LMFDB - Embedded newform 175.4.x.a.103.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,4,Mod(3,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([21, 10]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("175.3");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	175.x (of order $60$, degree $16$, 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:	$10.3253342510$
Analytic rank:	$0$
Dimension:	$928$
Relative dimension:	$58$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			103.6
Character	$\chi$	$=$	175.103
Dual form			175.4.x.a.17.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.89667 - 0.256624i) q^{2} +(5.67011 + 7.00201i) q^{3} +(15.9554 + 1.67698i) q^{4} +(-11.0694 + 1.57137i) q^{5} +(-25.9678 - 35.7416i) q^{6} +(17.8319 - 5.00240i) q^{7} +(-38.9538 - 6.16967i) q^{8} +(-11.2643 + 52.9944i) q^{9} +O(q^{10})$	\(q+(-4.89667 - 0.256624i) q^{2} +(5.67011 + 7.00201i) q^{3} +(15.9554 + 1.67698i) q^{4} +(-11.0694 + 1.57137i) q^{5} +(-25.9678 - 35.7416i) q^{6} +(17.8319 - 5.00240i) q^{7} +(-38.9538 - 6.16967i) q^{8} +(-11.2643 + 52.9944i) q^{9} +(54.6063 - 4.85381i) q^{10} +(46.2983 - 9.84101i) q^{11} +(78.7267 + 121.228i) q^{12} +(77.7071 + 39.5937i) q^{13} +(-88.6007 + 19.9190i) q^{14} +(-73.7673 - 68.5980i) q^{15} +(63.6192 + 13.5227i) q^{16} +(-1.45598 - 3.79297i) q^{17} +(68.7573 - 256.606i) q^{18} +(3.63625 + 34.5966i) q^{19} +(-179.251 + 6.50867i) q^{20} +(136.136 + 96.4948i) q^{21} +(-229.233 + 36.3070i) q^{22} +(7.51682 - 143.429i) q^{23} +(-177.672 - 307.738i) q^{24} +(120.062 - 34.7880i) q^{25} +(-370.346 - 213.819i) q^{26} +(-218.184 + 111.171i) q^{27} +(292.904 - 49.9115i) q^{28} +(-107.290 + 147.672i) q^{29} +(343.610 + 354.832i) q^{30} +(-58.5321 + 131.465i) q^{31} +(-3.28835 - 0.881111i) q^{32} +(331.424 + 268.382i) q^{33} +(6.15611 + 18.9466i) q^{34} +(-189.527 + 83.3938i) q^{35} +(-268.597 + 826.656i) q^{36} +(-72.6390 + 47.1723i) q^{37} +(-8.92723 - 170.342i) q^{38} +(163.372 + 768.607i) q^{39} +(440.888 + 7.08370i) q^{40} +(-30.3689 + 9.86746i) q^{41} +(-641.849 - 507.439i) q^{42} +(-68.8788 - 68.8788i) q^{43} +(755.211 - 79.3758i) q^{44} +(41.4151 - 604.315i) q^{45} +(-73.6149 + 700.399i) q^{46} +(-198.880 - 76.3428i) q^{47} +(266.042 + 522.137i) q^{48} +(292.952 - 178.404i) q^{49} +(-596.830 + 139.535i) q^{50} +(18.3028 - 31.7014i) q^{51} +(1173.45 + 762.047i) q^{52} +(-92.6207 + 75.0028i) q^{53} +(1096.91 - 488.374i) q^{54} +(-497.029 + 181.685i) q^{55} +(-725.483 + 84.8454i) q^{56} +(-221.628 + 221.628i) q^{57} +(563.262 - 695.570i) q^{58} +(-403.775 + 448.437i) q^{59} +(-1061.95 - 1218.21i) q^{60} +(-315.828 + 284.372i) q^{61} +(320.350 - 628.722i) q^{62} +(64.2352 + 1001.34i) q^{63} +(-478.982 - 155.631i) q^{64} +(-922.384 - 316.171i) q^{65} +(-1554.00 - 1399.23i) q^{66} +(301.722 - 115.820i) q^{67} +(-16.8701 - 62.9599i) q^{68} +(1046.92 - 760.629i) q^{69} +(949.453 - 359.715i) q^{70} +(471.023 + 342.218i) q^{71} +(765.746 - 1994.84i) q^{72} +(216.544 - 333.449i) q^{73} +(367.795 - 212.347i) q^{74} +(924.349 + 643.420i) q^{75} +558.101i q^{76} +(776.357 - 407.086i) q^{77} +(-602.739 - 3805.54i) q^{78} +(-411.874 - 925.085i) q^{79} +(-725.473 - 49.7184i) q^{80} +(-679.200 - 302.399i) q^{81} +(151.239 - 40.5244i) q^{82} +(-73.2488 + 462.475i) q^{83} +(2010.28 + 1767.91i) q^{84} +(22.0770 + 39.6978i) q^{85} +(319.601 + 354.953i) q^{86} +(-1642.35 + 86.0720i) q^{87} +(-1864.21 + 97.6991i) q^{88} +(328.469 + 364.801i) q^{89} +(-357.878 + 2948.50i) q^{90} +(1583.73 + 317.309i) q^{91} +(360.462 - 2275.87i) q^{92} +(-1252.40 + 335.581i) q^{93} +(954.259 + 424.863i) q^{94} +(-94.6150 - 377.249i) q^{95} +(-12.4758 - 28.0211i) q^{96} +(83.1014 + 524.682i) q^{97} +(-1480.27 + 798.409i) q^{98} +2564.40i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 928 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 24 q^{7} + 84 q^{8} - 10 q^{9}+O(q^{10}) $ 928 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 24 * q^7 + 84 * q^8 - 10 * q^9	\( 928 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 24 q^{7} + 84 q^{8} - 10 q^{9} - 96 q^{10} - 6 q^{11} - 72 q^{12} - 20 q^{14} - 368 q^{15} - 1670 q^{16} + 120 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} - 880 q^{22} + 296 q^{23} + 32 q^{25} - 48 q^{26} + 226 q^{28} - 200 q^{29} - 38 q^{30} - 18 q^{31} - 964 q^{32} - 1092 q^{33} + 288 q^{35} + 7400 q^{36} - 392 q^{37} + 5424 q^{38} + 2430 q^{39} + 2172 q^{40} - 2098 q^{42} + 1560 q^{43} - 10 q^{44} - 4224 q^{45} - 6 q^{46} + 96 q^{47} + 6232 q^{50} - 16 q^{51} - 8928 q^{52} - 2384 q^{53} - 30 q^{54} + 244 q^{56} + 1556 q^{57} + 640 q^{58} + 4890 q^{59} + 3676 q^{60} - 18 q^{61} + 224 q^{63} - 9700 q^{64} - 1116 q^{65} - 2610 q^{66} - 2404 q^{67} - 13614 q^{68} - 1700 q^{70} - 24 q^{71} - 518 q^{72} - 4200 q^{73} - 16104 q^{75} - 722 q^{77} - 356 q^{78} - 10 q^{79} + 6414 q^{80} - 6810 q^{81} + 1692 q^{82} + 20620 q^{84} + 2712 q^{85} - 6 q^{86} + 9102 q^{87} + 1650 q^{88} + 20370 q^{89} - 12 q^{91} + 1612 q^{92} - 4604 q^{93} - 30 q^{94} + 1652 q^{95} - 2610 q^{96} - 19478 q^{98}+O(q^{100}) \) 928 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 24 * q^7 + 84 * q^8 - 10 * q^9 - 96 * q^10 - 6 * q^11 - 72 * q^12 - 20 * q^14 - 368 * q^15 - 1670 * q^16 + 120 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 - 880 * q^22 + 296 * q^23 + 32 * q^25 - 48 * q^26 + 226 * q^28 - 200 * q^29 - 38 * q^30 - 18 * q^31 - 964 * q^32 - 1092 * q^33 + 288 * q^35 + 7400 * q^36 - 392 * q^37 + 5424 * q^38 + 2430 * q^39 + 2172 * q^40 - 2098 * q^42 + 1560 * q^43 - 10 * q^44 - 4224 * q^45 - 6 * q^46 + 96 * q^47 + 6232 * q^50 - 16 * q^51 - 8928 * q^52 - 2384 * q^53 - 30 * q^54 + 244 * q^56 + 1556 * q^57 + 640 * q^58 + 4890 * q^59 + 3676 * q^60 - 18 * q^61 + 224 * q^63 - 9700 * q^64 - 1116 * q^65 - 2610 * q^66 - 2404 * q^67 - 13614 * q^68 - 1700 * q^70 - 24 * q^71 - 518 * q^72 - 4200 * q^73 - 16104 * q^75 - 722 * q^77 - 356 * q^78 - 10 * q^79 + 6414 * q^80 - 6810 * q^81 + 1692 * q^82 + 20620 * q^84 + 2712 * q^85 - 6 * q^86 + 9102 * q^87 + 1650 * q^88 + 20370 * q^89 - 12 * q^91 + 1612 * q^92 - 4604 * q^93 - 30 * q^94 + 1652 * q^95 - 2610 * q^96 - 19478 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{20}\right)$

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 $

$2$	−4.89667	−	0.256624i	−1.73124	−	0.0907302i	−0.839521	−	0.543328i	$-0.817164\pi$
$2$	−4.89667	−	0.256624i	−1.73124	−	0.0907302i	−0.891715	+	0.452597i	$0.850498\pi$
$3$	5.67011	+	7.00201i	1.09121	+	1.34754i	0.932895	+	0.360149i	$0.117274\pi$
$3$	5.67011	+	7.00201i	1.09121	+	1.34754i	0.158319	+	0.987388i	$0.449392\pi$
$4$	15.9554	+	1.67698i	1.99442	+	0.209622i
$5$	−11.0694	+	1.57137i	−0.990074	+	0.140547i
$5$	−11.0694	+	1.57137i	−0.990074	+	0.140547i
$6$	−25.9678	−	35.7416i	−1.76689	−	2.43191i
$7$	17.8319	−	5.00240i	0.962831	−	0.270104i
$7$	17.8319	−	5.00240i	0.962831	−	0.270104i
$8$	−38.9538	−	6.16967i	−1.72153	−	0.272664i
$9$	−11.2643	+	52.9944i	−0.417197	+	1.96276i
$10$	54.6063	−	4.85381i	1.72680	−	0.153491i
$11$	46.2983	−	9.84101i	1.26904	−	0.269743i	0.476291	−	0.879288i	$-0.341981\pi$
$11$	46.2983	−	9.84101i	1.26904	−	0.269743i	0.792752	+	0.609545i	$0.208648\pi$
$12$	78.7267	+	121.228i	1.89387	+	2.91630i
$13$	77.7071	+	39.5937i	1.65785	+	0.844718i	0.995420	+	0.0955952i	$0.0304754\pi$
$13$	77.7071	+	39.5937i	1.65785	+	0.844718i	0.662431	+	0.749123i	$0.269525\pi$
$14$	−88.6007	+	19.9190i	−1.69139	+	0.380256i
$15$	−73.7673	−	68.5980i	−1.26978	−	1.18079i
$16$	63.6192	+	13.5227i	0.994050	+	0.211292i
$17$	−1.45598	−	3.79297i	−0.0207722	−	0.0541135i	0.922802	−	0.385274i	$-0.125893\pi$
$17$	−1.45598	−	3.79297i	−0.0207722	−	0.0541135i	−0.943574	+	0.331161i	$0.892560\pi$
$18$	68.7573	−	256.606i	0.900347	−	3.36014i
$19$	3.63625	+	34.5966i	0.0439060	+	0.417738i	0.994294	+	0.106672i	$0.0340194\pi$
$19$	3.63625	+	34.5966i	0.0439060	+	0.417738i	−0.950388	+	0.311066i	$0.899314\pi$
$20$	−179.251	+	6.50867i	−2.00409	+	0.0727691i
$21$	136.136	+	96.4948i	1.41463	+	1.00271i
$22$	−229.233	+	36.3070i	−2.22149	+	0.351849i
$23$	7.51682	−	143.429i	0.0681463	−	1.30031i	−0.723924	−	0.689880i	$-0.757663\pi$
$23$	7.51682	−	143.429i	0.0681463	−	1.30031i	0.792070	−	0.610430i	$-0.209003\pi$
$24$	−177.672	−	307.738i	−1.51113	−	2.61736i
$25$	120.062	−	34.7880i	0.960493	−	0.278304i
$26$	−370.346	−	213.819i	−2.79349	−	1.61282i
$27$	−218.184	+	111.171i	−1.55517	+	0.792399i
$28$	292.904	−	49.9115i	1.97691	−	0.336871i
$29$	−107.290	+	147.672i	−0.687010	+	0.945589i	−0.999991	−	0.00417070i	$-0.998672\pi$
$29$	−107.290	+	147.672i	−0.687010	+	0.945589i	0.312981	+	0.949759i	$0.398672\pi$
$30$	343.610	+	354.832i	2.09115	+	2.15944i
$31$	−58.5321	+	131.465i	−0.339118	+	0.761672i	0.660820	+	0.750545i	$0.270209\pi$
$31$	−58.5321	+	131.465i	−0.339118	+	0.761672i	−0.999938	+	0.0111278i	$0.996458\pi$
$32$	−3.28835	−	0.881111i	−0.0181658	−	0.00486750i
$33$	331.424	+	268.382i	1.74829	+	1.41573i
$34$	6.15611	+	18.9466i	0.0310519	+	0.0955679i
$35$	−189.527	+	83.3938i	−0.915312	+	0.402746i
$36$	−268.597	+	826.656i	−1.24350	+	3.82711i
$37$	−72.6390	+	47.1723i	−0.322751	+	0.209597i	−0.695837	−	0.718200i	$-0.744966\pi$
$37$	−72.6390	+	47.1723i	−0.322751	+	0.209597i	0.373086	+	0.927797i	$0.378300\pi$
$38$	−8.92723	−	170.342i	−0.0381102	−	0.727186i
$39$	163.372	+	768.607i	0.670783	+	3.15578i
$40$	440.888	+	7.08370i	1.74276	+	0.0280008i
$41$	−30.3689	+	9.86746i	−0.115679	+	0.0375863i	−0.366284	−	0.930503i	$-0.619370\pi$
$41$	−30.3689	+	9.86746i	−0.115679	+	0.0375863i	0.250606	+	0.968089i	$0.419370\pi$
$42$	−641.849	−	507.439i	−2.35808	−	1.86428i
$43$	−68.8788	−	68.8788i	−0.244277	−	0.244277i	0.574340	−	0.818617i	$-0.305259\pi$
$43$	−68.8788	−	68.8788i	−0.244277	−	0.244277i	−0.818617	+	0.574340i	$0.805259\pi$
$44$	755.211	−	79.3758i	2.58755	−	0.271963i
$45$	41.4151	−	604.315i	0.137196	−	2.00191i
$46$	−73.6149	+	700.399i	−0.235955	+	2.24496i
$47$	−198.880	−	76.3428i	−0.617226	−	0.236931i	0.0296082	−	0.999562i	$-0.490574\pi$
$47$	−198.880	−	76.3428i	−0.617226	−	0.236931i	−0.646834	+	0.762631i	$0.723907\pi$
$48$	266.042	+	522.137i	0.799998	+	1.57008i
$49$	292.952	−	178.404i	0.854088	−	0.520129i
$50$	−596.830	+	139.535i	−1.68809	+	0.394665i
$51$	18.3028	−	31.7014i	0.0502530	−	0.0870408i
$52$	1173.45	+	762.047i	3.12939	+	2.03225i
$53$	−92.6207	+	75.0028i	−0.240046	+	0.194385i	−0.741793	−	0.670629i	$-0.766024\pi$
$53$	−92.6207	+	75.0028i	−0.240046	+	0.194385i	0.501747	+	0.865014i	$0.332691\pi$
$54$	1096.91	−	488.374i	2.76426	−	1.23073i
$55$	−497.029	+	181.685i	−1.21853	+	0.445426i
$56$	−725.483	+	84.8454i	−1.73119	+	0.202463i
$57$	−221.628	+	221.628i	−0.515006	+	0.515006i
$58$	563.262	−	695.570i	1.27517	−	1.57470i
$59$	−403.775	+	448.437i	−0.890966	+	0.989518i	−0.999990	−	0.00452075i	$-0.998561\pi$
$59$	−403.775	+	448.437i	−0.890966	+	0.989518i	0.109023	+	0.994039i	$0.465228\pi$
$60$	−1061.95	−	1218.21i	−2.28495	−	2.62118i
$61$	−315.828	+	284.372i	−0.662911	+	0.596888i	−0.930344	−	0.366689i	$-0.880491\pi$
$61$	−315.828	+	284.372i	−0.662911	+	0.596888i	0.267432	+	0.963577i	$0.413825\pi$
$62$	320.350	−	628.722i	0.656201	−	1.28787i
$63$	64.2352	+	1001.34i	0.128458	+	2.00249i
$64$	−478.982	−	155.631i	−0.935511	−	0.303966i
$65$	−922.384	−	316.171i	−1.76012	−	0.603326i
$66$	−1554.00	−	1399.23i	−2.89825	−	2.60959i
$67$	301.722	−	115.820i	0.550168	−	0.211190i	−0.0673740	−	0.997728i	$-0.521462\pi$
$67$	301.722	−	115.820i	0.550168	−	0.211190i	0.617542	+	0.786538i	$0.288129\pi$
$68$	−16.8701	−	62.9599i	−0.0300852	−	0.112280i
$69$	1046.92	−	760.629i	1.82658	−	1.32709i
$70$	949.453	−	359.715i	1.62116	−	0.614202i
$71$	471.023	+	342.218i	0.787327	+	0.572026i	0.907169	−	0.420767i	$-0.138239\pi$
$71$	471.023	+	342.218i	0.787327	+	0.572026i	−0.119842	+	0.992793i	$0.538239\pi$
$72$	765.746	−	1994.84i	1.25339	−	3.26519i
$73$	216.544	−	333.449i	0.347186	−	0.534619i	−0.621337	−	0.783543i	$-0.713410\pi$
$73$	216.544	−	333.449i	0.347186	−	0.534619i	0.968523	+	0.248924i	$0.0800769\pi$
$74$	367.795	−	212.347i	0.577774	−	0.333578i
$75$	924.349	+	643.420i	1.42313	+	0.990610i
$76$			558.101i			0.842349i
$77$	776.357	−	407.086i	1.14901	−	0.602491i
$78$	−602.739	−	3805.54i	−0.874958	−	5.52427i
$79$	−411.874	−	925.085i	−0.586576	−	1.31747i	−0.926244	−	0.376925i	$-0.876981\pi$
$79$	−411.874	−	925.085i	−0.586576	−	1.31747i	0.339668	−	0.940545i	$-0.389685\pi$
$80$	−725.473	−	49.7184i	−1.01388	−	0.0694835i
$81$	−679.200	−	302.399i	−0.931687	−	0.414814i
$82$	151.239	−	40.5244i	0.203677	−	0.0545752i
$83$	−73.2488	+	462.475i	−0.0968686	+	0.611604i	0.890721	+	0.454550i	$0.150200\pi$
$83$	−73.2488	+	462.475i	−0.0968686	+	0.611604i	−0.987590	+	0.157055i	$0.949800\pi$
$84$	2010.28	+	1767.91i	2.61118	+	2.29637i
$85$	22.0770	+	39.6978i	0.0281715	+	0.0506569i
$86$	319.601	+	354.953i	0.400738	+	0.445065i
$87$	−1642.35	+	86.0720i	−2.02389	+	0.106068i
$88$	−1864.21	+	97.6991i	−2.25824	+	0.118350i
$89$	328.469	+	364.801i	0.391209	+	0.434482i	0.906288	−	0.422661i	$-0.138904\pi$
$89$	328.469	+	364.801i	0.391209	+	0.434482i	−0.515079	+	0.857143i	$0.672237\pi$
$90$	−357.878	+	2948.50i	−0.419152	+	3.45333i
$91$	1583.73	+	317.309i	1.82439	+	0.365528i
$92$	360.462	−	2275.87i	0.408487	−	2.57908i
$93$	−1252.40	+	335.581i	−1.39643	+	0.374173i
$94$	954.259	+	424.863i	1.04707	+	0.466184i
$95$	−94.6150	−	377.249i	−0.102182	−	0.407420i
$96$	−12.4758	−	28.0211i	−0.0132636	−	0.0297905i
$97$	83.1014	+	524.682i	0.0869863	+	0.549210i	0.992240	+	0.124338i	$0.0396808\pi$
$97$	83.1014	+	524.682i	0.0869863	+	0.549210i	−0.905254	+	0.424872i	$0.860319\pi$
$98$	−1480.27	+	798.409i	−1.52582	+	0.822975i
$99$			2564.40i			2.60336i
$100$	1973.97	−	353.716i	1.97397	−	0.353716i
$101$	419.295	−	242.080i	0.413083	−	0.238494i	−0.279030	−	0.960282i	$-0.590013\pi$
$101$	419.295	−	242.080i	0.413083	−	0.238494i	0.692114	+	0.721789i	$0.256680\pi$
$102$	−97.7581	+	150.534i	−0.0948970	+	0.146129i
$103$	278.948	−	726.684i	0.266850	−	0.695168i	−0.733038	−	0.680188i	$-0.761898\pi$
$103$	278.948	−	726.684i	0.266850	−	0.695168i	0.999888	−	0.0149798i	$-0.00476841\pi$
$104$	−2782.71	−	2021.75i	−2.62372	−	1.90624i
$105$	−1658.56	−	854.217i	−1.54152	−	0.793934i
$106$	472.781	−	343.495i	0.433213	−	0.314747i
$107$	206.031	+	768.917i	0.186147	+	0.694711i	0.994382	+	0.105850i	$0.0337565\pi$
$107$	206.031	+	768.917i	0.186147	+	0.694711i	−0.808235	+	0.588860i	$0.799577\pi$
$108$	−3667.65	+	1407.88i	−3.26777	+	1.25438i
$109$	4.61467	+	4.15507i	0.00405509	+	0.00365122i	0.671156	−	0.741316i	$-0.265798\pi$
$109$	4.61467	+	4.15507i	0.00405509	+	0.00365122i	−0.667101	+	0.744968i	$0.732465\pi$
$110$	2480.41	−	762.104i	2.14998	−	0.660580i
$111$	−742.172	−	241.146i	−0.634630	−	0.206204i
$112$	1202.10	−	77.1137i	1.01417	−	0.0650586i
$113$	968.995	−	1901.76i	0.806685	−	1.58321i	−0.00562592	−	0.999984i	$-0.501791\pi$
$113$	968.995	−	1901.76i	0.806685	−	1.58321i	0.812311	−	0.583224i	$-0.198209\pi$
$114$	1142.12	−	1028.37i	0.938324	−	0.844870i
$115$	142.174	+	1599.48i	0.115285	+	1.29698i
$116$	−1959.50	+	2176.25i	−1.56841	+	1.74189i
$117$	−2973.56	+	3672.05i	−2.34962	+	2.90154i
$118$	2092.23	−	2092.23i	1.63225	−	1.63225i
$119$	−44.9369	−	60.3523i	−0.0346164	−	0.0464915i
$120$	2450.29	+	3127.27i	1.86400	+	2.37900i
$121$	830.759	−	369.878i	0.624162	−	0.277895i
$122$	1619.48	−	1311.43i	1.20181	−	0.973208i
$123$	−241.287	−	156.694i	−0.176879	−	0.114867i
$124$	−1154.37	+	1999.42i	−0.836009	+	1.44801i
$125$	−1274.34	+	573.742i	−0.911844	+	0.410537i
$126$	−57.5717	−	4919.71i	−0.0407055	−	3.47844i
$127$	−923.154	−	1811.79i	−0.645013	−	1.26591i	−0.949612	−	0.313429i	$-0.898522\pi$
$127$	−923.154	−	1811.79i	−0.645013	−	1.26591i	0.304598	−	0.952481i	$-0.401478\pi$
$128$	2330.90	+	894.750i	1.60957	+	0.617855i
$129$	91.7393	−	872.841i	0.0626139	−	0.595731i
$130$	4435.48	+	1784.89i	2.99244	+	1.20420i
$131$	−43.1545	+	4.53572i	−0.0287819	+	0.00302510i	−0.118908	−	0.992905i	$-0.537940\pi$
$131$	−43.1545	+	4.53572i	−0.0287819	+	0.00302510i	0.0901266	+	0.995930i	$0.471273\pi$
$132$	4837.92	+	4837.92i	3.19005	+	3.19005i
$133$	237.907	+	598.733i	0.155107	+	0.390352i
$134$	−1507.16	+	489.705i	−0.971631	+	0.315702i
$135$	2240.47	−	1573.43i	1.42836	−	1.00311i
$136$	33.3147	+	156.733i	0.0210052	+	0.0988219i
$137$	−66.2139	−	1263.44i	−0.0412922	−	0.787902i	−0.938286	−	0.345860i	$-0.887587\pi$
$137$	−66.2139	−	1263.44i	−0.0412922	−	0.787902i	0.896994	−	0.442043i	$-0.145746\pi$
$138$	−5321.60	+	3455.89i	−3.28264	+	2.13177i
$139$	360.479	−	1109.44i	0.219967	−	0.676989i	−0.778797	−	0.627276i	$-0.784170\pi$
$139$	360.479	−	1109.44i	0.219967	−	0.676989i	0.998764	−	0.0497121i	$-0.0158304\pi$
$140$	−3163.83	+	1012.75i	−1.90994	+	0.611377i
$141$	−593.119	−	1825.43i	−0.354252	−	1.09028i
$142$	−2218.63	−	1796.61i	−1.31115	−	1.06175i
$143$	3987.35	+	1068.41i	2.33174	+	0.624788i
$144$	−1433.25	+	3219.14i	−0.829429	+	1.86293i
$145$	955.588	−	1803.23i	0.547291	−	1.03276i
$146$	−1145.92	+	1577.22i	−0.649567	+	0.894052i
$147$	2910.26	+	1039.68i	1.63289	+	0.583342i
$148$	−1238.09	+	630.839i	−0.687638	+	0.350369i
$149$	−1402.51	−	809.738i	−0.771127	−	0.445210i	0.0621498	−	0.998067i	$-0.480204\pi$
$149$	−1402.51	−	809.738i	−0.771127	−	0.445210i	−0.833276	+	0.552857i	$0.813538\pi$
$150$	−4361.12	−	3387.83i	−2.37389	−	1.84410i
$151$	−1133.48	−	1963.25i	−0.610870	−	1.05806i	−0.991094	−	0.133163i	$-0.957487\pi$
$151$	−1133.48	−	1963.25i	−0.610870	−	1.05806i	0.380224	−	0.924894i	$-0.375847\pi$
$152$	71.8042	−	1370.10i	0.0383164	−	0.731120i
$153$	217.407	−	34.4338i	0.114878	−	0.0181948i
$154$	−3906.04	+	1794.14i	−2.04388	+	0.938803i
$155$	441.333	−	1547.21i	0.228701	−	0.801774i
$156$	1317.73	+	12537.4i	0.676302	+	6.43458i
$157$	−106.159	+	396.190i	−0.0539643	+	0.201397i	−0.987645	−	0.156710i	$-0.949911\pi$
$157$	−106.159	+	396.190i	−0.0539643	+	0.201397i	0.933680	+	0.358107i	$0.116578\pi$
$158$	1779.42	+	4635.53i	0.895966	+	2.33407i
$159$	−1050.34	−	223.257i	−0.523883	−	0.111355i
$160$	37.7845	+	4.58614i	0.0186696	+	0.00226604i
$161$	−583.452	−	2595.22i	−0.285605	−	1.27039i
$162$	3248.22	+	1655.05i	1.57533	+	0.802672i
$163$	1563.45	+	2407.50i	0.751280	+	1.15687i	0.982914	+	0.184066i	$0.0589261\pi$
$163$	1563.45	+	2407.50i	0.751280	+	1.15687i	−0.231634	+	0.972803i	$0.574407\pi$
$164$	−501.096	+	106.511i	−0.238591	+	0.0507142i
$165$	−4090.37	−	2450.02i	−1.92991	−	1.15596i
$166$	477.357	−	2245.79i	0.223193	−	1.05004i
$167$	4006.75	+	634.607i	1.85660	+	0.294056i	0.981726	−	0.190301i	$-0.0609464\pi$
$167$	4006.75	+	634.607i	1.85660	+	0.294056i	0.874870	+	0.484357i	$0.160946\pi$
$168$	−4707.66	−	4598.75i	−2.16193	−	2.11191i
$169$	3179.37	+	4376.02i	1.44714	+	1.99182i
$170$	−97.9162	−	200.053i	−0.0441755	−	0.0902550i
$171$	−1874.39	−	197.006i	−0.838234	−	0.0881020i
$172$	−983.480	−	1214.50i	−0.435986	−	0.538398i
$173$	1673.42	+	87.7003i	0.735421	+	0.0385418i	0.416369	−	0.909196i	$-0.363302\pi$
$173$	1673.42	+	87.7003i	0.735421	+	0.0385418i	0.319052	+	0.947737i	$0.396636\pi$
$174$	8064.15			3.51346
$175$	1966.90	−	1220.93i	0.849621	−	0.527393i
$176$	3078.54			1.31849
$177$	−5429.41	−	284.544i	−2.30565	−	0.120834i
$178$	−1514.79	−	1870.61i	−0.637855	−	0.787685i
$179$	−827.624	−	86.9868i	−0.345584	−	0.0363223i	−0.0698533	−	0.997557i	$-0.522253\pi$
$179$	−827.624	−	86.9868i	−0.345584	−	0.0363223i	−0.275731	+	0.961235i	$0.588920\pi$
$180$	1674.22	−	9572.62i	0.693271	−	3.96390i
$181$	270.354	+	372.110i	0.111023	+	0.152811i	0.860913	−	0.508753i	$-0.169893\pi$
$181$	270.354	+	372.110i	0.111023	+	0.152811i	−0.749889	+	0.661563i	$0.769893\pi$
$182$	−7673.57	−	1960.18i	−3.12529	−	0.798343i
$183$	−3781.96	−	599.003i	−1.52771	−	0.241965i
$184$	−1177.72	+	5540.75i	−0.471863	+	2.21994i
$185$	729.942	−	636.310i	0.290089	−	0.252878i
$186$	6218.73	−	1321.83i	2.45150	−	0.521083i
$187$	−104.736	−	161.280i	−0.0409576	−	0.0630692i
$188$	−3045.18	−	1551.60i	−1.18134	−	0.601925i
$189$	−3334.52	+	3073.82i	−1.28334	+	1.18300i
$190$	366.488	+	1871.55i	0.139936	+	0.714612i
$191$	−3341.26	−	710.207i	−1.26579	−	0.269051i	−0.474368	−	0.880327i	$-0.657323\pi$
$191$	−3341.26	−	710.207i	−1.26579	−	0.269051i	−0.791418	+	0.611275i	$0.790657\pi$
$192$	−1626.15	−	4236.28i	−0.611237	−	1.59233i
$193$	−378.993	+	1414.42i	−0.141350	+	0.527524i	0.858541	+	0.512745i	$0.171371\pi$
$193$	−378.993	+	1414.42i	−0.141350	+	0.527524i	−0.999891	+	0.0147794i	$0.995295\pi$
$194$	−272.275	−	2590.52i	−0.100764	−	0.958704i
$195$	−3016.19	−	8251.27i	−1.10766	−	3.03018i
$196$	4973.34	−	2355.24i	1.81244	−	0.858322i
$197$	2738.56	−	433.746i	0.990429	−	0.156869i	0.359864	−	0.933005i	$-0.382823\pi$
$197$	2738.56	−	433.746i	0.990429	−	0.156869i	0.630565	+	0.776136i	$0.282823\pi$
$198$	658.087	−	12557.0i	0.236203	−	4.50702i
$199$	−1561.60	−	2704.77i	−0.556275	−	0.963497i	−0.997803	−	0.0662495i	$-0.978897\pi$
$199$	−1561.60	−	2704.77i	−0.556275	−	0.963497i	0.441528	−	0.897248i	$-0.354437\pi$
$200$	−4891.49	+	614.385i	−1.72940	+	0.217218i
$201$	2521.77	+	1455.95i	0.884936	+	0.510918i
$202$	−2115.27	+	1077.79i	−0.736783	+	0.375410i
$203$	−1174.47	+	3169.99i	−0.406068	+	1.09601i
$204$	345.191	−	475.114i	0.118471	−	0.163062i
$205$	320.659	−	156.947i	0.109248	−	0.0534716i
$206$	−1552.40	+	3486.75i	−0.525053	+	1.17929i
$207$	7516.29	+	2013.98i	2.52376	+	0.676239i
$208$	4408.25	+	3569.73i	1.46951	+	1.18998i
$209$	508.818	+	1565.98i	0.168400	+	0.518283i
$210$	7902.23	+	4608.45i	2.59669	+	1.51435i
$211$	−710.477	+	2186.62i	−0.231807	+	0.713429i	0.765722	+	0.643172i	$0.222382\pi$
$211$	−710.477	+	2186.62i	−0.231807	+	0.713429i	−0.997529	+	0.0702569i	$0.977618\pi$
$212$	−1603.58	+	1041.38i	−0.519501	+	0.337368i
$213$	274.540	+	5238.53i	0.0883152	+	1.68515i
$214$	−811.543	−	3818.01i	−0.259233	−	1.21960i
$215$	870.679	+	654.211i	0.276185	+	0.207520i
$216$	9185.00	−	2984.39i	2.89333	−	0.940101i
$217$	−386.096	+	2637.07i	−0.120783	+	0.824959i
$218$	−21.5302	−	21.5302i	−0.00668905	−	0.00668905i
$219$	3562.64	−	374.449i	1.09927	−	0.115538i
$220$	−8234.97	+	2065.35i	−2.52364	+	0.632937i
$221$	37.0375	−	352.388i	0.0112734	−	0.107259i
$222$	3572.29	+	1371.27i	1.07998	+	0.414567i
$223$	−40.2496	−	78.9943i	−0.0120866	−	0.0237213i	0.884884	−	0.465811i	$-0.154237\pi$
$223$	−40.2496	−	78.9943i	−0.0120866	−	0.0237213i	−0.896971	+	0.442090i	$0.854237\pi$
$224$	−63.0452	+	0.737771i	−0.0188053	+	0.000220064i
$225$	491.161	+	6754.46i	0.145529	+	2.00132i
$226$	−5232.89	+	9063.63i	−1.54021	+	2.66772i
$227$	153.300	+	99.5544i	0.0448234	+	0.0291086i	0.566856	−	0.823817i	$-0.308159\pi$
$227$	153.300	+	99.5544i	0.0448234	+	0.0291086i	−0.522033	+	0.852925i	$0.674826\pi$
$228$	−3907.83	+	3164.50i	−1.13510	+	0.919184i
$229$	−42.7842	+	19.0487i	−0.0123461	+	0.00549684i	−0.412900	−	0.910776i	$-0.635484\pi$
$229$	−42.7842	+	19.0487i	−0.0123461	+	0.00549684i	0.400554	+	0.916273i	$0.368818\pi$
$230$	−285.713	−	7868.64i	−0.0819103	−	2.25584i
$231$	7252.46	+	3127.84i	2.06570	+	0.890894i
$232$	5090.45	−	5090.45i	1.44054	−	1.44054i
$233$	−971.231	+	1199.37i	−0.273079	+	0.337225i	−0.895174	−	0.445717i	$-0.852949\pi$
$233$	−971.231	+	1199.37i	−0.273079	+	0.337225i	0.622095	+	0.782942i	$0.286282\pi$
$234$	15502.9	−	17217.7i	4.33101	−	4.81008i
$235$	2321.44	+	532.553i	0.644399	+	0.147830i
$236$	−7194.41	+	6477.87i	−1.98439	+	1.78675i
$237$	4142.08	−	8129.28i	1.13526	−	2.22807i
$238$	204.553	+	307.058i	0.0557110	+	0.0836285i
$239$	−6952.28	−	2258.93i	−1.88161	−	0.611373i	−0.986053	−	0.166430i	$-0.946776\pi$
$239$	−6952.28	−	2258.93i	−1.88161	−	0.611373i	−0.895559	−	0.444943i	$-0.853224\pi$
$240$	−3765.39	−	5361.68i	−1.01273	−	1.44206i
$241$	2035.55	+	1832.82i	0.544072	+	0.489885i	0.894723	−	0.446621i	$-0.147373\pi$
$241$	2035.55	+	1832.82i	0.544072	+	0.489885i	−0.350651	+	0.936506i	$0.614040\pi$
$242$	−4162.88	+	1597.98i	−1.10578	+	0.424471i
$243$	−22.5304	−	84.0845i	−0.00594784	−	0.0221976i
$244$	−5516.04	+	4007.64i	−1.44725	+	1.05149i
$245$	−2962.45	+	2435.16i	−0.772507	+	0.635006i
$246$	1141.29	+	829.199i	0.295798	+	0.214910i
$247$	−1087.25	+	2832.38i	−0.280081	+	0.729635i
$248$	3091.14	−	4759.94i	0.791483	−	1.21878i
$249$	−3653.58	+	2109.40i	−0.929864	+	0.536857i
$250$	6387.27	−	2482.40i	1.61587	−	0.628004i
$251$			134.048i			0.0337093i	0.999858	+	0.0168546i	$0.00536525\pi$
$251$			134.048i			0.0337093i	−0.999858	+	0.0168546i	$0.994635\pi$
$252$	−654.325	+	16084.5i	−0.163566	+	4.02074i
$253$	−1063.47	−	6714.52i	−0.264269	−	1.66853i
$254$	4055.44	+	9108.66i	1.00181	+	2.25011i
$255$	−152.786	+	379.674i	−0.0375209	+	0.0932397i
$256$	−7503.35	−	3340.70i	−1.83187	−	0.815602i
$257$	4792.04	−	1284.02i	1.16311	−	0.311654i	0.374902	−	0.927064i	$-0.377676\pi$
$257$	4792.04	−	1284.02i	1.16311	−	0.311654i	0.788207	+	0.615410i	$0.211010\pi$
$258$	−673.209	+	4250.48i	−0.162450	+	1.02567i
$259$	−1059.32	+	1204.54i	−0.254141	+	0.288983i
$260$	−14186.8	−	6591.45i	−3.38395	−	1.57225i
$261$	−6617.26	−	7349.21i	−1.56934	−	1.74293i
$262$	212.478	−	11.1355i	0.0501027	−	0.00262577i
$263$	2424.40	−	127.057i	0.568421	−	0.0297897i	0.234039	−	0.972227i	$-0.424806\pi$
$263$	2424.40	−	127.057i	0.568421	−	0.0297897i	0.334382	+	0.942438i	$0.391472\pi$
$264$	−11254.4	−	12499.3i	−2.62371	−	2.91392i
$265$	907.395	−	975.774i	0.210343	−	0.226194i
$266$	−1011.31	−	2992.85i	−0.233110	−	0.689864i
$267$	−691.888	+	4368.41i	−0.158587	+	1.00128i
$268$	5008.32	−	1341.98i	1.14154	−	0.305874i
$269$	−396.614	−	176.584i	−0.0898958	−	0.0400242i	0.361296	−	0.932451i	$-0.382334\pi$
$269$	−396.614	−	176.584i	−0.0898958	−	0.0400242i	−0.451192	+	0.892427i	$0.649001\pi$
$270$	−11374.6	+	7129.64i	−2.56385	+	1.60702i
$271$	−996.345	−	2237.83i	−0.223335	−	0.501618i	0.766775	−	0.641916i	$-0.221860\pi$
$271$	−996.345	−	2237.83i	−0.223335	−	0.501618i	−0.990109	+	0.140299i	$0.955194\pi$
$272$	−41.3374	−	260.994i	−0.00921489	−	0.0581805i
$273$	6758.12	+	12888.5i	1.49824	+	2.85731i
$274$			6203.63i			1.36779i
$275$	5216.30	−	2792.16i	1.14384	−	0.612267i
$276$	17979.5	−	10380.5i	3.92116	−	2.26388i
$277$	−1487.46	+	2290.49i	−0.322646	+	0.496831i	−0.962358	−	0.271783i	$-0.912387\pi$
$277$	−1487.46	+	2290.49i	−0.322646	+	0.496831i	0.639713	+	0.768614i	$0.279053\pi$
$278$	−2049.86	+	5340.06i	−0.442238	+	1.15207i
$279$	−6307.60	−	4582.74i	−1.35350	−	0.983374i
$280$	7897.31	−	2079.18i	1.68555	−	0.443768i
$281$	1988.17	−	1444.49i	0.422079	−	0.306659i	−0.356395	−	0.934336i	$-0.615994\pi$
$281$	1988.17	−	1444.49i	0.422079	−	0.306659i	0.778474	+	0.627677i	$0.215994\pi$
$282$	2435.86	+	9090.75i	0.514373	+	1.91967i
$283$	−6983.99	+	2680.90i	−1.46698	+	0.563121i	−0.955191	−	0.295991i	$-0.904350\pi$
$283$	−6983.99	+	2680.90i	−1.46698	+	0.563121i	−0.511789	+	0.859111i	$0.671017\pi$
$284$	6941.47	+	6250.13i	1.45035	+	1.30590i
$285$	2105.02	−	2801.54i	0.437511	−	0.582277i
$286$	−19250.6	−	6254.89i	−3.98011	−	1.29322i
$287$	−492.174	+	327.873i	−0.101227	+	0.0674346i
$288$	83.7350	−	164.339i	0.0171324	−	0.0336242i
$289$	3638.80	−	3276.39i	0.740648	−	0.666882i
$290$	−5141.95	+	8584.61i	−1.04119	+	1.73830i
$291$	−3202.63	+	3556.88i	−0.645160	+	0.716523i
$292$	4014.23	−	4957.16i	0.804504	−	0.993479i
$293$	100.749	−	100.749i	0.0200881	−	0.0200881i	−0.696991	−	0.717080i	$-0.745478\pi$
$293$	100.749	−	100.749i	0.0200881	−	0.0200881i	0.717080	+	0.696991i	$0.245478\pi$
$294$	−13983.8	−	5837.82i	−2.77398	−	1.15806i
$295$	3764.87	−	5598.40i	0.743049	−	1.10492i
$296$	3120.60	−	1389.38i	0.612775	−	0.272825i
$297$	−9007.54	+	7294.16i	−1.75983	+	1.42508i
$298$	6659.82	+	4324.94i	1.29461	+	0.840728i
$299$	6263.02	−	10847.9i	1.21137	−	2.09816i
$300$	13669.4	+	11816.1i	2.63067	+	2.27402i
$301$	−1572.80	−	883.680i	−0.301178	−	0.169217i
$302$	5046.47	+	9904.25i	0.961562	+	1.88717i
$303$	4072.50	+	1563.28i	0.772141	+	0.296397i
$304$	−236.504	+	2250.18i	−0.0446198	+	0.424529i
$305$	3049.16	−	3644.10i	0.572440	−	0.684134i
$306$	−1073.41	+	112.820i	−0.200531	+	0.0210767i
$307$	−6766.34	−	6766.34i	−1.25790	−	1.25790i	−0.952094	−	0.305806i	$-0.901074\pi$
$307$	−6766.34	−	6766.34i	−1.25790	−	1.25790i	−0.305806	−	0.952094i	$-0.598926\pi$
$308$	13069.8	−	5193.28i	2.41792	−	0.960763i
$309$	6669.91	−	2167.19i	1.22795	−	0.398987i
$310$	−2558.11	+	7462.93i	−0.468681	+	1.36731i
$311$	666.690	+	3136.53i	0.121558	+	0.571885i	0.996198	+	0.0871131i	$0.0277642\pi$
$311$	666.690	+	3136.53i	0.121558	+	0.571885i	−0.874640	+	0.484772i	$0.838903\pi$
$312$	−1621.92	−	30948.1i	−0.294305	−	5.61568i
$313$	4069.41	−	2642.71i	0.734878	−	0.477236i	−0.122146	−	0.992512i	$-0.538977\pi$
$313$	4069.41	−	2642.71i	0.734878	−	0.477236i	0.857024	+	0.515277i	$0.172311\pi$
$314$	621.497	−	1912.77i	0.111698	−	0.343770i
$315$	−2284.51	−	10983.2i	−0.408628	−	1.96456i
$316$	−5020.27	−	15450.8i	−0.893709	−	2.75055i
$317$	−2808.72	−	2274.46i	−0.497646	−	0.402985i	0.347369	−	0.937728i	$-0.387075\pi$
$317$	−2808.72	−	2274.46i	−0.497646	−	0.402985i	−0.845015	+	0.534743i	$0.820408\pi$
$318$	5085.88	+	1362.76i	0.896862	+	0.240313i
$319$	−3514.11	+	7892.83i	−0.616779	+	1.38531i
$320$	5546.57	+	970.076i	0.968947	+	0.169465i
$321$	−4215.75	+	5802.48i	−0.733022	+	1.00892i
$322$	2190.98	+	12857.7i	0.379188	+	2.22525i
$323$	125.930	−	64.1643i	0.0216932	−	0.0110532i
$324$	−10329.8	−	5963.90i	−1.77122	−	1.02262i
$325$	10707.0	+	2050.41i	1.82744	+	0.349958i
$326$	−7037.87	−	12189.9i	−1.19568	−	2.07098i
$327$	−2.92811	+	55.8717i	−0.000495183	+	0.00944865i
$328$	1243.86	−	197.009i	0.209393	−	0.0331646i
$329$	−3928.30	−	366.460i	−0.658280	−	0.0614091i
$330$	19400.5	+	13046.7i	3.23625	+	2.17635i
$331$	−306.052	−	2911.89i	−0.0508222	−	0.483541i	−0.990098	−	0.140378i	$-0.955168\pi$
$331$	−306.052	−	2911.89i	−0.0508222	−	0.483541i	0.939276	−	0.343163i	$-0.111498\pi$
$332$	−1944.27	+	7256.12i	−0.321403	+	1.19949i
$333$	−1681.64	−	4380.82i	−0.276737	−	0.720924i
$334$	−19456.9	−	4135.69i	−3.18753	−	0.677530i
$335$	−3157.88	+	1756.17i	−0.515024	+	0.286418i
$336$	7355.97	+	7979.84i	1.19435	+	1.29564i
$337$	101.949	+	51.9456i	0.0164793	+	0.00839660i	0.462211	−	0.886770i	$-0.347056\pi$
$337$	101.949	+	51.9456i	0.0164793	+	0.00839660i	−0.445731	+	0.895167i	$0.647056\pi$
$338$	−14445.3	−	22243.8i	−2.32462	−	3.57960i
$339$	18810.5	−	3998.29i	3.01370	−	0.640581i
$340$	285.674	+	670.417i	0.0455672	+	0.106937i
$341$	−1416.19	+	6662.63i	−0.224900	+	1.05807i
$342$	9127.71	+	1445.69i	1.44319	+	0.228578i
$343$	4331.44	−	4646.75i	0.681853	−	0.731489i
$344$	2258.13	+	3108.05i	0.353925	+	0.487136i
$345$	−10393.5	+	10064.8i	−1.62193	+	1.57063i
$346$	−8171.69	−	858.879i	−1.26969	−	0.133450i
$347$	−4849.42	−	5988.54i	−0.750232	−	0.926460i	0.248882	−	0.968534i	$-0.419937\pi$
$347$	−4849.42	−	5988.54i	−0.750232	−	0.926460i	−0.999114	+	0.0420740i	$0.986603\pi$
$348$	−26348.7	−	1380.88i	−4.05873	−	0.212709i
$349$	6249.45			0.958525			0.479262	−	0.877672i	$-0.340904\pi$
$349$	6249.45			0.958525			0.479262	+	0.877672i	$0.340904\pi$
$350$	−9944.59	+	5473.75i	−1.51875	+	0.835956i
$351$	−21356.1			−3.24760
$352$	−160.916	−	8.43326i	−0.0243661	−	0.00127697i
$353$	−4870.11	−	6014.08i	−0.734305	−	0.906791i	0.264028	−	0.964515i	$-0.414949\pi$
$353$	−4870.11	−	6014.08i	−0.734305	−	0.906791i	−0.998333	+	0.0577239i	$0.981616\pi$
$354$	26513.0	+	2786.63i	3.98066	+	0.418384i
$355$	−5751.68	−	3047.99i	−0.859908	−	0.455692i
$356$	4629.08	+	6371.38i	0.689160	+	0.948547i
$357$	167.790	−	656.853i	0.0248751	−	0.0973791i
$358$	4030.28	+	638.334i	0.594992	+	0.0942375i
$359$	1425.22	−	6705.15i	0.209528	−	0.985750i	−0.740131	−	0.672463i	$-0.765236\pi$
$359$	1425.22	−	6705.15i	0.209528	−	0.985750i	0.949658	−	0.313287i	$-0.101430\pi$
$360$	−5341.70	+	23284.8i	−0.782034	+	3.40894i
$361$	5525.41	−	1174.46i	0.805571	−	0.171229i
$362$	−1228.34	−	1891.48i	−0.178343	−	0.274624i
$363$	7300.39	+	3719.73i	1.05557	+	0.537838i
$364$	24736.9	+	7718.67i	3.56199	+	1.11145i
$365$	−1873.04	+	4031.33i	−0.268600	+	0.578109i
$366$	18365.3	+	3903.66i	2.62287	+	0.557508i
$367$	−4243.96	−	11055.9i	−0.603631	−	1.57251i	−0.805177	−	0.593034i	$-0.797930\pi$
$367$	−4243.96	−	11055.9i	−0.603631	−	1.57251i	0.201546	−	0.979479i	$-0.435403\pi$
$368$	2417.77	−	9023.22i	0.342486	−	1.27817i
$369$	−180.835	−	1720.53i	−0.0255120	−	0.242730i
$370$	−3737.58	+	2928.48i	−0.525156	+	0.411472i
$371$	−1276.41	+	1800.77i	−0.178619	+	0.251998i
$372$	−20545.4	+	3254.06i	−2.86351	+	0.453536i
$373$	−441.313	+	8420.76i	−0.0612610	+	1.16893i	0.779099	+	0.626900i	$0.215677\pi$
$373$	−441.313	+	8420.76i	−0.0612610	+	1.16893i	−0.840360	+	0.542028i	$0.817657\pi$
$374$	471.471	+	816.612i	0.0651850	+	0.112904i
$375$	−11243.0	−	5669.76i	−1.54823	−	0.780761i
$376$	7276.11	+	4200.87i	0.997971	+	0.576179i
$377$	−14184.1	+	7227.17i	−1.93772	+	0.987316i
$378$	17116.9	−	14195.8i	2.32909	−	1.93162i
$379$	1808.96	−	2489.82i	0.245172	−	0.337450i	−0.668641	−	0.743585i	$-0.733124\pi$
$379$	1808.96	−	2489.82i	0.245172	−	0.337450i	0.913813	+	0.406135i	$0.133124\pi$
$380$	−876.981	−	6177.82i	−0.118390	−	0.833988i
$381$	7451.79	−	16737.0i	1.00201	−	2.25056i
$382$	16178.8	+	4335.10i	2.16696	+	0.580636i
$383$	7376.76	+	5973.58i	0.984164	+	0.796960i	0.979173	−	0.203027i	$-0.0650780\pi$
$383$	7376.76	+	5973.58i	0.984164	+	0.796960i	0.00499090	+	0.999988i	$0.498411\pi$
$384$	6951.45	+	21394.3i	0.923801	+	2.84317i
$385$	−7954.10	+	5726.13i	−1.05293	+	0.758001i
$386$	2218.78	−	6828.70i	0.292572	−	0.900444i
$387$	4426.06	−	2874.32i	0.581368	−	0.377545i
$388$	446.035	+	8510.86i	0.0583608	+	1.11359i
$389$	−768.236	−	3614.27i	−0.100131	−	0.471081i	−0.999430	−	0.0337468i	$-0.989256\pi$
$389$	−768.236	−	3614.27i	−0.100131	−	0.471081i	0.899299	−	0.437334i	$-0.144077\pi$
$390$	12651.8	+	41177.8i	1.64269	+	5.34646i
$391$	−554.968	+	180.320i	−0.0717798	+	0.0233227i
$392$	−12512.3	+	5142.11i	−1.61216	+	0.662540i
$393$	−276.450	−	276.450i	−0.0354836	−	0.0354836i
$394$	−13521.2	+	1421.13i	−1.72890	+	0.181715i
$395$	6012.83	+	9592.89i	0.765920	+	1.22195i
$396$	−4300.45	+	40916.1i	−0.545722	+	5.19220i
$397$	−7558.28	−	2901.35i	−0.955514	−	0.366787i	−0.169870	−	0.985466i	$-0.554335\pi$
$397$	−7558.28	−	2901.35i	−0.955514	−	0.366787i	−0.785644	+	0.618679i	$0.787668\pi$
$398$	6952.53	+	13645.1i	0.875625	+	1.71851i
$399$	−2843.37	+	5060.72i	−0.356759	+	0.634969i
$400$	8108.65	−	589.633i	1.01358	−	0.0737041i
$401$	−3346.04	+	5795.52i	−0.416692	+	0.721731i	−0.995604	−	0.0936582i	$-0.970144\pi$
$401$	−3346.04	+	5795.52i	−0.416692	+	0.721731i	0.578913	+	0.815390i	$0.303477\pi$
$402$	−11974.7	−	7776.44i	−1.48568	−	0.964810i
$403$	−9753.56	+	7898.28i	−1.20561	+	0.976281i
$404$	7095.98	−	3159.33i	0.873856	−	0.389066i
$405$	7993.49	+	2280.09i	0.980740	+	0.279750i
$406$	6564.50	−	15221.0i	0.802440	−	1.86060i
$407$	−2898.84	+	2898.84i	−0.353047	+	0.353047i
$408$	−908.550	+	1121.97i	−0.110245	+	0.136141i
$409$	−10176.5	+	11302.1i	−1.23030	+	1.36639i	−0.322734	+	0.946490i	$0.604602\pi$
$409$	−10176.5	+	11302.1i	−1.23030	+	1.36639i	−0.907570	+	0.419901i	$0.862065\pi$
$410$	−1610.44	+	686.231i	−0.193985	+	0.0826598i
$411$	8471.15	−	7627.46i	1.01667	−	0.915413i
$412$	5669.35	−	11126.7i	0.677934	−	1.33052i
$413$	−4956.80	+	10016.3i	−0.590577	+	1.19339i
$414$	−36288.0	−	11790.7i	−4.30787	−	1.39971i
$415$	84.1004	−	5234.40i	0.00994777	−	0.619148i
$416$	−220.642	−	198.667i	−0.0260045	−	0.0234145i
$417$	9812.26	−	3766.57i	1.15230	−	0.442326i
$418$	−2089.65	−	7798.68i	−0.244517	−	0.912550i
$419$	2922.72	−	2123.48i	0.340774	−	0.247587i	−0.404214	−	0.914664i	$-0.632455\pi$
$419$	2922.72	−	2123.48i	0.340774	−	0.247587i	0.744988	+	0.667077i	$0.232455\pi$
$420$	−25030.5	−	16410.7i	−2.90801	−	1.90658i
$421$	−4616.53	−	3354.11i	−0.534432	−	0.388288i	0.287581	−	0.957756i	$-0.407149\pi$
$421$	−4616.53	−	3354.11i	−0.534432	−	0.388288i	−0.822013	+	0.569469i	$0.807149\pi$
$422$	4040.12	−	10524.9i	0.466042	−	1.21408i
$423$	6285.99	−	9679.57i	0.722542	−	1.11262i
$424$	4070.67	−	2350.20i	0.466248	−	0.269188i
$425$	−306.758	−	404.739i	−0.0350116	−	0.0461946i
$426$		−	25721.8i		−	2.92541i
$427$	−4209.26	+	6650.79i	−0.477050	+	0.753757i
$428$	1997.84	+	12613.9i	0.225629	+	1.42457i
$429$	15127.7	+	33977.5i	1.70250	+	3.82389i
$430$	−4095.54	−	3426.89i	−0.459313	−	0.384324i
$431$	9162.48	+	4079.40i	1.02399	+	0.455911i	0.848851	−	0.528632i	$-0.177295\pi$
$431$	9162.48	+	4079.40i	1.02399	+	0.455911i	0.175142	+	0.984543i	$0.443961\pi$
$432$	−15384.0	+	4122.14i	−1.71334	+	0.459089i
$433$	1186.22	−	7489.49i	0.131654	−	0.831229i	−0.830160	−	0.557525i	$-0.811751\pi$
$433$	1186.22	−	7489.49i	0.131654	−	0.831229i	0.961814	−	0.273704i	$-0.0882488\pi$
$434$	2567.32	−	12813.8i	0.283953	−	1.41724i
$435$	18044.5	−	3533.50i	1.98889	−	0.389467i
$436$	66.6609	+	74.0344i	0.00732220	+	0.00813212i
$437$	4989.51	−	261.489i	0.546180	−	0.0286241i
$438$	−17541.2	+	919.294i	−1.91358	+	0.100287i
$439$	−5490.89	−	6098.25i	−0.596961	−	0.662992i	0.366632	−	0.930366i	$-0.380511\pi$
$439$	−5490.89	−	6098.25i	−0.596961	−	0.662992i	−0.963593	+	0.267374i	$0.913844\pi$
$440$	20482.1	−	4010.82i	2.21920	−	0.434565i
$441$	6154.53	+	17534.4i	0.664564	+	1.89336i
$442$	−271.792	+	1716.03i	−0.0292485	+	0.184668i
$443$	12833.9	−	3438.84i	1.37643	−	0.368813i	0.506607	−	0.862177i	$-0.330900\pi$
$443$	12833.9	−	3438.84i	1.37643	−	0.368813i	0.869823	+	0.493364i	$0.164233\pi$
$444$	−11437.3	−	5092.19i	−1.22250	−	0.544290i
$445$	−4209.18	−	3521.97i	−0.448391	−	0.375186i
$446$	176.817	+	397.138i	0.0187725	+	0.0421638i
$447$	−2282.58	−	14411.7i	−0.241527	−	1.52494i
$448$	−9319.67	−	379.130i	−0.982841	−	0.0399826i
$449$			11553.6i			1.21436i	0.794563	+	0.607181i	$0.207700\pi$
$449$			11553.6i			1.21436i	−0.794563	+	0.607181i	$0.792300\pi$
$450$	−671.700	−	33200.4i	−0.0703650	−	3.47796i
$451$	−1308.92	+	755.708i	−0.136663	+	0.0789022i
$452$	18649.9	−	28718.3i	1.94075	−	2.98849i
$453$	7319.70	−	19068.5i	0.759182	−	1.97774i
$454$	−725.114	−	526.826i	−0.0749588	−	0.0544608i
$455$	−18029.5	−	1023.80i	−1.85766	−	0.105486i
$456$	10000.6	−	7265.88i	1.02702	−	0.746175i
$457$	−1560.02	−	5822.06i	−0.159681	−	0.595939i	−0.998659	−	0.0517732i	$-0.983513\pi$
$457$	−1560.02	−	5822.06i	−0.159681	−	0.595939i	0.838977	−	0.544166i	$-0.183154\pi$
$458$	214.389	−	82.2960i	0.0218727	−	0.00839616i
$459$	739.339	+	665.704i	0.0751838	+	0.0676958i
$460$	−413.864	+	25758.8i	−0.0419489	+	2.61089i
$461$	4358.33	+	1416.11i	0.440320	+	0.143069i	0.520783	−	0.853689i	$-0.325640\pi$
$461$	4358.33	+	1416.11i	0.440320	+	0.143069i	−0.0804631	+	0.996758i	$0.525640\pi$
$462$	−34710.2	−	17177.1i	−3.49538	−	1.72977i
$463$	−17.3044	+	33.9618i	−0.00173694	+	0.00340894i	−0.891873	−	0.452285i	$-0.850609\pi$
$463$	−17.3044	+	33.9618i	−0.00173694	+	0.00340894i	0.890136	+	0.455694i	$0.150609\pi$
$464$	−8822.65	+	7943.95i	−0.882718	+	0.794803i
$465$	13336.0	−	5682.65i	1.32998	−	0.566724i
$466$	5063.59	−	5623.68i	0.503361	−	0.559039i
$467$	581.452	−	718.034i	0.0576154	−	0.0711491i	−0.747524	−	0.664235i	$-0.768757\pi$
$467$	581.452	−	718.034i	0.0576154	−	0.0711491i	0.805139	+	0.593086i	$0.202091\pi$
$468$	−53602.3	+	53602.3i	−5.29438	+	5.29438i
$469$	4800.89	−	3574.63i	0.472675	−	0.351942i
$470$	−11230.7	−	3203.48i	−1.10219	−	0.314394i
$471$	−3376.06	+	1503.12i	−0.330277	+	0.147049i
$472$	18495.3	−	14977.2i	1.80363	−	1.46055i
$473$	−3866.81	−	2511.14i	−0.375890	−	0.244106i
$474$	−22368.6	+	38743.5i	−2.16756	+	3.75432i
$475$	1640.12	+	4027.23i	0.158430	+	0.389015i
$476$	−615.775	−	1038.30i	−0.0592942	−	0.0999801i
$477$	−2931.42	−	5753.23i	−0.281385	−	0.552248i
$478$	33463.3	+	12845.4i	3.20204	+	1.22915i
$479$	2094.33	−	19926.2i	0.199775	−	1.90073i	−0.193159	−	0.981167i	$-0.561873\pi$
$479$	2094.33	−	19926.2i	0.199775	−	1.90073i	0.392934	−	0.919567i	$-0.371460\pi$
$480$	182.130	+	290.571i	0.0173189	+	0.0276306i
$481$	−7512.29	+	789.574i	−0.712123	+	0.0748471i
$482$	−9497.09	−	9497.09i	−0.897470	−	0.897470i
$483$	14863.5	−	18800.5i	1.40023	−	1.77113i
$484$	13875.4	−	4508.38i	1.30310	−	0.423401i
$485$	−1744.35	−	5677.31i	−0.163313	−	0.531533i
$486$	88.7458	+	417.516i	0.00828311	+	0.0389690i
$487$	24.1091	+	460.029i	0.00224330	+	0.0428047i	0.999522	−	0.0309216i	$-0.00984422\pi$
$487$	24.1091	+	460.029i	0.00224330	+	0.0428047i	−0.997279	+	0.0737263i	$0.976511\pi$
$488$	14057.2	−	9128.83i	1.30397	−	0.846809i
$489$	−7992.39	+	24598.0i	−0.739117	+	2.27477i
$490$	15131.1	−	11163.9i	1.39501	−	1.02926i
$491$	5284.71	+	16264.7i	0.485734	+	1.49494i	0.830914	+	0.556400i	$0.187818\pi$
$491$	5284.71	+	16264.7i	0.485734	+	1.49494i	−0.345180	+	0.938537i	$0.612182\pi$
$492$	−3587.06	−	2904.75i	−0.328694	−	0.266171i
$493$	716.329	+	191.940i	0.0654399	+	0.0175346i
$494$	6050.76	−	13590.2i	0.551086	−	1.23776i
$495$	−4029.62	−	28386.3i	−0.365895	−	2.57752i
$496$	−5501.53	+	7572.20i	−0.498036	+	0.685488i
$497$	10111.1	+	3746.15i	0.912569	+	0.338105i
$498$	18431.7	−	9391.43i	1.65852	−	0.845060i
$499$	−786.343	−	453.996i	−0.0705442	−	0.0407287i	0.464313	−	0.885671i	$-0.346301\pi$
$499$	−786.343	−	453.996i	−0.0705442	−	0.0407287i	−0.534857	+	0.844942i	$0.679635\pi$
$500$	−21294.8	+	7017.24i	−1.90466	+	0.627641i
$501$	18275.2	+	31653.6i	1.62969	+	2.82271i
$502$	34.3999	−	656.389i	0.00305845	−	0.0583587i
$503$	7814.08	−	1237.63i	0.692669	−	0.109708i	0.199833	−	0.979830i	$-0.435960\pi$
$503$	7814.08	−	1237.63i	0.692669	−	0.109708i	0.492836	+	0.870122i	$0.335960\pi$
$504$	3675.73	−	39402.2i	0.324861	−	3.48237i
$505$	−4260.93	+	3338.54i	−0.375463	+	0.294184i
$506$	3484.39	+	33151.7i	0.306126	+	2.91260i
$507$	−12613.6	+	47074.5i	−1.10491	+	4.12357i
$508$	−11690.9	−	30456.0i	−1.02107	−	2.65997i
$509$	12141.7	+	2580.79i	1.05731	+	0.224738i	0.703584	−	0.710612i	$-0.251582\pi$
$509$	12141.7	+	2580.79i	1.05731	+	0.224738i	0.353724	+	0.935350i	$0.384915\pi$
$510$	845.576	−	1819.93i	0.0734171	−	0.158016i
$511$	2193.35	−	7029.26i	0.189878	−	0.608524i
$512$	18087.3	+	9215.92i	1.56123	+	0.795489i
$513$	−4639.50	−	7144.20i	−0.399296	−	0.614862i
$514$	−23794.6	+	5057.69i	−2.04189	+	0.434018i
$515$	−1945.89	+	8482.25i	−0.166497	+	0.725772i
$516$	2927.47	−	13772.7i	0.249757	−	1.17502i
$517$	−9959.09	−	1577.37i	−0.847196	−	0.134183i
$518$	5496.24	−	5626.40i	0.466198	−	0.477239i
$519$	8874.41	+	12214.6i	0.750565	+	1.03306i
$520$	33979.7	+	18006.9i	2.86559	+	1.51857i
$521$	12294.2	+	1292.17i	1.03382	+	0.108658i	0.606208	−	0.795306i	$-0.292690\pi$
$521$	12294.2	+	1292.17i	1.03382	+	0.108658i	0.427608	+	0.903964i	$0.359356\pi$
$522$	30516.6	+	37684.8i	2.55876	+	3.15981i
$523$	10090.1	+	528.801i	0.843614	+	0.0442119i	0.469245	−	0.883068i	$-0.344526\pi$
$523$	10090.1	+	528.801i	0.843614	+	0.0442119i	0.374369	+	0.927280i	$0.377859\pi$
$524$	−696.153			−0.0580374
$525$	19701.5	+	6849.43i	1.63780	+	0.569398i
$526$	−11904.1			−0.986773
$527$	583.865	+	30.5991i	0.0482610	+	0.00252925i
$528$	17455.7	+	21556.0i	1.43875	+	1.77671i
$529$	−8415.17	−	884.470i	−0.691639	−	0.0726942i
$530$	−4693.63	+	4545.19i	−0.384676	+	0.372510i
$531$	−19216.4	−	26449.1i	−1.57047	−	2.16157i
$532$	2791.84	+	9951.99i	0.227522	+	0.811040i
$533$	−2750.57	−	435.648i	−0.223528	−	0.0354034i
$534$	4508.99	−	21213.1i	0.365399	−	1.71907i
$535$	−3488.88	−	8187.68i	−0.281939	−	0.661652i
$536$	−12467.8	+	2650.11i	−1.00471	+	0.213559i
$537$	−4083.64	−	6288.26i	−0.328160	−	0.505323i
$538$	1896.77	+	966.454i	0.151999	+	0.0774476i
$539$	11807.5	−	11142.8i	0.943572	−	0.890450i
$540$	38386.2	−	21347.5i	3.05904	−	1.70121i
$541$	−6119.17	−	1300.67i	−0.486292	−	0.103365i	−0.0417601	−	0.999128i	$-0.513297\pi$
$541$	−6119.17	−	1300.67i	−0.486292	−	0.103365i	−0.444532	+	0.895763i	$0.646630\pi$
$542$	4304.50	+	11213.6i	0.341133	+	0.888681i
$543$	−1072.58	+	4002.92i	−0.0847676	+	0.316357i
$544$	1.44576	+	13.7555i	0.000113946	+	0.00108412i
$545$	−57.6106	−	38.7426i	−0.00452801	−	0.00304505i
$546$	−29784.8	−	64844.9i	−2.33456	−	5.08261i
$547$	−22813.7	+	3613.34i	−1.78326	+	0.282441i	−0.958925	−	0.283659i	$-0.908452\pi$
$547$	−22813.7	+	3613.34i	−1.78326	+	0.282441i	−0.824337	+	0.566100i	$0.808452\pi$
$548$	1062.29	−	20269.6i	0.0828078	−	1.58007i
$549$	−11512.6	−	19940.4i	−0.894981	−	1.55015i
$550$	−26259.1	+	12333.6i	−2.03580	+	0.956197i
$551$	−5499.10	−	3174.91i	−0.425172	−	0.245473i
$552$	−45474.2	+	23170.2i	−3.50636	+	1.78658i
$553$	−11972.1	−	14435.6i	−0.920627	−	1.11006i
$554$	7871.40	−	10834.1i	0.603653	−	0.830857i
$555$	8594.30	+	1503.11i	0.657312	+	0.114961i
$556$	7612.08	−	17097.0i	0.580619	−	1.30409i
$557$	1238.56	+	331.872i	0.0942184	+	0.0252457i	0.305620	−	0.952153i	$-0.401136\pi$
$557$	1238.56	+	331.872i	0.0942184	+	0.0252457i	−0.211402	+	0.977399i	$0.567803\pi$
$558$	29710.2	+	24058.9i	2.25400	+	1.82526i
$559$	−2625.20	−	8079.54i	−0.198630	−	0.611321i
$560$	−13185.3	+	2742.53i	−0.994963	+	0.206952i
$561$	535.415	−	1647.84i	0.0402945	−	0.124014i
$562$	−10106.1	+	6562.99i	−0.758542	+	0.492603i
$563$	−647.764	−	12360.1i	−0.0484902	−	0.925248i	−0.909254	−	0.416243i	$-0.863347\pi$
$563$	−647.764	−	12360.1i	−0.0484902	−	0.925248i	0.860763	−	0.509005i	$-0.169987\pi$
$564$	−6402.23	−	30120.1i	−0.477983	−	2.24873i
$565$	−7737.80	+	22573.9i	−0.576162	+	1.68087i
$566$	34886.3	−	11335.3i	2.59078	−	0.841795i
$567$	−13624.1	−	1994.72i	−1.00910	−	0.147743i
$568$	−16236.8	−	16236.8i	−1.19944	−	1.19944i
$569$	−16107.2	+	1692.93i	−1.18673	+	0.124730i	−0.677250	−	0.735753i	$-0.736828\pi$
$569$	−16107.2	+	1692.93i	−1.18673	+	0.124730i	−0.509479	+	0.860483i	$0.670162\pi$
$570$	−11026.6	+	13178.0i	−0.810266	+	0.968363i
$571$	−411.570	+	3915.83i	−0.0301641	+	0.286992i	0.969033	+	0.246931i	$0.0794220\pi$
$571$	−411.570	+	3915.83i	−0.0301641	+	0.286992i	−0.999197	+	0.0400613i	$0.987245\pi$
$572$	61828.0	+	23733.6i	4.51951	+	1.73488i
$573$	−13972.5	−	27422.5i	−1.01869	−	1.99929i
$574$	2494.16	−	1479.18i	0.181366	−	0.107561i
$575$	−4087.15	−	17481.9i	−0.296428	−	1.26790i
$576$	13642.9	−	23630.3i	0.986903	−	1.70937i
$577$	−3311.87	−	2150.75i	−0.238951	−	0.155177i	0.419609	−	0.907705i	$-0.362167\pi$
$577$	−3311.87	−	2150.75i	−0.238951	−	0.155177i	−0.658560	+	0.752528i	$0.728834\pi$
$578$	−18658.8	+	15109.6i	−1.34274	+	1.08733i
$579$	−12052.7	+	5366.21i	−0.865101	+	0.385168i
$580$	18270.8	−	27168.8i	1.30802	−	1.94504i
$581$	1007.32	+	8613.21i	0.0719287	+	0.615036i
$582$	16595.0	−	16595.0i	1.18193	−	1.18193i
$583$	−3550.08	+	4383.98i	−0.252194	+	0.311434i
$584$	−10492.5	+	11653.1i	−0.743462	+	0.825698i
$585$	27145.3	−	45319.8i	1.91850	−	3.20298i
$586$	−519.190	+	467.480i	−0.0365999	+	0.0329547i
$587$	−10221.7	+	20061.2i	−0.718730	+	1.41059i	0.185111	+	0.982718i	$0.440736\pi$
$587$	−10221.7	+	20061.2i	−0.718730	+	1.41059i	−0.903841	+	0.427869i	$0.859264\pi$
$588$	44690.8	+	21468.9i	3.13438	+	1.50572i
$589$	−4761.09	−	1546.97i	−0.333069	−	0.108221i
$590$	−19872.0	+	26447.4i	−1.38664	+	1.84546i
$591$	18565.1	+	16716.1i	1.29216	+	1.16346i
$592$	−5259.13	+	2018.79i	−0.365116	+	0.140155i
$593$	1428.47	+	5331.11i	0.0989209	+	0.369178i	0.997585	−	0.0694603i	$-0.0221277\pi$
$593$	1428.47	+	5331.11i	0.0989209	+	0.369178i	−0.898664	+	0.438638i	$0.855461\pi$
$594$	45978.8	−	33405.6i	3.17598	−	2.30749i
$595$	592.258	+	597.450i	0.0408071	+	0.0411648i
$596$	−21019.6	−	15271.7i	−1.44463	−	1.04958i
$597$	10084.4	−	26270.7i	0.691333	−	1.80098i
$598$	−33451.8	+	51511.3i	−2.28753	+	3.52249i
$599$	6205.52	−	3582.76i	0.423290	−	0.244387i	−0.273194	−	0.961959i	$-0.588080\pi$
$599$	6205.52	−	3582.76i	0.423290	−	0.244387i	0.696484	+	0.717572i	$0.254747\pi$
$600$	−32037.2	−	30766.6i	−2.17986	−	2.09340i
$601$		−	15331.0i		−	1.04054i	−0.854002	−	0.520270i	$-0.825831\pi$
$601$		−	15331.0i		−	1.04054i	0.854002	−	0.520270i	$-0.174169\pi$
$602$	7474.71	+	4730.71i	0.506057	+	0.320281i
$603$	2739.14	+	17294.2i	0.184985	+	1.16795i
$604$	−14792.8	−	33225.2i	−0.996541	−	2.23827i
$605$	−8614.76	+	5399.74i	−0.578909	+	0.362861i
$606$	−19540.5	−	8700.00i	−1.30987	−	0.583190i
$607$	−12669.2	+	3394.70i	−0.847161	+	0.226996i	−0.656186	−	0.754599i	$-0.727832\pi$
$607$	−12669.2	+	3394.70i	−0.847161	+	0.226996i	−0.190975	+	0.981595i	$0.561165\pi$
$608$	18.5262	−	116.970i	0.00123575	−	0.00780223i
$609$	−28855.7	+	9750.52i	−1.92002	+	0.648787i
$610$	−15865.9	+	17061.5i	−1.05310	+	1.13246i
$611$	−12431.7	−	13806.8i	−0.823129	−	0.914178i
$612$	3526.55	−	184.819i	0.232929	−	0.0122073i
$613$	−11735.9	+	615.050i	−0.773257	+	0.0405247i	−0.434883	−	0.900487i	$-0.643210\pi$
$613$	−11735.9	+	615.050i	−0.773257	+	0.0405247i	−0.338374	+	0.941012i	$0.609877\pi$
$614$	31396.1	+	34868.9i	2.06359	+	2.29185i
$615$	2917.12	+	1355.35i	0.191268	+	0.0888667i
$616$	−32753.7	+	11067.7i	−2.14234	+	0.723912i
$617$	−2743.15	+	17319.6i	−0.178987	+	1.13008i	0.720604	+	0.693347i	$0.243864\pi$
$617$	−2743.15	+	17319.6i	−0.178987	+	1.13008i	−0.899591	+	0.436733i	$0.856136\pi$
$618$	−33216.5	+	8900.34i	−2.16208	+	0.579327i
$619$	21604.1	+	9618.77i	1.40282	+	0.624574i	0.962006	−	0.273027i	$-0.0880248\pi$
$619$	21604.1	+	9618.77i	1.40282	+	0.624574i	0.440809	+	0.897601i	$0.354692\pi$
$620$	9636.28	−	23946.3i	0.624197	−	1.55114i
$621$	14305.1	+	32129.7i	0.924385	+	2.07620i
$622$	−2459.66	−	15529.7i	−0.158558	−	1.00110i
$623$	7682.10	+	4861.96i	0.494024	+	0.312665i
$624$			51107.4i			3.27874i
$625$	13204.6	−	8353.42i	0.845093	−	0.534619i
$626$	−20604.8	+	11896.2i	−1.31555	+	0.759532i
$627$	−8079.96	+	12442.0i	−0.514645	+	0.792484i
$628$	−2358.21	+	6143.34i	−0.149845	+	0.390360i
$629$	284.684	+	206.835i	0.0180463	+	0.0131114i
$630$	8367.95	+	54367.6i	0.529186	+	3.43819i
$631$	20104.4	−	14606.7i	1.26837	−	0.921526i	0.269235	−	0.963074i	$-0.413229\pi$
$631$	20104.4	−	14606.7i	1.26837	−	0.921526i	0.999136	+	0.0415484i	$0.0132291\pi$
$632$	10336.6	+	38576.7i	0.650581	+	2.42800i
$633$	−19339.3	+	7423.64i	−1.21432	+	0.466135i
$634$	13169.7	+	11858.1i	0.824979	+	0.742814i
$635$	13065.7	+	18604.8i	0.816531	+	1.16269i
$636$	−16384.2	−	5323.55i	−1.02150	−	0.331906i
$637$	29828.2	−	2264.21i	1.85531	−	0.140834i
$638$	19233.0	−	37746.8i	1.19348	−	2.34234i
$639$	−23441.4	+	21106.7i	−1.45122	+	1.30668i
$640$	−27207.6	−	6241.61i	−1.68043	−	0.385502i
$641$	13505.8	−	14999.7i	0.832212	−	0.924265i	−0.165871	−	0.986147i	$-0.553044\pi$
$641$	13505.8	−	14999.7i	0.832212	−	0.924265i	0.998083	+	0.0618823i	$0.0197103\pi$
$642$	22132.2	−	27331.0i	1.36057	−	1.68017i
$643$	22074.7	−	22074.7i	1.35387	−	1.35387i	0.472593	−	0.881281i	$-0.343318\pi$
$643$	22074.7	−	22074.7i	1.35387	−	1.35387i	0.881281	−	0.472593i	$-0.156682\pi$
$644$	−4957.08	−	42386.2i	−0.303317	−	2.59356i
$645$	356.057	+	9805.95i	0.0217360	+	0.598618i
$646$	−633.102	+	281.875i	−0.0385589	+	0.0171675i
$647$	16525.3	−	13381.9i	1.00414	−	0.813133i	0.0217057	−	0.999764i	$-0.493090\pi$
$647$	16525.3	−	13381.9i	1.00414	−	0.813133i	0.982430	+	0.186631i	$0.0597570\pi$
$648$	24591.7	+	15970.0i	1.49082	+	0.968152i
$649$	−14281.0	+	24735.5i	−0.863758	+	1.49607i
$650$	−51902.7	−	12787.9i	−3.13198	−	0.771664i
$651$	−20654.0	+	12249.1i	−1.24346	+	0.737448i
$652$	20908.1	+	41034.4i	1.25586	+	2.46477i
$653$	−24536.2	−	9418.57i	−1.47041	−	0.564437i	−0.514342	−	0.857585i	$-0.671964\pi$
$653$	−24536.2	−	9418.57i	−1.47041	−	0.564437i	−0.956067	+	0.293149i	$0.905297\pi$
$654$	28.6760	−	272.834i	0.00171456	−	0.0163129i
$655$	470.566	−	118.019i	0.0280710	−	0.00704029i
$656$	−2065.48	+	217.091i	−0.122932	+	0.0129207i
$657$	15231.7	+	15231.7i	0.904482	+	0.904482i
$658$	19141.6	+	2802.53i	1.13407	+	0.166040i
$659$	−72.2301	+	23.4690i	−0.00426963	+	0.00138729i	−0.311151	−	0.950360i	$-0.600715\pi$
$659$	−72.2301	+	23.4690i	−0.00426963	+	0.00138729i	0.306881	+	0.951748i	$0.400715\pi$
$660$	−61154.9	−	45950.6i	−3.60674	−	2.71004i
$661$	4952.54	+	23299.8i	0.291424	+	1.37104i	0.843447	+	0.537213i	$0.180523\pi$
$661$	4952.54	+	23299.8i	0.291424	+	1.37104i	−0.552022	+	0.833829i	$0.686144\pi$
$662$	751.378	+	14337.1i	0.0441135	+	0.841735i
$663$	2677.43	−	1738.75i	0.156837	−	0.101851i
$664$	5706.63	−	17563.2i	0.333525	−	1.02648i
$665$	−3574.31	−	6253.76i	−0.208430	−	0.364677i
$666$	7110.22	+	21883.0i	0.413687	+	1.27320i
$667$	20374.1	+	16498.6i	1.18274	+	0.957765i
$668$	62865.0	+	16844.6i	3.64120	+	0.975656i
$669$	324.899	−	729.735i	0.0187763	−	0.0421721i
$670$	15913.8	−	7789.02i	0.917615	−	0.449128i
$671$	−11823.8	+	16274.0i	−0.680256	+	0.936292i
$672$	−362.639	−	437.260i	−0.0208171	−	0.0251007i
$673$	−10492.9	+	5346.42i	−0.601000	+	0.306225i	−0.727892	−	0.685692i	$-0.759500\pi$
$673$	−10492.9	+	5346.42i	−0.601000	+	0.306225i	0.126892	+	0.991917i	$0.459500\pi$
$674$	−485.880	−	280.523i	−0.0277677	−	0.0160317i
$675$	−22328.2	+	20937.5i	−1.27320	+	1.19390i
$676$	43389.5	+	75152.8i	2.46868	+	4.27588i
$677$	878.238	−	16757.8i	0.0498573	−	0.951335i	−0.853138	−	0.521685i	$-0.825304\pi$
$677$	878.238	−	16757.8i	0.0498573	−	0.951335i	0.902996	−	0.429650i	$-0.141363\pi$
$678$	−93134.7	+	14751.1i	−5.27554	+	0.835564i
$679$	4106.52	+	8940.36i	0.232097	+	0.505301i
$680$	−615.058	−	1682.59i	−0.0346859	−	0.0948887i
$681$	172.150	+	1637.90i	0.00968692	+	0.0921649i
$682$	8644.39	−	32261.3i	0.485353	−	1.81136i
$683$	−928.769	−	2419.52i	−0.0520327	−	0.135550i	0.905101	−	0.425197i	$-0.139795\pi$
$683$	−928.769	−	2419.52i	−0.0520327	−	0.135550i	−0.957133	+	0.289647i	$0.906462\pi$
$684$	−29576.2	−	6286.62i	−1.65333	−	0.351425i
$685$	2718.27	+	13881.4i	0.151620	+	0.774278i
$686$	−22402.1	+	21642.1i	−1.24682	+	1.20452i
$687$	−375.971	−	191.567i	−0.0208794	−	0.0106386i
$688$	−3450.59	−	5313.44i	−0.191210	−	0.294438i
$689$	−10166.9	+	2161.05i	−0.562161	+	0.119491i
$690$	53476.3	−	46616.7i	2.95044	−	2.57198i
$691$	1849.94	−	8703.28i	0.101845	−	0.479144i	−0.897433	−	0.441151i	$-0.854570\pi$
$691$	1849.94	−	8703.28i	0.101845	−	0.479144i	0.999278	−	0.0379928i	$-0.0120964\pi$
$692$	26553.0	+	4205.58i	1.45866	+	0.231029i
$693$	12828.2	+	45728.1i	0.703177	+	2.50659i
$694$	22209.2	+	30568.4i	1.21477	+	1.67199i
$695$	−2246.93	+	12847.2i	−0.122635	+	0.701184i
$696$	64506.8	+	6779.94i	3.51311	+	0.369243i
$697$	81.6436	+	100.821i	0.00443683	+	0.00547903i
$698$	−30601.5	−	1603.76i	−1.65943	−	0.0869672i
$699$	−13905.0			−0.752411
$700$	33430.1	−	16182.0i	1.80506	−	0.873746i
$701$	−8579.73			−0.462271			−0.231135	−	0.972922i	$-0.574244\pi$
$701$	−8579.73			−0.462271			−0.231135	+	0.972922i	$0.574244\pi$
$702$	104574.	+	5480.49i	5.62235	+	0.294655i
$703$	−1896.14	−	2341.53i	−0.101727	−	0.125623i
$704$	−23707.6	−	2491.77i	−1.26920	−	0.133398i
$705$	9433.87	+	19274.4i	0.503972	+	1.02967i
$706$	22304.0	+	30698.8i	1.18898	+	1.63649i
$707$	6265.84	−	6414.22i	0.333311	−	0.341205i
$708$	−86151.2	−	13645.0i	−4.57311	−	0.724309i
$709$	2859.95	−	13455.0i	0.151492	−	0.712713i	−0.835178	−	0.549979i	$-0.814636\pi$
$709$	2859.95	−	13455.0i	0.151492	−	0.712713i	0.986670	−	0.162734i	$-0.0520311\pi$
$710$	27381.9	+	16401.0i	1.44736	+	0.866929i
$711$	53663.8	−	11406.6i	2.83059	−	0.601660i
$712$	−10544.4	−	16236.9i	−0.555011	−	0.854642i
$713$	18416.0	+	9383.43i	0.967300	+	0.492864i
$714$	−990.179	+	3173.34i	−0.0518999	+	0.166329i
$715$	−45816.3	−	5561.00i	−2.39641	−	0.290867i
$716$	−13059.2	−	2775.82i	−0.681627	−	0.144884i
$717$	−23603.1	−	61488.3i	−1.22939	−	3.20268i
$718$	−8699.56	+	32467.2i	−0.452179	+	1.68756i
$719$	−3778.49	−	35950.0i	−0.195986	−	1.86468i	−0.444133	−	0.895961i	$-0.646488\pi$
$719$	−3778.49	−	35950.0i	−0.195986	−	1.86468i	0.248147	−	0.968722i	$-0.420178\pi$
$720$	10806.7	−	37886.0i	0.559366	−	1.96101i
$721$	1339.00	−	14353.5i	0.0691637	−	0.741406i
$722$	−27357.5	+	4333.01i	−1.41017	+	0.223349i
$723$	−1291.60	+	24645.2i	−0.0664387	+	1.26773i
$724$	3689.58	+	6390.53i	0.189395	+	0.328042i
$725$	−7744.21	+	21462.2i	−0.396707	+	1.09943i
$726$	−34793.0	−	20087.8i	−1.77864	−	1.02690i
$727$	26031.9	−	13263.9i	1.32802	−	0.676658i	0.361286	−	0.932455i	$-0.382338\pi$
$727$	26031.9	−	13263.9i	1.32802	−	0.676658i	0.966731	+	0.255797i	$0.0823377\pi$
$728$	−59734.5	−	22131.5i	−3.04108	−	1.12671i
$729$	−11338.1	+	15605.6i	−0.576036	+	0.792845i
$730$	10206.2	−	19259.5i	0.517463	−	0.976472i
$731$	−160.969	+	361.542i	−0.00814452	+	0.0182929i
$732$	−59338.1	−	15899.6i	−2.99617	−	0.802822i
$733$	21423.5	+	17348.4i	1.07953	+	0.874187i	0.992528	−	0.122021i	$-0.0389375\pi$
$733$	21423.5	+	17348.4i	1.07953	+	0.874187i	0.0870036	+	0.996208i	$0.472271\pi$
$734$	17944.1	+	55226.2i	0.902354	+	2.77716i
$735$	−33848.4	−	6935.51i	−1.69867	−	0.348055i
$736$	−151.095	+	465.024i	−0.00756718	+	0.0232894i
$737$	12829.4	−	8331.53i	0.641219	−	0.416412i
$738$	443.962	+	8471.30i	0.0221443	+	0.422538i
$739$	−5999.16	−	28223.8i	−0.298623	−	1.40491i	−0.829994	−	0.557773i	$-0.811656\pi$
$739$	−5999.16	−	28223.8i	−0.298623	−	1.40491i	0.531370	−	0.847140i	$-0.321677\pi$
$740$	12713.6	−	8928.47i	0.631569	−	0.443537i
$741$	−25997.2	+	8446.99i	−1.28884	+	0.418769i
$742$	6712.27	−	8490.21i	0.332096	−	0.420061i
$743$	−14244.0	−	14244.0i	−0.703314	−	0.703314i	0.261806	−	0.965120i	$-0.415682\pi$
$743$	−14244.0	−	14244.0i	−0.703314	−	0.703314i	−0.965120	+	0.261806i	$0.915682\pi$
$744$	50856.3	−	5345.21i	2.50603	−	0.263394i
$745$	16797.3	+	6759.43i	0.826045	+	0.332411i
$746$	4321.94	−	41120.5i	0.212114	−	2.01813i
$747$	−23683.5	−	9091.23i	−1.16002	−	0.445289i
$748$	−1400.64	−	2748.92i	−0.0684661	−	0.134372i
$749$	7520.35	+	12680.6i	0.366872	+	0.618610i
$750$	53598.4	+	30648.2i	2.60951	+	1.49215i
$751$	−16788.6	+	29078.6i	−0.815743	+	1.41291i	0.0930502	+	0.995661i	$0.470338\pi$
$751$	−16788.6	+	29078.6i	−0.815743	+	1.41291i	−0.908793	+	0.417247i	$0.862995\pi$
$752$	−11620.2	−	7546.26i	−0.563492	−	0.365936i
$753$	−938.604	+	760.067i	−0.0454245	+	0.0367840i
$754$	71309.7	−	31749.1i	3.44422	−	1.53347i
$755$	15631.9	+	19950.8i	0.753513	+	0.961699i
$756$	−58358.3	+	43452.1i	−2.80750	+	2.09040i
$757$	18598.1	−	18598.1i	0.892946	−	0.892946i	−0.101853	−	0.994799i	$-0.532477\pi$
$757$	18598.1	−	18598.1i	0.892946	−	0.892946i	0.994799	+	0.101853i	$0.0324772\pi$
$758$	−9496.85	+	11727.6i	−0.455067	+	0.561961i
$759$	40985.1	−	45518.5i	1.96003	−	2.17684i
$760$	1358.11	+	15279.0i	0.0648208	+	0.729248i
$761$	−30365.0	+	27340.7i	−1.44642	+	1.30237i	−0.569276	+	0.822147i	$0.692776\pi$
$761$	−30365.0	+	27340.7i	−1.44642	+	1.30237i	−0.877148	+	0.480220i	$0.840557\pi$
$762$	−40784.1	+	80043.3i	−1.93891	+	3.80533i
$763$	103.074	+	51.0083i	0.00489058	+	0.00242021i
$764$	−52120.1	−	16934.9i	−2.46811	−	0.801939i
$765$	−2352.45	+	722.786i	−0.111180	+	0.0341600i
\(766\

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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	175.x (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.89667 - 0.256624i) q^{2} +(5.67011 + 7.00201i) q^{3} +(15.9554 + 1.67698i) q^{4} +(-11.0694 + 1.57137i) q^{5} +(-25.9678 - 35.7416i) q^{6} +(17.8319 - 5.00240i) q^{7} +(-38.9538 - 6.16967i) q^{8} +(-11.2643 + 52.9944i) q^{9} +O(q^{10})\)	\(q+(-4.89667 - 0.256624i) q^{2} +(5.67011 + 7.00201i) q^{3} +(15.9554 + 1.67698i) q^{4} +(-11.0694 + 1.57137i) q^{5} +(-25.9678 - 35.7416i) q^{6} +(17.8319 - 5.00240i) q^{7} +(-38.9538 - 6.16967i) q^{8} +(-11.2643 + 52.9944i) q^{9} +(54.6063 - 4.85381i) q^{10} +(46.2983 - 9.84101i) q^{11} +(78.7267 + 121.228i) q^{12} +(77.7071 + 39.5937i) q^{13} +(-88.6007 + 19.9190i) q^{14} +(-73.7673 - 68.5980i) q^{15} +(63.6192 + 13.5227i) q^{16} +(-1.45598 - 3.79297i) q^{17} +(68.7573 - 256.606i) q^{18} +(3.63625 + 34.5966i) q^{19} +(-179.251 + 6.50867i) q^{20} +(136.136 + 96.4948i) q^{21} +(-229.233 + 36.3070i) q^{22} +(7.51682 - 143.429i) q^{23} +(-177.672 - 307.738i) q^{24} +(120.062 - 34.7880i) q^{25} +(-370.346 - 213.819i) q^{26} +(-218.184 + 111.171i) q^{27} +(292.904 - 49.9115i) q^{28} +(-107.290 + 147.672i) q^{29} +(343.610 + 354.832i) q^{30} +(-58.5321 + 131.465i) q^{31} +(-3.28835 - 0.881111i) q^{32} +(331.424 + 268.382i) q^{33} +(6.15611 + 18.9466i) q^{34} +(-189.527 + 83.3938i) q^{35} +(-268.597 + 826.656i) q^{36} +(-72.6390 + 47.1723i) q^{37} +(-8.92723 - 170.342i) q^{38} +(163.372 + 768.607i) q^{39} +(440.888 + 7.08370i) q^{40} +(-30.3689 + 9.86746i) q^{41} +(-641.849 - 507.439i) q^{42} +(-68.8788 - 68.8788i) q^{43} +(755.211 - 79.3758i) q^{44} +(41.4151 - 604.315i) q^{45} +(-73.6149 + 700.399i) q^{46} +(-198.880 - 76.3428i) q^{47} +(266.042 + 522.137i) q^{48} +(292.952 - 178.404i) q^{49} +(-596.830 + 139.535i) q^{50} +(18.3028 - 31.7014i) q^{51} +(1173.45 + 762.047i) q^{52} +(-92.6207 + 75.0028i) q^{53} +(1096.91 - 488.374i) q^{54} +(-497.029 + 181.685i) q^{55} +(-725.483 + 84.8454i) q^{56} +(-221.628 + 221.628i) q^{57} +(563.262 - 695.570i) q^{58} +(-403.775 + 448.437i) q^{59} +(-1061.95 - 1218.21i) q^{60} +(-315.828 + 284.372i) q^{61} +(320.350 - 628.722i) q^{62} +(64.2352 + 1001.34i) q^{63} +(-478.982 - 155.631i) q^{64} +(-922.384 - 316.171i) q^{65} +(-1554.00 - 1399.23i) q^{66} +(301.722 - 115.820i) q^{67} +(-16.8701 - 62.9599i) q^{68} +(1046.92 - 760.629i) q^{69} +(949.453 - 359.715i) q^{70} +(471.023 + 342.218i) q^{71} +(765.746 - 1994.84i) q^{72} +(216.544 - 333.449i) q^{73} +(367.795 - 212.347i) q^{74} +(924.349 + 643.420i) q^{75} +558.101i q^{76} +(776.357 - 407.086i) q^{77} +(-602.739 - 3805.54i) q^{78} +(-411.874 - 925.085i) q^{79} +(-725.473 - 49.7184i) q^{80} +(-679.200 - 302.399i) q^{81} +(151.239 - 40.5244i) q^{82} +(-73.2488 + 462.475i) q^{83} +(2010.28 + 1767.91i) q^{84} +(22.0770 + 39.6978i) q^{85} +(319.601 + 354.953i) q^{86} +(-1642.35 + 86.0720i) q^{87} +(-1864.21 + 97.6991i) q^{88} +(328.469 + 364.801i) q^{89} +(-357.878 + 2948.50i) q^{90} +(1583.73 + 317.309i) q^{91} +(360.462 - 2275.87i) q^{92} +(-1252.40 + 335.581i) q^{93} +(954.259 + 424.863i) q^{94} +(-94.6150 - 377.249i) q^{95} +(-12.4758 - 28.0211i) q^{96} +(83.1014 + 524.682i) q^{97} +(-1480.27 + 798.409i) q^{98} +2564.40i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 928 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 24 q^{7} + 84 q^{8} - 10 q^{9}+O(q^{10}) \) 928 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 24 * q^7 + 84 * q^8 - 10 * q^9	\( 928 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 24 q^{7} + 84 q^{8} - 10 q^{9} - 96 q^{10} - 6 q^{11} - 72 q^{12} - 20 q^{14} - 368 q^{15} - 1670 q^{16} + 120 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} - 880 q^{22} + 296 q^{23} + 32 q^{25} - 48 q^{26} + 226 q^{28} - 200 q^{29} - 38 q^{30} - 18 q^{31} - 964 q^{32} - 1092 q^{33} + 288 q^{35} + 7400 q^{36} - 392 q^{37} + 5424 q^{38} + 2430 q^{39} + 2172 q^{40} - 2098 q^{42} + 1560 q^{43} - 10 q^{44} - 4224 q^{45} - 6 q^{46} + 96 q^{47} + 6232 q^{50} - 16 q^{51} - 8928 q^{52} - 2384 q^{53} - 30 q^{54} + 244 q^{56} + 1556 q^{57} + 640 q^{58} + 4890 q^{59} + 3676 q^{60} - 18 q^{61} + 224 q^{63} - 9700 q^{64} - 1116 q^{65} - 2610 q^{66} - 2404 q^{67} - 13614 q^{68} - 1700 q^{70} - 24 q^{71} - 518 q^{72} - 4200 q^{73} - 16104 q^{75} - 722 q^{77} - 356 q^{78} - 10 q^{79} + 6414 q^{80} - 6810 q^{81} + 1692 q^{82} + 20620 q^{84} + 2712 q^{85} - 6 q^{86} + 9102 q^{87} + 1650 q^{88} + 20370 q^{89} - 12 q^{91} + 1612 q^{92} - 4604 q^{93} - 30 q^{94} + 1652 q^{95} - 2610 q^{96} - 19478 q^{98}+O(q^{100}) \) 928 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 24 * q^7 + 84 * q^8 - 10 * q^9 - 96 * q^10 - 6 * q^11 - 72 * q^12 - 20 * q^14 - 368 * q^15 - 1670 * q^16 + 120 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 - 880 * q^22 + 296 * q^23 + 32 * q^25 - 48 * q^26 + 226 * q^28 - 200 * q^29 - 38 * q^30 - 18 * q^31 - 964 * q^32 - 1092 * q^33 + 288 * q^35 + 7400 * q^36 - 392 * q^37 + 5424 * q^38 + 2430 * q^39 + 2172 * q^40 - 2098 * q^42 + 1560 * q^43 - 10 * q^44 - 4224 * q^45 - 6 * q^46 + 96 * q^47 + 6232 * q^50 - 16 * q^51 - 8928 * q^52 - 2384 * q^53 - 30 * q^54 + 244 * q^56 + 1556 * q^57 + 640 * q^58 + 4890 * q^59 + 3676 * q^60 - 18 * q^61 + 224 * q^63 - 9700 * q^64 - 1116 * q^65 - 2610 * q^66 - 2404 * q^67 - 13614 * q^68 - 1700 * q^70 - 24 * q^71 - 518 * q^72 - 4200 * q^73 - 16104 * q^75 - 722 * q^77 - 356 * q^78 - 10 * q^79 + 6414 * q^80 - 6810 * q^81 + 1692 * q^82 + 20620 * q^84 + 2712 * q^85 - 6 * q^86 + 9102 * q^87 + 1650 * q^88 + 20370 * q^89 - 12 * q^91 + 1612 * q^92 - 4604 * q^93 - 30 * q^94 + 1652 * q^95 - 2610 * q^96 - 19478 * q^98

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