LMFDB - Embedded newform 507.2.q.b.16.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(16,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(78))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("507.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.q (of order $39$, degree $24$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$16$ over $\Q(\zeta_{39})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{39}]$

Embedding invariants

Embedding label			16.3
Character	$\chi$	$=$	507.16
Dual form			507.2.q.b.412.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00855 - 0.162147i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(2.03388 + 0.330538i) q^{4} +(-1.08961 - 0.965307i) q^{5} +(1.61095 + 1.21055i) q^{6} +(-3.04871 + 3.17404i) q^{7} +(-0.118504 - 0.0292085i) q^{8} +(0.428693 + 0.903450i) q^{9} +O(q^{10})$	\(q+(-2.00855 - 0.162147i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(2.03388 + 0.330538i) q^{4} +(-1.08961 - 0.965307i) q^{5} +(1.61095 + 1.21055i) q^{6} +(-3.04871 + 3.17404i) q^{7} +(-0.118504 - 0.0292085i) q^{8} +(0.428693 + 0.903450i) q^{9} +(2.03201 + 2.11554i) q^{10} +(-0.00113001 + 0.00238145i) q^{11} +(-1.54236 - 1.36641i) q^{12} +(3.51734 + 0.792647i) q^{13} +(6.63814 - 5.88088i) q^{14} +(0.405001 + 1.39823i) q^{15} +(-3.67576 - 1.22715i) q^{16} +(4.22368 - 4.39732i) q^{17} +(-0.714559 - 1.88414i) q^{18} +(-2.48570 + 4.30536i) q^{19} +(-1.89706 - 2.32348i) q^{20} +(4.27315 - 1.05324i) q^{21} +(0.00265584 - 0.00460004i) q^{22} +(-0.259672 - 0.449765i) q^{23} +(0.0845472 + 0.0880230i) q^{24} +(-0.347259 - 2.85994i) q^{25} +(-6.93624 - 2.16240i) q^{26} +(0.120537 - 0.992709i) q^{27} +(-7.24986 + 5.44791i) q^{28} +(-5.46329 - 0.441042i) q^{29} +(-0.586747 - 2.87408i) q^{30} +(-0.554660 + 4.56803i) q^{31} +(7.40855 + 3.15649i) q^{32} +(0.00222788 - 0.00140883i) q^{33} +(-9.19649 + 8.14738i) q^{34} +(6.38581 - 0.515516i) q^{35} +(0.573286 + 1.97921i) q^{36} +(8.51209 - 3.62666i) q^{37} +(5.69076 - 8.24448i) q^{38} +(-2.54918 - 2.54984i) q^{39} +(0.100927 + 0.146218i) q^{40} +(-9.50674 - 6.01170i) q^{41} +(-8.75362 + 1.42260i) q^{42} +(-8.81573 - 3.75603i) q^{43} +(-0.00308548 + 0.00447009i) q^{44} +(0.405001 - 1.39823i) q^{45} +(0.448637 + 0.945482i) q^{46} +(4.06035 - 10.7063i) q^{47} +(2.45085 + 3.00175i) q^{48} +(-0.498054 - 12.3591i) q^{49} +(0.233758 + 5.80063i) q^{50} +(-5.92003 + 1.45916i) q^{51} +(6.89187 + 2.77477i) q^{52} +(0.796395 + 0.196294i) q^{53} +(-0.403069 + 1.97436i) q^{54} +(0.00353010 - 0.00150404i) q^{55} +(0.453992 - 0.287087i) q^{56} +(4.40196 - 2.31033i) q^{57} +(10.9018 + 1.77171i) q^{58} +(3.02693 - 1.01054i) q^{59} +(0.361558 + 2.97770i) q^{60} +(1.70511 - 5.88672i) q^{61} +(1.85476 - 9.08519i) q^{62} +(-4.17454 - 1.39367i) q^{63} +(-7.50600 - 3.93945i) q^{64} +(-3.06737 - 4.25899i) q^{65} +(-0.00470325 + 0.00246846i) q^{66} +(11.4122 - 1.85466i) q^{67} +(10.0440 - 7.54754i) q^{68} +(-0.0209119 + 0.518923i) q^{69} -12.9098 q^{70} +(0.0175492 - 0.435479i) q^{71} +(-0.0244132 - 0.119584i) q^{72} +(-5.91984 - 8.57636i) q^{73} +(-17.6850 + 5.90413i) q^{74} +(-1.23504 + 2.60279i) q^{75} +(-6.47871 + 7.93498i) q^{76} +(-0.00411375 - 0.0108471i) q^{77} +(4.70671 + 5.53482i) q^{78} +(1.70281 - 4.48994i) q^{79} +(2.82056 + 4.88535i) q^{80} +(-0.632445 + 0.774605i) q^{81} +(18.1200 + 13.6163i) q^{82} +(-10.8774 - 5.70892i) q^{83} +(9.03923 - 0.729722i) q^{84} +(-8.84691 + 0.714196i) q^{85} +(17.0978 + 8.97363i) q^{86} +(4.38179 + 3.29270i) q^{87} +(0.000203470 - 0.000249205i) q^{88} +(2.44648 + 4.23742i) q^{89} +(-1.04018 + 2.74274i) q^{90} +(-13.2392 + 8.74764i) q^{91} +(-0.379478 - 1.00060i) q^{92} +(2.91025 - 3.56441i) q^{93} +(-9.89140 + 20.8457i) q^{94} +(6.86443 - 2.29168i) q^{95} +(-4.57460 - 6.62745i) q^{96} +(3.31342 + 16.2302i) q^{97} +(-1.00362 + 24.9046i) q^{98} -0.00263595 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9}+O(q^{10}) $ 384 * q + q^2 + 16 * q^3 + 17 * q^4 + 6 * q^5 + q^6 - 3 * q^7 - 18 * q^8 + 16 * q^9	\( 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9} + 3 q^{10} - 4 q^{11} - 34 q^{12} - 15 q^{13} + 24 q^{14} - 3 q^{15} + 11 q^{16} - 3 q^{17} - 2 q^{18} + 6 q^{19} + q^{20} + 6 q^{21} - 86 q^{22} - 52 q^{23} + 9 q^{24} - 74 q^{25} - 64 q^{26} - 32 q^{27} - 16 q^{28} - 44 q^{29} + 3 q^{30} - 28 q^{31} + 74 q^{32} - 17 q^{33} - 83 q^{34} + 70 q^{35} + 17 q^{36} + 11 q^{37} - 29 q^{38} + q^{39} - 5 q^{40} + q^{41} + 118 q^{42} - 79 q^{43} - 19 q^{44} - 3 q^{45} + 314 q^{46} + 11 q^{48} - 69 q^{49} - 76 q^{50} + 6 q^{51} - 37 q^{52} - 102 q^{53} + q^{54} - 73 q^{55} - 36 q^{56} + 14 q^{57} - 51 q^{58} + 194 q^{59} + 76 q^{60} + 4 q^{61} - 89 q^{62} - 3 q^{63} - 184 q^{64} - 49 q^{65} - 36 q^{66} - 73 q^{67} + 4 q^{68} - 100 q^{70} + 106 q^{71} + 9 q^{72} - 132 q^{73} - 45 q^{74} + 11 q^{75} + 24 q^{76} - 54 q^{77} - 39 q^{78} - 2 q^{79} + 177 q^{80} + 16 q^{81} - 76 q^{82} - 58 q^{83} - 16 q^{84} - 123 q^{85} - 157 q^{86} - 57 q^{87} + 476 q^{88} + 18 q^{89} - 6 q^{90} + 233 q^{91} - 12 q^{92} + q^{93} - 111 q^{94} + 64 q^{95} - 83 q^{96} - 143 q^{97} - 79 q^{98} - 18 q^{99}+O(q^{100}) \) 384 * q + q^2 + 16 * q^3 + 17 * q^4 + 6 * q^5 + q^6 - 3 * q^7 - 18 * q^8 + 16 * q^9 + 3 * q^10 - 4 * q^11 - 34 * q^12 - 15 * q^13 + 24 * q^14 - 3 * q^15 + 11 * q^16 - 3 * q^17 - 2 * q^18 + 6 * q^19 + q^20 + 6 * q^21 - 86 * q^22 - 52 * q^23 + 9 * q^24 - 74 * q^25 - 64 * q^26 - 32 * q^27 - 16 * q^28 - 44 * q^29 + 3 * q^30 - 28 * q^31 + 74 * q^32 - 17 * q^33 - 83 * q^34 + 70 * q^35 + 17 * q^36 + 11 * q^37 - 29 * q^38 + q^39 - 5 * q^40 + q^41 + 118 * q^42 - 79 * q^43 - 19 * q^44 - 3 * q^45 + 314 * q^46 + 11 * q^48 - 69 * q^49 - 76 * q^50 + 6 * q^51 - 37 * q^52 - 102 * q^53 + q^54 - 73 * q^55 - 36 * q^56 + 14 * q^57 - 51 * q^58 + 194 * q^59 + 76 * q^60 + 4 * q^61 - 89 * q^62 - 3 * q^63 - 184 * q^64 - 49 * q^65 - 36 * q^66 - 73 * q^67 + 4 * q^68 - 100 * q^70 + 106 * q^71 + 9 * q^72 - 132 * q^73 - 45 * q^74 + 11 * q^75 + 24 * q^76 - 54 * q^77 - 39 * q^78 - 2 * q^79 + 177 * q^80 + 16 * q^81 - 76 * q^82 - 58 * q^83 - 16 * q^84 - 123 * q^85 - 157 * q^86 - 57 * q^87 + 476 * q^88 + 18 * q^89 - 6 * q^90 + 233 * q^91 - 12 * q^92 + q^93 - 111 * q^94 + 64 * q^95 - 83 * q^96 - 143 * q^97 - 79 * q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{1}{39}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.00855	−	0.162147i	−1.42026	−	0.114655i	−0.653664	−	0.756785i	$-0.726769\pi$
$2$	−2.00855	−	0.162147i	−1.42026	−	0.114655i	−0.766596	+	0.642130i	$0.778051\pi$
$3$	−0.845190	−	0.534466i	−0.487971	−	0.308574i
$3$	−0.845190	−	0.534466i	−0.487971	−	0.308574i
$4$	2.03388	+	0.330538i	1.01694	+	0.165269i
$5$	−1.08961	−	0.965307i	−0.487287	−	0.431698i	0.383366	−	0.923596i	$-0.374765\pi$
$5$	−1.08961	−	0.965307i	−0.487287	−	0.431698i	−0.870653	+	0.491898i	$0.836303\pi$
$6$	1.61095	+	1.21055i	0.657666	+	0.494204i
$7$	−3.04871	+	3.17404i	−1.15230	+	1.19967i	−0.175740	+	0.984437i	$0.556232\pi$
$7$	−3.04871	+	3.17404i	−1.15230	+	1.19967i	−0.976562	+	0.215237i	$0.930948\pi$
$8$	−0.118504	−	0.0292085i	−0.0418974	−	0.0103268i
$9$	0.428693	+	0.903450i	0.142898	+	0.301150i
$10$	2.03201	+	2.11554i	0.642577	+	0.668994i
$11$	−0.00113001	+	0.00238145i	−0.000340712	+	0.000718035i	−0.903621	−	0.428334i	$-0.859101\pi$
$11$	−0.00113001	+	0.00238145i	−0.000340712	+	0.000718035i	0.903280	+	0.429052i	$0.141152\pi$
$12$	−1.54236	−	1.36641i	−0.445240	−	0.394448i
$13$	3.51734	+	0.792647i	0.975536	+	0.219841i
$13$	3.51734	+	0.792647i	0.975536	+	0.219841i
$14$	6.63814	−	5.88088i	1.77412	−	1.57173i
$15$	0.405001	+	1.39823i	0.104571	+	0.361020i
$16$	−3.67576	−	1.22715i	−0.918941	−	0.306788i
$17$	4.22368	−	4.39732i	1.02439	−	1.06651i	0.0266302	−	0.999645i	$-0.491522\pi$
$17$	4.22368	−	4.39732i	1.02439	−	1.06651i	0.997762	−	0.0668603i	$-0.0212982\pi$
$18$	−0.714559	−	1.88414i	−0.168423	−	0.444095i
$19$	−2.48570	+	4.30536i	−0.570259	+	0.987717i	0.426280	+	0.904591i	$0.359824\pi$
$19$	−2.48570	+	4.30536i	−0.570259	+	0.987717i	−0.996539	+	0.0831260i	$0.973510\pi$
$20$	−1.89706	−	2.32348i	−0.424196	−	0.519546i
$21$	4.27315	−	1.05324i	0.932478	−	0.229835i
$22$	0.00265584	−	0.00460004i	0.000566226	−	0.000980732i
$23$	−0.259672	−	0.449765i	−0.0541454	−	0.0937826i	0.837682	−	0.546158i	$-0.183910\pi$
$23$	−0.259672	−	0.449765i	−0.0541454	−	0.0937826i	−0.891828	+	0.452375i	$0.850577\pi$
$24$	0.0845472	+	0.0880230i	0.0172581	+	0.0179676i
$25$	−0.347259	−	2.85994i	−0.0694518	−	0.571987i
$26$	−6.93624	−	2.16240i	−1.36031	−	0.424081i
$27$	0.120537	−	0.992709i	0.0231973	−	0.191047i
$28$	−7.24986	+	5.44791i	−1.37009	+	1.02956i
$29$	−5.46329	−	0.441042i	−1.01451	−	0.0818995i	−0.437986	−	0.898982i	$-0.644308\pi$
$29$	−5.46329	−	0.441042i	−1.01451	−	0.0818995i	−0.576521	+	0.817082i	$0.695590\pi$
$30$	−0.586747	−	2.87408i	−0.107125	−	0.524732i
$31$	−0.554660	+	4.56803i	−0.0996198	+	0.820443i	0.854175	+	0.519985i	$0.174063\pi$
$31$	−0.554660	+	4.56803i	−0.0996198	+	0.820443i	−0.953795	+	0.300458i	$0.902860\pi$
$32$	7.40855	+	3.15649i	1.30966	+	0.557993i
$33$	0.00222788	−	0.00140883i	0.000387824	−	0.000245245i
$34$	−9.19649	+	8.14738i	−1.57718	+	1.39726i
$35$	6.38581	−	0.515516i	1.07940	−	0.0871381i
$36$	0.573286	+	1.97921i	0.0955477	+	0.329869i
$37$	8.51209	−	3.62666i	1.39938	−	0.596220i	0.445193	−	0.895434i	$-0.353135\pi$
$37$	8.51209	−	3.62666i	1.39938	−	0.596220i	0.954186	+	0.299215i	$0.0967247\pi$
$38$	5.69076	−	8.24448i	0.923163	−	1.33743i
$39$	−2.54918	−	2.54984i	−0.408196	−	0.408301i
$40$	0.100927	+	0.146218i	0.0159580	+	0.0231191i
$41$	−9.50674	−	6.01170i	−1.48470	−	0.938869i	−0.997860	−	0.0653798i	$-0.979174\pi$
$41$	−9.50674	−	6.01170i	−1.48470	−	0.938869i	−0.486843	−	0.873490i	$-0.661852\pi$
$42$	−8.75362	+	1.42260i	−1.35071	+	0.219512i
$43$	−8.81573	−	3.75603i	−1.34439	−	0.572790i	−0.404582	−	0.914502i	$-0.632583\pi$
$43$	−8.81573	−	3.75603i	−1.34439	−	0.572790i	−0.939805	+	0.341712i	$0.888993\pi$
$44$	−0.00308548	+	0.00447009i	−0.000465153	+	0.000673891i
$45$	0.405001	−	1.39823i	0.0603740	−	0.208435i
$46$	0.448637	+	0.945482i	0.0661479	+	0.139404i
$47$	4.06035	−	10.7063i	0.592262	−	1.56167i	−0.218217	−	0.975900i	$-0.570024\pi$
$47$	4.06035	−	10.7063i	0.592262	−	1.56167i	0.810479	−	0.585767i	$-0.199207\pi$
$48$	2.45085	+	3.00175i	0.353750	+	0.433265i
$49$	−0.498054	−	12.3591i	−0.0711506	−	1.76558i
$50$	0.233758	+	5.80063i	0.0330583	+	0.820333i
$51$	−5.92003	+	1.45916i	−0.828969	+	0.204323i
$52$	6.89187	+	2.77477i	0.955731	+	0.384791i
$53$	0.796395	+	0.196294i	0.109393	+	0.0269630i	0.293632	−	0.955918i	$-0.405136\pi$
$53$	0.796395	+	0.196294i	0.109393	+	0.0269630i	−0.184239	+	0.982881i	$0.558982\pi$
$54$	−0.403069	+	1.97436i	−0.0548507	+	0.268677i
$55$	0.00353010	−	0.00150404i	0.000475999	−	0.000202804i
$56$	0.453992	−	0.287087i	0.0606672	−	0.0383636i
$57$	4.40196	−	2.31033i	0.583053	−	0.306010i
$58$	10.9018	+	1.77171i	1.43147	+	0.232637i
$59$	3.02693	−	1.01054i	0.394073	−	0.131561i	−0.112724	−	0.993626i	$-0.535958\pi$
$59$	3.02693	−	1.01054i	0.394073	−	0.131561i	0.506797	+	0.862065i	$0.330829\pi$
$60$	0.361558	+	2.97770i	0.0466769	+	0.384419i
$61$	1.70511	−	5.88672i	0.218317	−	0.753717i	−0.774342	−	0.632768i	$-0.781919\pi$
$61$	1.70511	−	5.88672i	0.218317	−	0.753717i	0.992659	−	0.120950i	$-0.0385940\pi$
$62$	1.85476	−	9.08519i	0.235554	−	1.15382i
$63$	−4.17454	−	1.39367i	−0.525943	−	0.175586i
$64$	−7.50600	−	3.93945i	−0.938250	−	0.492432i
$65$	−3.06737	−	4.25899i	−0.380461	−	0.528263i
$66$	−0.00470325	+	0.00246846i	−0.000578930	+	0.000303846i
$67$	11.4122	−	1.85466i	1.39422	−	0.226583i	0.583545	−	0.812081i	$-0.301665\pi$
$67$	11.4122	−	1.85466i	1.39422	−	0.226583i	0.810674	+	0.585498i	$0.199101\pi$
$68$	10.0440	−	7.54754i	1.21801	−	0.915274i
$69$	−0.0209119	+	0.518923i	−0.00251750	+	0.0624710i
$70$	−12.9098			−1.54302
$71$	0.0175492	−	0.435479i	0.00208271	−	0.0516819i	−0.997813	−	0.0660934i	$-0.978946\pi$
$71$	0.0175492	−	0.435479i	0.00208271	−	0.0516819i	0.999896	+	0.0144115i	$0.00458749\pi$
$72$	−0.0244132	−	0.119584i	−0.00287712	−	0.0140931i
$73$	−5.91984	−	8.57636i	−0.692864	−	1.00379i	−0.998663	−	0.0516911i	$-0.983539\pi$
$73$	−5.91984	−	8.57636i	−0.692864	−	1.00379i	0.305799	−	0.952096i	$-0.401077\pi$
$74$	−17.6850	+	5.90413i	−2.05584	+	0.686341i
$75$	−1.23504	+	2.60279i	−0.142610	+	0.300544i
$76$	−6.47871	+	7.93498i	−0.743159	+	0.910205i
$77$	−0.00411375	−	0.0108471i	−0.000468805	−	0.00123614i
$78$	4.70671	+	5.53482i	0.532930	+	0.626695i
$79$	1.70281	−	4.48994i	0.191581	−	0.505158i	−0.804465	−	0.594001i	$-0.797548\pi$
$79$	1.70281	−	4.48994i	0.191581	−	0.505158i	0.996046	+	0.0888430i	$0.0283169\pi$
$80$	2.82056	+	4.88535i	0.315348	+	0.546199i
$81$	−0.632445	+	0.774605i	−0.0702717	+	0.0860672i
$82$	18.1200	+	13.6163i	2.00102	+	1.50367i
$83$	−10.8774	−	5.70892i	−1.19395	−	0.626635i	−0.253757	−	0.967268i	$-0.581666\pi$
$83$	−10.8774	−	5.70892i	−1.19395	−	0.626635i	−0.940196	+	0.340633i	$0.889359\pi$
$84$	9.03923	−	0.729722i	0.986261	−	0.0796192i
$85$	−8.84691	+	0.714196i	−0.959582	+	0.0774654i
$86$	17.0978	+	8.97363i	1.84370	+	0.967651i
$87$	4.38179	+	3.29270i	0.469778	+	0.353015i
$88$	0.000203470	0	0.000249205i	2.16899e−5	0	2.65653e-5i
$89$	2.44648	+	4.23742i	0.259326	+	0.449166i	0.966062	−	0.258312i	$-0.0831663\pi$
$89$	2.44648	+	4.23742i	0.259326	+	0.449166i	−0.706736	+	0.707478i	$0.749833\pi$
$90$	−1.04018	+	2.74274i	−0.109645	+	0.289110i
$91$	−13.2392	+	8.74764i	−1.38785	+	0.917001i
$92$	−0.379478	−	1.00060i	−0.0395634	−	0.104320i
$93$	2.91025	−	3.56441i	0.301779	−	0.369612i
$94$	−9.89140	+	20.8457i	−1.02022	+	2.15007i
$95$	6.86443	−	2.29168i	0.704275	−	0.235122i
$96$	−4.57460	−	6.62745i	−0.466893	−	0.676411i
$97$	3.31342	+	16.2302i	0.336426	+	1.64793i	0.698378	+	0.715729i	$0.253905\pi$
$97$	3.31342	+	16.2302i	0.336426	+	1.64793i	−0.361952	+	0.932197i	$0.617890\pi$
$98$	−1.00362	+	24.9046i	−0.101381	+	2.51575i
$99$	−0.00263595			−0.000264923
$100$	0.239034	−	5.93156i	0.0239034	−	0.593156i
$101$	8.33004	−	6.25962i	0.828870	−	0.622855i	−0.0992810	−	0.995059i	$-0.531654\pi$
$101$	8.33004	−	6.25962i	0.828870	−	0.622855i	0.928151	+	0.372204i	$0.121398\pi$
$102$	12.1273	−	1.97087i	1.20078	−	0.195146i
$103$	11.6284	−	6.10304i	1.14578	−	0.601350i	0.218541	−	0.975828i	$-0.429870\pi$
$103$	11.6284	−	6.10304i	1.14578	−	0.601350i	0.927236	+	0.374478i	$0.122178\pi$
$104$	−0.393666	−	0.196668i	−0.0386022	−	0.0192849i
$105$	−5.67275	−	2.97729i	−0.553604	−	0.290554i
$106$	−1.56777	−	0.523399i	−0.152275	−	0.0508370i
$107$	1.10521	−	5.41369i	0.106845	−	0.523361i	−0.890777	−	0.454440i	$-0.849839\pi$
$107$	1.10521	−	5.41369i	0.106845	−	0.523361i	0.997622	−	0.0689208i	$-0.0219556\pi$
$108$	0.573286	−	1.97921i	0.0551645	−	0.190450i
$109$	−0.677732	−	5.58163i	−0.0649150	−	0.534623i	−0.988499	−	0.151227i	$-0.951678\pi$
$109$	−0.677732	−	5.58163i	−0.0649150	−	0.534623i	0.923584	−	0.383396i	$-0.125246\pi$
$110$	−0.00733427	+	0.00244854i	−0.000699295	+	0.000233459i
$111$	−9.13266	−	1.48420i	−0.866834	−	0.140874i
$112$	15.1013	−	7.92580i	1.42694	−	0.748917i
$113$	−11.0313	+	6.97580i	−1.03774	+	0.656228i	−0.940765	−	0.339059i	$-0.889892\pi$
$113$	−11.0313	+	6.97580i	−1.03774	+	0.656228i	−0.0969765	+	0.995287i	$0.530917\pi$
$114$	−9.21617	+	3.92664i	−0.863173	+	0.367764i
$115$	−0.151221	+	0.740730i	−0.0141014	+	0.0690735i
$116$	−10.9659	−	2.70285i	−1.01816	−	0.250954i
$117$	0.791742	+	3.51755i	0.0731965	+	0.325197i
$118$	−6.24361	+	1.53891i	−0.574770	+	0.141668i
$119$	1.08050	+	26.8122i	0.0990489	+	2.45787i
$120$	−0.00715399	−	0.177524i	−0.000653067	−	0.0162057i
$121$	6.95689	+	8.52065i	0.632445	+	0.774604i
$122$	−4.37931	+	11.5473i	−0.396484	+	1.04544i
$123$	4.82195	+	10.1621i	0.434781	+	0.916282i
$124$	−2.63802	+	9.10752i	−0.236902	+	0.817879i
$125$	−6.51700	+	9.44150i	−0.582898	+	0.844473i
$126$	8.15880	+	3.47614i	0.726844	+	0.309679i
$127$	18.6827	−	3.03624i	1.65782	−	0.269423i	0.741822	−	0.670597i	$-0.233962\pi$
$127$	18.6827	−	3.03624i	1.65782	−	0.269423i	0.916002	+	0.401175i	$0.131398\pi$
$128$	0.824867	+	0.521614i	0.0729086	+	0.0461046i
$129$	5.44350	+	7.88627i	0.479273	+	0.694347i
$130$	5.47039	+	9.05176i	0.479785	+	0.793892i
$131$	2.50677	−	3.63169i	0.219018	−	0.317302i	−0.698038	−	0.716061i	$-0.745943\pi$
$131$	2.50677	−	3.63169i	0.219018	−	0.317302i	0.917056	+	0.398758i	$0.130559\pi$
$132$	0.00499692	−	0.00212899i	0.000434926	−	0.000185305i
$133$	−6.08721	−	21.0155i	−0.527828	−	1.82227i
$134$	−23.2227	+	1.87473i	−2.00613	+	0.161952i
$135$	−1.08961	+	0.965307i	−0.0937784	+	0.0830804i
$136$	−0.628961	+	0.397731i	−0.0539329	+	0.0341051i
$137$	10.7492	+	4.57981i	0.918367	+	0.391280i	0.798835	−	0.601550i	$-0.205450\pi$
$137$	10.7492	+	4.57981i	0.918367	+	0.391280i	0.119533	+	0.992830i	$0.461860\pi$
$138$	0.126144	−	1.03889i	0.0107381	−	0.0884364i
$139$	0.109328	+	0.535522i	0.00927305	+	0.0454224i	0.984164	−	0.177261i	$-0.0567236\pi$
$139$	0.109328	+	0.535522i	0.00927305	+	0.0454224i	−0.974891	+	0.222683i	$0.928518\pi$
$140$	13.1584	+	1.06226i	1.11209	+	0.0897770i
$141$	−9.15389	+	6.87870i	−0.770897	+	0.579291i
$142$	−0.105860	+	0.871837i	−0.00888359	+	0.0731629i
$143$	−0.00586230	+	0.00748069i	−0.000490230	+	0.000625567i
$144$	−0.467103	−	3.84694i	−0.0389253	−	0.320578i
$145$	5.52709	+	5.75431i	0.459000	+	0.477869i
$146$	10.4997	+	18.1859i	0.868958	+	1.50508i
$147$	−6.18456	+	10.7120i	−0.510094	+	0.883509i
$148$	18.5114	−	4.56264i	1.52162	−	0.375047i
$149$	−5.57872	−	6.83269i	−0.457026	−	0.559756i	0.493762	−	0.869597i	$-0.335621\pi$
$149$	−5.57872	−	6.83269i	−0.457026	−	0.559756i	−0.950788	+	0.309842i	$0.899724\pi$
$150$	2.90267	−	5.02757i	0.237002	−	0.410500i
$151$	−2.69727	−	7.11212i	−0.219501	−	0.578776i	0.779356	−	0.626582i	$-0.215546\pi$
$151$	−2.69727	−	7.11212i	−0.219501	−	0.578776i	−0.998857	+	0.0478055i	$0.984777\pi$
$152$	0.420318	−	0.437597i	0.0340923	−	0.0354938i
$153$	5.78342	+	1.93079i	0.467561	+	0.156095i
$154$	0.00650385	+	0.0224539i	0.000524095	+	0.00180939i
$155$	5.01392	−	4.44194i	0.402727	−	0.356785i
$156$	−4.34192	−	6.02868i	−0.347632	−	0.482681i
$157$	−13.5635	−	12.0162i	−1.08249	−	0.959000i	−0.0831913	−	0.996534i	$-0.526511\pi$
$157$	−13.5635	−	12.0162i	−1.08249	−	0.959000i	−0.999295	+	0.0375341i	$0.988050\pi$
$158$	−4.14821	+	8.74216i	−0.330014	+	0.695489i
$159$	−0.568193	−	0.591551i	−0.0450606	−	0.0469131i
$160$	−5.02542	−	10.5908i	−0.397294	−	0.837280i
$161$	2.21924	+	0.546993i	0.174900	+	0.0431091i
$162$	1.39590	−	1.45328i	0.109672	−	0.114181i
$163$	−7.92177	−	5.95283i	−0.620481	−	0.466261i	0.243421	−	0.969921i	$-0.421730\pi$
$163$	−7.92177	−	5.95283i	−0.620481	−	0.466261i	−0.863902	+	0.503659i	$0.831987\pi$
$164$	−17.3485	−	15.3694i	−1.35469	−	1.20015i
$165$	−0.00378746		0.000615523i	−0.000294854		4.79184e-5i
$166$	20.9222	+	13.2304i	1.62388	+	1.02688i
$167$	−12.4671	−	1.00645i	−0.964730	−	0.0778811i	−0.411948	−	0.911207i	$-0.635152\pi$
$167$	−12.4671	−	1.00645i	−0.964730	−	0.0778811i	−0.552782	+	0.833326i	$0.686434\pi$
$168$	−0.537148			−0.0414418
$169$	11.7434	+	5.57603i	0.903340	+	0.428925i
$170$	17.8853			1.37174
$171$	−4.95528	−	0.400032i	−0.378940	−	0.0305912i
$172$	−16.6887	−	10.5533i	−1.27250	−	0.804680i
$173$	6.56747	+	1.06732i	0.499315	+	0.0811466i	0.404853	−	0.914382i	$-0.367323\pi$
$173$	6.56747	+	1.06732i	0.499315	+	0.0811466i	0.0944624	+	0.995528i	$0.469887\pi$
$174$	−8.26715	−	7.32406i	−0.626731	−	0.555235i
$175$	10.1362	+	7.61689i	0.766227	+	0.575783i
$176$	0.00707606	−	0.00736696i	0.000533378	−	0.000555306i
$177$	−3.09843	−	0.763695i	−0.232892	−	0.0574028i
$178$	−4.22679	−	8.90777i	−0.316811	−	0.667665i
$179$	−1.36389	−	1.41996i	−0.101942	−	0.106133i	0.668277	−	0.743913i	$-0.267032\pi$
$179$	−1.36389	−	1.41996i	−0.101942	−	0.106133i	−0.770218	+	0.637780i	$0.779853\pi$
$180$	1.28589	−	2.70996i	0.0958447	−	0.201988i
$181$	−0.813913	−	0.721064i	−0.0604977	−	0.0535962i	0.632332	−	0.774697i	$-0.282098\pi$
$181$	−0.813913	−	0.721064i	−0.0604977	−	0.0535962i	−0.692830	+	0.721101i	$0.743636\pi$
$182$	28.0101	−	15.4234i	2.07625	−	1.14326i
$183$	−4.58739	+	4.06407i	−0.339110	+	0.300425i
$184$	0.0176351	+	0.0608835i	0.00130008	+	0.00448839i
$185$	−12.7757	−	4.26515i	−0.939286	−	0.313580i
$186$	−6.42335	+	6.68741i	−0.470983	+	0.490345i
$187$	0.00569919	+	0.0150275i	0.000416766	+	0.00109892i
$188$	11.7971	−	20.4332i	0.860392	−	1.49024i
$189$	2.78342	+	3.40906i	0.202464	+	0.247973i
$190$	−14.1591	+	3.48991i	−1.02721	+	0.253185i
$191$	−4.39139	+	7.60611i	−0.317750	+	0.550359i	−0.980018	−	0.198908i	$-0.936261\pi$
$191$	−4.39139	+	7.60611i	−0.317750	+	0.550359i	0.662268	+	0.749267i	$0.269594\pi$
$192$	4.23849	+	7.34129i	0.305887	+	0.529812i
$193$	8.21584	+	8.55359i	0.591389	+	0.615701i	0.947892	−	0.318593i	$-0.103210\pi$
$193$	8.21584	+	8.55359i	0.591389	+	0.615701i	−0.356503	+	0.934294i	$0.616031\pi$
$194$	−4.02349	−	33.1364i	−0.288870	−	2.37906i
$195$	0.316228	+	5.23906i	0.0226455	+	0.375177i
$196$	3.07217	−	25.3016i	0.219441	−	1.80726i
$197$	9.60333	−	7.21644i	0.684209	−	0.514150i	−0.200854	−	0.979621i	$-0.564372\pi$
$197$	9.60333	−	7.21644i	0.684209	−	0.514150i	0.885063	+	0.465471i	$0.154115\pi$
$198$	0.00529445		0.000427412i	0.000376260		3.03748e-5i
$199$	−0.591120	−	2.89550i	−0.0419034	−	0.205257i	0.953449	−	0.301554i	$-0.0975052\pi$
$199$	−0.591120	−	2.89550i	−0.0419034	−	0.205257i	−0.995353	+	0.0962971i	$0.969300\pi$
$200$	−0.0423831	+	0.349056i	−0.00299694	+	0.0246820i
$201$	−10.6367	−	4.53188i	−0.750255	−	0.319654i
$202$	−17.7463	+	11.2221i	−1.24862	+	0.789582i
$203$	18.0558	−	15.9961i	1.26727	−	1.12270i
$204$	−12.5230	+	1.01096i	−0.876782	+	0.0707812i
$205$	4.55547	+	15.7273i	0.318168	+	1.09844i
$206$	−24.3457	+	10.3728i	−1.69625	+	0.722704i
$207$	0.295021	−	0.427412i	0.0205054	−	0.0297072i
$208$	−11.9562	−	7.22989i	−0.829015	−	0.501303i
$209$	−0.00744414	−	0.0107847i	−0.000514922	−	0.000745993i
$210$	10.9112	+	6.89985i	0.752947	+	0.476135i
$211$	−11.3849	+	1.85022i	−0.783767	+	0.127375i	−0.539110	−	0.842235i	$-0.681239\pi$
$211$	−11.3849	+	1.85022i	−0.783767	+	0.127375i	−0.244657	+	0.969610i	$0.578675\pi$
$212$	1.55489	+	0.662478i	0.106790	+	0.0454991i
$213$	−0.247581	+	0.358683i	−0.0169640	+	0.0245766i
$214$	−3.09769	+	10.6945i	−0.211754	+	0.731058i
$215$	5.97995	+	12.6025i	0.407829	+	0.859482i
$216$	−0.0432796	+	0.114119i	−0.00294481	+	0.00776481i
$217$	−12.8081	−	15.6871i	−0.869472	−	1.06491i
$218$	0.456216	+	11.3209i	0.0308988	+	0.766746i
$219$	0.419614	+	10.4126i	0.0283549	+	0.703619i
$220$	0.00767696	−	0.00189220i	0.000517581	−	0.000127572i
$221$	18.3417	−	12.1190i	1.23379	−	0.815211i
$222$	18.1028	+	4.46193i	1.21498	+	0.299465i
$223$	−0.899436	+	4.40573i	−0.0602307	+	0.295030i	−0.998738	−	0.0502309i	$-0.984004\pi$
$223$	−0.899436	+	4.40573i	−0.0602307	+	0.295030i	0.938507	+	0.345260i	$0.112209\pi$
$224$	−32.6053	+	13.8918i	−2.17853	+	0.928186i
$225$	2.43494	−	1.53976i	0.162330	−	0.102651i
$226$	23.2881	−	12.2226i	1.54910	−	0.813032i
$227$	−14.8876	−	2.41947i	−0.988123	−	0.160586i	−0.355191	−	0.934794i	$-0.615584\pi$
$227$	−14.8876	−	2.41947i	−0.988123	−	0.160586i	−0.632931	+	0.774208i	$0.718148\pi$
$228$	9.71672	−	3.24392i	0.643506	−	0.214834i
$229$	−2.15633	−	17.7589i	−0.142494	−	1.17354i	−0.871978	−	0.489546i	$-0.837163\pi$
$229$	−2.15633	−	17.7589i	−0.142494	−	1.17354i	0.729484	−	0.683998i	$-0.239760\pi$
$230$	0.423843	−	1.46327i	0.0279474	−	0.0964855i
$231$	−0.00232048	+	0.0113665i	−0.000152677	+	0.000747859i
$232$	0.634538	+	0.211840i	0.0416594	+	0.0139080i
$233$	−13.6115	−	7.14387i	−0.891720	−	0.468011i	−0.0443512	−	0.999016i	$-0.514122\pi$
$233$	−13.6115	−	7.14387i	−0.891720	−	0.468011i	−0.847368	+	0.531005i	$0.821814\pi$
$234$	−1.01989	−	7.19355i	−0.0666725	−	0.470257i
$235$	−14.7590	+	7.74612i	−0.962771	+	0.505301i
$236$	6.49045	−	1.05480i	0.422493	−	0.0686617i
$237$	−3.83892	+	2.88476i	−0.249364	+	0.187385i
$238$	2.17729	−	54.0289i	0.141133	−	3.50218i
$239$	18.8480			1.21918			0.609589	−	0.792718i	$-0.291335\pi$
$239$	18.8480			1.21918			0.609589	+	0.792718i	$0.291335\pi$
$240$	0.227145	−	5.63654i	0.0146621	−	0.363837i
$241$	−2.85126	−	13.9664i	−0.183666	−	0.899655i	−0.962261	−	0.272128i	$-0.912272\pi$
$241$	−2.85126	−	13.9664i	−0.183666	−	0.899655i	0.778595	−	0.627527i	$-0.215933\pi$
$242$	−12.5917	−	18.2422i	−0.809424	−	1.17265i
$243$	0.948536	−	0.316668i	0.0608486	−	0.0203143i
$244$	5.41378	−	11.4093i	0.346582	−	0.730406i
$245$	−11.3876	+	13.9473i	−0.727529	+	0.891061i
$246$	−8.03740	−	21.1929i	−0.512446	−	1.35121i
$247$	−12.1557	+	13.1731i	−0.773448	+	0.838187i
$248$	0.199155	−	0.525128i	0.0126463	−	0.0333457i
$249$	6.14228	+	10.6387i	0.389251	+	0.674202i
$250$	14.6206	−	17.9070i	0.924690	−	1.13254i
$251$	13.7016	+	10.2961i	0.864837	+	0.649883i	0.937695	−	0.347460i	$-0.112956\pi$
$251$	13.7016	+	10.2961i	0.864837	+	0.649883i	−0.0728581	+	0.997342i	$0.523212\pi$
$252$	−8.02988	−	4.21441i	−0.505835	−	0.265483i
$253$	0.00136453		0.000110156i	8.57871e−5		6.92545e-6i
$254$	−38.0175	+	3.06909i	−2.38543	+	0.192572i
$255$	7.85903	+	4.12474i	0.492152	+	0.258301i
$256$	11.9815	+	9.00353i	0.748845	+	0.562721i
$257$	14.8579	−	18.1976i	0.926810	−	1.13514i	−0.0637376	−	0.997967i	$-0.520302\pi$
$257$	14.8579	−	18.1976i	0.926810	−	1.13514i	0.990548	−	0.137169i	$-0.0438005\pi$
$258$	−9.65481	−	16.7226i	−0.601082	−	1.04110i
$259$	−14.4397	+	38.0743i	−0.897239	+	2.36582i
$260$	−4.83092	−	9.67618i	−0.299601	−	0.600091i
$261$	−1.94361	−	5.12488i	−0.120306	−	0.317222i
$262$	−5.62385	+	6.88796i	−0.347443	+	0.425540i
$263$	4.61133	−	9.71817i	0.284347	−	0.599248i	−0.710146	−	0.704055i	$-0.751371\pi$
$263$	4.61133	−	9.71817i	0.284347	−	0.599248i	0.994493	+	0.104806i	$0.0334223\pi$
$264$	−0.000305162	0	0.000101878i	−1.87814e−5	0	6.27016e-6i
$265$	−0.678273	−	0.982648i	−0.0416660	−	0.0603636i
$266$	8.81887	+	43.1977i	0.540720	+	2.64862i
$267$	0.197019	−	4.88899i	0.0120574	−	0.299201i
$268$	23.8241			1.45529
$269$	0.690956	−	17.1459i	0.0421284	−	1.04540i	−0.830500	−	0.557019i	$-0.811945\pi$
$269$	0.690956	−	17.1459i	0.0421284	−	1.04540i	0.872628	−	0.488385i	$-0.162414\pi$
$270$	2.34505	−	1.76219i	0.142715	−	0.107244i
$271$	−4.24807	+	0.690379i	−0.258052	+	0.0419375i	−0.288061	−	0.957612i	$-0.593011\pi$
$271$	−4.24807	+	0.690379i	−0.258052	+	0.0419375i	0.0300089	+	0.999550i	$0.490446\pi$
$272$	−20.9214	+	10.9804i	−1.26855	+	0.665785i
$273$	15.8650	−	0.317495i	0.960193	−	0.0192157i
$274$	−20.8477	−	10.9417i	−1.25946	−	0.661015i
$275$	0.00720321	+	0.00240478i	0.000434370	+	0.000145014i
$276$	−0.214056	+	1.04852i	−0.0128847	+	0.0631133i
$277$	4.08785	−	14.1129i	0.245615	−	0.847962i	−0.739071	−	0.673627i	$-0.764735\pi$
$277$	4.08785	−	14.1129i	0.245615	−	0.847962i	0.984686	−	0.174335i	$-0.0557774\pi$
$278$	−0.132757	−	1.09335i	−0.00796222	−	0.0655748i
$279$	−4.36477	+	1.45717i	−0.261312	+	0.0872388i
$280$	−0.771800	−	0.125430i	−0.0461238	−	0.00749585i
$281$	−18.6892	+	9.80885i	−1.11490	+	0.585147i	−0.918518	−	0.395380i	$-0.870613\pi$
$281$	−18.6892	+	9.80885i	−1.11490	+	0.585147i	−0.196386	+	0.980527i	$0.562921\pi$
$282$	19.5014	−	12.3319i	1.16129	−	0.734357i
$283$	13.3625	−	5.69321i	0.794315	−	0.338426i	0.0435976	−	0.999049i	$-0.486118\pi$
$283$	13.3625	−	5.69321i	0.794315	−	0.338426i	0.750718	+	0.660623i	$0.229708\pi$
$284$	0.179636	−	0.879914i	0.0106594	−	0.0522133i
$285$	−7.02657	−	1.73189i	−0.416218	−	0.102589i
$286$	0.0129877	−	0.0140748i	0.000767979	−	0.000832260i
$287$	48.0646	−	11.8469i	2.83716	−	0.699298i
$288$	0.324260	+	8.04642i	0.0191072	+	0.474140i
$289$	−0.812399	−	20.1595i	−0.0477882	−	1.18585i
$290$	−10.1684	−	12.4540i	−0.597109	−	0.731326i
$291$	5.87401	−	15.4885i	0.344341	−	0.907952i
$292$	−9.20544	−	19.4001i	−0.538708	−	1.13530i
$293$	−0.264540	+	0.913299i	−0.0154546	+	0.0533555i	−0.967875	−	0.251432i	$-0.919098\pi$
$293$	−0.264540	+	0.913299i	−0.0154546	+	0.0533555i	0.952420	+	0.304788i	$0.0985856\pi$
$294$	14.1589	−	20.5127i	0.825765	−	1.19633i
$295$	−4.27365	−	1.82083i	−0.248821	−	0.106013i
$296$	−1.11464	+	0.181147i	−0.0647874	+	0.0105290i
$297$	0.00222788	+	0.00140883i	0.000129275	+	8.17484e-5i
$298$	10.0972	+	14.6284i	0.584917	+	0.847399i
$299$	−0.556851	−	1.78781i	−0.0322035	−	0.103392i
$300$	−3.37225	+	4.88554i	−0.194697	+	0.282067i
$301$	38.7984	−	16.5304i	2.23630	−	0.952798i
$302$	4.26440	+	14.7224i	0.245389	+	0.847179i
$303$	−10.3860	+	0.838446i	−0.596661	+	0.0481675i
$304$	14.4202	−	12.7752i	0.827053	−	0.732705i
$305$	−7.54039	+	4.76825i	−0.431761	+	0.273029i
$306$	−11.3032	−	4.81585i	−0.646162	−	0.275304i
$307$	−0.901267	+	7.42260i	−0.0514380	+	0.423630i	0.944129	+	0.329576i	$0.106906\pi$
$307$	−0.901267	+	7.42260i	−0.0514380	+	0.423630i	−0.995567	+	0.0940542i	$0.970017\pi$
$308$	−0.00478151	−	0.0234214i	−0.000272452	−	0.00133456i
$309$	−13.0900	−	1.05674i	−0.744666	−	0.0601157i
$310$	−10.7910	+	8.10888i	−0.612885	+	0.460553i
$311$	−0.451485	+	3.71831i	−0.0256013	+	0.210846i	−0.999896	−	0.0144320i	$-0.995406\pi$
$311$	−0.451485	+	3.71831i	−0.0256013	+	0.210846i	0.974295	+	0.225278i	$0.0723291\pi$
$312$	0.227610	+	0.376623i	0.0128859	+	0.0213221i
$313$	3.75044	+	30.8877i	0.211988	+	1.74587i	0.578700	+	0.815540i	$0.303560\pi$
$313$	3.75044	+	30.8877i	0.211988	+	1.74587i	−0.366713	+	0.930334i	$0.619517\pi$
$314$	25.2946	+	26.3345i	1.42746	+	1.48614i
$315$	3.20329	+	5.54826i	0.180485	+	0.312609i
$316$	4.94741	−	8.56917i	0.278314	−	0.482054i
$317$	−22.1398	+	5.45698i	−1.24350	+	0.306494i	−0.805562	−	0.592512i	$-0.798136\pi$
$317$	−22.1398	+	5.45698i	−1.24350	+	0.306494i	−0.437935	+	0.899007i	$0.644290\pi$
$318$	1.04533	+	1.28029i	0.0586189	+	0.0717952i
$319$	0.00722391	−	0.0125122i	0.000404461	−	0.000700547i
$320$	4.37580	+	11.5380i	0.244615	+	0.644996i
$321$	−3.82755	+	3.98490i	−0.213633	+	0.222415i
$322$	−4.36876	−	1.45850i	−0.243461	−	0.0812793i
$323$	8.43322	+	29.1149i	0.469237	+	1.61999i
$324$	−1.54236	+	1.36641i	−0.0856865	+	0.0759116i
$325$	1.04549	−	10.3346i	0.0579934	−	0.573262i
$326$	14.9461	+	13.2410i	0.827785	+	0.733354i
$327$	−2.41038	+	5.07976i	−0.133294	+	0.280911i
$328$	0.950991	+	0.990087i	0.0525097	+	0.0546684i
$329$	21.6033	+	45.5279i	1.19103	+	2.51003i
$330$	0.00750751	+	0.00185043i	0.000413275	+	0.000101863i
$331$	−8.91584	+	9.28237i	−0.490059	+	0.510205i	−0.919607	−	0.392838i	$-0.871493\pi$
$331$	−8.91584	+	9.28237i	−0.490059	+	0.510205i	0.429549	+	0.903044i	$0.358673\pi$
$332$	−20.2364	−	15.2067i	−1.11062	−	0.834575i
$333$	6.92558	+	6.13553i	0.379519	+	0.336225i
$334$	24.8775	+	4.04299i	1.36124	+	0.221223i
$335$	−14.2251	−	8.99540i	−0.777199	−	0.491471i
$336$	−16.9996	−	1.37235i	−0.927403	−	0.0748677i
$337$	−9.18096			−0.500119			−0.250059	−	0.968230i	$-0.580450\pi$
$337$	−9.18096			−0.500119			−0.250059	+	0.968230i	$0.580450\pi$
$338$	−22.6831	−	13.1039i	−1.23380	−	0.712758i
$339$	13.0519			0.708883
$340$	−18.2297	−	1.47165i	−0.988642	−	0.0798114i
$341$	−0.0102518	−	0.00648284i	−0.000555165	−	0.000351065i
$342$	9.88807	+	1.60697i	0.534685	+	0.0868948i
$343$	17.6871	+	15.6694i	0.955013	+	0.846068i
$344$	0.934989	+	0.702598i	0.0504112	+	0.0378816i
$345$	0.523706	−	0.545235i	0.0281954	−	0.0293545i
$346$	−13.0180	−	3.20866i	−0.699854	−	0.172498i
$347$	1.59231	+	3.35572i	0.0854795	+	0.180144i	0.941689	−	0.336485i	$-0.109238\pi$
$347$	1.59231	+	3.35572i	0.0854795	+	0.180144i	−0.856209	+	0.516629i	$0.827187\pi$
$348$	7.82370	+	8.14533i	0.419394	+	0.436636i
$349$	−1.23580	+	2.60440i	−0.0661510	+	0.139410i	−0.933833	−	0.357710i	$-0.883558\pi$
$349$	−1.23580	+	2.60440i	−0.0661510	+	0.139410i	0.867682	+	0.497120i	$0.165609\pi$
$350$	−19.1241	−	16.9425i	−1.02223	−	0.905613i
$351$	1.21084	−	3.39616i	0.0646297	−	0.181273i
$352$	−0.0158888	+	0.0140762i	−0.000846875	+	0.000750266i
$353$	3.77163	+	13.0212i	0.200744	+	0.693047i	0.996205	+	0.0870425i	$0.0277416\pi$
$353$	3.77163	+	13.0212i	0.200744	+	0.693047i	−0.795461	+	0.606005i	$0.792771\pi$
$354$	6.09953	+	2.03632i	0.324186	+	0.108229i
$355$	−0.439493	+	0.457561i	−0.0233259	+	0.0242848i
$356$	3.57522	+	9.42708i	0.189486	+	0.499634i
$357$	13.4170	−	23.2389i	0.710103	−	1.22993i
$358$	2.50920	+	3.07321i	0.132615	+	0.162424i
$359$	−28.8496	+	7.11078i	−1.52262	+	0.375293i	−0.909840	−	0.414959i	$-0.863796\pi$
$359$	−28.8496	+	7.11078i	−1.52262	+	0.375293i	−0.612782	+	0.790252i	$0.709950\pi$
$360$	−0.0888342	+	0.153865i	−0.00468197	+	0.00810942i
$361$	−2.85741	−	4.94918i	−0.150390	−	0.260483i
$362$	1.51787	+	1.58027i	0.0797773	+	0.0830570i
$363$	−1.32590	−	10.9198i	−0.0695918	−	0.573140i
$364$	−29.8185	+	13.4156i	−1.56291	+	0.703169i
$365$	−1.82853	+	15.0593i	−0.0957097	+	0.788241i
$366$	9.87299	−	7.41907i	0.516069	−	0.387801i
$367$	21.1267	+	1.70552i	1.10280	+	0.0890276i	0.618435	−	0.785836i	$-0.287767\pi$
$367$	21.1267	+	1.70552i	1.10280	+	0.0890276i	0.484369	+	0.874864i	$0.339049\pi$
$368$	0.402564	+	1.97189i	0.0209851	+	0.102792i
$369$	1.35580	−	11.1660i	0.0705803	−	0.581281i
$370$	24.9690	+	10.6383i	1.29808	+	0.553059i
$371$	−3.05102	+	1.92935i	−0.158401	+	0.100167i
$372$	7.09729	−	6.28765i	0.367977	−	0.325999i
$373$	−28.1532	+	2.27276i	−1.45772	+	0.117679i	−0.783748	−	0.621079i	$-0.786695\pi$
$373$	−28.1532	+	2.27276i	−1.45772	+	0.117679i	−0.673970	+	0.738758i	$0.735412\pi$
$374$	−0.00901044	−	0.0311076i	−0.000465919	−	0.00160854i
$375$	10.5543	−	4.49675i	0.545020	−	0.232211i
$376$	−0.793880	+	1.15013i	−0.0409412	+	0.0593136i
$377$	−18.8667	−	5.88176i	−0.971683	−	0.302926i
$378$	−5.03786	−	7.29860i	−0.259120	−	0.375400i
$379$	−27.2356	−	17.2227i	−1.39900	−	0.884673i	−0.399512	−	0.916728i	$-0.630820\pi$
$379$	−27.2356	−	17.2227i	−1.39900	−	0.884673i	−0.999486	+	0.0320552i	$0.989795\pi$
$380$	14.7189	−	2.39206i	0.755066	−	0.122710i
$381$	−17.4132	−	7.41908i	−0.892106	−	0.380091i
$382$	10.0536	−	14.5652i	0.514389	−	0.745221i
$383$	5.09792	−	17.6001i	0.260491	−	0.899321i	−0.718518	−	0.695508i	$-0.755179\pi$
$383$	5.09792	−	17.6001i	0.260491	−	0.899321i	0.979010	−	0.203813i	$-0.0653334\pi$
$384$	−0.418384	−	0.881727i	−0.0213506	−	0.0449954i
$385$	−0.00598837	+	0.0157900i	−0.000305196	+	0.000804735i
$386$	−15.1150	−	18.5125i	−0.769333	−	0.942262i
$387$	−0.385850	−	9.57476i	−0.0196138	−	0.486712i
$388$	1.37441	+	34.1055i	0.0697749	+	1.73145i
$389$	−15.4903	+	3.81803i	−0.785392	+	0.193582i	−0.611565	−	0.791194i	$-0.709460\pi$
$389$	−15.4903	+	3.81803i	−0.785392	+	0.193582i	−0.173827	+	0.984776i	$0.555613\pi$
$390$	0.214338	−	10.5742i	0.0108534	−	0.535445i
$391$	−3.07453	−	0.757804i	−0.155486	−	0.0383238i
$392$	−0.301970	+	1.47915i	−0.0152518	+	0.0747081i
$393$	−4.05971	+	1.72968i	−0.204785	+	0.0872509i
$394$	−20.4589	+	12.9374i	−1.03070	+	0.651778i
$395$	−6.18956	+	3.24853i	−0.311431	+	0.163451i
$396$	−0.00536122		0.000871284i	−0.000269412		4.37837e-5i
$397$	18.6078	−	6.21220i	0.933899	−	0.311781i	0.191311	−	0.981530i	$-0.438726\pi$
$397$	18.6078	−	6.21220i	0.933899	−	0.311781i	0.742588	+	0.669748i	$0.233598\pi$
$398$	0.717799	+	5.91161i	0.0359800	+	0.296322i
$399$	−6.08721	+	21.0155i	−0.304742	+	1.05209i
$400$	−2.23313	+	10.9386i	−0.111656	+	0.546929i
$401$	−4.02390	−	1.34338i	−0.200944	−	0.0670850i	0.214415	−	0.976743i	$-0.431216\pi$
$401$	−4.02390	−	1.34338i	−0.200944	−	0.0670850i	−0.415359	+	0.909658i	$0.636344\pi$
$402$	20.6295	+	10.8272i	1.02891	+	0.540012i
$403$	−5.57177	+	15.6277i	−0.277550	+	0.778471i
$404$	19.0114	−	9.97794i	0.945852	−	0.496421i
$405$	1.43685	−	0.233511i	0.0713975	−	0.0116032i
$406$	−38.8598	+	29.2012i	−1.92858	+	1.44923i
$407$	−0.000982050		0.0243693i	−4.86784e−5		0.00120794i
$408$	0.744165			0.0368417
$409$	−0.205404	+	5.09706i	−0.0101566	+	0.252033i	0.986132	+	0.165961i	$0.0530726\pi$
$409$	−0.205404	+	5.09706i	−0.0101566	+	0.252033i	−0.996289	+	0.0860722i	$0.972568\pi$
$410$	−6.59976	−	32.3277i	−0.325939	−	1.59655i
$411$	−6.63738	−	9.61590i	−0.327398	−	0.474317i
$412$	25.6680	−	8.56925i	1.26457	−	0.422177i
$413$	−6.02074	+	12.6884i	−0.296261	+	0.624357i
$414$	−0.661869	+	0.810642i	−0.0325291	+	0.0398409i
$415$	6.34126	+	16.7205i	0.311280	+	0.820779i
$416$	23.5564	+	16.9748i	1.15495	+	0.832259i
$417$	0.193816	−	0.511050i	0.00949119	−	0.0250262i
$418$	0.0132032	+	0.0228686i	0.000645791	+	0.00111854i
$419$	16.5913	−	20.3207i	0.810540	−	0.992731i	−0.189402	−	0.981900i	$-0.560655\pi$
$419$	16.5913	−	20.3207i	0.810540	−	0.992731i	0.999941	−	0.0108312i	$-0.00344773\pi$
$420$	−10.5536	−	7.93052i	−0.514963	−	0.386970i
$421$	12.9054	+	6.77326i	0.628969	+	0.330109i	0.748909	−	0.662673i	$-0.230578\pi$
$421$	12.9054	+	6.77326i	0.628969	+	0.330109i	−0.119940	+	0.992781i	$0.538270\pi$
$422$	23.1671	−	1.87024i	1.12776	−	0.0910420i
$423$	11.4132	−	0.921369i	0.554929	−	0.0447985i
$424$	−0.0886423	−	0.0465231i	−0.00430485	−	0.00225936i
$425$	−14.0427	−	10.5524i	−0.681173	−	0.511869i
$426$	0.555439	−	0.680289i	0.0269111	−	0.0329601i
$427$	13.4863	+	23.3590i	0.652648	+	1.13042i
$428$	4.03731	−	10.6455i	0.195151	−	0.514570i
$429$	0.00895293	−	0.00318940i	0.000432251	−	0.000153986i
$430$	−9.96758	−	26.2824i	−0.480680	−	1.26745i
$431$	−9.35691	+	11.4601i	−0.450707	+	0.552015i	−0.949116	−	0.314926i	$-0.898020\pi$
$431$	−9.35691	+	11.4601i	−0.450707	+	0.552015i	0.498409	+	0.866942i	$0.333918\pi$
$432$	−1.66127	+	3.50105i	−0.0799278	+	0.168444i
$433$	0.984799	−	0.328774i	0.0473264	−	0.0157999i	−0.292906	−	0.956141i	$-0.594622\pi$
$433$	0.984799	−	0.328774i	0.0473264	−	0.0157999i	0.340233	+	0.940341i	$0.389494\pi$
$434$	23.1821	+	33.5851i	1.11278	+	1.61214i
$435$	−1.59596	−	7.81753i	−0.0765204	−	0.374822i
$436$	0.466513	−	11.5764i	0.0223419	−	0.554409i
$437$	2.58187			0.123508
$438$	0.845557	−	20.9823i	0.0404023	−	1.00257i
$439$	−7.86534	+	5.91042i	−0.375392	+	0.282089i	−0.771646	−	0.636052i	$-0.780566\pi$
$439$	−7.86534	+	5.91042i	−0.375392	+	0.282089i	0.396254	+	0.918141i	$0.370310\pi$
$440$	−0.000462261	0	7.51247e-5i	−2.20374e−5	0	3.58143e-6i
$441$	10.9523	−	5.74822i	0.521539	−	0.273725i
$442$	−38.8052	+	21.3676i	−1.84578	+	1.01635i
$443$	−10.7414	−	5.63751i	−0.510339	−	0.267846i	0.189839	−	0.981815i	$-0.439203\pi$
$443$	−10.7414	−	5.63751i	−0.510339	−	0.267846i	−0.700177	+	0.713969i	$0.746896\pi$
$444$	−18.0842	−	6.03739i	−0.858238	−	0.286522i
$445$	1.42472	−	6.97872i	0.0675380	−	0.330823i
$446$	2.52094	−	8.70329i	0.119370	−	0.412113i
$447$	1.06324	+	8.75655i	0.0502894	+	0.414171i
$448$	35.3876	−	11.8141i	1.67190	−	0.558164i
$449$	16.2770	+	2.64526i	0.768157	+	0.124838i	0.531847	−	0.846840i	$-0.321498\pi$
$449$	16.2770	+	2.64526i	0.768157	+	0.124838i	0.236309	+	0.971678i	$0.424062\pi$
$450$	−5.14037	+	2.69788i	−0.242320	+	0.127179i
$451$	0.0250593	−	0.0158466i	0.00118000	−	0.000746185i
$452$	−24.7423	+	10.5417i	−1.16378	+	0.495839i
$453$	−1.52148	+	7.45269i	−0.0714853	+	0.350158i
$454$	29.5101	+	7.27359i	1.38498	+	0.341367i
$455$	22.8697	+	3.24845i	1.07215	+	0.152290i
$456$	−0.589129	+	0.145207i	−0.0275885	+	0.00679996i
$457$	0.391175	+	9.70692i	0.0182984	+	0.454070i	0.982203	+	0.187822i	$0.0601430\pi$
$457$	0.391175	+	9.70692i	0.0182984	+	0.454070i	−0.963905	+	0.266248i	$0.914216\pi$
$458$	1.45153	+	36.0194i	0.0678256	+	1.68308i
$459$	−3.85615	−	4.72292i	−0.179989	−	0.220447i
$460$	−0.552406	+	1.45658i	−0.0257561	+	0.0679132i
$461$	−13.6732	−	28.8156i	−0.636823	−	1.34208i	−0.923334	−	0.383998i	$-0.874547\pi$
$461$	−13.6732	−	28.8156i	−0.636823	−	1.34208i	0.286511	−	0.958077i	$-0.407504\pi$
$462$	0.00650385	−	0.0224539i	0.000302586	−	0.00104465i
$463$	−3.65941	+	5.30157i	−0.170067	+	0.246385i	−0.898745	−	0.438472i	$-0.855520\pi$
$463$	−3.65941	+	5.30157i	−0.170067	+	0.246385i	0.728678	+	0.684857i	$0.240135\pi$
$464$	19.5405	+	8.32544i	0.907146	+	0.386499i
$465$	−6.61178	+	1.07452i	−0.306614	+	0.0498296i
$466$	26.1811	+	16.5559i	1.21281	+	0.766937i
$467$	21.9353	+	31.7788i	1.01504	+	1.47055i	0.877220	+	0.480089i	$0.159396\pi$
$467$	21.9353	+	31.7788i	1.01504	+	1.47055i	0.137825	+	0.990457i	$0.455989\pi$
$468$	0.447626	+	7.41599i	0.0206915	+	0.342804i
$469$	−28.9056	+	41.8770i	−1.33474	+	1.93370i
$470$	30.9002	−	13.1653i	1.42532	−	0.607272i
$471$	5.04149	+	17.4052i	0.232300	+	0.801991i
$472$	−0.388219	+	0.0313403i	−0.0178692	+	0.00144255i
$473$	0.0189067	−	0.0167499i	0.000869331	−	0.000770160i
$474$	8.17841	−	5.17172i	0.375647	−	0.237545i
$475$	13.1762	+	5.61387i	0.604567	+	0.257582i
$476$	−6.66487	+	54.8901i	−0.305484	+	2.51589i
$477$	0.164067	+	0.803653i	0.00751211	+	0.0367967i
$478$	−37.8572	−	3.05615i	−1.73155	−	0.139785i
$479$	−13.3156	+	10.0060i	−0.608405	+	0.457187i	−0.859753	−	0.510710i	$-0.829383\pi$
$479$	−13.3156	+	10.0060i	−0.608405	+	0.457187i	0.251348	+	0.967897i	$0.419126\pi$
$480$	−1.41301	+	11.6372i	−0.0644949	+	0.531163i
$481$	32.8146	−	6.00914i	1.49622	−	0.273993i
$482$	3.46229	+	28.5146i	0.157703	+	1.29880i
$483$	−1.58333	−	1.64842i	−0.0720439	−	0.0750056i
$484$	11.3331	+	19.6295i	0.515142	+	0.892252i
$485$	12.0568	−	20.8830i	0.547471	−	0.948247i
$486$	−1.95653	+	0.482241i	−0.0887500	+	0.0218749i
$487$	−10.8354	−	13.2710i	−0.490999	−	0.601365i	0.468365	−	0.883535i	$-0.344843\pi$
$487$	−10.8354	−	13.2710i	−0.490999	−	0.601365i	−0.959364	+	0.282170i	$0.908946\pi$
$488$	−0.374004	+	0.647794i	−0.0169304	+	0.0293243i
$489$	3.51382	+	9.26519i	0.158901	+	0.418986i
$490$	25.1342	−	26.1674i	1.13545	−	1.18212i
$491$	−16.4942	−	5.50658i	−0.744374	−	0.248509i	−0.0809149	−	0.996721i	$-0.525784\pi$
$491$	−16.4942	−	5.50658i	−0.744374	−	0.248509i	−0.663459	+	0.748212i	$0.730912\pi$
$492$	6.44835	+	22.2623i	0.290714	+	1.00366i
$493$	−25.0146	+	22.1610i	−1.12660	+	0.998080i
$494$	26.5513	−	24.4879i	1.19460	−	1.10176i
$495$	0.00287215	+	0.00254450i	0.000129094	+	0.000114367i
$496$	7.64446	−	16.1104i	0.343247	−	0.723377i
$497$	1.32873	+	1.38335i	0.0596015	+	0.0620517i
$498$	−10.6120	−	22.3644i	−0.475537	−	1.00217i
$499$	−25.1478	−	6.19837i	−1.12577	−	0.277477i	−0.367888	−	0.929870i	$-0.619919\pi$
$499$	−25.1478	−	6.19837i	−1.12577	−	0.277477i	−0.757881	+	0.652393i	$0.773765\pi$
$500$	−16.3756	+	17.0488i	−0.732339	+	0.762446i
$501$	9.99913	+	7.51386i	0.446728	+	0.335694i
$502$	−25.8509	−	22.9019i	−1.15378	−	1.02216i
$503$	−23.6725	−	3.84715i	−1.05550	−	0.171536i	−0.392195	−	0.919882i	$-0.628284\pi$
$503$	−23.6725	−	3.84715i	−1.05550	−	0.171536i	−0.663309	+	0.748346i	$0.730848\pi$
$504$	0.453992	+	0.287087i	0.0202224	+	0.0127879i
$505$	−15.1189	−	1.22053i	−0.672783	−	0.0543127i
$506$	−0.00275859			−0.000122634
$507$	−6.94523	−	10.9893i	−0.308448	−	0.488050i
$508$	39.0021			1.73044
$509$	26.3673	+	2.12859i	1.16871	+	0.0943480i	0.649543	−	0.760325i	$-0.274960\pi$
$509$	26.3673	+	2.12859i	1.16871	+	0.0943480i	0.519167	+	0.854673i	$0.326242\pi$
$510$	−15.1164	−	9.55906i	−0.669368	−	0.423282i
$511$	45.2695	+	7.35702i	2.00261	+	0.325455i
$512$	−24.0666	−	21.3212i	−1.06360	−	0.942272i
$513$	3.97435	+	2.98653i	0.175472	+	0.131859i
$514$	−32.7935	+	34.1417i	−1.44646	+	1.50592i
$515$	−18.5616	−	4.57503i	−0.817924	−	0.201600i
$516$	8.46473	+	17.8390i	0.372639	+	0.785320i
$517$	0.0209082	+	0.0217677i	0.000919541	+	0.000957344i
$518$	35.1765	−	74.1329i	1.54557	−	3.25721i
$519$	−4.98031	−	4.41217i	−0.218612	−	0.193673i
$520$	0.239096	+	0.594300i	0.0104851	+	0.0260618i
$521$	19.4447	−	17.2265i	0.851888	−	0.754707i	−0.119341	−	0.992853i	$-0.538078\pi$
$521$	19.4447	−	17.2265i	0.851888	−	0.754707i	0.971229	+	0.238146i	$0.0765397\pi$
$522$	3.07286	+	10.6087i	0.134495	+	0.464332i
$523$	3.61430	+	1.20663i	0.158042	+	0.0527623i	0.394588	−	0.918858i	$-0.370887\pi$
$523$	3.61430	+	1.20663i	0.158042	+	0.0527623i	−0.236546	+	0.971620i	$0.576015\pi$
$524$	6.29890	−	6.55785i	0.275169	−	0.286481i
$525$	−4.49608	−	11.8552i	−0.196225	−	0.517403i
$526$	−10.8379	+	18.7717i	−0.472553	+	0.818486i
$527$	17.7444	+	21.7329i	0.772958	+	0.946701i
$528$	−0.00991801	+	0.00244457i	−0.000431626	+	0.000106386i
$529$	11.3651	−	19.6850i	0.494137	−	0.855870i
$530$	1.20301	+	2.08368i	0.0522555	+	0.0905092i
$531$	2.21060	+	2.30147i	0.0959317	+	0.0998754i
$532$	−5.43425	−	44.7551i	−0.235605	−	1.94038i
$533$	−28.6733	−	28.6807i	−1.24198	−	1.24230i
$534$	−1.18846	+	9.78783i	−0.0514296	+	0.423561i
$535$	−6.43012	+	4.83192i	−0.277998	+	0.208902i
$536$	−1.40656	−	0.113549i	−0.0607540	−	0.00490457i
$537$	0.393826	+	1.92909i	0.0169948	+	0.0832462i
$538$	−4.16798	+	34.3264i	−0.179694	+	1.47992i
$539$	0.0299954	+	0.0127798i	0.00129199	+	0.000550467i
$540$	−2.53520	+	1.60317i	−0.109098	+	0.0689893i
$541$	−18.3195	+	16.2297i	−0.787619	+	0.697769i	−0.957734	−	0.287655i	$-0.907124\pi$
$541$	−18.3195	+	16.2297i	−0.787619	+	0.697769i	0.170115	+	0.985424i	$0.445586\pi$
$542$	8.64441	−	0.697849i	0.371309	−	0.0299752i
$543$	0.302527	+	1.04444i	0.0129827	+	0.0448214i
$544$	45.1714	−	19.2457i	1.93671	−	0.825154i
$545$	−4.64952	+	6.73599i	−0.199164	+	0.288538i
$546$	−31.9171	−	1.93475i	−1.36593	−	0.0827998i
$547$	18.1144	+	26.2432i	0.774514	+	1.12208i	0.989368	+	0.145432i	$0.0464571\pi$
$547$	18.1144	+	26.2432i	0.774514	+	1.12208i	−0.214854	+	0.976646i	$0.568928\pi$
$548$	20.3489	+	12.8678i	0.869260	+	0.549687i
$549$	6.04933	−	0.983111i	0.258179	−	0.0419582i
$550$	−0.0140781	−	0.00599811i	−0.000600292	−	0.000255760i
$551$	15.4789	−	22.4251i	0.659425	−	0.955342i
$552$	0.0176351	−	0.0608835i	0.000750601	−	0.00259137i
$553$	9.05987	+	19.0933i	0.385265	+	0.811929i
$554$	−10.4990	+	27.6836i	−0.446060	+	1.17616i
$555$	8.51830	+	10.4330i	0.361582	+	0.442857i
$556$	0.0453491	+	1.12533i	0.00192323	+	0.0477245i
$557$	−1.72057	−	42.6954i	−0.0729028	−	1.80906i	−0.460952	−	0.887425i	$-0.652492\pi$
$557$	−1.72057	−	42.6954i	−0.0729028	−	1.80906i	0.388050	−	0.921639i	$-0.373149\pi$
$558$	9.00314	−	2.21908i	0.381133	−	0.0939409i
$559$	−28.0308	−	20.1990i	−1.18557	−	0.854328i
$560$	−24.1053	−	5.94143i	−1.01864	−	0.251071i
$561$	0.00321480	−	0.0157471i	0.000135729	−	0.000664844i
$562$	39.1287	−	16.6712i	1.65054	−	0.703231i
$563$	−17.5622	+	11.1057i	−0.740159	+	0.468048i	−0.850586	−	0.525836i	$-0.823753\pi$
$563$	−17.5622	+	11.1057i	−0.740159	+	0.468048i	0.110427	+	0.993884i	$0.464778\pi$
$564$	−20.8916	+	10.9648i	−0.879696	+	0.461700i
$565$	18.7536	+	3.04776i	0.788970	+	0.128220i
$566$	−27.7623	+	9.26842i	−1.16694	+	0.389581i
$567$	−0.530486	−	4.36895i	−0.0222783	−	0.183479i
$568$	−0.0147994	+	0.0510933i	−0.000620968	+	0.00214383i
$569$	−4.67903	+	22.9194i	−0.196155	+	0.960831i	0.755849	+	0.654746i	$0.227224\pi$
$569$	−4.67903	+	22.9194i	−0.196155	+	0.960831i	−0.952004	+	0.306085i	$0.900981\pi$
$570$	13.8324	+	4.61794i	0.579376	+	0.193424i
$571$	−3.18844	−	1.67342i	−0.133432	−	0.0700305i	0.396686	−	0.917954i	$-0.370160\pi$
$571$	−3.18844	−	1.67342i	−0.133432	−	0.0700305i	−0.530118	+	0.847924i	$0.677852\pi$
$572$	−0.0143959	+	0.0132771i	−0.000601923	+	0.000555145i
$573$	7.77677	−	4.08156i	0.324879	−	0.170510i
$574$	−98.4611	+	16.0015i	−4.10969	+	0.667889i
$575$	−1.19613	+	0.898831i	−0.0498819	+	0.0374838i
$576$	0.341334	−	8.47011i	0.0142222	−	0.352921i
$577$	1.66867			0.0694675			0.0347338	−	0.999397i	$-0.488942\pi$
$577$	1.66867			0.0694675			0.0347338	+	0.999397i	$0.488942\pi$
$578$	−1.63705	+	40.6231i	−0.0680925	+	1.68970i
$579$	−2.37234	−	11.6205i	−0.0985912	−	0.482931i
$580$	9.33944	+	13.5305i	0.387799	+	0.561824i
$581$	51.2824	−	17.1206i	2.12755	−	0.710281i
$582$	−14.3097	+	30.1570i	−0.593155	+	1.25005i
$583$	−0.00136740	+	0.00167476i	−5.66320e−5	+	6.93616e-5i
$584$	0.451019	+	1.18924i	0.0186633	+	0.0492111i
$585$	2.53283	−	4.59702i	0.104720	−	0.190063i
$586$	0.679431	−	1.79151i	0.0280670	−	0.0740067i
$587$	−19.4186	−	33.6339i	−0.801490	−	1.38822i	−0.918636	−	0.395106i	$-0.870708\pi$
$587$	−19.4186	−	33.6339i	−0.801490	−	1.38822i	0.117146	−	0.993115i	$-0.462625\pi$
$588$	−16.1194	+	19.7427i	−0.664753	+	0.814175i
$589$	−18.2883	−	13.7428i	−0.753557	−	0.566261i
$590$	8.28859	+	4.35019i	0.341236	+	0.179094i
$591$	−11.9736	+	0.966607i	−0.492527	+	0.0397609i
$592$	−35.7389	+	2.88514i	−1.46886	+	0.118579i
$593$	2.94411	+	1.54519i	0.120900	+	0.0634534i	0.524089	−	0.851663i	$-0.324406\pi$
$593$	2.94411	+	1.54519i	0.120900	+	0.0634534i	−0.403189	+	0.915117i	$0.632098\pi$
$594$	−0.00424638	−	0.00319094i	−0.000174231	−	0.000130926i
$595$	24.7047	−	30.2578i	1.01279	−	1.24045i
$596$	−9.08800	−	15.7409i	−0.372259	−	0.644771i
$597$	−1.04794	+	2.76318i	−0.0428892	+	0.113089i
$598$	0.828576	+	3.68119i	0.0338830	+	0.150535i
$599$	0.330196	+	0.870655i	0.0134914	+	0.0355740i	0.941593	−	0.336754i	$-0.109329\pi$
$599$	0.330196	+	0.870655i	0.0134914	+	0.0355740i	−0.928101	+	0.372328i	$0.878560\pi$
$600$	0.222380	−	0.272366i	0.00907863	−	0.0111193i
$601$	13.7070	−	28.8870i	0.559122	−	1.17832i	−0.405356	−	0.914159i	$-0.632852\pi$
$601$	13.7070	−	28.8870i	0.559122	−	1.17832i	0.964477	−	0.264165i	$-0.0850964\pi$
$602$	−80.6088	+	26.9112i	−3.28537	+	1.09682i
$603$	6.56790	+	9.51525i	0.267466	+	0.387491i
$604$	−3.13511	−	15.3568i	−0.127566	−	0.624859i
$605$	0.644766	−	15.9997i	0.0262134	−	0.650480i
$606$	20.9968			0.852937
$607$	−0.864744	+	21.4584i	−0.0350989	+	0.870970i	0.881746	+	0.471725i	$0.156369\pi$
$607$	−0.864744	+	21.4584i	−0.0350989	+	0.870970i	−0.916844	+	0.399245i	$0.869272\pi$
$608$	−32.0052	+	24.0504i	−1.29798	+	0.975372i
$609$	−23.8100	+	3.86950i	−0.964828	+	0.156800i
$610$	15.9184	−	8.35463i	0.644518	−	0.338269i
$611$	22.7679	−	34.4392i	0.921091	−	1.39326i
$612$	11.1246	+	5.83864i	0.449685	+	0.236013i
$613$	16.8724	+	5.63283i	0.681469	+	0.227508i	0.636266	−	0.771470i	$-0.280478\pi$
$613$	16.8724	+	5.63283i	0.681469	+	0.227508i	0.0452033	+	0.998978i	$0.485606\pi$
$614$	3.01379	−	14.7625i	0.121627	−	0.595767i
$615$	4.55547	−	15.7273i	0.183694	−	0.634186i
$616$	0.000170667		0.00140557i	6.87639e−6		5.66321e-5i
$617$	−7.12799	+	2.37967i	−0.286962	+	0.0958020i	−0.456505	−	0.889721i	$-0.650899\pi$
$617$	−7.12799	+	2.37967i	−0.286962	+	0.0958020i	0.169543	+	0.985523i	$0.445771\pi$
$618$	26.1207	+	4.24502i	1.05073	+	0.170760i
$619$	5.65811	−	2.96961i	0.227419	−	0.119359i	−0.347166	−	0.937804i	$-0.612856\pi$
$619$	5.65811	−	2.96961i	0.227419	−	0.119359i	0.574585	+	0.818445i	$0.305164\pi$
$620$	11.6660	−	7.37711i	0.468516	−	0.296272i
$621$	−0.477786	+	0.203566i	−0.0191729	+	0.00816881i
$622$	1.50974	−	7.39521i	0.0605352	−	0.296521i
$623$	−20.9083	−	5.15344i	−0.837674	−	0.206468i
$624$	6.24115	+	12.5008i	0.249846	+	0.500434i
$625$	2.22877	−	0.549343i	0.0891509	−	0.0219737i
$626$	−2.52461	−	62.6476i	−0.100904	−	2.50390i
$627$	0.000527660		0.0130938i	2.10727e−5		0.000522914i
$628$	−23.6148	−	28.9229i	−0.942333	−	1.15415i
$629$	20.0048	−	52.7482i	0.797642	−	2.10321i
$630$	−5.53434	−	11.6634i	−0.220493	−	0.464680i
$631$	−1.68429	+	5.81483i	−0.0670504	+	0.231485i	−0.987044	−	0.160448i	$-0.948706\pi$
$631$	−1.68429	+	5.81483i	−0.0670504	+	0.231485i	0.919994	+	0.391933i	$0.128193\pi$
$632$	−0.332934	+	0.482338i	−0.0132434	+	0.0191864i
$633$	10.6113	+	4.52104i	0.421760	+	0.179695i
$634$	45.3538	−	7.37071i	1.80123	−	0.292728i
$635$	−23.2877	−	14.7263i	−0.924145	−	0.584394i
$636$	−0.960108	−	1.39096i	−0.0380707	−	0.0551550i
$637$	8.04457	−	43.8660i	0.318738	−	1.73803i
$638$	−0.0165384	+	0.0239600i	−0.000654761	+	0.000948586i
$639$	0.400957	−	0.170832i	0.0158616	−	0.00675801i
$640$	−0.395262	−	1.36460i	−0.0156241	−	0.0539407i
$641$	6.77732	−	0.547122i	0.267688	−	0.0216100i	0.0541062	−	0.998535i	$-0.482769\pi$
$641$	6.77732	−	0.547122i	0.267688	−	0.0216100i	0.213582	+	0.976925i	$0.431487\pi$
$642$	8.33396	−	7.38325i	0.328915	−	0.291393i
$643$	−15.6873	+	9.92003i	−0.618646	+	0.391208i	−0.806709	−	0.590949i	$-0.798753\pi$
$643$	−15.6873	+	9.92003i	−0.618646	+	0.391208i	0.188063	+	0.982157i	$0.439779\pi$
$644$	4.33287	+	1.84606i	0.170739	+	0.0727451i
$645$	1.68140	−	13.8476i	0.0662050	−	0.545248i
$646$	−12.2177	−	59.8461i	−0.480698	−	2.35461i
$647$	16.8402	+	1.35948i	0.662058	+	0.0534469i	0.406929	−	0.913460i	$-0.366600\pi$
$647$	16.8402	+	1.35948i	0.662058	+	0.0534469i	0.255130	+	0.966907i	$0.417882\pi$
$648$	0.0975722	−	0.0733208i	0.00383300	−	0.00288031i
$649$	−0.00101392	+	0.00835042i	−3.98000e−5	+	0.000327783i
$650$	−3.77565	+	20.5881i	−0.148093	+	0.807532i
$651$	2.44108	+	20.1041i	0.0956734	+	0.787941i
$652$	−14.1443	−	14.7258i	−0.553935	−	0.576707i
$653$	3.52817	+	6.11098i	0.138068	+	0.239141i	0.926765	−	0.375641i	$-0.122577\pi$
$653$	3.52817	+	6.11098i	0.138068	+	0.239141i	−0.788697	+	0.614782i	$0.789244\pi$
$654$	5.66503	−	9.81212i	0.221520	−	0.383684i
$655$	−6.23709	+	1.53730i	−0.243703	+	0.0600674i
$656$	27.5673	+	33.7638i	1.07632	+	1.31825i
$657$	5.21053	−	9.02490i	0.203282	−	0.352095i
$658$	−36.0090	−	94.9480i	−1.40378	−	3.70146i
$659$	−19.6567	+	20.4648i	−0.765716	+	0.797195i	−0.983901	−	0.178713i	$-0.942807\pi$
$659$	−19.6567	+	20.4648i	−0.765716	+	0.797195i	0.218185	+	0.975907i	$0.429986\pi$
$660$	−0.00749981	−	0.00250380i	−0.000291930	−	9.74605e-5i
$661$	−4.42979	−	15.2934i	−0.172299	−	0.594845i	−0.999459	−	0.0328791i	$-0.989532\pi$
$661$	−4.42979	−	15.2934i	−0.172299	−	0.594845i	0.827160	−	0.561966i	$-0.189955\pi$
$662$	19.4130	−	17.1984i	0.754509	−	0.668436i
$663$	−21.9794	+	0.439858i	−0.853608	+	0.0170827i
$664$	1.12227	+	0.994242i	0.0435524	+	0.0385841i
$665$	−13.6537	+	28.7746i	−0.529469	+	1.11583i
$666$	−12.9155	−	13.4465i	−0.500466	−	0.521041i
$667$	1.22030	+	2.57172i	0.0472501	+	0.0995775i
$668$	−25.0239	−	6.16784i	−0.968204	−	0.238641i
$669$	3.11491	−	3.24296i	0.120429	−	0.125380i
$670$	27.1132	+	20.3743i	1.04748	+	0.787127i
$671$	0.0120922	+	0.0107127i	0.000466812	+	0.000413560i
$672$	34.9824	+	5.68519i	1.34947	+	0.219311i
$673$	27.2140	+	17.2091i	1.04902	+	0.663362i	0.943608	−	0.331066i	$-0.107408\pi$
$673$	27.2140	+	17.2091i	1.04902	+	0.663362i	0.105416	+	0.994428i	$0.466383\pi$
$674$	18.4404	+	1.48867i	0.710299	+	0.0573412i
$675$	−2.88094			−0.110887
$676$	22.0417	+	15.2226i	0.847756	+	0.585486i
$677$	49.9563			1.91998			0.959989	−	0.280039i	$-0.0903474\pi$
$677$	49.9563			1.91998			0.959989	+	0.280039i	$0.0903474\pi$
$678$	−26.2154	−	2.11633i	−1.00680	−	0.0812771i
$679$	−61.6169	−	38.9641i	−2.36464	−	1.49531i
$680$	1.06925	+	0.173770i	0.0410039	+	0.00666379i
$681$	11.2897	+	10.0018i	0.432622	+	0.383270i
$682$	0.0195401	+	0.0146834i	0.000748228	+	0.000562257i
$683$	27.5070	−	28.6379i	1.05253	−	1.09580i	0.0572862	−	0.998358i	$-0.481755\pi$
$683$	27.5070	−	28.6379i	1.05253	−	1.09580i	0.995241	−	0.0974395i	$-0.0310653\pi$
$684$	−9.94624	−	2.45153i	−0.380304	−	0.0937365i
$685$	−7.29149	−	15.3665i	−0.278593	−	0.587123i
$686$	−32.9847	−	34.3407i	−1.25936	−	1.31113i
$687$	−7.66904	+	16.1622i	−0.292592	+	0.616625i
$688$	27.7953	+	24.6245i	1.05969	+	0.938801i
$689$	2.64560	+	1.32169i	0.100789	+	0.0503525i
$690$	−1.14030	+	1.01022i	−0.0434104	+	0.0384583i
$691$	0.502231	+	1.73390i	0.0191058	+	0.0659607i	0.969505	−	0.245073i	$-0.0788119\pi$
$691$	0.502231	+	1.73390i	0.0191058	+	0.0659607i	−0.950399	+	0.311034i	$0.899325\pi$
$692$	13.0047	+	4.34160i	0.494364	+	0.165043i
$693$	0.00803624	−	0.00836662i	0.000305272	−	0.000317821i
$694$	−2.65411	−	6.99832i	−0.100749	−	0.265652i
$695$	0.397819	−	0.689043i	0.0150901	−	0.0261369i
$696$	−0.423084	−	0.518183i	−0.0160369	−	0.0196417i
$697$	−66.5887	+	16.4127i	−2.52223	+	0.621673i
$698$	2.90447	−	5.03069i	0.109936	−	0.190414i
$699$	7.68616	+	13.3128i	0.290717	+	0.503537i
$700$	18.0983	+	18.8423i	0.684050	+	0.712171i
$701$	−0.548919	−	4.52075i	−0.0207324	−	0.170746i	0.978665	−	0.205463i	$-0.0658701\pi$
$701$	−0.548919	−	4.52075i	−0.0207324	−	0.170746i	−0.999397	+	0.0347169i	$0.988947\pi$
$702$	−2.98270	+	6.62502i	−0.112575	+	0.250045i
$703$	−5.54442	+	45.6624i	−0.209112	+	1.72219i
$704$	0.0178635	−	0.0134236i	0.000673256	−	0.000505919i
$705$	16.6142	+	1.34124i	0.625727	+	0.0505139i
$706$	−5.46417	−	26.7653i	−0.205647	−	1.00732i
$707$	−5.52757	+	45.5236i	−0.207886	+	1.71209i
$708$	−6.04942	−	2.57742i	−0.227351	−	0.0968653i
$709$	−13.1906	+	8.34123i	−0.495384	+	0.313262i	−0.758691	−	0.651450i	$-0.774161\pi$
$709$	−13.1906	+	8.34123i	−0.495384	+	0.313262i	0.263308	+	0.964712i	$0.415187\pi$
$710$	0.956936	−	0.847772i	0.0359132	−	0.0318163i
$711$	4.78642	−	0.386400i	0.179505	−	0.0144911i
$712$	−0.166148	−	0.573608i	−0.00622665	−	0.0214969i
$713$	2.19857	−	0.936725i	0.0823372	−	0.0350806i
$714$	−30.7168	+	44.5010i	−1.14955	+	1.66541i
$715$	0.0136088	−	0.00249209i	0.000508939	−	9.31987e-5i
$716$	−2.30464	−	3.33885i	−0.0861285	−	0.124779i
$717$	−15.9302	−	10.0736i	−0.594923	−	0.376206i
$718$	59.0988	−	9.60449i	2.20555	−	0.358436i
$719$	−4.26594	−	1.81755i	−0.159093	−	0.0677831i	0.310952	−	0.950426i	$-0.399352\pi$
$719$	−4.26594	−	1.81755i	−0.159093	−	0.0677831i	−0.470045	+	0.882642i	$0.655762\pi$
$720$	−3.20452	+	4.64255i	−0.119425	+	0.173018i
$721$	−16.0802	+	55.5152i	−0.598857	+	2.06750i
$722$	4.93676	+	10.4040i	0.183727	+	0.387197i
$723$	−5.05471	+	13.3282i	−0.187987	+	0.495680i
$724$	−1.41707	−	1.73559i	−0.0526648	−	0.0645027i
$725$	0.635824	+	15.7778i	0.0236139	+	0.585973i
$726$	0.892532	+	22.1479i	0.0331250	+	0.821987i
$727$	10.9763	−	2.70542i	0.407089	−	0.100338i	−0.0304534	−	0.999536i	$-0.509695\pi$
$727$	10.9763	−	2.70542i	0.407089	−	0.100338i	0.437542	+	0.899198i	$0.355849\pi$
$728$	1.82440	−	0.649929i	0.0676169	−	0.0240880i
$729$	−0.970942	−	0.239316i	−0.0359608	−	0.00886354i
$730$	6.11452	−	29.9509i	0.226309	−	1.10853i
$731$	−53.7513	+	22.9013i	−1.98806	+	0.847034i
$732$	−10.6736	+	6.74955i	−0.394506	+	0.249471i
$733$	37.3406	−	19.5979i	1.37921	−	0.723863i	0.398101	−	0.917341i	$-0.369669\pi$
$733$	37.3406	−	19.5979i	1.37921	−	0.723863i	0.981105	+	0.193478i	$0.0619769\pi$
$734$	−42.1575	−	6.85126i	−1.55606	−	0.252885i
$735$	17.0791	−	5.70183i	0.629971	−	0.210315i
$736$	−0.504115	−	4.15176i	−0.0185819	−	0.153036i
$737$	−0.00847912	+	0.0292733i	−0.000312333	+	0.00107830i
$738$	−4.53374	+	22.2077i	−0.166889	+	0.817477i
$739$	−32.5503	−	10.8669i	−1.19738	−	0.399745i	−0.353071	−	0.935597i	$-0.614863\pi$
$739$	−32.5503	−	10.8669i	−1.19738	−	0.399745i	−0.844312	+	0.535851i	$0.819991\pi$
$740$	−24.5744	−	12.8977i	−0.903374	−	0.474128i
$741$	17.3145	−	4.63701i	0.636063	−	0.170345i
$742$	6.44096	−	3.38048i	0.236455	−	0.124101i
$743$	−14.8184	+	2.40822i	−0.543634	+	0.0883492i	−0.426026	−	0.904711i	$-0.640087\pi$
$743$	−14.8184	+	2.40822i	−0.543634	+	0.0883492i	−0.117608	+	0.993060i	$0.537523\pi$
$744$	−0.448987	+	0.337392i	−0.0164607	+	0.0123694i
$745$	−0.517036	+	12.8301i	−0.0189427	+	0.470059i
$746$	56.9157			2.08383
$747$	0.494649	−	12.2746i	0.0180983	−	0.449104i
$748$	0.00662431	+	0.0324480i	0.000242209	+	0.00118642i
$749$	13.8138	+	20.0127i	0.504745	+	0.731249i
$750$	−21.9279	+	7.32061i	−0.800694	+	0.267311i
$751$	−5.18716	+	10.9317i	−0.189282	+	0.398904i	−0.975800	−	0.218663i	$-0.929830\pi$
$751$	−5.18716	+	10.9317i	−0.189282	+	0.398904i	0.786518	+	0.617567i	$0.211882\pi$
$752$	−28.0631	+	34.3710i	−1.02335	+	1.25338i
$753$	−6.07755	−	16.0252i	−0.221478	−	0.583990i
$754$	36.9410	+	14.8730i	1.34531	+	0.541642i
$755$	−3.92641	+	10.3531i	−0.142897	+	0.376788i
$756$	4.53432	+	7.85367i	0.164912	+	0.285635i
$757$	−21.8001	+	26.7003i	−0.792338	+	0.970438i	−0.999970	−	0.00776917i	$-0.997527\pi$
$757$	−21.8001	+	26.7003i	−0.792338	+	0.970438i	0.207632	+	0.978207i	$0.433424\pi$
$758$	51.9114	+	39.0089i	1.88551	+	1.41687i
$759$	−0.00121216		0.000636191i	−4.39986e−5		2.30923e-5i
$760$	−0.880397	+	0.0710730i	−0.0319354	+	0.00257809i
$761$	−32.9432	+	2.65945i	−1.19419	+	0.0964049i	−0.661526	−	0.749922i	$-0.730091\pi$
$761$	−32.9432	+	2.65945i	−1.19419	+	0.0964049i	−0.532663	+	0.846327i	$0.678809\pi$
$762$	33.7723	+	17.7251i	1.22344	+	0.642112i
$763$	19.7825	+	14.8656i	0.716175	+	0.538170i
$764$	−11.4457	+	14.0184i	−0.414091	+	0.507169i
$765$	−4.43784	−	7.68657i	−0.160451	−	0.277909i
$766$	−13.0932	+	34.5240i	−0.473077	+	1.24740i
$767$	11.4478	−	1.15512i	0.413355	−	0.0417090i
$768$	−5.31459	−	14.0134i	−0.191774	−	0.505665i
$769$	5.60546	−	6.86544i	0.202138	−	0.247574i	−0.663581	−	0.748105i	$-0.730964\pi$
$769$	5.60546	−	6.86544i	0.202138	−	0.247574i	0.865719	+	0.500530i	$0.166862\pi$
$770$	0.0145883	−	0.0307441i	0.000525724	−	0.00110794i
$771$	−22.2837	+	7.43941i	−0.802530	+	0.267924i
$772$	13.8828	+	20.1127i	0.499652	+	0.723871i
$773$	5.19424	+	25.4431i	0.186824	+	0.915124i	0.959799	+	0.280688i	$0.0905625\pi$
$773$	5.19424	+	25.4431i	0.186824	+	0.915124i	−0.772975	+	0.634436i	$0.781232\pi$
$774$	−0.777520	+	19.2940i	−0.0279474	+	0.693507i
$775$	13.2569			0.476202
$776$	0.0814079	−	2.02012i	0.00292237	−	0.0725180i
$777$	32.5537	−	24.4625i	1.16786	−	0.877588i
$778$	31.7322	−	5.15699i	1.13766	−	0.184887i
$779$	49.5134	−	25.9866i	1.77400	−	0.931068i
$780$	−1.08854	+	10.7602i	−0.0389760	+	0.385276i
$781$	0.00101724		0.000533890i	3.63998e−5		1.91041e-5i
$782$	6.05248	+	2.02061i	0.216436	+	0.0722570i
$783$	−1.09635	+	5.37029i	−0.0391805	+	0.191919i
$784$	−13.3357	+	46.0403i	−0.476276	+	1.64430i
$785$	3.17955	+	26.1859i	0.113483	+	0.934615i
$786$	8.43460	−	2.81588i	0.300852	−	0.100439i
$787$	−20.9759	−	3.40892i	−0.747711	−	0.121515i	−0.225396	−	0.974267i	$-0.572368\pi$
$787$	−20.9759	−	3.40892i	−0.747711	−	0.121515i	−0.522315	+	0.852752i	$0.674932\pi$
$788$	21.9174	−	11.5031i	0.780774	−	0.409782i
$789$	−9.09148	+	5.74911i	−0.323665	+	0.204674i
$790$	12.9588	−	5.52122i	0.461053	−	0.196436i
$791$	11.4899	−	56.2811i	0.408533	−	2.00112i
$792$	0.000312370	0	7.69924e-5i	1.10996e−5	0	2.73580e-6i
$793$	10.6635	−	19.3541i	0.378674	−	0.687283i
$794$	−38.3820	+	9.46032i	−1.36213	+	0.335734i
$795$	0.0480778	+	1.19304i	0.00170514	+	0.0423127i
$796$	−0.245197	−	6.08450i	−0.00869078	−	0.215659i
$797$	0.722393	+	0.884771i	0.0255885	+	0.0313402i	0.787241	−	0.616646i	$-0.211509\pi$
$797$	0.722393	+	0.884771i	0.0255885	+	0.0313402i	−0.761652	+	0.647986i	$0.775612\pi$
$798$	15.6341	−	41.2236i	0.553440	−	1.45930i
$799$	−29.9292	−	63.0744i	−1.05882	−	2.23141i
$800$	6.45466	−	22.2841i	0.228207	−	0.787861i
$801$	−2.77951	+	4.02682i	−0.0982093	+	0.142281i
$802$	7.86438	+	3.35070i	0.277701	+	0.118317i
$803$	0.0271137	−	0.00440640i	0.000956822	−	0.000155499i
$804$	−20.1359	−	12.7332i	−0.710137	−	0.449064i
$805$	−1.89008	−	2.73825i	−0.0666165	−	0.0965106i
$806$	13.7252	−	30.4856i	0.483448	−	1.07381i
$807$	−9.74789	+	14.1223i	−0.343142	+	0.497127i
$808$	−1.16998	+	0.498480i	−0.0411596	+	0.0175365i
$809$	13.5738	+	46.8622i	0.477229	+	1.64759i	0.732538	+	0.680726i	$0.238336\pi$
$809$	13.5738	+	46.8622i	0.477229	+	1.64759i	−0.255309	+	0.966860i	$0.582177\pi$
$810$	−2.92385	+	0.236037i	−0.102733	+	0.00829350i
$811$	33.8144	−	29.9569i	1.18738	−	1.05193i	0.189845	−	0.981814i	$-0.439201\pi$
$811$	33.8144	−	29.9569i	1.18738	−	1.05193i	0.997539	−	0.0701165i	$-0.0223371\pi$
$812$	42.0108	−	26.5660i	1.47429	−	0.932284i
$813$	3.95941	+	1.68695i	0.138863	+	0.0591638i
$814$	0.00592391	−	0.0487878i	0.000207633	−	0.00171001i
$815$	2.88531	+	14.1332i	0.101068	+	0.495064i
$816$	23.5512	+	1.90125i	0.824458	+	0.0665571i
$817$	38.0843	−	28.6185i	1.33240	−	1.00124i
$818$	1.23904	−	10.2044i	0.0433219	−	0.356788i
$819$	−13.5786	−	8.21095i	−0.474475	−	0.286914i
$820$	4.06682	+	33.4933i	0.142020	+	1.16964i
$821$	34.3782	+	35.7915i	1.19981	+	1.24913i	0.960529	+	0.278179i	$0.0897310\pi$
$821$	34.3782	+	35.7915i	1.19981	+	1.24913i	0.239277	+	0.970951i	$0.423090\pi$
$822$	11.7723	+	20.3903i	0.410607	+	0.711192i
$823$	−10.2527	+	17.7581i	−0.357385	+	0.619009i	−0.987523	−	0.157474i	$-0.949665\pi$
$823$	−10.2527	+	17.7581i	−0.357385	+	0.619009i	0.630138	+	0.776483i	$0.282998\pi$
$824$	−1.55627	+	0.383585i	−0.0542151	+	0.0133628i
$825$	−0.00480281	−	0.00588237i	−0.000167212	−	0.000204798i
$826$	14.1504	−	24.5091i	0.492354	−	0.852782i
$827$	−4.89444	−	12.9056i	−0.170196	−	0.448771i	0.822595	−	0.568628i	$-0.192526\pi$
$827$	−4.89444	−	12.9056i	−0.170196	−	0.448771i	−0.992791	+	0.119857i	$0.961756\pi$
$828$	0.741315	−	0.771791i	0.0257625	−	0.0268216i
$829$	−16.7395	−	5.58848i	−0.581389	−	0.194096i	0.0107362	−	0.999942i	$-0.496583\pi$
$829$	−16.7395	−	5.58848i	−0.581389	−	0.194096i	−0.592125	+	0.805846i	$0.701711\pi$
$830$	−10.0256	−	34.6123i	−0.347992	−	1.20141i
$831$	−10.9979	+	9.74326i	−0.381512	+	0.337990i
$832$	−23.2786	−	19.8060i	−0.807040	−	0.686650i
$833$	−56.4504	−	50.0107i	−1.95589	−	1.73277i
$834$	−0.472154	+	0.995043i	−0.0163493	+	0.0344555i
$835$	12.6127	+	13.1312i	0.436479	+	0.454423i
$836$	−0.0115758	−	0.0243954i	−0.000400356	−	0.000843732i
$837$	4.46787	+	1.10123i	0.154432	+	0.0380641i
$838$	−36.6195	+	38.1249i	−1.26500	+	1.31700i
$839$	40.2075	+	30.2140i	1.38812	+	1.04310i	0.992179	+	0.124824i	$0.0398367\pi$
$839$	40.2075	+	30.2140i	1.38812	+	1.04310i	0.395937	+	0.918278i	$0.370420\pi$
$840$	0.585280	+	0.518512i	0.0201941	+	0.0178904i
$841$	1.02852	+	0.167151i	0.0354662	+	0.00576382i
$842$	−24.8228	−	15.6970i	−0.855451	−	0.540955i
$843$	21.0384	+	1.69840i	0.724601	+	0.0584959i
$844$	−23.7671			−0.818097
$845$	−7.41313	−	17.4117i	−0.255019	−	0.598980i
$846$	−23.0734			−0.793280
$847$	−48.2544	−	3.89550i	−1.65804	−	0.133851i
$848$	−2.68648	−	1.69882i	−0.0922540	−	0.0583379i
$849$	−14.3366	−	2.32993i	−0.492032	−	0.0799630i
$850$	26.4945	+	23.4721i	0.908755	+	0.805087i
$851$	−3.84150	−	2.88670i	−0.131685	−	0.0989548i
$852$	−0.622110	+	0.647686i	−0.0213132	+	0.0221893i
$853$	33.6844	+	8.30247i	1.15333	+	0.284271i	0.769201	−	0.639007i	$-0.220655\pi$
$853$	33.6844	+	8.30247i	1.15333	+	0.284271i	0.384132	+	0.923278i	$0.374501\pi$
$854$	−23.3003	−	49.1044i	−0.797321	−	1.68032i
$855$	5.01315	+	5.21924i	0.171446	+	0.178494i
$856$	−0.289098	+	0.609261i	−0.00988116	+	0.0208241i
$857$	0.310355	+	0.274951i	0.0106015	+	0.00939214i	0.668407	−	0.743796i	$-0.266977\pi$
$857$	0.310355	+	0.274951i	0.0106015	+	0.00939214i	−0.657805	+	0.753188i	$0.728515\pi$
$858$	−0.0184996	+	0.00495439i	−0.000631565	+	0.000169140i
$859$	19.1649	−	16.9786i	0.653898	−	0.579303i	−0.269569	−	0.962981i	$-0.586881\pi$
$859$	19.1649	−	16.9786i	0.653898	−	0.579303i	0.923467	+	0.383678i	$0.125343\pi$
$860$	7.99693	+	27.6086i	0.272693	+	0.941445i
$861$	−46.9555	−	15.6760i	−1.60024	−	0.534238i
$862$	20.6521	−	21.5011i	0.703412	−	0.732329i
$863$	−11.3432	−	29.9096i	−0.386127	−	1.01813i	−0.977351	−	0.211626i	$-0.932124\pi$
$863$	−11.3432	−	29.9096i	−0.386127	−	1.01813i	0.591223	−	0.806508i	$-0.298645\pi$
$864$	4.02647	−	6.97406i	0.136983	−	0.237262i
$865$	−6.12567	−	7.50258i	−0.208279	−	0.255095i
$866$	−2.03133	+	0.500677i	−0.0690273	+	0.0170137i
$867$	−10.0879	+	17.4728i	−0.342604	+	0.593407i
$868$	−20.8651	−	36.1393i	−0.708206	−	1.22665i
$869$	0.00876838	+	0.00912885i	0.000297447	+	0.000309675i
$870$	1.93798	+	15.9607i	0.0657036	+	0.541118i
$871$	41.6106	+	2.52236i	1.40992	+	0.0854668i
$872$	−0.0827174	+	0.681239i	−0.00280116	+	0.0230697i
$873$	−13.2427	+	9.95127i	−0.448198	+	0.336799i
$874$	−5.18581	−	0.418642i	−0.175413	−	0.0141608i
$875$	−10.0993	−	49.4695i	−0.341418	−	1.67238i
$876$	−2.58832	+	21.3167i	−0.0874512	+	0.720226i
$877$	−7.70126	−	3.28120i	−0.260053	−	0.110798i	0.258005	−	0.966143i	$-0.416935\pi$
$877$	−7.70126	−	3.28120i	−0.260053	−	0.110798i	−0.518058	+	0.855345i	$0.673345\pi$
$878$	16.7563	−	10.5960i	0.565498	−	0.357599i
$879$	0.711714	−	0.630523i	0.0240055	−	0.0212670i
$880$	−0.0148215	+	0.00119652i	−0.000499633	+	4.03345e-5i
$881$	2.04866	+	7.07280i	0.0690212	+	0.238289i	0.987611	−	0.156924i	$-0.0501579\pi$
$881$	2.04866	+	7.07280i	0.0690212	+	0.238289i	−0.918589	+	0.395213i	$0.870671\pi$
$882$	−22.9303	+	9.76970i	−0.772105	+	0.328963i
$883$	−7.52300	+	10.8990i	−0.253169	+	0.366779i	−0.928876	−	0.370392i	$-0.879223\pi$
$883$	−7.52300	+	10.8990i	−0.253169	+	0.366779i	0.675706	+	0.737171i	$0.263839\pi$
$884$	41.3106	−	18.5860i	1.38943	−	0.625115i
$885$	2.63887	+	3.82306i	0.0887047	+	0.128511i
$886$	20.6605	+	13.0649i	0.694104	+	0.438925i
$887$	19.3993	−	3.15270i	0.651366	−	0.105857i	0.174255	−	0.984701i	$-0.444248\pi$
$887$	19.3993	−	3.15270i	0.651366	−	0.105857i	0.477111	+	0.878843i	$0.341684\pi$
$888$	1.03890	+	0.442635i	0.0348633	+	0.0148539i
$889$	−47.3210	+	68.5563i	−1.58709	+	2.29930i
$890$	−3.99319	+	13.7861i	−0.133852	+	0.462111i
$891$	−0.00113001	−	0.00238145i	−3.78569e−5	−	7.97817e-5i
$892$	−3.28561	+	8.66345i	−0.110010	+	0.290074i
$893$	36.0015	+	44.0938i	1.20474	+	1.47554i
$894$	−0.715719	−	17.7604i	−0.0239372	−	0.593996i
$895$	0.115406	+	2.86377i	0.00385759	+	0.0957251i
$896$	−4.17040	+	1.02791i	−0.139323	+	0.0343401i
$897$	−0.484877	+	1.80866i	−0.0161896	+	0.0603892i
$898$	−32.2642	−	7.95240i	−1.07667	−	0.265375i
$899$	5.04496	−	24.7119i	0.168259	−	0.824186i
$900$	5.46134	−	2.32686i	0.182045	−	0.0775620i
$901$	4.22688	−	2.67292i	0.140818	−	0.0890478i
$902$	−0.0529024	+	0.0277653i	−0.00176146	+	0.000924484i
$903$	−41.6269	−	6.76504i	−1.38526	−	0.225126i
$904$	1.51101	−	0.504449i	0.0502554	−	0.0167777i
$905$	0.190797	+	1.57135i	0.00634229	+	0.0522335i
$906$	4.26440	−	14.7224i	0.141675	−	0.489119i
$907$	7.68724	−	37.6546i	0.255251	−	1.25030i	−0.626813	−	0.779170i	$-0.715641\pi$
$907$	7.68724	−	37.6546i	0.255251	−	1.25030i	0.882064	−	0.471130i	$-0.156154\pi$
$908$	−29.4799	−	9.84183i	−0.978324	−	0.326612i
$909$	9.22628	+	4.84233i	0.306016	+	0.160610i
$910$	−45.4083	−	10.2329i	−1.50527	−	0.339218i
$911$	−10.0517	+	5.27552i	−0.333027	+	0.174786i	−0.622945	−	0.782265i	$-0.714064\pi$
$911$	−10.0517	+	5.27552i	−0.333027	+	0.174786i	0.289919	+	0.957051i	$0.406372\pi$
$912$	−19.0157	+	3.09035i	−0.629672	+	0.102332i
$913$	0.0258872	−	0.0194529i	0.000856740	−	0.000643798i
$914$	0.788252	−	19.5603i	0.0260730	−	0.646996i
$915$	8.92153			0.294937
$916$	1.48429	−	36.8324i	0.0490425	−	1.21698i
$917$	3.88470	+	19.0285i	0.128284	+	0.628378i
$918$	6.97946	+	10.1115i	0.230356	+	0.333729i
$919$	−7.83107	+	2.61439i	−0.258323	+	0.0862409i	−0.442880	−	0.896581i	$-0.646043\pi$
$919$	−7.83107	+	2.61439i	−0.258323	+	0.0862409i	0.184557	+	0.982822i	$0.440915\pi$
$920$	0.0395559	−	0.0833624i	0.00130412	−	0.00274838i
$921$	4.72887	−	5.79181i	0.155821	−	0.190847i
$922$	22.7909	+	60.0946i	0.750578	+	1.97911i
$923$	0.406908	−	1.51782i	0.0133936	−	0.0499597i
$924$	−0.00847665	+	0.0223511i	−0.000278861	+	0.000735297i
$925$	−13.3279	−	23.0846i	−0.438219	−	0.759018i
$926$	8.20974	−	10.0551i	0.269789	−	0.330431i
$927$	10.4988	+	7.88932i	0.344825	+	0.259119i
$928$	−39.0829	−	20.5123i	−1.28296	−	0.673348i
$929$	−54.3002	+	4.38357i	−1.78153	+	0.143820i	−0.926874	−	0.375372i	$-0.877515\pi$
$929$	−54.3002	+	4.38357i	−1.78153	+	0.143820i	−0.854657	+	0.519192i	$0.826233\pi$
$930$	13.4543	−	1.08615i	0.441185	−	0.0356161i
$931$	54.4483	+	28.5767i	1.78447	+	0.936563i
$932$	−25.3229	−	19.0289i	−0.829480	−	0.623313i
$933$	2.36890	−	2.90138i	0.0775543	−	0.0949868i
$934$	−38.9053	−	67.3860i	−1.27302	−	2.20494i
$935$	0.00829630	−	0.0218755i	0.000271318	−	0.000715407i
$936$	0.00891813	−	0.439968i	0.000291498	−	0.0143808i
$937$	6.72598	+	17.7350i	0.219728	+	0.579376i	0.998873	−	0.0474685i	$-0.0151154\pi$
$937$	6.72598	+	17.7350i	0.219728	+	0.579376i	−0.779144	+	0.626844i	$0.784346\pi$
$938$	64.8486	−	79.4251i	2.11738	−	2.59332i
$939$	13.3386	−	28.1104i	0.435288	−	0.917350i
$940$	−32.5785	+	10.8763i	−1.06259	+	0.354746i
$941$	11.8472	+	17.1637i	0.386208	+	0.559519i	0.967079	−	0.254477i	$-0.0819032\pi$
$941$	11.8472	+	17.1637i	0.386208	+	0.559519i	−0.580871	+	0.813996i	$0.697288\pi$
$942$	−7.30388	−	35.7768i	−0.237973	−	1.16567i
$943$	−0.235218	+	5.83687i	−0.00765975	+	0.190075i
$944$	−12.3664			−0.402491
$945$	0.257967	−	6.40139i	0.00839167	−	0.208237i
$946$	−0.0406910	+	0.0305773i	−0.00132298	+	0.000994155i
$947$	48.4718	−	7.87743i	1.57512	−	0.255982i	0.690864	−	0.722984i	$-0.257230\pi$
$947$	48.4718	−	7.87743i	1.57512	−	0.255982i	0.884256	+	0.467002i	$0.154666\pi$
$948$	−8.76144	+	4.59836i	−0.284558	+	0.149348i
$949$	−14.0241	−	34.8584i	−0.455240	−	1.13155i
$950$	−25.5549	−	13.4122i	−0.829109	−	0.435150i
$951$	21.6289	+	7.22080i	0.701366	+	0.234150i
$952$	0.655104	−	3.20891i	0.0212320	−	0.104001i
$953$	−1.16721	+	4.02968i	−0.0378097	+	0.130534i	−0.977203	−	0.212307i	$-0.931902\pi$
$953$	−1.16721	+	4.02968i	−0.0378097	+	0.130534i	0.939393	+	0.342842i	$0.111389\pi$
$954$	−0.199227	−	1.64078i	−0.00645021	−	0.0531222i
$955$	12.1271	−	4.04863i	0.392424	−	0.131011i
$956$	38.3347	+	6.23000i	1.23983	+	0.201492i
$957$	−0.0127929	+	0.00671423i	−0.000413536	+	0.000217040i
$958$	28.3675	−	17.9385i	0.916512	−	0.579567i
$959$	−47.3077	+	20.1559i	−1.52764	+	0.650869i
$960$	2.46831	−	12.0906i	0.0796642	−	0.390221i
$961$	9.53990	+	2.35137i	0.307739	+	0.0758508i
$962$	−66.8842	+	6.74886i	−2.15643	+	0.217592i
$963$	5.36480	−	1.32230i	0.172878	−	0.0426106i
$964$	−1.18270	−	29.3485i	−0.0380923	−	0.945252i
$965$	−0.695186	−	17.2509i	−0.0223788	−	0.555325i
$966$	2.91291	+	3.56766i	0.0937213	+	0.114788i
$967$	−6.17734	+	16.2883i	−0.198650	+	0.523797i	−0.996913	−	0.0785119i	$-0.974983\pi$
$967$	−6.17734	+	16.2883i	−0.198650	+	0.523797i	0.798263	+	0.602309i	$0.205752\pi$
$968$	−0.575542	−	1.21293i	−0.0184986	−	0.0389850i
$969$	8.43322	−	29.1149i	0.270914	−	0.935304i
$970$	−27.6028	+	39.9895i	−0.886272	+	1.28399i
$971$	−16.3329	−	6.95882i	−0.524149	−	0.223319i	0.113651	−	0.993521i	$-0.463745\pi$
$971$	−16.3329	−	6.95882i	−0.524149	−	0.223319i	−0.637800	+	0.770202i	$0.720156\pi$
$972$	2.03388	−	0.330538i	0.0652369	−	0.0106020i
$973$	−2.03308	−	1.28564i	−0.0651774	−	0.0412157i
$974$	19.6116	+	28.4123i	0.628397	+	0.910390i
$975$	−6.40715	+	8.17595i	−0.205193	+	0.261840i
$976$	−13.4915	+	19.5458i	−0.431851	+	0.625645i
$977$	−9.32582	+	3.97336i	−0.298359	+	0.127119i	−0.535959	−	0.844244i	$-0.680050\pi$
$977$	−9.32582	+	3.97336i	−0.298359	+	0.127119i	0.237599	+	0.971363i	$0.423639\pi$
$978$	−5.55537	−	19.1794i	−0.177641	−	0.613288i
$979$	−0.0128558	+	0.00103783i	−0.000410872	+	3.31690e-5i
$980$	−27.7713	+	24.6032i	−0.887120	+	0.785920i
$981$	4.75218	−	3.00510i	0.151726	−	0.0959454i
$982$	32.2366	+	13.7347i	1.02871	+	0.438293i
$983$	3.99793	−	32.9259i	0.127514	−	1.05017i	−0.778712	−	0.627381i	$-0.784127\pi$
$983$	3.99793	−	32.9259i	0.127514	−	1.05017i	0.906226	−	0.422793i	$-0.138950\pi$
$984$	−0.274601	−	1.34508i	−0.00875395	−	0.0428797i
$985$	−17.4299	−	1.40709i	−0.555364	−	0.0448336i
$986$	53.8364	−	40.4554i	1.71450	−	1.28836i
$987$	6.07425	−	50.0259i	0.193345	−	1.59234i
$988$	−29.0775	+	22.7747i	−0.925079	+	0.724561i
$989$	0.599867	+	4.94035i	0.0190747	+	0.157094i
$990$	−0.00535628	−	0.00557648i	−0.000170234	−	0.000177232i
$991$	3.67148	+	6.35919i	0.116628	+	0.202006i	0.918430	−	0.395585i	$-0.129458\pi$
$991$	3.67148	+	6.35919i	0.116628	+	0.202006i	−0.801801	+	0.597591i	$0.796125\pi$
$992$	−18.5282	+	32.0917i	−0.588270	+	1.01891i
$993$	12.4967	−	3.08016i	0.396570	−	0.0977458i
$994$	−2.44451	−	2.99398i	−0.0775351	−	0.0949632i
$995$	−2.15096	+	3.72557i	−0.0681899	+	0.118108i
$996$	8.97617	+	23.6682i	0.284421	+	0.749956i
$997$	−15.5377	+	16.1765i	−0.492085	+	0.512315i	−0.920221	−	0.391400i	$-0.871991\pi$
$997$	−15.5377	+	16.1765i	−0.492085	+	0.512315i	0.428136	+	0.903714i	$0.359171\pi$
$998$	49.5056	+	16.5274i	1.56707	+	0.523165i
$999$	−2.57420	−	8.88717i	−0.0814441	−	0.281178i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.q.b.16.3	✓	384
169.74	even	39	inner	507.2.q.b.412.3	yes	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.q.b.16.3	✓	384	1.1	even	1	trivial
507.2.q.b.412.3	yes	384	169.74	even	39	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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.q (of order \(39\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.00855 - 0.162147i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(2.03388 + 0.330538i) q^{4} +(-1.08961 - 0.965307i) q^{5} +(1.61095 + 1.21055i) q^{6} +(-3.04871 + 3.17404i) q^{7} +(-0.118504 - 0.0292085i) q^{8} +(0.428693 + 0.903450i) q^{9} +O(q^{10})\)	\(q+(-2.00855 - 0.162147i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(2.03388 + 0.330538i) q^{4} +(-1.08961 - 0.965307i) q^{5} +(1.61095 + 1.21055i) q^{6} +(-3.04871 + 3.17404i) q^{7} +(-0.118504 - 0.0292085i) q^{8} +(0.428693 + 0.903450i) q^{9} +(2.03201 + 2.11554i) q^{10} +(-0.00113001 + 0.00238145i) q^{11} +(-1.54236 - 1.36641i) q^{12} +(3.51734 + 0.792647i) q^{13} +(6.63814 - 5.88088i) q^{14} +(0.405001 + 1.39823i) q^{15} +(-3.67576 - 1.22715i) q^{16} +(4.22368 - 4.39732i) q^{17} +(-0.714559 - 1.88414i) q^{18} +(-2.48570 + 4.30536i) q^{19} +(-1.89706 - 2.32348i) q^{20} +(4.27315 - 1.05324i) q^{21} +(0.00265584 - 0.00460004i) q^{22} +(-0.259672 - 0.449765i) q^{23} +(0.0845472 + 0.0880230i) q^{24} +(-0.347259 - 2.85994i) q^{25} +(-6.93624 - 2.16240i) q^{26} +(0.120537 - 0.992709i) q^{27} +(-7.24986 + 5.44791i) q^{28} +(-5.46329 - 0.441042i) q^{29} +(-0.586747 - 2.87408i) q^{30} +(-0.554660 + 4.56803i) q^{31} +(7.40855 + 3.15649i) q^{32} +(0.00222788 - 0.00140883i) q^{33} +(-9.19649 + 8.14738i) q^{34} +(6.38581 - 0.515516i) q^{35} +(0.573286 + 1.97921i) q^{36} +(8.51209 - 3.62666i) q^{37} +(5.69076 - 8.24448i) q^{38} +(-2.54918 - 2.54984i) q^{39} +(0.100927 + 0.146218i) q^{40} +(-9.50674 - 6.01170i) q^{41} +(-8.75362 + 1.42260i) q^{42} +(-8.81573 - 3.75603i) q^{43} +(-0.00308548 + 0.00447009i) q^{44} +(0.405001 - 1.39823i) q^{45} +(0.448637 + 0.945482i) q^{46} +(4.06035 - 10.7063i) q^{47} +(2.45085 + 3.00175i) q^{48} +(-0.498054 - 12.3591i) q^{49} +(0.233758 + 5.80063i) q^{50} +(-5.92003 + 1.45916i) q^{51} +(6.89187 + 2.77477i) q^{52} +(0.796395 + 0.196294i) q^{53} +(-0.403069 + 1.97436i) q^{54} +(0.00353010 - 0.00150404i) q^{55} +(0.453992 - 0.287087i) q^{56} +(4.40196 - 2.31033i) q^{57} +(10.9018 + 1.77171i) q^{58} +(3.02693 - 1.01054i) q^{59} +(0.361558 + 2.97770i) q^{60} +(1.70511 - 5.88672i) q^{61} +(1.85476 - 9.08519i) q^{62} +(-4.17454 - 1.39367i) q^{63} +(-7.50600 - 3.93945i) q^{64} +(-3.06737 - 4.25899i) q^{65} +(-0.00470325 + 0.00246846i) q^{66} +(11.4122 - 1.85466i) q^{67} +(10.0440 - 7.54754i) q^{68} +(-0.0209119 + 0.518923i) q^{69} -12.9098 q^{70} +(0.0175492 - 0.435479i) q^{71} +(-0.0244132 - 0.119584i) q^{72} +(-5.91984 - 8.57636i) q^{73} +(-17.6850 + 5.90413i) q^{74} +(-1.23504 + 2.60279i) q^{75} +(-6.47871 + 7.93498i) q^{76} +(-0.00411375 - 0.0108471i) q^{77} +(4.70671 + 5.53482i) q^{78} +(1.70281 - 4.48994i) q^{79} +(2.82056 + 4.88535i) q^{80} +(-0.632445 + 0.774605i) q^{81} +(18.1200 + 13.6163i) q^{82} +(-10.8774 - 5.70892i) q^{83} +(9.03923 - 0.729722i) q^{84} +(-8.84691 + 0.714196i) q^{85} +(17.0978 + 8.97363i) q^{86} +(4.38179 + 3.29270i) q^{87} +(0.000203470 - 0.000249205i) q^{88} +(2.44648 + 4.23742i) q^{89} +(-1.04018 + 2.74274i) q^{90} +(-13.2392 + 8.74764i) q^{91} +(-0.379478 - 1.00060i) q^{92} +(2.91025 - 3.56441i) q^{93} +(-9.89140 + 20.8457i) q^{94} +(6.86443 - 2.29168i) q^{95} +(-4.57460 - 6.62745i) q^{96} +(3.31342 + 16.2302i) q^{97} +(-1.00362 + 24.9046i) q^{98} -0.00263595 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9}+O(q^{10}) \) 384 * q + q^2 + 16 * q^3 + 17 * q^4 + 6 * q^5 + q^6 - 3 * q^7 - 18 * q^8 + 16 * q^9	\( 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9} + 3 q^{10} - 4 q^{11} - 34 q^{12} - 15 q^{13} + 24 q^{14} - 3 q^{15} + 11 q^{16} - 3 q^{17} - 2 q^{18} + 6 q^{19} + q^{20} + 6 q^{21} - 86 q^{22} - 52 q^{23} + 9 q^{24} - 74 q^{25} - 64 q^{26} - 32 q^{27} - 16 q^{28} - 44 q^{29} + 3 q^{30} - 28 q^{31} + 74 q^{32} - 17 q^{33} - 83 q^{34} + 70 q^{35} + 17 q^{36} + 11 q^{37} - 29 q^{38} + q^{39} - 5 q^{40} + q^{41} + 118 q^{42} - 79 q^{43} - 19 q^{44} - 3 q^{45} + 314 q^{46} + 11 q^{48} - 69 q^{49} - 76 q^{50} + 6 q^{51} - 37 q^{52} - 102 q^{53} + q^{54} - 73 q^{55} - 36 q^{56} + 14 q^{57} - 51 q^{58} + 194 q^{59} + 76 q^{60} + 4 q^{61} - 89 q^{62} - 3 q^{63} - 184 q^{64} - 49 q^{65} - 36 q^{66} - 73 q^{67} + 4 q^{68} - 100 q^{70} + 106 q^{71} + 9 q^{72} - 132 q^{73} - 45 q^{74} + 11 q^{75} + 24 q^{76} - 54 q^{77} - 39 q^{78} - 2 q^{79} + 177 q^{80} + 16 q^{81} - 76 q^{82} - 58 q^{83} - 16 q^{84} - 123 q^{85} - 157 q^{86} - 57 q^{87} + 476 q^{88} + 18 q^{89} - 6 q^{90} + 233 q^{91} - 12 q^{92} + q^{93} - 111 q^{94} + 64 q^{95} - 83 q^{96} - 143 q^{97} - 79 q^{98} - 18 q^{99}+O(q^{100}) \) 384 * q + q^2 + 16 * q^3 + 17 * q^4 + 6 * q^5 + q^6 - 3 * q^7 - 18 * q^8 + 16 * q^9 + 3 * q^10 - 4 * q^11 - 34 * q^12 - 15 * q^13 + 24 * q^14 - 3 * q^15 + 11 * q^16 - 3 * q^17 - 2 * q^18 + 6 * q^19 + q^20 + 6 * q^21 - 86 * q^22 - 52 * q^23 + 9 * q^24 - 74 * q^25 - 64 * q^26 - 32 * q^27 - 16 * q^28 - 44 * q^29 + 3 * q^30 - 28 * q^31 + 74 * q^32 - 17 * q^33 - 83 * q^34 + 70 * q^35 + 17 * q^36 + 11 * q^37 - 29 * q^38 + q^39 - 5 * q^40 + q^41 + 118 * q^42 - 79 * q^43 - 19 * q^44 - 3 * q^45 + 314 * q^46 + 11 * q^48 - 69 * q^49 - 76 * q^50 + 6 * q^51 - 37 * q^52 - 102 * q^53 + q^54 - 73 * q^55 - 36 * q^56 + 14 * q^57 - 51 * q^58 + 194 * q^59 + 76 * q^60 + 4 * q^61 - 89 * q^62 - 3 * q^63 - 184 * q^64 - 49 * q^65 - 36 * q^66 - 73 * q^67 + 4 * q^68 - 100 * q^70 + 106 * q^71 + 9 * q^72 - 132 * q^73 - 45 * q^74 + 11 * q^75 + 24 * q^76 - 54 * q^77 - 39 * q^78 - 2 * q^79 + 177 * q^80 + 16 * q^81 - 76 * q^82 - 58 * q^83 - 16 * q^84 - 123 * q^85 - 157 * q^86 - 57 * q^87 + 476 * q^88 + 18 * q^89 - 6 * q^90 + 233 * q^91 - 12 * q^92 + q^93 - 111 * q^94 + 64 * q^95 - 83 * q^96 - 143 * q^97 - 79 * q^98 - 18 * q^99

Introduction

L-functions

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