LMFDB - Embedded newform 117.3.k.a.29.12

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			29.12
Character	$\chi$	$=$	117.29
Dual form			117.3.k.a.113.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.487810i q^{2} +(1.50104 + 2.59748i) q^{3} +3.76204 q^{4} +(-6.04718 + 3.49134i) q^{5} +(1.26708 - 0.732220i) q^{6} +(3.63606 + 6.29784i) q^{7} -3.78640i q^{8} +(-4.49379 + 7.79781i) q^{9} +(1.70311 + 2.94987i) q^{10} -13.2988i q^{11} +(5.64696 + 9.77182i) q^{12} +(-6.86798 + 11.0377i) q^{13} +(3.07215 - 1.77371i) q^{14} +(-18.1457 - 10.4668i) q^{15} +13.2011 q^{16} +(10.7424 + 6.20212i) q^{17} +(3.80385 + 2.19211i) q^{18} +(15.6319 - 27.0752i) q^{19} +(-22.7497 + 13.1346i) q^{20} +(-10.9006 + 18.8979i) q^{21} -6.48729 q^{22} +(25.0371 + 14.4552i) q^{23} +(9.83509 - 5.68352i) q^{24} +(11.8789 - 20.5748i) q^{25} +(5.38430 + 3.35027i) q^{26} +(-27.0000 + 0.0322797i) q^{27} +(13.6790 + 23.6927i) q^{28} -27.2026i q^{29} +(-5.10580 + 8.85165i) q^{30} +(-3.11269 - 5.39134i) q^{31} -21.5852i q^{32} +(34.5433 - 19.9620i) q^{33} +(3.02546 - 5.24024i) q^{34} +(-43.9758 - 25.3894i) q^{35} +(-16.9058 + 29.3357i) q^{36} +(-2.38864 - 4.13724i) q^{37} +(-13.2076 - 7.62539i) q^{38} +(-38.9793 - 1.27144i) q^{39} +(13.2196 + 22.8970i) q^{40} +(-15.2056 - 8.77897i) q^{41} +(9.21857 + 5.31745i) q^{42} +(-34.2827 - 59.3793i) q^{43} -50.0306i q^{44} +(-0.0500886 - 62.8441i) q^{45} +(7.05138 - 12.2134i) q^{46} +(-33.6396 - 19.4218i) q^{47} +(19.8153 + 34.2896i) q^{48} +(-1.94186 + 3.36341i) q^{49} +(-10.0366 - 5.79464i) q^{50} +(0.0148298 + 37.2127i) q^{51} +(-25.8376 + 41.5243i) q^{52} +39.0799i q^{53} +(0.0157463 + 13.1709i) q^{54} +(46.4306 + 80.4202i) q^{55} +(23.8462 - 13.7676i) q^{56} +(93.7913 - 0.0373772i) q^{57} -13.2697 q^{58} +48.4526i q^{59} +(-68.2649 - 39.3765i) q^{60} +(34.3961 + 59.5759i) q^{61} +(-2.62995 + 1.51840i) q^{62} +(-65.4491 + 0.0521648i) q^{63} +42.2750 q^{64} +(2.99552 - 90.7254i) q^{65} +(-9.73765 - 16.8506i) q^{66} +(35.4579 - 61.4149i) q^{67} +(40.4133 + 23.3326i) q^{68} +(0.0345636 + 86.7311i) q^{69} +(-12.3852 + 21.4518i) q^{70} +(31.5031 + 18.1883i) q^{71} +(29.5256 + 17.0153i) q^{72} -65.7582 q^{73} +(-2.01819 + 1.16520i) q^{74} +(71.2733 - 0.0284034i) q^{75} +(58.8078 - 101.858i) q^{76} +(83.7537 - 48.3552i) q^{77} +(-0.620223 + 19.0145i) q^{78} +(14.2831 - 24.7390i) q^{79} +(-79.8295 + 46.0896i) q^{80} +(-40.6118 - 70.0834i) q^{81} +(-4.28247 + 7.41745i) q^{82} +(117.848 + 68.0393i) q^{83} +(-41.0087 + 71.0946i) q^{84} -86.6148 q^{85} +(-28.9658 + 16.7234i) q^{86} +(70.6581 - 40.8320i) q^{87} -50.3546 q^{88} +(-107.549 + 62.0934i) q^{89} +(-30.6560 + 0.0244337i) q^{90} +(-94.4861 - 3.11968i) q^{91} +(94.1906 + 54.3810i) q^{92} +(9.33163 - 16.1777i) q^{93} +(-9.47417 + 16.4097i) q^{94} +218.305i q^{95} +(56.0672 - 32.4002i) q^{96} +(16.5765 + 28.7113i) q^{97} +(1.64070 + 0.947261i) q^{98} +(103.702 + 59.7620i) 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 $

$2$		−	0.487810i		−	0.243905i	−0.992536	−	0.121952i	$-0.961084\pi$
$2$		−	0.487810i		−	0.243905i	0.992536	−	0.121952i	$-0.0389156\pi$
$3$	1.50104	+	2.59748i	0.500345	+	0.865826i
$3$	1.50104	+	2.59748i	0.500345	+	0.865826i
$4$	3.76204			0.940510
$5$	−6.04718	+	3.49134i	−1.20944	+	0.698268i	−0.962636	−	0.270799i	$-0.912712\pi$
$5$	−6.04718	+	3.49134i	−1.20944	+	0.698268i	−0.246799	+	0.969067i	$0.579379\pi$
$6$	1.26708	−	0.732220i	0.211179	−	0.122037i
$7$	3.63606	+	6.29784i	0.519437	+	0.899692i	0.999745	+	0.0225914i	$0.00719168\pi$
$7$	3.63606	+	6.29784i	0.519437	+	0.899692i	−0.480308	+	0.877100i	$0.659475\pi$
$8$		−	3.78640i		−	0.473300i
$9$	−4.49379	+	7.79781i	−0.499310	+	0.866424i
$10$	1.70311	+	2.94987i	0.170311	+	0.294987i
$11$		−	13.2988i		−	1.20898i	−0.796612	−	0.604491i	$-0.793377\pi$
$11$		−	13.2988i		−	1.20898i	0.796612	−	0.604491i	$-0.206623\pi$
$12$	5.64696	+	9.77182i	0.470580	+	0.814318i
$13$	−6.86798	+	11.0377i	−0.528306	+	0.849054i
$13$	−6.86798	+	11.0377i	−0.528306	+	0.849054i
$14$	3.07215	−	1.77371i	0.219439	−	0.126693i
$15$	−18.1457	−	10.4668i	−1.20971	−	0.697786i
$16$	13.2011			0.825070
$17$	10.7424	+	6.20212i	0.631905	+	0.364831i	0.781490	−	0.623918i	$-0.214460\pi$
$17$	10.7424	+	6.20212i	0.631905	+	0.364831i	−0.149584	+	0.988749i	$0.547794\pi$
$18$	3.80385	+	2.19211i	0.211325	+	0.121784i
$19$	15.6319	−	27.0752i	0.822731	−	1.42501i	−0.0809106	−	0.996721i	$-0.525783\pi$
$19$	15.6319	−	27.0752i	0.822731	−	1.42501i	0.903641	−	0.428290i	$-0.140884\pi$
$20$	−22.7497	+	13.1346i	−1.13749	+	0.656728i
$21$	−10.9006	+	18.8979i	−0.519079	+	0.899898i
$22$	−6.48729			−0.294877
$23$	25.0371	+	14.4552i	1.08857	+	0.628486i	0.933195	−	0.359370i	$-0.117008\pi$
$23$	25.0371	+	14.4552i	1.08857	+	0.628486i	0.155374	+	0.987856i	$0.450342\pi$
$24$	9.83509	−	5.68352i	0.409796	−	0.236813i
$25$	11.8789	−	20.5748i	0.475155	−	0.822993i
$26$	5.38430	+	3.35027i	0.207089	+	0.128856i
$27$	−27.0000	+	0.0322797i	−0.999999	+	0.00119554i
$28$	13.6790	+	23.6927i	0.488536	+	0.846169i
$29$		−	27.2026i		−	0.938020i	−0.883193	−	0.469010i	$-0.844611\pi$
$29$		−	27.2026i		−	0.938020i	0.883193	−	0.469010i	$-0.155389\pi$
$30$	−5.10580	+	8.85165i	−0.170193	+	0.295055i
$31$	−3.11269	−	5.39134i	−0.100409	−	0.173914i	0.811444	−	0.584430i	$-0.198682\pi$
$31$	−3.11269	−	5.39134i	−0.100409	−	0.173914i	−0.911853	+	0.410516i	$0.865349\pi$
$32$		−	21.5852i		−	0.674539i
$33$	34.5433	−	19.9620i	1.04677	−	0.604908i
$34$	3.02546	−	5.24024i	0.0889840	−	0.154125i
$35$	−43.9758	−	25.3894i	−1.25645	−	0.725412i
$36$	−16.9058	+	29.3357i	−0.469606	+	0.814880i
$37$	−2.38864	−	4.13724i	−0.0645577	−	0.111817i	0.831940	−	0.554866i	$-0.187230\pi$
$37$	−2.38864	−	4.13724i	−0.0645577	−	0.111817i	−0.896498	+	0.443048i	$0.853897\pi$
$38$	−13.2076	−	7.62539i	−0.347567	−	0.200668i
$39$	−38.9793	−	1.27144i	−0.999468	−	0.0326011i
$40$	13.2196	+	22.8970i	0.330490	+	0.572426i
$41$	−15.2056	−	8.77897i	−0.370869	−	0.214121i	0.302969	−	0.953000i	$-0.402022\pi$
$41$	−15.2056	−	8.77897i	−0.370869	−	0.214121i	−0.673838	+	0.738879i	$0.735355\pi$
$42$	9.21857	+	5.31745i	0.219490	+	0.126606i
$43$	−34.2827	−	59.3793i	−0.797272	−	1.38091i	−0.921387	−	0.388647i	$-0.872943\pi$
$43$	−34.2827	−	59.3793i	−0.797272	−	1.38091i	0.124115	−	0.992268i	$-0.460391\pi$
$44$		−	50.0306i		−	1.13706i
$45$	−0.0500886	−	62.8441i	−0.00111308	−	1.39653i
$46$	7.05138	−	12.2134i	0.153291	−	0.265508i
$47$	−33.6396	−	19.4218i	−0.715737	−	0.413231i	0.0974449	−	0.995241i	$-0.468933\pi$
$47$	−33.6396	−	19.4218i	−0.715737	−	0.413231i	−0.813181	+	0.582010i	$0.802266\pi$
$48$	19.8153	+	34.2896i	0.412820	+	0.714367i
$49$	−1.94186	+	3.36341i	−0.0396299	+	0.0686410i
$50$	−10.0366	−	5.79464i	−0.200732	−	0.115893i
$51$	0.0148298	+	37.2127i	0.000290781	+	0.729661i
$52$	−25.8376	+	41.5243i	−0.496877	+	0.798544i
$53$			39.0799i			0.737357i	0.929557	+	0.368678i	$0.120190\pi$
$53$			39.0799i			0.737357i	−0.929557	+	0.368678i	$0.879810\pi$
$54$	0.0157463	+	13.1709i	0.000291599	+	0.243905i
$55$	46.4306	+	80.4202i	0.844193	+	1.46218i
$56$	23.8462	−	13.7676i	0.425824	−	0.245850i
$57$	93.7913	−	0.0373772i	1.64546	−	0.000655740i
$58$	−13.2697			−0.228788
$59$			48.4526i			0.821230i	0.911809	+	0.410615i	$0.134686\pi$
$59$			48.4526i			0.821230i	−0.911809	+	0.410615i	$0.865314\pi$
$60$	−68.2649	−	39.3765i	−1.13775	−	0.656275i
$61$	34.3961	+	59.5759i	0.563871	+	0.976653i	0.997154	+	0.0753953i	$0.0240219\pi$
$61$	34.3961	+	59.5759i	0.563871	+	0.976653i	−0.433283	+	0.901258i	$0.642645\pi$
$62$	−2.62995	+	1.51840i	−0.0424186	+	0.0244904i
$63$	−65.4491	+	0.0521648i	−1.03887	+	0.000828013i
$64$	42.2750			0.660547
$65$	2.99552	−	90.7254i	0.0460848	−	1.39577i
$66$	−9.73765	−	16.8506i	−0.147540	−	0.255312i
$67$	35.4579	−	61.4149i	0.529222	−	0.916640i	−0.470197	−	0.882562i	$-0.655817\pi$
$67$	35.4579	−	61.4149i	0.529222	−	0.916640i	0.999419	−	0.0340783i	$-0.0108496\pi$
$68$	40.4133	+	23.3326i	0.594313	+	0.343127i
$69$	0.0345636	+	86.7311i	0.000500922	+	1.25697i
$70$	−12.3852	+	21.4518i	−0.176932	+	0.306455i
$71$	31.5031	+	18.1883i	0.443705	+	0.256173i	0.705168	−	0.709040i	$-0.250872\pi$
$71$	31.5031	+	18.1883i	0.443705	+	0.256173i	−0.261463	+	0.965214i	$0.584205\pi$
$72$	29.5256	+	17.0153i	0.410078	+	0.236323i
$73$	−65.7582			−0.900797			−0.450398	−	0.892828i	$-0.648718\pi$
$73$	−65.7582			−0.900797			−0.450398	+	0.892828i	$0.648718\pi$
$74$	−2.01819	+	1.16520i	−0.0272728	+	0.0157459i
$75$	71.2733	−	0.0284034i	0.950311	−	0.000378713i
$76$	58.8078	−	101.858i	0.773787	−	1.34024i
$77$	83.7537	−	48.3552i	1.08771	−	0.627990i
$78$	−0.620223	+	19.0145i	−0.00795157	+	0.243775i
$79$	14.2831	−	24.7390i	0.180798	−	0.313152i	−0.761354	−	0.648336i	$-0.775465\pi$
$79$	14.2831	−	24.7390i	0.180798	−	0.313152i	0.942153	+	0.335184i	$0.108799\pi$
$80$	−79.8295	+	46.0896i	−0.997869	+	0.576120i
$81$	−40.6118	−	70.0834i	−0.501380	−	0.865227i
$82$	−4.28247	+	7.41745i	−0.0522252	+	0.0904567i
$83$	117.848	+	68.0393i	1.41985	+	0.819751i	0.996285	−	0.0861146i	$-0.0274451\pi$
$83$	117.848	+	68.0393i	1.41985	+	0.819751i	0.423565	+	0.905866i	$0.360778\pi$
$84$	−41.0087	+	71.0946i	−0.488199	+	0.846364i
$85$	−86.6148			−1.01900
$86$	−28.9658	+	16.7234i	−0.336812	+	0.194459i
$87$	70.6581	−	40.8320i	0.812162	−	0.469334i
$88$	−50.3546			−0.572211
$89$	−107.549	+	62.0934i	−1.20842	+	0.697679i	−0.962413	−	0.271591i	$-0.912450\pi$
$89$	−107.549	+	62.0934i	−1.20842	+	0.697679i	−0.246002	+	0.969269i	$0.579117\pi$
$90$	−30.6560	+	0.0244337i	−0.340622	+	0.000271486i
$91$	−94.4861	−	3.11968i	−1.03831	−	0.0342822i
$92$	94.1906	+	54.3810i	1.02381	+	0.591098i
$93$	9.33163	−	16.1777i	0.100340	−	0.173954i
$94$	−9.47417	+	16.4097i	−0.100789	+	0.174572i
$95$			218.305i			2.29794i
$96$	56.0672	−	32.4002i	0.584033	−	0.337502i
$97$	16.5765	+	28.7113i	0.170891	+	0.295992i	0.938732	−	0.344649i	$-0.112002\pi$
$97$	16.5765	+	28.7113i	0.170891	+	0.295992i	−0.767840	+	0.640641i	$0.778669\pi$
$98$	1.64070	+	0.947261i	0.0167419	+	0.00966592i
$99$	103.702	+	59.7620i	1.04749	+	0.603656i
$100$	44.6889	−	77.4034i	0.446889	−	0.774034i
$101$		−	103.928i		−	1.02899i	−0.857493	−	0.514496i	$-0.827979\pi$
$101$		−	103.928i		−	1.02899i	0.857493	−	0.514496i	$-0.172021\pi$
$102$	18.1527	−	0.00723413i	0.177968	−	7.09228e-5i
$103$	55.7564	+	96.5729i	0.541324	+	0.937601i	0.998828	+	0.0483936i	$0.0154102\pi$
$103$	55.7564	+	96.5729i	0.541324	+	0.937601i	−0.457504	+	0.889208i	$0.651256\pi$
$104$	41.7932	+	26.0049i	0.401857	+	0.250047i
$105$	−0.0607083	−	152.337i	−0.000578175	−	1.45082i
$106$	19.0636			0.179845
$107$	−95.0812	+	54.8952i	−0.888609	+	0.513039i	−0.873487	−	0.486847i	$-0.838147\pi$
$107$	−95.0812	+	54.8952i	−0.888609	+	0.513039i	−0.0151221	+	0.999886i	$0.504814\pi$
$108$	−101.575	+	0.121437i	−0.940510	+	0.00112442i
$109$	−173.169			−1.58871			−0.794355	−	0.607454i	$-0.792191\pi$
$109$	−173.169			−1.58871			−0.794355	+	0.607454i	$0.792191\pi$
$110$	39.2298	−	22.6493i	0.356634	−	0.205903i
$111$	7.16096	−	12.4146i	0.0645131	−	0.111843i
$112$	48.0001	+	83.1386i	0.428572	+	0.742309i
$113$			67.6124i			0.598340i	0.954200	+	0.299170i	$0.0967097\pi$
$113$			67.6124i			0.598340i	−0.954200	+	0.299170i	$0.903290\pi$
$114$	−0.0182330	−	45.7523i	−0.000159938	−	0.401336i
$115$	−201.872			−1.75541
$116$		−	102.337i		−	0.882218i
$117$	−55.2067	−	103.156i	−0.471852	−	0.881678i
$118$	23.6356			0.200302
$119$			90.2051i			0.758026i
$120$	−39.6314	+	68.7069i	−0.330262	+	0.572557i
$121$	−55.8580			−0.461637
$122$	29.0617	−	16.7788i	0.238211	−	0.137531i
$123$	−0.0209913	−	52.6738i	−0.000170661	−	0.428242i
$124$	−11.7101	−	20.2825i	−0.0944361	−	0.163568i
$125$		−	8.67411i		−	0.0693929i
$126$	0.0254465	+	31.9267i	0.000201956	+	0.253387i
$127$	−80.7093	−	139.793i	−0.635506	−	1.10073i	−0.986408	−	0.164317i	$-0.947458\pi$
$127$	−80.7093	−	139.793i	−0.635506	−	1.10073i	0.350902	−	0.936412i	$-0.385875\pi$
$128$		−	106.963i		−	0.835650i
$129$	102.777	−	178.179i	0.796721	−	1.38123i
$130$	−44.2567	−	1.46124i	−0.340436	−	0.0112403i
$131$	115.941	−	66.9384i	0.885044	−	0.510980i	0.0127257	−	0.999919i	$-0.495949\pi$
$131$	115.941	−	66.9384i	0.885044	−	0.510980i	0.872318	+	0.488939i	$0.162616\pi$
$132$	129.953	−	75.0977i	0.984496	−	0.568922i
$133$	227.354			1.70943
$134$	−29.9588	−	17.2967i	−0.223573	−	0.129080i
$135$	163.161	−	94.4613i	1.20860	−	0.699713i
$136$	23.4837	−	40.6750i	0.172674	−	0.299081i
$137$	−56.9217	+	32.8638i	−0.415487	+	0.239882i	−0.693145	−	0.720798i	$-0.743775\pi$
$137$	−56.9217	+	32.8638i	−0.415487	+	0.239882i	0.277657	+	0.960680i	$0.410442\pi$
$138$	42.3083	−	0.0168605i	0.306582	−	0.000122177i
$139$	−106.816			−0.768459			−0.384229	−	0.923238i	$-0.625533\pi$
$139$	−106.816			−0.768459			−0.384229	+	0.923238i	$0.625533\pi$
$140$	−165.439	−	95.5161i	−1.18171	−	0.682258i
$141$	−0.0464393	−	116.531i	−0.000329357	−	0.826461i
$142$	8.87244	−	15.3675i	0.0624820	−	0.108222i
$143$	146.788	+	91.3359i	1.02649	+	0.638712i
$144$	−59.3230	+	102.940i	−0.411965	+	0.714860i
$145$	94.9734	+	164.499i	0.654989	+	1.13447i
$146$			32.0775i			0.219709i
$147$	−11.6512	+	0.00464316i	−0.0792597	+	3.15862e-5i
$148$	−8.98614	−	15.5645i	−0.0607172	−	0.105165i
$149$		−	72.8766i		−	0.489105i	−0.969636	−	0.244552i	$-0.921359\pi$
$149$		−	72.8766i		−	0.489105i	0.969636	−	0.244552i	$-0.0786410\pi$
$150$	−0.0138555	−	34.7678i	−9.23699e−5	−	0.231786i
$151$	−27.9610	+	48.4298i	−0.185172	+	0.320727i	−0.943634	−	0.330989i	$-0.892618\pi$
$151$	−27.9610	+	48.4298i	−0.185172	+	0.320727i	0.758462	+	0.651717i	$0.225951\pi$
$152$	−102.518	−	59.1886i	−0.674458	−	0.389399i
$153$	−96.6370	+	55.8961i	−0.631614	+	0.365334i
$154$	−23.5882	−	40.8559i	−0.153170	−	0.265298i
$155$	37.6460	+	21.7349i	0.242877	+	0.140225i
$156$	−146.642	−	4.78322i	−0.940010	−	0.0306617i
$157$	−53.6483	−	92.9215i	−0.341709	−	0.591857i	0.643041	−	0.765831i	$-0.277672\pi$
$157$	−53.6483	−	92.9215i	−0.341709	−	0.591857i	−0.984750	+	0.173975i	$0.944339\pi$
$158$	−12.0679	−	6.96742i	−0.0763793	−	0.0440976i
$159$	−101.509	+	58.6603i	−0.638423	+	0.368933i
$160$	75.3614	+	130.530i	0.471009	+	0.815811i
$161$			210.240i			1.30584i
$162$	−34.1874	+	19.8108i	−0.211033	+	0.122289i
$163$	−10.9857	+	19.0279i	−0.0673972	+	0.116735i	−0.897755	−	0.440495i	$-0.854803\pi$
$163$	−10.9857	+	19.0279i	−0.0673972	+	0.116735i	0.830358	+	0.557231i	$0.188136\pi$
$164$	−57.2042	−	33.0268i	−0.348806	−	0.201383i
$165$	−139.196	+	241.316i	−0.843610	+	1.46252i
$166$	33.1903	−	57.4872i	0.199941	−	0.346309i
$167$	89.1759	+	51.4858i	0.533988	+	0.308298i	0.742639	−	0.669692i	$-0.233574\pi$
$167$	89.1759	+	51.4858i	0.533988	+	0.308298i	−0.208651	+	0.977990i	$0.566907\pi$
$168$	71.5549	+	41.2742i	0.425922	+	0.245680i
$169$	−74.6617	−	151.613i	−0.441786	−	0.897121i
$170$			42.2516i			0.248539i
$171$	140.881	+	243.565i	0.823866	+	1.42436i
$172$	−128.973	−	223.388i	−0.749842	−	1.29876i
$173$	37.8574	−	21.8570i	0.218829	−	0.126341i	−0.386579	−	0.922256i	$-0.626343\pi$
$173$	37.8574	−	21.8570i	0.218829	−	0.126341i	0.605408	+	0.795915i	$0.293010\pi$
$174$	−19.9183	−	34.4677i	−0.114473	−	0.198090i
$175$	172.769			0.987253
$176$		−	175.559i		−	0.997495i
$177$	−125.854	+	72.7290i	−0.711042	+	0.410898i
$178$	30.2898	+	52.4634i	0.170167	+	0.294738i
$179$	−72.0040	+	41.5715i	−0.402257	+	0.232243i	−0.687457	−	0.726225i	$-0.741273\pi$
$179$	−72.0040	+	41.5715i	−0.402257	+	0.232243i	0.285200	+	0.958468i	$0.407940\pi$
$180$	−0.188435	−	236.422i	−0.00104686	−	1.31346i
$181$	187.685			1.03693			0.518467	−	0.855098i	$-0.326503\pi$
$181$	187.685			1.03693			0.518467	+	0.855098i	$0.326503\pi$
$182$	−1.52181	+	46.0912i	−0.00836161	+	0.253249i
$183$	−103.117	+	178.769i	−0.563482	+	0.976878i
$184$	54.7331	−	94.8005i	0.297463	−	0.515220i
$185$	28.8890	+	16.6791i	0.156157	+	0.0901571i
$186$	−7.89167	−	4.55206i	−0.0424283	−	0.0244735i
$187$	82.4807	−	142.861i	0.441073	−	0.763962i
$188$	−126.554	−	73.0658i	−0.673158	−	0.388648i
$189$	−98.3768	−	169.924i	−0.520512	−	0.899070i
$190$	106.491			0.560480
$191$	−20.2778	+	11.7074i	−0.106167	+	0.0612954i	−0.552143	−	0.833749i	$-0.686190\pi$
$191$	−20.2778	+	11.7074i	−0.106167	+	0.0612954i	0.445976	+	0.895045i	$0.352856\pi$
$192$	63.4562	+	109.808i	0.330501	+	0.571919i
$193$	−66.0165	+	114.344i	−0.342054	+	0.592456i	−0.984814	−	0.173612i	$-0.944456\pi$
$193$	−66.0165	+	114.344i	−0.342054	+	0.592456i	0.642760	+	0.766068i	$0.277789\pi$
$194$	14.0056	−	8.08616i	0.0721940	−	0.0416812i
$195$	240.154	−	128.401i	1.23156	−	0.658468i
$196$	−7.30537	+	12.6533i	−0.0372723	+	0.0645575i
$197$	174.634	−	100.825i	0.886468	−	0.511802i	0.0136824	−	0.999906i	$-0.495645\pi$
$197$	174.634	−	100.825i	0.886468	−	0.511802i	0.872786	+	0.488104i	$0.162311\pi$
$198$	29.1525	−	50.5866i	0.147235	−	0.255488i
$199$	−166.537	+	288.450i	−0.836868	+	1.44950i	0.0556333	+	0.998451i	$0.482282\pi$
$199$	−166.537	+	288.450i	−0.836868	+	1.44950i	−0.892501	+	0.451046i	$0.851051\pi$
$200$	−77.9046	−	44.9782i	−0.389523	−	0.224891i
$201$	212.747	−	0.0847829i	1.05844	−	0.000421805i
$202$	−50.6972			−0.250976
$203$	171.318	−	98.9102i	0.843929	−	0.487242i
$204$	0.0557903	+	139.996i	0.000273482	+	0.686254i
$205$	122.601			0.598055
$206$	47.1092	−	27.1985i	0.228686	−	0.132032i
$207$	−225.230	+	130.276i	−1.08807	+	0.629354i
$208$	−90.6650	+	145.710i	−0.435889	+	0.700529i
$209$	−360.068	−	207.885i	−1.72281	−	0.994666i
$210$	−74.3113	+	0.0296141i	−0.353863	+	0.000141020i
$211$	−78.6862	+	136.289i	−0.372921	+	0.645917i	−0.990013	−	0.140973i	$-0.954977\pi$
$211$	−78.6862	+	136.289i	−0.372921	+	0.645917i	0.617093	+	0.786890i	$0.288310\pi$
$212$			147.020i			0.693492i
$213$	0.0434898	+	109.130i	0.000204178	+	0.512347i
$214$	26.7784	+	46.3816i	0.125133	+	0.216736i
$215$	414.627	+	239.385i	1.92850	+	1.11342i
$216$	0.122224	+	102.233i	0.000565851	+	0.473300i
$217$	22.6359	−	39.2065i	0.104313	−	0.180675i
$218$			84.4737i			0.387494i
$219$	−98.7053	−	170.805i	−0.450709	−	0.779933i
$220$	174.674	+	302.544i	0.793972	+	1.37520i
$221$	−142.236	+	75.9752i	−0.643600	+	0.343779i
$222$	−6.05595	−	3.49319i	−0.0272791	−	0.0157351i
$223$	−205.234			−0.920334			−0.460167	−	0.887832i	$-0.652210\pi$
$223$	−205.234			−0.920334			−0.460167	+	0.887832i	$0.652210\pi$
$224$	135.940	−	78.4852i	0.606877	−	0.350381i
$225$	107.058	+	185.088i	0.475811	+	0.822614i
$226$	32.9820			0.145938
$227$	22.3106	−	12.8810i	0.0982846	−	0.0567447i	−0.450052	−	0.893002i	$-0.648595\pi$
$227$	22.3106	−	12.8810i	0.0982846	−	0.0567447i	0.548337	+	0.836258i	$0.315261\pi$
$228$	352.847	−	0.140615i	1.54757	−	0.000616730i
$229$	−130.146	−	225.419i	−0.568323	−	0.984364i	−0.996732	−	0.0807792i	$-0.974259\pi$
$229$	−130.146	−	225.419i	−0.568323	−	0.984364i	0.428409	−	0.903585i	$-0.359074\pi$
$230$			98.4750i			0.428152i
$231$	251.319	+	144.966i	1.08796	+	0.627556i
$232$	−103.000			−0.443965
$233$		−	294.729i		−	1.26493i	−0.774588	−	0.632466i	$-0.782043\pi$
$233$		−	294.729i		−	1.26493i	0.774588	−	0.632466i	$-0.217957\pi$
$234$	−50.3207	+	26.9304i	−0.215046	+	0.115087i
$235$	271.233			1.15418
$236$			182.281i			0.772375i
$237$	85.6984	−	0.0341520i	0.361596	−	0.000144101i
$238$	44.0030			0.184886
$239$	−108.604	+	62.7024i	−0.454409	+	0.262353i	−0.709690	−	0.704514i	$-0.751165\pi$
$239$	−108.604	+	62.7024i	−0.454409	+	0.262353i	0.255282	+	0.966867i	$0.417832\pi$
$240$	−239.544	−	138.173i	−0.998098	−	0.575722i
$241$	6.56320	+	11.3678i	0.0272332	+	0.0471693i	0.879321	−	0.476230i	$-0.157997\pi$
$241$	6.56320	+	11.3678i	0.0272332	+	0.0471693i	−0.852088	+	0.523399i	$0.824664\pi$
$242$			27.2481i			0.112595i
$243$	121.080	−	210.686i	0.498273	−	0.867020i
$244$	129.400	+	224.127i	0.530327	+	0.918553i
$245$		−	27.1188i		−	0.110689i
$246$	−25.6948	+	0.0102398i	−0.104450	+	4.16250e-5i
$247$	191.489	+	358.492i	0.775258	+	1.45138i
$248$	−20.4138	+	11.7859i	−0.0823137	+	0.0475238i
$249$	0.162688	+	408.236i	0.000653365	+	1.63950i
$250$	−4.23132			−0.0169253
$251$	−273.785	−	158.070i	−1.09078	−	0.629760i	−0.156993	−	0.987600i	$-0.550180\pi$
$251$	−273.785	−	158.070i	−1.09078	−	0.629760i	−0.933783	+	0.357840i	$0.883513\pi$
$252$	−246.222	+	0.196246i	−0.977072	+	0.000778755i
$253$	192.237	−	332.963i	0.759828	−	1.31606i
$254$	−68.1922	+	39.3708i	−0.268473	+	0.155003i
$255$	−130.012	−	224.980i	−0.509850	−	0.882275i
$256$	116.922			0.456728
$257$	−344.952	−	199.158i	−1.34223	−	0.774934i	−0.355092	−	0.934831i	$-0.615550\pi$
$257$	−344.952	−	199.158i	−1.34223	−	0.774934i	−0.987134	+	0.159897i	$0.948884\pi$
$258$	−86.9175	−	50.1357i	−0.336889	−	0.194324i
$259$	17.3704	−	30.0865i	0.0670673	−	0.116164i
$260$	11.2693	−	341.313i	0.0433433	−	1.31274i
$261$	212.121	+	122.243i	0.812723	+	0.468362i
$262$	−32.6532	−	56.5571i	−0.124631	−	0.215867i
$263$		−	275.471i		−	1.04742i	−0.851897	−	0.523709i	$-0.824548\pi$
$263$		−	275.471i		−	1.04742i	0.851897	−	0.523709i	$-0.175452\pi$
$264$	−75.5840	−	130.795i	−0.286303	−	0.495435i
$265$	−136.441	−	236.323i	−0.514872	−	0.891785i
$266$		−	110.905i		−	0.416938i
$267$	−322.721	−	186.152i	−1.20869	−	0.697197i
$268$	133.394	−	231.045i	0.497739	−	0.862109i
$269$	22.6267	+	13.0635i	0.0841140	+	0.0485632i	0.541467	−	0.840722i	$-0.317869\pi$
$269$	22.6267	+	13.0635i	0.0841140	+	0.0485632i	−0.457353	+	0.889285i	$0.651202\pi$
$270$	−46.0791	−	79.5915i	−0.170664	−	0.294783i
$271$	112.570	+	194.976i	0.415386	+	0.719470i	0.995469	−	0.0950874i	$-0.0303131\pi$
$271$	112.570	+	194.976i	0.415386	+	0.719470i	−0.580083	+	0.814558i	$0.696980\pi$
$272$	141.812	+	81.8749i	0.521366	+	0.301011i
$273$	−133.724	−	250.108i	−0.489830	−	0.916147i
$274$	16.0313	+	27.7670i	0.0585083	+	0.101339i
$275$	−273.621	−	157.975i	−0.994984	−	0.574454i
$276$	0.130030	+	326.286i	0.000471122	+	1.18220i
$277$	39.9487	+	69.1931i	0.144219	+	0.249795i	0.929081	−	0.369876i	$-0.120600\pi$
$277$	39.9487	+	69.1931i	0.144219	+	0.249795i	−0.784862	+	0.619670i	$0.787266\pi$
$278$			52.1058i			0.187431i
$279$	56.0285	−	0.0446563i	0.200819	−	0.000160058i
$280$	−96.1346	+	166.510i	−0.343338	+	0.594678i
$281$	−20.7840	−	11.9996i	−0.0739643	−	0.0427033i	0.462562	−	0.886587i	$-0.346930\pi$
$281$	−20.7840	−	11.9996i	−0.0739643	−	0.0427033i	−0.536526	+	0.843884i	$0.680264\pi$
$282$	−56.8450	+	0.0226536i	−0.201578	+	8.03318e-5i
$283$	143.648	−	248.806i	0.507591	−	0.879174i	−0.492370	−	0.870386i	$-0.663869\pi$
$283$	143.648	−	248.806i	0.507591	−	0.879174i	0.999961	−	0.00878782i	$-0.00279729\pi$
$284$	118.516	+	68.4252i	0.417310	+	0.240934i
$285$	−567.042	+	327.683i	−1.98962	+	1.14977i
$286$	44.5545	−	71.6047i	0.155785	−	0.250366i
$287$		−	127.683i		−	0.444890i
$288$	168.318	+	96.9995i	0.584436	+	0.336804i
$289$	−67.5674	−	117.030i	−0.233797	−	0.404949i
$290$	80.2441	−	46.3290i	0.276704	−	0.159755i
$291$	−49.6950	+	86.1536i	−0.170773	+	0.296061i
$292$	−247.385			−0.847209
$293$			273.356i			0.932954i	0.884533	+	0.466477i	$0.154477\pi$
$293$			273.356i			0.932954i	−0.884533	+	0.466477i	$0.845523\pi$
$294$	0.00226498	+	5.68356i	7.70402e−6	+	0.0193318i
$295$	−169.164	−	293.001i	−0.573438	−	0.993224i
$296$	−15.6652	+	9.04433i	−0.0529231	+	0.0305552i
$297$	0.429281	+	359.067i	0.00144539	+	1.20898i
$298$	−35.5499			−0.119295
$299$	−331.506	+	177.074i	−1.10872	+	0.592222i
$300$	268.133	−	0.106855i	0.893777	−	0.000356183i
$301$	249.308	−	431.814i	0.828265	−	1.43460i
$302$	23.6246	+	13.6396i	0.0782270	+	0.0451644i
$303$	269.951	−	156.000i	0.890928	−	0.514851i
$304$	206.358	−	357.423i	0.678810	−	1.17573i
$305$	−415.999	−	240.177i	−1.36393	−	0.787466i
$306$	27.2667	+	47.1405i	0.0891068	+	0.154054i
$307$	20.3839			0.0663972			0.0331986	−	0.999449i	$-0.489431\pi$
$307$	20.3839			0.0663972			0.0331986	+	0.999449i	$0.489431\pi$
$308$	315.085	−	181.914i	1.02300	−	0.590631i
$309$	−167.154	+	289.785i	−0.540951	+	0.937817i
$310$	10.6025	−	18.3641i	0.0342017	−	0.0592390i
$311$	335.207	−	193.532i	1.07783	−	0.622288i	0.147523	−	0.989059i	$-0.452870\pi$
$311$	335.207	−	193.532i	1.07783	−	0.622288i	0.930312	+	0.366770i	$0.119537\pi$
$312$	−4.81420	+	147.591i	−0.0154301	+	0.473049i
$313$	−220.375	+	381.701i	−0.704074	+	1.21949i	0.262951	+	0.964809i	$0.415304\pi$
$313$	−220.375	+	381.701i	−0.704074	+	1.21949i	−0.967025	+	0.254682i	$0.918029\pi$
$314$	−45.3280	+	26.1702i	−0.144357	+	0.0833444i
$315$	395.600	−	228.820i	1.25587	−	0.726413i
$316$	53.7335	−	93.0691i	0.170043	−	0.294522i
$317$	419.972	+	242.471i	1.32483	+	0.764892i	0.984495	−	0.175412i	$-0.0561257\pi$
$317$	419.972	+	242.471i	1.32483	+	0.764892i	0.340337	+	0.940304i	$0.389459\pi$
$318$	28.6151	+	49.5172i	0.0899846	+	0.155714i
$319$	−361.762			−1.13405
$320$	−255.644	+	147.596i	−0.798888	+	0.461238i
$321$	−285.309	−	164.572i	−0.888814	−	0.512685i
$322$	102.557			0.318500
$323$	335.847	−	193.902i	1.03978	−	0.600315i
$324$	−152.783	−	263.657i	−0.471553	−	0.813755i
$325$	145.515	+	272.423i	0.447738	+	0.838225i
$326$	9.28198	+	5.35895i	0.0284723	+	0.0164385i
$327$	−259.933	−	449.803i	−0.794903	−	1.37555i
$328$	−33.2407	+	57.5746i	−0.101344	+	0.175532i
$329$		−	282.476i		−	0.858590i
$330$	117.716	+	67.9010i	0.356716	+	0.205761i
$331$	196.505	+	340.357i	0.593671	+	1.02827i	0.993733	+	0.111780i	$0.0356551\pi$
$331$	196.505	+	340.357i	0.593671	+	1.02827i	−0.400062	+	0.916488i	$0.631012\pi$
$332$	443.347	+	255.967i	1.33538	+	0.770984i
$333$	42.9954	−	0.0342686i	0.129115	−	0.000102909i
$334$	25.1153	−	43.5009i	0.0751954	−	0.130242i
$335$			495.182i			1.47816i
$336$	−143.901	+	249.473i	−0.428276	+	0.742479i
$337$	214.778	+	372.007i	0.637324	+	1.10388i	0.986018	+	0.166641i	$0.0532922\pi$
$337$	214.778	+	372.007i	0.637324	+	1.10388i	−0.348693	+	0.937237i	$0.613374\pi$
$338$	−73.9585	+	36.4207i	−0.218812	+	0.107754i
$339$	−175.622	+	101.489i	−0.518058	+	0.299376i
$340$	−325.848			−0.958378
$341$	−71.6984	+	41.3951i	−0.210259	+	0.121393i
$342$	118.813	−	68.7232i	0.347407	−	0.200945i
$343$	328.091			0.956533
$344$	−224.834	+	129.808i	−0.653587	+	0.377349i
$345$	−303.017	−	524.357i	−0.878309	−	1.51988i
$346$	−10.6621	−	18.4672i	−0.0308152	−	0.0533735i
$347$		−	249.804i		−	0.719895i	−0.932972	−	0.359948i	$-0.882795\pi$
$347$		−	249.804i		−	0.719895i	0.932972	−	0.359948i	$-0.117205\pi$
$348$	265.819	−	153.612i	0.763847	−	0.441413i
$349$	387.832			1.11127			0.555634	−	0.831427i	$-0.312476\pi$
$349$	387.832			1.11127			0.555634	+	0.831427i	$0.312476\pi$
$350$		−	84.2786i		−	0.240796i
$351$	185.079	−	298.239i	0.527291	−	0.849685i
$352$	−287.058			−0.815505
$353$		−	286.323i		−	0.811114i	−0.914070	−	0.405557i	$-0.867078\pi$
$353$		−	286.323i		−	0.811114i	0.914070	−	0.405557i	$-0.132922\pi$
$354$	35.4779	+	61.3931i	0.100220	+	0.173427i
$355$	−254.006			−0.715511
$356$	−404.604	+	233.598i	−1.13653	+	0.656174i
$357$	−234.306	+	135.401i	−0.656319	+	0.379275i
$358$	20.2790	+	35.1243i	0.0566452	+	0.0981124i
$359$			481.579i			1.34145i	0.741708	+	0.670723i	$0.234016\pi$
$359$			481.579i			1.34145i	−0.741708	+	0.670723i	$0.765984\pi$
$360$	−237.953	+	0.189655i	−0.660980	+	0.000526820i
$361$	−308.212	−	533.838i	−0.853772	−	1.47878i
$362$		−	91.5546i		−	0.252913i
$363$	−83.8449	−	145.090i	−0.230978	−	0.399697i
$364$	−355.461	−	11.7364i	−0.976540	−	0.0322428i
$365$	397.651	−	229.584i	1.08946	−	0.628997i
$366$	87.2051	+	50.3016i	0.238265	+	0.137436i
$367$	−442.946			−1.20694			−0.603469	−	0.797387i	$-0.706215\pi$
$367$	−442.946			−1.20694			−0.603469	+	0.797387i	$0.706215\pi$
$368$	330.518	+	190.825i	0.898146	+	0.518545i
$369$	136.788	−	79.1197i	0.370698	−	0.214417i
$370$	8.13622	−	14.0923i	0.0219898	−	0.0380874i
$371$	−246.119	+	142.097i	−0.663394	+	0.383010i
$372$	35.1060	−	60.8614i	0.0943709	−	0.163606i
$373$	158.675			0.425401			0.212701	−	0.977117i	$-0.431774\pi$
$373$	158.675			0.425401			0.212701	+	0.977117i	$0.431774\pi$
$374$	−69.6889	−	40.2349i	−0.186334	−	0.107580i
$375$	22.5308	−	13.0201i	0.0600821	−	0.0347204i
$376$	−73.5389	+	127.373i	−0.195582	+	0.338758i
$377$	300.254	+	186.827i	0.796430	+	0.495562i
$378$	−82.8907	+	47.9892i	−0.219288	+	0.126956i
$379$	−234.605	−	406.347i	−0.619009	−	1.07216i	−0.989667	−	0.143386i	$-0.954201\pi$
$379$	−234.605	−	406.347i	−0.619009	−	1.07216i	0.370657	−	0.928770i	$-0.379132\pi$
$380$			821.272i			2.16124i
$381$	241.961	−	419.474i	0.635067	−	1.10098i
$382$	5.71099	+	9.89173i	0.0149502	+	0.0258946i
$383$			274.219i			0.715977i	0.933726	+	0.357989i	$0.116537\pi$
$383$			274.219i			0.715977i	−0.933726	+	0.357989i	$0.883463\pi$
$384$	277.834	−	160.555i	0.723527	−	0.418113i
$385$	−337.649	+	584.825i	−0.877010	+	1.51903i
$386$	55.7781	+	32.2035i	0.144503	+	0.0834288i
$387$	617.088	−	0.491837i	1.59454	−	0.00127090i
$388$	62.3613	+	108.013i	0.160725	+	0.278384i
$389$	−422.859	−	244.138i	−1.08704	−	0.627603i	−0.154254	−	0.988031i	$-0.549297\pi$
$389$	−422.859	−	244.138i	−1.08704	−	0.627603i	−0.932787	+	0.360428i	$0.882631\pi$
$390$	−62.6354	−	117.149i	−0.160604	−	0.300383i
$391$	179.306	+	310.566i	0.458582	+	0.794287i
$392$	12.7352	+	7.35268i	0.0324878	+	0.0187568i
$393$	347.902	+	200.677i	0.885247	+	0.510628i
$394$	−49.1835	−	85.1883i	−0.124831	−	0.216214i
$395$			199.468i			0.504982i
$396$	390.129	+	224.827i	0.985175	+	0.567745i
$397$	−188.010	+	325.643i	−0.473577	+	0.820260i	−0.999542	−	0.0302462i	$-0.990371\pi$
$397$	−188.010	+	325.643i	−0.473577	+	0.820260i	0.525965	+	0.850506i	$0.323704\pi$
$398$	140.709	+	81.2382i	0.353540	+	0.204116i
$399$	341.266	+	590.547i	0.855304	+	1.48007i
$400$	156.815	−	271.611i	0.392036	−	0.679027i
$401$	0.743410	+	0.429208i	0.00185389	+	0.00107034i	0.500927	−	0.865490i	$-0.332993\pi$
$401$	0.743410	+	0.429208i	0.00185389	+	0.00107034i	−0.499073	+	0.866560i	$0.666326\pi$
$402$	−0.0413579	−	103.780i	−0.000102880	−	0.258160i
$403$	80.8859	+	2.67064i	0.200710	+	0.00662691i
$404$		−	390.982i		−	0.967777i
$405$	490.271	+	282.017i	1.21055	+	0.696339i
$406$	−48.2494	−	83.5704i	−0.118841	−	0.205838i
$407$	−55.0203	+	31.7660i	−0.135185	+	0.0780491i
$408$	140.902	−	0.0561516i	0.345349	−	0.000137626i
$409$	331.210			0.809805			0.404903	−	0.914360i	$-0.367305\pi$
$409$	331.210			0.809805			0.404903	+	0.914360i	$0.367305\pi$
$410$		−	59.8062i		−	0.145869i
$411$	−170.805	−	98.5233i	−0.415583	−	0.239716i
$412$	209.758	+	363.311i	0.509121	+	0.881824i
$413$	−305.147	+	176.176i	−0.738854	+	0.426577i
$414$	63.5500	+	109.870i	0.153502	+	0.265385i
$415$	−950.193			−2.28962
$416$	238.251	+	148.247i	0.572720	+	0.356363i
$417$	−160.334	−	277.452i	−0.384494	−	0.665352i
$418$	−101.409	+	175.645i	−0.242604	+	0.420203i
$419$	−475.959	−	274.795i	−1.13594	−	0.655836i	−0.190519	−	0.981684i	$-0.561017\pi$
$419$	−475.959	−	274.795i	−1.13594	−	0.655836i	−0.945422	+	0.325848i	$0.894350\pi$
$420$	−0.228387	−	573.096i	−0.000543779	−	1.36452i
$421$	12.9173	−	22.3734i	0.0306824	−	0.0531435i	−0.850276	−	0.526336i	$-0.823565\pi$
$421$	12.9173	−	22.3734i	0.0306824	−	0.0531435i	0.880959	+	0.473193i	$0.156899\pi$
$422$	66.4829	+	38.3839i	0.157542	+	0.0909572i
$423$	302.617	−	175.038i	0.715407	−	0.413801i
$424$	147.972			0.348991
$425$	255.215	−	147.349i	0.600506	−	0.346702i
$426$	53.2346	−	0.0212148i	0.124964	−	4.97999e-5i
$427$	−250.133	+	433.243i	−0.585791	+	1.01462i
$428$	−357.699	+	206.518i	−0.835746	+	0.482518i
$429$	−16.9087	+	518.377i	−0.0394142	+	1.20834i
$430$	116.774	−	202.259i	0.271568	−	0.470370i
$431$	−319.892	+	184.690i	−0.742209	+	0.428514i	−0.822872	−	0.568227i	$-0.807630\pi$
$431$	−319.892	+	184.690i	−0.742209	+	0.428514i	0.0806632	+	0.996741i	$0.474296\pi$
$432$	−356.430	+	0.426128i	−0.825069	+	0.000986407i
$433$	201.061	−	348.248i	0.464344	−	0.804268i	−0.534827	−	0.844961i	$-0.679623\pi$
$433$	201.061	−	348.248i	0.464344	−	0.804268i	0.999172	+	0.0406935i	$0.0129567\pi$
$434$	−19.1253	−	11.0420i	−0.0440676	−	0.0254424i
$435$	−284.724	+	493.610i	−0.654537	+	1.13474i
$436$	−651.470			−1.49420
$437$	782.754	−	451.923i	1.79120	−	1.03415i
$438$	−83.3206	+	48.1494i	−0.190230	+	0.109930i
$439$	157.502			0.358774			0.179387	−	0.983779i	$-0.442589\pi$
$439$	157.502			0.358774			0.179387	+	0.983779i	$0.442589\pi$
$440$	304.503	−	175.805i	0.692052	−	0.399557i
$441$	−17.5009	−	30.2567i	−0.0396846	−	0.0686093i
$442$	37.0615	+	69.3840i	0.0838495	+	0.156977i
$443$	479.178	+	276.653i	1.08167	+	0.624500i	0.931345	−	0.364138i	$-0.118636\pi$
$443$	479.178	+	276.653i	1.08167	+	0.624500i	0.150320	+	0.988637i	$0.451970\pi$
$444$	26.9398	−	46.7041i	0.0606753	−	0.105189i
$445$	433.578	−	750.979i	0.974333	−	1.68759i
$446$			100.115i			0.224474i
$447$	189.295	−	109.390i	0.423480	−	0.244721i
$448$	153.714	+	266.241i	0.343112	+	0.594288i
$449$	581.789	+	335.896i	1.29574	+	0.748098i	0.979666	−	0.200635i	$-0.0643007\pi$
$449$	581.789	+	335.896i	1.29574	+	0.748098i	0.316078	+	0.948733i	$0.397634\pi$
$450$	90.2879	−	52.2237i	0.200640	−	0.116053i
$451$	−116.750	+	202.216i	−0.258869	+	0.448373i
$452$			254.361i			0.562745i
$453$	−167.766	+	0.0668571i	−0.370344	+	0.000147587i
$454$	−6.28350	−	10.8833i	−0.0138403	−	0.0239721i
$455$	582.266	−	311.018i	1.27970	−	0.683555i
$456$	−0.141525	−	355.131i	−0.000310362	−	0.778797i
$457$	448.574			0.981562			0.490781	−	0.871283i	$-0.336711\pi$
$457$	448.574			0.981562			0.490781	+	0.871283i	$0.336711\pi$
$458$	−109.962	+	63.4865i	−0.240091	+	0.138617i
$459$	−290.244	−	167.110i	−0.632341	−	0.364075i
$460$	−759.450			−1.65098
$461$	57.5536	−	33.2286i	0.124845	−	0.0720793i	−0.436277	−	0.899812i	$-0.643703\pi$
$461$	57.5536	−	33.2286i	0.124845	−	0.0720793i	0.561122	+	0.827733i	$0.310370\pi$
$462$	70.7156	−	122.596i	0.153064	−	0.265359i
$463$	−31.2533	−	54.1323i	−0.0675018	−	0.116916i	0.830299	−	0.557318i	$-0.188169\pi$
$463$	−31.2533	−	54.1323i	−0.0675018	−	0.116916i	−0.897801	+	0.440401i	$0.854836\pi$
$464$		−	359.105i		−	0.773932i
$465$	0.0519701	+	130.410i	0.000111764	+	0.280451i
$466$	−143.772			−0.308523
$467$		−	138.519i		−	0.296615i	−0.988941	−	0.148308i	$-0.952617\pi$
$467$		−	138.519i		−	0.296615i	0.988941	−	0.148308i	$-0.0473826\pi$
$468$	−207.690	−	388.078i	−0.443782	−	0.829227i
$469$	515.708			1.09959
$470$		−	132.310i		−	0.281511i
$471$	160.834	−	278.829i	0.341473	−	0.591993i
$472$	183.461			0.388688
$473$	−789.674	+	455.918i	−1.66950	+	0.963887i
$474$	−0.0166597	−	41.8045i	−3.51471e−5	−	0.0881952i
$475$	−371.379	−	643.247i	−0.781850	−	1.35420i
$476$			339.355i			0.712932i
$477$	−304.738	−	175.617i	−0.638863	−	0.368169i
$478$	30.5868	+	52.9780i	0.0639892	+	0.110833i
$479$			498.237i			1.04016i	0.854117	+	0.520081i	$0.174098\pi$
$479$			498.237i			1.04016i	−0.854117	+	0.520081i	$0.825902\pi$
$480$	−225.928	+	391.679i	−0.470684	+	0.815999i
$481$	62.0707	+	2.04941i	0.129045	+	0.00426073i
$482$	5.54533	−	3.20160i	0.0115048	−	0.00664232i
$483$	−546.093	+	315.577i	−1.13063	+	0.653369i
$484$	−210.140			−0.434174
$485$	−200.481	−	115.748i	−0.413364	−	0.238656i
$486$	−102.775	−	59.0642i	−0.211470	−	0.121531i
$487$	54.8187	−	94.9488i	0.112564	−	0.194967i	−0.804239	−	0.594306i	$-0.797427\pi$
$487$	54.8187	−	94.9488i	0.112564	−	0.194967i	0.916803	+	0.399339i	$0.130760\pi$
$488$	225.578	−	130.238i	0.462250	−	0.266880i
$489$	−65.9144	+	0.0262679i	−0.134794	+	5.37175e-5i
$490$	−13.2288			−0.0269976
$491$	258.961	+	149.511i	0.527416	+	0.304504i	0.739964	−	0.672647i	$-0.234843\pi$
$491$	258.961	+	149.511i	0.527416	+	0.304504i	−0.212548	+	0.977151i	$0.568176\pi$
$492$	−0.0789700	−	198.161i	−0.000160508	−	0.402766i
$493$	168.714	−	292.221i	0.342218	−	0.592740i
$494$	174.876	−	93.4101i	0.354000	−	0.189089i
$495$	−835.751	+	0.666118i	−1.68838	+	0.00134569i
$496$	−41.0910	−	71.1718i	−0.0828448	−	0.143491i
$497$			264.535i			0.532264i
$498$	199.142	−	0.0793608i	0.399883	−	0.000159359i
$499$	−146.467	−	253.688i	−0.293521	−	0.508394i	0.681119	−	0.732173i	$-0.261494\pi$
$499$	−146.467	−	253.688i	−0.293521	−	0.508394i	−0.974640	+	0.223779i	$0.928160\pi$
$500$		−	32.6324i		−	0.0652647i
$501$	0.123107	+	308.914i	0.000245722	+	0.616596i
$502$	−77.1080	+	133.555i	−0.153602	+	0.266046i
$503$	−695.889	−	401.772i	−1.38348	−	0.798751i	−0.390908	−	0.920430i	$-0.627839\pi$
$503$	−695.889	−	401.772i	−1.38348	−	0.798751i	−0.992570	+	0.121679i	$0.961172\pi$
$504$	0.197517	+	247.816i	0.000391899	+	0.491699i
$505$	362.848	+	628.472i	0.718512	+	1.24450i
$506$	−162.423	−	93.7749i	−0.320994	−	0.185326i
$507$	281.743	−	421.509i	0.555705	−	0.831379i
$508$	−303.632	−	525.905i	−0.597700	−	1.03525i
$509$	−518.067	−	299.106i	−1.01781	−	0.587634i	−0.104343	−	0.994541i	$-0.533274\pi$
$509$	−518.067	−	299.106i	−1.01781	−	0.587634i	−0.913470	+	0.406907i	$0.866607\pi$
$510$	−109.748	+	63.4211i	−0.215191	+	0.124355i
$511$	−239.101	−	414.134i	−0.467907	−	0.810439i
$512$		−	484.888i		−	0.947048i
$513$	−421.187	+	731.535i	−0.821026	+	1.42599i
$514$	−97.1513	+	168.271i	−0.189010	+	0.327376i
$515$	−674.337	−	389.329i	−1.30939	−	0.755978i
$516$	386.651	−	670.317i	0.749324	−	1.29906i
$517$	−258.287	+	447.367i	−0.499588	+	0.865312i
$518$	−14.6765	−	8.47347i	−0.0283330	−	0.0163581i
$519$	113.598	+	65.5257i	0.218879	+	0.126254i
$520$	−343.523	−	11.3422i	−0.660620	−	0.0218120i
$521$			133.778i			0.256772i	0.991724	+	0.128386i	$0.0409797\pi$
$521$			133.778i			0.256772i	−0.991724	+	0.128386i	$0.959020\pi$
$522$	59.6312	−	103.475i	0.114236	−	0.198227i
$523$	−42.9618	−	74.4120i	−0.0821449	−	0.142279i	0.822026	−	0.569450i	$-0.192844\pi$
$523$	−42.9618	−	74.4120i	−0.0821449	−	0.142279i	−0.904171	+	0.427171i	$0.859510\pi$
$524$	436.174	−	251.825i	0.832393	−	0.480582i
$525$	259.333	+	448.765i	0.493967	+	0.854790i
$526$	−134.377			−0.255471
$527$		−	77.2212i		−	0.146530i
$528$	456.011	−	263.520i	0.863657	−	0.499092i
$529$	153.404	+	265.704i	0.289990	+	0.502277i
$530$	−115.281	+	66.5574i	−0.217511	+	0.125580i
$531$	−377.824	−	217.735i	−0.711533	−	0.410048i
$532$	855.315			1.60773
$533$	201.331	−	107.541i	0.377733	−	0.201766i
$534$	−90.8066	+	157.427i	−0.170050	+	0.294806i
$535$	383.315	−	663.921i	0.716477	−	1.24097i
$536$	−232.541	−	134.258i	−0.433846	−	0.250481i
$537$	−216.062	−	124.628i	−0.402349	−	0.232083i
$538$	6.37251	−	11.0375i	0.0118448	−	0.0205158i
$539$	44.7293	+	25.8245i	0.0829857	+	0.0479118i
$540$	613.818	−	355.367i	1.13670	−	0.658087i
$541$	92.8838			0.171689			0.0858445	−	0.996309i	$-0.472641\pi$
$541$	92.8838			0.171689			0.0858445	+	0.996309i	$0.472641\pi$
$542$	95.1115	−	54.9126i	0.175482	−	0.101315i
$543$	281.722	+	487.508i	0.518825	+	0.897804i
$544$	133.874	−	231.877i	0.246092	−	0.426245i
$545$	1047.18	−	604.593i	1.92144	−	1.10934i
$546$	−122.005	+	65.2317i	−0.223453	+	0.119472i
$547$	−296.920	+	514.281i	−0.542815	+	0.940184i	0.455926	+	0.890018i	$0.349308\pi$
$547$	−296.920	+	514.281i	−0.542815	+	0.940184i	−0.998741	+	0.0501659i	$0.984025\pi$
$548$	−214.142	+	123.635i	−0.390770	+	0.225611i
$549$	−619.130	+	0.493465i	−1.12774	+	0.000898843i
$550$	−77.0617	+	133.475i	−0.140112	+	0.242681i
$551$	−736.516	−	425.228i	−1.33669	−	0.771738i
$552$	328.399	−	0.130872i	0.594925	−	0.000237086i
$553$	207.736			0.375653
$554$	33.7531	−	19.4874i	0.0609262	−	0.0351757i
$555$	0.0398811	+	100.074i	7.18578e−5	+	0.180314i
$556$	−401.845			−0.722743
$557$	−341.237	+	197.014i	−0.612635	+	0.353705i	−0.773996	−	0.633191i	$-0.781745\pi$
$557$	−341.237	+	197.014i	−0.612635	+	0.353705i	0.161361	+	0.986895i	$0.448412\pi$
$558$	−0.0217838	−	27.3312i	−3.90391e−5	−	0.0489807i
$559$	890.864	+	29.4140i	1.59367	+	0.0526190i
$560$	−580.530	−	335.169i	−1.03666	−	0.598516i
$561$	494.884	−	0.197219i	0.882147	−	0.000351548i
$562$	−5.85354	+	10.1386i	−0.0104156	+	0.0180403i
$563$			428.281i			0.760712i	0.924840	+	0.380356i	$0.124199\pi$
$563$			428.281i			0.760712i	−0.924840	+	0.380356i	$0.875801\pi$
$564$	−0.174707	−	438.395i	−0.000309764	−	0.777295i
$565$	−236.058	−	408.864i	−0.417801	−	0.723653i
$566$	−121.370	−	70.0731i	−0.214435	−	0.123804i
$567$	293.707	−	510.594i	0.518002	−	0.900518i
$568$	68.8683	−	119.283i	0.121247	−	0.210006i
$569$		−	305.673i		−	0.537211i	−0.963250	−	0.268605i	$-0.913437\pi$
$569$		−	305.673i		−	0.537211i	0.963250	−	0.268605i	$-0.0865628\pi$
$570$	159.847	+	276.609i	0.280434	+	0.485278i
$571$	557.263	+	965.207i	0.975941	+	1.69038i	0.676793	+	0.736173i	$0.263369\pi$
$571$	557.263	+	965.207i	0.975941	+	1.69038i	0.299148	+	0.954207i	$0.403297\pi$
$572$	552.223	+	343.609i	0.965425	+	0.600716i
$573$	−60.8475	−	35.0980i	−0.106191	−	0.0612530i
$574$	−62.2852			−0.108511
$575$	594.826	−	343.423i	1.03448	−	0.597257i
$576$	−189.975	+	329.652i	−0.329817	+	0.572313i
$577$	−701.400			−1.21560			−0.607799	−	0.794091i	$-0.707947\pi$
$577$	−701.400			−1.21560			−0.607799	+	0.794091i	$0.707947\pi$
$578$	−57.0885	+	32.9601i	−0.0987690	+	0.0570243i
$579$	−396.099	+	0.157851i	−0.684109	+	0.000272627i
$580$	357.294	+	618.851i	0.616024	+	1.06698i
$581$			989.580i			1.70324i
$582$	42.0266	+	24.2417i	0.0722106	+	0.0416525i
$583$	519.716			0.891451
$584$			248.987i			0.426347i
$585$	693.998	+	431.059i	1.18632	+	0.736853i
$586$	133.346			0.227552
$587$			361.472i			0.615795i	0.951419	+	0.307898i	$0.0996254\pi$
$587$			361.472i			0.615795i	−0.951419	+	0.307898i	$0.900375\pi$
$588$	−43.8322	+	0.0174678i	−0.0745446	+	2.97071e-5i
$589$	−194.629			−0.330440
$590$	−142.929	+	82.5200i	−0.242252	+	0.139864i
$591$	524.023	+	302.266i	0.886672	+	0.511449i
$592$	−31.5327	−	54.6162i	−0.0532646	−	0.0922571i
$593$		−	389.500i		−	0.656829i	−0.944534	−	0.328415i	$-0.893486\pi$
$593$		−	389.500i		−	0.656829i	0.944534	−	0.328415i	$-0.106514\pi$
$594$	175.157	−	0.209407i	0.294876	−	0.000352538i
$595$	−314.937	−	545.486i	−0.529305	−	0.916783i
$596$		−	274.165i		−	0.460008i
$597$	−999.220	+	0.398204i	−1.67373	+	0.000667008i
$598$	86.3786	+	161.712i	0.144446	+	0.270422i
$599$	−608.526	+	351.333i	−1.01590	+	0.586532i	−0.912915	−	0.408151i	$-0.866174\pi$
$599$	−608.526	+	351.333i	−1.01590	+	0.586532i	−0.102989	+	0.994683i	$0.532840\pi$
$600$	−0.107547	−	269.869i	−0.000179245	−	0.449782i
$601$	648.967			1.07981			0.539906	−	0.841725i	$-0.318460\pi$
$601$	648.967			1.07981			0.539906	+	0.841725i	$0.318460\pi$
$602$	−210.643	−	121.615i	−0.349905	−	0.202018i
$603$	319.561	+	552.479i	0.529953	+	0.916218i
$604$	−105.190	+	182.195i	−0.174156	+	0.301647i
$605$	337.783	−	195.019i	0.558319	−	0.322346i
$606$	−76.0983	−	131.685i	−0.125575	−	0.217302i
$607$	179.712			0.296066			0.148033	−	0.988982i	$-0.452706\pi$
$607$	179.712			0.296066			0.148033	+	0.988982i	$0.452706\pi$
$608$	−584.425	−	337.418i	−0.961226	−	0.554964i
$609$	514.071	+	296.526i	0.844123	+	0.486906i
$610$	−117.161	+	202.928i	−0.192067	+	0.332670i
$611$	445.409	−	237.915i	0.728983	−	0.389387i
$612$	−363.552	+	210.284i	−0.594040	+	0.343601i
$613$	232.871	+	403.344i	0.379887	+	0.657983i	0.991045	−	0.133525i	$-0.0426296\pi$
$613$	232.871	+	403.344i	0.379887	+	0.657983i	−0.611159	+	0.791508i	$0.709296\pi$
$614$		−	9.94349i		−	0.0161946i
$615$	184.029	+	318.454i	0.299234	+	0.517812i
$616$	−183.092	−	317.125i	−0.297228	−	0.514814i
$617$			408.565i			0.662180i	0.943599	+	0.331090i	$0.107416\pi$
$617$			408.565i			0.662180i	−0.943599	+	0.331090i	$0.892584\pi$
$618$	141.360	+	81.5393i	0.228738	+	0.131941i
$619$	490.018	−	848.736i	0.791628	−	1.37114i	−0.133330	−	0.991072i	$-0.542567\pi$
$619$	490.018	−	848.736i	0.791628	−	1.37114i	0.924958	−	0.380068i	$-0.124100\pi$
$620$	141.626	+	81.7677i	0.228429	+	0.131883i
$621$	−676.468	−	389.481i	−1.08932	−	0.627184i
$622$	−94.4067	−	163.517i	−0.151779	−	0.262889i
$623$	−782.109	−	451.551i	−1.25539	−	0.724801i
$624$	−514.570	−	16.7845i	−0.824632	−	0.0268982i
$625$	327.256	+	566.825i	0.523610	+	0.906919i
$626$	186.197	+	107.501i	0.297440	+	0.171727i
$627$	−0.497072	−	1247.31i	−0.000792778	−	1.98933i
$628$	−201.827	−	349.575i	−0.321381	−	0.556647i
$629$		−	59.2584i		−	0.0942105i
$630$	−111.621	−	192.978i	−0.177176	−	0.306314i
$631$	−215.458	+	373.184i	−0.341455	+	0.591417i	−0.984703	−	0.174241i	$-0.944253\pi$
$631$	−215.458	+	373.184i	−0.341455	+	0.591417i	0.643249	+	0.765657i	$0.277586\pi$
$632$	−93.6717	−	54.0814i	−0.148215	−	0.0855718i
$633$	−472.117	+	0.188146i	−0.745841	+	0.000297229i
$634$	118.280	−	204.866i	0.186561	−	0.323133i
$635$	976.126	+	563.567i	1.53721	+	0.887507i
$636$	−381.882	+	220.683i	−0.600443	+	0.346985i
$637$	−23.7876	−	44.5335i	−0.0373432	−	0.0699113i
$638$			176.471i			0.276600i
$639$	−283.397	+	163.921i	−0.443501	+	0.256527i
$640$	373.444	+	646.825i	0.583507	+	1.01066i
$641$	844.464	−	487.551i	1.31742	−	0.760610i	0.334104	−	0.942536i	$-0.391566\pi$
$641$	844.464	−	487.551i	1.31742	−	0.760610i	0.983312	+	0.181926i	$0.0582331\pi$
$642$	−80.2798	+	139.177i	−0.125046	+	0.216786i
$643$	−236.578			−0.367928			−0.183964	−	0.982933i	$-0.558893\pi$
$643$	−236.578			−0.367928			−0.183964	+	0.982933i	$0.558893\pi$
$644$			790.930i			1.22815i
$645$	0.572390	+	1436.31i	0.000887426	+	2.22684i
$646$	−94.5872	−	163.830i	−0.146420	−	0.253606i
$647$	456.680	−	263.665i	0.705843	−	0.407519i	−0.103677	−	0.994611i	$-0.533061\pi$
$647$	456.680	−	263.665i	0.705843	−	0.407519i	0.809520	+	0.587092i	$0.199727\pi$
$648$	−265.364	+	153.772i	−0.409512	+	0.237303i
$649$	644.361			0.992852
$650$	132.891	−	70.9836i	0.204447	−	0.109206i
$651$	135.815	−	0.0541243i	0.208626	−	8.31403e-5i
$652$	−41.3288	+	71.5836i	−0.0633877	+	0.109791i
$653$	−656.842	−	379.228i	−1.00588	−	0.580747i	−0.0958996	−	0.995391i	$-0.530573\pi$
$653$	−656.842	−	379.228i	−1.00588	−	0.580747i	−0.909984	+	0.414644i	$0.863906\pi$
$654$	−219.419	+	126.798i	−0.335502	+	0.193881i
$655$	−467.409	+	809.577i	−0.713602	+	1.23599i
$656$	−200.731	−	115.892i	−0.305993	−	0.176665i
$657$	295.503	−	512.770i	0.449776	−	0.780472i
$658$	−137.795			−0.209414
$659$	−604.853	+	349.212i	−0.917835	+	0.529912i	−0.882944	−	0.469479i	$-0.844442\pi$
$659$	−604.853	+	349.212i	−0.917835	+	0.529912i	−0.0348912	+	0.999391i	$0.511108\pi$
$660$	−523.660	+	907.841i	−0.793424	+	1.37552i
$661$	−449.994	+	779.413i	−0.680778	+	1.17914i	0.293966	+	0.955816i	$0.405025\pi$
$661$	−449.994	+	779.413i	−0.680778	+	1.17914i	−0.974744	+	0.223326i	$0.928309\pi$
$662$	166.029	−	95.8571i	0.250800	−	0.144799i
$663$	−410.845	−	255.412i	−0.619675	−	0.385237i
$664$	257.624	−	446.218i	0.387988	−	0.672015i
$665$	−1374.85	+	793.769i	−2.06744	+	1.19364i
$666$	−0.0167166	−	20.9736i	−2.50999e−5	−	0.0314919i
$667$	393.218	−	681.074i	0.589533	−	1.02110i
$668$	335.484	+	193.692i	0.502221	+	0.289957i
$669$	−308.064	−	533.092i	−0.460485	−	0.796849i
$670$	241.555			0.360529
$671$	792.287	−	457.427i	1.18076	−	0.681710i
$672$	407.915	+	235.293i	0.607016	+	0.350139i
$673$	902.419			1.34089			0.670445	−	0.741959i	$-0.266103\pi$
$673$	902.419			1.34089			0.670445	+	0.741959i	$0.266103\pi$
$674$	181.469	−	104.771i	0.269241	−	0.155447i
$675$	−320.065	+	555.903i	−0.474171	+	0.823561i
$676$	−280.881	−	570.376i	−0.415504	−	0.843751i
$677$	420.355	+	242.692i	0.620908	+	0.358482i	0.777223	−	0.629226i	$-0.216628\pi$
$677$	420.355	+	242.692i	0.620908	+	0.358482i	−0.156314	+	0.987707i	$0.549961\pi$
$678$	49.5071	+	85.6700i	0.0730194	+	0.126357i
$679$	−120.546	+	208.792i	−0.177535	+	0.307499i
$680$			327.958i			0.482292i
$681$	66.9472	+	38.6164i	0.0983072	+	0.0567055i
$682$	20.1929	+	34.9752i	0.0296084	+	0.0512833i
$683$	−788.943	−	455.497i	−1.15511	−	0.666906i	−0.204986	−	0.978765i	$-0.565715\pi$
$683$	−788.943	−	455.497i	−1.15511	−	0.666906i	−0.950128	+	0.311859i	$0.899048\pi$
$684$	530.001	+	916.301i	0.774855	+	1.33962i
$685$	229.477	−	397.466i	0.335003	−	0.580243i
$686$		−	160.046i		−	0.233303i
$687$	390.168	−	676.414i	0.567930	−	0.984590i
$688$	−452.570	−	783.874i	−0.657805	−	1.13935i
$689$	−431.352	−	268.400i	−0.626056	−	0.389550i
$690$	−255.787	+	147.814i	−0.370705	+	0.214224i
$691$	847.527			1.22652			0.613261	−	0.789880i	$-0.289857\pi$
$691$	847.527			1.22652			0.613261	+	0.789880i	$0.289857\pi$
$692$	142.421	−	82.2269i	0.205811	−	0.118825i
$693$	0.693729	+	870.394i	0.00100105	+	1.25598i
$694$	−121.857			−0.175586
$695$	645.934	−	372.930i	0.929401	−	0.536590i
$696$	−154.606	−	267.540i	−0.222136	−	0.384396i
$697$	−108.896	−	188.614i	−0.156236	−	0.270608i
$698$		−	189.189i		−	0.271044i
$699$	765.552	−	442.399i	1.09521	−	0.632902i
$700$	649.965			0.928522
$701$		−	127.812i		−	0.182328i	−0.995836	−	0.0911638i	$-0.970941\pi$
$701$		−	127.812i		−	0.182328i	0.995836	−	0.0911638i	$-0.0290587\pi$
$702$	−145.484	−	90.2834i	−0.207242	−	0.128609i
$703$	−149.355			−0.212454
$704$		−	562.207i		−	0.798589i
$705$	407.130	+	704.522i	0.577490	+	0.999321i
$706$	−139.671			−0.197835
$707$	654.523	−	377.889i	0.925775	−	0.534496i
$708$	−473.470	+	273.610i	−0.668743	+	0.386454i
$709$	267.367	+	463.093i	0.377104	+	0.653164i	0.990640	−	0.136504i	$-0.0435865\pi$
$709$	267.367	+	463.093i	0.377104	+	0.653164i	−0.613535	+	0.789667i	$0.710253\pi$
$710$			123.907i			0.174517i
$711$	128.725	+	222.548i	0.181048	+	0.313008i
$712$	235.111	+	407.223i	0.330211	+	0.571943i
$713$		−	179.978i		−	0.252424i
$714$	66.0500	+	114.297i	0.0925070	+	0.160079i
$715$	−1206.54	−	39.8368i	−1.68747	−	0.0557157i
$716$	−270.882	+	156.394i	−0.378327	+	0.218427i
$717$	−325.886	−	187.977i	−0.454513	−	0.262172i
$718$	234.919			0.327185
$719$	999.991	+	577.345i	1.39081	+	0.802984i	0.993405	−	0.114660i	$-0.0365779\pi$
$719$	999.991	+	577.345i	1.39081	+	0.802984i	0.397404	+	0.917644i	$0.369911\pi$
$720$	−0.661225	−	829.612i	−0.000918368	−	1.15224i
$721$	−405.467	+	702.290i	−0.562368	+	0.974050i
$722$	−260.412	+	150.349i	−0.360681	+	0.208239i
$723$	−19.6760	+	34.1112i	−0.0272144	+	0.0471801i
$724$	706.079			0.975247
$725$	−559.688	−	323.136i	−0.771984	−	0.445705i
$726$	−70.7764	+	40.9004i	−0.0974881	+	0.0563366i
$727$	−586.005	+	1014.99i	−0.806059	+	1.39614i	0.109515	+	0.993985i	$0.465070\pi$
$727$	−586.005	+	1014.99i	−0.806059	+	1.39614i	−0.915574	+	0.402150i	$0.868263\pi$
$728$	−11.8124	+	357.762i	−0.0162258	+	0.491432i
$729$	728.998	−	1.74310i	0.999997	−	0.00239108i
$730$	−111.993	−	193.978i	−0.153416	−	0.265724i
$731$		−	850.501i		−	1.16348i
$732$	−387.931	+	672.535i	−0.529961	+	0.918764i
$733$	320.692	+	555.455i	0.437506	+	0.757783i	0.997496	−	0.0707164i	$-0.0225285\pi$
$733$	320.692	+	555.455i	0.437506	+	0.757783i	−0.559990	+	0.828499i	$0.689195\pi$
$734$			216.074i			0.294378i
$735$	70.4405	−	40.7063i	0.0958374	−	0.0553827i
$736$	312.019	−	540.432i	0.423938	−	0.734283i
$737$	−816.744	−	471.547i	−1.10820	−	0.639820i
$738$	−38.5954	−	66.7263i	−0.0522973	−	0.0904151i
$739$	−553.660	−	958.967i	−0.749201	−	1.29766i	−0.948206	−	0.317656i	$-0.897104\pi$
$739$	−553.660	−	958.967i	−0.749201	−	1.29766i	0.199004	−	0.979999i	$-0.436229\pi$
$740$	108.682	+	62.7473i	0.146867	+	0.0847937i
$741$	−643.744	+	1035.50i	−0.868750	+	1.39743i
$742$	69.3163	+	120.059i	0.0934182	+	0.161805i
$743$	724.903	+	418.523i	0.975643	+	0.563288i	0.900952	−	0.433919i	$-0.142870\pi$
$743$	724.903	+	418.523i	0.975643	+	0.563288i	0.0746910	+	0.997207i	$0.476203\pi$
$744$	−61.2554	−	35.3333i	−0.0823326	−	0.0474910i
$745$	254.437	+	440.698i	0.341526	+	0.591540i
$746$		−	77.4031i		−	0.103758i
$747$	−1060.14	+	613.199i	−1.41920	+	0.820882i
$748$	310.296	−	537.448i	0.414834	−	0.718514i
$749$	−691.442	−	399.204i	−0.923154	−	0.532983i
$750$	−6.35135	−	10.9908i	−0.00846847	−	0.0146543i
$751$	660.189	−	1143.48i	0.879080	−	1.52261i	0.0267285	−	0.999643i	$-0.491491\pi$
$751$	660.189	−	1143.48i	0.879080	−	1.52261i	0.852352	−	0.522969i	$-0.175176\pi$
$752$	−444.081	−	256.390i	−0.590533	−	0.340944i
$753$	−0.377958	−	948.418i	−0.000501937	−	1.25952i
$754$	91.1359	−	146.467i	0.120870	−	0.194253i
$755$		−	390.485i		−	0.517199i
$756$	−370.098	−	639.262i	−0.489547	−	0.845585i
$757$	216.276	+	374.601i	0.285702	+	0.494850i	0.972779	−	0.231734i	$-0.0744400\pi$
$757$	216.276	+	374.601i	0.285702	+	0.494850i	−0.687077	+	0.726584i	$0.741107\pi$
$758$	−198.220	+	114.442i	−0.261504	+	0.150979i
$759$	1153.42	−	0.459654i	1.51966	−	0.000605605i
$760$	826.589			1.08762
$761$			564.390i			0.741642i	0.928704	+	0.370821i	$0.120924\pi$
$761$			564.390i			0.741642i	−0.928704	+	0.370821i	$0.879076\pi$
$762$	−204.624	−	118.031i	−0.268535	−	0.154896i
$763$	−629.654	−	1090.59i	−0.825234	−	1.42935i
$764$	−76.2861	+	44.0438i	−0.0998509	+	0.0576489i
$765$	389.228	−	675.406i	0.508795	−	0.882884i
$766$	133.767			0.174630
$767$	−534.805	−	332.771i	−0.697269	−	0.433861i
$768$	175.504	+	303.703i	0.228521	+	0.395447i
$769$	−387.663	+	671.452i	−0.504113	+	0.873149i	0.495876	+	0.868393i	$0.334847\pi$
$769$	−387.663	+	671.452i	−0.504113	+	0.873149i	−0.999989	+	0.00475571

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-0.487810i q^{2} +(1.50104 + 2.59748i) q^{3} +3.76204 q^{4} +(-6.04718 + 3.49134i) q^{5} +(1.26708 - 0.732220i) q^{6} +(3.63606 + 6.29784i) q^{7} -3.78640i q^{8} +(-4.49379 + 7.79781i) q^{9} +(1.70311 + 2.94987i) q^{10} -13.2988i q^{11} +(5.64696 + 9.77182i) q^{12} +(-6.86798 + 11.0377i) q^{13} +(3.07215 - 1.77371i) q^{14} +(-18.1457 - 10.4668i) q^{15} +13.2011 q^{16} +(10.7424 + 6.20212i) q^{17} +(3.80385 + 2.19211i) q^{18} +(15.6319 - 27.0752i) q^{19} +(-22.7497 + 13.1346i) q^{20} +(-10.9006 + 18.8979i) q^{21} -6.48729 q^{22} +(25.0371 + 14.4552i) q^{23} +(9.83509 - 5.68352i) q^{24} +(11.8789 - 20.5748i) q^{25} +(5.38430 + 3.35027i) q^{26} +(-27.0000 + 0.0322797i) q^{27} +(13.6790 + 23.6927i) q^{28} -27.2026i q^{29} +(-5.10580 + 8.85165i) q^{30} +(-3.11269 - 5.39134i) q^{31} -21.5852i q^{32} +(34.5433 - 19.9620i) q^{33} +(3.02546 - 5.24024i) q^{34} +(-43.9758 - 25.3894i) q^{35} +(-16.9058 + 29.3357i) q^{36} +(-2.38864 - 4.13724i) q^{37} +(-13.2076 - 7.62539i) q^{38} +(-38.9793 - 1.27144i) q^{39} +(13.2196 + 22.8970i) q^{40} +(-15.2056 - 8.77897i) q^{41} +(9.21857 + 5.31745i) q^{42} +(-34.2827 - 59.3793i) q^{43} -50.0306i q^{44} +(-0.0500886 - 62.8441i) q^{45} +(7.05138 - 12.2134i) q^{46} +(-33.6396 - 19.4218i) q^{47} +(19.8153 + 34.2896i) q^{48} +(-1.94186 + 3.36341i) q^{49} +(-10.0366 - 5.79464i) q^{50} +(0.0148298 + 37.2127i) q^{51} +(-25.8376 + 41.5243i) q^{52} +39.0799i q^{53} +(0.0157463 + 13.1709i) q^{54} +(46.4306 + 80.4202i) q^{55} +(23.8462 - 13.7676i) q^{56} +(93.7913 - 0.0373772i) q^{57} -13.2697 q^{58} +48.4526i q^{59} +(-68.2649 - 39.3765i) q^{60} +(34.3961 + 59.5759i) q^{61} +(-2.62995 + 1.51840i) q^{62} +(-65.4491 + 0.0521648i) q^{63} +42.2750 q^{64} +(2.99552 - 90.7254i) q^{65} +(-9.73765 - 16.8506i) q^{66} +(35.4579 - 61.4149i) q^{67} +(40.4133 + 23.3326i) q^{68} +(0.0345636 + 86.7311i) q^{69} +(-12.3852 + 21.4518i) q^{70} +(31.5031 + 18.1883i) q^{71} +(29.5256 + 17.0153i) q^{72} -65.7582 q^{73} +(-2.01819 + 1.16520i) q^{74} +(71.2733 - 0.0284034i) q^{75} +(58.8078 - 101.858i) q^{76} +(83.7537 - 48.3552i) q^{77} +(-0.620223 + 19.0145i) q^{78} +(14.2831 - 24.7390i) q^{79} +(-79.8295 + 46.0896i) q^{80} +(-40.6118 - 70.0834i) q^{81} +(-4.28247 + 7.41745i) q^{82} +(117.848 + 68.0393i) q^{83} +(-41.0087 + 71.0946i) q^{84} -86.6148 q^{85} +(-28.9658 + 16.7234i) q^{86} +(70.6581 - 40.8320i) q^{87} -50.3546 q^{88} +(-107.549 + 62.0934i) q^{89} +(-30.6560 + 0.0244337i) q^{90} +(-94.4861 - 3.11968i) q^{91} +(94.1906 + 54.3810i) q^{92} +(9.33163 - 16.1777i) q^{93} +(-9.47417 + 16.4097i) q^{94} +218.305i q^{95} +(56.0672 - 32.4002i) q^{96} +(16.5765 + 28.7113i) q^{97} +(1.64070 + 0.947261i) q^{98} +(103.702 + 59.7620i) 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

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Representations

Groups

Database

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