LMFDB - Embedded newform 156.3.f.a.79.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [156,3,Mod(79,156)]

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, 0]))

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

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

chi := DirichletCharacter("156.79");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 156 = 2^{2} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	156.f (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			79.11
Character	$\chi$	$=$	156.79
Dual form			156.3.f.a.79.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.337137 - 1.97138i) q^{2} +1.73205i q^{3} +(-3.77268 - 1.32925i) q^{4} -3.28562 q^{5} +(3.41453 + 0.583939i) q^{6} +11.8734i q^{7} +(-3.89237 + 6.98924i) q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(0.337137 - 1.97138i) q^{2} +1.73205i q^{3} +(-3.77268 - 1.32925i) q^{4} -3.28562 q^{5} +(3.41453 + 0.583939i) q^{6} +11.8734i q^{7} +(-3.89237 + 6.98924i) q^{8} -3.00000 q^{9} +(-1.10771 + 6.47720i) q^{10} +3.23214i q^{11} +(2.30233 - 6.53447i) q^{12} +3.60555 q^{13} +(23.4069 + 4.00296i) q^{14} -5.69086i q^{15} +(12.4662 + 10.0297i) q^{16} -12.7169 q^{17} +(-1.01141 + 5.91414i) q^{18} +19.4637i q^{19} +(12.3956 + 4.36742i) q^{20} -20.5653 q^{21} +(6.37178 + 1.08968i) q^{22} -6.77915i q^{23} +(-12.1057 - 6.74178i) q^{24} -14.2047 q^{25} +(1.21557 - 7.10791i) q^{26} -5.19615i q^{27} +(15.7827 - 44.7944i) q^{28} +14.6737 q^{29} +(-11.2188 - 1.91860i) q^{30} +4.99021i q^{31} +(23.9751 - 21.1942i) q^{32} -5.59824 q^{33} +(-4.28736 + 25.0699i) q^{34} -39.0114i q^{35} +(11.3180 + 3.98776i) q^{36} -16.5006 q^{37} +(38.3703 + 6.56193i) q^{38} +6.24500i q^{39} +(12.7888 - 22.9640i) q^{40} +13.4022 q^{41} +(-6.93333 + 40.5420i) q^{42} +53.3697i q^{43} +(4.29633 - 12.1938i) q^{44} +9.85686 q^{45} +(-13.3643 - 2.28551i) q^{46} -91.1714i q^{47} +(-17.3719 + 21.5921i) q^{48} -91.9770 q^{49} +(-4.78894 + 28.0029i) q^{50} -22.0264i q^{51} +(-13.6026 - 4.79269i) q^{52} +36.7750 q^{53} +(-10.2436 - 1.75182i) q^{54} -10.6196i q^{55} +(-82.9858 - 46.2156i) q^{56} -33.7120 q^{57} +(4.94705 - 28.9274i) q^{58} +89.2562i q^{59} +(-7.56459 + 21.4698i) q^{60} -50.6171 q^{61} +(9.83759 + 1.68239i) q^{62} -35.6201i q^{63} +(-33.6989 - 54.4094i) q^{64} -11.8465 q^{65} +(-1.88737 + 11.0362i) q^{66} -50.0554i q^{67} +(47.9769 + 16.9040i) q^{68} +11.7418 q^{69} +(-76.9063 - 13.1522i) q^{70} -46.7777i q^{71} +(11.6771 - 20.9677i) q^{72} +136.133 q^{73} +(-5.56297 + 32.5290i) q^{74} -24.6033i q^{75} +(25.8721 - 73.4301i) q^{76} -38.3764 q^{77} +(12.3113 + 2.10542i) q^{78} +101.057i q^{79} +(-40.9591 - 32.9537i) q^{80} +9.00000 q^{81} +(4.51838 - 26.4208i) q^{82} +160.838i q^{83} +(77.5862 + 27.3364i) q^{84} +41.7830 q^{85} +(105.212 + 17.9929i) q^{86} +25.4156i q^{87} +(-22.5902 - 12.5807i) q^{88} +171.832 q^{89} +(3.32312 - 19.4316i) q^{90} +42.8101i q^{91} +(-9.01120 + 25.5755i) q^{92} -8.64329 q^{93} +(-179.734 - 30.7373i) q^{94} -63.9502i q^{95} +(36.7094 + 41.5261i) q^{96} +174.529 q^{97} +(-31.0089 + 181.322i) q^{98} -9.69643i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{2} + 8 q^{4} - 12 q^{6} - 32 q^{8} - 72 q^{9}+O(q^{10}) $ 24 * q + 4 * q^2 + 8 * q^4 - 12 * q^6 - 32 * q^8 - 72 * q^9	$ 24 q + 4 q^{2} + 8 q^{4} - 12 q^{6} - 32 q^{8} - 72 q^{9} - 12 q^{10} + 12 q^{12} + 32 q^{14} + 4 q^{16} - 12 q^{18} + 84 q^{20} + 28 q^{22} - 36 q^{24} + 104 q^{25} - 96 q^{28} + 64 q^{29} - 12 q^{30} + 44 q^{32} + 48 q^{33} + 40 q^{34} - 24 q^{36} - 192 q^{37} - 104 q^{38} + 220 q^{40} - 220 q^{44} - 104 q^{46} - 144 q^{48} - 248 q^{49} + 100 q^{50} - 52 q^{52} + 336 q^{53} + 36 q^{54} + 168 q^{56} - 16 q^{58} + 60 q^{60} + 16 q^{61} + 152 q^{62} - 16 q^{64} - 132 q^{66} + 400 q^{68} - 192 q^{69} + 208 q^{70} + 96 q^{72} + 112 q^{73} - 104 q^{74} - 264 q^{76} - 272 q^{77} - 300 q^{80} + 216 q^{81} - 4 q^{82} + 96 q^{84} + 64 q^{85} + 288 q^{86} - 492 q^{88} + 36 q^{90} + 328 q^{92} - 96 q^{93} - 884 q^{94} + 72 q^{96} - 80 q^{97} - 572 q^{98}+O(q^{100}) $ 24 * q + 4 * q^2 + 8 * q^4 - 12 * q^6 - 32 * q^8 - 72 * q^9 - 12 * q^10 + 12 * q^12 + 32 * q^14 + 4 * q^16 - 12 * q^18 + 84 * q^20 + 28 * q^22 - 36 * q^24 + 104 * q^25 - 96 * q^28 + 64 * q^29 - 12 * q^30 + 44 * q^32 + 48 * q^33 + 40 * q^34 - 24 * q^36 - 192 * q^37 - 104 * q^38 + 220 * q^40 - 220 * q^44 - 104 * q^46 - 144 * q^48 - 248 * q^49 + 100 * q^50 - 52 * q^52 + 336 * q^53 + 36 * q^54 + 168 * q^56 - 16 * q^58 + 60 * q^60 + 16 * q^61 + 152 * q^62 - 16 * q^64 - 132 * q^66 + 400 * q^68 - 192 * q^69 + 208 * q^70 + 96 * q^72 + 112 * q^73 - 104 * q^74 - 264 * q^76 - 272 * q^77 - 300 * q^80 + 216 * q^81 - 4 * q^82 + 96 * q^84 + 64 * q^85 + 288 * q^86 - 492 * q^88 + 36 * q^90 + 328 * q^92 - 96 * q^93 - 884 * q^94 + 72 * q^96 - 80 * q^97 - 572 * q^98

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 $

$2$	0.337137	−	1.97138i	0.168569	−	0.985690i
$2$	0.337137	−	1.97138i	0.168569	−	0.985690i
$3$			1.73205i			0.577350i
$3$			1.73205i			0.577350i
$4$	−3.77268	−	1.32925i	−0.943169	−	0.332313i
$5$	−3.28562			−0.657124			−0.328562	−	0.944482i	$-0.606564\pi$
$5$	−3.28562			−0.657124			−0.328562	+	0.944482i	$0.606564\pi$
$6$	3.41453	+	0.583939i	0.569088	+	0.0973232i
$7$			11.8734i			1.69620i	0.529839	+	0.848098i	$0.322252\pi$
$7$			11.8734i			1.69620i	−0.529839	+	0.848098i	$0.677748\pi$
$8$	−3.89237	+	6.98924i	−0.486546	+	0.873655i
$9$	−3.00000			−0.333333
$10$	−1.10771	+	6.47720i	−0.110771	+	0.647720i
$11$			3.23214i			0.293831i	0.989149	+	0.146916i	$0.0469346\pi$
$11$			3.23214i			0.293831i	−0.989149	+	0.146916i	$0.953065\pi$
$12$	2.30233	−	6.53447i	0.191861	−	0.544539i
$13$	3.60555			0.277350
$13$	3.60555			0.277350
$14$	23.4069	+	4.00296i	1.67192	+	0.285926i
$15$		−	5.69086i		−	0.379391i
$16$	12.4662	+	10.0297i	0.779136	+	0.626855i
$17$	−12.7169			−0.748055			−0.374028	−	0.927418i	$-0.622024\pi$
$17$	−12.7169			−0.748055			−0.374028	+	0.927418i	$0.622024\pi$
$18$	−1.01141	+	5.91414i	−0.0561896	+	0.328563i
$19$			19.4637i			1.02440i	0.858865	+	0.512202i	$0.171170\pi$
$19$			19.4637i			1.02440i	−0.858865	+	0.512202i	$0.828830\pi$
$20$	12.3956	+	4.36742i	0.619779	+	0.218371i
$21$	−20.5653			−0.979299
$22$	6.37178	+	1.08968i	0.289626	+	0.0495307i
$23$		−	6.77915i		−	0.294746i	−0.989081	−	0.147373i	$-0.952918\pi$
$23$		−	6.77915i		−	0.294746i	0.989081	−	0.147373i	$-0.0470817\pi$
$24$	−12.1057	−	6.74178i	−0.504405	−	0.280908i
$25$	−14.2047			−0.568188
$26$	1.21557	−	7.10791i	0.0467525	−	0.273381i
$27$		−	5.19615i		−	0.192450i
$28$	15.7827	−	44.7944i	0.563668	−	1.59980i
$29$	14.6737			0.505989			0.252995	−	0.967468i	$-0.418584\pi$
$29$	14.6737			0.505989			0.252995	+	0.967468i	$0.418584\pi$
$30$	−11.2188	−	1.91860i	−0.373962	−	0.0639534i
$31$			4.99021i			0.160974i	0.996756	+	0.0804872i	$0.0256476\pi$
$31$			4.99021i			0.160974i	−0.996756	+	0.0804872i	$0.974352\pi$
$32$	23.9751	−	21.1942i	0.749222	−	0.662319i
$33$	−5.59824			−0.169644
$34$	−4.28736	+	25.0699i	−0.126099	+	0.737351i
$35$		−	39.0114i		−	1.11461i
$36$	11.3180	+	3.98776i	0.314390	+	0.110771i
$37$	−16.5006			−0.445962			−0.222981	−	0.974823i	$-0.571579\pi$
$37$	−16.5006			−0.445962			−0.222981	+	0.974823i	$0.571579\pi$
$38$	38.3703	+	6.56193i	1.00974	+	0.172682i
$39$			6.24500i			0.160128i
$40$	12.7888	−	22.9640i	0.319721	−	0.574100i
$41$	13.4022			0.326883			0.163442	−	0.986553i	$-0.447740\pi$
$41$	13.4022			0.326883			0.163442	+	0.986553i	$0.447740\pi$
$42$	−6.93333	+	40.5420i	−0.165079	+	0.965285i
$43$			53.3697i			1.24116i	0.784145	+	0.620578i	$0.213102\pi$
$43$			53.3697i			1.24116i	−0.784145	+	0.620578i	$0.786898\pi$
$44$	4.29633	−	12.1938i	0.0976439	−	0.277132i
$45$	9.85686			0.219041
$46$	−13.3643	−	2.28551i	−0.290528	−	0.0496849i
$47$		−	91.1714i		−	1.93982i	−0.243468	−	0.969909i	$-0.578285\pi$
$47$		−	91.1714i		−	1.93982i	0.243468	−	0.969909i	$-0.421715\pi$
$48$	−17.3719	+	21.5921i	−0.361915	+	0.449835i
$49$	−91.9770			−1.87708
$50$	−4.78894	+	28.0029i	−0.0957787	+	0.560057i
$51$		−	22.0264i		−	0.431890i
$52$	−13.6026	−	4.79269i	−0.261588	−	0.0921670i
$53$	36.7750			0.693867			0.346934	−	0.937890i	$-0.387223\pi$
$53$	36.7750			0.693867			0.346934	+	0.937890i	$0.387223\pi$
$54$	−10.2436	−	1.75182i	−0.189696	−	0.0324411i
$55$		−	10.6196i		−	0.193084i
$56$	−82.9858	−	46.2156i	−1.48189	−	0.825278i
$57$	−33.7120			−0.591439
$58$	4.94705	−	28.9274i	0.0852940	−	0.498749i
$59$			89.2562i			1.51282i	0.654100	+	0.756408i	$0.273048\pi$
$59$			89.2562i			1.51282i	−0.654100	+	0.756408i	$0.726952\pi$
$60$	−7.56459	+	21.4698i	−0.126076	+	0.357830i
$61$	−50.6171			−0.829788			−0.414894	−	0.909870i	$-0.636181\pi$
$61$	−50.6171			−0.829788			−0.414894	+	0.909870i	$0.636181\pi$
$62$	9.83759	+	1.68239i	0.158671	+	0.0271353i
$63$		−	35.6201i		−	0.565399i
$64$	−33.6989	−	54.4094i	−0.526545	−	0.850147i
$65$	−11.8465			−0.182253
$66$	−1.88737	+	11.0362i	−0.0285966	+	0.167216i
$67$		−	50.0554i		−	0.747096i	−0.927611	−	0.373548i	$-0.878141\pi$
$67$		−	50.0554i		−	0.747096i	0.927611	−	0.373548i	$-0.121859\pi$
$68$	47.9769	+	16.9040i	0.705543	+	0.248588i
$69$	11.7418			0.170171
$70$	−76.9063	−	13.1522i	−1.09866	−	0.187889i
$71$		−	46.7777i		−	0.658841i	−0.944183	−	0.329421i	$-0.893147\pi$
$71$		−	46.7777i		−	0.658841i	0.944183	−	0.329421i	$-0.106853\pi$
$72$	11.6771	−	20.9677i	0.162182	−	0.291218i
$73$	136.133			1.86484			0.932420	−	0.361378i	$-0.117693\pi$
$73$	136.133			1.86484			0.932420	+	0.361378i	$0.117693\pi$
$74$	−5.56297	+	32.5290i	−0.0751753	+	0.439581i
$75$		−	24.6033i		−	0.328044i
$76$	25.8721	−	73.4301i	0.340422	−	0.966185i
$77$	−38.3764			−0.498395
$78$	12.3113	+	2.10542i	0.157837	+	0.0269926i
$79$			101.057i			1.27920i	0.768706	+	0.639602i	$0.220901\pi$
$79$			101.057i			1.27920i	−0.768706	+	0.639602i	$0.779099\pi$
$80$	−40.9591	−	32.9537i	−0.511989	−	0.411921i
$81$	9.00000			0.111111
$82$	4.51838	−	26.4208i	0.0551023	−	0.322205i
$83$			160.838i			1.93781i	0.247431	+	0.968905i	$0.420414\pi$
$83$			160.838i			1.93781i	−0.247431	+	0.968905i	$0.579586\pi$
$84$	77.5862	+	27.3364i	0.923645	+	0.325434i
$85$	41.7830			0.491565
$86$	105.212	+	17.9929i	1.22339	+	0.209220i
$87$			25.4156i			0.292133i
$88$	−22.5902	−	12.5807i	−0.256707	−	0.142962i
$89$	171.832			1.93069			0.965346	−	0.260974i	$-0.0840438\pi$
$89$	171.832			1.93069			0.965346	+	0.260974i	$0.0840438\pi$
$90$	3.32312	−	19.4316i	0.0369235	−	0.215907i
$91$			42.8101i			0.470440i
$92$	−9.01120	+	25.5755i	−0.0979478	+	0.277995i
$93$	−8.64329			−0.0929386
$94$	−179.734	−	30.7373i	−1.91206	−	0.326993i
$95$		−	63.9502i		−	0.673160i
$96$	36.7094	+	41.5261i	0.382390	+	0.432564i
$97$	174.529			1.79926			0.899632	−	0.436648i	$-0.143834\pi$
$97$	174.529			1.79926			0.899632	+	0.436648i	$0.143834\pi$
$98$	−31.0089	+	181.322i	−0.316417	+	1.85022i
$99$		−	9.69643i		−	0.0979437i
$100$	53.5897	+	18.8816i	0.535897	+	0.188816i
$101$	−113.787			−1.12661			−0.563303	−	0.826250i	$-0.690470\pi$
$101$	−113.787			−1.12661			−0.563303	+	0.826250i	$0.690470\pi$
$102$	−43.4224	−	7.42592i	−0.425710	−	0.0728031i
$103$		−	37.9309i		−	0.368261i	−0.982902	−	0.184131i	$-0.941053\pi$
$103$		−	37.9309i		−	0.368261i	0.982902	−	0.184131i	$-0.0589469\pi$
$104$	−14.0341	+	25.2001i	−0.134944	+	0.242308i
$105$	67.5697			0.643521
$106$	12.3982	−	72.4974i	0.116964	−	0.683938i
$107$		−	100.080i		−	0.935329i	−0.883906	−	0.467665i	$-0.845095\pi$
$107$		−	100.080i		−	0.935329i	0.883906	−	0.467665i	$-0.154905\pi$
$108$	−6.90699	+	19.6034i	−0.0639537	+	0.181513i
$109$	106.094			0.973339			0.486669	−	0.873586i	$-0.338212\pi$
$109$	106.094			0.973339			0.486669	+	0.873586i	$0.338212\pi$
$110$	−20.9353	−	3.58026i	−0.190320	−	0.0325478i
$111$		−	28.5799i		−	0.257477i
$112$	−119.086	+	148.016i	−1.06327	+	1.32157i
$113$	−3.71070			−0.0328381			−0.0164190	−	0.999865i	$-0.505227\pi$
$113$	−3.71070			−0.0328381			−0.0164190	+	0.999865i	$0.505227\pi$
$114$	−11.3656	+	66.4592i	−0.0996982	+	0.582976i
$115$			22.2737i			0.193684i
$116$	−55.3591	−	19.5050i	−0.477234	−	0.168147i
$117$	−10.8167			−0.0924500
$118$	175.958	+	30.0916i	1.49117	+	0.255014i
$119$		−	150.993i		−	1.26885i
$120$	39.7748	+	22.1509i	0.331457	+	0.184591i
$121$	110.553			0.913663
$122$	−17.0649	+	99.7854i	−0.139876	+	0.817914i
$123$			23.2133i			0.188726i
$124$	6.63324	−	18.8264i	0.0534939	−	0.151826i
$125$	128.812			1.03049
$126$	−70.2208	−	12.0089i	−0.557308	−	0.0953085i
$127$			12.2878i			0.0967547i	0.998829	+	0.0483773i	$0.0154050\pi$
$127$			12.2878i			0.0967547i	−0.998829	+	0.0483773i	$0.984595\pi$
$128$	−118.623	+	48.0899i	−0.926740	+	0.375702i
$129$	−92.4390			−0.716581
$130$	−3.99389	+	23.3539i	−0.0307222	+	0.179645i
$131$			65.7642i			0.502017i	0.967985	+	0.251008i	$0.0807622\pi$
$131$			65.7642i			0.502017i	−0.967985	+	0.251008i	$0.919238\pi$
$132$	21.1203	+	7.44146i	0.160003	+	0.0563747i
$133$	−231.099			−1.73759
$134$	−98.6782	−	16.8756i	−0.736405	−	0.125937i
$135$			17.0726i			0.126464i
$136$	49.4990	−	88.8817i	0.363964	−	0.653542i
$137$	−170.828			−1.24692			−0.623459	−	0.781856i	$-0.714273\pi$
$137$	−170.828			−1.24692			−0.623459	+	0.781856i	$0.714273\pi$
$138$	3.95861	−	23.1476i	0.0286856	−	0.167736i
$139$			252.107i			1.81372i	0.421435	+	0.906859i	$0.361527\pi$
$139$			252.107i			1.81372i	−0.421435	+	0.906859i	$0.638473\pi$
$140$	−51.8560	+	147.177i	−0.370400	+	1.05127i
$141$	157.914			1.11995
$142$	−92.2167	−	15.7705i	−0.649413	−	0.111060i
$143$			11.6537i			0.0814941i
$144$	−37.3985	−	30.0890i	−0.259712	−	0.208952i
$145$	−48.2122			−0.332498
$146$	45.8956	−	268.370i	0.314353	−	1.83815i
$147$		−	159.309i		−	1.08373i
$148$	62.2515	+	21.9335i	0.420618	+	0.148199i
$149$	−174.527			−1.17132			−0.585662	−	0.810555i	$-0.699166\pi$
$149$	−174.527			−1.17132			−0.585662	+	0.810555i	$0.699166\pi$
$150$	−48.5024	−	8.29468i	−0.323349	−	0.0552979i
$151$			192.421i			1.27431i	0.770735	+	0.637156i	$0.219889\pi$
$151$			192.421i			1.27431i	−0.770735	+	0.637156i	$0.780111\pi$
$152$	−136.036	−	75.7598i	−0.894975	−	0.498420i
$153$	38.1508			0.249352
$154$	−12.9381	+	75.6545i	−0.0840138	+	0.491263i
$155$		−	16.3959i		−	0.105780i
$156$	8.30117	−	23.5604i	0.0532127	−	0.151028i
$157$	−111.221			−0.708412			−0.354206	−	0.935167i	$-0.615249\pi$
$157$	−111.221			−0.708412			−0.354206	+	0.935167i	$0.615249\pi$
$158$	199.222	+	34.0701i	1.26090	+	0.215634i
$159$			63.6961i			0.400605i
$160$	−78.7731	+	69.6361i	−0.492332	+	0.435225i
$161$	80.4914			0.499946
$162$	3.03424	−	17.7424i	0.0187299	−	0.109521i
$163$		−	101.620i		−	0.623433i	−0.950175	−	0.311717i	$-0.899096\pi$
$163$		−	101.620i		−	0.623433i	0.950175	−	0.311717i	$-0.100904\pi$
$164$	−50.5622	−	17.8149i	−0.308306	−	0.108627i
$165$	18.3937			0.111477
$166$	317.073	+	54.2246i	1.91008	+	0.326654i
$167$		−	48.0371i		−	0.287647i	−0.989603	−	0.143824i	$-0.954060\pi$
$167$		−	48.0371i		−	0.287647i	0.989603	−	0.143824i	$-0.0459398\pi$
$168$	80.0477	−	143.736i	0.476474	−	0.855569i
$169$	13.0000			0.0769231
$170$	14.0866	−	82.3702i	0.0828625	−	0.484531i
$171$		−	58.3910i		−	0.341468i
$172$	70.9417	−	201.347i	0.412452	−	1.17062i
$173$	−22.0593			−0.127510			−0.0637552	−	0.997966i	$-0.520308\pi$
$173$	−22.0593			−0.127510			−0.0637552	+	0.997966i	$0.520308\pi$
$174$	50.1038	+	8.56854i	0.287953	+	0.0492445i
$175$		−	168.658i		−	0.963758i
$176$	−32.4173	+	40.2925i	−0.184189	+	0.228935i
$177$	−154.596			−0.873425
$178$	57.9308	−	338.745i	0.325454	−	1.90306i
$179$			94.6864i			0.528974i	0.964389	+	0.264487i	$0.0852027\pi$
$179$			94.6864i			0.528974i	−0.964389	+	0.264487i	$0.914797\pi$
$180$	−37.1867	−	13.1022i	−0.206593	−	0.0727903i
$181$	264.251			1.45995			0.729976	−	0.683473i	$-0.239531\pi$
$181$	264.251			1.45995			0.729976	+	0.683473i	$0.239531\pi$
$182$	84.3949	+	14.4329i	0.463708	+	0.0793015i
$183$		−	87.6713i		−	0.479078i
$184$	47.3811	+	26.3870i	0.257506	+	0.143407i
$185$	54.2147			0.293053
$186$	−2.91398	+	17.0392i	−0.0156665	+	0.0916087i
$187$		−	41.1030i		−	0.219802i
$188$	−121.190	+	343.960i	−0.644626	+	1.82958i
$189$	61.6959			0.326433
$190$	−126.070	−	21.5600i	−0.663527	−	0.113474i
$191$		−	58.2134i		−	0.304782i	−0.988320	−	0.152391i	$-0.951303\pi$
$191$		−	58.2134i		−	0.304782i	0.988320	−	0.152391i	$-0.0486973\pi$
$192$	94.2399	−	58.3682i	0.490833	−	0.304001i
$193$	−263.901			−1.36737			−0.683683	−	0.729779i	$-0.739623\pi$
$193$	−263.901			−1.36737			−0.683683	+	0.729779i	$0.739623\pi$
$194$	58.8401	−	344.062i	0.303300	−	1.77352i
$195$		−	20.5187i		−	0.105224i
$196$	346.999	+	122.261i	1.77040	+	0.623778i
$197$	−301.259			−1.52923			−0.764616	−	0.644486i	$-0.777071\pi$
$197$	−301.259			−1.52923			−0.764616	+	0.644486i	$0.777071\pi$
$198$	−19.1153	−	3.26903i	−0.0965421	−	0.0165102i
$199$		−	269.251i		−	1.35302i	−0.736434	−	0.676510i	$-0.763492\pi$
$199$		−	269.251i		−	1.35302i	0.736434	−	0.676510i	$-0.236508\pi$
$200$	55.2900	−	99.2800i	0.276450	−	0.496400i
$201$	86.6985			0.431336
$202$	−38.3619	+	224.318i	−0.189911	+	1.11048i
$203$			174.226i			0.858257i
$204$	−29.2786	+	83.0984i	−0.143523	+	0.407345i
$205$	−44.0346			−0.214803
$206$	−74.7762	−	12.7879i	−0.362991	−	0.0620773i
$207$			20.3375i			0.0982486i
$208$	44.9475	+	36.1625i	0.216094	+	0.173858i
$209$	−62.9093			−0.301002
$210$	22.7803	−	133.206i	0.108477	−	0.634312i
$211$		−	59.3222i		−	0.281148i	−0.990070	−	0.140574i	$-0.955105\pi$
$211$		−	59.3222i		−	0.281148i	0.990070	−	0.140574i	$-0.0448948\pi$
$212$	−138.740	−	48.8832i	−0.654434	−	0.230581i
$213$	81.0214			0.380382
$214$	−197.296	−	33.7408i	−0.921945	−	0.157667i
$215$		−	175.352i		−	0.815593i
$216$	36.3171	+	20.2253i	0.168135	+	0.0936359i
$217$	−59.2506			−0.273044
$218$	35.7682	−	209.151i	0.164074	−	0.959410i
$219$			235.790i			1.07667i
$220$	−14.1161	+	40.0643i	−0.0641641	+	0.182110i
$221$	−45.8516			−0.207473
$222$	−56.3418	−	9.63535i	−0.253792	−	0.0434025i
$223$		−	258.093i		−	1.15737i	−0.815552	−	0.578684i	$-0.803567\pi$
$223$		−	258.093i		−	1.15737i	0.815552	−	0.578684i	$-0.196433\pi$
$224$	251.647	+	284.665i	1.12342	+	1.27083i
$225$	42.6141			0.189396
$226$	−1.25102	+	7.31520i	−0.00553547	+	0.0323681i
$227$			158.803i			0.699571i	0.936830	+	0.349785i	$0.113746\pi$
$227$			158.803i			0.699571i	−0.936830	+	0.349785i	$0.886254\pi$
$228$	127.185	+	44.8118i	0.557827	+	0.196543i
$229$	178.254			0.778401			0.389200	−	0.921153i	$-0.372751\pi$
$229$	178.254			0.778401			0.389200	+	0.921153i	$0.372751\pi$
$230$	43.9099	+	7.50930i	0.190913	+	0.0326491i
$231$		−	66.4699i		−	0.287749i
$232$	−57.1155	+	102.558i	−0.246187	+	0.442060i
$233$	−386.286			−1.65788			−0.828939	−	0.559339i	$-0.811055\pi$
$233$	−386.286			−1.65788			−0.828939	+	0.559339i	$0.811055\pi$
$234$	−3.64670	+	21.3237i	−0.0155842	+	0.0911271i
$235$			299.555i			1.27470i
$236$	118.644	−	336.735i	0.502729	−	1.42684i
$237$	−175.036			−0.738549
$238$	−297.665	−	50.9054i	−1.25069	−	0.213888i
$239$			316.936i			1.32609i	0.748579	+	0.663046i	$0.230737\pi$
$239$			316.936i			1.32609i	−0.748579	+	0.663046i	$0.769263\pi$
$240$	57.0775	−	70.9433i	0.237823	−	0.295597i
$241$	−126.129			−0.523359			−0.261679	−	0.965155i	$-0.584276\pi$
$241$	−126.129			−0.523359			−0.261679	+	0.965155i	$0.584276\pi$
$242$	37.2716	−	217.942i	0.154015	−	0.900589i
$243$			15.5885i			0.0641500i
$244$	190.962	+	67.2828i	0.782630	+	0.275749i
$245$	302.201			1.23347
$246$	45.7622	+	7.82607i	0.186025	+	0.0318133i
$247$			70.1772i			0.284118i
$248$	−34.8777	−	19.4237i	−0.140636	−	0.0783215i
$249$	−278.580			−1.11880
$250$	43.4273	−	253.937i	0.173709	−	1.01575i
$251$		−	10.8846i		−	0.0433651i	−0.999765	−	0.0216826i	$-0.993098\pi$
$251$		−	10.8846i		−	0.0433651i	0.999765	−	0.0216826i	$-0.00690231\pi$
$252$	−47.3481	+	134.383i	−0.187889	+	0.533267i
$253$	21.9112			0.0866055
$254$	24.2240	+	4.14269i	0.0953701	+	0.0163098i
$255$			72.3703i			0.283805i
$256$	54.8113	+	250.063i	0.214107	+	0.976810i
$257$	−111.386			−0.433407			−0.216704	−	0.976237i	$-0.569531\pi$
$257$	−111.386			−0.433407			−0.216704	+	0.976237i	$0.569531\pi$
$258$	−31.1646	+	182.232i	−0.120793	+	0.706327i
$259$		−	195.918i		−	0.756440i
$260$	44.6929	+	15.7469i	0.171896	+	0.0605652i
$261$	−44.0211			−0.168663
$262$	129.646	+	22.1716i	0.494833	+	0.0846243i
$263$			253.500i			0.963879i	0.876204	+	0.481940i	$0.160068\pi$
$263$			253.500i			0.963879i	−0.876204	+	0.481940i	$0.839932\pi$
$264$	21.7904	−	39.1274i	0.0825394	−	0.148210i
$265$	−120.829			−0.455957
$266$	−77.9122	+	455.584i	−0.292903	+	1.71272i
$267$			297.621i			1.11469i
$268$	−66.5362	+	188.843i	−0.248270	+	0.704638i
$269$	−5.40463			−0.0200916			−0.0100458	−	0.999950i	$-0.503198\pi$
$269$	−5.40463			−0.0200916			−0.0100458	+	0.999950i	$0.503198\pi$
$270$	33.6565	+	5.75581i	0.124654	+	0.0213178i
$271$		−	211.867i		−	0.781797i	−0.920434	−	0.390899i	$-0.872164\pi$
$271$		−	211.867i		−	0.781797i	0.920434	−	0.390899i	$-0.127836\pi$
$272$	−158.532	−	127.547i	−0.582837	−	0.468922i
$273$	−74.1492			−0.271609
$274$	−57.5925	+	336.767i	−0.210191	+	1.22908i
$275$		−	45.9116i		−	0.166951i
$276$	−44.2981	−	15.6079i	−0.160501	−	0.0565502i
$277$	302.153			1.09081			0.545403	−	0.838174i	$-0.316377\pi$
$277$	302.153			1.09081			0.545403	+	0.838174i	$0.316377\pi$
$278$	496.998	+	84.9946i	1.78776	+	0.305736i
$279$		−	14.9706i		−	0.0536581i
$280$	272.660	+	151.847i	0.973785	+	0.542310i
$281$	267.442			0.951749			0.475875	−	0.879513i	$-0.342132\pi$
$281$	267.442			0.951749			0.475875	+	0.879513i	$0.342132\pi$
$282$	53.2386	−	311.308i	0.188789	−	1.10393i
$283$		−	81.6996i		−	0.288691i	−0.989527	−	0.144346i	$-0.953892\pi$
$283$		−	81.6996i		−	0.288691i	0.989527	−	0.144346i	$-0.0461077\pi$
$284$	−62.1794	+	176.477i	−0.218941	+	0.621399i
$285$	110.765			0.388649
$286$	22.9738	+	3.92888i	0.0803279	+	0.0137374i
$287$			159.129i			0.554458i
$288$	−71.9253	+	63.5826i	−0.249741	+	0.220773i
$289$	−127.279			−0.440413
$290$	−16.2541	+	95.0445i	−0.0560487	+	0.327740i
$291$			302.293i			1.03881i
$292$	−513.587	−	180.955i	−1.75886	−	0.619710i
$293$	334.103			1.14028			0.570142	−	0.821546i	$-0.306888\pi$
$293$	334.103			1.14028			0.570142	+	0.821546i	$0.306888\pi$
$294$	−314.058	−	53.7089i	−1.06822	−	0.182683i
$295$		−	293.262i		−	0.994108i
$296$	64.2265	−	115.327i	0.216981	−	0.389617i
$297$	16.7947			0.0565478
$298$	−58.8397	+	344.060i	−0.197449	+	1.15456i
$299$		−	24.4426i		−	0.0817477i
$300$	−32.7039	+	92.8202i	−0.109013	+	0.309401i
$301$	−633.678			−2.10524
$302$	379.335	+	64.8723i	1.25608	+	0.214809i
$303$		−	197.085i		−	0.650447i
$304$	−195.214	+	242.637i	−0.642152	+	0.798150i
$305$	166.308			0.545273
$306$	12.8621	−	75.2098i	0.0420329	−	0.245784i
$307$		−	66.5686i		−	0.216836i	−0.994105	−	0.108418i	$-0.965422\pi$
$307$		−	66.5686i		−	0.216836i	0.994105	−	0.108418i	$-0.0345785\pi$
$308$	144.782	+	51.0119i	0.470071	+	0.165623i
$309$	65.6982			0.212616
$310$	−32.3226	−	5.52768i	−0.104266	−	0.0178312i
$311$		−	187.627i		−	0.603301i	−0.953419	−	0.301651i	$-0.902462\pi$
$311$		−	187.627i		−	0.603301i	0.953419	−	0.301651i	$-0.0975376\pi$
$312$	−43.6478	−	24.3078i	−0.139897	−	0.0779098i
$313$	−320.922			−1.02531			−0.512655	−	0.858595i	$-0.671338\pi$
$313$	−320.922			−1.02531			−0.512655	+	0.858595i	$0.671338\pi$
$314$	−37.4967	+	219.258i	−0.119416	+	0.698275i
$315$			117.034i			0.371537i
$316$	134.330	−	381.256i	0.425096	−	1.20651i
$317$	244.321			0.770729			0.385365	−	0.922764i	$-0.374076\pi$
$317$	244.321			0.770729			0.385365	+	0.922764i	$0.374076\pi$
$318$	125.569	+	21.4743i	0.394872	+	0.0675294i
$319$			47.4275i			0.148675i
$320$	110.722	+	178.769i	0.346006	+	0.558652i
$321$	173.344			0.540013
$322$	27.1367	−	158.679i	0.0842753	−	0.492792i
$323$		−	247.518i		−	0.766310i
$324$	−33.9541	−	11.9633i	−0.104797	−	0.0369237i
$325$	−51.2158			−0.157587
$326$	−200.331	−	34.2598i	−0.614512	−	0.105091i
$327$			183.760i			0.561958i
$328$	−52.1663	+	93.6712i	−0.159044	+	0.285583i
$329$	1082.51			3.29031
$330$	6.20120	−	36.2609i	0.0187915	−	0.109882i
$331$			239.954i			0.724937i	0.931996	+	0.362468i	$0.118066\pi$
$331$			239.954i			0.724937i	−0.931996	+	0.362468i	$0.881934\pi$
$332$	213.795	−	606.791i	0.643960	−	1.82768i
$333$	49.5018			0.148654
$334$	−94.6993	−	16.1951i	−0.283531	−	0.0484883i
$335$			164.463i			0.490935i
$336$	−256.371	−	206.263i	−0.763008	−	0.613878i
$337$	−145.754			−0.432503			−0.216252	−	0.976338i	$-0.569383\pi$
$337$	−145.754			−0.432503			−0.216252	+	0.976338i	$0.569383\pi$
$338$	4.38279	−	25.6279i	0.0129668	−	0.0758223i
$339$		−	6.42712i		−	0.0189591i
$340$	−157.634	−	55.5402i	−0.463629	−	0.163353i
$341$	−16.1291			−0.0472993
$342$	−115.111	−	19.6858i	−0.336581	−	0.0575608i
$343$		−	510.281i		−	1.48770i
$344$	−373.013	−	207.735i	−1.08434	−	0.603880i
$345$	−38.5792			−0.111824
$346$	−7.43701	+	43.4872i	−0.0214942	+	0.125686i
$347$		−	85.3813i		−	0.246056i	−0.992403	−	0.123028i	$-0.960740\pi$
$347$		−	85.3813i		−	0.246056i	0.992403	−	0.123028i	$-0.0392605\pi$
$348$	33.7837	−	95.8848i	0.0970796	−	0.275531i
$349$	639.148			1.83137			0.915684	−	0.401898i	$-0.131649\pi$
$349$	639.148			1.83137			0.915684	+	0.401898i	$0.131649\pi$
$350$	−332.488	−	56.8608i	−0.949967	−	0.162459i
$351$		−	18.7350i		−	0.0533761i
$352$	68.5027	+	77.4910i	0.194610	+	0.220145i
$353$	39.0265			0.110557			0.0552783	−	0.998471i	$-0.482395\pi$
$353$	39.0265			0.110557			0.0552783	+	0.998471i	$0.482395\pi$
$354$	−52.1202	+	304.768i	−0.147232	+	0.860926i
$355$			153.694i			0.432940i
$356$	−648.265	−	228.407i	−1.82097	−	0.641594i
$357$	261.528			0.732570
$358$	186.663	+	31.9223i	0.521404	+	0.0891685i
$359$		−	444.065i		−	1.23695i	−0.785804	−	0.618475i	$-0.787751\pi$
$359$		−	444.065i		−	1.23695i	0.785804	−	0.618475i	$-0.212249\pi$
$360$	−38.3665	+	68.8919i	−0.106574	+	0.191367i
$361$	−17.8340			−0.0494016
$362$	89.0890	−	520.940i	0.246102	−	1.43906i
$363$			191.484i			0.527504i
$364$	56.9053	−	161.508i	0.156333	−	0.443705i
$365$	−447.282			−1.22543
$366$	−172.833	−	29.5573i	−0.472223	−	0.0807576i
$367$		−	306.652i		−	0.835565i	−0.908547	−	0.417782i	$-0.862807\pi$
$367$		−	306.652i		−	0.835565i	0.908547	−	0.417782i	$-0.137193\pi$
$368$	67.9927	−	84.5101i	0.184763	−	0.229647i
$369$	−40.2066			−0.108961
$370$	18.2778	−	106.878i	0.0493995	−	0.288859i
$371$			436.643i			1.17694i
$372$	32.6083	+	11.4891i	0.0876569	+	0.0308847i
$373$	213.971			0.573648			0.286824	−	0.957983i	$-0.407401\pi$
$373$	213.971			0.573648			0.286824	+	0.957983i	$0.407401\pi$
$374$	−81.0296	−	13.8573i	−0.216657	−	0.0370517i
$375$			223.108i			0.594956i
$376$	637.219	+	354.873i	1.69473	+	0.943811i
$377$	52.9068			0.140336
$378$	20.8000	−	121.626i	0.0550264	−	0.321762i
$379$			661.037i			1.74416i	0.489363	+	0.872080i	$0.337229\pi$
$379$			661.037i			1.74416i	−0.489363	+	0.872080i	$0.662771\pi$
$380$	−85.0059	+	241.263i	−0.223700	+	0.634904i
$381$	−21.2832			−0.0558614
$382$	−114.761	−	19.6259i	−0.300421	−	0.0513767i
$383$			105.883i			0.276456i	0.990400	+	0.138228i	$0.0441407\pi$
$383$			105.883i			0.276456i	−0.990400	+	0.138228i	$0.955859\pi$
$384$	−83.2941	−	205.461i	−0.216912	−	0.535054i
$385$	126.090			0.327507
$386$	−88.9711	+	520.250i	−0.230495	+	1.34780i
$387$		−	160.109i		−	0.413718i
$388$	−658.440	−	231.993i	−1.69701	−	0.597919i
$389$	17.6934			0.0454843			0.0227421	−	0.999741i	$-0.492760\pi$
$389$	17.6934			0.0454843			0.0227421	+	0.999741i	$0.492760\pi$
$390$	−40.4501	−	6.91762i	−0.103718	−	0.0177375i
$391$			86.2101i			0.220486i
$392$	358.008	−	642.849i	0.913287	−	1.63992i
$393$	−113.907			−0.289840
$394$	−101.566	+	593.896i	−0.257781	+	1.50735i
$395$		−	332.035i		−	0.840596i
$396$	−12.8890	+	36.5815i	−0.0325480	+	0.0923775i
$397$	421.644			1.06208			0.531038	−	0.847348i	$-0.321802\pi$
$397$	421.644			1.06208			0.531038	+	0.847348i	$0.321802\pi$
$398$	−530.796	−	90.7745i	−1.33366	−	0.228077i
$399$		−	400.276i		−	1.00320i
$400$	−177.078	−	142.469i	−0.442696	−	0.356171i
$401$	238.424			0.594573			0.297287	−	0.954788i	$-0.403918\pi$
$401$	238.424			0.594573			0.297287	+	0.954788i	$0.403918\pi$
$402$	29.2293	−	170.916i	0.0727097	−	0.425163i
$403$			17.9924i			0.0446463i
$404$	429.283	+	151.252i	1.06258	+	0.374386i
$405$	−29.5706			−0.0730138
$406$	343.466	+	58.7382i	0.845976	+	0.144675i
$407$		−	53.3323i		−	0.131038i
$408$	153.948	+	85.7349i	0.377323	+	0.210134i
$409$	252.675			0.617787			0.308893	−	0.951097i	$-0.400041\pi$
$409$	252.675			0.617787			0.308893	+	0.951097i	$0.400041\pi$
$410$	−14.8457	+	86.8088i	−0.0362090	+	0.211729i
$411$		−	295.883i		−	0.719909i
$412$	−50.4197	+	143.101i	−0.122378	+	0.347333i
$413$	−1059.77			−2.56603
$414$	40.0928	+	6.85652i	0.0968426	+	0.0165616i
$415$		−	528.454i		−	1.27338i
$416$	86.4435	−	76.4168i	0.207797	−	0.183694i
$417$	−436.662			−1.04715
$418$	−21.2091	+	124.018i	−0.0507394	+	0.296694i
$419$		−	313.319i		−	0.747779i	−0.927473	−	0.373889i	$-0.878024\pi$
$419$		−	313.319i		−	0.747779i	0.927473	−	0.373889i	$-0.121976\pi$
$420$	−254.919	−	89.8171i	−0.606949	−	0.213850i
$421$	−240.111			−0.570335			−0.285167	−	0.958478i	$-0.592049\pi$
$421$	−240.111			−0.570335			−0.285167	+	0.958478i	$0.592049\pi$
$422$	−116.947	−	19.9997i	−0.277125	−	0.0473927i
$423$			273.514i			0.646606i
$424$	−143.142	+	257.029i	−0.337599	+	0.606201i
$425$	180.640			0.425036
$426$	27.3153	−	159.724i	0.0641205	−	0.374939i
$427$		−	600.995i		−	1.40748i
$428$	−133.032	+	377.570i	−0.310822	+	0.882174i
$429$	−20.1847			−0.0470506
$430$	−345.686	−	59.1179i	−0.803922	−	0.137483i
$431$			82.1676i			0.190644i	0.995446	+	0.0953221i	$0.0303881\pi$
$431$			82.1676i			0.190644i	−0.995446	+	0.0953221i	$0.969612\pi$
$432$	52.1157	−	64.7762i	0.120638	−	0.149945i
$433$	578.441			1.33589			0.667946	−	0.744210i	$-0.267174\pi$
$433$	578.441			1.33589			0.667946	+	0.744210i	$0.267174\pi$
$434$	−19.9756	+	116.805i	−0.0460267	+	0.269137i
$435$		−	83.5060i		−	0.191968i
$436$	−400.258	−	141.026i	−0.918023	−	0.323453i
$437$	131.947			0.301938
$438$	464.831	+	79.4935i	1.06126	+	0.181492i
$439$			9.44128i			0.0215063i	0.999942	+	0.0107532i	$0.00342290\pi$
$439$			9.44128i			0.0215063i	−0.999942	+	0.0107532i	$0.996577\pi$
$440$	74.2229	+	41.3354i	0.168688	+	0.0939441i
$441$	275.931			0.625694
$442$	−15.4583	+	90.3909i	−0.0349735	+	0.204504i
$443$		−	32.7106i		−	0.0738388i	−0.999318	−	0.0369194i	$-0.988246\pi$
$443$		−	32.7106i		−	0.0738388i	0.999318	−	0.0369194i	$-0.0117545\pi$
$444$	−37.9899	+	107.823i	−0.0855628	+	0.242844i
$445$	−564.573			−1.26870
$446$	−508.799	−	87.0128i	−1.14081	−	0.195096i
$447$		−	302.290i		−	0.676265i
$448$	646.023	−	400.120i	1.44202	−	0.893124i
$449$	265.915			0.592239			0.296120	−	0.955151i	$-0.404307\pi$
$449$	265.915			0.592239			0.296120	+	0.955151i	$0.404307\pi$
$450$	14.3668	−	84.0086i	0.0319262	−	0.186686i
$451$			43.3178i			0.0960484i
$452$	13.9993	+	4.93246i	0.0309718	+	0.0109125i
$453$	−333.283			−0.735724
$454$	313.060	+	53.5383i	0.689560	+	0.117926i
$455$		−	140.658i		−	0.309137i
$456$	131.220	−	235.622i	0.287763	−	0.516714i
$457$	−573.960			−1.25593			−0.627966	−	0.778241i	$-0.716112\pi$
$457$	−573.960			−1.25593			−0.627966	+	0.778241i	$0.716112\pi$
$458$	60.0960	−	351.406i	0.131214	−	0.767262i
$459$			66.0792i			0.143963i
$460$	29.6074	−	84.0315i	0.0643638	−	0.182677i
$461$	−736.689			−1.59802			−0.799012	−	0.601315i	$-0.794644\pi$
$461$	−736.689			−1.59802			−0.799012	+	0.601315i	$0.794644\pi$
$462$	−131.037	−	22.4095i	−0.283631	−	0.0485054i
$463$			344.820i			0.744752i	0.928082	+	0.372376i	$0.121457\pi$
$463$			344.820i			0.744752i	−0.928082	+	0.372376i	$0.878543\pi$
$464$	182.925	+	147.172i	0.394235	+	0.317182i
$465$	28.3986			0.0610722
$466$	−130.231	+	761.516i	−0.279466	+	1.63415i
$467$			261.010i			0.558909i	0.960159	+	0.279454i	$0.0901536\pi$
$467$			261.010i			0.558909i	−0.960159	+	0.279454i	$0.909846\pi$
$468$	40.8077	+	14.3781i	0.0871960	+	0.0307223i
$469$	594.327			1.26722
$470$	590.536	+	100.991i	1.25646	+	0.214875i
$471$		−	192.640i		−	0.409002i
$472$	−623.833	−	347.418i	−1.32168	−	0.736055i
$473$	−172.498			−0.364690
$474$	−59.0112	+	345.063i	−0.124496	+	0.727980i
$475$		−	276.475i		−	0.582054i
$476$	−200.708	+	569.648i	−0.421655	+	1.19674i
$477$	−110.325			−0.231289
$478$	624.801	+	106.851i	1.30712	+	0.223538i
$479$			640.105i			1.33634i	0.744010	+	0.668168i	$0.232921\pi$
$479$			640.105i			1.33634i	−0.744010	+	0.668168i	$0.767079\pi$
$480$	−120.613	−	136.439i	−0.251278	−	0.284248i
$481$	−59.4938			−0.123688
$482$	−42.5230	+	248.649i	−0.0882219	+	0.515869i
$483$			139.415i			0.288644i
$484$	−417.082	−	146.953i	−0.861739	−	0.303622i
$485$	−573.435			−1.18234
$486$	30.7308	+	5.25545i	0.0632320	+	0.0108137i
$487$			116.026i			0.238247i	0.992879	+	0.119124i	$0.0380085\pi$
$487$			116.026i			0.238247i	−0.992879	+	0.119124i	$0.961991\pi$
$488$	197.020	−	353.775i	0.403730	−	0.724948i
$489$	176.010			0.359939
$490$	101.883	−	595.754i	0.207925	−	1.21582i
$491$			633.134i			1.28948i	0.764402	+	0.644740i	$0.223034\pi$
$491$			633.134i			1.28948i	−0.764402	+	0.644740i	$0.776966\pi$
$492$	30.8563	−	87.5763i	0.0627161	−	0.178001i
$493$	−186.605			−0.378508
$494$	138.346	+	23.6594i	0.280053	+	0.0478934i
$495$			31.8588i			0.0643612i
$496$	−50.0502	+	62.2088i	−0.100908	+	0.125421i
$497$	555.409			1.11752
$498$	−93.9198	+	549.187i	−0.188594	+	1.10279i
$499$		−	230.887i		−	0.462699i	−0.972871	−	0.231350i	$-0.925686\pi$
$499$		−	230.887i		−	0.462699i	0.972871	−	0.231350i	$-0.0743141\pi$
$500$	−485.965	−	171.223i	−0.971930	−	0.342446i
$501$	83.2027			0.166073
$502$	−21.4578	−	3.66962i	−0.0427446	−	0.00731000i
$503$		−	306.383i		−	0.609111i	−0.952495	−	0.304556i	$-0.901492\pi$
$503$		−	306.383i		−	0.609111i	0.952495	−	0.304556i	$-0.0985079\pi$
$504$	248.957	+	138.647i	0.493963	+	0.275093i
$505$	373.862			0.740320
$506$	7.38708	−	43.1953i	0.0145990	−	0.0853661i
$507$			22.5167i			0.0444116i
$508$	16.3336	−	46.3581i	0.0321528	−	0.0912561i
$509$	808.903			1.58920			0.794600	−	0.607133i	$-0.207681\pi$
$509$	808.903			1.58920			0.794600	+	0.607133i	$0.207681\pi$
$510$	142.669	+	24.3987i	0.279744	+	0.0478407i
$511$			1616.36i			3.16313i
$512$	511.449	−	23.7481i	0.998924	−	0.0463830i
$513$	101.136			0.197146
$514$	−37.5523	+	219.584i	−0.0730589	+	0.427205i
$515$			124.627i			0.241993i
$516$	348.742	+	122.875i	0.675858	+	0.238129i
$517$	294.679			0.569979
$518$	−386.229	−	66.0513i	−0.745615	−	0.127512i
$519$		−	38.2078i		−	0.0736181i
$520$	46.1109	−	82.7978i	0.0886747	−	0.159227i
$521$	−547.022			−1.04995			−0.524973	−	0.851119i	$-0.675924\pi$
$521$	−547.022			−1.04995			−0.524973	+	0.851119i	$0.675924\pi$
$522$	−14.8412	+	86.7823i	−0.0284313	+	0.166250i
$523$			353.861i			0.676598i	0.941039	+	0.338299i	$0.109852\pi$
$523$			353.861i			0.676598i	−0.941039	+	0.338299i	$0.890148\pi$
$524$	87.4172	−	248.107i	0.166827	−	0.473487i
$525$	292.124			0.556426
$526$	499.745	+	85.4644i	0.950086	+	0.162480i
$527$		−	63.4602i		−	0.120418i
$528$	−69.7886	−	56.1485i	−0.132175	−	0.106342i
$529$	483.043			0.913125
$530$	−40.7358	+	238.199i	−0.0768601	+	0.449432i
$531$		−	267.769i		−	0.504272i
$532$	871.863	+	307.189i	1.63884	+	0.577423i
$533$	48.3223			0.0906611
$534$	586.724	+	100.339i	1.09873	+	0.187901i
$535$			328.826i			0.614627i
$536$	349.849	+	194.834i	0.652704	+	0.363497i
$537$	−164.002			−0.305403
$538$	−1.82210	+	10.6546i	−0.00338681	+	0.0198041i
$539$		−	297.283i		−	0.551545i
$540$	22.6938	−	64.4093i	0.0420255	−	0.119277i
$541$	−206.160			−0.381072			−0.190536	−	0.981680i	$-0.561023\pi$
$541$	−206.160			−0.381072			−0.190536	+	0.981680i	$0.561023\pi$
$542$	−417.670	−	71.4283i	−0.770610	−	0.131787i
$543$			457.697i			0.842903i
$544$	−304.890	+	269.525i	−0.560460	+	0.495451i
$545$	−348.584			−0.639604
$546$	−24.9985	+	146.176i	−0.0457847	+	0.267722i
$547$		−	675.217i		−	1.23440i	−0.786806	−	0.617200i	$-0.788267\pi$
$547$		−	675.217i		−	1.23440i	0.786806	−	0.617200i	$-0.211733\pi$
$548$	644.478	+	227.073i	1.17606	+	0.414367i
$549$	151.851			0.276596
$550$	−90.5092	−	15.4785i	−0.164562	−	0.0281428i
$551$			285.604i			0.518337i
$552$	−45.7036	+	82.0665i	−0.0827963	+	0.148671i
$553$	−1199.89			−2.16978
$554$	101.867	−	595.659i	0.183876	−	1.07520i
$555$			93.9027i			0.169194i
$556$	335.113	−	951.117i	0.602722	−	1.71064i
$557$	553.332			0.993415			0.496708	−	0.867918i	$-0.334542\pi$
$557$	553.332			0.993415			0.496708	+	0.867918i	$0.334542\pi$
$558$	−29.5128	−	5.04716i	−0.0528903	−	0.00904508i
$559$			192.427i			0.344235i
$560$	391.272	−	486.323i	0.698699	−	0.868434i
$561$	71.1924			0.126903
$562$	90.1646	−	527.229i	0.160435	−	0.938130i
$563$		−	899.000i		−	1.59680i	−0.602126	−	0.798401i	$-0.705680\pi$
$563$		−	899.000i		−	1.59680i	0.602126	−	0.798401i	$-0.294320\pi$
$564$	−595.757	−	209.907i	−1.05631	−	0.372175i
$565$	12.1920			0.0215787
$566$	−161.061	−	27.5440i	−0.284560	−	0.0486643i
$567$			106.860i			0.188466i
$568$	326.941	+	182.076i	0.575600	+	0.320557i
$569$	−607.676			−1.06797			−0.533986	−	0.845493i	$-0.679306\pi$
$569$	−607.676			−1.06797			−0.533986	+	0.845493i	$0.679306\pi$
$570$	37.3430	−	218.360i	0.0655141	−	0.383087i
$571$		−	17.8567i		−	0.0312727i	−0.999878	−	0.0156364i	$-0.995023\pi$
$571$		−	17.8567i		−	0.0312727i	0.999878	−	0.0156364i	$-0.00497741\pi$
$572$	15.4906	−	43.9655i	0.0270815	−	0.0768627i
$573$	100.829			0.175966
$574$	313.704	+	53.6485i	0.546523	+	0.0934642i
$575$			96.2958i			0.167471i
$576$	101.097	+	163.228i	0.175515	+	0.283382i
$577$	−706.376			−1.22422			−0.612111	−	0.790772i	$-0.709679\pi$
$577$	−706.376			−1.22422			−0.612111	+	0.790772i	$0.709679\pi$
$578$	−42.9106	+	250.916i	−0.0742399	+	0.434111i
$579$		−	457.091i		−	0.789449i
$580$	181.889	+	64.0861i	0.313602	+	0.110493i
$581$	−1909.69			−3.28691
$582$	595.933	+	101.914i	1.02394	+	0.175110i
$583$			118.862i			0.203880i
$584$	−529.881	+	951.468i	−0.907331	+	1.62923i
$585$	35.5394			0.0607511
$586$	112.639	−	658.644i	0.192216	−	1.12397i
$587$			329.703i			0.561675i	0.959755	+	0.280837i	$0.0906122\pi$
$587$			329.703i			0.561675i	−0.959755	+	0.280837i	$0.909388\pi$
$588$	−211.761	+	601.021i	−0.360139	+	1.02214i
$589$	−97.1277			−0.164903
$590$	−578.131	−	98.8696i	−0.979882	−	0.167576i
$591$		−	521.796i		−	0.882903i
$592$	−205.700	−	165.496i	−0.347466	−	0.279554i
$593$	423.306			0.713838			0.356919	−	0.934135i	$-0.383827\pi$
$593$	423.306			0.713838			0.356919	+	0.934135i	$0.383827\pi$
$594$	5.66212	−	33.1087i	0.00953219	−	0.0557386i
$595$			496.106i			0.833791i
$596$	658.435	+	231.991i	1.10476	+	0.389246i
$597$	466.356			0.781166
$598$	−48.1856	−	8.24051i	−0.0805779	−	0.0137801i
$599$		−	800.175i		−	1.33585i	−0.744228	−	0.667926i	$-0.767182\pi$
$599$		−	800.175i		−	1.33585i	0.744228	−	0.667926i	$-0.232818\pi$
$600$	171.958	+	95.7650i	0.286597	+	0.159608i
$601$	95.1851			0.158378			0.0791889	−	0.996860i	$-0.474767\pi$
$601$	95.1851			0.158378			0.0791889	+	0.996860i	$0.474767\pi$
$602$	−213.637	+	1249.22i	−0.354878	+	2.07512i
$603$			150.166i			0.249032i
$604$	255.776	−	725.942i	0.423470	−	1.20189i
$605$	−363.236			−0.600390
$606$	−388.530	−	66.4448i	−0.641139	−	0.109645i
$607$			557.802i			0.918950i	0.888191	+	0.459475i	$0.151962\pi$
$607$			557.802i			0.918950i	−0.888191	+	0.459475i	$0.848038\pi$
$608$	412.517	+	466.643i	0.678481	+	0.767506i
$609$	−301.769			−0.495515
$610$	56.0688	−	327.857i	0.0919160	−	0.537471i
$611$		−	328.723i		−	0.538009i
$612$	−143.931	−	50.7120i	−0.235181	−	0.0828628i
$613$	70.1273			0.114400			0.0572001	−	0.998363i	$-0.481783\pi$
$613$	70.1273			0.114400			0.0572001	+	0.998363i	$0.481783\pi$
$614$	−131.232	−	22.4428i	−0.213733	−	0.0365517i
$615$		−	76.2701i		−	0.124016i
$616$	149.375	−	268.222i	0.242492	−	0.435425i
$617$	−57.1204			−0.0925776			−0.0462888	−	0.998928i	$-0.514739\pi$
$617$	−57.1204			−0.0925776			−0.0462888	+	0.998928i	$0.514739\pi$
$618$	22.1493	−	129.516i	0.0358403	−	0.209573i
$619$		−	74.8935i		−	0.120991i	−0.998168	−	0.0604955i	$-0.980732\pi$
$619$		−	74.8935i		−	0.120991i	0.998168	−	0.0604955i	$-0.0192681\pi$
$620$	−21.7943	+	61.8565i	−0.0351521	+	0.0997686i
$621$	−35.2255			−0.0567238
$622$	−369.884	−	63.2560i	−0.594668	−	0.101698i
$623$			2040.22i			3.27483i
$624$	−62.6353	+	77.8513i	−0.100377	+	0.124762i
$625$	−68.1089			−0.108974
$626$	−108.195	+	632.659i	−0.172835	+	1.01064i
$627$		−	108.962i		−	0.173783i
$628$	419.600	+	147.840i	0.668152	+	0.235414i
$629$	209.837			0.333605
$630$	230.719	+	39.4566i	0.366220	+	0.0626295i
$631$		−	1194.39i		−	1.89285i	−0.322929	−	0.946423i	$-0.604667\pi$
$631$		−	1194.39i		−	1.89285i	0.322929	−	0.946423i	$-0.395333\pi$
$632$	−706.312	−	393.352i	−1.11758	−	0.622392i
$633$	102.749			0.162321
$634$	82.3698	−	481.650i	0.129921	−	0.759700i
$635$		−	40.3732i		−	0.0635798i
$636$	84.6682	−	240.305i	0.133126	−	0.377838i
$637$	−331.628			−0.520609
$638$	93.4976	+	15.9896i	0.146548	+	0.0250620i
$639$			140.333i			0.219614i
$640$	389.749	−	158.005i	0.608983	−	0.246883i
$641$	356.128			0.555582			0.277791	−	0.960642i	$-0.410398\pi$
$641$	356.128			0.555582			0.277791	+	0.960642i	$0.410398\pi$
$642$	58.4408	−	341.727i	0.0910292	−	0.532285i
$643$			392.830i			0.610933i	0.952203	+	0.305467i	$0.0988124\pi$
$643$			392.830i			0.610933i	−0.952203	+	0.305467i	$0.901188\pi$
$644$	−303.668	−	106.993i	−0.471534	−	0.166139i
$645$	303.719			0.470883
$646$	−487.952	−	83.4476i	−0.755344	−	0.129176i
$647$		−	798.420i		−	1.23403i	−0.786950	−	0.617017i	$-0.788341\pi$
$647$		−	798.420i		−	1.23403i	0.786950	−	0.617017i	$-0.211659\pi$
$648$	−35.0313	+	62.9031i	−0.0540607	+	0.0970728i
$649$	−288.489			−0.444513
$650$	−17.2668	+	100.966i	−0.0265642	+	0.155332i
$651$		−	102.625i		−	0.157642i
$652$	−135.078	+	383.378i	−0.207175	+	0.588003i
$653$	−928.782			−1.42233			−0.711165	−	0.703025i	$-0.751832\pi$
$653$	−928.782			−1.42233			−0.711165	+	0.703025i	$0.751832\pi$
$654$	362.261	+	61.9524i	0.553916	+	0.0947284i
$655$		−	216.076i		−	0.329887i
$656$	167.074	+	134.420i	0.254686	+	0.204908i
$657$	−408.400			−0.621613
$658$	364.955	−	2134.04i	0.554643	−	3.24323i
$659$			844.014i			1.28075i	0.768062	+	0.640375i	$0.221221\pi$
$659$			844.014i			1.28075i	−0.768062	+	0.640375i	$0.778779\pi$
$660$	−69.3934	−	24.4498i	−0.105141	−	0.0370452i
$661$	885.957			1.34033			0.670164	−	0.742213i	$-0.266224\pi$
$661$	885.957			1.34033			0.670164	+	0.742213i	$0.266224\pi$
$662$	473.041	+	80.8975i	0.714563	+	0.122202i
$663$		−	79.4173i		−	0.119785i
$664$	−1124.14	−	626.042i	−1.69298	−	0.942835i
$665$	759.304			1.14181
$666$	16.6889	−	97.5869i	0.0250584	−	0.146527i
$667$		−	99.4752i		−	0.149138i
$668$	−63.8534	+	181.228i	−0.0955889	+	0.271300i
$669$	447.030			0.668206
$670$	324.219	+	55.4467i	0.483909	+	0.0827562i
$671$		−	163.602i		−	0.243818i
$672$	−493.055	+	435.865i	−0.733713	+	0.648608i
$673$	−350.866			−0.521346			−0.260673	−	0.965427i	$-0.583944\pi$
$673$	−350.866			−0.521346			−0.260673	+	0.965427i	$0.583944\pi$
$674$	−49.1390	+	287.336i	−0.0729065	+	0.426314i
$675$			73.8098i			0.109348i
$676$	−49.0448	−	17.2803i	−0.0725515	−	0.0255625i
$677$	−148.197			−0.218903			−0.109451	−	0.993992i	$-0.534909\pi$
$677$	−148.197			−0.218903			−0.109451	+	0.993992i	$0.534909\pi$
$678$	−12.6703	−	2.16682i	−0.0186878	−	0.00319590i
$679$			2072.24i			3.05191i
$680$	−162.635	+	292.032i	−0.239169	+	0.429458i
$681$	−275.054			−0.403897
$682$	−5.43771	+	31.7965i	−0.00797318	+	0.0466224i
$683$		−	115.571i		−	0.169210i	−0.996415	−	0.0846051i	$-0.973037\pi$
$683$		−	115.571i		−	0.169210i	0.996415	−	0.0846051i	$-0.0269629\pi$
$684$	−77.6163	+	220.290i	−0.113474	+	0.322062i
$685$	561.276			0.819380
$686$	−1005.96	−	172.035i	−1.46641	−	0.250780i
$687$			308.745i			0.449410i
$688$	−535.281	+	665.316i	−0.778024	+	0.967029i
$689$	132.594			0.192444
$690$	−13.0065	+	76.0543i	−0.0188500	+	0.110224i
$691$		−	689.060i		−	0.997192i	−0.866834	−	0.498596i	$-0.833849\pi$
$691$		−	689.060i		−	0.997192i	0.866834	−	0.498596i	$-0.166151\pi$
$692$	83.2226	+	29.3223i	0.120264	+	0.0423733i
$693$	115.129			0.166132
$694$	−168.319	−	28.7852i	−0.242535	−	0.0414773i
$695$		−	828.327i		−	1.19184i
$696$	−177.636	−	98.9269i	−0.255224	−	0.142136i
$697$	−170.435			−0.244527
$698$	215.481	−	1260.00i	0.308711	−	1.80516i
$699$		−	669.066i		−	0.957176i
$700$	−224.189	+	636.291i	−0.320269	+	0.908987i
$701$	−9.25723			−0.0132058			−0.00660288	−	0.999978i	$-0.502102\pi$
$701$	−9.25723			−0.0132058			−0.00660288	+	0.999978i	$0.502102\pi$
$702$	−36.9338	−	6.31627i	−0.0526122	−	0.00899753i
$703$		−	321.162i		−	0.456845i
$704$	175.859	−	108.920i	0.249800	−	0.154715i
$705$	−518.844			−0.735949
$706$	13.1573	−	76.9360i	0.0186364	−	0.108975i
$707$		−	1351.04i		−	1.91095i
$708$	583.242	+	205.497i	0.823788	+	0.290250i
$709$	−126.321			−0.178168			−0.0890838	−	0.996024i	$-0.528394\pi$
$709$	−126.321			−0.178168			−0.0890838	+	0.996024i	$0.528394\pi$
$710$	302.989	+	51.8159i	0.426745	+	0.0729802i
$711$		−	303.171i		−	0.426401i
$712$	−668.832	+	1200.97i	−0.939371	+	1.68676i
$713$	33.8294			0.0474465
$714$	88.1707	−	515.570i	0.123488	−	0.722087i
$715$		−	38.2895i		−	0.0535517i
$716$	125.862	−	357.221i	0.175785	−	0.498912i
$717$	−548.949			−0.765620
$718$	−875.421	−	149.711i	−1.21925	−	0.208511i
$719$		−	914.836i		−	1.27237i	−0.771535	−	0.636187i	$-0.780511\pi$
$719$		−	914.836i		−	1.27237i	0.771535	−	0.636187i	$-0.219489\pi$
$720$	122.877	+	98.8611i	0.170663	+	0.137307i
$721$	450.368			0.624643
$722$	−6.01250	+	35.1575i	−0.00832756	+	0.0486946i
$723$		−	218.463i		−	0.302161i
$724$	−996.934	−	351.256i	−1.37698	−	0.485161i
$725$	−208.435			−0.287497
$726$	377.487	+	64.5564i	0.519955	+	0.0889206i
$727$		−	593.202i		−	0.815959i	−0.912991	−	0.407979i	$-0.866234\pi$
$727$		−	593.202i		−	0.815959i	0.912991	−	0.407979i	$-0.133766\pi$
$728$	−299.210	−	166.633i	−0.411002	−	0.228891i
$729$	−27.0000			−0.0370370
$730$	−150.796	+	881.763i	−0.206569	+	1.20789i
$731$		−	678.699i		−	0.928453i
$732$	−116.537	+	330.756i	−0.159204	+	0.451852i
$733$	761.188			1.03846			0.519228	−	0.854636i	$-0.326220\pi$
$733$	761.188			1.03846			0.519228	+	0.854636i	$0.326220\pi$
$734$	−604.528	−	103.384i	−0.823608	−	0.140850i
$735$			523.428i			0.712147i
$736$	−143.679	−	162.531i	−0.195216	−	0.220830i
$737$	161.786			0.219520
$738$	−13.5552	+	79.2625i	−0.0183674	+	0.107402i
$739$		−	716.713i		−	0.969841i	−0.874558	−	0.484921i	$-0.838848\pi$
$739$		−	716.713i		−	0.969841i	0.874558	−	0.484921i	$-0.161152\pi$
$740$	−204.535	−	72.0650i	−0.276398	−	0.0973852i
$741$	−121.551			−0.164036
$742$	860.789	+	147.209i	1.16009	+	0.198394i
$743$		−	80.3543i		−	0.108148i	−0.998537	−	0.0540742i	$-0.982779\pi$
$743$		−	80.3543i		−	0.108148i	0.998537	−	0.0540742i	$-0.0172208\pi$
$744$	33.6429	−	60.4100i	0.0452189	−	0.0811963i
$745$	573.431			0.769705
$746$	72.1375	−	421.817i	0.0966991	−	0.565439i
$747$		−	482.515i		−	0.645937i
$748$	−54.6362	+	155.068i	−0.0730430	+	0.207310i
$749$	1188.29			1.58650
$750$	439.832	+	75.2182i	0.586442	+	0.100291i
$751$			370.246i			0.493004i	0.969142	+	0.246502i	$0.0792812\pi$
$751$			370.246i			0.493004i	−0.969142	+	0.246502i	$0.920719\pi$
$752$	914.420	−	1136.56i	1.21598	−	1.51138i
$753$	18.8528			0.0250369
$754$	17.8368	−	104.299i	0.0236563	−	0.138328i
$755$		−	632.222i		−	0.837381i
$756$	−232.759	−	82.0093i	−0.307882	−	0.108478i
$757$	914.746			1.20838			0.604191	−	0.796839i	$-0.293496\pi$
$757$	914.746			1.20838			0.604191	+	0.796839i	$0.293496\pi$
$758$	1303.15	+	222.860i	1.71920	+	0.294011i
$759$			37.9513i			0.0500017i
$760$	446.963	+	248.918i	0.588109	+	0.327523i
$761$	145.895			0.191715			0.0958575	−	0.995395i	$-0.469441\pi$
$761$	145.895			0.191715			0.0958575	+	0.995395i	$0.469441\pi$
$762$	−7.17535	+	41.9572i	−0.00941648	+	0.0550620i
$763$			1259.69i			1.65097i
$764$	−77.3803	+	219.620i	−0.101283	+	0.287461i
$765$	−125.349			−0.163855
$766$	208.735	+	35.6970i	0.272500	+	0.0466019i
$767$			321.818i			0.419580i
$768$	−433.123	+	94.9359i	−0.563962	+	0.123614i
$769$	1156.46			1.50385			0.751925	−	0.659249i	$-0.229126\pi$
$769$	1156.46			1.50385			0.751925	+	0.659249i	$0.229126\pi$
$770$	42.5098	−	248.572i	0.0552075	−	0.322821i
$771$		−	192.926i		−	0.250228i
$772$	995.615	+	350.791i	1.28966	+	0.454393i
$773$	341.427			0.441691			0.220845	−	0.975309i	$-0.429118\pi$
$773$	341.427			0.441691			0.220845	+	0.975309i	$0.429118\pi$
$774$	−315.636	−	53.9787i	−0.407798	−	0.0697400i
$775$		−	70.8844i		−	0.0914638i
$776$	−679.330	+	1219.82i	−0.875426	+	1.57194i
$777$	339.340			0.436731
$778$	5.96510	−	34.8804i	0.00766722	−	0.0448334i
$779$			260.856i			0.334860i
$780$	−27.2745	+	77.4104i	−0.0349673	+	0.0992441i
$781$	151.192			0.193588
$782$	169.953	+	29.0646i	0.217331	+	0.0371671i
$783$		−	76.2468i		−	0.0973777i
$784$	−1146.60	−	922.499i	−1.46250	−	1.17666i
$785$	365.429			0.465515
$786$	−38.4023	+	224.554i	−0.0488579	+	0.285692i
$787$		−	817.162i		−	1.03833i	−0.854675	−	0.519163i	$-0.826244\pi$
$787$		−	817.162i		−	1.03833i	0.854675	−	0.519163i	$-0.173756\pi$
$788$	1136.55	+	400.449i	1.44232	+	0.508184i
$789$	−439.075			−0.556496
$790$	−654.568	−	111.942i	−0.828567	−	0.141698i
$791$		−	44.0585i		−	0.0556998i
$792$	67.7706	+	37.7421i	0.0855690	+	0.0476542i
$793$	−182.502			−0.230142
$794$	142.152	−	831.221i	0.179033	−	1.04688i
$795$		−	209.281i		−	0.263247i
$796$	−357.902	+	1015.80i	−0.449626	+	1.27613i
$797$	107.818			0.135280			0.0676398	−	0.997710i	$-0.478453\pi$
$797$	107.818			0.135280			0.0676398	+	0.997710i	$0.478453\pi$
$798$	−789.095	−	134.948i	−0.988841	−	0.169108i
$799$			1159.42i			1.45109i
$800$	−340.559	+	301.057i	−0.425699	+	0.376322i
$801$	−515.495			−0.643564
$802$	80.3816	−	470.024i	0.100226	−	0.586065i
$803$			440.002i			0.547948i
$804$	−327.085	−	115.244i	−0.406823	−	0.143339i
$805$	−264.464			−0.328527
$806$	35.4699	+	6.06593i	0.0440074	+	0.00752596i
$807$		−	9.36110i		−	0.0115999i
$808$	442.902	−	795.286i	0.548146	−	0.984265i
$809$	1301.75			1.60909			0.804545	−	0.593892i	$-0.202409\pi$
$809$	1301.75			1.60909			0.804545	+	0.593892i	$0.202409\pi$
$810$	−9.96935	+	58.2948i	−0.0123078	+	0.0719689i
$811$			1064.64i			1.31275i	0.754434	+	0.656376i	$0.227911\pi$
$811$			1064.64i			1.31275i	−0.754434	+	0.656376i	$0.772089\pi$
$812$	231.591	−	657.299i	0.285210	−	0.809482i
$813$	366.965			0.451371
$814$	−105.138	−	17.9803i	−0.129163	−	0.0220889i
$815$			333.883i			0.409673i
$816$	220.917	−	274.585i	0.270732	−	0.336501i
$817$	−1038.77			−1.27144
$818$	85.1861	−	498.118i	0.104139	−	0.608946i
$819$		−	128.430i		−	0.156813i
$820$	166.128	+	58.5330i	0.202595	+	0.0713817i
$821$	−1017.75			−1.23964			−0.619822	−	0.784742i	$-0.712795\pi$
$821$	−1017.75			−1.23964			−0.619822	+	0.784742i	$0.712795\pi$
$822$	−583.297	−	99.7531i	−0.709607	−	0.121354i
$823$			638.191i			0.775444i	0.921776	+	0.387722i	$0.126738\pi$
$823$			638.191i			0.775444i	−0.921776	+	0.387722i	$0.873262\pi$
$824$	265.108	+	147.641i	0.321733	+	0.179176i
$825$	79.5213			0.0963894
$826$	−357.289	+	2089.21i	−0.432553	+	2.52931i
$827$			7.34024i			0.00887574i	0.999990	+	0.00443787i	$0.00141262\pi$
$827$			7.34024i			0.00887574i	−0.999990	+	0.00443787i	$0.998587\pi$
$828$	27.0336	−	76.7266i	0.0326493	−	0.0926650i
$829$	247.816			0.298933			0.149467	−	0.988767i	$-0.452244\pi$
$829$	247.816			0.298933			0.149467	+	0.988767i	$0.452244\pi$
$830$	−1041.78	−	178.161i	−1.25516	−	0.214652i
$831$			523.345i			0.629777i
$832$	−121.503	−	196.176i	−0.146037	−	0.235788i
$833$	1169.67			1.40416
$834$	−147.215	+	860.826i	−0.176517	+	1.03217i
$835$			157.832i			0.189020i
$836$	237.337	+	83.6223i	0.283895	+	0.100027i
$837$	25.9299			0.0309795
$838$	−617.671	−	105.632i	−0.737078	−	0.126052i
$839$			845.310i			1.00752i	0.863843	+	0.503761i	$0.168051\pi$
$839$			845.310i			1.00752i	−0.863843	+	0.503761i	$0.831949\pi$
$840$	−263.006	+	472.261i	−0.313103	+	0.562215i
$841$	−625.683			−0.743975
$842$	−80.9503	+	473.350i	−0.0961406	+	0.562173i
$843$			463.222i			0.549493i
$844$	−78.8542	+	223.804i	−0.0934291	+	0.265170i
$845$	−42.7131			−0.0505480
$846$	539.201	+	92.2119i	0.637353	+	0.108998i
$847$			1312.64i			1.54975i
$848$	458.443	+	368.841i	0.540617	+	0.434954i
$849$	141.508			0.166676
$850$	60.9006	−	356.111i	0.0716478	−	0.418954i
$851$			111.860i			0.131446i
$852$	−305.668	−	107.698i	−0.358765	−	0.126406i
$853$	−995.183			−1.16669			−0.583343	−	0.812226i	$-0.698256\pi$
$853$	−995.183			−1.16669			−0.583343	+	0.812226i	$0.698256\pi$
$854$	−1184.79	−	202.618i	−1.38734	−	0.237258i
$855$			191.851i			0.224387i
$856$	699.485	+	389.549i	0.817155	+	0.455081i
$857$	1376.43			1.60611			0.803053	−	0.595907i	$-0.203207\pi$
$857$	1376.43			1.60611			0.803053	+	0.595907i	$0.203207\pi$
$858$	−6.80503	+	39.7918i	−0.00793127	+	0.0463773i
$859$			142.833i			0.166278i	0.996538	+	0.0831392i	$0.0264946\pi$
$859$			142.833i			0.166278i	−0.996538	+	0.0831392i	$0.973505\pi$
$860$	−233.088	+	661.548i	−0.271032	+	0.769242i
$861$	−275.620			−0.320116
$862$	161.984	+	27.7018i	0.187916	+	0.0321366i
$863$		−	91.2703i		−	0.105759i	−0.998601	−	0.0528796i	$-0.983160\pi$
$863$		−	91.2703i		−	0.105759i	0.998601	−	0.0528796i	$-0.0168400\pi$
$864$	−110.128	−	124.578i	−0.127463	−	0.144188i
$865$	72.4784			0.0837901
$866$	195.014	−	1140.33i	0.225189	−	1.31677i
$867$		−	220.454i		−	0.254273i
$868$	223.533	+	78.7589i	0.257527	+	0.0907361i
$869$	−326.631			−0.375870
$870$	−164.622	−	28.1530i	−0.189221	−	0.0323597i
$871$		−	180.477i		−	0.207207i
$872$	−412.957	+	741.516i	−0.473574	+	0.850362i
$873$	−523.586			−0.599755
$874$	44.4843	−	260.118i	0.0508974	−	0.297618i
$875$			1529.43i			1.74792i
$876$	313.424	−	889.558i	0.357790	−	1.01548i
$877$	60.0268			0.0684456			0.0342228	−	0.999414i	$-0.489104\pi$
$877$	60.0268			0.0684456			0.0342228	+	0.999414i	$0.489104\pi$
$878$	18.6123	+	3.18301i	0.0211986	+	0.00362529i
$879$			578.683i			0.658343i
$880$	106.511	−	132.386i	0.121035	−	0.150438i
$881$	394.095			0.447327			0.223664	−	0.974666i	$-0.428198\pi$
$881$	394.095			0.447327			0.223664	+	0.974666i	$0.428198\pi$
$882$	93.0266	−	543.965i	0.105472	−	0.616740i
$883$		−	522.361i		−	0.591575i	−0.955254	−	0.295787i	$-0.904418\pi$
$883$		−	522.361i		−	0.591575i	0.955254	−	0.295787i	$-0.0955820\pi$
$884$	172.983	+	60.9483i	0.195682	+	0.0689460i
$885$	507.945			0.573949
$886$	−64.4850	−	11.0280i	−0.0727822	−	0.0124469i
$887$		−	55.8245i		−	0.0629363i	−0.999505	−	0.0314682i	$-0.989982\pi$
$887$		−	55.8245i		−	0.0629363i	0.999505	−	0.0314682i	$-0.0100183\pi$
$888$	199.752	+	111.244i	0.224946	+	0.125274i
$889$	−145.898			−0.164115
$890$	−190.339	+	1112.99i	−0.213864	+	1.25055i
$891$			29.0893i			0.0326479i
$892$	−343.070	+	973.701i	−0.384608	+	1.09159i
$893$	1774.53			1.98716
$894$	−595.929	−	101.913i	−0.666587	−	0.113997i
$895$		−	311.103i		−	0.347602i
$896$	−570.989	−	1408.45i	−0.637265	−	1.57193i
$897$	42.3358			0.0471971
$898$	89.6500	−	524.220i	0.0998330	−	0.583764i
$899$			73.2248i			0.0814514i
$900$	−160.769	−	56.6449i	−0.178632	−	0.0629387i
$901$	−467.665			−0.519051
$902$	85.3959	+	14.6041i	0.0946740	+	0.0161908i
$903$		−	1097.56i		−	1.21546i
$904$	14.4434	−	25.9350i	0.0159772	−	0.0286891i
$905$	−868.229			−0.959369
$906$	−112.362	+	657.027i	−0.124020	+	0.725196i
$907$		−	1009.83i		−	1.11337i	−0.830722	−	0.556687i	$-0.812072\pi$
$907$		−	1009.83i		−	1.11337i	0.830722	−	0.556687i	$-0.187928\pi$
$908$	211.089	−	599.111i	0.232476	−	0.659814i
$909$	341.362			0.375536
$910$	−277.289	−	47.4209i	−0.304714	−	0.0521109i
$911$			1113.95i			1.22277i	0.791333	+	0.611386i	$0.209388\pi$
$911$			1113.95i			1.22277i	−0.791333	+	0.611386i	$0.790612\pi$
$912$	−420.260	−	338.121i	−0.460812	−	0.370747i
$913$	−519.852			−0.569389
$914$	−193.504	+	1131.49i	−0.211711	+	1.23796i
$915$			288.055i			0.314814i
$916$	−672.494	−	236.944i	−0.734164	−	0.258673i
$917$	−780.843			−0.851519
$918$	130.267	+	22.2778i	0.141903	+	0.0242677i
$919$		−	816.271i		−	0.888217i	−0.895973	−	0.444109i	$-0.853520\pi$
$919$		−	816.271i		−	0.888217i	0.895973	−	0.444109i	$-0.146480\pi$
$920$	−155.676	−	86.6975i	−0.169213	−	0.0942365i
$921$	115.300			0.125190
$922$	−248.366	+	1452.29i	−0.269377	+	1.57516i
$923$		−	168.660i		−	0.182730i
$924$	−88.3553	+	250.770i	−0.0956226	+	0.271396i
$925$	234.386			0.253391
$926$	679.771	+	116.252i	0.734094	+	0.125542i
$927$			113.793i			0.122754i
$928$	351.803	−	310.997i	0.379099	−	0.335126i
$929$	−1541.71			−1.65954			−0.829769	−	0.558107i	$-0.811528\pi$
$929$	−1541.71			−1.65954			−0.829769	+	0.558107i	$0.811528\pi$
$930$	9.57422	−	55.9844i	0.0102949	−	0.0601983i
$931$		−	1790.21i		−	1.92289i
$932$	1457.33	+	513.471i	1.56366	+	0.550934i
$933$	324.979			0.348316
$934$	514.551	+	87.9964i	0.550911	+	0.0942145i
$935$			135.049i			0.144437i
$936$	42.1024	−	75.6002i	0.0449812	−	0.0807694i
$937$	337.315			0.359995			0.179997	−	0.983667i	$-0.442391\pi$
$937$	337.315			0.359995			0.179997	+	0.983667i	$0.442391\pi$
$938$	200.370	−	1171.64i	0.213614	−	1.24909i
$939$		−	555.853i		−	0.591963i
$940$	398.184	−	1130.12i	0.423600	−	1.20226i
$941$	−646.195			−0.686711			−0.343355	−	0.939206i	$-0.611563\pi$
$941$	−646.195			−0.686711			−0.343355	+	0.939206i	$0.611563\pi$
$942$	−379.766	−	64.9461i	−0.403149	−	0.0689449i
$943$		−	90.8556i		−	0.0963474i
$944$	−895.210	+	1112.68i	−0.948316	+	1.17869i
$945$	−202.709			−0.214507
$946$	−58.1557	+	340.060i	−0.0614753	+	0.359471i
$947$			134.511i			0.142039i	0.997475	+	0.0710193i	$0.0226252\pi$
$947$			134.511i			0.142039i	−0.997475	+	0.0710193i	$0.977375\pi$
$948$	660.354	+	232.667i	0.696576	+	0.245429i
$949$	490.835			0.517213
$950$	−545.038	−	93.2102i	−0.573724	−	0.0981160i
$951$			423.177i			0.444981i
$952$	1055.33	+	587.721i	1.10854	+	0.617354i
$953$	−739.031			−0.775478			−0.387739	−	0.921769i	$-0.626744\pi$
$953$	−739.031			−0.775478			−0.387739	+	0.921769i	$0.626744\pi$
$954$	−37.1947	+	217.492i	−0.0389881	+	0.227979i
$955$			191.267i			0.200280i
$956$	421.288	−	1195.70i	0.440677	−	1.25073i
$957$	−82.1468			−0.0858378
$958$	1261.89	+	215.803i	1.31721	+	0.225264i
$959$		−	2028.30i		−	2.11502i
$960$	−309.636	+	191.776i	−0.322538	+	0.199766i
$961$	936.098			0.974087
$962$	−20.0576	+	117.285i	−0.0208499	+	0.121918i
$963$			300.241i			0.311776i
$964$	475.846	+	167.658i	0.493616	+	0.173919i
$965$	867.080			0.898528
$966$	274.840	+	47.0021i	0.284514	+	0.0486564i
$967$		−	956.992i		−	0.989650i	−0.868993	−	0.494825i	$-0.835232\pi$
$967$		−	956.992i		−	0.989650i	0.868993	−	0.494825i	$-0.164768\pi$
$968$	−430.314	+	772.683i	−0.444539	+	0.798226i
$969$	428.714			0.442429
$970$	−193.326	+	1130.46i	−0.199306	+	1.16542i
$971$		−	1072.25i		−	1.10428i	−0.833753	−	0.552138i	$-0.813812\pi$
$971$		−	1072.25i		−	1.10428i	0.833753	−	0.552138i	$-0.186188\pi$
$972$	20.7210	−	58.8102i	0.0213179	−	0.0605043i
$973$	−2993.36			−3.07642
$974$	228.732	+	39.1169i	0.234838	+	0.0401611i
$975$		−	88.7083i		−	0.0909829i
$976$	−631.001	−	507.673i	−0.646518	−	0.520156i
$977$	1279.30			1.30942			0.654708	−	0.755882i	$-0.272792\pi$
$977$	1279.30			1.30942			0.654708	+	0.755882i	$0.272792\pi$
$978$	59.3397	−	346.983i	0.0606745	−	0.354788i
$979$			555.384i			0.567297i
$980$	−1140.11	−	401.702i	−1.16338	−	0.409900i
$981$	−318.282			−0.324446
$982$	1248.15	+	213.453i	1.27103	+	0.217366i
$983$		−	946.789i		−	0.963163i	−0.876401	−	0.481581i	$-0.840063\pi$
$983$		−	946.789i		−	0.963163i	0.876401	−	0.481581i	$-0.159937\pi$
$984$	−162.243	−	90.3548i	−0.164881	−	0.0918240i
$985$	989.822			1.00490
$986$	−62.9114	+	367.868i	−0.0638046	+	0.373092i
$987$			1874.97i			1.89966i
$988$	93.2832	−	264.756i	0.0944162	−	0.267972i
$989$	361.801			0.365825
$990$	62.8058	+	10.7408i	0.0634402	+	0.0108493i
$991$			1113.13i			1.12324i	0.827395	+	0.561621i	$0.189822\pi$
$991$			1113.13i			1.12324i	−0.827395	+	0.561621i	$0.810178\pi$
$992$	105.763	+	119.641i	0.106616	+	0.120606i
$993$	−415.613			−0.418542
$994$	187.249	−	1094.92i	0.188380	−	1.10153i
$995$			884.656i			0.889101i
$996$	1050.99	+	370.303i	1.05521	+	0.371790i
$997$	−178.778			−0.179316			−0.0896578	−	0.995973i	$-0.528577\pi$
$997$	−178.778			−0.179316			−0.0896578	+	0.995973i	$0.528577\pi$
$998$	−455.166	−	77.8406i	−0.456078	−	0.0779966i
$999$			85.7397i			0.0858255i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	156.3.f.a.79.11	✓	24
3.2	odd	2		468.3.f.b.235.14		24
4.3	odd	2	inner	156.3.f.a.79.12	yes	24
8.3	odd	2		2496.3.k.e.703.22		24
8.5	even	2		2496.3.k.e.703.21		24
12.11	even	2		468.3.f.b.235.13		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
156.3.f.a.79.11	✓	24	1.1	even	1	trivial
156.3.f.a.79.12	yes	24	4.3	odd	2	inner
468.3.f.b.235.13		24	12.11	even	2
468.3.f.b.235.14		24	3.2	odd	2
2496.3.k.e.703.21		24	8.5	even	2
2496.3.k.e.703.22		24	8.3	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.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.337137 - 1.97138i) q^{2} +1.73205i q^{3} +(-3.77268 - 1.32925i) q^{4} -3.28562 q^{5} +(3.41453 + 0.583939i) q^{6} +11.8734i q^{7} +(-3.89237 + 6.98924i) q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(0.337137 - 1.97138i) q^{2} +1.73205i q^{3} +(-3.77268 - 1.32925i) q^{4} -3.28562 q^{5} +(3.41453 + 0.583939i) q^{6} +11.8734i q^{7} +(-3.89237 + 6.98924i) q^{8} -3.00000 q^{9} +(-1.10771 + 6.47720i) q^{10} +3.23214i q^{11} +(2.30233 - 6.53447i) q^{12} +3.60555 q^{13} +(23.4069 + 4.00296i) q^{14} -5.69086i q^{15} +(12.4662 + 10.0297i) q^{16} -12.7169 q^{17} +(-1.01141 + 5.91414i) q^{18} +19.4637i q^{19} +(12.3956 + 4.36742i) q^{20} -20.5653 q^{21} +(6.37178 + 1.08968i) q^{22} -6.77915i q^{23} +(-12.1057 - 6.74178i) q^{24} -14.2047 q^{25} +(1.21557 - 7.10791i) q^{26} -5.19615i q^{27} +(15.7827 - 44.7944i) q^{28} +14.6737 q^{29} +(-11.2188 - 1.91860i) q^{30} +4.99021i q^{31} +(23.9751 - 21.1942i) q^{32} -5.59824 q^{33} +(-4.28736 + 25.0699i) q^{34} -39.0114i q^{35} +(11.3180 + 3.98776i) q^{36} -16.5006 q^{37} +(38.3703 + 6.56193i) q^{38} +6.24500i q^{39} +(12.7888 - 22.9640i) q^{40} +13.4022 q^{41} +(-6.93333 + 40.5420i) q^{42} +53.3697i q^{43} +(4.29633 - 12.1938i) q^{44} +9.85686 q^{45} +(-13.3643 - 2.28551i) q^{46} -91.1714i q^{47} +(-17.3719 + 21.5921i) q^{48} -91.9770 q^{49} +(-4.78894 + 28.0029i) q^{50} -22.0264i q^{51} +(-13.6026 - 4.79269i) q^{52} +36.7750 q^{53} +(-10.2436 - 1.75182i) q^{54} -10.6196i q^{55} +(-82.9858 - 46.2156i) q^{56} -33.7120 q^{57} +(4.94705 - 28.9274i) q^{58} +89.2562i q^{59} +(-7.56459 + 21.4698i) q^{60} -50.6171 q^{61} +(9.83759 + 1.68239i) q^{62} -35.6201i q^{63} +(-33.6989 - 54.4094i) q^{64} -11.8465 q^{65} +(-1.88737 + 11.0362i) q^{66} -50.0554i q^{67} +(47.9769 + 16.9040i) q^{68} +11.7418 q^{69} +(-76.9063 - 13.1522i) q^{70} -46.7777i q^{71} +(11.6771 - 20.9677i) q^{72} +136.133 q^{73} +(-5.56297 + 32.5290i) q^{74} -24.6033i q^{75} +(25.8721 - 73.4301i) q^{76} -38.3764 q^{77} +(12.3113 + 2.10542i) q^{78} +101.057i q^{79} +(-40.9591 - 32.9537i) q^{80} +9.00000 q^{81} +(4.51838 - 26.4208i) q^{82} +160.838i q^{83} +(77.5862 + 27.3364i) q^{84} +41.7830 q^{85} +(105.212 + 17.9929i) q^{86} +25.4156i q^{87} +(-22.5902 - 12.5807i) q^{88} +171.832 q^{89} +(3.32312 - 19.4316i) q^{90} +42.8101i q^{91} +(-9.01120 + 25.5755i) q^{92} -8.64329 q^{93} +(-179.734 - 30.7373i) q^{94} -63.9502i q^{95} +(36.7094 + 41.5261i) q^{96} +174.529 q^{97} +(-31.0089 + 181.322i) q^{98} -9.69643i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{2} + 8 q^{4} - 12 q^{6} - 32 q^{8} - 72 q^{9}+O(q^{10}) \) 24 * q + 4 * q^2 + 8 * q^4 - 12 * q^6 - 32 * q^8 - 72 * q^9	\( 24 q + 4 q^{2} + 8 q^{4} - 12 q^{6} - 32 q^{8} - 72 q^{9} - 12 q^{10} + 12 q^{12} + 32 q^{14} + 4 q^{16} - 12 q^{18} + 84 q^{20} + 28 q^{22} - 36 q^{24} + 104 q^{25} - 96 q^{28} + 64 q^{29} - 12 q^{30} + 44 q^{32} + 48 q^{33} + 40 q^{34} - 24 q^{36} - 192 q^{37} - 104 q^{38} + 220 q^{40} - 220 q^{44} - 104 q^{46} - 144 q^{48} - 248 q^{49} + 100 q^{50} - 52 q^{52} + 336 q^{53} + 36 q^{54} + 168 q^{56} - 16 q^{58} + 60 q^{60} + 16 q^{61} + 152 q^{62} - 16 q^{64} - 132 q^{66} + 400 q^{68} - 192 q^{69} + 208 q^{70} + 96 q^{72} + 112 q^{73} - 104 q^{74} - 264 q^{76} - 272 q^{77} - 300 q^{80} + 216 q^{81} - 4 q^{82} + 96 q^{84} + 64 q^{85} + 288 q^{86} - 492 q^{88} + 36 q^{90} + 328 q^{92} - 96 q^{93} - 884 q^{94} + 72 q^{96} - 80 q^{97} - 572 q^{98}+O(q^{100}) \) 24 * q + 4 * q^2 + 8 * q^4 - 12 * q^6 - 32 * q^8 - 72 * q^9 - 12 * q^10 + 12 * q^12 + 32 * q^14 + 4 * q^16 - 12 * q^18 + 84 * q^20 + 28 * q^22 - 36 * q^24 + 104 * q^25 - 96 * q^28 + 64 * q^29 - 12 * q^30 + 44 * q^32 + 48 * q^33 + 40 * q^34 - 24 * q^36 - 192 * q^37 - 104 * q^38 + 220 * q^40 - 220 * q^44 - 104 * q^46 - 144 * q^48 - 248 * q^49 + 100 * q^50 - 52 * q^52 + 336 * q^53 + 36 * q^54 + 168 * q^56 - 16 * q^58 + 60 * q^60 + 16 * q^61 + 152 * q^62 - 16 * q^64 - 132 * q^66 + 400 * q^68 - 192 * q^69 + 208 * q^70 + 96 * q^72 + 112 * q^73 - 104 * q^74 - 264 * q^76 - 272 * q^77 - 300 * q^80 + 216 * q^81 - 4 * q^82 + 96 * q^84 + 64 * q^85 + 288 * q^86 - 492 * q^88 + 36 * q^90 + 328 * q^92 - 96 * q^93 - 884 * q^94 + 72 * q^96 - 80 * q^97 - 572 * q^98

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