LMFDB - Embedded newform 273.2.r.b.68.20

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			68.20
Character	$\chi$	$=$	273.68
Dual form			273.2.r.b.269.13

$q$-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} +(-1.29627 + 1.14878i) q^{3} +1.28912 q^{4} +(1.06280 - 1.84082i) q^{5} +(-0.968576 - 1.09293i) q^{6} +(2.34470 - 1.22572i) q^{7} +2.77318i q^{8} +(0.360617 - 2.97825i) q^{9} +(1.55206 + 0.896082i) q^{10} +(0.855509 + 0.493928i) q^{11} +(-1.67105 + 1.48092i) q^{12} +(3.08300 - 1.86952i) q^{13} +(1.03345 + 1.97690i) q^{14} +(0.737024 + 3.60711i) q^{15} +0.240083 q^{16} -1.84105 q^{17} +(2.51107 + 0.304049i) q^{18} +(-6.19875 + 3.57885i) q^{19} +(1.37008 - 2.37304i) q^{20} +(-1.63128 + 4.28240i) q^{21} +(-0.416448 + 0.721310i) q^{22} +1.62700i q^{23} +(-3.18576 - 3.59478i) 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} +(-3.04128 + 0.621411i) q^{30} +(-4.23375 + 2.44435i) q^{31} +5.74877i q^{32} +(-1.67638 + 0.342527i) q^{33} -1.55226i q^{34} +(0.235611 - 5.61886i) q^{35} +(0.464880 - 3.83933i) q^{36} +3.29157 q^{37} +(-3.01745 - 5.22638i) q^{38} +(-1.84872 + 5.96508i) q^{39} +(5.10491 + 2.94732i) q^{40} +(-4.93559 - 8.54870i) q^{41} +(-3.61064 - 1.37539i) 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} +(-0.311212 + 0.275803i) q^{48} +(3.99522 - 5.74789i) q^{49} +(-0.351833 + 0.203131i) q^{50} +(2.38649 - 2.11496i) 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} +(0.950114 + 4.65001i) q^{60} +(1.92009 - 1.10857i) q^{61} +(-2.06092 - 3.56962i) q^{62} +(-2.80496 - 7.42511i) q^{63} -4.36683 q^{64} +(-0.164850 - 7.66217i) q^{65} +(-0.288797 - 1.41342i) q^{66} +(1.22692 - 2.12509i) q^{67} -2.37334 q^{68} +(-1.86907 - 2.10903i) q^{69} +(4.73746 + 0.198652i) q^{70} +(2.48976 + 1.43746i) q^{71} +(8.25920 + 1.00005i) 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} +(-5.02937 - 1.55872i) q^{78} +(-7.27556 + 12.6016i) q^{79} +(0.255160 - 0.441950i) q^{80} +(-8.73991 - 2.14801i) q^{81} +(7.20771 - 4.16137i) q^{82} +14.4620 q^{83} +(-2.10291 + 5.52054i) 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} +(-6.60407 - 7.45195i) 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 $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$

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	$0.903649\pi$
$3$	−1.29627	+	1.14878i	−0.748400	+	0.663247i
$3$	−1.29627	+	1.14878i	−0.748400	+	0.663247i
$4$	1.28912			0.644561
$5$	1.06280	−	1.84082i	0.475297	−	0.823239i	−0.524302	−	0.851532i	$-0.675674\pi$
$5$	1.06280	−	1.84082i	0.475297	−	0.823239i	0.999600	+	0.0282929i	$0.00900711\pi$
$6$	−0.968576	−	1.09293i	−0.395419	−	0.446186i
$7$	2.34470	−	1.22572i	0.886213	−	0.463278i
$7$	2.34470	−	1.22572i	0.886213	−	0.463278i
$8$			2.77318i			0.980466i
$9$	0.360617	−	2.97825i	0.120206	−	0.992749i
$10$	1.55206	+	0.896082i	0.490804	+	0.283366i
$11$	0.855509	+	0.493928i	0.257946	+	0.148925i	0.623397	−	0.781905i	$-0.285752\pi$
$11$	0.855509	+	0.493928i	0.257946	+	0.148925i	−0.365451	+	0.930830i	$0.619085\pi$
$12$	−1.67105	+	1.48092i	−0.482390	+	0.427504i
$13$	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
$15$	0.737024	+	3.60711i	0.190299	+	0.931352i
$16$	0.240083			0.0600208
$17$	−1.84105			−0.446520			−0.223260	−	0.974759i	$-0.571670\pi$
$17$	−1.84105			−0.446520			−0.223260	+	0.974759i	$0.571670\pi$
$18$	2.51107	+	0.304049i	0.591864	+	0.0716650i
$19$	−6.19875	+	3.57885i	−1.42209	+	0.821044i	−0.996477	−	0.0838608i	$-0.973275\pi$
$19$	−6.19875	+	3.57885i	−1.42209	+	0.821044i	−0.425613	+	0.904905i	$0.639942\pi$
$20$	1.37008	−	2.37304i	0.306358	−	0.530628i
$21$	−1.63128	+	4.28240i	−0.355974	+	0.934496i
$22$	−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	$0.945744\pi$
$24$	−3.18576	−	3.59478i	−0.650291	−	0.733781i
$25$	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	$-0.649993\pi$
$29$	0.488355	−	0.281952i	0.0906852	−	0.0523571i	0.544657	+	0.838659i	$0.316660\pi$
$30$	−3.04128	+	0.621411i	−0.555260	+	0.113454i
$31$	−4.23375	+	2.44435i	−0.760403	+	0.439019i	−0.829440	−	0.558595i	$-0.811341\pi$
$31$	−4.23375	+	2.44435i	−0.760403	+	0.439019i	0.0690374	+	0.997614i	$0.478007\pi$
$32$			5.74877i			1.01625i
$33$	−1.67638	+	0.342527i	−0.291821	+	0.0596263i
$34$		−	1.55226i		−	0.266210i
$35$	0.235611	−	5.61886i	0.0398256	−	0.949760i
$36$	0.464880	−	3.83933i	0.0774799	−	0.639888i
$37$	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
$39$	−1.84872	+	5.96508i	−0.296033	+	0.955178i
$40$	5.10491	+	2.94732i	0.807158	+	0.466013i
$41$	−4.93559	−	8.54870i	−0.770810	−	1.33508i	−0.937120	−	0.349008i	$-0.886518\pi$
$41$	−4.93559	−	8.54870i	−0.770810	−	1.33508i	0.166310	−	0.986074i	$-0.446815\pi$
$42$	−3.61064	−	1.37539i	−0.557134	−	0.212227i
$43$	−0.214038	+	0.370726i	−0.0326406	+	0.0565351i	−0.881884	−	0.471466i	$-0.843725\pi$
$43$	−0.214038	+	0.370726i	−0.0326406	+	0.0565351i	0.849244	+	0.528001i	$0.177058\pi$
$44$	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	0.158119	−	0.987420i	$-0.449457\pi$
$47$	6.40449	−	11.0929i	0.934190	−	1.61807i	0.776071	−	0.630645i	$-0.217210\pi$
$48$	−0.311212	+	0.275803i	−0.0449196	+	0.0398087i
$49$	3.99522	−	5.74789i	0.570746	−	0.821127i
$50$	−0.351833	+	0.203131i	−0.0497567	+	0.0287270i
$51$	2.38649	−	2.11496i	0.334176	−	0.296154i
$52$	3.97436	−	2.41004i	0.551145	−	0.334213i
$53$	−6.59657	+	3.80853i	−0.906109	+	0.523142i	−0.879177	−	0.476495i	$-0.841907\pi$
$53$	−6.59657	+	3.80853i	−0.906109	+	0.523142i	−0.0269320	+	0.999637i	$0.508574\pi$
$54$	−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	$-0.782927\pi$
$59$	−11.9264			−1.55268			−0.776342	+	0.630312i	$0.782927\pi$
$60$	0.950114	+	4.65001i	0.122659	+	0.600314i
$61$	1.92009	−	1.10857i	0.245843	−	0.141937i	−0.372016	−	0.928226i	$-0.621333\pi$
$61$	1.92009	−	1.10857i	0.245843	−	0.141937i	0.617859	+	0.786289i	$0.288000\pi$
$62$	−2.06092	−	3.56962i	−0.261737	−	0.453342i
$63$	−2.80496	−	7.42511i	−0.353391	−	0.935476i
$64$	−4.36683			−0.545853
$65$	−0.164850	−	7.66217i	−0.0204471	−	0.950375i
$66$	−0.288797	−	1.41342i	−0.0355484	−	0.173980i
$67$	1.22692	−	2.12509i	0.149892	−	0.259621i	−0.781295	−	0.624162i	$-0.785441\pi$
$67$	1.22692	−	2.12509i	0.149892	−	0.259621i	0.931188	+	0.364540i	$0.118774\pi$
$68$	−2.37334			−0.287810
$69$	−1.86907	−	2.10903i	−0.225009	−	0.253898i
$70$	4.73746	+	0.198652i	0.566234	+	0.0237435i
$71$	2.48976	+	1.43746i	0.295480	+	0.170596i	0.640411	−	0.768033i	$-0.278764\pi$
$71$	2.48976	+	1.43746i	0.295480	+	0.170596i	−0.344930	+	0.938628i	$0.612097\pi$
$72$	8.25920	+	1.00005i	0.973356	+	0.117858i
$73$	−8.31343	+	4.79976i	−0.973013	+	0.561769i	−0.900154	−	0.435573i	$-0.856546\pi$
$73$	−8.31343	+	4.79976i	−0.973013	+	0.561769i	−0.0728598	+	0.997342i	$0.523213\pi$
$74$			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
$78$	−5.02937	−	1.55872i	−0.569464	−	0.176491i
$79$	−7.27556	+	12.6016i	−0.818565	+	1.41780i	0.0881750	+	0.996105i	$0.471897\pi$
$79$	−7.27556	+	12.6016i	−0.818565	+	1.41780i	−0.906740	+	0.421691i	$0.861437\pi$
$80$	0.255160	−	0.441950i	0.0285278	−	0.0494115i
$81$	−8.73991	−	2.14801i	−0.971101	−	0.238668i
$82$	7.20771	−	4.16137i	0.795958	−	0.459547i
$83$	14.4620			1.58741			0.793707	−	0.608301i	$-0.208149\pi$
$83$	14.4620			1.58741			0.793707	+	0.608301i	$0.208149\pi$
$84$	−2.10291	+	5.52054i	−0.229447	+	0.602340i
$85$	−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	$-0.588652\pi$
$89$	−5.18724			−0.549846			−0.274923	+	0.961466i	$0.588652\pi$
$90$	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
$96$	−6.60407	−	7.45195i	−0.674025	−	0.760561i
$97$	−0.172790	−	0.0997601i	−0.0175441	−	0.0101291i	0.491202	−	0.871046i	$-0.336558\pi$
$97$	−0.172790	−	0.0997601i	−0.0175441	−	0.0101291i	−0.508746	+	0.860916i	$0.669891\pi$
$98$	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	$-0.930048\pi$
$101$	−3.00678	+	5.20790i	−0.299186	+	0.518205i	0.676764	+	0.736200i	$0.263382\pi$
$102$	1.78320	+	2.01214i	0.176563	+	0.199231i
$103$	8.42274	+	4.86287i	0.829917	+	0.479153i	0.853824	−	0.520561i	$-0.174277\pi$
$103$	8.42274	+	4.86287i	0.829917	+	0.479153i	−0.0239072	+	0.999714i	$0.507611\pi$
$104$	5.18451	+	8.54970i	0.508384	+	0.838367i
$105$	6.14941	+	7.55421i	0.600121	+	0.737215i
$106$	−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	−0.997949	−	0.0640208i	$-0.979608\pi$
$109$	−5.78829	−	10.0256i	−0.554418	−	0.960280i	0.443531	−	0.896259i	$-0.353726\pi$
$110$	0.885200	+	1.53321i	0.0844005	+	0.146186i
$111$	−4.26675	+	3.78128i	−0.404982	+	0.358903i
$112$	0.562923	−	0.294275i	0.0531912	−	0.0278064i
$113$	−6.10760	−	3.52622i	−0.574554	−	0.331719i	0.184412	−	0.982849i	$-0.440962\pi$
$113$	−6.10760	−	3.52622i	−0.574554	−	0.331719i	−0.758966	+	0.651130i	$0.774295\pi$
$114$	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
$117$	−4.45612	−	9.85612i	−0.411968	−	0.911198i
$118$		−	10.0556i		−	0.925690i
$119$	−4.31671	+	2.25661i	−0.395712	+	0.206863i
$120$	−10.0032	+	2.04390i	−0.913159	+	0.186581i
$121$	−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
$126$	6.26037	−	2.36496i	0.557718	−	0.210687i
$127$	−5.43519	−	9.41402i	−0.482295	−	0.835359i	0.517499	−	0.855684i	$-0.326863\pi$
$127$	−5.43519	−	9.41402i	−0.482295	−	0.835359i	−0.999793	+	0.0203250i	$0.993530\pi$
$128$			7.81572i			0.690819i
$129$	−0.148430	−	0.726442i	−0.0130686	−	0.0639597i
$130$	6.46024	−	0.138990i	0.566601	−	0.0121903i
$131$	−8.66948	+	15.0160i	−0.757456	+	1.31195i	0.186688	+	0.982419i	$0.440225\pi$
$131$	−8.66948	+	15.0160i	−0.757456	+	1.31195i	−0.944144	+	0.329533i	$0.893109\pi$
$132$	−2.16106	+	0.441559i	−0.188096	+	0.0384328i
$133$	−10.1475	+	15.9893i	−0.879903	+	1.38644i
$134$	1.79174	+	1.03446i	0.154783	+	0.0893639i
$135$	11.0087	−	0.894252i	0.947474	−	0.0769650i
$136$		−	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	$-0.183496\pi$
$138$	1.77820	−	1.57588i	0.151370	−	0.134148i
$139$	−13.6009	−	7.85246i	−1.15361	−	0.666037i	−0.203846	−	0.979003i	$-0.565344\pi$
$139$	−13.6009	−	7.85246i	−1.15361	−	0.666037i	−0.949764	+	0.312966i	$0.898678\pi$
$140$	0.303732	−	7.24340i	0.0256700	−	0.612179i
$141$	4.44135	+	21.7367i	0.374029	+	1.83056i
$142$	−1.21198	+	2.09921i	−0.101707	+	0.176161i
$143$	3.56094	−	0.0766127i	0.297781	−	0.00640668i
$144$	0.0865782	−	0.715028i	0.00721485	−	0.0595856i
$145$		−	1.19863i		−	0.0995408i
$146$	−4.04685	−	7.00935i	−0.334920	−	0.580098i
$147$	1.42417	+	12.0404i	0.117464	+	0.993077i
$148$	4.24323			0.348792
$149$	6.51483	−	3.76134i	0.533715	−	0.308141i	−0.208813	−	0.977956i	$-0.566960\pi$
$149$	6.51483	−	3.76134i	0.533715	−	0.308141i	0.742528	+	0.669815i	$0.233627\pi$
$150$	0.222717	−	0.667490i	0.0181848	−	0.0545003i
$151$	1.77190	+	3.06902i	0.144195	+	0.249753i	0.929072	−	0.369898i	$-0.120607\pi$
$151$	1.77190	+	3.06902i	0.144195	+	0.249753i	−0.784877	+	0.619651i	$0.787274\pi$
$152$	−9.92478	−	17.1902i	−0.805006	−	1.39431i
$153$	−0.663914	+	5.48310i	−0.0536743	+	0.443283i
$154$	−0.0923223	+	2.20170i	−0.00743954	+	0.177418i
$155$			10.3914i			0.834658i
$156$	−2.38323	+	7.68973i	−0.190811	+	0.615671i
$157$	−12.7221	+	7.34511i	−1.01533	+	0.586204i	−0.912749	−	0.408521i	$-0.866045\pi$
$157$	−12.7221	+	7.34511i	−1.01533	+	0.586204i	−0.102585	+	0.994724i	$0.532711\pi$
$158$	−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
$162$	1.81107	−	7.36893i	0.142291	−	0.578958i
$163$	−0.446786	−	0.773855i	−0.0349949	−	0.0606130i	0.847997	−	0.530000i	$-0.177808\pi$
$163$	−0.446786	−	0.773855i	−0.0349949	−	0.0606130i	−0.882992	+	0.469387i	$0.844475\pi$
$164$	−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	$-0.0969271\pi$
$167$	2.80871	+	4.86483i	0.217345	+	0.376452i	−0.736651	+	0.676274i	$0.763594\pi$
$168$	−11.8758	−	4.52381i	−0.916241	−	0.349020i
$169$	6.00977	−	11.5275i	0.462290	−	0.886729i
$170$	−2.85742	−	1.64973i	−0.219154	−	0.126529i
$171$	8.42332	+	19.7520i	0.644148	+	1.51047i
$172$	−0.275922	+	0.477911i	−0.0210388	+	0.0364404i
$173$	7.20865	+	12.4858i	0.548064	+	0.949274i	0.998407	+	0.0564189i	$0.0179682\pi$
$173$	7.20865	+	12.4858i	0.548064	+	0.949274i	−0.450343	+	0.892855i	$0.648698\pi$
$174$	−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
$177$	15.4598	−	13.7008i	1.16203	−	1.02981i
$178$		−	4.37355i		−	0.327811i
$179$	19.3121	+	11.1499i	1.44346	+	0.833380i	0.998079	−	0.0619621i	$-0.0197358\pi$
$179$	19.3121	+	11.1499i	1.44346	+	0.833380i	0.445378	+	0.895342i	$0.353069\pi$
$180$	−6.57343	−	4.93619i	−0.489955	−	0.367922i
$181$			6.26949i			0.466007i	0.972476	+	0.233004i	$0.0748554\pi$
$181$			6.26949i			0.466007i	−0.972476	+	0.233004i	$0.925145\pi$
$182$	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
$189$	12.1658	+	6.40265i	0.884930	+	0.465724i
$190$	−12.8278			−0.930624
$191$	−4.27245	+	2.46670i	−0.309143	+	0.178484i	−0.646543	−	0.762877i	$-0.723786\pi$
$191$	−4.27245	+	2.46670i	−0.309143	+	0.178484i	0.337400	+	0.941361i	$0.390453\pi$
$192$	5.66058	−	5.01652i	0.408517	−	0.362036i
$193$	2.69080	−	4.66060i	0.193688	−	0.335477i	−0.752782	−	0.658270i	$-0.771288\pi$
$193$	2.69080	−	4.66060i	0.193688	−	0.335477i	0.946470	+	0.322793i	$0.104622\pi$
$194$	0.0841113	−	0.145685i	0.00603884	−	0.0104596i
$195$	9.01582	+	9.74284i	0.645636	+	0.697699i
$196$	5.15033	−	7.40973i	0.367881	−	0.529267i
$197$	1.73936	−	1.00422i	0.123924	−	0.0715477i	−0.436756	−	0.899580i	$-0.643873\pi$
$197$	1.73936	−	1.00422i	0.123924	−	0.0715477i	0.560681	+	0.828032i	$0.310540\pi$
$198$	1.99806	+	1.50040i	0.141996	+	0.106629i
$199$			1.88370i			0.133532i	0.997769	+	0.0667659i	$0.0212681\pi$
$199$			1.88370i			0.133532i	−0.997769	+	0.0667659i	$0.978732\pi$
$200$	−1.15722	+	0.668122i	−0.0818279	+	0.0472434i
$201$	0.850840	+	4.16415i	0.0600137	+	0.293716i
$202$	−4.39096	−	2.53512i	−0.308947	−	0.178371i
$203$	0.799451	−	1.25968i	0.0561104	−	0.0884120i
$204$	3.07648	−	2.72644i	0.215397	−	0.190889i
$205$	−20.9821			−1.46546
$206$	−4.10006	+	7.10151i	−0.285665	+	0.494786i
$207$	4.84562	+	0.586726i	0.336794	+	0.0407803i
$208$	0.740177	−	0.448841i	0.0513220	−	0.0311215i
$209$	−7.07078			−0.489096
$210$	−6.36922	+	5.18478i	−0.439518	+	0.357784i
$211$	3.68771	+	6.38731i	0.253873	+	0.439720i	0.964589	−	0.263759i	$-0.0849623\pi$
$211$	3.68771	+	6.38731i	0.253873	+	0.439720i	−0.710716	+	0.703479i	$0.751629\pi$
$212$	−8.50380	+	4.90967i	−0.584043	+	0.337197i
$213$	−4.87872	+	0.996846i	−0.334285	+	0.0683027i
$214$	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
$222$	−3.18813	−	3.59745i	−0.213973	−	0.241445i
$223$	−1.19481	+	0.689825i	−0.0800106	+	0.0461941i	−0.539472	−	0.842004i	$-0.681376\pi$
$223$	−1.19481	+	0.689825i	−0.0800106	+	0.0461941i	0.459461	+	0.888198i	$0.348043\pi$
$224$	7.04639	+	13.4791i	0.470806	+	0.900613i
$225$	1.32968	−	0.567046i	0.0886451	−	0.0378031i
$226$	2.97308	−	5.14953i	0.197767	−	0.342542i
$227$	−2.98238			−0.197947			−0.0989736	−	0.995090i	$-0.531556\pi$
$227$	−2.98238			−0.197947			−0.0989736	+	0.995090i	$0.531556\pi$
$228$	5.05843	−	15.1603i	0.335003	−	1.00401i
$229$	10.3410	+	5.97040i	0.683355	+	0.394535i	0.801118	−	0.598506i	$-0.204239\pi$
$229$	10.3410	+	5.97040i	0.683355	+	0.394535i	−0.117763	+	0.993042i	$0.537572\pi$
$230$	−1.45793	+	2.52521i	−0.0961331	+	0.166507i
$231$	−3.51077	+	2.85790i	−0.230992	+	0.188036i
$232$	0.781902	+	1.35429i	0.0513343	+	0.0889137i
$233$	−14.3523	−	8.28630i	−0.940250	−	0.542854i	−0.0502115	−	0.998739i	$-0.515990\pi$
$233$	−14.3523	−	8.28630i	−0.940250	−	0.542854i	−0.890039	+	0.455885i	$0.849323\pi$
$234$	8.31004	−	3.75711i	0.543244	−	0.245610i
$235$	−13.6133	−	23.5790i	−0.888037	−	1.53812i
$236$	−15.3746			−1.00080
$237$	−5.04542	−	24.6931i	−0.327735	−	1.60399i
$238$	−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	$-0.407936\pi$
$240$	0.176947	+	0.866008i	0.0114219	+	0.0559006i
$241$		−	18.1245i		−	1.16750i	−0.811933	−	0.583750i	$-0.801585\pi$
$241$		−	18.1245i		−	1.16750i	0.811933	−	0.583750i	$-0.198415\pi$
$242$	7.31939	−	4.22585i	0.470508	−	0.271648i
$243$	13.7969	−	7.25582i	0.885068	−	0.465461i
$244$	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
$249$	−18.7466	+	16.6137i	−1.18802	+	1.05285i
$250$			9.82437i			0.621348i
$251$	−3.79901	+	6.58007i	−0.239791	+	0.415330i	−0.960654	−	0.277747i	$-0.910412\pi$
$251$	−3.79901	+	6.58007i	−0.239791	+	0.415330i	0.720863	+	0.693077i	$0.243746\pi$
$252$	−3.61594	−	9.57187i	−0.227783	−	0.602971i
$253$	−0.803624	+	1.39192i	−0.0505234	+	0.0875091i
$254$	7.93729	−	4.58260i	0.498030	−	0.287538i
$255$	−1.35690	−	6.64088i	−0.0849723	−	0.415868i
$256$	−15.3234			−0.957710
$257$	23.7009			1.47842			0.739212	−	0.673473i	$-0.235198\pi$
$257$	23.7009			1.47842			0.739212	+	0.673473i	$0.235198\pi$
$258$	0.612489	−	0.125147i	0.0381319	−	0.00779131i
$259$	7.71773	−	4.03454i	0.479556	−	0.250694i
$260$	−0.212511	−	9.87748i	−0.0131794	−	0.612575i
$261$	−0.663613	−	1.55612i	−0.0410766	−	0.0963212i
$262$	−12.6605	−	7.30954i	−0.782168	−	0.451585i
$263$	−15.2086	−	8.78068i	−0.937801	−	0.541440i	−0.0485307	−	0.998822i	$-0.515454\pi$
$263$	−15.2086	−	8.78068i	−0.937801	−	0.541440i	−0.889270	+	0.457382i	$0.848787\pi$
$264$	−0.949887	−	4.64890i	−0.0584615	−	0.286120i
$265$			16.1908i			0.994593i
$266$	−13.4811	−	8.55574i	−0.826579	−	0.524586i
$267$	6.72405	−	5.95899i	0.411505	−	0.364684i
$268$	1.58165	−	2.73951i	0.0966149	−	0.167342i
$269$	23.7413			1.44753			0.723766	−	0.690045i	$-0.242409\pi$
$269$	23.7413			1.44753			0.723766	+	0.690045i	$0.242409\pi$
$270$	0.753976	+	9.28179i	0.0458855	+	0.564871i
$271$		−	30.3088i		−	1.84113i	−0.390590	−	0.920565i	$-0.627729\pi$
$271$		−	30.3088i		−	1.84113i	0.390590	−	0.920565i	$-0.372271\pi$
$272$	−0.442006			−0.0268005
$273$	2.97682	+	16.2523i	0.180165	+	0.983636i
$274$	10.7582			0.649925
$275$			0.475995i			0.0287036i
$276$	−2.40946	−	2.71880i	−0.145032	−	0.163653i
$277$	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
$279$	5.75313	+	13.4906i	0.344431	+	0.807662i
$280$	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	$0.699565\pi$
$282$	−18.3270	+	3.74466i	−1.09136	+	0.222991i
$283$	6.20370	+	3.58171i	0.368772	+	0.212910i	0.672922	−	0.739714i	$-0.265039\pi$
$283$	6.20370	+	3.58171i	0.368772	+	0.212910i	−0.304150	+	0.952624i	$0.598372\pi$
$284$	3.20961	+	1.85307i	0.190455	+	0.109959i
$285$	−17.4779	−	19.7219i	−1.03530	−	1.16822i
$286$	0.0645949	+	3.00236i	0.00381958	+	0.177533i
$287$	−22.0508	−	13.9945i	−1.30162	−	0.826067i
$288$	17.1213	+	2.07311i	1.00888	+	0.122159i
$289$	−13.6105			−0.800619
$290$	1.01061			0.0593449
$291$	0.338584	−	0.0691812i	0.0198481	−	0.00405547i
$292$	−10.7170	+	6.18748i	−0.627167	+	0.362095i
$293$	−11.3968	+	19.7398i	−0.665805	+	1.15321i	0.313261	+	0.949667i	$0.398579\pi$
$293$	−11.3968	+	19.7398i	−0.665805	+	1.15321i	−0.979066	+	0.203542i	$0.934755\pi$
$294$	−10.1517	+	1.20077i	−0.592059	+	0.0700303i
$295$	−12.6753	+	21.9543i	−0.737987	+	1.27823i
$296$			9.12809i			0.530560i
$297$	0.415598	+	5.11620i	0.0241154	+	0.296872i
$298$	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
$303$	−2.08513	−	10.2050i	−0.119788	−	0.586259i
$304$	−1.48822	+	0.859222i	−0.0853551	+	0.0492798i
$305$		−	4.71273i		−	0.269850i
$306$	−4.62300	−	0.559770i	−0.264279	−	0.0319999i
$307$		−	24.9738i		−	1.42533i	−0.701504	−	0.712665i	$-0.747488\pi$
$307$		−	24.9738i		−	1.42533i	0.701504	−	0.712665i	$-0.252512\pi$
$308$	3.36632	+	0.141157i	0.191814	+	0.00804319i
$309$	−16.5045	+	3.37228i	−0.938907	+	0.191842i
$310$	−8.76137			−0.497612
$311$	9.00463	+	15.5965i	0.510606	+	0.884395i	0.999924	+	0.0122902i	$0.00391219\pi$
$311$	9.00463	+	15.5965i	0.510606	+	0.884395i	−0.489319	+	0.872105i	$0.662754\pi$
$312$	−16.5422	−	5.12684i	−0.936519	−	0.290250i
$313$	17.5542	+	10.1349i	0.992223	+	0.572860i	0.905938	−	0.423410i	$-0.139167\pi$
$313$	17.5542	+	10.1349i	0.992223	+	0.572860i	0.0862849	+	0.996271i	$0.472500\pi$
$314$	−6.19292	−	10.7265i	−0.349487	−	0.605329i
$315$	−16.6494	−	2.72796i	−0.938086	−	0.153703i
$316$	−9.37909	+	16.2451i	−0.527615	+	0.913856i
$317$	−8.12697	−	4.69211i	−0.456456	−	0.263535i	0.254097	−	0.967179i	$-0.418222\pi$
$317$	−8.12697	−	4.69211i	−0.456456	−	0.263535i	−0.710553	+	0.703644i	$0.751555\pi$
$318$	10.5517	+	3.52073i	0.591712	+	0.197433i
$319$	0.557056			0.0311891
$320$	−4.64105	+	8.03854i	−0.259443	+	0.449368i
$321$	0.706159	+	0.796821i	0.0394139	+	0.0444742i
$322$	−3.21642	+	1.68142i	−0.179244	+	0.0937021i
$323$	11.4122	−	6.58884i	0.634993	−	0.366613i
$324$	−11.2668	−	2.76905i	−0.625934	−	0.153836i
$325$	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	0.999807	+	0.0196317i	$0.00624935\pi$
$331$	9.40426	+	16.2887i	0.516905	+	0.895306i	−0.482902	+	0.875674i	$0.660417\pi$
$332$	18.6433			1.02319
$333$	1.18700	−	9.80310i	0.0650469	−	0.537206i
$334$	−4.10171	+	2.36812i	−0.224436	+	0.129578i
$335$	−2.60794	−	4.51709i	−0.142487	−	0.246795i
$336$	−0.391642	+	1.02813i	−0.0213658	+	0.0560892i
$337$	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
$339$	11.9679	−	2.44535i	0.650008	−	0.132813i
$340$	−2.52238	+	4.36889i	−0.136795	+	0.236936i
$341$	−4.82934			−0.261524
$342$	−16.6536	+	7.10200i	−0.900524	+	0.384032i
$343$	2.32229	−	18.3741i	0.125392	−	0.992107i
$344$	−1.02809	−	0.593566i	−0.0554307	−	0.0320030i
$345$	−5.86879	+	1.19914i	−0.315965	+	0.0645596i
$346$	−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	−0.444383	−	0.895837i	$-0.646577\pi$
$349$	2.04081	−	1.17826i	0.109242	−	0.0630710i	0.553626	+	0.832766i	$0.313244\pi$
$350$	−0.575960	+	0.907529i	−0.0307864	+	0.0485095i
$351$	17.0988	+	7.65707i	0.912667	+	0.408704i
$352$	−2.83948	+	4.91813i	−0.151345	+	0.262137i
$353$	−11.3836	+	19.7170i	−0.605888	+	1.04943i	0.386023	+	0.922489i	$0.373849\pi$
$353$	−11.3836	+	19.7170i	−0.605888	+	1.04943i	−0.991911	+	0.126939i	$0.959485\pi$
$354$	11.5516	+	13.0347i	0.613961	+	0.692786i
$355$	5.29222	−	3.05547i	0.280882	−	0.162167i
$356$	−6.68699			−0.354410
$357$	3.00326	−	7.88411i	0.158949	−	0.417272i
$358$	−9.40085	+	16.2827i	−0.496850	+	0.860570i
$359$	5.83980	+	3.37161i	0.308213	+	0.177947i	0.646126	−	0.763230i	$-0.276388\pi$
$359$	5.83980	+	3.37161i	0.308213	+	0.177947i	−0.337914	+	0.941177i	$0.609721\pi$
$360$	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	0.760163	−	0.649733i	$-0.225119\pi$
$367$	11.0644	+	6.38805i	0.577559	+	0.333454i	−0.182604	+	0.983187i	$0.558453\pi$
$368$			0.390617i			0.0203623i
$369$	−27.2400	+	11.6166i	−1.41806	+	0.604736i
$370$	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	0.979151	+	0.203132i	$0.0651119\pi$
$373$	12.8528	+	22.2617i	0.665493	+	1.15267i	−0.313659	+	0.949536i	$0.601555\pi$
$374$	0.766703	−	1.32797i	0.0396452	−	0.0686676i
$375$	−15.1043	+	13.3858i	−0.779985	+	0.691239i
$376$	30.7625	+	17.7608i	1.58646	+	0.915942i
$377$	0.978482	−	1.78225i	0.0503944	−	0.0917904i
$378$	−5.39830	+	10.2574i	−0.277659	+	0.527583i
$379$	−15.2609	−	26.4326i	−0.783898	−	1.35775i	−0.929655	−	0.368431i	$-0.879895\pi$
$379$	−15.2609	−	26.4326i	−0.783898	−	1.35775i	0.145757	−	0.989320i	$-0.453438\pi$
$380$			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	$-0.0987575\pi$
$383$	4.14360	+	7.17693i	0.211728	+	0.366724i	−0.740527	+	0.672026i	$0.765424\pi$
$384$	−8.97853	−	10.1313i	−0.458184	−	0.517009i
$385$	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	$-0.428779\pi$
$389$	23.2193	−	13.4057i	1.17727	−	0.679695i	0.955381	+	0.295378i	$0.0954454\pi$
$390$	−8.21453	+	7.60156i	−0.415959	+	0.384920i
$391$		−	2.99540i		−	0.151484i
$392$	15.9399	+	11.0795i	0.805086	+	0.559597i
$393$	−6.01207	−	29.4240i	−0.303269	−	1.48425i
$394$	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	−0.621662	−	0.783286i	$-0.713542\pi$
$397$	−5.06386	+	2.92362i	−0.254148	+	0.146732i	0.367514	+	0.930018i	$0.380209\pi$
$398$	−1.58821			−0.0796099
$399$	−5.21419	−	32.3836i	−0.261036	−	1.62121i
$400$	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	$-0.0330390\pi$
$402$	−3.51094	+	0.717374i	−0.175110	+	0.0357793i
$403$	−8.48286	+	15.4510i	−0.422561	+	0.769670i
$404$	−3.87611	+	6.71362i	−0.192844	+	0.334015i
$405$	−13.2429	+	13.8057i	−0.658043	+	0.686010i
$406$	1.06208	+	0.674045i	0.0527101	+	0.0334523i
$407$	2.81596	+	1.62580i	0.139582	+	0.0805878i
$408$	5.86515	+	6.61817i	0.290368	+	0.327648i
$409$			10.6492i			0.526570i	0.964718	+	0.263285i	$0.0848060\pi$
$409$			10.6492i			0.526570i	−0.964718	+	0.263285i	$0.915194\pi$
$410$		−	17.6908i		−	0.873685i
$411$	14.6581	+	16.5400i	0.723030	+	0.815858i
$412$	10.8579	+	6.26884i	0.534933	+	0.308843i
$413$	−27.9638	+	14.6184i	−1.37601	+	0.719325i
$414$	−0.494689	+	4.08552i	−0.0243126	+	0.200792i
$415$	15.3702	−	26.6220i	0.754493	−	1.30682i
$416$	10.7475	+	17.7235i	0.526938	+	0.868964i
$417$	26.6511	−	5.44549i	1.30511	−	0.266667i
$418$		−	5.96162i		−	0.291593i
$419$	4.05247	+	7.01909i	0.197976	+	0.342905i	0.947872	−	0.318651i	$-0.103230\pi$
$419$	4.05247	+	7.01909i	0.197976	+	0.342905i	−0.749896	+	0.661556i	$0.769896\pi$
$420$	7.92734	+	9.73830i	0.386815	+	0.475180i
$421$	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
$426$	−0.840476	−	4.11342i	−0.0407212	−	0.199296i
$427$	3.14325	−	4.95275i	0.152113	−	0.239680i
$428$		−	0.792429i		−	0.0383035i
$429$	−4.52792	+	4.19004i	−0.218610	+	0.202297i
$430$	−0.664401	+	0.383592i	−0.0320403	+	0.0184985i
$431$	−11.9816	−	6.91758i	−0.577134	−	0.333208i	0.182860	−	0.983139i	$-0.441465\pi$
$431$	−11.9816	−	6.91758i	−0.577134	−	0.333208i	−0.759993	+	0.649931i	$0.774798\pi$
$432$	0.709180	+	1.02633i	0.0341204	+	0.0493791i
$433$	10.1569	+	5.86410i	0.488111	+	0.281811i	0.723790	−	0.690020i	$-0.242398\pi$
$433$	10.1569	+	5.86410i	0.488111	+	0.281811i	−0.235680	+	0.971831i	$0.575732\pi$
$434$	−9.20759	−	5.84357i	−0.441979	−	0.280500i
$435$	1.37696	+	1.55374i	0.0660202	+	0.0744964i
$436$	−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	$0.227348\pi$
$439$			27.4492i			1.31008i	−0.755595	+	0.655039i	$0.772652\pi$
$440$	2.91153	+	5.04292i	0.138802	+	0.240412i
$441$	−15.6779	−	13.9715i	−0.746566	−	0.665312i
$442$	−2.90198	−	4.78560i	−0.138033	−	0.227628i
$443$	23.7433	+	13.7082i	1.12808	+	0.651298i	0.943451	−	0.331511i	$-0.107558\pi$
$443$	23.7433	+	13.7082i	1.12808	+	0.651298i	0.184629	+	0.982808i	$0.440892\pi$
$444$	−5.50036	+	4.87453i	−0.261036	+	0.231335i
$445$	−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	$-0.381846\pi$
$449$	−5.57195	−	3.21697i	−0.262957	−	0.151818i	−0.625683	+	0.780078i	$0.715179\pi$
$450$	0.478097	+	1.12110i	0.0225377	+	0.0528490i
$451$		−	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	$-0.880313\pi$
$461$	−3.15743	+	5.46883i	−0.147056	+	0.254709i	0.783082	+	0.621918i	$0.213646\pi$
$462$	−2.40959	−	2.96005i	−0.112104	−	0.137714i
$463$	−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
$465$	−11.9374	−	13.4700i	−0.553585	−	0.624658i
$466$	6.98647	−	12.1009i	0.323642	−	0.560565i
$467$	−2.04445	+	3.54109i	−0.0946057	+	0.163862i	−0.909444	−	0.415826i	$-0.863492\pi$
$467$	−2.04445	+	3.54109i	−0.0946057	+	0.163862i	0.814838	+	0.579688i	$0.196826\pi$
$468$	−5.74448	−	12.7057i	−0.265539	−	0.587323i
$469$	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
$474$	20.8196	−	4.25397i	0.956277	−	0.195391i
$475$	−2.98684	−	1.72445i	−0.137046	−	0.0791234i
$476$	−5.56477	+	2.90905i	−0.255061	+	0.133336i
$477$	8.96392	+	21.0197i	0.410430	+	0.962424i
$478$	24.9863			1.14285
$479$	15.1680	−	26.2717i	0.693042	−	1.20038i	−0.277794	−	0.960641i	$-0.589603\pi$
$479$	15.1680	−	26.2717i	0.693042	−	1.20038i	0.970836	−	0.239744i	$-0.0770634\pi$
$480$	−20.7365	+	4.23698i	−0.946486	+	0.193391i
$481$	10.1479	−	6.15366i	0.462704	−	0.280583i
$482$	15.2814			0.696048
$483$	−6.96748	−	2.65409i	−0.317032	−	0.120765i
$484$	−6.46117	−	11.1911i	−0.293690	−	0.508686i
$485$	−0.367281	+	0.212050i	−0.0166774	+	0.00962867i
$486$	6.11764	+	11.6326i	0.277502	+	0.527666i
$487$	−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	$-0.857627\pi$
$491$	−21.6683	+	12.5102i	−0.977875	+	0.564577i	−0.0762474	+	0.997089i	$0.524294\pi$
$492$	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
$495$	−2.47107	−	5.79445i	−0.111066	−	0.260441i
$496$	−1.01645	+	0.586849i	−0.0456400	+	0.0263503i
$497$	7.59967	+	0.318671i	0.340892	+	0.0142944i
$498$	−14.0076	−	15.8060i	−0.627694	−	0.708282i
$499$	−8.03279	+	13.9132i	−0.359597	+	0.622841i	−0.987894	−	0.155133i	$-0.950419\pi$
$499$	−8.03279	+	13.9132i	−0.359597	+	0.622841i	0.628296	+	0.777974i	$0.283753\pi$
$500$	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	−0.00209081	+	0.999998i	$0.500666\pi$
$503$	−19.4463	+	33.6820i	−0.867069	+	1.50181i	−0.864978	+	0.501810i	$0.832668\pi$
$504$	20.5911	−	7.77864i	0.917202	−	0.346488i
$505$	6.39120	+	11.0699i	0.284405	+	0.492603i
$506$	−1.17357	−	0.677563i	−0.0521717	−	0.0301214i
$507$	5.45225	+	21.8466i	0.242143	+	0.970241i
$508$	−7.00662	−	12.1358i	−0.310869	−	0.538440i
$509$	30.1839			1.33788			0.668939	−	0.743317i	$-0.266749\pi$
$509$	30.1839			1.33788			0.668939	+	0.743317i	$0.266749\pi$
$510$	5.59916	−	1.14405i	0.247935	−	0.0506593i
$511$	−13.6093	+	21.4439i	−0.602041	+	0.948623i
$512$			2.71177i			0.119845i
$513$	−33.6095	−	15.9273i	−1.48390	−	0.703209i
$514$			19.9831i			0.881417i
$515$	17.9033	−	10.3365i	0.788915	−	0.455480i
$516$	−0.191345	−	0.936473i	−0.00842349	−	0.0412259i
$517$	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	−0.957841	−	0.287299i	$-0.907243\pi$
$521$	−16.6107	−	28.7706i	−0.727729	−	1.26046i	0.230112	−	0.973164i	$-0.426091\pi$
$522$	1.31202	−	0.559515i	0.0574254	−	0.0244893i
$523$			19.3414i			0.845740i	0.906190	+	0.422870i	$0.138977\pi$
$523$			19.3414i			0.845740i	−0.906190	+	0.422870i	$0.861023\pi$
$524$	−11.1760	+	19.3574i	−0.488227	+	0.845634i
$525$	−2.18002	+	0.351012i	−0.0951438	+	0.0153194i
$526$	7.40330	−	12.8229i	0.322799	−	0.559104i
$527$	7.79454	−	4.50018i	0.339536	−	0.196031i
$528$	−0.402471	+	0.0822350i	−0.0175153	+	0.00357882i
$529$	20.3529			0.884907
$530$	−13.6510			−0.592963
$531$	−4.30086	+	35.5197i	−0.186641	+	1.54143i
$532$	−13.0814	+	20.6121i	−0.567151	+	0.893648i
$533$	−31.1984	−	17.1284i	−1.35135	−	0.741914i
$534$	5.02423	+	5.66928i	0.217420	+	0.245334i
$535$	−1.13156	−	0.653306i	−0.0489216	−	0.0282449i
$536$	5.89325	+	3.40247i	0.254550	+	0.146964i
$537$	−37.8424	+	7.73216i	−1.63302	+	0.333667i
$538$			20.0171i			0.863000i
$539$	6.25699	−	2.94401i	0.269508	−	0.126808i
$540$	14.1915	−	1.15280i	0.610705	−	0.0496087i
$541$	−13.4353	+	23.2706i	−0.577629	+	1.00048i	0.418122	+	0.908391i	$0.362689\pi$
$541$	−13.4353	+	23.2706i	−0.577629	+	1.00048i	−0.995751	+	0.0920914i	$0.970645\pi$
$542$	25.5544			1.09766
$543$	−7.20225	−	8.12693i	−0.309078	−	0.348760i
$544$		−	10.5838i		−	0.453776i
$545$	−24.6071			−1.05405
$546$	−13.7029	+	2.50986i	−0.586431	+	0.107412i
$547$	−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
$549$	−2.60917	−	6.11828i	−0.111357	−	0.261122i
$550$	−0.401328			−0.0171127
$551$	−2.01813	+	3.49550i	−0.0859750	+	0.148913i
$552$	5.84872	−	5.18325i	0.248938	−	0.220614i
$553$	−1.61292	+	38.4649i	−0.0685882	+	1.63569i
$554$			14.8232i			0.629778i
$555$	2.42596	+	11.8730i	0.102976	+	0.503983i
$556$	−17.5332	−	10.1228i	−0.743573	−	0.429302i
$557$	23.3427	+	13.4769i	0.989060	+	0.571034i	0.904993	−	0.425426i	$-0.139876\pi$
$557$	23.3427	+	13.4769i	0.989060	+	0.571034i	0.0840671	+	0.996460i	$0.473209\pi$
$558$	−11.3744	+	4.85067i	−0.481517	+	0.205345i
$559$	0.0331993	+	1.54310i	0.00140418	+	0.0652660i
$560$	0.0565664	−	1.34899i	0.00239037	−	0.0570054i
$561$	3.08630	−	0.630610i	0.130304	−	0.0266244i
$562$	−22.8912			−0.965607
$563$	7.64099			0.322029			0.161015	−	0.986952i	$-0.448523\pi$
$563$	7.64099			0.322029			0.161015	+	0.986952i	$0.448523\pi$
$564$	5.72545	+	28.0213i	0.241085	+	1.17991i
$565$	−12.9823	+	7.49532i	−0.546169	+	0.315331i
$566$	−3.01986	+	5.23056i	−0.126934	+	0.219857i
$567$	−23.1253	+	5.67624i	−0.971172	+	0.238380i
$568$	−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	$-0.0249662\pi$
$570$	16.6282	−	14.7363i	0.696479	−	0.617234i
$571$	7.51056	+	13.0087i	0.314307	+	0.544396i	0.979290	−	0.202463i	$-0.0648945\pi$
$571$	7.51056	+	13.0087i	0.314307	+	0.544396i	−0.664983	+	0.746859i	$0.731561\pi$
$572$	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
$576$	−1.57475	+	13.0055i	−0.0656147	+	0.541895i
$577$	15.7668	−	9.10299i	0.656382	−	0.378963i	−0.134515	−	0.990912i	$-0.542948\pi$
$577$	15.7668	−	9.10299i	0.656382	−	0.378963i	0.790897	+	0.611949i	$0.209614\pi$
$578$		−	11.4755i		−	0.477319i
$579$	1.86600	+	9.13251i	0.0775483	+	0.379534i
$580$		−	1.54518i		−	0.0641602i
$581$	33.9091	−	17.7264i	1.40679	−	0.735414i
$582$	0.0583291	+	0.285472i	0.00241782	+	0.0118332i
$583$	−7.52457			−0.311636
$584$	−13.3106	−	23.0546i	−0.550796	−	0.954006i
$585$	−22.8793	−	2.27215i	−0.945942	−	0.0939417i
$586$	−16.6433	−	9.60900i	−0.687528	−	0.396944i
$587$	2.83282	+	4.90659i	0.116923	+	0.202516i	0.918547	−	0.395312i	$-0.129364\pi$
$587$	2.83282	+	4.90659i	0.116923	+	0.202516i	−0.801624	+	0.597829i	$0.796030\pi$
$588$	1.83593	+	15.5216i	0.0757125	+	0.640099i
$589$	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	$-0.810299\pi$
$593$	1.76064	−	3.04952i	0.0723010	−	0.125229i	0.899909	+	0.436077i	$0.143632\pi$
$594$	−4.31365	+	0.350405i	−0.176991	+	0.0143773i
$595$	−0.433772	+	10.3446i	−0.0177829	+	0.424087i
$596$	8.39841	−	4.84883i	0.344012	−	0.198616i
$597$	−2.16395	−	2.44178i	−0.0885646	−	0.0999352i
$598$	−4.22921	+	2.56458i	−0.172945	+	0.104874i
$599$	22.9515	−	13.2511i	0.937774	−	0.541424i	0.0485125	−	0.998823i	$-0.484552\pi$
$599$	22.9515	−	13.2511i	0.937774	−	0.541424i	0.889262	+	0.457398i	$0.151219\pi$
$600$	0.732544	−	2.19546i	0.0299060	−	0.0896291i
$601$	−24.6360	+	14.2236i	−1.00492	+	0.580194i	−0.909702	−	0.415262i	$-0.863690\pi$
$601$	−24.6360	+	14.2236i	−1.00492	+	0.580194i	−0.0952232	+	0.995456i	$0.530356\pi$
$602$	−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
$606$	8.60416	−	1.75805i	0.349520	−	0.0714157i
$607$	8.40141	−	4.85056i	0.341003	−	0.196878i	−0.319713	−	0.947515i	$-0.603586\pi$
$607$	8.40141	−	4.85056i	0.341003	−	0.196878i	0.660715	+	0.750637i	$0.270253\pi$
$608$	−20.5740	−	35.6352i	−0.834386	−	1.44520i
$609$	0.410789	+	2.55127i	0.0166460	+	0.103383i
$610$	3.97347			0.160881
$611$	−0.993394	−	46.1727i	−0.0401884	−	1.86795i
$612$	−0.855867	+	7.06840i	−0.0345964	+	0.285723i
$613$	4.23217	−	7.33033i	0.170936	−	0.296069i	−0.767812	−	0.640676i	$-0.778654\pi$
$613$	4.23217	−	7.33033i	0.170936	−	0.296069i	0.938747	+	0.344606i	$0.111988\pi$
$614$	21.0563			0.849763
$615$	27.1985	−	24.1038i	1.09675	−	0.971960i
$616$	−0.303659	+	7.24167i	−0.0122348	+	0.291775i
$617$	−10.0946	−	5.82812i	−0.406393	−	0.234631i	0.282846	−	0.959165i	$-0.408722\pi$
$617$	−10.0946	−	5.82812i	−0.406393	−	0.234631i	−0.689239	+	0.724534i	$0.742055\pi$
$618$	−2.84329	−	13.9155i	−0.114374	−	0.559764i
$619$	25.2951	−	14.6041i	1.01669	−	0.586989i	0.103550	−	0.994624i	$-0.466980\pi$
$619$	25.2951	−	14.6041i	1.01669	−	0.586989i	0.913145	+	0.407635i	$0.133646\pi$
$620$			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
$624$	−0.443848	+	1.43212i	−0.0177681	+	0.0573306i
$625$	11.1793	−	19.3631i	0.447172	−	0.774524i
$626$	−8.54512	+	14.8006i	−0.341532	+	0.591550i
$627$	9.16562	−	8.12276i	0.366040	−	0.324392i
$628$	−16.4004	+	9.46875i	−0.654445	+	0.377844i
$629$	−6.05994			−0.241626
$630$	2.30004	−	14.0377i	0.0916359	−	0.559275i
$631$	12.7791	−	22.1340i	0.508727	−	0.881141i	−0.491222	−	0.871034i	$-0.663450\pi$
$631$	12.7791	−	22.1340i	0.508727	−	0.881141i	0.999949	−	0.0101065i	$-0.00321706\pi$
$632$	−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	$-0.236712\pi$
$642$	−0.671828	+	0.595387i	−0.0265149	+	0.0234981i
$643$	−19.3892	−	11.1943i	−0.764634	−	0.441462i	0.0663229	−	0.997798i	$-0.478873\pi$
$643$	−19.3892	−	11.1943i	−0.764634	−	0.441462i	−0.830957	+	0.556336i	$0.812207\pi$
$644$	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	$-0.700571\pi$
$647$	10.3042	−	17.8473i	0.405098	−	0.701651i	0.994333	+	0.106311i	$0.0339040\pi$
$648$	5.95682	−	24.2373i	0.234006	−	0.952131i
$649$	−10.2031	−	5.89078i	−0.400508	−	0.231233i
$650$	−0.704943	+	1.28401i	−0.0276501	+	0.0503631i
$651$	−3.56129	−	22.1180i	−0.139578	−	0.866873i
$652$	−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
$657$	11.2969	+	26.4903i	0.440734	+	1.03349i
$658$	28.5482	+	1.19709i	1.11293	+	0.0466675i
$659$	−33.0777	−	19.0974i	−1.28852	−	0.743929i	−0.310132	−	0.950693i	$-0.600373\pi$
$659$	−33.0777	−	19.0974i	−1.28852	−	0.743929i	−0.978391	+	0.206764i	$0.933707\pi$
$660$	−1.48394	+	4.44741i	−0.0577623	+	0.173115i
$661$	−5.78197	−	3.33822i	−0.224893	−	0.129842i	0.383321	−	0.923615i	$-0.374780\pi$
$661$	−5.78197	−	3.33822i	−0.224893	−	0.129842i	−0.608214	+	0.793773i	$0.708114\pi$
$662$	−13.7335	+	7.92907i	−0.533770	+	0.308172i
$663$	3.40359	−	10.9820i	0.132185	−	0.426506i
$664$			40.1057i			1.55640i
$665$	18.6486	+	35.6731i	0.723160	+	1.38334i
$666$	8.26534	+	1.00080i	0.320275	+	0.0387801i
$667$	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
$672$	−24.6185	−	9.37783i	−0.949681	−	0.361758i
$673$	5.54228	+	9.59951i	0.213639	+	0.370034i	0.952851	−	0.303439i	$-0.0981350\pi$
$673$	5.54228	+	9.59951i	0.213639	+	0.370034i	−0.739212	+	0.673473i	$0.764802\pi$
$674$			17.5227i			0.674950i
$675$	−1.07221	+	2.26255i	−0.0412692	+	0.0870855i
$676$	7.74733	−	14.8603i	0.297974	−	0.571551i
$677$	14.9397	−	25.8763i	0.574178	−	0.994506i	−0.421952	−	0.906618i	$-0.638655\pi$
$677$	14.9397	−	25.8763i	0.574178	−	0.994506i	0.996130	−	0.0878879i	$-0.0280117\pi$
$678$	2.06176	+	10.0906i	0.0791814	+	0.387526i
$679$	−0.527417	−	0.0221158i	−0.0202404	−	0.000848726i
$680$	−9.39841	−	5.42617i	−0.360413	−	0.208084i
$681$	3.86595	−	3.42609i	0.148144	−	0.131288i
$682$		−	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	$0.976785\pi$
$684$	10.8587	+	25.4628i	0.415193	+	0.973593i
$685$	−23.4883	−	13.5610i	−0.897443	−	0.518139i
$686$	15.4918	+	1.95801i	0.591481	+	0.0747571i
$687$	−20.2634	+	4.14033i	−0.773098	+	0.157963i
$688$	−0.0513871	+	0.0890050i	−0.00195911	+	0.00339329i
$689$	−13.2171	+	24.0742i	−0.503531	+	0.917152i
$690$	−1.01104	−	4.94818i	−0.0384896	−	0.188374i
$691$		−	32.3395i		−	1.23025i	−0.788428	−	0.615127i	$-0.789105\pi$
$691$		−	32.3395i		−	1.23025i	0.788428	−	0.615127i	$-0.210895\pi$
$692$	9.29284	+	16.0957i	0.353261	+	0.611866i
$693$	1.26780	−	7.73769i	0.0481599	−	0.293931i
$694$	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
$699$	28.1235	−	5.74635i	1.06373	−	0.217347i
$700$	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	$0.949338\pi$
$702$	−6.45594	+	14.4166i	−0.243664	+	0.544120i
$703$	−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
$708$	19.9296	−	17.6620i	0.748999	−	0.663778i
$709$	−13.5979	−	23.5522i	−0.510679	−	0.884523i	−0.999923	−	0.0123757i	$-0.996061\pi$
$709$	−13.5979	−	23.5522i	−0.510679	−	0.884523i	0.489244	−	0.872147i	$-0.337273\pi$
$710$	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
$714$	6.64738	+	2.53216i	0.248772	+	0.0947635i
$715$	3.64353	−	6.63648i	0.136260	−	0.248190i
$716$	24.8957	+	14.3735i	0.930397	+	0.537165i
$717$	34.0441	+	38.4149i	1.27140	+	1.43463i
$718$	−2.84272	+	4.92374i	−0.106089	+	0.183752i
$719$	−14.7050	−	25.4699i	−0.548405	−	0.949866i	−0.998384	−	0.0568265i	$-0.981902\pi$
$719$	−14.7050	−	25.4699i	−0.548405	−	0.949866i	0.449979	−	0.893039i	$-0.351432\pi$
$720$	−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
$723$	20.8210	+	23.4942i	0.774341	+	0.873757i
$724$			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	$-0.798782\pi$
$727$		−	31.8635i		−	1.18175i	0.806763	−	0.590876i	$-0.201218\pi$
$728$	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	0.344177	−	0.938905i	$-0.388158\pi$
$733$	−8.03692	−	4.64012i	−0.296850	−	0.171387i	−0.641027	+	0.767518i	$0.721491\pi$
$734$	−5.38599	+	9.32881i	−0.198801	+	0.344333i
$735$	23.6778	+	10.1749i	0.873370	+	0.375306i
$736$	−9.35328			−0.344767
$737$	2.09929	−	1.21202i	0.0773282	−	0.0446455i
$738$	−9.79437	−	22.9670i	−0.360536	−	0.845427i
$739$	−19.1664	+	33.1971i	−0.705046	+	1.22118i	0.261629	+	0.965169i	$0.415740\pi$
$739$	−19.1664	+	33.1971i	−0.705046	+	1.22118i	−0.966675	+	0.256007i	$0.917593\pi$
$740$	4.50970	−	7.81103i	0.165780	−	0.287139i
$741$	−9.88836	−	43.5924i	−0.363258	−	1.60141i
$742$	−14.3463	−	9.10484i	−0.526669	−	0.334249i
$743$	41.4254	−	23.9170i	1.51975	−	0.877428i	0.520022	−	0.854153i	$-0.325924\pi$
$743$	41.4254	−	23.9170i	1.51975	−	0.877428i	0.999729	−	0.0232753i	$-0.00740942\pi$
$744$	22.2746	+	7.43223i	0.816627	+	0.272479i
$745$		−	15.9902i		−	0.585834i
$746$	−18.7696	+	10.8367i	−0.687205	+	0.396758i
$747$	5.21525	−	43.0715i	0.190816	−	1.57590i
$748$	−2.03041	−	1.17226i	−0.0742393	−	0.0428621i
$749$	−0.753455	−	1.44130i	−0.0275306	−	0.0526638i
$750$	−11.2860	−	12.7350i	−0.412107	−	0.465017i
$751$	−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
$753$	−2.63452	−	12.8937i	−0.0960071	−	0.469874i
$754$	1.50268	+	0.824993i	0.0547242	+	0.0300445i
$755$	7.53267			0.274142
$756$	15.6832	+	8.25380i	0.570392	+	0.300188i
$757$	−6.86398	−	11.8888i	−0.249476	−	0.432105i	0.713905	−	0.700243i	$-0.246925\pi$
$757$	−6.86398	−	11.8888i	−0.249476	−	0.432105i	−0.963380	+	0.268138i	$0.913592\pi$
$758$	22.2862	−	12.8670i	0.809473	−	0.467349i
$759$	−0.557293	−	2.72748i	−0.0202285	−	0.0990013i
$760$	−42.1921			−1.53047
$761$	11.3944	+	19.7356i	0.413045	+	0.715415i	0.995221	−	0.0976477i	$-0.0311318\pi$
$761$	11.3944	+	19.7356i	0.413045	+	0.715415i	−0.582176	+	0.813063i	$0.697798\pi$
$762$	−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
$768$	19.8632	−	17.6031i	0.716751	−	0.635199i
$769$	20.0316	−	11.5653i	0.722359	−	0.417054i	−0.0932614	−	0.995642i	$-0.529729\pi$
$769$	20.0316	−	11.5653i	0.722359	−	0.417054i	0.815620	+	0.578588i	$0.196396\pi$
$770$	3.95482	+	2.50991i	0.142522	+	0.0904510i
$771$	−30.7228	+	27.2271i	−1.10645	+	0.980561i
$772$	3.46877	−	6.00808i	0.124844	−	0.216236i
$773$	1.27842			0.0459815			0.0229908	−	0.999736i	$-0.492681\pi$
$773$	1.27842			0.0459815			0.0229908	+	0.999736i	$0.492681\pi$
$774$	−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
$777$	−5.36945	+	14.0958i	−0.192628	+	0.505684i
$778$	11.3028	+	19.5770i	0.405225	+	0.701871i
$779$	61.1890	+	35.3275i	2.19232	+	1.26574i
$780$	11.6225	+	12.5597i	0.416152	+	0.449710i
$781$	1.42001	+	2.45953i	0.0508119	+	0.0880088i
$782$	2.52553			0.0903126
$783$	2.64785	+	1.25480i	0.0946265	+	0.0448429i
$784$	0.959187	−	1.37997i	0.0342567	−	0.0492847i
$785$			31.2255i			1.11448i
$786$	24.8084	−	5.06899i	0.884887	−	0.180805i
$787$			55.0921i			1.96382i	0.189341	+	0.981911i	$0.439365\pi$
$787$			55.0921i			1.96382i	−0.189341	+	0.981911i	$0.560635\pi$
$788$	2.24225	−	1.29456i	0.0798768	−	0.0461169i
$789$	29.8014	−	6.08918i	1.06096	−	0.216781i
$790$	−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
$795$	−18.5996	−	20.9876i	−0.659661	−	0.744354i
$796$			2.42832i			0.0860694i
$797$	12.6676	−	21.9409i	0.448710	−	0.777188i	−0.549593	−	0.835433i	$-0.685217\pi$
$797$	12.6676	−	21.9409i	0.448710	−	0.777188i	0.998302	+	0.0582448i	$0.0185504\pi$
$798$	27.3038	−	4.39627i	0.966543	−	0.155626i
$799$	−11.7910	+	20.4226i	−0.417135	+	0.722499i
$800$	−2.39891	+	1.38501i	−0.0848143	+	0.0489676i
$801$	−1.87061	+	15.4489i	−0.0660947	+	0.545859i
$802$	3.49861			0.123540
$803$	−9.48295			−0.334646
$804$	1.09684	+	5.36810i	0.0386825	+	0.189318i
$805$	9.14191	+	0.383341i	0.322210	+	0.0135110i
$806$	−13.0273	−	7.15220i	−0.458867	−	0.251925i
$807$	−30.7751	+	27.2735i	−1.08333	+	0.960072i
$808$	−14.4424	−	8.33833i	−0.508083	−	0.293342i
$809$	21.5893	+	12.4646i	0.759039	+	0.438231i	0.828950	−	0.559322i	$-0.188938\pi$
$809$	21.5893	+	12.4646i	0.759039	+	0.438231i	−0.0699118	+	0.997553i	$0.522272\pi$
$810$	−11.6401	−	11.1655i	−0.408990	−	0.392316i
$811$			13.2404i			0.464932i	0.972605	+	0.232466i	$0.0746794\pi$
$811$			13.2404i			0.464932i	−0.972605	+	0.232466i	$0.925321\pi$
$812$	1.03059	−	1.62388i	0.0361666	−	0.0569870i
$813$	34.8181	+	39.2883i	1.22112	+	1.37790i
$814$	−1.37077	+	2.37424i	−0.0480454	+	0.0832170i
$815$	−1.89937			−0.0665320
$816$	0.572958	−	0.507767i	0.0200575	−	0.0177754i
$817$		−	3.06405i		−	0.107197i
$818$	−8.97874			−0.313934
$819$	−22.5291	−	17.6477i	−0.787230	−	0.616659i
$820$	−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	$0.856369\pi$
$822$	−13.9455	+	12.3587i	−0.486404	+	0.431061i
$823$	−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
$825$	−0.546812	−	0.617016i	−0.0190376	−	0.0214818i
$826$	−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	$0.810442\pi$
$828$	6.24660	+	0.756362i	0.217084	+	0.0262854i
$829$	26.9798	+	15.5768i	0.937048	+	0.541005i	0.889034	−	0.457842i	$-0.151377\pi$
$829$	26.9798	+	15.5768i	0.937048	+	0.541005i	0.0480145	+	0.998847i	$0.484711\pi$
$830$	22.4459	+	12.9592i	0.779109	+	0.449819i
$831$	−22.7898	+	20.1968i	−0.790568	+	0.700618i
$832$	−13.4629	+	8.16388i	−0.466743	+	0.283032i
$833$	−7.35541	+	10.5822i	−0.254850	+	0.366650i
$834$	4.59128	+	22.4705i	0.158983	+	0.778089i
$835$	11.9404			0.413214
$836$	−9.11510			−0.315252
$837$	−22.9553	−	10.8784i	−0.793452	−	0.376012i
$838$	−5.91804	+	3.41678i	−0.204435	+	0.118031i
$839$	22.8424	−	39.5642i	0.788608	−	1.36591i	−0.138211	−	0.990403i	$-0.544135\pi$
$839$	22.8424	−	39.5642i	0.788608	−	1.36591i	0.926820	−	0.375507i	$-0.122531\pi$
$840$	−20.9491	+	17.0534i	−0.722814	+	0.588398i
$841$	−14.3410	+	24.8394i	−0.494517	+	0.856529i
$842$			14.1558i			0.487842i
$843$	−31.1894	−	35.1938i	−1.07422	−	1.21214i
$844$	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
$849$	−12.1562	+	2.48383i	−0.417201	+	0.0852447i
$850$	0.647742	−	0.373974i	0.0222174	−	0.0128272i
$851$			5.35540i			0.183581i
$852$	−6.28927	+	1.28506i	−0.215467	+	0.0440253i
$853$		−	15.6593i		−	0.536165i	−0.963396	−	0.268082i	$-0.913610\pi$
$853$		−	15.6593i		−	0.536165i	0.963396	−	0.268082i	$-0.0863900\pi$
$854$	4.17584	+	2.65018i	0.142894	+	0.0906874i
$855$	45.3121	+	5.48656i	1.54964	+	0.187636i
$856$	1.70468			0.0582648
$857$	−0.325260	−	0.563367i	−0.0111107	−	0.0192443i	0.860417	−	0.509591i	$-0.170203\pi$
$857$	−0.325260	−	0.563367i	−0.0111107	−	0.0192443i	−0.871527	+	0.490347i	$0.836870\pi$
$858$	−3.53277	−	3.81765i	−0.120607	−	0.130332i
$859$	20.5321	+	11.8542i	0.700547	+	0.404461i	0.807551	−	0.589798i	$-0.200792\pi$
$859$	20.5321	+	11.8542i	0.700547	+	0.404461i	−0.107004	+	0.994259i	$0.534126\pi$
$860$	0.586498	+	1.01584i	0.0199994	+	0.0346400i
$861$	44.6602	−	7.19089i	1.52202	−	0.245065i
$862$	5.83246	−	10.1021i	0.198654	−	0.344079i
$863$	−7.67159	−	4.42919i	−0.261144	−	0.150771i	0.363712	−	0.931511i	$-0.381509\pi$
$863$	−7.67159	−	4.42919i	−0.261144	−	0.150771i	−0.624856	+	0.780740i	$0.714842\pi$
$864$	−24.5753	+	16.9812i	−0.836068	+	0.577714i
$865$	30.6454			1.04197
$866$	−4.94423	+	8.56366i	−0.168012	+	0.291005i
$867$	17.6429	−	15.6355i	0.599184	−	0.531009i
$868$	−8.93461	+	14.0781i	−0.303260	+	0.477841i
$869$	−12.4486	+	7.18721i	−0.422290	+	0.243809i
$870$	−1.31002	+	1.16096i	−0.0444137	+	0.0393604i
$871$	−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	0.933316	−	0.359056i	$-0.116901\pi$
$877$	4.61113	+	7.98670i	0.155707	+	0.269692i	−0.777609	+	0.628748i	$0.783568\pi$
$878$	−23.1434			−0.781051
$879$	−7.90336	−	38.6803i	−0.266574	−	1.30466i
$880$	0.436583	−	0.252061i	0.0147172	−	0.00849699i
$881$	9.25255	+	16.0259i	0.311726	+	0.539926i	0.978736	−	0.205123i	$-0.0657595\pi$
$881$	9.25255	+	16.0259i	0.311726	+	0.539926i	−0.667010	+	0.745049i	$0.732426\pi$
$882$	11.7799	−	13.2186i	0.396650	−	0.445093i
$883$	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
$885$	−8.79003	−	43.0198i	−0.295474	−	1.44610i
$886$	−11.5579	+	20.0189i	−0.388295	+	0.672547i
$887$	−29.8003			−1.00060			−0.500298	−	0.865853i	$-0.666776\pi$
$887$	−29.8003			−1.00060			−0.500298	+	0.865853i	$0.666776\pi$
$888$	−10.4862	−	11.8324i	−0.351892	−	0.397071i
$889$	−24.2828	−	15.4110i	−0.814420	−	0.516869i
$890$	−8.05091	−	4.64819i	−0.269867	−	0.155808i
$891$	−6.41611	−	6.15453i	−0.214948	−	0.206185i
$892$	−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
$897$	−9.70522	−	3.00788i	−0.324048	−	0.100430i
$898$	2.71234	−	4.69791i	0.0905120	−	0.156771i
$899$	−1.37838	+	2.38742i	−0.0459715	+	0.0796250i
$900$	1.71412	−	0.730992i	0.0571372	−	0.0243664i
$901$	12.1446	−	7.01171i	0.404596	−	0.233594i
$902$	8.22168			0.273752
$903$	−1.23844	−	1.52135i	−0.0412127	−	0.0506275i
$904$	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	−0.577443	−	0.816431i	$-0.695949\pi$
$907$	12.5986	−	21.8214i	0.418329	−	0.724567i	0.995772	+	0.0918646i	$0.0292827\pi$
$908$	−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
$915$	5.41388	+	6.10895i	0.178977	+	0.201956i
$916$	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	−0.968934	−	0.247320i	$-0.920450\pi$
$919$	−21.1797	−	36.6842i	−0.698652	−	1.21010i	0.270282	−	0.962781i	$-0.412883\pi$
$920$	−4.79531	+	8.30572i	−0.158097	+	0.273832i
$921$	28.6894	+	32.3727i	0.945347	+	1.06672i
$922$	−4.61096	−	2.66214i	−0.151854	−	0.0876729i
$923$	10.3633	−	0.222964i	0.341112	−	0.00733894i
$924$	−4.52581	+	3.68418i	−0.148888	+	0.121201i
$925$	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	$-0.00120633\pi$
$929$	15.1396	+	26.2226i	0.496714	+	0.860335i	−0.503278	+	0.864124i	$0.667873\pi$
$930$	11.3571	−	10.0649i	0.372413	−	0.330040i
$931$	−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
$936$	27.3327	−	12.3576i	0.893399	−	0.403921i
$937$			1.23501i			0.0403459i	0.999797	+	0.0201730i	$0.00642169\pi$
$937$			1.23501i			0.0403459i	−0.999797	+	0.0201730i	$0.993578\pi$
$938$	5.46905	+	0.229330i	0.178571	+	0.00748788i
$939$	−34.3977	+	7.02832i	−1.12253	+	0.229361i
$940$	−17.5493	−	30.3962i	−0.572394	−	0.991416i
$941$	−8.91584	−	15.4427i	−0.290648	−	0.503417i	0.683315	−	0.730124i	$-0.260538\pi$
$941$	−8.91584	−	15.4427i	−0.290648	−	0.503417i	−0.973963	+	0.226706i	$0.927204\pi$
$942$	20.3500	+	6.79006i	0.663039	+	0.221232i
$943$	13.9088	−	8.03023i	0.452932	−	0.261500i
$944$	−2.86333			−0.0931934
$945$	24.7159	−	15.5903i	0.804007	−	0.507152i
$946$	−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	$0.922511\pi$
$948$	−6.50417	−	31.8324i	−0.211246	−	1.03387i
$949$	−16.6570	+	30.3398i	−0.540710	+	0.984872i
$950$	1.45395	−	2.51831i	0.0471723	−	0.0817049i
$951$	15.9249	−	3.25386i	0.516401	−	0.105514i
$952$	−6.25798	−	11.9710i	−0.202822	−	0.387982i
$953$	−2.58732	−	1.49379i	−0.0838116	−	0.0483887i	0.457508	−	0.889205i	$-0.348742\pi$
$953$	−2.58732	−	1.49379i	−0.0838116	−	0.0483887i	−0.541320	+	0.840817i	$0.682075\pi$
$954$	−17.7224	+	7.55780i	−0.573784	+	0.244693i
$955$			10.4864i			0.339332i
$956$		−	38.2032i		−	1.23558i
$957$	−0.722093	+	0.639933i	−0.0233419	+	0.0206861i
$958$	22.1506	+	12.7887i	0.715653	+	0.413183i
$959$	−15.6398	−	29.9177i	−0.505037	−	0.966093i
$960$	−3.21846	−	15.7516i	−0.103875	−	0.508382i
$961$	−3.55027	+	6.14924i	−0.114525	+	0.198363i
$962$	5.18837	+	8.55605i	0.167280	+	0.275858i
$963$	−1.83074	−	0.221673i	−0.0589948	−	0.00714331i
$964$		−	23.3647i		−	0.752526i
$965$	−5.71954	−	9.90654i	−0.184119	−	0.318903i
$966$	2.23776	−	5.87453i	0.0719987	−	0.189010i
$967$	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	−0.998760	−	0.0497845i	$-0.984147\pi$
$971$	−16.9046	−	29.2796i	−0.542495	−	0.939628i	0.456265	−	0.889844i	$-0.349187\pi$
$972$	17.7858	−	9.35364i	0.570481	−	0.300018i
$973$	−41.5149	−	1.74081i	−1.33091	−	0.0558078i
$974$		−	30.8111i		−	0.987251i
$975$	−2.93458	+	0.665670i	−0.0939816	+	0.0213185i
$976$	0.460983	−	0.266148i	0.0147557	−	0.00851921i
$977$	−23.7118	−	13.6900i	−0.758607	−	0.437982i	0.0701884	−	0.997534i	$-0.477640\pi$
$977$	−23.7118	−	13.6900i	−0.758607	−	0.437982i	−0.828795	+	0.559552i	$0.810973\pi$
$978$	−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
$981$	−31.9461	+	13.6236i	−1.01996	+	0.434967i
$982$	−10.5478	−	18.2693i	−0.336593	−	0.582996i
$983$	−16.3929	−	28.3933i	−0.522851	−	0.905605i	−0.999646	−	0.0265906i	$-0.991535\pi$
$983$	−16.3929	−	28.3933i	−0.522851	−	0.905605i	0.476795	−	0.879014i	$-0.341798\pi$
$984$	−15.0070	+	44.9765i	−0.478406	+	1.43380i
$985$		−	4.26913i		−	0.136026i
$986$	−0.437661	−	0.758051i	−0.0139380	−	0.0241413i
$987$	37.0567	+	45.5221i	1.17953	+	1.44899i
$988$	−16.0109	+	29.1629i	−0.509375	+	0.927796i
$989$	−0.603172	−	0.348242i	−0.0191798	−	0.0110734i
$990$	4.88550	−	2.08344i	0.155271	−	0.0662162i
$991$	7.02081	−	12.1604i	0.223023	−	0.386288i	−0.732701	−	0.680550i	$-0.761741\pi$
$991$	7.02081	−	12.1604i	0.223023	−	0.386288i	0.955725	+	0.294263i	$0.0950740\pi$
$992$	−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
$996$	−24.1667	+	21.4170i	−0.765752	+	0.678625i
$997$		−	42.8725i		−	1.35779i	−0.734237	−	0.678893i	$-0.762460\pi$
$997$		−	42.8725i		−	1.35779i	0.734237	−	0.678893i	$-0.237540\pi$
$998$	−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.68.20	yes	64
3.2	odd	2	inner	273.2.r.b.68.13	✓	64
7.3	odd	6		273.2.bf.b.185.13	yes	64
13.9	even	3		273.2.bf.b.152.20	yes	64
21.17	even	6		273.2.bf.b.185.20	yes	64
39.35	odd	6		273.2.bf.b.152.13	yes	64
91.87	odd	6	inner	273.2.r.b.269.20	yes	64
273.269	even	6	inner	273.2.r.b.269.13	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.r.b.68.13	✓	64	3.2	odd	2	inner
273.2.r.b.68.20	yes	64	1.1	even	1	trivial
273.2.r.b.269.13	yes	64	273.269	even	6	inner
273.2.r.b.269.20	yes	64	91.87	odd	6	inner
273.2.bf.b.152.13	yes	64	39.35	odd	6
273.2.bf.b.152.20	yes	64	13.9	even	3
273.2.bf.b.185.13	yes	64	7.3	odd	6
273.2.bf.b.185.20	yes	64	21.17	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+0.843135i q^{2} +(-1.29627 + 1.14878i) q^{3} +1.28912 q^{4} +(1.06280 - 1.84082i) q^{5} +(-0.968576 - 1.09293i) q^{6} +(2.34470 - 1.22572i) q^{7} +2.77318i q^{8} +(0.360617 - 2.97825i) q^{9} +(1.55206 + 0.896082i) q^{10} +(0.855509 + 0.493928i) q^{11} +(-1.67105 + 1.48092i) q^{12} +(3.08300 - 1.86952i) q^{13} +(1.03345 + 1.97690i) q^{14} +(0.737024 + 3.60711i) q^{15} +0.240083 q^{16} -1.84105 q^{17} +(2.51107 + 0.304049i) q^{18} +(-6.19875 + 3.57885i) q^{19} +(1.37008 - 2.37304i) q^{20} +(-1.63128 + 4.28240i) q^{21} +(-0.416448 + 0.721310i) q^{22} +1.62700i q^{23} +(-3.18576 - 3.59478i) 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} +(-3.04128 + 0.621411i) q^{30} +(-4.23375 + 2.44435i) q^{31} +5.74877i q^{32} +(-1.67638 + 0.342527i) q^{33} -1.55226i q^{34} +(0.235611 - 5.61886i) q^{35} +(0.464880 - 3.83933i) q^{36} +3.29157 q^{37} +(-3.01745 - 5.22638i) q^{38} +(-1.84872 + 5.96508i) q^{39} +(5.10491 + 2.94732i) q^{40} +(-4.93559 - 8.54870i) q^{41} +(-3.61064 - 1.37539i) 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} +(-0.311212 + 0.275803i) q^{48} +(3.99522 - 5.74789i) q^{49} +(-0.351833 + 0.203131i) q^{50} +(2.38649 - 2.11496i) 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} +(0.950114 + 4.65001i) q^{60} +(1.92009 - 1.10857i) q^{61} +(-2.06092 - 3.56962i) q^{62} +(-2.80496 - 7.42511i) q^{63} -4.36683 q^{64} +(-0.164850 - 7.66217i) q^{65} +(-0.288797 - 1.41342i) q^{66} +(1.22692 - 2.12509i) q^{67} -2.37334 q^{68} +(-1.86907 - 2.10903i) q^{69} +(4.73746 + 0.198652i) q^{70} +(2.48976 + 1.43746i) q^{71} +(8.25920 + 1.00005i) 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} +(-5.02937 - 1.55872i) q^{78} +(-7.27556 + 12.6016i) q^{79} +(0.255160 - 0.441950i) q^{80} +(-8.73991 - 2.14801i) q^{81} +(7.20771 - 4.16137i) q^{82} +14.4620 q^{83} +(-2.10291 + 5.52054i) 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} +(-6.60407 - 7.45195i) 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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