 - 1.80093i) 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} +(5.97722 + 5.51565i) q^{65} -0.825600i q^{66} +(11.2463 + 6.49307i) q^{67} +1.48428 q^{68} +(1.93975 + 1.11991i) q^{69} +(-2.30886 - 0.520331i) 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} +(1.64331 + 1.51642i) 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} +(-8.33102 + 9.02819i) 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 18 q^{2} - 18 q^{4} + 2 q^{5} + 36 q^{8} + 18 q^{9}+O(q^{10}) \) 36 * q - 18 * q^2 - 18 * q^4 + 2 * q^5 + 36 * q^8 + 18 * q^9	\( 36 q - 18 q^{2} - 18 q^{4} + 2 q^{5} + 36 q^{8} + 18 q^{9} + 2 q^{10} + 4 q^{11} - 14 q^{13} - 2 q^{15} - 18 q^{16} + 18 q^{18} + 6 q^{19} - 4 q^{20} - 2 q^{22} - 20 q^{23} + 4 q^{25} + 28 q^{26} - 2 q^{30} - 18 q^{32} - 6 q^{33} - 40 q^{35} - 36 q^{36} + 20 q^{37} + 6 q^{39} + 2 q^{40} + 10 q^{41} - 2 q^{44} - 2 q^{45} + 10 q^{46} + 10 q^{49} - 2 q^{50} - 14 q^{52} - 12 q^{53} + 56 q^{55} + 8 q^{57} + 30 q^{58} + 18 q^{59} + 4 q^{60} - 6 q^{61} - 12 q^{62} + 36 q^{64} + 40 q^{65} + 36 q^{67} + 12 q^{69} + 20 q^{70} - 24 q^{71} + 18 q^{72} - 34 q^{74} + 8 q^{75} - 6 q^{76} - 24 q^{77} - 6 q^{78} + 2 q^{80} - 18 q^{81} - 20 q^{82} + 36 q^{83} + 26 q^{85} - 10 q^{87} + 4 q^{88} + 4 q^{90} - 36 q^{91} + 10 q^{92} + 12 q^{93} + 12 q^{94} - 30 q^{95} + 52 q^{97} + 10 q^{98} + 2 q^{99}+O(q^{100}) \) 36 * q - 18 * q^2 - 18 * q^4 + 2 * 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 - 4 * q^20 - 2 * q^22 - 20 * q^23 + 4 * q^25 + 28 * q^26 - 2 * q^30 - 18 * q^32 - 6 * q^33 - 40 * q^35 - 36 * q^36 + 20 * q^37 + 6 * q^39 + 2 * q^40 + 10 * q^41 - 2 * q^44 - 2 * q^45 + 10 * q^46 + 10 * q^49 - 2 * q^50 - 14 * q^52 - 12 * q^53 + 56 * q^55 + 8 * q^57 + 30 * q^58 + 18 * q^59 + 4 * q^60 - 6 * q^61 - 12 * q^62 + 36 * q^64 + 40 * q^65 + 36 * q^67 + 12 * q^69 + 20 * 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 + 4 * q^90 - 36 * q^91 + 10 * q^92 + 12 * q^93 + 12 * q^94 - 30 * q^95 + 52 * q^97 + 10 * q^98 + 2 * q^99

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