LMFDB - Embedded newform 637.2.bl.a.235.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(53,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([10, 0]))

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

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

chi := DirichletCharacter("637.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bl (of order $21$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$324$
Relative dimension:	$27$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			235.9
Character	$\chi$	$=$	637.235
Dual form			637.2.bl.a.534.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.14314 - 0.172300i) q^{2} +(1.61990 - 1.10443i) q^{3} +(-0.634071 - 0.195585i) q^{4} +(0.136884 + 1.82659i) q^{5} +(-2.04206 + 0.983405i) q^{6} +(-1.31108 - 2.29806i) q^{7} +(2.77426 + 1.33601i) q^{8} +(0.308291 - 0.785514i) q^{9} +O(q^{10})$	\(q+(-1.14314 - 0.172300i) q^{2} +(1.61990 - 1.10443i) q^{3} +(-0.634071 - 0.195585i) q^{4} +(0.136884 + 1.82659i) q^{5} +(-2.04206 + 0.983405i) q^{6} +(-1.31108 - 2.29806i) q^{7} +(2.77426 + 1.33601i) q^{8} +(0.308291 - 0.785514i) q^{9} +(0.158245 - 2.11163i) q^{10} +(1.56251 + 3.98121i) q^{11} +(-1.24314 + 0.383459i) q^{12} +(-0.623490 + 0.781831i) q^{13} +(1.10278 + 2.85290i) q^{14} +(2.23908 + 2.80772i) q^{15} +(-1.84466 - 1.25767i) q^{16} +(5.56863 + 5.16694i) q^{17} +(-0.487763 + 0.844831i) q^{18} +(-2.12170 - 3.67489i) q^{19} +(0.270460 - 1.18496i) q^{20} +(-4.66186 - 2.27464i) q^{21} +(-1.10020 - 4.82029i) q^{22} +(6.53253 - 6.06130i) q^{23} +(5.96956 - 0.899766i) q^{24} +(1.62644 - 0.245147i) q^{25} +(0.847444 - 0.786313i) q^{26} +(0.940662 + 4.12131i) q^{27} +(0.381850 + 1.71356i) q^{28} +(-1.32015 + 5.78396i) q^{29} +(-2.07581 - 3.59541i) q^{30} +(-0.638205 + 1.10540i) q^{31} +(-2.62242 - 2.43325i) q^{32} +(6.92808 + 4.72348i) q^{33} +(-5.47545 - 6.86599i) q^{34} +(4.01816 - 2.70937i) q^{35} +(-0.349113 + 0.437774i) q^{36} +(1.83197 - 0.565089i) q^{37} +(1.79221 + 4.56647i) q^{38} +(-0.146514 + 1.95509i) q^{39} +(-2.06060 + 5.25033i) q^{40} +(-0.00976311 - 0.00470167i) q^{41} +(4.93723 + 3.40346i) q^{42} +(7.66443 - 3.69099i) q^{43} +(-0.212077 - 2.82997i) q^{44} +(1.47702 + 0.455599i) q^{45} +(-8.51194 + 5.80334i) q^{46} +(-2.99702 - 0.451729i) q^{47} -4.37717 q^{48} +(-3.56215 + 6.02587i) q^{49} -1.90149 q^{50} +(14.7272 + 2.21976i) q^{51} +(0.548251 - 0.373791i) q^{52} +(-1.96219 - 0.605257i) q^{53} +(-0.365203 - 4.87330i) q^{54} +(-7.05817 + 3.39904i) q^{55} +(-0.567031 - 8.12703i) q^{56} +(-7.49560 - 3.60969i) q^{57} +(2.50569 - 6.38439i) q^{58} +(0.564081 - 7.52714i) q^{59} +(-0.870590 - 2.21823i) q^{60} +(7.53001 - 2.32270i) q^{61} +(0.920018 - 1.15367i) q^{62} +(-2.20935 + 0.321397i) q^{63} +(5.36254 + 6.72441i) q^{64} +(-1.51344 - 1.03184i) q^{65} +(-7.10588 - 6.59330i) q^{66} +(-5.07276 + 8.78627i) q^{67} +(-2.52033 - 4.36535i) q^{68} +(3.88777 - 17.0334i) q^{69} +(-5.06013 + 2.40486i) q^{70} +(-0.556031 - 2.43613i) q^{71} +(1.90474 - 1.76734i) q^{72} +(8.96678 - 1.35152i) q^{73} +(-2.19156 + 0.330324i) q^{74} +(2.36393 - 2.19341i) q^{75} +(0.626554 + 2.74511i) q^{76} +(7.10048 - 8.81041i) q^{77} +(0.504348 - 2.20969i) q^{78} +(-2.73663 - 4.73998i) q^{79} +(2.04474 - 3.54160i) q^{80} +(7.93123 + 7.35910i) q^{81} +(0.0103505 + 0.00705683i) q^{82} +(8.68971 + 10.8966i) q^{83} +(2.51107 + 2.35407i) q^{84} +(-8.67564 + 10.8789i) q^{85} +(-9.39745 + 2.89873i) q^{86} +(4.24946 + 10.8275i) q^{87} +(-0.984140 + 13.1324i) q^{88} +(-2.71299 + 6.91260i) q^{89} +(-1.60993 - 0.775302i) q^{90} +(2.61414 + 0.407775i) q^{91} +(-5.32759 + 2.56563i) q^{92} +(0.187012 + 2.49550i) q^{93} +(3.34818 + 1.03278i) q^{94} +(6.42211 - 4.37852i) q^{95} +(-6.93541 - 1.04534i) q^{96} -5.12462 q^{97} +(5.11029 - 6.27463i) q^{98} +3.60900 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9}+O(q^{10}) $ 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9} - 5 q^{10} - 18 q^{11} - 40 q^{12} + 54 q^{13} - 15 q^{14} + 6 q^{15} + 29 q^{16} - 6 q^{17} + 49 q^{18} - 24 q^{19} + 11 q^{20} - 6 q^{22} - 42 q^{23} + 20 q^{24} + 14 q^{25} + 3 q^{26} - 33 q^{27} + 7 q^{28} - 22 q^{29} + 57 q^{30} - 31 q^{31} - 139 q^{32} + 6 q^{33} + 50 q^{34} + 42 q^{35} - 78 q^{36} - 4 q^{37} - 90 q^{38} + 40 q^{40} + 8 q^{41} + 20 q^{42} + 34 q^{43} - 256 q^{44} + 19 q^{45} + 85 q^{46} + 34 q^{47} - 10 q^{48} + 51 q^{49} - 54 q^{50} + 74 q^{51} - 25 q^{52} + 10 q^{53} + 111 q^{54} - 10 q^{55} - 196 q^{56} - 5 q^{57} - 21 q^{58} + 65 q^{59} + 87 q^{60} + 3 q^{61} - 54 q^{62} - 35 q^{63} - 28 q^{64} - q^{65} - 110 q^{66} + 135 q^{67} - 158 q^{68} + 42 q^{69} + 44 q^{70} + 9 q^{71} - 133 q^{72} + 31 q^{73} - 97 q^{74} - 315 q^{75} - 177 q^{76} + 6 q^{77} - 25 q^{78} + 43 q^{79} - 20 q^{80} - 259 q^{81} + 96 q^{82} + 59 q^{83} + 285 q^{84} + 6 q^{85} + 95 q^{86} - 206 q^{87} + 228 q^{88} + 43 q^{89} - 61 q^{90} - 7 q^{91} + 53 q^{92} - 10 q^{93} - 36 q^{94} - 17 q^{95} + 277 q^{96} + 66 q^{97} + 260 q^{98} - 206 q^{99}+O(q^{100}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9 - 5 * q^10 - 18 * q^11 - 40 * q^12 + 54 * q^13 - 15 * q^14 + 6 * q^15 + 29 * q^16 - 6 * q^17 + 49 * q^18 - 24 * q^19 + 11 * q^20 - 6 * q^22 - 42 * q^23 + 20 * q^24 + 14 * q^25 + 3 * q^26 - 33 * q^27 + 7 * q^28 - 22 * q^29 + 57 * q^30 - 31 * q^31 - 139 * q^32 + 6 * q^33 + 50 * q^34 + 42 * q^35 - 78 * q^36 - 4 * q^37 - 90 * q^38 + 40 * q^40 + 8 * q^41 + 20 * q^42 + 34 * q^43 - 256 * q^44 + 19 * q^45 + 85 * q^46 + 34 * q^47 - 10 * q^48 + 51 * q^49 - 54 * q^50 + 74 * q^51 - 25 * q^52 + 10 * q^53 + 111 * q^54 - 10 * q^55 - 196 * q^56 - 5 * q^57 - 21 * q^58 + 65 * q^59 + 87 * q^60 + 3 * q^61 - 54 * q^62 - 35 * q^63 - 28 * q^64 - q^65 - 110 * q^66 + 135 * q^67 - 158 * q^68 + 42 * q^69 + 44 * q^70 + 9 * q^71 - 133 * q^72 + 31 * q^73 - 97 * q^74 - 315 * q^75 - 177 * q^76 + 6 * q^77 - 25 * q^78 + 43 * q^79 - 20 * q^80 - 259 * q^81 + 96 * q^82 + 59 * q^83 + 285 * q^84 + 6 * q^85 + 95 * q^86 - 206 * q^87 + 228 * q^88 + 43 * q^89 - 61 * q^90 - 7 * q^91 + 53 * q^92 - 10 * q^93 - 36 * q^94 - 17 * q^95 + 277 * q^96 + 66 * q^97 + 260 * q^98 - 206 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{17}{21}\right)$

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 $

$2$	−1.14314	−	0.172300i	−0.808320	−	0.121835i	−0.268135	−	0.963381i	$-0.586407\pi$
$2$	−1.14314	−	0.172300i	−0.808320	−	0.121835i	−0.540184	+	0.841547i	$0.681646\pi$
$3$	1.61990	−	1.10443i	0.935250	−	0.637643i	0.00320905	−	0.999995i	$-0.498979\pi$
$3$	1.61990	−	1.10443i	0.935250	−	0.637643i	0.932041	+	0.362352i	$0.118026\pi$
$4$	−0.634071	−	0.195585i	−0.317035	−	0.0977925i
$5$	0.136884	+	1.82659i	0.0612165	+	0.816878i	0.940330	+	0.340265i	$0.110517\pi$
$5$	0.136884	+	1.82659i	0.0612165	+	0.816878i	−0.879113	+	0.476613i	$0.841864\pi$
$6$	−2.04206	+	0.983405i	−0.833668	+	0.401474i
$7$	−1.31108	−	2.29806i	−0.495541	−	0.868585i
$7$	−1.31108	−	2.29806i	−0.495541	−	0.868585i
$8$	2.77426	+	1.33601i	0.980849	+	0.472352i
$9$	0.308291	−	0.785514i	0.102764	−	0.261838i
$10$	0.158245	−	2.11163i	0.0500415	−	0.667757i
$11$	1.56251	+	3.98121i	0.471114	+	1.20038i	0.947103	+	0.320928i	$0.103995\pi$
$11$	1.56251	+	3.98121i	0.471114	+	1.20038i	−0.475989	+	0.879451i	$0.657910\pi$
$12$	−1.24314	+	0.383459i	−0.358864	+	0.110695i
$13$	−0.623490	+	0.781831i	−0.172925	+	0.216841i
$13$	−0.623490	+	0.781831i	−0.172925	+	0.216841i
$14$	1.10278	+	2.85290i	0.294732	+	0.762468i
$15$	2.23908	+	2.80772i	0.578129	+	0.724951i
$16$	−1.84466	−	1.25767i	−0.461165	−	0.314417i
$17$	5.56863	+	5.16694i	1.35059	+	1.25317i	0.939925	+	0.341380i	$0.110894\pi$
$17$	5.56863	+	5.16694i	1.35059	+	1.25317i	0.410667	+	0.911786i	$0.365296\pi$
$18$	−0.487763	+	0.844831i	−0.114967	+	0.199129i
$19$	−2.12170	−	3.67489i	−0.486751	−	0.843078i	0.513133	−	0.858309i	$-0.328485\pi$
$19$	−2.12170	−	3.67489i	−0.486751	−	0.843078i	−0.999884	+	0.0152315i	$0.995151\pi$
$20$	0.270460	−	1.18496i	0.0604767	−	0.264966i
$21$	−4.66186	−	2.27464i	−1.01730	−	0.496366i
$22$	−1.10020	−	4.82029i	−0.234563	−	1.02769i
$23$	6.53253	−	6.06130i	1.36213	−	1.26387i	0.429480	−	0.903076i	$-0.358697\pi$
$23$	6.53253	−	6.06130i	1.36213	−	1.26387i	0.932646	−	0.360792i	$-0.117494\pi$
$24$	5.96956	−	0.899766i	1.21853	−	0.183664i
$25$	1.62644	−	0.245147i	0.325289	−	0.0490294i
$26$	0.847444	−	0.786313i	0.166197	−	0.154209i
$27$	0.940662	+	4.12131i	0.181031	+	0.793147i
$28$	0.381850	+	1.71356i	0.0721629	+	0.323832i
$29$	−1.32015	+	5.78396i	−0.245146	+	1.07405i	0.691114	+	0.722746i	$0.257120\pi$
$29$	−1.32015	+	5.78396i	−0.245146	+	1.07405i	−0.936260	+	0.351308i	$0.885737\pi$
$30$	−2.07581	−	3.59541i	−0.378989	−	0.656429i
$31$	−0.638205	+	1.10540i	−0.114625	+	0.198536i	−0.917630	−	0.397436i	$-0.869900\pi$
$31$	−0.638205	+	1.10540i	−0.114625	+	0.198536i	0.803005	+	0.595973i	$0.203233\pi$
$32$	−2.62242	−	2.43325i	−0.463582	−	0.430141i
$33$	6.92808	+	4.72348i	1.20602	+	0.822253i
$34$	−5.47545	−	6.86599i	−0.939031	−	1.17751i
$35$	4.01816	−	2.70937i	0.679192	−	0.457968i
$36$	−0.349113	+	0.437774i	−0.0581855	+	0.0729624i
$37$	1.83197	−	0.565089i	0.301174	−	0.0929000i	−0.140485	−	0.990083i	$-0.544866\pi$
$37$	1.83197	−	0.565089i	0.301174	−	0.0929000i	0.441659	+	0.897183i	$0.354390\pi$
$38$	1.79221	+	4.56647i	0.290735	+	0.740780i
$39$	−0.146514	+	1.95509i	−0.0234610	+	0.313065i
$40$	−2.06060	+	5.25033i	−0.325810	+	0.830149i
$41$	−0.00976311	−	0.00470167i	−0.00152474	−	0.000734277i	0.433121	−	0.901336i	$-0.357412\pi$
$41$	−0.00976311	−	0.00470167i	−0.00152474	−	0.000734277i	−0.434646	+	0.900601i	$0.643126\pi$
$42$	4.93723	+	3.40346i	0.761830	+	0.525165i
$43$	7.66443	−	3.69099i	1.16881	−	0.562871i	0.254182	−	0.967157i	$-0.418194\pi$
$43$	7.66443	−	3.69099i	1.16881	−	0.562871i	0.914633	+	0.404285i	$0.132480\pi$
$44$	−0.212077	−	2.82997i	−0.0319718	−	0.426634i
$45$	1.47702	+	0.455599i	0.220180	+	0.0679167i
$46$	−8.51194	+	5.80334i	−1.25502	+	0.855656i
$47$	−2.99702	−	0.451729i	−0.437161	−	0.0658914i	−0.0732251	−	0.997315i	$-0.523329\pi$
$47$	−2.99702	−	0.451729i	−0.437161	−	0.0658914i	−0.363936	+	0.931424i	$0.618567\pi$
$48$	−4.37717			−0.631791
$49$	−3.56215	+	6.02587i	−0.508879	+	0.860838i
$50$	−1.90149			−0.268911
$51$	14.7272	+	2.21976i	2.06221	+	0.310829i
$52$	0.548251	−	0.373791i	0.0760288	−	0.0518355i
$53$	−1.96219	−	0.605257i	−0.269528	−	0.0831384i	0.157045	−	0.987591i	$-0.449803\pi$
$53$	−1.96219	−	0.605257i	−0.269528	−	0.0831384i	−0.426573	+	0.904453i	$0.640279\pi$
$54$	−0.365203	−	4.87330i	−0.0496979	−	0.663172i
$55$	−7.05817	+	3.39904i	−0.951724	+	0.458326i
$56$	−0.567031	−	8.12703i	−0.0757727	−	1.08602i
$57$	−7.49560	−	3.60969i	−0.992817	−	0.478115i
$58$	2.50569	−	6.38439i	0.329013	−	0.838312i
$59$	0.564081	−	7.52714i	0.0734371	−	0.979950i	−0.831809	−	0.555062i	$-0.812694\pi$
$59$	0.564081	−	7.52714i	0.0734371	−	0.979950i	0.905246	−	0.424888i	$-0.139686\pi$
$60$	−0.870590	−	2.21823i	−0.112393	−	0.286372i
$61$	7.53001	−	2.32270i	0.964120	−	0.297392i	0.227560	−	0.973764i	$-0.426925\pi$
$61$	7.53001	−	2.32270i	0.964120	−	0.297392i	0.736560	+	0.676373i	$0.236449\pi$
$62$	0.920018	−	1.15367i	0.116842	−	0.146516i
$63$	−2.20935	+	0.321397i	−0.278352	+	0.0404922i
$64$	5.36254	+	6.72441i	0.670317	+	0.840551i
$65$	−1.51344	−	1.03184i	−0.187719	−	0.127984i
$66$	−7.10588	−	6.59330i	−0.874674	−	0.811579i
$67$	−5.07276	+	8.78627i	−0.619736	+	1.07341i	0.369798	+	0.929112i	$0.379427\pi$
$67$	−5.07276	+	8.78627i	−0.619736	+	1.07341i	−0.989534	+	0.144302i	$0.953906\pi$
$68$	−2.52033	−	4.36535i	−0.305635	−	0.529376i
$69$	3.88777	−	17.0334i	0.468032	−	2.05058i
$70$	−5.06013	+	2.40486i	−0.604801	+	0.287435i
$71$	−0.556031	−	2.43613i	−0.0659887	−	0.289115i	0.931157	−	0.364619i	$-0.118801\pi$
$71$	−0.556031	−	2.43613i	−0.0659887	−	0.289115i	−0.997146	+	0.0755036i	$0.975944\pi$
$72$	1.90474	−	1.76734i	0.224475	−	0.208283i
$73$	8.96678	−	1.35152i	1.04948	−	0.158184i	0.398416	−	0.917205i	$-0.369560\pi$
$73$	8.96678	−	1.35152i	1.04948	−	0.158184i	0.651066	+	0.759021i	$0.274322\pi$
$74$	−2.19156	+	0.330324i	−0.254764	+	0.0383994i
$75$	2.36393	−	2.19341i	0.272963	−	0.253273i
$76$	0.626554	+	2.74511i	0.0718707	+	0.314886i
$77$	7.10048	−	8.81041i	0.809175	−	1.00404i
$78$	0.504348	−	2.20969i	0.0571061	−	0.250198i
$79$	−2.73663	−	4.73998i	−0.307895	−	0.533290i	0.670007	−	0.742355i	$-0.266291\pi$
$79$	−2.73663	−	4.73998i	−0.307895	−	0.533290i	−0.977902	+	0.209065i	$0.932958\pi$
$80$	2.04474	−	3.54160i	0.228609	−	0.395963i
$81$	7.93123	+	7.35910i	0.881247	+	0.817678i
$82$	0.0103505	+	0.00705683i	0.00114302	+	0.000779297i
$83$	8.68971	+	10.8966i	0.953820	+	1.19605i	0.980522	+	0.196408i	$0.0629279\pi$
$83$	8.68971	+	10.8966i	0.953820	+	1.19605i	−0.0267026	+	0.999643i	$0.508501\pi$
$84$	2.51107	+	2.35407i	0.273980	+	0.256850i
$85$	−8.67564	+	10.8789i	−0.941005	+	1.17998i
$86$	−9.39745	+	2.89873i	−1.01335	+	0.312578i
$87$	4.24946	+	10.8275i	0.455590	+	1.16082i
$88$	−0.984140	+	13.1324i	−0.104910	+	1.39992i
$89$	−2.71299	+	6.91260i	−0.287577	+	0.732734i	0.711958	+	0.702222i	$0.247809\pi$
$89$	−2.71299	+	6.91260i	−0.287577	+	0.732734i	−0.999534	+	0.0305113i	$0.990286\pi$
$90$	−1.60993	−	0.775302i	−0.169702	−	0.0817240i
$91$	2.61414	+	0.407775i	0.274036	+	0.0427465i
$92$	−5.32759	+	2.56563i	−0.555439	+	0.267485i
$93$	0.187012	+	2.49550i	0.0193922	+	0.258771i
$94$	3.34818	+	1.03278i	0.345338	+	0.106523i
$95$	6.42211	−	4.37852i	0.658894	−	0.449227i
$96$	−6.93541	−	1.04534i	−0.707842	−	0.106690i
$97$	−5.12462			−0.520326			−0.260163	−	0.965565i	$-0.583776\pi$
$97$	−5.12462			−0.520326			−0.260163	+	0.965565i	$0.583776\pi$
$98$	5.11029	−	6.27463i	0.516217	−	0.633833i
$99$	3.60900			0.362718
$100$	−1.07923	−	0.162667i	−0.107923	−	0.0162667i
$101$	−1.30150	+	0.887345i	−0.129504	+	0.0882941i	−0.626339	−	0.779551i	$-0.715448\pi$
$101$	−1.30150	+	0.887345i	−0.129504	+	0.0882941i	0.496836	+	0.867845i	$0.334495\pi$
$102$	−16.4527	−	5.07498i	−1.62906	−	0.502498i
$103$	−0.526597	−	7.02695i	−0.0518871	−	0.692386i	−0.961126	−	0.276111i	$-0.910954\pi$
$103$	−0.526597	−	7.02695i	−0.0518871	−	0.692386i	0.909239	−	0.416275i	$-0.136665\pi$
$104$	−2.77426	+	1.33601i	−0.272038	+	0.131007i
$105$	3.51670	−	8.82669i	0.343195	−	0.861397i
$106$	2.13877	+	1.02998i	0.207736	+	0.100040i
$107$	−4.12304	+	10.5053i	−0.398589	+	1.01559i	0.580879	+	0.813990i	$0.302709\pi$
$107$	−4.12304	+	10.5053i	−0.398589	+	1.01559i	−0.979468	+	0.201599i	$0.935386\pi$
$108$	0.209620	−	2.79718i	0.0201707	−	0.269159i
$109$	3.23109	+	8.23268i	0.309482	+	0.788548i	0.997993	+	0.0633220i	$0.0201695\pi$
$109$	3.23109	+	8.23268i	0.309482	+	0.788548i	−0.688511	+	0.725226i	$0.741735\pi$
$110$	8.65411	−	2.66944i	0.825137	−	0.254521i
$111$	2.34351	−	2.93867i	0.222436	−	0.278926i
$112$	−0.471704	+	5.88804i	−0.0445718	+	0.556367i
$113$	−3.89481	−	4.88394i	−0.366393	−	0.459442i	0.564125	−	0.825690i	$-0.309214\pi$
$113$	−3.89481	−	4.88394i	−0.366393	−	0.459442i	−0.930517	+	0.366248i	$0.880642\pi$
$114$	7.94655	+	5.41787i	0.744263	+	0.507430i
$115$	11.9657	+	11.1026i	1.11581	+	1.03532i
$116$	1.96832	−	3.40924i	0.182754	−	0.316540i
$117$	0.421923	+	0.730792i	0.0390068	+	0.0675617i
$118$	−1.94175	+	8.50736i	−0.178752	+	0.783166i
$119$	4.57302	−	19.5713i	0.419208	−	1.79410i
$120$	2.46065	+	10.7808i	0.224625	+	0.984148i
$121$	−5.34502	+	4.95945i	−0.485911	+	0.450859i
$122$	−9.00804	+	1.35774i	−0.815550	+	0.122924i
$123$	−0.0210079	+	0.00316644i	−0.00189422	+	0.000285508i
$124$	0.620868	−	0.576081i	0.0557556	−	0.0517336i
$125$	2.70840	+	11.8663i	0.242246	+	1.06135i
$126$	2.58097	+	0.0132706i	0.229931	+	0.00118224i
$127$	4.27287	−	18.7207i	0.379156	−	1.66119i	−0.320908	−	0.947110i	$-0.603988\pi$
$127$	4.27287	−	18.7207i	0.379156	−	1.66119i	0.700064	−	0.714080i	$-0.253155\pi$
$128$	−1.39410	−	2.41466i	−0.123222	−	0.213427i
$129$	8.33917	−	14.4439i	0.734223	−	1.27171i
$130$	1.55228	+	1.44030i	0.136144	+	0.126323i
$131$	−16.6490	−	11.3511i	−1.45463	−	0.991752i	−0.994593	−	0.103854i	$-0.966883\pi$
$131$	−16.6490	−	11.3511i	−1.45463	−	0.991752i	−0.460040	−	0.887898i	$-0.652165\pi$
$132$	−3.46905	−	4.35005i	−0.301942	−	0.378623i
$133$	−5.66341	+	9.69386i	−0.491080	+	0.840564i
$134$	7.31273	−	9.16988i	0.631724	−	0.792157i
$135$	−7.39920	+	2.28235i	−0.636822	+	0.196434i
$136$	8.54574	+	21.7742i	0.732791	+	1.86712i
$137$	−0.642864	+	8.57842i	−0.0549236	+	0.732904i	0.899969	+	0.435953i	$0.143589\pi$
$137$	−0.642864	+	8.57842i	−0.0549236	+	0.732904i	−0.954893	+	0.296951i	$0.904030\pi$
$138$	−7.37911	+	18.8017i	−0.628152	+	1.60050i
$139$	−3.84859	−	1.85338i	−0.326433	−	0.157202i	0.263488	−	0.964663i	$-0.415127\pi$
$139$	−3.84859	−	1.85338i	−0.326433	−	0.157202i	−0.589921	+	0.807461i	$0.700841\pi$
$140$	−3.07771	+	0.932045i	−0.260114	+	0.0787722i
$141$	−5.35379	+	2.57825i	−0.450870	+	0.217128i
$142$	0.215874	+	2.88063i	0.0181157	+	0.241737i
$143$	−4.08684	−	1.26062i	−0.341759	−	0.105419i
$144$	−1.55661	+	1.06128i	−0.129717	+	0.0884398i
$145$	−10.7457	−	1.61965i	−0.892378	−	0.134504i
$146$	−10.4831			−0.867589
$147$	0.884811	+	13.6955i	0.0729780	+	1.12958i
$148$	−1.27212			−0.104568
$149$	−13.4908	−	2.03341i	−1.10521	−	0.166584i	−0.429009	−	0.903300i	$-0.641137\pi$
$149$	−13.4908	−	2.03341i	−1.10521	−	0.166584i	−0.676202	+	0.736717i	$0.736375\pi$
$150$	−3.08022	+	2.10006i	−0.251499	+	0.171469i
$151$	−2.91198	−	0.898227i	−0.236974	−	0.0730966i	0.173994	−	0.984747i	$-0.444333\pi$
$151$	−2.91198	−	0.898227i	−0.236974	−	0.0730966i	−0.410967	+	0.911650i	$0.634809\pi$
$152$	−0.976442	−	13.0297i	−0.0791999	−	1.05685i
$153$	5.77546	−	2.78131i	0.466918	−	0.224856i
$154$	−9.63486	+	8.84809i	−0.776399	+	0.712999i
$155$	−2.10649	−	1.01443i	−0.169197	−	0.0814810i
$156$	0.475287	−	1.21101i	0.0380534	−	0.0969584i
$157$	−0.843512	+	11.2559i	−0.0673196	+	0.898318i	0.856661	+	0.515879i	$0.172535\pi$
$157$	−0.843512	+	11.2559i	−0.0673196	+	0.898318i	−0.923981	+	0.382438i	$0.875084\pi$
$158$	2.31164	+	5.88997i	0.183904	+	0.468581i
$159$	−3.84702	+	1.18665i	−0.305089	+	0.0941075i
$160$	4.08559	−	5.12317i	0.322994	−	0.405022i
$161$	−22.4939	−	7.06530i	−1.77277	−	0.556824i
$162$	−7.79850	−	9.77901i	−0.612708	−	0.768312i
$163$	−16.5005	−	11.2499i	−1.29242	−	0.881158i	−0.295185	−	0.955440i	$-0.595381\pi$
$163$	−16.5005	−	11.2499i	−1.29242	−	0.881158i	−0.997237	+	0.0742818i	$0.976334\pi$
$164$	0.00527093	+	0.00489071i	0.000411590	+	0.000381900i
$165$	−7.67954	+	13.3014i	−0.597852	+	1.03551i
$166$	−8.05605	−	13.9535i	−0.625271	−	1.08300i
$167$	1.81910	−	7.97001i	0.140766	−	0.616738i	−0.854491	−	0.519466i	$-0.826131\pi$
$167$	1.81910	−	7.97001i	0.140766	−	0.616738i	0.995258	−	0.0972724i	$-0.0310118\pi$
$168$	−9.89427	−	12.5387i	−0.763359	−	0.967384i
$169$	−0.222521	−	0.974928i	−0.0171170	−	0.0749945i
$170$	11.7919	−	10.9413i	0.904396	−	0.839157i
$171$	−3.54078	+	0.533686i	−0.270770	+	0.0408120i
$172$	−5.58170	+	0.841305i	−0.425600	+	0.0641489i
$173$	−5.98060	+	5.54918i	−0.454696	+	0.421896i	−0.873982	−	0.485958i	$-0.838471\pi$
$173$	−5.98060	+	5.54918i	−0.454696	+	0.421896i	0.419286	+	0.907854i	$0.362280\pi$
$174$	−2.99214	−	13.1094i	−0.226834	−	0.993824i
$175$	−2.69576	−	3.41626i	−0.203780	−	0.258245i
$176$	2.12474	−	9.30909i	0.160158	−	0.701699i
$177$	−7.39944	−	12.8162i	−0.556176	−	0.963325i
$178$	4.29237	−	7.43459i	0.321726	−	0.557246i
$179$	7.83203	+	7.26706i	0.585393	+	0.543166i	0.916297	−	0.400499i	$-0.131163\pi$
$179$	7.83203	+	7.26706i	0.585393	+	0.543166i	−0.330904	+	0.943664i	$0.607354\pi$
$180$	−0.847424	−	0.577764i	−0.0631633	−	0.0430640i
$181$	−0.578085	−	0.724896i	−0.0429688	−	0.0538811i	0.759883	−	0.650060i	$-0.225256\pi$
$181$	−0.578085	−	0.724896i	−0.0429688	−	0.0538811i	−0.802852	+	0.596179i	$0.796685\pi$
$182$	−2.91806	−	0.916559i	−0.216301	−	0.0679399i
$183$	9.63262	−	12.0789i	0.712064	−	0.892900i
$184$	26.2209	−	8.08808i	1.93303	−	0.596261i
$185$	1.28296	+	3.26892i	0.0943248	+	0.240336i
$186$	0.216195	−	2.88492i	0.0158522	−	0.211533i
$187$	−11.8696	+	30.2433i	−0.867992	+	2.21161i
$188$	1.81197	+	0.872601i	0.132152	+	0.0636410i
$189$	8.23774	−	7.56505i	0.599207	−	0.550277i
$190$	−8.09577	+	3.89872i	−0.587329	+	0.282843i
$191$	0.151900	+	2.02696i	0.0109911	+	0.146666i	0.999999	−	0.00119486i	$-0.000380334\pi$
$191$	0.151900	+	2.02696i	0.0109911	+	0.146666i	−0.989008	+	0.147861i	$0.952761\pi$
$192$	16.1134	+	4.97033i	1.16289	+	0.358703i
$193$	−0.154559	+	0.105377i	−0.0111254	+	0.00758518i	−0.568870	−	0.822427i	$-0.692619\pi$
$193$	−0.154559	+	0.105377i	−0.0111254	+	0.00758518i	0.557745	+	0.830013i	$0.311667\pi$
$194$	5.85814	+	0.882972i	0.420590	+	0.0633937i
$195$	−3.59121			−0.257172
$196$	3.43723	−	3.12412i	0.245516	−	0.223152i
$197$	−23.6083			−1.68202			−0.841009	−	0.541021i	$-0.818038\pi$
$197$	−23.6083			−1.68202			−0.841009	+	0.541021i	$0.818038\pi$
$198$	−4.12558	−	0.621832i	−0.293192	−	0.0441916i
$199$	−8.65513	+	5.90096i	−0.613546	+	0.418308i	−0.829825	−	0.558023i	$-0.811560\pi$
$199$	−8.65513	+	5.90096i	−0.613546	+	0.418308i	0.216280	+	0.976331i	$0.430608\pi$
$200$	4.83969	+	1.49285i	0.342218	+	0.105560i
$201$	1.48646	+	19.8354i	0.104847	+	1.39908i
$202$	1.64068	−	0.790109i	0.115438	−	0.0555919i
$203$	15.0227	−	4.54943i	1.05439	−	0.319307i
$204$	−8.90391	−	4.28790i	−0.623398	−	0.300213i
$205$	0.00725162	−	0.0184768i	0.000506475	−	0.00129048i
$206$	−0.608772	+	8.12350i	−0.0424151	+	0.565991i
$207$	−2.74731	−	7.00004i	−0.190951	−	0.486536i
$208$	2.13341	−	0.658070i	0.147925	−	0.0456290i
$209$	11.3153	−	14.1890i	0.782698	−	0.981472i
$210$	−5.54091	+	9.48419i	−0.382359	+	0.654471i
$211$	−1.82910	−	2.29362i	−0.125921	−	0.157899i	0.714875	−	0.699252i	$-0.246484\pi$
$211$	−1.82910	−	2.29362i	−0.125921	−	0.157899i	−0.840795	+	0.541353i	$0.817912\pi$
$212$	1.12579	+	0.767551i	0.0773197	+	0.0527157i
$213$	−3.59125	−	3.33219i	−0.246068	−	0.228318i
$214$	6.52327	−	11.2986i	0.445921	−	0.772358i
$215$	7.79109	+	13.4946i	0.531348	+	0.920322i
$216$	−2.89648	+	12.6903i	−0.197081	+	0.863467i
$217$	3.37702	+	0.0173637i	0.229247	+	0.00117872i
$218$	−2.27509	−	9.96780i	−0.154088	−	0.675105i
$219$	13.0326	−	12.0925i	0.880663	−	0.817136i
$220$	5.14018	−	0.774758i	0.346551	−	0.0522342i
$221$	−7.51166	+	1.13220i	−0.505289	+	0.0761600i
$222$	−3.18529	+	2.95552i	−0.213783	+	0.198361i
$223$	4.15366	+	18.1984i	0.278150	+	1.21865i	0.900131	+	0.435620i	$0.143471\pi$
$223$	4.15366	+	18.1984i	0.278150	+	1.21865i	−0.621981	+	0.783032i	$0.713672\pi$
$224$	−2.15356	+	9.21664i	−0.143890	+	0.615813i
$225$	0.308852	−	1.35317i	0.0205902	−	0.0902113i
$226$	3.61080	+	6.25408i	0.240187	+	0.416015i
$227$	8.15537	−	14.1255i	0.541291	−	0.937543i	−0.457540	−	0.889189i	$-0.651269\pi$
$227$	8.15537	−	14.1255i	0.541291	−	0.937543i	0.998830	−	0.0483536i	$-0.0153974\pi$
$228$	4.04674	+	3.75483i	0.268002	+	0.248670i
$229$	−14.2136	−	9.69066i	−0.939261	−	0.640377i	−0.00615559	−	0.999981i	$-0.501959\pi$
$229$	−14.2136	−	9.69066i	−0.939261	−	0.640377i	−0.933105	+	0.359604i	$0.882912\pi$
$230$	−11.7655	−	14.7535i	−0.775794	−	0.972815i
$231$	1.77160	−	22.1140i	0.116563	−	1.45499i
$232$	−11.3899	+	14.2825i	−0.747782	+	0.937689i
$233$	17.1652	−	5.29477i	1.12453	−	0.346872i	0.323937	−	0.946079i	$-0.394993\pi$
$233$	17.1652	−	5.29477i	1.12453	−	0.346872i	0.800595	+	0.599206i	$0.204517\pi$
$234$	−0.356400	−	0.908092i	−0.0232986	−	0.0593638i
$235$	0.414880	−	5.53618i	0.0270638	−	0.361141i
$236$	−1.82986	+	4.66241i	−0.119114	+	0.303497i
$237$	−9.66805	−	4.65589i	−0.628007	−	0.302432i
$238$	−8.59972	+	21.5847i	−0.557437	+	1.39913i
$239$	1.83021	−	0.881383i	0.118386	−	0.0570119i	−0.373753	−	0.927528i	$-0.621929\pi$
$239$	1.83021	−	0.881383i	0.118386	−	0.0570119i	0.492140	+	0.870516i	$0.336215\pi$
$240$	−0.599166	−	7.99532i	−0.0386760	−	0.516096i
$241$	−25.8473	−	7.97283i	−1.66497	−	0.513575i	−0.687775	−	0.725924i	$-0.741412\pi$
$241$	−25.8473	−	7.97283i	−1.66497	−	0.513575i	−0.977194	+	0.212349i	$0.931889\pi$
$242$	6.96460	−	4.74838i	0.447701	−	0.305238i
$243$	8.43517	+	1.27140i	0.541116	+	0.0815602i
$244$	−5.22885			−0.334743
$245$	−11.4944	−	5.68176i	−0.734351	−	0.362995i
$246$	0.0245605			0.00156592
$247$	4.19600	+	0.632446i	0.266985	+	0.0402416i
$248$	−3.24738	+	2.21403i	−0.206209	+	0.140591i
$249$	26.1109	+	8.05416i	1.65471	+	0.510412i
$250$	−1.05151	−	14.0314i	−0.0665033	−	0.887424i
$251$	−1.71262	+	0.824753i	−0.108099	+	0.0520580i	−0.487152	−	0.873317i	$-0.661964\pi$
$251$	−1.71262	+	0.824753i	−0.108099	+	0.0520580i	0.379053	+	0.925375i	$0.376250\pi$
$252$	1.46375	+	0.228327i	0.0922073	+	0.0143833i
$253$	34.3384	+	16.5365i	2.15884	+	1.03964i
$254$	−8.11005	+	20.6641i	−0.508870	+	1.29658i
$255$	−2.03869	+	27.2044i	−0.127668	+	1.70361i
$256$	−5.10688	−	13.0121i	−0.319180	−	0.813257i
$257$	−13.0780	+	4.03404i	−0.815786	+	0.251637i	−0.674446	−	0.738325i	$-0.735617\pi$
$257$	−13.0780	+	4.03404i	−0.815786	+	0.251637i	−0.141340	+	0.989961i	$0.545141\pi$
$258$	−12.0215	+	15.0745i	−0.748426	+	0.938496i
$259$	−3.70046	−	3.46911i	−0.229936	−	0.215560i
$260$	0.757812	+	0.950267i	0.0469975	+	0.0589330i
$261$	4.13639	+	2.82014i	0.256036	+	0.174562i
$262$	17.0763	+	15.8445i	1.05498	+	0.978877i
$263$	15.7624	−	27.3013i	0.971953	−	1.68347i	0.282308	−	0.959324i	$-0.408900\pi$
$263$	15.7624	−	27.3013i	0.971953	−	1.68347i	0.689645	−	0.724148i	$-0.257767\pi$
$264$	12.9096	+	22.3602i	0.794534	+	1.37617i
$265$	0.836965	−	3.66698i	0.0514144	−	0.225261i
$266$	8.14430	−	10.1056i	0.499359	−	0.619614i
$267$	3.23970	+	14.1940i	0.198266	+	0.868661i
$268$	4.93495	−	4.57897i	0.301450	−	0.279705i
$269$	30.4428	−	4.58852i	1.85613	−	0.279767i	0.876625	−	0.481174i	$-0.159790\pi$
$269$	30.4428	−	4.58852i	1.85613	−	0.279767i	0.979508	+	0.201407i	$0.0645514\pi$
$270$	8.85155	−	1.33416i	0.538688	−	0.0811942i
$271$	−5.35914	+	4.97255i	−0.325544	+	0.302061i	−0.825965	−	0.563721i	$-0.809369\pi$
$271$	−5.35914	+	4.97255i	−0.325544	+	0.302061i	0.500421	+	0.865782i	$0.333179\pi$
$272$	−3.77394	−	16.5347i	−0.228829	−	1.00257i
$273$	4.68501	−	2.22658i	0.283549	−	0.134759i
$274$	2.21294	−	9.69554i	0.133689	−	0.585729i
$275$	3.51731	+	6.09217i	0.212102	+	0.367371i
$276$	−5.79660	+	10.0400i	−0.348915	+	0.604338i
$277$	−0.0322710	−	0.0299432i	−0.00193898	−	0.00179911i	0.679203	−	0.733951i	$-0.262326\pi$
$277$	−0.0322710	−	0.0299432i	−0.00193898	−	0.00179911i	−0.681142	+	0.732152i	$0.738516\pi$
$278$	4.08012	+	2.78178i	0.244709	+	0.166840i
$279$	0.671557	+	0.842106i	0.0402051	+	0.0504155i
$280$	14.7672	−	2.14820i	0.882507	−	0.128379i
$281$	16.7043	−	20.9466i	0.996496	−	1.24957i	0.0282415	−	0.999601i	$-0.491009\pi$
$281$	16.7043	−	20.9466i	0.996496	−	1.24957i	0.968255	−	0.249966i	$-0.0804193\pi$
$282$	6.56434	−	2.02483i	0.390901	−	0.120577i
$283$	−4.32231	−	11.0131i	−0.256934	−	0.654658i	0.742958	−	0.669338i	$-0.233422\pi$
$283$	−4.32231	−	11.0131i	−0.256934	−	0.654658i	−0.999892	+	0.0146800i	$0.995327\pi$
$284$	−0.123907	+	1.65343i	−0.00735255	+	0.0981130i
$285$	5.56741	−	14.1855i	0.329785	−	0.840279i
$286$	4.45462	+	2.14523i	0.263407	+	0.126850i
$287$	0.00199548	+	0.0286004i	0.000117790	+	0.00168823i
$288$	−2.71982	+	1.30980i	−0.160267	+	0.0771804i
$289$	3.04203	+	40.5931i	0.178943	+	2.38783i
$290$	12.0047	+	3.70296i	0.704939	+	0.217445i
$291$	−8.30137	+	5.65978i	−0.486635	+	0.331782i
$292$	−5.94991	−	0.896805i	−0.348192	−	0.0524815i
$293$	−1.82258			−0.106476			−0.0532382	−	0.998582i	$-0.516954\pi$
$293$	−1.82258			−0.106476			−0.0532382	+	0.998582i	$0.516954\pi$
$294$	1.34827	−	15.8082i	0.0786327	−	0.921955i
$295$	13.8262			0.804995
$296$	5.83733	+	0.879836i	0.339288	+	0.0511394i
$297$	−14.9380	+	10.1846i	−0.866791	+	0.590968i
$298$	15.0715	+	4.64894i	0.873068	+	0.269306i
$299$	0.665951	+	8.88649i	0.0385129	+	0.513919i
$300$	−1.92790	+	0.928426i	−0.111307	+	0.0536027i
$301$	−18.5308	−	12.7741i	−1.06810	−	0.736289i
$302$	3.17403	+	1.52853i	0.182645	+	0.0879570i
$303$	−1.12828	+	2.87482i	−0.0648183	+	0.165154i
$304$	−0.707978	+	9.44732i	−0.0406054	+	0.541841i
$305$	5.27338	+	13.4363i	0.301953	+	0.769363i
$306$	−7.08136	+	2.18431i	−0.404815	+	0.124869i
$307$	0.306479	−	0.384312i	0.0174917	−	0.0219339i	−0.773009	−	0.634395i	$-0.781249\pi$
$307$	0.306479	−	0.384312i	0.0174917	−	0.0219339i	0.790500	+	0.612462i	$0.209821\pi$
$308$	−6.22539	+	4.19768i	−0.354725	+	0.239185i
$309$	−8.61381	−	10.8014i	−0.490022	−	0.614469i
$310$	2.23322	+	1.52258i	0.126838	+	0.0864768i
$311$	−5.20922	−	4.83345i	−0.295388	−	0.274080i	0.518530	−	0.855059i	$-0.326479\pi$
$311$	−5.20922	−	4.83345i	−0.295388	−	0.274080i	−0.813918	+	0.580979i	$0.802670\pi$
$312$	−3.01849	+	5.22818i	−0.170889	+	0.295988i
$313$	−1.23687	−	2.14232i	−0.0699119	−	0.121091i	0.828950	−	0.559322i	$-0.188938\pi$
$313$	−1.23687	−	2.14232i	−0.0699119	−	0.121091i	−0.898862	+	0.438231i	$0.855605\pi$
$314$	2.90364	−	12.7217i	0.163862	−	0.717926i
$315$	−0.889488	−	3.99159i	−0.0501170	−	0.224901i
$316$	0.808148	+	3.54073i	0.0454619	+	0.199182i
$317$	5.91303	−	5.48649i	0.332109	−	0.308152i	−0.496437	−	0.868072i	$-0.665359\pi$
$317$	5.91303	−	5.48649i	0.332109	−	0.308152i	0.828546	+	0.559920i	$0.189168\pi$
$318$	4.60214	−	0.693660i	0.258075	−	0.0388985i
$319$	−25.0899	+	3.78169i	−1.40476	+	0.211734i
$320$	−11.5487	+	10.7157i	−0.645593	+	0.599023i
$321$	4.92348	+	21.5712i	0.274802	+	1.20399i
$322$	24.4962	+	11.9523i	1.36512	+	0.666076i
$323$	7.17296	−	31.4268i	0.399114	−	1.74863i
$324$	−3.58963	−	6.21742i	−0.199424	−	0.345412i
$325$	−0.822407	+	1.42445i	−0.0456190	+	0.0790143i
$326$	16.9240	+	15.7032i	0.937335	+	0.869720i
$327$	14.3265	+	9.76762i	0.792255	+	0.540151i
$328$	−0.0208039	−	0.0260873i	−0.00114870	−	0.00144043i
$329$	2.89123	+	7.47959i	0.159399	+	0.412363i
$330$	11.0706	−	13.8821i	0.609416	−	0.764184i
$331$	8.98040	−	2.77009i	0.493607	−	0.152258i	−0.0379507	−	0.999280i	$-0.512083\pi$
$331$	8.98040	−	2.77009i	0.493607	−	0.152258i	0.531558	+	0.847022i	$0.321607\pi$
$332$	−3.37869	−	8.60876i	−0.185430	−	0.472467i
$333$	0.120896	−	1.61325i	0.00662508	−	0.0884056i
$334$	−3.45272	+	8.79738i	−0.188924	+	0.481371i
$335$	−16.7433	−	8.06317i	−0.914786	−	0.440538i
$336$	5.73881	+	10.0590i	0.313078	+	0.548764i
$337$	16.5749	−	7.98205i	0.902893	−	0.434810i	0.0759598	−	0.997111i	$-0.475798\pi$
$337$	16.5749	−	7.98205i	0.902893	−	0.434810i	0.826933	+	0.562301i	$0.190084\pi$
$338$	0.0863917	+	1.15282i	0.00469909	+	0.0627049i
$339$	−11.7032	−	3.60995i	−0.635629	−	0.196066i
$340$	7.62872	−	5.20117i	0.413726	−	0.282073i
$341$	−5.39805	−	0.813625i	−0.292321	−	0.0440602i
$342$	4.13955			0.223841
$343$	18.5181	+	0.285664i	0.999881	+	0.0154244i
$344$	26.1943			1.41230
$345$	31.6453	+	4.76977i	1.70373	+	0.256796i
$346$	7.79276	−	5.31302i	0.418942	−	0.285630i
$347$	1.02663	+	0.316673i	0.0551124	+	0.0169999i	0.322189	−	0.946675i	$-0.395581\pi$
$347$	1.02663	+	0.316673i	0.0551124	+	0.0169999i	−0.267076	+	0.963675i	$0.586058\pi$
$348$	−0.576773	−	7.69650i	−0.0309183	−	0.412576i
$349$	7.30173	−	3.51633i	0.390853	−	0.188225i	−0.228128	−	0.973631i	$-0.573260\pi$
$349$	7.30173	−	3.51633i	0.390853	−	0.188225i	0.618980	+	0.785406i	$0.287546\pi$
$350$	2.49300	+	4.36973i	0.133256	+	0.233572i
$351$	−3.80866	−	1.83416i	−0.203291	−	0.0979000i
$352$	5.58971	−	14.2424i	0.297933	−	0.759120i
$353$	−0.672285	+	8.97102i	−0.0357821	+	0.477479i	0.950313	+	0.311296i	$0.100763\pi$
$353$	−0.672285	+	8.97102i	−0.0357821	+	0.477479i	−0.986095	+	0.166183i	$0.946856\pi$
$354$	6.25034	+	15.9256i	0.332202	+	0.846436i
$355$	4.37371	−	1.34911i	0.232132	−	0.0716033i
$356$	3.07223	−	3.85246i	0.162828	−	0.204180i
$357$	−14.2073	−	36.7542i	−0.751930	−	1.94524i
$358$	−7.70096	−	9.65670i	−0.407009	−	0.510373i
$359$	7.40536	+	5.04889i	0.390840	+	0.266470i	0.742757	−	0.669561i	$-0.233518\pi$
$359$	7.40536	+	5.04889i	0.390840	+	0.266470i	−0.351917	+	0.936031i	$0.614470\pi$
$360$	3.48894	+	3.23726i	0.183883	+	0.170619i
$361$	0.496786	−	0.860459i	0.0261466	−	0.0452873i
$362$	0.535931	+	0.928260i	0.0281679	+	0.0487883i
$363$	−3.18103	+	13.9370i	−0.166961	+	0.731504i
$364$	−1.57779	−	0.769845i	−0.0826989	−	0.0403508i
$365$	3.69610	+	16.1937i	0.193463	+	0.847615i
$366$	−13.0926	+	12.1482i	−0.684361	+	0.634994i
$367$	−18.1597	+	2.73713i	−0.947927	+	0.142877i	−0.604769	−	0.796401i	$-0.706735\pi$
$367$	−18.1597	+	2.73713i	−0.947927	+	0.142877i	−0.343158	+	0.939278i	$0.611497\pi$
$368$	−19.6734	+	2.96529i	−1.02555	+	0.154576i
$369$	−0.00670310	+	0.00621957i	−0.000348950	+	0.000323778i
$370$	−0.903359	−	3.95787i	−0.0469634	−	0.205760i
$371$	1.18167	+	5.30278i	0.0613494	+	0.275306i
$372$	0.369503	−	1.61890i	0.0191579	−	0.0839361i
$373$	2.92095	+	5.05924i	0.151241	+	0.261958i	0.931684	−	0.363270i	$-0.118340\pi$
$373$	2.92095	+	5.05924i	0.151241	+	0.261958i	−0.780443	+	0.625227i	$0.785006\pi$
$374$	18.7795	−	32.5271i	0.971065	−	1.68193i
$375$	17.4928	+	16.2309i	0.903323	+	0.838161i
$376$	−7.71101	−	5.25728i	−0.397665	−	0.271123i
$377$	−3.69898	−	4.63837i	−0.190507	−	0.238888i
$378$	−10.7203	+	7.22853i	−0.551394	+	0.371795i
$379$	1.41525	−	1.77466i	0.0726963	−	0.0911582i	−0.744154	−	0.668009i	$-0.767147\pi$
$379$	1.41525	−	1.77466i	0.0726963	−	0.0911582i	0.816850	+	0.576850i	$0.195718\pi$
$380$	−4.92845	+	1.52022i	−0.252824	+	0.0779858i
$381$	−13.7540	−	35.0447i	−0.704640	−	1.79539i
$382$	0.175604	−	2.34327i	0.00898466	−	0.119892i
$383$	−0.0694781	+	0.177027i	−0.00355016	+	0.00904567i	−0.932638	−	0.360814i	$-0.882499\pi$
$383$	−0.0694781	+	0.177027i	−0.00355016	+	0.00904567i	0.929088	+	0.369860i	$0.120594\pi$
$384$	−4.92513	−	2.37182i	−0.251334	−	0.121036i
$385$	17.0650	+	11.7637i	0.869713	+	0.599534i
$386$	0.194839	−	0.0938294i	0.00991703	−	0.00477579i
$387$	−0.536449	−	7.15842i	−0.0272692	−	0.363883i
$388$	3.24937	+	1.00230i	0.164962	+	0.0508840i
$389$	30.2339	−	20.6131i	1.53292	−	1.04513i	0.556088	−	0.831124i	$-0.312302\pi$
$389$	30.2339	−	20.6131i	1.53292	−	1.04513i	0.976833	−	0.214004i	$-0.0686505\pi$
$390$	4.10525	+	0.618767i	0.207877	+	0.0313325i
$391$	67.6956			3.42351
$392$	−17.9330	+	11.9582i	−0.905752	+	0.603982i
$393$	−39.5063			−1.99283
$394$	26.9875	+	4.06771i	1.35961	+	0.204928i
$395$	8.28343	−	5.64754i	0.416784	−	0.284159i
$396$	−2.28836	−	0.705867i	−0.114995	−	0.0354711i
$397$	−2.87412	−	38.3524i	−0.144248	−	1.92485i	−0.333183	−	0.942862i	$-0.608123\pi$
$397$	−2.87412	−	38.3524i	−0.144248	−	1.92485i	0.188935	−	0.981990i	$-0.439496\pi$
$398$	10.9107	−	5.25433i	0.546906	−	0.263376i
$399$	1.53203	+	21.9579i	0.0766973	+	1.09927i
$400$	−3.30855	−	1.59331i	−0.165427	−	0.0796657i
$401$	11.8127	−	30.0984i	0.589900	−	1.50304i	−0.254361	−	0.967109i	$-0.581865\pi$
$401$	11.8127	−	30.0984i	0.589900	−	1.50304i	0.844261	−	0.535931i	$-0.180039\pi$
$402$	1.71842	−	22.9307i	0.0857069	−	1.14368i
$403$	−0.466325	−	1.18818i	−0.0232293	−	0.0591873i
$404$	0.998792	−	0.308087i	0.0496918	−	0.0153279i
$405$	−12.3564	+	15.4945i	−0.613996	+	0.769927i
$406$	−17.9569	+	2.61221i	−0.891184	+	0.129642i
$407$	5.11221	+	6.41051i	0.253403	+	0.317757i
$408$	37.8913	+	25.8339i	1.87590	+	1.27897i
$409$	−8.44177	−	7.83282i	−0.417419	−	0.387308i	0.443313	−	0.896367i	$-0.353803\pi$
$409$	−8.44177	−	7.83282i	−0.417419	−	0.387308i	−0.860732	+	0.509059i	$0.829994\pi$
$410$	−0.0114732	+	0.0198721i	−0.000566619	+	0.000981412i
$411$	8.43289	+	14.6062i	0.415964	+	0.720470i
$412$	−1.04047	+	4.55858i	−0.0512601	+	0.224585i
$413$	−18.0374	+	8.57237i	−0.887561	+	0.421819i
$414$	1.93445	+	8.47536i	0.0950728	+	0.416541i
$415$	−18.7141	+	17.3641i	−0.918639	+	0.852372i
$416$	3.53744	−	0.533183i	0.173437	−	0.0261415i
$417$	−8.28126	+	1.24820i	−0.405535	+	0.0611246i
$418$	−15.3797	+	14.2703i	−0.752247	+	0.697984i
$419$	5.54720	+	24.3039i	0.270999	+	1.18732i	0.908837	+	0.417152i	$0.136972\pi$
$419$	5.54720	+	24.3039i	0.270999	+	1.18732i	−0.637838	+	0.770171i	$0.720171\pi$
$420$	−3.95621	+	4.90894i	−0.193043	+	0.239532i
$421$	6.18252	−	27.0874i	0.301317	−	1.32016i	−0.566823	−	0.823839i	$-0.691828\pi$
$421$	6.18252	−	27.0874i	0.301317	−	1.32016i	0.868141	−	0.496318i	$-0.165315\pi$
$422$	1.69572	+	2.93708i	0.0825465	+	0.142975i
$423$	−1.27880	+	2.21494i	−0.0621772	+	0.107694i
$424$	−4.63500	−	4.30066i	−0.225096	−	0.208858i
$425$	10.3237	+	7.03860i	0.500774	+	0.341422i
$426$	3.53115	+	4.42792i	0.171085	+	0.214534i
$427$	−15.2101	−	14.2592i	−0.736070	−	0.690050i
$428$	4.66898	−	5.85472i	0.225684	−	0.282999i
$429$	−8.01255	+	2.47155i	−0.386850	+	0.119327i
$430$	−6.58117	−	16.7685i	−0.317372	−	0.808651i
$431$	1.88592	−	25.1659i	0.0908418	−	1.21220i	−0.746450	−	0.665442i	$-0.768243\pi$
$431$	1.88592	−	25.1659i	0.0908418	−	1.21220i	0.837291	−	0.546757i	$-0.184138\pi$
$432$	3.44804	−	8.78546i	0.165894	−	0.422691i
$433$	−31.9446	−	15.3837i	−1.53516	−	0.739294i	−0.540387	−	0.841416i	$-0.681722\pi$
$433$	−31.9446	−	15.3837i	−1.53516	−	0.739294i	−0.994772	+	0.102123i	$0.967437\pi$
$434$	−3.85741	−	0.601710i	−0.185161	−	0.0288830i
$435$	−19.1957	+	9.24415i	−0.920362	+	0.443223i
$436$	−0.438551	−	5.85206i	−0.0210028	−	0.280263i
$437$	−36.1347	−	11.1461i	−1.72856	−	0.533189i
$438$	−16.9816	+	11.5779i	−0.811413	+	0.553212i
$439$	16.0641	+	2.42127i	0.766696	+	0.115561i	0.520734	−	0.853719i	$-0.325658\pi$
$439$	16.0641	+	2.42127i	0.766696	+	0.115561i	0.245961	+	0.969280i	$0.420896\pi$
$440$	−24.1223			−1.14999
$441$	3.63522	+	4.65584i	0.173106	+	0.221707i
$442$	8.78193			0.417714
$443$	−27.5415	−	4.15121i	−1.30854	−	0.197230i	−0.542516	−	0.840046i	$-0.682528\pi$
$443$	−27.5415	−	4.15121i	−1.30854	−	0.197230i	−0.766021	+	0.642816i	$0.777766\pi$
$444$	−2.06071	+	1.40497i	−0.0977971	+	0.0666770i
$445$	−12.9979	−	4.00931i	−0.616158	−	0.190060i
$446$	−1.61262	−	21.5189i	−0.0763597	−	1.01895i
$447$	−24.0995	+	11.6057i	−1.13987	+	0.548932i
$448$	8.42239	−	21.1397i	0.397921	−	0.998755i
$449$	20.8608	+	10.0460i	0.984482	+	0.474102i	0.855645	−	0.517564i	$-0.173161\pi$
$449$	20.8608	+	10.0460i	0.984482	+	0.474102i	0.128838	+	0.991666i	$0.458875\pi$
$450$	−0.586212	+	1.49364i	−0.0276343	+	0.0704110i
$451$	0.00346336	−	0.0462154i	0.000163083	−	0.00217620i
$452$	1.51436	+	3.85853i	0.0712295	+	0.181490i
$453$	−5.70915	+	1.76104i	−0.268239	+	0.0827408i
$454$	−11.7565	+	14.7422i	−0.551761	+	0.691887i
$455$	−0.387005	+	4.83079i	−0.0181431	+	0.226471i
$456$	−15.9721	−	20.0284i	−0.747964	−	0.937918i
$457$	−3.86109	−	2.63245i	−0.180614	−	0.123141i	0.469638	−	0.882859i	$-0.344384\pi$
$457$	−3.86109	−	2.63245i	−0.180614	−	0.123141i	−0.650252	+	0.759718i	$0.725337\pi$
$458$	14.5784	+	13.5268i	0.681203	+	0.632064i
$459$	−16.0563	+	27.8104i	−0.749446	+	1.29808i
$460$	−5.41563	−	9.38014i	−0.252505	−	0.437351i
$461$	6.63739	−	29.0803i	0.309134	−	1.35440i	−0.546776	−	0.837279i	$-0.684145\pi$
$461$	6.63739	−	29.0803i	0.309134	−	1.35440i	0.855910	−	0.517125i	$-0.172998\pi$
$462$	−5.83542	+	24.9741i	−0.271489	+	1.16190i
$463$	−1.10846	−	4.85649i	−0.0515146	−	0.225700i	0.942617	−	0.333875i	$-0.108356\pi$
$463$	−1.10846	−	4.85649i	−0.0515146	−	0.225700i	−0.994132	+	0.108175i	$0.965499\pi$
$464$	9.70953	−	9.00912i	0.450753	−	0.418238i
$465$	−4.53267	+	0.683190i	−0.210197	+	0.0316822i
$466$	−20.5345	+	3.09508i	−0.951243	+	0.143377i
$467$	−23.9741	+	22.2447i	−1.10939	+	1.02936i	−0.110015	+	0.993930i	$0.535090\pi$
$467$	−23.9741	+	22.2447i	−1.10939	+	1.02936i	−0.999372	+	0.0354311i	$0.988720\pi$
$468$	−0.124597	−	0.545895i	−0.00575950	−	0.0252340i
$469$	26.8422	+	0.138015i	1.23946	+	0.00637293i
$470$	−1.42815	+	6.25713i	−0.0658756	+	0.288620i
$471$	11.0649	+	19.1650i	0.509845	+	0.883078i
$472$	11.6213	−	20.1286i	0.534912	−	0.926494i
$473$	26.6704	+	24.7465i	1.22630	+	1.13784i
$474$	10.2497	+	6.98812i	0.470784	+	0.320975i
$475$	−4.35171	−	5.45687i	−0.199670	−	0.250379i
$476$	−6.72747	+	11.5152i	−0.308353	+	0.527797i
$477$	−1.08036	+	1.35473i	−0.0494665	+	0.0620290i
$478$	−2.24404	+	0.692196i	−0.102640	+	0.0316603i
$479$	12.1330	+	30.9145i	0.554373	+	1.41252i	0.883589	+	0.468264i	$0.155120\pi$
$479$	12.1330	+	30.9145i	0.554373	+	1.41252i	−0.329216	+	0.944255i	$0.606784\pi$
$480$	0.960072	−	12.8113i	0.0438211	−	0.584752i
$481$	−0.700412	+	1.78462i	−0.0319360	+	0.0813717i
$482$	28.1732	+	13.5675i	1.28326	+	0.617984i
$483$	−44.2410	+	13.3978i	−2.01303	+	0.609622i
$484$	4.35911	−	2.09924i	0.198142	−	0.0954199i
$485$	−0.701480	−	9.36060i	−0.0318526	−	0.425043i
$486$	−9.42349	−	2.90676i	−0.427458	−	0.131853i
$487$	16.1531	−	11.0130i	0.731967	−	0.499046i	−0.139059	−	0.990284i	$-0.544408\pi$
$487$	16.1531	−	11.0130i	0.731967	−	0.499046i	0.871026	+	0.491238i	$0.163455\pi$
$488$	23.9934	+	3.61642i	1.08613	+	0.163708i
$489$	−39.1539			−1.77060
$490$	12.1607	+	8.47552i	0.549366	+	0.382885i
$491$	2.93953			0.132659			0.0663296	−	0.997798i	$-0.478871\pi$
$491$	2.93953			0.132659			0.0663296	+	0.997798i	$0.478871\pi$
$492$	0.0139398	+	0.00210109i	0.000628456	+	9.47245e-5i
$493$	−37.2368	+	25.3876i	−1.67706	+	1.14340i
$494$	−4.68764	−	1.44594i	−0.210907	−	0.0650561i
$495$	0.494016	+	6.59218i	0.0222044	+	0.296297i
$496$	2.56750	−	1.23644i	0.115284	−	0.0555180i
$497$	−4.86937	+	4.47174i	−0.218421	+	0.200585i
$498$	−28.4607	−	13.7059i	−1.27535	−	0.614177i
$499$	−15.9701	+	40.6910i	−0.714918	+	1.82158i	−0.165140	+	0.986270i	$0.552808\pi$
$499$	−15.9701	+	40.6910i	−0.714918	+	1.82158i	−0.549778	+	0.835311i	$0.685288\pi$
$500$	0.603547	−	8.05377i	0.0269914	−	0.360175i
$501$	−5.85555	−	14.9197i	−0.261607	−	0.666563i
$502$	2.09986	−	0.647722i	0.0937214	−	0.0289092i
$503$	−7.72735	+	9.68979i	−0.344545	+	0.432046i	−0.923668	−	0.383194i	$-0.874824\pi$
$503$	−7.72735	+	9.68979i	−0.344545	+	0.432046i	0.579122	+	0.815241i	$0.303395\pi$
$504$	−6.55870	−	2.06008i	−0.292148	−	0.0917633i
$505$	−1.79897	−	2.25584i	−0.0800533	−	0.100384i
$506$	−36.4043	−	24.8200i	−1.61837	−	1.10338i
$507$	−1.43720	−	1.33353i	−0.0638284	−	0.0592241i
$508$	−6.37078	+	11.0345i	−0.282658	+	0.489578i
$509$	−10.8949	−	18.8706i	−0.482909	−	0.836423i	0.516899	−	0.856047i	$-0.327086\pi$
$509$	−10.8949	−	18.8706i	−0.482909	−	0.836423i	−0.999807	+	0.0196240i	$0.993753\pi$
$510$	7.01782	−	30.7471i	0.310754	−	1.36150i
$511$	−14.8620	−	18.8342i	−0.657457	−	0.833177i
$512$	4.83674	+	21.1911i	0.213756	+	0.936525i
$513$	13.1496	−	12.2010i	0.580567	−	0.538688i
$514$	15.6451	−	2.35811i	0.690074	−	0.104012i
$515$	12.7633	−	1.92376i	0.562418	−	0.0847709i
$516$	−8.11263	+	7.52742i	−0.357139	+	0.331376i
$517$	−2.88445	−	12.6376i	−0.126858	−	0.555801i
$518$	3.63241	+	4.60325i	0.159599	+	0.202255i
$519$	−3.55929	+	15.5943i	−0.156236	+	0.684513i
$520$	−2.82011	−	4.88457i	−0.123670	−	0.214202i
$521$	−21.3586	+	36.9941i	−0.935735	+	1.62074i	−0.162417	+	0.986722i	$0.551929\pi$
$521$	−21.3586	+	36.9941i	−0.935735	+	1.62074i	−0.773318	+	0.634019i	$0.781404\pi$
$522$	−4.24254	−	3.93651i	−0.185691	−	0.172296i
$523$	5.72644	+	3.90422i	0.250400	+	0.170720i	0.682015	−	0.731338i	$-0.261104\pi$
$523$	5.72644	+	3.90422i	0.250400	+	0.170720i	−0.431615	+	0.902058i	$0.642056\pi$
$524$	8.33656	+	10.4537i	0.364184	+	0.456673i
$525$	−8.13987	−	2.55673i	−0.355253	−	0.111585i
$526$	−22.7226	+	28.4933i	−0.990754	+	1.24237i
$527$	−9.26549	+	2.85802i	−0.403611	+	0.124497i
$528$	−6.83937	−	17.4264i	−0.297646	−	0.758388i
$529$	4.21577	−	56.2555i	0.183294	−	2.44589i
$530$	−1.58859	+	4.04766i	−0.0690038	+	0.175819i
$531$	−5.73877	−	2.76364i	−0.249041	−	0.119932i
$532$	5.48697	−	5.03892i	0.237890	−	0.218465i
$533$	0.00976311	−	0.00470167i	0.000422887	−	0.000203652i
$534$	−1.25778	−	16.7839i	−0.0544295	−	0.726311i
$535$	−19.7534	−	6.09310i	−0.854012	−	0.263428i
$536$	−25.8117	+	17.5981i	−1.11490	+	0.760123i
$537$	20.7131	+	3.12199i	0.893835	+	0.134724i
$538$	−35.5909			−1.53443
$539$	−29.5561	−	4.76620i	−1.27307	−	0.205295i
$540$	5.13801			0.221105
$541$	−2.86376	−	0.431643i	−0.123123	−	0.0185578i	0.0871918	−	0.996192i	$-0.472211\pi$
$541$	−2.86376	−	0.431643i	−0.123123	−	0.0185578i	−0.210315	+	0.977634i	$0.567449\pi$
$542$	6.98300	−	4.76093i	0.299945	−	0.204499i
$543$	−1.73704	−	0.535805i	−0.0745435	−	0.0229936i
$544$	−2.03084	−	27.0997i	−0.0870717	−	1.16189i
$545$	−14.5955	+	7.02882i	−0.625202	+	0.301081i
$546$	−5.73924	+	1.73806i	−0.245617	+	0.0743819i
$547$	27.6977	+	13.3385i	1.18427	+	0.570314i	0.919152	−	0.393902i	$-0.128875\pi$
$547$	27.6977	+	13.3385i	1.18427	+	0.570314i	0.265117	+	0.964216i	$0.414589\pi$
$548$	2.08543	−	5.31359i	0.0890852	−	0.226985i
$549$	0.496925	−	6.63100i	0.0212082	−	0.283004i
$550$	−2.97109	−	7.57021i	−0.126688	−	0.322795i
$551$	24.0564	−	7.42041i	1.02484	−	0.316120i
$552$	33.5425	−	42.0610i	1.42767	−	1.79024i
$553$	−7.30483	+	12.5034i	−0.310633	+	0.531700i
$554$	0.0317310	+	0.0397894i	0.00134812	+	0.00169049i
$555$	5.68855	+	3.87839i	0.241466	+	0.164628i
$556$	2.07778	+	1.92790i	0.0881176	+	0.0817612i
$557$	−0.944964	+	1.63673i	−0.0400394	+	0.0693503i	−0.885351	−	0.464924i	$-0.846082\pi$
$557$	−0.944964	+	1.63673i	−0.0400394	+	0.0693503i	0.845311	+	0.534274i	$0.179415\pi$
$558$	−0.622587	−	1.07835i	−0.0263562	−	0.0456503i
$559$	−1.89296	+	8.29359i	−0.0800636	+	0.350781i
$560$	−10.8196	−	0.0556315i	−0.457213	−	0.00235086i
$561$	14.1740	+	62.1003i	0.598426	+	2.62188i
$562$	−22.7044	+	21.0666i	−0.957728	+	0.888642i
$563$	−18.9389	+	2.85458i	−0.798179	+	0.120306i	−0.535454	−	0.844565i	$-0.679859\pi$
$563$	−18.9389	+	2.85458i	−0.798179	+	0.120306i	−0.262725	+	0.964871i	$0.584621\pi$
$564$	3.89895	−	0.587672i	0.164175	−	0.0247454i
$565$	8.38783	−	7.78277i	0.352879	−	0.327424i
$566$	3.04344	+	13.3342i	0.127925	+	0.560477i
$567$	6.51320	−	27.8748i	0.273529	−	1.17063i
$568$	1.71213	−	7.50132i	0.0718392	−	0.314748i
$569$	8.17261	+	14.1554i	0.342614	+	0.593424i	0.984917	−	0.173026i	$-0.0553545\pi$
$569$	8.17261	+	14.1554i	0.342614	+	0.593424i	−0.642304	+	0.766450i	$0.722021\pi$
$570$	−8.80849	+	15.2567i	−0.368947	+	0.639035i
$571$	15.9496	+	14.7991i	0.667471	+	0.619322i	0.939330	−	0.343015i	$-0.111448\pi$
$571$	15.9496	+	14.7991i	0.667471	+	0.619322i	−0.271859	+	0.962337i	$0.587639\pi$
$572$	2.34479	+	1.59865i	0.0980406	+	0.0668429i
$573$	2.48470	+	3.11571i	0.103800	+	0.130161i
$574$	0.00264675	−	0.0330380i	0.000110473	−	0.00137898i
$575$	9.13888	−	11.4598i	0.381118	−	0.477906i
$576$	6.93534	−	2.13927i	0.288972	−	0.0891362i
$577$	−1.88571	−	4.80470i	−0.0785030	−	0.200022i	0.886234	−	0.463238i	$-0.153312\pi$
$577$	−1.88571	−	4.80470i	−0.0785030	−	0.200022i	−0.964737	+	0.263215i	$0.915217\pi$
$578$	3.51674	−	46.9276i	0.146277	−	1.95193i
$579$	−0.133989	+	0.341400i	−0.00556841	+	0.0141881i
$580$	6.49673	+	3.12866i	0.269762	+	0.129911i
$581$	13.6480	−	34.2557i	0.566216	−	1.42117i
$582$	10.4648	−	5.03958i	0.433779	−	0.208897i
$583$	−0.656293	−	8.75762i	−0.0271809	−	0.362704i
$584$	26.6818	+	8.23025i	1.10410	+	0.340570i
$585$	−1.27711	+	0.870716i	−0.0528018	+	0.0359997i
$586$	2.08346	+	0.314031i	0.0860670	+	0.0129725i
$587$	−11.8148			−0.487648			−0.243824	−	0.969819i	$-0.578402\pi$
$587$	−11.8148			−0.487648			−0.243824	+	0.969819i	$0.578402\pi$
$588$	2.11759	−	8.85695i	0.0873281	−	0.365254i
$589$	5.41632			0.223176
$590$	−15.8053	−	2.38226i	−0.650693	−	0.0980763i
$591$	−38.2430	+	26.0737i	−1.57311	+	1.07253i
$592$	−4.09006	−	1.26162i	−0.168100	−	0.0518521i
$593$	0.689949	+	9.20673i	0.0283328	+	0.378075i	0.993289	+	0.115663i	$0.0368991\pi$
$593$	0.689949	+	9.20673i	0.0283328	+	0.378075i	−0.964956	+	0.262413i	$0.915482\pi$
$594$	18.8310	−	9.06852i	0.772645	−	0.372086i
$595$	36.3748	+	5.67405i	1.49122	+	0.232613i
$596$	8.15643	+	3.92793i	0.334100	+	0.160894i
$597$	−7.50325	+	19.1180i	−0.307087	+	0.782446i
$598$	0.769872	−	10.2732i	0.0314824	−	0.420103i
$599$	−15.9936	−	40.7511i	−0.653482	−	1.66504i	−0.743193	−	0.669077i	$-0.766690\pi$
$599$	−15.9936	−	40.7511i	−0.653482	−	1.66504i	0.0897112	−	0.995968i	$-0.471406\pi$
$600$	9.48857	−	2.92684i	0.387369	−	0.119488i
$601$	12.2370	−	15.3448i	0.499159	−	0.625926i	−0.466880	−	0.884320i	$-0.654622\pi$
$601$	12.2370	−	15.3448i	0.499159	−	0.625926i	0.966039	+	0.258395i	$0.0831936\pi$
$602$	18.9822	+	17.7954i	0.773658	+	0.725288i
$603$	5.33785	+	6.69345i	0.217374	+	0.272578i
$604$	1.67072	+	1.13908i	0.0679807	+	0.0463485i
$605$	−9.79055	−	9.08431i	−0.398043	−	0.369330i
$606$	1.78512	−	3.09191i	0.0725154	−	0.125600i
$607$	−12.7554	−	22.0930i	−0.517725	−	0.896725i	−0.999788	−	0.0205891i	$-0.993446\pi$
$607$	−12.7554	−	22.0930i	−0.517725	−	0.896725i	0.482063	−	0.876136i	$-0.339888\pi$
$608$	−3.37794	+	14.7997i	−0.136993	+	0.600208i
$609$	19.3108	−	23.9611i	0.782511	−	0.970954i
$610$	−3.71311	−	16.2682i	−0.150339	−	0.658679i
$611$	2.22179	−	2.06152i	0.0898840	−	0.0834002i
$612$	−4.20603	+	0.633958i	−0.170019	+	0.0256262i
$613$	−38.1700	+	5.75320i	−1.54167	+	0.232369i	−0.864188	−	0.503169i	$-0.832167\pi$
$613$	−38.1700	+	5.75320i	−1.54167	+	0.232369i	−0.677483	+	0.735539i	$0.736929\pi$
$614$	−0.416564	+	0.386515i	−0.0168112	+	0.0155985i
$615$	−0.00865945	−	0.0379395i	−0.000349183	−	0.00152987i
$616$	31.4694	−	14.9560i	1.26794	−	0.602595i
$617$	−7.45513	+	32.6630i	−0.300132	+	1.31496i	0.569796	+	0.821786i	$0.307022\pi$
$617$	−7.45513	+	32.6630i	−0.300132	+	1.31496i	−0.869928	+	0.493179i	$0.835835\pi$
$618$	7.98568	+	13.8316i	0.321231	+	0.556389i
$619$	−12.5697	+	21.7714i	−0.505220	+	0.875067i	0.494761	+	0.869029i	$0.335255\pi$
$619$	−12.5697	+	21.7714i	−0.505220	+	0.875067i	−0.999982	+	0.00603845i	$0.998078\pi$
$620$	1.13725	+	1.05522i	0.0456732	+	0.0423786i
$621$	31.1254	+	21.2209i	1.24902	+	0.851567i
$622$	5.12205	+	6.42285i	0.205376	+	0.257533i
$623$	19.4425	−	2.82833i	0.778947	−	0.113314i
$624$	2.72912	−	3.42221i	0.109252	−	0.136998i
$625$	−13.4454	+	4.14736i	−0.537816	+	0.165894i
$626$	1.04479	+	2.66208i	0.0417581	+	0.106398i
$627$	2.65899	−	35.4817i	0.106190	−	1.41700i
$628$	2.73633	−	6.97205i	0.109191	−	0.278215i
$629$	13.1214	+	6.31891i	0.523183	+	0.251952i
$630$	0.329054	+	4.71620i	0.0131098	+	0.187898i
$631$	3.35494	−	1.61565i	0.133558	−	0.0643182i	−0.365911	−	0.930650i	$-0.619243\pi$
$631$	3.35494	−	1.61565i	0.133558	−	0.0643182i	0.499469	+	0.866332i	$0.333528\pi$
$632$	−1.25944	−	16.8061i	−0.0500980	−	0.668511i
$633$	−5.49611	−	1.69532i	−0.218451	−	0.0673831i
$634$	−7.70473	+	5.25299i	−0.305994	+	0.208623i
$635$	34.7799	+	5.24223i	1.38020	+	0.208032i
$636$	2.67138			0.105927
$637$	−2.49025	−	6.54207i	−0.0986671	−	0.259206i
$638$	29.3328			1.16130
$639$	−2.08503	−	0.314268i	−0.0824826	−	0.0124322i
$640$	4.21977	−	2.87699i	0.166801	−	0.113723i
$641$	−24.7529	−	7.63525i	−0.977680	−	0.301574i	−0.235574	−	0.971856i	$-0.575697\pi$
$641$	−24.7529	−	7.63525i	−0.977680	−	0.301574i	−0.742106	+	0.670282i	$0.766173\pi$
$642$	−1.91150	−	25.5071i	−0.0754408	−	1.00669i
$643$	−28.6633	+	13.8035i	−1.13037	+	0.544358i	−0.903081	−	0.429469i	$-0.858701\pi$
$643$	−28.6633	+	13.8035i	−1.13037	+	0.544358i	−0.227289	+	0.973827i	$0.572986\pi$
$644$	12.8808	+	8.87937i	0.507576	+	0.349896i
$645$	27.5246	+	13.2551i	1.08378	+	0.521921i
$646$	−13.6145	+	34.6892i	−0.535656	+	1.36483i
$647$	0.590632	−	7.88144i	0.0232201	−	0.309851i	−0.973486	−	0.228748i	$-0.926537\pi$
$647$	0.590632	−	7.88144i	0.0232201	−	0.309851i	0.996706	−	0.0811029i	$-0.0258442\pi$
$648$	12.1714	+	31.0123i	0.478139	+	1.21828i
$649$	30.8485	−	9.51550i	1.21091	−	0.373516i
$650$	1.18556	−	1.48664i	0.0465014	−	0.0583109i
$651$	5.48962	−	3.70156i	0.215155	−	0.145075i
$652$	8.26221	+	10.3605i	0.323573	+	0.405748i
$653$	−40.8668	−	27.8625i	−1.59924	−	1.09034i	−0.941455	−	0.337139i	$-0.890541\pi$
$653$	−40.8668	−	27.8625i	−1.59924	−	1.09034i	−0.657786	−	0.753205i	$-0.728507\pi$
$654$	−14.6942	−	13.6342i	−0.574587	−	0.533139i
$655$	18.4549	−	31.9648i	0.721093	−	1.24897i
$656$	0.0120965	+	0.0209517i	0.000472288	+	0.000818027i
$657$	1.70274	−	7.46019i	0.0664302	−	0.291050i
$658$	−2.01634	−	9.04836i	−0.0786050	−	0.352742i
$659$	−10.0150	−	43.8786i	−0.390130	−	1.70927i	−0.664196	−	0.747558i	$-0.731226\pi$
$659$	−10.0150	−	43.8786i	−0.390130	−	1.70927i	0.274067	−	0.961711i	$-0.411631\pi$
$660$	7.47092	−	6.93200i	0.290805	−	0.269828i
$661$	−5.41525	+	0.816218i	−0.210629	+	0.0317472i	−0.253509	−	0.967333i	$-0.581585\pi$
$661$	−5.41525	+	0.816218i	−0.210629	+	0.0317472i	0.0428801	+	0.999080i	$0.486347\pi$
$662$	−10.7431	+	1.61926i	−0.417543	+	0.0629344i
$663$	−10.9177	+	10.1302i	−0.424009	+	0.393423i
$664$	9.54957	+	41.8394i	0.370595	+	1.62368i
$665$	−18.4820	−	9.01781i	−0.716700	−	0.349696i
$666$	−0.416165	+	1.82334i	−0.0161260	+	0.0706528i
$667$	26.4344	+	45.7857i	1.02354	+	1.77283i
$668$	−2.71226	+	4.69776i	−0.104940	+	0.181762i
$669$	26.8273	+	24.8921i	1.03720	+	0.962385i
$670$	17.7506	+	12.1022i	0.685767	+	0.467548i
$671$	21.0129	+	26.3493i	0.811193	+	1.01720i
$672$	6.69059	+	17.3085i	0.258095	+	0.667690i
$673$	19.1172	−	23.9722i	0.736914	−	0.924060i	−0.262248	−	0.965001i	$-0.584464\pi$
$673$	19.1172	−	23.9722i	0.736914	−	0.924060i	0.999162	+	0.0409401i	$0.0130353\pi$
$674$	−20.3227	+	6.26872i	−0.782801	+	0.241462i
$675$	2.54026	+	6.47248i	0.0977747	+	0.249126i
$676$	−0.0495872	+	0.661695i	−0.00190720	+	0.0254498i
$677$	−4.96082	+	12.6400i	−0.190660	+	0.485793i	−0.993955	−	0.109788i	$-0.964983\pi$
$677$	−4.96082	+	12.6400i	−0.190660	+	0.485793i	0.803295	+	0.595581i	$0.203078\pi$
$678$	12.7563	+	6.14313i	0.489904	+	0.235925i
$679$	6.71877	+	11.7767i	0.257843	+	0.451947i
$680$	−38.6028	+	18.5901i	−1.48035	+	0.712899i
$681$	−2.38975	−	31.8890i	−0.0915753	−	1.22199i
$682$	6.03052	+	1.86017i	0.230921	+	0.0712295i
$683$	1.33602	−	0.910880i	0.0511212	−	0.0348539i	−0.537490	−	0.843270i	$-0.680627\pi$
$683$	1.33602	−	0.910880i	0.0511212	−	0.0348539i	0.588611	+	0.808416i	$0.299675\pi$
$684$	2.34949	+	0.354128i	0.0898348	+	0.0135404i
$685$	−15.7573			−0.602055
$686$	−21.1195	−	3.51722i	−0.806344	−	0.134288i
$687$	−33.7273			−1.28678
$688$	−18.7803	−	2.83068i	−0.715993	−	0.107919i
$689$	1.69662	−	1.15673i	0.0646360	−	0.0440680i
$690$	−35.3531	−	10.9050i	−1.34587	−	0.415146i
$691$	3.05678	+	40.7899i	0.116285	+	1.55172i	0.684606	+	0.728914i	$0.259974\pi$
$691$	3.05678	+	40.7899i	0.116285	+	1.55172i	−0.568320	+	0.822807i	$0.692407\pi$
$692$	4.87746	−	2.34886i	0.185413	−	0.0892903i
$693$	−4.73168	−	8.29370i	−0.179742	−	0.315052i
$694$	−1.11902	−	0.538890i	−0.0424773	−	0.0204560i
$695$	2.85856	−	7.28350i	0.108432	−	0.276279i
$696$	−2.67651	+	35.7155i	−0.101453	+	1.35379i
$697$	−0.0300740	−	0.0766272i	−0.00113913	−	0.00290246i
$698$	−8.95274	+	2.76156i	−0.338866	+	0.104526i
$699$	21.9583	−	27.5348i	0.830538	−	1.04146i
$700$	1.04113	+	2.69340i	0.0393511	+	0.101801i
$701$	−17.5198	−	21.9691i	−0.661713	−	0.829762i	0.331816	−	0.943344i	$-0.392339\pi$
$701$	−17.5198	−	21.9691i	−0.661713	−	0.829762i	−0.993529	+	0.113583i	$0.963767\pi$
$702$	4.03780	+	2.75292i	0.152397	+	0.103902i
$703$	−5.96353	−	5.53335i	−0.224919	−	0.208694i
$704$	−18.3923	+	31.8563i	−0.693185	+	1.20063i
$705$	−5.44226	−	9.42628i	−0.204967	−	0.355014i
$706$	2.31422	−	10.1393i	0.0870969	−	0.381596i
$707$	3.74553	+	1.82754i	0.140865	+	0.0687316i
$708$	2.18511	+	9.57360i	0.0821216	+	0.359798i
$709$	11.1494	−	10.3451i	0.418725	−	0.388520i	−0.442479	−	0.896779i	$-0.645901\pi$
$709$	11.1494	−	10.3451i	0.418725	−	0.388520i	0.861205	+	0.508258i	$0.169711\pi$
$710$	−5.23220	+	0.788627i	−0.196361	+	0.0295966i
$711$	−4.56700	+	0.688365i	−0.171276	+	0.0258157i
$712$	−16.7619	+	15.5527i	−0.628177	+	0.582863i
$713$	2.53109	+	11.0894i	0.0947901	+	0.415303i
$714$	9.90813	+	44.4629i	0.370803	+	1.66398i
$715$	1.74322	−	7.63756i	0.0651929	−	0.285629i
$716$	−3.54473	−	6.13966i	−0.132473	−	0.229450i
$717$	1.99133	−	3.44909i	0.0743677	−	0.128809i
$718$	−7.59542	−	7.04752i	−0.283459	−	0.263011i
$719$	20.7908	+	14.1749i	0.775367	+	0.528636i	0.885142	−	0.465320i	$-0.154061\pi$
$719$	20.7908	+	14.1749i	0.775367	+	0.528636i	−0.109776	+	0.993956i	$0.535013\pi$
$720$	−2.15160	−	2.69802i	−0.0801854	−	0.100549i
$721$	−15.4579	+	10.4230i	−0.575684	+	0.388174i
$722$	−0.716152	+	0.898026i	−0.0266524	+	0.0334211i
$723$	−50.6754	+	15.6313i	−1.88464	+	0.581335i
$724$	0.224768	+	0.572701i	0.00835345	+	0.0212842i
$725$	−0.729231	+	9.73091i	−0.0270830	+	0.361397i
$726$	6.03771	−	15.3838i	0.224080	−	0.570947i
$727$	−0.192728	−	0.0928130i	−0.00714789	−	0.00344224i	0.430306	−	0.902683i	$-0.358406\pi$
$727$	−0.192728	−	0.0928130i	−0.00714789	−	0.00344224i	−0.437454	+	0.899241i	$0.644120\pi$
$728$	6.70750	+	4.62380i	0.248597	+	0.171369i
$729$	−14.1757	+	6.82665i	−0.525025	+	0.252839i
$730$	−1.43498	−	19.1484i	−0.0531108	−	0.708715i
$731$	61.7515	+	19.0478i	2.28396	+	0.704509i
$732$	−8.47022	+	5.77490i	−0.313068	+	0.213446i
$733$	5.30822	+	0.800086i	0.196064	+	0.0295518i	0.246340	−	0.969184i	$-0.420772\pi$
$733$	5.30822	+	0.800086i	0.196064	+	0.0295518i	−0.0502762	+	0.998735i	$0.516010\pi$
$734$	21.2306			0.783635
$735$	−24.8949	+	3.49088i	−0.918263	+	0.128763i
$736$	−31.8797			−1.17510
$737$	−42.9062	−	6.46707i	−1.58047	−	0.238218i
$738$	0.00873420	−	0.00595488i	0.000321510	−	0.000219202i
$739$	20.7131	+	6.38915i	0.761944	+	0.235029i	0.651289	−	0.758830i	$-0.274229\pi$
$739$	20.7131	+	6.38915i	0.761944	+	0.235029i	0.110656	+	0.993859i	$0.464705\pi$
$740$	−0.174134	−	2.32365i	−0.00640128	−	0.0854192i
$741$	7.49560	−	3.60969i	0.275358	−	0.132605i
$742$	−0.437144	−	6.26540i	−0.0160480	−	0.230010i
$743$	22.0807	+	10.6335i	0.810061	+	0.390105i	0.792599	−	0.609743i	$-0.208727\pi$
$743$	22.0807	+	10.6335i	0.810061	+	0.390105i	0.0174617	+	0.999848i	$0.494441\pi$
$744$	−2.81520	+	7.17301i	−0.103210	+	0.262975i
$745$	1.86754	−	24.9206i	0.0684214	−	0.913020i
$746$	−2.46734	−	6.28669i	−0.0903358	−	0.230172i
$747$	11.2384	−	3.46657i	0.411190	−	0.126835i
$748$	13.4413	−	16.8549i	0.491463	−	0.616275i
$749$	29.5475	−	4.29831i	1.07964	−	0.157057i
$750$	−17.2000	−	21.5682i	−0.628057	−	0.787559i
$751$	−25.5671	−	17.4313i	−0.932956	−	0.636078i	−0.00152572	−	0.999999i	$-0.500486\pi$
$751$	−25.5671	−	17.4313i	−0.932956	−	0.636078i	−0.931430	+	0.363920i	$0.881438\pi$
$752$	4.96037	+	4.60255i	0.180886	+	0.167838i
$753$	−1.86339	+	3.22749i	−0.0679057	+	0.117616i
$754$	3.42925	+	5.93963i	0.124886	+	0.216309i
$755$	1.24209	−	5.44196i	0.0452043	−	0.198053i
$756$	−6.70292	+	3.18560i	−0.243783	+	0.115859i
$757$	2.53803	+	11.1198i	0.0922461	+	0.404157i	0.999878	−	0.0156100i	$-0.00496902\pi$
$757$	2.53803	+	11.1198i	0.0922461	+	0.404157i	−0.907632	+	0.419767i	$0.862112\pi$
$758$	−1.92359	+	1.78483i	−0.0698681	+	0.0648281i
$759$	73.8883	−	11.1369i	2.68198	−	0.404243i
$760$	23.6663	−	3.56713i	0.858469	−	0.129393i
$761$	38.4171	−	35.6459i	1.39262	−	1.29216i	0.483674	−	0.875248i	$-0.339302\pi$
$761$	38.4171	−	35.6459i	1.39262	−	1.29216i	0.908946	−	0.416914i	$-0.136888\pi$
$762$	9.68453	+	42.4307i	0.350834	+	1.53710i
$763$	14.6830	−	18.2189i	0.531560	−	0.659569i
$764$	0.300128	−	1.31495i	0.0108583	−	0.0475731i
$765$	5.87090	+	10.1687i	0.212263	+	0.367650i
$766$	0.109925	−	0.190395i	0.00397174	−	0.00687926i
$767$	5.53325	+	5.13411i	0.199794	+	0.185382i
$768$	−22.6436	−	15.4381i	−0.817081	−	0.557076i
$769$	−14.7060	−	18.4408i	−0.530313	−	0.664991i	0.442450	−	0.896793i	$-0.354109\pi$
$769$	−14.7060	−	18.4408i	−0.530313	−	0.664991i	−0.972763	+	0.231802i	$0.925538\pi$
$770$	−17.4807	−	16.3878i	−0.629962	−	0.590576i
$771$	−16.7298	+	20.9785i	−0.602510	+	0.755523i
$772$	0.118612	−	0.0365868i	0.00426892	−	0.00131679i
$773$	−0.278648	−	0.709983i	−0.0100223	−	0.0255363i	0.925775	−	0.378075i	$-0.123414\pi$
$773$	−0.278648	−	0.709983i	−0.0100223	−	0.0255363i	−0.935797	+	0.352538i	$0.885319\pi$
$774$	−0.620161	+	8.27548i	−0.0222912	+	0.297456i
$775$	−0.767019	+	1.95433i	−0.0275521	+	0.0702017i
$776$	−14.2170	−	6.84655i	−0.510361	−	0.245777i
$777$	−9.82577	−	1.53271i	−0.352498	−	0.0549855i
$778$	−38.1132	+	18.3543i	−1.36642	+	0.658035i
$779$	0.00343627	+	0.0458539i	0.000123117	+	0.00164289i
$780$	2.27708	+	0.702387i	0.0815327	+	0.0251495i
$781$	8.82993	−	6.02015i	0.315960	−	0.215418i
$782$	−77.3853	−	11.6640i	−2.76729	−	0.417102i
$783$	−25.0793			−0.896261
$784$	14.1495	−	6.63567i	0.505339	−	0.236988i
$785$	−20.6754			−0.737937
$786$	45.1611	+	6.80694i	1.61084	+	0.242796i
$787$	40.2070	−	27.4126i	1.43322	−	0.977155i	0.436217	−	0.899842i	$-0.356318\pi$
$787$	40.2070	−	27.4126i	1.43322	−	0.977155i	0.997007	−	0.0773135i	$-0.0246342\pi$
$788$	14.9693	+	4.61742i	0.533260	+	0.164489i
$789$	−4.61882	−	61.6339i	−0.164435	−	2.19423i
$790$	−10.4422	+	5.02868i	−0.371515	+	0.178912i
$791$	−6.11718	+	15.3537i	−0.217502	+	0.545915i
$792$	10.0123	+	4.82167i	0.355772	+	0.171331i
$793$	−2.87893	+	7.33538i	−0.102234	+	0.260487i
$794$	−3.32262	+	44.3373i	−0.117915	+	1.57347i
$795$	−2.69413	−	6.86452i	−0.0955508	−	0.243459i
$796$	6.64210	−	2.04882i	0.235423	−	0.0726184i
$797$	−31.5365	+	39.5455i	−1.11708	+	1.40077i	−0.211092	+	0.977466i	$0.567702\pi$
$797$	−31.5365	+	39.5455i	−1.11708	+	1.40077i	−0.905987	+	0.423306i	$0.860870\pi$
$798$	2.03204	−	25.3649i	0.0719333	−	0.897907i
$799$	−14.3553	−	18.0009i	−0.507853	−	0.636828i
$800$	−4.86172	−	3.31466i	−0.171888	−	0.117191i
$801$	4.59355	+	4.26219i	0.162305	+	0.150597i
$802$	−18.6895	+	32.3712i	−0.659950	+	1.14307i
$803$	19.3914	+	33.5868i	0.684307	+	1.18525i
$804$	2.93699	−	12.8678i	0.103580	−	0.453812i
$805$	9.82639	−	42.0543i	0.346335	−	1.48222i
$806$	0.328350	+	1.43860i	0.0115657	+	0.0506724i
$807$	44.2467	−	41.0549i	1.55756	−	1.44520i
$808$	−4.79619	+	0.722909i	−0.168729	+	0.0254319i
$809$	32.9170	−	4.96145i	1.15730	−	0.174435i	0.457793	−	0.889059i	$-0.348640\pi$
$809$	32.9170	−	4.96145i	1.15730	−	0.174435i	0.699509	+	0.714624i	$0.253402\pi$
$810$	16.7948	−	15.5833i	0.590109	−	0.547541i
$811$	−8.00067	−	35.0532i	−0.280942	−	1.23089i	−0.896589	−	0.442864i	$-0.853963\pi$
$811$	−8.00067	−	35.0532i	−0.280942	−	1.23089i	0.615647	−	0.788022i	$-0.288895\pi$
$812$	−10.4153	−	0.0535523i	−0.365504	−	0.00187932i
$813$	−3.18944	+	13.9738i	−0.111858	+	0.490084i
$814$	−4.73942	−	8.20892i	−0.166117	−	0.287723i
$815$	18.2903	−	31.6797i	0.640681	−	1.10969i
$816$	−24.3749	−	22.6166i	−0.853291	−	0.791738i
$817$	−29.8256	−	20.3348i	−1.04347	−	0.711423i
$818$	8.30050	+	10.4085i	0.290220	+	0.363925i
$819$	1.12623	−	1.92773i	0.0393536	−	0.0673603i
$820$	−0.00821183	+	0.0102973i	−0.000286770	+	0.000359598i
$821$	−35.1714	+	10.8489i	−1.22749	+	0.378631i	−0.839666	−	0.543102i	$-0.817250\pi$
$821$	−35.1714	+	10.8489i	−1.22749	+	0.378631i	−0.387825	+	0.921733i	$0.626773\pi$
$822$	−7.12330	−	18.1499i	−0.248453	−	0.633049i
$823$	−0.782918	+	10.4473i	−0.0272908	+	0.364170i	0.966793	+	0.255559i	$0.0822595\pi$
$823$	−0.782918	+	10.4473i	−0.0272908	+	0.364170i	−0.994084	+	0.108611i	$0.965360\pi$
$824$	7.92717	−	20.1981i	0.276156	−	0.703635i
$825$	12.4261	+	5.98408i	0.432620	+	0.208339i
$826$	22.0962	−	6.69155i	0.768825	−	0.232829i
$827$	−1.90522	+	0.917504i	−0.0662509	+	0.0319048i	−0.466716	−	0.884407i	$-0.654563\pi$
$827$	−1.90522	+	0.917504i	−0.0662509	+	0.0319048i	0.400465	+	0.916312i	$0.368849\pi$
$828$	0.372889	+	4.97585i	0.0129588	+	0.172923i
$829$	26.9365	+	8.30880i	0.935542	+	0.288576i	0.724795	−	0.688964i	$-0.241934\pi$
$829$	26.9365	+	8.30880i	0.935542	+	0.288576i	0.210747	+	0.977541i	$0.432411\pi$
$830$	24.3846	−	16.6252i	0.846403	−	0.577067i
$831$	−0.0853460	−	0.0128638i	−0.00296062	−	0.000446242i
$832$	−8.60084			−0.298181
$833$	−50.9716	+	15.1504i	−1.76606	+	0.524931i
$834$	9.68168			0.335249
$835$	14.8070	+	2.23179i	0.512417	+	0.0772344i
$836$	−9.94987	+	6.78371i	−0.344124	+	0.234619i
$837$	−5.15605	−	1.59043i	−0.178219	−	0.0549733i
$838$	−2.15365	−	28.7385i	−0.0743966	−	0.992753i
$839$	9.89027	−	4.76290i	0.341450	−	0.164434i	−0.255298	−	0.966862i	$-0.582174\pi$
$839$	9.89027	−	4.76290i	0.341450	−	0.164434i	0.596748	+	0.802429i	$0.296459\pi$
$840$	21.5488	−	19.7892i	0.743505	−	0.682791i
$841$	−5.58326	−	2.68876i	−0.192526	−	0.0927158i
$842$	−11.7346	+	29.8993i	−0.404402	+	1.03040i
$843$	3.92535	−	52.3801i	0.135196	−	1.80407i
$844$	0.711182	+	1.81206i	0.0244799	+	0.0623738i
$845$	1.75034	−	0.539908i	0.0602135	−	0.0185734i
$846$	1.84347	−	2.31164i	0.0633799	−	0.0794759i
$847$	18.4048	+	5.78094i	0.632398	+	0.198636i
$848$	2.85837	+	3.58428i	0.0981568	+	0.123085i
$849$	−19.1649	−	13.0664i	−0.657736	−	0.448437i
$850$	−10.5887	−	9.82486i	−0.363189	−	0.336990i
$851$	8.54224	−	14.7956i	0.292824	−	0.507186i
$852$	1.62538	+	2.81524i	0.0556846	+	0.0964485i
$853$	−10.9529	+	47.9880i	−0.375022	+	1.64308i	0.337426	+	0.941352i	$0.390444\pi$
$853$	−10.9529	+	47.9880i	−0.375022	+	1.64308i	−0.712447	+	0.701726i	$0.752413\pi$
$854$	14.9304	+	18.9209i	0.510908	+	0.647460i
$855$	−1.45951	−	6.39451i	−0.0499140	−	0.218688i
$856$	−25.4736	+	23.6361i	−0.870670	+	0.807864i
$857$	−54.8987	+	8.27465i	−1.87530	+	0.282657i	−0.984980	−	0.172671i	$-0.944760\pi$
$857$	−54.8987	+	8.27465i	−1.87530	+	0.282657i	−0.890324	+	0.455327i	$0.849522\pi$
$858$	9.58529	−	1.44475i	0.327236	−	0.0493230i
$859$	−9.55981	+	8.87021i	−0.326177	+	0.302648i	−0.826214	−	0.563356i	$-0.809510\pi$
$859$	−9.55981	+	8.87021i	−0.326177	+	0.302648i	0.500038	+	0.866004i	$0.333319\pi$
$860$	−2.30077	−	10.0803i	−0.0784556	−	0.343737i
$861$	0.0348197	+	0.0441260i	0.00118665	+	0.00150381i
$862$	−6.49196	+	28.4431i	−0.221117	+	0.968777i
$863$	−23.0864	−	39.9868i	−0.785871	−	1.36117i	−0.928478	−	0.371388i	$-0.878882\pi$
$863$	−23.0864	−	39.9868i	−0.785871	−	1.36117i	0.142607	−	0.989779i	$-0.454452\pi$
$864$	7.56136	−	13.0967i	0.257243	−	0.445557i
$865$	−10.9548	−	10.1645i	−0.372473	−	0.345604i
$866$	33.8664	+	23.0897i	1.15083	+	0.784621i
$867$	49.7600	+	62.3971i	1.68994	+	2.11912i
$868$	−2.13788	−	0.671505i	−0.0725642	−	0.0227923i
$869$	14.5949	−	18.3014i	0.495096	−	0.620831i
$870$	23.5361	−	7.25991i	0.797947	−	0.246134i
$871$	−3.70657	−	9.44419i	−0.125592	−	0.320004i
$872$	−2.03509	+	27.1564i	−0.0689168	+	0.919631i
$873$	−1.57988	+	4.02546i	−0.0534707	+	0.136241i
$874$	39.3864	+	18.9675i	1.33227	+	0.641585i
$875$	23.7184	−	21.7816i	0.801830	−	0.736353i
$876$	−10.6287	+	5.11852i	−0.359111	+	0.172939i
$877$	−2.25561	−	30.0990i	−0.0761666	−	1.01637i	−0.896082	−	0.443888i	$-0.853599\pi$
$877$	−2.25561	−	30.0990i	−0.0761666	−	1.01637i	0.819916	−	0.572484i	$-0.194020\pi$
$878$	−17.9462	−	5.53568i	−0.605656	−	0.186820i
$879$	−2.95240	+	2.01291i	−0.0995821	+	0.0678939i
$880$	17.2948	+	2.60677i	0.583007	+	0.0878742i
$881$	−3.22775			−0.108746			−0.0543728	−	0.998521i	$-0.517316\pi$
$881$	−3.22775			−0.108746			−0.0543728	+	0.998521i	$0.517316\pi$
$882$	−3.35335	−	5.94861i	−0.112913	−	0.200300i
$883$	54.1137			1.82107			0.910536	−	0.413431i	$-0.135670\pi$
$883$	54.1137			1.82107			0.910536	+	0.413431i	$0.135670\pi$
$884$	4.98437	+	0.751272i	0.167642	+	0.0252680i
$885$	22.3971	−	15.2701i	0.752872	−	0.513299i
$886$	30.7685	+	9.49081i	1.03369	+	0.318850i
$887$	−3.90505	−	52.1093i	−0.131119	−	1.74966i	−0.544192	−	0.838961i	$-0.683164\pi$
$887$	−3.90505	−	52.1093i	−0.131119	−	1.74966i	0.413073	−	0.910698i	$-0.364455\pi$
$888$	10.4276	−	5.02167i	0.349928	−	0.168516i
$889$	−48.6233	+	14.7249i	−1.63077	+	0.493858i
$890$	14.1675	+	6.82273i	0.474897	+	0.228698i
$891$	−16.9055	+	43.0745i	−0.566356	+	1.44305i
$892$	0.925613	−	12.3514i	0.0309918	−	0.413557i
$893$	4.69873	+	11.9722i	0.157237	+	0.400633i
$894$	29.5487	−	9.11458i	0.988258	−	0.304837i
$895$	−12.2019	+	15.3007i	−0.407864	+	0.511446i
$896$	−3.72125	+	6.36953i	−0.124318	+	0.212791i
$897$	10.8933	+	13.6597i	0.363716	+	0.456086i
$898$	−22.1158	−	15.0783i	−0.738015	−	0.503170i
$899$	−5.55108	−	5.15065i	−0.185139	−	0.171784i
$900$	−0.460494	+	0.797599i	−0.0153498	+	0.0265866i
$901$	−7.79942	−	13.5090i	−0.259836	−	0.450050i
$902$	−0.0119220	+	0.0522338i	−0.000396960	+	0.00173919i
$903$	−44.1262	−	0.226884i	−1.46843	−	0.00755024i
$904$	−4.28021	−	18.7528i	−0.142358	−	0.623709i
$905$	1.24496	−	1.15515i	0.0413839	−	0.0383986i
$906$	6.82976	−	1.02942i	0.226904	−	0.0342002i
$907$	−42.7572	+	6.44460i	−1.41973	+	0.213990i	−0.813622	−	0.581394i	$-0.802507\pi$
$907$	−42.7572	+	6.44460i	−1.41973	+	0.213990i	−0.606106	+	0.795384i	$0.707269\pi$
$908$	−7.93382	+	7.36151i	−0.263293	+	0.244300i
$909$	0.295781	+	1.29590i	0.00981045	+	0.0429824i
$910$	1.27475	−	5.45557i	0.0422574	−	0.180850i
$911$	−9.73476	+	42.6508i	−0.322527	+	1.41308i	0.510513	+	0.859870i	$0.329456\pi$
$911$	−9.73476	+	42.6508i	−0.322527	+	1.41308i	−0.833040	+	0.553213i	$0.813401\pi$
$912$	9.28704	+	16.0856i	0.307525	+	0.532649i
$913$	−29.8037	+	51.6215i	−0.986358	+	1.70842i
$914$	3.96019	+	3.67452i	0.130991	+	0.121542i
$915$	23.3818	+	15.9415i	0.772980	+	0.527009i
$916$	7.11708	+	8.92453i	0.235155	+	0.294875i
$917$	−4.25738	+	53.1427i	−0.140591	+	1.75493i
$918$	23.1463	−	29.0246i	0.763943	−	0.957954i
$919$	0.418895	−	0.129212i	0.0138181	−	0.00426231i	−0.287838	−	0.957679i	$-0.592937\pi$
$919$	0.418895	−	0.129212i	0.0138181	−	0.00426231i	0.301657	+	0.953417i	$0.402460\pi$
$920$	18.3629	+	46.7878i	0.605406	+	1.54255i
$921$	0.0720194	−	0.961032i	0.00237312	−	0.0316671i
$922$	−12.5980	+	32.0991i	−0.414892	+	1.05713i
$923$	2.25132	+	1.08418i	0.0741032	+	0.0356862i
$924$	−5.44848	+	13.6753i	−0.179242	+	0.449885i
$925$	2.84107	−	1.36819i	0.0934138	−	0.0449857i
$926$	0.430350	+	5.74262i	0.0141422	+	0.188714i
$927$	−5.68211	−	1.75270i	−0.186625	−	0.0575662i
$928$	17.5358	−	11.9557i	0.575640	−	0.392465i
$929$	−24.1960	−	3.64696i	−0.793844	−	0.119653i	−0.260414	−	0.965497i	$-0.583859\pi$
$929$	−24.1960	−	3.64696i	−0.793844	−	0.119653i	−0.533430	+	0.845844i	$0.679097\pi$
$930$	5.29917			0.173767
$931$	29.7022	+	0.305449i	0.973451	+	0.0100107i
$932$	−11.9196			−0.390438
$933$	−13.7766	−	2.07649i	−0.451027	−	0.0679814i
$934$	31.2384	−	21.2980i	1.02215	−	0.696891i
$935$	−56.8670	−	17.5411i	−1.85975	−	0.573656i
$936$	0.194176	+	2.59110i	0.00634684	+	0.0846927i
$937$	−9.70193	+	4.67220i	−0.316948	+	0.152634i	−0.585593	−	0.810605i	$-0.699138\pi$
$937$	−9.70193	+	4.67220i	−0.316948	+	0.152634i	0.268645	+	0.963239i	$0.413424\pi$
$938$	−30.6605	−	4.78268i	−1.00110	−	0.156160i
$939$	−4.36964	−	2.10431i	−0.142598	−	0.0686715i
$940$	−1.34586	+	3.42919i	−0.0438970	+	0.111848i
$941$	−1.76478	+	23.5493i	−0.0575301	+	0.767686i	0.891604	+	0.452815i	$0.149580\pi$
$941$	−1.76478	+	23.5493i	−0.0575301	+	0.767686i	−0.949135	+	0.314871i	$0.898039\pi$
$942$	−9.34660	−	23.8147i	−0.304529	−	0.775926i
$943$	−0.0922760	+	0.0284634i	−0.00300492	+	0.000926895i
$944$	−10.5072	+	13.1756i	−0.341979	+	0.428829i
$945$	14.9459	+	14.0115i	0.486190	+	0.455793i
$946$	−26.2241	−	32.8839i	−0.852617	−	1.06915i
$947$	39.6462	+	27.0303i	1.28833	+	0.878368i	0.996935	−	0.0782355i	$-0.0249286\pi$
$947$	39.6462	+	27.0303i	1.28833	+	0.878368i	0.291394	+	0.956603i	$0.405881\pi$
$948$	5.21961	+	4.84309i	0.169525	+	0.157296i
$949$	−4.53403	+	7.85317i	−0.147181	+	0.254925i
$950$	4.03438	+	6.98775i	0.130893	+	0.226713i
$951$	3.51908	−	15.4181i	0.114114	−	0.499966i
$952$	38.8342	−	48.1862i	1.25863	−	1.56173i
$953$	2.72490	+	11.9386i	0.0882683	+	0.386729i	0.999694	−	0.0247359i	$-0.00787448\pi$
$953$	2.72490	+	11.9386i	0.0882683	+	0.386729i	−0.911426	+	0.411465i	$0.865017\pi$
$954$	1.46843	−	1.36250i	0.0475420	−	0.0441126i
$955$	−3.68164	+	0.554919i	−0.119135	+	0.0179567i
$956$	−1.33287	+	0.200898i	−0.0431080	+	0.00649749i
$957$	−36.4665	+	33.8360i	−1.17880	+	1.09376i
$958$	−8.54315	−	37.4300i	−0.276017	−	1.20931i
$959$	20.5566	−	9.76963i	0.663806	−	0.315478i
$960$	−6.87311	+	30.1131i	−0.221829	+	0.971895i
$961$	14.6854	+	25.4358i	0.473722	+	0.820511i
$962$	1.10816	−	1.91938i	0.0357284	−	0.0618834i
$963$	6.98098	+	6.47740i	0.224959	+	0.208731i
$964$	14.8296	+	10.1107i	0.477630	+	0.325643i
$965$	−0.213637	−	0.267893i	−0.00687722	−	0.00862377i
$966$	52.8819	−	7.69281i	1.70145	−	0.247512i
$967$	−32.0056	+	40.1338i	−1.02923	+	1.29062i	−0.0732116	+	0.997316i	$0.523325\pi$
$967$	−32.0056	+	40.1338i	−1.02923	+	1.29062i	−0.956021	+	0.293300i	$0.905247\pi$
$968$	−21.4543	+	6.61779i	−0.689569	+	0.212704i
$969$	−23.0892	−	58.8303i	−0.741732	−	1.88990i
$970$	−0.810945	+	10.8213i	−0.0260379	+	0.347451i
$971$	−16.0492	+	40.8928i	−0.515044	+	1.31231i	0.402770	+	0.915301i	$0.368047\pi$
$971$	−16.0492	+	40.8928i	−0.515044	+	1.31231i	−0.917814	+	0.397010i	$0.870048\pi$
$972$	−5.09983	−	2.45595i	−0.163577	−	0.0787746i
$973$	0.786613	+	11.2742i	0.0252176	+	0.361434i
$974$	−20.3627	+	9.80618i	−0.652464	+	0.314210i
$975$	0.240988	+	3.21576i	0.00771779	+	0.102987i
$976$	−16.8115	−	5.18566i	−0.538123	−	0.165989i
$977$	36.1835	−	24.6695i	1.15761	−	0.789247i	0.176809	−	0.984245i	$-0.443423\pi$
$977$	36.1835	−	24.6695i	1.15761	−	0.789247i	0.980804	+	0.194999i	$0.0624702\pi$
$978$	44.7583	+	6.74623i	1.43121	+	0.215721i
$979$	−31.7596			−1.01504
$980$	6.17701	+	5.85078i	0.197317	+	0.186896i
$981$	7.46300			0.238275
$982$	−3.36029	−	0.506482i	−0.107231	−	0.0161625i
$983$	−21.6442	+	14.7567i	−0.690341	+	0.470667i	−0.856979	−	0.515351i	$-0.827661\pi$
$983$	−21.6442	+	14.7567i	−0.690341	+	0.470667i	0.166638	+	0.986018i	$0.446709\pi$
$984$	−0.0625118	−	0.0192823i	−0.00199280	−	0.000614699i
$985$	−3.23160	−	43.1227i	−0.102967	−	1.37400i
$986$	46.9410	−	22.6056i	1.49491	−	0.719909i
$987$	12.9442	+	8.92304i	0.412018	+	0.284023i
$988$	−2.53687	−	1.22169i	−0.0807085	−	0.0388672i
$989$	27.6959	−	70.5679i	0.880677	−	2.24393i
$990$	0.571106	−	7.62089i	0.0181510	−	0.242208i
$991$	7.21475	+	18.3829i	0.229184	+	0.583952i	0.998490	−	0.0549286i	$-0.0174931\pi$
$991$	7.21475	+	18.3829i	0.229184	+	0.583952i	−0.769306	+	0.638880i	$0.779398\pi$
$992$	4.36336	−	1.34592i	0.138537	−	0.0427330i
$993$	11.4880	−	14.4055i	0.364560	−	0.457144i
$994$	6.33684	−	4.27282i	0.200992	−	0.135526i
$995$	−11.9634	−	15.0017i	−0.379266	−	0.475584i
$996$	−14.9809	−	10.2138i	−0.474689	−	0.323637i
$997$	−1.32593	−	1.23029i	−0.0419928	−	0.0389636i	0.658897	−	0.752233i	$-0.271023\pi$
$997$	−1.32593	−	1.23029i	−0.0419928	−	0.0389636i	−0.700890	+	0.713269i	$0.747214\pi$
$998$	25.2670	−	43.7638i	0.799814	−	1.38532i
$999$	4.05217	+	7.01857i	0.128205	+	0.222058i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bl.a.235.9	✓	324
49.44	even	21	inner	637.2.bl.a.534.9	yes	324

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.bl.a.235.9	✓	324	1.1	even	1	trivial
637.2.bl.a.534.9	yes	324	49.44	even	21	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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bl (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.14314 - 0.172300i) q^{2} +(1.61990 - 1.10443i) q^{3} +(-0.634071 - 0.195585i) q^{4} +(0.136884 + 1.82659i) q^{5} +(-2.04206 + 0.983405i) q^{6} +(-1.31108 - 2.29806i) q^{7} +(2.77426 + 1.33601i) q^{8} +(0.308291 - 0.785514i) q^{9} +O(q^{10})\)	\(q+(-1.14314 - 0.172300i) q^{2} +(1.61990 - 1.10443i) q^{3} +(-0.634071 - 0.195585i) q^{4} +(0.136884 + 1.82659i) q^{5} +(-2.04206 + 0.983405i) q^{6} +(-1.31108 - 2.29806i) q^{7} +(2.77426 + 1.33601i) q^{8} +(0.308291 - 0.785514i) q^{9} +(0.158245 - 2.11163i) q^{10} +(1.56251 + 3.98121i) q^{11} +(-1.24314 + 0.383459i) q^{12} +(-0.623490 + 0.781831i) q^{13} +(1.10278 + 2.85290i) q^{14} +(2.23908 + 2.80772i) q^{15} +(-1.84466 - 1.25767i) q^{16} +(5.56863 + 5.16694i) q^{17} +(-0.487763 + 0.844831i) q^{18} +(-2.12170 - 3.67489i) q^{19} +(0.270460 - 1.18496i) q^{20} +(-4.66186 - 2.27464i) q^{21} +(-1.10020 - 4.82029i) q^{22} +(6.53253 - 6.06130i) q^{23} +(5.96956 - 0.899766i) q^{24} +(1.62644 - 0.245147i) q^{25} +(0.847444 - 0.786313i) q^{26} +(0.940662 + 4.12131i) q^{27} +(0.381850 + 1.71356i) q^{28} +(-1.32015 + 5.78396i) q^{29} +(-2.07581 - 3.59541i) q^{30} +(-0.638205 + 1.10540i) q^{31} +(-2.62242 - 2.43325i) q^{32} +(6.92808 + 4.72348i) q^{33} +(-5.47545 - 6.86599i) q^{34} +(4.01816 - 2.70937i) q^{35} +(-0.349113 + 0.437774i) q^{36} +(1.83197 - 0.565089i) q^{37} +(1.79221 + 4.56647i) q^{38} +(-0.146514 + 1.95509i) q^{39} +(-2.06060 + 5.25033i) q^{40} +(-0.00976311 - 0.00470167i) q^{41} +(4.93723 + 3.40346i) q^{42} +(7.66443 - 3.69099i) q^{43} +(-0.212077 - 2.82997i) q^{44} +(1.47702 + 0.455599i) q^{45} +(-8.51194 + 5.80334i) q^{46} +(-2.99702 - 0.451729i) q^{47} -4.37717 q^{48} +(-3.56215 + 6.02587i) q^{49} -1.90149 q^{50} +(14.7272 + 2.21976i) q^{51} +(0.548251 - 0.373791i) q^{52} +(-1.96219 - 0.605257i) q^{53} +(-0.365203 - 4.87330i) q^{54} +(-7.05817 + 3.39904i) q^{55} +(-0.567031 - 8.12703i) q^{56} +(-7.49560 - 3.60969i) q^{57} +(2.50569 - 6.38439i) q^{58} +(0.564081 - 7.52714i) q^{59} +(-0.870590 - 2.21823i) q^{60} +(7.53001 - 2.32270i) q^{61} +(0.920018 - 1.15367i) q^{62} +(-2.20935 + 0.321397i) q^{63} +(5.36254 + 6.72441i) q^{64} +(-1.51344 - 1.03184i) q^{65} +(-7.10588 - 6.59330i) q^{66} +(-5.07276 + 8.78627i) q^{67} +(-2.52033 - 4.36535i) q^{68} +(3.88777 - 17.0334i) q^{69} +(-5.06013 + 2.40486i) q^{70} +(-0.556031 - 2.43613i) q^{71} +(1.90474 - 1.76734i) q^{72} +(8.96678 - 1.35152i) q^{73} +(-2.19156 + 0.330324i) q^{74} +(2.36393 - 2.19341i) q^{75} +(0.626554 + 2.74511i) q^{76} +(7.10048 - 8.81041i) q^{77} +(0.504348 - 2.20969i) q^{78} +(-2.73663 - 4.73998i) q^{79} +(2.04474 - 3.54160i) q^{80} +(7.93123 + 7.35910i) q^{81} +(0.0103505 + 0.00705683i) q^{82} +(8.68971 + 10.8966i) q^{83} +(2.51107 + 2.35407i) q^{84} +(-8.67564 + 10.8789i) q^{85} +(-9.39745 + 2.89873i) q^{86} +(4.24946 + 10.8275i) q^{87} +(-0.984140 + 13.1324i) q^{88} +(-2.71299 + 6.91260i) q^{89} +(-1.60993 - 0.775302i) q^{90} +(2.61414 + 0.407775i) q^{91} +(-5.32759 + 2.56563i) q^{92} +(0.187012 + 2.49550i) q^{93} +(3.34818 + 1.03278i) q^{94} +(6.42211 - 4.37852i) q^{95} +(-6.93541 - 1.04534i) q^{96} -5.12462 q^{97} +(5.11029 - 6.27463i) q^{98} +3.60900 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9}+O(q^{10}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9} - 5 q^{10} - 18 q^{11} - 40 q^{12} + 54 q^{13} - 15 q^{14} + 6 q^{15} + 29 q^{16} - 6 q^{17} + 49 q^{18} - 24 q^{19} + 11 q^{20} - 6 q^{22} - 42 q^{23} + 20 q^{24} + 14 q^{25} + 3 q^{26} - 33 q^{27} + 7 q^{28} - 22 q^{29} + 57 q^{30} - 31 q^{31} - 139 q^{32} + 6 q^{33} + 50 q^{34} + 42 q^{35} - 78 q^{36} - 4 q^{37} - 90 q^{38} + 40 q^{40} + 8 q^{41} + 20 q^{42} + 34 q^{43} - 256 q^{44} + 19 q^{45} + 85 q^{46} + 34 q^{47} - 10 q^{48} + 51 q^{49} - 54 q^{50} + 74 q^{51} - 25 q^{52} + 10 q^{53} + 111 q^{54} - 10 q^{55} - 196 q^{56} - 5 q^{57} - 21 q^{58} + 65 q^{59} + 87 q^{60} + 3 q^{61} - 54 q^{62} - 35 q^{63} - 28 q^{64} - q^{65} - 110 q^{66} + 135 q^{67} - 158 q^{68} + 42 q^{69} + 44 q^{70} + 9 q^{71} - 133 q^{72} + 31 q^{73} - 97 q^{74} - 315 q^{75} - 177 q^{76} + 6 q^{77} - 25 q^{78} + 43 q^{79} - 20 q^{80} - 259 q^{81} + 96 q^{82} + 59 q^{83} + 285 q^{84} + 6 q^{85} + 95 q^{86} - 206 q^{87} + 228 q^{88} + 43 q^{89} - 61 q^{90} - 7 q^{91} + 53 q^{92} - 10 q^{93} - 36 q^{94} - 17 q^{95} + 277 q^{96} + 66 q^{97} + 260 q^{98} - 206 q^{99}+O(q^{100}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9 - 5 * q^10 - 18 * q^11 - 40 * q^12 + 54 * q^13 - 15 * q^14 + 6 * q^15 + 29 * q^16 - 6 * q^17 + 49 * q^18 - 24 * q^19 + 11 * q^20 - 6 * q^22 - 42 * q^23 + 20 * q^24 + 14 * q^25 + 3 * q^26 - 33 * q^27 + 7 * q^28 - 22 * q^29 + 57 * q^30 - 31 * q^31 - 139 * q^32 + 6 * q^33 + 50 * q^34 + 42 * q^35 - 78 * q^36 - 4 * q^37 - 90 * q^38 + 40 * q^40 + 8 * q^41 + 20 * q^42 + 34 * q^43 - 256 * q^44 + 19 * q^45 + 85 * q^46 + 34 * q^47 - 10 * q^48 + 51 * q^49 - 54 * q^50 + 74 * q^51 - 25 * q^52 + 10 * q^53 + 111 * q^54 - 10 * q^55 - 196 * q^56 - 5 * q^57 - 21 * q^58 + 65 * q^59 + 87 * q^60 + 3 * q^61 - 54 * q^62 - 35 * q^63 - 28 * q^64 - q^65 - 110 * q^66 + 135 * q^67 - 158 * q^68 + 42 * q^69 + 44 * q^70 + 9 * q^71 - 133 * q^72 + 31 * q^73 - 97 * q^74 - 315 * q^75 - 177 * q^76 + 6 * q^77 - 25 * q^78 + 43 * q^79 - 20 * q^80 - 259 * q^81 + 96 * q^82 + 59 * q^83 + 285 * q^84 + 6 * q^85 + 95 * q^86 - 206 * q^87 + 228 * q^88 + 43 * q^89 - 61 * q^90 - 7 * q^91 + 53 * q^92 - 10 * q^93 - 36 * q^94 - 17 * q^95 + 277 * q^96 + 66 * q^97 + 260 * q^98 - 206 * q^99

Introduction

L-functions

Modular forms

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