LMFDB - Embedded newform 546.2.bq.c.419.20

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			419.20
Character	$\chi$	$=$	546.419
Dual form			546.2.bq.c.503.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-1.16613 + 1.28068i) q^{3} +(0.500000 - 0.866025i) q^{4} +3.03607 q^{5} +(-0.369559 + 1.69217i) q^{6} +(2.25111 + 1.39014i) q^{7} -1.00000i q^{8} +(-0.280280 - 2.98688i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(-1.16613 + 1.28068i) q^{3} +(0.500000 - 0.866025i) q^{4} +3.03607 q^{5} +(-0.369559 + 1.69217i) q^{6} +(2.25111 + 1.39014i) q^{7} -1.00000i q^{8} +(-0.280280 - 2.98688i) 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} +(-3.54046 + 3.88824i) 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} +(1.28068 + 1.16613i) q^{24} +4.21775 q^{25} +(3.46911 + 0.982495i) q^{26} +(4.15208 + 3.12414i) q^{27} +(2.32945 - 1.25445i) q^{28} +(5.09714 - 2.94283i) q^{29} +(-1.12201 + 5.13754i) q^{30} +8.58125i q^{31} +(-0.866025 - 0.500000i) q^{32} +(1.04484 - 4.78421i) q^{33} -0.465162i q^{34} +(6.83455 + 4.22056i) q^{35} +(-2.72685 - 1.25071i) q^{36} +(-0.0269566 - 0.0466902i) q^{37} -6.15292 q^{38} +(-6.24168 + 0.203523i) q^{39} -3.03607i q^{40} +(4.15653 + 7.19932i) q^{41} +(-3.18426 + 3.29552i) q^{42} +(-1.40564 + 2.43464i) q^{43} +2.82727i q^{44} +(-0.850950 - 9.06839i) q^{45} +(2.60482 - 4.51168i) q^{46} -6.13208 q^{47} +(1.69217 + 0.369559i) q^{48} +(3.13503 + 6.25872i) q^{49} +(3.65268 - 2.10887i) q^{50} +(0.244692 + 0.767629i) q^{51} +(3.49558 - 0.883688i) q^{52} -8.84822i q^{53} +(5.15787 + 0.629548i) q^{54} +(-7.43380 + 4.29190i) q^{55} +(1.39014 - 2.25111i) 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} +(3.52123 - 7.11343i) 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} +(-1.92527 + 8.81558i) q^{69} +(8.02918 + 0.237838i) q^{70} +(-9.26650 - 5.35002i) q^{71} +(-2.98688 + 0.280280i) q^{72} -7.57692i q^{73} +(-0.0466902 - 0.0269566i) q^{74} +(-4.91844 + 5.40158i) q^{75} +(-5.32858 + 3.07646i) q^{76} +(-7.47698 - 0.221481i) q^{77} +(-5.30369 + 3.29710i) q^{78} -14.2092 q^{79} +(-1.51804 - 2.62932i) q^{80} +(-8.84289 + 1.67432i) q^{81} +(7.19932 + 4.15653i) q^{82} -1.88916 q^{83} +(-1.10989 + 4.44614i) q^{84} +(0.706134 - 1.22306i) q^{85} +2.81129i q^{86} +(-2.17510 + 9.95952i) q^{87} +(1.41364 + 2.44849i) q^{88} +(-1.27938 - 2.21594i) q^{89} +(-5.27114 - 7.42798i) q^{90} +(2.06316 + 9.31361i) q^{91} -5.20964i q^{92} +(-10.9898 - 10.0069i) 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} +(5.84438 + 3.85269i) 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
$3$	−1.16613	+	1.28068i	−0.673266	+	0.739401i
$3$	−1.16613	+	1.28068i	−0.673266	+	0.739401i
$4$	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	$0.262463\pi$
$6$	−0.369559	+	1.69217i	−0.150872	+	0.690824i
$7$	2.25111	+	1.39014i	0.850841	+	0.525423i
$7$	2.25111	+	1.39014i	0.850841	+	0.525423i
$8$		−	1.00000i		−	0.353553i
$9$	−0.280280	−	2.98688i	−0.0934265	−	0.995626i
$10$	2.62932	−	1.51804i	0.831463	−	0.480046i
$11$	−2.44849	+	1.41364i	−0.738247	+	0.426227i	−0.821432	−	0.570307i	$-0.806824\pi$
$11$	−2.44849	+	1.41364i	−0.738247	+	0.426227i	0.0831844	+	0.996534i	$0.473491\pi$
$12$	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
$15$	−3.54046	+	3.88824i	−0.914143	+	1.00394i
$16$	−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	−0.257019	−	0.966406i	$-0.582740\pi$
$19$	−5.32858	−	3.07646i	−1.22246	−	0.705788i	−0.965442	+	0.260618i	$0.916074\pi$
$20$	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	0.0505552	−	0.998721i	$-0.483901\pi$
$23$	4.51168	−	2.60482i	0.940751	−	0.543143i	0.890196	+	0.455579i	$0.150568\pi$
$24$	1.28068	+	1.16613i	0.261418	+	0.238035i
$25$	4.21775			0.843550
$26$	3.46911	+	0.982495i	0.680348	+	0.192683i
$27$	4.15208	+	3.12414i	0.799067	+	0.601241i
$28$	2.32945	−	1.25445i	0.440225	−	0.237069i
$29$	5.09714	−	2.94283i	0.946514	−	0.546470i	0.0545179	−	0.998513i	$-0.482638\pi$
$29$	5.09714	−	2.94283i	0.946514	−	0.546470i	0.891996	+	0.452042i	$0.149304\pi$
$30$	−1.12201	+	5.13754i	−0.204850	+	0.937983i
$31$			8.58125i			1.54124i	0.637296	+	0.770619i	$0.280053\pi$
$31$			8.58125i			1.54124i	−0.637296	+	0.770619i	$0.719947\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	1.04484	−	4.78421i	0.181884	−	0.832825i
$34$		−	0.465162i		−	0.0797747i
$35$	6.83455	+	4.22056i	1.15525	+	0.713405i
$36$	−2.72685	−	1.25071i	−0.454475	−	0.208452i
$37$	−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
$39$	−6.24168	+	0.203523i	−0.999469	+	0.0325897i
$40$		−	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	$0.608462\pi$
$42$	−3.18426	+	3.29552i	−0.491343	+	0.508510i
$43$	−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
$45$	−0.850950	−	9.06839i	−0.126852	−	1.35184i
$46$	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	$0.647589\pi$
$48$	1.69217	+	0.369559i	0.244243	+	0.0533412i
$49$	3.13503	+	6.25872i	0.447862	+	0.894103i
$50$	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	$-0.792093\pi$
$53$		−	8.84822i		−	1.21540i	0.794168	−	0.607698i	$-0.207907\pi$
$54$	5.15787	+	0.629548i	0.701898	+	0.0856706i
$55$	−7.43380	+	4.29190i	−1.00237	+	0.578720i
$56$	1.39014	−	2.25111i	0.185765	−	0.300818i
$57$	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	−0.478009	−	0.878355i	$-0.658641\pi$
$61$	−11.5411	−	6.66328i	−1.47769	−	0.853146i	−0.999682	+	0.0252092i	$0.991975\pi$
$62$	4.29062	+	7.43158i	0.544910	+	0.943812i
$63$	3.52123	−	7.11343i	0.443633	−	0.896208i
$64$	−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
$69$	−1.92527	+	8.81558i	−0.231775	+	1.06127i
$70$	8.02918	+	0.237838i	0.959670	+	0.0284271i
$71$	−9.26650	−	5.35002i	−1.09973	−	0.634930i	−0.163581	−	0.986530i	$-0.552304\pi$
$71$	−9.26650	−	5.35002i	−1.09973	−	0.634930i	−0.936150	+	0.351600i	$0.885638\pi$
$72$	−2.98688	+	0.280280i	−0.352007	+	0.0330313i
$73$		−	7.57692i		−	0.886811i	−0.896321	−	0.443406i	$-0.853770\pi$
$73$		−	7.57692i		−	0.886811i	0.896321	−	0.443406i	$-0.146230\pi$
$74$	−0.0466902	−	0.0269566i	−0.00542763	−	0.00313364i
$75$	−4.91844	+	5.40158i	−0.567933	+	0.623721i
$76$	−5.32858	+	3.07646i	−0.611230	+	0.352894i
$77$	−7.47698	−	0.221481i	−0.852081	−	0.0252401i
$78$	−5.30369	+	3.29710i	−0.600525	+	0.373323i
$79$	−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
$81$	−8.84289	+	1.67432i	−0.982543	+	0.186036i
$82$	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	$0.533062\pi$
$84$	−1.10989	+	4.44614i	−0.121099	+	0.485113i
$85$	0.706134	−	1.22306i	0.0765910	−	0.132659i
$86$			2.81129i			0.303149i
$87$	−2.17510	+	9.95952i	−0.233195	+	1.06777i
$88$	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
$91$	2.06316	+	9.31361i	0.216278	+	0.976332i
$92$		−	5.20964i		−	0.543143i
$93$	−10.9898	−	10.0069i	−1.13959	−	1.03766i
$94$	−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	0.0964702	−	0.995336i	$-0.469245\pi$
$97$	−7.06440	−	4.07863i	−0.717281	−	0.414122i	−0.813751	+	0.581214i	$0.802578\pi$
$98$	5.84438	+	3.85269i	0.590371	+	0.389181i
$99$	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	$0.826856\pi$
$102$	0.595724	+	0.542440i	0.0589855	+	0.0537096i
$103$			13.3326i			1.31370i	0.754020	+	0.656852i	$0.228112\pi$
$103$			13.3326i			1.31370i	−0.754020	+	0.656852i	$0.771888\pi$
$104$	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	$-0.319115\pi$
$107$	15.9007	−	9.18025i	1.53718	−	0.887488i	0.999003	−	0.0446537i	$-0.0142184\pi$
$108$	4.78162	−	2.03373i	0.460112	−	0.195696i
$109$	−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
$111$	0.0912301	+	0.0199241i	0.00865918	+	0.00189111i
$112$	0.0783374	−	2.64459i	0.00740219	−	0.249890i
$113$	−2.01785	−	1.16500i	−0.189823	−	0.109594i	0.402077	−	0.915606i	$-0.368289\pi$
$113$	−2.01785	−	1.16500i	−0.189823	−	0.109594i	−0.591900	+	0.806012i	$0.701622\pi$
$114$	7.17511	−	7.87992i	0.672010	−	0.738022i
$115$	13.6978	−	7.90843i	1.27733	−	0.737465i
$116$		−	5.88567i		−	0.546470i
$117$	7.01797	−	8.23093i	0.648811	−	0.760949i
$118$		−	10.8238i		−	0.996412i
$119$	1.08357	−	0.583525i	0.0993310	−	0.0534916i
$120$	3.88824	+	3.54046i	0.354946	+	0.323198i
$121$	−1.50327	+	2.60374i	−0.136661	+	0.236703i
$122$	−13.3266			−1.20653
$123$	−14.0671	−	3.07216i	−1.26839	−	0.277008i
$124$	7.43158	+	4.29062i	0.667376	+	0.385309i
$125$	−2.37497			−0.212424
$126$	−0.507241	−	7.92103i	−0.0451886	−	0.705661i
$127$	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	$0.779643\pi$
$132$	−3.62083	−	3.29697i	−0.315153	−	0.286964i
$133$	−7.71855	−	14.3329i	−0.669283	−	1.24282i
$134$	−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	0.443310	−	0.896369i	$-0.353804\pi$
$137$	−1.30289	−	0.752224i	−0.111313	−	0.0642669i	−0.554623	+	0.832102i	$0.687138\pi$
$138$	2.74046	+	8.59715i	0.233283	+	0.731838i
$139$	9.48078	+	5.47373i	0.804150	+	0.464276i	0.844920	−	0.534893i	$-0.179648\pi$
$139$	9.48078	+	5.47373i	0.804150	+	0.464276i	−0.0407705	+	0.999169i	$0.512981\pi$
$140$	7.07239	−	3.80861i	0.597726	−	0.321887i
$141$	7.15081	−	7.85323i	0.602207	−	0.661362i
$142$	−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
$147$	−11.6713	−	3.28351i	−0.962630	−	0.270819i
$148$	−0.0539132			−0.00443164
$149$	13.4874	+	7.78696i	1.10493	+	0.637933i	0.937512	−	0.347953i	$-0.113123\pi$
$149$	13.4874	+	7.78696i	1.10493	+	0.637933i	0.167420	+	0.985886i	$0.446456\pi$
$150$	−1.55871	+	7.13713i	−0.127268	+	0.582744i
$151$	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
$153$	−1.26843	−	0.581783i	−0.102546	−	0.0470344i
$154$	−6.58599	+	3.54668i	−0.530715	+	0.285800i
$155$			26.0533i			2.09265i
$156$	−2.94458	+	5.50722i	−0.235755	+	0.440930i
$157$			0.641256i			0.0511778i	0.999673	+	0.0255889i	$0.00814609\pi$
$157$			0.641256i			0.0511778i	−0.999673	+	0.0255889i	$0.991854\pi$
$158$	−12.3056	+	7.10462i	−0.978978	+	0.565213i
$159$	11.3317	+	10.3182i	0.898665	+	0.818285i
$160$	−2.62932	−	1.51804i	−0.207866	−	0.120011i
$161$	13.7774	+	0.408110i	1.08581	+	0.0321635i
$162$	−6.82100	+	5.87145i	−0.535909	+	0.461305i
$163$	−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
$165$	3.17222	−	14.5252i	0.246957	−	1.13079i
$166$	−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
$171$	−7.69552	+	16.7781i	−0.588491	+	1.28305i
$172$	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
$175$	9.49464	+	5.86325i	0.717727	+	0.443220i
$176$	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	0.340051	−	0.940407i	$-0.389556\pi$
$179$	17.7205	−	10.2309i	1.32449	−	0.764696i	0.984442	+	0.175711i	$0.0562224\pi$
$180$	−8.27893	−	3.79725i	−0.617075	−	0.283030i
$181$		−	20.7135i		−	1.53962i	−0.638272	−	0.769811i	$-0.720350\pi$
$181$		−	20.7135i		−	1.53962i	0.638272	−	0.769811i	$-0.279650\pi$
$182$	6.44355	+	7.03425i	0.477628	+	0.521413i
$183$	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
$186$	−14.5209	−	3.17128i	−1.06472	−	0.232529i
$187$			1.31514i			0.0961726i
$188$	−3.06604	+	5.31054i	−0.223614	+	0.387311i
$189$	5.00381	+	12.8048i	0.363974	+	0.931409i
$190$	−18.6807			−1.35524
$191$	−1.91936	−	1.10814i	−0.138880	−	0.0801825i	0.428950	−	0.903328i	$-0.358884\pi$
$191$	−1.91936	−	1.10814i	−0.138880	−	0.0801825i	−0.567830	+	0.823146i	$0.692217\pi$
$192$	1.16613	−	1.28068i	0.0841582	−	0.0924251i
$193$	−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
$195$	−18.9502	+	0.617910i	−1.35705	+	0.0442494i
$196$	6.98773	+	0.414341i	0.499123	+	0.0295958i
$197$	−14.8759	+	8.58860i	−1.05986	+	0.611912i	−0.925394	−	0.379006i	$-0.876266\pi$
$197$	−14.8759	+	8.58860i	−1.05986	+	0.611912i	−0.134469	+	0.990918i	$0.542933\pi$
$198$	7.70955	+	3.53610i	0.547894	+	0.251299i
$199$	6.23877	+	3.60195i	0.442254	+	0.255336i	0.704553	−	0.709651i	$-0.251147\pi$
$199$	6.23877	+	3.60195i	0.442254	+	0.255336i	−0.262299	+	0.964987i	$0.584481\pi$
$200$		−	4.21775i		−	0.298240i
$201$	5.78763	+	1.26398i	0.408228	+	0.0891546i
$202$	0.354186	+	0.204489i	0.0249205	+	0.0143878i
$203$	15.5652	+	0.461068i	1.09246	+	0.0323606i
$204$	0.787132	+	0.171905i	0.0551103	+	0.0120357i
$205$	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
$210$	−9.66766	+	10.0055i	−0.667132	+	0.690442i
$211$	−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
$217$	−11.9291	+	19.3174i	−0.809801	+	1.31135i
$218$	−5.76644	+	3.32926i	−0.390553	+	0.225486i
$219$	9.70360	+	8.83567i	0.655709	+	0.597060i
$220$			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	−0.783025	−	0.621990i	$-0.786324\pi$
$223$	−9.49568	+	5.48233i	−0.635878	+	0.367124i	0.147147	+	0.989115i	$0.452991\pi$
$224$	−1.25445	−	2.32945i	−0.0838167	−	0.155643i
$225$	−1.18215	−	12.5979i	−0.0788099	−	0.839860i
$226$	−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	$0.975197\pi$
$228$	2.27387	−	10.4118i	0.150590	−	0.689536i
$229$			6.45518i			0.426570i	0.976990	+	0.213285i	$0.0684163\pi$
$229$			6.45518i			0.426570i	−0.976990	+	0.213285i	$0.931584\pi$
$230$	7.90843	−	13.6978i	0.521466	−	0.903206i
$231$	9.00278	−	9.31734i	0.592339	−	0.613036i
$232$	−2.94283	−	5.09714i	−0.193206	−	0.334643i
$233$		−	5.44256i		−	0.356554i	−0.983980	−	0.178277i	$-0.942948\pi$
$233$		−	5.44256i		−	0.356554i	0.983980	−	0.178277i	$-0.0570523\pi$
$234$	1.96227	−	10.6372i	0.128278	−	0.695374i
$235$	−18.6175			−1.21447
$236$	−5.41190	−	9.37369i	−0.352285	−	0.610175i
$237$	16.5698	−	18.1975i	1.07633	−	1.18205i
$238$	0.646640	−	1.04713i	0.0419154	−	0.0678756i
$239$		−	24.8962i		−	1.61040i	−0.593001	−	0.805202i	$-0.702057\pi$
$239$		−	24.8962i		−	1.61040i	0.593001	−	0.805202i	$-0.297943\pi$
$240$	5.13754	+	1.12201i	0.331627	+	0.0724253i
$241$	−3.77906	−	2.18184i	−0.243431	−	0.140545i	0.373322	−	0.927702i	$-0.378219\pi$
$241$	−3.77906	−	2.18184i	−0.243431	−	0.140545i	−0.616752	+	0.787157i	$0.711552\pi$
$242$			3.00653i			0.193267i
$243$	8.16769	−	13.2774i	0.523957	−	0.851744i
$244$	−11.5411	+	6.66328i	−0.738846	+	0.426573i
$245$	9.51820	+	19.0019i	0.608095	+	1.21399i
$246$	−13.7185	+	4.37296i	−0.874661	+	0.278810i
$247$	−5.43726	−	21.5080i	−0.345964	−	1.36852i
$248$	8.58125			0.544910
$249$	2.20301	−	2.41941i	0.139610	−	0.153324i
$250$	−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	$0.812630\pi$
$258$	−3.60036	−	3.27833i	−0.224148	−	0.204100i
$259$	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	−0.843640	−	0.536908i	$-0.819592\pi$
$263$	−12.9817	+	7.49497i	−0.800484	+	0.462160i	0.0431562	+	0.999068i	$0.486259\pi$
$264$	−4.78421	−	1.04484i	−0.294448	−	0.0643057i
$265$		−	26.8639i		−	1.65023i
$266$	−13.8509	−	8.55340i	−0.849255	−	0.524443i
$267$	4.32983	+	0.945609i	0.264981	+	0.0578703i
$268$	−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	$0.189886\pi$
$270$	15.6597	+	1.91135i	0.953018	+	0.116321i
$271$	2.48498	−	1.43471i	0.150952	−	0.0871522i	−0.422622	−	0.906306i	$-0.638890\pi$
$271$	2.48498	−	1.43471i	0.150952	−	0.0871522i	0.573573	+	0.819154i	$0.305557\pi$
$272$	−0.465162			−0.0282046
$273$	−14.3337	−	8.21864i	−0.867513	−	0.497415i
$274$	−1.50445			−0.0908871
$275$	−10.3271	+	5.96236i	−0.622748	+	0.359544i
$276$	6.67188	+	6.07512i	0.401600	+	0.365679i
$277$	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
$279$	25.6312	−	2.40515i	1.53450	−	0.143993i
$280$	4.22056	−	6.83455i	0.252227	−	0.408443i
$281$			28.6157i			1.70707i	0.521034	+	0.853536i	$0.325547\pi$
$281$			28.6157i			1.70707i	−0.521034	+	0.853536i	$0.674453\pi$
$282$	2.26617	−	10.3765i	0.134948	−	0.617912i
$283$	−7.61788	+	4.39819i	−0.452836	+	0.261445i	−0.709027	−	0.705181i	$-0.750866\pi$
$283$	−7.61788	+	4.39819i	−0.452836	+	0.261445i	0.256191	+	0.966626i	$0.417532\pi$
$284$	−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
$288$	−1.25071	+	2.72685i	−0.0736988	+	0.160681i
$289$	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
$297$	−14.5827	−	1.77990i	−0.846175	−	0.103280i
$298$	15.5739			0.902173
$299$	18.0728	+	5.11845i	1.04518	+	0.296008i
$300$	2.21869	+	6.96029i	0.128096	+	0.401853i
$301$	−6.54875	+	3.52663i	−0.377464	+	0.203271i
$302$	9.01615	−	5.20547i	0.518821	−	0.299541i
$303$	−0.692060	−	0.151142i	−0.0397578	−	0.00868287i
$304$			6.15292i			0.352894i
$305$	−35.0398	−	20.2302i	−2.00637	−	1.15838i
$306$	−1.38938	+	0.130376i	−0.0794258	+	0.00745307i
$307$			15.8994i			0.907425i	0.891148	+	0.453712i	$0.149901\pi$
$307$			15.8994i			0.907425i	−0.891148	+	0.453712i	$0.850099\pi$
$308$	−3.93030	+	6.36451i	−0.223949	+	0.362652i
$309$	−17.0748	−	15.5476i	−0.971354	−	0.884472i
$310$	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	$0.255158\pi$
$312$	0.203523	+	6.24168i	0.0115222	+	0.353366i
$313$			14.2440i			0.805116i	0.915394	+	0.402558i	$0.131879\pi$
$313$			14.2440i			0.805116i	−0.915394	+	0.402558i	$0.868121\pi$
$314$	0.320628	+	0.555344i	0.0180941	+	0.0313399i
$315$	10.6907	−	21.5969i	0.602354	−	1.21685i
$316$	−7.10462	+	12.3056i	−0.399666	+	0.692242i
$317$		−	9.51590i		−	0.534466i	−0.963632	−	0.267233i	$-0.913891\pi$
$317$		−	9.51590i		−	0.534466i	0.963632	−	0.267233i	$-0.0861094\pi$
$318$	14.9727	+	3.26994i	0.839625	+	0.183369i
$319$	−8.32019	+	14.4110i	−0.465841	+	0.806860i
$320$	−3.03607			−0.169722
$321$	−6.78529	+	31.0690i	−0.378718	+	1.73410i
$322$	12.1356	−	6.53525i	0.676291	−	0.364195i
$323$	−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
$327$	7.76469	−	8.52742i	0.429388	−	0.471567i
$328$	7.19932	−	4.15653i	0.397516	−	0.229506i
$329$	−13.8040	−	8.52444i	−0.761040	−	0.469968i
$330$	−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
$336$	3.29552	+	3.18426i	0.179785	+	0.173716i
$337$	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
$342$	1.72454	+	18.3780i	0.0932523	+	0.993769i
$343$	−1.64316	+	18.4472i	−0.0887224	+	0.996056i
$344$	2.43464	+	1.40564i	0.131267	+	0.0757872i
$345$	−5.84526	+	26.7648i	−0.314698	+	1.44097i
$346$		−	3.13596i		−	0.168590i
$347$	−3.25509	−	1.87933i	−0.174742	−	0.100888i	0.410078	−	0.912051i	$-0.365502\pi$
$347$	−3.25509	−	1.87933i	−0.174742	−	0.100888i	−0.584820	+	0.811163i	$0.698835\pi$
$348$	7.53765	+	6.86345i	0.404060	+	0.367920i
$349$	9.98836	−	5.76679i	0.534665	−	0.308689i	−0.208249	−	0.978076i	$-0.566776\pi$
$349$	9.98836	−	5.76679i	0.534665	−	0.308689i	0.742914	+	0.669387i	$0.233443\pi$
$350$	11.1542	+	0.330407i	0.596218	+	0.0176610i
$351$	2.35731	+	18.5861i	0.125824	+	0.992053i
$352$	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	$0.852704\pi$
$354$	13.8618	+	12.6220i	0.736748	+	0.670850i
$355$	−28.1338	−	16.2430i	−1.49319	−	0.862091i
$356$	−2.55875			−0.135614
$357$	−0.516280	+	2.06818i	−0.0273244	+	0.109459i
$358$	10.2309	−	17.7205i	0.540722	−	0.936558i
$359$			34.0398i			1.79655i	0.439433	+	0.898275i	$0.355179\pi$
$359$			34.0398i			1.79655i	−0.439433	+	0.898275i	$0.644821\pi$
$360$	−9.06839	+	0.850950i	−0.477946	+	0.0448490i
$361$	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
$364$	9.09740	+	2.87006i	0.476834	+	0.150432i
$365$		−	23.0041i		−	1.20409i
$366$	15.5405	−	17.0671i	0.812315	−	0.892109i
$367$	12.6014	−	7.27540i	0.657786	−	0.379773i	−0.133647	−	0.991029i	$-0.542669\pi$
$367$	12.6014	−	7.27540i	0.657786	−	0.379773i	0.791433	+	0.611256i	$0.209335\pi$
$368$	−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
$371$	12.3002	−	19.9184i	0.638597	−	1.03411i
$372$	−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
$375$	2.76953	−	3.04158i	0.143018	−	0.157067i
$376$			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
$381$	−11.4943	−	2.51029i	−0.588873	−	0.128606i
$382$	−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	$0.954451\pi$
$384$	0.369559	−	1.69217i	0.0188590	−	0.0863530i
$385$	−22.7007	−	0.672433i	−1.15693	−	0.0342704i
$386$	−10.7846	−	6.22651i	−0.548924	−	0.316921i
$387$	7.66596	+	3.51610i	0.389683	+	0.178734i
$388$	−7.06440	+	4.07863i	−0.358640	+	0.207061i
$389$			25.7858i			1.30739i	0.756756	+	0.653697i	$0.226783\pi$
$389$			25.7858i			1.30739i	−0.756756	+	0.653697i	$0.773217\pi$
$390$	−16.1024	+	10.0102i	−0.815377	+	0.506888i
$391$		−	2.42333i		−	0.122553i
$392$	6.25872	−	3.13503i	0.316113	−	0.158343i
$393$	20.5489	−	22.5674i	1.03656	−	1.13838i
$394$	−8.58860	+	14.8759i	−0.432687	+	0.749436i
$395$	−43.1403			−2.17062
$396$	8.44472	−	0.792427i	0.424363	−	0.0398209i
$397$	1.64285	+	0.948501i	0.0824524	+	0.0476039i	0.540659	−	0.841242i	$-0.318175\pi$
$397$	1.64285	+	0.948501i	0.0824524	+	0.0476039i	−0.458207	+	0.888846i	$0.651508\pi$
$398$	7.20391			0.361099
$399$	27.3567	+	6.82907i	1.36955	+	0.341881i
$400$	−2.10887	−	3.65268i	−0.105444	−	0.182634i
$401$	−6.75706	+	3.90119i	−0.337431	+	0.194816i	−0.659136	−	0.752024i	$-0.729078\pi$
$401$	−6.75706	+	3.90119i	−0.337431	+	0.194816i	0.321704	+	0.946840i	$0.395744\pi$
$402$	5.64423	−	1.79917i	0.281509	−	0.0897347i
$403$	−22.1861	+	21.5654i	−1.10517	+	1.07425i
$404$	0.408979			0.0203475
$405$	−26.8477	+	5.08337i	−1.33407	+	0.252595i
$406$	13.7104	−	7.38329i	0.680434	−	0.366427i
$407$	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	0.795462	−	0.606004i	$-0.207228\pi$
$409$	13.5171	+	7.80411i	0.668378	+	0.385888i	−0.127084	+	0.991892i	$0.540562\pi$
$410$	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
$413$	25.2135	−	13.5780i	1.24068	−	0.668128i
$414$	−14.2059	−	6.51575i	−0.698183	−	0.320232i
$415$	−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	$0.627595\pi$
$420$	−3.36971	+	13.4988i	−0.164425	+	0.658674i
$421$	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
$423$	1.71870	+	18.3158i	0.0835660	+	0.890544i
$424$	−8.84822			−0.429708
$425$	0.980969	−	1.69909i	0.0475840	−	0.0824179i
$426$	12.4776	−	13.7033i	0.604543	−	0.663927i
$427$	−16.7175	−	31.0436i	−0.809019	−	1.50230i
$428$		−	18.3605i		−	0.887488i
$429$	14.9950	−	9.32179i	0.723965	−	0.450060i
$430$			8.53527i			0.411607i
$431$	2.98264	−	1.72203i	0.143669	−	0.0829472i	−0.426443	−	0.904515i	$-0.640233\pi$
$431$	2.98264	−	1.72203i	0.143669	−	0.0829472i	0.570111	+	0.821567i	$0.306900\pi$
$432$	0.629548	−	5.15787i	0.0302891	−	0.248158i
$433$	24.3487	+	14.0577i	1.17012	+	0.675571i	0.953709	−	0.300731i	$-0.0972307\pi$
$433$	24.3487	+	14.0577i	1.17012	+	0.675571i	0.216414	+	0.976302i	$0.430564\pi$
$434$	−0.672233	+	22.6939i	−0.0322682	+	1.08934i
$435$	−6.60377	+	30.2379i	−0.316626	+	1.44979i
$436$	−3.32926	+	5.76644i	−0.159442	+	0.276162i
$437$	−32.0545			−1.53337
$438$	12.8214	+	2.80012i	0.612630	+	0.133795i
$439$	2.77253	−	1.60072i	0.132326	−	0.0763982i	−0.432376	−	0.901693i	$-0.642325\pi$
$439$	2.77253	−	1.60072i	0.132326	−	0.0763982i	0.564701	+	0.825295i	$0.308991\pi$
$440$	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	$-0.933710\pi$
$443$		−	8.70328i		−	0.413505i	0.978393	−	0.206753i	$-0.0662896\pi$
$444$	0.0628698	−	0.0690456i	0.00298367	−	0.00327676i
$445$	−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
$448$	−2.25111	−	1.39014i	−0.106355	−	0.0656778i
$449$	−1.72047	−	0.993316i	−0.0811942	−	0.0468775i	0.458853	−	0.888512i	$-0.348260\pi$
$449$	−1.72047	−	0.993316i	−0.0811942	−	0.0468775i	−0.540047	+	0.841635i	$0.681594\pi$
$450$	−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
$453$	−12.1405	+	13.3331i	−0.570412	+	0.626443i
$454$			17.0522i			0.800298i
$455$	6.26390	+	28.2768i	0.293656	+	1.32564i
$456$	−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
$459$	2.22423	−	0.946016i	0.103818	−	0.0441563i
$460$		−	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	$0.152576\pi$
$462$	3.13797	−	12.5704i	0.145991	−	0.584830i
$463$	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
$465$	−33.3659	−	30.3816i	−1.54731	−	1.40891i
$466$	−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	$0.816215\pi$
$468$	−3.61921	−	10.1932i	−0.167298	−	0.471181i
$469$	0.267933	−	9.04517i	0.0123720	−	0.417667i
$470$	−16.1232	+	9.30873i	−0.743708	+	0.429380i
$471$	−0.821243	−	0.747788i	−0.0378409	−	0.0344563i
$472$	−9.37369	−	5.41190i	−0.431459	−	0.249103i
$473$		−	7.94827i		−	0.365462i
$474$	5.25115	−	24.0444i	0.241193	−	1.10440i
$475$	−22.4746	−	12.9757i	−1.03121	−	0.595367i
$476$	0.0364396	−	1.23016i	0.00167021	−	0.0563845i
$477$	−26.4286	+	2.47998i	−1.21008	+	0.113550i
$478$	−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
$483$	−16.5889	+	17.1685i	−0.754820	+	0.781193i
$484$	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
$490$	17.7440	+	11.6971i	0.801591	+	0.528419i
$491$	4.02666	−	2.32479i	0.181721	−	0.104916i	−0.406380	−	0.913704i	$-0.633209\pi$
$491$	4.02666	−	2.32479i	0.181721	−	0.104916i	0.588101	+	0.808788i	$0.299876\pi$
$492$	−9.69411	+	10.6464i	−0.437044	+	0.479975i
$493$		−	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
$497$	−13.4227	−	24.9252i	−0.602090	−	1.11805i
$498$	0.698157	−	3.19678i	0.0312851	−	0.143251i
$499$	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
$501$	12.8939	+	2.81594i	0.576055	+	0.125807i
$502$		−	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	$-0.0361891\pi$
$504$	−7.11343	−	3.52123i	−0.316857	−	0.156848i
$505$	0.620845	+	1.07534i	0.0276273	+	0.0478518i
$506$			14.7291i			0.654787i
$507$	−16.2121	−	15.6259i	−0.720004	−	0.693970i
$508$	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	$-0.359075\pi$
$510$	1.80866	+	1.64689i	0.0800889	+	0.0729254i
$511$	10.5330	−	17.0565i	0.465951	−	0.754536i
$512$			1.00000i			0.0441942i
$513$	−12.5134	−	29.4209i	−0.552480	−	1.29897i
$514$	1.80474	+	1.04197i	0.0796039	+	0.0459593i
$515$			40.4789i			1.78371i
$516$	−4.75716	−	1.03894i	−0.209422	−	0.0457366i
$517$	15.0143	−	8.66853i	0.660330	−	0.381242i
$518$	−0.0676316	−	0.125588i	−0.00297156	−	0.00551803i
$519$	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	$0.504949\pi$
$522$	−16.0493	−	7.36126i	−0.702461	−	0.322194i
$523$	−23.3251	+	13.4668i	−1.01994	+	0.588861i	−0.914086	−	0.405521i	$-0.867090\pi$
$523$	−23.3251	+	13.4668i	−1.01994	+	0.588861i	−0.105851	+	0.994382i	$0.533757\pi$
$524$	−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
$531$	−29.5149	−	13.5374i	−1.28084	−	0.587475i
$532$	−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
$537$	−7.56187	+	34.6249i	−0.326319	+	1.49417i
$538$			2.39067i			0.103069i
$539$	−16.5236	−	10.8926i	−0.711724	−	0.469178i
$540$	14.5174	−	6.17456i	0.624728	−	0.265711i
$541$	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
$543$	26.5273	+	24.1546i	1.13840	+	1.03657i
$544$	−0.402842	+	0.232581i	−0.0172717	+	0.00997184i
$545$	−20.2157			−0.865947
$546$	−16.5226	+	0.0492773i	−0.707104	+	0.00210888i
$547$	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
$549$	−16.6677	+	36.3396i	−0.711358	+	1.55093i
$550$	−5.96236	+	10.3271i	−0.254236	+	0.440350i
$551$	−36.2140			−1.54277
$552$	8.81558	+	1.92527i	0.375216	+	0.0819449i
$553$	−31.9866	−	19.7528i	−1.36021	−	0.839974i
$554$		−	10.9518i		−	0.465298i
$555$	0.276981	+	0.0604911i	0.0117572	+	0.00256770i
$556$	9.48078	−	5.47373i	0.402075	−	0.232138i
$557$	21.2756	−	12.2835i	0.901476	−	0.520468i	0.0237975	−	0.999717i	$-0.492424\pi$
$557$	21.2756	−	12.2835i	0.901476	−	0.520468i	0.877679	+	0.479249i	$0.159091\pi$
$558$	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
$561$	−1.68427	−	1.53363i	−0.0711101	−	0.0647497i
$562$	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	−0.640283	−	0.768139i	$-0.721183\pi$
$569$	−7.04152	+	4.06542i	−0.295196	+	0.170431i	0.345087	+	0.938571i	$0.387849\pi$
$570$	21.7842	−	23.9240i	0.912438	−	1.00207i
$571$	−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
$574$	10.4283	+	19.3649i	0.435271	+	0.808274i
$575$	19.0291	−	10.9865i	0.793570	−	0.458168i
$576$	0.280280	+	2.98688i	0.0116783	+	0.124453i
$577$		−	9.90231i		−	0.412239i	−0.978527	−	0.206119i	$-0.933916\pi$
$577$		−	9.90231i		−	0.412239i	0.978527	−	0.206119i	$-0.0660835\pi$
$578$	14.5350	+	8.39181i	0.604578	+	0.349053i
$579$	21.0726	+	4.60213i	0.875747	+	0.191258i
$580$		−	17.8693i		−	0.741983i
$581$	−4.25272	−	2.62620i	−0.176433	−	0.108953i
$582$	9.51243	−	10.4468i	0.394303	−	0.433035i
$583$	12.5082	+	21.6648i	0.518035	+	0.897263i
$584$	−7.57692			−0.313535
$585$	21.3071	−	24.9897i	0.880939	−	1.03320i
$586$			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	$0.869547\pi$
$588$	−8.67924	+	8.46586i	−0.357926	+	0.349126i
$589$	26.3999	−	45.7259i	1.08779	−	1.88410i
$590$		−	32.8619i		−	1.35290i
$591$	6.34798	−	29.0667i	0.261121	−	1.19564i
$592$	−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	$0.421124\pi$
$594$	−13.5190	+	5.74992i	−0.554689	+	0.235922i
$595$	3.28981	−	1.77162i	0.134869	−	0.0726295i
$596$	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	$0.00248515\pi$
$599$			0.382157i			0.0156145i	−0.999970	+	0.00780725i	$0.997515\pi$
$600$	5.40158	+	4.91844i	0.220519	+	0.200795i
$601$	−37.2367	+	21.4986i	−1.51892	+	0.876948i	−0.519166	+	0.854673i	$0.673757\pi$
$601$	−37.2367	+	21.4986i	−1.51892	+	0.876948i	−0.999752	+	0.0222741i	$0.992909\pi$
$602$	−3.90807	+	6.32853i	−0.159281	+	0.257931i
$603$	−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	0.534000	−	0.845485i	$-0.320688\pi$
$607$	1.69476	+	0.978470i	0.0687882	+	0.0397149i	−0.465211	+	0.885200i	$0.654022\pi$
$608$	3.07646	+	5.32858i	0.124767	+	0.216103i
$609$	−18.7415	+	19.3963i	−0.759444	+	0.785979i
$610$	−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
$615$	−42.7087	−	9.32732i	−1.72218	−	0.376114i
$616$	−0.221481	+	7.47698i	−0.00892373	+	0.301256i
$617$	18.5603	+	10.7158i	0.747208	+	0.431401i	0.824684	−	0.565593i	$-0.191353\pi$
$617$	18.5603	+	10.7158i	0.747208	+	0.431401i	−0.0774759	+	0.996994i	$0.524686\pi$
$618$	−22.5610	−	4.92720i	−0.907538	−	0.198201i
$619$			4.27262i			0.171731i	0.996307	+	0.0858656i	$0.0273656\pi$
$619$			4.27262i			0.171731i	−0.996307	+	0.0858656i	$0.972634\pi$
$620$	22.5628	+	13.0267i	0.906145	+	0.523163i
$621$	26.8707	+	3.27972i	1.07828	+	0.131611i
$622$	21.2458	−	12.2663i	0.851879	−	0.491833i
$623$	0.200446	−	6.76685i	0.00803069	−	0.271108i
$624$	3.29710	+	5.30369i	0.131989	+	0.212318i
$625$	−28.2993			−1.13197
$626$	7.12198	+	12.3356i	0.284652	+	0.493031i
$627$	−20.2860	+	22.2787i	−0.810144	+	0.889724i
$628$	0.555344	+	0.320628i	0.0221606	+	0.0127944i
$629$	−0.0250784			−0.000999941
$630$	−1.54002	−	24.0488i	−0.0613559	−	0.958129i
$631$	−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
$633$	18.0285	+	3.93731i	0.716568	+	0.156494i
$634$	−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
$637$	−8.30280	+	23.8341i	−0.328969	+	0.944341i
$638$			16.6404i			0.658799i
$639$	−13.3826	+	29.1774i	−0.529409	+	1.15424i
$640$	−2.62932	+	1.51804i	−0.103933	+	0.0600057i
$641$	29.4525	+	17.0044i	1.16331	+	0.671635i	0.952094	−	0.305806i	$-0.0989258\pi$
$641$	29.4525	+	17.0044i	1.16331	+	0.671635i	0.211212	+	0.977440i	$0.432259\pi$
$642$	9.65828	+	30.2992i	0.381182	+	1.19581i
$643$	−36.5123	−	21.0804i	−1.43990	−	0.831329i	−0.442062	−	0.896984i	$-0.645753\pi$
$643$	−36.5123	−	21.0804i	−1.43990	−	0.831329i	−0.997842	+	0.0656552i	$0.979086\pi$
$644$	7.24212	−	11.7275i	0.285380	−	0.462128i
$645$	−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	$0.853854\pi$
$648$	1.67432	+	8.84289i	0.0657736	+	0.347381i
$649$			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	−0.572101	−	0.820183i	$-0.693871\pi$
$653$	−3.77819	+	2.18134i	−0.147852	+	0.0853624i	0.424249	+	0.905546i	$0.360538\pi$
$654$	2.46071	−	11.2673i	0.0962214	−	0.440587i
$655$	−53.5001			−2.09042
$656$	4.15653	−	7.19932i	0.162285	−	0.281086i
$657$	−22.6313	+	2.12366i	−0.882932	+	0.0828517i
$658$	−16.2169	−	0.480371i	−0.632199	−	0.0187268i
$659$	−31.7835	−	18.3502i	−1.23811	−	0.714823i	−0.269403	−	0.963028i	$-0.586826\pi$
$659$	−31.7835	−	18.3502i	−1.23811	−	0.714823i	−0.968708	+	0.248204i	$0.920160\pi$
$660$	−10.9931	−	10.0098i	−0.427906	−	0.389632i
$661$	−39.4869	+	22.7978i	−1.53586	+	0.886732i	−0.536790	+	0.843716i	$0.680363\pi$
$661$	−39.4869	+	22.7978i	−1.53586	+	0.886732i	−0.999074	+	0.0430156i	$0.986303\pi$
$662$		−	28.4574i		−	1.10603i
$663$	−1.36971	+	2.56175i	−0.0531951	+	0.0994901i
$664$			1.88916i			0.0733137i
$665$	−23.4341	−	43.5158i	−0.908735	−	1.68747i
$666$	−0.0674298	+	0.147013i	−0.00261285	+	0.00569665i
$667$	15.3311	−	26.5543i	0.593623	−	1.02818i
$668$	−7.61973			−0.294816
$669$	4.05209	−	18.5540i	0.156663	−	0.717340i
$670$	−8.99293	−	5.19207i	−0.347427	−	0.200587i
$671$	37.6778			1.45454
$672$	4.44614	+	1.10989i	0.171513	+	0.0428150i
$673$	−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	$0.732313\pi$
$678$	2.71709	−	2.98399i	0.104349	−	0.114600i
$679$	−10.2329	−	19.0020i	−0.392703	−	0.729228i
$680$	−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	0.164245	−	0.986420i	$-0.447481\pi$
$683$	−15.8870	−	9.17234i	−0.607898	−	0.350970i	−0.772142	+	0.635450i	$0.780815\pi$
$684$	10.6825	+	15.0536i	0.408456	+	0.575587i
$685$	−3.95567	−	2.28381i	−0.151139	−	0.0872599i
$686$	7.80059	+	16.7973i	0.297828	+	0.641326i
$687$	−8.26701	−	7.52758i	−0.315406	−	0.287195i
$688$	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	0.118691	−	0.992931i	$-0.462130\pi$
$691$	27.2842	−	15.7526i	1.03794	−	0.599255i	0.919249	+	0.393676i	$0.128797\pi$
$692$	−1.56798	−	2.71582i	−0.0596056	−	0.103240i
$693$	1.43411	+	22.3949i	0.0544772	+	0.850712i
$694$	−3.75865			−0.142677
$695$	28.7844	+	16.6187i	1.09185	+	0.630382i
$696$	9.95952	+	2.17510i	0.377515	+	0.0824469i
$697$	3.86692			0.146470
$698$	5.76679	−	9.98836i	0.218276	−	0.378065i
$699$	6.97018	+	6.34674i	0.263636	+	0.240056i
$700$	9.82504	−	5.29097i	0.371352	−	0.199980i
$701$			34.1901i			1.29134i	0.763616	+	0.645671i	$0.223422\pi$
$701$			34.1901i			1.29134i	−0.763616	+	0.645671i	$0.776578\pi$
$702$	11.3345	+	14.9174i	0.427795	+	0.563020i
$703$			0.331724i			0.0125112i
$704$	2.44849	−	1.41364i	0.0922809	−	0.0532784i
$705$	21.7104	−	23.8430i	0.817661	−	0.897979i
$706$	−1.97910	−	1.14263i	−0.0744843	−	0.0430035i
$707$	−0.0320383	+	1.08158i	−0.00120493	+	0.0406771i
$708$	18.3157	+	4.00003i	0.688345	+	0.150330i
$709$	−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
$711$	3.98256	+	42.4413i	0.149358	+	1.59167i
$712$	−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
$717$	31.8841	+	29.0323i	1.19073	+	1.08423i
$718$	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
$721$	−18.5342	+	30.0133i	−0.690250	+	1.11775i
$722$	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
$726$	−3.85041	−	3.50601i	−0.142902	−	0.130120i
$727$			39.6594i			1.47088i	0.677588	+	0.735442i	$0.263025\pi$
$727$			39.6594i			1.47088i	−0.677588	+	0.735442i	$0.736975\pi$
$728$	9.31361	−	2.06316i	0.345185	−	0.0764657i
$729$	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
$732$	4.92495	−	22.5508i	0.182031	−	0.833500i
$733$			25.2243i			0.931681i	0.884869	+	0.465840i	$0.154248\pi$
$733$			25.2243i			0.931681i	−0.884869	+	0.465840i	$0.845752\pi$
$734$	7.27540	−	12.6014i	0.268540	−	0.465125i
$735$	−35.4348	−	9.96898i	−1.30703	−	0.367711i
$736$	−5.20964			−0.192030
$737$	8.37445	+	4.83499i	0.308477	+	0.178099i
$738$	10.3972	−	22.6685i	0.382727	−	0.834438i
$739$	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
$741$	33.8854	+	18.1178i	1.24481	+	0.665574i
$742$	0.693146	−	23.3999i	0.0254462	−	0.859038i
$743$	23.6670	−	13.6642i	0.868258	−	0.501289i	0.00148913	−	0.999999i	$-0.499526\pi$
$743$	23.6670	−	13.6642i	0.868258	−	0.501289i	0.866769	+	0.498710i	$0.166193\pi$
$744$	−10.0069	+	10.9898i	−0.366869	+	0.402907i
$745$	40.9488	+	23.6418i	1.50025	+	0.866169i
$746$			13.7856i			0.504726i
$747$	0.529494	+	5.64270i	0.0193732	+	0.206456i
$748$	1.13895	+	0.657570i	0.0416440	+	0.0240432i
$749$	48.5560	+	1.43831i	1.77420	+	0.0525548i
$750$	0.877693	−	4.01885i	0.0320488	−	0.146748i
$751$	−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
$756$	13.5912	+	2.06895i	0.494305	+	0.0752470i
$757$	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
$763$	−14.9891	−	9.25625i	−0.542641	−	0.335099i
$764$	−1.91936	+	1.10814i	−0.0694401	+	0.0400913i
$765$	−3.85105	−	1.76634i	−0.139235	−	0.0638621i
$766$			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	−0.636531	−	0.771252i	$-0.719631\pi$
$769$	−7.95521	+	4.59295i	−0.286872	+	0.165626i	0.349658	+	0.936877i	$0.386298\pi$
$770$	−19.9956	+	10.7680i	−0.720590	+	0.388051i
$771$	−3.52637	−	0.770138i	−0.126999	−	0.0277359i
$772$	−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	$0.0765923\pi$
$774$	8.39697	−	0.787946i	0.301823	−	0.0283221i
$775$			36.1936i			1.30011i
$776$	−4.07863	+	7.06440i	−0.146414	+	0.253597i
$777$	0.177672	+	0.171674i	0.00637396	+	0.00615877i
$778$	12.8929	+	22.3312i	0.462234	+	0.800612i
$779$		−	51.1495i		−	1.83262i
$780$	−8.93998	+	16.7203i	−0.320103	+	0.598683i
$781$	30.2519			1.08250
$782$	−1.21166	−	2.09866i	−0.0433290	−	0.0750481i
$783$	30.3575	+	3.70531i	1.08489	+	0.132417i
$784$	3.85269	−	5.84438i	0.137596	−	0.208728i
$785$			1.94690i			0.0694879i
$786$	6.51217	−	29.8184i	0.232281	−	1.06359i
$787$	9.70952	+	5.60579i	0.346107	+	0.199825i	0.662969	−	0.748647i	$-0.269296\pi$
$787$	9.70952	+	5.60579i	0.346107	+	0.199825i	−0.316862	+	0.948472i	$0.602629\pi$
$788$			17.1772i			0.611912i
$789$	5.53967	−	25.3655i	0.197217	−	0.903035i
$790$	−37.3606	+	21.5701i	−1.32923	+	0.767431i
$791$	−2.92289	−	5.42764i	−0.103926	−	0.192985i
$792$	6.91713	−	4.90862i	0.245789	−	0.174420i
$793$	−11.7765	−	46.5841i	−0.418196	−	1.65425i
$794$	1.89700			0.0673221
$795$	34.4040	+	31.3268i	1.22018	+	1.11105i
$796$	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
$804$	3.98846	−	4.38025i	0.140662	−	0.154479i
$805$	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	−0.0866990	−	0.996235i	$-0.527632\pi$
$809$	20.8406	−	12.0323i	0.732716	−	0.423034i	0.819415	+	0.573201i	$0.194299\pi$
$810$	−20.7091	+	17.8262i	−0.727643	+	0.626347i
$811$			9.95856i			0.349692i	0.984596	+	0.174846i	$0.0559428\pi$
$811$			9.95856i			0.349692i	−0.984596	+	0.174846i	$0.944057\pi$
$812$	8.18189	−	13.2493i	0.287128	−	0.464960i
$813$	−1.06042	+	4.85552i	−0.0371904	+	0.170291i
$814$	0.152427			0.00534258
$815$	−5.04137	+	8.73190i	−0.176591	+	0.305865i
$816$	0.542440	−	0.595724i	0.0189892	−	0.0208545i
$817$	14.9802	−	8.64880i	0.524090	−	0.302583i
$818$	15.6082			0.545728
$819$	27.2404	−	8.77282i	0.951856	−	0.306547i
$820$	25.2391			0.881386
$821$	−46.0440	+	26.5835i	−1.60695	+	0.927770i	−0.616897	+	0.787044i	$0.711610\pi$
$821$	−46.0440	+	26.5835i	−1.60695	+	0.927770i	−0.990049	+	0.140726i	$0.955056\pi$
$822$	1.75438	−	1.92672i	0.0611912	−	0.0672020i
$823$	−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
$825$	4.40689	−	20.1786i	0.153428	−	0.702529i
$826$	15.0466	−	24.3656i	0.523537	−	0.847788i
$827$		−	47.9790i		−	1.66839i	−0.551468	−	0.834196i	$-0.685932\pi$
$827$		−	47.9790i		−	1.66839i	0.551468	−	0.834196i	$-0.314068\pi$
$828$	−15.5606	+	1.46016i	−0.540767	+	0.0507439i
$829$	38.8652	−	22.4388i	1.34984	−	0.779333i	0.361617	−	0.932327i	$-0.382225\pi$
$829$	38.8652	−	22.4388i	1.34984	−	0.779333i	0.988227	+	0.152994i	$0.0488915\pi$
$830$	−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
$834$	−12.7662	+	14.0202i	−0.442056	+	0.485480i
$835$	−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
$843$	−36.6476	−	33.3697i	−1.26221	−	1.14931i
$844$	−10.6541			−0.366729
$845$	−1.11966	+	39.4531i	−0.0385176	+	1.35723i
$846$	10.6463	+	15.0026i	0.366028	+	0.515800i
$847$	−7.00358	+	3.77156i	−0.240646	+	0.129592i
$848$	−7.66278	+	4.42411i	−0.263141	+	0.151925i
$849$	3.25078	−	14.8849i	0.111566	−	0.510849i
$850$		−	1.96194i		−	0.0672939i
$851$	−0.243239	−	0.140434i	−0.00833814	−	0.00481403i
$852$	3.95429	−	18.1062i	0.135472	−	0.620309i
$853$		−	3.96594i		−	0.135791i	−0.997692	−	0.0678956i	$-0.978372\pi$
$853$		−	3.96594i		−	0.135791i	0.997692	−	0.0678956i	$-0.0216285\pi$
$854$	−29.9996	−	18.5258i	−1.02657	−	0.633938i
$855$	−23.3642	+	50.9396i	−0.799037	+	1.74210i
$856$	−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	$0.629895\pi$
$858$	8.32514	−	15.5704i	0.284216	−	0.531565i
$859$		−	45.9665i		−	1.56836i	−0.620535	−	0.784179i	$-0.713084\pi$
$859$		−	45.9665i		−	1.56836i	0.620535	−	0.784179i	$-0.286916\pi$
$860$	4.26764	+	7.39176i	0.145525	+	0.252057i
$861$	−27.3959	−	26.4710i	−0.933648	−	0.902128i
$862$	1.72203	−	2.98264i	0.0586525	−	0.101589i
$863$		−	1.54791i		−	0.0526915i	−0.999653	−	0.0263458i	$-0.991613\pi$
$863$		−	1.54791i		−	0.0526915i	0.999653	−	0.0263458i	$-0.00838709\pi$
$864$	−2.03373	−	4.78162i	−0.0691890	−	0.162674i
$865$	4.76050	−	8.24543i	0.161862	−	0.280353i
$866$	28.1154			0.955401
$867$	−28.4007	−	6.20254i	−0.964538	−	0.210649i
$868$	10.7648	+	19.9896i	0.365380	+	0.678492i
$869$	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
$873$	−10.2024	+	22.2437i	−0.345298	+	0.752834i
$874$	−27.7600	+	16.0272i	−0.938996	+	0.542130i
$875$	−5.34634	−	3.30154i	−0.180739	−	0.111612i
$876$	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	$0.490451\pi$
$882$	9.86947	−	18.5363i	0.332322	−	0.624149i
$883$	−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	$-0.342309\pi$
$888$	0.0199241	−	0.0912301i	0.000668609	−	0.00306148i
$889$	−0.532121	+	17.9639i	−0.0178468	+	0.602488i
$890$	−6.72777	−	3.88428i	−0.225515	−	0.130201i
$891$	19.2848	−	16.6002i	0.646066	−	0.556127i
$892$			10.9647i			0.367124i
$893$	32.6753	+	18.8651i	1.09344	+	0.631297i
$894$	−18.1612	+	19.9452i	−0.607402	+	0.667068i
$895$	53.8008	−	31.0619i	1.79836	−	1.03828i
$896$	−2.64459	−	0.0783374i	−0.0883496	−	0.00261707i
$897$	−27.6303	+	17.1767i	−0.922550	+	0.573513i
$898$	−1.98663			−0.0662948
$899$	25.2532	+	43.7398i	0.842241	+	1.45880i
$900$	−11.5012	−	5.27518i	−0.383373	−	0.175839i
$901$	−3.56444	−	2.05793i	−0.118749	−	0.0685596i
$902$	−23.5033			−0.782573
$903$	3.12022	−	12.4994i	0.103835	−	0.415953i
$904$	−1.16500	+	2.01785i	−0.0387475	+	0.0671126i
$905$		−	62.8877i		−	2.09046i
$906$	−3.84746	+	17.6171i	−0.127823	+	0.585287i
$907$	−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
$910$	19.5631	+	21.3565i	0.648511	+	0.707961i
$911$			0.152718i			0.00505976i	0.999997	+	0.00252988i	$0.000805287\pi$
$911$			0.152718i			0.00505976i	−0.999997	+	0.00252988i	$0.999195\pi$
$912$	−7.87992	−	7.17511i	−0.260930	−	0.237591i
$913$	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
$917$	−39.6679	−	24.4963i	−1.30995	−	0.808938i
$918$	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
$921$	−20.3620	−	18.5407i	−0.670950	−	0.610938i
$922$		−	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
$927$	39.8230	−	3.73687i	1.30796	−	0.122735i
$928$	−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	$0.224784\pi$
$930$	−44.0865	−	9.62823i	−1.44565	−	0.315722i
$931$	2.54940	−	42.9949i	0.0835533	−	1.40910i
$932$	−4.71340	−	2.72128i	−0.154392	−	0.0891385i
$933$	−28.6081	+	31.4183i	−0.936588	+	1.02859i
$934$	−31.3625	+	18.1071i	−1.02621	+	0.592483i
$935$			3.99286i			0.130581i
$936$	−8.23093	−	7.01797i	−0.269036	−	0.229389i
$937$		−	24.6387i		−	0.804910i	−0.915440	−	0.402455i	$-0.868157\pi$
$937$		−	24.6387i		−	0.804910i	0.915440	−	0.402455i	$-0.131843\pi$
$938$	−4.29055	−	7.96731i	−0.140091	−	0.260142i
$939$	−18.2419	−	16.6103i	−0.595303	−	0.542057i
$940$	−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	$0.625094\pi$
$942$	−1.08511	−	0.236982i	−0.0353548	−	0.00772129i
$943$	37.5059	+	21.6540i	1.22136	+	0.705152i
$944$	−10.8238			−0.352285
$945$	15.1919	+	38.8762i	0.494194	+	1.26464i
$946$	−3.97413	−	6.88340i	−0.129210	−	0.223799i
$947$	−24.5958	+	14.2004i	−0.799257	+	0.461451i	−0.843211	−	0.537582i	$-0.819338\pi$
$947$	−24.5958	+	14.2004i	−0.799257	+	0.461451i	0.0439545	+	0.999034i	$0.486004\pi$
$948$	−7.47456	−	23.4486i	−0.242763	−	0.761576i
$949$	19.5895	−	19.0415i	0.635902	−	0.618112i
$950$	−25.9515			−0.841977
$951$	12.1868	+	11.0968i	0.395185	+	0.359838i
$952$	−0.583525	−	1.08357i	−0.0189121	−	0.0351188i
$953$	47.1399	+	27.2162i	1.52701	+	0.881621i	0.999485	+	0.0320819i	$0.0102137\pi$
$953$	47.1399	+	27.2162i	1.52701	+	0.881621i	0.527526	+	0.849539i	$0.323120\pi$
$954$	−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
$959$	−1.88726	−	3.50454i	−0.0609428	−	0.113168i
$960$	3.54046	−	3.88824i	0.114268	−	0.125492i
$961$	−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
$966$	−5.78214	+	23.1628i	−0.186037	+	0.745250i
$967$	−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
$969$	1.05772	−	4.84316i	0.0339788	−	0.155585i
$970$	−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	$-0.00551055\pi$
$972$	−7.41471	−	13.7121i	−0.237827	−	0.439816i
$973$	13.7331	+	25.5016i	0.440263	+	0.817544i
$974$		−	13.4306i		−	0.430346i
$975$	−26.3258	+	0.858407i	−0.843102	+	0.0274910i
$976$			13.3266i			0.426573i
$977$	27.5938	−	15.9313i	0.882803	−	0.509686i	0.0112213	−	0.999937i	$-0.496428\pi$
$977$	27.5938	−	15.9313i	0.882803	−	0.509686i	0.871582	+	0.490251i	$0.163095\pi$
$978$	−4.25311	−	3.87269i	−0.135999	−	0.123835i
$979$	6.26507	+	3.61714i	0.200233	+	0.115604i
$980$	21.2153	+	1.25797i	0.677697	+	0.0401844i
$981$	1.86624	+	19.8882i	0.0595846	+	0.634980i
$982$	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	$0.417072\pi$
$984$	−3.07216	+	14.0671i	−0.0979370	+	0.448442i
$985$	−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
$990$	23.4068	+	10.7359i	0.743916	+	0.341208i
$991$	−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
$994$	−24.0870	−	14.8745i	−0.763993	−	0.471791i
$995$	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	−0.469059	−	0.883167i	$-0.655407\pi$
$997$	−46.3662	−	26.7696i	−1.46843	−	0.847800i	−0.999374	+	0.0353669i	$0.988740\pi$
$998$	16.9113	−	9.76376i	0.535318	−	0.309066i
$999$	0.0339409	−	0.278078i	0.00107384	−	0.00879799i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-1.16613 + 1.28068i) q^{3} +(0.500000 - 0.866025i) q^{4} +3.03607 q^{5} +(-0.369559 + 1.69217i) q^{6} +(2.25111 + 1.39014i) q^{7} -1.00000i q^{8} +(-0.280280 - 2.98688i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(-1.16613 + 1.28068i) q^{3} +(0.500000 - 0.866025i) q^{4} +3.03607 q^{5} +(-0.369559 + 1.69217i) q^{6} +(2.25111 + 1.39014i) q^{7} -1.00000i q^{8} +(-0.280280 - 2.98688i) 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} +(-3.54046 + 3.88824i) 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} +(1.28068 + 1.16613i) q^{24} +4.21775 q^{25} +(3.46911 + 0.982495i) q^{26} +(4.15208 + 3.12414i) q^{27} +(2.32945 - 1.25445i) q^{28} +(5.09714 - 2.94283i) q^{29} +(-1.12201 + 5.13754i) q^{30} +8.58125i q^{31} +(-0.866025 - 0.500000i) q^{32} +(1.04484 - 4.78421i) q^{33} -0.465162i q^{34} +(6.83455 + 4.22056i) q^{35} +(-2.72685 - 1.25071i) q^{36} +(-0.0269566 - 0.0466902i) q^{37} -6.15292 q^{38} +(-6.24168 + 0.203523i) q^{39} -3.03607i q^{40} +(4.15653 + 7.19932i) q^{41} +(-3.18426 + 3.29552i) q^{42} +(-1.40564 + 2.43464i) q^{43} +2.82727i q^{44} +(-0.850950 - 9.06839i) q^{45} +(2.60482 - 4.51168i) q^{46} -6.13208 q^{47} +(1.69217 + 0.369559i) q^{48} +(3.13503 + 6.25872i) q^{49} +(3.65268 - 2.10887i) q^{50} +(0.244692 + 0.767629i) q^{51} +(3.49558 - 0.883688i) q^{52} -8.84822i q^{53} +(5.15787 + 0.629548i) q^{54} +(-7.43380 + 4.29190i) q^{55} +(1.39014 - 2.25111i) 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} +(3.52123 - 7.11343i) 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} +(-1.92527 + 8.81558i) q^{69} +(8.02918 + 0.237838i) q^{70} +(-9.26650 - 5.35002i) q^{71} +(-2.98688 + 0.280280i) q^{72} -7.57692i q^{73} +(-0.0466902 - 0.0269566i) q^{74} +(-4.91844 + 5.40158i) q^{75} +(-5.32858 + 3.07646i) q^{76} +(-7.47698 - 0.221481i) q^{77} +(-5.30369 + 3.29710i) q^{78} -14.2092 q^{79} +(-1.51804 - 2.62932i) q^{80} +(-8.84289 + 1.67432i) q^{81} +(7.19932 + 4.15653i) q^{82} -1.88916 q^{83} +(-1.10989 + 4.44614i) q^{84} +(0.706134 - 1.22306i) q^{85} +2.81129i q^{86} +(-2.17510 + 9.95952i) q^{87} +(1.41364 + 2.44849i) q^{88} +(-1.27938 - 2.21594i) q^{89} +(-5.27114 - 7.42798i) q^{90} +(2.06316 + 9.31361i) q^{91} -5.20964i q^{92} +(-10.9898 - 10.0069i) 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} +(5.84438 + 3.85269i) 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

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