LMFDB - Embedded newform 117.3.k.a.29.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,3,Mod(29,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 2]))

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

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

chi := DirichletCharacter("117.29");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	117.k (of order $6$, degree $2$, 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:	$3.18801909302$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			29.18
Character	$\chi$	$=$	117.29
Dual form			117.3.k.a.113.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.28020i q^{2} +(1.42433 - 2.64032i) q^{3} +2.36108 q^{4} +(2.95232 - 1.70452i) q^{5} +(3.38014 + 1.82343i) q^{6} +(-5.94919 - 10.3043i) q^{7} +8.14347i q^{8} +(-4.94255 - 7.52139i) q^{9} +(2.18213 + 3.77956i) q^{10} +0.388888i q^{11} +(3.36297 - 6.23401i) q^{12} +(-0.0928942 + 12.9997i) q^{13} +(13.1916 - 7.61616i) q^{14} +(-0.295390 - 10.2229i) q^{15} -0.980943 q^{16} +(15.0463 + 8.68699i) q^{17} +(9.62889 - 6.32745i) q^{18} +(-0.621191 + 1.07593i) q^{19} +(6.97067 - 4.02452i) q^{20} +(-35.6802 + 1.03098i) q^{21} -0.497854 q^{22} +(26.5009 + 15.3003i) q^{23} +(21.5013 + 11.5990i) q^{24} +(-6.68922 + 11.5861i) q^{25} +(-16.6422 - 0.118923i) q^{26} +(-26.8987 + 2.33692i) q^{27} +(-14.0465 - 24.3293i) q^{28} +31.0599i q^{29} +(13.0873 - 0.378159i) q^{30} +(-5.37627 - 9.31197i) q^{31} +31.3181i q^{32} +(1.02679 + 0.553906i) q^{33} +(-11.1211 + 19.2623i) q^{34} +(-35.1278 - 20.2810i) q^{35} +(-11.6698 - 17.7586i) q^{36} +(-19.8258 - 34.3393i) q^{37} +(-1.37741 - 0.795249i) q^{38} +(34.1909 + 18.7611i) q^{39} +(13.8807 + 24.0421i) q^{40} +(-10.3721 - 5.98834i) q^{41} +(-1.31987 - 45.6779i) q^{42} +(-22.6657 - 39.2581i) q^{43} +0.918196i q^{44} +(-27.4123 - 13.7808i) q^{45} +(-19.5875 + 33.9265i) q^{46} +(-19.2574 - 11.1183i) q^{47} +(-1.39719 + 2.59000i) q^{48} +(-46.2857 + 80.1692i) q^{49} +(-14.8325 - 8.56355i) q^{50} +(44.3674 - 27.3539i) q^{51} +(-0.219331 + 30.6933i) q^{52} -62.8432i q^{53} +(-2.99173 - 34.4357i) q^{54} +(0.662867 + 1.14812i) q^{55} +(83.9127 - 48.4470i) q^{56} +(1.95602 + 3.17263i) q^{57} -39.7630 q^{58} +86.0767i q^{59} +(-0.697442 - 24.1370i) q^{60} +(51.8074 + 89.7331i) q^{61} +(11.9212 - 6.88271i) q^{62} +(-48.0985 + 95.6756i) q^{63} -44.0172 q^{64} +(21.8839 + 38.5375i) q^{65} +(-0.709111 + 1.31449i) q^{66} +(35.6269 - 61.7076i) q^{67} +(35.5256 + 20.5107i) q^{68} +(78.1438 - 48.1781i) q^{69} +(25.9638 - 44.9706i) q^{70} +(-21.8910 - 12.6388i) q^{71} +(61.2502 - 40.2495i) q^{72} +38.2777 q^{73} +(43.9612 - 25.3810i) q^{74} +(21.0632 + 34.1641i) q^{75} +(-1.46668 + 2.54037i) q^{76} +(4.00721 - 2.31357i) q^{77} +(-24.0180 + 43.7713i) q^{78} +(25.4640 - 44.1049i) q^{79} +(-2.89605 + 1.67204i) q^{80} +(-32.1425 + 74.3496i) q^{81} +(7.66628 - 13.2784i) q^{82} +(-83.8496 - 48.4106i) q^{83} +(-84.2441 + 2.43424i) q^{84} +59.2286 q^{85} +(50.2582 - 29.0166i) q^{86} +(82.0081 + 44.2397i) q^{87} -3.16689 q^{88} +(-126.762 + 73.1861i) q^{89} +(17.6422 - 35.0933i) q^{90} +(134.505 - 76.3803i) q^{91} +(62.5709 + 36.1253i) q^{92} +(-32.2441 + 0.931698i) q^{93} +(14.2336 - 24.6534i) q^{94} +4.23533i q^{95} +(82.6896 + 44.6074i) q^{96} +(-53.4485 - 92.5755i) q^{97} +(-102.633 - 59.2550i) q^{98} +(2.92497 - 1.92209i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - q^{3} - 98 q^{4} - 6 q^{5} + 12 q^{6} - q^{7} - 3 q^{9} - 6 q^{10} - 39 q^{12} + 4 q^{13} - 6 q^{14} - 25 q^{15} + 166 q^{16} + 34 q^{18} + 5 q^{19} + 21 q^{20} - 91 q^{21} + 30 q^{22} - 75 q^{23}+ \cdots + 522 q^{99}+O(q^{100}) $ 52 * q - q^3 - 98 * q^4 - 6 * q^5 + 12 * q^6 - q^7 - 3 * q^9 - 6 * q^10 - 39 * q^12 + 4 * q^13 - 6 * q^14 - 25 * q^15 + 166 * q^16 + 34 * q^18 + 5 * q^19 + 21 * q^20 - 91 * q^21 + 30 * q^22 - 75 * q^23 - 24 * q^24 + 88 * q^25 - 132 * q^26 - 34 * q^27 - 22 * q^28 + 70 * q^30 + 14 * q^31 + 95 * q^33 - 6 * q^34 + 228 * q^35 - 58 * q^36 - 13 * q^37 - 192 * q^38 - 111 * q^39 + 72 * q^40 + 33 * q^41 + 159 * q^42 - 31 * q^43 - 47 * q^45 + 6 * q^46 - 69 * q^47 + 293 * q^48 - 123 * q^49 - 168 * q^50 + 235 * q^51 - 92 * q^52 - 339 * q^54 - 27 * q^55 + 168 * q^56 + 189 * q^57 + 210 * q^58 + 213 * q^60 + 8 * q^61 + 471 * q^62 + 169 * q^63 - 98 * q^64 - 246 * q^65 - 576 * q^66 - 34 * q^67 + 18 * q^68 - 193 * q^69 - 57 * q^70 + 144 * q^71 + 36 * q^72 - 106 * q^73 - 465 * q^74 - 58 * q^75 - 79 * q^76 + 282 * q^77 - 76 * q^78 - 25 * q^79 - 1050 * q^80 - 279 * q^81 + 81 * q^82 + 219 * q^83 + 395 * q^84 - 108 * q^85 - 24 * q^86 - 518 * q^87 + 30 * q^88 + 99 * q^89 + 183 * q^90 + 2 * q^91 + 888 * q^92 + 582 * q^93 + 303 * q^94 - 439 * q^96 + 212 * q^97 - 405 * q^98 + 522 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$			1.28020i			0.640101i	0.947401	+	0.320050i	$0.103700\pi$
$2$			1.28020i			0.640101i	−0.947401	+	0.320050i	$0.896300\pi$
$3$	1.42433	−	2.64032i	0.474778	−	0.880106i
$3$	1.42433	−	2.64032i	0.474778	−	0.880106i
$4$	2.36108			0.590271
$5$	2.95232	−	1.70452i	0.590463	−	0.340904i	−0.174818	−	0.984601i	$-0.555934\pi$
$5$	2.95232	−	1.70452i	0.590463	−	0.340904i	0.765281	+	0.643697i	$0.222600\pi$
$6$	3.38014	+	1.82343i	0.563356	+	0.303906i
$7$	−5.94919	−	10.3043i	−0.849884	−	1.47204i	−0.881311	−	0.472537i	$-0.843338\pi$
$7$	−5.94919	−	10.3043i	−0.849884	−	1.47204i	0.0314269	−	0.999506i	$-0.489995\pi$
$8$			8.14347i			1.01793i
$9$	−4.94255	−	7.52139i	−0.549172	−	0.835709i
$10$	2.18213	+	3.77956i	0.218213	+	0.377956i
$11$			0.388888i			0.0353534i	0.999844	+	0.0176767i	$0.00562696\pi$
$11$			0.388888i			0.0353534i	−0.999844	+	0.0176767i	$0.994373\pi$
$12$	3.36297	−	6.23401i	0.280248	−	0.519501i
$13$	−0.0928942	+	12.9997i	−0.00714571	+	0.999974i
$13$	−0.0928942	+	12.9997i	−0.00714571	+	0.999974i
$14$	13.1916	−	7.61616i	0.942255	−	0.544011i
$15$	−0.295390	−	10.2229i	−0.0196927	−	0.681524i
$16$	−0.980943			−0.0613089
$17$	15.0463	+	8.68699i	0.885077	+	0.511000i	0.872329	−	0.488919i	$-0.162609\pi$
$17$	15.0463	+	8.68699i	0.885077	+	0.511000i	0.0127482	+	0.999919i	$0.495942\pi$
$18$	9.62889	−	6.32745i	0.534938	−	0.351525i
$19$	−0.621191	+	1.07593i	−0.0326942	+	0.0566281i	−0.881910	−	0.471419i	$-0.843742\pi$
$19$	−0.621191	+	1.07593i	−0.0326942	+	0.0566281i	0.849215	+	0.528047i	$0.177075\pi$
$20$	6.97067	−	4.02452i	0.348533	−	0.201226i
$21$	−35.6802	+	1.03098i	−1.69906	+	0.0490945i
$22$	−0.497854			−0.0226297
$23$	26.5009	+	15.3003i	1.15221	+	0.665231i	0.949426	−	0.313992i	$-0.101666\pi$
$23$	26.5009	+	15.3003i	1.15221	+	0.665231i	0.202788	+	0.979223i	$0.435000\pi$
$24$	21.5013	+	11.5990i	0.895889	+	0.483292i
$25$	−6.68922	+	11.5861i	−0.267569	+	0.463443i
$26$	−16.6422	−	0.118923i	−0.640084	−	0.00457397i
$27$	−26.8987	+	2.33692i	−0.996247	+	0.0865528i
$28$	−14.0465	−	24.3293i	−0.501662	−	0.868904i
$29$			31.0599i			1.07103i	0.844525	+	0.535516i	$0.179883\pi$
$29$			31.0599i			1.07103i	−0.844525	+	0.535516i	$0.820117\pi$
$30$	13.0873	−	0.378159i	0.436244	−	0.0126053i
$31$	−5.37627	−	9.31197i	−0.173428	−	0.300386i	0.766188	−	0.642616i	$-0.222151\pi$
$31$	−5.37627	−	9.31197i	−0.173428	−	0.300386i	−0.939616	+	0.342230i	$0.888818\pi$
$32$			31.3181i			0.978690i
$33$	1.02679	+	0.553906i	0.0311147	+	0.0167850i
$34$	−11.1211	+	19.2623i	−0.327091	+	0.566539i
$35$	−35.1278	−	20.2810i	−1.00365	−	0.579458i
$36$	−11.6698	−	17.7586i	−0.324160	−	0.493295i
$37$	−19.8258	−	34.3393i	−0.535832	−	0.928088i	−0.999123	−	0.0418816i	$-0.986665\pi$
$37$	−19.8258	−	34.3393i	−0.535832	−	0.928088i	0.463291	−	0.886206i	$-0.346669\pi$
$38$	−1.37741	−	0.795249i	−0.0362477	−	0.0209276i
$39$	34.1909	+	18.7611i	0.876691	+	0.481055i
$40$	13.8807	+	24.0421i	0.347018	+	0.601052i
$41$	−10.3721	−	5.98834i	−0.252978	−	0.146057i	0.368149	−	0.929767i	$-0.379992\pi$
$41$	−10.3721	−	5.98834i	−0.252978	−	0.146057i	−0.621127	+	0.783710i	$0.713325\pi$
$42$	−1.31987	−	45.6779i	−0.0314254	−	1.08757i
$43$	−22.6657	−	39.2581i	−0.527108	−	0.912978i	−0.999501	−	0.0315902i	$-0.989943\pi$
$43$	−22.6657	−	39.2581i	−0.527108	−	0.912978i	0.472393	−	0.881388i	$-0.343390\pi$
$44$			0.918196i			0.0208681i
$45$	−27.4123	−	13.7808i	−0.609162	−	0.306241i
$46$	−19.5875	+	33.9265i	−0.425815	+	0.737533i
$47$	−19.2574	−	11.1183i	−0.409733	−	0.236559i	0.280942	−	0.959725i	$-0.409353\pi$
$47$	−19.2574	−	11.1183i	−0.409733	−	0.236559i	−0.690675	+	0.723165i	$0.742686\pi$
$48$	−1.39719	+	2.59000i	−0.0291081	+	0.0539583i
$49$	−46.2857	+	80.1692i	−0.944606	+	1.63611i
$50$	−14.8325	−	8.56355i	−0.296650	−	0.171271i
$51$	44.3674	−	27.3539i	0.869949	−	0.536350i
$52$	−0.219331	+	30.6933i	−0.00421790	+	0.590256i
$53$		−	62.8432i		−	1.18572i	−0.805305	−	0.592861i	$-0.797998\pi$
$53$		−	62.8432i		−	1.18572i	0.805305	−	0.592861i	$-0.202002\pi$
$54$	−2.99173	−	34.4357i	−0.0554025	−	0.637699i
$55$	0.662867	+	1.14812i	0.0120521	+	0.0208749i
$56$	83.9127	−	48.4470i	1.49844	−	0.865126i
$57$	1.95602	+	3.17263i	0.0343162	+	0.0556602i
$58$	−39.7630			−0.685569
$59$			86.0767i			1.45893i	0.684020	+	0.729464i	$0.260230\pi$
$59$			86.0767i			1.45893i	−0.684020	+	0.729464i	$0.739770\pi$
$60$	−0.697442	−	24.1370i	−0.0116240	−	0.402284i
$61$	51.8074	+	89.7331i	0.849302	+	1.47103i	0.881832	+	0.471563i	$0.156310\pi$
$61$	51.8074	+	89.7331i	0.849302	+	1.47103i	−0.0325305	+	0.999471i	$0.510357\pi$
$62$	11.9212	−	6.88271i	0.192277	−	0.111011i
$63$	−48.0985	+	95.6756i	−0.763467	+	1.51866i
$64$	−44.0172			−0.687769
$65$	21.8839	+	38.5375i	0.336676	+	0.592884i
$66$	−0.709111	+	1.31449i	−0.0107441	+	0.0199166i
$67$	35.6269	−	61.7076i	0.531745	−	0.921009i	−0.467569	−	0.883957i	$-0.654870\pi$
$67$	35.6269	−	61.7076i	0.531745	−	0.921009i	0.999313	−	0.0370522i	$-0.0117968\pi$
$68$	35.5256	+	20.5107i	0.522436	+	0.301628i
$69$	78.1438	−	48.1781i	1.13252	−	0.698233i
$70$	25.9638	−	44.9706i	0.370911	−	0.642437i
$71$	−21.8910	−	12.6388i	−0.308325	−	0.178011i	0.337852	−	0.941199i	$-0.390300\pi$
$71$	−21.8910	−	12.6388i	−0.308325	−	0.178011i	−0.646177	+	0.763188i	$0.723633\pi$
$72$	61.2502	−	40.2495i	0.850697	−	0.559020i
$73$	38.2777			0.524353			0.262176	−	0.965020i	$-0.415560\pi$
$73$	38.2777			0.524353			0.262176	+	0.965020i	$0.415560\pi$
$74$	43.9612	−	25.3810i	0.594070	−	0.342986i
$75$	21.0632	+	34.1641i	0.280843	+	0.455521i
$76$	−1.46668	+	2.54037i	−0.0192985	+	0.0334259i
$77$	4.00721	−	2.31357i	0.0520417	−	0.0300463i
$78$	−24.0180	+	43.7713i	−0.307924	+	0.561170i
$79$	25.4640	−	44.1049i	0.322329	−	0.558290i	−0.658639	−	0.752459i	$-0.728868\pi$
$79$	25.4640	−	44.1049i	0.322329	−	0.558290i	0.980968	+	0.194169i	$0.0622010\pi$
$80$	−2.89605	+	1.67204i	−0.0362007	+	0.0209005i
$81$	−32.1425	+	74.3496i	−0.396821	+	0.917896i
$82$	7.66628	−	13.2784i	0.0934912	−	0.161932i
$83$	−83.8496	−	48.4106i	−1.01024	−	0.583260i	−0.0989755	−	0.995090i	$-0.531557\pi$
$83$	−83.8496	−	48.4106i	−1.01024	−	0.583260i	−0.911261	+	0.411830i	$0.864890\pi$
$84$	−84.2441	+	2.43424i	−1.00291	+	0.0289791i
$85$	59.2286			0.696807
$86$	50.2582	−	29.0166i	0.584398	−	0.337402i
$87$	82.0081	+	44.2397i	0.942622	+	0.508503i
$88$	−3.16689			−0.0359874
$89$	−126.762	+	73.1861i	−1.42429	+	0.822316i	−0.996662	−	0.0816370i	$-0.973985\pi$
$89$	−126.762	+	73.1861i	−1.42429	+	0.822316i	−0.427631	+	0.903953i	$0.640652\pi$
$90$	17.6422	−	35.0933i	0.196025	−	0.389925i
$91$	134.505	−	76.3803i	1.47808	−	0.839344i
$92$	62.5709	+	36.1253i	0.680118	+	0.392667i
$93$	−32.2441	+	0.931698i	−0.346711	+	0.0100183i
$94$	14.2336	−	24.6534i	0.151422	−	0.262270i
$95$			4.23533i			0.0445824i
$96$	82.6896	+	44.6074i	0.861350	+	0.464660i
$97$	−53.4485	−	92.5755i	−0.551016	−	0.954387i	−0.998202	−	0.0599460i	$-0.980907\pi$
$97$	−53.4485	−	92.5755i	−0.551016	−	0.954387i	0.447186	−	0.894441i	$-0.352426\pi$
$98$	−102.633	−	59.2550i	−1.04727	−	0.604643i
$99$	2.92497	−	1.92209i	0.0295452	−	0.0194151i
$100$	−15.7938	+	27.3557i	−0.157938	+	0.273557i
$101$		−	142.272i		−	1.40863i	−0.709887	−	0.704315i	$-0.751254\pi$
$101$		−	142.272i		−	1.40863i	0.709887	−	0.704315i	$-0.248746\pi$
$102$	35.0184	+	56.7992i	0.343318	+	0.556855i
$103$	−45.7825	−	79.2975i	−0.444490	−	0.769879i	0.553527	−	0.832831i	$-0.313282\pi$
$103$	−45.7825	−	79.2975i	−0.444490	−	0.769879i	−0.998017	+	0.0629525i	$0.979948\pi$
$104$	−105.862	−	0.756481i	−1.01791	−	0.00727386i
$105$	−103.582	+	63.8615i	−0.986495	+	0.608205i
$106$	80.4520			0.758981
$107$	58.7386	−	33.9128i	0.548959	−	0.316942i	−0.199743	−	0.979848i	$-0.564011\pi$
$107$	58.7386	−	33.9128i	0.548959	−	0.316942i	0.748702	+	0.662907i	$0.230677\pi$
$108$	−63.5100	+	5.51768i	−0.588056	+	0.0510896i
$109$	−0.979347			−0.00898483			−0.00449242	−	0.999990i	$-0.501430\pi$
$109$	−0.979347			−0.00898483			−0.00449242	+	0.999990i	$0.501430\pi$
$110$	−1.46982	+	0.848603i	−0.0133620	+	0.00771457i
$111$	−118.905	+	3.43577i	−1.07122	+	0.0309529i
$112$	5.83581	+	10.1079i	0.0521055	+	0.0902493i
$113$		−	37.4854i		−	0.331729i	−0.986149	−	0.165865i	$-0.946959\pi$
$113$		−	37.4854i		−	0.331729i	0.986149	−	0.165865i	$-0.0530414\pi$
$114$	−4.06160	+	2.50410i	−0.0356281	+	0.0219658i
$115$	104.319			0.907120
$116$			73.3351i			0.632199i
$117$	98.2346	−	63.5528i	0.839612	−	0.543186i
$118$	−110.196			−0.933860
$119$		−	206.722i		−	1.73716i
$120$	83.2495	−	2.40550i	0.693746	−	0.0200459i
$121$	120.849			0.998750
$122$	−114.876	+	66.3239i	−0.941610	+	0.543639i
$123$	−30.5845	+	18.8563i	−0.248654	+	0.153303i
$124$	−12.6938	−	21.9863i	−0.102370	−	0.177309i
$125$			130.834i			1.04667i
$126$	−122.484	−	61.5757i	−0.972096	−	0.488696i
$127$	99.3066	+	172.004i	0.781942	+	1.35436i	0.930809	+	0.365506i	$0.119104\pi$
$127$	99.3066	+	172.004i	0.781942	+	1.35436i	−0.148867	+	0.988857i	$0.547563\pi$
$128$			68.9214i			0.538448i
$129$	−135.937	+	3.92792i	−1.05378	+	0.0304490i
$130$	−49.3357	+	28.0159i	−0.379505	+	0.215507i
$131$	−54.3776	+	31.3949i	−0.415096	+	0.239656i	−0.692977	−	0.720960i	$-0.743701\pi$
$131$	−54.3776	+	31.3949i	−0.415096	+	0.239656i	0.277881	+	0.960616i	$0.410368\pi$
$132$	2.42433	+	1.30782i	0.0183661	+	0.00990771i
$133$	14.7823			0.111145
$134$	78.9982	+	45.6096i	0.589539	+	0.340370i
$135$	−75.4300	+	52.7487i	−0.558741	+	0.390731i
$136$	−70.7423	+	122.529i	−0.520164	+	0.900950i
$137$	35.3721	−	20.4221i	0.258190	−	0.149066i	−0.365318	−	0.930883i	$-0.619040\pi$
$137$	35.3721	−	20.4221i	0.258190	−	0.149066i	0.623509	+	0.781816i	$0.285707\pi$
$138$	61.6776	+	100.040i	0.446939	+	0.724926i
$139$	33.2143			0.238952			0.119476	−	0.992837i	$-0.461879\pi$
$139$	33.2143			0.238952			0.119476	+	0.992837i	$0.461879\pi$
$140$	−82.9396	−	47.8852i	−0.592426	−	0.342037i
$141$	−56.7848	+	35.0096i	−0.402729	+	0.248295i
$142$	16.1802	−	28.0250i	0.113945	−	0.197359i
$143$	−5.05541	−	0.0361254i	−0.0353525	−	0.000252625i
$144$	4.84836	+	7.37805i	0.0336691	+	0.0512365i
$145$	52.9423	+	91.6987i	0.365119	+	0.632405i
$146$			49.0032i			0.335639i
$147$	145.746	+	236.397i	0.991468	+	1.60814i
$148$	−46.8103	−	81.0779i	−0.316286	−	0.547824i
$149$			176.203i			1.18257i	0.806463	+	0.591285i	$0.201379\pi$
$149$			176.203i			1.18257i	−0.806463	+	0.591285i	$0.798621\pi$
$150$	−43.7369	+	26.9652i	−0.291580	+	0.179768i
$151$	−47.8186	+	82.8242i	−0.316679	+	0.548505i	−0.979793	−	0.200014i	$-0.935901\pi$
$151$	−47.8186	+	82.8242i	−0.316679	+	0.548505i	0.663114	+	0.748519i	$0.269235\pi$
$152$	−8.76183	−	5.05865i	−0.0576436	−	0.0332806i
$153$	−9.02888	−	156.105i	−0.0590123	−	1.02029i
$154$	2.96183	+	5.13004i	0.0192327	+	0.0333120i
$155$	−31.7449	−	18.3279i	−0.204806	−	0.118245i
$156$	80.7277	+	44.2966i	0.517485	+	0.283953i
$157$	−139.108	−	240.942i	−0.886038	−	1.53466i	−0.844519	−	0.535526i	$-0.820114\pi$
$157$	−139.108	−	240.942i	−0.886038	−	1.53466i	−0.0415193	−	0.999138i	$-0.513220\pi$
$158$	56.4631	+	32.5990i	0.357362	+	0.206323i
$159$	−165.926	−	89.5097i	−1.04356	−	0.562954i
$160$	53.3823	+	92.4608i	0.333639	+	0.577880i
$161$		−	364.098i		−	2.26148i
$162$	−95.1824	−	41.1488i	−0.587546	−	0.254005i
$163$	132.114	−	228.828i	0.810513	−	1.40385i	−0.101992	−	0.994785i	$-0.532522\pi$
$163$	132.114	−	228.828i	0.810513	−	1.40385i	0.912505	−	0.409065i	$-0.134145\pi$
$164$	−24.4894	−	14.1390i	−0.149326	−	0.0862133i
$165$	3.97554	−	0.114874i	0.0240942	−	0.000696204i
$166$	61.9753	−	107.344i	0.373345	−	0.646653i
$167$	129.454	+	74.7404i	0.775175	+	0.447547i	0.834718	−	0.550678i	$-0.185631\pi$
$167$	129.454	+	74.7404i	0.775175	+	0.447547i	−0.0595426	+	0.998226i	$0.518964\pi$
$168$	−8.39579	−	290.561i	−0.0499749	−	1.72953i
$169$	−168.983	−	2.41519i	−0.999898	−	0.0142910i
$170$			75.8246i			0.446027i
$171$	11.1628	−	0.645638i	0.0652794	−	0.00377566i
$172$	−53.5155	−	92.6916i	−0.311137	−	0.538905i
$173$	−119.431	+	68.9533i	−0.690351	+	0.398574i	−0.803743	−	0.594976i	$-0.797162\pi$
$173$	−119.431	+	68.9533i	−0.690351	+	0.398574i	0.113393	+	0.993550i	$0.463828\pi$
$174$	−56.6358	+	104.987i	−0.325493	+	0.603373i
$175$	159.182			0.909610
$176$		−	0.381477i		−	0.00216748i
$177$	227.270	+	122.602i	1.28401	+	0.692667i
$178$	−93.6930	−	162.281i	−0.526365	−	0.911691i
$179$	−217.128	+	125.359i	−1.21301	+	0.700331i	−0.963413	−	0.268020i	$-0.913631\pi$
$179$	−217.128	+	125.359i	−1.21301	+	0.700331i	−0.249595	+	0.968350i	$0.580297\pi$
$180$	−64.7228	−	32.5377i	−0.359571	−	0.180765i
$181$	−50.9136			−0.281290			−0.140645	−	0.990060i	$-0.544918\pi$
$181$	−50.9136			−0.281290			−0.140645	+	0.990060i	$0.544918\pi$
$182$	97.7821	+	172.194i	0.537264	+	0.946119i
$183$	310.715	−	8.97814i	1.69789	−	0.0490609i
$184$	−124.598	+	215.809i	−0.677161	+	1.17288i
$185$	−117.064	−	67.5869i	−0.632778	−	0.365334i
$186$	−1.19276	−	41.2790i	−0.00641269	−	0.221930i
$187$	−3.37826	+	5.85133i	−0.0180656	+	0.0312905i
$188$	−45.4684	−	26.2512i	−0.241853	−	0.139634i
$189$	184.106	+	263.269i	0.974104	+	1.39296i
$190$	−5.42207			−0.0285372
$191$	255.354	−	147.428i	1.33693	−	0.771877i	0.350579	−	0.936533i	$-0.385985\pi$
$191$	255.354	−	147.428i	1.33693	−	0.771877i	0.986351	+	0.164656i	$0.0526515\pi$
$192$	−62.6952	+	116.219i	−0.326538	+	0.605309i
$193$	−167.362	+	289.879i	−0.867159	+	1.50196i	−0.00227209	+	0.999997i	$0.500723\pi$
$193$	−167.362	+	289.879i	−0.867159	+	1.50196i	−0.864887	+	0.501966i	$0.832610\pi$
$194$	118.515	−	68.4249i	0.610904	−	0.352705i
$195$	132.921	−	2.89033i	0.681647	−	0.0148222i
$196$	−109.284	+	189.286i	−0.557574	+	0.965746i
$197$	70.7200	−	40.8302i	0.358985	−	0.207260i	−0.309651	−	0.950850i	$-0.600212\pi$
$197$	70.7200	−	40.8302i	0.358985	−	0.207260i	0.668635	+	0.743591i	$0.266879\pi$
$198$	2.46067	+	3.74456i	0.0124276	+	0.0189119i
$199$	8.22234	−	14.2415i	0.0413183	−	0.0715654i	−0.844627	−	0.535356i	$-0.820178\pi$
$199$	8.22234	−	14.2415i	0.0413183	−	0.0715654i	0.885945	+	0.463790i	$0.153511\pi$
$200$	−94.3508	−	54.4735i	−0.471754	−	0.272367i
$201$	−112.183	−	181.959i	−0.558125	−	0.905266i
$202$	182.136			0.901665
$203$	320.051	−	184.781i	1.57661	−	0.910253i
$204$	104.755	−	64.5848i	0.513506	−	0.316592i
$205$	−40.8290			−0.199166
$206$	101.517	−	58.6108i	0.492800	−	0.284518i
$207$	−15.9025	−	274.946i	−0.0768235	−	1.32824i
$208$	0.0911239	−	12.7519i	0.000438096	−	0.0613074i
$209$	−0.418417	−	0.241573i	−0.00200200	−	0.00115585i
$210$	−81.7556	−	132.606i	−0.389312	−	0.631456i
$211$	28.1476	−	48.7530i	0.133401	−	0.231057i	−0.791585	−	0.611060i	$-0.790744\pi$
$211$	28.1476	−	48.7530i	0.133401	−	0.231057i	0.924985	+	0.380003i	$0.124077\pi$
$212$		−	148.378i		−	0.699897i
$213$	−64.5506	+	39.7974i	−0.303054	+	0.186842i
$214$	43.4152	+	75.1973i	0.202875	+	0.351389i
$215$	−133.832	−	77.2681i	−0.622476	−	0.359387i
$216$	−19.0307	−	219.049i	−0.0881050	−	1.01411i
$217$	−63.9689	+	110.797i	−0.294787	+	0.510587i
$218$		−	1.25376i		−	0.00575120i
$219$	54.5203	−	101.065i	0.248951	−	0.461486i
$220$	1.56508	+	2.71081i	0.00711402	+	0.0123218i
$221$	−114.326	+	194.790i	−0.517311	+	0.881403i
$222$	−4.39848	−	152.222i	−0.0198130	−	0.685687i
$223$	255.002			1.14351			0.571754	−	0.820425i	$-0.306263\pi$
$223$	255.002			1.14351			0.571754	+	0.820425i	$0.306263\pi$
$224$	322.711	−	186.317i	1.44067	−	0.831773i
$225$	120.205	−	6.95248i	0.534245	−	0.0308999i
$226$	47.9888			0.212340
$227$	4.66796	−	2.69505i	0.0205637	−	0.0118725i	−0.489683	−	0.871901i	$-0.662887\pi$
$227$	4.66796	−	2.69505i	0.0205637	−	0.0118725i	0.510247	+	0.860028i	$0.329554\pi$
$228$	4.61834	+	7.49085i	0.0202559	+	0.0328546i
$229$	25.9402	+	44.9298i	0.113276	+	0.196200i	0.917089	−	0.398682i	$-0.130532\pi$
$229$	25.9402	+	44.9298i	0.113276	+	0.196200i	−0.803813	+	0.594882i	$0.797199\pi$
$230$			133.549i			0.580648i
$231$	−0.400937	−	13.8756i	−0.00173566	−	0.0600676i
$232$	−252.936			−1.09024
$233$			239.911i			1.02966i	0.857292	+	0.514830i	$0.172145\pi$
$233$			239.911i			1.02966i	−0.857292	+	0.514830i	$0.827855\pi$
$234$	81.3603	+	125.760i	0.347694	+	0.537436i
$235$	−75.8053			−0.322576
$236$			203.234i			0.861163i
$237$	−80.1817	−	130.053i	−0.338319	−	0.548747i
$238$	264.646			1.11196
$239$	367.788	−	212.343i	1.53886	−	0.888463i	0.539958	−	0.841692i	$-0.318440\pi$
$239$	367.788	−	212.343i	1.53886	−	0.888463i	0.998906	−	0.0467711i	$-0.0148931\pi$
$240$	0.289761	+	10.0280i	0.00120734	+	0.0417835i
$241$	−87.7783	−	152.037i	−0.364226	−	0.630857i	0.624426	−	0.781084i	$-0.285333\pi$
$241$	−87.7783	−	152.037i	−0.364226	−	0.630857i	−0.988652	+	0.150227i	$0.952000\pi$
$242$			154.711i			0.639301i
$243$	150.525	+	190.765i	0.619444	+	0.785041i
$244$	122.322	+	211.867i	0.501318	+	0.868309i
$245$			315.580i			1.28808i
$246$	−24.1398	−	39.1543i	−0.0981293	−	0.159164i
$247$	−13.9291	−	8.17522i	−0.0563930	−	0.0330981i
$248$	75.8317	−	43.7815i	0.305773	−	0.176538i
$249$	−247.249	+	152.437i	−0.992969	+	0.612196i
$250$	−167.493			−0.669974
$251$	−192.539	−	111.163i	−0.767088	−	0.442879i	0.0647468	−	0.997902i	$-0.479376\pi$
$251$	−192.539	−	111.163i	−0.767088	−	0.442879i	−0.831835	+	0.555023i	$0.812709\pi$
$252$	−113.565	+	225.898i	−0.450653	+	0.896421i
$253$	−5.95010	+	10.3059i	−0.0235182	+	0.0407347i
$254$	−220.200	+	127.132i	−0.866929	+	0.500522i
$255$	84.3613	−	156.382i	0.330829	−	0.613264i
$256$	−264.302			−1.03243
$257$	−166.959	−	96.3938i	−0.649646	−	0.375073i	0.138675	−	0.990338i	$-0.455716\pi$
$257$	−166.959	−	96.3938i	−0.649646	−	0.375073i	−0.788321	+	0.615265i	$0.789049\pi$
$258$	−5.02853	−	174.027i	−0.0194904	−	0.674523i
$259$	−235.895	+	408.581i	−0.910790	+	1.57753i
$260$	51.6698	+	90.9902i	0.198730	+	0.349962i
$261$	233.614	−	153.515i	0.895072	−	0.588181i
$262$	−40.1918	−	69.6143i	−0.153404	−	0.265704i
$263$			33.4747i			0.127280i	0.997973	+	0.0636402i	$0.0202710\pi$
$263$			33.4747i			0.127280i	−0.997973	+	0.0636402i	$0.979729\pi$
$264$	−4.51071	+	8.36160i	−0.0170860	+	0.0316727i
$265$	−107.118	−	185.533i	−0.404217	−	0.700125i
$266$			18.9244i			0.0711442i
$267$	12.6830	+	438.934i	0.0475020	+	1.64395i
$268$	84.1181	−	145.697i	0.313874	−	0.543645i
$269$	189.997	+	109.695i	0.706308	+	0.407787i	0.809692	−	0.586854i	$-0.199634\pi$
$269$	189.997	+	109.695i	0.706308	+	0.407787i	−0.103385	+	0.994641i	$0.532967\pi$
$270$	−67.5289	−	96.5656i	−0.250107	−	0.357651i
$271$	−95.0457	−	164.624i	−0.350722	−	0.607468i	0.635654	−	0.771974i	$-0.280730\pi$
$271$	−95.0457	−	164.624i	−0.350722	−	0.607468i	−0.986376	+	0.164506i	$0.947397\pi$
$272$	−14.7596	−	8.52144i	−0.0542631	−	0.0313288i
$273$	−10.0880	−	463.927i	−0.0369523	−	1.69937i
$274$	26.1444	+	45.2834i	0.0954174	+	0.165268i
$275$	−4.50568	−	2.60136i	−0.0163843	−	0.00945947i
$276$	184.504	−	113.752i	0.668493	−	0.412147i
$277$	−138.346	−	239.622i	−0.499443	−	0.865061i	0.500556	−	0.865704i	$-0.333129\pi$
$277$	−138.346	−	239.622i	−0.499443	−	0.865061i	−1.00000		0.000642640i	$0.999795\pi$
$278$			42.5210i			0.152953i
$279$	−43.4665	+	86.4618i	−0.155794	+	0.309899i
$280$	165.158	−	286.062i	0.589850	−	1.02165i
$281$	−294.212	−	169.863i	−1.04702	−	0.604496i	−0.125204	−	0.992131i	$-0.539959\pi$
$281$	−294.212	−	169.863i	−1.04702	−	0.604496i	−0.921813	+	0.387635i	$0.873292\pi$
$282$	−44.8193	−	72.6960i	−0.158934	−	0.257787i
$283$	−104.166	+	180.421i	−0.368079	+	0.637531i	−0.989265	−	0.146132i	$-0.953318\pi$
$283$	−104.166	+	180.421i	−0.368079	+	0.637531i	0.621186	+	0.783663i	$0.286651\pi$
$284$	−51.6866	−	29.8413i	−0.181995	−	0.105075i
$285$	11.1826	+	6.03252i	0.0392372	+	0.0211667i
$286$	0.0462478	−	6.47194i	0.000161706	−	0.0226292i
$287$			142.503i			0.496526i
$288$	235.555	−	154.791i	0.817900	−	0.537469i
$289$	6.42771	+	11.1331i	0.0222412	+	0.0385229i
$290$	−117.393	+	67.7768i	−0.404803	+	0.233713i
$291$	−320.557	+	9.26254i	−1.10157	+	0.0318300i
$292$	90.3770			0.309510
$293$		−	0.824535i		−	0.00281411i	−0.999999	−	0.00140706i	$-0.999552\pi$
$293$		−	0.824535i		−	0.00281411i	0.999999	−	0.00140706i	$-0.000447880\pi$
$294$	−302.635	+	186.584i	−1.02937	+	0.634639i
$295$	146.720	+	254.126i	0.497354	+	0.861443i
$296$	279.641	−	161.451i	0.944732	−	0.545441i
$297$	−0.908801	−	10.4606i	−0.00305994	−	0.0352207i
$298$	−225.575			−0.756963
$299$	−201.361	+	343.082i	−0.673447	+	1.14743i
$300$	49.7320	+	80.6643i	0.165773	+	0.268881i
$301$	−269.685	+	467.107i	−0.895962	+	1.55185i
$302$	−106.032	−	61.2174i	−0.351098	−	0.202707i
$303$	−375.642	−	202.642i	−1.23974	−	0.668787i
$304$	0.609353	−	1.05543i	0.00200445	−	0.00347181i
$305$	305.904	+	176.614i	1.00296	+	0.579061i
$306$	199.846	−	11.5588i	0.653091	−	0.0377738i
$307$	−316.281			−1.03023			−0.515116	−	0.857121i	$-0.672251\pi$
$307$	−316.281			−1.03023			−0.515116	+	0.857121i	$0.672251\pi$
$308$	9.46137	−	5.46252i	0.0307187	−	0.0177355i
$309$	−274.580	+	7.93402i	−0.888609	+	0.0256764i
$310$	23.4634	−	40.6398i	0.0756885	−	0.131096i
$311$	−56.9212	+	32.8634i	−0.183026	+	0.105670i	−0.588714	−	0.808342i	$-0.700365\pi$
$311$	−56.9212	+	32.8634i	−0.183026	+	0.105670i	0.405688	+	0.914012i	$0.367032\pi$
$312$	−152.781	+	278.433i	−0.489682	+	0.892413i
$313$	48.7457	−	84.4300i	0.155737	−	0.269744i	−0.777590	−	0.628772i	$-0.783558\pi$
$313$	48.7457	−	84.4300i	0.155737	−	0.269744i	0.933327	+	0.359027i	$0.116891\pi$
$314$	308.454	−	178.086i	0.982339	−	0.567154i
$315$	21.0792	+	364.449i	0.0669181	+	1.15698i
$316$	60.1226	−	104.135i	0.190261	−	0.329542i
$317$	199.509	+	115.187i	0.629366	+	0.363365i	0.780507	−	0.625148i	$-0.214961\pi$
$317$	199.509	+	115.187i	0.629366	+	0.363365i	−0.151140	+	0.988512i	$0.548295\pi$
$318$	114.590	−	212.419i	0.360347	−	0.667983i
$319$	−12.0788			−0.0378647
$320$	−129.953	+	75.0282i	−0.406102	+	0.234463i
$321$	−5.87703	−	203.392i	−0.0183085	−	0.633619i
$322$	466.118			1.44757
$323$	−18.6933	+	10.7926i	−0.0578739	+	0.0334135i
$324$	−75.8911	+	175.546i	−0.234232	+	0.541808i
$325$	−149.994	−	88.0339i	−0.461519	−	0.270874i
$326$	292.945	+	169.132i	0.898605	+	0.518810i
$327$	−1.39492	+	2.58579i	−0.00426580	+	0.00790760i
$328$	48.7659	−	84.4649i	0.148676	−	0.257515i
$329$			264.579i			0.804192i
$330$	0.147061	+	5.08949i	0.000445641	+	0.0154227i
$331$	−31.9013	−	55.2546i	−0.0963785	−	0.166932i	0.813805	−	0.581139i	$-0.197393\pi$
$331$	−31.9013	−	55.2546i	−0.0963785	−	0.166932i	−0.910183	+	0.414206i	$0.864059\pi$
$332$	−197.976	−	114.302i	−0.596313	−	0.344282i
$333$	−160.289	+	318.841i	−0.481348	+	0.957480i
$334$	−95.6828	+	165.727i	−0.286475	+	0.496190i
$335$		−	242.907i		−	0.725096i
$336$	35.0003	−	1.01134i	0.104167	−	0.00300993i
$337$	−175.733	−	304.378i	−0.521463	−	0.903200i	−0.999688	−	0.0249629i	$-0.992053\pi$
$337$	−175.733	−	304.378i	−0.521463	−	0.903200i	0.478226	−	0.878237i	$-0.341280\pi$
$338$	3.09193	−	216.332i	0.00914771	−	0.640035i
$339$	−98.9733	−	53.3917i	−0.291957	−	0.157498i
$340$	139.844			0.411305
$341$	3.62131	−	2.09076i	0.0106197	−	0.00613127i
$342$	0.826547	+	14.2906i	0.00241680	+	0.0417854i
$343$	518.429			1.51146
$344$	319.697	−	184.577i	0.929351	−	0.536561i
$345$	148.585	−	275.435i	0.430680	−	0.798361i
$346$	−88.2741	−	152.895i	−0.255128	−	0.441894i
$347$		−	303.213i		−	0.873812i	−0.899507	−	0.436906i	$-0.856074\pi$
$347$		−	303.213i		−	0.873812i	0.899507	−	0.436906i	$-0.143926\pi$
$348$	193.628	+	104.454i	0.556402	+	0.300154i
$349$	130.278			0.373290			0.186645	−	0.982427i	$-0.440239\pi$
$349$	130.278			0.373290			0.186645	+	0.982427i	$0.440239\pi$
$350$			203.785i			0.582242i
$351$	−27.8805	−	349.891i	−0.0794317	−	0.996840i
$352$	−12.1792			−0.0346000
$353$		−	555.897i		−	1.57478i	−0.616455	−	0.787390i	$-0.711432\pi$
$353$		−	555.897i		−	1.57478i	0.616455	−	0.787390i	$-0.288568\pi$
$354$	−156.955	+	290.951i	−0.443376	+	0.821896i
$355$	−86.1724			−0.242739
$356$	−299.296	+	172.799i	−0.840719	+	0.485390i
$357$	−545.812	−	294.442i	−1.52889	−	0.824766i
$358$	−160.485	−	277.968i	−0.448282	−	0.776447i
$359$			387.457i			1.07927i	0.841900	+	0.539633i	$0.181437\pi$
$359$			387.457i			1.07927i	−0.841900	+	0.539633i	$0.818563\pi$
$360$	112.224	−	223.231i	0.311733	−	0.620087i
$361$	179.728	+	311.298i	0.497862	+	0.862323i
$362$		−	65.1796i		−	0.180054i
$363$	172.129	−	319.079i	0.474185	−	0.879006i
$364$	317.578	−	180.340i	0.872467	−	0.495440i
$365$	113.008	−	65.2452i	0.309611	−	0.178754i
$366$	11.4938	+	397.777i	0.0314039	+	1.08682i
$367$	355.512			0.968697			0.484349	−	0.874875i	$-0.339057\pi$
$367$	355.512			0.968697			0.484349	+	0.874875i	$0.339057\pi$
$368$	−25.9959	−	15.0087i	−0.0706410	−	0.0407846i
$369$	6.22402	+	107.610i	0.0168673	+	0.291627i
$370$	86.5248	−	149.865i	0.233851	−	0.405042i
$371$	−647.555	+	373.866i	−1.74543	+	1.00773i
$372$	−76.1312	+	2.19982i	−0.204654	+	0.00591349i
$373$	80.4668			0.215729			0.107864	−	0.994166i	$-0.465599\pi$
$373$	80.4668			0.215729			0.107864	+	0.994166i	$0.465599\pi$
$374$	−7.49087	−	4.32486i	−0.0200291	−	0.0115638i
$375$	345.442	+	186.351i	0.921180	+	0.496935i
$376$	90.5414	−	156.822i	0.240802	−	0.417081i
$377$	−403.769	−	2.88529i	−1.07101	−	0.00765328i
$378$	−337.038	+	235.692i	−0.891634	+	0.623525i
$379$	−43.1053	−	74.6606i	−0.113734	−	0.196994i	0.803539	−	0.595252i	$-0.202948\pi$
$379$	−43.1053	−	74.6606i	−0.113734	−	0.196994i	−0.917273	+	0.398259i	$0.869615\pi$
$380$			9.99997i			0.0263157i
$381$	595.591	−	17.2097i	1.56323	−	0.0451697i
$382$	188.738	+	326.904i	0.494079	+	0.855770i
$383$		−	210.045i		−	0.548419i	−0.961670	−	0.274210i	$-0.911584\pi$
$383$		−	210.045i		−	0.548419i	0.961670	−	0.274210i	$-0.0884162\pi$
$384$	181.974	+	98.1671i	0.473891	+	0.255643i
$385$	7.88704	−	13.6608i	0.0204858	−	0.0354825i
$386$	−371.104	−	214.257i	−0.961408	−	0.555069i
$387$	−183.249	+	364.512i	−0.473512	+	0.941891i
$388$	−126.196	−	218.579i	−0.325249	−	0.563347i
$389$	530.326	+	306.184i	1.36331	+	0.787105i	0.990062	−	0.140629i	$-0.0449123\pi$
$389$	530.326	+	306.184i	1.36331	+	0.787105i	0.373243	+	0.927734i	$0.378246\pi$
$390$	3.70021	+	170.166i	0.00948772	+	0.436323i
$391$	265.827	+	460.427i	0.679865	+	1.17756i
$392$	−652.855	−	376.926i	−1.66545	−	0.961546i
$393$	5.44069	+	188.291i	0.0138440	+	0.479112i
$394$	52.2709	+	90.5358i	0.132667	+	0.229786i
$395$		−	173.615i		−	0.439533i
$396$	6.90611	−	4.53823i	0.0174397	−	0.0114602i
$397$	5.75102	−	9.96106i	0.0144862	−	0.0250908i	−0.858691	−	0.512493i	$-0.828722\pi$
$397$	5.75102	−	9.96106i	0.0144862	−	0.0250908i	0.873178	+	0.487402i	$0.162055\pi$
$398$	18.2320	+	10.5263i	0.0458091	+	0.0264479i
$399$	21.0550	−	39.0300i	0.0527693	−	0.0978196i
$400$	6.56174	−	11.3653i	0.0164044	−	0.0284132i
$401$	126.952	+	73.2957i	0.316588	+	0.182782i	0.649871	−	0.760045i	$-0.274823\pi$
$401$	126.952	+	73.2957i	0.316588	+	0.182782i	−0.333282	+	0.942827i	$0.608156\pi$
$402$	232.944	−	143.617i	0.579462	−	0.357256i
$403$	121.552	−	69.0247i	0.301618	−	0.171277i
$404$		−	335.915i		−	0.831474i
$405$	31.8357	+	274.291i	0.0786066	+	0.677262i
$406$	236.557	+	409.730i	0.582654	+	1.00919i
$407$	13.3541	−	7.71000i	0.0328111	−	0.0189435i
$408$	222.755	+	361.304i	0.545969	+	0.885550i
$409$	−33.5225			−0.0819622			−0.0409811	−	0.999160i	$-0.513048\pi$
$409$	−33.5225			−0.0819622			−0.0409811	+	0.999160i	$0.513048\pi$
$410$		−	52.2693i		−	0.127486i
$411$	−3.53911	−	122.481i	−0.00861098	−	0.298008i
$412$	−108.096	−	187.228i	−0.262369	−	0.454437i
$413$	886.960	−	512.087i	2.14760	−	1.23992i
$414$	351.986	−	20.3584i	0.850209	−	0.0491748i
$415$	−330.067			−0.795343
$416$	−407.125	−	2.90927i	−0.978665	−	0.00699343i
$417$	47.3083	−	87.6963i	0.113449	−	0.210303i
$418$	0.309263	−	0.535658i	0.000739863	−	0.00128148i
$419$	−507.592	−	293.058i	−1.21144	−	0.699423i	−0.248364	−	0.968667i	$-0.579893\pi$
$419$	−507.592	−	293.058i	−1.21144	−	0.699423i	−0.963072	+	0.269244i	$0.913226\pi$
$420$	−244.566	+	150.782i	−0.582300	+	0.359006i
$421$	14.6994	−	25.4601i	0.0349154	−	0.0604752i	−0.848040	−	0.529933i	$-0.822217\pi$
$421$	14.6994	−	25.4601i	0.0349154	−	0.0604752i	0.882955	+	0.469458i	$0.155550\pi$
$422$	62.4137	+	36.0346i	0.147900	+	0.0853900i
$423$	11.5559	+	199.795i	0.0273188	+	0.472329i
$424$	511.762			1.20699
$425$	−201.296	+	116.218i	−0.473638	+	0.273455i
$426$	−50.9487	−	82.6378i	−0.119598	−	0.193985i
$427$	616.424	−	1067.68i	1.44362	−	2.50042i
$428$	138.687	−	80.0709i	0.324035	−	0.187082i
$429$	−7.29597	+	13.2964i	−0.0170069	+	0.0309940i
$430$	98.9188	−	171.332i	0.230044	−	0.398447i
$431$	−309.247	+	178.544i	−0.717510	+	0.414255i	−0.813836	−	0.581095i	$-0.802624\pi$
$431$	−309.247	+	178.544i	−0.717510	+	0.414255i	0.0963253	+	0.995350i	$0.469291\pi$
$432$	26.3861	−	2.29239i	0.0610789	−	0.00530646i
$433$	−66.0808	+	114.455i	−0.152612	+	0.264331i	−0.932187	−	0.361978i	$-0.882102\pi$
$433$	−66.0808	+	114.455i	−0.152612	+	0.264331i	0.779575	+	0.626309i	$0.215435\pi$
$434$	−141.843	−	81.8930i	−0.326827	−	0.188694i
$435$	317.521	−	9.17481i	0.729934	−	0.0210915i
$436$	−2.31232			−0.00530349
$437$	−32.9242	+	19.0088i	−0.0753415	+	0.0434984i
$438$	129.384	+	69.7970i	0.295397	+	0.159354i
$439$	−241.481			−0.550071			−0.275036	−	0.961434i	$-0.588690\pi$
$439$	−241.481			−0.550071			−0.275036	+	0.961434i	$0.588690\pi$
$440$	−9.34967	+	5.39803i	−0.0212493	+	0.0122683i
$441$	831.753	−	48.1073i	1.88606	−	0.109087i
$442$	−249.371	−	146.360i	−0.564187	−	0.331131i
$443$	−390.576	−	225.499i	−0.881661	−	0.509028i	−0.0104556	−	0.999945i	$-0.503328\pi$
$443$	−390.576	−	225.499i	−0.881661	−	0.509028i	−0.871206	+	0.490918i	$0.836662\pi$
$444$	−280.745	+	8.11215i	−0.632308	+	0.0182706i
$445$	−249.495	+	432.137i	−0.560662	+	0.971095i
$446$			326.454i			0.731961i
$447$	465.231	+	250.972i	1.04079	+	0.561458i
$448$	261.867	+	453.566i	0.584524	+	1.01243i
$449$	687.272	+	396.797i	1.53067	+	0.883734i	0.999331	+	0.0365769i	$0.0116454\pi$
$449$	687.272	+	396.797i	1.53067	+	0.883734i	0.531342	+	0.847157i	$0.321688\pi$
$450$	8.90058	+	153.887i	0.0197791	+	0.341971i
$451$	2.32879	−	4.03358i	0.00516362	−	0.00894365i
$452$		−	88.5062i		−	0.195810i
$453$	150.573	+	244.226i	0.332390	+	0.539129i
$454$	3.45020	+	5.97593i	0.00759957	+	0.0131628i
$455$	266.910	−	454.765i	0.586615	−	0.999484i
$456$	−25.8362	+	15.9288i	−0.0566583	+	0.0349316i
$457$	439.912			0.962609			0.481304	−	0.876554i	$-0.340163\pi$
$457$	439.912			0.962609			0.481304	+	0.876554i	$0.340163\pi$
$458$	−57.5192	+	33.2087i	−0.125588	+	0.0725081i
$459$	−425.027	−	198.507i	−0.925984	−	0.432476i
$460$	246.305			0.535446
$461$	510.523	−	294.750i	1.10742	−	0.639372i	0.169264	−	0.985571i	$-0.445861\pi$
$461$	510.523	−	294.750i	1.10742	−	0.639372i	0.938161	+	0.346199i	$0.112528\pi$
$462$	17.7636	−	0.513280i	0.0384493	−	0.00111100i
$463$	−98.6145	−	170.805i	−0.212990	−	0.368910i	0.739659	−	0.672982i	$-0.234987\pi$
$463$	−98.6145	−	170.805i	−0.212990	−	0.368910i	−0.952649	+	0.304072i	$0.901654\pi$
$464$		−	30.4680i		−	0.0656638i
$465$	−93.6068	+	57.7115i	−0.201305	+	0.124111i
$466$	−307.134			−0.659086
$467$			822.756i			1.76179i	0.473313	+	0.880895i	$0.343058\pi$
$467$			822.756i			1.76179i	−0.473313	+	0.880895i	$0.656942\pi$
$468$	231.940	−	150.053i	0.495599	−	0.320627i
$469$	−847.805			−1.80769
$470$		−	97.0461i		−	0.206481i
$471$	−834.300	+	24.1072i	−1.77134	+	0.0511830i
$472$	−700.963			−1.48509
$473$	15.2670	−	8.81439i	0.0322769	−	0.0186351i
$474$	166.494	−	102.649i	0.351253	−	0.216558i
$475$	−8.31056	−	14.3943i	−0.0174959	−	0.0303038i
$476$		−	488.089i		−	1.02540i
$477$	−472.668	+	310.606i	−0.990919	+	0.651165i
$478$	271.841	+	470.843i	0.568706	+	0.985028i
$479$		−	472.641i		−	0.986724i	−0.869824	−	0.493362i	$-0.835768\pi$
$479$		−	472.641i		−	0.986724i	0.869824	−	0.493362i	$-0.164232\pi$
$480$	320.160	−	9.25106i	0.667000	−	0.0192730i
$481$	448.241	−	254.539i	0.931893	−	0.529186i
$482$	194.637	−	112.374i	0.403812	−	0.233141i
$483$	−961.333	−	518.597i	−1.99034	−	1.07370i
$484$	285.334			0.589533
$485$	−315.594	−	182.208i	−0.650709	−	0.375687i
$486$	−244.218	+	192.702i	−0.502505	+	0.396506i
$487$	−254.911	+	441.518i	−0.523431	+	0.906609i	0.476197	+	0.879338i	$0.342015\pi$
$487$	−254.911	+	441.518i	−0.523431	+	0.906609i	−0.999628	+	0.0272702i	$0.991319\pi$
$488$	−730.738	+	421.892i	−1.49741	+	0.864533i
$489$	−416.003	−	674.749i	−0.850722	−	1.37985i
$490$	−404.006			−0.824501
$491$	−377.657	−	218.041i	−0.769160	−	0.444075i	0.0634150	−	0.997987i	$-0.479801\pi$
$491$	−377.657	−	218.041i	−0.769160	−	0.444075i	−0.832575	+	0.553913i	$0.813134\pi$
$492$	−72.2125	+	44.5212i	−0.146773	+	0.0904903i
$493$	−269.817	+	467.338i	−0.547297	+	0.947946i
$494$	10.4659	−	17.8320i	0.0211861	−	0.0360972i
$495$	5.35919	−	10.6603i	0.0108267	−	0.0215360i
$496$	5.27381	+	9.13451i	0.0106327	+	0.0184163i
$497$			300.763i			0.605156i
$498$	−195.150	−	316.529i	−0.391867	−	0.635600i
$499$	−81.6627	−	141.444i	−0.163653	−	0.283455i	0.772523	−	0.634986i	$-0.218994\pi$
$499$	−81.6627	−	141.444i	−0.163653	−	0.283455i	−0.936176	+	0.351532i	$0.885661\pi$
$500$			308.909i			0.617819i
$501$	381.724	−	235.345i	0.761925	−	0.469750i
$502$	142.310	−	246.489i	0.283487	−	0.491014i
$503$	91.9955	+	53.1136i	0.182894	+	0.105594i	0.588652	−	0.808387i	$-0.299659\pi$
$503$	91.9955	+	53.1136i	0.182894	+	0.105594i	−0.405758	+	0.913981i	$0.632992\pi$
$504$	−779.131	−	391.688i	−1.54590	−	0.777159i
$505$	−242.505	−	420.031i	−0.480208	−	0.831744i
$506$	−13.1936	−	7.61733i	−0.0260743	−	0.0150540i
$507$	−247.065	+	442.728i	−0.487307	+	0.873231i
$508$	234.471	+	406.116i	0.461558	+	0.799441i
$509$	781.981	+	451.477i	1.53631	+	0.886988i	0.999050	+	0.0435700i	$0.0138731\pi$
$509$	781.981	+	451.477i	1.53631	+	0.886988i	0.537258	+	0.843418i	$0.319460\pi$
$510$	200.201	+	107.999i	0.392551	+	0.211764i
$511$	−227.722	−	394.425i	−0.445639	−	0.771869i
$512$		−	62.6743i		−	0.122411i
$513$	14.1948	−	30.3929i	0.0276702	−	0.0592454i
$514$	123.404	−	213.741i	0.240085	−	0.415839i
$515$	−270.328	−	156.074i	−0.524910	−	0.303057i
$516$	−320.959	+	9.27415i	−0.622014	+	0.0179732i
$517$	4.32376	−	7.48897i	0.00836318	−	0.0144854i
$518$	−523.067	−	301.993i	−1.00978	−	0.582997i
$519$	11.9495	+	413.547i	0.0230241	+	0.796816i
$520$	−313.829	+	178.211i	−0.603517	+	0.342714i
$521$			712.668i			1.36789i	0.729536	+	0.683943i	$0.239736\pi$
$521$			712.668i			1.36789i	−0.729536	+	0.683943i	$0.760264\pi$
$522$	196.530	+	299.073i	0.376495	+	0.572936i
$523$	−132.996	−	230.356i	−0.254295	−	0.440452i	0.710409	−	0.703789i	$-0.248510\pi$
$523$	−132.996	−	230.356i	−0.254295	−	0.440452i	−0.964704	+	0.263337i	$0.915177\pi$
$524$	−128.390	+	74.1261i	−0.245019	+	0.141462i
$525$	226.728	−	420.290i	0.431863	−	0.800553i
$526$	−42.8544			−0.0814723
$527$		−	186.814i		−	0.354487i
$528$	−1.00722	−	0.543350i	−0.00190761	−	0.00102907i
$529$	203.699	+	352.817i	0.385064	+	0.666951i
$530$	237.520	−	137.132i	0.448150	−	0.258740i
$531$	647.416	−	425.438i	1.21924	−	0.801202i
$532$	34.9023			0.0656059
$533$	78.8099	−	134.278i	0.147861	−	0.251928i
$534$	−561.923	+	16.2368i	−1.05229	+	0.0304061i
$535$	115.610	−	200.242i	0.216093	−	0.374285i
$536$	502.514	+	290.127i	0.937526	+	0.541281i
$537$	21.7245	+	751.841i	0.0404554	+	1.40008i
$538$	−140.431	+	243.234i	−0.261025	+	0.452108i
$539$	−31.1768	−	17.9999i	−0.0578419	−	0.0333951i
$540$	−178.097	+	124.544i	−0.329809	+	0.230637i
$541$	−160.358			−0.296410			−0.148205	−	0.988957i	$-0.547350\pi$
$541$	−160.358			−0.296410			−0.148205	+	0.988957i	$0.547350\pi$
$542$	210.752	−	121.678i	0.388841	−	0.224497i
$543$	−72.5179	+	134.428i	−0.133551	+	0.247565i
$544$	−272.060	+	471.222i	−0.500110	+	0.866216i
$545$	−2.89134	+	1.66932i	−0.00530521	+	0.00306297i
$546$	593.920	−	12.9146i	1.08777	−	0.0236532i
$547$	−26.1612	+	45.3124i	−0.0478266	+	0.0828381i	−0.888948	−	0.458009i	$-0.848563\pi$
$547$	−26.1612	+	45.3124i	−0.0478266	+	0.0828381i	0.841121	+	0.540847i	$0.181896\pi$
$548$	83.5165	−	48.2183i	0.152402	−	0.0879895i
$549$	418.856	−	833.173i	0.762944	−	1.51762i
$550$	3.33026	−	5.76818i	0.00605502	−	0.0104876i
$551$	−33.4184	−	19.2941i	−0.0606505	−	0.0350166i
$552$	392.337	+	636.362i	0.710755	+	1.15283i
$553$	−605.960			−1.09577
$554$	306.764	−	177.110i	0.553726	−	0.319694i
$555$	−345.189	+	212.820i	−0.621962	+	0.383459i
$556$	78.4218			0.141046
$557$	−408.417	+	235.800i	−0.733245	+	0.423339i	−0.819608	−	0.572925i	$-0.805809\pi$
$557$	−408.417	+	235.800i	−0.733245	+	0.423339i	0.0863633	+	0.996264i	$0.472475\pi$
$558$	−110.689	−	55.6458i	−0.198367	−	0.0997237i
$559$	512.447	−	290.999i	0.916722	−	0.520571i
$560$	34.4583	+	19.8945i	0.0615327	+	0.0355259i
$561$	10.6376	+	17.2539i	0.0189618	+	0.0307557i
$562$	217.459	−	376.650i	0.386938	−	0.670196i
$563$			276.668i			0.491417i	0.969344	+	0.245709i	$0.0790206\pi$
$563$			276.668i			0.491417i	−0.969344	+	0.245709i	$0.920979\pi$
$564$	−134.074	+	82.6605i	−0.237719	+	0.146561i
$565$	−63.8946	−	110.669i	−0.113088	−	0.195874i
$566$	−230.976	−	133.354i	−0.408084	−	0.235608i
$567$	957.342	−	111.114i	1.68843	−	0.195969i
$568$	102.924	−	178.269i	0.181204	−	0.313854i
$569$			137.321i			0.241338i	0.992693	+	0.120669i	$0.0385039\pi$
$569$			137.321i			0.241338i	−0.992693	+	0.120669i	$0.961496\pi$
$570$	−7.72284	+	14.3160i	−0.0135488	+	0.0251158i
$571$	232.326	+	402.400i	0.406875	+	0.704728i	0.994538	−	0.104378i	$-0.0332852\pi$
$571$	232.326	+	402.400i	0.406875	+	0.704728i	−0.587663	+	0.809106i	$0.699952\pi$
$572$	−11.9362	−	0.0852951i	−0.0208676	−	0.000149117i
$573$	−25.5491	−	884.202i	−0.0445883	−	1.54311i
$574$	−182.433			−0.317827
$575$	−354.541	+	204.694i	−0.616593	+	0.355990i
$576$	217.557	+	331.070i	0.377703	+	0.574775i
$577$	882.703			1.52981			0.764907	−	0.644141i	$-0.222785\pi$
$577$	882.703			1.52981			0.764907	+	0.644141i	$0.222785\pi$
$578$	−14.2526	+	8.22877i	−0.0246586	+	0.0142366i
$579$	526.993	+	854.772i	0.910179	+	1.47629i
$580$	125.001	+	216.508i	0.215519	+	0.373290i
$581$			1152.02i			1.98281i
$582$	−11.8579	−	410.378i	−0.0203744	−	0.705117i
$583$	24.4390			0.0419193
$584$			311.714i			0.533756i
$585$	181.693	−	355.071i	0.310586	−	0.606959i
$586$	1.05557			0.00180132
$587$			134.791i			0.229626i	0.993387	+	0.114813i	$0.0366269\pi$
$587$			134.791i			0.229626i	−0.993387	+	0.114813i	$0.963373\pi$
$588$	344.118	+	558.152i	0.585235	+	0.949239i
$589$	13.3587			0.0226804
$590$	−325.332	+	187.831i	−0.551410	+	0.318357i
$591$	−7.07580	−	244.879i	−0.0119726	−	0.414347i
$592$	19.4480	+	33.6848i	0.0328513	+	0.0569001i
$593$			50.7063i			0.0855080i	0.999086	+	0.0427540i	$0.0136132\pi$
$593$			50.7063i			0.0855080i	−0.999086	+	0.0427540i	$0.986387\pi$
$594$	13.3916	−	1.16345i	0.0225448	−	0.00195867i
$595$	−352.362	−	610.309i	−0.592206	−	1.02573i
$596$			416.030i			0.698037i
$597$	−25.8908	−	41.9943i	−0.0433681	−	0.0703422i
$598$	−439.214	−	257.782i	−0.734471	−	0.431074i
$599$	144.221	−	83.2662i	0.240770	−	0.139009i	−0.374761	−	0.927122i	$-0.622275\pi$
$599$	144.221	−	83.2662i	0.240770	−	0.139009i	0.615531	+	0.788113i	$0.288942\pi$
$600$	−278.214	+	171.528i	−0.463691	+	0.285879i
$601$	−79.1116			−0.131633			−0.0658166	−	0.997832i	$-0.520965\pi$
$601$	−79.1116			−0.131633			−0.0658166	+	0.997832i	$0.520965\pi$
$602$	−597.992	−	345.251i	−0.993341	−	0.573506i
$603$	−640.214	+	37.0290i	−1.06172	+	0.0614080i
$604$	−112.904	+	195.555i	−0.186927	+	0.323767i
$605$	356.784	−	205.989i	0.589725	−	0.340478i
$606$	259.423	−	480.898i	0.428091	−	0.793561i
$607$	366.740			0.604185			0.302092	−	0.953279i	$-0.402315\pi$
$607$	366.740			0.604185			0.302092	+	0.953279i	$0.402315\pi$
$608$	−33.6962	−	19.4545i	−0.0554213	−	0.0319975i
$609$	−32.0223	−	1108.23i	−0.0525818	−	1.81975i
$610$	−226.101	+	391.618i	−0.370657	+	0.641997i
$611$	146.323	−	249.307i	0.239481	−	0.408032i
$612$	−21.3179	−	368.577i	−0.0348332	−	0.602250i
$613$	603.549	+	1045.38i	0.984582	+	1.70535i	0.643778	+	0.765212i	$0.277366\pi$
$613$	603.549	+	1045.38i	0.984582	+	1.70535i	0.340804	+	0.940134i	$0.389301\pi$
$614$		−	404.903i		−	0.659452i
$615$	−58.1541	+	107.801i	−0.0945595	+	0.175287i
$616$	18.8405	+	32.6326i	0.0305852	+	0.0529750i
$617$		−	157.601i		−	0.255430i	−0.991811	−	0.127715i	$-0.959236\pi$
$617$		−	157.601i		−	0.255430i	0.991811	−	0.127715i	$-0.0407644\pi$
$618$	−10.1571	−	351.518i	−0.0164355	−	0.568799i
$619$	−269.359	+	466.544i	−0.435152	+	0.753706i	−0.997308	−	0.0733253i	$-0.976639\pi$
$619$	−269.359	+	466.544i	−0.435152	+	0.753706i	0.562156	+	0.827031i	$0.309972\pi$
$620$	−74.9523	−	43.2737i	−0.120891	−	0.0697964i
$621$	−748.595	−	349.627i	−1.20547	−	0.563007i
$622$	−42.0718	−	72.8705i	−0.0676396	−	0.117155i
$623$	1508.26	+	870.796i	2.42097	+	1.39775i
$624$	−33.5393	−	18.4036i	−0.0537490	−	0.0294930i
$625$	55.7781	+	96.6104i	0.0892449	+	0.154577i
$626$	108.087	+	62.4043i	0.172664	+	0.0996874i
$627$	−1.23380	+	0.760673i	−0.00196778	+	0.00121319i
$628$	−328.446	−	568.885i	−0.523003	−	0.905867i
$629$		−	688.906i		−	1.09524i
$630$	−466.569	+	26.9856i	−0.740585	+	0.0428343i
$631$	511.749	−	886.375i	0.811012	−	1.40471i	−0.101144	−	0.994872i	$-0.532250\pi$
$631$	511.749	−	886.375i	0.811012	−	1.40471i	0.912156	−	0.409842i	$-0.134416\pi$
$632$	359.167	+	207.365i	0.568302	+	0.328109i
$633$	−88.6319	−	143.759i	−0.140019	−	0.227108i
$634$	−147.462	+	255.412i	−0.232590	+	0.402858i
$635$	586.369	+	338.540i	0.923416	+	0.533134i
$636$	−391.765	−	211.340i	−0.615983	−	0.332296i
$637$	−1037.87	−	609.146i	−1.62931	−	0.956273i
$638$		−	15.4633i		−	0.0242372i
$639$	13.1362	+	227.119i	0.0205575	+	0.355429i
$640$	117.478	+	203.478i	0.183559	+	0.317934i
$641$	824.358	−	475.943i	1.28605	−	0.742501i	0.308102	−	0.951353i	$-0.400306\pi$
$641$	824.358	−	475.943i	1.28605	−	0.742501i	0.977947	+	0.208853i	$0.0669729\pi$
$642$	260.382	−	7.52378i	0.405580	−	0.0117193i
$643$	−76.8350			−0.119495			−0.0597473	−	0.998214i	$-0.519029\pi$
$643$	−76.8350			−0.119495			−0.0597473	+	0.998214i	$0.519029\pi$
$644$		−	859.666i		−	1.33488i
$645$	−394.634	+	243.304i	−0.611836	+	0.377216i
$646$	−13.8166	−	23.9311i	−0.0213880	−	0.0370451i
$647$	189.920	−	109.651i	0.293540	−	0.169475i	−0.345997	−	0.938236i	$-0.612459\pi$
$647$	189.920	−	109.651i	0.293540	−	0.169475i	0.639537	+	0.768760i	$0.279126\pi$
$648$	−605.464	−	261.751i	−0.934357	−	0.403937i
$649$	−33.4742			−0.0515781
$650$	112.701	−	192.022i	0.173386	−	0.295419i
$651$	201.427	+	326.710i	0.309412	+	0.501859i
$652$	311.931	−	540.281i	0.478422	−	0.828652i
$653$	796.282	+	459.733i	1.21942	+	0.704033i	0.964794	−	0.263007i	$-0.0847141\pi$
$653$	796.282	+	459.733i	1.21942	+	0.704033i	0.254627	+	0.967039i	$0.418047\pi$
$654$	−3.31033	−	1.78577i	−0.00506166	−	0.00273054i
$655$	−107.027	+	185.376i	−0.163399	+	0.283016i
$656$	10.1744	+	5.87422i	0.0155098	+	0.00895460i
$657$	−189.190	−	287.902i	−0.287960	−	0.438207i
$658$	−338.714			−0.514764
$659$	−205.439	+	118.610i	−0.311744	+	0.179985i	−0.647706	−	0.761890i	$-0.724272\pi$
$659$	−205.439	+	118.610i	−0.311744	+	0.179985i	0.335963	+	0.941875i	$0.390938\pi$
$660$	9.38659	−	0.271226i	0.0142221	−	0.000410949i
$661$	288.800	−	500.216i	0.436914	−	0.756756i	−0.560536	−	0.828130i	$-0.689405\pi$
$661$	288.800	−	500.216i	0.436914	−	0.756756i	0.997450	+	0.0713735i	$0.0227382\pi$
$662$	70.7370	−	40.8401i	0.106854	−	0.0616919i
$663$	351.470	+	579.302i	0.530120	+	0.873759i
$664$	394.230	−	682.827i	0.593720	−	1.02835i
$665$	43.6421	−	25.1968i	0.0656272	−	0.0378899i
$666$	−408.180	−	205.202i	−0.612883	−	0.308111i
$667$	−475.227	+	823.117i	−0.712484	+	1.23406i
$668$	305.652	+	176.468i	0.457563	+	0.264174i
$669$	363.208	−	673.287i	0.542913	−	1.00641i
$670$	310.970			0.464134
$671$	−34.8961	+	20.1473i	−0.0520061	+	0.0300257i
$672$	−32.2884	−	1117.44i	−0.0480483	−	1.66285i
$673$	372.561			0.553582			0.276791	−	0.960930i	$-0.410729\pi$
$673$	372.561			0.553582			0.276791	+	0.960930i	$0.410729\pi$
$674$	389.666	−	224.974i	0.578139	−	0.333789i
$675$	152.855	−	327.282i	0.226453	−	0.484863i
$676$	−398.983	−	5.70246i	−0.590211	−	0.00843559i
$677$	685.482	+	395.763i	1.01253	+	0.584584i	0.911931	−	0.410343i	$-0.134591\pi$
$677$	685.482	+	395.763i	1.01253	+	0.584584i	0.100598	+	0.994927i	$0.467924\pi$
$678$	68.3521	−	126.706i	0.100814	−	0.186882i
$679$	−635.951	+	1101.50i	−0.936599	+	1.62224i
$680$			482.326i			0.709304i
$681$	−0.467047	−	16.1635i	−0.000685826	−	0.0237350i
$682$	2.67660	+	4.63601i	0.00392463	+	0.00679766i
$683$	−352.092	−	203.280i	−0.515508	−	0.297629i	0.219587	−	0.975593i	$-0.429529\pi$
$683$	−352.092	−	203.280i	−0.515508	−	0.297629i	−0.735095	+	0.677964i	$0.762862\pi$
$684$	26.3563	−	1.52441i	0.0385325	−	0.00222866i
$685$	69.6197	−	120.585i	0.101635	−	0.176036i
$686$			663.694i			0.967483i
$687$	155.576	−	4.49540i	0.226458	−	0.00654352i
$688$	22.2337	+	38.5099i	0.0323164	+	0.0559737i
$689$	816.941	+	5.83777i	1.18569	+	0.00847282i
$690$	352.612	+	190.218i	0.511031	+	0.275679i
$691$	−1045.70			−1.51332			−0.756658	−	0.653811i	$-0.773169\pi$
$691$	−1045.70			−1.51332			−0.756658	+	0.653811i	$0.773169\pi$
$692$	−281.986	+	162.805i	−0.407494	+	0.235267i
$693$	−37.2071	−	18.7049i	−0.0536898	−	0.0269912i
$694$	388.173			0.559328
$695$	98.0591	−	56.6145i	0.141092	−	0.0814596i
$696$	−360.265	+	667.830i	−0.517622	+	0.959526i
$697$	−104.041	−	180.205i	−0.149270	−	0.258544i
$698$			166.782i			0.238943i
$699$	633.440	+	341.713i	0.906209	+	0.488860i
$700$	375.842			0.536917
$701$		−	1179.32i		−	1.68234i	−0.540772	−	0.841169i	$-0.681868\pi$
$701$		−	1179.32i		−	1.68234i	0.540772	−	0.841169i	$-0.318132\pi$
$702$	447.931	−	35.6927i	0.638078	−	0.0508443i
$703$	49.2624			0.0700745
$704$		−	17.1177i		−	0.0243150i
$705$	−107.972	+	200.150i	−0.153152	+	0.283901i
$706$	711.661			1.00802
$707$	−1466.01	+	846.401i	−2.07356	+	1.19717i
$708$	536.603	+	289.474i	0.757914	+	0.408861i
$709$	33.3380	+	57.7431i	0.0470211	+	0.0814430i	0.888578	−	0.458725i	$-0.151694\pi$
$709$	33.3380	+	57.7431i	0.0470211	+	0.0814430i	−0.841557	+	0.540168i	$0.818361\pi$
$710$		−	110.318i		−	0.155377i
$711$	−457.587	+	26.4661i	−0.643582	+	0.0372238i
$712$	−595.989	−	1032.28i	−0.837063	−	1.44984i
$713$		−	329.034i		−	0.461479i
$714$	376.944	−	698.750i	0.527933	−	0.978641i
$715$	−14.9867	+	8.51039i	−0.0209605	+	0.0119026i
$716$	−512.659	+	295.984i	−0.716004	+	0.413385i
$717$	−36.7986	−	1273.52i	−0.0513231	−	1.77619i
$718$	−496.022			−0.690839
$719$	−1116.38	−	644.541i	−1.55268	−	0.896441i	−0.997922	−	0.0644306i	$-0.979477\pi$
$719$	−1116.38	−	644.541i	−1.55268	−	0.896441i	−0.554760	−	0.832011i	$-0.687190\pi$
$720$	26.8899	+	13.5182i	0.0373471	+	0.0187753i
$721$	−544.737	+	943.512i	−0.755530	+	1.30862i
$722$	−398.525	+	230.088i	−0.551973	+	0.318682i
$723$	−526.450	+	15.2118i	−0.728147	+	0.0210399i
$724$	−120.211			−0.166038
$725$	−359.863	−	207.767i	−0.496362	−	0.286575i
$726$	408.485	+	220.360i	0.562652	+	0.303526i
$727$	157.164	−	272.216i	0.216182	−	0.374438i	−0.737456	−	0.675395i	$-0.763973\pi$
$727$	157.164	−	272.216i	0.216182	−	0.374438i	0.953637	+	0.300958i	$0.0973063\pi$
$728$	622.000	+	1095.34i	0.854396	+	1.50459i
$729$	718.078	−	125.720i	0.985017	−	0.172456i
$730$	83.5270	+	144.673i	0.114421	+	0.198182i
$731$		−	787.586i		−	1.07741i
$732$	733.624	−	21.1981i	1.00222	−	0.0289592i
$733$	364.601	+	631.508i	0.497410	+	0.861539i	0.999996	−	0.00298843i	$-0.000951249\pi$
$733$	364.601	+	631.508i	0.497410	+	0.861539i	−0.502586	+	0.864527i	$0.667618\pi$
$734$			455.127i			0.620064i
$735$	833.230	+	449.491i	1.13365	+	0.611552i
$736$	−479.176	+	829.958i	−0.651055	+	1.12766i
$737$	23.9973	+	13.8549i	0.0325608	+	0.0187990i
$738$	−137.763	+	7.96800i	−0.186670	+	0.0107967i
$739$	626.860	+	1085.75i	0.848254	+	1.46922i	0.882765	+	0.469815i	$0.155679\pi$
$739$	626.860	+	1085.75i	0.848254	+	1.46922i	−0.0345112	+	0.999404i	$0.510987\pi$
$740$	−276.398	−	159.578i	−0.373510	−	0.215646i
$741$	−41.4248	+	25.1329i	−0.0559040	+	0.0339176i
$742$	−478.624	−	829.001i	−0.645046	−	1.11725i
$743$	883.125	+	509.873i	1.18859	+	0.686235i	0.957987	−	0.286812i	$-0.0925954\pi$
$743$	883.125	+	509.873i	1.18859	+	0.686235i	0.230607	+	0.973047i	$0.425929\pi$
$744$	−7.58725	−	262.579i	−0.0101979	−	0.352929i
$745$	300.341	+	520.206i	0.403143	+	0.698264i
$746$			103.014i			0.138088i
$747$	50.3159	+	869.937i	0.0673572	+	1.16457i
$748$	−7.97637	+	13.8155i	−0.0106636	+	0.0184699i
$749$	−698.895	−	403.507i	−0.933104	−	0.538728i
$750$	−238.567	+	442.236i	−0.318089	+	0.589648i
$751$	430.676	−	745.953i	0.573470	−	0.993280i	−0.422736	−	0.906253i	$-0.638930\pi$
$751$	430.676	−	745.953i	0.573470	−	0.993280i	0.996206	−	0.0870265i	$-0.0277365\pi$
$752$	18.8904	+	10.9064i	0.0251203	+	0.0145032i
$753$	−567.744	+	350.032i	−0.753976	+	0.464850i
$754$	3.69375	−	516.906i	0.00489887	−	0.685551i
$755$			326.031i			0.431829i
$756$	434.689	+	621.601i	0.574986	+	0.822223i
$757$	−561.757	−	972.991i	−0.742083	−	1.28533i	−0.951545	−	0.307509i	$-0.900505\pi$
$757$	−561.757	−	972.991i	−0.742083	−	1.28533i	0.209462	−	0.977817i	$-0.432829\pi$
$758$	95.5806	−	55.1835i	0.126096	−	0.0728014i
$759$	18.7359	+	30.3892i	0.0246849	+	0.0400384i
$760$	−34.4903			−0.0453819
$761$		−	16.6977i		−	0.0219417i	−0.999940	−	0.0109709i	$-0.996508\pi$
$761$		−	16.6977i		−	0.0219417i	0.999940	−	0.0109709i	$-0.00349220\pi$
$762$	22.0318	+	762.477i	0.0289132	+	1.00063i
$763$	5.82632	+	10.0915i	0.00763607	+	0.0132261i
$764$	602.911	−	348.091i	0.789151	−	0.455617i
$765$	−292.740	−	445.481i	−0.382667	−	0.582328i
$766$	268.899			0.351044
$767$	−1118.97	−	7.99603i	−1.45889	−	0.0104251i
$768$	−376.454	+	697.841i	−0.490175	+	0.908648i
$769$	−407.017	+	704.973i	−0.529280	+	0.916740i	0.470137	+	0.882594i	$0.344205\pi$
$769$	−407.017	+	704.973i	−0.529280	+	0.916740i	−0.999417

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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	117.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.28020i q^{2} +(1.42433 - 2.64032i) q^{3} +2.36108 q^{4} +(2.95232 - 1.70452i) q^{5} +(3.38014 + 1.82343i) q^{6} +(-5.94919 - 10.3043i) q^{7} +8.14347i q^{8} +(-4.94255 - 7.52139i) q^{9} +(2.18213 + 3.77956i) q^{10} +0.388888i q^{11} +(3.36297 - 6.23401i) q^{12} +(-0.0928942 + 12.9997i) q^{13} +(13.1916 - 7.61616i) q^{14} +(-0.295390 - 10.2229i) q^{15} -0.980943 q^{16} +(15.0463 + 8.68699i) q^{17} +(9.62889 - 6.32745i) q^{18} +(-0.621191 + 1.07593i) q^{19} +(6.97067 - 4.02452i) q^{20} +(-35.6802 + 1.03098i) q^{21} -0.497854 q^{22} +(26.5009 + 15.3003i) q^{23} +(21.5013 + 11.5990i) q^{24} +(-6.68922 + 11.5861i) q^{25} +(-16.6422 - 0.118923i) q^{26} +(-26.8987 + 2.33692i) q^{27} +(-14.0465 - 24.3293i) q^{28} +31.0599i q^{29} +(13.0873 - 0.378159i) q^{30} +(-5.37627 - 9.31197i) q^{31} +31.3181i q^{32} +(1.02679 + 0.553906i) q^{33} +(-11.1211 + 19.2623i) q^{34} +(-35.1278 - 20.2810i) q^{35} +(-11.6698 - 17.7586i) q^{36} +(-19.8258 - 34.3393i) q^{37} +(-1.37741 - 0.795249i) q^{38} +(34.1909 + 18.7611i) q^{39} +(13.8807 + 24.0421i) q^{40} +(-10.3721 - 5.98834i) q^{41} +(-1.31987 - 45.6779i) q^{42} +(-22.6657 - 39.2581i) q^{43} +0.918196i q^{44} +(-27.4123 - 13.7808i) q^{45} +(-19.5875 + 33.9265i) q^{46} +(-19.2574 - 11.1183i) q^{47} +(-1.39719 + 2.59000i) q^{48} +(-46.2857 + 80.1692i) q^{49} +(-14.8325 - 8.56355i) q^{50} +(44.3674 - 27.3539i) q^{51} +(-0.219331 + 30.6933i) q^{52} -62.8432i q^{53} +(-2.99173 - 34.4357i) q^{54} +(0.662867 + 1.14812i) q^{55} +(83.9127 - 48.4470i) q^{56} +(1.95602 + 3.17263i) q^{57} -39.7630 q^{58} +86.0767i q^{59} +(-0.697442 - 24.1370i) q^{60} +(51.8074 + 89.7331i) q^{61} +(11.9212 - 6.88271i) q^{62} +(-48.0985 + 95.6756i) q^{63} -44.0172 q^{64} +(21.8839 + 38.5375i) q^{65} +(-0.709111 + 1.31449i) q^{66} +(35.6269 - 61.7076i) q^{67} +(35.5256 + 20.5107i) q^{68} +(78.1438 - 48.1781i) q^{69} +(25.9638 - 44.9706i) q^{70} +(-21.8910 - 12.6388i) q^{71} +(61.2502 - 40.2495i) q^{72} +38.2777 q^{73} +(43.9612 - 25.3810i) q^{74} +(21.0632 + 34.1641i) q^{75} +(-1.46668 + 2.54037i) q^{76} +(4.00721 - 2.31357i) q^{77} +(-24.0180 + 43.7713i) q^{78} +(25.4640 - 44.1049i) q^{79} +(-2.89605 + 1.67204i) q^{80} +(-32.1425 + 74.3496i) q^{81} +(7.66628 - 13.2784i) q^{82} +(-83.8496 - 48.4106i) q^{83} +(-84.2441 + 2.43424i) q^{84} +59.2286 q^{85} +(50.2582 - 29.0166i) q^{86} +(82.0081 + 44.2397i) q^{87} -3.16689 q^{88} +(-126.762 + 73.1861i) q^{89} +(17.6422 - 35.0933i) q^{90} +(134.505 - 76.3803i) q^{91} +(62.5709 + 36.1253i) q^{92} +(-32.2441 + 0.931698i) q^{93} +(14.2336 - 24.6534i) q^{94} +4.23533i q^{95} +(82.6896 + 44.6074i) q^{96} +(-53.4485 - 92.5755i) q^{97} +(-102.633 - 59.2550i) q^{98} +(2.92497 - 1.92209i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - q^{3} - 98 q^{4} - 6 q^{5} + 12 q^{6} - q^{7} - 3 q^{9} - 6 q^{10} - 39 q^{12} + 4 q^{13} - 6 q^{14} - 25 q^{15} + 166 q^{16} + 34 q^{18} + 5 q^{19} + 21 q^{20} - 91 q^{21} + 30 q^{22} - 75 q^{23}+ \cdots + 522 q^{99}+O(q^{100}) \) 52 * q - q^3 - 98 * q^4 - 6 * q^5 + 12 * q^6 - q^7 - 3 * q^9 - 6 * q^10 - 39 * q^12 + 4 * q^13 - 6 * q^14 - 25 * q^15 + 166 * q^16 + 34 * q^18 + 5 * q^19 + 21 * q^20 - 91 * q^21 + 30 * q^22 - 75 * q^23 - 24 * q^24 + 88 * q^25 - 132 * q^26 - 34 * q^27 - 22 * q^28 + 70 * q^30 + 14 * q^31 + 95 * q^33 - 6 * q^34 + 228 * q^35 - 58 * q^36 - 13 * q^37 - 192 * q^38 - 111 * q^39 + 72 * q^40 + 33 * q^41 + 159 * q^42 - 31 * q^43 - 47 * q^45 + 6 * q^46 - 69 * q^47 + 293 * q^48 - 123 * q^49 - 168 * q^50 + 235 * q^51 - 92 * q^52 - 339 * q^54 - 27 * q^55 + 168 * q^56 + 189 * q^57 + 210 * q^58 + 213 * q^60 + 8 * q^61 + 471 * q^62 + 169 * q^63 - 98 * q^64 - 246 * q^65 - 576 * q^66 - 34 * q^67 + 18 * q^68 - 193 * q^69 - 57 * q^70 + 144 * q^71 + 36 * q^72 - 106 * q^73 - 465 * q^74 - 58 * q^75 - 79 * q^76 + 282 * q^77 - 76 * q^78 - 25 * q^79 - 1050 * q^80 - 279 * q^81 + 81 * q^82 + 219 * q^83 + 395 * q^84 - 108 * q^85 - 24 * q^86 - 518 * q^87 + 30 * q^88 + 99 * q^89 + 183 * q^90 + 2 * q^91 + 888 * q^92 + 582 * q^93 + 303 * q^94 - 439 * q^96 + 212 * q^97 - 405 * q^98 + 522 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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