LMFDB - Embedded newform 546.2.bv.a.317.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(317,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 4, 9]))

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

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

chi := DirichletCharacter("546.317");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bv (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$36$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			317.19
Character	$\chi$	$=$	546.317
Dual form			546.2.bv.a.515.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 - 0.258819i) q^{2} +(-1.73129 + 0.0513637i) q^{3} +(0.866025 - 0.500000i) q^{4} +(2.92144 - 0.782798i) q^{5} +(-1.65900 + 0.497704i) q^{6} +(-0.584700 + 2.58033i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.99472 - 0.177851i) q^{9} +O(q^{10})$	\(q+(0.965926 - 0.258819i) q^{2} +(-1.73129 + 0.0513637i) q^{3} +(0.866025 - 0.500000i) q^{4} +(2.92144 - 0.782798i) q^{5} +(-1.65900 + 0.497704i) q^{6} +(-0.584700 + 2.58033i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.99472 - 0.177851i) q^{9} +(2.61929 - 1.51225i) q^{10} +(-1.60292 - 0.429501i) q^{11} +(-1.47366 + 0.910127i) q^{12} +(3.59768 + 0.238040i) q^{13} +(0.103063 + 2.64374i) q^{14} +(-5.01765 + 1.50531i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.580520 - 1.00549i) q^{17} +(2.84665 - 0.946882i) q^{18} +(1.29627 + 4.83773i) q^{19} +(2.13864 - 2.13864i) q^{20} +(0.879749 - 4.49734i) q^{21} -1.65946 q^{22} +(1.67821 - 2.90674i) q^{23} +(-1.18789 + 1.26053i) q^{24} +(3.59192 - 2.07380i) q^{25} +(3.53671 - 0.701220i) q^{26} +(-5.17560 + 0.461731i) q^{27} +(0.783803 + 2.52699i) q^{28} -6.25536i q^{29} +(-4.45708 + 2.75268i) q^{30} +(9.23517 + 2.47456i) q^{31} +(0.258819 - 0.965926i) q^{32} +(2.79718 + 0.661258i) q^{33} +(-0.820979 - 0.820979i) q^{34} +(0.311715 + 7.99600i) q^{35} +(2.50458 - 1.65138i) q^{36} +(4.84229 - 1.29749i) q^{37} +(2.50419 + 4.33739i) q^{38} +(-6.24086 - 0.227326i) q^{39} +(1.51225 - 2.61929i) q^{40} +(-1.39464 - 1.39464i) q^{41} +(-0.314225 - 4.57179i) q^{42} -0.835305i q^{43} +(-1.60292 + 0.429501i) q^{44} +(8.60969 - 2.86384i) q^{45} +(0.868703 - 3.24204i) q^{46} +(-0.406755 - 1.51803i) q^{47} +(-0.821162 + 1.52502i) q^{48} +(-6.31625 - 3.01744i) q^{49} +(2.93279 - 2.93279i) q^{50} +(1.05669 + 1.71098i) q^{51} +(3.23471 - 1.59269i) q^{52} +(-9.00444 + 5.19871i) q^{53} +(-4.87974 + 1.78554i) q^{54} -5.01905 q^{55} +(1.41113 + 2.23802i) q^{56} +(-2.49269 - 8.30893i) q^{57} +(-1.61901 - 6.04222i) q^{58} +(2.14595 + 0.575005i) q^{59} +(-3.59276 + 3.81246i) q^{60} +(-2.85717 + 4.94876i) q^{61} +9.56095 q^{62} +(-1.29210 + 7.83138i) q^{63} -1.00000i q^{64} +(10.6968 - 2.12084i) q^{65} +(2.87301 - 0.0852361i) q^{66} +(-12.8449 - 3.44179i) q^{67} +(-1.00549 - 0.580520i) q^{68} +(-2.75616 + 5.11860i) q^{69} +(2.37061 + 7.64286i) q^{70} +(-4.08659 - 4.08659i) q^{71} +(1.99183 - 2.24335i) q^{72} +(-3.80315 + 14.1935i) q^{73} +(4.34148 - 2.50656i) q^{74} +(-6.11214 + 3.77484i) q^{75} +(3.54146 + 3.54146i) q^{76} +(2.04548 - 3.88494i) q^{77} +(-6.08704 + 1.39567i) q^{78} +(3.33349 - 5.77377i) q^{79} +(0.782798 - 2.92144i) q^{80} +(8.93674 - 1.06523i) q^{81} +(-1.70807 - 0.986157i) q^{82} +(0.280924 + 0.280924i) q^{83} +(-1.48678 - 4.33468i) q^{84} +(-2.48305 - 2.48305i) q^{85} +(-0.216193 - 0.806843i) q^{86} +(0.321298 + 10.8298i) q^{87} +(-1.43714 + 0.829732i) q^{88} +(2.01247 + 7.51064i) q^{89} +(7.57510 - 4.99461i) q^{90} +(-2.71779 + 9.14405i) q^{91} -3.35641i q^{92} +(-16.1158 - 3.80982i) q^{93} +(-0.785790 - 1.36103i) q^{94} +(7.57393 + 13.1184i) q^{95} +(-0.398477 + 1.68559i) q^{96} +(-7.91821 + 7.91821i) q^{97} +(-6.88200 - 1.27986i) q^{98} +(-4.87669 - 1.00116i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 16 q^{7}+O(q^{10}) $ 144 * q - 16 * q^7	$ 144 q - 16 q^{7} + 72 q^{16} + 16 q^{18} + 8 q^{19} + 8 q^{21} + 24 q^{27} - 8 q^{28} - 8 q^{31} + 12 q^{33} - 8 q^{37} + 16 q^{39} - 40 q^{45} + 8 q^{46} + 8 q^{52} - 12 q^{54} - 32 q^{55} + 16 q^{57} + 8 q^{58} - 32 q^{61} - 40 q^{63} - 32 q^{66} - 8 q^{67} + 16 q^{72} + 80 q^{73} - 16 q^{76} + 16 q^{78} - 112 q^{79} - 48 q^{81} + 16 q^{84} - 80 q^{85} + 96 q^{87} - 32 q^{91} + 36 q^{93} - 64 q^{94} - 144 q^{97} - 32 q^{99}+O(q^{100}) $ 144 * q - 16 * q^7 + 72 * q^16 + 16 * q^18 + 8 * q^19 + 8 * q^21 + 24 * q^27 - 8 * q^28 - 8 * q^31 + 12 * q^33 - 8 * q^37 + 16 * q^39 - 40 * q^45 + 8 * q^46 + 8 * q^52 - 12 * q^54 - 32 * q^55 + 16 * q^57 + 8 * q^58 - 32 * q^61 - 40 * q^63 - 32 * q^66 - 8 * q^67 + 16 * q^72 + 80 * q^73 - 16 * q^76 + 16 * q^78 - 112 * q^79 - 48 * q^81 + 16 * q^84 - 80 * q^85 + 96 * q^87 - 32 * q^91 + 36 * q^93 - 64 * q^94 - 144 * q^97 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$3$	−1.73129	+	0.0513637i	−0.999560	+	0.0296548i
$3$	−1.73129	+	0.0513637i	−0.999560	+	0.0296548i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	2.92144	−	0.782798i	1.30651	−	0.350078i	0.462601	−	0.886567i	$-0.346916\pi$
$5$	2.92144	−	0.782798i	1.30651	−	0.350078i	0.843907	+	0.536489i	$0.180250\pi$
$6$	−1.65900	+	0.497704i	−0.677285	+	0.203187i
$7$	−0.584700	+	2.58033i	−0.220996	+	0.975275i
$7$	−0.584700	+	2.58033i	−0.220996	+	0.975275i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	2.99472	−	0.177851i	0.998241	−	0.0592836i
$10$	2.61929	−	1.51225i	0.828293	−	0.478215i
$11$	−1.60292	−	0.429501i	−0.483298	−	0.129499i	0.00893972	−	0.999960i	$-0.497154\pi$
$11$	−1.60292	−	0.429501i	−0.483298	−	0.129499i	−0.492238	+	0.870461i	$0.663821\pi$
$12$	−1.47366	+	0.910127i	−0.425409	+	0.262731i
$13$	3.59768	+	0.238040i	0.997818	+	0.0660204i
$13$	3.59768	+	0.238040i	0.997818	+	0.0660204i
$14$	0.103063	+	2.64374i	0.0275448	+	0.706570i
$15$	−5.01765	+	1.50531i	−1.29555	+	0.388668i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−0.580520	−	1.00549i	−0.140797	−	0.243867i	0.787000	−	0.616953i	$-0.211633\pi$
$17$	−0.580520	−	1.00549i	−0.140797	−	0.243867i	−0.927797	+	0.373086i	$0.878300\pi$
$18$	2.84665	−	0.946882i	0.670962	−	0.223182i
$19$	1.29627	+	4.83773i	0.297384	+	1.10985i	0.939306	+	0.343081i	$0.111471\pi$
$19$	1.29627	+	4.83773i	0.297384	+	1.10985i	−0.641922	+	0.766770i	$0.721863\pi$
$20$	2.13864	−	2.13864i	0.478215	−	0.478215i
$21$	0.879749	−	4.49734i	0.191977	−	0.981399i
$22$	−1.65946			−0.353799
$23$	1.67821	−	2.90674i	0.349930	−	0.606097i	−0.636307	−	0.771436i	$-0.719539\pi$
$23$	1.67821	−	2.90674i	0.349930	−	0.606097i	0.986237	+	0.165340i	$0.0528720\pi$
$24$	−1.18789	+	1.26053i	−0.242476	+	0.257304i
$25$	3.59192	−	2.07380i	0.718384	−	0.414759i
$26$	3.53671	−	0.701220i	0.693605	−	0.137521i
$27$	−5.17560	+	0.461731i	−0.996044	+	0.0888602i
$28$	0.783803	+	2.52699i	0.148125	+	0.477555i
$29$		−	6.25536i		−	1.16159i	−0.814049	−	0.580796i	$-0.802741\pi$
$29$		−	6.25536i		−	1.16159i	0.814049	−	0.580796i	$-0.197259\pi$
$30$	−4.45708	+	2.75268i	−0.813747	+	0.502568i
$31$	9.23517	+	2.47456i	1.65869	+	0.444443i	0.962026	−	0.272959i	$-0.0880022\pi$
$31$	9.23517	+	2.47456i	1.65869	+	0.444443i	0.696659	+	0.717402i	$0.254669\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$	2.79718	+	0.661258i	0.486926	+	0.115110i
$34$	−0.820979	−	0.820979i	−0.140797	−	0.140797i
$35$	0.311715	+	7.99600i	0.0526894	+	1.35157i
$36$	2.50458	−	1.65138i	0.417430	−	0.275231i
$37$	4.84229	−	1.29749i	0.796068	−	0.213306i	0.162211	−	0.986756i	$-0.448137\pi$
$37$	4.84229	−	1.29749i	0.796068	−	0.213306i	0.633857	+	0.773450i	$0.281471\pi$
$38$	2.50419	+	4.33739i	0.406234	+	0.703617i
$39$	−6.24086	−	0.227326i	−0.999337	−	0.0364012i
$40$	1.51225	−	2.61929i	0.239108	−	0.414147i
$41$	−1.39464	−	1.39464i	−0.217806	−	0.217806i	0.589767	−	0.807573i	$-0.299219\pi$
$41$	−1.39464	−	1.39464i	−0.217806	−	0.217806i	−0.807573	+	0.589767i	$0.799219\pi$
$42$	−0.314225	−	4.57179i	−0.0484859	−	0.705442i
$43$		−	0.835305i		−	0.127383i	−0.997970	−	0.0636914i	$-0.979713\pi$
$43$		−	0.835305i		−	0.127383i	0.997970	−	0.0636914i	$-0.0202873\pi$
$44$	−1.60292	+	0.429501i	−0.241649	+	0.0647497i
$45$	8.60969	−	2.86384i	1.28346	−	0.426917i
$46$	0.868703	−	3.24204i	0.128083	−	0.478013i
$47$	−0.406755	−	1.51803i	−0.0593313	−	0.221427i	0.929894	−	0.367827i	$-0.119898\pi$
$47$	−0.406755	−	1.51803i	−0.0593313	−	0.221427i	−0.989226	+	0.146400i	$0.953231\pi$
$48$	−0.821162	+	1.52502i	−0.118525	+	0.220118i
$49$	−6.31625	−	3.01744i	−0.902322	−	0.431063i
$50$	2.93279	−	2.93279i	0.414759	−	0.414759i
$51$	1.05669	+	1.71098i	0.147967	+	0.239584i
$52$	3.23471	−	1.59269i	0.448573	−	0.220867i
$53$	−9.00444	+	5.19871i	−1.23685	+	0.714098i	−0.968450	−	0.249208i	$-0.919830\pi$
$53$	−9.00444	+	5.19871i	−1.23685	+	0.714098i	−0.268404	+	0.963306i	$0.586496\pi$
$54$	−4.87974	+	1.78554i	−0.664048	+	0.242981i
$55$	−5.01905			−0.676768
$56$	1.41113	+	2.23802i	0.188570	+	0.299068i
$57$	−2.49269	−	8.30893i	−0.330165	−	1.10054i
$58$	−1.61901	−	6.04222i	−0.212586	−	0.793382i
$59$	2.14595	+	0.575005i	0.279379	+	0.0748593i	0.395788	−	0.918342i	$-0.370472\pi$
$59$	2.14595	+	0.575005i	0.279379	+	0.0748593i	−0.116409	+	0.993201i	$0.537138\pi$
$60$	−3.59276	+	3.81246i	−0.463824	+	0.492186i
$61$	−2.85717	+	4.94876i	−0.365823	+	0.633624i	−0.988908	−	0.148530i	$-0.952546\pi$
$61$	−2.85717	+	4.94876i	−0.365823	+	0.633624i	0.623085	+	0.782154i	$0.285879\pi$
$62$	9.56095			1.21424
$63$	−1.29210	+	7.83138i	−0.162789	+	0.986661i
$64$		−	1.00000i		−	0.125000i
$65$	10.6968	−	2.12084i	1.32677	−	0.263058i
$66$	2.87301	−	0.0852361i	0.353643	−	0.0104918i
$67$	−12.8449	−	3.44179i	−1.56926	−	0.420482i	−0.633680	−	0.773596i	$-0.718456\pi$
$67$	−12.8449	−	3.44179i	−1.56926	−	0.420482i	−0.935580	+	0.353114i	$0.885123\pi$
$68$	−1.00549	−	0.580520i	−0.121934	−	0.0703983i
$69$	−2.75616	+	5.11860i	−0.331803	+	0.616207i
$70$	2.37061	+	7.64286i	0.283342	+	0.913497i
$71$	−4.08659	−	4.08659i	−0.484988	−	0.484988i	0.421732	−	0.906720i	$-0.361422\pi$
$71$	−4.08659	−	4.08659i	−0.484988	−	0.484988i	−0.906720	+	0.421732i	$0.861422\pi$
$72$	1.99183	−	2.24335i	0.234739	−	0.264381i
$73$	−3.80315	+	14.1935i	−0.445125	+	1.66123i	0.270482	+	0.962725i	$0.412817\pi$
$73$	−3.80315	+	14.1935i	−0.445125	+	1.66123i	−0.715607	+	0.698503i	$0.753850\pi$
$74$	4.34148	−	2.50656i	0.504687	−	0.291381i
$75$	−6.11214	+	3.77484i	−0.705769	+	0.435881i
$76$	3.54146	+	3.54146i	0.406234	+	0.406234i
$77$	2.04548	−	3.88494i	0.233104	−	0.442730i
$78$	−6.08704	+	1.39567i	−0.689222	+	0.158029i
$79$	3.33349	−	5.77377i	0.375047	−	0.649600i	−0.615287	−	0.788303i	$-0.710960\pi$
$79$	3.33349	−	5.77377i	0.375047	−	0.649600i	0.990334	+	0.138703i	$0.0442934\pi$
$80$	0.782798	−	2.92144i	0.0875195	−	0.326627i
$81$	8.93674	−	1.06523i	0.992971	−	0.118359i
$82$	−1.70807	−	0.986157i	−0.188625	−	0.108903i
$83$	0.280924	+	0.280924i	0.0308354	+	0.0308354i	0.722356	−	0.691521i	$-0.243059\pi$
$83$	0.280924	+	0.280924i	0.0308354	+	0.0308354i	−0.691521	+	0.722356i	$0.743059\pi$
$84$	−1.48678	−	4.33468i	−0.162221	−	0.472953i
$85$	−2.48305	−	2.48305i	−0.269324	−	0.269324i
$86$	−0.216193	−	0.806843i	−0.0233127	−	0.0870041i
$87$	0.321298	+	10.8298i	0.0344468	+	1.16108i
$88$	−1.43714	+	0.829732i	−0.153199	+	0.0884497i
$89$	2.01247	+	7.51064i	0.213321	+	0.796126i	0.986751	+	0.162244i	$0.0518730\pi$
$89$	2.01247	+	7.51064i	0.213321	+	0.796126i	−0.773429	+	0.633882i	$0.781460\pi$
$90$	7.57510	−	4.99461i	0.798486	−	0.526478i
$91$	−2.71779	+	9.14405i	−0.284902	+	0.958557i
$92$		−	3.35641i		−	0.349930i
$93$	−16.1158	−	3.80982i	−1.67114	−	0.395060i
$94$	−0.785790	−	1.36103i	−0.0810481	−	0.140379i
$95$	7.57393	+	13.1184i	0.777069	+	1.34592i
$96$	−0.398477	+	1.68559i	−0.0406694	+	0.172035i
$97$	−7.91821	+	7.91821i	−0.803972	+	0.803972i	−0.983714	−	0.179742i	$-0.942474\pi$
$97$	−7.91821	+	7.91821i	−0.803972	+	0.803972i	0.179742	+	0.983714i	$0.442474\pi$
$98$	−6.88200	−	1.27986i	−0.695187	−	0.129285i
$99$	−4.87669	−	1.00116i	−0.490125	−	0.100620i
$100$	2.07380	−	3.59192i	0.207380	−	0.359192i
$101$	−5.70049	−	9.87354i	−0.567220	−	0.982454i	−0.996839	−	0.0794437i	$-0.974686\pi$
$101$	−5.70049	−	9.87354i	−0.567220	−	0.982454i	0.429619	−	0.903010i	$-0.358648\pi$
$102$	1.46352	+	1.37918i	0.144910	+	0.136559i
$103$	−7.97390	−	4.60373i	−0.785692	−	0.453619i	0.0527519	−	0.998608i	$-0.483201\pi$
$103$	−7.97390	−	4.60373i	−0.785692	−	0.453619i	−0.838444	+	0.544988i	$0.816534\pi$
$104$	2.71227	−	2.37563i	0.265960	−	0.232949i
$105$	−0.950372	−	13.8274i	−0.0927468	−	1.34941i
$106$	−7.35209	+	7.35209i	−0.714098	+	0.714098i
$107$	−9.93441	−	5.73564i	−0.960396	−	0.554485i	−0.0641012	−	0.997943i	$-0.520418\pi$
$107$	−9.93441	−	5.73564i	−0.960396	−	0.554485i	−0.896295	+	0.443458i	$0.853751\pi$
$108$	−4.25133	+	2.98767i	−0.409085	+	0.287489i
$109$	−12.9615	−	3.47302i	−1.24148	−	0.332655i	−0.422443	−	0.906390i	$-0.638827\pi$
$109$	−12.9615	−	3.47302i	−1.24148	−	0.332655i	−0.819041	+	0.573735i	$0.805494\pi$
$110$	−4.84803	+	1.29902i	−0.462241	+	0.123857i
$111$	−8.31677	+	2.49505i	−0.789393	+	0.236819i
$112$	1.94229	+	1.79653i	0.183529	+	0.169756i
$113$			10.2704i			0.966154i	0.875578	+	0.483077i	$0.160481\pi$
$113$			10.2704i			0.966154i	−0.875578	+	0.483077i	$0.839519\pi$
$114$	−4.55827	−	7.38065i	−0.426921	−	0.691261i
$115$	2.62739	−	9.80556i	0.245006	−	0.914373i
$116$	−3.12768	−	5.41730i	−0.290398	−	0.502984i
$117$	10.8164	+	0.0730131i	0.999977	+	0.00675007i
$118$	2.22165			0.204520
$119$	2.93393	−	0.910025i	0.268953	−	0.0834219i
$120$	−2.48360	+	4.61243i	−0.226721	+	0.421055i
$121$	−7.14140	−	4.12309i	−0.649218	−	0.374826i
$122$	−1.47898	+	5.51963i	−0.133900	+	0.499723i
$123$	2.48615	+	2.34288i	0.224169	+	0.211251i
$124$	9.23517	−	2.47456i	0.829343	−	0.222222i
$125$	−1.82299	+	1.82299i	−0.163053	+	0.163053i
$126$	0.778838	+	7.89895i	0.0693844	+	0.703694i
$127$		−	9.79749i		−	0.869386i	−0.900579	−	0.434693i	$-0.856857\pi$
$127$		−	9.79749i		−	0.869386i	0.900579	−	0.434693i	$-0.143143\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$	0.0429043	+	1.44615i	0.00377752	+	0.127327i
$130$	9.78337	−	4.81710i	0.858058	−	0.422488i
$131$	−14.1078	−	8.14512i	−1.23260	−	0.711642i	−0.265029	−	0.964240i	$-0.585382\pi$
$131$	−14.1078	−	8.14512i	−1.23260	−	0.711642i	−0.967571	+	0.252598i	$0.918715\pi$
$132$	2.75306	−	0.825922i	0.239623	−	0.0718873i
$133$	−13.2409	+	0.516180i	−1.14813	+	0.0447585i
$134$	−13.2981			−1.14878
$135$	−14.7588	+	5.40037i	−1.27023	+	0.464790i
$136$	−1.12148	−	0.300499i	−0.0961659	−	0.0257676i
$137$	12.2697	+	3.28765i	1.04827	+	0.280883i	0.741536	−	0.670913i	$-0.234098\pi$
$137$	12.2697	+	3.28765i	1.04827	+	0.280883i	0.306733	+	0.951796i	$0.400764\pi$
$138$	−1.33745	+	5.65754i	−0.113852	+	0.481602i
$139$	13.5672			1.15075			0.575376	−	0.817889i	$-0.304856\pi$
$139$	13.5672			1.15075			0.575376	+	0.817889i	$0.304856\pi$
$140$	4.26795	+	6.76888i	0.360708	+	0.572075i
$141$	0.782182	+	2.60726i	0.0658716	+	0.219571i
$142$	−5.00502	−	2.88965i	−0.420012	−	0.242494i
$143$	−5.66456	−	1.92677i	−0.473694	−	0.161124i
$144$	1.34334	−	2.68243i	0.111945	−	0.223536i
$145$	−4.89669	−	18.2747i	−0.406648	−	1.51763i
$146$			14.6942i			1.21610i
$147$	11.0902	+	4.89964i	0.914708	+	0.404115i
$148$	3.54481	−	3.54481i	0.291381	−	0.291381i
$149$	6.50715	−	1.74358i	0.533086	−	0.142840i	0.0177731	−	0.999842i	$-0.494342\pi$
$149$	6.50715	−	1.74358i	0.533086	−	0.142840i	0.515313	+	0.857002i	$0.327676\pi$
$150$	−4.92687	+	5.22815i	−0.402277	+	0.426877i
$151$	−3.09576	+	11.5536i	−0.251930	+	0.940215i	0.717843	+	0.696205i	$0.245130\pi$
$151$	−3.09576	+	11.5536i	−0.251930	+	0.940215i	−0.969773	+	0.244010i	$0.921537\pi$
$152$	4.33739	+	2.50419i	0.351809	+	0.203117i
$153$	−1.91732	−	2.90792i	−0.155006	−	0.235091i
$154$	0.970288	−	4.28197i	0.0781880	−	0.345051i
$155$	28.9171			2.32268
$156$	−5.51841	+	2.92356i	−0.441826	+	0.234072i
$157$	2.78090	+	4.81666i	0.221940	+	0.384412i	0.955397	−	0.295324i	$-0.0954277\pi$
$157$	2.78090	+	4.81666i	0.221940	+	0.384412i	−0.733457	+	0.679736i	$0.762094\pi$
$158$	1.72554	−	6.43980i	0.137277	−	0.512323i
$159$	15.3223	−	9.46298i	1.21513	−	0.750463i
$160$		−	3.02450i		−	0.239108i
$161$	6.51911	+	6.02990i	0.513778	+	0.475223i
$162$	8.35653	−	3.34193i	0.656551	−	0.262567i
$163$	−12.2384	+	3.27927i	−0.958585	+	0.256852i	−0.704001	−	0.710199i	$-0.748605\pi$
$163$	−12.2384	+	3.27927i	−0.958585	+	0.256852i	−0.254584	+	0.967051i	$0.581938\pi$
$164$	−1.90511	−	0.510472i	−0.148764	−	0.0398612i
$165$	8.68942	−	0.257797i	0.676470	−	0.0200694i
$166$	0.344060	+	0.198643i	0.0267042	+	0.0154177i
$167$	−6.67954	+	6.67954i	−0.516878	+	0.516878i	−0.916625	−	0.399747i	$-0.869098\pi$
$167$	−6.67954	+	6.67954i	−0.516878	+	0.516878i	0.399747	+	0.916625i	$0.369098\pi$
$168$	−2.55802	−	3.80217i	−0.197356	−	0.293344i
$169$	12.8867	+	1.71279i	0.991283	+	0.131753i
$170$	−3.04110	−	1.75578i	−0.233242	−	0.134662i
$171$	4.74235	+	14.2571i	0.362657	+	1.09027i
$172$	−0.417653	−	0.723396i	−0.0318457	−	0.0551584i
$173$	9.13449	−	15.8214i	0.694482	−	1.20288i	−0.275873	−	0.961194i	$-0.588967\pi$
$173$	9.13449	−	15.8214i	0.694482	−	1.20288i	0.970355	−	0.241684i	$-0.0776998\pi$
$174$	3.11332	+	10.3777i	0.236020	+	0.786729i
$175$	3.25089	+	10.4809i	0.245745	+	0.792282i
$176$	−1.17342	+	1.17342i	−0.0884497	+	0.0884497i
$177$	−3.74479	−	0.885277i	−0.281476	−	0.0665415i
$178$	3.88779	+	6.73385i	0.291402	+	0.504724i
$179$	12.4226	+	21.5165i	0.928507	+	1.60822i	0.785821	+	0.618454i	$0.212241\pi$
$179$	12.4226	+	21.5165i	0.928507	+	1.60822i	0.142686	+	0.989768i	$0.454426\pi$
$180$	6.02429	−	6.78501i	0.449024	−	0.505724i
$181$			0.149928i			0.0111440i	0.999984	+	0.00557202i	$0.00177364\pi$
$181$			0.149928i			0.0111440i	−0.999984	+	0.00557202i	$0.998226\pi$
$182$	−0.258527	+	9.53589i	−0.0191633	+	0.706847i
$183$	4.69240	−	8.71449i	0.346872	−	0.644194i
$184$	−0.868703	−	3.24204i	−0.0640417	−	0.239007i
$185$	13.1308	−	7.58108i	0.965396	−	0.557372i
$186$	−16.5528	+	0.491085i	−1.21371	+	0.0360081i
$187$	0.498667	+	1.86105i	0.0364662	+	0.136094i
$188$	−1.11128	−	1.11128i	−0.0810481	−	0.0810481i
$189$	1.83475	−	13.6247i	0.133458	−	0.991054i
$190$	10.7112	+	10.7112i	0.777069	+	0.777069i
$191$	0.868360	+	0.501348i	0.0628323	+	0.0362763i	0.531087	−	0.847317i	$-0.321784\pi$
$191$	0.868360	+	0.501348i	0.0628323	+	0.0362763i	−0.468255	+	0.883594i	$0.655117\pi$
$192$	0.0513637	+	1.73129i	0.00370685	+	0.124945i
$193$	4.72680	−	17.6407i	0.340243	−	1.26980i	−0.557830	−	0.829956i	$-0.688366\pi$
$193$	4.72680	−	17.6407i	0.340243	−	1.26980i	0.898072	−	0.439848i	$-0.144968\pi$
$194$	−5.59902	+	9.69779i	−0.401986	+	0.696260i
$195$	−18.4103	+	4.22121i	−1.31839	+	0.302287i
$196$	−6.97876	+	0.544946i	−0.498483	+	0.0389247i
$197$	2.15178	+	2.15178i	0.153308	+	0.153308i	0.779594	−	0.626286i	$-0.215426\pi$
$197$	2.15178	+	2.15178i	0.153308	+	0.153308i	−0.626286	+	0.779594i	$0.715426\pi$
$198$	−4.96964	+	0.295137i	−0.353177	+	0.0209745i
$199$	21.4123	−	12.3624i	1.51788	−	0.876349i	0.518102	−	0.855319i	$-0.326639\pi$
$199$	21.4123	−	12.3624i	1.51788	−	0.876349i	0.999779	−	0.0210302i	$-0.00669462\pi$
$200$	1.07348	−	4.00627i	0.0759062	−	0.283286i
$201$	22.4151	+	5.29898i	1.58104	+	0.373761i
$202$	−8.06171	−	8.06171i	−0.567220	−	0.567220i
$203$	16.1409	+	3.65751i	1.13287	+	0.256707i
$204$	1.77061	+	0.953402i	0.123968	+	0.0667515i
$205$	−5.16607	−	2.98263i	−0.360814	−	0.208316i
$206$	−8.89373	−	2.38307i	−0.619656	−	0.166036i
$207$	4.50880	−	9.00335i	0.313383	−	0.625776i
$208$	2.00499	−	2.99667i	0.139021	−	0.207781i
$209$		−	8.31123i		−	0.574900i
$210$	−4.49678	−	13.1102i	−0.310307	−	0.904693i
$211$	17.5610			1.20895			0.604474	−	0.796625i	$-0.293383\pi$
$211$	17.5610			1.20895			0.604474	+	0.796625i	$0.293383\pi$
$212$	−5.19871	+	9.00444i	−0.357049	+	0.618427i
$213$	7.28496	+	6.86516i	0.499157	+	0.470393i
$214$	−11.0804	−	2.96898i	−0.757441	−	0.202956i
$215$	−0.653875	−	2.44030i	−0.0445939	−	0.166427i
$216$	−3.33321	+	3.98619i	−0.226796	+	0.271226i
$217$	−11.7850	+	22.3830i	−0.800017	+	1.51945i
$218$	−13.4187			−0.908829
$219$	5.85532	−	24.7685i	0.395666	−	1.67370i
$220$	−4.34662	+	2.50952i	−0.293049	+	0.169192i
$221$	−1.84918	−	3.75562i	−0.124389	−	0.252630i
$222$	−7.38762	+	4.56257i	−0.495824	+	0.306219i
$223$	−5.75356	+	5.75356i	−0.385287	+	0.385287i	−0.873003	−	0.487716i	$-0.837830\pi$
$223$	−5.75356	+	5.75356i	−0.385287	+	0.385287i	0.487716	+	0.873003i	$0.337830\pi$
$224$	2.34108	+	1.23262i	0.156420	+	0.0823576i
$225$	10.3880	−	6.84927i	0.692532	−	0.456618i
$226$	2.65816	+	9.92040i	0.176818	+	0.659895i
$227$	4.13784	−	15.4426i	0.274638	−	1.02496i	−0.681445	−	0.731869i	$-0.738648\pi$
$227$	4.13784	−	15.4426i	0.274638	−	1.02496i	0.956083	−	0.293095i	$-0.0946851\pi$
$228$	−6.31320	−	5.94939i	−0.418102	−	0.394008i
$229$	6.20039	−	1.66139i	0.409733	−	0.109788i	−0.0480642	−	0.998844i	$-0.515305\pi$
$229$	6.20039	−	1.66139i	0.409733	−	0.109788i	0.457797	+	0.889057i	$0.348639\pi$
$230$		−	10.1515i		−	0.669368i
$231$	−3.34178	+	6.83101i	−0.219873	+	0.449448i
$232$	−4.42321	−	4.42321i	−0.290398	−	0.290398i
$233$	−7.09411	+	12.2874i	−0.464751	+	0.804972i	−0.999190	−	0.0402351i	$-0.987189\pi$
$233$	−7.09411	+	12.2874i	−0.464751	+	0.804972i	0.534440	+	0.845207i	$0.320523\pi$
$234$	10.4667	−	2.72897i	0.684232	−	0.178398i
$235$	−2.37662	−	4.11643i	−0.155034	−	0.268526i
$236$	2.14595	−	0.575005i	0.139689	−	0.0374297i
$237$	−5.47467	+	10.1673i	−0.355618	+	0.660436i
$238$	2.59843	−	1.63837i	0.168431	−	0.106200i
$239$	−20.3363	−	20.3363i	−1.31544	−	1.31544i	−0.917340	−	0.398105i	$-0.869668\pi$
$239$	−20.3363	−	20.3363i	−1.31544	−	1.31544i	−0.398105	−	0.917340i	$-0.630332\pi$
$240$	−1.20519	+	5.09807i	−0.0777949	+	0.329079i
$241$	1.96287	−	7.32554i	0.126440	−	0.471880i	−0.873447	−	0.486919i	$-0.838121\pi$
$241$	1.96287	−	7.32554i	0.126440	−	0.471880i	0.999887	+	0.0150393i	$0.00478734\pi$
$242$	−7.96520	−	2.13427i	−0.512022	−	0.137196i
$243$	−15.4174	+	2.30324i	−0.989024	+	0.147753i
$244$			5.71434i			0.365823i
$245$	−20.8146	−	3.87093i	−1.32980	−	0.247305i
$246$	3.00782	+	1.61959i	0.191772	+	0.103261i
$247$	3.51198	+	17.7132i	0.223462	+	1.12706i
$248$	8.28003	−	4.78048i	0.525782	−	0.303560i
$249$	−0.500789	−	0.471931i	−0.0317362	−	0.0299074i
$250$	−1.28905	+	2.23270i	−0.0815267	+	0.141208i
$251$	−22.1156			−1.39593			−0.697963	−	0.716133i	$-0.745910\pi$
$251$	−22.1156			−1.39593			−0.697963	+	0.716133i	$0.745910\pi$
$252$	2.79670	+	7.42822i	0.176175	+	0.467934i
$253$	−3.93847	+	3.93847i	−0.247610	+	0.247610i
$254$	−2.53578	−	9.46365i	−0.159109	−	0.593802i
$255$	4.42641	+	4.17134i	0.277193	+	0.261219i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−13.8247	+	23.9451i	−0.862360	+	1.49365i	0.00728386	+	0.999973i	$0.497681\pi$
$257$	−13.8247	+	23.9451i	−0.862360	+	1.49365i	−0.869644	+	0.493679i	$0.835652\pi$
$258$	0.415735	+	1.38577i	0.0258825	+	0.0862745i
$259$	0.516668	+	13.2534i	0.0321042	+	0.823525i
$260$	8.20325	−	7.18508i	0.508744	−	0.445600i
$261$	−1.11252	−	18.7331i	−0.0688633	−	1.15955i
$262$	−15.7352	−	4.21622i	−0.972121	−	0.260479i
$263$	−7.75957	+	4.47999i	−0.478475	+	0.276248i	−0.719781	−	0.694201i	$-0.755758\pi$
$263$	−7.75957	+	4.47999i	−0.478475	+	0.276248i	0.241305	+	0.970449i	$0.422424\pi$
$264$	2.44548	−	1.51032i	0.150509	−	0.0929539i
$265$	−22.2364	+	22.2364i	−1.36597	+	1.36597i
$266$	−12.6561	+	3.92559i	−0.775996	+	0.240693i
$267$	−3.86994	−	12.8997i	−0.236836	−	0.789450i
$268$	−12.8449	+	3.44179i	−0.784630	+	0.210241i
$269$	18.1732	−	10.4923i	1.10804	−	0.639725i	0.169716	−	0.985493i	$-0.445715\pi$
$269$	18.1732	−	10.4923i	1.10804	−	0.639725i	0.938320	+	0.345768i	$0.112381\pi$
$270$	−12.8582	+	9.03620i	−0.782522	+	0.549926i
$271$	25.6168	−	6.86399i	1.55611	−	0.416958i	0.624679	−	0.780881i	$-0.285230\pi$
$271$	25.6168	−	6.86399i	1.55611	−	0.416958i	0.931429	+	0.363923i	$0.118563\pi$
$272$	−1.16104			−0.0703983
$273$	4.23560	−	15.9706i	0.256350	−	0.966584i
$274$	12.7025			0.767386
$275$	−6.64826	+	1.78140i	−0.400905	+	0.107422i
$276$	0.172398	+	5.81092i	0.0103771	+	0.349776i
$277$	4.18469	−	2.41603i	0.251434	−	0.145165i	−0.368987	−	0.929435i	$-0.620295\pi$
$277$	4.18469	−	2.41603i	0.251434	−	0.145165i	0.620421	+	0.784269i	$0.286962\pi$
$278$	13.1049	−	3.51144i	0.785978	−	0.210602i
$279$	28.0969	+	5.76813i	1.68212	+	0.345329i
$280$	5.87444	+	5.43361i	0.351065	+	0.324720i
$281$	−16.2214	+	16.2214i	−0.967687	+	0.967687i	−0.999494	−	0.0318072i	$-0.989874\pi$
$281$	−16.2214	+	16.2214i	−0.967687	+	0.967687i	0.0318072	+	0.999494i	$0.489874\pi$
$282$	1.43034	+	2.31597i	0.0851754	+	0.137914i
$283$	−19.0956	+	11.0249i	−1.13512	+	0.655361i	−0.945217	−	0.326443i	$-0.894150\pi$
$283$	−19.0956	+	11.0249i	−1.13512	+	0.655361i	−0.189901	+	0.981803i	$0.560817\pi$
$284$	−5.58238	−	1.49579i	−0.331253	−	0.0887590i
$285$	−13.7865	−	22.3228i	−0.816640	−	1.32229i
$286$	−5.97023	−	0.395019i	−0.353027	−	0.0233579i
$287$	4.41407	−	2.78318i	0.260554	−	0.164286i
$288$	0.603301	−	2.93871i	0.0355498	−	0.173165i
$289$	7.82599	−	13.5550i	0.460353	−	0.797354i
$290$	−9.45967	−	16.3846i	−0.555491	−	0.962139i
$291$	13.3020	−	14.1154i	0.779777	−	0.827460i
$292$	3.80315	+	14.1935i	0.222562	+	0.830614i
$293$	23.7231	−	23.7231i	1.38592	−	1.38592i	0.552217	−	0.833700i	$-0.313782\pi$
$293$	23.7231	−	23.7231i	1.38592	−	1.38592i	0.833700	−	0.552217i	$-0.186218\pi$
$294$	11.9805	+	1.86232i	0.698715	+	0.108613i
$295$	6.71938			0.391217
$296$	2.50656	−	4.34148i	0.145691	−	0.252344i
$297$	8.49438	+	1.48281i	0.492894	+	0.0860411i
$298$	5.83415	−	3.36835i	0.337963	−	0.195123i
$299$	6.72958	−	10.0580i	0.389181	−	0.581672i
$300$	−3.40585	+	6.32517i	−0.196637	+	0.365184i
$301$	2.15537	+	0.488403i	0.124233	+	0.0281511i
$302$			11.9611i			0.688285i
$303$	10.3763	+	16.8012i	0.596105	+	0.965201i
$304$	4.83773	+	1.29627i	0.277463	+	0.0743459i
$305$	−4.47317	+	16.6941i	−0.256133	+	0.955901i
$306$	−2.60462	−	2.31259i	−0.148896	−	0.132202i
$307$	−20.8725	−	20.8725i	−1.19126	−	1.19126i	−0.976715	−	0.214543i	$-0.931174\pi$
$307$	−20.8725	−	20.8725i	−1.19126	−	1.19126i	−0.214543	−	0.976715i	$-0.568826\pi$
$308$	−0.171030	−	4.38720i	−0.00974532	−	0.249984i
$309$	14.0416	+	7.56082i	0.798798	+	0.430120i
$310$	27.9318	−	7.48429i	1.58642	−	0.425079i
$311$	0.229149	+	0.396898i	0.0129938	+	0.0225060i	0.872449	−	0.488705i	$-0.162530\pi$
$311$	0.229149	+	0.396898i	0.0129938	+	0.0225060i	−0.859455	+	0.511211i	$0.829197\pi$
$312$	−4.57370	+	4.25221i	−0.258935	+	0.240734i
$313$	−8.34185	+	14.4485i	−0.471509	+	0.816678i	−0.999469	−	0.0325918i	$-0.989624\pi$
$313$	−8.34185	+	14.4485i	−0.471509	+	0.816678i	0.527960	+	0.849269i	$0.322957\pi$
$314$	3.93279	+	3.93279i	0.221940	+	0.221940i
$315$	2.35559	+	23.8904i	0.132723	+	1.34607i
$316$		−	6.66697i		−	0.375047i
$317$	19.9682	−	5.35045i	1.12152	−	0.300511i	0.350024	−	0.936741i	$-0.386174\pi$
$317$	19.9682	−	5.35045i	1.12152	−	0.300511i	0.771500	+	0.636230i	$0.219507\pi$
$318$	12.3510	−	13.1062i	0.692608	−	0.734961i
$319$	−2.68668	+	10.0268i	−0.150425	+	0.561395i
$320$	−0.782798	−	2.92144i	−0.0437597	−	0.163314i
$321$	17.4939	+	9.41978i	0.976417	+	0.525761i
$322$	7.85763	+	4.13717i	0.437889	+	0.230555i
$323$	4.11178	−	4.11178i	0.228785	−	0.228785i
$324$	7.20683	−	5.39088i	0.400379	−	0.299494i
$325$	13.4162	−	6.60585i	0.744200	−	0.366426i
$326$	−10.9726	+	6.33506i	−0.607719	+	0.350867i
$327$	22.6184	+	5.34705i	1.25080	+	0.295692i
$328$	−1.97231			−0.108903
$329$	4.15486	−	0.161972i	0.229065	−	0.00892982i
$330$	8.32661	−	2.49800i	0.458365	−	0.137510i
$331$	−2.10415	−	7.85278i	−0.115654	−	0.431628i	0.883681	−	0.468090i	$-0.155058\pi$
$331$	−2.10415	−	7.85278i	−0.115654	−	0.431628i	−0.999335	+	0.0364624i	$0.988391\pi$
$332$	0.383749	+	0.102825i	0.0210610	+	0.00564327i
$333$	14.2706	−	4.74683i	0.782023	−	0.260124i
$334$	−4.72315	+	8.18073i	−0.258439	+	0.447630i
$335$	−40.2200			−2.19745
$336$	−3.45493	−	3.01055i	−0.188482	−	0.164239i
$337$		−	9.06558i		−	0.493834i	−0.969037	−	0.246917i	$-0.920583\pi$
$337$		−	9.06558i		−	0.493834i	0.969037	−	0.246917i	$-0.0794175\pi$
$338$	12.8909	−	1.68089i	0.701171	−	0.0914285i
$339$	−0.527523	−	17.7810i	−0.0286511	−	0.965729i
$340$	−3.39191	−	0.908859i	−0.183952	−	0.0492898i
$341$	−13.7404	−	7.93303i	−0.744085	−	0.429597i
$342$	8.27077	+	12.5439i	0.447232	+	0.678297i
$343$	11.4791	−	14.5337i	0.619814	−	0.784749i
$344$	−0.590650	−	0.590650i	−0.0318457	−	0.0318457i
$345$	−4.04513	+	17.1112i	−0.217782	+	0.921237i
$346$	4.72836	−	17.6465i	0.254198	−	0.948680i
$347$	−12.6080	+	7.27922i	−0.676832	+	0.390769i	−0.798660	−	0.601782i	$-0.794458\pi$
$347$	−12.6080	+	7.27922i	−0.676832	+	0.390769i	0.121828	+	0.992551i	$0.461124\pi$
$348$	5.69317	+	9.21827i	0.305186	+	0.494151i
$349$	0.0763433	+	0.0763433i	0.00408656	+	0.00408656i	0.709147	−	0.705061i	$-0.249080\pi$
$349$	0.0763433	+	0.0763433i	0.00408656	+	0.00408656i	−0.705061	+	0.709147i	$0.749080\pi$
$350$	5.85278	+	9.28239i	0.312844	+	0.496164i
$351$	−18.7301	+	0.429163i	−0.999738	+	0.0229071i
$352$	−0.829732	+	1.43714i	−0.0442249	+	0.0765997i
$353$	−4.69405	+	17.5184i	−0.249839	+	0.932412i	0.721050	+	0.692883i	$0.243660\pi$
$353$	−4.69405	+	17.5184i	−0.249839	+	0.932412i	−0.970889	+	0.239529i	$0.923007\pi$
$354$	−3.84632	+	0.114112i	−0.204430	+	0.00606499i
$355$	−15.1377	−	8.73975i	−0.803425	−	0.463858i
$356$	5.49817	+	5.49817i	0.291402	+	0.291402i
$357$	−5.03274	+	1.72621i	−0.266361	+	0.0913610i
$358$	17.5682	+	17.5682i	0.928507	+	0.928507i
$359$	6.33367	+	23.6376i	0.334278	+	1.24754i	0.904650	+	0.426156i	$0.140133\pi$
$359$	6.33367	+	23.6376i	0.334278	+	1.24754i	−0.570371	+	0.821387i	$0.693201\pi$
$360$	4.06293	−	8.11301i	0.214135	−	0.427593i
$361$	−5.26883	+	3.04196i	−0.277307	+	0.160103i
$362$	0.0388042	+	0.144819i	0.00203950	+	0.00761152i
$363$	12.5756	+	6.77145i	0.660048	+	0.355409i
$364$	2.21835	+	9.27787i	0.116273	+	0.486293i
$365$			44.4427i			2.32624i
$366$	2.27703	−	9.63203i	0.119022	−	0.503474i
$367$	−3.99222	−	6.91472i	−0.208392	−	0.360946i	0.742816	−	0.669495i	$-0.233490\pi$
$367$	−3.99222	−	6.91472i	−0.208392	−	0.360946i	−0.951208	+	0.308550i	$0.900156\pi$
$368$	−1.67821	−	2.90674i	−0.0874825	−	0.151524i
$369$	−4.42459	−	3.92851i	−0.230335	−	0.204510i
$370$	10.7213	−	10.7213i	0.557372	−	0.557372i
$371$	−8.14953	−	26.2741i	−0.423102	−	1.36409i
$372$	−15.8616	+	4.75852i	−0.822388	+	0.246718i
$373$	−4.87694	+	8.44712i	−0.252519	+	0.437375i	−0.964219	−	0.265109i	$-0.914592\pi$
$373$	−4.87694	+	8.44712i	−0.252519	+	0.437375i	0.711700	+	0.702484i	$0.247926\pi$
$374$	0.963351	+	1.66857i	0.0498137	+	0.0862799i
$375$	3.06249	−	3.24976i	0.158146	−	0.167817i
$376$	−1.36103	−	0.785790i	−0.0701897	−	0.0405240i
$377$	1.48903	−	22.5048i	0.0766888	−	1.15906i
$378$	−1.75411	−	13.6354i	−0.0902218	−	0.701327i
$379$	21.5486	−	21.5486i	1.10688	−	1.10688i	0.113321	−	0.993558i	$-0.463851\pi$
$379$	21.5486	−	21.5486i	1.10688	−	1.10688i	0.993558	−	0.113321i	$-0.0361488\pi$
$380$	13.1184	+	7.57393i	0.672961	+	0.388534i
$381$	0.503235	+	16.9623i	0.0257815	+	0.869004i
$382$	0.968530	+	0.259517i	0.0495543	+	0.0132780i
$383$	−27.7841	+	7.44472i	−1.41970	+	0.380407i	−0.885377	−	0.464874i	$-0.846100\pi$
$383$	−27.7841	+	7.44472i	−1.41970	+	0.380407i	−0.534322	+	0.845281i	$0.679433\pi$
$384$	0.497704	+	1.65900i	0.0253984	+	0.0846606i
$385$	2.93463	−	12.9508i	0.149563	−	0.660035i
$386$		−	18.2630i		−	0.929561i
$387$	−0.148560	−	2.50151i	−0.00755171	−	0.127159i
$388$	−2.89827	+	10.8165i	−0.147137	+	0.549123i
$389$	−18.2199	−	31.5578i	−0.923785	−	1.60004i	−0.793503	−	0.608566i	$-0.791745\pi$
$389$	−18.2199	−	31.5578i	−0.923785	−	1.60004i	−0.130282	−	0.991477i	$-0.541588\pi$
$390$	−16.6904	+	8.84230i	−0.845152	+	0.447747i
$391$	−3.89693			−0.197076
$392$	−6.59992	+	2.33261i	−0.333346	+	0.117815i
$393$	24.8430	+	13.3769i	1.25316	+	0.674777i
$394$	2.63538	+	1.52154i	0.132769	+	0.0766540i
$395$	5.21889	−	19.4772i	0.262591	−	0.980003i
$396$	−4.72391	+	1.57132i	−0.237386	+	0.0789616i
$397$	7.37303	−	1.97560i	0.370042	−	0.0991523i	−0.0690058	−	0.997616i	$-0.521983\pi$
$397$	7.37303	−	1.97560i	0.370042	−	0.0991523i	0.439047	+	0.898464i	$0.355316\pi$
$398$	17.4831	−	17.4831i	0.876349	−	0.876349i
$399$	22.8973	−	1.57376i	1.14630	−	0.0787864i
$400$		−	4.14759i		−	0.207380i
$401$	3.89458	+	14.5348i	0.194486	+	0.725832i	0.992399	+	0.123059i	$0.0392706\pi$
$401$	3.89458	+	14.5348i	0.194486	+	0.725832i	−0.797913	+	0.602772i	$0.794063\pi$
$402$	23.0228	−	0.683037i	1.14827	−	0.0340668i
$403$	32.6362	+	11.1010i	1.62572	+	0.552981i
$404$	−9.87354	−	5.70049i	−0.491227	−	0.283610i
$405$	25.2743	−	10.1077i	1.25589	−	0.502254i
$406$	16.5376	−	0.644698i	0.820746	−	0.0319958i
$407$	−8.31908			−0.412361
$408$	1.95704	+	0.462648i	0.0968878	+	0.0229045i
$409$	−1.43431	−	0.384321i	−0.0709219	−	0.0190035i	0.223184	−	0.974776i	$-0.428355\pi$
$409$	−1.43431	−	0.384321i	−0.0709219	−	0.0190035i	−0.294106	+	0.955773i	$0.595022\pi$
$410$	−5.76200	−	1.54392i	−0.284565	−	0.0762489i
$411$	−21.4112	−	5.06166i	−1.05614	−	0.249673i
$412$	−9.20747			−0.453619
$413$	−2.73844	+	5.20106i	−0.134750	+	0.255928i
$414$	2.02493	−	9.86353i	0.0995197	−	0.484766i
$415$	1.04061	+	0.600796i	0.0510815	+	0.0294919i
$416$	1.16108	−	3.41349i	0.0569265	−	0.167360i
$417$	−23.4887	+	0.696859i	−1.15025	+	0.0341253i
$418$	−2.15111	−	8.02804i	−0.105214	−	0.392664i
$419$		−	13.4415i		−	0.656661i	−0.944563	−	0.328331i	$-0.893514\pi$
$419$		−	13.4415i		−	0.656661i	0.944563	−	0.328331i	$-0.106486\pi$
$420$	−7.73673	−	11.4997i	−0.377514	−	0.561126i
$421$	−6.65545	+	6.65545i	−0.324367	+	0.324367i	−0.850440	−	0.526073i	$-0.823664\pi$
$421$	−6.65545	+	6.65545i	−0.324367	+	0.324367i	0.526073	+	0.850440i	$0.323664\pi$
$422$	16.9626	−	4.54512i	0.825727	−	0.221253i
$423$	−1.48810	−	4.47374i	−0.0723540	−	0.217521i
$424$	−2.69105	+	10.0431i	−0.130689	+	0.487738i
$425$	−4.17036	−	2.40776i	−0.202292	−	0.116793i
$426$	8.81357	+	4.74575i	0.427019	+	0.229932i
$427$	−11.0989	−	10.2660i	−0.537112	−	0.496806i
$428$	−11.4713			−0.554485
$429$	9.90596	+	3.04484i	0.478264	+	0.147006i
$430$	−1.26319	−	2.18791i	−0.0609164	−	0.105510i
$431$	−6.26821	+	23.3933i	−0.301929	+	1.12681i	0.633628	+	0.773638i	$0.281565\pi$
$431$	−6.26821	+	23.3933i	−0.301929	+	1.12681i	−0.935557	+	0.353176i	$0.885102\pi$
$432$	−2.18793	+	4.71306i	−0.105267	+	0.226757i
$433$			24.7173i			1.18784i	0.804525	+	0.593919i	$0.202420\pi$
$433$			24.7173i			1.18784i	−0.804525	+	0.593919i	$0.797580\pi$
$434$	−5.59028	+	24.6704i	−0.268342	+	1.18422i
$435$	9.41623	+	31.3872i	0.451474	+	1.50490i
$436$	−12.9615	+	3.47302i	−0.620742	+	0.166327i
$437$	16.2374	+	4.35080i	0.776741	+	0.208127i
$438$	−0.754750	−	25.4400i	−0.0360633	−	1.21557i
$439$	−16.8340	−	9.71913i	−0.803444	−	0.463869i	0.0412297	−	0.999150i	$-0.486872\pi$
$439$	−16.8340	−	9.71913i	−0.803444	−	0.463869i	−0.844674	+	0.535281i	$0.820206\pi$
$440$	−3.54900	+	3.54900i	−0.169192	+	0.169192i
$441$	−19.4521	−	7.91305i	−0.926290	−	0.376812i
$442$	−2.75820	−	3.14905i	−0.131194	−	0.149785i
$443$	14.4432	+	8.33879i	0.686218	+	0.396188i	0.802194	−	0.597064i	$-0.203666\pi$
$443$	14.4432	+	8.33879i	0.686218	+	0.396188i	−0.115976	+	0.993252i	$0.536999\pi$
$444$	−5.95501	+	6.31916i	−0.282612	+	0.299894i
$445$	11.7586	+	20.3665i	0.557412	+	0.965466i
$446$	−4.06838	+	7.04665i	−0.192644	+	0.333668i
$447$	−11.1762	+	3.35288i	−0.528616	+	0.158586i
$448$	2.58033	+	0.584700i	0.121909	+	0.0276245i
$449$	18.8402	−	18.8402i	0.889123	−	0.889123i	−0.105316	−	0.994439i	$-0.533585\pi$
$449$	18.8402	−	18.8402i	0.889123	−	0.889123i	0.994439	+	0.105316i	$0.0335854\pi$
$450$	8.26130	−	9.30450i	0.389441	−	0.438618i
$451$	1.63649	+	2.83449i	0.0770594	+	0.133471i
$452$	5.13518	+	8.89439i	0.241538	+	0.418357i
$453$	4.76623	−	20.1615i	0.223937	−	0.947272i
$454$		−	15.9874i		−	0.750325i
$455$	−0.781916	+	28.8413i	−0.0366568	+	1.35210i
$456$	−7.63790	−	4.11270i	−0.357677	−	0.192595i
$457$	2.23990	+	8.35943i	0.104778	+	0.391038i	0.998320	−	0.0579425i	$-0.0184540\pi$
$457$	2.23990	+	8.35943i	0.104778	+	0.391038i	−0.893542	+	0.448980i	$0.851787\pi$
$458$	5.55912	−	3.20956i	0.259760	−	0.149973i
$459$	3.46880	+	4.93596i	0.161910	+	0.230391i
$460$	−2.62739	−	9.80556i	−0.122503	−	0.457187i
$461$	−16.7940	−	16.7940i	−0.782176	−	0.782176i	0.198021	−	0.980198i	$-0.436548\pi$
$461$	−16.7940	−	16.7940i	−0.782176	−	0.782176i	−0.980198	+	0.198021i	$0.936548\pi$
$462$	−1.45991	+	7.46317i	−0.0679212	+	0.347218i
$463$	11.3073	+	11.3073i	0.525497	+	0.525497i	0.919226	−	0.393730i	$-0.128815\pi$
$463$	11.3073	+	11.3073i	0.525497	+	0.525497i	−0.393730	+	0.919226i	$0.628815\pi$
$464$	−5.41730	−	3.12768i	−0.251492	−	0.145199i
$465$	−50.0638	+	1.48529i	−2.32165	+	0.0688786i
$466$	−3.67218	+	13.7048i	−0.170110	+	0.634861i
$467$	−7.32346	+	12.6846i	−0.338889	+	0.586974i	−0.984224	−	0.176926i	$-0.943385\pi$
$467$	−7.32346	+	12.6846i	−0.338889	+	0.586974i	0.645335	+	0.763900i	$0.276718\pi$
$468$	9.40379	−	5.34497i	0.434690	−	0.247071i
$469$	16.3914	−	31.1318i	0.756885	−	1.43753i
$470$	−3.36105	−	3.36105i	−0.155034	−	0.155034i
$471$	−5.06195	−	8.19620i	−0.233242	−	0.377661i
$472$	1.92401	−	1.11083i	0.0885595	−	0.0511299i
$473$	−0.358764	+	1.33893i	−0.0164960	+	0.0615639i
$474$	−2.65664	+	11.2378i	−0.122023	+	0.516169i
$475$	14.6886	+	14.6886i	0.673957	+	0.673957i
$476$	2.08584	−	2.25507i	0.0956045	−	0.103361i
$477$	−26.0412	+	17.1702i	−1.19234	+	0.786167i
$478$	−24.9068	−	14.3799i	−1.13921	−	0.657722i
$479$	6.53578	+	1.75126i	0.298627	+	0.0800169i	0.405022	−	0.914307i	$-0.367264\pi$
$479$	6.53578	+	1.75126i	0.298627	+	0.0800169i	−0.106394	+	0.994324i	$0.533931\pi$
$480$	0.155349	+	5.23628i	0.00709070	+	0.239002i
$481$	17.7299	−	3.51530i	0.808414	−	0.160284i
$482$		−	7.58396i		−	0.345440i
$483$	−11.5962	−	10.1047i	−0.527645	−	0.459778i
$484$	−8.24618			−0.374826
$485$	−16.9342	+	29.3309i	−0.768944	+	1.33185i
$486$	−14.2959	+	6.21507i	−0.648476	+	0.281921i
$487$	15.1040	+	4.04712i	0.684430	+	0.183392i	0.584246	−	0.811577i	$-0.301390\pi$
$487$	15.1040	+	4.04712i	0.684430	+	0.183392i	0.100184	+	0.994969i	$0.468057\pi$
$488$	1.47898	+	5.51963i	0.0669502	+	0.249862i
$489$	21.0198	−	6.30597i	0.950547	−	0.285166i
$490$	−21.1072	+	1.64819i	−0.953528	+	0.0744575i
$491$	2.12133			0.0957341			0.0478670	−	0.998854i	$-0.484758\pi$
$491$	2.12133			0.0957341			0.0478670	+	0.998854i	$0.484758\pi$
$492$	3.32451	+	0.785922i	0.149881	+	0.0354321i
$493$	−6.28970	+	3.63136i	−0.283274	+	0.163548i
$494$	7.97682	+	16.2007i	0.358894	+	0.728902i
$495$	−15.0307	+	0.892641i	−0.675578	+	0.0401212i
$496$	6.76061	−	6.76061i	0.303560	−	0.303560i
$497$	12.9342	−	8.15533i	0.580177	−	0.365817i
$498$	−0.605870	−	0.326236i	−0.0271497	−	0.0146190i
$499$	0.734964	+	2.74292i	0.0329015	+	0.122790i	0.980423	−	0.196901i	$-0.0630876\pi$
$499$	0.734964	+	2.74292i	0.0329015	+	0.122790i	−0.947522	+	0.319691i	$0.896421\pi$
$500$	−0.667262	+	2.49025i	−0.0298409	+	0.111368i
$501$	11.2211	−	11.9073i	0.501323	−	0.531979i
$502$	−21.3621	+	5.72395i	−0.953436	+	0.255472i
$503$			34.5946i			1.54250i	0.636534	+	0.771248i	$0.280367\pi$
$503$			34.5946i			1.54250i	−0.636534	+	0.771248i	$0.719633\pi$
$504$	4.62397	+	6.45127i	0.205968	+	0.287363i
$505$	−24.3826	−	24.3826i	−1.08501	−	1.08501i
$506$	−2.78492	+	4.82363i	−0.123805	+	0.214436i
$507$	−22.3985	−	2.30342i	−0.994754	−	0.102298i
$508$	−4.89874	−	8.48487i	−0.217347	−	0.376455i
$509$	2.53040	−	0.678019i	0.112158	−	0.0300527i	−0.202303	−	0.979323i	$-0.564843\pi$
$509$	2.53040	−	0.678019i	0.112158	−	0.0300527i	0.314462	+	0.949270i	$0.398176\pi$
$510$	5.35521	+	2.88356i	0.237133	+	0.127686i
$511$	−34.4004	−	18.1124i	−1.52178	−	0.801243i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−8.94268	−	24.4396i	−0.394829	−	1.07904i
$514$	−7.15619	+	26.7073i	−0.315646	+	1.17801i
$515$	−26.8991	−	7.20759i	−1.18532	−	0.317604i
$516$	0.760234	+	1.23095i	0.0334674	+	0.0541898i
$517$			2.60798i			0.114699i
$518$	3.92929	+	12.6681i	0.172643	+	0.556603i
$519$	−15.0018	+	27.8606i	−0.658506	+	1.22294i
$520$	6.06409	−	9.06341i	0.265928	−	0.397457i
$521$	−3.73840	+	2.15836i	−0.163782	+	0.0945596i	−0.579651	−	0.814865i	$-0.696811\pi$
$521$	−3.73840	+	2.15836i	−0.163782	+	0.0945596i	0.415869	+	0.909425i	$0.363478\pi$
$522$	−5.92309	−	17.8068i	−0.259247	−	0.779384i
$523$	12.4994	−	21.6496i	0.546561	−	0.946672i	−0.451946	−	0.892045i	$-0.649270\pi$
$523$	12.4994	−	21.6496i	0.546561	−	0.946672i	0.998507	−	0.0546262i	$-0.0173967\pi$
$524$	−16.2902			−0.711642
$525$	−6.16658	−	17.9785i	−0.269131	−	0.784646i
$526$	−6.33566	+	6.33566i	−0.276248	+	0.276248i
$527$	−2.87306	−	10.7224i	−0.125152	−	0.467075i
$528$	1.97125	−	2.09180i	0.0857879	−	0.0910338i
$529$	5.86725	+	10.1624i	0.255098	+	0.441842i
$530$	−15.7235	+	27.2339i	−0.682985	+	1.18297i
$531$	6.52879	+	1.34032i	0.283325	+	0.0581651i
$532$	−11.2089	+	7.06747i	−0.485965	+	0.306414i
$533$	−4.68548	−	5.34944i	−0.202951	−	0.231710i
$534$	−7.07677	−	11.4586i	−0.306242	−	0.495860i
$535$	−33.5127	−	8.97969i	−1.44888	−	0.388226i
$536$	−11.5165	+	6.64903i	−0.497435	+	0.287195i
$537$	−22.6122	−	36.6133i	−0.975791	−	1.57998i
$538$	14.8383	−	14.8383i	0.639725	−	0.639725i
$539$	8.82845	+	7.54955i	0.380268	+	0.325182i
$540$	−10.0813	+	12.0562i	−0.433829	+	0.518818i
$541$	3.42635	−	0.918088i	0.147310	−	0.0394717i	−0.184410	−	0.982849i	$-0.559038\pi$
$541$	3.42635	−	0.918088i	0.147310	−	0.0394717i	0.331721	+	0.943378i	$0.392371\pi$
$542$	22.9674	−	13.2602i	0.986533	−	0.569575i
$543$	−0.00770084	−	0.259568i	−0.000330475	−	0.0111391i
$544$	−1.12148	+	0.300499i	−0.0480830	+	0.0128838i
$545$	−40.5849			−1.73846
$546$	−0.0422124	−	16.5227i	−0.00180652	−	0.707104i
$547$	17.5248			0.749307			0.374653	−	0.927165i	$-0.377762\pi$
$547$	17.5248			0.749307			0.374653	+	0.927165i	$0.377762\pi$
$548$	12.2697	−	3.28765i	0.524135	−	0.140441i
$549$	−7.67629	+	15.3283i	−0.327616	+	0.654197i
$550$	−5.96066	+	3.44139i	−0.254164	+	0.146741i
$551$	30.2618	−	8.10861i	1.28919	−	0.345439i
$552$	1.67050	+	5.56830i	0.0711012	+	0.237002i
$553$	12.9492	+	11.9774i	0.550655	+	0.509332i
$554$	3.41679	−	3.41679i	0.145165	−	0.145165i
$555$	−22.3438	+	13.7995i	−0.948443	+	0.585755i
$556$	11.7495	−	6.78358i	0.498290	−	0.287688i
$557$	19.9768	+	5.35276i	0.846443	+	0.226804i	0.655874	−	0.754870i	$-0.272300\pi$
$557$	19.9768	+	5.35276i	0.846443	+	0.226804i	0.190569	+	0.981674i	$0.438967\pi$
$558$	28.6324	−	1.70042i	1.21211	−	0.0719846i
$559$	0.198836	−	3.00517i	0.00840987	−	0.127105i
$560$	7.08060	+	3.72805i	0.299210	+	0.157539i
$561$	−0.958928	−	3.19641i	−0.0404860	−	0.134952i
$562$	−11.4703	+	19.8671i	−0.483843	+	0.838041i
$563$	10.6903	+	18.5162i	0.450544	+	0.780364i	0.998420	−	0.0561950i	$-0.0178969\pi$
$563$	10.6903	+	18.5162i	0.450544	+	0.780364i	−0.547876	+	0.836559i	$0.684564\pi$
$564$	1.98102	+	1.86686i	0.0834159	+	0.0786090i
$565$	8.03961	+	30.0042i	0.338229	+	1.26229i
$566$	−15.5915	+	15.5915i	−0.655361	+	0.655361i
$567$	−2.47666	+	23.6826i	−0.104010	+	0.994576i
$568$	−5.77930			−0.242494
$569$	22.3188	−	38.6572i	0.935651	−	1.62060i	0.162182	−	0.986761i	$-0.448147\pi$
$569$	22.3188	−	38.6572i	0.935651	−	1.62060i	0.773469	−	0.633834i	$-0.218520\pi$
$570$	−19.0943	−	17.9939i	−0.799771	−	0.753683i
$571$	−12.0819	+	6.97550i	−0.505613	+	0.291916i	−0.731028	−	0.682347i	$-0.760959\pi$
$571$	−12.0819	+	6.97550i	−0.505613	+	0.291916i	0.225416	+	0.974263i	$0.427626\pi$
$572$	−5.86904	+	1.16365i	−0.245397	+	0.0486547i
$573$	−1.52913	−	0.823376i	−0.0638804	−	0.0343970i
$574$	3.54332	−	3.83080i	0.147896	−	0.159894i
$575$		−	13.9210i		−	0.580547i
$576$	−0.177851	−	2.99472i	−0.00741045	−	0.124780i
$577$	15.3639	+	4.11675i	0.639608	+	0.171382i	0.564026	−	0.825757i	$-0.309252\pi$
$577$	15.3639	+	4.11675i	0.639608	+	0.171382i	0.0755822	+	0.997140i	$0.475918\pi$
$578$	4.05103	−	15.1187i	0.168501	−	0.628853i
$579$	−7.27737	+	30.7839i	−0.302437	+	1.27933i
$580$	−13.3780	−	13.3780i	−0.555491	−	0.555491i
$581$	−0.889133	+	0.560621i	−0.0368874	+	0.0232585i
$582$	9.19541	−	17.0773i	0.381162	−	0.707875i
$583$	16.6662	−	4.46570i	0.690245	−	0.184951i
$584$	7.34712	+	12.7256i	0.304026	+	0.526588i
$585$	31.6567	−	8.25376i	1.30884	−	0.341251i
$586$	16.7748	−	29.0547i	0.692959	−	1.20024i
$587$	9.65450	+	9.65450i	0.398484	+	0.398484i	0.877698	−	0.479214i	$-0.159078\pi$
$587$	9.65450	+	9.65450i	0.398484	+	0.398484i	−0.479214	+	0.877698i	$0.659078\pi$
$588$	12.0543	−	1.30191i	0.497109	−	0.0536900i
$589$			47.8849i			1.97306i
$590$	6.49042	−	1.73910i	0.267206	−	0.0715978i
$591$	−3.83588	−	3.61483i	−0.157787	−	0.148694i
$592$	1.29749	−	4.84229i	0.0533265	−	0.199017i
$593$	−9.61177	−	35.8716i	−0.394708	−	1.47307i	−0.822277	−	0.569088i	$-0.807297\pi$
$593$	−9.61177	−	35.8716i	−0.394708	−	1.47307i	0.427569	−	0.903983i	$-0.359370\pi$
$594$	8.58872	−	0.766226i	0.352399	−	0.0314386i
$595$	7.85894	−	4.95526i	0.322185	−	0.203146i
$596$	4.76356	−	4.76356i	0.195123	−	0.195123i
$597$	−36.4360	+	22.5027i	−1.49123	+	0.920976i
$598$	3.89706	−	11.4571i	0.159363	−	0.468514i
$599$	5.41427	−	3.12593i	0.221221	−	0.127722i	−0.385294	−	0.922794i	$-0.625900\pi$
$599$	5.41427	−	3.12593i	0.221221	−	0.127722i	0.606516	+	0.795072i	$0.292567\pi$
$600$	−1.65272	+	6.99115i	−0.0674721	+	0.285412i
$601$	−22.2269			−0.906655			−0.453327	−	0.891344i	$-0.649763\pi$
$601$	−22.2269			−0.906655			−0.453327	+	0.891344i	$0.649763\pi$
$602$	2.20833	−	0.0860893i	0.0900049	−	0.00350874i
$603$	−39.0792	−	8.02274i	−1.59143	−	0.326711i
$604$	3.09576	+	11.5536i	0.125965	+	0.470107i
$605$	−24.0907	−	6.45509i	−0.979428	−	0.262437i
$606$	14.3712	+	13.5431i	0.583791	+	0.550150i
$607$	−6.41924	+	11.1184i	−0.260549	+	0.451284i	−0.966388	−	0.257088i	$-0.917237\pi$
$607$	−6.41924	+	11.1184i	−0.260549	+	0.451284i	0.705839	+	0.708372i	$0.250570\pi$
$608$	5.00839			0.203117
$609$	−28.1325	−	5.50315i	−1.13999	−	0.222999i
$610$			17.2830i			0.699768i
$611$	−1.10202	−	5.55822i	−0.0445831	−	0.224861i
$612$	−3.11441	−	1.55967i	−0.125893	−	0.0630459i
$613$	−27.5468	−	7.38115i	−1.11261	−	0.298122i	−0.344718	−	0.938706i	$-0.612026\pi$
$613$	−27.5468	−	7.38115i	−1.11261	−	0.298122i	−0.767888	+	0.640584i	$0.778692\pi$
$614$	−25.5635	−	14.7591i	−1.03166	−	0.595629i
$615$	9.09715	+	4.89845i	0.366833	+	0.197524i
$616$	−1.30069	−	4.19344i	−0.0524064	−	0.168959i
$617$	−9.57893	−	9.57893i	−0.385633	−	0.385633i	0.487494	−	0.873127i	$-0.337911\pi$
$617$	−9.57893	−	9.57893i	−0.385633	−	0.385633i	−0.873127	+	0.487494i	$0.837911\pi$
$618$	15.5200	+	3.66896i	0.624307	+	0.147587i
$619$	10.5264	−	39.2850i	0.423091	−	1.57900i	−0.344967	−	0.938615i	$-0.612110\pi$
$619$	10.5264	−	39.2850i	0.423091	−	1.57900i	0.768057	−	0.640381i	$-0.221224\pi$
$620$	25.0429	−	14.4585i	1.00575	−	0.580669i
$621$	−7.34359	+	15.8190i	−0.294688	+	0.634794i
$622$	0.324065	+	0.324065i	0.0129938	+	0.0129938i
$623$	−20.5566	+	0.801377i	−0.823585	+	0.0321065i
$624$	−3.31730	+	5.29108i	−0.132798	+	0.211813i
$625$	−14.2677	+	24.7124i	−0.570709	+	0.988496i
$626$	−4.31806	+	16.1152i	−0.172584	+	0.644093i
$627$	0.426895	+	14.3892i	0.0170486	+	0.574647i
$628$	4.81666	+	2.78090i	0.192206	+	0.110970i
$629$	−4.11566	−	4.11566i	−0.164102	−	0.164102i
$630$	8.45861	+	22.4666i	0.336999	+	0.895093i
$631$	3.44931	+	3.44931i	0.137315	+	0.137315i	0.772423	−	0.635108i	$-0.219044\pi$
$631$	3.44931	+	3.44931i	0.137315	+	0.137315i	−0.635108	+	0.772423i	$0.719044\pi$
$632$	−1.72554	−	6.43980i	−0.0686383	−	0.256162i
$633$	−30.4032	+	0.901997i	−1.20842	+	0.0358512i
$634$	17.9030	−	10.3363i	0.711017	−	0.410506i
$635$	−7.66945	−	28.6228i	−0.304353	−	1.13586i
$636$	8.53797	−	15.8563i	0.338553	−	0.628743i
$637$	−22.0056	−	12.3593i	−0.871894	−	0.489694i
$638$			10.3806i			0.410970i
$639$	−12.9650	−	11.5114i	−0.512887	−	0.455384i
$640$	−1.51225	−	2.61929i	−0.0597769	−	0.103537i
$641$	11.6885	+	20.2450i	0.461666	+	0.799630i	0.999044	−	0.0437119i	$-0.0139184\pi$
$641$	11.6885	+	20.2450i	0.461666	+	0.799630i	−0.537378	+	0.843342i	$0.680585\pi$
$642$	19.3359	+	4.57104i	0.763126	+	0.180405i
$643$	12.7687	−	12.7687i	0.503548	−	0.503548i	−0.408991	−	0.912539i	$-0.634119\pi$
$643$	12.7687	−	12.7687i	0.503548	−	0.503548i	0.912539	+	0.408991i	$0.134119\pi$
$644$	8.66067	+	1.96249i	0.341278	+	0.0773331i
$645$	1.25739	+	4.19127i	0.0495097	+	0.165031i
$646$	2.90747	−	5.03588i	0.114393	−	0.198134i
$647$	15.0344	+	26.0404i	0.591064	+	1.02375i	0.994089	+	0.108565i	$0.0346255\pi$
$647$	15.0344	+	26.0404i	0.591064	+	1.02375i	−0.403025	+	0.915189i	$0.632041\pi$
$648$	5.56600	−	7.07246i	0.218653	−	0.277832i
$649$	−3.19282	−	1.84337i	−0.125329	−	0.0723588i
$650$	11.2494	−	9.85314i	0.441237	−	0.386472i
$651$	19.2535	−	39.3567i	0.754606	−	1.54251i
$652$	−8.95913	+	8.95913i	−0.350867	+	0.350867i
$653$	−22.4490	−	12.9609i	−0.878497	−	0.507200i	−0.00833439	−	0.999965i	$-0.502653\pi$
$653$	−22.4490	−	12.9609i	−0.878497	−	0.507200i	−0.870163	+	0.492765i	$0.835986\pi$
$654$	23.2317	−	0.689234i	0.908429	−	0.0269512i
$655$	−47.5910	−	12.7520i	−1.85953	−	0.498260i
$656$	−1.90511	+	0.510472i	−0.0743820	+	0.0199306i
$657$	−8.86505	+	43.1821i	−0.345858	+	1.68470i
$658$	3.97136	−	1.23181i	0.154820	−	0.0480209i
$659$		−	9.59163i		−	0.373637i	−0.982394	−	0.186818i	$-0.940182\pi$
$659$		−	9.59163i		−	0.373637i	0.982394	−	0.186818i	$-0.0598176\pi$
$660$	7.39636	−	4.56797i	0.287903	−	0.177808i
$661$	−3.74781	+	13.9870i	−0.145773	+	0.544032i	0.853947	+	0.520360i	$0.174202\pi$
$661$	−3.74781	+	13.9870i	−0.145773	+	0.544032i	−0.999720	+	0.0236717i	$0.992464\pi$
$662$	−4.06490	−	7.04061i	−0.157987	−	0.273641i
$663$	3.39437	+	6.40708i	0.131826	+	0.248831i
$664$	0.397286			0.0154177
$665$	−38.2784	+	11.8729i	−1.48437	+	0.460412i
$666$	12.5557	−	8.27858i	0.486525	−	0.320788i
$667$	−18.1827	−	10.4978i	−0.704037	−	0.406476i
$668$	−2.44488	+	9.12442i	−0.0945953	+	0.353034i
$669$	9.66556	−	10.2566i	0.373692	−	0.396543i
$670$	−38.8495	+	10.4097i	−1.50089	+	0.402162i
$671$	6.70531	−	6.70531i	0.258855	−	0.258855i
$672$	−4.11640	−	2.01377i	−0.158794	−	0.0776828i
$673$		−	26.9899i		−	1.04039i	−0.854049	−	0.520193i	$-0.825860\pi$
$673$		−	26.9899i		−	1.04039i	0.854049	−	0.520193i	$-0.174140\pi$
$674$	−2.34635	−	8.75668i	−0.0903778	−	0.337295i
$675$	−17.6328	+	12.3916i	−0.678687	+	0.476954i
$676$	12.0166	−	4.96002i	0.462176	−	0.190770i
$677$	40.4765	+	23.3691i	1.55564	+	0.898148i	0.997666	+	0.0682885i	$0.0217538\pi$
$677$	40.4765	+	23.3691i	1.55564	+	0.898148i	0.557972	+	0.829859i	$0.311579\pi$
$678$	−5.11160	−	17.0386i	−0.196310	−	0.654362i
$679$	−15.8019	−	25.0614i	−0.606419	−	0.961768i
$680$	−3.51156			−0.134662
$681$	−6.37061	+	26.9482i	−0.244122	+	1.03266i
$682$	−15.3254	−	4.10644i	−0.586841	−	0.157244i
$683$	−4.03279	−	1.08058i	−0.154310	−	0.0413473i	0.180837	−	0.983513i	$-0.442119\pi$
$683$	−4.03279	−	1.08058i	−0.154310	−	0.0413473i	−0.335147	+	0.942166i	$0.608786\pi$
$684$	11.2356	+	9.97585i	0.429602	+	0.381436i
$685$	38.4187			1.46790
$686$	7.32637	−	17.0095i	0.279722	−	0.649427i
$687$	−10.6493	+	3.19482i	−0.406297	+	0.121890i
$688$	−0.723396	−	0.417653i	−0.0275792	−	0.0159229i
$689$	−33.6326	+	16.5599i	−1.28130	+	0.630883i
$690$	0.521416	+	17.5751i	0.0198500	+	0.669073i
$691$	9.93409	+	37.0745i	0.377911	+	1.41038i	0.849045	+	0.528321i	$0.177178\pi$
$691$	9.93409	+	37.0745i	0.377911	+	1.41038i	−0.471134	+	0.882062i	$0.656155\pi$
$692$		−	18.2690i		−	0.694482i
$693$	5.43471	−	11.9981i	0.206448	−	0.455770i
$694$	−10.2944	+	10.2944i	−0.390769	+	0.390769i
$695$	39.6357	−	10.6203i	1.50347	−	0.402853i
$696$	7.88505	+	7.43066i	0.298882	+	0.281659i
$697$	−0.592678	+	2.21191i	−0.0224493	+	0.0837819i
$698$	0.0935010	+	0.0539829i	0.00353907	+	0.00204328i
$699$	11.6508	−	21.6373i	0.440675	−	0.818400i
$700$	8.05581	+	7.45129i	0.304481	+	0.281632i
$701$	−1.65602			−0.0625472			−0.0312736	−	0.999511i	$-0.509956\pi$
$701$	−1.65602			−0.0625472			−0.0312736	+	0.999511i	$0.509956\pi$
$702$	−17.9808	+	5.26224i	−0.678641	+	0.198610i
$703$	12.5538	+	21.7438i	0.473476	+	0.820084i
$704$	−0.429501	+	1.60292i	−0.0161874	+	0.0604123i
$705$	4.32605	+	7.00466i	0.162929	+	0.263811i
$706$			18.1364i			0.682573i
$707$	28.8101	−	8.93612i	1.08352	−	0.336077i
$708$	−3.68572	+	1.10572i	−0.138518	+	0.0415557i
$709$	27.5601	−	7.38472i	1.03504	−	0.277339i	0.298985	−	0.954258i	$-0.403352\pi$
$709$	27.5601	−	7.38472i	1.03504	−	0.277339i	0.736058	+	0.676919i	$0.236685\pi$
$710$	−16.8839	−	4.52403i	−0.633641	−	0.169784i
$711$	8.95600	−	17.8837i	0.335876	−	0.670691i
$712$	6.73385	+	3.88779i	0.252362	+	0.145701i
$713$	22.6914	−	22.6914i	0.849800	−	0.849800i
$714$	−4.41447	+	2.96996i	−0.165207	+	0.111148i
$715$	−18.0569	−	1.19473i	−0.675292	−	0.0446805i
$716$	21.5165	+	12.4226i	0.804111	+	0.464254i
$717$	36.2525	+	34.1634i	1.35388	+	1.27586i
$718$	12.2357	+	21.1929i	0.456632	+	0.790911i
$719$	−0.628392	+	1.08841i	−0.0234351	+	0.0405907i	−0.877505	−	0.479567i	$-0.840794\pi$
$719$	−0.628392	+	1.08841i	−0.0234351	+	0.0405907i	0.854070	+	0.520158i	$0.174127\pi$
$720$	1.82468	−	8.88813i	0.0680019	−	0.331241i
$721$	16.5415	−	17.8835i	0.616038	−	0.666017i
$722$	−4.30198	+	4.30198i	−0.160103	+	0.160103i
$723$	−3.02203	+	12.7835i	−0.112391	+	0.475422i
$724$	0.0749639	+	0.129841i	0.00278601	+	0.00482551i
$725$	−12.9724	−	22.4688i	−0.481781	−	0.834469i
$726$	13.8997	+	3.28591i	0.515866	+	0.121952i
$727$			17.2192i			0.638627i	0.947649	+	0.319313i	$0.103452\pi$
$727$			17.2192i			0.638627i	−0.947649	+	0.319313i	$0.896548\pi$
$728$	4.54405	+	8.38759i	0.168414	+	0.310865i
$729$	26.5736	−	4.77947i	0.984208	−	0.177017i
$730$	11.5026	+	42.9284i	0.425731	+	1.58885i
$731$	−0.839891	+	0.484911i	−0.0310645	+	0.0179351i
$732$	−0.293509	−	9.89317i	−0.0108484	−	0.365662i
$733$	11.4862	+	42.8670i	0.424251	+	1.58333i	0.765552	+	0.643374i	$0.222466\pi$
$733$	11.4862	+	42.8670i	0.424251	+	1.58333i	−0.341301	+	0.939954i	$0.610867\pi$
$734$	−5.64585	−	5.64585i	−0.208392	−	0.208392i
$735$	36.2349	+	5.63258i	1.33655	+	0.207761i
$736$	−2.37334	−	2.37334i	−0.0874825	−	0.0874825i
$737$	19.1112	+	11.0338i	0.703968	+	0.406436i
$738$	−5.29060	−	2.64948i	−0.194750	−	0.0975289i
$739$	0.728651	−	2.71936i	0.0268039	−	0.100033i	−0.951228	−	0.308489i	$-0.900177\pi$
$739$	0.728651	−	2.71936i	0.0268039	−	0.100033i	0.978032	+	0.208455i	$0.0668435\pi$
$740$	7.58108	−	13.1308i	0.278686	−	0.482698i
$741$	−6.99007	−	30.4863i	−0.256787	−	1.11994i
$742$	−14.6721	−	23.2696i	−0.538629	−	0.854255i
$743$	10.8955	+	10.8955i	0.399715	+	0.399715i	0.878133	−	0.478417i	$-0.158789\pi$
$743$	10.8955	+	10.8955i	0.399715	+	0.399715i	−0.478417	+	0.878133i	$0.658789\pi$
$744$	−14.0896	+	8.70168i	−0.516549	+	0.319019i
$745$	17.6454	−	10.1876i	0.646476	−	0.373243i
$746$	−2.52449	+	9.42153i	−0.0924282	+	0.344947i
$747$	0.891251	+	0.791326i	0.0326092	+	0.0289531i
$748$	1.36238	+	1.36238i	0.0498137	+	0.0498137i
$749$	20.6085	−	22.2805i	0.753019	−	0.814111i
$750$	2.11704	−	3.93166i	0.0773034	−	0.143564i
$751$	19.7285	+	11.3903i	0.719904	+	0.415637i	0.814717	−	0.579858i	$-0.196892\pi$
$751$	19.7285	+	11.3903i	0.719904	+	0.415637i	−0.0948132	+	0.995495i	$0.530225\pi$
$752$	−1.51803	−	0.406755i	−0.0553569	−	0.0148328i
$753$	38.2886	−	1.13594i	1.39531	−	0.0413960i
$754$	−4.38639	−	22.1234i	−0.159743	−	0.805686i
$755$			36.1764i			1.31659i
$756$	−5.22343	−	12.7168i	−0.189974	−	0.462504i
$757$	−48.5293			−1.76383			−0.881913	−	0.471411i	$-0.843745\pi$
$757$	−48.5293			−1.76383			−0.881913	+	0.471411i	$0.843745\pi$
$758$	15.2372	−	26.3916i	0.553440	−	0.958586i
$759$	6.61634	−	7.02093i	0.240158	−	0.254844i
$760$	14.6317	+	3.92055i	0.530748	+	0.142213i
$761$	14.1003	+	52.6229i	0.511134	+	1.90758i	0.408206	+	0.912890i	$0.366154\pi$
$761$	14.1003	+	52.6229i	0.511134	+	1.90758i	0.102928	+	0.994689i	$0.467179\pi$
$762$	4.87625	+	16.2541i	0.176648	+	0.588822i
$763$	16.5401	−	31.4143i	0.598792	−	1.13727i
$764$	1.00270			0.0362763
$765$	−7.87766	−	6.99443i	−0.284817	−	0.252884i
$766$	−24.9105	+	14.3821i	−0.900053	+	0.519646i
$767$	7.58358	+	2.57951i	0.273827	+	0.0931407i
$768$	0.910127	+	1.47366i	0.0328414	+	0.0531761i
$769$	7.37109	−	7.37109i	0.265808	−	0.265808i	−0.561600	−	0.827409i	$-0.689814\pi$
$769$	7.37109	−	7.37109i	0.265808	−	0.265808i	0.827409	+	0.561600i	$0.189814\pi$
$770$	−0.517279	−	13.2691i	−0.0186415	−	0.478184i
$771$	22.7046	−	42.1659i	0.817687	−	1.51857i
$772$	−4.72680	−	17.6407i	−0.170121	−	0.634902i
$773$	−1.93188	+	7.20989i	−0.0694850	+	0.259322i	−0.991926	−	0.126816i	$-0.959524\pi$
$773$	−1.93188	+	7.20989i	−0.0694850	+	0.259322i	0.922441	+	0.386137i	$0.126191\pi$
$774$	−0.790936	−	2.37782i	−0.0284296	−	0.0854690i
$775$	38.3037	−	10.2635i	1.37591	−	0.368674i
$776$			11.1980i			0.401986i
$777$	−1.57524	−	22.9189i	−0.0565115	−	0.822211i
$778$	−25.7668	−	25.7668i	−0.923785	−	0.923785i
$779$	4.93905	−	8.55469i	0.176960	−	0.306504i
$780$	−13.8331	+	12.8608i	−0.495306	+	0.460491i
$781$	4.79527	+	8.30566i	0.171588	+	0.297200i
$782$	−3.76414	+	1.00860i	−0.134605	+	0.0360674i
$783$	2.88830	+	32.3752i	0.103219	+	1.15700i
$784$	−5.77131	+	3.96131i	−0.206118	+	0.141476i
$785$	11.8947	+	11.8947i	0.424541	+	0.424541i
$786$	27.4587	+	6.49129i	0.979418	+	0.231536i
$787$	6.28978	−	23.4738i	0.224207	−	0.836750i	−0.758514	−	0.651656i	$-0.774074\pi$
$787$	6.28978	−	23.4738i	0.224207	−	0.836750i	0.982721	−	0.185094i	$-0.0592589\pi$
$788$	2.93939	+	0.787606i	0.104711	+	0.0280573i
$789$	13.2039	−	8.15472i	0.470073	−	0.290316i
$790$		−	20.1643i		−	0.717412i
$791$	−26.5010	−	6.00507i	−0.942265	−	0.213516i
$792$	−4.15626	+	2.74041i	−0.147686	+	0.0973764i
$793$	−11.4572	+	17.1240i	−0.406857	+	0.608090i
$794$	6.61047	−	3.81656i	0.234597	−	0.135445i
$795$	37.3555	−	39.6398i	1.32486	−	1.40588i
$796$	12.3624	−	21.4123i	0.438174	−	0.758940i
$797$	18.6559			0.660824			0.330412	−	0.943837i	$-0.392812\pi$
$797$	18.6559			0.660824			0.330412	+	0.943837i	$0.392812\pi$
$798$	21.7098	−	7.44639i	0.768517	−	0.263599i
$799$	−1.29023	+	1.29023i	−0.0456452	+	0.0456452i
$800$	−1.07348	−	4.00627i	−0.0379531	−	0.141643i
$801$	7.36256	+	22.1344i	0.260143	+	0.782079i
$802$	7.52375	+	13.0315i	0.265673	+	0.460159i
$803$	12.1923	−	21.1176i	0.430256	−	0.745225i
$804$	22.0615	−	6.61850i	0.778050	−	0.233417i
$805$	23.7654	+	12.5129i	0.837620	+	0.441020i
$806$	34.3973	+	2.27589i	1.21159	+	0.0801647i
$807$	−30.9241	+	19.0986i	−1.08858	+	0.672303i
$808$	−11.0125	−	2.95079i	−0.387418	−	0.103808i
$809$	3.44305	−	1.98785i	0.121051	−	0.0698889i	−0.438252	−	0.898852i	$-0.644402\pi$
$809$	3.44305	−	1.98785i	0.121051	−	0.0698889i	0.559303	+	0.828963i	$0.311069\pi$
$810$	21.7970	−	16.3047i	0.765870	−	0.572889i
$811$	27.2199	−	27.2199i	0.955819	−	0.955819i	−0.0432450	−	0.999064i	$-0.513770\pi$
$811$	27.2199	−	27.2199i	0.955819	−	0.955819i	0.999064	+	0.0432450i	$0.0137696\pi$
$812$	15.8072	−	4.90297i	0.554724	−	0.172061i
$813$	−43.9975	+	13.1993i	−1.54306	+	0.462921i
$814$	−8.03561	+	2.15314i	−0.281648	+	0.0754674i
$815$	−33.1868	+	19.1604i	−1.16248	+	0.671159i
$816$	2.01009	−	0.0596352i	0.0703674	−	0.00208765i
$817$	4.04098	−	1.08278i	0.141376	−	0.0378816i
$818$	−1.48490			−0.0519185
$819$	−6.51275	+	27.8673i	−0.227574	+	0.973761i
$820$	−5.96526			−0.208316
$821$	23.9158	−	6.40822i	0.834667	−	0.223648i	0.183918	−	0.982942i	$-0.441122\pi$
$821$	23.9158	−	6.40822i	0.834667	−	0.223648i	0.650749	+	0.759293i	$0.274455\pi$
$822$	−21.9917	+	0.652447i	−0.767049	+	0.0227567i
$823$	7.45979	−	4.30691i	0.260032	−	0.150129i	−0.364317	−	0.931275i	$-0.618698\pi$
$823$	7.45979	−	4.30691i	0.260032	−	0.150129i	0.624349	+	0.781145i	$0.285364\pi$
$824$	−8.89373	+	2.38307i	−0.309828	+	0.0830181i
$825$	11.4186	−	3.42559i	0.397543	−	0.119264i
$826$	−1.29900	+	5.73260i	−0.0451979	+	0.199463i
$827$	12.5373	−	12.5373i	0.435965	−	0.435965i	−0.454687	−	0.890651i	$-0.650249\pi$
$827$	12.5373	−	12.5373i	0.435965	−	0.435965i	0.890651	+	0.454687i	$0.150249\pi$
$828$	−0.596940	−	10.0515i	−0.0207451	−	0.349315i
$829$	−19.3504	+	11.1720i	−0.672068	+	0.388019i	−0.796860	−	0.604164i	$-0.793507\pi$
$829$	−19.3504	+	11.1720i	−0.672068	+	0.388019i	0.124792	+	0.992183i	$0.460174\pi$
$830$	1.16065	+	0.310995i	0.0402867	+	0.0107948i
$831$	−7.12081	+	4.39779i	−0.247018	+	0.152558i
$832$	0.238040	−	3.59768i	0.00825255	−	0.124727i
$833$	0.632703	+	8.10261i	0.0219219	+	0.280739i
$834$	−22.5080	+	6.75243i	−0.779387	+	0.233818i
$835$	−14.2852	+	24.7426i	−0.494358	+	0.856253i
$836$	−4.15562	−	7.19774i	−0.143725	−	0.248939i
$837$	−48.9401	−	8.54314i	−1.69162	−	0.295294i
$838$	−3.47892	−	12.9835i	−0.120177	−	0.448508i
$839$	−6.99080	+	6.99080i	−0.241349	+	0.241349i	−0.817408	−	0.576059i	$-0.804590\pi$
$839$	−6.99080	+	6.99080i	−0.241349	+	0.241349i	0.576059	+	0.817408i	$0.304590\pi$
$840$	−10.4494	−	9.10542i	−0.360540	−	0.314167i
$841$	−10.1296			−0.349296
$842$	−4.70612	+	8.15123i	−0.162183	+	0.280910i
$843$	27.2507	−	28.9171i	0.938565	−	0.995958i
$844$	15.2083	−	8.78050i	0.523490	−	0.302237i
$845$	38.9884	−	5.08386i	1.34124	−	0.174890i
$846$	−2.59528	−	3.93615i	−0.0892277	−	0.135328i
$847$	14.8145	−	16.0164i	0.509033	−	0.550331i
$848$			10.3974i			0.357049i
$849$	32.4938	−	20.0681i	1.11518	−	0.688734i
$850$	−4.65143	−	1.24635i	−0.159543	−	0.0427494i
$851$	4.35491	−	16.2527i	0.149284	−	0.557137i
$852$	9.74154	+	2.30292i	0.333740	+	0.0788967i
$853$	−35.2320	−	35.2320i	−1.20632	−	1.20632i	−0.972210	−	0.234110i	$-0.924782\pi$
$853$	−35.2320	−	35.2320i	−1.20632	−	1.20632i	−0.234110	−	0.972210i	$-0.575218\pi$
$854$	−13.3777	−	7.04358i	−0.457776	−	0.241026i
$855$	25.0149	+	37.9390i	0.855493	+	1.29749i
$856$	−11.0804	+	2.96898i	−0.378720	+	0.101478i
$857$	−7.20533	−	12.4800i	−0.246130	−	0.426309i	0.716319	−	0.697773i	$-0.245826\pi$
$857$	−7.20533	−	12.4800i	−0.246130	−	0.426309i	−0.962449	+	0.271464i	$0.912492\pi$
$858$	10.3565	+	0.377239i	0.353564	+	0.0128787i
$859$	−5.03498	+	8.72085i	−0.171791	+	0.297552i	−0.939046	−	0.343791i	$-0.888289\pi$
$859$	−5.03498	+	8.72085i	−0.171791	+	0.297552i	0.767255	+	0.641342i	$0.221622\pi$
$860$	−1.78642	−	1.78642i	−0.0609164	−	0.0609164i
$861$	−7.49908	+	5.04522i	−0.255568	+	0.171941i
$862$			24.2185i			0.824885i
$863$	34.0557	−	9.12520i	1.15927	−	0.310625i	0.372596	−	0.927994i	$-0.378468\pi$
$863$	34.0557	−	9.12520i	1.15927	−	0.310625i	0.786674	+	0.617368i	$0.211801\pi$
$864$	−0.893545	+	5.11875i	−0.0303990	+	0.174143i
$865$	14.3009	−	53.3717i	0.486246	−	1.81469i
$866$	6.39731	+	23.8751i	0.217389	+	0.811308i
$867$	−12.8528	+	23.8696i	−0.436505	+	0.810655i
$868$	0.985383	+	25.2767i	0.0334461	+	0.857947i
$869$	−7.82315	+	7.82315i	−0.265382	+	0.265382i
$870$	17.2190	+	27.8806i	0.583779	+	0.945243i
$871$	−45.3928	−	15.4401i	−1.53808	−	0.523168i
$872$	−11.6209	+	6.70935i	−0.393535	+	0.227207i
$873$	−22.3046	+	25.1211i	−0.754896	+	0.850221i
$874$	16.8102			0.568614
$875$	−3.63803	−	5.76984i	−0.122988	−	0.195056i
$876$	−7.31338	−	24.3778i	−0.247096	−	0.823649i
$877$	−3.79319	−	14.1564i	−0.128087	−	0.478026i	0.871844	−	0.489783i	$-0.162924\pi$
$877$	−3.79319	−	14.1564i	−0.128087	−	0.478026i	−0.999931	+	0.0117571i	$0.996257\pi$
$878$	−18.7759	−	5.03099i	−0.633657	−	0.169788i
$879$	−39.8530	+	42.2900i	−1.34421	+	1.42641i
$880$	−2.50952	+	4.34662i	−0.0845960	+	0.146525i
$881$	20.5780			0.693291			0.346645	−	0.937996i	$-0.387321\pi$
$881$	20.5780			0.693291			0.346645	+	0.937996i	$0.387321\pi$
$882$	−20.8373	−	2.60885i	−0.701629	−	0.0878446i
$883$			36.4936i			1.22811i	0.789264	+	0.614054i	$0.210462\pi$
$883$			36.4936i			1.22811i	−0.789264	+	0.614054i	$0.789538\pi$
$884$	−3.47925	−	2.32787i	−0.117020	−	0.0782949i
$885$	−11.6332	+	0.345132i	−0.391045	+	0.0116015i
$886$	16.1093	+	4.31648i	0.541203	+	0.145015i
$887$	2.47311	+	1.42785i	0.0830388	+	0.0479425i	0.540944	−	0.841058i	$-0.318067\pi$
$887$	2.47311	+	1.42785i	0.0830388	+	0.0479425i	−0.457906	+	0.889001i	$0.651400\pi$
$888$	−4.11658	+	7.64511i	−0.138143	+	0.256553i
$889$	25.2808	+	5.72859i	0.847891	+	0.192131i
$890$	16.6292	+	16.6292i	0.557412	+	0.557412i
$891$	−14.7824	−	2.13086i	−0.495229	−	0.0713866i
$892$	−2.10595	+	7.85951i	−0.0705124	+	0.263156i
$893$	6.81656	−	3.93554i	0.228107	−	0.131698i
$894$	−9.92759	+	6.13124i	−0.332028	+	0.205060i
$895$	53.1350	+	53.1350i	1.77611	+	1.77611i
$896$	2.64374	−	0.103063i	0.0883213	−	0.00344310i
$897$	−11.1342	+	17.7590i	−0.371761	+	0.592957i
$898$	13.3220	−	23.0744i	0.444561	−	0.770003i
$899$	15.4792	−	57.7693i	0.516262	−	1.92672i
$900$	5.57162	−	11.1256i	0.185721	−	0.370855i
$901$	10.4545	+	6.03591i	0.348290	+	0.201085i
$902$	2.31435	+	2.31435i	0.0770594	+	0.0770594i
$903$	−3.75665	−	0.734859i	−0.125013	−	0.0244546i
$904$	7.26224	+	7.26224i	0.241538	+	0.241538i
$905$	0.117363	+	0.438005i	0.00390128	+	0.0145598i
$906$	−0.614367	−	20.7082i	−0.0204110	−	0.687982i
$907$	28.1413	−	16.2474i	0.934416	−	0.539486i	0.0462108	−	0.998932i	$-0.485285\pi$
$907$	28.1413	−	16.2474i	0.934416	−	0.539486i	0.888206	+	0.459446i	$0.151952\pi$
$908$	−4.13784	−	15.4426i	−0.137319	−	0.512482i
$909$	−18.8274	−	28.5547i	−0.624466	−	0.947099i
$910$	6.70940	+	28.0609i	0.222414	+	0.930210i
$911$			3.28273i			0.108762i	0.998520	+	0.0543809i	$0.0173185\pi$
$911$			3.28273i			0.108762i	−0.998520	+	0.0543809i	$0.982681\pi$
$912$	−8.44209	−	1.99573i	−0.279545	−	0.0660851i
$913$	−0.329641	−	0.570955i	−0.0109095	−	0.0188958i
$914$	4.32716	+	7.49486i	0.143130	+	0.247908i
$915$	6.88688	−	29.1321i	0.227673	−	0.963077i
$916$	4.53900	−	4.53900i	0.149973	−	0.149973i
$917$	29.2659	−	31.6403i	0.966446	−	1.04485i
$918$	4.62813	+	3.86998i	0.152751	+	0.127728i
$919$	−12.1884	+	21.1110i	−0.402060	+	0.696388i	−0.993974	−	0.109613i	$-0.965039\pi$
$919$	−12.1884	+	21.1110i	−0.402060	+	0.696388i	0.591915	+	0.806001i	$0.298372\pi$
$920$	−5.07573	−	8.79143i	−0.167342	−	0.289845i
$921$	37.2084	+	35.0643i	1.22606	+	1.15541i
$922$	−20.5684	−	11.8752i	−0.677385	−	0.391088i
$923$	−13.7295	−	15.6750i	−0.451911	−	0.515949i
$924$	0.521444	+	7.58672i	0.0171543	+	0.249585i
$925$	14.7024	−	14.7024i	0.483412	−	0.483412i
$926$	13.8486	+	7.99550i	0.455094	+	0.262748i
$927$	−24.6984	−	12.3687i	−0.811202	−	0.406243i
$928$	−6.04222	−	1.61901i	−0.198346	−	0.0531465i
$929$	−47.5051	+	12.7290i	−1.55859	+	0.417624i	−0.932218	−	0.361898i	$-0.882129\pi$
$929$	−47.5051	+	12.7290i	−1.55859	+	0.417624i	−0.626375	+	0.779522i	$0.715462\pi$
$930$	−47.9735	+	14.3922i	−1.57311	+	0.471937i
$931$	6.41002	−	34.4677i	0.210080	−	1.12963i
$932$			14.1882i			0.464751i
$933$	−0.417109	−	0.675374i	−0.0136555	−	0.0221108i
$934$	−3.79090	+	14.1478i	−0.124042	+	0.462932i
$935$	2.91366	+	5.04660i	0.0952867	+	0.165041i
$936$	7.69998	−	7.59673i	0.251682	−	0.248307i
$937$	−49.3899			−1.61350			−0.806749	−	0.590895i	$-0.798775\pi$
$937$	−49.3899			−1.61350			−0.806749	+	0.590895i	$0.798775\pi$
$938$	7.77537	−	34.3135i	0.253875	−	1.12037i
$939$	13.7000	−	25.4430i	0.447083	−	0.830301i
$940$	−4.11643	−	2.37662i	−0.134263	−	0.0775169i
$941$	−12.5436	+	46.8133i	−0.408909	+	1.52607i	0.387820	+	0.921735i	$0.373228\pi$
$941$	−12.5436	+	46.8133i	−0.408909	+	1.52607i	−0.796730	+	0.604336i	$0.793439\pi$
$942$	−7.01080	−	6.60679i	−0.228424	−	0.215261i
$943$	−6.39433	+	1.71336i	−0.208228	+	0.0557945i
$944$	1.57094	−	1.57094i	0.0511299	−	0.0511299i
$945$	−5.30531	−	41.2401i	−0.172582	−	1.34154i
$946$			1.38616i			0.0450679i
$947$	−0.107633	−	0.401692i	−0.00349760	−	0.0130532i	0.964155	−	0.265340i	$-0.0854841\pi$
$947$	−0.107633	−	0.401692i	−0.00349760	−	0.0130532i	−0.967653	+	0.252287i	$0.918817\pi$
$948$	0.342440	+	11.5425i	0.0111219	+	0.374882i
$949$	−17.0612	+	50.1586i	−0.553829	+	1.62822i
$950$	17.9897	+	10.3864i	0.583664	+	0.336978i
$951$	−34.2958	+	10.2888i	−1.11212	+	0.333638i
$952$	1.43112	−	2.71809i	0.0463827	−	0.0880937i
$953$	−17.5490			−0.568468			−0.284234	−	0.958755i	$-0.591739\pi$
$953$	−17.5490			−0.568468			−0.284234	+	0.958755i	$0.591739\pi$
$954$	−20.7099	+	23.3251i	−0.670508	+	0.755177i
$955$	2.92932	+	0.784908i	0.0947905	+	0.0253990i
$956$	−27.7799	−	7.44360i	−0.898465	−	0.240743i
$957$	4.13641	−	17.4974i	0.133711	−	0.565609i
$958$	6.76633			0.218610
$959$	−15.6573	+	29.7376i	−0.505601	+	0.960277i
$960$	1.50531	+	5.01765i	0.0485835	+	0.161944i
$961$	52.3181	+	30.2059i	1.68768	+	0.974383i
$962$	16.2159	−	7.98435i	0.522823	−	0.257426i
$963$	−30.7709	−	15.4098i	−0.991579	−	0.496574i
$964$	−1.96287	−	7.32554i	−0.0632199	−	0.235940i
$965$		−	55.2363i		−	1.77812i
$966$	−13.8163	−	6.75904i	−0.444533	−	0.217468i
$967$	11.2055	−	11.2055i	0.360345	−	0.360345i	−0.503595	−	0.863940i	$-0.667989\pi$
$967$	11.2055	−	11.2055i	0.360345	−	0.360345i	0.863940	+	0.503595i	$0.167989\pi$
$968$	−7.96520	+	2.13427i	−0.256011	+	0.0685980i
$969$	−6.90748	+	7.32987i	−0.221900	+	0.235469i
$970$	−8.76580	+	32.7144i	−0.281453	+	1.05040i
$971$	−21.2615	−	12.2753i	−0.682315	−	0.393935i	0.118412	−	0.992965i	$-0.462220\pi$
$971$	−21.2615	−	12.2753i	−0.682315	−	0.393935i	−0.800727	+	0.599030i	$0.795553\pi$
$972$	−12.2002	+	9.70335i	−0.391322	+	0.311235i
$973$	−7.93271	+	35.0078i	−0.254311	+	1.12230i
$974$	15.6369			0.501037
$975$	−22.8881	+	12.1257i	−0.733006	+	0.388334i
$976$	2.85717	+	4.94876i	0.0914557	+	0.158406i
$977$	−12.2182	+	45.5989i	−0.390894	+	1.45884i	0.437767	+	0.899088i	$0.355769\pi$
$977$	−12.2182	+	45.5989i	−0.390894	+	1.45884i	−0.828662	+	0.559750i	$0.810897\pi$
$978$	18.6714	−	11.5314i	0.597047	−	0.368734i
$979$		−	12.9033i		−	0.412391i
$980$	−19.9614	+	7.05498i	−0.637645	+	0.225363i
$981$	−39.4337	−	8.09552i	−1.25902	−	0.258470i
$982$	2.04904	−	0.549039i	0.0653876	−	0.0175206i
$983$	50.0435	+	13.4091i	1.59614	+	0.427685i	0.943874	−	0.330305i	$-0.107152\pi$
$983$	50.0435	+	13.4091i	1.59614	+	0.427685i	0.652266	+	0.757990i	$0.273818\pi$
$984$	3.41464	−	0.101305i	0.108855	−	0.00322949i
$985$	7.97071	+	4.60189i	0.253968	+	0.146628i
$986$	−5.13552	+	5.13552i	−0.163548	+	0.163548i
$987$	−7.18494	+	0.493829i	−0.228699	+	0.0157188i
$988$	11.8981	+	13.5841i	0.378528	+	0.432167i
$989$	−2.42801	−	1.40181i	−0.0772063	−	0.0445751i
$990$	−14.2875	+	4.75245i	−0.454086	+	0.151043i
$991$	−8.55384	−	14.8157i	−0.271722	−	0.470636i	0.697581	−	0.716506i	$-0.254260\pi$
$991$	−8.55384	−	14.8157i	−0.271722	−	0.470636i	−0.969303	+	0.245870i	$0.920926\pi$
$992$	4.78048	−	8.28003i	0.151780	−	0.262891i
$993$	4.04623	+	13.4874i	0.128403	+	0.428008i
$994$	10.3827	−	11.2251i	0.329319	−	0.356037i
$995$	52.8776	−	52.8776i	1.67633	−	1.67633i
$996$	−0.669662	−	0.158309i	−0.0212190	−	0.00501622i
$997$	6.18994	+	10.7213i	0.196037	+	0.339546i	0.947240	−	0.320525i	$-0.103859\pi$
$997$	6.18994	+	10.7213i	0.196037	+	0.339546i	−0.751203	+	0.660071i	$0.770526\pi$
$998$	1.41984	+	2.45924i	0.0449443	+	0.0778458i
$999$	−24.4627	+	8.95112i	−0.773965	+	0.283201i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bv.a.317.19	yes	144
3.2	odd	2	inner	546.2.bv.a.317.13	✓	144
7.4	even	3	inner	546.2.bv.a.473.13	yes	144
13.8	odd	4	inner	546.2.bv.a.359.19	yes	144
21.11	odd	6	inner	546.2.bv.a.473.19	yes	144
39.8	even	4	inner	546.2.bv.a.359.13	yes	144
91.60	odd	12	inner	546.2.bv.a.515.13	yes	144
273.242	even	12	inner	546.2.bv.a.515.19	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bv.a.317.13	✓	144	3.2	odd	2	inner
546.2.bv.a.317.19	yes	144	1.1	even	1	trivial
546.2.bv.a.359.13	yes	144	39.8	even	4	inner
546.2.bv.a.359.19	yes	144	13.8	odd	4	inner
546.2.bv.a.473.13	yes	144	7.4	even	3	inner
546.2.bv.a.473.19	yes	144	21.11	odd	6	inner
546.2.bv.a.515.13	yes	144	91.60	odd	12	inner
546.2.bv.a.515.19	yes	144	273.242	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bv (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{2} +(-1.73129 + 0.0513637i) q^{3} +(0.866025 - 0.500000i) q^{4} +(2.92144 - 0.782798i) q^{5} +(-1.65900 + 0.497704i) q^{6} +(-0.584700 + 2.58033i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.99472 - 0.177851i) q^{9} +O(q^{10})\)	\(q+(0.965926 - 0.258819i) q^{2} +(-1.73129 + 0.0513637i) q^{3} +(0.866025 - 0.500000i) q^{4} +(2.92144 - 0.782798i) q^{5} +(-1.65900 + 0.497704i) q^{6} +(-0.584700 + 2.58033i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.99472 - 0.177851i) q^{9} +(2.61929 - 1.51225i) q^{10} +(-1.60292 - 0.429501i) q^{11} +(-1.47366 + 0.910127i) q^{12} +(3.59768 + 0.238040i) q^{13} +(0.103063 + 2.64374i) q^{14} +(-5.01765 + 1.50531i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.580520 - 1.00549i) q^{17} +(2.84665 - 0.946882i) q^{18} +(1.29627 + 4.83773i) q^{19} +(2.13864 - 2.13864i) q^{20} +(0.879749 - 4.49734i) q^{21} -1.65946 q^{22} +(1.67821 - 2.90674i) q^{23} +(-1.18789 + 1.26053i) q^{24} +(3.59192 - 2.07380i) q^{25} +(3.53671 - 0.701220i) q^{26} +(-5.17560 + 0.461731i) q^{27} +(0.783803 + 2.52699i) q^{28} -6.25536i q^{29} +(-4.45708 + 2.75268i) q^{30} +(9.23517 + 2.47456i) q^{31} +(0.258819 - 0.965926i) q^{32} +(2.79718 + 0.661258i) q^{33} +(-0.820979 - 0.820979i) q^{34} +(0.311715 + 7.99600i) q^{35} +(2.50458 - 1.65138i) q^{36} +(4.84229 - 1.29749i) q^{37} +(2.50419 + 4.33739i) q^{38} +(-6.24086 - 0.227326i) q^{39} +(1.51225 - 2.61929i) q^{40} +(-1.39464 - 1.39464i) q^{41} +(-0.314225 - 4.57179i) q^{42} -0.835305i q^{43} +(-1.60292 + 0.429501i) q^{44} +(8.60969 - 2.86384i) q^{45} +(0.868703 - 3.24204i) q^{46} +(-0.406755 - 1.51803i) q^{47} +(-0.821162 + 1.52502i) q^{48} +(-6.31625 - 3.01744i) q^{49} +(2.93279 - 2.93279i) q^{50} +(1.05669 + 1.71098i) q^{51} +(3.23471 - 1.59269i) q^{52} +(-9.00444 + 5.19871i) q^{53} +(-4.87974 + 1.78554i) q^{54} -5.01905 q^{55} +(1.41113 + 2.23802i) q^{56} +(-2.49269 - 8.30893i) q^{57} +(-1.61901 - 6.04222i) q^{58} +(2.14595 + 0.575005i) q^{59} +(-3.59276 + 3.81246i) q^{60} +(-2.85717 + 4.94876i) q^{61} +9.56095 q^{62} +(-1.29210 + 7.83138i) q^{63} -1.00000i q^{64} +(10.6968 - 2.12084i) q^{65} +(2.87301 - 0.0852361i) q^{66} +(-12.8449 - 3.44179i) q^{67} +(-1.00549 - 0.580520i) q^{68} +(-2.75616 + 5.11860i) q^{69} +(2.37061 + 7.64286i) q^{70} +(-4.08659 - 4.08659i) q^{71} +(1.99183 - 2.24335i) q^{72} +(-3.80315 + 14.1935i) q^{73} +(4.34148 - 2.50656i) q^{74} +(-6.11214 + 3.77484i) q^{75} +(3.54146 + 3.54146i) q^{76} +(2.04548 - 3.88494i) q^{77} +(-6.08704 + 1.39567i) q^{78} +(3.33349 - 5.77377i) q^{79} +(0.782798 - 2.92144i) q^{80} +(8.93674 - 1.06523i) q^{81} +(-1.70807 - 0.986157i) q^{82} +(0.280924 + 0.280924i) q^{83} +(-1.48678 - 4.33468i) q^{84} +(-2.48305 - 2.48305i) q^{85} +(-0.216193 - 0.806843i) q^{86} +(0.321298 + 10.8298i) q^{87} +(-1.43714 + 0.829732i) q^{88} +(2.01247 + 7.51064i) q^{89} +(7.57510 - 4.99461i) q^{90} +(-2.71779 + 9.14405i) q^{91} -3.35641i q^{92} +(-16.1158 - 3.80982i) q^{93} +(-0.785790 - 1.36103i) q^{94} +(7.57393 + 13.1184i) q^{95} +(-0.398477 + 1.68559i) q^{96} +(-7.91821 + 7.91821i) q^{97} +(-6.88200 - 1.27986i) q^{98} +(-4.87669 - 1.00116i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 16 q^{7}+O(q^{10}) \) 144 * q - 16 * q^7	\( 144 q - 16 q^{7} + 72 q^{16} + 16 q^{18} + 8 q^{19} + 8 q^{21} + 24 q^{27} - 8 q^{28} - 8 q^{31} + 12 q^{33} - 8 q^{37} + 16 q^{39} - 40 q^{45} + 8 q^{46} + 8 q^{52} - 12 q^{54} - 32 q^{55} + 16 q^{57} + 8 q^{58} - 32 q^{61} - 40 q^{63} - 32 q^{66} - 8 q^{67} + 16 q^{72} + 80 q^{73} - 16 q^{76} + 16 q^{78} - 112 q^{79} - 48 q^{81} + 16 q^{84} - 80 q^{85} + 96 q^{87} - 32 q^{91} + 36 q^{93} - 64 q^{94} - 144 q^{97} - 32 q^{99}+O(q^{100}) \) 144 * q - 16 * q^7 + 72 * q^16 + 16 * q^18 + 8 * q^19 + 8 * q^21 + 24 * q^27 - 8 * q^28 - 8 * q^31 + 12 * q^33 - 8 * q^37 + 16 * q^39 - 40 * q^45 + 8 * q^46 + 8 * q^52 - 12 * q^54 - 32 * q^55 + 16 * q^57 + 8 * q^58 - 32 * q^61 - 40 * q^63 - 32 * q^66 - 8 * q^67 + 16 * q^72 + 80 * q^73 - 16 * q^76 + 16 * q^78 - 112 * q^79 - 48 * q^81 + 16 * q^84 - 80 * q^85 + 96 * q^87 - 32 * q^91 + 36 * q^93 - 64 * q^94 - 144 * q^97 - 32 * q^99

Introduction

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