LMFDB - Embedded newform 156.3.e.c.103.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [156,3,Mod(103,156)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(156, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("156.103");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 156 = 2^{2} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	156.e (of order $2$, degree $1$, 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:	$4.25069212402$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			103.1
Character	$\chi$	$=$	156.103
Dual form			156.3.e.c.103.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.99484 - 0.143522i) q^{2} +1.73205i q^{3} +(3.95880 + 0.572609i) q^{4} +8.96077i q^{5} +(0.248588 - 3.45517i) q^{6} -7.15347 q^{7} +(-7.81501 - 1.71044i) q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(-1.99484 - 0.143522i) q^{2} +1.73205i q^{3} +(3.95880 + 0.572609i) q^{4} +8.96077i q^{5} +(0.248588 - 3.45517i) q^{6} -7.15347 q^{7} +(-7.81501 - 1.71044i) q^{8} -3.00000 q^{9} +(1.28607 - 17.8753i) q^{10} +9.63996 q^{11} +(-0.991787 + 6.85685i) q^{12} +(0.746915 - 12.9785i) q^{13} +(14.2701 + 1.02668i) q^{14} -15.5205 q^{15} +(15.3442 + 4.53369i) q^{16} -18.0668 q^{17} +(5.98453 + 0.430567i) q^{18} -23.1718 q^{19} +(-5.13101 + 35.4739i) q^{20} -12.3902i q^{21} +(-19.2302 - 1.38355i) q^{22} +25.4726i q^{23} +(2.96257 - 13.5360i) q^{24} -55.2954 q^{25} +(-3.35269 + 25.7829i) q^{26} -5.19615i q^{27} +(-28.3192 - 4.09614i) q^{28} -2.34438 q^{29} +(30.9610 + 2.22754i) q^{30} +40.4034 q^{31} +(-29.9587 - 11.2462i) q^{32} +16.6969i q^{33} +(36.0404 + 2.59299i) q^{34} -64.1006i q^{35} +(-11.8764 - 1.71783i) q^{36} +20.7540i q^{37} +(46.2241 + 3.32566i) q^{38} +(22.4795 + 1.29370i) q^{39} +(15.3269 - 70.0285i) q^{40} +43.4609i q^{41} +(-1.77827 + 24.7165i) q^{42} +20.0005i q^{43} +(38.1627 + 5.51993i) q^{44} -26.8823i q^{45} +(3.65589 - 50.8139i) q^{46} +19.7391 q^{47} +(-7.85258 + 26.5770i) q^{48} +2.17215 q^{49} +(110.306 + 7.93611i) q^{50} -31.2926i q^{51} +(10.3885 - 50.9517i) q^{52} -55.3961 q^{53} +(-0.745763 + 10.3655i) q^{54} +86.3815i q^{55} +(55.9045 + 12.2356i) q^{56} -40.1347i q^{57} +(4.67667 + 0.336471i) q^{58} -45.1980 q^{59} +(-61.4426 - 8.88718i) q^{60} +106.826 q^{61} +(-80.5986 - 5.79879i) q^{62} +21.4604 q^{63} +(58.1488 + 26.7342i) q^{64} +(116.298 + 6.69294i) q^{65} +(2.39638 - 33.3077i) q^{66} +62.9302 q^{67} +(-71.5229 - 10.3452i) q^{68} -44.1199 q^{69} +(-9.19986 + 127.871i) q^{70} +4.89257 q^{71} +(23.4450 + 5.13132i) q^{72} -70.7434i q^{73} +(2.97866 - 41.4010i) q^{74} -95.7744i q^{75} +(-91.7325 - 13.2684i) q^{76} -68.9592 q^{77} +(-44.6573 - 5.80702i) q^{78} +86.8826i q^{79} +(-40.6254 + 137.496i) q^{80} +9.00000 q^{81} +(6.23761 - 86.6978i) q^{82} -68.7350 q^{83} +(7.09472 - 49.0503i) q^{84} -161.892i q^{85} +(2.87052 - 39.8979i) q^{86} -4.06059i q^{87} +(-75.3364 - 16.4886i) q^{88} +64.1247i q^{89} +(-3.85821 + 53.6260i) q^{90} +(-5.34304 + 92.8415i) q^{91} +(-14.5858 + 100.841i) q^{92} +69.9808i q^{93} +(-39.3764 - 2.83300i) q^{94} -207.637i q^{95} +(19.4791 - 51.8899i) q^{96} +118.454i q^{97} +(-4.33309 - 0.311751i) q^{98} -28.9199 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{4} - 72 q^{9}+O(q^{10}) $ 24 * q + 8 * q^4 - 72 * q^9	$ 24 q + 8 q^{4} - 72 q^{9} + 28 q^{10} + 36 q^{12} + 48 q^{13} - 40 q^{14} + 100 q^{16} + 32 q^{17} + 84 q^{22} - 312 q^{25} - 16 q^{26} - 80 q^{29} + 60 q^{30} - 24 q^{36} + 120 q^{38} - 204 q^{40} - 96 q^{42} - 144 q^{48} + 392 q^{49} + 28 q^{52} - 224 q^{53} + 800 q^{56} - 96 q^{61} - 352 q^{62} - 184 q^{64} - 112 q^{65} + 252 q^{66} - 344 q^{68} + 144 q^{69} + 232 q^{74} - 16 q^{77} - 168 q^{78} + 216 q^{81} + 20 q^{82} - 92 q^{88} - 84 q^{90} - 616 q^{92} - 684 q^{94}+O(q^{100}) $ 24 * q + 8 * q^4 - 72 * q^9 + 28 * q^10 + 36 * q^12 + 48 * q^13 - 40 * q^14 + 100 * q^16 + 32 * q^17 + 84 * q^22 - 312 * q^25 - 16 * q^26 - 80 * q^29 + 60 * q^30 - 24 * q^36 + 120 * q^38 - 204 * q^40 - 96 * q^42 - 144 * q^48 + 392 * q^49 + 28 * q^52 - 224 * q^53 + 800 * q^56 - 96 * q^61 - 352 * q^62 - 184 * q^64 - 112 * q^65 + 252 * q^66 - 344 * q^68 + 144 * q^69 + 232 * q^74 - 16 * q^77 - 168 * q^78 + 216 * q^81 + 20 * q^82 - 92 * q^88 - 84 * q^90 - 616 * q^92 - 684 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/156\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.99484	−	0.143522i	−0.997422	−	0.0717611i
$2$	−1.99484	−	0.143522i	−0.997422	−	0.0717611i
$3$			1.73205i			0.577350i
$3$			1.73205i			0.577350i
$4$	3.95880	+	0.572609i	0.989701	+	0.143152i
$5$			8.96077i			1.79215i	0.443899	+	0.896077i	$0.353595\pi$
$5$			8.96077i			1.79215i	−0.443899	+	0.896077i	$0.646405\pi$
$6$	0.248588	−	3.45517i	0.0414313	−	0.575862i
$7$	−7.15347			−1.02192			−0.510962	−	0.859603i	$-0.670711\pi$
$7$	−7.15347			−1.02192			−0.510962	+	0.859603i	$0.670711\pi$
$8$	−7.81501	−	1.71044i	−0.976876	−	0.213805i
$9$	−3.00000			−0.333333
$10$	1.28607	−	17.8753i	0.128607	−	1.78753i
$11$	9.63996			0.876360			0.438180	−	0.898887i	$-0.355623\pi$
$11$	9.63996			0.876360			0.438180	+	0.898887i	$0.355623\pi$
$12$	−0.991787	+	6.85685i	−0.0826490	+	0.571404i
$13$	0.746915	−	12.9785i	0.0574550	−	0.998348i
$13$	0.746915	−	12.9785i	0.0574550	−	0.998348i
$14$	14.2701	+	1.02668i	1.01929	+	0.0733344i
$15$	−15.5205			−1.03470
$16$	15.3442	+	4.53369i	0.959015	+	0.283356i
$17$	−18.0668			−1.06275			−0.531376	−	0.847136i	$-0.678325\pi$
$17$	−18.0668			−1.06275			−0.531376	+	0.847136i	$0.678325\pi$
$18$	5.98453	+	0.430567i	0.332474	+	0.0239204i
$19$	−23.1718			−1.21957			−0.609783	−	0.792568i	$-0.708744\pi$
$19$	−23.1718			−1.21957			−0.609783	+	0.792568i	$0.708744\pi$
$20$	−5.13101	+	35.4739i	−0.256551	+	1.77370i
$21$		−	12.3902i		−	0.590008i
$22$	−19.2302	−	1.38355i	−0.874101	−	0.0628886i
$23$			25.4726i			1.10751i	0.832681	+	0.553753i	$0.186805\pi$
$23$			25.4726i			1.10751i	−0.832681	+	0.553753i	$0.813195\pi$
$24$	2.96257	−	13.5360i	0.123440	−	0.564000i
$25$	−55.2954			−2.21182
$26$	−3.35269	+	25.7829i	−0.128949	+	0.991651i
$27$		−	5.19615i		−	0.192450i
$28$	−28.3192	−	4.09614i	−1.01140	−	0.146291i
$29$	−2.34438			−0.0808407			−0.0404204	−	0.999183i	$-0.512870\pi$
$29$	−2.34438			−0.0808407			−0.0404204	+	0.999183i	$0.512870\pi$
$30$	30.9610	+	2.22754i	1.03203	+	0.0742512i
$31$	40.4034			1.30334			0.651668	−	0.758504i	$-0.274069\pi$
$31$	40.4034			1.30334			0.651668	+	0.758504i	$0.274069\pi$
$32$	−29.9587	−	11.2462i	−0.936208	−	0.351445i
$33$			16.6969i			0.505967i
$34$	36.0404	+	2.59299i	1.06001	+	0.0762643i
$35$		−	64.1006i		−	1.83145i
$36$	−11.8764	−	1.71783i	−0.329900	−	0.0477174i
$37$			20.7540i			0.560920i	0.959866	+	0.280460i	$0.0904870\pi$
$37$			20.7540i			0.560920i	−0.959866	+	0.280460i	$0.909513\pi$
$38$	46.2241	+	3.32566i	1.21642	+	0.0875175i
$39$	22.4795	+	1.29370i	0.576397	+	0.0331717i
$40$	15.3269	−	70.0285i	0.383172	−	1.75071i
$41$			43.4609i			1.06002i	0.847990	+	0.530012i	$0.177812\pi$
$41$			43.4609i			1.06002i	−0.847990	+	0.530012i	$0.822188\pi$
$42$	−1.77827	+	24.7165i	−0.0423397	+	0.588487i
$43$			20.0005i			0.465128i	0.972581	+	0.232564i	$0.0747116\pi$
$43$			20.0005i			0.465128i	−0.972581	+	0.232564i	$0.925288\pi$
$44$	38.1627	+	5.51993i	0.867334	+	0.125453i
$45$		−	26.8823i		−	0.597385i
$46$	3.65589	−	50.8139i	0.0794758	−	1.10465i
$47$	19.7391			0.419981			0.209990	−	0.977703i	$-0.432657\pi$
$47$	19.7391			0.419981			0.209990	+	0.977703i	$0.432657\pi$
$48$	−7.85258	+	26.5770i	−0.163595	+	0.553688i
$49$	2.17215			0.0443295
$50$	110.306	+	7.93611i	2.20611	+	0.158722i
$51$		−	31.2926i		−	0.613580i
$52$	10.3885	−	50.9517i	0.199779	−	0.979841i
$53$	−55.3961			−1.04521			−0.522605	−	0.852575i	$-0.675040\pi$
$53$	−55.3961			−1.04521			−0.522605	+	0.852575i	$0.675040\pi$
$54$	−0.745763	+	10.3655i	−0.0138104	+	0.191954i
$55$			86.3815i			1.57057i
$56$	55.9045	+	12.2356i	0.998294	+	0.218493i
$57$		−	40.1347i		−	0.704117i
$58$	4.67667	+	0.336471i	0.0806323	+	0.00580122i
$59$	−45.1980			−0.766067			−0.383034	−	0.923734i	$-0.625121\pi$
$59$	−45.1980			−0.766067			−0.383034	+	0.923734i	$0.625121\pi$
$60$	−61.4426	−	8.88718i	−1.02404	−	0.148120i
$61$	106.826			1.75125			0.875626	−	0.482989i	$-0.160449\pi$
$61$	106.826			1.75125			0.875626	+	0.482989i	$0.160449\pi$
$62$	−80.5986	−	5.79879i	−1.29998	−	0.0935289i
$63$	21.4604			0.340641
$64$	58.1488	+	26.7342i	0.908575	+	0.417722i
$65$	116.298	+	6.69294i	1.78919	+	0.102968i
$66$	2.39638	−	33.3077i	0.0363087	−	0.504662i
$67$	62.9302			0.939256			0.469628	−	0.882864i	$-0.344388\pi$
$67$	62.9302			0.939256			0.469628	+	0.882864i	$0.344388\pi$
$68$	−71.5229	−	10.3452i	−1.05181	−	0.152135i
$69$	−44.1199			−0.639419
$70$	−9.19986	+	127.871i	−0.131427	+	1.82672i
$71$	4.89257			0.0689094			0.0344547	−	0.999406i	$-0.489031\pi$
$71$	4.89257			0.0689094			0.0344547	+	0.999406i	$0.489031\pi$
$72$	23.4450	+	5.13132i	0.325625	+	0.0712684i
$73$		−	70.7434i		−	0.969088i	−0.874767	−	0.484544i	$-0.838985\pi$
$73$		−	70.7434i		−	0.969088i	0.874767	−	0.484544i	$-0.161015\pi$
$74$	2.97866	−	41.4010i	0.0402522	−	0.559474i
$75$		−	95.7744i		−	1.27699i
$76$	−91.7325	−	13.2684i	−1.20701	−	0.174584i
$77$	−68.9592			−0.895574
$78$	−44.6573	−	5.80702i	−0.572530	−	0.0744490i
$79$			86.8826i			1.09978i	0.835237	+	0.549890i	$0.185330\pi$
$79$			86.8826i			1.09978i	−0.835237	+	0.549890i	$0.814670\pi$
$80$	−40.6254	+	137.496i	−0.507817	+	1.71870i
$81$	9.00000			0.111111
$82$	6.23761	−	86.6978i	0.0760684	−	1.05729i
$83$	−68.7350			−0.828132			−0.414066	−	0.910247i	$-0.635892\pi$
$83$	−68.7350			−0.828132			−0.414066	+	0.910247i	$0.635892\pi$
$84$	7.09472	−	49.0503i	0.0844610	−	0.583932i
$85$		−	161.892i		−	1.90462i
$86$	2.87052	−	39.8979i	0.0333781	−	0.463929i
$87$		−	4.06059i		−	0.0466734i
$88$	−75.3364	−	16.4886i	−0.856096	−	0.187370i
$89$			64.1247i			0.720502i	0.932855	+	0.360251i	$0.117309\pi$
$89$			64.1247i			0.720502i	−0.932855	+	0.360251i	$0.882691\pi$
$90$	−3.85821	+	53.6260i	−0.0428690	+	0.595844i
$91$	−5.34304	+	92.8415i	−0.0587147	+	1.02024i
$92$	−14.5858	+	100.841i	−0.158542	+	1.09610i
$93$			69.9808i			0.752482i
$94$	−39.3764	−	2.83300i	−0.418898	−	0.0301383i
$95$		−	207.637i		−	2.18565i
$96$	19.4791	−	51.8899i	0.202907	−	0.540520i
$97$			118.454i			1.22118i	0.791948	+	0.610589i	$0.209067\pi$
$97$			118.454i			1.22118i	−0.791948	+	0.610589i	$0.790933\pi$
$98$	−4.33309	−	0.311751i	−0.0442152	−	0.00318114i
$99$	−28.9199			−0.292120
$100$	−218.903	−	31.6626i	−2.18903	−	0.316626i
$101$	84.8930			0.840525			0.420262	−	0.907403i	$-0.361938\pi$
$101$	84.8930			0.840525			0.420262	+	0.907403i	$0.361938\pi$
$102$	−4.49118	+	62.4239i	−0.0440312	+	0.611999i
$103$			61.9501i			0.601457i	0.953710	+	0.300729i	$0.0972298\pi$
$103$			61.9501i			0.601457i	−0.953710	+	0.300729i	$0.902770\pi$
$104$	−28.0362	+	100.150i	−0.269578	+	0.962978i
$105$	111.025			1.05739
$106$	110.507	+	7.95057i	1.04251	+	0.0750054i
$107$			154.774i			1.44648i	0.690594	+	0.723242i	$0.257349\pi$
$107$			154.774i			1.44648i	−0.690594	+	0.723242i	$0.742651\pi$
$108$	2.97536	−	20.5705i	0.0275497	−	0.190468i
$109$			195.399i			1.79265i	0.443395	+	0.896326i	$0.353774\pi$
$109$			195.399i			1.79265i	−0.443395	+	0.896326i	$0.646226\pi$
$110$	12.3977	−	172.318i	0.112706	−	1.56652i
$111$	−35.9470			−0.323847
$112$	−109.765	−	32.4316i	−0.980041	−	0.289568i
$113$	92.5267			0.818820			0.409410	−	0.912350i	$-0.365735\pi$
$113$	92.5267			0.818820			0.409410	+	0.912350i	$0.365735\pi$
$114$	−5.76022	+	80.0624i	−0.0505282	+	0.702302i
$115$	−228.254			−1.98482
$116$	−9.28094	−	1.34241i	−0.0800081	−	0.0115725i
$117$	−2.24075	+	38.9356i	−0.0191517	+	0.332783i
$118$	90.1629	+	6.48691i	0.764092	+	0.0549738i
$119$	129.240			1.08605
$120$	121.293	+	26.5469i	1.01077	+	0.221224i
$121$	−28.0711			−0.231993
$122$	−213.102	−	15.3320i	−1.74674	−	0.125672i
$123$	−75.2766			−0.612005
$124$	159.949	+	23.1354i	1.28991	+	0.186576i
$125$		−	271.470i		−	2.17176i
$126$	−42.8102	−	3.08005i	−0.339763	−	0.0244448i
$127$		−	168.057i		−	1.32328i	−0.749820	−	0.661642i	$-0.769860\pi$
$127$		−	168.057i		−	1.32328i	0.749820	−	0.661642i	$-0.230140\pi$
$128$	−112.161	−	61.6763i	−0.876256	−	0.481846i
$129$	−34.6419			−0.268542
$130$	−231.035	−	30.0426i	−1.77719	−	0.231097i
$131$		−	190.771i		−	1.45626i	−0.685437	−	0.728132i	$-0.740389\pi$
$131$		−	190.771i		−	1.45626i	0.685437	−	0.728132i	$-0.259611\pi$
$132$	−9.56079	+	66.0997i	−0.0724303	+	0.500756i
$133$	165.759			1.24630
$134$	−125.536	−	9.03188i	−0.936835	−	0.0674021i
$135$	46.5615			0.344900
$136$	141.192	+	30.9022i	1.03818	+	0.227222i
$137$			6.18337i			0.0451341i	0.999745	+	0.0225670i	$0.00718392\pi$
$137$			6.18337i			0.0451341i	−0.999745	+	0.0225670i	$0.992816\pi$
$138$	88.0123	+	6.33218i	0.637770	+	0.0458854i
$139$			58.0376i			0.417537i	0.977965	+	0.208769i	$0.0669455\pi$
$139$			58.0376i			0.417537i	−0.977965	+	0.208769i	$0.933054\pi$
$140$	36.7046	−	253.762i	0.262175	−	1.81258i
$141$			34.1891i			0.242476i
$142$	−9.75991	−	0.702192i	−0.0687317	−	0.00494501i
$143$	7.20024	−	125.112i	0.0503513	−	0.874913i
$144$	−46.0327	−	13.6011i	−0.319672	−	0.0944519i
$145$		−	21.0075i		−	0.144879i
$146$	−10.1533	+	141.122i	−0.0695428	+	0.966590i
$147$			3.76227i			0.0255937i
$148$	−11.8839	+	82.1611i	−0.0802969	+	0.555143i
$149$		−	16.3306i		−	0.109601i	−0.998497	−	0.0548006i	$-0.982548\pi$
$149$		−	16.3306i		−	0.109601i	0.998497	−	0.0548006i	$-0.0174523\pi$
$150$	−13.7458	+	191.055i	−0.0916384	+	1.27370i
$151$	2.78196			0.0184236			0.00921179	−	0.999958i	$-0.497068\pi$
$151$	2.78196			0.0184236			0.00921179	+	0.999958i	$0.497068\pi$
$152$	181.088	+	39.6339i	1.19137	+	0.260750i
$153$	54.2004			0.354251
$154$	137.563	+	9.89718i	0.893265	+	0.0642674i
$155$			362.046i			2.33578i
$156$	88.2510	+	17.9934i	0.565711	+	0.115342i
$157$	3.45959			0.0220356			0.0110178	−	0.999939i	$-0.496493\pi$
$157$	3.45959			0.0220356			0.0110178	+	0.999939i	$0.496493\pi$
$158$	12.4696	−	173.317i	0.0789214	−	1.09694i
$159$		−	95.9489i		−	0.603452i
$160$	100.775	−	268.453i	0.629844	−	1.67783i
$161$		−	182.218i		−	1.13179i
$162$	−17.9536	−	1.29170i	−0.110825	−	0.00797346i
$163$	81.7175			0.501335			0.250667	−	0.968073i	$-0.419350\pi$
$163$	81.7175			0.501335			0.250667	+	0.968073i	$0.419350\pi$
$164$	−24.8861	+	172.053i	−0.151745	+	1.04911i
$165$	−149.617			−0.906770
$166$	137.116	+	9.86500i	0.825997	+	0.0594277i
$167$	58.7346			0.351704			0.175852	−	0.984417i	$-0.443732\pi$
$167$	58.7346			0.351704			0.175852	+	0.984417i	$0.443732\pi$
$168$	−21.1927	+	96.8294i	−0.126147	+	0.576365i
$169$	−167.884	−	19.3877i	−0.993398	−	0.114720i
$170$	−23.2351	+	322.950i	−0.136677	+	1.89971i
$171$	69.5153			0.406522
$172$	−11.4525	+	79.1781i	−0.0665842	+	0.460338i
$173$	−110.454			−0.638462			−0.319231	−	0.947677i	$-0.603425\pi$
$173$	−110.454			−0.638462			−0.319231	+	0.947677i	$0.603425\pi$
$174$	−0.582784	+	8.10023i	−0.00334934	+	0.0465531i
$175$	395.554			2.26031
$176$	147.918	+	43.7046i	0.840442	+	0.248322i
$177$		−	78.2852i		−	0.442289i
$178$	9.20332	−	127.919i	0.0517040	−	0.718644i
$179$			37.1266i			0.207411i	0.994608	+	0.103706i	$0.0330700\pi$
$179$			37.1266i			0.207411i	−0.994608	+	0.103706i	$0.966930\pi$
$180$	15.3930	−	106.422i	0.0855169	−	0.591232i
$181$	195.926			1.08246			0.541232	−	0.840873i	$-0.317958\pi$
$181$	195.926			1.08246			0.541232	+	0.840873i	$0.317958\pi$
$182$	23.9833	−	184.437i	0.131777	−	1.01339i
$183$			185.029i			1.01109i
$184$	43.5694	−	199.069i	0.236790	−	1.08190i
$185$	−185.972			−1.00525
$186$	10.0438	−	139.601i	0.0539989	−	0.750542i
$187$	−174.163			−0.931354
$188$	78.1432	+	11.3028i	0.415655	+	0.0601212i
$189$			37.1705i			0.196669i
$190$	−29.8005	+	414.203i	−0.156845	+	2.18002i
$191$			64.5134i			0.337767i	0.985636	+	0.168883i	$0.0540161\pi$
$191$			64.5134i			0.337767i	−0.985636	+	0.168883i	$0.945984\pi$
$192$	−46.3050	+	100.717i	−0.241172	+	0.524566i
$193$			215.920i			1.11876i	0.828913	+	0.559378i	$0.188960\pi$
$193$			215.920i			1.11876i	−0.828913	+	0.559378i	$0.811040\pi$
$194$	17.0008	−	236.298i	0.0876331	−	1.21803i
$195$	−11.5925	+	201.433i	−0.0594487	+	1.03299i
$196$	8.59910	+	1.24379i	0.0438730	+	0.00634587i
$197$			80.2124i			0.407170i	0.979057	+	0.203585i	$0.0652592\pi$
$197$			80.2124i			0.407170i	−0.979057	+	0.203585i	$0.934741\pi$
$198$	57.6907	+	4.15065i	0.291367	+	0.0209629i
$199$		−	230.080i		−	1.15618i	−0.815973	−	0.578090i	$-0.803798\pi$
$199$		−	230.080i		−	1.15618i	0.815973	−	0.578090i	$-0.196202\pi$
$200$	432.134	+	94.5795i	2.16067	+	0.472897i
$201$			108.998i			0.542280i
$202$	−169.348	−	12.1840i	−0.838358	−	0.0603170i
$203$	16.7705			0.0826131
$204$	17.9184	−	123.881i	0.0878354	−	0.607261i
$205$	−389.443			−1.89972
$206$	8.89121	−	123.581i	0.0431612	−	0.599907i
$207$		−	76.4179i		−	0.369168i
$208$	70.3015	−	195.759i	0.337988	−	0.941150i
$209$	−223.375			−1.06878
$210$	−221.479	−	15.9346i	−1.05466	−	0.0758792i
$211$		−	192.934i		−	0.914380i	−0.889369	−	0.457190i	$-0.848856\pi$
$211$		−	192.934i		−	0.914380i	0.889369	−	0.457190i	$-0.151144\pi$
$212$	−219.302	−	31.7203i	−1.03444	−	0.149624i
$213$			8.47417i			0.0397849i
$214$	22.2135	−	308.750i	0.103801	−	1.44276i
$215$	−179.220			−0.833582
$216$	−8.88771	+	40.6080i	−0.0411468	+	0.188000i
$217$	−289.025			−1.33191
$218$	28.0441	−	389.791i	0.128643	−	1.78803i
$219$	122.531			0.559503
$220$	−49.4628	+	341.967i	−0.224831	+	1.55440i
$221$	−13.4944	+	234.480i	−0.0610605	+	1.06100i
$222$	71.7087	+	5.15920i	0.323012	+	0.0232396i
$223$	29.0156			0.130115			0.0650573	−	0.997882i	$-0.479277\pi$
$223$	29.0156			0.130115			0.0650573	+	0.997882i	$0.479277\pi$
$224$	214.308	+	80.4497i	0.956734	+	0.359150i
$225$	165.886			0.737272
$226$	−184.576	−	13.2796i	−0.816709	−	0.0587595i
$227$	−405.207			−1.78505			−0.892526	−	0.450996i	$-0.851069\pi$
$227$	−405.207			−1.78505			−0.892526	+	0.450996i	$0.851069\pi$
$228$	22.9815	−	158.885i	0.100796	−	0.696865i
$229$		−	122.661i		−	0.535637i	−0.963469	−	0.267818i	$-0.913697\pi$
$229$		−	122.661i		−	0.535637i	0.963469	−	0.267818i	$-0.0863027\pi$
$230$	455.332	+	32.7596i	1.97970	+	0.142433i
$231$		−	119.441i		−	0.517060i
$232$	18.3214	+	4.00992i	0.0789714	+	0.0172842i
$233$	256.411			1.10047			0.550237	−	0.835008i	$-0.314537\pi$
$233$	256.411			1.10047			0.550237	+	0.835008i	$0.314537\pi$
$234$	10.0581	−	77.3488i	0.0429832	−	0.330550i
$235$			176.878i			0.752670i
$236$	−178.930	−	25.8808i	−0.758177	−	0.109664i
$237$	−150.485			−0.634958
$238$	−257.814	−	18.5489i	−1.08325	−	0.0779364i
$239$	383.513			1.60466			0.802328	−	0.596883i	$-0.203594\pi$
$239$	383.513			1.60466			0.802328	+	0.596883i	$0.203594\pi$
$240$	−238.150	−	70.3652i	−0.992293	−	0.293188i
$241$		−	185.925i		−	0.771475i	−0.922609	−	0.385737i	$-0.873947\pi$
$241$		−	185.925i		−	0.771475i	0.922609	−	0.385737i	$-0.126053\pi$
$242$	55.9975	+	4.02883i	0.231395	+	0.0166481i
$243$			15.5885i			0.0641500i
$244$	422.905	+	61.1697i	1.73322	+	0.250696i
$245$			19.4641i			0.0794453i
$246$	150.165	+	10.8039i	0.610427	+	0.0439181i
$247$	−17.3073	+	300.735i	−0.0700702	+	1.21755i
$248$	−315.753	−	69.1077i	−1.27320	−	0.278660i
$249$		−	119.052i		−	0.478122i
$250$	−38.9620	+	541.540i	−0.155848	+	2.16616i
$251$		−	264.427i		−	1.05349i	−0.850023	−	0.526746i	$-0.823412\pi$
$251$		−	264.427i		−	1.05349i	0.850023	−	0.526746i	$-0.176588\pi$
$252$	84.9575	+	12.2884i	0.337133	+	0.0487636i
$253$			245.555i			0.970574i
$254$	−24.1199	+	335.248i	−0.0949604	+	1.31987i
$255$	280.406			1.09963
$256$	214.891	+	139.132i	0.839419	+	0.543485i
$257$	44.4283			0.172873			0.0864364	−	0.996257i	$-0.472452\pi$
$257$	44.4283			0.172873			0.0864364	+	0.996257i	$0.472452\pi$
$258$	69.1052	+	4.97189i	0.267850	+	0.0192709i
$259$		−	148.463i		−	0.573218i
$260$	456.567	+	93.0890i	1.75603	+	0.358035i
$261$	7.03314			0.0269469
$262$	−27.3798	+	380.557i	−0.104503	+	1.45251i
$263$			397.499i			1.51140i	0.654917	+	0.755701i	$0.272704\pi$
$263$			397.499i			1.51140i	−0.654917	+	0.755701i	$0.727296\pi$
$264$	28.5591	−	130.486i	0.108178	−	0.494267i
$265$		−	496.392i		−	1.87318i
$266$	−330.662	−	23.7900i	−1.24309	−	0.0894362i
$267$	−111.067			−0.415982
$268$	249.128	+	36.0344i	0.929582	+	0.134457i
$269$	−107.526			−0.399726			−0.199863	−	0.979824i	$-0.564050\pi$
$269$	−107.526			−0.399726			−0.199863	+	0.979824i	$0.564050\pi$
$270$	−92.8830	−	6.68261i	−0.344011	−	0.0247504i
$271$	−110.427			−0.407478			−0.203739	−	0.979025i	$-0.565309\pi$
$271$	−110.427			−0.407478			−0.203739	+	0.979025i	$0.565309\pi$
$272$	−277.221	−	81.9092i	−1.01920	−	0.301137i
$273$	−160.806	−	9.25441i	−0.589034	−	0.0338989i
$274$	0.887451	−	12.3349i	0.00323887	−	0.0450177i
$275$	−533.045			−1.93835
$276$	−174.662	−	25.2634i	−0.632833	−	0.0915342i
$277$	299.860			1.08253			0.541264	−	0.840852i	$-0.317946\pi$
$277$	299.860			1.08253			0.541264	+	0.840852i	$0.317946\pi$
$278$	8.32969	−	115.776i	0.0299629	−	0.416461i
$279$	−121.210			−0.434446
$280$	−109.640	+	500.947i	−0.391573	+	1.78910i
$281$			88.8074i			0.316040i	0.987436	+	0.158020i	$0.0505111\pi$
$281$			88.8074i			0.316040i	−0.987436	+	0.158020i	$0.949489\pi$
$282$	4.90690	−	68.2020i	0.0174004	−	0.241851i
$283$		−	402.310i		−	1.42159i	−0.703399	−	0.710795i	$-0.748335\pi$
$283$		−	402.310i		−	1.42159i	0.703399	−	0.710795i	$-0.251665\pi$
$284$	19.3687	+	2.80153i	0.0681997	+	0.00986453i
$285$	359.638			1.26189
$286$	−32.3198	+	248.546i	−0.113006	+	0.869044i
$287$		−	310.897i		−	1.08326i
$288$	89.8760	+	33.7387i	0.312069	+	0.117148i
$289$	37.4090			0.129443
$290$	−3.01504	+	41.9066i	−0.0103967	+	0.144505i
$291$	−205.169			−0.705048
$292$	40.5083	−	280.059i	0.138727	−	0.959107i
$293$		−	538.815i		−	1.83896i	−0.393137	−	0.919480i	$-0.628610\pi$
$293$		−	538.815i		−	1.83896i	0.393137	−	0.919480i	$-0.371390\pi$
$294$	0.539969	−	7.50514i	0.00183663	−	0.0255277i
$295$		−	405.009i		−	1.37291i
$296$	35.4985	−	162.193i	0.119928	−	0.547949i
$297$		−	50.0907i		−	0.168656i
$298$	−2.34380	+	32.5769i	−0.00786510	+	0.109319i
$299$	330.597	+	19.0259i	1.10568	+	0.0636318i
$300$	54.8413	−	379.152i	0.182804	−	1.26384i
$301$		−	143.073i		−	0.475326i
$302$	−5.54957	−	0.399273i	−0.0183761	−	0.00132210i
$303$			147.039i			0.485277i
$304$	−355.553	−	105.054i	−1.16958	−	0.345571i
$305$			957.247i			3.13851i
$306$	−108.121	−	7.77896i	−0.353338	−	0.0254214i
$307$	−541.889			−1.76511			−0.882555	−	0.470208i	$-0.844179\pi$
$307$	−541.889			−1.76511			−0.882555	+	0.470208i	$0.844179\pi$
$308$	−272.996	−	39.4866i	−0.886350	−	0.128203i
$309$	−107.301			−0.347251
$310$	51.9616	−	722.225i	0.167618	−	2.32976i
$311$			297.786i			0.957512i	0.877948	+	0.478756i	$0.158912\pi$
$311$			297.786i			0.957512i	−0.877948	+	0.478756i	$0.841088\pi$
$312$	−173.464	−	48.5600i	−0.555976	−	0.155641i
$313$	157.927			0.504559			0.252280	−	0.967654i	$-0.418820\pi$
$313$	157.927			0.504559			0.252280	+	0.967654i	$0.418820\pi$
$314$	−6.90134	−	0.496528i	−0.0219788	−	0.00158130i
$315$			192.302i			0.610482i
$316$	−49.7498	+	343.951i	−0.157436	+	1.08845i
$317$		−	42.1595i		−	0.132995i	−0.997787	−	0.0664977i	$-0.978818\pi$
$317$		−	42.1595i		−	0.132995i	0.997787	−	0.0664977i	$-0.0211825\pi$
$318$	−13.7708	+	191.403i	−0.0433044	+	0.601896i
$319$	−22.5997			−0.0708456
$320$	−239.559	+	521.058i	−0.748623	+	1.62831i
$321$	−268.076			−0.835128
$322$	−26.1523	+	363.496i	−0.0812183	+	1.12887i
$323$	418.640			1.29610
$324$	35.6292	+	5.15348i	0.109967	+	0.0159058i
$325$	−41.3010	+	717.652i	−0.127080	+	2.20816i
$326$	−163.014	−	11.7283i	−0.500042	−	0.0359763i
$327$	−338.441			−1.03499
$328$	74.3374	−	339.648i	0.226638	−	1.03551i
$329$	−141.203			−0.429189
$330$	298.463	+	21.4734i	0.904432	+	0.0650708i
$331$	−102.961			−0.311062			−0.155531	−	0.987831i	$-0.549709\pi$
$331$	−102.961			−0.311062			−0.155531	+	0.987831i	$0.549709\pi$
$332$	−272.108	−	39.3583i	−0.819603	−	0.118549i
$333$		−	62.2621i		−	0.186973i
$334$	−117.166	−	8.42971i	−0.350797	−	0.0252387i
$335$			563.903i			1.68329i
$336$	56.1732	−	190.118i	0.167182	−	0.565827i
$337$	259.348			0.769578			0.384789	−	0.923005i	$-0.374274\pi$
$337$	259.348			0.769578			0.384789	+	0.923005i	$0.374274\pi$
$338$	332.120	+	62.7706i	0.982604	+	0.185712i
$339$			160.261i			0.472746i
$340$	92.7010	−	640.900i	0.272650	−	1.88500i
$341$	389.488			1.14219
$342$	−138.672	−	9.97699i	−0.405474	−	0.0291725i
$343$	334.982			0.976623
$344$	34.2097	−	156.304i	0.0994469	−	0.454373i
$345$		−	395.348i		−	1.14594i
$346$	220.338	+	15.8526i	0.636816	+	0.0458168i
$347$		−	331.490i		−	0.955304i	−0.878549	−	0.477652i	$-0.841488\pi$
$347$		−	331.490i		−	0.955304i	0.878549	−	0.477652i	$-0.158512\pi$
$348$	2.32513	−	16.0751i	0.00668140	−	0.0461927i
$349$			31.3006i			0.0896867i	0.998994	+	0.0448433i	$0.0142789\pi$
$349$			31.3006i			0.0896867i	−0.998994	+	0.0448433i	$0.985721\pi$
$350$	−789.068	−	56.7708i	−2.25448	−	0.162202i
$351$	−67.4384	−	3.88109i	−0.192132	−	0.0110572i
$352$	−288.800	−	108.413i	−0.820456	−	0.307992i
$353$		−	251.339i		−	0.712009i	−0.934484	−	0.356005i	$-0.884139\pi$
$353$		−	251.339i		−	0.712009i	0.934484	−	0.356005i	$-0.115861\pi$
$354$	−11.2357	+	156.167i	−0.0317392	+	0.441149i
$355$			43.8412i			0.123496i
$356$	−36.7184	+	253.857i	−0.103141	+	0.713081i
$357$			223.851i			0.627033i
$358$	5.32850	−	74.0618i	0.0148841	−	0.206877i
$359$	270.471			0.753402			0.376701	−	0.926335i	$-0.377058\pi$
$359$	270.471			0.753402			0.376701	+	0.926335i	$0.377058\pi$
$360$	−45.9806	+	210.086i	−0.127724	+	0.583571i
$361$	175.931			0.487343
$362$	−390.842	−	28.1197i	−1.07967	−	0.0776788i
$363$		−	48.6206i		−	0.133941i
$364$	−74.3139	+	364.482i	−0.204159	+	1.00132i
$365$	633.916			1.73676
$366$	26.5557	−	369.104i	0.0725567	−	1.00848i
$367$			345.056i			0.940208i	0.882611	+	0.470104i	$0.155784\pi$
$367$			345.056i			0.940208i	−0.882611	+	0.470104i	$0.844216\pi$
$368$	−115.485	+	390.858i	−0.313818	+	1.06211i
$369$		−	130.383i		−	0.353341i
$370$	370.985	+	26.6911i	1.00266	+	0.0721382i
$371$	396.274			1.06812
$372$	−40.0716	+	277.040i	−0.107719	+	0.744732i
$373$	−194.494			−0.521431			−0.260715	−	0.965416i	$-0.583958\pi$
$373$	−194.494			−0.521431			−0.260715	+	0.965416i	$0.583958\pi$
$374$	347.428	+	24.9963i	0.928953	+	0.0668350i
$375$	470.200			1.25387
$376$	−154.261	−	33.7626i	−0.410269	−	0.0897941i
$377$	−1.75105	+	30.4266i	−0.00464470	+	0.0807072i
$378$	5.33480	−	74.1494i	0.0141132	−	0.196162i
$379$	483.006			1.27442			0.637212	−	0.770689i	$-0.280088\pi$
$379$	483.006			1.27442			0.637212	+	0.770689i	$0.280088\pi$
$380$	118.895	−	821.993i	0.312881	−	2.16314i
$381$	291.084			0.763999
$382$	9.25911	−	128.694i	0.0242385	−	0.336896i
$383$	556.781			1.45374			0.726868	−	0.686778i	$-0.240975\pi$
$383$	556.781			1.45374			0.726868	+	0.686778i	$0.240975\pi$
$384$	106.826	−	194.268i	0.278194	−	0.505907i
$385$		−	617.927i		−	1.60501i
$386$	30.9893	−	430.726i	0.0802832	−	1.11587i
$387$		−	60.0016i		−	0.155043i
$388$	−67.8280	+	468.937i	−0.174814	+	1.20860i
$389$	−763.729			−1.96331			−0.981657	−	0.190655i	$-0.938939\pi$
$389$	−763.729			−1.96331			−0.981657	+	0.190655i	$0.938939\pi$
$390$	52.0354	−	400.164i	0.133424	−	1.02606i
$391$		−	460.209i		−	1.17700i
$392$	−16.9753	−	3.71533i	−0.0433045	−	0.00947788i
$393$	330.424			0.840774
$394$	11.5123	−	160.011i	0.0292189	−	0.406120i
$395$	−778.535			−1.97098
$396$	−114.488	−	16.5598i	−0.289111	−	0.0418176i
$397$			248.024i			0.624745i	0.949960	+	0.312373i	$0.101124\pi$
$397$			248.024i			0.624745i	−0.949960	+	0.312373i	$0.898876\pi$
$398$	−33.0216	+	458.973i	−0.0829688	+	1.15320i
$399$			287.102i			0.719554i
$400$	−848.465	−	250.692i	−2.12116	−	0.626730i
$401$			605.027i			1.50880i	0.656417	+	0.754398i	$0.272071\pi$
$401$			605.027i			1.50880i	−0.656417	+	0.754398i	$0.727929\pi$
$402$	15.6437	−	217.434i	0.0389146	−	0.540882i
$403$	30.1780	−	524.377i	0.0748833	−	1.30118i
$404$	336.075	+	48.6105i	0.831868	+	0.120323i
$405$			80.6469i			0.199128i
$406$	−33.4544	−	2.40693i	−0.0824001	−	0.00592841i
$407$			200.068i			0.491568i
$408$	−53.5242	+	244.552i	−0.131187	+	0.599392i
$409$		−	216.943i		−	0.530423i	−0.964190	−	0.265211i	$-0.914558\pi$
$409$		−	216.943i		−	0.530423i	0.964190	−	0.265211i	$-0.0854417\pi$
$410$	776.879	+	55.8938i	1.89483	+	0.136326i
$411$	−10.7099			−0.0260582
$412$	−35.4732	+	245.248i	−0.0860999	+	0.595263i
$413$	323.322			0.782863
$414$	−10.9677	+	152.442i	−0.0264919	+	0.368217i
$415$		−	615.918i		−	1.48414i
$416$	−168.336	+	380.419i	−0.404654	+	0.914470i
$417$	−100.524			−0.241065
$418$	445.598	+	32.0593i	1.06602	+	0.0766968i
$419$		−	168.374i		−	0.401848i	−0.979607	−	0.200924i	$-0.935606\pi$
$419$		−	168.374i		−	0.401848i	0.979607	−	0.200924i	$-0.0643944\pi$
$420$	439.528	+	63.5742i	1.04650	+	0.151367i
$421$		−	689.983i		−	1.63891i	−0.573140	−	0.819457i	$-0.694275\pi$
$421$		−	689.983i		−	1.63891i	0.573140	−	0.819457i	$-0.305725\pi$
$422$	−27.6903	+	384.874i	−0.0656169	+	0.912023i
$423$	−59.2173			−0.139994
$424$	432.921	+	94.7518i	1.02104	+	0.223471i
$425$	999.010			2.35061
$426$	1.21623	−	16.9047i	0.00285501	−	0.0396823i
$427$	−764.180			−1.78965
$428$	−88.6248	+	612.719i	−0.207067	+	1.43159i
$429$	216.701	+	12.4712i	0.505131	+	0.0290703i
$430$	357.516	+	25.7221i	0.831433	+	0.0598187i
$431$	157.729			0.365960			0.182980	−	0.983117i	$-0.441426\pi$
$431$	157.729			0.365960			0.182980	+	0.983117i	$0.441426\pi$
$432$	23.5577	−	79.7310i	0.0545318	−	0.184563i
$433$	482.476			1.11426			0.557132	−	0.830424i	$-0.311902\pi$
$433$	482.476			1.11426			0.557132	+	0.830424i	$0.311902\pi$
$434$	576.559	+	41.4815i	1.32848	+	0.0955795i
$435$	36.3860			0.0836459
$436$	−111.887	+	773.547i	−0.256622	+	1.77419i
$437$		−	590.246i		−	1.35068i
$438$	−244.431	−	17.5860i	−0.558061	−	0.0401506i
$439$			133.554i			0.304223i	0.988363	+	0.152111i	$0.0486072\pi$
$439$			133.554i			0.304223i	−0.988363	+	0.152111i	$0.951393\pi$
$440$	147.750	−	675.072i	0.335796	−	1.53425i
$441$	−6.51644			−0.0147765
$442$	60.5723	−	465.815i	0.137041	−	1.05388i
$443$			388.850i			0.877765i	0.898545	+	0.438882i	$0.144626\pi$
$443$			388.850i			0.877765i	−0.898545	+	0.438882i	$0.855374\pi$
$444$	−142.307	−	20.5836i	−0.320512	−	0.0463594i
$445$	−574.606			−1.29125
$446$	−57.8815	−	4.16438i	−0.129779	−	0.00933717i
$447$	28.2854			0.0632783
$448$	−415.966	−	191.243i	−0.928495	−	0.426881i
$449$		−	196.054i		−	0.436647i	−0.975876	−	0.218323i	$-0.929941\pi$
$449$		−	196.054i		−	0.436647i	0.975876	−	0.218323i	$-0.0700588\pi$
$450$	−330.917	−	23.8083i	−0.735371	−	0.0529074i
$451$			418.962i			0.928962i
$452$	366.295	+	52.9816i	0.810387	+	0.117216i
$453$			4.81850i			0.0106369i
$454$	808.324	+	58.1562i	1.78045	+	0.128097i
$455$	−831.931	−	47.8777i	−1.82842	−	0.105226i
$456$	−68.6480	+	313.653i	−0.150544	+	0.687835i
$457$			531.008i			1.16194i	0.813924	+	0.580972i	$0.197327\pi$
$457$			531.008i			1.16194i	−0.813924	+	0.580972i	$0.802673\pi$
$458$	−17.6045	+	244.689i	−0.0384379	+	0.534256i
$459$			93.8778i			0.204527i
$460$	−903.614	−	130.700i	−1.96438	−	0.284131i
$461$			161.575i			0.350488i	0.984525	+	0.175244i	$0.0560714\pi$
$461$			161.575i			0.350488i	−0.984525	+	0.175244i	$0.943929\pi$
$462$	−17.1424	+	238.266i	−0.0371048	+	0.515727i
$463$	−202.497			−0.437358			−0.218679	−	0.975797i	$-0.570175\pi$
$463$	−202.497			−0.437358			−0.218679	+	0.975797i	$0.570175\pi$
$464$	−35.9727	−	10.6287i	−0.0775274	−	0.0229067i
$465$	−627.082			−1.34856
$466$	−511.499	−	36.8006i	−1.09764	−	0.0789713i
$467$		−	296.012i		−	0.633858i	−0.948449	−	0.316929i	$-0.897348\pi$
$467$		−	296.012i		−	0.633858i	0.948449	−	0.316929i	$-0.102652\pi$
$468$	−31.1655	+	152.855i	−0.0665930	+	0.326614i
$469$	−450.169			−0.959849
$470$	25.3859	−	352.843i	0.0540125	−	0.750730i
$471$			5.99219i			0.0127223i
$472$	353.223	+	77.3085i	0.748353	+	0.163789i
$473$			192.804i			0.407620i
$474$	300.194	+	21.5980i	0.633321	+	0.0455653i
$475$	1281.29			2.69746
$476$	511.637	+	74.0041i	1.07487	+	0.155471i
$477$	166.188			0.348403
$478$	−765.048	−	55.0426i	−1.60052	−	0.115152i
$479$	−178.050			−0.371711			−0.185856	−	0.982577i	$-0.559506\pi$
$479$	−178.050			−0.371711			−0.185856	+	0.982577i	$0.559506\pi$
$480$	464.974	+	174.547i	0.968695	+	0.363640i
$481$	269.357	+	15.5015i	0.559993	+	0.0322277i
$482$	−26.6844	+	370.892i	−0.0553619	+	0.769486i
$483$	315.610			0.653437
$484$	−111.128	−	16.0738i	−0.229603	−	0.0332103i
$485$	−1061.44			−2.18854
$486$	2.23729	−	31.0965i	0.00460348	−	0.0639846i
$487$	629.282			1.29216			0.646080	−	0.763270i	$-0.276407\pi$
$487$	629.282			1.29216			0.646080	+	0.763270i	$0.276407\pi$
$488$	−834.850	−	182.720i	−1.71076	−	0.374427i
$489$			141.539i			0.289446i
$490$	2.79353	−	38.8278i	0.00570108	−	0.0792405i
$491$		−	151.056i		−	0.307649i	−0.988098	−	0.153824i	$-0.950841\pi$
$491$		−	151.056i		−	0.307649i	0.988098	−	0.153824i	$-0.0491590\pi$
$492$	−298.005	−	43.1040i	−0.605701	−	0.0876098i
$493$	42.3554			0.0859137
$494$	77.6877	−	597.436i	0.157262	−	1.20938i
$495$		−	259.144i		−	0.523524i
$496$	619.960	+	183.177i	1.24992	+	0.369308i
$497$	−34.9988			−0.0704202
$498$	−17.0867	+	237.491i	−0.0343106	+	0.476890i
$499$	−129.655			−0.259831			−0.129915	−	0.991525i	$-0.541471\pi$
$499$	−129.655			−0.259831			−0.129915	+	0.991525i	$0.541471\pi$
$500$	155.446	−	1074.70i	0.310892	−	2.14939i
$501$			101.731i			0.203056i
$502$	−37.9511	+	527.490i	−0.0755998	+	1.05078i
$503$		−	57.9337i		−	0.115176i	−0.998340	−	0.0575882i	$-0.981659\pi$
$503$		−	57.9337i		−	0.115176i	0.998340	−	0.0575882i	$-0.0183410\pi$
$504$	−167.713	−	36.7068i	−0.332765	−	0.0728309i
$505$			760.707i			1.50635i
$506$	35.2426	−	489.844i	0.0696494	−	0.968071i
$507$	33.5805	−	290.784i	0.0662338	−	0.573539i
$508$	96.2310	−	665.305i	0.189431	−	1.30966i
$509$		−	370.869i		−	0.728622i	−0.931277	−	0.364311i	$-0.881304\pi$
$509$		−	370.869i		−	0.728622i	0.931277	−	0.364311i	$-0.118696\pi$
$510$	−559.366	−	40.2445i	−1.09680	−	0.0789107i
$511$			506.061i			0.990335i
$512$	−408.706	−	308.388i	−0.798254	−	0.602321i
$513$			120.404i			0.234706i
$514$	−88.6275	−	6.37645i	−0.172427	−	0.0124055i
$515$	−555.120			−1.07790
$516$	−137.141	−	19.8363i	−0.265776	−	0.0384424i
$517$	190.284			0.368054
$518$	−21.3078	+	296.161i	−0.0411347	+	0.571740i
$519$		−	191.312i		−	0.368616i
$520$	−897.419	−	251.225i	−1.72581	−	0.483126i
$521$	−686.693			−1.31803			−0.659014	−	0.752131i	$-0.729026\pi$
$521$	−686.693			−1.31803			−0.659014	+	0.752131i	$0.729026\pi$
$522$	−14.0300	−	1.00941i	−0.0268774	−	0.00193374i
$523$		−	183.477i		−	0.350817i	−0.984496	−	0.175408i	$-0.943875\pi$
$523$		−	183.477i		−	0.350817i	0.984496	−	0.175408i	$-0.0561246\pi$
$524$	109.237	−	755.223i	0.208467	−	1.44127i
$525$			685.119i			1.30499i
$526$	57.0499	−	792.948i	0.108460	−	1.50751i
$527$	−729.961			−1.38512
$528$	−75.6986	+	256.201i	−0.143369	+	0.485230i
$529$	−119.855			−0.226568
$530$	−71.2432	+	990.224i	−0.134421	+	1.86835i
$531$	135.594			0.255356
$532$	656.205	+	94.9148i	1.23347	+	0.178411i
$533$	564.059	+	32.4616i	1.05827	+	0.0609037i
$534$	221.562	+	15.9406i	0.414910	+	0.0298513i
$535$	−1386.89			−2.59232
$536$	−491.800	−	107.638i	−0.917537	−	0.200818i
$537$	−64.3052			−0.119749
$538$	214.498	+	15.4324i	0.398695	+	0.0286848i
$539$	20.9394			0.0388486
$540$	184.328	+	26.6615i	0.341348	+	0.0493732i
$541$			30.8671i			0.0570556i	0.999593	+	0.0285278i	$0.00908191\pi$
$541$			30.8671i			0.0570556i	−0.999593	+	0.0285278i	$0.990918\pi$
$542$	220.284	+	15.8487i	0.406428	+	0.0292411i
$543$			339.354i			0.624961i
$544$	541.257	+	203.184i	0.994958	+	0.373499i
$545$	−1750.93			−3.21271
$546$	319.455	+	41.5404i	0.585082	+	0.0760813i
$547$			661.135i			1.20866i	0.796736	+	0.604328i	$0.206558\pi$
$547$			661.135i			1.20866i	−0.796736	+	0.604328i	$0.793442\pi$
$548$	−3.54065	+	24.4787i	−0.00646104	+	0.0446692i
$549$	−320.479			−0.583751
$550$	1063.34	+	76.5038i	1.93335	+	0.139098i
$551$	54.3234			0.0985906
$552$	344.797	+	75.4645i	0.624633	+	0.136711i
$553$		−	621.512i		−	1.12389i
$554$	−598.175	−	43.0366i	−1.07974	−	0.0776835i
$555$		−	322.113i		−	0.580384i
$556$	−33.2329	+	229.760i	−0.0597713	+	0.413237i
$557$		−	968.340i		−	1.73849i	−0.494380	−	0.869246i	$-0.664605\pi$
$557$		−	968.340i		−	1.73849i	0.494380	−	0.869246i	$-0.335395\pi$
$558$	241.796	+	17.3964i	0.433326	+	0.0311763i
$559$	259.577	+	14.9387i	0.464360	+	0.0267240i
$560$	290.612	−	983.575i	0.518950	−	1.75638i
$561$		−	301.660i		−	0.537717i
$562$	12.7458	−	177.157i	0.0226794	−	0.315226i
$563$			791.962i			1.40668i	0.710853	+	0.703341i	$0.248309\pi$
$563$			791.962i			1.40668i	−0.710853	+	0.703341i	$0.751691\pi$
$564$	−19.5770	+	135.348i	−0.0347110	+	0.239979i
$565$			829.110i			1.46745i
$566$	−57.7405	+	802.546i	−0.102015	+	1.41793i
$567$	−64.3812			−0.113547
$568$	−38.2355	−	8.36845i	−0.0673160	−	0.0147332i
$569$	394.766			0.693788			0.346894	−	0.937904i	$-0.387236\pi$
$569$	394.766			0.693788			0.346894	+	0.937904i	$0.387236\pi$
$570$	−717.421	−	51.6160i	−1.25863	−	0.0905543i
$571$			714.833i			1.25190i	0.779864	+	0.625948i	$0.215288\pi$
$571$			714.833i			1.25190i	−0.779864	+	0.625948i	$0.784712\pi$
$572$	100.145	−	491.173i	0.175078	−	0.858694i
$573$	−111.741			−0.195010
$574$	−44.6206	+	620.190i	−0.0777362	+	1.08047i
$575$		−	1408.52i		−	2.44960i
$576$	−174.446	−	80.2027i	−0.302858	−	0.139241i
$577$			456.320i			0.790849i	0.918498	+	0.395425i	$0.129403\pi$
$577$			456.320i			0.790849i	−0.918498	+	0.395425i	$0.870597\pi$
$578$	−74.6252	−	5.36903i	−0.129109	−	0.00928897i
$579$	−373.984			−0.645914
$580$	12.0291	−	83.1644i	0.0207397	−	0.143387i
$581$	491.694			0.846289
$582$	409.280	+	29.4463i	0.703230	+	0.0505950i
$583$	−534.016			−0.915980
$584$	−121.003	+	552.861i	−0.207196	+	0.946679i
$585$	−348.893	−	20.0788i	−0.596398	−	0.0343227i
$586$	−77.3320	+	1074.85i	−0.131966	+	1.83422i
$587$	940.348			1.60196			0.800978	−	0.598694i	$-0.204313\pi$
$587$	940.348			1.60196			0.800978	+	0.598694i	$0.204313\pi$
$588$	−2.15431	+	14.8941i	−0.00366379	+	0.0253301i
$589$	−936.219			−1.58951
$590$	−58.1277	+	807.929i	−0.0985216	+	1.36937i
$591$	−138.932			−0.235079
$592$	−94.0923	+	318.455i	−0.158940	+	0.537930i
$593$		−	132.854i		−	0.224038i	−0.993706	−	0.112019i	$-0.964268\pi$
$593$		−	132.854i		−	0.224038i	0.993706	−	0.112019i	$-0.0357317\pi$
$594$	−7.18913	+	99.9231i	−0.0121029	+	0.168221i
$595$			1158.09i			1.94637i
$596$	9.35103	−	64.6495i	0.0156896	−	0.108472i
$597$	398.510			0.667521
$598$	−656.759	−	85.4017i	−1.09826	−	0.142812i
$599$			294.961i			0.492422i	0.969216	+	0.246211i	$0.0791857\pi$
$599$			294.961i			0.492422i	−0.969216	+	0.246211i	$0.920814\pi$
$600$	−163.816	+	748.478i	−0.273027	+	1.24746i
$601$	−676.783			−1.12610			−0.563048	−	0.826424i	$-0.690371\pi$
$601$	−676.783			−1.12610			−0.563048	+	0.826424i	$0.690371\pi$
$602$	−20.5342	+	285.409i	−0.0341099	+	0.474101i
$603$	−188.790			−0.313085
$604$	11.0132	+	1.59297i	0.0182338	+	0.00263738i
$605$		−	251.539i		−	0.415767i
$606$	21.1034	−	293.320i	0.0348240	−	0.484026i
$607$			943.492i			1.55435i	0.629283	+	0.777176i	$0.283348\pi$
$607$			943.492i			1.55435i	−0.629283	+	0.777176i	$0.716652\pi$
$608$	694.195	+	260.595i	1.14177	+	0.428611i
$609$			29.0473i			0.0476967i
$610$	137.386	−	1909.56i	0.225223	−	3.13042i
$611$	14.7434	−	256.184i	0.0241300	−	0.419287i
$612$	214.569	+	31.0356i	0.350602	+	0.0507118i
$613$		−	78.6962i		−	0.128379i	−0.997938	−	0.0641894i	$-0.979554\pi$
$613$		−	78.6962i		−	0.128379i	0.997938	−	0.0641894i	$-0.0204462\pi$
$614$	1080.98	+	77.7731i	1.76056	+	0.126666i
$615$		−	674.536i		−	1.09681i
$616$	538.917	+	117.951i	0.874865	+	0.191478i
$617$		−	677.179i		−	1.09753i	−0.835975	−	0.548767i	$-0.815097\pi$
$617$		−	677.179i		−	1.09753i	0.835975	−	0.548767i	$-0.184903\pi$
$618$	214.048	+	15.4000i	0.346356	+	0.0249192i
$619$	194.411			0.314072			0.157036	−	0.987593i	$-0.449806\pi$
$619$	194.411			0.314072			0.157036	+	0.987593i	$0.449806\pi$
$620$	−207.311	+	1433.27i	−0.334372	+	2.31172i
$621$	132.360			0.213140
$622$	42.7389	−	594.037i	0.0687121	−	0.955043i
$623$		−	458.714i		−	0.736299i
$624$	339.065	+	121.766i	0.543373	+	0.195137i
$625$	1050.19			1.68031
$626$	−315.040	−	22.6660i	−0.503259	−	0.0362077i
$627$		−	386.897i		−	0.617060i
$628$	13.6958	+	1.98099i	0.0218087	+	0.00315445i
$629$		−	374.959i		−	0.596119i
$630$	27.5996	−	383.612i	0.0438089	−	0.608908i
$631$	−329.979			−0.522946			−0.261473	−	0.965211i	$-0.584208\pi$
$631$	−329.979			−0.522946			−0.261473	+	0.965211i	$0.584208\pi$
$632$	148.608	−	678.989i	0.235139	−	1.07435i
$633$	334.172			0.527918
$634$	−6.05083	+	84.1017i	−0.00954389	+	0.132652i
$635$	1505.92			2.37153
$636$	54.9412	−	379.843i	0.0863855	−	0.597237i
$637$	1.62241	−	28.1913i	0.00254695	−	0.0442563i
$638$	45.0829	+	3.24356i	0.0706629	+	0.00508396i
$639$	−14.6777			−0.0229698
$640$	552.667	−	1005.05i	0.863542	−	1.57039i
$641$	−0.0265537			−4.14254e−5			−2.07127e−5	−	1.00000i	$-0.500007\pi$
$641$	−0.0265537			−4.14254e−5			−2.07127e−5		1.00000i	$0.500007\pi$
$642$	534.770	+	38.4749i	0.832975	+	0.0599297i
$643$	−603.043			−0.937859			−0.468929	−	0.883236i	$-0.655360\pi$
$643$	−603.043			−0.937859			−0.468929	+	0.883236i	$0.655360\pi$
$644$	104.339	−	721.364i	0.162018	−	1.12013i
$645$		−	310.418i		−	0.481269i
$646$	−835.120	−	60.0841i	−1.29276	−	0.0930094i
$647$		−	1205.80i		−	1.86368i	−0.362873	−	0.931839i	$-0.618204\pi$
$647$		−	1205.80i		−	1.86368i	0.362873	−	0.931839i	$-0.381796\pi$
$648$	−70.3351	−	15.3940i	−0.108542	−	0.0237561i
$649$	−435.707			−0.671351
$650$	185.388	−	1425.68i	0.285212	−	2.19335i
$651$		−	500.606i		−	0.768980i
$652$	323.504	+	46.7922i	0.496171	+	0.0717672i
$653$	956.801			1.46524			0.732619	−	0.680639i	$-0.238298\pi$
$653$	956.801			1.46524			0.732619	+	0.680639i	$0.238298\pi$
$654$	675.137	+	48.5738i	1.03232	+	0.0742719i
$655$	1709.45			2.60985
$656$	−197.038	+	666.875i	−0.300364	+	1.01658i
$657$			212.230i			0.323029i
$658$	281.678	+	20.2658i	0.428082	+	0.0307991i
$659$			765.970i			1.16232i	0.813789	+	0.581161i	$0.197401\pi$
$659$			765.970i			1.16232i	−0.813789	+	0.581161i	$0.802599\pi$
$660$	−592.305	−	85.6721i	−0.897431	−	0.129806i
$661$		−	204.901i		−	0.309986i	−0.987916	−	0.154993i	$-0.950464\pi$
$661$		−	204.901i		−	0.309986i	0.987916	−	0.154993i	$-0.0495355\pi$
$662$	205.392	+	14.7773i	0.310260	+	0.0223221i
$663$	−406.132	−	23.3729i	−0.612567	−	0.0352533i
$664$	537.165	+	117.567i	0.808983	+	0.177059i
$665$			1485.32i			2.23357i
$666$	−8.93599	+	124.203i	−0.0134174	+	0.186491i
$667$		−	59.7175i		−	0.0895315i
$668$	232.519	+	33.6319i	0.348082	+	0.0503472i
$669$			50.2564i			0.0751217i
$670$	80.9326	−	1124.90i	0.120795	−	1.67895i
$671$	1029.80			1.53473
$672$	−139.343	+	371.193i	−0.207356	+	0.552371i
$673$	548.057			0.814349			0.407174	−	0.913350i	$-0.366514\pi$
$673$	548.057			0.814349			0.407174	+	0.913350i	$0.366514\pi$
$674$	−517.358	−	37.2222i	−0.767594	−	0.0552258i
$675$			287.323i			0.425664i
$676$	−653.519	−	172.884i	−0.966744	−	0.255746i
$677$	−594.743			−0.878498			−0.439249	−	0.898365i	$-0.644755\pi$
$677$	−594.743			−0.878498			−0.439249	+	0.898365i	$0.644755\pi$
$678$	23.0010	−	319.696i	0.0339248	−	0.471527i
$679$		−	847.359i		−	1.24795i
$680$	−276.907	+	1265.19i	−0.407217	+	1.86057i
$681$		−	701.839i		−	1.03060i
$682$	−776.967	−	55.9001i	−1.13925	−	0.0819650i
$683$	44.7137			0.0654666			0.0327333	−	0.999464i	$-0.489579\pi$
$683$	44.7137			0.0654666			0.0327333	+	0.999464i	$0.489579\pi$
$684$	275.197	+	39.8051i	0.402335	+	0.0581945i
$685$	−55.4077			−0.0808872
$686$	−668.236	−	48.0773i	−0.974105	−	0.0700835i
$687$	212.455			0.309250
$688$	−90.6762	+	306.893i	−0.131797	+	0.446065i
$689$	−41.3762	+	718.960i	−0.0600525	+	1.04348i
$690$	−56.7412	+	788.658i	−0.0822337	+	1.14298i
$691$	−284.878			−0.412269			−0.206135	−	0.978524i	$-0.566088\pi$
$691$	−284.878			−0.412269			−0.206135	+	0.978524i	$0.566088\pi$
$692$	−437.266	−	63.2469i	−0.631887	−	0.0913973i
$693$	206.878			0.298525
$694$	−47.5762	+	661.271i	−0.0685536	+	0.952841i
$695$	−520.062			−0.748291
$696$	−6.94539	+	31.7335i	−0.00997901	+	0.0455941i
$697$		−	785.200i		−	1.12654i
$698$	4.49234	−	62.4399i	0.00643601	−	0.0894554i
$699$			444.116i			0.635359i
$700$	1565.92	+	226.498i	2.23703	+	0.323568i
$701$	−264.562			−0.377407			−0.188703	−	0.982034i	$-0.560428\pi$
$701$	−264.562			−0.377407			−0.188703	+	0.982034i	$0.560428\pi$
$702$	133.972	+	17.4211i	0.190843	+	0.0248163i
$703$		−	480.908i		−	0.684079i
$704$	560.552	+	257.717i	0.796239	+	0.366075i
$705$	−306.361			−0.434554
$706$	−36.0728	+	501.383i	−0.0510946	+	0.710174i
$707$	−607.280			−0.858953
$708$	44.8268	−	309.916i	0.0633147	−	0.437734i
$709$		−	153.842i		−	0.216984i	−0.994097	−	0.108492i	$-0.965398\pi$
$709$		−	153.842i		−	0.216984i	0.994097	−	0.108492i	$-0.0346022\pi$
$710$	6.29218	−	87.4563i	0.00886223	−	0.123178i
$711$		−	260.648i		−	0.366593i
$712$	109.681	−	501.135i	0.154047	−	0.703841i
$713$			1029.18i			1.44345i
$714$	32.1276	−	446.547i	0.0449966	−	0.625416i
$715$	1121.10	+	64.5196i	1.56798	+	0.0902373i
$716$	−21.2590	+	146.977i	−0.0296914	+	0.205275i
$717$			664.264i			0.926449i
$718$	−539.548	−	38.8186i	−0.751459	−	0.0540649i
$719$			400.635i			0.557211i	0.960406	+	0.278606i	$0.0898723\pi$
$719$			400.635i			0.557211i	−0.960406	+	0.278606i	$0.910128\pi$
$720$	121.876	−	412.489i	0.169272	−	0.572901i
$721$		−	443.158i		−	0.614644i
$722$	−350.954	−	25.2500i	−0.486086	−	0.0349723i
$723$	322.032			0.445411
$724$	775.633	+	112.189i	1.07132	+	0.154957i
$725$	129.633			0.178805
$726$	−6.97814	+	96.9906i	−0.00961176	+	0.133596i
$727$			794.012i			1.09218i	0.837728	+	0.546088i	$0.183884\pi$
$727$			794.012i			1.09218i	−0.837728	+	0.546088i	$0.816116\pi$
$728$	200.556	−	716.418i	0.275489	−	0.984091i
$729$	−27.0000			−0.0370370
$730$	−1264.56	−	90.9810i	−1.73228	−	0.124631i
$731$		−	361.345i		−	0.494316i
$732$	−105.949	+	732.493i	−0.144739	+	1.00067i
$733$			693.526i			0.946148i	0.881023	+	0.473074i	$0.156856\pi$
$733$			693.526i			0.946148i	−0.881023	+	0.473074i	$0.843144\pi$
$734$	49.5232	−	688.333i	0.0674703	−	0.937784i
$735$	−33.7128			−0.0458678
$736$	286.471	−	763.126i	0.389227	−	1.03686i
$737$	606.644			0.823127
$738$	−18.7128	+	260.093i	−0.0253561	+	0.352430i
$739$	−54.3708			−0.0735734			−0.0367867	−	0.999323i	$-0.511712\pi$
$739$	−54.3708			−0.0735734			−0.0367867	+	0.999323i	$0.511712\pi$
$740$	−736.227	−	106.489i	−0.994901	−	0.143904i
$741$	−520.889	−	29.9772i	−0.702954	−	0.0404551i
$742$	−790.505	−	56.8742i	−1.06537	−	0.0766498i
$743$	−430.157			−0.578947			−0.289473	−	0.957186i	$-0.593480\pi$
$743$	−430.157			−0.578947			−0.289473	+	0.957186i	$0.593480\pi$
$744$	119.698	−	546.901i	0.160884	−	0.735082i
$745$	146.335			0.196422
$746$	387.984	+	27.9142i	0.520086	+	0.0374184i
$747$	206.205			0.276044
$748$	−689.478	−	99.7274i	−0.921762	−	0.133325i
$749$		−	1107.17i		−	1.47820i
$750$	−937.975	−	67.4841i	−1.25063	−	0.0899788i
$751$			1403.65i			1.86904i	0.355906	+	0.934522i	$0.384172\pi$
$751$			1403.65i			1.86904i	−0.355906	+	0.934522i	$0.615828\pi$
$752$	302.881	+	89.4910i	0.402768	+	0.119004i
$753$	458.000			0.608234
$754$	7.85997	−	60.4450i	0.0104244	−	0.0801658i
$755$			24.9285i			0.0330179i
$756$	−21.2842	+	147.151i	−0.0281537	+	0.194644i
$757$	1062.91			1.40410			0.702052	−	0.712126i	$-0.252267\pi$
$757$	1062.91			1.40410			0.702052	+	0.712126i	$0.252267\pi$
$758$	−963.522	−	69.3222i	−1.27114	−	0.0914540i
$759$	−425.314			−0.560361
$760$	−355.151	+	1622.68i	−0.467303	+	2.13511i
$761$			500.997i			0.658340i	0.944271	+	0.329170i	$0.106769\pi$
$761$			500.997i			0.658340i	−0.944271	+	0.329170i	$0.893231\pi$
$762$	−580.666	−	41.7770i	−0.762029	−	0.0548254i
$763$		−	1397.78i		−	1.83196i
$764$	−36.9410	+	255.396i	−0.0483520	+	0.334288i
$765$			485.677i			0.634872i
$766$	−1110.69	−	79.9104i	−1.44999	−	0.104322i
$767$	−33.7591	+	586.603i	−0.0440144	+	0.764802i
$768$	−240.984	+	372.203i	−0.313781	+	0.484639i
$769$			303.302i			0.394411i	0.980362	+	0.197205i	$0.0631866\pi$
$769$			303.302i			0.394411i	−0.980362	+	0.197205i	$0.936813\pi$
$770$	−88.6863	+	1232.67i	−0.115177	+	1.60087i
$771$			76.9521i			0.0998081i
$772$	−123.638	+	854.784i	−0.160152	+	1.10723i
$773$		−	40.4275i		−	0.0522995i	−0.999658	−	0.0261498i	$-0.991675\pi$
$773$		−	40.4275i		−	0.0522995i	0.999658	−	0.0261498i	$-0.00832468\pi$
$774$	−8.61156	+	119.694i	−0.0111260	+	0.154643i
$775$	−2234.12			−2.88274
$776$	202.609	−	925.721i	0.261094	−	1.19294i
$777$	257.146			0.330947
$778$	1523.52	+	109.612i	1.95825	+	0.140890i
$779$		−	1007.07i		−	1.29277i
$780$	−161.235	+	790.797i	−0.206711	+	1.01384i
$781$	47.1642			0.0603895
$782$	−66.0502	+	918.044i	−0.0844631	+	1.17397i
$783$			12.1818i			0.0155578i
$784$	33.3299	+	9.84784i	0.0425127	+	0.0125610i
$785$			31.0006i			0.0394912i
$786$	−659.145	−	47.4232i	−0.838607	−	0.0603349i
$787$	541.043			0.687475			0.343737	−	0.939066i	$-0.388307\pi$
$787$	541.043			0.687475			0.343737	+	0.939066i	$0.388307\pi$
$788$	−45.9303	+	317.545i	−0.0582872	+	0.402976i
$789$	−688.488			−0.872608
$790$	1553.06	+	111.737i	1.96589	+	0.141439i
$791$	−661.887			−0.836773
$792$	226.009	+	49.4658i	0.285365	+	0.0624568i
$793$	79.7903	−	1386.45i	0.100618	−	1.74836i
$794$	35.5969	−	494.769i	0.0448324	−	0.623134i
$795$	859.775			1.08148
$796$	131.746	−	910.841i	0.165510	−	1.14427i
$797$	594.102			0.745423			0.372711	−	0.927947i	$-0.378428\pi$
$797$	594.102			0.745423			0.372711	+	0.927947i	$0.378428\pi$
$798$	41.2055	−	572.724i	0.0516360	−	0.717699i
$799$	−356.622			−0.446336
$800$	1656.58	+	621.865i	2.07072	+	0.777332i
$801$		−	192.374i		−	0.240167i
$802$	86.8349	−	1206.93i	0.108273	−	1.50491i
$803$		−	681.964i		−	0.849270i
$804$	−62.4133	+	431.503i	−0.0776285	+	0.536695i
$805$	1632.81			2.02834
$806$	−135.460	+	1041.72i	−0.168065	+	1.29246i
$807$		−	186.241i		−	0.230782i
$808$	−663.440	−	145.205i	−0.821089	−	0.179709i
$809$	−268.111			−0.331411			−0.165705	−	0.986175i	$-0.552990\pi$
$809$	−268.111			−0.331411			−0.165705	+	0.986175i	$0.552990\pi$
$810$	11.5746	−	160.878i	0.0142897	−	0.198615i
$811$	1210.73			1.49288			0.746441	−	0.665452i	$-0.231761\pi$
$811$	1210.73			1.49288			0.746441	+	0.665452i	$0.231761\pi$
$812$	66.3909	+	9.60291i	0.0817622	+	0.0118262i
$813$		−	191.265i		−	0.235258i
$814$	28.7142	−	399.105i	0.0352754	−	0.490300i
$815$			732.252i			0.898469i
$816$	141.871	−	480.161i	0.173861	−	0.588433i
$817$		−	463.447i		−	0.567255i
$818$	−31.1361	+	432.767i	−0.0380637	+	0.529055i
$819$	16.0291	−	278.525i	0.0195716	−	0.340079i
$820$	−1541.73	−	222.999i	−1.88016	−	0.271950i
$821$		−	9.06751i		−	0.0110445i	−0.999985	−	0.00552223i	$-0.998242\pi$
$821$		−	9.06751i		−	0.0110445i	0.999985	−	0.00552223i	$-0.00175779\pi$
$822$	21.3646	+	1.53711i	0.0259910	+	0.00186996i
$823$			391.114i			0.475229i	0.971359	+	0.237615i	$0.0763656\pi$
$823$			391.114i			0.475229i	−0.971359	+	0.237615i	$0.923634\pi$
$824$	105.962	−	484.141i	0.128595	−	0.587549i
$825$		−	923.262i		−	1.11910i
$826$	−644.978	−	46.4039i	−0.780845	−	0.0561791i
$827$	575.381			0.695744			0.347872	−	0.937542i	$-0.386904\pi$
$827$	575.381			0.695744			0.347872	+	0.937542i	$0.386904\pi$
$828$	43.7575	−	302.523i	0.0528473	−	0.365366i
$829$	−684.323			−0.825480			−0.412740	−	0.910849i	$-0.635428\pi$
$829$	−684.323			−0.825480			−0.412740	+	0.910849i	$0.635428\pi$
$830$	−88.3980	+	1228.66i	−0.106504	+	1.48031i
$831$			519.374i			0.624998i
$832$	390.403	−	734.717i	0.469235	−	0.883074i
$833$	−39.2437			−0.0471113
$834$	200.530	+	14.4274i	0.240444	+	0.0172991i
$835$			526.307i			0.630307i
$836$	−884.297	−	127.906i	−1.05777	−	0.152998i
$837$		−	209.942i		−	0.250827i
$838$	−24.1654	+	335.880i	−0.0288371	+	0.400812i
$839$	−1239.98			−1.47793			−0.738966	−	0.673743i	$-0.764685\pi$
$839$	−1239.98			−1.47793			−0.738966	+	0.673743i	$0.764685\pi$
$840$	−867.665	−	189.903i	−1.03294	−	0.226074i
$841$	−835.504			−0.993465
$842$	−99.0279	+	1376.41i	−0.117610	+	1.63469i
$843$	−153.819			−0.182466
$844$	110.476	−	763.789i	0.130896	−	0.904963i
$845$	173.729	−	1504.37i	0.205596	−	1.78032i
$846$	118.129	+	8.49900i	0.139633	+	0.0100461i
$847$	200.806			0.237079
$848$	−850.011	−	251.149i	−1.00237	−	0.296166i
$849$	696.822			0.820756
$850$	−1992.87	−	143.380i	−2.34455	−	0.168683i
$851$	−528.660			−0.621222
$852$	−4.85239	+	33.5476i	−0.00569529	+	0.0393751i
$853$			1300.90i			1.52509i	0.646935	+	0.762545i	$0.276050\pi$
$853$			1300.90i			1.52509i	−0.646935	+	0.762545i	$0.723950\pi$
$854$	1524.42	+	109.677i	1.78503	+	0.128427i
$855$			622.911i			0.728550i
$856$	264.732	−	1209.56i	0.309266	−	1.41304i
$857$	1399.44			1.63295			0.816477	−	0.577378i	$-0.195924\pi$
$857$	1399.44			1.63295			0.816477	+	0.577378i	$0.195924\pi$
$858$	−430.495	−	55.9795i	−0.501743	−	0.0652441i
$859$		−	1316.15i		−	1.53219i	−0.642727	−	0.766095i	$-0.722197\pi$
$859$		−	1316.15i		−	1.53219i	0.642727	−	0.766095i	$-0.277803\pi$
$860$	−709.497	−	102.623i	−0.824996	−	0.119329i
$861$	538.489			0.625422
$862$	−314.645	−	22.6376i	−0.365017	−	0.0262617i
$863$	−689.042			−0.798427			−0.399213	−	0.916858i	$-0.630717\pi$
$863$	−689.042			−0.798427			−0.399213	+	0.916858i	$0.630717\pi$
$864$	−58.4372	+	155.670i	−0.0676356	+	0.180173i
$865$		−	989.753i		−	1.14422i
$866$	−962.464	−	69.2460i	−1.11139	−	0.0799608i
$867$			64.7943i			0.0747340i
$868$	−1144.19	−	165.498i	−1.31819	−	0.190666i
$869$			837.545i			0.963804i
$870$	−72.5843	−	5.22220i	−0.0834303	−	0.00600252i
$871$	47.0035	−	816.741i	0.0539650	−	0.937705i
$872$	334.219	−	1527.05i	0.383278	−	1.75120i
$873$		−	355.363i		−	0.407059i
$874$	−84.7134	+	1177.45i	−0.0969261	+	1.34719i
$875$			1941.95i			2.21937i
$876$	485.077	+	70.1625i	0.553741	+	0.0800941i
$877$			672.682i			0.767026i	0.923535	+	0.383513i	$0.125286\pi$
$877$			672.682i			0.767026i	−0.923535	+	0.383513i	$0.874714\pi$
$878$	19.1679	−	266.419i	0.0218314	−	0.303438i
$879$	933.255			1.06172
$880$	−391.627	+	1325.46i	−0.445030	+	1.50620i
$881$	689.782			0.782953			0.391477	−	0.920188i	$-0.371964\pi$
$881$	689.782			0.782953			0.391477	+	0.920188i	$0.371964\pi$
$882$	12.9993	+	0.935254i	0.0147384	+	0.00106038i
$883$		−	759.459i		−	0.860089i	−0.902808	−	0.430045i	$-0.858498\pi$
$883$		−	759.459i		−	0.860089i	0.902808	−	0.430045i	$-0.141502\pi$
$884$	−187.687	+	920.534i	−0.212316	+	1.04133i
$885$	701.495			0.792650
$886$	55.8086	−	775.695i	0.0629894	−	0.875502i
$887$			303.051i			0.341659i	0.985301	+	0.170829i	$0.0546447\pi$
$887$			303.051i			0.341659i	−0.985301	+	0.170829i	$0.945355\pi$
$888$	280.926	+	61.4853i	0.316359	+	0.0692402i
$889$			1202.19i			1.35230i
$890$	1146.25	+	82.4688i	1.28792	+	0.0926616i
$891$	86.7597			0.0973734
$892$	114.867	+	16.6146i	0.128775	+	0.0186262i
$893$	−457.390			−0.512195
$894$	−56.4249	−	4.05958i	−0.0631151	−	0.00454092i
$895$	−332.683			−0.371713
$896$	802.339	+	441.199i	0.895467	+	0.492410i
$897$	−32.9538	+	572.611i	−0.0367378	+	0.638362i
$898$	−28.1382	+	391.098i	−0.0313343	+	0.435521i
$899$	−94.7210			−0.105363
$900$	656.710	+	94.9879i	0.729678	+	0.105542i
$901$	1000.83			1.11080
$902$	60.1303	−	835.763i	0.0666633	−	0.926567i
$903$	247.810			0.274430
$904$	−723.097	−	158.261i	−0.799886	−	0.175068i
$905$			1755.65i			1.93994i
$906$	0.691561	−	9.61215i	0.000763313	−	0.0106094i
$907$		−	1136.35i		−	1.25286i	−0.779477	−	0.626431i	$-0.784515\pi$
$907$		−	1136.35i		−	1.25286i	0.779477	−	0.626431i	$-0.215485\pi$
$908$	−1604.13	−	232.025i	−1.76667	−	0.255534i
$909$	−254.679			−0.280175
$910$	1652.70	+	214.909i	1.81616	+	0.236164i
$911$			1357.93i			1.49059i	0.666735	+	0.745295i	$0.267691\pi$
$911$			1357.93i			1.49059i	−0.666735	+	0.745295i	$0.732309\pi$
$912$	181.958	−	615.836i	0.199516	−	0.675259i
$913$	−662.603			−0.725742
$914$	76.2114	−	1059.28i	0.0833823	−	1.15895i
$915$	−1658.00			−1.81202
$916$	70.2366	−	485.590i	0.0766775	−	0.530120i
$917$			1364.67i			1.48819i
$918$	13.4736	−	187.272i	0.0146771	−	0.204000i
$919$			1496.08i			1.62794i	0.580908	+	0.813969i	$0.302698\pi$
$919$			1496.08i			1.62794i	−0.580908	+	0.813969i	$0.697302\pi$
$920$	1783.81	+	390.416i	1.93892	+	0.424365i
$921$		−	938.579i		−	1.01909i
$922$	23.1896	−	322.316i	0.0251514	−	0.349584i
$923$	3.65433	−	63.4983i	0.00395919	−	0.0687956i
$924$	68.3929	−	472.843i	0.0740182	−	0.511734i
$925$		−	1147.60i		−	1.24065i
$926$	403.949	+	29.0628i	0.436230	+	0.0313853i
$927$		−	185.850i		−	0.200486i
$928$	70.2345	+	26.3655i	0.0756838	+	0.0284111i
$929$			225.727i			0.242979i	0.992593	+	0.121489i	$0.0387670\pi$
$929$			225.727i			0.242979i	−0.992593	+	0.121489i	$0.961233\pi$
$930$	1250.93	+	90.0002i	1.34509	+	0.0967744i
$931$	−50.3325			−0.0540628
$932$	1015.08	+	146.823i	1.08914	+	0.157535i
$933$	−515.781			−0.552820
$934$	−42.4842	+	590.497i	−0.0454863	+	0.632224i
$935$		−	1560.64i		−	1.66913i
$936$	84.1085	−	300.449i	0.0898595	−	0.320993i
$937$	−1034.66			−1.10422			−0.552111	−	0.833771i	$-0.686177\pi$
$937$	−1034.66			−1.10422			−0.552111	+	0.833771i	$0.686177\pi$
$938$	898.017	+	64.6093i	0.957374	+	0.0688798i
$939$			273.538i			0.291307i
$940$	−101.282	+	700.223i	−0.107746	+	0.744918i
$941$			1046.73i			1.11236i	0.831062	+	0.556180i	$0.187734\pi$
$941$			1046.73i			1.11236i	−0.831062	+	0.556180i	$0.812266\pi$
$942$	0.860012	−	11.9535i	0.000912964	−	0.0126895i
$943$	−1107.06			−1.17398
$944$	−693.528	−	204.914i	−0.734670	−	0.217069i
$945$	−333.076			−0.352462
$946$	27.6717	−	384.614i	0.0292513	−	0.406569i
$947$	156.424			0.165178			0.0825891	−	0.996584i	$-0.473681\pi$
$947$	156.424			0.165178			0.0825891	+	0.996584i	$0.473681\pi$
$948$	−595.741	−	86.1691i	−0.628419	−	0.0908957i
$949$	−918.146	−	52.8394i	−0.967487	−	0.0556790i
$950$	−2555.98	−	183.894i	−2.69050	−	0.193572i
$951$	73.0224			0.0767849
$952$	−1010.01	−	221.058i	−1.06094	−	0.232204i
$953$	835.890			0.877114			0.438557	−	0.898703i	$-0.355490\pi$
$953$	835.890			0.877114			0.438557	+	0.898703i	$0.355490\pi$
$954$	−331.520	−	23.8517i	−0.347505	−	0.0250018i
$955$	−578.090			−0.605330
$956$	1518.25	+	219.603i	1.58813	+	0.229710i
$957$		−	39.1439i		−	0.0409027i
$958$	355.181	+	25.5541i	0.370753	+	0.0266744i
$959$		−	44.2325i		−	0.0461236i
$960$	−902.499	−	414.929i	−0.940103	−	0.432218i
$961$	671.438			0.698687
$962$	−535.100	−	69.5817i	−0.556237	−	0.0723303i
$963$		−	464.321i		−	0.482161i
$964$	106.463	−	736.042i	0.110438	−	0.763529i
$965$	−1934.81			−2.00498
$966$	−629.593	−	45.2971i	−0.651753	−	0.0468914i
$967$	684.654			0.708018			0.354009	−	0.935242i	$-0.384818\pi$
$967$	684.654			0.708018			0.354009	+	0.935242i	$0.384818\pi$
$968$	219.376	+	48.0140i	0.226628	+	0.0496013i
$969$			725.105i			0.748302i
$970$	2117.41	+	152.340i	2.18290	+	0.157052i
$971$		−	1753.07i		−	1.80543i	−0.430239	−	0.902715i	$-0.641571\pi$
$971$		−	1753.07i		−	1.80543i	0.430239	−	0.902715i	$-0.358429\pi$
$972$	−8.92609	+	61.7116i	−0.00918322	+	0.0634893i
$973$		−	415.171i		−	0.426691i
$974$	−1255.32	−	90.3160i	−1.28883	−	0.0927268i
$975$	−1243.01	−	71.5354i	−1.27488	−	0.0733696i
$976$	1639.17	+	484.318i	1.67948	+	0.496227i
$977$		−	1610.15i		−	1.64805i	−0.566550	−	0.824027i	$-0.691722\pi$
$977$		−	1610.15i		−	1.64805i	0.566550	−	0.824027i	$-0.308278\pi$
$978$	20.3140	−	282.348i	0.0207709	−	0.288699i
$979$			618.160i			0.631419i
$980$	−11.1453	+	77.0545i	−0.0113728	+	0.0786271i
$981$		−	586.197i		−	0.597551i
$982$	−21.6798	+	301.332i	−0.0220772	+	0.306856i
$983$	541.189			0.550549			0.275274	−	0.961366i	$-0.411231\pi$
$983$	541.189			0.550549			0.275274	+	0.961366i	$0.411231\pi$
$984$	588.287	+	128.756i	0.597853	+	0.130850i
$985$	−718.765			−0.729710
$986$	−84.4925	−	6.07895i	−0.0856922	−	0.00616526i
$987$		−	244.571i		−	0.247792i
$988$	−240.720	+	1180.64i	−0.243644	+	1.19498i
$989$	−509.466			−0.515132
$990$	−37.1930	+	516.953i	−0.0375687	+	0.522174i
$991$			263.541i			0.265935i	0.991120	+	0.132967i	$0.0424505\pi$
$991$			263.541i			0.265935i	−0.991120	+	0.132967i	$0.957549\pi$
$992$	−1210.43	−	454.387i	−1.22020	−	0.458051i
$993$		−	178.334i		−	0.179592i
$994$	69.8172	+	5.02311i	0.0702386	+	0.00505343i
$995$	2061.69			2.07205
$996$	68.1705	−	471.305i	0.0684443	−	0.473198i
$997$	−222.859			−0.223530			−0.111765	−	0.993735i	$-0.535650\pi$
$997$	−222.859			−0.223530			−0.111765	+	0.993735i	$0.535650\pi$
$998$	258.642	+	18.6084i	0.259161	+	0.0186457i
$999$	107.841			0.107949

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	156.3.e.c.103.1	✓	24
3.2	odd	2		468.3.e.m.415.24		24
4.3	odd	2	inner	156.3.e.c.103.23	yes	24
12.11	even	2		468.3.e.m.415.2		24
13.12	even	2	inner	156.3.e.c.103.24	yes	24
39.38	odd	2		468.3.e.m.415.1		24
52.51	odd	2	inner	156.3.e.c.103.2	yes	24
156.155	even	2		468.3.e.m.415.23		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
156.3.e.c.103.1	✓	24	1.1	even	1	trivial
156.3.e.c.103.2	yes	24	52.51	odd	2	inner
156.3.e.c.103.23	yes	24	4.3	odd	2	inner
156.3.e.c.103.24	yes	24	13.12	even	2	inner
468.3.e.m.415.1		24	39.38	odd	2
468.3.e.m.415.2		24	12.11	even	2
468.3.e.m.415.23		24	156.155	even	2
468.3.e.m.415.24		24	3.2	odd	2

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:	\( N \)	\(=\)	\( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	156.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.99484 - 0.143522i) q^{2} +1.73205i q^{3} +(3.95880 + 0.572609i) q^{4} +8.96077i q^{5} +(0.248588 - 3.45517i) q^{6} -7.15347 q^{7} +(-7.81501 - 1.71044i) q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(-1.99484 - 0.143522i) q^{2} +1.73205i q^{3} +(3.95880 + 0.572609i) q^{4} +8.96077i q^{5} +(0.248588 - 3.45517i) q^{6} -7.15347 q^{7} +(-7.81501 - 1.71044i) q^{8} -3.00000 q^{9} +(1.28607 - 17.8753i) q^{10} +9.63996 q^{11} +(-0.991787 + 6.85685i) q^{12} +(0.746915 - 12.9785i) q^{13} +(14.2701 + 1.02668i) q^{14} -15.5205 q^{15} +(15.3442 + 4.53369i) q^{16} -18.0668 q^{17} +(5.98453 + 0.430567i) q^{18} -23.1718 q^{19} +(-5.13101 + 35.4739i) q^{20} -12.3902i q^{21} +(-19.2302 - 1.38355i) q^{22} +25.4726i q^{23} +(2.96257 - 13.5360i) q^{24} -55.2954 q^{25} +(-3.35269 + 25.7829i) q^{26} -5.19615i q^{27} +(-28.3192 - 4.09614i) q^{28} -2.34438 q^{29} +(30.9610 + 2.22754i) q^{30} +40.4034 q^{31} +(-29.9587 - 11.2462i) q^{32} +16.6969i q^{33} +(36.0404 + 2.59299i) q^{34} -64.1006i q^{35} +(-11.8764 - 1.71783i) q^{36} +20.7540i q^{37} +(46.2241 + 3.32566i) q^{38} +(22.4795 + 1.29370i) q^{39} +(15.3269 - 70.0285i) q^{40} +43.4609i q^{41} +(-1.77827 + 24.7165i) q^{42} +20.0005i q^{43} +(38.1627 + 5.51993i) q^{44} -26.8823i q^{45} +(3.65589 - 50.8139i) q^{46} +19.7391 q^{47} +(-7.85258 + 26.5770i) q^{48} +2.17215 q^{49} +(110.306 + 7.93611i) q^{50} -31.2926i q^{51} +(10.3885 - 50.9517i) q^{52} -55.3961 q^{53} +(-0.745763 + 10.3655i) q^{54} +86.3815i q^{55} +(55.9045 + 12.2356i) q^{56} -40.1347i q^{57} +(4.67667 + 0.336471i) q^{58} -45.1980 q^{59} +(-61.4426 - 8.88718i) q^{60} +106.826 q^{61} +(-80.5986 - 5.79879i) q^{62} +21.4604 q^{63} +(58.1488 + 26.7342i) q^{64} +(116.298 + 6.69294i) q^{65} +(2.39638 - 33.3077i) q^{66} +62.9302 q^{67} +(-71.5229 - 10.3452i) q^{68} -44.1199 q^{69} +(-9.19986 + 127.871i) q^{70} +4.89257 q^{71} +(23.4450 + 5.13132i) q^{72} -70.7434i q^{73} +(2.97866 - 41.4010i) q^{74} -95.7744i q^{75} +(-91.7325 - 13.2684i) q^{76} -68.9592 q^{77} +(-44.6573 - 5.80702i) q^{78} +86.8826i q^{79} +(-40.6254 + 137.496i) q^{80} +9.00000 q^{81} +(6.23761 - 86.6978i) q^{82} -68.7350 q^{83} +(7.09472 - 49.0503i) q^{84} -161.892i q^{85} +(2.87052 - 39.8979i) q^{86} -4.06059i q^{87} +(-75.3364 - 16.4886i) q^{88} +64.1247i q^{89} +(-3.85821 + 53.6260i) q^{90} +(-5.34304 + 92.8415i) q^{91} +(-14.5858 + 100.841i) q^{92} +69.9808i q^{93} +(-39.3764 - 2.83300i) q^{94} -207.637i q^{95} +(19.4791 - 51.8899i) q^{96} +118.454i q^{97} +(-4.33309 - 0.311751i) q^{98} -28.9199 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{4} - 72 q^{9}+O(q^{10}) \) 24 * q + 8 * q^4 - 72 * q^9	\( 24 q + 8 q^{4} - 72 q^{9} + 28 q^{10} + 36 q^{12} + 48 q^{13} - 40 q^{14} + 100 q^{16} + 32 q^{17} + 84 q^{22} - 312 q^{25} - 16 q^{26} - 80 q^{29} + 60 q^{30} - 24 q^{36} + 120 q^{38} - 204 q^{40} - 96 q^{42} - 144 q^{48} + 392 q^{49} + 28 q^{52} - 224 q^{53} + 800 q^{56} - 96 q^{61} - 352 q^{62} - 184 q^{64} - 112 q^{65} + 252 q^{66} - 344 q^{68} + 144 q^{69} + 232 q^{74} - 16 q^{77} - 168 q^{78} + 216 q^{81} + 20 q^{82} - 92 q^{88} - 84 q^{90} - 616 q^{92} - 684 q^{94}+O(q^{100}) \) 24 * q + 8 * q^4 - 72 * q^9 + 28 * q^10 + 36 * q^12 + 48 * q^13 - 40 * q^14 + 100 * q^16 + 32 * q^17 + 84 * q^22 - 312 * q^25 - 16 * q^26 - 80 * q^29 + 60 * q^30 - 24 * q^36 + 120 * q^38 - 204 * q^40 - 96 * q^42 - 144 * q^48 + 392 * q^49 + 28 * q^52 - 224 * q^53 + 800 * q^56 - 96 * q^61 - 352 * q^62 - 184 * q^64 - 112 * q^65 + 252 * q^66 - 344 * q^68 + 144 * q^69 + 232 * q^74 - 16 * q^77 - 168 * q^78 + 216 * q^81 + 20 * q^82 - 92 * q^88 - 84 * q^90 - 616 * q^92 - 684 * q^94

Introduction

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