LMFDB - Embedded newform 175.4.x.a.103.5

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			103.5
Character	$\chi$	$=$	175.103
Dual form			175.4.x.a.17.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.92278 - 0.257992i) q^{2} +(6.01798 + 7.43159i) q^{3} +(16.2110 + 1.70384i) q^{4} +(10.4321 + 4.02129i) q^{5} +(-27.7079 - 38.1366i) q^{6} +(-17.0686 - 7.18780i) q^{7} +(-40.4127 - 6.40074i) q^{8} +(-13.3988 + 63.0363i) q^{9} +O(q^{10})$	\(q+(-4.92278 - 0.257992i) q^{2} +(6.01798 + 7.43159i) q^{3} +(16.2110 + 1.70384i) q^{4} +(10.4321 + 4.02129i) q^{5} +(-27.7079 - 38.1366i) q^{6} +(-17.0686 - 7.18780i) q^{7} +(-40.4127 - 6.40074i) q^{8} +(-13.3988 + 63.0363i) q^{9} +(-50.3175 - 22.4873i) q^{10} +(-36.2070 + 7.69603i) q^{11} +(84.8951 + 130.727i) q^{12} +(-55.0114 - 28.0297i) q^{13} +(82.1703 + 39.7875i) q^{14} +(32.8957 + 101.727i) q^{15} +(69.7388 + 14.8234i) q^{16} +(-22.1540 - 57.7131i) q^{17} +(82.2220 - 306.857i) q^{18} +(10.8269 + 103.011i) q^{19} +(162.263 + 82.9638i) q^{20} +(-49.3015 - 170.102i) q^{21} +(180.224 - 28.5447i) q^{22} +(1.82815 - 34.8831i) q^{23} +(-195.635 - 338.850i) q^{24} +(92.6584 + 83.9012i) q^{25} +(263.577 + 152.176i) q^{26} +(-319.043 + 162.560i) q^{27} +(-264.451 - 145.603i) q^{28} +(-31.4695 + 43.3140i) q^{29} +(-135.694 - 509.267i) q^{30} +(-118.998 + 267.273i) q^{31} +(-23.3058 - 6.24476i) q^{32} +(-275.087 - 222.761i) q^{33} +(94.1696 + 289.824i) q^{34} +(-149.157 - 143.622i) q^{35} +(-324.611 + 999.051i) q^{36} +(-39.8493 + 25.8784i) q^{37} +(-26.7225 - 509.895i) q^{38} +(-122.752 - 577.504i) q^{39} +(-395.851 - 229.285i) q^{40} +(33.6968 - 10.9488i) q^{41} +(198.815 + 850.096i) q^{42} +(155.660 + 155.660i) q^{43} +(-600.064 + 63.0692i) q^{44} +(-393.265 + 603.722i) q^{45} +(-17.9991 + 171.250i) q^{46} +(-161.941 - 62.1633i) q^{47} +(309.525 + 607.477i) q^{48} +(239.671 + 245.371i) q^{49} +(-434.491 - 436.932i) q^{50} +(295.578 - 511.956i) q^{51} +(-844.030 - 548.120i) q^{52} +(33.8061 - 27.3756i) q^{53} +(1612.52 - 717.938i) q^{54} +(-408.664 - 65.3129i) q^{55} +(643.779 + 399.730i) q^{56} +(-700.382 + 700.382i) q^{57} +(166.092 - 205.106i) q^{58} +(270.639 - 300.575i) q^{59} +(359.945 + 1705.15i) q^{60} +(323.167 - 290.981i) q^{61} +(654.754 - 1285.03i) q^{62} +(681.790 - 979.631i) q^{63} +(-429.340 - 139.501i) q^{64} +(-461.170 - 513.626i) q^{65} +(1296.72 + 1167.57i) q^{66} +(161.366 - 61.9427i) q^{67} +(-260.804 - 973.334i) q^{68} +(270.239 - 196.340i) q^{69} +(697.213 + 745.498i) q^{70} +(-258.285 - 187.655i) q^{71} +(944.961 - 2461.71i) q^{72} +(-426.964 + 657.467i) q^{73} +(202.846 - 117.113i) q^{74} +(-65.9027 + 1193.52i) q^{75} +1688.36i q^{76} +(673.318 + 128.888i) q^{77} +(455.291 + 2874.59i) q^{78} +(350.279 + 786.739i) q^{79} +(667.914 + 435.080i) q^{80} +(-1538.50 - 684.986i) q^{81} +(-168.707 + 45.2048i) q^{82} +(-27.2857 + 172.275i) q^{83} +(-509.397 - 2841.53i) q^{84} +(0.968099 - 691.158i) q^{85} +(-726.122 - 806.440i) q^{86} +(-511.275 + 26.7948i) q^{87} +(1512.48 - 79.2659i) q^{88} +(426.238 + 473.385i) q^{89} +(2091.71 - 2870.53i) q^{90} +(737.493 + 873.837i) q^{91} +(89.0715 - 562.375i) q^{92} +(-2702.39 + 724.104i) q^{93} +(781.162 + 347.796i) q^{94} +(-301.291 + 1118.17i) q^{95} +(-93.8452 - 210.780i) q^{96} +(234.636 + 1481.43i) q^{97} +(-1116.54 - 1269.74i) q^{98} -2385.47i 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 $

$2$	−4.92278	−	0.257992i	−1.74046	−	0.0912138i	−0.844560	−	0.535461i	$-0.820138\pi$
$2$	−4.92278	−	0.257992i	−1.74046	−	0.0912138i	−0.895904	+	0.444247i	$0.853471\pi$
$3$	6.01798	+	7.43159i	1.15816	+	1.43021i	0.883352	+	0.468711i	$0.155281\pi$
$3$	6.01798	+	7.43159i	1.15816	+	1.43021i	0.274809	+	0.961499i	$0.411385\pi$
$4$	16.2110	+	1.70384i	2.02637	+	0.212980i
$5$	10.4321	+	4.02129i	0.933078	+	0.359675i
$5$	10.4321	+	4.02129i	0.933078	+	0.359675i
$6$	−27.7079	−	38.1366i	−1.88528	−	2.59487i
$7$	−17.0686	−	7.18780i	−0.921615	−	0.388105i
$7$	−17.0686	−	7.18780i	−0.921615	−	0.388105i
$8$	−40.4127	−	6.40074i	−1.78601	−	0.282876i
$9$	−13.3988	+	63.0363i	−0.496251	+	2.33468i
$10$	−50.3175	−	22.4873i	−1.59118	−	0.711111i
$11$	−36.2070	+	7.69603i	−0.992438	+	0.210949i	−0.675390	−	0.737460i	$-0.736025\pi$
$11$	−36.2070	+	7.69603i	−0.992438	+	0.210949i	−0.317048	+	0.948410i	$0.602691\pi$
$12$	84.8951	+	130.727i	2.04226	+	3.14480i
$13$	−55.0114	−	28.0297i	−1.17365	−	0.598003i	−0.245202	−	0.969472i	$-0.578854\pi$
$13$	−55.0114	−	28.0297i	−1.17365	−	0.598003i	−0.928445	+	0.371469i	$0.878854\pi$
$14$	82.1703	+	39.7875i	1.56864	+	0.759546i
$15$	32.8957	+	101.727i	0.566243	+	1.75106i
$16$	69.7388	+	14.8234i	1.08967	+	0.231616i
$17$	−22.1540	−	57.7131i	−0.316067	−	0.823382i	−0.995937	−	0.0900498i	$-0.971297\pi$
$17$	−22.1540	−	57.7131i	−0.316067	−	0.823382i	0.679871	−	0.733332i	$-0.262036\pi$
$18$	82.2220	−	306.857i	1.07666	−	4.01816i
$19$	10.8269	+	103.011i	0.130730	+	1.24381i	0.841449	+	0.540336i	$0.181703\pi$
$19$	10.8269	+	103.011i	0.130730	+	1.24381i	−0.710719	+	0.703476i	$0.751630\pi$
$20$	162.263	+	82.9638i	1.81416	+	0.927563i
$21$	−49.3015	−	170.102i	−0.512308	−	1.76759i
$22$	180.224	−	28.5447i	1.74654	−	0.276625i
$23$	1.82815	−	34.8831i	0.0165737	−	0.316245i	−0.977745	−	0.209798i	$-0.932719\pi$
$23$	1.82815	−	34.8831i	0.0165737	−	0.316245i	0.994318	−	0.106447i	$-0.0339474\pi$
$24$	−195.635	−	338.850i	−1.66391	−	2.88198i
$25$	92.6584	+	83.9012i	0.741267	+	0.671210i
$26$	263.577	+	152.176i	1.98814	+	1.14786i
$27$	−319.043	+	162.560i	−2.27407	+	1.15870i
$28$	−264.451	−	145.603i	−1.78488	−	0.982731i
$29$	−31.4695	+	43.3140i	−0.201508	+	0.277352i	−0.897797	−	0.440410i	$-0.854833\pi$
$29$	−31.4695	+	43.3140i	−0.201508	+	0.277352i	0.696289	+	0.717762i	$0.254833\pi$
$30$	−135.694	−	509.267i	−0.825805	−	3.09930i
$31$	−118.998	+	267.273i	−0.689440	+	1.54851i	0.140148	+	0.990131i	$0.455242\pi$
$31$	−118.998	+	267.273i	−0.689440	+	1.54851i	−0.829588	+	0.558376i	$0.811425\pi$
$32$	−23.3058	−	6.24476i	−0.128747	−	0.0344978i
$33$	−275.087	−	222.761i	−1.45110	−	1.17508i
$34$	94.1696	+	289.824i	0.474999	+	1.46190i
$35$	−149.157	−	143.622i	−0.720347	−	0.693614i
$36$	−324.611	+	999.051i	−1.50283	+	4.62524i
$37$	−39.8493	+	25.8784i	−0.177059	+	0.114984i	−0.630126	−	0.776493i	$-0.716997\pi$
$37$	−39.8493	+	25.8784i	−0.177059	+	0.114984i	0.453067	+	0.891477i	$0.350330\pi$
$38$	−26.7225	−	509.895i	−0.114078	−	2.17673i
$39$	−122.752	−	577.504i	−0.504003	−	2.37115i
$40$	−395.851	−	229.285i	−1.56474	−	0.906327i
$41$	33.6968	−	10.9488i	0.128355	−	0.0417051i	−0.244135	−	0.969741i	$-0.578504\pi$
$41$	33.6968	−	10.9488i	0.128355	−	0.0417051i	0.372490	+	0.928036i	$0.378504\pi$
$42$	198.815	+	850.096i	0.730424	+	3.12316i
$43$	155.660	+	155.660i	0.552046	+	0.552046i	0.927031	−	0.374985i	$-0.122352\pi$
$43$	155.660	+	155.660i	0.552046	+	0.552046i	−0.374985	+	0.927031i	$0.622352\pi$
$44$	−600.064	+	63.0692i	−2.05598	+	0.216092i
$45$	−393.265	+	603.722i	−1.30277	+	1.99995i
$46$	−17.9991	+	171.250i	−0.0576919	+	0.548902i
$47$	−161.941	−	62.1633i	−0.502586	−	0.192925i	0.0938487	−	0.995586i	$-0.470083\pi$
$47$	−161.941	−	62.1633i	−0.502586	−	0.192925i	−0.596434	+	0.802662i	$0.703416\pi$
$48$	309.525	+	607.477i	0.930751	+	1.82670i
$49$	239.671	+	245.371i	0.698749	+	0.715366i
$50$	−434.491	−	436.932i	−1.22893	−	1.23583i
$51$	295.578	−	511.956i	0.811553	−	1.40565i
$52$	−844.030	−	548.120i	−2.25088	−	1.46174i
$53$	33.8061	−	27.3756i	0.0876155	−	0.0709496i	−0.584512	−	0.811385i	$-0.698714\pi$
$53$	33.8061	−	27.3756i	0.0876155	−	0.0709496i	0.672127	+	0.740435i	$0.265381\pi$
$54$	1612.52	−	717.938i	4.06362	−	1.80924i
$55$	−408.664	−	65.3129i	−1.00189	−	0.160123i
$56$	643.779	+	399.730i	1.53623	+	0.953860i
$57$	−700.382	+	700.382i	−1.62751	+	1.62751i
$58$	166.092	−	205.106i	0.376016	−	0.464341i
$59$	270.639	−	300.575i	0.597190	−	0.663247i	−0.366454	−	0.930436i	$-0.619428\pi$
$59$	270.639	−	300.575i	0.597190	−	0.663247i	0.963644	+	0.267189i	$0.0860948\pi$
$60$	359.945	+	1705.15i	0.774478	+	3.66890i
$61$	323.167	−	290.981i	0.678317	−	0.610759i	−0.256223	−	0.966618i	$-0.582478\pi$
$61$	323.167	−	290.981i	0.678317	−	0.610759i	0.934540	+	0.355858i	$0.115811\pi$
$62$	654.754	−	1285.03i	1.34119	−	2.63223i
$63$	681.790	−	979.631i	1.36345	−	1.95908i
$64$	−429.340	−	139.501i	−0.838555	−	0.272463i
$65$	−461.170	−	513.626i	−0.880017	−	0.980115i
$66$	1296.72	+	1167.57i	2.41841	+	2.17755i
$67$	161.366	−	61.9427i	0.294239	−	0.112948i	−0.206771	−	0.978389i	$-0.566295\pi$
$67$	161.366	−	61.9427i	0.294239	−	0.112948i	0.501010	+	0.865442i	$0.332962\pi$
$68$	−260.804	−	973.334i	−0.465105	−	1.73579i
$69$	270.239	−	196.340i	0.471492	−	0.342559i
$70$	697.213	+	745.498i	1.19047	+	1.27292i
$71$	−258.285	−	187.655i	−0.431729	−	0.313669i	0.350611	−	0.936521i	$-0.385974\pi$
$71$	−258.285	−	187.655i	−0.431729	−	0.313669i	−0.782340	+	0.622852i	$0.785974\pi$
$72$	944.961	−	2461.71i	1.54673	−	4.02937i
$73$	−426.964	+	657.467i	−0.684553	+	1.05412i	0.310085	+	0.950709i	$0.399642\pi$
$73$	−426.964	+	657.467i	−0.684553	+	1.05412i	−0.994639	+	0.103411i	$0.967024\pi$
$74$	202.846	−	117.113i	0.318653	−	0.183974i
$75$	−65.9027	+	1193.52i	−0.101464	+	1.83754i
$76$			1688.36i			2.54827i
$77$	673.318	+	128.888i	0.996516	+	0.190756i
$78$	455.291	+	2874.59i	0.660917	+	4.17287i
$79$	350.279	+	786.739i	0.498853	+	1.12044i	0.971034	+	0.238941i	$0.0768004\pi$
$79$	350.279	+	786.739i	0.498853	+	1.12044i	−0.472181	+	0.881502i	$0.656533\pi$
$80$	667.914	+	435.080i	0.933438	+	0.608042i
$81$	−1538.50	−	684.986i	−2.11043	−	0.939624i
$82$	−168.707	+	45.2048i	−0.227202	+	0.0608785i
$83$	−27.2857	+	172.275i	−0.0360842	+	0.227827i	−0.999139	−	0.0414771i	$-0.986794\pi$
$83$	−27.2857	+	172.275i	−0.0360842	+	0.227827i	0.963055	+	0.269304i	$0.0867937\pi$
$84$	−509.397	−	2841.53i	−0.661664	−	3.69091i
$85$	0.968099	−	691.158i	0.00123535	−	0.881961i
$86$	−726.122	−	806.440i	−0.910462	−	1.01117i
$87$	−511.275	+	26.7948i	−0.630050	+	0.0330195i
$88$	1512.48	−	79.2659i	1.83217	−	0.0960201i
$89$	426.238	+	473.385i	0.507653	+	0.563806i	0.941427	−	0.337216i	$-0.109485\pi$
$89$	426.238	+	473.385i	0.507653	+	0.563806i	−0.433774	+	0.901022i	$0.642818\pi$
$90$	2091.71	−	2870.53i	2.44984	−	3.36200i
$91$	737.493	+	873.837i	0.849563	+	1.00663i
$92$	89.0715	−	562.375i	0.100939	−	0.637301i
$93$	−2702.39	+	724.104i	−3.01317	+	0.807377i
$94$	781.162	+	347.796i	0.857135	+	0.381621i
$95$	−301.291	+	1118.17i	−0.325387	+	1.20759i
$96$	−93.8452	−	210.780i	−0.0997712	−	0.224090i
$97$	234.636	+	1481.43i	0.245605	+	1.55069i	0.734660	+	0.678435i	$0.237342\pi$
$97$	234.636	+	1481.43i	0.245605	+	1.55069i	−0.489056	+	0.872253i	$0.662658\pi$
$98$	−1116.54	−	1269.74i	−1.15090	−	1.30881i
$99$		−	2385.47i		−	2.42171i
$100$	1359.13	+	1518.00i	1.35913	+	1.51800i
$101$	1509.14	−	871.302i	1.48678	−	0.858394i	0.486896	−	0.873460i	$-0.338129\pi$
$101$	1509.14	−	871.302i	1.48678	−	0.858394i	0.999887	+	0.0150659i	$0.00479581\pi$
$102$	−1587.14	+	2443.99i	−1.54069	+	2.37246i
$103$	184.931	−	481.762i	0.176911	−	0.460869i	−0.816239	−	0.577714i	$-0.803945\pi$
$103$	184.931	−	481.762i	0.176911	−	0.460869i	0.993150	+	0.116845i	$0.0372782\pi$
$104$	2043.75	+	1484.87i	1.92698	+	1.40003i
$105$	169.713	−	1972.79i	0.157736	−	1.83356i
$106$	−173.482	+	126.042i	−0.158963	+	0.115494i
$107$	100.389	+	374.657i	0.0907008	+	0.338500i	0.996333	−	0.0855650i	$-0.0272695\pi$
$107$	100.389	+	374.657i	0.0907008	+	0.338500i	−0.905632	+	0.424065i	$0.860603\pi$
$108$	−5448.97	+	2091.67i	−4.85489	+	1.86362i
$109$	−1271.59	−	1144.94i	−1.11739	−	1.00611i	−0.999915	−	0.0130302i	$-0.995852\pi$
$109$	−1271.59	−	1144.94i	−1.11739	−	1.00611i	−0.117478	−	0.993075i	$-0.537481\pi$
$110$	1994.91	+	426.953i	1.72916	+	0.370076i
$111$	−432.130	−	140.408i	−0.369513	−	0.120062i
$112$	−1083.79	−	754.283i	−0.914363	−	0.636366i
$113$	180.313	−	353.885i	0.150110	−	0.294608i	−0.803691	−	0.595047i	$-0.797133\pi$
$113$	180.313	−	353.885i	0.150110	−	0.294608i	0.953801	+	0.300439i	$0.0971333\pi$
$114$	3628.52	−	3267.13i	2.98107	−	2.68416i
$115$	159.347	−	356.554i	0.129210	−	0.289120i
$116$	−583.951	+	648.544i	−0.467401	+	0.519101i
$117$	2503.97	−	3092.15i	1.97857	−	2.44333i
$118$	−1409.84	+	1409.84i	−1.09989	+	1.09989i
$119$	−36.6938	+	1144.32i	−0.0282665	+	0.881508i
$120$	−678.276	−	4321.63i	−0.515982	−	3.28758i
$121$	35.7879	−	15.9338i	0.0268880	−	0.0119713i
$122$	−1665.95	+	1349.06i	−1.23630	+	1.00113i
$123$	284.154	+	184.531i	0.208303	+	0.135274i
$124$	−2384.46	+	4130.01i	−1.72686	+	2.99101i
$125$	629.233	+	1247.87i	0.450242	+	0.892906i
$126$	−3609.04	+	4646.61i	−2.55173	+	3.28534i
$127$	−498.630	−	978.616i	−0.348395	−	0.683765i	0.648608	−	0.761123i	$-0.275352\pi$
$127$	−498.630	−	978.616i	−0.348395	−	0.683765i	−0.997003	+	0.0773581i	$0.975352\pi$
$128$	2257.76	+	866.672i	1.55906	+	0.598466i
$129$	−220.043	+	2093.56i	−0.150183	+	1.42890i
$130$	2137.72	+	2647.44i	1.44224	+	1.78612i
$131$	−499.532	+	52.5029i	−0.333163	+	0.0350168i	−0.269633	−	0.962963i	$-0.586902\pi$
$131$	−499.532	+	52.5029i	−0.333163	+	0.0350168i	−0.0635297	+	0.997980i	$0.520236\pi$
$132$	−4079.88	−	4079.88i	−2.69021	−	2.69021i
$133$	555.625	−	1836.08i	0.362247	−	1.19705i
$134$	−810.350	+	263.299i	−0.522415	+	0.169743i
$135$	−3982.00	+	412.886i	−2.53864	+	0.263227i
$136$	525.896	+	2474.15i	0.331582	+	1.55997i
$137$	−20.7036	−	395.047i	−0.0129111	−	0.246359i	−0.997459	−	0.0712432i	$-0.977303\pi$
$137$	−20.7036	−	395.047i	−0.0129111	−	0.246359i	0.984548	−	0.175116i	$-0.0560300\pi$
$138$	−1380.98	+	896.819i	−0.851861	+	0.553205i
$139$	−852.904	+	2624.97i	−0.520449	+	1.60178i	0.252695	+	0.967546i	$0.418683\pi$
$139$	−852.904	+	2624.97i	−0.520449	+	1.60178i	−0.773144	+	0.634231i	$0.781317\pi$
$140$	−2173.27	−	2582.39i	−1.31196	−	1.55894i
$141$	−512.586	−	1577.58i	−0.306152	−	0.942240i
$142$	1223.06	+	990.417i	0.722797	+	0.585310i
$143$	2207.51	+	591.502i	1.29092	+	0.345901i
$144$	−1868.83	+	4197.46i	−1.08150	+	2.42908i
$145$	−502.472	+	325.309i	−0.287779	+	0.186314i
$146$	2271.47	−	3126.41i	1.28759	−	1.77222i
$147$	−381.158	+	3257.77i	−0.213860	+	1.82787i
$148$	−690.089	+	351.618i	−0.383277	+	0.195289i
$149$	989.355	+	571.204i	0.543967	+	0.314060i	0.746685	−	0.665178i	$-0.231644\pi$
$149$	989.355	+	571.204i	0.543967	+	0.314060i	−0.202718	+	0.979237i	$0.564978\pi$
$150$	632.341	−	5858.40i	0.344203	−	3.18891i
$151$	992.086	+	1718.34i	0.534667	+	0.926071i	0.999179	+	0.0405042i	$0.0128964\pi$
$151$	992.086	+	1718.34i	0.534667	+	0.926071i	−0.464512	+	0.885567i	$0.653770\pi$
$152$	221.804	−	4232.27i	0.118360	−	2.25844i
$153$	3934.86	−	623.221i	2.07918	−	0.329310i
$154$	−3281.34	−	808.199i	−1.71700	−	0.422900i
$155$	−2316.18	+	2309.70i	−1.20026	+	1.19690i
$156$	−1005.96	−	9571.06i	−0.516290	−	4.91217i
$157$	494.103	−	1844.02i	0.251170	−	0.937380i	−0.719011	−	0.694999i	$-0.755405\pi$
$157$	494.103	−	1844.02i	0.251170	−	0.937380i	0.970181	−	0.242381i	$-0.0779285\pi$
$158$	−1521.37	−	3963.31i	−0.766036	−	1.99559i
$159$	406.889	+	86.4868i	0.202946	+	0.0431374i
$160$	−218.017	−	158.865i	−0.107723	−	0.0784963i
$161$	−281.937	+	582.265i	−0.138011	+	0.285024i
$162$	7396.98	+	3768.95i	3.58742	+	1.82788i
$163$	−28.2611	−	43.5182i	−0.0135802	−	0.0209117i	0.831815	−	0.555053i	$-0.187302\pi$
$163$	−28.2611	−	43.5182i	−0.0135802	−	0.0209117i	−0.845395	+	0.534141i	$0.820635\pi$
$164$	564.914	−	120.076i	0.268978	−	0.0571730i
$165$	−1973.95	−	3430.07i	−0.931345	−	1.61837i
$166$	178.767	−	841.032i	0.0835843	−	0.393233i
$167$	−1645.25	−	260.583i	−0.762357	−	0.120745i	−0.236863	−	0.971543i	$-0.576119\pi$
$167$	−1645.25	−	260.583i	−0.762357	−	0.120745i	−0.525494	+	0.850797i	$0.676119\pi$
$168$	903.623	+	7189.87i	0.414977	+	3.30185i
$169$	949.224	+	1306.50i	0.432055	+	0.594672i
$170$	−183.079	+	3402.17i	−0.0825971	+	1.53491i
$171$	−6638.53	−	697.737i	−2.96878	−	0.312031i
$172$	2258.19	+	2788.63i	1.00108	+	1.23623i
$173$	2581.66	+	135.299i	1.13457	+	0.0594601i	0.610355	−	0.792128i	$-0.291027\pi$
$173$	2581.66	+	135.299i	1.13457	+	0.0594601i	0.524211	+	0.851588i	$0.324360\pi$
$174$	2523.80			1.09959
$175$	−978.480	−	2098.08i	−0.422664	−	0.906287i
$176$	−2639.11			−1.13029
$177$	3862.45	+	202.423i	1.64023	+	0.0859606i
$178$	−1976.14	−	2440.33i	−0.832125	−	1.02759i
$179$	2164.61	+	227.509i	0.903856	+	0.0949991i	0.545041	−	0.838410i	$-0.316514\pi$
$179$	2164.61	+	227.509i	0.903856	+	0.0949991i	0.358815	+	0.933409i	$0.383181\pi$
$180$	−7403.86	+	9116.87i	−3.06584	+	3.77517i
$181$	−1573.37	−	2165.56i	−0.646121	−	0.889309i	0.352802	−	0.935698i	$-0.385229\pi$
$181$	−1573.37	−	2165.56i	−0.646121	−	0.889309i	−0.998923	+	0.0463884i	$0.985229\pi$
$182$	−3405.07	−	4491.97i	−1.38682	−	1.82949i
$183$	4107.27	+	650.527i	1.65911	+	0.262778i
$184$	−297.159	+	1398.02i	−0.119059	+	0.560128i
$185$	−519.778	+	109.721i	−0.206567	+	0.0436048i
$186$	13490.1	−	2867.41i	5.31796	−	1.13037i
$187$	1246.29	+	1919.12i	0.487368	+	0.750481i
$188$	−2519.31	−	1283.65i	−0.977337	−	0.497978i
$189$	6614.05	−	481.456i	2.54551	−	0.185295i
$190$	1771.67	−	5426.75i	0.676474	−	2.07209i
$191$	1612.81	+	342.813i	0.610988	+	0.129869i	0.503005	−	0.864283i	$-0.332228\pi$
$191$	1612.81	+	342.813i	0.610988	+	0.129869i	0.107982	+	0.994153i	$0.465561\pi$
$192$	−1547.05	−	4030.19i	−0.581502	−	1.51487i
$193$	181.036	−	675.634i	0.0675194	−	0.251986i	−0.923914	−	0.382601i	$-0.875029\pi$
$193$	181.036	−	675.634i	0.0675194	−	0.251986i	0.991433	+	0.130615i	$0.0416952\pi$
$194$	−772.862	−	7353.29i	−0.286022	−	2.72132i
$195$	1041.75	−	6518.22i	0.382569	−	2.39374i
$196$	3467.23	+	4386.06i	1.26357	+	1.59842i
$197$	−3685.21	+	583.679i	−1.33279	+	0.211094i	−0.781859	−	0.623455i	$-0.785728\pi$
$197$	−3685.21	+	583.679i	−1.33279	+	0.211094i	−0.550934	+	0.834549i	$0.685728\pi$
$198$	−615.432	+	11743.1i	−0.220893	+	4.21489i
$199$	2352.37	+	4074.42i	0.837965	+	1.45140i	0.891593	+	0.452837i	$0.149588\pi$
$199$	2352.37	+	4074.42i	0.837965	+	1.45140i	−0.0536280	+	0.998561i	$0.517079\pi$
$200$	−3207.55	−	3983.76i	−1.13404	−	1.40847i
$201$	1431.43	+	826.437i	0.502315	+	0.290012i
$202$	−7653.94	+	3899.88i	−2.66599	+	1.35839i
$203$	848.471	−	513.111i	0.293355	−	0.177406i
$204$	5663.90	−	7795.69i	1.94388	−	2.67553i
$205$	395.558	+	21.2859i	0.134766	+	0.00725206i
$206$	−1034.67	+	2323.90i	−0.349945	+	0.785988i
$207$	2174.41	+	582.632i	0.730106	+	0.195631i
$208$	−3420.93	−	2770.21i	−1.14038	−	0.923461i
$209$	−1184.79	−	3646.41i	−0.392123	−	1.20683i
$210$	−1344.42	+	9667.80i	−0.441780	+	3.17686i
$211$	−367.436	+	1130.85i	−0.119883	+	0.368962i	−0.992934	−	0.118666i	$-0.962138\pi$
$211$	−367.436	+	1130.85i	−0.119883	+	0.368962i	0.873051	+	0.487629i	$0.162138\pi$
$212$	594.673	−	386.185i	0.192652	−	0.125110i
$213$	−159.779	−	3048.77i	−0.0513985	−	0.980742i
$214$	−397.535	−	1870.25i	−0.126986	−	0.597420i
$215$	997.913	+	2249.82i	0.316545	+	0.713659i
$216$	13933.9	−	4527.40i	4.38927	−	1.42616i
$217$	3952.23	−	3706.64i	1.23638	−	1.15955i
$218$	5964.35	+	5964.35i	1.85301	+	1.85301i
$219$	−7455.49	+	783.603i	−2.30044	+	0.241785i
$220$	−6513.56	−	1755.08i	−1.99611	−	0.537854i
$221$	−398.960	+	3795.85i	−0.121434	+	1.15537i
$222$	2091.06	+	802.681i	0.632173	+	0.242669i
$223$	272.746	+	535.293i	0.0819031	+	0.160744i	0.928326	−	0.371768i	$-0.121248\pi$
$223$	272.746	+	535.293i	0.0819031	+	0.160744i	−0.846423	+	0.532512i	$0.821248\pi$
$224$	352.910	+	274.106i	0.105267	+	0.0817611i
$225$	−6530.33	+	4716.67i	−1.93491	+	1.39753i
$226$	−978.942	+	1695.58i	−0.288134	+	0.499063i
$227$	4227.50	+	2745.37i	1.23608	+	0.802717i	0.986200	−	0.165561i	$-0.0529434\pi$
$227$	4227.50	+	2745.37i	1.23608	+	0.802717i	0.249876	+	0.968278i	$0.419610\pi$
$228$	−12547.2	+	10160.5i	−3.64456	+	2.95131i
$229$	7.88300	−	3.50974i	0.00227478	−	0.00101280i	−0.405599	−	0.914051i	$-0.632937\pi$
$229$	7.88300	−	3.50974i	0.00227478	−	0.00101280i	0.407874	+	0.913038i	$0.366270\pi$
$230$	−876.416	+	1714.12i	−0.251257	+	0.491417i
$231$	3094.17	+	5779.47i	0.881305	+	1.64615i
$232$	1549.01	−	1549.01i	0.438351	−	0.438351i
$233$	−2125.80	+	2625.14i	−0.597706	+	0.738106i	−0.982780	−	0.184780i	$-0.940843\pi$
$233$	−2125.80	+	2625.14i	−0.597706	+	0.738106i	0.385074	+	0.922886i	$0.374176\pi$
$234$	−13124.3	+	14576.0i	−3.66649	+	4.07205i
$235$	−1439.41	−	1299.71i	−0.399561	−	0.360781i
$236$	4899.46	−	4411.50i	1.35139	−	1.21680i
$237$	−3738.75	+	7337.70i	−1.02472	+	2.01112i
$238$	475.860	−	5623.76i	0.129603	−	1.53166i
$239$	−5250.48	−	1705.99i	−1.42103	−	0.461720i	−0.505099	−	0.863061i	$-0.668544\pi$
$239$	−5250.48	−	1705.99i	−1.42103	−	0.461720i	−0.915928	+	0.401342i	$0.868544\pi$
$240$	786.161	+	7581.96i	0.211444	+	2.03922i
$241$	−3075.88	−	2769.53i	−0.822135	−	0.740254i	0.146374	−	0.989229i	$-0.453240\pi$
$241$	−3075.88	−	2769.53i	−0.822135	−	0.740254i	−0.968510	+	0.248975i	$0.919906\pi$
$242$	−180.287	+	69.2056i	−0.0478895	+	0.0183831i
$243$	−1665.92	−	6217.28i	−0.439788	−	1.64131i
$244$	5734.64	−	4166.46i	1.50460	−	1.09316i
$245$	1513.57	+	3523.52i	0.394688	+	0.918815i
$246$	−1351.22	−	981.716i	−0.350205	−	0.254439i
$247$	2291.77	−	5970.28i	0.590373	−	1.53797i
$248$	6519.77	−	10039.6i	1.66938	−	2.57062i
$249$	−1444.48	+	833.972i	−0.367632	+	0.212252i
$250$	−2775.63	−	6305.34i	−0.702185	−	1.59514i
$251$		−	1735.74i		−	0.436489i	−0.975894	−	0.218245i	$-0.929967\pi$
$251$		−	1735.74i		−	0.436489i	0.975894	−	0.218245i	$-0.0700331\pi$
$252$	12721.6	−	14719.1i	3.18011	−	3.67943i
$253$	202.270	+	1277.08i	0.0502633	+	0.317350i
$254$	2202.17	+	4946.15i	0.544001	+	1.22185i
$255$	5142.23	−	4152.18i	1.26282	−	1.01969i
$256$	−7591.59	−	3379.99i	−1.85341	−	0.825193i
$257$	−6258.22	+	1676.88i	−1.51898	+	0.407008i	−0.919405	−	0.393313i	$-0.871329\pi$
$257$	−6258.22	+	1676.88i	−1.51898	+	0.407008i	−0.599571	+	0.800321i	$0.704662\pi$
$258$	1623.34	−	10249.4i	0.391724	−	2.47325i
$259$	866.179	−	155.279i	0.207806	−	0.0372531i
$260$	−6600.88	−	9112.14i	−1.57450	−	2.17350i
$261$	−2308.70	−	2564.07i	−0.547529	−	0.608093i
$262$	2472.63	−	129.585i	0.583052	−	0.0305565i
$263$	5566.74	−	291.740i	1.30517	−	0.0684010i	0.612969	−	0.790107i	$-0.289975\pi$
$263$	5566.74	−	291.740i	1.30517	−	0.0684010i	0.692200	+	0.721706i	$0.256642\pi$
$264$	9691.16	+	10763.1i	2.25928	+	2.50918i
$265$	462.754	−	149.642i	0.107271	−	0.0346884i
$266$	−3208.91	+	8895.25i	−0.739665	+	2.05039i
$267$	−952.912	+	6016.45i	−0.218417	+	1.37903i
$268$	2721.44	−	729.209i	0.620294	−	0.166207i
$269$	118.571	+	52.7911i	0.0268751	+	0.0119655i	0.420130	−	0.907464i	$-0.361984\pi$
$269$	118.571	+	52.7911i	0.0268751	+	0.0119655i	−0.393255	+	0.919429i	$0.628651\pi$
$270$	19709.0	−	1005.22i	4.44241	−	0.226578i
$271$	−806.810	−	1812.12i	−0.180849	−	0.406195i	0.800259	−	0.599655i	$-0.204696\pi$
$271$	−806.810	−	1812.12i	−0.180849	−	0.406195i	−0.981108	+	0.193460i	$0.938029\pi$
$272$	−689.486	−	4353.24i	−0.153699	−	0.970419i
$273$	−2055.78	+	10739.5i	−0.455756	+	2.38089i
$274$			1950.07i			0.429956i
$275$	−4000.59	−	2324.71i	−0.877253	−	0.509764i
$276$	4715.37	−	2722.42i	1.02838	−	0.593734i
$277$	−1059.47	+	1631.43i	−0.229809	+	0.353875i	−0.934698	−	0.355443i	$-0.884330\pi$
$277$	−1059.47	+	1631.43i	−0.229809	+	0.353875i	0.704889	+	0.709318i	$0.250997\pi$
$278$	4875.88	−	12702.1i	1.05193	−	2.74036i
$279$	−15253.5	−	11082.3i	−3.27313	−	2.37807i
$280$	5108.55	+	6758.86i	1.09034	+	1.44257i
$281$	796.307	−	578.551i	0.169052	−	0.122824i	−0.500042	−	0.866001i	$-0.666682\pi$
$281$	796.307	−	578.551i	0.169052	−	0.122824i	0.669094	+	0.743177i	$0.266682\pi$
$282$	2116.34	+	7898.30i	0.446902	+	1.66786i
$283$	1574.62	−	604.440i	0.330747	−	0.126962i	−0.187327	−	0.982298i	$-0.559982\pi$
$283$	1574.62	−	604.440i	0.330747	−	0.126962i	0.518074	+	0.855336i	$0.326649\pi$
$284$	−3867.31	−	3482.14i	−0.808038	−	0.727560i
$285$	−10122.9	+	4490.03i	−2.10396	+	0.933216i
$286$	−10714.5	−	3481.35i	−2.21525	−	0.719778i
$287$	−653.854	−	55.3265i	−0.134480	−	0.0113792i
$288$	705.916	−	1385.44i	0.144432	−	0.283464i
$289$	811.064	−	730.285i	0.165085	−	0.148643i
$290$	2557.48	−	1471.79i	0.517864	−	0.298022i
$291$	−9597.36	+	10659.0i	−1.93336	+	2.14721i
$292$	−8041.73	+	9930.71i	−1.61167	+	1.99024i
$293$	−6901.04	+	6901.04i	−1.37598	+	1.37598i	−0.524687	+	0.851295i	$0.675818\pi$
$293$	−6901.04	+	6901.04i	−1.37598	+	1.37598i	−0.851295	+	0.524687i	$0.824182\pi$
$294$	2716.83	−	15938.9i	0.538942	−	3.16183i
$295$	4032.04	−	2047.32i	0.795779	−	0.404066i
$296$	1776.06	−	790.753i	0.348755	−	0.155276i
$297$	10300.5	−	8341.19i	2.01244	−	1.62965i
$298$	−4723.00	−	3067.16i	−0.918108	−	0.596227i
$299$	−1078.33	+	1867.73i	−0.208567	+	0.361249i
$300$	−3101.91	+	19235.8i	−0.596963	+	3.70192i
$301$	−1538.04	−	3775.75i	−0.294522	−	0.723026i
$302$	−4440.50	−	8714.96i	−0.846099	−	1.66056i
$303$	15557.1	+	5971.82i	2.94962	+	1.13225i
$304$	−771.925	+	7344.38i	−0.145635	+	1.38562i
$305$	4541.44	−	1736.00i	0.852597	−	0.325912i
$306$	−19531.2	+	2052.81i	−3.64878	+	0.383502i
$307$	107.493	+	107.493i	0.0199835	+	0.0199835i	0.717028	−	0.697044i	$-0.245502\pi$
$307$	107.493	+	107.493i	0.0199835	+	0.0199835i	−0.697044	+	0.717028i	$0.745502\pi$
$308$	10695.5	+	3236.64i	1.97869	+	0.598781i
$309$	4693.17	−	1524.90i	0.864030	−	0.280740i
$310$	11997.9	−	10772.6i	2.19818	−	1.97369i
$311$	1909.40	+	8983.03i	0.348142	+	1.63788i	0.708963	+	0.705245i	$0.249163\pi$
$311$	1909.40	+	8983.03i	0.348142	+	1.63788i	−0.360821	+	0.932635i	$0.617503\pi$
$312$	1264.30	+	24124.2i	0.229412	+	4.37745i
$313$	5209.53	−	3383.11i	0.940767	−	0.610941i	0.0194740	−	0.999810i	$-0.493801\pi$
$313$	5209.53	−	3383.11i	0.940767	−	0.610941i	0.921293	+	0.388869i	$0.127134\pi$
$314$	−2908.10	+	8950.21i	−0.522655	+	1.60857i
$315$	11051.9	−	7477.96i	1.97684	−	1.33757i
$316$	4337.88	+	13350.6i	0.772231	+	2.37668i
$317$	−612.187	−	495.739i	−0.108466	−	0.0878343i	0.573553	−	0.819168i	$-0.305565\pi$
$317$	−612.187	−	495.739i	−0.108466	−	0.0878343i	−0.682019	+	0.731334i	$0.738898\pi$
$318$	−1980.71	−	530.729i	−0.349285	−	0.0935906i
$319$	806.069	−	1810.46i	0.141477	−	0.317763i
$320$	−3917.95	−	3181.79i	−0.684438	−	0.555836i
$321$	−2180.16	+	3000.73i	−0.379080	+	0.521758i
$322$	1538.13	−	2793.62i	0.266201	−	0.483486i
$323$	5705.25	−	2906.97i	0.982813	−	0.500768i
$324$	−23773.5	−	13725.7i	−4.07639	−	2.35351i
$325$	−2745.54	−	7212.71i	−0.468601	−	1.23104i
$326$	127.895	+	221.521i	0.0217285	+	0.0376348i
$327$	856.351	−	16340.1i	0.144820	−	2.76334i
$328$	−1431.86	+	226.784i	−0.241040	+	0.0381771i
$329$	2317.28	+	2225.04i	0.388316	+	0.372858i
$330$	8832.39	+	17394.7i	1.47336	+	2.90166i
$331$	1013.70	+	9644.68i	0.168332	+	1.60157i	0.673926	+	0.738799i	$0.264607\pi$
$331$	1013.70	+	9644.68i	0.168332	+	1.60157i	−0.505595	+	0.862771i	$0.668727\pi$
$332$	−735.857	+	2746.26i	−0.121643	+	0.453977i
$333$	−1097.35	−	2858.69i	−0.180584	−	0.470437i
$334$	8031.99	+	1707.25i	1.31584	+	0.279691i
$335$	1932.48	+	2.70681i	0.315172	+	0.000441459i
$336$	−916.721	−	12593.6i	−0.148843	−	2.04475i
$337$	2090.30	+	1065.06i	0.337881	+	0.172159i	0.614696	−	0.788764i	$-0.289279\pi$
$337$	2090.30	+	1065.06i	0.337881	+	0.172159i	−0.276815	+	0.960923i	$0.589279\pi$
$338$	−4335.75	−	6676.47i	−0.697733	−	1.07442i
$339$	3715.05	−	789.659i	0.595203	−	0.126514i
$340$	1193.32	−	11202.7i	0.190344	−	1.78692i
$341$	2251.61	−	10593.0i	0.357570	−	1.68223i
$342$	32500.0	+	5147.49i	5.13859	+	0.813872i
$343$	−2327.16	−	5910.83i	−0.366341	−	0.930481i
$344$	−5294.32	−	7287.00i	−0.829798	−	1.14212i
$345$	3608.71	−	961.535i	0.563149	−	0.150050i
$346$	−12674.0	−	1332.09i	−1.96925	−	0.206976i
$347$	2276.52	+	2811.27i	0.352191	+	0.434919i	0.922197	−	0.386721i	$-0.126392\pi$
$347$	2276.52	+	2811.27i	0.352191	+	0.434919i	−0.570006	+	0.821641i	$0.693059\pi$
$348$	−8333.92	−	436.762i	−1.28375	−	0.0672785i
$349$	590.411			0.0905559			0.0452779	−	0.998974i	$-0.485583\pi$
$349$	590.411			0.0905559			0.0452779	+	0.998974i	$0.485583\pi$
$350$	4275.55	+	10580.8i	0.652965	+	1.61591i
$351$	22107.5			3.36186
$352$	891.892	+	46.7421i	0.135051	+	0.00707773i
$353$	339.465	+	419.204i	0.0511839	+	0.0632068i	0.802095	−	0.597196i	$-0.203719\pi$
$353$	339.465	+	419.204i	0.0511839	+	0.0632068i	−0.750911	+	0.660403i	$0.770385\pi$
$354$	−18961.8	−	1992.96i	−2.84691	−	0.299223i
$355$	−1939.84	−	2996.27i	−0.290017	−	0.447960i
$356$	6103.16	+	8400.28i	0.908615	+	1.25060i
$357$	−8724.92	+	6613.79i	−1.29348	+	0.980502i
$358$	−10597.2	−	1678.43i	−1.56446	−	0.247787i
$359$	2591.20	−	12190.7i	0.380943	−	1.79220i	−0.201677	−	0.979452i	$-0.564639\pi$
$359$	2591.20	−	12190.7i	0.380943	−	1.79220i	0.582621	−	0.812744i	$-0.302027\pi$
$360$	19757.2	−	21880.9i	2.89249	−	3.20340i
$361$	−3785.01	+	804.529i	−0.551831	+	0.117295i
$362$	7186.67	+	11066.5i	1.04343	+	1.60675i
$363$	333.784	+	170.072i	0.0482621	+	0.0245908i
$364$	10466.6	+	15422.3i	1.50714	+	2.22074i
$365$	−7098.01	+	5141.83i	−1.01788	+	0.737358i
$366$	−20051.3	−	4262.04i	−2.86366	−	0.608689i
$367$	1617.65	+	4214.11i	0.230083	+	0.599387i	0.999211	−	0.0397075i	$-0.0126426\pi$
$367$	1617.65	+	4214.11i	0.230083	+	0.599387i	−0.769128	+	0.639094i	$0.779309\pi$
$368$	644.581	−	2405.61i	0.0913073	−	0.340764i
$369$	238.673	+	2270.82i	0.0336716	+	0.320364i
$370$	2587.06	−	406.036i	0.363499	−	0.0570508i
$371$	−773.791	+	224.271i	−0.108284	+	0.0313843i
$372$	−45042.2	+	7133.98i	−6.27776	+	0.994300i
$373$	201.187	−	3838.87i	0.0279277	−	0.532893i	−0.948464	−	0.316885i	$-0.897363\pi$
$373$	201.187	−	3838.87i	0.0279277	−	0.532893i	0.976392	−	0.216008i	$-0.0693037\pi$
$374$	−5640.10	−	9768.93i	−0.779793	−	1.35064i
$375$	−5486.98	+	12185.9i	−0.755590	+	1.67807i
$376$	6146.58	+	3548.73i	0.843047	+	0.486734i
$377$	2945.26	−	1500.68i	0.402357	−	0.205011i
$378$	−32683.7	+	663.728i	−4.44727	+	0.0903134i
$379$	−2159.62	+	2972.47i	−0.292698	+	0.402864i	−0.929888	−	0.367843i	$-0.880096\pi$
$379$	−2159.62	+	2972.47i	−0.292698	+	0.402864i	0.637190	+	0.770706i	$0.280096\pi$
$380$	−6789.40	+	17613.2i	−0.916550	+	2.37773i
$381$	4271.93	−	9594.90i	0.574429	−	1.29019i
$382$	−7851.04	−	2103.68i	−1.05156	−	0.281764i
$383$	−2503.70	−	2027.45i	−0.334029	−	0.270491i	0.447602	−	0.894233i	$-0.352278\pi$
$383$	−2503.70	−	2027.45i	−0.334029	−	0.270491i	−0.781630	+	0.623742i	$0.785612\pi$
$384$	7146.39	+	21994.3i	0.949708	+	2.92290i
$385$	6505.84	+	4052.19i	0.861217	+	0.536412i
$386$	−1065.51	+	3279.29i	−0.140500	+	0.432413i
$387$	−11897.9	+	7726.60i	−1.56280	+	1.01490i
$388$	1279.55	+	24415.3i	0.167421	+	3.19458i
$389$	−1745.40	−	8211.44i	−0.227494	−	1.07027i	−0.932527	−	0.361100i	$-0.882401\pi$
$389$	−1745.40	−	8211.44i	−0.227494	−	1.07027i	0.705033	−	0.709174i	$-0.250932\pi$
$390$	−6809.92	+	31819.0i	−0.884190	+	4.13132i
$391$	−2053.72	+	667.293i	−0.265629	+	0.0863081i
$392$	−8115.20	−	11450.2i	−1.04561	−	1.47531i
$393$	−3396.36	−	3396.36i	−0.435938	−	0.435938i
$394$	18292.0	−	1922.57i	2.33893	−	0.245832i
$395$	490.444	+	9615.93i	0.0624733	+	1.22489i
$396$	4064.47	−	38670.9i	0.515776	−	4.90728i
$397$	−6622.91	−	2542.30i	−0.837265	−	0.321396i	−0.0983142	−	0.995155i	$-0.531345\pi$
$397$	−6622.91	−	2542.30i	−0.837265	−	0.321396i	−0.738951	+	0.673760i	$0.764678\pi$
$398$	−10529.0	−	20664.4i	−1.32606	−	2.60254i
$399$	16988.7	−	6920.30i	2.13158	−	0.868292i
$400$	5218.18	+	7224.68i	0.652272	+	0.903085i
$401$	3380.50	−	5855.19i	0.420982	−	0.729163i	−0.575054	−	0.818116i	$-0.695019\pi$
$401$	3380.50	−	5855.19i	0.420982	−	0.729163i	0.996036	+	0.0889530i	$0.0283521\pi$
$402$	−6833.40	−	4437.66i	−0.847808	−	0.550573i
$403$	14037.8	−	11367.6i	1.73517	−	1.40511i
$404$	25949.2	−	11553.3i	3.19560	−	1.42277i
$405$	−13295.3	−	13332.6i	−1.63123	−	1.63581i
$406$	−4309.21	+	2307.03i	−0.526755	+	0.282010i
$407$	1243.66	−	1243.66i	0.151464	−	0.151464i
$408$	−15222.0	+	18797.6i	−1.84706	+	2.28093i
$409$	−4962.73	+	5511.67i	−0.599978	+	0.666343i	−0.964264	−	0.264944i	$-0.914646\pi$
$409$	−4962.73	+	5511.67i	−0.599978	+	0.666343i	0.364286	+	0.931287i	$0.381313\pi$
$410$	−1941.75	−	206.836i	−0.233893	−	0.0249144i
$411$	2811.23	−	2531.25i	0.337392	−	0.303789i
$412$	3818.76	−	7494.75i	0.456643	−	0.896213i
$413$	−6779.90	+	3185.09i	−0.807789	+	0.379486i
$414$	−10553.8	−	3429.14i	−1.25288	−	0.407085i
$415$	−977.416	+	1687.47i	−0.115613	+	0.199602i
$416$	1107.04	+	996.787i	0.130474	+	0.117480i
$417$	−24640.5	+	9458.58i	−2.89364	+	1.11076i
$418$	4891.71	+	18256.1i	0.572396	+	2.13621i
$419$	9436.79	−	6856.23i	1.10028	−	0.799400i	0.119175	−	0.992873i	$-0.461975\pi$
$419$	9436.79	−	6856.23i	1.10028	−	0.799400i	0.981106	+	0.193473i	$0.0619752\pi$
$420$	6112.53	−	31691.6i	0.710145	−	3.68189i
$421$	6441.65	+	4680.13i	0.745717	+	0.541795i	0.894496	−	0.447076i	$-0.147535\pi$
$421$	6441.65	+	4680.13i	0.745717	+	0.541795i	−0.148780	+	0.988870i	$0.547535\pi$
$422$	2100.56	−	5472.14i	0.242307	−	0.631231i
$423$	6088.36	−	9375.25i	0.699825	−	1.07764i
$424$	−1541.42	+	889.939i	−0.176552	+	0.101932i
$425$	2789.45	−	7206.36i	0.318372	−	0.822493i
$426$			15049.6i			1.71163i
$427$	−7607.51	+	2643.77i	−0.862186	+	0.299627i
$428$	989.049	+	6244.61i	0.111700	+	0.705244i
$429$	8888.98	+	19965.0i	1.00038	+	2.24690i
$430$	−4332.06	−	11332.8i	−0.485839	−	1.27097i
$431$	3484.03	+	1551.19i	0.389374	+	0.173360i	0.592080	−	0.805879i	$-0.298307\pi$
$431$	3484.03	+	1551.19i	0.389374	+	0.173360i	−0.202706	+	0.979240i	$0.564974\pi$
$432$	−24659.4	+	6607.45i	−2.74635	+	0.735883i
$433$	−289.267	+	1826.36i	−0.0321046	+	0.202700i	−0.998527	−	0.0542585i	$-0.982721\pi$
$433$	−289.267	+	1826.36i	−0.0321046	+	0.202700i	0.966422	+	0.256959i	$0.0827205\pi$
$434$	−20412.2	+	17227.3i	−2.25764	+	1.90538i
$435$	−5441.43	−	1776.46i	−0.599762	−	0.195804i
$436$	−18662.9	−	20727.2i	−2.04997	−	2.27673i
$437$	3613.16	−	189.357i	0.395516	−	0.0207281i
$438$	36903.9	−	1934.05i	4.02588	−	0.210987i
$439$	6913.95	+	7678.71i	0.751673	+	0.834818i	0.990681	−	0.136200i	$-0.0434889\pi$
$439$	6913.95	+	7678.71i	0.751673	+	0.834818i	−0.239008	+	0.971018i	$0.576822\pi$
$440$	16097.2	+	5255.22i	1.74410	+	0.569393i
$441$	−18678.6	+	11820.3i	−2.01691	+	1.27635i
$442$	2943.29	−	18583.2i	0.316737	−	1.99980i
$443$	−6181.59	+	1656.35i	−0.662971	+	0.177643i	−0.574586	−	0.818444i	$-0.694837\pi$
$443$	−6181.59	+	1656.35i	−0.662971	+	0.177643i	−0.0883845	+	0.996086i	$0.528170\pi$
$444$	−6766.02	−	3012.43i	−0.723201	−	0.321990i
$445$	2542.95	+	6652.44i	0.270893	+	0.708665i
$446$	−1204.56	−	2705.49i	−0.127887	−	0.287240i
$447$	1708.96	+	10790.0i	0.180830	+	1.14172i
$448$	6325.51	+	5467.09i	0.667081	+	0.576553i
$449$		−	1239.49i		−	0.130279i	−0.997876	−	0.0651394i	$-0.979251\pi$
$449$		−	1239.49i		−	0.130279i	0.997876	−	0.0651394i	$-0.0207492\pi$
$450$	33364.2	−	21534.3i	3.49512	−	2.25586i
$451$	−1135.80	+	655.754i	−0.118587	+	0.0684661i
$452$	3526.02	−	5429.60i	0.366925	−	0.565015i
$453$	−6799.66	+	17713.7i	−0.705245	+	1.83723i
$454$	−20102.8	−	14605.5i	−2.07813	−	1.50985i
$455$	4179.66	+	12081.7i	0.430650	+	1.24483i
$456$	32787.3	−	23821.4i	3.36712	−	2.44635i
$457$	−1564.33	−	5838.15i	−0.160123	−	0.597587i	−0.998612	−	0.0526687i	$-0.983227\pi$
$457$	−1564.33	−	5838.15i	−0.160123	−	0.597587i	0.838489	−	0.544918i	$-0.183439\pi$
$458$	−39.7117	+	15.2439i	−0.00405155	+	0.00155524i
$459$	16449.9	+	14811.6i	1.67281	+	1.50620i
$460$	3190.68	−	5508.59i	0.323405	−	0.558346i
$461$	12933.5	+	4202.34i	1.30666	+	0.424561i	0.877895	−	0.478853i	$-0.158947\pi$
$461$	12933.5	+	4202.34i	1.30666	+	0.424561i	0.428769	+	0.903414i	$0.358947\pi$
$462$	−13740.9	−	29249.3i	−1.38373	−	2.94546i
$463$	3335.59	−	6546.47i	0.334812	−	0.657106i	−0.660812	−	0.750551i	$-0.729788\pi$
$463$	3335.59	−	6546.47i	0.334812	−	0.657106i	0.995624	+	0.0934451i	$0.0297880\pi$
$464$	−2836.70	+	2554.18i	−0.283816	+	0.255549i
$465$	−31103.5	−	3313.17i	−3.10192	−	0.330418i
$466$	11142.1	−	12374.5i	1.10761	−	1.23013i
$467$	−967.593	+	1194.88i	−0.0958777	+	0.118399i	−0.822827	−	0.568292i	$-0.807604\pi$
$467$	−967.593	+	1194.88i	−0.0958777	+	0.118399i	0.726949	+	0.686691i	$0.240938\pi$
$468$	45860.4	−	45860.4i	4.52970	−	4.52970i
$469$	−3199.52	−	102.596i	−0.315011	−	0.0101011i
$470$	6750.59	+	6769.52i	0.662513	+	0.664372i
$471$	16677.5	−	7425.30i	1.63155	−	0.726411i
$472$	−12861.2	+	10414.8i	−1.25420	+	1.01563i
$473$	−6833.96	−	4438.03i	−0.664325	−	0.431418i
$474$	20298.1	−	35157.3i	1.96692	−	3.40681i
$475$	−7639.58	+	10453.3i	−0.737953	+	1.00974i
$476$	−2544.58	+	18488.0i	−0.245022	+	1.78024i
$477$	1272.70	+	2497.81i	0.122165	+	0.239763i
$478$	25406.8	+	9752.76i	2.43113	+	0.933224i
$479$	2.77140	−	26.3681i	0.000264360	−	0.00251522i	−0.994389	−	0.105786i	$-0.966264\pi$
$479$	2.77140	−	26.3681i	0.000264360	−	0.00251522i	0.994653	+	0.103271i	$0.0329308\pi$
$480$	−131.398	−	2576.26i	−0.0124947	−	0.244978i
$481$	2917.53	−	306.645i	0.276565	−	0.0290682i
$482$	14427.3	+	14427.3i	1.36338	+	1.36338i
$483$	−6023.84	+	1408.82i	−0.567483	+	0.132719i
$484$	607.306	−	197.326i	0.0570347	−	0.0185317i
$485$	−3509.52	+	16398.0i	−0.328576	+	1.53525i
$486$	6596.92	+	31036.1i	0.615725	+	2.89676i
$487$	780.148	+	14886.1i	0.0725912	+	1.38512i	0.755754	+	0.654856i	$0.227271\pi$
$487$	780.148	+	14886.1i	0.0725912	+	1.38512i	−0.683163	+	0.730266i	$0.739396\pi$
$488$	−14922.6	+	9690.82i	−1.38425	+	0.898941i
$489$	153.335	−	471.916i	0.0141800	−	0.0436417i
$490$	−6541.93	−	17736.0i	−0.603131	−	1.63517i
$491$	−2978.81	−	9167.83i	−0.273792	−	0.842645i	−0.989537	−	0.144283i	$-0.953913\pi$
$491$	−2978.81	−	9167.83i	−0.273792	−	0.842645i	0.715745	−	0.698362i	$-0.246087\pi$
$492$	4292.00	+	3475.59i	0.393289	+	0.318479i
$493$	3196.96	+	856.623i	0.292057	+	0.0782563i
$494$	−12822.2	+	28799.1i	−1.16781	+	2.62294i
$495$	9592.68	−	24885.5i	0.871028	−	2.25964i
$496$	−12260.7	+	16875.4i	−1.10992	+	1.52767i
$497$	3059.72	+	5059.49i	0.276151	+	0.456638i
$498$	7326.02	−	3732.79i	0.659210	−	0.335884i
$499$	−12786.8	−	7382.45i	−1.14712	−	0.662293i	−0.198939	−	0.980012i	$-0.563750\pi$
$499$	−12786.8	−	7382.45i	−1.14712	−	0.662293i	−0.948185	+	0.317719i	$0.897083\pi$
$500$	8074.30	+	21301.4i	0.722187	+	1.90525i
$501$	−7964.57	−	13795.0i	−0.710241	−	1.23017i
$502$	−447.806	+	8544.65i	−0.0398139	+	0.759694i
$503$	−17347.2	+	2747.52i	−1.53772	+	0.243551i	−0.867056	−	0.498211i	$-0.833991\pi$
$503$	−17347.2	+	2747.52i	−1.53772	+	0.243551i	−0.670664	+	0.741762i	$0.733991\pi$
$504$	−33823.4	+	35225.6i	−2.98931	+	3.11324i
$505$	19247.3	−	3020.84i	1.69603	−	0.266190i
$506$	−666.253	−	6338.98i	−0.0585347	−	0.556921i
$507$	−3996.92	+	14916.7i	−0.350117	+	1.30666i
$508$	−6415.87	−	16713.9i	−0.560351	−	1.45976i
$509$	−11819.7	−	2512.36i	−1.02928	−	0.218779i	−0.337829	−	0.941207i	$-0.609693\pi$
$509$	−11819.7	−	2512.36i	−1.02928	−	0.218779i	−0.691446	+	0.722428i	$0.743026\pi$
$510$	−26385.3	+	19113.6i	−2.29090	+	1.65954i
$511$	12013.4	−	8153.08i	1.04000	−	0.705814i
$512$	19261.3	+	9814.12i	1.66257	+	0.847123i
$513$	−20199.8	−	31105.0i	−1.73849	−	2.67704i
$514$	31240.4	−	6640.36i	2.68085	−	0.569832i
$515$	3866.53	−	4282.14i	0.330835	−	0.366396i
$516$	−7134.21	+	33563.8i	−0.608655	+	2.86350i
$517$	6341.81	+	1004.44i	0.539482	+	0.0854456i
$518$	−4304.07	+	540.935i	−0.365077	+	0.0458829i
$519$	14530.9	+	20000.1i	1.22897	+	1.69153i
$520$	15349.5	+	23708.9i	1.29447	+	1.99943i
$521$	16635.0	+	1748.41i	1.39883	+	0.147023i	0.773728	−	0.633518i	$-0.218390\pi$
$521$	16635.0	+	1748.41i	1.39883	+	0.147023i	0.625104	+	0.780542i	$0.285057\pi$
$522$	10703.7	+	13218.0i	0.897488	+	1.10831i
$523$	−20004.3	−	1048.38i	−1.67252	−	0.0876532i	−0.807655	−	0.589655i	$-0.799264\pi$
$523$	−20004.3	−	1048.38i	−1.67252	−	0.0876532i	−0.864867	+	0.502002i	$0.832597\pi$
$524$	−8187.36			−0.682570
$525$	9703.61	−	19897.9i	0.806667	−	1.65412i
$526$	−27479.1			−2.27784
$527$	18061.5	+	946.561i	1.49292	+	0.0782407i
$528$	−15882.1	−	19612.8i	−1.30905	−	1.61655i
$529$	10886.9	+	1144.25i	0.894786	+	0.0940458i
$530$	−2316.64	+	617.266i	−0.189865	+	0.0505893i
$531$	15320.9	+	21087.5i	1.25211	+	1.72339i
$532$	12135.6	−	28817.9i	0.988996	−	2.34852i
$533$	−2160.60	−	342.205i	−0.175583	−	0.0278097i
$534$	6243.16	−	29371.8i	0.505933	−	2.38023i
$535$	−459.334	+	4312.16i	−0.0371192	+	0.348469i
$536$	−6917.72	+	1470.41i	−0.557463	+	0.118492i
$537$	11335.8	+	17455.6i	0.910942	+	1.40273i
$538$	−570.078	−	290.469i	−0.0456836	−	0.0232770i
$539$	−10566.1	−	7039.62i	−0.844371	−	0.562556i
$540$	−65255.6	−	91.4029i	−5.20028	−	0.00728399i
$541$	−10356.9	−	2201.44i	−0.823068	−	0.174948i	−0.222919	−	0.974837i	$-0.571559\pi$
$541$	−10356.9	−	2201.44i	−0.823068	−	0.174948i	−0.600149	+	0.799889i	$0.704892\pi$
$542$	3504.23	+	9128.83i	0.277711	+	0.723463i
$543$	6625.04	−	24725.0i	0.523587	−	1.95405i
$544$	155.911	+	1483.40i	0.0122879	+	0.116912i
$545$	−8661.20	−	17057.6i	−0.680744	−	1.34067i
$546$	12890.8	−	52337.7i	1.01040	−	4.10228i
$547$	−9017.17	+	1428.18i	−0.704838	+	0.111635i	−0.498556	−	0.866857i	$-0.666136\pi$
$547$	−9017.17	+	1428.18i	−0.704838	+	0.111635i	−0.206282	+	0.978493i	$0.566136\pi$
$548$	337.474	−	6439.38i	0.0263069	−	0.501965i
$549$	14012.3	+	24270.1i	1.08931	+	1.88674i
$550$	19094.2	+	12476.1i	1.48033	+	0.967244i
$551$	−4802.55	−	2772.76i	−0.371317	−	0.214380i
$552$	−12177.8	+	6204.90i	−0.938989	+	0.478439i
$553$	−323.830	−	15946.2i	−0.0249017	−	1.22622i
$554$	5636.41	−	7757.85i	0.432253	−	0.594945i
$555$	−3943.42	−	3202.47i	−0.301601	−	0.244932i
$556$	−18299.0	+	41100.1i	−1.39577	+	3.13495i
$557$	−11522.5	−	3087.46i	−0.876528	−	0.234865i	−0.207619	−	0.978210i	$-0.566571\pi$
$557$	−11522.5	−	3087.46i	−0.876528	−	0.234865i	−0.668908	+	0.743345i	$0.733238\pi$
$558$	72230.4	+	58491.0i	5.47985	+	4.43750i
$559$	−4199.98	−	12926.2i	−0.317782	−	0.978033i
$560$	−8273.06	−	12227.0i	−0.624287	−	0.922653i
$561$	−6761.96	+	20811.2i	−0.508895	+	1.56622i
$562$	−4069.30	+	2642.64i	−0.305433	+	0.198350i
$563$	−552.626	−	10544.7i	−0.0413684	−	0.789355i	−0.938012	−	0.346603i	$-0.887335\pi$
$563$	−552.626	−	10544.7i	−0.0413684	−	0.789355i	0.896644	−	0.442753i	$-0.145998\pi$
$564$	−5621.57	−	26447.4i	−0.419700	−	1.97453i
$565$	3304.13	−	2966.68i	0.246028	−	0.220901i
$566$	−7907.44	+	2569.28i	−0.587234	+	0.190804i
$567$	21336.5	+	22750.2i	1.58033	+	1.68504i
$568$	9236.85	+	9236.85i	0.682341	+	0.682341i
$569$	−24930.8	+	2620.33i	−1.83682	+	0.193058i	−0.958516	−	0.285040i	$-0.907993\pi$
$569$	−24930.8	+	2620.33i	−1.83682	+	0.193058i	−0.878307	+	0.478098i	$0.841326\pi$
$570$	50991.2	−	19491.8i	3.74699	−	1.43232i
$571$	−769.682	+	7323.04i	−0.0564102	+	0.536707i	0.929428	+	0.369005i	$0.120301\pi$
$571$	−769.682	+	7323.04i	−0.0564102	+	0.536707i	−0.985838	+	0.167702i	$0.946365\pi$
$572$	34778.1	+	13350.1i	2.54222	+	0.975865i
$573$	7158.20	+	14048.8i	0.521882	+	1.02425i
$574$	3204.50	+	441.049i	0.233020	+	0.0320715i
$575$	3096.13	−	3078.83i	0.224552	−	0.223298i
$576$	14546.3	−	25194.9i	1.05225	−	1.82255i
$577$	−14384.7	−	9341.55i	−1.03786	−	0.673993i	−0.0910678	−	0.995845i	$-0.529028\pi$
$577$	−14384.7	−	9341.55i	−1.03786	−	0.673993i	−0.946790	+	0.321852i	$0.895695\pi$
$578$	−4181.09	+	3385.78i	−0.300883	+	0.243650i
$579$	6110.51	−	2720.57i	0.438591	−	0.195273i
$580$	−8699.83	+	4417.45i	−0.622829	+	0.316249i
$581$	1704.01	−	2744.36i	0.121677	−	0.195964i
$582$	49995.6	−	49995.6i	3.56080	−	3.56080i
$583$	−1013.33	+	1251.36i	−0.0719862	+	0.0888955i
$584$	21463.1	−	23837.1i	1.52080	−	1.68902i
$585$	38556.2	−	22188.5i	2.72496	−	1.56817i
$586$	35752.7	−	32191.8i	2.52036	−	2.26934i
$587$	1768.38	−	3470.63i	0.124342	−	0.244035i	−0.820441	−	0.571731i	$-0.806272\pi$
$587$	1768.38	−	3470.63i	0.124342	−	0.244035i	0.944783	+	0.327696i	$0.106272\pi$
$588$	−11729.7	+	52162.3i	−0.822659	+	3.65839i
$589$	−28820.6	−	9364.38i	−2.01618	−	0.655097i
$590$	−20377.0	+	9038.26i	−1.42188	+	0.630677i
$591$	−26515.2	−	23874.4i	−1.84550	−	1.66169i
$592$	−3162.65	+	1214.03i	−0.219568	+	0.0842841i
$593$	−2705.16	−	10095.8i	−0.187332	−	0.699131i	−0.994119	−	0.108290i	$-0.965463\pi$
$593$	−2705.16	−	10095.8i	−0.187332	−	0.699131i	0.806788	−	0.590841i	$-0.201204\pi$
$594$	−52859.0	+	38404.3i	−3.65123	+	2.65278i
$595$	−4984.43	+	11790.1i	−0.343432	+	0.812349i
$596$	15065.2	+	10945.5i	1.03539	+	0.752256i
$597$	−16122.9	+	42001.6i	−1.10531	+	2.87942i
$598$	5790.25	−	8916.20i	0.395955	−	0.609717i
$599$	−968.133	+	558.952i	−0.0660381	+	0.0381271i	−0.532656	−	0.846332i	$-0.678806\pi$
$599$	−968.133	+	558.952i	−0.0660381	+	0.0381271i	0.466617	+	0.884459i	$0.345473\pi$
$600$	10302.7	−	47811.4i	0.701009	−	3.25315i
$601$		−	25984.5i		−	1.76361i	−0.471612	−	0.881806i	$-0.656328\pi$
$601$		−	25984.5i		−	1.76361i	0.471612	−	0.881806i	$-0.343672\pi$
$602$	6597.32	+	18984.0i	0.446656	+	1.28526i
$603$	1742.53	+	11001.9i	0.117680	+	0.743004i
$604$	13154.9	+	29546.4i	0.886200	+	1.99044i
$605$	437.418	−	22.3098i	0.0293944	−	0.00149921i
$606$	−75043.6	−	33411.6i	−5.03042	−	2.23969i
$607$	13482.8	−	3612.71i	0.901566	−	0.241574i	0.221877	−	0.975075i	$-0.428782\pi$
$607$	13482.8	−	3612.71i	0.901566	−	0.241574i	0.679689	+	0.733501i	$0.262115\pi$
$608$	390.952	−	2468.37i	0.0260776	−	0.164648i
$609$	8919.31	+	3217.59i	0.593479	+	0.214094i
$610$	−22804.4	+	7374.29i	−1.51364	+	0.489469i
$611$	7166.18	+	7958.85i	0.474489	+	0.526973i
$612$	64849.8	−	3398.64i	4.28333	−	0.224480i
$613$	6753.08	−	353.914i	0.444950	−	0.0233188i	0.171454	−	0.985192i	$-0.445153\pi$
$613$	6753.08	−	353.914i	0.444950	−	0.0233188i	0.273496	+	0.961873i	$0.411820\pi$
$614$	−501.431	−	556.895i	−0.0329578	−	0.0366034i
$615$	2222.27	+	3067.72i	0.145708	+	0.201142i
$616$	−26385.6	−	9518.47i	−1.72582	−	0.622581i
$617$	951.939	−	6010.30i	0.0621128	−	0.392165i	−0.936972	−	0.349403i	$-0.886384\pi$
$617$	951.939	−	6010.30i	0.0621128	−	0.392165i	0.999085	−	0.0427617i	$-0.0136156\pi$
$618$	−23496.8	+	6295.96i	−1.52942	+	0.409807i
$619$	12187.5	+	5426.22i	0.791367	+	0.352339i	0.762288	−	0.647238i	$-0.224076\pi$
$619$	12187.5	+	5426.22i	0.791367	+	0.352339i	0.0290791	+	0.999577i	$0.490743\pi$
$620$	−41483.0	+	33496.2i	−2.68709	+	2.16974i
$621$	5087.36	+	11426.4i	0.328742	+	0.738367i
$622$	−7082.01	−	44714.0i	−0.456532	−	2.88243i
$623$	−3872.67	−	11143.7i	−0.249045	−	0.716635i
$624$		−	42094.0i		−	2.70050i
$625$	1546.17	+	15548.3i	0.0989548	+	0.995092i
$626$	−26518.2	+	15310.3i	−1.69310	+	0.977510i
$627$	19968.6	−	30748.9i	1.27188	−	1.95852i
$628$	11151.8	−	29051.5i	0.708608	−	1.84599i
$629$	2376.35	+	1726.52i	0.150638	+	0.109445i
$630$	−56335.3	+	33961.0i	−3.56262	+	2.14768i
$631$	6723.70	−	4885.05i	0.424194	−	0.308195i	−0.355129	−	0.934817i	$-0.615563\pi$
$631$	6723.70	−	4885.05i	0.424194	−	0.308195i	0.779323	+	0.626622i	$0.215563\pi$
$632$	−9119.99	−	34036.3i	−0.574009	−	2.14223i
$633$	−10615.3	+	4074.81i	−0.666538	+	0.255860i
$634$	2885.76	+	2598.35i	0.180770	+	0.162766i
$635$	−1266.47	−	12214.2i	−0.0791468	−	0.763315i
$636$	6448.70	+	2095.31i	0.402056	+	0.130636i
$637$	−6306.97	−	20216.1i	−0.392294	−	1.25744i
$638$	−4435.18	+	8704.53i	−0.275220	+	0.540150i
$639$	15289.8	−	13767.0i	0.946563	−	0.852289i
$640$	20068.1	+	18120.3i	1.23947	+	1.11917i
$641$	3022.54	−	3356.87i	0.186245	−	0.206846i	−0.642790	−	0.766042i	$-0.722223\pi$
$641$	3022.54	−	3356.87i	0.186245	−	0.206846i	0.829036	+	0.559196i	$0.188890\pi$
$642$	11506.6	−	14209.5i	0.707366	−	0.873524i
$643$	−16990.3	+	16990.3i	−1.04204	+	1.04204i	−0.0429655	+	0.999077i	$0.513681\pi$
$643$	−16990.3	+	16990.3i	−1.04204	+	1.04204i	−0.999077	+	0.0429655i	$0.986319\pi$
$644$	−5562.56	+	8958.70i	−0.340366	+	0.548171i
$645$	−10714.3	+	20955.5i	−0.654073	+	1.27926i
$646$	−28835.6	+	12838.5i	−1.75623	+	0.781923i
$647$	22231.2	−	18002.4i	1.35085	−	1.09389i	0.364145	−	0.931342i	$-0.381361\pi$
$647$	22231.2	−	18002.4i	1.35085	−	1.09389i	0.986700	−	0.162551i	$-0.0519722\pi$
$648$	57790.7	+	37529.7i	3.50344	+	2.27516i
$649$	−7485.80	+	12965.8i	−0.452763	+	0.784209i
$650$	11654.9	+	36214.9i	0.703295	+	2.18533i
$651$	51330.6	+	7064.85i	3.09033	+	0.425335i
$652$	−383.991	−	753.625i	−0.0230648	−	0.0452672i
$653$	18422.1	+	7071.56i	1.10400	+	0.423785i	0.841013	−	0.541015i	$-0.181960\pi$
$653$	18422.1	+	7071.56i	1.10400	+	0.423785i	0.262985	+	0.964800i	$0.415293\pi$
$654$	−8431.24	+	80217.9i	−0.504110	+	4.79628i
$655$	−5422.31	−	1461.05i	−0.323461	−	0.0871570i
$656$	2512.27	−	264.051i	0.149524	−	0.0157156i
$657$	−35723.5	−	35723.5i	−2.12132	−	2.12132i
$658$	−10833.4	−	11551.2i	−0.641840	−	0.684366i
$659$	−8999.51	+	2924.12i	−0.531974	+	0.172849i	−0.562673	−	0.826680i	$-0.690227\pi$
$659$	−8999.51	+	2924.12i	−0.531974	+	0.172849i	0.0306985	+	0.999529i	$0.490227\pi$
$660$	−26155.4	−	58968.1i	−1.54257	−	3.47778i
$661$	−5493.47	−	25844.8i	−0.323255	−	1.52079i	−0.776907	−	0.629615i	$-0.783213\pi$
$661$	−5493.47	−	25844.8i	−0.323255	−	1.52079i	0.453653	−	0.891178i	$-0.350121\pi$
$662$	−2501.95	−	47740.1i	−0.146890	−	2.80283i
$663$	−30610.1	+	19878.4i	−1.79306	+	1.16443i
$664$	2205.38	−	6787.45i	0.128893	−	0.396693i
$665$	13179.8	−	16919.9i	0.768555	−	0.986653i
$666$	4664.49	+	14355.8i	0.271389	+	0.835250i
$667$	1453.40	+	1176.94i	0.0843715	+	0.0683227i
$668$	−26227.2	−	7027.56i	−1.51910	−	0.407042i
$669$	−2336.70	+	5248.32i	−0.135041	+	0.303306i
$670$	−9512.47	−	511.889i	−0.548506	−	0.0295164i
$671$	−9461.51	+	13022.7i	−0.544348	+	0.749231i
$672$	86.7591	+	4272.25i	0.00498036	+	0.245246i
$673$	−9506.30	+	4843.70i	−0.544489	+	0.277431i	−0.704524	−	0.709680i	$-0.748839\pi$
$673$	−9506.30	+	4843.70i	−0.544489	+	0.277431i	0.160035	+	0.987111i	$0.448839\pi$
$674$	−10015.3	−	5782.33i	−0.572366	−	0.330456i
$675$	−43201.0	−	11705.5i	−2.46342	−	0.667473i
$676$	13161.8	+	22796.9i	0.748850	+	1.29705i
$677$	−1351.49	+	25787.9i	−0.0767236	+	1.46397i	0.640944	+	0.767588i	$0.278543\pi$
$677$	−1351.49	+	25787.9i	−0.0767236	+	1.46397i	−0.717667	+	0.696386i	$0.754790\pi$
$678$	−18492.1	+	2928.86i	−1.04747	+	0.165903i
$679$	6643.35	−	26972.4i	0.375476	−	1.52446i
$680$	−4463.05	+	27925.4i	−0.251691	+	1.57484i
$681$	5038.56	+	47938.6i	0.283521	+	2.69752i
$682$	−13817.1	+	51565.9i	−0.775780	+	2.89525i
$683$	−3990.11	−	10394.6i	−0.223539	−	0.582340i	0.775244	−	0.631662i	$-0.217627\pi$
$683$	−3990.11	−	10394.6i	−0.223539	−	0.582340i	−0.998783	+	0.0493226i	$0.984294\pi$
$684$	−106428.	−	22622.0i	−5.94939	−	1.26458i
$685$	1372.62	−	4204.44i	0.0765621	−	0.234516i
$686$	9931.16	+	29698.1i	0.552731	+	1.65288i
$687$	73.5227	+	37.4617i	0.00408307	+	0.00208043i
$688$	8548.14	+	13163.0i	0.473684	+	0.729410i
$689$	−2627.05	+	558.397i	−0.145258	+	0.0308755i
$690$	−18012.9	+	3802.40i	−0.993826	+	0.209790i
$691$	4716.93	−	22191.4i	0.259683	−	1.22171i	−0.634115	−	0.773239i	$-0.718635\pi$
$691$	4716.93	−	22191.4i	0.259683	−	1.22171i	0.893797	−	0.448471i	$-0.148031\pi$
$692$	41620.7	+	6592.07i	2.28639	+	0.362128i
$693$	−17146.3	+	40716.6i	−0.939876	+	2.23188i
$694$	−10481.5	−	14426.6i	−0.573305	−	0.789086i
$695$	−19453.4	+	23954.2i	−1.06174	+	1.30739i
$696$	20833.5	+	2189.69i	1.13461	+	0.119253i
$697$	−1378.41	−	1702.19i	−0.0749080	−	0.0925037i
$698$	−2906.46	−	152.321i	−0.157609	−	0.00825995i
$699$	−32302.0			−1.74789
$700$	−12287.3	−	35679.2i	−0.663453	−	1.92649i
$701$	−6475.19			−0.348880			−0.174440	−	0.984668i	$-0.555811\pi$
$701$	−6475.19			−0.348880			−0.174440	+	0.984668i	$0.555811\pi$
$702$	−108830.	−	5703.55i	−5.85119	−	0.306648i
$703$	−3097.22	−	3824.75i	−0.166165	−	0.205197i
$704$	16618.7	+	1746.70i	0.889689	+	0.0935101i
$705$	996.538	−	18518.7i	0.0532366	−	0.989299i
$706$	−1562.96	−	2151.23i	−0.0833183	−	0.114678i
$707$	−32021.6	+	4024.47i	−1.70339	+	0.214082i
$708$	62269.3	+	9862.49i	3.30540	+	0.523524i
$709$	−1839.76	+	8655.37i	−0.0974520	+	0.458476i	0.902180	+	0.431359i	$0.141966\pi$
$709$	−1839.76	+	8655.37i	−0.0974520	+	0.458476i	−0.999632	+	0.0271165i	$0.991367\pi$
$710$	8776.39	+	15250.4i	0.463904	+	0.806111i
$711$	−54286.4	+	11538.9i	−2.86343	+	0.608641i
$712$	−14195.4	−	21859.0i	−0.747185	−	1.15056i
$713$	9105.79	+	4639.63i	0.478281	+	0.243696i
$714$	44657.1	−	30307.3i	2.34069	−	1.58854i
$715$	20650.5	+	15047.7i	1.08012	+	0.787065i
$716$	34702.7	+	7376.29i	1.81132	+	0.385007i
$717$	−18919.1	−	49286.0i	−0.985422	−	2.56711i
$718$	−15901.0	+	59343.4i	−0.826491	+	3.08451i
$719$	386.213	+	3674.57i	0.0200324	+	0.190596i	0.999962	−	0.00874956i	$-0.00278511\pi$
$719$	386.213	+	3674.57i	0.0200324	+	0.190596i	−0.979929	+	0.199345i	$0.936118\pi$
$720$	−36375.1	+	36273.3i	−1.88280	+	1.87754i
$721$	−6619.32	+	6893.74i	−0.341909	+	0.356084i
$722$	18840.3	−	2984.01i	0.971142	−	0.153814i
$723$	2071.45	−	39525.6i	0.106553	−	2.03316i
$724$	−21816.1	−	37786.7i	−1.11988	−	1.93968i
$725$	−6550.01	+	1373.08i	−0.335533	+	0.0703379i
$726$	−1599.27	−	923.338i	−0.0817554	−	0.0472015i
$727$	−1608.37	+	819.507i	−0.0820513	+	0.0418072i	−0.494535	−	0.869158i	$-0.664661\pi$
$727$	−1608.37	+	819.507i	−0.0820513	+	0.0418072i	0.412483	+	0.910965i	$0.364661\pi$
$728$	−24210.9	−	40034.6i	−1.23258	−	2.03816i
$729$	9451.81	−	13009.3i	0.480202	−	0.660941i
$730$	36268.5	−	23480.9i	1.83884	−	1.19050i
$731$	5535.15	−	12432.1i	0.280061	−	0.629028i
$732$	65474.4	+	17543.8i	3.30602	+	0.885844i
$733$	26220.1	+	21232.6i	1.32123	+	1.06991i	0.992077	+	0.125635i	$0.0400967\pi$
$733$	26220.1	+	21232.6i	1.32123	+	1.06991i	0.329153	+	0.944276i	$0.393237\pi$
$734$	−6876.11	−	21162.5i	−0.345779	−	1.06420i
$735$	−17076.7	+	32452.7i	−0.856986	+	1.62862i
$736$	−260.443	+	801.562i	−0.0130436	+	0.0401440i
$737$	−5365.87	+	3484.64i	−0.268188	+	0.174163i
$738$	−589.081	−	11240.3i	−0.0293826	−	0.560654i
$739$	1623.63	+	7638.56i	0.0808201	+	0.380228i	0.999904	−	0.0138326i	$-0.00440319\pi$
$739$	1623.63	+	7638.56i	0.0808201	+	0.380228i	−0.919084	+	0.394061i	$0.871070\pi$
$740$	−8613.05	+	893.073i	−0.427868	+	0.0443649i
$741$	58160.5	−	18897.5i	2.88337	−	0.936864i
$742$	3867.06	−	904.404i	0.191326	−	0.0447462i
$743$	18980.3	+	18980.3i	0.937175	+	0.937175i	0.998140	−	0.0609650i	$-0.0194178\pi$
$743$	18980.3	+	18980.3i	0.937175	+	0.937175i	−0.0609650	+	0.998140i	$0.519418\pi$
$744$	113846.	−	11965.7i	5.60993	−	0.589628i
$745$	8024.09	+	9937.36i	0.394604	+	0.488693i
$746$	−1980.79	+	18846.0i	−0.0972145	+	0.924934i
$747$	−10494.0	−	4028.26i	−0.513996	−	0.197305i
$748$	16933.7	+	33234.3i	0.827752	+	1.62455i
$749$	979.464	−	7116.43i	0.0477822	−	0.347168i
$750$	30155.0	−	58572.8i	1.46814	−	2.85170i
$751$	3524.31	−	6104.29i	0.171244	−	0.296603i	−0.767611	−	0.640916i	$-0.778555\pi$
$751$	3524.31	−	6104.29i	0.171244	−	0.296603i	0.938855	+	0.344313i	$0.111888\pi$
$752$	−10372.1	−	6735.71i	−0.502967	−	0.326631i
$753$	12899.3	−	10445.6i	0.624271	−	0.505525i
$754$	−14886.0	+	6627.68i	−0.718987	+	0.320114i
$755$	3439.60	+	21915.4i	0.165801	+	1.05640i
$756$	108041.	+	3464.43i	5.19762	+	0.166667i
$757$	−14662.2	+	14662.2i	−0.703972	+	0.703972i	−0.965261	−	0.261289i	$-0.915852\pi$
$757$	−14662.2	+	14662.2i	−0.703972	+	0.703972i	0.261289	+	0.965261i	$0.415852\pi$
$758$	11398.2	−	14075.6i	0.546176	−	0.674472i
$759$	−8273.50	+	9188.65i	−0.395664	+	0.439429i
$760$	19333.1	−	43259.6i	0.922743	−	2.06473i
$761$	15891.4	−	14308.7i	0.756983	−	0.681590i	−0.197351	−	0.980333i	$-0.563234\pi$
$761$	15891.4	−	14308.7i	0.756983	−	0.681590i	0.954334	+	0.298743i	$0.0965672\pi$
$762$	−23505.1	+	46131.4i	−1.11746	+	2.19313i
$763$	13474.5	+	28682.4i	0.639333	+	1.36091i
$764$	25561.1	+	8305.30i	1.21043	+	0.393292i
$765$	43555.1	+	9321.71i	2.05848	+	0.440558i
$766$	11802.1	+

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)

\(f(q)\)	\(=\)	\(q+(-4.92278 - 0.257992i) q^{2} +(6.01798 + 7.43159i) q^{3} +(16.2110 + 1.70384i) q^{4} +(10.4321 + 4.02129i) q^{5} +(-27.7079 - 38.1366i) q^{6} +(-17.0686 - 7.18780i) q^{7} +(-40.4127 - 6.40074i) q^{8} +(-13.3988 + 63.0363i) q^{9} +O(q^{10})\)	\(q+(-4.92278 - 0.257992i) q^{2} +(6.01798 + 7.43159i) q^{3} +(16.2110 + 1.70384i) q^{4} +(10.4321 + 4.02129i) q^{5} +(-27.7079 - 38.1366i) q^{6} +(-17.0686 - 7.18780i) q^{7} +(-40.4127 - 6.40074i) q^{8} +(-13.3988 + 63.0363i) q^{9} +(-50.3175 - 22.4873i) q^{10} +(-36.2070 + 7.69603i) q^{11} +(84.8951 + 130.727i) q^{12} +(-55.0114 - 28.0297i) q^{13} +(82.1703 + 39.7875i) q^{14} +(32.8957 + 101.727i) q^{15} +(69.7388 + 14.8234i) q^{16} +(-22.1540 - 57.7131i) q^{17} +(82.2220 - 306.857i) q^{18} +(10.8269 + 103.011i) q^{19} +(162.263 + 82.9638i) q^{20} +(-49.3015 - 170.102i) q^{21} +(180.224 - 28.5447i) q^{22} +(1.82815 - 34.8831i) q^{23} +(-195.635 - 338.850i) q^{24} +(92.6584 + 83.9012i) q^{25} +(263.577 + 152.176i) q^{26} +(-319.043 + 162.560i) q^{27} +(-264.451 - 145.603i) q^{28} +(-31.4695 + 43.3140i) q^{29} +(-135.694 - 509.267i) q^{30} +(-118.998 + 267.273i) q^{31} +(-23.3058 - 6.24476i) q^{32} +(-275.087 - 222.761i) q^{33} +(94.1696 + 289.824i) q^{34} +(-149.157 - 143.622i) q^{35} +(-324.611 + 999.051i) q^{36} +(-39.8493 + 25.8784i) q^{37} +(-26.7225 - 509.895i) q^{38} +(-122.752 - 577.504i) q^{39} +(-395.851 - 229.285i) q^{40} +(33.6968 - 10.9488i) q^{41} +(198.815 + 850.096i) q^{42} +(155.660 + 155.660i) q^{43} +(-600.064 + 63.0692i) q^{44} +(-393.265 + 603.722i) q^{45} +(-17.9991 + 171.250i) q^{46} +(-161.941 - 62.1633i) q^{47} +(309.525 + 607.477i) q^{48} +(239.671 + 245.371i) q^{49} +(-434.491 - 436.932i) q^{50} +(295.578 - 511.956i) q^{51} +(-844.030 - 548.120i) q^{52} +(33.8061 - 27.3756i) q^{53} +(1612.52 - 717.938i) q^{54} +(-408.664 - 65.3129i) q^{55} +(643.779 + 399.730i) q^{56} +(-700.382 + 700.382i) q^{57} +(166.092 - 205.106i) q^{58} +(270.639 - 300.575i) q^{59} +(359.945 + 1705.15i) q^{60} +(323.167 - 290.981i) q^{61} +(654.754 - 1285.03i) q^{62} +(681.790 - 979.631i) q^{63} +(-429.340 - 139.501i) q^{64} +(-461.170 - 513.626i) q^{65} +(1296.72 + 1167.57i) q^{66} +(161.366 - 61.9427i) q^{67} +(-260.804 - 973.334i) q^{68} +(270.239 - 196.340i) q^{69} +(697.213 + 745.498i) q^{70} +(-258.285 - 187.655i) q^{71} +(944.961 - 2461.71i) q^{72} +(-426.964 + 657.467i) q^{73} +(202.846 - 117.113i) q^{74} +(-65.9027 + 1193.52i) q^{75} +1688.36i q^{76} +(673.318 + 128.888i) q^{77} +(455.291 + 2874.59i) q^{78} +(350.279 + 786.739i) q^{79} +(667.914 + 435.080i) q^{80} +(-1538.50 - 684.986i) q^{81} +(-168.707 + 45.2048i) q^{82} +(-27.2857 + 172.275i) q^{83} +(-509.397 - 2841.53i) q^{84} +(0.968099 - 691.158i) q^{85} +(-726.122 - 806.440i) q^{86} +(-511.275 + 26.7948i) q^{87} +(1512.48 - 79.2659i) q^{88} +(426.238 + 473.385i) q^{89} +(2091.71 - 2870.53i) q^{90} +(737.493 + 873.837i) q^{91} +(89.0715 - 562.375i) q^{92} +(-2702.39 + 724.104i) q^{93} +(781.162 + 347.796i) q^{94} +(-301.291 + 1118.17i) q^{95} +(-93.8452 - 210.780i) q^{96} +(234.636 + 1481.43i) q^{97} +(-1116.54 - 1269.74i) q^{98} -2385.47i 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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