LMFDB - Embedded newform 460.2.w.a.163.46

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(3,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([22, 33, 32]))

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

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

chi := DirichletCharacter("460.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.w (of order $44$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$1360$
Relative dimension:	$68$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			163.46
Character	$\chi$	$=$	460.163
Dual form			460.2.w.a.127.46

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.680913 - 1.23950i) q^{2} +(0.876446 + 0.656099i) q^{3} +(-1.07271 - 1.68798i) q^{4} +(-1.79976 - 1.32697i) q^{5} +(1.41002 - 0.639607i) q^{6} +(3.86395 - 0.276355i) q^{7} +(-2.82268 + 0.180260i) q^{8} +(-0.507507 - 1.72841i) q^{9} +O(q^{10})$	\(q+(0.680913 - 1.23950i) q^{2} +(0.876446 + 0.656099i) q^{3} +(-1.07271 - 1.68798i) q^{4} +(-1.79976 - 1.32697i) q^{5} +(1.41002 - 0.639607i) q^{6} +(3.86395 - 0.276355i) q^{7} +(-2.82268 + 0.180260i) q^{8} +(-0.507507 - 1.72841i) q^{9} +(-2.87026 + 1.32725i) q^{10} +(-0.203396 - 0.316490i) q^{11} +(0.167307 - 2.18323i) q^{12} +(0.0210304 - 0.294043i) q^{13} +(2.28847 - 4.97753i) q^{14} +(-0.706769 - 2.34384i) q^{15} +(-1.69857 + 3.62145i) q^{16} +(-2.18106 - 5.84765i) q^{17} +(-2.48793 - 0.547842i) q^{18} +(1.39450 + 3.05353i) q^{19} +(-0.309273 + 4.46143i) q^{20} +(3.56786 + 2.29292i) q^{21} +(-0.530784 + 0.0366066i) q^{22} +(4.04881 - 2.57044i) q^{23} +(-2.59219 - 1.69397i) q^{24} +(1.47829 + 4.77647i) q^{25} +(-0.350146 - 0.226285i) q^{26} +(1.83700 - 4.92519i) q^{27} +(-4.61140 - 6.22582i) q^{28} +(-3.83568 - 1.75170i) q^{29} +(-3.38644 - 0.719913i) q^{30} +(-2.71234 - 0.389975i) q^{31} +(3.33220 + 4.57126i) q^{32} +(0.0293834 - 0.410834i) q^{33} +(-8.73326 - 1.27832i) q^{34} +(-7.32090 - 4.62998i) q^{35} +(-2.37311 + 2.71075i) q^{36} +(-3.43953 + 6.29902i) q^{37} +(4.73438 + 0.350707i) q^{38} +(0.211353 - 0.243915i) q^{39} +(5.31935 + 3.42119i) q^{40} +(10.4928 + 3.08097i) q^{41} +(5.27147 - 2.86107i) q^{42} +(1.44920 + 1.08486i) q^{43} +(-0.316044 + 0.682832i) q^{44} +(-1.38016 + 3.78417i) q^{45} +(-0.429177 - 6.76874i) q^{46} +(0.303446 + 0.303446i) q^{47} +(-3.86473 + 2.05957i) q^{48} +(7.92496 - 1.13944i) q^{49} +(6.92702 + 1.42002i) q^{50} +(1.92505 - 6.55613i) q^{51} +(-0.518899 + 0.279926i) q^{52} +(7.03398 - 0.503081i) q^{53} +(-4.85393 - 5.63059i) q^{54} +(-0.0539092 + 0.839507i) q^{55} +(-10.8569 + 1.47657i) q^{56} +(-0.781214 + 3.59118i) q^{57} +(-4.78299 + 3.56157i) q^{58} +(7.04726 + 8.13298i) q^{59} +(-3.19820 + 3.70729i) q^{60} +(0.209492 - 1.45705i) q^{61} +(-2.33024 + 3.09640i) q^{62} +(-2.43863 - 6.53823i) q^{63} +(7.93501 - 1.01763i) q^{64} +(-0.428037 + 0.501301i) q^{65} +(-0.489221 - 0.316163i) q^{66} +(2.96943 + 13.6502i) q^{67} +(-7.53107 + 9.95444i) q^{68} +(5.23502 + 0.403563i) q^{69} +(-10.7237 + 5.92164i) q^{70} +(1.89316 - 2.94581i) q^{71} +(1.74409 + 4.78726i) q^{72} +(-3.18524 + 8.53995i) q^{73} +(5.46561 + 8.55238i) q^{74} +(-1.83819 + 5.15622i) q^{75} +(3.65840 - 5.62946i) q^{76} +(-0.873374 - 1.16669i) q^{77} +(-0.158419 - 0.428057i) q^{78} +(-3.89266 - 4.49237i) q^{79} +(7.86257 - 4.26379i) q^{80} +(0.295203 - 0.189716i) q^{81} +(10.9636 - 10.9080i) q^{82} +(-3.11091 + 5.69721i) q^{83} +(0.0431189 - 8.48213i) q^{84} +(-3.83427 + 13.4186i) q^{85} +(2.33146 - 1.05759i) q^{86} +(-2.21248 - 4.05185i) q^{87} +(0.631171 + 0.856685i) q^{88} +(-8.15971 + 1.17319i) q^{89} +(3.75071 + 4.28740i) q^{90} -1.14198i q^{91} +(-8.68207 - 4.07696i) q^{92} +(-2.12135 - 2.12135i) q^{93} +(0.582742 - 0.169501i) q^{94} +(1.54218 - 7.34609i) q^{95} +(-0.0787053 + 6.19272i) q^{96} +(-0.999441 + 0.545736i) q^{97} +(3.98388 - 10.5988i) q^{98} +(-0.443799 + 0.512172i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8}+O(q^{10}) $ 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8	$ 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8} - 18 q^{10} - 6 q^{12} - 36 q^{13} - 44 q^{16} - 36 q^{17} - 38 q^{18} - 14 q^{20} - 88 q^{21} - 28 q^{22} - 36 q^{25} - 36 q^{26} - 34 q^{28} + 2 q^{30} + 2 q^{32} - 60 q^{33} - 36 q^{36} - 36 q^{37} - 10 q^{38} + 2 q^{40} - 56 q^{41} - 202 q^{42} - 120 q^{45} - 44 q^{46} - 50 q^{48} - 34 q^{50} - 250 q^{52} - 84 q^{53} - 84 q^{56} - 44 q^{57} - 58 q^{58} - 42 q^{60} - 136 q^{61} - 82 q^{62} - 68 q^{65} - 84 q^{66} - 4 q^{68} + 16 q^{70} - 104 q^{72} - 36 q^{73} + 4 q^{76} - 44 q^{77} - 50 q^{78} + 204 q^{80} + 80 q^{81} - 10 q^{82} - 252 q^{85} + 44 q^{86} - 50 q^{88} + 264 q^{90} - 22 q^{92} - 88 q^{93} + 52 q^{96} - 36 q^{97} + 30 q^{98}+O(q^{100}) $ 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8 - 18 * q^10 - 6 * q^12 - 36 * q^13 - 44 * q^16 - 36 * q^17 - 38 * q^18 - 14 * q^20 - 88 * q^21 - 28 * q^22 - 36 * q^25 - 36 * q^26 - 34 * q^28 + 2 * q^30 + 2 * q^32 - 60 * q^33 - 36 * q^36 - 36 * q^37 - 10 * q^38 + 2 * q^40 - 56 * q^41 - 202 * q^42 - 120 * q^45 - 44 * q^46 - 50 * q^48 - 34 * q^50 - 250 * q^52 - 84 * q^53 - 84 * q^56 - 44 * q^57 - 58 * q^58 - 42 * q^60 - 136 * q^61 - 82 * q^62 - 68 * q^65 - 84 * q^66 - 4 * q^68 + 16 * q^70 - 104 * q^72 - 36 * q^73 + 4 * q^76 - 44 * q^77 - 50 * q^78 + 204 * q^80 + 80 * q^81 - 10 * q^82 - 252 * q^85 + 44 * q^86 - 50 * q^88 + 264 * q^90 - 22 * q^92 - 88 * q^93 + 52 * q^96 - 36 * q^97 + 30 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{11}\right)$

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 $

$2$	0.680913	−	1.23950i	0.481478	−	0.876458i
$2$	0.680913	−	1.23950i	0.481478	−	0.876458i
$3$	0.876446	+	0.656099i	0.506016	+	0.378799i	0.821569	−	0.570109i	$-0.193099\pi$
$3$	0.876446	+	0.656099i	0.506016	+	0.378799i	−0.315553	+	0.948908i	$0.602190\pi$
$4$	−1.07271	−	1.68798i	−0.536357	−	0.843991i
$5$	−1.79976	−	1.32697i	−0.804878	−	0.593440i
$5$	−1.79976	−	1.32697i	−0.804878	−	0.593440i
$6$	1.41002	−	0.639607i	0.575637	−	0.261118i
$7$	3.86395	−	0.276355i	1.46043	−	0.104452i	0.681620	−	0.731706i	$-0.261276\pi$
$7$	3.86395	−	0.276355i	1.46043	−	0.104452i	0.778815	+	0.627254i	$0.215821\pi$
$8$	−2.82268	+	0.180260i	−0.997967	+	0.0637314i
$9$	−0.507507	−	1.72841i	−0.169169	−	0.576136i
$10$	−2.87026	+	1.32725i	−0.907657	+	0.419714i
$11$	−0.203396	−	0.316490i	−0.0613261	−	0.0954253i	0.809236	−	0.587483i	$-0.199881\pi$
$11$	−0.203396	−	0.316490i	−0.0613261	−	0.0954253i	−0.870562	+	0.492058i	$0.836245\pi$
$12$	0.167307	−	2.18323i	0.0482974	−	0.630245i
$13$	0.0210304	−	0.294043i	0.00583278	−	0.0815529i	−0.993702	−	0.112056i	$-0.964256\pi$
$13$	0.0210304	−	0.294043i	0.00583278	−	0.0815529i	0.999535	+	0.0305031i	$0.00971094\pi$
$14$	2.28847	−	4.97753i	0.611619	−	1.33030i
$15$	−0.706769	−	2.34384i	−0.182487	−	0.605177i
$16$	−1.69857	+	3.62145i	−0.424642	+	0.905362i
$17$	−2.18106	−	5.84765i	−0.528985	−	1.41826i	−0.876871	−	0.480726i	$-0.840373\pi$
$17$	−2.18106	−	5.84765i	−0.528985	−	1.41826i	0.347887	−	0.937537i	$-0.386899\pi$
$18$	−2.48793	−	0.547842i	−0.586410	−	0.129128i
$19$	1.39450	+	3.05353i	0.319920	+	0.700528i	0.999451	−	0.0331190i	$-0.0105440\pi$
$19$	1.39450	+	3.05353i	0.319920	+	0.700528i	−0.679531	+	0.733647i	$0.737817\pi$
$20$	−0.309273	+	4.46143i	−0.0691555	+	0.997606i
$21$	3.56786	+	2.29292i	0.778570	+	0.500357i
$22$	−0.530784	+	0.0366066i	−0.113163	+	0.00780456i
$23$	4.04881	−	2.57044i	0.844234	−	0.535974i
$23$	4.04881	−	2.57044i	0.844234	−	0.535974i
$24$	−2.59219	−	1.69397i	−0.529129	−	0.345780i
$25$	1.47829	+	4.77647i	0.295658	+	0.955294i
$26$	−0.350146	−	0.226285i	−0.0686693	−	0.0443781i
$27$	1.83700	−	4.92519i	0.353531	−	0.947854i
$28$	−4.61140	−	6.22582i	−0.871472	−	1.17657i
$29$	−3.83568	−	1.75170i	−0.712267	−	0.325282i	0.0261196	−	0.999659i	$-0.491685\pi$
$29$	−3.83568	−	1.75170i	−0.712267	−	0.325282i	−0.738387	+	0.674377i	$0.764412\pi$
$30$	−3.38644	−	0.719913i	−0.618276	−	0.131437i
$31$	−2.71234	−	0.389975i	−0.487150	−	0.0700416i	−0.105636	−	0.994405i	$-0.533688\pi$
$31$	−2.71234	−	0.389975i	−0.487150	−	0.0700416i	−0.381514	+	0.924363i	$0.624597\pi$
$32$	3.33220	+	4.57126i	0.589056	+	0.808092i
$33$	0.0293834	−	0.410834i	0.00511500	−	0.0715170i
$34$	−8.73326	−	1.27832i	−1.49774	−	0.219230i
$35$	−7.32090	−	4.62998i	−1.23746	−	0.782609i
$36$	−2.37311	+	2.71075i	−0.395519	+	0.451792i
$37$	−3.43953	+	6.29902i	−0.565455	+	1.03555i	0.425953	+	0.904745i	$0.359939\pi$
$37$	−3.43953	+	6.29902i	−0.565455	+	1.03555i	−0.991408	+	0.130808i	$0.958243\pi$
$38$	4.73438	+	0.350707i	0.768018	+	0.0568921i
$39$	0.211353	−	0.243915i	0.0338436	−	0.0390576i
$40$	5.31935	+	3.42119i	0.841063	+	0.540937i
$41$	10.4928	+	3.08097i	1.63870	+	0.481167i	0.965956	−	0.258705i	$-0.0832959\pi$
$41$	10.4928	+	3.08097i	1.63870	+	0.481167i	0.672747	+	0.739872i	$0.265114\pi$
$42$	5.27147	−	2.86107i	0.813406	−	0.441473i
$43$	1.44920	+	1.08486i	0.221001	+	0.165439i	0.704042	−	0.710159i	$-0.251377\pi$
$43$	1.44920	+	1.08486i	0.221001	+	0.165439i	−0.483041	+	0.875598i	$0.660468\pi$
$44$	−0.316044	+	0.682832i	−0.0476454	+	0.102941i
$45$	−1.38016	+	3.78417i	−0.205742	+	0.564111i
$46$	−0.429177	−	6.76874i	−0.0632787	−	0.997996i
$47$	0.303446	+	0.303446i	0.0442622	+	0.0442622i	0.728891	−	0.684629i	$-0.240036\pi$
$47$	0.303446	+	0.303446i	0.0442622	+	0.0442622i	−0.684629	+	0.728891i	$0.740036\pi$
$48$	−3.86473	+	2.05957i	−0.557825	+	0.297274i
$49$	7.92496	−	1.13944i	1.13214	−	0.162777i
$50$	6.92702	+	1.42002i	0.979628	+	0.200821i
$51$	1.92505	−	6.55613i	0.269562	−	0.918042i
$52$	−0.518899	+	0.279926i	−0.0719584	+	0.0388187i
$53$	7.03398	−	0.503081i	0.966192	−	0.0691034i	0.420682	−	0.907208i	$-0.361791\pi$
$53$	7.03398	−	0.503081i	0.966192	−	0.0691034i	0.545510	+	0.838105i	$0.316336\pi$
$54$	−4.85393	−	5.63059i	−0.660537	−	0.766227i
$55$	−0.0539092	+	0.839507i	−0.00726912	+	0.113199i
$56$	−10.8569	+	1.47657i	−1.45081	+	0.197316i
$57$	−0.781214	+	3.59118i	−0.103474	+	0.475664i
$58$	−4.78299	+	3.56157i	−0.628037	+	0.467656i
$59$	7.04726	+	8.13298i	0.917476	+	1.05882i	0.998071	+	0.0620766i	$0.0197723\pi$
$59$	7.04726	+	8.13298i	0.917476	+	1.05882i	−0.0805956	+	0.996747i	$0.525682\pi$
$60$	−3.19820	+	3.70729i	−0.412886	+	0.478609i
$61$	0.209492	−	1.45705i	0.0268227	−	0.186556i	−0.972005	−	0.234959i	$-0.924504\pi$
$61$	0.209492	−	1.45705i	0.0268227	−	0.186556i	0.998828	+	0.0484036i	$0.0154134\pi$
$62$	−2.33024	+	3.09640i	−0.295941	+	0.393243i
$63$	−2.43863	−	6.53823i	−0.307239	−	0.823739i
$64$	7.93501	−	1.01763i	0.991877	−	0.127204i
$65$	−0.428037	+	0.501301i	−0.0530914	+	0.0621788i
$66$	−0.489221	−	0.316163i	−0.0602189	−	0.0389170i
$67$	2.96943	+	13.6502i	0.362773	+	1.66764i	0.690855	+	0.722993i	$0.257234\pi$
$67$	2.96943	+	13.6502i	0.362773	+	1.66764i	−0.328082	+	0.944649i	$0.606402\pi$
$68$	−7.53107	+	9.95444i	−0.913276	+	1.20715i
$69$	5.23502	+	0.403563i	0.630223	+	0.0485833i
$70$	−10.7237	+	5.92164i	−1.28173	+	0.707771i
$71$	1.89316	−	2.94581i	0.224676	−	0.349603i	−0.710554	−	0.703642i	$-0.751556\pi$
$71$	1.89316	−	2.94581i	0.224676	−	0.349603i	0.935231	+	0.354039i	$0.115192\pi$
$72$	1.74409	+	4.78726i	0.205543	+	0.564184i
$73$	−3.18524	+	8.53995i	−0.372804	+	0.999525i	0.606133	+	0.795363i	$0.292720\pi$
$73$	−3.18524	+	8.53995i	−0.372804	+	0.999525i	−0.978937	+	0.204162i	$0.934553\pi$
$74$	5.46561	+	8.55238i	0.635365	+	0.994194i
$75$	−1.83819	+	5.15622i	−0.212256	+	0.595389i
$76$	3.65840	−	5.62946i	0.419647	−	0.645743i
$77$	−0.873374	−	1.16669i	−0.0995302	−	0.132957i
$78$	−0.158419	−	0.428057i	−0.0179374	−	0.0484679i
$79$	−3.89266	−	4.49237i	−0.437959	−	0.505431i	0.493265	−	0.869879i	$-0.335803\pi$
$79$	−3.89266	−	4.49237i	−0.437959	−	0.505431i	−0.931224	+	0.364448i	$0.881258\pi$
$80$	7.86257	−	4.26379i	0.879062	−	0.476707i
$81$	0.295203	−	0.189716i	0.0328003	−	0.0210795i
$82$	10.9636	−	10.9080i	1.21072	−	1.20458i
$83$	−3.11091	+	5.69721i	−0.341467	+	0.625350i	−0.990828	−	0.135130i	$-0.956855\pi$
$83$	−3.11091	+	5.69721i	−0.341467	+	0.625350i	0.649361	+	0.760480i	$0.275036\pi$
$84$	0.0431189	−	8.48213i	0.00470466	−	0.925476i
$85$	−3.83427	+	13.4186i	−0.415885	+	1.45545i
$86$	2.33146	−	1.05759i	0.251408	−	0.114043i
$87$	−2.21248	−	4.05185i	−0.237202	−	0.434404i
$88$	0.631171	+	0.856685i	0.0672830	+	0.0913229i
$89$	−8.15971	+	1.17319i	−0.864927	+	0.124358i	−0.560477	−	0.828170i	$-0.689382\pi$
$89$	−8.15971	+	1.17319i	−0.864927	+	0.124358i	−0.304451	+	0.952528i	$0.598473\pi$
$90$	3.75071	+	4.28740i	0.395359	+	0.451931i
$91$		−	1.14198i		−	0.119712i
$92$	−8.68207	−	4.07696i	−0.905169	−	0.425052i
$93$	−2.12135	−	2.12135i	−0.219974	−	0.219974i
$94$	0.582742	−	0.169501i	0.0601052	−	0.0174827i
$95$	1.54218	−	7.34609i	0.158224	−	0.753693i
$96$	−0.0787053	+	6.19272i	−0.00803282	+	0.632041i
$97$	−0.999441	+	0.545736i	−0.101478	+	0.0554111i	−0.529186	−	0.848506i	$-0.677503\pi$
$97$	−0.999441	+	0.545736i	−0.101478	+	0.0554111i	0.427709	+	0.903917i	$0.359321\pi$
$98$	3.98388	−	10.5988i	0.402433	−	1.07064i
$99$	−0.443799	+	0.512172i	−0.0446035	+	0.0514752i
$100$	6.47681	−	7.61912i	0.647681	−	0.761912i
$101$	7.76712	−	2.28063i	0.772857	−	0.226931i	0.128555	−	0.991702i	$-0.458966\pi$
$101$	7.76712	−	2.28063i	0.772857	−	0.226931i	0.644302	+	0.764771i	$0.277148\pi$
$102$	−6.81553	−	6.85026i	−0.674838	−	0.678277i
$103$	0.799608	−	3.67574i	0.0787877	−	0.362181i	−0.920826	−	0.389974i	$-0.872484\pi$
$103$	0.799608	−	3.67574i	0.0787877	−	0.362181i	0.999614	+	0.0277924i	$0.00884775\pi$
$104$	−0.00635785	+	0.833780i	−0.000623439	+	0.0817588i
$105$	−3.37865	−	8.86116i	−0.329723	−	0.864761i
$106$	4.16596	−	9.06117i	0.404634	−	0.880099i
$107$	−4.58202	+	3.43005i	−0.442960	+	0.331596i	−0.797366	−	0.603496i	$-0.793774\pi$
$107$	−4.58202	+	3.43005i	−0.442960	+	0.331596i	0.354406	+	0.935092i	$0.384683\pi$
$108$	−10.2842	+	2.18250i	−0.989599	+	0.210011i
$109$	2.43499	+	1.11202i	0.233230	+	0.106513i	0.528602	−	0.848870i	$-0.322716\pi$
$109$	2.43499	+	1.11202i	0.233230	+	0.106513i	−0.295372	+	0.955382i	$0.595444\pi$
$110$	1.00386	+	0.638452i	0.0957143	+	0.0608740i
$111$	−7.14734	+	3.26408i	−0.678396	+	0.309813i
$112$	−5.56237	+	14.4625i	−0.525594	+	1.36658i
$113$	−0.405946	−	1.86610i	−0.0381882	−	0.175548i	0.954103	−	0.299480i	$-0.0968132\pi$
$113$	−0.405946	−	1.86610i	−0.0381882	−	0.175548i	−0.992291	+	0.123932i	$0.960450\pi$
$114$	3.91933	+	3.41360i	0.367079	+	0.319713i
$115$	−10.6978	−	0.746464i	−0.997574	−	0.0696081i
$116$	1.15776	+	8.35362i	0.107495	+	0.775614i
$117$	−0.518900	+	0.112880i	−0.0479723	+	0.0104357i
$118$	14.8794	−	3.19723i	1.36976	−	0.294329i
$119$	−10.0435	−	21.9922i	−0.920688	−	2.01603i
$120$	2.41748	+	6.48851i	0.220685	+	0.592317i
$121$	4.51077	−	9.87721i	0.410070	−	0.897928i
$122$	−1.66336	−	1.25179i	−0.150594	−	0.113332i
$123$	7.17497	+	9.58463i	0.646945	+	0.864217i
$124$	2.25129	+	4.99671i	0.202172	+	0.448718i
$125$	3.67767	−	10.5582i	0.328941	−	0.944351i
$126$	−9.76462	−	1.42928i	−0.869902	−	0.127331i
$127$	16.7080	+	3.63460i	1.48259	+	0.322518i	0.879786	−	0.475369i	$-0.157685\pi$
$127$	16.7080	+	3.63460i	1.48259	+	0.322518i	0.602807	+	0.797887i	$0.294049\pi$
$128$	4.14170	−	10.5284i	0.366078	−	0.930584i
$129$	0.558371	+	1.90164i	0.0491619	+	0.167430i
$130$	0.329906	+	0.871893i	0.0289347	+	0.0764701i
$131$	11.1082	+	9.62530i	0.970527	+	0.840966i	0.987296	−	0.158893i	$-0.0507925\pi$
$131$	11.1082	+	9.62530i	0.970527	+	0.840966i	−0.0167690	+	0.999859i	$0.505338\pi$
$132$	−0.725000	+	0.391109i	−0.0631032	+	0.0340417i
$133$	6.23213	+	11.4133i	0.540394	+	0.989658i
$134$	18.9414	+	5.61402i	1.63629	+	0.484978i
$135$	−9.84176	+	6.42653i	−0.847044	+	0.553108i
$136$	7.21052	+	16.1129i	0.618297	+	1.38167i
$137$	−11.4790	+	11.4790i	−0.980719	+	0.980719i	−0.999818	−	0.0190988i	$-0.993920\pi$
$137$	−11.4790	+	11.4790i	−0.980719	+	0.980719i	0.0190988	+	0.999818i	$0.493920\pi$
$138$	4.06481	−	6.21401i	0.346020	−	0.528972i
$139$	−2.50752			−0.212685			−0.106343	−	0.994330i	$-0.533914\pi$
$139$	−2.50752			−0.212685			−0.106343	+	0.994330i	$0.533914\pi$
$140$	0.0379241	+	17.3242i	0.00320517	+	1.46416i
$141$	0.0668633	+	0.465045i	0.00563091	+	0.0391638i
$142$	−2.36225	−	4.35240i	−0.198236	−	0.365246i
$143$	−0.0973392	+	0.0531512i	−0.00813991	+	0.00444473i
$144$	7.12137	+	1.09791i	0.593448	+	0.0914924i
$145$	4.57886	+	8.24247i	0.380253	+	0.684500i
$146$	8.41639	+	9.76306i	0.696545	+	0.807996i
$147$	7.69338	+	4.20091i	0.634540	+	0.346485i
$148$	14.3223	−	0.951196i	1.17728	−	0.0781878i
$149$	−11.1651	−	17.3733i	−0.914683	−	1.42328i	−0.905984	−	0.423313i	$-0.860867\pi$
$149$	−11.1651	−	17.3733i	−0.914683	−	1.42328i	−0.00869976	−	0.999962i	$-0.502769\pi$
$150$	5.13948	+	5.78938i	0.419637	+	0.472701i
$151$	11.0208	−	9.54960i	0.896862	−	0.777136i	−0.0786910	−	0.996899i	$-0.525074\pi$
$151$	11.0208	−	9.54960i	0.896862	−	0.777136i	0.975553	+	0.219764i	$0.0705286\pi$
$152$	−4.48665	−	8.36775i	−0.363915	−	0.678715i
$153$	−9.00022	+	6.73748i	−0.727625	+	0.544693i
$154$	−2.04080	+	0.288131i	−0.164453	+	0.0232182i
$155$	4.36408	+	4.30106i	0.350531	+	0.345469i
$156$	−0.638446	−	0.0951097i	−0.0511166	−	0.00761487i
$157$	−20.0783	−	7.48883i	−1.60243	−	0.597674i	−0.620045	−	0.784566i	$-0.712886\pi$
$157$	−20.0783	−	7.48883i	−1.60243	−	0.597674i	−0.982380	+	0.186892i	$0.940158\pi$
$158$	−8.21886	+	1.76604i	−0.653857	+	0.140498i
$159$	6.49498	+	4.17407i	0.515085	+	0.331025i
$160$	0.0687616	−	12.6489i	0.00543608	−	0.999985i
$161$	14.9340	−	11.0510i	1.17697	−	0.870938i
$162$	−0.0341445	−	0.495084i	−0.00268265	−	0.0388975i
$163$	20.7971	−	4.52414i	1.62896	−	0.354358i	0.697041	−	0.717031i	$-0.254499\pi$
$163$	20.7971	−	4.52414i	1.62896	−	0.354358i	0.931917	+	0.362673i	$0.118136\pi$
$164$	−6.05518	−	21.0167i	−0.472830	−	1.64113i
$165$	−0.598048	+	0.700412i	−0.0465580	+	0.0545270i
$166$	4.94342	+	7.73528i	0.383684	+	0.600374i
$167$	−23.3432	+	8.70656i	−1.80635	+	0.673734i	−0.810191	+	0.586166i	$0.800637\pi$
$167$	−23.3432	+	8.70656i	−1.80635	+	0.673734i	−0.996159	+	0.0875679i	$0.972091\pi$
$168$	−10.4842	−	5.82904i	−0.808876	−	0.449720i
$169$	12.7817	+	1.83773i	0.983205	+	0.141363i
$170$	14.0215	+	13.8895i	1.07540	+	1.06527i
$171$	4.57003	−	3.95995i	0.349479	−	0.302825i
$172$	0.276642	−	3.60997i	0.0210937	−	0.275257i
$173$	−11.1565	−	2.42695i	−0.848212	−	0.184517i	−0.232606	−	0.972571i	$-0.574725\pi$
$173$	−11.1565	−	2.42695i	−0.848212	−	0.184517i	−0.615606	+	0.788054i	$0.711089\pi$
$174$	−6.52877	−	0.0165944i	−0.494945	−	0.00125802i
$175$	7.03204	+	18.0475i	0.531572	+	1.36426i
$176$	1.49163	−	0.199008i	0.112436	−	0.0150008i
$177$	0.840506	+	11.7518i	0.0631763	+	0.883321i
$178$	−4.10189	+	10.9128i	−0.307449	+	0.817948i
$179$	−20.8900	−	6.13386i	−1.56139	−	0.458466i	−0.616911	−	0.787033i	$-0.711616\pi$
$179$	−20.8900	−	6.13386i	−1.56139	−	0.458466i	−0.944481	+	0.328567i	$0.893434\pi$
$180$	7.86813	−	1.72965i	0.586456	−	0.128921i
$181$	−0.171837	−	1.19516i	−0.0127726	−	0.0888352i	0.982438	−	0.186589i	$-0.0597433\pi$
$181$	−0.171837	−	1.19516i	−0.0127726	−	0.0888352i	−0.995211	+	0.0977539i	$0.968834\pi$
$182$	−1.41548	−	0.777588i	−0.104922	−	0.0576387i
$183$	1.13958	−	1.13958i	0.0842399	−	0.0842399i
$184$	−10.9651	+	7.98537i	−0.808360	+	0.588689i
$185$	14.5490	−	6.77259i	1.06966	−	0.497931i
$186$	−4.07387	+	1.18496i	−0.298711	+	0.0868853i
$187$	−1.40710	+	1.87967i	−0.102898	+	0.137455i
$188$	0.186700	−	0.837723i	0.0136165	−	0.0610972i
$189$	5.73698	−	19.5384i	0.417304	−	1.42121i
$190$	−8.05538	−	6.91358i	−0.584399	−	0.501564i
$191$	3.40203	+	2.94787i	0.246162	+	0.213301i	0.769199	−	0.639009i	$-0.220656\pi$
$191$	3.40203	+	2.94787i	0.246162	+	0.213301i	−0.523037	+	0.852310i	$0.675201\pi$
$192$	7.62227	+	4.31426i	0.550090	+	0.311355i
$193$	−21.2214	−	11.5878i	−1.52755	−	0.834105i	−0.527666	−	0.849452i	$-0.676933\pi$
$193$	−21.2214	−	11.5878i	−1.52755	−	0.834105i	−0.999882	+	0.0153472i	$0.995115\pi$
$194$	−0.00409322	+	1.61041i	−0.000293876	+	0.115620i
$195$	−0.704054	+	0.158529i	−0.0504184	+	0.0113525i
$196$	−10.4246	−	12.1549i	−0.744613	−	0.868208i
$197$	17.8281	+	1.27509i	1.27020	+	0.0908465i	0.690109	−	0.723705i	$-0.257562\pi$
$197$	17.8281	+	1.27509i	1.27020	+	0.0908465i	0.580091	+	0.814552i	$0.303017\pi$
$198$	0.332647	+	0.898833i	0.0236402	+	0.0638773i
$199$	0.590349	−	4.10597i	0.0418487	−	0.291064i	−0.958140	−	0.286300i	$-0.907575\pi$
$199$	0.590349	−	4.10597i	0.0418487	−	0.291064i	0.999989	−	0.00476390i	$-0.00151640\pi$
$200$	−5.03374	−	13.2160i	−0.355939	−	0.934509i
$201$	−6.35337	+	13.9119i	−0.448132	+	0.981272i
$202$	2.46189	−	11.1802i	0.173218	−	0.786639i
$203$	−15.3049	−	5.70845i	−1.07420	−	0.400655i
$204$	−13.1317	+	3.78340i	−0.919401	+	0.264891i
$205$	−14.7962	−	19.4687i	−1.03341	−	1.35975i
$206$	−4.01161	−	3.49397i	−0.279502	−	0.243436i
$207$	−6.49757	−	5.69347i	−0.451612	−	0.395724i
$208$	1.02914	+	0.575612i	0.0713580	+	0.0399115i
$209$	0.682776	−	1.06242i	0.0472286	−	0.0734891i
$210$	−13.2840	−	1.84585i	−0.916681	−	0.127375i
$211$	−2.91785	+	1.33254i	−0.200873	+	0.0917358i	−0.513312	−	0.858202i	$-0.671582\pi$
$211$	−2.91785	+	1.33254i	−0.200873	+	0.0917358i	0.312438	+	0.949938i	$0.398854\pi$
$212$	−8.39465	−	11.3336i	−0.576547	−	0.778393i
$213$	3.59199	−	1.33974i	0.246119	−	0.0917976i
$214$	1.13159	+	8.01497i	0.0773542	+	0.547892i
$215$	−1.16864	−	3.87554i	−0.0797007	−	0.264309i
$216$	−4.29745	+	14.2334i	−0.292405	+	0.968458i
$217$	−10.5881	−	0.757276i	−0.718767	−	0.0514072i
$218$	3.03637	−	2.26098i	0.205649	−	0.153133i
$219$	−8.39474	+	5.39497i	−0.567264	+	0.364558i
$220$	1.47490	−	0.809554i	0.0994379	−	0.0545801i
$221$	−1.76533	+	0.518347i	−0.118749	+	0.0348678i
$222$	−0.820893	+	11.0817i	−0.0550947	+	0.743754i
$223$	−0.106808	−	1.49337i	−0.00715239	−	0.100003i	0.992622	−	0.121251i	$-0.0386907\pi$
$223$	−0.106808	−	1.49337i	−0.00715239	−	0.100003i	−0.999774	+	0.0212478i	$0.993236\pi$
$224$	14.1387	+	16.7422i	0.944685	+	1.11864i
$225$	7.50545	−	4.97918i	0.500363	−	0.331945i
$226$	−2.58945	−	0.767485i	−0.172247	−	0.0510523i
$227$	−11.9900	+	16.0167i	−0.795802	+	1.06307i	0.200712	+	0.979650i	$0.435674\pi$
$227$	−11.9900	+	16.0167i	−0.795802	+	1.06307i	−0.996515	+	0.0834174i	$0.973417\pi$
$228$	6.89987	−	2.53364i	0.456955	−	0.167794i
$229$		−	11.5431i		−	0.762789i	−0.924412	−	0.381395i	$-0.875444\pi$
$229$		−	11.5431i		−	0.762789i	0.924412	−	0.381395i	$-0.124556\pi$
$230$	−8.20951	+	12.7516i	−0.541319	+	0.840817i
$231$		−	1.59556i		−	0.104980i
$232$	11.1426	+	4.25305i	0.731550	+	0.279227i
$233$	12.5080	−	16.7087i	0.819427	−	1.09463i	−0.174508	−	0.984656i	$-0.555833\pi$
$233$	12.5080	−	16.7087i	0.819427	−	1.09463i	0.993935	−	0.109971i	$-0.0350757\pi$
$234$	−0.213411	+	0.720037i	−0.0139511	+	0.0470703i
$235$	−0.143466	−	0.948796i	−0.00935872	−	0.0618926i
$236$	6.16861	−	20.6200i	0.401543	−	1.34225i
$237$	−0.464266	−	6.49129i	−0.0301573	−	0.421655i
$238$	−34.0981	−	2.52587i	−2.21025	−	0.163728i
$239$	14.6630	−	4.30543i	0.948468	−	0.278495i	0.229319	−	0.973351i	$-0.426350\pi$
$239$	14.6630	−	4.30543i	0.948468	−	0.278495i	0.719149	+	0.694856i	$0.244532\pi$
$240$	9.68859	+	1.42164i	0.625396	+	0.0917667i
$241$	−20.2396	+	13.0072i	−1.30375	+	0.837868i	−0.993615	−	0.112825i	$-0.964010\pi$
$241$	−20.2396	+	13.0072i	−1.30375	+	0.837868i	−0.310133	+	0.950693i	$0.600374\pi$
$242$	−9.17134	−	12.3166i	−0.589556	−	0.791742i
$243$	−15.3465	−	1.09760i	−0.984478	−	0.0704113i
$244$	−2.68420	+	1.20938i	−0.171838	+	0.0774225i
$245$	−15.7751	−	8.46549i	−1.00783	−	0.540840i
$246$	16.7657	−	2.36706i	1.06894	−	0.150918i
$247$	0.927196	−	0.345826i	0.0589961	−	0.0220044i
$248$	7.72635	+	0.611849i	0.490624	+	0.0388524i
$249$	−6.46448	+	2.95223i	−0.409670	+	0.187090i
$250$	−10.5827	−	11.7477i	−0.669306	−	0.742987i
$251$	−1.91664	+	2.98236i	−0.120977	+	0.188245i	−0.896460	−	0.443124i	$-0.853870\pi$
$251$	−1.91664	+	2.98236i	−0.120977	+	0.188245i	0.775483	+	0.631369i	$0.217506\pi$
$252$	−8.42045	+	11.1300i	−0.530439	+	0.701125i
$253$	−1.63703	−	0.758589i	−0.102919	−	0.0476921i
$254$	15.8818	−	18.2347i	0.996510	−	1.14414i
$255$	−12.1644	+	9.24499i	−0.761767	+	0.578944i
$256$	−10.2297	−	12.3025i	−0.639359	−	0.768908i
$257$	2.90871	+	1.08489i	0.181440	+	0.0676738i	0.438542	−	0.898711i	$-0.355495\pi$
$257$	2.90871	+	1.08489i	0.181440	+	0.0676738i	−0.257102	+	0.966384i	$0.582768\pi$
$258$	2.73728	+	0.602750i	0.170416	+	0.0375256i
$259$	−11.5494	+	25.2896i	−0.717644	+	1.57142i
$260$	1.30535	+	0.184765i	0.0809543	+	0.0114586i
$261$	−1.08101	+	7.51862i	−0.0669131	+	0.465391i
$262$	19.4943	−	7.21459i	1.20436	−	0.445719i
$263$	−16.1722	−	1.15666i	−0.997222	−	0.0713227i	−0.436825	−	0.899547i	$-0.643897\pi$
$263$	−16.1722	−	1.15666i	−0.997222	−	0.0713227i	−0.560397	+	0.828224i	$0.689352\pi$
$264$	−0.00888312	+	1.16495i	−0.000546718	+	0.0716976i
$265$	−13.3271	−	8.42847i	−0.818676	−	0.517757i
$266$	18.3903	+	0.0467433i	1.12758	+	0.00286601i
$267$	−7.92127	−	4.32534i	−0.484774	−	0.264707i
$268$	19.8560	−	19.6552i	1.21290	−	1.20063i
$269$	3.03447	+	2.62938i	0.185015	+	0.160316i	0.742444	−	0.669908i	$-0.233667\pi$
$269$	3.03447	+	2.62938i	0.185015	+	0.160316i	−0.557429	+	0.830225i	$0.688212\pi$
$270$	1.26429	+	16.5748i	0.0769423	+	1.00871i
$271$	−1.77897	+	6.05862i	−0.108065	+	0.368035i	−0.995714	−	0.0924852i	$-0.970519\pi$
$271$	−1.77897	+	6.05862i	−0.108065	+	0.368035i	0.887649	+	0.460520i	$0.152337\pi$
$272$	24.8816	+	2.03402i	1.50867	+	0.123331i
$273$	0.749251	−	1.00088i	0.0453467	−	0.0605762i
$274$	6.41202	+	22.0444i	0.387364	+	1.33175i
$275$	1.21103	−	1.43938i	0.0730276	−	0.0867977i
$276$	−4.93448	−	9.26953i	−0.297021	−	0.557960i
$277$	−12.3119	+	12.3119i	−0.739751	+	0.739751i	−0.972530	−	0.232779i	$-0.925218\pi$
$277$	−12.3119	+	12.3119i	−0.739751	+	0.739751i	0.232779	+	0.972530i	$0.425218\pi$
$278$	−1.70741	+	3.10807i	−0.102403	+	0.186410i
$279$	0.702492	+	4.88594i	0.0420571	+	0.292514i
$280$	21.4991	+	11.7493i	1.28482	+	0.702153i
$281$	16.2856	+	4.78188i	0.971517	+	0.285263i	0.728718	−	0.684814i	$-0.240116\pi$
$281$	16.2856	+	4.78188i	0.971517	+	0.285263i	0.242799	+	0.970077i	$0.421935\pi$
$282$	0.621951	+	0.233778i	0.0370366	+	0.0139213i
$283$	−0.370022	−	5.17359i	−0.0219955	−	0.307538i	−0.996526	−	0.0832825i	$-0.973460\pi$
$283$	−0.370022	−	5.17359i	−0.0219955	−	0.307538i	0.974530	−	0.224255i	$-0.0719949\pi$
$284$	−7.00329	−	0.0356012i	−0.415569	−	0.00211254i
$285$	6.17140	−	5.42663i	0.365562	−	0.321446i
$286$	−0.000398654		0.156843i	−2.35729e−5		0.00927433i
$287$	41.3952	+	9.00496i	2.44348	+	0.531546i
$288$	6.20989	−	8.07935i	0.365921	−	0.476080i
$289$	−16.5902	+	14.3755i	−0.975894	+	0.845617i
$290$	13.3343	−	0.0630827i	0.783019	−	0.00370434i
$291$	−1.23401	−	0.177424i	−0.0723391	−	0.0104008i
$292$	17.8321	−	3.78431i	1.04355	−	0.221460i
$293$	−15.6276	+	5.82881i	−0.912976	+	0.340523i	−0.761671	−	0.647965i	$-0.775620\pi$
$293$	−15.6276	+	5.82881i	−0.912976	+	0.340523i	−0.151306	+	0.988487i	$0.548348\pi$
$294$	10.4455	−	6.67549i	0.609196	−	0.389322i
$295$	−1.89117	−	23.9890i	−0.110108	−	1.39669i
$296$	8.57322	−	18.4001i	0.498308	−	1.06949i
$297$	−1.93241	+	0.420371i	−0.112130	+	0.0243924i
$298$	−29.1367	+	2.00947i	−1.68784	+	0.116406i
$299$	−0.670673	−	1.24458i	−0.0387860	−	0.0719760i
$300$	10.6755	−	2.42831i	0.616348	−	0.140199i
$301$	5.89944	+	3.79134i	0.340038	+	0.218529i
$302$	−4.33249	−	20.1628i	−0.249307	−	1.16024i
$303$	8.30378	+	3.09715i	0.477040	+	0.177927i
$304$	−13.4268	−	0.136514i	−0.770082	−	0.00782963i
$305$	−2.31050	+	2.34435i	−0.132299	+	0.134237i
$306$	2.22273	+	15.7434i	0.127065	+	0.899990i
$307$	−0.387817	+	0.290316i	−0.0221339	+	0.0165692i	−0.610287	−	0.792180i	$-0.708946\pi$
$307$	−0.387817	+	0.290316i	−0.0221339	+	0.0165692i	0.588153	+	0.808749i	$0.299855\pi$
$308$	−1.03247	+	2.72577i	−0.0588305	+	0.155315i
$309$	3.11246	−	2.69696i	0.177062	−	0.153425i
$310$	8.30271	−	2.48062i	0.471562	−	0.140890i
$311$	−13.4528	−	20.9329i	−0.762836	−	1.18700i	−0.977629	−	0.210337i	$-0.932544\pi$
$311$	−13.4528	−	20.9329i	−0.762836	−	1.18700i	0.214793	−	0.976660i	$-0.431092\pi$
$312$	−0.552614	+	0.726591i	−0.0312856	+	0.0411351i
$313$	−3.93531	−	2.14884i	−0.222437	−	0.121460i	0.364167	−	0.931334i	$-0.381354\pi$
$313$	−3.93531	−	2.14884i	−0.222437	−	0.121460i	−0.586604	+	0.809874i	$0.699536\pi$
$314$	−22.9540	+	19.7878i	−1.29537	+	1.11669i
$315$	−4.28708	+	15.0033i	−0.241550	+	0.845338i
$316$	−3.40733	+	11.3898i	−0.191677	+	0.640725i
$317$	−17.1588	+	9.36943i	−0.963735	+	0.526239i	−0.882427	−	0.470450i	$-0.844092\pi$
$317$	−17.1588	+	9.36943i	−0.963735	+	0.526239i	−0.0813086	+	0.996689i	$0.525910\pi$
$318$	9.59627	−	5.20834i	0.538132	−	0.292069i
$319$	0.225766	+	1.57024i	0.0126405	+	0.0879166i
$320$	−15.6315	−	8.69805i	−0.873828	−	0.486236i
$321$	−6.26634			−0.349753
$322$	−3.52889	−	26.0354i	−0.196657	−	1.45090i
$323$	14.8145	−	14.8145i	0.824299	−	0.824299i
$324$	−0.636905	−	0.294787i	−0.0353836	−	0.0163771i
$325$	1.43558	−	0.334230i	0.0796315	−	0.0185398i
$326$	8.55338	−	28.8586i	0.473728	−	1.59833i
$327$	1.40454	+	2.57223i	0.0776713	+	0.142244i
$328$	−30.1732	−	6.80515i	−1.66604	−	0.375752i
$329$	1.25636	+	1.08864i	0.0692653	+	0.0600187i
$330$	0.460942	+	1.21820i	0.0253740	+	0.0670597i
$331$	4.50374	+	15.3383i	0.247548	+	0.843071i	0.985710	+	0.168448i	$0.0538756\pi$
$331$	4.50374	+	15.3383i	0.247548	+	0.843071i	−0.738162	+	0.674623i	$0.764306\pi$
$332$	12.9539	−	0.860318i	0.710938	−	0.0472161i
$333$	12.6329	+	2.74811i	0.692277	+	0.150596i
$334$	−5.10291	+	34.8623i	−0.279219	+	1.90758i
$335$	12.7692	−	28.5075i	0.697657	−	1.55753i
$336$	−14.3639	+	9.02612i	−0.783617	+	0.492415i
$337$	11.6506	+	15.5634i	0.634649	+	0.847792i	0.996426	−	0.0844728i	$-0.0269206\pi$
$337$	11.6506	+	15.5634i	0.634649	+	0.847792i	−0.361777	+	0.932265i	$0.617830\pi$
$338$	10.9811	−	14.5915i	0.597291	−	0.793674i
$339$	0.868559	−	1.90188i	0.0471737	−	0.103296i
$340$	26.7634	−	7.92212i	1.45145	−	0.429637i
$341$	0.428254	+	0.937746i	0.0231913	+	0.0507818i
$342$	−1.79656	−	8.36093i	−0.0971471	−	0.452107i
$343$	3.80974	−	0.828757i	0.205706	−	0.0447487i
$344$	−4.28618	−	2.80097i	−0.231095	−	0.151018i
$345$	−8.88628	−	7.67305i	−0.478421	−	0.413103i
$346$	−10.6048	+	12.1759i	−0.570117	+	0.654581i
$347$	−0.582755	−	2.67888i	−0.0312839	−	0.143810i	0.958856	−	0.283894i	$-0.0916263\pi$
$347$	−0.582755	−	2.67888i	−0.0312839	−	0.143810i	−0.990140	+	0.140084i	$0.955263\pi$
$348$	−4.46609	+	8.08110i	−0.239408	+	0.433192i
$349$	7.98588	−	3.64703i	0.427474	−	0.195221i	−0.190047	−	0.981775i	$-0.560864\pi$
$349$	7.98588	−	3.64703i	0.427474	−	0.195221i	0.617522	+	0.786554i	$0.288137\pi$
$350$	27.1581	+	3.57257i	1.45166	+	0.190962i
$351$	−1.40959	−	0.643737i	−0.0752382	−	0.0343601i
$352$	0.769002	−	1.98438i	0.0409879	−	0.105768i
$353$	17.0159	−	12.7380i	0.905667	−	0.677974i	−0.0413544	−	0.999145i	$-0.513167\pi$
$353$	17.0159	−	12.7380i	0.905667	−	0.677974i	0.947021	+	0.321171i	$0.104076\pi$
$354$	15.1387	+	6.96016i	0.804611	+	0.369928i
$355$	−7.31623	+	2.78959i	−0.388305	+	0.148056i
$356$	10.7334	+	12.5149i	0.568867	+	0.663291i
$357$	5.62649	−	25.8646i	0.297785	−	1.36890i
$358$	−21.8272	+	21.7165i	−1.15360	+	1.14775i
$359$	−9.50461	+	2.79080i	−0.501634	+	0.147293i	−0.522753	−	0.852484i	$-0.675095\pi$
$359$	−9.50461	+	2.79080i	−0.501634	+	0.147293i	0.0211194	+	0.999777i	$0.493277\pi$
$360$	3.21361	−	10.9303i	0.169372	−	0.576077i
$361$	5.06294	−	5.84295i	0.266471	−	0.307524i
$362$	−1.59840	−	0.600805i	−0.0840101	−	0.0315776i
$363$	10.4339	−	5.69732i	0.547636	−	0.299032i
$364$	−1.92764	+	1.22502i	−0.101036	+	0.0642084i
$365$	17.0649	−	11.1432i	0.893220	−	0.583260i
$366$	−0.636551	−	2.18846i	−0.0332730	−	0.114392i
$367$	0.928291	+	0.928291i	0.0484564	+	0.0484564i	0.730920	−	0.682463i	$-0.239091\pi$
$367$	0.928291	+	0.928291i	0.0484564	+	0.0484564i	−0.682463	+	0.730920i	$0.739091\pi$
$368$	2.43156	+	19.0286i	0.126754	+	0.991934i
$369$		−	19.6995i		−	1.02551i
$370$	1.51196	−	22.6450i	0.0786030	−	1.17726i
$371$	27.0399	−	3.88775i	1.40384	−	0.201842i
$372$	−1.30520	+	5.85641i	−0.0676714	+	0.303641i
$373$	14.6412	+	26.8133i	0.758090	+	1.38834i	0.916120	+	0.400904i	$0.131304\pi$
$373$	14.6412	+	26.8133i	0.758090	+	1.38834i	−0.158030	+	0.987434i	$0.550514\pi$
$374$	1.37173	+	3.02399i	0.0709306	+	0.156367i
$375$	10.1505	−	6.84074i	0.524168	−	0.353254i
$376$	−0.911230	−	0.801831i	−0.0469931	−	0.0413513i
$377$	−0.595740	+	1.09102i	−0.0306822	+	0.0561902i
$378$	−20.3114	−	20.4149i	−1.04470	−	1.05003i
$379$	27.5301	−	17.6925i	1.41412	−	0.908803i	0.414126	−	0.910220i	$-0.364087\pi$
$379$	27.5301	−	17.6925i	1.41412	−	0.908803i	0.999999	+	0.00141704i	$0.000451057\pi$
$380$	−14.0544	+	5.27709i	−0.720975	+	0.270709i
$381$	12.2590	+	14.1476i	0.628046	+	0.724804i
$382$	5.97037	−	2.20956i	0.305471	−	0.113051i
$383$	18.5986	+	24.8448i	0.950343	+	1.26951i	0.962975	+	0.269590i	$0.0868880\pi$
$383$	18.5986	+	24.8448i	0.950343	+	1.26951i	−0.0126322	+	0.999920i	$0.504021\pi$
$384$	10.5376	−	6.51017i	0.537746	−	0.332220i
$385$	0.0236995	+	3.25871i	0.00120784	+	0.166079i
$386$	−28.8129	+	18.4136i	−1.46654	+	0.937229i
$387$	1.13960	−	3.05538i	0.0579291	−	0.155314i
$388$	1.99331	+	1.10162i	0.101195	+	0.0559263i
$389$	0.287460	−	0.447296i	0.0145748	−	0.0226788i	−0.833890	−	0.551931i	$-0.813891\pi$
$389$	0.287460	−	0.447296i	0.0145748	−	0.0226788i	0.848465	+	0.529252i	$0.177527\pi$
$390$	−0.282903	+	0.980618i	−0.0143254	+	0.0496555i
$391$	−23.8617	−	18.0697i	−1.20674	−	0.913823i
$392$	−22.1642	+	4.64482i	−1.11946	+	0.234599i
$393$	3.42057	+	15.7241i	0.172545	+	0.793177i
$394$	13.7199	−	21.2297i	0.691197	−	1.06954i
$395$	1.04462	+	13.2507i	0.0525604	+	0.666713i
$396$	1.34061	+	0.199711i	0.0673680	+	0.0100359i
$397$	−0.269779	−	0.723305i	−0.0135398	−	0.0363016i	0.930004	−	0.367549i	$-0.119803\pi$
$397$	−0.269779	−	0.723305i	−0.0135398	−	0.0363016i	−0.943544	+	0.331248i	$0.892530\pi$
$398$	−4.68736	−	3.52754i	−0.234956	−	0.176820i
$399$	−2.02613	+	14.0920i	−0.101433	+	0.705484i
$400$	−19.8087	−	2.75960i	−0.990435	−	0.137980i
$401$	−10.2651	−	11.8465i	−0.512613	−	0.591587i	0.439152	−	0.898413i	$-0.355279\pi$
$401$	−10.2651	−	11.8465i	−0.512613	−	0.591587i	−0.951766	+	0.306825i	$0.900733\pi$
$402$	12.9177	+	17.3478i	0.644278	+	0.865230i
$403$	−0.171711	+	0.789343i	−0.00855353	+	0.0393200i
$404$	−12.1816	−	10.6643i	−0.606056	−	0.530568i
$405$	−0.783043	−	0.0502834i	−0.0389097	−	0.00249860i
$406$	−17.4970	+	15.0835i	−0.868359	+	0.748582i
$407$	2.69316	−	0.192619i	0.133495	−	0.00954776i
$408$	−4.25200	+	18.8529i	−0.210505	+	0.933356i
$409$	−9.43962	+	32.1484i	−0.466759	+	1.58964i	0.304107	+	0.952638i	$0.401642\pi$
$409$	−9.43962	+	32.1484i	−0.466759	+	1.58964i	−0.770866	+	0.636998i	$0.780176\pi$
$410$	−34.2064	+	5.08342i	−1.68933	+	0.251052i
$411$	−17.5921	+	2.52936i	−0.867755	+	0.124764i
$412$	−7.06233	+	2.59329i	−0.347936	+	0.127762i
$413$	29.4778	+	29.4778i	1.45051	+	1.45051i
$414$	−11.4813	+	4.17697i	−0.564277	+	0.205287i
$415$	13.1589	−	6.12553i	0.645947	−	0.300691i
$416$	1.41423	−	0.883676i	0.0693381	−	0.0433258i
$417$	−2.19771	−	1.64518i	−0.107622	−	0.0805650i
$418$	−0.851957	−	1.56972i	−0.0416706	−	0.0767773i
$419$	22.9975	+	6.75268i	1.12350	+	0.329890i	0.790151	−	0.612912i	$-0.210002\pi$
$419$	22.9975	+	6.75268i	1.12350	+	0.329890i	0.333352	+	0.942802i	$0.391820\pi$
$420$	−11.3331	+	15.2086i	−0.553001	+	0.742104i
$421$	−6.79651	+	7.84360i	−0.331242	+	0.382273i	−0.896801	−	0.442434i	$-0.854115\pi$
$421$	−6.79651	+	7.84360i	−0.331242	+	0.382273i	0.565559	+	0.824708i	$0.308660\pi$
$422$	−0.335124	+	4.52402i	−0.0163136	+	0.220226i
$423$	0.370478	−	0.678480i	0.0180133	−	0.0329888i
$424$	−19.7640	+	2.68798i	−0.959824	+	0.130540i
$425$	24.7069	−	19.0623i	1.19846	−	0.924656i
$426$	0.785223	−	5.36451i	0.0380442	−	0.259912i
$427$	0.406803	−	5.68785i	0.0196866	−	0.275254i
$428$	10.7051	+	4.05489i	0.517449	+	0.196001i
$429$	−0.120185	−	0.0172800i	−0.00580258	−	0.000834285i
$430$	−5.59946	−	1.19037i	−0.270030	−	0.0574049i
$431$	−12.4430	−	5.68255i	−0.599360	−	0.273719i	0.0925432	−	0.995709i	$-0.470500\pi$
$431$	−12.4430	−	5.68255i	−0.599360	−	0.273719i	−0.691903	+	0.721990i	$0.743228\pi$
$432$	14.7161	+	15.0184i	0.708027	+	0.722572i
$433$	1.83740	−	4.92627i	0.0883000	−	0.236741i	−0.885292	−	0.465035i	$-0.846042\pi$
$433$	1.83740	−	4.92627i	0.0883000	−	0.236741i	0.973592	+	0.228293i	$0.0733145\pi$
$434$	−8.14822	+	12.6083i	−0.391127	+	0.605218i
$435$	−1.39476	+	10.2283i	−0.0668735	+	0.490408i
$436$	−0.734977	−	5.30311i	−0.0351990	−	0.253973i
$437$	13.4950	+	8.77866i	0.645552	+	0.419940i
$438$	0.970973	+	14.0788i	0.0463949	+	0.672710i
$439$	15.7299	+	10.1090i	0.750748	+	0.482477i	0.859209	−	0.511624i	$-0.170956\pi$
$439$	15.7299	+	10.1090i	0.750748	+	0.482477i	−0.108461	+	0.994101i	$0.534592\pi$
$440$	0.000839088	−	2.37937i	4.00019e−5	−	0.113432i
$441$	−5.99139	−	13.1193i	−0.285304	−	0.624729i
$442$	−0.559545	+	2.54107i	−0.0266148	+	0.120866i
$443$	2.56451	+	6.87572i	0.121844	+	0.326675i	0.983524	−	0.180775i	$-0.0578607\pi$
$443$	2.56451	+	6.87572i	0.121844	+	0.326675i	−0.861681	+	0.507451i	$0.830588\pi$
$444$	13.1768	+	8.56316i	0.625342	+	0.406389i
$445$	16.2423	+	8.71624i	0.769960	+	0.413190i
$446$	−1.92376	−	0.884467i	−0.0910925	−	0.0418807i
$447$	1.61296	−	22.5522i	0.0762905	−	1.06668i
$448$	30.3792	−	6.12495i	1.43528	−	0.289377i
$449$	11.3708	+	17.6933i	0.536622	+	0.835001i	0.998654	−	0.0518626i	$-0.0165158\pi$
$449$	11.3708	+	17.6933i	0.536622	+	0.835001i	−0.462032	+	0.886863i	$0.652879\pi$
$450$	−1.06113	−	12.6934i	−0.0500222	−	0.598372i
$451$	−1.15910	−	3.94753i	−0.0545798	−	0.185882i
$452$	−2.71449	+	2.68703i	−0.127679	+	0.126387i
$453$	15.9246	−	1.13895i	0.748205	−	0.0535127i
$454$	11.6886	+	25.7676i	0.548573	+	1.20933i
$455$	−1.51537	+	2.05529i	−0.0710418	+	0.0963535i
$456$	1.55777	−	10.2776i	0.0729492	−	0.481291i
$457$	3.54913	+	2.65685i	0.166021	+	0.124282i	0.679058	−	0.734085i	$-0.262389\pi$
$457$	3.54913	+	2.65685i	0.166021	+	0.124282i	−0.513036	+	0.858367i	$0.671479\pi$
$458$	−14.3077	−	7.85984i	−0.668553	−	0.367266i
$459$	−32.8074			−1.53132
$460$	10.2157	+	18.8584i	0.476308	+	0.879279i
$461$	3.48127			0.162139			0.0810694	−	0.996708i	$-0.474166\pi$
$461$	3.48127			0.162139			0.0810694	+	0.996708i	$0.474166\pi$
$462$	−1.97770	−	1.08644i	−0.0920107	−	0.0505457i
$463$	−16.3625	−	12.2488i	−0.760429	−	0.569250i	0.147158	−	0.989113i	$-0.452987\pi$
$463$	−16.3625	−	12.2488i	−0.760429	−	0.569250i	−0.907588	+	0.419863i	$0.862078\pi$
$464$	12.8588	−	10.9153i	0.596956	−	0.506731i
$465$	1.00296	+	6.63291i	0.0465110	+	0.307594i
$466$	−12.1936	−	26.8809i	−0.564858	−	1.24523i
$467$	−39.6067	+	2.83273i	−1.83278	+	0.131083i	−0.944561	−	0.328335i	$-0.893513\pi$
$467$	−39.6067	+	2.83273i	−1.83278	+	0.131083i	−0.888220	+	0.459418i	$0.848058\pi$
$468$	0.747170	+	0.754806i	0.0345380	+	0.0348909i
$469$	15.2460	+	51.9232i	0.703996	+	2.39759i
$470$	−1.27372	−	0.468221i	−0.0587523	−	0.0215974i
$471$	−12.6842	−	19.7369i	−0.584455	−	0.909430i
$472$	−21.3582	−	21.6864i	−0.983091	−	0.998199i
$473$	0.0485854	−	0.679313i	0.00223396	−	0.0312348i
$474$	−8.36207	−	3.84455i	−0.384083	−	0.176586i
$475$	−12.5236	+	11.1748i	−0.574623	+	0.512735i
$476$	−26.3487	+	40.5447i	−1.20769	+	1.85836i
$477$	−4.43932	−	11.9023i	−0.203263	−	0.544968i
$478$	4.64762	−	21.1064i	0.212577	−	0.965382i
$479$	−12.5676	−	27.5192i	−0.574229	−	1.25739i	−0.944515	−	0.328468i	$-0.893468\pi$
$479$	−12.5676	−	27.5192i	−0.574229	−	1.25739i	0.370286	−	0.928918i	$-0.379260\pi$
$480$	8.35921	−	11.0410i	0.381544	−	0.503949i
$481$	1.77985	+	1.14384i	0.0811542	+	0.0521546i
$482$	2.34100	+	33.9438i	0.106630	+	1.54610i
$483$	20.3394	+	0.112623i	0.925474	+	0.00512452i
$484$	−21.5113	+	2.98133i	−0.977787	+	0.135515i
$485$	2.52293	+	0.344035i	0.114561	+	0.0156218i
$486$	−11.8101	+	18.2746i	−0.535717	+	0.828952i
$487$	7.94948	−	21.3134i	0.360225	−	0.965802i	−0.622808	−	0.782375i	$-0.714008\pi$
$487$	7.94948	−	21.3134i	0.360225	−	0.965802i	0.983033	−	0.183427i	$-0.0587191\pi$
$488$	−0.328681	+	4.15054i	−0.0148787	+	0.187886i
$489$	21.1958	+	9.67982i	0.958509	+	0.437737i
$490$	−21.2344	+	13.7889i	−0.959273	+	0.622919i
$491$	11.8037	+	1.69711i	0.532692	+	0.0765895i	0.403412	−	0.915019i	$-0.367824\pi$
$491$	11.8037	+	1.69711i	0.532692	+	0.0765895i	0.129280	+	0.991608i	$0.458733\pi$
$492$	8.48200	−	22.3928i	0.382398	−	1.00955i
$493$	−1.87745	+	26.2502i	−0.0845563	+	1.18225i
$494$	0.202689	−	1.38474i	0.00911940	−	0.0623022i
$495$	1.47837	−	0.332878i	0.0664478	−	0.0149618i
$496$	6.01936	−	9.16018i	0.270277	−	0.411304i
$497$	6.50096	−	11.9056i	0.291608	−	0.534040i
$498$	−0.742464	+	10.0229i	−0.0332706	+	0.449138i
$499$	8.04258	−	9.28163i	0.360035	−	0.415503i	−0.546616	−	0.837383i	$-0.684084\pi$
$499$	8.04258	−	9.28163i	0.360035	−	0.415503i	0.906651	+	0.421880i	$0.138630\pi$
$500$	−21.7671	+	5.11806i	−0.973453	+	0.228886i
$501$	−26.1714	−	7.68461i	−1.16925	−	0.343323i
$502$	2.39156	+	4.40640i	0.106740	+	0.196667i
$503$	18.5723	+	13.9031i	0.828099	+	0.619907i	0.926946	−	0.375195i	$-0.122424\pi$
$503$	18.5723	+	13.9031i	0.828099	+	0.619907i	−0.0988466	+	0.995103i	$0.531515\pi$
$504$	8.06205	+	18.0157i	0.359112	+	0.802484i
$505$	−17.0053	−	6.20215i	−0.756726	−	0.275992i
$506$	−2.05494	+	1.51256i	−0.0913534	+	0.0672416i
$507$	9.99670	+	9.99670i	0.443969	+	0.443969i
$508$	−11.7878	−	32.1016i	−0.522997	−	1.42428i
$509$	−27.9311	+	4.01588i	−1.23802	+	0.178001i	−0.730063	−	0.683380i	$-0.760509\pi$
$509$	−27.9311	+	4.01588i	−1.23802	+	0.178001i	−0.507960	+	0.861381i	$0.669600\pi$
$510$	3.17622	+	21.3729i	0.140646	+	0.946406i
$511$	−9.94753	+	33.8782i	−0.440053	+	1.49868i
$512$	−22.2145	+	4.30280i	−0.981753	+	0.190159i
$513$	17.6009	−	1.25884i	0.777100	−	0.0555793i
$514$	3.32530	−	2.86663i	0.146673	−	0.126441i
$515$	−6.31671	+	5.55440i	−0.278347	+	0.244756i
$516$	2.61096	−	2.98244i	0.114941	−	0.131294i
$517$	0.0343180	−	0.157757i	0.00150930	−	0.00693816i
$518$	23.4823	+	31.5355i	1.03175	+	1.38559i
$519$	−8.18574	−	9.44684i	−0.359314	−	0.414670i
$520$	1.11785	−	1.49217i	0.0490207	−	0.0654359i
$521$	−2.28779	+	15.9120i	−0.100230	+	0.697115i	0.876305	+	0.481757i	$0.160001\pi$
$521$	−2.28779	+	15.9120i	−0.100230	+	0.697115i	−0.976535	+	0.215359i	$0.930908\pi$
$522$	8.58324	+	6.45944i	0.375678	+	0.282722i
$523$	−10.2872	−	27.5810i	−0.449827	−	1.20603i	−0.942023	−	0.335548i	$-0.891079\pi$
$523$	−10.2872	−	27.5810i	−0.449827	−	1.20603i	0.492197	−	0.870484i	$-0.336194\pi$
$524$	4.33141	−	29.0756i	0.189219	−	1.27017i
$525$	−5.67774	+	20.4314i	−0.247797	+	0.891698i
$526$	−12.4456	+	19.2579i	−0.542652	+	0.839683i
$527$	3.63533	+	16.7113i	0.158357	+	0.727957i
$528$	1.43790	+	0.804239i	0.0625767	+	0.0350000i
$529$	9.78564	−	20.8144i	0.425463	−	0.904976i
$530$	−19.5217	+	10.7798i	−0.847967	+	0.468246i
$531$	10.4806	−	16.3081i	0.454818	−	0.707711i
$532$	12.5801	−	22.7629i	0.545418	−	0.986899i
$533$	1.12661	−	3.02055i	0.0487987	−	0.130834i
$534$	−10.7550	+	6.87322i	−0.465412	+	0.297433i
$535$	12.7981	−	0.0930765i	0.553311	−	0.00402405i
$536$	−10.8423	−	37.9950i	−0.468317	−	1.64113i
$537$	−14.2845	−	19.0819i	−0.616423	−	0.823445i
$538$	5.32533	−	1.97084i	0.229591	−	0.0849690i
$539$	−1.97252	−	2.27641i	−0.0849626	−	0.0980521i
$540$	21.4053	+	9.71889i	0.921136	+	0.418234i
$541$	−1.42580	+	0.916309i	−0.0613001	+	0.0393952i	−0.570932	−	0.820997i	$-0.693418\pi$
$541$	−1.42580	+	0.916309i	−0.0613001	+	0.0393952i	0.509632	+	0.860393i	$0.329782\pi$
$542$	6.29833	+	6.33043i	0.270536	+	0.271915i
$543$	0.633534	−	1.16023i	0.0271876	−	0.0497903i
$544$	19.4634	−	29.4557i	0.834486	−	1.26290i
$545$	−2.90679	−	5.23255i	−0.124513	−	0.224138i
$546$	−0.730418	−	1.61021i	−0.0312590	−	0.0689106i
$547$	3.18448	+	5.83193i	0.136158	+	0.249356i	0.936858	−	0.349711i	$-0.113720\pi$
$547$	3.18448	+	5.83193i	0.136158	+	0.249356i	−0.800699	+	0.599067i	$0.795538\pi$
$548$	31.6901	+	7.06266i	1.35373	+	0.301702i
$549$	−2.62469	+	0.377374i	−0.112019	+	0.0161059i
$550$	−0.959503	−	2.48116i	−0.0409133	−	0.105797i
$551$		−	14.1551i		−	0.603027i
$552$	−14.8495	−	0.195465i	−0.632038	−	0.00831956i
$553$	−16.2825	−	16.2825i	−0.692404	−	0.692404i
$554$	6.87726	+	23.6439i	0.292187	+	1.00454i
$555$	17.1949	+	3.60975i	0.729881	+	0.153225i
$556$	2.68986	+	4.23265i	0.114075	+	0.179504i
$557$	−25.9669	+	14.1790i	−1.10025	+	0.600784i	−0.923549	−	0.383479i	$-0.874726\pi$
$557$	−25.9669	+	14.1790i	−1.10025	+	0.600784i	−0.176705	+	0.984264i	$0.556544\pi$
$558$	6.53445	+	2.45616i	0.276626	+	0.103978i
$559$	0.349472	−	0.403313i	0.0147811	−	0.0170583i
$560$	29.2022	−	18.6479i	1.23402	−	0.788019i
$561$	−2.46650	+	0.724229i	−0.104136	+	0.0305770i
$562$	17.0162	−	16.9299i	0.717785	−	0.714146i
$563$	−8.97167	+	41.2421i	−0.378111	+	1.73815i	0.257629	+	0.966244i	$0.417059\pi$
$563$	−8.97167	+	41.2421i	−0.378111	+	1.73815i	−0.635740	+	0.771903i	$0.719305\pi$
$564$	0.713262	−	0.611725i	0.0300337	−	0.0257582i
$565$	−1.74566	+	3.89722i	−0.0734405	+	0.163957i
$566$	−6.66461	−	3.06412i	−0.280134	−	0.128795i
$567$	1.08822	−	0.814632i	0.0457010	−	0.0342113i
$568$	−4.81276	+	8.65632i	−0.201939	+	0.363211i
$569$	−32.2487	−	14.7275i	−1.35193	−	0.617408i	−0.397990	−	0.917390i	$-0.630292\pi$
$569$	−32.2487	−	14.7275i	−1.35193	−	0.617408i	−0.953945	+	0.299982i	$0.903019\pi$
$570$	−2.52411	−	11.3445i	−0.105723	−	0.475169i
$571$	17.9411	−	8.19342i	0.750811	−	0.342884i	−0.00298222	−	0.999996i	$-0.500949\pi$
$571$	17.9411	−	8.19342i	0.750811	−	0.342884i	0.753793	+	0.657112i	$0.228222\pi$
$572$	0.194135	+	0.107291i	0.00811721	+	0.00448605i
$573$	1.04760	+	4.81572i	0.0437639	+	0.201179i
$574$	39.3481	−	45.1776i	1.64236	−	1.88568i
$575$	18.2630	+	15.5391i	0.761618	+	0.648027i
$576$	−5.78595	−	13.1985i	−0.241081	−	0.549937i
$577$	37.7472	−	8.21140i	1.57144	−	0.341845i	0.659348	−	0.751838i	$-0.270833\pi$
$577$	37.7472	−	8.21140i	1.57144	−	0.341845i	0.912089	+	0.409993i	$0.134469\pi$
$578$	6.52192	+	30.3520i	0.271276	+	1.26248i
$579$	−10.9967	−	24.0794i	−0.457006	−	1.00070i
$580$	9.00133	−	16.5709i	0.373760	−	0.688067i
$581$	−10.4459	+	22.8734i	−0.433371	+	0.948950i
$582$	−1.06017	+	1.40875i	−0.0439456	+	0.0583944i
$583$	−1.58990	−	2.12386i	−0.0658470	−	0.0879613i
$584$	7.45148	−	24.6797i	0.308345	−	1.02125i
$585$	1.08368	+	0.485409i	0.0448048	+	0.0200692i
$586$	−3.41626	+	23.3393i	−0.141124	+	0.964139i
$587$	−19.7520	−	4.29678i	−0.815252	−	0.177347i	−0.214440	−	0.976737i	$-0.568792\pi$
$587$	−19.7520	−	4.29678i	−0.815252	−	0.177347i	−0.600812	+	0.799390i	$0.705156\pi$
$588$	−1.16175	−	17.4927i	−0.0479099	−	0.721385i
$589$	−2.59155	−	8.82602i	−0.106783	−	0.363670i
$590$	−31.0220	−	13.9903i	−1.27716	−	0.575971i
$591$	14.7888	+	12.8146i	0.608329	+	0.527120i
$592$	−16.9693	−	23.1554i	−0.697434	−	0.951680i
$593$	14.1242	+	25.8665i	0.580010	+	1.06221i	0.988753	+	0.149559i	$0.0477855\pi$
$593$	14.1242	+	25.8665i	0.580010	+	1.06221i	−0.408743	+	0.912650i	$0.634033\pi$
$594$	−0.794756	+	2.68146i	−0.0326092	+	0.110022i
$595$	−11.1071	+	52.9083i	−0.455348	+	2.16903i
$596$	−17.3488	+	37.4831i	−0.710634	+	1.53537i
$597$	3.21133	−	3.21133i	0.131431	−	0.131431i
$598$	−1.99933	−	0.0161526i	−0.0817585	−	0.000660530i
$599$	37.6122			1.53679			0.768396	−	0.639975i	$-0.221055\pi$
$599$	37.6122			1.53679			0.768396	+	0.639975i	$0.221055\pi$
$600$	4.25917	−	14.8857i	0.173880	−	0.607706i
$601$	1.62585	+	11.3080i	0.0663198	+	0.461264i	0.995737	+	0.0922344i	$0.0294009\pi$
$601$	1.62585	+	11.3080i	0.0663198	+	0.461264i	−0.929418	+	0.369030i	$0.879690\pi$
$602$	8.71637	−	4.73078i	0.355253	−	0.192812i
$603$	22.0862	−	12.0600i	0.899419	−	0.491120i
$604$	−27.9418	−	8.35896i	−1.13693	−	0.340121i
$605$	−21.2251	+	11.7910i	−0.862923	+	0.479371i
$606$	9.49306	−	8.18363i	0.385629	−	0.332437i
$607$	23.0722	+	12.5984i	0.936472	+	0.511352i	0.873587	−	0.486668i	$-0.161788\pi$
$607$	23.0722	+	12.5984i	0.936472	+	0.511352i	0.0628851	+	0.998021i	$0.479970\pi$
$608$	−9.31172	+	16.5496i	−0.377640	+	0.671175i
$609$	−9.66864	−	15.0447i	−0.391793	−	0.609642i
$610$	1.33257	+	4.46016i	0.0539543	+	0.180587i
$611$	0.0956078	−	0.0828447i	0.00386788	−	0.00335154i
$612$	21.0274	+	7.96481i	0.849983	+	0.321959i
$613$	20.7623	−	15.5425i	0.838582	−	0.627754i	−0.0912136	−	0.995831i	$-0.529075\pi$
$613$	20.7623	−	15.5425i	0.838582	−	0.627754i	0.929795	+	0.368077i	$0.119984\pi$
$614$	0.0957769	+	0.678379i	0.00386524	+	0.0273772i
$615$	−0.194697	−	26.7710i	−0.00785093	−	1.07951i
$616$	2.67556	+	3.13576i	0.107801	+	0.126343i
$617$	38.6166	+	14.4033i	1.55465	+	0.579854i	0.972433	−	0.233182i	$-0.0749137\pi$
$617$	38.6166	+	14.4033i	1.55465	+	0.579854i	0.582214	+	0.813035i	$0.302186\pi$
$618$	−1.22357	−	5.69429i	−0.0492191	−	0.229058i
$619$	8.71858	+	5.60309i	0.350429	+	0.225207i	0.703999	−	0.710201i	$-0.251396\pi$
$619$	8.71858	+	5.60309i	0.350429	+	0.225207i	−0.353570	+	0.935408i	$0.615032\pi$
$620$	2.57870	−	11.9803i	0.103563	−	0.481140i
$621$	−5.22227	−	24.6631i	−0.209562	−	0.989695i
$622$	−35.1065	+	2.42119i	−1.40764	+	0.0970810i
$623$	−31.2045	+	6.78812i	−1.25018	+	0.271960i
$624$	0.524327	+	1.17971i	0.0209899	+	0.0472262i
$625$	−20.6293	+	14.1220i	−0.825173	+	0.564881i
$626$	−5.34310	+	3.41464i	−0.213553	+	0.136476i
$627$	1.29547	−	0.483185i	0.0517360	−	0.0192965i
$628$	8.89731	+	41.9252i	0.355041	+	1.67300i
$629$	44.3363	+	6.37459i	1.76780	+	0.254172i
$630$	15.6774	+	15.5297i	0.624602	+	0.618720i
$631$	23.4750	−	20.3412i	0.934527	−	0.809772i	−0.0474308	−	0.998875i	$-0.515103\pi$
$631$	23.4750	−	20.3412i	0.934527	−	0.809772i	0.981957	+	0.189103i	$0.0605579\pi$
$632$	11.7975	+	11.9788i	0.469280	+	0.476492i
$633$	−3.43162	−	0.746503i	−0.136395	−	0.0296708i
$634$	−0.0702741	+	27.6481i	−0.00279094	+	1.09805i
$635$	−25.2474	−	28.7124i	−1.00191	−	1.13942i
$636$	0.0784943	−	15.4410i	0.00311250	−	0.612275i
$637$	−0.168379	−	2.35424i	−0.00667141	−	0.0932786i
$638$	2.10004	+	0.789360i	0.0831413	+	0.0312511i
$639$	−6.05235	−	1.77713i	−0.239427	−	0.0703022i
$640$	−21.4249	+	13.4526i	−0.846894	+	0.531761i
$641$	−3.51306	−	24.4338i	−0.138757	−	0.965079i	−0.933614	−	0.358281i	$-0.883363\pi$
$641$	−3.51306	−	24.4338i	−0.138757	−	0.965079i	0.794856	−	0.606798i	$-0.207546\pi$
$642$	−4.26684	+	7.76713i	−0.168399	+	0.306544i
$643$	−17.0841	+	17.0841i	−0.673733	+	0.673733i	−0.958575	−	0.284842i	$-0.908059\pi$
$643$	−17.0841	+	17.0841i	−0.673733	+	0.673733i	0.284842	+	0.958575i	$0.408059\pi$
$644$	−34.6738	−	13.3538i	−1.36634	−	0.526214i
$645$	1.51848	−	4.16344i	0.0597903	−	0.163935i
$646$	−8.27515	−	28.4499i	−0.325581	−	1.11935i
$647$	−13.0614	+	17.4480i	−0.513497	+	0.685952i	−0.980098	−	0.198516i	$-0.936388\pi$
$647$	−13.0614	+	17.4480i	−0.513497	+	0.685952i	0.466600	+	0.884468i	$0.345479\pi$
$648$	−0.799065	+	0.588719i	−0.0313902	+	0.0231271i
$649$	1.14062	−	3.88460i	0.0447733	−	0.152484i
$650$	0.563225	−	2.00698i	0.0220915	−	0.0787201i
$651$	−8.78304	−	7.61055i	−0.344235	−	0.298281i
$652$	−29.9461	−	30.2521i	−1.17278	−	1.18476i
$653$	−32.5022	−	17.7475i	−1.27191	−	0.694514i	−0.305663	−	0.952140i	$-0.598878\pi$
$653$	−32.5022	−	17.7475i	−1.27191	−	0.694514i	−0.966245	+	0.257625i	$0.917060\pi$
$654$	4.14464	+	0.0105346i	0.162068	+	0.000411935i
$655$	−7.21960	−	32.0635i	−0.282093	−	1.25282i
$656$	−28.9803	+	32.7660i	−1.13149	+	1.27930i
$657$	16.3770	+	1.17131i	0.638930	+	0.0456971i
$658$	2.20484	−	0.815985i	0.0859536	−	0.0318104i
$659$	2.35778	−	16.3987i	0.0918460	−	0.638803i	−0.890949	−	0.454103i	$-0.849960\pi$
$659$	2.35778	−	16.3987i	0.0918460	−	0.638803i	0.982795	−	0.184700i	$-0.0591312\pi$
$660$	1.82382	+	0.258152i	0.0709920	+	0.0100485i
$661$	5.17228	−	11.3257i	0.201178	−	0.440519i	−0.781973	−	0.623312i	$-0.785787\pi$
$661$	5.17228	−	11.3257i	0.201178	−	0.440519i	0.983151	+	0.182793i	$0.0585138\pi$
$662$	22.0785	+	4.86169i	0.858106	+	0.188955i
$663$	−1.88730	−	0.703927i	−0.0732967	−	0.0273383i
$664$	7.75412	−	16.6422i	0.300918	−	0.645841i
$665$	3.92877	−	28.8111i	0.152351	−	1.11725i
$666$	12.0082	−	13.7872i	0.465307	−	0.534243i
$667$	−20.0325	+	2.76712i	−0.775663	+	0.107143i
$668$	39.7371	+	30.0632i	1.53747	+	1.16318i
$669$	0.886187	−	1.37893i	0.0342620	−	0.0533127i
$670$	−26.6403	−	35.2386i	−1.02921	−	1.36139i
$671$	−0.503751	+	0.230055i	−0.0194471	+	0.00888118i
$672$	1.40727	+	23.9501i	0.0542868	+	0.923894i
$673$	−4.19188	+	1.56349i	−0.161585	+	0.0602682i	−0.428955	−	0.903326i	$-0.641118\pi$
$673$	−4.19188	+	1.56349i	−0.161585	+	0.0602682i	0.267370	+	0.963594i	$0.413845\pi$
$674$	27.2239	−	3.84360i	1.04862	−	0.148050i
$675$	26.2407	+	1.49352i	1.01000	+	0.0574855i
$676$	−10.6090	−	23.5466i	−0.408040	−	0.905637i
$677$	−18.7657	−	1.34215i	−0.721225	−	0.0515830i	−0.294099	−	0.955775i	$-0.595019\pi$
$677$	−18.7657	−	1.34215i	−0.721225	−	0.0515830i	−0.427126	+	0.904192i	$0.640474\pi$
$678$	−1.76596	−	2.37159i	−0.0678214	−	0.0910805i
$679$	−3.71097	+	2.38490i	−0.142414	+	0.0915239i
$680$	8.40409	−	38.5675i	0.322282	−	1.47900i
$681$	−21.0171	+	6.17118i	−0.805378	+	0.236480i
$682$	1.45394	+	0.107703i	0.0556742	+	0.00412416i
$683$	−0.949197	−	13.2715i	−0.0363200	−	0.507820i	−0.982753	−	0.184921i	$-0.940797\pi$
$683$	−0.949197	−	13.2715i	−0.0363200	−	0.507820i	0.946433	−	0.322899i	$-0.104658\pi$
$684$	−11.5867	−	3.46623i	−0.443027	−	0.132534i
$685$	35.8918	−	5.42717i	1.37136	−	0.207362i
$686$	1.56686	−	5.28647i	0.0598228	−	0.201839i
$687$	7.57341	−	10.1169i	0.288944	−	0.385984i
$688$	−6.39032	+	3.40550i	−0.243629	+	0.129833i
$689$		−	2.07887i		−	0.0791988i
$690$	−15.5615	+	5.78986i	−0.592417	+	0.220416i
$691$			43.0263i			1.63680i	0.574651	+	0.818399i	$0.305138\pi$
$691$			43.0263i			1.63680i	−0.574651	+	0.818399i	$0.694862\pi$
$692$	7.87109	+	21.4354i	0.299214	+	0.814850i
$693$	−1.57328	+	2.10165i	−0.0597638	+	0.0798351i
$694$	−3.71727	−	1.10176i	−0.141106	−	0.0418223i
$695$	4.51295	+	3.32741i	0.171186	+	0.126216i
$696$	6.97549	+	11.0382i	0.264405	+	0.418404i
$697$	−4.86904	−	68.0781i	−0.184428	−	2.57864i
$698$	0.917202	−	12.3818i	0.0347166	−	0.468658i
$699$	21.9252	−	6.43782i	0.829287	−	0.243501i
$700$	22.9205	−	31.2298i	0.866312	−	1.18037i
$701$	−4.22786	+	2.71708i	−0.159684	+	0.102623i	−0.618042	−	0.786145i	$-0.712074\pi$
$701$	−4.22786	+	2.71708i	−0.159684	+	0.102623i	0.458358	+	0.888767i	$0.348438\pi$
$702$	−1.75772	+	1.30885i	−0.0663408	+	0.0493995i
$703$	−24.0307	−	1.71871i	−0.906334	−	0.0648223i
$704$	−1.93602	−	2.30437i	−0.0729664	−	0.0868492i
$705$	0.496763	−	0.925696i	0.0187092	−	0.0348637i
$706$	−4.20233	−	29.7647i	−0.158157	−	1.12021i
$707$	29.3815	−	10.9587i	1.10500	−	0.412145i
$708$	18.9352	−	14.0251i	0.711629	−	0.527096i
$709$	−15.5057	+	7.08120i	−0.582328	+	0.265940i	−0.684723	−	0.728804i	$-0.740077\pi$
$709$	−15.5057	+	7.08120i	−0.582328	+	0.265940i	0.102395	+	0.994744i	$0.467349\pi$
$710$	−1.52403	+	10.9679i	−0.0571957	+	0.411619i
$711$	−5.78910	+	9.00802i	−0.217108	+	0.337827i
$712$	22.8207	−	4.78240i	0.855244	−	0.179228i
$713$	−11.9841	+	5.39297i	−0.448809	+	0.201968i
$714$	−28.2279	−	24.5855i	−1.05640	−	0.920091i
$715$	0.245718	+	0.0335068i	0.00918931	+	0.00125308i
$716$	12.0552	+	41.8418i	0.450523	+	1.56370i
$717$	15.6761	+	5.84688i	0.585434	+	0.218356i
$718$	−3.01261	+	13.6812i	−0.112430	+	0.510580i
$719$	−8.78351	+	19.2332i	−0.327570	+	0.717277i	−0.999733	−	0.0231259i	$-0.992638\pi$
$719$	−8.78351	+	19.2332i	−0.327570	+	0.717277i	0.672163	+	0.740403i	$0.265365\pi$
$720$	−11.3599	−	11.4258i	−0.423358	−	0.425816i
$721$	2.07383	−	14.4238i	0.0772336	−	0.537172i
$722$	−3.79490	−	10.2541i	−0.141232	−	0.381616i
$723$	−26.2729	−	1.87908i	−0.977101	−	0.0698836i
$724$	−1.83307	+	1.57212i	−0.0681255	+	0.0584274i
$725$	2.69667	−	20.9105i	0.100152	−	0.776597i
$726$	0.0427320	−	16.8122i	0.00158593	−	0.623957i
$727$	−0.163222	−	0.0891261i	−0.00605358	−	0.00330550i	0.476219	−	0.879327i	$-0.342007\pi$
$727$	−0.163222	−	0.0891261i	−0.00605358	−	0.00330550i	−0.482273	+	0.876021i	$0.660189\pi$
$728$	0.205853	+	3.22344i	0.00762941	+	0.119469i
$729$	−13.5258	−	11.7202i	−0.500957	−	0.434081i
$730$	−2.19219	−	28.7395i	−0.0811367	−	1.06370i
$731$	3.18307	−	10.8406i	0.117730	−	0.400952i
$732$	−3.14602	−	0.701144i	−0.116280	−	0.0259150i
$733$	8.84856	−	11.8203i	0.326829	−	0.436592i	−0.606789	−	0.794863i	$-0.707543\pi$
$733$	8.84856	−	11.8203i	0.326829	−	0.436592i	0.933618	+	0.358271i	$0.116634\pi$
$734$	1.78270	−	0.518530i	0.0658007	−	0.0191393i
$735$	−8.27178	−	17.7695i	−0.305109	−	0.655439i
$736$	25.2416	+	9.94291i	0.930418	+	0.366500i
$737$	3.71619	−	3.71619i	0.136888	−	0.136888i
$738$	−24.4175	−	13.4136i	−0.898821	−	0.493763i
$739$	2.01060	+	13.9840i	0.0739611	+	0.514411i	0.992801	+	0.119779i	$0.0382187\pi$
$739$	2.01060	+	13.9840i	0.0739611	+	0.514411i	−0.918839	+	0.394632i	$0.870872\pi$
$740$	−27.0389	−	17.2933i	−0.993970	−	0.635715i
$741$	1.03953	+	0.305235i	0.0381882	+	0.0112131i
$742$	13.5930	−	36.1632i	0.499014	−	1.32759i
$743$	−1.03577	−	14.4820i	−0.0379989	−	0.531294i	−0.980427	−	0.196884i	$-0.936918\pi$
$743$	−1.03577	−	14.4820i	−0.0379989	−	0.531294i	0.942428	−	0.334409i	$-0.108537\pi$
$744$	6.37029	+	5.60550i	0.233546	+	0.205508i
$745$	−2.95927	+	46.0836i	−0.108419	+	1.68837i
$746$	43.2044	+	0.109814i	1.58182	+	0.00402058i
$747$	11.4259	+	2.48556i	0.418052	+	0.0909417i
$748$	4.68227	+	0.358815i	0.171201	+	0.0131196i
$749$	−16.7568	+	14.5198i	−0.612279	+	0.530542i
$750$	−1.56750	−	17.2395i	−0.0572369	−	0.629496i
$751$	−15.9037	−	2.28661i	−0.580335	−	0.0834395i	−0.154105	−	0.988054i	$-0.549249\pi$
$751$	−15.9037	−	2.28661i	−0.580335	−	0.0834395i	−0.426230	+	0.904615i	$0.640158\pi$
$752$	−1.61434	+	0.583491i	−0.0588688	+	0.0212777i
$753$	−3.63655	+	1.35636i	−0.132523	+	0.0494287i
$754$	0.946666	+	1.48131i	0.0344755	+	0.0539460i
$755$	−32.5069	+	2.56269i	−1.18305	+	0.0932657i
$756$	−39.1345	+	11.2752i	−1.42331	+	0.410074i
$757$	43.7289	−	9.51263i	1.58935	−	0.345743i	0.670985	−	0.741471i	$-0.265871\pi$
$757$	43.7289	−	9.51263i	1.58935	−	0.345743i	0.918368	+	0.395728i	$0.129508\pi$
$758$	−3.18425	−	46.1705i	−0.115657	−	1.67699i
$759$	−0.937057	−	1.73891i	−0.0340130	−	0.0631186i
$760$	−3.02887	+	21.0136i	−0.109869	+	0.762245i
$761$	−39.7433	−	25.5415i	−1.44069	−	0.925878i	−0.999596	−	0.0284193i	$-0.990953\pi$
$761$	−39.7433	−	25.5415i	−1.44069	−	0.925878i	−0.441098	−	0.897459i	$-0.645411\pi$
$762$	25.8832	−	5.56169i	0.937651	−	0.201479i
$763$	9.71600	+	3.62388i	0.351743	+	0.131193i
$764$	1.32655	−	8.90479i	0.0479930	−	0.322164i
$765$	25.1387	−	0.182825i	0.908892	−	0.00661007i
$766$	43.4591	−	6.13577i	1.57024	−	0.221695i
$767$	2.53965	−	1.90116i	0.0917015	−	0.0686469i
$768$	−0.894138	−	17.4942i	−0.0322644	−	0.631269i
$769$	−39.6515	+	34.3582i	−1.42987	+	1.23899i	−0.502640	+	0.864496i	$0.667638\pi$
$769$	−39.6515	+	34.3582i	−1.42987	+	1.23899i	−0.927230	+	0.374493i	$0.877817\pi$
$770$	4.05530	+	2.18952i	0.146143	+	0.0789049i
$771$	1.83753	+	2.85925i	0.0661770	+	0.102973i
$772$	3.20457	+	48.2517i	0.115335	+	1.73662i
$773$	−37.3773	−	20.4096i	−1.34437	−	0.734081i	−0.364027	−	0.931389i	$-0.618598\pi$
$773$	−37.3773	−	20.4096i	−1.34437	−	0.734081i	−0.980342	+	0.197308i	$0.936780\pi$
$774$	−3.01118	−	3.49298i	−0.108235	−	0.125553i
$775$	−2.14692	−	13.5319i	−0.0771196	−	0.486080i
$776$	2.72273	−	1.72060i	0.0977402	−	0.0617658i
$777$	−26.7149	+	14.5874i	−0.958392	+	0.523322i
$778$	−0.358688	−	0.660876i	−0.0128596	−	0.0236936i
$779$	5.22441	+	36.3366i	0.187184	+	1.30189i
$780$	1.02284	+	1.01837i	0.0366236	+	0.0364637i
$781$	−1.31738			−0.0471395
$782$	−38.6451	+	17.2727i	−1.38195	+	0.617670i
$783$	−15.6736	+	15.6736i	−0.560128	+	0.560128i
$784$	−9.33466	+	30.6352i	−0.333381	+	1.09412i
$785$	26.1988	+	40.1215i	0.935074	+	1.43200i
$786$	21.8191	+	6.46696i	0.778263	+	0.230669i
$787$	6.97929	+	12.7816i	0.248785	+	0.455616i	0.971991	−	0.235016i	$-0.0755143\pi$
$787$	6.97929	+	12.7816i	0.248785	+	0.455616i	−0.723207	+	0.690632i	$0.757333\pi$
$788$	−16.9721	−	31.4613i	−0.604608	−	1.12076i
$789$	−13.4152	−	11.6243i	−0.477593	−	0.413837i
$790$	17.1355	+	7.72775i	0.609653	+	0.274941i
$791$	−2.08426	−	7.09834i	−0.0741078	−	0.252388i
$792$	1.16038	−	1.52569i	0.0412322	−	0.0542132i
$793$	−0.424029	−	0.0922419i	−0.0150577	−	0.00327561i
$794$	−1.08023	−	0.158117i	−0.0383360	−	0.00561137i
$795$	−6.15054	−	16.1310i	−0.218137	−	0.572107i
$796$	−7.56407	+	3.40803i	−0.268101	+	0.120794i
$797$	−20.7695	−	27.7448i	−0.735694	−	0.982773i	−0.999833	−	0.0182878i	$-0.994178\pi$
$797$	−20.7695	−	27.7448i	−0.735694	−	0.982773i	0.264138	−	0.964485i	$-0.414912\pi$
$798$	16.0874	+	12.1068i	0.569489	+	0.428577i
$799$	1.11261	−	2.43628i	0.0393614	−	0.0861894i
$800$	−16.9085	+	22.6738i	−0.597807	+	0.801640i
$801$	6.16886	+	13.5079i	0.217966	+	0.477279i
$802$	−21.6734	+	4.65709i	−0.765314	+	0.164448i
$803$	3.35067	−	0.728894i	0.118243	−	0.0257221i
$804$	30.2984	−	4.19917i	1.06854	−	0.148093i
$805$	−41.5420	+	0.0720926i	−1.46416	+	0.00254093i
$806$	0.861469	+	0.750309i	0.0303440	+	0.0264285i
$807$	0.934412	+	4.29542i	0.0328929	+	0.151206i
$808$	−21.5130	+	7.83759i	−0.756823	+	0.275725i
$809$	21.7957	−	9.95377i	0.766297	−	0.349956i	0.00638275	−	0.999980i	$-0.497968\pi$
$809$	21.7957	−	9.95377i	0.766297	−	0.349956i	0.759914	+	0.650024i	$0.225241\pi$
$810$	−0.595510	+	0.936342i	−0.0209241	+	0.0328997i
$811$	19.3713	+	8.84657i	0.680218	+	0.310645i	0.725394	−	0.688334i	$-0.241658\pi$
$811$	19.3713	+	8.84657i	0.680218	+	0.310645i	−0.0451760	+	0.998979i	$0.514385\pi$
$812$	6.78208	+	31.9580i	0.238004	+	1.12151i
$813$	−5.53423	+	4.14287i	−0.194094	+	0.145297i
$814$	1.59506	−	3.46933i	0.0559068	−	0.121600i
$815$	−43.4333	−	19.4548i	−1.52140	−	0.681473i
$816$	20.4729	+	18.1075i	0.716693	+	0.633890i
$817$	−1.29174	+	5.93801i	−0.0451921	+	0.207745i
$818$	33.4203	+	33.5907i	1.16851	+	1.17447i
$819$	−1.97381	+	0.579562i	−0.0689704	+	0.0202515i
$820$	−16.9907	+	45.8601i	−0.593340	+	1.60151i
$821$	−2.38290	+	2.75001i	−0.0831637	+	0.0959760i	−0.795806	−	0.605551i	$-0.792953\pi$
$821$	−2.38290	+	2.75001i	−0.0831637	+	0.0959760i	0.712643	+	0.701527i	$0.247498\pi$
$822$	−8.84355	+	23.5277i	−0.308454	+	0.820622i
$823$	−26.9825	+	14.7335i	−0.940549	+	0.513579i	−0.874921	−	0.484265i	$-0.839087\pi$
$823$	−26.9825	+	14.7335i	−0.940549	+	0.513579i	−0.0656282	+	0.997844i	$0.520905\pi$
$824$	−1.59445	+	10.5196i	−0.0555452	+	0.366466i
$825$	2.00577	−	0.466983i	0.0698320	−	0.0162583i
$826$	56.6096	−	16.4659i	1.96970	−	0.572922i
$827$	−24.7860	−	24.7860i	−0.861892	−	0.861892i	0.129666	−	0.991558i	$-0.458610\pi$
$827$	−24.7860	−	24.7860i	−0.861892	−	0.861892i	−0.991558	+	0.129666i	$0.958610\pi$
$828$	−2.64044	+	17.0753i	−0.0917616	+	0.593406i
$829$			3.20982i			0.111482i	0.998445	+	0.0557408i	$0.0177520\pi$
$829$			3.20982i			0.111482i	−0.998445	+	0.0557408i	$0.982248\pi$
$830$	1.36750	−	20.4814i	0.0474668	−	0.710921i
$831$	−18.8686	+	2.71289i	−0.654543	+	0.0941091i
$832$	−0.132351	−	2.35464i	−0.00458844	−	0.0816324i
$833$	−23.9478	−	43.8572i	−0.829744	−	1.51956i
$834$	−3.53565	+	1.60383i	−0.122430	+	0.0555361i
$835$	53.5655	+	15.3060i	1.85371	+	0.529686i
$836$	−2.52577	−	0.0128398i	−0.0873555	−	0.000444072i
$837$	−6.90327	+	12.6424i	−0.238612	+	0.436985i
$838$	24.0293	−	23.9074i	0.830077	−	0.825868i
$839$	−2.97213	+	1.91007i	−0.102609	+	0.0659431i	−0.590939	−	0.806716i	$-0.701243\pi$
$839$	−2.97213	+	1.91007i	−0.102609	+	0.0659431i	0.488330	+	0.872659i	$0.337606\pi$
$840$	11.1341	+	24.4032i	0.384165	+	0.841989i
$841$	−7.34698	−	8.47886i	−0.253344	−	0.292375i
$842$	5.09429	+	13.7651i	0.175561	+	0.474376i
$843$	11.1360	+	14.8760i	0.383546	+	0.512357i
$844$	5.37933	+	3.49585i	0.185164	+	0.120332i
$845$	−20.5653	−	20.2684i	−0.707469	−	0.697253i
$846$	−0.588712	−	0.921193i	−0.0202403	−	0.0316713i
$847$	14.6998	−	39.4116i	0.505090	−	1.35420i
$848$	−10.1258	+	26.3277i	−0.347722	+	0.904097i
$849$	3.07008	−	4.77714i	0.105365	−	0.163951i
$850$	−6.80445	−	43.6039i	−0.233391	−	1.49560i
$851$	2.26531	+	34.3446i	0.0776537	+	1.17732i
$852$	−6.11464	−	4.62605i	−0.209484	−	0.158486i
$853$	−5.05593	−	23.2417i	−0.173112	−	0.795781i	−0.979024	−	0.203746i	$-0.934688\pi$
$853$	−5.05593	−	23.2417i	−0.173112	−	0.795781i	0.805912	−	0.592035i	$-0.201675\pi$
$854$	−6.77309	−	4.37716i	−0.231770	−	0.149783i
$855$	−13.4797	+	1.06267i	−0.460996	+	0.0363427i
$856$	12.3153	−	10.5079i	0.420927	−	0.359152i
$857$	1.15143	+	3.08711i	0.0393321	+	0.105454i	0.955131	−	0.296184i	$-0.0957140\pi$
$857$	1.15143	+	3.08711i	0.0393321	+	0.105454i	−0.915799	+	0.401637i	$0.868441\pi$
$858$	−0.103254	+	0.137203i	−0.00352503	+	0.00468403i
$859$	−4.42397	+	30.7694i	−0.150944	+	1.04984i	0.763698	+	0.645574i	$0.223382\pi$
$859$	−4.42397	+	30.7694i	−0.150944	+	1.04984i	−0.914642	+	0.404265i	$0.867527\pi$
$860$	−5.28822	+	6.12999i	−0.180327	+	0.209031i
$861$	30.3725	+	35.0517i	1.03509	+	1.19456i
$862$	−15.5161	+	11.5538i	−0.528482	+	0.393525i
$863$	1.84743	−	8.49250i	0.0628873	−	0.289088i	−0.934953	−	0.354771i	$-0.884559\pi$
$863$	1.84743	−	8.49250i	0.0628873	−	0.289088i	0.997841	+	0.0656827i	$0.0209225\pi$
$864$	28.6356	−	8.01433i	0.974203	−	0.272653i
$865$	16.8585	+	19.1723i	0.573208	+	0.651877i
$866$	−4.85499	−	5.63182i	−0.164979	−	0.191377i
$867$	−23.9721	+	1.71452i	−0.814137	+	0.0582282i
$868$	10.0797	+	18.6849i	0.342129	+	0.634205i
$869$	−0.630039	+	2.14572i	−0.0213726	+	0.0727885i
$870$	11.7282	+	8.69336i	0.397624	+	0.294732i
$871$	4.07621	−	0.586070i	0.138117	−	0.0198582i
$872$	−7.07366	−	2.69996i	−0.239544	−	0.0914320i
$873$	1.45048	+	1.45048i	0.0490913	+	0.0490913i
$874$	20.0700	−	10.7495i	0.678880	−	0.363608i
$875$	11.2925	−	41.8125i	0.381757	−	1.41352i
$876$	18.1118	+	8.38290i	0.611940	+	0.283232i
$877$	−4.34479	−	3.25247i	−0.146713	−	0.109828i	0.523400	−	0.852087i	$-0.324663\pi$
$877$	−4.34479	−	3.25247i	−0.146713	−	0.109828i	−0.670113	+	0.742259i	$0.733754\pi$
$878$	23.2408	−	12.6139i	0.784339	−	0.425697i
$879$	−17.5210	−	5.14464i	−0.590970	−	0.173525i
$880$	−2.94866	−	1.62119i	−0.0993993	−	0.0546502i
$881$	−10.5494	+	12.1747i	−0.355419	+	0.410175i	−0.905100	−	0.425200i	$-0.860204\pi$
$881$	−10.5494	+	12.1747i	−0.355419	+	0.410175i	0.549681	+	0.835375i	$0.314749\pi$
$882$	−20.3410	−	1.50679i	−0.684916	−	0.0507363i
$883$	−24.9229	+	45.6428i	−0.838721	+	1.53600i	0.00548491	+	0.999985i	$0.498254\pi$
$883$	−24.9229	+	45.6428i	−0.838721	+	1.53600i	−0.844206	+	0.536018i	$0.819928\pi$
$884$	2.76865	+	2.42380i	0.0931199	+	0.0815213i
$885$	14.0816	−	22.2658i	0.473348	−	0.748457i
$886$	10.2687	+	1.50306i	0.344982	+	0.0504962i
$887$	1.63026	−	22.7940i	0.0547389	−	0.765349i	−0.893755	−	0.448555i	$-0.851939\pi$
$887$	1.63026	−	22.7940i	0.0547389	−	0.765349i	0.948494	−	0.316794i	$-0.102607\pi$
$888$	19.5863	−	10.5018i	0.657272	−	0.352418i
$889$	65.5632	+	9.42656i	2.19892	+	0.316157i
$890$	21.8634	−	14.1973i	0.732862	−	0.475896i
$891$	−0.120086	−	0.0548415i	−0.00402304	−	0.00183726i
$892$	−2.40621	+	1.78225i	−0.0805657	+	0.0596741i
$893$	−0.503426	+	1.34974i	−0.0168465	+	0.0451672i
$894$	−26.8551	−	17.3553i	−0.898169	−	0.580449i
$895$	29.4576	+	38.7599i	0.984658	+	1.29560i
$896$	13.0938	−	41.8256i	0.437432	−	1.39729i
$897$	0.228760	−	1.53084i	0.00763806	−	0.0511131i
$898$	29.6734	−	2.04649i	0.990215	−	0.0682923i
$899$	9.72053	+	6.24701i	0.324198	+	0.208349i
$900$	−16.4560	−	7.32782i	−0.548532	−	0.244261i
$901$	−18.2834	−	40.0350i	−0.609107	−	1.33376i
$902$	−5.68220	−	1.25122i	−0.189197	−	0.0416611i
$903$	2.68304	+	7.19352i	0.0892861	+	0.239385i
$904$	1.48224	+	5.19423i	0.0492985	+	0.172758i
$905$	−1.27667	+	2.37902i	−0.0424380	+	0.0790813i
$906$	9.43156	−	20.5141i	0.313343	−	0.681535i
$907$	0.610515	−	8.53612i	0.0202718	−	0.283437i	−0.977197	−	0.212334i	$-0.931894\pi$
$907$	0.610515	−	8.53612i	0.0202718	−	0.283437i	0.997469	−	0.0711031i	$-0.0226519\pi$
$908$	39.8978	+	3.05748i	1.32405	+	0.101466i
$909$	−7.88373	−	12.2673i	−0.261487	−	0.406881i
$910$	1.51569	+	3.27778i	0.0502447	+	0.108657i
$911$	12.6304	+	43.0153i	0.418465	+	1.42516i	0.851772	+	0.523913i	$0.175528\pi$
$911$	12.6304	+	43.0153i	0.418465	+	1.42516i	−0.433307	+	0.901246i	$0.642653\pi$
$912$	−11.6783	−	8.92898i	−0.386708	−	0.295668i
$913$	2.43586	−	0.174216i	0.0806150	−	0.00576570i
$914$	5.70981	−	2.59006i	0.188864	−	0.0856717i
$915$	−3.56315	+	0.538781i	−0.117794	+	0.0178115i
$916$	−19.4845	+	12.3824i	−0.643787	+	0.409128i
$917$	45.5814	+	34.1218i	1.50523	+	1.12680i
$918$	−22.3390	+	40.6647i	−0.737297	+	1.34214i
$919$	−37.3913			−1.23342			−0.616712	−	0.787189i	$-0.711536\pi$
$919$	−37.3913			−1.23342			−0.616712	+	0.787189i	$0.711536\pi$
$920$	30.3310	+	0.178645i	0.999983	+	0.00588974i
$921$	−0.530377			−0.0174765
$922$	2.37044	−	4.31503i	0.0780663	−	0.142108i
$923$	−0.826381	−	0.618621i	−0.0272006	−	0.0203622i
$924$	−2.69328	+	1.71158i	−0.0886023	+	0.0563069i
$925$	−35.1717	−	7.11701i	−1.15644	−	0.234006i
$926$	−26.3238	+	11.9409i	−0.865054	+	0.392403i
$927$	−6.75898	+	0.483412i	−0.221994	+	0.0158773i
$928$	−4.77380	−	23.3709i	−0.156708	−	0.767187i
$929$	2.44903	+	8.34064i	0.0803502	+	0.273648i	0.989862	−	0.142030i	$-0.0453628\pi$
$929$	2.44903	+	8.34064i	0.0803502	+	0.273648i	−0.909512	+	0.415677i	$0.863545\pi$
$930$	8.90441	+	3.27327i	0.291987	+	0.107335i
$931$	14.5307	+	22.6102i	0.476223	+	0.741018i
$932$	−41.6216	−	3.18958i	−1.36336	−	0.104478i
$933$	1.94344	−	27.1729i	0.0636255	−	0.889601i
$934$	−23.4576	+	51.0214i	−0.767556	+	1.66947i
$935$	5.02672	−	1.51577i	0.164391	−	0.0495710i
$936$	1.44434	−	0.412160i	0.0472097	−	0.0134719i
$937$	−7.93614	−	21.2776i	−0.259262	−	0.695109i	−0.999735	−	0.0230226i	$-0.992671\pi$
$937$	−7.93614	−	21.2776i	−0.259262	−	0.695109i	0.740473	−	0.672086i	$-0.234602\pi$
$938$	74.7400	+	16.4578i	2.44035	+	0.537365i
$939$	−2.03923	−	4.46530i	−0.0665479	−	0.145720i
$940$	−1.44765	+	1.25996i	−0.0472172	+	0.0410952i
$941$	15.3868	+	9.88848i	0.501594	+	0.322355i	0.766854	−	0.641822i	$-0.221821\pi$
$941$	15.3868	+	9.88848i	0.501594	+	0.322355i	−0.265259	+	0.964177i	$0.585458\pi$
$942$	−33.1007	+	2.28286i	−1.07848	+	0.0743796i
$943$	50.4029	−	14.4970i	1.64134	−	0.472086i
$944$	−41.4234	+	11.7069i	−1.34822	+	0.381027i
$945$	−36.2520	+	27.5516i	−1.17928	+	0.896253i
$946$	−0.808925	−	0.522774i	−0.0263004	−	0.0169969i
$947$	3.68102	−	9.86918i	0.119617	−	0.320705i	−0.863318	−	0.504661i	$-0.831618\pi$
$947$	3.68102	−	9.86918i	0.119617	−	0.320705i	0.982935	+	0.183956i	$0.0588902\pi$
$948$	−10.4592	+	7.74698i	−0.339698	+	0.251610i
$949$	2.44413	+	1.11620i	0.0793397	+	0.0362332i
$950$	5.32365	+	23.1321i	0.172722	+	0.750503i
$951$	−21.1860	−	3.04609i	−0.687005	−	0.0987763i
$952$	32.3139	+	60.2666i	1.04730	+	1.95325i
$953$	1.49892	−	20.9577i	0.0485549	−	0.678886i	−0.913640	−	0.406524i	$-0.866741\pi$
$953$	1.49892	−	20.9577i	0.0485549	−	0.678886i	0.962195	−	0.272362i	$-0.0878048\pi$
$954$	−17.7757	−	2.60189i	−0.575508	−	0.0842392i
$955$	−2.21110	−	9.81987i	−0.0715494	−	0.317763i
$956$	−22.9967	−	20.1323i	−0.743765	−	0.651126i
$957$	−0.832361	+	1.52436i	−0.0269064	+	0.0492754i
$958$	−42.6675	−	3.16066i	−1.37852	−	0.102116i
$959$	−41.1820	+	47.5266i	−1.32984	+	1.53471i
$960$	−7.99338	−	17.8792i	−0.257985	−	0.577048i
$961$	−22.5396	−	6.61822i	−0.727084	−	0.213491i
$962$	2.62971	−	1.42727i	0.0847853	−	0.0460169i
$963$	8.25394	+	6.17882i	0.265980	+	0.199110i
$964$	43.6673	+	20.2111i	1.40643	+	0.650955i
$965$	22.8168	+	49.0154i	0.734500	+	1.57786i
$966$	13.9889	−	25.1339i	0.450087	−	0.808671i
$967$	−28.8666	−	28.8666i	−0.928286	−	0.928286i	0.0693094	−	0.997595i	$-0.477920\pi$
$967$	−28.8666	−	28.8666i	−0.928286	−	0.928286i	−0.997595	+	0.0693094i	$0.977920\pi$
$968$	−10.9520	+	28.6933i	−0.352010	+	0.922237i
$969$	22.7038	−	3.26432i	0.729352	−	0.104865i
$970$	2.14433	−	2.89292i	0.0688503	−	0.0928859i
$971$	−5.93349	+	20.2076i	−0.190415	+	0.648493i	0.807838	+	0.589405i	$0.200638\pi$
$971$	−5.93349	+	20.2076i	−0.190415	+	0.648493i	−0.998253	+	0.0590886i	$0.981181\pi$
$972$	14.6097	+	27.0820i	0.468606	+	0.868656i
$973$	−9.68894	+	0.692966i	−0.310613	+	0.0222155i
$974$	−21.0050	−	24.3659i	−0.673044	−	0.780735i
$975$	1.47749	+	0.648946i	0.0473177	+	0.0207829i
$976$	4.92079	+	3.23356i	0.157510	+	0.103504i
$977$	−10.0452	+	46.1772i	−0.321376	+	1.47734i	0.478986	+	0.877822i	$0.341004\pi$
$977$	−10.0452	+	46.1772i	−0.321376	+	1.47734i	−0.800362	+	0.599517i	$0.795359\pi$
$978$	26.4307	−	19.6811i	0.845159	−	0.629333i
$979$	2.03095	+	2.34384i	0.0649095	+	0.0749096i
$980$	2.63254	+	35.7091i	0.0840936	+	1.14068i
$981$	0.686257	−	4.77302i	0.0219105	−	0.152391i
$982$	10.1408	−	13.4750i	0.323607	−	0.430006i
$983$	9.09754	+	24.3914i	0.290166	+	0.777966i	0.997472	+	0.0710585i	$0.0226377\pi$
$983$	9.09754	+	24.3914i	0.290166	+	0.777966i	−0.707306	+	0.706908i	$0.750090\pi$
$984$	−21.9803	−	25.7610i	−0.700708	−	0.821230i
$985$	−30.3944	−	25.9523i	−0.968445	−	0.826908i
$986$	31.2587	+	20.2012i	0.995481	+	0.643338i
$987$	0.386874	+	1.77843i	0.0123143	+	0.0566081i
$988$	−1.57837	−	1.19412i	−0.0502145	−	0.0379899i
$989$	8.65610	+	0.667291i	0.275248	+	0.0212186i
$990$	0.594040	−	2.05910i	0.0188798	−	0.0654425i
$991$	−20.3579	+	31.6775i	−0.646691	+	1.00627i	0.350867	+	0.936425i	$0.385887\pi$
$991$	−20.3579	+	31.6775i	−0.646691	+	1.00627i	−0.997558	+	0.0698451i	$0.977750\pi$
$992$	−7.25538	−	13.6983i	−0.230358	−	0.434921i
$993$	−6.11618	+	16.3981i	−0.194091	+	0.520379i
$994$	−10.3304	−	16.1646i	−0.327661	−	0.512711i
$995$	−6.51099	+	6.60639i	−0.206412	+	0.209437i
$996$	11.9178	+	7.74502i	0.377632	+	0.245410i
$997$	11.1360	+	14.8760i	0.352682	+	0.471128i	0.941440	−	0.337182i	$-0.109474\pi$
$997$	11.1360	+	14.8760i	0.352682	+	0.471128i	−0.588758	+	0.808309i	$0.700383\pi$
$998$	−6.02827	−	16.2887i	−0.190822	−	0.515611i
$999$	24.7055	+	28.5117i	0.781647	+	0.902069i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.w.a.163.46	yes	1360
4.3	odd	2	inner	460.2.w.a.163.56	yes	1360
5.2	odd	4	inner	460.2.w.a.347.57	yes	1360
20.7	even	4	inner	460.2.w.a.347.22	yes	1360
23.12	even	11	inner	460.2.w.a.403.22	yes	1360
92.35	odd	22	inner	460.2.w.a.403.57	yes	1360
115.12	odd	44	inner	460.2.w.a.127.56	yes	1360
460.127	even	44	inner	460.2.w.a.127.46	✓	1360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.w.a.127.46	✓	1360	460.127	even	44	inner
460.2.w.a.127.56	yes	1360	115.12	odd	44	inner
460.2.w.a.163.46	yes	1360	1.1	even	1	trivial
460.2.w.a.163.56	yes	1360	4.3	odd	2	inner
460.2.w.a.347.22	yes	1360	20.7	even	4	inner
460.2.w.a.347.57	yes	1360	5.2	odd	4	inner
460.2.w.a.403.22	yes	1360	23.12	even	11	inner
460.2.w.a.403.57	yes	1360	92.35	odd	22	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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.w (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.680913 - 1.23950i) q^{2} +(0.876446 + 0.656099i) q^{3} +(-1.07271 - 1.68798i) q^{4} +(-1.79976 - 1.32697i) q^{5} +(1.41002 - 0.639607i) q^{6} +(3.86395 - 0.276355i) q^{7} +(-2.82268 + 0.180260i) q^{8} +(-0.507507 - 1.72841i) q^{9} +O(q^{10})\)	\(q+(0.680913 - 1.23950i) q^{2} +(0.876446 + 0.656099i) q^{3} +(-1.07271 - 1.68798i) q^{4} +(-1.79976 - 1.32697i) q^{5} +(1.41002 - 0.639607i) q^{6} +(3.86395 - 0.276355i) q^{7} +(-2.82268 + 0.180260i) q^{8} +(-0.507507 - 1.72841i) q^{9} +(-2.87026 + 1.32725i) q^{10} +(-0.203396 - 0.316490i) q^{11} +(0.167307 - 2.18323i) q^{12} +(0.0210304 - 0.294043i) q^{13} +(2.28847 - 4.97753i) q^{14} +(-0.706769 - 2.34384i) q^{15} +(-1.69857 + 3.62145i) q^{16} +(-2.18106 - 5.84765i) q^{17} +(-2.48793 - 0.547842i) q^{18} +(1.39450 + 3.05353i) q^{19} +(-0.309273 + 4.46143i) q^{20} +(3.56786 + 2.29292i) q^{21} +(-0.530784 + 0.0366066i) q^{22} +(4.04881 - 2.57044i) q^{23} +(-2.59219 - 1.69397i) q^{24} +(1.47829 + 4.77647i) q^{25} +(-0.350146 - 0.226285i) q^{26} +(1.83700 - 4.92519i) q^{27} +(-4.61140 - 6.22582i) q^{28} +(-3.83568 - 1.75170i) q^{29} +(-3.38644 - 0.719913i) q^{30} +(-2.71234 - 0.389975i) q^{31} +(3.33220 + 4.57126i) q^{32} +(0.0293834 - 0.410834i) q^{33} +(-8.73326 - 1.27832i) q^{34} +(-7.32090 - 4.62998i) q^{35} +(-2.37311 + 2.71075i) q^{36} +(-3.43953 + 6.29902i) q^{37} +(4.73438 + 0.350707i) q^{38} +(0.211353 - 0.243915i) q^{39} +(5.31935 + 3.42119i) q^{40} +(10.4928 + 3.08097i) q^{41} +(5.27147 - 2.86107i) q^{42} +(1.44920 + 1.08486i) q^{43} +(-0.316044 + 0.682832i) q^{44} +(-1.38016 + 3.78417i) q^{45} +(-0.429177 - 6.76874i) q^{46} +(0.303446 + 0.303446i) q^{47} +(-3.86473 + 2.05957i) q^{48} +(7.92496 - 1.13944i) q^{49} +(6.92702 + 1.42002i) q^{50} +(1.92505 - 6.55613i) q^{51} +(-0.518899 + 0.279926i) q^{52} +(7.03398 - 0.503081i) q^{53} +(-4.85393 - 5.63059i) q^{54} +(-0.0539092 + 0.839507i) q^{55} +(-10.8569 + 1.47657i) q^{56} +(-0.781214 + 3.59118i) q^{57} +(-4.78299 + 3.56157i) q^{58} +(7.04726 + 8.13298i) q^{59} +(-3.19820 + 3.70729i) q^{60} +(0.209492 - 1.45705i) q^{61} +(-2.33024 + 3.09640i) q^{62} +(-2.43863 - 6.53823i) q^{63} +(7.93501 - 1.01763i) q^{64} +(-0.428037 + 0.501301i) q^{65} +(-0.489221 - 0.316163i) q^{66} +(2.96943 + 13.6502i) q^{67} +(-7.53107 + 9.95444i) q^{68} +(5.23502 + 0.403563i) q^{69} +(-10.7237 + 5.92164i) q^{70} +(1.89316 - 2.94581i) q^{71} +(1.74409 + 4.78726i) q^{72} +(-3.18524 + 8.53995i) q^{73} +(5.46561 + 8.55238i) q^{74} +(-1.83819 + 5.15622i) q^{75} +(3.65840 - 5.62946i) q^{76} +(-0.873374 - 1.16669i) q^{77} +(-0.158419 - 0.428057i) q^{78} +(-3.89266 - 4.49237i) q^{79} +(7.86257 - 4.26379i) q^{80} +(0.295203 - 0.189716i) q^{81} +(10.9636 - 10.9080i) q^{82} +(-3.11091 + 5.69721i) q^{83} +(0.0431189 - 8.48213i) q^{84} +(-3.83427 + 13.4186i) q^{85} +(2.33146 - 1.05759i) q^{86} +(-2.21248 - 4.05185i) q^{87} +(0.631171 + 0.856685i) q^{88} +(-8.15971 + 1.17319i) q^{89} +(3.75071 + 4.28740i) q^{90} -1.14198i q^{91} +(-8.68207 - 4.07696i) q^{92} +(-2.12135 - 2.12135i) q^{93} +(0.582742 - 0.169501i) q^{94} +(1.54218 - 7.34609i) q^{95} +(-0.0787053 + 6.19272i) q^{96} +(-0.999441 + 0.545736i) q^{97} +(3.98388 - 10.5988i) q^{98} +(-0.443799 + 0.512172i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8}+O(q^{10}) \) 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8	\( 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8} - 18 q^{10} - 6 q^{12} - 36 q^{13} - 44 q^{16} - 36 q^{17} - 38 q^{18} - 14 q^{20} - 88 q^{21} - 28 q^{22} - 36 q^{25} - 36 q^{26} - 34 q^{28} + 2 q^{30} + 2 q^{32} - 60 q^{33} - 36 q^{36} - 36 q^{37} - 10 q^{38} + 2 q^{40} - 56 q^{41} - 202 q^{42} - 120 q^{45} - 44 q^{46} - 50 q^{48} - 34 q^{50} - 250 q^{52} - 84 q^{53} - 84 q^{56} - 44 q^{57} - 58 q^{58} - 42 q^{60} - 136 q^{61} - 82 q^{62} - 68 q^{65} - 84 q^{66} - 4 q^{68} + 16 q^{70} - 104 q^{72} - 36 q^{73} + 4 q^{76} - 44 q^{77} - 50 q^{78} + 204 q^{80} + 80 q^{81} - 10 q^{82} - 252 q^{85} + 44 q^{86} - 50 q^{88} + 264 q^{90} - 22 q^{92} - 88 q^{93} + 52 q^{96} - 36 q^{97} + 30 q^{98}+O(q^{100}) \) 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8 - 18 * q^10 - 6 * q^12 - 36 * q^13 - 44 * q^16 - 36 * q^17 - 38 * q^18 - 14 * q^20 - 88 * q^21 - 28 * q^22 - 36 * q^25 - 36 * q^26 - 34 * q^28 + 2 * q^30 + 2 * q^32 - 60 * q^33 - 36 * q^36 - 36 * q^37 - 10 * q^38 + 2 * q^40 - 56 * q^41 - 202 * q^42 - 120 * q^45 - 44 * q^46 - 50 * q^48 - 34 * q^50 - 250 * q^52 - 84 * q^53 - 84 * q^56 - 44 * q^57 - 58 * q^58 - 42 * q^60 - 136 * q^61 - 82 * q^62 - 68 * q^65 - 84 * q^66 - 4 * q^68 + 16 * q^70 - 104 * q^72 - 36 * q^73 + 4 * q^76 - 44 * q^77 - 50 * q^78 + 204 * q^80 + 80 * q^81 - 10 * q^82 - 252 * q^85 + 44 * q^86 - 50 * q^88 + 264 * q^90 - 22 * q^92 - 88 * q^93 + 52 * q^96 - 36 * q^97 + 30 * q^98

Introduction

L-functions

Modular forms

Varieties

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