LMFDB - Embedded newform 276.3.f.b.139.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [276,3,Mod(139,276)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(276, 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("276.139");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 276 = 2^{2} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	276.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:	$7.52045529634$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			139.18
Character	$\chi$	$=$	276.139
Dual form			276.3.f.b.139.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0758829 + 1.99856i) q^{2} +1.73205i q^{3} +(-3.98848 - 0.303313i) q^{4} +1.44548 q^{5} +(-3.46161 - 0.131433i) q^{6} -10.3854i q^{7} +(0.908847 - 7.94821i) q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(-0.0758829 + 1.99856i) q^{2} +1.73205i q^{3} +(-3.98848 - 0.303313i) q^{4} +1.44548 q^{5} +(-3.46161 - 0.131433i) q^{6} -10.3854i q^{7} +(0.908847 - 7.94821i) q^{8} -3.00000 q^{9} +(-0.109688 + 2.88889i) q^{10} -19.0259i q^{11} +(0.525354 - 6.90826i) q^{12} +20.2068 q^{13} +(20.7557 + 0.788071i) q^{14} +2.50365i q^{15} +(15.8160 + 2.41952i) q^{16} -27.6069 q^{17} +(0.227649 - 5.99568i) q^{18} +5.26346i q^{19} +(-5.76529 - 0.438434i) q^{20} +17.9880 q^{21} +(38.0243 + 1.44374i) q^{22} -4.79583i q^{23} +(13.7667 + 1.57417i) q^{24} -22.9106 q^{25} +(-1.53335 + 40.3845i) q^{26} -5.19615i q^{27} +(-3.15001 + 41.4218i) q^{28} +1.54674 q^{29} +(-5.00370 - 0.189984i) q^{30} -27.7834i q^{31} +(-6.03572 + 31.4256i) q^{32} +32.9538 q^{33} +(2.09489 - 55.1740i) q^{34} -15.0119i q^{35} +(11.9655 + 0.909939i) q^{36} +42.8386 q^{37} +(-10.5193 - 0.399407i) q^{38} +34.9992i q^{39} +(1.31372 - 11.4890i) q^{40} +36.9794 q^{41} +(-1.36498 + 35.9500i) q^{42} -6.35454i q^{43} +(-5.77079 + 75.8843i) q^{44} -4.33645 q^{45} +(9.58476 + 0.363922i) q^{46} -0.999114i q^{47} +(-4.19073 + 27.3941i) q^{48} -58.8555 q^{49} +(1.73852 - 45.7882i) q^{50} -47.8166i q^{51} +(-80.5945 - 6.12899i) q^{52} -36.9393 q^{53} +(10.3848 + 0.394299i) q^{54} -27.5016i q^{55} +(-82.5449 - 9.43870i) q^{56} -9.11658 q^{57} +(-0.117372 + 3.09126i) q^{58} +41.4643i q^{59} +(0.759390 - 9.98577i) q^{60} +49.1239 q^{61} +(55.5268 + 2.10828i) q^{62} +31.1561i q^{63} +(-62.3480 - 14.4474i) q^{64} +29.2086 q^{65} +(-2.50063 + 65.8601i) q^{66} -85.3226i q^{67} +(110.110 + 8.37354i) q^{68} +8.30662 q^{69} +(30.0021 + 1.13914i) q^{70} +5.34813i q^{71} +(-2.72654 + 23.8446i) q^{72} +100.619 q^{73} +(-3.25072 + 85.6155i) q^{74} -39.6823i q^{75} +(1.59648 - 20.9932i) q^{76} -197.590 q^{77} +(-69.9480 - 2.65584i) q^{78} -136.777i q^{79} +(22.8618 + 3.49738i) q^{80} +9.00000 q^{81} +(-2.80611 + 73.9056i) q^{82} +58.3493i q^{83} +(-71.7447 - 5.45598i) q^{84} -39.9053 q^{85} +(12.6999 + 0.482201i) q^{86} +2.67904i q^{87} +(-151.221 - 17.2916i) q^{88} -76.4726 q^{89} +(0.329063 - 8.66666i) q^{90} -209.855i q^{91} +(-1.45464 + 19.1281i) q^{92} +48.1222 q^{93} +(1.99679 + 0.0758157i) q^{94} +7.60825i q^{95} +(-54.4308 - 10.4542i) q^{96} +47.7398 q^{97} +(4.46613 - 117.626i) q^{98} +57.0776i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{2} + 8 q^{4} + 4 q^{5} - 12 q^{6} - 44 q^{8} - 120 q^{9}+O(q^{10}) $ 40 * q + 4 * q^2 + 8 * q^4 + 4 * q^5 - 12 * q^6 - 44 * q^8 - 120 * q^9	$ 40 q + 4 q^{2} + 8 q^{4} + 4 q^{5} - 12 q^{6} - 44 q^{8} - 120 q^{9} - 24 q^{10} + 48 q^{12} + 8 q^{13} + 4 q^{14} + 40 q^{16} + 40 q^{17} - 12 q^{18} + 12 q^{20} + 24 q^{21} - 8 q^{22} + 36 q^{24} + 144 q^{25} - 128 q^{26} - 24 q^{28} - 72 q^{29} + 60 q^{30} + 44 q^{32} + 12 q^{33} - 80 q^{34} - 24 q^{36} + 68 q^{37} + 56 q^{38} + 140 q^{40} - 192 q^{41} + 36 q^{42} + 104 q^{44} - 12 q^{45} - 96 q^{48} - 200 q^{49} + 140 q^{50} - 184 q^{52} - 76 q^{53} + 36 q^{54} - 236 q^{56} + 84 q^{57} + 304 q^{58} + 96 q^{60} - 452 q^{61} + 40 q^{62} - 376 q^{64} + 744 q^{65} - 156 q^{66} + 300 q^{68} - 480 q^{70} + 132 q^{72} + 344 q^{73} + 500 q^{74} - 284 q^{76} - 56 q^{77} + 24 q^{78} - 228 q^{80} + 360 q^{81} + 144 q^{82} - 360 q^{84} + 96 q^{85} - 144 q^{86} + 300 q^{88} - 752 q^{89} + 72 q^{90} + 24 q^{93} - 200 q^{94} + 12 q^{96} - 40 q^{97} - 556 q^{98}+O(q^{100}) $ 40 * q + 4 * q^2 + 8 * q^4 + 4 * q^5 - 12 * q^6 - 44 * q^8 - 120 * q^9 - 24 * q^10 + 48 * q^12 + 8 * q^13 + 4 * q^14 + 40 * q^16 + 40 * q^17 - 12 * q^18 + 12 * q^20 + 24 * q^21 - 8 * q^22 + 36 * q^24 + 144 * q^25 - 128 * q^26 - 24 * q^28 - 72 * q^29 + 60 * q^30 + 44 * q^32 + 12 * q^33 - 80 * q^34 - 24 * q^36 + 68 * q^37 + 56 * q^38 + 140 * q^40 - 192 * q^41 + 36 * q^42 + 104 * q^44 - 12 * q^45 - 96 * q^48 - 200 * q^49 + 140 * q^50 - 184 * q^52 - 76 * q^53 + 36 * q^54 - 236 * q^56 + 84 * q^57 + 304 * q^58 + 96 * q^60 - 452 * q^61 + 40 * q^62 - 376 * q^64 + 744 * q^65 - 156 * q^66 + 300 * q^68 - 480 * q^70 + 132 * q^72 + 344 * q^73 + 500 * q^74 - 284 * q^76 - 56 * q^77 + 24 * q^78 - 228 * q^80 + 360 * q^81 + 144 * q^82 - 360 * q^84 + 96 * q^85 - 144 * q^86 + 300 * q^88 - 752 * q^89 + 72 * q^90 + 24 * q^93 - 200 * q^94 + 12 * q^96 - 40 * q^97 - 556 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/276\mathbb{Z}\right)^\times$.

$n$	$97$	$139$	$185$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	−0.0758829	+	1.99856i	−0.0379415	+	0.999280i
$2$	−0.0758829	+	1.99856i	−0.0379415	+	0.999280i
$3$			1.73205i			0.577350i
$3$			1.73205i			0.577350i
$4$	−3.98848	−	0.303313i	−0.997121	−	0.0758283i
$5$	1.44548			0.289097			0.144548	−	0.989498i	$-0.453827\pi$
$5$	1.44548			0.289097			0.144548	+	0.989498i	$0.453827\pi$
$6$	−3.46161	−	0.131433i	−0.576935	−	0.0219055i
$7$		−	10.3854i		−	1.48362i	−0.670609	−	0.741811i	$-0.733967\pi$
$7$		−	10.3854i		−	1.48362i	0.670609	−	0.741811i	$-0.266033\pi$
$8$	0.908847	−	7.94821i	0.113606	−	0.993526i
$9$	−3.00000			−0.333333
$10$	−0.109688	+	2.88889i	−0.0109688	+	0.288889i
$11$		−	19.0259i		−	1.72962i	−0.502096	−	0.864812i	$-0.667438\pi$
$11$		−	19.0259i		−	1.72962i	0.502096	−	0.864812i	$-0.332562\pi$
$12$	0.525354	−	6.90826i	0.0437795	−	0.575688i
$13$	20.2068			1.55437			0.777185	−	0.629272i	$-0.216647\pi$
$13$	20.2068			1.55437			0.777185	+	0.629272i	$0.216647\pi$
$14$	20.7557	+	0.788071i	1.48255	+	0.0562908i
$15$			2.50365i			0.166910i
$16$	15.8160	+	2.41952i	0.988500	+	0.151220i
$17$	−27.6069			−1.62394			−0.811968	−	0.583702i	$-0.801603\pi$
$17$	−27.6069			−1.62394			−0.811968	+	0.583702i	$0.801603\pi$
$18$	0.227649	−	5.99568i	0.0126472	−	0.333093i
$19$			5.26346i			0.277024i	0.990361	+	0.138512i	$0.0442320\pi$
$19$			5.26346i			0.277024i	−0.990361	+	0.138512i	$0.955768\pi$
$20$	−5.76529	−	0.438434i	−0.288264	−	0.0219217i
$21$	17.9880			0.856569
$22$	38.0243	+	1.44374i	1.72838	+	0.0656245i
$23$		−	4.79583i		−	0.208514i
$23$		−	4.79583i		−	0.208514i
$24$	13.7667	+	1.57417i	0.573612	+	0.0655904i
$25$	−22.9106			−0.916423
$26$	−1.53335	+	40.3845i	−0.0589751	+	1.55325i
$27$		−	5.19615i		−	0.192450i
$28$	−3.15001	+	41.4218i	−0.112500	+	1.47935i
$29$	1.54674			0.0533360			0.0266680	−	0.999644i	$-0.491510\pi$
$29$	1.54674			0.0533360			0.0266680	+	0.999644i	$0.491510\pi$
$30$	−5.00370	−	0.189984i	−0.166790	−	0.00633281i
$31$		−	27.7834i		−	0.896238i	−0.893974	−	0.448119i	$-0.852094\pi$
$31$		−	27.7834i		−	0.896238i	0.893974	−	0.448119i	$-0.147906\pi$
$32$	−6.03572	+	31.4256i	−0.188616	+	0.982051i
$33$	32.9538			0.998599
$34$	2.09489	−	55.1740i	0.0616145	−	1.62277i
$35$		−	15.0119i		−	0.428910i
$36$	11.9655	+	0.909939i	0.332374	+	0.0252761i
$37$	42.8386			1.15780			0.578900	−	0.815399i	$-0.303482\pi$
$37$	42.8386			1.15780			0.578900	+	0.815399i	$0.303482\pi$
$38$	−10.5193	−	0.399407i	−0.276825	−	0.0105107i
$39$			34.9992i			0.897416i
$40$	1.31372	−	11.4890i	0.0328431	−	0.287225i
$41$	36.9794			0.901937			0.450968	−	0.892540i	$-0.351079\pi$
$41$	36.9794			0.901937			0.450968	+	0.892540i	$0.351079\pi$
$42$	−1.36498	+	35.9500i	−0.0324995	+	0.855952i
$43$		−	6.35454i		−	0.147780i	−0.997266	−	0.0738900i	$-0.976459\pi$
$43$		−	6.35454i		−	0.147780i	0.997266	−	0.0738900i	$-0.0235414\pi$
$44$	−5.77079	+	75.8843i	−0.131154	+	1.72464i
$45$	−4.33645			−0.0963656
$46$	9.58476	+	0.363922i	0.208364	+	0.00791134i
$47$		−	0.999114i		−	0.0212577i	−0.999944	−	0.0106289i	$-0.996617\pi$
$47$		−	0.999114i		−	0.0212577i	0.999944	−	0.0106289i	$-0.00338334\pi$
$48$	−4.19073	+	27.3941i	−0.0873069	+	0.570711i
$49$	−58.8555			−1.20113
$50$	1.73852	−	45.7882i	0.0347704	−	0.915763i
$51$		−	47.8166i		−	0.937579i
$52$	−80.5945	−	6.12899i	−1.54989	−	0.117865i
$53$	−36.9393			−0.696968			−0.348484	−	0.937315i	$-0.613303\pi$
$53$	−36.9393			−0.696968			−0.348484	+	0.937315i	$0.613303\pi$
$54$	10.3848	+	0.394299i	0.192312	+	0.00730184i
$55$		−	27.5016i		−	0.500029i
$56$	−82.5449	−	9.43870i	−1.47402	−	0.168548i
$57$	−9.11658			−0.159940
$58$	−0.117372	+	3.09126i	−0.00202365	+	0.0532976i
$59$			41.4643i			0.702785i	0.936228	+	0.351392i	$0.114292\pi$
$59$			41.4643i			0.702785i	−0.936228	+	0.351392i	$0.885708\pi$
$60$	0.759390	−	9.98577i	0.0126565	−	0.166430i
$61$	49.1239			0.805309			0.402655	−	0.915352i	$-0.368088\pi$
$61$	49.1239			0.805309			0.402655	+	0.915352i	$0.368088\pi$
$62$	55.5268	+	2.10828i	0.895593	+	0.0340046i
$63$			31.1561i			0.494540i
$64$	−62.3480	−	14.4474i	−0.974187	−	0.225741i
$65$	29.2086			0.449363
$66$	−2.50063	+	65.8601i	−0.0378883	+	0.997880i
$67$		−	85.3226i		−	1.27347i	−0.771082	−	0.636736i	$-0.780284\pi$
$67$		−	85.3226i		−	1.27347i	0.771082	−	0.636736i	$-0.219716\pi$
$68$	110.110	+	8.37354i	1.61926	+	0.123140i
$69$	8.30662			0.120386
$70$	30.0021	+	1.13914i	0.428601	+	0.0162735i
$71$			5.34813i			0.0753258i	0.999291	+	0.0376629i	$0.0119913\pi$
$71$			5.34813i			0.0753258i	−0.999291	+	0.0376629i	$0.988009\pi$
$72$	−2.72654	+	23.8446i	−0.0378686	+	0.331175i
$73$	100.619			1.37834			0.689170	−	0.724600i	$-0.257976\pi$
$73$	100.619			1.37834			0.689170	+	0.724600i	$0.257976\pi$
$74$	−3.25072	+	85.6155i	−0.0439286	+	1.15697i
$75$		−	39.6823i		−	0.529097i
$76$	1.59648	−	20.9932i	0.0210063	−	0.276227i
$77$	−197.590			−2.56611
$78$	−69.9480	−	2.65584i	−0.896770	−	0.0340493i
$79$		−	136.777i		−	1.73135i	−0.500604	−	0.865676i	$-0.666889\pi$
$79$		−	136.777i		−	1.73135i	0.500604	−	0.865676i	$-0.333111\pi$
$80$	22.8618	+	3.49738i	0.285772	+	0.0437172i
$81$	9.00000			0.111111
$82$	−2.80611	+	73.9056i	−0.0342208	+	0.901287i
$83$			58.3493i			0.703004i	0.936187	+	0.351502i	$0.114329\pi$
$83$			58.3493i			0.703004i	−0.936187	+	0.351502i	$0.885671\pi$
$84$	−71.7447	−	5.45598i	−0.854103	−	0.0649522i
$85$	−39.9053			−0.469474
$86$	12.6999	+	0.482201i	0.147674	+	0.00560699i
$87$			2.67904i			0.0307936i
$88$	−151.221	−	17.2916i	−1.71843	−	0.196496i
$89$	−76.4726			−0.859243			−0.429621	−	0.903009i	$-0.641353\pi$
$89$	−76.4726			−0.859243			−0.429621	+	0.903009i	$0.641353\pi$
$90$	0.329063	−	8.66666i	0.00365625	−	0.0962962i
$91$		−	209.855i		−	2.30610i
$92$	−1.45464	+	19.1281i	−0.0158113	+	0.207914i
$93$	48.1222			0.517443
$94$	1.99679	+	0.0758157i	0.0212424	+	0.000806550i
$95$			7.60825i			0.0800868i
$96$	−54.4308	−	10.4542i	−0.566987	−	0.108898i
$97$	47.7398			0.492163			0.246082	−	0.969249i	$-0.420857\pi$
$97$	47.7398			0.492163			0.246082	+	0.969249i	$0.420857\pi$
$98$	4.46613	−	117.626i	0.0455727	−	1.20027i
$99$			57.0776i			0.576541i
$100$	91.3785	+	6.94908i	0.913785	+	0.0694908i
$101$	−172.054			−1.70351			−0.851754	−	0.523942i	$-0.824461\pi$
$101$	−172.054			−1.70351			−0.851754	+	0.523942i	$0.824461\pi$
$102$	95.5642	+	3.62846i	0.936904	+	0.0355731i
$103$			196.928i			1.91192i	0.293493	+	0.955961i	$0.405182\pi$
$103$			196.928i			1.91192i	−0.293493	+	0.955961i	$0.594818\pi$
$104$	18.3649	−	160.608i	0.176586	−	1.54431i
$105$	26.0013			0.247631
$106$	2.80306	−	73.8254i	0.0264440	−	0.696466i
$107$		−	160.552i		−	1.50048i	−0.661163	−	0.750242i	$-0.729937\pi$
$107$		−	160.552i		−	1.50048i	0.661163	−	0.750242i	$-0.270063\pi$
$108$	−1.57606	+	20.7248i	−0.0145932	+	0.191896i
$109$	−53.8076			−0.493648			−0.246824	−	0.969060i	$-0.579387\pi$
$109$	−53.8076			−0.493648			−0.246824	+	0.969060i	$0.579387\pi$
$110$	54.9635	+	2.08690i	0.499669	+	0.0189718i
$111$			74.1986i			0.668456i
$112$	25.1276	−	164.255i	0.224353	−	1.46656i
$113$	165.840			1.46761			0.733805	−	0.679360i	$-0.237742\pi$
$113$	165.840			1.46761			0.733805	+	0.679360i	$0.237742\pi$
$114$	0.691793	−	18.2200i	0.00606836	−	0.159825i
$115$		−	6.93230i		−	0.0602808i
$116$	−6.16917	−	0.469148i	−0.0531825	−	0.00404438i
$117$	−60.6204			−0.518123
$118$	−82.8689	−	3.14643i	−0.702279	−	0.0266647i
$119$			286.707i			2.40931i
$120$	19.8995	+	2.27544i	0.165829	+	0.0189620i
$121$	−240.983			−1.99160
$122$	−3.72766	+	98.1770i	−0.0305546	+	0.804729i
$123$			64.0502i			0.520734i
$124$	−8.42707	+	110.814i	−0.0679602	+	0.893658i
$125$	−69.2540			−0.554032
$126$	−62.2672	−	2.36421i	−0.494184	−	0.0187636i
$127$			18.4052i			0.144923i	0.997371	+	0.0724615i	$0.0230854\pi$
$127$			18.4052i			0.144923i	−0.997371	+	0.0724615i	$0.976915\pi$
$128$	33.6052	−	123.510i	0.262540	−	0.964921i
$129$	11.0064			0.0853209
$130$	−2.21644	+	58.3752i	−0.0170495	+	0.449040i
$131$			152.412i			1.16345i	0.813385	+	0.581726i	$0.197622\pi$
$131$			152.412i			1.16345i	−0.813385	+	0.581726i	$0.802378\pi$
$132$	−131.436	−	9.99531i	−0.995724	−	0.0757220i
$133$	54.6629			0.410999
$134$	170.522	+	6.47453i	1.27256	+	0.0483174i
$135$		−	7.51095i		−	0.0556367i
$136$	−25.0905	+	219.425i	−0.184489	+	1.61342i
$137$	17.3433			0.126593			0.0632967	−	0.997995i	$-0.479839\pi$
$137$	17.3433			0.126593			0.0632967	+	0.997995i	$0.479839\pi$
$138$	−0.630331	+	16.6013i	−0.00456762	+	0.120299i
$139$			114.003i			0.820166i	0.912048	+	0.410083i	$0.134500\pi$
$139$			114.003i			0.820166i	−0.912048	+	0.410083i	$0.865500\pi$
$140$	−4.55329	+	59.8745i	−0.0325235	+	0.427675i
$141$	1.73052			0.0122732
$142$	−10.6886	−	0.405832i	−0.0752716	−	0.00285797i
$143$		−	384.452i		−	2.68848i
$144$	−47.4480	−	7.25856i	−0.329500	−	0.0504066i
$145$	2.23579			0.0154193
$146$	−7.63525	+	201.093i	−0.0522962	+	1.37735i
$147$		−	101.941i		−	0.693474i
$148$	−170.861	−	12.9935i	−1.15447	−	0.0877940i
$149$	177.114			1.18869			0.594344	−	0.804211i	$-0.297412\pi$
$149$	177.114			1.18869			0.594344	+	0.804211i	$0.297412\pi$
$150$	79.3074	+	3.01121i	0.528716	+	0.0200747i
$151$			208.085i			1.37805i	0.724739	+	0.689024i	$0.241960\pi$
$151$			208.085i			1.37805i	−0.724739	+	0.689024i	$0.758040\pi$
$152$	41.8351	+	4.78368i	0.275231	+	0.0314716i
$153$	82.8207			0.541312
$154$	14.9937	−	394.896i	0.0973619	−	2.56426i
$155$		−	40.1604i		−	0.259100i
$156$	10.6157	−	139.594i	0.0680495	−	0.894832i
$157$	40.3152			0.256785			0.128392	−	0.991723i	$-0.459018\pi$
$157$	40.3152			0.256785			0.128392	+	0.991723i	$0.459018\pi$
$158$	273.357	+	10.3790i	1.73011	+	0.0656900i
$159$		−	63.9807i		−	0.402394i
$160$	−8.72453	+	45.4252i	−0.0545283	+	0.283908i
$161$	−49.8064			−0.309356
$162$	−0.682946	+	17.9870i	−0.00421572	+	0.111031i
$163$		−	37.1199i		−	0.227730i	−0.993496	−	0.113865i	$-0.963677\pi$
$163$		−	37.1199i		−	0.227730i	0.993496	−	0.113865i	$-0.0363231\pi$
$164$	−147.492	−	11.2163i	−0.899340	−	0.0683923i
$165$	47.6341			0.288692
$166$	−116.615	−	4.42772i	−0.702498	−	0.0266730i
$167$			211.568i			1.26687i	0.773795	+	0.633436i	$0.218356\pi$
$167$			211.568i			1.26687i	−0.773795	+	0.633436i	$0.781644\pi$
$168$	16.3483	−	142.972i	0.0973113	−	0.851024i
$169$	239.315			1.41607
$170$	3.02813	−	79.7532i	0.0178125	−	0.469136i
$171$		−	15.7904i		−	0.0923414i
$172$	−1.92742	+	25.3450i	−0.0112059	+	0.147355i
$173$	16.5044			0.0954012			0.0477006	−	0.998862i	$-0.484811\pi$
$173$	16.5044			0.0954012			0.0477006	+	0.998862i	$0.484811\pi$
$174$	−5.35422	−	0.203293i	−0.0307714	−	0.00116835i
$175$			237.934i			1.35962i
$176$	46.0334	−	300.913i	0.261554	−	1.70973i
$177$	−71.8183			−0.405753
$178$	5.80297	−	152.835i	0.0326009	−	0.858624i
$179$		−	72.0214i		−	0.402354i	−0.979555	−	0.201177i	$-0.935523\pi$
$179$		−	72.0214i		−	0.402354i	0.979555	−	0.201177i	$-0.0644767\pi$
$180$	17.2959	+	1.31530i	0.0960881	+	0.00730724i
$181$	296.997			1.64086			0.820432	−	0.571744i	$-0.193733\pi$
$181$	296.997			1.64086			0.820432	+	0.571744i	$0.193733\pi$
$182$	419.407	+	15.9244i	2.30444	+	0.0874967i
$183$			85.0850i			0.464945i
$184$	−38.1183	−	4.35868i	−0.207164	−	0.0236885i
$185$	61.9225			0.334716
$186$	−3.65166	+	96.1752i	−0.0196326	+	0.517071i
$187$			525.245i			2.80880i
$188$	−0.303044	+	3.98495i	−0.00161194	+	0.0211965i
$189$	−53.9639			−0.285523
$190$	−15.2055	−	0.577336i	−0.0800291	−	0.00303861i
$191$			6.55362i			0.0343121i	0.999853	+	0.0171561i	$0.00546121\pi$
$191$			6.55362i			0.0343121i	−0.999853	+	0.0171561i	$0.994539\pi$
$192$	25.0237	−	107.990i	0.130332	−	0.562447i
$193$	128.442			0.665501			0.332750	−	0.943015i	$-0.392023\pi$
$193$	128.442			0.665501			0.332750	+	0.943015i	$0.392023\pi$
$194$	−3.62264	+	95.4109i	−0.0186734	+	0.491809i
$195$			50.5908i			0.259440i
$196$	234.744	+	17.8516i	1.19767	+	0.0910798i
$197$	−226.137			−1.14791			−0.573953	−	0.818888i	$-0.694591\pi$
$197$	−226.137			−1.14791			−0.573953	+	0.818888i	$0.694591\pi$
$198$	−114.073	−	4.33121i	−0.576126	−	0.0218748i
$199$		−	187.075i		−	0.940075i	−0.882646	−	0.470037i	$-0.844240\pi$
$199$		−	187.075i		−	0.940075i	0.882646	−	0.470037i	$-0.155760\pi$
$200$	−20.8222	+	182.098i	−0.104111	+	0.910490i
$201$	147.783			0.735239
$202$	13.0560	−	343.861i	0.0646336	−	1.70228i
$203$		−	16.0635i		−	0.0791305i
$204$	−14.5034	+	190.716i	−0.0710950	+	0.934880i
$205$	53.4531			0.260747
$206$	−393.572	−	14.9435i	−1.91055	−	0.0725411i
$207$			14.3875i			0.0695048i
$208$	319.591	+	48.8908i	1.53650	+	0.235052i
$209$	100.142			0.479148
$210$	−1.97305	+	51.9651i	−0.00939550	+	0.247453i
$211$			116.404i			0.551680i	0.961204	+	0.275840i	$0.0889560\pi$
$211$			116.404i			0.551680i	−0.961204	+	0.275840i	$0.911044\pi$
$212$	147.332	+	11.2042i	0.694961	+	0.0528499i
$213$	−9.26324			−0.0434894
$214$	320.873	+	12.1831i	1.49940	+	0.0569306i
$215$		−	9.18539i		−	0.0427227i
$216$	−41.3001	−	4.72251i	−0.191204	−	0.0218635i
$217$	−288.540			−1.32968
$218$	4.08308	−	107.538i	0.0187297	−	0.493292i
$219$			174.277i			0.795784i
$220$	−8.34159	+	109.690i	−0.0379163	+	0.498589i
$221$	−557.847			−2.52420
$222$	−148.290	−	5.63041i	−0.667975	−	0.0253622i
$223$		−	388.945i		−	1.74415i	−0.489373	−	0.872074i	$-0.662774\pi$
$223$		−	388.945i		−	1.74415i	0.489373	−	0.872074i	$-0.337226\pi$
$224$	326.366	+	62.6831i	1.45699	+	0.279835i
$225$	68.7317			0.305474
$226$	−12.5844	+	331.441i	−0.0556833	+	1.46655i
$227$			41.9888i			0.184973i	0.995714	+	0.0924864i	$0.0294815\pi$
$227$			41.9888i			0.184973i	−0.995714	+	0.0924864i	$0.970519\pi$
$228$	36.3613	+	2.76518i	0.159480	+	0.0121280i
$229$	10.2438			0.0447327			0.0223664	−	0.999750i	$-0.492880\pi$
$229$	10.2438			0.0447327			0.0223664	+	0.999750i	$0.492880\pi$
$230$	13.8546	+	0.526043i	0.0602374	+	0.00228714i
$231$		−	342.236i		−	1.48154i
$232$	1.40575	−	12.2938i	0.00605929	−	0.0529907i
$233$	272.456			1.16934			0.584671	−	0.811271i	$-0.301224\pi$
$233$	272.456			1.16934			0.584671	+	0.811271i	$0.301224\pi$
$234$	4.60006	−	121.154i	0.0196584	−	0.517750i
$235$		−	1.44420i		−	0.00614554i
$236$	12.5767	−	165.380i	0.0532910	−	0.700761i
$237$	236.904			0.999597
$238$	−573.002	−	21.7562i	−2.40757	−	0.0914126i
$239$		−	75.0354i		−	0.313955i	−0.987602	−	0.156978i	$-0.949825\pi$
$239$		−	75.0354i		−	0.313955i	0.987602	−	0.156978i	$-0.0501751\pi$
$240$	−6.05763	+	39.5978i	−0.0252401	+	0.164991i
$241$	252.898			1.04937			0.524685	−	0.851296i	$-0.324183\pi$
$241$	252.898			1.04937			0.524685	+	0.851296i	$0.324183\pi$
$242$	18.2865	−	481.620i	0.0755642	−	1.99016i
$243$			15.5885i			0.0641500i
$244$	−195.930	−	14.8999i	−0.802991	−	0.0610652i
$245$	−85.0747			−0.347244
$246$	−128.008	−	4.86032i	−0.520359	−	0.0197574i
$247$			106.358i			0.430598i
$248$	−220.828	−	25.2509i	−0.890436	−	0.101818i
$249$	−101.064			−0.405879
$250$	5.25519	−	138.408i	0.0210208	−	0.553633i
$251$			251.991i			1.00395i	0.864883	+	0.501974i	$0.167393\pi$
$251$			251.991i			1.00395i	−0.864883	+	0.501974i	$0.832607\pi$
$252$	9.45004	−	124.265i	0.0375002	−	0.493117i
$253$	−91.2448			−0.360652
$254$	−36.7839	−	1.39664i	−0.144819	−	0.00549859i
$255$		−	69.1180i		−	0.271051i
$256$	244.292	+	76.5342i	0.954265	+	0.298962i
$257$	−409.405			−1.59302			−0.796509	−	0.604627i	$-0.793322\pi$
$257$	−409.405			−1.59302			−0.796509	+	0.604627i	$0.793322\pi$
$258$	−0.835197	+	21.9969i	−0.00323720	+	0.0852594i
$259$		−	444.894i		−	1.71774i
$260$	−116.498	−	8.85936i	−0.448070	−	0.0340745i
$261$	−4.64023			−0.0177787
$262$	−304.605	−	11.5655i	−1.16261	−	0.0441430i
$263$			158.053i			0.600962i	0.953788	+	0.300481i	$0.0971471\pi$
$263$			158.053i			0.600962i	−0.953788	+	0.300481i	$0.902853\pi$
$264$	29.9499	−	261.923i	0.113447	−	0.992134i
$265$	−53.3951			−0.201491
$266$	−4.14798	+	109.247i	−0.0155939	+	0.410703i
$267$		−	132.454i		−	0.496084i
$268$	−25.8795	+	340.308i	−0.0965652	+	1.26981i
$269$	427.662			1.58982			0.794911	−	0.606726i	$-0.207517\pi$
$269$	427.662			1.58982			0.794911	+	0.606726i	$0.207517\pi$
$270$	15.0111	+	0.569953i	0.0555966	+	0.00211094i
$271$			304.015i			1.12183i	0.827874	+	0.560914i	$0.189550\pi$
$271$			304.015i			1.12183i	−0.827874	+	0.560914i	$0.810450\pi$
$272$	−436.631	−	66.7954i	−1.60526	−	0.245571i
$273$	363.479			1.33143
$274$	−1.31606	+	34.6616i	−0.00480314	+	0.126502i
$275$			435.893i			1.58507i
$276$	−33.1308	−	2.51951i	−0.120039	−	0.00912865i
$277$	−187.916			−0.678398			−0.339199	−	0.940715i	$-0.610156\pi$
$277$	−187.916			−0.678398			−0.339199	+	0.940715i	$0.610156\pi$
$278$	−227.842	−	8.65089i	−0.819576	−	0.0311183i
$279$			83.3502i			0.298746i
$280$	−119.317	−	13.6435i	−0.426133	−	0.0487267i
$281$	57.7947			0.205675			0.102837	−	0.994698i	$-0.467208\pi$
$281$	57.7947			0.205675			0.102837	+	0.994698i	$0.467208\pi$
$282$	−0.131317	+	3.45854i	−0.000465662	+	0.0122643i
$283$		−	159.311i		−	0.562935i	−0.959571	−	0.281468i	$-0.909179\pi$
$283$		−	159.311i		−	0.562935i	0.959571	−	0.281468i	$-0.0908212\pi$
$284$	1.62216	−	21.3309i	0.00571183	−	0.0751090i
$285$	−13.1779			−0.0462381
$286$	768.350	+	29.1733i	2.68654	+	0.102005i
$287$		−	384.044i		−	1.33813i
$288$	18.1072	−	94.2769i	0.0628721	−	0.327350i
$289$	473.141			1.63717
$290$	−0.169659	+	4.46837i	−0.000585030	+	0.0154082i
$291$			82.6878i			0.284151i
$292$	−401.316	−	30.5190i	−1.37437	−	0.104517i
$293$	−42.9966			−0.146746			−0.0733731	−	0.997305i	$-0.523376\pi$
$293$	−42.9966			−0.146746			−0.0733731	+	0.997305i	$0.523376\pi$
$294$	203.735	+	7.73556i	0.692975	+	0.0263114i
$295$			59.9359i			0.203173i
$296$	38.9337	−	340.490i	0.131533	−	1.15030i
$297$	−98.8613			−0.332866
$298$	−13.4400	+	353.974i	−0.0451006	+	1.18783i
$299$		−	96.9085i		−	0.324109i
$300$	−12.0362	+	158.272i	−0.0401205	+	0.527574i
$301$	−65.9942			−0.219250
$302$	−415.871	−	15.7901i	−1.37705	−	0.0522851i
$303$		−	298.007i		−	0.983521i
$304$	−12.7350	+	83.2469i	−0.0418916	+	0.273838i
$305$	71.0077			0.232812
$306$	−6.28468	+	165.522i	−0.0205382	+	0.540922i
$307$		−	137.871i		−	0.449091i	−0.974464	−	0.224546i	$-0.927910\pi$
$307$		−	137.871i		−	0.449091i	0.974464	−	0.224546i	$-0.0720898\pi$
$308$	788.085	+	59.9317i	2.55872	+	0.194584i
$309$	−341.089			−1.10385
$310$	80.2630	+	3.04749i	0.258913	+	0.00983062i
$311$		−	171.383i		−	0.551071i	−0.961291	−	0.275535i	$-0.911145\pi$
$311$		−	171.383i		−	0.551071i	0.961291	−	0.275535i	$-0.0888551\pi$
$312$	278.181	+	31.8090i	0.891606	+	0.101952i
$313$	−226.654			−0.724135			−0.362068	−	0.932152i	$-0.617929\pi$
$313$	−226.654			−0.724135			−0.362068	+	0.932152i	$0.617929\pi$
$314$	−3.05923	+	80.5723i	−0.00974279	+	0.256600i
$315$			45.0356i			0.142970i
$316$	−41.4862	+	545.532i	−0.131285	+	1.72637i
$317$	−358.933			−1.13228			−0.566140	−	0.824309i	$-0.691564\pi$
$317$	−358.933			−1.13228			−0.566140	+	0.824309i	$0.691564\pi$
$318$	127.869	+	4.85504i	0.402105	+	0.0152674i
$319$		−	29.4282i		−	0.0922513i
$320$	−90.1230	−	20.8835i	−0.281634	−	0.0652609i
$321$	278.084			0.866305
$322$	3.77945	−	99.5411i	0.0117374	−	0.309134i
$323$		−	145.308i		−	0.449869i
$324$	−35.8964	−	2.72982i	−0.110791	−	0.00842537i
$325$	−462.950			−1.42446
$326$	74.1864	+	2.81677i	0.227566	+	0.00864039i
$327$		−	93.1975i		−	0.285008i
$328$	33.6086	−	293.920i	0.102465	−	0.896098i
$329$	−10.3761			−0.0315384
$330$	−3.61462	+	95.1996i	−0.0109534	+	0.288484i
$331$			339.163i			1.02466i	0.858788	+	0.512331i	$0.171218\pi$
$331$			339.163i			1.02466i	−0.858788	+	0.512331i	$0.828782\pi$
$332$	17.6981	−	232.725i	0.0533076	−	0.700980i
$333$	−128.516			−0.385933
$334$	−422.830	−	16.0544i	−1.26596	−	0.0480670i
$335$		−	123.332i		−	0.368157i
$336$	284.498	+	43.5222i	0.846719	+	0.129530i
$337$	−265.196			−0.786931			−0.393465	−	0.919339i	$-0.628724\pi$
$337$	−265.196			−0.786931			−0.393465	+	0.919339i	$0.628724\pi$
$338$	−18.1599	+	478.286i	−0.0537276	+	1.41505i
$339$			287.243i			0.847326i
$340$	159.162	+	12.1038i	0.468123	+	0.0355994i
$341$	−528.603			−1.55016
$342$	31.5580	+	1.19822i	0.0922749	+	0.00350357i
$343$			102.353i			0.298405i
$344$	−50.5072	−	5.77531i	−0.146823	−	0.0167887i
$345$	12.0071			0.0348032
$346$	−1.25240	+	32.9850i	−0.00361966	+	0.0953325i
$347$		−	587.088i		−	1.69190i	−0.533266	−	0.845948i	$-0.679036\pi$
$347$		−	587.088i		−	1.69190i	0.533266	−	0.845948i	$-0.320964\pi$
$348$	0.812588	−	10.6853i	0.00233502	−	0.0307049i
$349$	−153.866			−0.440877			−0.220438	−	0.975401i	$-0.570749\pi$
$349$	−153.866			−0.440877			−0.220438	+	0.975401i	$0.570749\pi$
$350$	−475.526	−	18.0552i	−1.35865	−	0.0515862i
$351$		−	104.998i		−	0.299139i
$352$	597.900	+	114.835i	1.69858	+	0.326235i
$353$	−316.498			−0.896595			−0.448297	−	0.893884i	$-0.647969\pi$
$353$	−316.498			−0.896595			−0.448297	+	0.893884i	$0.647969\pi$
$354$	5.44978	−	143.533i	0.0153949	−	0.405461i
$355$			7.73064i			0.0217764i
$356$	305.010	+	23.1951i	0.856769	+	0.0651549i
$357$	−496.592			−1.39101
$358$	143.939	+	5.46520i	0.402064	+	0.0152659i
$359$			137.500i			0.383008i	0.981492	+	0.191504i	$0.0613366\pi$
$359$			137.500i			0.383008i	−0.981492	+	0.191504i	$0.938663\pi$
$360$	−3.94117	+	34.4670i	−0.0109477	+	0.0957417i
$361$	333.296			0.923258
$362$	−22.5370	+	593.565i	−0.0622568	+	1.63968i
$363$		−	417.396i		−	1.14985i
$364$	−63.6517	+	837.002i	−0.174867	+	2.29946i
$365$	145.443			0.398473
$366$	−170.048	−	6.45650i	−0.464611	−	0.0176407i
$367$			290.884i			0.792601i	0.918121	+	0.396300i	$0.129706\pi$
$367$			290.884i			0.792601i	−0.918121	+	0.396300i	$0.870294\pi$
$368$	11.6036	−	75.8509i	0.0315315	−	0.206117i
$369$	−110.938			−0.300646
$370$	−4.69886	+	123.756i	−0.0126996	+	0.334475i
$371$			383.627i			1.03404i
$372$	−191.935	−	14.5961i	−0.515954	−	0.0392368i
$373$	−116.006			−0.311008			−0.155504	−	0.987835i	$-0.549700\pi$
$373$	−116.006			−0.311008			−0.155504	+	0.987835i	$0.549700\pi$
$374$	−1049.73	−	39.8571i	−2.80677	−	0.106570i
$375$		−	119.951i		−	0.319870i
$376$	−7.94116	−	0.908042i	−0.0211201	−	0.00241500i
$377$	31.2548			0.0829039
$378$	4.09494	−	107.850i	0.0108332	−	0.285317i
$379$			236.473i			0.623939i	0.950092	+	0.311970i	$0.100989\pi$
$379$			236.473i			0.623939i	−0.950092	+	0.311970i	$0.899011\pi$
$380$	2.30768	−	30.3454i	0.00607284	−	0.0798562i
$381$	−31.8788			−0.0836713
$382$	−13.0978	−	0.497308i	−0.0342874	−	0.00130185i
$383$		−	212.752i		−	0.555489i	−0.960655	−	0.277745i	$-0.910413\pi$
$383$		−	212.752i		−	0.555489i	0.960655	−	0.277745i	$-0.0895869\pi$
$384$	213.925	+	58.2059i	0.557097	+	0.151578i
$385$	−285.613			−0.741853
$386$	−9.74653	+	256.698i	−0.0252501	+	0.665021i
$387$			19.0636i			0.0492600i
$388$	−190.410	−	14.4801i	−0.490746	−	0.0373199i
$389$	343.786			0.883769			0.441884	−	0.897072i	$-0.354310\pi$
$389$	343.786			0.883769			0.441884	+	0.897072i	$0.354310\pi$
$390$	−101.109	−	3.83898i	−0.259253	−	0.00984353i
$391$			132.398i			0.338614i
$392$	−53.4907	+	467.796i	−0.136456	+	1.19336i
$393$	−263.986			−0.671719
$394$	17.1600	−	451.949i	0.0435532	−	1.14708i
$395$		−	197.709i		−	0.500528i
$396$	17.3124	−	227.653i	0.0437181	−	0.574881i
$397$	475.637			1.19808			0.599039	−	0.800720i	$-0.295550\pi$
$397$	475.637			1.19808			0.599039	+	0.800720i	$0.295550\pi$
$398$	373.880	+	14.1958i	0.939398	+	0.0356678i
$399$			94.6789i			0.237290i
$400$	−362.354	−	55.4326i	−0.905884	−	0.138581i
$401$	293.540			0.732021			0.366010	−	0.930611i	$-0.380723\pi$
$401$	293.540			0.732021			0.366010	+	0.930611i	$0.380723\pi$
$402$	−11.2142	+	295.353i	−0.0278961	+	0.734710i
$403$		−	561.414i		−	1.39309i
$404$	686.236	+	52.1863i	1.69860	+	0.129174i
$405$	13.0094			0.0321219
$406$	32.1038	+	1.21894i	0.0790735	+	0.00300233i
$407$		−	815.041i		−	2.00256i
$408$	−380.056	−	43.4579i	−0.931509	−	0.106515i
$409$	481.840			1.17809			0.589047	−	0.808099i	$-0.299503\pi$
$409$	481.840			1.17809			0.589047	+	0.808099i	$0.299503\pi$
$410$	−4.05618	+	106.829i	−0.00989312	+	0.260559i
$411$			30.0395i			0.0730887i
$412$	59.7309	−	785.444i	0.144978	−	1.90642i
$413$	430.621			1.04267
$414$	−28.7543	−	1.09177i	−0.0694548	−	0.00263711i
$415$			84.3430i			0.203236i
$416$	−121.963	+	635.012i	−0.293179	+	1.52647i
$417$	−197.459			−0.473523
$418$	−7.59906	+	200.140i	−0.0181796	+	0.478803i
$419$			49.3476i			0.117775i	0.998265	+	0.0588873i	$0.0187553\pi$
$419$			49.3476i			0.117775i	−0.998265	+	0.0588873i	$0.981245\pi$
$420$	−103.706	−	7.88653i	−0.246918	−	0.0187775i
$421$	−714.534			−1.69723			−0.848615	−	0.529010i	$-0.822563\pi$
$421$	−714.534			−1.69723			−0.848615	+	0.529010i	$0.822563\pi$
$422$	−232.641	−	8.83311i	−0.551283	−	0.0209315i
$423$			2.99734i			0.00708591i
$424$	−33.5722	+	293.601i	−0.0791796	+	0.692455i
$425$	632.490			1.48821
$426$	0.702922	−	18.5131i	0.00165005	−	0.0434581i
$427$		−	510.168i		−	1.19477i
$428$	−48.6975	+	640.359i	−0.113779	+	1.49616i
$429$	665.890			1.55219
$430$	18.3575	+	0.697014i	0.0426920	+	0.00162096i
$431$			580.388i			1.34661i	0.739366	+	0.673304i	$0.235126\pi$
$431$			580.388i			1.34661i	−0.739366	+	0.673304i	$0.764874\pi$
$432$	12.5722	−	82.1824i	0.0291023	−	0.190237i
$433$	725.100			1.67460			0.837298	−	0.546747i	$-0.184134\pi$
$433$	725.100			1.67460			0.837298	+	0.546747i	$0.184134\pi$
$434$	21.8953	−	576.665i	0.0504499	−	1.32872i
$435$			3.87251i			0.00890232i
$436$	214.611	+	16.3206i	0.492227	+	0.0374325i
$437$	25.2427			0.0577635
$438$	−348.303	−	13.2246i	−0.795211	−	0.0301932i
$439$			574.926i			1.30963i	0.755791	+	0.654813i	$0.227253\pi$
$439$			574.926i			1.30963i	−0.755791	+	0.654813i	$0.772747\pi$
$440$	−218.588	−	24.9947i	−0.496791	−	0.0568062i
$441$	176.566			0.400378
$442$	42.3311	−	1114.89i	0.0957717	−	2.52238i
$443$		−	443.805i		−	1.00182i	−0.865500	−	0.500909i	$-0.832999\pi$
$443$		−	443.805i		−	1.00182i	0.865500	−	0.500909i	$-0.167001\pi$
$444$	22.5054	−	295.940i	0.0506879	−	0.666531i
$445$	−110.540			−0.248404
$446$	777.330	+	29.5143i	1.74289	+	0.0661756i
$447$			306.771i			0.686289i
$448$	−150.041	+	647.506i	−0.334914	+	1.44533i
$449$	247.515			0.551258			0.275629	−	0.961264i	$-0.411114\pi$
$449$	247.515			0.551258			0.275629	+	0.961264i	$0.411114\pi$
$450$	−5.21557	+	137.364i	−0.0115901	+	0.305254i
$451$		−	703.565i		−	1.56001i
$452$	−661.450	−	50.3015i	−1.46339	−	0.111286i
$453$	−360.414			−0.795616
$454$	−83.9172	−	3.18623i	−0.184840	−	0.00701814i
$455$		−	303.342i		−	0.666685i
$456$	−8.28558	+	72.4605i	−0.0181701	+	0.158905i
$457$	140.398			0.307218			0.153609	−	0.988132i	$-0.450910\pi$
$457$	140.398			0.307218			0.153609	+	0.988132i	$0.450910\pi$
$458$	−0.777329	+	20.4728i	−0.00169722	+	0.0447005i
$459$			143.450i			0.312526i
$460$	−2.10266	+	27.6493i	−0.00457099	+	0.0601073i
$461$	466.948			1.01290			0.506451	−	0.862269i	$-0.330957\pi$
$461$	466.948			1.01290			0.506451	+	0.862269i	$0.330957\pi$
$462$	683.980	+	25.9699i	1.48048	+	0.0562119i
$463$			67.1091i			0.144944i	0.997370	+	0.0724721i	$0.0230888\pi$
$463$			67.1091i			0.144944i	−0.997370	+	0.0724721i	$0.976911\pi$
$464$	24.4633	+	3.74238i	0.0527227	+	0.00806547i
$465$	69.5599			0.149591
$466$	−20.6748	+	544.521i	−0.0443665	+	1.16850i
$467$		−	624.347i		−	1.33693i	−0.743743	−	0.668466i	$-0.766951\pi$
$467$		−	624.347i		−	1.33693i	0.743743	−	0.668466i	$-0.233049\pi$
$468$	241.784	+	18.3870i	0.516632	+	0.0392884i
$469$	−886.105			−1.88935
$470$	2.88633	+	0.109590i	0.00614112	+	0.000233171i
$471$			69.8280i			0.148255i
$472$	329.567	+	37.6847i	0.698235	+	0.0798405i
$473$	−120.901			−0.255604
$474$	−17.9770	+	473.468i	−0.0379262	+	0.998877i
$475$		−	120.589i		−	0.253871i
$476$	86.9621	−	1143.53i	0.182693	−	2.40237i
$477$	110.818			0.232323
$478$	149.963	+	5.69390i	0.313729	+	0.0119119i
$479$		−	107.202i		−	0.223804i	−0.993719	−	0.111902i	$-0.964306\pi$
$479$		−	107.202i		−	0.223804i	0.993719	−	0.111902i	$-0.0356942\pi$
$480$	−78.6788	−	15.1113i	−0.163914	−	0.0314819i
$481$	865.631			1.79965
$482$	−19.1907	+	505.432i	−0.0398146	+	1.04861i
$483$		−	86.2672i		−	0.178607i
$484$	961.159	+	73.0935i	1.98586	+	0.151020i
$485$	69.0071			0.142283
$486$	−31.1545	−	1.18290i	−0.0641038	−	0.00243395i
$487$			237.798i			0.488292i	0.969739	+	0.244146i	$0.0785075\pi$
$487$			237.798i			0.488292i	−0.969739	+	0.244146i	$0.921492\pi$
$488$	44.6461	−	390.447i	0.0914879	−	0.800096i
$489$	64.2936			0.131480
$490$	6.45571	−	170.027i	0.0131749	−	0.346993i
$491$			557.173i			1.13477i	0.823452	+	0.567385i	$0.192045\pi$
$491$			557.173i			1.13477i	−0.823452	+	0.567385i	$0.807955\pi$
$492$	19.4273	−	255.463i	0.0394863	−	0.519234i
$493$	−42.7008			−0.0866143
$494$	−212.562	−	8.07074i	−0.430288	−	0.0163375i
$495$			82.5047i			0.166676i
$496$	67.2224	−	439.422i	0.135529	−	0.885932i
$497$	55.5422			0.111755
$498$	7.66903	−	201.982i	0.0153997	−	0.405587i
$499$		−	496.785i		−	0.995561i	−0.867303	−	0.497781i	$-0.834148\pi$
$499$		−	496.785i		−	0.995561i	0.867303	−	0.497781i	$-0.165852\pi$
$500$	276.218	+	21.0056i	0.552437	+	0.0420113i
$501$	−366.446			−0.731429
$502$	−503.619	−	19.1218i	−1.00322	−	0.0380912i
$503$		−	251.401i		−	0.499804i	−0.968271	−	0.249902i	$-0.919602\pi$
$503$		−	251.401i		−	0.499804i	0.968271	−	0.249902i	$-0.0803983\pi$
$504$	247.635	+	28.3161i	0.491339	+	0.0561827i
$505$	−248.702			−0.492479
$506$	6.92393	−	182.358i	0.0136836	−	0.360392i
$507$			414.506i			0.817566i
$508$	5.58254	−	73.4089i	0.0109893	−	0.144506i
$509$	611.634			1.20164			0.600820	−	0.799385i	$-0.294841\pi$
$509$	611.634			1.20164			0.600820	+	0.799385i	$0.294841\pi$
$510$	138.137	+	5.24488i	0.270856	+	0.0102841i
$511$		−	1044.96i		−	2.04493i
$512$	−171.496	+	482.424i	−0.334953	+	0.942235i
$513$	27.3497			0.0533133
$514$	31.0669	−	818.221i	0.0604414	−	1.59187i
$515$			284.656i			0.552730i
$516$	−43.8988	−	3.33838i	−0.0850752	−	0.00646974i
$517$	−19.0090			−0.0367679
$518$	889.147	+	33.7598i	1.71650	+	0.0651734i
$519$			28.5865i			0.0550799i
$520$	26.5462	−	232.156i	0.0510503	−	0.446454i
$521$	−107.916			−0.207133			−0.103567	−	0.994623i	$-0.533025\pi$
$521$	−107.916			−0.207133			−0.103567	+	0.994623i	$0.533025\pi$
$522$	0.352115	−	9.27379i	0.000674549	−	0.0177659i
$523$		−	569.689i		−	1.08927i	−0.838672	−	0.544636i	$-0.816668\pi$
$523$		−	569.689i		−	1.08927i	0.838672	−	0.544636i	$-0.183332\pi$
$524$	46.2286	−	607.893i	0.0882225	−	1.16010i
$525$	−412.114			−0.784980
$526$	−315.878	−	11.9935i	−0.600529	−	0.0228014i
$527$			767.013i			1.45543i
$528$	521.197	+	79.7323i	0.987115	+	0.151008i
$529$	−23.0000			−0.0434783
$530$	4.05178	−	106.713i	0.00764486	−	0.201346i
$531$		−	124.393i		−	0.234262i
$532$	−218.022	−	16.5800i	−0.409816	−	0.0311654i
$533$	747.236			1.40194
$534$	264.718	+	10.0510i	0.495727	+	0.0188222i
$535$		−	232.075i		−	0.433785i
$536$	−678.162	−	77.5453i	−1.26523	−	0.144674i
$537$	124.745			0.232299
$538$	−32.4523	+	854.708i	−0.0603202	+	1.58868i
$539$			1119.78i			2.07751i
$540$	−2.27817	+	29.9573i	−0.00421884	+	0.0554765i
$541$	−881.063			−1.62858			−0.814291	−	0.580457i	$-0.802874\pi$
$541$	−881.063			−1.62858			−0.814291	+	0.580457i	$0.802874\pi$
$542$	−607.593	−	23.0696i	−1.12102	−	0.0425638i
$543$			514.413i			0.947354i
$544$	166.627	−	867.564i	0.306301	−	1.59479i
$545$	−77.7780			−0.142712
$546$	−27.5819	+	726.435i	−0.0505162	+	1.33047i
$547$		−	476.107i		−	0.870396i	−0.900335	−	0.435198i	$-0.856678\pi$
$547$		−	476.107i		−	0.870396i	0.900335	−	0.435198i	$-0.143322\pi$
$548$	−69.1734	−	5.26045i	−0.126229	−	0.00959936i
$549$	−147.372			−0.268436
$550$	−871.159	−	33.0769i	−1.58393	−	0.0601398i
$551$			8.14123i			0.0147754i
$552$	7.54945	−	66.0228i	0.0136765	−	0.119606i
$553$	−1420.48			−2.56867
$554$	14.2596	−	375.562i	0.0257394	−	0.677910i
$555$			107.253i			0.193248i
$556$	34.5786	−	454.700i	0.0621918	−	0.817805i
$557$	241.426			0.433440			0.216720	−	0.976234i	$-0.430464\pi$
$557$	241.426			0.433440			0.216720	+	0.976234i	$0.430464\pi$
$558$	−166.580	−	6.32485i	−0.298531	−	0.0113349i
$559$		−	128.405i		−	0.229705i
$560$	36.3215	−	237.428i	0.0648598	−	0.423978i
$561$	−909.751			−1.62166
$562$	−4.38563	+	115.506i	−0.00780361	+	0.205527i
$563$			991.134i			1.76045i	0.474555	+	0.880226i	$0.342609\pi$
$563$			991.134i			1.76045i	−0.474555	+	0.880226i	$0.657391\pi$
$564$	−6.90213	−	0.524888i	−0.0122378	−	0.000930653i
$565$	239.719			0.424282
$566$	318.392	+	12.0890i	0.562530	+	0.0213586i
$567$		−	93.4682i		−	0.164847i
$568$	42.5081	+	4.86064i	0.0748382	+	0.00855746i
$569$	903.207			1.58736			0.793679	−	0.608337i	$-0.208163\pi$
$569$	903.207			1.58736			0.793679	+	0.608337i	$0.208163\pi$
$570$	0.999975	−	26.3368i	0.00175434	−	0.0462048i
$571$			508.809i			0.891085i	0.895261	+	0.445542i	$0.146989\pi$
$571$			508.809i			0.891085i	−0.895261	+	0.445542i	$0.853011\pi$
$572$	−116.609	+	1533.38i	−0.203863	+	2.68074i
$573$	−11.3512			−0.0198101
$574$	767.535	+	29.1424i	1.33717	+	0.0507707i
$575$			109.875i			0.191087i
$576$	187.044	+	43.3422i	0.324729	+	0.0752469i
$577$	479.819			0.831576			0.415788	−	0.909462i	$-0.363506\pi$
$577$	479.819			0.831576			0.415788	+	0.909462i	$0.363506\pi$
$578$	−35.9033	+	945.600i	−0.0621165	+	1.63599i
$579$			222.467i			0.384227i
$580$	−8.91743	−	0.678146i	−0.0153749	−	0.00116922i
$581$	605.978			1.04299
$582$	−165.257	−	6.27459i	−0.283946	−	0.0107811i
$583$			702.802i			1.20549i
$584$	91.4471	−	799.739i	0.156587	−	1.36942i
$585$	−87.6258			−0.149788
$586$	3.26271	−	85.9313i	0.00556776	−	0.146640i
$587$		−	313.927i		−	0.534799i	−0.963586	−	0.267400i	$-0.913836\pi$
$587$		−	313.927i		−	0.534799i	0.963586	−	0.267400i	$-0.0861644\pi$
$588$	−30.9200	+	406.589i	−0.0525850	+	0.691478i
$589$	146.237			0.248280
$590$	−119.786	−	4.54812i	−0.203026	−	0.00770867i
$591$		−	391.682i		−	0.662744i
$592$	677.535	+	103.649i	1.14449	+	0.175082i
$593$	478.213			0.806430			0.403215	−	0.915105i	$-0.367893\pi$
$593$	478.213			0.806430			0.403215	+	0.915105i	$0.367893\pi$
$594$	7.50188	−	197.580i	0.0126294	−	0.332627i
$595$			414.431i			0.696522i
$596$	−706.418	−	53.7211i	−1.18527	−	0.0901362i
$597$	324.023			0.542753
$598$	193.677	+	7.35370i	0.323875	+	0.0122972i
$599$			81.5265i			0.136104i	0.997682	+	0.0680522i	$0.0216784\pi$
$599$			81.5265i			0.136104i	−0.997682	+	0.0680522i	$0.978322\pi$
$600$	−315.403	−	36.0651i	−0.525672	−	0.0601086i
$601$	−566.865			−0.943203			−0.471601	−	0.881812i	$-0.656324\pi$
$601$	−566.865			−0.943203			−0.471601	+	0.881812i	$0.656324\pi$
$602$	5.00783	−	131.893i	0.00831865	−	0.219092i
$603$			255.968i			0.424491i
$604$	63.1149	−	829.944i	0.104495	−	1.37408i
$605$	−348.338			−0.575765
$606$	595.584	+	22.6136i	0.982812	+	0.0373162i
$607$		−	176.145i		−	0.290190i	−0.989418	−	0.145095i	$-0.953651\pi$
$607$		−	176.145i		−	0.290190i	0.989418	−	0.145095i	$-0.0463487\pi$
$608$	−165.408	−	31.7688i	−0.272052	−	0.0522513i
$609$	27.8228			0.0456860
$610$	−5.38827	+	141.913i	−0.00883324	+	0.232645i
$611$		−	20.1889i		−	0.0330424i
$612$	−330.329	−	25.1206i	−0.539753	−	0.0410467i
$613$	601.868			0.981841			0.490920	−	0.871204i	$-0.336661\pi$
$613$	601.868			0.981841			0.490920	+	0.871204i	$0.336661\pi$
$614$	275.543	+	10.4621i	0.448768	+	0.0170392i
$615$			92.5835i			0.150542i
$616$	−179.579	+	1570.49i	−0.291525	+	2.54949i
$617$	882.213			1.42984			0.714922	−	0.699205i	$-0.246462\pi$
$617$	882.213			1.42984			0.714922	+	0.699205i	$0.246462\pi$
$618$	25.8829	−	681.687i	0.0418816	−	1.10305i
$619$			374.977i			0.605779i	0.953026	+	0.302889i	$0.0979513\pi$
$619$			374.977i			0.605779i	−0.953026	+	0.302889i	$0.902049\pi$
$620$	−12.1812	+	160.179i	−0.0196471	+	0.258354i
$621$	−24.9199			−0.0401286
$622$	342.519	+	13.0050i	0.550674	+	0.0209084i
$623$			794.195i			1.27479i
$624$	−84.6813	+	553.548i	−0.135707	+	0.887096i
$625$	472.659			0.756254
$626$	17.1992	−	452.982i	0.0274748	−	0.723614i
$627$			173.451i			0.276636i
$628$	−160.796	−	12.2281i	−0.256045	−	0.0194715i
$629$	−1182.64			−1.88019
$630$	−90.0063	−	3.41743i	−0.142867	−	0.00542449i
$631$			518.746i			0.822101i	0.911613	+	0.411050i	$0.134838\pi$
$631$			518.746i			0.822101i	−0.911613	+	0.411050i	$0.865162\pi$
$632$	−1087.13	−	124.309i	−1.72014	−	0.196692i
$633$	−201.618			−0.318512
$634$	27.2369	−	717.349i	0.0429604	−	1.13147i
$635$			26.6044i			0.0418967i
$636$	−19.4062	+	255.186i	−0.0305129	+	0.401236i
$637$	−1189.28			−1.86700
$638$	58.8139	+	2.23309i	0.0921848	+	0.00350015i
$639$		−	16.0444i		−	0.0251086i
$640$	48.5757	−	178.532i	0.0758996	−	0.278956i
$641$	−548.751			−0.856087			−0.428043	−	0.903758i	$-0.640797\pi$
$641$	−548.751			−0.856087			−0.428043	+	0.903758i	$0.640797\pi$
$642$	−21.1018	+	555.768i	−0.0328689	+	0.865682i
$643$			718.325i			1.11715i	0.829455	+	0.558573i	$0.188651\pi$
$643$			718.325i			1.11715i	−0.829455	+	0.558573i	$0.811349\pi$
$644$	198.652	+	15.1069i	0.308466	+	0.0234580i
$645$	15.9096			0.0246660
$646$	290.406	+	11.0264i	0.449545	+	0.0170687i
$647$		−	85.7707i		−	0.132567i	−0.997801	−	0.0662833i	$-0.978886\pi$
$647$		−	85.7707i		−	0.132567i	0.997801	−	0.0662833i	$-0.0211141\pi$
$648$	8.17963	−	71.5339i	0.0126229	−	0.110392i
$649$	788.894			1.21555
$650$	35.1300	−	925.233i	0.0540461	−	1.42343i
$651$		−	499.766i		−	0.767690i
$652$	−11.2590	+	148.052i	−0.0172683	+	0.227074i
$653$	−489.690			−0.749908			−0.374954	−	0.927043i	$-0.622341\pi$
$653$	−489.690			−0.749908			−0.374954	+	0.927043i	$0.622341\pi$
$654$	186.261	+	7.07210i	0.284803	+	0.0108136i
$655$			220.309i			0.336350i
$656$	584.866	+	89.4724i	0.891565	+	0.136391i
$657$	−301.856			−0.459446
$658$	0.787372	−	20.7373i	0.00119661	−	0.0315157i
$659$			123.275i			0.187063i	0.995616	+	0.0935315i	$0.0298156\pi$
$659$			123.275i			0.187063i	−0.995616	+	0.0935315i	$0.970184\pi$
$660$	−189.988	−	14.4481i	−0.287860	−	0.0218910i
$661$	−181.684			−0.274863			−0.137431	−	0.990511i	$-0.543885\pi$
$661$	−181.684			−0.274863			−0.137431	+	0.990511i	$0.543885\pi$
$662$	−677.837	−	25.7367i	−1.02392	−	0.0388772i
$663$		−	966.220i		−	1.45735i
$664$	463.772	+	53.0306i	0.698452	+	0.0798654i
$665$	79.0143			0.118818
$666$	9.75215	−	256.846i	0.0146429	−	0.385655i
$667$		−	7.41793i		−	0.0111213i
$668$	64.1712	−	843.834i	0.0960647	−	1.26322i
$669$	673.673			1.00698
$670$	246.487	+	9.35883i	0.367892	+	0.0139684i
$671$		−	934.624i		−	1.39288i
$672$	−108.570	+	565.283i	−0.161563	+	0.841195i
$673$	−532.225			−0.790825			−0.395412	−	0.918504i	$-0.629398\pi$
$673$	−532.225			−0.790825			−0.395412	+	0.918504i	$0.629398\pi$
$674$	20.1238	−	530.009i	0.0298573	−	0.786364i
$675$			119.047i			0.176366i
$676$	−954.505	−	72.5874i	−1.41199	−	0.107378i
$677$	−598.769			−0.884444			−0.442222	−	0.896906i	$-0.645810\pi$
$677$	−598.769			−0.884444			−0.442222	+	0.896906i	$0.645810\pi$
$678$	−574.073	−	21.7969i	−0.846715	−	0.0321488i
$679$		−	495.795i		−	0.730184i
$680$	−36.2678	+	317.176i	−0.0533351	+	0.466435i
$681$	−72.7268			−0.106794
$682$	40.1119	−	1056.44i	0.0588152	−	1.54904i
$683$			45.2719i			0.0662839i	0.999451	+	0.0331420i	$0.0105513\pi$
$683$			45.2719i			0.0662839i	−0.999451	+	0.0331420i	$0.989449\pi$
$684$	−4.78943	+	62.9797i	−0.00700209	+	0.0920755i
$685$	25.0694			0.0365977
$686$	−204.558	−	7.76683i	−0.298190	−	0.0113219i
$687$			17.7428i			0.0258264i
$688$	15.3749	−	100.503i	0.0223473	−	0.146081i
$689$	−746.425			−1.08335
$690$	−0.911133	+	23.9969i	−0.00132048	+	0.0347781i
$691$			972.602i			1.40753i	0.710434	+	0.703764i	$0.248499\pi$
$691$			972.602i			1.40753i	−0.710434	+	0.703764i	$0.751501\pi$
$692$	−65.8276	−	5.00600i	−0.0951265	−	0.00723411i
$693$	592.771			0.855369
$694$	1173.33	+	44.5499i	1.69068	+	0.0641930i
$695$			164.790i			0.237107i
$696$	21.2936	+	2.43484i	0.0305942	+	0.00349833i
$697$	−1020.89			−1.46469
$698$	11.6758	−	307.510i	0.0167275	−	0.440559i
$699$			471.908i			0.675119i
$700$	72.1686	−	948.997i	0.103098	−	1.35571i
$701$	610.691			0.871171			0.435586	−	0.900147i	$-0.356541\pi$
$701$	610.691			0.871171			0.435586	+	0.900147i	$0.356541\pi$
$702$	209.844	+	7.96753i	0.298923	+	0.0113498i
$703$			225.479i			0.320739i
$704$	−274.875	+	1186.22i	−0.390447	+	1.68498i
$705$	2.50143			0.00354813
$706$	24.0168	−	632.540i	0.0340181	−	0.895949i
$707$			1786.84i			2.52736i
$708$	286.446	+	21.7834i	0.404585	+	0.0307675i
$709$	397.424			0.560542			0.280271	−	0.959921i	$-0.409576\pi$
$709$	397.424			0.560542			0.280271	+	0.959921i	$0.409576\pi$
$710$	−15.4501	−	0.586624i	−0.0217608	−	0.000826230i
$711$			410.331i			0.577117i
$712$	−69.5019	+	607.820i	−0.0976151	+	0.853680i
$713$	−133.244			−0.186879
$714$	37.6828	−	992.468i	0.0527771	−	1.39001i
$715$		−	555.719i		−	0.777229i
$716$	−21.8450	+	287.256i	−0.0305098	+	0.401196i
$717$	129.965			0.181262
$718$	−274.802	−	10.4339i	−0.382733	−	0.0145319i
$719$		−	822.580i		−	1.14406i	−0.820232	−	0.572031i	$-0.806156\pi$
$719$		−	822.580i		−	1.14406i	0.820232	−	0.572031i	$-0.193844\pi$
$720$	−68.5853	−	10.4921i	−0.0952574	−	0.0145724i
$721$	2045.17			2.83657
$722$	−25.2915	+	666.112i	−0.0350297	+	0.922593i
$723$			438.033i			0.605854i
$724$	−1184.57	−	90.0830i	−1.63614	−	0.124424i
$725$	−35.4368			−0.0488784
$726$	834.190	+	31.6732i	1.14902	+	0.0436270i
$727$		−	622.314i		−	0.856003i	−0.903778	−	0.428002i	$-0.859218\pi$
$727$		−	622.314i		−	0.856003i	0.903778	−	0.428002i	$-0.140782\pi$
$728$	−1667.97	−	190.726i	−2.29117	−	0.261986i
$729$	−27.0000			−0.0370370
$730$	−11.0366	+	290.676i	−0.0151187	+	0.398186i
$731$			175.429i			0.239985i
$732$	25.8074	−	339.360i	0.0352560	−	0.463607i
$733$	−359.822			−0.490890			−0.245445	−	0.969411i	$-0.578934\pi$
$733$	−359.822			−0.490890			−0.245445	+	0.969411i	$0.578934\pi$
$734$	−581.350	−	22.0732i	−0.792030	−	0.0300724i
$735$		−	147.354i		−	0.200481i
$736$	150.712	+	28.9463i	0.204772	+	0.0393292i
$737$	−1623.34			−2.20263
$738$	8.41832	−	221.717i	0.0114069	−	0.300429i
$739$		−	78.7282i		−	0.106533i	−0.998580	−	0.0532667i	$-0.983037\pi$
$739$		−	78.7282i		−	0.106533i	0.998580	−	0.0532667i	$-0.0169634\pi$
$740$	−246.977	−	18.7819i	−0.333752	−	0.0253810i
$741$	−184.217			−0.248606
$742$	−766.702	−	29.1108i	−1.03329	−	0.0392328i
$743$		−	128.331i		−	0.172720i	−0.996264	−	0.0863602i	$-0.972476\pi$
$743$		−	128.331i		−	0.172720i	0.996264	−	0.0863602i	$-0.0275236\pi$
$744$	43.7358	−	382.485i	0.0587846	−	0.514093i
$745$	256.016			0.343646
$746$	8.80288	−	231.845i	0.0118001	−	0.310784i
$747$		−	175.048i		−	0.234335i
$748$	159.314	−	2094.93i	0.212986	−	2.80071i
$749$	−1667.39			−2.22615
$750$	239.730	+	9.10226i	0.319640	+	0.0121363i
$751$		−	178.977i		−	0.238319i	−0.992875	−	0.119159i	$-0.961980\pi$
$751$		−	178.977i		−	0.238319i	0.992875	−	0.119159i	$-0.0380199\pi$
$752$	2.41737	−	15.8020i	0.00321459	−	0.0210133i
$753$	−436.461			−0.579629
$754$	−2.37170	+	62.4645i	−0.00314550	+	0.0828442i
$755$			300.784i			0.398389i
$756$	215.234	+	16.3679i	0.284701	+	0.0216507i
$757$	−399.508			−0.527752			−0.263876	−	0.964557i	$-0.585001\pi$
$757$	−399.508			−0.527752			−0.263876	+	0.964557i	$0.585001\pi$
$758$	−472.605	−	17.9443i	−0.623490	−	0.0236732i
$759$		−	158.041i		−	0.208222i
$760$	60.4719	+	6.91473i	0.0795683	+	0.00909833i
$761$	417.858			0.549091			0.274546	−	0.961574i	$-0.411473\pi$
$761$	417.858			0.549091			0.274546	+	0.961574i	$0.411473\pi$
$762$	2.41905	−	63.7116i	0.00317461	−	0.0836110i
$763$			558.811i			0.732387i
$764$	1.98780	−	26.1390i	0.00260183	−	0.0342133i
$765$	119.716			0.156491
$766$	425.198	+	16.1443i	0.555089	+	0.0210761i
$767$			837.861i			1.09239i
$768$	−132.561	+	423.126i	−0.172606	+	0.550945i
$769$	−1273.07			−1.65549			−0.827746	−	0.561103i	$-0.810377\pi$
$769$	−1273.07			−1.65549			−0.827746	+	0.561103i	$0.810377\pi$
$770$	21.6732	−	570.816i	0.0281470	−	0.741319i
$771$		−	709.111i		−	0.919729i
$772$	−512.287	−	38.9580i	−0.663585	−	0.0504638i
$773$	246.538			0.318937			0.159468	−	0.987203i	$-0.449022\pi$
$773$	246.538			0.318937			0.159468	+	0.987203i	$0.449022\pi$
$774$	−38.0998	−	1.44660i	−0.0492246	−	0.00186900i
$775$			636.533i			0.821333i
$776$	43.3882	−	379.446i	0.0559126	−	0.488977i
$777$	770.579			0.991736
$778$	−26.0875	+	687.077i	−0.0335315	+	0.883132i
$779$			194.640i			0.249858i
$780$	15.3449	−	201.781i	0.0196729	−	0.258693i
$781$	101.753			0.130285
$782$	−264.605	−	10.0468i	−0.338370	−	0.0128475i
$783$		−	8.03712i		−	0.0102645i
$784$	−930.859	−	142.402i	−1.18732	−	0.181635i
$785$	58.2750			0.0742356
$786$	20.0320	−	527.591i	0.0254860	−	0.671235i
$787$		−	380.874i		−	0.483957i	−0.970282	−	0.241979i	$-0.922204\pi$
$787$		−	380.874i		−	0.483957i	0.970282	−	0.241979i	$-0.0777964\pi$
$788$	901.946	+	68.5905i	1.14460	+	0.0870437i
$789$	−273.756			−0.346965
$790$	395.133	+	15.0027i	0.500168	+	0.0189908i
$791$		−	1722.31i		−	2.17738i
$792$	453.664	+	51.8748i	0.572809	+	0.0654985i
$793$	992.637			1.25175
$794$	−36.0927	+	950.589i	−0.0454568	+	1.19721i
$795$		−	92.4831i		−	0.116331i
$796$	−56.7423	+	746.145i	−0.0712843	+	0.937368i
$797$	1047.16			1.31388			0.656940	−	0.753943i	$-0.271850\pi$
$797$	1047.16			1.31388			0.656940	+	0.753943i	$0.271850\pi$
$798$	−189.221	−	7.18451i	−0.237120	−	0.00900315i
$799$			27.5824i			0.0345212i
$800$	138.282	−	719.979i	0.172852	−	0.899974i
$801$	229.418			0.286414
$802$	−22.2747	+	586.658i	−0.0277739	+	0.731494i
$803$		−	1914.36i		−	2.38401i
$804$	−589.431	−	44.8246i	−0.733123	−	0.0557520i
$805$	−71.9943			−0.0894339
$806$	1122.02	+	42.6017i	1.39208	+	0.0528557i
$807$			740.733i			0.917884i
$808$	−156.371	+	1367.52i	−0.193529	+	1.69248i
$809$	138.547			0.171257			0.0856286	−	0.996327i	$-0.472710\pi$
$809$	138.547			0.171257			0.0856286	+	0.996327i	$0.472710\pi$
$810$	−0.987188	+	26.0000i	−0.00121875	+	0.0320987i
$811$		−	707.714i		−	0.872644i	−0.899791	−	0.436322i	$-0.856281\pi$
$811$		−	707.714i		−	0.872644i	0.899791	−	0.436322i	$-0.143719\pi$
$812$	−4.87227	+	64.0689i	−0.00600033	+	0.0789026i
$813$	−526.570			−0.647687
$814$	1628.91	+	61.8477i	2.00112	+	0.0759800i
$815$		−	53.6562i		−	0.0658359i
$816$	115.693	−	756.267i	0.141781	−	0.926797i
$817$	33.4469			0.0409387
$818$	−36.5635	+	962.987i	−0.0446986	+	1.17725i
$819$			629.564i			0.768699i
$820$	−213.197	−	16.2130i	−0.259996	−	0.0197720i
$821$	382.691			0.466128			0.233064	−	0.972461i	$-0.425125\pi$
$821$	382.691			0.466128			0.233064	+	0.972461i	$0.425125\pi$
$822$	−60.0357	−	2.27948i	−0.0730361	−	0.00277309i
$823$		−	892.869i		−	1.08490i	−0.840090	−	0.542448i	$-0.817498\pi$
$823$		−	892.869i		−	1.08490i	0.840090	−	0.542448i	$-0.182502\pi$
$824$	1565.22	+	178.977i	1.89954	+	0.217206i
$825$	−754.990			−0.915139
$826$	−32.6768	+	860.622i	−0.0395603	+	1.04192i
$827$		−	1623.07i		−	1.96260i	−0.192497	−	0.981298i	$-0.561659\pi$
$827$		−	1623.07i		−	1.96260i	0.192497	−	0.981298i	$-0.438341\pi$
$828$	4.36392	−	57.3843i	0.00527043	−	0.0693047i
$829$	−377.724			−0.455638			−0.227819	−	0.973704i	$-0.573159\pi$
$829$	−377.724			−0.455638			−0.227819	+	0.973704i	$0.573159\pi$
$830$	−168.564	−	6.40019i	−0.203090	−	0.00771107i
$831$		−	325.480i		−	0.391673i
$832$	−1259.85	−	291.936i	−1.51425	−	0.350885i
$833$	1624.82			1.95056
$834$	14.9838	−	394.634i	0.0179662	−	0.473182i
$835$			305.817i			0.366248i
$836$	−399.414	−	30.3743i	−0.477768	−	0.0363330i
$837$	−144.367			−0.172481
$838$	−98.6241	−	3.74464i	−0.117690	−	0.00446854i
$839$			444.985i			0.530376i	0.964197	+	0.265188i	$0.0854340\pi$
$839$			444.985i			0.530376i	−0.964197	+	0.265188i	$0.914566\pi$
$840$	23.6312	−	206.664i	0.0281324	−	0.246028i
$841$	−838.608			−0.997155
$842$	54.2209	−	1428.04i	0.0643954	−	1.69601i
$843$			100.103i			0.118747i
$844$	35.3070	−	464.277i	0.0418329	−	0.550091i
$845$	345.926			0.409380
$846$	−5.99037	−	0.227447i	−0.00708081	−	0.000268850i
$847$			2502.70i			2.95478i
$848$	−584.232	−	89.3753i	−0.688952	−	0.105395i
$849$	275.934			0.325011
$850$	−47.9952	+	1264.07i	−0.0564649	+	1.48714i
$851$		−	205.447i		−	0.241418i
$852$	36.9463	+	2.80966i	0.0433642	+	0.00329773i
$853$	618.686			0.725306			0.362653	−	0.931924i	$-0.381871\pi$
$853$	618.686			0.725306			0.362653	+	0.931924i	$0.381871\pi$
$854$	1019.60	+	38.7131i	1.19391	+	0.0453315i
$855$		−	22.8247i		−	0.0266956i
$856$	−1276.10	−	145.917i	−1.49077	−	0.170464i
$857$	565.340			0.659673			0.329836	−	0.944038i	$-0.393006\pi$
$857$	565.340			0.659673			0.329836	+	0.944038i	$0.393006\pi$
$858$	−50.5297	+	1330.82i	−0.0588924	+	1.55107i
$859$		−	483.623i		−	0.563007i	−0.959560	−	0.281504i	$-0.909167\pi$
$859$		−	483.623i		−	0.563007i	0.959560	−	0.281504i	$-0.0908331\pi$
$860$	−2.78605	+	36.6358i	−0.00323959	+	0.0425997i
$861$	665.184			0.772571
$862$	−1159.94	−	44.0416i	−1.34564	−	0.0510923i
$863$		−	922.057i		−	1.06843i	−0.845348	−	0.534216i	$-0.820607\pi$
$863$		−	922.057i		−	1.06843i	0.845348	−	0.534216i	$-0.179393\pi$
$864$	163.292	+	31.3625i	0.188996	+	0.0362992i
$865$	23.8569			0.0275802
$866$	−55.0227	+	1449.16i	−0.0635366	+	1.67339i
$867$			819.504i			0.945218i
$868$	1150.84	+	87.5180i	1.32585	+	0.100827i
$869$	−2602.30			−2.99459
$870$	−7.73944	−	0.293857i	−0.00889591	−	0.000337767i
$871$		−	1724.10i		−	1.97945i
$872$	−48.9029	+	427.674i	−0.0560813	+	0.490452i
$873$	−143.219			−0.164054
$874$	−1.91549	+	50.4490i	−0.00219163	+	0.0577220i
$875$			719.227i			0.821973i
$876$	52.8604	−	695.100i	0.0603430	−	0.793493i
$877$	1391.35			1.58649			0.793245	−	0.608903i	$-0.208390\pi$
$877$	1391.35			1.58649			0.793245	+	0.608903i	$0.208390\pi$
$878$	−1149.02	−	43.6271i	−1.30868	−	0.0496892i
$879$		−	74.4723i		−	0.0847239i
$880$	66.5406	−	434.965i	0.0756143	−	0.494278i
$881$	−97.6998			−0.110896			−0.0554482	−	0.998462i	$-0.517659\pi$
$881$	−97.6998			−0.110896			−0.0554482	+	0.998462i	$0.517659\pi$
$882$	−13.3984	+	352.879i	−0.0151909	+	0.400089i
$883$			1429.58i			1.61900i	0.587121	+	0.809499i	$0.300261\pi$
$883$			1429.58i			1.61900i	−0.587121	+	0.809499i	$0.699739\pi$
$884$	2224.97	+	169.202i	2.51693	+	0.191405i
$885$	−103.812			−0.117302
$886$	886.971	+	33.6772i	1.00110	+	0.0380104i
$887$			1193.96i			1.34606i	0.739615	+	0.673031i	$0.235008\pi$
$887$			1193.96i			1.34606i	−0.739615	+	0.673031i	$0.764992\pi$
$888$	589.746	+	67.4352i	0.664128	+	0.0759406i
$889$	191.145			0.215011
$890$	8.38809	−	220.921i	0.00942482	−	0.248225i
$891$		−	171.233i		−	0.192180i
$892$	−117.972	+	1551.30i	−0.132256	+	1.73913i
$893$	5.25880			0.00588891
$894$	−613.101	−	23.2787i	−0.685795	−	0.0260388i
$895$		−	104.106i		−	0.116319i
$896$	−1282.69	−	349.001i	−1.43158	−	0.389511i
$897$	167.850			0.187124
$898$	−18.7821	+	494.673i	−0.0209155	+	0.550861i
$899$		−	42.9738i		−	0.0478018i
$900$	−274.135	−	20.8472i	−0.304595	−	0.0231636i
$901$	1019.78			1.13183
$902$	1406.12	+	53.3886i	1.55889	+	0.0591891i
$903$		−	114.305i		−	0.126584i
$904$	150.723	−	1318.13i	0.166729	−	1.45811i
$905$	429.304			0.474369
$906$	27.3493	−	720.309i	0.0301868	−	0.795043i
$907$		−	1598.38i		−	1.76227i	−0.472868	−	0.881133i	$-0.656781\pi$
$907$		−	1598.38i		−	1.76227i	0.472868	−	0.881133i	$-0.343219\pi$
$908$	12.7358	−	167.472i	0.0140262	−	0.184440i
$909$	516.163			0.567836
$910$	606.247	+	23.0185i	0.666205	+	0.0252950i
$911$			853.834i			0.937249i	0.883397	+	0.468624i	$0.155250\pi$
$911$			853.834i			0.937249i	−0.883397	+	0.468624i	$0.844750\pi$
$912$	−144.188	−	22.0577i	−0.158101	−	0.0241861i
$913$	1110.15			1.21593
$914$	−10.6538	+	280.595i	−0.0116563	+	0.306996i
$915$			122.989i			0.134414i
$916$	−40.8572	−	3.10708i	−0.0446039	−	0.00339201i
$917$	1582.85			1.72612
$918$	−286.693	−	10.8854i	−0.312301	−	0.0118577i
$919$			373.609i			0.406538i	0.979123	+	0.203269i	$0.0651566\pi$
$919$			373.609i			0.406538i	−0.979123	+	0.203269i	$0.934843\pi$
$920$	−55.0993	−	6.30040i	−0.0598906	−	0.00684826i
$921$	238.800			0.259283
$922$	−35.4334	+	933.224i	−0.0384310	+	1.01217i
$923$			108.069i			0.117084i
$924$	−103.805	+	1365.00i	−0.112343	+	1.47728i
$925$	−981.457			−1.06103
$926$	−134.122	−	5.09244i	−0.144840	−	0.00549939i
$927$		−	590.784i		−	0.637307i
$928$	−9.33572	+	48.6074i	−0.0100600	+	0.0523787i
$929$	1373.92			1.47892			0.739461	−	0.673200i	$-0.235080\pi$
$929$	1373.92			1.47892			0.739461	+	0.673200i	$0.235080\pi$
$930$	−5.27841	+	139.020i	−0.00567571	+	0.149483i
$931$		−	309.784i		−	0.332743i
$932$	−1086.69	−	82.6396i	−1.16597	−	0.0886691i
$933$	296.844			0.318161
$934$	1247.80	+	47.3773i	1.33597	+	0.0507252i
$935$			759.233i			0.812014i
$936$	−55.0947	+	481.824i	−0.0588619	+	0.514769i
$937$	−1616.84			−1.72555			−0.862774	−	0.505589i	$-0.831275\pi$
$937$	−1616.84			−1.72555			−0.862774	+	0.505589i	$0.831275\pi$
$938$	67.2403	−	1770.93i	0.0716847	−	1.88799i
$939$		−	392.577i		−	0.418080i
$940$	−0.438046	+	5.76018i	−0.000466006	+	0.00612785i
$941$	−343.085			−0.364596			−0.182298	−	0.983243i	$-0.558354\pi$
$941$	−343.085			−0.364596			−0.182298	+	0.983243i	$0.558354\pi$
$942$	−139.555	−	5.29875i	−0.148148	−	0.00562500i
$943$		−	177.347i		−	0.188067i
$944$	−100.324	+	655.799i	−0.106275	+	0.694703i
$945$	−78.0039			−0.0825438
$946$	9.17430	−	241.627i	0.00969799	−	0.255420i
$947$		−	258.643i		−	0.273118i	−0.990632	−	0.136559i	$-0.956396\pi$
$947$		−	258.643i		−	0.273118i	0.990632	−	0.136559i	$-0.0436044\pi$
$948$	−944.889	−	71.8562i	−0.996719	−	0.0757977i
$949$	2033.18			2.14245
$950$	241.004	+	9.15064i	0.253689	+	0.00963225i
$951$		−	621.690i		−	0.653723i
$952$	2278.81	+	260.573i	2.39371	+	0.273711i
$953$	−1572.61			−1.65017			−0.825084	−	0.565009i	$-0.808873\pi$
$953$	−1572.61			−1.65017			−0.825084	+	0.565009i	$0.808873\pi$
$954$	−8.40918	+	221.476i	−0.00881466	+	0.232155i
$955$			9.47315i			0.00991952i
$956$	−22.7592	+	299.277i	−0.0238067	+	0.313052i
$957$	50.9711			0.0532613
$958$	214.250	+	8.13480i	0.223643	+	0.00849144i
$959$		−	180.116i		−	0.187817i
$960$	36.1713	−	156.098i	0.0376784	−	0.162602i
$961$	189.084			0.196757
$962$	−65.6866	+	1730.02i	−0.0682813	+	1.79835i
$963$			481.656i			0.500162i
$964$	−1008.68	−	76.7074i	−1.04635	−	0.0795720i
$965$	185.660			0.192394
$966$	172.410	+	6.54621i	0.178478	+	0.00677661i
$967$			1228.87i			1.27080i	0.772182	+	0.635401i	$0.219165\pi$
$967$			1228.87i			1.27080i	−0.772182	+	0.635401i	$0.780835\pi$
$968$	−219.017	+	1915.39i	−0.226257	+	1.97870i
$969$	251.681			0.259732
$970$	−5.23646	+	137.915i	−0.00539842	+	0.142180i
$971$		−	647.638i		−	0.666980i	−0.942754	−	0.333490i	$-0.891774\pi$
$971$		−	647.638i		−	0.666980i	0.942754	−	0.333490i	$-0.108226\pi$
$972$	4.72818	−	62.1743i	0.00486439	−	0.0639653i
$973$	1183.96			1.21682
$974$	−475.253	−	18.0448i	−0.487940	−	0.0185265i
$975$		−	801.852i		−	0.822413i
$976$	776.943	+	118.856i	0.796048	+	0.121779i
$977$	1935.15			1.98070			0.990351	−	0.138579i	$-0.0442533\pi$
$977$	1935.15			1.98070			0.990351	+	0.138579i	$0.0442533\pi$
$978$	−4.87878	+	128.495i	−0.00498853	+	0.131385i
$979$			1454.96i			1.48617i
$980$	339.319	+	25.8043i	0.346244	+	0.0263309i
$981$	161.423			0.164549
$982$	−1113.54	−	42.2799i	−1.13395	−	0.0430549i
$983$		−	1454.52i		−	1.47967i	−0.672786	−	0.739837i	$-0.734902\pi$
$983$		−	1454.52i		−	1.47967i	0.672786	−	0.739837i	$-0.265098\pi$
$984$	509.084	+	58.2119i	0.517362	+	0.0591584i
$985$	−326.878			−0.331856
$986$	3.24026	−	85.3402i	0.00328627	−	0.0865519i
$987$		−	17.9720i		−	0.0182087i
$988$	32.2597	−	424.206i	0.0326515	−	0.429358i
$989$	−30.4753			−0.0308143
$990$	−164.891	−	6.26070i	−0.166556	−	0.00632394i
$991$			201.298i			0.203127i	0.994829	+	0.101563i	$0.0323844\pi$
$991$			201.298i			0.203127i	−0.994829	+	0.101563i	$0.967616\pi$
$992$	873.110	+	167.693i	0.880152	+	0.169045i
$993$	−587.447			−0.591589
$994$	−4.21471	+	111.004i	−0.00424015	+	0.111675i
$995$		−	270.414i		−	0.271773i
$996$	403.092	+	30.6540i	0.404711	+	0.0307771i
$997$	−1110.59			−1.11394			−0.556968	−	0.830534i	$-0.688036\pi$
$997$	−1110.59			−1.11394			−0.556968	+	0.830534i	$0.688036\pi$
$998$	992.855	+	37.6975i	0.994844	+	0.0377731i
$999$		−	222.596i		−	0.222819i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.3.f.b.139.18	yes	40
4.3	odd	2	inner	276.3.f.b.139.17	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.3.f.b.139.17	✓	40	4.3	odd	2	inner
276.3.f.b.139.18	yes	40	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	276.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0758829 + 1.99856i) q^{2} +1.73205i q^{3} +(-3.98848 - 0.303313i) q^{4} +1.44548 q^{5} +(-3.46161 - 0.131433i) q^{6} -10.3854i q^{7} +(0.908847 - 7.94821i) q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(-0.0758829 + 1.99856i) q^{2} +1.73205i q^{3} +(-3.98848 - 0.303313i) q^{4} +1.44548 q^{5} +(-3.46161 - 0.131433i) q^{6} -10.3854i q^{7} +(0.908847 - 7.94821i) q^{8} -3.00000 q^{9} +(-0.109688 + 2.88889i) q^{10} -19.0259i q^{11} +(0.525354 - 6.90826i) q^{12} +20.2068 q^{13} +(20.7557 + 0.788071i) q^{14} +2.50365i q^{15} +(15.8160 + 2.41952i) q^{16} -27.6069 q^{17} +(0.227649 - 5.99568i) q^{18} +5.26346i q^{19} +(-5.76529 - 0.438434i) q^{20} +17.9880 q^{21} +(38.0243 + 1.44374i) q^{22} -4.79583i q^{23} +(13.7667 + 1.57417i) q^{24} -22.9106 q^{25} +(-1.53335 + 40.3845i) q^{26} -5.19615i q^{27} +(-3.15001 + 41.4218i) q^{28} +1.54674 q^{29} +(-5.00370 - 0.189984i) q^{30} -27.7834i q^{31} +(-6.03572 + 31.4256i) q^{32} +32.9538 q^{33} +(2.09489 - 55.1740i) q^{34} -15.0119i q^{35} +(11.9655 + 0.909939i) q^{36} +42.8386 q^{37} +(-10.5193 - 0.399407i) q^{38} +34.9992i q^{39} +(1.31372 - 11.4890i) q^{40} +36.9794 q^{41} +(-1.36498 + 35.9500i) q^{42} -6.35454i q^{43} +(-5.77079 + 75.8843i) q^{44} -4.33645 q^{45} +(9.58476 + 0.363922i) q^{46} -0.999114i q^{47} +(-4.19073 + 27.3941i) q^{48} -58.8555 q^{49} +(1.73852 - 45.7882i) q^{50} -47.8166i q^{51} +(-80.5945 - 6.12899i) q^{52} -36.9393 q^{53} +(10.3848 + 0.394299i) q^{54} -27.5016i q^{55} +(-82.5449 - 9.43870i) q^{56} -9.11658 q^{57} +(-0.117372 + 3.09126i) q^{58} +41.4643i q^{59} +(0.759390 - 9.98577i) q^{60} +49.1239 q^{61} +(55.5268 + 2.10828i) q^{62} +31.1561i q^{63} +(-62.3480 - 14.4474i) q^{64} +29.2086 q^{65} +(-2.50063 + 65.8601i) q^{66} -85.3226i q^{67} +(110.110 + 8.37354i) q^{68} +8.30662 q^{69} +(30.0021 + 1.13914i) q^{70} +5.34813i q^{71} +(-2.72654 + 23.8446i) q^{72} +100.619 q^{73} +(-3.25072 + 85.6155i) q^{74} -39.6823i q^{75} +(1.59648 - 20.9932i) q^{76} -197.590 q^{77} +(-69.9480 - 2.65584i) q^{78} -136.777i q^{79} +(22.8618 + 3.49738i) q^{80} +9.00000 q^{81} +(-2.80611 + 73.9056i) q^{82} +58.3493i q^{83} +(-71.7447 - 5.45598i) q^{84} -39.9053 q^{85} +(12.6999 + 0.482201i) q^{86} +2.67904i q^{87} +(-151.221 - 17.2916i) q^{88} -76.4726 q^{89} +(0.329063 - 8.66666i) q^{90} -209.855i q^{91} +(-1.45464 + 19.1281i) q^{92} +48.1222 q^{93} +(1.99679 + 0.0758157i) q^{94} +7.60825i q^{95} +(-54.4308 - 10.4542i) q^{96} +47.7398 q^{97} +(4.46613 - 117.626i) q^{98} +57.0776i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{2} + 8 q^{4} + 4 q^{5} - 12 q^{6} - 44 q^{8} - 120 q^{9}+O(q^{10}) \) 40 * q + 4 * q^2 + 8 * q^4 + 4 * q^5 - 12 * q^6 - 44 * q^8 - 120 * q^9	\( 40 q + 4 q^{2} + 8 q^{4} + 4 q^{5} - 12 q^{6} - 44 q^{8} - 120 q^{9} - 24 q^{10} + 48 q^{12} + 8 q^{13} + 4 q^{14} + 40 q^{16} + 40 q^{17} - 12 q^{18} + 12 q^{20} + 24 q^{21} - 8 q^{22} + 36 q^{24} + 144 q^{25} - 128 q^{26} - 24 q^{28} - 72 q^{29} + 60 q^{30} + 44 q^{32} + 12 q^{33} - 80 q^{34} - 24 q^{36} + 68 q^{37} + 56 q^{38} + 140 q^{40} - 192 q^{41} + 36 q^{42} + 104 q^{44} - 12 q^{45} - 96 q^{48} - 200 q^{49} + 140 q^{50} - 184 q^{52} - 76 q^{53} + 36 q^{54} - 236 q^{56} + 84 q^{57} + 304 q^{58} + 96 q^{60} - 452 q^{61} + 40 q^{62} - 376 q^{64} + 744 q^{65} - 156 q^{66} + 300 q^{68} - 480 q^{70} + 132 q^{72} + 344 q^{73} + 500 q^{74} - 284 q^{76} - 56 q^{77} + 24 q^{78} - 228 q^{80} + 360 q^{81} + 144 q^{82} - 360 q^{84} + 96 q^{85} - 144 q^{86} + 300 q^{88} - 752 q^{89} + 72 q^{90} + 24 q^{93} - 200 q^{94} + 12 q^{96} - 40 q^{97} - 556 q^{98}+O(q^{100}) \) 40 * q + 4 * q^2 + 8 * q^4 + 4 * q^5 - 12 * q^6 - 44 * q^8 - 120 * q^9 - 24 * q^10 + 48 * q^12 + 8 * q^13 + 4 * q^14 + 40 * q^16 + 40 * q^17 - 12 * q^18 + 12 * q^20 + 24 * q^21 - 8 * q^22 + 36 * q^24 + 144 * q^25 - 128 * q^26 - 24 * q^28 - 72 * q^29 + 60 * q^30 + 44 * q^32 + 12 * q^33 - 80 * q^34 - 24 * q^36 + 68 * q^37 + 56 * q^38 + 140 * q^40 - 192 * q^41 + 36 * q^42 + 104 * q^44 - 12 * q^45 - 96 * q^48 - 200 * q^49 + 140 * q^50 - 184 * q^52 - 76 * q^53 + 36 * q^54 - 236 * q^56 + 84 * q^57 + 304 * q^58 + 96 * q^60 - 452 * q^61 + 40 * q^62 - 376 * q^64 + 744 * q^65 - 156 * q^66 + 300 * q^68 - 480 * q^70 + 132 * q^72 + 344 * q^73 + 500 * q^74 - 284 * q^76 - 56 * q^77 + 24 * q^78 - 228 * q^80 + 360 * q^81 + 144 * q^82 - 360 * q^84 + 96 * q^85 - 144 * q^86 + 300 * q^88 - 752 * q^89 + 72 * q^90 + 24 * q^93 - 200 * q^94 + 12 * q^96 - 40 * q^97 - 556 * q^98

Introduction

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