LMFDB - Embedded newform 175.4.x.a.103.26

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			103.26
Character	$\chi$	$=$	175.103
Dual form			175.4.x.a.17.26

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.757961 - 0.0397231i) q^{2} +(-6.12747 - 7.56679i) q^{3} +(-7.38325 - 0.776011i) q^{4} +(10.8983 + 2.49552i) q^{5} +(4.34381 + 5.97873i) q^{6} +(2.54741 + 18.3442i) q^{7} +(11.5626 + 1.83134i) q^{8} +(-14.0969 + 66.3205i) q^{9} +O(q^{10})$	\(q+(-0.757961 - 0.0397231i) q^{2} +(-6.12747 - 7.56679i) q^{3} +(-7.38325 - 0.776011i) q^{4} +(10.8983 + 2.49552i) q^{5} +(4.34381 + 5.97873i) q^{6} +(2.54741 + 18.3442i) q^{7} +(11.5626 + 1.83134i) q^{8} +(-14.0969 + 66.3205i) q^{9} +(-8.16134 - 2.32442i) q^{10} +(32.3675 - 6.87992i) q^{11} +(39.3687 + 60.6225i) q^{12} +(-26.8007 - 13.6556i) q^{13} +(-1.20215 - 14.0054i) q^{14} +(-47.8957 - 97.7562i) q^{15} +(49.4022 + 10.5008i) q^{16} +(-20.5510 - 53.5371i) q^{17} +(13.3193 - 49.7084i) q^{18} +(7.59237 + 72.2366i) q^{19} +(-78.5281 - 26.8822i) q^{20} +(123.198 - 131.679i) q^{21} +(-24.8066 + 3.92898i) q^{22} +(2.68398 - 51.2135i) q^{23} +(-56.9923 - 98.7136i) q^{24} +(112.545 + 54.3937i) q^{25} +(19.7715 + 11.4151i) q^{26} +(353.975 - 180.359i) q^{27} +(-4.57285 - 137.417i) q^{28} +(132.793 - 182.775i) q^{29} +(32.4199 + 75.9979i) q^{30} +(-109.713 + 246.419i) q^{31} +(-127.491 - 34.1611i) q^{32} +(-250.390 - 202.762i) q^{33} +(13.4502 + 41.3954i) q^{34} +(-18.0160 + 206.278i) q^{35} +(155.546 - 478.721i) q^{36} +(233.258 - 151.480i) q^{37} +(-2.88526 - 55.0541i) q^{38} +(60.8911 + 286.470i) q^{39} +(121.443 + 48.8133i) q^{40} +(-145.309 + 47.2138i) q^{41} +(-98.6098 + 94.9140i) q^{42} +(234.929 + 234.929i) q^{43} +(-244.316 + 25.6787i) q^{44} +(-319.136 + 687.600i) q^{45} +(-4.06871 + 38.7112i) q^{46} +(276.801 + 106.254i) q^{47} +(-223.253 - 438.159i) q^{48} +(-330.021 + 93.4606i) q^{49} +(-83.1439 - 45.6990i) q^{50} +(-279.179 + 483.552i) q^{51} +(187.279 + 121.621i) q^{52} +(407.159 - 329.711i) q^{53} +(-275.464 + 122.644i) q^{54} +(369.919 + 5.79445i) q^{55} +(-4.13976 + 216.773i) q^{56} +(500.077 - 500.077i) q^{57} +(-107.913 + 133.261i) q^{58} +(371.186 - 412.244i) q^{59} +(277.766 + 758.926i) q^{60} +(79.3325 - 71.4313i) q^{61} +(92.9464 - 182.418i) q^{62} +(-1252.51 - 89.6504i) q^{63} +(-288.995 - 93.9003i) q^{64} +(-258.004 - 215.705i) q^{65} +(181.731 + 163.632i) q^{66} +(-69.2096 + 26.5671i) q^{67} +(110.188 + 411.226i) q^{68} +(-403.968 + 293.500i) q^{69} +(21.8494 - 155.635i) q^{70} +(646.549 + 469.746i) q^{71} +(-284.452 + 741.024i) q^{72} +(382.526 - 589.039i) q^{73} +(-182.818 + 105.550i) q^{74} +(-278.028 - 1184.90i) q^{75} -539.232i q^{76} +(208.660 + 576.231i) q^{77} +(-34.7736 - 219.552i) q^{78} +(194.697 + 437.297i) q^{79} +(512.194 + 237.724i) q^{80} +(-1861.32 - 828.714i) q^{81} +(112.014 - 30.0141i) q^{82} +(67.8602 - 428.453i) q^{83} +(-1011.78 + 876.618i) q^{84} +(-90.3672 - 634.748i) q^{85} +(-168.735 - 187.399i) q^{86} +(-2196.70 + 115.124i) q^{87} +(386.853 - 20.2741i) q^{88} +(85.3692 + 94.8122i) q^{89} +(269.206 - 508.497i) q^{90} +(182.230 - 526.425i) q^{91} +(-59.5587 + 376.039i) q^{92} +(2536.86 - 679.749i) q^{93} +(-205.583 - 91.5316i) q^{94} +(-97.5241 + 806.201i) q^{95} +(522.706 + 1174.02i) q^{96} +(-35.2334 - 222.455i) q^{97} +(253.856 - 57.7300i) q^{98} +2243.61i 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 $

$2$	−0.757961	−	0.0397231i	−0.267980	−	0.0140442i	−0.0821272	−	0.996622i	$-0.526171\pi$
$2$	−0.757961	−	0.0397231i	−0.267980	−	0.0140442i	−0.185853	+	0.982578i	$0.559505\pi$
$3$	−6.12747	−	7.56679i	−1.17923	−	1.45623i	−0.861286	−	0.508120i	$-0.830341\pi$
$3$	−6.12747	−	7.56679i	−1.17923	−	1.45623i	−0.317945	−	0.948109i	$-0.602993\pi$
$4$	−7.38325	−	0.776011i	−0.922906	−	0.0970013i
$5$	10.8983	+	2.49552i	0.974771	+	0.223206i
$5$	10.8983	+	2.49552i	0.974771	+	0.223206i
$6$	4.34381	+	5.97873i	0.295558	+	0.406801i
$7$	2.54741	+	18.3442i	0.137547	+	0.990495i
$7$	2.54741	+	18.3442i	0.137547	+	0.990495i
$8$	11.5626	+	1.83134i	0.511002	+	0.0809347i
$9$	−14.0969	+	66.3205i	−0.522106	+	2.45631i
$10$	−8.16134	−	2.32442i	−0.258084	−	0.0735046i
$11$	32.3675	−	6.87992i	0.887197	−	0.188580i	0.258297	−	0.966066i	$-0.416839\pi$
$11$	32.3675	−	6.87992i	0.887197	−	0.188580i	0.628900	+	0.777486i	$0.283505\pi$
$12$	39.3687	+	60.6225i	0.947063	+	1.45835i
$13$	−26.8007	−	13.6556i	−0.571783	−	0.291338i	0.144094	−	0.989564i	$-0.453973\pi$
$13$	−26.8007	−	13.6556i	−0.571783	−	0.291338i	−0.715878	+	0.698226i	$0.753973\pi$
$14$	−1.20215	−	14.0054i	−0.0229492	−	0.267364i
$15$	−47.8957	−	97.7562i	−0.824441	−	1.68270i
$16$	49.4022	+	10.5008i	0.771909	+	0.164074i
$17$	−20.5510	−	53.5371i	−0.293197	−	0.763804i	−0.998492	−	0.0548904i	$-0.982519\pi$
$17$	−20.5510	−	53.5371i	−0.293197	−	0.763804i	0.705296	−	0.708913i	$-0.250814\pi$
$18$	13.3193	−	49.7084i	0.174411	−	0.650910i
$19$	7.59237	+	72.2366i	0.0916742	+	0.872221i	0.939639	+	0.342168i	$0.111161\pi$
$19$	7.59237	+	72.2366i	0.0916742	+	0.872221i	−0.847965	+	0.530053i	$0.822172\pi$
$20$	−78.5281	−	26.8822i	−0.877971	−	0.300552i
$21$	123.198	−	131.679i	1.28019	−	1.36832i
$22$	−24.8066	+	3.92898i	−0.240399	+	0.0380755i
$23$	2.68398	−	51.2135i	0.0243326	−	0.464293i	−0.959105	−	0.283049i	$-0.908654\pi$
$23$	2.68398	−	51.2135i	0.0243326	−	0.464293i	0.983438	−	0.181245i	$-0.0580125\pi$
$24$	−56.9923	−	98.7136i	−0.484730	−	0.839576i
$25$	112.545	+	54.3937i	0.900358	+	0.435150i
$26$	19.7715	+	11.4151i	0.149135	+	0.0861030i
$27$	353.975	−	180.359i	2.52306	−	1.28556i
$28$	−4.57285	−	137.417i	−0.0308639	−	0.927476i
$29$	132.793	−	182.775i	0.850315	−	1.17036i	−0.133478	−	0.991052i	$-0.542615\pi$
$29$	132.793	−	182.775i	0.850315	−	1.17036i	0.983793	−	0.179306i	$-0.0573853\pi$
$30$	32.4199	+	75.9979i	0.197301	+	0.462509i
$31$	−109.713	+	246.419i	−0.635644	+	1.42768i	0.252263	+	0.967659i	$0.418825\pi$
$31$	−109.713	+	246.419i	−0.635644	+	1.42768i	−0.887908	+	0.460022i	$0.847842\pi$
$32$	−127.491	−	34.1611i	−0.704294	−	0.188715i
$33$	−250.390	−	202.762i	−1.32083	−	1.06958i
$34$	13.4502	+	41.3954i	0.0678438	+	0.208802i
$35$	−18.0160	+	206.278i	−0.0870074	+	0.996208i
$36$	155.546	−	478.721i	0.720120	−	2.21630i
$37$	233.258	−	151.480i	1.03642	−	0.673057i	0.0899789	−	0.995944i	$-0.471320\pi$
$37$	233.258	−	151.480i	1.03642	−	0.673057i	0.946438	+	0.322887i	$0.104653\pi$
$38$	−2.88526	−	55.0541i	−0.0123171	−	0.235025i
$39$	60.8911	+	286.470i	0.250010	+	1.17620i
$40$	121.443	+	48.8133i	0.480045	+	0.192951i
$41$	−145.309	+	47.2138i	−0.553499	+	0.179843i	−0.572394	−	0.819979i	$-0.693985\pi$
$41$	−145.309	+	47.2138i	−0.553499	+	0.179843i	0.0188948	+	0.999821i	$0.493985\pi$
$42$	−98.6098	+	94.9140i	−0.362282	+	0.348704i
$43$	234.929	+	234.929i	0.833172	+	0.833172i	0.987949	−	0.154778i	$-0.0494661\pi$
$43$	234.929	+	234.929i	0.833172	+	0.833172i	−0.154778	+	0.987949i	$0.549466\pi$
$44$	−244.316	+	25.6787i	−0.837092	+	0.0879819i
$45$	−319.136	+	687.600i	−1.05720	+	2.27781i
$46$	−4.06871	+	38.7112i	−0.0130413	+	0.124080i
$47$	276.801	+	106.254i	0.859053	+	0.329760i	0.747713	−	0.664023i	$-0.231152\pi$
$47$	276.801	+	106.254i	0.859053	+	0.329760i	0.111341	+	0.993782i	$0.464485\pi$
$48$	−223.253	−	438.159i	−0.671330	−	1.31756i
$49$	−330.021	+	93.4606i	−0.962161	+	0.272480i
$50$	−83.1439	−	45.6990i	−0.235166	−	0.129256i
$51$	−279.179	+	483.552i	−0.766527	+	1.32766i
$52$	187.279	+	121.621i	0.499442	+	0.324341i
$53$	407.159	−	329.711i	1.05524	−	0.854515i	0.0655633	−	0.997848i	$-0.479116\pi$
$53$	407.159	−	329.711i	1.05524	−	0.854515i	0.989674	+	0.143334i	$0.0457823\pi$
$54$	−275.464	+	122.644i	−0.694183	+	0.309070i
$55$	369.919	+	5.79445i	0.906906	+	0.0142059i
$56$	−4.13976	+	216.773i	−0.00987855	+	0.517277i
$57$	500.077	−	500.077i	1.16205	−	1.16205i
$58$	−107.913	+	133.261i	−0.244304	+	0.301690i
$59$	371.186	−	412.244i	0.819055	−	0.909653i	−0.178177	−	0.983998i	$-0.557020\pi$
$59$	371.186	−	412.244i	0.819055	−	0.909653i	0.997233	+	0.0743452i	$0.0236867\pi$
$60$	277.766	+	758.926i	0.597658	+	1.63295i
$61$	79.3325	−	71.4313i	0.166516	−	0.149932i	−0.581660	−	0.813432i	$-0.697597\pi$
$61$	79.3325	−	71.4313i	0.166516	−	0.149932i	0.748176	+	0.663500i	$0.230930\pi$
$62$	92.9464	−	182.418i	0.190390	−	0.373662i
$63$	−1252.51	−	89.6504i	−2.50478	−	0.179284i
$64$	−288.995	−	93.9003i	−0.564444	−	0.183399i
$65$	−258.004	−	215.705i	−0.492329	−	0.411614i
$66$	181.731	+	163.632i	0.338933	+	0.305177i
$67$	−69.2096	+	26.5671i	−0.126198	+	0.0484431i	−0.420648	−	0.907224i	$-0.638197\pi$
$67$	−69.2096	+	26.5671i	−0.126198	+	0.0484431i	0.294449	+	0.955667i	$0.404864\pi$
$68$	110.188	+	411.226i	0.196503	+	0.733360i
$69$	−403.968	+	293.500i	−0.704811	+	0.512075i
$70$	21.8494	−	155.635i	0.0373072	−	0.265742i
$71$	646.549	+	469.746i	1.08072	+	0.785191i	0.977809	−	0.209499i	$-0.0671835\pi$
$71$	646.549	+	469.746i	1.08072	+	0.785191i	0.102914	+	0.994690i	$0.467183\pi$
$72$	−284.452	+	741.024i	−0.465598	+	1.21292i
$73$	382.526	−	589.039i	0.613306	−	0.944408i	−0.386450	−	0.922310i	$-0.626299\pi$
$73$	382.526	−	589.039i	0.613306	−	0.944408i	0.999756	−	0.0220979i	$-0.00703455\pi$
$74$	−182.818	+	105.550i	−0.287191	+	0.165810i
$75$	−278.028	−	1184.90i	−0.428052	−	1.82427i
$76$		−	539.232i		−	0.813871i
$77$	208.660	+	576.231i	0.308819	+	0.852826i
$78$	−34.7736	−	219.552i	−0.0504787	−	0.318710i
$79$	194.697	+	437.297i	0.277280	+	0.622781i	0.997477	−	0.0709883i	$-0.0226153\pi$
$79$	194.697	+	437.297i	0.277280	+	0.622781i	−0.720197	+	0.693770i	$0.755949\pi$
$80$	512.194	+	237.724i	0.715813	+	0.332230i
$81$	−1861.32	−	828.714i	−2.55325	−	1.13678i
$82$	112.014	−	30.0141i	0.150852	−	0.0404208i
$83$	67.8602	−	428.453i	0.0897425	−	0.566612i	−0.901314	−	0.433167i	$-0.857396\pi$
$83$	67.8602	−	428.453i	0.0897425	−	0.566612i	0.991056	−	0.133445i	$-0.0426040\pi$
$84$	−1011.78	+	876.618i	−1.31422	+	1.13865i
$85$	−90.3672	−	634.748i	−0.115314	−	0.809977i
$86$	−168.735	−	187.399i	−0.211572	−	0.234974i
$87$	−2196.70	+	115.124i	−2.70703	+	0.141869i
$88$	386.853	−	20.2741i	0.468622	−	0.0245594i
$89$	85.3692	+	94.8122i	0.101676	+	0.112922i	0.791835	−	0.610736i	$-0.209126\pi$
$89$	85.3692	+	94.8122i	0.101676	+	0.112922i	−0.690159	+	0.723658i	$0.742459\pi$
$90$	269.206	−	508.497i	0.315298	−	0.595559i
$91$	182.230	−	526.425i	0.209922	−	0.606421i
$92$	−59.5587	+	376.039i	−0.0674938	+	0.426139i
$93$	2536.86	−	679.749i	2.82860	−	0.757921i
$94$	−205.583	−	91.5316i	−0.225578	−	0.100434i
$95$	−97.5241	+	806.201i	−0.105324	+	0.870679i
$96$	522.706	+	1174.02i	0.555713	+	1.24815i
$97$	−35.2334	−	222.455i	−0.0368806	−	0.232855i	0.962362	−	0.271771i	$-0.0876094\pi$
$97$	−35.2334	−	222.455i	−0.0368806	−	0.232855i	−0.999242	+	0.0389165i	$0.987609\pi$
$98$	253.856	−	57.7300i	0.261667	−	0.0595063i
$99$			2243.61i			2.27769i
$100$	−788.736	−	488.938i	−0.788736	−	0.488938i
$101$	−165.100	+	95.3206i	−0.162654	+	0.0939085i	−0.579118	−	0.815244i	$-0.696603\pi$
$101$	−165.100	+	95.3206i	−0.162654	+	0.0939085i	0.416463	+	0.909153i	$0.363269\pi$
$102$	230.815	−	355.424i	0.224060	−	0.345022i
$103$	−337.721	+	879.792i	−0.323074	+	0.841636i	0.671821	+	0.740714i	$0.265513\pi$
$103$	−337.721	+	879.792i	−0.323074	+	0.841636i	−0.994894	+	0.100922i	$0.967821\pi$
$104$	−284.879	−	206.977i	−0.268603	−	0.195151i
$105$	1671.25	−	1127.64i	1.55331	−	1.04806i
$106$	−321.708	+	233.734i	−0.294783	+	0.214173i
$107$	2.09282	+	7.81049i	0.00189084	+	0.00705672i	0.966865	−	0.255289i	$-0.0821706\pi$
$107$	2.09282	+	7.81049i	0.00189084	+	0.00705672i	−0.964974	+	0.262346i	$0.915504\pi$
$108$	−2753.45	+	1056.95i	−2.45325	+	0.941713i
$109$	1622.36	+	1460.78i	1.42564	+	1.28365i	0.902021	+	0.431692i	$0.142083\pi$
$109$	1622.36	+	1460.78i	1.42564	+	1.28365i	0.523614	+	0.851955i	$0.324583\pi$
$110$	−280.154	−	19.0863i	−0.242833	−	0.0165437i
$111$	−2575.50	−	836.829i	−2.20230	−	0.715570i
$112$	−66.7806	+	932.995i	−0.0563409	+	0.787141i
$113$	79.6542	−	156.330i	0.0663118	−	0.130144i	−0.855471	−	0.517850i	$-0.826732\pi$
$113$	79.6542	−	156.330i	0.0663118	−	0.130144i	0.921783	+	0.387706i	$0.126732\pi$
$114$	−398.904	+	359.174i	−0.327726	+	0.295086i
$115$	157.055	−	551.441i	0.127352	−	0.447149i
$116$	−1122.28	+	1246.42i	−0.898287	+	0.997649i
$117$	1283.46	−	1584.94i	1.01415	−	1.25237i
$118$	−297.720	+	297.720i	−0.232266	+	0.232266i
$119$	929.746	−	513.373i	0.716216	−	0.395469i
$120$	−374.776	−	1218.03i	−0.285102	−	0.926589i
$121$	−215.608	+	95.9948i	−0.161989	+	0.0721223i
$122$	−62.9685	+	50.9909i	−0.0467287	+	0.0378401i
$123$	1247.63	+	810.223i	0.914596	+	0.593946i
$124$	1001.26	−	1734.23i	0.725127	−	1.25596i
$125$	1090.80	+	873.655i	0.780515	+	0.625137i
$126$	945.792	+	117.705i	0.668713	+	0.0832222i
$127$	276.611	+	542.881i	0.193270	+	0.379314i	0.967223	−	0.253930i	$-0.0817232\pi$
$127$	276.611	+	542.881i	0.193270	+	0.379314i	−0.773953	+	0.633243i	$0.781723\pi$
$128$	1201.09	+	461.055i	0.829394	+	0.318374i
$129$	338.139	−	3217.18i	0.230787	−	2.19579i
$130$	186.988	+	173.745i	0.126154	+	0.117218i
$131$	−1438.62	+	151.205i	−0.959484	+	0.100846i	−0.571305	−	0.820738i	$-0.693563\pi$
$131$	−1438.62	+	151.205i	−0.959484	+	0.100846i	−0.388179	+	0.921584i	$0.626896\pi$
$132$	1691.34	+	1691.34i	1.11525	+	1.11525i
$133$	−1305.78	+	323.292i	−0.851322	+	0.210774i
$134$	53.5135	−	17.3876i	0.0344990	−	0.0112094i
$135$	4307.81	−	1082.25i	2.74635	−	0.689967i
$136$	−139.579	−	656.667i	−0.0880058	−	0.414035i
$137$	65.3597	+	1247.14i	0.0407595	+	0.777738i	0.940185	+	0.340664i	$0.110652\pi$
$137$	65.3597	+	1247.14i	0.0407595	+	0.777738i	−0.899426	+	0.437074i	$0.856015\pi$
$138$	317.851	−	206.415i	0.196067	−	0.127327i
$139$	343.028	−	1055.73i	0.209318	−	0.644216i	−0.790190	−	0.612862i	$-0.790018\pi$
$139$	343.028	−	1055.73i	0.209318	−	0.644216i	0.999508	−	0.0313538i	$-0.00998185\pi$
$140$	293.090	−	1509.02i	0.176933	−	0.910966i
$141$	−892.086	−	2745.56i	−0.532817	−	1.63984i
$142$	−471.400	−	381.732i	−0.278584	−	0.225593i
$143$	−961.422	−	257.612i	−0.562225	−	0.150648i
$144$	−1392.83	+	3128.35i	−0.806037	+	1.81039i
$145$	1903.34	−	1660.54i	1.09009	−	0.951036i
$146$	−313.339	+	431.274i	−0.177617	+	0.244469i
$147$	2729.39	+	1924.53i	1.53140	+	1.07981i
$148$	−1839.75	+	937.401i	−1.02180	+	0.520634i
$149$	2033.09	+	1173.80i	1.11783	+	0.645381i	0.940847	−	0.338832i	$-0.110032\pi$
$149$	2033.09	+	1173.80i	1.11783	+	0.645381i	0.176986	+	0.984213i	$0.443365\pi$
$150$	163.667	+	909.151i	0.0890889	+	0.494879i
$151$	−418.122	−	724.208i	−0.225339	−	0.390299i	0.731082	−	0.682290i	$-0.239016\pi$
$151$	−418.122	−	724.208i	−0.225339	−	0.390299i	−0.956421	+	0.291991i	$0.905682\pi$
$152$	−44.5021	+	849.150i	−0.0237473	+	0.453126i
$153$	3840.31	−	608.246i	2.02922	−	0.321397i
$154$	−135.267	−	445.049i	−0.0707799	−	0.232877i
$155$	−1810.62	+	2411.75i	−0.938275	+	1.24978i
$156$	−227.270	−	2162.33i	−0.116642	−	1.10978i
$157$	40.8011	−	152.272i	0.0207406	−	0.0774051i	−0.954780	−	0.297314i	$-0.903909\pi$
$157$	40.8011	−	152.272i	0.0207406	−	0.0774051i	0.975520	+	0.219909i	$0.0705759\pi$
$158$	−130.202	−	339.188i	−0.0655590	−	0.170787i
$159$	−4989.71	−	1060.59i	−2.48874	−	0.528998i
$160$	−1304.18	−	690.453i	−0.644403	−	0.341157i
$161$	946.309	−	81.2262i	0.463227	−	0.0397610i
$162$	1377.89	+	702.071i	0.668255	+	0.340493i
$163$	−2237.00	−	3444.68i	−1.07494	−	1.65526i	−0.673091	−	0.739560i	$-0.735034\pi$
$163$	−2237.00	−	3444.68i	−1.07494	−	1.65526i	−0.401851	−	0.915705i	$-0.631633\pi$
$164$	1109.49	−	235.830i	0.528273	−	0.112288i
$165$	−2222.82	−	2834.60i	−1.04877	−	1.33742i
$166$	−68.4549	+	322.055i	−0.0320068	+	0.150580i
$167$	3020.72	+	478.435i	1.39970	+	0.221691i	0.810237	−	0.586102i	$-0.199338\pi$
$167$	3020.72	+	478.435i	1.39970	+	0.221691i	0.589466	+	0.807793i	$0.299338\pi$
$168$	1665.64	−	1296.94i	0.764923	−	0.595604i
$169$	−759.562	−	1045.45i	−0.345727	−	0.475853i
$170$	43.2807	+	484.704i	0.0195264	+	0.218677i
$171$	−4897.79	−	514.779i	−2.19031	−	0.230211i
$172$	−1552.23	−	1916.85i	−0.688120	−	0.849758i
$173$	139.202	+	7.29526i	0.0611752	+	0.00320606i	0.0828990	−	0.996558i	$-0.473582\pi$
$173$	139.202	+	7.29526i	0.0611752	+	0.00320606i	−0.0217238	+	0.999764i	$0.506915\pi$
$174$	1669.59			0.727421
$175$	−711.113	+	2203.11i	−0.307172	+	0.951654i
$176$	1671.27			0.715777
$177$	−5393.79	−	282.676i	−2.29052	−	0.120041i
$178$	−60.9404	−	75.2551i	−0.0256611	−	0.0316888i
$179$	528.037	+	55.4989i	0.220488	+	0.0231742i	0.214128	−	0.976806i	$-0.431309\pi$
$179$	528.037	+	55.4989i	0.220488	+	0.0231742i	0.00635961	+	0.999980i	$0.497976\pi$
$180$	2889.84	−	4829.07i	1.19664	−	1.99965i
$181$	1005.93	+	1384.54i	0.413093	+	0.568574i	0.963970	−	0.266013i	$-0.0857063\pi$
$181$	1005.93	+	1384.54i	0.413093	+	0.568574i	−0.550876	+	0.834587i	$0.685706\pi$
$182$	−159.034	+	391.771i	−0.0647715	+	0.159560i
$183$	−1026.61	−	162.600i	−0.414696	−	0.0656815i
$184$	124.823	−	587.248i	0.0500114	−	0.235285i
$185$	2920.13	−	1068.77i	1.16050	−	0.424742i
$186$	−1949.84	+	414.452i	−0.768652	+	0.163382i
$187$	−1033.52	−	1591.47i	−0.404161	−	0.622353i
$188$	−1961.23	−	999.298i	−0.760838	−	0.387667i
$189$	4210.27	+	6033.95i	1.62038	+	2.32225i
$190$	105.944	−	607.195i	0.0404527	−	0.231845i
$191$	2626.41	+	558.262i	0.994977	+	0.211489i	0.676501	−	0.736442i	$-0.263495\pi$
$191$	2626.41	+	558.262i	0.994977	+	0.211489i	0.318477	+	0.947931i	$0.396829\pi$
$192$	1060.29	+	2762.14i	0.398539	+	1.03823i
$193$	435.257	−	1624.40i	0.162334	−	0.605839i	−0.836031	−	0.548682i	$-0.815130\pi$
$193$	435.257	−	1624.40i	0.162334	−	0.605839i	0.998365	−	0.0571572i	$-0.0182036\pi$
$194$	17.8690	+	170.012i	0.00661298	+	0.0629183i
$195$	−51.2840	+	3273.98i	−0.0188335	+	1.20233i
$196$	2509.16	−	433.943i	0.914415	−	0.158142i
$197$	−3900.69	+	617.809i	−1.41073	+	0.223437i	−0.814865	−	0.579651i	$-0.803189\pi$
$197$	−3900.69	+	617.809i	−1.41073	+	0.223437i	−0.595860	+	0.803088i	$0.703189\pi$
$198$	89.1232	−	1700.57i	0.0319884	−	0.610376i
$199$	1370.04	+	2372.97i	0.488037	+	0.845304i	0.999905	−	0.0137594i	$-0.00437988\pi$
$199$	1370.04	+	2372.97i	0.488037	+	0.845304i	−0.511869	+	0.859064i	$0.671047\pi$
$200$	1201.70	+	835.043i	0.424866	+	0.295232i
$201$	625.107	+	360.906i	0.219361	+	0.126648i
$202$	128.926	−	65.6911i	0.0449069	−	0.0228812i
$203$	3691.14	+	1970.39i	1.27619	+	0.681253i
$204$	2436.49	−	3353.54i	0.836217	−	1.15095i
$205$	−1701.44	+	151.927i	−0.579677	+	0.0517612i
$206$	290.927	−	653.433i	0.0983974	−	0.221004i
$207$	3358.67	+	899.952i	1.12775	+	0.302179i
$208$	−1180.62	−	956.047i	−0.393564	−	0.318702i
$209$	742.728	+	2285.88i	0.245816	+	0.756544i
$210$	−1311.54	+	788.317i	−0.430974	+	0.259043i
$211$	−1551.01	+	4773.53i	−0.506048	+	1.55746i	0.292954	+	0.956127i	$0.405362\pi$
$211$	−1551.01	+	4773.53i	−0.506048	+	1.55746i	−0.799002	+	0.601329i	$0.794638\pi$
$212$	−3262.02	+	2118.38i	−1.05677	+	0.686277i
$213$	−407.243	−	7770.65i	−0.131004	−	2.49970i
$214$	−1.27602	−	6.00318i	−0.000407601	−	0.00191761i
$215$	1974.05	+	3146.59i	0.626183	+	0.998121i
$216$	4423.19	−	1437.18i	1.39333	−	0.452721i
$217$	−4799.84	−	1384.86i	−1.50154	−	0.433229i
$218$	−1171.66	−	1171.66i	−0.364014	−	0.364014i
$219$	−6801.05	+	714.819i	−2.09850	+	0.220562i
$220$	−2726.71	−	329.843i	−0.835611	−	0.101082i
$221$	−180.303	+	1715.47i	−0.0548801	+	0.522150i
$222$	1918.88	+	736.591i	0.580122	+	0.222688i
$223$	46.3331	+	90.9338i	0.0139134	+	0.0273066i	0.897859	−	0.440284i	$-0.145122\pi$
$223$	46.3331	+	90.9338i	0.0139134	+	0.0273066i	−0.883945	+	0.467591i	$0.845122\pi$
$224$	301.887	−	2425.74i	0.0900476	−	0.723557i
$225$	−5193.95	+	6697.24i	−1.53895	+	1.98437i
$226$	−66.5847	+	115.328i	−0.0195980	+	0.0339447i
$227$	3503.20	+	2275.01i	1.02430	+	0.665187i	0.943442	−	0.331538i	$-0.107568\pi$
$227$	3503.20	+	2275.01i	1.02430	+	0.665187i	0.0808570	+	0.996726i	$0.474234\pi$
$228$	−4080.26	+	3304.13i	−1.18518	+	0.959742i
$229$	−1988.06	+	885.143i	−0.573690	+	0.255423i	−0.673011	−	0.739632i	$-0.734999\pi$
$229$	−1988.06	+	885.143i	−0.573690	+	0.255423i	0.0993214	+	0.995055i	$0.468333\pi$
$230$	−140.947	+	411.732i	−0.0404076	+	0.118038i
$231$	3081.66	−	5109.72i	0.877741	−	1.45539i
$232$	1870.17	−	1870.17i	0.529235	−	0.529235i
$233$	1853.04	−	2288.32i	0.521016	−	0.643402i	−0.446927	−	0.894571i	$-0.647482\pi$
$233$	1853.04	−	2288.32i	0.521016	−	0.643402i	0.967943	+	0.251169i	$0.0808149\pi$
$234$	−1035.77	+	1150.34i	−0.289360	+	0.321367i
$235$	2751.49	+	1848.74i	0.763776	+	0.513186i
$236$	−3060.46	+	2755.65i	−0.844149	+	0.760075i
$237$	2115.93	−	4152.75i	0.579935	−	1.13819i
$238$	−725.104	+	352.185i	−0.197485	+	0.0959190i
$239$	−864.320	−	280.835i	−0.233926	−	0.0760070i	0.189708	−	0.981840i	$-0.439246\pi$
$239$	−864.320	−	280.835i	−0.233926	−	0.0760070i	−0.423634	+	0.905833i	$0.639246\pi$
$240$	−1339.64	−	5332.31i	−0.360306	−	1.43416i
$241$	−3959.80	−	3565.42i	−1.05839	−	0.952982i	−0.0594186	−	0.998233i	$-0.518925\pi$
$241$	−3959.80	−	3565.42i	−1.05839	−	0.952982i	−0.998976	+	0.0452507i	$0.985591\pi$
$242$	167.236	−	64.1957i	0.0444228	−	0.0170523i
$243$	2358.28	+	8801.20i	0.622566	+	2.32345i
$244$	−641.163	+	465.832i	−0.168222	+	0.122221i
$245$	−3829.90	+	194.984i	−0.998707	+	0.0508452i
$246$	−913.473	−	663.677i	−0.236752	−	0.172010i
$247$	782.956	−	2039.67i	0.201694	−	0.525430i
$248$	−1719.85	+	2648.33i	−0.440364	+	0.678101i
$249$	−3657.82	+	2111.85i	−0.930944	+	0.537481i
$250$	−792.082	−	705.527i	−0.200383	−	0.178486i
$251$		−	112.858i		−	0.0283806i	−0.999899	−	0.0141903i	$-0.995483\pi$
$251$		−	112.858i		−	0.0283806i	0.999899	−	0.0141903i	$-0.00451706\pi$
$252$	9178.01	+	1633.87i	2.29429	+	0.408429i
$253$	−265.471	−	1676.12i	−0.0659684	−	0.416508i
$254$	−188.096	−	422.470i	−0.0464653	−	0.104363i
$255$	−4249.28	+	4573.19i	−1.04353	+	1.12307i
$256$	1328.71	+	591.580i	0.324392	+	0.144429i
$257$	−6633.08	+	1777.33i	−1.60996	+	0.431388i	−0.948031	−	0.318177i	$-0.896929\pi$
$257$	−6633.08	+	1777.33i	−1.60996	+	0.431388i	−0.661930	+	0.749565i	$0.730263\pi$
$258$	−384.093	+	2425.07i	−0.0926844	+	0.585186i
$259$	3372.98	+	3893.06i	0.809216	+	0.933988i
$260$	1737.52	+	1792.82i	0.414447	+	0.427637i
$261$	10249.7	+	11383.5i	2.43081	+	2.69969i
$262$	1096.42	−	57.4610i	0.258539	−	0.0135494i
$263$	−2342.54	+	122.768i	−0.549230	+	0.0287839i	−0.324933	−	0.945737i	$-0.605342\pi$
$263$	−2342.54	+	122.768i	−0.549230	+	0.0287839i	−0.224297	+	0.974521i	$0.572008\pi$
$264$	−2523.84	−	2803.01i	−0.588377	−	0.653459i
$265$	5260.13	−	2577.21i	1.21935	−	0.597421i
$266$	1002.58	−	193.173i	0.231097	−	0.0445271i
$267$	194.326	−	1226.93i	0.0445415	−	0.281224i
$268$	531.608	−	142.444i	0.121168	−	0.0324670i
$269$	−2774.22	−	1235.16i	−0.628800	−	0.279960i	0.0674906	−	0.997720i	$-0.478501\pi$
$269$	−2774.22	−	1235.16i	−0.628800	−	0.279960i	−0.696290	+	0.717760i	$0.745167\pi$
$270$	−3308.14	+	649.187i	−0.745656	+	0.146327i
$271$	−545.495	−	1225.20i	−0.122275	−	0.274634i	0.842029	−	0.539432i	$-0.181361\pi$
$271$	−545.495	−	1225.20i	−0.122275	−	0.274634i	−0.964304	+	0.264799i	$0.914694\pi$
$272$	−453.083	−	2860.65i	−0.101001	−	0.637693i
$273$	−5099.95	+	1846.76i	−1.13063	+	0.409417i
$274$		−	947.878i		−	0.208991i
$275$	4017.02	+	986.289i	0.880855	+	0.216274i
$276$	3210.35	−	1853.50i	0.700147	−	0.404230i
$277$	1105.47	−	1702.28i	0.239789	−	0.369242i	−0.698203	−	0.715900i	$-0.746017\pi$
$277$	1105.47	−	1702.28i	0.239789	−	0.369242i	0.937992	+	0.346657i	$0.112683\pi$
$278$	−301.939	+	786.578i	−0.0651406	+	0.169697i
$279$	−14796.0	−	10749.9i	−3.17496	−	2.30674i
$280$	−586.078	+	2352.12i	−0.125089	+	0.502022i
$281$	−908.221	+	659.861i	−0.192811	+	0.140086i	−0.680003	−	0.733210i	$-0.738021\pi$
$281$	−908.221	+	659.861i	−0.192811	+	0.140086i	0.487191	+	0.873295i	$0.338021\pi$
$282$	567.105	+	2116.46i	0.119754	+	0.446927i
$283$	−7513.79	+	2884.28i	−1.57826	+	0.605839i	−0.980619	−	0.195922i	$-0.937230\pi$
$283$	−7513.79	+	2884.28i	−1.57826	+	0.605839i	−0.597645	+	0.801761i	$0.703897\pi$
$284$	−4409.11	−	3969.98i	−0.921241	−	0.829489i
$285$	6697.93	−	4202.02i	1.39211	−	0.873356i
$286$	718.487	+	233.451i	0.148549	+	0.0482665i
$287$	−1236.26	−	2545.31i	−0.254266	−	0.523501i
$288$	4062.80	−	7973.69i	0.831259	−	1.63144i
$289$	1207.19	−	1086.96i	0.245713	−	0.221241i
$290$	−1508.62	+	1183.02i	−0.305480	+	0.239549i
$291$	−1467.38	+	1629.69i	−0.295599	+	0.328296i
$292$	−3281.39	+	4052.18i	−0.657633	+	0.812109i
$293$	1883.35	−	1883.35i	0.375516	−	0.375516i	−0.493965	−	0.869482i	$-0.664453\pi$
$293$	1883.35	−	1883.35i	0.375516	−	0.375516i	0.869482	+	0.493965i	$0.164453\pi$
$294$	−1992.32	−	1567.14i	−0.395220	−	0.310875i
$295$	5074.05	−	3566.44i	1.00143	−	0.703886i
$296$	2974.49	−	1324.33i	0.584084	−	0.260051i
$297$	10216.4	−	8273.10i	1.99602	−	1.61634i
$298$	−1494.38	−	970.459i	−0.290493	−	0.188648i
$299$	−771.286	+	1335.91i	−0.149179	+	0.258386i
$300$	1133.26	+	8964.15i	0.218096	+	1.72515i
$301$	−3711.13	+	4908.06i	−0.710652	+	0.939853i
$302$	288.152	+	565.531i	0.0549050	+	0.107757i
$303$	1732.92	+	665.204i	0.328559	+	0.126122i
$304$	−383.459	+	3648.37i	−0.0723451	+	0.688317i
$305$	1042.85	−	580.502i	0.195781	−	0.108982i
$306$	−2934.97	+	308.478i	−0.548304	+	0.0576291i
$307$	339.385	+	339.385i	0.0630936	+	0.0630936i	0.737950	−	0.674856i	$-0.235794\pi$
$307$	339.385	+	339.385i	0.0630936	+	0.0630936i	−0.674856	+	0.737950i	$0.735794\pi$
$308$	−1093.43	−	4416.38i	−0.202285	−	0.817034i
$309$	8726.57	−	2835.44i	1.60659	−	0.522014i
$310$	1468.18	−	1756.09i	0.268991	−	0.321739i
$311$	−1695.66	−	7977.46i	−0.309171	−	1.45453i	−0.808692	−	0.588233i	$-0.799824\pi$
$311$	−1695.66	−	7977.46i	−0.309171	−	1.45453i	0.499521	−	0.866302i	$-0.333509\pi$
$312$	179.437	+	3423.86i	0.0325597	+	0.621276i
$313$	−3612.40	+	2345.92i	−0.652348	+	0.423640i	−0.827935	−	0.560824i	$-0.810484\pi$
$313$	−3612.40	+	2345.92i	−0.652348	+	0.423640i	0.175587	+	0.984464i	$0.443818\pi$
$314$	−36.9743	+	113.795i	−0.00664517	+	0.0204517i
$315$	−13426.5	−	4102.69i	−2.40157	−	0.733843i
$316$	−1098.15	−	3379.76i	−0.195493	−	0.601665i
$317$	−7083.27	−	5735.92i	−1.25500	−	1.01628i	−0.998766	−	0.0496688i	$-0.984183\pi$
$317$	−7083.27	−	5735.92i	−1.25500	−	1.01628i	−0.256238	−	0.966614i	$-0.582483\pi$
$318$	3739.87	+	1002.10i	0.659502	+	0.176713i
$319$	3040.72	−	6829.56i	0.533691	−	1.19869i
$320$	−2915.22	−	1744.55i	−0.509268	−	0.304759i
$321$	46.2767	−	63.6944i	0.00804646	−	0.0110750i
$322$	−720.492	+	23.9760i	−0.124694	+	0.00414947i
$323$	3711.31	−	1891.01i	0.639327	−	0.325754i
$324$	13099.5	+	7563.01i	2.24614	+	1.29681i
$325$	−2273.50	−	2994.66i	−0.388034	−	0.511120i
$326$	1558.73	+	2699.79i	0.264816	+	0.458674i
$327$	1112.46	−	21227.0i	0.188132	−	3.58977i
$328$	−1766.62	+	279.805i	−0.297395	+	0.0471027i
$329$	−1244.02	+	5348.36i	−0.208465	+	0.896246i
$330$	1572.21	+	2236.82i	0.262265	+	0.373129i
$331$	793.484	+	7549.50i	0.131764	+	1.25365i	0.837999	+	0.545672i	$0.183726\pi$
$331$	793.484	+	7549.50i	0.131764	+	1.25365i	−0.706235	+	0.707977i	$0.749608\pi$
$332$	−833.513	+	3110.71i	−0.137786	+	0.514224i
$333$	6758.00	+	17605.2i	1.11212	+	2.89717i
$334$	−2270.58	−	482.628i	−0.371979	−	0.0790665i
$335$	−820.564	+	116.821i	−0.133827	+	0.0190526i
$336$	7468.97	−	5211.58i	1.21270	−	0.846175i
$337$	6561.45	+	3343.23i	1.06061	+	0.540407i	0.895130	−	0.445806i	$-0.147083\pi$
$337$	6561.45	+	3343.23i	1.06061	+	0.540407i	0.165479	+	0.986213i	$0.447083\pi$
$338$	534.190	+	822.581i	0.0859649	+	0.132374i
$339$	−1671.00	+	355.181i	−0.267717	+	0.0569050i
$340$	174.633	+	4756.63i	0.0278552	+	0.758719i
$341$	−1855.78	+	8730.77i	−0.294710	+	1.38650i
$342$	3691.89	+	584.738i	0.583727	+	0.0924532i
$343$	−2555.16	−	5815.91i	−0.402233	−	0.915537i
$344$	2286.17	+	3146.64i	0.358319	+	0.493184i
$345$	−5134.98	+	2190.53i	−0.801328	+	0.341838i
$346$	−105.220	−	11.0590i	−0.0163487	−	0.00171832i
$347$	3559.06	+	4395.07i	0.550606	+	0.679941i	0.974142	−	0.225938i	$-0.0725447\pi$
$347$	3559.06	+	4395.07i	0.550606	+	0.679941i	−0.423536	+	0.905879i	$0.639211\pi$
$348$	16308.1	+	854.674i	2.51209	+	0.131653i
$349$	9481.19			1.45420			0.727101	−	0.686530i	$-0.240867\pi$
$349$	9481.19			1.45420			0.727101	+	0.686530i	$0.240867\pi$
$350$	626.510	−	1641.62i	0.0956811	−	0.250710i
$351$	−11949.7			−1.81717
$352$	−4361.58	−	228.581i	−0.660435	−	0.0346119i
$353$	3008.66	+	3715.39i	0.453640	+	0.560199i	0.951734	−	0.306924i	$-0.0992998\pi$
$353$	3008.66	+	3715.39i	0.453640	+	0.560199i	−0.498094	+	0.867123i	$0.665966\pi$
$354$	4077.05	+	428.516i	0.612127	+	0.0643371i
$355$	5874.01	+	6732.89i	0.878198	+	1.00661i
$356$	−556.727	−	766.269i	−0.0828834	−	0.114079i
$357$	−9581.57	−	3889.51i	−1.42048	−	0.576624i
$358$	−398.027	−	63.0412i	−0.0587608	−	0.00930679i
$359$	−2156.65	+	10146.2i	−0.317057	+	1.49164i	0.474343	+	0.880340i	$0.342686\pi$
$359$	−2156.65	+	10146.2i	−0.317057	+	1.49164i	−0.791401	+	0.611298i	$0.790648\pi$
$360$	−4949.28	+	7366.03i	−0.724583	+	1.07840i
$361$	1548.64	−	329.173i	0.225782	−	0.0479914i
$362$	−707.455	−	1089.39i	−0.102716	−	0.158168i
$363$	2047.50	+	1043.25i	0.296049	+	0.150845i
$364$	−1753.96	+	3745.31i	−0.252562	+	0.539307i
$365$	5638.84	−	5464.91i	0.808631	−	0.783688i
$366$	771.674	+	164.024i	0.110208	+	0.0234254i
$367$	281.499	+	733.329i	0.0400384	+	0.104304i	0.952142	−	0.305657i	$-0.0988759\pi$
$367$	281.499	+	733.329i	0.0400384	+	0.104304i	−0.912103	+	0.409960i	$0.865543\pi$
$368$	670.375	−	2501.87i	0.0949612	−	0.354400i
$369$	−1082.84	−	10302.5i	−0.152765	−	1.45347i
$370$	−2255.80	+	694.087i	−0.316956	+	0.0975239i
$371$	7085.49	+	6629.11i	0.991538	+	0.927672i
$372$	−19257.7	+	3050.13i	−2.68405	+	0.425112i
$373$	152.911	−	2917.72i	0.0212264	−	0.405024i	−0.967267	−	0.253761i	$-0.918332\pi$
$373$	152.911	−	2917.72i	0.0212264	−	0.405024i	0.988493	−	0.151263i	$-0.0483342\pi$
$374$	720.146	+	1247.33i	0.0995665	+	0.172454i
$375$	−73.0905	−	13607.2i	−0.0100650	−	1.87379i
$376$	3005.96	+	1735.49i	0.412289	+	0.238035i
$377$	−6054.87	+	3085.11i	−0.827166	+	0.421462i
$378$	−2951.54	−	4740.75i	−0.401616	−	0.645073i
$379$	6069.38	−	8353.79i	0.822594	−	1.13220i	−0.166662	−	0.986014i	$-0.553299\pi$
$379$	6069.38	−	8353.79i	0.822594	−	1.13220i	0.989257	−	0.146190i	$-0.0467011\pi$
$380$	1345.66	−	5876.70i	0.181661	−	0.793338i
$381$	2412.94	−	5419.54i	0.324458	−	0.728744i
$382$	−1968.54	−	527.470i	−0.263664	−	0.0706485i
$383$	−1293.05	−	1047.09i	−0.172511	−	0.139697i	0.539177	−	0.842193i	$-0.318735\pi$
$383$	−1293.05	−	1047.09i	−0.172511	−	0.139697i	−0.711688	+	0.702496i	$0.752069\pi$
$384$	−3870.93	−	11913.5i	−0.514421	−	1.58322i
$385$	836.041	+	6800.64i	0.110672	+	0.900240i
$386$	−394.434	+	1213.94i	−0.0520108	+	0.160073i
$387$	−18892.4	+	12268.9i	−2.48154	+	1.61153i
$388$	87.5096	+	1669.78i	0.0114501	+	0.218480i
$389$	−555.132	−	2611.69i	−0.0723556	−	0.340406i	0.927048	−	0.374943i	$-0.122338\pi$
$389$	−555.132	−	2611.69i	−0.0723556	−	0.340406i	−0.999403	+	0.0345368i	$0.989004\pi$
$390$	168.924	−	2479.51i	0.0219328	−	0.321936i
$391$	−2796.98	+	908.795i	−0.361763	+	0.117544i
$392$	−3987.08	+	476.269i	−0.513719	+	0.0613654i
$393$	9959.20	+	9959.20i	1.27831	+	1.27831i
$394$	2981.12	−	313.328i	0.381184	−	0.0400640i
$395$	1030.58	+	5251.65i	0.131276	+	0.668960i
$396$	1741.07	−	16565.2i	0.220939	−	2.10210i
$397$	1363.46	+	523.384i	0.172368	+	0.0661660i	0.443022	−	0.896511i	$-0.353906\pi$
$397$	1363.46	+	523.384i	0.172368	+	0.0661660i	−0.270654	+	0.962677i	$0.587240\pi$
$398$	−944.173	−	1853.04i	−0.118912	−	0.233379i
$399$	10447.4	+	7899.62i	1.31084	+	0.991167i
$400$	4988.78	+	3868.98i	0.623598	+	0.483622i
$401$	1405.44	−	2434.29i	0.175023	−	0.303149i	−0.765146	−	0.643857i	$-0.777333\pi$
$401$	1405.44	−	2434.29i	0.175023	−	0.303149i	0.940169	+	0.340708i	$0.110667\pi$
$402$	−459.470	−	298.384i	−0.0570057	−	0.0370200i
$403$	6305.38	−	5106.00i	0.779388	−	0.631136i
$404$	1292.95	−	575.656i	0.159224	−	0.0708910i
$405$	−18217.1	−	13676.5i	−2.23510	−	1.67800i
$406$	−2719.47	−	1640.10i	−0.332426	−	0.200485i
$407$	6507.81	−	6507.81i	0.792581	−	0.792581i
$408$	−4113.60	+	5079.87i	−0.499150	+	0.616399i
$409$	6123.27	−	6800.58i	0.740284	−	0.822169i	−0.248949	−	0.968517i	$-0.580085\pi$
$409$	6123.27	−	6800.58i	0.740284	−	0.822169i	0.989233	+	0.146348i	$0.0467519\pi$
$410$	1295.66	−	47.5683i	0.156069	−	0.00572983i
$411$	9036.33	−	8136.35i	1.08450	−	0.976488i
$412$	3176.20	−	6233.65i	0.379807	−	0.745412i
$413$	8507.85	+	5758.96i	1.01367	+	0.686150i
$414$	−2509.99	−	815.545i	−0.297969	−	0.0968161i
$415$	1808.77	−	4500.05i	0.213950	−	0.532286i
$416$	2950.35	+	2656.51i	0.347724	+	0.313092i
$417$	−10090.4	+	3873.34i	−1.18496	+	0.454864i
$418$	−472.157	−	1762.11i	−0.0552487	−	0.206191i
$419$	6860.13	−	4984.18i	0.799855	−	0.581129i	−0.111017	−	0.993819i	$-0.535411\pi$
$419$	6860.13	−	4984.18i	0.799855	−	0.581129i	0.910872	+	0.412690i	$0.135411\pi$
$420$	−13214.3	+	7028.70i	−1.53522	+	0.816584i
$421$	11332.0	+	8233.16i	1.31184	+	0.953111i	0.999996	+	0.00297904i	$0.000948258\pi$
$421$	11332.0	+	8233.16i	1.31184	+	0.953111i	0.311849	+	0.950132i	$0.399052\pi$
$422$	1365.23	−	3556.54i	0.157484	−	0.410259i
$423$	−10948.8	+	16859.7i	−1.25851	+	1.93794i
$424$	5311.65	−	3066.68i	0.608388	−	0.351253i
$425$	599.179	−	7143.17i	0.0683870	−	0.815281i
$426$			5906.03i			0.671709i
$427$	1512.45	+	1273.33i	0.171411	+	0.144311i
$428$	−9.39075	−	59.2909i	−0.00106056	−	0.00669610i
$429$	3941.78	+	8853.39i	0.443615	+	0.996377i
$430$	−1371.26	−	2463.41i	−0.153786	−	0.276270i
$431$	10705.3	+	4766.33i	1.19642	+	0.532682i	0.905616	−	0.424100i	$-0.139409\pi$
$431$	10705.3	+	4766.33i	1.19642	+	0.532682i	0.290808	+	0.956782i	$0.406076\pi$
$432$	19381.1	−	5193.14i	2.15850	−	0.578368i
$433$	−1131.82	+	7146.06i	−0.125617	+	0.793113i	0.841775	+	0.539828i	$0.181511\pi$
$433$	−1131.82	+	7146.06i	−0.125617	+	0.793113i	−0.967392	+	0.253284i	$0.918489\pi$
$434$	3583.08	+	1240.34i	0.396298	+	0.137185i
$435$	−24227.6	−	4227.26i	−2.67040	−	0.465935i
$436$	−10844.7	−	12044.3i	−1.19121	−	1.32297i
$437$	3719.86	−	194.950i	0.407197	−	0.0213403i
$438$	5183.33	−	271.647i	0.565454	−	0.0296342i
$439$	−6229.67	−	6918.75i	−0.677280	−	0.752196i	0.302308	−	0.953210i	$-0.402243\pi$
$439$	−6229.67	−	6918.75i	−0.677280	−	0.752196i	−0.979588	+	0.201014i	$0.935576\pi$
$440$	4266.63	+	744.447i	0.462281	+	0.0806594i
$441$	−1546.09	−	23204.7i	−0.166946	−	2.50563i
$442$	204.807	−	1293.10i	0.0220400	−	0.139155i
$443$	−5377.64	+	1440.94i	−0.576748	+	0.154539i	−0.535390	−	0.844605i	$-0.679835\pi$
$443$	−5377.64	+	1440.94i	−0.576748	+	0.154539i	−0.0413586	+	0.999144i	$0.513169\pi$
$444$	18366.1	+	8177.13i	1.96310	+	0.874030i
$445$	693.772	+	1246.33i	0.0739055	+	0.132768i
$446$	−31.5065	−	70.7648i	−0.00334501	−	0.00751303i
$447$	−3575.75	−	22576.4i	−0.378361	−	2.38887i
$448$	986.338	−	5540.60i	0.104018	−	0.584305i
$449$		−	11421.2i		−	1.20044i	−0.799834	−	0.600222i	$-0.795079\pi$
$449$		−	11421.2i		−	1.20044i	0.799834	−	0.600222i	$-0.204921\pi$
$450$	4202.84	−	4869.93i	0.440276	−	0.510157i
$451$	−4378.46	+	2527.91i	−0.457148	+	0.263935i
$452$	−709.420	+	1092.41i	−0.0738237	+	0.113679i
$453$	−2917.90	+	7601.40i	−0.302638	+	0.788399i
$454$	−2564.92	−	1863.53i	−0.265149	−	0.192642i
$455$	3299.70	−	5282.37i	0.339983	−	0.544266i
$456$	6698.02	−	4866.40i	0.687859	−	0.499759i
$457$	779.714	+	2909.93i	0.0798107	+	0.297857i	0.994281	−	0.106795i	$-0.0340590\pi$
$457$	779.714	+	2909.93i	0.0798107	+	0.297857i	−0.914470	+	0.404653i	$0.867392\pi$
$458$	1542.04	−	591.932i	0.157325	−	0.0603912i
$459$	−16930.5	−	15244.3i	−1.72167	−	1.55020i
$460$	−1587.50	+	3949.55i	−0.160908	+	0.400323i
$461$	−13045.9	−	4238.86i	−1.31802	−	0.428251i	−0.436206	−	0.899847i	$-0.643678\pi$
$461$	−13045.9	−	4238.86i	−1.31802	−	0.428251i	−0.881815	+	0.471596i	$0.843678\pi$
$462$	−2538.75	+	3750.56i	−0.255657	+	0.377688i
$463$	−6104.68	+	11981.1i	−0.612762	+	1.20261i	0.351132	+	0.936326i	$0.385797\pi$
$463$	−6104.68	+	11981.1i	−0.612762	+	1.20261i	−0.963894	+	0.266287i	$0.914203\pi$
$464$	8479.56	−	7635.03i	0.848392	−	0.763895i
$465$	29343.7	−	1077.31i	2.92641	−	0.107439i
$466$	−1495.43	+	1660.85i	−0.148658	+	0.165101i
$467$	−11611.3	+	14338.8i	−1.15055	+	1.42082i	−0.260196	+	0.965556i	$0.583787\pi$
$467$	−11611.3	+	14338.8i	−1.15055	+	1.42082i	−0.890358	+	0.455261i	$0.849546\pi$
$468$	−10706.0	+	10706.0i	−1.05745	+	1.05745i
$469$	−663.658	−	1201.92i	−0.0653409	−	0.118336i
$470$	−2012.08	−	1510.57i	−0.197469	−	0.148250i
$471$	−1402.22	+	624.306i	−0.137178	+	0.0610754i
$472$	5046.85	−	4086.86i	0.492161	−	0.398544i
$473$	9220.37	+	5987.78i	0.896306	+	0.582068i
$474$	−1768.75	+	3063.57i	−0.171396	+	0.296866i
$475$	−3074.73	+	8542.82i	−0.297007	+	0.825203i
$476$	−7262.93	+	3068.87i	−0.699361	+	0.295507i
$477$	16126.9	+	31650.9i	1.54801	+	3.03814i
$478$	643.966	+	247.195i	0.0616199	+	0.0236537i
$479$	1053.20	−	10020.5i	0.100463	−	0.955841i	−0.821930	−	0.569588i	$-0.807103\pi$
$479$	1053.20	−	10020.5i	0.100463	−	0.955841i	0.922393	−	0.386253i	$-0.126231\pi$
$480$	2766.81	+	14099.2i	0.263098	+	1.34070i
$481$	−8320.04	+	874.471i	−0.788693	+	0.0828949i
$482$	2859.74	+	2859.74i	0.270244	+	0.270244i
$483$	−6413.10	−	6662.81i	−0.604153	−	0.627678i
$484$	1666.38	−	541.439i	0.156497	−	0.0508489i
$485$	171.158	−	2512.30i	0.0160245	−	0.235212i
$486$	−1437.87	−	6764.65i	−0.134204	−	0.631380i
$487$	165.325	+	3154.59i	0.0153831	+	0.293528i	0.995478	+	0.0949962i	$0.0302839\pi$
$487$	165.325	+	3154.59i	0.0153831	+	0.293528i	−0.980094	+	0.198532i	$0.936383\pi$
$488$	1048.11	−	680.650i	0.0972248	−	0.0631385i
$489$	−12358.0	+	38034.1i	−1.14284	+	3.51730i
$490$	2910.66	+	4.34484i	0.268347	+	0.000400572i
$491$	−1224.40	−	3768.31i	−0.112538	−	0.346357i	0.878887	−	0.477029i	$-0.158287\pi$
$491$	−1224.40	−	3768.31i	−0.112538	−	0.346357i	−0.991426	+	0.130672i	$0.958287\pi$
$492$	−8582.84	−	6950.25i	−0.786473	−	0.636873i
$493$	−12514.3	−	3353.19i	−1.14323	−	0.306329i
$494$	−674.472	+	1514.89i	−0.0614290	+	0.137972i
$495$	−5598.98	+	24451.5i	−0.508395	+	2.22023i
$496$	−8007.63	+	11021.6i	−0.724906	+	0.997747i
$497$	−6970.09	+	13057.1i	−0.629077	+	1.17845i
$498$	2856.38	−	1455.40i	0.257023	−	0.130960i
$499$	−14393.6	−	8310.15i	−1.29127	−	0.745518i	−0.312394	−	0.949953i	$-0.601131\pi$
$499$	−14393.6	−	8310.15i	−1.29127	−	0.745518i	−0.978880	+	0.204435i	$0.934464\pi$
$500$	−7375.70	−	7296.89i	−0.659703	−	0.652654i
$501$	−14889.1	−	25788.7i	−1.32774	−	2.29971i
$502$	−4.48306	+	85.5419i	−0.000398583	+	0.00760542i
$503$	−7172.93	+	1136.08i	−0.635836	+	0.100706i	−0.466027	−	0.884771i	$-0.654315\pi$
$503$	−7172.93	+	1136.08i	−0.635836	+	0.100706i	−0.169809	+	0.985477i	$0.554315\pi$
$504$	−14318.1	−	3330.37i	−1.26544	−	0.294338i
$505$	−2037.18	+	626.819i	−0.179512	+	0.0552339i
$506$	134.636	+	1280.98i	0.0118287	+	0.112542i
$507$	−3256.49	+	12153.4i	−0.285258	+	1.06460i
$508$	−1621.01	−	4222.87i	−0.141576	−	0.368818i
$509$	4342.11	+	922.944i	0.378115	+	0.0803709i	0.393049	−	0.919518i	$-0.371420\pi$
$509$	4342.11	+	922.944i	0.378115	+	0.0803709i	−0.0149336	+	0.999888i	$0.504754\pi$
$510$	3402.45	−	3297.50i	0.295418	−	0.286306i
$511$	11779.9	+	5516.63i	1.01979	+	0.477576i
$512$	−10154.1	−	5173.80i	−0.876473	−	0.446585i
$513$	15716.0	+	24200.6i	1.35259	+	2.08281i
$514$	5098.22	−	1083.66i	0.437496	−	0.0929926i
$515$	−5876.11	+	8745.43i	−0.502781	+	0.748291i
$516$	−4993.13	+	23490.8i	−0.425989	+	2.00412i
$517$	9690.36	+	1534.80i	0.824335	+	0.130562i
$518$	−2401.95	−	3084.77i	−0.203736	−	0.261655i
$519$	−797.752	−	1098.01i	−0.0674710	−	0.0928659i
$520$	−2588.18	−	2966.61i	−0.218267	−	0.250182i
$521$	−610.844	−	64.2023i	−0.0513658	−	0.00539876i	0.0788107	−	0.996890i	$-0.474888\pi$
$521$	−610.844	−	64.2023i	−0.0513658	−	0.00539876i	−0.130176	+	0.991491i	$0.541554\pi$
$522$	−7316.71	−	9035.38i	−0.613494	−	0.757602i
$523$	−2488.84	−	130.434i	−0.208086	−	0.0109053i	−0.0519921	−	0.998647i	$-0.516557\pi$
$523$	−2488.84	−	130.434i	−0.208086	−	0.0109053i	−0.156094	+	0.987742i	$0.549890\pi$
$524$	10739.0			0.895296
$525$	21027.8	−	8118.64i	1.74805	−	0.674907i
$526$	1780.43			0.147587
$527$	15447.3	+	809.556i	1.27684	+	0.0669162i
$528$	−10240.6	−	12646.1i	−0.844066	−	1.04233i
$529$	9484.73	+	996.885i	0.779546	+	0.0819335i
$530$	−4089.35	+	1744.47i	−0.335151	+	0.142972i
$531$	22107.6	+	30428.6i	1.80676	+	2.48679i
$532$	9891.80	−	1373.65i	0.806135	−	0.111946i
$533$	4539.12	+	718.927i	0.368877	+	0.0584243i
$534$	−196.029	+	922.246i	−0.0158858	+	0.0747368i
$535$	3.31683	+	90.3436i	0.000268036	+	0.00730073i
$536$	−848.899	+	180.439i	−0.0684083	+	0.0145406i
$537$	−2815.58	−	4335.61i	−0.226259	−	0.348408i
$538$	2053.69	+	1046.41i	0.164574	+	0.0838545i
$539$	−10039.0	+	5295.61i	−0.802243	+	0.423187i
$540$	−32645.5	+	4647.64i	−2.60155	+	0.370375i
$541$	289.493	+	61.5336i	0.0230061	+	0.00489009i	0.219400	−	0.975635i	$-0.429590\pi$
$541$	289.493	+	61.5336i	0.0230061	+	0.00489009i	−0.196394	+	0.980525i	$0.562923\pi$
$542$	364.795	+	950.325i	0.0289102	+	0.0753135i
$543$	4312.74	−	16095.3i	0.340842	−	1.27204i
$544$	791.176	+	7527.54i	0.0623555	+	0.593273i
$545$	14035.5	+	19968.7i	1.10315	+	1.56947i
$546$	3938.93	−	1197.18i	0.308737	−	0.0938365i
$547$	3615.72	−	572.674i	0.282627	−	0.0447637i	−0.0135115	−	0.999909i	$-0.504301\pi$
$547$	3615.72	−	572.674i	0.282627	−	0.0447637i	0.296139	+	0.955145i	$0.404301\pi$
$548$	485.225	−	9258.64i	0.0378244	−	0.721733i
$549$	3619.02	+	6268.33i	0.281341	+	0.487297i
$550$	−3005.56	−	907.137i	−0.233014	−	0.0703281i
$551$	14211.2	+	8204.85i	1.09876	+	0.634371i
$552$	−5208.43	+	2653.83i	−0.401604	+	0.204628i
$553$	−7525.90	+	4685.54i	−0.578723	+	0.360306i
$554$	−905.527	+	1246.35i	−0.0694443	+	0.0955819i
$555$	−25980.1	−	15547.2i	−1.98702	−	1.18908i
$556$	−3351.92	+	7528.53i	−0.255671	+	0.574246i
$557$	−23756.6	−	6365.56i	−1.80718	−	0.484232i	−0.812118	−	0.583493i	$-0.801686\pi$
$557$	−23756.6	−	6365.56i	−1.80718	−	0.484232i	−0.995062	+	0.0992601i	$0.968352\pi$
$558$	10787.8	+	8735.77i	0.818428	+	0.662750i
$559$	−3088.16	−	9504.39i	−0.233659	−	0.719128i
$560$	−3056.10	+	10001.4i	−0.230614	+	0.754706i
$561$	−5709.52	+	17572.1i	−0.429690	+	1.32245i
$562$	714.608	−	464.072i	0.0536369	−	0.0348322i
$563$	−372.921	−	7115.75i	−0.0279161	−	0.532670i	−0.976417	−	0.215895i	$-0.930733\pi$
$563$	−372.921	−	7115.75i	−0.0279161	−	0.532670i	0.948501	−	0.316775i	$-0.102600\pi$
$564$	4455.91	+	20963.4i	0.332673	+	1.56510i
$565$	1258.22	−	1504.95i	0.0936878	−	0.112060i
$566$	5809.74	−	1887.70i	0.431451	−	0.140187i
$567$	10460.6	−	36255.6i	0.774784	−	2.68535i
$568$	6615.56	+	6615.56i	0.488702	+	0.488702i
$569$	2941.01	−	309.112i	0.216684	−	0.0227744i	0.00443581	−	0.999990i	$-0.498588\pi$
$569$	2941.01	−	309.112i	0.216684	−	0.0227744i	0.212249	+	0.977216i	$0.431921\pi$
$570$	−5243.69	+	2918.91i	−0.385323	+	0.214491i
$571$	277.970	−	2644.70i	0.0203725	−	0.193831i	−0.979602	−	0.200946i	$-0.935598\pi$
$571$	277.970	−	2644.70i	0.0203725	−	0.193831i	0.999975	+	0.00711550i	$0.00226495\pi$
$572$	6898.51	+	2648.09i	0.504268	+	0.193570i
$573$	−11869.0	−	23294.3i	−0.865332	−	1.69831i
$574$	835.932	+	1978.35i	0.0607859	+	0.143859i
$575$	3087.76	−	5617.82i	0.223945	−	0.407442i
$576$	10301.4	−	17842.6i	0.745185	−	1.29070i
$577$	−5394.05	−	3502.94i	−0.389181	−	0.252737i	0.335186	−	0.942152i	$-0.391201\pi$
$577$	−5394.05	−	3502.94i	−0.389181	−	0.252737i	−0.724366	+	0.689415i	$0.757868\pi$
$578$	−958.179	+	775.918i	−0.0689533	+	0.0558372i
$579$	−14958.5	+	6659.97i	−1.07367	+	0.478029i
$580$	−15341.4	+	10783.2i	−1.09831	+	0.771976i
$581$	8032.50	+	153.398i	0.573570	+	0.0109536i
$582$	1176.95	−	1176.95i	0.0838252	−	0.0838252i
$583$	10910.3	−	13473.1i	0.775060	−	0.957119i
$584$	5501.75	−	6110.31i	0.389836	−	0.432956i
$585$	17942.7	−	14070.2i	1.26810	−	0.994410i
$586$	−1502.32	+	1352.69i	−0.105905	+	0.0953570i
$587$	−999.538	+	1961.70i	−0.0702817	+	0.137936i	−0.923474	−	0.383661i	$-0.874663\pi$
$587$	−999.538	+	1961.70i	−0.0702817	+	0.137936i	0.853192	+	0.521596i	$0.174663\pi$
$588$	−18658.3	−	16327.3i	−1.30860	−	1.14511i
$589$	−18633.4	−	6054.36i	−1.30353	−	0.423541i
$590$	−3987.60	+	2501.67i	−0.278249	+	0.174563i
$591$	28576.2	+	25730.1i	1.98895	+	1.79086i
$592$	13114.1	−	5034.04i	0.910451	−	0.349489i
$593$	684.405	+	2554.23i	0.0473949	+	0.176880i	0.985566	−	0.169292i	$-0.0541481\pi$
$593$	684.405	+	2554.23i	0.0473949	+	0.176880i	−0.938171	+	0.346172i	$0.887481\pi$
$594$	−8072.29	+	5864.86i	−0.557593	+	0.405115i
$595$	11413.8	−	3274.68i	0.786418	−	0.225628i
$596$	−14099.9	−	10244.2i	−0.969052	−	0.704057i
$597$	9560.93	−	24907.1i	0.655449	−	1.70750i
$598$	637.671	−	981.928i	0.0436059	−	0.0671472i
$599$	15701.3	−	9065.16i	1.07102	−	0.618352i	0.142557	−	0.989787i	$-0.454467\pi$
$599$	15701.3	−	9065.16i	1.07102	−	0.618352i	0.928459	+	0.371435i	$0.121134\pi$
$600$	−1044.79	−	14209.7i	−0.0710887	−	0.966849i
$601$		−	23451.0i		−	1.59166i	−0.605523	−	0.795828i	$-0.707036\pi$
$601$		−	23451.0i		−	1.59166i	0.605523	−	0.795828i	$-0.292964\pi$
$602$	3007.86	−	3572.70i	0.203640	−	0.241881i
$603$	−786.304	−	4964.53i	−0.0531024	−	0.335276i
$604$	2525.10	+	5671.47i	0.170108	+	0.382068i
$605$	−2589.31	+	508.124i	−0.174001	+	0.0341457i
$606$	−1287.06	−	573.036i	−0.0862759	−	0.0384125i
$607$	−15355.4	+	4114.47i	−1.02678	+	0.275125i	−0.732626	−	0.680632i	$-0.761705\pi$
$607$	−15355.4	+	4114.47i	−1.02678	+	0.275125i	−0.294157	+	0.955757i	$0.595039\pi$
$608$	1499.72	−	9468.86i	0.100036	−	0.631601i
$609$	−7707.78	−	40003.6i	−0.512865	−	2.66178i
$610$	−813.496	+	398.573i	−0.0539959	+	0.0264553i
$611$	−5967.49	−	6627.57i	−0.395121	−	0.438826i
$612$	−28826.0	+	1510.71i	−1.90396	+	0.0997822i
$613$	−4855.74	+	254.479i	−0.319937	+	0.0167672i	−0.211629	−	0.977350i	$-0.567877\pi$
$613$	−4855.74	+	254.479i	−0.319937	+	0.0167672i	−0.108308	+	0.994117i	$0.534543\pi$
$614$	−243.759	−	270.722i	−0.0160217	−	0.0177939i
$615$	11575.1	+	11943.5i	0.758950	+	0.783105i
$616$	1357.39	+	7044.88i	0.0887836	+	0.460789i
$617$	−205.043	+	1294.59i	−0.0133788	+	0.0844703i	−0.993474	−	0.114056i	$-0.963616\pi$
$617$	−205.043	+	1294.59i	−0.0133788	+	0.0844703i	0.980096	+	0.198527i	$0.0636156\pi$
$618$	−6727.04	+	1802.50i	−0.437866	+	0.117326i
$619$	−3098.72	−	1379.64i	−0.201208	−	0.0895837i	0.303659	−	0.952781i	$-0.401792\pi$
$619$	−3098.72	−	1379.64i	−0.201208	−	0.0895837i	−0.504867	+	0.863197i	$0.668458\pi$
$620$	15239.8	−	16401.5i	0.987170	−	1.06242i
$621$	−8286.76	−	18612.4i	−0.535485	−	1.20272i
$622$	968.356	+	6113.96i	0.0624237	+	0.394128i
$623$	−1521.79	+	1807.56i	−0.0978636	+	0.116241i
$624$			14791.6i			0.948942i
$625$	9707.65	+	12243.5i	0.621289	+	0.783581i
$626$	2831.25	−	1634.62i	0.180766	−	0.104365i
$627$	12745.7	−	19626.7i	0.811828	−	1.25011i
$628$	−419.409	+	1092.60i	−0.0266501	+	0.0694258i
$629$	−12903.5	−	9374.92i	−0.817957	−	0.594281i
$630$	10013.8	+	3643.02i	0.633266	+	0.230383i
$631$	−9383.63	+	6817.60i	−0.592007	+	0.430118i	−0.843033	−	0.537862i	$-0.819232\pi$
$631$	−9383.63	+	6817.60i	−0.592007	+	0.430118i	0.251026	+	0.967980i	$0.419232\pi$
$632$	1450.37	+	5412.86i	0.0912859	+	0.340684i
$633$	45624.0	−	17513.4i	2.86476	−	1.09968i
$634$	5141.00	+	4628.98i	0.322043	+	0.289969i
$635$	1659.82	+	6606.75i	0.103729	+	0.412883i
$636$	36017.2	+	11702.7i	2.24556	+	0.729626i
$637$	10121.1	+	2001.85i	0.629532	+	0.124515i
$638$	−2576.04	+	5055.76i	−0.159853	+	0.313729i
$639$	−40268.1	+	36257.5i	−2.49293	+	2.24464i
$640$	11939.2	+	8022.05i	0.737406	+	0.495468i
$641$	−11663.1	+	12953.2i	−0.718666	+	0.798160i	−0.986230	−	0.165380i	$-0.947115\pi$
$641$	−11663.1	+	12953.2i	−0.718666	+	0.798160i	0.267564	+	0.963540i	$0.413781\pi$
$642$	−37.6061	+	46.4396i	−0.00231183	+	0.00285487i
$643$	13969.1	−	13969.1i	0.856746	−	0.856746i	−0.134207	−	0.990953i	$-0.542849\pi$
$643$	13969.1	−	13969.1i	0.856746	−	0.856746i	0.990953	+	0.134207i	$0.0428487\pi$
$644$	−7049.87	−	134.633i	−0.431372	−	0.00823801i
$645$	11713.7	−	34217.9i	0.715078	−	2.08888i
$646$	−2888.14	+	1285.88i	−0.175902	+	0.0783165i
$647$	10238.7	−	8291.12i	0.622139	−	0.503799i	−0.265637	−	0.964073i	$-0.585582\pi$
$647$	10238.7	−	8291.12i	0.622139	−	0.503799i	0.887777	+	0.460274i	$0.152249\pi$
$648$	−20004.1	−	12990.8i	−1.21271	−	0.787544i
$649$	9178.15	−	15897.0i	0.555122	−	0.961499i
$650$	1604.27	+	2360.15i	0.0968070	+	0.142419i
$651$	18931.9	+	44805.1i	1.13978	+	2.69747i
$652$	13843.2	+	27168.9i	0.831507	+	1.63192i
$653$	−19952.4	−	7659.01i	−1.19571	−	0.458990i	−0.322610	−	0.946532i	$-0.604560\pi$
$653$	−19952.4	−	7659.01i	−1.19571	−	0.458990i	−0.873100	+	0.487542i	$0.837894\pi$
$654$	−1686.40	+	16045.0i	−0.100831	+	0.959343i
$655$	−16055.8	−	1942.22i	−0.957787	−	0.115861i
$656$	−7674.37	+	806.609i	−0.456759	+	0.0480073i
$657$	33672.9	+	33672.9i	1.99955	+	1.99955i
$658$	1155.37	−	4004.44i	0.0684515	−	0.237248i
$659$	−7017.47	+	2280.12i	−0.414813	+	0.134781i	−0.508986	−	0.860775i	$-0.669979\pi$
$659$	−7017.47	+	2280.12i	−0.414813	+	0.134781i	0.0941726	+	0.995556i	$0.469979\pi$
$660$	14211.9	+	22653.5i	0.838180	+	1.33604i
$661$	3416.42	+	16073.0i	0.201034	+	0.945789i	0.956755	+	0.290895i	$0.0939532\pi$
$661$	3416.42	+	16073.0i	0.201034	+	0.945789i	−0.755721	+	0.654893i	$0.772713\pi$
$662$	−301.541	−	5753.75i	−0.0177035	−	0.337803i
$663$	14085.4	−	9147.17i	0.825086	−	0.535817i
$664$	1569.29	−	4829.77i	0.0917171	−	0.282276i
$665$	−15037.6	+	264.721i	−0.876890	+	0.0154368i
$666$	−4422.97	−	13612.5i	−0.257337	−	0.792002i
$667$	−9004.11	−	7291.38i	−0.522699	−	0.423273i
$668$	−21931.5	−	5876.52i	−1.27029	−	0.340373i
$669$	404.173	−	907.786i	0.0233576	−	0.0524620i
$670$	626.596	−	55.9507i	0.0361306	−	0.00322622i
$671$	2076.35	−	2857.86i	0.119459	−	0.164421i
$672$	−20204.9	+	12579.3i	−1.15985	+	0.722111i
$673$	1851.35	−	943.310i	0.106039	−	0.0540296i	−0.400167	−	0.916442i	$-0.631048\pi$
$673$	1851.35	−	943.310i	0.106039	−	0.0540296i	0.506206	+	0.862413i	$0.331048\pi$
$674$	−4840.52	−	2794.68i	−0.276632	−	0.159714i
$675$	49648.5	−	1044.47i	2.83107	−	0.0595581i
$676$	4796.76	+	8308.23i	0.272915	+	0.472703i
$677$	1000.02	−	19081.6i	0.0567711	−	1.08326i	−0.810602	−	0.585598i	$-0.800860\pi$
$677$	1000.02	−	19081.6i	0.0567711	−	1.08326i	0.867373	−	0.497659i	$-0.165807\pi$
$678$	1280.66	−	202.836i	0.0725419	−	0.0114895i
$679$	3991.01	−	1213.02i	0.225569	−	0.0685585i
$680$	117.557	−	7504.86i	0.00662956	−	0.423233i
$681$	−4251.26	−	40448.0i	−0.239220	−	2.27602i
$682$	1753.42	−	6543.87i	0.0984488	−	0.367416i
$683$	1854.48	+	4831.09i	0.103894	+	0.270654i	0.975667	−	0.219256i	$-0.0703630\pi$
$683$	1854.48	+	4831.09i	0.103894	+	0.270654i	−0.871773	+	0.489910i	$0.837030\pi$
$684$	35762.1	+	7601.48i	1.99912	+	0.424927i
$685$	−2399.95	+	13754.7i	−0.133865	+	0.767214i
$686$	1705.69	+	4509.73i	0.0949322	+	0.250995i
$687$	18879.5	+	9619.58i	1.04847	+	0.534221i
$688$	9139.09	+	14073.0i	0.506431	+	0.779835i
$689$	−15414.6	+	3276.47i	−0.852320	+	0.181166i
$690$	3979.13	−	1456.36i	0.219541	−	0.0803517i
$691$	5232.49	−	24616.9i	0.288065	−	1.35524i	−0.561377	−	0.827560i	$-0.689728\pi$
$691$	5232.49	−	24616.9i	0.288065	−	1.35524i	0.849442	−	0.527681i	$-0.176938\pi$
$692$	−1022.10	−	161.885i	−0.0561480	−	0.00889297i
$693$	−41157.4	+	5715.41i	−2.25604	+	0.313290i
$694$	−2523.04	−	3472.67i	−0.138002	−	0.189943i
$695$	6373.01	−	10649.6i	0.347830	−	0.581242i
$696$	−25610.5	−	2691.78i	−1.39478	−	0.146597i
$697$	5513.94	+	6809.14i	0.299649	+	0.370036i
$698$	−7186.38	−	376.622i	−0.389697	−	0.0204231i
$699$	−28669.7			−1.55134
$700$	6959.96	−	15714.3i	0.375803	−	0.848491i
$701$	−18557.3			−0.999858			−0.499929	−	0.866066i	$-0.666641\pi$
$701$	−18557.3			−0.999858			−0.499929	+	0.866066i	$0.666641\pi$
$702$	9057.42	+	474.679i	0.486966	+	0.0255208i
$703$	12713.4	+	15699.7i	0.682067	+	0.842283i
$704$	−10000.1	−	1051.05i	−0.535358	−	0.0562684i
$705$	−2870.60	−	32148.1i	−0.153352	−	1.71740i
$706$	−2132.86	−	2935.63i	−0.113699	−	0.156493i
$707$	−2169.16	−	2785.81i	−0.115389	−	0.148191i
$708$	39604.3	+	6272.71i	2.10229	+	0.332970i
$709$	4505.01	−	21194.4i	0.238631	−	1.12267i	−0.681731	−	0.731603i	$-0.738773\pi$
$709$	4505.01	−	21194.4i	0.238631	−	1.12267i	0.920362	−	0.391067i	$-0.127894\pi$
$710$	−4184.82	−	5336.61i	−0.221202	−	0.282083i
$711$	−31746.3	+	6747.89i	−1.67452	+	0.355929i
$712$	813.461	+	1252.62i	0.0428170	+	0.0659325i
$713$	12325.5	+	6280.15i	0.647396	+	0.329865i
$714$	7107.96	+	3328.71i	0.372561	+	0.174473i
$715$	−9834.96	−	5206.78i	−0.514415	−	0.272339i
$716$	−3855.56	−	819.524i	−0.201242	−	0.0427752i
$717$	3171.07	+	8260.93i	0.165169	+	0.430279i
$718$	2037.70	−	7604.79i	0.105914	−	0.395276i
$719$	3621.46	+	34455.9i	0.187841	+	1.78719i	0.530457	+	0.847712i	$0.322020\pi$
$719$	3621.46	+	34455.9i	0.187841	+	1.78719i	−0.342616	+	0.939475i	$0.611313\pi$
$720$	−22986.3	+	30617.8i	−1.18979	+	1.58480i
$721$	−16999.4	−	3954.03i	−0.878074	−	0.204238i
$722$	−1186.88	+	187.984i	−0.0611789	+	0.00968979i
$723$	−2715.24	+	51809.9i	−0.139669	+	2.66505i
$724$	−6352.59	−	11003.0i	−0.326094	−	0.564811i
$725$	24887.0	−	13347.2i	1.27487	−	0.683727i
$726$	−1510.49	−	872.079i	−0.0772168	−	0.0445811i
$727$	127.254	−	64.8391i	0.00649187	−	0.00330777i	−0.450742	−	0.892654i	$-0.648840\pi$
$727$	127.254	−	64.8391i	0.00649187	−	0.00330777i	0.457233	+	0.889347i	$0.348840\pi$
$728$	3071.12	−	5753.14i	0.156351	−	0.292892i
$729$	19811.5	−	27268.2i	1.00653	−	1.38537i
$730$	−4491.10	+	3918.20i	−0.227703	+	0.198656i
$731$	7749.41	−	17405.5i	0.392096	−	0.880663i
$732$	7453.56	+	1997.18i	0.376355	+	0.100844i
$733$	−20738.2	−	16793.5i	−1.04500	−	0.846224i	−0.0566452	−	0.998394i	$-0.518040\pi$
$733$	−20738.2	−	16793.5i	−1.04500	−	0.846224i	−0.988354	+	0.152170i	$0.951374\pi$
$734$	−184.235	−	567.017i	−0.00926463	−	0.0285136i
$735$	24943.0	+	27785.3i	1.25175	+	1.39439i
$736$	−2091.69	+	6437.56i	−0.104756	+	0.322407i
$737$	−2057.36	+	1336.07i	−0.102828	+	0.0667770i
$738$	411.503	+	7851.94i	0.0205252	+	0.391645i
$739$	3513.28	+	16528.7i	0.174882	+	0.822757i	0.974876	+	0.222749i	$0.0715029\pi$
$739$	3513.28	+	16528.7i	0.174882	+	0.822757i	−0.799993	+	0.600009i	$0.795164\pi$
$740$	−22389.4	+	5624.91i	−1.11223	+	0.279427i
$741$	−20231.3	+	6573.55i	−1.00299	+	0.325891i
$742$	−5107.20	−	5306.07i	−0.252684	−	0.262523i
$743$	−12768.6	−	12768.6i	−0.630464	−	0.630464i	0.317721	−	0.948184i	$-0.397083\pi$
$743$	−12768.6	−	12768.6i	−0.630464	−	0.630464i	−0.948184	+	0.317721i	$0.897083\pi$
$744$	30577.6	−	3213.84i	1.50676	−	0.158367i
$745$	19227.9	+	17866.1i	0.945579	+	0.878606i
$746$	−231.802	+	2205.45i	−0.0113765	+	0.108240i
$747$	27458.6	+	10540.4i	1.34492	+	0.516267i
$748$	6395.70	+	12552.3i	0.312634	+	0.613578i
$749$	−137.946	+	58.2876i	−0.00672957	+	0.00284350i
$750$	−485.119	+	10316.6i	−0.0236187	+	0.502279i
$751$	7212.31	−	12492.1i	0.350441	−	0.606981i	−0.635886	−	0.771783i	$-0.719365\pi$
$751$	7212.31	−	12492.1i	0.350441	−	0.606981i	0.986327	+	0.164802i	$0.0526985\pi$
$752$	12558.8	+	8155.79i	0.609006	+	0.395493i
$753$	−853.972	+	691.533i	−0.0413286	+	0.0334673i
$754$	4711.90	−	2097.87i	0.227583	−	0.101326i
$755$	−2749.53	−	8936.05i	−0.132537	−	0.430750i
$756$	−26403.1	−	47817.4i	−1.27020	−	2.30040i
$757$	9550.09	−	9550.09i	0.458526	−	0.458526i	−0.439646	−	0.898171i	$-0.644896\pi$
$757$	9550.09	−	9550.09i	0.458526	−	0.458526i	0.898171	+	0.439646i	$0.144896\pi$
$758$	−4932.20	+	6090.75i	−0.236340	+	0.291855i
$759$	−11056.2	+	12279.1i	−0.528740	+	0.587225i
$760$	−2604.07	+	9143.21i	−0.124289	+	0.436394i
$761$	−3516.16	+	3165.96i	−0.167491	+	0.150809i	−0.748614	−	0.663006i	$-0.769280\pi$
$761$	−3516.16	+	3165.96i	−0.167491	+	0.150809i	0.581123	+	0.813816i	$0.302614\pi$
$762$	−2044.19	+	4011.95i	−0.0971828	+	0.190732i
$763$	−22664.1	+	33482.2i	−1.07535	+	1.58865i
$764$	−18958.3	−	6159.91i	−0.897756	−	0.291699i
$765$	43370.7	+	2954.75i	2.04977	+	0.139646i

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)

\(f(q)\)	\(=\)	\(q+(-0.757961 - 0.0397231i) q^{2} +(-6.12747 - 7.56679i) q^{3} +(-7.38325 - 0.776011i) q^{4} +(10.8983 + 2.49552i) q^{5} +(4.34381 + 5.97873i) q^{6} +(2.54741 + 18.3442i) q^{7} +(11.5626 + 1.83134i) q^{8} +(-14.0969 + 66.3205i) q^{9} +O(q^{10})\)	\(q+(-0.757961 - 0.0397231i) q^{2} +(-6.12747 - 7.56679i) q^{3} +(-7.38325 - 0.776011i) q^{4} +(10.8983 + 2.49552i) q^{5} +(4.34381 + 5.97873i) q^{6} +(2.54741 + 18.3442i) q^{7} +(11.5626 + 1.83134i) q^{8} +(-14.0969 + 66.3205i) q^{9} +(-8.16134 - 2.32442i) q^{10} +(32.3675 - 6.87992i) q^{11} +(39.3687 + 60.6225i) q^{12} +(-26.8007 - 13.6556i) q^{13} +(-1.20215 - 14.0054i) q^{14} +(-47.8957 - 97.7562i) q^{15} +(49.4022 + 10.5008i) q^{16} +(-20.5510 - 53.5371i) q^{17} +(13.3193 - 49.7084i) q^{18} +(7.59237 + 72.2366i) q^{19} +(-78.5281 - 26.8822i) q^{20} +(123.198 - 131.679i) q^{21} +(-24.8066 + 3.92898i) q^{22} +(2.68398 - 51.2135i) q^{23} +(-56.9923 - 98.7136i) q^{24} +(112.545 + 54.3937i) q^{25} +(19.7715 + 11.4151i) q^{26} +(353.975 - 180.359i) q^{27} +(-4.57285 - 137.417i) q^{28} +(132.793 - 182.775i) q^{29} +(32.4199 + 75.9979i) q^{30} +(-109.713 + 246.419i) q^{31} +(-127.491 - 34.1611i) q^{32} +(-250.390 - 202.762i) q^{33} +(13.4502 + 41.3954i) q^{34} +(-18.0160 + 206.278i) q^{35} +(155.546 - 478.721i) q^{36} +(233.258 - 151.480i) q^{37} +(-2.88526 - 55.0541i) q^{38} +(60.8911 + 286.470i) q^{39} +(121.443 + 48.8133i) q^{40} +(-145.309 + 47.2138i) q^{41} +(-98.6098 + 94.9140i) q^{42} +(234.929 + 234.929i) q^{43} +(-244.316 + 25.6787i) q^{44} +(-319.136 + 687.600i) q^{45} +(-4.06871 + 38.7112i) q^{46} +(276.801 + 106.254i) q^{47} +(-223.253 - 438.159i) q^{48} +(-330.021 + 93.4606i) q^{49} +(-83.1439 - 45.6990i) q^{50} +(-279.179 + 483.552i) q^{51} +(187.279 + 121.621i) q^{52} +(407.159 - 329.711i) q^{53} +(-275.464 + 122.644i) q^{54} +(369.919 + 5.79445i) q^{55} +(-4.13976 + 216.773i) q^{56} +(500.077 - 500.077i) q^{57} +(-107.913 + 133.261i) q^{58} +(371.186 - 412.244i) q^{59} +(277.766 + 758.926i) q^{60} +(79.3325 - 71.4313i) q^{61} +(92.9464 - 182.418i) q^{62} +(-1252.51 - 89.6504i) q^{63} +(-288.995 - 93.9003i) q^{64} +(-258.004 - 215.705i) q^{65} +(181.731 + 163.632i) q^{66} +(-69.2096 + 26.5671i) q^{67} +(110.188 + 411.226i) q^{68} +(-403.968 + 293.500i) q^{69} +(21.8494 - 155.635i) q^{70} +(646.549 + 469.746i) q^{71} +(-284.452 + 741.024i) q^{72} +(382.526 - 589.039i) q^{73} +(-182.818 + 105.550i) q^{74} +(-278.028 - 1184.90i) q^{75} -539.232i q^{76} +(208.660 + 576.231i) q^{77} +(-34.7736 - 219.552i) q^{78} +(194.697 + 437.297i) q^{79} +(512.194 + 237.724i) q^{80} +(-1861.32 - 828.714i) q^{81} +(112.014 - 30.0141i) q^{82} +(67.8602 - 428.453i) q^{83} +(-1011.78 + 876.618i) q^{84} +(-90.3672 - 634.748i) q^{85} +(-168.735 - 187.399i) q^{86} +(-2196.70 + 115.124i) q^{87} +(386.853 - 20.2741i) q^{88} +(85.3692 + 94.8122i) q^{89} +(269.206 - 508.497i) q^{90} +(182.230 - 526.425i) q^{91} +(-59.5587 + 376.039i) q^{92} +(2536.86 - 679.749i) q^{93} +(-205.583 - 91.5316i) q^{94} +(-97.5241 + 806.201i) q^{95} +(522.706 + 1174.02i) q^{96} +(-35.2334 - 222.455i) q^{97} +(253.856 - 57.7300i) q^{98} +2243.61i 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

Introduction

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