LMFDB - Embedded newform 546.2.bq.c.419.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(419,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([3, 3, 2]))

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

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

chi := DirichletCharacter("546.419");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			419.14
Character	$\chi$	$=$	546.419
Dual form			546.2.bq.c.503.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(1.69217 - 0.369559i) q^{3} +(0.500000 - 0.866025i) q^{4} +3.03607 q^{5} +(-1.28068 + 1.16613i) q^{6} +(-2.32945 - 1.25445i) q^{7} +1.00000i q^{8} +(2.72685 - 1.25071i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(1.69217 - 0.369559i) q^{3} +(0.500000 - 0.866025i) q^{4} +3.03607 q^{5} +(-1.28068 + 1.16613i) q^{6} +(-2.32945 - 1.25445i) q^{7} +1.00000i q^{8} +(2.72685 - 1.25071i) q^{9} +(-2.62932 + 1.51804i) q^{10} +(2.44849 - 1.41364i) q^{11} +(0.526036 - 1.65024i) q^{12} +(-2.51309 - 2.58542i) q^{13} +(2.64459 - 0.0783374i) q^{14} +(5.13754 - 1.12201i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.232581 - 0.402842i) q^{17} +(-1.73617 + 2.44657i) q^{18} +(5.32858 + 3.07646i) q^{19} +(1.51804 - 2.62932i) q^{20} +(-4.40541 - 1.26187i) q^{21} +(-1.41364 + 2.44849i) q^{22} +(-4.51168 + 2.60482i) q^{23} +(0.369559 + 1.69217i) q^{24} +4.21775 q^{25} +(3.46911 + 0.982495i) q^{26} +(4.15208 - 3.12414i) q^{27} +(-2.25111 + 1.39014i) q^{28} +(-5.09714 + 2.94283i) q^{29} +(-3.88824 + 3.54046i) q^{30} -8.58125i q^{31} +(0.866025 + 0.500000i) q^{32} +(3.62083 - 3.29697i) q^{33} +0.465162i q^{34} +(-7.07239 - 3.80861i) q^{35} +(0.280280 - 2.98688i) q^{36} +(-0.0269566 - 0.0466902i) q^{37} -6.15292 q^{38} +(-5.20803 - 3.44623i) q^{39} +3.03607i q^{40} +(4.15653 + 7.19932i) q^{41} +(4.44614 - 1.10989i) q^{42} +(-1.40564 + 2.43464i) q^{43} -2.82727i q^{44} +(8.27893 - 3.79725i) q^{45} +(2.60482 - 4.51168i) q^{46} -6.13208 q^{47} +(-1.16613 - 1.28068i) q^{48} +(3.85269 + 5.84438i) q^{49} +(-3.65268 + 2.10887i) q^{50} +(0.244692 - 0.767629i) q^{51} +(-3.49558 + 0.883688i) q^{52} +8.84822i q^{53} +(-2.03373 + 4.78162i) q^{54} +(7.43380 - 4.29190i) q^{55} +(1.25445 - 2.32945i) q^{56} +(10.1538 + 3.23665i) q^{57} +(2.94283 - 5.09714i) q^{58} +(5.41190 - 9.37369i) q^{59} +(1.59708 - 5.01025i) q^{60} +(11.5411 + 6.66328i) q^{61} +(4.29062 + 7.43158i) q^{62} +(-7.92103 - 0.507241i) q^{63} -1.00000 q^{64} +(-7.62992 - 7.84953i) q^{65} +(-1.48725 + 4.66567i) q^{66} +(-1.71013 - 2.96202i) q^{67} +(-0.232581 - 0.402842i) q^{68} +(-6.67188 + 6.07512i) q^{69} +(8.02918 - 0.237838i) q^{70} +(9.26650 + 5.35002i) q^{71} +(1.25071 + 2.72685i) q^{72} +7.57692i q^{73} +(0.0466902 + 0.0269566i) q^{74} +(7.13713 - 1.55871i) q^{75} +(5.32858 - 3.07646i) q^{76} +(-7.47698 + 0.221481i) q^{77} +(6.23340 + 0.380506i) q^{78} -14.2092 q^{79} +(-1.51804 - 2.62932i) q^{80} +(5.87145 - 6.82100i) q^{81} +(-7.19932 - 4.15653i) q^{82} -1.88916 q^{83} +(-3.29552 + 3.18426i) q^{84} +(0.706134 - 1.22306i) q^{85} -2.81129i q^{86} +(-7.53765 + 6.86345i) q^{87} +(1.41364 + 2.44849i) q^{88} +(-1.27938 - 2.21594i) q^{89} +(-5.27114 + 7.42798i) q^{90} +(2.61083 + 9.17516i) q^{91} +5.20964i q^{92} +(-3.17128 - 14.5209i) q^{93} +(5.31054 - 3.06604i) q^{94} +(16.1780 + 9.34036i) q^{95} +(1.65024 + 0.526036i) q^{96} +(7.06440 + 4.07863i) q^{97} +(-6.25872 - 3.13503i) q^{98} +(4.90862 - 6.91713i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 32 q^{4} + 16 q^{7} + 16 q^{9}+O(q^{10}) $ 64 * q + 32 * q^4 + 16 * q^7 + 16 * q^9	$ 64 q + 32 q^{4} + 16 q^{7} + 16 q^{9} - 12 q^{15} - 32 q^{16} - 24 q^{18} + 16 q^{21} - 16 q^{28} + 8 q^{30} - 16 q^{36} - 48 q^{39} + 20 q^{42} - 8 q^{43} + 8 q^{46} + 8 q^{49} - 8 q^{51} + 8 q^{57} + 16 q^{58} - 24 q^{60} + 32 q^{63} - 64 q^{64} + 24 q^{67} + 48 q^{70} - 12 q^{72} - 12 q^{78} + 96 q^{79} + 68 q^{81} + 8 q^{84} - 112 q^{85} - 16 q^{91} - 56 q^{93}+O(q^{100}) $ 64 * q + 32 * q^4 + 16 * q^7 + 16 * q^9 - 12 * q^15 - 32 * q^16 - 24 * q^18 + 16 * q^21 - 16 * q^28 + 8 * q^30 - 16 * q^36 - 48 * q^39 + 20 * q^42 - 8 * q^43 + 8 * q^46 + 8 * q^49 - 8 * q^51 + 8 * q^57 + 16 * q^58 - 24 * q^60 + 32 * q^63 - 64 * q^64 + 24 * q^67 + 48 * q^70 - 12 * q^72 - 12 * q^78 + 96 * q^79 + 68 * q^81 + 8 * q^84 - 112 * q^85 - 16 * q^91 - 56 * q^93

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	1.69217	−	0.369559i	0.976973	−	0.213365i
$3$	1.69217	−	0.369559i	0.976973	−	0.213365i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	3.03607			1.35777			0.678887	−	0.734243i	$-0.262463\pi$
$5$	3.03607			1.35777			0.678887	+	0.734243i	$0.262463\pi$
$6$	−1.28068	+	1.16613i	−0.522835	+	0.476071i
$7$	−2.32945	−	1.25445i	−0.880450	−	0.474139i
$7$	−2.32945	−	1.25445i	−0.880450	−	0.474139i
$8$			1.00000i			0.353553i
$9$	2.72685	−	1.25071i	0.908951	−	0.416903i
$10$	−2.62932	+	1.51804i	−0.831463	+	0.480046i
$11$	2.44849	−	1.41364i	0.738247	−	0.426227i	−0.0831844	−	0.996534i	$-0.526509\pi$
$11$	2.44849	−	1.41364i	0.738247	−	0.426227i	0.821432	+	0.570307i	$0.193176\pi$
$12$	0.526036	−	1.65024i	0.151853	−	0.476383i
$13$	−2.51309	−	2.58542i	−0.697005	−	0.717066i
$13$	−2.51309	−	2.58542i	−0.697005	−	0.717066i
$14$	2.64459	−	0.0783374i	0.706797	−	0.0209365i
$15$	5.13754	−	1.12201i	1.32651	−	0.289701i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.232581	−	0.402842i	0.0564092	−	0.0977037i	−0.836442	−	0.548056i	$-0.815368\pi$
$17$	0.232581	−	0.402842i	0.0564092	−	0.0977037i	0.892851	+	0.450352i	$0.148702\pi$
$18$	−1.73617	+	2.44657i	−0.409219	+	0.576663i
$19$	5.32858	+	3.07646i	1.22246	+	0.705788i	0.965442	−	0.260618i	$-0.0839264\pi$
$19$	5.32858	+	3.07646i	1.22246	+	0.705788i	0.257019	+	0.966406i	$0.417260\pi$
$20$	1.51804	−	2.62932i	0.339443	−	0.587933i
$21$	−4.40541	−	1.26187i	−0.961340	−	0.275364i
$22$	−1.41364	+	2.44849i	−0.301388	+	0.522020i
$23$	−4.51168	+	2.60482i	−0.940751	+	0.543143i	−0.890196	−	0.455579i	$-0.849432\pi$
$23$	−4.51168	+	2.60482i	−0.940751	+	0.543143i	−0.0505552	+	0.998721i	$0.516099\pi$
$24$	0.369559	+	1.69217i	0.0754359	+	0.345412i
$25$	4.21775			0.843550
$26$	3.46911	+	0.982495i	0.680348	+	0.192683i
$27$	4.15208	−	3.12414i	0.799067	−	0.601241i
$28$	−2.25111	+	1.39014i	−0.425421	+	0.262711i
$29$	−5.09714	+	2.94283i	−0.946514	+	0.546470i	−0.891996	−	0.452042i	$-0.850696\pi$
$29$	−5.09714	+	2.94283i	−0.946514	+	0.546470i	−0.0545179	+	0.998513i	$0.517362\pi$
$30$	−3.88824	+	3.54046i	−0.709892	+	0.646396i
$31$		−	8.58125i		−	1.54124i	−0.637296	−	0.770619i	$-0.719947\pi$
$31$		−	8.58125i		−	1.54124i	0.637296	−	0.770619i	$-0.280053\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	3.62083	−	3.29697i	0.630305	−	0.573928i
$34$			0.465162i			0.0797747i
$35$	−7.07239	−	3.80861i	−1.19545	−	0.643773i
$36$	0.280280	−	2.98688i	0.0467133	−	0.497813i
$37$	−0.0269566	−	0.0466902i	−0.00443164	−	0.00767582i	0.863801	−	0.503833i	$-0.168077\pi$
$37$	−0.0269566	−	0.0466902i	−0.00443164	−	0.00767582i	−0.868233	+	0.496157i	$0.834744\pi$
$38$	−6.15292			−0.998135
$39$	−5.20803	−	3.44623i	−0.833952	−	0.551838i
$40$			3.03607i			0.480046i
$41$	4.15653	+	7.19932i	0.649141	+	1.12434i	0.983329	+	0.181838i	$0.0582046\pi$
$41$	4.15653	+	7.19932i	0.649141	+	1.12434i	−0.334188	+	0.942506i	$0.608462\pi$
$42$	4.44614	−	1.10989i	0.686054	−	0.171260i
$43$	−1.40564	+	2.43464i	−0.214358	+	0.371280i	−0.953074	−	0.302738i	$-0.902099\pi$
$43$	−1.40564	+	2.43464i	−0.214358	+	0.371280i	0.738715	+	0.674017i	$0.235433\pi$
$44$		−	2.82727i		−	0.426227i
$45$	8.27893	−	3.79725i	1.23415	−	0.566060i
$46$	2.60482	−	4.51168i	0.384060	−	0.665211i
$47$	−6.13208			−0.894456			−0.447228	−	0.894420i	$-0.647589\pi$
$47$	−6.13208			−0.894456			−0.447228	+	0.894420i	$0.647589\pi$
$48$	−1.16613	−	1.28068i	−0.168316	−	0.184850i
$49$	3.85269	+	5.84438i	0.550385	+	0.834911i
$50$	−3.65268	+	2.10887i	−0.516567	+	0.298240i
$51$	0.244692	−	0.767629i	0.0342637	−	0.107490i
$52$	−3.49558	+	0.883688i	−0.484750	+	0.122545i
$53$			8.84822i			1.21540i	0.794168	+	0.607698i	$0.207907\pi$
$53$			8.84822i			1.21540i	−0.794168	+	0.607698i	$0.792093\pi$
$54$	−2.03373	+	4.78162i	−0.276756	+	0.650697i
$55$	7.43380	−	4.29190i	1.00237	−	0.578720i
$56$	1.25445	−	2.32945i	0.167633	−	0.311286i
$57$	10.1538	+	3.23665i	1.34490	+	0.428705i
$58$	2.94283	−	5.09714i	0.386413	−	0.669287i
$59$	5.41190	−	9.37369i	0.704570	−	1.22035i	−0.262277	−	0.964993i	$-0.584473\pi$
$59$	5.41190	−	9.37369i	0.704570	−	1.22035i	0.966847	−	0.255358i	$-0.0821932\pi$
$60$	1.59708	−	5.01025i	0.206183	−	0.646820i
$61$	11.5411	+	6.66328i	1.47769	+	0.853146i	0.999682	−	0.0252092i	$-0.00802519\pi$
$61$	11.5411	+	6.66328i	1.47769	+	0.853146i	0.478009	+	0.878355i	$0.341359\pi$
$62$	4.29062	+	7.43158i	0.544910	+	0.943812i
$63$	−7.92103	−	0.507241i	−0.997956	−	0.0639063i
$64$	−1.00000			−0.125000
$65$	−7.62992	−	7.84953i	−0.946375	−	0.973614i
$66$	−1.48725	+	4.66567i	−0.183067	+	0.574305i
$67$	−1.71013	−	2.96202i	−0.208925	−	0.361869i	0.742451	−	0.669900i	$-0.233663\pi$
$67$	−1.71013	−	2.96202i	−0.208925	−	0.361869i	−0.951376	+	0.308031i	$0.900330\pi$
$68$	−0.232581	−	0.402842i	−0.0282046	−	0.0488518i
$69$	−6.67188	+	6.07512i	−0.803200	+	0.731359i
$70$	8.02918	−	0.237838i	0.959670	−	0.0284271i
$71$	9.26650	+	5.35002i	1.09973	+	0.634930i	0.936150	−	0.351600i	$-0.114362\pi$
$71$	9.26650	+	5.35002i	1.09973	+	0.634930i	0.163581	+	0.986530i	$0.447696\pi$
$72$	1.25071	+	2.72685i	0.147398	+	0.321363i
$73$			7.57692i			0.886811i	0.896321	+	0.443406i	$0.146230\pi$
$73$			7.57692i			0.886811i	−0.896321	+	0.443406i	$0.853770\pi$
$74$	0.0466902	+	0.0269566i	0.00542763	+	0.00313364i
$75$	7.13713	−	1.55871i	0.824125	−	0.179984i
$76$	5.32858	−	3.07646i	0.611230	−	0.352894i
$77$	−7.47698	+	0.221481i	−0.852081	+	0.0252401i
$78$	6.23340	+	0.380506i	0.705793	+	0.0430838i
$79$	−14.2092			−1.59866			−0.799332	−	0.600890i	$-0.794813\pi$
$79$	−14.2092			−1.59866			−0.799332	+	0.600890i	$0.794813\pi$
$80$	−1.51804	−	2.62932i	−0.169722	−	0.293967i
$81$	5.87145	−	6.82100i	0.652383	−	0.757889i
$82$	−7.19932	−	4.15653i	−0.795032	−	0.459012i
$83$	−1.88916			−0.207362			−0.103681	−	0.994611i	$-0.533062\pi$
$83$	−1.88916			−0.207362			−0.103681	+	0.994611i	$0.533062\pi$
$84$	−3.29552	+	3.18426i	−0.359571	+	0.347432i
$85$	0.706134	−	1.22306i	0.0765910	−	0.132659i
$86$		−	2.81129i		−	0.303149i
$87$	−7.53765	+	6.86345i	−0.808121	+	0.735839i
$88$	1.41364	+	2.44849i	0.150694	+	0.261010i
$89$	−1.27938	−	2.21594i	−0.135614	−	0.234890i	0.790218	−	0.612826i	$-0.209967\pi$
$89$	−1.27938	−	2.21594i	−0.135614	−	0.234890i	−0.925832	+	0.377936i	$0.876634\pi$
$90$	−5.27114	+	7.42798i	−0.555627	+	0.782978i
$91$	2.61083	+	9.17516i	0.273689	+	0.961818i
$92$			5.20964i			0.543143i
$93$	−3.17128	−	14.5209i	−0.328846	−	1.50575i
$94$	5.31054	−	3.06604i	0.547740	−	0.316238i
$95$	16.1780	+	9.34036i	1.65983	+	0.958301i
$96$	1.65024	+	0.526036i	0.168427	+	0.0536883i
$97$	7.06440	+	4.07863i	0.717281	+	0.414122i	0.813751	−	0.581214i	$-0.197422\pi$
$97$	7.06440	+	4.07863i	0.717281	+	0.414122i	−0.0964702	+	0.995336i	$0.530755\pi$
$98$	−6.25872	−	3.13503i	−0.632226	−	0.316686i
$99$	4.90862	−	6.91713i	0.493335	−	0.695197i
$100$	2.10887	−	3.65268i	0.210887	−	0.365268i
$101$	0.204489	+	0.354186i	0.0203475	+	0.0352428i	0.876020	−	0.482275i	$-0.160189\pi$
$101$	0.204489	+	0.354186i	0.0203475	+	0.0352428i	−0.855672	+	0.517518i	$0.826856\pi$
$102$	0.171905	+	0.787132i	0.0170211	+	0.0779377i
$103$		−	13.3326i		−	1.31370i	−0.754020	−	0.656852i	$-0.771888\pi$
$103$		−	13.3326i		−	1.31370i	0.754020	−	0.656852i	$-0.228112\pi$
$104$	2.58542	−	2.51309i	0.253521	−	0.246428i
$105$	−13.3752	−	3.83114i	−1.30528	−	0.373881i
$106$	−4.42411	−	7.66278i	−0.429708	−	0.744275i
$107$	−15.9007	+	9.18025i	−1.53718	+	0.887488i	−0.538173	+	0.842835i	$0.680885\pi$
$107$	−15.9007	+	9.18025i	−1.53718	+	0.887488i	−0.999003	+	0.0446537i	$0.985782\pi$
$108$	−0.629548	−	5.15787i	−0.0605783	−	0.496317i
$109$	−6.65851			−0.637770			−0.318885	−	0.947793i	$-0.603308\pi$
$109$	−6.65851			−0.637770			−0.318885	+	0.947793i	$0.603308\pi$
$110$	−4.29190	+	7.43380i	−0.409217	+	0.708785i
$111$	−0.0628698	−	0.0690456i	−0.00596734	−	0.00655351i
$112$	0.0783374	+	2.64459i	0.00740219	+	0.249890i
$113$	2.01785	+	1.16500i	0.189823	+	0.109594i	0.591900	−	0.806012i	$-0.298378\pi$
$113$	2.01785	+	1.16500i	0.189823	+	0.109594i	−0.402077	+	0.915606i	$0.631711\pi$
$114$	−10.4118	+	2.27387i	−0.975151	+	0.212967i
$115$	−13.6978	+	7.90843i	−1.27733	+	0.737465i
$116$			5.88567i			0.546470i
$117$	−10.0864	−	3.90691i	−0.932491	−	0.361194i
$118$			10.8238i			0.996412i
$119$	−1.04713	+	0.646640i	−0.0959906	+	0.0592774i
$120$	1.12201	+	5.13754i	0.102425	+	0.468991i
$121$	−1.50327	+	2.60374i	−0.136661	+	0.236703i
$122$	−13.3266			−1.20653
$123$	9.69411	+	10.6464i	0.874088	+	0.959950i
$124$	−7.43158	−	4.29062i	−0.667376	−	0.385309i
$125$	−2.37497			−0.212424
$126$	7.11343	−	3.52123i	0.633715	−	0.313696i
$127$	3.39634	+	5.88263i	0.301376	+	0.521999i	0.976448	−	0.215753i	$-0.0692206\pi$
$127$	3.39634	+	5.88263i	0.301376	+	0.521999i	−0.675072	+	0.737752i	$0.735887\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−1.47884	+	4.63929i	−0.130204	+	0.408467i
$130$	10.5325	+	2.98293i	0.923758	+	0.261620i
$131$	−17.6215			−1.53959			−0.769797	−	0.638289i	$-0.779643\pi$
$131$	−17.6215			−1.53959			−0.769797	+	0.638289i	$0.779643\pi$
$132$	−1.04484	−	4.78421i	−0.0909419	−	0.416412i
$133$	−8.55340	−	13.8509i	−0.741674	−	1.20103i
$134$	2.96202	+	1.71013i	0.255880	+	0.147732i
$135$	12.6060	−	9.48513i	1.08495	−	0.816350i
$136$	0.402842	+	0.232581i	0.0345435	+	0.0199437i
$137$	1.30289	+	0.752224i	0.111313	+	0.0642669i	0.554623	−	0.832102i	$-0.312862\pi$
$137$	1.30289	+	0.752224i	0.111313	+	0.0642669i	−0.443310	+	0.896369i	$0.646196\pi$
$138$	2.74046	−	8.59715i	0.233283	−	0.731838i
$139$	−9.48078	−	5.47373i	−0.804150	−	0.464276i	0.0407705	−	0.999169i	$-0.487019\pi$
$139$	−9.48078	−	5.47373i	−0.804150	−	0.464276i	−0.844920	+	0.534893i	$0.820352\pi$
$140$	−6.83455	+	4.22056i	−0.577625	+	0.356703i
$141$	−10.3765	+	2.26617i	−0.873859	+	0.190846i
$142$	−10.7000			−0.897927
$143$	−9.80811	−	2.77778i	−0.820195	−	0.232290i
$144$	−2.44657	−	1.73617i	−0.203881	−	0.144681i
$145$	−15.4753	+	8.93466i	−1.28515	+	0.741983i
$146$	−3.78846	−	6.56180i	−0.313535	−	0.543059i
$147$	8.67924	+	8.46586i	0.715851	+	0.698253i
$148$	−0.0539132			−0.00443164
$149$	−13.4874	−	7.78696i	−1.10493	−	0.637933i	−0.167420	−	0.985886i	$-0.553544\pi$
$149$	−13.4874	−	7.78696i	−1.10493	−	0.637933i	−0.937512	+	0.347953i	$0.886877\pi$
$150$	−5.40158	+	4.91844i	−0.441037	+	0.401589i
$151$	10.4109			0.847231			0.423615	−	0.905842i	$-0.360761\pi$
$151$	10.4109			0.847231			0.423615	+	0.905842i	$0.360761\pi$
$152$	−3.07646	+	5.32858i	−0.249534	+	0.432205i
$153$	0.130376	−	1.38938i	0.0105402	−	0.112325i
$154$	6.36451	−	3.93030i	0.512867	−	0.316712i
$155$		−	26.0533i		−	2.09265i
$156$	−5.58853	+	2.78717i	−0.447441	+	0.223152i
$157$		−	0.641256i		−	0.0511778i	−0.999673	−	0.0255889i	$-0.991854\pi$
$157$		−	0.641256i		−	0.0511778i	0.999673	−	0.0255889i	$-0.00814609\pi$
$158$	12.3056	−	7.10462i	0.978978	−	0.565213i
$159$	3.26994	+	14.9727i	0.259323	+	1.18741i
$160$	2.62932	+	1.51804i	0.207866	+	0.120011i
$161$	13.7774	−	0.408110i	1.08581	−	0.0321635i
$162$	−1.67432	+	8.84289i	−0.131547	+	0.694763i
$163$	−1.66049	+	2.87605i	−0.130059	+	0.225270i	−0.923699	−	0.383118i	$-0.874850\pi$
$163$	−1.66049	+	2.87605i	−0.130059	+	0.225270i	0.793640	+	0.608388i	$0.208183\pi$
$164$	8.31306			0.649141
$165$	10.9931	−	10.0098i	0.855812	−	0.779265i
$166$	1.63606	−	0.944581i	0.126983	−	0.0733137i
$167$	−3.80987	−	6.59888i	−0.294816	−	0.510637i	0.680126	−	0.733095i	$-0.261925\pi$
$167$	−3.80987	−	6.59888i	−0.294816	−	0.510637i	−0.974942	+	0.222459i	$0.928592\pi$
$168$	1.26187	−	4.40541i	0.0973557	−	0.339885i
$169$	−0.368787	+	12.9948i	−0.0283682	+	0.999598i
$170$			1.41227i			0.108316i
$171$	18.3780	+	1.72454i	1.40540	+	0.131879i
$172$	1.40564	+	2.43464i	0.107179	+	0.185640i
$173$	1.56798	−	2.71582i	0.119211	−	0.206480i	−0.800244	−	0.599674i	$-0.795297\pi$
$173$	1.56798	−	2.71582i	0.119211	−	0.206480i	0.919455	+	0.393194i	$0.128630\pi$
$174$	3.09607	−	9.71275i	0.234712	−	0.736322i
$175$	−9.82504	−	5.29097i	−0.742703	−	0.399960i
$176$	−2.44849	−	1.41364i	−0.184562	−	0.106557i
$177$	5.69371	−	17.8619i	0.427965	−	1.34258i
$178$	2.21594	+	1.27938i	0.166092	+	0.0958932i
$179$	−17.7205	+	10.2309i	−1.32449	+	0.764696i	−0.984442	−	0.175711i	$-0.943778\pi$
$179$	−17.7205	+	10.2309i	−1.32449	+	0.764696i	−0.340051	+	0.940407i	$0.610444\pi$
$180$	0.850950	−	9.06839i	0.0634261	−	0.675918i
$181$			20.7135i			1.53962i	0.638272	+	0.769811i	$0.279650\pi$
$181$			20.7135i			1.53962i	−0.638272	+	0.769811i	$0.720350\pi$
$182$	−6.84862	−	6.64051i	−0.507654	−	0.492227i
$183$	21.9920	+	7.01025i	1.62570	+	0.518212i
$184$	−2.60482	−	4.51168i	−0.192030	−	0.332606i
$185$	−0.0818423	−	0.141755i	−0.00601716	−	0.0104220i
$186$	10.0069	+	10.9898i	0.733738	+	0.805813i
$187$		−	1.31514i		−	0.0961726i
$188$	−3.06604	+	5.31054i	−0.223614	+	0.387311i
$189$	−13.5912	+	2.06895i	−0.988611	+	0.150494i
$190$	−18.6807			−1.35524
$191$	1.91936	+	1.10814i	0.138880	+	0.0801825i	0.567830	−	0.823146i	$-0.307783\pi$
$191$	1.91936	+	1.10814i	0.138880	+	0.0801825i	−0.428950	+	0.903328i	$0.641116\pi$
$192$	−1.69217	+	0.369559i	−0.122122	+	0.0266706i
$193$	−6.22651	−	10.7846i	−0.448194	−	0.776295i	0.550074	−	0.835116i	$-0.314599\pi$
$193$	−6.22651	−	10.7846i	−0.448194	−	0.776295i	−0.998269	+	0.0588206i	$0.981266\pi$
$194$	−8.15726			−0.585657
$195$	−15.8120	−	10.4630i	−1.13232	−	0.749271i
$196$	6.98773	−	0.414341i	0.499123	−	0.0295958i
$197$	14.8759	−	8.58860i	1.05986	−	0.611912i	0.134469	−	0.990918i	$-0.457067\pi$
$197$	14.8759	−	8.58860i	1.05986	−	0.611912i	0.925394	+	0.379006i	$0.123734\pi$
$198$	−0.792427	+	8.44472i	−0.0563153	+	0.600140i
$199$	−6.23877	−	3.60195i	−0.442254	−	0.255336i	0.262299	−	0.964987i	$-0.415519\pi$
$199$	−6.23877	−	3.60195i	−0.442254	−	0.255336i	−0.704553	+	0.709651i	$0.748853\pi$
$200$			4.21775i			0.298240i
$201$	−3.98846	−	4.38025i	−0.281324	−	0.308959i
$202$	−0.354186	−	0.204489i	−0.0249205	−	0.0143878i
$203$	15.5652	−	0.461068i	1.09246	−	0.0323606i
$204$	−0.542440	−	0.595724i	−0.0379784	−	0.0417090i
$205$	12.6195	+	21.8577i	0.881386	+	1.52661i
$206$	6.66632	+	11.5464i	0.464465	+	0.804476i
$207$	−9.04482	+	12.7458i	−0.628658	+	0.885892i
$208$	−0.982495	+	3.46911i	−0.0681238	+	0.240539i
$209$	17.3960			1.20330
$210$	13.4988	−	3.36971i	0.931506	−	0.232532i
$211$	−5.32704	−	9.22671i	−0.366729	−	0.635193i	0.622323	−	0.782760i	$-0.286189\pi$
$211$	−5.32704	−	9.22671i	−0.366729	−	0.635193i	−0.989052	+	0.147567i	$0.952856\pi$
$212$	7.66278	+	4.42411i	0.526282	+	0.303849i
$213$	17.6576	+	5.62860i	1.20988	+	0.385665i
$214$	9.18025	−	15.9007i	0.627549	−	1.08695i
$215$	−4.26764	+	7.39176i	−0.291050	+	0.504114i
$216$	3.12414	+	4.15208i	0.212571	+	0.282513i
$217$	−10.7648	+	19.9896i	−0.730761	+	1.35698i
$218$	5.76644	−	3.32926i	0.390553	−	0.225486i
$219$	2.80012	+	12.8214i	0.189214	+	0.866390i
$220$		−	8.58381i		−	0.578720i
$221$	−1.62601	+	0.411058i	−0.109378	+	0.0276508i
$222$	0.0889697	+	0.0283603i	0.00597125	+	0.00190342i
$223$	9.49568	−	5.48233i	0.635878	−	0.367124i	−0.147147	−	0.989115i	$-0.547009\pi$
$223$	9.49568	−	5.48233i	0.635878	−	0.367124i	0.783025	+	0.621990i	$0.213676\pi$
$224$	−1.39014	−	2.25111i	−0.0928825	−	0.150409i
$225$	11.5012	−	5.27518i	0.766745	−	0.351679i
$226$	−2.33001			−0.154990
$227$	−8.52609	+	14.7676i	−0.565896	+	0.980161i	0.431069	+	0.902319i	$0.358136\pi$
$227$	−8.52609	+	14.7676i	−0.565896	+	0.980161i	−0.996966	+	0.0778425i	$0.975197\pi$
$228$	7.87992	−	7.17511i	0.521860	−	0.475183i
$229$		−	6.45518i		−	0.426570i	−0.976990	−	0.213285i	$-0.931584\pi$
$229$		−	6.45518i		−	0.426570i	0.976990	−	0.213285i	$-0.0684163\pi$
$230$	7.90843	−	13.6978i	0.521466	−	0.903206i
$231$	−12.5704	+	3.13797i	−0.827074	+	0.206463i
$232$	−2.94283	−	5.09714i	−0.193206	−	0.334643i
$233$			5.44256i			0.356554i	0.983980	+	0.178277i	$0.0570523\pi$
$233$			5.44256i			0.356554i	−0.983980	+	0.178277i	$0.942948\pi$
$234$	10.6886	−	1.65973i	0.698733	−	0.108500i
$235$	−18.6175			−1.21447
$236$	−5.41190	−	9.37369i	−0.352285	−	0.610175i
$237$	−24.0444	+	5.25115i	−1.56185	+	0.341099i
$238$	0.583525	−	1.08357i	0.0378243	−	0.0702376i
$239$			24.8962i			1.61040i	0.593001	+	0.805202i	$0.297943\pi$
$239$			24.8962i			1.61040i	−0.593001	+	0.805202i	$0.702057\pi$
$240$	−3.54046	−	3.88824i	−0.228536	−	0.250985i
$241$	3.77906	+	2.18184i	0.243431	+	0.140545i	0.616752	−	0.787157i	$-0.288448\pi$
$241$	3.77906	+	2.18184i	0.243431	+	0.140545i	−0.373322	+	0.927702i	$0.621781\pi$
$242$		−	3.00653i		−	0.193267i
$243$	7.41471	−	13.7121i	0.475654	−	0.879633i
$244$	11.5411	−	6.66328i	0.738846	−	0.426573i
$245$	11.6971	+	17.7440i	0.747298	+	1.13362i
$246$	−13.7185	−	4.37296i	−0.874661	−	0.278810i
$247$	−5.43726	−	21.5080i	−0.345964	−	1.36852i
$248$	8.58125			0.544910
$249$	−3.19678	+	0.698157i	−0.202587	+	0.0442439i
$250$	2.05679	−	1.18749i	0.130083	−	0.0751033i
$251$	9.80578	−	16.9841i	0.618936	−	1.07203i	−0.370745	−	0.928735i	$-0.620898\pi$
$251$	9.80578	−	16.9841i	0.618936	−	1.07203i	0.989680	−	0.143293i	$-0.0457691\pi$
$252$	−4.39980	+	6.60619i	−0.277161	+	0.416151i
$253$	−7.36454	+	12.7558i	−0.463004	+	0.801947i
$254$	−5.88263	−	3.39634i	−0.369109	−	0.213105i
$255$	0.742903	−	2.33058i	0.0465224	−	0.145946i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	1.04197	+	1.80474i	0.0649963	+	0.112577i	0.896692	−	0.442654i	$-0.145963\pi$
$257$	1.04197	+	1.80474i	0.0649963	+	0.112577i	−0.831696	+	0.555231i	$0.812630\pi$
$258$	−1.03894	−	4.75716i	−0.0646813	−	0.296168i
$259$	0.00422342	+	0.142578i	0.000262431	+	0.00885939i
$260$	−10.6128	+	2.68294i	−0.658181	+	0.166389i
$261$	−10.2185	+	14.3997i	−0.632510	+	0.891320i
$262$	15.2606	−	8.81073i	0.942805	−	0.544329i
$263$	12.9817	−	7.49497i	0.800484	−	0.462160i	−0.0431562	−	0.999068i	$-0.513741\pi$
$263$	12.9817	−	7.49497i	0.800484	−	0.462160i	0.843640	+	0.536908i	$0.180408\pi$
$264$	3.29697	+	3.62083i	0.202914	+	0.222847i
$265$			26.8639i			1.65023i
$266$	14.3329	+	7.71855i	0.878808	+	0.473255i
$267$	−2.98384	−	3.27694i	−0.182608	−	0.200545i
$268$	−3.42025			−0.208925
$269$	−1.19534	+	2.07038i	−0.0728809	+	0.126233i	−0.900163	−	0.435554i	$-0.856553\pi$
$269$	−1.19534	+	2.07038i	−0.0728809	+	0.126233i	0.827282	+	0.561787i	$0.189886\pi$
$270$	−6.17456	+	14.5174i	−0.375772	+	0.883499i
$271$	−2.48498	+	1.43471i	−0.150952	+	0.0871522i	−0.573573	−	0.819154i	$-0.694443\pi$
$271$	−2.48498	+	1.43471i	−0.150952	+	0.0871522i	0.422622	+	0.906306i	$0.361110\pi$
$272$	−0.465162			−0.0282046
$273$	7.80872	+	14.5610i	0.472605	+	0.881274i
$274$	−1.50445			−0.0908871
$275$	10.3271	−	5.96236i	0.622748	−	0.359544i
$276$	1.92527	+	8.81558i	0.115888	+	0.530636i
$277$	5.47591	−	9.48455i	0.329015	−	0.569871i	−0.653301	−	0.757098i	$-0.726617\pi$
$277$	5.47591	−	9.48455i	0.329015	−	0.569871i	0.982317	+	0.187227i	$0.0599499\pi$
$278$	10.9475			0.656585
$279$	−10.7327	−	23.3998i	−0.642547	−	1.40091i
$280$	3.80861	−	7.07239i	0.227608	−	0.422656i
$281$		−	28.6157i		−	1.70707i	−0.521034	−	0.853536i	$-0.674453\pi$
$281$		−	28.6157i		−	1.70707i	0.521034	−	0.853536i	$-0.325547\pi$
$282$	7.85323	−	7.15081i	0.467653	−	0.425825i
$283$	7.61788	−	4.39819i	0.452836	−	0.261445i	−0.256191	−	0.966626i	$-0.582468\pi$
$283$	7.61788	−	4.39819i	0.452836	−	0.261445i	0.709027	+	0.705181i	$0.249134\pi$
$284$	9.26650	−	5.35002i	0.549865	−	0.317465i
$285$	30.8276	+	9.82672i	1.82607	+	0.582085i
$286$	9.88296	−	2.49842i	0.584392	−	0.147735i
$287$	−0.651223	−	21.9846i	−0.0384405	−	1.29771i
$288$	2.98688	+	0.280280i	0.176004	+	0.0165156i
$289$	8.39181	+	14.5350i	0.493636	+	0.855003i
$290$	8.93466	−	15.4753i	0.524661	−	0.908740i
$291$	13.4614	+	4.29101i	0.789123	+	0.251544i
$292$	6.56180	+	3.78846i	0.384000	+	0.221703i
$293$	−5.88594	+	10.1947i	−0.343860	+	0.595583i	−0.985146	−	0.171719i	$-0.945068\pi$
$293$	−5.88594	+	10.1947i	−0.343860	+	0.595583i	0.641286	+	0.767302i	$0.278401\pi$
$294$	−11.7494	−	2.99203i	−0.685237	−	0.174499i
$295$	16.4309	−	28.4592i	0.956646	−	1.65696i
$296$	0.0466902	−	0.0269566i	0.00271381	−	0.00156682i
$297$	5.74992	−	13.5190i	0.333644	−	0.784449i
$298$	15.5739			0.902173
$299$	18.0728	+	5.11845i	1.04518	+	0.296008i
$300$	2.21869	−	6.96029i	0.128096	−	0.401853i
$301$	6.32853	−	3.90807i	0.364770	−	0.225258i
$302$	−9.01615	+	5.20547i	−0.518821	+	0.299541i
$303$	0.476923	+	0.523771i	0.0273985	+	0.0300899i
$304$		−	6.15292i		−	0.352894i
$305$	35.0398	+	20.2302i	2.00637	+	1.15838i
$306$	0.581783	+	1.26843i	0.0332583	+	0.0725113i
$307$		−	15.8994i		−	0.907425i	−0.891148	−	0.453712i	$-0.850099\pi$
$307$		−	15.8994i		−	0.907425i	0.891148	−	0.453712i	$-0.149901\pi$
$308$	−3.54668	+	6.58599i	−0.202091	+	0.375272i
$309$	−4.92720	−	22.5610i	−0.280298	−	1.28345i
$310$	13.0267	+	22.5628i	0.739864	+	1.28148i
$311$	24.5325			1.39111			0.695556	−	0.718472i	$-0.255158\pi$
$311$	24.5325			1.39111			0.695556	+	0.718472i	$0.255158\pi$
$312$	3.44623	−	5.20803i	0.195104	−	0.294846i
$313$		−	14.2440i		−	0.805116i	−0.915394	−	0.402558i	$-0.868121\pi$
$313$		−	14.2440i		−	0.805116i	0.915394	−	0.402558i	$-0.131879\pi$
$314$	0.320628	+	0.555344i	0.0180941	+	0.0313399i
$315$	−24.0488	−	1.54002i	−1.35500	−	0.0867704i
$316$	−7.10462	+	12.3056i	−0.399666	+	0.692242i
$317$			9.51590i			0.534466i	0.963632	+	0.267233i	$0.0861094\pi$
$317$			9.51590i			0.534466i	−0.963632	+	0.267233i	$0.913891\pi$
$318$	−10.3182	−	11.3317i	−0.578615	−	0.635452i
$319$	−8.32019	+	14.4110i	−0.465841	+	0.806860i
$320$	−3.03607			−0.169722
$321$	−23.5139	+	21.4107i	−1.31242	+	1.19503i
$322$	−11.7275	+	7.24212i	−0.653548	+	0.403588i
$323$	2.47866	−	1.43105i	0.137916	−	0.0796259i
$324$	−2.97144	−	8.49533i	−0.165080	−	0.471963i
$325$	−10.5996	−	10.9046i	−0.587958	−	0.604881i
$326$		−	3.32098i		−	0.183932i
$327$	−11.2673	+	2.46071i	−0.623083	+	0.136078i
$328$	−7.19932	+	4.15653i	−0.397516	+	0.229506i
$329$	14.2844	+	7.69241i	0.787524	+	0.424097i
$330$	−4.51539	+	14.1653i	−0.248564	+	0.779776i
$331$	14.2287	−	24.6448i	0.782080	−	1.35460i	−0.148648	−	0.988890i	$-0.547492\pi$
$331$	14.2287	−	24.6448i	0.782080	−	1.35460i	0.930728	−	0.365712i	$-0.119174\pi$
$332$	−0.944581	+	1.63606i	−0.0518406	+	0.0897906i
$333$	−0.131903	−	0.0936024i	−0.00722822	−	0.00512938i
$334$	6.59888	+	3.80987i	0.361075	+	0.208467i
$335$	−5.19207	−	8.99293i	−0.283673	−	0.491336i
$336$	1.10989	+	4.44614i	0.0605496	+	0.242557i
$337$	26.4091			1.43860			0.719298	−	0.694702i	$-0.244464\pi$
$337$	26.4091			1.43860			0.719298	+	0.694702i	$0.244464\pi$
$338$	−6.17801	−	11.4382i	−0.336039	−	0.622156i
$339$	3.84507	+	1.22567i	0.208835	+	0.0665691i
$340$	−0.706134	−	1.22306i	−0.0382955	−	0.0663297i
$341$	−12.1308	−	21.0111i	−0.656918	−	1.13781i
$342$	−16.7781	+	7.69552i	−0.907256	+	0.416126i
$343$	−1.64316	−	18.4472i	−0.0887224	−	0.996056i
$344$	−2.43464	−	1.40564i	−0.131267	−	0.0757872i
$345$	−20.2563	+	18.4445i	−1.09056	+	0.993020i
$346$			3.13596i			0.168590i
$347$	3.25509	+	1.87933i	0.174742	+	0.100888i	0.584820	−	0.811163i	$-0.301165\pi$
$347$	3.25509	+	1.87933i	0.174742	+	0.100888i	−0.410078	+	0.912051i	$0.634498\pi$
$348$	2.17510	+	9.95952i	0.116598	+	0.533887i
$349$	−9.98836	+	5.76679i	−0.534665	+	0.308689i	−0.742914	−	0.669387i	$-0.766557\pi$
$349$	−9.98836	+	5.76679i	−0.534665	+	0.308689i	0.208249	+	0.978076i	$0.433224\pi$
$350$	11.1542	−	0.330407i	0.596218	−	0.0176610i
$351$	−18.5117	−	2.88362i	−0.988084	−	0.153916i
$352$	2.82727			0.150694
$353$	−1.14263	−	1.97910i	−0.0608161	−	0.105337i	0.834014	−	0.551743i	$-0.186037\pi$
$353$	−1.14263	−	1.97910i	−0.0608161	−	0.105337i	−0.894830	+	0.446406i	$0.852704\pi$
$354$	4.00003	+	18.3157i	0.212599	+	0.973467i
$355$	28.1338	+	16.2430i	1.49319	+	0.862091i
$356$	−2.55875			−0.135614
$357$	−1.53295	+	1.48120i	−0.0811325	+	0.0783934i
$358$	10.2309	−	17.7205i	0.540722	−	0.936558i
$359$		−	34.0398i		−	1.79655i	−0.439433	−	0.898275i	$-0.644821\pi$
$359$		−	34.0398i		−	1.79655i	0.439433	−	0.898275i	$-0.355179\pi$
$360$	3.79725	+	8.27893i	0.200133	+	0.436338i
$361$	9.42920	+	16.3319i	0.496274	+	0.859571i
$362$	−10.3567	−	17.9384i	−0.544339	−	0.942822i
$363$	−1.58154	+	4.96150i	−0.0830096	+	0.260411i
$364$	9.25134	+	2.32654i	0.484902	+	0.121944i
$365$			23.0041i			1.20409i
$366$	−22.5508	+	4.92495i	−1.17875	+	0.257431i
$367$	−12.6014	+	7.27540i	−0.657786	+	0.379773i	−0.791433	−	0.611256i	$-0.790665\pi$
$367$	−12.6014	+	7.27540i	−0.657786	+	0.379773i	0.133647	+	0.991029i	$0.457331\pi$
$368$	4.51168	+	2.60482i	0.235188	+	0.135786i
$369$	20.3385	+	14.4329i	1.05878	+	0.751345i
$370$	0.141755	+	0.0818423i	0.00736949	+	0.00425478i
$371$	11.0997	−	20.6115i	0.576267	−	1.07010i
$372$	−14.1611	−	4.51404i	−0.734219	−	0.234042i
$373$	−6.89279	+	11.9387i	−0.356895	+	0.618160i	−0.987440	−	0.157992i	$-0.949498\pi$
$373$	−6.89279	+	11.9387i	−0.356895	+	0.618160i	0.630545	+	0.776152i	$0.282831\pi$
$374$	0.657570	+	1.13895i	0.0340022	+	0.0588935i
$375$	−4.01885	+	0.877693i	−0.207533	+	0.0453239i
$376$		−	6.13208i		−	0.316238i
$377$	20.4180	+	5.78264i	1.05158	+	0.297821i
$378$	10.7358	−	8.58734i	0.552190	−	0.441685i
$379$	0.775475	+	1.34316i	0.0398335	+	0.0689936i	0.885255	−	0.465106i	$-0.153984\pi$
$379$	0.775475	+	1.34316i	0.0398335	+	0.0689936i	−0.845421	+	0.534100i	$0.820651\pi$
$380$	16.1780	−	9.34036i	0.829913	−	0.479150i
$381$	7.92115	+	8.69924i	0.405813	+	0.445676i
$382$	−2.21629			−0.113395
$383$	−12.1022	+	20.9615i	−0.618391	+	1.07108i	0.371388	+	0.928478i	$0.378882\pi$
$383$	−12.1022	+	20.9615i	−0.618391	+	1.07108i	−0.989779	+	0.142607i	$0.954451\pi$
$384$	1.28068	−	1.16613i	0.0653544	−	0.0595088i
$385$	−22.7007	+	0.672433i	−1.15693	+	0.0342704i
$386$	10.7846	+	6.22651i	0.548924	+	0.316921i
$387$	−0.787946	+	8.39697i	−0.0400535	+	0.426842i
$388$	7.06440	−	4.07863i	0.358640	−	0.207061i
$389$		−	25.7858i		−	1.30739i	−0.756756	−	0.653697i	$-0.773217\pi$
$389$		−	25.7858i		−	1.30739i	0.756756	−	0.653697i	$-0.226783\pi$
$390$	18.9251	+	1.15525i	0.958307	+	0.0584981i
$391$			2.42333i			0.122553i
$392$	−5.84438	+	3.85269i	−0.295186	+	0.194590i
$393$	−29.8184	+	6.51217i	−1.50414	+	0.328495i
$394$	−8.58860	+	14.8759i	−0.432687	+	0.749436i
$395$	−43.1403			−2.17062
$396$	−3.53610	−	7.70955i	−0.177696	−	0.387420i
$397$	−1.64285	−	0.948501i	−0.0824524	−	0.0476039i	0.458207	−	0.888846i	$-0.348492\pi$
$397$	−1.64285	−	0.948501i	−0.0824524	−	0.0476039i	−0.540659	+	0.841242i	$0.681825\pi$
$398$	7.20391			0.361099
$399$	−19.5925	−	20.2771i	−0.980852	−	1.01512i
$400$	−2.10887	−	3.65268i	−0.105444	−	0.182634i
$401$	6.75706	−	3.90119i	0.337431	−	0.194816i	−0.321704	−	0.946840i	$-0.604256\pi$
$401$	6.75706	−	3.90119i	0.337431	−	0.194816i	0.659136	+	0.752024i	$0.270922\pi$
$402$	5.64423	+	1.79917i	0.281509	+	0.0897347i
$403$	−22.1861	+	21.5654i	−1.10517	+	1.07425i
$404$	0.408979			0.0203475
$405$	17.8262	−	20.7091i	0.885789	−	1.02904i
$406$	−13.2493	+	8.18189i	−0.657552	+	0.406060i
$407$	−0.132006	−	0.0762137i	−0.00654329	−	0.00377777i
$408$	0.767629	+	0.244692i	0.0380033	+	0.0121141i
$409$	−13.5171	−	7.80411i	−0.668378	−	0.385888i	0.127084	−	0.991892i	$-0.459438\pi$
$409$	−13.5171	−	7.80411i	−0.668378	−	0.385888i	−0.795462	+	0.606004i	$0.792772\pi$
$410$	−21.8577	−	12.6195i	−1.07947	−	0.623234i
$411$	2.48270	+	0.791394i	0.122463	+	0.0390366i
$412$	−11.5464	−	6.66632i	−0.568851	−	0.328426i
$413$	−24.3656	+	15.0466i	−1.19895	+	0.740394i
$414$	1.46016	−	15.5606i	0.0717628	−	0.764760i
$415$	−5.73564			−0.281551
$416$	−0.883688	−	3.49558i	−0.0433263	−	0.171385i
$417$	−18.0659	−	5.75876i	−0.884692	−	0.282008i
$418$	−15.0654	+	8.69799i	−0.736871	+	0.425432i
$419$	12.3282	+	21.3531i	0.602273	+	1.04317i	0.992476	+	0.122439i	$0.0390717\pi$
$419$	12.3282	+	21.3531i	0.602273	+	1.04317i	−0.390203	+	0.920729i	$0.627595\pi$
$420$	−10.0055	+	9.66766i	−0.488216	+	0.471734i
$421$	23.3182			1.13646			0.568230	−	0.822870i	$-0.307628\pi$
$421$	23.3182			1.13646			0.568230	+	0.822870i	$0.307628\pi$
$422$	9.22671	+	5.32704i	0.449149	+	0.259316i
$423$	−16.7213	+	7.66946i	−0.813017	+	0.372902i
$424$	−8.84822			−0.429708
$425$	0.980969	−	1.69909i	0.0475840	−	0.0824179i
$426$	−18.1062	+	3.95429i	−0.877250	+	0.191586i
$427$	−18.5258	−	29.9996i	−0.896524	−	1.45178i
$428$			18.3605i			0.887488i
$429$	−17.6235	−	1.07579i	−0.850871	−	0.0519398i
$430$		−	8.53527i		−	0.411607i
$431$	−2.98264	+	1.72203i	−0.143669	+	0.0829472i	−0.570111	−	0.821567i	$-0.693100\pi$
$431$	−2.98264	+	1.72203i	−0.143669	+	0.0829472i	0.426443	+	0.904515i	$0.359767\pi$
$432$	−4.78162	−	2.03373i	−0.230056	−	0.0978480i
$433$	−24.3487	−	14.0577i	−1.17012	−	0.675571i	−0.216414	−	0.976302i	$-0.569436\pi$
$433$	−24.3487	−	14.0577i	−1.17012	−	0.675571i	−0.953709	+	0.300731i	$0.902769\pi$
$434$	−0.672233	−	22.6939i	−0.0322682	−	1.08934i
$435$	−22.8849	+	20.8380i	−1.09725	+	0.999104i
$436$	−3.32926	+	5.76644i	−0.159442	+	0.276162i
$437$	−32.0545			−1.53337
$438$	−8.83567	−	9.70360i	−0.422185	−	0.463656i
$439$	−2.77253	+	1.60072i	−0.132326	+	0.0763982i	−0.564701	−	0.825295i	$-0.691009\pi$
$439$	−2.77253	+	1.60072i	−0.132326	+	0.0763982i	0.432376	+	0.901693i	$0.357675\pi$
$440$	4.29190	+	7.43380i	0.204608	+	0.354392i
$441$	17.8153	+	11.1182i	0.848350	+	0.529436i
$442$	1.20264	−	1.16899i	0.0572037	−	0.0556034i
$443$			8.70328i			0.413505i	0.978393	+	0.206753i	$0.0662896\pi$
$443$			8.70328i			0.413505i	−0.978393	+	0.206753i	$0.933710\pi$
$444$	−0.0912301	+	0.0199241i	−0.00432959	+	0.000945556i
$445$	−3.88428	−	6.72777i	−0.184132	−	0.318927i
$446$	−5.48233	+	9.49568i	−0.259596	+	0.449633i
$447$	−25.7007	−	8.19244i	−1.21560	−	0.387489i
$448$	2.32945	+	1.25445i	0.110056	+	0.0592674i
$449$	1.72047	+	0.993316i	0.0811942	+	0.0468775i	0.540047	−	0.841635i	$-0.318406\pi$
$449$	1.72047	+	0.993316i	0.0811942	+	0.0468775i	−0.458853	+	0.888512i	$0.651740\pi$
$450$	−7.32272	+	10.3190i	−0.345196	+	0.486444i
$451$	20.3544	+	11.7516i	0.958452	+	0.553363i
$452$	2.01785	−	1.16500i	0.0949115	−	0.0547972i
$453$	17.6171	−	3.84746i	0.827721	−	0.180769i
$454$		−	17.0522i		−	0.800298i
$455$	7.92667	+	27.8565i	0.371608	+	1.30593i
$456$	−3.23665	+	10.1538i	−0.151570	+	0.475494i
$457$	4.88049	+	8.45325i	0.228300	+	0.395427i	0.957304	−	0.289082i	$-0.0933501\pi$
$457$	4.88049	+	8.45325i	0.228300	+	0.395427i	−0.729005	+	0.684509i	$0.760017\pi$
$458$	3.22759	+	5.59035i	0.150815	+	0.261220i
$459$	−0.292842	−	2.39925i	−0.0136687	−	0.111987i
$460$			15.8169i			0.737465i
$461$	0.950125	−	1.64567i	0.0442517	−	0.0766463i	−0.843051	−	0.537833i	$-0.819243\pi$
$461$	0.950125	−	1.64567i	0.0442517	−	0.0766463i	0.887303	+	0.461187i	$0.152576\pi$
$462$	9.31734	−	9.00278i	0.433482	−	0.418847i
$463$	0.757226			0.0351913			0.0175956	−	0.999845i	$-0.494399\pi$
$463$	0.757226			0.0351913			0.0175956	+	0.999845i	$0.494399\pi$
$464$	5.09714	+	2.94283i	0.236629	+	0.136618i
$465$	−9.62823	−	44.0865i	−0.446499	−	2.04446i
$466$	−2.72128	−	4.71340i	−0.126061	−	0.218344i
$467$	−36.2142			−1.67580			−0.837898	−	0.545827i	$-0.816215\pi$
$467$	−36.2142			−1.67580			−0.837898	+	0.545827i	$0.816215\pi$
$468$	−8.42670	+	6.78165i	−0.389524	+	0.313482i
$469$	0.267933	+	9.04517i	0.0123720	+	0.417667i
$470$	16.1232	−	9.30873i	0.743708	−	0.429380i
$471$	−0.236982	−	1.08511i	−0.0109195	−	0.0499993i
$472$	9.37369	+	5.41190i	0.431459	+	0.249103i
$473$			7.94827i			0.365462i
$474$	18.1975	−	16.5698i	0.835838	−	0.761077i
$475$	22.4746	+	12.9757i	1.03121	+	0.595367i
$476$	0.0364396	+	1.23016i	0.00167021	+	0.0563845i
$477$	11.0666	+	24.1278i	0.506703	+	1.10474i
$478$	−12.4481	−	21.5608i	−0.569364	−	0.986167i
$479$	17.3954	+	30.1297i	0.794816	+	1.37666i	0.922956	+	0.384905i	$0.125766\pi$
$479$	17.3954	+	30.1297i	0.794816	+	1.37666i	−0.128141	+	0.991756i	$0.540901\pi$
$480$	5.01025	+	1.59708i	0.228685	+	0.0728966i
$481$	−0.0529695	+	0.187031i	−0.00241520	+	0.00852787i
$482$	−4.36368			−0.198760
$483$	23.1628	−	5.78214i	1.05394	−	0.263096i
$484$	1.50327	+	2.60374i	0.0683303	+	0.118352i
$485$	21.4480	+	12.3830i	0.973905	+	0.562284i
$486$	0.434735	+	15.5824i	0.0197200	+	0.706832i
$487$	6.71532	−	11.6313i	0.304300	−	0.527064i	−0.672805	−	0.739820i	$-0.734911\pi$
$487$	6.71532	−	11.6313i	0.304300	−	0.527064i	0.977105	+	0.212756i	$0.0682440\pi$
$488$	−6.66328	+	11.5411i	−0.301633	+	0.522443i
$489$	−1.74695	+	5.48040i	−0.0789999	+	0.247832i
$490$	−19.0019	−	9.51820i	−0.858420	−	0.429988i
$491$	−4.02666	+	2.32479i	−0.181721	+	0.104916i	−0.588101	−	0.808788i	$-0.700124\pi$
$491$	−4.02666	+	2.32479i	−0.181721	+	0.104916i	0.406380	+	0.913704i	$0.366791\pi$
$492$	14.0671	−	3.07216i	0.634193	−	0.138504i
$493$			2.73779i			0.123304i
$494$	15.4628	+	15.9079i	0.695705	+	0.715729i
$495$	14.9029	−	21.0009i	0.669837	−	0.943921i
$496$	−7.43158	+	4.29062i	−0.333688	+	0.192655i
$497$	−14.8745	−	24.0870i	−0.667213	−	1.08045i
$498$	2.41941	−	2.20301i	0.108416	−	0.0987192i
$499$	19.5275			0.874171			0.437086	−	0.899420i	$-0.356011\pi$
$499$	19.5275			0.874171			0.437086	+	0.899420i	$0.356011\pi$
$500$	−1.18749	+	2.05679i	−0.0531060	+	0.0919823i
$501$	−8.88560	−	9.75844i	−0.396979	−	0.435975i
$502$			19.6116i			0.875307i
$503$	13.3449	−	23.1140i	0.595020	−	1.03060i	−0.398525	−	0.917158i	$-0.630478\pi$
$503$	13.3449	−	23.1140i	0.595020	−	1.03060i	0.993544	−	0.113446i	$-0.0361891\pi$
$504$	0.507241	−	7.92103i	0.0225943	−	0.352831i
$505$	0.620845	+	1.07534i	0.0276273	+	0.0478518i
$506$		−	14.7291i		−	0.654787i
$507$	4.17828	+	22.1256i	0.185564	+	0.982632i
$508$	6.79268			0.301376
$509$	−12.8220	−	22.2084i	−0.568325	−	0.984368i	−0.996732	−	0.0807821i	$-0.974258\pi$
$509$	−12.8220	−	22.2084i	−0.568325	−	0.984368i	0.428406	−	0.903586i	$-0.359075\pi$
$510$	0.521916	+	2.38979i	0.0231108	+	0.105822i
$511$	9.50489	−	17.6501i	0.420472	−	0.780793i
$512$		−	1.00000i		−	0.0441942i
$513$	31.7360	−	3.87356i	1.40118	−	0.171022i
$514$	−1.80474	−	1.04197i	−0.0796039	−	0.0459593i
$515$		−	40.4789i		−	1.78371i
$516$	3.27833	+	3.60036i	0.144320	+	0.158497i
$517$	−15.0143	+	8.66853i	−0.660330	+	0.381242i
$518$	−0.0749468	−	0.121365i	−0.00329297	−	0.00533246i
$519$	1.64963	−	5.17508i	0.0724105	−	0.227161i
$520$	7.84953	−	7.62992i	0.344224	−	0.334594i
$521$	−0.709723			−0.0310935			−0.0155468	−	0.999879i	$-0.504949\pi$
$521$	−0.709723			−0.0310935			−0.0155468	+	0.999879i	$0.504949\pi$
$522$	1.64963	−	17.5798i	0.0722024	−	0.769446i
$523$	23.3251	−	13.4668i	1.01994	−	0.588861i	0.105851	−	0.994382i	$-0.466243\pi$
$523$	23.3251	−	13.4668i	1.01994	−	0.588861i	0.914086	+	0.405521i	$0.132910\pi$
$524$	−8.81073	+	15.2606i	−0.384899	+	0.666664i
$525$	−18.5809	−	5.32227i	−0.810938	−	0.232283i
$526$	−7.49497	+	12.9817i	−0.326796	+	0.566028i
$527$	−3.45689	−	1.99584i	−0.150585	−	0.0869400i
$528$	−4.66567	−	1.48725i	−0.203047	−	0.0647241i
$529$	2.07018	−	3.58566i	0.0900080	−	0.155898i
$530$	−13.4319	−	23.2648i	−0.583446	−	1.01056i
$531$	3.03369	−	32.3294i	0.131651	−	1.40298i
$532$	−16.2720	+	0.482003i	−0.705479	+	0.0208975i
$533$	8.16754	−	28.8389i	0.353775	−	1.24915i
$534$	4.22255	+	1.34599i	0.182728	+	0.0582469i
$535$	−48.2756	+	27.8719i	−2.08714	+	1.20501i
$536$	2.96202	−	1.71013i	0.127940	−	0.0738662i
$537$	−26.2051	+	23.8612i	−1.13083	+	1.02969i
$538$		−	2.39067i		−	0.103069i
$539$	17.6951	+	8.86359i	0.762182	+	0.381782i
$540$	−1.91135	−	15.6597i	−0.0822516	−	0.673886i
$541$	38.5039			1.65541			0.827705	−	0.561163i	$-0.189646\pi$
$541$	38.5039			1.65541			0.827705	+	0.561163i	$0.189646\pi$
$542$	1.43471	−	2.48498i	0.0616259	−	0.106739i
$543$	7.65486	+	35.0507i	0.328501	+	1.50417i
$544$	0.402842	−	0.232581i	0.0172717	−	0.00997184i
$545$	−20.2157			−0.865947
$546$	−14.0431	−	8.70588i	−0.600988	−	0.372577i
$547$	42.8003			1.83001			0.915003	−	0.403446i	$-0.132188\pi$
$547$	42.8003			1.83001			0.915003	+	0.403446i	$0.132188\pi$
$548$	1.30289	−	0.752224i	0.0556567	−	0.0321334i
$549$	39.8048	+	3.73516i	1.69883	+	0.159413i
$550$	−5.96236	+	10.3271i	−0.254236	+	0.440350i
$551$	−36.2140			−1.54277
$552$	−6.07512	−	6.67188i	−0.258574	−	0.283974i
$553$	33.0997	+	17.8248i	1.40754	+	0.757989i
$554$			10.9518i			0.465298i
$555$	−0.190878	−	0.209627i	−0.00810230	−	0.00889819i
$556$	−9.48078	+	5.47373i	−0.402075	+	0.232138i
$557$	−21.2756	+	12.2835i	−0.901476	+	0.520468i	−0.877679	−	0.479249i	$-0.840909\pi$
$557$	−21.2756	+	12.2835i	−0.901476	+	0.520468i	−0.0237975	+	0.999717i	$0.507576\pi$
$558$	20.9947	+	14.8985i	0.888775	+	0.630704i
$559$	9.82708	−	2.48430i	0.415641	−	0.105075i
$560$	0.237838	+	8.02918i	0.0100505	+	0.339295i
$561$	−0.486022	−	2.22544i	−0.0205199	−	0.0939580i
$562$	14.3079	+	24.7820i	0.603541	+	1.04536i
$563$	20.0367	−	34.7046i	0.844447	−	1.46263i	−0.0416528	−	0.999132i	$-0.513262\pi$
$563$	20.0367	−	34.7046i	0.844447	−	1.46263i	0.886100	−	0.463494i	$-0.153404\pi$
$564$	−3.22570	+	10.1194i	−0.135826	+	0.426104i
$565$	6.12633	+	3.53704i	0.257737	+	0.148804i
$566$	−4.39819	+	7.61788i	−0.184870	+	0.320203i
$567$	−22.2339	+	8.52374i	−0.933736	+	0.357963i
$568$	−5.35002	+	9.26650i	−0.224482	+	0.388814i
$569$	7.04152	−	4.06542i	0.295196	−	0.170431i	−0.345087	−	0.938571i	$-0.612151\pi$
$569$	7.04152	−	4.06542i	0.295196	−	0.170431i	0.640283	+	0.768139i	$0.278817\pi$
$570$	−31.6109	+	6.90362i	−1.32403	+	0.289161i
$571$	−9.23752			−0.386578			−0.193289	−	0.981142i	$-0.561916\pi$
$571$	−9.23752			−0.386578			−0.193289	+	0.981142i	$0.561916\pi$
$572$	−7.30968	+	7.10518i	−0.305633	+	0.297083i
$573$	3.65740	+	1.16585i	0.152790	+	0.0487040i
$574$	11.5563	+	18.7136i	0.482350	+	0.781092i
$575$	−19.0291	+	10.9865i	−0.793570	+	0.458168i
$576$	−2.72685	+	1.25071i	−0.113619	+	0.0521129i
$577$			9.90231i			0.412239i	0.978527	+	0.206119i	$0.0660835\pi$
$577$			9.90231i			0.412239i	−0.978527	+	0.206119i	$0.933916\pi$
$578$	−14.5350	−	8.39181i	−0.604578	−	0.349053i
$579$	−14.5219	−	15.9483i	−0.603508	−	0.662790i
$580$			17.8693i			0.741983i
$581$	4.40071	+	2.36987i	0.182572	+	0.0983186i
$582$	−13.8034	+	3.01459i	−0.572171	+	0.124959i
$583$	12.5082	+	21.6648i	0.518035	+	0.897263i
$584$	−7.57692			−0.313535
$585$	−30.6231	−	11.8617i	−1.26611	−	0.490420i
$586$		−	11.7719i		−	0.486291i
$587$	−2.75048	−	4.76396i	−0.113524	−	0.196630i	0.803665	−	0.595083i	$-0.202881\pi$
$587$	−2.75048	−	4.76396i	−0.113524	−	0.196630i	−0.917189	+	0.398453i	$0.869547\pi$
$588$	11.6713	−	3.28351i	0.481315	−	0.135410i
$589$	26.3999	−	45.7259i	1.08779	−	1.88410i
$590$			32.8619i			1.35290i
$591$	21.9985	−	20.0308i	0.904896	−	0.823959i
$592$	−0.0269566	+	0.0466902i	−0.00110791	+	0.00191896i
$593$	11.9453			0.490534			0.245267	−	0.969456i	$-0.421124\pi$
$593$	11.9453			0.490534			0.245267	+	0.969456i	$0.421124\pi$
$594$	1.77990	+	14.5827i	0.0730303	+	0.598336i
$595$	−3.17918	+	1.96325i	−0.130334	+	0.0804853i
$596$	−13.4874	+	7.78696i	−0.552466	+	0.318966i
$597$	−11.8882	−	3.78951i	−0.486550	−	0.155094i
$598$	−18.2107	+	4.60370i	−0.744692	+	0.188259i
$599$		−	0.382157i		−	0.0156145i	−0.999970	−	0.00780725i	$-0.997515\pi$
$599$		−	0.382157i		−	0.0156145i	0.999970	−	0.00780725i	$-0.00248515\pi$
$600$	1.55871	+	7.13713i	0.0636339	+	0.291372i
$601$	37.2367	−	21.4986i	1.51892	−	0.876948i	0.519166	−	0.854673i	$-0.326243\pi$
$601$	37.2367	−	21.4986i	1.51892	−	0.876948i	0.999752	−	0.0222741i	$-0.00709065\pi$
$602$	−3.52663	+	6.54875i	−0.143735	+	0.266907i
$603$	−8.36789	−	5.93813i	−0.340767	−	0.241819i
$604$	5.20547	−	9.01615i	0.211808	−	0.366862i
$605$	−4.56403	+	7.90513i	−0.185554	+	0.321389i
$606$	−0.674913	−	0.215138i	−0.0274165	−	0.00873936i
$607$	−1.69476	−	0.978470i	−0.0687882	−	0.0397149i	0.465211	−	0.885200i	$-0.345978\pi$
$607$	−1.69476	−	0.978470i	−0.0687882	−	0.0397149i	−0.534000	+	0.845485i	$0.679312\pi$
$608$	3.07646	+	5.32858i	0.124767	+	0.216103i
$609$	26.1685	−	6.53245i	1.06040	−	0.264708i
$610$	−40.4604			−1.63819
$611$	15.4105	+	15.8540i	0.623441	+	0.641385i
$612$	−1.13805	−	0.807600i	−0.0460031	−	0.0326453i
$613$	−4.39722	−	7.61620i	−0.177602	−	0.307616i	0.763457	−	0.645859i	$-0.223501\pi$
$613$	−4.39722	−	7.61620i	−0.177602	−	0.307616i	−0.941059	+	0.338243i	$0.890167\pi$
$614$	7.94968	+	13.7693i	0.320823	+	0.555682i
$615$	29.4320	+	32.3231i	1.18681	+	1.30339i
$616$	−0.221481	−	7.47698i	−0.00892373	−	0.301256i
$617$	−18.5603	−	10.7158i	−0.747208	−	0.431401i	0.0774759	−	0.996994i	$-0.475314\pi$
$617$	−18.5603	−	10.7158i	−0.747208	−	0.431401i	−0.824684	+	0.565593i	$0.808647\pi$
$618$	15.5476	+	17.0748i	0.625416	+	0.686851i
$619$		−	4.27262i		−	0.171731i	−0.996307	−	0.0858656i	$-0.972634\pi$
$619$		−	4.27262i		−	0.171731i	0.996307	−	0.0858656i	$-0.0273656\pi$
$620$	−22.5628	−	13.0267i	−0.906145	−	0.523163i
$621$	−10.5950	+	24.9105i	−0.425164	+	0.999626i
$622$	−21.2458	+	12.2663i	−0.851879	+	0.491833i
$623$	0.200446	+	6.76685i	0.00803069	+	0.271108i
$624$	−0.380506	+	6.23340i	−0.0152324	+	0.249536i
$625$	−28.2993			−1.13197
$626$	7.12198	+	12.3356i	0.284652	+	0.493031i
$627$	29.4369	−	6.42884i	1.17560	−	0.256743i
$628$	−0.555344	−	0.320628i	−0.0221606	−	0.0127944i
$629$	−0.0250784			−0.000999941
$630$	21.5969	−	10.6907i	0.860442	−	0.425928i
$631$	−18.9403	+	32.8055i	−0.754001	+	1.30597i	0.191869	+	0.981421i	$0.438545\pi$
$631$	−18.9403	+	32.8055i	−0.754001	+	1.30597i	−0.945870	+	0.324547i	$0.894788\pi$
$632$		−	14.2092i		−	0.565213i
$633$	−12.4241	−	13.6445i	−0.493812	−	0.542319i
$634$	−4.75795	−	8.24101i	−0.188962	−	0.327292i
$635$	10.3115	+	17.8601i	0.409201	+	0.708757i
$636$	14.6017	+	4.65448i	0.578994	+	0.184562i
$637$	5.42802	−	24.6483i	0.215066	−	0.976600i
$638$		−	16.6404i		−	0.658799i
$639$	31.9597	+	2.99900i	1.26431	+	0.118639i
$640$	2.62932	−	1.51804i	0.103933	−	0.0600057i
$641$	−29.4525	−	17.0044i	−1.16331	−	0.671635i	−0.211212	−	0.977440i	$-0.567741\pi$
$641$	−29.4525	−	17.0044i	−1.16331	−	0.671635i	−0.952094	+	0.305806i	$0.901074\pi$
$642$	9.65828	−	30.2992i	0.381182	−	1.19581i
$643$	36.5123	+	21.0804i	1.43990	+	0.831329i	0.997842	−	0.0656552i	$-0.0209137\pi$
$643$	36.5123	+	21.0804i	1.43990	+	0.831329i	0.442062	+	0.896984i	$0.354247\pi$
$644$	6.53525	−	12.1356i	0.257525	−	0.478210i
$645$	−4.48986	+	14.0852i	−0.176788	+	0.554605i
$646$	−1.43105	+	2.47866i	−0.0563040	+	0.0975214i
$647$	−1.63864	−	2.83821i	−0.0644217	−	0.111582i	0.832016	−	0.554752i	$-0.187187\pi$
$647$	−1.63864	−	2.83821i	−0.0644217	−	0.111582i	−0.896437	+	0.443171i	$0.853854\pi$
$648$	6.82100	+	5.87145i	0.267954	+	0.230652i
$649$		−	30.6018i		−	1.20123i
$650$	14.6318	+	4.14392i	0.573907	+	0.162538i
$651$	−10.8285	+	37.8040i	−0.424401	+	1.48165i
$652$	1.66049	+	2.87605i	0.0650297	+	0.112635i
$653$	3.77819	−	2.18134i	0.147852	−	0.0853624i	−0.424249	−	0.905546i	$-0.639462\pi$
$653$	3.77819	−	2.18134i	0.147852	−	0.0853624i	0.572101	+	0.820183i	$0.306129\pi$
$654$	8.52742	−	7.76469i	0.333448	−	0.303623i
$655$	−53.5001			−2.09042
$656$	4.15653	−	7.19932i	0.162285	−	0.281086i
$657$	9.47653	+	20.6611i	0.369715	+	0.806068i
$658$	−16.2169	+	0.480371i	−0.632199	+	0.0187268i
$659$	31.7835	+	18.3502i	1.23811	+	0.714823i	0.968708	−	0.248204i	$-0.0798404\pi$
$659$	31.7835	+	18.3502i	1.23811	+	0.714823i	0.269403	+	0.963028i	$0.413174\pi$
$660$	−3.17222	−	14.5252i	−0.123479	−	0.565394i
$661$	39.4869	−	22.7978i	1.53586	−	0.886732i	0.536790	−	0.843716i	$-0.319637\pi$
$661$	39.4869	−	22.7978i	1.53586	−	0.886732i	0.999074	−	0.0430156i	$-0.0136965\pi$
$662$			28.4574i			1.10603i
$663$	−2.59957	+	1.29649i	−0.100959	+	0.0503514i
$664$		−	1.88916i		−	0.0733137i
$665$	−25.9688	−	42.0524i	−1.00703	−	1.63072i
$666$	0.161032	+	0.0151108i	0.00623987	+	0.000585531i
$667$	15.3311	−	26.5543i	0.593623	−	1.02818i
$668$	−7.61973			−0.294816
$669$	14.0422	−	12.7862i	0.542904	−	0.494344i
$670$	8.99293	+	5.19207i	0.347427	+	0.200587i
$671$	37.6778			1.45454
$672$	−3.18426	−	3.29552i	−0.122836	−	0.127128i
$673$	−11.5760	−	20.0503i	−0.446223	−	0.772881i	0.551914	−	0.833901i	$-0.313898\pi$
$673$	−11.5760	−	20.0503i	−0.446223	−	0.772881i	−0.998137	+	0.0610205i	$0.980564\pi$
$674$	−22.8710	+	13.2046i	−0.880956	+	0.508620i
$675$	17.5124	−	13.1768i	0.674053	−	0.507177i
$676$	11.0694	+	6.81676i	0.425746	+	0.262183i
$677$	−34.6964			−1.33349			−0.666745	−	0.745286i	$-0.732313\pi$
$677$	−34.6964			−1.33349			−0.666745	+	0.745286i	$0.732313\pi$
$678$	−3.94276	+	0.861075i	−0.151421	+	0.0330694i
$679$	−11.3397	−	18.3629i	−0.435179	−	0.704705i
$680$	1.22306	+	0.706134i	0.0469022	+	0.0270790i
$681$	−8.97005	+	28.1402i	−0.343733	+	1.07833i
$682$	21.0111	+	12.1308i	0.804556	+	0.464511i
$683$	15.8870	+	9.17234i	0.607898	+	0.350970i	0.772142	−	0.635450i	$-0.219185\pi$
$683$	15.8870	+	9.17234i	0.607898	+	0.350970i	−0.164245	+	0.986420i	$0.552519\pi$
$684$	10.6825	−	15.0536i	0.408456	−	0.575587i
$685$	3.95567	+	2.28381i	0.151139	+	0.0872599i
$686$	10.6466	+	15.1542i	0.406490	+	0.578589i
$687$	−2.38557	−	10.9232i	−0.0910151	−	0.416747i
$688$	2.81129			0.107179
$689$	22.8764	−	22.2363i	0.871520	−	0.847137i
$690$	8.32023	−	26.1016i	0.316746	−	0.993671i
$691$	−27.2842	+	15.7526i	−1.03794	+	0.599255i	−0.919249	−	0.393676i	$-0.871203\pi$
$691$	−27.2842	+	15.7526i	−1.03794	+	0.599255i	−0.118691	+	0.992931i	$0.537870\pi$
$692$	−1.56798	−	2.71582i	−0.0596056	−	0.103240i
$693$	−20.1116	+	9.95548i	−0.763977	+	0.378177i
$694$	−3.75865			−0.142677
$695$	−28.7844	−	16.6187i	−1.09185	−	0.630382i
$696$	−6.86345	−	7.53765i	−0.260159	−	0.285714i
$697$	3.86692			0.146470
$698$	5.76679	−	9.98836i	0.218276	−	0.378065i
$699$	2.01135	+	9.20972i	0.0760761	+	0.348344i
$700$	−9.49464	+	5.86325i	−0.358863	+	0.221610i
$701$		−	34.1901i		−	1.29134i	−0.763616	−	0.645671i	$-0.776578\pi$
$701$		−	34.1901i		−	1.29134i	0.763616	−	0.645671i	$-0.223422\pi$
$702$	17.4735	−	6.75859i	0.659493	−	0.255086i
$703$		−	0.331724i		−	0.0125112i
$704$	−2.44849	+	1.41364i	−0.0922809	+	0.0532784i
$705$	−31.5038	+	6.88025i	−1.18650	+	0.259125i
$706$	1.97910	+	1.14263i	0.0744843	+	0.0430035i
$707$	−0.0320383	−	1.08158i	−0.00120493	−	0.0406771i
$708$	−12.6220	−	13.8618i	−0.474363	−	0.520959i
$709$	−12.7384	+	22.0635i	−0.478399	+	0.828612i	−0.999693	−	0.0247651i	$-0.992116\pi$
$709$	−12.7384	+	22.0635i	−0.478399	+	0.828612i	0.521294	+	0.853377i	$0.325450\pi$
$710$	−32.4861			−1.21918
$711$	−38.7465	+	17.7716i	−1.45311	+	0.666488i
$712$	2.21594	−	1.27938i	0.0830460	−	0.0479466i
$713$	22.3526	+	38.7159i	0.837112	+	1.44992i
$714$	0.586976	−	2.04923i	0.0219670	−	0.0766906i
$715$	−29.7781	−	8.43355i	−1.11364	−	0.315397i
$716$			20.4619i			0.764696i
$717$	9.20063	+	42.1286i	0.343604	+	1.57332i
$718$	17.0199	+	29.4793i	0.635177	+	1.10016i
$719$	4.89874	−	8.48486i	0.182692	−	0.316432i	−0.760104	−	0.649801i	$-0.774852\pi$
$719$	4.89874	−	8.48486i	0.182692	−	0.316432i	0.942796	+	0.333369i	$0.108186\pi$
$720$	−7.42798	−	5.27114i	−0.276824	−	0.196444i
$721$	−16.7252	+	31.0577i	−0.622878	+	1.15665i
$722$	−16.3319	−	9.42920i	−0.607809	−	0.350919i
$723$	7.20111	+	2.29545i	0.267812	+	0.0853688i
$724$	17.9384	+	10.3567i	0.666676	+	0.384905i
$725$	−21.4984	+	12.4121i	−0.798432	+	0.460975i
$726$	−1.11109	−	5.08756i	−0.0412365	−	0.188817i
$727$		−	39.6594i		−	1.47088i	−0.677588	−	0.735442i	$-0.736975\pi$
$727$		−	39.6594i		−	1.47088i	0.677588	−	0.735442i	$-0.263025\pi$
$728$	−9.17516	+	2.61083i	−0.340054	+	0.0967637i
$729$	7.47948	−	25.9433i	0.277018	−	0.960865i
$730$	−11.5020	−	19.9221i	−0.425710	−	0.737351i
$731$	0.653852	+	1.13251i	0.0241836	+	0.0418872i
$732$	17.0671	−	15.5405i	0.630816	−	0.574394i
$733$		−	25.2243i		−	0.931681i	−0.884869	−	0.465840i	$-0.845752\pi$
$733$		−	25.2243i		−	0.931681i	0.884869	−	0.465840i	$-0.154248\pi$
$734$	7.27540	−	12.6014i	0.268540	−	0.465125i
$735$	26.3508	+	25.7030i	0.971964	+	0.948069i
$736$	−5.20964			−0.192030
$737$	−8.37445	−	4.83499i	−0.308477	−	0.178099i
$738$	−24.8301	−	2.32998i	−0.914008	−	0.0857678i
$739$	6.81162	+	11.7981i	0.250569	+	0.433999i	0.963683	−	0.267050i	$-0.0860488\pi$
$739$	6.81162	+	11.7981i	0.250569	+	0.433999i	−0.713113	+	0.701049i	$0.752716\pi$
$740$	−0.163685			−0.00601716
$741$	−17.1492	−	34.3858i	−0.629993	−	1.26319i
$742$	0.693146	+	23.3999i	0.0254462	+	0.859038i
$743$	−23.6670	+	13.6642i	−0.868258	+	0.501289i	−0.866769	−	0.498710i	$-0.833807\pi$
$743$	−23.6670	+	13.6642i	−0.868258	+	0.501289i	−0.00148913	+	0.999999i	$0.500474\pi$
$744$	14.5209	−	3.17128i	0.532362	−	0.116265i
$745$	−40.9488	−	23.6418i	−1.50025	−	0.866169i
$746$		−	13.7856i		−	0.504726i
$747$	−5.15147	+	2.36279i	−0.188482	+	0.0864501i
$748$	−1.13895	−	0.657570i	−0.0416440	−	0.0240432i
$749$	48.5560	−	1.43831i	1.77420	−	0.0525548i
$750$	3.04158	−	2.76953i	0.111063	−	0.101129i
$751$	−10.9387	−	18.9464i	−0.399160	−	0.691365i	0.594463	−	0.804123i	$-0.297365\pi$
$751$	−10.9387	−	18.9464i	−0.399160	−	0.691365i	−0.993622	+	0.112758i	$0.964031\pi$
$752$	3.06604	+	5.31054i	0.111807	+	0.193655i
$753$	10.3164	−	32.3638i	0.375950	−	1.17940i
$754$	−20.5738	+	5.20109i	−0.749255	+	0.189412i
$755$	31.6084			1.15035
$756$	−5.00381	+	12.8048i	−0.181987	+	0.465705i
$757$	16.2004	+	28.0600i	0.588815	+	1.01986i	0.994388	+	0.105794i	$0.0337385\pi$
$757$	16.2004	+	28.0600i	0.588815	+	1.01986i	−0.405573	+	0.914062i	$0.632928\pi$
$758$	−1.34316	−	0.775475i	−0.0487859	−	0.0281665i
$759$	−7.74802	+	24.3065i	−0.281235	+	0.882269i
$760$	−9.34036	+	16.1780i	−0.338810	+	0.586837i
$761$	−4.54101	+	7.86526i	−0.164611	+	0.285115i	−0.936517	−	0.350622i	$-0.885970\pi$
$761$	−4.54101	+	7.86526i	−0.164611	+	0.285115i	0.771906	+	0.635737i	$0.219304\pi$
$762$	−11.2095	−	3.57319i	−0.406079	−	0.129443i
$763$	15.5107	+	8.35279i	0.561524	+	0.302391i
$764$	1.91936	−	1.10814i	0.0694401	−	0.0400913i
$765$	0.395830	−	4.21827i	0.0143113	−	0.152512i
$766$		−	24.2043i		−	0.874537i
$767$	−37.8355	+	9.56486i	−1.36616	+	0.345367i
$768$	−0.526036	+	1.65024i	−0.0189817	+	0.0595478i
$769$	7.95521	−	4.59295i	0.286872	−	0.165626i	−0.349658	−	0.936877i	$-0.613702\pi$
$769$	7.95521	−	4.59295i	0.286872	−	0.165626i	0.636531	+	0.771252i	$0.280369\pi$
$770$	19.3231	−	11.9327i	0.696357	−	0.430024i
$771$	2.43015	+	2.66886i	0.0875195	+	0.0961166i
$772$	−12.4530			−0.448194
$773$	7.76299	−	13.4459i	0.279215	−	0.483615i	−0.691975	−	0.721922i	$-0.743259\pi$
$773$	7.76299	−	13.4459i	0.279215	−	0.483615i	0.971190	+	0.238307i	$0.0765923\pi$
$774$	−3.51610	−	7.66596i	−0.126384	−	0.275547i
$775$		−	36.1936i		−	1.30011i
$776$	−4.07863	+	7.06440i	−0.146414	+	0.253597i
$777$	0.0598379	+	0.239706i	0.00214667	+	0.00859939i
$778$	12.8929	+	22.3312i	0.462234	+	0.800612i
$779$			51.1495i			1.83262i
$780$	−16.9672	+	8.46205i	−0.607523	+	0.302990i
$781$	30.2519			1.08250
$782$	−1.21166	−	2.09866i	−0.0433290	−	0.0750481i
$783$	−11.9699	+	28.1430i	−0.427768	+	1.00575i
$784$	3.13503	−	6.25872i	0.111965	−	0.223526i
$785$		−	1.94690i		−	0.0694879i
$786$	22.5674	−	20.5489i	0.804954	−	0.732956i
$787$	−9.70952	−	5.60579i	−0.346107	−	0.199825i	0.316862	−	0.948472i	$-0.397371\pi$
$787$	−9.70952	−	5.60579i	−0.346107	−	0.199825i	−0.662969	+	0.748647i	$0.730704\pi$
$788$		−	17.1772i		−	0.611912i
$789$	19.1973	−	17.4802i	0.683443	−	0.622313i
$790$	37.3606	−	21.5701i	1.32923	−	0.767431i
$791$	−3.23903	−	5.24511i	−0.115167	−	0.186495i
$792$	6.91713	+	4.90862i	0.245789	+	0.174420i
$793$	−11.7765	−	46.5841i	−0.418196	−	1.65425i
$794$	1.89700			0.0673221
$795$	9.92778	+	45.4581i	0.352102	+	1.61223i
$796$	−6.23877	+	3.60195i	−0.221127	+	0.127668i
$797$	12.1591	−	21.0602i	0.430697	−	0.745989i	−0.566236	−	0.824243i	$-0.691601\pi$
$797$	12.1591	−	21.0602i	0.430697	−	0.745989i	0.996933	+	0.0782535i	$0.0249344\pi$
$798$	27.1062	+	7.76421i	0.959547	+	0.274850i
$799$	−1.42621	+	2.47026i	−0.0504556	+	0.0873917i
$800$	3.65268	+	2.10887i	0.129142	+	0.0745600i
$801$	−6.26017	−	4.44242i	−0.221192	−	0.156965i
$802$	−3.90119	+	6.75706i	−0.137756	+	0.238600i
$803$	10.7110	+	18.5520i	0.377983	+	0.654686i
$804$	−5.78763	+	1.26398i	−0.204114	+	0.0445773i
$805$	41.8291	−	1.23905i	1.47428	−	0.0436708i
$806$	8.43104	−	29.7693i	0.296971	−	1.04858i
$807$	−1.25758	+	3.94518i	−0.0442689	+	0.138877i
$808$	−0.354186	+	0.204489i	−0.0124602	+	0.00719391i
$809$	−20.8406	+	12.0323i	−0.732716	+	0.423034i	−0.819415	−	0.573201i	$-0.805701\pi$
$809$	−20.8406	+	12.0323i	−0.732716	+	0.423034i	0.0866990	+	0.996235i	$0.472368\pi$
$810$	−5.08337	+	26.8477i	−0.178611	+	0.943331i
$811$		−	9.95856i		−	0.349692i	−0.984596	−	0.174846i	$-0.944057\pi$
$811$		−	9.95856i		−	0.349692i	0.984596	−	0.174846i	$-0.0559428\pi$
$812$	7.38329	−	13.7104i	0.259103	−	0.481140i
$813$	−3.67480	+	3.34611i	−0.128881	+	0.117353i
$814$	0.152427			0.00534258
$815$	−5.04137	+	8.73190i	−0.176591	+	0.305865i
$816$	−0.787132	+	0.171905i	−0.0275551	+	0.00601787i
$817$	−14.9802	+	8.64880i	−0.524090	+	0.302583i
$818$	15.6082			0.545728
$819$	18.5948	+	21.7539i	0.649755	+	0.760144i
$820$	25.2391			0.881386
$821$	46.0440	−	26.5835i	1.60695	−	0.927770i	0.616897	−	0.787044i	$-0.288390\pi$
$821$	46.0440	−	26.5835i	1.60695	−	0.927770i	0.990049	−	0.140726i	$-0.0449437\pi$
$822$	−2.54578	+	0.555982i	−0.0887942	+	0.0193921i
$823$	−2.07366	+	3.59169i	−0.0722834	+	0.125199i	−0.899902	−	0.436093i	$-0.856362\pi$
$823$	−2.07366	+	3.59169i	−0.0722834	+	0.125199i	0.827618	+	0.561291i	$0.189695\pi$
$824$	13.3326			0.464465
$825$	15.2717	−	13.9058i	0.531694	−	0.484137i
$826$	13.5780	−	25.2135i	0.472438	−	0.877291i
$827$			47.9790i			1.66839i	0.551468	+	0.834196i	$0.314068\pi$
$827$			47.9790i			1.66839i	−0.551468	+	0.834196i	$0.685932\pi$
$828$	6.51575	+	14.2059i	0.226438	+	0.493690i
$829$	−38.8652	+	22.4388i	−1.34984	+	0.779333i	−0.988227	−	0.152994i	$-0.951108\pi$
$829$	−38.8652	+	22.4388i	−1.34984	+	0.779333i	−0.361617	+	0.932327i	$0.617775\pi$
$830$	4.96721	−	2.86782i	0.172414	−	0.0995434i
$831$	5.76105	−	18.0731i	0.199848	−	0.626949i
$832$	2.51309	+	2.58542i	0.0871256	+	0.0896333i
$833$	3.25043	−	0.192736i	0.112621	−	0.00667790i
$834$	18.5249	−	4.04573i	0.641466	−	0.140092i
$835$	−11.5670	−	20.0347i	−0.400294	−	0.693329i
$836$	8.69799	−	15.0654i	0.300826	−	0.521046i
$837$	−26.8090	−	35.6300i	−0.926656	−	1.23155i
$838$	−21.3531	−	12.3282i	−0.737631	−	0.425872i
$839$	−4.16815	+	7.21944i	−0.143900	+	0.249243i	−0.928962	−	0.370175i	$-0.879298\pi$
$839$	−4.16815	+	7.21944i	−0.143900	+	0.249243i	0.785062	+	0.619418i	$0.212631\pi$
$840$	3.83114	−	13.3752i	0.132187	−	0.461487i
$841$	2.82053	−	4.88530i	0.0972596	−	0.168459i
$842$	−20.1942	+	11.6591i	−0.695937	+	0.401799i
$843$	−10.5752	−	48.4226i	−0.364229	−	1.66776i
$844$	−10.6541			−0.366729
$845$	−1.11966	+	39.4531i	−0.0385176	+	1.35723i
$846$	10.6463	−	15.0026i	0.366028	−	0.515800i
$847$	6.76805	−	4.17950i	0.232553	−	0.143609i
$848$	7.66278	−	4.42411i	0.263141	−	0.151925i
$849$	11.2653	−	10.2577i	0.386625	−	0.352044i
$850$			1.96194i			0.0672939i
$851$	0.243239	+	0.140434i	0.00833814	+	0.00481403i
$852$	13.7033	−	12.4776i	0.469468	−	0.427477i
$853$			3.96594i			0.135791i	0.997692	+	0.0678956i	$0.0216285\pi$
$853$			3.96594i			0.135791i	−0.997692	+	0.0678956i	$0.978372\pi$
$854$	31.0436	+	16.7175i	1.06229	+	0.572063i
$855$	55.7970	+	5.23582i	1.90822	+	0.179061i
$856$	−9.18025	−	15.9007i	−0.313775	−	0.543473i
$857$	−23.2349			−0.793688			−0.396844	−	0.917886i	$-0.629895\pi$
$857$	−23.2349			−0.793688			−0.396844	+	0.917886i	$0.629895\pi$
$858$	15.8003	−	7.88009i	0.539413	−	0.269022i
$859$			45.9665i			1.56836i	0.620535	+	0.784179i	$0.286916\pi$
$859$			45.9665i			1.56836i	−0.620535	+	0.784179i	$0.713084\pi$
$860$	4.26764	+	7.39176i	0.145525	+	0.252057i
$861$	−9.22659	−	36.9610i	−0.314441	−	1.25963i
$862$	1.72203	−	2.98264i	0.0586525	−	0.101589i
$863$			1.54791i			0.0526915i	0.999653	+	0.0263458i	$0.00838709\pi$
$863$			1.54791i			0.0526915i	−0.999653	+	0.0263458i	$0.991613\pi$
$864$	5.15787	−	0.629548i	0.175474	−	0.0214176i
$865$	4.76050	−	8.24543i	0.161862	−	0.280353i
$866$	28.1154			0.955401
$867$	19.5719	+	21.4944i	0.664696	+	0.729990i
$868$	11.9291	+	19.3174i	0.404901	+	0.655674i
$869$	−34.7912	+	20.0867i	−1.18021	+	0.681394i
$870$	9.39990	−	29.4886i	0.318686	−	0.999758i
$871$	−3.36038	+	11.8652i	−0.113862	+	0.402038i
$872$		−	6.65851i		−	0.225486i
$873$	24.3648	+	2.28631i	0.824622	+	0.0773800i
$874$	27.7600	−	16.0272i	0.938996	−	0.542130i
$875$	5.53239	+	2.97929i	0.187029	+	0.100719i
$876$	12.5037	+	3.98573i	0.422462	+	0.134665i
$877$	−24.5132	+	42.4581i	−0.827752	+	1.43371i	0.0720452	+	0.997401i	$0.477047\pi$
$877$	−24.5132	+	42.4581i	−0.827752	+	1.43371i	−0.899798	+	0.436308i	$0.856286\pi$
$878$	1.60072	−	2.77253i	0.0540217	−	0.0935683i
$879$	−6.19242	+	19.4264i	−0.208865	+	0.655236i
$880$	−7.43380	−	4.29190i	−0.250593	−	0.144680i
$881$	26.1386	+	45.2735i	0.880633	+	1.52530i	0.850638	+	0.525752i	$0.176216\pi$
$881$	26.1386	+	45.2735i	0.880633	+	1.52530i	0.0299951	+	0.999550i	$0.490451\pi$
$882$	−20.9876	−	0.720932i	−0.706690	−	0.0242750i
$883$	−3.96893			−0.133565			−0.0667826	−	0.997768i	$-0.521273\pi$
$883$	−3.96893			−0.133565			−0.0667826	+	0.997768i	$0.521273\pi$
$884$	−0.457020	+	1.61370i	−0.0153712	+	0.0542745i
$885$	17.2865	−	54.2299i	0.581080	−	1.82292i
$886$	−4.35164	−	7.53726i	−0.146196	−	0.253219i
$887$	−15.6126	−	27.0417i	−0.524218	−	0.907973i	−0.999602	−	0.0281944i	$-0.991024\pi$
$887$	−15.6126	−	27.0417i	−0.524218	−	0.907973i	0.475384	−	0.879778i	$-0.342309\pi$
$888$	0.0690456	−	0.0628698i	0.00231702	−	0.00210977i
$889$	−0.532121	−	17.9639i	−0.0178468	−	0.602488i
$890$	6.72777	+	3.88428i	0.225515	+	0.130201i
$891$	4.73376	−	25.0012i	0.158587	−	0.837573i
$892$		−	10.9647i		−	0.367124i
$893$	−32.6753	−	18.8651i	−1.09344	−	0.631297i
$894$	26.3537	−	5.75548i	0.881399	−	0.192492i
$895$	−53.8008	+	31.0619i	−1.79836	+	1.03828i
$896$	−2.64459	+	0.0783374i	−0.0883496	+	0.00261707i
$897$	32.4738	+	1.98230i	1.08427	+	0.0661871i
$898$	−1.98663			−0.0662948
$899$	25.2532	+	43.7398i	0.842241	+	1.45880i
$900$	1.18215	−	12.5979i	0.0394050	−	0.419930i
$901$	3.56444	+	2.05793i	0.118749	+	0.0685596i
$902$	−23.5033			−0.782573
$903$	9.26465	−	8.95187i	0.308308	−	0.297900i
$904$	−1.16500	+	2.01785i	−0.0387475	+	0.0671126i
$905$			62.8877i			2.09046i
$906$	−13.3331	+	12.1405i	−0.442962	+	0.403342i
$907$	−7.90610	−	13.6938i	−0.262518	−	0.454694i	0.704393	−	0.709811i	$-0.251220\pi$
$907$	−7.90610	−	13.6938i	−0.262518	−	0.454694i	−0.966910	+	0.255117i	$0.917886\pi$
$908$	8.52609	+	14.7676i	0.282948	+	0.490081i
$909$	1.00060	+	0.710056i	0.0331877	+	0.0235511i
$910$	−20.7929	−	20.1611i	−0.689279	−	0.668333i
$911$		−	0.152718i		−	0.00505976i	−0.999997	−	0.00252988i	$-0.999195\pi$
$911$		−	0.152718i		−	0.00505976i	0.999997	−	0.00252988i	$-0.000805287\pi$
$912$	−2.27387	−	10.4118i	−0.0752952	−	0.344768i
$913$	−4.62559	+	2.67059i	−0.153085	+	0.0883835i
$914$	−8.45325	−	4.88049i	−0.279609	−	0.161432i
$915$	66.7693	+	21.2836i	2.20733	+	0.703615i
$916$	−5.59035	−	3.22759i	−0.184710	−	0.106643i
$917$	41.0483	+	22.1053i	1.35554	+	0.729981i
$918$	1.45323	+	1.93139i	0.0479638	+	0.0637454i
$919$	19.6574	−	34.0476i	0.648437	−	1.12313i	−0.335059	−	0.942197i	$-0.608756\pi$
$919$	19.6574	−	34.0476i	0.648437	−	1.12313i	0.983496	−	0.180929i	$-0.0579104\pi$
$920$	−7.90843	−	13.6978i	−0.260733	−	0.451603i
$921$	−5.87575	−	26.9044i	−0.193613	−	0.886529i
$922$			1.90025i			0.0625814i
$923$	−9.45548	−	37.4028i	−0.311231	−	1.23113i
$924$	−3.56766	+	12.4553i	−0.117367	+	0.409749i
$925$	−0.113696	−	0.196928i	−0.00373831	−	0.00647494i
$926$	−0.655777	+	0.378613i	−0.0215502	+	0.0124420i
$927$	−16.6753	−	36.3561i	−0.547688	−	1.19409i
$928$	−5.88567			−0.193206
$929$	−5.53410	+	9.58534i	−0.181568	+	0.314485i	−0.942415	−	0.334447i	$-0.891451\pi$
$929$	−5.53410	+	9.58534i	−0.181568	+	0.314485i	0.760847	+	0.648932i	$0.224784\pi$
$930$	30.3816	+	33.3659i	0.996251	+	1.09411i
$931$	2.54940	+	42.9949i	0.0835533	+	1.40910i
$932$	4.71340	+	2.72128i	0.154392	+	0.0891385i
$933$	41.5131	−	9.06622i	1.35908	−	0.296815i
$934$	31.3625	−	18.1071i	1.02621	−	0.592483i
$935$		−	3.99286i		−	0.130581i
$936$	3.90691	−	10.0864i	0.127701	−	0.329685i
$937$			24.6387i			0.804910i	0.915440	+	0.402455i	$0.131843\pi$
$937$			24.6387i			0.804910i	−0.915440	+	0.402455i	$0.868157\pi$
$938$	−4.75462	−	7.69938i	−0.155244	−	0.251394i
$939$	−5.26398	−	24.1031i	−0.171784	−	0.786576i
$940$	−9.30873	+	16.1232i	−0.303617	+	0.525881i
$941$	−23.4949			−0.765911			−0.382956	−	0.923767i	$-0.625094\pi$
$941$	−23.4949			−0.765911			−0.382956	+	0.923767i	$0.625094\pi$
$942$	0.747788	+	0.821243i	0.0243643	+	0.0267576i
$943$	−37.5059	−	21.6540i	−1.22136	−	0.705152i
$944$	−10.8238			−0.352285
$945$	−41.2638	+	6.28149i	−1.34231	+	0.204337i
$946$	−3.97413	−	6.88340i	−0.129210	−	0.223799i
$947$	24.5958	−	14.2004i	0.799257	−	0.461451i	−0.0439545	−	0.999034i	$-0.513996\pi$
$947$	24.5958	−	14.2004i	0.799257	−	0.461451i	0.843211	+	0.537582i	$0.180662\pi$
$948$	−7.47456	+	23.4486i	−0.242763	+	0.761576i
$949$	19.5895	−	19.0415i	0.635902	−	0.618112i
$950$	−25.9515			−0.841977
$951$	3.51668	+	16.1025i	0.114036	+	0.522159i
$952$	−0.646640	−	1.04713i	−0.0209577	−	0.0339378i
$953$	−47.1399	−	27.2162i	−1.52701	−	0.881621i	−0.999485	−	0.0320819i	$-0.989786\pi$
$953$	−47.1399	−	27.2162i	−1.52701	−	0.881621i	−0.527526	−	0.849539i	$-0.676880\pi$
$954$	−21.6478	−	15.3620i	−0.700874	−	0.497363i
$955$	5.82733	+	3.36441i	0.188568	+	0.108870i
$956$	21.5608	+	12.4481i	0.697325	+	0.402601i
$957$	−8.75343	+	27.4606i	−0.282958	+	0.887675i
$958$	−30.1297	−	17.3954i	−0.973446	−	0.562020i
$959$	−2.09139	−	3.38669i	−0.0675346	−	0.109362i
$960$	−5.13754	+	1.12201i	−0.165813	+	0.0362127i
$961$	−42.6378			−1.37541
$962$	−0.0476424	−	0.188458i	−0.00153605	−	0.00607613i
$963$	−31.8769	+	44.9203i	−1.02722	+	1.44754i
$964$	3.77906	−	2.18184i	0.121715	−	0.0702723i
$965$	−18.9042	−	32.7430i	−0.608546	−	1.05403i
$966$	−17.1685	+	16.5889i	−0.552387	+	0.533738i
$967$	−15.1916			−0.488528			−0.244264	−	0.969709i	$-0.578546\pi$
$967$	−15.1916			−0.488528			−0.244264	+	0.969709i	$0.578546\pi$
$968$	−2.60374	−	1.50327i	−0.0836872	−	0.0483168i
$969$	3.66544	−	3.33759i	0.117751	−	0.107219i
$970$	−24.7661			−0.795190
$971$	16.0453	−	27.7912i	0.514917	−	0.891862i	−0.484933	−	0.874551i	$-0.661156\pi$
$971$	16.0453	−	27.7912i	0.514917	−	0.891862i	0.999850	−	0.0173110i	$-0.00551055\pi$
$972$	−8.16769	−	13.2774i	−0.261979	−	0.425872i
$973$	15.2185	+	24.6440i	0.487882	+	0.790050i
$974$			13.4306i			0.430346i
$975$	−21.9661	−	14.5353i	−0.703480	−	0.465503i
$976$		−	13.3266i		−	0.426573i
$977$	−27.5938	+	15.9313i	−0.882803	+	0.509686i	−0.871582	−	0.490251i	$-0.836905\pi$
$977$	−27.5938	+	15.9313i	−0.882803	+	0.509686i	−0.0112213	+	0.999937i	$0.503572\pi$
$978$	−1.22730	−	5.61964i	−0.0392446	−	0.179696i
$979$	−6.26507	−	3.61714i	−0.200233	−	0.115604i
$980$	21.2153	−	1.25797i	0.677697	−	0.0401844i
$981$	−18.1568	+	8.32787i	−0.579701	+	0.265888i
$982$	2.32479	−	4.02666i	0.0741871	−	0.128496i
$983$	16.1522			0.515176			0.257588	−	0.966255i	$-0.417072\pi$
$983$	16.1522			0.515176			0.257588	+	0.966255i	$0.417072\pi$
$984$	−10.6464	+	9.69411i	−0.339394	+	0.309037i
$985$	45.1643	−	26.0756i	1.43905	−	0.830838i
$986$	−1.36890	−	2.37100i	−0.0435945	−	0.0755079i
$987$	27.0144	+	7.73792i	0.859877	+	0.246301i
$988$	−21.3451	−	6.04521i	−0.679079	−	0.192324i
$989$		−	14.6458i		−	0.465709i
$990$	−2.40587	+	25.6388i	−0.0764635	+	0.814854i
$991$	−18.8682	−	32.6806i	−0.599367	−	1.03813i	−0.992915	−	0.118830i	$-0.962086\pi$
$991$	−18.8682	−	32.6806i	−0.599367	−	1.03813i	0.393547	−	0.919304i	$-0.371248\pi$
$992$	4.29062	−	7.43158i	0.136227	−	0.235953i
$993$	14.9696	−	46.9615i	0.475046	−	1.49028i
$994$	24.9252	+	13.4227i	0.790580	+	0.425742i
$995$	−18.9414	−	10.9358i	−0.600481	−	0.346688i
$996$	−0.993767	+	3.11757i	−0.0314887	+	0.0987839i
$997$	46.3662	+	26.7696i	1.46843	+	0.847800i	0.999374	−	0.0353669i	$-0.0112600\pi$
$997$	46.3662	+	26.7696i	1.46843	+	0.847800i	0.469059	+	0.883167i	$0.344593\pi$
$998$	−16.9113	+	9.76376i	−0.535318	+	0.309066i
$999$	−0.257793	−	0.109645i	−0.00815620	−	0.00346902i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bq.c.419.14	yes	64
3.2	odd	2	inner	546.2.bq.c.419.29	yes	64
7.6	odd	2	inner	546.2.bq.c.419.3	✓	64
13.9	even	3	inner	546.2.bq.c.503.20	yes	64
21.20	even	2	inner	546.2.bq.c.419.20	yes	64
39.35	odd	6	inner	546.2.bq.c.503.3	yes	64
91.48	odd	6	inner	546.2.bq.c.503.29	yes	64
273.230	even	6	inner	546.2.bq.c.503.14	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bq.c.419.3	✓	64	7.6	odd	2	inner
546.2.bq.c.419.14	yes	64	1.1	even	1	trivial
546.2.bq.c.419.20	yes	64	21.20	even	2	inner
546.2.bq.c.419.29	yes	64	3.2	odd	2	inner
546.2.bq.c.503.3	yes	64	39.35	odd	6	inner
546.2.bq.c.503.14	yes	64	273.230	even	6	inner
546.2.bq.c.503.20	yes	64	13.9	even	3	inner
546.2.bq.c.503.29	yes	64	91.48	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(1.69217 - 0.369559i) q^{3} +(0.500000 - 0.866025i) q^{4} +3.03607 q^{5} +(-1.28068 + 1.16613i) q^{6} +(-2.32945 - 1.25445i) q^{7} +1.00000i q^{8} +(2.72685 - 1.25071i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(1.69217 - 0.369559i) q^{3} +(0.500000 - 0.866025i) q^{4} +3.03607 q^{5} +(-1.28068 + 1.16613i) q^{6} +(-2.32945 - 1.25445i) q^{7} +1.00000i q^{8} +(2.72685 - 1.25071i) q^{9} +(-2.62932 + 1.51804i) q^{10} +(2.44849 - 1.41364i) q^{11} +(0.526036 - 1.65024i) q^{12} +(-2.51309 - 2.58542i) q^{13} +(2.64459 - 0.0783374i) q^{14} +(5.13754 - 1.12201i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.232581 - 0.402842i) q^{17} +(-1.73617 + 2.44657i) q^{18} +(5.32858 + 3.07646i) q^{19} +(1.51804 - 2.62932i) q^{20} +(-4.40541 - 1.26187i) q^{21} +(-1.41364 + 2.44849i) q^{22} +(-4.51168 + 2.60482i) q^{23} +(0.369559 + 1.69217i) q^{24} +4.21775 q^{25} +(3.46911 + 0.982495i) q^{26} +(4.15208 - 3.12414i) q^{27} +(-2.25111 + 1.39014i) q^{28} +(-5.09714 + 2.94283i) q^{29} +(-3.88824 + 3.54046i) q^{30} -8.58125i q^{31} +(0.866025 + 0.500000i) q^{32} +(3.62083 - 3.29697i) q^{33} +0.465162i q^{34} +(-7.07239 - 3.80861i) q^{35} +(0.280280 - 2.98688i) q^{36} +(-0.0269566 - 0.0466902i) q^{37} -6.15292 q^{38} +(-5.20803 - 3.44623i) q^{39} +3.03607i q^{40} +(4.15653 + 7.19932i) q^{41} +(4.44614 - 1.10989i) q^{42} +(-1.40564 + 2.43464i) q^{43} -2.82727i q^{44} +(8.27893 - 3.79725i) q^{45} +(2.60482 - 4.51168i) q^{46} -6.13208 q^{47} +(-1.16613 - 1.28068i) q^{48} +(3.85269 + 5.84438i) q^{49} +(-3.65268 + 2.10887i) q^{50} +(0.244692 - 0.767629i) q^{51} +(-3.49558 + 0.883688i) q^{52} +8.84822i q^{53} +(-2.03373 + 4.78162i) q^{54} +(7.43380 - 4.29190i) q^{55} +(1.25445 - 2.32945i) q^{56} +(10.1538 + 3.23665i) q^{57} +(2.94283 - 5.09714i) q^{58} +(5.41190 - 9.37369i) q^{59} +(1.59708 - 5.01025i) q^{60} +(11.5411 + 6.66328i) q^{61} +(4.29062 + 7.43158i) q^{62} +(-7.92103 - 0.507241i) q^{63} -1.00000 q^{64} +(-7.62992 - 7.84953i) q^{65} +(-1.48725 + 4.66567i) q^{66} +(-1.71013 - 2.96202i) q^{67} +(-0.232581 - 0.402842i) q^{68} +(-6.67188 + 6.07512i) q^{69} +(8.02918 - 0.237838i) q^{70} +(9.26650 + 5.35002i) q^{71} +(1.25071 + 2.72685i) q^{72} +7.57692i q^{73} +(0.0466902 + 0.0269566i) q^{74} +(7.13713 - 1.55871i) q^{75} +(5.32858 - 3.07646i) q^{76} +(-7.47698 + 0.221481i) q^{77} +(6.23340 + 0.380506i) q^{78} -14.2092 q^{79} +(-1.51804 - 2.62932i) q^{80} +(5.87145 - 6.82100i) q^{81} +(-7.19932 - 4.15653i) q^{82} -1.88916 q^{83} +(-3.29552 + 3.18426i) q^{84} +(0.706134 - 1.22306i) q^{85} -2.81129i q^{86} +(-7.53765 + 6.86345i) q^{87} +(1.41364 + 2.44849i) q^{88} +(-1.27938 - 2.21594i) q^{89} +(-5.27114 + 7.42798i) q^{90} +(2.61083 + 9.17516i) q^{91} +5.20964i q^{92} +(-3.17128 - 14.5209i) q^{93} +(5.31054 - 3.06604i) q^{94} +(16.1780 + 9.34036i) q^{95} +(1.65024 + 0.526036i) q^{96} +(7.06440 + 4.07863i) q^{97} +(-6.25872 - 3.13503i) q^{98} +(4.90862 - 6.91713i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 32 q^{4} + 16 q^{7} + 16 q^{9}+O(q^{10}) \) 64 * q + 32 * q^4 + 16 * q^7 + 16 * q^9	\( 64 q + 32 q^{4} + 16 q^{7} + 16 q^{9} - 12 q^{15} - 32 q^{16} - 24 q^{18} + 16 q^{21} - 16 q^{28} + 8 q^{30} - 16 q^{36} - 48 q^{39} + 20 q^{42} - 8 q^{43} + 8 q^{46} + 8 q^{49} - 8 q^{51} + 8 q^{57} + 16 q^{58} - 24 q^{60} + 32 q^{63} - 64 q^{64} + 24 q^{67} + 48 q^{70} - 12 q^{72} - 12 q^{78} + 96 q^{79} + 68 q^{81} + 8 q^{84} - 112 q^{85} - 16 q^{91} - 56 q^{93}+O(q^{100}) \) 64 * q + 32 * q^4 + 16 * q^7 + 16 * q^9 - 12 * q^15 - 32 * q^16 - 24 * q^18 + 16 * q^21 - 16 * q^28 + 8 * q^30 - 16 * q^36 - 48 * q^39 + 20 * q^42 - 8 * q^43 + 8 * q^46 + 8 * q^49 - 8 * q^51 + 8 * q^57 + 16 * q^58 - 24 * q^60 + 32 * q^63 - 64 * q^64 + 24 * q^67 + 48 * q^70 - 12 * q^72 - 12 * q^78 + 96 * q^79 + 68 * q^81 + 8 * q^84 - 112 * q^85 - 16 * q^91 - 56 * q^93

Introduction

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