LMFDB - Embedded newform 177.4.e.b.4.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,4,Mod(4,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(58))

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

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

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

chi := DirichletCharacter("177.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	177.e (of order $29$, degree $28$, 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:	$10.4433380710$
Analytic rank:	$0$
Dimension:	$420$
Relative dimension:	$15$ over $\Q(\zeta_{29})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			4.10
Character	$\chi$	$=$	177.4
Dual form			177.4.e.b.133.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.00109 + 0.217632i) q^{2} +(1.94216 - 2.28649i) q^{3} +(-3.85597 - 0.848763i) q^{4} +(-3.87099 - 2.94265i) q^{5} +(4.38404 - 4.15279i) q^{6} +(5.75041 - 14.4324i) q^{7} +(-22.7916 - 7.67938i) q^{8} +(-1.45604 - 8.88144i) q^{9} +O(q^{10})$	\(q+(2.00109 + 0.217632i) q^{2} +(1.94216 - 2.28649i) q^{3} +(-3.85597 - 0.848763i) q^{4} +(-3.87099 - 2.94265i) q^{5} +(4.38404 - 4.15279i) q^{6} +(5.75041 - 14.4324i) q^{7} +(-22.7916 - 7.67938i) q^{8} +(-1.45604 - 8.88144i) q^{9} +(-7.10578 - 6.73095i) q^{10} +(-55.5415 + 25.6962i) q^{11} +(-9.42959 + 7.16819i) q^{12} +(-6.50110 + 39.6549i) q^{13} +(14.6480 - 27.6291i) q^{14} +(-14.2464 + 3.13587i) q^{15} +(-15.2698 - 7.06458i) q^{16} +(-12.6125 - 31.6550i) q^{17} +(-0.980780 - 18.0894i) q^{18} +(-32.7981 - 48.3736i) q^{19} +(12.4288 + 14.6323i) q^{20} +(-21.8314 - 41.1783i) q^{21} +(-116.736 + 39.3329i) q^{22} +(7.86701 - 145.099i) q^{23} +(-61.8237 + 37.1981i) q^{24} +(-27.1157 - 97.6618i) q^{25} +(-21.6394 + 77.9382i) q^{26} +(-23.1351 - 13.9200i) q^{27} +(-34.4231 + 50.7703i) q^{28} +(57.7340 - 6.27895i) q^{29} +(-29.1908 + 3.17469i) q^{30} +(-20.3860 + 30.0671i) q^{31} +(135.844 + 81.7348i) q^{32} +(-49.1163 + 176.901i) q^{33} +(-18.3496 - 66.0893i) q^{34} +(-64.7294 + 38.9464i) q^{35} +(-1.92380 + 35.4824i) q^{36} +(183.478 - 61.8210i) q^{37} +(-55.1043 - 103.938i) q^{38} +(78.0443 + 91.8809i) q^{39} +(65.6282 + 96.7944i) q^{40} +(-7.42872 - 137.015i) q^{41} +(-34.7248 - 87.1527i) q^{42} +(43.8662 + 20.2947i) q^{43} +(235.976 - 51.9423i) q^{44} +(-20.4986 + 38.6646i) q^{45} +(47.3206 - 288.643i) q^{46} +(-154.726 + 117.620i) q^{47} +(-45.8095 + 21.1937i) q^{48} +(73.7882 + 69.8959i) q^{49} +(-33.0066 - 201.331i) q^{50} +(-96.8741 - 32.6407i) q^{51} +(58.7257 - 147.390i) q^{52} +(-214.196 + 202.897i) q^{53} +(-43.2661 - 32.8900i) q^{54} +(290.615 + 63.9693i) q^{55} +(-241.893 + 284.779i) q^{56} +(-174.305 - 18.9568i) q^{57} +116.897 q^{58} +(37.1557 - 451.662i) q^{59} +57.5953 q^{60} +(48.6850 + 5.29481i) q^{61} +(-47.3377 + 55.7303i) q^{62} +(-136.554 - 30.0577i) q^{63} +(361.202 + 274.578i) q^{64} +(141.856 - 134.373i) q^{65} +(-136.785 + 343.305i) q^{66} +(277.967 + 93.6579i) q^{67} +(21.7658 + 132.766i) q^{68} +(-316.487 - 299.792i) q^{69} +(-138.005 + 63.8480i) q^{70} +(-111.705 + 84.9159i) q^{71} +(-35.0185 + 213.604i) q^{72} +(482.360 - 909.827i) q^{73} +(380.610 - 83.7787i) q^{74} +(-275.965 - 127.675i) q^{75} +(85.4108 + 214.365i) q^{76} +(51.4730 + 949.363i) q^{77} +(136.177 + 200.847i) q^{78} +(95.1092 + 111.971i) q^{79} +(38.3208 + 72.2807i) q^{80} +(-76.7599 + 25.8634i) q^{81} +(14.9532 - 275.795i) q^{82} +(-410.652 + 247.081i) q^{83} +(49.2305 + 177.312i) q^{84} +(-44.3266 + 159.650i) q^{85} +(83.3635 + 50.1581i) q^{86} +(97.7718 - 144.203i) q^{87} +(1463.21 - 159.134i) q^{88} +(312.065 - 33.9392i) q^{89} +(-49.4343 + 72.9101i) q^{90} +(534.934 + 321.859i) q^{91} +(-153.489 + 552.818i) q^{92} +(29.1552 + 105.007i) q^{93} +(-335.219 + 201.695i) q^{94} +(-15.3854 + 283.767i) q^{95} +(450.717 - 151.864i) q^{96} +(-359.128 - 677.388i) q^{97} +(132.445 + 155.927i) q^{98} +(309.090 + 455.873i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 420 q + 2 q^{2} - 45 q^{3} - 56 q^{4} - 14 q^{5} + 6 q^{6} + 6 q^{7} + 66 q^{8} - 135 q^{9}+O(q^{10}) $ 420 * q + 2 * q^2 - 45 * q^3 - 56 * q^4 - 14 * q^5 + 6 * q^6 + 6 * q^7 + 66 * q^8 - 135 * q^9	\( 420 q + 2 q^{2} - 45 q^{3} - 56 q^{4} - 14 q^{5} + 6 q^{6} + 6 q^{7} + 66 q^{8} - 135 q^{9} - 754 q^{10} + 64 q^{11} - 168 q^{12} + 90 q^{13} + 1024 q^{14} - 42 q^{15} - 172 q^{16} + 96 q^{17} + 18 q^{18} + 16 q^{19} - 178 q^{20} - 243 q^{21} - 604 q^{22} + 48 q^{23} + 198 q^{24} - 173 q^{25} + 156 q^{26} - 405 q^{27} + 84 q^{28} - 50 q^{29} + 174 q^{30} + 222 q^{31} - 45 q^{32} + 192 q^{33} - 64 q^{34} - 132 q^{35} - 504 q^{36} + 30 q^{37} - 108 q^{38} + 270 q^{39} + 6984 q^{40} + 400 q^{41} + 114 q^{42} + 1220 q^{43} + 1180 q^{44} - 126 q^{45} + 4938 q^{46} + 370 q^{47} - 516 q^{48} + 771 q^{49} + 1048 q^{50} + 288 q^{51} - 1964 q^{52} - 822 q^{53} + 54 q^{54} - 2342 q^{55} - 13824 q^{56} + 48 q^{57} - 13150 q^{58} - 3423 q^{59} - 534 q^{60} - 2182 q^{61} + 845 q^{62} + 54 q^{63} - 8018 q^{64} + 4140 q^{65} - 1812 q^{66} + 506 q^{67} + 4826 q^{68} - 3684 q^{69} + 6882 q^{70} + 5874 q^{71} + 594 q^{72} + 206 q^{73} + 11124 q^{74} - 867 q^{75} + 16940 q^{76} + 9940 q^{77} + 468 q^{78} - 1762 q^{79} - 28954 q^{80} - 1215 q^{81} + 3770 q^{82} - 1216 q^{83} - 8013 q^{84} - 420 q^{85} - 2256 q^{86} + 5940 q^{87} + 13458 q^{88} - 1580 q^{89} + 522 q^{90} - 12204 q^{91} + 4562 q^{92} + 666 q^{93} + 176 q^{94} - 28456 q^{95} + 2040 q^{96} + 2574 q^{97} + 50690 q^{98} + 576 q^{99}+O(q^{100}) \) 420 * q + 2 * q^2 - 45 * q^3 - 56 * q^4 - 14 * q^5 + 6 * q^6 + 6 * q^7 + 66 * q^8 - 135 * q^9 - 754 * q^10 + 64 * q^11 - 168 * q^12 + 90 * q^13 + 1024 * q^14 - 42 * q^15 - 172 * q^16 + 96 * q^17 + 18 * q^18 + 16 * q^19 - 178 * q^20 - 243 * q^21 - 604 * q^22 + 48 * q^23 + 198 * q^24 - 173 * q^25 + 156 * q^26 - 405 * q^27 + 84 * q^28 - 50 * q^29 + 174 * q^30 + 222 * q^31 - 45 * q^32 + 192 * q^33 - 64 * q^34 - 132 * q^35 - 504 * q^36 + 30 * q^37 - 108 * q^38 + 270 * q^39 + 6984 * q^40 + 400 * q^41 + 114 * q^42 + 1220 * q^43 + 1180 * q^44 - 126 * q^45 + 4938 * q^46 + 370 * q^47 - 516 * q^48 + 771 * q^49 + 1048 * q^50 + 288 * q^51 - 1964 * q^52 - 822 * q^53 + 54 * q^54 - 2342 * q^55 - 13824 * q^56 + 48 * q^57 - 13150 * q^58 - 3423 * q^59 - 534 * q^60 - 2182 * q^61 + 845 * q^62 + 54 * q^63 - 8018 * q^64 + 4140 * q^65 - 1812 * q^66 + 506 * q^67 + 4826 * q^68 - 3684 * q^69 + 6882 * q^70 + 5874 * q^71 + 594 * q^72 + 206 * q^73 + 11124 * q^74 - 867 * q^75 + 16940 * q^76 + 9940 * q^77 + 468 * q^78 - 1762 * q^79 - 28954 * q^80 - 1215 * q^81 + 3770 * q^82 - 1216 * q^83 - 8013 * q^84 - 420 * q^85 - 2256 * q^86 + 5940 * q^87 + 13458 * q^88 - 1580 * q^89 + 522 * q^90 - 12204 * q^91 + 4562 * q^92 + 666 * q^93 + 176 * q^94 - 28456 * q^95 + 2040 * q^96 + 2574 * q^97 + 50690 * q^98 + 576 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/177\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{1}{29}\right)$	$1$

Coefficient data

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

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

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

$2$	2.00109	+	0.217632i	0.707492	+	0.0769444i	0.454789	−	0.890599i	$-0.349715\pi$
$2$	2.00109	+	0.217632i	0.707492	+	0.0769444i	0.252703	+	0.967544i	$0.418680\pi$
$3$	1.94216	−	2.28649i	0.373769	−	0.440034i
$3$	1.94216	−	2.28649i	0.373769	−	0.440034i
$4$	−3.85597	−	0.848763i	−0.481996	−	0.106095i
$5$	−3.87099	−	2.94265i	−0.346232	−	0.263199i	0.417576	−	0.908642i	$-0.362880\pi$
$5$	−3.87099	−	2.94265i	−0.346232	−	0.263199i	−0.763808	+	0.645443i	$0.776673\pi$
$6$	4.38404	−	4.15279i	0.298296	−	0.282561i
$7$	5.75041	−	14.4324i	0.310493	−	0.779279i	−0.688068	−	0.725646i	$-0.741541\pi$
$7$	5.75041	−	14.4324i	0.310493	−	0.779279i	0.998561	−	0.0536323i	$-0.0170799\pi$
$8$	−22.7916	−	7.67938i	−1.00726	−	0.339384i
$9$	−1.45604	−	8.88144i	−0.0539273	−	0.328942i
$10$	−7.10578	−	6.73095i	−0.224704	−	0.212851i
$11$	−55.5415	+	25.6962i	−1.52240	+	0.704337i	−0.989857	−	0.142067i	$-0.954625\pi$
$11$	−55.5415	+	25.6962i	−1.52240	+	0.704337i	−0.532541	+	0.846404i	$0.678763\pi$
$12$	−9.42959	+	7.16819i	−0.226841	+	0.172440i
$13$	−6.50110	+	39.6549i	−0.138698	+	0.846023i	0.822215	+	0.569176i	$0.192738\pi$
$13$	−6.50110	+	39.6549i	−0.138698	+	0.846023i	−0.960914	+	0.276847i	$0.910710\pi$
$14$	14.6480	−	27.6291i	0.279632	−	0.527443i
$15$	−14.2464	+	3.13587i	−0.245227	+	0.0539785i
$16$	−15.2698	−	7.06458i	−0.238591	−	0.110384i
$17$	−12.6125	−	31.6550i	−0.179940	−	0.451615i	0.811145	−	0.584845i	$-0.198845\pi$
$17$	−12.6125	−	31.6550i	−0.179940	−	0.451615i	−0.991085	+	0.133230i	$0.957465\pi$
$18$	−0.980780	−	18.0894i	−0.0128429	−	0.236873i
$19$	−32.7981	−	48.3736i	−0.396021	−	0.584088i	0.576444	−	0.817137i	$-0.304440\pi$
$19$	−32.7981	−	48.3736i	−0.396021	−	0.584088i	−0.972465	+	0.233049i	$0.925130\pi$
$20$	12.4288	+	14.6323i	0.138958	+	0.163594i
$21$	−21.8314	−	41.1783i	−0.226857	−	0.427898i
$22$	−116.736	+	39.3329i	−1.13128	+	0.381172i
$23$	7.86701	−	145.099i	0.0713211	−	1.31544i	−0.715654	−	0.698455i	$-0.753871\pi$
$23$	7.86701	−	145.099i	0.0713211	−	1.31544i	0.786975	−	0.616985i	$-0.211646\pi$
$24$	−61.8237	+	37.1981i	−0.525821	+	0.316376i
$25$	−27.1157	−	97.6618i	−0.216925	−	0.781295i
$26$	−21.6394	+	77.9382i	−0.163225	+	0.587883i
$27$	−23.1351	−	13.9200i	−0.164902	−	0.0992184i
$28$	−34.4231	+	50.7703i	−0.232334	+	0.342668i
$29$	57.7340	−	6.27895i	0.369687	−	0.0402059i	0.0786099	−	0.996905i	$-0.474952\pi$
$29$	57.7340	−	6.27895i	0.369687	−	0.0402059i	0.291077	+	0.956700i	$0.405986\pi$
$30$	−29.1908	+	3.17469i	−0.177649	+	0.0193205i
$31$	−20.3860	+	30.0671i	−0.118111	+	0.174200i	−0.882149	−	0.470971i	$-0.843904\pi$
$31$	−20.3860	+	30.0671i	−0.118111	+	0.174200i	0.764038	+	0.645171i	$0.223214\pi$
$32$	135.844	+	81.7348i	0.750441	+	0.451525i
$33$	−49.1163	+	176.901i	−0.259092	+	0.933167i
$34$	−18.3496	−	66.0893i	−0.0925568	−	0.333359i
$35$	−64.7294	+	38.9464i	−0.312608	+	0.188090i
$36$	−1.92380	+	35.4824i	−0.00890648	+	0.164270i
$37$	183.478	−	61.8210i	0.815233	−	0.274684i	0.119362	−	0.992851i	$-0.461915\pi$
$37$	183.478	−	61.8210i	0.815233	−	0.274684i	0.695871	+	0.718167i	$0.255019\pi$
$38$	−55.1043	−	103.938i	−0.235240	−	0.443709i
$39$	78.0443	+	91.8809i	0.320438	+	0.377249i
$40$	65.6282	+	96.7944i	0.259418	+	0.382614i
$41$	−7.42872	−	137.015i	−0.0282969	−	0.521905i	−0.977981	−	0.208695i	$-0.933078\pi$
$41$	−7.42872	−	137.015i	−0.0282969	−	0.521905i	0.949684	−	0.313210i	$-0.101404\pi$
$42$	−34.7248	−	87.1527i	−0.127575	−	0.320189i
$43$	43.8662	+	20.2947i	0.155571	+	0.0719746i	0.496129	−	0.868249i	$-0.334754\pi$
$43$	43.8662	+	20.2947i	0.155571	+	0.0719746i	−0.340559	+	0.940223i	$0.610616\pi$
$44$	235.976	−	51.9423i	0.808517	−	0.177968i
$45$	−20.4986	+	38.6646i	−0.0679057	+	0.128084i
$46$	47.3206	−	288.643i	0.151675	−	0.925176i
$47$	−154.726	+	117.620i	−0.480195	+	0.365035i	−0.817092	−	0.576507i	$-0.804415\pi$
$47$	−154.726	+	117.620i	−0.480195	+	0.365035i	0.336898	+	0.941541i	$0.390622\pi$
$48$	−45.8095	+	21.1937i	−0.137751	+	0.0637302i
$49$	73.7882	+	69.8959i	0.215126	+	0.203778i
$50$	−33.0066	−	201.331i	−0.0933567	−	0.569451i
$51$	−96.8741	−	32.6407i	−0.265982	−	0.0896198i
$52$	58.7257	−	147.390i	0.156611	−	0.393065i
$53$	−214.196	+	202.897i	−0.555134	+	0.525850i	−0.913020	−	0.407915i	$-0.866256\pi$
$53$	−214.196	+	202.897i	−0.555134	+	0.525850i	0.357886	+	0.933765i	$0.383497\pi$
$54$	−43.2661	−	32.8900i	−0.109033	−	0.0828845i
$55$	290.615	+	63.9693i	0.712483	+	0.156829i
$56$	−241.893	+	284.779i	−0.577220	+	0.679556i
$57$	−174.305	−	18.9568i	−0.405039	−	0.0440507i
$58$	116.897			0.264644
$59$	37.1557	−	451.662i	0.0819874	−	0.996633i
$59$	37.1557	−	451.662i	0.0819874	−	0.996633i
$60$	57.5953			0.123925
$61$	48.6850	+	5.29481i	0.102188	+	0.0111136i	0.159070	−	0.987267i	$-0.449150\pi$
$61$	48.6850	+	5.29481i	0.102188	+	0.0111136i	−0.0568821	+	0.998381i	$0.518116\pi$
$62$	−47.3377	+	55.7303i	−0.0969661	+	0.114157i
$63$	−136.554	−	30.0577i	−0.273082	−	0.0601098i
$64$	361.202	+	274.578i	0.705472	+	0.536286i
$65$	141.856	−	134.373i	0.270694	−	0.256415i
$66$	−136.785	+	343.305i	−0.255108	+	0.640272i
$67$	277.967	+	93.6579i	0.506851	+	0.170778i	0.561098	−	0.827749i	$-0.310379\pi$
$67$	277.967	+	93.6579i	0.506851	+	0.170778i	−0.0542465	+	0.998528i	$0.517276\pi$
$68$	21.7658	+	132.766i	0.0388161	+	0.236768i
$69$	−316.487	−	299.792i	−0.552182	−	0.523054i
$70$	−138.005	+	63.8480i	−0.235640	+	0.109019i
$71$	−111.705	+	84.9159i	−0.186717	+	0.141939i	−0.694357	−	0.719631i	$-0.744311\pi$
$71$	−111.705	+	84.9159i	−0.186717	+	0.141939i	0.507640	+	0.861569i	$0.330518\pi$
$72$	−35.0185	+	213.604i	−0.0573191	+	0.349631i
$73$	482.360	−	909.827i	0.773369	−	1.45873i	−0.111935	−	0.993715i	$-0.535705\pi$
$73$	482.360	−	909.827i	0.773369	−	1.45873i	0.885304	−	0.465013i	$-0.153950\pi$
$74$	380.610	−	83.7787i	0.597906	−	0.131609i
$75$	−275.965	−	127.675i	−0.424876	−	0.196569i
$76$	85.4108	+	214.365i	0.128912	+	0.323544i
$77$	51.4730	+	949.363i	0.0761804	+	1.40506i
$78$	136.177	+	200.847i	0.197680	+	0.291557i
$79$	95.1092	+	111.971i	0.135451	+	0.159465i	0.825705	−	0.564101i	$-0.190777\pi$
$79$	95.1092	+	111.971i	0.135451	+	0.159465i	−0.690255	+	0.723567i	$0.742501\pi$
$80$	38.3208	+	72.2807i	0.0535549	+	0.101015i
$81$	−76.7599	+	25.8634i	−0.105295	+	0.0354779i
$82$	14.9532	−	275.795i	0.0201378	−	0.371421i
$83$	−410.652	+	247.081i	−0.543072	+	0.326755i	−0.760518	−	0.649317i	$-0.775055\pi$
$83$	−410.652	+	247.081i	−0.543072	+	0.326755i	0.217446	+	0.976072i	$0.430227\pi$
$84$	49.2305	+	177.312i	0.0639462	+	0.230314i
$85$	−44.3266	+	159.650i	−0.0565635	+	0.203723i
$86$	83.3635	+	50.1581i	0.104527	+	0.0628917i
$87$	97.7718	−	144.203i	0.120485	−	0.177703i
$88$	1463.21	−	159.134i	1.77248	−	0.192769i
$89$	312.065	−	33.9392i	0.371673	−	0.0404218i	0.0796231	−	0.996825i	$-0.474628\pi$
$89$	312.065	−	33.9392i	0.371673	−	0.0404218i	0.292050	+	0.956403i	$0.405663\pi$
$90$	−49.4343	+	72.9101i	−0.0578981	+	0.0853933i
$91$	534.934	+	321.859i	0.616223	+	0.370769i
$92$	−153.489	+	552.818i	−0.173939	+	0.626471i
$93$	29.1552	+	105.007i	0.0325080	+	0.117083i
$94$	−335.219	+	201.695i	−0.367821	+	0.221311i
$95$	−15.3854	+	283.767i	−0.0166159	+	0.306462i
$96$	450.717	−	151.864i	0.479178	−	0.161454i
$97$	−359.128	−	677.388i	−0.375917	−	0.709055i	0.621303	−	0.783571i	$-0.286604\pi$
$97$	−359.128	−	677.388i	−0.375917	−	0.709055i	−0.997220	+	0.0745159i	$0.976259\pi$
$98$	132.445	+	155.927i	0.136520	+	0.160724i
$99$	309.090	+	455.873i	0.313785	+	0.462798i
$100$	21.6655	+	399.596i	0.0216655	+	0.399596i
$101$	−137.678	−	345.545i	−0.135638	−	0.340426i	0.845431	−	0.534085i	$-0.179344\pi$
$101$	−137.678	−	345.545i	−0.135638	−	0.340426i	−0.981069	+	0.193659i	$0.937965\pi$
$102$	−186.750	−	86.3998i	−0.181284	−	0.0838711i
$103$	932.419	−	205.241i	0.891980	−	0.196340i	0.254744	−	0.967008i	$-0.418009\pi$
$103$	932.419	−	205.241i	0.891980	−	0.196340i	0.637236	+	0.770669i	$0.280078\pi$
$104$	452.696	−	853.875i	0.426831	−	0.805090i
$105$	−36.6644	+	223.643i	−0.0340769	+	0.207860i
$106$	−472.782	+	359.400i	−0.433214	+	0.329320i
$107$	−1297.91	+	600.476i	−1.17265	+	0.542525i	−0.906830	−	0.421497i	$-0.861505\pi$
$107$	−1297.91	+	600.476i	−1.17265	+	0.542525i	−0.265820	+	0.964023i	$0.585643\pi$
$108$	77.3937	+	73.3112i	0.0689557	+	0.0653183i
$109$	−92.6785	−	565.314i	−0.0814403	−	0.496764i	−0.995777	−	0.0918082i	$-0.970735\pi$
$109$	−92.6785	−	565.314i	−0.0814403	−	0.496764i	0.914336	−	0.404955i	$-0.132713\pi$
$110$	567.625	+	191.255i	0.492009	+	0.165777i
$111$	214.991	−	539.586i	0.183838	−	0.461399i
$112$	−189.767	+	179.757i	−0.160101	+	0.151656i
$113$	−1666.94	−	1267.17i	−1.38772	−	1.05492i	−0.990547	−	0.137170i	$-0.956199\pi$
$113$	−1666.94	−	1267.17i	−1.38772	−	1.05492i	−0.397170	−	0.917745i	$-0.630008\pi$
$114$	−344.674	−	75.8684i	−0.283172	−	0.0623310i
$115$	−457.427	+	538.525i	−0.370916	+	0.436676i
$116$	−227.950	−	24.7910i	−0.182453	−	0.0198430i
$117$	361.659			0.285772
$118$	172.648	−	895.729i	0.134691	−	0.698802i
$119$	−529.386			−0.407804
$120$	348.780	+	37.9321i	0.265326	+	0.0288559i
$121$	1562.89	−	1839.97i	1.17422	−	1.38240i
$122$	96.2706	+	21.1908i	0.0714421	+	0.0157256i
$123$	−327.710	−	249.119i	−0.240233	−	0.182620i
$124$	104.128	−	98.6349i	0.0754108	−	0.0714329i
$125$	−407.394	+	1022.48i	−0.291507	+	0.731628i
$126$	−266.715	−	89.8666i	−0.188578	−	0.0635393i
$127$	332.490	+	2028.10i	0.232312	+	1.41704i	0.803050	+	0.595911i	$0.203209\pi$
$127$	332.490	+	2028.10i	0.232312	+	1.41704i	−0.570738	+	0.821132i	$0.693343\pi$
$128$	−257.742	−	244.146i	−0.177980	−	0.168591i
$129$	131.599	−	60.8840i	0.0898187	−	0.0415546i
$130$	313.111	−	238.021i	0.211243	−	0.160583i
$131$	−116.064	+	707.961i	−0.0774091	+	0.472174i	0.919465	+	0.393171i	$0.128622\pi$
$131$	−116.064	+	707.961i	−0.0774091	+	0.472174i	−0.996874	+	0.0790032i	$0.974826\pi$
$132$	339.538	−	640.437i	0.223886	−	0.422294i
$133$	−886.752	+	195.189i	−0.578129	+	0.127256i
$134$	535.853	+	247.912i	0.345453	+	0.159824i
$135$	48.5943	+	121.963i	0.0309803	+	0.0777546i
$136$	44.3682	+	818.323i	0.0279746	+	0.515960i
$137$	1267.31	+	1869.15i	0.790320	+	1.16564i	0.982861	+	0.184346i	$0.0590167\pi$
$137$	1267.31	+	1869.15i	0.790320	+	1.16564i	−0.192541	+	0.981289i	$0.561673\pi$
$138$	−568.074	−	668.788i	−0.350418	−	0.412544i
$139$	−552.599	−	1042.31i	−0.337200	−	0.636027i	0.655694	−	0.755027i	$-0.272376\pi$
$139$	−552.599	−	1042.31i	−0.337200	−	0.636027i	−0.992894	+	0.119000i	$0.962031\pi$
$140$	282.651	−	95.2362i	0.170631	−	0.0574923i
$141$	−31.5668	+	582.216i	−0.0188540	+	0.347741i
$142$	−242.012	+	145.614i	−0.143022	+	0.0860538i
$143$	−657.902	−	2369.55i	−0.384731	−	1.38568i
$144$	−40.5102	+	145.904i	−0.0234434	+	0.0844354i
$145$	−241.964	−	145.585i	−0.138580	−	0.0833806i
$146$	1163.25	−	1715.67i	0.659393	−	0.972532i
$147$	303.125	−	32.9668i	0.170077	−	0.0184970i
$148$	−759.958	+	82.6504i	−0.422082	+	0.0459042i
$149$	−681.052	+	1004.48i	−0.374456	+	0.552281i	−0.967494	−	0.252893i	$-0.918618\pi$
$149$	−681.052	+	1004.48i	−0.374456	+	0.552281i	0.593038	+	0.805174i	$0.297928\pi$
$150$	−524.445	−	315.548i	−0.285472	−	0.171763i
$151$	790.466	−	2847.00i	0.426008	−	1.53434i	−0.369986	−	0.929037i	$-0.620638\pi$
$151$	790.466	−	2847.00i	0.426008	−	1.53434i	0.795994	−	0.605304i	$-0.206949\pi$
$152$	376.042	+	1354.38i	0.200665	+	0.722729i
$153$	−262.777	+	158.108i	−0.138852	+	0.0835442i
$154$	−103.609	+	1910.96i	−0.0542148	+	0.999933i
$155$	167.391	−	56.4005i	0.0867429	−	0.0292271i
$156$	−222.951	−	420.531i	−0.114426	−	0.215830i
$157$	−1950.71	−	2296.55i	−0.991616	−	1.16742i	−0.985883	−	0.167437i	$-0.946451\pi$
$157$	−1950.71	−	2296.55i	−0.991616	−	1.16742i	−0.00573295	−	0.999984i	$-0.501825\pi$
$158$	165.954	+	244.763i	0.0835605	+	0.123243i
$159$	47.9190	+	883.815i	0.0239008	+	0.440824i
$160$	−285.335	−	716.137i	−0.140986	−	0.353847i
$161$	−2048.89	−	947.916i	−1.00295	−	0.464014i
$162$	−159.232	+	35.0496i	−0.0772250	+	0.0169985i
$163$	−918.405	+	1732.30i	−0.441319	+	0.832416i	0.558676	+	0.829386i	$0.311309\pi$
$163$	−918.405	+	1732.30i	−0.441319	+	0.832416i	−0.999995	+	0.00303050i	$0.999035\pi$
$164$	−87.6481	+	534.630i	−0.0417327	+	0.254558i
$165$	710.686	−	540.249i	0.335314	−	0.254899i
$166$	−875.525	+	405.061i	−0.409361	+	0.189390i
$167$	−3028.88	−	2869.11i	−1.40348	−	1.32945i	−0.878010	−	0.478643i	$-0.841129\pi$
$167$	−3028.88	−	2869.11i	−1.40348	−	1.32945i	−0.525475	−	0.850809i	$-0.676112\pi$
$168$	181.348	+	1106.17i	0.0832813	+	0.507994i
$169$	551.743	+	185.904i	0.251135	+	0.0846172i
$170$	−123.446	+	309.827i	−0.0556936	+	0.139780i
$171$	−381.872	+	361.728i	−0.170775	+	0.161766i
$172$	−151.921	−	115.488i	−0.0673483	−	0.0511968i
$173$	−863.266	−	190.019i	−0.379381	−	0.0835081i	0.0211860	−	0.999776i	$-0.493256\pi$
$173$	−863.266	−	190.019i	−0.379381	−	0.0835081i	−0.400567	+	0.916267i	$0.631187\pi$
$174$	227.033	−	267.284i	0.0989157	−	0.116453i
$175$	−1565.43	−	170.250i	−0.676200	−	0.0735412i
$176$	1029.64			0.440978
$177$	−960.556	−	962.155i	−0.407909	−	0.408588i
$178$	631.857			0.266066
$179$	−3159.66	−	343.633i	−1.31935	−	0.143488i	−0.578790	−	0.815477i	$-0.696475\pi$
$179$	−3159.66	−	343.633i	−1.31935	−	0.143488i	−0.740562	+	0.671989i	$0.765440\pi$
$180$	111.859	−	131.691i	0.0463194	−	0.0545314i
$181$	3641.94	+	801.652i	1.49560	+	0.329206i	0.886068	−	0.463556i	$-0.153427\pi$
$181$	3641.94	+	801.652i	1.49560	+	0.329206i	0.609531	+	0.792762i	$0.291358\pi$
$182$	1000.40	+	760.487i	0.407444	+	0.309731i
$183$	106.660	−	101.034i	0.0430851	−	0.0408123i
$184$	−1293.57	+	3246.61i	−0.518278	+	1.30078i
$185$	−892.159	−	300.603i	−0.354556	−	0.119464i
$186$	35.4891	+	216.474i	0.0139903	+	0.0853369i
$187$	1513.93	+	1434.07i	0.592029	+	0.560800i
$188$	696.452	−	322.213i	0.270181	−	0.124999i
$189$	−333.936	+	253.851i	−0.128520	+	0.0976982i
$190$	−92.5442	+	564.495i	−0.0353361	+	0.215541i
$191$	1656.04	−	3123.63i	0.627367	−	1.18334i	−0.342456	−	0.939534i	$-0.611259\pi$
$191$	1656.04	−	3123.63i	0.627367	−	1.18334i	0.969824	−	0.243807i	$-0.0783963\pi$
$192$	1329.33	−	292.608i	0.499668	−	0.109985i
$193$	−2725.11	−	1260.77i	−1.01636	−	0.470218i	−0.160286	−	0.987071i	$-0.551242\pi$
$193$	−2725.11	−	1260.77i	−1.01636	−	0.470218i	−0.856075	+	0.516852i	$0.827104\pi$
$194$	−571.227	−	1433.67i	−0.211400	−	0.530575i
$195$	−31.7355	−	585.327i	−0.0116545	−	0.214955i
$196$	−225.200	−	332.145i	−0.0820700	−	0.121044i
$197$	1845.30	+	2172.46i	0.667372	+	0.785691i	0.986804	−	0.161918i	$-0.0517681\pi$
$197$	1845.30	+	2172.46i	0.667372	+	0.785691i	−0.319432	+	0.947609i	$0.603492\pi$
$198$	519.304	+	979.511i	0.186391	+	0.351570i
$199$	−2737.67	+	922.430i	−0.975219	+	0.328590i	−0.761399	−	0.648284i	$-0.775487\pi$
$199$	−2737.67	+	922.430i	−0.975219	+	0.328590i	−0.213820	+	0.976873i	$0.568591\pi$
$200$	−131.973	+	2434.10i	−0.0466595	+	0.860584i
$201$	754.003	−	453.669i	0.264593	−	0.159201i
$202$	−200.304	−	721.430i	−0.0697691	−	0.251285i
$203$	241.373	−	869.349i	0.0834537	−	0.300573i
$204$	345.839	+	208.085i	0.118694	+	0.0714159i
$205$	−374.430	+	552.242i	−0.127567	+	0.188148i
$206$	1910.52	−	207.782i	0.646176	−	0.0702759i
$207$	−1300.14	+	141.399i	−0.436550	+	0.0474777i
$208$	379.416	−	559.597i	0.126480	−	0.186544i
$209$	3064.67	+	1843.95i	1.01430	+	0.610282i
$210$	−122.040	+	439.550i	−0.0401028	+	0.144437i
$211$	−1182.47	−	4258.86i	−0.385803	−	1.38954i	−0.860529	−	0.509402i	$-0.829867\pi$
$211$	−1182.47	−	4258.86i	−0.385803	−	1.38954i	0.474726	−	0.880133i	$-0.342547\pi$
$212$	998.145	−	600.564i	0.323363	−	0.194561i
$213$	−22.7897	+	420.332i	−0.00733111	+	0.135214i
$214$	−2727.91	+	919.141i	−0.871384	+	0.293604i
$215$	−110.086	−	207.643i	−0.0349199	−	0.0658659i
$216$	420.390	+	494.921i	0.132426	+	0.155903i
$217$	316.714	+	467.118i	0.0990780	+	0.146129i
$218$	−62.4278	−	1151.41i	−0.0193952	−	0.357723i
$219$	−1143.49	−	2869.94i	−0.352830	−	0.885536i
$220$	−1066.31	−	493.327i	−0.326775	−	0.151182i
$221$	1337.27	−	294.356i	0.407034	−	0.0895950i
$222$	547.647	−	1032.97i	0.165566	−	0.312291i
$223$	−263.282	+	1605.95i	−0.0790613	+	0.482252i	0.917384	+	0.398004i	$0.130297\pi$
$223$	−263.282	+	1605.95i	−0.0790613	+	0.482252i	−0.996445	+	0.0842481i	$0.973151\pi$
$224$	1960.79	−	1490.56i	0.584871	−	0.444607i
$225$	−827.896	+	383.026i	−0.245303	+	0.113489i
$226$	−3059.91	−	2898.50i	−0.900629	−	0.853121i
$227$	424.904	+	2591.80i	0.124237	+	0.757814i	0.973303	+	0.229526i	$0.0737175\pi$
$227$	424.904	+	2591.80i	0.124237	+	0.757814i	−0.849065	+	0.528288i	$0.822834\pi$
$228$	656.024	+	221.040i	0.190554	+	0.0642050i
$229$	−560.280	+	1406.20i	−0.161678	+	0.405782i	−0.987389	−	0.158311i	$-0.949395\pi$
$229$	−560.280	+	1406.20i	−0.161678	+	0.405782i	0.825711	+	0.564094i	$0.190774\pi$
$230$	−1032.55	+	978.086i	−0.296020	+	0.280405i
$231$	2270.67	+	1726.12i	0.646751	+	0.491647i
$232$	−1364.07	−	300.254i	−0.386015	−	0.0849682i
$233$	2317.91	−	2728.86i	0.651723	−	0.767268i	−0.332710	−	0.943029i	$-0.607963\pi$
$233$	2317.91	−	2728.86i	0.651723	−	0.767268i	0.984433	+	0.175761i	$0.0562387\pi$
$234$	723.712	+	78.7084i	0.202182	+	0.0219886i
$235$	945.058			0.262335
$236$	−526.625	+	1710.06i	−0.145256	+	0.471675i
$237$	440.738			0.120798
$238$	−1059.35	−	115.211i	−0.288518	−	0.0313782i
$239$	1366.33	−	1608.57i	0.369793	−	0.435354i	−0.545520	−	0.838098i	$-0.683668\pi$
$239$	1366.33	−	1608.57i	0.369793	−	0.435354i	0.915313	+	0.402744i	$0.131944\pi$
$240$	239.694	+	52.7606i	0.0644674	+	0.0141903i
$241$	4359.27	+	3313.83i	1.16517	+	0.885737i	0.995019	−	0.0996818i	$-0.0317825\pi$
$241$	4359.27	+	3313.83i	1.16517	+	0.885737i	0.170147	+	0.985419i	$0.445576\pi$
$242$	3527.91	−	3341.82i	0.937120	−	0.887687i
$243$	−89.9436	+	225.741i	−0.0237444	+	0.0595939i
$244$	−183.234	−	61.7386i	−0.0480751	−	0.0161984i
$245$	−79.9542	−	487.699i	−0.0208493	−	0.127175i
$246$	−601.561	−	569.828i	−0.155911	−	0.147687i
$247$	2131.48	−	986.126i	0.549079	−	0.254031i
$248$	695.526	−	528.725i	0.178088	−	0.135379i
$249$	−232.604	+	1418.82i	−0.0591995	+	0.361101i
$250$	−1037.76	+	1957.41i	−0.262534	+	0.495191i
$251$	3604.98	−	793.515i	0.906550	−	0.199547i	0.262861	−	0.964834i	$-0.415334\pi$
$251$	3604.98	−	793.515i	0.906550	−	0.199547i	0.643689	+	0.765287i	$0.277403\pi$
$252$	501.035	+	231.804i	0.125247	+	0.0579454i
$253$	3291.54	+	8261.14i	0.817934	+	2.05286i
$254$	223.963	+	4130.76i	0.0553257	+	1.02042i
$255$	278.948	+	411.418i	0.0685036	+	0.101035i
$256$	−2812.48	−	3311.10i	−0.686640	−	0.808375i
$257$	2928.02	+	5522.83i	0.710680	+	1.34048i	0.930986	+	0.365054i	$0.118950\pi$
$257$	2928.02	+	5522.83i	0.710680	+	1.34048i	−0.220306	+	0.975431i	$0.570706\pi$
$258$	276.591	−	93.1943i	0.0667434	−	0.0224885i
$259$	162.847	−	3003.53i	0.0390688	−	0.720581i
$260$	−661.045	+	397.737i	−0.157678	+	0.0948717i
$261$	−139.829	−	503.618i	−0.0331617	−	0.119437i
$262$	−386.330	+	1391.43i	−0.0910974	+	0.328103i
$263$	2927.41	+	1761.37i	0.686358	+	0.412968i	0.815577	−	0.578648i	$-0.196420\pi$
$263$	2927.41	+	1761.37i	0.686358	+	0.412968i	−0.129219	+	0.991616i	$0.541247\pi$
$264$	2477.93	−	3654.67i	0.577674	−	0.852005i
$265$	1426.21	−	155.109i	0.330608	−	0.0359558i
$266$	−1816.95	+	197.605i	−0.418813	+	0.0455487i
$267$	528.479	−	779.448i	0.121133	−	0.178657i
$268$	−992.338	−	597.070i	−0.226182	−	0.136089i
$269$	539.627	−	1943.56i	0.122311	−	0.440525i	−0.876881	−	0.480707i	$-0.840380\pi$
$269$	539.627	−	1943.56i	0.122311	−	0.440525i	0.999192	+	0.0401824i	$0.0127939\pi$
$270$	70.6987	+	254.634i	0.0159355	+	0.0573945i
$271$	−2732.59	+	1644.14i	−0.612519	+	0.368541i	−0.787758	−	0.615985i	$-0.788758\pi$
$271$	−2732.59	+	1644.14i	−0.612519	+	0.368541i	0.175238	+	0.984526i	$0.443930\pi$
$272$	−31.0383	+	572.468i	−0.00691902	+	0.127614i
$273$	1774.85	−	598.018i	0.393476	−	0.132578i
$274$	2129.22	+	4016.14i	0.469456	+	0.885488i
$275$	4015.58	+	4727.51i	0.880541	+	1.03665i
$276$	965.911	+	1424.61i	0.210656	+	0.310694i
$277$	393.750	+	7262.30i	0.0854086	+	1.57527i	0.656464	+	0.754357i	$0.272051\pi$
$277$	393.750	+	7262.30i	0.0854086	+	1.57527i	−0.571056	+	0.820911i	$0.693466\pi$
$278$	−878.959	−	2206.02i	−0.189628	−	0.475929i
$279$	296.722	+	137.278i	0.0636712	+	0.0294574i
$280$	1774.37	−	390.568i	0.378710	−	0.0833604i
$281$	207.683	−	391.732i	0.0440901	−	0.0831628i	−0.860488	−	0.509471i	$-0.829841\pi$
$281$	207.683	−	391.732i	0.0440901	−	0.0831628i	0.904578	+	0.426308i	$0.140186\pi$
$282$	−189.877	+	1158.20i	−0.0400957	+	0.244573i
$283$	3059.17	−	2325.52i	0.642574	−	0.488472i	−0.232414	−	0.972617i	$-0.574662\pi$
$283$	3059.17	−	2325.52i	0.642574	−	0.488472i	0.874988	+	0.484145i	$0.160869\pi$
$284$	502.804	−	232.622i	0.105056	−	0.0486042i
$285$	618.949	+	586.299i	0.128643	+	0.121857i
$286$	−800.832	−	4884.86i	−0.165574	−	1.00996i
$287$	−2020.17	−	680.676i	−0.415495	−	0.139997i
$288$	528.128	−	1325.50i	0.108056	−	0.271201i
$289$	2723.85	−	2580.17i	0.554418	−	0.525172i
$290$	−452.508	−	343.988i	−0.0916282	−	0.0696540i
$291$	−2246.32	−	494.453i	−0.452514	−	0.0996060i
$292$	−2632.19	+	3098.86i	−0.527525	+	0.621051i
$293$	−3127.10	−	340.092i	−0.623505	−	0.0678103i	−0.209087	−	0.977897i	$-0.567049\pi$
$293$	−3127.10	−	340.092i	−0.623505	−	0.0678103i	−0.414418	+	0.910087i	$0.636015\pi$
$294$	613.754			0.121751
$295$	−1472.91	+	1639.04i	−0.290699	+	0.323487i
$296$	−4656.50			−0.914371
$297$	1642.65	+	178.649i	0.320930	+	0.0349032i
$298$	−1581.45	+	1861.83i	−0.307420	+	0.361922i
$299$	5702.73	+	1255.27i	1.10300	+	0.242789i
$300$	955.748	+	726.541i	0.183934	+	0.139823i
$301$	545.151	−	516.394i	0.104392	−	0.0988853i
$302$	2201.39	−	5525.07i	0.419456	−	1.05276i
$303$	−1057.48	−	356.306i	−0.200497	−	0.0675552i
$304$	159.083	+	970.362i	0.0300132	+	0.183073i
$305$	−172.878	−	163.759i	−0.0324557	−	0.0307436i
$306$	−560.250	+	259.199i	−0.104665	+	0.0484230i
$307$	−3823.59	+	2906.62i	−0.710826	+	0.540356i	−0.896929	−	0.442174i	$-0.854207\pi$
$307$	−3823.59	+	2906.62i	−0.710826	+	0.540356i	0.186103	+	0.982530i	$0.440414\pi$
$308$	607.306	−	3704.40i	0.112352	−	0.685318i
$309$	1341.63	−	2530.57i	0.246998	−	0.465888i
$310$	347.239	−	76.4330i	0.0636188	−	0.0140036i
$311$	−5742.74	−	2656.88i	−1.04708	−	0.484430i	−0.180553	−	0.983565i	$-0.557789\pi$
$311$	−5742.74	−	2656.88i	−1.04708	−	0.484430i	−0.866524	+	0.499136i	$0.833651\pi$
$312$	−1073.17	−	2693.44i	−0.194731	−	0.488738i
$313$	103.988	+	1917.95i	0.0187788	+	0.346355i	0.992791	+	0.119859i	$0.0382442\pi$
$313$	103.988	+	1917.95i	0.0187788	+	0.346355i	−0.974012	+	0.226496i	$0.927273\pi$
$314$	−3403.74	−	5020.15i	−0.611734	−	0.902240i
$315$	440.148	+	518.183i	0.0787287	+	0.0926866i
$316$	−271.701	−	512.483i	−0.0483683	−	0.0912324i
$317$	3417.30	−	1151.42i	0.605472	−	0.204007i	0.000165815	−	1.00000i	$-0.499947\pi$
$317$	3417.30	−	1151.42i	0.605472	−	0.204007i	0.605306	+	0.795993i	$0.293051\pi$
$318$	−96.4557	+	1779.02i	−0.0170093	+	0.313719i
$319$	−3045.28	+	1832.29i	−0.534493	+	0.321594i
$320$	−590.220	−	2125.78i	−0.103107	−	0.371358i
$321$	−1147.76	+	4133.87i	−0.199570	+	0.718785i
$322$	−3893.71	−	2342.77i	−0.673876	−	0.405458i
$323$	−1117.60	+	1648.34i	−0.192523	+	0.283950i
$324$	317.936	−	34.5776i	0.0545157	−	0.00592894i
$325$	4049.06	−	440.361i	0.691081	−	0.0751596i
$326$	−2214.81	+	3266.60i	−0.376280	+	0.554971i
$327$	−1472.58	−	886.021i	−0.249033	−	0.149838i
$328$	−882.875	+	3179.83i	−0.148624	+	0.535295i
$329$	807.803	+	2909.44i	0.135367	+	0.487546i
$330$	1539.72	−	926.420i	0.256845	−	0.154539i
$331$	35.0580	−	646.607i	0.00582164	−	0.107374i	−0.994178	−	0.107748i	$-0.965636\pi$
$331$	35.0580	−	646.607i	0.00582164	−	0.107374i	1.00000		0.000373662i	$0.000118940\pi$
$332$	1793.18	−	604.192i	0.296426	−	0.0998775i
$333$	−816.210	−	1539.54i	−0.134318	−	0.253352i
$334$	−5436.66	−	6400.53i	−0.890660	−	1.04857i
$335$	−800.404	−	1180.51i	−0.130540	−	0.192531i
$336$	42.4539	+	783.016i	0.00689300	+	0.127134i
$337$	1571.22	+	3943.46i	0.253975	+	0.637430i	0.999581	−	0.0289576i	$-0.00921879\pi$
$337$	1571.22	+	3943.46i	0.253975	+	0.637430i	−0.745605	+	0.666388i	$0.767839\pi$
$338$	1063.63	+	492.087i	0.171165	+	0.0791894i
$339$	−6134.82	+	1350.38i	−0.982884	+	0.216349i
$340$	306.427	−	577.983i	0.0488775	−	0.0921928i
$341$	359.657	−	2193.81i	0.0571160	−	0.348392i
$342$	−842.883	+	640.743i	−0.133269	+	0.101308i
$343$	6269.37	−	2900.52i	0.986921	−	0.456598i
$344$	−843.930	−	799.413i	−0.132272	−	0.125295i
$345$	342.933	+	2091.80i	0.0535157	+	0.326431i
$346$	−1686.12	−	568.119i	−0.261983	−	0.0882725i
$347$	−143.879	+	361.108i	−0.0222588	+	0.0558654i	−0.939686	−	0.342038i	$-0.888883\pi$
$347$	−143.879	+	361.108i	−0.0222588	+	0.0558654i	0.917427	+	0.397904i	$0.130262\pi$
$348$	−499.399	+	473.056i	−0.0769270	+	0.0728691i
$349$	207.507	+	157.743i	0.0318269	+	0.0241942i	0.620967	−	0.783837i	$-0.286740\pi$
$349$	207.507	+	157.743i	0.0318269	+	0.0241942i	−0.589140	+	0.808031i	$0.700533\pi$
$350$	−3095.50	−	681.372i	−0.472748	−	0.104060i
$351$	702.399	−	826.928i	0.106813	−	0.125750i
$352$	−9645.27	−	1048.99i	−1.46050	−	0.158838i
$353$	−9903.06			−1.49316			−0.746582	−	0.665294i	$-0.768306\pi$
$353$	−9903.06			−1.49316			−0.746582	+	0.665294i	$0.768306\pi$
$354$	−1712.76	−	2134.41i	−0.257154	−	0.320459i
$355$	682.286			0.102006
$356$	−1232.12	−	134.001i	−0.183433	−	0.0199496i
$357$	−1028.15	+	1210.43i	−0.152424	+	0.179448i
$358$	−6247.97	−	1375.28i	−0.922390	−	0.203033i
$359$	−304.550	−	231.513i	−0.0447731	−	0.0340356i	0.582548	−	0.812796i	$-0.302056\pi$
$359$	−304.550	−	231.513i	−0.0447731	−	0.0340356i	−0.627321	+	0.778760i	$0.715849\pi$
$360$	764.117	−	723.810i	0.111868	−	0.105967i
$361$	1274.49	−	3198.72i	0.185813	−	0.466354i
$362$	7113.39	+	2396.78i	1.03279	+	0.347989i
$363$	−1171.70	−	7147.04i	−0.169417	−	1.03340i
$364$	−1789.51	−	1695.11i	−0.257680	−	0.244088i
$365$	−4544.51	+	2102.51i	−0.651700	+	0.301508i
$366$	235.425	−	178.966i	0.0336226	−	0.0255592i
$367$	1628.03	−	9930.52i	0.231559	−	1.41245i	−0.573476	−	0.819222i	$-0.694405\pi$
$367$	1628.03	−	9930.52i	0.231559	−	1.41245i	0.805035	−	0.593227i	$-0.202146\pi$
$368$	−1145.19	+	2160.05i	−0.162220	+	0.305980i
$369$	−1206.07	+	265.476i	−0.170151	+	0.0374530i
$370$	−1719.87	−	795.696i	−0.241653	−	0.111801i
$371$	1696.59	+	4258.11i	0.237419	+	0.595877i
$372$	−23.2950	−	429.651i	−0.00324675	−	0.0598827i
$373$	−7803.48	−	11509.3i	−1.08324	−	1.59766i	−0.758273	−	0.651937i	$-0.773957\pi$
$373$	−7803.48	−	11509.3i	−1.08324	−	1.59766i	−0.324969	−	0.945725i	$-0.605354\pi$
$374$	2717.41	+	3199.18i	0.375705	+	0.442315i
$375$	1546.67	+	2917.32i	0.212985	+	0.401733i
$376$	4429.71	−	1492.54i	0.607566	−	0.204713i
$377$	−126.343	+	2330.26i	−0.0172599	+	0.318340i
$378$	−723.481	+	435.304i	−0.0984440	+	0.0592318i
$379$	−1802.39	−	6491.61i	−0.244281	−	0.879820i	−0.979408	−	0.201891i	$-0.935291\pi$
$379$	−1802.39	−	6491.61i	−0.244281	−	0.879820i	0.735127	−	0.677929i	$-0.237122\pi$
$380$	300.177	−	1081.14i	0.0405230	−	0.145951i
$381$	5282.96	+	3178.65i	0.710379	+	0.427421i
$382$	3993.69	−	5890.26i	0.534909	−	0.788931i
$383$	−6407.97	+	696.908i	−0.854913	+	0.0929774i	−0.525071	−	0.851059i	$-0.675961\pi$
$383$	−6407.97	+	696.908i	−0.854913	+	0.0929774i	−0.329842	+	0.944036i	$0.606996\pi$
$384$	−1058.81	+	115.153i	−0.140709	+	0.0153031i
$385$	2594.39	−	3826.44i	0.343435	−	0.506528i
$386$	−5178.80	−	3115.98i	−0.682886	−	0.410879i
$387$	116.375	−	419.145i	0.0152860	−	0.0550551i
$388$	809.846	+	2916.80i	0.105963	+	0.381645i
$389$	−6296.30	+	3788.36i	−0.820655	+	0.493772i	−0.862924	−	0.505334i	$-0.831369\pi$
$389$	−6296.30	+	3788.36i	−0.820655	+	0.493772i	0.0422682	+	0.999106i	$0.486542\pi$
$390$	63.8800	−	1178.20i	0.00829408	−	0.152975i
$391$	−4692.31	+	1581.02i	−0.606906	+	0.204491i
$392$	−1144.99	−	2159.69i	−0.147528	−	0.278267i
$393$	1393.33	+	1640.35i	0.178840	+	0.210547i
$394$	3219.82	+	4748.87i	0.411706	+	0.607220i
$395$	−38.6747	−	713.313i	−0.00492642	−	0.0908624i
$396$	−804.913	−	2020.18i	−0.102142	−	0.256358i
$397$	12483.2	+	5775.36i	1.57812	+	0.730118i	0.996520	−	0.0833543i	$-0.0265633\pi$
$397$	12483.2	+	5775.36i	1.57812	+	0.730118i	0.581604	+	0.813472i	$0.302425\pi$
$398$	−5679.08	+	1250.06i	−0.715243	+	0.157437i
$399$	−1275.92	+	2406.63i	−0.160090	+	0.301961i
$400$	−275.888	+	1682.84i	−0.0344860	+	0.210355i
$401$	1386.53	−	1054.01i	0.172668	−	0.131259i	−0.515271	−	0.857027i	$-0.672309\pi$
$401$	1386.53	−	1054.01i	0.172668	−	0.131259i	0.687939	+	0.725768i	$0.258516\pi$
$402$	1607.56	−	743.737i	0.199447	−	0.0922741i
$403$	−1059.78	−	1003.87i	−0.130996	−	0.124086i
$404$	237.596	+	1449.27i	0.0292595	+	0.178475i
$405$	373.244	+	125.760i	0.0457941	+	0.0154298i
$406$	672.208	−	1687.11i	0.0821702	−	0.206232i
$407$	−8602.08	+	8148.32i	−1.04764	+	0.992377i
$408$	1957.25	+	1487.87i	0.237496	+	0.180540i
$409$	15307.9	+	3369.53i	1.85068	+	0.407366i	0.994084	−	0.108617i	$-0.0346421\pi$
$409$	15307.9	+	3369.53i	1.85068	+	0.407366i	0.856599	+	0.515983i	$0.172573\pi$
$410$	−869.452	+	1023.60i	−0.104730	+	0.123297i
$411$	6735.10	+	732.486i	0.808316	+	0.0879097i
$412$	−3769.58			−0.450762
$413$	−6304.92	−	3133.49i	−0.751199	−	0.373339i
$414$	−2632.47			−0.312509
$415$	2316.70	+	251.957i	0.274030	+	0.0298026i
$416$	−4124.33	+	4855.53i	−0.486086	+	0.572265i
$417$	−3456.47	−	760.826i	−0.405909	−	0.0893472i
$418$	5731.38	+	4356.89i	0.670649	+	0.509814i
$419$	809.868	−	767.148i	0.0944263	−	0.0894454i	−0.639031	−	0.769181i	$-0.720664\pi$
$419$	809.868	−	767.148i	0.0944263	−	0.0894454i	0.733457	+	0.679736i	$0.237906\pi$
$420$	331.197	−	831.241i	0.0384780	−	0.0965724i
$421$	13097.1	+	4412.91i	1.51618	+	0.510860i	0.949685	−	0.313206i	$-0.101403\pi$
$421$	13097.1	+	4412.91i	1.51618	+	0.510860i	0.566494	+	0.824066i	$0.308299\pi$
$422$	−1439.36	−	8779.70i	−0.166035	−	1.01277i
$423$	1269.92	+	1202.93i	0.145971	+	0.138271i
$424$	6439.99	−	2979.46i	0.737626	−	0.341262i
$425$	−2749.49	+	2090.10i	−0.313811	+	0.238553i
$426$	−137.082	+	836.162i	−0.0155907	+	0.0950990i
$427$	356.376	−	672.196i	0.0403893	−	0.0761823i
$428$	5514.36	−	1213.80i	0.622772	−	0.137083i
$429$	−6695.69	−	3097.76i	−0.753545	−	0.348627i
$430$	−175.101	−	439.471i	−0.0196375	−	0.0492864i
$431$	−272.226	−	5020.90i	−0.0304238	−	0.561133i	−0.973518	−	0.228609i	$-0.926582\pi$
$431$	−272.226	−	5020.90i	−0.0304238	−	0.561133i	0.943095	−	0.332525i	$-0.107900\pi$
$432$	254.931	+	375.995i	0.0283921	+	0.0418752i
$433$	208.135	+	245.036i	0.0231001	+	0.0271956i	0.773591	−	0.633685i	$-0.218459\pi$
$433$	208.135	+	245.036i	0.0231001	+	0.0271956i	−0.750491	+	0.660881i	$0.770183\pi$
$434$	532.113	+	1003.67i	0.0588531	+	0.111009i
$435$	−802.811	+	270.499i	−0.0884870	+	0.0298147i
$436$	−122.452	+	2258.49i	−0.0134504	+	0.248079i
$437$	−7276.96	+	4378.40i	−0.796577	+	0.479285i
$438$	−1663.63	−	5991.86i	−0.181487	−	0.653658i
$439$	−227.059	+	817.793i	−0.0246855	+	0.0889091i	−0.974867	−	0.222789i	$-0.928484\pi$
$439$	−227.059	+	817.793i	−0.0246855	+	0.0889091i	0.950181	+	0.311698i	$0.100898\pi$
$440$	−6132.34	−	3689.71i	−0.664427	−	0.399772i
$441$	513.338	−	757.117i	0.0554301	−	0.0817532i
$442$	2740.06	−	297.999i	0.294867	−	0.0320688i
$443$	14067.5	−	1529.94i	1.50873	−	0.164084i	0.683947	−	0.729532i	$-0.260262\pi$
$443$	14067.5	−	1529.94i	1.50873	−	0.164084i	0.824785	+	0.565447i	$0.191296\pi$
$444$	−1286.98	+	1898.15i	−0.137562	+	0.202888i
$445$	−1307.87	−	786.921i	−0.139324	−	0.0838284i
$446$	−876.356	+	3156.35i	−0.0930418	+	0.335106i
$447$	974.011	+	3508.07i	0.103063	+	0.371199i
$448$	6039.90	−	3634.09i	0.636961	−	0.383246i
$449$	−862.670	+	15911.0i	−0.0906724	+	1.67235i	0.500444	+	0.865769i	$0.333170\pi$
$449$	−862.670	+	15911.0i	−0.0906724	+	1.67235i	−0.591117	+	0.806586i	$0.701313\pi$
$450$	−1740.05	+	586.292i	−0.182282	+	0.0614179i
$451$	3933.36	+	7419.11i	0.410676	+	0.774616i
$452$	5352.12	+	6301.01i	0.556953	+	0.655696i
$453$	−4974.42	−	7336.71i	−0.515935	−	0.760947i
$454$	286.213	+	5278.89i	0.0295873	+	0.545706i
$455$	−1123.60	−	2820.04i	−0.115770	−	0.290561i
$456$	3827.11	+	1770.61i	0.393028	+	0.181834i
$457$	1380.94	−	303.969i	0.141352	−	0.0311139i	−0.143731	−	0.989617i	$-0.545910\pi$
$457$	1380.94	−	303.969i	0.141352	−	0.0311139i	0.285083	+	0.958503i	$0.407979\pi$
$458$	−1427.20	+	2691.99i	−0.145609	+	0.274647i
$459$	−148.844	+	907.907i	−0.0151360	+	0.0923257i
$460$	2220.91	−	1688.29i	0.225109	−	0.171124i
$461$	13812.2	−	6390.18i	1.39544	−	0.645598i	0.429189	−	0.903215i	$-0.358799\pi$
$461$	13812.2	−	6390.18i	1.39544	−	0.645598i	0.966247	+	0.257617i	$0.0829373\pi$
$462$	4168.16	+	3948.29i	0.419741	+	0.397600i
$463$	−2471.16	−	15073.4i	−0.248044	−	1.51300i	−0.757688	−	0.652616i	$-0.773671\pi$
$463$	−2471.16	−	15073.4i	−0.248044	−	1.51300i	0.509644	−	0.860385i	$-0.329777\pi$
$464$	−925.946	−	311.988i	−0.0926422	−	0.0312148i
$465$	196.141	−	492.276i	0.0195609	−	0.0490941i
$466$	5232.24	−	4956.24i	0.520126	−	0.492689i
$467$	459.480	+	349.288i	0.0455293	+	0.0346105i	0.627691	−	0.778462i	$-0.284000\pi$
$467$	459.480	+	349.288i	0.0455293	+	0.0346105i	−0.582162	+	0.813073i	$0.697793\pi$
$468$	−1394.55	−	306.963i	−0.137741	−	0.0303191i
$469$	2950.14	−	3473.17i	0.290458	−	0.341953i
$470$	1891.15	+	205.674i	0.185600	+	0.0201852i
$471$	−9039.63			−0.884340
$472$	−4315.32	+	10008.8i	−0.420823	+	0.976039i
$473$	−2957.89			−0.287535
$474$	881.956	+	95.9185i	0.0854632	+	0.00929469i
$475$	−3834.91	+	4514.81i	−0.370438	+	0.436113i
$476$	2041.29	+	449.323i	0.196560	+	0.0432661i
$477$	2113.90	+	1606.94i	0.202911	+	0.154249i
$478$	3084.22	−	2921.53i	0.295123	−	0.279556i
$479$	638.747	−	1603.13i	0.0609292	−	0.152921i	−0.895360	−	0.445343i	$-0.853082\pi$
$479$	638.747	−	1603.13i	0.0609292	−	0.152921i	0.956289	+	0.292422i	$0.0944612\pi$
$480$	−2191.60	−	738.437i	−0.208401	−	0.0702185i
$481$	1258.70	+	7677.72i	0.119317	+	0.727804i
$482$	8002.09	+	7579.98i	0.756194	+	0.716305i
$483$	−6146.66	+	2843.75i	−0.579054	+	0.267899i
$484$	−7588.15	+	5768.36i	−0.712636	+	0.541732i
$485$	−603.133	+	3678.95i	−0.0564677	+	0.344438i
$486$	−229.114	+	432.154i	−0.0213844	+	0.0403352i
$487$	−12832.6	+	2824.67i	−1.19405	+	0.262829i	−0.767148	−	0.641471i	$-0.778325\pi$
$487$	−12832.6	+	2824.67i	−1.19405	+	0.262829i	−0.426898	+	0.904300i	$0.640394\pi$
$488$	−1068.95	−	494.547i	−0.0991577	−	0.0458752i
$489$	2177.18	+	5464.31i	0.201341	+	0.505327i
$490$	−53.8568	−	993.330i	−0.00496531	−	0.0915797i
$491$	−8987.49	−	13255.6i	−0.826069	−	1.21836i	−0.973363	−	0.229268i	$-0.926367\pi$
$491$	−8987.49	−	13255.6i	−0.826069	−	1.21836i	0.147295	−	0.989093i	$-0.452943\pi$
$492$	1052.20	+	1238.74i	0.0964161	+	0.113510i
$493$	−926.929	−	1748.37i	−0.0846791	−	0.159722i
$494$	4479.89	−	1509.45i	0.408016	−	0.137476i
$495$	144.992	−	2674.22i	0.0131655	−	0.242823i
$496$	523.702	−	315.101i	0.0474091	−	0.0285251i
$497$	583.195	+	2100.48i	0.0526355	+	0.189576i
$498$	−774.242	+	2788.57i	−0.0696679	+	0.250921i
$499$	−1065.02	−	640.804i	−0.0955452	−	0.0574876i	0.466979	−	0.884268i	$-0.345342\pi$
$499$	−1065.02	−	640.804i	−0.0955452	−	0.0574876i	−0.562525	+	0.826781i	$0.690170\pi$
$500$	2438.74	−	3596.88i	0.218128	−	0.321714i
$501$	−12442.8	+	1353.23i	−1.10958	+	0.120674i
$502$	7386.57	−	803.338i	0.656731	−	0.0714238i
$503$	12431.5	−	18335.1i	1.10197	−	1.62529i	0.393894	−	0.919156i	$-0.371128\pi$
$503$	12431.5	−	18335.1i	1.10197	−	1.62529i	0.708080	−	0.706133i	$-0.249562\pi$
$504$	2881.45	+	1733.71i	0.254663	+	0.153225i
$505$	−483.869	+	1742.74i	−0.0426374	+	0.153566i
$506$	4788.78	+	17247.6i	0.420725	+	1.51532i
$507$	1496.64	−	900.498i	0.131101	−	0.0788807i
$508$	439.304	−	8102.49i	0.0383680	−	0.707657i
$509$	15802.4	−	5324.45i	1.37609	−	0.463658i	0.468479	−	0.883475i	$-0.344802\pi$
$509$	15802.4	−	5324.45i	1.37609	−	0.463658i	0.907609	+	0.419817i	$0.137906\pi$
$510$	468.663	+	883.992i	0.0406917	+	0.0767526i
$511$	−10357.3	−	12193.5i	−0.896630	−	1.05559i
$512$	−3313.56	−	4887.14i	−0.286016	−	0.421842i
$513$	85.4308	+	1575.68i	0.00735256	+	0.135610i
$514$	4657.28	+	11688.9i	0.399658	+	1.00306i
$515$	−4213.34	−	1949.30i	−0.360508	−	0.166789i
$516$	−559.117	+	123.071i	−0.0477010	+	0.0104998i
$517$	5571.34	−	10508.7i	0.473941	−	0.893947i
$518$	979.535	−	5974.90i	0.0830855	−	0.506799i
$519$	−2111.08	+	1604.80i	−0.178547	+	0.135728i
$520$	−4265.03	+	1973.21i	−0.359681	+	0.166406i
$521$	601.545	+	569.814i	0.0505838	+	0.0479156i	0.712574	−	0.701597i	$-0.247529\pi$
$521$	601.545	+	569.814i	0.0505838	+	0.0479156i	−0.661990	+	0.749513i	$0.730288\pi$
$522$	−170.207	−	1038.22i	−0.0142716	−	0.0870527i
$523$	18331.5	+	6176.60i	1.53266	+	0.516413i	0.954167	−	0.299276i	$-0.0967450\pi$
$523$	18331.5	+	6176.60i	1.53266	+	0.516413i	0.578492	+	0.815688i	$0.303642\pi$
$524$	1048.43	−	2631.37i	0.0874064	−	0.219374i
$525$	−3429.58	+	3248.67i	−0.285103	+	0.270064i
$526$	5474.69	+	4161.75i	0.453817	+	0.344983i
$527$	1208.89	+	266.097i	0.0999243	+	0.0219950i
$528$	1999.73	−	2354.26i	0.164824	−	0.194046i
$529$	−8896.01	−	967.500i	−0.731159	−	0.0795183i
$530$	2887.72			0.236669
$531$	−4065.51	+	327.641i	−0.332256	+	0.0267767i
$532$	3584.96			0.292157
$533$	5481.60	+	596.160i	0.445468	+	0.0484476i
$534$	1227.17	−	1444.73i	0.0994470	−	0.117078i
$535$	6791.18	+	1494.85i	0.548800	+	0.120800i
$536$	−5616.07	−	4269.22i	−0.452569	−	0.344034i
$537$	−6922.27	+	6557.12i	−0.556272	+	0.526929i
$538$	1502.82	−	3771.80i	0.120430	−	0.302256i
$539$	−5894.37	−	1986.04i	−0.471036	−	0.158710i
$540$	−83.8610	−	511.529i	−0.00668296	−	0.0407643i
$541$	6255.42	+	5925.45i	0.497119	+	0.470896i	0.894698	−	0.446672i	$-0.147391\pi$
$541$	6255.42	+	5925.45i	0.497119	+	0.470896i	−0.397579	+	0.917568i	$0.630149\pi$
$542$	−5825.97	+	2695.38i	−0.461710	+	0.213610i
$543$	8906.20	−	6770.31i	0.703870	−	0.535068i
$544$	873.977	−	5331.03i	0.0688814	−	0.420158i
$545$	−1304.76	+	2461.04i	−0.102550	+	0.193430i
$546$	3681.79	−	810.422i	0.288582	−	0.0635218i
$547$	−18476.8	−	8548.30i	−1.44426	−	0.668188i	−0.467794	−	0.883838i	$-0.654951\pi$
$547$	−18476.8	−	8548.30i	−1.44426	−	0.668188i	−0.976471	+	0.215650i	$0.930813\pi$
$548$	−3300.26	−	8283.02i	−0.257263	−	0.645681i
$549$	−23.8616	−	440.102i	−0.00185499	−	0.0342133i
$550$	7006.69	+	10334.1i	0.543211	+	0.801176i
$551$	−2197.30	−	2586.86i	−0.169888	−	0.200007i
$552$	4911.02	+	9263.16i	0.378672	+	0.714251i
$553$	2162.94	−	728.778i	0.166324	−	0.0560412i
$554$	−792.576	+	14618.2i	−0.0607822	+	1.12106i
$555$	−2420.04	+	1456.09i	−0.185090	+	0.111365i
$556$	1246.13	+	4488.15i	0.0950497	+	0.342338i
$557$	2412.16	−	8687.83i	0.183495	−	0.660889i	−0.813369	−	0.581749i	$-0.802369\pi$
$557$	2412.16	−	8687.83i	0.183495	−	0.660889i	0.996863	−	0.0791404i	$-0.0252175\pi$
$558$	563.891	+	339.282i	0.0427803	+	0.0257400i
$559$	−1089.96	+	1607.58i	−0.0824696	+	0.121634i
$560$	1263.55	−	137.419i	0.0953475	−	0.0103697i
$561$	6219.27	−	676.387i	0.468053	−	0.0509039i
$562$	500.845	−	738.692i	0.0375923	−	0.0554445i
$563$	11492.0	+	6914.53i	0.860269	+	0.517607i	0.876023	−	0.482269i	$-0.160187\pi$
$563$	11492.0	+	6914.53i	0.860269	+	0.517607i	−0.0157542	+	0.999876i	$0.505015\pi$
$564$	615.884	−	2218.22i	0.0459812	−	0.165609i
$565$	2723.85	+	9810.41i	0.202820	+	0.730490i
$566$	6627.77	−	3987.80i	0.492201	−	0.296148i
$567$	−68.1286	+	1256.56i	−0.00504609	+	0.0930697i
$568$	3198.03	−	1077.54i	0.236244	−	0.0795998i
$569$	9478.79	+	17878.9i	0.698368	+	1.31726i	0.938080	+	0.346418i	$0.112602\pi$
$569$	9478.79	+	17878.9i	0.698368	+	1.31726i	−0.239712	+	0.970844i	$0.577053\pi$
$570$	1110.97	+	1307.94i	0.0816379	+	0.0961115i
$571$	−1590.43	−	2345.71i	−0.116563	−	0.171918i	0.764932	−	0.644111i	$-0.222773\pi$
$571$	−1590.43	−	2345.71i	−0.116563	−	0.171918i	−0.881495	+	0.472194i	$0.843462\pi$
$572$	525.664	+	9695.31i	0.0384251	+	0.708708i
$573$	−3925.84	−	9853.11i	−0.286220	−	0.718359i
$574$	−3894.41	−	1801.75i	−0.283188	−	0.131017i
$575$	−14383.9	+	3166.14i	−1.04322	+	0.229630i
$576$	1912.73	−	3607.79i	0.138363	−	0.260980i
$577$	−1893.78	+	11551.5i	−0.136636	+	0.833444i	0.826204	+	0.563371i	$0.190496\pi$
$577$	−1893.78	+	11551.5i	−0.136636	+	0.833444i	−0.962840	+	0.270072i	$0.912952\pi$
$578$	6012.20	−	4570.36i	0.432655	−	0.328896i
$579$	−8175.32	+	3782.31i	−0.586796	+	0.271481i
$580$	809.440	+	766.742i	0.0579485	+	0.0548918i
$581$	1204.57	+	7347.54i	0.0860136	+	0.524660i
$582$	−4387.48	−	1478.31i	−0.312486	−	0.105289i
$583$	6683.07	−	16773.2i	0.474759	−	1.19155i
$584$	−17980.6	+	17032.2i	−1.27405	+	1.20684i
$585$	−1399.98	−	1064.24i	−0.0989435	−	0.0752149i
$586$	−6183.59	−	1361.11i	−0.435907	−	0.0959504i
$587$	6454.03	−	7598.27i	0.453810	−	0.534266i	−0.486910	−	0.873452i	$-0.661876\pi$
$587$	6454.03	−	7598.27i	0.453810	−	0.534266i	0.940719	+	0.339186i	$0.110152\pi$
$588$	−1196.82	−	130.162i	−0.0839388	−	0.00912890i
$589$	2123.08			0.148523
$590$	−3304.13	+	2959.32i	−0.230558	+	0.206497i
$591$	8551.16			0.595174
$592$	−3238.42	−	352.199i	−0.224828	−	0.0244515i
$593$	1381.61	−	1626.56i	0.0956763	−	0.112639i	−0.712240	−	0.701936i	$-0.752319\pi$
$593$	1381.61	−	1626.56i	0.0956763	−	0.112639i	0.807917	+	0.589297i	$0.200595\pi$
$594$	3248.21	+	714.985i	0.224370	+	0.0493875i
$595$	2049.25	+	1557.80i	0.141195	+	0.107333i
$596$	3478.68	−	3295.18i	0.239081	−	0.226470i
$597$	−3207.88	+	8051.16i	−0.219916	+	0.551946i
$598$	11138.5	+	3752.99i	0.761683	+	0.256641i
$599$	−1279.29	−	7803.31i	−0.0872625	−	0.532278i	−0.993893	−	0.110352i	$-0.964802\pi$
$599$	−1279.29	−	7803.31i	−0.0872625	−	0.532278i	0.906630	−	0.421926i	$-0.138646\pi$
$600$	5309.22	+	5029.16i	0.361247	+	0.342191i
$601$	−17241.5	+	7976.75i	−1.17021	+	0.541395i	−0.906085	−	0.423095i	$-0.860944\pi$
$601$	−17241.5	+	7976.75i	−1.17021	+	0.541395i	−0.264121	+	0.964490i	$0.585082\pi$
$602$	1203.28	−	914.709i	0.0814651	−	0.0619281i
$603$	427.087	−	2605.11i	0.0288430	−	0.175934i
$604$	−5464.44	+	10307.0i	−0.368121	+	0.694349i
$605$	−11464.3	+	2523.49i	−0.770398	+	0.169577i
$606$	−2038.56	−	943.140i	−0.136652	−	0.0632218i
$607$	−8907.47	−	22356.1i	−0.595623	−	1.49490i	−0.849460	−	0.527653i	$-0.823072\pi$
$607$	−8907.47	−	22356.1i	−0.595623	−	1.49490i	0.253837	−	0.967247i	$-0.418307\pi$
$608$	−501.630	−	9252.03i	−0.0334602	−	0.617137i
$609$	−1518.97	−	2240.31i	−0.101070	−	0.149067i
$610$	−310.305	−	365.320i	−0.0205966	−	0.0242481i
$611$	−3658.32	−	6900.32i	−0.242226	−	0.456886i
$612$	1147.46	−	386.624i	0.0757896	−	0.0255365i
$613$	1343.69	−	24782.8i	0.0885333	−	1.63290i	−0.530605	−	0.847619i	$-0.678035\pi$
$613$	1343.69	−	24782.8i	0.0885333	−	1.63290i	0.619138	−	0.785282i	$-0.287482\pi$
$614$	−8283.91	+	4984.26i	−0.544481	+	0.327603i
$615$	535.493	+	1928.67i	0.0351108	+	0.126458i
$616$	6117.37	−	22032.8i	0.400123	−	1.44111i
$617$	−10097.3	−	6075.34i	−0.658835	−	0.396408i	0.146514	−	0.989209i	$-0.453195\pi$
$617$	−10097.3	−	6075.34i	−0.658835	−	0.396408i	−0.805349	+	0.592800i	$0.798022\pi$
$618$	3235.44	−	4771.92i	0.210597	−	0.310607i
$619$	−6955.51	+	756.457i	−0.451640	+	0.0491188i	−0.331113	−	0.943591i	$-0.607424\pi$
$619$	−6955.51	+	756.457i	−0.451640	+	0.0491188i	−0.120527	+	0.992710i	$0.538459\pi$
$620$	−693.325	+	75.4036i	−0.0449106	+	0.00488433i
$621$	−2201.77	+	3247.37i	−0.142277	+	0.209843i
$622$	−10913.5	−	6566.45i	−0.703524	−	0.423297i
$623$	1304.68	−	4699.03i	0.0839019	−	0.302187i
$624$	−542.624	−	1954.36i	−0.0348115	−	0.125380i
$625$	−6270.16	+	3772.63i	−0.401290	+	0.241448i
$626$	−209.317	+	3860.62i	−0.0133642	+	0.246488i
$627$	10168.3	−	3426.09i	0.647657	−	0.218221i
$628$	5572.65	+	10511.1i	0.354097	+	0.667898i
$629$	−4271.06	−	5028.28i	−0.270744	−	0.318745i
$630$	768.003	+	1132.72i	0.0485682	+	0.0716328i
$631$	894.168	+	16492.0i	0.0564125	+	1.04047i	0.880513	+	0.474023i	$0.157199\pi$
$631$	894.168	+	16492.0i	0.0564125	+	1.04047i	−0.824100	+	0.566444i	$0.808319\pi$
$632$	−1307.82	−	3282.38i	−0.0823138	−	0.206592i
$633$	−12034.4	−	5567.69i	−0.755644	−	0.349598i
$634$	7088.91	−	1560.39i	0.444064	−	0.0977458i
$635$	4680.91	−	8829.14i	0.292530	−	0.551770i
$636$	565.375	−	3448.64i	0.0352493	−	0.215011i
$637$	−3251.42	+	2471.67i	−0.202239	+	0.153738i
$638$	−6492.65	+	3003.82i	−0.402894	+	0.186399i
$639$	916.822	+	868.460i	0.0567589	+	0.0537649i
$640$	279.280	+	1703.53i	0.0172492	+	0.105216i
$641$	−3790.16	−	1277.06i	−0.233545	−	0.0786905i	0.200096	−	0.979776i	$-0.435875\pi$
$641$	−3790.16	−	1277.06i	−0.233545	−	0.0786905i	−0.433641	+	0.901086i	$0.642771\pi$
$642$	−3196.44	+	8022.45i	−0.196500	+	0.493179i
$643$	−2737.50	+	2593.09i	−0.167895	+	0.159038i	−0.767034	−	0.641607i	$-0.778268\pi$
$643$	−2737.50	+	2593.09i	−0.167895	+	0.159038i	0.599139	+	0.800645i	$0.295510\pi$
$644$	7095.89	+	5394.16i	0.434188	+	0.330061i
$645$	−688.577	−	151.567i	−0.0420352	−	0.00925265i
$646$	−2595.14	+	3055.24i	−0.158057	+	0.186079i
$647$	−2653.49	−	288.584i	−0.161235	−	0.0175354i	0.0271452	−	0.999632i	$-0.491358\pi$
$647$	−2653.49	−	288.584i	−0.161235	−	0.0175354i	−0.188381	+	0.982096i	$0.560324\pi$
$648$	1948.10			0.118099
$649$	9542.32	+	26040.7i	0.577148	+	1.57502i
$650$	8198.36			0.494717
$651$	1683.17	+	183.055i	0.101334	+	0.0110208i
$652$	5011.65	−	5900.17i	0.301030	−	0.354400i
$653$	13328.7	+	2933.87i	0.798764	+	0.175821i	0.595555	−	0.803314i	$-0.296932\pi$
$653$	13328.7	+	2933.87i	0.798764	+	0.175821i	0.203208	+	0.979136i	$0.434863\pi$
$654$	−2753.93	−	2093.49i	−0.164660	−	0.125171i
$655$	2532.56	−	2398.97i	0.151077	−	0.143108i
$656$	−854.515	+	2144.67i	−0.0508586	+	0.127645i
$657$	−8782.90	−	2959.30i	−0.521543	−	0.175728i
$658$	983.299	+	5997.86i	0.0582568	+	0.355351i
$659$	16729.9	+	15847.4i	0.988927	+	0.936761i	0.998001	−	0.0631973i	$-0.0201298\pi$
$659$	16729.9	+	15847.4i	0.988927	+	0.936761i	−0.00907398	+	0.999959i	$0.502888\pi$
$660$	−3198.93	+	1479.98i	−0.188664	+	0.0872852i
$661$	−23628.4	+	17961.9i	−1.39038	+	1.05694i	−0.400305	+	0.916382i	$0.631096\pi$
$661$	−23628.4	+	17961.9i	−1.39038	+	1.05694i	−0.990073	+	0.140556i	$0.955111\pi$
$662$	210.876	−	1286.29i	0.0123806	−	0.0755182i
$663$	1924.15	−	3629.34i	0.112712	−	0.212597i
$664$	11256.9	−	2477.82i	0.657907	−	0.144816i
$665$	4006.98	+	1853.83i	0.233660	+	0.108103i
$666$	−1298.26	−	3258.38i	−0.0755353	−	0.189579i
$667$	−456.872	−	8426.51i	−0.0265220	−	0.489169i
$668$	9244.09	+	13634.0i	0.535426	+	0.789694i
$669$	3160.64	+	3721.00i	0.182657	+	0.215040i
$670$	−1344.76	−	2536.49i	−0.0775414	−	0.146259i
$671$	−2840.09	+	956.938i	−0.163399	+	0.0550554i
$672$	400.036	−	7378.23i	0.0229639	−	0.423544i
$673$	−6110.28	+	3676.43i	−0.349976	+	0.210574i	−0.679677	−	0.733512i	$-0.737880\pi$
$673$	−6110.28	+	3676.43i	−0.349976	+	0.210574i	0.329700	+	0.944086i	$0.393052\pi$
$674$	2285.93	+	8233.16i	0.130639	+	0.470519i
$675$	−732.123	+	2636.87i	−0.0417473	+	0.150360i
$676$	−1969.72	−	1185.14i	−0.112069	−	0.0674294i
$677$	6878.66	−	10145.3i	0.390500	−	0.575944i	−0.580728	−	0.814098i	$-0.697232\pi$
$677$	6878.66	−	10145.3i	0.390500	−	0.575944i	0.971227	+	0.238154i	$0.0765423\pi$
$678$	−12570.2	+	1367.09i	−0.712030	+	0.0774379i
$679$	−11841.5	+	1287.84i	−0.669271	+	0.0727876i
$680$	2236.29	−	3298.28i	0.126114	−	0.186005i
$681$	6751.34	+	4062.15i	0.379900	+	0.228578i
$682$	1197.15	−	4311.74i	0.0672159	−	0.242090i
$683$	−6152.55	−	22159.5i	−0.344686	−	1.24145i	−0.909317	−	0.416104i	$-0.863395\pi$
$683$	−6152.55	−	22159.5i	−0.344686	−	1.24145i	0.564631	−	0.825344i	$-0.309019\pi$
$684$	1779.51	−	1070.69i	0.0994755	−	0.0598524i
$685$	594.489	−	10964.7i	0.0331595	−	0.611591i
$686$	13176.8	−	4439.78i	0.733371	−	0.247102i
$687$	2127.10	+	4012.13i	0.118128	+	0.222813i
$688$	−526.457	−	619.793i	−0.0291729	−	0.0343450i
$689$	−6653.37	−	9812.99i	−0.367886	−	0.542591i
$690$	230.998	+	4260.51i	0.0127449	+	0.235065i
$691$	1392.17	+	3494.08i	0.0766435	+	0.192361i	0.962306	−	0.271969i	$-0.0876747\pi$
$691$	1392.17	+	3494.08i	0.0766435	+	0.192361i	−0.885663	+	0.464329i	$0.846295\pi$
$692$	3167.45	+	1465.42i	0.174000	+	0.0805012i
$693$	8356.76	−	1839.46i	0.458077	−	0.100830i
$694$	−366.502	+	691.297i	−0.0200465	+	0.0378116i
$695$	−928.054	+	5660.88i	−0.0506520	+	0.308963i
$696$	−3335.76	+	2535.78i	−0.181669	+	0.138101i
$697$	−4243.50	+	1963.25i	−0.230608	+	0.106691i
$698$	380.910	+	360.817i	0.0206557	+	0.0195661i
$699$	−1737.74	−	10599.8i	−0.0940306	−	0.573561i
$700$	5891.73	+	1985.16i	0.318124	+	0.107188i
$701$	9848.63	−	24718.2i	0.530638	−	1.33180i	−0.382426	−	0.923986i	$-0.624911\pi$
$701$	9848.63	−	24718.2i	0.530638	−	1.33180i	0.913064	−	0.407816i	$-0.133709\pi$
$702$	1585.53	−	1501.89i	0.0852449	−	0.0807483i
$703$	−9008.24	−	6847.89i	−0.483289	−	0.367387i
$704$	−27117.3	−	5968.97i	−1.45174	−	0.319551i
$705$	1835.45	−	2160.86i	0.0980527	−	0.115437i
$706$	−19816.9	−	2155.22i	−1.05640	−	0.114891i
$707$	−5778.77			−0.307402
$708$	2887.24	+	4525.33i	0.153261	+	0.240215i
$709$	7795.73			0.412941			0.206470	−	0.978453i	$-0.433802\pi$
$709$	7795.73			0.412941			0.206470	+	0.978453i	$0.433802\pi$
$710$	1365.32	+	148.487i	0.0721681	+	0.00784876i
$711$	855.983	−	1007.74i	0.0451503	−	0.0531551i
$712$	−7373.10	−	1622.94i	−0.388088	−	0.0854246i
$713$	4202.31	+	3194.52i	0.220726	+	0.167792i
$714$	−2320.85	+	2198.43i	−0.121647	+	0.115230i
$715$	−4426.02	+	11108.5i	−0.231502	+	0.581025i
$716$	11891.9	+	4006.84i	0.620699	+	0.209138i
$717$	−1024.34	−	6248.18i	−0.0533537	−	0.325443i
$718$	−559.047	−	529.557i	−0.0290577	−	0.0275249i
$719$	−29825.6	+	13798.8i	−1.54702	+	0.715729i	−0.993147	−	0.116871i	$-0.962713\pi$
$719$	−29825.6	+	13798.8i	−1.54702	+	0.715729i	−0.553875	+	0.832600i	$0.686851\pi$
$720$	586.160	−	445.587i	0.0303401	−	0.0230640i
$721$	2399.66	−	14637.3i	0.123950	−	0.756063i
$722$	3246.51	−	6123.56i	0.167344	−	0.315645i
$723$	16043.4	−	3531.42i	0.825258	−	0.181653i
$724$	−13362.8	−	6182.29i	−0.685946	−	0.317352i
$725$	−2178.71	−	5468.15i	−0.111607	−	0.280113i
$726$	−789.251	−	14556.9i	−0.0403469	−	0.744154i
$727$	−1624.88	−	2396.53i	−0.0828936	−	0.122259i	0.783982	−	0.620784i	$-0.213186\pi$
$727$	−1624.88	−	2396.53i	−0.0828936	−	0.122259i	−0.866875	+	0.498525i	$0.833875\pi$
$728$	−9720.31	−	11443.6i	−0.494861	−	0.582595i
$729$	341.470	+	644.080i	0.0173485	+	0.0327227i
$730$	−9551.54	+	3218.29i	−0.484272	+	0.163170i
$731$	89.1649	−	1644.55i	0.00451147	−	0.0832092i
$732$	−497.033	+	299.055i	−0.0250968	+	0.0151003i
$733$	1214.85	+	4375.48i	0.0612160	+	0.220480i	0.987831	−	0.155532i	$-0.0497090\pi$
$733$	1214.85	+	4375.48i	0.0612160	+	0.220480i	−0.926615	+	0.376012i	$0.877295\pi$
$734$	5419.02	−	19517.5i	0.272506	−	0.981479i
$735$	−1270.40	−	764.375i	−0.0637544	−	0.0383597i
$736$	12928.3	−	19067.8i	0.647477	−	0.954957i
$737$	−17845.3	+	1940.80i	−0.891915	+	0.0970016i
$738$	−2471.23	+	268.763i	−0.123262	+	0.0134055i
$739$	−18282.5	+	26964.6i	−0.910056	+	1.34223i	0.0294019	+	0.999568i	$0.490640\pi$
$739$	−18282.5	+	26964.6i	−0.910056	+	1.34223i	−0.939458	+	0.342664i	$0.888671\pi$
$740$	3185.00	+	1916.35i	0.158220	+	0.0951979i
$741$	1884.90	−	6788.81i	0.0934462	−	0.336563i
$742$	2468.32	+	8890.10i	0.122123	+	0.439846i
$743$	−13850.6	+	8333.63i	−0.683889	+	0.411482i	−0.814667	−	0.579929i	$-0.803080\pi$
$743$	−13850.6	+	8333.63i	−0.683889	+	0.411482i	0.130778	+	0.991412i	$0.458253\pi$
$744$	141.899	−	2617.18i	0.00699231	−	0.128966i
$745$	5592.17	−	1884.22i	0.275008	−	0.0926611i
$746$	−13110.7	−	24729.4i	−0.643454	−	1.21368i
$747$	2792.36	+	3287.42i	0.136770	+	0.161018i
$748$	−4620.48	−	6814.70i	−0.225858	−	0.333115i
$749$	1202.83	+	22185.0i	0.0586790	+	1.08227i
$750$	2460.12	+	6174.42i	0.119774	+	0.300611i
$751$	201.689	+	93.3110i	0.00979989	+	0.00453391i	0.424783	−	0.905295i	$-0.360350\pi$
$751$	201.689	+	93.3110i	0.00979989	+	0.00453391i	−0.414983	+	0.909829i	$0.636212\pi$
$752$	3193.58	−	702.960i	0.154864	−	0.0340882i
$753$	5187.07	−	9783.86i	0.251033	−	0.473498i
$754$	−759.961	+	4635.56i	−0.0367058	+	0.223895i
$755$	−11437.6	+	8694.64i	−0.551334	+	0.419113i
$756$	1503.11	−	695.411i	0.0723114	−	0.0334548i
$757$	−17097.7	−	16195.8i	−0.820907	−	0.777604i	0.156788	−	0.987632i	$-0.449886\pi$
$757$	−17097.7	−	16195.8i	−0.820907	−	0.777604i	−0.977695	+	0.210028i	$0.932645\pi$
$758$	−2193.96	−	13382.6i	−0.105129	−	0.641261i
$759$	25281.7	+	8518.38i	1.20905	+	0.407375i
$760$	2529.81	−	6349.35i	0.120745	−	0.303046i
$761$	−382.728	+	362.539i	−0.0182311	+	0.0172694i	−0.696761	−	0.717304i	$-0.745376\pi$
$761$	−382.728	+	362.539i	−0.0182311	+	0.0172694i	0.678530	+	0.734573i	$0.262617\pi$
$762$	9879.90	+	7510.51i	0.469700	+	0.357056i
$763$	−8691.80	−	1913.21i	−0.412404	−	0.0907770i
$764$	−9036.88	+	10639.0i	−0.427936	+	0.503805i
$765$	1482.46	+	161.228i	0.0700635	+	0.00761987i
$766$	−12974.6			−0.611998
$767$	17669.1	+	4409.70i	0.831804	+	0.207595i
$768$	−13033.1			−0.612357
$769$	−1215.65	−	132.210i	−0.0570056	−	0.00619974i	0.0795717	−	0.996829i	$-0.474645\pi$
$769$	−1215.65	−	132.210i	−0.0570056	−	0.00619974i	−0.136577	+	0.990629i	$0.543610\pi$
$770$	6024.36	−	7092.43i	0.281952	−	0.331939i
$771$	18314.6	+	4031.34i	0.855490	+	0.188307i
$772$	9437.84	+	7174.46i	0.439994	+	0.334475i
$773$	13867.2	−	13135.7i	0.645238	−	0.611202i	−0.293448	−	0.955975i	$-0.594803\pi$
$773$	13867.2	−	13135.7i	0.645238	−	0.611202i	0.938686	+	0.344773i	$0.112044\pi$
$774$	324.096	−	813.420i	0.0150509	−	0.0377749i
$775$	3489.19	+	1175.64i	0.161723	+	0.0544908i
$776$	2983.18	+	18196.6i	0.138003	+	0.841779i
$777$	−6551.27	−	6205.69i	−0.302478	−	0.286522i
$778$	−13423.9	+	6210.57i	−0.618600	+	0.286195i
$779$	−6384.25	+	4853.18i	−0.293632	+	0.223213i
$780$	−374.433	+	2283.94i	−0.0171883	+	0.104844i
$781$	4022.24	−	7586.75i	0.184286	−	0.347599i
$782$	−9733.81	+	2142.57i	−0.445116	+	0.0979774i
$783$	−1423.09	−	658.390i	−0.0649514	−	0.0300497i
$784$	−632.949	−	1588.58i	−0.0288333	−	0.0723661i
$785$	793.226	+	14630.2i	0.0360655	+	0.665190i
$786$	2431.18	+	3585.72i	0.110327	+	0.162721i
$787$	7113.12	+	8374.21i	0.322180	+	0.379299i	0.899279	−	0.437374i	$-0.144092\pi$
$787$	7113.12	+	8374.21i	0.322180	+	0.379299i	−0.577100	+	0.816674i	$0.695816\pi$
$788$	−5271.53	−	9943.15i	−0.238313	−	0.449505i
$789$	9712.84	−	3272.64i	0.438259	−	0.147667i
$790$	77.8478	−	1435.82i	0.00350595	−	0.0646635i
$791$	−27873.9	+	16771.2i	−1.25295	+	0.753875i
$792$	−3543.82	−	12763.7i	−0.158995	−	0.572649i
$793$	−526.471	+	1896.18i	−0.0235757	+	0.0849120i
$794$	23723.1	+	14273.7i	1.06033	+	0.637980i
$795$	2415.26	−	3562.25i	0.107749	−	0.158918i
$796$	11339.3	−	1233.22i	0.504914	−	0.0549127i
$797$	13865.9	−	1508.01i	0.616255	−	0.0670217i	0.205333	−	0.978692i	$-0.434172\pi$
$797$	13865.9	−	1508.01i	0.616255	−	0.0670217i	0.410922	+	0.911670i	$0.365207\pi$
$798$	−3076.98	+	4538.21i	−0.136496	+	0.201317i
$799$	5674.74	+	3414.38i	0.251261	+	0.151179i
$800$	4298.86	−	15483.1i	0.189985	−	0.684263i
$801$	−755.808	−	2722.17i	−0.0333398	−	0.120079i
$802$	3003.95	−	1807.42i	0.132261	−	0.0795787i
$803$	−3411.85	+	62927.9i	−0.149940	+	2.76548i
$804$	−3292.47	+	1109.36i	−0.144424	+	0.0486619i
$805$	5141.84	+	9698.53i	0.225125	+	0.424631i
$806$	−1902.23	−	2239.48i	−0.0831307	−	0.0978691i
$807$	−3395.89	−	5008.56i	−0.148130	−	0.218475i
$808$	484.323	+	8932.81i	0.0210871	+	0.388930i
$809$	−9703.55	−	24354.1i	−0.421704	−	1.05840i	−0.974361	−	0.224989i	$-0.927765\pi$
$809$	−9703.55	−	24354.1i	−0.421704	−	1.05840i	0.552657	−	0.833409i	$-0.313614\pi$
$810$	719.524	+	332.887i	0.0312117	+	0.0144401i
$811$	−38312.3	+	8433.18i	−1.65885	+	0.365141i	−0.942917	−	0.333028i	$-0.891930\pi$
$811$	−38312.3	+	8433.18i	−1.65885	+	0.365141i	−0.715934	+	0.698168i	$0.753999\pi$
$812$	−1668.60	+	3147.31i	−0.0721138	+	0.136021i
$813$	−1547.81	+	9441.21i	−0.0667699	+	0.407279i
$814$	−18986.9	+	14433.4i	−0.817554	+	0.621489i
$815$	8652.67	−	4003.15i	0.371889	−	0.172054i
$816$	1248.66	+	1182.79i	0.0535684	+	0.0507427i
$817$	−457.003	−	2787.59i	−0.0195698	−	0.119370i
$818$	29899.2	+	10074.2i	1.27800	+	0.430608i
$819$	2079.69	−	5219.62i	0.0887303	−	0.222696i
$820$	1912.51	−	1811.63i	0.0814486	−	0.0771522i
$821$	−6852.89	−	5209.43i	−0.291313	−	0.221450i	0.449302	−	0.893380i	$-0.351673\pi$
$821$	−6852.89	−	5209.43i	−0.291313	−	0.221450i	−0.740615	+	0.671930i	$0.765466\pi$
$822$	13318.1	+	2931.54i	0.565113	+	0.124391i
$823$	7269.67	−	8558.51i	0.307904	−	0.362492i	−0.586346	−	0.810061i	$-0.699434\pi$
$823$	7269.67	−	8558.51i	0.307904	−	0.362492i	0.894250	+	0.447569i	$0.147710\pi$
$824$	−22827.4	−	2482.63i	−0.965086	−	0.104959i
$825$	18608.3			0.785282
$826$	−11934.8	−	7642.54i	−0.502741	−	0.321935i
$827$	34484.1			1.44998			0.724989	−	0.688761i	$-0.241845\pi$
$827$	34484.1			1.44998			0.724989	+	0.688761i	$0.241845\pi$
$828$	5133.31	+	558.281i	0.215453	+	0.0234319i
$829$	20096.8	−	23659.8i	0.841968	−	0.991241i	−0.158025	−	0.987435i	$-0.550513\pi$
$829$	20096.8	−	23659.8i	0.841968	−	0.991241i	0.999993	−	0.00380582i	$-0.00121143\pi$
$830$	4581.10	+	1008.38i	0.191581	+	0.0421702i
$831$	17369.9	+	13204.2i	0.725095	+	0.551203i
$832$	−13236.6	+	12538.4i	−0.551558	+	0.522464i
$833$	1281.90	−	3217.33i	0.0533196	−	0.133822i
$834$	−6751.12	−	2274.72i	−0.280302	−	0.0944448i
$835$	3281.99	+	20019.2i	0.136021	+	0.829693i
$836$	−10252.2	−	9711.41i	−0.424139	−	0.401766i
$837$	890.166	−	411.834i	0.0367606	−	0.0170073i
$838$	1787.57	−	1358.88i	0.0736882	−	0.0560163i
$839$	−2317.26	+	14134.6i	−0.0953523	+	0.581623i	0.895327	+	0.445409i	$0.146942\pi$
$839$	−2317.26	+	14134.6i	−0.0953523	+	0.581623i	−0.990679	+	0.136214i	$0.956506\pi$
$840$	2553.08	−	4815.62i	0.104869	−	0.197803i
$841$	−20525.0	+	4517.90i	−0.841568	+	0.185243i
$842$	25248.0	+	11681.0i	1.03338	+	0.478091i
$843$	−492.336	−	1235.67i	−0.0201150	−	0.0504848i
$844$	944.792	+	17425.7i	0.0385321	+	0.710683i
$845$	−1588.74	−	2343.22i	−0.0646797	−	0.0953955i
$846$	2279.43	+	2683.55i	0.0926340	+	0.109057i
$847$	−17568.1	−	33136.9i	−0.712687	−	1.34427i
$848$	4704.12	−	1585.00i	0.190495	−	0.0641854i
$849$	624.122	−	11511.3i	0.0252295	−	0.465330i
$850$	−5956.84	+	3584.11i	−0.240374	+	0.144628i
$851$	−7526.71	−	27108.8i	−0.303187	−	1.09198i
$852$	444.639	−	1601.44i	0.0178792	−	0.0643951i
$853$	35558.5	+	21394.8i	1.42732	+	0.858787i	0.998994	−	0.0448392i	$-0.0142775\pi$
$853$	35558.5	+	21394.8i	1.42732	+	0.858787i	0.428321	+	0.903626i	$0.359105\pi$
$854$	859.430	−	1267.56i	0.0344369	−	0.0507906i
$855$	2542.66	−	276.531i	0.101704	−	0.0110610i
$856$	34192.7	−	3718.68i	1.36528	−	0.148483i
$857$	5017.82	−	7400.73i	0.200006	−	0.294987i	−0.714438	−	0.699699i	$-0.753318\pi$
$857$	5017.82	−	7400.73i	0.200006	−	0.294987i	0.914445	+	0.404711i	$0.132628\pi$
$858$	−12724.5	−	7656.08i	−0.506302	−	0.304632i
$859$	−9243.12	+	33290.7i	−0.367137	+	1.32231i	0.517361	+	0.855767i	$0.326914\pi$
$859$	−9243.12	+	33290.7i	−0.367137	+	1.32231i	−0.884499	+	0.466542i	$0.845500\pi$
$860$	248.247	+	894.103i	0.00984318	+	0.0354519i
$861$	−5479.86	+	3297.12i	−0.216902	+	0.130506i
$862$	547.960	−	10106.5i	0.0216515	−	0.399338i
$863$	39903.3	−	13445.0i	1.57396	−	0.530327i	0.609097	−	0.793096i	$-0.291532\pi$
$863$	39903.3	−	13445.0i	1.57396	−	0.530327i	0.964859	+	0.262769i	$0.0846356\pi$
$864$	−2005.03	−	3781.89i	−0.0789498	−	0.148915i
$865$	2782.53	+	3275.85i	0.109375	+	0.128766i
$866$	363.170	+	535.636i	0.0142506	+	0.0210181i
$867$	−609.369	−	11239.2i	−0.0238700	−	0.440256i
$868$	−824.767	−	2070.01i	−0.0322516	−	0.0809454i
$869$	−8159.75	−	3775.10i	−0.318527	−	0.147367i
$870$	−1665.37	+	366.575i	−0.0648979	+	0.0142851i
$871$	−5521.09	+	10413.9i	−0.214782	+	0.405122i
$872$	−2228.97	+	13596.1i	−0.0865624	+	0.528007i
$873$	−5493.27	+	4175.88i	−0.212966	+	0.161892i
$874$	−15514.7	+	7177.88i	−0.600450	+	0.277798i
$875$	12414.2	+	11759.4i	0.479631	+	0.454331i
$876$	1973.36	+	12036.9i	0.0761113	+	0.464259i
$877$	−12297.9	−	4143.64i	−0.473512	−	0.159545i	0.0724202	−	0.997374i	$-0.476928\pi$
$877$	−12297.9	−	4143.64i	−0.473512	−	0.159545i	−0.545932	+	0.837830i	$0.683824\pi$
$878$	−632.343	+	1587.06i	−0.0243058	+	0.0610031i
$879$	−6850.94	+	6489.55i	−0.262886	+	0.249018i
$880$	−3985.73	−	3029.87i	−0.152681	−	0.116065i
$881$	25845.3	+	5688.98i	0.988365	+	0.217556i	0.679600	−	0.733583i	$-0.262153\pi$
$881$	25845.3	+	5688.98i	0.988365	+	0.217556i	0.308765	+	0.951138i	$0.400084\pi$
$882$	1192.01	−	1403.34i	0.0455068	−	0.0535747i
$883$	−11638.8	−	1265.80i	−0.443577	−	0.0482419i	−0.116394	−	0.993203i	$-0.537134\pi$
$883$	−11638.8	−	1265.80i	−0.443577	−	0.0482419i	−0.327182	+	0.944961i	$0.606099\pi$
$884$	−5406.32			−0.205695
$885$	887.019	+	6551.07i	0.0336913	+	0.248827i
$886$	28483.3			1.08004
$887$	20773.8	+	2259.29i	0.786377	+	0.0855236i	0.492492	−	0.870317i	$-0.336086\pi$
$887$	20773.8	+	2259.29i	0.786377	+	0.0855236i	0.293885	+	0.955841i	$0.405052\pi$
$888$	−9043.67	+	10647.0i	−0.341763	+	0.402355i
$889$	31182.3	+	6863.75i	1.17640	+	0.258946i
$890$	−2445.91	−	1859.33i	−0.0921204	−	0.0700281i
$891$	3598.77	−	3408.93i	0.135312	−	0.128175i
$892$	2378.28	−	5969.03i	0.0892720	−	0.224056i
$893$	10764.4	+	3626.96i	0.403380	+	0.135914i
$894$	1185.62	+	7231.93i	0.0443545	+	0.270550i
$895$	11219.8	+	10628.0i	0.419035	+	0.396931i
$896$	−5005.75	+	2315.91i	−0.186641	+	0.0863494i
$897$	13945.8	−	10601.3i	0.519103	−	0.394612i
$898$	−5189.02	+	31651.6i	−0.192828	+	1.17620i
$899$	−988.175	+	1863.89i	−0.0366601	+	0.0691484i
$900$	3517.44	−	774.247i	0.130276	−	0.0286758i
$901$	9124.25	+	4221.33i	0.337373	+	0.156085i
$902$	6256.37	+	15702.3i	0.230947	+	0.579634i
$903$	−121.959	−	2249.40i	−0.00449450	−	0.0828962i
$904$	28261.0	+	41681.9i	1.03976	+	1.53354i
$905$	−11738.9	−	13820.1i	−0.431177	−	0.507621i
$906$	−8357.55	−	15764.0i	−0.306469	−	0.578062i
$907$	23666.0	−	7974.01i	0.866392	−	0.291921i	0.149208	−	0.988806i	$-0.452327\pi$
$907$	23666.0	−	7974.01i	0.866392	−	0.291921i	0.717184	+	0.696884i	$0.245431\pi$
$908$	561.407	−	10354.5i	0.0205187	−	0.378444i
$909$	−2868.48	+	1725.90i	−0.104666	+	0.0629754i
$910$	−1634.70	−	5887.67i	−0.0595494	−	0.214477i
$911$	5598.22	−	20163.0i	0.203598	−	0.733292i	−0.789268	−	0.614049i	$-0.789540\pi$
$911$	5598.22	−	20163.0i	0.203598	−	0.733292i	0.992865	−	0.119243i	$-0.0380467\pi$
$912$	2527.68	+	1520.86i	0.0917763	+	0.0552199i
$913$	16459.2	−	24275.5i	0.596626	−	0.879957i
$914$	2829.54	−	307.731i	0.102399	−	0.0111366i
$915$	−710.189	+	77.2377i	−0.0256592	+	0.00279060i
$916$	3353.95	−	4946.71i	0.120980	−	0.178432i
$917$	9550.19	+	5746.16i	0.343920	+	0.206930i
$918$	−495.439	+	1784.41i	−0.0178126	+	0.0641550i
$919$	−6913.03	−	24898.5i	−0.248139	−	0.893716i	−0.977736	−	0.209838i	$-0.932706\pi$
$919$	−6913.03	−	24898.5i	−0.248139	−	0.893716i	0.729597	−	0.683877i	$-0.239708\pi$
$920$	14561.0	−	8761.08i	0.521807	−	0.313961i
$921$	−780.078	+	14387.7i	−0.0279093	+	0.514756i
$922$	29030.1	−	9781.36i	1.03693	−	0.349384i
$923$	−2641.13	−	4981.70i	−0.0941862	−	0.177654i
$924$	−7290.58	−	8583.14i	−0.259570	−	0.305589i
$925$	−11012.7	−	16242.5i	−0.391454	−	0.577351i
$926$	−1664.56	−	30701.0i	−0.0590722	−	1.08952i
$927$	−3180.47	−	7982.38i	−0.112687	−	0.282822i
$928$	8356.04	+	3865.92i	0.295582	+	0.136751i
$929$	23244.0	−	5116.40i	0.820896	−	0.180693i	0.215384	−	0.976529i	$-0.430900\pi$
$929$	23244.0	−	5116.40i	0.820896	−	0.180693i	0.605512	+	0.795837i	$0.292969\pi$
$930$	499.629	−	942.401i	0.0176167	−	0.0332286i
$931$	961.003	−	5861.86i	0.0338299	−	0.206353i
$932$	−11254.0	+	8555.04i	−0.395532	+	0.300675i
$933$	−17228.2	+	7970.63i	−0.604530	+	0.279686i
$934$	843.444	+	798.953i	0.0295485	+	0.0279899i
$935$	−1640.44	−	10006.2i	−0.0573776	−	0.349988i
$936$	−8242.78	−	2777.32i	−0.287846	−	0.0969865i
$937$	20117.3	−	50490.7i	0.701392	−	1.76036i	0.0535785	−	0.998564i	$-0.482937\pi$
$937$	20117.3	−	50490.7i	0.701392	−	1.76036i	0.647814	−	0.761799i	$-0.275683\pi$
$938$	6659.36	−	6308.08i	0.231808	−	0.219580i
$939$	4587.33	+	3487.20i	0.159427	+	0.121193i
$940$	−3644.12	−	802.130i	−0.126445	−	0.0278326i
$941$	−12627.1	+	14865.8i	−0.437441	+	0.514996i	−0.936067	−	0.351822i	$-0.885562\pi$
$941$	−12627.1	+	14865.8i	−0.437441	+	0.514996i	0.498626	+	0.866817i	$0.333838\pi$
$942$	−18089.1	−	1967.31i	−0.625663	−	0.0680450i
$943$	−19939.1			−0.688553
$944$	−3758.16	+	6634.31i	−0.129574	+	0.228738i
$945$	2039.66			0.0702116
$946$	−5919.00	−	643.730i	−0.203429	−	0.0221242i
$947$	−21471.2	+	25277.9i	−0.736770	+	0.867392i	−0.995121	−	0.0986586i	$-0.968545\pi$
$947$	−21471.2	+	25277.9i	−0.736770	+	0.867392i	0.258352	+	0.966051i	$0.416821\pi$
$948$	−1699.47	−	374.082i	−0.0582239	−	0.0128161i
$949$	32943.3	+	25042.8i	1.12685	+	0.856611i
$950$	−8656.57	+	8199.93i	−0.295638	+	0.280043i
$951$	4004.23	−	10049.9i	0.136536	−	0.342680i
$952$	12065.5	+	4065.35i	0.410763	+	0.138402i
$953$	−3327.35	−	20295.9i	−0.113099	−	0.689873i	−0.981128	−	0.193360i	$-0.938062\pi$
$953$	−3327.35	−	20295.9i	−0.113099	−	0.689873i	0.868029	−	0.496514i	$-0.165387\pi$
$954$	3880.37	+	3675.69i	0.131689	+	0.124743i
$955$	−15602.3	+	7218.38i	−0.528668	+	0.244588i
$956$	−6633.81	+	5042.89i	−0.224428	+	0.170606i
$957$	−1724.93	+	10521.6i	−0.0582643	+	0.355397i
$958$	1627.08	−	3069.00i	0.0548733	−	0.103502i
$959$	34263.9	−	7542.06i	1.15374	−	0.253958i
$960$	−6006.87	−	2779.07i	−0.201949	−	0.0934314i
$961$	10538.3	+	26449.3i	0.353743	+	0.887827i
$962$	847.853	+	15637.7i	0.0284157	+	0.524097i
$963$	7222.89	+	10653.0i	0.241697	+	0.356477i
$964$	−13996.6	−	16478.0i	−0.467633	−	0.550541i
$965$	6838.86	+	12899.5i	0.228135	+	0.430309i
$966$	−12918.9	+	4352.89i	−0.430289	+	0.144981i
$967$	224.883	−	4147.73i	0.00747855	−	0.137934i	−0.992410	−	0.122977i	$-0.960756\pi$
$967$	224.883	−	4147.73i	0.00747855	−	0.137934i	0.999888	−	0.0149573i	$-0.00476122\pi$
$968$	−49750.6	+	29933.9i	−1.65190	+	0.993918i
$969$	1598.34	+	5756.70i	0.0529888	+	0.190848i
$970$	−2007.58	+	7230.64i	−0.0664530	+	0.239342i
$971$	4627.85	+	2784.48i	0.152950	+	0.0920271i	0.589972	−	0.807424i	$-0.299139\pi$
$971$	4627.85	+	2784.48i	0.152950	+	0.0920271i	−0.437021	+	0.899451i	$0.643967\pi$
$972$	538.421	−	794.111i	0.0177673	−	0.0262049i
$973$	−18220.8	+	1981.63i	−0.600341	+	0.0652910i
$974$	−26293.9	+	2859.63i	−0.865001	+	0.0940745i
$975$	6857.03	−	10113.4i	0.225232	−	0.332192i
$976$	−706.006	−	424.789i	−0.0231544	−	0.0139315i
$977$	−9031.22	+	32527.5i	−0.295736	+	1.06515i	0.655123	+	0.755522i	$0.272617\pi$
$977$	−9031.22	+	32527.5i	−0.295736	+	1.06515i	−0.950859	+	0.309623i	$0.899797\pi$
$978$	3167.53	+	11408.4i	0.103565	+	0.373007i
$979$	−16460.5	+	9903.93i	−0.537363	+	0.323321i
$980$	−105.640	+	1948.42i	−0.00344342	+	0.0635101i
$981$	−4885.86	+	1646.24i	−0.159015	+	0.0535783i
$982$	−15099.9	−	28481.5i	−0.490691	−	0.925541i
$983$	−11654.8	−	13721.0i	−0.378158	−	0.445202i	0.539852	−	0.841760i	$-0.318480\pi$
$983$	−11654.8	−	13721.0i	−0.378158	−	0.445202i	−0.918009	+	0.396558i	$0.870204\pi$
$984$	5555.95	+	8194.42i	0.179997	+	0.265476i
$985$	−750.363	−	13839.6i	−0.0242726	−	0.447682i
$986$	−1474.37	−	3700.38i	−0.0476201	−	0.119517i
$987$	8221.28	+	3803.57i	0.265133	+	0.122664i
$988$	−9055.90	+	1993.35i	−0.291606	+	0.0641873i
$989$	3289.82	−	6205.27i	0.105774	−	0.199511i
$990$	872.138	−	5319.81i	0.0279983	−	0.170782i
$991$	−13581.8	+	10324.6i	−0.435357	+	0.330950i	−0.799790	−	0.600280i	$-0.795056\pi$
$991$	−13581.8	+	10324.6i	−0.435357	+	0.330950i	0.364433	+	0.931230i	$0.381263\pi$
$992$	−5226.85	+	2418.20i	−0.167291	+	0.0773970i
$993$	−1410.37	−	1335.97i	−0.0450723	−	0.0426947i
$994$	709.894	+	4330.16i	0.0226524	+	0.138173i
$995$	13311.9	+	4485.30i	0.424136	+	0.142908i
$996$	2101.16	−	5273.51i	0.0668451	−	0.167769i
$997$	−37448.4	+	35473.0i	−1.18957	+	1.12682i	−0.200452	+	0.979703i	$0.564241\pi$
$997$	−37448.4	+	35473.0i	−1.18957	+	1.12682i	−0.989119	+	0.147118i	$0.953000\pi$
$998$	−1991.75	−	1514.09i	−0.0631741	−	0.0480237i
$999$	−5105.34	−	1123.77i	−0.161687	−	0.0355901i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.4.e.b.4.10	✓	420
59.15	even	29	inner	177.4.e.b.133.10	yes	420

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.4.e.b.4.10	✓	420	1.1	even	1	trivial
177.4.e.b.133.10	yes	420	59.15	even	29	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	177.e (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(2.00109 + 0.217632i) q^{2} +(1.94216 - 2.28649i) q^{3} +(-3.85597 - 0.848763i) q^{4} +(-3.87099 - 2.94265i) q^{5} +(4.38404 - 4.15279i) q^{6} +(5.75041 - 14.4324i) q^{7} +(-22.7916 - 7.67938i) q^{8} +(-1.45604 - 8.88144i) q^{9} +O(q^{10})\)	\(q+(2.00109 + 0.217632i) q^{2} +(1.94216 - 2.28649i) q^{3} +(-3.85597 - 0.848763i) q^{4} +(-3.87099 - 2.94265i) q^{5} +(4.38404 - 4.15279i) q^{6} +(5.75041 - 14.4324i) q^{7} +(-22.7916 - 7.67938i) q^{8} +(-1.45604 - 8.88144i) q^{9} +(-7.10578 - 6.73095i) q^{10} +(-55.5415 + 25.6962i) q^{11} +(-9.42959 + 7.16819i) q^{12} +(-6.50110 + 39.6549i) q^{13} +(14.6480 - 27.6291i) q^{14} +(-14.2464 + 3.13587i) q^{15} +(-15.2698 - 7.06458i) q^{16} +(-12.6125 - 31.6550i) q^{17} +(-0.980780 - 18.0894i) q^{18} +(-32.7981 - 48.3736i) q^{19} +(12.4288 + 14.6323i) q^{20} +(-21.8314 - 41.1783i) q^{21} +(-116.736 + 39.3329i) q^{22} +(7.86701 - 145.099i) q^{23} +(-61.8237 + 37.1981i) q^{24} +(-27.1157 - 97.6618i) q^{25} +(-21.6394 + 77.9382i) q^{26} +(-23.1351 - 13.9200i) q^{27} +(-34.4231 + 50.7703i) q^{28} +(57.7340 - 6.27895i) q^{29} +(-29.1908 + 3.17469i) q^{30} +(-20.3860 + 30.0671i) q^{31} +(135.844 + 81.7348i) q^{32} +(-49.1163 + 176.901i) q^{33} +(-18.3496 - 66.0893i) q^{34} +(-64.7294 + 38.9464i) q^{35} +(-1.92380 + 35.4824i) q^{36} +(183.478 - 61.8210i) q^{37} +(-55.1043 - 103.938i) q^{38} +(78.0443 + 91.8809i) q^{39} +(65.6282 + 96.7944i) q^{40} +(-7.42872 - 137.015i) q^{41} +(-34.7248 - 87.1527i) q^{42} +(43.8662 + 20.2947i) q^{43} +(235.976 - 51.9423i) q^{44} +(-20.4986 + 38.6646i) q^{45} +(47.3206 - 288.643i) q^{46} +(-154.726 + 117.620i) q^{47} +(-45.8095 + 21.1937i) q^{48} +(73.7882 + 69.8959i) q^{49} +(-33.0066 - 201.331i) q^{50} +(-96.8741 - 32.6407i) q^{51} +(58.7257 - 147.390i) q^{52} +(-214.196 + 202.897i) q^{53} +(-43.2661 - 32.8900i) q^{54} +(290.615 + 63.9693i) q^{55} +(-241.893 + 284.779i) q^{56} +(-174.305 - 18.9568i) q^{57} +116.897 q^{58} +(37.1557 - 451.662i) q^{59} +57.5953 q^{60} +(48.6850 + 5.29481i) q^{61} +(-47.3377 + 55.7303i) q^{62} +(-136.554 - 30.0577i) q^{63} +(361.202 + 274.578i) q^{64} +(141.856 - 134.373i) q^{65} +(-136.785 + 343.305i) q^{66} +(277.967 + 93.6579i) q^{67} +(21.7658 + 132.766i) q^{68} +(-316.487 - 299.792i) q^{69} +(-138.005 + 63.8480i) q^{70} +(-111.705 + 84.9159i) q^{71} +(-35.0185 + 213.604i) q^{72} +(482.360 - 909.827i) q^{73} +(380.610 - 83.7787i) q^{74} +(-275.965 - 127.675i) q^{75} +(85.4108 + 214.365i) q^{76} +(51.4730 + 949.363i) q^{77} +(136.177 + 200.847i) q^{78} +(95.1092 + 111.971i) q^{79} +(38.3208 + 72.2807i) q^{80} +(-76.7599 + 25.8634i) q^{81} +(14.9532 - 275.795i) q^{82} +(-410.652 + 247.081i) q^{83} +(49.2305 + 177.312i) q^{84} +(-44.3266 + 159.650i) q^{85} +(83.3635 + 50.1581i) q^{86} +(97.7718 - 144.203i) q^{87} +(1463.21 - 159.134i) q^{88} +(312.065 - 33.9392i) q^{89} +(-49.4343 + 72.9101i) q^{90} +(534.934 + 321.859i) q^{91} +(-153.489 + 552.818i) q^{92} +(29.1552 + 105.007i) q^{93} +(-335.219 + 201.695i) q^{94} +(-15.3854 + 283.767i) q^{95} +(450.717 - 151.864i) q^{96} +(-359.128 - 677.388i) q^{97} +(132.445 + 155.927i) q^{98} +(309.090 + 455.873i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 420 q + 2 q^{2} - 45 q^{3} - 56 q^{4} - 14 q^{5} + 6 q^{6} + 6 q^{7} + 66 q^{8} - 135 q^{9}+O(q^{10}) \) 420 * q + 2 * q^2 - 45 * q^3 - 56 * q^4 - 14 * q^5 + 6 * q^6 + 6 * q^7 + 66 * q^8 - 135 * q^9	\( 420 q + 2 q^{2} - 45 q^{3} - 56 q^{4} - 14 q^{5} + 6 q^{6} + 6 q^{7} + 66 q^{8} - 135 q^{9} - 754 q^{10} + 64 q^{11} - 168 q^{12} + 90 q^{13} + 1024 q^{14} - 42 q^{15} - 172 q^{16} + 96 q^{17} + 18 q^{18} + 16 q^{19} - 178 q^{20} - 243 q^{21} - 604 q^{22} + 48 q^{23} + 198 q^{24} - 173 q^{25} + 156 q^{26} - 405 q^{27} + 84 q^{28} - 50 q^{29} + 174 q^{30} + 222 q^{31} - 45 q^{32} + 192 q^{33} - 64 q^{34} - 132 q^{35} - 504 q^{36} + 30 q^{37} - 108 q^{38} + 270 q^{39} + 6984 q^{40} + 400 q^{41} + 114 q^{42} + 1220 q^{43} + 1180 q^{44} - 126 q^{45} + 4938 q^{46} + 370 q^{47} - 516 q^{48} + 771 q^{49} + 1048 q^{50} + 288 q^{51} - 1964 q^{52} - 822 q^{53} + 54 q^{54} - 2342 q^{55} - 13824 q^{56} + 48 q^{57} - 13150 q^{58} - 3423 q^{59} - 534 q^{60} - 2182 q^{61} + 845 q^{62} + 54 q^{63} - 8018 q^{64} + 4140 q^{65} - 1812 q^{66} + 506 q^{67} + 4826 q^{68} - 3684 q^{69} + 6882 q^{70} + 5874 q^{71} + 594 q^{72} + 206 q^{73} + 11124 q^{74} - 867 q^{75} + 16940 q^{76} + 9940 q^{77} + 468 q^{78} - 1762 q^{79} - 28954 q^{80} - 1215 q^{81} + 3770 q^{82} - 1216 q^{83} - 8013 q^{84} - 420 q^{85} - 2256 q^{86} + 5940 q^{87} + 13458 q^{88} - 1580 q^{89} + 522 q^{90} - 12204 q^{91} + 4562 q^{92} + 666 q^{93} + 176 q^{94} - 28456 q^{95} + 2040 q^{96} + 2574 q^{97} + 50690 q^{98} + 576 q^{99}+O(q^{100}) \) 420 * q + 2 * q^2 - 45 * q^3 - 56 * q^4 - 14 * q^5 + 6 * q^6 + 6 * q^7 + 66 * q^8 - 135 * q^9 - 754 * q^10 + 64 * q^11 - 168 * q^12 + 90 * q^13 + 1024 * q^14 - 42 * q^15 - 172 * q^16 + 96 * q^17 + 18 * q^18 + 16 * q^19 - 178 * q^20 - 243 * q^21 - 604 * q^22 + 48 * q^23 + 198 * q^24 - 173 * q^25 + 156 * q^26 - 405 * q^27 + 84 * q^28 - 50 * q^29 + 174 * q^30 + 222 * q^31 - 45 * q^32 + 192 * q^33 - 64 * q^34 - 132 * q^35 - 504 * q^36 + 30 * q^37 - 108 * q^38 + 270 * q^39 + 6984 * q^40 + 400 * q^41 + 114 * q^42 + 1220 * q^43 + 1180 * q^44 - 126 * q^45 + 4938 * q^46 + 370 * q^47 - 516 * q^48 + 771 * q^49 + 1048 * q^50 + 288 * q^51 - 1964 * q^52 - 822 * q^53 + 54 * q^54 - 2342 * q^55 - 13824 * q^56 + 48 * q^57 - 13150 * q^58 - 3423 * q^59 - 534 * q^60 - 2182 * q^61 + 845 * q^62 + 54 * q^63 - 8018 * q^64 + 4140 * q^65 - 1812 * q^66 + 506 * q^67 + 4826 * q^68 - 3684 * q^69 + 6882 * q^70 + 5874 * q^71 + 594 * q^72 + 206 * q^73 + 11124 * q^74 - 867 * q^75 + 16940 * q^76 + 9940 * q^77 + 468 * q^78 - 1762 * q^79 - 28954 * q^80 - 1215 * q^81 + 3770 * q^82 - 1216 * q^83 - 8013 * q^84 - 420 * q^85 - 2256 * q^86 + 5940 * q^87 + 13458 * q^88 - 1580 * q^89 + 522 * q^90 - 12204 * q^91 + 4562 * q^92 + 666 * q^93 + 176 * q^94 - 28456 * q^95 + 2040 * q^96 + 2574 * q^97 + 50690 * q^98 + 576 * q^99

Introduction

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