LMFDB - Embedded newform 966.2.bd.a.59.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(59,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([33, 11, 42]))

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

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

chi := DirichletCharacter("966.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.bd (of order $66$, degree $20$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$1280$
Relative dimension:	$64$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			59.9
Character	$\chi$	$=$	966.59
Dual form			966.2.bd.a.131.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.945001 - 0.327068i) q^{2} +(-1.02432 - 1.39670i) q^{3} +(0.786053 + 0.618159i) q^{4} +(-3.14301 + 0.300121i) q^{5} +(0.511165 + 1.65491i) q^{6} +(1.51112 - 2.17176i) q^{7} +(-0.540641 - 0.841254i) q^{8} +(-0.901547 + 2.86133i) q^{9} +O(q^{10})$	\(q+(-0.945001 - 0.327068i) q^{2} +(-1.02432 - 1.39670i) q^{3} +(0.786053 + 0.618159i) q^{4} +(-3.14301 + 0.300121i) q^{5} +(0.511165 + 1.65491i) q^{6} +(1.51112 - 2.17176i) q^{7} +(-0.540641 - 0.841254i) q^{8} +(-0.901547 + 2.86133i) q^{9} +(3.06831 + 0.744364i) q^{10} +(-1.84462 + 0.638428i) q^{11} +(0.0582153 - 1.73107i) q^{12} +(0.634938 + 2.16240i) q^{13} +(-2.13832 + 1.55807i) q^{14} +(3.63862 + 4.08243i) q^{15} +(0.235759 + 0.971812i) q^{16} +(-0.844945 - 0.338265i) q^{17} +(1.78781 - 2.40909i) q^{18} +(0.870072 + 2.17333i) q^{19} +(-2.65610 - 1.70697i) q^{20} +(-4.58116 + 0.113987i) q^{21} +1.95197 q^{22} +(-2.37468 + 4.16664i) q^{23} +(-0.621192 + 1.61682i) q^{24} +(4.87882 - 0.940315i) q^{25} +(0.107235 - 2.25114i) q^{26} +(4.91989 - 1.67172i) q^{27} +(2.53031 - 0.773004i) q^{28} +(6.37350 - 0.916371i) q^{29} +(-2.10327 - 5.04798i) q^{30} +(-9.67729 + 0.460986i) q^{31} +(0.0950560 - 0.995472i) q^{32} +(2.78117 + 1.92243i) q^{33} +(0.687838 + 0.596015i) q^{34} +(-4.09767 + 7.27938i) q^{35} +(-2.47742 + 1.69186i) q^{36} +(2.28768 - 3.21259i) q^{37} +(-0.111391 - 2.33838i) q^{38} +(2.36985 - 3.10180i) q^{39} +(1.95172 + 2.48181i) q^{40} +(4.32526 - 9.47100i) q^{41} +(4.36648 + 1.39063i) q^{42} +(6.16838 + 3.96418i) q^{43} +(-1.84462 - 0.638428i) q^{44} +(1.97483 - 9.26377i) q^{45} +(3.60685 - 3.16079i) q^{46} +(3.87019 + 6.70337i) q^{47} +(1.11584 - 1.32473i) q^{48} +(-2.43304 - 6.56356i) q^{49} +(-4.91803 - 0.707106i) q^{50} +(0.393037 + 1.52663i) q^{51} +(-0.837613 + 2.09225i) q^{52} +(3.64600 + 3.82382i) q^{53} +(-5.19607 - 0.0293639i) q^{54} +(5.60605 - 2.56020i) q^{55} +(-2.64397 - 0.0970937i) q^{56} +(2.14427 - 3.44142i) q^{57} +(-6.32268 - 1.21860i) q^{58} +(-1.05820 + 4.36195i) q^{59} +(0.336560 + 5.45825i) q^{60} +(2.17263 - 4.21432i) q^{61} +(9.29582 + 2.72950i) q^{62} +(4.85177 + 6.28175i) q^{63} +(-0.415415 + 0.909632i) q^{64} +(-2.64460 - 6.60590i) q^{65} +(-1.99944 - 2.72632i) q^{66} +(12.6356 - 2.43532i) q^{67} +(-0.455070 - 0.788205i) q^{68} +(8.25198 - 0.951239i) q^{69} +(6.25316 - 5.53880i) q^{70} +(6.85569 - 5.94049i) q^{71} +(2.89452 - 0.788522i) q^{72} +(-2.52214 + 3.20716i) q^{73} +(-3.21259 + 2.28768i) q^{74} +(-6.31080 - 5.85107i) q^{75} +(-0.659544 + 2.24620i) q^{76} +(-1.40092 + 4.97080i) q^{77} +(-3.25401 + 2.15611i) q^{78} +(-0.532359 - 0.507603i) q^{79} +(-1.03265 - 2.98366i) q^{80} +(-7.37442 - 5.15925i) q^{81} +(-7.18504 + 7.53545i) q^{82} +(0.126573 + 0.277156i) q^{83} +(-3.67150 - 2.74228i) q^{84} +(2.75719 + 0.809585i) q^{85} +(-4.53257 - 5.76363i) q^{86} +(-7.80839 - 7.96322i) q^{87} +(1.53436 + 1.20663i) q^{88} +(0.534057 - 11.2112i) q^{89} +(-4.89610 + 8.10837i) q^{90} +(5.65567 + 1.88871i) q^{91} +(-4.44227 + 1.80727i) q^{92} +(10.5565 + 13.0441i) q^{93} +(-1.46488 - 7.60050i) q^{94} +(-3.38691 - 6.56969i) q^{95} +(-1.48774 + 0.886914i) q^{96} +(-0.429571 - 0.196179i) q^{97} +(0.152500 + 6.99834i) q^{98} +(-0.163744 - 5.85363i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1280 q - 64 q^{4} + 4 q^{9}+O(q^{10}) $ 1280 * q - 64 * q^4 + 4 * q^9	$ 1280 q - 64 q^{4} + 4 q^{9} + 16 q^{15} + 64 q^{16} - 44 q^{18} + 120 q^{21} - 16 q^{22} - 12 q^{24} + 56 q^{25} + 32 q^{30} - 24 q^{33} + 8 q^{36} - 44 q^{37} - 20 q^{39} + 4 q^{42} + 136 q^{43} + 12 q^{45} + 12 q^{46} + 92 q^{49} + 4 q^{51} - 36 q^{54} - 56 q^{57} - 28 q^{58} + 8 q^{60} + 72 q^{61} - 134 q^{63} + 128 q^{64} + 24 q^{67} - 72 q^{70} - 44 q^{72} - 72 q^{73} + 48 q^{75} - 16 q^{78} - 72 q^{79} + 40 q^{81} + 48 q^{82} - 10 q^{84} - 32 q^{85} + 222 q^{87} - 8 q^{88} - 8 q^{91} - 16 q^{93} + 72 q^{94} - 12 q^{96} - 68 q^{99}+O(q^{100}) $ 1280 * q - 64 * q^4 + 4 * q^9 + 16 * q^15 + 64 * q^16 - 44 * q^18 + 120 * q^21 - 16 * q^22 - 12 * q^24 + 56 * q^25 + 32 * q^30 - 24 * q^33 + 8 * q^36 - 44 * q^37 - 20 * q^39 + 4 * q^42 + 136 * q^43 + 12 * q^45 + 12 * q^46 + 92 * q^49 + 4 * q^51 - 36 * q^54 - 56 * q^57 - 28 * q^58 + 8 * q^60 + 72 * q^61 - 134 * q^63 + 128 * q^64 + 24 * q^67 - 72 * q^70 - 44 * q^72 - 72 * q^73 + 48 * q^75 - 16 * q^78 - 72 * q^79 + 40 * q^81 + 48 * q^82 - 10 * q^84 - 32 * q^85 + 222 * q^87 - 8 * q^88 - 8 * q^91 - 16 * q^93 + 72 * q^94 - 12 * q^96 - 68 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{11}\right)$

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 $

$2$	−0.945001	−	0.327068i	−0.668216	−	0.231272i
$2$	−0.945001	−	0.327068i	−0.668216	−	0.231272i
$3$	−1.02432	−	1.39670i	−0.591390	−	0.806386i
$3$	−1.02432	−	1.39670i	−0.591390	−	0.806386i
$4$	0.786053	+	0.618159i	0.393027	+	0.309079i
$5$	−3.14301	+	0.300121i	−1.40560	+	0.134218i	−0.770119	−	0.637900i	$-0.779803\pi$
$5$	−3.14301	+	0.300121i	−1.40560	+	0.134218i	−0.635479	+	0.772118i	$0.719197\pi$
$6$	0.511165	+	1.65491i	0.208682	+	0.675612i
$7$	1.51112	−	2.17176i	0.571149	−	0.820846i
$7$	1.51112	−	2.17176i	0.571149	−	0.820846i
$8$	−0.540641	−	0.841254i	−0.191145	−	0.297428i
$9$	−0.901547	+	2.86133i	−0.300516	+	0.953777i
$10$	3.06831	+	0.744364i	0.970285	+	0.235389i
$11$	−1.84462	+	0.638428i	−0.556173	+	0.192493i	−0.590673	−	0.806911i	$-0.701137\pi$
$11$	−1.84462	+	0.638428i	−0.556173	+	0.192493i	0.0344995	+	0.999405i	$0.489016\pi$
$12$	0.0582153	−	1.73107i	0.0168053	−	0.499718i
$13$	0.634938	+	2.16240i	0.176100	+	0.599742i	0.999480	+	0.0322512i	$0.0102677\pi$
$13$	0.634938	+	2.16240i	0.176100	+	0.599742i	−0.823380	+	0.567491i	$0.807914\pi$
$14$	−2.13832	+	1.55807i	−0.571490	+	0.416412i
$15$	3.63862	+	4.08243i	0.939489	+	1.05408i
$16$	0.235759	+	0.971812i	0.0589397	+	0.242953i
$17$	−0.844945	−	0.338265i	−0.204929	−	0.0820413i	0.266927	−	0.963717i	$-0.413992\pi$
$17$	−0.844945	−	0.338265i	−0.204929	−	0.0820413i	−0.471856	+	0.881675i	$0.656416\pi$
$18$	1.78781	−	2.40909i	0.421391	−	0.567829i
$19$	0.870072	+	2.17333i	0.199608	+	0.498597i	0.994073	−	0.108713i	$-0.0346729\pi$
$19$	0.870072	+	2.17333i	0.199608	+	0.498597i	−0.794465	+	0.607310i	$0.792249\pi$
$20$	−2.65610	−	1.70697i	−0.593922	−	0.381690i
$21$	−4.58116	+	0.113987i	−0.999691	+	0.0248740i
$22$	1.95197			0.416162
$23$	−2.37468	+	4.16664i	−0.495156	+	0.868804i
$23$	−2.37468	+	4.16664i	−0.495156	+	0.868804i
$24$	−0.621192	+	1.61682i	−0.126800	+	0.330033i
$25$	4.87882	−	0.940315i	0.975763	−	0.188063i
$26$	0.107235	−	2.25114i	0.0210305	−	0.441485i
$27$	4.91989	−	1.67172i	0.946834	−	0.321722i
$28$	2.53031	−	0.773004i	0.478183	−	0.146084i
$29$	6.37350	−	0.916371i	1.18353	−	0.170166i	0.477684	−	0.878532i	$-0.341476\pi$
$29$	6.37350	−	0.916371i	1.18353	−	0.170166i	0.705845	+	0.708366i	$0.250567\pi$
$30$	−2.10327	−	5.04798i	−0.384003	−	0.921630i
$31$	−9.67729	+	0.460986i	−1.73809	+	0.0827955i	−0.892504	−	0.451040i	$-0.851053\pi$
$31$	−9.67729	+	0.460986i	−1.73809	+	0.0827955i	−0.845588	+	0.533836i	$0.820750\pi$
$32$	0.0950560	−	0.995472i	0.0168037	−	0.175976i
$33$	2.78117	+	1.92243i	0.484139	+	0.334651i
$34$	0.687838	+	0.596015i	0.117963	+	0.102216i
$35$	−4.09767	+	7.27938i	−0.692633	+	1.23044i
$36$	−2.47742	+	1.69186i	−0.412904	+	0.281976i
$37$	2.28768	−	3.21259i	0.376092	−	0.528147i	−0.582538	−	0.812804i	$-0.697940\pi$
$37$	2.28768	−	3.21259i	0.376092	−	0.528147i	0.958630	+	0.284656i	$0.0918795\pi$
$38$	−0.111391	−	2.33838i	−0.0180699	−	0.379335i
$39$	2.36985	−	3.10180i	0.379480	−	0.496686i
$40$	1.95172	+	2.48181i	0.308594	+	0.392409i
$41$	4.32526	−	9.47100i	0.675492	−	1.47912i	−0.191858	−	0.981423i	$-0.561451\pi$
$41$	4.32526	−	9.47100i	0.675492	−	1.47912i	0.867350	−	0.497699i	$-0.165822\pi$
$42$	4.36648	+	1.39063i	0.673762	+	0.214579i
$43$	6.16838	+	3.96418i	0.940670	+	0.604532i	0.918585	−	0.395224i	$-0.129333\pi$
$43$	6.16838	+	3.96418i	0.940670	+	0.604532i	0.0220851	+	0.999756i	$0.492970\pi$
$44$	−1.84462	−	0.638428i	−0.278086	−	0.0962467i
$45$	1.97483	−	9.26377i	0.294390	−	1.38096i
$46$	3.60685	−	3.16079i	0.531801	−	0.466034i
$47$	3.87019	+	6.70337i	0.564525	+	0.977786i	0.997094	+	0.0761853i	$0.0242740\pi$
$47$	3.87019	+	6.70337i	0.564525	+	0.977786i	−0.432568	+	0.901601i	$0.642393\pi$
$48$	1.11584	−	1.32473i	0.161057	−	0.191208i
$49$	−2.43304	−	6.56356i	−0.347578	−	0.937651i
$50$	−4.91803	−	0.707106i	−0.695515	−	0.0999999i
$51$	0.393037	+	1.52663i	0.0550362	+	0.213770i
$52$	−0.837613	+	2.09225i	−0.116156	+	0.290144i
$53$	3.64600	+	3.82382i	0.500817	+	0.525242i	0.924813	−	0.380422i	$-0.124221\pi$
$53$	3.64600	+	3.82382i	0.500817	+	0.525242i	−0.423996	+	0.905664i	$0.639373\pi$
$54$	−5.19607	−	0.0293639i	−0.707095	−	0.00399592i
$55$	5.60605	−	2.56020i	0.755920	−	0.345217i
$56$	−2.64397	−	0.0970937i	−0.353315	−	0.0129747i
$57$	2.14427	−	3.44142i	0.284015	−	0.455827i
$58$	−6.32268	−	1.21860i	−0.830209	−	0.160010i
$59$	−1.05820	+	4.36195i	−0.137766	+	0.567878i	0.860524	+	0.509411i	$0.170137\pi$
$59$	−1.05820	+	4.36195i	−0.137766	+	0.567878i	−0.998289	+	0.0584674i	$0.981379\pi$
$60$	0.336560	+	5.45825i	0.0434497	+	0.704658i
$61$	2.17263	−	4.21432i	0.278177	−	0.539588i	−0.707812	−	0.706401i	$-0.750317\pi$
$61$	2.17263	−	4.21432i	0.278177	−	0.539588i	0.985988	+	0.166813i	$0.0533478\pi$
$62$	9.29582	+	2.72950i	1.18057	+	0.346647i
$63$	4.85177	+	6.28175i	0.611265	+	0.791426i
$64$	−0.415415	+	0.909632i	−0.0519269	+	0.113704i
$65$	−2.64460	−	6.60590i	−0.328023	−	0.819361i
$66$	−1.99944	−	2.72632i	−0.246114	−	0.335587i
$67$	12.6356	−	2.43532i	1.54369	−	0.297522i	0.654856	−	0.755754i	$-0.272729\pi$
$67$	12.6356	−	2.43532i	1.54369	−	0.297522i	0.888833	+	0.458232i	$0.151517\pi$
$68$	−0.455070	−	0.788205i	−0.0551854	−	0.0955839i
$69$	8.25198	−	0.951239i	0.993421	−	0.114516i
$70$	6.25316	−	5.53880i	0.747395	−	0.662013i
$71$	6.85569	−	5.94049i	0.813621	−	0.705007i	−0.145081	−	0.989420i	$-0.546344\pi$
$71$	6.85569	−	5.94049i	0.813621	−	0.705007i	0.958702	+	0.284413i	$0.0917987\pi$
$72$	2.89452	−	0.788522i	0.341122	−	0.0929282i
$73$	−2.52214	+	3.20716i	−0.295194	+	0.375370i	−0.910915	−	0.412595i	$-0.864623\pi$
$73$	−2.52214	+	3.20716i	−0.295194	+	0.375370i	0.615721	+	0.787965i	$0.288865\pi$
$74$	−3.21259	+	2.28768i	−0.373457	+	0.265937i
$75$	−6.31080	−	5.85107i	−0.728708	−	0.675623i
$76$	−0.659544	+	2.24620i	−0.0756548	+	0.257657i
$77$	−1.40092	+	4.97080i	−0.159650	+	0.566475i
$78$	−3.25401	+	2.15611i	−0.368444	+	0.244131i
$79$	−0.532359	−	0.507603i	−0.0598950	−	0.0571098i	0.659540	−	0.751669i	$-0.270751\pi$
$79$	−0.532359	−	0.507603i	−0.0598950	−	0.0571098i	−0.719435	+	0.694559i	$0.755599\pi$
$80$	−1.03265	−	2.98366i	−0.115454	−	0.333583i
$81$	−7.37442	−	5.15925i	−0.819381	−	0.573250i
$82$	−7.18504	+	7.53545i	−0.793454	+	0.832151i
$83$	0.126573	+	0.277156i	0.0138932	+	0.0304218i	0.916451	−	0.400146i	$-0.131041\pi$
$83$	0.126573	+	0.277156i	0.0138932	+	0.0304218i	−0.902558	+	0.430568i	$0.858313\pi$
$84$	−3.67150	−	2.74228i	−0.400593	−	0.299208i
$85$	2.75719	+	0.809585i	0.299060	+	0.0878119i
$86$	−4.53257	−	5.76363i	−0.488760	−	0.621509i
$87$	−7.80839	−	7.96322i	−0.837147	−	0.853747i
$88$	1.53436	+	1.20663i	0.163563	+	0.128627i
$89$	0.534057	−	11.2112i	0.0566100	−	1.18839i	−0.774607	−	0.632442i	$-0.782053\pi$
$89$	0.534057	−	11.2112i	0.0566100	−	1.18839i	0.831217	−	0.555947i	$-0.187644\pi$
$90$	−4.89610	+	8.10837i	−0.516094	+	0.854697i
$91$	5.65567	+	1.88871i	0.592876	+	0.197991i
$92$	−4.44227	+	1.80727i	−0.463139	+	0.188421i
$93$	10.5565	+	13.0441i	1.09466	+	1.35261i
$94$	−1.46488	−	7.60050i	−0.151090	−	0.783932i
$95$	−3.38691	−	6.56969i	−0.347490	−	0.674036i
$96$	−1.48774	+	0.886914i	−0.151842	+	0.0905203i
$97$	−0.429571	−	0.196179i	−0.0436164	−	0.0199189i	0.393487	−	0.919330i	$-0.371268\pi$
$97$	−0.429571	−	0.196179i	−0.0436164	−	0.0199189i	−0.437104	+	0.899411i	$0.643996\pi$
$98$	0.152500	+	6.99834i	0.0154048	+	0.706939i
$99$	−0.163744	−	5.85363i	−0.0164569	−	0.588312i
$100$	4.41627	+	2.27675i	0.441627	+	0.227675i
$101$	7.56582	+	0.722448i	0.752827	+	0.0718863i	0.464412	−	0.885619i	$-0.346266\pi$
$101$	7.56582	+	0.722448i	0.752827	+	0.0718863i	0.288415	+	0.957505i	$0.406872\pi$
$102$	0.127890	−	1.57121i	0.0126630	−	0.155573i
$103$	2.23307	−	11.5863i	0.220031	−	1.14163i	−0.688955	−	0.724804i	$-0.741930\pi$
$103$	2.23307	−	11.5863i	0.220031	−	1.14163i	0.908986	−	0.416826i	$-0.136858\pi$
$104$	1.47585	−	1.70323i	0.144719	−	0.167015i
$105$	14.3644	−	1.73317i	1.40182	−	0.169140i
$106$	−2.19483	−	4.80600i	−0.213181	−	0.466800i
$107$	−2.93443	+	5.69200i	−0.283682	+	0.550266i	−0.987022	−	0.160588i	$-0.948661\pi$
$107$	−2.93443	+	5.69200i	−0.283682	+	0.550266i	0.703340	+	0.710854i	$0.251691\pi$
$108$	4.90069	+	1.72722i	0.471569	+	0.166202i
$109$	16.4567	+	6.58829i	1.57627	+	0.631043i	0.984551	−	0.175100i	$-0.0560250\pi$
$109$	16.4567	+	6.58829i	1.57627	+	0.631043i	0.591720	+	0.806144i	$0.298449\pi$
$110$	−6.13508	+	0.585829i	−0.584957	+	0.0558566i
$111$	−6.83034	+	0.0955144i	−0.648307	+	0.00906582i
$112$	2.46680	+	0.956511i	0.233090	+	0.0903818i
$113$	1.69903	−	1.47222i	0.159832	−	0.138495i	−0.571273	−	0.820760i	$-0.693550\pi$
$113$	1.69903	−	1.47222i	0.159832	−	0.138495i	0.731105	+	0.682265i	$0.239005\pi$
$114$	−3.15191	+	2.55082i	−0.295204	+	0.238906i
$115$	6.21316	−	13.8085i	0.579380	−	1.28765i
$116$	5.57637	+	3.21952i	0.517753	+	0.298925i
$117$	−6.75977	−	0.132739i	−0.624941	−	0.0122717i
$118$	2.42665	−	3.77595i	0.223392	−	0.347604i
$119$	−2.01144	+	1.32386i	−0.184388	+	0.121358i
$120$	1.46717	−	5.26813i	0.133934	−	0.480913i
$121$	−5.65156	+	4.44444i	−0.513778	+	0.404040i
$122$	−3.43151	+	3.27193i	−0.310674	+	0.296227i
$123$	−17.6586	+	3.66022i	−1.59222	+	0.330030i
$124$	−7.89182	−	5.61974i	−0.708707	−	0.504668i
$125$	0.0951053	−	0.0279254i	0.00850648	−	0.00249773i
$126$	−2.53036	−	7.52311i	−0.225423	−	0.670212i
$127$	−11.1760	+	12.8978i	−0.991713	+	1.14450i	−0.00220836	+	0.999998i	$0.500703\pi$
$127$	−11.1760	+	12.8978i	−0.991713	+	1.14450i	−0.989505	+	0.144500i	$0.953843\pi$
$128$	0.690079	−	0.723734i	0.0609949	−	0.0639697i
$129$	−0.781610	−	12.6760i	−0.0688169	−	1.11606i
$130$	0.338574	+	7.10754i	0.0296949	+	0.623373i
$131$	−2.10329	−	8.66987i	−0.183765	−	0.757490i	−0.986852	−	0.161628i	$-0.948326\pi$
$131$	−2.10329	−	8.66987i	−0.183765	−	0.757490i	0.803087	−	0.595862i	$-0.203190\pi$
$132$	0.997780	+	3.23033i	0.0868456	+	0.281164i
$133$	6.03473	+	1.39458i	0.523278	+	0.120926i
$134$	−12.7372	−	1.83133i	−1.10033	−	0.158203i
$135$	−14.9616	+	6.73080i	−1.28769	+	0.579295i
$136$	0.172245	+	0.893693i	0.0147699	+	0.0766335i
$137$	20.1281	+	11.6209i	1.71966	+	0.992845i	0.919535	+	0.393008i	$0.128565\pi$
$137$	20.1281	+	11.6209i	1.71966	+	0.992845i	0.800122	+	0.599837i	$0.204768\pi$
$138$	−8.10925	−	1.80004i	−0.690305	−	0.153229i
$139$			5.80158i			0.492084i	0.969259	+	0.246042i	$0.0791301\pi$
$139$			5.80158i			0.492084i	−0.969259	+	0.246042i	$0.920870\pi$
$140$	−7.72080	+	3.18896i	−0.652527	+	0.269516i
$141$	5.39829	−	12.2719i	0.454618	−	1.03348i
$142$	−8.42158	+	3.37149i	−0.706723	+	0.282929i
$143$	−2.55176	−	3.58344i	−0.213389	−	0.299662i
$144$	−2.99322	−	0.201550i	−0.249435	−	0.0167958i
$145$	−19.7570	+	4.79299i	−1.64073	+	0.398036i
$146$	3.43238	−	2.20586i	0.284066	−	0.182558i
$147$	−6.67512	+	10.1214i	−0.550554	+	0.834799i
$148$	3.78413	−	1.11112i	0.311054	−	0.0913336i
$149$	−1.69868	+	8.81358i	−0.139161	+	0.722037i	0.843573	+	0.537014i	$0.180448\pi$
$149$	−1.69868	+	8.81358i	−0.139161	+	0.722037i	−0.982734	+	0.185022i	$0.940764\pi$
$150$	4.05001	+	7.59332i	0.330682	+	0.619992i
$151$	−0.691785	+	2.85158i	−0.0562967	+	0.232058i	−0.993008	−	0.118043i	$-0.962338\pi$
$151$	−0.691785	+	2.85158i	−0.0562967	+	0.232058i	0.936712	+	0.350102i	$0.113853\pi$
$152$	1.35793	−	1.90694i	0.110143	−	0.154674i
$153$	1.72965	−	2.11271i	0.139834	−	0.170802i
$154$	2.94966	−	4.23921i	0.237691	−	0.341605i
$155$	30.2775	−	4.35325i	2.43195	−	0.349661i
$156$	3.78024	−	0.973239i	0.302661	−	0.0779215i
$157$	−11.0343	+	14.0313i	−0.880634	+	1.11982i	0.111391	+	0.993777i	$0.464469\pi$
$157$	−11.0343	+	14.0313i	−0.880634	+	1.11982i	−0.992025	+	0.126040i	$0.959773\pi$
$158$	0.337059	+	0.653803i	0.0268150	+	0.0520138i
$159$	1.60607	−	9.00918i	0.127369	−	0.714475i
$160$			3.15731i			0.249607i
$161$	5.46050	+	11.4535i	0.430347	+	0.902663i
$162$	5.28141	+	7.28743i	0.414947	+	0.572555i
$163$	−5.86261	+	16.9389i	−0.459195	+	1.32676i	0.443422	+	0.896313i	$0.353764\pi$
$163$	−5.86261	+	16.9389i	−0.459195	+	1.32676i	−0.902617	+	0.430445i	$0.858357\pi$
$164$	9.25447	−	4.77101i	0.722653	−	0.372553i
$165$	−9.31821	−	5.20752i	−0.725421	−	0.405405i
$166$	−0.0289626	−	0.303310i	−0.00224794	−	0.0235415i
$167$	−1.75777	−	12.2256i	−0.136020	−	0.946042i	−0.937491	−	0.348008i	$-0.886858\pi$
$167$	−1.75777	−	12.2256i	−0.136020	−	0.946042i	0.801471	−	0.598033i	$-0.204051\pi$
$168$	2.57265	+	3.79229i	0.198484	+	0.292581i
$169$	6.66346	−	4.28235i	0.512574	−	0.329411i
$170$	−2.34076	−	1.66685i	−0.179528	−	0.127841i
$171$	−7.00304	+	0.530199i	−0.535536	+	0.0405454i
$172$	2.39818	+	6.92910i	0.182860	+	0.528339i
$173$	15.9092	+	3.06625i	1.20955	+	0.233122i	0.753873	−	0.657021i	$-0.228184\pi$
$173$	15.9092	+	3.06625i	1.20955	+	0.233122i	0.455681	+	0.890143i	$0.349396\pi$
$174$	4.77442	+	10.0791i	0.361948	+	0.764096i
$175$	5.33033	−	12.0165i	0.402935	−	0.908364i
$176$	−1.05532	−	1.64211i	−0.0795475	−	0.123778i
$177$	7.17628	−	2.99004i	0.539402	−	0.224745i
$178$	−4.17152	+	10.4200i	−0.312669	+	0.781009i
$179$	−2.86685	+	2.04147i	−0.214278	+	0.152587i	−0.682157	−	0.731206i	$-0.738958\pi$
$179$	−2.86685	+	2.04147i	−0.214278	+	0.152587i	0.467879	+	0.883793i	$0.345018\pi$
$180$	7.27881	−	6.06106i	0.542530	−	0.451765i
$181$	−7.95749	+	12.3821i	−0.591476	+	0.920354i	0.408496	+	0.912760i	$0.366054\pi$
$181$	−7.95749	+	12.3821i	−0.591476	+	0.920354i	−0.999971	+	0.00759365i	$0.997583\pi$
$182$	−4.72688	−	3.63462i	−0.350380	−	0.269416i
$183$	−8.11160	+	1.28228i	−0.599627	+	0.0947890i
$184$	4.78905	−	0.254945i	0.353053	−	0.0187948i
$185$	−6.22603	+	10.7838i	−0.457747	+	0.792841i
$186$	−5.70958	−	15.7794i	−0.418646	−	1.15700i
$187$	1.77456	+	0.0845326i	0.129769	+	0.00618164i
$188$	−1.10157	+	7.66159i	−0.0803403	+	0.558779i
$189$	3.80398	−	13.2110i	0.276698	−	0.960957i
$190$	1.05190	+	7.31612i	0.0763128	+	0.530767i
$191$	−2.09768	+	0.508892i	−0.151783	+	0.0368222i	−0.310930	−	0.950433i	$-0.600641\pi$
$191$	−2.09768	+	0.508892i	−0.151783	+	0.0368222i	0.159147	+	0.987255i	$0.449125\pi$
$192$	1.69600	−	0.351541i	0.122398	−	0.0253703i
$193$	22.7109	+	2.16863i	1.63477	+	0.156101i	0.871639	−	0.490148i	$-0.163057\pi$
$193$	22.7109	+	2.16863i	1.63477	+	0.156101i	0.763126	+	0.646249i	$0.223663\pi$
$194$	0.341782	+	0.325888i	0.0245385	+	0.0233974i
$195$	−6.51755	+	10.4603i	−0.466732	+	0.749074i
$196$	2.14482	−	6.66331i	0.153201	−	0.475951i
$197$	−1.24927	−	4.25461i	−0.0890065	−	0.303128i	0.902943	−	0.429760i	$-0.141402\pi$
$197$	−1.24927	−	4.25461i	−0.0890065	−	0.303128i	−0.991950	+	0.126631i	$0.959583\pi$
$198$	−1.75980	+	5.58524i	−0.125063	+	0.396926i
$199$	19.1788	−	0.913599i	1.35955	−	0.0647633i	0.644911	−	0.764258i	$-0.276894\pi$
$199$	19.1788	−	0.913599i	1.35955	−	0.0647633i	0.714638	+	0.699494i	$0.246591\pi$
$200$	−3.42873	−	3.59595i	−0.242448	−	0.254272i
$201$	−16.3443	−	15.1537i	−1.15284	−	1.06886i
$202$	−6.91342	−	3.15725i	−0.486426	−	0.222143i
$203$	7.64098	−	15.2264i	0.536292	−	1.06869i
$204$	−0.634750	+	1.44297i	−0.0444414	+	0.101028i
$205$	−10.7519	+	31.0656i	−0.750946	+	2.16971i
$206$	−5.89976	+	10.2187i	−0.411056	+	0.711969i
$207$	−9.78124	−	10.5512i	−0.679843	−	0.733357i
$208$	−1.95175	+	1.12685i	−0.135330	+	0.0781327i
$209$	−2.99247	−	3.45349i	−0.206993	−	0.238883i
$210$	−14.1413	−	3.06030i	−0.975840	−	0.211181i
$211$	−3.37136	+	23.4483i	−0.232094	+	1.61425i	0.456926	+	0.889505i	$0.348950\pi$
$211$	−3.37136	+	23.4483i	−0.232094	+	1.61425i	−0.689020	+	0.724742i	$0.741959\pi$
$212$	0.502225	+	5.25953i	0.0344929	+	0.361226i
$213$	−15.3195	−	3.49040i	−1.04967	−	0.239159i
$214$	4.63471	−	4.41918i	0.316822	−	0.302089i
$215$	−20.5770	−	10.6082i	−1.40334	−	0.723474i
$216$	−4.06623	−	3.23508i	−0.276672	−	0.220119i
$217$	−13.6224	+	21.7133i	−0.924747	+	1.47400i
$218$	−13.3968	−	11.6084i	−0.907347	−	0.786221i
$219$	7.06292	+	0.237523i	0.477268	+	0.0160503i
$220$	5.98926	+	1.45298i	0.403796	+	0.0979598i
$221$	0.194977	−	2.04189i	0.0131155	−	0.137352i
$222$	6.48592	+	2.14372i	0.435306	+	0.143877i
$223$	−0.325395	+	1.10819i	−0.0217900	+	0.0742101i	−0.969670	−	0.244417i	$-0.921404\pi$
$223$	−0.325395	+	1.10819i	−0.0217900	+	0.0742101i	0.947880	+	0.318627i	$0.103222\pi$
$224$	−2.01828	−	1.71071i	−0.134852	−	0.114302i
$225$	−1.70793	+	14.8076i	−0.113862	+	0.987176i
$226$	−2.08710	+	0.835550i	−0.138832	+	0.0555800i
$227$	−4.31661	+	2.22537i	−0.286504	+	0.147703i	−0.595488	−	0.803364i	$-0.703041\pi$
$227$	−4.31661	+	2.22537i	−0.286504	+	0.147703i	0.308984	+	0.951067i	$0.400011\pi$
$228$	3.81285	−	1.37964i	0.252512	−	0.0913686i
$229$	−10.6256	+	6.13469i	−0.702158	+	0.405391i	−0.808151	−	0.588976i	$-0.799531\pi$
$229$	−10.6256	+	6.13469i	−0.702158	+	0.405391i	0.105992	+	0.994367i	$0.466198\pi$
$230$	−10.3878	+	11.0169i	−0.684949	+	0.726434i
$231$	8.37771	−	3.13500i	0.551213	−	0.206268i
$232$	−4.21668	−	4.86630i	−0.276838	−	0.319488i
$233$	7.03288	+	0.335017i	0.460739	+	0.0219477i	0.276669	−	0.960965i	$-0.410770\pi$
$233$	7.03288	+	0.335017i	0.460739	+	0.0219477i	0.184070	+	0.982913i	$0.441073\pi$
$234$	6.34457	+	2.33634i	0.414758	+	0.152732i
$235$	−14.1759	−	19.9072i	−0.924733	−	1.29861i
$236$	−3.52818	+	2.77459i	−0.229665	+	0.180611i
$237$	−0.163665	+	1.26349i	−0.0106312	+	0.0820727i
$238$	2.33380	−	0.593167i	0.151278	−	0.0384493i
$239$	−15.3993	+	7.03261i	−0.996095	+	0.454902i	−0.845662	−	0.533719i	$-0.820794\pi$
$239$	−15.3993	+	7.03261i	−0.996095	+	0.454902i	−0.150433	+	0.988620i	$0.548067\pi$
$240$	−3.10952	+	4.49853i	−0.200718	+	0.290379i
$241$	−4.50463	+	1.55907i	−0.290168	+	0.100428i	−0.468275	−	0.883583i	$-0.655124\pi$
$241$	−4.50463	+	1.55907i	−0.290168	+	0.100428i	0.178106	+	0.984011i	$0.443003\pi$
$242$	6.79436	−	2.35155i	0.436758	−	0.151164i
$243$	0.347823	+	15.5846i	0.0223129	+	0.999751i
$244$	4.31292	−	1.96964i	0.276106	−	0.126094i
$245$	9.61696	+	19.8991i	0.614405	+	1.27131i
$246$	17.8845	+	2.31665i	1.14028	+	0.147705i
$247$	−4.14718	+	3.26138i	−0.263879	+	0.207517i
$248$	5.61974	+	7.89182i	0.356854	+	0.501131i
$249$	0.257453	−	0.460680i	0.0163154	−	0.0291944i
$250$	−0.0990081	−	0.00471634i	−0.00626182	−	0.000298287i
$251$	15.0018	+	17.3130i	0.946903	+	1.09278i	0.995575	+	0.0939690i	$0.0299554\pi$
$251$	15.0018	+	17.3130i	0.946903	+	1.09278i	−0.0486726	+	0.998815i	$0.515499\pi$
$252$	−0.0693735	+	7.93695i	−0.00437012	+	0.499981i
$253$	1.72028	−	9.20192i	0.108153	−	0.578520i
$254$	14.7798	−	8.53314i	0.927369	−	0.535417i
$255$	−1.69349	−	4.68025i	−0.106051	−	0.293089i
$256$	−0.888835	+	0.458227i	−0.0555522	+	0.0286392i
$257$	−12.3352	+	4.93828i	−0.769450	+	0.308041i	−0.722971	−	0.690878i	$-0.757224\pi$
$257$	−12.3352	+	4.93828i	−0.769450	+	0.308041i	−0.0464784	+	0.998919i	$0.514800\pi$
$258$	−3.40728	+	12.2344i	−0.212128	+	0.761683i
$259$	−3.52002	−	9.82289i	−0.218723	−	0.610364i
$260$	2.00470	−	6.82737i	0.124326	−	0.423416i
$261$	−3.12397	+	19.0628i	−0.193369	+	1.17996i
$262$	−0.848028	+	8.88095i	−0.0523913	+	0.548667i
$263$	−4.83163	−	1.17214i	−0.297931	−	0.0722772i	0.0840073	−	0.996465i	$-0.473228\pi$
$263$	−4.83163	−	1.17214i	−0.297931	−	0.0722772i	−0.381938	+	0.924188i	$0.624743\pi$
$264$	0.113635	−	3.37901i	0.00699374	−	0.207964i
$265$	−12.6070	−	10.9241i	−0.774445	−	0.671060i
$266$	−5.24671	−	3.29165i	−0.321696	−	0.201824i
$267$	−16.2058	+	10.7380i	−0.991779	+	0.657152i
$268$	11.4377	+	5.89654i	0.698668	+	0.360189i
$269$	3.32695	−	3.17225i	0.202848	−	0.193415i	−0.581845	−	0.813300i	$-0.697669\pi$
$269$	3.32695	−	3.17225i	0.202848	−	0.193415i	0.784693	+	0.619884i	$0.212821\pi$
$270$	16.3401	−	1.46716i	0.994429	−	0.0892885i
$271$	−0.668481	−	7.00064i	−0.0406073	−	0.425259i	−0.992802	−	0.119767i	$-0.961785\pi$
$271$	−0.668481	−	7.00064i	−0.0406073	−	0.425259i	0.952195	−	0.305492i	$-0.0988208\pi$
$272$	0.129526	−	0.900876i	0.00785370	−	0.0546237i
$273$	−3.15524	−	9.83393i	−0.190964	−	0.595176i
$274$	−15.2202	−	17.5651i	−0.919486	−	1.06114i
$275$	−8.39923	+	4.84930i	−0.506492	+	0.292424i
$276$	7.07451	+	4.35331i	0.425835	+	0.262038i
$277$	−1.54972	+	2.68419i	−0.0931135	+	0.161277i	−0.908820	−	0.417189i	$-0.863015\pi$
$277$	−1.54972	+	2.68419i	−0.0931135	+	0.161277i	0.815706	+	0.578466i	$0.196349\pi$
$278$	1.89751	−	5.48250i	0.113805	−	0.328819i
$279$	7.40550	−	28.1055i	0.443356	−	1.68263i
$280$	8.33917	−	0.488345i	0.498361	−	0.0291842i
$281$	−25.9255	−	11.8398i	−1.54658	−	0.706301i	−0.554535	−	0.832160i	$-0.687104\pi$
$281$	−25.9255	−	11.8398i	−1.54658	−	0.706301i	−0.992048	+	0.125859i	$0.959831\pi$
$282$	−9.11513	+	9.83132i	−0.542798	+	0.585447i
$283$	−9.85478	−	10.3354i	−0.585806	−	0.614375i	0.362404	−	0.932021i	$-0.381956\pi$
$283$	−9.85478	−	10.3354i	−0.585806	−	0.614375i	−0.948209	+	0.317646i	$0.897108\pi$
$284$	9.06111	−	0.431634i	0.537678	−	0.0256128i
$285$	−5.70662	+	11.4600i	−0.338031	+	0.678829i
$286$	1.23938	+	4.22095i	0.0732863	+	0.249590i
$287$	−14.0327	−	23.7052i	−0.828325	−	1.39927i
$288$	2.76268	+	1.16945i	0.162792	+	0.0689106i
$289$	−11.7040	−	11.1597i	−0.688469	−	0.656454i
$290$	20.2380	+	1.93249i	1.18842	+	0.113480i
$291$	0.166015	+	0.800932i	0.00973194	+	0.0469515i
$292$	−3.96507	+	0.961916i	−0.232038	+	0.0562919i
$293$	−0.0903330	−	0.628280i	−0.00527731	−	0.0367045i	0.987013	−	0.160643i	$-0.0513567\pi$
$293$	−0.0903330	−	0.628280i	−0.00527731	−	0.0367045i	−0.992290	+	0.123938i	$0.960448\pi$
$294$	9.61838	−	7.38152i	0.560955	−	0.430499i
$295$	2.01682	−	14.0273i	0.117424	−	0.816699i
$296$	−3.93942	−	0.187658i	−0.228974	−	0.0109074i
$297$	−8.00805	+	6.22468i	−0.464674	+	0.361193i
$298$	4.48789	−	7.77326i	0.259977	−	0.450293i
$299$	−10.5177	−	2.48946i	−0.608256	−	0.143969i
$300$	−1.34373	−	8.50033i	−0.0775803	−	0.490766i
$301$	17.9304	−	7.40588i	1.03349	−	0.426868i
$302$	1.58640	−	2.46848i	0.0912869	−	0.142045i
$303$	−6.74076	−	11.3072i	−0.387246	−	0.649582i
$304$	−1.90694	+	1.35793i	−0.109371	+	0.0778826i
$305$	−5.56380	+	13.8977i	−0.318582	+	0.795780i
$306$	−2.32552	+	1.43080i	−0.132941	+	0.0817932i
$307$	−4.56102	−	7.09709i	−0.260311	−	0.405052i	0.686356	−	0.727266i	$-0.259209\pi$
$307$	−4.56102	−	7.09709i	−0.260311	−	0.405052i	−0.946667	+	0.322214i	$0.895573\pi$
$308$	−4.17394	+	3.04132i	−0.237833	+	0.173295i
$309$	−18.4700	+	8.74910i	−1.05072	+	0.497719i
$310$	−30.0361	−	5.78898i	−1.70593	−	0.328792i
$311$	7.96999	+	23.0278i	0.451936	+	1.30578i	0.909165	+	0.416436i	$0.136721\pi$
$311$	7.96999	+	23.0278i	0.451936	+	1.30578i	−0.457229	+	0.889349i	$0.651158\pi$
$312$	−3.89064	−	0.316682i	−0.220264	−	0.0179286i
$313$	16.9772	+	12.0894i	0.959610	+	0.683335i	0.948558	−	0.316604i	$-0.102542\pi$
$313$	16.9772	+	12.0894i	0.959610	+	0.683335i	0.0110523	+	0.999939i	$0.496482\pi$
$314$	15.0166	−	9.65059i	0.847436	−	0.544614i
$315$	−17.1345	−	18.2875i	−0.965417	−	1.03038i
$316$	−0.104683	−	0.728085i	−0.00588887	−	0.0409580i
$317$	−0.0482496	−	0.505292i	−0.00270997	−	0.0283800i	0.994016	−	0.109236i	$-0.0348406\pi$
$317$	−0.0482496	−	0.505292i	−0.00270997	−	0.0283800i	−0.996726	+	0.0808564i	$0.974234\pi$
$318$	−4.46435	+	7.98839i	−0.250348	+	0.447967i
$319$	−11.1716	+	5.75938i	−0.625491	+	0.322463i
$320$	1.03265	−	2.98366i	0.0577272	−	0.166792i
$321$	10.9558	−	1.73189i	0.611493	−	0.0966648i
$322$	−1.41409	−	12.6095i	−0.0788044	−	0.702702i
$323$		−	2.13066i		−	0.118553i
$324$	−2.60745	−	8.61401i	−0.144858	−	0.478556i
$325$	5.13109	+	9.95292i	0.284621	+	0.552089i
$326$	11.0803	−	14.0898i	0.613684	−	0.780362i
$327$	−7.65507	−	29.7337i	−0.423326	−	1.64427i
$328$	−10.3059	+	1.48177i	−0.569050	+	0.0818170i
$329$	20.4064	+	1.72447i	1.12504	+	0.0950731i
$330$	7.10250	+	7.96880i	0.390980	+	0.438668i
$331$	10.5532	−	14.8199i	0.580056	−	0.814574i	−0.415416	−	0.909631i	$-0.636364\pi$
$331$	10.5532	−	14.8199i	0.580056	−	0.814574i	0.995472	+	0.0950574i	$0.0303035\pi$
$332$	−0.0718334	+	0.296101i	−0.00394237	+	0.0162507i
$333$	7.12984	+	9.44211i	0.390713	+	0.517424i
$334$	−2.33749	+	12.1281i	−0.127902	+	0.663618i
$335$	−38.9831	+	11.4465i	−2.12987	+	0.625387i
$336$	−1.19082	−	4.42515i	−0.0649647	−	0.241412i
$337$	26.9379	−	17.3120i	1.46740	−	0.943043i	0.469202	−	0.883091i	$-0.344541\pi$
$337$	26.9379	−	17.3120i	1.46740	−	0.943043i	0.998201	−	0.0599524i	$-0.0190949\pi$
$338$	−7.69760	+	1.86742i	−0.418694	+	0.101574i
$339$	−3.79660	−	0.865020i	−0.206203	−	0.0469814i
$340$	1.66685	+	2.34076i	0.0903976	+	0.126946i
$341$	17.5566	−	7.02860i	0.950742	−	0.380620i
$342$	6.79129	+	1.78943i	0.367231	+	0.0967614i
$343$	−17.9311	−	4.63433i	−0.968186	−	0.250230i
$344$		−	7.33237i		−	0.395335i
$345$	−25.6506	+	5.46635i	−1.38098	+	0.294299i
$346$	−14.0313	−	8.10100i	−0.754329	−	0.435512i
$347$	6.03129	+	31.2933i	0.323776	+	1.67991i	0.670473	+	0.741934i	$0.266091\pi$
$347$	6.03129	+	31.2933i	0.323776	+	1.67991i	−0.346697	+	0.937977i	$0.612697\pi$
$348$	−1.21527	−	11.0863i	−0.0651453	−	0.594290i
$349$	5.92741	+	0.852232i	0.317287	+	0.0456189i	0.299118	−	0.954216i	$-0.403307\pi$
$349$	5.92741	+	0.852232i	0.317287	+	0.0456189i	0.0181683	+	0.999835i	$0.494217\pi$
$350$	−8.96739	+	9.61224i	−0.479327	+	0.513796i
$351$	6.73876	+	9.57735i	0.359688	+	0.511201i
$352$	0.460195	+	1.89695i	0.0245285	+	0.101108i
$353$	−0.404183	−	8.48484i	−0.0215125	−	0.451602i	−0.983767	−	0.179451i	$-0.942568\pi$
$353$	−0.404183	−	8.48484i	−0.0215125	−	0.451602i	0.962254	−	0.272151i	$-0.0877352\pi$
$354$	−7.75953	+	0.478459i	−0.412414	+	0.0254298i
$355$	−19.7647	+	20.7286i	−1.04900	+	1.10016i
$356$	7.35013	−	8.48250i	0.389556	−	0.449572i
$357$	3.90938	+	1.45333i	0.206907	+	0.0769185i
$358$	3.37687	−	0.991539i	0.178473	−	0.0524045i
$359$	−7.57131	−	5.39150i	−0.399598	−	0.284553i	0.362538	−	0.931969i	$-0.381910\pi$
$359$	−7.57131	−	5.39150i	−0.399598	−	0.284553i	−0.762137	+	0.647416i	$0.775850\pi$
$360$	−8.86086	+	3.34704i	−0.467008	+	0.176405i
$361$	9.78459	−	9.32959i	0.514978	−	0.491031i
$362$	11.5696	−	9.09845i	0.608086	−	0.478204i
$363$	11.9965	+	3.34103i	0.629655	+	0.175358i
$364$	3.27813	+	4.98073i	0.171821	+	0.261061i
$365$	6.96458	−	10.8371i	0.364543	−	0.567240i
$366$	8.08486	+	1.44129i	0.422603	+	0.0753373i
$367$	28.0551	+	16.1976i	1.46446	+	0.845508i	0.999213	−	0.0396718i	$-0.0126312\pi$
$367$	28.0551	+	16.1976i	1.46446	+	0.845508i	0.465250	+	0.885180i	$0.345965\pi$
$368$	−4.60904	−	1.32542i	−0.240263	−	0.0690924i
$369$	23.2002	+	20.9146i	1.20776	+	1.08877i
$370$	9.41065	−	8.15437i	0.489236	−	0.423926i
$371$	13.8139	−	2.13999i	0.717184	−	0.111103i
$372$	0.234634	+	16.7789i	0.0121652	+	0.869946i
$373$	15.8947	−	1.51776i	0.822995	−	0.0785865i	0.324943	−	0.945734i	$-0.394655\pi$
$373$	15.8947	−	1.51776i	0.822995	−	0.0785865i	0.498052	+	0.867147i	$0.334049\pi$
$374$	−1.64931	−	0.660285i	−0.0852838	−	0.0341425i
$375$	−0.136421	−	0.104229i	−0.00704478	−	0.00538237i
$376$	3.54685	−	6.87992i	0.182915	−	0.354805i
$377$	6.02834	+	13.2002i	0.310475	+	0.679846i
$378$	−7.91565	+	11.2402i	−0.407137	+	0.578135i
$379$	18.2767	−	21.0925i	0.938812	−	1.08345i	−0.0575598	−	0.998342i	$-0.518332\pi$
$379$	18.2767	−	21.0925i	0.938812	−	1.08345i	0.996372	−	0.0851050i	$-0.0271226\pi$
$380$	1.39882	−	7.25778i	0.0717581	−	0.372316i
$381$	29.4622	+	2.39811i	1.50940	+	0.122859i
$382$	2.14875	+	0.205181i	0.109940	+	0.0104980i
$383$	29.1166	+	15.0107i	1.48779	+	0.767009i	0.994685	−	0.102960i	$-0.0328314\pi$
$383$	29.1166	+	15.0107i	1.48779	+	0.767009i	0.493105	+	0.869970i	$0.335862\pi$
$384$	−1.71770	−	0.222501i	−0.0876560	−	0.0113544i
$385$	2.91128	−	16.0437i	0.148373	−	0.817664i
$386$	−20.7525	−	9.47736i	−1.05628	−	0.482385i
$387$	−16.9039	+	14.0759i	−0.859274	+	0.715518i
$388$	−0.216396	−	0.419750i	−0.0109859	−	0.0213096i
$389$	2.63624	+	13.6781i	0.133663	+	0.693508i	0.985497	+	0.169696i	$0.0542785\pi$
$389$	2.63624	+	13.6781i	0.133663	+	0.693508i	−0.851834	+	0.523812i	$0.824509\pi$
$390$	9.58031	−	7.75327i	0.485118	−	0.392602i
$391$	3.41590	−	2.71731i	0.172750	−	0.137420i
$392$	−4.20621	+	5.59533i	−0.212446	+	0.282607i
$393$	−9.95478	+	11.8184i	−0.502152	+	0.596157i
$394$	−0.210989	+	4.42920i	−0.0106295	+	0.223140i
$395$	1.82555	+	1.43563i	0.0918536	+	0.0722344i
$396$	3.48976	−	4.70249i	0.175367	−	0.236309i
$397$	1.13489	+	1.44313i	0.0569585	+	0.0724287i	0.813698	−	0.581288i	$-0.197451\pi$
$397$	1.13489	+	1.44313i	0.0569585	+	0.0724287i	−0.756739	+	0.653717i	$0.773209\pi$
$398$	−18.4228	−	5.40942i	−0.923451	−	0.271150i
$399$	−4.23367	−	9.85721i	−0.211949	−	0.493478i
$400$	2.06403	+	4.51960i	0.103202	+	0.225980i
$401$	19.3652	−	20.3097i	0.967054	−	1.01422i	−0.0328373	−	0.999461i	$-0.510454\pi$
$401$	19.3652	−	20.3097i	0.967054	−	1.01422i	0.999891	−	0.0147562i	$-0.00469721\pi$
$402$	10.4891	+	19.6659i	0.523149	+	0.980847i
$403$	−7.14132	−	20.6335i	−0.355734	−	1.02783i
$404$	5.50055	+	5.24476i	0.273662	+	0.260937i
$405$	24.7263	+	14.0024i	1.22866	+	0.695783i
$406$	−12.2008	+	11.8899i	−0.605516	+	0.590084i
$407$	−2.16888	+	7.38652i	−0.107507	+	0.366136i
$408$	1.07179	−	1.15600i	0.0530614	−	0.0572305i
$409$	−0.969811	+	0.690599i	−0.0479541	+	0.0341479i	−0.603783	−	0.797149i	$-0.706341\pi$
$409$	−0.969811	+	0.690599i	−0.0479541	+	0.0341479i	0.555829	+	0.831297i	$0.312401\pi$
$410$	20.3211	−	25.8404i	1.00359	−	1.27617i
$411$	−4.38655	−	40.0164i	−0.216372	−	1.97387i
$412$	8.91748	−	7.72704i	0.439333	−	0.380684i
$413$	7.87403	+	8.88957i	0.387456	+	0.437427i
$414$	5.79233	+	13.1700i	0.284678	+	0.647270i
$415$	−0.481001	−	0.833117i	−0.0236114	−	0.0408961i
$416$	2.21296	−	0.426514i	0.108500	−	0.0209116i
$417$	8.10308	−	5.94266i	0.396809	−	0.291013i
$418$	1.69836	+	4.24229i	0.0830694	+	0.207497i
$419$	−4.07621	+	8.92565i	−0.199136	+	0.436047i	−0.982685	−	0.185283i	$-0.940680\pi$
$419$	−4.07621	+	8.92565i	−0.199136	+	0.436047i	0.783549	+	0.621329i	$0.213407\pi$
$420$	12.3626	+	7.51714i	0.603232	+	0.366799i
$421$	18.8795	+	5.54352i	0.920131	+	0.270175i	0.707299	−	0.706914i	$-0.249913\pi$
$421$	18.8795	+	5.54352i	0.920131	+	0.270175i	0.212832	+	0.977089i	$0.431731\pi$
$422$	10.8551	−	21.0560i	0.528419	−	1.02499i
$423$	−22.6697	+	5.03049i	−1.10224	+	0.244591i
$424$	1.24562	−	5.13453i	0.0604928	−	0.249355i
$425$	−4.44041	−	0.855818i	−0.215391	−	0.0415133i
$426$	13.3353	+	8.30895i	0.646099	+	0.402570i
$427$	−5.86936	−	11.0868i	−0.284038	−	0.536525i
$428$	−5.82517	+	2.66027i	−0.281570	+	0.128589i
$429$	−2.39119	+	7.23462i	−0.115448	+	0.349291i
$430$	15.9757	+	16.7549i	0.770418	+	0.807991i
$431$	0.377587	−	0.943168i	0.0181877	−	0.0454308i	−0.918996	−	0.394267i	$-0.870999\pi$
$431$	0.377587	−	0.943168i	0.0181877	−	0.0454308i	0.937184	+	0.348836i	$0.113423\pi$
$432$	2.78450	+	4.38709i	0.133970	+	0.211074i
$433$	−4.73749	−	0.681149i	−0.227669	−	0.0327339i	0.0275358	−	0.999621i	$-0.491234\pi$
$433$	−4.73749	−	0.681149i	−0.227669	−	0.0327339i	−0.255205	+	0.966887i	$0.582143\pi$
$434$	19.9749	−	16.0636i	0.958825	−	0.771080i
$435$	26.9318	+	22.6850i	1.29128	+	1.08766i
$436$	8.86327	+	15.3516i	0.424474	+	0.735210i
$437$	−11.1216	−	1.53571i	−0.532021	−	0.0734627i
$438$	−6.59678	−	2.53451i	−0.315206	−	0.121104i
$439$	−16.6421	−	5.75988i	−0.794283	−	0.274904i	−0.100358	−	0.994951i	$-0.531999\pi$
$439$	−16.6421	−	5.75988i	−0.794283	−	0.274904i	−0.693925	+	0.720048i	$0.744120\pi$
$440$	−5.18463	−	3.33196i	−0.247168	−	0.158845i
$441$	20.9740	−	1.04439i	0.998763	−	0.0497327i
$442$	−0.852089	+	1.86581i	−0.0405297	+	0.0887478i
$443$	−20.4510	−	26.0055i	−0.971655	−	1.23556i	−0.971860	−	0.235559i	$-0.924308\pi$
$443$	−20.4510	−	26.0055i	−0.971655	−	1.23556i	0.000205392	−	1.00000i	$-0.499935\pi$
$444$	−5.42805	−	4.14716i	−0.257604	−	0.196815i
$445$	1.68618	+	35.3974i	0.0799328	+	1.67800i
$446$	0.669953	−	0.940817i	0.0317232	−	0.0445490i
$447$	14.0499	−	6.65536i	0.664539	−	0.314788i
$448$	1.34776	+	2.27674i	0.0636755	+	0.107566i
$449$	17.5822	+	15.2351i	0.829758	+	0.718989i	0.962242	−	0.272196i	$-0.0877499\pi$
$449$	17.5822	+	15.2351i	0.829758	+	0.718989i	−0.132484	+	0.991185i	$0.542295\pi$
$450$	6.45710	−	13.4346i	0.304391	−	0.633314i
$451$	−1.93190	+	20.2317i	−0.0909695	+	0.952675i
$452$	2.24560	−	0.106971i	0.105624	−	0.00503149i
$453$	4.69141	−	1.95470i	0.220422	−	0.0918400i
$454$	4.80705	−	0.691150i	0.225606	−	0.0324373i
$455$	−18.3427	−	4.23886i	−0.859919	−	0.198721i
$456$	−4.05438	+	0.0566958i	−0.189864	+	0.00265502i
$457$	0.335638	−	7.04590i	0.0157005	−	0.329593i	−0.977329	−	0.211727i	$-0.932091\pi$
$457$	0.335638	−	7.04590i	0.0157005	−	0.329593i	0.993029	−	0.117867i	$-0.0376056\pi$
$458$	12.0476	−	2.32199i	0.562950	−	0.108500i
$459$	−4.72252	−	0.251717i	−0.220429	−	0.0117491i
$460$	13.4197	−	7.01349i	0.625698	−	0.327006i
$461$	0.103447			0.00481799			0.00240899	−	0.999997i	$-0.499233\pi$
$461$	0.103447			0.00481799			0.00240899	+	0.999997i	$0.499233\pi$
$462$	−8.94230	+	0.222500i	−0.416034	+	0.0103516i
$463$	10.8683	+	6.98461i	0.505091	+	0.324602i	0.768250	−	0.640150i	$-0.221128\pi$
$463$	10.8683	+	6.98461i	0.505091	+	0.324602i	−0.263159	+	0.964753i	$0.584764\pi$
$464$	2.39315	+	5.97780i	0.111099	+	0.277512i
$465$	−37.0939	−	37.8295i	−1.72019	−	1.75430i
$466$	−6.53650	−	2.61682i	−0.302798	−	0.121222i
$467$	−1.50663	−	6.21041i	−0.0697184	−	0.287383i	0.926271	−	0.376859i	$-0.122996\pi$
$467$	−1.50663	−	6.21041i	−0.0697184	−	0.287383i	−0.995989	+	0.0894759i	$0.971481\pi$
$468$	−5.23149	−	4.28295i	−0.241826	−	0.197980i
$469$	13.8050	−	31.1216i	0.637457	−	1.43706i
$470$	6.88520	+	23.4488i	0.317591	+	1.08161i
$471$	30.9001	+	1.03916i	1.42380	+	0.0478819i
$472$	4.24161	−	1.46804i	0.195236	−	0.0675719i
$473$	−13.9091	−	3.37432i	−0.639543	−	0.155152i
$474$	0.567912	−	1.14047i	0.0260851	−	0.0523836i
$475$	6.28854	+	9.78516i	0.288538	+	0.448974i
$476$	−2.39945	−	0.202769i	−0.109979	−	0.00929391i
$477$	−14.2283	+	6.98507i	−0.651467	+	0.319824i
$478$	16.8525	−	1.60921i	0.770813	−	0.0736038i
$479$	12.5556	+	9.87385i	0.573681	+	0.451148i	0.862372	−	0.506274i	$-0.168978\pi$
$479$	12.5556	+	9.87385i	0.573681	+	0.451148i	−0.288691	+	0.957422i	$0.593220\pi$
$480$	4.40982	−	3.23409i	0.201280	−	0.147615i
$481$	8.39945	+	2.90708i	0.382982	+	0.132551i
$482$	4.76680			0.217122
$483$	10.4039	−	19.3587i	0.473392	−	0.880852i
$484$	−7.18980			−0.326809
$485$	1.40903	+	0.487669i	0.0639806	+	0.0221439i
$486$	4.76852	−	14.8412i	0.216305	−	0.673210i
$487$	0.785749	+	0.617920i	0.0356057	+	0.0280006i	0.635803	−	0.771851i	$-0.280669\pi$
$487$	0.785749	+	0.617920i	0.0356057	+	0.0280006i	−0.600198	+	0.799852i	$0.704911\pi$
$488$	−4.71992	+	0.450698i	−0.213661	+	0.0204021i
$489$	29.6638	−	9.16250i	1.34144	−	0.414343i
$490$	−2.57966	−	21.9501i	−0.116537	−	0.991605i
$491$	0.457816	+	0.712376i	0.0206610	+	0.0321491i	0.851430	−	0.524468i	$-0.175736\pi$
$491$	0.457816	+	0.712376i	0.0206610	+	0.0321491i	−0.830769	+	0.556617i	$0.812099\pi$
$492$	−16.1432	−	8.03870i	−0.727791	−	0.362412i
$493$	−5.69524	−	1.38165i	−0.256501	−	0.0622263i
$494$	4.98578	−	1.72560i	0.224321	−	0.0776382i
$495$	2.27145	+	18.3489i	0.102094	+	0.824722i
$496$	−2.72950	−	9.29582i	−0.122558	−	0.417395i
$497$	−2.54154	−	23.8657i	−0.114003	−	1.07052i
$498$	−0.393967	+	0.351138i	−0.0176541	+	0.0157349i
$499$	−7.80677	−	32.1799i	−0.349479	−	1.44057i	−0.827124	−	0.562019i	$-0.810025\pi$
$499$	−7.80677	−	32.1799i	−0.349479	−	1.44057i	0.477645	−	0.878553i	$-0.341490\pi$
$500$	0.0920202	+	0.0368393i	0.00411527	+	0.00164750i
$501$	−15.2749	+	14.9779i	−0.682433	+	0.669164i
$502$	−8.51416	−	21.2673i	−0.380006	−	0.949208i
$503$	25.8503	+	16.6130i	1.15261	+	0.740735i	0.970156	−	0.242480i	$-0.0779609\pi$
$503$	25.8503	+	16.6130i	1.15261	+	0.740735i	0.182450	+	0.983215i	$0.441597\pi$
$504$	2.66148	−	7.47774i	0.118552	−	0.333085i
$505$	−23.9963			−1.06782
$506$	−4.63532	+	8.13317i	−0.206065	+	0.361564i
$507$	−12.8067	−	4.92038i	−0.568764	−	0.218522i
$508$	−16.7579	+	3.22982i	−0.743510	+	0.143300i
$509$	0.165721	−	3.47891i	0.00734545	−	0.154200i	−0.992215	−	0.124540i	$-0.960255\pi$
$509$	0.165721	−	3.47891i	0.00734545	−	0.154200i	0.999560	−	0.0296600i	$-0.00944245\pi$
$510$	0.0695937	+	4.97673i	0.00308166	+	0.220373i
$511$	3.15392	+	10.3239i	0.139521	+	0.456701i
$512$	0.989821	−	0.142315i	0.0437443	−	0.00628949i
$513$	7.91387	+	9.23806i	0.349406	+	0.407870i
$514$	13.2719	−	0.632221i	0.585400	−	0.0278861i
$515$	−3.54129	+	37.0860i	−0.156048	+	1.63421i
$516$	7.22138	−	10.4471i	0.317903	−	0.459910i
$517$	−11.4186	−	9.89430i	−0.502191	−	0.435151i
$518$	0.113668	+	10.4339i	0.00499430	+	0.458440i
$519$	−12.0134	−	25.3612i	−0.527332	−	1.11323i
$520$	−4.12745	+	5.79620i	−0.181001	+	0.254180i
$521$	−1.23431	−	25.9114i	−0.0540762	−	1.13520i	−0.848967	−	0.528447i	$-0.822775\pi$
$521$	−1.23431	−	25.9114i	−0.0540762	−	1.13520i	0.794890	−	0.606753i	$-0.207528\pi$
$522$	9.18700	−	16.9927i	0.402104	−	0.743748i
$523$	4.92602	+	6.26394i	0.215400	+	0.273903i	0.881731	−	0.471753i	$-0.156379\pi$
$523$	4.92602	+	6.26394i	0.215400	+	0.273903i	−0.666331	+	0.745656i	$0.732136\pi$
$524$	3.70606	−	8.11514i	0.161900	−	0.354512i
$525$	−22.2434	+	4.86385i	−0.970784	+	0.212276i
$526$	4.18252	+	2.68794i	0.182367	+	0.117200i
$527$	8.33271	+	2.88398i	0.362979	+	0.125628i
$528$	−1.21255	+	3.15600i	−0.0527695	+	0.137347i
$529$	−11.7218	−	19.7889i	−0.509642	−	0.860387i
$530$	8.34076	+	14.4466i	0.362299	+	0.627521i
$531$	−11.5270	−	6.96036i	−0.500228	−	0.302054i
$532$	3.88155	+	4.82664i	0.168286	+	0.209261i
$533$	23.2264	+	3.33945i	1.00605	+	0.144648i
$534$	18.8265	−	4.84698i	0.814704	−	0.209749i
$535$	7.51466	−	18.7707i	0.324887	−	0.811528i
$536$	−8.88006	−	9.31314i	−0.383560	−	0.402266i
$537$	5.78789	+	1.91301i	0.249766	+	0.0825526i
$538$	−4.18151	+	1.90963i	−0.180278	+	0.0823302i
$539$	8.67840	+	10.5539i	0.373805	+	0.454590i
$540$	−15.9213	−	3.95786i	−0.685143	−	0.170319i
$541$	−34.2199	−	6.59534i	−1.47123	−	0.283556i	−0.610254	−	0.792206i	$-0.708932\pi$
$541$	−34.2199	−	6.59534i	−1.47123	−	0.283556i	−0.860973	+	0.508650i	$0.830145\pi$
$542$	−1.65797	+	6.83425i	−0.0712160	+	0.293556i
$543$	25.4451	−	1.56896i	1.09195	−	0.0673307i
$544$	−0.417050	+	0.808965i	−0.0178809	+	0.0346841i
$545$	−53.7011	−	15.7681i	−2.30030	−	0.675429i
$546$	−0.234659	+	10.3250i	−0.0100425	+	0.441871i
$547$	−9.37268	+	20.5233i	−0.400747	+	0.877513i	0.596447	+	0.802652i	$0.296579\pi$
$547$	−9.37268	+	20.5233i	−0.400747	+	0.877513i	−0.997194	+	0.0748610i	$0.976149\pi$
$548$	8.63814	+	21.5770i	0.369003	+	0.921725i
$549$	10.0998	+	10.0160i	0.431050	+	0.427473i
$550$	9.52332	−	1.83547i	0.406076	−	0.0782647i
$551$	7.53699	+	13.0544i	0.321086	+	0.556138i
$552$	−5.26159	−	6.42773i	−0.223948	−	0.273582i
$553$	−1.90685	+	0.389105i	−0.0810874	+	0.0165464i
$554$	2.34240	−	2.02970i	0.0995189	−	0.0862336i
$555$	21.4392	−	2.35013i	0.910043	−	0.0997577i
$556$	−3.58630	+	4.56035i	−0.152093	+	0.193402i
$557$	−27.5089	+	19.5890i	−1.16559	+	0.830013i	−0.988055	−	0.154102i	$-0.950752\pi$
$557$	−27.5089	+	19.5890i	−1.16559	+	0.830013i	−0.177535	+	0.984114i	$0.556812\pi$
$558$	−16.1906	+	24.1376i	−0.685403	+	1.02183i
$559$	−4.65560	+	15.8555i	−0.196911	+	0.670617i
$560$	−8.04024	−	2.26599i	−0.339762	−	0.0957555i
$561$	−1.69964	−	2.56512i	−0.0717590	−	0.108299i
$562$	20.6272	+	19.6680i	0.870105	+	0.829643i
$563$	−8.85649	−	25.5892i	−0.373257	−	1.07845i	−0.962683	−	0.270632i	$-0.912767\pi$
$563$	−8.85649	−	25.5892i	−0.373257	−	1.07845i	0.589426	−	0.807822i	$-0.299354\pi$
$564$	11.8293	−	6.30934i	0.498104	−	0.265671i
$565$	−4.89824	+	5.13712i	−0.206070	+	0.216120i
$566$	5.93240	+	12.9901i	0.249357	+	0.546016i
$567$	−22.3483	+	8.21921i	−0.938539	+	0.345175i
$568$	−8.70393	−	2.55570i	−0.365209	−	0.107235i
$569$	9.64944	+	12.2703i	0.404526	+	0.514396i	0.945047	−	0.326934i	$-0.106015\pi$
$569$	9.64944	+	12.2703i	0.404526	+	0.514396i	−0.540521	+	0.841330i	$0.681773\pi$
$570$	9.14095	−	8.96321i	0.382872	−	0.375428i
$571$	−0.809597	−	0.636674i	−0.0338806	−	0.0266440i	0.601075	−	0.799193i	$-0.294739\pi$
$571$	−0.809597	−	0.636674i	−0.0338806	−	0.0266440i	−0.634956	+	0.772549i	$0.718982\pi$
$572$	0.209320	−	4.39416i	0.00875210	−	0.183729i
$573$	2.85946	+	2.40857i	0.119456	+	0.100619i
$574$	5.50772	+	26.9911i	0.229888	+	1.12659i
$575$	−7.66769	+	22.5612i	−0.319765	+	0.940868i
$576$	−2.22824	−	2.00872i	−0.0928434	−	0.0836965i
$577$	7.97860	+	41.3969i	0.332154	+	1.72338i	0.636903	+	0.770944i	$0.280215\pi$
$577$	7.97860	+	41.3969i	0.332154	+	1.72338i	−0.304749	+	0.952433i	$0.598573\pi$
$578$	7.41028	+	14.3739i	0.308227	+	0.597877i
$579$	−20.2342	−	33.9417i	−0.840906	−	1.41057i
$580$	−18.4929	−	8.44541i	−0.767874	−	0.350676i
$581$	0.793181	+	0.143930i	0.0329067	+	0.00597122i
$582$	0.105075	−	0.811179i	0.00435551	−	0.0336245i
$583$	−9.16671	−	4.72577i	−0.379647	−	0.195721i
$584$	4.06161	+	0.387836i	0.168071	+	0.0160488i
$585$	21.2859	−	1.61155i	0.880063	−	0.0666295i
$586$	−0.120125	+	0.623270i	−0.00496234	+	0.0257470i
$587$	24.3109	−	28.0563i	1.00342	−	1.15801i	0.0160022	−	0.999872i	$-0.494906\pi$
$587$	24.3109	−	28.0563i	1.00342	−	1.15801i	0.987417	−	0.158136i	$-0.0505484\pi$
$588$	−11.5036	+	3.82968i	−0.474402	+	0.157933i
$589$	−9.42181	−	20.6309i	−0.388219	−	0.850081i
$590$	−6.49376	+	12.5961i	−0.267344	+	0.518575i
$591$	−4.66277	+	6.10292i	−0.191801	+	0.251041i
$592$	3.66138	+	1.46579i	0.150482	+	0.0602438i
$593$	−36.5217	+	3.48740i	−1.49977	+	0.143211i	−0.812401	−	0.583099i	$-0.801840\pi$
$593$	−36.5217	+	3.48740i	−1.49977	+	0.143211i	−0.687367	+	0.726310i	$0.741234\pi$
$594$	9.60351	−	3.26315i	0.394037	−	0.133889i
$595$	5.92467	−	4.76457i	0.242888	−	0.195328i
$596$	−6.78345	+	5.87789i	−0.277861	+	0.240768i
$597$	−20.9212	−	25.8512i	−0.856248	−	1.05802i
$598$	9.12503	+	5.79255i	0.373150	+	0.236875i
$599$	−12.0018	−	6.92924i	−0.490380	−	0.283121i	0.234352	−	0.972152i	$-0.424703\pi$
$599$	−12.0018	−	6.92924i	−0.490380	−	0.283121i	−0.724732	+	0.689031i	$0.758037\pi$
$600$	−1.51036	+	8.47231i	−0.0616601	+	0.345880i
$601$	6.24835	−	9.72262i	0.254875	−	0.396594i	−0.690111	−	0.723704i	$-0.742438\pi$
$601$	6.24835	−	9.72262i	0.254875	−	0.396594i	0.944986	+	0.327110i	$0.106075\pi$
$602$	−19.3665	+	1.13411i	−0.789318	+	0.0462227i
$603$	−4.42337	+	38.3503i	−0.180134	+	1.56174i
$604$	−2.30651	+	1.81386i	−0.0938505	+	0.0738048i
$605$	16.4291	−	15.6651i	0.667936	−	0.636876i
$606$	2.67180	+	12.8900i	0.108534	+	0.523621i
$607$	−6.89947	−	4.91309i	−0.280041	−	0.199416i	0.431403	−	0.902159i	$-0.358019\pi$
$607$	−6.89947	−	4.91309i	−0.280041	−	0.199416i	−0.711443	+	0.702743i	$0.751958\pi$
$608$	2.24620	−	0.659544i	0.0910954	−	0.0267480i
$609$	−29.0936	+	4.92454i	−1.17893	+	0.199552i
$610$	9.80329	−	11.3136i	0.396924	−	0.458074i
$611$	−12.0380	+	12.6251i	−0.487007	+	0.510758i
$612$	2.66558	−	0.591502i	0.107750	−	0.0239101i
$613$	0.766846	+	16.0981i	0.0309726	+	0.650195i	0.959969	+	0.280106i	$0.0903697\pi$
$613$	0.766846	+	16.0981i	0.0309726	+	0.650195i	−0.928996	+	0.370089i	$0.879327\pi$
$614$	1.98894	+	8.19852i	0.0802671	+	0.330865i
$615$	54.4027	−	16.8038i	2.19373	−	0.677596i
$616$	4.93910	−	1.50888i	0.199002	−	0.0607947i
$617$	11.8813	+	1.70827i	0.478323	+	0.0687725i	0.377260	−	0.926107i	$-0.376866\pi$
$617$	11.8813	+	1.70827i	0.478323	+	0.0687725i	0.101063	+	0.994880i	$0.467775\pi$
$618$	20.3157	−	2.22698i	0.817216	−	0.0895821i
$619$	−7.14792	−	37.0869i	−0.287299	−	1.49065i	−0.782926	−	0.622115i	$-0.786274\pi$
$619$	−7.14792	−	37.0869i	−0.287299	−	1.49065i	0.495627	−	0.868535i	$-0.334938\pi$
$620$	26.4907	+	15.2944i	1.06389	+	0.614239i
$621$	−4.71774	+	24.4692i	−0.189316	+	0.981916i
$622$		−	24.3680i		−	0.977067i
$623$	−23.5411	−	18.1014i	−0.943153	−	0.725216i
$624$	3.57308	+	1.57177i	0.143038	+	0.0629211i
$625$	−23.3540	+	9.34953i	−0.934160	+	0.373981i
$626$	−12.0894	−	16.9772i	−0.483191	−	0.678547i
$627$	−1.75826	+	7.71706i	−0.0702181	+	0.308190i
$628$	−17.3471	+	4.20836i	−0.692225	+	0.167932i
$629$	−3.01967	+	1.94062i	−0.120402	+	0.0773778i
$630$	10.2108	+	22.8858i	0.406809	+	0.911793i
$631$	−7.94047	+	2.33153i	−0.316105	+	0.0928168i	−0.435936	−	0.899977i	$-0.643583\pi$
$631$	−7.94047	+	2.33153i	−0.316105	+	0.0928168i	0.119831	+	0.992794i	$0.461765\pi$
$632$	−0.139208	+	0.722280i	−0.00553740	+	0.0287307i
$633$	36.2036	−	19.3097i	1.43896	−	0.767492i
$634$	−0.119669	+	0.493282i	−0.00475266	+	0.0195907i
$635$	31.2555	−	43.8922i	1.24034	−	1.74181i
$636$	6.83156	−	6.08889i	0.270889	−	0.241440i
$637$	12.6482	−	9.42867i	0.501140	−	0.373578i
$638$	12.4409	−	1.78873i	0.492540	−	0.0708166i
$639$	10.8170	+	24.9720i	0.427913	+	0.987879i
$640$	−1.95172	+	2.48181i	−0.0771485	+	0.0981023i
$641$	−11.6513	−	22.6003i	−0.460198	−	0.892659i	−0.998746	−	0.0500645i	$-0.984057\pi$
$641$	−11.6513	−	22.6003i	−0.460198	−	0.892659i	0.538548	−	0.842595i	$-0.318973\pi$
$642$	−10.9197	−	1.94665i	−0.430966	−	0.0768282i
$643$		−	10.3727i		−	0.409059i	−0.978860	−	0.204530i	$-0.934433\pi$
$643$		−	10.3727i		−	0.409059i	0.978860	−	0.204530i	$-0.0655665\pi$
$644$	−2.78785	+	12.3785i	−0.109857	+	0.487782i
$645$	6.26094	+	39.6062i	0.246524	+	1.55949i
$646$	−0.696872	+	2.01348i	−0.0274181	+	0.0792193i
$647$	−34.8594	+	17.9712i	−1.37046	+	0.706523i	−0.977084	−	0.212854i	$-0.931724\pi$
$647$	−34.8594	+	17.9712i	−1.37046	+	0.706523i	−0.393379	+	0.919377i	$0.628694\pi$
$648$	−0.353322	+	8.99306i	−0.0138798	+	0.353281i
$649$	−0.832823	−	8.72172i	−0.0326912	−	0.342357i
$650$	−1.59360	−	11.0837i	−0.0625061	−	0.434740i
$651$	44.2806	−	3.21494i	1.73549	−	0.126003i
$652$	−15.0793	+	9.69085i	−0.590550	+	0.379523i
$653$	24.6036	+	17.5201i	0.962811	+	0.685615i	0.949326	−	0.314294i	$-0.101768\pi$
$653$	24.6036	+	17.5201i	0.962811	+	0.685615i	0.0134857	+	0.999909i	$0.495707\pi$
$654$	−2.49088	+	30.6021i	−0.0974012	+	1.19663i
$655$	9.21267	+	26.6183i	0.359969	+	1.04006i
$656$	10.2237	+	1.97047i	0.399170	+	0.0769338i
$657$	−6.90292	−	10.1081i	−0.269309	−	0.394354i
$658$	−18.7200	−	8.30390i	−0.729783	−	0.323720i
$659$	24.4028	+	37.9714i	0.950596	+	1.47916i	0.876211	+	0.481927i	$0.160063\pi$
$659$	24.4028	+	37.9714i	0.950596	+	1.47916i	0.0743851	+	0.997230i	$0.476301\pi$
$660$	−4.10553	−	9.85352i	−0.159807	−	0.383548i
$661$	1.94540	−	4.85936i	0.0756671	−	0.189007i	−0.885712	−	0.464235i	$-0.846329\pi$
$661$	1.94540	−	4.85936i	0.0756671	−	0.189007i	0.961379	+	0.275228i	$0.0887534\pi$
$662$	−14.8199	+	10.5532i	−0.575991	+	0.410161i
$663$	−3.05162	+	1.81922i	−0.118515	+	0.0706525i
$664$	0.164728	−	0.256322i	0.00639268	−	0.00994721i
$665$	−19.3858	−	2.57204i	−0.751749	−	0.0997393i
$666$	−3.64950	−	11.2547i	−0.141415	−	0.436112i
$667$	−11.3169	+	28.7322i	−0.438191	+	1.11251i
$668$	6.17564	−	10.6965i	0.238943	−	0.413861i
$669$	1.88112	−	0.680662i	0.0727283	−	0.0263159i
$670$	40.5828	+	1.93320i	1.56785	+	0.0746859i
$671$	−1.31713	+	9.16087i	−0.0508474	+	0.353651i
$672$	−0.321996	+	4.57125i	−0.0124213	+	0.176340i
$673$	−6.72526	−	46.7752i	−0.259240	−	1.80305i	−0.538273	−	0.842771i	$-0.680923\pi$
$673$	−6.72526	−	46.7752i	−0.259240	−	1.80305i	0.279033	−	0.960281i	$-0.409986\pi$
$674$	−31.1186	+	7.54928i	−1.19864	+	0.290788i
$675$	22.4313	−	12.7823i	0.863382	−	0.491989i
$676$	7.88501	+	0.752927i	0.303270	+	0.0289587i
$677$	0.910847	+	0.868491i	0.0350067	+	0.0333788i	0.707381	−	0.706833i	$-0.249877\pi$
$677$	0.910847	+	0.868491i	0.0350067	+	0.0333788i	−0.672374	+	0.740212i	$0.734725\pi$
$678$	3.30487	+	2.05919i	0.126923	+	0.0790828i
$679$	−1.07519	+	0.636475i	−0.0412618	+	0.0244257i
$680$	−0.809585	−	2.75719i	−0.0310462	−	0.105734i
$681$	7.52976	+	3.74954i	0.288541	+	0.143683i
$682$	−18.8898	+	0.899833i	−0.723328	+	0.0344564i
$683$	−24.3415	−	25.5287i	−0.931403	−	0.976827i	0.0683804	−	0.997659i	$-0.478217\pi$
$683$	−24.3415	−	25.5287i	−0.931403	−	0.976827i	−0.999783	+	0.0208324i	$0.993368\pi$
$684$	−5.83251	−	3.91223i	−0.223012	−	0.149588i
$685$	−66.7505	−	30.4839i	−2.55041	−	1.16473i
$686$	15.4291	+	10.2441i	0.589087	+	0.391122i
$687$	19.4523	+	8.55690i	0.742151	+	0.326466i
$688$	−2.39818	+	6.92910i	−0.0914299	+	0.264169i
$689$	−5.95364	+	10.3120i	−0.226816	+	0.392856i
$690$	26.0277	+	3.22378i	0.990858	+	0.122727i
$691$	40.1768	−	23.1961i	1.52840	−	0.882421i	0.528969	−	0.848641i	$-0.322579\pi$
$691$	40.1768	−	23.1961i	1.52840	−	0.882421i	0.999429	−	0.0337803i	$-0.0107546\pi$
$692$	10.6100	+	12.2446i	0.403333	+	0.465472i
$693$	−12.9601	−	8.48992i	−0.492313	−	0.322505i
$694$	4.53546	−	31.5448i	0.172164	−	1.19742i
$695$	−1.74118	−	18.2345i	−0.0660467	−	0.691672i
$696$	−2.47756	+	10.8741i	−0.0939115	+	0.412181i
$697$	−6.85832	+	6.53939i	−0.259777	+	0.247697i
$698$	−5.32267	−	2.74402i	−0.201466	−	0.103863i
$699$	−6.73598	−	10.1660i	−0.254778	−	0.384513i
$700$	11.6180	−	6.15063i	0.439121	−	0.232472i
$701$	20.6562	+	17.8987i	0.780175	+	0.676026i	0.950971	−	0.309281i	$-0.100088\pi$
$701$	20.6562	+	17.8987i	0.780175	+	0.676026i	−0.170795	+	0.985307i	$0.554634\pi$
$702$	−3.23569	−	11.2546i	−0.122123	−	0.424779i
$703$	8.97249	+	2.17670i	0.338404	+	0.0820959i
$704$	0.185547	−	1.94314i	0.00699306	−	0.0732347i
$705$	−13.2839	+	40.1908i	−0.500299	+	1.51367i
$706$	−2.39317	+	8.15038i	−0.0900680	+	0.306743i
$707$	13.0018	−	15.3394i	0.488984	−	0.576898i
$708$	7.48925	+	2.08575i	0.281463	+	0.0783873i
$709$	33.3957	−	13.3696i	1.25420	−	0.502106i	0.353047	−	0.935605i	$-0.385145\pi$
$709$	33.3957	−	13.3696i	1.25420	−	0.502106i	0.901154	+	0.433499i	$0.142721\pi$
$710$	25.4573	−	13.1241i	0.955395	−	0.492540i
$711$	1.93237	−	1.06563i	0.0724694	−	0.0399641i
$712$	−9.72023	+	5.61198i	−0.364281	+	0.210318i
$713$	21.0597	−	41.4165i	0.788693	−	1.55106i
$714$	−3.21903	−	2.65203i	−0.120469	−	0.0992499i
$715$	9.09567	+	10.4970i	0.340159	+	0.392564i
$716$	−3.51545	−	0.167461i	−0.131378	−	0.00625833i
$717$	25.5962	+	14.3045i	0.955907	+	0.534213i
$718$	5.39150	+	7.57131i	0.201209	+	0.282559i
$719$	−32.7259	+	25.7359i	−1.22047	+	0.959787i	−0.999879	−	0.0155797i	$-0.995041\pi$
$719$	−32.7259	+	25.7359i	−1.22047	+	0.959787i	−0.220590	+	0.975367i	$0.570798\pi$
$720$	9.46823	−	0.264856i	0.352860	−	0.00987060i
$721$	−21.7881	−	22.3579i	−0.811433	−	0.832653i
$722$	−12.2979	+	5.61624i	−0.457679	+	0.209015i
$723$	6.79172	+	4.69464i	0.252587	+	0.174595i
$724$	−13.9091	+	4.81399i	−0.516928	+	0.178911i
$725$	30.2335	−	10.4639i	1.12284	−	0.388620i
$726$	−10.2440	−	7.08096i	−0.380191	−	0.262799i
$727$	−17.5241	+	8.00299i	−0.649933	+	0.296814i	−0.712968	−	0.701197i	$-0.752649\pi$
$727$	−17.5241	+	8.00299i	−0.649933	+	0.296814i	0.0630348	+	0.998011i	$0.479922\pi$
$728$	−1.46880	−	5.77897i	−0.0544374	−	0.214183i
$729$	21.4107	−	16.4494i	0.792989	−	0.609236i
$730$	−10.1260	+	7.96318i	−0.374780	+	0.294730i
$731$	−3.87100	−	5.43606i	−0.143174	−	0.201060i
$732$	−7.16880	−	4.00632i	−0.264967	−	0.148078i
$733$	−1.71837	−	0.0818561i	−0.0634695	−	0.00302342i	0.0158232	−	0.999875i	$-0.494963\pi$
$733$	−1.71837	−	0.0818561i	−0.0634695	−	0.00302342i	−0.0792926	+	0.996851i	$0.525266\pi$
$734$	−21.2143	−	24.4827i	−0.783036	−	0.903671i
$735$	17.9423	−	33.8151i	0.661813	−	1.24729i
$736$	3.92204	+	2.75999i	0.144568	+	0.101735i
$737$	−21.7531	+	12.5592i	−0.801287	+	0.462623i
$738$	−15.0838	−	27.3523i	−0.555241	−	1.00685i
$739$	42.5727	−	21.9477i	1.56606	−	0.807360i	0.566203	−	0.824266i	$-0.308412\pi$
$739$	42.5727	−	21.9477i	1.56606	−	0.807360i	0.999857	+	0.0169055i	$0.00538144\pi$
$740$	−11.5601	+	4.62797i	−0.424958	+	0.170127i
$741$	8.80320	+	2.45168i	0.323394	+	0.0900648i
$742$	−13.7541	−	2.49581i	−0.504929	−	0.0916240i
$743$	−10.7139	+	36.4882i	−0.393055	+	1.33862i	0.490967	+	0.871178i	$0.336644\pi$
$743$	−10.7139	+	36.4882i	−0.393055	+	1.33862i	−0.884022	+	0.467445i	$0.845175\pi$
$744$	5.26612	−	15.9328i	0.193065	−	0.584126i
$745$	2.69383	−	28.2110i	0.0986941	−	1.03357i
$746$	−15.5169	−	3.76436i	−0.568114	−	0.137823i
$747$	−0.907146	+	0.112298i	−0.0331907	+	0.00410876i
$748$	1.34264	+	1.16341i	0.0490919	+	0.0425383i
$749$	7.92736	+	14.9741i	0.289659	+	0.547143i
$750$	0.0948284	+	0.143116i	0.00346264	+	0.00522585i
$751$	−23.4915	−	12.1107i	−0.857218	−	0.441927i	−0.0271781	−	0.999631i	$-0.508652\pi$
$751$	−23.4915	−	12.1107i	−0.857218	−	0.441927i	−0.830040	+	0.557704i	$0.811682\pi$
$752$	−5.60198	+	5.34147i	−0.204283	+	0.194783i
$753$	8.81445	−	38.6869i	0.321217	−	1.40983i
$754$	−1.37942	−	14.4459i	−0.0502354	−	0.526089i
$755$	1.31847	−	9.17017i	0.0479841	−	0.333737i
$756$	11.1566	−	8.03306i	0.405762	−	0.292160i
$757$	−12.2476	−	14.1345i	−0.445146	−	0.513726i	0.488186	−	0.872740i	$-0.337659\pi$
$757$	−12.2476	−	14.1345i	−0.445146	−	0.513726i	−0.933332	+	0.359013i	$0.883113\pi$
$758$	−24.1702	+	13.9547i	−0.877901	+	0.506856i
$759$	−14.6144	+	7.02297i	−0.530471	+	0.254918i
$760$	−3.69567	+	6.40110i	−0.134056	+	0.232192i
$761$	−3.62814	+	10.4828i	−0.131520	+	0.380002i	−0.991463	−	0.130388i	$-0.958378\pi$
$761$	−3.62814	+	10.4828i	−0.131520	+	0.380002i	0.859943	+	0.510390i	$0.170499\pi$
$762$	−27.0575	−	11.9024i	−0.980190	−	0.431177i
$763$	39.1762	−	25.7843i	1.41827	−	0.933456i
$764$	−1.96347	−	0.896685i	−0.0710357	−	0.0324409i
$765$	−4.80223	+	7.15936i	−0.173625	+	0.258847i
$766$	−22.6057	−	23.7082i	−0.816779	−	0.856613i
$767$	−10.1042	+	0.481322i	−0.364841	+	0.0173795i
$768$	1.55046	+	0.772068i	0.0559472	+	0.0278596i
$769$	12.9477	+	44.0958i	0.466905	+	1.59013i	0.770570	+	0.637355i	$0.219971\pi$
$769$	12.9477	+	44.0958i	0.466905	+	1.59013i	−0.303665	+	0.952779i	$0.598210\pi$
$770$	−7.99855	+	14.2092i	−0.288248	+	0.512062i
$771$	19.5325	+	12.1702i	0.703445	+	0.438301i
$772$	16.5114	+	15.7436i	0.594259	+	0.566624i
$773$	37.4036	+	3.57161i	1.34531	+	0.128462i	0.742729	−	0.669593i	$-0.233531\pi$
$773$	37.4036	+	3.57161i	1.34531	+	0.128462i	0.602585	+	0.798054i	$0.294137\pi$
$774$	20.5780	−	7.77300i	0.739660	−	0.279395i
$775$	−46.7802	+	11.3488i	−1.68040	+	0.407660i
$776$	0.0672078	+	0.467441i	0.00241262	+	0.0167801i
$777$	−10.1140	+	14.9782i	−0.362838	+	0.537339i
$778$	1.98242	−	13.7881i	0.0710733	−	0.494326i
$779$	24.3469	+	1.15979i	0.872320	+	0.0415537i
$780$	−11.5892	+	4.19343i	−0.414961	+	0.150149i
$781$	−8.85355	+	15.3348i	−0.316805	+	0.548722i
$782$	−4.11678	+	1.45063i	−0.147216	+	0.0518743i
$783$	29.8250	−	15.1632i	1.06586	−	0.541887i
$784$	5.80493	−	3.91188i	0.207319	−	0.139710i
$785$	30.4699	−	47.4121i	1.08752	−	1.69221i
$786$	13.2727	−	7.91247i	0.473421	−	0.282228i
$787$	−41.2100	+	29.3455i	−1.46898	+	1.04605i	−0.483673	+	0.875249i	$0.660698\pi$
$787$	−41.2100	+	29.3455i	−1.46898	+	1.04605i	−0.985305	+	0.170806i	$0.945363\pi$
$788$	1.64803	−	4.11659i	0.0587088	−	0.146648i
$789$	3.31199	+	7.94898i	0.117910	+	0.282991i
$790$	−1.25560	−	1.95375i	−0.0446723	−	0.0695114i
$791$	−0.629864	−	5.91458i	−0.0223954	−	0.210298i
$792$	−4.83586	+	3.30246i	−0.171835	+	0.117348i
$793$	10.4925	+	2.02227i	0.372601	+	0.0718129i
$794$	−0.600471	−	1.73495i	−0.0213099	−	0.0615710i
$795$	−2.34404	+	28.7980i	−0.0831345	+	1.02136i
$796$	15.6403	+	11.1374i	0.554356	+	0.394755i
$797$	−12.1363	+	7.79955i	−0.429891	+	0.276274i	−0.737641	−	0.675193i	$-0.764060\pi$
$797$	−12.1363	+	7.79955i	−0.429891	+	0.276274i	0.307750	+	0.951467i	$0.400424\pi$
$798$	0.776843	+	10.6998i	0.0274999	+	0.378768i
$799$	−1.00258	−	6.97313i	−0.0354689	−	0.246691i
$800$	−0.472296	−	4.94611i	−0.0166982	−	0.174871i
$801$	31.5976	+	11.6356i	1.11645	+	0.411123i
$802$	−24.9428	+	12.8589i	−0.880761	+	0.454064i
$803$	2.60484	−	7.52619i	0.0919228	−	0.265593i
$804$	−3.48013	−	22.0150i	−0.122735	−	0.776408i
$805$	−20.5999	−	34.3597i	−0.726049	−	1.21102i
$806$			21.8343i			0.769082i
$807$	−7.83854	−	1.39738i	−0.275930	−	0.0491899i
$808$	−3.48263	−	6.75536i	−0.122518	−	0.237653i
$809$	4.08251	−	5.19133i	0.143533	−	0.182517i	−0.708971	−	0.705238i	$-0.750840\pi$
$809$	4.08251	−	5.19133i	0.143533	−	0.182517i	0.852504	+	0.522720i	$0.175083\pi$
$810$	−18.7867	−	21.3194i	−0.660096	−	0.749089i
$811$	5.21124	−	0.749263i	0.182991	−	0.0263102i	−0.0502098	−	0.998739i	$-0.515989\pi$
$811$	5.21124	−	0.749263i	0.182991	−	0.0263102i	0.233201	+	0.972428i	$0.425080\pi$
$812$	15.4186	−	7.24544i	0.541086	−	0.254265i
$813$	−9.09307	+	8.10455i	−0.318908	+	0.284239i
$814$	4.46549	−	6.27090i	0.156515	−	0.219795i
$815$	13.3425	−	54.9987i	0.467369	−	1.92652i
$816$	−1.39093	+	0.741874i	−0.0486923	+	0.0259708i
$817$	−3.24855	+	16.8551i	−0.113652	+	0.589685i
$818$	1.14235	−	0.335423i	0.0399412	−	0.0117278i
$819$	−10.5031	+	14.4800i	−0.367008	+	0.505972i
$820$	−27.6550	+	17.7728i	−0.965756	+	0.620654i
$821$	9.15038	−	2.21986i	0.319351	−	0.0774736i	−0.0728795	−	0.997341i	$-0.523219\pi$
$821$	9.15038	−	2.21986i	0.319351	−	0.0774736i	0.392230	+	0.919867i	$0.371704\pi$
$822$	−8.94280	+	39.2503i	−0.311916	+	1.36901i
$823$	−5.01182	−	7.03812i	−0.174701	−	0.245333i	0.717936	−	0.696109i	$-0.245087\pi$
$823$	−5.01182	−	7.03812i	−0.174701	−	0.245333i	−0.892637	+	0.450776i	$0.851147\pi$
$824$	−10.9543	+	4.38544i	−0.381611	+	0.152774i
$825$	15.3765	+	6.76399i	0.535341	+	0.235492i
$826$	−4.53347	−	10.9760i	−0.157740	−	0.381904i
$827$		−	29.8864i		−	1.03925i	−0.854394	−	0.519626i	$-0.826071\pi$
$827$		−	29.8864i		−	1.03925i	0.854394	−	0.519626i	$-0.173929\pi$
$828$	−1.16627	−	14.3401i	−0.0405308	−	0.498355i
$829$	−21.0516	−	12.1541i	−0.731152	−	0.422131i	0.0876915	−	0.996148i	$-0.472051\pi$
$829$	−21.0516	−	12.1541i	−0.731152	−	0.422131i	−0.818843	+	0.574017i	$0.805384\pi$
$830$	0.182060	+	0.944617i	0.00631939	+	0.0327881i
$831$	5.33641	−	0.584970i	0.185118	−	0.0202924i
$832$	−2.23075	−	0.320734i	−0.0773374	−	0.0111194i
$833$	−0.164433	+	6.36886i	−0.00569726	+	0.220668i
$834$	−9.60107	+	2.96556i	−0.332458	+	0.102689i
$835$	9.19384	+	37.8975i	0.318166	+	1.31150i
$836$	−0.217432	−	4.56445i	−0.00752003	−	0.157865i
$837$	−46.8406	+	18.4457i	−1.61905	+	0.637577i
$838$	6.77131	−	7.10155i	0.233911	−	0.245319i
$839$	−25.2083	+	29.0919i	−0.870288	+	1.00437i	0.129630	+	0.991562i	$0.458621\pi$
$839$	−25.2083	+	29.0919i	−0.870288	+	1.00437i	−0.999918	+	0.0128030i	$0.995925\pi$
$840$	−9.22403	−	11.1471i	−0.318259	−	0.384612i
$841$	11.9565	−	3.51074i	0.412293	−	0.121060i
$842$	−16.0280	−	11.4135i	−0.552363	−	0.393336i
$843$	10.0193	+	48.3378i	0.345083	+	1.66484i
$844$	−17.1448	+	16.3476i	−0.590150	+	0.562706i
$845$	−19.6581	+	15.4593i	−0.676260	+	0.531817i
$846$	23.0682	+	2.66072i	0.793101	+	0.0914773i
$847$	1.11205	+	18.9899i	0.0382107	+	0.652500i
$848$	−2.85645	+	4.44473i	−0.0980910	+	0.152633i
$849$	−4.34103	+	24.3509i	−0.148984	+	0.835721i
$850$	3.91628	+	2.26106i	0.134327	+	0.0775539i
$851$	7.95321	+	17.1608i	0.272633	+	0.588265i
$852$	−9.88431	−	12.2135i	−0.338631	−	0.418429i
$853$	−28.6635	+	24.8371i	−0.981421	+	0.850406i	−0.988752	−	0.149567i	$-0.952212\pi$
$853$	−28.6635	+	24.8371i	−0.981421	+	0.850406i	0.00733056	+	0.999973i	$0.497667\pi$
$854$	1.92043	+	12.3967i	0.0657158	+	0.424205i
$855$	21.8515	−	3.76819i	0.747306	−	0.128869i
$856$	6.37488	−	0.608727i	0.217889	−	0.0208059i
$857$	−49.4999	−	19.8168i	−1.69089	−	0.676928i	−0.691901	−	0.721992i	$-0.743227\pi$
$857$	−49.4999	−	19.8168i	−1.69089	−	0.676928i	−0.998984	+	0.0450641i	$0.985651\pi$
$858$	4.62588	−	6.05464i	0.157925	−	0.206702i
$859$	−8.89244	+	17.2489i	−0.303406	+	0.588526i	−0.990415	−	0.138123i	$-0.955893\pi$
$859$	−8.89244	+	17.2489i	−0.303406	+	0.588526i	0.687009	+	0.726649i	$0.258923\pi$
$860$	−9.61709	−	21.0585i	−0.327940	−	0.718089i
$861$	−18.7351	+	43.8812i	−0.638492	+	1.49547i
$862$	−0.665300	+	0.767797i	−0.0226602	+	0.0261513i
$863$	5.73877	−	29.7756i	0.195350	−	1.01357i	−0.743367	−	0.668883i	$-0.766773\pi$
$863$	5.73877	−	29.7756i	0.195350	−	1.01357i	0.938717	−	0.344688i	$-0.112015\pi$
$864$	−1.19648	−	5.05652i	−0.0407052	−	0.172026i
$865$	−50.9231	−	4.86256i	−1.73144	−	0.165332i
$866$	4.25415	+	2.19317i	0.144562	+	0.0745269i
$867$	−3.59820	+	27.7780i	−0.122201	+	0.943392i
$868$	−24.1302	+	8.64702i	−0.819032	+	0.293499i
$869$	1.30607	+	0.596460i	0.0443053	+	0.0202335i
$870$	−18.0310	−	30.2459i	−0.611309	−	1.02543i
$871$	13.2890	+	25.7770i	0.450280	+	0.873422i
$872$	−3.35477	−	17.4062i	−0.113607	−	0.589448i
$873$	0.948611	−	1.05228i	0.0321056	−	0.0356143i
$874$	10.0077	+	5.08878i	0.338515	+	0.172130i
$875$	0.0830681	−	0.248744i	0.00280821	−	0.00840908i
$876$	5.40500	+	4.55271i	0.182618	+	0.153822i
$877$	−1.05568	+	22.1615i	−0.0356478	+	0.748340i	0.908315	+	0.418288i	$0.137370\pi$
$877$	−1.05568	+	22.1615i	−0.0356478	+	0.748340i	−0.943962	+	0.330053i	$0.892933\pi$
$878$	13.8429	+	10.8862i	0.467175	+	0.367391i
$879$	−0.784989	+	0.769726i	−0.0264770	+	0.0259622i
$880$	3.80971	+	4.84444i	0.128425	+	0.163306i
$881$	−46.3557	−	13.6113i	−1.56176	−	0.458575i	−0.617174	−	0.786827i	$-0.711722\pi$
$881$	−46.3557	−	13.6113i	−1.56176	−	0.458575i	−0.944590	+	0.328252i	$0.893541\pi$
$882$	−20.1620	−	5.87298i	−0.678891	−	0.197754i
$883$	−6.76626	−	14.8160i	−0.227703	−	0.498600i	0.760951	−	0.648809i	$-0.224733\pi$
$883$	−6.76626	−	14.8160i	−0.227703	−	0.498600i	−0.988654	+	0.150209i	$0.952005\pi$
$884$	1.41547	−	1.48451i	0.0476075	−	0.0499293i
$885$	−21.6578	+	11.5515i	−0.728017	+	0.388299i
$886$	10.8206	+	31.2641i	0.363525	+	1.05034i
$887$	−0.461832	−	0.440356i	−0.0155068	−	0.0147857i	0.682286	−	0.731085i	$-0.260986\pi$
$887$	−0.461832	−	0.440356i	−0.0155068	−	0.0147857i	−0.697793	+	0.716300i	$0.745834\pi$
$888$	3.77311	+	5.69441i	0.126617	+	0.191092i
$889$	11.1226	+	43.7618i	0.373041	+	1.46772i
$890$	9.98390	−	34.0020i	0.334661	−	1.13975i
$891$	16.8968	+	4.80880i	0.566064	+	0.161101i
$892$	−0.940817	+	0.669953i	−0.0315009	+	0.0224317i
$893$	−11.2013	+	14.2436i	−0.374838	+	0.476645i
$894$	−15.4539	+	1.69404i	−0.516857	+	0.0566572i
$895$	8.39785	−	7.27678i	0.280709	−	0.243236i
$896$	−0.528983	−	2.59233i	−0.0176721	−	0.0866037i
$897$	7.29646	+	17.2401i	0.243622	+	0.575630i
$898$	−11.6323	−	20.1478i	−0.388176	−	0.672340i
$899$	−61.2558	+	11.8061i	−2.04299	+	0.393755i
$900$	−10.4960	+	10.5838i	−0.349867	+	0.352794i
$901$	−1.78721	−	4.46423i	−0.0595406	−	0.148725i
$902$	8.44280	−	18.4871i	0.281114	−	0.615555i
$903$	−28.7102	−	17.4574i	−0.955416	−	0.580946i
$904$	−2.15708	−	0.633375i	−0.0717433	−	0.0210657i
$905$	21.2944	−	41.3053i	0.707849	−	1.37303i
$906$	−5.07271	+	0.312787i	−0.168529	+	0.0103917i
$907$	8.41548	−	34.6891i	0.279431	−	1.15183i	−0.643061	−	0.765815i	$-0.722336\pi$
$907$	8.41548	−	34.6891i	0.279431	−	1.15183i	0.922492	−	0.386016i	$-0.126149\pi$
$908$	−4.76872	−	0.919096i	−0.158256	−	0.0305013i
$909$	−8.88811	+	20.9970i	−0.294800	+	0.696426i
$910$	15.9475	+	10.0050i	0.528654	+	0.331664i
$911$	−46.4005	+	21.1904i	−1.53732	+	0.702070i	−0.990795	−	0.135374i	$-0.956776\pi$
$911$	−46.4005	+	21.1904i	−1.53732	+	0.702070i	−0.546524	+	0.837444i	$0.684049\pi$
$912$	3.84994	+	1.27248i	0.127484	+	0.0421361i
$913$	−0.410423	−	0.430439i	−0.0135830	−	0.0142454i
$914$	−2.62167	+	6.54861i	−0.0867170	+	0.216609i
$915$	25.1100	−	6.46469i	0.830112	−	0.213716i
$916$	−12.1445	−	1.74611i	−0.401265	−	0.0576932i
$917$	−22.0071	−	8.53337i	−0.726740	−	0.281797i
$918$	4.38046	+	1.78246i	0.144577	+	0.0588299i
$919$	4.08912	+	7.08256i	0.134888	+	0.233632i	0.925554	−	0.378614i	$-0.123599\pi$
$919$	4.08912	+	7.08256i	0.134888	+	0.233632i	−0.790667	+	0.612247i	$0.790266\pi$
$920$	−14.9755	+	2.23859i	−0.493729	+	0.0738042i
$921$	−5.24058	+	13.6401i	−0.172683	+	0.449455i
$922$	−0.0977571	−	0.0338341i	−0.00321946	−	0.00111427i
$923$	17.1987	+	11.0529i	0.566101	+	0.363811i
$924$	8.52325	+	2.71448i	0.280394	+	0.0892998i
$925$	8.14031	−	17.8248i	0.267652	−	0.586076i
$926$	−7.98608	−	10.1551i	−0.262439	−	0.333718i
$927$	31.1390	+	16.8351i	1.02274	+	0.552939i
$928$	−0.306382	−	6.43175i	−0.0100575	−	0.211132i
$929$	27.1230	−	38.0889i	0.889875	−	1.24966i	−0.0776755	−	0.996979i	$-0.524750\pi$
$929$	27.1230	−	38.0889i	0.889875	−	1.24966i	0.967551	−	0.252676i	$-0.0813108\pi$
$930$	22.6810	+	47.8811i	0.743739	+	1.57008i
$931$	12.1479	−	10.9986i	0.398131	−	0.360464i
$932$	5.32112	+	4.61078i	0.174299	+	0.151031i
$933$	23.9991	−	34.7194i	0.785695	−	1.13666i
$934$	−0.607460	+	6.36161i	−0.0198767	+	0.208158i
$935$	−5.60283	+	0.266896i	−0.183232	+	0.00872842i
$936$	3.54294	+	5.75845i	0.115805	+	0.188221i
$937$	−34.4992	+	4.96024i	−1.12704	+	0.162044i	−0.680520	−	0.732730i	$-0.738246\pi$
$937$	−34.4992	+	4.96024i	−1.12704	+	0.162044i	−0.446520	+	0.894774i	$0.647337\pi$
$938$	−23.2246	+	24.8947i	−0.758311	+	0.812842i
$939$	−0.504754	−	36.0955i	−0.0164720	−	1.17793i
$940$	1.16284	−	24.4111i	0.0379278	−	0.796202i
$941$	52.8724	−	10.1903i	1.72359	−	0.332195i	0.771089	−	0.636728i	$-0.219713\pi$
$941$	52.8724	−	10.1903i	1.72359	−	0.332195i	0.952502	+	0.304533i	$0.0985004\pi$
$942$	−28.8608	−	11.0884i	−0.940334	−	0.361281i
$943$	29.1911	+	40.5124i	0.950594	+	1.31927i
$944$	−4.48848			−0.146087
$945$	−7.99105	+	42.6639i	−0.259949	+	1.38786i
$946$	12.0405	+	7.73798i	0.391471	+	0.251583i
$947$	21.4822	+	53.6600i	0.698079	+	1.74372i	0.667990	+	0.744170i	$0.267155\pi$
$947$	21.4822	+	53.6600i	0.698079	+	1.74372i	0.0300889	+	0.999547i	$0.490421\pi$
$948$	−0.909689	+	0.892001i	−0.0295453	+	0.0289709i
$949$	−8.53657	−	3.41753i	−0.277109	−	0.110938i
$950$	−2.74226	−	11.3038i	−0.0889708	−	0.366743i
$951$	−0.656319	+	0.584970i	−0.0212826	+	0.0189689i
$952$	2.20117	+	0.976401i	0.0713402	+	0.0316453i
$953$	5.25354	+	17.8919i	0.170179	+	0.579576i	0.999775	+	0.0212120i	$0.00675251\pi$
$953$	5.25354	+	17.8919i	0.170179	+	0.579576i	−0.829596	+	0.558364i	$0.811429\pi$
$954$	15.7303	−	1.94729i	0.509287	−	0.0630458i
$955$	6.44032	−	2.22902i	0.208404	−	0.0721292i
$956$	−16.4519	−	3.99119i	−0.532093	−	0.129084i
$957$	19.4874	+	9.70400i	0.629939	+	0.313686i
$958$	−8.63566	−	13.4373i	−0.279005	−	0.434141i
$959$	55.6538	−	26.1526i	1.79715	−	0.844513i
$960$	−5.22505	+	1.61391i	−0.168638	+	0.0520886i
$961$	62.5777	−	5.97545i	2.01864	−	0.192756i
$962$	−6.98668	−	5.49438i	−0.225260	−	0.177146i
$963$	−13.6412	−	13.5280i	−0.439580	−	0.435933i
$964$	−4.50463	−	1.55907i	−0.145084	−	0.0502141i
$965$	−72.0315			−2.31878
$966$	−16.1633	+	14.8912i	−0.520045	+	0.479118i
$967$	−21.8421			−0.702394			−0.351197	−	0.936302i	$-0.614225\pi$
$967$	−21.8421			−0.702394			−0.351197	+	0.936302i	$0.614225\pi$
$968$	6.79436	+	2.35155i	0.218379	+	0.0755818i
$969$	−2.97590	+	2.18248i	−0.0955997	+	0.0701112i
$970$	−1.17203	−	0.921694i	−0.0376316	−	0.0295938i
$971$	5.21833	−	0.498291i	0.167464	−	0.0159909i	−0.0109870	−	0.999940i	$-0.503497\pi$
$971$	5.21833	−	0.498291i	0.167464	−	0.0159909i	0.178451	+	0.983949i	$0.442891\pi$
$972$	−9.36034	+	12.4653i	−0.300233	+	0.399825i
$973$	12.5996	+	8.76688i	0.403925	+	0.281053i
$974$	−0.540432	−	0.840928i	−0.0173165	−	0.0269451i
$975$	8.64539	−	17.3615i	0.276874	−	0.556014i
$976$	4.60774	+	1.11783i	0.147490	+	0.0357807i
$977$	−9.62025	+	3.32960i	−0.307779	+	0.106523i	−0.476592	−	0.879125i	$-0.658128\pi$
$977$	−9.62025	+	3.32960i	−0.307779	+	0.106523i	0.168813	+	0.985648i	$0.446007\pi$
$978$	−31.0290	−	1.04350i	−0.992199	−	0.0333673i
$979$	6.17244	+	21.0214i	0.197272	+	0.671847i
$980$	−4.74140	+	21.5866i	−0.151458	+	0.689558i
$981$	−33.6878	+	41.1485i	−1.07557	+	1.31377i
$982$	−0.199641	−	0.822933i	−0.00637082	−	0.0262609i
$983$	35.7351	+	14.3062i	1.13977	+	0.456296i	0.863283	−	0.504721i	$-0.168405\pi$
$983$	35.7351	+	14.3062i	1.13977	+	0.456296i	0.276490	+	0.961017i	$0.410829\pi$
$984$	12.6261	+	12.8765i	0.402506	+	0.410488i
$985$	5.20336	+	12.9974i	0.165793	+	0.414130i
$986$	4.93011	+	3.16839i	0.157007	+	0.100902i
$987$	−18.4940	−	30.2680i	−0.588672	−	0.963442i
$988$	−5.27595			−0.167850
$989$	−31.1653	+	16.2878i	−0.990998	+	0.517921i
$990$	3.85481	−	18.0826i	0.122514	−	0.574704i
$991$	−51.9912	+	10.0205i	−1.65156	+	0.318311i	−0.928177	−	0.372140i	$-0.878624\pi$
$991$	−51.9912	+	10.0205i	−1.65156	+	0.318311i	−0.723379	+	0.690451i	$0.757412\pi$
$992$	−0.460986	+	9.67729i	−0.0146363	+	0.307254i
$993$	−31.5087	+	0.440613i	−0.999900	+	0.0139824i
$994$	−5.40395	+	23.3843i	−0.171403	+	0.741706i
$995$	−60.0050	+	8.62742i	−1.90229	+	0.273508i
$996$	0.487145	−	0.202972i	0.0154358	−	0.00643141i
$997$	31.6187	−	1.50618i	1.00137	−	0.0477014i	0.459515	−	0.888170i	$-0.348023\pi$
$997$	31.6187	−	1.50618i	1.00137	−	0.0477014i	0.541860	+	0.840469i	$0.317720\pi$
$998$	−3.14762	+	32.9634i	−0.0996363	+	1.04344i
$999$	5.88458	−	19.6300i	0.186180	−	0.621065i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.bd.a.59.9	✓	1280
3.2	odd	2	inner	966.2.bd.a.59.47	yes	1280
7.5	odd	6	inner	966.2.bd.a.887.34	yes	1280
21.5	even	6	inner	966.2.bd.a.887.3	yes	1280
23.16	even	11	inner	966.2.bd.a.269.3	yes	1280
69.62	odd	22	inner	966.2.bd.a.269.34	yes	1280
161.131	odd	66	inner	966.2.bd.a.131.47	yes	1280
483.131	even	66	inner	966.2.bd.a.131.9	yes	1280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.bd.a.59.9	✓	1280	1.1	even	1	trivial
966.2.bd.a.59.47	yes	1280	3.2	odd	2	inner
966.2.bd.a.131.9	yes	1280	483.131	even	66	inner
966.2.bd.a.131.47	yes	1280	161.131	odd	66	inner
966.2.bd.a.269.3	yes	1280	23.16	even	11	inner
966.2.bd.a.269.34	yes	1280	69.62	odd	22	inner
966.2.bd.a.887.3	yes	1280	21.5	even	6	inner
966.2.bd.a.887.34	yes	1280	7.5	odd	6	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.bd (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.945001 - 0.327068i) q^{2} +(-1.02432 - 1.39670i) q^{3} +(0.786053 + 0.618159i) q^{4} +(-3.14301 + 0.300121i) q^{5} +(0.511165 + 1.65491i) q^{6} +(1.51112 - 2.17176i) q^{7} +(-0.540641 - 0.841254i) q^{8} +(-0.901547 + 2.86133i) q^{9} +O(q^{10})\)	\(q+(-0.945001 - 0.327068i) q^{2} +(-1.02432 - 1.39670i) q^{3} +(0.786053 + 0.618159i) q^{4} +(-3.14301 + 0.300121i) q^{5} +(0.511165 + 1.65491i) q^{6} +(1.51112 - 2.17176i) q^{7} +(-0.540641 - 0.841254i) q^{8} +(-0.901547 + 2.86133i) q^{9} +(3.06831 + 0.744364i) q^{10} +(-1.84462 + 0.638428i) q^{11} +(0.0582153 - 1.73107i) q^{12} +(0.634938 + 2.16240i) q^{13} +(-2.13832 + 1.55807i) q^{14} +(3.63862 + 4.08243i) q^{15} +(0.235759 + 0.971812i) q^{16} +(-0.844945 - 0.338265i) q^{17} +(1.78781 - 2.40909i) q^{18} +(0.870072 + 2.17333i) q^{19} +(-2.65610 - 1.70697i) q^{20} +(-4.58116 + 0.113987i) q^{21} +1.95197 q^{22} +(-2.37468 + 4.16664i) q^{23} +(-0.621192 + 1.61682i) q^{24} +(4.87882 - 0.940315i) q^{25} +(0.107235 - 2.25114i) q^{26} +(4.91989 - 1.67172i) q^{27} +(2.53031 - 0.773004i) q^{28} +(6.37350 - 0.916371i) q^{29} +(-2.10327 - 5.04798i) q^{30} +(-9.67729 + 0.460986i) q^{31} +(0.0950560 - 0.995472i) q^{32} +(2.78117 + 1.92243i) q^{33} +(0.687838 + 0.596015i) q^{34} +(-4.09767 + 7.27938i) q^{35} +(-2.47742 + 1.69186i) q^{36} +(2.28768 - 3.21259i) q^{37} +(-0.111391 - 2.33838i) q^{38} +(2.36985 - 3.10180i) q^{39} +(1.95172 + 2.48181i) q^{40} +(4.32526 - 9.47100i) q^{41} +(4.36648 + 1.39063i) q^{42} +(6.16838 + 3.96418i) q^{43} +(-1.84462 - 0.638428i) q^{44} +(1.97483 - 9.26377i) q^{45} +(3.60685 - 3.16079i) q^{46} +(3.87019 + 6.70337i) q^{47} +(1.11584 - 1.32473i) q^{48} +(-2.43304 - 6.56356i) q^{49} +(-4.91803 - 0.707106i) q^{50} +(0.393037 + 1.52663i) q^{51} +(-0.837613 + 2.09225i) q^{52} +(3.64600 + 3.82382i) q^{53} +(-5.19607 - 0.0293639i) q^{54} +(5.60605 - 2.56020i) q^{55} +(-2.64397 - 0.0970937i) q^{56} +(2.14427 - 3.44142i) q^{57} +(-6.32268 - 1.21860i) q^{58} +(-1.05820 + 4.36195i) q^{59} +(0.336560 + 5.45825i) q^{60} +(2.17263 - 4.21432i) q^{61} +(9.29582 + 2.72950i) q^{62} +(4.85177 + 6.28175i) q^{63} +(-0.415415 + 0.909632i) q^{64} +(-2.64460 - 6.60590i) q^{65} +(-1.99944 - 2.72632i) q^{66} +(12.6356 - 2.43532i) q^{67} +(-0.455070 - 0.788205i) q^{68} +(8.25198 - 0.951239i) q^{69} +(6.25316 - 5.53880i) q^{70} +(6.85569 - 5.94049i) q^{71} +(2.89452 - 0.788522i) q^{72} +(-2.52214 + 3.20716i) q^{73} +(-3.21259 + 2.28768i) q^{74} +(-6.31080 - 5.85107i) q^{75} +(-0.659544 + 2.24620i) q^{76} +(-1.40092 + 4.97080i) q^{77} +(-3.25401 + 2.15611i) q^{78} +(-0.532359 - 0.507603i) q^{79} +(-1.03265 - 2.98366i) q^{80} +(-7.37442 - 5.15925i) q^{81} +(-7.18504 + 7.53545i) q^{82} +(0.126573 + 0.277156i) q^{83} +(-3.67150 - 2.74228i) q^{84} +(2.75719 + 0.809585i) q^{85} +(-4.53257 - 5.76363i) q^{86} +(-7.80839 - 7.96322i) q^{87} +(1.53436 + 1.20663i) q^{88} +(0.534057 - 11.2112i) q^{89} +(-4.89610 + 8.10837i) q^{90} +(5.65567 + 1.88871i) q^{91} +(-4.44227 + 1.80727i) q^{92} +(10.5565 + 13.0441i) q^{93} +(-1.46488 - 7.60050i) q^{94} +(-3.38691 - 6.56969i) q^{95} +(-1.48774 + 0.886914i) q^{96} +(-0.429571 - 0.196179i) q^{97} +(0.152500 + 6.99834i) q^{98} +(-0.163744 - 5.85363i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1280 q - 64 q^{4} + 4 q^{9}+O(q^{10}) \) 1280 * q - 64 * q^4 + 4 * q^9	\( 1280 q - 64 q^{4} + 4 q^{9} + 16 q^{15} + 64 q^{16} - 44 q^{18} + 120 q^{21} - 16 q^{22} - 12 q^{24} + 56 q^{25} + 32 q^{30} - 24 q^{33} + 8 q^{36} - 44 q^{37} - 20 q^{39} + 4 q^{42} + 136 q^{43} + 12 q^{45} + 12 q^{46} + 92 q^{49} + 4 q^{51} - 36 q^{54} - 56 q^{57} - 28 q^{58} + 8 q^{60} + 72 q^{61} - 134 q^{63} + 128 q^{64} + 24 q^{67} - 72 q^{70} - 44 q^{72} - 72 q^{73} + 48 q^{75} - 16 q^{78} - 72 q^{79} + 40 q^{81} + 48 q^{82} - 10 q^{84} - 32 q^{85} + 222 q^{87} - 8 q^{88} - 8 q^{91} - 16 q^{93} + 72 q^{94} - 12 q^{96} - 68 q^{99}+O(q^{100}) \) 1280 * q - 64 * q^4 + 4 * q^9 + 16 * q^15 + 64 * q^16 - 44 * q^18 + 120 * q^21 - 16 * q^22 - 12 * q^24 + 56 * q^25 + 32 * q^30 - 24 * q^33 + 8 * q^36 - 44 * q^37 - 20 * q^39 + 4 * q^42 + 136 * q^43 + 12 * q^45 + 12 * q^46 + 92 * q^49 + 4 * q^51 - 36 * q^54 - 56 * q^57 - 28 * q^58 + 8 * q^60 + 72 * q^61 - 134 * q^63 + 128 * q^64 + 24 * q^67 - 72 * q^70 - 44 * q^72 - 72 * q^73 + 48 * q^75 - 16 * q^78 - 72 * q^79 + 40 * q^81 + 48 * q^82 - 10 * q^84 - 32 * q^85 + 222 * q^87 - 8 * q^88 - 8 * q^91 - 16 * q^93 + 72 * q^94 - 12 * q^96 - 68 * q^99

Introduction

L-functions

Modular forms

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