LMFDB - Embedded newform 115.4.g.a.6.11

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			6.11
Character	$\chi$	$=$	115.6
Dual form			115.4.g.a.96.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.10300 - 4.60492i) q^{2} +(-0.871970 - 0.256034i) q^{3} +(-11.5438 - 13.3223i) q^{4} +(4.20627 - 2.70320i) q^{5} +(-3.01277 + 3.47692i) q^{6} +(1.35658 - 9.43524i) q^{7} +(-46.7662 + 13.7318i) q^{8} +(-22.0191 - 14.1508i) q^{9} +O(q^{10})$	\(q+(2.10300 - 4.60492i) q^{2} +(-0.871970 - 0.256034i) q^{3} +(-11.5438 - 13.3223i) q^{4} +(4.20627 - 2.70320i) q^{5} +(-3.01277 + 3.47692i) q^{6} +(1.35658 - 9.43524i) q^{7} +(-46.7662 + 13.7318i) q^{8} +(-22.0191 - 14.1508i) q^{9} +(-3.60228 - 25.0544i) q^{10} +(0.553380 + 1.21173i) q^{11} +(6.65493 + 14.5723i) q^{12} +(5.90684 + 41.0829i) q^{13} +(-40.5957 - 26.0892i) q^{14} +(-4.35985 + 1.28017i) q^{15} +(-15.0456 + 104.644i) q^{16} +(9.34884 - 10.7891i) q^{17} +(-111.469 + 71.6370i) q^{18} +(-3.15281 - 3.63853i) q^{19} +(-84.5694 - 24.8318i) q^{20} +(-3.59864 + 7.87992i) q^{21} +6.74370 q^{22} +(76.0429 - 79.9029i) q^{23} +44.2945 q^{24} +(10.3854 - 22.7408i) q^{25} +(201.606 + 59.1968i) q^{26} +(31.6453 + 36.5206i) q^{27} +(-141.359 + 90.8461i) q^{28} +(149.195 - 172.180i) q^{29} +(-3.27368 + 22.7690i) q^{30} +(128.425 - 37.7088i) q^{31} +(122.214 + 78.5423i) q^{32} +(-0.172287 - 1.19828i) q^{33} +(-30.0226 - 65.7403i) q^{34} +(-19.7992 - 43.3543i) q^{35} +(65.6634 + 456.699i) q^{36} +(-87.5208 - 56.2462i) q^{37} +(-23.3855 + 6.86661i) q^{38} +(5.36803 - 37.3354i) q^{39} +(-159.591 + 184.178i) q^{40} +(-60.8847 + 39.1282i) q^{41} +(28.7185 + 33.1429i) q^{42} +(-391.109 - 114.840i) q^{43} +(9.75495 - 21.3604i) q^{44} -130.871 q^{45} +(-208.029 - 518.208i) q^{46} +300.953 q^{47} +(39.9118 - 87.3947i) q^{48} +(241.923 + 71.0349i) q^{49} +(-82.8792 - 95.6477i) q^{50} +(-10.9143 + 7.01419i) q^{51} +(479.132 - 552.948i) q^{52} +(32.8270 - 228.317i) q^{53} +(234.725 - 68.9214i) q^{54} +(5.60323 + 3.60098i) q^{55} +(66.1205 + 459.878i) q^{56} +(1.81757 + 3.97992i) q^{57} +(-479.119 - 1049.12i) q^{58} +(83.3086 + 579.424i) q^{59} +(67.3842 + 43.3052i) q^{60} +(456.855 - 134.145i) q^{61} +(96.4302 - 670.687i) q^{62} +(-163.387 + 188.558i) q^{63} +(-92.8048 + 59.6420i) q^{64} +(135.901 + 156.838i) q^{65} +(-5.88030 - 1.72661i) q^{66} +(230.888 - 505.573i) q^{67} -251.658 q^{68} +(-86.7650 + 50.2034i) q^{69} -241.281 q^{70} +(-86.9387 + 190.369i) q^{71} +(1224.06 + 359.417i) q^{72} +(-189.879 - 219.132i) q^{73} +(-443.066 + 284.741i) q^{74} +(-14.8781 + 17.1703i) q^{75} +(-12.0781 + 84.0053i) q^{76} +(12.1837 - 3.57746i) q^{77} +(-160.638 - 103.236i) q^{78} +(144.682 + 1006.28i) q^{79} +(219.590 + 480.834i) q^{80} +(275.331 + 602.891i) q^{81} +(52.1420 + 362.656i) q^{82} +(1052.24 + 676.234i) q^{83} +(146.521 - 43.0224i) q^{84} +(10.1585 - 70.6538i) q^{85} +(-1351.33 + 1559.52i) q^{86} +(-174.177 + 111.937i) q^{87} +(-42.5187 - 49.0692i) q^{88} +(690.778 + 202.831i) q^{89} +(-275.221 + 602.649i) q^{90} +395.640 q^{91} +(-1942.32 - 90.6804i) q^{92} -121.637 q^{93} +(632.903 - 1385.86i) q^{94} +(-23.0972 - 6.78196i) q^{95} +(-86.4577 - 99.7775i) q^{96} +(-455.825 + 292.941i) q^{97} +(835.874 - 964.649i) q^{98} +(4.96208 - 34.5120i) 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 $

$2$	2.10300	−	4.60492i	0.743522	−	1.62809i	−0.0341499	−	0.999417i	$-0.510872\pi$
$2$	2.10300	−	4.60492i	0.743522	−	1.62809i	0.777672	−	0.628670i	$-0.216400\pi$
$3$	−0.871970	−	0.256034i	−0.167811	−	0.0492737i	0.196748	−	0.980454i	$-0.436962\pi$
$3$	−0.871970	−	0.256034i	−0.167811	−	0.0492737i	−0.364559	+	0.931180i	$0.618780\pi$
$4$	−11.5438	−	13.3223i	−1.44298	−	1.66529i
$5$	4.20627	−	2.70320i	0.376220	−	0.241782i
$5$	4.20627	−	2.70320i	0.376220	−	0.241782i
$6$	−3.01277	+	3.47692i	−0.204993	+	0.236574i
$7$	1.35658	−	9.43524i	0.0732486	−	0.509455i	−0.919859	−	0.392249i	$-0.871697\pi$
$7$	1.35658	−	9.43524i	0.0732486	−	0.509455i	0.993108	−	0.117206i	$-0.0373938\pi$
$8$	−46.7662	+	13.7318i	−2.06679	+	0.606865i
$9$	−22.0191	−	14.1508i	−0.815521	−	0.524104i
$10$	−3.60228	−	25.0544i	−0.113914	−	0.792289i
$11$	0.553380	+	1.21173i	0.0151682	+	0.0332138i	0.917064	−	0.398739i	$-0.130552\pi$
$11$	0.553380	+	1.21173i	0.0151682	+	0.0332138i	−0.901896	+	0.431953i	$0.857825\pi$
$12$	6.65493	+	14.5723i	0.160093	+	0.350554i
$13$	5.90684	+	41.0829i	0.126020	+	0.876489i	0.950528	+	0.310639i	$0.100543\pi$
$13$	5.90684	+	41.0829i	0.126020	+	0.876489i	−0.824508	+	0.565850i	$0.808548\pi$
$14$	−40.5957	−	26.0892i	−0.774975	−	0.498046i
$15$	−4.35985	+	1.28017i	−0.0750472	+	0.0220359i
$16$	−15.0456	+	104.644i	−0.235088	+	1.63507i
$17$	9.34884	−	10.7891i	0.133378	−	0.153927i	−0.685131	−	0.728419i	$-0.740255\pi$
$17$	9.34884	−	10.7891i	0.133378	−	0.153927i	0.818510	+	0.574493i	$0.194801\pi$
$18$	−111.469	+	71.6370i	−1.45964	+	0.938056i
$19$	−3.15281	−	3.63853i	−0.0380686	−	0.0439335i	0.736396	−	0.676551i	$-0.236526\pi$
$19$	−3.15281	−	3.63853i	−0.0380686	−	0.0439335i	−0.774465	+	0.632617i	$0.781981\pi$
$20$	−84.5694	−	24.8318i	−0.945515	−	0.277628i
$21$	−3.59864	+	7.87992i	−0.0373946	+	0.0818828i
$22$	6.74370			0.0653528
$23$	76.0429	−	79.9029i	0.689393	−	0.724387i
$23$	76.0429	−	79.9029i	0.689393	−	0.724387i
$24$	44.2945			0.376732
$25$	10.3854	−	22.7408i	0.0830830	−	0.181926i
$26$	201.606	+	59.1968i	1.52070	+	0.446517i
$27$	31.6453	+	36.5206i	0.225561	+	0.260311i
$28$	−141.359	+	90.8461i	−0.954085	+	0.613153i
$29$	149.195	−	172.180i	0.955336	−	1.10252i	−0.0393149	−	0.999227i	$-0.512518\pi$
$29$	149.195	−	172.180i	0.955336	−	1.10252i	0.994651	−	0.103290i	$-0.0329370\pi$
$30$	−3.27368	+	22.7690i	−0.0199230	+	0.138568i
$31$	128.425	−	37.7088i	0.744056	−	0.218474i	0.112335	−	0.993670i	$-0.464167\pi$
$31$	128.425	−	37.7088i	0.744056	−	0.218474i	0.631721	+	0.775196i	$0.282349\pi$
$32$	122.214	+	78.5423i	0.675144	+	0.433889i
$33$	−0.172287	−	1.19828i	−0.000908825	−	0.00632102i
$34$	−30.0226	−	65.7403i	−0.151436	−	0.331599i
$35$	−19.7992	−	43.3543i	−0.0956194	−	0.209377i
$36$	65.6634	+	456.699i	0.303997	+	2.11435i
$37$	−87.5208	−	56.2462i	−0.388874	−	0.249914i	0.331565	−	0.943432i	$-0.392423\pi$
$37$	−87.5208	−	56.2462i	−0.388874	−	0.249914i	−0.720439	+	0.693518i	$0.756060\pi$
$38$	−23.3855	+	6.86661i	−0.0998324	+	0.0293134i
$39$	5.36803	−	37.3354i	0.0220403	−	0.153294i
$40$	−159.591	+	184.178i	−0.630839	+	0.728027i
$41$	−60.8847	+	39.1282i	−0.231917	+	0.149044i	−0.651439	−	0.758701i	$-0.725834\pi$
$41$	−60.8847	+	39.1282i	−0.231917	+	0.149044i	0.419522	+	0.907745i	$0.362198\pi$
$42$	28.7185	+	33.1429i	0.105509	+	0.121763i
$43$	−391.109	−	114.840i	−1.38706	−	0.407277i	−0.498839	−	0.866695i	$-0.666240\pi$
$43$	−391.109	−	114.840i	−1.38706	−	0.407277i	−0.888220	+	0.459418i	$0.848058\pi$
$44$	9.75495	−	21.3604i	0.0334230	−	0.0731862i
$45$	−130.871			−0.433534
$46$	−208.029	−	518.208i	−0.666786	−	1.66099i
$47$	300.953			0.934010			0.467005	−	0.884255i	$-0.345333\pi$
$47$	300.953			0.934010			0.467005	+	0.884255i	$0.345333\pi$
$48$	39.9118	−	87.3947i	0.120016	−	0.262799i
$49$	241.923	+	71.0349i	0.705314	+	0.207099i
$50$	−82.8792	−	95.6477i	−0.234418	−	0.270533i
$51$	−10.9143	+	7.01419i	−0.0299668	+	0.0192585i
$52$	479.132	−	552.948i	1.27776	−	1.47462i
$53$	32.8270	−	228.317i	0.0850781	−	0.591731i	−0.902030	−	0.431674i	$-0.857923\pi$
$53$	32.8270	−	228.317i	0.0850781	−	0.591731i	0.987108	−	0.160057i	$-0.0511679\pi$
$54$	234.725	−	68.9214i	0.591518	−	0.173685i
$55$	5.60323	+	3.60098i	0.0137371	+	0.00882828i
$56$	66.1205	+	459.878i	0.157781	+	1.09739i
$57$	1.81757	+	3.97992i	0.00422355	+	0.00924829i
$58$	−479.119	−	1049.12i	−1.08468	−	2.37512i
$59$	83.3086	+	579.424i	0.183828	+	1.27855i	0.847608	+	0.530624i	$0.178042\pi$
$59$	83.3086	+	579.424i	0.183828	+	1.27855i	−0.663780	+	0.747928i	$0.731049\pi$
$60$	67.3842	+	43.3052i	0.144988	+	0.0931780i
$61$	456.855	−	134.145i	0.958922	−	0.281565i	0.235425	−	0.971892i	$-0.424352\pi$
$61$	456.855	−	134.145i	0.958922	−	0.281565i	0.723497	+	0.690327i	$0.242534\pi$
$62$	96.4302	−	670.687i	0.197527	−	1.37383i
$63$	−163.387	+	188.558i	−0.326743	+	0.377081i
$64$	−92.8048	+	59.6420i	−0.181259	+	0.116488i
$65$	135.901	+	156.838i	0.259330	+	0.299283i
$66$	−5.88030	−	1.72661i	−0.0109669	−	0.00322017i
$67$	230.888	−	505.573i	0.421006	−	0.921875i	−0.573695	−	0.819069i	$-0.694491\pi$
$67$	230.888	−	505.573i	0.421006	−	0.921875i	0.994701	−	0.102806i	$-0.0327821\pi$
$68$	−251.658			−0.448794
$69$	−86.7650	+	50.2034i	−0.151381	+	0.0875910i
$70$	−241.281			−0.411980
$71$	−86.9387	+	190.369i	−0.145320	+	0.318206i	−0.968270	−	0.249908i	$-0.919600\pi$
$71$	−86.9387	+	190.369i	−0.145320	+	0.318206i	0.822950	+	0.568114i	$0.192327\pi$
$72$	1224.06	+	359.417i	2.00357	+	0.588302i
$73$	−189.879	−	219.132i	−0.304433	−	0.351335i	0.582833	−	0.812592i	$-0.301944\pi$
$73$	−189.879	−	219.132i	−0.304433	−	0.351335i	−0.887267	+	0.461257i	$0.847399\pi$
$74$	−443.066	+	284.741i	−0.696018	+	0.447304i
$75$	−14.8781	+	17.1703i	−0.0229064	+	0.0264354i
$76$	−12.0781	+	84.0053i	−0.0182297	+	0.126790i
$77$	12.1837	−	3.57746i	0.0180320	−	0.00529466i
$78$	−160.638	−	103.236i	−0.233188	−	0.149861i
$79$	144.682	+	1006.28i	0.206050	+	1.43311i	0.785883	+	0.618375i	$0.212209\pi$
$79$	144.682	+	1006.28i	0.206050	+	1.43311i	−0.579833	+	0.814736i	$0.696882\pi$
$80$	219.590	+	480.834i	0.306886	+	0.671986i
$81$	275.331	+	602.891i	0.377683	+	0.827011i
$82$	52.1420	+	362.656i	0.0702210	+	0.488398i
$83$	1052.24	+	676.234i	1.39155	+	0.894293i	0.999669	−	0.0257249i	$-0.00818940\pi$
$83$	1052.24	+	676.234i	1.39155	+	0.894293i	0.391877	+	0.920017i	$0.371826\pi$
$84$	146.521	−	43.0224i	0.190318	−	0.0558824i
$85$	10.1585	−	70.6538i	0.0129629	−	0.0901586i
$86$	−1351.33	+	1559.52i	−1.69439	+	1.95543i
$87$	−174.177	+	111.937i	−0.214641	+	0.137941i
$88$	−42.5187	−	49.0692i	−0.0515058	−	0.0594409i
$89$	690.778	+	202.831i	0.822723	+	0.241573i	0.665888	−	0.746052i	$-0.268053\pi$
$89$	690.778	+	202.831i	0.822723	+	0.241573i	0.156835	+	0.987625i	$0.449871\pi$
$90$	−275.221	+	602.649i	−0.322342	+	0.705831i
$91$	395.640			0.455762
$92$	−1942.32	−	90.6804i	−2.20109	−	0.102762i
$93$	−121.637			−0.135626
$94$	632.903	−	1385.86i	0.694457	−	1.52065i
$95$	−23.0972	−	6.78196i	−0.0249445	−	0.00732437i
$96$	−86.4577	−	99.7775i	−0.0919172	−	0.106078i
$97$	−455.825	+	292.941i	−0.477134	+	0.306636i	−0.757013	−	0.653400i	$-0.773342\pi$
$97$	−455.825	+	292.941i	−0.477134	+	0.306636i	0.279879	+	0.960035i	$0.409706\pi$
$98$	835.874	−	964.649i	0.861592	−	0.994330i
$99$	4.96208	−	34.5120i	0.00503745	−	0.0350362i
$100$	−422.847	+	124.159i	−0.422847	+	0.124159i
$101$	−1458.90	−	937.580i	−1.43729	−	0.923690i	−0.999699	−	0.0245162i	$-0.992195\pi$
$101$	−1458.90	−	937.580i	−1.43729	−	0.923690i	−0.437591	−	0.899174i	$-0.644168\pi$
$102$	9.34708	+	65.0103i	0.00907351	+	0.0631077i
$103$	607.242	+	1329.67i	0.580906	+	1.27201i	0.940784	+	0.339008i	$0.110091\pi$
$103$	607.242	+	1329.67i	0.580906	+	1.27201i	−0.359877	+	0.933000i	$0.617181\pi$
$104$	−840.382	−	1840.18i	−0.792368	−	1.73504i
$105$	6.16419	+	42.8729i	0.00572917	+	0.0398473i
$106$	−982.348	−	631.316i	−0.900132	−	0.578480i
$107$	−1146.61	+	336.675i	−1.03595	+	0.304183i	−0.755129	−	0.655577i	$-0.772426\pi$
$107$	−1146.61	+	336.675i	−1.03595	+	0.304183i	−0.280823	+	0.959760i	$0.590607\pi$
$108$	121.230	−	843.176i	0.108013	−	0.751247i
$109$	440.343	−	508.183i	0.386947	−	0.446560i	−0.528540	−	0.848908i	$-0.677260\pi$
$109$	440.343	−	508.183i	0.386947	−	0.446560i	0.915487	+	0.402348i	$0.131806\pi$
$110$	28.3658	−	18.2296i	0.0245870	−	0.0158011i
$111$	61.9146	+	71.4533i	0.0529430	+	0.0610995i
$112$	966.935	+	283.918i	0.815775	+	0.239533i
$113$	−518.918	+	1136.27i	−0.431997	+	0.945942i	0.561001	+	0.827815i	$0.310416\pi$
$113$	−518.918	+	1136.27i	−0.431997	+	0.945942i	−0.992998	+	0.118127i	$0.962311\pi$
$114$	22.1496			0.0181973
$115$	103.863	−	541.653i	0.0842198	−	0.439212i
$116$	−4016.11			−3.21454
$117$	451.293	−	988.194i	0.356599	−	0.780843i
$118$	2843.40	+	834.898i	2.21827	+	0.651344i
$119$	−89.1156	−	102.845i	−0.0686489	−	0.0792250i
$120$	186.314	−	119.737i	0.141734	−	0.0910871i
$121$	870.458	−	1004.56i	0.653988	−	0.754742i
$122$	343.039	−	2385.89i	0.254568	−	1.77056i
$123$	63.1078	−	18.5301i	0.0462621	−	0.0135838i
$124$	−1984.88	−	1275.61i	−1.43748	−	0.923812i
$125$	−17.7894	−	123.728i	−0.0127290	−	0.0885323i
$126$	524.695	+	1148.92i	0.370981	+	0.812334i
$127$	−227.408	−	497.953i	−0.158891	−	0.347923i	0.813397	−	0.581709i	$-0.197616\pi$
$127$	−227.408	−	497.953i	−0.158891	−	0.347923i	−0.972288	+	0.233786i	$0.924888\pi$
$128$	244.878	+	1703.17i	0.169097	+	1.17609i
$129$	311.632	+	200.274i	0.212695	+	0.136691i
$130$	1008.03	−	295.984i	0.680077	−	0.199689i
$131$	−380.652	+	2647.50i	−0.253876	+	1.76575i	0.320590	+	0.947218i	$0.396119\pi$
$131$	−380.652	+	2647.50i	−0.253876	+	1.76575i	−0.574466	+	0.818529i	$0.694790\pi$
$132$	−13.9750	+	16.1280i	−0.00921490	+	0.0106346i
$133$	−38.6075	+	24.8115i	−0.0251706	+	0.0161762i
$134$	−1842.57	−	2126.44i	−1.18786	−	1.37087i
$135$	231.831	+	68.0718i	0.147799	+	0.0433977i
$136$	−289.055	+	632.943i	−0.182252	+	0.399076i
$137$	−1478.52			−0.922032			−0.461016	−	0.887392i	$-0.652515\pi$
$137$	−1478.52			−0.922032			−0.461016	+	0.887392i	$0.652515\pi$
$138$	48.7163	+	505.124i	0.0300508	+	0.311587i
$139$	−895.364			−0.546358			−0.273179	−	0.961963i	$-0.588075\pi$
$139$	−895.364			−0.546358			−0.273179	+	0.961963i	$0.588075\pi$
$140$	−349.019	+	764.246i	−0.210697	+	0.461361i
$141$	−262.422	−	77.0540i	−0.156737	−	0.0460221i
$142$	693.804	+	800.692i	0.410019	+	0.473187i
$143$	−46.5128	+	29.8920i	−0.0272000	+	0.0174804i
$144$	1812.09	−	2091.27i	1.04866	−	1.21022i
$145$	162.115	−	1127.54i	0.0928480	−	0.645772i
$146$	−1408.40	+	413.544i	−0.798357	+	0.234419i
$147$	−192.762	−	123.881i	−0.108155	−	0.0695068i
$148$	260.997	+	1815.28i	0.144958	+	1.00821i
$149$	1439.50	+	3152.07i	0.791467	+	1.73307i	0.672403	+	0.740185i	$0.265262\pi$
$149$	1439.50	+	3152.07i	0.791467	+	1.73307i	0.119064	+	0.992887i	$0.462011\pi$
$150$	47.7792	+	104.622i	0.0260077	+	0.0569489i
$151$	−14.7216	−	102.391i	−0.00793398	−	0.0551820i	0.985470	−	0.169851i	$-0.0543285\pi$
$151$	−14.7216	−	102.391i	−0.00793398	−	0.0551820i	−0.993404	+	0.114669i	$0.963419\pi$
$152$	197.408	+	126.867i	0.105342	+	0.0676989i
$153$	−358.528	+	105.273i	−0.189446	+	0.0556264i
$154$	9.14838	−	63.6284i	0.00478700	−	0.0332943i
$155$	438.253	−	505.771i	0.227105	−	0.262094i
$156$	−559.362	+	359.480i	−0.287082	+	0.184496i
$157$	−1209.14	−	1395.42i	−0.614649	−	0.709343i	0.360033	−	0.932940i	$-0.382765\pi$
$157$	−1209.14	−	1395.42i	−0.614649	−	0.709343i	−0.974682	+	0.223597i	$0.928220\pi$
$158$	4938.13	+	1449.96i	2.48643	+	0.730082i
$159$	−87.0810	+	190.681i	−0.0434338	+	0.0951068i
$160$	726.381			0.358909
$161$	−650.744	−	825.878i	−0.318546	−	0.404275i
$162$	3355.29			1.62726
$163$	2.32810	−	5.09783i	0.00111872	−	0.00244965i	−0.909072	−	0.416639i	$-0.863208\pi$
$163$	2.32810	−	5.09783i	0.00111872	−	0.00244965i	0.910191	+	0.414190i	$0.135935\pi$
$164$	1224.12	+	359.434i	0.582852	+	0.171141i
$165$	−3.96388	−	4.57456i	−0.00187023	−	0.00215836i
$166$	5326.86	−	3423.37i	2.49063	−	1.60063i
$167$	1451.25	−	1674.83i	0.672463	−	0.776063i	−0.312297	−	0.949985i	$-0.601098\pi$
$167$	1451.25	−	1674.83i	0.672463	−	0.776063i	0.984760	+	0.173921i	$0.0556439\pi$
$168$	60.0891	−	417.929i	0.0275951	−	0.191928i
$169$	455.089	−	133.626i	0.207141	−	0.0608221i
$170$	−303.992	−	195.364i	−0.137148	−	0.0881396i
$171$	17.9337	+	124.732i	0.00802004	+	0.0557806i
$172$	2984.97	+	6536.16i	1.32326	+	2.89755i
$173$	−480.896	−	1053.02i	−0.211340	−	0.462770i	0.774041	−	0.633136i	$-0.218233\pi$
$173$	−480.896	−	1053.02i	−0.211340	−	0.462770i	−0.985381	+	0.170365i	$0.945505\pi$
$174$	149.166	+	1037.48i	0.0649901	+	0.452016i
$175$	−200.476	−	128.838i	−0.0865976	−	0.0556529i
$176$	−135.127	+	39.6769i	−0.0578727	+	0.0169930i
$177$	75.7093	−	526.570i	0.0321506	−	0.223613i
$178$	2386.72	−	2754.43i	1.00501	−	1.15985i
$179$	535.970	−	344.447i	0.223800	−	0.143828i	−0.423936	−	0.905692i	$-0.639352\pi$
$179$	535.970	−	344.447i	0.223800	−	0.143828i	0.647737	+	0.761864i	$0.275716\pi$
$180$	1510.75	+	1743.50i	0.625581	+	0.721959i
$181$	691.043	+	202.909i	0.283784	+	0.0833264i	0.420527	−	0.907280i	$-0.361845\pi$
$181$	691.043	+	202.909i	0.283784	+	0.0833264i	−0.136743	+	0.990607i	$0.543663\pi$
$182$	832.031	−	1821.89i	0.338870	−	0.742021i
$183$	−432.709			−0.174791
$184$	−2459.03	+	4780.96i	−0.985227	+	1.91553i
$185$	−520.181			−0.206727
$186$	−255.803	+	560.130i	−0.100841	+	0.220810i
$187$	18.2470	+	5.35781i	0.00713559	+	0.00209520i
$188$	−3474.15	−	4009.38i	−1.34776	−	1.55539i
$189$	387.510	−	249.038i	0.149139	−	0.0958456i
$190$	−79.8039	+	92.0986i	−0.0304715	+	0.0351660i
$191$	132.204	−	919.496i	0.0500833	−	0.348337i	−0.949336	−	0.314263i	$-0.898243\pi$
$191$	132.204	−	919.496i	0.0500833	−	0.348337i	0.999419	−	0.0340743i	$-0.0108483\pi$
$192$	96.1934	−	28.2449i	0.0361571	−	0.0106167i
$193$	−621.497	−	399.412i	−0.231795	−	0.148965i	0.419588	−	0.907715i	$-0.362174\pi$
$193$	−621.497	−	399.412i	−0.231795	−	0.148965i	−0.651383	+	0.758749i	$0.725811\pi$
$194$	390.372	+	2715.09i	0.144469	+	1.00481i
$195$	−78.3460	−	171.554i	−0.0287717	−	0.0630011i
$196$	−1846.37	−	4042.98i	−0.672875	−	1.47339i
$197$	−737.037	−	5126.21i	−0.266557	−	1.85394i	−0.480365	−	0.877069i	$-0.659496\pi$
$197$	−737.037	−	5126.21i	−0.266557	−	1.85394i	0.213808	−	0.976876i	$-0.431413\pi$
$198$	−148.490	−	95.4287i	−0.0532966	−	0.0342516i
$199$	393.620	−	115.577i	0.140216	−	0.0411711i	−0.210871	−	0.977514i	$-0.567630\pi$
$199$	393.620	−	115.577i	0.140216	−	0.0411711i	0.351087	+	0.936343i	$0.385812\pi$
$200$	−173.412	+	1206.11i	−0.0613105	+	0.426424i
$201$	−330.771	+	381.730i	−0.116074	+	0.133956i
$202$	−7385.56	+	4746.41i	−2.57251	+	1.65325i
$203$	−1422.16	−	1641.26i	−0.491706	−	0.567459i
$204$	219.438	+	64.4328i	0.0753124	+	0.0221137i
$205$	−150.326	+	329.167i	−0.0512156	+	0.112147i
$206$	7400.08			2.50286
$207$	−2805.08	+	683.320i	−0.941869	+	0.229440i
$208$	−4387.97			−1.46275
$209$	2.66423	−	5.83385i	0.000881764	−	0.00193079i
$210$	210.390	+	61.7760i	0.0691346	+	0.0202998i
$211$	−1223.23	−	1411.68i	−0.399103	−	0.460589i	0.520256	−	0.854011i	$-0.325837\pi$
$211$	−1223.23	−	1411.68i	−0.399103	−	0.460589i	−0.919358	+	0.393422i	$0.871291\pi$
$212$	−3420.66	+	2198.32i	−1.10817	+	0.712177i
$213$	124.549	−	143.737i	0.0400655	−	0.0462380i
$214$	−860.955	+	5988.07i	−0.275017	+	1.91279i
$215$	−1955.54	+	574.200i	−0.620312	+	0.182140i
$216$	−1981.42	−	1273.38i	−0.624160	−	0.401124i
$217$	−181.573	−	1262.87i	−0.0568019	−	0.395066i
$218$	−1414.10	−	3096.45i	−0.439335	−	0.962010i
$219$	109.464	+	239.692i	0.0337756	+	0.0739583i
$220$	−16.7095	−	116.217i	−0.00512069	−	0.0356152i
$221$	498.472	+	320.348i	0.151723	+	0.0975066i
$222$	459.244	−	134.846i	0.138840	−	0.0407670i
$223$	3.58195	−	24.9130i	0.00107563	−	0.00748116i	−0.989277	−	0.146054i	$-0.953343\pi$
$223$	3.58195	−	24.9130i	0.00107563	−	0.00748116i	0.990352	+	0.138573i	$0.0442516\pi$
$224$	906.859	−	1046.57i	0.270500	−	0.312174i
$225$	−550.477	+	353.770i	−0.163104	+	0.104821i
$226$	4141.16	+	4779.16i	1.21888	+	1.40666i
$227$	848.495	+	249.141i	0.248091	+	0.0728460i	0.403414	−	0.915018i	$-0.367824\pi$
$227$	848.495	+	249.141i	0.248091	+	0.0728460i	−0.155323	+	0.987864i	$0.549642\pi$
$228$	32.0399	−	70.1577i	0.00930657	−	0.0203785i
$229$	3672.44			1.05975			0.529873	−	0.848077i	$-0.322240\pi$
$229$	3672.44			1.05975			0.529873	+	0.848077i	$0.322240\pi$
$230$	−2275.85	−	1617.38i	−0.652456	−	0.463681i
$231$	−11.5398			−0.00328684
$232$	−4612.92	+	10100.9i	−1.30540	+	2.85843i
$233$	−3125.07	−	917.602i	−0.878669	−	0.258000i	−0.188871	−	0.982002i	$-0.560483\pi$
$233$	−3125.07	−	917.602i	−0.878669	−	0.258000i	−0.689798	+	0.724002i	$0.742301\pi$
$234$	−3601.49	−	4156.34i	−1.00614	−	1.16115i
$235$	1265.89	−	813.536i	0.351393	−	0.225827i
$236$	6757.56	−	7798.64i	1.86390	−	2.15105i
$237$	131.484	−	914.493i	0.0360372	−	0.250644i
$238$	−661.003	+	194.088i	−0.180027	+	0.0528607i
$239$	5343.05	+	3433.77i	1.44608	+	0.929339i	0.999400	+	0.0346447i	$0.0110299\pi$
$239$	5343.05	+	3433.77i	1.44608	+	0.929339i	0.446680	+	0.894694i	$0.352606\pi$
$240$	−68.3659	−	475.495i	−0.0183875	−	0.127888i
$241$	−2405.42	−	5267.14i	−0.642934	−	1.40783i	−0.897605	−	0.440800i	$-0.854695\pi$
$241$	−2405.42	−	5267.14i	−0.642934	−	1.40783i	0.254672	−	0.967028i	$-0.418033\pi$
$242$	−2795.36	−	6120.98i	−0.742531	−	1.62592i
$243$	−271.404	−	1887.66i	−0.0716485	−	0.498326i
$244$	−7060.98	−	4537.81i	−1.85259	−	1.19059i
$245$	1209.61	−	355.175i	0.315426	−	0.0926174i
$246$	47.3858	−	329.575i	0.0122813	−	0.0854185i
$247$	130.859	−	151.019i	0.0337098	−	0.0389032i
$248$	−5488.11	+	3526.99i	−1.40522	+	0.903082i
$249$	−744.384	−	859.064i	−0.189451	−	0.218639i
$250$	−607.168	−	178.280i	−0.153603	−	0.0451018i
$251$	−2602.87	+	5699.48i	−0.654547	+	1.43326i	0.232970	+	0.972484i	$0.425156\pi$
$251$	−2602.87	+	5699.48i	−0.654547	+	1.43326i	−0.887517	+	0.460775i	$0.847572\pi$
$252$	4398.14			1.09943
$253$	138.902	+	47.9271i	0.0345165	+	0.0119097i
$254$	−2771.28			−0.684588
$255$	−26.9477	+	59.0071i	−0.00661776	+	0.0144909i
$256$	7511.14	+	2205.47i	1.83378	+	0.538445i
$257$	−1502.96	−	1734.51i	−0.364793	−	0.420994i	0.543446	−	0.839444i	$-0.317119\pi$
$257$	−1502.96	−	1734.51i	−0.364793	−	0.420994i	−0.908240	+	0.418450i	$0.862574\pi$
$258$	1577.61	−	1013.87i	0.380689	−	0.244654i
$259$	−649.426	+	749.477i	−0.155804	+	0.179808i
$260$	520.626	−	3621.04i	0.124184	−	0.863720i
$261$	−5721.61	+	1680.02i	−1.35693	+	0.398431i
$262$	11391.0	+	7320.56i	2.68603	+	1.72620i
$263$	401.297	+	2791.08i	0.0940877	+	0.654394i	0.981222	+	0.192883i	$0.0617836\pi$
$263$	401.297	+	2791.08i	0.0940877	+	0.654394i	−0.887134	+	0.461512i	$0.847307\pi$
$264$	24.5117	+	53.6731i	0.00571436	+	0.0125127i
$265$	−479.108	−	1049.10i	−0.111062	−	0.243192i
$266$	33.0637	+	229.963i	0.00762130	+	0.0530073i
$267$	−550.406	−	353.725i	−0.126158	−	0.0810771i
$268$	−9400.73	+	2760.30i	−2.14269	+	0.629151i
$269$	985.045	−	6851.14i	0.223269	−	1.55287i	−0.502286	−	0.864702i	$-0.667507\pi$
$269$	985.045	−	6851.14i	0.223269	−	1.55287i	0.725554	−	0.688165i	$-0.241583\pi$
$270$	801.006	−	924.410i	0.180547	−	0.208362i
$271$	2385.43	−	1533.02i	0.534704	−	0.343633i	−0.245261	−	0.969457i	$-0.578874\pi$
$271$	2385.43	−	1533.02i	0.534704	−	0.343633i	0.779964	+	0.625824i	$0.215237\pi$
$272$	988.365	+	1140.63i	0.220325	+	0.254269i
$273$	−344.987	−	101.297i	−0.0764818	−	0.0224571i
$274$	−3109.32	+	6808.47i	−0.685551	+	1.50115i
$275$	33.3028			0.00730268
$276$	1670.43	+	576.369i	0.364304	+	0.125701i
$277$	7402.87			1.60576			0.802880	−	0.596141i	$-0.203300\pi$
$277$	7402.87			1.60576			0.802880	+	0.596141i	$0.203300\pi$
$278$	−1882.95	+	4123.09i	−0.406230	+	0.889519i
$279$	−3361.40	−	986.995i	−0.721296	−	0.211792i
$280$	1521.26	+	1755.63i	0.324689	+	0.374711i
$281$	3950.06	−	2538.55i	0.838580	−	0.538923i	−0.0494137	−	0.998778i	$-0.515735\pi$
$281$	3950.06	−	2538.55i	0.838580	−	0.538923i	0.887994	+	0.459856i	$0.152099\pi$
$282$	−906.700	+	1046.39i	−0.191465	+	0.220963i
$283$	−654.578	+	4552.69i	−0.137493	+	0.956287i	0.797928	+	0.602753i	$0.205929\pi$
$283$	−654.578	+	4552.69i	−0.137493	+	0.956287i	−0.935421	+	0.353535i	$0.884980\pi$
$284$	3539.76	−	1039.37i	0.739599	−	0.217166i
$285$	18.4037	+	11.8273i	0.00382506	+	0.00245821i
$286$	39.8339	+	277.051i	0.00823576	+	0.0572810i
$287$	286.589	+	627.542i	0.0589436	+	0.129068i
$288$	−1579.61	−	3458.86i	−0.323192	−	0.707691i
$289$	670.188	+	4661.26i	0.136411	+	0.948761i
$290$	−4851.30	−	3117.74i	−0.982338	−	0.631310i
$291$	472.469	−	138.729i	0.0951773	−	0.0279466i
$292$	−727.410	+	5059.25i	−0.145782	+	1.01394i
$293$	−5325.50	+	6145.96i	−1.06184	+	1.22543i	−0.0884972	+	0.996076i	$0.528206\pi$
$293$	−5325.50	+	6145.96i	−1.06184	+	1.22543i	−0.973343	+	0.229353i	$0.926339\pi$
$294$	−975.839	+	627.134i	−0.193579	+	0.124405i
$295$	1916.72	+	2212.01i	0.378290	+	0.436570i
$296$	4865.37	+	1428.60i	0.955386	+	0.280527i
$297$	−26.7414	+	58.5554i	−0.00522455	+	0.0114402i
$298$	17542.3			3.41006
$299$	3731.82	+	2652.09i	0.721795	+	0.512958i
$300$	400.499			0.0770760
$301$	−1614.11	+	3534.41i	−0.309089	+	0.676812i
$302$	−502.464	−	147.537i	−0.0957402	−	0.0281119i
$303$	1032.07	+	1191.07i	0.195679	+	0.225826i
$304$	428.188	−	275.180i	0.0807838	−	0.0519166i
$305$	1559.03	−	1799.22i	0.292688	−	0.337780i
$306$	−269.208	+	1872.38i	−0.0502928	+	0.349794i
$307$	517.813	−	152.044i	0.0962643	−	0.0282657i	−0.233246	−	0.972418i	$-0.574935\pi$
$307$	517.813	−	152.044i	0.0962643	−	0.0282657i	0.329510	+	0.944152i	$0.393116\pi$
$308$	−188.307	−	121.017i	−0.0348369	−	0.0223883i
$309$	−189.056	−	1314.91i	−0.0348058	−	0.242080i
$310$	−1407.39	−	3081.76i	−0.257853	−	0.564620i
$311$	3798.28	+	8317.06i	0.692542	+	1.51645i	0.848786	+	0.528736i	$0.177334\pi$
$311$	3798.28	+	8317.06i	0.692542	+	1.51645i	−0.156245	+	0.987718i	$0.549939\pi$
$312$	261.640	+	1819.75i	0.0474758	+	0.330202i
$313$	−6970.99	−	4479.98i	−1.25886	−	0.809021i	−0.270733	−	0.962654i	$-0.587266\pi$
$313$	−6970.99	−	4479.98i	−1.25886	−	0.809021i	−0.988128	+	0.153633i	$0.950903\pi$
$314$	−8968.63	+	2633.43i	−1.61188	+	0.473290i
$315$	−177.537	+	1234.79i	−0.0317557	+	0.220866i
$316$	11735.8	−	13543.9i	2.08922	−	2.41108i
$317$	−8951.59	+	5752.84i	−1.58603	+	1.01928i	−0.612570	+	0.790416i	$0.709864\pi$
$317$	−8951.59	+	5752.84i	−1.58603	+	1.01928i	−0.973459	+	0.228863i	$0.926499\pi$
$318$	694.940	+	802.003i	0.122548	+	0.141428i
$319$	291.197	+	85.5033i	0.0511095	+	0.0150071i
$320$	−229.137	+	501.741i	−0.0400286	+	0.0876505i
$321$	1086.01			0.188832
$322$	−5171.62	+	1259.81i	−0.895041	+	0.218032i
$323$	−68.7317			−0.0118400
$324$	4853.52	−	10627.7i	0.832222	−	1.82231i
$325$	995.604	+	292.336i	0.169927	+	0.0498950i
$326$	−18.5791	−	21.4415i	−0.00315645	−	0.00364274i
$327$	−514.078	+	330.378i	−0.0869375	+	0.0558713i
$328$	2310.04	−	2665.93i	0.388874	−	0.448785i
$329$	408.267	−	2839.56i	0.0684149	−	0.475836i
$330$	−29.4015	+	8.63307i	−0.00490455	+	0.00144010i
$331$	−1430.28	−	919.188i	−0.237509	−	0.152638i	0.416472	−	0.909148i	$-0.363266\pi$
$331$	−1430.28	−	919.188i	−0.237509	−	0.152638i	−0.653982	+	0.756510i	$0.726903\pi$
$332$	−3137.90	−	21824.6i	−0.518719	−	3.60777i
$333$	1131.20	+	2476.98i	0.186154	+	0.407620i
$334$	−4660.50	−	10205.1i	−0.763507	−	1.67185i
$335$	−395.493	−	2750.71i	−0.0645017	−	0.448619i
$336$	−770.446	−	495.136i	−0.125093	−	0.0803924i
$337$	1922.09	−	564.377i	0.310692	−	0.0912273i	−0.122670	−	0.992448i	$-0.539146\pi$
$337$	1922.09	−	564.377i	0.310692	−	0.0912273i	0.433361	+	0.901220i	$0.357327\pi$
$338$	341.713	−	2376.66i	0.0549903	−	0.382466i
$339$	743.405	−	857.935i	0.119104	−	0.137453i
$340$	−1058.54	+	680.282i	−0.168845	+	0.108510i
$341$	116.761	+	134.749i	0.0185424	+	0.0213990i
$342$	612.095	+	179.727i	0.0967787	+	0.0284168i
$343$	2356.65	−	5160.34i	0.370982	−	0.812338i
$344$	19867.6			3.11392
$345$	−229.247	+	445.712i	−0.0357746	+	0.0695546i
$346$	−5860.38			−0.910566
$347$	−3678.72	+	8055.28i	−0.569119	+	1.24620i	0.378146	+	0.925746i	$0.376562\pi$
$347$	−3678.72	+	8055.28i	−0.569119	+	1.24620i	−0.947265	+	0.320451i	$0.896166\pi$
$348$	3501.93	+	1028.26i	0.539434	+	0.158392i
$349$	−2474.58	−	2855.82i	−0.379545	−	0.438018i	0.533548	−	0.845770i	$-0.320858\pi$
$349$	−2474.58	−	2855.82i	−0.379545	−	0.438018i	−0.913093	+	0.407752i	$0.866313\pi$
$350$	−1014.89	+	652.231i	−0.154995	+	0.0996092i
$351$	−1313.45	+	1515.80i	−0.199734	+	0.230506i
$352$	−27.5414	+	191.555i	−0.00417035	+	0.0290054i
$353$	6483.58	−	1903.75i	0.977582	−	0.287044i	0.246356	−	0.969179i	$-0.420767\pi$
$353$	6483.58	−	1903.75i	0.977582	−	0.287044i	0.731226	+	0.682136i	$0.238949\pi$
$354$	−2265.60	−	1456.01i	−0.340156	−	0.218605i
$355$	148.919	+	1035.76i	0.0222643	+	0.154851i
$356$	−5272.06	−	11544.2i	−0.784884	−	1.71866i
$357$	51.3744	+	112.494i	0.00761631	+	0.0166774i
$358$	−459.008	−	3192.47i	−0.0677635	−	0.471305i
$359$	6732.45	+	4326.68i	0.989763	+	0.636082i	0.932080	−	0.362253i	$-0.117992\pi$
$359$	6732.45	+	4326.68i	0.989763	+	0.636082i	0.0576834	+	0.998335i	$0.481629\pi$
$360$	6120.31	−	1797.09i	0.896025	−	0.263097i
$361$	972.839	−	6766.24i	0.141834	−	0.986476i
$362$	2387.64	−	2755.49i	0.346662	−	0.400069i
$363$	−1016.21	+	653.081i	−0.146935	+	0.0944294i
$364$	−4567.21	−	5270.84i	−0.657656	−	0.758976i
$365$	−1391.04	−	408.446i	−0.199480	−	0.0585727i
$366$	−909.987	+	1992.59i	−0.129961	+	0.284575i
$367$	−8712.97			−1.23927			−0.619637	−	0.784889i	$-0.712720\pi$
$367$	−8712.97			−1.23927			−0.619637	+	0.784889i	$0.712720\pi$
$368$	7217.29	+	9159.66i	1.02236	+	1.29750i
$369$	1894.32			0.267247
$370$	−1093.94	+	2395.39i	−0.153706	+	0.336569i
$371$	−2109.69	−	619.462i	−0.295229	−	0.0866869i
$372$	1404.16	+	1620.49i	0.195705	+	0.225856i
$373$	5408.62	−	3475.91i	0.750798	−	0.482508i	−0.108429	−	0.994104i	$-0.534582\pi$
$373$	5408.62	−	3475.91i	0.750798	−	0.482508i	0.859226	+	0.511596i	$0.170945\pi$
$374$	63.0458	−	72.7587i	0.00871663	−	0.0100595i
$375$	−16.1667	+	112.442i	−0.00222625	+	0.0154839i
$376$	−14074.4	+	4132.62i	−1.93040	+	0.566817i
$377$	7954.92	+	5112.32i	1.08674	+	0.698403i
$378$	−331.866	−	2308.18i	−0.0451570	−	0.314074i
$379$	1476.37	+	3232.79i	0.200095	+	0.438146i	0.982905	−	0.184115i	$-0.0589417\pi$
$379$	1476.37	+	3232.79i	0.200095	+	0.438146i	−0.782810	+	0.622260i	$0.786214\pi$
$380$	176.280	+	385.998i	0.0237972	+	0.0521087i
$381$	70.7999	+	492.424i	0.00952019	+	0.0662144i
$382$	−3956.19	−	2542.49i	−0.529885	−	0.340537i
$383$	−11277.6	+	3311.40i	−1.50459	+	0.441788i	−0.927165	−	0.374654i	$-0.877762\pi$
$383$	−11277.6	+	3311.40i	−1.50459	+	0.441788i	−0.577428	+	0.816442i	$0.695943\pi$
$384$	222.541	−	1547.81i	0.0295742	−	0.205693i
$385$	41.5773	−	47.9828i	0.00550383	−	0.00635176i
$386$	−3146.27	+	2021.98i	−0.414873	+	0.266623i
$387$	6986.78	+	8063.17i	0.917720	+	1.05911i
$388$	9164.62	+	2690.98i	1.19913	+	0.352097i
$389$	−4803.72	+	10518.7i	−0.626114	+	1.37100i	0.284874	+	0.958565i	$0.408048\pi$
$389$	−4803.72	+	10518.7i	−0.626114	+	1.37100i	−0.910988	+	0.412433i	$0.864679\pi$
$390$	−954.754			−0.123964
$391$	−151.170	−	1567.44i	−0.0195525	−	0.202733i
$392$	−12289.2			−1.58342
$393$	1009.77	−	2211.08i	0.129608	−	0.283802i
$394$	−25155.8	−	7386.40i	−3.21657	−	0.944471i
$395$	3328.76	+	3841.59i	0.424021	+	0.489346i
$396$	−517.061	+	332.295i	−0.0656144	+	0.0421678i
$397$	1538.02	−	1774.97i	0.194436	−	0.224391i	−0.650157	−	0.759800i	$-0.725297\pi$
$397$	1538.02	−	1774.97i	0.194436	−	0.224391i	0.844593	+	0.535409i	$0.179842\pi$
$398$	295.558	−	2055.65i	0.0372235	−	0.258895i
$399$	40.0171	−	11.7501i	0.00502096	−	0.00147429i
$400$	2223.44	+	1428.92i	0.277931	+	0.178615i
$401$	368.454	+	2562.65i	0.0458845	+	0.319134i	0.999817	+	0.0191135i	$0.00608439\pi$
$401$	368.454	+	2562.65i	0.0458845	+	0.319134i	−0.953933	+	0.300020i	$0.903007\pi$
$402$	1062.23	+	2325.95i	0.131789	+	0.288577i
$403$	2307.77	+	5053.32i	0.285256	+	0.624624i
$404$	4350.62	+	30259.2i	0.535771	+	3.72637i
$405$	2787.85	+	1791.64i	0.342048	+	0.219821i
$406$	−10548.7	+	3097.38i	−1.28947	+	0.378621i
$407$	19.7231	−	137.177i	0.00240206	−	0.0167067i
$408$	414.102	−	477.899i	0.0502478	−	0.0579891i
$409$	10889.2	−	6998.08i	1.31647	−	0.846046i	0.321571	−	0.946886i	$-0.395789\pi$
$409$	10889.2	−	6998.08i	1.31647	−	0.846046i	0.994903	+	0.100839i	$0.0321528\pi$
$410$	1199.66	+	1384.48i	0.144504	+	0.166767i
$411$	1289.22	+	378.550i	0.154727	+	0.0454319i
$412$	10704.4	−	23439.4i	1.28002	−	2.80286i
$413$	5580.02			0.664830
$414$	−2752.45	+	14354.2i	−0.326753	+	1.70404i
$415$	6254.00			0.739751
$416$	−2504.85	+	5484.85i	−0.295217	+	0.646435i
$417$	780.731	+	229.243i	0.0916848	+	0.0269211i
$418$	−21.2616	−	24.5372i	−0.00248789	−	0.00287118i
$419$	−789.889	+	507.631i	−0.0920969	+	0.0591871i	−0.585879	−	0.810399i	$-0.699251\pi$
$419$	−789.889	+	507.631i	−0.0920969	+	0.0591871i	0.493782	+	0.869586i	$0.335614\pi$
$420$	500.007	−	577.039i	0.0580901	−	0.0670396i
$421$	523.510	−	3641.09i	0.0606041	−	0.421511i	−0.936822	−	0.349807i	$-0.886247\pi$
$421$	523.510	−	3641.09i	0.0606041	−	0.421511i	0.997426	−	0.0717039i	$-0.0228437\pi$
$422$	−9073.14	+	2664.12i	−1.04662	+	0.307315i
$423$	−6626.70	−	4258.72i	−0.761704	−	0.489518i
$424$	1600.01	+	11128.3i	0.183262	+	1.27462i
$425$	−148.262	−	324.649i	−0.0169218	−	0.0370537i
$426$	−399.972	−	875.817i	−0.0454899	−	0.0996091i
$427$	−645.926	−	4492.51i	−0.0732050	−	0.509152i
$428$	17721.6	+	11388.9i	2.00141	+	1.28623i
$429$	48.2112	−	14.1561i	0.00542577	−	0.00159315i
$430$	−1468.36	+	10212.7i	−0.164676	+	1.14535i
$431$	−1565.18	+	1806.31i	−0.174923	+	0.201872i	−0.836441	−	0.548058i	$-0.815367\pi$
$431$	−1565.18	+	1806.31i	−0.174923	+	0.201872i	0.661517	+	0.749930i	$0.269913\pi$
$432$	−4297.80	+	2762.03i	−0.478653	+	0.307612i
$433$	−2330.18	−	2689.18i	−0.258618	−	0.298461i	0.611561	−	0.791198i	$-0.290542\pi$
$433$	−2330.18	−	2689.18i	−0.258618	−	0.298461i	−0.870178	+	0.492737i	$0.835997\pi$
$434$	−6197.27	−	1819.68i	−0.685435	−	0.201262i
$435$	−430.047	+	941.673i	−0.0474005	+	0.103793i
$436$	−11853.4			−1.30201
$437$	−530.478	−	24.7663i	−0.0580691	−	0.00271106i
$438$	1333.96			0.145524
$439$	3630.33	−	7949.32i	0.394684	−	0.864237i	−0.603098	−	0.797667i	$-0.706067\pi$
$439$	3630.33	−	7949.32i	0.394684	−	0.864237i	0.997782	−	0.0665702i	$-0.0212056\pi$
$440$	−311.489	−	91.4615i	−0.0337492	−	0.00990967i
$441$	−4321.71	−	4987.52i	−0.466657	−	0.538551i
$442$	2523.46	−	1621.73i	0.271559	−	0.174520i
$443$	3217.35	−	3713.02i	0.345058	−	0.398219i	−0.556520	−	0.830834i	$-0.687864\pi$
$443$	3217.35	−	3713.02i	0.345058	−	0.398219i	0.901579	+	0.432615i	$0.142409\pi$
$444$	237.190	−	1649.69i	0.0253525	−	0.176331i
$445$	3453.89	−	1014.15i	0.367933	−	0.108035i
$446$	−107.190	−	68.8866i	−0.0113802	−	0.00731362i
$447$	−448.167	−	3117.07i	−0.0474219	−	0.329827i
$448$	436.839	+	956.545i	0.0460686	+	0.100876i
$449$	2272.37	+	4975.81i	0.238842	+	0.522991i	0.990656	−	0.136384i	$-0.0435482\pi$
$449$	2272.37	+	4975.81i	0.238842	+	0.522991i	−0.751814	+	0.659375i	$0.770821\pi$
$450$	471.432	+	3278.88i	0.0493856	+	0.343484i
$451$	−81.1053	−	52.1232i	−0.00846807	−	0.00544210i
$452$	21128.1	−	6203.76i	2.19863	−	0.645576i
$453$	−13.3788	+	93.0514i	−0.00138762	+	0.00965108i
$454$	2931.66	−	3383.32i	0.303061	−	0.349751i
$455$	1664.17	−	1069.50i	0.171467	−	0.110195i
$456$	−139.652	−	161.167i	−0.0143417	−	0.0165512i
$457$	6142.02	+	1803.46i	0.628691	+	0.184600i	0.580529	−	0.814239i	$-0.302846\pi$
$457$	6142.02	+	1803.46i	0.628691	+	0.184600i	0.0481613	+	0.998840i	$0.484664\pi$
$458$	7723.14	−	16911.3i	0.787945	−	1.72536i
$459$	689.873			0.0701536
$460$	−8415.04	+	4869.06i	−0.852942	+	0.493524i
$461$	−7507.40			−0.758470			−0.379235	−	0.925300i	$-0.623813\pi$
$461$	−7507.40			−0.758470			−0.379235	+	0.925300i	$0.623813\pi$
$462$	−24.2681	+	53.1398i	−0.00244384	+	0.00535127i
$463$	−10334.3	−	3034.44i	−1.03732	−	0.304584i	−0.281634	−	0.959522i	$-0.590876\pi$
$463$	−10334.3	−	3034.44i	−1.03732	−	0.304584i	−0.755682	+	0.654938i	$0.772695\pi$
$464$	15772.9	+	18202.9i	1.57810	+	1.82123i
$465$	−511.638	+	328.810i	−0.0510251	+	0.0327918i
$466$	−10797.5	+	12461.0i	−1.07336	+	1.23872i
$467$	1768.35	−	12299.1i	0.175223	−	1.21871i	−0.692411	−	0.721503i	$-0.743452\pi$
$467$	1768.35	−	12299.1i	0.175223	−	1.21871i	0.867635	−	0.497202i	$-0.165639\pi$
$468$	−18374.7	+	5395.29i	−1.81489	+	0.532901i
$469$	−4456.99	−	2864.33i	−0.438815	−	0.282010i
$470$	−1084.11	−	7540.18i	−0.106397	−	0.740006i
$471$	697.059	+	1526.35i	0.0681928	+	0.149321i
$472$	−11852.5	−	25953.4i	−1.15584	−	2.53094i
$473$	−77.2765	−	537.470i	−0.00751200	−	0.0522471i
$474$	−3934.66	−	2528.65i	−0.381276	−	0.245031i
$475$	−115.486	+	33.9098i	−0.0111555	+	0.00327556i
$476$	−341.394	+	2374.45i	−0.0328735	+	0.228640i
$477$	−3953.69	+	4562.80i	−0.379511	+	0.437980i
$478$	27048.7	−	17383.1i	2.58824	−	1.66336i
$479$	−4177.92	−	4821.58i	−0.398526	−	0.459924i	0.520650	−	0.853770i	$-0.325690\pi$
$479$	−4177.92	−	4821.58i	−0.398526	−	0.459924i	−0.919176	+	0.393846i	$0.871144\pi$
$480$	−633.383	−	185.978i	−0.0602288	−	0.0176848i
$481$	1793.79	−	3927.85i	0.170041	−	0.372338i
$482$	−29313.4			−2.77010
$483$	355.977	+	886.753i	0.0335353	+	0.0835376i
$484$	−23431.5			−2.20055
$485$	−1125.44	+	2464.38i	−0.105369	+	0.230725i
$486$	−9263.28	−	2719.94i	−0.864590	−	0.253867i
$487$	11002.0	+	12697.0i	1.02371	+	1.18143i	0.983253	+	0.182246i	$0.0583366\pi$
$487$	11002.0	+	12697.0i	1.02371	+	1.18143i	0.0404590	+	0.999181i	$0.487118\pi$
$488$	−19523.3	+	12546.9i	−1.81102	+	1.16387i
$489$	−3.33525	+	3.84909i	−0.000308436	+	0.000355954i
$490$	908.263	−	6317.11i	0.0837371	−	0.582404i
$491$	328.106	−	96.3407i	0.0301573	−	0.00885498i	−0.266619	−	0.963802i	$-0.585907\pi$
$491$	328.106	−	96.3407i	0.0301573	−	0.00885498i	0.296776	+	0.954947i	$0.404088\pi$
$492$	−975.370	−	626.832i	−0.0893761	−	0.0574386i
$493$	−462.875	−	3219.36i	−0.0422857	−	0.294103i
$494$	−420.235	−	920.186i	−0.0382738	−	0.0838079i
$495$	−72.4212	−	158.580i	−0.00657594	−	0.0143993i
$496$	2013.80	+	14006.3i	0.182303	+	1.26794i
$497$	1678.24	+	1078.54i	0.151467	+	0.0973422i
$498$	−5521.36	+	1621.22i	−0.496824	+	0.145881i
$499$	2859.66	−	19889.4i	0.256545	−	1.78431i	−0.300451	−	0.953797i	$-0.597137\pi$
$499$	2859.66	−	19889.4i	0.256545	−	1.78431i	0.556996	−	0.830515i	$-0.311954\pi$
$500$	−1442.98	+	1665.29i	−0.129064	+	0.148948i
$501$	−1694.26	+	1088.84i	−0.151086	+	0.0970970i
$502$	20771.9	+	23972.0i	1.84680	+	2.13132i
$503$	14214.9	+	4173.86i	1.26006	+	0.369986i	0.842516	−	0.538671i	$-0.181074\pi$
$503$	14214.9	+	4173.86i	1.26006	+	0.369986i	0.417542	+	0.908658i	$0.362892\pi$
$504$	5051.73	−	11061.7i	0.446472	−	0.977637i
$505$	−8671.01			−0.764069
$506$	512.811	−	538.841i	0.0450538	−	0.0473407i
$507$	−431.037			−0.0377574
$508$	−4008.73	+	8777.89i	−0.350115	+	0.766645i
$509$	3977.30	+	1167.84i	0.346347	+	0.101697i	0.450280	−	0.892888i	$-0.351324\pi$
$509$	3977.30	+	1167.84i	0.346347	+	0.101697i	−0.103932	+	0.994584i	$0.533142\pi$
$510$	215.053	+	248.184i	0.0186719	+	0.0215486i
$511$	−2325.15	+	1494.28i	−0.201289	+	0.129360i
$512$	16937.5	−	19546.9i	1.46199	−	1.68723i
$513$	33.1100	−	230.285i	0.00284959	−	0.0198193i
$514$	−11148.0	+	3273.34i	−0.956647	+	0.280897i
$515$	6148.61	+	3951.47i	0.526097	+	0.338102i
$516$	−929.324	−	6463.59i	−0.0792853	−	0.551441i
$517$	166.541	+	364.674i	0.0141673	+	0.0310220i
$518$	2085.54	+	4566.71i	0.176899	+	0.387354i
$519$	149.720	+	1041.32i	0.0126627	+	0.0880714i
$520$	−8509.25	−	5468.56i	−0.717607	−	0.461178i
$521$	−6857.14	+	2013.44i	−0.576615	+	0.169310i	−0.557021	−	0.830498i	$-0.688056\pi$
$521$	−6857.14	+	2013.44i	−0.576615	+	0.169310i	−0.0195944	+	0.999808i	$0.506238\pi$
$522$	−4296.19	+	29880.6i	−0.360228	+	2.50544i
$523$	−5659.37	+	6531.26i	−0.473168	+	0.546065i	−0.941290	−	0.337598i	$-0.890385\pi$
$523$	−5659.37	+	6531.26i	−0.473168	+	0.546065i	0.468122	+	0.883664i	$0.344931\pi$
$524$	39664.9	−	25491.1i	3.30681	−	2.12516i
$525$	141.822	+	163.672i	0.0117898	+	0.0136061i
$526$	13696.7	+	4021.70i	1.13537	+	0.333374i
$527$	793.775	−	1738.12i	0.0656117	−	0.143670i
$528$	127.985			0.0105490
$529$	−601.948	−	12152.1i	−0.0494738	−	0.998775i
$530$	−5838.59			−0.478514
$531$	6364.93	−	13937.3i	0.520178	−	1.13903i
$532$	776.225	+	227.920i	0.0632587	+	0.0185744i
$533$	−1967.14	−	2270.20i	−0.159862	−	0.184490i
$534$	−2786.38	+	1790.70i	−0.225802	+	0.145114i
$535$	−3912.84	+	4515.66i	−0.316200	+	0.364914i
$536$	−3855.30	+	26814.2i	−0.310679	+	2.16082i
$537$	−555.540	+	163.121i	−0.0446430	+	0.0131084i
$538$	−29477.4	−	18944.0i	−2.36220	−	1.51809i
$539$	47.7998	+	332.455i	0.00381982	+	0.0265675i
$540$	−1769.35	−	3874.34i	−0.141001	−	0.308750i
$541$	2247.97	+	4922.38i	0.178647	+	0.391182i	0.977678	−	0.210107i	$-0.0673813\pi$
$541$	2247.97	+	4922.38i	0.178647	+	0.391182i	−0.799032	+	0.601289i	$0.794654\pi$
$542$	−2042.90	−	14208.7i	−0.161901	−	1.12604i
$543$	−550.618	−	353.861i	−0.0435161	−	0.0279661i
$544$	1989.96	−	584.306i	0.156836	−	0.0460513i
$545$	478.478	−	3327.89i	0.0376069	−	0.261562i
$546$	−1191.97	+	1375.61i	−0.0934280	+	0.107822i
$547$	−855.778	+	549.975i	−0.0668929	+	0.0429894i	−0.573660	−	0.819094i	$-0.694477\pi$
$547$	−855.778	+	549.975i	−0.0668929	+	0.0429894i	0.506767	+	0.862083i	$0.330840\pi$
$548$	17067.8	+	19697.3i	1.33047	+	1.53545i
$549$	−11957.8	−	3511.12i	−0.929590	−	0.272952i
$550$	70.0358	−	153.357i	0.00542971	−	0.0118894i
$551$	−1096.86			−0.0848058
$552$	3368.28	−	3539.26i	0.259717	−	0.272900i
$553$	9690.80			0.745198
$554$	15568.2	−	34089.7i	1.19392	−	2.61432i
$555$	453.582	+	133.184i	0.0346910	+	0.0101862i
$556$	10335.9	+	11928.3i	0.788384	+	0.909844i
$557$	−12919.7	+	8302.96i	−0.982807	+	0.631611i	−0.930219	−	0.367005i	$-0.880383\pi$
$557$	−12919.7	+	8302.96i	−0.982807	+	0.631611i	−0.0525875	+	0.998616i	$0.516747\pi$
$558$	−11614.1	+	13403.3i	−0.881115	+	1.01686i
$559$	2407.75	−	16746.2i	0.182177	−	1.26707i
$560$	4834.67	−	1419.59i	0.364825	−	0.107122i
$561$	−14.5391	−	9.34370i	−0.00109419	−	0.000703193i
$562$	−3382.86	−	23528.3i	−0.253910	−	1.76598i
$563$	−5295.40	−	11595.3i	−0.396402	−	0.868000i	−0.997622	−	0.0689166i	$-0.978046\pi$
$563$	−5295.40	−	11595.3i	−0.396402	−	0.868000i	0.601220	−	0.799083i	$-0.294682\pi$
$564$	2002.82	+	4385.56i	0.149528	+	0.327421i
$565$	888.867	+	6182.21i	0.0661857	+	0.460332i
$566$	19588.2	+	12588.6i	1.45469	+	0.934872i
$567$	6061.93	−	1779.94i	0.448989	−	0.131835i
$568$	1451.68	−	10096.7i	0.107238	−	0.745856i
$569$	−300.053	+	346.280i	−0.0221070	+	0.0255128i	−0.766695	−	0.642011i	$-0.778100\pi$
$569$	−300.053	+	346.280i	−0.0221070	+	0.0255128i	0.744588	+	0.667524i	$0.232646\pi$
$570$	93.1670	−	59.8748i	0.00684620	−	0.00439979i
$571$	6402.30	+	7388.65i	0.469226	+	0.541515i	0.940196	−	0.340634i	$-0.110642\pi$
$571$	6402.30	+	7388.65i	0.469226	+	0.541515i	−0.470970	+	0.882149i	$0.656096\pi$
$572$	935.167	+	274.590i	0.0683589	+	0.0200720i
$573$	−350.700	+	767.925i	−0.0255684	+	0.0559870i
$574$	3492.48			0.253960
$575$	−1027.32	−	2559.10i	−0.0745083	−	0.185603i
$576$	2887.46			0.208873
$577$	2915.97	−	6385.09i	0.210387	−	0.460684i	−0.774791	−	0.632217i	$-0.782145\pi$
$577$	2915.97	−	6385.09i	0.210387	−	0.460684i	0.985178	+	0.171534i	$0.0548722\pi$
$578$	22874.2	+	6716.46i	1.64609	+	0.483335i
$579$	439.664	+	507.399i	0.0315575	+	0.0364193i
$580$	−16892.8	+	10856.4i	−1.20937	+	0.777218i
$581$	7807.87	−	9010.77i	0.557531	−	0.643425i
$582$	354.763	−	2467.43i	0.0252670	−	0.175736i
$583$	294.825	−	86.5685i	0.0209441	−	0.00614974i
$584$	11889.0	+	7640.58i	0.842413	+	0.541386i
$585$	−773.031	−	5376.55i	−0.0546340	−	0.379988i
$586$	17102.2	+	37448.5i	1.20560	+	2.63990i
$587$	8953.43	+	19605.3i	0.629553	+	1.37853i	0.908363	+	0.418182i	$0.137333\pi$
$587$	8953.43	+	19605.3i	0.629553	+	1.37853i	−0.278810	+	0.960346i	$0.589940\pi$
$588$	574.839	+	3998.09i	0.0403163	+	0.280406i
$589$	−542.102	−	348.388i	−0.0379235	−	0.0243720i
$590$	14217.0	−	4174.49i	0.992042	−	0.291290i
$591$	−669.806	+	4658.61i	−0.0466196	+	0.324246i
$592$	7202.66	−	8312.31i	0.500047	−	0.577084i
$593$	−7235.60	+	4650.04i	−0.501063	+	0.322014i	−0.766641	−	0.642075i	$-0.778074\pi$
$593$	−7235.60	+	4650.04i	−0.501063	+	0.322014i	0.265578	+	0.964089i	$0.414437\pi$
$594$	213.406	+	246.284i	0.0147410	+	0.0170120i
$595$	−652.855	−	191.695i	−0.0449823	−	0.0132080i
$596$	25375.5	−	55564.5i	1.74399	−	3.81881i
$597$	−372.817			−0.0255584
$598$	20060.7	−	11607.4i	1.37181	−	0.793749i
$599$	−9582.78			−0.653659			−0.326830	−	0.945083i	$-0.605980\pi$
$599$	−9582.78			−0.653659			−0.326830	+	0.945083i	$0.605980\pi$
$600$	460.015	−	1007.29i	0.0313001	−	0.0685375i
$601$	−7946.70	−	2333.36i	−0.539355	−	0.158369i	0.000698035	−	1.00000i	$-0.499778\pi$
$601$	−7946.70	−	2333.36i	−0.539355	−	0.158369i	−0.540053	+	0.841631i	$0.681596\pi$
$602$	12881.2	+	14865.7i	0.872093	+	1.00645i
$603$	−12238.2	+	7865.01i	−0.826497	+	0.531157i
$604$	−1194.14	+	1378.12i	−0.0804454	+	0.0928389i
$605$	945.843	−	6578.48i	0.0635603	−	0.442071i
$606$	7655.23	−	2247.78i	0.513156	−	0.150676i
$607$	−7427.92	−	4773.63i	−0.496688	−	0.319202i	0.268202	−	0.963363i	$-0.413571\pi$
$607$	−7427.92	−	4773.63i	−0.496688	−	0.319202i	−0.764890	+	0.644161i	$0.777207\pi$
$608$	−99.5390	−	692.309i	−0.00663954	−	0.0461790i
$609$	819.865	+	1795.25i	0.0545527	+	0.119454i
$610$	−5006.63	−	10963.0i	−0.332316	−	0.727669i
$611$	1777.68	+	12364.0i	0.117704	+	0.818649i
$612$	5541.27	+	3561.16i	0.366001	+	0.235214i
$613$	−26059.3	+	7651.69i	−1.71700	+	0.504158i	−0.984317	−	0.176408i	$-0.943552\pi$
$613$	−26059.3	+	7651.69i	−1.71700	+	0.504158i	−0.732687	+	0.680566i	$0.761734\pi$
$614$	388.811	−	2704.24i	0.0255556	−	0.177743i
$615$	215.357	−	248.536i	0.0141204	−	0.0162958i
$616$	−520.660	+	334.608i	−0.0340552	+	0.0218859i
$617$	19840.9	+	22897.7i	1.29460	+	1.49404i	0.761821	+	0.647788i	$0.224306\pi$
$617$	19840.9	+	22897.7i	1.29460	+	1.49404i	0.532776	+	0.846256i	$0.321149\pi$
$618$	−6452.65	−	1894.67i	−0.420006	−	0.123325i
$619$	−6696.16	+	14662.5i	−0.434800	+	0.952080i	0.557723	+	0.830027i	$0.311675\pi$
$619$	−6696.16	+	14662.5i	−0.434800	+	0.952080i	−0.992524	+	0.122053i	$0.961052\pi$
$620$	−11797.2			−0.764170
$621$	5324.50	+	248.583i	0.344066	+	0.0160633i
$622$	46287.2			2.98384
$623$	2850.85	−	6242.50i	0.183334	−	0.401445i
$624$	3826.18	+	1123.47i	0.245465	+	0.0720749i
$625$	−409.288	−	472.343i	−0.0261944	−	0.0302300i
$626$	−35290.0	+	22679.5i	−2.25315	+	1.44801i
$627$	−3.81679	+	4.40481i	−0.000243107	+	0.000280560i
$628$	−4632.11	+	32217.1i	−0.294334	+	2.04713i
$629$	−1425.07	+	418.437i	−0.0903357	+	0.0265249i
$630$	5312.78	+	3414.31i	0.335978	+	0.215920i
$631$	−1738.05	−	12088.4i	−0.109652	−	0.762649i	−0.968247	−	0.249994i	$-0.919571\pi$
$631$	−1738.05	−	12088.4i	−0.109652	−	0.762649i	0.858595	−	0.512655i	$-0.171338\pi$
$632$	−20584.3	−	45073.3i	−1.29557	−	2.83690i
$633$	705.182	+	1544.13i	0.0442788	+	0.0969570i
$634$	7666.20	+	53319.6i	0.480227	+	3.34005i
$635$	−2302.61	−	1479.80i	−0.143899	−	0.0924786i
$636$	3545.56	−	1041.07i	0.221054	−	0.0649074i
$637$	−1489.33	+	10358.5i	−0.0926362	+	0.644299i
$638$	1006.12	−	1161.13i	0.0624339	−	0.0720526i
$639$	4608.18	−	2961.50i	0.285285	−	0.183341i
$640$	5634.03	+	6502.02i	0.347976	+	0.401586i
$641$	−366.219	−	107.532i	−0.0225660	−	0.00662596i	0.270430	−	0.962740i	$-0.412834\pi$
$641$	−366.219	−	107.532i	−0.0225660	−	0.00662596i	−0.292996	+	0.956114i	$0.594652\pi$
$642$	2283.87	−	5000.99i	0.140401	−	0.307435i
$643$	−20261.9			−1.24269			−0.621346	−	0.783537i	$-0.713414\pi$
$643$	−20261.9			−1.24269			−0.621346	+	0.783537i	$0.713414\pi$
$644$	−3490.51	+	18203.2i	−0.213579	+	1.11383i
$645$	1852.19			0.113070
$646$	−144.543	+	316.504i	−0.00880334	+	0.0192766i
$647$	−4807.13	−	1411.50i	−0.292098	−	0.0857678i	0.132400	−	0.991196i	$-0.457732\pi$
$647$	−4807.13	−	1411.50i	−0.292098	−	0.0857678i	−0.424499	+	0.905428i	$0.639550\pi$
$648$	−21154.9	−	24414.1i	−1.28248	−	1.48006i
$649$	−656.006	+	421.589i	−0.0396772	+	0.0254990i
$650$	3439.94	−	3969.90i	0.207578	−	0.239557i
$651$	−165.011	+	1147.67i	−0.00993438	+	0.0690951i
$652$	−94.7901	+	27.8329i	−0.00569366	+	0.00167181i
$653$	−1309.20	−	841.371i	−0.0784577	−	0.0504217i	0.500824	−	0.865549i	$-0.333030\pi$
$653$	−1309.20	−	841.371i	−0.0784577	−	0.0504217i	−0.579282	+	0.815128i	$0.696667\pi$
$654$	440.260	+	3062.07i	0.0263234	+	0.183083i
$655$	5555.60	+	12165.1i	0.331412	+	0.725692i
$656$	−3178.50	−	6959.95i	−0.189176	−	0.414239i
$657$	1080.06	+	7512.02i	0.0641360	+	0.446076i
$658$	−12217.4	−	7851.63i	−0.723834	−	0.465180i
$659$	−12697.2	+	3728.22i	−0.750548	+	0.220381i	−0.634564	−	0.772870i	$-0.718820\pi$
$659$	−12697.2	+	3728.22i	−0.750548	+	0.220381i	−0.115984	+	0.993251i	$0.537002\pi$
$660$	−15.1853	+	105.616i	−0.000895585	+	0.00622893i
$661$	−20695.5	+	23883.9i	−1.21780	+	1.40541i	−0.330758	+	0.943716i	$0.607304\pi$
$661$	−20695.5	+	23883.9i	−1.21780	+	1.40541i	−0.887038	+	0.461696i	$0.847241\pi$
$662$	−7240.68	+	4653.30i	−0.425101	+	0.273196i
$663$	−352.633	−	406.960i	−0.0206563	−	0.0238386i
$664$	−58495.1	−	17175.7i	−3.41875	−	1.00384i
$665$	−95.3227	+	208.728i	−0.00555858	+	0.0121716i
$666$	13785.2			0.802051
$667$	−2412.47	−	25014.1i	−0.140047	−	1.45210i
$668$	−39065.7			−2.26272
$669$	−9.50192	+	20.8063i	−0.000549126	+	0.00120242i
$670$	−13498.5	−	3963.53i	−0.778350	−	0.228544i
$671$	415.362	+	479.353i	0.0238970	+	0.0275786i
$672$	−1058.71	+	680.392i	−0.0607748	+	0.0390576i
$673$	5638.25	−	6506.89i	0.322940	−	0.372693i	−0.570946	−	0.820988i	$-0.693423\pi$
$673$	5638.25	−	6506.89i	0.322940	−	0.372693i	0.893886	+	0.448295i	$0.147969\pi$
$674$	1443.24	−	10038.0i	0.0824802	−	0.573662i
$675$	1159.16	−	340.359i	0.0660977	−	0.0194080i
$676$	−7033.68	−	4520.27i	−0.400187	−	0.257184i
$677$	448.492	+	3119.33i	0.0254608	+	0.177084i	0.998584	−	0.0532024i	$-0.0169429\pi$
$677$	448.492	+	3119.33i	0.0254608	+	0.177084i	−0.973123	+	0.230286i	$0.926034\pi$
$678$	−2387.35	−	5227.56i	−0.135229	−	0.296111i
$679$	2145.60	+	4698.22i	0.121268	+	0.265539i
$680$	495.130	+	3443.70i	0.0279226	+	0.194206i
$681$	−676.074	−	434.487i	−0.0380429	−	0.0244487i
$682$	866.056	−	254.297i	0.0486261	−	0.0142779i
$683$	4768.19	−	33163.5i	0.267130	−	1.85793i	−0.208151	−	0.978097i	$-0.566744\pi$
$683$	4768.19	−	33163.5i	0.267130	−	1.85793i	0.475281	−	0.879834i	$-0.342347\pi$
$684$	1454.69	−	1678.80i	0.0813180	−	0.0938459i
$685$	−6219.05	+	3996.74i	−0.346887	+	0.222931i
$686$	−18806.9	−	21704.4i	−1.04672	−	1.20798i
$687$	−3202.26	−	940.269i	−0.177837	−	0.0522176i
$688$	17901.8	−	39199.5i	0.992007	−	2.17219i
$689$	9573.84			0.529368
$690$	1570.37	+	1993.00i	0.0866418	+	0.109960i
$691$	29516.4			1.62497			0.812486	−	0.582981i	$-0.198114\pi$
$691$	29516.4			1.62497			0.812486	+	0.582981i	$0.198114\pi$
$692$	−8477.20	+	18562.5i	−0.465686	+	1.01971i
$693$	−318.897	−	93.6368i	−0.0174804	−	0.00513271i
$694$	29357.6	+	33880.5i	1.60576	+	1.85315i
$695$	−3766.14	+	2420.35i	−0.205551	+	0.132100i
$696$	6608.50	−	7626.62i	0.359906	−	0.415354i
$697$	−147.042	+	1022.70i	−0.00799081	+	0.0555773i
$698$	−18354.8	+	5389.47i	−0.995331	+	0.292256i
$699$	2490.03	+	1600.24i	0.134737	+	0.0865905i
$700$	597.844	+	4158.09i	0.0322805	+	0.224516i
$701$	−3464.87	−	7587.00i	−0.186685	−	0.408783i	0.793029	−	0.609184i	$-0.208503\pi$
$701$	−3464.87	−	7587.00i	−0.186685	−	0.408783i	−0.979714	+	0.200401i	$0.935776\pi$
$702$	4217.97	+	9236.07i	0.226777	+	0.496571i
$703$	71.2825	+	495.781i	0.00382428	+	0.0265985i
$704$	−123.627	−	79.4500i	−0.00661840	−	0.00425339i
$705$	−1312.11	+	385.270i	−0.0700948	+	0.0205817i
$706$	4868.33	−	33860.0i	0.259521	−	1.80501i
$707$	−10825.4	+	12493.2i	−0.575858	+	0.664576i
$708$	−7889.10	+	5070.02i	−0.418772	+	0.269128i
$709$	1687.19	+	1947.12i	0.0893705	+	0.103139i	0.798673	−	0.601765i	$-0.205536\pi$
$709$	1687.19	+	1947.12i	0.0893705	+	0.103139i	−0.709303	+	0.704904i	$0.750990\pi$
$710$	5082.76	+	1492.43i	0.268665	+	0.0788873i
$711$	11054.0	−	24204.8i	0.583060	−	1.27672i
$712$	−35090.3			−1.84700
$713$	6752.73	−	13129.0i	0.354687	−	0.689599i
$714$	626.068			0.0328151
$715$	−114.841	+	251.467i	−0.00600674	+	0.0131529i
$716$	−10776.0	−	3164.11i	−0.562454	−	0.165151i
$717$	−3779.82	−	4362.14i	−0.196876	−	0.227207i
$718$	34082.4	−	21903.4i	1.77151	−	1.13848i
$719$	−3349.90	+	3865.99i	−0.173756	+	0.200525i	−0.835947	−	0.548810i	$-0.815081\pi$
$719$	−3349.90	+	3865.99i	−0.173756	+	0.200525i	0.662192	+	0.749335i	$0.269627\pi$
$720$	1969.03	−	13694.9i	0.101918	−	0.708859i
$721$	13369.6	−	3925.66i	0.690581	−	0.202773i
$722$	−29112.2	−	18709.2i	−1.50061	−	0.964385i
$723$	748.893	+	5208.66i	0.0385223	+	0.267928i
$724$	−5274.08	−	11548.6i	−0.270732	−	0.592820i
$725$	−2366.06	−	5180.96i	−0.121205	−	0.265401i
$726$	870.293	+	6053.02i	0.0444898	+	0.309433i
$727$	3185.37	+	2047.11i	0.162502	+	0.104433i	0.619364	−	0.785104i	$-0.287390\pi$
$727$	3185.37	+	2047.11i	0.162502	+	0.104433i	−0.456862	+	0.889537i	$0.651027\pi$
$728$	−18502.6	+	5432.85i	−0.941966	+	0.276586i
$729$	2300.11	−	15997.6i	0.116857	−	0.812762i
$730$	−4806.22	+	5546.67i	−0.243680	+	0.281221i
$731$	−4895.44	+	3146.11i	−0.247694	+	0.159183i
$732$	4995.13	+	5764.68i	0.252220	+	0.291078i
$733$	8173.05	+	2399.82i	0.411840	+	0.120927i	0.481088	−	0.876672i	$-0.340242\pi$
$733$	8173.05	+	2399.82i	0.411840	+	0.120927i	−0.0692481	+	0.997599i	$0.522060\pi$
$734$	−18323.4	+	40122.6i	−0.921427	+	2.01764i
$735$	−1145.68			−0.0574955
$736$	15569.3	−	3792.68i	0.779744	−	0.189946i
$737$	740.389			0.0370048
$738$	3983.75	−	8723.20i	0.198704	−	0.435102i
$739$	−28901.1	−	8486.13i	−1.43863	−	0.422419i	−0.532862	−	0.846202i	$-0.678884\pi$
$739$	−28901.1	−	8486.13i	−1.43863	−	0.422419i	−0.905764	+	0.423783i	$0.860702\pi$
$740$	6004.89	+	6930.01i	0.298303	+	0.344260i
$741$	−152.771	+	98.1797i	−0.00757378	+	0.00486737i
$742$	−7289.26	+	8412.25i	−0.360643	+	0.416204i
$743$	−1532.69	+	10660.1i	−0.0756781	+	0.526353i	0.916354	+	0.400369i	$0.131118\pi$
$743$	−1532.69	+	10660.1i	−0.0756781	+	0.526353i	−0.992032	+	0.125984i	$0.959791\pi$
$744$	5688.50	−	1670.29i	0.280310	−	0.0823064i
$745$	14575.6	+	9367.18i	0.716791	+	0.460654i
$746$	−4631.98	−	32216.1i	−0.227331	−	1.58112i
$747$	−13600.1	−	29780.1i	−0.666133	−	1.45863i
$748$	−139.262	−	304.942i	−0.00680740	−	0.0149061i
$749$	1621.14	+	11275.3i	0.0790855	+	0.550052i
$750$	483.786	+	310.911i	0.0235538	+	0.0151371i
$751$	−29582.1	+	8686.09i	−1.43737	+	0.422050i	−0.905345	−	0.424677i	$-0.860388\pi$
$751$	−29582.1	+	8686.09i	−1.43737	+	0.422050i	−0.532027	+	0.846728i	$0.678569\pi$
$752$	−4528.01	+	31493.0i	−0.219574	+	1.52717i
$753$	3728.88	−	4303.36i	0.180462	−	0.208264i
$754$	40271.0	−	25880.6i	1.94507	−	1.25002i
$755$	−338.708	−	390.890i	−0.0163269	−	0.0188423i
$756$	−7791.11	−	2287.68i	−0.374815	−	0.110056i
$757$	−13123.9	+	28737.4i	−0.630116	+	1.37976i	0.277812	+	0.960635i	$0.410391\pi$
$757$	−13123.9	+	28737.4i	−0.630116	+	1.37976i	−0.907928	+	0.419126i	$0.862337\pi$
$758$	17991.6			0.862114
$759$	−108.847	−	77.3545i	−0.00520540	−	0.00369933i
$760$	1173.30			0.0560000
$761$	−2036.43	+	4459.15i	−0.0970044	+	0.212410i	−0.951913	−	0.306369i	$-0.900886\pi$
$761$	−2036.43	+	4459.15i	−0.0970044	+	0.212410i	0.854908	+	0.518779i	$0.173613\pi$
$762$	2416.47	+	709.539i	0.114881	+	0.0337322i
$763$	−4197.46	−	4844.13i	−0.199159	−	0.229842i
$764$	−13775.9	+	8853.26i	−0.652351	+	0.419241i

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)

\(f(q)\)	\(=\)	\(q+(2.10300 - 4.60492i) q^{2} +(-0.871970 - 0.256034i) q^{3} +(-11.5438 - 13.3223i) q^{4} +(4.20627 - 2.70320i) q^{5} +(-3.01277 + 3.47692i) q^{6} +(1.35658 - 9.43524i) q^{7} +(-46.7662 + 13.7318i) q^{8} +(-22.0191 - 14.1508i) q^{9} +O(q^{10})\)	\(q+(2.10300 - 4.60492i) q^{2} +(-0.871970 - 0.256034i) q^{3} +(-11.5438 - 13.3223i) q^{4} +(4.20627 - 2.70320i) q^{5} +(-3.01277 + 3.47692i) q^{6} +(1.35658 - 9.43524i) q^{7} +(-46.7662 + 13.7318i) q^{8} +(-22.0191 - 14.1508i) q^{9} +(-3.60228 - 25.0544i) q^{10} +(0.553380 + 1.21173i) q^{11} +(6.65493 + 14.5723i) q^{12} +(5.90684 + 41.0829i) q^{13} +(-40.5957 - 26.0892i) q^{14} +(-4.35985 + 1.28017i) q^{15} +(-15.0456 + 104.644i) q^{16} +(9.34884 - 10.7891i) q^{17} +(-111.469 + 71.6370i) q^{18} +(-3.15281 - 3.63853i) q^{19} +(-84.5694 - 24.8318i) q^{20} +(-3.59864 + 7.87992i) q^{21} +6.74370 q^{22} +(76.0429 - 79.9029i) q^{23} +44.2945 q^{24} +(10.3854 - 22.7408i) q^{25} +(201.606 + 59.1968i) q^{26} +(31.6453 + 36.5206i) q^{27} +(-141.359 + 90.8461i) q^{28} +(149.195 - 172.180i) q^{29} +(-3.27368 + 22.7690i) q^{30} +(128.425 - 37.7088i) q^{31} +(122.214 + 78.5423i) q^{32} +(-0.172287 - 1.19828i) q^{33} +(-30.0226 - 65.7403i) q^{34} +(-19.7992 - 43.3543i) q^{35} +(65.6634 + 456.699i) q^{36} +(-87.5208 - 56.2462i) q^{37} +(-23.3855 + 6.86661i) q^{38} +(5.36803 - 37.3354i) q^{39} +(-159.591 + 184.178i) q^{40} +(-60.8847 + 39.1282i) q^{41} +(28.7185 + 33.1429i) q^{42} +(-391.109 - 114.840i) q^{43} +(9.75495 - 21.3604i) q^{44} -130.871 q^{45} +(-208.029 - 518.208i) q^{46} +300.953 q^{47} +(39.9118 - 87.3947i) q^{48} +(241.923 + 71.0349i) q^{49} +(-82.8792 - 95.6477i) q^{50} +(-10.9143 + 7.01419i) q^{51} +(479.132 - 552.948i) q^{52} +(32.8270 - 228.317i) q^{53} +(234.725 - 68.9214i) q^{54} +(5.60323 + 3.60098i) q^{55} +(66.1205 + 459.878i) q^{56} +(1.81757 + 3.97992i) q^{57} +(-479.119 - 1049.12i) q^{58} +(83.3086 + 579.424i) q^{59} +(67.3842 + 43.3052i) q^{60} +(456.855 - 134.145i) q^{61} +(96.4302 - 670.687i) q^{62} +(-163.387 + 188.558i) q^{63} +(-92.8048 + 59.6420i) q^{64} +(135.901 + 156.838i) q^{65} +(-5.88030 - 1.72661i) q^{66} +(230.888 - 505.573i) q^{67} -251.658 q^{68} +(-86.7650 + 50.2034i) q^{69} -241.281 q^{70} +(-86.9387 + 190.369i) q^{71} +(1224.06 + 359.417i) q^{72} +(-189.879 - 219.132i) q^{73} +(-443.066 + 284.741i) q^{74} +(-14.8781 + 17.1703i) q^{75} +(-12.0781 + 84.0053i) q^{76} +(12.1837 - 3.57746i) q^{77} +(-160.638 - 103.236i) q^{78} +(144.682 + 1006.28i) q^{79} +(219.590 + 480.834i) q^{80} +(275.331 + 602.891i) q^{81} +(52.1420 + 362.656i) q^{82} +(1052.24 + 676.234i) q^{83} +(146.521 - 43.0224i) q^{84} +(10.1585 - 70.6538i) q^{85} +(-1351.33 + 1559.52i) q^{86} +(-174.177 + 111.937i) q^{87} +(-42.5187 - 49.0692i) q^{88} +(690.778 + 202.831i) q^{89} +(-275.221 + 602.649i) q^{90} +395.640 q^{91} +(-1942.32 - 90.6804i) q^{92} -121.637 q^{93} +(632.903 - 1385.86i) q^{94} +(-23.0972 - 6.78196i) q^{95} +(-86.4577 - 99.7775i) q^{96} +(-455.825 + 292.941i) q^{97} +(835.874 - 964.649i) q^{98} +(4.96208 - 34.5120i) 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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