LMFDB - Embedded newform 525.2.bm.a.131.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(131,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 12, 25]))

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

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

chi := DirichletCharacter("525.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bm (of order $30$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$608$
Relative dimension:	$76$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			131.15
Character	$\chi$	$=$	525.131
Dual form			525.2.bm.a.521.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.406505 + 1.91245i) q^{2} +(1.66519 + 0.476610i) q^{3} +(-1.66514 - 0.741369i) q^{4} +(-0.898652 - 2.04754i) q^{5} +(-1.58840 + 2.99085i) q^{6} +(2.59781 + 0.501390i) q^{7} +(-0.203728 + 0.280407i) q^{8} +(2.54569 + 1.58729i) q^{9} +O(q^{10})$	\(q+(-0.406505 + 1.91245i) q^{2} +(1.66519 + 0.476610i) q^{3} +(-1.66514 - 0.741369i) q^{4} +(-0.898652 - 2.04754i) q^{5} +(-1.58840 + 2.99085i) q^{6} +(2.59781 + 0.501390i) q^{7} +(-0.203728 + 0.280407i) q^{8} +(2.54569 + 1.58729i) q^{9} +(4.28113 - 0.886296i) q^{10} +(-0.0390194 - 0.0351332i) q^{11} +(-2.41943 - 2.02814i) q^{12} +(5.80558 + 1.88635i) q^{13} +(-2.01491 + 4.76437i) q^{14} +(-0.520544 - 3.83784i) q^{15} +(-2.89273 - 3.21271i) q^{16} +(0.443226 - 4.21701i) q^{17} +(-4.07045 + 4.22327i) q^{18} +(-0.0972966 - 0.218532i) q^{19} +(-0.0215998 + 4.07568i) q^{20} +(4.08687 + 2.07305i) q^{21} +(0.0830522 - 0.0603410i) q^{22} +(-1.37371 + 6.46278i) q^{23} +(-0.472890 + 0.369832i) q^{24} +(-3.38485 + 3.68005i) q^{25} +(-5.96754 + 10.3361i) q^{26} +(3.48252 + 3.85643i) q^{27} +(-3.95401 - 2.76082i) q^{28} +(-1.20721 - 1.66159i) q^{29} +(7.55130 + 0.564584i) q^{30} +(-3.08920 - 0.324688i) q^{31} +(6.71973 - 3.87964i) q^{32} +(-0.0482297 - 0.0771003i) q^{33} +(7.88466 + 2.56188i) q^{34} +(-1.30791 - 5.76969i) q^{35} +(-3.06216 - 4.53036i) q^{36} +(1.02316 + 1.13633i) q^{37} +(0.457483 - 0.0972411i) q^{38} +(8.76831 + 5.90811i) q^{39} +(0.757226 + 0.165152i) q^{40} +(-3.19900 + 9.84551i) q^{41} +(-5.62594 + 6.97324i) q^{42} -8.68665 q^{43} +(0.0389262 + 0.0874296i) q^{44} +(0.962351 - 6.63882i) q^{45} +(-11.8013 - 5.25430i) q^{46} +(-1.02878 - 9.78819i) q^{47} +(-3.28573 - 6.72846i) q^{48} +(6.49722 + 2.60503i) q^{49} +(-5.66198 - 7.96933i) q^{50} +(2.74792 - 6.81086i) q^{51} +(-8.26864 - 7.44511i) q^{52} +(1.15517 - 2.59456i) q^{53} +(-8.79090 + 5.09251i) q^{54} +(-0.0368718 + 0.111466i) q^{55} +(-0.669840 + 0.626298i) q^{56} +(-0.0578625 - 0.410268i) q^{57} +(3.66845 - 1.63330i) q^{58} +(2.85577 - 0.607013i) q^{59} +(-1.97848 + 6.77647i) q^{60} +(1.77896 - 8.36934i) q^{61} +(1.87672 - 5.77596i) q^{62} +(5.81735 + 5.39985i) q^{63} +(2.01619 + 6.20519i) q^{64} +(-1.35482 - 13.5823i) q^{65} +(0.167056 - 0.0608954i) q^{66} +(1.36572 - 12.9939i) q^{67} +(-3.86440 + 6.69333i) q^{68} +(-5.36770 + 10.1070i) q^{69} +(11.5659 - 0.155909i) q^{70} +(2.65223 + 3.65048i) q^{71} +(-0.963715 + 0.390454i) q^{72} +(-0.621829 - 0.559897i) q^{73} +(-2.58910 + 1.49482i) q^{74} +(-7.39035 + 4.51472i) q^{75} +0.436019i q^{76} +(-0.0837494 - 0.110833i) q^{77} +(-14.8634 + 14.3673i) q^{78} +(-0.238900 - 2.27298i) q^{79} +(-3.97859 + 8.81010i) q^{80} +(3.96103 + 8.08147i) q^{81} +(-17.5287 - 10.1202i) q^{82} +(-7.90211 - 5.74122i) q^{83} +(-5.26832 - 6.48180i) q^{84} +(-9.03281 + 2.88210i) q^{85} +(3.53116 - 16.6128i) q^{86} +(-1.21831 - 3.34222i) q^{87} +(0.0178010 - 0.00378371i) q^{88} +(-2.73025 - 0.580332i) q^{89} +(12.3052 + 4.53916i) q^{90} +(14.1360 + 7.81123i) q^{91} +(7.07872 - 9.74303i) q^{92} +(-4.98934 - 2.01301i) q^{93} +(19.1377 + 2.01145i) q^{94} +(-0.360017 + 0.395603i) q^{95} +(13.0387 - 3.25763i) q^{96} +(5.20118 + 7.15881i) q^{97} +(-7.62315 + 11.3667i) q^{98} +(-0.0435646 - 0.151373i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 608 q - 9 q^{3} - 78 q^{4} - 36 q^{7} - 3 q^{9}+O(q^{10}) $ 608 * q - 9 * q^3 - 78 * q^4 - 36 * q^7 - 3 * q^9	$ 608 q - 9 q^{3} - 78 q^{4} - 36 q^{7} - 3 q^{9} - 30 q^{10} + 3 q^{12} + 16 q^{15} + 50 q^{16} - 8 q^{18} - 18 q^{19} - 21 q^{21} - 24 q^{22} - 66 q^{24} - 10 q^{25} - 30 q^{28} - 7 q^{30} - 36 q^{31} + 36 q^{33} - 100 q^{36} - 14 q^{37} - 31 q^{39} - 30 q^{40} + 20 q^{42} - 96 q^{43} - 117 q^{45} + 42 q^{46} - 28 q^{49} - 8 q^{51} - 66 q^{52} + 3 q^{54} + 48 q^{57} - 38 q^{58} - 49 q^{60} - 18 q^{61} + 4 q^{63} - 32 q^{64} - 3 q^{66} - 22 q^{67} - 270 q^{70} + 45 q^{72} + 102 q^{73} + 135 q^{75} + 58 q^{78} - 34 q^{79} - 55 q^{81} + 108 q^{82} - 75 q^{84} - 96 q^{85} - 9 q^{87} + 36 q^{88} + 38 q^{91} - 22 q^{93} + 30 q^{94} - 81 q^{96} + 36 q^{99}+O(q^{100}) $ 608 * q - 9 * q^3 - 78 * q^4 - 36 * q^7 - 3 * q^9 - 30 * q^10 + 3 * q^12 + 16 * q^15 + 50 * q^16 - 8 * q^18 - 18 * q^19 - 21 * q^21 - 24 * q^22 - 66 * q^24 - 10 * q^25 - 30 * q^28 - 7 * q^30 - 36 * q^31 + 36 * q^33 - 100 * q^36 - 14 * q^37 - 31 * q^39 - 30 * q^40 + 20 * q^42 - 96 * q^43 - 117 * q^45 + 42 * q^46 - 28 * q^49 - 8 * q^51 - 66 * q^52 + 3 * q^54 + 48 * q^57 - 38 * q^58 - 49 * q^60 - 18 * q^61 + 4 * q^63 - 32 * q^64 - 3 * q^66 - 22 * q^67 - 270 * q^70 + 45 * q^72 + 102 * q^73 + 135 * q^75 + 58 * q^78 - 34 * q^79 - 55 * q^81 + 108 * q^82 - 75 * q^84 - 96 * q^85 - 9 * q^87 + 36 * q^88 + 38 * q^91 - 22 * q^93 + 30 * q^94 - 81 * q^96 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.406505	+	1.91245i	−0.287442	+	1.35231i	0.563094	+	0.826393i	$0.309611\pi$
$2$	−0.406505	+	1.91245i	−0.287442	+	1.35231i	−0.850536	+	0.525916i	$0.823722\pi$
$3$	1.66519	+	0.476610i	0.961395	+	0.275171i
$3$	1.66519	+	0.476610i	0.961395	+	0.275171i
$4$	−1.66514	−	0.741369i	−0.832571	−	0.370685i
$5$	−0.898652	−	2.04754i	−0.401890	−	0.915688i
$5$	−0.898652	−	2.04754i	−0.401890	−	0.915688i
$6$	−1.58840	+	2.99085i	−0.648462	+	1.22101i
$7$	2.59781	+	0.501390i	0.981879	+	0.189508i
$7$	2.59781	+	0.501390i	0.981879	+	0.189508i
$8$	−0.203728	+	0.280407i	−0.0720287	+	0.0991390i
$9$	2.54569	+	1.58729i	0.848562	+	0.529096i
$10$	4.28113	−	0.886296i	1.35381	−	0.280271i
$11$	−0.0390194	−	0.0351332i	−0.0117648	−	0.0105931i	0.663227	−	0.748418i	$-0.269186\pi$
$11$	−0.0390194	−	0.0351332i	−0.0117648	−	0.0105931i	−0.674992	+	0.737825i	$0.735853\pi$
$12$	−2.41943	−	2.02814i	−0.698429	−	0.585474i
$13$	5.80558	+	1.88635i	1.61018	+	0.523178i	0.969596	−	0.244712i	$-0.0786933\pi$
$13$	5.80558	+	1.88635i	1.61018	+	0.523178i	0.640582	+	0.767890i	$0.278693\pi$
$14$	−2.01491	+	4.76437i	−0.538506	+	1.27333i
$15$	−0.520544	−	3.83784i	−0.134404	−	0.990927i
$16$	−2.89273	−	3.21271i	−0.723183	−	0.803176i
$17$	0.443226	−	4.21701i	0.107498	−	1.02278i	−0.799220	−	0.601038i	$-0.794754\pi$
$17$	0.443226	−	4.21701i	0.107498	−	1.02278i	0.906718	−	0.421737i	$-0.138579\pi$
$18$	−4.07045	+	4.22327i	−0.959414	+	0.995434i
$19$	−0.0972966	−	0.218532i	−0.0223214	−	0.0501346i	0.902041	−	0.431651i	$-0.142069\pi$
$19$	−0.0972966	−	0.218532i	−0.0223214	−	0.0501346i	−0.924362	+	0.381516i	$0.875402\pi$
$20$	−0.0215998	+	4.07568i	−0.00482985	+	0.911350i
$21$	4.08687	+	2.07305i	0.891827	+	0.452376i
$22$	0.0830522	−	0.0603410i	0.0177068	−	0.0128647i
$23$	−1.37371	+	6.46278i	−0.286438	+	1.34758i	0.565850	+	0.824508i	$0.308548\pi$
$23$	−1.37371	+	6.46278i	−0.286438	+	1.34758i	−0.852287	+	0.523074i	$0.824785\pi$
$24$	−0.472890	+	0.369832i	−0.0965282	+	0.0754916i
$25$	−3.38485	+	3.68005i	−0.676970	+	0.736011i
$26$	−5.96754	+	10.3361i	−1.17033	+	2.02707i
$27$	3.48252	+	3.85643i	0.670212	+	0.742170i
$28$	−3.95401	−	2.76082i	−0.747237	−	0.521746i
$29$	−1.20721	−	1.66159i	−0.224174	−	0.308549i	0.682084	−	0.731274i	$-0.261074\pi$
$29$	−1.20721	−	1.66159i	−0.224174	−	0.308549i	−0.906258	+	0.422725i	$0.861074\pi$
$30$	7.55130	+	0.564584i	1.37867	+	0.103078i
$31$	−3.08920	−	0.324688i	−0.554837	−	0.0583157i	−0.177039	−	0.984204i	$-0.556652\pi$
$31$	−3.08920	−	0.324688i	−0.554837	−	0.0583157i	−0.377798	+	0.925888i	$0.623319\pi$
$32$	6.71973	−	3.87964i	1.18789	−	0.685829i
$33$	−0.0482297	−	0.0771003i	−0.00839571	−	0.0134214i
$34$	7.88466	+	2.56188i	1.35221	+	0.439359i
$35$	−1.30791	−	5.76969i	−0.221077	−	0.975256i
$36$	−3.06216	−	4.53036i	−0.510361	−	0.755059i
$37$	1.02316	+	1.13633i	0.168206	+	0.186812i	0.821354	−	0.570418i	$-0.193219\pi$
$37$	1.02316	+	1.13633i	0.168206	+	0.186812i	−0.653148	+	0.757230i	$0.726552\pi$
$38$	0.457483	−	0.0972411i	0.0742136	−	0.0157746i
$39$	8.76831	+	5.90811i	1.40405	+	0.946055i
$40$	0.757226	+	0.165152i	0.119728	+	0.0261129i
$41$	−3.19900	+	9.84551i	−0.499600	+	1.53761i	0.310063	+	0.950716i	$0.399650\pi$
$41$	−3.19900	+	9.84551i	−0.499600	+	1.53761i	−0.809663	+	0.586895i	$0.800350\pi$
$42$	−5.62594	+	6.97324i	−0.868101	+	1.07599i
$43$	−8.68665			−1.32470			−0.662350	−	0.749194i	$-0.730441\pi$
$43$	−8.68665			−1.32470			−0.662350	+	0.749194i	$0.730441\pi$
$44$	0.0389262	+	0.0874296i	0.00586834	+	0.0131805i
$45$	0.962351	−	6.63882i	0.143459	−	0.989656i
$46$	−11.8013	−	5.25430i	−1.74001	−	0.774704i
$47$	−1.02878	−	9.78819i	−0.150063	−	1.42775i	−0.767457	−	0.641100i	$-0.778478\pi$
$47$	−1.02878	−	9.78819i	−0.150063	−	1.42775i	0.617394	−	0.786654i	$-0.288188\pi$
$48$	−3.28573	−	6.72846i	−0.474254	−	0.971169i
$49$	6.49722	+	2.60503i	0.928174	+	0.372147i
$50$	−5.66198	−	7.96933i	−0.800725	−	1.12703i
$51$	2.74792	−	6.81086i	0.384786	−	0.953711i
$52$	−8.26864	−	7.44511i	−1.14665	−	1.03245i
$53$	1.15517	−	2.59456i	0.158675	−	0.356390i	−0.816660	−	0.577119i	$-0.804177\pi$
$53$	1.15517	−	2.59456i	0.158675	−	0.356390i	0.975335	+	0.220729i	$0.0708436\pi$
$54$	−8.79090	+	5.09251i	−1.19629	+	0.693002i
$55$	−0.0368718	+	0.111466i	−0.00497180	+	0.0150301i
$56$	−0.669840	+	0.626298i	−0.0895111	+	0.0836925i
$57$	−0.0578625	−	0.410268i	−0.00766407	−	0.0543414i
$58$	3.66845	−	1.63330i	0.481691	−	0.214462i
$59$	2.85577	−	0.607013i	0.371790	−	0.0790264i	−0.0182274	−	0.999834i	$-0.505802\pi$
$59$	2.85577	−	0.607013i	0.371790	−	0.0790264i	0.390017	+	0.920807i	$0.372469\pi$
$60$	−1.97848	+	6.77647i	−0.255420	+	0.874839i
$61$	1.77896	−	8.36934i	0.227772	−	1.07158i	−0.704466	−	0.709738i	$-0.748813\pi$
$61$	1.77896	−	8.36934i	0.227772	−	1.07158i	0.932238	−	0.361846i	$-0.117853\pi$
$62$	1.87672	−	5.77596i	0.238344	−	0.733548i
$63$	5.81735	+	5.39985i	0.732918	+	0.680317i
$64$	2.01619	+	6.20519i	0.252024	+	0.775649i
$65$	−1.35482	−	13.5823i	−0.168045	−	1.68468i
$66$	0.167056	−	0.0608954i	0.0205632	−	0.00749570i
$67$	1.36572	−	12.9939i	0.166849	−	1.58746i	−0.515795	−	0.856712i	$-0.672503\pi$
$67$	1.36572	−	12.9939i	0.166849	−	1.58746i	0.682644	−	0.730751i	$-0.260830\pi$
$68$	−3.86440	+	6.69333i	−0.468627	+	0.811685i
$69$	−5.36770	+	10.1070i	−0.646195	+	1.21674i
$70$	11.5659	−	0.155909i	1.38239	−	0.0186347i
$71$	2.65223	+	3.65048i	0.314761	+	0.433232i	0.936859	−	0.349708i	$-0.113719\pi$
$71$	2.65223	+	3.65048i	0.314761	+	0.433232i	−0.622097	+	0.782940i	$0.713719\pi$
$72$	−0.963715	+	0.390454i	−0.113575	+	0.0460155i
$73$	−0.621829	−	0.559897i	−0.0727795	−	0.0655310i	0.631938	−	0.775019i	$-0.282260\pi$
$73$	−0.621829	−	0.559897i	−0.0727795	−	0.0655310i	−0.704718	+	0.709488i	$0.748926\pi$
$74$	−2.58910	+	1.49482i	−0.300977	+	0.173769i
$75$	−7.39035	+	4.51472i	−0.853364	+	0.521315i
$76$			0.436019i			0.0500148i
$77$	−0.0837494	−	0.110833i	−0.00954413	−	0.0126306i
$78$	−14.8634	+	14.3673i	−1.68294	+	1.62678i
$79$	−0.238900	−	2.27298i	−0.0268783	−	0.255730i	−0.999707	−	0.0242040i	$-0.992295\pi$
$79$	−0.238900	−	2.27298i	−0.0268783	−	0.255730i	0.972829	−	0.231526i	$-0.0743718\pi$
$80$	−3.97859	+	8.81010i	−0.444819	+	0.984999i
$81$	3.96103	+	8.08147i	0.440115	+	0.897942i
$82$	−17.5287	−	10.1202i	−1.93572	−	1.11759i
$83$	−7.90211	−	5.74122i	−0.867369	−	0.630180i	0.0625107	−	0.998044i	$-0.480089\pi$
$83$	−7.90211	−	5.74122i	−0.867369	−	0.630180i	−0.929880	+	0.367864i	$0.880089\pi$
$84$	−5.26832	−	6.48180i	−0.574821	−	0.707222i
$85$	−9.03281	+	2.88210i	−0.979745	+	0.312608i
$86$	3.53116	−	16.6128i	0.380775	−	1.79141i
$87$	−1.21831	−	3.34222i	−0.130616	−	0.358324i
$88$	0.0178010	−	0.00378371i	0.00189759	−	0.000403345i
$89$	−2.73025	−	0.580332i	−0.289406	−	0.0615151i	0.0609212	−	0.998143i	$-0.480596\pi$
$89$	−2.73025	−	0.580332i	−0.289406	−	0.0615151i	−0.350327	+	0.936628i	$0.613929\pi$
$90$	12.3052	+	4.53916i	1.29709	+	0.478470i
$91$	14.1360	+	7.81123i	1.48185	+	0.818839i
$92$	7.07872	−	9.74303i	0.738008	−	1.01578i
$93$	−4.98934	−	2.01301i	−0.517370	−	0.208739i
$94$	19.1377	+	2.01145i	1.97390	+	0.207465i
$95$	−0.360017	+	0.395603i	−0.0369369	+	0.0405880i
$96$	13.0387	−	3.25763i	1.33075	−	0.332480i
$97$	5.20118	+	7.15881i	0.528100	+	0.726867i	0.986839	−	0.161704i	$-0.0516989\pi$
$97$	5.20118	+	7.15881i	0.528100	+	0.726867i	−0.458739	+	0.888571i	$0.651699\pi$
$98$	−7.62315	+	11.3667i	−0.770054	+	1.14821i
$99$	−0.0435646	−	0.151373i	−0.00437840	−	0.0152136i
$100$	8.36454	−	3.61839i	0.836454	−	0.361839i
$101$	3.17488	+	5.49905i	0.315912	+	0.547176i	0.979631	−	0.200806i	$-0.0643562\pi$
$101$	3.17488	+	5.49905i	0.315912	+	0.547176i	−0.663719	+	0.747982i	$0.731023\pi$
$102$	11.9084	+	8.02392i	1.17911	+	0.794486i
$103$	6.26269	−	0.658235i	0.617081	−	0.0648579i	0.209170	−	0.977879i	$-0.432924\pi$
$103$	6.26269	−	0.658235i	0.617081	−	0.0648579i	0.407911	+	0.913021i	$0.366257\pi$
$104$	−1.71170	+	1.24363i	−0.167846	+	0.121948i
$105$	0.571982	−	10.2310i	0.0558197	−	0.998441i
$106$	4.49239	+	3.26391i	0.436340	+	0.317019i
$107$	−13.8737	−	8.00998i	−1.34122	−	0.774354i	−0.354234	−	0.935157i	$-0.615258\pi$
$107$	−13.8737	−	8.00998i	−1.34122	−	0.774354i	−0.986987	+	0.160803i	$0.948592\pi$
$108$	−2.93986	−	9.00334i	−0.282888	−	0.866347i
$109$	−16.3843	+	3.48259i	−1.56933	+	0.333572i	−0.908802	−	0.417228i	$-0.863002\pi$
$109$	−16.3843	+	3.48259i	−1.56933	+	0.333572i	−0.660530	+	0.750800i	$0.729668\pi$
$110$	−0.198186	−	0.115827i	−0.0188963	−	0.0110437i
$111$	1.16216	+	2.37985i	0.110307	+	0.225885i
$112$	−5.90395	−	9.79638i	−0.557871	−	0.925671i
$113$	8.14890	+	2.64774i	0.766584	+	0.249078i	0.666102	−	0.745861i	$-0.267962\pi$
$113$	8.14890	+	2.64774i	0.766584	+	0.249078i	0.100482	+	0.994939i	$0.467962\pi$
$114$	0.808140	+	0.0561167i	0.0756893	+	0.00525581i
$115$	14.4673	−	2.99507i	1.34908	−	0.279292i
$116$	0.778333	+	3.66177i	0.0722664	+	0.339987i
$117$	11.7850	+	14.0172i	1.08952	+	1.29589i
$118$			5.70829i			0.525491i
$119$	3.26578	−	10.7328i	0.299374	−	0.983870i
$120$	1.18221	+	0.635911i	0.107920	+	0.0580505i
$121$	−1.14952	−	10.9370i	−0.104502	−	0.994273i
$122$	15.2828	+	6.80435i	1.38364	+	0.616037i
$123$	−10.0194	+	14.8699i	−0.903419	+	1.34078i
$124$	4.90324	+	2.83089i	0.440324	+	0.254221i
$125$	10.5769	+	3.62353i	0.946024	+	0.324098i
$126$	−12.6917	+	8.93035i	−1.13067	+	0.795579i
$127$	−1.84122	−	5.66670i	−0.163382	−	0.502838i	0.835531	−	0.549443i	$-0.185160\pi$
$127$	−1.84122	−	5.66670i	−0.163382	−	0.502838i	−0.998913	+	0.0466045i	$0.985160\pi$
$128$	2.74680	−	0.288700i	0.242785	−	0.0255177i
$129$	−14.4649	−	4.14014i	−1.27356	−	0.364519i
$130$	26.5263	+	2.93024i	2.32651	+	0.256999i
$131$	16.1394	−	7.18571i	1.41010	−	0.627818i	0.446410	−	0.894829i	$-0.352702\pi$
$131$	16.1394	−	7.18571i	1.41010	−	0.627818i	0.963694	+	0.267010i	$0.0860357\pi$
$132$	0.0231495	+	0.164139i	0.00201490	+	0.0142865i
$133$	−0.143188	−	0.616487i	−0.0124160	−	0.0534562i
$134$	24.2952	+	7.89397i	2.09878	+	0.681936i
$135$	4.76662	−	10.5962i	0.410245	−	0.911975i
$136$	1.09218	+	0.983406i	0.0936540	+	0.0843264i
$137$	−2.74850	−	12.9307i	−0.234820	−	1.10474i	−0.924664	−	0.380784i	$-0.875654\pi$
$137$	−2.74850	−	12.9307i	−0.234820	−	1.10474i	0.689843	−	0.723959i	$-0.257679\pi$
$138$	−17.1472	−	14.3740i	−1.45967	−	1.22360i
$139$	1.06649	−	0.346524i	0.0904586	−	0.0293918i	−0.263438	−	0.964676i	$-0.584856\pi$
$139$	1.06649	−	0.346524i	0.0904586	−	0.0293918i	0.353897	+	0.935285i	$0.384856\pi$
$140$	−2.09962	+	10.5770i	−0.177450	+	0.893921i
$141$	2.95204	−	16.7895i	0.248607	−	1.41393i
$142$	−8.05951	+	3.58833i	−0.676339	+	0.301126i
$143$	−0.160257	−	0.277573i	−0.0134013	−	0.0232118i
$144$	−2.26450	−	12.7701i	−0.188708	−	1.06418i
$145$	−2.31730	+	3.96501i	−0.192441	+	0.329276i
$146$	1.32355	−	0.961618i	0.109538	−	0.0795841i
$147$	9.57749	+	7.43450i	0.789938	+	0.613187i
$148$	−0.861262	−	2.65069i	−0.0707953	−	0.217886i
$149$	6.66736	+	3.84940i	0.546211	+	0.315355i	0.747593	−	0.664158i	$-0.231210\pi$
$149$	6.66736	+	3.84940i	0.546211	+	0.315355i	−0.201381	+	0.979513i	$0.564543\pi$
$150$	−5.62998	−	15.9690i	−0.459686	−	1.30386i
$151$	−6.58949	−	11.4133i	−0.536245	−	0.928804i	−0.999102	−	0.0423710i	$-0.986509\pi$
$151$	−6.58949	−	11.4133i	−0.536245	−	0.928804i	0.462857	−	0.886433i	$-0.346824\pi$
$152$	0.0810999	+	0.0172383i	0.00657807	+	0.00139821i
$153$	7.82192	−	10.0317i	0.632365	−	0.811011i
$154$	0.246008	−	0.115113i	0.0198239	−	0.00927604i
$155$	2.11130	+	6.61704i	0.169584	+	0.531494i
$156$	−10.2204	−	16.3384i	−0.818287	−	1.30812i
$157$	−15.4308	+	8.90900i	−1.23151	+	0.711015i	−0.967346	−	0.253461i	$-0.918431\pi$
$157$	−15.4308	+	8.90900i	−1.23151	+	0.711015i	−0.264169	+	0.964476i	$0.585098\pi$
$158$	4.44408	+	0.467091i	0.353552	+	0.0371598i
$159$	3.16017	−	3.76986i	0.250618	−	0.298969i
$160$	−13.9824	−	10.2725i	−1.10541	−	0.812110i
$161$	−6.80900	+	16.1003i	−0.536624	+	1.26888i
$162$	−17.0656	+	4.29013i	−1.34080	+	0.337065i
$163$	−6.06227	−	6.73283i	−0.474833	−	0.527356i	0.457377	−	0.889273i	$-0.348789\pi$
$163$	−6.06227	−	6.73283i	−0.474833	−	0.527356i	−0.932210	+	0.361917i	$0.882122\pi$
$164$	12.6260	−	14.0225i	0.985921	−	1.09498i
$165$	−0.114524	+	0.168039i	−0.00891571	+	0.0130818i
$166$	14.1921	−	12.7786i	1.10152	−	0.991811i
$167$	−6.98596	−	5.07560i	−0.540590	−	0.392762i	0.283714	−	0.958909i	$-0.408433\pi$
$167$	−6.98596	−	5.07560i	−0.540590	−	0.392762i	−0.824304	+	0.566147i	$0.808433\pi$
$168$	−1.41391	+	0.723649i	−0.109085	+	0.0558308i
$169$	19.6292	+	14.2615i	1.50994	+	1.09703i
$170$	−1.84001	−	18.4464i	−0.141122	−	1.41478i
$171$	0.0991862	−	0.710751i	0.00758496	−	0.0543525i
$172$	14.4645	+	6.44001i	1.10291	+	0.491046i
$173$	−10.6830	−	2.27074i	−0.812214	−	0.172641i	−0.216961	−	0.976180i	$-0.569615\pi$
$173$	−10.6830	−	2.27074i	−0.812214	−	0.172641i	−0.595252	+	0.803539i	$0.702948\pi$
$174$	6.88709	−	0.971325i	0.522109	−	0.0736360i
$175$	−10.6383	+	7.86295i	−0.804182	+	0.594383i
$176$			0.226989i			0.0171099i
$177$	5.04470	+	0.350300i	0.379183	+	0.0263302i
$178$	2.21972	−	4.98556i	0.166375	−	0.373684i
$179$	1.76165	−	3.95673i	0.131672	−	0.295740i	−0.835663	−	0.549243i	$-0.814916\pi$
$179$	1.76165	−	3.95673i	0.131672	−	0.295740i	0.967335	+	0.253503i	$0.0815828\pi$
$180$	−6.52427	+	10.3411i	−0.486290	+	0.770782i
$181$	−13.5032	+	18.5855i	−1.00368	+	1.38145i	−0.0806428	+	0.996743i	$0.525697\pi$
$181$	−13.5032	+	18.5855i	−1.00368	+	1.38145i	−0.923039	+	0.384706i	$0.874303\pi$
$182$	−20.6850	+	23.8591i	−1.53327	+	1.76856i
$183$	6.95121	−	13.0886i	0.513848	−	0.967540i
$184$	−1.53235	−	1.70185i	−0.112966	−	0.125462i
$185$	1.40722	−	3.11612i	0.103461	−	0.229102i
$186$	5.87798	−	8.72359i	0.430994	−	0.639644i
$187$	−0.165451	+	0.148973i	−0.0120990	+	0.0108940i
$188$	−5.54360	+	17.0614i	−0.404309	+	1.24433i
$189$	7.11335	+	11.7644i	0.517420	+	0.855732i
$190$	−0.610223	−	0.849330i	−0.0442703	−	0.0616169i
$191$	9.63163	−	8.67236i	0.696921	−	0.627510i	−0.242550	−	0.970139i	$-0.577984\pi$
$191$	9.63163	−	8.67236i	0.696921	−	0.627510i	0.939471	+	0.342629i	$0.111317\pi$
$192$	0.399872	+	11.2937i	0.0288583	+	0.815055i
$193$	4.24419	+	7.35115i	0.305503	+	0.529147i	0.977373	−	0.211522i	$-0.0678419\pi$
$193$	4.24419	+	7.35115i	0.305503	+	0.529147i	−0.671870	+	0.740669i	$0.734509\pi$
$194$	−15.8052	+	7.03693i	−1.13475	+	0.505222i
$195$	4.21744	−	23.2628i	0.302017	−	1.66588i
$196$	−8.88750	−	9.15459i	−0.634822	−	0.653899i
$197$	5.71855	+	7.87091i	0.407430	+	0.560779i	0.962589	−	0.270965i	$-0.0873427\pi$
$197$	5.71855	+	7.87091i	0.407430	+	0.560779i	−0.555159	+	0.831744i	$0.687343\pi$
$198$	0.307203	−	0.0217813i	0.0218320	−	0.00154793i
$199$	−16.0191	+	9.24865i	−1.13557	+	0.655619i	−0.945329	−	0.326119i	$-0.894259\pi$
$199$	−16.0191	+	9.24865i	−1.13557	+	0.655619i	−0.190237	+	0.981738i	$0.560926\pi$
$200$	−0.342327	−	1.69887i	−0.0242061	−	0.120128i
$201$	8.46722	−	20.9864i	0.597232	−	1.48027i
$202$	−11.8073	+	3.83642i	−0.830757	+	0.269929i
$203$	−2.30301	−	4.92177i	−0.161639	−	0.345440i
$204$	−9.62504	+	9.30383i	−0.673888	+	0.651398i
$205$	23.0339	−	2.29761i	1.60876	−	0.160472i
$206$	−1.28697	+	12.2447i	−0.0896673	+	0.853128i
$207$	−13.7553	+	14.2717i	−0.956061	+	0.991954i
$208$	−10.7337	−	24.1083i	−0.744249	−	1.67161i
$209$	−0.00388127	+	0.0119453i	−0.000268473	+	0.000826274i
$210$	19.3338	+	5.25283i	1.33416	+	0.362480i
$211$	3.55376	+	10.9374i	0.244651	+	0.752959i	0.995694	+	0.0927049i	$0.0295513\pi$
$211$	3.55376	+	10.9374i	0.244651	+	0.752959i	−0.751042	+	0.660254i	$0.770449\pi$
$212$	−3.84705	+	3.46390i	−0.264217	+	0.237902i
$213$	2.67660	+	7.34280i	0.183397	+	0.503120i
$214$	20.9584	−	23.2767i	1.43269	−	1.59116i
$215$	7.80627	+	17.7863i	0.532383	+	1.21301i
$216$	−1.79086	+	0.190863i	−0.121852	+	0.0129866i
$217$	−7.86235	−	2.39237i	−0.533731	−	0.162405i
$218$		−	32.7499i		−	2.21810i
$219$	−0.768608	−	1.22870i	−0.0519377	−	0.0830280i
$220$	0.144035	−	0.158272i	0.00971081	−	0.0106707i
$221$	10.5279	−	23.6461i	0.708185	−	1.59061i
$222$	−5.02378	+	1.25516i	−0.337174	+	0.0842407i
$223$	−7.00692	+	2.27669i	−0.469218	+	0.152458i	−0.534076	−	0.845436i	$-0.679340\pi$
$223$	−7.00692	+	2.27669i	−0.469218	+	0.152458i	0.0648583	+	0.997894i	$0.479340\pi$
$224$	19.4018	−	6.70935i	1.29634	−	0.448287i
$225$	−14.4581	+	3.99553i	−0.963871	+	0.266369i
$226$	−8.37624	+	14.5081i	−0.557179	+	0.965063i
$227$	2.78260	−	3.09039i	0.184688	−	0.205116i	−0.643690	−	0.765286i	$-0.722597\pi$
$227$	2.78260	−	3.09039i	0.184688	−	0.205116i	0.828378	+	0.560170i	$0.189264\pi$
$228$	−0.207811	+	0.726053i	−0.0137626	+	0.0480840i
$229$	−13.2256	+	1.39006i	−0.873970	+	0.0918579i	−0.530882	−	0.847446i	$-0.678139\pi$
$229$	−13.2256	+	1.39006i	−0.873970	+	0.0918579i	−0.343087	+	0.939303i	$0.611473\pi$
$230$	−0.153084	+	28.8855i	−0.0100940	+	1.90466i
$231$	−0.0866341	−	0.224474i	−0.00570010	−	0.0147693i
$232$	0.711864			0.0467362
$233$	8.09207	+	18.1751i	0.530129	+	1.19069i	0.957979	+	0.286840i	$0.0926047\pi$
$233$	8.09207	+	18.1751i	0.530129	+	1.19069i	−0.427849	+	0.903850i	$0.640729\pi$
$234$	−31.5978	+	16.8402i	−2.06562	+	1.10088i
$235$	−19.1172	+	10.9026i	−1.24707	+	0.711210i
$236$	−5.20529	−	1.10642i	−0.338836	−	0.0720217i
$237$	0.685512	−	3.89879i	0.0445288	−	0.253254i
$238$	19.1983	+	10.6086i	1.24444	+	0.687652i
$239$	−26.0684	+	8.47014i	−1.68623	+	0.547888i	−0.986103	−	0.166135i	$-0.946871\pi$
$239$	−26.0684	+	8.47014i	−1.68623	+	0.547888i	−0.700122	+	0.714023i	$0.746871\pi$
$240$	−10.8241	+	12.7742i	−0.698690	+	0.824572i
$241$	−1.43743	−	6.76259i	−0.0925932	−	0.435617i	−0.999886	−	0.0151167i	$-0.995188\pi$
$241$	−1.43743	−	6.76259i	−0.0925932	−	0.435617i	0.907293	−	0.420500i	$-0.138145\pi$
$242$	21.3838	+	2.24753i	1.37460	+	0.144477i
$243$	2.74414	+	15.3450i	0.176037	+	0.984384i
$244$	−9.16699	+	12.6173i	−0.586856	+	0.807739i
$245$	−0.504830	−	15.6443i	−0.0322524	−	0.999480i
$246$	−24.3651	−	25.2063i	−1.55346	−	1.60710i
$247$	−0.152636	−	1.45224i	−0.00971202	−	0.0924037i
$248$	0.720401	−	0.800086i	0.0457455	−	0.0508055i
$249$	−10.4222	−	13.3264i	−0.660477	−	0.844527i
$250$	−11.2294	+	18.7548i	−0.710208	+	1.18616i
$251$	11.2596			0.710702			0.355351	−	0.934733i	$-0.384361\pi$
$251$	11.2596			0.710702			0.355351	+	0.934733i	$0.384361\pi$
$252$	−5.68344	−	13.3043i	−0.358023	−	0.838094i
$253$	0.280659	−	0.203911i	0.0176449	−	0.0128198i
$254$	11.5858	−	1.21771i	0.726956	−	0.0764061i
$255$	−16.4149	+	0.494110i	−1.02794	+	0.0309424i
$256$	−1.92846	+	18.3481i	−0.120529	+	1.14675i
$257$	−4.92901	+	8.53729i	−0.307463	+	0.532542i	−0.977807	−	0.209509i	$-0.932813\pi$
$257$	−4.92901	+	8.53729i	−0.307463	+	0.532542i	0.670344	+	0.742051i	$0.266147\pi$
$258$	13.7979	−	25.9804i	0.859018	−	1.61747i
$259$	2.08822	+	3.46497i	0.129756	+	0.215303i
$260$	−7.81355	+	23.6209i	−0.484576	+	1.46491i
$261$	−0.435769	−	6.14607i	−0.0269734	−	0.380432i
$262$	7.18161	+	33.7868i	0.443681	+	2.08736i
$263$	0.825226	+	3.88238i	0.0508856	+	0.239398i	0.996239	−	0.0866500i	$-0.0276162\pi$
$263$	0.825226	+	3.88238i	0.0508856	+	0.239398i	−0.945353	+	0.326048i	$0.894283\pi$
$264$	0.0314452	+	0.00218353i	0.00193532	+	0.000134387i
$265$	−6.35056	−	0.0336559i	−0.390112	−	0.00206746i
$266$	1.23721	−	0.0232361i	0.0758582	−	0.00142469i
$267$	−4.26978	−	2.26762i	−0.261306	−	0.138776i
$268$	−11.9074	+	20.6243i	−0.727362	+	1.25983i
$269$	1.57389	−	14.9746i	0.0959619	−	0.913017i	−0.835577	−	0.549374i	$-0.814866\pi$
$269$	1.57389	−	14.9746i	0.0959619	−	0.913017i	0.931539	−	0.363643i	$-0.118467\pi$
$270$	18.3271	+	13.4233i	1.11535	+	0.816919i
$271$	−25.0729	+	2.63527i	−1.52307	+	0.160081i	−0.828764	−	0.559598i	$-0.810956\pi$
$271$	−25.0729	+	2.63527i	−1.52307	+	0.160081i	−0.694307	+	0.719679i	$0.744289\pi$
$272$	−14.8301	+	10.7747i	−0.899210	+	0.653314i
$273$	19.8161	+	19.7445i	1.19933	+	1.19499i
$274$	25.8466			1.56145
$275$	0.261367	−	0.0246729i	0.0157610	−	0.00148783i
$276$	16.4310	−	12.8502i	0.989031	−	0.773489i
$277$	8.14676	−	9.04789i	0.489491	−	0.543635i	−0.446904	−	0.894582i	$-0.647473\pi$
$277$	8.14676	−	9.04789i	0.489491	−	0.543635i	0.936395	+	0.350947i	$0.114140\pi$
$278$	0.229178	+	2.18048i	0.0137452	+	0.130776i
$279$	−7.34876	−	5.73000i	−0.439959	−	0.343046i
$280$	1.88432	+	0.808700i	0.112610	+	0.0483291i
$281$	0.0891879	−	0.122757i	0.00532050	−	0.00732305i	−0.806348	−	0.591441i	$-0.798559\pi$
$281$	0.0891879	−	0.122757i	0.00532050	−	0.00732305i	0.811669	+	0.584118i	$0.198559\pi$
$282$	30.9091	+	12.4706i	1.84061	+	0.742616i
$283$	8.41295	+	0.884237i	0.500098	+	0.0525624i	0.351220	−	0.936293i	$-0.385767\pi$
$283$	8.41295	+	0.884237i	0.500098	+	0.0525624i	0.148878	+	0.988856i	$0.452434\pi$
$284$	−1.70998	−	8.04485i	−0.101469	−	0.477374i
$285$	−0.788043	+	0.487164i	−0.0466796	+	0.0288571i
$286$	0.595990	−	0.193649i	0.0352416	−	0.0114507i
$287$	−13.2468	+	23.9728i	−0.781936	+	1.41507i
$288$	23.2644	+	0.789809i	1.37087	+	0.0465399i
$289$	−0.958211	−	0.203674i	−0.0563654	−	0.0119808i
$290$	−6.64090	−	6.04353i	−0.389967	−	0.354888i
$291$	5.24897	+	14.3997i	0.307700	+	0.844124i
$292$	0.620343	+	1.39331i	0.0363028	+	0.0815375i
$293$	23.7034			1.38476			0.692382	−	0.721531i	$-0.256561\pi$
$293$	23.7034			1.38476			0.692382	+	0.721531i	$0.256561\pi$
$294$	−18.1114	+	15.2943i	−1.05628	+	0.891984i
$295$	−3.80923	−	5.30182i	−0.221782	−	0.308684i
$296$	−0.527082	+	0.0553985i	−0.0306360	+	0.00321997i
$297$	−0.000397126	−	0.272828i	−2.30436e−5	−	0.0158311i
$298$	−10.0721	+	11.1862i	−0.583462	+	0.648000i
$299$	−20.1662	+	34.9289i	−1.16624	+	2.01999i
$300$	15.6531	−	2.03868i	0.903730	−	0.117703i
$301$	−22.5662	−	4.35540i	−1.30070	−	0.251041i
$302$	24.5061	−	7.96253i	1.41017	−	0.458192i
$303$	2.66586	+	10.6701i	0.153150	+	0.612982i
$304$	−0.420625	+	0.944739i	−0.0241245	+	0.0541845i
$305$	−18.7352	+	3.87864i	−1.07278	+	0.222090i
$306$	16.0054	+	19.0370i	0.914969	+	1.08827i
$307$		−	28.7606i		−	1.64145i	−0.571320	−	0.820727i	$-0.693569\pi$
$307$		−	28.7606i		−	1.64145i	0.571320	−	0.820727i	$-0.306431\pi$
$308$	0.0572864	+	0.246643i	0.00326419	+	0.0140538i
$309$	10.7423	+	1.88878i	0.611106	+	0.107449i
$310$	−13.5130	+	1.34791i	−0.767489	+	0.0765563i
$311$	−19.8163	+	22.0082i	−1.12368	+	1.24797i	−0.158220	+	0.987404i	$0.550576\pi$
$311$	−19.8163	+	22.0082i	−1.12368	+	1.24797i	−0.965456	+	0.260565i	$0.916091\pi$
$312$	−3.44303	+	1.25505i	−0.194923	+	0.0710533i
$313$	10.8831	−	9.79921i	0.615151	−	0.553884i	−0.301554	−	0.953449i	$-0.597505\pi$
$313$	10.8831	−	9.79921i	0.615151	−	0.553884i	0.916705	+	0.399565i	$0.130839\pi$
$314$	−10.7653	−	33.1323i	−0.607523	−	1.86976i
$315$	5.82864	−	16.7639i	0.328407	−	0.944536i
$316$	−1.28731	+	3.96195i	−0.0724171	+	0.222877i
$317$	−10.0820	−	22.6445i	−0.566260	−	1.27184i	−0.939004	−	0.343907i	$-0.888250\pi$
$317$	−10.0820	−	22.6445i	−0.566260	−	1.27184i	0.372744	−	0.927934i	$-0.378417\pi$
$318$	5.92505	+	7.57614i	0.332260	+	0.424849i
$319$	−0.0112722	+	0.107247i	−0.000631119	+	0.00600470i
$320$	10.8935	−	9.70454i	0.608967	−	0.542500i
$321$	−19.2846	−	19.9504i	−1.07636	−	1.11353i
$322$	−28.0232	−	19.5667i	−1.56167	−	1.09041i
$323$	−0.964674	+	0.313442i	−0.0536759	+	0.0174404i
$324$	−0.604327	−	16.3934i	−0.0335737	−	0.910744i
$325$	−26.5929	+	14.9798i	−1.47511	+	0.830932i
$326$	15.3406	−	8.85688i	0.849635	−	0.490537i
$327$	−28.9427	−	2.00976i	−1.60054	−	0.111140i
$328$	−2.10903	−	2.90283i	−0.116452	−	0.160282i
$329$	2.23513	−	25.9437i	0.123227	−	1.43032i
$330$	−0.274811	−	0.287331i	−0.0151279	−	0.0158171i
$331$	−16.0460	+	7.14413i	−0.881966	+	0.392677i	−0.797194	−	0.603724i	$-0.793683\pi$
$331$	−16.0460	+	7.14413i	−0.881966	+	0.392677i	−0.0847725	+	0.996400i	$0.527016\pi$
$332$	8.90178	+	15.4183i	0.488548	+	0.846191i
$333$	0.800952	+	4.51679i	0.0438919	+	0.247519i
$334$	12.5467	−	11.2971i	0.686523	−	0.618149i
$335$	−27.8329	+	8.88068i	−1.52068	+	0.485203i
$336$	−5.16211	−	19.1267i	−0.281616	−	1.04345i
$337$	10.3420	−	31.8294i	0.563365	−	1.73386i	−0.109396	−	0.993998i	$-0.534892\pi$
$337$	10.3420	−	31.8294i	0.563365	−	1.73386i	0.672760	−	0.739860i	$-0.265108\pi$
$338$	−35.2537	+	31.7426i	−1.91755	+	1.72657i
$339$	12.3075	+	8.29282i	0.668451	+	0.450404i
$340$	17.1776	+	1.89753i	0.931587	+	0.102908i
$341$	0.109131	+	0.121203i	0.00590979	+	0.00656349i
$342$	1.31896	+	0.478613i	0.0713211	+	0.0258804i
$343$	15.5724	+	10.0250i	0.840830	+	0.541300i
$344$	1.76971	−	2.43580i	0.0954165	−	0.131330i
$345$	25.5182	+	1.90791i	1.37385	+	0.102718i
$346$	8.68538	−	19.5077i	0.466929	−	1.04874i
$347$	−5.41289	+	12.1575i	−0.290579	+	0.652651i	−0.998564	−	0.0535767i	$-0.982938\pi$
$347$	−5.41289	+	12.1575i	−0.290579	+	0.652651i	0.707985	+	0.706228i	$0.249604\pi$
$348$	−0.449167	+	6.46849i	−0.0240779	+	0.346747i
$349$			19.8476i			1.06242i	0.847241	+	0.531209i	$0.178262\pi$
$349$			19.8476i			1.06242i	−0.847241	+	0.531209i	$0.821738\pi$
$350$	−10.7130	−	23.5416i	−0.572634	−	1.25835i
$351$	12.9435	+	28.9580i	0.690872	+	1.54567i
$352$	−0.398504	−	0.0847046i	−0.0212403	−	0.00451477i
$353$	−0.0264269	−	0.0117660i	−0.00140656	−	0.000626242i	0.406033	−	0.913858i	$-0.366912\pi$
$353$	−0.0264269	−	0.0117660i	−0.00140656	−	0.000626242i	−0.407440	+	0.913232i	$0.633578\pi$
$354$	−2.72063	+	9.50536i	−0.144600	+	0.505204i
$355$	5.09107	−	8.71105i	0.270206	−	0.462335i
$356$	4.11601	+	2.99046i	0.218148	+	0.158494i
$357$	10.5535	−	16.3155i	0.558549	−	0.863509i
$358$	6.85095	+	4.97751i	0.362084	+	0.263069i
$359$	−8.73228	+	7.86258i	−0.460872	+	0.414971i	−0.866585	−	0.499029i	$-0.833690\pi$
$359$	−8.73228	+	7.86258i	−0.460872	+	0.414971i	0.405713	+	0.914001i	$0.367023\pi$
$360$	1.66552	+	1.62236i	0.0877804	+	0.0855060i
$361$	12.6752	−	14.0772i	0.667115	−	0.740907i
$362$	−30.0548	−	33.3793i	−1.57965	−	1.75437i
$363$	3.29851	−	18.7600i	0.173127	−	0.984645i
$364$	−17.7474	−	23.4868i	−0.930218	−	1.23104i
$365$	−0.587604	+	1.77637i	−0.0307566	+	0.0929796i
$366$	22.2057	+	18.6144i	1.16071	+	0.972993i
$367$	−0.842962	−	0.0885989i	−0.0440023	−	0.00462483i	0.0825017	−	0.996591i	$-0.473709\pi$
$367$	−0.842962	−	0.0885989i	−0.0440023	−	0.00462483i	−0.126504	+	0.991966i	$0.540376\pi$
$368$	24.7368	−	14.2818i	1.28949	−	0.744489i
$369$	−23.7713	+	19.9858i	−1.23749	+	1.04042i
$370$	5.38740	+	3.95797i	0.280078	+	0.205765i
$371$	4.30180	−	6.16098i	0.223338	−	0.319862i
$372$	6.81558	+	7.05089i	0.353371	+	0.365572i
$373$	12.1803	+	2.58900i	0.630672	+	0.134053i	0.512147	−	0.858898i	$-0.328850\pi$
$373$	12.1803	+	2.58900i	0.630672	+	0.134053i	0.118525	+	0.992951i	$0.462184\pi$
$374$	−0.217648	−	0.376977i	−0.0112543	−	0.0194930i
$375$	15.8854	+	11.0749i	0.820320	+	0.571904i
$376$	2.95427	+	1.70565i	0.152355	+	0.0879622i
$377$	−3.87424	−	11.9237i	−0.199534	−	0.614102i
$378$	−25.3904	+	8.82168i	−1.30594	+	0.453738i
$379$	18.6400	−	13.5428i	0.957474	−	0.695646i	0.00491145	−	0.999988i	$-0.498437\pi$
$379$	18.6400	−	13.5428i	0.957474	−	0.695646i	0.952563	+	0.304342i	$0.0984366\pi$
$380$	0.892767	−	0.391830i	0.0457980	−	0.0201004i
$381$	−0.365171	−	10.3137i	−0.0187083	−	0.528384i
$382$	12.6702	+	21.9454i	0.648263	+	1.12282i
$383$	−1.81210	+	0.806799i	−0.0925940	+	0.0412255i	−0.452511	−	0.891759i	$-0.649472\pi$
$383$	−1.81210	+	0.806799i	−0.0925940	+	0.0412255i	0.359917	+	0.932984i	$0.382805\pi$
$384$	4.71153	+	0.828412i	0.240434	+	0.0422747i
$385$	−0.151674	+	0.271081i	−0.00773003	+	0.0138156i
$386$	−15.7840	+	5.12854i	−0.803386	+	0.261036i
$387$	−22.1135	−	13.7882i	−1.12409	−	0.700894i
$388$	−3.35339	−	15.7764i	−0.170242	−	0.800927i
$389$	9.92878	+	8.93991i	0.503409	+	0.453272i	0.881285	−	0.472585i	$-0.156679\pi$
$389$	9.92878	+	8.93991i	0.503409	+	0.453272i	−0.377876	+	0.925856i	$0.623346\pi$
$390$	42.7747	+	17.5221i	2.16598	+	0.887266i
$391$	26.6447	+	8.65740i	1.34748	+	0.437824i
$392$	−2.05413	+	1.29115i	−0.103749	+	0.0652129i
$393$	30.2998	−	4.27336i	1.52842	−	0.215562i
$394$	−17.3774	+	7.73690i	−0.875459	+	0.389780i
$395$	−4.43933	+	2.53177i	−0.223367	+	0.127387i
$396$	−0.0396822	+	0.284355i	−0.00199410	+	0.0142894i
$397$	14.3328	−	1.50644i	0.719342	−	0.0756058i	0.262218	−	0.965009i	$-0.415546\pi$
$397$	14.3328	−	1.50644i	0.719342	−	0.0756058i	0.457124	+	0.889403i	$0.348880\pi$
$398$	−11.1758	−	34.3955i	−0.560190	−	1.72409i
$399$	0.0553889	−	1.09481i	0.00277291	−	0.0548091i
$400$	21.6144	+	0.229105i	1.08072	+	0.0114552i
$401$	2.50278	+	1.44498i	0.124983	+	0.0721589i	0.561188	−	0.827688i	$-0.310344\pi$
$401$	2.50278	+	1.44498i	0.124983	+	0.0721589i	−0.436205	+	0.899847i	$0.643678\pi$
$402$	36.6936	+	24.7242i	1.83011	+	1.23313i
$403$	−17.3221	−	7.71230i	−0.862876	−	0.384177i
$404$	−1.20980	−	11.5105i	−0.0601897	−	0.572667i
$405$	12.9876	−	15.3728i	0.645357	−	0.763881i
$406$	10.3488	−	2.40367i	0.513604	−	0.119292i
$407$		−	0.0802858i		−	0.00397962i
$408$	1.34999	+	2.15810i	0.0668343	+	0.106842i
$409$	−2.49594	−	11.7425i	−0.123416	−	0.580628i	−0.995780	−	0.0917711i	$-0.970747\pi$
$409$	−2.49594	−	11.7425i	−0.123416	−	0.580628i	0.872364	−	0.488857i	$-0.162586\pi$
$410$	−4.96931	+	44.9852i	−0.245417	+	2.22166i
$411$	1.58613	−	22.8420i	0.0782379	−	1.12671i
$412$	−10.9163	−	3.54691i	−0.537806	−	0.174744i
$413$	7.72310	−	0.145048i	0.380029	−	0.00713734i
$414$	−21.7024	−	32.1079i	−1.06662	−	1.57802i
$415$	−4.65413	+	21.3392i	−0.228462	+	1.04750i
$416$	46.3302	−	9.84780i	2.27153	−	0.482828i
$417$	1.94106	−	0.0687264i	0.0950543	−	0.00336555i
$418$	−0.0212671	−	0.0122786i	−0.00104021	−	0.000600564i
$419$	23.9092	+	17.3711i	1.16804	+	0.848633i	0.990773	−	0.135530i	$-0.0432737\pi$
$419$	23.9092	+	17.3711i	1.16804	+	0.848633i	0.177269	+	0.984162i	$0.443274\pi$
$420$	−8.53736	+	16.6120i	−0.416581	+	0.810582i
$421$	−1.21664	+	0.883944i	−0.0592956	+	0.0430808i	−0.617038	−	0.786933i	$-0.711668\pi$
$421$	−1.21664	+	0.883944i	−0.0592956	+	0.0430808i	0.557743	+	0.830014i	$0.311668\pi$
$422$	−22.3618	+	2.35032i	−1.08856	+	0.114412i
$423$	12.9177	−	26.5506i	0.628081	−	1.29094i
$424$	0.492193	+	0.852503i	0.0239030	+	0.0414012i
$425$	14.0186	+	15.9050i	0.680001	+	0.771507i
$426$	−15.1308	+	2.13398i	−0.733090	+	0.103392i
$427$	8.81769	−	20.8500i	0.426718	−	1.00900i
$428$	17.1633	+	23.6233i	0.829621	+	1.14187i
$429$	−0.134563	−	0.538590i	−0.00649677	−	0.0260034i
$430$	−37.1887	+	7.69894i	−1.79340	+	0.371276i
$431$	−21.5665	−	2.26673i	−1.03882	−	0.109185i	−0.430271	−	0.902700i	$-0.641582\pi$
$431$	−21.5665	−	2.26673i	−1.03882	−	0.109185i	−0.608550	+	0.793515i	$0.708249\pi$
$432$	2.31556	−	22.3439i	0.111408	−	1.07502i
$433$	5.95075	−	8.19050i	0.285975	−	0.393610i	−0.641727	−	0.766933i	$-0.721782\pi$
$433$	5.95075	−	8.19050i	0.285975	−	0.393610i	0.927701	+	0.373323i	$0.121782\pi$
$434$	7.77138	−	14.0639i	0.373038	−	0.675088i
$435$	−5.74850	+	5.49802i	−0.275620	+	0.263610i
$436$	29.8641	+	6.34781i	1.43023	+	0.304005i
$437$	1.54598	−	0.328608i	0.0739542	−	0.0157194i
$438$	2.66228	−	0.970453i	0.127209	−	0.0463701i
$439$	−6.97666	+	32.8226i	−0.332978	+	1.56654i	0.419398	+	0.907803i	$0.362241\pi$
$439$	−6.97666	+	32.8226i	−0.332978	+	1.56654i	−0.752376	+	0.658734i	$0.771092\pi$
$440$	−0.0237442	−	0.0330479i	−0.00113196	−	0.00157550i
$441$	12.4049	+	16.9445i	0.590711	+	0.806883i
$442$	40.9424	+	29.7464i	1.94743	+	1.41489i
$443$	−3.20379	−	1.84971i	−0.152217	−	0.0878823i	0.421957	−	0.906616i	$-0.361343\pi$
$443$	−3.20379	−	1.84971i	−0.152217	−	0.0878823i	−0.574174	+	0.818733i	$0.694677\pi$
$444$	−0.170815	−	4.82438i	−0.00810651	−	0.228955i
$445$	1.26529	+	6.11181i	0.0599805	+	0.289728i
$446$	−1.50571	−	14.3259i	−0.0712975	−	0.678351i
$447$	9.26773	+	9.58770i	0.438349	+	0.453483i
$448$	2.12645	+	17.1308i	0.100465	+	0.809354i
$449$		−	26.6623i		−	1.25827i	−0.777295	−	0.629136i	$-0.783409\pi$
$449$		−	26.6623i		−	1.25827i	0.777295	−	0.629136i	$-0.216591\pi$
$450$	−1.76400	−	29.2746i	−0.0831558	−	1.38002i
$451$	0.470727	−	0.271775i	0.0221657	−	0.0127974i
$452$	−11.6061	−	10.4502i	−0.545906	−	0.491536i
$453$	−5.53302	−	22.1459i	−0.259964	−	1.04051i
$454$	4.77909	+	6.57785i	0.224294	+	0.308714i
$455$	3.29047	−	35.9636i	0.154260	−	1.68600i
$456$	0.126830	+	0.0673580i	0.00593938	+	0.00315433i
$457$	−10.9935	+	19.0413i	−0.514255	+	0.890716i	0.485608	+	0.874177i	$0.338598\pi$
$457$	−10.9935	+	19.0413i	−0.514255	+	0.890716i	−0.999863	+	0.0165393i	$0.994735\pi$
$458$	2.71782	−	25.8583i	0.126995	−	1.20828i
$459$	17.8061	−	12.9766i	0.831119	−	0.605694i
$460$	−26.3106	−	5.73838i	−1.22674	−	0.267553i
$461$	8.64062	+	26.5931i	0.402434	+	1.23856i	0.923019	+	0.384754i	$0.125714\pi$
$461$	8.64062	+	26.5931i	0.402434	+	1.23856i	−0.520586	+	0.853809i	$0.674286\pi$
$462$	0.464513	−	0.0744341i	0.0216111	−	0.00346299i
$463$	1.51474	−	4.66190i	0.0703961	−	0.216657i	−0.909669	−	0.415334i	$-0.863665\pi$
$463$	1.51474	−	4.66190i	0.0703961	−	0.216657i	0.980065	+	0.198677i	$0.0636646\pi$
$464$	−1.84604	+	8.68495i	−0.0857004	+	0.403189i
$465$	0.361964	+	12.0249i	0.0167857	+	0.557640i
$466$	−38.0485	+	8.08745i	−1.76256	+	0.374644i
$467$	28.4808	−	12.6805i	1.31793	−	0.586782i	0.377265	−	0.926106i	$-0.376865\pi$
$467$	28.4808	−	12.6805i	1.31793	−	0.586782i	0.940670	+	0.339323i	$0.110198\pi$
$468$	−9.23181	−	32.0776i	−0.426741	−	1.48279i
$469$	10.0629	−	33.0710i	0.464662	−	1.52708i
$470$	−13.0796	−	40.9928i	−0.603316	−	1.89085i
$471$	−29.9413	+	7.48064i	−1.37962	+	0.344690i
$472$	−0.411590	+	0.924446i	−0.0189450	+	0.0425511i
$473$	0.338948	+	0.305190i	0.0155848	+	0.0140326i
$474$	7.17759	+	2.89589i	0.329678	+	0.133012i
$475$	1.13354	+	0.381640i	0.0520105	+	0.0175108i
$476$	−13.3949	+	15.4504i	−0.613956	+	0.708169i
$477$	7.05902	−	4.77134i	0.323210	−	0.218465i
$478$	−5.60182	−	53.2978i	−0.256221	−	2.43778i
$479$	7.68063	+	3.41964i	0.350937	+	0.156247i	0.574632	−	0.818412i	$-0.305145\pi$
$479$	7.68063	+	3.41964i	0.350937	+	0.156247i	−0.223695	+	0.974659i	$0.571812\pi$
$480$	−18.3873	−	23.7697i	−0.839264	−	1.08493i
$481$	3.79651	+	8.52709i	0.173106	+	0.388802i
$482$	13.5175			0.615704
$483$	−19.0118	+	23.5647i	−0.865067	+	1.07223i
$484$	−6.19423	+	19.0639i	−0.281556	+	0.866540i
$485$	9.98391	−	17.0829i	0.453346	−	0.775695i
$486$	−30.4622	−	0.989777i	−1.38179	−	0.0448972i
$487$	−2.52853	+	0.537455i	−0.114579	+	0.0243544i	−0.264844	−	0.964291i	$-0.585320\pi$
$487$	−2.52853	+	0.537455i	−0.114579	+	0.0243544i	0.150265	+	0.988646i	$0.451987\pi$
$488$	1.98440	+	2.20390i	0.0898296	+	0.0997659i
$489$	−6.88587	−	14.1007i	−0.311390	−	0.637658i
$490$	30.1243	+	5.39403i	1.36088	+	0.243677i
$491$	3.65695	+	1.18822i	0.165036	+	0.0536234i	0.390370	−	0.920658i	$-0.372347\pi$
$491$	3.65695	+	1.18822i	0.165036	+	0.0536234i	−0.225334	+	0.974282i	$0.572347\pi$
$492$	27.7078	−	17.3325i	1.24917	−	0.781409i
$493$	−7.54200	+	4.35437i	−0.339674	+	0.196111i
$494$	2.83938	+	0.298431i	0.127750	+	0.0134271i
$495$	−0.270793	+	0.225232i	−0.0121713	+	0.0101234i
$496$	7.89310	+	10.8639i	0.354411	+	0.487805i
$497$	5.05966	+	10.8130i	0.226957	+	0.485031i
$498$	29.7228	−	14.5146i	1.33191	−	0.650417i
$499$	−16.2162	+	28.0873i	−0.725937	+	1.25736i	0.232651	+	0.972560i	$0.425260\pi$
$499$	−16.2162	+	28.0873i	−0.725937	+	1.25736i	−0.958587	+	0.284799i	$0.908073\pi$
$500$	−14.9256	−	13.8751i	−0.667494	−	0.620511i
$501$	−9.21384	−	11.7814i	−0.411644	−	0.526354i
$502$	−4.57710	+	21.5335i	−0.204286	+	0.961089i
$503$	−13.0717	+	9.49713i	−0.582837	+	0.423456i	−0.839746	−	0.542980i	$-0.817296\pi$
$503$	−13.0717	+	9.49713i	−0.582837	+	0.423456i	0.256909	+	0.966436i	$0.417296\pi$
$504$	−2.69932	+	0.531128i	−0.120237	+	0.0236583i
$505$	8.40642	−	11.4424i	0.374081	−	0.509181i
$506$	0.275881	+	0.619639i	0.0122644	+	0.0275463i
$507$	25.8891	+	33.1034i	1.14978	+	1.47018i
$508$	−1.13522	+	10.8009i	−0.0503672	+	0.479212i
$509$	1.38978	+	1.54351i	0.0616008	+	0.0684147i	0.773158	−	0.634214i	$-0.218676\pi$
$509$	1.38978	+	1.54351i	0.0616008	+	0.0684147i	−0.711557	+	0.702629i	$0.752010\pi$
$510$	5.72778	−	31.5937i	0.253631	−	1.39899i
$511$	−1.33466	−	1.76628i	−0.0590421	−	0.0781358i
$512$	−29.0524	−	9.43969i	−1.28395	−	0.417179i
$513$	0.503914	−	1.13626i	0.0222484	−	0.0501670i
$514$	−14.3235	−	12.8969i	−0.631783	−	0.568860i
$515$	−6.97575	−	12.2316i	−0.307388	−	0.538988i
$516$	21.0167	+	17.6177i	0.925209	+	0.775578i
$517$	−0.303748	+	0.418074i	−0.0133588	+	0.0183869i
$518$	−7.47547	+	2.58510i	−0.328453	+	0.113583i
$519$	−16.7069	−	8.87283i	−0.733353	−	0.389474i
$520$	4.08460	+	2.38720i	0.179122	+	0.104685i
$521$	−3.35561	−	1.49402i	−0.147012	−	0.0654540i	0.331912	−	0.943310i	$-0.392306\pi$
$521$	−3.35561	−	1.49402i	−0.147012	−	0.0654540i	−0.478924	+	0.877856i	$0.658973\pi$
$522$	11.9312	+	1.66502i	0.522216	+	0.0728759i
$523$	−1.18458	+	5.57301i	−0.0517980	+	0.243691i	−0.996428	−	0.0844470i	$-0.973088\pi$
$523$	−1.18458	+	5.57301i	−0.0517980	+	0.243691i	0.944630	+	0.328138i	$0.106421\pi$
$524$	−32.2016			−1.40673
$525$	−21.4624	+	8.02293i	−0.936694	+	0.350149i
$526$	−7.76034			−0.338367
$527$	−2.73842	+	12.8833i	−0.119288	+	0.561204i
$528$	−0.108185	+	0.377978i	−0.00470815	+	0.0164494i
$529$	−18.8689	−	8.40097i	−0.820387	−	0.365260i
$530$	2.64590	−	12.1315i	0.114931	−	0.526958i
$531$	8.23341	+	2.98767i	0.357299	+	0.129654i
$532$	−0.218616	+	1.13269i	−0.00947819	+	0.0491085i
$533$	−37.1441	+	51.1245i	−1.60889	+	2.21445i
$534$	6.07241	−	7.24395i	0.262779	−	0.313476i
$535$	−3.93314	+	35.6051i	−0.170044	+	1.53934i
$536$	3.36536	+	3.03019i	0.145362	+	0.130884i
$537$	4.81929	−	5.74907i	0.207968	−	0.248091i
$538$	27.9984	+	9.09724i	1.20710	+	0.392210i
$539$	−0.161994	−	0.329915i	−0.00697759	−	0.0142104i
$540$	−15.7928	+	14.1104i	−0.679614	+	0.607213i
$541$	18.1195	+	20.1237i	0.779017	+	0.865186i	0.993766	−	0.111483i	$-0.0355600\pi$
$541$	18.1195	+	20.1237i	0.779017	+	0.865186i	−0.214749	+	0.976669i	$0.568893\pi$
$542$	5.15243	−	49.0221i	0.221316	−	2.10568i
$543$	−31.3433	+	24.5126i	−1.34507	+	1.05193i
$544$	−13.3821	−	30.0567i	−0.573753	−	1.28867i
$545$	21.8545	+	30.4179i	0.936146	+	1.30296i
$546$	−45.8158	+	29.8712i	−1.96073	+	1.27837i
$547$	−18.5595	+	13.4843i	−0.793548	+	0.576546i	−0.909014	−	0.416765i	$-0.863164\pi$
$547$	−18.5595	+	13.4843i	−0.793548	+	0.576546i	0.115466	+	0.993311i	$0.463164\pi$
$548$	−5.00977	+	23.5691i	−0.214007	+	1.00682i
$549$	17.8132	−	18.4820i	0.760250	−	0.788792i
$550$	−0.0590611	+	0.509882i	−0.00251837	+	0.0217414i
$551$	−0.245652	+	0.425481i	−0.0104651	+	0.0181261i
$552$	−1.74053	−	3.56422i	−0.0740818	−	0.151703i
$553$	0.519033	−	6.02454i	0.0220715	−	0.256190i
$554$	13.9920	+	19.2583i	0.594462	+	0.818207i
$555$	3.82846	−	4.51823i	0.162509	−	0.191788i
$556$	−2.03276	−	0.213652i	−0.0862084	−	0.00906086i
$557$	21.9041	−	12.6464i	0.928108	−	0.535843i	0.0418951	−	0.999122i	$-0.486660\pi$
$557$	21.9041	−	12.6464i	0.928108	−	0.535843i	0.886213	+	0.463279i	$0.153327\pi$
$558$	13.9457	−	11.7249i	0.590367	−	0.496354i
$559$	−50.4310	−	16.3860i	−2.13300	−	0.693055i
$560$	−14.7529	+	20.8921i	−0.623424	+	0.882853i
$561$	−0.346509	+	0.169212i	−0.0146296	+	0.00714414i
$562$	0.198511	+	0.220469i	0.00837368	+	0.00929992i
$563$	33.2929	−	7.07662i	1.40313	−	0.298244i	0.556684	−	0.830724i	$-0.312073\pi$
$563$	33.2929	−	7.07662i	1.40313	−	0.298244i	0.846442	+	0.532480i	$0.178740\pi$
$564$	−17.3628	+	25.7683i	−0.731105	+	1.08504i
$565$	−1.90167	−	19.0646i	−0.0800040	−	0.802054i
$566$	−5.11096	+	15.7299i	−0.214830	+	0.661178i
$567$	6.23803	+	22.9801i	0.261973	+	0.965075i
$568$	−1.56395			−0.0656220
$569$	9.19001	+	20.6411i	0.385265	+	0.865320i	0.997226	+	0.0744321i	$0.0237144\pi$
$569$	9.19001	+	20.6411i	0.385265	+	0.865320i	−0.611961	+	0.790888i	$0.709619\pi$
$570$	−0.611336	−	1.70513i	−0.0256061	−	0.0714200i
$571$	9.67786	+	4.30886i	0.405006	+	0.180320i	0.599121	−	0.800659i	$-0.295517\pi$
$571$	9.67786	+	4.30886i	0.405006	+	0.180320i	−0.194115	+	0.980979i	$0.562184\pi$
$572$	0.0610663	+	0.581007i	0.00255331	+	0.0242931i
$573$	20.1718	−	9.85056i	0.842689	−	0.411513i
$574$	−40.4620	−	35.0790i	−1.68885	−	1.46417i
$575$	−19.1336	−	26.9308i	−0.797926	−	1.12309i
$576$	−4.71685	+	18.9967i	−0.196535	+	0.791531i
$577$	29.1751	+	26.2694i	1.21458	+	1.09361i	0.992957	+	0.118475i	$0.0378005\pi$
$577$	29.1751	+	26.2694i	1.21458	+	1.09361i	0.221618	+	0.975134i	$0.428866\pi$
$578$	0.779035	−	1.74974i	0.0324036	−	0.0727796i
$579$	3.56373	+	14.2639i	0.148104	+	0.592786i
$580$	6.79818	−	4.88433i	0.282279	−	0.202811i
$581$	−17.6496	−	18.8766i	−0.732228	−	0.783134i
$582$	−29.6725	+	4.18487i	−1.22996	+	0.173469i
$583$	−0.136229	+	0.0606532i	−0.00564204	+	0.00251200i
$584$	0.283683	−	0.0602987i	0.0117389	−	0.00249518i
$585$	18.1101	−	36.7268i	0.748761	−	1.51847i
$586$	−9.63552	+	45.3316i	−0.398040	+	1.87263i
$587$	2.79701	−	8.60831i	0.115445	−	0.355303i	−0.876595	−	0.481230i	$-0.840190\pi$
$587$	2.79701	−	8.60831i	0.115445	−	0.355303i	0.992040	+	0.125927i	$0.0401904\pi$
$588$	−10.4362	−	19.4800i	−0.430381	−	0.803340i
$589$	0.229614	+	0.706679i	0.00946107	+	0.0291182i
$590$	11.6880	−	5.12977i	0.481186	−	0.211189i
$591$	5.77109	+	15.8320i	0.237391	+	0.651243i
$592$	0.690977	−	6.57421i	0.0283990	−	0.270198i
$593$	−5.99911	+	10.3908i	−0.246354	+	0.426697i	−0.962511	−	0.271241i	$-0.912566\pi$
$593$	−5.99911	+	10.3908i	−0.246354	+	0.426697i	0.716158	+	0.697939i	$0.245899\pi$
$594$	0.521932	+	0.110146i	0.0214151	+	0.00451935i
$595$	−24.9106	+	2.95819i	−1.02123	+	0.121274i
$596$	−8.24828	−	11.3528i	−0.337863	−	0.465028i
$597$	−31.0828	+	7.76584i	−1.27213	+	0.317835i
$598$	−58.6022	−	52.7657i	−2.39642	−	2.15775i
$599$	−36.1023	+	20.8437i	−1.47510	+	0.851649i	−0.999606	−	0.0280703i	$-0.991064\pi$
$599$	−36.1023	+	20.8437i	−1.47510	+	0.851649i	−0.475493	+	0.879719i	$0.657730\pi$
$600$	0.239659	−	2.99208i	0.00978406	−	0.122151i
$601$			29.5606i			1.20580i	0.797817	+	0.602900i	$0.205988\pi$
$601$			29.5606i			1.20580i	−0.797817	+	0.602900i	$0.794012\pi$
$602$	17.5028	−	41.3864i	0.713360	−	1.68678i
$603$	24.1018	−	30.9107i	0.981503	−	1.25878i
$604$	2.51095	+	23.8901i	0.102169	+	0.972074i
$605$	−21.3609	+	12.1823i	−0.868445	+	0.495279i
$606$	−21.4898	+	0.760880i	−0.872963	+	0.0309086i
$607$	32.2398	+	18.6137i	1.30858	+	0.755506i	0.981858	−	0.189616i	$-0.0607243\pi$
$607$	32.2398	+	18.6137i	1.30858	+	0.755506i	0.326717	+	0.945122i	$0.394058\pi$
$608$	−1.50163	−	1.09100i	−0.0608991	−	0.0442458i
$609$	−1.48917	−	9.29329i	−0.0603441	−	0.376583i
$610$	0.198244	−	37.4069i	0.00802668	−	1.51456i
$611$	12.4913	−	58.7667i	0.505342	−	2.37745i
$612$	−20.4618	+	10.9052i	−0.827118	+	0.440817i
$613$	−13.6495	+	2.90129i	−0.551299	+	0.117182i	−0.475135	−	0.879913i	$-0.657601\pi$
$613$	−13.6495	+	2.90129i	−0.551299	+	0.117182i	−0.0761641	+	0.997095i	$0.524267\pi$
$614$	55.0033	+	11.6913i	2.21975	+	0.471823i
$615$	39.4507	+	7.15224i	1.59081	+	0.288406i
$616$	0.0481406		0.000904130i	0.00193964		3.64284e-5i
$617$	−9.32928	+	12.8407i	−0.375583	+	0.516945i	−0.954408	−	0.298507i	$-0.903511\pi$
$617$	−9.32928	+	12.8407i	−0.375583	+	0.516945i	0.578825	+	0.815452i	$0.303511\pi$
$618$	−7.97898	+	19.7763i	−0.320962	+	0.795519i
$619$	23.2362	+	2.44223i	0.933943	+	0.0981614i	0.559261	−	0.828992i	$-0.311085\pi$
$619$	23.2362	+	2.44223i	0.933943	+	0.0981614i	0.374682	+	0.927153i	$0.377752\pi$
$620$	1.39005	−	12.5836i	0.0558258	−	0.505369i
$621$	−29.7072	+	17.2092i	−1.19211	+	0.690580i
$622$	−34.0342	−	46.8441i	−1.36465	−	1.87828i
$623$	−6.80169	−	2.87651i	−0.272504	−	0.115245i
$624$	−6.38336	−	45.2606i	−0.255539	−	1.81187i
$625$	−2.08561	−	24.9129i	−0.0834242	−	0.996514i
$626$	14.3165	+	24.7969i	0.572202	+	0.991084i
$627$	−0.0121563	+	0.0180413i	−0.000485475	+	0.000720500i
$628$	32.2994	−	3.39480i	1.28889	−	0.135467i
$629$	5.24541	−	3.81101i	0.209148	−	0.151955i
$630$	29.6907	+	17.9616i	1.18291	+	0.715607i
$631$	−5.39736	−	3.92141i	−0.214865	−	0.156109i	0.475147	−	0.879906i	$-0.342395\pi$
$631$	−5.39736	−	3.92141i	−0.214865	−	0.156109i	−0.690012	+	0.723798i	$0.742395\pi$
$632$	0.686030	+	0.396080i	0.0272888	+	0.0157552i
$633$	0.704820	+	19.9065i	0.0280141	+	0.791212i
$634$	47.4049	−	10.0762i	1.88269	−	0.400178i
$635$	−9.94818	+	8.86237i	−0.394781	+	0.351692i
$636$	−8.05699	+	3.93450i	−0.319480	+	0.156013i
$637$	32.8061	+	27.3797i	1.29982	+	1.08482i
$638$	−0.200523	−	0.0651540i	−0.00793880	−	0.00257947i
$639$	0.957377	+	13.5028i	0.0378732	+	0.534163i
$640$	−3.05954	−	5.36474i	−0.120939	−	0.212060i
$641$	0.474812	+	2.23381i	0.0187539	+	0.0882303i	0.986529	−	0.163585i	$-0.0523058\pi$
$641$	0.474812	+	2.23381i	0.0187539	+	0.0882303i	−0.967775	+	0.251815i	$0.918972\pi$
$642$	45.9936	−	28.7710i	1.81522	−	1.13550i
$643$			17.2363i			0.679734i	0.940474	+	0.339867i	$0.110382\pi$
$643$			17.2363i			0.679734i	−0.940474	+	0.339867i	$0.889618\pi$
$644$	23.2742	−	21.7613i	0.917133	−	0.857516i
$645$	4.52178	+	33.3380i	0.178045	+	1.31268i
$646$	−0.207298	−	1.97231i	−0.00815604	−	0.0775995i
$647$	−10.9523	−	4.87626i	−0.430578	−	0.191706i	0.179992	−	0.983668i	$-0.442393\pi$
$647$	−10.9523	−	4.87626i	−0.430578	−	0.191706i	−0.610570	+	0.791962i	$0.709060\pi$
$648$	−3.07308	−	0.535719i	−0.120722	−	0.0210450i
$649$	−0.132757	−	0.0766472i	−0.00521116	−	0.00300867i
$650$	−17.8381	−	56.9470i	−0.699670	−	2.23364i
$651$	−11.9520	−	7.73102i	−0.468438	−	0.303002i
$652$	5.10303	+	15.7055i	0.199850	+	0.615075i
$653$	−8.58103	+	0.901902i	−0.335802	+	0.0352942i	−0.270929	−	0.962599i	$-0.587331\pi$
$653$	−8.58103	+	0.901902i	−0.335802	+	0.0352942i	−0.0648727	+	0.997894i	$0.520664\pi$
$654$	15.6089	−	54.5347i	0.610358	−	2.13248i
$655$	−29.2167	−	26.5886i	−1.14159	−	1.03890i
$656$	40.8846	−	18.2030i	1.59628	−	0.710707i
$657$	−0.694262	−	2.41234i	−0.0270858	−	0.0941145i
$658$	48.7075	+	14.8208i	1.89881	+	0.577775i
$659$	12.5195	+	4.06784i	0.487691	+	0.158460i	0.542533	−	0.840035i	$-0.317465\pi$
$659$	12.5195	+	4.06784i	0.487691	+	0.158460i	−0.0548418	+	0.998495i	$0.517465\pi$
$660$	0.315278	−	0.194903i	0.0122722	−	0.00758661i
$661$	−13.1180	−	11.8115i	−0.510230	−	0.459413i	0.373352	−	0.927690i	$-0.378208\pi$
$661$	−13.1180	−	11.8115i	−0.510230	−	0.459413i	−0.883582	+	0.468277i	$0.844875\pi$
$662$	−7.14005	−	33.5913i	−0.277506	−	1.30556i
$663$	28.8009	−	34.3574i	1.11853	−	1.33433i
$664$	3.21976	−	1.04616i	0.124951	−	0.0405990i
$665$	−1.13361	+	0.847191i	−0.0439593	+	0.0328527i
$666$	−8.96374	−	0.304312i	−0.347338	−	0.0117919i
$667$	12.3968	−	5.51942i	0.480007	−	0.213713i
$668$	7.86973	+	13.6308i	0.304489	+	0.527391i
$669$	−12.7529	+	0.451537i	−0.493056	+	0.0174574i
$670$	−5.66966	−	56.8393i	−0.219038	−	2.19589i
$671$	−0.363456	+	0.264066i	−0.0140310	+	0.0101942i
$672$	35.5053	−	1.92523i	1.36965	−	0.0742672i
$673$	5.05017	+	15.5428i	0.194670	+	0.599132i	0.999980	+	0.00627874i	$0.00199860\pi$
$673$	5.05017	+	15.5428i	0.194670	+	0.599132i	−0.805310	+	0.592853i	$0.798001\pi$
$674$	56.6682	+	32.7174i	2.18278	+	1.26023i
$675$	−25.9797	−	0.237556i	−0.999958	−	0.00914352i
$676$	−22.1124	−	38.2998i	−0.850478	−	1.47307i
$677$	39.8796	+	8.47667i	1.53270	+	0.325785i	0.895552	−	0.444958i	$-0.146781\pi$
$677$	39.8796	+	8.47667i	1.53270	+	0.325785i	0.637146	+	0.770743i	$0.280115\pi$
$678$	−20.8627	+	20.1664i	−0.801227	+	0.774487i
$679$	9.92231	+	21.2050i	0.380783	+	0.813775i
$680$	1.03207	−	3.12003i	0.0395781	−	0.119648i
$681$	6.10645	−	3.81986i	0.234000	−	0.146377i
$682$	−0.276157	+	0.159439i	−0.0105746	+	0.00610524i
$683$	−21.6481	−	2.27531i	−0.828341	−	0.0870622i	−0.319138	−	0.947708i	$-0.603393\pi$
$683$	−21.6481	−	2.27531i	−0.828341	−	0.0870622i	−0.509203	+	0.860646i	$0.670060\pi$
$684$	−0.692088	+	1.10997i	−0.0264626	+	0.0424407i
$685$	−24.0062	+	17.2479i	−0.917228	+	0.659007i
$686$	−25.5026	+	25.7063i	−0.973694	+	0.981469i
$687$	−22.6855	−	3.98872i	−0.865507	−	0.152179i
$688$	25.1281	+	27.9076i	0.958002	+	1.06397i
$689$	11.6007	−	12.8839i	0.441951	−	0.490836i
$690$	−14.0220	+	48.0268i	−0.533810	+	1.82835i
$691$	5.07128	−	4.56620i	0.192920	−	0.173706i	−0.567010	−	0.823711i	$-0.691900\pi$
$691$	5.07128	−	4.56620i	0.192920	−	0.173706i	0.759930	+	0.650005i	$0.225233\pi$
$692$	16.1053	+	11.7012i	0.612230	+	0.444811i
$693$	−0.0372754	−	0.415081i	−0.00141597	−	0.0157676i
$694$	−21.0504	−	15.2940i	−0.799061	−	0.580552i
$695$	−1.66793	−	1.87228i	−0.0632681	−	0.0710196i
$696$	1.18539	+	0.339282i	0.0449320	+	0.0128604i
$697$	40.1007	+	17.8540i	1.51892	+	0.676268i
$698$	−37.9576	−	8.06814i	−1.43672	−	0.305384i
$699$	4.81237	+	34.1217i	0.182021	+	1.29060i
$700$	23.5437	−	5.20600i	0.889868	−	0.196768i
$701$			47.1635i			1.78134i	0.454651	+	0.890670i	$0.349764\pi$
$701$			47.1635i			1.78134i	−0.454651	+	0.890670i	$0.650236\pi$
$702$	−60.6425	+	12.9822i	−2.28880	+	0.489983i
$703$	0.148775	−	0.334153i	0.00561114	−	0.0126028i
$704$	0.139338	−	0.312958i	0.00525149	−	0.0117950i
$705$	−37.0300	+	9.04348i	−1.39463	+	0.340597i
$706$	0.0332447	−	0.0457573i	0.00125118	−	0.00172210i
$707$	5.49055	+	15.8773i	0.206494	+	0.597128i
$708$	−8.14045	−	4.32329i	−0.305937	−	0.162479i
$709$	−28.6130	−	31.7780i	−1.07458	−	1.19345i	−0.980220	−	0.197909i	$-0.936585\pi$
$709$	−28.6130	−	31.7780i	−1.07458	−	1.19345i	−0.0943640	−	0.995538i	$-0.530082\pi$
$710$	14.5899	+	13.2775i	0.547551	+	0.498297i
$711$	2.99971	−	6.16549i	0.112498	−	0.231224i
$712$	0.718957	−	0.647352i	0.0269441	−	0.0242605i
$713$	6.34204	−	19.5188i	0.237511	−	0.730984i
$714$	26.9126	+	26.8154i	1.00718	+	1.00354i
$715$	−0.424326	+	0.577573i	−0.0158689	+	0.0216000i
$716$	−5.86680	+	5.28249i	−0.219253	+	0.197416i
$717$	−47.4457	+	1.67989i	−1.77189	+	0.0627366i
$718$	−11.4871	−	19.8963i	−0.428695	−	0.742522i
$719$	35.9611	−	16.0109i	1.34112	−	0.597107i	0.394337	−	0.918966i	$-0.370974\pi$
$719$	35.9611	−	16.0109i	1.34112	−	0.597107i	0.946788	+	0.321859i	$0.104308\pi$
$720$	−24.1124	+	16.1126i	−0.898616	+	0.600480i
$721$	16.5993	+	1.43008i	0.618190	+	0.0532590i
$722$	21.7695	+	29.9632i	0.810178	+	1.11511i
$723$	0.829526	−	11.9461i	0.0308504	−	0.444279i
$724$	36.2634	−	20.9367i	1.34772	−	0.778106i
$725$	10.2010	+	1.18161i	0.378854	+	0.0438838i
$726$	34.5368	+	13.9343i	1.28178	+	0.517150i
$727$	−29.7534	+	9.66748i	−1.10349	+	0.358547i	−0.803446	−	0.595377i	$-0.797003\pi$
$727$	−29.7534	+	9.66748i	−1.10349	+	0.358547i	−0.300048	+	0.953924i	$0.597003\pi$
$728$	−5.07022	+	2.37247i	−0.187915	+	0.0879296i
$729$	−2.74409	+	26.8602i	−0.101633	+	0.994822i
$730$	−3.15837	−	1.84587i	−0.116896	−	0.0683187i
$731$	−3.85014	+	36.6317i	−0.142403	+	1.35487i
$732$	−21.2783	+	16.6410i	−0.786467	+	0.615070i
$733$	−7.31322	−	16.4258i	−0.270120	−	0.606700i	0.726650	−	0.687008i	$-0.241076\pi$
$733$	−7.31322	−	16.4258i	−0.270120	−	0.606700i	−0.996770	+	0.0803082i	$0.974410\pi$
$734$	0.512109	−	1.57611i	0.0189023	−	0.0581753i
$735$	6.61561	−	26.2913i	0.244020	−	0.969770i
$736$	15.8423	+	48.7576i	0.583955	+	1.79723i
$737$	−0.509809	+	0.459034i	−0.0187790	+	0.0169087i
$738$	−28.5589	−	53.5859i	−1.05127	−	1.97252i
$739$	−8.80093	+	9.77442i	−0.323747	+	0.359558i	−0.882945	−	0.469477i	$-0.844443\pi$
$739$	−8.80093	+	9.77442i	−0.323747	+	0.359558i	0.559198	+	0.829034i	$0.311109\pi$
$740$	−4.65343	+	4.14552i	−0.171063	+	0.152392i
$741$	0.437983	−	2.49099i	0.0160897	−	0.0915089i
$742$	10.0339	+	10.7315i	0.368355	+	0.393964i
$743$		−	15.0724i		−	0.552954i	−0.961020	−	0.276477i	$-0.910833\pi$
$743$		−	15.0724i		−	0.552954i	0.961020	−	0.276477i	$-0.0891670\pi$
$744$	1.58093	−	0.988942i	0.0579597	−	0.0362564i
$745$	1.89017	−	17.1110i	0.0692505	−	0.626897i
$746$	−9.90269	+	22.2418i	−0.362563	+	0.814331i
$747$	−11.0033	−	27.1583i	−0.402590	−	0.993669i
$748$	0.385944	−	0.125401i	0.0141115	−	0.00458511i
$749$	−32.0251	−	27.7645i	−1.17017	−	1.01449i
$750$	−27.6377	+	25.8782i	−1.00919	+	0.944937i
$751$	16.2897	−	28.2146i	0.594419	−	1.02956i	−0.399209	−	0.916860i	$-0.630715\pi$
$751$	16.2897	−	28.2146i	0.594419	−	1.02956i	0.993629	−	0.112704i	$-0.0359513\pi$
$752$	−28.4706	+	31.6198i	−1.03822	+	1.15306i
$753$	18.7494	+	5.36646i	0.683266	+	0.195565i
$754$	24.3784	−	2.56227i	0.887809	−	0.0933125i
$755$	−17.4476	+	23.7489i	−0.634984	+	0.864310i
$756$	−3.12300	−	24.8630i	−0.113582	−	0.904257i
$757$	49.3650			1.79420			0.897101	−	0.441826i	$-0.145669\pi$
$757$	49.3650			1.79420			0.897101	+	0.441826i	$0.145669\pi$
$758$	18.3227	+	41.1534i	0.665510	+	1.49476i
$759$	0.564536	−	0.205784i	0.0204914	−	0.00746950i
$760$	−0.0375845	−	0.181547i	−0.00136333	−	0.00658539i
$761$	−17.7316	−	3.76897i	−0.642770	−	0.136625i	−0.125016	−	0.992155i	$-0.539898\pi$
$761$	−17.7316	−	3.76897i	−0.642770	−	0.136625i	−0.517754	+	0.855530i	$0.673232\pi$
$762$	19.8728	+	3.49417i	0.719916	+	0.126581i
$763$	−44.3094	+	0.832177i	−1.60411	+	0.0301268i
$764$	−22.4675	+	7.30012i	−0.812845	+	0.264109i
$765$	−27.5694	−	7.00074i	−0.996774	−	0.253112i
$766$	−0.806339	−	3.79353i	−0.0291342	−	0.137066i
$767$	17.7245	+	1.86291i	0.639993	+	0.0672660i
$768$	−11.9561	+	29.6338i	−0.431429	+	1.06932i
$769$	13.1153	−	18.0516i	0.472948	−	0.650958i	−0.504182	−	0.863597i	$-0.668206\pi$
$769$	13.1153	−	18.0516i	0.472948	−	0.650958i	0.977131	+	0.212640i	$0.0682060\pi$
$770$	−0.456774	−	0.400265i	−0.0164610	−	0.0144246i
$771$	−12.2767	+	11.8670i	−0.442134	+	0.427378i
$772$	−1.61726	−	15.3872i	−0.0582066	−	0.553799i
$773$	8.51663	−	9.45868i	0.306322	−	0.340205i	−0.570254	−	0.821468i	$-0.693155\pi$
$773$	8.51663	−	9.45868i	0.306322	−	0.340205i	0.876576	+	0.481263i	$0.159822\pi$
$774$	35.3585	−	36.6860i	1.27094	−	1.31865i
$775$	11.6513	−	10.2694i	0.418528	−	0.368888i
$776$	−3.06701			−0.110099
$777$	1.82584	+	6.76509i	0.0655015	+	0.242696i
$778$	−21.1333	+	15.3542i	−0.757664	+	0.550475i
$779$	2.46281	−	0.258852i	0.0882392	−	0.00927432i
$780$	−24.2690	+	35.6092i	−0.868969	+	1.27502i
$781$	0.0247647	−	0.235621i	0.000886152	−	0.00843117i
$782$	−27.3881	+	47.4376i	−0.979396	+	1.69636i
$783$	2.20364	−	10.4420i	0.0787518	−	0.373168i
$784$	−10.4255	−	28.4093i	−0.372340	−	1.01462i
$785$	32.1085	+	23.5892i	1.14600	+	0.841934i
$786$	−4.14442	+	59.6842i	−0.147827	+	2.12886i
$787$	6.32196	+	29.7425i	0.225354	+	1.06021i	0.934725	+	0.355371i	$0.115645\pi$
$787$	6.32196	+	29.7425i	0.225354	+	1.06021i	−0.709372	+	0.704834i	$0.751021\pi$
$788$	−3.68695	−	17.3458i	−0.131342	−	0.617917i
$789$	−0.476228	+	6.85820i	−0.0169542	+	0.244158i
$790$	−3.03729	−	9.51918i	−0.108062	−	0.338677i
$791$	19.8417	+	10.9641i	0.705490	+	0.389838i
$792$	0.0513215	+	0.0186231i	0.00182363	+	0.000661743i
$793$	26.1153	−	45.2331i	0.927383	−	1.60627i
$794$	−2.94535	+	28.0232i	−0.104527	+	0.994505i
$795$	−10.5588	−	3.08279i	−0.374483	−	0.109335i
$796$	33.5308	−	3.52423i	1.18847	−	0.124913i
$797$	22.7448	−	16.5251i	0.805664	−	0.585349i	−0.106906	−	0.994269i	$-0.534095\pi$
$797$	22.7448	−	16.5251i	0.805664	−	0.585349i	0.912570	+	0.408920i	$0.134095\pi$
$798$	2.07126	+	0.550974i	0.0733217	+	0.0195043i
$799$	−41.7329			−1.47640
$800$	−8.46798	+	37.8609i	−0.299388	+	1.33859i
$801$	−6.02920	−	5.81103i	−0.213031	−	0.205323i
$802$	−3.78085	+	4.19906i	−0.133507	+	0.148274i
$803$	0.00459239	+	0.0436937i	0.000162062	+	0.00154192i
$804$	−29.6578	+	28.6681i	−1.04595	+	1.01104i
$805$	39.0849	−	0.526866i	1.37756	−	0.0185696i
$806$	21.7909	−	29.9927i	0.767553	−	1.05645i
$807$	9.75786	−	24.1853i	0.343493	−	0.851364i
$808$	−2.18879	−	0.230051i	−0.0770012	−	0.00809315i
$809$	10.8809	+	51.1906i	0.382552	+	1.79977i	0.574660	+	0.818392i	$0.305134\pi$
$809$	10.8809	+	51.1906i	0.382552	+	1.79977i	−0.192108	+	0.981374i	$0.561532\pi$
$810$	24.1203	+	31.0872i	0.847501	+	1.09229i
$811$	46.3848	−	15.0713i	1.62879	−	0.529226i	0.654797	−	0.755805i	$-0.272754\pi$
$811$	46.3848	−	15.0713i	1.62879	−	0.529226i	0.973993	+	0.226579i	$0.0727542\pi$
$812$	0.185985	+	9.90283i	0.00652680	+	0.347521i
$813$	−43.0071	−	7.56179i	−1.50832	−	0.265204i
$814$	0.153543	+	0.0326365i	0.00538167	+	0.00114391i
$815$	−8.33788	+	18.4632i	−0.292063	+	0.646738i
$816$	−29.8303	+	10.8737i	−1.04427	+	0.380657i
$817$	0.845181	+	1.89831i	0.0295691	+	0.0664134i
$818$	23.4716			0.820664
$819$	23.5871	+	42.3228i	0.824200	+	1.47888i
$820$	−40.0581	−	13.2508i	−1.39889	−	0.462737i
$821$	−37.8733	+	3.98064i	−1.32179	+	0.138925i	−0.739003	−	0.673702i	$-0.764703\pi$
$821$	−37.8733	+	3.98064i	−1.32179	+	0.138925i	−0.582783	+	0.812628i	$0.698036\pi$
$822$	43.0394	+	12.3188i	1.50117	+	0.429666i
$823$	8.41405	−	9.34475i	0.293295	−	0.325738i	−0.578430	−	0.815732i	$-0.696334\pi$
$823$	8.41405	−	9.34475i	0.293295	−	0.325738i	0.871726	+	0.489994i	$0.163001\pi$
$824$	−1.09131	+	1.89021i	−0.0380176	+	0.0658484i
$825$	0.446984	+	0.0834851i	0.0155620	+	0.00290658i
$826$	−2.86208	+	14.8290i	−0.0995845	+	0.515968i
$827$	9.18671	−	2.98494i	0.319453	−	0.103797i	−0.144901	−	0.989446i	$-0.546286\pi$
$827$	9.18671	−	2.98494i	0.319453	−	0.103797i	0.464354	+	0.885649i	$0.346286\pi$
$828$	33.4852	−	13.5667i	1.16369	−	0.471476i
$829$	7.37743	−	16.5700i	0.256229	−	0.575499i	−0.738930	−	0.673782i	$-0.764668\pi$
$829$	7.37743	−	16.5700i	0.256229	−	0.575499i	0.995158	+	0.0982833i	$0.0313351\pi$
$830$	−38.9184	−	17.5753i	−1.35088	−	0.610048i
$831$	17.8782	−	11.1836i	0.620187	−	0.387955i
$832$			39.8280i			1.38079i
$833$	13.8652	−	26.2442i	0.480400	−	0.909308i
$834$	−0.657615	+	3.74013i	−0.0227713	+	0.129510i
$835$	−4.11455	+	18.8652i	−0.142390	+	0.652859i
$836$	0.0153188	−	0.0170132i	0.000529810	−	0.000588414i
$837$	−9.50607	−	13.0440i	−0.328578	−	0.450867i
$838$	−42.9406	+	38.6639i	−1.48336	+	1.33562i
$839$	−4.44164	−	13.6700i	−0.153343	−	0.471940i	0.844647	−	0.535324i	$-0.179811\pi$
$839$	−4.44164	−	13.6700i	−0.153343	−	0.471940i	−0.997989	+	0.0633843i	$0.979811\pi$
$840$	2.75231	+	2.24472i	0.0949638	+	0.0774503i
$841$	7.65799	−	23.5689i	0.264068	−	0.812719i
$842$	−1.19593	−	2.68610i	−0.0412145	−	0.0925692i
$843$	0.207021	−	0.161905i	0.00713020	−	0.00557629i
$844$	2.19110	−	20.8469i	0.0754207	−	0.717580i
$845$	11.5611	−	53.0077i	0.397713	−	1.82352i
$846$	45.5257	+	35.4975i	1.56521	+	1.22043i
$847$	2.49746	−	28.9886i	0.0858137	−	0.996060i
$848$	−11.6772	+	3.79414i	−0.400995	+	0.130291i
$849$	13.5877	+	5.48211i	0.466328	+	0.188146i
$850$	−36.1163	+	20.3444i	−1.23878	+	0.697807i
$851$	−8.74938	+	5.05146i	−0.299925	+	0.173162i
$852$	0.986812	−	14.2112i	0.0338076	−	0.486866i
$853$	32.0108	+	44.0590i	1.09603	+	1.50855i	0.840547	+	0.541739i	$0.182234\pi$
$853$	32.0108	+	44.0590i	1.09603	+	1.50855i	0.255481	+	0.966814i	$0.417766\pi$
$854$	36.2902	+	25.3390i	1.24183	+	0.867084i
$855$	−1.54442	+	0.435630i	−0.0528182	+	0.0148982i
$856$	5.07252	−	2.25843i	0.173375	−	0.0771915i
$857$	−1.82862	−	3.16727i	−0.0624646	−	0.108192i	0.833102	−	0.553120i	$-0.186563\pi$
$857$	−1.82862	−	3.16727i	−0.0624646	−	0.108192i	−0.895567	+	0.444928i	$0.853229\pi$
$858$	1.08473	−	0.0384065i	0.0370320	−	0.00131118i
$859$	−15.9707	+	14.3801i	−0.544915	+	0.490643i	−0.894995	−	0.446076i	$-0.852821\pi$
$859$	−15.9707	+	14.3801i	−0.544915	+	0.490643i	0.350080	+	0.936720i	$0.386154\pi$
$860$	0.187629	−	35.4040i	0.00639811	−	1.20727i
$861$	−33.4841	+	33.6056i	−1.14114	+	1.14528i
$862$	13.1019	−	40.3235i	0.446252	−	1.37342i
$863$	−26.7669	+	24.1010i	−0.911155	+	0.820408i	−0.984225	−	0.176919i	$-0.943387\pi$
$863$	−26.7669	+	24.1010i	−0.911155	+	0.820408i	0.0730704	+	0.997327i	$0.476720\pi$
$864$	38.3631	+	12.4032i	1.30514	+	0.421967i
$865$	4.95087	+	23.9145i	0.168335	+	0.813117i
$866$	13.2450	+	14.7100i	0.450082	+	0.499867i
$867$	−1.49853	−	0.795848i	−0.0508926	−	0.0270284i
$868$	11.3183	+	9.81255i	0.384168	+	0.333060i
$869$	−0.0705353	+	0.0970835i	−0.00239275	+	0.00329333i
$870$	−8.17793	−	13.2287i	−0.277258	−	0.448495i
$871$	32.4399	−	72.8612i	1.09918	−	2.46881i
$872$	2.36140	−	5.30378i	0.0799670	−	0.179609i
$873$	1.87748	+	26.4799i	0.0635429	+	0.896207i
$874$			3.09019i			0.104527i
$875$	25.6599	+	14.7164i	0.867462	+	0.497504i
$876$	0.368919	+	2.61579i	0.0124646	+	0.0883793i
$877$	28.3822	+	6.03282i	0.958398	+	0.203714i	0.660451	−	0.750869i	$-0.270365\pi$
$877$	28.3822	+	6.03282i	0.958398	+	0.203714i	0.297947	+	0.954583i	$0.403698\pi$
$878$	−59.9357	−	26.6851i	−2.02273	−	0.900578i
$879$	39.4705	+	11.2973i	1.33131	+	0.381047i
$880$	0.464769	−	0.203984i	0.0156674	−	0.00687630i
$881$	−17.2237	−	12.5137i	−0.580280	−	0.421598i	0.258545	−	0.965999i	$-0.416757\pi$
$881$	−17.2237	−	12.5137i	−0.580280	−	0.421598i	−0.838825	+	0.544401i	$0.816757\pi$
$882$	−37.4483	+	16.8358i	−1.26095	+	0.566892i
$883$	−2.03295	−	1.47703i	−0.0684143	−	0.0497059i	0.553052	−	0.833146i	$-0.313463\pi$
$883$	−2.03295	−	1.47703i	−0.0684143	−	0.0497059i	−0.621467	+	0.783441i	$0.713463\pi$
$884$	−35.0610	+	31.5691i	−1.17923	+	1.06178i
$885$	−3.81618	−	10.6440i	−0.128279	−	0.357795i
$886$	4.83984	−	5.37518i	0.162597	−	0.180583i
$887$	17.0309	+	18.9148i	0.571843	+	0.635096i	0.957805	−	0.287418i	$-0.0927970\pi$
$887$	17.0309	+	18.9148i	0.571843	+	0.635096i	−0.385962	+	0.922515i	$0.626130\pi$
$888$	−0.904092	−	0.158964i	−0.0303393	−	0.00533447i
$889$	−1.94192	−	15.6442i	−0.0651297	−	0.524689i
$890$	−12.2029	−	0.0646713i	−0.409042	−	0.00216779i
$891$	0.129371	−	0.454498i	0.00433409	−	0.0152263i
$892$	13.3554	+	1.40371i	0.447171	+	0.0469996i
$893$	−2.03893	+	1.17718i	−0.0682303	+	0.0393928i
$894$	−22.1034	+	13.8267i	−0.739249	+	0.462433i
$895$	−9.68468	−	0.0513256i	−0.323723	−	0.00171563i
$896$	7.28041	+	0.627230i	0.243221	+	0.0209543i
$897$	−50.2279	+	48.5517i	−1.67706	+	1.62109i
$898$	50.9904	+	10.8383i	1.70157	+	0.361680i
$899$	3.18983	+	5.52494i	0.106387	+	0.184267i
$900$	27.0369	+	4.06563i	0.901231	+	0.135521i
$901$	−10.4293	−	6.02135i	−0.347450	−	0.200600i
$902$	0.328404	+	1.01072i	0.0109346	+	0.0336534i
$903$	−35.5011	−	18.0078i	−1.18140	−	0.599263i
$904$	−2.40260	+	1.74559i	−0.0799094	+	0.0580576i
$905$	50.1892	+	10.9464i	1.66835	+	0.363869i
$906$	44.6023	−	1.57921i	1.48181	−	0.0524659i
$907$	−18.9728	−	32.8619i	−0.629983	−	1.09116i	−0.987555	−	0.157277i	$-0.949729\pi$
$907$	−18.9728	−	32.8619i	−0.629983	−	1.09116i	0.357572	−	0.933886i	$-0.383605\pi$
$908$	−6.92454	+	3.08301i	−0.229799	+	0.102313i
$909$	−0.646335	+	19.0383i	−0.0214376	+	0.631461i
$910$	67.4411	+	20.9122i	2.23565	+	0.693234i
$911$	22.5678	−	7.33272i	0.747704	−	0.242944i	0.0897110	−	0.995968i	$-0.471406\pi$
$911$	22.5678	−	7.33272i	0.747704	−	0.242944i	0.657993	+	0.753024i	$0.271406\pi$
$912$	−1.15069	+	1.37269i	−0.0381032	+	0.0454544i
$913$	0.106628	+	0.501645i	0.00352887	+	0.0166020i
$914$	−31.9467	−	28.7650i	−1.05670	−	0.951461i
$915$	−33.0462	−	2.47075i	−1.09247	−	0.0816804i
$916$	23.0530	+	7.49037i	0.761693	+	0.247489i
$917$	45.5298	−	10.5750i	1.50353	−	0.349217i
$918$	17.5788	+	39.3285i	0.580187	+	1.29803i
$919$	−36.3734	+	16.1945i	−1.19985	+	0.534207i	−0.906666	−	0.421849i	$-0.861381\pi$
$919$	−36.3734	+	16.1945i	−1.19985	+	0.534207i	−0.293183	+	0.956056i	$0.594715\pi$
$920$	−2.10755	+	4.66691i	−0.0694839	+	0.153864i
$921$	13.7076	−	47.8918i	0.451681	−	1.57809i
$922$	−54.3705	+	5.71457i	−1.79060	+	0.188199i
$923$	8.51164	+	26.1961i	0.280164	+	0.862257i
$924$	−0.0221599	+	0.438009i	−0.000729006	+	0.0144094i
$925$	−7.64500	−	0.0810341i	−0.251366	−	0.00266439i
$926$	8.29992	+	4.79196i	0.272752	+	0.157474i
$927$	16.9877	+	8.26504i	0.557948	+	0.271459i
$928$	−14.5585	−	6.48186i	−0.477906	−	0.212778i
$929$	−1.60257	−	15.2475i	−0.0525787	−	0.500253i	−0.988844	−	0.148958i	$-0.952408\pi$
$929$	−1.60257	−	15.2475i	−0.0525787	−	0.500253i	0.936265	−	0.351295i	$-0.114259\pi$
$930$	−23.1442	−	4.19593i	−0.758927	−	0.137590i
$931$	−0.0628751	−	1.67331i	−0.00206065	−	0.0548404i
$932$		−	36.2633i		−	1.18785i
$933$	−43.4871	+	27.2031i	−1.42370	+	0.890589i
$934$	12.6732	+	59.6229i	0.414681	+	1.95092i
$935$	0.453712	+	0.204894i	0.0148380	+	0.00670074i
$936$	−6.33145	+	0.448913i	−0.206950	+	0.0146732i
$937$	−29.8277	−	9.69159i	−0.974427	−	0.316611i	−0.221825	−	0.975086i	$-0.571201\pi$
$937$	−29.8277	−	9.69159i	−0.974427	−	0.316611i	−0.752602	+	0.658476i	$0.771201\pi$
$938$	59.1562	+	32.6884i	1.93152	+	1.06731i
$939$	22.7928	−	11.1305i	0.743816	−	0.363230i
$940$	39.9158	−	3.98156i	1.30191	−	0.129864i
$941$	−53.6770	+	11.4094i	−1.74982	+	0.371936i	−0.967879	−	0.251415i	$-0.919104\pi$
$941$	−53.6770	+	11.4094i	−1.74982	+	0.371936i	−0.781942	+	0.623351i	$0.785771\pi$
$942$	−2.13510	−	60.3023i	−0.0695653	−	1.96476i
$943$	−59.2349	−	34.1993i	−1.92895	−	1.11368i
$944$	−10.2111	−	7.41883i	−0.332345	−	0.241462i
$945$	17.6956	−	25.1369i	0.575638	−	0.817705i
$946$	−0.721445	+	0.524160i	−0.0234562	+	0.0170419i
$947$	32.2335	−	3.38787i	1.04745	−	0.110091i	0.434863	−	0.900497i	$-0.356797\pi$
$947$	32.2335	−	3.38787i	1.04745	−	0.110091i	0.612584	+	0.790406i	$0.290130\pi$
$948$	−4.03192	+	5.98383i	−0.130951	+	0.194346i
$949$	−2.55391	−	4.42351i	−0.0829036	−	0.143593i
$950$	−1.19066	+	2.01271i	−0.0386301	+	0.0653009i
$951$	−5.99577	−	42.5124i	−0.194426	−	1.37856i
$952$	2.34421	+	3.10231i	0.0759764	+	0.100546i
$953$	−8.92185	−	12.2799i	−0.289007	−	0.397784i	0.639684	−	0.768638i	$-0.279065\pi$
$953$	−8.92185	−	12.2799i	−0.289007	−	0.397784i	−0.928691	+	0.370854i	$0.879065\pi$
$954$	6.25545	+	15.4396i	0.202528	+	0.499876i
$955$	−26.4125	−	11.9277i	−0.854689	−	0.385972i
$956$	49.6871	+	5.22233i	1.60700	+	0.168902i
$957$	−0.0698854	+	0.173214i	−0.00225907	+	0.00559923i
$958$	−9.66211	+	13.2988i	−0.312169	+	0.429663i
$959$	−0.656764	−	34.9695i	−0.0212080	−	1.12922i
$960$	22.7650	−	10.9679i	0.734738	−	0.353987i
$961$	−20.8848	−	4.43921i	−0.673705	−	0.143200i
$962$	−17.8510	+	3.79434i	−0.575538	+	0.122334i
$963$	−22.6039	−	42.4124i	−0.728401	−	1.36672i
$964$	−2.62005	+	12.3263i	−0.0843860	+	0.397005i
$965$	11.2377	−	15.2963i	0.361755	−	0.492405i
$966$	−37.3381	−	45.9384i	−1.20133	−	1.47804i
$967$	2.90859	+	2.11321i	0.0935338	+	0.0679563i	0.633569	−	0.773686i	$-0.281589\pi$
$967$	2.90859	+	2.11321i	0.0935338	+	0.0679563i	−0.540035	+	0.841642i	$0.681589\pi$
$968$	3.30101	+	1.90584i	0.106098	+	0.0612559i
$969$	−1.75575	+	0.0621651i	−0.0564029	+	0.00199703i
$970$	28.6118	+	26.0380i	0.918669	+	0.836031i
$971$	0.824574	+	7.84530i	0.0264618	+	0.251768i	0.999754	+	0.0221961i	$0.00706581\pi$
$971$	0.824574	+	7.84530i	0.0264618	+	0.251768i	−0.973292	+	0.229572i	$0.926268\pi$
$972$	6.80694	−	27.5861i	0.218333	−	0.884824i
$973$	2.94428	−	0.365475i	0.0943894	−	0.0117166i
$974$		−	5.05417i		−	0.161946i
$975$	−51.4216	+	12.2698i	−1.64681	+	0.392948i
$976$	−32.0343	+	18.4950i	−1.02539	+	0.592010i
$977$	−2.99219	−	2.69418i	−0.0957286	−	0.0861944i	0.619877	−	0.784699i	$-0.287182\pi$
$977$	−2.99219	−	2.69418i	−0.0957286	−	0.0861944i	−0.715606	+	0.698505i	$0.753849\pi$
$978$	29.7662	−	7.43688i	0.951817	−	0.237805i
$979$	0.0861436	+	0.118567i	0.00275316	+	0.00378940i
$980$	−10.7576	+	26.4243i	−0.343639	+	0.844094i
$981$	−47.2372	−	17.1410i	−1.50817	−	0.547271i
$982$	−3.75897	+	6.51073i	−0.119954	+	0.207766i
$983$	−0.599501	+	5.70387i	−0.0191211	+	0.181925i	−0.999914	−	0.0131278i	$-0.995821\pi$
$983$	−0.599501	+	5.70387i	−0.0191211	+	0.181925i	0.980793	+	0.195053i	$0.0624878\pi$
$984$	−2.12841	−	5.83893i	−0.0678511	−	0.186138i
$985$	10.9770	−	18.7822i	0.349757	−	0.598450i
$986$	−5.26168	−	16.1938i	−0.167566	−	0.515715i
$987$	16.0869	−	42.1357i	0.512052	−	1.34120i
$988$	−0.822483	+	2.53134i	−0.0261667	+	0.0805327i
$989$	11.9329	−	56.1399i	0.379444	−	1.78514i
$990$	−0.320667	−	0.609437i	−0.0101915	−	0.0193692i
$991$	−26.4308	+	5.61804i	−0.839602	+	0.178463i	−0.607591	−	0.794250i	$-0.707864\pi$
$991$	−26.4308	+	5.61804i	−0.839602	+	0.178463i	−0.232011	+	0.972713i	$0.574531\pi$
$992$	−22.0182	+	9.80316i	−0.699080	+	0.311251i
$993$	−30.1245	+	4.24862i	−0.955971	+	0.134826i
$994$	−22.7362	+	5.28082i	−0.721149	+	0.167498i
$995$	33.3326	+	24.4885i	1.05671	+	0.776338i
$996$	7.47458	+	29.9171i	0.236841	+	0.947958i
$997$	4.54811	−	10.2152i	0.144040	−	0.323519i	−0.827090	−	0.562069i	$-0.810005\pi$
$997$	4.54811	−	10.2152i	0.144040	−	0.323519i	0.971130	+	0.238550i	$0.0766721\pi$
$998$	−47.1237	−	42.4303i	−1.49167	−	1.34311i
$999$	−0.819013	+	7.90303i	−0.0259124	+	0.250041i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bm.a.131.15	✓	608
3.2	odd	2	inner	525.2.bm.a.131.62	yes	608
7.3	odd	6	inner	525.2.bm.a.206.15	yes	608
21.17	even	6	inner	525.2.bm.a.206.62	yes	608
25.21	even	5	inner	525.2.bm.a.446.62	yes	608
75.71	odd	10	inner	525.2.bm.a.446.15	yes	608
175.171	odd	30	inner	525.2.bm.a.521.62	yes	608
525.521	even	30	inner	525.2.bm.a.521.15	yes	608

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bm.a.131.15	✓	608	1.1	even	1	trivial
525.2.bm.a.131.62	yes	608	3.2	odd	2	inner
525.2.bm.a.206.15	yes	608	7.3	odd	6	inner
525.2.bm.a.206.62	yes	608	21.17	even	6	inner
525.2.bm.a.446.15	yes	608	75.71	odd	10	inner
525.2.bm.a.446.62	yes	608	25.21	even	5	inner
525.2.bm.a.521.15	yes	608	525.521	even	30	inner
525.2.bm.a.521.62	yes	608	175.171	odd	30	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bm (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.406505 + 1.91245i) q^{2} +(1.66519 + 0.476610i) q^{3} +(-1.66514 - 0.741369i) q^{4} +(-0.898652 - 2.04754i) q^{5} +(-1.58840 + 2.99085i) q^{6} +(2.59781 + 0.501390i) q^{7} +(-0.203728 + 0.280407i) q^{8} +(2.54569 + 1.58729i) q^{9} +O(q^{10})\)	\(q+(-0.406505 + 1.91245i) q^{2} +(1.66519 + 0.476610i) q^{3} +(-1.66514 - 0.741369i) q^{4} +(-0.898652 - 2.04754i) q^{5} +(-1.58840 + 2.99085i) q^{6} +(2.59781 + 0.501390i) q^{7} +(-0.203728 + 0.280407i) q^{8} +(2.54569 + 1.58729i) q^{9} +(4.28113 - 0.886296i) q^{10} +(-0.0390194 - 0.0351332i) q^{11} +(-2.41943 - 2.02814i) q^{12} +(5.80558 + 1.88635i) q^{13} +(-2.01491 + 4.76437i) q^{14} +(-0.520544 - 3.83784i) q^{15} +(-2.89273 - 3.21271i) q^{16} +(0.443226 - 4.21701i) q^{17} +(-4.07045 + 4.22327i) q^{18} +(-0.0972966 - 0.218532i) q^{19} +(-0.0215998 + 4.07568i) q^{20} +(4.08687 + 2.07305i) q^{21} +(0.0830522 - 0.0603410i) q^{22} +(-1.37371 + 6.46278i) q^{23} +(-0.472890 + 0.369832i) q^{24} +(-3.38485 + 3.68005i) q^{25} +(-5.96754 + 10.3361i) q^{26} +(3.48252 + 3.85643i) q^{27} +(-3.95401 - 2.76082i) q^{28} +(-1.20721 - 1.66159i) q^{29} +(7.55130 + 0.564584i) q^{30} +(-3.08920 - 0.324688i) q^{31} +(6.71973 - 3.87964i) q^{32} +(-0.0482297 - 0.0771003i) q^{33} +(7.88466 + 2.56188i) q^{34} +(-1.30791 - 5.76969i) q^{35} +(-3.06216 - 4.53036i) q^{36} +(1.02316 + 1.13633i) q^{37} +(0.457483 - 0.0972411i) q^{38} +(8.76831 + 5.90811i) q^{39} +(0.757226 + 0.165152i) q^{40} +(-3.19900 + 9.84551i) q^{41} +(-5.62594 + 6.97324i) q^{42} -8.68665 q^{43} +(0.0389262 + 0.0874296i) q^{44} +(0.962351 - 6.63882i) q^{45} +(-11.8013 - 5.25430i) q^{46} +(-1.02878 - 9.78819i) q^{47} +(-3.28573 - 6.72846i) q^{48} +(6.49722 + 2.60503i) q^{49} +(-5.66198 - 7.96933i) q^{50} +(2.74792 - 6.81086i) q^{51} +(-8.26864 - 7.44511i) q^{52} +(1.15517 - 2.59456i) q^{53} +(-8.79090 + 5.09251i) q^{54} +(-0.0368718 + 0.111466i) q^{55} +(-0.669840 + 0.626298i) q^{56} +(-0.0578625 - 0.410268i) q^{57} +(3.66845 - 1.63330i) q^{58} +(2.85577 - 0.607013i) q^{59} +(-1.97848 + 6.77647i) q^{60} +(1.77896 - 8.36934i) q^{61} +(1.87672 - 5.77596i) q^{62} +(5.81735 + 5.39985i) q^{63} +(2.01619 + 6.20519i) q^{64} +(-1.35482 - 13.5823i) q^{65} +(0.167056 - 0.0608954i) q^{66} +(1.36572 - 12.9939i) q^{67} +(-3.86440 + 6.69333i) q^{68} +(-5.36770 + 10.1070i) q^{69} +(11.5659 - 0.155909i) q^{70} +(2.65223 + 3.65048i) q^{71} +(-0.963715 + 0.390454i) q^{72} +(-0.621829 - 0.559897i) q^{73} +(-2.58910 + 1.49482i) q^{74} +(-7.39035 + 4.51472i) q^{75} +0.436019i q^{76} +(-0.0837494 - 0.110833i) q^{77} +(-14.8634 + 14.3673i) q^{78} +(-0.238900 - 2.27298i) q^{79} +(-3.97859 + 8.81010i) q^{80} +(3.96103 + 8.08147i) q^{81} +(-17.5287 - 10.1202i) q^{82} +(-7.90211 - 5.74122i) q^{83} +(-5.26832 - 6.48180i) q^{84} +(-9.03281 + 2.88210i) q^{85} +(3.53116 - 16.6128i) q^{86} +(-1.21831 - 3.34222i) q^{87} +(0.0178010 - 0.00378371i) q^{88} +(-2.73025 - 0.580332i) q^{89} +(12.3052 + 4.53916i) q^{90} +(14.1360 + 7.81123i) q^{91} +(7.07872 - 9.74303i) q^{92} +(-4.98934 - 2.01301i) q^{93} +(19.1377 + 2.01145i) q^{94} +(-0.360017 + 0.395603i) q^{95} +(13.0387 - 3.25763i) q^{96} +(5.20118 + 7.15881i) q^{97} +(-7.62315 + 11.3667i) q^{98} +(-0.0435646 - 0.151373i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 608 q - 9 q^{3} - 78 q^{4} - 36 q^{7} - 3 q^{9}+O(q^{10}) \) 608 * q - 9 * q^3 - 78 * q^4 - 36 * q^7 - 3 * q^9	\( 608 q - 9 q^{3} - 78 q^{4} - 36 q^{7} - 3 q^{9} - 30 q^{10} + 3 q^{12} + 16 q^{15} + 50 q^{16} - 8 q^{18} - 18 q^{19} - 21 q^{21} - 24 q^{22} - 66 q^{24} - 10 q^{25} - 30 q^{28} - 7 q^{30} - 36 q^{31} + 36 q^{33} - 100 q^{36} - 14 q^{37} - 31 q^{39} - 30 q^{40} + 20 q^{42} - 96 q^{43} - 117 q^{45} + 42 q^{46} - 28 q^{49} - 8 q^{51} - 66 q^{52} + 3 q^{54} + 48 q^{57} - 38 q^{58} - 49 q^{60} - 18 q^{61} + 4 q^{63} - 32 q^{64} - 3 q^{66} - 22 q^{67} - 270 q^{70} + 45 q^{72} + 102 q^{73} + 135 q^{75} + 58 q^{78} - 34 q^{79} - 55 q^{81} + 108 q^{82} - 75 q^{84} - 96 q^{85} - 9 q^{87} + 36 q^{88} + 38 q^{91} - 22 q^{93} + 30 q^{94} - 81 q^{96} + 36 q^{99}+O(q^{100}) \) 608 * q - 9 * q^3 - 78 * q^4 - 36 * q^7 - 3 * q^9 - 30 * q^10 + 3 * q^12 + 16 * q^15 + 50 * q^16 - 8 * q^18 - 18 * q^19 - 21 * q^21 - 24 * q^22 - 66 * q^24 - 10 * q^25 - 30 * q^28 - 7 * q^30 - 36 * q^31 + 36 * q^33 - 100 * q^36 - 14 * q^37 - 31 * q^39 - 30 * q^40 + 20 * q^42 - 96 * q^43 - 117 * q^45 + 42 * q^46 - 28 * q^49 - 8 * q^51 - 66 * q^52 + 3 * q^54 + 48 * q^57 - 38 * q^58 - 49 * q^60 - 18 * q^61 + 4 * q^63 - 32 * q^64 - 3 * q^66 - 22 * q^67 - 270 * q^70 + 45 * q^72 + 102 * q^73 + 135 * q^75 + 58 * q^78 - 34 * q^79 - 55 * q^81 + 108 * q^82 - 75 * q^84 - 96 * q^85 - 9 * q^87 + 36 * q^88 + 38 * q^91 - 22 * q^93 + 30 * q^94 - 81 * q^96 + 36 * q^99

Introduction

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