LMFDB - Embedded newform 285.2.bi.a.47.35

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [285,2,Mod(17,285)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(285, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([18, 9, 20]))

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

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

chi := DirichletCharacter("285.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 285 = 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	285.bi (of order $36$, degree $12$, 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:	$2.27573645761$
Analytic rank:	$0$
Dimension:	$432$
Relative dimension:	$36$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			47.35
Character	$\chi$	$=$	285.47
Dual form			285.2.bi.a.188.35

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.17284 + 1.52144i) q^{2} +(0.975768 - 1.43104i) q^{3} +(1.72241 + 4.73229i) q^{4} +(0.814392 - 2.08249i) q^{5} +(4.29743 - 1.62485i) q^{6} +(-2.75201 + 0.737399i) q^{7} +(-2.08430 + 7.77872i) q^{8} +(-1.09575 - 2.79273i) q^{9} +O(q^{10})$	\(q+(2.17284 + 1.52144i) q^{2} +(0.975768 - 1.43104i) q^{3} +(1.72241 + 4.73229i) q^{4} +(0.814392 - 2.08249i) q^{5} +(4.29743 - 1.62485i) q^{6} +(-2.75201 + 0.737399i) q^{7} +(-2.08430 + 7.77872i) q^{8} +(-1.09575 - 2.79273i) q^{9} +(4.93792 - 3.28587i) q^{10} +(-3.73301 + 2.15525i) q^{11} +(8.45278 + 2.15277i) q^{12} +(2.33571 - 0.204348i) q^{13} +(-7.10158 - 2.58476i) q^{14} +(-2.18547 - 3.19745i) q^{15} +(-8.64810 + 7.25662i) q^{16} +(1.11405 + 0.780068i) q^{17} +(1.86806 - 7.73527i) q^{18} +(3.45298 - 2.66025i) q^{19} +(11.2577 + 0.267031i) q^{20} +(-1.63008 + 4.65777i) q^{21} +(-11.3903 - 0.996523i) q^{22} +(-5.89829 - 2.75042i) q^{23} +(9.09787 + 10.5730i) q^{24} +(-3.67353 - 3.39193i) q^{25} +(5.38603 + 3.10963i) q^{26} +(-5.06571 - 1.15698i) q^{27} +(-8.22969 - 11.7532i) q^{28} +(-0.862815 + 4.89327i) q^{29} +(0.116054 - 10.2726i) q^{30} +(-0.652248 + 1.12973i) q^{31} +(-13.7864 + 1.20616i) q^{32} +(-0.558295 + 7.44512i) q^{33} +(1.23383 + 3.38992i) q^{34} +(-0.705589 + 6.33157i) q^{35} +(11.3287 - 9.99566i) q^{36} +(5.44328 + 5.44328i) q^{37} +(11.5502 - 0.526793i) q^{38} +(1.98668 - 3.54190i) q^{39} +(14.5017 + 10.6755i) q^{40} +(0.663443 + 0.790660i) q^{41} +(-10.6284 + 7.64052i) q^{42} +(3.89049 - 1.81417i) q^{43} +(-16.6291 - 13.9535i) q^{44} +(-6.70820 + 0.00752364i) q^{45} +(-8.63143 - 14.9501i) q^{46} +(-5.96012 - 8.51193i) q^{47} +(1.94598 + 19.4566i) q^{48} +(0.967628 - 0.558660i) q^{49} +(-2.82139 - 12.9592i) q^{50} +(2.20337 - 0.833089i) q^{51} +(4.99010 + 10.7013i) q^{52} +(4.06282 + 1.89452i) q^{53} +(-9.24668 - 10.2211i) q^{54} +(1.44816 + 9.52918i) q^{55} -22.9441i q^{56} +(-0.437615 - 7.53714i) q^{57} +(-9.31956 + 9.31956i) q^{58} +(-0.369884 - 2.09772i) q^{59} +(11.3670 - 15.8496i) q^{60} +(10.6360 - 3.87117i) q^{61} +(-3.13604 + 1.46236i) q^{62} +(5.07488 + 6.87761i) q^{63} +(-12.2372 - 7.06514i) q^{64} +(1.47663 - 5.03052i) q^{65} +(-12.5404 + 15.3276i) q^{66} +(7.56854 - 5.29955i) q^{67} +(-1.77265 + 6.61562i) q^{68} +(-9.69131 + 5.75692i) q^{69} +(-11.1662 + 12.6840i) q^{70} +(-2.25823 + 6.20442i) q^{71} +(24.0077 - 2.70268i) q^{72} +(-0.0524530 + 0.599541i) q^{73} +(3.54576 + 20.1090i) q^{74} +(-8.43850 + 1.94724i) q^{75} +(18.5365 + 11.7585i) q^{76} +(8.68400 - 8.68400i) q^{77} +(9.70552 - 4.67336i) q^{78} +(4.26050 + 5.07747i) q^{79} +(8.06889 + 23.9193i) q^{80} +(-6.59865 + 6.12028i) q^{81} +(0.238613 + 2.72736i) q^{82} +(-1.13311 + 0.303617i) q^{83} +(-24.8496 + 0.308610i) q^{84} +(2.53176 - 1.68472i) q^{85} +(11.2136 + 1.97725i) q^{86} +(6.16056 + 6.00942i) q^{87} +(-8.98441 - 33.5303i) q^{88} +(-2.53368 - 2.12601i) q^{89} +(-14.5873 - 10.1898i) q^{90} +(-6.27722 + 2.28472i) q^{91} +(2.85648 - 32.6498i) q^{92} +(0.980242 + 2.03574i) q^{93} -27.5630i q^{94} +(-2.72786 - 9.35728i) q^{95} +(-11.7263 + 20.9059i) q^{96} +(2.89333 - 4.13210i) q^{97} +(2.95247 + 0.258307i) q^{98} +(10.1095 + 8.06365i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 432 q - 12 q^{3} - 24 q^{6} - 12 q^{7}+O(q^{10}) $ 432 * q - 12 * q^3 - 24 * q^6 - 12 * q^7	$ 432 q - 12 q^{3} - 24 q^{6} - 12 q^{7} - 24 q^{10} - 6 q^{12} - 24 q^{13} + 6 q^{15} - 108 q^{16} + 24 q^{18} - 24 q^{21} - 72 q^{22} - 6 q^{27} - 72 q^{28} - 6 q^{30} - 24 q^{31} - 102 q^{33} - 24 q^{36} - 48 q^{37} - 24 q^{40} + 24 q^{42} - 36 q^{43} + 12 q^{45} - 24 q^{46} - 156 q^{48} - 72 q^{51} - 48 q^{52} + 12 q^{55} - 90 q^{57} + 96 q^{58} + 132 q^{60} - 24 q^{61} + 18 q^{63} - 72 q^{66} - 120 q^{67} + 24 q^{70} + 168 q^{72} - 24 q^{73} - 192 q^{75} - 168 q^{76} - 6 q^{78} + 72 q^{81} - 312 q^{82} + 42 q^{87} - 204 q^{88} + 156 q^{90} + 72 q^{91} + 138 q^{93} + 240 q^{96} - 48 q^{97}+O(q^{100}) $ 432 * q - 12 * q^3 - 24 * q^6 - 12 * q^7 - 24 * q^10 - 6 * q^12 - 24 * q^13 + 6 * q^15 - 108 * q^16 + 24 * q^18 - 24 * q^21 - 72 * q^22 - 6 * q^27 - 72 * q^28 - 6 * q^30 - 24 * q^31 - 102 * q^33 - 24 * q^36 - 48 * q^37 - 24 * q^40 + 24 * q^42 - 36 * q^43 + 12 * q^45 - 24 * q^46 - 156 * q^48 - 72 * q^51 - 48 * q^52 + 12 * q^55 - 90 * q^57 + 96 * q^58 + 132 * q^60 - 24 * q^61 + 18 * q^63 - 72 * q^66 - 120 * q^67 + 24 * q^70 + 168 * q^72 - 24 * q^73 - 192 * q^75 - 168 * q^76 - 6 * q^78 + 72 * q^81 - 312 * q^82 + 42 * q^87 - 204 * q^88 + 156 * q^90 + 72 * q^91 + 138 * q^93 + 240 * q^96 - 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/285\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$211$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{4}{9}\right)$

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 $

$2$	2.17284	+	1.52144i	1.53643	+	1.07582i	0.967321	+	0.253556i	$0.0816003\pi$
$2$	2.17284	+	1.52144i	1.53643	+	1.07582i	0.569108	+	0.822263i	$0.307289\pi$
$3$	0.975768	−	1.43104i	0.563360	−	0.826212i
$3$	0.975768	−	1.43104i	0.563360	−	0.826212i
$4$	1.72241	+	4.73229i	0.861207	+	2.36615i
$5$	0.814392	−	2.08249i	0.364207	−	0.931318i
$5$	0.814392	−	2.08249i	0.364207	−	0.931318i
$6$	4.29743	−	1.62485i	1.75442	−	0.663342i
$7$	−2.75201	+	0.737399i	−1.04016	+	0.278711i	−0.738181	−	0.674603i	$-0.764315\pi$
$7$	−2.75201	+	0.737399i	−1.04016	+	0.278711i	−0.301982	+	0.953314i	$0.597648\pi$
$8$	−2.08430	+	7.77872i	−0.736912	+	2.75019i
$9$	−1.09575	−	2.79273i	−0.365251	−	0.930909i
$10$	4.93792	−	3.28587i	1.56151	−	1.03908i
$11$	−3.73301	+	2.15525i	−1.12554	+	0.649834i	−0.942811	−	0.333329i	$-0.891828\pi$
$11$	−3.73301	+	2.15525i	−1.12554	+	0.649834i	−0.182734	+	0.983162i	$0.558495\pi$
$12$	8.45278	+	2.15277i	2.44011	+	0.621453i
$13$	2.33571	−	0.204348i	0.647810	−	0.0566761i	0.241485	−	0.970405i	$-0.422366\pi$
$13$	2.33571	−	0.204348i	0.647810	−	0.0566761i	0.406325	+	0.913728i	$0.366810\pi$
$14$	−7.10158	−	2.58476i	−1.89798	−	0.690807i
$15$	−2.18547	−	3.19745i	−0.564286	−	0.825579i
$16$	−8.64810	+	7.25662i	−2.16202	+	1.81415i
$17$	1.11405	+	0.780068i	0.270197	+	0.189194i	0.700821	−	0.713338i	$-0.252817\pi$
$17$	1.11405	+	0.780068i	0.270197	+	0.189194i	−0.430623	+	0.902532i	$0.641706\pi$
$18$	1.86806	−	7.73527i	0.440307	−	1.82322i
$19$	3.45298	−	2.66025i	0.792168	−	0.610303i
$19$	3.45298	−	2.66025i	0.792168	−	0.610303i
$20$	11.2577	+	0.267031i	2.51729	+	0.0597099i
$21$	−1.63008	+	4.65777i	−0.355712	+	1.01641i
$22$	−11.3903	−	0.996523i	−2.42842	−	0.212459i
$23$	−5.89829	−	2.75042i	−1.22988	−	0.573501i	−0.304487	−	0.952516i	$-0.598485\pi$
$23$	−5.89829	−	2.75042i	−1.22988	−	0.573501i	−0.925390	+	0.379015i	$0.876263\pi$
$24$	9.09787	+	10.5730i	1.85710	+	2.15819i
$25$	−3.67353	−	3.39193i	−0.734706	−	0.678385i
$26$	5.38603	+	3.10963i	1.05629	+	0.609848i
$27$	−5.06571	−	1.15698i	−0.974896	−	0.222662i
$28$	−8.22969	−	11.7532i	−1.55526	−	2.22115i
$29$	−0.862815	+	4.89327i	−0.160221	+	0.908657i	0.793636	+	0.608393i	$0.208186\pi$
$29$	−0.862815	+	4.89327i	−0.160221	+	0.908657i	−0.953856	+	0.300263i	$0.902925\pi$
$30$	0.116054	−	10.2726i	0.0211885	−	1.87551i
$31$	−0.652248	+	1.12973i	−0.117147	+	0.202905i	−0.918636	−	0.395105i	$-0.870708\pi$
$31$	−0.652248	+	1.12973i	−0.117147	+	0.202905i	0.801489	+	0.598010i	$0.204042\pi$
$32$	−13.7864	+	1.20616i	−2.43712	+	0.213221i
$33$	−0.558295	+	7.44512i	−0.0971866	+	1.29603i
$34$	1.23383	+	3.38992i	0.211600	+	0.581367i
$35$	−0.705589	+	6.33157i	−0.119266	+	1.07023i
$36$	11.3287	−	9.99566i	1.88811	−	1.66594i
$37$	5.44328	+	5.44328i	0.894870	+	0.894870i	0.994977	−	0.100107i	$-0.0319184\pi$
$37$	5.44328	+	5.44328i	0.894870	+	0.894870i	−0.100107	+	0.994977i	$0.531918\pi$
$38$	11.5502	−	0.526793i	1.87369	−	0.0854571i
$39$	1.98668	−	3.54190i	0.318124	−	0.567158i
$40$	14.5017	+	10.6755i	2.29292	+	1.68794i
$41$	0.663443	+	0.790660i	0.103612	+	0.123480i	0.815359	−	0.578956i	$-0.196540\pi$
$41$	0.663443	+	0.790660i	0.103612	+	0.123480i	−0.711746	+	0.702437i	$0.752095\pi$
$42$	−10.6284	+	7.64052i	−1.64000	+	1.17896i
$43$	3.89049	−	1.81417i	0.593295	−	0.276658i	−0.102691	−	0.994713i	$-0.532745\pi$
$43$	3.89049	−	1.81417i	0.593295	−	0.276658i	0.695986	+	0.718055i	$0.254968\pi$
$44$	−16.6291	−	13.9535i	−2.50693	−	2.10356i
$45$	−6.70820	+	0.00752364i	−0.999999	+	0.00112156i
$46$	−8.63143	−	14.9501i	−1.27264	−	2.20427i
$47$	−5.96012	−	8.51193i	−0.869373	−	1.24159i	−0.969122	−	0.246581i	$-0.920693\pi$
$47$	−5.96012	−	8.51193i	−0.869373	−	1.24159i	0.0997493	−	0.995013i	$-0.468196\pi$
$48$	1.94598	+	19.4566i	0.280877	+	2.80831i
$49$	0.967628	−	0.558660i	0.138233	−	0.0798086i
$50$	−2.82139	−	12.9592i	−0.399004	−	1.83270i
$51$	2.20337	−	0.833089i	0.308533	−	0.116656i
$52$	4.99010	+	10.7013i	0.692002	+	1.48400i
$53$	4.06282	+	1.89452i	0.558071	+	0.260233i	0.681125	−	0.732167i	$-0.261491\pi$
$53$	4.06282	+	1.89452i	0.558071	+	0.260233i	−0.123054	+	0.992400i	$0.539269\pi$
$54$	−9.24668	−	10.2211i	−1.25831	−	1.39092i
$55$	1.44816	+	9.52918i	0.195270	+	1.28491i
$56$		−	22.9441i		−	3.06603i
$57$	−0.437615	−	7.53714i	−0.0579635	−	0.998319i
$58$	−9.31956	+	9.31956i	−1.22372	+	1.22372i
$59$	−0.369884	−	2.09772i	−0.0481548	−	0.273100i	0.951218	−	0.308521i	$-0.0998339\pi$
$59$	−0.369884	−	2.09772i	−0.0481548	−	0.273100i	−0.999372	+	0.0354210i	$0.988723\pi$
$60$	11.3670	−	15.8496i	1.46747	−	2.04618i
$61$	10.6360	−	3.87117i	1.36180	−	0.495653i	0.445186	−	0.895438i	$-0.353137\pi$
$61$	10.6360	−	3.87117i	1.36180	−	0.495653i	0.916609	+	0.399785i	$0.130915\pi$
$62$	−3.13604	+	1.46236i	−0.398277	+	0.185720i
$63$	5.07488	+	6.87761i	0.639375	+	0.866497i
$64$	−12.2372	−	7.06514i	−1.52965	−	0.883143i
$65$	1.47663	−	5.03052i	0.183154	−	0.623959i
$66$	−12.5404	+	15.3276i	−1.54361	+	1.88670i
$67$	7.56854	−	5.29955i	0.924644	−	0.647443i	−0.0111699	−	0.999938i	$-0.503556\pi$
$67$	7.56854	−	5.29955i	0.924644	−	0.647443i	0.935814	+	0.352495i	$0.114667\pi$
$68$	−1.77265	+	6.61562i	−0.214965	+	0.802262i
$69$	−9.69131	+	5.75692i	−1.16670	+	0.693052i
$70$	−11.1662	+	12.6840i	−1.33462	+	1.51602i
$71$	−2.25823	+	6.20442i	−0.268002	+	0.736330i	0.730566	+	0.682842i	$0.239256\pi$
$71$	−2.25823	+	6.20442i	−0.268002	+	0.736330i	−0.998568	+	0.0534880i	$0.982966\pi$
$72$	24.0077	−	2.70268i	2.82934	−	0.318514i
$73$	−0.0524530	+	0.599541i	−0.00613916	+	0.0701709i	−0.998646	−	0.0520162i	$-0.983435\pi$
$73$	−0.0524530	+	0.599541i	−0.00613916	+	0.0701709i	0.992507	+	0.122187i	$0.0389908\pi$
$74$	3.54576	+	20.1090i	0.412186	+	2.33762i
$75$	−8.43850	+	1.94724i	−0.974394	+	0.224848i
$76$	18.5365	+	11.7585i	2.12629	+	1.34879i
$77$	8.68400	−	8.68400i	0.989634	−	0.989634i
$78$	9.70552	−	4.67336i	1.09893	−	0.529153i
$79$	4.26050	+	5.07747i	0.479344	+	0.571260i	0.950474	−	0.310804i	$-0.100598\pi$
$79$	4.26050	+	5.07747i	0.479344	+	0.571260i	−0.471130	+	0.882064i	$0.656154\pi$
$80$	8.06889	+	23.9193i	0.902130	+	2.67426i
$81$	−6.59865	+	6.12028i	−0.733183	+	0.680032i
$82$	0.238613	+	2.72736i	0.0263504	+	0.301187i
$83$	−1.13311	+	0.303617i	−0.124375	+	0.0333263i	−0.320470	−	0.947259i	$-0.603841\pi$
$83$	−1.13311	+	0.303617i	−0.124375	+	0.0333263i	0.196094	+	0.980585i	$0.437174\pi$
$84$	−24.8496	+	0.308610i	−2.71131	+	0.0336722i
$85$	2.53176	−	1.68472i	0.274608	−	0.182734i
$86$	11.2136	+	1.97725i	1.20919	+	0.213213i
$87$	6.16056	+	6.00942i	0.660481	+	0.644277i
$88$	−8.98441	−	33.5303i	−0.957741	−	3.57434i
$89$	−2.53368	−	2.12601i	−0.268570	−	0.225357i	0.498549	−	0.866861i	$-0.333866\pi$
$89$	−2.53368	−	2.12601i	−0.268570	−	0.225357i	−0.767119	+	0.641504i	$0.778311\pi$
$90$	−14.5873	−	10.1898i	−1.53763	−	1.07410i
$91$	−6.27722	+	2.28472i	−0.658032	+	0.239504i
$92$	2.85648	−	32.6498i	0.297809	−	3.40397i
$93$	0.980242	+	2.03574i	0.101646	+	0.211097i
$94$		−	27.5630i		−	2.84291i
$95$	−2.72786	−	9.35728i	−0.279873	−	0.960037i
$96$	−11.7263	+	20.9059i	−1.19681	+	2.13370i
$97$	2.89333	−	4.13210i	0.293773	−	0.419551i	−0.644950	−	0.764225i	$-0.723122\pi$
$97$	2.89333	−	4.13210i	0.293773	−	0.419551i	0.938722	+	0.344674i	$0.112011\pi$
$98$	2.95247	+	0.258307i	0.298244	+	0.0260930i
$99$	10.1095	+	8.06365i	1.01604	+	0.810427i
$100$	9.72424	−	23.2265i	0.972424	−	2.32265i
$101$	3.69874	−	4.40798i	0.368038	−	0.438611i	−0.549963	−	0.835189i	$-0.685358\pi$
$101$	3.69874	−	4.40798i	0.368038	−	0.438611i	0.918001	+	0.396578i	$0.129803\pi$
$102$	6.05505	+	1.54212i	0.599539	+	0.152692i
$103$	0.439584	+	0.117786i	0.0433135	+	0.0116058i	0.280411	−	0.959880i	$-0.409529\pi$
$103$	0.439584	+	0.117786i	0.0433135	+	0.0116058i	−0.237097	+	0.971486i	$0.576196\pi$
$104$	−3.27876	+	18.5948i	−0.321509	+	1.82337i
$105$	8.37224	+	7.18787i	0.817047	+	0.701464i
$106$	5.94544	+	10.2978i	0.577473	+	1.00021i
$107$	2.71613	+	10.1367i	0.262578	+	0.979955i	0.963716	+	0.266930i	$0.0860091\pi$
$107$	2.71613	+	10.1367i	0.262578	+	0.979955i	−0.701138	+	0.713026i	$0.747324\pi$
$108$	−3.25005	−	25.9652i	−0.312737	−	2.49850i
$109$	−2.43112	+	6.67944i	−0.232859	+	0.639775i	−0.999999	−	0.00170560i	$-0.999457\pi$
$109$	−2.43112	+	6.67944i	−0.232859	+	0.639775i	0.767140	+	0.641480i	$0.221679\pi$
$110$	−11.3514	+	22.9087i	−1.08232	+	2.18425i
$111$	13.1009	−	2.47818i	1.24349	−	0.235218i
$112$	18.4486	−	26.3474i	1.74323	−	2.48959i
$113$	0.478861	+	0.478861i	0.0450475	+	0.0450475i	0.729272	−	0.684224i	$-0.239859\pi$
$113$	0.478861	+	0.478861i	0.0450475	+	0.0450475i	−0.684224	+	0.729272i	$0.739859\pi$
$114$	10.5164	−	17.0428i	0.984953	−	1.59620i
$115$	−10.5312	+	10.0432i	−0.982042	+	0.936534i
$116$	−24.6425	+	4.34514i	−2.28800	+	0.403436i
$117$	−3.13006	−	6.29909i	−0.289374	−	0.582351i
$118$	2.38785	−	5.12076i	0.219819	−	0.471404i
$119$	−3.64111	−	1.32525i	−0.333780	−	0.121486i
$120$	29.4273	−	10.3357i	2.68633	−	0.943517i
$121$	3.79024	−	6.56489i	0.344568	−	0.596808i
$122$	29.0000	+	7.77052i	2.62553	+	0.703510i
$123$	1.77883	−	0.177913i	0.160392	−	0.0160418i
$124$	−6.46964	−	1.14077i	−0.580991	−	0.102444i
$125$	−10.0553	+	4.88774i	−0.899378	+	0.437173i
$126$	0.563047	+	22.6650i	0.0501603	+	2.01916i
$127$	−0.358406	−	4.09660i	−0.0318034	−	0.363514i	−0.995375	−	0.0960643i	$-0.969375\pi$
$127$	−0.358406	−	4.09660i	−0.0318034	−	0.363514i	0.963572	−	0.267450i	$-0.0861810\pi$
$128$	−4.14293	−	8.88455i	−0.366187	−	0.785291i
$129$	1.20007	−	7.33766i	0.105660	−	0.646045i
$130$	10.8621	−	8.68390i	0.952670	−	0.761629i
$131$	−5.65868	+	0.997778i	−0.494401	+	0.0871763i	−0.415289	−	0.909689i	$-0.636320\pi$
$131$	−5.65868	+	0.997778i	−0.494401	+	0.0871763i	−0.0791121	+	0.996866i	$0.525209\pi$
$132$	−36.1941	+	10.1816i	−3.15029	+	0.886191i
$133$	−7.54098	+	9.86726i	−0.653886	+	0.855600i
$134$	24.5081			2.11718
$135$	−6.53488	+	9.60705i	−0.562433	+	0.826843i
$136$	−8.38995	+	7.04001i	−0.719433	+	0.603676i
$137$	6.73391	−	14.4409i	0.575317	−	1.23377i	−0.376304	−	0.926496i	$-0.622805\pi$
$137$	6.73391	−	14.4409i	0.575317	−	1.23377i	0.951621	−	0.307274i	$-0.0994170\pi$
$138$	−29.8164	−	2.23588i	−2.53814	−	0.190331i
$139$	−13.5058	+	16.0955i	−1.14554	+	1.36521i	−0.225099	+	0.974336i	$0.572270\pi$
$139$	−13.5058	+	16.0955i	−1.14554	+	1.36521i	−0.920446	+	0.390871i	$0.872174\pi$
$140$	−31.1781	+	7.56652i	−2.63503	+	0.639488i
$141$	−17.9966	+	0.223502i	−1.51559	+	0.0188223i
$142$	−14.3464	+	10.0455i	−1.20392	+	0.842996i
$143$	−8.27882	+	5.79689i	−0.692310	+	0.484760i
$144$	29.7419	+	16.2003i	2.47849	+	1.35003i
$145$	9.48751	+	5.78184i	0.787895	+	0.480156i
$146$	−1.02614	+	1.22290i	−0.0849236	+	0.101208i
$147$	0.144715	−	1.92984i	0.0119359	−	0.159170i
$148$	−16.3836	+	35.1348i	−1.34672	+	2.88806i
$149$	−5.85791	+	4.91537i	−0.479899	+	0.402683i	−0.850390	−	0.526153i	$-0.823634\pi$
$149$	−5.85791	+	4.91537i	−0.479899	+	0.402683i	0.370491	+	0.928836i	$0.379189\pi$
$150$	−21.2981	−	8.60761i	−1.73898	−	0.702809i
$151$	−4.11264			−0.334682			−0.167341	−	0.985899i	$-0.553518\pi$
$151$	−4.11264			−0.334682			−0.167341	+	0.985899i	$0.553518\pi$
$152$	13.4963	+	32.4046i	1.09469	+	2.62836i
$153$	0.957789	−	3.96601i	0.0774326	−	0.320633i
$154$	32.0811	−	5.65676i	2.58517	−	0.455835i
$155$	1.82146	+	2.27834i	0.146303	+	0.183001i
$156$	20.1832	+	3.30095i	1.61595	+	0.264288i
$157$	−9.33892	−	20.0274i	−0.745327	−	1.59836i	−0.800105	−	0.599860i	$-0.795223\pi$
$157$	−9.33892	−	20.0274i	−0.745327	−	1.59836i	0.0547786	−	0.998499i	$-0.482555\pi$
$158$	1.53233	+	17.5146i	0.121906	+	1.39339i
$159$	6.67550	−	3.96544i	0.529402	−	0.314480i
$160$	−8.71576	+	29.6924i	−0.689041	+	2.34739i
$161$	18.2603	+	3.21978i	1.43911	+	0.253754i
$162$	−23.6494	+	3.25896i	−1.85807	+	0.256048i
$163$	10.6545	+	2.85486i	0.834525	+	0.223610i	0.650687	−	0.759346i	$-0.274481\pi$
$163$	10.6545	+	2.85486i	0.834525	+	0.223610i	0.183838	+	0.982957i	$0.441148\pi$
$164$	−2.59891	+	4.50145i	−0.202941	+	0.351504i
$165$	15.0497	+	7.22589i	1.17162	+	0.562534i
$166$	−2.92401	−	1.06425i	−0.226947	−	0.0826020i
$167$	−3.71923	+	7.97591i	−0.287803	+	0.617195i	−0.996052	−	0.0887673i	$-0.971707\pi$
$167$	−3.71923	+	7.97591i	−0.287803	+	0.617195i	0.708250	+	0.705962i	$0.249485\pi$
$168$	−32.8339	−	22.3881i	−2.53319	−	1.72728i
$169$	−7.38870	+	1.30283i	−0.568362	+	0.100217i
$170$	8.06430	+	0.191284i	0.618504	+	0.0146708i
$171$	−11.2130	−	6.72826i	−0.857477	−	0.514523i
$172$	15.2862	+	15.2862i	1.16556	+	1.16556i
$173$	4.98152	−	7.11435i	0.378738	−	0.540894i	−0.583851	−	0.811861i	$-0.698455\pi$
$173$	4.98152	−	7.11435i	0.378738	−	0.540894i	0.962589	+	0.270967i	$0.0873435\pi$
$174$	4.24294	+	22.4304i	0.321657	+	1.70044i
$175$	12.6108	+	6.62576i	0.953287	+	0.500860i
$176$	16.6436	−	45.7279i	1.25456	−	3.44687i
$177$	−3.36284	−	1.51757i	−0.252767	−	0.114067i
$178$	−2.27069	−	8.47433i	−0.170195	−	0.635178i
$179$	−7.22714	−	12.5178i	−0.540182	−	0.935622i	−0.998893	−	0.0470367i	$-0.985022\pi$
$179$	−7.22714	−	12.5178i	−0.540182	−	0.935622i	0.458712	−	0.888585i	$-0.348311\pi$
$180$	−11.5899	−	31.7322i	−0.863860	−	2.36518i
$181$	−4.40651	+	24.9905i	−0.327533	+	1.85753i	0.163708	+	0.986509i	$0.447655\pi$
$181$	−4.40651	+	24.9905i	−0.327533	+	1.85753i	−0.491241	+	0.871024i	$0.663457\pi$
$182$	−17.1155	−	4.58607i	−1.26868	−	0.339942i
$183$	4.83842	−	18.9979i	0.357667	−	1.40436i
$184$	33.6885	−	40.1484i	2.48355	−	2.95978i
$185$	15.7685	−	6.90262i	1.15933	−	0.507490i
$186$	−0.967351	+	5.91472i	−0.0709296	+	0.433688i
$187$	−5.84001	−	0.510935i	−0.427064	−	0.0373633i
$188$	30.0152	−	42.8661i	2.18908	−	3.12633i
$189$	14.7940	−	0.551414i	1.07611	−	0.0401095i
$190$	8.30932	−	24.4821i	0.602822	−	1.77612i
$191$			24.4106i			1.76629i	0.469104	+	0.883143i	$0.344577\pi$
$191$			24.4106i			1.76629i	−0.469104	+	0.883143i	$0.655423\pi$
$192$	−22.0512	+	10.6180i	−1.59141	+	0.766286i
$193$	0.845202	−	9.66070i	0.0608390	−	0.695393i	−0.903128	−	0.429371i	$-0.858735\pi$
$193$	0.845202	−	9.66070i	0.0608390	−	0.695393i	0.963967	−	0.266022i	$-0.0857092\pi$
$194$	12.5735	−	4.57637i	0.902722	−	0.328564i
$195$	−5.75803	−	7.02174i	−0.412341	−	0.502837i
$196$	4.31040	+	3.61686i	0.307886	+	0.258347i
$197$	−2.78188	−	10.3821i	−0.198201	−	0.739695i	−0.991415	−	0.130753i	$-0.958261\pi$
$197$	−2.78188	−	10.3821i	−0.198201	−	0.739695i	0.793214	−	0.608943i	$-0.208406\pi$
$198$	9.69797	+	32.9020i	0.689204	+	2.33824i
$199$	−9.16098	−	1.61533i	−0.649405	−	0.114508i	−0.160764	−	0.986993i	$-0.551396\pi$
$199$	−9.16098	−	1.61533i	−0.649405	−	0.114508i	−0.488640	+	0.872485i	$0.662507\pi$
$200$	34.0416	−	21.5056i	2.40711	−	1.52067i
$201$	−0.198731	−	16.0020i	−0.0140174	−	1.12869i
$202$	14.7432	−	3.95044i	1.03733	−	0.277952i
$203$	−1.23381	−	14.1026i	−0.0865968	−	0.989806i
$204$	7.73753	+	8.99204i	0.541735	+	0.629569i
$205$	2.18684	−	0.737706i	0.152736	−	0.0515236i
$206$	0.775941	+	0.924730i	0.0540624	+	0.0644290i
$207$	−1.21809	+	19.4861i	−0.0846630	+	1.35438i
$208$	−18.7166	+	18.7166i	−1.29776	+	1.29776i
$209$	−7.15650	+	17.3728i	−0.495026	+	1.20170i
$210$	7.25563	+	28.3559i	0.500686	+	1.95674i
$211$	−3.67600	−	20.8476i	−0.253066	−	1.43521i	−0.800988	−	0.598681i	$-0.795692\pi$
$211$	−3.67600	−	20.8476i	−0.253066	−	1.43521i	0.547922	−	0.836530i	$-0.315419\pi$
$212$	−1.96758	+	22.4896i	−0.135134	+	1.54459i
$213$	6.67528	+	9.28569i	0.457383	+	0.636245i
$214$	−9.52070	+	26.1579i	−0.650822	+	1.78812i
$215$	−0.609599	−	9.57936i	−0.0415743	−	0.653307i
$216$	19.5583	−	36.9932i	1.33078	−	2.51707i
$217$	0.961934	−	3.58999i	0.0653004	−	0.243704i
$218$	−15.4448	+	10.8146i	−1.04605	+	0.732454i
$219$	0.806785	+	0.660075i	0.0545175	+	0.0446037i
$220$	−42.6005	+	23.2663i	−2.87213	+	1.56861i
$221$	2.76151	+	1.59436i	0.185759	+	0.107248i
$222$	32.2366	+	14.5476i	2.16358	+	0.976370i
$223$	−1.50633	+	0.702414i	−0.100871	+	0.0470371i	−0.472399	−	0.881385i	$-0.656612\pi$
$223$	−1.50633	+	0.702414i	−0.100871	+	0.0470371i	0.371528	+	0.928422i	$0.378834\pi$
$224$	37.0510	−	13.4855i	2.47558	−	0.901036i
$225$	−5.44744	+	13.9759i	−0.363162	+	0.931726i
$226$	0.311930	+	1.76905i	0.0207493	+	0.117675i
$227$	12.7737	−	12.7737i	0.847822	−	0.847822i	−0.142039	−	0.989861i	$-0.545366\pi$
$227$	12.7737	−	12.7737i	0.847822	−	0.847822i	0.989861	+	0.142039i	$0.0453660\pi$
$228$	34.9142	−	15.0530i	2.31225	−	0.996909i
$229$			8.57575i			0.566701i	0.959016	+	0.283351i	$0.0914460\pi$
$229$			8.57575i			0.566701i	−0.959016	+	0.283351i	$0.908554\pi$
$230$	−38.1628	+	5.79965i	−2.51638	+	0.382418i
$231$	−3.95359	−	20.9007i	−0.260127	−	1.37517i
$232$	−36.2650	−	16.9107i	−2.38091	−	1.11024i
$233$	0.0891381	+	0.191157i	0.00583963	+	0.0125231i	0.909206	−	0.416347i	$-0.136690\pi$
$233$	0.0891381	+	0.191157i	0.00583963	+	0.0125231i	−0.903366	+	0.428870i	$0.858912\pi$
$234$	2.78257	−	18.4491i	0.181902	−	1.20606i
$235$	−22.5799	+	5.47984i	−1.47295	+	0.357466i
$236$	9.28992	−	5.36354i	0.604722	−	0.349137i
$237$	11.4233	−	1.14252i	0.742024	−	0.0742147i
$238$	−5.89524	−	8.41928i	−0.382132	−	0.545741i
$239$	−11.2172	−	19.4288i	−0.725583	−	1.25675i	−0.958733	−	0.284306i	$-0.908237\pi$
$239$	−11.2172	−	19.4288i	−0.725583	−	1.25675i	0.233150	−	0.972441i	$-0.425097\pi$
$240$	42.1029	+	11.7928i	2.71773	+	0.761221i
$241$	4.19197	+	3.51748i	0.270029	+	0.226581i	0.767740	−	0.640762i	$-0.221381\pi$
$241$	4.19197	+	3.51748i	0.270029	+	0.226581i	−0.497711	+	0.867343i	$0.665826\pi$
$242$	18.2237	−	8.49783i	1.17146	−	0.546261i
$243$	2.31963	+	15.4149i	0.148804	+	0.988867i
$244$	36.6390	+	43.6647i	2.34557	+	2.79535i
$245$	−0.375376	−	2.47005i	−0.0239819	−	0.157805i
$246$	4.13580	+	2.31981i	0.263689	+	0.147906i
$247$	7.52156	−	6.91919i	0.478585	−	0.440257i
$248$	−7.42835	−	7.42835i	−0.471701	−	0.471701i
$249$	−0.671168	+	1.91779i	−0.0425336	+	0.121535i
$250$	−29.2850	−	4.67832i	−1.85215	−	0.295883i
$251$	−4.73281	−	13.0033i	−0.298732	−	0.820760i	−0.994712	−	0.102699i	$-0.967252\pi$
$251$	−4.73281	−	13.0033i	−0.298732	−	0.820760i	0.695980	−	0.718061i	$-0.254970\pi$
$252$	−23.8058	+	35.8619i	−1.49962	+	2.25909i
$253$	27.9462	−	2.44498i	1.75696	−	0.153714i
$254$	5.45396	−	9.44653i	0.342212	−	0.592728i
$255$	0.0595029	−	5.26695i	0.00372622	−	0.329829i
$256$	−0.392033	+	2.22333i	−0.0245020	+	0.138958i
$257$	1.88979	+	2.69891i	0.117882	+	0.168353i	0.873757	−	0.486363i	$-0.161677\pi$
$257$	1.88979	+	2.69891i	0.117882	+	0.168353i	−0.755874	+	0.654717i	$0.772788\pi$
$258$	13.7714	−	14.1177i	0.857367	−	0.878931i
$259$	−18.9938	−	10.9661i	−1.18022	−	0.681400i
$260$	26.3493	−	1.67678i	1.63411	−	0.103990i
$261$	14.6110	−	2.95221i	0.904398	−	0.182737i
$262$	−13.8135	−	6.44132i	−0.853398	−	0.397946i
$263$	−10.9509	−	0.958083i	−0.675264	−	0.0590780i	−0.255635	−	0.966773i	$-0.582284\pi$
$263$	−10.9509	−	0.958083i	−0.675264	−	0.0590780i	−0.419629	+	0.907696i	$0.637840\pi$
$264$	−56.7499	−	19.8607i	−3.49271	−	1.22234i
$265$	7.25405	−	6.91789i	0.445613	−	0.424963i
$266$	−31.3977	+	9.96683i	−1.92512	+	0.611105i
$267$	−5.51470	+	1.55131i	−0.337494	+	0.0949386i
$268$	38.1151	+	26.6885i	2.32825	+	1.63026i
$269$	−15.9918	+	13.4187i	−0.975035	+	0.818151i	−0.983333	−	0.181814i	$-0.941803\pi$
$269$	−15.9918	+	13.4187i	−0.975035	+	0.818151i	0.00829816	+	0.999966i	$0.497359\pi$
$270$	−28.8158	+	10.9321i	−1.75367	+	0.665309i
$271$	30.3391	+	11.0425i	1.84297	+	0.670786i	0.988487	+	0.151308i	$0.0483486\pi$
$271$	30.3391	+	11.0425i	1.84297	+	0.670786i	0.854484	+	0.519478i	$0.173874\pi$
$272$	−15.2951	+	1.33815i	−0.927401	+	0.0811371i
$273$	−2.85558	+	11.2123i	−0.172828	+	0.678600i
$274$	36.6026	−	21.1325i	2.21125	−	1.27666i
$275$	21.0238	+	4.74470i	1.26778	+	0.286116i
$276$	−43.9359	−	35.9463i	−2.64463	−	2.16371i
$277$	2.52278	−	9.41515i	0.151579	−	0.565701i	−0.847795	−	0.530324i	$-0.822070\pi$
$277$	2.52278	−	9.41515i	0.151579	−	0.565701i	0.999374	−	0.0353770i	$-0.0112632\pi$
$278$	−53.8342	+	14.4248i	−3.22876	+	0.865144i
$279$	3.86972	+	0.583648i	0.231674	+	0.0349421i
$280$	−47.7809	−	18.6855i	−2.85545	−	1.11667i
$281$	0.589999	+	1.62101i	0.0351964	+	0.0967013i	0.956046	−	0.293216i	$-0.0947257\pi$
$281$	0.589999	+	1.62101i	0.0351964	+	0.0967013i	−0.920850	+	0.389918i	$0.872503\pi$
$282$	−39.4438	−	26.8951i	−2.34884	−	1.60158i
$283$	−17.0459	−	11.9356i	−1.01327	−	0.709500i	−0.0559221	−	0.998435i	$-0.517810\pi$
$283$	−17.0459	−	11.9356i	−1.01327	−	0.709500i	−0.957349	+	0.288935i	$0.906699\pi$
$284$	−33.2507			−1.97307
$285$	−16.0524	−	5.22686i	−0.950863	−	0.309612i
$286$	−26.8081			−1.58520
$287$	−2.40883	−	1.68668i	−0.142189	−	0.0995618i
$288$	18.4750	+	37.1801i	1.08865	+	2.19086i
$289$	−5.18174	−	14.2367i	−0.304808	−	0.837453i
$290$	11.8181	+	26.9977i	0.693984	+	1.58536i
$291$	−3.08999	−	8.17244i	−0.181138	−	0.479077i
$292$	−2.92755	+	0.784434i	−0.171322	+	0.0459055i
$293$	−0.605000	+	2.25789i	−0.0353445	+	0.131907i	−0.981344	−	0.192261i	$-0.938418\pi$
$293$	−0.605000	+	2.25789i	−0.0353445	+	0.131907i	0.945999	+	0.324169i	$0.105085\pi$
$294$	3.25057	−	3.97305i	0.189577	−	0.231713i
$295$	−4.66971	−	0.938084i	−0.271881	−	0.0546174i
$296$	−53.6872	+	30.9963i	−3.12051	+	1.80163i
$297$	21.4039	−	6.59885i	1.24198	−	0.382904i
$298$	−20.2067	+	1.76786i	−1.17054	+	0.102409i
$299$	−14.3387	−	5.21888i	−0.829231	−	0.301815i
$300$	−23.7495	−	36.5795i	−1.37118	−	2.11192i
$301$	−9.36892	+	7.86145i	−0.540015	+	0.453127i
$302$	−8.93611	−	6.25713i	−0.514215	−	0.360058i
$303$	−2.69889	−	9.59421i	−0.155047	−	0.551173i
$304$	−10.5573	+	48.0631i	−0.605504	+	2.75661i
$305$	0.600159	−	25.3019i	0.0343650	−	1.44878i
$306$	8.11515	−	7.16027i	0.463912	−	0.409326i
$307$	17.5963	+	1.53948i	1.00427	+	0.0878627i	0.577411	−	0.816453i	$-0.304063\pi$
$307$	17.5963	+	1.53948i	1.00427	+	0.0878627i	0.426863	+	0.904316i	$0.359618\pi$
$308$	56.0527	+	26.1378i	3.19390	+	1.48934i
$309$	0.597489	−	0.514131i	0.0339900	−	0.0292479i
$310$	0.491384	+	7.72170i	0.0279087	+	0.438563i
$311$	18.4668	+	10.6618i	1.04716	+	0.604576i	0.921852	−	0.387542i	$-0.126676\pi$
$311$	18.4668	+	10.6618i	1.04716	+	0.604576i	0.125305	+	0.992118i	$0.460009\pi$
$312$	23.4106	+	22.8362i	1.32536	+	1.29285i
$313$	0.537379	+	0.767457i	0.0303745	+	0.0433792i	0.834052	−	0.551686i	$-0.186015\pi$
$313$	0.537379	+	0.767457i	0.0303745	+	0.0433792i	−0.803678	+	0.595065i	$0.797126\pi$
$314$	10.1784	−	57.7248i	0.574403	−	3.25760i
$315$	18.4555	−	4.96733i	1.03985	−	0.279877i
$316$	−16.6897	+	28.9074i	−0.938870	+	1.62617i
$317$	9.59121	−	0.839122i	0.538696	−	0.0471298i	0.185438	−	0.982656i	$-0.440630\pi$
$317$	9.59121	−	0.839122i	0.538696	−	0.0471298i	0.353258	+	0.935526i	$0.385074\pi$
$318$	20.5380	+	1.54010i	1.15171	+	0.0863646i
$319$	−7.32534	−	20.1262i	−0.410140	−	1.12685i
$320$	−24.6790	+	19.7300i	−1.37960	+	1.10294i
$321$	17.1564	+	6.00421i	0.957577	+	0.335122i
$322$	34.7780	+	34.7780i	1.93810	+	1.93810i
$323$	5.92198	−	0.270096i	0.329508	−	0.0150285i
$324$	−40.3286	−	20.6851i	−2.24048	−	1.14917i
$325$	−9.27345	−	7.17189i	−0.514399	−	0.397825i
$326$	18.8070	+	22.4133i	1.04162	+	1.24136i
$327$	7.18635	+	9.99661i	0.397406	+	0.552814i
$328$	−7.53314	+	3.51276i	−0.415948	+	0.193960i
$329$	22.6790	+	19.0299i	1.25033	+	1.04916i
$330$	21.7069	+	38.5979i	1.19492	+	2.12474i
$331$	−15.6934	−	27.1818i	−0.862589	−	1.49405i	−0.869422	−	0.494071i	$-0.835508\pi$
$331$	−15.6934	−	27.1818i	−0.862589	−	1.49405i	0.00683323	−	0.999977i	$-0.497825\pi$
$332$	−3.38850	−	4.83927i	−0.185968	−	0.265590i
$333$	9.23710	−	21.1661i	0.506190	−	1.15989i
$334$	−20.2161	+	11.6718i	−1.10618	+	0.638652i
$335$	−4.87250	−	20.0773i	−0.266213	−	1.09694i
$336$	−19.7026	−	52.1097i	−1.07486	−	2.84282i
$337$	−15.0473	−	32.2689i	−0.819676	−	1.75780i	−0.631033	−	0.775756i	$-0.717369\pi$
$337$	−15.0473	−	32.2689i	−0.819676	−	1.75780i	−0.188643	−	0.982046i	$-0.560409\pi$
$338$	−18.0366	−	8.41062i	−0.981063	−	0.457477i
$339$	1.15253	−	0.218012i	0.0625967	−	0.0118408i
$340$	12.3333	+	9.07923i	0.668869	+	0.492391i
$341$		−	5.62304i		−	0.304505i
$342$	−14.1273	−	31.6792i	−0.763919	−	1.71302i
$343$	11.8513	−	11.8513i	0.639911	−	0.639911i
$344$	6.00294	+	34.0444i	0.323657	+	1.83555i
$345$	4.09620	+	24.8705i	0.220532	+	1.33898i
$346$	21.6481	−	7.87925i	1.16381	−	0.423591i
$347$	−18.9890	+	8.85470i	−1.01938	+	0.475345i	−0.859144	−	0.511734i	$-0.829004\pi$
$347$	−18.9890	+	8.85470i	−1.01938	+	0.475345i	−0.160237	+	0.987079i	$0.551226\pi$
$348$	−17.8273	+	39.5042i	−0.955643	+	2.11765i
$349$	−22.7744	−	13.1488i	−1.21908	−	0.703839i	−0.254362	−	0.967109i	$-0.581866\pi$
$349$	−22.7744	−	13.1488i	−1.21908	−	0.703839i	−0.964722	+	0.263270i	$0.915199\pi$
$350$	17.3206	+	33.5833i	0.925823	+	1.79510i
$351$	−12.0685	−	1.66721i	−0.644167	−	0.0889893i
$352$	48.8654	−	34.2159i	2.60453	−	1.82371i
$353$	−1.42721	+	5.32640i	−0.0759625	+	0.283496i	−0.993450	−	0.114269i	$-0.963547\pi$
$353$	−1.42721	+	5.32640i	−0.0759625	+	0.283496i	0.917487	+	0.397765i	$0.130214\pi$
$354$	−4.99803	−	8.41378i	−0.265642	−	0.447187i
$355$	11.0816	+	9.75557i	0.588149	+	0.517772i
$356$	5.69686	−	15.6520i	0.301933	−	0.829555i
$357$	−5.44937	+	3.91743i	−0.288411	+	0.207332i
$358$	3.34161	−	38.1947i	0.176609	−	2.01865i
$359$	1.67434	+	9.49563i	0.0883681	+	0.501160i	0.996579	+	0.0826472i	$0.0263375\pi$
$359$	1.67434	+	9.49563i	0.0883681	+	0.501160i	−0.908211	+	0.418513i	$0.862551\pi$
$360$	13.9234	−	52.1969i	0.733827	−	2.75102i
$361$	4.84616	−	18.3716i	0.255061	−	0.966925i
$362$	−47.5962	+	47.5962i	−2.50160	+	2.50160i
$363$	−5.69623	−	11.8298i	−0.298975	−	0.620904i
$364$	−21.6239	−	25.7704i	−1.13340	−	1.35074i
$365$	1.20582	+	0.597494i	0.0631155	+	0.0312743i
$366$	39.4172	−	33.9179i	2.06037	−	1.77292i
$367$	1.11396	+	12.7326i	0.0581480	+	0.664635i	0.968206	+	0.250154i	$0.0804813\pi$
$367$	1.11396	+	12.7326i	0.0581480	+	0.664635i	−0.910058	+	0.414481i	$0.863963\pi$
$368$	70.9677	−	19.0157i	3.69945	−	0.991263i
$369$	1.48113	−	2.71918i	0.0771044	−	0.141555i
$370$	44.7644	+	8.99259i	2.32719	+	0.467502i
$371$	−12.5779	−	2.21783i	−0.653014	−	0.115144i
$372$	−7.94536	+	8.14519i	−0.411948	+	0.422308i
$373$	6.27713	+	23.4266i	0.325018	+	1.21298i	0.914294	+	0.405051i	$0.132746\pi$
$373$	6.27713	+	23.4266i	0.325018	+	1.21298i	−0.589276	+	0.807931i	$0.700587\pi$
$374$	−11.9120	−	9.99540i	−0.615957	−	0.516850i
$375$	−2.81713	+	19.1589i	−0.145476	+	0.989362i
$376$	78.6347	−	28.6207i	4.05527	−	1.47600i
$377$	−1.01536	+	11.6056i	−0.0522936	+	0.597718i
$378$	32.9840	+	21.3101i	1.69651	+	1.09607i
$379$			10.0922i			0.518401i	0.965824	+	0.259200i	$0.0834590\pi$
$379$			10.0922i			0.518401i	−0.965824	+	0.259200i	$0.916541\pi$
$380$	39.5829	−	29.0261i	2.03056	−	1.48901i
$381$	−6.21212	−	3.48443i	−0.318256	−	0.178513i
$382$	−37.1391	+	53.0402i	−1.90020	+	2.71377i
$383$	8.98122	+	0.785755i	0.458919	+	0.0401502i	0.314272	−	0.949333i	$-0.398240\pi$
$383$	8.98122	+	0.785755i	0.458919	+	0.0401502i	0.144647	+	0.989483i	$0.453795\pi$
$384$	−16.7567	−	2.74055i	−0.855111	−	0.139853i
$385$	−11.0122	−	25.1565i	−0.561232	−	1.28210i
$386$	16.5346	−	19.7052i	0.841591	−	1.00297i
$387$	−9.32950	−	8.87721i	−0.474245	−	0.451254i
$388$	24.5378	+	6.57488i	1.24572	+	0.333789i
$389$	−4.66720	+	26.4690i	−0.236636	+	1.34203i	0.602503	+	0.798116i	$0.294170\pi$
$389$	−4.66720	+	26.4690i	−0.236636	+	1.34203i	−0.839140	+	0.543916i	$0.816941\pi$
$390$	−1.82812	−	24.0176i	−0.0925706	−	1.21618i
$391$	−4.42549	−	7.66517i	−0.223807	−	0.387644i
$392$	2.32884	+	8.69133i	0.117624	+	0.438979i
$393$	−4.09370	+	9.07140i	−0.206500	+	0.457592i
$394$	9.75117	−	26.7911i	0.491257	−	1.34972i
$395$	14.0435	−	4.73740i	0.706605	−	0.238365i
$396$	−20.7468	+	61.7300i	−1.04257	+	3.10205i
$397$	−7.88266	+	11.2576i	−0.395619	+	0.565003i	−0.966707	−	0.255886i	$-0.917633\pi$
$397$	−7.88266	+	11.2576i	−0.395619	+	0.565003i	0.571088	+	0.820889i	$0.306522\pi$
$398$	−17.4477	−	17.4477i	−0.874575	−	0.874575i
$399$	6.76220	+	20.4196i	0.338534	+	1.02226i
$400$	56.3830	+	2.67630i	2.81915	+	0.133815i
$401$	7.74107	−	1.36496i	0.386570	−	0.0681628i	0.0230144	−	0.999735i	$-0.492674\pi$
$401$	7.74107	−	1.36496i	0.386570	−	0.0681628i	0.363556	+	0.931572i	$0.381563\pi$
$402$	23.9142	−	35.0721i	1.19273	−	1.74924i
$403$	−1.29261	+	2.77200i	−0.0643893	+	0.138083i
$404$	27.2306	+	9.91114i	1.35477	+	0.493097i
$405$	7.37155	+	18.7259i	0.366295	+	0.930499i
$406$	18.7753	−	32.5198i	0.931802	−	1.61393i
$407$	−32.0515	−	8.58817i	−1.58873	−	0.425700i
$408$	1.88789	+	18.8758i	0.0934644	+	0.934490i
$409$	12.5288	+	2.20917i	0.619512	+	0.109237i	0.474591	−	0.880207i	$-0.342596\pi$
$409$	12.5288	+	2.20917i	0.619512	+	0.109237i	0.144921	+	0.989443i	$0.453707\pi$
$410$	5.87403	+	1.72423i	0.290098	+	0.0851538i
$411$	−14.0948	−	23.7275i	−0.695245	−	1.17039i
$412$	0.199747	+	2.28312i	0.00984082	+	0.112481i
$413$	2.56478	+	5.50019i	0.126205	+	0.270647i
$414$	−32.2936	+	40.4869i	−1.58714	+	1.98982i
$415$	−0.290519	+	2.60696i	−0.0142610	+	0.127971i
$416$	−31.9547	+	5.63448i	−1.56671	+	0.276253i
$417$	9.85489	+	35.0328i	0.482596	+	1.71556i
$418$	−41.9815	+	26.8601i	−2.05338	+	1.31377i
$419$	6.44150			0.314688			0.157344	−	0.987544i	$-0.449707\pi$
$419$	6.44150			0.314688			0.157344	+	0.987544i	$0.449707\pi$
$420$	−19.5946	+	52.0004i	−0.956120	+	2.53736i
$421$	−2.00561	+	1.68290i	−0.0977473	+	0.0820197i	−0.690352	−	0.723474i	$-0.742544\pi$
$421$	−2.00561	+	1.68290i	−0.0977473	+	0.0820197i	0.592604	+	0.805494i	$0.298100\pi$
$422$	23.7310	−	50.8913i	1.15521	−	2.47735i
$423$	−17.2407	+	25.9720i	−0.838271	+	1.26280i
$424$	−23.2051	+	27.6548i	−1.12694	+	1.34303i
$425$	−1.44657	−	6.64439i	−0.0701692	−	0.322300i
$426$	0.376701	+	30.3323i	0.0182512	+	1.46961i
$427$	−26.4157	+	18.4965i	−1.27834	+	0.895106i
$428$	−43.2917	+	30.3132i	−2.09258	+	1.46524i
$429$	0.217381	+	17.5037i	0.0104953	+	0.845089i
$430$	13.2498	−	21.7419i	0.638964	−	1.04849i
$431$	−11.3033	+	13.4707i	−0.544459	+	0.648861i	−0.966181	−	0.257864i	$-0.916981\pi$
$431$	−11.3033	+	13.4707i	−0.544459	+	0.648861i	0.421722	+	0.906725i	$0.361426\pi$
$432$	52.2045	−	26.7542i	2.51169	−	1.28721i
$433$	9.03144	−	19.3680i	0.434023	−	0.930766i	−0.560685	−	0.828029i	$-0.689462\pi$
$433$	9.03144	−	19.3680i	0.434023	−	0.930766i	0.994709	−	0.102737i	$-0.0327600\pi$
$434$	7.55207	−	6.33694i	0.362511	−	0.304183i
$435$	17.5317	−	7.93528i	0.840579	−	0.380468i
$436$	−35.7965			−1.71434
$437$	−27.6835	+	6.19377i	−1.32428	+	0.296288i
$438$	0.748751	+	2.66171i	0.0357767	+	0.127181i
$439$	16.5082	−	2.91084i	0.787894	−	0.138927i	0.234798	−	0.972044i	$-0.424557\pi$
$439$	16.5082	−	2.91084i	0.787894	−	0.138927i	0.553097	+	0.833117i	$0.313446\pi$
$440$	−77.1433	−	8.59683i	−3.67766	−	0.409838i
$441$	−2.62047	−	2.09017i	−0.124784	−	0.0995318i
$442$	3.57460	+	7.66576i	0.170026	+	0.364623i
$443$	−2.18722	−	25.0000i	−0.103918	−	1.18779i	−0.851768	−	0.523919i	$-0.824469\pi$
$443$	−2.18722	−	25.0000i	−0.103918	−	1.18779i	0.747850	−	0.663868i	$-0.231086\pi$
$444$	34.2927	+	57.7290i	1.62746	+	2.73970i
$445$	−6.49081	+	3.54497i	−0.307694	+	0.168047i
$446$	−4.34169	−	0.765558i	−0.205585	−	0.0362502i
$447$	1.31813	+	13.1792i	0.0623456	+	0.623354i
$448$	38.8867	+	10.4197i	1.83722	+	0.492283i
$449$	16.7274	−	28.9728i	0.789417	−	1.36731i	−0.136908	−	0.990584i	$-0.543716\pi$
$449$	16.7274	−	28.9728i	0.789417	−	1.36731i	0.926325	−	0.376726i	$-0.122950\pi$
$450$	−33.0998	+	22.0794i	−1.56034	+	1.04083i
$451$	−4.18071	−	1.52165i	−0.196862	−	0.0716519i
$452$	−1.44131	+	3.09091i	−0.0677937	+	0.145384i
$453$	−4.01299	+	5.88536i	−0.188547	+	0.276518i
$454$	47.1897	−	8.32081i	2.21472	−	0.390515i
$455$	−0.354207	+	14.9329i	−0.0166055	+	0.700066i
$456$	59.5415	+	12.3056i	2.78828	+	0.576262i
$457$	16.9746	+	16.9746i	0.794038	+	0.794038i	0.982148	−	0.188110i	$-0.0602362\pi$
$457$	16.9746	+	16.9746i	0.794038	+	0.794038i	−0.188110	+	0.982148i	$0.560236\pi$
$458$	−13.0475	+	18.6337i	−0.609668	+	0.870696i
$459$	−4.74094	−	5.24054i	−0.221288	−	0.244607i
$460$	−65.6665	−	32.5383i	−3.06172	−	1.51711i
$461$	9.46215	−	25.9971i	0.440696	−	1.21080i	−0.498339	−	0.866982i	$-0.666056\pi$
$461$	9.46215	−	25.9971i	0.440696	−	1.21080i	0.939035	−	0.343821i	$-0.111721\pi$
$462$	23.2086	−	51.4290i	1.07976	−	2.39270i
$463$	9.83134	+	36.6911i	0.456901	+	1.70518i	0.682438	+	0.730943i	$0.260920\pi$
$463$	9.83134	+	36.6911i	0.456901	+	1.70518i	−0.225537	+	0.974235i	$0.572414\pi$
$464$	−28.0469	−	48.5786i	−1.30204	−	2.25520i
$465$	5.03772	−	0.383451i	0.233619	−	0.0177821i
$466$	−0.0971512	+	0.550972i	−0.00450044	+	0.0255233i
$467$	41.3539	+	11.0807i	1.91363	+	0.512755i	0.992280	+	0.124020i	$0.0395787\pi$
$467$	41.3539	+	11.0807i	1.91363	+	0.512755i	0.921349	+	0.388735i	$0.127088\pi$
$468$	24.4179	−	25.6620i	1.12872	−	1.18623i
$469$	−16.9208	+	20.1654i	−0.781330	+	0.931153i
$470$	−57.3997	−	22.4471i	−2.64765	−	1.03541i
$471$	−37.7726	−	6.17770i	−1.74047	−	0.284653i
$472$	17.0885	+	1.49505i	0.786563	+	0.0688153i
$473$	−10.6133	+	15.1573i	−0.487998	+	0.696934i
$474$	26.5593	+	14.8974i	1.21991	+	0.684258i
$475$	−21.7080	−	1.93975i	−0.996031	−	0.0890019i
$476$		−	19.5134i		−	0.894396i
$477$	0.839035	−	13.4223i	0.0384168	−	0.614563i
$478$	5.18651	−	59.2821i	0.237225	−	2.71150i
$479$	−16.6628	+	6.06477i	−0.761344	+	0.277106i	−0.693371	−	0.720581i	$-0.743875\pi$
$479$	−16.6628	+	6.06477i	−0.761344	+	0.277106i	−0.0679727	+	0.997687i	$0.521653\pi$
$480$	33.9865	+	41.4455i	1.55126	+	1.89172i
$481$	13.8263	+	11.6016i	0.630424	+	0.528988i
$482$	3.75685	+	14.0208i	0.171120	+	0.638628i
$483$	22.4255	−	22.9895i	1.02039	−	1.04606i
$484$	37.5954	+	6.62907i	1.70888	+	0.301322i
$485$	−6.24875	−	9.39047i	−0.283741	−	0.426399i
$486$	−18.4126	+	37.0233i	−0.835214	+	1.67941i
$487$	−13.8823	+	3.71974i	−0.629065	+	0.168558i	−0.559246	−	0.829002i	$-0.688909\pi$
$487$	−13.8823	+	3.71974i	−0.629065	+	0.168558i	−0.0698199	+	0.997560i	$0.522242\pi$
$488$	7.94423	+	90.8029i	0.359618	+	4.11045i
$489$	14.4817	−	12.4613i	0.654887	−	0.563521i
$490$	2.94239	−	5.93812i	0.132924	−	0.268257i
$491$	12.1688	+	14.5022i	0.549171	+	0.654477i	0.967218	−	0.253949i	$-0.0817295\pi$
$491$	12.1688	+	14.5022i	0.549171	+	0.654477i	−0.418047	+	0.908426i	$0.637285\pi$
$492$	3.90582	+	8.11152i	0.176088	+	0.365695i
$493$	−4.77830	+	4.77830i	−0.215204	+	0.215204i
$494$	26.8702	−	3.59070i	1.20895	−	0.161553i
$495$	25.0256	−	14.4860i	1.12482	−	0.651096i
$496$	−2.55729	−	14.5031i	−0.114826	−	0.651209i
$497$	1.63952	−	18.7399i	0.0735427	−	0.840597i
$498$	−4.37614	+	3.14591i	−0.196100	+	0.140972i
$499$	4.27036	−	11.7327i	0.191167	−	0.525228i	−0.806667	−	0.591006i	$-0.798731\pi$
$499$	4.27036	−	11.7327i	0.191167	−	0.525228i	0.997834	+	0.0657783i	$0.0209530\pi$
$500$	−40.4497	−	39.1661i	−1.80896	−	1.75156i
$501$	7.78475	+	13.1050i	0.347797	+	0.585489i
$502$	9.50006	−	35.4547i	0.424009	−	1.58242i
$503$	11.9549	−	8.37091i	0.533043	−	0.373240i	−0.275846	−	0.961202i	$-0.588958\pi$
$503$	11.9549	−	8.37091i	0.533043	−	0.373240i	0.808889	+	0.587961i	$0.200069\pi$
$504$	−64.0766	+	25.1411i	−2.85420	+	1.11987i
$505$	−6.16736	−	11.2924i	−0.274444	−	0.502506i
$506$	64.4425	+	37.2059i	2.86482	+	1.65400i
$507$	−5.34526	+	11.8448i	−0.237391	+	0.526045i
$508$	18.7690	−	8.75211i	0.832738	−	0.388312i
$509$	22.1716	−	8.06979i	0.982737	−	0.357687i	0.199834	−	0.979830i	$-0.435960\pi$
$509$	22.1716	−	8.06979i	0.982737	−	0.357687i	0.782904	+	0.622143i	$0.213738\pi$
$510$	8.14262	−	11.3537i	0.360561	−	0.502750i
$511$	−0.297749	−	1.68862i	−0.0131717	−	0.0747002i
$512$	−18.0980	+	18.0980i	−0.799828	+	0.799828i
$513$	−20.5697	+	9.48099i	−0.908173	+	0.418596i
$514$			8.73949i			0.385483i
$515$	0.603282	−	0.819505i	0.0265838	−	0.0361117i
$516$	36.7910	−	6.95939i	1.61963	−	0.306370i
$517$	40.5946	+	18.9296i	1.78535	+	0.832521i
$518$	−24.5863	−	52.7255i	−1.08026	−	2.31663i
$519$	−5.32011	−	14.0707i	−0.233527	−	0.617635i
$520$	36.0533	+	21.9714i	1.58104	+	0.963512i
$521$	−19.8465	+	11.4584i	−0.869490	+	0.502000i	−0.867179	−	0.497997i	$-0.834069\pi$
$521$	−19.8465	+	11.4584i	−0.869490	+	0.502000i	−0.00231129	+	0.999997i	$0.500736\pi$
$522$	36.2389	+	15.8150i	1.58613	+	0.692205i
$523$	8.48991	+	12.1248i	0.371238	+	0.530182i	0.960691	−	0.277620i	$-0.0895457\pi$
$523$	8.48991	+	12.1248i	0.371238	+	0.530182i	−0.589453	+	0.807803i	$0.700657\pi$
$524$	−14.4684	−	25.0599i	−0.632054	−	1.09475i
$525$	21.7869	−	11.5814i	0.950860	−	0.505452i
$526$	−22.3370	−	18.7429i	−0.973938	−	0.817231i
$527$	−1.60790	+	0.749777i	−0.0700413	+	0.0326608i
$528$	−49.1982	−	68.4374i	−2.14108	−	2.97836i
$529$	12.4409	+	14.8264i	0.540907	+	0.644628i
$530$	26.2870	−	3.99488i	1.14183	−	0.173526i
$531$	−5.45305	+	3.33157i	−0.236642	+	0.144578i
$532$	−59.6834	−	18.6906i	−2.58760	−	0.810341i
$533$	1.71118	+	1.71118i	0.0741195	+	0.0741195i
$534$	−14.3428	−	5.01953i	−0.620672	−	0.217216i
$535$	23.3217	+	2.59896i	1.00828	+	0.112363i
$536$	25.4486	+	69.9194i	1.09921	+	3.02006i
$537$	−24.9654	−	1.87211i	−1.07734	−	0.0807875i
$538$	−55.1632	+	4.82615i	−2.37825	+	0.208070i
$539$	−2.40811	+	4.17097i	−0.103725	+	0.179656i
$540$	−56.7191	−	14.3776i	−2.44080	−	0.618715i
$541$	−5.89747	+	33.4462i	−0.253552	+	1.43797i	0.546210	+	0.837648i	$0.316070\pi$
$541$	−5.89747	+	33.4462i	−0.253552	+	1.43797i	−0.799762	+	0.600317i	$0.795041\pi$
$542$	49.1215	+	70.1527i	2.10995	+	3.01332i
$543$	31.4628	+	30.6909i	1.35020	+	1.31707i
$544$	−16.2997	−	9.41064i	−0.698844	−	0.403478i
$545$	11.9300	+	10.5025i	0.511025	+	0.449876i
$546$	−23.2636	+	20.0180i	−0.995589	+	0.856690i
$547$	−9.74744	−	4.54531i	−0.416770	−	0.194343i	0.202910	−	0.979197i	$-0.434960\pi$
$547$	−9.74744	−	4.54531i	−0.416770	−	0.194343i	−0.619681	+	0.784854i	$0.712738\pi$
$548$	79.9372	+	6.99360i	3.41475	+	0.298752i
$549$	−22.4655	−	25.4615i	−0.958805	−	1.08667i
$550$	38.4625	+	42.2959i	1.64005	+	1.80350i
$551$	10.0380	+	19.1917i	0.427634	+	0.817592i
$552$	−24.5818	−	87.3852i	−1.04627	−	3.71936i
$553$	−15.4691	−	10.8316i	−0.657812	−	0.460605i
$554$	19.8062	−	16.6193i	0.841483	−	0.706088i
$555$	5.50851	−	29.3008i	0.233823	−	1.24375i
$556$	−99.4313	−	36.1900i	−4.21683	−	1.53480i
$557$	3.25175	−	0.284491i	0.137781	−	0.0120543i	−0.0180565	−	0.999837i	$-0.505748\pi$
$557$	3.25175	−	0.284491i	0.137781	−	0.0120543i	0.155838	+	0.987783i	$0.450192\pi$
$558$	7.52030	+	7.15571i	0.318360	+	0.302926i
$559$	8.71636	−	5.03239i	0.368663	−	0.212847i
$560$	−39.8438	−	59.8762i	−1.68371	−	2.53023i
$561$	−6.42967	+	7.85874i	−0.271461	+	0.331796i
$562$	−1.18429	+	4.41984i	−0.0499564	+	0.186440i
$563$	−27.4678	+	7.35998i	−1.15763	+	0.310186i	−0.786019	−	0.618202i	$-0.787861\pi$
$563$	−27.4678	+	7.35998i	−1.15763	+	0.310186i	−0.371611	+	0.928388i	$0.621195\pi$
$564$	−32.0553	−	84.7803i	−1.34977	−	3.56989i
$565$	1.38720	−	0.607243i	0.0583601	−	0.0255469i
$566$	−18.8786	−	51.8684i	−0.793525	−	2.18019i
$567$	13.6465	−	21.7089i	0.573097	−	0.911689i
$568$	−43.5557	−	30.4980i	−1.82756	−	1.27967i
$569$	27.5407			1.15456			0.577282	−	0.816545i	$-0.304113\pi$
$569$	27.5407			1.15456			0.577282	+	0.816545i	$0.304113\pi$
$570$	−26.9270	−	35.7799i	−1.12785	−	1.49865i
$571$	−2.98783			−0.125037			−0.0625185	−	0.998044i	$-0.519913\pi$
$571$	−2.98783			−0.125037			−0.0625185	+	0.998044i	$0.519913\pi$
$572$	−41.6921	−	29.1931i	−1.74324	−	1.22063i
$573$	34.9325	+	23.8190i	1.45933	+	0.995054i
$574$	−2.66782	−	7.32978i	−0.111353	−	0.305939i
$575$	12.3383	+	30.1103i	0.514544	+	1.25569i
$576$	−6.32207	+	41.9168i	−0.263419	+	1.74653i
$577$	−22.5551	+	6.04363i	−0.938982	+	0.251600i	−0.695681	−	0.718351i	$-0.744897\pi$
$577$	−22.5551	+	6.04363i	−0.938982	+	0.251600i	−0.243302	+	0.969951i	$0.578230\pi$
$578$	10.4012	−	38.8177i	0.432632	−	1.61461i
$579$	−13.0001	−	10.6361i	−0.540267	−	0.442022i
$580$	−11.0199	+	54.8564i	−0.457578	+	2.27779i
$581$	2.89446	−	1.67112i	0.120082	−	0.0693295i
$582$	5.71982	−	22.4586i	0.237094	−	0.930939i
$583$	−19.2497	+	1.68413i	−0.797241	+	0.0697496i
$584$	−4.55433	−	1.65764i	−0.188460	−	0.0685937i
$585$	−15.6669	+	1.38838i	−0.647746	+	0.0574026i
$586$	−4.74981	+	3.98556i	−0.196213	+	0.164642i
$587$	0.445063	+	0.311637i	0.0183697	+	0.0128626i	0.582725	−	0.812669i	$-0.301986\pi$
$587$	0.445063	+	0.311637i	0.0183697	+	0.0128626i	−0.564356	+	0.825532i	$0.690875\pi$
$588$	9.38182	−	2.63915i	0.386900	−	0.108837i
$589$	0.753153	+	5.63607i	0.0310331	+	0.232230i
$590$	−8.71928	−	9.14298i	−0.358967	−	0.376410i
$591$	−17.5717	−	6.14955i	−0.722803	−	0.252959i
$592$	−86.5738	−	7.57423i	−3.55816	−	0.311299i
$593$	−11.1879	−	5.21700i	−0.459431	−	0.214236i	0.179102	−	0.983831i	$-0.442681\pi$
$593$	−11.1879	−	5.21700i	−0.459431	−	0.214236i	−0.638533	+	0.769594i	$0.720459\pi$
$594$	56.5470	+	18.2265i	2.32015	+	0.747843i
$595$	−5.72512	+	6.50329i	−0.234707	+	0.266609i
$596$	−33.3507	−	19.2551i	−1.36610	−	0.788718i
$597$	−11.2506	+	11.5335i	−0.460456	+	0.472037i
$598$	−23.2156	−	33.1553i	−0.949356	−	1.35582i
$599$	−6.54489	+	37.1179i	−0.267417	+	1.51660i	0.494647	+	0.869094i	$0.335297\pi$
$599$	−6.54489	+	37.1179i	−0.267417	+	1.51660i	−0.762064	+	0.647502i	$0.775814\pi$
$600$	2.44134	−	69.6994i	0.0996673	−	2.84547i
$601$	−14.7171	+	25.4908i	−0.600323	+	1.03979i	0.392449	+	0.919774i	$0.371628\pi$
$601$	−14.7171	+	25.4908i	−0.600323	+	1.03979i	−0.992772	+	0.120016i	$0.961705\pi$
$602$	−32.3179	+	2.82745i	−1.31718	+	0.115238i
$603$	−23.0934	−	15.3299i	−0.940437	−	0.624280i
$604$	−7.08367	−	19.4622i	−0.288231	−	0.791907i
$605$	−10.5846	−	13.2395i	−0.430324	−	0.538264i
$606$	8.73274	−	24.9529i	0.354743	−	1.01364i
$607$	−20.3389	−	20.3389i	−0.825532	−	0.825532i	0.161363	−	0.986895i	$-0.448411\pi$
$607$	−20.3389	−	20.3389i	−0.825532	−	0.825532i	−0.986895	+	0.161363i	$0.948411\pi$
$608$	−44.3957	+	40.8402i	−1.80048	+	1.65629i
$609$	−21.3853	−	11.9952i	−0.866574	−	0.486070i
$610$	39.7994	−	54.0639i	1.61143	−	2.18898i
$611$	−15.6605	−	18.6635i	−0.633558	−	0.755044i
$612$	20.4180	−	2.29857i	0.825349	−	0.0929140i
$613$	−14.2020	+	6.62249i	−0.573612	+	0.267480i	−0.687705	−	0.725990i	$-0.741382\pi$
$613$	−14.2020	+	6.62249i	−0.573612	+	0.267480i	0.114093	+	0.993470i	$0.463604\pi$
$614$	35.8917	+	30.1167i	1.44847	+	1.21541i
$615$	1.07817	−	3.84929i	0.0434758	−	0.155218i
$616$	49.4504	+	85.6505i	1.99241	+	3.45096i
$617$	−1.71798	−	2.45352i	−0.0691631	−	0.0987752i	0.783080	−	0.621921i	$-0.213647\pi$
$617$	−1.71798	−	2.45352i	−0.0691631	−	0.0987752i	−0.852243	+	0.523145i	$0.824758\pi$
$618$	2.08046	−	0.208081i	0.0836886	−	0.00837023i
$619$	11.2889	−	6.51763i	0.453738	−	0.261966i	−0.255670	−	0.966764i	$-0.582296\pi$
$619$	11.2889	−	6.51763i	0.453738	−	0.261966i	0.709407	+	0.704799i	$0.248963\pi$
$620$	−7.64447	+	12.5439i	−0.307009	+	0.503776i
$621$	26.6968	+	20.7570i	1.07131	+	0.832951i
$622$	23.9041	+	51.2625i	0.958468	+	2.05544i
$623$	8.54045	+	3.98248i	0.342166	+	0.159555i
$624$	8.52116	+	45.0473i	0.341119	+	1.80333i
$625$	1.98967	+	24.9207i	0.0795869	+	0.996828i
$626$			2.48515i			0.0993265i
$627$	17.8781	+	27.1931i	0.713982	+	1.08599i
$628$	78.6899	−	78.6899i	3.14007	−	3.14007i
$629$	1.81797	+	10.3102i	0.0724873	+	0.411096i
$630$	47.6583	+	17.2857i	1.89875	+	0.688678i
$631$	20.8571	−	7.59137i	0.830308	−	0.302208i	0.108323	−	0.994116i	$-0.465452\pi$
$631$	20.8571	−	7.59137i	0.830308	−	0.302208i	0.721985	+	0.691908i	$0.243230\pi$
$632$	−48.3764	+	22.5583i	−1.92431	+	0.897320i
$633$	−33.4207	−	15.0819i	−1.32835	−	0.599454i
$634$	22.1168	+	12.7691i	0.878371	+	0.507128i
$635$	−8.82301	−	2.58986i	−0.350130	−	0.102775i
$636$	30.2636	+	24.7603i	1.20003	+	0.981810i
$637$	2.14594	−	1.50260i	0.0850253	−	0.0595353i
$638$	14.7040	−	54.8760i	0.582136	−	2.17256i
$639$	19.8017	−	0.491916i	0.783344	−	0.0194599i
$640$	−21.8760	+	1.39211i	−0.864723	+	0.0550281i
$641$	−0.525380	+	1.44347i	−0.0207513	+	0.0570136i	−0.949636	−	0.313356i	$-0.898547\pi$
$641$	−0.525380	+	1.44347i	−0.0207513	+	0.0570136i	0.928884	+	0.370370i	$0.120769\pi$
$642$	28.1430	+	39.1486i	1.11072	+	1.54507i
$643$	−0.984458	+	11.2524i	−0.0388232	+	0.443752i	0.951760	+	0.306842i	$0.0992724\pi$
$643$	−0.984458	+	11.2524i	−0.0388232	+	0.443752i	−0.990584	+	0.136909i	$0.956283\pi$
$644$	16.2148	+	91.9589i	0.638954	+	3.62369i
$645$	−14.3033	−	8.47487i	−0.563191	−	0.333698i
$646$	13.2784	+	8.42304i	0.522433	+	0.331400i
$647$	−21.2552	+	21.2552i	−0.835628	+	0.835628i	−0.988280	−	0.152652i	$-0.951219\pi$
$647$	−21.2552	+	21.2552i	−0.835628	+	0.835628i	0.152652	+	0.988280i	$0.451219\pi$
$648$	−33.8544	−	64.0856i	−1.32993	−	2.51752i
$649$	5.90190	+	7.03361i	0.231670	+	0.276093i
$650$	−9.23813	−	29.6923i	−0.362349	−	1.16463i
$651$	−4.19879	−	4.87956i	−0.164564	−	0.191245i
$652$	4.84140	+	55.3375i	0.189604	+	2.16718i
$653$	−9.62023	+	2.57773i	−0.376469	+	0.100874i	−0.442091	−	0.896970i	$-0.645763\pi$
$653$	−9.62023	+	2.57773i	−0.376469	+	0.100874i	0.0656227	+	0.997845i	$0.479097\pi$
$654$	0.405542	+	32.6546i	0.0158579	+	1.27690i
$655$	−2.53052	+	12.5967i	−0.0988756	+	0.492195i
$656$	−11.4750	−	2.02336i	−0.448025	−	0.0789989i
$657$	1.73183	−	0.510462i	0.0675651	−	0.0199150i
$658$	20.3249	+	75.8537i	0.792349	+	2.95709i
$659$	17.9458	+	15.0583i	0.699067	+	0.586587i	0.921508	−	0.388359i	$-0.126958\pi$
$659$	17.9458	+	15.0583i	0.699067	+	0.586587i	−0.222441	+	0.974946i	$0.571402\pi$
$660$	−8.27317	+	83.6656i	−0.322033	+	3.25668i
$661$	−4.53415	+	1.65030i	−0.176358	+	0.0641891i	−0.428690	−	0.903452i	$-0.641025\pi$
$661$	−4.53415	+	1.65030i	−0.176358	+	0.0641891i	0.252332	+	0.967641i	$0.418803\pi$
$662$	7.25616	−	82.9382i	0.282019	−	3.22349i
$663$	4.97619	−	2.39611i	0.193259	−	0.0930573i
$664$		−	9.44701i		−	0.366615i
$665$	14.4072	+	23.7398i	0.558686	+	0.920591i
$666$	52.2736	−	31.9368i	2.02556	−	1.23753i
$667$	18.5476	−	26.4888i	0.718168	−	1.02565i
$668$	−44.1504	−	3.86266i	−1.70823	−	0.149451i
$669$	−0.464647	+	2.84102i	−0.0179643	+	0.109840i
$670$	19.9592	−	51.0379i	0.771092	−	1.97177i
$671$	−31.3608	+	37.3743i	−1.21067	+	1.44282i
$672$	16.8549	−	66.1802i	0.650194	−	2.55296i
$673$	−35.4739	−	9.50520i	−1.36742	−	0.366398i	−0.500883	−	0.865515i	$-0.666991\pi$
$673$	−35.4739	−	9.50520i	−1.36742	−	0.366398i	−0.866535	+	0.499117i	$0.833658\pi$
$674$	16.3999	−	93.0087i	0.631702	−	3.58256i
$675$	14.6846	+	21.4327i	0.565212	+	0.824946i
$676$	−18.8918	−	32.7215i	−0.726606	−	1.25852i
$677$	−7.05498	−	26.3295i	−0.271145	−	1.01193i	−0.958381	−	0.285492i	$-0.907843\pi$
$677$	−7.05498	−	26.3295i	−0.271145	−	1.01193i	0.687236	−	0.726434i	$-0.258824\pi$
$678$	2.83595	+	1.27979i	0.108914	+	0.0491501i
$679$	−4.91546	+	13.5051i	−0.188638	+	0.518279i
$680$	7.82804	+	23.2053i	0.300192	+	0.889884i
$681$	−5.81553	−	30.7439i	−0.222851	−	1.17811i
$682$	8.55511	−	12.2180i	0.327592	−	0.467850i
$683$	−10.9376	−	10.9376i	−0.418514	−	0.418514i	0.466177	−	0.884691i	$-0.345631\pi$
$683$	−10.9376	−	10.9376i	−0.418514	−	0.418514i	−0.884691	+	0.466177i	$0.845631\pi$
$684$	12.5267	−	64.6519i	0.478971	−	2.47203i
$685$	−24.5890	−	25.7839i	−0.939498	−	0.985151i
$686$	43.7820	−	7.71995i	1.67161	−	0.294749i
$687$	12.2722	+	8.36794i	0.468215	+	0.319257i
$688$	−20.4807	+	43.9209i	−0.780818	+	1.67447i
$689$	9.87672	+	3.59483i	0.376273	+	0.136952i
$690$	−28.9385	+	60.2716i	−1.10167	+	2.29450i
$691$	8.01630	−	13.8846i	0.304954	−	0.528197i	−0.672297	−	0.740282i	$-0.734692\pi$
$691$	8.01630	−	13.8846i	0.304954	−	0.528197i	0.977251	+	0.212085i	$0.0680254\pi$
$692$	42.2474	+	11.3202i	1.60600	+	0.430328i
$693$	−33.7676	−	14.7365i	−1.28272	−	0.559794i
$694$	−54.7318	−	9.65070i	−2.07759	−	0.366335i
$695$	22.5198	+	41.2337i	0.854226	+	1.56408i
$696$	−59.5861	+	35.3958i	−2.25860	+	1.34168i
$697$	0.122341	+	1.39837i	0.00463401	+	0.0529669i
$698$	−29.4800	−	63.2200i	−1.11583	−	2.39291i
$699$	0.360532	+	0.0589649i	0.0136366	+	0.00223026i
$700$	−9.63401	+	71.0903i	−0.364131	+	2.68696i
$701$	3.96523	−	0.699177i	0.149765	−	0.0264075i	−0.0982631	−	0.995160i	$-0.531329\pi$
$701$	3.96523	−	0.699177i	0.149765	−	0.0264075i	0.248028	+	0.968753i	$0.420218\pi$
$702$	−23.6863	−	21.9840i	−0.893981	−	0.829733i
$703$	33.2760	+	4.31507i	1.25503	+	0.162746i
$704$	60.9087			2.29558
$705$	−14.1909	+	37.6598i	−0.534459	+	1.41835i
$706$	−11.2049	+	9.40201i	−0.421701	+	0.353849i
$707$	−6.92852	+	14.8583i	−0.260574	+	0.558803i
$708$	1.38936	−	18.5278i	0.0522155	−	0.696318i
$709$	13.0986	−	15.6103i	0.491928	−	0.586256i	−0.461779	−	0.886995i	$-0.652789\pi$
$709$	13.0986	−	15.6103i	0.491928	−	0.586256i	0.953707	+	0.300739i	$0.0972331\pi$
$710$	9.23598	+	38.0572i	0.346620	+	1.42826i
$711$	9.51152	−	17.4621i	0.356710	−	0.654879i
$712$	21.8186	−	15.2776i	0.817688	−	0.572551i
$713$	6.95436	−	4.86950i	0.260443	−	0.182364i
$714$	−17.8007	+	0.221070i	−0.666175	+	0.00827332i
$715$	5.32977	+	21.9615i	0.199322	+	0.821314i
$716$	46.7896	−	55.7617i	1.74861	−	2.08391i
$717$	−38.7489	−	2.90570i	−1.44710	−	0.108515i
$718$	−10.8090	+	23.1799i	−0.403386	+	0.865065i
$719$	2.88616	−	2.42178i	0.107636	−	0.0903170i	−0.587382	−	0.809310i	$-0.699841\pi$
$719$	2.88616	−	2.42178i	0.107636	−	0.0903170i	0.695017	+	0.718993i	$0.255397\pi$
$720$	57.9586	−	48.7439i	2.15999	−	1.81658i
$721$	−1.29660			−0.0482877
$722$	38.4811	−	32.5453i	1.43212	−	1.21121i
$723$	9.12406	−	2.56664i	0.339327	−	0.0954543i
$724$	−125.852	+	22.1912i	−4.67727	+	0.824728i
$725$	19.7672	−	15.0490i	0.734135	−	0.558905i
$726$	5.62132	−	34.3707i	0.208627	−	1.27562i
$727$	14.2060	+	30.4649i	0.526872	+	1.12988i	0.972122	+	0.234474i	$0.0753368\pi$
$727$	14.2060	+	30.4649i	0.526872	+	1.12988i	−0.445251	+	0.895406i	$0.646885\pi$
$728$	−4.68859	−	53.5908i	−0.173771	−	1.98621i
$729$	24.3228	+	11.7219i	0.900844	+	0.434144i
$730$	1.71100	+	3.13284i	0.0633271	+	0.115952i
$731$	5.74939	+	1.01377i	0.212649	+	0.0374957i
$732$	98.2372	−	9.82534i	3.63095	−	0.363155i
$733$	−25.3115	−	6.78219i	−0.934901	−	0.250506i	−0.240958	−	0.970536i	$-0.577462\pi$
$733$	−25.3115	−	6.78219i	−0.934901	−	0.250506i	−0.693943	+	0.720029i	$0.744128\pi$
$734$	−16.9514	+	29.3607i	−0.625687	+	1.08372i
$735$	−3.90101	−	1.87301i	−0.143891	−	0.0690871i
$736$	84.6338	+	30.8042i	3.11964	+	1.13546i
$737$	−16.8315	+	36.0954i	−0.619998	+	1.32959i
$738$	7.35532	−	3.65490i	0.270753	−	0.134539i
$739$	26.1233	−	4.60625i	0.960962	−	0.169444i	0.328903	−	0.944364i	$-0.393321\pi$
$739$	26.1233	−	4.60625i	0.960962	−	0.169444i	0.632059	+	0.774920i	$0.282210\pi$
$740$	59.8251	+	62.7322i	2.19922	+	2.30608i
$741$	−2.56235	−	17.5152i	−0.0941301	−	0.643436i
$742$	−23.9555	−	23.9555i	−0.879435	−	0.879435i
$743$	−1.18129	+	1.68705i	−0.0433373	+	0.0618920i	−0.840236	−	0.542221i	$-0.817584\pi$
$743$	−1.18129	+	1.68705i	−0.0433373	+	0.0618920i	0.796899	+	0.604113i	$0.206472\pi$
$744$	−17.8786	+	3.38193i	−0.655462	+	0.123987i
$745$	5.46558	+	16.2021i	0.200243	+	0.593599i
$746$	−22.0029	+	60.4524i	−0.805583	+	2.21332i
$747$	2.08953	+	2.83179i	0.0764521	+	0.103610i
$748$	−7.64102	−	28.5167i	−0.279383	−	1.04267i
$749$	−14.9496	−	25.8935i	−0.546248	−	0.946129i
$750$	−35.2703	+	37.3431i	−1.28789	+	1.36358i
$751$	1.29044	−	7.31846i	0.0470889	−	0.267055i	−0.952169	−	0.305572i	$-0.901152\pi$
$751$	1.29044	−	7.31846i	0.0470889	−	0.267055i	0.999258	+	0.0385173i	$0.0122635\pi$
$752$	113.312	+	30.3617i	4.13205	+	1.10718i
$753$	−23.2264	−	5.91535i	−0.846416	−	0.215567i
$754$	−19.8634	+	23.6723i	−0.723382	+	0.862093i
$755$	−3.34930	+	8.56454i	−0.121894	+	0.311696i
$756$	28.0909	+	69.0599i	1.02166	+	2.51169i
$757$	28.6205	+	2.50397i	1.04023	+	0.0910084i	0.594449	−	0.804133i	$-0.297370\pi$
$757$	28.6205	+	2.50397i	1.04023	+	0.0910084i	0.445781	+	0.895142i	$0.352926\pi$
$758$	−15.3546	+	21.9287i	−0.557706	+	0.796486i
$759$	23.7701	−	42.3779i	0.862802	−	1.53822i
$760$	78.4734	−	1.71587i	2.84653	−	0.0622410i
$761$		−	24.8615i		−	0.901229i	−0.892719	−	0.450614i	$-0.851205\pi$
$761$		−	24.8615i		−	0.901229i	0.892719	−	0.450614i	$-0.148795\pi$
$762$	−8.19658	−	17.0225i	−0.296931	−	0.616659i
$763$	1.76505	−	20.1746i	0.0638991	−	0.730370i
$764$	−115.518	+	42.0451i	−4.17929	+	1.52114i
$765$	−7.47915	−	5.22447i	−0.270409	−	0.188891i
$766$	18.3193	+	15.3717i	0.661902	+	0.555402i
$767$	−1.29261	−	4.82408i	−0.0466734	−	0.174188i
$768$	2.79914	+	2.73047i	0.101005	+	0.0985272i
$769$	−26.1155	−	4.60486i	−0.941748	−	0.166056i	−0.318362	−	0.947969i	$-0.603133\pi$
$769$	−26.1155	−	4.60486i	−0.941748	−	0.166056i	−0.623387	+	0.781914i	$0.714244\pi$
$770$	14.3464	−	71.4154i	0.517009	−	2.57363i
$771$	5.70625	−	0.0708667i	0.205505	−	0.00255220i
$772$	47.1731	−	12.6400i	1.69780	−	0.454923i
$773$	−4.07430	−	46.5695i	−0.146542	−	1.67499i	−0.612722	−	0.790298i	$-0.709926\pi$
$773$	−4.07430	−	46.5695i	−0.146542	−	1.67499i	0.466180	−	0.884690i	$-0.345630\pi$
$774$	−6.76538	−	33.4830i	−0.243176	−	1.20352i
$775$	6.22801	−	1.93771i	0.223717	−	0.0696046i
$776$	26.1119	+	31.1189i	0.937362	+	1.11710i
$777$	−34.2265	+	16.4806i	−1.22787	+	0.591238i
$778$	−50.4120	+	50.4120i	−1.80736	+	1.80736i
$779$	4.39421	+	0.965213i	0.157439	+	0.0345823i
$780$	23.3112	−	39.3430i	0.834676	−	1.40871i
$781$	−4.94213	−	28.0282i	−0.176843	−	1.00293i
$782$	2.04621	−	23.3883i	0.0731723	−	0.836363i
$783$	10.0322	−	23.7896i	0.358522	−	0.850171i
$784$	−4.31416	+	11.8531i	−0.154077	+	0.423324i
$785$	−49.3123	+	3.13808i	−1.76003	+	0.112003i
$786$	−22.6965	+	13.4824i	−0.809558	+	0.480901i
$787$	8.51768	−	31.7884i	0.303623	−	1.13313i	−0.630502	−	0.776188i	$-0.717151\pi$
$787$	8.51768	−	31.7884i	0.303623	−	1.13313i	0.934125	−	0.356947i	$-0.116182\pi$
$788$	44.3397	−	31.0470i	1.57953	−	1.10600i
$789$	−12.0566	+	14.7364i	−0.429228	+	0.524629i
$790$	37.7219	+	11.0727i	1.34209	+	0.393949i
$791$	−1.67094	−	0.964720i	−0.0594119	−	0.0343015i
$792$	−83.7961	+	61.8319i	−2.97757	+	2.19710i
$793$	24.0515	−	11.2154i	0.854094	−	0.398270i
$794$	−34.2555	+	12.4680i	−1.21568	+	0.442472i
$795$	−2.82152	−	17.1311i	−0.100069	−	0.607577i
$796$	−8.13479	−	46.1347i	−0.288330	−	1.63520i
$797$	12.6377	−	12.6377i	0.447652	−	0.447652i	−0.446921	−	0.894573i	$-0.647480\pi$
$797$	12.6377	−	12.6377i	0.447652	−	0.447652i	0.894573	+	0.446921i	$0.147480\pi$
$798$	−16.3740	+	54.6568i	−0.579632	+	1.93483i
$799$		−	14.1320i		−	0.499956i
$800$	54.7361	+	42.3318i	1.93522	+	1.49665i
$801$	−3.16108	+	9.40548i	−0.111691	+	0.332326i
$802$	18.8968	+	8.81171i	0.667269	+	0.311152i
$803$	−1.09636	−	2.35114i	−0.0386895	−	0.0829700i
$804$	75.3839	−	28.5025i	2.65858	−	1.00521i
$805$	21.5762	−	35.4047i	0.760461	−	1.24785i
$806$	−7.02606	+	4.05650i	−0.247482	+	0.142884i
$807$	3.59843	+	35.9784i	0.126671	+	1.26650i
$808$	26.5792	+	37.9590i	0.935053	+	1.33539i
$809$	0.886828	+	1.53603i	0.0311792	+	0.0540040i	0.881194	−	0.472755i	$-0.156740\pi$
$809$	0.886828	+	1.53603i	0.0311792	+	0.0540040i	−0.850015	+	0.526759i	$0.823407\pi$
$810$	−12.4731	+	51.9038i	−0.438262	+	1.82371i
$811$	18.5956	+	15.6036i	0.652980	+	0.547915i	0.907973	−	0.419028i	$-0.137629\pi$
$811$	18.5956	+	15.6036i	0.652980	+	0.547915i	−0.254994	+	0.966943i	$0.582073\pi$
$812$	64.6123	−	30.1292i	2.26745	−	1.05733i
$813$	45.4063	−	32.6416i	1.59247	−	1.14479i
$814$	−56.5763	−	67.4250i	−1.98300	−	2.36325i
$815$	14.6222	−	19.8629i	0.512192	−	0.695768i
$816$	−13.0095	+	23.1936i	−0.455424	+	0.811939i
$817$	8.60767	−	16.6140i	0.301144	−	0.581249i
$818$	23.8620	+	23.8620i	0.834317	+	0.834317i
$819$	13.2589	+	15.0271i	0.463303	+	0.525088i
$820$	7.25769	+	9.07815i	0.253449	+	0.317023i
$821$	6.29547	+	17.2967i	0.219713	+	0.603658i	0.999756	−	0.0220682i	$-0.00702510\pi$
$821$	6.29547	+	17.2967i	0.219713	+	0.603658i	−0.780043	+	0.625726i	$0.784803\pi$
$822$	5.47415	−	73.0003i	0.190933	−	2.54618i
$823$	−7.35676	+	0.643633i	−0.256441	+	0.0224357i	−0.214651	−	0.976691i	$-0.568861\pi$
$823$	−7.35676	+	0.643633i	−0.256441	+	0.0224357i	−0.0417895	+	0.999126i	$0.513306\pi$
$824$	−1.83245	+	3.17390i	−0.0638365	+	0.110568i
$825$	27.3042	−	25.4562i	0.950610	−	0.886270i
$826$	−2.79534	+	15.8532i	−0.0972624	+	0.551603i
$827$	2.27488	+	3.24887i	0.0791054	+	0.112974i	0.856755	−	0.515724i	$-0.172477\pi$
$827$	2.27488	+	3.24887i	0.0791054	+	0.112974i	−0.777649	+	0.628698i	$0.783588\pi$
$828$	−94.3119	+	27.7987i	−3.27756	+	0.966073i
$829$	−10.7856	−	6.22705i	−0.374598	−	0.216274i	0.300867	−	0.953666i	$-0.402724\pi$
$829$	−10.7856	−	6.22705i	−0.374598	−	0.216274i	−0.675465	+	0.737392i	$0.736057\pi$
$830$	−4.59758	+	5.22250i	−0.159584	+	0.181276i
$831$	−11.0118	−	12.7972i	−0.381995	−	0.443930i
$832$	−30.0263	−	14.0015i	−1.04098	−	0.485415i
$833$	1.51378	+	0.132439i	0.0524494	+	0.00458873i
$834$	−31.8872	+	91.1143i	−1.10416	+	3.15503i
$835$	13.5809	+	14.2408i	0.469985	+	0.492822i
$836$	−94.5395	−	3.94354i	−3.26972	−	0.136390i
$837$	4.61117	−	4.96823i	0.159386	−	0.171727i
$838$	13.9963	+	9.80034i	0.483495	+	0.338547i
$839$	36.3302	−	30.4847i	1.25426	−	1.05245i	0.257990	−	0.966147i	$-0.416940\pi$
$839$	36.3302	−	30.4847i	1.25426	−	1.05245i	0.996269	−	0.0863012i	$-0.0275047\pi$
$840$	−73.3627	+	50.1437i	−2.53125	+	1.73012i
$841$	4.05147	+	1.47462i	0.139706	+	0.0508488i
$842$	−6.91829	+	0.605272i	−0.238420	+	0.0208591i
$843$	2.89543	+	0.737416i	0.0997240	+	0.0253980i
$844$	92.3255	−	53.3041i	3.17797	−	1.83480i
$845$	−3.30417	+	16.4479i	−0.113667	+	0.565825i
$846$	−76.9760	+	30.2023i	−2.64649	+	1.03838i
$847$	−5.58984	+	20.8616i	−0.192069	+	0.716812i
$848$	−48.8835	+	13.0983i	−1.67866	+	0.449797i
$849$	−33.7132	+	12.7469i	−1.15703	+	0.437472i
$850$	6.96585	−	16.6381i	0.238927	−	0.570680i
$851$	−17.1347	−	47.0773i	−0.587371	−	1.61379i
$852$	−32.4450	+	47.5832i	−1.11155	+	1.63017i
$853$	32.1397	+	22.5045i	1.10044	+	0.770538i	0.975142	−	0.221581i	$-0.0711217\pi$
$853$	32.1397	+	22.5045i	1.10044	+	0.770538i	0.125300	+	0.992119i	$0.460011\pi$
$854$	−85.5382			−2.92706
$855$	−23.1433	+	17.8715i	−0.791483	+	0.611191i
$856$	−84.5121			−2.88856
$857$	5.11532	+	3.58179i	0.174736	+	0.122352i	0.657673	−	0.753304i	$-0.271541\pi$
$857$	5.11532	+	3.58179i	0.174736	+	0.122352i	−0.482937	+	0.875655i	$0.660430\pi$
$858$	−26.1585	+	38.3635i	−0.893037	+	1.30971i
$859$	8.90335	+	24.4618i	0.303778	+	0.834624i	0.993835	+	0.110869i	$0.0353634\pi$
$859$	8.90335	+	24.4618i	0.303778	+	0.834624i	−0.690057	+	0.723755i	$0.742414\pi$
$860$	44.2823	−	19.3844i	1.51002	−	0.661003i
$861$	−4.76417	+	1.80133i	−0.162363	+	0.0613891i
$862$	−45.0550	+	12.0724i	−1.53458	+	0.411189i
$863$	−14.8266	+	55.3336i	−0.504703	+	1.88358i	−0.0377688	+	0.999287i	$0.512025\pi$
$863$	−14.8266	+	55.3336i	−0.504703	+	1.88358i	−0.466934	+	0.884292i	$0.654642\pi$
$864$	71.2336	+	9.84066i	2.42342	+	0.334786i
$865$	−10.7586	−	16.1678i	−0.365805	−	0.549723i
$866$	49.0910	−	28.3427i	1.66818	−	0.963125i
$867$	−25.4295	−	6.47644i	−0.863630	−	0.219951i
$868$	18.6457	−	1.63129i	0.632877	−	0.0553696i
$869$	−26.8477	−	9.77177i	−0.910747	−	0.331485i
$870$	50.1665	+	9.43125i	1.70080	+	0.319749i
$871$	16.5950	−	13.9248i	0.562299	−	0.471825i
$872$	−46.8904	−	32.8330i	−1.58791	−	1.11186i
$873$	−14.7102	−	3.55251i	−0.497865	−	0.120234i
$874$	−69.5751	−	28.6606i	−2.35341	−	0.969459i
$875$	24.0682	−	20.8659i	0.813654	−	0.705397i
$876$	−1.73405	+	4.95486i	−0.0585881	+	0.167409i
$877$	−22.1173	−	1.93501i	−0.746847	−	0.0653407i	−0.292623	−	0.956228i	$-0.594528\pi$
$877$	−22.1173	−	1.93501i	−0.746847	−	0.0653407i	−0.454224	+	0.890887i	$0.650084\pi$
$878$	40.2984	+	18.7914i	1.36000	+	0.634180i
$879$	2.64079	+	3.06896i	0.0890718	+	0.103513i
$880$	−81.6735	−	71.9005i	−2.75321	−	2.42377i
$881$	34.1754	+	19.7312i	1.15140	+	0.664761i	0.949228	−	0.314590i	$-0.101867\pi$
$881$	34.1754	+	19.7312i	1.15140	+	0.664761i	0.202171	+	0.979350i	$0.435200\pi$
$882$	−2.51380	−	8.52848i	−0.0846439	−	0.287169i
$883$	27.7835	+	39.6790i	0.934990	+	1.33530i	0.942101	+	0.335330i	$0.108848\pi$
$883$	27.7835	+	39.6790i	0.934990	+	1.33530i	−0.00711049	+	0.999975i	$0.502263\pi$
$884$	−2.78851	+	15.8144i	−0.0937878	+	0.531897i
$885$	−5.89899	+	5.76719i	−0.198292	+	0.193862i
$886$	33.2835	−	57.6487i	1.11818	−	1.93675i
$887$	19.9974	−	1.74954i	0.671446	−	0.0587439i	0.253665	−	0.967292i	$-0.418364\pi$
$887$	19.9974	−	1.74954i	0.671446	−	0.0587439i	0.417780	+	0.908548i	$0.362808\pi$
$888$	−8.02926	+	107.074i	−0.269444	+	3.59316i
$889$	4.00716	+	11.0096i	0.134396	+	0.369250i
$890$	−19.4969	−	2.17273i	−0.653539	−	0.0728302i
$891$	11.4420	−	37.0688i	0.383323	−	1.24185i
$892$	−5.91855	−	5.91855i	−0.198168	−	0.198168i
$893$	−43.2240	−	13.5362i	−1.44644	−	0.452970i
$894$	−17.1872	+	30.6417i	−0.574826	+	1.02481i
$895$	−31.9539	+	4.85607i	−1.06810	+	0.162321i
$896$	17.9529	+	21.3954i	0.599763	+	0.714769i
$897$	−21.4597	+	15.4269i	−0.716519	+	0.515090i
$898$	80.4263	−	37.5034i	2.68386	−	1.25150i
$899$	−4.96529	−	4.16637i	−0.165602	−	0.138956i
$900$	−75.5207	−	1.70660i	−2.51736	−	0.0568866i
$901$	3.04833	+	5.27987i	0.101555	+	0.175898i
$902$	−6.76891	−	9.66700i	−0.225380	−	0.321876i
$903$	2.10817	+	21.0783i	0.0701556	+	0.701440i
$904$	−4.72302	+	2.72684i	−0.157085	+	0.0906933i
$905$	48.4539	+	29.5286i	1.61066	+	0.981564i
$906$	−17.6738	+	6.68243i	−0.587172	+	0.222009i
$907$	−13.3870	−	28.7086i	−0.444509	−	0.953253i	−0.993112	−	0.117170i	$-0.962618\pi$
$907$	−13.3870	−	28.7086i	−0.444509	−	0.953253i	0.548603	−	0.836083i	$-0.315160\pi$
$908$	82.4506	+	38.4473i	2.73622	+	1.27592i
$909$	−16.3632	−	5.49950i	−0.542733	−	0.182407i
$910$	−23.4891	+	31.9079i	−0.778657	+	1.05774i
$911$		−	25.2858i		−	0.837757i	−0.908042	−	0.418878i	$-0.862423\pi$
$911$		−	25.2858i		−	0.837757i	0.908042	−	0.418878i	$-0.137577\pi$
$912$	58.4787	+	62.0063i	1.93642	+	2.05324i
$913$	3.57556	−	3.57556i	0.118334	−	0.118334i
$914$	11.0573	+	62.7088i	0.365742	+	2.07422i
$915$	−35.6225	−	25.5477i	−1.17764	−	0.844580i
$916$	−40.5829	+	14.7710i	−1.34090	+	0.488047i
$917$	14.8370	−	6.91860i	0.489961	−	0.228472i
$918$	−2.32814	−	18.5999i	−0.0768400	−	0.613887i
$919$	−12.1545	−	7.01740i	−0.400940	−	0.231483i	0.285950	−	0.958245i	$-0.407691\pi$
$919$	−12.1545	−	7.01740i	−0.400940	−	0.231483i	−0.686889	+	0.726762i	$0.741024\pi$
$920$	−56.1731	−	102.853i	−1.85197	−	3.39095i
$921$	19.3730	−	23.6789i	0.638361	−	0.780245i
$922$	60.1126	−	42.0913i	1.97970	−	1.38620i
$923$	−4.00670	+	14.9532i	−0.131882	+	0.492191i
$924$	92.0986	−	54.7092i	3.02982	−	1.79980i
$925$	−1.53286	−	38.4593i	−0.0504001	−	1.26453i
$926$	−34.4612	+	94.6815i	−1.13247	+	3.11143i
$927$	−0.152731	−	1.35670i	−0.00501636	−	0.0445600i
$928$	5.99310	−	68.5015i	0.196733	−	2.24867i
$929$	−7.95765	−	45.1301i	−0.261082	−	1.48067i	−0.779964	−	0.625824i	$-0.784763\pi$
$929$	−7.95765	−	45.1301i	−0.261082	−	1.48067i	0.518882	−	0.854846i	$-0.326348\pi$
$930$	11.5295	+	6.83140i	0.378069	+	0.224010i
$931$	1.85503	−	4.50318i	0.0607961	−	0.147586i
$932$	−0.751079	+	0.751079i	−0.0246024	+	0.0246024i
$933$	33.2768	−	16.0233i	1.08943	−	0.524579i
$934$	72.9966	+	86.9940i	2.38852	+	2.84653i
$935$	−5.82008	+	11.7457i	−0.190337	+	0.384124i
$936$	55.5229	−	11.2186i	1.81482	−	0.366693i
$937$	1.36396	+	15.5901i	0.0445586	+	0.509307i	0.985376	+	0.170393i	$0.0545039\pi$
$937$	1.36396	+	15.5901i	0.0445586	+	0.509307i	−0.940818	+	0.338914i	$0.889941\pi$
$938$	−67.4466	+	18.0723i	−2.20221	+	0.590081i
$939$	1.62262	−	0.0201515i	0.0529522	−	0.000657620i
$940$	−64.8241	−	97.4161i	−2.11433	−	3.17736i
$941$	18.0009	+	3.17404i	0.586812	+	0.103471i	0.459168	−	0.888349i	$-0.348147\pi$
$941$	18.0009	+	3.17404i	0.586812	+	0.103471i	0.127644	+	0.991820i	$0.459259\pi$
$942$	−72.6748	−	70.8918i	−2.36787	−	2.30978i
$943$	−1.73853	−	6.48828i	−0.0566143	−	0.211288i
$944$	18.4211	+	15.4572i	0.599557	+	0.503088i
$945$	10.8998	−	31.2575i	0.354571	−	1.01681i
$946$	−46.1218	+	16.7870i	−1.49955	+	0.545791i
$947$	−2.23439	+	25.5392i	−0.0726080	+	0.829913i	0.869353	+	0.494191i	$0.164536\pi$
$947$	−2.23439	+	25.5392i	−0.0726080	+	0.829913i	−0.941961	+	0.335722i	$0.891020\pi$
$948$	25.0824	+	52.0906i	0.814639	+	1.69182i
$949$			1.41107i			0.0458054i
$950$	−44.2168	−	37.2421i	−1.43458	−	1.20829i
$951$	8.15797	−	14.5442i	0.264540	−	0.471628i
$952$	17.8980	−	25.5609i	0.580076	−	0.828434i
$953$	−2.36819	−	0.207190i	−0.0767133	−	0.00671155i	0.0487344	−	0.998812i	$-0.484481\pi$
$953$	−2.36819	−	0.207190i	−0.0767133	−	0.00671155i	−0.125448	+	0.992100i	$0.540037\pi$
$954$	22.2442	−	27.8879i	0.720183	−	0.902903i
$955$	50.8347	+	19.8798i	1.64497	+	0.643294i
$956$	72.6222	−	86.5478i	2.34877	−	2.79915i
$957$	−35.9492	−	9.15564i	−1.16207	−	0.295960i
$958$	−45.4328	−	12.1737i	−1.46787	−	0.393314i
$959$	−7.88307	+	44.7071i	−0.254558	+	1.44367i
$960$	4.15354	+	54.5685i	0.134055	+	1.76119i
$961$	14.6491	+	25.3731i	0.472553	+	0.818486i
$962$	12.3911	+	46.2443i	0.399505	+	1.49097i
$963$	25.3329	−	18.6928i	0.816342	−	0.602367i
$964$	−9.42545	+	25.8962i	−0.303573	+	0.834061i
$965$	−19.4300	−	9.62772i	−0.625474	−	0.309927i
$966$	83.7039	−	15.8335i	2.69313	−	0.509433i
$967$	23.2491	−	33.2032i	0.747642	−	1.06774i	−0.247461	−	0.968898i	$-0.579596\pi$
$967$	23.2491	−	33.2032i	0.747642	−	1.06774i	0.995103	−	0.0988457i	$-0.0315150\pi$
$968$	43.1665	+	43.1665i	1.38742	+	1.38742i
$969$	5.39196	−	8.73814i	0.173215	−	0.280709i
$970$	0.709487	−	29.9111i	0.0227803	−	0.960387i
$971$	12.7188	−	2.24266i	0.408165	−	0.0719705i	0.0342039	−	0.999415i	$-0.489110\pi$
$971$	12.7188	−	2.24266i	0.408165	−	0.0719705i	0.373961	+	0.927444i	$0.377999\pi$
$972$	−68.9525	+	37.5280i	−2.21165	+	1.20371i
$973$	25.2992	−	54.2543i	0.811054	−	1.73931i
$974$	−35.8233	−	13.0386i	−1.14785	−	0.417784i
$975$	−19.3120	+	6.27259i	−0.618479	+	0.200884i
$976$	−63.8892	+	110.659i	−2.04504	+	3.54212i
$977$	−30.4231	−	8.15185i	−0.973322	−	0.260801i	−0.263092	−	0.964771i	$-0.584742\pi$
$977$	−30.4231	−	8.15185i	−0.973322	−	0.260801i	−0.710230	+	0.703970i	$0.751409\pi$
$978$	50.4256	−	5.04339i	1.61243	−	0.161270i
$979$	14.0404	+	2.47570i	0.448732	+	0.0791236i
$980$	11.0424	−	6.03083i	0.352737	−	0.192648i
$981$	21.3178	−	0.529578i	0.680624	−	0.0169081i
$982$	4.37663	+	50.0251i	0.139664	+	1.59637i
$983$	12.4032	+	26.5988i	0.395601	+	0.848369i	0.998713	+	0.0507127i	$0.0161493\pi$
$983$	12.4032	+	26.5988i	0.395601	+	0.848369i	−0.603112	+	0.797656i	$0.706073\pi$
$984$	−2.32369	+	14.2079i	−0.0740766	+	0.452930i
$985$	−23.8862	−	2.66187i	−0.761078	−	0.0848143i
$986$	−17.6524	+	3.11259i	−0.562166	+	0.0991250i
$987$	49.3621	−	13.8858i	1.57121	−	0.441989i
$988$	45.6989	+	23.6765i	1.45387	+	0.753250i
$989$	−27.9370			−0.888344
$990$	76.4160	+	6.59918i	2.42866	+	0.209736i
$991$	−15.7050	+	13.1780i	−0.498884	+	0.418614i	−0.857197	−	0.514988i	$-0.827796\pi$
$991$	−15.7050	+	13.1780i	−0.498884	+	0.418614i	0.358313	+	0.933601i	$0.383352\pi$
$992$	7.62956	−	16.3616i	0.242239	−	0.519482i
$993$	−54.2114	−	4.06521i	−1.72035	−	0.129005i
$994$	32.0739	−	38.2242i	1.01732	−	1.21240i
$995$	−10.8245	+	17.7621i	−0.343161	+	0.563098i
$996$	−10.2316	+	0.127067i	−0.324200	+	0.00402629i
$997$	25.0377	−	17.5316i	0.792950	−	0.555230i	−0.105441	−	0.994426i	$-0.533625\pi$
$997$	25.0377	−	17.5316i	0.792950	−	0.555230i	0.898391	+	0.439196i	$0.144737\pi$
$998$	27.1294	−	18.9962i	0.858765	−	0.601314i
$999$	−21.2763	−	33.8719i	−0.673152	−	1.07166i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	285.2.bi.a.47.35	yes	432
3.2	odd	2	inner	285.2.bi.a.47.2	yes	432
5.3	odd	4	inner	285.2.bi.a.218.35	yes	432
15.8	even	4	inner	285.2.bi.a.218.2	yes	432
19.17	even	9	inner	285.2.bi.a.17.2	✓	432
57.17	odd	18	inner	285.2.bi.a.17.35	yes	432
95.93	odd	36	inner	285.2.bi.a.188.2	yes	432
285.188	even	36	inner	285.2.bi.a.188.35	yes	432

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.2.bi.a.17.2	✓	432	19.17	even	9	inner
285.2.bi.a.17.35	yes	432	57.17	odd	18	inner
285.2.bi.a.47.2	yes	432	3.2	odd	2	inner
285.2.bi.a.47.35	yes	432	1.1	even	1	trivial
285.2.bi.a.188.2	yes	432	95.93	odd	36	inner
285.2.bi.a.188.35	yes	432	285.188	even	36	inner
285.2.bi.a.218.2	yes	432	15.8	even	4	inner
285.2.bi.a.218.35	yes	432	5.3	odd	4	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:	\( N \)	\(=\)	\( 285 = 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	285.bi (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(2.17284 + 1.52144i) q^{2} +(0.975768 - 1.43104i) q^{3} +(1.72241 + 4.73229i) q^{4} +(0.814392 - 2.08249i) q^{5} +(4.29743 - 1.62485i) q^{6} +(-2.75201 + 0.737399i) q^{7} +(-2.08430 + 7.77872i) q^{8} +(-1.09575 - 2.79273i) q^{9} +O(q^{10})\)	\(q+(2.17284 + 1.52144i) q^{2} +(0.975768 - 1.43104i) q^{3} +(1.72241 + 4.73229i) q^{4} +(0.814392 - 2.08249i) q^{5} +(4.29743 - 1.62485i) q^{6} +(-2.75201 + 0.737399i) q^{7} +(-2.08430 + 7.77872i) q^{8} +(-1.09575 - 2.79273i) q^{9} +(4.93792 - 3.28587i) q^{10} +(-3.73301 + 2.15525i) q^{11} +(8.45278 + 2.15277i) q^{12} +(2.33571 - 0.204348i) q^{13} +(-7.10158 - 2.58476i) q^{14} +(-2.18547 - 3.19745i) q^{15} +(-8.64810 + 7.25662i) q^{16} +(1.11405 + 0.780068i) q^{17} +(1.86806 - 7.73527i) q^{18} +(3.45298 - 2.66025i) q^{19} +(11.2577 + 0.267031i) q^{20} +(-1.63008 + 4.65777i) q^{21} +(-11.3903 - 0.996523i) q^{22} +(-5.89829 - 2.75042i) q^{23} +(9.09787 + 10.5730i) q^{24} +(-3.67353 - 3.39193i) q^{25} +(5.38603 + 3.10963i) q^{26} +(-5.06571 - 1.15698i) q^{27} +(-8.22969 - 11.7532i) q^{28} +(-0.862815 + 4.89327i) q^{29} +(0.116054 - 10.2726i) q^{30} +(-0.652248 + 1.12973i) q^{31} +(-13.7864 + 1.20616i) q^{32} +(-0.558295 + 7.44512i) q^{33} +(1.23383 + 3.38992i) q^{34} +(-0.705589 + 6.33157i) q^{35} +(11.3287 - 9.99566i) q^{36} +(5.44328 + 5.44328i) q^{37} +(11.5502 - 0.526793i) q^{38} +(1.98668 - 3.54190i) q^{39} +(14.5017 + 10.6755i) q^{40} +(0.663443 + 0.790660i) q^{41} +(-10.6284 + 7.64052i) q^{42} +(3.89049 - 1.81417i) q^{43} +(-16.6291 - 13.9535i) q^{44} +(-6.70820 + 0.00752364i) q^{45} +(-8.63143 - 14.9501i) q^{46} +(-5.96012 - 8.51193i) q^{47} +(1.94598 + 19.4566i) q^{48} +(0.967628 - 0.558660i) q^{49} +(-2.82139 - 12.9592i) q^{50} +(2.20337 - 0.833089i) q^{51} +(4.99010 + 10.7013i) q^{52} +(4.06282 + 1.89452i) q^{53} +(-9.24668 - 10.2211i) q^{54} +(1.44816 + 9.52918i) q^{55} -22.9441i q^{56} +(-0.437615 - 7.53714i) q^{57} +(-9.31956 + 9.31956i) q^{58} +(-0.369884 - 2.09772i) q^{59} +(11.3670 - 15.8496i) q^{60} +(10.6360 - 3.87117i) q^{61} +(-3.13604 + 1.46236i) q^{62} +(5.07488 + 6.87761i) q^{63} +(-12.2372 - 7.06514i) q^{64} +(1.47663 - 5.03052i) q^{65} +(-12.5404 + 15.3276i) q^{66} +(7.56854 - 5.29955i) q^{67} +(-1.77265 + 6.61562i) q^{68} +(-9.69131 + 5.75692i) q^{69} +(-11.1662 + 12.6840i) q^{70} +(-2.25823 + 6.20442i) q^{71} +(24.0077 - 2.70268i) q^{72} +(-0.0524530 + 0.599541i) q^{73} +(3.54576 + 20.1090i) q^{74} +(-8.43850 + 1.94724i) q^{75} +(18.5365 + 11.7585i) q^{76} +(8.68400 - 8.68400i) q^{77} +(9.70552 - 4.67336i) q^{78} +(4.26050 + 5.07747i) q^{79} +(8.06889 + 23.9193i) q^{80} +(-6.59865 + 6.12028i) q^{81} +(0.238613 + 2.72736i) q^{82} +(-1.13311 + 0.303617i) q^{83} +(-24.8496 + 0.308610i) q^{84} +(2.53176 - 1.68472i) q^{85} +(11.2136 + 1.97725i) q^{86} +(6.16056 + 6.00942i) q^{87} +(-8.98441 - 33.5303i) q^{88} +(-2.53368 - 2.12601i) q^{89} +(-14.5873 - 10.1898i) q^{90} +(-6.27722 + 2.28472i) q^{91} +(2.85648 - 32.6498i) q^{92} +(0.980242 + 2.03574i) q^{93} -27.5630i q^{94} +(-2.72786 - 9.35728i) q^{95} +(-11.7263 + 20.9059i) q^{96} +(2.89333 - 4.13210i) q^{97} +(2.95247 + 0.258307i) q^{98} +(10.1095 + 8.06365i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 432 q - 12 q^{3} - 24 q^{6} - 12 q^{7}+O(q^{10}) \) 432 * q - 12 * q^3 - 24 * q^6 - 12 * q^7	\( 432 q - 12 q^{3} - 24 q^{6} - 12 q^{7} - 24 q^{10} - 6 q^{12} - 24 q^{13} + 6 q^{15} - 108 q^{16} + 24 q^{18} - 24 q^{21} - 72 q^{22} - 6 q^{27} - 72 q^{28} - 6 q^{30} - 24 q^{31} - 102 q^{33} - 24 q^{36} - 48 q^{37} - 24 q^{40} + 24 q^{42} - 36 q^{43} + 12 q^{45} - 24 q^{46} - 156 q^{48} - 72 q^{51} - 48 q^{52} + 12 q^{55} - 90 q^{57} + 96 q^{58} + 132 q^{60} - 24 q^{61} + 18 q^{63} - 72 q^{66} - 120 q^{67} + 24 q^{70} + 168 q^{72} - 24 q^{73} - 192 q^{75} - 168 q^{76} - 6 q^{78} + 72 q^{81} - 312 q^{82} + 42 q^{87} - 204 q^{88} + 156 q^{90} + 72 q^{91} + 138 q^{93} + 240 q^{96} - 48 q^{97}+O(q^{100}) \) 432 * q - 12 * q^3 - 24 * q^6 - 12 * q^7 - 24 * q^10 - 6 * q^12 - 24 * q^13 + 6 * q^15 - 108 * q^16 + 24 * q^18 - 24 * q^21 - 72 * q^22 - 6 * q^27 - 72 * q^28 - 6 * q^30 - 24 * q^31 - 102 * q^33 - 24 * q^36 - 48 * q^37 - 24 * q^40 + 24 * q^42 - 36 * q^43 + 12 * q^45 - 24 * q^46 - 156 * q^48 - 72 * q^51 - 48 * q^52 + 12 * q^55 - 90 * q^57 + 96 * q^58 + 132 * q^60 - 24 * q^61 + 18 * q^63 - 72 * q^66 - 120 * q^67 + 24 * q^70 + 168 * q^72 - 24 * q^73 - 192 * q^75 - 168 * q^76 - 6 * q^78 + 72 * q^81 - 312 * q^82 + 42 * q^87 - 204 * q^88 + 156 * q^90 + 72 * q^91 + 138 * q^93 + 240 * q^96 - 48 * q^97

Introduction

L-functions

Modular forms

Varieties

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