LMFDB - Embedded newform 117.3.k.a.29.13

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			29.13
Character	$\chi$	$=$	117.29
Dual form			117.3.k.a.113.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.434891i q^{2} +(-0.475458 - 2.96208i) q^{3} +3.81087 q^{4} +(3.11857 - 1.80051i) q^{5} +(-1.28818 + 0.206772i) q^{6} +(3.94503 + 6.83299i) q^{7} -3.39687i q^{8} +(-8.54788 + 2.81669i) q^{9} +(-0.783024 - 1.35624i) q^{10} -11.0466i q^{11} +(-1.81191 - 11.2881i) q^{12} +(-10.9334 - 7.03289i) q^{13} +(2.97160 - 1.71566i) q^{14} +(-6.81600 - 8.38140i) q^{15} +13.7662 q^{16} +(15.8468 + 9.14913i) q^{17} +(1.22495 + 3.71739i) q^{18} +(-6.43665 + 11.1486i) q^{19} +(11.8845 - 6.86150i) q^{20} +(18.3642 - 14.9343i) q^{21} -4.80408 q^{22} +(-28.7611 - 16.6052i) q^{23} +(-10.0618 + 1.61507i) q^{24} +(-6.01635 + 10.4206i) q^{25} +(-3.05854 + 4.75482i) q^{26} +(12.4074 + 23.9803i) q^{27} +(15.0340 + 26.0396i) q^{28} +12.5996i q^{29} +(-3.64499 + 2.96422i) q^{30} +(10.2010 + 17.6687i) q^{31} -19.5743i q^{32} +(-32.7211 + 5.25221i) q^{33} +(3.97887 - 6.89161i) q^{34} +(24.6057 + 14.2061i) q^{35} +(-32.5749 + 10.7340i) q^{36} +(1.01336 + 1.75519i) q^{37} +(4.84842 + 2.79924i) q^{38} +(-15.6337 + 35.7294i) q^{39} +(-6.11610 - 10.5934i) q^{40} +(15.8294 + 9.13910i) q^{41} +(-6.49479 - 7.98642i) q^{42} +(26.4882 + 45.8790i) q^{43} -42.0973i q^{44} +(-21.5857 + 24.1746i) q^{45} +(-7.22145 + 12.5079i) q^{46} +(-16.9294 - 9.77417i) q^{47} +(-6.54525 - 40.7767i) q^{48} +(-6.62652 + 11.4775i) q^{49} +(4.53183 + 2.61645i) q^{50} +(19.5660 - 51.2894i) q^{51} +(-41.6656 - 26.8014i) q^{52} +89.9664i q^{53} +(10.4288 - 5.39588i) q^{54} +(-19.8895 - 34.4497i) q^{55} +(23.2108 - 13.4008i) q^{56} +(36.0834 + 13.7652i) q^{57} +5.47946 q^{58} -79.2173i q^{59} +(-25.9749 - 31.9404i) q^{60} +(35.6480 + 61.7441i) q^{61} +(7.68394 - 4.43633i) q^{62} +(-52.9681 - 47.2957i) q^{63} +46.5522 q^{64} +(-46.7592 - 2.24698i) q^{65} +(2.28414 + 14.2301i) q^{66} +(11.9507 - 20.6993i) q^{67} +(60.3899 + 34.8661i) q^{68} +(-35.5113 + 93.0877i) q^{69} +(6.17811 - 10.7008i) q^{70} +(17.1555 + 9.90476i) q^{71} +(9.56795 + 29.0361i) q^{72} -96.8588 q^{73} +(0.763315 - 0.440700i) q^{74} +(33.7273 + 12.8664i) q^{75} +(-24.5292 + 42.4859i) q^{76} +(75.4816 - 43.5793i) q^{77} +(15.5384 + 6.79894i) q^{78} +(50.7374 - 87.8797i) q^{79} +(42.9309 - 24.7862i) q^{80} +(65.1325 - 48.1535i) q^{81} +(3.97451 - 6.88405i) q^{82} +(-101.767 - 58.7549i) q^{83} +(69.9836 - 56.9127i) q^{84} +65.8923 q^{85} +(19.9523 - 11.5195i) q^{86} +(37.3211 - 5.99059i) q^{87} -37.5240 q^{88} +(-97.3912 + 56.2288i) q^{89} +(10.5133 + 9.38741i) q^{90} +(4.92328 - 102.453i) q^{91} +(-109.605 - 63.2803i) q^{92} +(47.4859 - 38.6170i) q^{93} +(-4.25070 + 7.36242i) q^{94} +46.3569i q^{95} +(-57.9807 + 9.30675i) q^{96} +(-80.5671 - 139.546i) q^{97} +(4.99144 + 2.88181i) q^{98} +(31.1150 + 94.4253i) 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 $

$2$		−	0.434891i		−	0.217445i	−0.994072	−	0.108723i	$-0.965324\pi$
$2$		−	0.434891i		−	0.217445i	0.994072	−	0.108723i	$-0.0346760\pi$
$3$	−0.475458	−	2.96208i	−0.158486	−	0.987361i
$3$	−0.475458	−	2.96208i	−0.158486	−	0.987361i
$4$	3.81087			0.952718
$5$	3.11857	−	1.80051i	0.623714	−	0.360101i	−0.154600	−	0.987977i	$-0.549409\pi$
$5$	3.11857	−	1.80051i	0.623714	−	0.360101i	0.778314	+	0.627876i	$0.216075\pi$
$6$	−1.28818	+	0.206772i	−0.214697	+	0.0344620i
$7$	3.94503	+	6.83299i	0.563576	+	0.976142i	0.997181	+	0.0750386i	$0.0239080\pi$
$7$	3.94503	+	6.83299i	0.563576	+	0.976142i	−0.433605	+	0.901103i	$0.642759\pi$
$8$		−	3.39687i		−	0.424609i
$9$	−8.54788	+	2.81669i	−0.949764	+	0.312966i
$10$	−0.783024	−	1.35624i	−0.0783024	−	0.135624i
$11$		−	11.0466i		−	1.00424i	−0.864798	−	0.502120i	$-0.832554\pi$
$11$		−	11.0466i		−	1.00424i	0.864798	−	0.502120i	$-0.167446\pi$
$12$	−1.81191	−	11.2881i	−0.150992	−	0.940676i
$13$	−10.9334	−	7.03289i	−0.841028	−	0.540992i
$13$	−10.9334	−	7.03289i	−0.841028	−	0.540992i
$14$	2.97160	−	1.71566i	0.212257	−	0.122547i
$15$	−6.81600	−	8.38140i	−0.454400	−	0.558760i
$16$	13.7662			0.860388
$17$	15.8468	+	9.14913i	0.932162	+	0.538184i	0.887495	−	0.460818i	$-0.152444\pi$
$17$	15.8468	+	9.14913i	0.932162	+	0.538184i	0.0446674	+	0.999002i	$0.485777\pi$
$18$	1.22495	+	3.71739i	0.0680530	+	0.206522i
$19$	−6.43665	+	11.1486i	−0.338771	+	0.586768i	−0.984202	−	0.177050i	$-0.943344\pi$
$19$	−6.43665	+	11.1486i	−0.338771	+	0.586768i	0.645431	+	0.763819i	$0.276678\pi$
$20$	11.8845	−	6.86150i	0.594223	−	0.343075i
$21$	18.3642	−	14.9343i	0.874486	−	0.711158i
$22$	−4.80408			−0.218367
$23$	−28.7611	−	16.6052i	−1.25048	−	0.721965i	−0.279276	−	0.960211i	$-0.590094\pi$
$23$	−28.7611	−	16.6052i	−1.25048	−	0.721965i	−0.971205	+	0.238246i	$0.923428\pi$
$24$	−10.0618	+	1.61507i	−0.419243	+	0.0672946i
$25$	−6.01635	+	10.4206i	−0.240654	+	0.416825i
$26$	−3.05854	+	4.75482i	−0.117636	+	0.182878i
$27$	12.4074	+	23.9803i	0.459535	+	0.888160i
$28$	15.0340	+	26.0396i	0.536928	+	0.929987i
$29$			12.5996i			0.434470i	0.976119	+	0.217235i	$0.0697037\pi$
$29$			12.5996i			0.434470i	−0.976119	+	0.217235i	$0.930296\pi$
$30$	−3.64499	+	2.96422i	−0.121500	+	0.0988072i
$31$	10.2010	+	17.6687i	0.329065	+	0.569957i	0.982327	−	0.187175i	$-0.0599332\pi$
$31$	10.2010	+	17.6687i	0.329065	+	0.569957i	−0.653262	+	0.757132i	$0.726600\pi$
$32$		−	19.5743i		−	0.611697i
$33$	−32.7211	+	5.25221i	−0.991547	+	0.159158i
$34$	3.97887	−	6.89161i	0.117026	−	0.202694i
$35$	24.6057	+	14.2061i	0.703020	+	0.405889i
$36$	−32.5749	+	10.7340i	−0.904857	+	0.298168i
$37$	1.01336	+	1.75519i	0.0273881	+	0.0474375i	0.879395	−	0.476094i	$-0.157948\pi$
$37$	1.01336	+	1.75519i	0.0273881	+	0.0474375i	−0.852007	+	0.523531i	$0.824614\pi$
$38$	4.84842	+	2.79924i	0.127590	+	0.0736641i
$39$	−15.6337	+	35.7294i	−0.400863	+	0.916138i
$40$	−6.11610	−	10.5934i	−0.152902	−	0.264835i
$41$	15.8294	+	9.13910i	0.386083	+	0.222905i	0.680461	−	0.732784i	$-0.261779\pi$
$41$	15.8294	+	9.13910i	0.386083	+	0.222905i	−0.294379	+	0.955689i	$0.595113\pi$
$42$	−6.49479	−	7.98642i	−0.154638	−	0.190153i
$43$	26.4882	+	45.8790i	0.616006	+	1.06695i	0.990207	+	0.139606i	$0.0445835\pi$
$43$	26.4882	+	45.8790i	0.616006	+	1.06695i	−0.374202	+	0.927347i	$0.622083\pi$
$44$		−	42.0973i		−	0.956756i
$45$	−21.5857	+	24.1746i	−0.479682	+	0.537213i
$46$	−7.22145	+	12.5079i	−0.156988	+	0.271911i
$47$	−16.9294	−	9.77417i	−0.360199	−	0.207961i	0.308969	−	0.951072i	$-0.400016\pi$
$47$	−16.9294	−	9.77417i	−0.360199	−	0.207961i	−0.669168	+	0.743111i	$0.733349\pi$
$48$	−6.54525	−	40.7767i	−0.136359	−	0.849514i
$49$	−6.62652	+	11.4775i	−0.135235	+	0.234234i
$50$	4.53183	+	2.61645i	0.0906366	+	0.0523291i
$51$	19.5660	−	51.2894i	0.383647	−	1.00568i
$52$	−41.6656	−	26.8014i	−0.801262	−	0.515412i
$53$			89.9664i			1.69748i	0.528811	+	0.848739i	$0.322638\pi$
$53$			89.9664i			1.69748i	−0.528811	+	0.848739i	$0.677362\pi$
$54$	10.4288	−	5.39588i	0.193126	−	0.0999237i
$55$	−19.8895	−	34.4497i	−0.361628	−	0.626358i
$56$	23.2108	−	13.4008i	0.414479	−	0.239299i
$57$	36.0834	+	13.7652i	0.633043	+	0.241495i
$58$	5.47946			0.0944734
$59$		−	79.2173i		−	1.34267i	−0.741156	−	0.671333i	$-0.765722\pi$
$59$		−	79.2173i		−	1.34267i	0.741156	−	0.671333i	$-0.234278\pi$
$60$	−25.9749	−	31.9404i	−0.432915	−	0.532340i
$61$	35.6480	+	61.7441i	0.584393	+	1.01220i	0.994951	+	0.100363i	$0.0320006\pi$
$61$	35.6480	+	61.7441i	0.584393	+	1.01220i	−0.410558	+	0.911834i	$0.634666\pi$
$62$	7.68394	−	4.43633i	0.123935	−	0.0715536i
$63$	−52.9681	−	47.2957i	−0.840763	−	0.750725i
$64$	46.5522			0.727378
$65$	−46.7592	−	2.24698i	−0.719373	−	0.0345689i
$66$	2.28414	+	14.2301i	0.0346081	+	0.215607i
$67$	11.9507	−	20.6993i	0.178369	−	0.308945i	−0.762953	−	0.646454i	$-0.776251\pi$
$67$	11.9507	−	20.6993i	0.178369	−	0.308945i	0.941322	+	0.337509i	$0.109584\pi$
$68$	60.3899	+	34.8661i	0.888087	+	0.512737i
$69$	−35.5113	+	93.0877i	−0.514657	+	1.34910i
$70$	6.17811	−	10.7008i	0.0882586	−	0.152868i
$71$	17.1555	+	9.90476i	0.241627	+	0.139504i	0.615924	−	0.787805i	$-0.288783\pi$
$71$	17.1555	+	9.90476i	0.241627	+	0.139504i	−0.374297	+	0.927309i	$0.622116\pi$
$72$	9.56795	+	29.0361i	0.132888	+	0.403279i
$73$	−96.8588			−1.32683			−0.663416	−	0.748250i	$-0.730894\pi$
$73$	−96.8588			−1.32683			−0.663416	+	0.748250i	$0.730894\pi$
$74$	0.763315	−	0.440700i	0.0103151	−	0.00595541i
$75$	33.7273	+	12.8664i	0.449697	+	0.171551i
$76$	−24.5292	+	42.4859i	−0.322753	+	0.559024i
$77$	75.4816	−	43.5793i	0.980280	−	0.565965i
$78$	15.5384	+	6.79894i	0.199210	+	0.0871659i
$79$	50.7374	−	87.8797i	0.642245	−	1.11240i	−0.342686	−	0.939450i	$-0.611337\pi$
$79$	50.7374	−	87.8797i	0.642245	−	1.11240i	0.984930	−	0.172951i	$-0.0553301\pi$
$80$	42.9309	−	24.7862i	0.536636	−	0.309827i
$81$	65.1325	−	48.1535i	0.804105	−	0.594488i
$82$	3.97451	−	6.88405i	0.0484696	−	0.0839518i
$83$	−101.767	−	58.7549i	−1.22610	−	0.707891i	−0.259890	−	0.965638i	$-0.583686\pi$
$83$	−101.767	−	58.7549i	−1.22610	−	0.707891i	−0.966212	+	0.257747i	$0.917020\pi$
$84$	69.9836	−	56.9127i	0.833138	−	0.677532i
$85$	65.8923			0.775203
$86$	19.9523	−	11.5195i	0.232004	−	0.133948i
$87$	37.3211	−	5.99059i	0.428978	−	0.0688573i
$88$	−37.5240			−0.426409
$89$	−97.3912	+	56.2288i	−1.09428	+	0.631785i	−0.934713	−	0.355402i	$-0.884344\pi$
$89$	−97.3912	+	56.2288i	−1.09428	+	0.631785i	−0.159569	+	0.987187i	$0.551011\pi$
$90$	10.5133	+	9.38741i	0.116814	+	0.104305i
$91$	4.92328	−	102.453i	0.0541019	−	1.12585i
$92$	−109.605	−	63.2803i	−1.19135	−	0.687829i
$93$	47.4859	−	38.6170i	0.510601	−	0.415236i
$94$	−4.25070	+	7.36242i	−0.0452202	+	0.0783237i
$95$			46.3569i			0.487967i
$96$	−57.9807	+	9.30675i	−0.603966	+	0.0969453i
$97$	−80.5671	−	139.546i	−0.830589	−	1.43862i	−0.897572	−	0.440868i	$-0.854671\pi$
$97$	−80.5671	−	139.546i	−0.830589	−	1.43862i	0.0669831	−	0.997754i	$-0.478663\pi$
$98$	4.99144	+	2.88181i	0.0509331	+	0.0294062i
$99$	31.1150	+	94.4253i	0.314293	+	0.953791i
$100$	−22.9275	+	39.7116i	−0.229275	+	0.397116i
$101$			49.3422i			0.488537i	0.969708	+	0.244269i	$0.0785478\pi$
$101$			49.3422i			0.488537i	−0.969708	+	0.244269i	$0.921452\pi$
$102$	−22.3053	−	8.50908i	−0.218679	−	0.0834224i
$103$	−90.4062	−	156.588i	−0.877730	−	1.52027i	−0.853825	−	0.520560i	$-0.825723\pi$
$103$	−90.4062	−	156.588i	−0.877730	−	1.52027i	−0.0239051	−	0.999714i	$-0.507610\pi$
$104$	−23.8899	+	37.1393i	−0.229710	+	0.357108i
$105$	30.3807	−	79.6386i	0.289340	−	0.758463i
$106$	39.1255			0.369109
$107$	−70.0533	+	40.4453i	−0.654704	+	0.377993i	−0.790256	−	0.612777i	$-0.790052\pi$
$107$	−70.0533	+	40.4453i	−0.654704	+	0.377993i	0.135552	+	0.990770i	$0.456719\pi$
$108$	47.2831	+	91.3859i	0.437807	+	0.846165i
$109$	164.989			1.51366			0.756830	−	0.653612i	$-0.226747\pi$
$109$	164.989			1.51366			0.756830	+	0.653612i	$0.226747\pi$
$110$	−14.9819	+	8.64978i	−0.136199	+	0.0786343i
$111$	4.71720	−	3.83617i	0.0424973	−	0.0345601i
$112$	54.3081	+	94.0644i	0.484894	+	0.839861i
$113$			56.7986i			0.502642i	0.967904	+	0.251321i	$0.0808650\pi$
$113$			56.7986i			0.502642i	−0.967904	+	0.251321i	$0.919135\pi$
$114$	5.98635	−	15.6923i	0.0525119	−	0.137652i
$115$	−119.591			−1.03992
$116$			48.0155i			0.413927i
$117$	113.267	+	29.3204i	0.968090	+	0.250602i
$118$	−34.4508			−0.291956
$119$			144.374i			1.21323i
$120$	−28.4706	+	23.1531i	−0.237255	+	0.192943i
$121$	−1.02810			−0.00849666
$122$	26.8519	−	15.5030i	0.220098	−	0.127073i
$123$	19.5446	−	51.2332i	0.158899	−	0.416530i
$124$	38.8747	+	67.3330i	0.313506	+	0.543008i
$125$			133.355i			1.06684i
$126$	−20.5684	+	23.0353i	−0.163242	+	0.182820i
$127$	−19.0725	−	33.0345i	−0.150177	−	0.260114i	0.781115	−	0.624387i	$-0.214651\pi$
$127$	−19.0725	−	33.0345i	−0.150177	−	0.260114i	−0.931292	+	0.364272i	$0.881318\pi$
$128$		−	98.5423i		−	0.769862i
$129$	123.303	−	100.274i	0.955840	−	0.777317i
$130$	−0.977190	+	20.3352i	−0.00751685	+	0.156424i
$131$	76.4250	−	44.1240i	0.583397	−	0.336825i	−0.179085	−	0.983834i	$-0.557314\pi$
$131$	76.4250	−	44.1240i	0.583397	−	0.336825i	0.762482	+	0.647009i	$0.223980\pi$
$132$	−124.696	+	20.0155i	−0.944664	+	0.151632i
$133$	−101.571			−0.763692
$134$	−9.00193	−	5.19727i	−0.0671786	−	0.0387856i
$135$	81.8702	+	52.4446i	0.606446	+	0.388479i
$136$	31.0784	−	53.8294i	0.228518	−	0.395805i
$137$	−227.617	+	131.415i	−1.66144	+	0.959232i	−0.689409	+	0.724372i	$0.742130\pi$
$137$	−227.617	+	131.415i	−1.66144	+	0.959232i	−0.972029	+	0.234860i	$0.924537\pi$
$138$	40.4830	+	15.4435i	0.293355	+	0.111910i
$139$	−8.06479			−0.0580201			−0.0290100	−	0.999579i	$-0.509235\pi$
$139$	−8.06479			−0.0580201			−0.0290100	+	0.999579i	$0.509235\pi$
$140$	93.7691	+	54.1376i	0.669780	+	0.386697i
$141$	−20.9027	+	54.7934i	−0.148246	+	0.388606i
$142$	4.30749	−	7.46079i	0.0303344	−	0.0525408i
$143$	−77.6898	+	120.777i	−0.543285	+	0.844593i
$144$	−117.672	+	38.7752i	−0.817166	+	0.269272i
$145$	22.6857	+	39.2928i	0.156453	+	0.270985i
$146$			42.1230i			0.288514i
$147$	37.1479	+	14.1713i	0.252706	+	0.0964031i
$148$	3.86178	+	6.68879i	0.0260931	+	0.0451945i
$149$		−	75.2287i		−	0.504890i	−0.967611	−	0.252445i	$-0.918765\pi$
$149$		−	75.2287i		−	0.504890i	0.967611	−	0.252445i	$-0.0812347\pi$
$150$	5.59546	−	14.6677i	0.0373031	−	0.0977845i
$151$	−40.9836	+	70.9857i	−0.271415	+	0.470104i	−0.969224	−	0.246179i	$-0.920825\pi$
$151$	−40.9836	+	70.9857i	−0.271415	+	0.470104i	0.697810	+	0.716283i	$0.254158\pi$
$152$	37.8704	+	21.8645i	0.249147	+	0.143845i
$153$	−161.226	−	33.5702i	−1.05377	−	0.219413i
$154$	−18.9522	−	32.8262i	−0.123066	−	0.213157i
$155$	63.6252	+	36.7340i	0.410485	+	0.236994i
$156$	−59.5779	+	136.160i	−0.381910	+	0.872821i
$157$	28.5135	+	49.3869i	0.181615	+	0.314566i	0.942431	−	0.334402i	$-0.108534\pi$
$157$	28.5135	+	49.3869i	0.181615	+	0.314566i	−0.760816	+	0.648968i	$0.775201\pi$
$158$	−38.2180	−	22.0652i	−0.241886	−	0.139653i
$159$	266.488	−	42.7752i	1.67602	−	0.269027i
$160$	−35.2437	−	61.0438i	−0.220273	−	0.381524i
$161$		−	262.032i		−	1.62753i
$162$	−20.9415	−	28.3255i	−0.129269	−	0.174849i
$163$	78.4808	−	135.933i	0.481478	−	0.833944i	−0.518296	−	0.855201i	$-0.673434\pi$
$163$	78.4808	−	135.933i	0.481478	−	0.833944i	0.999774	+	0.0212574i	$0.00676694\pi$
$164$	60.3237	+	34.8279i	0.367828	+	0.212365i
$165$	−92.5863	+	75.2939i	−0.561129	+	0.456327i
$166$	−25.5520	+	44.2573i	−0.153928	+	0.266610i
$167$	−195.434	−	112.834i	−1.17026	−	0.675653i	−0.216522	−	0.976278i	$-0.569471\pi$
$167$	−195.434	−	112.834i	−1.17026	−	0.675653i	−0.953742	+	0.300625i	$0.902805\pi$
$168$	−50.7300	−	62.3809i	−0.301964	−	0.371315i
$169$	70.0768	+	153.786i	0.414656	+	0.909978i
$170$		−	28.6559i		−	0.168564i
$171$	23.6175	−	113.427i	0.138114	−	0.663315i
$172$	100.943	+	174.839i	0.586879	+	1.01650i
$173$	61.9470	−	35.7651i	0.358075	−	0.206735i	−0.310161	−	0.950684i	$-0.600383\pi$
$173$	61.9470	−	35.7651i	0.358075	−	0.206735i	0.668236	+	0.743949i	$0.267050\pi$
$174$	−2.60525	−	16.2306i	−0.0149727	−	0.0932794i
$175$	−94.9387			−0.542507
$176$		−	152.070i		−	0.864036i
$177$	−234.648	+	37.6645i	−1.32570	+	0.212794i
$178$	24.4534	+	42.3545i	0.137379	+	0.237947i
$179$	211.264	−	121.974i	1.18025	−	0.681416i	0.224176	−	0.974549i	$-0.428031\pi$
$179$	211.264	−	121.974i	1.18025	−	0.681416i	0.956072	+	0.293132i	$0.0946976\pi$
$180$	−82.2603	+	92.1262i	−0.457001	+	0.511812i
$181$	−139.111			−0.768572			−0.384286	−	0.923214i	$-0.625552\pi$
$181$	−139.111			−0.768572			−0.384286	+	0.923214i	$0.625552\pi$
$182$	−44.5557	−	2.14109i	−0.244811	−	0.0117642i
$183$	165.942	−	134.949i	0.906787	−	0.737426i
$184$	−56.4058	+	97.6977i	−0.306553	+	0.530966i
$185$	6.32046	+	3.64912i	0.0341646	+	0.0197250i
$186$	−16.7942	−	20.6512i	−0.0902912	−	0.111028i
$187$	101.067	−	175.053i	0.540466	−	0.936114i
$188$	−64.5156	−	37.2481i	−0.343168	−	0.198128i
$189$	−114.910	+	179.383i	−0.607987	+	0.949116i
$190$	20.1602			0.106106
$191$	114.551	−	66.1359i	0.599742	−	0.346261i	−0.169198	−	0.985582i	$-0.554118\pi$
$191$	114.551	−	66.1359i	0.599742	−	0.346261i	0.768940	+	0.639321i	$0.220784\pi$
$192$	−22.1336	−	137.891i	−0.115279	−	0.718184i
$193$	131.583	−	227.909i	0.681780	−	1.18088i	−0.292658	−	0.956217i	$-0.594540\pi$
$193$	131.583	−	227.909i	0.681780	−	1.18088i	0.974437	−	0.224660i	$-0.0721271\pi$
$194$	−60.6874	+	35.0379i	−0.312822	+	0.180608i
$195$	15.5763	+	139.573i	0.0798785	+	0.715760i
$196$	−25.2528	+	43.7391i	−0.128841	+	0.223159i
$197$	221.466	−	127.864i	1.12420	−	0.649054i	0.181727	−	0.983349i	$-0.441831\pi$
$197$	221.466	−	127.864i	1.12420	−	0.649054i	0.942469	+	0.334295i	$0.108498\pi$
$198$	41.0647	−	13.5316i	0.207397	−	0.0683415i
$199$	−50.2310	+	87.0026i	−0.252417	+	0.437199i	−0.964191	−	0.265210i	$-0.914559\pi$
$199$	−50.2310	+	87.0026i	−0.252417	+	0.437199i	0.711774	+	0.702409i	$0.247892\pi$
$200$	35.3975	+	20.4368i	0.176988	+	0.102184i
$201$	−66.9951	−	25.5575i	−0.333309	−	0.127152i
$202$	21.4585			0.106230
$203$	−86.0931	+	49.7059i	−0.424104	+	0.244856i
$204$	74.5636	−	195.457i	0.365508	−	0.958125i
$205$	65.8201			0.321073
$206$	−68.0987	+	39.3168i	−0.330576	+	0.190858i
$207$	292.618	+	60.9282i	1.41361	+	0.294339i
$208$	−150.511	−	96.8163i	−0.723610	−	0.465463i
$209$	123.154	+	71.1033i	0.589256	+	0.340207i
$210$	−34.6341	−	13.2123i	−0.164924	−	0.0629157i
$211$	41.7337	−	72.2848i	0.197790	−	0.342582i	−0.750022	−	0.661413i	$-0.769957\pi$
$211$	41.7337	−	72.2848i	0.197790	−	0.342582i	0.947812	+	0.318831i	$0.103290\pi$
$212$			342.850i			1.61722i
$213$	21.1820	−	55.5255i	0.0994460	−	0.260683i
$214$	17.5893	+	30.4655i	0.0821929	+	0.142362i
$215$	165.211	+	95.3845i	0.768423	+	0.443649i
$216$	81.4581	−	42.1465i	0.377121	−	0.195123i
$217$	−80.4866	+	139.407i	−0.370906	+	0.642428i
$218$		−	71.7521i		−	0.329138i
$219$	46.0523	+	286.904i	0.210284	+	1.31006i
$220$	−75.7965	−	131.283i	−0.344529	−	0.596742i
$221$	−108.913	−	211.479i	−0.492821	−	0.956920i
$222$	−1.66831	−	2.05147i	−0.00751493	−	0.00924085i
$223$	112.700			0.505381			0.252691	−	0.967547i	$-0.418685\pi$
$223$	112.700			0.505381			0.252691	+	0.967547i	$0.418685\pi$
$224$	133.751	−	77.2212i	0.597103	−	0.344737i
$225$	22.0753	−	106.020i	0.0981126	−	0.471202i
$226$	24.7012			0.109297
$227$	133.355	−	76.9927i	0.587468	−	0.339175i	−0.176628	−	0.984278i	$-0.556519\pi$
$227$	133.355	−	76.9927i	0.587468	−	0.339175i	0.764096	+	0.645103i	$0.223186\pi$
$228$	137.509	+	52.4574i	0.603111	+	0.230076i
$229$	−28.5160	−	49.3911i	−0.124524	−	0.215682i	0.797023	−	0.603949i	$-0.206407\pi$
$229$	−28.5160	−	49.3911i	−0.124524	−	0.215682i	−0.921547	+	0.388267i	$0.873074\pi$
$230$			52.0091i			0.226126i
$231$	−164.974	−	202.863i	−0.714172	−	0.878193i
$232$	42.7993			0.184480
$233$			189.973i			0.815337i	0.913130	+	0.407668i	$0.133658\pi$
$233$			189.973i			0.815337i	−0.913130	+	0.407668i	$0.866342\pi$
$234$	12.7512	−	49.2586i	0.0544922	−	0.210507i
$235$	−70.3939			−0.299548
$236$		−	301.887i		−	1.27918i
$237$	−284.430	−	108.505i	−1.20013	−	0.457828i
$238$	62.7871			0.263811
$239$	17.0447	−	9.84074i	0.0713165	−	0.0411746i	−0.463918	−	0.885878i	$-0.653557\pi$
$239$	17.0447	−	9.84074i	0.0713165	−	0.0411746i	0.535234	+	0.844704i	$0.320223\pi$
$240$	−93.8305	−	115.380i	−0.390961	−	0.480751i
$241$	−71.6552	−	124.110i	−0.297324	−	0.514981i	0.678199	−	0.734879i	$-0.262761\pi$
$241$	−71.6552	−	124.110i	−0.297324	−	0.514981i	−0.975523	+	0.219898i	$0.929428\pi$
$242$			0.447110i			0.00184756i
$243$	−173.602	−	170.033i	−0.714413	−	0.699724i
$244$	135.850	+	235.299i	0.556761	+	0.964339i
$245$			47.7244i			0.194793i
$246$	−22.2808	−	8.49975i	−0.0905726	−	0.0345518i
$247$	148.781	−	76.6234i	0.602353	−	0.310216i
$248$	60.0183	−	34.6516i	0.242009	−	0.139724i
$249$	−125.651	+	329.376i	−0.504624	+	1.32280i
$250$	57.9950			0.231980
$251$	−203.239	−	117.340i	−0.809716	−	0.467490i	0.0371413	−	0.999310i	$-0.488175\pi$
$251$	−203.239	−	117.340i	−0.809716	−	0.467490i	−0.846857	+	0.531820i	$0.821508\pi$
$252$	−201.854	−	180.238i	−0.801010	−	0.715229i
$253$	−183.432	+	317.713i	−0.725026	+	1.25578i
$254$	−14.3664	+	8.29445i	−0.0565607	+	0.0326553i
$255$	−31.3290	−	195.178i	−0.122859	−	0.765406i
$256$	143.354			0.559975
$257$	62.0316	+	35.8140i	0.241368	+	0.139354i	0.615805	−	0.787898i	$-0.288831\pi$
$257$	62.0316	+	35.8140i	0.241368	+	0.139354i	−0.374437	+	0.927252i	$0.622164\pi$
$258$	−43.6082	−	53.6235i	−0.169024	−	0.207843i
$259$	−7.99546	+	13.8485i	−0.0308705	+	0.0534693i
$260$	−178.193	−	8.56294i	−0.685359	−	0.0329344i
$261$	−35.4892	−	107.700i	−0.135974	−	0.412644i
$262$	−19.1891	−	33.2365i	−0.0732409	−	0.126857i
$263$		−	326.720i		−	1.24228i	−0.783700	−	0.621140i	$-0.786670\pi$
$263$		−	326.720i		−	1.24228i	0.783700	−	0.621140i	$-0.213330\pi$
$264$	17.8411	+	111.149i	0.0675799	+	0.421020i
$265$	161.985	+	280.566i	0.611265	+	1.05874i
$266$			44.1723i			0.166061i
$267$	212.860	+	261.746i	0.797228	+	0.980324i
$268$	45.5427	−	78.8823i	0.169936	−	0.294337i
$269$	−205.679	−	118.749i	−0.764608	−	0.441446i	0.0663401	−	0.997797i	$-0.478868\pi$
$269$	−205.679	−	118.749i	−0.764608	−	0.441446i	−0.830948	+	0.556351i	$0.812201\pi$
$270$	22.8077	−	35.6046i	0.0844729	−	0.131869i
$271$	−14.0335	−	24.3067i	−0.0517841	−	0.0896928i	0.838971	−	0.544176i	$-0.183157\pi$
$271$	−14.0335	−	24.3067i	−0.0517841	−	0.0896928i	−0.890756	+	0.454483i	$0.849824\pi$
$272$	218.150	+	125.949i	0.802021	+	0.463047i
$273$	−305.814	+	34.1287i	−1.12020	+	0.125014i
$274$	57.1511	+	98.9885i	0.208580	+	0.361272i
$275$	115.113	+	66.4604i	0.418592	+	0.241674i
$276$	−135.329	+	354.745i	−0.490323	+	1.28531i
$277$	220.842	+	382.510i	0.797264	+	1.38090i	0.921391	+	0.388636i	$0.127054\pi$
$277$	220.842	+	382.510i	0.797264	+	1.38090i	−0.124127	+	0.992266i	$0.539613\pi$
$278$			3.50730i			0.0126162i
$279$	−136.964	−	122.297i	−0.490911	−	0.438339i
$280$	48.2564	−	83.5825i	0.172344	−	0.298509i
$281$	−227.027	−	131.074i	−0.807926	−	0.466456i	0.0383092	−	0.999266i	$-0.487803\pi$
$281$	−227.027	−	131.074i	−0.807926	−	0.466456i	−0.846235	+	0.532810i	$0.821136\pi$
$282$	23.8291	+	9.09040i	0.0845005	+	0.0322355i
$283$	−128.358	+	222.323i	−0.453562	+	0.785592i	−0.998604	−	0.0528164i	$-0.983180\pi$
$283$	−128.358	+	222.323i	−0.453562	+	0.785592i	0.545042	+	0.838408i	$0.316514\pi$
$284$	65.3776	+	37.7458i	0.230203	+	0.132908i
$285$	137.313	−	22.0408i	0.481800	−	0.0773360i
$286$	52.5247	+	33.7866i	0.183653	+	0.118135i
$287$			144.216i			0.502495i
$288$	55.1348	+	167.319i	0.191440	+	0.580968i
$289$	22.9131	+	39.6867i	0.0792841	+	0.137324i
$290$	17.0881	−	9.86580i	0.0589244	−	0.0340200i
$291$	−375.042	+	304.995i	−1.28880	+	1.04809i
$292$	−369.116			−1.26410
$293$		−	419.339i		−	1.43119i	−0.698516	−	0.715595i	$-0.746156\pi$
$293$		−	419.339i		−	1.43119i	0.698516	−	0.715595i	$-0.253844\pi$
$294$	6.16295	−	16.1553i	0.0209624	−	0.0549498i
$295$	−142.631	−	247.045i	−0.483496	−	0.837439i
$296$	5.96215	−	3.44225i	0.0201424	−	0.0116292i
$297$	264.902	−	137.060i	0.891925	−	0.461483i
$298$	−32.7162			−0.109786
$299$	197.672	+	383.824i	0.661112	+	1.28369i
$300$	128.530	+	49.0320i	0.428434	+	0.163440i
$301$	−208.994	+	361.988i	−0.694332	+	1.20262i
$302$	30.8710	+	17.8234i	0.102222	+	0.0590179i
$303$	146.156	−	23.4602i	0.482363	−	0.0774263i
$304$	−88.6082	+	153.474i	−0.291474	+	0.504848i
$305$	222.341	+	128.369i	0.728988	+	0.420881i
$306$	−14.5994	+	70.1159i	−0.0477104	+	0.229137i
$307$	12.4727			0.0406277			0.0203139	−	0.999794i	$-0.493533\pi$
$307$	12.4727			0.0406277			0.0203139	+	0.999794i	$0.493533\pi$
$308$	287.650	−	166.075i	0.933930	−	0.539205i
$309$	−420.843	+	342.242i	−1.36195	+	1.10758i
$310$	15.9753	−	27.6700i	0.0515331	−	0.0892580i
$311$	−370.614	+	213.974i	−1.19168	+	0.688019i	−0.958688	−	0.284458i	$-0.908186\pi$
$311$	−370.614	+	213.974i	−1.19168	+	0.688019i	−0.232996	+	0.972478i	$0.574853\pi$
$312$	121.368	+	53.1056i	0.389001	+	0.170210i
$313$	−147.784	+	255.969i	−0.472154	+	0.817794i	−0.999492	−	0.0318612i	$-0.989857\pi$
$313$	−147.784	+	255.969i	−0.472154	+	0.817794i	0.527339	+	0.849655i	$0.323190\pi$
$314$	21.4779	−	12.4003i	0.0684009	−	0.0394913i
$315$	−250.341	−	52.1254i	−0.794733	−	0.165478i
$316$	193.353	−	334.898i	0.611878	−	1.05980i
$317$	311.087	+	179.606i	0.981347	+	0.566581i	0.902677	−	0.430319i	$-0.141599\pi$
$317$	311.087	+	179.606i	0.981347	+	0.566581i	0.0786708	+	0.996901i	$0.474932\pi$
$318$	−18.6025	−	115.893i	−0.0584986	−	0.364444i
$319$	139.183			0.436311
$320$	145.176	−	83.8175i	0.453676	−	0.261930i
$321$	153.110	+	188.274i	0.476977	+	0.586523i
$322$	−113.955			−0.353899
$323$	−204.000	+	117.779i	−0.631579	+	0.364642i
$324$	248.211	−	183.507i	0.766085	−	0.566379i
$325$	139.066	−	71.6200i	0.427895	−	0.220369i
$326$	−59.1159	−	34.1306i	−0.181337	−	0.104695i
$327$	−78.4452	−	488.711i	−0.239894	−	1.49453i
$328$	31.0444	−	53.7704i	0.0946475	−	0.163934i
$329$		−	154.238i		−	0.468807i
$330$	32.7446	+	40.2649i	0.0992261	+	0.122015i
$331$	5.36870	+	9.29886i	0.0162196	+	0.0280932i	0.874021	−	0.485888i	$-0.161504\pi$
$331$	5.36870	+	9.29886i	0.0162196	+	0.0280932i	−0.857802	+	0.513981i	$0.828170\pi$
$332$	−387.819	−	223.907i	−1.16813	−	0.674420i
$333$	−13.6059	−	12.1488i	−0.0408585	−	0.0364829i
$334$	−49.0705	+	84.9925i	−0.146918	+	0.254469i
$335$		−	86.0696i		−	0.256924i
$336$	252.805	−	205.589i	0.752397	−	0.611872i
$337$	−168.540	−	291.920i	−0.500119	−	0.866232i	−1.00000		0.000137943i	$-0.999956\pi$
$337$	−168.540	−	291.920i	−0.500119	−	0.866232i	0.499881	−	0.866094i	$-0.333377\pi$
$338$	66.8803	−	30.4757i	0.197871	−	0.0901649i
$339$	168.242	−	27.0053i	0.496290	−	0.0796618i
$340$	251.107			0.738550
$341$	195.179	−	112.687i	0.572373	−	0.330460i
$342$	−49.3283	−	10.2710i	−0.144235	−	0.0300323i
$343$	282.046			0.822291
$344$	155.845	−	89.9772i	0.453038	−	0.261562i
$345$	56.8606	+	354.239i	0.164813	+	1.02678i
$346$	−15.5539	−	26.9402i	−0.0449535	−	0.0778617i
$347$			665.816i			1.91878i	0.282087	+	0.959389i	$0.408973\pi$
$347$			665.816i			1.91878i	−0.282087	+	0.959389i	$0.591027\pi$
$348$	142.226	−	22.8294i	0.408695	−	0.0656016i
$349$	5.14846			0.0147520			0.00737602	−	0.999973i	$-0.497652\pi$
$349$	5.14846			0.0147520			0.00737602	+	0.999973i	$0.497652\pi$
$350$			41.2879i			0.117966i
$351$	32.9961	−	349.446i	0.0940059	−	0.995572i
$352$	−216.230			−0.614290
$353$			28.1359i			0.0797052i	0.999206	+	0.0398526i	$0.0126888\pi$
$353$			28.1359i			0.0797052i	−0.999206	+	0.0398526i	$0.987311\pi$
$354$	16.3799	+	102.046i	0.0462710	+	0.288266i
$355$	71.3344			0.200942
$356$	−371.145	+	214.281i	−1.04254	+	0.601912i
$357$	427.649	−	68.6439i	1.19790	−	0.192280i
$358$	−53.0452	−	91.8769i	−0.148171	−	0.256639i
$359$		−	196.366i		−	0.546980i	−0.961875	−	0.273490i	$-0.911822\pi$
$359$		−	196.366i		−	0.546980i	0.961875	−	0.273490i	$-0.0881780\pi$
$360$	82.1180	+	73.3239i	0.228106	+	0.203677i
$361$	97.6392	+	169.116i	0.270469	+	0.468466i
$362$			60.4983i			0.167122i
$363$	0.488816	+	3.04531i	0.00134660	+	0.00838928i
$364$	18.7620	−	390.433i	0.0515439	−	1.07262i
$365$	−302.061	+	174.395i	−0.827564	+	0.477794i
$366$	−58.6880	−	72.1666i	−0.160350	−	0.197177i
$367$	−173.165			−0.471839			−0.235919	−	0.971773i	$-0.575810\pi$
$367$	−173.165			−0.471839			−0.235919	+	0.971773i	$0.575810\pi$
$368$	−395.931	−	228.591i	−1.07590	−	0.621171i
$369$	−161.050	−	33.5334i	−0.436449	−	0.0908765i
$370$	1.58697	−	2.74871i	0.00428910	−	0.00742894i
$371$	−614.740	+	354.920i	−1.65698	+	0.956658i
$372$	180.963	−	147.164i	0.486459	−	0.395603i
$373$	−95.5823			−0.256253			−0.128126	−	0.991758i	$-0.540896\pi$
$373$	−95.5823			−0.256253			−0.128126	+	0.991758i	$0.540896\pi$
$374$	−76.1290	−	43.9531i	−0.203554	−	0.117522i
$375$	395.009	−	63.4048i	1.05336	−	0.169080i
$376$	−33.2016	+	57.5069i	−0.0883022	+	0.152944i
$377$	88.6118	−	137.756i	0.235045	−	0.365401i
$378$	78.0120	+	49.9731i	0.206381	+	0.132204i
$379$	35.1129	+	60.8173i	0.0926462	+	0.160468i	0.908624	−	0.417616i	$-0.137134\pi$
$379$	35.1129	+	60.8173i	0.0926462	+	0.160468i	−0.815978	+	0.578084i	$0.803801\pi$
$380$			176.660i			0.464895i
$381$	−88.7829	+	72.2009i	−0.233026	+	0.189504i
$382$	−28.7619	−	49.8170i	−0.0752929	−	0.130411i
$383$			435.200i			1.13629i	0.822928	+	0.568146i	$0.192339\pi$
$383$			435.200i			1.13629i	−0.822928	+	0.568146i	$0.807661\pi$
$384$	−291.890	+	46.8527i	−0.760132	+	0.122012i
$385$	156.930	−	271.810i	0.407610	−	0.706000i
$386$	−99.1156	−	57.2244i	−0.256776	−	0.148250i
$387$	−355.645	−	317.559i	−0.918980	−	0.820565i
$388$	−307.031	−	531.793i	−0.791317	−	1.37060i
$389$	21.8657	+	12.6242i	0.0562100	+	0.0324528i	0.527842	−	0.849343i	$-0.323001\pi$
$389$	21.8657	+	12.6242i	0.0562100	+	0.0324528i	−0.471632	+	0.881796i	$0.656335\pi$
$390$	60.6990	−	6.77399i	0.155639	−	0.0173692i
$391$	−303.846	−	526.277i	−0.777101	−	1.34598i
$392$	38.9875	+	22.5095i	0.0994580	+	0.0574221i
$393$	−167.036	−	205.398i	−0.425028	−	0.522642i
$394$	−55.6067	−	96.3137i	−0.141134	−	0.244451i
$395$		−	365.412i		−	0.925093i
$396$	118.575	+	359.843i	0.299432	+	0.908693i
$397$	352.580	−	610.687i	0.888112	−	1.53825i	0.0460070	−	0.998941i	$-0.485350\pi$
$397$	352.580	−	610.687i	0.888112	−	1.53825i	0.842105	−	0.539314i	$-0.181316\pi$
$398$	37.8366	+	21.8450i	0.0950669	+	0.0548869i
$399$	48.2927	+	300.862i	0.121034	+	0.754040i
$400$	−82.8223	+	143.452i	−0.207056	+	0.358631i
$401$	477.752	+	275.830i	1.19140	+	0.687856i	0.958625	−	0.284674i	$-0.0918852\pi$
$401$	477.752	+	275.830i	1.19140	+	0.687856i	0.232778	+	0.972530i	$0.425219\pi$
$402$	−11.1147	+	29.1356i	−0.0276485	+	0.0724765i
$403$	12.7306	−	264.921i	0.0315895	−	0.657371i
$404$			188.037i			0.465438i
$405$	116.420	−	267.442i	0.287456	−	0.660350i
$406$	21.6166	+	37.4411i	0.0532429	+	0.0922194i
$407$	19.3889	−	11.1942i	0.0476386	−	0.0275042i
$408$	−174.224	−	66.4633i	−0.427019	−	0.162900i
$409$	607.179			1.48455			0.742273	−	0.670098i	$-0.233748\pi$
$409$	607.179			1.48455			0.742273	+	0.670098i	$0.233748\pi$
$410$		−	28.6245i		−	0.0698159i
$411$	497.484	+	611.739i	1.21042	+	1.48841i
$412$	−344.526	−	596.737i	−0.836229	−	1.44839i
$413$	541.291	−	312.514i	1.31063	−	0.756694i
$414$	26.4971	−	127.257i	0.0640027	−	0.307383i
$415$	−423.155			−1.01965
$416$	−137.664	+	214.013i	−0.330923	+	0.514454i
$417$	3.83447	+	23.8886i	0.00919537	+	0.0572868i
$418$	30.9221	−	53.5587i	0.0739764	−	0.128131i
$419$	−511.942	−	295.570i	−1.22182	−	0.705418i	−0.256514	−	0.966541i	$-0.582574\pi$
$419$	−511.942	−	295.570i	−1.22182	−	0.705418i	−0.965306	+	0.261123i	$0.915907\pi$
$420$	115.777	−	303.492i	0.275659	−	0.722601i
$421$	−224.617	+	389.048i	−0.533532	+	0.924105i	0.465701	+	0.884942i	$0.345802\pi$
$421$	−224.617	+	389.048i	−0.533532	+	0.924105i	−0.999233	+	0.0391625i	$0.987531\pi$
$422$	−31.4360	−	18.1496i	−0.0744929	−	0.0430085i
$423$	172.241	+	35.8637i	0.407189	+	0.0847841i
$424$	305.605			0.720765
$425$	−190.679	+	110.089i	−0.448657	+	0.259032i
$426$	−24.1475	−	9.21185i	−0.0566843	−	0.0216241i
$427$	−281.264	+	487.164i	−0.658699	+	1.14090i
$428$	−266.964	+	154.132i	−0.623748	+	0.360121i
$429$	394.689	+	172.699i	0.920022	+	0.402563i
$430$	41.4819	−	71.8487i	0.0964694	−	0.167090i
$431$	654.630	−	377.951i	1.51886	−	0.876916i	0.519109	−	0.854708i	$-0.326264\pi$
$431$	654.630	−	377.951i	1.51886	−	0.876916i	0.999753	−	0.0222075i	$-0.00706945\pi$
$432$	170.803	+	330.118i	0.395378	+	0.764162i
$433$	147.022	−	254.650i	0.339543	−	0.588106i	−0.644804	−	0.764348i	$-0.723061\pi$
$433$	147.022	−	254.650i	0.339543	−	0.588106i	0.984347	+	0.176242i	$0.0563942\pi$
$434$	60.6268	+	35.0029i	0.139693	+	0.0806518i
$435$	105.602	−	85.8790i	0.242764	−	0.197423i
$436$	628.751			1.44209
$437$	370.249	−	213.764i	0.847253	−	0.489162i
$438$	124.772	−	20.0277i	0.284867	−	0.0457254i
$439$	633.805			1.44375			0.721873	−	0.692025i	$-0.243281\pi$
$439$	633.805			1.44375			0.721873	+	0.692025i	$0.243281\pi$
$440$	−117.021	+	67.5623i	−0.265958	+	0.153551i
$441$	24.3142	−	116.773i	0.0551342	−	0.264791i
$442$	−91.9704	+	47.3654i	−0.208078	+	0.107162i
$443$	−46.2937	−	26.7277i	−0.104501	−	0.0603334i	0.446839	−	0.894614i	$-0.352550\pi$
$443$	−46.2937	−	26.7277i	−0.104501	−	0.0603334i	−0.551339	+	0.834281i	$0.685883\pi$
$444$	17.9767	−	14.6191i	0.0404880	−	0.0329260i
$445$	−202.481	+	350.707i	−0.455013	+	0.788106i
$446$		−	49.0122i		−	0.109893i
$447$	−222.834	+	35.7681i	−0.498509	+	0.0800180i
$448$	183.650	+	318.091i	0.409932	+	0.710024i
$449$	−610.311	−	352.363i	−1.35927	−	0.784773i	−0.369742	−	0.929135i	$-0.620554\pi$
$449$	−610.311	−	352.363i	−1.35927	−	0.784773i	−0.989525	+	0.144362i	$0.953887\pi$
$450$	−46.1073	−	9.60036i	−0.102461	−	0.0213341i
$451$	100.956	−	174.861i	0.223850	−	0.387719i
$452$			216.452i			0.478876i
$453$	229.752	+	87.6462i	0.507178	+	0.193479i
$454$	−33.4834	−	57.9949i	−0.0737520	−	0.127742i
$455$	−169.113	−	328.370i	−0.371677	−	0.721692i
$456$	46.7586	−	122.571i	0.102541	−	0.268796i
$457$	−858.234			−1.87797			−0.938987	−	0.343953i	$-0.888234\pi$
$457$	−858.234			−1.87797			−0.938987	+	0.343953i	$0.888234\pi$
$458$	−21.4797	+	12.4013i	−0.0468990	+	0.0270771i
$459$	−22.7814	+	493.527i	−0.0496327	+	1.07522i
$460$	−455.746			−0.990753
$461$	401.655	−	231.896i	0.871269	−	0.503028i	0.00349951	−	0.999994i	$-0.498886\pi$
$461$	401.655	−	231.896i	0.871269	−	0.503028i	0.867770	+	0.496966i	$0.165553\pi$
$462$	−88.2230	+	71.7456i	−0.190959	+	0.155293i
$463$	−163.427	−	283.065i	−0.352975	−	0.611371i	0.633794	−	0.773502i	$-0.281497\pi$
$463$	−163.427	−	283.065i	−0.352975	−	0.611371i	−0.986769	+	0.162131i	$0.948163\pi$
$464$			173.449i			0.373813i
$465$	78.5581	−	205.928i	0.168942	−	0.442857i
$466$	82.6177			0.177291
$467$			889.917i			1.90560i	0.303594	+	0.952802i	$0.401814\pi$
$467$			889.917i			1.90560i	−0.303594	+	0.952802i	$0.598186\pi$
$468$	431.644	+	111.736i	0.922317	+	0.238753i
$469$	188.584			0.402098
$470$			30.6136i			0.0651354i
$471$	132.731	−	107.941i	0.281807	−	0.229174i
$472$	−269.091			−0.570108
$473$	506.808	−	292.606i	1.07148	−	0.618617i
$474$	−47.1879	+	123.696i	−0.0995525	+	0.260962i
$475$	−77.4502	−	134.148i	−0.163053	−	0.282416i
$476$			550.192i			1.15587i
$477$	−253.408	−	769.022i	−0.531253	−	1.61220i
$478$	−4.27964	−	7.41256i	−0.00895323	−	0.0155075i
$479$			653.524i			1.36435i	0.731189	+	0.682175i	$0.238966\pi$
$479$			653.524i			1.36435i	−0.731189	+	0.682175i	$0.761034\pi$
$480$	−164.060	+	133.418i	−0.341792	+	0.277955i
$481$	1.26464	−	26.3169i	0.00262919	−	0.0547130i
$482$	−53.9745	+	31.1622i	−0.111980	+	0.0646518i
$483$	−776.161	+	124.585i	−1.60696	+	0.257940i
$484$	−3.91794			−0.00809492
$485$	−502.508	−	290.123i	−1.03610	−	0.598193i
$486$	−73.9457	+	75.4981i	−0.152152	+	0.155346i
$487$	−257.806	+	446.533i	−0.529376	+	0.916906i	0.470037	+	0.882647i	$0.344240\pi$
$487$	−257.806	+	446.533i	−0.529376	+	0.916906i	−0.999413	+	0.0342590i	$0.989093\pi$
$488$	209.737	−	121.092i	0.429789	−	0.248139i
$489$	−439.959	−	167.837i	−0.899711	−	0.343224i
$490$	20.7549			0.0423569
$491$	−217.965	−	125.842i	−0.443921	−	0.256298i	0.261339	−	0.965247i	$-0.415836\pi$
$491$	−217.965	−	125.842i	−0.443921	−	0.256298i	−0.705259	+	0.708949i	$0.749169\pi$
$492$	74.4818	−	195.243i	0.151386	−	0.396836i
$493$	−115.276	+	199.663i	−0.233825	+	0.404996i
$494$	−33.3228	−	64.7035i	−0.0674551	−	0.130979i
$495$	267.048	+	238.449i	0.539490	+	0.481716i
$496$	140.429	+	243.231i	0.283124	+	0.490384i
$497$			156.298i			0.314484i
$498$	143.243	+	54.6446i	0.287636	+	0.109728i
$499$	330.409	+	572.286i	0.662143	+	1.14686i	0.980052	+	0.198743i	$0.0636861\pi$
$499$	330.409	+	572.286i	0.662143	+	1.14686i	−0.317909	+	0.948121i	$0.602981\pi$
$500$			508.200i			1.01640i
$501$	−241.303	+	632.540i	−0.481643	+	1.26256i
$502$	−51.0300	+	88.3866i	−0.101653	+	0.176069i
$503$	124.243	+	71.7317i	0.247004	+	0.142608i	0.618392	−	0.785870i	$-0.287785\pi$
$503$	124.243	+	71.7317i	0.247004	+	0.142608i	−0.371388	+	0.928478i	$0.621118\pi$
$504$	−160.657	+	179.926i	−0.318765	+	0.356996i
$505$	88.8411	+	153.877i	0.175923	+	0.304707i
$506$	138.170	+	79.7727i	0.273064	+	0.157654i
$507$	422.210	−	280.692i	0.832760	−	0.553634i
$508$	−72.6828	−	125.890i	−0.143076	−	0.247816i
$509$	−74.1781	−	42.8268i	−0.145733	−	0.0841390i	0.425360	−	0.905024i	$-0.360147\pi$
$509$	−74.1781	−	42.8268i	−0.145733	−	0.0841390i	−0.571094	+	0.820885i	$0.693481\pi$
$510$	−84.8813	+	13.6247i	−0.166434	+	0.0267151i
$511$	−382.111	−	661.835i	−0.747771	−	1.29518i
$512$		−	456.512i		−	0.891626i
$513$	−347.209	−	16.0273i	−0.676821	−	0.0312423i
$514$	15.5752	−	26.9770i	0.0303019	−	0.0524844i
$515$	−563.876	−	325.554i	−1.09491	−	0.632144i
$516$	469.893	−	382.131i	0.910645	−	0.740564i
$517$	−107.972	+	187.012i	−0.208843	+	0.361726i
$518$	6.02260	+	3.47715i	0.0116266	+	0.00671264i
$519$	−135.392	−	166.487i	−0.260872	−	0.320785i
$520$	−7.63270	+	158.835i	−0.0146783	+	0.305452i
$521$			39.8935i			0.0765710i	0.999267	+	0.0382855i	$0.0121896\pi$
$521$			39.8935i			0.0765710i	−0.999267	+	0.0382855i	$0.987810\pi$
$522$	−46.8377	+	15.4339i	−0.0897275	+	0.0295669i
$523$	211.748	+	366.758i	0.404872	+	0.701258i	0.994307	−	0.106558i	$-0.0339829\pi$
$523$	211.748	+	366.758i	0.404872	+	0.701258i	−0.589435	+	0.807816i	$0.700650\pi$
$524$	291.246	−	168.151i	0.555813	−	0.320899i
$525$	45.1393	+	281.216i	0.0859797	+	0.535650i
$526$	−142.087			−0.270128
$527$			373.322i			0.708390i
$528$	−450.445	+	72.3030i	−0.853115	+	0.136938i
$529$	286.966	+	497.039i	0.542468	+	0.939582i
$530$	122.016	−	70.4458i	0.230218	−	0.132917i
$531$	223.131	+	677.140i	0.420208	+	1.27522i
$532$	−387.074			−0.727583
$533$	−108.794	−	211.247i	−0.204116	−	0.396337i
$534$	113.831	−	92.5708i	0.213167	−	0.173354i
$535$	−145.644	+	252.263i	−0.272232	+	0.471520i
$536$	−70.3129	−	40.5952i	−0.131181	−	0.0757373i
$537$	−461.743	−	567.790i	−0.859857	−	1.05734i
$538$	−51.6429	+	89.4481i	−0.0959905	+	0.166260i
$539$	126.787	+	73.2007i	0.235227	+	0.135808i
$540$	311.997	+	199.860i	0.577772	+	0.370110i
$541$	−189.199			−0.349722			−0.174861	−	0.984593i	$-0.555948\pi$
$541$	−189.199			−0.349722			−0.174861	+	0.984593i	$0.555948\pi$
$542$	−10.5708	+	6.10304i	−0.0195033	+	0.0112602i
$543$	66.1416	+	412.060i	0.121808	+	0.758858i
$544$	179.088	−	310.189i	0.329205	−	0.570201i
$545$	514.529	−	297.064i	0.944090	−	0.545071i
$546$	14.8423	+	132.996i	0.0271836	+	0.243582i
$547$	175.857	−	304.594i	0.321494	−	0.556845i	−0.659302	−	0.751878i	$-0.729148\pi$
$547$	175.857	−	304.594i	0.321494	−	0.556845i	0.980797	+	0.195033i	$0.0624815\pi$
$548$	−867.419	+	500.805i	−1.58288	+	0.913877i
$549$	−478.628	−	427.372i	−0.871819	−	0.778455i
$550$	28.9030	−	50.0615i	0.0525509	−	0.0910208i
$551$	−140.468	−	81.0993i	−0.254933	−	0.147186i
$552$	316.207	+	120.628i	0.572839	+	0.218528i
$553$	800.641			1.44781
$554$	166.350	−	96.0422i	0.300271	−	0.173361i
$555$	7.80388	−	20.4567i	0.0140610	−	0.0368590i
$556$	−30.7339			−0.0552767
$557$	524.604	−	302.880i	0.941838	−	0.543770i	0.0513020	−	0.998683i	$-0.483663\pi$
$557$	524.604	−	302.880i	0.941838	−	0.543770i	0.890536	+	0.454913i	$0.150330\pi$
$558$	−53.1856	+	59.5645i	−0.0953148	+	0.106746i
$559$	33.0565	−	687.900i	0.0591351	−	1.23059i
$560$	338.727	+	195.564i	0.604870	+	0.349222i
$561$	−566.576	−	216.139i	−1.00994	−	0.385274i
$562$	−57.0029	+	98.7320i	−0.101429	+	0.175680i
$563$		−	461.212i		−	0.819204i	−0.912264	−	0.409602i	$-0.865668\pi$
$563$		−	461.212i		−	0.819204i	0.912264	−	0.409602i	$-0.134332\pi$
$564$	−79.6576	+	208.811i	−0.141237	+	0.370232i
$565$	102.266	+	177.130i	0.181002	+	0.313505i
$566$	96.6860	+	55.8217i	0.170823	+	0.0986249i
$567$	585.982	+	255.083i	1.03348	+	0.449882i
$568$	33.6452	−	58.2752i	0.0592346	−	0.102597i
$569$		−	308.963i		−	0.542992i	−0.962439	−	0.271496i	$-0.912482\pi$
$569$		−	308.963i		−	0.542992i	0.962439	−	0.271496i	$-0.0875185\pi$
$570$	−9.58532	−	59.7162i	−0.0168164	−	0.104765i
$571$	−46.7472	−	80.9685i	−0.0818690	−	0.141801i	0.822184	−	0.569222i	$-0.192756\pi$
$571$	−46.7472	−	80.9685i	−0.0818690	−	0.141801i	−0.904053	+	0.427421i	$0.859422\pi$
$572$	−296.066	+	460.265i	−0.517597	+	0.804659i
$573$	−250.364	−	307.864i	−0.436936	−	0.537284i
$574$	62.7182			0.109265
$575$	346.073	−	199.805i	0.601866	−	0.347488i
$576$	−397.922	+	131.123i	−0.690837	+	0.227644i
$577$	478.102			0.828600			0.414300	−	0.910140i	$-0.364027\pi$
$577$	478.102			0.828600			0.414300	+	0.910140i	$0.364027\pi$
$578$	17.2594	−	9.96470i	0.0298605	−	0.0172400i
$579$	−737.649	−	281.400i	−1.27400	−	0.486010i
$580$	86.4523	+	149.740i	0.149056	+	0.258172i
$581$		−	927.160i		−	1.59580i
$582$	132.639	+	163.102i	0.227903	+	0.280244i
$583$	993.826			1.70468
$584$			329.017i			0.563386i
$585$	406.021	−	112.499i	0.694054	−	0.192307i
$586$	−182.366			−0.311205
$587$		−	209.513i		−	0.356922i	−0.983947	−	0.178461i	$-0.942888\pi$
$587$		−	209.513i		−	0.356922i	0.983947	−	0.178461i	$-0.0571119\pi$
$588$	141.566	+	54.0048i	0.240758	+	0.0918449i
$589$	−262.641			−0.445910
$590$	−107.437	+	62.0290i	−0.182097	+	0.105134i
$591$	−484.041	−	595.208i	−0.819020	−	1.00712i
$592$	13.9501	+	24.1623i	0.0235644	+	0.0408147i
$593$			806.812i			1.36056i	0.732953	+	0.680280i	$0.238142\pi$
$593$			806.812i			1.36056i	−0.732953	+	0.680280i	$0.761858\pi$
$594$	−59.6063	−	115.203i	−0.100347	−	0.193945i
$595$	259.947	+	450.242i	0.436886	+	0.756708i
$596$		−	286.687i		−	0.481018i
$597$	281.592	+	107.422i	0.471678	+	0.179937i
$598$	166.922	−	85.9659i	0.279133	−	0.143756i
$599$	−463.319	+	267.498i	−0.773488	+	0.446574i	−0.834118	−	0.551587i	$-0.814023\pi$
$599$	−463.319	+	267.498i	−0.773488	+	0.446574i	0.0606294	+	0.998160i	$0.480689\pi$
$600$	43.7054	−	114.567i	0.0728423	−	0.190945i
$601$	318.353			0.529705			0.264852	−	0.964289i	$-0.414677\pi$
$601$	318.353			0.529705			0.264852	+	0.964289i	$0.414677\pi$
$602$	157.425	+	90.8895i	0.261504	+	0.150979i
$603$	−43.8500	+	210.597i	−0.0727197	+	0.349248i
$604$	−156.183	+	270.517i	−0.258582	+	0.447876i
$605$	−3.20619	+	1.85110i	−0.00529949	+	0.00305966i
$606$	−10.2026	−	63.5618i	−0.0168360	−	0.104888i
$607$	−519.920			−0.856541			−0.428271	−	0.903651i	$-0.640877\pi$
$607$	−519.920			−0.856541			−0.428271	+	0.903651i	$0.640877\pi$
$608$	218.226	+	125.993i	0.358924	+	0.207225i
$609$	188.167	+	231.382i	0.308976	+	0.379937i
$610$	55.8264	−	96.6942i	0.0915187	−	0.158515i
$611$	116.354	+	225.927i	0.190432	+	0.369766i
$612$	−614.413	−	127.932i	−1.00394	−	0.209039i
$613$	239.689	+	415.154i	0.391010	+	0.677249i	0.992583	−	0.121569i	$-0.0387925\pi$
$613$	239.689	+	415.154i	0.391010	+	0.677249i	−0.601573	+	0.798818i	$0.705459\pi$
$614$		−	5.42426i		−	0.00883431i
$615$	−31.2947	−	194.965i	−0.0508856	−	0.317016i
$616$	−148.033	−	256.401i	−0.240314	−	0.416236i
$617$			240.049i			0.389058i	0.980897	+	0.194529i	$0.0623179\pi$
$617$			240.049i			0.389058i	−0.980897	+	0.194529i	$0.937682\pi$
$618$	148.838	+	183.021i	0.240838	+	0.296150i
$619$	−86.1248	+	149.172i	−0.139135	+	0.240989i	−0.927170	−	0.374642i	$-0.877766\pi$
$619$	−86.1248	+	149.172i	−0.139135	+	0.240989i	0.788034	+	0.615631i	$0.211099\pi$
$620$	242.467	+	139.988i	0.391076	+	0.225788i
$621$	41.3471	−	895.727i	0.0665815	−	1.44239i
$622$	93.0553	+	161.177i	0.149607	+	0.259126i
$623$	−768.422	−	443.649i	−1.23342	−	0.712117i
$624$	−215.216	+	491.858i	−0.344898	+	0.788234i
$625$	89.6985	+	155.362i	0.143518	+	0.248580i
$626$	111.319	+	64.2699i	0.177825	+	0.102668i
$627$	152.059	−	398.600i	0.242518	−	0.635726i
$628$	108.661	+	188.207i	0.173028	+	0.299693i
$629$			37.0854i			0.0589593i
$630$	−22.6689	+	108.871i	−0.0359823	+	0.172811i
$631$	−484.961	+	839.977i	−0.768559	+	1.33118i	0.169785	+	0.985481i	$0.445693\pi$
$631$	−484.961	+	839.977i	−0.768559	+	1.33118i	−0.938344	+	0.345702i	$0.887641\pi$
$632$	−298.516	−	172.348i	−0.472336	−	0.272703i
$633$	−233.956	−	89.2502i	−0.369599	−	0.140996i
$634$	78.1091	−	135.289i	0.123200	−	0.213389i
$635$	−118.958	−	68.6803i	−0.187335	−	0.108158i
$636$	1015.55	−	163.011i	1.59678	−	0.256306i
$637$	153.170	−	78.8837i	0.240455	−	0.123836i
$638$		−	60.5295i		−	0.0948739i
$639$	−174.542	−	36.3428i	−0.273149	−	0.0568745i
$640$	−177.426	−	307.311i	−0.277228	−	0.480174i
$641$	272.656	−	157.418i	0.425360	−	0.245582i	−0.272008	−	0.962295i	$-0.587688\pi$
$641$	272.656	−	157.418i	0.425360	−	0.245582i	0.697368	+	0.716713i	$0.254354\pi$
$642$	81.8785	−	66.5860i	0.127537	−	0.103717i
$643$	−883.910			−1.37466			−0.687332	−	0.726343i	$-0.741218\pi$
$643$	−883.910			−1.37466			−0.687332	+	0.726343i	$0.741218\pi$
$644$		−	998.570i		−	1.55058i
$645$	203.986	−	534.720i	0.316258	−	0.829023i
$646$	51.2212	+	88.7177i	0.0792897	+	0.137334i
$647$	1006.62	−	581.171i	1.55582	−	0.898255i	0.558174	−	0.829724i	$-0.311502\pi$
$647$	1006.62	−	581.171i	1.55582	−	0.898255i	0.997649	−	0.0685315i	$-0.0218314\pi$
$648$	−163.571	−	221.247i	−0.252425	−	0.341430i
$649$	−875.084			−1.34836
$650$	−31.1469	−	60.4785i	−0.0479183	−	0.0930439i
$651$	451.203	+	172.126i	0.693092	+	0.264402i
$652$	299.080	−	518.022i	0.458712	−	0.794513i
$653$	131.909	+	76.1578i	0.202005	+	0.116627i	0.597590	−	0.801802i	$-0.296125\pi$
$653$	131.909	+	76.1578i	0.202005	+	0.116627i	−0.395585	+	0.918429i	$0.629458\pi$
$654$	−212.536	+	34.1151i	−0.324978	+	0.0521638i
$655$	158.891	−	275.208i	0.242582	−	0.420164i
$656$	217.911	+	125.811i	0.332181	+	0.191785i
$657$	827.937	−	272.821i	1.26018	−	0.415253i
$658$	−67.0765			−0.101940
$659$	586.936	−	338.868i	0.890647	−	0.514215i	0.0164930	−	0.999864i	$-0.494750\pi$
$659$	586.936	−	338.868i	0.890647	−	0.514215i	0.874154	+	0.485649i	$0.161417\pi$
$660$	−352.834	+	286.935i	−0.534597	+	0.434750i
$661$	414.883	−	718.598i	0.627659	−	1.08714i	−0.360361	−	0.932813i	$-0.617346\pi$
$661$	414.883	−	718.598i	0.627659	−	1.08714i	0.988020	−	0.154325i	$-0.0493203\pi$
$662$	4.04399	−	2.33480i	0.00610874	−	0.00352689i
$663$	−574.636	+	423.160i	−0.866720	+	0.638251i
$664$	−199.583	+	345.688i	−0.300577	+	0.520615i
$665$	−316.756	+	182.879i	−0.476325	+	0.275007i
$666$	−5.28341	+	5.91707i	−0.00793304	+	0.00888449i
$667$	209.219	−	362.378i	0.313672	−	0.543296i
$668$	−744.774	−	429.996i	−1.11493	−	0.643706i
$669$	−53.5841	−	333.827i	−0.0800958	−	0.498994i
$670$	−37.4309			−0.0558670
$671$	682.064	−	393.790i	1.01649	−	0.586870i
$672$	−292.329	−	359.466i	−0.435013	−	0.534920i
$673$	−614.686			−0.913353			−0.456676	−	0.889633i	$-0.650960\pi$
$673$	−614.686			−0.913353			−0.456676	+	0.889633i	$0.650960\pi$
$674$	−126.953	+	73.2966i	−0.188358	+	0.108749i
$675$	−324.537	−	14.9808i	−0.480796	−	0.0221937i
$676$	267.054	+	586.060i	0.395050	+	0.866952i
$677$	534.883	+	308.815i	0.790078	+	0.456152i	0.839990	−	0.542602i	$-0.182561\pi$
$677$	534.883	+	308.815i	0.790078	+	0.456152i	−0.0499121	+	0.998754i	$0.515894\pi$
$678$	−11.7444	−	73.1670i	−0.0173221	−	0.107916i
$679$	635.679	−	1101.03i	0.936199	−	1.62154i
$680$		−	223.828i		−	0.329159i
$681$	−291.463	−	358.402i	−0.427993	−	0.526288i
$682$	−49.0065	−	84.8817i	−0.0718570	−	0.124460i
$683$	−101.555	−	58.6329i	−0.148690	−	0.0858461i	0.423809	−	0.905751i	$-0.360693\pi$
$683$	−101.555	−	58.6329i	−0.148690	−	0.0858461i	−0.572499	+	0.819905i	$0.694026\pi$
$684$	90.0032	−	432.255i	0.131584	−	0.631952i
$685$	−473.227	+	819.652i	−0.690842	+	1.19657i
$686$		−	122.659i		−	0.178803i
$687$	−132.742	+	107.950i	−0.193220	+	0.157133i
$688$	364.643	+	631.580i	0.530004	+	0.917994i
$689$	632.724	−	983.635i	0.918322	−	1.42763i
$690$	154.055	−	24.7281i	0.223269	−	0.0358379i
$691$	110.872			0.160451			0.0802254	−	0.996777i	$-0.474436\pi$
$691$	110.872			0.160451			0.0802254	+	0.996777i	$0.474436\pi$
$692$	236.072	−	136.296i	0.341144	−	0.196960i
$693$	−522.458	+	585.119i	−0.753907	+	0.844327i
$694$	289.557			0.417229
$695$	−25.1506	+	14.5207i	−0.0361879	+	0.0208931i
$696$	−20.3493	−	126.775i	−0.0292375	−	0.182148i
$697$	167.230	+	289.650i	0.239928	+	0.415567i
$698$		−	2.23902i		−	0.00320776i
$699$	562.717	−	90.3244i	0.805032	−	0.129219i
$700$	−361.799			−0.516856
$701$			1172.51i			1.67263i	0.548250	+	0.836315i	$0.315294\pi$
$701$			1172.51i			1.67263i	−0.548250	+	0.836315i	$0.684706\pi$
$702$	−151.971	−	14.3497i	−0.216482	−	0.0204411i
$703$	−26.0905			−0.0371131
$704$		−	514.245i		−	0.730461i
$705$	33.4693	+	208.513i	0.0474742	+	0.295763i
$706$	12.2360			0.0173315
$707$	−337.155	+	194.657i	−0.476881	+	0.275328i
$708$	−894.214	+	143.534i	−1.26301	+	0.202732i
$709$	292.951	+	507.405i	0.413188	+	0.715663i	0.995236	−	0.0974912i	$-0.0310818\pi$
$709$	292.951	+	507.405i	0.413188	+	0.715663i	−0.582048	+	0.813154i	$0.697748\pi$
$710$		−	31.0227i		−	0.0436939i
$711$	−186.167	+	894.096i	−0.261838	+	1.25752i
$712$	191.002	+	330.826i	0.268262	+	0.464643i
$713$		−	677.560i		−	0.950294i
$714$	−29.8526	−	185.981i	−0.0418104	−	0.260477i
$715$	−24.8215	+	516.532i	−0.0347154	+	0.722423i
$716$	805.101	−	464.825i	1.12444	−	0.649197i
$717$	−37.2531	−	45.8088i	−0.0519569	−	0.0638896i
$718$	−85.3977			−0.118938
$719$	115.750	+	66.8285i	0.160988	+	0.0929464i	0.578330	−	0.815803i	$-0.303705\pi$
$719$	115.750	+	66.8285i	0.160988	+	0.0929464i	−0.417342	+	0.908750i	$0.637038\pi$
$720$	−297.153	+	332.792i	−0.412713	+	0.462211i
$721$	713.311	−	1235.49i	0.989335	−	1.71358i
$722$	73.5470	−	42.4624i	0.101866	−	0.0588122i
$723$	−333.556	+	271.258i	−0.461350	+	0.375184i
$724$	−530.136			−0.732232
$725$	−131.296	−	75.8037i	−0.181098	−	0.104557i
$726$	1.32438	−	0.212582i	0.00182421	−	0.000292812i
$727$	−50.8543	+	88.0822i	−0.0699509	+	0.121159i	−0.898879	−	0.438196i	$-0.855618\pi$
$727$	−50.8543	+	88.0822i	−0.0699509	+	0.121159i	0.828929	+	0.559354i	$0.188951\pi$
$728$	−348.018	−	16.7238i	−0.478047	−	0.0229722i
$729$	−421.111	+	595.068i	−0.577656	+	0.816280i
$730$	75.8427	+	131.363i	0.103894	+	0.179950i
$731$			969.377i			1.32610i
$732$	632.383	−	514.273i	0.863912	−	0.702559i
$733$	326.946	+	566.287i	0.446038	+	0.772561i	0.998124	−	0.0612267i	$-0.0195013\pi$
$733$	326.946	+	566.287i	0.446038	+	0.772561i	−0.552086	+	0.833787i	$0.686168\pi$
$734$			75.3077i			0.102599i
$735$	141.364	−	22.6909i	0.192331	−	0.0308720i
$736$	−325.035	+	562.977i	−0.441624	+	0.764915i
$737$	−228.657	−	132.015i	−0.310254	−	0.179125i
$738$	−14.5834	+	70.0390i	−0.0197607	+	0.0949038i
$739$	163.941	+	283.953i	0.221841	+	0.384240i	0.955367	−	0.295421i	$-0.0954600\pi$
$739$	163.941	+	283.953i	0.221841	+	0.384240i	−0.733526	+	0.679661i	$0.762127\pi$
$740$	24.0864	+	13.9063i	0.0325492	+	0.0187923i
$741$	−297.704	−	404.271i	−0.401760	−	0.545575i
$742$	154.351	+	267.345i	0.208021	+	0.360303i
$743$	497.490	+	287.226i	0.669570	+	0.386576i	0.795914	−	0.605410i	$-0.206991\pi$
$743$	497.490	+	287.226i	0.669570	+	0.386576i	−0.126344	+	0.991987i	$0.540324\pi$
$744$	−131.177	−	161.304i	−0.176313	−	0.216806i
$745$	−135.450	−	234.606i	−0.181812	−	0.314907i
$746$			41.5679i			0.0557210i
$747$	1035.38	+	215.585i	1.38605	+	0.288601i
$748$	385.153	−	667.105i	0.514911	−	0.891852i
$749$	−552.725	−	319.116i	−0.737950	−	0.426056i
$750$	−27.5742	−	171.786i	−0.0367656	−	0.229048i
$751$	−251.966	+	436.417i	−0.335507	+	0.581115i	−0.983582	−	0.180462i	$-0.942241\pi$
$751$	−251.966	+	436.417i	−0.335507	+	0.581115i	0.648075	+	0.761576i	$0.275574\pi$
$752$	−233.053	−	134.553i	−0.309911	−	0.178927i
$753$	−250.939	+	657.800i	−0.333253	+	0.873573i
$754$	−59.9089	−	38.5364i	−0.0794547	−	0.0511093i
$755$			295.165i			0.390947i
$756$	−437.906	+	683.605i	−0.579240	+	0.904240i
$757$	−171.376	−	296.832i	−0.226389	−	0.392117i	0.730346	−	0.683077i	$-0.239359\pi$
$757$	−171.376	−	296.832i	−0.226389	−	0.392117i	−0.956735	+	0.290960i	$0.906025\pi$
$758$	26.4489	−	15.2703i	0.0348930	−	0.0201455i
$759$	1028.31	+	392.281i	1.35482	+	0.516839i
$760$	157.469			0.207196
$761$			679.506i			0.892912i	0.894806	+	0.446456i	$0.147314\pi$
$761$			679.506i			0.892912i	−0.894806	+	0.446456i	$0.852686\pi$
$762$	31.3995	+	38.6108i	0.0412067	+	0.0506704i
$763$	650.886	+	1127.37i	0.853061	+	1.47755i
$764$	436.538	−	252.035i	0.571385	−	0.329889i
$765$	−563.239	+	185.598i	−0.736261	+	0.242612i
$766$	189.264			0.247081
$767$	−557.127	+	866.111i	−0.726371	+	1.12922i
$768$	−68.1586	−	424.625i	−0.0887481	−	0.552897i
$769$	−186.936	+	323.782i	−0.243089	+	0.421043i	−0.961593	−	0.274481i	$-0.911494\pi$
$769$	−186.936	+	323.782i	−0.243089	+	0.421043i	0.718503	+	0.695523i	$0.244827\pi$

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-0.434891i q^{2} +(-0.475458 - 2.96208i) q^{3} +3.81087 q^{4} +(3.11857 - 1.80051i) q^{5} +(-1.28818 + 0.206772i) q^{6} +(3.94503 + 6.83299i) q^{7} -3.39687i q^{8} +(-8.54788 + 2.81669i) q^{9} +(-0.783024 - 1.35624i) q^{10} -11.0466i q^{11} +(-1.81191 - 11.2881i) q^{12} +(-10.9334 - 7.03289i) q^{13} +(2.97160 - 1.71566i) q^{14} +(-6.81600 - 8.38140i) q^{15} +13.7662 q^{16} +(15.8468 + 9.14913i) q^{17} +(1.22495 + 3.71739i) q^{18} +(-6.43665 + 11.1486i) q^{19} +(11.8845 - 6.86150i) q^{20} +(18.3642 - 14.9343i) q^{21} -4.80408 q^{22} +(-28.7611 - 16.6052i) q^{23} +(-10.0618 + 1.61507i) q^{24} +(-6.01635 + 10.4206i) q^{25} +(-3.05854 + 4.75482i) q^{26} +(12.4074 + 23.9803i) q^{27} +(15.0340 + 26.0396i) q^{28} +12.5996i q^{29} +(-3.64499 + 2.96422i) q^{30} +(10.2010 + 17.6687i) q^{31} -19.5743i q^{32} +(-32.7211 + 5.25221i) q^{33} +(3.97887 - 6.89161i) q^{34} +(24.6057 + 14.2061i) q^{35} +(-32.5749 + 10.7340i) q^{36} +(1.01336 + 1.75519i) q^{37} +(4.84842 + 2.79924i) q^{38} +(-15.6337 + 35.7294i) q^{39} +(-6.11610 - 10.5934i) q^{40} +(15.8294 + 9.13910i) q^{41} +(-6.49479 - 7.98642i) q^{42} +(26.4882 + 45.8790i) q^{43} -42.0973i q^{44} +(-21.5857 + 24.1746i) q^{45} +(-7.22145 + 12.5079i) q^{46} +(-16.9294 - 9.77417i) q^{47} +(-6.54525 - 40.7767i) q^{48} +(-6.62652 + 11.4775i) q^{49} +(4.53183 + 2.61645i) q^{50} +(19.5660 - 51.2894i) q^{51} +(-41.6656 - 26.8014i) q^{52} +89.9664i q^{53} +(10.4288 - 5.39588i) q^{54} +(-19.8895 - 34.4497i) q^{55} +(23.2108 - 13.4008i) q^{56} +(36.0834 + 13.7652i) q^{57} +5.47946 q^{58} -79.2173i q^{59} +(-25.9749 - 31.9404i) q^{60} +(35.6480 + 61.7441i) q^{61} +(7.68394 - 4.43633i) q^{62} +(-52.9681 - 47.2957i) q^{63} +46.5522 q^{64} +(-46.7592 - 2.24698i) q^{65} +(2.28414 + 14.2301i) q^{66} +(11.9507 - 20.6993i) q^{67} +(60.3899 + 34.8661i) q^{68} +(-35.5113 + 93.0877i) q^{69} +(6.17811 - 10.7008i) q^{70} +(17.1555 + 9.90476i) q^{71} +(9.56795 + 29.0361i) q^{72} -96.8588 q^{73} +(0.763315 - 0.440700i) q^{74} +(33.7273 + 12.8664i) q^{75} +(-24.5292 + 42.4859i) q^{76} +(75.4816 - 43.5793i) q^{77} +(15.5384 + 6.79894i) q^{78} +(50.7374 - 87.8797i) q^{79} +(42.9309 - 24.7862i) q^{80} +(65.1325 - 48.1535i) q^{81} +(3.97451 - 6.88405i) q^{82} +(-101.767 - 58.7549i) q^{83} +(69.9836 - 56.9127i) q^{84} +65.8923 q^{85} +(19.9523 - 11.5195i) q^{86} +(37.3211 - 5.99059i) q^{87} -37.5240 q^{88} +(-97.3912 + 56.2288i) q^{89} +(10.5133 + 9.38741i) q^{90} +(4.92328 - 102.453i) q^{91} +(-109.605 - 63.2803i) q^{92} +(47.4859 - 38.6170i) q^{93} +(-4.25070 + 7.36242i) q^{94} +46.3569i q^{95} +(-57.9807 + 9.30675i) q^{96} +(-80.5671 - 139.546i) q^{97} +(4.99144 + 2.88181i) q^{98} +(31.1150 + 94.4253i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - q^{3} - 98 q^{4} - 6 q^{5} + 12 q^{6} - q^{7} - 3 q^{9} - 6 q^{10} - 39 q^{12} + 4 q^{13} - 6 q^{14} - 25 q^{15} + 166 q^{16} + 34 q^{18} + 5 q^{19} + 21 q^{20} - 91 q^{21} + 30 q^{22} - 75 q^{23}+ \cdots + 522 q^{99}+O(q^{100}) \) 52 * q - q^3 - 98 * q^4 - 6 * q^5 + 12 * q^6 - q^7 - 3 * q^9 - 6 * q^10 - 39 * q^12 + 4 * q^13 - 6 * q^14 - 25 * q^15 + 166 * q^16 + 34 * q^18 + 5 * q^19 + 21 * q^20 - 91 * q^21 + 30 * q^22 - 75 * q^23 - 24 * q^24 + 88 * q^25 - 132 * q^26 - 34 * q^27 - 22 * q^28 + 70 * q^30 + 14 * q^31 + 95 * q^33 - 6 * q^34 + 228 * q^35 - 58 * q^36 - 13 * q^37 - 192 * q^38 - 111 * q^39 + 72 * q^40 + 33 * q^41 + 159 * q^42 - 31 * q^43 - 47 * q^45 + 6 * q^46 - 69 * q^47 + 293 * q^48 - 123 * q^49 - 168 * q^50 + 235 * q^51 - 92 * q^52 - 339 * q^54 - 27 * q^55 + 168 * q^56 + 189 * q^57 + 210 * q^58 + 213 * q^60 + 8 * q^61 + 471 * q^62 + 169 * q^63 - 98 * q^64 - 246 * q^65 - 576 * q^66 - 34 * q^67 + 18 * q^68 - 193 * q^69 - 57 * q^70 + 144 * q^71 + 36 * q^72 - 106 * q^73 - 465 * q^74 - 58 * q^75 - 79 * q^76 + 282 * q^77 - 76 * q^78 - 25 * q^79 - 1050 * q^80 - 279 * q^81 + 81 * q^82 + 219 * q^83 + 395 * q^84 - 108 * q^85 - 24 * q^86 - 518 * q^87 + 30 * q^88 + 99 * q^89 + 183 * q^90 + 2 * q^91 + 888 * q^92 + 582 * q^93 + 303 * q^94 - 439 * q^96 + 212 * q^97 - 405 * q^98 + 522 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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