LMFDB - Embedded newform 273.2.r.b.269.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(68,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 2]))

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

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

chi := DirichletCharacter("273.68");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.r (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:	$2.17991597518$
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			269.20
Character	$\chi$	$=$	273.269
Dual form			273.2.r.b.68.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.843135i q^{2} +(0.346738 + 1.69699i) q^{3} +1.28912 q^{4} +(-1.06280 - 1.84082i) q^{5} +(-1.43079 + 0.292347i) q^{6} +(2.34470 + 1.22572i) q^{7} +2.77318i q^{8} +(-2.75955 + 1.17682i) q^{9} +(1.55206 - 0.896082i) q^{10} +(-0.855509 + 0.493928i) q^{11} +(0.446987 + 2.18763i) q^{12} +(3.08300 + 1.86952i) q^{13} +(-1.03345 + 1.97690i) q^{14} +(2.75534 - 2.44184i) q^{15} +0.240083 q^{16} +1.84105 q^{17} +(-0.992218 - 2.32667i) q^{18} +(-6.19875 - 3.57885i) q^{19} +(-1.37008 - 2.37304i) q^{20} +(-1.26704 + 4.40393i) q^{21} +(-0.416448 - 0.721310i) q^{22} +1.62700i q^{23} +(-4.70605 + 0.961564i) q^{24} +(0.240923 - 0.417291i) q^{25} +(-1.57626 + 2.59939i) q^{26} +(-2.95389 - 4.27487i) q^{27} +(3.02260 + 1.58010i) q^{28} +(-0.488355 - 0.281952i) q^{29} +(2.05880 + 2.32312i) q^{30} +(-4.23375 - 2.44435i) q^{31} +5.74877i q^{32} +(-1.13483 - 1.28053i) q^{33} +1.55226i q^{34} +(-0.235611 - 5.61886i) q^{35} +(-3.55739 + 1.51707i) q^{36} +3.29157 q^{37} +(3.01745 - 5.22638i) q^{38} +(-2.10357 + 5.88005i) q^{39} +(5.10491 - 2.94732i) q^{40} +(4.93559 - 8.54870i) q^{41} +(-3.71311 - 1.06828i) q^{42} +(-0.214038 - 0.370726i) q^{43} +(-1.10286 + 0.636734i) q^{44} +(5.09915 + 3.82910i) q^{45} -1.37179 q^{46} +(-6.40449 - 11.0929i) q^{47} +(0.0832459 + 0.407419i) q^{48} +(3.99522 + 5.74789i) q^{49} +(0.351833 + 0.203131i) q^{50} +(0.638362 + 3.12424i) q^{51} +(3.97436 + 2.41004i) q^{52} +(6.59657 + 3.80853i) q^{53} +(3.60430 - 2.49053i) q^{54} +(1.81847 + 1.04989i) q^{55} +(-3.39914 + 6.50226i) q^{56} +(3.92393 - 11.7601i) q^{57} +(0.237723 - 0.411749i) q^{58} +11.9264 q^{59} +(3.55197 - 3.14783i) q^{60} +(1.92009 + 1.10857i) q^{61} +(2.06092 - 3.56962i) q^{62} +(-7.91276 - 0.623142i) q^{63} -4.36683 q^{64} +(0.164850 - 7.66217i) q^{65} +(1.07966 - 0.956814i) q^{66} +(1.22692 + 2.12509i) q^{67} +2.37334 q^{68} +(-2.76101 + 0.564144i) q^{69} +(4.73746 - 0.198652i) q^{70} +(-2.48976 + 1.43746i) q^{71} +(-3.26353 - 7.65271i) q^{72} +(-8.31343 - 4.79976i) q^{73} +2.77524i q^{74} +(0.791675 + 0.264153i) q^{75} +(-7.99095 - 4.61358i) q^{76} +(-2.61133 + 0.109499i) q^{77} +(-4.95768 - 1.77359i) q^{78} +(-7.27556 - 12.6016i) q^{79} +(-0.255160 - 0.441950i) q^{80} +(6.23019 - 6.49498i) q^{81} +(7.20771 + 4.16137i) q^{82} -14.4620 q^{83} +(-1.63337 + 5.67721i) q^{84} +(-1.95666 - 3.38904i) q^{85} +(0.312572 - 0.180463i) q^{86} +(0.309138 - 0.926496i) q^{87} +(-1.36975 - 2.37248i) q^{88} +5.18724 q^{89} +(-3.22845 + 4.29927i) q^{90} +(4.93719 + 8.16236i) q^{91} +2.09741i q^{92} +(2.68004 - 8.03217i) q^{93} +(9.35281 - 5.39985i) q^{94} +15.2144i q^{95} +(-9.75561 + 1.99332i) q^{96} +(-0.172790 + 0.0997601i) q^{97} +(-4.84625 + 3.36851i) q^{98} +(1.77955 - 2.36980i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 64 q^{4} + 12 q^{6} - 10 q^{7} - 4 q^{9} - 6 q^{10} + 6 q^{12} + 12 q^{13} - 9 q^{15} + 32 q^{16} + 2 q^{18} - 36 q^{19} + 10 q^{21} + 10 q^{22} - 18 q^{24} - 24 q^{25} - 14 q^{28} + 8 q^{30} - 24 q^{31}+ \cdots + 22 q^{99}+O(q^{100}) $ 64 * q - 64 * q^4 + 12 * q^6 - 10 * q^7 - 4 * q^9 - 6 * q^10 + 6 * q^12 + 12 * q^13 - 9 * q^15 + 32 * q^16 + 2 * q^18 - 36 * q^19 + 10 * q^21 + 10 * q^22 - 18 * q^24 - 24 * q^25 - 14 * q^28 + 8 * q^30 - 24 * q^31 - 45 * q^33 + 33 * q^39 + 90 * q^40 + 3 * q^42 - 20 * q^43 - 6 * q^48 - 6 * q^49 - 10 * q^51 - 48 * q^52 - 18 * q^55 + 4 * q^57 + 30 * q^58 + 55 * q^60 - 18 * q^61 + 31 * q^63 - 84 * q^64 + 75 * q^66 + 44 * q^67 + 33 * q^69 + 20 * q^70 + 17 * q^72 + 84 * q^73 - 18 * q^76 - 71 * q^78 + 20 * q^79 + 16 * q^81 - 18 * q^82 - 135 * q^84 - 2 * q^85 - 46 * q^88 - 10 * q^91 - 56 * q^93 + 36 * q^94 + 30 * q^96 - 24 * q^97 + 22 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$			0.843135i			0.596187i	0.954537	+	0.298093i	$0.0963507\pi$
$2$			0.843135i			0.596187i	−0.954537	+	0.298093i	$0.903649\pi$
$3$	0.346738	+	1.69699i	0.200189	+	0.979757i
$3$	0.346738	+	1.69699i	0.200189	+	0.979757i
$4$	1.28912			0.644561
$5$	−1.06280	−	1.84082i	−0.475297	−	0.823239i	0.524302	−	0.851532i	$-0.324326\pi$
$5$	−1.06280	−	1.84082i	−0.475297	−	0.823239i	−0.999600	+	0.0282929i	$0.990993\pi$
$6$	−1.43079	+	0.292347i	−0.584118	+	0.119350i
$7$	2.34470	+	1.22572i	0.886213	+	0.463278i
$7$	2.34470	+	1.22572i	0.886213	+	0.463278i
$8$			2.77318i			0.980466i
$9$	−2.75955	+	1.17682i	−0.919849	+	0.392273i
$10$	1.55206	−	0.896082i	0.490804	−	0.283366i
$11$	−0.855509	+	0.493928i	−0.257946	+	0.148925i	−0.623397	−	0.781905i	$-0.714248\pi$
$11$	−0.855509	+	0.493928i	−0.257946	+	0.148925i	0.365451	+	0.930830i	$0.380915\pi$
$12$	0.446987	+	2.18763i	0.129034	+	0.631514i
$13$	3.08300	+	1.86952i	0.855070	+	0.518512i
$13$	3.08300	+	1.86952i	0.855070	+	0.518512i
$14$	−1.03345	+	1.97690i	−0.276200	+	0.528348i
$15$	2.75534	−	2.44184i	0.711425	−	0.630480i
$16$	0.240083			0.0600208
$17$	1.84105			0.446520			0.223260	−	0.974759i	$-0.428330\pi$
$17$	1.84105			0.446520			0.223260	+	0.974759i	$0.428330\pi$
$18$	−0.992218	−	2.32667i	−0.233868	−	0.548402i
$19$	−6.19875	−	3.57885i	−1.42209	−	0.821044i	−0.425613	−	0.904905i	$-0.639942\pi$
$19$	−6.19875	−	3.57885i	−1.42209	−	0.821044i	−0.996477	+	0.0838608i	$0.973275\pi$
$20$	−1.37008	−	2.37304i	−0.306358	−	0.530628i
$21$	−1.26704	+	4.40393i	−0.276490	+	0.961017i
$22$	−0.416448	−	0.721310i	−0.0887871	−	0.153784i
$23$			1.62700i			0.339254i	0.985508	+	0.169627i	$0.0542563\pi$
$23$			1.62700i			0.339254i	−0.985508	+	0.169627i	$0.945744\pi$
$24$	−4.70605	+	0.961564i	−0.960618	+	0.196278i
$25$	0.240923	−	0.417291i	0.0481846	−	0.0834582i
$26$	−1.57626	+	2.59939i	−0.309130	+	0.509781i
$27$	−2.95389	−	4.27487i	−0.568476	−	0.822700i
$28$	3.02260	+	1.58010i	0.571219	+	0.298611i
$29$	−0.488355	−	0.281952i	−0.0906852	−	0.0523571i	0.453972	−	0.891016i	$-0.350007\pi$
$29$	−0.488355	−	0.281952i	−0.0906852	−	0.0523571i	−0.544657	+	0.838659i	$0.683340\pi$
$30$	2.05880	+	2.32312i	0.375884	+	0.424142i
$31$	−4.23375	−	2.44435i	−0.760403	−	0.439019i	0.0690374	−	0.997614i	$-0.478007\pi$
$31$	−4.23375	−	2.44435i	−0.760403	−	0.439019i	−0.829440	+	0.558595i	$0.811341\pi$
$32$			5.74877i			1.01625i
$33$	−1.13483	−	1.28053i	−0.197548	−	0.222911i
$34$			1.55226i			0.266210i
$35$	−0.235611	−	5.61886i	−0.0398256	−	0.949760i
$36$	−3.55739	+	1.51707i	−0.592899	+	0.252844i
$37$	3.29157			0.541130			0.270565	−	0.962702i	$-0.412789\pi$
$37$	3.29157			0.541130			0.270565	+	0.962702i	$0.412789\pi$
$38$	3.01745	−	5.22638i	0.489496	−	0.847831i
$39$	−2.10357	+	5.88005i	−0.336841	+	0.941562i
$40$	5.10491	−	2.94732i	0.807158	−	0.466013i
$41$	4.93559	−	8.54870i	0.770810	−	1.33508i	−0.166310	−	0.986074i	$-0.553185\pi$
$41$	4.93559	−	8.54870i	0.770810	−	1.33508i	0.937120	−	0.349008i	$-0.113482\pi$
$42$	−3.71311	−	1.06828i	−0.572945	−	0.164840i
$43$	−0.214038	−	0.370726i	−0.0326406	−	0.0565351i	0.849244	−	0.528001i	$-0.177058\pi$
$43$	−0.214038	−	0.370726i	−0.0326406	−	0.0565351i	−0.881884	+	0.471466i	$0.843725\pi$
$44$	−1.10286	+	0.636734i	−0.166262	+	0.0959913i
$45$	5.09915	+	3.82910i	0.760137	+	0.570809i
$46$	−1.37179			−0.202259
$47$	−6.40449	−	11.0929i	−0.934190	−	1.61807i	−0.776071	−	0.630645i	$-0.782790\pi$
$47$	−6.40449	−	11.0929i	−0.934190	−	1.61807i	−0.158119	−	0.987420i	$-0.550543\pi$
$48$	0.0832459	+	0.407419i	0.0120155	+	0.0588059i
$49$	3.99522	+	5.74789i	0.570746	+	0.821127i
$50$	0.351833	+	0.203131i	0.0497567	+	0.0287270i
$51$	0.638362	+	3.12424i	0.0893885	+	0.437482i
$52$	3.97436	+	2.41004i	0.551145	+	0.334213i
$53$	6.59657	+	3.80853i	0.906109	+	0.523142i	0.879177	−	0.476495i	$-0.158093\pi$
$53$	6.59657	+	3.80853i	0.906109	+	0.523142i	0.0269320	+	0.999637i	$0.491426\pi$
$54$	3.60430	−	2.49053i	0.490483	−	0.338918i
$55$	1.81847	+	1.04989i	0.245202	+	0.141567i
$56$	−3.39914	+	6.50226i	−0.454229	+	0.868901i
$57$	3.92393	−	11.7601i	0.519737	−	1.55767i
$58$	0.237723	−	0.411749i	0.0312146	−	0.0540653i
$59$	11.9264			1.55268			0.776342	−	0.630312i	$-0.217073\pi$
$59$	11.9264			1.55268			0.776342	+	0.630312i	$0.217073\pi$
$60$	3.55197	−	3.14783i	0.458557	−	0.406383i
$61$	1.92009	+	1.10857i	0.245843	+	0.141937i	0.617859	−	0.786289i	$-0.288000\pi$
$61$	1.92009	+	1.10857i	0.245843	+	0.141937i	−0.372016	+	0.928226i	$0.621333\pi$
$62$	2.06092	−	3.56962i	0.261737	−	0.453342i
$63$	−7.91276	−	0.623142i	−0.996913	−	0.0785085i
$64$	−4.36683			−0.545853
$65$	0.164850	−	7.66217i	0.0204471	−	0.950375i
$66$	1.07966	−	0.956814i	0.132897	−	0.117776i
$67$	1.22692	+	2.12509i	0.149892	+	0.259621i	0.931188	−	0.364540i	$-0.118774\pi$
$67$	1.22692	+	2.12509i	0.149892	+	0.259621i	−0.781295	+	0.624162i	$0.785441\pi$
$68$	2.37334			0.287810
$69$	−2.76101	+	0.564144i	−0.332387	+	0.0679149i
$70$	4.73746	−	0.198652i	0.566234	−	0.0237435i
$71$	−2.48976	+	1.43746i	−0.295480	+	0.170596i	−0.640411	−	0.768033i	$-0.721236\pi$
$71$	−2.48976	+	1.43746i	−0.295480	+	0.170596i	0.344930	+	0.938628i	$0.387903\pi$
$72$	−3.26353	−	7.65271i	−0.384611	−	0.901880i
$73$	−8.31343	−	4.79976i	−0.973013	−	0.561769i	−0.0728598	−	0.997342i	$-0.523213\pi$
$73$	−8.31343	−	4.79976i	−0.973013	−	0.561769i	−0.900154	+	0.435573i	$0.856546\pi$
$74$			2.77524i			0.322615i
$75$	0.791675	+	0.264153i	0.0914148	+	0.0305018i
$76$	−7.99095	−	4.61358i	−0.916625	−	0.529214i
$77$	−2.61133	+	0.109499i	−0.297588	+	0.0124785i
$78$	−4.95768	−	1.77359i	−0.561347	−	0.200820i
$79$	−7.27556	−	12.6016i	−0.818565	−	1.41780i	−0.906740	−	0.421691i	$-0.861437\pi$
$79$	−7.27556	−	12.6016i	−0.818565	−	1.41780i	0.0881750	−	0.996105i	$-0.471897\pi$
$80$	−0.255160	−	0.441950i	−0.0285278	−	0.0494115i
$81$	6.23019	−	6.49498i	0.692243	−	0.721664i
$82$	7.20771	+	4.16137i	0.795958	+	0.459547i
$83$	−14.4620			−1.58741			−0.793707	−	0.608301i	$-0.791851\pi$
$83$	−14.4620			−1.58741			−0.793707	+	0.608301i	$0.791851\pi$
$84$	−1.63337	+	5.67721i	−0.178215	+	0.619434i
$85$	−1.95666	−	3.38904i	−0.212230	−	0.367593i
$86$	0.312572	−	0.180463i	0.0337055	−	0.0194599i
$87$	0.309138	−	0.926496i	0.0331431	−	0.0993308i
$88$	−1.36975	−	2.37248i	−0.146016	−	0.252907i
$89$	5.18724			0.549846			0.274923	−	0.961466i	$-0.411348\pi$
$89$	5.18724			0.549846			0.274923	+	0.961466i	$0.411348\pi$
$90$	−3.22845	+	4.29927i	−0.340309	+	0.453183i
$91$	4.93719	+	8.16236i	0.517558	+	0.855648i
$92$			2.09741i			0.218670i
$93$	2.68004	−	8.03217i	0.277908	−	0.832897i
$94$	9.35281	−	5.39985i	0.964669	−	0.556952i
$95$			15.2144i			1.56096i
$96$	−9.75561	+	1.99332i	−0.995678	+	0.203442i
$97$	−0.172790	+	0.0997601i	−0.0175441	+	0.0101291i	−0.508746	−	0.860916i	$-0.669891\pi$
$97$	−0.172790	+	0.0997601i	−0.0175441	+	0.0101291i	0.491202	+	0.871046i	$0.336558\pi$
$98$	−4.84625	+	3.36851i	−0.489545	+	0.340271i
$99$	1.77955	−	2.36980i	0.178852	−	0.238174i
$100$	0.310579	−	0.537939i	0.0310579	−	0.0537939i
$101$	3.00678	+	5.20790i	0.299186	+	0.518205i	0.975950	−	0.217995i	$-0.0699516\pi$
$101$	3.00678	+	5.20790i	0.299186	+	0.518205i	−0.676764	+	0.736200i	$0.736618\pi$
$102$	−2.63416	+	0.538225i	−0.260821	+	0.0532922i
$103$	8.42274	−	4.86287i	0.829917	−	0.479153i	−0.0239072	−	0.999714i	$-0.507611\pi$
$103$	8.42274	−	4.86287i	0.829917	−	0.479153i	0.853824	+	0.520561i	$0.174277\pi$
$104$	−5.18451	+	8.54970i	−0.508384	+	0.838367i
$105$	9.45345	−	2.34810i	0.922562	−	0.229151i
$106$	−3.21111	+	5.56181i	−0.311891	+	0.540210i
$107$		−	0.614704i		−	0.0594257i	−0.999558	−	0.0297128i	$-0.990541\pi$
$107$		−	0.614704i		−	0.0594257i	0.999558	−	0.0297128i	$-0.00945928\pi$
$108$	−3.80793	−	5.51084i	−0.366418	−	0.530280i
$109$	−5.78829	+	10.0256i	−0.554418	+	0.960280i	0.443531	+	0.896259i	$0.353726\pi$
$109$	−5.78829	+	10.0256i	−0.554418	+	0.960280i	−0.997949	+	0.0640208i	$0.979608\pi$
$110$	−0.885200	+	1.53321i	−0.0844005	+	0.146186i
$111$	1.14131	+	5.58575i	0.108328	+	0.530176i
$112$	0.562923	+	0.294275i	0.0531912	+	0.0278064i
$113$	6.10760	−	3.52622i	0.574554	−	0.331719i	−0.184412	−	0.982849i	$-0.559038\pi$
$113$	6.10760	−	3.52622i	0.574554	−	0.331719i	0.758966	+	0.651130i	$0.225705\pi$
$114$	9.91538	+	3.30840i	0.928661	+	0.309860i
$115$	2.99502	−	1.72918i	0.279287	−	0.161247i
$116$	−0.629549	−	0.363470i	−0.0584522	−	0.0337474i
$117$	−10.7078	−	1.53090i	−0.989934	−	0.141532i
$118$			10.0556i			0.925690i
$119$	4.31671	+	2.25661i	0.395712	+	0.206863i
$120$	6.77164	+	7.64104i	0.618164	+	0.697528i
$121$	−5.01207	+	8.68116i	−0.455643	+	0.789196i
$122$	−0.934672	+	1.61890i	−0.0846212	+	0.146568i
$123$	16.2184	+	5.41149i	1.46236	+	0.487938i
$124$	−5.45782	−	3.15107i	−0.490127	−	0.282975i
$125$	−11.6522			−1.04220
$126$	0.525393	−	6.67152i	0.0468057	−	0.594347i
$127$	−5.43519	+	9.41402i	−0.482295	+	0.835359i	−0.999793	−	0.0203250i	$-0.993530\pi$
$127$	−5.43519	+	9.41402i	−0.482295	+	0.835359i	0.517499	+	0.855684i	$0.326863\pi$
$128$			7.81572i			0.690819i
$129$	0.554902	−	0.491766i	0.0488564	−	0.0432975i
$130$	6.46024	+	0.138990i	0.566601	+	0.0121903i
$131$	8.66948	+	15.0160i	0.757456	+	1.31195i	0.944144	+	0.329533i	$0.106891\pi$
$131$	8.66948	+	15.0160i	0.757456	+	1.31195i	−0.186688	+	0.982419i	$0.559775\pi$
$132$	−1.46293	−	1.65076i	−0.127332	−	0.143680i
$133$	−10.1475	−	15.9893i	−0.879903	−	1.38644i
$134$	−1.79174	+	1.03446i	−0.154783	+	0.0893639i
$135$	−4.72988	+	9.98090i	−0.407083	+	0.859019i
$136$			5.10556i			0.437798i
$137$		−	12.7597i		−	1.09014i	−0.838392	−	0.545068i	$-0.816504\pi$
$137$		−	12.7597i		−	1.09014i	0.838392	−	0.545068i	$-0.183496\pi$
$138$	−0.475650	−	2.32791i	−0.0404900	−	0.198164i
$139$	−13.6009	+	7.85246i	−1.15361	+	0.666037i	−0.949764	−	0.312966i	$-0.898678\pi$
$139$	−13.6009	+	7.85246i	−1.15361	+	0.666037i	−0.203846	+	0.979003i	$0.565344\pi$
$140$	−0.303732	−	7.24340i	−0.0256700	−	0.612179i
$141$	16.6039	−	14.7147i	1.39830	−	1.23920i
$142$	−1.21198	−	2.09921i	−0.101707	−	0.176161i
$143$	−3.56094	−	0.0766127i	−0.297781	−	0.00640668i
$144$	−0.662521	+	0.282535i	−0.0552101	+	0.0235446i
$145$			1.19863i			0.0995408i
$146$	4.04685	−	7.00935i	0.334920	−	0.580098i
$147$	−8.36881	+	8.77286i	−0.690248	+	0.723573i
$148$	4.24323			0.348792
$149$	−6.51483	−	3.76134i	−0.533715	−	0.308141i	0.208813	−	0.977956i	$-0.433040\pi$
$149$	−6.51483	−	3.76134i	−0.533715	−	0.308141i	−0.742528	+	0.669815i	$0.766373\pi$
$150$	−0.222717	+	0.667490i	−0.0181848	+	0.0545003i
$151$	1.77190	−	3.06902i	0.144195	−	0.249753i	−0.784877	−	0.619651i	$-0.787274\pi$
$151$	1.77190	−	3.06902i	0.144195	−	0.249753i	0.929072	+	0.369898i	$0.120607\pi$
$152$	9.92478	−	17.1902i	0.805006	−	1.39431i
$153$	−5.08047	+	2.16659i	−0.410731	+	0.175158i
$154$	−0.0923223	−	2.20170i	−0.00743954	−	0.177418i
$155$			10.3914i			0.834658i
$156$	−2.71176	+	7.58011i	−0.217114	+	0.606894i
$157$	−12.7221	−	7.34511i	−1.01533	−	0.586204i	−0.102585	−	0.994724i	$-0.532711\pi$
$157$	−12.7221	−	7.34511i	−1.01533	−	0.586204i	−0.912749	+	0.408521i	$0.866045\pi$
$158$	10.6249	−	6.13428i	0.845271	−	0.488017i
$159$	−4.17576	+	12.5149i	−0.331159	+	0.992495i
$160$	10.5825	−	6.10978i	0.836616	−	0.483021i
$161$	−1.99425	+	3.81484i	−0.157169	+	0.300651i
$162$	5.47615	+	5.25289i	0.430247	+	0.412706i
$163$	−0.446786	+	0.773855i	−0.0349949	+	0.0606130i	−0.882992	−	0.469387i	$-0.844475\pi$
$163$	−0.446786	+	0.773855i	−0.0349949	+	0.0606130i	0.847997	+	0.530000i	$0.177808\pi$
$164$	6.36258	−	11.0203i	0.496834	−	0.860542i
$165$	−1.15112	+	3.44995i	−0.0896149	+	0.268578i
$166$		−	12.1934i		−	0.946395i
$167$	−2.80871	+	4.86483i	−0.217345	+	0.376452i	−0.953995	−	0.299821i	$-0.903073\pi$
$167$	−2.80871	+	4.86483i	−0.217345	+	0.376452i	0.736651	+	0.676274i	$0.236406\pi$
$168$	−12.2129	−	3.51372i	−0.942244	−	0.271089i
$169$	6.00977	+	11.5275i	0.462290	+	0.886729i
$170$	2.85742	−	1.64973i	0.219154	−	0.126529i
$171$	21.3174	+	2.58119i	1.63018	+	0.197388i
$172$	−0.275922	−	0.477911i	−0.0210388	−	0.0364404i
$173$	−7.20865	+	12.4858i	−0.548064	+	0.949274i	0.450343	+	0.892855i	$0.351302\pi$
$173$	−7.20865	+	12.4858i	−0.548064	+	0.949274i	−0.998407	+	0.0564189i	$0.982032\pi$
$174$	0.781161	+	0.260645i	0.0592197	+	0.0197595i
$175$	1.07637	−	0.683117i	0.0813662	−	0.0516388i
$176$	−0.205393	+	0.118584i	−0.0154821	+	0.00893860i
$177$	4.13533	+	20.2390i	0.310830	+	1.52125i
$178$			4.37355i			0.327811i
$179$	−19.3121	+	11.1499i	−1.44346	+	0.833380i	−0.998079	−	0.0619621i	$-0.980264\pi$
$179$	−19.3121	+	11.1499i	−1.44346	+	0.833380i	−0.445378	+	0.895342i	$0.646931\pi$
$180$	6.57343	+	4.93619i	0.489955	+	0.367922i
$181$		−	6.26949i		−	0.466007i	−0.972476	−	0.233004i	$-0.925145\pi$
$181$		−	6.26949i		−	0.466007i	0.972476	−	0.233004i	$-0.0748554\pi$
$182$	−6.88197	+	4.16272i	−0.510126	+	0.308561i
$183$	−1.21546	+	3.64276i	−0.0898492	+	0.269281i
$184$	−4.51197			−0.332627
$185$	−3.49827	−	6.05918i	−0.257198	−	0.445480i
$186$	6.77221	+	2.25964i	0.496562	+	0.165685i
$187$	−1.57504	+	0.909347i	−0.115178	+	0.0664980i
$188$	−8.25617	−	14.3001i	−0.602143	−	1.04294i
$189$	−1.68618	−	13.6439i	−0.122652	−	0.992450i
$190$	−12.8278			−0.930624
$191$	4.27245	+	2.46670i	0.309143	+	0.178484i	0.646543	−	0.762877i	$-0.276214\pi$
$191$	4.27245	+	2.46670i	0.309143	+	0.178484i	−0.337400	+	0.941361i	$0.609547\pi$
$192$	−1.51414	−	7.41046i	−0.109274	−	0.534804i
$193$	2.69080	+	4.66060i	0.193688	+	0.335477i	0.946470	−	0.322793i	$-0.104622\pi$
$193$	2.69080	+	4.66060i	0.193688	+	0.335477i	−0.752782	+	0.658270i	$0.771288\pi$
$194$	−0.0841113	−	0.145685i	−0.00603884	−	0.0104596i
$195$	13.0598	−	2.37701i	0.935230	−	0.170221i
$196$	5.15033	+	7.40973i	0.367881	+	0.529267i
$197$	−1.73936	−	1.00422i	−0.123924	−	0.0715477i	0.436756	−	0.899580i	$-0.356127\pi$
$197$	−1.73936	−	1.00422i	−0.123924	−	0.0715477i	−0.560681	+	0.828032i	$0.689460\pi$
$198$	1.99806	+	1.50040i	0.141996	+	0.106629i
$199$		−	1.88370i		−	0.133532i	−0.997769	−	0.0667659i	$-0.978732\pi$
$199$		−	1.88370i		−	0.133532i	0.997769	−	0.0667659i	$-0.0212681\pi$
$200$	1.15722	+	0.668122i	0.0818279	+	0.0472434i
$201$	−3.18084	+	2.81892i	−0.224359	+	0.198832i
$202$	−4.39096	+	2.53512i	−0.308947	+	0.178371i
$203$	−0.799451	−	1.25968i	−0.0561104	−	0.0884120i
$204$	0.822926	+	4.02753i	0.0576164	+	0.281984i
$205$	−20.9821			−1.46546
$206$	4.10006	+	7.10151i	0.285665	+	0.494786i
$207$	−1.91469	−	4.48980i	−0.133080	−	0.312062i
$208$	0.740177	+	0.448841i	0.0513220	+	0.0311215i
$209$	7.07078			0.489096
$210$	1.97977	+	7.97054i	0.136617	+	0.550019i
$211$	3.68771	−	6.38731i	0.253873	−	0.439720i	−0.710716	−	0.703479i	$-0.751629\pi$
$211$	3.68771	−	6.38731i	0.253873	−	0.439720i	0.964589	+	0.263759i	$0.0849623\pi$
$212$	8.50380	+	4.90967i	0.584043	+	0.337197i
$213$	−3.30266	−	3.72668i	−0.226294	−	0.255348i
$214$	0.518279			0.0354288
$215$	−0.454959	+	0.788012i	−0.0310280	+	0.0537420i
$216$	11.8550	−	8.19165i	0.806629	−	0.557371i
$217$	−6.93076	−	10.9207i	−0.470491	−	0.741343i
$218$	−8.45295	−	4.88031i	−0.572506	−	0.330537i
$219$	5.26256	−	15.7721i	0.355611	−	1.06578i
$220$	2.34422	+	1.35344i	0.158048	+	0.0912488i
$221$	5.67596	+	3.44189i	0.381806	+	0.231526i
$222$	−4.70955	+	0.962279i	−0.316084	+	0.0645839i
$223$	−1.19481	−	0.689825i	−0.0800106	−	0.0461941i	0.459461	−	0.888198i	$-0.348043\pi$
$223$	−1.19481	−	0.689825i	−0.0800106	−	0.0461941i	−0.539472	+	0.842004i	$0.681376\pi$
$224$	−7.04639	+	13.4791i	−0.470806	+	0.900613i
$225$	−0.173762	+	1.43506i	−0.0115841	+	0.0956705i
$226$	2.97308	+	5.14953i	0.197767	+	0.342542i
$227$	2.98238			0.197947			0.0989736	−	0.995090i	$-0.468444\pi$
$227$	2.98238			0.197947			0.0989736	+	0.995090i	$0.468444\pi$
$228$	5.05843	−	15.1603i	0.335003	−	1.00401i
$229$	10.3410	−	5.97040i	0.683355	−	0.394535i	−0.117763	−	0.993042i	$-0.537572\pi$
$229$	10.3410	−	5.97040i	0.683355	−	0.394535i	0.801118	+	0.598506i	$0.204239\pi$
$230$	1.45793	+	2.52521i	0.0961331	+	0.166507i
$231$	−1.09126	−	4.39343i	−0.0717999	−	0.289066i
$232$	0.781902	−	1.35429i	0.0513343	−	0.0889137i
$233$	14.3523	−	8.28630i	0.940250	−	0.542854i	0.0502115	−	0.998739i	$-0.484010\pi$
$233$	14.3523	−	8.28630i	0.940250	−	0.542854i	0.890039	+	0.455885i	$0.150677\pi$
$234$	1.29076	−	9.02810i	0.0843793	−	0.590185i
$235$	−13.6133	+	23.5790i	−0.888037	+	1.53812i
$236$	15.3746			1.00080
$237$	18.8621	−	16.7160i	1.22523	−	1.08582i
$238$	−1.90263	+	3.63957i	−0.123329	+	0.235918i
$239$		−	29.6350i		−	1.91693i	−0.285211	−	0.958465i	$-0.592064\pi$
$239$		−	29.6350i		−	1.91693i	0.285211	−	0.958465i	$-0.407936\pi$
$240$	0.661511	−	0.586245i	0.0427004	−	0.0378419i
$241$			18.1245i			1.16750i	0.811933	+	0.583750i	$0.198415\pi$
$241$			18.1245i			1.16750i	−0.811933	+	0.583750i	$0.801585\pi$
$242$	−7.31939	−	4.22585i	−0.470508	−	0.271648i
$243$	13.1821	+	8.32051i	0.845635	+	0.533761i
$244$	2.47524	+	1.42908i	0.158461	+	0.0914874i
$245$	6.33471	−	13.4633i	0.404710	−	0.860140i
$246$	−4.56262	+	13.6743i	−0.290902	+	0.871842i
$247$	−12.4200	−	22.6223i	−0.790266	−	1.43942i
$248$	6.77862	−	11.7409i	0.430443	−	0.745549i
$249$	−5.01453	−	24.5419i	−0.317783	−	1.55528i
$250$		−	9.82437i		−	0.621348i
$251$	3.79901	+	6.58007i	0.239791	+	0.415330i	0.960654	−	0.277747i	$-0.0895877\pi$
$251$	3.79901	+	6.58007i	0.239791	+	0.415330i	−0.720863	+	0.693077i	$0.756254\pi$
$252$	−10.2005	−	0.803307i	−0.642572	−	0.0506036i
$253$	−0.803624	−	1.39192i	−0.0505234	−	0.0875091i
$254$	−7.93729	−	4.58260i	−0.498030	−	0.287538i
$255$	5.07272	−	4.49555i	0.317666	−	0.281522i
$256$	−15.3234			−0.957710
$257$	−23.7009			−1.47842			−0.739212	−	0.673473i	$-0.764802\pi$
$257$	−23.7009			−1.47842			−0.739212	+	0.673473i	$0.764802\pi$
$258$	0.414625	+	0.467858i	0.0258134	+	0.0291275i
$259$	7.71773	+	4.03454i	0.479556	+	0.250694i
$260$	0.212511	−	9.87748i	0.0131794	−	0.612575i
$261$	1.67944	+	0.203353i	0.103955	+	0.0125872i
$262$	−12.6605	+	7.30954i	−0.782168	+	0.451585i
$263$	15.2086	−	8.78068i	0.937801	−	0.541440i	0.0485307	−	0.998822i	$-0.484546\pi$
$263$	15.2086	−	8.78068i	0.937801	−	0.541440i	0.889270	+	0.457382i	$0.151213\pi$
$264$	3.55112	−	3.14708i	0.218557	−	0.193689i
$265$		−	16.1908i		−	0.994593i
$266$	13.4811	−	8.55574i	0.826579	−	0.524586i
$267$	1.79861	+	8.80269i	0.110073	+	0.538716i
$268$	1.58165	+	2.73951i	0.0966149	+	0.167342i
$269$	−23.7413			−1.44753			−0.723766	−	0.690045i	$-0.757591\pi$
$269$	−23.7413			−1.44753			−0.723766	+	0.690045i	$0.757591\pi$
$270$	−8.41525	−	3.98793i	−0.512136	−	0.242698i
$271$			30.3088i			1.84113i	0.390590	+	0.920565i	$0.372271\pi$
$271$			30.3088i			1.84113i	−0.390590	+	0.920565i	$0.627729\pi$
$272$	0.442006			0.0268005
$273$	−12.1395	+	11.2086i	−0.734718	+	0.678373i
$274$	10.7582			0.649925
$275$			0.475995i			0.0287036i
$276$	−3.55928	+	0.727251i	−0.214244	+	0.0437753i
$277$	17.5811			1.05634			0.528172	−	0.849137i	$-0.322878\pi$
$277$	17.5811			1.05634			0.528172	+	0.849137i	$0.322878\pi$
$278$	−6.62069	−	11.4674i	−0.397083	−	0.687767i
$279$	14.5598	+	1.76295i	0.871671	+	0.105545i
$280$	15.5821	−	0.653392i	0.931207	−	0.0390476i
$281$			27.1501i			1.61964i	0.586680	+	0.809819i	$0.300435\pi$
$281$			27.1501i			1.61964i	−0.586680	+	0.809819i	$0.699565\pi$
$282$	12.4065	+	13.9993i	0.738794	+	0.833646i
$283$	6.20370	−	3.58171i	0.368772	−	0.212910i	−0.304150	−	0.952624i	$-0.598372\pi$
$283$	6.20370	−	3.58171i	0.368772	−	0.212910i	0.672922	+	0.739714i	$0.265039\pi$
$284$	−3.20961	+	1.85307i	−0.190455	+	0.109959i
$285$	−25.8186	+	5.27539i	−1.52936	+	0.312487i
$286$	0.0645949	−	3.00236i	0.00381958	−	0.177533i
$287$	22.0508	−	13.9945i	1.30162	−	0.826067i
$288$	−6.76527	−	15.8640i	−0.398647	−	0.934796i
$289$	−13.6105			−0.800619
$290$	−1.01061			−0.0593449
$291$	−0.229204	−	0.258631i	−0.0134362	−	0.0151612i
$292$	−10.7170	−	6.18748i	−0.627167	−	0.362095i
$293$	11.3968	+	19.7398i	0.665805	+	1.15321i	0.979066	+	0.203542i	$0.0652452\pi$
$293$	11.3968	+	19.7398i	0.665805	+	1.15321i	−0.313261	+	0.949667i	$0.601421\pi$
$294$	−7.39671	−	7.05604i	−0.431385	−	0.411516i
$295$	−12.6753	−	21.9543i	−0.737987	−	1.27823i
$296$			9.12809i			0.530560i
$297$	4.63856	+	2.19818i	0.269156	+	0.127551i
$298$	3.17132	−	5.49288i	0.183709	−	0.318194i
$299$	−3.04172	+	5.01606i	−0.175907	+	0.290086i
$300$	1.02057	+	0.340526i	0.0589225	+	0.0196603i
$301$	−0.0474501	−	1.13159i	−0.00273498	−	0.0652238i
$302$	2.58760	+	1.49395i	0.148899	+	0.0859671i
$303$	−7.79519	+	6.90825i	−0.447822	+	0.396869i
$304$	−1.48822	−	0.859222i	−0.0853551	−	0.0492798i
$305$		−	4.71273i		−	0.269850i
$306$	−1.82672	−	4.28352i	−0.104427	−	0.244873i
$307$			24.9738i			1.42533i	0.701504	+	0.712665i	$0.252512\pi$
$307$			24.9738i			1.42533i	−0.701504	+	0.712665i	$0.747488\pi$
$308$	−3.36632	+	0.141157i	−0.191814	+	0.00804319i
$309$	11.1727	+	12.6072i	0.635594	+	0.717196i
$310$	−8.76137			−0.497612
$311$	−9.00463	+	15.5965i	−0.510606	+	0.884395i	0.489319	+	0.872105i	$0.337246\pi$
$311$	−9.00463	+	15.5965i	−0.510606	+	0.884395i	−0.999924	+	0.0122902i	$0.996088\pi$
$312$	−16.3064	−	5.83357i	−0.923169	−	0.330261i
$313$	17.5542	−	10.1349i	0.992223	−	0.572860i	0.0862849	−	0.996271i	$-0.472500\pi$
$313$	17.5542	−	10.1349i	0.992223	−	0.572860i	0.905938	+	0.423410i	$0.139167\pi$
$314$	6.19292	−	10.7265i	0.349487	−	0.605329i
$315$	7.26256	+	15.2282i	0.409199	+	0.858013i
$316$	−9.37909	−	16.2451i	−0.527615	−	0.913856i
$317$	8.12697	−	4.69211i	0.456456	−	0.263535i	−0.254097	−	0.967179i	$-0.581778\pi$
$317$	8.12697	−	4.69211i	0.456456	−	0.263535i	0.710553	+	0.703644i	$0.248445\pi$
$318$	−10.5517	−	3.52073i	−0.591712	−	0.197433i
$319$	0.557056			0.0311891
$320$	4.64105	+	8.03854i	0.259443	+	0.449368i
$321$	1.04315	−	0.213141i	0.0582228	−	0.0118964i
$322$	−3.21642	−	1.68142i	−0.179244	−	0.0937021i
$323$	−11.4122	−	6.58884i	−0.634993	−	0.366613i
$324$	8.03148	−	8.37282i	0.446193	−	0.465157i
$325$	1.52290	−	0.836097i	0.0844753	−	0.0463783i
$326$	−0.652465	−	0.376701i	−0.0361367	−	0.0208635i
$327$	−19.0204	−	6.34641i	−1.05183	−	0.350957i
$328$	23.7070	+	13.6873i	1.30900	+	0.755753i
$329$	−1.41981	−	33.8596i	−0.0782766	−	1.86674i
$330$	−2.90878	−	0.970553i	−0.160123	−	0.0534272i
$331$	9.40426	−	16.2887i	0.516905	−	0.895306i	−0.482902	−	0.875674i	$-0.660417\pi$
$331$	9.40426	−	16.2887i	0.516905	−	0.895306i	0.999807	−	0.0196317i	$-0.00624935\pi$
$332$	−18.6433			−1.02319
$333$	−9.08323	+	3.87358i	−0.497758	+	0.212271i
$334$	−4.10171	−	2.36812i	−0.224436	−	0.129578i
$335$	2.60794	−	4.51709i	0.142487	−	0.246795i
$336$	−0.304195	+	1.05731i	−0.0165952	+	0.0576810i
$337$	20.7828			1.13211			0.566056	−	0.824367i	$-0.308469\pi$
$337$	20.7828			1.13211			0.566056	+	0.824367i	$0.308469\pi$
$338$	−9.71922	+	5.06705i	−0.528656	+	0.275611i
$339$	8.10170	+	9.14185i	0.440024	+	0.496517i
$340$	−2.52238	−	4.36889i	−0.136795	−	0.236936i
$341$	4.82934			0.261524
$342$	−2.17629	+	17.9734i	−0.117680	+	0.971893i
$343$	2.32229	+	18.3741i	0.125392	+	0.992107i
$344$	1.02809	−	0.593566i	0.0554307	−	0.0320030i
$345$	3.97288	+	4.48295i	0.213893	+	0.241354i
$346$	−10.5272	−	6.07787i	−0.565945	−	0.326748i
$347$		−	2.62990i		−	0.141180i	−0.997505	−	0.0705902i	$-0.977512\pi$
$347$		−	2.62990i		−	0.141180i	0.997505	−	0.0705902i	$-0.0224883\pi$
$348$	0.398517	−	1.19437i	0.0213628	−	0.0640248i
$349$	2.04081	+	1.17826i	0.109242	+	0.0630710i	0.553626	−	0.832766i	$-0.313244\pi$
$349$	2.04081	+	1.17826i	0.109242	+	0.0630710i	−0.444383	+	0.895837i	$0.646577\pi$
$350$	0.575960	+	0.907529i	0.0307864	+	0.0485095i
$351$	−1.11487	−	18.7018i	−0.0595072	−	0.998228i
$352$	−2.83948	−	4.91813i	−0.151345	−	0.262137i
$353$	11.3836	+	19.7170i	0.605888	+	1.04943i	0.991911	+	0.126939i	$0.0405152\pi$
$353$	11.3836	+	19.7170i	0.605888	+	1.04943i	−0.386023	+	0.922489i	$0.626151\pi$
$354$	−17.0642	+	3.48664i	−0.906951	+	0.185313i
$355$	5.29222	+	3.05547i	0.280882	+	0.162167i
$356$	6.68699			0.354410
$357$	−2.33268	+	8.10786i	−0.123459	+	0.429114i
$358$	−9.40085	−	16.2827i	−0.496850	−	0.860570i
$359$	−5.83980	+	3.37161i	−0.308213	+	0.177947i	−0.646126	−	0.763230i	$-0.723612\pi$
$359$	−5.83980	+	3.37161i	−0.308213	+	0.177947i	0.337914	+	0.941177i	$0.390279\pi$
$360$	−10.6188	+	14.1408i	−0.559659	+	0.745288i
$361$	16.1163	+	27.9143i	0.848228	+	1.46917i
$362$	5.28602			0.277827
$363$	−16.4697	−	5.49535i	−0.864436	−	0.288431i
$364$	6.36465	+	10.5223i	0.333598	+	0.551518i
$365$			20.4047i			1.06803i
$366$	−3.07134	−	1.02480i	−0.160542	−	0.0535669i
$367$	11.0644	−	6.38805i	0.577559	−	0.333454i	−0.182604	−	0.983187i	$-0.558453\pi$
$367$	11.0644	−	6.38805i	0.577559	−	0.333454i	0.760163	+	0.649733i	$0.225119\pi$
$368$			0.390617i			0.0203623i
$369$	−3.55972	+	29.3988i	−0.185311	+	1.53044i
$370$	5.10871	−	2.94951i	0.265589	−	0.153338i
$371$	10.7988	+	17.0154i	0.560645	+	0.883396i
$372$	3.45491	−	10.3545i	0.179129	−	0.536853i
$373$	12.8528	−	22.2617i	0.665493	−	1.15267i	−0.313659	−	0.949536i	$-0.601555\pi$
$373$	12.8528	−	22.2617i	0.665493	−	1.15267i	0.979151	−	0.203132i	$-0.0651119\pi$
$374$	−0.766703	−	1.32797i	−0.0396452	−	0.0686676i
$375$	−4.04025	−	19.7736i	−0.208638	−	1.02111i
$376$	30.7625	−	17.7608i	1.58646	−	0.915942i
$377$	−0.978482	−	1.78225i	−0.0503944	−	0.0917904i
$378$	11.5037	−	1.42168i	0.591685	−	0.0731234i
$379$	−15.2609	+	26.4326i	−0.783898	+	1.35775i	0.145757	+	0.989320i	$0.453438\pi$
$379$	−15.2609	+	26.4326i	−0.783898	+	1.35775i	−0.929655	+	0.368431i	$0.879895\pi$
$380$			19.6132i			1.00614i
$381$	−17.8601	−	5.95926i	−0.914999	−	0.305302i
$382$	−2.07976	+	3.60225i	−0.106410	+	0.184307i
$383$	−4.14360	+	7.17693i	−0.211728	+	0.366724i	−0.952255	−	0.305302i	$-0.901242\pi$
$383$	−4.14360	+	7.17693i	−0.211728	+	0.366724i	0.740527	+	0.672026i	$0.234576\pi$
$384$	−13.2632	+	2.71000i	−0.676835	+	0.138294i
$385$	2.97688	+	4.69061i	0.151716	+	0.239055i
$386$	−3.92951	+	2.26871i	−0.200007	+	0.115474i
$387$	1.02693	+	0.771149i	0.0522016	+	0.0391997i
$388$	−0.222747	+	0.128603i	−0.0113083	+	0.00652883i
$389$	−23.2193	−	13.4057i	−1.17727	−	0.679695i	−0.221886	−	0.975073i	$-0.571221\pi$
$389$	−23.2193	−	13.4057i	−1.17727	−	0.679695i	−0.955381	+	0.295378i	$0.904555\pi$
$390$	2.00414	+	11.0112i	0.101484	+	0.557572i
$391$			2.99540i			0.151484i
$392$	−15.9399	+	11.0795i	−0.805086	+	0.559597i
$393$	−22.4759	+	19.9186i	−1.13376	+	1.00476i
$394$	0.846693	−	1.46652i	0.0426558	−	0.0738820i
$395$	−15.4649	+	26.7860i	−0.778124	+	1.34775i
$396$	2.29406	−	3.05496i	0.115281	−	0.153518i
$397$	−5.06386	−	2.92362i	−0.254148	−	0.146732i	0.367514	−	0.930018i	$-0.380209\pi$
$397$	−5.06386	−	2.92362i	−0.254148	−	0.146732i	−0.621662	+	0.783286i	$0.713542\pi$
$398$	1.58821			0.0796099
$399$	23.6151	−	22.7643i	1.18223	−	1.13964i
$400$	0.0578416	−	0.100185i	0.00289208	−	0.00500923i
$401$		−	4.14953i		−	0.207218i	−0.994618	−	0.103609i	$-0.966961\pi$
$401$		−	4.14953i		−	0.207218i	0.994618	−	0.103609i	$-0.0330390\pi$
$402$	−2.37673	−	2.68188i	−0.118541	−	0.133760i
$403$	−8.48286	−	15.4510i	−0.422561	−	0.769670i
$404$	3.87611	+	6.71362i	0.192844	+	0.334015i
$405$	−18.5775	−	4.56581i	−0.923124	−	0.226877i
$406$	1.06208	−	0.674045i	0.0527101	−	0.0334523i
$407$	−2.81596	+	1.62580i	−0.139582	+	0.0805878i
$408$	−8.66408	+	1.77029i	−0.428936	+	0.0876423i
$409$		−	10.6492i		−	0.526570i	−0.964718	−	0.263285i	$-0.915194\pi$
$409$		−	10.6492i		−	0.526570i	0.964718	−	0.263285i	$-0.0848060\pi$
$410$		−	17.6908i		−	0.873685i
$411$	21.6531	−	4.42427i	1.06807	−	0.218233i
$412$	10.8579	−	6.26884i	0.534933	−	0.308843i
$413$	27.9638	+	14.6184i	1.37601	+	0.719325i
$414$	3.78550	−	1.61434i	0.186047	−	0.0793407i
$415$	15.3702	+	26.6220i	0.754493	+	1.30682i
$416$	−10.7475	+	17.7235i	−0.526938	+	0.868964i
$417$	−18.0415	−	20.3578i	−0.883495	−	0.996925i
$418$			5.96162i			0.291593i
$419$	−4.05247	+	7.01909i	−0.197976	+	0.342905i	−0.947872	−	0.318651i	$-0.896770\pi$
$419$	−4.05247	+	7.01909i	−0.197976	+	0.342905i	0.749896	+	0.661556i	$0.230104\pi$
$420$	12.1867	−	3.02699i	0.594648	−	0.147702i
$421$	16.7895			0.818270			0.409135	−	0.912474i	$-0.365830\pi$
$421$	16.7895			0.818270			0.409135	+	0.912474i	$0.365830\pi$
$422$	5.38536	+	3.10924i	0.262155	+	0.151355i
$423$	30.7278	+	23.0744i	1.49404	+	1.12192i
$424$	−10.5617	+	18.2935i	−0.512923	+	0.888409i
$425$	0.443552	−	0.768254i	0.0215154	−	0.0372658i
$426$	3.14209	−	2.78459i	0.152235	−	0.134914i
$427$	3.14325	+	4.95275i	0.152113	+	0.239680i
$428$		−	0.792429i		−	0.0383035i
$429$	−1.10470	−	6.06945i	−0.0533355	−	0.293036i
$430$	−0.664401	−	0.383592i	−0.0320403	−	0.0184985i
$431$	11.9816	−	6.91758i	0.577134	−	0.333208i	−0.182860	−	0.983139i	$-0.558535\pi$
$431$	11.9816	−	6.91758i	0.577134	−	0.333208i	0.759993	+	0.649931i	$0.225202\pi$
$432$	−0.709180	−	1.02633i	−0.0341204	−	0.0493791i
$433$	10.1569	−	5.86410i	0.488111	−	0.281811i	−0.235680	−	0.971831i	$-0.575732\pi$
$433$	10.1569	−	5.86410i	0.488111	−	0.281811i	0.723790	+	0.690020i	$0.242398\pi$
$434$	9.20759	−	5.84357i	0.441979	−	0.280500i
$435$	−2.03406	+	0.415610i	−0.0975258	+	0.0199270i
$436$	−7.46182	+	12.9243i	−0.357356	+	0.618959i
$437$	5.82281	−	10.0854i	0.278543	−	0.482450i
$438$	13.2980	+	4.43705i	0.635402	+	0.212011i
$439$		−	27.4492i		−	1.31008i	−0.755595	−	0.655039i	$-0.772652\pi$
$439$		−	27.4492i		−	1.31008i	0.755595	−	0.655039i	$-0.227348\pi$
$440$	−2.91153	+	5.04292i	−0.138802	+	0.240412i
$441$	−17.7892	−	11.1599i	−0.847106	−	0.531424i
$442$	−2.90198	+	4.78560i	−0.138033	+	0.227628i
$443$	−23.7433	+	13.7082i	−1.12808	+	0.651298i	−0.943451	−	0.331511i	$-0.892442\pi$
$443$	−23.7433	+	13.7082i	−1.12808	+	0.651298i	−0.184629	+	0.982808i	$0.559108\pi$
$444$	1.47129	+	7.20072i	0.0698243	+	0.341731i
$445$	−5.51299	−	9.54877i	−0.261341	−	0.452655i
$446$	0.581616	−	1.00739i	0.0275403	−	0.0477012i
$447$	4.12401	−	12.3598i	0.195059	−	0.584598i
$448$	−10.2389	−	5.35251i	−0.483742	−	0.252882i
$449$	5.57195	−	3.21697i	0.262957	−	0.151818i	−0.362726	−	0.931896i	$-0.618154\pi$
$449$	5.57195	−	3.21697i	0.262957	−	0.151818i	0.625683	+	0.780078i	$0.284821\pi$
$450$	−1.20995	−	0.146505i	−0.0570375	−	0.00690630i
$451$			9.75131i			0.459171i
$452$	7.87344	−	4.54573i	0.370336	−	0.213813i
$453$	5.82247	+	1.94275i	0.273564	+	0.0912782i
$454$			2.51455i			0.118013i
$455$	9.77819	−	17.7634i	0.458409	−	0.832762i
$456$	32.6129	+	10.8817i	1.52724	+	0.509585i
$457$	23.9957			1.12247			0.561235	−	0.827656i	$-0.310326\pi$
$457$	23.9957			1.12247			0.561235	+	0.827656i	$0.310326\pi$
$458$	5.03386	+	8.71890i	0.235217	+	0.407407i
$459$	−5.43826	−	7.87026i	−0.253836	−	0.367352i
$460$	3.86095	−	2.22912i	0.180018	−	0.103933i
$461$	3.15743	+	5.46883i	0.147056	+	0.254709i	0.930138	−	0.367210i	$-0.119687\pi$
$461$	3.15743	+	5.46883i	0.147056	+	0.254709i	−0.783082	+	0.621918i	$0.786354\pi$
$462$	3.70425	−	0.920083i	0.172338	−	0.0428061i
$463$	−4.43562			−0.206141			−0.103070	−	0.994674i	$-0.532867\pi$
$463$	−4.43562			−0.206141			−0.103070	+	0.994674i	$0.532867\pi$
$464$	−0.117246	−	0.0676919i	−0.00544300	−	0.00314252i
$465$	−17.6341	+	3.60309i	−0.817763	+	0.167089i
$466$	6.98647	+	12.1009i	0.323642	+	0.560565i
$467$	2.04445	+	3.54109i	0.0946057	+	0.163862i	0.909444	−	0.415826i	$-0.136508\pi$
$467$	2.04445	+	3.54109i	0.0946057	+	0.163862i	−0.814838	+	0.579688i	$0.803174\pi$
$468$	−13.8036	−	1.97352i	−0.638073	−	0.0912259i
$469$	0.271996	+	6.48656i	0.0125596	+	0.299522i
$470$	−19.8803	−	11.4779i	−0.917009	−	0.529436i
$471$	8.05334	−	24.1361i	0.371078	−	1.11213i
$472$			33.0740i			1.52235i
$473$	0.366224	+	0.211439i	0.0168390	+	0.00972199i
$474$	14.0939	+	15.9033i	0.647353	+	0.730465i
$475$	−2.98684	+	1.72445i	−0.137046	+	0.0791234i
$476$	5.56477	+	2.90905i	0.255061	+	0.133336i
$477$	−22.6855	−	2.74684i	−1.03870	−	0.125769i
$478$	24.9863			1.14285
$479$	−15.1680	−	26.2717i	−0.693042	−	1.20038i	−0.970836	−	0.239744i	$-0.922937\pi$
$479$	−15.1680	−	26.2717i	−0.693042	−	1.20038i	0.277794	−	0.960641i	$-0.410397\pi$
$480$	14.0376	+	15.8398i	0.640725	+	0.722986i
$481$	10.1479	+	6.15366i	0.462704	+	0.280583i
$482$	−15.2814			−0.696048
$483$	−7.16522	−	2.06148i	−0.326029	−	0.0938005i
$484$	−6.46117	+	11.1911i	−0.293690	+	0.508686i
$485$	0.367281	+	0.212050i	0.0166774	+	0.00962867i
$486$	−7.01532	+	11.1143i	−0.318221	+	0.504157i
$487$	−36.5435			−1.65594			−0.827971	−	0.560771i	$-0.810505\pi$
$487$	−36.5435			−1.65594			−0.827971	+	0.560771i	$0.810505\pi$
$488$	−3.07425	+	5.32476i	−0.139165	+	0.241040i
$489$	−1.46814	−	0.489866i	−0.0663917	−	0.0221525i
$490$	11.3514	+	5.34102i	0.512804	+	0.241282i
$491$	21.6683	+	12.5102i	0.977875	+	0.564577i	0.901628	−	0.432512i	$-0.142373\pi$
$491$	21.6683	+	12.5102i	0.977875	+	0.564577i	0.0762474	+	0.997089i	$0.475706\pi$
$492$	20.9075	+	6.97608i	0.942583	+	0.314506i
$493$	−0.899086	−	0.519087i	−0.0404928	−	0.0233785i
$494$	19.0737	−	10.4717i	0.858164	−	0.471146i
$495$	−6.25367	−	0.757217i	−0.281082	−	0.0340344i
$496$	−1.01645	−	0.586849i	−0.0456400	−	0.0263503i
$497$	−7.59967	+	0.318671i	−0.340892	+	0.0142944i
$498$	20.6921	−	4.22792i	0.927237	−	0.189458i
$499$	−8.03279	−	13.9132i	−0.359597	−	0.622841i	0.628296	−	0.777974i	$-0.283753\pi$
$499$	−8.03279	−	13.9132i	−0.359597	−	0.622841i	−0.987894	+	0.155133i	$0.950419\pi$
$500$	−15.0211			−0.671764
$501$	−9.22946	−	3.07954i	−0.412342	−	0.137583i
$502$	−5.54789	+	3.20308i	−0.247614	+	0.142960i
$503$	19.4463	+	33.6820i	0.867069	+	1.50181i	0.864978	+	0.501810i	$0.167332\pi$
$503$	19.4463	+	33.6820i	0.867069	+	1.50181i	0.00209081	+	0.999998i	$0.499334\pi$
$504$	1.72808	−	21.9435i	0.0769749	−	0.977439i
$505$	6.39120	−	11.0699i	0.284405	−	0.492603i
$506$	1.17357	−	0.677563i	0.0521717	−	0.0301214i
$507$	−17.4782	+	14.1955i	−0.776234	+	0.630445i
$508$	−7.00662	+	12.1358i	−0.310869	+	0.538440i
$509$	−30.1839			−1.33788			−0.668939	−	0.743317i	$-0.733251\pi$
$509$	−30.1839			−1.33788			−0.668939	+	0.743317i	$0.733251\pi$
$510$	3.79035	+	4.27699i	0.167840	+	0.189388i
$511$	−13.6093	−	21.4439i	−0.602041	−	0.948623i
$512$			2.71177i			0.119845i
$513$	3.01129	+	37.0704i	0.132952	+	1.63670i
$514$		−	19.9831i		−	0.881417i
$515$	−17.9033	−	10.3365i	−0.788915	−	0.455480i
$516$	0.715337	−	0.633946i	0.0314910	−	0.0279079i
$517$	10.9582	+	6.32671i	0.481941	+	0.278249i
$518$	−3.40166	+	6.50709i	−0.149460	+	0.285905i
$519$	−23.6877	−	7.90373i	−1.03977	−	0.346935i
$520$	21.2485	+	0.457157i	0.931810	+	0.0200476i
$521$	16.6107	−	28.7706i	0.727729	−	1.26046i	−0.230112	−	0.973164i	$-0.573909\pi$
$521$	16.6107	−	28.7706i	0.727729	−	1.26046i	0.957841	−	0.287299i	$-0.0927573\pi$
$522$	−0.171454	+	1.41600i	−0.00750435	+	0.0619766i
$523$		−	19.3414i		−	0.845740i	−0.906190	−	0.422870i	$-0.861023\pi$
$523$		−	19.3414i		−	0.845740i	0.906190	−	0.422870i	$-0.138977\pi$
$524$	11.1760	+	19.3574i	0.488227	+	0.845634i
$525$	1.53246	+	1.58973i	0.0668821	+	0.0693816i
$526$	7.40330	+	12.8229i	0.322799	+	0.559104i
$527$	−7.79454	−	4.50018i	−0.339536	−	0.196031i
$528$	−0.272453	−	0.307433i	−0.0118570	−	0.0133793i
$529$	20.3529			0.884907
$530$	13.6510			0.592963
$531$	−32.9114	+	14.0352i	−1.42823	+	0.609077i
$532$	−13.0814	−	20.6121i	−0.567151	−	0.893648i
$533$	31.1984	−	17.1284i	1.35135	−	0.741914i
$534$	−7.42186	+	1.51647i	−0.321175	+	0.0656242i
$535$	−1.13156	+	0.653306i	−0.0489216	+	0.0282449i
$536$	−5.89325	+	3.40247i	−0.254550	+	0.146964i
$537$	−25.6175	−	28.9064i	−1.10547	−	1.24740i
$538$		−	20.0171i		−	0.863000i
$539$	−6.25699	−	2.94401i	−0.269508	−	0.126808i
$540$	−6.09740	+	12.8666i	−0.262390	+	0.553691i
$541$	−13.4353	−	23.2706i	−0.577629	−	1.00048i	−0.995751	−	0.0920914i	$-0.970645\pi$
$541$	−13.4353	−	23.2706i	−0.577629	−	1.00048i	0.418122	−	0.908391i	$-0.362689\pi$
$542$	−25.5544			−1.09766
$543$	10.6393	−	2.17387i	0.456574	−	0.0932895i
$544$			10.5838i			0.453776i
$545$	24.6071			1.05405
$546$	−9.45033	−	10.2353i	−0.404437	−	0.438029i
$547$	−30.2508			−1.29343			−0.646716	−	0.762731i	$-0.723858\pi$
$547$	−30.2508			−1.29343			−0.646716	+	0.762731i	$0.723858\pi$
$548$		−	16.4488i		−	0.702660i
$549$	−6.60317	−	0.799536i	−0.281816	−	0.0341234i
$550$	−0.401328			−0.0171127
$551$	2.01813	+	3.49550i	0.0859750	+	0.148913i
$552$	−1.56447	−	7.65677i	−0.0665883	−	0.325894i
$553$	−1.61292	−	38.4649i	−0.0685882	−	1.63569i
$554$			14.8232i			0.629778i
$555$	9.06938	−	8.03747i	0.384974	−	0.341172i
$556$	−17.5332	+	10.1228i	−0.743573	+	0.429302i
$557$	−23.3427	+	13.4769i	−0.989060	+	0.571034i	−0.904993	−	0.425426i	$-0.860124\pi$
$557$	−23.3427	+	13.4769i	−0.989060	+	0.571034i	−0.0840671	+	0.996460i	$0.526791\pi$
$558$	−1.48641	+	12.2759i	−0.0629246	+	0.519679i
$559$	0.0331993	−	1.54310i	0.00140418	−	0.0652660i
$560$	−0.0565664	−	1.34899i	−0.00239037	−	0.0570054i
$561$	−2.08928	−	2.35751i	−0.0882093	−	0.0995343i
$562$	−22.8912			−0.965607
$563$	−7.64099			−0.322029			−0.161015	−	0.986952i	$-0.551477\pi$
$563$	−7.64099			−0.322029			−0.161015	+	0.986952i	$0.551477\pi$
$564$	21.4044	−	18.9690i	0.901288	−	0.798740i
$565$	−12.9823	−	7.49532i	−0.546169	−	0.315331i
$566$	3.01986	+	5.23056i	0.126934	+	0.219857i
$567$	22.5689	−	7.59230i	0.947806	−	0.318847i
$568$	−3.98634	−	6.90454i	−0.167263	−	0.289708i
$569$		−	3.73804i		−	0.156707i	−0.996926	−	0.0783534i	$-0.975034\pi$
$569$		−	3.73804i		−	0.156707i	0.996926	−	0.0783534i	$-0.0249662\pi$
$570$	−4.44787	−	21.7686i	−0.186301	−	0.911786i
$571$	7.51056	−	13.0087i	0.314307	−	0.544396i	−0.664983	−	0.746859i	$-0.731561\pi$
$571$	7.51056	−	13.0087i	0.314307	−	0.544396i	0.979290	+	0.202463i	$0.0648945\pi$
$572$	−4.59049	−	0.0987632i	−0.191938	−	0.00412950i
$573$	−2.70454	+	8.10559i	−0.112984	+	0.338616i
$574$	11.7992	+	18.5918i	0.492490	+	0.776006i
$575$	0.678935	+	0.391983i	0.0283135	+	0.0163468i
$576$	12.0505	−	5.13897i	0.502103	−	0.214124i
$577$	15.7668	+	9.10299i	0.656382	+	0.378963i	0.790897	−	0.611949i	$-0.209614\pi$
$577$	15.7668	+	9.10299i	0.656382	+	0.378963i	−0.134515	+	0.990912i	$0.542948\pi$
$578$		−	11.4755i		−	0.477319i
$579$	−6.97598	+	6.18226i	−0.289912	+	0.256926i
$580$			1.54518i			0.0641602i
$581$	−33.9091	−	17.7264i	−1.40679	−	0.735414i
$582$	0.218061	−	0.193250i	0.00903893	−	0.00801049i
$583$	−7.52457			−0.311636
$584$	13.3106	−	23.0546i	0.550796	−	0.954006i
$585$	8.56208	+	21.3381i	0.353999	+	0.882222i
$586$	−16.6433	+	9.60900i	−0.687528	+	0.396944i
$587$	−2.83282	+	4.90659i	−0.116923	+	0.202516i	−0.918547	−	0.395312i	$-0.870636\pi$
$587$	−2.83282	+	4.90659i	−0.116923	+	0.202516i	0.801624	+	0.597829i	$0.203970\pi$
$588$	−10.7884	+	11.3093i	−0.444907	+	0.466387i
$589$	17.4959	+	30.3039i	0.720908	+	1.24865i
$590$	18.5105	−	10.6870i	0.762064	−	0.439978i
$591$	1.10105	−	3.29988i	0.0452911	−	0.135739i
$592$	0.790250			0.0324791
$593$	−1.76064	−	3.04952i	−0.0723010	−	0.125229i	0.827608	−	0.561306i	$-0.189701\pi$
$593$	−1.76064	−	3.04952i	−0.0723010	−	0.125229i	−0.899909	+	0.436077i	$0.856368\pi$
$594$	−1.85336	+	3.91093i	−0.0760445	+	0.160468i
$595$	−0.433772	−	10.3446i	−0.0177829	−	0.424087i
$596$	−8.39841	−	4.84883i	−0.344012	−	0.198616i
$597$	3.19661	−	0.653149i	0.130829	−	0.0267316i
$598$	−4.22921	−	2.56458i	−0.172945	−	0.104874i
$599$	−22.9515	−	13.2511i	−0.937774	−	0.541424i	−0.0485125	−	0.998823i	$-0.515448\pi$
$599$	−22.9515	−	13.2511i	−0.937774	−	0.541424i	−0.889262	+	0.457398i	$0.848781\pi$
$600$	−0.732544	+	2.19546i	−0.0299060	+	0.0896291i
$601$	−24.6360	−	14.2236i	−1.00492	−	0.580194i	−0.0952232	−	0.995456i	$-0.530356\pi$
$601$	−24.6360	−	14.2236i	−1.00492	−	0.580194i	−0.909702	+	0.415262i	$0.863690\pi$
$602$	0.954084	−	0.0400069i	0.0388856	−	0.00163056i
$603$	−5.88660	−	4.42042i	−0.239721	−	0.180014i
$604$	2.28419	−	3.95634i	0.0929425	−	0.160981i
$605$	21.3073			0.866263
$606$	−5.82459	−	6.57240i	−0.236608	−	0.266985i
$607$	8.40141	+	4.85056i	0.341003	+	0.196878i	0.660715	−	0.750637i	$-0.270253\pi$
$607$	8.40141	+	4.85056i	0.341003	+	0.196878i	−0.319713	+	0.947515i	$0.603586\pi$
$608$	20.5740	−	35.6352i	0.834386	−	1.44520i
$609$	1.86046	−	1.79344i	0.0753896	−	0.0726737i
$610$	3.97347			0.160881
$611$	0.993394	−	46.1727i	0.0401884	−	1.86795i
$612$	−6.54934	+	2.79299i	−0.264742	+	0.112900i
$613$	4.23217	+	7.33033i	0.170936	+	0.296069i	0.938747	−	0.344606i	$-0.111988\pi$
$613$	4.23217	+	7.33033i	0.170936	+	0.296069i	−0.767812	+	0.640676i	$0.778654\pi$
$614$	−21.0563			−0.849763
$615$	−7.27530	−	35.6065i	−0.293368	−	1.43579i
$616$	−0.303659	−	7.24167i	−0.0122348	−	0.291775i
$617$	10.0946	−	5.82812i	0.406393	−	0.234631i	−0.282846	−	0.959165i	$-0.591278\pi$
$617$	10.0946	−	5.82812i	0.406393	−	0.234631i	0.689239	+	0.724534i	$0.257945\pi$
$618$	−10.6295	+	9.42011i	−0.427583	+	0.378933i
$619$	25.2951	+	14.6041i	1.01669	+	0.586989i	0.913145	−	0.407635i	$-0.133646\pi$
$619$	25.2951	+	14.6041i	1.01669	+	0.586989i	0.103550	+	0.994624i	$0.466980\pi$
$620$			13.3958i			0.537989i
$621$	6.95524	−	4.80599i	0.279104	−	0.192858i
$622$	−13.1499	−	7.59212i	−0.527265	−	0.304416i
$623$	12.1625	+	6.35810i	0.487281	+	0.254732i
$624$	−0.505032	+	1.41170i	−0.0202175	+	0.0565133i
$625$	11.1793	+	19.3631i	0.447172	+	0.774524i
$626$	8.54512	+	14.8006i	0.341532	+	0.591550i
$627$	2.45170	+	11.9990i	0.0979117	+	0.479195i
$628$	−16.4004	−	9.46875i	−0.654445	−	0.377844i
$629$	6.05994			0.241626
$630$	−12.8395	+	6.12332i	−0.511536	+	0.243959i
$631$	12.7791	+	22.1340i	0.508727	+	0.881141i	0.999949	+	0.0101065i	$0.00321706\pi$
$631$	12.7791	+	22.1340i	0.508727	+	0.881141i	−0.491222	+	0.871034i	$0.663450\pi$
$632$	34.9466	−	20.1764i	1.39010	−	0.802575i
$633$	12.1179	+	4.04329i	0.481642	+	0.160706i
$634$	3.95608	+	6.85214i	0.157116	+	0.272133i
$635$	23.1060			0.916934
$636$	−5.38307	+	16.1332i	−0.213453	+	0.639724i
$637$	1.57146	+	25.1899i	0.0622637	+	0.998060i
$638$			0.469673i			0.0185945i
$639$	5.17897	−	6.89675i	0.204877	−	0.272831i
$640$	14.3873	−	8.30653i	0.568709	−	0.328344i
$641$		−	34.2795i		−	1.35396i	−0.736002	−	0.676980i	$-0.763288\pi$
$641$		−	34.2795i		−	1.35396i	0.736002	−	0.676980i	$-0.236712\pi$
$642$	0.179707	+	0.879514i	0.00709246	+	0.0347116i
$643$	−19.3892	+	11.1943i	−0.764634	+	0.441462i	−0.830957	−	0.556336i	$-0.812207\pi$
$643$	−19.3892	+	11.1943i	−0.764634	+	0.441462i	0.0663229	+	0.997798i	$0.478873\pi$
$644$	−2.57084	+	4.91779i	−0.101305	+	0.193788i
$645$	−1.49500	−	0.498827i	−0.0588656	−	0.0196413i
$646$	5.55529	−	9.62204i	0.218570	−	0.378574i
$647$	−10.3042	−	17.8473i	−0.405098	−	0.701651i	0.589235	−	0.807962i	$-0.299429\pi$
$647$	−10.3042	−	17.8473i	−0.405098	−	0.701651i	−0.994333	+	0.106311i	$0.966096\pi$
$648$	18.0117	+	17.2774i	0.707567	+	0.678721i
$649$	−10.2031	+	5.89078i	−0.400508	+	0.231233i
$650$	0.704943	+	1.28401i	0.0276501	+	0.0503631i
$651$	16.1291	−	15.5480i	0.632149	−	0.609376i
$652$	−0.575962	+	0.997595i	−0.0225564	+	0.0390688i
$653$		−	27.5127i		−	1.07665i	−0.842736	−	0.538327i	$-0.819056\pi$
$653$		−	27.5127i		−	1.07665i	0.842736	−	0.538327i	$-0.180944\pi$
$654$	5.35089	−	16.0368i	0.209236	−	0.627087i
$655$	18.4278	−	31.9179i	0.720034	−	1.24713i
$656$	1.18495	−	2.05240i	0.0462647	−	0.0801328i
$657$	28.5897	+	3.46175i	1.11539	+	0.135056i
$658$	28.5482	−	1.19709i	1.11293	−	0.0466675i
$659$	33.0777	−	19.0974i	1.28852	−	0.743929i	0.310132	−	0.950693i	$-0.399627\pi$
$659$	33.0777	−	19.0974i	1.28852	−	0.743929i	0.978391	+	0.206764i	$0.0662933\pi$
$660$	−1.48394	+	4.44741i	−0.0577623	+	0.173115i
$661$	−5.78197	+	3.33822i	−0.224893	+	0.129842i	−0.608214	−	0.793773i	$-0.708114\pi$
$661$	−5.78197	+	3.33822i	−0.224893	+	0.129842i	0.383321	+	0.923615i	$0.374780\pi$
$662$	13.7335	+	7.92907i	0.533770	+	0.308172i
$663$	−3.87278	+	10.8255i	−0.150406	+	0.420427i
$664$		−	40.1057i		−	1.55640i
$665$	−18.6486	+	35.6731i	−0.723160	+	1.38334i
$666$	−3.26595	−	7.65839i	−0.126553	−	0.296757i
$667$	0.458737	−	0.794555i	0.0177624	−	0.0307653i
$668$	−3.62078	+	6.27137i	−0.140092	+	0.242646i
$669$	0.756340	−	2.26677i	0.0292418	−	0.0876385i
$670$	3.80851	+	2.19885i	0.147136	+	0.0849489i
$671$	−2.19021			−0.0845521
$672$	−25.3172	−	7.28392i	−0.976632	−	0.280983i
$673$	5.54228	−	9.59951i	0.213639	−	0.370034i	−0.739212	−	0.673473i	$-0.764802\pi$
$673$	5.54228	−	9.59951i	0.213639	−	0.370034i	0.952851	+	0.303439i	$0.0981350\pi$
$674$			17.5227i			0.674950i
$675$	−2.49553	+	0.202716i	−0.0960528	+	0.00780254i
$676$	7.74733	+	14.8603i	0.297974	+	0.571551i
$677$	−14.9397	−	25.8763i	−0.574178	−	0.994506i	−0.996130	−	0.0878879i	$-0.971988\pi$
$677$	−14.9397	−	25.8763i	−0.574178	−	0.994506i	0.421952	−	0.906618i	$-0.361345\pi$
$678$	−7.70782	+	6.83083i	−0.296017	+	0.262336i
$679$	−0.527417	+	0.0221158i	−0.0202404	+	0.000848726i
$680$	9.39841	−	5.42617i	0.360413	−	0.208084i
$681$	1.03410	+	5.06106i	0.0396269	+	0.193940i
$682$			4.07179i			0.155917i
$683$			3.80861i			0.145732i	0.997342	+	0.0728662i	$0.0232146\pi$
$683$			3.80861i			0.145732i	−0.997342	+	0.0728662i	$0.976785\pi$
$684$	27.4807	+	3.32747i	1.05075	+	0.127229i
$685$	−23.4883	+	13.5610i	−0.897443	+	0.518139i
$686$	−15.4918	+	1.95801i	−0.591481	+	0.0747571i
$687$	13.7173	+	15.4785i	0.523349	+	0.590541i
$688$	−0.0513871	−	0.0890050i	−0.00195911	−	0.00339329i
$689$	13.2171	+	24.0742i	0.503531	+	0.917152i
$690$	−3.77973	+	3.34968i	−0.143892	+	0.127520i
$691$			32.3395i			1.23025i	0.788428	+	0.615127i	$0.210895\pi$
$691$			32.3395i			1.23025i	−0.788428	+	0.615127i	$0.789105\pi$
$692$	−9.29284	+	16.0957i	−0.353261	+	0.611866i
$693$	7.07722	−	3.37523i	0.268841	−	0.128214i
$694$	2.21736			0.0841699
$695$	28.9099	+	16.6912i	1.09662	+	0.633132i
$696$	2.56934	+	0.857294i	0.0973904	+	0.0324957i
$697$	9.08668	−	15.7386i	0.344182	−	0.596141i
$698$	−0.993435	+	1.72068i	−0.0376021	+	0.0651287i
$699$	19.0382	+	21.4825i	0.720093	+	0.812544i
$700$	1.38758	−	0.880622i	0.0524455	−	0.0332844i
$701$			8.39232i			0.316974i	0.987361	+	0.158487i	$0.0506616\pi$
$701$			8.39232i			0.316974i	−0.987361	+	0.158487i	$0.949338\pi$
$702$	15.7681	−	0.939984i	0.595130	−	0.0354774i
$703$	−20.4036	−	11.7800i	−0.769536	−	0.444292i
$704$	3.73586	−	2.15690i	0.140800	−	0.0812912i
$705$	−44.7336	−	14.9260i	−1.68476	−	0.562145i
$706$	−16.6241	+	9.59791i	−0.625655	+	0.361222i
$707$	0.666573	+	15.8964i	0.0250690	+	0.597847i
$708$	5.33095	+	26.0905i	0.200349	+	0.980541i
$709$	−13.5979	+	23.5522i	−0.510679	+	0.884523i	0.489244	+	0.872147i	$0.337273\pi$
$709$	−13.5979	+	23.5522i	−0.510679	+	0.884523i	−0.999923	+	0.0123757i	$0.996061\pi$
$710$	−2.57617	+	4.46206i	−0.0966820	+	0.167458i
$711$	34.9071	+	26.2128i	1.30912	+	0.983056i
$712$			14.3851i			0.539105i
$713$	3.97698	−	6.88832i	0.148939	−	0.257970i
$714$	−6.83603	−	1.96677i	−0.255832	−	0.0736044i
$715$	3.64353	+	6.63648i	0.136260	+	0.248190i
$716$	−24.8957	+	14.3735i	−0.930397	+	0.537165i
$717$	50.2903	−	10.2756i	1.87813	−	0.383748i
$718$	−2.84272	−	4.92374i	−0.106089	−	0.183752i
$719$	14.7050	−	25.4699i	0.548405	−	0.949866i	−0.449979	−	0.893039i	$-0.648568\pi$
$719$	14.7050	−	25.4699i	0.548405	−	0.949866i	0.998384	−	0.0568265i	$-0.0180982\pi$
$720$	1.22422	+	0.919304i	0.0456240	+	0.0342604i
$721$	25.7093	−	1.07805i	0.957464	−	0.0401486i
$722$	−23.5355	+	13.5882i	−0.875902	+	0.505702i
$723$	−30.7570	+	6.28444i	−1.14387	+	0.233721i
$724$		−	8.08214i		−	0.300370i
$725$	−0.235312	+	0.135857i	−0.00873926	+	0.00504561i
$726$	4.63332	−	13.8862i	0.171959	−	0.515365i
$727$			31.8635i			1.18175i	0.806763	+	0.590876i	$0.201218\pi$
$727$			31.8635i			1.18175i	−0.806763	+	0.590876i	$0.798782\pi$
$728$	−22.6357	+	13.6917i	−0.838933	+	0.507448i
$729$	−9.54908	+	25.2550i	−0.353669	+	0.935370i
$730$	−17.2039			−0.636746
$731$	−0.394056	−	0.682525i	−0.0145747	−	0.0252441i
$732$	−1.56687	+	4.69597i	−0.0579133	+	0.173568i
$733$	−8.03692	+	4.64012i	−0.296850	+	0.171387i	−0.641027	−	0.767518i	$-0.721491\pi$
$733$	−8.03692	+	4.64012i	−0.296850	+	0.171387i	0.344177	+	0.938905i	$0.388158\pi$
$734$	5.38599	+	9.32881i	0.198801	+	0.344333i
$735$	25.0436	+	6.08169i	0.923747	+	0.224327i
$736$	−9.35328			−0.344767
$737$	−2.09929	−	1.21202i	−0.0773282	−	0.0446455i
$738$	−24.7872	−	3.00132i	−0.912429	−	0.110480i
$739$	−19.1664	−	33.1971i	−0.705046	−	1.22118i	−0.966675	−	0.256007i	$-0.917593\pi$
$739$	−19.1664	−	33.1971i	−0.705046	−	1.22118i	0.261629	−	0.965169i	$-0.415740\pi$
$740$	−4.50970	−	7.81103i	−0.165780	−	0.287139i
$741$	34.0833	−	28.9206i	1.25208	−	1.06242i
$742$	−14.3463	+	9.10484i	−0.526669	+	0.334249i
$743$	−41.4254	−	23.9170i	−1.51975	−	0.877428i	−0.999729	−	0.0232753i	$-0.992591\pi$
$743$	−41.4254	−	23.9170i	−1.51975	−	0.877428i	−0.520022	−	0.854153i	$-0.674076\pi$
$744$	22.2746	+	7.43223i	0.816627	+	0.272479i
$745$			15.9902i			0.585834i
$746$	18.7696	+	10.8367i	0.687205	+	0.396758i
$747$	39.9086	−	17.0192i	1.46018	−	0.622700i
$748$	−2.03041	+	1.17226i	−0.0742393	+	0.0428621i
$749$	0.753455	−	1.44130i	0.0275306	−	0.0526638i
$750$	16.6718	−	3.40648i	0.608770	−	0.124387i
$751$	−19.6118			−0.715646			−0.357823	−	0.933789i	$-0.616481\pi$
$751$	−19.6118			−0.715646			−0.357823	+	0.933789i	$0.616481\pi$
$752$	−1.53761	−	2.66322i	−0.0560709	−	0.0971176i
$753$	−9.84905	+	8.72843i	−0.358919	+	0.318082i
$754$	1.50268	−	0.824993i	0.0547242	−	0.0300445i
$755$	−7.53267			−0.274142
$756$	−2.17370	−	17.5887i	−0.0790567	−	0.639695i
$757$	−6.86398	+	11.8888i	−0.249476	+	0.432105i	−0.963380	−	0.268138i	$-0.913592\pi$
$757$	−6.86398	+	11.8888i	−0.249476	+	0.432105i	0.713905	+	0.700243i	$0.246925\pi$
$758$	−22.2862	−	12.8670i	−0.809473	−	0.467349i
$759$	2.08342	−	1.84637i	0.0756234	−	0.0670190i
$760$	−42.1921			−1.53047
$761$	−11.3944	+	19.7356i	−0.413045	+	0.715415i	−0.995221	−	0.0976477i	$-0.968868\pi$
$761$	−11.3944	+	19.7356i	−0.413045	+	0.715415i	0.582176	+	0.813063i	$0.302202\pi$
$762$	5.02446	−	15.0585i	0.182017	−	0.545510i
$763$	−25.8604	+	16.4122i	−0.936209	+	0.594162i
$764$	5.50771	+	3.17988i	0.199262	+	0.115044i
$765$	9.38780	+	7.04958i	0.339417	+	0.254878i
$766$	−6.05112	−	3.49362i	−0.218636	−	0.126230i
$767$	36.7691	+	22.2967i	1.32765	+	0.805086i
$768$	−5.31319	−	26.0036i	−0.191723	−	0.938324i
$769$	20.0316	+	11.5653i	0.722359	+	0.417054i	0.815620	−	0.578588i	$-0.196396\pi$
$769$	20.0316	+	11.5653i	0.722359	+	0.417054i	−0.0932614	+	0.995642i	$0.529729\pi$
$770$	−3.95482	+	2.50991i	−0.142522	+	0.0904510i
$771$	−8.21801	−	40.2202i	−0.295964	−	1.44850i
$772$	3.46877	+	6.00808i	0.124844	+	0.216236i
$773$	−1.27842			−0.0459815			−0.0229908	−	0.999736i	$-0.507319\pi$
$773$	−1.27842			−0.0459815			−0.0229908	+	0.999736i	$0.507319\pi$
$774$	−0.650183	+	0.865838i	−0.0233704	+	0.0311219i
$775$	−2.04001	+	1.17780i	−0.0732795	+	0.0423079i
$776$	−0.276652	−	0.479176i	−0.00993124	−	0.0172014i
$777$	−4.17054	+	14.4958i	−0.149617	+	0.520035i
$778$	11.3028	−	19.5770i	0.405225	−	0.701871i
$779$	−61.1890	+	35.3275i	−2.19232	+	1.26574i
$780$	16.8357	−	3.06426i	0.602813	−	0.109718i
$781$	1.42001	−	2.45953i	0.0508119	−	0.0880088i
$782$	−2.52553			−0.0903126
$783$	0.237238	+	2.92051i	0.00847819	+	0.104370i
$784$	0.959187	+	1.37997i	0.0342567	+	0.0492847i
$785$			31.2255i			1.11448i
$786$	−16.7941	−	18.9502i	−0.599025	−	0.675933i
$787$		−	55.0921i		−	1.96382i	−0.189341	−	0.981911i	$-0.560635\pi$
$787$		−	55.0921i		−	1.96382i	0.189341	−	0.981911i	$-0.439365\pi$
$788$	−2.24225	−	1.29456i	−0.0798768	−	0.0461169i
$789$	20.1741	+	22.7642i	0.718217	+	0.810427i
$790$	−22.5842	−	13.0390i	−0.803510	−	0.463907i
$791$	18.6426	−	0.781727i	0.662856	−	0.0277950i
$792$	6.57186	+	4.93501i	0.233521	+	0.175358i
$793$	3.84716	+	7.00737i	0.136617	+	0.248839i
$794$	2.46501	−	4.26952i	0.0874798	−	0.151519i
$795$	27.4756	−	5.61396i	0.974460	−	0.199107i
$796$		−	2.42832i		−	0.0860694i
$797$	−12.6676	−	21.9409i	−0.448710	−	0.777188i	0.549593	−	0.835433i	$-0.314783\pi$
$797$	−12.6676	−	21.9409i	−0.448710	−	0.777188i	−0.998302	+	0.0582448i	$0.981450\pi$
$798$	19.1934	+	19.9107i	0.679439	+	0.704831i
$799$	−11.7910	−	20.4226i	−0.417135	−	0.722499i
$800$	2.39891	+	1.38501i	0.0848143	+	0.0489676i
$801$	−14.3144	+	6.10445i	−0.505775	+	0.215690i
$802$	3.49861			0.123540
$803$	9.48295			0.334646
$804$	−4.10049	+	3.63394i	−0.144613	+	0.128159i
$805$	9.14191	−	0.383341i	0.322210	−	0.0135110i
$806$	13.0273	−	7.15220i	0.458867	−	0.251925i
$807$	−8.23200	−	40.2887i	−0.289780	−	1.41823i
$808$	−14.4424	+	8.33833i	−0.508083	+	0.293342i
$809$	−21.5893	+	12.4646i	−0.759039	+	0.438231i	−0.828950	−	0.559322i	$-0.811062\pi$
$809$	−21.5893	+	12.4646i	−0.759039	+	0.438231i	0.0699118	+	0.997553i	$0.477728\pi$
$810$	3.84959	−	15.6634i	0.135261	−	0.550354i
$811$		−	13.2404i		−	0.464932i	−0.972605	−	0.232466i	$-0.925321\pi$
$811$		−	13.2404i		−	0.464932i	0.972605	−	0.232466i	$-0.0746794\pi$
$812$	−1.03059	−	1.62388i	−0.0361666	−	0.0569870i
$813$	−51.4337	+	10.5092i	−1.80386	+	0.368574i
$814$	−1.37077	−	2.37424i	−0.0480454	−	0.0832170i
$815$	1.89937			0.0665320
$816$	0.153260	+	0.750079i	0.00536517	+	0.0262580i
$817$			3.06405i			0.107197i
$818$	8.97874			0.313934
$819$	−23.2300	−	16.7142i	−0.811723	−	0.584042i
$820$	−27.0486			−0.944577
$821$			24.9896i			0.872144i	0.899912	+	0.436072i	$0.143631\pi$
$821$			24.9896i			0.872144i	−0.899912	+	0.436072i	$0.856369\pi$
$822$	3.73026	+	18.2565i	0.130108	+	0.636768i
$823$	−23.5272			−0.820107			−0.410054	−	0.912061i	$-0.634490\pi$
$823$	−23.5272			−0.820107			−0.410054	+	0.912061i	$0.634490\pi$
$824$	13.4856	+	23.3577i	0.469793	+	0.813705i
$825$	−0.807758	+	0.165045i	−0.0281225	+	0.00574614i
$826$	−12.3253	+	23.5773i	−0.428852	+	0.820358i
$827$			32.2623i			1.12187i	0.827860	+	0.560934i	$0.189558\pi$
$827$			32.2623i			1.12187i	−0.827860	+	0.560934i	$0.810442\pi$
$828$	−2.46827	−	5.78790i	−0.0857784	−	0.201143i
$829$	26.9798	−	15.5768i	0.937048	−	0.541005i	0.0480145	−	0.998847i	$-0.484711\pi$
$829$	26.9798	−	15.5768i	0.937048	−	0.541005i	0.889034	+	0.457842i	$0.151377\pi$
$830$	−22.4459	+	12.9592i	−0.779109	+	0.449819i
$831$	6.09602	+	29.8349i	0.211469	+	1.03496i
$832$	−13.4629	−	8.16388i	−0.466743	−	0.283032i
$833$	7.35541	+	10.5822i	0.254850	+	0.366650i
$834$	17.1644	−	15.2114i	0.594353	−	0.526728i
$835$	11.9404			0.413214
$836$	9.11510			0.315252
$837$	2.05671	+	25.3191i	0.0710904	+	0.875155i
$838$	−5.91804	−	3.41678i	−0.204435	−	0.118031i
$839$	−22.8424	−	39.5642i	−0.788608	−	1.36591i	−0.926820	−	0.375507i	$-0.877469\pi$
$839$	−22.8424	−	39.5642i	−0.788608	−	1.36591i	0.138211	−	0.990403i	$-0.455865\pi$
$840$	6.51169	+	26.2161i	0.224675	+	0.904540i
$841$	−14.3410	−	24.8394i	−0.494517	−	0.856529i
$842$			14.1558i			0.487842i
$843$	−46.0734	+	9.41396i	−1.58685	+	0.324234i
$844$	4.75391	−	8.23402i	0.163636	−	0.283427i
$845$	14.8328	−	23.3143i	0.510265	−	0.802035i
$846$	−19.4549	+	25.9077i	−0.668872	+	0.890725i
$847$	−22.3925	+	14.2113i	−0.769414	+	0.488306i
$848$	1.58373	+	0.914366i	0.0543854	+	0.0313995i
$849$	8.22918	+	9.28570i	0.282425	+	0.318684i
$850$	0.647742	+	0.373974i	0.0222174	+	0.0128272i
$851$			5.35540i			0.183581i
$852$	−4.25753	−	4.80414i	−0.145861	−	0.164587i
$853$			15.6593i			0.536165i	0.963396	+	0.268082i	$0.0863900\pi$
$853$			15.6593i			0.536165i	−0.963396	+	0.268082i	$0.913610\pi$
$854$	−4.17584	+	2.65018i	−0.142894	+	0.0906874i
$855$	−17.9046	−	41.9848i	−0.612323	−	1.43585i
$856$	1.70468			0.0582648
$857$	0.325260	−	0.563367i	0.0111107	−	0.0192443i	−0.860417	−	0.509591i	$-0.829797\pi$
$857$	0.325260	−	0.563367i	0.0111107	−	0.0192443i	0.871527	+	0.490347i	$0.163130\pi$
$858$	5.11736	−	0.931413i	0.174704	−	0.0317979i
$859$	20.5321	−	11.8542i	0.700547	−	0.404461i	−0.107004	−	0.994259i	$-0.534126\pi$
$859$	20.5321	−	11.8542i	0.700547	−	0.404461i	0.807551	+	0.589798i	$0.200792\pi$
$860$	−0.586498	+	1.01584i	−0.0199994	+	0.0346400i
$861$	31.3943	+	32.5675i	1.06991	+	1.10990i
$862$	5.83246	+	10.1021i	0.198654	+	0.344079i
$863$	7.67159	−	4.42919i	0.261144	−	0.150771i	−0.363712	−	0.931511i	$-0.618491\pi$
$863$	7.67159	−	4.42919i	0.261144	−	0.150771i	0.624856	+	0.780740i	$0.285158\pi$
$864$	24.5753	−	16.9812i	0.836068	−	0.577714i
$865$	30.6454			1.04197
$866$	4.94423	+	8.56366i	0.168012	+	0.291005i
$867$	−4.71928	−	23.0969i	−0.160275	−	0.784413i
$868$	−8.93461	−	14.0781i	−0.303260	−	0.477841i
$869$	12.4486	+	7.18721i	0.422290	+	0.243809i
$870$	−0.350416	−	1.71499i	−0.0118802	−	0.0581436i
$871$	−0.190307	+	8.84542i	−0.00644830	+	0.299716i
$872$	−27.8028	−	16.0520i	−0.941522	−	0.543588i
$873$	0.359421	−	0.478635i	0.0121646	−	0.0161993i
$874$	8.50335	+	4.90941i	0.287630	+	0.166063i
$875$	−27.3209	−	14.2823i	−0.923614	−	0.482830i
$876$	6.78409	−	20.3321i	0.229213	−	0.686959i
$877$	4.61113	−	7.98670i	0.155707	−	0.269692i	−0.777609	−	0.628748i	$-0.783568\pi$
$877$	4.61113	−	7.98670i	0.155707	−	0.269692i	0.933316	+	0.359056i	$0.116901\pi$
$878$	23.1434			0.781051
$879$	−29.5465	+	26.1847i	−0.996578	+	0.883187i
$880$	0.436583	+	0.252061i	0.0147172	+	0.00849699i
$881$	−9.25255	+	16.0259i	−0.311726	+	0.539926i	−0.978736	−	0.205123i	$-0.934240\pi$
$881$	−9.25255	+	16.0259i	−0.311726	+	0.539926i	0.667010	+	0.745049i	$0.267574\pi$
$882$	9.40931	−	14.9987i	0.316828	−	0.505033i
$883$	38.1017			1.28223			0.641113	−	0.767447i	$-0.278473\pi$
$883$	38.1017			1.28223			0.641113	+	0.767447i	$0.278473\pi$
$884$	7.31701	+	4.43701i	0.246098	+	0.149233i
$885$	32.8613	−	29.1223i	1.10462	−	0.978936i
$886$	−11.5579	−	20.0189i	−0.388295	−	0.672547i
$887$	29.8003			1.00060			0.500298	−	0.865853i	$-0.333224\pi$
$887$	29.8003			1.00060			0.500298	+	0.865853i	$0.333224\pi$
$888$	−15.4903	+	3.16505i	−0.519820	+	0.106212i
$889$	−24.2828	+	15.4110i	−0.814420	+	0.516869i
$890$	8.05091	−	4.64819i	0.269867	−	0.155808i
$891$	−2.12193	+	8.63378i	−0.0710873	+	0.289242i
$892$	−1.54026	−	0.889269i	−0.0515717	−	0.0297749i
$893$			91.6828i			3.06805i
$894$	10.4210	+	3.47710i	0.348529	+	0.116292i
$895$	41.0498	+	23.7001i	1.37214	+	0.792207i
$896$	−9.57988	+	18.3255i	−0.320041	+	0.612212i
$897$	−9.56687	−	3.42252i	−0.319429	−	0.114274i
$898$	2.71234	+	4.69791i	0.0905120	+	0.156771i
$899$	1.37838	+	2.38742i	0.0459715	+	0.0796250i
$900$	−0.224000	+	1.84996i	−0.00746668	+	0.0616655i
$901$	12.1446	+	7.01171i	0.404596	+	0.233594i
$902$	−8.22168			−0.273752
$903$	1.90384	−	0.472887i	0.0633560	−	0.0157367i
$904$	9.77884	+	16.9374i	0.325239	+	0.563331i
$905$	−11.5410	+	6.66319i	−0.383635	+	0.221492i
$906$	−1.63800	+	4.90913i	−0.0544189	+	0.163095i
$907$	12.5986	+	21.8214i	0.418329	+	0.724567i	0.995772	−	0.0918646i	$-0.0292827\pi$
$907$	12.5986	+	21.8214i	0.418329	+	0.724567i	−0.577443	+	0.816431i	$0.695949\pi$
$908$	3.84465			0.127589
$909$	−14.4261	−	10.8330i	−0.478484	−	0.359308i
$910$	14.9770	+	8.24434i	0.496481	+	0.273297i
$911$		−	29.5095i		−	0.977692i	−0.872370	−	0.488846i	$-0.837418\pi$
$911$		−	29.5095i		−	0.977692i	0.872370	−	0.488846i	$-0.162582\pi$
$912$	0.942071	−	2.82341i	0.0311951	−	0.0934925i
$913$	12.3724	−	7.14320i	0.409466	−	0.236405i
$914$			20.2316i			0.669202i
$915$	7.99745	−	1.63408i	0.264388	−	0.0540210i
$916$	13.3309	−	7.69658i	0.440464	−	0.254302i
$917$	1.92193	+	45.8343i	0.0634679	+	1.51358i
$918$	6.63569	−	4.58519i	0.219011	−	0.151334i
$919$	−21.1797	+	36.6842i	−0.698652	+	1.21010i	0.270282	+	0.962781i	$0.412883\pi$
$919$	−21.1797	+	36.6842i	−0.698652	+	1.21010i	−0.968934	+	0.247320i	$0.920450\pi$
$920$	4.79531	+	8.30572i	0.158097	+	0.273832i
$921$	−42.3803	+	8.65936i	−1.39648	+	0.285336i
$922$	−4.61096	+	2.66214i	−0.151854	+	0.0876729i
$923$	−10.3633	−	0.222964i	−0.341112	−	0.00733894i
$924$	−1.40677	−	5.66367i	−0.0462794	−	0.186321i
$925$	0.793014	−	1.37354i	0.0260742	−	0.0451618i
$926$		−	3.73983i		−	0.122898i
$927$	−17.5202	+	23.3314i	−0.575439	+	0.766302i
$928$	1.62088	−	2.80744i	0.0532079	−	0.0921587i
$929$	−15.1396	+	26.2226i	−0.496714	+	0.860335i	−0.999993	−	0.00378978i	$-0.998794\pi$
$929$	−15.1396	+	26.2226i	−0.496714	+	0.860335i	0.503278	+	0.864124i	$0.332127\pi$
$930$	−3.03790	−	14.8679i	−0.0996165	−	0.487539i
$931$	−4.19456	−	49.9280i	−0.137471	−	1.63632i
$932$	18.5019	−	10.6821i	0.606049	−	0.349903i
$933$	−29.5893	−	9.87288i	−0.968710	−	0.323224i
$934$	−2.98561	+	1.72375i	−0.0976923	+	0.0564027i
$935$	3.34789	+	1.93290i	0.109488	+	0.0632127i
$936$	4.24545	−	29.6945i	0.138767	−	0.970596i
$937$		−	1.23501i		−	0.0403459i	−0.999797	−	0.0201730i	$-0.993578\pi$
$937$		−	1.23501i		−	0.0403459i	0.999797	−	0.0201730i	$-0.00642169\pi$
$938$	−5.46905	+	0.229330i	−0.178571	+	0.00748788i
$939$	23.2856	+	26.2752i	0.759896	+	0.857457i
$940$	−17.5493	+	30.3962i	−0.572394	+	0.991416i
$941$	8.91584	−	15.4427i	0.290648	−	0.503417i	−0.683315	−	0.730124i	$-0.739462\pi$
$941$	8.91584	−	15.4427i	0.290648	−	0.503417i	0.973963	+	0.226706i	$0.0727958\pi$
$942$	20.3500	+	6.79006i	0.663039	+	0.221232i
$943$	13.9088	+	8.03023i	0.452932	+	0.261500i
$944$	2.86333			0.0931934
$945$	−23.3239	+	17.6047i	−0.758728	+	0.572681i
$946$	−0.178272	+	0.308776i	−0.00579612	+	0.0100392i
$947$			14.8353i			0.482082i	0.970515	+	0.241041i	$0.0774889\pi$
$947$			14.8353i			0.482082i	−0.970515	+	0.241041i	$0.922511\pi$
$948$	24.3156	−	21.5490i	0.789735	−	0.699879i
$949$	−16.6570	−	30.3398i	−0.540710	−	0.984872i
$950$	−1.45395	−	2.51831i	−0.0471723	−	0.0817049i
$951$	10.7804	+	12.1645i	0.349578	+	0.394460i
$952$	−6.25798	+	11.9710i	−0.202822	+	0.387982i
$953$	2.58732	−	1.49379i	0.0838116	−	0.0483887i	−0.457508	−	0.889205i	$-0.651258\pi$
$953$	2.58732	−	1.49379i	0.0838116	−	0.0483887i	0.541320	+	0.840817i	$0.317925\pi$
$954$	2.31596	−	19.1270i	0.0749820	−	0.619258i
$955$		−	10.4864i		−	0.339332i
$956$		−	38.2032i		−	1.23558i
$957$	0.193152	+	0.945317i	0.00624372	+	0.0305578i
$958$	22.1506	−	12.7887i	0.715653	−	0.413183i
$959$	15.6398	−	29.9177i	0.505037	−	0.966093i
$960$	−12.0321	+	10.6631i	−0.388334	+	0.344149i
$961$	−3.55027	−	6.14924i	−0.114525	−	0.198363i
$962$	−5.18837	+	8.55605i	−0.167280	+	0.275858i
$963$	0.723396	+	1.69630i	0.0233111	+	0.0546626i
$964$			23.3647i			0.752526i
$965$	5.71954	−	9.90654i	0.184119	−	0.318903i
$966$	1.73810	−	6.04125i	0.0559226	−	0.194374i
$967$	13.1157			0.421773			0.210887	−	0.977511i	$-0.432365\pi$
$967$	13.1157			0.421773			0.210887	+	0.977511i	$0.432365\pi$
$968$	−24.0744	−	13.8993i	−0.773780	−	0.446742i
$969$	7.22416	−	21.6510i	0.232073	−	0.695530i
$970$	−0.178786	+	0.309667i	−0.00574049	+	0.00994282i
$971$	16.9046	−	29.2796i	0.542495	−	0.939628i	−0.456265	−	0.889844i	$-0.650813\pi$
$971$	16.9046	−	29.2796i	0.542495	−	0.939628i	0.998760	−	0.0497845i	$-0.0158534\pi$
$972$	16.9934	+	10.7262i	0.545064	+	0.344042i
$973$	−41.5149	+	1.74081i	−1.33091	+	0.0558078i
$974$		−	30.8111i		−	0.987251i
$975$	1.94689	+	2.29444i	0.0623505	+	0.0734809i
$976$	0.460983	+	0.266148i	0.0147557	+	0.00851921i
$977$	23.7118	−	13.6900i	0.758607	−	0.437982i	−0.0701884	−	0.997534i	$-0.522360\pi$
$977$	23.7118	−	13.6900i	0.758607	−	0.437982i	0.828795	+	0.559552i	$0.189027\pi$
$978$	0.413023	−	1.23784i	0.0132070	−	0.0395818i
$979$	−4.43773	+	2.56212i	−0.141830	+	0.0818858i
$980$	8.16622	−	17.3559i	0.260860	−	0.554413i
$981$	4.17471	−	34.4779i	0.133288	−	1.10080i
$982$	−10.5478	+	18.2693i	−0.336593	+	0.582996i
$983$	16.3929	−	28.3933i	0.522851	−	0.905605i	−0.476795	−	0.879014i	$-0.658202\pi$
$983$	16.3929	−	28.3933i	0.522851	−	0.905605i	0.999646	−	0.0265906i	$-0.00846504\pi$
$984$	−15.0070	+	44.9765i	−0.478406	+	1.43380i
$985$			4.26913i			0.136026i
$986$	0.437661	−	0.758051i	0.0139380	−	0.0241413i
$987$	56.9671	−	14.1498i	1.81328	−	0.450393i
$988$	−16.0109	−	29.1629i	−0.509375	−	0.927796i
$989$	0.603172	−	0.348242i	0.0191798	−	0.0110734i
$990$	0.638437	−	5.27269i	0.0202909	−	0.167577i
$991$	7.02081	+	12.1604i	0.223023	+	0.386288i	0.955725	−	0.294263i	$-0.0950740\pi$
$991$	7.02081	+	12.1604i	0.223023	+	0.386288i	−0.732701	+	0.680550i	$0.761741\pi$
$992$	14.0520	−	24.3388i	0.446153	−	0.772759i
$993$	30.9025	+	10.3110i	0.980661	+	0.327211i
$994$	−0.268683	−	6.40755i	−0.00852210	−	0.203235i
$995$	−3.46755	+	2.00199i	−0.109929	+	0.0634673i
$996$	−6.46434	−	31.6375i	−0.204830	−	1.00247i
$997$			42.8725i			1.35779i	0.734237	+	0.678893i	$0.237540\pi$
$997$			42.8725i			1.35779i	−0.734237	+	0.678893i	$0.762460\pi$
$998$	11.7307	−	6.77273i	0.371329	−	0.214387i
$999$	−9.72292	−	14.0710i	−0.307620	−	0.445188i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.r.b.269.20	yes	64
3.2	odd	2	inner	273.2.r.b.269.13	yes	64
7.5	odd	6		273.2.bf.b.152.20	yes	64
13.3	even	3		273.2.bf.b.185.13	yes	64
21.5	even	6		273.2.bf.b.152.13	yes	64
39.29	odd	6		273.2.bf.b.185.20	yes	64
91.68	odd	6	inner	273.2.r.b.68.20	yes	64
273.68	even	6	inner	273.2.r.b.68.13	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.r.b.68.13	✓	64	273.68	even	6	inner
273.2.r.b.68.20	yes	64	91.68	odd	6	inner
273.2.r.b.269.13	yes	64	3.2	odd	2	inner
273.2.r.b.269.20	yes	64	1.1	even	1	trivial
273.2.bf.b.152.13	yes	64	21.5	even	6
273.2.bf.b.152.20	yes	64	7.5	odd	6
273.2.bf.b.185.13	yes	64	13.3	even	3
273.2.bf.b.185.20	yes	64	39.29	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.843135i q^{2} +(0.346738 + 1.69699i) q^{3} +1.28912 q^{4} +(-1.06280 - 1.84082i) q^{5} +(-1.43079 + 0.292347i) q^{6} +(2.34470 + 1.22572i) q^{7} +2.77318i q^{8} +(-2.75955 + 1.17682i) q^{9} +(1.55206 - 0.896082i) q^{10} +(-0.855509 + 0.493928i) q^{11} +(0.446987 + 2.18763i) q^{12} +(3.08300 + 1.86952i) q^{13} +(-1.03345 + 1.97690i) q^{14} +(2.75534 - 2.44184i) q^{15} +0.240083 q^{16} +1.84105 q^{17} +(-0.992218 - 2.32667i) q^{18} +(-6.19875 - 3.57885i) q^{19} +(-1.37008 - 2.37304i) q^{20} +(-1.26704 + 4.40393i) q^{21} +(-0.416448 - 0.721310i) q^{22} +1.62700i q^{23} +(-4.70605 + 0.961564i) q^{24} +(0.240923 - 0.417291i) q^{25} +(-1.57626 + 2.59939i) q^{26} +(-2.95389 - 4.27487i) q^{27} +(3.02260 + 1.58010i) q^{28} +(-0.488355 - 0.281952i) q^{29} +(2.05880 + 2.32312i) q^{30} +(-4.23375 - 2.44435i) q^{31} +5.74877i q^{32} +(-1.13483 - 1.28053i) q^{33} +1.55226i q^{34} +(-0.235611 - 5.61886i) q^{35} +(-3.55739 + 1.51707i) q^{36} +3.29157 q^{37} +(3.01745 - 5.22638i) q^{38} +(-2.10357 + 5.88005i) q^{39} +(5.10491 - 2.94732i) q^{40} +(4.93559 - 8.54870i) q^{41} +(-3.71311 - 1.06828i) q^{42} +(-0.214038 - 0.370726i) q^{43} +(-1.10286 + 0.636734i) q^{44} +(5.09915 + 3.82910i) q^{45} -1.37179 q^{46} +(-6.40449 - 11.0929i) q^{47} +(0.0832459 + 0.407419i) q^{48} +(3.99522 + 5.74789i) q^{49} +(0.351833 + 0.203131i) q^{50} +(0.638362 + 3.12424i) q^{51} +(3.97436 + 2.41004i) q^{52} +(6.59657 + 3.80853i) q^{53} +(3.60430 - 2.49053i) q^{54} +(1.81847 + 1.04989i) q^{55} +(-3.39914 + 6.50226i) q^{56} +(3.92393 - 11.7601i) q^{57} +(0.237723 - 0.411749i) q^{58} +11.9264 q^{59} +(3.55197 - 3.14783i) q^{60} +(1.92009 + 1.10857i) q^{61} +(2.06092 - 3.56962i) q^{62} +(-7.91276 - 0.623142i) q^{63} -4.36683 q^{64} +(0.164850 - 7.66217i) q^{65} +(1.07966 - 0.956814i) q^{66} +(1.22692 + 2.12509i) q^{67} +2.37334 q^{68} +(-2.76101 + 0.564144i) q^{69} +(4.73746 - 0.198652i) q^{70} +(-2.48976 + 1.43746i) q^{71} +(-3.26353 - 7.65271i) q^{72} +(-8.31343 - 4.79976i) q^{73} +2.77524i q^{74} +(0.791675 + 0.264153i) q^{75} +(-7.99095 - 4.61358i) q^{76} +(-2.61133 + 0.109499i) q^{77} +(-4.95768 - 1.77359i) q^{78} +(-7.27556 - 12.6016i) q^{79} +(-0.255160 - 0.441950i) q^{80} +(6.23019 - 6.49498i) q^{81} +(7.20771 + 4.16137i) q^{82} -14.4620 q^{83} +(-1.63337 + 5.67721i) q^{84} +(-1.95666 - 3.38904i) q^{85} +(0.312572 - 0.180463i) q^{86} +(0.309138 - 0.926496i) q^{87} +(-1.36975 - 2.37248i) q^{88} +5.18724 q^{89} +(-3.22845 + 4.29927i) q^{90} +(4.93719 + 8.16236i) q^{91} +2.09741i q^{92} +(2.68004 - 8.03217i) q^{93} +(9.35281 - 5.39985i) q^{94} +15.2144i q^{95} +(-9.75561 + 1.99332i) q^{96} +(-0.172790 + 0.0997601i) q^{97} +(-4.84625 + 3.36851i) q^{98} +(1.77955 - 2.36980i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 64 q^{4} + 12 q^{6} - 10 q^{7} - 4 q^{9} - 6 q^{10} + 6 q^{12} + 12 q^{13} - 9 q^{15} + 32 q^{16} + 2 q^{18} - 36 q^{19} + 10 q^{21} + 10 q^{22} - 18 q^{24} - 24 q^{25} - 14 q^{28} + 8 q^{30} - 24 q^{31}+ \cdots + 22 q^{99}+O(q^{100}) \) 64 * q - 64 * q^4 + 12 * q^6 - 10 * q^7 - 4 * q^9 - 6 * q^10 + 6 * q^12 + 12 * q^13 - 9 * q^15 + 32 * q^16 + 2 * q^18 - 36 * q^19 + 10 * q^21 + 10 * q^22 - 18 * q^24 - 24 * q^25 - 14 * q^28 + 8 * q^30 - 24 * q^31 - 45 * q^33 + 33 * q^39 + 90 * q^40 + 3 * q^42 - 20 * q^43 - 6 * q^48 - 6 * q^49 - 10 * q^51 - 48 * q^52 - 18 * q^55 + 4 * q^57 + 30 * q^58 + 55 * q^60 - 18 * q^61 + 31 * q^63 - 84 * q^64 + 75 * q^66 + 44 * q^67 + 33 * q^69 + 20 * q^70 + 17 * q^72 + 84 * q^73 - 18 * q^76 - 71 * q^78 + 20 * q^79 + 16 * q^81 - 18 * q^82 - 135 * q^84 - 2 * q^85 - 46 * q^88 - 10 * q^91 - 56 * q^93 + 36 * q^94 + 30 * q^96 - 24 * q^97 + 22 * q^99

Introduction

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