LMFDB - Embedded newform 115.4.g.a.6.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,4,Mod(6,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("115.6");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	115.g (of order $11$, degree $10$, 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:	$6.78521965066$
Analytic rank:	$0$
Dimension:	$110$
Relative dimension:	$11$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			6.6
Character	$\chi$	$=$	115.6
Dual form			115.4.g.a.96.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.502951 + 1.10131i) q^{2} +(-7.38951 - 2.16976i) q^{3} +(4.27896 + 4.93819i) q^{4} +(4.20627 - 2.70320i) q^{5} +(6.10614 - 7.04686i) q^{6} +(2.63135 - 18.3014i) q^{7} +(-16.8840 + 4.95759i) q^{8} +(27.1832 + 17.4696i) q^{9} +O(q^{10})$	\(q+(-0.502951 + 1.10131i) q^{2} +(-7.38951 - 2.16976i) q^{3} +(4.27896 + 4.93819i) q^{4} +(4.20627 - 2.70320i) q^{5} +(6.10614 - 7.04686i) q^{6} +(2.63135 - 18.3014i) q^{7} +(-16.8840 + 4.95759i) q^{8} +(27.1832 + 17.4696i) q^{9} +(0.861517 + 5.99198i) q^{10} +(12.9405 + 28.3358i) q^{11} +(-20.9048 - 45.7751i) q^{12} +(6.69273 + 46.5490i) q^{13} +(18.8321 + 12.1027i) q^{14} +(-36.9476 + 10.8488i) q^{15} +(-4.40727 + 30.6532i) q^{16} +(-47.8147 + 55.1811i) q^{17} +(-32.9113 + 21.1508i) q^{18} +(57.1420 + 65.9454i) q^{19} +(31.3474 + 9.20442i) q^{20} +(-59.1540 + 129.529i) q^{21} -37.7150 q^{22} +(97.8235 + 50.9663i) q^{23} +135.521 q^{24} +(10.3854 - 22.7408i) q^{25} +(-54.6310 - 16.0411i) q^{26} +(-26.7943 - 30.9223i) q^{27} +(101.635 - 65.3170i) q^{28} +(-116.249 + 134.159i) q^{29} +(6.63496 - 46.1471i) q^{30} +(101.005 - 29.6576i) q^{31} +(-149.969 - 96.3792i) q^{32} +(-34.1424 - 237.466i) q^{33} +(-36.7230 - 80.4122i) q^{34} +(-38.4043 - 84.0937i) q^{35} +(30.0479 + 208.988i) q^{36} +(-234.483 - 150.693i) q^{37} +(-101.366 + 29.7638i) q^{38} +(51.5439 - 358.496i) q^{39} +(-57.6173 + 66.4939i) q^{40} +(38.6455 - 24.8359i) q^{41} +(-112.900 - 130.294i) q^{42} +(94.7313 + 27.8156i) q^{43} +(-84.5555 + 185.151i) q^{44} +161.564 q^{45} +(-105.330 + 82.1004i) q^{46} +436.665 q^{47} +(99.0777 - 216.950i) q^{48} +(1.08806 + 0.319483i) q^{49} +(19.8213 + 22.8750i) q^{50} +(473.057 - 304.015i) q^{51} +(-201.230 + 232.231i) q^{52} +(-26.6367 + 185.262i) q^{53} +(47.5313 - 13.9564i) q^{54} +(131.029 + 84.2071i) q^{55} +(46.3033 + 322.046i) q^{56} +(-279.166 - 611.289i) q^{57} +(-89.2827 - 195.502i) q^{58} +(29.5870 + 205.782i) q^{59} +(-211.671 - 136.032i) q^{60} +(175.617 - 51.5657i) q^{61} +(-18.1382 + 126.154i) q^{62} +(391.247 - 451.523i) q^{63} +(-26.8481 + 17.2542i) q^{64} +(153.983 + 177.706i) q^{65} +(278.695 + 81.8323i) q^{66} +(88.4106 - 193.592i) q^{67} -477.092 q^{68} +(-612.284 - 588.869i) q^{69} +111.929 q^{70} +(-400.051 + 875.989i) q^{71} +(-545.569 - 160.193i) q^{72} +(487.835 + 562.992i) q^{73} +(283.893 - 182.447i) q^{74} +(-126.085 + 145.510i) q^{75} +(-81.1422 + 564.356i) q^{76} +(552.637 - 162.269i) q^{77} +(368.891 + 237.072i) q^{78} +(-178.998 - 1244.96i) q^{79} +(64.3238 + 140.849i) q^{80} +(-231.523 - 506.965i) q^{81} +(7.91527 + 55.0519i) q^{82} +(-741.416 - 476.479i) q^{83} +(-892.757 + 262.137i) q^{84} +(-51.9556 + 361.359i) q^{85} +(-78.2788 + 90.3386i) q^{86} +(1150.12 - 739.136i) q^{87} +(-358.965 - 414.268i) q^{88} +(-1316.89 - 386.673i) q^{89} +(-81.2587 + 177.932i) q^{90} +869.523 q^{91} +(166.902 + 701.154i) q^{92} -810.724 q^{93} +(-219.621 + 480.903i) q^{94} +(418.619 + 122.918i) q^{95} +(899.079 + 1037.59i) q^{96} +(-183.511 + 117.935i) q^{97} +(-0.899091 + 1.03761i) q^{98} +(-143.250 + 996.325i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 110 q - 2 q^{2} + 6 q^{3} - 40 q^{4} - 55 q^{5} - 3 q^{6} - 10 q^{7} + 243 q^{8} - 233 q^{9}+O(q^{10}) $ 110 * q - 2 * q^2 + 6 * q^3 - 40 * q^4 - 55 * q^5 - 3 * q^6 - 10 * q^7 + 243 * q^8 - 233 * q^9	\( 110 q - 2 q^{2} + 6 q^{3} - 40 q^{4} - 55 q^{5} - 3 q^{6} - 10 q^{7} + 243 q^{8} - 233 q^{9} - 10 q^{10} + 2 q^{11} - 57 q^{12} + 34 q^{13} - 154 q^{14} + 30 q^{15} + 16 q^{16} + 252 q^{17} - 33 q^{18} - 160 q^{19} - 200 q^{20} - 684 q^{21} - 704 q^{22} + 127 q^{23} - 3090 q^{24} - 275 q^{25} - 567 q^{26} + 384 q^{27} - 188 q^{28} + 340 q^{29} - 15 q^{30} + 582 q^{31} - 1364 q^{32} + 1760 q^{33} + 1819 q^{34} + 665 q^{35} + 2794 q^{36} + 312 q^{37} + 3123 q^{38} - 1560 q^{39} - 1205 q^{40} + 1324 q^{41} + 1454 q^{42} - 1740 q^{43} - 369 q^{44} + 3730 q^{45} - 4322 q^{46} - 2858 q^{47} - 2686 q^{48} + 2015 q^{49} - 325 q^{50} - 1426 q^{51} + 1717 q^{52} + 882 q^{53} + 2541 q^{54} + 450 q^{55} + 7755 q^{56} + 3688 q^{57} + 6622 q^{58} + 2605 q^{59} + 1530 q^{60} - 104 q^{61} - 9360 q^{62} - 7618 q^{63} + 3483 q^{64} + 170 q^{65} - 1766 q^{66} - 166 q^{67} - 5018 q^{68} - 1194 q^{69} - 770 q^{70} - 1222 q^{71} + 3303 q^{72} - 922 q^{73} + 1245 q^{74} + 150 q^{75} + 1360 q^{76} - 3093 q^{77} - 1600 q^{78} + 2448 q^{79} + 2115 q^{80} - 1371 q^{81} + 6609 q^{82} + 6704 q^{83} + 3894 q^{84} - 720 q^{85} - 5074 q^{86} - 6324 q^{87} + 1918 q^{88} - 5380 q^{89} - 165 q^{90} + 7828 q^{91} - 16225 q^{92} - 24948 q^{93} - 16490 q^{94} + 685 q^{95} + 675 q^{96} - 4400 q^{97} + 8790 q^{98} - 3626 q^{99}+O(q^{100}) \) 110 * q - 2 * q^2 + 6 * q^3 - 40 * q^4 - 55 * q^5 - 3 * q^6 - 10 * q^7 + 243 * q^8 - 233 * q^9 - 10 * q^10 + 2 * q^11 - 57 * q^12 + 34 * q^13 - 154 * q^14 + 30 * q^15 + 16 * q^16 + 252 * q^17 - 33 * q^18 - 160 * q^19 - 200 * q^20 - 684 * q^21 - 704 * q^22 + 127 * q^23 - 3090 * q^24 - 275 * q^25 - 567 * q^26 + 384 * q^27 - 188 * q^28 + 340 * q^29 - 15 * q^30 + 582 * q^31 - 1364 * q^32 + 1760 * q^33 + 1819 * q^34 + 665 * q^35 + 2794 * q^36 + 312 * q^37 + 3123 * q^38 - 1560 * q^39 - 1205 * q^40 + 1324 * q^41 + 1454 * q^42 - 1740 * q^43 - 369 * q^44 + 3730 * q^45 - 4322 * q^46 - 2858 * q^47 - 2686 * q^48 + 2015 * q^49 - 325 * q^50 - 1426 * q^51 + 1717 * q^52 + 882 * q^53 + 2541 * q^54 + 450 * q^55 + 7755 * q^56 + 3688 * q^57 + 6622 * q^58 + 2605 * q^59 + 1530 * q^60 - 104 * q^61 - 9360 * q^62 - 7618 * q^63 + 3483 * q^64 + 170 * q^65 - 1766 * q^66 - 166 * q^67 - 5018 * q^68 - 1194 * q^69 - 770 * q^70 - 1222 * q^71 + 3303 * q^72 - 922 * q^73 + 1245 * q^74 + 150 * q^75 + 1360 * q^76 - 3093 * q^77 - 1600 * q^78 + 2448 * q^79 + 2115 * q^80 - 1371 * q^81 + 6609 * q^82 + 6704 * q^83 + 3894 * q^84 - 720 * q^85 - 5074 * q^86 - 6324 * q^87 + 1918 * q^88 - 5380 * q^89 - 165 * q^90 + 7828 * q^91 - 16225 * q^92 - 24948 * q^93 - 16490 * q^94 + 685 * q^95 + 675 * q^96 - 4400 * q^97 + 8790 * q^98 - 3626 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$e\left(\frac{9}{11}\right)$

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 $

$2$	−0.502951	+	1.10131i	−0.177820	+	0.389372i	−0.977464	−	0.211103i	$-0.932294\pi$
$2$	−0.502951	+	1.10131i	−0.177820	+	0.389372i	0.799644	+	0.600475i	$0.205022\pi$
$3$	−7.38951	−	2.16976i	−1.42211	−	0.417570i	−0.521895	−	0.853010i	$-0.674775\pi$
$3$	−7.38951	−	2.16976i	−1.42211	−	0.417570i	−0.900218	+	0.435440i	$0.856593\pi$
$4$	4.27896	+	4.93819i	0.534870	+	0.617273i
$5$	4.20627	−	2.70320i	0.376220	−	0.241782i
$5$	4.20627	−	2.70320i	0.376220	−	0.241782i
$6$	6.10614	−	7.04686i	0.415470	−	0.479478i
$7$	2.63135	−	18.3014i	0.142079	−	0.988184i	−0.786643	−	0.617408i	$-0.788183\pi$
$7$	2.63135	−	18.3014i	0.142079	−	0.988184i	0.928722	−	0.370776i	$-0.120908\pi$
$8$	−16.8840	+	4.95759i	−0.746175	+	0.219097i
$9$	27.1832	+	17.4696i	1.00679	+	0.647022i
$10$	0.861517	+	5.99198i	0.0272436	+	0.189483i
$11$	12.9405	+	28.3358i	0.354702	+	0.776688i	0.999919	+	0.0126895i	$0.00403931\pi$
$11$	12.9405	+	28.3358i	0.354702	+	0.776688i	−0.645218	+	0.763999i	$0.723233\pi$
$12$	−20.9048	−	45.7751i	−0.502891	−	1.10118i
$13$	6.69273	+	46.5490i	0.142787	+	0.993105i	0.927654	+	0.373441i	$0.121822\pi$
$13$	6.69273	+	46.5490i	0.142787	+	0.993105i	−0.784867	+	0.619664i	$0.787269\pi$
$14$	18.8321	+	12.1027i	0.359506	+	0.231041i
$15$	−36.9476	+	10.8488i	−0.635988	+	0.186743i
$16$	−4.40727	+	30.6532i	−0.0688636	+	0.478957i
$17$	−47.8147	+	55.1811i	−0.682163	+	0.787258i	−0.986228	−	0.165394i	$-0.947111\pi$
$17$	−47.8147	+	55.1811i	−0.682163	+	0.787258i	0.304065	+	0.952651i	$0.401656\pi$
$18$	−32.9113	+	21.1508i	−0.430959	+	0.276961i
$19$	57.1420	+	65.9454i	0.689962	+	0.796259i	0.987360	−	0.158495i	$-0.0506641\pi$
$19$	57.1420	+	65.9454i	0.689962	+	0.796259i	−0.297397	+	0.954754i	$0.596119\pi$
$20$	31.3474	+	9.20442i	0.350474	+	0.102909i
$21$	−59.1540	+	129.529i	−0.614689	+	1.34598i
$22$	−37.7150			−0.365494
$23$	97.8235	+	50.9663i	0.886853	+	0.462052i
$23$	97.8235	+	50.9663i	0.886853	+	0.462052i
$24$	135.521			1.15263
$25$	10.3854	−	22.7408i	0.0830830	−	0.181926i
$26$	−54.6310	−	16.0411i	−0.412077	−	0.120997i
$27$	−26.7943	−	30.9223i	−0.190984	−	0.220407i
$28$	101.635	−	65.3170i	0.685974	−	0.440848i
$29$	−116.249	+	134.159i	−0.744378	+	0.859058i	−0.994011	−	0.109283i	$-0.965145\pi$
$29$	−116.249	+	134.159i	−0.744378	+	0.859058i	0.249633	+	0.968341i	$0.419690\pi$
$30$	6.63496	−	46.1471i	0.0403791	−	0.280842i
$31$	101.005	−	29.6576i	0.585192	−	0.171828i	0.0242827	−	0.999705i	$-0.492270\pi$
$31$	101.005	−	29.6576i	0.585192	−	0.171828i	0.560909	+	0.827877i	$0.310452\pi$
$32$	−149.969	−	96.3792i	−0.828470	−	0.532425i
$33$	−34.1424	−	237.466i	−0.180104	−	1.25265i
$34$	−36.7230	−	80.4122i	−0.185234	−	0.405605i
$35$	−38.4043	−	84.0937i	−0.185472	−	0.406127i
$36$	30.0479	+	208.988i	0.139111	+	0.967535i
$37$	−234.483	−	150.693i	−1.04186	−	0.669561i	−0.0964121	−	0.995342i	$-0.530737\pi$
$37$	−234.483	−	150.693i	−1.04186	−	0.669561i	−0.945446	+	0.325780i	$0.894373\pi$
$38$	−101.366	+	29.7638i	−0.432730	+	0.127061i
$39$	51.5439	−	358.496i	0.211632	−	1.47193i
$40$	−57.6173	+	66.4939i	−0.227752	+	0.262840i
$41$	38.6455	−	24.8359i	0.147205	−	0.0946030i	−0.464965	−	0.885329i	$-0.653933\pi$
$41$	38.6455	−	24.8359i	0.147205	−	0.0946030i	0.612170	+	0.790726i	$0.290297\pi$
$42$	−112.900	−	130.294i	−0.414783	−	0.478685i
$43$	94.7313	+	27.8156i	0.335962	+	0.0986475i	0.445363	−	0.895350i	$-0.353075\pi$
$43$	94.7313	+	27.8156i	0.335962	+	0.0986475i	−0.109400	+	0.993998i	$0.534893\pi$
$44$	−84.5555	+	185.151i	−0.289709	+	0.634375i
$45$	161.564			0.535211
$46$	−105.330	+	82.1004i	−0.337610	+	0.263153i
$47$	436.665			1.35519			0.677597	−	0.735433i	$-0.263021\pi$
$47$	436.665			1.35519			0.677597	+	0.735433i	$0.263021\pi$
$48$	99.0777	−	216.950i	0.297930	−	0.652375i
$49$	1.08806	+	0.319483i	0.00317219	+	0.000931438i
$50$	19.8213	+	22.8750i	0.0560632	+	0.0647004i
$51$	473.057	−	304.015i	1.29885	−	0.834719i
$52$	−201.230	+	232.231i	−0.536645	+	0.619321i
$53$	−26.6367	+	185.262i	−0.0690346	+	0.480146i	0.925749	+	0.378139i	$0.123436\pi$
$53$	−26.6367	+	185.262i	−0.0690346	+	0.480146i	−0.994784	+	0.102008i	$0.967473\pi$
$54$	47.5313	−	13.9564i	0.119781	−	0.0351710i
$55$	131.029	+	84.2071i	0.321235	+	0.206445i
$56$	46.3033	+	322.046i	0.110492	+	0.768487i
$57$	−279.166	−	611.289i	−0.648710	−	1.42048i
$58$	−89.2827	−	195.502i	−0.202128	−	0.442597i
$59$	29.5870	+	205.782i	0.0652864	+	0.454077i	0.996075	+	0.0885179i	$0.0282131\pi$
$59$	29.5870	+	205.782i	0.0652864	+	0.454077i	−0.930788	+	0.365559i	$0.880878\pi$
$60$	−211.671	−	136.032i	−0.455443	−	0.292695i
$61$	175.617	−	51.5657i	0.368614	−	0.108235i	−0.0921793	−	0.995742i	$-0.529383\pi$
$61$	175.617	−	51.5657i	0.368614	−	0.108235i	0.460793	+	0.887508i	$0.347565\pi$
$62$	−18.1382	+	126.154i	−0.0371540	+	0.258412i
$63$	391.247	−	451.523i	0.782420	−	0.902961i
$64$	−26.8481	+	17.2542i	−0.0524377	+	0.0336996i
$65$	153.983	+	177.706i	0.293834	+	0.339103i
$66$	278.695	+	81.8323i	0.519773	+	0.152619i
$67$	88.4106	−	193.592i	0.161210	−	0.353001i	−0.811739	−	0.584020i	$-0.801479\pi$
$67$	88.4106	−	193.592i	0.161210	−	0.353001i	0.972949	+	0.231020i	$0.0742061\pi$
$68$	−477.092			−0.850822
$69$	−612.284	−	588.869i	−1.06827	−	1.02741i
$70$	111.929			0.191115
$71$	−400.051	+	875.989i	−0.668694	+	1.46424i	0.205499	+	0.978657i	$0.434118\pi$
$71$	−400.051	+	875.989i	−0.668694	+	1.46424i	−0.874193	+	0.485578i	$0.838609\pi$
$72$	−545.569	−	160.193i	−0.892998	−	0.262208i
$73$	487.835	+	562.992i	0.782148	+	0.902647i	0.997263	−	0.0739417i	$-0.0235579\pi$
$73$	487.835	+	562.992i	0.782148	+	0.902647i	−0.215114	+	0.976589i	$0.569012\pi$
$74$	283.893	−	182.447i	0.445972	−	0.286609i
$75$	−126.085	+	145.510i	−0.194120	+	0.224027i
$76$	−81.1422	+	564.356i	−0.122469	+	0.851791i
$77$	552.637	−	162.269i	0.817906	−	0.240159i
$78$	368.891	+	237.072i	0.535496	+	0.344142i
$79$	−178.998	−	1244.96i	−0.254922	−	1.77302i	−0.567742	−	0.823207i	$-0.692183\pi$
$79$	−178.998	−	1244.96i	−0.254922	−	1.77302i	0.312820	−	0.949812i	$-0.398726\pi$
$80$	64.3238	+	140.849i	0.0898953	+	0.196843i
$81$	−231.523	−	506.965i	−0.317590	−	0.695426i
$82$	7.91527	+	55.0519i	0.0106597	+	0.0741399i
$83$	−741.416	−	476.479i	−0.980493	−	0.630125i	−0.0508968	−	0.998704i	$-0.516208\pi$
$83$	−741.416	−	476.479i	−0.980493	−	0.630125i	−0.929596	+	0.368579i	$0.879844\pi$
$84$	−892.757	+	262.137i	−1.15962	+	0.340494i
$85$	−51.9556	+	361.359i	−0.0662986	+	0.461117i
$86$	−78.2788	+	90.3386i	−0.0981514	+	0.113273i
$87$	1150.12	−	739.136i	1.41731	−	0.910847i
$88$	−358.965	−	414.268i	−0.434839	−	0.501831i
$89$	−1316.89	−	386.673i	−1.56842	−	0.460531i	−0.621882	−	0.783111i	$-0.713632\pi$
$89$	−1316.89	−	386.673i	−1.56842	−	0.460531i	−0.946542	+	0.322580i	$0.895450\pi$
$90$	−81.2587	+	177.932i	−0.0951714	+	0.208396i
$91$	869.523			1.00166
$92$	166.902	+	701.154i	0.189139	+	0.794569i
$93$	−810.724			−0.903959
$94$	−219.621	+	480.903i	−0.240981	+	0.527674i
$95$	418.619	+	122.918i	0.452099	+	0.132748i
$96$	899.079	+	1037.59i	0.955852	+	1.10311i
$97$	−183.511	+	117.935i	−0.192090	+	0.123449i	−0.633151	−	0.774029i	$-0.718239\pi$
$97$	−183.511	+	117.935i	−0.192090	+	0.123449i	0.441061	+	0.897477i	$0.354602\pi$
$98$	−0.899091	+	1.03761i	−0.000926755	+	0.00106953i
$99$	−143.250	+	996.325i	−0.145426	+	1.01146i
$100$	156.737	−	46.0221i	0.156737	−	0.0460221i
$101$	180.502	+	116.002i	0.177828	+	0.114283i	0.626527	−	0.779400i	$-0.284476\pi$
$101$	180.502	+	116.002i	0.177828	+	0.114283i	−0.448699	+	0.893683i	$0.648112\pi$
$102$	96.8903	+	673.887i	0.0940546	+	0.654164i
$103$	616.716	+	1350.42i	0.589969	+	1.29185i	0.935461	+	0.353430i	$0.114985\pi$
$103$	616.716	+	1350.42i	0.589969	+	1.29185i	−0.345492	+	0.938422i	$0.612288\pi$
$104$	−343.771	−	752.753i	−0.324130	−	0.709745i
$105$	101.326	+	704.740i	0.0941756	+	0.655005i
$106$	−190.634	−	122.513i	−0.174680	−	0.112260i
$107$	−685.279	+	201.216i	−0.619144	+	0.181797i	−0.576238	−	0.817282i	$-0.695480\pi$
$107$	−685.279	+	201.216i	−0.619144	+	0.181797i	−0.0429060	+	0.999079i	$0.513662\pi$
$108$	38.0482	−	264.631i	0.0338999	−	0.235779i
$109$	946.278	−	1092.06i	0.831532	−	0.959639i	−0.168127	−	0.985765i	$-0.553772\pi$
$109$	946.278	−	1092.06i	0.831532	−	0.959639i	0.999659	+	0.0261266i	$0.00831731\pi$
$110$	−158.639	+	101.951i	−0.137506	+	0.0883697i
$111$	1405.75	+	1622.32i	1.20205	+	1.38724i
$112$	549.401	+	161.319i	0.463513	+	0.136100i
$113$	−488.356	+	1069.35i	−0.406555	+	0.890231i	0.590009	+	0.807397i	$0.299124\pi$
$113$	−488.356	+	1069.35i	−0.406555	+	0.890231i	−0.996563	+	0.0828338i	$0.973603\pi$
$114$	813.626			0.668448
$115$	549.244	−	50.0590i	0.445368	−	0.0405916i
$116$	−1159.93			−0.928419
$117$	−631.262	+	1382.27i	−0.498805	+	1.09223i
$118$	−241.511	−	70.9139i	−0.188414	−	0.0553233i
$119$	884.075	+	1020.28i	0.681034	+	0.785955i
$120$	570.039	−	366.342i	0.433643	−	0.278686i
$121$	236.159	−	272.542i	0.177430	−	0.204765i
$122$	−31.5368	+	219.344i	−0.0234034	+	0.162774i
$123$	−339.459	+	99.6742i	−0.248846	+	0.0730677i
$124$	578.649	+	371.875i	0.419067	+	0.269318i
$125$	−17.7894	−	123.728i	−0.0127290	−	0.0885323i
$126$	300.489	+	657.978i	0.212458	+	0.465217i
$127$	−1081.71	−	2368.61i	−0.755797	−	1.65497i	−0.755659	−	0.654965i	$-0.772683\pi$
$127$	−1081.71	−	2368.61i	−0.755797	−	1.65497i	−0.000138140	−	1.00000i	$-0.500044\pi$
$128$	−208.461	−	1449.88i	−0.143949	−	1.00119i
$129$	−639.665	−	411.088i	−0.436584	−	0.280576i
$130$	−273.155	+	80.2055i	−0.184287	+	0.0541114i
$131$	−12.9129	+	89.8114i	−0.00861228	+	0.0598997i	−0.993674	−	0.112300i	$-0.964178\pi$
$131$	−12.9129	+	89.8114i	−0.00861228	+	0.0598997i	0.985062	+	0.172200i	$0.0550874\pi$
$132$	1026.56	−	1184.71i	0.676895	−	0.781179i
$133$	1357.26	−	872.255i	0.884880	−	0.568678i
$134$	168.739	+	194.735i	0.108782	+	0.125541i
$135$	−196.293	−	57.6370i	−0.125143	−	0.0367452i
$136$	533.738	−	1168.72i	0.336527	−	0.736891i
$137$	−2087.63			−1.30188			−0.650942	−	0.759127i	$-0.725626\pi$
$137$	−2087.63			−1.30188			−0.650942	+	0.759127i	$0.725626\pi$
$138$	956.476	−	378.141i	0.590005	−	0.233257i
$139$	2441.76			1.48998			0.744990	−	0.667076i	$-0.232454\pi$
$139$	2441.76			1.48998			0.744990	+	0.667076i	$0.232454\pi$
$140$	250.940	−	549.482i	0.151488	−	0.331712i
$141$	−3226.74	−	947.457i	−1.92724	−	0.565888i
$142$	−763.529	−	881.159i	−0.451225	−	0.520741i
$143$	−1232.40	+	792.013i	−0.720686	+	0.463157i
$144$	−655.304	+	756.261i	−0.379227	+	0.437651i
$145$	−126.317	+	878.554i	−0.0723452	+	0.503172i
$146$	−865.386	+	254.100i	−0.490547	+	0.144038i
$147$	−7.34704	−	4.72165i	−0.00412227	−	0.00264922i
$148$	−259.193	−	1802.73i	−0.143956	−	1.00124i
$149$	−13.2973	−	29.1169i	−0.00731110	−	0.0160091i	0.905941	−	0.423403i	$-0.139165\pi$
$149$	−13.2973	−	29.1169i	−0.00731110	−	0.0160091i	−0.913252	+	0.407394i	$0.866437\pi$
$150$	−96.8367	−	212.043i	−0.0527112	−	0.115421i
$151$	−204.225	−	1420.42i	−0.110064	−	0.765510i	−0.967855	−	0.251511i	$-0.919073\pi$
$151$	−204.225	−	1420.42i	−0.110064	−	0.765510i	0.857791	−	0.513999i	$-0.171836\pi$
$152$	−1291.72	−	830.136i	−0.689290	−	0.442980i
$153$	−2263.75	+	664.697i	−1.19617	+	0.351226i
$154$	−99.2412	+	690.238i	−0.0519291	+	0.361175i
$155$	344.682	−	397.784i	0.178616	−	0.206134i
$156$	1990.87	−	1279.46i	1.02178	−	0.656657i
$157$	−675.784	−	779.896i	−0.343525	−	0.396449i	0.557528	−	0.830158i	$-0.311750\pi$
$157$	−675.784	−	779.896i	−0.343525	−	0.396449i	−0.901053	+	0.433709i	$0.857205\pi$
$158$	1461.11	+	429.021i	0.735694	+	0.216019i
$159$	598.807	−	1311.20i	0.298670	−	0.653995i
$160$	−891.343			−0.440418
$161$	1190.16	−	1656.20i	0.582596	−	0.810725i
$162$	674.771			0.327253
$163$	−1675.46	+	3668.74i	−0.805104	+	1.76293i	−0.177946	+	0.984040i	$0.556945\pi$
$163$	−1675.46	+	3668.74i	−0.805104	+	1.76293i	−0.627158	+	0.778892i	$0.715782\pi$
$164$	288.007	+	84.5665i	0.137132	+	0.0402655i
$165$	−785.530	−	906.550i	−0.370627	−	0.427726i
$166$	897.647	−	576.883i	0.419704	−	0.269728i
$167$	2494.95	−	2879.32i	1.15608	−	1.33418i	0.222867	−	0.974849i	$-0.428459\pi$
$167$	2494.95	−	2879.32i	1.15608	−	1.33418i	0.933209	−	0.359334i	$-0.116996\pi$
$168$	356.604	−	2480.23i	0.163765	−	1.13901i
$169$	−14.0087	+	4.11333i	−0.00637630	+	0.00187225i
$170$	−371.837	−	238.965i	−0.167757	−	0.107811i
$171$	401.265	+	2790.86i	0.179447	+	1.24808i
$172$	267.993	+	586.823i	0.118804	+	0.260144i
$173$	1567.10	+	3431.47i	0.688697	+	1.50804i	0.853158	+	0.521652i	$0.174684\pi$
$173$	1567.10	+	3431.47i	0.688697	+	1.50804i	−0.164462	+	0.986383i	$0.552589\pi$
$174$	235.564	+	1638.39i	0.102633	+	0.713826i
$175$	−388.861	−	249.906i	−0.167972	−	0.107949i
$176$	−925.617	+	271.786i	−0.396426	+	0.116401i
$177$	227.864	−	1584.83i	0.0967642	−	0.673010i
$178$	1088.18	−	1255.82i	0.458215	−	0.528809i
$179$	1007.90	−	647.739i	0.420861	−	0.270471i	−0.313023	−	0.949745i	$-0.601342\pi$
$179$	1007.90	−	647.739i	0.420861	−	0.270471i	0.733884	+	0.679275i	$0.237705\pi$
$180$	691.325	+	797.832i	0.286269	+	0.330372i
$181$	1318.03	+	387.009i	0.541263	+	0.158929i	0.540925	−	0.841071i	$-0.318074\pi$
$181$	1318.03	+	387.009i	0.541263	+	0.158929i	0.000338039		1.00000i	$0.499892\pi$
$182$	−437.328	+	957.615i	−0.178115	+	0.390017i
$183$	−1409.61			−0.569406
$184$	−1904.32	−	375.546i	−0.762981	−	0.150465i
$185$	−1393.65			−0.553855
$186$	407.755	−	892.859i	0.160742	−	0.351976i
$187$	−2182.35	−	640.795i	−0.853418	−	0.250586i
$188$	1868.47	+	2156.33i	0.724853	+	0.836525i
$189$	−636.428	+	409.007i	−0.244938	+	0.157412i
$190$	−345.915	+	399.207i	−0.132081	+	0.152429i
$191$	318.442	−	2214.81i	0.120637	−	0.839049i	−0.836200	−	0.548424i	$-0.815228\pi$
$191$	318.442	−	2214.81i	0.120637	−	0.839049i	0.956837	−	0.290625i	$-0.0938631\pi$
$192$	235.832	−	69.2465i	0.0886442	−	0.0260283i
$193$	−377.047	−	242.314i	−0.140624	−	0.0903737i	0.468437	−	0.883497i	$-0.344817\pi$
$193$	−377.047	−	242.314i	−0.140624	−	0.0903737i	−0.609061	+	0.793123i	$0.708454\pi$
$194$	−37.5862	−	261.418i	−0.0139100	−	0.0967459i
$195$	−752.280	−	1647.26i	−0.276266	−	0.604938i
$196$	3.07810	+	6.74010i	0.00112176	+	0.00245631i
$197$	429.297	+	2985.83i	0.155260	+	1.07986i	0.907223	+	0.420650i	$0.138198\pi$
$197$	429.297	+	2985.83i	0.155260	+	1.07986i	−0.751963	+	0.659205i	$0.770893\pi$
$198$	−1025.21	−	658.865i	−0.367974	−	0.236482i
$199$	−1610.37	+	472.848i	−0.573650	+	0.168439i	−0.555675	−	0.831400i	$-0.687540\pi$
$199$	−1610.37	+	472.848i	−0.573650	+	0.168439i	−0.0179751	+	0.999838i	$0.505722\pi$
$200$	−62.6071	+	435.442i	−0.0221350	+	0.153952i
$201$	−1073.36	+	1238.72i	−0.376661	+	0.434690i
$202$	−218.537	+	140.445i	−0.0761199	+	0.0489193i
$203$	2149.41	+	2480.55i	0.743146	+	0.857636i
$204$	3525.48	+	1035.17i	1.20996	+	0.355278i
$205$	95.4166	−	208.933i	0.0325082	−	0.0711831i
$206$	−1797.41			−0.607919
$207$	1768.80	+	3094.37i	0.593913	+	1.03900i
$208$	−1456.37			−0.485487
$209$	−1129.17	+	2472.54i	−0.373714	+	0.818320i
$210$	−827.099	−	242.858i	−0.271787	−	0.0798039i
$211$	2751.03	+	3174.85i	0.897576	+	1.03586i	0.999158	+	0.0410306i	$0.0130641\pi$
$211$	2751.03	+	3174.85i	0.897576	+	1.03586i	−0.101582	+	0.994827i	$0.532390\pi$
$212$	−1028.84	+	661.194i	−0.333306	+	0.214203i
$213$	4856.86	−	5605.12i	1.56238	−	1.80308i
$214$	123.061	−	855.906i	0.0393096	−	0.273404i
$215$	473.656	−	139.078i	0.150247	−	0.0441165i
$216$	605.696	+	389.257i	0.190798	+	0.122618i
$217$	−276.998	−	1926.57i	−0.0866538	−	0.602690i
$218$	726.768	+	1591.40i	0.225793	+	0.494418i
$219$	−2383.31	−	5218.72i	−0.735385	−	1.61027i
$220$	144.837	+	1007.36i	0.0443860	+	0.308711i
$221$	−2888.63	−	1856.41i	−0.879234	−	0.565049i
$222$	−2493.70	+	732.216i	−0.753901	+	0.221365i
$223$	662.276	−	4606.23i	0.198876	−	1.38321i	−0.608678	−	0.793417i	$-0.708300\pi$
$223$	662.276	−	4606.23i	0.198876	−	1.38321i	0.807554	−	0.589794i	$-0.200791\pi$
$224$	−2158.50	+	2491.04i	−0.643842	+	0.743034i
$225$	679.581	−	436.740i	0.201357	−	0.129404i
$226$	−932.067	−	1075.66i	−0.274337	−	0.316602i
$227$	5571.73	+	1636.01i	1.62911	+	0.478351i	0.963447	−	0.267899i	$-0.0863294\pi$
$227$	5571.73	+	1636.01i	1.62911	+	0.478351i	0.665666	+	0.746250i	$0.268148\pi$
$228$	1824.12	−	3994.26i	0.529847	−	1.16020i
$229$	2827.95			0.816053			0.408026	−	0.912970i	$-0.366217\pi$
$229$	2827.95			0.816053			0.408026	+	0.912970i	$0.366217\pi$
$230$	−221.113	+	630.065i	−0.0633901	+	0.180632i
$231$	−4435.80			−1.26344
$232$	1297.65	−	2841.45i	0.367219	−	0.804098i
$233$	−536.905	−	157.649i	−0.150960	−	0.0443260i	0.205379	−	0.978682i	$-0.434157\pi$
$233$	−536.905	−	157.649i	−0.150960	−	0.0443260i	−0.356340	+	0.934356i	$0.615975\pi$
$234$	−1204.81	−	1390.43i	−0.336586	−	0.388441i
$235$	1836.73	−	1180.39i	0.509851	−	0.327661i
$236$	−889.588	+	1026.64i	−0.245370	+	0.283172i
$237$	−1378.55	+	9588.00i	−0.377832	+	2.62788i
$238$	−1568.29	+	460.491i	−0.427130	+	0.125417i
$239$	−3267.08	−	2099.62i	−0.884224	−	0.568256i	0.0178485	−	0.999841i	$-0.494318\pi$
$239$	−3267.08	−	2099.62i	−0.884224	−	0.568256i	−0.902073	+	0.431584i	$0.857955\pi$
$240$	−169.712	−	1180.38i	−0.0456454	−	0.317471i
$241$	−2392.02	−	5237.78i	−0.639350	−	1.39998i	−0.900574	−	0.434702i	$-0.856854\pi$
$241$	−2392.02	−	5237.78i	−0.639350	−	1.39998i	0.261225	−	0.965278i	$-0.415874\pi$
$242$	181.376	+	397.159i	0.0481790	+	0.105497i
$243$	768.073	+	5342.07i	0.202765	+	1.41026i
$244$	1006.10	+	646.581i	0.263971	+	0.169644i
$245$	5.44030	−	1.59742i	0.00141865	−	0.000416552i
$246$	60.9593	−	423.981i	0.0157993	−	0.109886i
$247$	−2687.26	+	3101.26i	−0.692251	+	0.798900i
$248$	−1558.33	+	1001.48i	−0.399008	+	0.256427i
$249$	4444.86	+	5129.64i	1.13125	+	1.30553i
$250$	145.210	+	42.6374i	0.0367355	+	0.0107865i
$251$	1157.46	−	2534.48i	0.291068	−	0.637349i	−0.706450	−	0.707763i	$-0.749705\pi$
$251$	1157.46	−	2534.48i	0.291068	−	0.637349i	0.997518	+	0.0704133i	$0.0224318\pi$
$252$	3903.84			0.975867
$253$	−178.283	+	3431.44i	−0.0443026	+	0.852699i
$254$	3152.63			0.778793
$255$	1167.99	−	2557.54i	0.286833	−	0.628076i
$256$	1456.64	+	427.707i	0.355624	+	0.104421i
$257$	2611.18	+	3013.46i	0.633778	+	0.731419i	0.978262	−	0.207373i	$-0.0664914\pi$
$257$	2611.18	+	3013.46i	0.633778	+	0.731419i	−0.344483	+	0.938792i	$0.611946\pi$
$258$	774.455	−	497.712i	0.186882	−	0.120102i
$259$	−3374.90	+	3894.84i	−0.809676	+	0.934416i
$260$	−218.657	+	1520.79i	−0.0521558	+	0.362752i
$261$	−5503.73	+	1616.04i	−1.30526	+	0.383258i
$262$	−92.4156	−	59.3919i	−0.0217918	−	0.0140048i
$263$	−200.204	−	1392.45i	−0.0469396	−	0.326472i	−0.999738	−	0.0228699i	$-0.992720\pi$
$263$	−200.204	−	1392.45i	−0.0469396	−	0.326472i	0.952799	−	0.303602i	$-0.0981895\pi$
$264$	1753.72	+	3840.11i	0.408841	+	0.895236i
$265$	388.761	+	851.268i	0.0901185	+	0.197332i
$266$	277.990	+	1933.46i	0.0640776	+	0.445670i
$267$	8892.17	+	5714.65i	2.03817	+	1.30985i
$268$	1334.30	−	391.786i	0.304124	−	0.0892990i
$269$	241.079	−	1676.74i	0.0546427	−	0.380048i	−0.944089	−	0.329692i	$-0.893055\pi$
$269$	241.079	−	1676.74i	0.0546427	−	0.380048i	0.998731	−	0.0503563i	$-0.0160357\pi$
$270$	162.202	−	187.191i	0.0365604	−	0.0421930i
$271$	−6374.07	+	4096.36i	−1.42877	+	0.918215i	−0.428881	+	0.903361i	$0.641092\pi$
$271$	−6374.07	+	4096.36i	−1.42877	+	0.918215i	−0.999890	+	0.0148545i	$0.995271\pi$
$272$	−1480.75	−	1708.87i	−0.330086	−	0.380940i
$273$	−6425.35	−	1886.65i	−1.42447	−	0.418262i
$274$	1049.98	−	2299.13i	0.231501	−	0.506917i
$275$	778.771			0.170770
$276$	288.008	−	5543.32i	0.0628117	−	1.20894i
$277$	95.9776			0.0208185			0.0104093	−	0.999946i	$-0.496687\pi$
$277$	95.9776			0.0208185			0.0104093	+	0.999946i	$0.496687\pi$
$278$	−1228.08	+	2689.13i	−0.264948	+	0.580156i
$279$	3263.74	+	958.319i	0.700340	+	0.205638i
$280$	1065.32	+	1229.45i	0.227375	+	0.262405i
$281$	−1944.93	+	1249.93i	−0.412900	+	0.265355i	−0.730558	−	0.682850i	$-0.760740\pi$
$281$	−1944.93	+	1249.93i	−0.412900	+	0.265355i	0.317658	+	0.948205i	$0.397104\pi$
$282$	2666.34	−	3077.12i	0.563043	−	0.649786i
$283$	306.814	−	2133.94i	0.0644459	−	0.448231i	−0.931893	−	0.362735i	$-0.881843\pi$
$283$	306.814	−	2133.94i	0.0644459	−	0.448231i	0.996338	−	0.0854968i	$-0.0272477\pi$
$284$	−6037.60	+	1772.80i	−1.26150	+	0.370409i
$285$	−2826.69	−	1816.60i	−0.587504	−	0.377566i
$286$	−252.416	−	1755.59i	−0.0521877	−	0.362973i
$287$	−352.843	−	772.619i	−0.0725703	−	0.158907i
$288$	−2392.93	−	5239.80i	−0.489601	−	1.07208i
$289$	−59.5159	−	413.942i	−0.0121140	−	0.0842544i
$290$	−904.028	−	580.984i	−0.183056	−	0.117643i
$291$	1611.95	−	473.310i	0.324722	−	0.0953468i
$292$	−692.730	+	4818.04i	−0.138832	+	0.965598i
$293$	−3181.31	+	3671.43i	−0.634315	+	0.732039i	−0.978359	−	0.206915i	$-0.933658\pi$
$293$	−3181.31	+	3671.43i	−0.634315	+	0.732039i	0.344044	+	0.938954i	$0.388203\pi$
$294$	8.89520	−	5.71660i	0.00176455	−	0.00113401i
$295$	680.722	+	785.595i	0.134350	+	0.155048i
$296$	4706.08	+	1381.83i	0.924106	+	0.271342i
$297$	529.476	−	1159.39i	0.103445	−	0.226514i
$298$	38.7547			0.00753355
$299$	−1717.72	+	4894.69i	−0.332236	+	0.946713i
$300$	−1258.07			−0.242115
$301$	758.336	−	1660.52i	0.145215	−	0.317977i
$302$	1667.04	+	489.486i	0.317639	+	0.0932673i
$303$	−1082.13	−	1248.84i	−0.205170	−	0.236779i
$304$	−2273.28	+	1460.95i	−0.428887	+	0.275629i
$305$	599.299	−	691.627i	0.112511	−	0.129844i
$306$	406.519	−	2827.40i	0.0759448	−	0.528208i
$307$	−283.030	+	83.1051i	−0.0526169	+	0.0154497i	−0.307935	−	0.951407i	$-0.599638\pi$
$307$	−283.030	+	83.1051i	−0.0526169	+	0.0154497i	0.255318	+	0.966857i	$0.417820\pi$
$308$	3166.03	+	2034.68i	0.585718	+	0.376418i
$309$	−1627.15	−	11317.1i	−0.299564	−	2.08351i
$310$	264.725	+	579.667i	0.0485012	+	0.106203i
$311$	−1608.58	−	3522.30i	−0.293293	−	0.642223i	0.704422	−	0.709782i	$-0.251206\pi$
$311$	−1608.58	−	3522.30i	−0.293293	−	0.642223i	−0.997715	+	0.0675585i	$0.978479\pi$
$312$	907.008	+	6308.38i	0.164581	+	1.14468i
$313$	4040.46	+	2596.65i	0.729650	+	0.468918i	0.851982	−	0.523572i	$-0.175401\pi$
$313$	4040.46	+	2596.65i	0.729650	+	0.468918i	−0.122332	+	0.992489i	$0.539037\pi$
$314$	1198.79	−	351.998i	0.215452	−	0.0632623i
$315$	425.130	−	2956.85i	0.0760425	−	0.528887i
$316$	5381.90	−	6211.05i	0.958087	−	1.10569i
$317$	3237.86	−	2080.84i	0.573679	−	0.368681i	−0.221404	−	0.975182i	$-0.571064\pi$
$317$	3237.86	−	2080.84i	0.573679	−	0.368681i	0.795083	+	0.606501i	$0.207427\pi$
$318$	1142.87	+	1318.94i	0.201538	+	0.232587i
$319$	−5305.83	−	1557.93i	−0.931252	−	0.273440i
$320$	−66.2886	+	145.152i	−0.0115801	+	0.0253570i
$321$	5500.46			0.956405
$322$	1225.39	+	2143.73i	0.212076	+	0.371010i
$323$	−6371.17			−1.09753
$324$	1512.81	−	3312.59i	0.259398	−	0.568003i
$325$	1128.07	+	331.231i	0.192535	+	0.0565334i
$326$	−3197.75	−	3690.40i	−0.543272	−	0.626970i
$327$	−9362.04	+	6016.62i	−1.58325	+	1.01749i
$328$	−529.364	+	610.919i	−0.0891135	+	0.102842i
$329$	1149.02	−	7991.59i	0.192545	−	1.33918i
$330$	1393.48	−	409.162i	0.232450	−	0.0682533i
$331$	−73.3444	−	47.1356i	−0.0121794	−	0.00782721i	0.534537	−	0.845145i	$-0.320486\pi$
$331$	−73.3444	−	47.1356i	−0.0121794	−	0.00782721i	−0.546716	+	0.837318i	$0.684122\pi$
$332$	−819.548	−	5700.08i	−0.135478	−	0.942267i
$333$	−3741.45	−	8192.64i	−0.615707	−	1.34821i
$334$	1916.19	+	4195.87i	0.313920	+	0.687388i
$335$	−151.441	−	1053.29i	−0.0246988	−	0.171784i
$336$	−3709.78	−	2384.13i	−0.602337	−	0.387099i
$337$	−281.865	+	82.7632i	−0.0455614	+	0.0133780i	−0.304434	−	0.952533i	$-0.598467\pi$
$337$	−281.865	+	82.7632i	−0.0455614	+	0.0133780i	0.258872	+	0.965912i	$0.416649\pi$
$338$	2.51565	−	17.4968i	0.000404833	−	0.00281567i
$339$	5928.95	−	6842.37i	0.949900	−	1.09624i
$340$	−2006.78	+	1289.68i	−0.320096	+	0.205713i
$341$	2147.43	+	2478.26i	0.341025	+	0.393564i
$342$	−3275.42	−	961.749i	−0.517878	−	0.152063i
$343$	2643.25	−	5787.90i	0.416099	−	0.911129i
$344$	−1737.34			−0.272300
$345$	−4167.26	−	821.814i	−0.650313	−	0.128246i
$346$	−4567.29			−0.709651
$347$	1730.09	−	3788.36i	0.267654	−	0.586080i	−0.727311	−	0.686308i	$-0.759230\pi$
$347$	1730.09	−	3788.36i	0.267654	−	0.586080i	0.994964	+	0.100228i	$0.0319574\pi$
$348$	8571.30	+	2516.76i	1.32032	+	0.387680i
$349$	−184.493	−	212.916i	−0.0282971	−	0.0326566i	0.741425	−	0.671036i	$-0.234150\pi$
$349$	−184.493	−	212.916i	−0.0282971	−	0.0326566i	−0.769722	+	0.638380i	$0.779605\pi$
$350$	470.802	−	302.566i	0.0719013	−	0.0462081i
$351$	1260.07	−	1454.20i	0.191618	−	0.221139i
$352$	790.305	−	5496.69i	0.119669	−	0.832314i
$353$	4285.69	−	1258.39i	0.646187	−	0.189738i	0.0578142	−	0.998327i	$-0.481587\pi$
$353$	4285.69	−	1258.39i	0.646187	−	0.189738i	0.588373	+	0.808590i	$0.299769\pi$
$354$	1630.78	+	1048.04i	0.244845	+	0.157352i
$355$	685.256	+	4766.06i	0.102450	+	0.712553i
$356$	−3725.45	−	8157.59i	−0.554630	−	1.21447i
$357$	−4319.13	−	9457.58i	−0.640316	−	1.40210i
$358$	206.436	+	1435.79i	0.0304762	+	0.211967i
$359$	5639.11	+	3624.04i	0.829028	+	0.532784i	0.884969	−	0.465650i	$-0.154180\pi$
$359$	5639.11	+	3624.04i	0.829028	+	0.532784i	−0.0559412	+	0.998434i	$0.517816\pi$
$360$	−2727.84	+	800.967i	−0.399361	+	0.117263i
$361$	−107.450	+	747.329i	−0.0156655	+	0.108956i
$362$	−1089.12	+	1256.92i	−0.158130	+	0.182492i
$363$	−2336.45	+	1501.54i	−0.337828	+	0.217109i
$364$	3720.66	+	4293.87i	0.535757	+	0.618296i
$365$	3573.85	+	1049.38i	0.512504	+	0.150485i
$366$	708.964	−	1552.41i	0.101252	−	0.221710i
$367$	13801.3			1.96300			0.981499	−	0.191467i	$-0.0613246\pi$
$367$	13801.3			1.96300			0.981499	+	0.191467i	$0.0613246\pi$
$368$	−1993.42	+	2773.99i	−0.282375	+	0.392946i
$369$	1484.38			0.209414
$370$	700.939	−	1534.84i	0.0984867	−	0.215656i
$371$	3320.48	+	974.980i	0.464664	+	0.136438i
$372$	−3469.06	−	4003.51i	−0.483501	−	0.557990i
$373$	−1803.92	+	1159.31i	−0.250412	+	0.160930i	−0.659825	−	0.751419i	$-0.729370\pi$
$373$	−1803.92	+	1159.31i	−0.250412	+	0.160930i	0.409413	+	0.912349i	$0.365733\pi$
$374$	1803.33	−	2081.15i	0.249326	−	0.287738i
$375$	−137.004	+	952.886i	−0.0188663	+	0.131218i
$376$	−7372.65	+	2164.81i	−1.01121	+	0.296918i
$377$	−7022.98	−	4513.40i	−0.959422	−	0.616583i
$378$	−130.351	−	906.615i	−0.0177369	−	0.123363i
$379$	5045.48	+	11048.1i	0.683823	+	1.49736i	0.858541	+	0.512745i	$0.171372\pi$
$379$	5045.48	+	11048.1i	0.683823	+	1.49736i	−0.174717	+	0.984619i	$0.555901\pi$
$380$	1184.26	+	2593.18i	0.159872	+	0.350071i
$381$	2853.99	+	19850.0i	0.383765	+	2.66914i
$382$	2279.04	+	1464.65i	0.305250	+	0.196172i
$383$	−250.350	+	73.5093i	−0.0334002	+	0.00980717i	−0.298390	−	0.954444i	$-0.596450\pi$
$383$	−250.350	+	73.5093i	−0.0334002	+	0.00980717i	0.264990	+	0.964251i	$0.414631\pi$
$384$	−1605.46	+	11166.2i	−0.213355	+	1.48391i
$385$	1885.89	−	2176.44i	0.249647	−	0.288108i
$386$	456.499	−	293.374i	0.0601948	−	0.0386848i
$387$	2089.17	+	2411.03i	0.274415	+	0.316692i
$388$	−1367.62	−	401.570i	−0.178945	−	0.0525429i
$389$	5673.42	−	12423.1i	0.739470	−	1.61921i	−0.0449535	−	0.998989i	$-0.514314\pi$
$389$	5673.42	−	12423.1i	0.739470	−	1.61921i	0.784424	−	0.620225i	$-0.212959\pi$
$390$	2192.51			0.284672
$391$	−7489.78	+	2961.07i	−0.968732	+	0.382987i
$392$	−19.9547			−0.00257108
$393$	290.289	−	635.645i	0.0372599	−	0.0815879i
$394$	−3504.24	−	1028.94i	−0.448073	−	0.131566i
$395$	−4118.28	−	4752.75i	−0.524591	−	0.605410i
$396$	−5533.00	+	3555.84i	−0.702130	+	0.451232i
$397$	526.336	−	607.425i	0.0665392	−	0.0767903i	−0.721504	−	0.692410i	$-0.756549\pi$
$397$	526.336	−	607.425i	0.0665392	−	0.0767903i	0.788043	+	0.615620i	$0.211094\pi$
$398$	289.187	−	2011.34i	0.0364212	−	0.253315i
$399$	−11922.0	+	3500.63i	−1.49586	+	0.439224i
$400$	651.308	+	418.570i	0.0814135	+	0.0523213i
$401$	1636.58	+	11382.7i	0.203808	+	1.41752i	0.792851	+	0.609415i	$0.208596\pi$
$401$	1636.58	+	11382.7i	0.203808	+	1.41752i	−0.589043	+	0.808102i	$0.700495\pi$
$402$	−824.370	−	1805.12i	−0.102278	−	0.223958i
$403$	2056.53	+	4503.17i	0.254201	+	0.556622i
$404$	199.524	+	1387.72i	0.0245710	+	0.170895i
$405$	−2344.28	−	1506.58i	−0.287625	−	0.184845i
$406$	−3812.90	+	1119.57i	−0.466086	+	0.136855i
$407$	1235.67	−	8594.31i	0.150492	−	1.04669i
$408$	−6479.91	+	7478.22i	−0.786283	+	0.907419i
$409$	−5747.84	+	3693.91i	−0.694896	+	0.446583i	−0.839823	−	0.542860i	$-0.817342\pi$
$409$	−5747.84	+	3693.91i	−0.694896	+	0.446583i	0.144927	+	0.989442i	$0.453705\pi$
$410$	182.110	+	210.167i	0.0219361	+	0.0253156i
$411$	15426.6	+	4529.65i	1.85143	+	0.543628i
$412$	−4029.72	+	8823.85i	−0.481869	+	1.05515i
$413$	3843.96			0.457987
$414$	−4297.47	+	391.679i	−0.510167	+	0.0464975i
$415$	−4406.61			−0.521234
$416$	3482.65	−	7625.94i	0.410459	−	0.898781i
$417$	−18043.4	−	5298.02i	−2.11892	−	0.622171i
$418$	−2155.11	−	2487.13i	−0.252177	−	0.291028i
$419$	1476.61	−	948.957i	0.172164	−	0.110643i	−0.451721	−	0.892159i	$-0.649190\pi$
$419$	1476.61	−	948.957i	0.172164	−	0.110643i	0.623885	+	0.781516i	$0.285553\pi$
$420$	−3046.57	+	3515.92i	−0.353946	+	0.408475i
$421$	1457.13	−	10134.6i	0.168684	−	1.17323i	−0.712923	−	0.701242i	$-0.752629\pi$
$421$	1457.13	−	10134.6i	0.168684	−	1.17323i	0.881607	−	0.471984i	$-0.156462\pi$
$422$	−4880.13	+	1432.94i	−0.562941	+	0.165294i
$423$	11870.0	+	7628.36i	1.36439	+	0.876840i
$424$	−468.721	−	3260.03i	−0.0536866	−	0.373398i
$425$	758.289	+	1660.42i	0.0865468	+	0.189511i
$426$	3730.21	+	8168.01i	0.424247	+	0.928970i
$427$	−481.618	−	3349.72i	−0.0545834	−	0.379636i
$428$	−3925.92	−	2523.04i	−0.443380	−	0.284943i
$429$	10825.3	−	3178.59i	1.21830	−	0.357724i
$430$	−85.0581	+	591.592i	−0.00953922	+	0.0663467i
$431$	8788.44	−	10142.4i	0.982191	−	1.13351i	−0.00885120	−	0.999961i	$-0.502817\pi$
$431$	8788.44	−	10142.4i	0.982191	−	1.13351i	0.991042	−	0.133548i	$-0.0426371\pi$
$432$	1065.96	−	685.050i	0.118718	−	0.0762951i
$433$	5031.12	+	5806.23i	0.558384	+	0.644410i	0.962816	−	0.270159i	$-0.0870761\pi$
$433$	5031.12	+	5806.23i	0.558384	+	0.644410i	−0.404432	+	0.914568i	$0.632531\pi$
$434$	2261.06	+	663.908i	0.250079	+	0.0734300i
$435$	2839.67	−	6218.01i	0.312992	−	0.685358i
$436$	9441.89			1.03712
$437$	2228.84	+	9363.33i	0.243981	+	1.02496i
$438$	6946.12			0.757759
$439$	−2924.72	+	6404.23i	−0.317970	+	0.696258i	−0.999364	−	0.0356590i	$-0.988647\pi$
$439$	−2924.72	+	6404.23i	−0.317970	+	0.696258i	0.681394	+	0.731917i	$0.261374\pi$
$440$	−2629.76	−	772.166i	−0.284929	−	0.0836626i
$441$	23.9957	+	27.6926i	0.00259105	+	0.00299023i
$442$	3497.33	−	2247.60i	0.376360	−	0.241872i
$443$	6259.27	−	7223.58i	0.671302	−	0.774724i	−0.313277	−	0.949662i	$-0.601427\pi$
$443$	6259.27	−	7223.58i	0.671302	−	0.774724i	0.984580	+	0.174938i	$0.0559724\pi$
$444$	−1996.17	+	13883.7i	−0.213365	+	1.48399i
$445$	−6584.44	+	1933.36i	−0.701421	+	0.205956i
$446$	4739.79	+	3046.08i	0.503219	+	0.323399i
$447$	35.0836	+	244.012i	0.00371230	+	0.0258196i
$448$	245.130	+	536.760i	0.0258511	+	0.0566061i
$449$	−1475.39	−	3230.65i	−0.155073	−	0.339563i	0.816110	−	0.577896i	$-0.196126\pi$
$449$	−1475.39	−	3230.65i	−0.155073	−	0.339563i	−0.971183	+	0.238333i	$0.923399\pi$
$450$	139.190	+	968.088i	0.0145811	+	0.101414i
$451$	1203.84	+	773.661i	0.125691	+	0.0807767i
$452$	−7370.31	+	2164.12i	−0.766970	+	0.225203i
$453$	−1572.84	+	10939.3i	−0.163131	+	1.13460i
$454$	−4604.06	+	5313.37i	−0.475945	+	0.549270i
$455$	3657.45	−	2350.50i	0.376844	−	0.242183i
$456$	7743.97	+	8937.01i	0.795273	+	0.917794i
$457$	−16098.5	−	4726.96i	−1.64783	−	0.483846i	−0.679532	−	0.733646i	$-0.737817\pi$
$457$	−16098.5	−	4726.96i	−1.64783	−	0.483846i	−0.968297	+	0.249800i	$0.919635\pi$
$458$	−1422.32	+	3114.45i	−0.145111	+	0.317748i
$459$	2987.49			0.303800
$460$	2597.40	+	2498.07i	0.263270	+	0.253202i
$461$	−10881.1			−1.09932			−0.549659	−	0.835389i	$-0.685242\pi$
$461$	−10881.1			−1.09932			−0.549659	+	0.835389i	$0.685242\pi$
$462$	2230.99	−	4885.19i	0.224665	−	0.491947i
$463$	−4001.86	−	1175.05i	−0.401690	−	0.117947i	0.0746463	−	0.997210i	$-0.476217\pi$
$463$	−4001.86	−	1175.05i	−0.401690	−	0.117947i	−0.476336	+	0.879263i	$0.658035\pi$
$464$	−3600.06	−	4154.69i	−0.360191	−	0.415683i
$465$	−3410.12	+	2191.55i	−0.340087	+	0.218561i
$466$	443.658	−	512.008i	0.0441031	−	0.0508977i
$467$	1741.48	−	12112.2i	0.172561	−	1.20019i	−0.700888	−	0.713271i	$-0.747213\pi$
$467$	1741.48	−	12112.2i	0.172561	−	1.20019i	0.873449	−	0.486916i	$-0.161878\pi$
$468$	−9527.06	+	2797.40i	−0.941001	+	0.276303i
$469$	−3310.37	−	2127.45i	−0.325925	−	0.209459i
$470$	376.194	+	2616.49i	0.0369203	+	0.256786i
$471$	3301.53	+	7229.34i	0.322986	+	0.707241i
$472$	−1519.73	−	3327.74i	−0.148202	−	0.324517i
$473$	437.695	+	3044.24i	0.0425481	+	0.295928i
$474$	−9866.02	−	6340.51i	−0.956037	−	0.614407i
$475$	2093.09	−	614.588i	0.202185	−	0.0593668i
$476$	−1255.39	+	8731.46i	−0.120884	+	0.840768i
$477$	−3960.53	+	4570.70i	−0.380168	+	0.438738i
$478$	3955.51	−	2542.05i	0.378496	−	0.243245i
$479$	1129.41	+	1303.41i	0.107733	+	0.124331i	0.807055	−	0.590476i	$-0.201060\pi$
$479$	1129.41	+	1303.41i	0.107733	+	0.124331i	−0.699322	+	0.714807i	$0.746515\pi$
$480$	6586.59	+	1934.00i	0.626323	+	0.183905i
$481$	5445.27	−	11923.5i	0.516181	−	1.13028i
$482$	6971.49			0.658802
$483$	−12388.3	+	9656.14i	−1.16705	+	0.909668i
$484$	2356.38			0.221297
$485$	−453.093	+	992.134i	−0.0424204	+	0.0928876i
$486$	−6269.57	−	1840.91i	−0.585172	−	0.171822i
$487$	−7435.62	−	8581.16i	−0.691869	−	0.798459i	0.295761	−	0.955262i	$-0.404427\pi$
$487$	−7435.62	−	8581.16i	−0.691869	−	0.798459i	−0.987630	+	0.156803i	$0.949881\pi$
$488$	−2709.47	+	1741.27i	−0.251336	+	0.161524i
$489$	20341.1	−	23474.9i	1.88110	−	2.17090i
$490$	−0.976956	+	6.79488i	−9.00702e−5	+	0.000626452i
$491$	16428.2	−	4823.76i	1.50997	−	0.443367i	0.581118	−	0.813819i	$-0.302615\pi$
$491$	16428.2	−	4823.76i	1.50997	−	0.443367i	0.928852	+	0.370452i	$0.120797\pi$
$492$	−1944.74	−	1249.81i	−0.178203	−	0.114524i
$493$	−1844.61	−	12829.5i	−0.168513	−	1.17203i
$494$	−2063.89	−	4519.28i	−0.187973	−	0.411604i
$495$	2090.72	+	4578.04i	0.189840	+	0.415692i
$496$	463.948	+	3226.83i	0.0419997	+	0.292114i
$497$	14979.2	+	9626.52i	1.35193	+	0.868830i
$498$	−7884.87	+	2315.21i	−0.709497	+	0.208327i
$499$	−621.956	+	4325.80i	−0.0557968	+	0.388075i	0.942718	+	0.333591i	$0.108260\pi$
$499$	−621.956	+	4325.80i	−0.0557968	+	0.388075i	−0.998515	+	0.0544839i	$0.982649\pi$
$500$	534.870	−	617.273i	0.0478403	−	0.0552106i
$501$	−24683.9	+	15863.4i	−2.20118	+	1.41462i
$502$	2209.10	+	2549.44i	0.196408	+	0.226667i
$503$	12020.9	+	3529.65i	1.06558	+	0.312882i	0.767095	−	0.641533i	$-0.221701\pi$
$503$	12020.9	+	3529.65i	1.06558	+	0.312882i	0.298482	+	0.954415i	$0.403520\pi$
$504$	−4367.35	+	9563.16i	−0.385986	+	0.845192i
$505$	1072.81			0.0945339
$506$	−3689.41	−	1922.19i	−0.324139	−	0.168877i
$507$	112.443			0.00984961
$508$	7068.06	−	15476.9i	0.617312	−	1.35173i
$509$	−13516.8	−	3968.90i	−1.17706	−	0.345616i	−0.366020	−	0.930607i	$-0.619280\pi$
$509$	−13516.8	−	3968.90i	−1.17706	−	0.345616i	−0.811040	+	0.584991i	$0.801098\pi$
$510$	2229.20	+	2572.64i	0.193550	+	0.223369i
$511$	11587.2	−	7446.65i	1.00311	−	0.644659i
$512$	6470.20	−	7467.01i	0.558486	−	0.644528i
$513$	508.102	−	3533.93i	0.0437296	−	0.304146i
$514$	−4632.06	+	1360.09i	−0.397493	+	0.116714i
$515$	6244.53	+	4013.12i	0.534305	+	0.343377i
$516$	−707.075	−	4917.81i	−0.0603241	−	0.419563i
$517$	5650.68	+	12373.3i	0.480689	+	1.05256i
$518$	−2592.02	−	5675.73i	−0.219859	−	0.481423i
$519$	−4134.65	−	28757.2i	−0.349694	−	2.43217i
$520$	−3480.84	−	2237.00i	−0.293548	−	0.188652i
$521$	1329.63	−	390.415i	0.111808	−	0.0328299i	−0.225350	−	0.974278i	$-0.572352\pi$
$521$	1329.63	−	390.415i	0.111808	−	0.0328299i	0.337158	+	0.941448i	$0.390534\pi$
$522$	988.347	−	6874.10i	0.0828712	−	0.576382i
$523$	897.678	−	1035.98i	0.0750530	−	0.0866157i	−0.716981	−	0.697092i	$-0.754477\pi$
$523$	897.678	−	1035.98i	0.0750530	−	0.0866157i	0.792034	+	0.610477i	$0.209022\pi$
$524$	−498.760	+	320.533i	−0.0415809	+	0.0267224i
$525$	2331.26	+	2690.42i	0.193799	+	0.223656i
$526$	1634.21	+	479.848i	0.135466	+	0.0397764i
$527$	−3192.96	+	6991.61i	−0.263923	+	0.577912i
$528$	7429.57			0.612368
$529$	6971.87	+	9971.40i	0.573015	+	0.819545i
$530$	−1133.04			−0.0928604
$531$	−2790.66	+	6110.69i	−0.228068	+	0.499400i
$532$	10115.0	+	2970.03i	0.824325	+	0.242044i
$533$	1414.73	+	1632.69i	0.114970	+	0.132682i
$534$	−10765.9	+	6918.84i	−0.872448	+	0.560688i
$535$	−2338.54	+	2698.82i	−0.188979	+	0.218093i
$536$	−532.974	+	3706.91i	−0.0429496	+	0.298721i
$537$	−8853.34	+	2599.58i	−0.711452	+	0.208901i
$538$	1725.36	+	1108.82i	0.138263	+	0.0888565i
$539$	5.02726	+	34.9654i	0.000401743	+	0.00279418i
$540$	−555.310	−	1215.96i	−0.0442533	−	0.0969011i
$541$	6971.40	+	15265.2i	0.554019	+	1.21313i	0.954880	+	0.296993i	$0.0959837\pi$
$541$	6971.40	+	15265.2i	0.554019	+	1.21313i	−0.400861	+	0.916139i	$0.631289\pi$
$542$	−1305.52	−	9080.09i	−0.103463	−	0.719600i
$543$	−8899.91	−	5719.62i	−0.703373	−	0.452030i
$544$	12489.0	−	3667.11i	0.984307	−	0.289019i
$545$	1028.23	−	7151.49i	0.0808156	−	0.562085i
$546$	5309.43	−	6127.41i	0.416159	−	0.480273i
$547$	12152.6	−	7810.01i	0.949923	−	0.610479i	0.0287315	−	0.999587i	$-0.490853\pi$
$547$	12152.6	−	7810.01i	0.949923	−	0.610479i	0.921192	+	0.389108i	$0.127217\pi$
$548$	−8932.88	−	10309.1i	−0.696339	−	0.803618i
$549$	5674.66	+	1666.23i	0.441145	+	0.129532i
$550$	−391.684	+	857.669i	−0.0303663	+	0.0664929i
$551$	−15489.9			−1.19763
$552$	13257.2	+	6907.02i	1.02222	+	0.532577i
$553$	−23255.5			−1.78829
$554$	−48.2721	+	105.701i	−0.00370196	+	0.00810615i
$555$	10298.4	+	3023.88i	0.787645	+	0.231273i
$556$	10448.2	+	12057.9i	0.796946	+	0.919724i
$557$	6689.92	−	4299.35i	0.508906	−	0.327054i	−0.260864	−	0.965376i	$-0.584007\pi$
$557$	6689.92	−	4299.35i	0.508906	−	0.327054i	0.769770	+	0.638321i	$0.220371\pi$
$558$	−2696.91	+	3112.40i	−0.204604	+	0.236126i
$559$	−660.777	+	4595.81i	−0.0499962	+	0.347731i
$560$	2747.00	−	806.593i	0.207289	−	0.0608657i
$561$	14736.1	+	9470.33i	1.10902	+	0.712723i
$562$	−398.356	−	2770.63i	−0.0298997	−	0.207957i
$563$	−4978.03	−	10900.4i	−0.372645	−	0.815978i	−0.999326	−	0.0367026i	$-0.988315\pi$
$563$	−4978.03	−	10900.4i	−0.372645	−	0.815978i	0.626682	−	0.779275i	$-0.284413\pi$
$564$	−9128.39	−	19988.4i	−0.681515	−	1.49231i
$565$	836.517	+	5818.10i	0.0622877	+	0.433220i
$566$	2195.81	+	1411.16i	0.163069	+	0.104798i
$567$	−9887.40	+	2903.20i	−0.732331	+	0.215032i
$568$	2411.66	−	16773.5i	0.178153	−	1.23908i
$569$	6280.45	−	7248.02i	0.462724	−	0.534012i	−0.475649	−	0.879635i	$-0.657787\pi$
$569$	6280.45	−	7248.02i	0.462724	−	0.534012i	0.938374	+	0.345623i	$0.112332\pi$
$570$	3422.33	−	2199.40i	0.251483	−	0.161619i
$571$	−11727.6	−	13534.3i	−0.859515	−	0.991933i	−0.999998	−	0.00185038i	$-0.999411\pi$
$571$	−11727.6	−	13534.3i	−0.859515	−	0.991933i	0.140483	−	0.990083i	$-0.455134\pi$
$572$	−9184.48	−	2696.81i	−0.671368	−	0.197131i
$573$	−7158.74	+	15675.5i	−0.521921	+	1.14285i
$574$	1028.36			0.0747783
$575$	2174.95	−	1695.28i	0.157742	−	0.122953i
$576$	−1031.24			−0.0745979
$577$	−9027.13	+	19766.7i	−0.651307	+	1.42616i	0.239098	+	0.970995i	$0.423148\pi$
$577$	−9027.13	+	19766.7i	−0.651307	+	1.42616i	−0.890405	+	0.455169i	$0.849579\pi$
$578$	485.812	+	142.647i	0.0349604	+	0.0102653i
$579$	2260.44	+	2608.68i	0.162246	+	0.187242i
$580$	−4878.97	+	3135.52i	−0.349290	+	0.224475i
$581$	−10671.2	+	12315.2i	−0.761987	+	0.879380i
$582$	−289.469	+	2013.30i	−0.0206167	+	0.143392i
$583$	−5594.26	+	1642.62i	−0.397411	+	0.116690i
$584$	−11027.7	−	7087.07i	−0.781386	−	0.502166i
$585$	1081.30	+	7520.63i	0.0764212	+	0.531521i
$586$	−2443.34	−	5350.17i	−0.172241	−	0.377156i
$587$	−2789.57	−	6108.30i	−0.196146	−	0.429500i	0.785846	−	0.618422i	$-0.212228\pi$
$587$	−2789.57	−	6108.30i	−0.196146	−	0.429500i	−0.981992	+	0.188922i	$0.939501\pi$
$588$	−8.12129	−	56.4848i	−0.000569586	−	0.00396155i
$589$	7727.39	+	4966.09i	0.540580	+	0.347410i
$590$	−1207.55	+	354.569i	−0.0842613	+	0.0247413i
$591$	3306.22	−	22995.3i	0.230118	−	1.60051i
$592$	5652.66	−	6523.51i	0.392437	−	0.452897i
$593$	10040.3	−	6452.49i	0.695286	−	0.446833i	−0.144676	−	0.989479i	$-0.546214\pi$
$593$	10040.3	−	6452.49i	0.695286	−	0.446833i	0.839961	+	0.542646i	$0.182578\pi$
$594$	1010.55	+	1166.23i	0.0698035	+	0.0805575i
$595$	6476.68	+	1901.72i	0.446248	+	0.131030i
$596$	86.8864	−	190.255i	0.00597149	−	0.0130757i
$597$	12925.8			0.886130
$598$	−4526.64	−	4353.53i	−0.309545	−	0.297708i
$599$	−8192.86			−0.558850			−0.279425	−	0.960168i	$-0.590144\pi$
$599$	−8192.86			−0.558850			−0.279425	+	0.960168i	$0.590144\pi$
$600$	1407.44	−	3081.86i	0.0957642	−	0.209694i
$601$	−24080.9	−	7070.79i	−1.63441	−	0.479906i	−0.669571	−	0.742748i	$-0.733522\pi$
$601$	−24080.9	−	7070.79i	−1.63441	−	0.479906i	−0.964839	+	0.262842i	$0.915340\pi$
$602$	1447.35	+	1670.33i	0.0979890	+	0.113085i
$603$	5785.26	−	3717.96i	0.390703	−	0.251090i
$604$	6140.41	−	7086.42i	0.413659	−	0.477388i
$605$	256.611	−	1784.77i	0.0172442	−	0.119936i
$606$	1919.62	−	563.650i	0.128678	−	0.0377834i
$607$	−18608.4	−	11958.9i	−1.24430	−	0.799663i	−0.258245	−	0.966079i	$-0.583144\pi$
$607$	−18608.4	−	11958.9i	−1.24430	−	0.799663i	−0.986056	+	0.166416i	$0.946780\pi$
$608$	−2213.77	−	15397.1i	−0.147665	−	1.02703i
$609$	−10500.9	−	22993.7i	−0.698714	−	1.52997i
$610$	460.278	+	1007.87i	0.0305510	+	0.0668974i
$611$	2922.48	+	20326.3i	0.193504	+	1.34585i
$612$	−12968.9	−	8334.60i	−0.856595	−	0.550500i
$613$	19054.5	−	5594.90i	1.25547	−	0.368639i	0.414663	−	0.909975i	$-0.363899\pi$
$613$	19054.5	−	5594.90i	1.25547	−	0.368639i	0.840807	+	0.541336i	$0.182081\pi$
$614$	50.8259	−	353.502i	0.00334066	−	0.0232348i
$615$	−1158.42	+	1336.88i	−0.0759543	+	0.0876559i
$616$	−8526.26	+	5479.49i	−0.557683	+	0.358401i
$617$	−15753.7	−	18180.7i	−1.02791	−	1.18627i	−0.982301	−	0.187309i	$-0.940023\pi$
$617$	−15753.7	−	18180.7i	−1.02791	−	1.18627i	−0.0456068	−	0.998959i	$-0.514522\pi$
$618$	13282.0	+	3899.94i	0.864530	+	0.253849i
$619$	−2971.55	+	6506.78i	−0.192951	+	0.422504i	−0.981237	−	0.192805i	$-0.938241\pi$
$619$	−2971.55	+	6506.78i	−0.192951	+	0.422504i	0.788286	+	0.615309i	$0.210969\pi$
$620$	3439.21			0.222777
$621$	−1045.12	−	4390.54i	−0.0675350	−	0.283714i
$622$	4688.18			0.302217
$623$	−10541.9	+	23083.4i	−0.677930	+	1.48446i
$624$	10761.9	+	3159.98i	0.690418	+	0.202725i
$625$	−409.288	−	472.343i	−0.0261944	−	0.0302300i
$626$	−4891.87	+	3143.81i	−0.312330	+	0.200722i
$627$	13708.8	−	15820.8i	0.873169	−	1.00769i
$628$	959.619	−	6674.29i	0.0609760	−	0.424098i
$629$	19527.1	−	5733.68i	1.23783	−	0.363461i
$630$	3042.58	+	1955.35i	0.192412	+	0.123656i
$631$	3144.80	+	21872.5i	0.198403	+	1.37992i	0.808919	+	0.587920i	$0.200053\pi$
$631$	3144.80	+	21872.5i	0.198403	+	1.37992i	−0.610516	+	0.792004i	$0.709038\pi$
$632$	9194.18	+	20132.4i	0.578679	+	1.26713i
$633$	−13440.1	−	29429.7i	−0.843911	−	1.84791i
$634$	663.170	+	4612.45i	0.0415423	+	0.288933i
$635$	−10952.8	−	7038.94i	−0.684487	−	0.439893i
$636$	9037.24	−	2653.57i	0.563443	−	0.165442i
$637$	−7.58953	+	52.7863i	−0.000472069	+	0.00328331i
$638$	4384.34	−	5059.80i	0.272065	−	0.313980i
$639$	−26177.8	+	16823.5i	−1.62062	+	1.04151i
$640$	−4796.16	−	5535.06i	−0.296226	−	0.341863i
$641$	18661.4	+	5479.47i	1.14989	+	0.337638i	0.800496	−	0.599338i	$-0.204569\pi$
$641$	18661.4	+	5479.47i	1.14989	+	0.337638i	0.349394	+	0.936976i	$0.386388\pi$
$642$	−2766.47	+	6057.72i	−0.170068	+	0.372397i
$643$	−2762.60			−0.169434			−0.0847171	−	0.996405i	$-0.526999\pi$
$643$	−2762.60			−0.169434			−0.0847171	+	0.996405i	$0.526999\pi$
$644$	13271.3	−	1209.57i	0.812052	−	0.0740118i
$645$	−3801.86			−0.232090
$646$	3204.39	−	7016.63i	0.195163	−	0.427346i
$647$	18183.7	+	5339.23i	1.10491	+	0.324431i	0.782801	−	0.622272i	$-0.213790\pi$
$647$	18183.7	+	5339.23i	1.10491	+	0.324431i	0.322109	+	0.946703i	$0.395608\pi$
$648$	6422.37	+	7411.81i	0.389343	+	0.449326i
$649$	−5448.13	+	3501.30i	−0.329519	+	0.211769i
$650$	−932.151	+	1075.76i	−0.0562492	+	0.0649150i
$651$	−2133.30	+	14837.4i	−0.128434	+	0.893278i
$652$	−25286.1	+	7424.68i	−1.51884	+	0.445971i
$653$	3754.63	+	2412.95i	0.225007	+	0.144603i	0.648288	−	0.761395i	$-0.275485\pi$
$653$	3754.63	+	2412.95i	0.225007	+	0.144603i	−0.423281	+	0.905999i	$0.639122\pi$
$654$	−1917.51	−	13336.6i	−0.114649	−	0.797403i
$655$	188.463	+	412.677i	0.0112426	+	0.0246178i
$656$	590.981	+	1294.07i	0.0351737	+	0.0770196i
$657$	3425.69	+	23826.2i	0.203423	+	1.41484i
$658$	8223.31	+	5284.80i	0.487201	+	0.313105i
$659$	−27192.0	+	7984.28i	−1.60736	+	0.471963i	−0.957581	−	0.288163i	$-0.906955\pi$
$659$	−27192.0	+	7984.28i	−1.60736	+	0.471963i	−0.649776	+	0.760126i	$0.725137\pi$
$660$	1115.46	−	7758.19i	0.0657867	−	0.457556i
$661$	13355.3	−	15412.8i	0.785870	−	0.906943i	−0.211648	−	0.977346i	$-0.567883\pi$
$661$	13355.3	−	15412.8i	0.785870	−	0.906943i	0.997519	+	0.0704032i	$0.0224286\pi$
$662$	88.7995	−	57.0680i	0.00521343	−	0.00335047i
$663$	17317.6	+	19985.6i	1.01442	+	1.17070i
$664$	14880.3	+	4369.24i	0.869677	+	0.255360i
$665$	3351.10	−	7337.88i	0.195413	−	0.427896i
$666$	10904.4			0.634440
$667$	−18209.5	+	7199.09i	−1.05708	+	0.417916i
$668$	24894.4			1.44191
$669$	−14888.3	+	32600.8i	−0.860411	+	1.88404i
$670$	1236.17	+	362.972i	0.0712796	+	0.0209296i
$671$	3733.73	+	4308.96i	0.214812	+	0.247907i
$672$	21355.2	−	13724.2i	1.22588	−	0.787828i
$673$	−5419.43	+	6254.35i	−0.310406	+	0.358228i	−0.889421	−	0.457089i	$-0.848892\pi$
$673$	−5419.43	+	6254.35i	−0.310406	+	0.358228i	0.579014	+	0.815317i	$0.303437\pi$
$674$	50.6167	−	352.047i	0.00289271	−	0.0201192i
$675$	−981.467	+	288.185i	−0.0559655	+	0.0164329i
$676$	−80.2552	−	51.5769i	−0.00456618	−	0.00293451i
$677$	−1519.02	−	10565.0i	−0.0862341	−	0.599771i	−0.986417	−	0.164260i	$-0.947477\pi$
$677$	−1519.02	−	10565.0i	−0.0862341	−	0.599771i	0.900183	−	0.435512i	$-0.143433\pi$
$678$	4553.60	+	9970.99i	0.257935	+	0.564798i
$679$	1675.50	+	3668.84i	0.0946979	+	0.207359i
$680$	−914.253	−	6358.77i	−0.0515588	−	0.358599i
$681$	−37622.6	−	24178.6i	−2.11704	−	1.36054i
$682$	−3809.38	+	1118.54i	−0.213884	+	0.0628020i
$683$	−4825.24	+	33560.3i	−0.270326	+	1.88016i	0.174669	+	0.984627i	$0.444114\pi$
$683$	−4825.24	+	33560.3i	−0.270326	+	1.88016i	−0.444996	+	0.895533i	$0.646795\pi$
$684$	−12064.8	+	13923.5i	−0.674427	+	0.778331i
$685$	−8781.12	+	5643.29i	−0.489795	+	0.314772i
$686$	5044.85	+	5822.07i	0.280777	+	0.324034i
$687$	−20897.2	−	6135.96i	−1.16052	−	0.340759i
$688$	−1270.15	+	2781.23i	−0.0703835	+	0.154118i
$689$	−8802.05			−0.486693
$690$	3001.00	−	4176.11i	0.165574	−	0.230409i
$691$	−16308.8			−0.897853			−0.448927	−	0.893569i	$-0.648194\pi$
$691$	−16308.8			−0.897853			−0.448927	+	0.893569i	$0.648194\pi$
$692$	−10239.7	+	22421.8i	−0.562506	+	1.23172i
$693$	17857.2	+	5243.35i	0.978845	+	0.287415i
$694$	3302.01	+	3810.72i	0.180609	+	0.208434i
$695$	10270.7	−	6600.57i	0.560560	−	0.360250i
$696$	−15754.3	+	18181.4i	−0.857994	+	0.990178i
$697$	−477.347	+	3320.02i	−0.0259409	+	0.180423i
$698$	327.278	−	96.0974i	0.0177473	−	0.00521109i
$699$	3625.40	+	2329.90i	0.196174	+	0.126073i
$700$	−429.841	−	2989.61i	−0.0232092	−	0.161424i
$701$	7126.20	+	15604.2i	0.383956	+	0.840746i	0.998648	+	0.0519789i	$0.0165529\pi$
$701$	7126.20	+	15604.2i	0.383956	+	0.840746i	−0.614692	+	0.788767i	$0.710720\pi$
$702$	967.773	+	2119.13i	0.0520317	+	0.113933i
$703$	−3461.31	−	24074.0i	−0.185698	−	1.29156i
$704$	−836.341	−	537.484i	−0.0447738	−	0.0287744i
$705$	−16133.7	+	4737.28i	−0.861887	+	0.253073i
$706$	−769.613	+	5352.78i	−0.0410266	+	0.285346i
$707$	2597.96	−	2998.20i	0.138198	−	0.159489i
$708$	8801.18	−	5656.18i	0.467187	−	0.300243i
$709$	20736.9	+	23931.6i	1.09843	+	1.26766i	0.960820	+	0.277175i	$0.0893981\pi$
$709$	20736.9	+	23931.6i	1.09843	+	1.26766i	0.137615	+	0.990486i	$0.456056\pi$
$710$	−5593.56	−	1642.42i	−0.295666	−	0.0868152i
$711$	16883.2	−	36968.9i	0.890531	−	1.94999i
$712$	24151.3			1.27122
$713$	11392.2	+	2246.62i	0.598373	+	0.118003i
$714$	12588.0			0.659798
$715$	−3042.81	+	6662.83i	−0.159154	+	0.348498i
$716$	7511.43	+	2205.56i	0.392061	+	0.115119i
$717$	19586.4	+	22603.9i	1.02018	+	1.17735i
$718$	−6827.38	+	4387.69i	−0.354869	+	0.228060i
$719$	5224.11	−	6028.94i	0.270969	−	0.312714i	−0.603914	−	0.797050i	$-0.706393\pi$
$719$	5224.11	−	6028.94i	0.270969	−	0.312714i	0.874883	+	0.484335i	$0.160938\pi$
$720$	−712.055	+	4952.45i	−0.0368566	+	0.256343i
$721$	26337.4	−	7733.35i	1.36041	−	0.399452i
$722$	−768.999	−	494.206i	−0.0396388	−	0.0254743i
$723$	6311.11	+	43894.8i	0.324637	+	2.25790i
$724$	3728.69	+	8164.69i	0.191403	+	0.419114i
$725$	1843.59	+	4036.89i	0.0944401	+	0.206795i
$726$	−478.545	−	3328.35i	−0.0244635	−	0.170147i
$727$	20464.7	+	13151.9i	1.04401	+	0.670943i	0.945975	−	0.324240i	$-0.105108\pi$
$727$	20464.7	+	13151.9i	1.04401	+	0.670943i	0.0980332	+	0.995183i	$0.468745\pi$
$728$	−14681.0	+	4310.74i	−0.747411	+	0.219460i
$729$	3773.76	−	26247.1i	0.191727	−	1.33349i
$730$	−2953.16	+	3408.13i	−0.149728	+	0.172795i
$731$	−6064.44	+	3897.38i	−0.306842	+	0.197195i
$732$	−6031.66	−	6960.91i	−0.304558	−	0.351479i
$733$	−11281.6	−	3312.57i	−0.568479	−	0.166920i	−0.0151527	−	0.999885i	$-0.504823\pi$
$733$	−11281.6	−	3312.57i	−0.568479	−	0.166920i	−0.553326	+	0.832965i	$0.686642\pi$
$734$	−6941.37	+	15199.5i	−0.349061	+	0.764336i
$735$	−43.6672			−0.00219141
$736$	−9758.40	−	17071.5i	−0.488722	−	0.854979i
$737$	6629.67			0.331353
$738$	−746.572	+	1634.77i	−0.0372381	+	0.0815400i
$739$	10048.6	+	2950.53i	0.500193	+	0.146870i	0.522090	−	0.852890i	$-0.325152\pi$
$739$	10048.6	+	2950.53i	0.500193	+	0.146870i	−0.0218970	+	0.999760i	$0.506971\pi$
$740$	−5963.38	−	6882.11i	−0.296241	−	0.341880i
$741$	26586.5	−	17086.1i	1.31806	−	0.847063i
$742$	−2743.79	+	3166.51i	−0.135752	+	0.156666i
$743$	1931.66	−	13435.0i	0.0953776	−	0.663366i	−0.884906	−	0.465770i	$-0.845777\pi$
$743$	1931.66	−	13435.0i	0.0953776	−	0.663366i	0.980284	−	0.197596i	$-0.0633134\pi$
$744$	13688.3	−	4019.24i	0.674511	−	0.198054i
$745$	−134.641	−	86.5284i	−0.00662129	−	0.00425524i
$746$	−369.475	−	2569.76i	−0.0181333	−	0.126120i
$747$	−11830.2	−	25904.5i	−0.579442	−	1.26880i
$748$	−6173.82	−	13518.8i	−0.301788	−	0.660823i
$749$	1879.33	+	13071.0i	0.0916813	+	0.637657i
$750$	−980.516	−	630.139i	−0.0477378	−	0.0306793i
$751$	−25627.2	+	7524.81i	−1.24520	+	0.365625i	−0.836968	−	0.547252i	$-0.815674\pi$
$751$	−25627.2	+	7524.81i	−1.24520	+	0.365625i	−0.408236	+	0.912876i	$0.633856\pi$
$752$	−1924.50	+	13385.2i	−0.0933236	+	0.649080i
$753$	−14052.2	+	16217.1i	−0.680069	+	0.784842i
$754$	8502.87	−	5464.46i	0.410685	−	0.263931i
$755$	−4698.70	−	5422.59i	−0.226495	−	0.261389i
$756$	−4743.00	−	1392.67i	−0.228176	−	0.0669986i
$757$	2057.17	−	4504.58i	0.0987704	−	0.216277i	−0.853796	−	0.520608i	$-0.825705\pi$
$757$	2057.17	−	4504.58i	0.0987704	−	0.216277i	0.952566	+	0.304331i	$0.0984328\pi$
$758$	−14705.0			−0.704629
$759$	8762.82	−	24969.8i	0.419065	−	1.19413i
$760$	−7677.33			−0.366429
$761$	8408.04	−	18411.0i	0.400514	−	0.877003i	−0.596704	−	0.802462i	$-0.703523\pi$
$761$	8408.04	−	18411.0i	0.400514	−	0.877003i	0.997218	−	0.0745419i	$-0.0237494\pi$
$762$	−23296.4	−	6840.43i	−1.10753	−	0.325200i
$763$	−17496.3	−	20191.8i	−0.830156	−	0.958051i
$764$	12299.8	−	7904.58i	0.582448	−	0.374316i
$765$	−7725.12

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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	115.g (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.502951 + 1.10131i) q^{2} +(-7.38951 - 2.16976i) q^{3} +(4.27896 + 4.93819i) q^{4} +(4.20627 - 2.70320i) q^{5} +(6.10614 - 7.04686i) q^{6} +(2.63135 - 18.3014i) q^{7} +(-16.8840 + 4.95759i) q^{8} +(27.1832 + 17.4696i) q^{9} +O(q^{10})\)	\(q+(-0.502951 + 1.10131i) q^{2} +(-7.38951 - 2.16976i) q^{3} +(4.27896 + 4.93819i) q^{4} +(4.20627 - 2.70320i) q^{5} +(6.10614 - 7.04686i) q^{6} +(2.63135 - 18.3014i) q^{7} +(-16.8840 + 4.95759i) q^{8} +(27.1832 + 17.4696i) q^{9} +(0.861517 + 5.99198i) q^{10} +(12.9405 + 28.3358i) q^{11} +(-20.9048 - 45.7751i) q^{12} +(6.69273 + 46.5490i) q^{13} +(18.8321 + 12.1027i) q^{14} +(-36.9476 + 10.8488i) q^{15} +(-4.40727 + 30.6532i) q^{16} +(-47.8147 + 55.1811i) q^{17} +(-32.9113 + 21.1508i) q^{18} +(57.1420 + 65.9454i) q^{19} +(31.3474 + 9.20442i) q^{20} +(-59.1540 + 129.529i) q^{21} -37.7150 q^{22} +(97.8235 + 50.9663i) q^{23} +135.521 q^{24} +(10.3854 - 22.7408i) q^{25} +(-54.6310 - 16.0411i) q^{26} +(-26.7943 - 30.9223i) q^{27} +(101.635 - 65.3170i) q^{28} +(-116.249 + 134.159i) q^{29} +(6.63496 - 46.1471i) q^{30} +(101.005 - 29.6576i) q^{31} +(-149.969 - 96.3792i) q^{32} +(-34.1424 - 237.466i) q^{33} +(-36.7230 - 80.4122i) q^{34} +(-38.4043 - 84.0937i) q^{35} +(30.0479 + 208.988i) q^{36} +(-234.483 - 150.693i) q^{37} +(-101.366 + 29.7638i) q^{38} +(51.5439 - 358.496i) q^{39} +(-57.6173 + 66.4939i) q^{40} +(38.6455 - 24.8359i) q^{41} +(-112.900 - 130.294i) q^{42} +(94.7313 + 27.8156i) q^{43} +(-84.5555 + 185.151i) q^{44} +161.564 q^{45} +(-105.330 + 82.1004i) q^{46} +436.665 q^{47} +(99.0777 - 216.950i) q^{48} +(1.08806 + 0.319483i) q^{49} +(19.8213 + 22.8750i) q^{50} +(473.057 - 304.015i) q^{51} +(-201.230 + 232.231i) q^{52} +(-26.6367 + 185.262i) q^{53} +(47.5313 - 13.9564i) q^{54} +(131.029 + 84.2071i) q^{55} +(46.3033 + 322.046i) q^{56} +(-279.166 - 611.289i) q^{57} +(-89.2827 - 195.502i) q^{58} +(29.5870 + 205.782i) q^{59} +(-211.671 - 136.032i) q^{60} +(175.617 - 51.5657i) q^{61} +(-18.1382 + 126.154i) q^{62} +(391.247 - 451.523i) q^{63} +(-26.8481 + 17.2542i) q^{64} +(153.983 + 177.706i) q^{65} +(278.695 + 81.8323i) q^{66} +(88.4106 - 193.592i) q^{67} -477.092 q^{68} +(-612.284 - 588.869i) q^{69} +111.929 q^{70} +(-400.051 + 875.989i) q^{71} +(-545.569 - 160.193i) q^{72} +(487.835 + 562.992i) q^{73} +(283.893 - 182.447i) q^{74} +(-126.085 + 145.510i) q^{75} +(-81.1422 + 564.356i) q^{76} +(552.637 - 162.269i) q^{77} +(368.891 + 237.072i) q^{78} +(-178.998 - 1244.96i) q^{79} +(64.3238 + 140.849i) q^{80} +(-231.523 - 506.965i) q^{81} +(7.91527 + 55.0519i) q^{82} +(-741.416 - 476.479i) q^{83} +(-892.757 + 262.137i) q^{84} +(-51.9556 + 361.359i) q^{85} +(-78.2788 + 90.3386i) q^{86} +(1150.12 - 739.136i) q^{87} +(-358.965 - 414.268i) q^{88} +(-1316.89 - 386.673i) q^{89} +(-81.2587 + 177.932i) q^{90} +869.523 q^{91} +(166.902 + 701.154i) q^{92} -810.724 q^{93} +(-219.621 + 480.903i) q^{94} +(418.619 + 122.918i) q^{95} +(899.079 + 1037.59i) q^{96} +(-183.511 + 117.935i) q^{97} +(-0.899091 + 1.03761i) q^{98} +(-143.250 + 996.325i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 110 q - 2 q^{2} + 6 q^{3} - 40 q^{4} - 55 q^{5} - 3 q^{6} - 10 q^{7} + 243 q^{8} - 233 q^{9}+O(q^{10}) \) 110 * q - 2 * q^2 + 6 * q^3 - 40 * q^4 - 55 * q^5 - 3 * q^6 - 10 * q^7 + 243 * q^8 - 233 * q^9	\( 110 q - 2 q^{2} + 6 q^{3} - 40 q^{4} - 55 q^{5} - 3 q^{6} - 10 q^{7} + 243 q^{8} - 233 q^{9} - 10 q^{10} + 2 q^{11} - 57 q^{12} + 34 q^{13} - 154 q^{14} + 30 q^{15} + 16 q^{16} + 252 q^{17} - 33 q^{18} - 160 q^{19} - 200 q^{20} - 684 q^{21} - 704 q^{22} + 127 q^{23} - 3090 q^{24} - 275 q^{25} - 567 q^{26} + 384 q^{27} - 188 q^{28} + 340 q^{29} - 15 q^{30} + 582 q^{31} - 1364 q^{32} + 1760 q^{33} + 1819 q^{34} + 665 q^{35} + 2794 q^{36} + 312 q^{37} + 3123 q^{38} - 1560 q^{39} - 1205 q^{40} + 1324 q^{41} + 1454 q^{42} - 1740 q^{43} - 369 q^{44} + 3730 q^{45} - 4322 q^{46} - 2858 q^{47} - 2686 q^{48} + 2015 q^{49} - 325 q^{50} - 1426 q^{51} + 1717 q^{52} + 882 q^{53} + 2541 q^{54} + 450 q^{55} + 7755 q^{56} + 3688 q^{57} + 6622 q^{58} + 2605 q^{59} + 1530 q^{60} - 104 q^{61} - 9360 q^{62} - 7618 q^{63} + 3483 q^{64} + 170 q^{65} - 1766 q^{66} - 166 q^{67} - 5018 q^{68} - 1194 q^{69} - 770 q^{70} - 1222 q^{71} + 3303 q^{72} - 922 q^{73} + 1245 q^{74} + 150 q^{75} + 1360 q^{76} - 3093 q^{77} - 1600 q^{78} + 2448 q^{79} + 2115 q^{80} - 1371 q^{81} + 6609 q^{82} + 6704 q^{83} + 3894 q^{84} - 720 q^{85} - 5074 q^{86} - 6324 q^{87} + 1918 q^{88} - 5380 q^{89} - 165 q^{90} + 7828 q^{91} - 16225 q^{92} - 24948 q^{93} - 16490 q^{94} + 685 q^{95} + 675 q^{96} - 4400 q^{97} + 8790 q^{98} - 3626 q^{99}+O(q^{100}) \) 110 * q - 2 * q^2 + 6 * q^3 - 40 * q^4 - 55 * q^5 - 3 * q^6 - 10 * q^7 + 243 * q^8 - 233 * q^9 - 10 * q^10 + 2 * q^11 - 57 * q^12 + 34 * q^13 - 154 * q^14 + 30 * q^15 + 16 * q^16 + 252 * q^17 - 33 * q^18 - 160 * q^19 - 200 * q^20 - 684 * q^21 - 704 * q^22 + 127 * q^23 - 3090 * q^24 - 275 * q^25 - 567 * q^26 + 384 * q^27 - 188 * q^28 + 340 * q^29 - 15 * q^30 + 582 * q^31 - 1364 * q^32 + 1760 * q^33 + 1819 * q^34 + 665 * q^35 + 2794 * q^36 + 312 * q^37 + 3123 * q^38 - 1560 * q^39 - 1205 * q^40 + 1324 * q^41 + 1454 * q^42 - 1740 * q^43 - 369 * q^44 + 3730 * q^45 - 4322 * q^46 - 2858 * q^47 - 2686 * q^48 + 2015 * q^49 - 325 * q^50 - 1426 * q^51 + 1717 * q^52 + 882 * q^53 + 2541 * q^54 + 450 * q^55 + 7755 * q^56 + 3688 * q^57 + 6622 * q^58 + 2605 * q^59 + 1530 * q^60 - 104 * q^61 - 9360 * q^62 - 7618 * q^63 + 3483 * q^64 + 170 * q^65 - 1766 * q^66 - 166 * q^67 - 5018 * q^68 - 1194 * q^69 - 770 * q^70 - 1222 * q^71 + 3303 * q^72 - 922 * q^73 + 1245 * q^74 + 150 * q^75 + 1360 * q^76 - 3093 * q^77 - 1600 * q^78 + 2448 * q^79 + 2115 * q^80 - 1371 * q^81 + 6609 * q^82 + 6704 * q^83 + 3894 * q^84 - 720 * q^85 - 5074 * q^86 - 6324 * q^87 + 1918 * q^88 - 5380 * q^89 - 165 * q^90 + 7828 * q^91 - 16225 * q^92 - 24948 * q^93 - 16490 * q^94 + 685 * q^95 + 675 * q^96 - 4400 * q^97 + 8790 * q^98 - 3626 * q^99

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