LMFDB - Embedded newform 115.4.g.a.16.3

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			16.3
Character	$\chi$	$=$	115.16
Dual form			115.4.g.a.36.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.62935 + 3.03443i) q^{2} +(5.69405 - 3.65935i) q^{3} +(-1.15577 - 8.03858i) q^{4} +(2.07708 + 4.54816i) q^{5} +(-3.86762 + 26.8999i) q^{6} +(-1.94859 + 0.572159i) q^{7} +(0.409529 + 0.263188i) q^{8} +(7.81524 - 17.1130i) q^{9} +O(q^{10})$	\(q+(-2.62935 + 3.03443i) q^{2} +(5.69405 - 3.65935i) q^{3} +(-1.15577 - 8.03858i) q^{4} +(2.07708 + 4.54816i) q^{5} +(-3.86762 + 26.8999i) q^{6} +(-1.94859 + 0.572159i) q^{7} +(0.409529 + 0.263188i) q^{8} +(7.81524 - 17.1130i) q^{9} +(-19.2624 - 5.65596i) q^{10} +(27.2835 + 31.4869i) q^{11} +(-35.9970 - 41.5427i) q^{12} +(77.0341 + 22.6192i) q^{13} +(3.38736 - 7.41728i) q^{14} +(28.4703 + 18.2967i) q^{15} +(60.4628 - 17.7535i) q^{16} +(0.200228 - 1.39261i) q^{17} +(31.3792 + 68.7108i) q^{18} +(-0.0722497 - 0.502508i) q^{19} +(34.1601 - 21.9534i) q^{20} +(-9.00167 + 10.3885i) q^{21} -167.283 q^{22} +(26.6576 + 107.034i) q^{23} +3.29498 q^{24} +(-16.3715 + 18.8937i) q^{25} +(-271.186 + 174.281i) q^{26} +(7.88616 + 54.8494i) q^{27} +(6.85148 + 15.0026i) q^{28} +(-8.79452 + 61.1672i) q^{29} +(-130.378 + 38.2826i) q^{30} +(-163.860 - 105.307i) q^{31} +(-106.724 + 233.693i) q^{32} +(270.575 + 79.4481i) q^{33} +(3.69932 + 4.26925i) q^{34} +(-6.64965 - 7.67410i) q^{35} +(-146.597 - 43.0447i) q^{36} +(85.9359 - 188.173i) q^{37} +(1.71480 + 1.10203i) q^{38} +(521.408 - 153.099i) q^{39} +(-0.346400 + 2.40926i) q^{40} +(-10.0827 - 22.0781i) q^{41} +(-7.85460 - 54.6299i) q^{42} +(331.768 - 213.215i) q^{43} +(221.576 - 255.712i) q^{44} +94.0654 q^{45} +(-394.881 - 200.540i) q^{46} -44.0009 q^{47} +(279.312 - 322.344i) q^{48} +(-285.080 + 183.210i) q^{49} +(-14.2853 - 99.3565i) q^{50} +(-3.95595 - 8.66233i) q^{51} +(92.7927 - 645.387i) q^{52} +(185.992 - 54.6123i) q^{53} +(-187.172 - 120.288i) q^{54} +(-86.5374 + 189.490i) q^{55} +(-0.948591 - 0.278531i) q^{56} +(-2.25025 - 2.59692i) q^{57} +(-162.484 - 187.516i) q^{58} +(-140.501 - 41.2550i) q^{59} +(114.175 - 250.007i) q^{60} +(-728.355 - 468.085i) q^{61} +(750.391 - 220.335i) q^{62} +(-5.43738 + 37.8178i) q^{63} +(-219.090 - 479.740i) q^{64} +(57.1296 + 397.345i) q^{65} +(-952.516 + 612.145i) q^{66} +(252.738 - 291.675i) q^{67} -11.4261 q^{68} +(543.466 + 511.911i) q^{69} +40.7708 q^{70} +(376.397 - 434.385i) q^{71} +(7.70450 - 4.95138i) q^{72} +(-36.2942 - 252.432i) q^{73} +(345.044 + 755.540i) q^{74} +(-24.0816 + 167.491i) q^{75} +(-3.95595 + 1.16157i) q^{76} +(-71.1800 - 45.7446i) q^{77} +(-906.395 + 1984.73i) q^{78} +(-910.012 - 267.204i) q^{79} +(206.331 + 238.119i) q^{80} +(578.256 + 667.343i) q^{81} +(93.5054 + 27.4557i) q^{82} +(437.641 - 958.300i) q^{83} +(93.9126 + 60.3540i) q^{84} +(6.74972 - 1.98190i) q^{85} +(-225.350 + 1567.34i) q^{86} +(173.756 + 380.472i) q^{87} +(2.88642 + 20.0755i) q^{88} +(-817.408 + 525.316i) q^{89} +(-247.331 + 285.435i) q^{90} -163.050 q^{91} +(829.595 - 337.997i) q^{92} -1318.38 q^{93} +(115.694 - 133.518i) q^{94} +(2.13542 - 1.37235i) q^{95} +(247.471 + 1721.20i) q^{96} +(152.393 + 333.694i) q^{97} +(193.638 - 1346.78i) q^{98} +(752.061 - 220.825i) 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 $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$e\left(\frac{4}{11}\right)$

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 $

$2$	−2.62935	+	3.03443i	−0.929615	+	1.07283i	0.0675594	+	0.997715i	$0.478479\pi$
$2$	−2.62935	+	3.03443i	−0.929615	+	1.07283i	−0.997175	+	0.0751179i	$0.976067\pi$
$3$	5.69405	−	3.65935i	1.09582	−	0.704242i	0.137663	−	0.990479i	$-0.456041\pi$
$3$	5.69405	−	3.65935i	1.09582	−	0.704242i	0.958159	+	0.286238i	$0.0924046\pi$
$4$	−1.15577	−	8.03858i	−0.144472	−	1.00482i
$5$	2.07708	+	4.54816i	0.185779	+	0.406800i
$5$	2.07708	+	4.54816i	0.185779	+	0.406800i
$6$	−3.86762	+	26.8999i	−0.263158	+	1.83031i
$7$	−1.94859	+	0.572159i	−0.105214	+	0.0308937i	−0.333916	−	0.942603i	$-0.608370\pi$
$7$	−1.94859	+	0.572159i	−0.105214	+	0.0308937i	0.228702	+	0.973497i	$0.426552\pi$
$8$	0.409529	+	0.263188i	0.0180988	+	0.0116314i
$9$	7.81524	−	17.1130i	0.289453	−	0.633814i
$10$	−19.2624	−	5.65596i	−0.609132	−	0.178857i
$11$	27.2835	+	31.4869i	0.747845	+	0.863059i	0.994358	−	0.106081i	$-0.0338302\pi$
$11$	27.2835	+	31.4869i	0.747845	+	0.863059i	−0.246513	+	0.969140i	$0.579285\pi$
$12$	−35.9970	−	41.5427i	−0.865953	−	0.999363i
$13$	77.0341	+	22.6192i	1.64349	+	0.482573i	0.967191	−	0.254051i	$-0.0817631\pi$
$13$	77.0341	+	22.6192i	1.64349	+	0.482573i	0.676302	+	0.736624i	$0.263581\pi$
$14$	3.38736	−	7.41728i	0.0646650	−	0.141597i
$15$	28.4703	+	18.2967i	0.490066	+	0.314946i
$16$	60.4628	−	17.7535i	0.944731	−	0.277398i
$17$	0.200228	−	1.39261i	0.00285661	−	0.0198682i	−0.988343	−	0.152242i	$-0.951351\pi$
$17$	0.200228	−	1.39261i	0.00285661	−	0.0198682i	0.991200	+	0.132374i	$0.0422599\pi$
$18$	31.3792	+	68.7108i	0.410897	+	0.899738i
$19$	−0.0722497	−	0.502508i	−0.000872380	−	0.00606754i	0.989381	−	0.145348i	$-0.0464302\pi$
$19$	−0.0722497	−	0.502508i	−0.000872380	−	0.00606754i	−0.990253	+	0.139280i	$0.955521\pi$
$20$	34.1601	−	21.9534i	0.381922	−	0.245446i
$21$	−9.00167	+	10.3885i	−0.0935394	+	0.107950i
$22$	−167.283			−1.62113
$23$	26.6576	+	107.034i	0.241673	+	0.970358i
$23$	26.6576	+	107.034i	0.241673	+	0.970358i
$24$	3.29498			0.0280243
$25$	−16.3715	+	18.8937i	−0.130972	+	0.151150i
$26$	−271.186	+	174.281i	−2.04554	+	1.31459i
$27$	7.88616	+	54.8494i	0.0562108	+	0.390955i
$28$	6.85148	+	15.0026i	0.0462431	+	0.101258i
$29$	−8.79452	+	61.1672i	−0.0563139	+	0.391671i	0.942098	+	0.335337i	$0.108850\pi$
$29$	−8.79452	+	61.1672i	−0.0563139	+	0.391671i	−0.998412	+	0.0563341i	$0.982059\pi$
$30$	−130.378	+	38.2826i	−0.793458	+	0.232980i
$31$	−163.860	−	105.307i	−0.949360	−	0.610117i	−0.0283261	−	0.999599i	$-0.509018\pi$
$31$	−163.860	−	105.307i	−0.949360	−	0.610117i	−0.921034	+	0.389482i	$0.872654\pi$
$32$	−106.724	+	233.693i	−0.589572	+	1.29098i
$33$	270.575	+	79.4481i	1.42731	+	0.419095i
$34$	3.69932	+	4.26925i	0.0186597	+	0.0215344i
$35$	−6.64965	−	7.67410i	−0.0321142	−	0.0370617i
$36$	−146.597	−	43.0447i	−0.678689	−	0.199281i
$37$	85.9359	−	188.173i	0.381832	−	0.836095i	−0.616962	−	0.786993i	$-0.711637\pi$
$37$	85.9359	−	188.173i	0.381832	−	0.836095i	0.998794	−	0.0491021i	$-0.0156360\pi$
$38$	1.71480	+	1.10203i	0.00732044	+	0.00470456i
$39$	521.408	−	153.099i	2.14082	−	0.628602i
$40$	−0.346400	+	2.40926i	−0.00136927	+	0.00952345i
$41$	−10.0827	−	22.0781i	−0.0384063	−	0.0840980i	0.889456	−	0.457020i	$-0.151083\pi$
$41$	−10.0827	−	22.0781i	−0.0384063	−	0.0840980i	−0.927863	+	0.372922i	$0.878356\pi$
$42$	−7.85460	−	54.6299i	−0.0288569	−	0.200704i
$43$	331.768	−	213.215i	1.17661	−	0.756161i	0.201850	−	0.979417i	$-0.435305\pi$
$43$	331.768	−	213.215i	1.17661	−	0.756161i	0.974760	+	0.223255i	$0.0716684\pi$
$44$	221.576	−	255.712i	0.759179	−	0.876139i
$45$	94.0654			0.311610
$46$	−394.881	−	200.540i	−1.26570	−	0.642784i
$47$	−44.0009			−0.136557			−0.0682786	−	0.997666i	$-0.521751\pi$
$47$	−44.0009			−0.136557			−0.0682786	+	0.997666i	$0.521751\pi$
$48$	279.312	−	322.344i	0.839901	−	0.969298i
$49$	−285.080	+	183.210i	−0.831138	+	0.534140i
$50$	−14.2853	−	99.3565i	−0.0404049	−	0.281023i
$51$	−3.95595	−	8.66233i	−0.0108616	−	0.0237837i
$52$	92.7927	−	645.387i	0.247462	−	1.72114i
$53$	185.992	−	54.6123i	0.482038	−	0.141539i	−0.0316803	−	0.999498i	$-0.510086\pi$
$53$	185.992	−	54.6123i	0.482038	−	0.141539i	0.513718	+	0.857959i	$0.328268\pi$
$54$	−187.172	−	120.288i	−0.471684	−	0.303133i
$55$	−86.5374	+	189.490i	−0.212158	+	0.464561i
$56$	−0.948591	−	0.278531i	−0.00226359	−	0.000664649i
$57$	−2.25025	−	2.59692i	−0.00522899	−	0.00603457i
$58$	−162.484	−	187.516i	−0.367848	−	0.424519i
$59$	−140.501	−	41.2550i	−0.310029	−	0.0910328i	0.123017	−	0.992405i	$-0.460743\pi$
$59$	−140.501	−	41.2550i	−0.310029	−	0.0910328i	−0.433046	+	0.901372i	$0.642561\pi$
$60$	114.175	−	250.007i	0.245665	−	0.537930i
$61$	−728.355	−	468.085i	−1.52879	−	0.982495i	−0.990158	−	0.139954i	$-0.955304\pi$
$61$	−728.355	−	468.085i	−1.52879	−	0.982495i	−0.538633	−	0.842540i	$-0.681059\pi$
$62$	750.391	−	220.335i	1.53709	−	0.451331i
$63$	−5.43738	+	37.8178i	−0.0108737	+	0.0756285i
$64$	−219.090	−	479.740i	−0.427910	−	0.936992i
$65$	57.1296	+	397.345i	0.109016	+	0.758225i
$66$	−952.516	+	612.145i	−1.77646	+	1.14166i
$67$	252.738	−	291.675i	0.460849	−	0.531848i	−0.476995	−	0.878906i	$-0.658274\pi$
$67$	252.738	−	291.675i	0.460849	−	0.531848i	0.937844	+	0.347058i	$0.112819\pi$
$68$	−11.4261			−0.0203767
$69$	543.466	+	511.911i	0.948197	+	0.893142i
$70$	40.7708			0.0696148
$71$	376.397	−	434.385i	0.629156	−	0.726085i	−0.348262	−	0.937397i	$-0.613228\pi$
$71$	376.397	−	434.385i	0.629156	−	0.726085i	0.977419	+	0.211312i	$0.0677736\pi$
$72$	7.70450	−	4.95138i	0.0126109	−	0.00810453i
$73$	−36.2942	−	252.432i	−0.0581906	−	0.404725i	−0.998010	−	0.0630534i	$-0.979916\pi$
$73$	−36.2942	−	252.432i	−0.0581906	−	0.404725i	0.939820	−	0.341671i	$-0.110993\pi$
$74$	345.044	+	755.540i	0.542034	+	1.18689i
$75$	−24.0816	+	167.491i	−0.0370760	+	0.257869i
$76$	−3.95595	+	1.16157i	−0.00597077	+	0.00175318i
$77$	−71.1800	−	45.7446i	−0.105347	−	0.0677024i
$78$	−906.395	+	1984.73i	−1.31576	+	2.88110i
$79$	−910.012	−	267.204i	−1.29600	−	0.380541i	−0.440227	−	0.897886i	$-0.645102\pi$
$79$	−910.012	−	267.204i	−1.29600	−	0.380541i	−0.855777	+	0.517345i	$0.826920\pi$
$80$	206.331	+	238.119i	0.288357	+	0.332782i
$81$	578.256	+	667.343i	0.793218	+	0.915422i
$82$	93.5054	+	27.4557i	0.125926	+	0.0369753i
$83$	437.641	−	958.300i	0.578763	−	1.26731i	−0.363235	−	0.931697i	$-0.618328\pi$
$83$	437.641	−	958.300i	0.578763	−	1.26731i	0.941998	−	0.335617i	$-0.108945\pi$
$84$	93.9126	+	60.3540i	0.121985	+	0.0783947i
$85$	6.74972	−	1.98190i	0.00861306	−	0.00252902i
$86$	−225.350	+	1567.34i	−0.282560	+	1.96524i
$87$	173.756	+	380.472i	0.214121	+	0.468860i
$88$	2.88642	+	20.0755i	0.00349651	+	0.0243188i
$89$	−817.408	+	525.316i	−0.973540	+	0.625656i	−0.927714	−	0.373293i	$-0.878229\pi$
$89$	−817.408	+	525.316i	−0.973540	+	0.625656i	−0.0458269	+	0.998949i	$0.514592\pi$
$90$	−247.331	+	285.435i	−0.289677	+	0.334305i
$91$	−163.050			−0.187827
$92$	829.595	−	337.997i	0.940122	−	0.383028i
$93$	−1318.38			−1.47000
$94$	115.694	−	133.518i	0.126946	−	0.146503i
$95$	2.13542	−	1.37235i	0.00230620	−	0.00148211i
$96$	247.471	+	1721.20i	0.263098	+	1.82989i
$97$	152.393	+	333.694i	0.159517	+	0.349294i	0.972467	−	0.233040i	$-0.0748672\pi$
$97$	152.393	+	333.694i	0.159517	+	0.349294i	−0.812950	+	0.582333i	$0.802140\pi$
$98$	193.638	−	1346.78i	0.199595	−	1.38822i
$99$	752.061	−	220.825i	0.763485	−	0.224179i
$100$	170.801	+	109.767i	0.170801	+	0.109767i
$101$	−79.4449	+	173.960i	−0.0782680	+	0.171383i	−0.944721	−	0.327876i	$-0.893667\pi$
$101$	−79.4449	+	173.960i	−0.0782680	+	0.171383i	0.866453	+	0.499259i	$0.166394\pi$
$102$	36.6868	+	10.7722i	0.0356131	+	0.0104569i
$103$	−42.8680	−	49.4723i	−0.0410088	−	0.0473267i	0.734875	−	0.678203i	$-0.237241\pi$
$103$	−42.8680	−	49.4723i	−0.0410088	−	0.0473267i	−0.775883	+	0.630876i	$0.782696\pi$
$104$	25.5946	+	29.5377i	0.0241322	+	0.0278501i
$105$	−65.9457	−	19.3634i	−0.0612918	−	0.0179969i
$106$	−323.322	+	707.975i	−0.296262	+	0.648723i
$107$	166.868	+	107.240i	0.150764	+	0.0968903i	0.613848	−	0.789424i	$-0.289621\pi$
$107$	166.868	+	107.240i	0.150764	+	0.0968903i	−0.463084	+	0.886314i	$0.653257\pi$
$108$	431.797	−	126.787i	0.384719	−	0.112964i
$109$	287.447	−	1999.24i	0.252591	−	1.75681i	−0.329943	−	0.944001i	$-0.607030\pi$
$109$	287.447	−	1999.24i	0.252591	−	1.75681i	0.582534	−	0.812807i	$-0.302061\pi$
$110$	−347.459	−	760.828i	−0.301172	−	0.659474i
$111$	−199.268	−	1385.94i	−0.170393	−	1.18511i
$112$	−107.660	+	69.1886i	−0.0908293	+	0.0583724i
$113$	−1083.47	+	1250.39i	−0.901982	+	1.04094i	0.0969755	+	0.995287i	$0.469083\pi$
$113$	−1083.47	+	1250.39i	−0.901982	+	1.04094i	−0.998957	+	0.0456556i	$0.985462\pi$
$114$	13.7969			0.0113350
$115$	−431.440	+	343.561i	−0.349843	+	0.278585i
$116$	501.862			0.401696
$117$	989.122	−	1141.51i	0.781576	−	0.901987i
$118$	494.613	−	317.868i	0.385871	−	0.247984i
$119$	0.406634	+	2.82820i	0.000313245	+	0.00217866i
$120$	6.84391	+	14.9861i	0.00520634	+	0.0114003i
$121$	−57.6109	+	400.693i	−0.0432840	+	0.301046i
$122$	3335.47	−	979.383i	2.47524	−	0.726796i
$123$	−138.203	−	88.8177i	−0.101312	−	0.0651091i
$124$	−657.130	+	1438.91i	−0.475903	+	1.04208i
$125$	−119.937	−	35.2166i	−0.0858197	−	0.0251989i
$126$	−100.459	−	115.936i	−0.0710284	−	0.0819711i
$127$	1038.40	+	1198.37i	0.725535	+	0.837312i	0.991961	−	0.126544i	$-0.0403884\pi$
$127$	1038.40	+	1198.37i	0.725535	+	0.837312i	−0.266426	+	0.963855i	$0.585843\pi$
$128$	59.7805	+	17.5531i	0.0412805	+	0.0121210i
$129$	1108.88	−	2428.11i	0.756834	−	1.65724i
$130$	−1355.93	−	871.403i	−0.914792	−	0.587901i
$131$	2671.58	−	784.447i	1.78181	−	0.523187i	0.786300	−	0.617844i	$-0.211994\pi$
$131$	2671.58	−	784.447i	1.78181	−	0.523187i	0.995510	+	0.0946576i	$0.0301756\pi$
$132$	325.926	−	2266.86i	0.214911	−	1.49474i
$133$	0.428300	+	0.937846i	0.000279235	+	0.000611440i
$134$	220.532	+	1533.83i	0.142172	+	0.988828i
$135$	−233.084	+	149.794i	−0.148598	+	0.0954978i
$136$	0.448519	−	0.517618i	0.000282795	−	0.000326363i
$137$	−1387.08			−0.865006			−0.432503	−	0.901632i	$-0.642370\pi$
$137$	−1387.08			−0.865006			−0.432503	+	0.901632i	$0.642370\pi$
$138$	−2982.32	+	303.117i	−1.83965	+	0.186979i
$139$	−906.751			−0.553306			−0.276653	−	0.960970i	$-0.589225\pi$
$139$	−906.751			−0.553306			−0.276653	+	0.960970i	$0.589225\pi$
$140$	−54.0034	+	62.3232i	−0.0326009	+	0.0376234i
$141$	−250.543	+	161.014i	−0.149642	+	0.0961692i
$142$	328.433	+	2284.30i	0.194095	+	1.34996i
$143$	1389.55	+	3042.69i	0.812589	+	1.77932i
$144$	168.716	−	1173.45i	0.0976366	−	0.679078i
$145$	−296.465	+	87.0501i	−0.169794	+	0.0498560i
$146$	861.417	+	553.599i	0.488297	+	0.313809i
$147$	−952.834	+	2086.42i	−0.534615	+	1.17064i
$148$	−1611.97	−	473.317i	−0.895291	−	0.262881i
$149$	713.926	+	823.915i	0.392531	+	0.453005i	0.917275	−	0.398255i	$-0.130384\pi$
$149$	713.926	+	823.915i	0.392531	+	0.453005i	−0.524744	+	0.851260i	$0.675839\pi$
$150$	−444.921	−	513.466i	−0.242184	−	0.279496i
$151$	−3155.13	−	926.431i	−1.70041	−	0.499284i	−0.719619	−	0.694369i	$-0.755684\pi$
$151$	−3155.13	−	926.431i	−1.70041	−	0.499284i	−0.980786	+	0.195085i	$0.937502\pi$
$152$	0.102666	−	0.224807i	5.47849e−5	−	0.000119962i
$153$	−22.2670	−	14.3101i	−0.0117659	−	0.00756146i
$154$	325.966	−	95.7122i	0.170565	−	0.0500825i
$155$	138.601	−	963.992i	0.0718240	−	0.499547i
$156$	−1833.33	−	4014.43i	−0.940922	−	2.06033i
$157$	32.6918	+	227.376i	0.0166184	+	0.115584i	0.996442	−	0.0842803i	$-0.0268591\pi$
$157$	32.6918	+	227.376i	0.0166184	+	0.115584i	−0.979824	+	0.199864i	$0.935950\pi$
$158$	3203.55	−	2058.80i	1.61304	−	1.03664i
$159$	859.205	−	991.576i	0.428550	−	0.494573i
$160$	−1284.55			−0.634701
$161$	−113.185	−	193.314i	−0.0554054	−	0.0946292i
$162$	−3545.44			−1.71948
$163$	136.545	−	157.582i	0.0656139	−	0.0757224i	−0.721994	−	0.691900i	$-0.756774\pi$
$163$	136.545	−	157.582i	0.0656139	−	0.0757224i	0.787608	+	0.616177i	$0.211319\pi$
$164$	−165.823	+	106.568i	−0.0789550	+	0.0507413i
$165$	200.663	+	1395.64i	0.0946761	+	0.658487i
$166$	1757.18	+	3847.70i	0.821590	+	1.79903i
$167$	−295.527	+	2055.43i	−0.136937	+	0.952421i	0.799270	+	0.600972i	$0.205220\pi$
$167$	−295.527	+	2055.43i	−0.136937	+	0.952421i	−0.936207	+	0.351448i	$0.885689\pi$
$168$	−6.42057	+	1.88525i	−0.00294856	+	0.000865775i
$169$	3574.39	+	2297.12i	1.62694	+	1.04557i
$170$	−11.7334	+	25.6927i	−0.00529361	+	0.0115914i
$171$	−9.16406	−	2.69081i	−0.00409821	−	0.00120334i
$172$	−2097.39	−	2420.52i	−0.929795	−	1.07304i
$173$	−608.084	−	701.766i	−0.267236	−	0.308406i	0.606233	−	0.795287i	$-0.292680\pi$
$173$	−608.084	−	701.766i	−0.267236	−	0.308406i	−0.873468	+	0.486881i	$0.838135\pi$
$174$	−1611.38	−	473.144i	−0.702060	−	0.206143i
$175$	21.0912	−	46.1833i	0.00911055	−	0.0199493i
$176$	2208.64	+	1419.41i	0.945923	+	0.607908i
$177$	−950.989	+	279.236i	−0.403846	+	0.118580i
$178$	555.215	−	3861.61i	0.233793	−	1.62607i
$179$	−788.421	−	1726.40i	−0.329214	−	0.720878i	0.670566	−	0.741850i	$-0.266051\pi$
$179$	−788.421	−	1726.40i	−0.329214	−	0.720878i	−0.999780	+	0.0209716i	$0.993324\pi$
$180$	−108.718	−	756.152i	−0.0450188	−	0.313113i
$181$	149.186	−	95.8757i	0.0612645	−	0.0393723i	−0.509650	−	0.860382i	$-0.670225\pi$
$181$	149.186	−	95.8757i	0.0612645	−	0.0393723i	0.570915	+	0.821009i	$0.306589\pi$
$182$	428.715	−	494.764i	0.174607	−	0.201507i
$183$	−5860.18			−2.36720
$184$	−17.2532	+	50.8497i	−0.00691261	+	0.0203733i
$185$	1034.34			0.411060
$186$	3466.49	−	4000.54i	1.36653	−	1.57706i
$187$	49.3120	−	31.6909i	0.0192837	−	0.0123929i
$188$	50.8550	+	353.705i	0.0197286	+	0.137216i
$189$	−46.7495	−	102.367i	−0.0179922	−	0.0393974i
$190$	−1.45046	+	10.0882i	−0.000553828	+	0.00385196i
$191$	−1871.47	+	549.513i	−0.708977	+	0.208175i	−0.616288	−	0.787521i	$-0.711364\pi$
$191$	−1871.47	+	549.513i	−0.708977	+	0.208175i	−0.0926890	+	0.995695i	$0.529546\pi$
$192$	−3003.04	−	1929.94i	−1.12878	−	0.725424i
$193$	1570.25	−	3438.37i	0.585643	−	1.28238i	−0.352396	−	0.935851i	$-0.614633\pi$
$193$	1570.25	−	3438.37i	0.585643	−	1.28238i	0.938039	−	0.346529i	$-0.112640\pi$
$194$	−1413.26	−	414.972i	−0.523023	−	0.153573i
$195$	1779.32	+	2053.45i	0.653436	+	0.754105i
$196$	1802.24	+	2079.89i	0.656792	+	0.757978i
$197$	−5053.55	−	1483.86i	−1.82767	−	0.536652i	−0.827959	−	0.560789i	$-0.810498\pi$
$197$	−5053.55	−	1483.86i	−1.82767	−	0.536652i	−0.999709	+	0.0241378i	$0.992316\pi$
$198$	−1307.35	+	2862.70i	−0.469240	+	1.02749i
$199$	3850.54	+	2474.59i	1.37165	+	0.881503i	0.998921	−	0.0464389i	$-0.0147873\pi$
$199$	3850.54	+	2474.59i	1.37165	+	0.881503i	0.372725	+	0.927942i	$0.378424\pi$
$200$	−11.6772	+	3.42874i	−0.00412852	+	0.00121224i
$201$	371.763	−	2585.67i	0.130459	−	0.907359i
$202$	−318.981	−	698.472i	−0.111106	−	0.243289i
$203$	−17.8604	−	124.222i	−0.00617515	−	0.0429491i
$204$	−65.0606	+	41.8119i	−0.0223292	+	0.0143501i
$205$	79.4721	−	91.7157i	0.0270760	−	0.0312473i
$206$	262.835			0.0888961
$207$	2040.01	+	380.309i	0.684979	+	0.127697i
$208$	5059.27			1.68652
$209$	13.8512	−	15.9851i	0.00458424	−	0.00529049i
$210$	232.151	−	149.194i	0.0762854	−	0.0490257i
$211$	849.631	+	5909.31i	0.277209	+	1.92803i	0.363156	+	0.931728i	$0.381699\pi$
$211$	849.631	+	5909.31i	0.277209	+	1.92803i	−0.0859472	+	0.996300i	$0.527392\pi$
$212$	−653.970	−	1431.99i	−0.211863	−	0.463914i
$213$	553.659	−	3850.78i	0.178104	−	1.23874i
$214$	−764.167	+	224.380i	−0.244100	+	0.0716742i
$215$	1658.84	+	1066.07i	0.526196	+	0.338166i
$216$	−11.2061	+	24.5380i	−0.00353000	+	0.00772962i
$217$	379.549	+	111.446i	0.118735	+	0.0348637i
$218$	5310.74	+	6128.92i	1.64995	+	1.90414i
$219$	−1130.40	−	1304.55i	−0.348791	−	0.402526i
$220$	1623.25	+	476.630i	0.497453	+	0.146065i
$221$	46.9243	−	102.750i	0.0142827	−	0.0312747i
$222$	4729.48	+	3039.45i	1.42983	+	0.918895i
$223$	−2197.45	+	645.229i	−0.659874	+	0.193757i	−0.594489	−	0.804104i	$-0.702646\pi$
$223$	−2197.45	+	645.229i	−0.659874	+	0.193757i	−0.0653849	+	0.997860i	$0.520828\pi$
$224$	74.2522	−	516.435i	0.0221481	−	0.154044i
$225$	195.381	+	427.825i	0.0578906	+	0.126763i
$226$	−945.401	−	6575.41i	−0.278262	−	1.93535i
$227$	3535.78	−	2272.31i	1.03382	−	0.664398i	0.0903718	−	0.995908i	$-0.471194\pi$
$227$	3535.78	−	2272.31i	1.03382	−	0.664398i	0.943452	+	0.331510i	$0.107558\pi$
$228$	−18.2748	+	21.0902i	−0.00530823	+	0.00612603i
$229$	−832.300			−0.240174			−0.120087	−	0.992763i	$-0.538317\pi$
$229$	−832.300			−0.240174			−0.120087	+	0.992763i	$0.538317\pi$
$230$	91.8930	−	2212.52i	0.0263446	−	0.634300i
$231$	−572.698			−0.163120
$232$	−19.7001	+	22.7351i	−0.00557489	+	0.00643377i
$233$	136.524	−	87.7387i	0.0383862	−	0.0246693i	−0.521307	−	0.853369i	$-0.674555\pi$
$233$	136.524	−	87.7387i	0.0383862	−	0.0246693i	0.559693	+	0.828700i	$0.310919\pi$
$234$	863.079	+	6002.85i	0.241116	+	1.67700i
$235$	−91.3931	−	200.123i	−0.0253695	−	0.0555514i
$236$	−169.243	+	1177.11i	−0.0466814	+	0.324676i
$237$	−6159.45	+	1808.58i	−1.68818	+	0.495695i
$238$	−9.65117	−	6.20243i	−0.00262854	−	0.00168926i
$239$	−1549.68	+	3393.33i	−0.419416	+	0.918394i	0.575511	+	0.817794i	$0.304803\pi$
$239$	−1549.68	+	3393.33i	−0.419416	+	0.918394i	−0.994927	+	0.100600i	$0.967924\pi$
$240$	2046.22	+	600.825i	0.550346	+	0.161596i
$241$	−4150.68	−	4790.14i	−1.10941	−	1.28033i	−0.956385	−	0.292110i	$-0.905643\pi$
$241$	−4150.68	−	4790.14i	−1.10941	−	1.28033i	−0.153029	−	0.988222i	$-0.548903\pi$
$242$	−1064.40	−	1228.38i	−0.282735	−	0.326294i
$243$	4299.10	+	1262.33i	1.13493	+	0.333245i
$244$	−2920.93	+	6395.94i	−0.766366	+	1.67811i
$245$	−1425.40	−	916.050i	−0.371696	−	0.238875i
$246$	632.895	−	185.835i	0.164032	−	0.0481642i
$247$	5.80066	−	40.3445i	0.00149428	−	0.0103929i
$248$	−39.3900	−	86.2522i	−0.0100858	−	0.0220847i
$249$	−1014.80	−	7058.09i	−0.258275	−	1.79634i
$250$	422.217	−	271.343i	0.106814	−	0.0686449i
$251$	−418.027	+	482.429i	−0.105122	+	0.121317i	−0.805872	−	0.592089i	$-0.798303\pi$
$251$	−418.027	+	482.429i	−0.105122	+	0.121317i	0.700750	+	0.713407i	$0.252849\pi$
$252$	310.286			0.0775642
$253$	−2642.87	+	3759.64i	−0.656742	+	0.934255i
$254$	−6366.70			−1.57276
$255$	31.1808	−	35.9846i	0.00765733	−	0.00883703i
$256$	3338.97	−	2145.82i	0.815178	−	0.523883i
$257$	645.281	+	4488.03i	0.156621	+	1.08932i	0.904804	+	0.425829i	$0.140017\pi$
$257$	645.281	+	4488.03i	0.156621	+	1.08932i	−0.748183	+	0.663493i	$0.769073\pi$
$258$	4452.30	+	9749.18i	1.07437	+	2.35255i
$259$	−59.7891	+	415.843i	−0.0143441	+	0.0997653i
$260$	3128.06	−	918.482i	0.746132	−	0.219084i
$261$	978.023	+	628.537i	0.231947	+	0.149063i
$262$	−4644.17	+	10169.3i	−1.09511	+	2.39795i
$263$	−3660.00	−	1074.67i	−0.858118	−	0.251966i	−0.177064	−	0.984199i	$-0.556660\pi$
$263$	−3660.00	−	1074.67i	−0.858118	−	0.251966i	−0.681054	+	0.732233i	$0.738478\pi$
$264$	89.8986	+	103.748i	0.0209579	+	0.0241867i
$265$	634.705	+	732.489i	0.147131	+	0.169798i
$266$	−3.97198	−	1.16628i	−0.000915555	−	0.000268831i
$267$	−2732.05	+	5982.36i	−0.626213	+	1.37122i
$268$	−2636.76	−	1694.55i	−0.600992	−	0.386234i
$269$	−1416.10	+	415.805i	−0.320971	+	0.0942456i	−0.438249	−	0.898854i	$-0.644401\pi$
$269$	−1416.10	+	415.805i	−0.320971	+	0.0942456i	0.117278	+	0.993099i	$0.462583\pi$
$270$	158.320	−	1101.14i	0.0356853	−	0.248197i
$271$	716.245	+	1568.36i	0.160549	+	0.351554i	0.972761	−	0.231808i	$-0.0744642\pi$
$271$	716.245	+	1568.36i	0.160549	+	0.351554i	−0.812212	+	0.583362i	$0.801737\pi$
$272$	−12.6174	−	87.7561i	−0.00281266	−	0.0195625i
$273$	−928.416	+	596.656i	−0.205825	+	0.132276i
$274$	3647.11	−	4208.98i	0.804123	−	0.928007i
$275$	−1041.58			−0.228398
$276$	3486.91	−	4960.35i	0.760462	−	1.08180i
$277$	3593.23			0.779408			0.389704	−	0.920940i	$-0.372577\pi$
$277$	3593.23			0.779408			0.389704	+	0.920940i	$0.372577\pi$
$278$	2384.16	−	2751.47i	0.514362	−	0.593605i
$279$	−3082.72	+	1981.14i	−0.661496	+	0.425118i
$280$	−0.703489	−	4.89287i	−0.000150148	−	0.00104430i
$281$	−1998.48	−	4376.06i	−0.424268	−	0.929018i	−0.994222	−	0.107341i	$-0.965766\pi$
$281$	−1998.48	−	4376.06i	−0.424268	−	0.929018i	0.569954	−	0.821677i	$-0.306961\pi$
$282$	170.179	−	1183.62i	0.0359362	−	0.249942i
$283$	6518.83	−	1914.10i	1.36927	−	0.402055i	0.487251	−	0.873262i	$-0.338000\pi$
$283$	6518.83	−	1914.10i	1.36927	−	0.402055i	0.882023	+	0.471207i	$0.156182\pi$
$284$	−3926.87	−	2523.65i	−0.820482	−	0.527292i
$285$	7.13729	−	15.6285i	0.00148343	−	0.00324825i
$286$	−12886.5	−	3783.81i	−2.66431	−	0.782312i
$287$	32.2793	+	37.2523i	0.00663898	+	0.00766179i
$288$	3165.11	+	3652.73i	0.647589	+	0.747358i
$289$	4712.09	+	1383.59i	0.959106	+	0.281619i
$290$	515.363	−	1128.49i	0.104356	−	0.228507i
$291$	2088.84	+	1342.41i	0.420789	+	0.270425i
$292$	−1987.25	+	583.508i	−0.398270	+	0.116943i
$293$	974.970	−	6781.07i	0.194397	−	1.35206i	−0.625801	−	0.779983i	$-0.715228\pi$
$293$	974.970	−	6781.07i	0.194397	−	1.35206i	0.820198	−	0.572079i	$-0.193863\pi$
$294$	−3825.75	−	8377.22i	−0.758919	−	1.66180i
$295$	−104.198	−	724.713i	−0.0205649	−	0.143032i
$296$	84.7183	−	54.4451i	0.0166356	−	0.0106911i
$297$	−1511.87	+	1744.80i	−0.295380	+	0.340887i
$298$	−4377.27			−0.850901
$299$	−367.498	+	8848.28i	−0.0710800	+	1.71140i
$300$	1374.22			0.264469
$301$	−524.489	+	605.293i	−0.100435	+	0.115909i
$302$	11107.1	−	7138.13i	2.11637	−	1.36011i
$303$	184.217	+	1281.26i	0.0349273	+	0.242925i
$304$	−13.2897	−	29.1004i	−0.00250729	−	0.00549020i
$305$	616.079	−	4284.92i	0.115661	−	0.804439i
$306$	101.971	−	29.9413i	0.0190499	−	0.00559356i
$307$	8866.99	+	5698.47i	1.64842	+	1.05938i	0.932482	+	0.361218i	$0.117639\pi$
$307$	8866.99	+	5698.47i	1.64842	+	1.05938i	0.715942	+	0.698160i	$0.245997\pi$
$308$	−285.454	+	625.057i	−0.0528092	+	0.115636i
$309$	−425.129	−	124.829i	−0.0782678	−	0.0229815i
$310$	2560.74	+	2955.25i	0.469161	+	0.541441i
$311$	2305.94	+	2661.20i	0.420443	+	0.485218i	0.925972	−	0.377592i	$-0.123248\pi$
$311$	2305.94	+	2661.20i	0.420443	+	0.485218i	−0.505529	+	0.862810i	$0.668702\pi$
$312$	253.825	+	74.5299i	0.0460578	+	0.0135238i
$313$	1983.25	−	4342.70i	0.358146	−	0.784230i	−0.641705	−	0.766952i	$-0.721773\pi$
$313$	1983.25	−	4342.70i	0.358146	−	0.784230i	0.999851	−	0.0172784i	$-0.00550016\pi$
$314$	−775.916	−	498.651i	−0.139451	−	0.0896194i
$315$	−183.295	+	53.8204i	−0.0327858	+	0.00962677i
$316$	−1096.17	+	7624.03i	−0.195140	+	1.35723i
$317$	110.795	+	242.608i	0.0196306	+	0.0429849i	0.919193	−	0.393807i	$-0.128842\pi$
$317$	110.795	+	242.608i	0.0196306	+	0.0429849i	−0.899563	+	0.436792i	$0.856115\pi$
$318$	749.717	+	5214.40i	0.132208	+	0.919525i
$319$	−2165.91	+	1391.95i	−0.380149	+	0.244307i
$320$	1726.87	−	1992.91i	0.301671	−	0.348147i
$321$	1342.59			0.233445
$322$	884.203	+	164.837i	0.153027	+	0.0285280i
$323$	−0.714266			−0.000123043
$324$	4696.16	−	5419.65i	0.805240	−	0.929296i
$325$	−1688.53	+	1085.15i	−0.288193	+	0.185210i
$326$	119.145	+	828.675i	0.0202419	+	0.140785i
$327$	−5679.16	−	12435.6i	−0.960423	−	2.10303i
$328$	1.68153	−	11.6953i	0.000283069	−	0.00196879i
$329$	85.7398	−	25.1755i	0.0143678	−	0.00421875i
$330$	−4762.58	−	3060.73i	−0.794459	−	0.510568i
$331$	1346.51	−	2948.44i	0.223598	−	0.489611i	−0.764272	−	0.644894i	$-0.776902\pi$
$331$	1346.51	−	2948.44i	0.223598	−	0.489611i	0.987870	+	0.155283i	$0.0496289\pi$
$332$	−8209.19	−	2410.43i	−1.35704	−	0.398463i
$333$	−2548.60	−	2941.24i	−0.419406	−	0.484021i
$334$	−5460.03	−	6301.21i	−0.894489	−	1.03230i
$335$	1851.54	+	543.662i	0.301972	+	0.0886669i
$336$	−359.835	+	787.928i	−0.0584244	+	0.127932i
$337$	−9086.63	−	5839.62i	−1.46878	−	0.943930i	−0.998099	−	0.0616280i	$-0.980371\pi$
$337$	−9086.63	−	5839.62i	−1.46878	−	0.943930i	−0.470684	−	0.882302i	$-0.655993\pi$
$338$	−16368.8	+	4806.30i	−2.63415	+	0.773456i
$339$	−1593.72	+	11084.5i	−0.255336	+	1.77590i
$340$	−23.7328	−	51.9676i	−0.00378556	−	0.00828923i
$341$	−1154.91	−	8032.58i	−0.183407	−	1.27563i
$342$	32.2606	−	20.7326i	0.00510074	−	0.00327805i
$343$	906.846	−	1046.56i	0.142755	−	0.164749i
$344$	191.984			0.0300904
$345$	−1199.43	+	3535.05i	−0.187175	+	0.551654i
$346$	3728.32			0.579295
$347$	7796.82	−	8998.01i	1.20621	−	1.39204i	0.308635	−	0.951181i	$-0.400128\pi$
$347$	7796.82	−	8998.01i	1.20621	−	1.39204i	0.897576	−	0.440860i	$-0.145327\pi$
$348$	2857.63	−	1836.49i	0.440187	−	0.282891i
$349$	−913.763	−	6355.36i	−0.140151	−	0.974770i	−0.931587	−	0.363518i	$-0.881575\pi$
$349$	−913.763	−	6355.36i	−0.140151	−	0.974770i	0.791436	−	0.611251i	$-0.209334\pi$
$350$	84.6839	+	185.432i	0.0129330	+	0.0283193i
$351$	−633.150	+	4403.65i	−0.0962822	+	0.669657i
$352$	−10270.1	+	3015.56i	−1.55510	+	0.456619i
$353$	−3267.67	−	2100.00i	−0.492693	−	0.316634i	0.270595	−	0.962693i	$-0.412780\pi$
$353$	−3267.67	−	2100.00i	−0.492693	−	0.316634i	−0.763287	+	0.646059i	$0.776416\pi$
$354$	1653.16	−	3619.92i	0.248205	−	0.543493i
$355$	2757.46	+	809.663i	0.412255	+	0.121049i
$356$	5167.54	+	5963.66i	0.769323	+	0.887846i
$357$	12.6648	+	14.6159i	0.00187757	+	0.00216683i
$358$	7311.67	+	2146.90i	1.07942	+	0.316948i
$359$	2295.16	−	5025.71i	0.337421	−	0.738849i	−0.662527	−	0.749038i	$-0.730516\pi$
$359$	2295.16	−	5025.71i	0.337421	−	0.738849i	0.999948	+	0.0101890i	$0.00324333\pi$
$360$	38.5225	+	24.7569i	0.00563976	+	0.00362445i
$361$	6580.92	−	1932.33i	0.959457	−	0.281722i
$362$	−101.333	+	704.784i	−0.0147125	+	0.102328i
$363$	1138.23	+	2492.39i	0.164578	+	0.360376i
$364$	188.449	+	1310.69i	0.0271357	+	0.188733i
$365$	1072.71	−	689.392i	0.153831	−	0.0988614i
$366$	15408.5	−	17782.3i	2.20058	−	2.53961i
$367$	−1981.82			−0.281881			−0.140940	−	0.990018i	$-0.545013\pi$
$367$	−1981.82			−0.281881			−0.140940	+	0.990018i	$0.545013\pi$
$368$	3512.02	+	5998.34i	0.497492	+	0.849687i
$369$	−456.621			−0.0644193
$370$	−2719.64	+	3138.63i	−0.382127	+	0.440998i
$371$	−331.177	+	212.834i	−0.0463446	+	0.0297838i
$372$	1523.75	+	10597.9i	0.212373	+	1.47709i
$373$	−3168.37	−	6937.77i	−0.439818	−	0.963067i	−0.991632	−	0.129099i	$-0.958791\pi$
$373$	−3168.37	−	6937.77i	−0.439818	−	0.963067i	0.551814	−	0.833967i	$-0.313936\pi$
$374$	−33.4946	+	232.960i	−0.00463092	+	0.0322088i
$375$	−811.795	+	238.365i	−0.111789	+	0.0328243i
$376$	−18.0196	−	11.5805i	−0.00247152	−	0.00158835i
$377$	−2061.03	+	4513.04i	−0.281562	+	0.616534i
$378$	433.547	+	127.301i	0.0589927	+	0.0173218i
$379$	4458.61	+	5145.51i	0.604283	+	0.697380i	0.972643	−	0.232303i	$-0.0746262\pi$
$379$	4458.61	+	5145.51i	0.604283	+	0.697380i	−0.368361	+	0.929683i	$0.620081\pi$
$380$	−13.4998	−	15.5796i	−0.00182244	−	0.00210320i
$381$	10298.0	+	3023.75i	1.38473	+	0.406592i
$382$	3253.28	−	7123.70i	0.435740	−	0.954137i
$383$	−6700.43	−	4306.11i	−0.893933	−	0.574496i	0.0110524	−	0.999939i	$-0.496482\pi$
$383$	−6700.43	−	4306.11i	−0.893933	−	0.574496i	−0.904985	+	0.425443i	$0.860118\pi$
$384$	404.626	−	118.809i	0.0537721	−	0.0157889i
$385$	60.2076	−	418.753i	0.00797003	−	0.0554328i
$386$	6304.76	+	13805.5i	0.831357	+	1.82042i
$387$	−1055.89	−	7343.87i	−0.138692	−	0.964625i
$388$	2506.29	−	1610.70i	0.327932	−	0.210749i
$389$	1773.79	−	2047.07i	0.231195	−	0.266813i	−0.628284	−	0.777984i	$-0.716243\pi$
$389$	1773.79	−	2047.07i	0.231195	−	0.266813i	0.859479	+	0.511171i	$0.170788\pi$
$390$	−10909.5			−1.41647
$391$	154.395	−	15.6925i	0.0199696	−	0.00202967i
$392$	−164.967			−0.0212554
$393$	12341.6	−	14242.9i	1.58410	−	1.82814i
$394$	17790.2	−	11433.1i	2.27476	−	1.46190i
$395$	−674.878	−	4693.88i	−0.0859666	−	0.597911i
$396$	−2644.33	−	5790.28i	−0.335562	−	0.734779i
$397$	−2129.68	+	14812.3i	−0.269234	+	1.87256i	0.186515	+	0.982452i	$0.440281\pi$
$397$	−2129.68	+	14812.3i	−0.269234	+	1.87256i	−0.455749	+	0.890108i	$0.650628\pi$
$398$	−17633.4	+	5177.63i	−2.22081	+	0.652088i
$399$	5.87067	+	3.77285i	0.000736594	+	0.000473380i
$400$	−654.438	+	1433.02i	−0.0818048	+	0.179127i
$401$	−11155.7	−	3275.61i	−1.38925	−	0.407921i	−0.500272	−	0.865868i	$-0.666767\pi$
$401$	−11155.7	−	3275.61i	−1.38925	−	0.407921i	−0.888979	+	0.457947i	$0.848585\pi$
$402$	6868.55	+	7926.72i	0.852169	+	0.983455i
$403$	−10240.9	−	11818.6i	−1.26584	−	1.46086i
$404$	1490.21	+	437.566i	0.183517	+	0.0538855i
$405$	−1834.10	+	4016.12i	−0.225030	+	0.492747i
$406$	423.904	+	272.427i	0.0518178	+	0.0333013i
$407$	8269.62	−	2428.18i	1.00715	−	0.295726i
$408$	0.659746	−	4.58863i	8.00546e−5	−	0.000556792i
$409$	1597.52	+	3498.08i	0.193135	+	0.422907i	0.981281	−	0.192582i	$-0.0616860\pi$
$409$	1597.52	+	3498.08i	0.193135	+	0.422907i	−0.788146	+	0.615489i	$0.788959\pi$
$410$	69.3450	+	482.305i	0.00835294	+	0.0580960i
$411$	−7898.08	+	5075.79i	−0.947892	+	0.609173i
$412$	−348.142	+	401.777i	−0.0416304	+	0.0480440i
$413$	297.385			0.0354318
$414$	−6517.93	+	5190.31i	−0.773765	+	0.616159i
$415$	5267.52			0.623065
$416$	−13507.3	+	15588.3i	−1.59195	+	1.83721i
$417$	−5163.09	+	3318.12i	−0.606325	+	0.389661i
$418$	12.0861	+	84.0609i	0.00141424	+	0.00983625i
$419$	2264.50	+	4958.57i	0.264029	+	0.578143i	0.994492	−	0.104809i	$-0.0334230\pi$
$419$	2264.50	+	4958.57i	0.264029	+	0.578143i	−0.730463	+	0.682952i	$0.760696\pi$
$420$	−79.4359	+	552.489i	−0.00922876	+	0.0641874i
$421$	8777.70	−	2577.37i	1.01615	−	0.298368i	0.269083	−	0.963117i	$-0.413280\pi$
$421$	8777.70	−	2577.37i	1.01615	−	0.298368i	0.747067	+	0.664749i	$0.231461\pi$
$422$	−20165.4	−	12959.5i	−2.32615	−	1.49493i
$423$	−343.877	+	752.986i	−0.0395269	+	0.0865519i
$424$	90.5425	+	26.5857i	0.0103706	+	0.00304508i
$425$	23.0337	+	26.5823i	0.00262893	+	0.00303395i
$426$	10229.2	+	11805.1i	1.16339	+	1.34262i
$427$	1687.09	+	495.373i	0.191203	+	0.0561424i
$428$	669.194	−	1465.33i	0.0755764	−	0.165489i
$429$	19046.5	+	12240.4i	2.14352	+	1.37756i
$430$	−7596.60	+	2230.56i	−0.851955	+	0.250157i
$431$	−984.628	+	6848.24i	−0.110041	+	0.765355i	0.857834	+	0.513926i	$0.171810\pi$
$431$	−984.628	+	6848.24i	−0.110041	+	0.765355i	−0.967876	+	0.251429i	$0.919100\pi$
$432$	1450.59	+	3176.34i	0.161554	+	0.353754i
$433$	1540.71	+	10715.9i	0.170997	+	1.18931i	0.876783	+	0.480887i	$0.159685\pi$
$433$	1540.71	+	10715.9i	0.170997	+	1.18931i	−0.705786	+	0.708426i	$0.749406\pi$
$434$	−1336.14	+	858.686i	−0.147781	+	0.0949729i
$435$	−1369.54	+	1580.54i	−0.150953	+	0.174209i
$436$	−16403.2			−1.80177
$437$	51.8597	−	21.1289i	0.00567685	−	0.00231288i
$438$	6930.77			0.756084
$439$	−4028.14	+	4648.72i	−0.437933	+	0.505401i	−0.931216	−	0.364467i	$-0.881251\pi$
$439$	−4028.14	+	4648.72i	−0.437933	+	0.505401i	0.493284	+	0.869869i	$0.335796\pi$
$440$	−85.3112	+	54.8262i	−0.00924330	+	0.00594031i
$441$	907.299	+	6310.40i	0.0979699	+	0.681395i
$442$	188.407	+	412.553i	0.0202751	+	0.0443963i
$443$	−1018.29	+	7082.39i	−0.109211	+	0.759581i	0.859454	+	0.511212i	$0.170803\pi$
$443$	−1018.29	+	7082.39i	−0.109211	+	0.759581i	−0.968666	+	0.248368i	$0.920106\pi$
$444$	−10910.7	+	3203.66i	−1.16621	+	0.342430i
$445$	−4087.04	−	2626.58i	−0.435381	−	0.279802i
$446$	3819.95	−	8364.53i	0.405561	−	0.888054i
$447$	7080.12	+	2078.91i	0.749169	+	0.219976i
$448$	701.404	+	809.464i	0.0739693	+	0.0853651i
$449$	4621.55	+	5333.55i	0.485755	+	0.560592i	0.944726	−	0.327860i	$-0.106327\pi$
$449$	4621.55	+	5333.55i	0.485755	+	0.560592i	−0.458971	+	0.888451i	$0.651782\pi$
$450$	−1811.93	−	532.030i	−0.189811	−	0.0557336i
$451$	420.077	−	919.841i	0.0438596	−	0.0960391i
$452$	11303.6	+	7264.37i	1.17627	+	0.755945i
$453$	−21355.6	+	6270.58i	−2.21496	+	0.650370i
$454$	−2401.64	+	16703.8i	−0.248270	+	1.72675i
$455$	−338.667	−	741.577i	−0.0348944	−	0.0764081i
$456$	−0.238061	−	1.65575i	−2.44479e−5	−	0.000170039i
$457$	7097.49	−	4561.28i	0.726491	−	0.466888i	−0.124398	−	0.992232i	$-0.539700\pi$
$457$	7097.49	−	4561.28i	0.726491	−	0.466888i	0.850889	+	0.525345i	$0.176064\pi$
$458$	2188.41	−	2525.56i	0.223270	−	0.257667i
$459$	77.9632			0.00792812
$460$	3260.39	+	3071.09i	0.330471	+	0.311283i
$461$	−13550.0			−1.36895			−0.684475	−	0.729036i	$-0.739968\pi$
$461$	−13550.0			−1.36895			−0.684475	+	0.729036i	$0.739968\pi$
$462$	1505.82	−	1737.81i	0.151639	−	0.175001i
$463$	−11260.3	+	7236.55i	−1.13026	+	0.726374i	−0.965614	−	0.259979i	$-0.916284\pi$
$463$	−11260.3	+	7236.55i	−1.13026	+	0.726374i	−0.164645	+	0.986353i	$0.552648\pi$
$464$	554.190	+	3854.48i	0.0554475	+	0.385646i
$465$	−2738.38	−	5996.21i	−0.273095	−	0.597995i
$466$	−92.7324	+	644.968i	−0.00921834	+	0.0641150i
$467$	4238.58	−	1244.56i	0.419996	−	0.123322i	−0.0649040	−	0.997892i	$-0.520674\pi$
$467$	4238.58	−	1244.56i	0.419996	−	0.123322i	0.484900	+	0.874569i	$0.338856\pi$
$468$	−10319.3	−	6631.82i	−1.01925	−	0.655034i
$469$	−325.599	+	712.963i	−0.0320571	+	0.0701953i
$470$	847.564	+	248.867i	0.0831813	+	0.0244242i
$471$	1018.20	+	1175.06i	0.0996095	+	0.114956i
$472$	−46.6816	−	53.8734i	−0.00455232	−	0.00525366i
$473$	15765.3	+	4629.10i	1.53253	+	0.449992i
$474$	10707.3	−	23445.8i	1.03756	−	2.27194i
$475$	10.6771	+	6.86175i	0.00103137	+	0.000662818i
$476$	22.2648	−	6.53752i	0.00214392	−	0.000629510i
$477$	518.995	−	3609.69i	0.0498179	−	0.346491i
$478$	−6222.17	−	13624.6i	−0.595388	−	1.30372i
$479$	364.503	+	2535.17i	0.0347694	+	0.241827i	0.999793	−	0.0203357i	$-0.00647351\pi$
$479$	364.503	+	2535.17i	0.0347694	+	0.241827i	−0.965024	+	0.262162i	$0.915564\pi$
$480$	−7314.27	+	4700.60i	−0.695519	+	0.446983i
$481$	10876.3	−	12552.0i	1.03101	−	1.18985i
$482$	25448.9			2.40491
$483$	−1351.89	−	686.558i	−0.127356	−	0.0646779i
$484$	3287.59			0.308752
$485$	−1201.16	+	1386.21i	−0.112458	+	0.129783i
$486$	−15134.3	+	9726.22i	−1.41256	+	0.907799i
$487$	−2173.15	−	15114.6i	−0.202207	−	1.40638i	−0.797717	−	0.603032i	$-0.793959\pi$
$487$	−2173.15	−	15114.6i	−0.202207	−	1.40638i	0.595510	−	0.803348i	$-0.296950\pi$
$488$	−175.088	−	383.389i	−0.0162415	−	0.0355639i
$489$	200.851	−	1396.95i	0.0185742	−	0.129186i
$490$	6527.57	−	1916.67i	0.601807	−	0.176706i
$491$	3165.56	+	2034.38i	0.290957	+	0.186986i	0.677974	−	0.735086i	$-0.262858\pi$
$491$	3165.56	+	2034.38i	0.290957	+	0.186986i	−0.387017	+	0.922072i	$0.626495\pi$
$492$	−554.237	+	1213.61i	−0.0507864	+	0.111207i
$493$	83.4215	+	24.4948i	0.00762092	+	0.00223770i
$494$	107.171	+	123.681i	0.00976079	+	0.0112646i
$495$	2566.44	+	2961.82i	0.233036	+	0.268938i
$496$	−11777.0	−	3458.04i	−1.06614	−	0.313046i
$497$	−484.908	+	1061.80i	−0.0437647	+	0.0958314i
$498$	24085.6	+	15478.8i	2.16727	+	1.39282i
$499$	18455.8	−	5419.12i	1.65570	−	0.486159i	0.685424	−	0.728144i	$-0.259617\pi$
$499$	18455.8	−	5419.12i	1.65570	−	0.486159i	0.970280	+	0.241985i	$0.0777986\pi$
$500$	−144.472	+	1004.82i	−0.0129219	+	0.0898741i
$501$	5838.80	+	12785.2i	0.520675	+	1.14012i
$502$	−364.758	−	2536.95i	−0.0324302	−	0.225557i
$503$	−5160.94	+	3316.73i	−0.457485	+	0.294008i	−0.749014	−	0.662554i	$-0.769472\pi$
$503$	−5160.94	+	3316.73i	−0.457485	+	0.294008i	0.291529	+	0.956562i	$0.405836\pi$
$504$	−12.1800	+	14.0564i	−0.00107647	+	0.00124231i
$505$	−956.212			−0.0842591
$506$	−4459.35	−	17905.0i	−0.391783	−	1.57307i
$507$	28758.7			2.51917
$508$	8433.08	−	9732.29i	0.736530	−	0.850001i
$509$	12897.4	−	8288.64i	1.12312	−	0.721783i	0.159004	−	0.987278i	$-0.449172\pi$
$509$	12897.4	−	8288.64i	1.12312	−	0.721783i	0.964112	+	0.265495i	$0.0855355\pi$
$510$	27.2075	+	189.232i	0.00236229	+	0.0164301i
$511$	215.154	+	471.121i	0.0186259	+	0.0407851i
$512$	−2338.89	+	16267.3i	−0.201885	+	1.40414i
$513$	26.9925	−	7.92571i	0.00232310	−	0.000682123i
$514$	−15315.3	−	9842.54i	−1.31426	−	0.844622i
$515$	135.968	−	297.728i	0.0116339	−	0.0254747i
$516$	−20800.2	−	6107.49i	−1.77457	−	0.521060i
$517$	−1200.50	−	1385.45i	−0.102124	−	0.117857i
$518$	−1104.64	−	1274.82i	−0.0936970	−	0.108132i
$519$	−6030.47	−	1770.71i	−0.510035	−	0.149760i
$520$	−81.1803	+	177.760i	−0.00684614	+	0.0149910i
$521$	−11293.8	−	7258.09i	−0.949694	−	0.610331i	−0.0285663	−	0.999592i	$-0.509094\pi$
$521$	−11293.8	−	7258.09i	−0.949694	−	0.610331i	−0.921128	+	0.389261i	$0.872731\pi$
$522$	−4478.81	+	1315.10i	−0.375541	+	0.110269i
$523$	1691.15	−	11762.2i	0.141393	−	0.983412i	−0.788356	−	0.615219i	$-0.789068\pi$
$523$	1691.15	−	11762.2i	0.141393	−	0.983412i	0.929749	−	0.368193i	$-0.120023\pi$
$524$	−9393.58	−	20569.1i	−0.783131	−	1.71482i
$525$	−48.9063	−	340.151i	−0.00406561	−	0.0282769i
$526$	12884.4	−	8280.32i	1.06804	−	0.686386i
$527$	−179.461	+	207.109i	−0.0148338	+	0.0171192i
$528$	17770.2			1.46468
$529$	−10745.7	+	5706.56i	−0.883188	+	0.469019i
$530$	−3891.55			−0.318940
$531$	−1804.05	+	2081.98i	−0.147437	+	0.170151i
$532$	7.04393	−	4.52686i	0.000574047	−	0.000368918i
$533$	−277.324	−	1928.83i	−0.0225370	−	0.156748i
$534$	−10969.5	−	24019.9i	−0.888948	−	1.94652i
$535$	−141.146	+	981.689i	−0.0114061	+	0.0793311i
$536$	180.269	−	52.9318i	0.0145269	−	0.00426549i
$537$	−10806.8	−	6945.11i	−0.868432	−	0.558108i
$538$	2461.69	−	5390.36i	0.197270	−	0.431961i
$539$	−13546.7	−	3977.67i	−1.08256	−	0.317867i
$540$	1473.52	+	1700.54i	0.117426	+	0.135517i
$541$	11307.5	+	13049.6i	0.898610	+	1.03705i	0.999113	+	0.0421145i	$0.0134094\pi$
$541$	11307.5	+	13049.6i	0.898610	+	1.03705i	−0.100503	+	0.994937i	$0.532045\pi$
$542$	−6642.33	−	1950.37i	−0.526407	−	0.154567i
$543$	498.628	−	1091.84i	0.0394073	−	0.0862900i
$544$	304.075	+	195.417i	0.0239653	+	0.0154015i
$545$	9689.89	−	2845.21i	0.761595	−	0.223624i
$546$	630.616	−	4386.03i	0.0494283	−	0.343782i
$547$	−5773.70	−	12642.6i	−0.451308	−	0.988227i	−0.989383	−	0.145330i	$-0.953576\pi$
$547$	−5773.70	−	12642.6i	−0.451308	−	0.988227i	0.538075	−	0.842897i	$-0.319152\pi$
$548$	1603.15	+	11150.1i	0.124969	+	0.869178i
$549$	−13702.6	+	8806.12i	−1.06523	+	0.684583i
$550$	2738.67	−	3160.59i	0.212322	−	0.245033i
$551$	31.3724			0.00242561
$552$	87.8361	+	352.676i	0.00677274	+	0.0271936i
$553$	1926.13			0.148114
$554$	−9447.85	+	10903.4i	−0.724550	+	0.836175i
$555$	5889.58	−	3785.00i	0.450448	−	0.289485i
$556$	1048.00	+	7288.99i	0.0799371	+	0.555975i
$557$	−9271.83	−	20302.5i	−0.705314	−	1.54442i	−0.833407	−	0.552660i	$-0.813613\pi$
$557$	−9271.83	−	20302.5i	−0.705314	−	1.54442i	0.128093	−	0.991762i	$-0.459115\pi$
$558$	2093.90	−	14563.4i	0.158856	−	1.10487i
$559$	30380.2	−	8920.44i	2.29865	−	0.674945i
$560$	−538.298	−	345.943i	−0.0406201	−	0.0261049i
$561$	164.817	−	360.899i	0.0124039	−	0.0271608i
$562$	18533.6	+	5441.95i	1.39109	+	0.408460i
$563$	7960.58	+	9187.00i	0.595912	+	0.687719i	0.970948	−	0.239291i	$-0.0769151\pi$
$563$	7960.58	+	9187.00i	0.595912	+	0.687719i	−0.375036	+	0.927010i	$0.622370\pi$
$564$	1583.90	+	1827.92i	0.118252	+	0.136470i
$565$	−7937.40	−	2330.63i	−0.591025	−	0.173540i
$566$	−11332.1	+	24813.8i	−0.841559	+	1.84276i
$567$	−1508.61	−	969.526i	−0.111739	−	0.0718100i
$568$	268.470	−	78.8300i	0.0198323	−	0.00582330i
$569$	−2066.79	+	14374.8i	−0.152275	+	1.05909i	0.760120	+	0.649783i	$0.225140\pi$
$569$	−2066.79	+	14374.8i	−0.152275	+	1.05909i	−0.912395	+	0.409311i	$0.865769\pi$
$570$	28.6571	+	62.7503i	0.00210581	+	0.00461109i
$571$	−1523.55	−	10596.5i	−0.111661	−	0.776620i	−0.966304	−	0.257404i	$-0.917133\pi$
$571$	−1523.55	−	10596.5i	−0.111661	−	0.776620i	0.854643	−	0.519216i	$-0.173776\pi$
$572$	22852.9	−	14686.7i	1.67051	−	1.07357i
$573$	−8645.39	+	9977.31i	−0.630307	+	0.727414i
$574$	−197.913			−0.0143915
$575$	−2458.71	−	1248.66i	−0.178322	−	0.0905609i
$576$	−9922.01			−0.717738
$577$	−5894.40	+	6802.49i	−0.425281	+	0.490800i	−0.927438	−	0.373976i	$-0.877994\pi$
$577$	−5894.40	+	6802.49i	−0.425281	+	0.490800i	0.502158	+	0.864776i	$0.332540\pi$
$578$	−16588.1	+	10660.6i	−1.19373	+	0.767164i
$579$	−3641.09	−	25324.4i	−0.261345	−	1.81769i
$580$	1042.41	+	2282.55i	0.0746268	+	0.163410i
$581$	−304.485	+	2117.74i	−0.0217421	+	0.151220i
$582$	−9565.73	+	2808.75i	−0.681293	+	0.200046i
$583$	6794.09	+	4366.30i	0.482646	+	0.310178i
$584$	51.5735	−	112.930i	0.00365433	−	0.00800186i
$585$	7246.24	+	2127.69i	0.512129	+	0.150375i
$586$	18013.1	+	20788.3i	1.26982	+	1.46545i
$587$	−6811.96	−	7861.42i	−0.478977	−	0.552769i	0.463909	−	0.885883i	$-0.346446\pi$
$587$	−6811.96	−	7861.42i	−0.478977	−	0.552769i	−0.942887	+	0.333113i	$0.891901\pi$
$588$	17873.1	+	5248.01i	1.25353	+	0.368068i
$589$	−41.0785	+	89.9495i	−0.00287370	+	0.00629253i
$590$	2473.06	+	1589.34i	0.172567	+	0.110902i
$591$	−34205.1	+	10043.5i	−2.38073	+	0.699045i
$592$	1855.19	−	12903.1i	0.128797	−	0.895804i
$593$	7445.47	+	16303.3i	0.515597	+	1.12900i	0.971080	+	0.238755i	$0.0767392\pi$
$593$	7445.47	+	16303.3i	0.515597	+	1.12900i	−0.455483	+	0.890244i	$0.650534\pi$
$594$	−1319.22	−	9175.36i	−0.0911248	−	0.633787i
$595$	−12.0185	+	7.72383i	−0.000828086	+	0.000532178i
$596$	5797.97	−	6691.21i	0.398480	−	0.459870i
$597$	30980.6			2.12387
$598$	−25883.2	−	24380.3i	−1.76997	−	1.66720i
$599$	−23377.4			−1.59462			−0.797309	−	0.603571i	$-0.793744\pi$
$599$	−23377.4			−1.59462			−0.797309	+	0.603571i	$0.793744\pi$
$600$	−53.9438	+	62.2544i	−0.00367041	+	0.00423588i
$601$	−15001.1	+	9640.61i	−1.01815	+	0.654324i	−0.939489	−	0.342578i	$-0.888700\pi$
$601$	−15001.1	+	9640.61i	−1.01815	+	0.654324i	−0.0786580	+	0.996902i	$0.525064\pi$
$602$	−457.654	−	3183.05i	−0.0309844	−	0.215501i
$603$	−3016.23	−	6604.61i	−0.203699	−	0.446038i
$604$	−3800.57	+	26433.6i	−0.256032	+	1.78074i
$605$	−1942.08	+	570.245i	−0.130507	+	0.0383203i
$606$	−4372.25	−	2809.87i	−0.293087	−	0.188355i
$607$	−11120.4	+	24350.2i	−0.743595	+	1.62825i	0.0339533	+	0.999423i	$0.489190\pi$
$607$	−11120.4	+	24350.2i	−0.743595	+	1.62825i	−0.777548	+	0.628823i	$0.783537\pi$
$608$	125.143	+	36.7454i	0.00834742	+	0.00245102i
$609$	−556.270	−	641.969i	−0.0370134	−	0.0427158i
$610$	11382.4	+	13136.0i	0.755509	+	0.871904i
$611$	−3389.57	−	995.267i	−0.224431	−	0.0658988i
$612$	−89.2974	+	195.534i	−0.00589809	+	0.0129150i
$613$	2164.65	+	1391.13i	0.142625	+	0.0916597i	0.610007	−	0.792396i	$-0.291166\pi$
$613$	2164.65	+	1391.13i	0.142625	+	0.0916597i	−0.467382	+	0.884055i	$0.654803\pi$
$614$	−40606.0	+	11923.0i	−2.66893	+	0.783670i
$615$	116.899	−	813.050i	0.00766475	−	0.0533095i
$616$	−17.1108	−	37.4675i	−0.00111918	−	0.00245066i
$617$	−1620.75	−	11272.5i	−0.105752	−	0.735519i	−0.971842	−	0.235632i	$-0.924284\pi$
$617$	−1620.75	−	11272.5i	−0.105752	−	0.735519i	0.866091	−	0.499887i	$-0.166625\pi$
$618$	1496.60	−	961.806i	0.0974143	−	0.0626044i
$619$	−9578.15	+	11053.8i	−0.621936	+	0.717752i	−0.976073	−	0.217441i	$-0.930229\pi$
$619$	−9578.15	+	11053.8i	−0.621936	+	0.717752i	0.354138	+	0.935193i	$0.384774\pi$
$620$	−7909.32			−0.512332
$621$	−5660.55	+	2306.24i	−0.365781	+	0.149028i
$622$	−14138.3			−0.911408
$623$	1292.23	−	1491.32i	0.0831015	−	0.0959042i
$624$	28807.7	−	18513.6i	1.84813	−	1.18772i
$625$	−88.9468	−	618.638i	−0.00569259	−	0.0395929i
$626$	7962.98	+	17436.5i	0.508410	+	1.11326i
$627$	20.3743	−	141.706i	0.00129772	−	0.00902585i
$628$	1790.00	−	525.591i	0.113740	−	0.0333971i
$629$	−244.846	−	157.353i	−0.0155209	−	0.00997469i
$630$	318.633	−	697.709i	0.0201502	−	0.0441229i
$631$	−10019.5	−	2941.98i	−0.632121	−	0.185608i	−0.0500518	−	0.998747i	$-0.515939\pi$
$631$	−10019.5	−	2941.98i	−0.632121	−	0.185608i	−0.582069	+	0.813139i	$0.697757\pi$
$632$	−302.351	−	348.932i	−0.0190299	−	0.0219617i
$633$	26462.1	+	30538.9i	1.66157	+	1.91755i
$634$	−1027.50	−	301.700i	−0.0643645	−	0.0188991i
$635$	−3293.57	+	7211.91i	−0.205829	+	0.450702i
$636$	−8963.91	−	5760.75i	−0.558871	−	0.359165i
$637$	−26105.0	+	7665.11i	−1.62373	+	0.476770i
$638$	1471.17	−	10232.2i	0.0912918	−	0.634949i
$639$	−4491.99	−	9836.10i	−0.278092	−	0.608936i
$640$	44.3341	+	308.350i	0.00273822	+	0.0190447i
$641$	4320.94	−	2776.90i	0.266251	−	0.171109i	−0.400703	−	0.916208i	$-0.631234\pi$
$641$	4320.94	−	2776.90i	0.266251	−	0.171109i	0.666954	+	0.745099i	$0.267598\pi$
$642$	−3530.12	+	4073.98i	−0.217014	+	0.250447i
$643$	17570.3			1.07761			0.538807	−	0.842429i	$-0.318875\pi$
$643$	17570.3			1.07761			0.538807	+	0.842429i	$0.318875\pi$
$644$	−1423.16	+	1133.28i	−0.0870811	+	0.0693438i
$645$	13346.7			0.814767
$646$	1.87806	−	2.16739i	0.000114383	−	0.000132004i
$647$	16523.7	−	10619.1i	1.00404	−	0.645257i	0.0681956	−	0.997672i	$-0.478276\pi$
$647$	16523.7	−	10619.1i	1.00404	−	0.645257i	0.935844	+	0.352415i	$0.114639\pi$
$648$	61.1757	+	425.486i	0.00370865	+	0.0257943i
$649$	−2534.39	−	5549.53i	−0.153287	−	0.335652i
$650$	1146.91	−	7976.96i	0.0692087	−	0.481357i
$651$	2568.99	−	754.324i	0.154665	−	0.0454137i
$652$	−1424.55	−	915.502i	−0.0855670	−	0.0549906i
$653$	−3471.51	+	7601.55i	−0.208041	+	0.455546i	−0.984674	−	0.174408i	$-0.944199\pi$
$653$	−3471.51	+	7601.55i	−0.208041	+	0.455546i	0.776632	+	0.629954i	$0.216926\pi$
$654$	52667.5	+	15464.6i	3.14903	+	0.924637i
$655$	9116.87	+	10521.4i	0.543856	+	0.627643i
$656$	−1001.59	−	1155.90i	−0.0596122	−	0.0687962i
$657$	−4603.51	−	1351.71i	−0.273364	−	0.0802668i
$658$	−149.047	+	326.367i	−0.00883046	+	0.0193360i
$659$	−373.854	−	240.261i	−0.0220990	−	0.0142022i	0.529545	−	0.848282i	$-0.322363\pi$
$659$	−373.854	−	240.261i	−0.0220990	−	0.0142022i	−0.551644	+	0.834080i	$0.685999\pi$
$660$	10987.0	−	3226.09i	0.647985	−	0.190265i
$661$	470.864	−	3274.93i	0.0277073	−	0.192708i	−0.971267	−	0.237993i	$-0.923510\pi$
$661$	470.864	−	3274.93i	0.0277073	−	0.192708i	0.998974	+	0.0452849i	$0.0144195\pi$
$662$	5406.41	+	11838.4i	0.317411	+	0.695033i
$663$	−108.808	−	756.775i	−0.00637367	−	0.0443299i
$664$	431.440	−	277.270i	0.0252155	−	0.0162050i
$665$	−3.37586	+	3.89595i	−0.000196858	+	0.000227186i
$666$	15626.1			0.909160
$667$	−6781.44	+	689.253i	−0.393671	+	0.0400120i
$668$	16864.3			0.976797
$669$	−10151.3	+	11715.2i	−0.586653	+	0.677033i
$670$	−6518.05	+	4188.90i	−0.375842	+	0.241539i
$671$	−5133.55	−	35704.6i	−0.295348	−	2.05419i
$672$	−1467.02	−	3212.33i	−0.0842136	−	0.184402i
$673$	−1131.14	+	7867.26i	−0.0647880	+	0.450610i	0.931444	+	0.363884i	$0.118550\pi$
$673$	−1131.14	+	7867.26i	−0.0647880	+	0.450610i	−0.996232	+	0.0867261i	$0.972360\pi$
$674$	41611.8	−	12218.3i	2.37808	−	0.698268i
$675$	−1165.42	−	748.969i	−0.0664548	−	0.0427079i
$676$	14334.4	−	31387.9i	0.815566	−	1.78584i
$677$	−20883.5	−	6131.94i	−1.18555	−	0.348109i	−0.371238	−	0.928538i	$-0.621067\pi$
$677$	−20883.5	−	6131.94i	−1.18555	−	0.348109i	−0.814311	+	0.580429i	$0.802885\pi$
$678$	−29444.9	−	33981.2i	−1.66788	−	1.92484i
$679$	−487.878	−	563.041i	−0.0275744	−	0.0318226i
$680$	3.28582	+	0.964803i	0.000185302	+	5.44096e-5i
$681$	11817.8	−	25877.3i	0.664989	−	1.45612i
$682$	27411.0	+	17616.0i	1.53903	+	0.989076i
$683$	−6646.01	+	1951.45i	−0.372332	+	0.109327i	−0.462545	−	0.886596i	$-0.653063\pi$
$683$	−6646.01	+	1951.45i	−0.372332	+	0.109327i	0.0902127	+	0.995923i	$0.471245\pi$
$684$	−11.0387	+	76.7760i	−0.000617070	+	0.00429182i
$685$	−2881.06	−	6308.64i	−0.160700	−	0.351884i
$686$	791.287	+	5503.52i	0.0440401	+	0.306305i
$687$	−4739.16	+	3045.68i	−0.263188	+	0.169141i
$688$	16274.3	−	18781.6i	0.901822	−	1.04076i
$689$	15563.0			0.860529
$690$	−7573.13	−	12934.5i	−0.417832	−	0.713633i
$691$	2811.47			0.154781			0.0773903	−	0.997001i	$-0.475341\pi$
$691$	2811.47			0.154781			0.0773903	+	0.997001i	$0.475341\pi$
$692$	−4938.40	+	5699.21i	−0.271286	+	0.313080i
$693$	−1339.12	+	860.597i	−0.0734037	+	0.0471737i
$694$	6803.27	+	47317.8i	0.372116	+	2.58812i
$695$	−1883.39	−	4124.05i	−0.102793	−	0.225085i
$696$	−28.9777	+	201.545i	−0.00157816	+	0.0109763i
$697$	−32.7651	+	9.62070i	−0.00178058	+	0.000522827i
$698$	21687.5	+	13937.7i	1.17605	+	0.755802i
$699$	456.309	−	999.178i	0.0246913	−	0.0540663i
$700$	−395.625	−	116.166i	−0.0213618	−	0.00627238i
$701$	−7282.13	−	8404.02i	−0.392357	−	0.452804i	0.524862	−	0.851187i	$-0.324117\pi$
$701$	−7282.13	−	8404.02i	−0.392357	−	0.452804i	−0.917219	+	0.398383i	$0.869571\pi$
$702$	−11697.8	−	13500.0i	−0.628925	−	0.725818i
$703$	−100.767	−	29.5880i	−0.00540614	−	0.00158739i
$704$	9127.96	−	19987.4i	0.488669	−	1.07004i
$705$	−1252.72	−	805.072i	−0.0669221	−	0.0430082i
$706$	14964.2	−	4393.87i	0.797710	−	0.234229i
$707$	55.2731	−	384.433i	0.00294025	−	0.0204499i
$708$	3343.79	+	7321.87i	0.177496	+	0.388662i
$709$	5047.74	+	35107.8i	0.267379	+	1.85966i	0.473039	+	0.881041i	$0.343157\pi$
$709$	5047.74	+	35107.8i	0.267379	+	1.85966i	−0.205660	+	0.978624i	$0.565934\pi$
$710$	−9707.18	+	6238.43i	−0.513104	+	0.329752i
$711$	−11684.6	+	13484.8i	−0.616325	+	0.711277i
$712$	−473.009			−0.0248972
$713$	6903.32	−	20345.9i	0.362596	−	1.06867i
$714$	−77.6511			−0.00407006
$715$	−10952.5	+	12639.8i	−0.572865	+	0.661122i
$716$	−12966.6	+	8333.11i	−0.676793	+	0.434948i
$717$	3593.40	+	24992.6i	0.187166	+	1.30177i
$718$	9215.38	+	20178.9i	0.478990	+	1.04884i
$719$	2651.46	−	18441.3i	0.137528	−	0.956531i	−0.797843	−	0.602865i	$-0.794026\pi$
$719$	2651.46	−	18441.3i	0.137528	−	0.956531i	0.935372	−	0.353666i	$-0.115065\pi$
$720$	5687.46	−	1669.99i	0.294387	−	0.0864400i
$721$	111.838	+	71.8742i	0.00577681	+	0.00371253i
$722$	−11440.0	+	25050.1i	−0.589685	+	1.29123i
$723$	−41163.0	−	12086.5i	−2.11738	−	0.621719i
$724$	−943.130	−	1088.43i	−0.0484132	−	0.0558718i
$725$	−1011.70	−	1167.56i	−0.0518256	−	0.0598099i
$726$	−10555.8	−	3099.46i	−0.539617	−	0.158446i
$727$	10193.5	−	22320.6i	0.520020	−	1.13868i	−0.449412	−	0.893325i	$-0.648366\pi$
$727$	10193.5	−	22320.6i	0.520020	−	1.13868i	0.969432	−	0.245360i	$-0.0789063\pi$
$728$	−66.7737	−	42.9128i	−0.00339945	−	0.00218469i
$729$	6222.80	−	1827.18i	0.316151	−	0.0928304i
$730$	−728.629	+	5067.73i	−0.0369422	+	0.256938i
$731$	−230.497	−	504.717i	−0.0116624	−	0.0255371i
$732$	6773.04	+	47107.5i	0.341993	+	2.37861i
$733$	−13445.3	+	8640.75i	−0.677507	+	0.435407i	−0.833625	−	0.552331i	$-0.813738\pi$
$733$	−13445.3	+	8640.75i	−0.677507	+	0.435407i	0.156118	+	0.987738i	$0.450102\pi$
$734$	5210.90	−	6013.70i	0.262040	−	0.302411i
$735$	−11468.5			−0.575538
$736$	−27858.2	−	5193.45i	−1.39520	−	0.260100i
$737$	16079.5			0.803659
$738$	1200.62	−	1385.58i	0.0598852	−	0.0691112i
$739$	−24696.9	+	15871.7i	−1.22935	+	0.790054i	−0.983789	−	0.179327i	$-0.942608\pi$
$739$	−24696.9	+	15871.7i	−1.22935	+	0.790054i	−0.245559	+	0.969382i	$0.578972\pi$
$740$	−1195.46	−	8314.61i	−0.0593865	−	0.413042i
$741$	−114.605	−	250.950i	−0.00568168	−	0.0124411i
$742$	224.948	−	1564.55i	0.0111295	−	0.0774075i
$743$	24573.7	−	7215.50i	1.21335	−	0.356273i	0.388410	−	0.921487i	$-0.373024\pi$
$743$	24573.7	−	7215.50i	1.21335	−	0.356273i	0.824945	+	0.565213i	$0.191206\pi$
$744$	−539.916	−	346.983i	−0.0266052	−	0.0170981i
$745$	−2264.42	+	4958.38i	−0.111358	+	0.243840i
$746$	29382.9	+	8627.61i	1.44207	+	0.423430i
$747$	−12979.1	−	14978.7i	−0.635717	−	0.733656i
$748$	−311.743	−	359.771i	−0.0152386	−	0.0175863i
$749$	−386.517	−	113.492i	−0.0188558	−	0.00553657i
$750$	1411.19	−	3090.08i	0.0687059	−	0.150445i
$751$	−21029.9	−	13515.1i	−1.02183	−	0.656690i	−0.0814008	−	0.996681i	$-0.525939\pi$
$751$	−21029.9	−	13515.1i	−1.02183	−	0.656690i	−0.940428	+	0.339992i	$0.889576\pi$
$752$	−2660.42	+	781.168i	−0.129010	+	0.0378807i
$753$	−614.894	+	4276.68i	−0.0297583	+	0.206973i
$754$	−8275.32	−	18120.4i	−0.399694	−	0.875208i
$755$	−2339.89	−	16274.3i	−0.112791	−	0.784481i
$756$	−768.855	+	494.113i	−0.0369881	+	0.0237708i
$757$	−23728.7	+	27384.4i	−1.13928	+	1.31480i	−0.196836	+	0.980436i	$0.563067\pi$
$757$	−23728.7	+	27384.4i	−1.13928	+	1.31480i	−0.942444	+	0.334364i	$0.891479\pi$
$758$	−27336.9			−1.30992
$759$	−1290.80	+	31078.8i	−0.0617301	+	1.48628i
$760$	1.23570			5.89784e−5
$761$	16783.7	−	19369.5i	0.799487	−	0.922657i	−0.198866	−	0.980027i	$-0.563726\pi$
$761$	16783.7	−	19369.5i	0.799487	−	0.922657i	0.998353	+	0.0573695i	$0.0182713\pi$
$762$	−36252.3	+	23297.9i	−1.72347	+	1.10761i
$763$	583.763	+	4060.16i	0.0276981	+	0.192645i
$764$	6580.30	+	14408.8i

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)

\(f(q)\)	\(=\)	\(q+(-2.62935 + 3.03443i) q^{2} +(5.69405 - 3.65935i) q^{3} +(-1.15577 - 8.03858i) q^{4} +(2.07708 + 4.54816i) q^{5} +(-3.86762 + 26.8999i) q^{6} +(-1.94859 + 0.572159i) q^{7} +(0.409529 + 0.263188i) q^{8} +(7.81524 - 17.1130i) q^{9} +O(q^{10})\)	\(q+(-2.62935 + 3.03443i) q^{2} +(5.69405 - 3.65935i) q^{3} +(-1.15577 - 8.03858i) q^{4} +(2.07708 + 4.54816i) q^{5} +(-3.86762 + 26.8999i) q^{6} +(-1.94859 + 0.572159i) q^{7} +(0.409529 + 0.263188i) q^{8} +(7.81524 - 17.1130i) q^{9} +(-19.2624 - 5.65596i) q^{10} +(27.2835 + 31.4869i) q^{11} +(-35.9970 - 41.5427i) q^{12} +(77.0341 + 22.6192i) q^{13} +(3.38736 - 7.41728i) q^{14} +(28.4703 + 18.2967i) q^{15} +(60.4628 - 17.7535i) q^{16} +(0.200228 - 1.39261i) q^{17} +(31.3792 + 68.7108i) q^{18} +(-0.0722497 - 0.502508i) q^{19} +(34.1601 - 21.9534i) q^{20} +(-9.00167 + 10.3885i) q^{21} -167.283 q^{22} +(26.6576 + 107.034i) q^{23} +3.29498 q^{24} +(-16.3715 + 18.8937i) q^{25} +(-271.186 + 174.281i) q^{26} +(7.88616 + 54.8494i) q^{27} +(6.85148 + 15.0026i) q^{28} +(-8.79452 + 61.1672i) q^{29} +(-130.378 + 38.2826i) q^{30} +(-163.860 - 105.307i) q^{31} +(-106.724 + 233.693i) q^{32} +(270.575 + 79.4481i) q^{33} +(3.69932 + 4.26925i) q^{34} +(-6.64965 - 7.67410i) q^{35} +(-146.597 - 43.0447i) q^{36} +(85.9359 - 188.173i) q^{37} +(1.71480 + 1.10203i) q^{38} +(521.408 - 153.099i) q^{39} +(-0.346400 + 2.40926i) q^{40} +(-10.0827 - 22.0781i) q^{41} +(-7.85460 - 54.6299i) q^{42} +(331.768 - 213.215i) q^{43} +(221.576 - 255.712i) q^{44} +94.0654 q^{45} +(-394.881 - 200.540i) q^{46} -44.0009 q^{47} +(279.312 - 322.344i) q^{48} +(-285.080 + 183.210i) q^{49} +(-14.2853 - 99.3565i) q^{50} +(-3.95595 - 8.66233i) q^{51} +(92.7927 - 645.387i) q^{52} +(185.992 - 54.6123i) q^{53} +(-187.172 - 120.288i) q^{54} +(-86.5374 + 189.490i) q^{55} +(-0.948591 - 0.278531i) q^{56} +(-2.25025 - 2.59692i) q^{57} +(-162.484 - 187.516i) q^{58} +(-140.501 - 41.2550i) q^{59} +(114.175 - 250.007i) q^{60} +(-728.355 - 468.085i) q^{61} +(750.391 - 220.335i) q^{62} +(-5.43738 + 37.8178i) q^{63} +(-219.090 - 479.740i) q^{64} +(57.1296 + 397.345i) q^{65} +(-952.516 + 612.145i) q^{66} +(252.738 - 291.675i) q^{67} -11.4261 q^{68} +(543.466 + 511.911i) q^{69} +40.7708 q^{70} +(376.397 - 434.385i) q^{71} +(7.70450 - 4.95138i) q^{72} +(-36.2942 - 252.432i) q^{73} +(345.044 + 755.540i) q^{74} +(-24.0816 + 167.491i) q^{75} +(-3.95595 + 1.16157i) q^{76} +(-71.1800 - 45.7446i) q^{77} +(-906.395 + 1984.73i) q^{78} +(-910.012 - 267.204i) q^{79} +(206.331 + 238.119i) q^{80} +(578.256 + 667.343i) q^{81} +(93.5054 + 27.4557i) q^{82} +(437.641 - 958.300i) q^{83} +(93.9126 + 60.3540i) q^{84} +(6.74972 - 1.98190i) q^{85} +(-225.350 + 1567.34i) q^{86} +(173.756 + 380.472i) q^{87} +(2.88642 + 20.0755i) q^{88} +(-817.408 + 525.316i) q^{89} +(-247.331 + 285.435i) q^{90} -163.050 q^{91} +(829.595 - 337.997i) q^{92} -1318.38 q^{93} +(115.694 - 133.518i) q^{94} +(2.13542 - 1.37235i) q^{95} +(247.471 + 1721.20i) q^{96} +(152.393 + 333.694i) q^{97} +(193.638 - 1346.78i) q^{98} +(752.061 - 220.825i) 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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