LMFDB - Embedded newform 117.3.k.a.29.17

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			29.17
Character	$\chi$	$=$	117.29
Dual form			117.3.k.a.113.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.15571i q^{2} +(2.85130 - 0.932773i) q^{3} +2.66432 q^{4} +(-3.81803 + 2.20434i) q^{5} +(1.07802 + 3.29529i) q^{6} +(2.07846 + 3.60000i) q^{7} +7.70206i q^{8} +(7.25987 - 5.31924i) q^{9} +(-2.54759 - 4.41256i) q^{10} -1.19738i q^{11} +(7.59680 - 2.48521i) q^{12} +(5.79208 - 11.6384i) q^{13} +(-4.16057 + 2.40211i) q^{14} +(-8.83022 + 9.84661i) q^{15} +1.75592 q^{16} +(-4.88116 - 2.81814i) q^{17} +(6.14752 + 8.39034i) q^{18} +(-5.38154 + 9.32111i) q^{19} +(-10.1725 + 5.87308i) q^{20} +(9.28430 + 8.32596i) q^{21} +1.38383 q^{22} +(-18.2404 - 10.5311i) q^{23} +(7.18427 + 21.9609i) q^{24} +(-2.78175 + 4.81813i) q^{25} +(13.4506 + 6.69399i) q^{26} +(15.7385 - 21.9386i) q^{27} +(5.53769 + 9.59156i) q^{28} -3.47455i q^{29} +(-11.3799 - 10.2052i) q^{30} +(-22.8806 - 39.6303i) q^{31} +32.8376i q^{32} +(-1.11689 - 3.41410i) q^{33} +(3.25697 - 5.64123i) q^{34} +(-15.8713 - 9.16327i) q^{35} +(19.3426 - 14.1722i) q^{36} +(4.09898 + 7.09965i) q^{37} +(-10.7725 - 6.21953i) q^{38} +(5.65902 - 38.5872i) q^{39} +(-16.9780 - 29.4067i) q^{40} +(-58.4348 - 33.7374i) q^{41} +(-9.62243 + 10.7300i) q^{42} +(-26.9088 - 46.6073i) q^{43} -3.19021i q^{44} +(-15.9930 + 36.3123i) q^{45} +(12.1709 - 21.0806i) q^{46} +(51.4209 + 29.6879i) q^{47} +(5.00666 - 1.63787i) q^{48} +(15.8600 - 27.4703i) q^{49} +(-5.56838 - 3.21491i) q^{50} +(-16.5464 - 3.48236i) q^{51} +(15.4320 - 31.0084i) q^{52} +37.7140i q^{53} +(25.3547 + 18.1892i) q^{54} +(2.63944 + 4.57165i) q^{55} +(-27.7274 + 16.0084i) q^{56} +(-6.64994 + 31.5971i) q^{57} +4.01558 q^{58} -41.4775i q^{59} +(-23.5266 + 26.2346i) q^{60} +(29.9579 + 51.8886i) q^{61} +(45.8013 - 26.4434i) q^{62} +(34.2386 + 15.0797i) q^{63} -30.9272 q^{64} +(3.54062 + 57.2034i) q^{65} +(3.94573 - 1.29080i) q^{66} +(-27.5080 + 47.6453i) q^{67} +(-13.0050 - 7.50844i) q^{68} +(-61.8319 - 13.0132i) q^{69} +(10.5901 - 18.3426i) q^{70} +(62.4404 + 36.0500i) q^{71} +(40.9691 + 55.9159i) q^{72} +11.5245 q^{73} +(-8.20517 + 4.73726i) q^{74} +(-3.43739 + 16.3327i) q^{75} +(-14.3382 + 24.8345i) q^{76} +(4.31057 - 2.48871i) q^{77} +(44.5958 + 6.54021i) q^{78} +(-65.9834 + 114.287i) q^{79} +(-6.70416 + 3.87065i) q^{80} +(24.4114 - 77.2339i) q^{81} +(38.9908 - 67.5340i) q^{82} +(-28.0525 - 16.1961i) q^{83} +(24.7364 + 22.1830i) q^{84} +24.8486 q^{85} +(53.8648 - 31.0988i) q^{86} +(-3.24096 - 9.90698i) q^{87} +9.22230 q^{88} +(73.3992 - 42.3771i) q^{89} +(-41.9666 - 18.4833i) q^{90} +(53.9367 - 3.33843i) q^{91} +(-48.5982 - 28.0582i) q^{92} +(-102.206 - 91.6557i) q^{93} +(-34.3107 + 59.4279i) q^{94} -47.4511i q^{95} +(30.6300 + 93.6299i) q^{96} +(29.7342 + 51.5011i) q^{97} +(31.7479 + 18.3296i) q^{98} +(-6.36916 - 8.69284i) 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 $

$2$			1.15571i			0.577857i	0.957351	+	0.288929i	$0.0932990\pi$
$2$			1.15571i			0.577857i	−0.957351	+	0.288929i	$0.906701\pi$
$3$	2.85130	−	0.932773i	0.950435	−	0.310924i
$3$	2.85130	−	0.932773i	0.950435	−	0.310924i
$4$	2.66432			0.666081
$5$	−3.81803	+	2.20434i	−0.763607	+	0.440869i	−0.830589	−	0.556886i	$-0.811996\pi$
$5$	−3.81803	+	2.20434i	−0.763607	+	0.440869i	0.0669825	+	0.997754i	$0.478663\pi$
$6$	1.07802	+	3.29529i	0.179670	+	0.549216i
$7$	2.07846	+	3.60000i	0.296923	+	0.514285i	0.975430	−	0.220308i	$-0.0707063\pi$
$7$	2.07846	+	3.60000i	0.296923	+	0.514285i	−0.678508	+	0.734593i	$0.737373\pi$
$8$			7.70206i			0.962757i
$9$	7.25987	−	5.31924i	0.806652	−	0.591026i
$10$	−2.54759	−	4.41256i	−0.254759	−	0.441256i
$11$		−	1.19738i		−	0.108853i	−0.998518	−	0.0544265i	$-0.982667\pi$
$11$		−	1.19738i		−	0.108853i	0.998518	−	0.0544265i	$-0.0173330\pi$
$12$	7.59680	−	2.48521i	0.633066	−	0.207101i
$13$	5.79208	−	11.6384i	0.445545	−	0.895260i
$13$	5.79208	−	11.6384i	0.445545	−	0.895260i
$14$	−4.16057	+	2.40211i	−0.297184	+	0.171579i
$15$	−8.83022	+	9.84661i	−0.588682	+	0.656441i
$16$	1.75592			0.109745
$17$	−4.88116	−	2.81814i	−0.287127	−	0.165773i	0.349518	−	0.936930i	$-0.386345\pi$
$17$	−4.88116	−	2.81814i	−0.287127	−	0.165773i	−0.636646	+	0.771157i	$0.719679\pi$
$18$	6.14752	+	8.39034i	0.341529	+	0.466130i
$19$	−5.38154	+	9.32111i	−0.283239	+	0.490585i	−0.972181	−	0.234232i	$-0.924742\pi$
$19$	−5.38154	+	9.32111i	−0.283239	+	0.490585i	0.688941	+	0.724817i	$0.258076\pi$
$20$	−10.1725	+	5.87308i	−0.508624	+	0.293654i
$21$	9.28430	+	8.32596i	0.442110	+	0.396474i
$22$	1.38383			0.0629015
$23$	−18.2404	−	10.5311i	−0.793059	−	0.457873i	0.0479795	−	0.998848i	$-0.484722\pi$
$23$	−18.2404	−	10.5311i	−0.793059	−	0.457873i	−0.841038	+	0.540976i	$0.818055\pi$
$24$	7.18427	+	21.9609i	0.299345	+	0.915038i
$25$	−2.78175	+	4.81813i	−0.111270	+	0.192725i
$26$	13.4506	+	6.69399i	0.517332	+	0.257461i
$27$	15.7385	−	21.9386i	0.582906	−	0.812540i
$28$	5.53769	+	9.59156i	0.197775	+	0.342556i
$29$		−	3.47455i		−	0.119812i	−0.998204	−	0.0599059i	$-0.980920\pi$
$29$		−	3.47455i		−	0.119812i	0.998204	−	0.0599059i	$-0.0190801\pi$
$30$	−11.3799	−	10.2052i	−0.379329	−	0.340174i
$31$	−22.8806	−	39.6303i	−0.738083	−	1.27840i	−0.953358	−	0.301843i	$-0.902398\pi$
$31$	−22.8806	−	39.6303i	−0.738083	−	1.27840i	0.215275	−	0.976554i	$-0.430935\pi$
$32$			32.8376i			1.02617i
$33$	−1.11689	−	3.41410i	−0.0338450	−	0.103458i
$34$	3.25697	−	5.64123i	0.0957931	−	0.165919i
$35$	−15.8713	−	9.16327i	−0.453464	−	0.261808i
$36$	19.3426	−	14.1722i	0.537296	−	0.393671i
$37$	4.09898	+	7.09965i	0.110783	+	0.191882i	0.916086	−	0.400981i	$-0.131331\pi$
$37$	4.09898	+	7.09965i	0.110783	+	0.191882i	−0.805303	+	0.592863i	$0.797997\pi$
$38$	−10.7725	−	6.21953i	−0.283488	−	0.163672i
$39$	5.65902	−	38.5872i	0.145103	−	0.989417i
$40$	−16.9780	−	29.4067i	−0.424449	−	0.735168i
$41$	−58.4348	−	33.7374i	−1.42524	−	0.822863i	−0.428500	−	0.903542i	$-0.640958\pi$
$41$	−58.4348	−	33.7374i	−1.42524	−	0.822863i	−0.996740	+	0.0806793i	$0.974291\pi$
$42$	−9.62243	+	10.7300i	−0.229105	+	0.255476i
$43$	−26.9088	−	46.6073i	−0.625785	−	1.08389i	−0.988388	−	0.151948i	$-0.951445\pi$
$43$	−26.9088	−	46.6073i	−0.625785	−	1.08389i	0.362603	−	0.931944i	$-0.381888\pi$
$44$		−	3.19021i		−	0.0725049i
$45$	−15.9930	+	36.3123i	−0.355400	+	0.806939i
$46$	12.1709	−	21.0806i	0.264585	−	0.458275i
$47$	51.4209	+	29.6879i	1.09406	+	0.631657i	0.934655	−	0.355556i	$-0.115709\pi$
$47$	51.4209	+	29.6879i	1.09406	+	0.631657i	0.159407	+	0.987213i	$0.449042\pi$
$48$	5.00666	−	1.63787i	0.104305	−	0.0341224i
$49$	15.8600	−	27.4703i	0.323674	−	0.560619i
$50$	−5.56838	−	3.21491i	−0.111368	−	0.0642981i
$51$	−16.5464	−	3.48236i	−0.324439	−	0.0682816i
$52$	15.4320	−	31.0084i	0.296769	−	0.596316i
$53$			37.7140i			0.711584i	0.934565	+	0.355792i	$0.115789\pi$
$53$			37.7140i			0.711584i	−0.934565	+	0.355792i	$0.884211\pi$
$54$	25.3547	+	18.1892i	0.469532	+	0.336836i
$55$	2.63944	+	4.57165i	0.0479898	+	0.0831208i
$56$	−27.7274	+	16.0084i	−0.495132	+	0.285864i
$57$	−6.64994	+	31.5971i	−0.116666	+	0.554335i
$58$	4.01558			0.0692342
$59$		−	41.4775i		−	0.703008i	−0.936186	−	0.351504i	$-0.885670\pi$
$59$		−	41.4775i		−	0.703008i	0.936186	−	0.351504i	$-0.114330\pi$
$60$	−23.5266	+	26.2346i	−0.392110	+	0.437243i
$61$	29.9579	+	51.8886i	0.491113	+	0.850633i	0.999948	−	0.0102316i	$-0.00325689\pi$
$61$	29.9579	+	51.8886i	0.491113	+	0.850633i	−0.508835	+	0.860864i	$0.669924\pi$
$62$	45.8013	−	26.4434i	0.738731	−	0.426506i
$63$	34.2386	+	15.0797i	0.543470	+	0.239360i
$64$	−30.9272			−0.483237
$65$	3.54062	+	57.2034i	0.0544711	+	0.880053i
$66$	3.94573	−	1.29080i	0.0597837	−	0.0195576i
$67$	−27.5080	+	47.6453i	−0.410567	+	0.711124i	−0.994952	−	0.100353i	$-0.968003\pi$
$67$	−27.5080	+	47.6453i	−0.410567	+	0.711124i	0.584384	+	0.811477i	$0.301336\pi$
$68$	−13.0050	−	7.50844i	−0.191250	−	0.110418i
$69$	−61.8319	−	13.0132i	−0.896114	−	0.188597i
$70$	10.5901	−	18.3426i	0.151288	−	0.262038i
$71$	62.4404	+	36.0500i	0.879442	+	0.507746i	0.870475	−	0.492213i	$-0.163812\pi$
$71$	62.4404	+	36.0500i	0.879442	+	0.507746i	0.00896786	+	0.999960i	$0.497145\pi$
$72$	40.9691	+	55.9159i	0.569015	+	0.776610i
$73$	11.5245			0.157870			0.0789352	−	0.996880i	$-0.474848\pi$
$73$	11.5245			0.157870			0.0789352	+	0.996880i	$0.474848\pi$
$74$	−8.20517	+	4.73726i	−0.110881	+	0.0640170i
$75$	−3.43739	+	16.3327i	−0.0458319	+	0.217769i
$76$	−14.3382	+	24.8345i	−0.188660	+	0.326769i
$77$	4.31057	−	2.48871i	0.0559815	−	0.0323209i
$78$	44.5958	+	6.54021i	0.571742	+	0.0838488i
$79$	−65.9834	+	114.287i	−0.835232	+	1.44666i	0.0586088	+	0.998281i	$0.481334\pi$
$79$	−65.9834	+	114.287i	−0.835232	+	1.44666i	−0.893841	+	0.448384i	$0.852000\pi$
$80$	−6.70416	+	3.87065i	−0.0838019	+	0.0483831i
$81$	24.4114	−	77.2339i	0.301376	−	0.953506i
$82$	38.9908	−	67.5340i	0.475497	−	0.823585i
$83$	−28.0525	−	16.1961i	−0.337981	−	0.195134i	0.321398	−	0.946944i	$-0.395847\pi$
$83$	−28.0525	−	16.1961i	−0.337981	−	0.195134i	−0.659379	+	0.751811i	$0.729181\pi$
$84$	24.7364	+	22.1830i	0.294481	+	0.264084i
$85$	24.8486			0.292336
$86$	53.8648	−	31.0988i	0.626335	−	0.361614i
$87$	−3.24096	−	9.90698i	−0.0372524	−	0.113873i
$88$	9.22230			0.104799
$89$	73.3992	−	42.3771i	0.824711	−	0.476147i	−0.0273276	−	0.999627i	$-0.508700\pi$
$89$	73.3992	−	42.3771i	0.824711	−	0.476147i	0.852038	+	0.523480i	$0.175366\pi$
$90$	−41.9666	−	18.4833i	−0.466296	−	0.205371i
$91$	53.9367	−	3.33843i	0.592711	−	0.0366860i
$92$	−48.5982	−	28.0582i	−0.528241	−	0.304980i
$93$	−102.206	−	91.6557i	−1.09898	−	0.985545i
$94$	−34.3107	+	59.4279i	−0.365007	+	0.632211i
$95$		−	47.4511i		−	0.499485i
$96$	30.6300	+	93.6299i	0.319062	+	0.975311i
$97$	29.7342	+	51.5011i	0.306538	+	0.530939i	0.977603	−	0.210460i	$-0.0674961\pi$
$97$	29.7342	+	51.5011i	0.306538	+	0.530939i	−0.671065	+	0.741399i	$0.734163\pi$
$98$	31.7479	+	18.3296i	0.323958	+	0.187037i
$99$	−6.36916	−	8.69284i	−0.0643350	−	0.0878065i
$100$	−7.41148	+	12.8371i	−0.0741148	+	0.128371i
$101$			91.5231i			0.906170i	0.891467	+	0.453085i	$0.149677\pi$
$101$			91.5231i			0.906170i	−0.891467	+	0.453085i	$0.850323\pi$
$102$	4.02461	−	19.1229i	0.0394570	−	0.187479i
$103$	63.5803	+	110.124i	0.617284	+	1.06917i	0.989979	+	0.141214i	$0.0451005\pi$
$103$	63.5803	+	110.124i	0.617284	+	1.06917i	−0.372695	+	0.927954i	$0.621566\pi$
$104$	89.6394	+	44.6109i	0.861918	+	0.428951i
$105$	−53.8010	−	11.3230i	−0.512391	−	0.107838i
$106$	−43.5866			−0.411194
$107$	109.268	−	63.0859i	1.02120	−	0.589588i	0.106745	−	0.994286i	$-0.465957\pi$
$107$	109.268	−	63.0859i	1.02120	−	0.589588i	0.914450	+	0.404699i	$0.132624\pi$
$108$	41.9323	−	58.4515i	0.388262	−	0.541217i
$109$	−161.530			−1.48193			−0.740965	−	0.671543i	$-0.765632\pi$
$109$	−161.530			−1.48193			−0.740965	+	0.671543i	$0.765632\pi$
$110$	−5.28352	+	3.05044i	−0.0480320	+	0.0277313i
$111$	18.3098	+	16.4198i	0.164953	+	0.147926i
$112$	3.64961	+	6.32130i	0.0325858	+	0.0564402i
$113$		−	174.160i		−	1.54124i	−0.637296	−	0.770619i	$-0.719947\pi$
$113$		−	174.160i		−	1.54124i	0.637296	−	0.770619i	$-0.280053\pi$
$114$	−36.5172	−	7.68544i	−0.320326	−	0.0674161i
$115$	92.8564			0.807447
$116$		−	9.25731i		−	0.0798044i
$117$	−19.8576	−	115.303i	−0.169723	−	0.985492i
$118$	47.9361			0.406239
$119$		−	23.4296i		−	0.196887i
$120$	−75.8391	−	68.0109i	−0.631993	−	0.566757i
$121$	119.566			0.988151
$122$	−59.9684	+	34.6228i	−0.491544	+	0.283793i
$123$	−198.085	−	41.6891i	−1.61045	−	0.338936i
$124$	−60.9612	−	105.588i	−0.491623	−	0.851516i
$125$		−	134.745i		−	1.07796i
$126$	−17.4278	+	39.5700i	−0.138316	+	0.314048i
$127$	124.490	+	215.623i	0.980236	+	1.69782i	0.661445	+	0.749993i	$0.269943\pi$
$127$	124.490	+	215.623i	0.980236	+	1.69782i	0.318791	+	0.947825i	$0.396723\pi$
$128$			95.6073i			0.746932i
$129$	−120.199	−	107.792i	−0.931776	−	0.835596i
$130$	−66.1108	+	4.09195i	−0.508545	+	0.0314765i
$131$	24.0170	−	13.8662i	0.183336	−	0.105849i	−0.405523	−	0.914085i	$-0.632911\pi$
$131$	24.0170	−	13.8662i	0.183336	−	0.105849i	0.588859	+	0.808236i	$0.299577\pi$
$132$	−2.97574	−	9.09627i	−0.0225435	−	0.0689111i
$133$	−44.7413			−0.336401
$134$	−55.0643	−	31.7914i	−0.410928	−	0.237249i
$135$	−11.7298	+	118.455i	−0.0868876	+	0.877446i
$136$	21.7055	−	37.5950i	0.159599	−	0.276434i
$137$	−168.362	+	97.2037i	−1.22892	+	0.709516i	−0.966804	−	0.255520i	$-0.917753\pi$
$137$	−168.362	+	97.2037i	−1.22892	+	0.709516i	−0.262115	+	0.965037i	$0.584420\pi$
$138$	15.0395	−	71.4600i	0.108982	−	0.517826i
$139$	−29.3031			−0.210814			−0.105407	−	0.994429i	$-0.533615\pi$
$139$	−29.3031			−0.210814			−0.105407	+	0.994429i	$0.533615\pi$
$140$	−42.2862	−	24.4139i	−0.302044	−	0.174385i
$141$	174.309	+	36.6851i	1.23623	+	0.260178i
$142$	−41.6635	+	72.1633i	−0.293405	+	0.508192i
$143$	−13.9356	−	6.93533i	−0.0974516	−	0.0484988i
$144$	12.7477	−	9.34015i	0.0885260	−	0.0648621i
$145$	7.65909	+	13.2659i	0.0528213	+	0.0914892i
$146$			13.3191i			0.0912265i
$147$	19.5981	−	93.1201i	0.133321	−	0.633470i
$148$	10.9210	+	18.9158i	0.0737907	+	0.127809i
$149$			86.7158i			0.581985i	0.956725	+	0.290993i	$0.0939855\pi$
$149$			86.7158i			0.581985i	−0.956725	+	0.290993i	$0.906015\pi$
$150$	−18.8759	−	3.97264i	−0.125840	−	0.0264843i
$151$	−17.7929	+	30.8181i	−0.117834	+	0.204094i	−0.918909	−	0.394470i	$-0.870928\pi$
$151$	−17.7929	+	30.8181i	−0.117834	+	0.204094i	0.801075	+	0.598563i	$0.204262\pi$
$152$	−71.7917	−	41.4490i	−0.472314	−	0.272690i
$153$	−50.4270	+	5.50473i	−0.329588	+	0.0359786i
$154$	2.87624	+	4.98179i	0.0186769	+	0.0323493i
$155$	174.718	+	100.873i	1.12721	+	0.650795i
$156$	15.0775	−	102.809i	0.0966503	−	0.659032i
$157$	40.5945	+	70.3117i	0.258564	+	0.447845i	0.965857	−	0.259074i	$-0.0834175\pi$
$157$	40.5945	+	70.3117i	0.258564	+	0.447845i	−0.707294	+	0.706920i	$0.750084\pi$
$158$	−132.083	−	76.2579i	−0.835966	−	0.482645i
$159$	35.1786	+	107.534i	0.221249	+	0.676314i
$160$	−72.3852	−	125.375i	−0.452408	−	0.783593i
$161$		−	87.5536i		−	0.543811i
$162$	89.2604	+	28.2126i	0.550990	+	0.174152i
$163$	22.6376	−	39.2095i	0.138881	−	0.240549i	−0.788192	−	0.615429i	$-0.788983\pi$
$163$	22.6376	−	39.2095i	0.138881	−	0.240549i	0.927073	+	0.374880i	$0.122316\pi$
$164$	−155.689	−	89.8873i	−0.949325	−	0.548093i
$165$	11.7902	+	10.5732i	0.0714555	+	0.0640797i
$166$	18.7181	−	32.4206i	0.112759	−	0.195305i
$167$	173.506	+	100.174i	1.03896	+	0.599842i	0.919538	−	0.393002i	$-0.128563\pi$
$167$	173.506	+	100.174i	1.03896	+	0.599842i	0.119420	+	0.992844i	$0.461897\pi$
$168$	−64.1270	+	71.5082i	−0.381708	+	0.425644i
$169$	−101.904	−	134.821i	−0.602980	−	0.797756i
$170$			28.7179i			0.168929i
$171$	10.5119	+	96.2957i	0.0614730	+	0.563133i
$172$	−71.6937	−	124.177i	−0.416824	−	0.721960i
$173$	163.868	−	94.6091i	0.947212	−	0.546873i	0.0549983	−	0.998486i	$-0.482485\pi$
$173$	163.868	−	94.6091i	0.947212	−	0.546873i	0.892214	+	0.451613i	$0.149151\pi$
$174$	11.4496	−	3.74563i	0.0658026	−	0.0215266i
$175$	−23.1270			−0.132154
$176$		−	2.10251i		−	0.0119461i
$177$	−38.6891	−	118.265i	−0.218582	−	0.668164i
$178$	48.9758	+	84.8286i	0.275145	+	0.476565i
$179$	−78.8621	+	45.5311i	−0.440571	+	0.254364i	−0.703840	−	0.710359i	$-0.748533\pi$
$179$	−78.8621	+	45.5311i	−0.440571	+	0.254364i	0.263269	+	0.964722i	$0.415199\pi$
$180$	−42.6105	+	96.7476i	−0.236725	+	0.537487i
$181$	−324.465			−1.79262			−0.896312	−	0.443423i	$-0.853764\pi$
$181$	−324.465			−1.79262			−0.896312	+	0.443423i	$0.853764\pi$
$182$	3.85827	+	62.3355i	0.0211993	+	0.342503i
$183$	133.819	+	120.006i	0.731253	+	0.655772i
$184$	81.1109	−	140.488i	0.440820	−	0.763523i
$185$	−31.3001	−	18.0711i	−0.169190	−	0.0976818i
$186$	105.928	−	118.120i	0.569504	−	0.635056i
$187$	−3.37439	+	5.84462i	−0.0180449	+	0.0312546i
$188$	137.002	+	79.0981i	0.728734	+	0.420734i
$189$	111.691	+	11.0600i	0.590955	+	0.0585184i
$190$	54.8399			0.288631
$191$	208.761	−	120.528i	1.09299	−	0.631038i	0.158619	−	0.987340i	$-0.449296\pi$
$191$	208.761	−	120.528i	1.09299	−	0.631038i	0.934371	+	0.356301i	$0.115962\pi$
$192$	−88.1828	+	28.8480i	−0.459285	+	0.150250i
$193$	54.5580	−	94.4973i	0.282684	−	0.489623i	−0.689361	−	0.724418i	$-0.742109\pi$
$193$	54.5580	−	94.4973i	0.282684	−	0.489623i	0.972045	+	0.234795i	$0.0754418\pi$
$194$	−59.5205	+	34.3642i	−0.306807	+	0.177135i
$195$	63.4532	+	159.802i	0.325401	+	0.819496i
$196$	42.2562	−	73.1899i	0.215593	−	0.373418i
$197$	50.5241	−	29.1701i	0.256467	−	0.148072i	−0.366255	−	0.930515i	$-0.619360\pi$
$197$	50.5241	−	29.1701i	0.256467	−	0.148072i	0.622722	+	0.782443i	$0.286027\pi$
$198$	10.0464	−	7.36093i	0.0507396	−	0.0371764i
$199$	−40.2524	+	69.7192i	−0.202273	+	0.350348i	−0.949261	−	0.314491i	$-0.898166\pi$
$199$	−40.2524	+	69.7192i	−0.202273	+	0.350348i	0.746987	+	0.664839i	$0.231500\pi$
$200$	−37.1095	−	21.4252i	−0.185548	−	0.107126i
$201$	−33.9915	+	161.510i	−0.169112	+	0.803532i
$202$	−105.775			−0.523637
$203$	12.5084	−	7.22170i	0.0616175	−	0.0355749i
$204$	−44.0849	−	9.27814i	−0.216102	−	0.0454811i
$205$	297.475			1.45110
$206$	−127.272	+	73.4807i	−0.617826	+	0.356702i
$207$	−188.440	+	20.5706i	−0.910337	+	0.0993746i
$208$	10.1704	−	20.4360i	0.0488962	−	0.0982502i
$209$	11.1609	+	6.44377i	0.0534016	+	0.0308314i
$210$	13.0862	−	62.1786i	0.0623150	−	0.296089i
$211$	−100.746	+	174.497i	−0.477469	+	0.827000i	−0.999666	−	0.0258242i	$-0.991779\pi$
$211$	−100.746	+	174.497i	−0.477469	+	0.827000i	0.522198	+	0.852824i	$0.325112\pi$
$212$			100.482i			0.473973i
$213$	211.663	+	44.5468i	0.993723	+	0.209140i
$214$	72.9092	+	126.283i	0.340697	+	0.590105i
$215$	205.477	+	118.632i	0.955707	+	0.551778i
$216$	168.972	+	121.218i	0.782278	+	0.561197i
$217$	95.1127	−	164.740i	0.438307	−	0.759170i
$218$		−	186.683i		−	0.856344i
$219$	32.8600	−	10.7498i	0.150045	−	0.0490857i
$220$	7.03232	+	12.1803i	0.0319651	+	0.0553652i
$221$	−61.0707	+	40.4859i	−0.276338	+	0.183194i
$222$	−18.9766	+	21.1609i	−0.0854804	+	0.0953194i
$223$	279.259			1.25228			0.626141	−	0.779710i	$-0.284633\pi$
$223$	279.259			1.25228			0.626141	+	0.779710i	$0.284633\pi$
$224$	−118.215	+	68.2515i	−0.527746	+	0.304694i
$225$	5.43364	+	49.7758i	0.0241495	+	0.221226i
$226$	201.279			0.890616
$227$	156.883	−	90.5764i	0.691115	−	0.399015i	−0.112915	−	0.993605i	$-0.536019\pi$
$227$	156.883	−	90.5764i	0.691115	−	0.399015i	0.804029	+	0.594589i	$0.202685\pi$
$228$	−17.7176	+	84.1848i	−0.0777088	+	0.369232i
$229$	−92.1879	−	159.674i	−0.402567	−	0.697267i	0.591468	−	0.806329i	$-0.298549\pi$
$229$	−92.1879	−	159.674i	−0.402567	−	0.697267i	−0.994035	+	0.109062i	$0.965215\pi$
$230$			107.315i			0.466589i
$231$	9.96935	−	11.1169i	0.0431574	−	0.0481249i
$232$	26.7611			0.115350
$233$			365.754i			1.56976i	0.619648	+	0.784880i	$0.287275\pi$
$233$			365.754i			1.56976i	−0.619648	+	0.784880i	$0.712725\pi$
$234$	133.257	−	22.9497i	0.569474	−	0.0980755i
$235$	−261.769			−1.11391
$236$		−	110.509i		−	0.468261i
$237$	−81.5352	+	387.413i	−0.344031	+	1.63465i
$238$	27.0779			0.113773
$239$	−383.341	+	221.322i	−1.60394	+	0.926033i	−0.613246	+	0.789892i	$0.710137\pi$
$239$	−383.341	+	221.322i	−1.60394	+	0.926033i	−0.990690	+	0.136141i	$0.956530\pi$
$240$	−15.5052	+	17.2898i	−0.0646048	+	0.0720410i
$241$	−169.035	−	292.778i	−0.701392	−	1.21485i	−0.967978	−	0.251035i	$-0.919229\pi$
$241$	−169.035	−	292.778i	−0.701392	−	1.21485i	0.266586	−	0.963811i	$-0.414104\pi$
$242$			138.184i			0.571010i
$243$	−2.43734	−	242.988i	−0.0100302	−	0.999950i
$244$	79.8175	+	138.248i	0.327121	+	0.566590i
$245$			139.844i			0.570790i
$246$	48.1807	−	228.929i	0.195856	−	0.930608i
$247$	77.3122	+	116.621i	0.313005	+	0.472150i
$248$	305.235	−	176.227i	1.23079	−	0.710594i
$249$	−95.0933	−	20.0134i	−0.381901	−	0.0803752i
$250$	155.727			0.622906
$251$	−165.872	−	95.7661i	−0.660843	−	0.381538i	0.131755	−	0.991282i	$-0.457939\pi$
$251$	−165.872	−	95.7661i	−0.660843	−	0.381538i	−0.792598	+	0.609744i	$0.791272\pi$
$252$	91.2227	+	40.1772i	0.361995	+	0.159433i
$253$	−12.6097	+	21.8407i	−0.0498408	+	0.0863268i
$254$	−249.199	+	143.875i	−0.981097	+	0.566436i
$255$	70.8509	−	23.1781i	0.277847	−	0.0908945i
$256$	−234.203			−0.914857
$257$	−348.494	−	201.203i	−1.35601	−	0.782892i	−0.366926	−	0.930250i	$-0.619590\pi$
$257$	−348.494	−	201.203i	−1.35601	−	0.782892i	−0.989083	+	0.147358i	$0.952923\pi$
$258$	124.577	−	138.916i	0.482855	−	0.538434i
$259$	−17.0391	+	29.5127i	−0.0657882	+	0.113949i
$260$	9.43336	+	152.408i	0.0362822	+	0.586186i
$261$	−18.4819	−	25.2247i	−0.0708120	−	0.0966465i
$262$	16.0254	+	27.7568i	0.0611657	+	0.105942i
$263$		−	120.218i		−	0.457102i	−0.973532	−	0.228551i	$-0.926601\pi$
$263$		−	120.218i		−	0.457102i	0.973532	−	0.228551i	$-0.0733988\pi$
$264$	26.2956	−	8.60231i	0.0996045	−	0.0325845i
$265$	−83.1345	−	143.993i	−0.313715	−	0.543370i
$266$		−	51.7082i		−	0.194392i
$267$	169.755	−	189.295i	0.635788	−	0.708969i
$268$	−73.2903	+	126.942i	−0.273471	+	0.473666i
$269$	−263.310	−	152.022i	−0.978849	−	0.565138i	−0.0769263	−	0.997037i	$-0.524511\pi$
$269$	−263.310	−	152.022i	−0.978849	−	0.565138i	−0.901922	+	0.431898i	$0.857844\pi$
$270$	−136.900	−	13.5563i	−0.507038	−	0.0502086i
$271$	−132.718	−	229.874i	−0.489734	−	0.848245i	0.510196	−	0.860058i	$-0.329573\pi$
$271$	−132.718	−	229.874i	−0.489734	−	0.848245i	−0.999930	+	0.0118135i	$0.996240\pi$
$272$	−8.57093	−	4.94843i	−0.0315108	−	0.0181927i
$273$	150.676	−	59.8296i	0.551927	−	0.219156i
$274$	−112.340	−	194.578i	−0.409999	−	0.710139i
$275$	5.76914	+	3.33082i	0.0209787	+	0.0121121i
$276$	−164.740	−	34.6713i	−0.596885	−	0.125621i
$277$	−138.120	−	239.230i	−0.498627	−	0.863647i	0.501372	−	0.865232i	$-0.332829\pi$
$277$	−138.120	−	239.230i	−0.498627	−	0.863647i	−0.999999	+	0.00158455i	$0.999496\pi$
$278$		−	33.8661i		−	0.121820i
$279$	−376.913	−	166.004i	−1.35094	−	0.594995i
$280$	70.5760	−	122.241i	0.252057	−	0.436576i
$281$	43.7580	+	25.2637i	0.155723	+	0.0899065i	0.575836	−	0.817565i	$-0.304677\pi$
$281$	43.7580	+	25.2637i	0.155723	+	0.0899065i	−0.420114	+	0.907471i	$0.638010\pi$
$282$	−42.3975	+	201.451i	−0.150346	+	0.714365i
$283$	76.0755	−	131.767i	0.268818	−	0.465606i	−0.699739	−	0.714399i	$-0.746700\pi$
$283$	76.0755	−	131.767i	0.268818	−	0.465606i	0.968557	+	0.248792i	$0.0800336\pi$
$284$	166.361	+	96.0488i	0.585780	+	0.338200i
$285$	−44.2611	−	135.297i	−0.155302	−	0.474728i
$286$	8.01526	−	16.1056i	0.0280254	−	0.0563131i
$287$		−	280.487i		−	0.977307i
$288$	174.671	+	238.396i	0.606496	+	0.827765i
$289$	−128.616	−	222.770i	−0.445039	−	0.770829i
$290$	−15.3316	+	8.85172i	−0.0528677	+	0.0305232i
$291$	132.820	+	119.110i	0.456426	+	0.409313i
$292$	30.7051			0.105154
$293$			285.933i			0.975882i	0.872877	+	0.487941i	$0.162252\pi$
$293$			285.933i			0.975882i	−0.872877	+	0.487941i	$0.837748\pi$
$294$	107.620	+	22.6498i	0.366055	+	0.0770403i
$295$	91.4306	+	158.362i	0.309934	+	0.536822i
$296$	−54.6819	+	31.5706i	−0.184736	+	0.106657i
$297$	−26.2689	−	18.8449i	−0.0884473	−	0.0634510i
$298$	−100.219			−0.336304
$299$	−228.214	+	151.291i	−0.763258	+	0.505991i
$300$	−9.15832	+	43.5156i	−0.0305277	+	0.145052i
$301$	111.858	−	193.743i	0.371620	−	0.643664i
$302$	−35.6170	−	20.5635i	−0.117937	−	0.0680909i
$303$	85.3703	+	260.960i	0.281750	+	0.861255i
$304$	−9.44955	+	16.3671i	−0.0310841	+	0.0538392i
$305$	−228.760	−	132.075i	−0.750034	−	0.433032i
$306$	−6.36190	−	58.2792i	−0.0207905	−	0.190455i
$307$	225.537			0.734647			0.367323	−	0.930093i	$-0.380274\pi$
$307$	225.537			0.734647			0.367323	+	0.930093i	$0.380274\pi$
$308$	11.4848	−	6.63073i	0.0372882	−	0.0215283i
$309$	284.008	+	254.692i	0.919119	+	0.824246i
$310$	−116.581	+	201.924i	−0.376067	+	0.651366i
$311$	387.790	−	223.890i	1.24691	−	0.719905i	0.276419	−	0.961037i	$-0.410852\pi$
$311$	387.790	−	223.890i	1.24691	−	0.719905i	0.970492	+	0.241132i	$0.0775188\pi$
$312$	297.201	+	43.5861i	0.952568	+	0.139699i
$313$	−143.843	+	249.143i	−0.459562	+	0.795985i	−0.998938	−	0.0460803i	$-0.985327\pi$
$313$	−143.843	+	249.143i	−0.459562	+	0.795985i	0.539376	+	0.842065i	$0.318660\pi$
$314$	−81.2603	+	46.9156i	−0.258791	+	0.149413i
$315$	−163.965	+	17.8988i	−0.520523	+	0.0568216i
$316$	−175.801	+	304.496i	−0.556332	+	0.963596i
$317$	−373.302	−	215.526i	−1.17761	−	0.679893i	−0.222149	−	0.975013i	$-0.571307\pi$
$317$	−373.302	−	215.526i	−1.17761	−	0.679893i	−0.955460	+	0.295119i	$0.904641\pi$
$318$	−124.279	+	40.6564i	−0.390813	+	0.127850i
$319$	−4.16036			−0.0130419
$320$	118.081	−	68.1741i	0.369003	−	0.213044i
$321$	252.711	−	281.799i	0.787263	−	0.877879i
$322$	101.187			0.314245
$323$	52.5364	−	30.3319i	0.162651	−	0.0939068i
$324$	65.0399	−	205.776i	0.200741	−	0.635112i
$325$	39.9631	+	60.2820i	0.122963	+	0.185483i
$326$	45.3150	+	26.1626i	0.139003	+	0.0802534i
$327$	−460.572	+	150.671i	−1.40848	+	0.460768i
$328$	259.847	−	450.068i	0.792217	−	1.37216i
$329$			246.820i			0.750213i
$330$	−12.2195	+	13.6261i	−0.0370289	+	0.0412911i
$331$	−37.8138	−	65.4955i	−0.114241	−	0.197872i	0.803235	−	0.595662i	$-0.203110\pi$
$331$	−37.8138	−	65.4955i	−0.114241	−	0.197872i	−0.917476	+	0.397791i	$0.869777\pi$
$332$	−74.7408	−	43.1516i	−0.225123	−	0.129975i
$333$	67.5228	+	29.7391i	0.202771	+	0.0893065i
$334$	−115.772	+	200.523i	−0.346623	+	0.600369i
$335$		−	242.548i		−	0.724025i
$336$	16.3025	+	14.6197i	0.0485193	+	0.0435110i
$337$	179.237	+	310.448i	0.531861	+	0.921211i	0.999308	+	0.0371897i	$0.0118406\pi$
$337$	179.237	+	310.448i	0.531861	+	0.921211i	−0.467447	+	0.884021i	$0.654826\pi$
$338$	155.814	−	117.772i	0.460989	−	0.348436i
$339$	−162.452	−	496.583i	−0.479208	−	1.46485i
$340$	66.2047			0.194720
$341$	−47.4526	+	27.3968i	−0.139157	+	0.0803425i
$342$	−111.290	+	12.1487i	−0.325410	+	0.0355226i
$343$	335.547			0.978270
$344$	358.972	−	207.253i	1.04352	−	0.602479i
$345$	264.762	−	86.6139i	0.767425	−	0.251055i
$346$	109.341	+	189.384i	0.316015	+	0.547353i
$347$			401.016i			1.15567i	0.816155	+	0.577833i	$0.196102\pi$
$347$			401.016i			1.15567i	−0.816155	+	0.577833i	$0.803898\pi$
$348$	−8.63497	−	26.3954i	−0.0248131	−	0.0758489i
$349$	−620.263			−1.77726			−0.888629	−	0.458628i	$-0.848341\pi$
$349$	−620.263			−1.77726			−0.888629	+	0.458628i	$0.848341\pi$
$350$		−	26.7282i		−	0.0763663i
$351$	−164.171	−	310.240i	−0.467724	−	0.883875i
$352$	39.3191			0.111702
$353$		−	91.5844i		−	0.259446i	−0.991550	−	0.129723i	$-0.958591\pi$
$353$		−	91.5844i		−	0.259446i	0.991550	−	0.129723i	$-0.0414088\pi$
$354$	136.681	−	44.7135i	0.386103	−	0.126309i
$355$	−317.866			−0.895397
$356$	195.559	−	112.906i	0.549324	−	0.317152i
$357$	−21.8545	−	66.8048i	−0.0612170	−	0.187128i
$358$	−52.6209	−	91.1421i	−0.146986	−	0.254587i
$359$			539.362i			1.50240i	0.660074	+	0.751201i	$0.270525\pi$
$359$			539.362i			1.50240i	−0.660074	+	0.751201i	$0.729475\pi$
$360$	−279.679	−	123.179i	−0.776886	−	0.342164i
$361$	122.578	+	212.311i	0.339551	+	0.588120i
$362$		−	374.989i		−	1.03588i
$363$	340.920	−	111.528i	0.939173	−	0.307240i
$364$	143.705	−	8.89465i	0.394794	−	0.0244359i
$365$	−44.0011	+	25.4040i	−0.120551	+	0.0696001i
$366$	−138.693	+	154.657i	−0.378942	+	0.422560i
$367$	242.757			0.661463			0.330731	−	0.943725i	$-0.392705\pi$
$367$	242.757			0.661463			0.330731	+	0.943725i	$0.392705\pi$
$368$	−32.0286	−	18.4917i	−0.0870342	−	0.0502492i
$369$	−603.686	+	65.8999i	−1.63601	+	0.178590i
$370$	20.8851	−	36.1740i	0.0564461	−	0.0977676i
$371$	−135.770	+	78.3869i	−0.365957	+	0.211286i
$372$	−272.309	−	244.200i	−0.732012	−	0.656453i
$373$	216.538			0.580531			0.290266	−	0.956946i	$-0.406256\pi$
$373$	216.538			0.580531			0.290266	+	0.956946i	$0.406256\pi$
$374$	−6.75471	−	3.89983i	−0.0180607	−	0.0104274i
$375$	−125.686	−	384.198i	−0.335163	−	1.02453i
$376$	−228.658	+	396.047i	−0.608132	+	1.05332i
$377$	−40.4381	−	20.1248i	−0.107263	−	0.0533815i
$378$	−12.7822	+	129.082i	−0.0338153	+	0.341488i
$379$	282.977	+	490.130i	0.746641	+	1.29322i	0.949424	+	0.313996i	$0.101668\pi$
$379$	282.977	+	490.130i	0.746641	+	1.29322i	−0.202783	+	0.979224i	$0.564999\pi$
$380$		−	126.425i		−	0.332697i
$381$	556.086	+	498.686i	1.45954	+	1.30889i
$382$	139.296	+	241.268i	0.364650	+	0.631593i
$383$		−	191.318i		−	0.499525i	−0.968307	−	0.249762i	$-0.919648\pi$
$383$		−	191.318i		−	0.499525i	0.968307	−	0.249762i	$-0.0803525\pi$
$384$	89.1799	+	272.605i	0.232239	+	0.709910i
$385$	−10.9719	+	19.0040i	−0.0284985	+	0.0493609i
$386$	109.212	+	63.0535i	0.282932	+	0.163351i
$387$	−443.270	−	195.229i	−1.14540	−	0.504468i
$388$	79.2214	+	137.216i	0.204179	+	0.353648i
$389$	458.688	+	264.823i	1.17915	+	0.680780i	0.955817	−	0.293963i	$-0.0949742\pi$
$389$	458.688	+	264.823i	1.17915	+	0.680780i	0.223329	+	0.974743i	$0.428308\pi$
$390$	−184.685	+	73.3338i	−0.473552	+	0.188035i
$391$	59.3561	+	102.808i	0.151806	+	0.262935i
$392$	211.578	+	122.155i	0.539740	+	0.311619i
$393$	55.5458	−	61.9393i	0.141338	−	0.157606i
$394$	33.7123	+	58.3914i	0.0855642	+	0.148202i
$395$		−	581.800i		−	1.47291i
$396$	−16.9695	−	23.1605i	−0.0428523	−	0.0584862i
$397$	247.437	−	428.574i	0.623267	−	1.07953i	−0.365606	−	0.930770i	$-0.619138\pi$
$397$	247.437	−	428.574i	0.623267	−	1.07953i	0.988873	−	0.148761i	$-0.0475285\pi$
$398$	−80.5755	−	46.5203i	−0.202451	−	0.116885i
$399$	−127.571	+	41.7335i	−0.319727	+	0.104595i
$400$	−4.88452	+	8.46024i	−0.0122113	+	0.0211506i
$401$	135.312	+	78.1223i	0.337436	+	0.194819i	0.659138	−	0.752022i	$-0.270921\pi$
$401$	135.312	+	78.1223i	0.337436	+	0.194819i	−0.321702	+	0.946841i	$0.604255\pi$
$402$	−186.659	−	39.2845i	−0.464327	−	0.0977226i
$403$	−593.758	+	36.7508i	−1.47335	+	0.0911931i
$404$			243.847i			0.603582i
$405$	77.0465	+	348.693i	0.190238	+	0.860970i
$406$	8.34622	+	14.4561i	0.0205572	+	0.0356061i
$407$	8.50099	−	4.90805i	0.0208870	−	0.0120591i
$408$	26.8213	−	127.441i	0.0657386	−	0.312356i
$409$	59.9988			0.146696			0.0733481	−	0.997306i	$-0.476632\pi$
$409$	59.9988			0.146696			0.0733481	+	0.997306i	$0.476632\pi$
$410$			343.796i			0.838527i
$411$	−389.382	+	434.201i	−0.947401	+	1.05645i
$412$	169.398	+	293.407i	0.411161	+	0.712152i
$413$	149.319	−	86.2093i	0.361547	−	0.208739i
$414$	−23.7737	−	217.783i	−0.0574244	−	0.526045i
$415$	142.807			0.344113
$416$	382.176	+	190.198i	0.918692	+	0.457206i
$417$	−83.5521	+	27.3332i	−0.200365	+	0.0655472i
$418$	−7.44715	+	12.8988i	−0.0178162	+	0.0308585i
$419$	246.976	+	142.592i	0.589442	+	0.340314i	0.764877	−	0.644177i	$-0.222800\pi$
$419$	246.976	+	142.592i	0.589442	+	0.340314i	−0.175435	+	0.984491i	$0.556133\pi$
$420$	−143.343	−	30.1682i	−0.341294	−	0.0718289i
$421$	193.967	−	335.961i	0.460729	−	0.798006i	−0.538268	−	0.842773i	$-0.680921\pi$
$421$	193.967	−	335.961i	0.460729	−	0.798006i	0.998997	+	0.0447674i	$0.0142547\pi$
$422$	−201.669	−	116.434i	−0.477888	−	0.275909i
$423$	531.226	−	57.9899i	1.25585	−	0.137092i
$424$	−290.475			−0.685083
$425$	27.1563	−	15.6787i	0.0638973	−	0.0368911i
$426$	−51.4833	+	244.622i	−0.120853	+	0.574230i
$427$	−124.533	+	215.697i	−0.291645	+	0.505144i
$428$	291.125	−	168.081i	0.680199	−	0.392713i
$429$	−46.2037	−	6.77601i	−0.107701	−	0.0157949i
$430$	−137.105	+	237.473i	−0.318849	+	0.552262i
$431$	187.461	−	108.231i	0.434945	−	0.251116i	−0.266506	−	0.963833i	$-0.585869\pi$
$431$	187.461	−	108.231i	0.434945	−	0.251116i	0.701451	+	0.712718i	$0.252536\pi$
$432$	27.6354	−	38.5223i	0.0639709	−	0.0891721i
$433$	41.6487	−	72.1376i	0.0961863	−	0.166600i	−0.813917	−	0.580981i	$-0.802669\pi$
$433$	41.6487	−	72.1376i	0.0961863	−	0.166600i	0.910103	+	0.414382i	$0.136002\pi$
$434$	190.392	+	109.923i	0.438692	+	0.253279i
$435$	34.2125	+	30.6810i	0.0786494	+	0.0705311i
$436$	−430.369			−0.987086
$437$	196.323	−	113.347i	0.449251	−	0.259375i
$438$	12.4237	+	37.9767i	0.0283645	+	0.0867049i
$439$	285.081			0.649388			0.324694	−	0.945819i	$-0.394739\pi$
$439$	285.081			0.649388			0.324694	+	0.945819i	$0.394739\pi$
$440$	−35.2111	+	20.3291i	−0.0800251	+	0.0462025i
$441$	−30.9797	−	283.794i	−0.0702487	−	0.643525i
$442$	−46.7902	−	70.5803i	−0.105860	−	0.159684i
$443$	434.480	+	250.847i	0.980767	+	0.566246i	0.902502	−	0.430686i	$-0.141728\pi$
$443$	434.480	+	250.847i	0.980767	+	0.566246i	0.0782655	+	0.996933i	$0.475062\pi$
$444$	48.7833	+	43.7478i	0.109872	+	0.0985310i
$445$	−186.827	+	323.594i	−0.419836	+	0.727178i
$446$			322.744i			0.723641i
$447$	80.8861	+	247.253i	0.180953	+	0.553139i
$448$	−64.2809	−	111.338i	−0.143484	−	0.248522i
$449$	−153.082	−	88.3819i	−0.340940	−	0.196842i	0.319748	−	0.947503i	$-0.396402\pi$
$449$	−153.082	−	88.3819i	−0.340940	−	0.196842i	−0.660688	+	0.750661i	$0.729735\pi$
$450$	−57.5266	+	6.27974i	−0.127837	+	0.0139550i
$451$	−40.3965	+	69.9688i	−0.0895710	+	0.155142i
$452$		−	464.018i		−	1.02659i
$453$	−21.9865	+	104.469i	−0.0485354	+	0.230615i
$454$	104.681	+	181.312i	0.230574	+	0.399366i
$455$	−198.573	+	131.641i	−0.436425	+	0.289321i
$456$	−243.362	−	51.2182i	−0.533689	−	0.112321i
$457$	159.859			0.349802			0.174901	−	0.984586i	$-0.444040\pi$
$457$	159.859			0.349802			0.174901	+	0.984586i	$0.444040\pi$
$458$	184.538	−	106.543i	0.402921	−	0.232626i
$459$	−138.648	+	62.7326i	−0.302065	+	0.136672i
$460$	247.399			0.537825
$461$	85.3515	−	49.2777i	0.185144	−	0.106893i	−0.404563	−	0.914510i	$-0.632576\pi$
$461$	85.3515	−	49.2777i	0.185144	−	0.106893i	0.589707	+	0.807617i	$0.299243\pi$
$462$	12.8479	+	11.5217i	0.0278093	+	0.0249388i
$463$	−192.657	−	333.692i	−0.416107	−	0.720718i	0.579437	−	0.815017i	$-0.303272\pi$
$463$	−192.657	−	333.692i	−0.416107	−	0.720718i	−0.995544	+	0.0942990i	$0.969939\pi$
$464$		−	6.10102i		−	0.0131487i
$465$	592.265	+	124.648i	1.27369	+	0.268061i
$466$	−422.707			−0.907097
$467$		−	511.214i		−	1.09468i	−0.836912	−	0.547338i	$-0.815641\pi$
$467$		−	511.214i		−	1.09468i	0.836912	−	0.547338i	$-0.184359\pi$
$468$	−52.9070	−	307.203i	−0.113049	−	0.656417i
$469$	−228.697			−0.487627
$470$		−	302.530i		−	0.643681i
$471$	181.332	+	162.615i	0.384994	+	0.345254i
$472$	319.462			0.676826
$473$	−55.8068	+	32.2201i	−0.117985	+	0.0681185i
$474$	−447.739	−	94.2315i	−0.944597	−	0.198801i
$475$	−29.9402	−	51.8579i	−0.0630320	−	0.109175i
$476$		−	62.4240i		−	0.131143i
$477$	200.610	+	273.798i	0.420565	+	0.574001i
$478$	−255.785	−	443.032i	−0.535115	−	0.926846i
$479$		−	71.9581i		−	0.150226i	−0.997175	−	0.0751128i	$-0.976068\pi$
$479$		−	71.9581i		−	0.150226i	0.997175	−	0.0751128i	$-0.0239317\pi$
$480$	−323.339	−	289.963i	−0.673622	−	0.604090i
$481$	106.370	−	6.58380i	0.221144	−	0.0136877i
$482$	338.368	−	195.357i	0.702008	−	0.405304i
$483$	−81.6676	−	249.642i	−0.169084	−	0.516857i
$484$	318.563			0.658189
$485$	−227.052	−	131.089i	−0.468149	−	0.270286i
$486$	280.824	−	2.81687i	0.577828	−	0.00579602i
$487$	−7.75168	+	13.4263i	−0.0159172	+	0.0275694i	−0.873874	−	0.486152i	$-0.838400\pi$
$487$	−7.75168	+	13.4263i	−0.0159172	+	0.0275694i	0.857957	+	0.513721i	$0.171733\pi$
$488$	−399.649	+	230.737i	−0.818952	+	0.472822i
$489$	27.9732	−	132.914i	0.0572048	−	0.271808i
$490$	−161.619			−0.329835
$491$	−583.945	−	337.141i	−1.18930	−	0.686641i	−0.231151	−	0.972918i	$-0.574249\pi$
$491$	−583.945	−	337.141i	−1.18930	−	0.686641i	−0.958147	+	0.286277i	$0.907582\pi$
$492$	−527.762	−	111.073i	−1.07269	−	0.225759i
$493$	−9.79176	+	16.9598i	−0.0198616	+	0.0344013i
$494$	−134.781	+	89.3509i	−0.272835	+	0.180872i
$495$	43.4797	+	19.1497i	0.0878377	+	0.0386863i
$496$	−40.1764	−	69.5876i	−0.0810008	−	0.140298i
$497$			299.714i			0.603046i
$498$	23.1298	−	109.901i	0.0464454	−	0.220684i
$499$	−339.947	−	588.805i	−0.681256	−	1.17997i	−0.974598	−	0.223962i	$-0.928101\pi$
$499$	−339.947	−	588.805i	−0.681256	−	1.17997i	0.293342	−	0.956007i	$-0.405232\pi$
$500$		−	359.004i		−	0.718008i
$501$	588.157	+	123.784i	1.17397	+	0.247074i
$502$	110.678	−	191.700i	0.220475	−	0.381873i
$503$	80.1083	+	46.2505i	0.159261	+	0.0919494i	0.577512	−	0.816382i	$-0.304024\pi$
$503$	80.1083	+	46.2505i	0.159261	+	0.0919494i	−0.418251	+	0.908331i	$0.637357\pi$
$504$	−116.145	+	263.708i	−0.230446	+	0.523229i
$505$	−201.748	−	349.438i	−0.399502	−	0.691957i
$506$	−25.2416	−	14.5732i	−0.0498845	−	0.0288009i
$507$	−416.315	−	289.362i	−0.821135	−	0.570734i
$508$	331.682	+	574.489i	0.652917	+	1.13088i
$509$	−204.617	−	118.136i	−0.401999	−	0.232094i	0.285347	−	0.958424i	$-0.407891\pi$
$509$	−204.617	−	118.136i	−0.401999	−	0.232094i	−0.687346	+	0.726330i	$0.741224\pi$
$510$	26.7873	+	81.8834i	0.0525240	+	0.160556i
$511$	23.9533	+	41.4883i	0.0468753	+	0.0811904i
$512$			111.757i			0.218275i
$513$	119.795	+	264.763i	0.233518	+	0.516108i
$514$	232.534	−	402.760i	0.452400	−	0.783580i
$515$	−485.503	−	280.305i	−0.942725	−	0.544282i
$516$	−320.249	−	287.193i	−0.620638	−	0.556575i
$517$	35.5477	−	61.5705i	0.0687577	−	0.119092i
$518$	−34.1082	−	19.6924i	−0.0658460	−	0.0380162i
$519$	378.988	−	422.610i	0.730227	−	0.814278i
$520$	−440.584	+	27.2701i	−0.847277	+	0.0524424i
$521$			114.601i			0.219963i	0.993934	+	0.109981i	$0.0350791\pi$
$521$			114.601i			0.219963i	−0.993934	+	0.109981i	$0.964921\pi$
$522$	29.1526	−	21.3598i	0.0558479	−	0.0409192i
$523$	294.538	+	510.154i	0.563169	+	0.975438i	0.997217	+	0.0745483i	$0.0237515\pi$
$523$	294.538	+	510.154i	0.563169	+	0.975438i	−0.434048	+	0.900890i	$0.642915\pi$
$524$	63.9891	−	36.9441i	0.122117	−	0.0705041i
$525$	−65.9421	+	21.5722i	−0.125604	+	0.0410900i
$526$	138.937			0.264140
$527$			257.923i			0.489417i
$528$	−1.96116	−	5.99488i	−0.00371432	−	0.0113539i
$529$	−42.6931	−	73.9466i	−0.0807052	−	0.139786i
$530$	166.415	−	96.0797i	0.313990	−	0.181282i
$531$	−220.629	−	301.121i	−0.415497	−	0.567083i
$532$	−119.205			−0.224070
$533$	−731.107	+	484.677i	−1.37168	+	0.909338i
$534$	218.771	+	196.189i	0.409683	+	0.367395i
$535$	−278.126	+	481.728i	−0.519861	+	0.900426i
$536$	−366.967	−	211.868i	−0.684639	−	0.395277i
$537$	−182.390	+	203.383i	−0.339646	+	0.378740i
$538$	175.694	−	304.311i	0.326569	−	0.565635i
$539$	−32.8925	−	18.9905i	−0.0610251	−	0.0352328i
$540$	−31.2520	+	315.603i	−0.0578742	+	0.584450i
$541$	−151.415			−0.279880			−0.139940	−	0.990160i	$-0.544691\pi$
$541$	−151.415			−0.279880			−0.139940	+	0.990160i	$0.544691\pi$
$542$	265.669	−	153.384i	0.490164	−	0.282997i
$543$	−925.149	+	302.652i	−1.70377	+	0.557371i
$544$	92.5409	−	160.286i	0.170112	−	0.294643i
$545$	616.729	−	356.068i	1.13161	−	0.653336i
$546$	69.1459	+	174.138i	0.126641	+	0.318935i
$547$	458.959	−	794.940i	0.839048	−	1.45327i	−0.0516444	−	0.998666i	$-0.516446\pi$
$547$	458.959	−	794.940i	0.839048	−	1.45327i	0.890692	−	0.454607i	$-0.150220\pi$
$548$	−448.570	+	258.982i	−0.818559	+	0.472595i
$549$	493.498	+	217.351i	0.898904	+	0.395904i
$550$	−3.84947	+	6.66748i	−0.00699904	+	0.0121227i
$551$	32.3866	+	18.6984i	0.0587779	+	0.0339354i
$552$	100.228	−	476.233i	0.181573	−	0.862740i
$553$	−548.575			−0.991998
$554$	276.482	−	159.627i	0.499065	−	0.288135i
$555$	−106.102	−	22.3304i	−0.191176	−	0.0402349i
$556$	−78.0730			−0.140419
$557$	−368.714	+	212.877i	−0.661964	+	0.382185i	−0.793025	−	0.609189i	$-0.791495\pi$
$557$	−368.714	+	212.877i	−0.661964	+	0.382185i	0.131061	+	0.991374i	$0.458162\pi$
$558$	191.853	−	435.604i	0.343822	−	0.780652i
$559$	−698.291	+	43.2209i	−1.24918	+	0.0773183i
$560$	−27.8686	−	16.0900i	−0.0497654	−	0.0287321i
$561$	−4.16972	+	19.8123i	−0.00743265	+	0.0353161i
$562$	−29.1976	+	50.5718i	−0.0519531	+	0.0899854i
$563$			978.187i			1.73745i	0.495291	+	0.868727i	$0.335061\pi$
$563$			978.187i			1.73745i	−0.495291	+	0.868727i	$0.664939\pi$
$564$	464.415	+	97.7410i	0.823430	+	0.173300i
$565$	383.908	+	664.948i	0.679483	+	1.17690i
$566$	152.285	+	87.9216i	0.269054	+	0.155338i
$567$	328.780	−	72.6466i	0.579859	−	0.128124i
$568$	−277.659	+	480.920i	−0.488836	+	0.846689i
$569$			700.782i			1.23160i	0.787901	+	0.615802i	$0.211168\pi$
$569$			700.782i			1.23160i	−0.787901	+	0.615802i	$0.788832\pi$
$570$	156.365	−	51.1532i	0.274325	−	0.0897424i
$571$	−389.201	−	674.116i	−0.681613	−	1.18059i	−0.974489	−	0.224437i	$-0.927946\pi$
$571$	−389.201	−	674.116i	−0.681613	−	1.18059i	0.292876	−	0.956150i	$-0.405388\pi$
$572$	−37.1289	−	18.4780i	−0.0649107	−	0.0323041i
$573$	482.816	−	538.390i	0.842611	−	0.939598i
$574$	324.163			0.564744
$575$	101.480	−	58.5896i	0.176487	−	0.101895i
$576$	−224.527	+	164.509i	−0.389804	+	0.285606i
$577$	986.504			1.70971			0.854856	−	0.518866i	$-0.173646\pi$
$577$	986.504			1.70971			0.854856	+	0.518866i	$0.173646\pi$
$578$	257.458	−	148.644i	0.445429	−	0.257169i
$579$	67.4171	−	320.331i	0.116437	−	0.553248i
$580$	20.4063	+	35.3447i	0.0351833	+	0.0609392i
$581$		−	134.652i		−	0.231758i
$582$	−137.657	+	153.502i	−0.236524	+	0.263749i
$583$	45.1580			0.0774580
$584$			88.7626i			0.151991i
$585$	329.983	+	396.456i	0.564074	+	0.677703i
$586$	−330.457			−0.563921
$587$		−	609.714i		−	1.03869i	−0.854563	−	0.519347i	$-0.826175\pi$
$587$		−	609.714i		−	1.03869i	0.854563	−	0.519347i	$-0.173825\pi$
$588$	52.2158	−	248.102i	0.0888023	−	0.421942i
$589$	492.531			0.836216
$590$	−183.022	+	105.668i	−0.310206	+	0.179098i
$591$	116.850	−	130.300i	0.197716	−	0.220474i
$592$	7.19748	+	12.4664i	0.0121579	+	0.0210581i
$593$			1034.59i			1.74467i	0.488911	+	0.872334i	$0.337394\pi$
$593$			1034.59i			1.74467i	−0.488911	+	0.872334i	$0.662606\pi$
$594$	21.7794	−	30.3593i	0.0366656	−	0.0511099i
$595$	51.6468	+	89.4549i	0.0868013	+	0.150344i
$596$			231.039i			0.387649i
$597$	−49.7397	+	236.337i	−0.0833161	+	0.395875i
$598$	−174.850	−	263.750i	−0.292391	−	0.441054i
$599$	−859.469	+	496.214i	−1.43484	+	0.828405i	−0.997485	−	0.0708843i	$-0.977418\pi$
$599$	−859.469	+	496.214i	−1.43484	+	0.828405i	−0.437355	+	0.899289i	$0.644085\pi$
$600$	−125.795	−	26.4750i	−0.209659	−	0.0441250i
$601$	432.270			0.719251			0.359625	−	0.933097i	$-0.382904\pi$
$601$	432.270			0.719251			0.359625	+	0.933097i	$0.382904\pi$
$602$	223.912	+	129.275i	0.371946	+	0.214743i
$603$	53.7320	+	492.220i	0.0891077	+	0.816286i
$604$	−47.4059	+	82.1095i	−0.0784867	+	0.135943i
$605$	−456.508	+	263.565i	−0.754559	+	0.435645i
$606$	−301.596	+	98.6637i	−0.497682	+	0.162811i
$607$	535.692			0.882525			0.441262	−	0.897378i	$-0.354531\pi$
$607$	535.692			0.882525			0.441262	+	0.897378i	$0.354531\pi$
$608$	−306.082	−	176.717i	−0.503425	−	0.290653i
$609$	28.9289	−	32.2587i	0.0475023	−	0.0529700i
$610$	152.641	−	264.382i	0.250231	−	0.433413i
$611$	643.352	−	426.501i	1.05295	−	0.698038i
$612$	−134.354	+	14.6664i	−0.219532	+	0.0239647i
$613$	−343.288	−	594.593i	−0.560014	−	0.969972i	−0.997494	−	0.0707444i	$-0.977463\pi$
$613$	−343.288	−	594.593i	−0.560014	−	0.969972i	0.437481	−	0.899228i	$-0.355871\pi$
$614$			260.656i			0.424521i
$615$	848.191	−	277.476i	1.37917	−	0.451181i
$616$	19.1682	+	33.2003i	0.0311172	+	0.0538965i
$617$			198.229i			0.321278i	0.987013	+	0.160639i	$0.0513555\pi$
$617$			198.229i			0.321278i	−0.987013	+	0.160639i	$0.948644\pi$
$618$	−294.351	+	328.232i	−0.476296	+	0.531119i
$619$	−348.839	+	604.207i	−0.563552	+	0.976101i	0.433630	+	0.901091i	$0.357232\pi$
$619$	−348.839	+	604.207i	−0.563552	+	0.976101i	−0.997183	+	0.0750105i	$0.976101\pi$
$620$	465.504	+	268.759i	0.750813	+	0.433482i
$621$	−518.112	+	234.424i	−0.834318	+	0.377495i
$622$	258.753	+	448.174i	0.416002	+	0.720537i
$623$	305.115	+	176.158i	0.489751	+	0.282758i
$624$	9.93677	−	67.7561i	0.0159243	−	0.108583i
$625$	227.480	+	394.007i	0.363968	+	0.630411i
$626$	−287.939	−	166.241i	−0.459966	−	0.265561i
$627$	37.8338	+	7.96252i	0.0603409	+	0.0126994i
$628$	108.157	+	187.333i	0.172224	+	0.298301i
$629$		−	46.2061i		−	0.0734596i
$630$	−20.6859	−	189.497i	−0.0328348	−	0.300788i
$631$	−169.170	+	293.012i	−0.268099	+	0.464361i	−0.968371	−	0.249515i	$-0.919729\pi$
$631$	−169.170	+	293.012i	−0.268099	+	0.464361i	0.700272	+	0.713876i	$0.253062\pi$
$632$	−880.241	−	508.207i	−1.39279	−	0.804126i
$633$	−124.491	+	591.517i	−0.196668	+	0.934466i
$634$	249.087	−	431.431i	0.392881	−	0.680490i
$635$	−950.614	−	548.837i	−1.49703	−	0.864310i
$636$	93.7271	+	286.505i	0.147370	+	0.450480i
$637$	−227.848	−	343.695i	−0.357689	−	0.539553i
$638$		−	4.80819i		−	0.00753634i
$639$	645.068	−	70.4172i	1.00950	−	0.110199i
$640$	−210.751	−	365.032i	−0.329299	−	0.570362i
$641$	−97.0449	+	56.0289i	−0.151396	+	0.0874086i	−0.573784	−	0.819006i	$-0.694525\pi$
$641$	−97.0449	+	56.0289i	−0.151396	+	0.0874086i	0.422388	+	0.906415i	$0.361192\pi$
$642$	325.679	+	292.062i	0.507289	+	0.454925i
$643$	133.008			0.206855			0.103427	−	0.994637i	$-0.467019\pi$
$643$	133.008			0.206855			0.103427	+	0.994637i	$0.467019\pi$
$644$		−	233.271i		−	0.362222i
$645$	696.535	+	146.593i	1.07990	+	0.227276i
$646$	35.0550	+	60.7171i	0.0542647	+	0.0939893i
$647$	513.330	−	296.371i	0.793400	−	0.458070i	−0.0477580	−	0.998859i	$-0.515208\pi$
$647$	513.330	−	296.371i	0.793400	−	0.458070i	0.841158	+	0.540789i	$0.181874\pi$
$648$	594.860	+	188.018i	0.917994	+	0.290151i
$649$	−49.6644			−0.0765245
$650$	−69.6688	+	46.1859i	−0.107183	+	0.0710553i
$651$	117.530	−	558.442i	0.180538	−	0.857822i
$652$	60.3139	−	104.467i	0.0925060	−	0.160225i
$653$	−759.015	−	438.217i	−1.16235	−	0.671083i	−0.210484	−	0.977597i	$-0.567504\pi$
$653$	−759.015	−	438.217i	−1.16235	−	0.671083i	−0.951866	+	0.306514i	$0.900837\pi$
$654$	−174.133	−	532.290i	−0.266258	−	0.813899i
$655$	−61.1319	+	105.884i	−0.0933311	+	0.161654i
$656$	−102.607	−	59.2401i	−0.156413	−	0.0903050i
$657$	83.6666	−	61.3017i	0.127346	−	0.0933056i
$658$	−285.254			−0.433516
$659$	482.911	−	278.809i	0.732794	−	0.423079i	−0.0866495	−	0.996239i	$-0.527616\pi$
$659$	482.911	−	278.809i	0.732794	−	0.423079i	0.819443	+	0.573160i	$0.194283\pi$
$660$	31.4128	+	28.1703i	0.0475951	+	0.0426823i
$661$	312.862	−	541.893i	0.473317	−	0.819808i	−0.526217	−	0.850350i	$-0.676390\pi$
$661$	312.862	−	541.893i	0.473317	−	0.819808i	0.999533	+	0.0305420i	$0.00972334\pi$
$662$	75.6941	−	43.7020i	0.114342	−	0.0660151i
$663$	−136.367	+	172.403i	−0.205682	+	0.260034i
$664$	124.743	−	216.062i	0.187866	−	0.325394i
$665$	170.824	−	98.6251i	0.256878	−	0.148308i
$666$	−34.3699	+	78.0371i	−0.0516064	+	0.117173i
$667$	−36.5907	+	63.3769i	−0.0548586	+	0.0950179i
$668$	462.276	+	266.895i	0.692030	+	0.399544i
$669$	796.252	−	260.485i	1.19021	−	0.389365i
$670$	280.317			0.418383
$671$	62.1305	−	35.8710i	0.0925939	−	0.0534591i
$672$	−273.404	+	304.874i	−0.406851	+	0.453681i
$673$	−176.438			−0.262167			−0.131083	−	0.991371i	$-0.541846\pi$
$673$	−176.438			−0.262167			−0.131083	+	0.991371i	$0.541846\pi$
$674$	−358.789	+	207.147i	−0.532328	+	0.307340i
$675$	61.9225	+	136.858i	0.0917370	+	0.202752i
$676$	−271.504	−	359.206i	−0.401634	−	0.531370i
$677$	−104.644	−	60.4161i	−0.154570	−	0.0892409i	0.420720	−	0.907190i	$-0.361777\pi$
$677$	−104.644	−	60.4161i	−0.154570	−	0.0892409i	−0.575290	+	0.817950i	$0.695111\pi$
$678$	573.908	−	187.748i	0.846472	−	0.276914i
$679$	−123.603	+	214.086i	−0.182036	+	0.315296i
$680$			191.385i			0.281449i
$681$	362.834	−	404.597i	0.532796	−	0.594122i
$682$	−31.6629	−	54.8417i	−0.0464265	−	0.0804130i
$683$	0.634589	+	0.366380i	0.000929120	+	0.000536428i	0.500464	−	0.865757i	$-0.333163\pi$
$683$	0.634589	+	0.366380i	0.000929120	+	0.000536428i	−0.499535	+	0.866293i	$0.666496\pi$
$684$	28.0070	+	256.563i	0.0409460	+	0.375092i
$685$	428.541	−	742.254i	0.625607	−	1.08358i
$686$			387.796i			0.565300i
$687$	−411.795	−	369.289i	−0.599411	−	0.537538i
$688$	−47.2496	−	81.8387i	−0.0686767	−	0.118952i
$689$	438.929	+	218.442i	0.637053	+	0.317042i
$690$	100.101	+	305.989i	0.145074	+	0.443462i
$691$	1152.96			1.66854			0.834271	−	0.551354i	$-0.185889\pi$
$691$	1152.96			1.66854			0.834271	+	0.551354i	$0.185889\pi$
$692$	436.597	−	252.069i	0.630920	−	0.364262i
$693$	18.0562	−	40.9967i	0.0260551	−	0.0591583i
$694$	−463.460			−0.667810
$695$	111.880	−	64.5941i	0.160979	−	0.0929412i
$696$	76.3041	−	24.9621i	0.109632	−	0.0358650i
$697$	190.153	+	329.355i	0.272817	+	0.472533i
$698$		−	716.847i		−	1.02700i
$699$	341.165	+	1042.88i	0.488076	+	1.49195i
$700$	−61.6178			−0.0880255
$701$			678.495i			0.967896i	0.875097	+	0.483948i	$0.160798\pi$
$701$			678.495i			0.967896i	−0.875097	+	0.483948i	$0.839202\pi$
$702$	358.549	−	189.735i	0.510753	−	0.270278i
$703$	−88.2355			−0.125513
$704$			37.0316i			0.0526018i
$705$	−746.383	+	244.171i	−1.05870	+	0.346342i
$706$	105.845			0.149923
$707$	−329.483	+	190.227i	−0.466030	+	0.269062i
$708$	−103.080	−	315.096i	−0.145594	−	0.445051i
$709$	−247.180	−	428.129i	−0.348632	−	0.603848i	0.637375	−	0.770554i	$-0.280020\pi$
$709$	−247.180	−	428.129i	−0.348632	−	0.603848i	−0.986007	+	0.166706i	$0.946687\pi$
$710$		−	367.362i		−	0.517412i
$711$	128.887	+	1180.69i	0.181275	+	1.66060i
$712$	326.391	+	565.325i	0.458414	+	0.793996i
$713$			963.827i			1.35179i
$714$	77.2073	−	25.2575i	0.108133	−	0.0353747i
$715$	68.4944	−	4.23948i	0.0957963	−	0.00592934i
$716$	−210.114	+	121.310i	−0.293456	+	0.169427i
$717$	−886.578	+	988.625i	−1.23651	+	1.37884i
$718$	−623.349			−0.868174
$719$	51.9602	+	29.9992i	0.0722673	+	0.0417236i	0.535698	−	0.844409i	$-0.320048\pi$
$719$	51.9602	+	29.9992i	0.0722673	+	0.0417236i	−0.463431	+	0.886133i	$0.653382\pi$
$720$	−28.0824	+	63.7614i	−0.0390033	+	0.0885575i
$721$	−264.298	+	457.778i	−0.366572	+	0.634921i
$722$	−245.371	+	141.665i	−0.339849	+	0.196212i
$723$	−755.067	−	677.127i	−1.04435	−	0.936552i
$724$	−864.480			−1.19403
$725$	16.7408	+	9.66531i	0.0230908	+	0.0133315i
$726$	128.895	+	394.006i	0.177541	+	0.542708i
$727$	−429.204	+	743.403i	−0.590377	+	1.02256i	0.403805	+	0.914845i	$0.367687\pi$
$727$	−429.204	+	743.403i	−0.590377	+	1.02256i	−0.994182	+	0.107717i	$0.965646\pi$
$728$	25.7127	+	415.424i	0.0353197	+	0.570637i
$729$	−233.602	−	690.559i	−0.320442	−	0.947268i
$730$	−29.3598	−	50.8527i	−0.0402189	−	0.0696612i
$731$			303.331i			0.414953i
$732$	356.538	+	319.736i	0.487074	+	0.436797i
$733$	−720.827	−	1248.51i	−0.983393	−	1.70329i	−0.648871	−	0.760899i	$-0.724758\pi$
$733$	−720.827	−	1248.51i	−0.983393	−	1.70329i	−0.334522	−	0.942388i	$-0.608575\pi$
$734$			280.558i			0.382231i
$735$	130.442	+	398.737i	0.177473	+	0.542499i
$736$	345.815	−	598.969i	0.469857	−	0.813816i
$737$	57.0496	+	32.9376i	0.0774079	+	0.0446915i
$738$	−76.1614	−	697.689i	−0.103200	−	0.945378i
$739$	−534.141	−	925.158i	−0.722788	−	1.25191i	−0.959878	−	0.280418i	$-0.909527\pi$
$739$	−534.141	−	925.158i	−0.722788	−	1.25191i	0.237090	−	0.971488i	$-0.423806\pi$
$740$	−83.3937	−	48.1473i	−0.112694	−	0.0650640i
$741$	329.222	+	260.407i	0.444294	+	0.351427i
$742$	−90.5929	−	156.912i	−0.122093	−	0.211471i
$743$	350.296	+	202.244i	0.471462	+	0.272199i	0.716851	−	0.697226i	$-0.245583\pi$
$743$	350.296	+	202.244i	0.471462	+	0.272199i	−0.245390	+	0.969425i	$0.578916\pi$
$744$	705.937	−	787.193i	0.948840	−	1.05805i
$745$	−191.151	−	331.084i	−0.256579	−	0.444408i
$746$			250.256i			0.335464i
$747$	−289.808	+	31.6361i	−0.387963	+	0.0423509i
$748$	−8.99047	+	15.5720i	−0.0120194	+	0.0208181i
$749$	454.218	+	262.243i	0.606432	+	0.350124i
$750$	444.024	−	145.257i	0.592032	−	0.193677i
$751$	−304.195	+	526.882i	−0.405054	+	0.701574i	−0.994328	−	0.106360i	$-0.966081\pi$
$751$	−304.195	+	526.882i	−0.405054	+	0.701574i	0.589274	+	0.807933i	$0.299414\pi$
$752$	90.2909	+	52.1295i	0.120068	+	0.0693211i
$753$	−562.279	−	118.338i	−0.746718	−	0.157155i
$754$	23.2586	−	46.7349i	0.0308469	−	0.0619826i
$755$		−	156.886i		−	0.207796i
$756$	297.580	+	29.4673i	0.393624	+	0.0389780i
$757$	395.079	+	684.296i	0.521900	+	0.903958i	0.999675	+	0.0254758i	$0.00811008\pi$
$757$	395.079	+	684.296i	0.521900	+	0.903958i	−0.477775	+	0.878482i	$0.658557\pi$
$758$	−566.451	+	327.040i	−0.747296	+	0.431452i
$759$	−15.5818	+	74.0364i	−0.0205293	+	0.0975447i
$760$	365.471			0.480883
$761$		−	1002.58i		−	1.31744i	−0.752386	−	0.658722i	$-0.771097\pi$
$761$		−	1002.58i		−	1.31744i	0.752386	−	0.658722i	$-0.228903\pi$
$762$	−576.338	+	642.677i	−0.756350	+	0.843408i
$763$	−335.734	−	581.509i	−0.440019	−	0.762135i
$764$	556.207	−	321.127i	0.728020	−	0.420323i
$765$	180.398	−	132.176i	0.235814	−	0.172779i
$766$	221.109			0.288654
$767$	−482.731	−	240.241i	−0.629375	−	0.313222i
$768$	−667.785	+	218.459i	−0.869512	+	0.284451i
$769$	−101.034	+	174.996i	−0.131384	+	0.227563i	−0.924210	−	0.381884i	$-0.875275\pi$
$769$	−101.034	+	174.996i	−0.131384	+	0.227563i	0.792826	+	0.609447i	$0.208609\pi$

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+1.15571i q^{2} +(2.85130 - 0.932773i) q^{3} +2.66432 q^{4} +(-3.81803 + 2.20434i) q^{5} +(1.07802 + 3.29529i) q^{6} +(2.07846 + 3.60000i) q^{7} +7.70206i q^{8} +(7.25987 - 5.31924i) q^{9} +(-2.54759 - 4.41256i) q^{10} -1.19738i q^{11} +(7.59680 - 2.48521i) q^{12} +(5.79208 - 11.6384i) q^{13} +(-4.16057 + 2.40211i) q^{14} +(-8.83022 + 9.84661i) q^{15} +1.75592 q^{16} +(-4.88116 - 2.81814i) q^{17} +(6.14752 + 8.39034i) q^{18} +(-5.38154 + 9.32111i) q^{19} +(-10.1725 + 5.87308i) q^{20} +(9.28430 + 8.32596i) q^{21} +1.38383 q^{22} +(-18.2404 - 10.5311i) q^{23} +(7.18427 + 21.9609i) q^{24} +(-2.78175 + 4.81813i) q^{25} +(13.4506 + 6.69399i) q^{26} +(15.7385 - 21.9386i) q^{27} +(5.53769 + 9.59156i) q^{28} -3.47455i q^{29} +(-11.3799 - 10.2052i) q^{30} +(-22.8806 - 39.6303i) q^{31} +32.8376i q^{32} +(-1.11689 - 3.41410i) q^{33} +(3.25697 - 5.64123i) q^{34} +(-15.8713 - 9.16327i) q^{35} +(19.3426 - 14.1722i) q^{36} +(4.09898 + 7.09965i) q^{37} +(-10.7725 - 6.21953i) q^{38} +(5.65902 - 38.5872i) q^{39} +(-16.9780 - 29.4067i) q^{40} +(-58.4348 - 33.7374i) q^{41} +(-9.62243 + 10.7300i) q^{42} +(-26.9088 - 46.6073i) q^{43} -3.19021i q^{44} +(-15.9930 + 36.3123i) q^{45} +(12.1709 - 21.0806i) q^{46} +(51.4209 + 29.6879i) q^{47} +(5.00666 - 1.63787i) q^{48} +(15.8600 - 27.4703i) q^{49} +(-5.56838 - 3.21491i) q^{50} +(-16.5464 - 3.48236i) q^{51} +(15.4320 - 31.0084i) q^{52} +37.7140i q^{53} +(25.3547 + 18.1892i) q^{54} +(2.63944 + 4.57165i) q^{55} +(-27.7274 + 16.0084i) q^{56} +(-6.64994 + 31.5971i) q^{57} +4.01558 q^{58} -41.4775i q^{59} +(-23.5266 + 26.2346i) q^{60} +(29.9579 + 51.8886i) q^{61} +(45.8013 - 26.4434i) q^{62} +(34.2386 + 15.0797i) q^{63} -30.9272 q^{64} +(3.54062 + 57.2034i) q^{65} +(3.94573 - 1.29080i) q^{66} +(-27.5080 + 47.6453i) q^{67} +(-13.0050 - 7.50844i) q^{68} +(-61.8319 - 13.0132i) q^{69} +(10.5901 - 18.3426i) q^{70} +(62.4404 + 36.0500i) q^{71} +(40.9691 + 55.9159i) q^{72} +11.5245 q^{73} +(-8.20517 + 4.73726i) q^{74} +(-3.43739 + 16.3327i) q^{75} +(-14.3382 + 24.8345i) q^{76} +(4.31057 - 2.48871i) q^{77} +(44.5958 + 6.54021i) q^{78} +(-65.9834 + 114.287i) q^{79} +(-6.70416 + 3.87065i) q^{80} +(24.4114 - 77.2339i) q^{81} +(38.9908 - 67.5340i) q^{82} +(-28.0525 - 16.1961i) q^{83} +(24.7364 + 22.1830i) q^{84} +24.8486 q^{85} +(53.8648 - 31.0988i) q^{86} +(-3.24096 - 9.90698i) q^{87} +9.22230 q^{88} +(73.3992 - 42.3771i) q^{89} +(-41.9666 - 18.4833i) q^{90} +(53.9367 - 3.33843i) q^{91} +(-48.5982 - 28.0582i) q^{92} +(-102.206 - 91.6557i) q^{93} +(-34.3107 + 59.4279i) q^{94} -47.4511i q^{95} +(30.6300 + 93.6299i) q^{96} +(29.7342 + 51.5011i) q^{97} +(31.7479 + 18.3296i) q^{98} +(-6.36916 - 8.69284i) 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

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