LMFDB - Embedded newform 117.3.k.a.29.15

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			29.15
Character	$\chi$	$=$	117.29
Dual form			117.3.k.a.113.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.306140i q^{2} +(-0.721810 + 2.91187i) q^{3} +3.90628 q^{4} +(5.23834 - 3.02436i) q^{5} +(-0.891441 - 0.220975i) q^{6} +(0.307870 + 0.533246i) q^{7} +2.42043i q^{8} +(-7.95798 - 4.20363i) q^{9} +(0.925877 + 1.60367i) q^{10} -1.57095i q^{11} +(-2.81959 + 11.3746i) q^{12} +(8.42234 + 9.90273i) q^{13} +(-0.163248 + 0.0942513i) q^{14} +(5.02545 + 17.4364i) q^{15} +14.8841 q^{16} +(-6.92854 - 4.00019i) q^{17} +(1.28690 - 2.43626i) q^{18} +(-13.8170 + 23.9317i) q^{19} +(20.4624 - 11.8140i) q^{20} +(-1.77497 + 0.511574i) q^{21} +0.480931 q^{22} +(-18.1819 - 10.4973i) q^{23} +(-7.04798 - 1.74709i) q^{24} +(5.79345 - 10.0345i) q^{25} +(-3.03163 + 2.57842i) q^{26} +(17.9846 - 20.1384i) q^{27} +(1.20262 + 2.08301i) q^{28} -48.8876i q^{29} +(-5.33797 + 1.53849i) q^{30} +(-16.9689 - 29.3909i) q^{31} +14.2383i q^{32} +(4.57440 + 1.13393i) q^{33} +(1.22462 - 2.12111i) q^{34} +(3.22545 + 1.86221i) q^{35} +(-31.0861 - 16.4206i) q^{36} +(-6.37439 - 11.0408i) q^{37} +(-7.32647 - 4.22994i) q^{38} +(-34.9148 + 17.3769i) q^{39} +(7.32024 + 12.6790i) q^{40} +(-20.7315 - 11.9693i) q^{41} +(-0.156613 - 0.543389i) q^{42} +(28.2980 + 49.0136i) q^{43} -6.13656i q^{44} +(-54.3999 + 2.04771i) q^{45} +(3.21365 - 5.56621i) q^{46} +(13.5831 + 7.84221i) q^{47} +(-10.7435 + 43.3406i) q^{48} +(24.3104 - 42.1069i) q^{49} +(3.07198 + 1.77361i) q^{50} +(16.6491 - 17.2876i) q^{51} +(32.9000 + 38.6828i) q^{52} -28.8222i q^{53} +(6.16517 + 5.50581i) q^{54} +(-4.75111 - 8.22916i) q^{55} +(-1.29068 + 0.745177i) q^{56} +(-59.7129 - 57.5074i) q^{57} +14.9665 q^{58} +43.1040i q^{59} +(19.6308 + 68.1113i) q^{60} +(-31.2772 - 54.1737i) q^{61} +(8.99775 - 5.19485i) q^{62} +(-0.208450 - 5.53773i) q^{63} +55.1776 q^{64} +(74.0685 + 26.4017i) q^{65} +(-0.347141 + 1.40041i) q^{66} +(-13.6099 + 23.5730i) q^{67} +(-27.0648 - 15.6259i) q^{68} +(43.6907 - 45.3662i) q^{69} +(-0.570099 + 0.987440i) q^{70} +(-110.895 - 64.0252i) q^{71} +(10.1746 - 19.2617i) q^{72} +27.8685 q^{73} +(3.38002 - 1.95146i) q^{74} +(25.0375 + 24.1128i) q^{75} +(-53.9730 + 93.4840i) q^{76} +(0.837702 - 0.483647i) q^{77} +(-5.31976 - 10.6888i) q^{78} +(-26.8055 + 46.4286i) q^{79} +(77.9680 - 45.0149i) q^{80} +(45.6589 + 66.9049i) q^{81} +(3.66430 - 6.34675i) q^{82} +(137.735 + 79.5215i) q^{83} +(-6.93351 + 1.99835i) q^{84} -48.3920 q^{85} +(-15.0050 + 8.66317i) q^{86} +(142.354 + 35.2876i) q^{87} +3.80237 q^{88} +(-91.3979 + 52.7686i) q^{89} +(-0.626885 - 16.6540i) q^{90} +(-2.68761 + 7.53993i) q^{91} +(-71.0235 - 41.0054i) q^{92} +(97.8309 - 28.1965i) q^{93} +(-2.40082 + 4.15834i) q^{94} +167.150i q^{95} +(-41.4602 - 10.2774i) q^{96} +(-46.6339 - 80.7723i) q^{97} +(12.8906 + 7.44240i) q^{98} +(-6.60370 + 12.5016i) 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 $

$2$			0.306140i			0.153070i	0.997067	+	0.0765351i	$0.0243857\pi$
$2$			0.306140i			0.153070i	−0.997067	+	0.0765351i	$0.975614\pi$
$3$	−0.721810	+	2.91187i	−0.240603	+	0.970624i
$3$	−0.721810	+	2.91187i	−0.240603	+	0.970624i
$4$	3.90628			0.976570
$5$	5.23834	−	3.02436i	1.04767	−	0.604871i	0.125672	−	0.992072i	$-0.459891\pi$
$5$	5.23834	−	3.02436i	1.04767	−	0.604871i	0.921995	+	0.387201i	$0.126558\pi$
$6$	−0.891441	−	0.220975i	−0.148573	−	0.0368292i
$7$	0.307870	+	0.533246i	0.0439814	+	0.0761780i	0.887178	−	0.461427i	$-0.152662\pi$
$7$	0.307870	+	0.533246i	0.0439814	+	0.0761780i	−0.843197	+	0.537605i	$0.819329\pi$
$8$			2.42043i			0.302554i
$9$	−7.95798	−	4.20363i	−0.884220	−	0.467071i
$10$	0.925877	+	1.60367i	0.0925877	+	0.160367i
$11$		−	1.57095i		−	0.142814i	−0.997447	−	0.0714068i	$-0.977251\pi$
$11$		−	1.57095i		−	0.142814i	0.997447	−	0.0714068i	$-0.0227488\pi$
$12$	−2.81959	+	11.3746i	−0.234966	+	0.947881i
$13$	8.42234	+	9.90273i	0.647873	+	0.761749i
$13$	8.42234	+	9.90273i	0.647873	+	0.761749i
$14$	−0.163248	+	0.0942513i	−0.0116606	+	0.00673223i
$15$	5.02545	+	17.4364i	0.335030	+	1.16242i
$16$	14.8841			0.930258
$17$	−6.92854	−	4.00019i	−0.407561	−	0.235306i	0.282180	−	0.959361i	$-0.408942\pi$
$17$	−6.92854	−	4.00019i	−0.407561	−	0.235306i	−0.689741	+	0.724056i	$0.742276\pi$
$18$	1.28690	−	2.43626i	0.0714945	−	0.135348i
$19$	−13.8170	+	23.9317i	−0.727210	+	1.25956i	0.230848	+	0.972990i	$0.425850\pi$
$19$	−13.8170	+	23.9317i	−0.727210	+	1.25956i	−0.958058	+	0.286575i	$0.907483\pi$
$20$	20.4624	−	11.8140i	1.02312	−	0.590699i
$21$	−1.77497	+	0.511574i	−0.0845222	+	0.0243607i
$22$	0.480931			0.0218605
$23$	−18.1819	−	10.4973i	−0.790517	−	0.456405i	0.0496277	−	0.998768i	$-0.484197\pi$
$23$	−18.1819	−	10.4973i	−0.790517	−	0.456405i	−0.840144	+	0.542363i	$0.817530\pi$
$24$	−7.04798	−	1.74709i	−0.293666	−	0.0727954i
$25$	5.79345	−	10.0345i	0.231738	−	0.401382i
$26$	−3.03163	+	2.57842i	−0.116601	+	0.0991699i
$27$	17.9846	−	20.1384i	0.666096	−	0.745866i
$28$	1.20262	+	2.08301i	0.0429509	+	0.0743931i
$29$		−	48.8876i		−	1.68578i	−0.538087	−	0.842889i	$-0.680853\pi$
$29$		−	48.8876i		−	1.68578i	0.538087	−	0.842889i	$-0.319147\pi$
$30$	−5.33797	+	1.53849i	−0.177932	+	0.0512831i
$31$	−16.9689	−	29.3909i	−0.547383	−	0.948095i	−0.998453	−	0.0556061i	$-0.982291\pi$
$31$	−16.9689	−	29.3909i	−0.547383	−	0.948095i	0.451070	−	0.892489i	$-0.351042\pi$
$32$			14.2383i			0.444948i
$33$	4.57440	+	1.13393i	0.138618	+	0.0343614i
$34$	1.22462	−	2.12111i	0.0360183	−	0.0623854i
$35$	3.22545	+	1.86221i	0.0921557	+	0.0532061i
$36$	−31.0861	−	16.4206i	−0.863502	−	0.456127i
$37$	−6.37439	−	11.0408i	−0.172281	−	0.298399i	0.766936	−	0.641723i	$-0.221780\pi$
$37$	−6.37439	−	11.0408i	−0.172281	−	0.298399i	−0.939217	+	0.343324i	$0.888447\pi$
$38$	−7.32647	−	4.22994i	−0.192802	−	0.111314i
$39$	−34.9148	+	17.3769i	−0.895252	+	0.445561i
$40$	7.32024	+	12.6790i	0.183006	+	0.316976i
$41$	−20.7315	−	11.9693i	−0.505647	−	0.291935i	0.225396	−	0.974267i	$-0.427633\pi$
$41$	−20.7315	−	11.9693i	−0.505647	−	0.291935i	−0.731042	+	0.682332i	$0.760966\pi$
$42$	−0.156613	−	0.543389i	−0.00372889	−	0.0129378i
$43$	28.2980	+	49.0136i	0.658094	+	1.13985i	0.981109	+	0.193458i	$0.0619702\pi$
$43$	28.2980	+	49.0136i	0.658094	+	1.13985i	−0.323015	+	0.946394i	$0.604696\pi$
$44$		−	6.13656i		−	0.139467i
$45$	−54.3999	+	2.04771i	−1.20889	+	0.0455046i
$46$	3.21365	−	5.56621i	0.0698620	−	0.121004i
$47$	13.5831	+	7.84221i	0.289002	+	0.166856i	0.637492	−	0.770457i	$-0.279972\pi$
$47$	13.5831	+	7.84221i	0.289002	+	0.166856i	−0.348489	+	0.937313i	$0.613305\pi$
$48$	−10.7435	+	43.3406i	−0.223823	+	0.902930i
$49$	24.3104	−	42.1069i	0.496131	−	0.859325i
$50$	3.07198	+	1.77361i	0.0614396	+	0.0354722i
$51$	16.6491	−	17.2876i	0.326454	−	0.338973i
$52$	32.9000	+	38.6828i	0.632693	+	0.743901i
$53$		−	28.8222i		−	0.543815i	−0.962323	−	0.271908i	$-0.912345\pi$
$53$		−	28.8222i		−	0.543815i	0.962323	−	0.271908i	$-0.0876545\pi$
$54$	6.16517	+	5.50581i	0.114170	+	0.101959i
$55$	−4.75111	−	8.22916i	−0.0863838	−	0.149621i
$56$	−1.29068	+	0.745177i	−0.0230479	+	0.0133067i
$57$	−59.7129	−	57.5074i	−1.04759	−	1.00890i
$58$	14.9665			0.258042
$59$			43.1040i			0.730576i	0.930895	+	0.365288i	$0.119029\pi$
$59$			43.1040i			0.730576i	−0.930895	+	0.365288i	$0.880971\pi$
$60$	19.6308	+	68.1113i	0.327180	+	1.13519i
$61$	−31.2772	−	54.1737i	−0.512741	−	0.888094i	−0.999891	−	0.0147756i	$-0.995297\pi$
$61$	−31.2772	−	54.1737i	−0.512741	−	0.888094i	0.487149	−	0.873319i	$-0.338037\pi$
$62$	8.99775	−	5.19485i	0.145125	−	0.0837879i
$63$	−0.208450	−	5.53773i	−0.00330873	−	0.0879005i
$64$	55.1776			0.862149
$65$	74.0685	+	26.4017i	1.13951	+	0.406180i
$66$	−0.347141	+	1.40041i	−0.00525971	+	0.0212183i
$67$	−13.6099	+	23.5730i	−0.203132	+	0.351835i	−0.949536	−	0.313658i	$-0.898445\pi$
$67$	−13.6099	+	23.5730i	−0.203132	+	0.351835i	0.746404	+	0.665493i	$0.231779\pi$
$68$	−27.0648	−	15.6259i	−0.398012	−	0.229792i
$69$	43.6907	−	45.3662i	0.633198	−	0.657482i
$70$	−0.570099	+	0.987440i	−0.00814427	+	0.0141063i
$71$	−110.895	−	64.0252i	−1.56190	−	0.901763i	−0.997065	−	0.0765591i	$-0.975607\pi$
$71$	−110.895	−	64.0252i	−1.56190	−	0.901763i	−0.564835	−	0.825204i	$-0.691060\pi$
$72$	10.1746	−	19.2617i	0.141314	−	0.267524i
$73$	27.8685			0.381760			0.190880	−	0.981613i	$-0.438866\pi$
$73$	27.8685			0.381760			0.190880	+	0.981613i	$0.438866\pi$
$74$	3.38002	−	1.95146i	0.0456760	−	0.0263710i
$75$	25.0375	+	24.1128i	0.333834	+	0.321504i
$76$	−53.9730	+	93.4840i	−0.710171	+	1.23005i
$77$	0.837702	−	0.483647i	0.0108792	−	0.00628114i
$78$	−5.31976	−	10.6888i	−0.0682021	−	0.137036i
$79$	−26.8055	+	46.4286i	−0.339311	+	0.587703i	−0.984303	−	0.176486i	$-0.943527\pi$
$79$	−26.8055	+	46.4286i	−0.339311	+	0.587703i	0.644993	+	0.764189i	$0.276860\pi$
$80$	77.9680	−	45.0149i	0.974601	−	0.562686i
$81$	45.6589	+	66.9049i	0.563690	+	0.825986i
$82$	3.66430	−	6.34675i	0.0446866	−	0.0773994i
$83$	137.735	+	79.5215i	1.65946	+	0.958090i	0.972964	+	0.230956i	$0.0741854\pi$
$83$	137.735	+	79.5215i	1.65946	+	0.958090i	0.686496	+	0.727133i	$0.259148\pi$
$84$	−6.93351	+	1.99835i	−0.0825418	+	0.0237899i
$85$	−48.3920			−0.569318
$86$	−15.0050	+	8.66317i	−0.174477	+	0.100734i
$87$	142.354	+	35.2876i	1.63626	+	0.405604i
$88$	3.80237			0.0432088
$89$	−91.3979	+	52.7686i	−1.02694	+	0.592905i	−0.916107	−	0.400933i	$-0.868686\pi$
$89$	−91.3979	+	52.7686i	−1.02694	+	0.592905i	−0.110835	+	0.993839i	$0.535353\pi$
$90$	−0.626885	−	16.6540i	−0.00696539	−	0.185044i
$91$	−2.68761	+	7.53993i	−0.0295341	+	0.0828564i
$92$	−71.0235	−	41.0054i	−0.771995	−	0.445711i
$93$	97.8309	−	28.1965i	1.05195	−	0.303188i
$94$	−2.40082	+	4.15834i	−0.0255406	+	0.0442376i
$95$			167.150i			1.75947i
$96$	−41.4602	−	10.2774i	−0.431877	−	0.107056i
$97$	−46.6339	−	80.7723i	−0.480762	−	0.832704i	0.518994	−	0.854778i	$-0.326307\pi$
$97$	−46.6339	−	80.7723i	−0.480762	−	0.832704i	−0.999756	+	0.0220735i	$0.992973\pi$
$98$	12.8906	+	7.44240i	0.131537	+	0.0759429i
$99$	−6.60370	+	12.5016i	−0.0667040	+	0.126279i
$100$	22.6308	−	39.1977i	0.226308	−	0.391977i
$101$			126.382i			1.25130i	0.780102	+	0.625652i	$0.215167\pi$
$101$			126.382i			1.25130i	−0.780102	+	0.625652i	$0.784833\pi$
$102$	5.29244	+	5.09697i	0.0518867	+	0.0499703i
$103$	−55.1093	−	95.4521i	−0.535042	−	0.926720i	−0.999161	−	0.0409470i	$-0.986963\pi$
$103$	−55.1093	−	95.4521i	−0.535042	−	0.926720i	0.464120	−	0.885773i	$-0.346371\pi$
$104$	−23.9689	+	20.3857i	−0.230470	+	0.196016i
$105$	−7.75069	+	8.04793i	−0.0738161	+	0.0766469i
$106$	8.82364			0.0832419
$107$	43.5421	−	25.1390i	0.406935	−	0.234944i	−0.282537	−	0.959256i	$-0.591176\pi$
$107$	43.5421	−	25.1390i	0.406935	−	0.234944i	0.689472	+	0.724312i	$0.257843\pi$
$108$	70.2528	−	78.6661i	0.650489	−	0.728390i
$109$	−92.5282			−0.848882			−0.424441	−	0.905456i	$-0.639529\pi$
$109$	−92.5282			−0.848882			−0.424441	+	0.905456i	$0.639529\pi$
$110$	2.51928	−	1.45451i	0.0229025	−	0.0132228i
$111$	36.7504	−	10.5921i	0.331084	−	0.0954239i
$112$	4.58237	+	7.93689i	0.0409140	+	0.0708651i
$113$			151.769i			1.34309i	0.740966	+	0.671543i	$0.234368\pi$
$113$			151.769i			1.34309i	−0.740966	+	0.671543i	$0.765632\pi$
$114$	17.6053	−	18.2805i	0.154433	−	0.160355i
$115$	−126.990			−1.10426
$116$		−	190.969i		−	1.64628i
$117$	−25.3974	−	114.210i	−0.217072	−	0.976156i
$118$	−13.1959			−0.111829
$119$		−	4.92615i		−	0.0413962i
$120$	−42.2035	+	12.1637i	−0.351696	+	0.101365i
$121$	118.532			0.979604
$122$	16.5848	−	9.57522i	0.135941	−	0.0784854i
$123$	49.8174	−	51.7279i	0.405019	−	0.420552i
$124$	−66.2851	−	114.809i	−0.534557	−	0.925880i
$125$			81.1320i			0.649056i
$126$	1.69532	−	0.0638149i	0.0134549	−	0.000506467i
$127$	−16.1533	−	27.9783i	−0.127191	−	0.220301i	0.795396	−	0.606090i	$-0.207263\pi$
$127$	−16.1533	−	27.9783i	−0.127191	−	0.220301i	−0.922587	+	0.385788i	$0.873929\pi$
$128$			73.8455i			0.576918i
$129$	−163.147	+	47.0217i	−1.26471	+	0.364509i
$130$	−8.08262	+	22.6753i	−0.0621740	+	0.174426i
$131$	2.31769	−	1.33812i	0.0176923	−	0.0102146i	−0.491128	−	0.871088i	$-0.663415\pi$
$131$	2.31769	−	1.33812i	0.0176923	−	0.0102146i	0.508820	+	0.860873i	$0.330082\pi$
$132$	17.8689	+	4.42943i	0.135370	+	0.0335563i
$133$	−17.0153			−0.127935
$134$	−7.21664	−	4.16653i	−0.0538555	−	0.0310935i
$135$	33.3037	−	159.883i	0.246694	−	1.18432i
$136$	9.68219	−	16.7700i	0.0711926	−	0.123309i
$137$	11.7960	−	6.81045i	0.0861025	−	0.0497113i	−0.456331	−	0.889810i	$-0.650837\pi$
$137$	11.7960	−	6.81045i	0.0861025	−	0.0497113i	0.542433	+	0.840099i	$0.317503\pi$
$138$	13.8884	+	13.3755i	0.100641	+	0.0969238i
$139$	55.9416			0.402457			0.201229	−	0.979544i	$-0.435507\pi$
$139$	55.9416			0.402457			0.201229	+	0.979544i	$0.435507\pi$
$140$	12.5995	+	7.27433i	0.0899964	+	0.0519595i
$141$	−32.6399	+	33.8917i	−0.231489	+	0.240367i
$142$	19.6007	−	33.9494i	0.138033	−	0.239080i
$143$	15.5567	−	13.2311i	0.108788	−	0.0925250i
$144$	−118.448	−	62.5674i	−0.822552	−	0.434496i
$145$	−147.853	−	256.090i	−1.01968	−	1.76614i
$146$			8.53166i			0.0584361i
$147$	105.062	+	101.182i	0.714710	+	0.688313i
$148$	−24.9001	−	43.1283i	−0.168244	−	0.291407i
$149$		−	100.302i		−	0.673171i	−0.941653	−	0.336586i	$-0.890728\pi$
$149$		−	100.302i		−	0.673171i	0.941653	−	0.336586i	$-0.109272\pi$
$150$	−7.38190	+	7.66500i	−0.0492127	+	0.0511000i
$151$	35.1292	−	60.8455i	0.232643	−	0.402950i	−0.725942	−	0.687756i	$-0.758596\pi$
$151$	35.1292	−	60.8455i	0.232643	−	0.402950i	0.958585	+	0.284806i	$0.0919292\pi$
$152$	−57.9251	−	33.4431i	−0.381086	−	0.220020i
$153$	38.3218	+	60.9585i	0.250470	+	0.398422i
$154$	0.148064	+	0.256454i	0.000961454	+	0.00166529i
$155$	−177.777	−	102.640i	−1.14695	−	0.662192i
$156$	−136.387	+	67.8789i	−0.874275	+	0.435121i
$157$	44.5950	+	77.2408i	0.284045	+	0.491980i	0.972377	−	0.233416i	$-0.0749903\pi$
$157$	44.5950	+	77.2408i	0.284045	+	0.491980i	−0.688332	+	0.725395i	$0.741657\pi$
$158$	−14.2136	−	8.20625i	−0.0899598	−	0.0519383i
$159$	83.9266	+	20.8042i	0.527840	+	0.130844i
$160$	43.0618	+	74.5853i	0.269136	+	0.466158i
$161$		−	12.9272i		−	0.0802933i
$162$	−20.4823	+	13.9780i	−0.126434	+	0.0862841i
$163$	−128.595	+	222.733i	−0.788925	+	1.36646i	0.137701	+	0.990474i	$0.456029\pi$
$163$	−128.595	+	222.733i	−0.788925	+	1.36646i	−0.926626	+	0.375984i	$0.877305\pi$
$164$	−80.9831	−	46.7556i	−0.493799	−	0.285095i
$165$	27.3917	−	7.89472i	0.166010	−	0.0478468i
$166$	−24.3447	+	42.1663i	−0.146655	+	0.254014i
$167$	141.423	+	81.6504i	0.846843	+	0.488925i	0.859584	−	0.510994i	$-0.170723\pi$
$167$	141.423	+	81.6504i	0.846843	+	0.488925i	−0.0127417	+	0.999919i	$0.504056\pi$
$168$	−1.23823	−	4.29618i	−0.00737041	−	0.0255725i
$169$	−27.1283	+	166.808i	−0.160522	+	0.987032i
$170$		−	14.8148i		−	0.0871456i
$171$	210.556	−	132.367i	1.23132	−	0.774074i
$172$	110.540	+	191.461i	0.642674	+	1.11314i
$173$	237.609	−	137.184i	1.37346	−	0.792970i	0.382102	−	0.924120i	$-0.375200\pi$
$173$	237.609	−	137.184i	1.37346	−	0.792970i	0.991363	+	0.131150i	$0.0418670\pi$
$174$	−10.8029	+	43.5804i	−0.0620859	+	0.250462i
$175$	7.13451			0.0407686
$176$		−	23.3822i		−	0.132853i
$177$	−125.513	−	31.1129i	−0.709114	−	0.175779i
$178$	−16.1546	−	27.9806i	−0.0907561	−	0.157194i
$179$	−231.140	+	133.449i	−1.29128	+	0.745524i	−0.978882	−	0.204426i	$-0.934467\pi$
$179$	−231.140	+	133.449i	−1.29128	+	0.745524i	−0.312403	+	0.949950i	$0.601134\pi$
$180$	−212.501	+	7.99891i	−1.18056	+	0.0444384i
$181$	256.842			1.41902			0.709508	−	0.704697i	$-0.248917\pi$
$181$	256.842			1.41902			0.709508	+	0.704697i	$0.248917\pi$
$182$	−2.30828	−	0.822785i	−0.0126828	−	0.00452080i
$183$	180.323	−	51.9721i	0.985372	−	0.284000i
$184$	25.4080	−	44.0080i	0.138087	−	0.239174i
$185$	−66.7824	−	38.5568i	−0.360986	−	0.208415i
$186$	8.63207	+	29.9500i	0.0464090	+	0.161021i
$187$	−6.28410	+	10.8844i	−0.0336048	+	0.0582053i
$188$	53.0594	+	30.6339i	0.282231	+	0.162946i
$189$	16.2756	+	3.39021i	0.0861144	+	0.0179376i
$190$	−51.1713			−0.269323
$191$	83.4394	−	48.1738i	0.436856	−	0.252219i	−0.265407	−	0.964136i	$-0.585506\pi$
$191$	83.4394	−	48.1738i	0.436856	−	0.252219i	0.702263	+	0.711918i	$0.252173\pi$
$192$	−39.8277	+	160.670i	−0.207436	+	0.836822i
$193$	−76.3158	+	132.183i	−0.395418	+	0.684885i	−0.993155	−	0.116808i	$-0.962734\pi$
$193$	−76.3158	+	132.183i	−0.395418	+	0.684885i	0.597736	+	0.801693i	$0.296067\pi$
$194$	24.7277	−	14.2765i	0.127462	−	0.0735903i
$195$	−130.342	+	196.621i	−0.668419	+	1.00831i
$196$	94.9633	−	164.481i	0.484507	−	0.839190i
$197$	−135.576	+	78.2746i	−0.688201	+	0.397333i	−0.802938	−	0.596063i	$-0.796731\pi$
$197$	−135.576	+	78.2746i	−0.688201	+	0.397333i	0.114737	+	0.993396i	$0.463398\pi$
$198$	−3.82724	−	2.02166i	−0.0193295	−	0.0102104i
$199$	−2.35518	+	4.07929i	−0.0118351	+	0.0204989i	−0.871882	−	0.489716i	$-0.837101\pi$
$199$	−2.35518	+	4.07929i	−0.0118351	+	0.0204989i	0.860047	+	0.510214i	$0.170434\pi$
$200$	24.2879	+	14.0226i	0.121440	+	0.0701132i
$201$	−58.8177	−	56.6454i	−0.292625	−	0.281818i
$202$	−38.6905			−0.191537
$203$	26.0691	−	15.0510i	0.128419	−	0.0741429i
$204$	65.0362	−	67.5303i	0.318805	−	0.331031i
$205$	−144.798			−0.706333
$206$	29.2217	−	16.8712i	0.141853	−	0.0818989i
$207$	100.564	+	159.967i	0.485817	+	0.772790i
$208$	125.359	+	147.393i	0.602688	+	0.708623i
$209$	37.5955	+	21.7058i	0.179883	+	0.103855i
$210$	−2.46379	−	2.37280i	−0.0117324	−	0.0112990i
$211$	158.647	−	274.785i	0.751881	−	1.30230i	−0.195028	−	0.980798i	$-0.562480\pi$
$211$	158.647	−	274.785i	0.751881	−	1.30230i	0.946910	−	0.321499i	$-0.104187\pi$
$212$		−	112.588i		−	0.531074i
$213$	266.478	−	276.698i	1.25107	−	1.29905i
$214$	7.69607	+	13.3300i	0.0359629	+	0.0622896i
$215$	296.469	+	171.167i	1.37893	+	0.796124i
$216$	48.7436	+	43.5304i	0.225665	+	0.201530i
$217$	10.4484	−	18.0971i	0.0481493	−	0.0833970i
$218$		−	28.3266i		−	0.129939i
$219$	−20.1157	+	81.1494i	−0.0918527	+	0.370545i
$220$	−18.5592	−	32.1454i	−0.0843598	−	0.146115i
$221$	−18.7417	−	102.303i	−0.0848040	−	0.462907i
$222$	3.24266	+	11.2508i	0.0146066	+	0.0506791i
$223$	328.042			1.47104			0.735521	−	0.677502i	$-0.236937\pi$
$223$	328.042			1.47104			0.735521	+	0.677502i	$0.236937\pi$
$224$	−7.59254	+	4.38355i	−0.0338953	+	0.0195694i
$225$	−88.2857	+	55.5012i	−0.392381	+	0.246672i
$226$	−46.4625			−0.205586
$227$	−103.945	+	60.0129i	−0.457909	+	0.264374i	−0.711165	−	0.703026i	$-0.751832\pi$
$227$	−103.945	+	60.0129i	−0.457909	+	0.264374i	0.253256	+	0.967399i	$0.418499\pi$
$228$	−233.255	−	224.640i	−1.02305	−	0.985264i
$229$	61.4253	+	106.392i	0.268233	+	0.464593i	0.968406	−	0.249381i	$-0.0802270\pi$
$229$	61.4253	+	106.392i	0.268233	+	0.464593i	−0.700173	+	0.713973i	$0.746894\pi$
$230$		−	38.8769i		−	0.169030i
$231$	0.803657	+	2.78838i	0.00347904	+	0.0120709i
$232$	118.329			0.510039
$233$		−	146.633i		−	0.629324i	−0.949204	−	0.314662i	$-0.898109\pi$
$233$		−	146.633i		−	0.629324i	0.949204	−	0.314662i	$-0.101891\pi$
$234$	34.9643	−	7.77516i	0.149420	−	0.0332272i
$235$	94.8706			0.403705
$236$			168.376i			0.713458i
$237$	−115.845	−	111.567i	−0.488799	−	0.470746i
$238$	1.50809			0.00633653
$239$	−134.259	+	77.5146i	−0.561754	+	0.324329i	−0.753849	−	0.657048i	$-0.771805\pi$
$239$	−134.259	+	77.5146i	−0.561754	+	0.324329i	0.192095	+	0.981376i	$0.438472\pi$
$240$	74.7994	+	259.525i	0.311664	+	1.08135i
$241$	223.189	+	386.575i	0.926097	+	1.60405i	0.789788	+	0.613380i	$0.210191\pi$
$241$	223.189	+	386.575i	0.926097	+	1.60405i	0.136309	+	0.990666i	$0.456476\pi$
$242$			36.2875i			0.149948i
$243$	−227.775	+	84.6602i	−0.937347	+	0.348396i
$244$	−122.178	−	211.618i	−0.500728	−	0.867286i
$245$		−	294.094i		−	1.20038i
$246$	15.8360	+	15.2511i	0.0643739	+	0.0619964i
$247$	−353.361	+	64.7353i	−1.43061	+	0.262086i
$248$	71.1387	−	41.0719i	0.286850	−	0.165613i
$249$	−330.975	+	343.668i	−1.32922	+	1.38019i
$250$	−24.8378			−0.0993510
$251$	267.883	+	154.662i	1.06726	+	0.616185i	0.927432	−	0.373991i	$-0.122011\pi$
$251$	267.883	+	154.662i	1.06726	+	0.616185i	0.139831	+	0.990175i	$0.455344\pi$
$252$	−0.814263	−	21.6319i	−0.00323120	−	0.0858409i
$253$	−16.4907	+	28.5628i	−0.0651808	+	0.112897i
$254$	8.56528	−	4.94517i	0.0337216	−	0.0194692i
$255$	34.9299	−	140.911i	0.136980	−	0.552594i
$256$	198.103			0.773840
$257$	12.7353	+	7.35271i	0.0495535	+	0.0286098i	0.524572	−	0.851366i	$-0.324225\pi$
$257$	12.7353	+	7.35271i	0.0495535	+	0.0286098i	−0.475019	+	0.879976i	$0.657559\pi$
$258$	−14.3952	−	49.9459i	−0.0557955	−	0.193589i
$259$	3.92496	−	6.79823i	0.0151543	−	0.0262480i
$260$	289.332	+	103.132i	1.11282	+	0.396663i
$261$	−205.506	+	389.046i	−0.787378	+	1.49060i
$262$	0.409651	+	0.709537i	0.00156356	+	0.00270816i
$263$			102.835i			0.391009i	0.980703	+	0.195504i	$0.0626343\pi$
$263$			102.835i			0.391009i	−0.980703	+	0.195504i	$0.937366\pi$
$264$	−2.74459	+	11.0720i	−0.0103962	+	0.0419395i
$265$	−87.1686	−	150.980i	−0.328938	−	0.569738i
$266$		−	5.20908i		−	0.0195830i
$267$	−87.6834	−	304.228i	−0.328402	−	1.13943i
$268$	−53.1639	+	92.0826i	−0.198373	+	0.343592i
$269$	−310.001	−	178.979i	−1.15242	−	0.665351i	−0.202945	−	0.979190i	$-0.565051\pi$
$269$	−310.001	−	178.979i	−1.15242	−	0.665351i	−0.949476	+	0.313839i	$0.898385\pi$
$270$	48.9468	+	10.1956i	0.181284	+	0.0377615i
$271$	129.545	+	224.378i	0.478025	+	0.827964i	0.999683	−	0.0251911i	$-0.00801942\pi$
$271$	129.545	+	224.378i	0.478025	+	0.827964i	−0.521657	+	0.853155i	$0.674686\pi$
$272$	−103.125	−	59.5394i	−0.379137	−	0.218895i
$273$	−20.0154	−	13.2684i	−0.0733163	−	0.0486021i
$274$	2.08495	+	3.61125i	0.00760932	+	0.0131797i
$275$	−15.7638	−	9.10122i	−0.0573228	−	0.0330953i
$276$	170.668	−	177.213i	0.618362	−	0.642076i
$277$	−70.4088	−	121.952i	−0.254184	−	0.440259i	0.710490	−	0.703707i	$-0.248473\pi$
$277$	−70.4088	−	121.952i	−0.254184	−	0.440259i	−0.964673	+	0.263449i	$0.915140\pi$
$278$			17.1260i			0.0616042i
$279$	11.4891	+	305.223i	0.0411797	+	1.09399i
$280$	−4.50736	+	7.80697i	−0.0160977	+	0.0278820i
$281$	−203.585	−	117.540i	−0.724503	−	0.418292i	0.0919046	−	0.995768i	$-0.470705\pi$
$281$	−203.585	−	117.540i	−0.724503	−	0.418292i	−0.816408	+	0.577476i	$0.804038\pi$
$282$	−10.3756	−	9.99240i	−0.0367929	−	0.0354340i
$283$	123.871	−	214.551i	0.437706	−	0.758129i	−0.559806	−	0.828624i	$-0.689124\pi$
$283$	123.871	−	214.551i	0.437706	−	0.758129i	0.997512	+	0.0704944i	$0.0224577\pi$
$284$	−433.186	−	250.100i	−1.52530	−	0.880634i
$285$	−486.719	−	120.651i	−1.70779	−	0.423335i
$286$	4.05056	+	4.76253i	0.0141628	+	0.0166522i
$287$		−	14.7400i		−	0.0513588i
$288$	59.8528	−	113.309i	0.207822	−	0.393432i
$289$	−112.497	−	194.850i	−0.389263	−	0.674223i
$290$	78.3994	−	45.2639i	0.270343	−	0.156082i
$291$	268.859	−	77.4897i	0.923915	−	0.266287i
$292$	108.862			0.372815
$293$		−	497.182i		−	1.69687i	−0.529301	−	0.848434i	$-0.677546\pi$
$293$		−	497.182i		−	1.69687i	0.529301	−	0.848434i	$-0.322454\pi$
$294$	−30.9759	+	32.1638i	−0.105360	+	0.109401i
$295$	130.362	+	225.793i	0.441904	+	0.765400i
$296$	26.7234	−	15.4288i	0.0902817	−	0.0521242i
$297$	−31.6364	−	28.2529i	−0.106520	−	0.0951275i
$298$	30.7066			0.103042
$299$	−49.1819	−	268.462i	−0.164488	−	0.897867i
$300$	97.8036	+	94.1914i	0.326012	+	0.313971i
$301$	−17.4242	+	30.1796i	−0.0578877	+	0.100264i
$302$	18.6273	+	10.7544i	0.0616796	+	0.0356108i
$303$	−368.007	−	91.2236i	−1.21455	−	0.301068i
$304$	−205.654	+	356.203i	−0.676493	+	1.17172i
$305$	−327.681	−	189.187i	−1.07437	−	0.620285i
$306$	−18.6619	+	11.7319i	−0.0609865	+	0.0383394i
$307$	−101.797			−0.331587			−0.165793	−	0.986161i	$-0.553018\pi$
$307$	−101.797			−0.331587			−0.165793	+	0.986161i	$0.553018\pi$
$308$	3.27230	−	1.88926i	0.0106243	−	0.00613397i
$309$	317.723	−	91.5729i	1.02823	−	0.296352i
$310$	31.4222	−	54.4248i	0.101362	−	0.175564i
$311$	221.012	−	127.602i	0.710650	−	0.410294i	−0.100651	−	0.994922i	$-0.532093\pi$
$311$	221.012	−	127.602i	0.710650	−	0.410294i	0.811302	+	0.584628i	$0.198759\pi$
$312$	−42.0595	−	84.5089i	−0.134806	−	0.270862i
$313$	132.574	−	229.625i	0.423559	−	0.733626i	−0.572725	−	0.819747i	$-0.694114\pi$
$313$	132.574	−	229.625i	0.423559	−	0.733626i	0.996285	+	0.0861210i	$0.0274472\pi$
$314$	−23.6465	+	13.6523i	−0.0753074	+	0.0434787i
$315$	−17.8400	−	28.3781i	−0.0566349	−	0.0900891i
$316$	−104.710	+	181.363i	−0.331360	+	0.573933i
$317$	−106.667	−	61.5840i	−0.336488	−	0.194271i	0.322230	−	0.946661i	$-0.395568\pi$
$317$	−106.667	−	61.5840i	−0.336488	−	0.194271i	−0.658718	+	0.752390i	$0.728901\pi$
$318$	−6.36899	+	25.6933i	−0.0200283	+	0.0807965i
$319$	−76.7999			−0.240752
$320$	289.039	−	166.877i	0.903246	−	0.521489i
$321$	41.7725	+	144.935i	0.130132	+	0.451509i
$322$	3.95754			0.0122905
$323$	191.463	−	110.541i	0.592765	−	0.342233i
$324$	178.356	+	261.349i	0.550483	+	0.806633i
$325$	148.164	−	27.1434i	0.455889	−	0.0835182i
$326$	−68.1874	−	39.3680i	−0.209164	−	0.120761i
$327$	66.7878	−	269.430i	0.204244	−	0.823945i
$328$	28.9710	−	50.1792i	0.0883261	−	0.152985i
$329$			9.65752i			0.0293542i
$330$	2.41689	+	8.38569i	0.00732392	+	0.0254112i
$331$	−282.112	−	488.633i	−0.852303	−	1.47623i	−0.879124	−	0.476592i	$-0.841872\pi$
$331$	−282.112	−	488.633i	−0.852303	−	1.47623i	0.0268211	−	0.999640i	$-0.491462\pi$
$332$	538.032	+	310.633i	1.62058	+	0.935641i
$333$	4.31592	+	114.658i	0.0129607	+	0.344318i
$334$	−24.9965	+	43.2952i	−0.0748398	+	0.129626i
$335$			164.644i			0.491475i
$336$	−26.4188	+	7.61433i	−0.0786274	+	0.0226617i
$337$	232.929	+	403.445i	0.691184	+	1.19717i	0.971450	+	0.237244i	$0.0762439\pi$
$337$	232.929	+	403.445i	0.691184	+	1.19717i	−0.280266	+	0.959922i	$0.590423\pi$
$338$	−51.0668	−	8.30506i	−0.151085	−	0.0245712i
$339$	−441.931	−	109.548i	−1.30363	−	0.323151i
$340$	−189.033			−0.555979
$341$	−46.1717	+	26.6572i	−0.135401	+	0.0781737i
$342$	40.5228	+	64.4595i	0.118488	+	0.188478i
$343$	60.1090			0.175245
$344$	−118.634	+	68.4934i	−0.344866	+	0.199109i
$345$	91.6630	−	369.780i	0.265690	−	1.07183i
$346$	41.9975	+	72.7418i	0.121380	+	0.210236i
$347$			390.942i			1.12663i	0.826241	+	0.563317i	$0.190475\pi$
$347$			390.942i			1.12663i	−0.826241	+	0.563317i	$0.809525\pi$
$348$	556.076	+	137.843i	1.59792	+	0.396101i
$349$	568.350			1.62851			0.814256	−	0.580507i	$-0.197145\pi$
$349$	568.350			1.62851			0.814256	+	0.580507i	$0.197145\pi$
$350$			2.18416i			0.00624046i
$351$	350.897	+	8.48422i	0.999708	+	0.0241716i
$352$	22.3677			0.0635447
$353$			612.552i			1.73528i	0.497196	+	0.867638i	$0.334363\pi$
$353$			612.552i			1.73528i	−0.497196	+	0.867638i	$0.665637\pi$
$354$	9.52491	−	38.4246i	0.0269065	−	0.108544i
$355$	−774.540			−2.18180
$356$	−357.026	+	206.129i	−1.00288	+	0.579013i
$357$	14.3443	+	3.55575i	0.0401802	+	0.00996007i
$358$	−40.8540	−	70.7613i	−0.114117	−	0.197657i
$359$			403.717i			1.12456i	0.826947	+	0.562280i	$0.190076\pi$
$359$			403.717i			1.12456i	−0.826947	+	0.562280i	$0.809924\pi$
$360$	−4.95633	−	131.671i	−0.0137676	−	0.365753i
$361$	−201.318	−	348.694i	−0.557669	−	0.965911i
$362$			78.6297i			0.217209i
$363$	−85.5577	+	345.150i	−0.235696	+	0.950827i
$364$	−10.4985	+	29.4531i	−0.0288421	+	0.0809150i
$365$	145.985	−	84.2842i	0.399958	−	0.230916i
$366$	15.9107	+	55.2042i	0.0434720	+	0.150831i
$367$	−560.461			−1.52714			−0.763572	−	0.645723i	$-0.776556\pi$
$367$	−560.461			−1.52714			−0.763572	+	0.645723i	$0.776556\pi$
$368$	−270.621	−	156.243i	−0.735384	−	0.424574i
$369$	114.666	+	182.400i	0.310749	+	0.494308i
$370$	11.8038	−	20.4448i	0.0319022	−	0.0552561i
$371$	15.3693	−	8.87348i	0.0414268	−	0.0239177i
$372$	382.155	−	110.143i	1.02730	−	0.296084i
$373$	182.480			0.489224			0.244612	−	0.969621i	$-0.421339\pi$
$373$	182.480			0.489224			0.244612	+	0.969621i	$0.421339\pi$
$374$	−3.33215	−	1.92382i	−0.00890949	−	0.00514390i
$375$	−236.246	−	58.5619i	−0.629989	−	0.156165i
$376$	−18.9815	+	32.8770i	−0.0504828	+	0.0874388i
$377$	484.121	−	411.748i	1.28414	−	1.09217i
$378$	−1.03788	+	4.98262i	−0.00274571	+	0.0131815i
$379$	−150.775	−	261.150i	−0.397823	−	0.689050i	0.595634	−	0.803256i	$-0.296901\pi$
$379$	−150.775	−	261.150i	−0.397823	−	0.689050i	−0.993457	+	0.114206i	$0.963568\pi$
$380$			652.934i			1.71825i
$381$	93.1287	−	26.8412i	0.244432	−	0.0704494i
$382$	14.7479	+	25.5442i	0.0386072	+	0.0668696i
$383$			196.029i			0.511825i	0.966700	+	0.255913i	$0.0823759\pi$
$383$			196.029i			0.511825i	−0.966700	+	0.255913i	$0.917624\pi$
$384$	−215.028	−	53.3024i	−0.559970	−	0.138808i
$385$	2.92544	−	5.06702i	0.00759855	−	0.0131611i
$386$	−40.4665	−	23.3633i	−0.104835	−	0.0605268i
$387$	−19.1598	−	509.004i	−0.0495085	−	1.31526i
$388$	−182.165	−	315.519i	−0.469498	−	0.813194i
$389$	−343.282	−	198.194i	−0.882474	−	0.509496i	−0.0110004	−	0.999939i	$-0.503502\pi$
$389$	−343.282	−	198.194i	−0.882474	−	0.509496i	−0.871473	+	0.490443i	$0.836835\pi$
$390$	−60.1935	−	39.9028i	−0.154342	−	0.102315i
$391$	83.9826	+	145.462i	0.214789	+	0.372026i
$392$	101.917	+	58.8417i	0.259992	+	0.150106i
$393$	2.22349	+	7.71467i	0.00565775	+	0.0196302i
$394$	−23.9630	−	41.5052i	−0.0608198	−	0.105343i
$395$			324.278i			0.820957i
$396$	−25.7959	+	48.8347i	−0.0651411	+	0.123320i
$397$	−363.884	+	630.265i	−0.916583	+	1.58757i	−0.112017	+	0.993706i	$0.535731\pi$
$397$	−363.884	+	630.265i	−0.916583	+	1.58757i	−0.804566	+	0.593863i	$0.797602\pi$
$398$	−1.24883	−	0.721015i	−0.00313777	−	0.00181160i
$399$	12.2818	−	49.5464i	0.0307815	−	0.124176i
$400$	86.2304	−	149.355i	0.215576	−	0.373389i
$401$	563.043	+	325.073i	1.40410	+	0.810656i	0.994810	−	0.101750i	$-0.0324440\pi$
$401$	563.043	+	325.073i	1.40410	+	0.810656i	0.409287	+	0.912406i	$0.365777\pi$
$402$	17.3414	−	18.0065i	0.0431379	−	0.0447922i
$403$	148.133	−	415.579i	0.367576	−	1.03121i
$404$			493.682i			1.22199i
$405$	441.521	+	212.382i	1.09018	+	0.524399i
$406$	4.60772	+	7.98080i	0.0113491	+	0.0196571i
$407$	−17.3445	+	10.0138i	−0.0426154	+	0.0246040i
$408$	41.8435	+	40.2981i	0.102558	+	0.0987698i
$409$	430.699			1.05305			0.526527	−	0.850159i	$-0.323494\pi$
$409$	430.699			1.05305			0.526527	+	0.850159i	$0.323494\pi$
$410$		−	44.3286i		−	0.108118i
$411$	11.3166	+	39.2644i	0.0275344	+	0.0955339i
$412$	−215.272	−	372.863i	−0.522506	−	0.905006i
$413$	−22.9850	+	13.2704i	−0.0556538	+	0.0321317i
$414$	−48.9725	+	30.7868i	−0.118291	+	0.0743641i
$415$	962.005			2.31808
$416$	−140.999	+	119.920i	−0.338939	+	0.288270i
$417$	−40.3792	+	162.895i	−0.0968326	+	0.390635i
$418$	−6.64502	+	11.5095i	−0.0158972	+	0.0275347i
$419$	177.836	+	102.674i	0.424430	+	0.245045i	0.696971	−	0.717100i	$-0.254531\pi$
$419$	177.836	+	102.674i	0.424430	+	0.245045i	−0.272541	+	0.962144i	$0.587864\pi$
$420$	−30.2763	+	31.4374i	−0.0720865	+	0.0748510i
$421$	28.6735	−	49.6640i	0.0681082	−	0.117967i	−0.829960	−	0.557822i	$-0.811637\pi$
$421$	28.6735	−	49.6640i	0.0681082	−	0.117967i	0.898069	+	0.439856i	$0.144970\pi$
$422$	84.1226	+	48.5682i	0.199343	+	0.115091i
$423$	−75.1283	−	119.507i	−0.177608	−	0.282522i
$424$	69.7622			0.164533
$425$	−80.2803	+	46.3499i	−0.188895	+	0.109058i
$426$	84.7083	+	81.5797i	0.198846	+	0.191502i
$427$	19.2586	−	33.3569i	0.0451021	−	0.0781192i
$428$	170.087	−	98.2001i	0.397401	−	0.229439i
$429$	27.2982	+	54.8494i	0.0636322	+	0.127854i
$430$	−52.4010	+	90.7612i	−0.121863	+	0.211072i
$431$	−596.019	+	344.111i	−1.38287	+	0.798402i	−0.992499	−	0.122254i	$-0.960988\pi$
$431$	−596.019	+	344.111i	−1.38287	+	0.798402i	−0.390375	+	0.920656i	$0.627655\pi$
$432$	267.685	−	299.742i	0.619641	−	0.693848i
$433$	67.6852	−	117.234i	0.156317	−	0.270749i	−0.777221	−	0.629228i	$-0.783371\pi$
$433$	67.6852	−	117.234i	0.156317	−	0.270749i	0.933538	+	0.358479i	$0.116705\pi$
$434$	5.54027	+	3.19867i	0.0127656	+	0.00737022i
$435$	852.422	−	245.682i	1.95959	−	0.564786i
$436$	−361.441			−0.828993
$437$	502.438	−	290.083i	1.14974	−	0.663805i
$438$	−24.8431	−	6.15824i	−0.0567194	−	0.0140599i
$439$	−430.958			−0.981680			−0.490840	−	0.871250i	$-0.663310\pi$
$439$	−430.958			−0.981680			−0.490840	+	0.871250i	$0.663310\pi$
$440$	19.9181	−	11.4997i	0.0452684	−	0.0261357i
$441$	−370.464	+	232.894i	−0.840054	+	0.528104i
$442$	31.3189	−	5.73758i	0.0708573	−	0.0129810i
$443$	−600.974	−	346.972i	−1.35660	−	0.783233i	−0.367436	−	0.930049i	$-0.619764\pi$
$443$	−600.974	−	346.972i	−1.35660	−	0.783233i	−0.989164	+	0.146815i	$0.953098\pi$
$444$	143.557	−	41.3755i	0.323327	−	0.0931881i
$445$	−319.182	+	552.839i	−0.717263	+	1.24234i
$446$			100.427i			0.225173i
$447$	292.068	+	72.3993i	0.653396	+	0.161967i
$448$	16.9875	+	29.4232i	0.0379185	+	0.0656768i
$449$	258.289	+	149.123i	0.575253	+	0.332122i	0.759245	−	0.650805i	$-0.225569\pi$
$449$	258.289	+	149.123i	0.575253	+	0.332122i	−0.183992	+	0.982928i	$0.558902\pi$
$450$	−16.9912	−	27.0278i	−0.0377581	−	0.0600618i
$451$	−18.8032	+	32.5682i	−0.0416923	+	0.0722132i
$452$			592.851i			1.31162i
$453$	151.818	+	146.210i	0.335138	+	0.322760i
$454$	−18.3724	−	31.8218i	−0.0404677	−	0.0700922i
$455$	8.72483	+	47.6250i	0.0191755	+	0.104670i
$456$	139.193	−	144.531i	0.305247	−	0.316953i
$457$	−287.081			−0.628186			−0.314093	−	0.949392i	$-0.601700\pi$
$457$	−287.081			−0.628186			−0.314093	+	0.949392i	$0.601700\pi$
$458$	−32.5708	+	18.8048i	−0.0711153	+	0.0410584i
$459$	−205.164	+	67.5877i	−0.446981	+	0.147250i
$460$	−496.060			−1.07839
$461$	247.094	−	142.660i	0.535995	−	0.309457i	−0.207459	−	0.978244i	$-0.566519\pi$
$461$	247.094	−	142.660i	0.535995	−	0.309457i	0.743454	+	0.668787i	$0.233186\pi$
$462$	−0.853636	+	0.246032i	−0.00184770	+	0.000532536i
$463$	79.9846	+	138.537i	0.172753	+	0.299217i	0.939381	−	0.342874i	$-0.111400\pi$
$463$	79.9846	+	138.537i	0.172753	+	0.299217i	−0.766628	+	0.642091i	$0.778067\pi$
$464$		−	727.649i		−	1.56821i
$465$	427.195	−	443.578i	0.918699	−	0.953931i
$466$	44.8901			0.0963307
$467$			28.8347i			0.0617446i	0.999523	+	0.0308723i	$0.00982851\pi$
$467$			28.8347i			0.0617446i	−0.999523	+	0.0308723i	$0.990171\pi$
$468$	−99.2092	−	446.137i	−0.211985	−	0.953284i
$469$	−16.7602			−0.0357361
$470$			29.0437i			0.0617951i
$471$	−257.104	+	74.1017i	−0.545869	+	0.157328i
$472$	−104.330			−0.221038
$473$	76.9979	−	44.4548i	0.162786	−	0.0939847i
$474$	34.1551	−	35.4650i	0.0720572	−	0.0748206i
$475$	160.096	+	277.295i	0.337044	+	0.583778i
$476$		−	19.2429i		−	0.0404263i
$477$	−121.158	+	229.367i	−0.254000	+	0.480853i
$478$	−23.7303	−	41.1021i	−0.0496450	−	0.0859877i
$479$		−	746.658i		−	1.55878i	−0.626536	−	0.779392i	$-0.715528\pi$
$479$		−	746.658i		−	1.55878i	0.626536	−	0.779392i	$-0.284472\pi$
$480$	−248.265	+	71.5541i	−0.517219	+	0.149071i
$481$	55.6465	−	156.113i	0.115689	−	0.324559i
$482$	−118.346	+	68.3272i	−0.245532	+	0.141758i
$483$	37.6424	+	9.33099i	0.0779345	+	0.0193188i
$484$	463.019			0.956652
$485$	−488.568	−	282.075i	−1.00736	−	0.581598i
$486$	−25.9179	−	69.7312i	−0.0533290	−	0.143480i
$487$	201.902	−	349.705i	0.414584	−	0.718081i	−0.580801	−	0.814046i	$-0.697260\pi$
$487$	201.902	−	349.705i	0.414584	−	0.718081i	0.995385	+	0.0959652i	$0.0305937\pi$
$488$	131.124	−	75.7043i	0.268696	−	0.155132i
$489$	−555.748	−	535.222i	−1.13650	−	1.09452i
$490$	90.0339			0.183743
$491$	−364.055	−	210.187i	−0.741456	−	0.428080i	0.0811426	−	0.996703i	$-0.474143\pi$
$491$	−364.055	−	210.187i	−0.741456	−	0.428080i	−0.822598	+	0.568623i	$0.807476\pi$
$492$	194.601	−	202.064i	0.395530	−	0.410698i
$493$	−195.560	+	338.720i	−0.396673	+	0.687058i
$494$	−19.8181	−	108.178i	−0.0401176	−	0.218984i
$495$	3.21684	+	85.4594i	0.00649867	+	0.172645i
$496$	−252.567	−	437.458i	−0.509207	−	0.881972i
$497$		−	78.8456i		−	0.158643i
$498$	−105.211	−	101.325i	−0.211266	−	0.203463i
$499$	−186.101	−	322.337i	−0.372948	−	0.645965i	0.617069	−	0.786909i	$-0.288320\pi$
$499$	−186.101	−	322.337i	−0.372948	−	0.645965i	−0.990018	+	0.140944i	$0.954986\pi$
$500$			316.924i			0.633848i
$501$	−339.836	+	352.869i	−0.678315	+	0.704328i
$502$	−47.3484	+	82.0098i	−0.0943195	+	0.163366i
$503$	143.625	+	82.9219i	0.285537	+	0.164855i	0.635927	−	0.771749i	$-0.280618\pi$
$503$	143.625	+	82.9219i	0.285537	+	0.164855i	−0.350391	+	0.936604i	$0.613951\pi$
$504$	13.4037	−	0.504538i	0.0265946	−	0.00100107i
$505$	382.223	+	662.030i	0.756878	+	1.31095i
$506$	−8.74423	−	5.04848i	−0.0172811	−	0.00997724i
$507$	−466.143	−	199.398i	−0.919414	−	0.393290i
$508$	−63.0992	−	109.291i	−0.124211	−	0.215140i
$509$	−253.659	−	146.450i	−0.498347	−	0.287721i	0.229683	−	0.973265i	$-0.426231\pi$
$509$	−253.659	−	146.450i	−0.498347	−	0.287721i	−0.728031	+	0.685544i	$0.759564\pi$
$510$	43.1386	+	10.6934i	0.0845856	+	0.0209675i
$511$	8.57986	+	14.8607i	0.0167903	+	0.0290817i
$512$			356.029i			0.695370i
$513$	233.453	+	708.654i	0.455075	+	1.38139i
$514$	−2.25096	+	3.89878i	−0.00437930	+	0.00758517i
$515$	−577.362	−	333.340i	−1.12109	−	0.647263i
$516$	−637.298	+	183.680i	−1.23507	+	0.355968i
$517$	12.3197	−	21.3384i	0.0238292	−	0.0412735i
$518$	2.08121	+	1.20159i	0.00401778	+	0.00231967i
$519$	227.953	+	790.908i	0.439215	+	1.52391i
$520$	−63.9035	+	179.278i	−0.122891	+	0.344764i
$521$		−	811.721i		−	1.55801i	−0.627020	−	0.779003i	$-0.715725\pi$
$521$		−	811.721i		−	1.55801i	0.627020	−	0.779003i	$-0.284275\pi$
$522$	−119.103	−	62.9135i	−0.228166	−	0.120524i
$523$	−267.247	−	462.886i	−0.510989	−	0.885059i	−0.999919	−	0.0127359i	$-0.995946\pi$
$523$	−267.247	−	462.886i	−0.510989	−	0.885059i	0.488930	−	0.872323i	$-0.337387\pi$
$524$	9.05353	−	5.22706i	0.0172777	−	0.00997530i
$525$	−5.14976	+	20.7748i	−0.00980906	+	0.0395710i
$526$	−31.4820			−0.0598517
$527$			271.515i			0.515209i
$528$	68.0859	+	16.8775i	0.128951	+	0.0319650i
$529$	−44.1127	−	76.4055i	−0.0833889	−	0.144434i
$530$	46.2212	−	26.6858i	0.0872098	−	0.0503506i
$531$	181.193	−	343.021i	0.341230	−	0.645990i
$532$	−66.4666			−0.124937
$533$	−56.0787	−	306.109i	−0.105213	−	0.574313i
$534$	93.1363	−	26.8434i	0.174413	−	0.0502686i
$535$	152.059	−	263.373i	0.284222	−	0.492287i
$536$	−57.0567	−	32.9417i	−0.106449	−	0.0614584i
$537$	−221.746	−	769.374i	−0.412935	−	1.43273i
$538$	54.7928	−	94.9039i	0.101845	−	0.176401i
$539$	−66.1478	−	38.1905i	−0.122723	−	0.0708543i
$540$	130.094	−	624.549i	0.240914	−	1.15657i
$541$	177.353			0.327825			0.163913	−	0.986475i	$-0.447589\pi$
$541$	177.353			0.327825			0.163913	+	0.986475i	$0.447589\pi$
$542$	−68.6912	+	39.6589i	−0.126737	+	0.0731714i
$543$	−185.391	+	747.891i	−0.341420	+	1.37733i
$544$	56.9562	−	98.6510i	0.104699	−	0.181344i
$545$	−484.694	+	279.838i	−0.889346	+	0.513464i
$546$	4.06198	−	6.12751i	0.00743952	−	0.0112225i
$547$	43.1845	−	74.7978i	0.0789480	−	0.136742i	−0.823848	−	0.566810i	$-0.808177\pi$
$547$	43.1845	−	74.7978i	0.0789480	−	0.136742i	0.902796	+	0.430068i	$0.141511\pi$
$548$	46.0786	−	26.6035i	0.0840851	−	0.0485466i
$549$	21.1769	+	562.592i	0.0385736	+	1.02476i
$550$	2.78625	−	4.82592i	0.00506591	−	0.00877441i
$551$	1169.96	+	675.479i	2.12335	+	1.22592i
$552$	109.806	+	105.750i	0.198924	+	0.191577i
$553$	−33.0104			−0.0596934
$554$	37.3343	−	21.5550i	0.0673905	−	0.0389079i
$555$	160.477	−	166.631i	0.289147	−	0.300236i
$556$	218.523			0.393028
$557$	670.505	−	387.116i	1.20378	−	0.695002i	0.242386	−	0.970180i	$-0.422070\pi$
$557$	670.505	−	387.116i	1.20378	−	0.695002i	0.961393	+	0.275178i	$0.0887367\pi$
$558$	−93.4412	+	3.51729i	−0.167457	+	0.00630338i
$559$	−247.033	+	693.037i	−0.441920	+	1.23978i
$560$	48.0080	+	27.7174i	0.0857285	+	0.0494954i
$561$	−27.1580	−	26.1550i	−0.0484100	−	0.0466220i
$562$	35.9838	−	62.3257i	0.0640280	−	0.110900i
$563$			425.709i			0.756143i	0.925776	+	0.378072i	$0.123413\pi$
$563$			425.709i			0.756143i	−0.925776	+	0.378072i	$0.876587\pi$
$564$	−127.501	+	132.390i	−0.226065	+	0.234735i
$565$	459.003	+	795.016i	0.812394	+	1.40711i
$566$	65.6826	+	37.9219i	0.116047	+	0.0669997i
$567$	−21.6198	+	44.9454i	−0.0381301	+	0.0792688i
$568$	154.968	−	268.413i	0.272832	−	0.472559i
$569$			858.981i			1.50963i	0.655936	+	0.754816i	$0.272274\pi$
$569$			858.981i			1.50963i	−0.655936	+	0.754816i	$0.727726\pi$
$570$	36.9360	−	149.004i	0.0648000	−	0.261411i
$571$	97.9094	+	169.584i	0.171470	+	0.296995i	0.938934	−	0.344097i	$-0.111815\pi$
$571$	97.9094	+	169.584i	0.171470	+	0.296995i	−0.767464	+	0.641092i	$0.778482\pi$
$572$	60.7688	−	51.6843i	0.106239	−	0.0903571i
$573$	80.0484	+	277.737i	0.139701	+	0.484707i
$574$	4.51250			0.00786151
$575$	−210.672	+	121.631i	−0.366385	+	0.211533i
$576$	−439.102	−	231.946i	−0.762330	−	0.402685i
$577$	150.939			0.261593			0.130796	−	0.991409i	$-0.458247\pi$
$577$	150.939			0.261593			0.130796	+	0.991409i	$0.458247\pi$
$578$	59.6515	−	34.4398i	0.103203	−	0.0595845i
$579$	−329.814	−	317.633i	−0.569626	−	0.548588i
$580$	−577.557	−	1000.36i	−0.995787	−	1.72475i
$581$			97.9289i			0.168552i
$582$	23.7227	+	82.3087i	0.0407607	+	0.141424i
$583$	−45.2782			−0.0776642
$584$			67.4537i			0.115503i
$585$	−478.452	−	521.461i	−0.817867	−	0.891386i
$586$	152.208			0.259740
$587$		−	936.372i		−	1.59518i	−0.603198	−	0.797591i	$-0.706107\pi$
$587$		−	936.372i		−	1.59518i	0.603198	−	0.797591i	$-0.293893\pi$
$588$	410.403	+	395.245i	0.697964	+	0.672186i
$589$	937.834			1.59225
$590$	−69.1244	+	39.9090i	−0.117160	+	0.0676423i
$591$	−130.066	−	451.278i	−0.220077	−	0.763584i
$592$	−94.8772	−	164.332i	−0.160265	−	0.277588i
$593$			86.5327i			0.145924i	0.997335	+	0.0729618i	$0.0232451\pi$
$593$			86.5327i			0.145924i	−0.997335	+	0.0729618i	$0.976755\pi$
$594$	8.64934	−	9.68517i	0.0145612	−	0.0163050i
$595$	−14.8984	−	25.8048i	−0.0250394	−	0.0433695i
$596$		−	391.809i		−	0.657398i
$597$	−10.1784	−	9.80244i	−0.0170492	−	0.0164195i
$598$	82.1871	−	15.0566i	0.137437	−	0.0251782i
$599$	351.701	−	203.055i	0.587147	−	0.338989i	−0.176822	−	0.984243i	$-0.556582\pi$
$599$	351.701	−	203.055i	0.587147	−	0.338989i	0.763969	+	0.645253i	$0.223248\pi$
$600$	−58.3634	+	60.6016i	−0.0972723	+	0.101003i
$601$	−124.589			−0.207303			−0.103651	−	0.994614i	$-0.533053\pi$
$601$	−124.589			−0.207303			−0.103651	+	0.994614i	$0.533053\pi$
$602$	−9.23919	−	5.33425i	−0.0153475	−	0.00886088i
$603$	207.399	−	130.382i	0.343946	−	0.216223i
$604$	137.224	−	237.679i	0.227192	−	0.393509i
$605$	620.911	−	358.483i	1.02630	−	0.592534i
$606$	27.9272	−	112.662i	0.0460845	−	0.185911i
$607$	−1061.72			−1.74912			−0.874560	−	0.484917i	$-0.838850\pi$
$607$	−1061.72			−1.74912			−0.874560	+	0.484917i	$0.838850\pi$
$608$	−340.748	−	196.731i	−0.560441	−	0.323571i
$609$	25.0096	+	86.7738i	0.0410667	+	0.142486i
$610$	57.9177	−	100.316i	0.0949471	−	0.164453i
$611$	36.7423	+	200.560i	0.0601347	+	0.328248i
$612$	149.696	+	238.121i	0.244601	+	0.389087i
$613$	148.204	+	256.696i	0.241768	+	0.418754i	0.961218	−	0.275790i	$-0.0889394\pi$
$613$	148.204	+	256.696i	0.241768	+	0.418754i	−0.719450	+	0.694544i	$0.755606\pi$
$614$		−	31.1642i		−	0.0507560i
$615$	104.517	−	421.634i	0.169946	−	0.685583i
$616$	1.17063	+	2.02760i	0.00190038	+	0.00329156i
$617$			412.450i			0.668477i	0.942489	+	0.334238i	$0.108479\pi$
$617$			412.450i			0.668477i	−0.942489	+	0.334238i	$0.891521\pi$
$618$	28.0341	+	97.2677i	0.0453627	+	0.157391i
$619$	184.087	−	318.849i	0.297395	−	0.515103i	−0.678144	−	0.734929i	$-0.737216\pi$
$619$	184.087	−	318.849i	0.297395	−	0.515103i	0.975539	+	0.219826i	$0.0705490\pi$
$620$	−694.447	−	400.939i	−1.12008	−	0.646676i
$621$	−538.393	+	177.364i	−0.866977	+	0.285610i
$622$	39.0640	+	67.6608i	0.0628038	+	0.108779i
$623$	−56.2772	−	32.4917i	−0.0903327	−	0.0521536i
$624$	−519.676	+	258.640i	−0.832815	+	0.414487i
$625$	390.208	+	675.860i	0.624333	+	1.08138i
$626$	70.2975	+	40.5863i	0.112296	+	0.0648343i
$627$	−90.3413	+	93.8059i	−0.144085	+	0.149611i
$628$	174.200	+	301.724i	0.277389	+	0.480452i
$629$			101.995i			0.162154i
$630$	8.68767	−	5.46154i	0.0137900	−	0.00866911i
$631$	−148.481	+	257.176i	−0.235310	+	0.407569i	−0.959363	−	0.282176i	$-0.908944\pi$
$631$	−148.481	+	257.176i	−0.235310	+	0.407569i	0.724053	+	0.689745i	$0.242277\pi$
$632$	−112.377	−	64.8809i	−0.177812	−	0.102660i
$633$	685.624	+	660.302i	1.08313	+	1.04313i
$634$	18.8534	−	32.6550i	0.0297371	−	0.0515063i
$635$	−169.233	−	97.7065i	−0.266508	−	0.153868i
$636$	327.841	+	81.2669i	0.515473	+	0.127778i
$637$	621.724	−	113.899i	0.976019	−	0.178805i
$638$		−	23.5115i		−	0.0368520i
$639$	613.361	+	975.673i	0.959876	+	1.52687i
$640$	223.335	+	386.827i	0.348961	+	0.604418i
$641$	440.939	−	254.577i	0.687893	−	0.397155i	−0.114929	−	0.993374i	$-0.536664\pi$
$641$	440.939	−	254.577i	0.687893	−	0.397155i	0.802822	+	0.596218i	$0.203331\pi$
$642$	−44.3703	+	12.7882i	−0.0691126	+	0.0199194i
$643$	615.541			0.957295			0.478648	−	0.878007i	$-0.341127\pi$
$643$	615.541			0.957295			0.478648	+	0.878007i	$0.341127\pi$
$644$		−	50.4973i		−	0.0784120i
$645$	−712.409	+	739.730i	−1.10451	+	1.14687i
$646$	33.8411	+	58.6146i	0.0523857	+	0.0907346i
$647$	145.240	−	83.8541i	0.224481	−	0.129604i	−0.383542	−	0.923523i	$-0.625296\pi$
$647$	145.240	−	83.8541i	0.224481	−	0.129604i	0.608024	+	0.793919i	$0.291963\pi$
$648$	−161.939	+	110.514i	−0.249905	+	0.170547i
$649$	67.7142			0.104336
$650$	8.30970	+	45.3589i	0.0127841	+	0.0697830i
$651$	45.1548	+	43.4871i	0.0693622	+	0.0668004i
$652$	−502.327	+	870.056i	−0.770440	+	1.33444i
$653$	−980.552	−	566.122i	−1.50161	−	0.866956i	−0.999998	−	0.00186411i	$-0.999407\pi$
$653$	−980.552	−	566.122i	−1.50161	−	0.866956i	−0.501613	−	0.865092i	$-0.667260\pi$
$654$	82.4834	+	20.4464i	0.126121	+	0.0312636i
$655$	8.09388	−	14.0190i	0.0123571	−	0.0214031i
$656$	−308.570	−	178.153i	−0.470382	−	0.271575i
$657$	−221.777	−	117.149i	−0.337560	−	0.178309i
$658$	−2.95655			−0.00449324
$659$	241.022	−	139.154i	0.365739	−	0.211160i	−0.305856	−	0.952078i	$-0.598943\pi$
$659$	241.022	−	139.154i	0.365739	−	0.211160i	0.671595	+	0.740918i	$0.265609\pi$
$660$	106.999	−	30.8390i	0.162120	−	0.0467257i
$661$	277.015	−	479.804i	0.419084	−	0.725876i	−0.576763	−	0.816911i	$-0.695684\pi$
$661$	277.015	−	479.804i	0.419084	−	0.725876i	0.995848	+	0.0910359i	$0.0290178\pi$
$662$	149.590	−	86.3660i	0.225967	−	0.130462i
$663$	311.420	+	19.2696i	0.469713	+	0.0290643i
$664$	−192.476	+	333.378i	−0.289874	+	0.502076i
$665$	−89.1320	+	51.4604i	−0.134033	+	0.0773840i
$666$	−35.1014	+	1.32128i	−0.0527047	+	0.00198390i
$667$	−513.188	+	888.868i	−0.769398	+	1.33264i
$668$	552.436	+	318.949i	0.827001	+	0.477469i
$669$	−236.784	+	955.217i	−0.353938	+	1.42783i
$670$	−50.4042			−0.0752302
$671$	−85.1042	+	49.1349i	−0.126832	+	0.0732264i
$672$	−7.28397	−	25.2726i	−0.0108392	−	0.0376080i
$673$	599.236			0.890395			0.445198	−	0.895432i	$-0.353133\pi$
$673$	599.236			0.890395			0.445198	+	0.895432i	$0.353133\pi$
$674$	−123.511	+	71.3090i	−0.183250	+	0.105800i
$675$	−97.8868	−	297.138i	−0.145017	−	0.440204i
$676$	−105.971	+	651.600i	−0.156761	+	0.963906i
$677$	703.476	+	406.152i	1.03911	+	0.599929i	0.919581	−	0.392901i	$-0.128529\pi$
$677$	703.476	+	406.152i	1.03911	+	0.599929i	0.119528	+	0.992831i	$0.461862\pi$
$678$	33.5371	−	135.293i	0.0494648	−	0.199547i
$679$	28.7143	−	49.7347i	0.0422891	−	0.0732469i
$680$		−	117.130i		−	0.172249i
$681$	−99.7209	−	345.993i	−0.146433	−	0.508066i
$682$	−8.16085	−	14.1350i	−0.0119661	−	0.0207258i
$683$	−142.444	−	82.2401i	−0.208556	−	0.120410i	0.392084	−	0.919929i	$-0.371754\pi$
$683$	−142.444	−	82.2401i	−0.208556	−	0.120410i	−0.600640	+	0.799519i	$0.705088\pi$
$684$	822.489	−	517.061i	1.20247	−	0.755937i
$685$	41.1944	−	71.3509i	0.0601379	−	0.104162i
$686$			18.4018i			0.0268248i
$687$	−354.136	+	102.068i	−0.515482	+	0.148570i
$688$	421.191	+	729.525i	0.612197	+	1.06036i
$689$	285.419	−	242.751i	0.414251	−	0.352323i
$690$	113.204	+	28.0617i	0.164064	+	0.0406692i
$691$	−422.774			−0.611830			−0.305915	−	0.952059i	$-0.598962\pi$
$691$	−422.774			−0.611830			−0.305915	+	0.952059i	$0.598962\pi$
$692$	928.168	−	535.878i	1.34128	−	0.774390i
$693$	−8.69949	+	0.327464i	−0.0125534	+	0.000472531i
$694$	−119.683			−0.172454
$695$	293.041	−	169.187i	0.421642	−	0.243435i
$696$	−85.4111	+	344.559i	−0.122717	+	0.495056i
$697$	95.7594	+	165.860i	0.137388	+	0.237963i
$698$			173.995i			0.249276i
$699$	426.975	+	105.841i	0.610837	+	0.151417i
$700$	27.8694			0.0398134
$701$		−	524.630i		−	0.748402i	−0.927348	−	0.374201i	$-0.877917\pi$
$701$		−	524.630i		−	0.748402i	0.927348	−	0.374201i	$-0.122083\pi$
$702$	−2.59736	+	107.424i	−0.00369995	+	0.153025i
$703$	352.299			0.501137
$704$		−	86.6811i		−	0.123127i
$705$	−68.4785	+	276.251i	−0.0971327	+	0.391845i
$706$	−187.527			−0.265619
$707$	−67.3925	+	38.9091i	−0.0953218	+	0.0550341i
$708$	−490.289	−	121.536i	−0.692499	−	0.171660i
$709$	−13.9544	−	24.1697i	−0.0196818	−	0.0340899i	0.856017	−	0.516948i	$-0.172932\pi$
$709$	−13.9544	−	24.1697i	−0.0196818	−	0.0340899i	−0.875699	+	0.482858i	$0.839599\pi$
$710$		−	237.118i		−	0.333969i
$711$	408.487	−	256.797i	0.574524	−	0.361177i
$712$	−127.723	−	221.222i	−0.179386	−	0.310705i
$713$			712.510i			0.999313i
$714$	−1.08856	+	4.39137i	−0.00152459	+	0.00615038i
$715$	41.4757	−	116.358i	0.0580080	−	0.162738i
$716$	−902.897	+	521.288i	−1.26103	+	0.728056i
$717$	−128.803	−	446.896i	−0.179641	−	0.623286i
$718$	−123.594			−0.172137
$719$	−772.065	−	445.752i	−1.07380	−	0.619961i	−0.144586	−	0.989492i	$-0.546185\pi$
$719$	−772.065	−	445.752i	−1.07380	−	0.619961i	−0.929218	+	0.369531i	$0.879518\pi$
$720$	−809.694	+	30.4783i	−1.12458	+	0.0423310i
$721$	33.9330	−	58.7736i	0.0470637	−	0.0815168i
$722$	106.749	−	61.6317i	0.147852	−	0.0853624i
$723$	−1286.76	+	370.865i	−1.77975	+	0.512952i
$724$	1003.30			1.38577
$725$	−490.565	−	283.228i	−0.676641	−	0.390659i
$726$	−105.664	−	26.1926i	−0.145543	−	0.0360780i
$727$	363.448	−	629.511i	0.499929	−	0.865903i	−0.500071	−	0.865984i	$-0.666693\pi$
$727$	363.448	−	629.511i	0.499929	−	0.865903i	1.00000		8.19289e-5i	$2.60788e-5\pi$
$728$	−18.2499	−	6.50517i	−0.0250685	−	0.00893567i
$729$	−82.1090	−	724.361i	−0.112632	−	0.993637i
$730$	25.8028	+	44.6917i	0.0353463	+	0.0612216i
$731$		−	452.790i		−	0.619412i
$732$	704.392	−	203.017i	0.962285	−	0.277346i
$733$	57.5796	+	99.7308i	0.0785534	+	0.136058i	0.902626	−	0.430426i	$-0.141637\pi$
$733$	57.5796	+	99.7308i	0.0785534	+	0.136058i	−0.824073	+	0.566484i	$0.808303\pi$
$734$		−	171.580i		−	0.233760i
$735$	856.362	+	212.280i	1.16512	+	0.288816i
$736$	149.464	−	258.880i	0.203077	−	0.351739i
$737$	37.0319	+	21.3804i	0.0502469	+	0.0290100i
$738$	−55.8398	+	35.1040i	−0.0756637	+	0.0475663i
$739$	−273.890	−	474.391i	−0.370622	−	0.641936i	0.619039	−	0.785360i	$-0.287522\pi$
$739$	−273.890	−	474.391i	−0.370622	−	0.641936i	−0.989661	+	0.143424i	$0.954189\pi$
$740$	−260.871	−	150.614i	−0.352528	−	0.203532i
$741$	66.5588	−	1075.67i	0.0898229	−	1.45164i
$742$	2.71653	+	4.70517i	0.00366109	+	0.00634120i
$743$	71.8996	+	41.5113i	0.0967694	+	0.0558698i	0.547604	−	0.836738i	$-0.315540\pi$
$743$	71.8996	+	41.5113i	0.0967694	+	0.0558698i	−0.450834	+	0.892608i	$0.648873\pi$
$744$	68.2476	+	236.793i	0.0917306	+	0.318270i
$745$	−303.350	−	525.418i	−0.407182	−	0.705259i
$746$			55.8646i			0.0748855i
$747$	−761.815	−	1211.82i	−1.01983	−	1.62225i
$748$	−24.5475	+	42.5174i	−0.0328175	+	0.0568415i
$749$	26.8106	+	15.4791i	0.0357951	+	0.0206663i
$750$	17.9281	−	72.3243i	0.0239042	−	0.0964325i
$751$	213.802	−	370.317i	0.284690	−	0.493098i	−0.687844	−	0.725859i	$-0.741443\pi$
$751$	213.802	−	370.317i	0.284690	−	0.493098i	0.972534	+	0.232761i	$0.0747759\pi$
$752$	202.173	+	116.724i	0.268847	+	0.155219i
$753$	−643.717	+	668.404i	−0.854870	+	0.887655i
$754$	126.053	+	148.209i	0.167179	+	0.196563i
$755$		−	424.972i		−	0.562877i
$756$	63.5771	+	13.2431i	0.0840967	+	0.0175173i
$757$	−59.7285	−	103.453i	−0.0789016	−	0.136662i	0.823875	−	0.566772i	$-0.191808\pi$
$757$	−59.7285	−	103.453i	−0.0789016	−	0.136662i	−0.902776	+	0.430110i	$0.858475\pi$
$758$	79.9485	−	46.1583i	0.105473	−	0.0608949i
$759$	−71.2680	−	68.6359i	−0.0938973	−	0.0904293i
$760$	−404.575			−0.532335
$761$			392.322i			0.515535i	0.966207	+	0.257767i	$0.0829868\pi$
$761$			392.322i			0.515535i	−0.966207	+	0.257767i	$0.917013\pi$
$762$	8.21718	+	28.5105i	0.0107837	+	0.0374153i
$763$	−28.4866	−	49.3402i	−0.0373350	−	0.0646661i
$764$	325.938	−	188.180i	0.426620	−	0.246309i
$765$	385.103	+	203.422i	0.503403	+	0.265912i
$766$	−60.0124			−0.0783451
$767$	−426.847	+	363.036i	−0.556515	+	0.473320i
$768$	−142.993	+	576.851i	−0.186189	+	0.751108i
$769$	605.521	−	1048.79i	0.787414	−	1.36384i	−0.140132	−	0.990133i	$-0.544753\pi$
$769$	605.521	−	1048.79i	0.787414	−	1.36384i	0.927546	−	0.373708i	$-0.121914\pi$

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+0.306140i q^{2} +(-0.721810 + 2.91187i) q^{3} +3.90628 q^{4} +(5.23834 - 3.02436i) q^{5} +(-0.891441 - 0.220975i) q^{6} +(0.307870 + 0.533246i) q^{7} +2.42043i q^{8} +(-7.95798 - 4.20363i) q^{9} +(0.925877 + 1.60367i) q^{10} -1.57095i q^{11} +(-2.81959 + 11.3746i) q^{12} +(8.42234 + 9.90273i) q^{13} +(-0.163248 + 0.0942513i) q^{14} +(5.02545 + 17.4364i) q^{15} +14.8841 q^{16} +(-6.92854 - 4.00019i) q^{17} +(1.28690 - 2.43626i) q^{18} +(-13.8170 + 23.9317i) q^{19} +(20.4624 - 11.8140i) q^{20} +(-1.77497 + 0.511574i) q^{21} +0.480931 q^{22} +(-18.1819 - 10.4973i) q^{23} +(-7.04798 - 1.74709i) q^{24} +(5.79345 - 10.0345i) q^{25} +(-3.03163 + 2.57842i) q^{26} +(17.9846 - 20.1384i) q^{27} +(1.20262 + 2.08301i) q^{28} -48.8876i q^{29} +(-5.33797 + 1.53849i) q^{30} +(-16.9689 - 29.3909i) q^{31} +14.2383i q^{32} +(4.57440 + 1.13393i) q^{33} +(1.22462 - 2.12111i) q^{34} +(3.22545 + 1.86221i) q^{35} +(-31.0861 - 16.4206i) q^{36} +(-6.37439 - 11.0408i) q^{37} +(-7.32647 - 4.22994i) q^{38} +(-34.9148 + 17.3769i) q^{39} +(7.32024 + 12.6790i) q^{40} +(-20.7315 - 11.9693i) q^{41} +(-0.156613 - 0.543389i) q^{42} +(28.2980 + 49.0136i) q^{43} -6.13656i q^{44} +(-54.3999 + 2.04771i) q^{45} +(3.21365 - 5.56621i) q^{46} +(13.5831 + 7.84221i) q^{47} +(-10.7435 + 43.3406i) q^{48} +(24.3104 - 42.1069i) q^{49} +(3.07198 + 1.77361i) q^{50} +(16.6491 - 17.2876i) q^{51} +(32.9000 + 38.6828i) q^{52} -28.8222i q^{53} +(6.16517 + 5.50581i) q^{54} +(-4.75111 - 8.22916i) q^{55} +(-1.29068 + 0.745177i) q^{56} +(-59.7129 - 57.5074i) q^{57} +14.9665 q^{58} +43.1040i q^{59} +(19.6308 + 68.1113i) q^{60} +(-31.2772 - 54.1737i) q^{61} +(8.99775 - 5.19485i) q^{62} +(-0.208450 - 5.53773i) q^{63} +55.1776 q^{64} +(74.0685 + 26.4017i) q^{65} +(-0.347141 + 1.40041i) q^{66} +(-13.6099 + 23.5730i) q^{67} +(-27.0648 - 15.6259i) q^{68} +(43.6907 - 45.3662i) q^{69} +(-0.570099 + 0.987440i) q^{70} +(-110.895 - 64.0252i) q^{71} +(10.1746 - 19.2617i) q^{72} +27.8685 q^{73} +(3.38002 - 1.95146i) q^{74} +(25.0375 + 24.1128i) q^{75} +(-53.9730 + 93.4840i) q^{76} +(0.837702 - 0.483647i) q^{77} +(-5.31976 - 10.6888i) q^{78} +(-26.8055 + 46.4286i) q^{79} +(77.9680 - 45.0149i) q^{80} +(45.6589 + 66.9049i) q^{81} +(3.66430 - 6.34675i) q^{82} +(137.735 + 79.5215i) q^{83} +(-6.93351 + 1.99835i) q^{84} -48.3920 q^{85} +(-15.0050 + 8.66317i) q^{86} +(142.354 + 35.2876i) q^{87} +3.80237 q^{88} +(-91.3979 + 52.7686i) q^{89} +(-0.626885 - 16.6540i) q^{90} +(-2.68761 + 7.53993i) q^{91} +(-71.0235 - 41.0054i) q^{92} +(97.8309 - 28.1965i) q^{93} +(-2.40082 + 4.15834i) q^{94} +167.150i q^{95} +(-41.4602 - 10.2774i) q^{96} +(-46.6339 - 80.7723i) q^{97} +(12.8906 + 7.44240i) q^{98} +(-6.60370 + 12.5016i) 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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