LMFDB - Embedded newform 273.2.r.b.269.13

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			269.13
Character	$\chi$	$=$	273.269
Dual form			273.2.r.b.68.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.843135i q^{2} +(-1.29627 - 1.14878i) q^{3} +1.28912 q^{4} +(1.06280 + 1.84082i) q^{5} +(-0.968576 + 1.09293i) q^{6} +(2.34470 + 1.22572i) q^{7} -2.77318i q^{8} +(0.360617 + 2.97825i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 64 * q - 64 * q^4 + 12 * q^6 - 10 * q^7 - 4 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

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	$-0.903649\pi$
$2$		−	0.843135i		−	0.596187i	0.954537	−	0.298093i	$-0.0963507\pi$
$3$	−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	0.999600	−	0.0282929i	$-0.00900711\pi$
$5$	1.06280	+	1.84082i	0.475297	+	0.823239i	−0.524302	+	0.851532i	$0.675674\pi$
$6$	−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	−0.365451	−	0.930830i	$-0.619085\pi$
$11$	0.855509	−	0.493928i	0.257946	−	0.148925i	0.623397	+	0.781905i	$0.285752\pi$
$12$	−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	−0.425613	−	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
$21$	−1.63128	−	4.28240i	−0.355974	−	0.934496i
$22$	−0.416448	−	0.721310i	−0.0887871	−	0.153784i
$23$		−	1.62700i		−	0.339254i	−0.985508	−	0.169627i	$-0.945744\pi$
$23$		−	1.62700i		−	0.339254i	0.985508	−	0.169627i	$-0.0542563\pi$
$24$	−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	0.544657	−	0.838659i	$-0.316660\pi$
$29$	0.488355	+	0.281952i	0.0906852	+	0.0523571i	−0.453972	+	0.891016i	$0.649993\pi$
$30$	−3.04128	−	0.621411i	−0.555260	−	0.113454i
$31$	−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
$33$	−1.67638	−	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	0.166310	+	0.986074i	$0.446815\pi$
$41$	−4.93559	+	8.54870i	−0.770810	+	1.33508i	−0.937120	+	0.349008i	$0.886518\pi$
$42$	−3.61064	+	1.37539i	−0.557134	+	0.212227i
$43$	−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	$0.217210\pi$
$47$	6.40449	+	11.0929i	0.934190	+	1.61807i	0.158119	+	0.987420i	$0.449457\pi$
$48$	−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	−0.0269320	−	0.999637i	$-0.508574\pi$
$53$	−6.59657	−	3.80853i	−0.906109	−	0.523142i	−0.879177	+	0.476495i	$0.841907\pi$
$54$	−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	0.617859	−	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
$63$	−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	0.931188	−	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
$69$	−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	−0.344930	−	0.938628i	$-0.612097\pi$
$71$	2.48976	−	1.43746i	0.295480	−	0.170596i	0.640411	+	0.768033i	$0.278764\pi$
$72$	8.25920	−	1.00005i	0.973356	−	0.117858i
$73$	−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
$78$	−5.02937	+	1.55872i	−0.569464	+	0.176491i
$79$	−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
$81$	−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	−0.508746	−	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	0.676764	−	0.736200i	$-0.263382\pi$
$101$	−3.00678	−	5.20790i	−0.299186	−	0.518205i	−0.975950	+	0.217995i	$0.930048\pi$
$102$	1.78320	−	2.01214i	0.176563	−	0.199231i
$103$	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
$105$	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	$0.00945928\pi$
$107$			0.614704i			0.0594257i	−0.999558	+	0.0297128i	$0.990541\pi$
$108$	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
$111$	−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	−0.758966	−	0.651130i	$-0.774295\pi$
$113$	−6.10760	+	3.52622i	−0.574554	+	0.331719i	0.184412	+	0.982849i	$0.440962\pi$
$114$	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	−0.999793	−	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
$129$	−0.148430	+	0.726442i	−0.0130686	+	0.0639597i
$130$	6.46024	+	0.138990i	0.566601	+	0.0121903i
$131$	−8.66948	−	15.0160i	−0.757456	−	1.31195i	−0.944144	−	0.329533i	$-0.893109\pi$
$131$	−8.66948	−	15.0160i	−0.757456	−	1.31195i	0.186688	−	0.982419i	$-0.440225\pi$
$132$	−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	$0.183496\pi$
$137$			12.7597i			1.09014i	−0.838392	+	0.545068i	$0.816504\pi$
$138$	1.77820	+	1.57588i	0.151370	+	0.134148i
$139$	−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
$141$	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	0.742528	−	0.669815i	$-0.233627\pi$
$149$	6.51483	+	3.76134i	0.533715	+	0.308141i	−0.208813	+	0.977956i	$0.566960\pi$
$150$	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
$153$	−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	−0.102585	−	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
$162$	1.81107	+	7.36893i	0.142291	+	0.578958i
$163$	−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	−0.736651	−	0.676274i	$-0.763594\pi$
$167$	2.80871	−	4.86483i	0.217345	−	0.376452i	0.953995	+	0.299821i	$0.0969271\pi$
$168$	−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	−0.450343	−	0.892855i	$-0.648698\pi$
$173$	7.20865	−	12.4858i	0.548064	−	0.949274i	0.998407	−	0.0564189i	$-0.0179682\pi$
$174$	−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	0.445378	−	0.895342i	$-0.353069\pi$
$179$	19.3121	−	11.1499i	1.44346	−	0.833380i	0.998079	+	0.0619621i	$0.0197358\pi$
$180$	−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
$189$	12.1658	−	6.40265i	0.884930	−	0.465724i
$190$	−12.8278			−0.930624
$191$	−4.27245	−	2.46670i	−0.309143	−	0.178484i	0.337400	−	0.941361i	$-0.390453\pi$
$191$	−4.27245	−	2.46670i	−0.309143	−	0.178484i	−0.646543	+	0.762877i	$0.723786\pi$
$192$	5.66058	+	5.01652i	0.408517	+	0.362036i
$193$	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
$195$	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	0.560681	−	0.828032i	$-0.310540\pi$
$197$	1.73936	+	1.00422i	0.123924	+	0.0715477i	−0.436756	+	0.899580i	$0.643873\pi$
$198$	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
$201$	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	−0.710716	−	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
$213$	−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	0.459461	−	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
$225$	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	−0.117763	−	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
$231$	−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	−0.890039	−	0.455885i	$-0.849323\pi$
$233$	−14.3523	+	8.28630i	−0.940250	+	0.542854i	−0.0502115	+	0.998739i	$0.515990\pi$
$234$	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	$0.407936\pi$
$239$			29.6350i			1.91693i	−0.285211	+	0.958465i	$0.592064\pi$
$240$	0.176947	−	0.866008i	0.0114219	−	0.0559006i
$241$			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
$243$	13.7969	+	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	0.720863	−	0.693077i	$-0.243746\pi$
$251$	−3.79901	−	6.58007i	−0.239791	−	0.415330i	−0.960654	+	0.277747i	$0.910412\pi$
$252$	−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	−0.889270	−	0.457382i	$-0.848787\pi$
$263$	−15.2086	+	8.78068i	−0.937801	+	0.541440i	−0.0485307	+	0.998822i	$0.515454\pi$
$264$	−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	$0.372271\pi$
$271$			30.3088i			1.84113i	−0.390590	+	0.920565i	$0.627729\pi$
$272$	−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	$-0.699565\pi$
$281$		−	27.1501i		−	1.61964i	0.586680	−	0.809819i	$-0.300435\pi$
$282$	−18.3270	−	3.74466i	−1.09136	−	0.222991i
$283$	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
$285$	−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	−0.979066	−	0.203542i	$-0.934755\pi$
$293$	−11.3968	−	19.7398i	−0.665805	−	1.15321i	0.313261	−	0.949667i	$-0.398579\pi$
$294$	−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	$0.252512\pi$
$307$			24.9738i			1.42533i	−0.701504	+	0.712665i	$0.747488\pi$
$308$	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	−0.489319	−	0.872105i	$-0.662754\pi$
$311$	9.00463	−	15.5965i	0.510606	−	0.884395i	0.999924	−	0.0122902i	$-0.00391219\pi$
$312$	−16.5422	+	5.12684i	−0.936519	+	0.290250i
$313$	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
$315$	−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	−0.710553	−	0.703644i	$-0.751555\pi$
$317$	−8.12697	+	4.69211i	−0.456456	+	0.263535i	0.254097	+	0.967179i	$0.418222\pi$
$318$	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	−0.482902	−	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
$333$	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	$0.0224883\pi$
$347$			2.62990i			0.141180i	−0.997505	+	0.0705902i	$0.977512\pi$
$348$	−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
$351$	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	−0.991911	−	0.126939i	$-0.959485\pi$
$353$	−11.3836	−	19.7170i	−0.605888	−	1.04943i	0.386023	−	0.922489i	$-0.373849\pi$
$354$	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	−0.337914	−	0.941177i	$-0.609721\pi$
$359$	5.83980	−	3.37161i	0.308213	−	0.177947i	0.646126	+	0.763230i	$0.276388\pi$
$360$	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
$369$	−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	−0.313659	−	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
$375$	−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	0.145757	+	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	−0.740527	−	0.672026i	$-0.765424\pi$
$383$	4.14360	−	7.17693i	0.211728	−	0.366724i	0.952255	+	0.305302i	$0.0987575\pi$
$384$	−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	0.955381	−	0.295378i	$-0.0954454\pi$
$389$	23.2193	+	13.4057i	1.17727	+	0.679695i	0.221886	+	0.975073i	$0.428779\pi$
$390$	−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	0.367514	−	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
$399$	−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	$0.0330390\pi$
$401$			4.14953i			0.207218i	−0.994618	+	0.103609i	$0.966961\pi$
$402$	−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	$-0.915194\pi$
$409$		−	10.6492i		−	0.526570i	0.964718	−	0.263285i	$-0.0848060\pi$
$410$			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	−0.749896	−	0.661556i	$-0.769896\pi$
$419$	4.05247	−	7.01909i	0.197976	−	0.342905i	0.947872	+	0.318651i	$0.103230\pi$
$420$	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	−0.759993	−	0.649931i	$-0.774798\pi$
$431$	−11.9816	+	6.91758i	−0.577134	+	0.333208i	0.182860	+	0.983139i	$0.441465\pi$
$432$	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
$435$	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	$-0.772652\pi$
$439$		−	27.4492i		−	1.31008i	0.755595	−	0.655039i	$-0.227348\pi$
$440$	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	0.184629	−	0.982808i	$-0.440892\pi$
$443$	23.7433	−	13.7082i	1.12808	−	0.651298i	0.943451	+	0.331511i	$0.107558\pi$
$444$	−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	−0.625683	−	0.780078i	$-0.715179\pi$
$449$	−5.57195	+	3.21697i	−0.262957	+	0.151818i	0.362726	+	0.931896i	$0.381846\pi$
$450$	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	0.783082	−	0.621918i	$-0.213646\pi$
$461$	−3.15743	−	5.46883i	−0.147056	−	0.254709i	−0.930138	+	0.367210i	$0.880313\pi$
$462$	−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	0.814838	−	0.579688i	$-0.196826\pi$
$467$	−2.04445	−	3.54109i	−0.0946057	−	0.163862i	−0.909444	+	0.415826i	$0.863492\pi$
$468$	−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	0.970836	+	0.239744i	$0.0770634\pi$
$479$	15.1680	+	26.2717i	0.693042	+	1.20038i	−0.277794	+	0.960641i	$0.589603\pi$
$480$	−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	−0.0762474	−	0.997089i	$-0.524294\pi$
$491$	−21.6683	−	12.5102i	−0.977875	−	0.564577i	−0.901628	+	0.432512i	$0.857627\pi$
$492$	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	0.628296	−	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	$-0.832668\pi$
$503$	−19.4463	−	33.6820i	−0.867069	−	1.50181i	−0.00209081	−	0.999998i	$-0.500666\pi$
$504$	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	0.230112	+	0.973164i	$0.426091\pi$
$521$	−16.6107	+	28.7706i	−0.727729	+	1.26046i	−0.957841	+	0.287299i	$0.907243\pi$
$522$	1.31202	+	0.559515i	0.0574254	+	0.0244893i
$523$		−	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
$525$	−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	−0.995751	−	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
$543$	−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	0.0840671	−	0.996460i	$-0.473209\pi$
$557$	23.3427	−	13.4769i	0.989060	−	0.571034i	0.904993	+	0.425426i	$0.139876\pi$
$558$	−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	$0.0249662\pi$
$569$			3.73804i			0.156707i	−0.996926	+	0.0783534i	$0.975034\pi$
$570$	16.6282	+	14.7363i	0.696479	+	0.617234i
$571$	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
$576$	−1.57475	−	13.0055i	−0.0656147	−	0.541895i
$577$	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
$579$	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	−0.801624	−	0.597829i	$-0.796030\pi$
$587$	2.83282	−	4.90659i	0.116923	−	0.202516i	0.918547	+	0.395312i	$0.129364\pi$
$588$	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	0.899909	−	0.436077i	$-0.143632\pi$
$593$	1.76064	+	3.04952i	0.0723010	+	0.125229i	−0.827608	+	0.561306i	$0.810299\pi$
$594$	−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	0.889262	−	0.457398i	$-0.151219\pi$
$599$	22.9515	+	13.2511i	0.937774	+	0.541424i	0.0485125	+	0.998823i	$0.484552\pi$
$600$	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
$606$	8.60416	+	1.75805i	0.349520	+	0.0714157i
$607$	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
$609$	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	0.938747	−	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
$615$	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	−0.689239	−	0.724534i	$-0.742055\pi$
$617$	−10.0946	+	5.82812i	−0.406393	+	0.234631i	0.282846	+	0.959165i	$0.408722\pi$
$618$	−2.84329	+	13.9155i	−0.114374	+	0.559764i
$619$	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
$624$	−0.443848	−	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	0.999949	+	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	$0.236712\pi$
$641$			34.2795i			1.35396i	−0.736002	+	0.676980i	$0.763288\pi$
$642$	−0.671828	−	0.595387i	−0.0265149	−	0.0234981i
$643$	−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	0.994333	−	0.106311i	$-0.0339040\pi$
$647$	10.3042	+	17.8473i	0.405098	+	0.701651i	−0.589235	+	0.807962i	$0.700571\pi$
$648$	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	$0.180944\pi$
$653$			27.5127i			1.07665i	−0.842736	+	0.538327i	$0.819056\pi$
$654$	−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	−0.978391	−	0.206764i	$-0.933707\pi$
$659$	−33.0777	+	19.0974i	−1.28852	+	0.743929i	−0.310132	+	0.950693i	$0.600373\pi$
$660$	−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
$663$	3.40359	+	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	−0.739212	−	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
$675$	−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	0.996130	+	0.0878879i	$0.0280117\pi$
$677$	14.9397	+	25.8763i	0.574178	+	0.994506i	−0.421952	+	0.906618i	$0.638655\pi$
$678$	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	$-0.976785\pi$
$683$		−	3.80861i		−	0.145732i	0.997342	−	0.0728662i	$-0.0232146\pi$
$684$	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	$0.210895\pi$
$691$			32.3395i			1.23025i	−0.788428	+	0.615127i	$0.789105\pi$
$692$	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	$-0.949338\pi$
$701$		−	8.39232i		−	0.316974i	0.987361	−	0.158487i	$-0.0506616\pi$
$702$	−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	0.489244	+	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
$714$	6.64738	−	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	0.449979	+	0.893039i	$0.351432\pi$
$719$	−14.7050	+	25.4699i	−0.548405	+	0.949866i	−0.998384	+	0.0568265i	$0.981902\pi$
$720$	−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	$0.201218\pi$
$727$			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
$735$	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	−0.966675	−	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
$741$	−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	0.999729	+	0.0232753i	$0.00740942\pi$
$743$	41.4254	+	23.9170i	1.51975	+	0.877428i	0.520022	+	0.854153i	$0.325924\pi$
$744$	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	−0.963380	−	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
$759$	−0.557293	+	2.72748i	−0.0202285	+	0.0990013i
$760$	−42.1921			−1.53047
$761$	11.3944	−	19.7356i	0.413045	−	0.715415i	−0.582176	−	0.813063i	$-0.697798\pi$
$761$	11.3944	−	19.7356i	0.413045	−	0.715415i	0.995221	+	0.0976477i	$0.0311318\pi$
$762$	−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

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)

\(f(q)\)	\(=\)	\(q-0.843135i q^{2} +(-1.29627 - 1.14878i) q^{3} +1.28912 q^{4} +(1.06280 + 1.84082i) q^{5} +(-0.968576 + 1.09293i) q^{6} +(2.34470 + 1.22572i) q^{7} -2.77318i q^{8} +(0.360617 + 2.97825i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 64 q^{4} + 12 q^{6} - 10 q^{7} - 4 q^{9}+O(q^{10}) \) 64 * q - 64 * q^4 + 12 * q^6 - 10 * q^7 - 4 * q^9	\( 64 q - 64 q^{4} + 12 q^{6} - 10 q^{7} - 4 q^{9} - 6 q^{10} + 6 q^{12} + 12 q^{13} - 9 q^{15} + 32 q^{16} + 2 q^{18} - 36 q^{19} + 10 q^{21} + 10 q^{22} - 18 q^{24} - 24 q^{25} - 14 q^{28} + 8 q^{30} - 24 q^{31} - 45 q^{33} + 33 q^{39} + 90 q^{40} + 3 q^{42} - 20 q^{43} - 6 q^{48} - 6 q^{49} - 10 q^{51} - 48 q^{52} - 18 q^{55} + 4 q^{57} + 30 q^{58} + 55 q^{60} - 18 q^{61} + 31 q^{63} - 84 q^{64} + 75 q^{66} + 44 q^{67} + 33 q^{69} + 20 q^{70} + 17 q^{72} + 84 q^{73} - 18 q^{76} - 71 q^{78} + 20 q^{79} + 16 q^{81} - 18 q^{82} - 135 q^{84} - 2 q^{85} - 46 q^{88} - 10 q^{91} - 56 q^{93} + 36 q^{94} + 30 q^{96} - 24 q^{97} + 22 q^{99}+O(q^{100}) \) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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