LMFDB - Embedded Newform 27.8.e.a.4.3

Newspace parameters

Level:	$ N $	=	$ 27 = 3^{3} $
Weight:	$ k $	=	$ 8 $
Character orbit:	$[\chi]$	=	27.e (of order $9$ and degree $6$)

Newform invariants

Self dual:	No
Analytic conductor:	$8.43439568807$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$20$ over $\Q(\zeta_{9})$
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			4.3
Character	$\chi$	=	27.4
Dual form			27.8.e.a.7.3

$q$-expansion

$f(q)$	$=$	$q+(-16.4594 - 5.99073i) q^{2} +(7.02376 + 46.2349i) q^{3} +(136.969 + 114.931i) q^{4} +(-40.0449 + 227.106i) q^{5} +(161.374 - 803.077i) q^{6} +(882.649 - 740.631i) q^{7} +(-444.907 - 770.602i) q^{8} +(-2088.33 + 649.486i) q^{9} +O(q^{10})$	\(q+(-16.4594 - 5.99073i) q^{2} +(7.02376 + 46.2349i) q^{3} +(136.969 + 114.931i) q^{4} +(-40.0449 + 227.106i) q^{5} +(161.374 - 803.077i) q^{6} +(882.649 - 740.631i) q^{7} +(-444.907 - 770.602i) q^{8} +(-2088.33 + 649.486i) q^{9} +(2019.65 - 3498.13i) q^{10} +(647.465 + 3671.95i) q^{11} +(-4351.78 + 7140.02i) q^{12} +(-7567.07 + 2754.19i) q^{13} +(-18964.8 + 6902.62i) q^{14} +(-10781.5 - 256.335i) q^{15} +(-1267.76 - 7189.84i) q^{16} +(-10746.9 + 18614.2i) q^{17} +(38263.6 + 1820.50i) q^{18} +(-5562.25 - 9634.10i) q^{19} +(-31586.5 + 26504.2i) q^{20} +(40442.5 + 35607.2i) q^{21} +(11340.8 - 64317.0i) q^{22} +(-79672.0 - 66852.8i) q^{23} +(32503.8 - 25982.8i) q^{24} +(23439.9 + 8531.43i) q^{25} +141049. q^{26} +(-44696.9 - 91992.1i) q^{27} +206017. q^{28} +(-132448. - 48207.1i) q^{29} +(175921. + 68808.2i) q^{30} +(-10109.4 - 8482.81i) q^{31} +(-41983.7 + 238101. i) q^{32} +(-165225. + 55726.4i) q^{33} +(288400. - 241996. i) q^{34} +(132856. + 230114. i) q^{35} +(-360684. - 151055. i) q^{36} +(-203213. + 351975. i) q^{37} +(33836.0 + 191894. i) q^{38} +(-180489. - 330518. i) q^{39} +(192825. - 70182.5i) q^{40} +(-121630. + 44269.8i) q^{41} +(-452346. - 828354. i) q^{42} +(6197.05 + 35145.2i) q^{43} +(-333339. + 577359. i) q^{44} +(-63875.0 - 500282. i) q^{45} +(910857. + 1.57765e6i) q^{46} +(814928. - 683806. i) q^{47} +(323517. - 109115. i) q^{48} +(87529.3 - 496403. i) q^{49} +(-334697. - 280844. i) q^{50} +(-936108. - 366140. i) q^{51} +(-1.35300e6 - 492451. i) q^{52} +666315. q^{53} +(184584. + 1.78190e6i) q^{54} -859851. q^{55} +(-963429. - 350659. i) q^{56} +(406364. - 324838. i) q^{57} +(1.89122e6 + 1.58692e6i) q^{58} +(-293561. + 1.66487e6i) q^{59} +(-1.44727e6 - 1.27424e6i) q^{60} +(-1.87164e6 + 1.57049e6i) q^{61} +(115577. + 200185. i) q^{62} +(-1.36224e6 + 2.11995e6i) q^{63} +(1.65018e6 - 2.85819e6i) q^{64} +(-322470. - 1.82882e6i) q^{65} +(3.05334e6 + 72594.8i) q^{66} +(3.89129e6 - 1.41632e6i) q^{67} +(-3.61134e6 + 1.31442e6i) q^{68} +(2.53133e6 - 4.15319e6i) q^{69} +(-808184. - 4.58344e6i) q^{70} +(-2.19506e6 + 3.80195e6i) q^{71} +(1.42961e6 + 1.32031e6i) q^{72} +(1.13112e6 + 1.95915e6i) q^{73} +(5.45336e6 - 4.57591e6i) q^{74} +(-229813. + 1.14366e6i) q^{75} +(345399. - 1.95885e6i) q^{76} +(3.29105e6 + 2.76152e6i) q^{77} +(990694. + 6.52139e6i) q^{78} +(-7.23906e6 - 2.63480e6i) q^{79} +1.68362e6 q^{80} +(3.93931e6 - 2.71269e6i) q^{81} +2.26717e6 q^{82} +(-1.87778e6 - 683455. i) q^{83} +(1.44702e6 + 9.52520e6i) q^{84} +(-3.79703e6 - 3.18609e6i) q^{85} +(108546. - 615594. i) q^{86} +(1.29857e6 - 6.46231e6i) q^{87} +(2.54155e6 - 2.13262e6i) q^{88} +(-3.29415e6 - 5.70564e6i) q^{89} +(-1.94571e6 + 8.61700e6i) q^{90} +(-4.63923e6 + 8.03539e6i) q^{91} +(-3.22918e6 - 1.83136e7i) q^{92} +(321196. - 526989. i) q^{93} +(-1.75097e7 + 6.37302e6i) q^{94} +(2.41070e6 - 877424. i) q^{95} +(-1.13035e7 - 268746. i) q^{96} +(1.19613e6 + 6.78360e6i) q^{97} +(-4.41450e6 + 7.64614e6i) q^{98} +(-3.73700e6 - 7.24775e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120q - 6q^{2} - 6q^{3} - 6q^{4} - 219q^{5} + 1386q^{6} - 6q^{7} - 4611q^{8} - 1728q^{9} + O(q^{10}) $	\( 120q - 6q^{2} - 6q^{3} - 6q^{4} - 219q^{5} + 1386q^{6} - 6q^{7} - 4611q^{8} - 1728q^{9} - 3q^{10} + 9399q^{11} - 10545q^{12} - 6q^{13} + 16647q^{14} + 11709q^{15} + 378q^{16} - 58959q^{17} - 156051q^{18} - 3q^{19} + 240243q^{20} - 516q^{21} + 105762q^{22} - 144084q^{23} - 150894q^{24} - 107997q^{25} + 443202q^{26} + 114363q^{27} - 12q^{28} + 107886q^{29} - 179901q^{30} + 297975q^{31} - 639576q^{32} - 31338q^{33} - 265806q^{34} - 450672q^{35} + 51264q^{36} - 3q^{37} - 145596q^{38} + 1919661q^{39} + 283521q^{40} + 227085q^{41} + 3792042q^{42} - 1080969q^{43} - 1205115q^{44} - 4430925q^{45} - 3q^{46} - 5184339q^{47} - 2424039q^{48} + 976008q^{49} + 2324559q^{50} + 2918034q^{51} - 3366135q^{52} + 5631750q^{53} + 11971422q^{54} - 12q^{55} + 5254923q^{56} - 284637q^{57} + 3884295q^{58} - 12534492q^{59} - 29390886q^{60} + 3865440q^{61} - 9923646q^{62} + 3292389q^{63} - 10223619q^{64} + 17158395q^{65} + 39100653q^{66} + 5567061q^{67} + 19858455q^{68} - 12682935q^{69} - 1020993q^{70} - 18563877q^{71} - 33138540q^{72} + 3770934q^{73} - 36278085q^{74} - 26317941q^{75} - 1156998q^{76} + 8471751q^{77} + 36593658q^{78} + 16415526q^{79} + 101080590q^{80} + 45736524q^{81} - 12q^{82} + 3147699q^{83} - 27588054q^{84} - 7672131q^{85} - 70854834q^{86} - 55384731q^{87} - 34323078q^{88} - 54647613q^{89} - 25256970q^{90} + 3315066q^{91} + 73858515q^{92} + 69808065q^{93} + 22126539q^{94} + 32541447q^{95} + 33014034q^{96} + 41250117q^{97} - 88493274q^{98} - 111262167q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Character Values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{9}\right)$

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 $

$2$	−16.4594	−	5.99073i	−1.45482	−	0.529511i	−0.510887	−	0.859648i	$-0.670683\pi$
$2$	−16.4594	−	5.99073i	−1.45482	−	0.529511i	−0.943933	+	0.330137i	$0.892905\pi$
$3$	7.02376	+	46.2349i	0.150191	+	0.988657i
$3$	7.02376	+	46.2349i	0.150191	+	0.988657i
$4$	136.969	+	114.931i	1.07007	+	0.897898i
$5$	−40.0449	+	227.106i	−0.143269	+	0.812520i	0.825472	+	0.564444i	$0.190909\pi$
$5$	−40.0449	+	227.106i	−0.143269	+	0.812520i	−0.968741	+	0.248076i	$0.920202\pi$
$6$	161.374	−	803.077i	0.305003	−	1.51785i
$7$	882.649	−	740.631i	0.972624	−	0.816129i	−0.0103360	−	0.999947i	$-0.503290\pi$
$7$	882.649	−	740.631i	0.972624	−	0.816129i	0.982960	+	0.183818i	$0.0588457\pi$
$8$	−444.907	−	770.602i	−0.307224	−	0.532127i
$9$	−2088.33	+	649.486i	−0.954885	+	0.296976i
$10$	2019.65	−	3498.13i	0.638669	−	1.10621i
$11$	647.465	+	3671.95i	0.146670	+	0.831808i	0.966011	+	0.258501i	$0.0832285\pi$
$11$	647.465	+	3671.95i	0.146670	+	0.831808i	−0.819341	+	0.573307i	$0.805660\pi$
$12$	−4351.78	+	7140.02i	−0.726998	+	1.19279i
$13$	−7567.07	+	2754.19i	−0.955270	+	0.347690i	−0.772178	−	0.635406i	$-0.780833\pi$
$13$	−7567.07	+	2754.19i	−0.955270	+	0.347690i	−0.183092	+	0.983096i	$0.558610\pi$
$14$	−18964.8	+	6902.62i	−1.84714	+	0.672305i
$15$	−10781.5	−	256.335i	−0.824821	−	0.0196105i
$16$	−1267.76	−	7189.84i	−0.0773781	−	0.438833i
$17$	−10746.9	+	18614.2i	−0.530532	+	0.918909i	0.468833	+	0.883287i	$0.344675\pi$
$17$	−10746.9	+	18614.2i	−0.530532	+	0.918909i	−0.999365	+	0.0356221i	$0.988659\pi$
$18$	38263.6	+	1820.50i	1.54644	+	0.0735762i
$19$	−5562.25	−	9634.10i	−0.186043	−	0.322236i	0.757885	−	0.652389i	$-0.226233\pi$
$19$	−5562.25	−	9634.10i	−0.186043	−	0.322236i	−0.943927	+	0.330153i	$0.892900\pi$
$20$	−31586.5	+	26504.2i	−0.882868	+	0.740815i
$21$	40442.5	+	35607.2i	0.952951	+	0.839016i
$22$	11340.8	−	64317.0i	0.227073	−	1.28779i
$23$	−79672.0	−	66852.8i	−1.36540	−	1.14570i	−0.974275	−	0.225364i	$-0.927643\pi$
$23$	−79672.0	−	66852.8i	−1.36540	−	1.14570i	−0.391121	−	0.920339i	$-0.627913\pi$
$24$	32503.8	−	25982.8i	0.479949	−	0.383660i
$25$	23439.9	+	8531.43i	0.300031	+	0.109202i
$26$	141049.			1.57385
$27$	−44696.9	−	91992.1i	−0.437023	−	0.899451i
$28$	206017.			1.77358
$29$	−132448.	−	48207.1i	−1.00844	−	0.367044i	−0.215609	−	0.976480i	$-0.569174\pi$
$29$	−132448.	−	48207.1i	−1.00844	−	0.367044i	−0.792835	+	0.609436i	$0.791396\pi$
$30$	175921.	+	68808.2i	1.18958	+	0.465282i
$31$	−10109.4	−	8482.81i	−0.0609481	−	0.0511415i	0.611805	−	0.791009i	$-0.290444\pi$
$31$	−10109.4	−	8482.81i	−0.0609481	−	0.0511415i	−0.672753	+	0.739867i	$0.734888\pi$
$32$	−41983.7	+	238101.i	−0.226493	+	1.28451i
$33$	−165225.	+	55726.4i	−0.800344	+	0.269937i
$34$	288400.	−	241996.i	1.25840	−	1.05592i
$35$	132856.	+	230114.i	0.523773	+	0.907202i
$36$	−360684.	−	151055.i	−1.28845	−	0.539604i
$37$	−203213.	+	351975.i	−0.659547	+	1.14237i	0.321186	+	0.947016i	$0.395919\pi$
$37$	−203213.	+	351975.i	−0.659547	+	1.14237i	−0.980733	+	0.195353i	$0.937415\pi$
$38$	33836.0	+	191894.i	0.100031	+	0.567307i
$39$	−180489.	−	330518.i	−0.487219	−	0.892214i
$40$	192825.	−	70182.5i	0.476379	−	0.173388i
$41$	−121630.	+	44269.8i	−0.275612	+	0.100315i	−0.476129	−	0.879376i	$-0.657960\pi$
$41$	−121630.	+	44269.8i	−0.275612	+	0.100315i	0.200516	+	0.979690i	$0.435738\pi$
$42$	−452346.	−	828354.i	−0.942104	−	1.72522i
$43$	6197.05	+	35145.2i	0.0118863	+	0.0674104i	0.990174	−	0.139841i	$-0.0446592\pi$
$43$	6197.05	+	35145.2i	0.0118863	+	0.0674104i	−0.978288	+	0.207252i	$0.933548\pi$
$44$	−333339.	+	577359.i	−0.589931	+	1.02179i
$45$	−63875.0	−	500282.i	−0.104493	−	0.818410i
$46$	910857.	+	1.57765e6i	1.37974	+	2.38978i
$47$	814928.	−	683806.i	1.14492	−	0.960705i	0.145335	−	0.989382i	$-0.453574\pi$
$47$	814928.	−	683806.i	1.14492	−	0.960705i	0.999589	+	0.0286771i	$0.00912944\pi$
$48$	323517.	−	109115.i	0.422234	−	0.142409i
$49$	87529.3	−	496403.i	0.106284	−	0.602765i
$50$	−334697.	−	280844.i	−0.378667	−	0.317739i
$51$	−936108.	−	366140.i	−0.988167	−	0.386502i
$52$	−1.35300e6	−	492451.i	−1.33440	−	0.485681i
$53$	666315.			0.614772			0.307386	−	0.951585i	$-0.400546\pi$
$53$	666315.			0.614772			0.307386	+	0.951585i	$0.400546\pi$
$54$	184584.	+	1.78190e6i	0.159520	+	1.53995i
$55$	−859851.			−0.696873
$56$	−963429.	−	350659.i	−0.733097	−	0.266826i
$57$	406364.	−	324838.i	0.290639	−	0.232330i
$58$	1.89122e6	+	1.58692e6i	1.27275	+	1.06797i
$59$	−293561.	+	1.66487e6i	−0.186087	+	1.05535i	0.738463	+	0.674294i	$0.235552\pi$
$59$	−293561.	+	1.66487e6i	−0.186087	+	1.05535i	−0.924550	+	0.381060i	$0.875559\pi$
$60$	−1.44727e6	−	1.27424e6i	−0.865011	−	0.761590i
$61$	−1.87164e6	+	1.57049e6i	−1.05577	+	0.885893i	−0.993688	−	0.112178i	$-0.964217\pi$
$61$	−1.87164e6	+	1.57049e6i	−1.05577	+	0.885893i	−0.0620779	+	0.998071i	$0.519773\pi$
$62$	115577.	+	200185.i	0.0615885	+	0.106674i
$63$	−1.36224e6	+	2.11995e6i	−0.686374	+	1.06815i
$64$	1.65018e6	−	2.85819e6i	0.786867	−	1.36289i
$65$	−322470.	−	1.82882e6i	−0.145644	−	0.825988i
$66$	3.05334e6	+	72594.8i	1.30729	+	0.0310815i
$67$	3.89129e6	−	1.41632e6i	1.58064	−	0.575305i	0.605295	−	0.796001i	$-0.293055\pi$
$67$	3.89129e6	−	1.41632e6i	1.58064	−	0.575305i	0.975343	+	0.220696i	$0.0708329\pi$
$68$	−3.61134e6	+	1.31442e6i	−1.39280	+	0.506936i
$69$	2.53133e6	−	4.15319e6i	0.927636	−	1.52198i
$70$	−808184.	−	4.58344e6i	−0.281622	−	1.59716i
$71$	−2.19506e6	+	3.80195e6i	−0.727850	+	1.26067i	0.229940	+	0.973205i	$0.426147\pi$
$71$	−2.19506e6	+	3.80195e6i	−0.727850	+	1.26067i	−0.957790	+	0.287468i	$0.907186\pi$
$72$	1.42961e6	+	1.32031e6i	0.451392	+	0.416882i
$73$	1.13112e6	+	1.95915e6i	0.340313	+	0.589439i	0.984491	−	0.175437i	$-0.0561337\pi$
$73$	1.13112e6	+	1.95915e6i	0.340313	+	0.589439i	−0.644178	+	0.764876i	$0.722800\pi$
$74$	5.45336e6	−	4.57591e6i	1.56442	−	1.31270i
$75$	−229813.	+	1.14366e6i	−0.0629015	+	0.313029i
$76$	345399.	−	1.95885e6i	0.0902554	−	0.511864i
$77$	3.29105e6	+	2.76152e6i	0.821517	+	0.689335i
$78$	990694.	+	6.52139e6i	0.236379	+	1.55600i
$79$	−7.23906e6	−	2.63480e6i	−1.65191	−	0.601247i	−0.662852	−	0.748751i	$-0.730654\pi$
$79$	−7.23906e6	−	2.63480e6i	−1.65191	−	0.601247i	−0.989062	+	0.147504i	$0.952876\pi$
$80$	1.68362e6			0.367646
$81$	3.93931e6	−	2.71269e6i	0.823611	−	0.567155i
$82$	2.26717e6			0.454084
$83$	−1.87778e6	−	683455.i	−0.360471	−	0.131201i	0.155434	−	0.987846i	$-0.450322\pi$
$83$	−1.87778e6	−	683455.i	−0.360471	−	0.131201i	−0.515906	+	0.856645i	$0.672544\pi$
$84$	1.44702e6	+	9.52520e6i	0.266377	+	1.75346i
$85$	−3.79703e6	−	3.18609e6i	−0.670623	−	0.562719i
$86$	108546.	−	615594.i	0.0184022	−	0.104364i
$87$	1.29857e6	−	6.46231e6i	0.211421	−	1.05213i
$88$	2.54155e6	−	2.13262e6i	0.397567	−	0.333598i
$89$	−3.29415e6	−	5.70564e6i	−0.495312	−	0.857906i	0.504673	−	0.863310i	$-0.331613\pi$
$89$	−3.29415e6	−	5.70564e6i	−0.495312	−	0.857906i	−0.999985	+	0.00540466i	$0.998280\pi$
$90$	−1.94571e6	+	8.61700e6i	−0.281339	+	1.24597i
$91$	−4.63923e6	+	8.03539e6i	−0.645359	+	1.11779i
$92$	−3.22918e6	−	1.83136e7i	−0.432349	−	2.45197i
$93$	321196.	−	526989.i	0.0414076	−	0.0679378i
$94$	−1.75097e7	+	6.37302e6i	−2.17436	+	0.791403i
$95$	2.41070e6	−	877424.i	0.288477	−	0.104997i
$96$	−1.13035e7	−	268746.i	−1.30396	−	0.0310022i
$97$	1.19613e6	+	6.78360e6i	0.133069	+	0.754674i	0.976185	+	0.216941i	$0.0696080\pi$
$97$	1.19613e6	+	6.78360e6i	0.133069	+	0.754674i	−0.843115	+	0.537733i	$0.819281\pi$
$98$	−4.41450e6	+	7.64614e6i	−0.473795	+	0.820636i
$99$	−3.73700e6	−	7.24775e6i	−0.387080	−	0.750723i
$100$	2.23002e6	+	3.86252e6i	0.223002	+	0.386252i
$101$	−132538.	+	111213.i	−0.0128002	+	0.0107406i	−0.649165	−	0.760647i	$-0.724882\pi$
$101$	−132538.	+	111213.i	−0.0128002	+	0.0107406i	0.636365	+	0.771388i	$0.280437\pi$
$102$	1.32143e7	+	1.16344e7i	1.23295	+	1.08554i
$103$	−3.57406e6	+	2.02695e7i	−0.322279	+	1.82773i	0.205869	+	0.978580i	$0.433998\pi$
$103$	−3.57406e6	+	2.02695e7i	−0.322279	+	1.82773i	−0.528147	+	0.849153i	$0.677113\pi$
$104$	5.48903e6	+	4.60584e6i	0.478496	+	0.401506i
$105$	−9.70613e6	+	7.75885e6i	−0.818246	+	0.654086i
$106$	−1.09671e7	−	3.99171e6i	−0.894382	−	0.325528i
$107$	2.02493e7			1.59797			0.798983	−	0.601353i	$-0.205371\pi$
$107$	2.02493e7			1.59797			0.798983	+	0.601353i	$0.205371\pi$
$108$	4.45064e6	−	1.77372e7i	0.339969	−	1.35488i
$109$	6.50872e6			0.481396			0.240698	−	0.970600i	$-0.422624\pi$
$109$	6.50872e6			0.481396			0.240698	+	0.970600i	$0.422624\pi$
$110$	1.41526e7	+	5.15114e6i	1.01382	+	0.369002i
$111$	−1.77009e7	−	6.92335e6i	−1.22847	−	0.480492i
$112$	−6.44401e6	−	5.40717e6i	−0.433404	−	0.363669i
$113$	1.93666e6	−	1.09834e7i	0.126264	−	0.716078i	−0.854285	−	0.519804i	$-0.826005\pi$
$113$	1.93666e6	−	1.09834e7i	0.126264	−	0.716078i	0.980549	−	0.196274i	$-0.0628841\pi$
$114$	−8.63453e6	+	2.91222e6i	−0.545848	+	0.184101i
$115$	1.83731e7	−	1.54169e7i	1.12653	−	0.945267i
$116$	−1.26008e7	−	2.18253e7i	−0.749542	−	1.29825i
$117$	1.40138e7	−	1.06664e7i	0.808917	−	0.615695i
$118$	1.48056e7	−	2.56441e7i	0.829545	−	1.43681i
$119$	4.30049e6	+	2.43893e7i	0.233939	+	1.32674i
$120$	4.59923e6	+	8.42229e6i	0.242969	+	0.444934i
$121$	5.24791e6	−	1.91008e6i	0.269301	−	0.0980175i
$122$	4.02145e7	−	1.46369e7i	2.00504	−	0.729775i
$123$	−2.90111e6	−	5.31263e6i	−0.140571	−	0.257420i
$124$	−409744.	−	2.32377e6i	−0.0192991	−	0.109450i
$125$	−1.18844e7	+	2.05843e7i	−0.544241	+	0.942653i
$126$	3.51217e7	−	2.67324e7i	1.56415	−	1.19053i
$127$	5.90579e6	+	1.02291e7i	0.255838	+	0.443124i	0.965123	−	0.261798i	$-0.0843154\pi$
$127$	5.90579e6	+	1.02291e7i	0.255838	+	0.443124i	−0.709285	+	0.704922i	$0.750982\pi$
$128$	−2.05768e7	+	1.72660e7i	−0.867246	+	0.727706i
$129$	−1.58141e6	+	533372.i	−0.0648605	+	0.0218759i
$130$	−5.64830e6	+	3.20331e7i	−0.225484	+	1.27878i
$131$	7.08938e6	+	5.94870e6i	0.275524	+	0.231192i	0.770070	−	0.637960i	$-0.220221\pi$
$131$	7.08938e6	+	5.94870e6i	0.275524	+	0.231192i	−0.494546	+	0.869151i	$0.664666\pi$
$132$	−2.90354e7	−	1.13566e7i	−1.09880	−	0.429775i
$133$	−1.20448e7	−	4.38396e6i	−0.443936	−	0.161579i
$134$	−7.25332e7			−2.60417
$135$	2.26818e7	−	6.46711e6i	0.793433	−	0.226226i
$136$	1.91255e7			0.651968
$137$	−7.83598e6	−	2.85206e6i	−0.260358	−	0.0947627i	0.208543	−	0.978013i	$-0.433128\pi$
$137$	−7.83598e6	−	2.85206e6i	−0.260358	−	0.0947627i	−0.468901	+	0.883250i	$0.655350\pi$
$138$	−6.65449e7	+	5.31944e7i	−2.15545	+	1.72302i
$139$	2.03804e7	+	1.71012e7i	0.643667	+	0.540101i	0.905142	−	0.425109i	$-0.139764\pi$
$139$	2.03804e7	+	1.71012e7i	0.643667	+	0.540101i	−0.261475	+	0.965210i	$0.584209\pi$
$140$	−8.24995e6	+	4.67878e7i	−0.254099	+	1.44107i
$141$	3.73396e7	+	3.28752e7i	1.12177	+	0.987647i
$142$	5.89058e7	−	4.94279e7i	1.72643	−	1.44865i
$143$	−1.50127e7	−	2.60027e7i	−0.429320	−	0.743605i
$144$	7.31721e6	+	1.41914e7i	0.204210	+	0.396056i
$145$	1.62520e7	−	2.81493e7i	0.442709	−	0.766795i
$146$	−6.88076e6	−	3.90228e7i	−0.182979	−	1.03773i
$147$	2.35659e7	+	560292.i	0.611891	+	0.0145480i
$148$	−6.82869e7	+	2.48544e7i	−1.73150	+	0.630213i
$149$	−2.76199e7	+	1.00528e7i	−0.684022	+	0.248964i	−0.660574	−	0.750761i	$-0.729687\pi$
$149$	−2.76199e7	+	1.00528e7i	−0.684022	+	0.248964i	−0.0234486	+	0.999725i	$0.507465\pi$
$150$	1.06340e7	−	1.74473e7i	0.257262	−	0.422093i
$151$	7.34521e6	+	4.16568e7i	0.173614	+	0.984615i	0.939731	+	0.341914i	$0.111075\pi$
$151$	7.34521e6	+	4.16568e7i	0.173614	+	0.984615i	−0.766117	+	0.642701i	$0.777814\pi$
$152$	−4.94937e6	+	8.57257e6i	−0.114314	+	0.197997i
$153$	1.03535e7	−	4.58526e7i	0.233704	−	1.03501i
$154$	−3.76252e7	−	6.51687e7i	−0.830149	−	1.43786i
$155$	2.33133e6	−	1.95622e6i	0.0502855	−	0.0421945i
$156$	1.32653e7	−	6.60146e7i	0.279757	−	1.39221i
$157$	4.90430e6	−	2.78137e7i	0.101141	−	0.573600i	−0.891550	−	0.452921i	$-0.850382\pi$
$157$	4.90430e6	−	2.78137e7i	0.101141	−	0.573600i	0.992692	−	0.120679i	$-0.0385071\pi$
$158$	1.03366e8	+	8.67345e7i	2.08487	+	1.74941i
$159$	4.68003e6	+	3.08070e7i	0.0923335	+	0.607798i
$160$	−5.23930e7	−	1.90695e7i	−1.01124	−	0.368061i
$161$	−1.19836e8			−2.26306
$162$	−8.10896e7	+	2.10499e7i	−1.49852	+	0.388997i
$163$	9.63217e7			1.74208			0.871039	−	0.491214i	$-0.163447\pi$
$163$	9.63217e7			1.74208			0.871039	+	0.491214i	$0.163447\pi$
$164$	−2.17476e7	−	7.91549e6i	−0.384998	−	0.140128i
$165$	−6.03939e6	−	3.97551e7i	−0.104664	−	0.688969i
$166$	2.68127e7	+	2.24985e7i	0.454948	+	0.381747i
$167$	1.67672e6	−	9.50917e6i	0.0278583	−	0.157992i	−0.967705	−	0.252085i	$-0.918884\pi$
$167$	1.67672e6	−	9.50917e6i	0.0278583	−	0.157992i	0.995563	+	0.0940926i	$0.0299950\pi$
$168$	9.44582e6	−	4.70070e7i	0.153694	−	0.764857i
$169$	1.60683e6	−	1.34829e6i	0.0256074	−	0.0214872i
$170$	4.34099e7	+	7.51881e7i	0.677669	+	1.17376i
$171$	1.78730e7	+	1.65066e7i	0.273346	+	0.252448i
$172$	−3.19047e6	+	5.52605e6i	−0.0478085	+	0.0828067i
$173$	3.17168e6	+	1.79875e7i	0.0465723	+	0.264125i	0.999199	−	0.0400174i	$-0.0127413\pi$
$173$	3.17168e6	+	1.79875e7i	0.0465723	+	0.264125i	−0.952627	+	0.304142i	$0.901630\pi$
$174$	−6.00877e7	+	9.85864e7i	−0.864695	+	1.41871i
$175$	2.70078e7	−	9.83005e6i	0.380940	−	0.138651i
$176$	2.55799e7	−	9.31034e6i	0.353676	−	0.128727i
$177$	−7.90370e7	−	1.87914e6i	−1.07133	−	0.0254715i
$178$	2.00388e7	+	1.13646e8i	0.266319	+	1.51037i
$179$	−1.56516e7	+	2.71094e7i	−0.203973	+	0.353292i	−0.949805	−	0.312842i	$-0.898719\pi$
$179$	−1.56516e7	+	2.71094e7i	−0.203973	+	0.353292i	0.745832	+	0.666134i	$0.232052\pi$
$180$	4.87490e7	−	7.58645e7i	0.623034	−	0.969583i
$181$	1.38544e7	+	2.39965e7i	0.173665	+	0.300796i	0.939698	−	0.342004i	$-0.111106\pi$
$181$	1.38544e7	+	2.39965e7i	0.173665	+	0.300796i	−0.766034	+	0.642801i	$0.777772\pi$
$182$	1.24497e8	−	1.04465e8i	1.53077	−	1.28446i
$183$	−8.57575e7	−	7.55043e7i	−1.03441	−	0.910737i
$184$	−1.60702e7	+	9.11387e7i	−0.190178	+	1.07855i
$185$	−7.17981e7	−	6.02458e7i	−0.833704	−	0.699561i
$186$	−8.44374e6	+	6.74973e6i	−0.0962143	+	0.0769115i
$187$	−7.53086e7	−	2.74101e7i	−0.842169	−	0.306524i
$188$	1.90211e8			2.08777
$189$	−1.07584e8	−	4.80929e7i	−1.15913	−	0.518161i
$190$	−4.49352e7			−0.475279
$191$	3.13583e6	+	1.14135e6i	0.0325639	+	0.0118523i	0.358251	−	0.933625i	$-0.383373\pi$
$191$	3.13583e6	+	1.14135e6i	0.0325639	+	0.0118523i	−0.325687	+	0.945478i	$0.605596\pi$
$192$	1.43739e8	+	5.62206e7i	1.46561	+	0.573246i
$193$	−2.79276e7	−	2.34341e7i	−0.279630	−	0.234637i	0.492176	−	0.870496i	$-0.336202\pi$
$193$	−2.79276e7	−	2.34341e7i	−0.279630	−	0.234637i	−0.771806	+	0.635859i	$0.780646\pi$
$194$	2.09511e7	−	1.18820e8i	0.206016	−	1.16838i
$195$	8.22903e7	−	2.77546e7i	0.794745	−	0.268048i
$196$	6.90410e7	−	5.79322e7i	0.654954	−	0.549571i
$197$	−938749.	−	1.62596e6i	−0.00874818	−	0.0151523i	0.861618	−	0.507557i	$-0.169451\pi$
$197$	−938749.	−	1.62596e6i	−0.00874818	−	0.0151523i	−0.870366	+	0.492405i	$0.836118\pi$
$198$	1.80895e7	+	1.41681e8i	0.165615	+	1.29713i
$199$	−8.42423e7	+	1.45912e8i	−0.757783	+	1.31252i	0.186196	+	0.982513i	$0.440384\pi$
$199$	−8.42423e7	+	1.45912e8i	−0.757783	+	1.31252i	−0.943979	+	0.330006i	$0.892949\pi$
$200$	−3.85425e6	−	2.18585e7i	−0.0340671	−	0.193204i
$201$	9.28147e7	+	1.69966e8i	0.806178	+	1.47630i
$202$	2.84775e6	−	1.03650e6i	0.0243093	−	0.00884785i
$203$	−1.52609e8	+	5.55450e7i	−1.28039	+	0.466025i
$204$	−8.61373e7	−	1.57738e8i	−0.710372	−	1.30086i
$205$	−5.18327e6	−	2.93958e7i	−0.0420209	−	0.238312i
$206$	1.80256e8	−	3.12213e8i	1.43666	−	2.48837i
$207$	2.09802e8	+	8.78651e7i	1.64404	+	0.688525i
$208$	2.93954e7	+	5.09144e7i	0.226495	+	0.392300i
$209$	3.17746e7	−	2.66621e7i	0.240751	−	0.202014i
$210$	2.06238e8	−	6.95593e7i	1.53675	−	0.518307i
$211$	1.85769e7	−	1.05355e8i	0.136139	−	0.772085i	−0.837920	−	0.545793i	$-0.816228\pi$
$211$	1.85769e7	−	1.05355e8i	0.136139	−	0.772085i	0.974059	−	0.226292i	$-0.0726604\pi$
$212$	9.12648e7	+	7.65802e7i	0.657851	+	0.552003i
$213$	−1.91200e8	−	7.47843e7i	−1.35569	−	0.530252i
$214$	−3.33292e8	−	1.21308e8i	−2.32475	−	0.846141i
$215$	−8.22985e6			−0.0564752
$216$	−5.10033e7	+	7.53714e7i	−0.344358	+	0.508884i
$217$	−1.52057e7			−0.101018
$218$	−1.07130e8	−	3.89920e7i	−0.700344	−	0.254905i
$219$	−8.26366e7	+	6.60578e7i	−0.531641	+	0.424981i
$220$	−1.17773e8	−	9.88235e7i	−0.745706	−	0.625721i
$221$	3.00556e7	−	1.70454e8i	0.187306	−	1.06227i
$222$	2.49870e8	+	2.19995e8i	1.53278	+	1.34952i
$223$	4.75147e7	−	3.98696e7i	0.286920	−	0.240755i	−0.487955	−	0.872869i	$-0.662257\pi$
$223$	4.75147e7	−	3.98696e7i	0.286920	−	0.240755i	0.774875	+	0.632114i	$0.217813\pi$
$224$	1.39288e8	+	2.41254e8i	0.828031	+	1.43419i
$225$	−5.44914e7	−	2.59258e6i	−0.318925	−	0.0151738i
$226$	−9.76746e7	+	1.69177e8i	−0.562862	+	0.974906i
$227$	1.33534e7	+	7.57308e7i	0.0757706	+	0.429717i	0.998969	+	0.0453933i	$0.0144541\pi$
$227$	1.33534e7	+	7.57308e7i	0.0757706	+	0.429717i	−0.923199	+	0.384323i	$0.874435\pi$
$228$	9.29934e7	+	2.21096e6i	0.519613	+	0.0123541i
$229$	2.44709e8	−	8.90666e7i	1.34656	−	0.490107i	0.434686	−	0.900582i	$-0.356859\pi$
$229$	2.44709e8	−	8.90666e7i	1.34656	−	0.490107i	0.911872	+	0.410475i	$0.134637\pi$
$230$	−3.94769e8	+	1.43684e8i	−2.13942	+	0.778685i
$231$	−1.04563e8	+	1.71557e8i	−0.558131	+	0.915731i
$232$	2.17786e7	+	1.23512e8i	0.114504	+	0.649385i
$233$	−1.04965e8	+	1.81804e8i	−0.543622	+	0.941581i	0.455070	+	0.890455i	$0.349614\pi$
$233$	−1.04965e8	+	1.81804e8i	−0.543622	+	0.941581i	−0.998692	+	0.0511252i	$0.983719\pi$
$234$	−2.94557e8	+	9.16093e7i	−1.50285	+	0.467395i
$235$	1.22663e8	+	2.12458e8i	0.616560	+	1.06791i
$236$	−2.31554e8	+	1.94297e8i	−1.14673	+	0.962219i
$237$	7.09744e7	−	3.53203e8i	0.346324	−	1.72348i
$238$	7.53262e7	−	4.27196e8i	0.362182	−	2.05403i
$239$	−2.89505e8	−	2.42923e8i	−1.37171	−	1.15100i	−0.972167	−	0.234289i	$-0.924724\pi$
$239$	−2.89505e8	−	2.42923e8i	−1.37171	−	1.15100i	−0.399544	−	0.916714i	$-0.630832\pi$
$240$	1.18254e7	+	7.78422e7i	0.0552173	+	0.363476i
$241$	−2.21320e8	−	8.05539e7i	−1.01850	−	0.370704i	−0.221809	−	0.975090i	$-0.571196\pi$
$241$	−2.21320e8	−	8.05539e7i	−1.01850	−	0.370704i	−0.796691	+	0.604387i	$0.793418\pi$
$242$	−9.78203e7			−0.443685
$243$	1.53089e8	+	1.63080e8i	0.684421	+	0.729087i
$244$	−4.36855e8			−1.92519
$245$	1.09231e8	+	3.97569e7i	0.474531	+	0.172715i
$246$	1.59241e7	+	1.04823e8i	0.0681995	+	0.448933i
$247$	6.86241e7	+	5.75824e7i	0.289759	+	0.243137i
$248$	−2.03912e6	+	1.15644e7i	−0.00848909	+	0.0481440i
$249$	1.84104e7	−	9.16192e7i	0.0755729	−	0.376088i
$250$	3.18925e8	−	2.67610e8i	1.29092	−	1.08321i
$251$	1.28760e8	+	2.23019e8i	0.513954	+	0.890194i	0.999869	+	0.0161879i	$0.00515300\pi$
$251$	1.28760e8	+	2.23019e8i	0.513954	+	0.890194i	−0.485915	+	0.874006i	$0.661514\pi$
$252$	−4.30233e8	+	1.33805e8i	−1.69357	+	0.526710i
$253$	1.93896e8	−	3.35837e8i	0.752742	−	1.30379i
$254$	−3.59258e7	−	2.03745e8i	−0.137559	−	0.780134i
$255$	1.20639e8	−	1.97934e8i	0.455614	−	0.747531i
$256$	4.51480e7	−	1.64325e7i	0.168189	−	0.0612160i
$257$	3.87015e8	−	1.40862e8i	1.42220	−	0.517640i	0.487518	−	0.873113i	$-0.337902\pi$
$257$	3.87015e8	−	1.40862e8i	1.42220	−	0.517640i	0.934687	+	0.355473i	$0.115680\pi$
$258$	2.92243e7	+	694823.i	0.105944	+	0.00251887i
$259$	8.13179e7	+	4.61177e8i	0.290829	+	1.64937i
$260$	1.66019e8	−	2.87554e8i	0.585804	−	1.01464i
$261$	3.07905e8	+	1.46495e7i	1.07195	+	0.0510012i
$262$	−8.10499e7	−	1.40383e8i	−0.278418	−	0.482235i
$263$	1.05346e8	−	8.83958e7i	0.357086	−	0.299631i	−0.446542	−	0.894763i	$-0.647345\pi$
$263$	1.05346e8	−	8.83958e7i	0.357086	−	0.299631i	0.803628	+	0.595132i	$0.202900\pi$
$264$	1.16453e8	+	1.02530e8i	0.389525	+	0.342954i
$265$	−2.66825e7	+	1.51324e8i	−0.0880778	+	0.499514i
$266$	1.71988e8	+	1.44315e8i	0.560288	+	0.470138i
$267$	2.40663e8	−	1.92380e8i	0.773783	−	0.618544i
$268$	6.95767e8	+	2.53238e8i	2.20796	+	0.803633i
$269$	2.29185e8			0.717883			0.358941	−	0.933360i	$-0.383138\pi$
$269$	2.29185e8			0.717883			0.358941	+	0.933360i	$0.383138\pi$
$270$	−4.12072e8	−	2.94361e7i	−1.27409	−	0.0910137i
$271$	−2.08163e8			−0.635348			−0.317674	−	0.948200i	$-0.602902\pi$
$271$	−2.08163e8			−0.635348			−0.317674	+	0.948200i	$0.602902\pi$
$272$	1.47457e8	+	5.36701e7i	0.444299	+	0.161712i
$273$	−4.04100e8	−	1.58056e8i	−1.20204	−	0.470155i
$274$	1.11890e8	+	9.38866e7i	0.328597	+	0.275725i
$275$	−1.61505e7	+	9.15940e7i	−0.0468297	+	0.265585i
$276$	8.24045e8	−	2.77931e8i	2.35922	−	0.795710i
$277$	−3.90805e8	+	3.27924e8i	−1.10479	+	0.927032i	−0.997738	−	0.0672212i	$-0.978587\pi$
$277$	−3.90805e8	+	3.27924e8i	−1.10479	+	0.927032i	−0.107055	+	0.994253i	$0.534142\pi$
$278$	−2.33001e8	−	4.03569e8i	−0.650430	−	1.12658i
$279$	2.66213e7	+	1.11490e7i	0.0733862	+	0.0307342i
$280$	1.18217e8	−	2.04758e8i	0.321831	−	0.557428i
$281$	1.96864e7	+	1.11647e8i	0.0529291	+	0.300176i	0.999768	−	0.0215318i	$-0.00685430\pi$
$281$	1.96864e7	+	1.11647e8i	0.0529291	+	0.300176i	−0.946839	+	0.321708i	$0.895743\pi$
$282$	−4.17640e8	−	7.64798e8i	−1.10900	−	2.03084i
$283$	2.48118e8	−	9.03076e7i	0.650737	−	0.236849i	0.00450515	−	0.999990i	$-0.498566\pi$
$283$	2.48118e8	−	9.03076e7i	0.650737	−	0.236849i	0.646232	+	0.763141i	$0.276344\pi$
$284$	−7.37618e8	+	2.68471e8i	−1.91081	+	0.695478i
$285$	5.74998e7	+	1.05296e8i	0.147133	+	0.269435i
$286$	9.13243e7	+	5.17926e8i	0.230837	+	1.30914i
$287$	−7.45694e7	+	1.29158e8i	−0.186198	+	0.322504i
$288$	−6.69674e7	−	5.24503e8i	−0.165192	−	1.29382i
$289$	−2.58223e7	−	4.47255e7i	−0.0629291	−	0.108996i
$290$	−4.36133e8	+	3.65959e8i	−1.05009	+	0.881129i
$291$	−3.05238e8	+	1.02949e8i	−0.726128	+	0.244906i
$292$	−7.02390e7	+	3.98345e8i	−0.165097	+	0.936309i
$293$	3.16343e8	+	2.65443e8i	0.734720	+	0.616503i	0.931414	−	0.363962i	$-0.118576\pi$
$293$	3.16343e8	+	2.65443e8i	0.734720	+	0.616503i	−0.196694	+	0.980465i	$0.563021\pi$
$294$	−3.84525e8	−	1.50399e8i	−0.882488	−	0.345168i
$295$	−3.66346e8	−	1.33339e8i	−0.830835	−	0.302399i
$296$	3.61644e8			0.810514
$297$	3.08851e8	−	2.23686e8i	0.684072	−	0.495441i
$298$	5.14831e8			1.12696
$299$	7.87009e8	+	2.86448e8i	1.70267	+	0.619721i
$300$	−1.62920e8	+	1.30234e8i	−0.348377	+	0.278485i
$301$	3.14995e7	+	2.64312e7i	0.0665764	+	0.0558642i
$302$	1.28657e8	−	7.29649e8i	0.268787	−	1.52437i
$303$	−6.07283e6	−	5.34676e6i	−0.0125413	−	0.0110418i
$304$	−6.22161e7	+	5.22055e7i	−0.127012	+	0.106576i
$305$	−2.81719e8	−	4.87951e8i	−0.568547	−	0.984752i
$306$	−4.45102e8	+	6.92681e8i	−0.888045	+	1.38200i
$307$	−1.67717e8	+	2.90494e8i	−0.330821	+	0.572998i	−0.982673	−	0.185348i	$-0.940659\pi$
$307$	−1.67717e8	+	2.90494e8i	−0.330821	+	0.572998i	0.651852	+	0.758346i	$0.273992\pi$
$308$	1.33389e8	+	7.56487e8i	0.260131	+	1.47528i
$309$	−9.62261e8	−	2.28783e7i	−1.85540	−	0.0441132i
$310$	−5.00915e7	+	1.82318e7i	−0.0954988	+	0.0347587i
$311$	−2.37574e8	+	8.64698e7i	−0.447855	+	0.163006i	−0.556095	−	0.831119i	$-0.687701\pi$
$311$	−2.37574e8	+	8.64698e7i	−0.447855	+	0.163006i	0.108240	+	0.994125i	$0.465479\pi$
$312$	−1.74397e8	+	2.86135e8i	−0.325086	+	0.533372i
$313$	−4.63659e7	−	2.62954e8i	−0.0854660	−	0.484702i	−0.997255	−	0.0740429i	$-0.976410\pi$
$313$	−4.63659e7	−	2.62954e8i	−0.0854660	−	0.484702i	0.911789	−	0.410659i	$-0.134701\pi$
$314$	−2.47346e8	+	4.28416e8i	−0.450870	+	0.780929i
$315$	−4.26903e8	−	3.94266e8i	−0.769560	−	0.710726i
$316$	−6.88709e8	−	1.19288e9i	−1.22781	−	2.12663i
$317$	−5.13358e8	+	4.30758e8i	−0.905133	+	0.759497i	−0.971187	−	0.238319i	$-0.923404\pi$
$317$	−5.13358e8	+	4.30758e8i	−0.905133	+	0.759497i	0.0660535	+	0.997816i	$0.478959\pi$
$318$	1.07526e8	−	5.35102e8i	0.187507	−	0.933129i
$319$	9.12589e7	−	5.17555e8i	0.157401	−	0.892667i
$320$	5.83032e8	+	4.89222e8i	0.994644	+	0.834605i
$321$	1.42227e8	+	9.36227e8i	0.240001	+	1.57984i
$322$	1.97242e9	+	7.17904e8i	3.29234	+	1.19831i
$323$	2.39108e8			0.394807
$324$	8.51336e8	+	8.11934e7i	1.39057	+	0.132621i
$325$	−2.00868e8			−0.324579
$326$	−1.58540e9	−	5.77038e8i	−2.53441	−	0.922449i
$327$	4.57156e7	+	3.00930e8i	0.0723016	+	0.475936i
$328$	8.82287e7	+	7.40327e7i	0.138055	+	0.115842i
$329$	2.12848e8	−	1.20712e9i	0.329522	−	1.86881i
$330$	−1.38758e8	+	6.90526e8i	−0.212549	+	1.05775i
$331$	−2.33055e7	+	1.95556e7i	−0.0353232	+	0.0296397i	−0.660278	−	0.751021i	$-0.729562\pi$
$331$	−2.33055e7	+	1.95556e7i	−0.0353232	+	0.0296397i	0.624955	+	0.780661i	$0.285117\pi$
$332$	−1.78648e8	−	3.09427e8i	−0.267926	−	0.464061i
$333$	1.95774e8	−	8.67026e8i	0.290536	−	1.28670i
$334$	−8.45648e7	+	1.46471e8i	−0.124187	+	0.215099i
$335$	1.65827e8	+	9.40453e8i	0.240990	+	1.36672i
$336$	2.04739e8	−	3.35917e8i	0.294451	−	0.483108i
$337$	−6.64502e8	+	2.41859e8i	−0.945784	+	0.344237i	−0.768447	−	0.639913i	$-0.778970\pi$
$337$	−6.64502e8	+	2.41859e8i	−0.945784	+	0.344237i	−0.177337	+	0.984150i	$0.556748\pi$
$338$	−3.45247e7	+	1.25660e7i	−0.0486319	+	0.0177006i
$339$	5.21417e8	+	1.23970e7i	0.726919	+	0.0172829i
$340$	−1.53897e8	−	8.72794e8i	−0.212351	−	1.20430i
$341$	2.46030e7	−	4.26136e7i	0.0336007	−	0.0581980i
$342$	−1.95293e8	−	3.78762e8i	−0.263995	−	0.512006i
$343$	1.84056e8	+	3.18795e8i	0.246275	+	0.426562i
$344$	2.43259e7	−	2.04118e7i	0.0322191	−	0.0270351i
$345$	8.41847e8	+	7.41196e8i	1.10374	+	0.971776i
$346$	5.55543e7	−	3.15064e8i	0.0721026	−	0.408914i
$347$	−1.57729e7	−	1.32350e7i	−0.0202655	−	0.0170048i	0.632599	−	0.774480i	$-0.281988\pi$
$347$	−1.57729e7	−	1.32350e7i	−0.0202655	−	0.0170048i	−0.652864	+	0.757475i	$0.726433\pi$
$348$	9.20584e8	−	7.35893e8i	1.17094	−	0.936025i
$349$	−1.24307e8	−	4.52439e7i	−0.156533	−	0.0569733i	0.262565	−	0.964914i	$-0.415431\pi$
$349$	−1.24307e8	−	4.52439e7i	−0.156533	−	0.0569733i	−0.419098	+	0.907941i	$0.637654\pi$
$350$	−5.03422e8			−0.627616
$351$	5.91588e8	+	5.73007e8i	0.730204	+	0.707270i
$352$	−9.01480e8			−1.10168
$353$	5.68285e8	+	2.06839e8i	0.687630	+	0.250277i	0.662120	−	0.749398i	$-0.269657\pi$
$353$	5.68285e8	+	2.06839e8i	0.687630	+	0.250277i	0.0255098	+	0.999675i	$0.491879\pi$
$354$	1.28964e9	+	5.04419e8i	1.54511	+	0.604338i
$355$	−7.75546e8	−	6.50760e8i	−0.920043	−	0.772008i
$356$	2.04557e8	−	1.16010e9i	0.240292	−	1.36276i
$357$	−1.09743e9	+	3.70137e8i	−1.27655	+	0.430550i
$358$	4.20021e8	−	3.52439e8i	0.483816	−	0.405970i
$359$	−5.23792e8	−	9.07235e8i	−0.597487	−	1.03488i	−0.993191	−	0.116500i	$-0.962833\pi$
$359$	−5.23792e8	−	9.07235e8i	−0.597487	−	1.03488i	0.395704	−	0.918378i	$-0.370501\pi$
$360$	−3.57100e8	+	2.71801e8i	−0.403395	+	0.307038i
$361$	3.85059e8	−	6.66941e8i	0.430776	−	0.746126i
$362$	−8.42782e7	−	4.77966e8i	−0.0933760	−	0.529562i
$363$	1.25173e8	+	2.29221e8i	0.137352	+	0.251525i
$364$	−1.55895e9	+	5.67411e8i	−1.69425	+	0.616656i
$365$	−4.90232e8	+	1.78430e8i	−0.527687	+	0.192062i
$366$	9.59191e8	+	1.75651e9i	1.02264	+	1.87269i
$367$	−1.79776e8	−	1.01956e9i	−0.189846	−	1.07667i	−0.919569	−	0.392928i	$-0.871462\pi$
$367$	−1.79776e8	−	1.01956e9i	−0.189846	−	1.07667i	0.729723	−	0.683743i	$-0.239649\pi$
$368$	−3.79656e8	+	6.57583e8i	−0.397121	+	0.687833i
$369$	2.25252e8	−	1.71447e8i	0.233387	−	0.177639i
$370$	8.20838e8	+	1.42173e9i	0.842464	+	1.45919i
$371$	5.88122e8	−	4.93493e8i	0.597942	−	0.501733i
$372$	1.04561e8	−	3.52661e7i	0.105310	−	0.0355187i
$373$	−1.43167e8	+	8.11942e8i	−0.142844	+	0.810110i	0.826228	+	0.563335i	$0.190482\pi$
$373$	−1.43167e8	+	8.11942e8i	−0.142844	+	0.810110i	−0.969073	+	0.246775i	$0.920629\pi$
$374$	1.07533e9	+	9.02308e8i	1.06290	+	0.891875i
$375$	−1.03519e9	−	4.04894e8i	−1.01370	−	0.396489i
$376$	−8.89510e8	−	3.23755e8i	−0.862965	−	0.314094i
$377$	1.13501e9			1.09095
$378$	1.48265e9	+	1.43609e9i	1.41195	+	1.36760i
$379$	2.48784e8			0.234739			0.117369	−	0.993088i	$-0.462554\pi$
$379$	2.48784e8			0.234739			0.117369	+	0.993088i	$0.462554\pi$
$380$	4.31036e8	+	1.56884e8i	0.402968	+	0.146668i
$381$	−4.31462e8	+	3.44900e8i	−0.399673	+	0.319489i
$382$	−4.47764e7	−	3.75718e7i	−0.0410986	−	0.0344858i
$383$	8.95175e6	−	5.07679e7i	0.00814165	−	0.0461736i	−0.980466	−	0.196687i	$-0.936982\pi$
$383$	8.95175e6	−	5.07679e7i	0.00814165	−	0.0461736i	0.988608	+	0.150514i	$0.0480928\pi$
$384$	−9.42817e8	−	8.30093e8i	−0.849705	−	0.748114i
$385$	−7.58947e8	+	6.36832e8i	−0.677796	+	0.568738i
$386$	3.19285e8	+	5.53018e8i	0.282568	+	0.489422i
$387$	−3.57678e7	−	6.93700e7i	−0.0313692	−	0.0608392i
$388$	−6.15813e8	+	1.06662e9i	−0.535227	+	0.927040i
$389$	−1.45469e8	−	8.24998e8i	−0.125299	−	0.710607i	−0.981130	−	0.193351i	$-0.938065\pi$
$389$	−1.45469e8	−	8.24998e8i	−0.125299	−	0.710607i	0.855831	−	0.517256i	$-0.173047\pi$
$390$	−1.52072e9	−	3.61559e7i	−1.29814	−	0.0308640i
$391$	2.10064e9	−	7.64569e8i	1.77718	−	0.646842i
$392$	−4.21472e8	+	1.53403e8i	−0.353401	+	0.128627i
$393$	−2.25243e8	+	3.69559e8i	−0.187188	+	0.307121i
$394$	5.71055e6	+	3.23861e7i	0.00470372	+	0.0266761i
$395$	8.88267e8	−	1.53852e9i	0.725193	−	1.25607i
$396$	3.21135e8	−	1.42222e9i	0.259869	−	1.15089i
$397$	−3.58350e8	−	6.20681e8i	−0.287436	−	0.497853i	0.685761	−	0.727827i	$-0.259469\pi$
$397$	−3.58350e8	−	6.20681e8i	−0.287436	−	0.497853i	−0.973197	+	0.229973i	$0.926136\pi$
$398$	2.26070e9	−	1.89695e9i	1.79743	−	1.50822i
$399$	1.18092e8	−	5.87684e8i	0.0930712	−	0.463168i
$400$	3.16234e7	−	1.79345e8i	0.0247058	−	0.140113i
$401$	−4.22468e7	−	3.54493e7i	−0.0327181	−	0.0274538i	0.626282	−	0.779597i	$-0.284576\pi$
$401$	−4.22468e7	−	3.54493e7i	−0.0327181	−	0.0274538i	−0.659000	+	0.752143i	$0.729020\pi$
$402$	−5.09455e8	−	3.35356e9i	−0.391124	−	2.57463i
$403$	9.98619e7	+	3.63468e7i	0.0760033	+	0.0276629i
$404$	−3.09355e7			−0.0233412
$405$	4.58318e8	+	1.00327e9i	0.342827	+	0.750456i
$406$	2.84460e9			2.10951
$407$	−1.42401e9	−	5.18298e8i	−1.04697	−	0.381065i
$408$	1.34333e8	+	8.84265e8i	0.0979201	+	0.644573i
$409$	7.02207e8	+	5.89222e8i	0.507497	+	0.425841i	0.860247	−	0.509877i	$-0.170309\pi$
$409$	7.02207e8	+	5.89222e8i	0.507497	+	0.425841i	−0.352750	+	0.935718i	$0.614753\pi$
$410$	−9.07888e7	+	5.14889e8i	−0.0650562	+	0.368952i
$411$	7.68269e7	−	3.82328e8i	0.0545842	−	0.271638i
$412$	−2.81913e9	+	2.36553e9i	−1.98598	+	1.66643i
$413$	9.73942e8	+	1.68692e9i	0.680312	+	1.17833i
$414$	−2.92684e9	−	2.70307e9i	−2.02720	−	1.87222i
$415$	2.30412e8	−	3.99086e8i	0.158248	−	0.274093i
$416$	−3.38082e8	−	1.91736e9i	−0.230248	−	1.30580i
$417$	−6.47525e8	+	1.06240e9i	−0.437301	+	0.717485i
$418$	−6.82717e8	+	2.48489e8i	−0.457218	+	0.166414i
$419$	−1.71682e9	+	6.24871e8i	−1.14019	+	0.414994i	−0.841980	−	0.539508i	$-0.818610\pi$
$419$	−1.71682e9	+	6.24871e8i	−1.14019	+	0.414994i	−0.298205	+	0.954502i	$0.596388\pi$
$420$	−2.22118e9	−	5.28096e7i	−1.46289	−	0.0347808i
$421$	−4.30655e8	−	2.44236e9i	−0.281282	−	1.59523i	−0.718272	−	0.695763i	$-0.755067\pi$
$421$	−4.30655e8	−	2.44236e9i	−0.281282	−	1.59523i	0.436990	−	0.899466i	$-0.356045\pi$
$422$	−9.36916e8	+	1.62279e9i	−0.606886	+	1.05116i
$423$	−1.25772e9	+	1.95730e9i	−0.807965	+	1.25738i
$424$	−2.96448e8	−	5.13464e8i	−0.188872	−	0.327137i
$425$	−4.10712e8	+	3.44628e8i	−0.259523	+	0.217766i
$426$	2.69903e9	+	2.37634e9i	1.69151	+	1.48927i
$427$	−4.88847e8	+	2.77239e9i	−0.303861	+	1.72328i
$428$	2.77354e9	+	2.32728e9i	1.70994	+	1.43481i
$429$	1.09679e9	−	8.76746e8i	0.670690	−	0.536134i
$430$	1.35458e8	+	4.93029e7i	0.0821612	+	0.0299042i
$431$	−1.25952e9			−0.757765			−0.378883	−	0.925445i	$-0.623692\pi$
$431$	−1.25952e9			−0.757765			−0.378883	+	0.925445i	$0.623692\pi$
$432$	−6.04744e8	+	4.37988e8i	−0.360893	+	0.261378i
$433$	−8.82502e8			−0.522406			−0.261203	−	0.965284i	$-0.584119\pi$
$433$	−8.82502e8			−0.522406			−0.261203	+	0.965284i	$0.584119\pi$
$434$	2.50277e8	+	9.10933e7i	0.146963	+	0.0534900i
$435$	1.41563e9	+	5.53696e8i	0.824588	+	0.322522i
$436$	8.91495e8	+	7.48053e8i	0.515129	+	0.432245i
$437$	−2.00911e8	+	1.13942e9i	−0.115164	+	0.653129i
$438$	1.75588e9	−	5.92218e8i	0.998474	−	0.336761i
$439$	−2.45599e9	+	2.06082e9i	−1.38548	+	1.16256i	−0.418351	+	0.908286i	$0.637392\pi$
$439$	−2.45599e9	+	2.06082e9i	−1.38548	+	1.16256i	−0.967133	+	0.254273i	$0.918164\pi$
$440$	3.82554e8	+	6.62603e8i	0.214096	+	0.370825i
$441$	1.39616e8	+	1.09350e9i	0.0775178	+	0.607135i
$442$	−1.51584e9	+	2.62551e9i	−0.834979	+	1.44623i
$443$	−2.35212e8	−	1.33395e9i	−0.128543	−	0.729001i	−0.979141	−	0.203184i	$-0.934871\pi$
$443$	−2.35212e8	−	1.33395e9i	−0.128543	−	0.729001i	0.850598	−	0.525817i	$-0.176240\pi$
$444$	−1.62877e9	−	2.98267e9i	−0.883120	−	1.61720i
$445$	1.42770e9	−	5.19641e8i	0.768028	−	0.279539i
$446$	−1.02091e9	+	3.71582e8i	−0.544899	+	0.198327i
$447$	−6.58787e8	−	1.20639e9i	−0.348874	−	0.638871i
$448$	−6.60337e8	−	3.74496e9i	−0.346971	−	1.96777i
$449$	4.55200e8	−	7.88429e8i	0.237323	−	0.411056i	−0.722622	−	0.691243i	$-0.757063\pi$
$449$	4.55200e8	−	7.88429e8i	0.237323	−	0.411056i	0.959945	+	0.280188i	$0.0903967\pi$
$450$	8.81364e8	+	3.69116e8i	0.455944	+	0.190950i
$451$	−2.41308e8	−	4.17958e8i	−0.123867	−	0.214543i
$452$	1.52759e9	−	1.28180e9i	0.778077	−	0.652884i
$453$	−1.87441e9	+	6.32192e8i	−0.947371	+	0.319526i
$454$	2.33894e8	−	1.32648e9i	0.117307	−	0.665282i
$455$	−1.63911e9	−	1.37537e9i	−0.815770	−	0.684512i
$456$	−4.31115e8	−	1.68622e8i	−0.212920	−	0.0832794i
$457$	3.65382e8	+	1.32988e8i	0.179077	+	0.0651788i	0.430003	−	0.902828i	$-0.358513\pi$
$457$	3.65382e8	+	1.32988e8i	0.179077	+	0.0651788i	−0.250925	+	0.968006i	$0.580735\pi$
$458$	−4.56133e9			−2.21852
$459$	2.19271e9	+	1.56634e8i	1.05837	+	0.0756037i
$460$	4.28844e9			2.05422
$461$	9.51312e8	+	3.46249e8i	0.452241	+	0.164602i	0.558091	−	0.829780i	$-0.311534\pi$
$461$	9.51312e8	+	3.46249e8i	0.452241	+	0.164602i	−0.105850	+	0.994382i	$0.533756\pi$
$462$	2.74880e9	−	2.19733e9i	1.29687	−	1.03669i
$463$	−4.67271e7	−	3.92087e7i	−0.0218794	−	0.0183590i	0.631782	−	0.775146i	$-0.282324\pi$
$463$	−4.67271e7	−	3.92087e7i	−0.0218794	−	0.0183590i	−0.653662	+	0.756787i	$0.726768\pi$
$464$	−1.78689e8	+	1.01339e9i	−0.0830395	+	0.470940i
$465$	1.06820e8	+	9.40488e7i	0.0492684	+	0.0433778i
$466$	2.81679e9	−	2.36357e9i	1.28945	−	1.08198i
$467$	9.95176e8	+	1.72370e9i	0.452159	+	0.783162i	0.998520	−	0.0543880i	$-0.0173208\pi$
$467$	9.95176e8	+	1.72370e9i	0.452159	+	0.783162i	−0.546361	+	0.837550i	$0.683987\pi$
$468$	3.14535e9	+	1.49649e8i	1.41843	+	0.0674861i
$469$	2.38568e9	−	4.13212e9i	1.06784	−	1.84956i
$470$	−7.46176e8	−	4.23177e9i	−0.331512	−	1.88010i
$471$	1.32041e9	+	3.13934e7i	0.582284	+	0.0138441i
$472$	1.41356e9	−	5.14494e8i	0.618753	−	0.225208i
$473$	−1.25039e8	+	4.55106e7i	−0.0543291	+	0.0197742i
$474$	−3.28414e9	+	5.38833e9i	−1.41644	+	2.32397i
$475$	−4.81860e7	−	2.73276e8i	−0.0206297	−	0.116997i
$476$	−2.21405e9	+	3.83484e9i	−0.940942	+	1.62976i
$477$	−1.39149e9	+	4.32762e8i	−0.587036	+	0.182572i
$478$	3.30978e9	+	5.73271e9i	1.38612	+	2.40084i
$479$	−8.28100e8	+	6.94859e8i	−0.344278	+	0.288883i	−0.798487	−	0.602012i	$-0.794366\pi$
$479$	−8.28100e8	+	6.94859e8i	−0.344278	+	0.288883i	0.454210	+	0.890895i	$0.349922\pi$
$480$	5.13681e8	−	2.55633e9i	0.212006	−	1.05505i
$481$	5.68321e8	−	3.22311e9i	0.232855	−	1.32059i
$482$	3.16022e9	+	2.65174e9i	1.28544	+	1.07861i
$483$	−8.41697e8	−	5.54059e9i	−0.339892	−	2.23739i
$484$	9.38331e8	+	3.41525e8i	0.376181	+	0.136919i
$485$	−1.58850e9			−0.632252
$486$	−1.54279e9	−	3.60132e9i	−0.609650	−	1.42310i
$487$	6.04240e8			0.237060			0.118530	−	0.992950i	$-0.462182\pi$
$487$	6.04240e8			0.237060			0.118530	+	0.992950i	$0.462182\pi$
$488$	2.04293e9	+	7.43566e8i	0.795764	+	0.289634i
$489$	6.76540e8	+	4.45342e9i	0.261645	+	1.72232i
$490$	−1.55971e9	−	1.30875e9i	−0.598903	−	0.502539i
$491$	2.57128e8	−	1.45825e9i	0.0980312	−	0.555962i	−0.895745	−	0.444568i	$-0.853357\pi$
$491$	2.57128e8	−	1.45825e9i	0.0980312	−	0.555962i	0.993776	−	0.111394i	$-0.0355317\pi$
$492$	2.13222e8	−	1.06110e9i	0.0807149	−	0.401677i
$493$	2.32074e9	−	1.94733e9i	0.872293	−	0.731940i
$494$	−7.84550e8	−	1.35888e9i	−0.292804	−	0.507151i
$495$	1.79566e9	−	5.58461e8i	0.665434	−	0.206954i
$496$	−4.81737e7	+	8.34393e7i	−0.0177266	+	0.0307033i
$497$	8.78376e8	+	4.98152e9i	0.320947	+	1.82018i
$498$	−8.51891e8	+	1.39771e9i	−0.309087	+	0.507123i
$499$	−2.58862e9	+	9.42180e8i	−0.932644	+	0.339455i	−0.763257	−	0.646095i	$-0.776401\pi$
$499$	−2.58862e9	+	9.42180e8i	−0.932644	+	0.339455i	−0.169387	+	0.985550i	$0.554179\pi$
$500$	−3.99357e9	+	1.45354e9i	−1.42878	+	0.520035i
$501$	4.51433e8	+	1.07330e7i	0.160384	+	0.00381321i
$502$	−7.83268e8	−	4.44213e9i	−0.276342	−	1.56722i
$503$	1.60198e9	−	2.77472e9i	0.561268	−	0.972145i	−0.436118	−	0.899889i	$-0.643647\pi$
$503$	1.60198e9	−	2.77472e9i	0.561268	−	0.972145i	0.997386	−	0.0722554i	$-0.0230197\pi$
$504$	2.23971e9	+	1.06561e8i	0.779264	+	0.0370758i
$505$	−1.99496e7	−	3.45538e7i	−0.00689311	−	0.0119392i
$506$	−5.20331e9	+	4.36610e9i	−1.78547	+	1.49819i
$507$	7.36240e7	+	6.48215e7i	0.0250895	+	0.0220898i
$508$	−3.66731e8	+	2.07983e9i	−0.124115	+	0.703892i
$509$	3.51368e9	+	2.94833e9i	1.18100	+	0.990976i	0.999972	+	0.00749826i	$0.00238679\pi$
$509$	3.51368e9	+	2.94833e9i	1.18100	+	0.990976i	0.181028	+	0.983478i	$0.442058\pi$
$510$	−3.17142e9	+	2.53516e9i	−1.05866	+	0.846270i
$511$	2.44939e9	+	8.91506e8i	0.812054	+	0.295564i
$512$	2.59667e9			0.855010
$513$	−6.37646e8	+	9.42297e8i	−0.208530	+	0.308161i
$514$	−7.21391e9			−2.34315
$515$	−4.46020e9	−	1.62338e9i	−1.43890	−	0.523715i
$516$	−2.77906e8	−	1.08697e8i	−0.0890478	−	0.0348293i
$517$	3.03854e9	+	2.54964e9i	0.967048	+	0.811450i
$518$	1.42434e9	−	8.07785e9i	0.450257	−	2.55353i
$519$	−8.09372e8	+	2.72982e8i	−0.254134	+	0.0857133i
$520$	−1.26582e9	+	1.06215e9i	−0.394785	+	0.331264i
$521$	4.84337e8	+	8.38897e8i	0.150043	+	0.259882i	0.931243	−	0.364399i	$-0.118725\pi$
$521$	4.84337e8	+	8.38897e8i	0.150043	+	0.259882i	−0.781200	+	0.624281i	$0.785392\pi$
$522$	−4.98018e9	−	2.08570e9i	−1.53249	−	0.641808i
$523$	5.98358e8	−	1.03639e9i	0.182896	−	0.316786i	−0.759969	−	0.649959i	$-0.774786\pi$
$523$	5.98358e8	−	1.03639e9i	0.182896	−	0.316786i	0.942866	+	0.333173i	$0.108119\pi$
$524$	2.87339e8	+	1.62958e9i	0.0872438	+	0.494784i
$525$	6.44188e8	+	1.17966e9i	0.194292	+	0.355795i
$526$	−2.26349e9	+	8.23842e8i	−0.678154	+	0.246828i
$527$	2.66545e8	−	9.70146e7i	0.0793294	−	0.0288735i
$528$	6.10130e8	+	1.11729e9i	0.180386	+	0.330330i
$529$	1.28710e9	+	7.29950e9i	0.378022	+	2.14387i
$530$	1.34572e9	−	2.33086e9i	0.392636	−	0.680065i
$531$	−4.68255e8	−	3.66747e9i	−0.135722	−	1.06301i
$532$	−1.14592e9	−	1.98479e9i	−0.329962	−	0.571511i
$533$	7.98458e8	−	6.69986e8i	0.228406	−	0.191655i
$534$	−5.11366e9	+	1.72472e9i	−1.45324	+	0.490143i
$535$	−8.10884e8	+	4.59875e9i	−0.228939	+	1.29838i
$536$	−2.82268e9	−	2.36851e9i	−0.791745	−	0.664353i
$537$	−1.36333e9	−	5.33241e8i	−0.379919	−	0.148598i
$538$	−3.77225e9	−	1.37299e9i	−1.04439	−	0.380127i
$539$	1.87944e9			0.516974
$540$	3.84999e9	+	1.72105e9i	1.05216	+	0.470344i
$541$	−2.76050e9			−0.749544			−0.374772	−	0.927117i	$-0.622279\pi$
$541$	−2.76050e9			−0.749544			−0.374772	+	0.927117i	$0.622279\pi$
$542$	3.42624e9	+	1.24705e9i	0.924316	+	0.336424i
$543$	−1.01217e9	+	8.09101e8i	−0.271301	+	0.216872i
$544$	−3.98086e9	−	3.34034e9i	−1.06018	−	0.889600i
$545$	−2.60641e8	+	1.47817e9i	−0.0689692	+	0.391144i
$546$	5.70438e9	+	5.02236e9i	1.49980	+	1.32049i
$547$	−1.62513e9	+	1.36365e9i	−0.424553	+	0.356243i	−0.829892	−	0.557924i	$-0.811598\pi$
$547$	−1.62513e9	+	1.36365e9i	−0.424553	+	0.356243i	0.405339	+	0.914167i	$0.367154\pi$
$548$	−7.45500e8	−	1.29124e9i	−0.193515	−	0.335178i
$549$	2.88859e9	−	4.49531e9i	0.745047	−	1.15946i
$550$	8.14543e8	−	1.41083e9i	0.208759	−	0.361581i
$551$	2.72277e8	+	1.54416e9i	0.0693393	+	0.393243i
$552$	−4.32666e9	−	1.02869e8i	−1.09488	−	0.0260313i
$553$	−8.34097e9	+	3.03586e9i	−2.09739	+	0.763386i
$554$	8.39693e9	−	3.05623e9i	2.09815	−	0.763664i
$555$	2.28117e9	−	3.74273e9i	0.566411	−	0.929316i
$556$	8.26036e8	+	4.68468e9i	0.203816	+	1.15590i
$557$	3.23479e9	−	5.60281e9i	0.793145	−	1.37377i	−0.130866	−	0.991400i	$-0.541776\pi$
$557$	3.23479e9	−	5.60281e9i	0.793145	−	1.37377i	0.924011	−	0.382367i	$-0.124891\pi$
$558$	−3.71380e8	−	3.42987e8i	−0.0904896	−	0.0835715i
$559$	−1.43690e8	−	2.48878e8i	−0.0347925	−	0.0602623i
$560$	1.48605e9	−	1.24694e9i	0.357582	−	0.300047i
$561$	7.38354e8	−	3.67441e9i	0.176561	−	0.878653i
$562$	3.44822e8	−	1.95558e9i	0.0819441	−	0.464728i
$563$	−3.43877e9	−	2.88547e9i	−0.812128	−	0.681456i	0.138987	−	0.990294i	$-0.455615\pi$
$563$	−3.43877e9	−	2.88547e9i	−0.812128	−	0.681456i	−0.951115	+	0.308838i	$0.900060\pi$
$564$	1.33599e9	+	8.79437e9i	0.313565	+	2.06409i
$565$	2.41683e9	+	8.79655e8i	0.563738	+	0.205184i
$566$	−4.62488e9			−1.07212
$567$	1.46793e9	−	5.31192e9i	0.338192	−	1.22380i
$568$	3.90639e9			0.894451
$569$	3.71235e9	+	1.35119e9i	0.844805	+	0.307484i	0.727920	−	0.685662i	$-0.240487\pi$
$569$	3.71235e9	+	1.35119e9i	0.844805	+	0.307484i	0.116885	+	0.993145i	$0.462709\pi$
$570$	−3.15614e8	−	2.07757e9i	−0.0713828	−	0.469888i
$571$	6.17683e9	+	5.18298e9i	1.38848	+	1.16507i	0.965952	+	0.258722i	$0.0833013\pi$
$571$	6.17683e9	+	5.18298e9i	1.38848	+	1.16507i	0.422527	+	0.906350i	$0.361143\pi$
$572$	9.32240e8	−	5.28699e9i	0.208277	−	1.18120i
$573$	−3.07448e7	+	1.53001e8i	−0.00682702	+	0.0339746i
$574$	2.00112e9	−	1.67914e9i	0.441653	−	0.370591i
$575$	−1.29715e9	−	2.24674e9i	−0.284547	−	0.492850i
$576$	−1.58977e9	+	7.04063e9i	−0.346621	+	1.53509i
$577$	7.53097e8	−	1.30440e9i	0.163206	−	0.282681i	−0.772811	−	0.634636i	$-0.781150\pi$
$577$	7.53097e8	−	1.30440e9i	0.163206	−	0.282681i	0.936017	+	0.351956i	$0.114483\pi$
$578$	1.57081e8	+	8.90849e8i	0.0338357	+	0.191892i
$579$	8.87315e8	−	1.45583e9i	0.189978	−	0.311698i
$580$	5.46125e9	−	1.98773e9i	1.16224	−	0.423019i
$581$	−2.16361e9	+	7.87488e8i	−0.457680	+	0.166582i
$582$	5.64078e9	+	1.34112e8i	1.18607	+	0.0281993i
$583$	4.31415e8	+	2.44668e9i	0.0901687	+	0.511372i
$584$	1.00649e9	−	1.74328e9i	0.209104	−	0.362179i
$585$	1.86122e9	+	3.60974e9i	0.384372	+	0.745471i
$586$	−3.61662e9	−	6.26417e9i	−0.742439	−	1.28594i
$587$	1.05438e9	−	8.84728e8i	0.215161	−	0.180541i	−0.528837	−	0.848723i	$-0.677372\pi$
$587$	1.05438e9	−	8.84728e8i	0.215161	−	0.180541i	0.743998	+	0.668182i	$0.232927\pi$
$588$	3.16342e9	+	2.78520e9i	0.641706	+	0.564983i
$589$	−2.54931e7	+	1.44579e8i	−0.00514067	+	0.0291542i
$590$	5.23104e9	+	4.38937e9i	1.04859	+	0.879873i
$591$	6.85826e7	−	5.48233e7i	0.0136665	−	0.0109247i
$592$	2.78827e9	+	1.01485e9i	0.552344	+	0.201037i
$593$	4.57156e9			0.900271			0.450136	−	0.892960i	$-0.351376\pi$
$593$	4.57156e9			0.900271			0.450136	+	0.892960i	$0.351376\pi$
$594$	−6.42355e9	+	1.83150e9i	−1.25754	+	0.358554i
$595$	−5.71117e9			−1.11152
$596$	−4.93846e9	−	1.79745e9i	−0.955498	−	0.347773i
$597$	−7.33793e9	−	2.87009e9i	−1.41144	−	0.552058i
$598$	−1.12377e10	−	9.42952e9i	−2.14893	−	1.80317i
$599$	−1.12694e9	+	6.39119e9i	−0.214243	+	1.21503i	0.667972	+	0.744186i	$0.267162\pi$
$599$	−1.12694e9	+	6.39119e9i	−0.214243	+	1.21503i	−0.882215	+	0.470846i	$0.843949\pi$
$600$	9.83556e8	−	3.31730e8i	0.185896	−	0.0626982i
$601$	5.32078e9	−	4.46466e9i	0.999803	−	0.838934i	0.0128458	−	0.999917i	$-0.495911\pi$
$601$	5.32078e9	−	4.46466e9i	0.999803	−	0.838934i	0.986957	+	0.160983i	$0.0514665\pi$
$602$	−3.60120e8	−	6.23746e8i	−0.0672759	−	0.116525i
$603$	−7.20645e9	+	5.48508e9i	−1.33848	+	1.01876i
$604$	−3.78158e9	+	6.54990e9i	−0.698304	+	1.20950i
$605$	2.23639e8	+	1.26832e9i	0.0410586	+	0.232855i
$606$	6.79242e7	+	1.24385e8i	0.0123985	+	0.0227046i
$607$	1.18260e9	−	4.30431e8i	0.214624	−	0.0781166i	−0.232471	−	0.972603i	$-0.574681\pi$
$607$	1.18260e9	−	4.30431e8i	0.214624	−	0.0781166i	0.447094	+	0.894487i	$0.352459\pi$
$608$	2.52742e9	−	9.19904e8i	0.456052	−	0.165989i
$609$	−3.64001e9	−	6.66572e9i	−0.653043	−	1.19588i
$610$	1.71374e9	+	9.71908e9i	0.305696	+	1.73369i
$611$	−4.28329e9	+	7.41887e9i	−0.759684	+	1.31581i
$612$	6.68799e9	−	5.09046e9i	1.17941	−	0.897692i
$613$	−3.71922e9	−	6.44188e9i	−0.652140	−	1.12954i	−0.982603	−	0.185720i	$-0.940538\pi$
$613$	−3.71922e9	−	6.44188e9i	−0.652140	−	1.12954i	0.330463	−	0.943819i	$-0.392795\pi$
$614$	4.50079e9	−	3.77661e9i	0.784693	−	0.658436i
$615$	1.32271e9	−	4.46117e8i	0.229298	−	0.0773367i
$616$	6.63819e8	−	3.76471e9i	0.114424	−	0.648931i
$617$	1.32701e9	+	1.11349e9i	0.227444	+	0.190848i	0.749387	−	0.662132i	$-0.230348\pi$
$617$	1.32701e9	+	1.11349e9i	0.227444	+	0.190848i	−0.521943	+	0.852980i	$0.674793\pi$
$618$	1.57012e10	+	6.14121e9i	2.67592	+	1.04663i
$619$	−7.25643e9	−	2.64112e9i	−1.22972	−	0.447581i	−0.356217	−	0.934403i	$-0.615934\pi$
$619$	−7.25643e9	−	2.64112e9i	−1.22972	−	0.447581i	−0.873501	+	0.486822i	$0.838156\pi$
$620$	5.44151e8			0.0916956
$621$	−2.58884e9	+	1.03173e10i	−0.433794	+	1.72880i
$622$	4.42834e9			0.737861
$623$	−7.13336e9	−	2.59633e9i	−1.18191	−	0.430182i
$624$	−2.14756e9	+	1.71671e9i	−0.353833	+	0.282846i
$625$	−2.70608e9	−	2.27067e9i	−0.443364	−	0.372026i
$626$	−8.12133e8	+	4.60583e9i	−0.132317	+	0.750409i
$627$	1.45590e9	+	1.28183e9i	0.235882	+	0.207680i
$628$	3.86839e9	−	3.24596e9i	0.623263	−	0.522980i
$629$	−4.36782e9	−	7.56529e9i	−0.699822	−	1.21213i
$630$	4.66464e9	+	9.04684e9i	0.743234	+	1.44147i
$631$	5.50653e9	−	9.53759e9i	0.872520	−	1.51125i	0.0131385	−	0.999914i	$-0.495818\pi$
$631$	5.50653e9	−	9.53759e9i	0.872520	−	1.51125i	0.859381	−	0.511335i	$-0.170849\pi$
$632$	1.19033e9	+	6.75068e9i	0.187567	+	1.06374i
$633$	5.00154e9	+	1.18914e8i	0.783774	+	0.0186346i
$634$	1.10301e10	−	4.01463e9i	1.71897	−	0.625653i
$635$	−2.55959e9	+	9.31616e8i	−0.396701	+	0.144387i
$636$	−2.89966e9	+	4.75750e9i	−0.446938	+	0.733295i
$637$	7.04848e8	+	3.99739e9i	0.108046	+	0.612757i
$638$	−4.60260e9	+	7.97194e9i	−0.701667	+	1.21532i
$639$	2.11470e9	−	9.36540e9i	0.320624	−	1.41995i
$640$	−3.09721e9	−	5.36453e9i	−0.467026	−	0.808912i
$641$	−8.26242e9	+	6.93300e9i	−1.23909	+	1.03972i	−0.241500	+	0.970401i	$0.577639\pi$
$641$	−8.26242e9	+	6.93300e9i	−1.23909	+	1.03972i	−0.997594	+	0.0693229i	$0.977916\pi$
$642$	3.26772e9	−	1.62618e10i	0.487385	−	2.42547i
$643$	−5.08411e8	+	2.88334e9i	−0.0754183	+	0.427718i	0.923598	+	0.383364i	$0.125234\pi$
$643$	−5.08411e8	+	2.88334e9i	−0.0754183	+	0.427718i	−0.999016	+	0.0443549i	$0.985877\pi$
$644$	−1.64138e10	−	1.37728e10i	−2.42164	−	2.03200i
$645$	−5.78045e7	−	3.80507e8i	−0.00848209	−	0.0558346i
$646$	−3.93557e9	−	1.43243e9i	−0.574373	−	0.209055i
$647$	6.62258e9			0.961307			0.480654	−	0.876911i	$-0.340399\pi$
$647$	6.62258e9			0.961307			0.480654	+	0.876911i	$0.340399\pi$
$648$	−3.84303e9	−	1.82874e9i	−0.554831	−	0.264022i
$649$	−6.30340e9			−0.905145
$650$	3.30618e9	+	1.20335e9i	0.472203	+	0.171868i
$651$	−1.06801e8	−	7.03034e8i	−0.0151720	−	0.0998718i
$652$	1.31931e10	+	1.10703e10i	1.86415	+	1.56421i
$653$	3.30249e8	−	1.87294e9i	0.0464136	−	0.263225i	−0.952767	−	0.303703i	$-0.901777\pi$
$653$	3.30249e8	−	1.87294e9i	0.0464136	−	0.263225i	0.999180	+	0.0404781i	$0.0128881\pi$
$654$	1.05034e9	−	5.22700e9i	0.146827	−	0.730685i
$655$	−1.63488e9	+	1.37183e9i	−0.227322	+	0.190746i
$656$	4.72492e8	+	8.18380e8i	0.0653478	+	0.113186i
$657$	−3.63460e9	−	3.35672e9i	−0.500008	−	0.461782i
$658$	−1.07349e10	+	1.85934e10i	−1.46895	+	2.54430i
$659$	8.20340e8	+	4.65238e9i	0.111659	+	0.633252i	0.988350	+	0.152197i	$0.0486349\pi$
$659$	8.20340e8	+	4.65238e9i	0.111659	+	0.633252i	−0.876691	+	0.481054i	$0.840254\pi$
$660$	3.74189e9	−	6.13935e9i	0.506625	−	0.831225i
$661$	5.17660e9	−	1.88413e9i	0.697171	−	0.253750i	0.0309686	−	0.999520i	$-0.490141\pi$
$661$	5.17660e9	−	1.88413e9i	0.697171	−	0.253750i	0.666203	+	0.745771i	$0.267919\pi$
$662$	5.00747e8	−	1.82257e8i	0.0670834	−	0.0244164i
$663$	8.09201e9	+	1.92392e8i	1.07835	+	0.0256383i
$664$	3.08765e8	+	1.75109e9i	0.0409298	+	0.232124i
$665$	1.47796e9	−	2.55990e9i	0.194889	−	0.337557i
$666$	−8.41644e9	+	1.30979e10i	−1.10400	+	1.71807i
$667$	7.32962e9	+	1.26953e10i	0.956403	+	1.65654i
$668$	1.32256e9	−	1.10976e9i	0.171671	−	0.144049i
$669$	2.17710e9	+	1.91680e9i	0.281117	+	0.247506i
$670$	2.90459e9	−	1.64727e10i	0.373098	−	2.11594i
$671$	−6.97859e9	−	5.85574e9i	−0.891742	−	0.748260i
$672$	−1.01760e10	+	8.13449e9i	−1.29356	+	1.03404i
$673$	−1.19084e10	−	4.33429e9i	−1.50591	−	0.548107i	−0.548328	−	0.836263i	$-0.684735\pi$
$673$	−1.19084e10	−	4.33429e9i	−1.50591	−	0.548107i	−0.957583	+	0.288157i	$0.906958\pi$
$674$	1.23862e10			1.55822
$675$	−2.62866e8	−	2.53761e9i	−0.0328982	−	0.317587i
$676$	3.75047e8			0.0466952
$677$	6.06415e8	+	2.20717e8i	0.0751120	+	0.0273385i	0.379303	−	0.925273i	$-0.376164\pi$
$677$	6.06415e8	+	2.20717e8i	0.0751120	+	0.0273385i	−0.304191	+	0.952611i	$0.598386\pi$
$678$	−8.50795e9	−	3.32772e9i	−1.04838	−	0.410055i
$679$	6.07991e9	+	5.10165e9i	0.745338	+	0.625413i
$680$	−7.65879e8	+	4.34352e9i	−0.0934069	+	0.529737i
$681$	−3.40762e9	+	1.14931e9i	−0.413462	+	0.139451i
$682$	−6.60238e8	+	5.54005e8i	−0.0796994	+	0.0668757i
$683$	−1.59602e9	−	2.76439e9i	−0.191675	−	0.331992i	0.754130	−	0.656725i	$-0.228059\pi$
$683$	−1.59602e9	−	2.76439e9i	−0.191675	−	0.331992i	−0.945806	+	0.324733i	$0.894725\pi$
$684$	5.50939e8	+	4.31507e9i	0.0658275	+	0.515574i
$685$	9.61513e8	−	1.66539e9i	0.114298	−	0.197970i
$686$	−1.11964e9	−	6.34980e9i	−0.132417	−	0.750976i
$687$	5.83676e9	+	1.06885e10i	0.686789	+	1.25767i
$688$	2.44832e8	−	8.91116e7i	0.0286622	−	0.0104322i
$689$	−5.04205e9	+	1.83516e9i	−0.587273	+	0.213750i
$690$	−9.41599e9	−	1.72429e10i	−1.09117	−	1.99820i
$691$	−9.59221e8	−	5.44001e9i	−0.110598	−	0.627230i	−0.988836	−	0.149007i	$-0.952392\pi$
$691$	−9.59221e8	−	5.44001e9i	−0.110598	−	0.627230i	0.878239	−	0.478223i	$-0.158719\pi$
$692$	−1.63290e9	+	2.82826e9i	−0.187321	+	0.324450i
$693$	−8.66637e9	−	3.62948e9i	−0.989170	−	0.414265i
$694$	1.80325e8	+	3.12331e8i	0.0204784	+	0.0354697i
$695$	−4.69992e9	+	3.94370e9i	−0.531060	+	0.445612i
$696$	−5.55761e9	+	1.87445e9i	−0.624822	+	0.210737i
$697$	4.83103e8	−	2.73981e9i	0.0540412	−	0.306483i
$698$	1.77497e9	+	1.48938e9i	0.197559	+	0.165772i
$699$	−9.14293e9	−	3.57608e9i	−1.01255	−	0.396038i
$700$	4.82903e9	+	1.75762e9i	0.532129	+	0.193679i
$701$	1.18768e10			1.30222			0.651112	−	0.758982i	$-0.274303\pi$
$701$	1.18768e10			1.30222			0.651112	+	0.758982i	$0.274303\pi$
$702$	−6.30445e9	−	1.29754e10i	−0.687808	−	1.41560i
$703$	4.52129e9			0.490816
$704$	1.15636e10	+	4.20880e9i	1.24907	+	0.454626i
$705$	−8.96143e9	+	7.16355e9i	−0.963197	+	0.769957i
$706$	−8.11452e9	−	6.80889e9i	−0.867853	−	0.728215i
$707$	−3.46172e7	+	1.96324e8i	−0.00368404	+	0.0208932i
$708$	−1.06097e10	−	9.34119e9i	−1.12353	−	0.989204i
$709$	−1.20839e9	+	1.01396e9i	−0.127335	+	0.106846i	−0.704231	−	0.709971i	$-0.748708\pi$
$709$	−1.20839e9	+	1.01396e9i	−0.127335	+	0.106846i	0.576896	+	0.816817i	$0.304264\pi$
$710$	8.86649e9	+	1.53572e10i	0.929710	+	1.61031i
$711$	1.68288e10	+	8.00681e8i	1.75594	+	0.0835441i
$712$	−2.93119e9	+	5.07696e9i	−0.304343	+	0.527138i
$713$	2.38339e8	+	1.35169e9i	0.0246253	+	0.139657i
$714$	2.02804e10	+	4.82178e8i	2.08513	+	0.0495751i
$715$	6.50655e9	−	2.36819e9i	0.665702	−	0.242296i
$716$	−5.25950e9	+	1.91430e9i	−0.535486	+	0.194901i
$717$	9.19812e9	−	1.50914e10i	0.931927	−	1.52902i
$718$	3.18631e9	+	1.80704e10i	0.321257	+	1.82194i
$719$	2.09939e9	−	3.63626e9i	0.210641	−	0.364841i	−0.741274	−	0.671202i	$-0.765778\pi$
$719$	2.09939e9	−	3.63626e9i	0.210641	−	0.364841i	0.951915	+	0.306361i	$0.0991116\pi$
$720$	−3.51597e9	+	1.09349e9i	−0.351060	+	0.109182i
$721$	1.18576e10	+	2.05379e10i	1.17821	+	2.04072i
$722$	−1.03333e10	+	8.67067e9i	−1.02178	+	0.857378i
$723$	2.16990e9	−	1.07985e10i	0.213529	−	1.06262i
$724$	−8.60313e8	+	4.87908e9i	−0.0842504	+	0.477807i
$725$	−2.69329e9	−	2.25994e9i	−0.262482	−	0.220249i
$726$	−6.87066e8	−	4.52271e9i	−0.0666378	−	0.438653i
$727$	1.16901e10	+	4.25486e9i	1.12836	+	0.410690i	0.837697	−	0.546135i	$-0.183901\pi$
$727$	1.16901e10	+	4.25486e9i	1.12836	+	0.410690i	0.290665	+	0.956825i	$0.406124\pi$
$728$	8.25611e9			0.793078
$729$	−6.46473e9	+	8.22351e9i	−0.618023	+	0.786160i
$730$	9.13785e9			0.869388
$731$	−7.20798e8	−	2.62349e8i	−0.0682500	−	0.0248410i
$732$	−3.06837e9	−	2.01980e10i	−0.289147	−	1.90335i
$733$	−6.19618e9	−	5.19921e9i	−0.581112	−	0.487611i	0.304200	−	0.952608i	$-0.401611\pi$
$733$	−6.19618e9	−	5.19921e9i	−0.581112	−	0.487611i	−0.885312	+	0.464997i	$0.846055\pi$
$734$	−3.14892e9	+	1.78584e10i	−0.293917	+	1.66689i
$735$	−1.07094e9	+	5.32953e9i	−0.0994856	+	0.495089i
$736$	1.92627e10	−	1.61633e10i	1.78092	−	1.49437i
$737$	7.72012e9	+	1.33716e10i	0.710375	+	1.23041i
$738$	−4.73461e9	+	1.47250e9i	−0.433598	+	0.134852i
$739$	−1.58506e8	+	2.74541e8i	−0.0144474	+	0.0250237i	−0.873159	−	0.487436i	$-0.837932\pi$
$739$	−1.58506e8	+	2.74541e8i	−0.0144474	+	0.0250237i	0.858711	+	0.512460i	$0.171266\pi$
$740$	−2.91004e9	−	1.65037e10i	−0.263990	−	1.49716i
$741$	−2.18032e9	+	3.57727e9i	−0.196860	+	0.322989i
$742$	−1.26365e10	+	4.59932e9i	−1.13557	+	0.413314i
$743$	6.68477e8	−	2.43306e8i	0.0597896	−	0.0217616i	−0.311952	−	0.950098i	$-0.600983\pi$
$743$	6.68477e8	−	2.43306e8i	0.0597896	−	0.0217616i	0.371742	+	0.928336i	$0.378761\pi$
$744$	−5.49001e8	−	1.30528e7i	−0.0488729	−	0.00116198i
$745$	−1.17702e9	−	6.67521e9i	−0.104289	−	0.591450i
$746$	7.22058e9	−	1.25064e10i	0.636775	−	1.10293i
$747$	4.36532e9	+	2.07693e8i	0.383172	+	0.0182305i
$748$	−7.16471e9	−	1.24096e10i	−0.625955	−	1.08419i
$749$	1.78731e10	−	1.49973e10i	1.55422	−	1.30415i
$750$	1.46130e10	+	1.28658e10i	1.26481	+	1.11359i
$751$	−4.04775e7	+	2.29559e8i	−0.00348717	+	0.0197767i	−0.986502	−	0.163751i	$-0.947641\pi$
$751$	−4.04775e7	+	2.29559e8i	−0.00348717	+	0.0197767i	0.983015	+	0.183528i	$0.0587517\pi$
$752$	−5.94959e9	−	4.99230e9i	−0.510181	−	0.428093i
$753$	−9.40690e9	+	7.51965e9i	−0.802905	+	0.641823i
$754$	−1.86817e10	−	6.79957e9i	−1.58714	−	0.577672i
$755$	−9.75465e9			−0.824892
$756$	−9.20833e9	−	1.89520e10i

Introduction	Features
Universe	News

Level:	\( N \)	=	\( 27 = 3^{3} \)
Weight:	\( k \)	=	\( 8 \)
Character orbit:	\([\chi]\)	=	27.e (of order \(9\) and degree \(6\))

\(f(q)\)	\(=\)	\(q+(-16.4594 - 5.99073i) q^{2} +(7.02376 + 46.2349i) q^{3} +(136.969 + 114.931i) q^{4} +(-40.0449 + 227.106i) q^{5} +(161.374 - 803.077i) q^{6} +(882.649 - 740.631i) q^{7} +(-444.907 - 770.602i) q^{8} +(-2088.33 + 649.486i) q^{9} +O(q^{10})\)	\(q+(-16.4594 - 5.99073i) q^{2} +(7.02376 + 46.2349i) q^{3} +(136.969 + 114.931i) q^{4} +(-40.0449 + 227.106i) q^{5} +(161.374 - 803.077i) q^{6} +(882.649 - 740.631i) q^{7} +(-444.907 - 770.602i) q^{8} +(-2088.33 + 649.486i) q^{9} +(2019.65 - 3498.13i) q^{10} +(647.465 + 3671.95i) q^{11} +(-4351.78 + 7140.02i) q^{12} +(-7567.07 + 2754.19i) q^{13} +(-18964.8 + 6902.62i) q^{14} +(-10781.5 - 256.335i) q^{15} +(-1267.76 - 7189.84i) q^{16} +(-10746.9 + 18614.2i) q^{17} +(38263.6 + 1820.50i) q^{18} +(-5562.25 - 9634.10i) q^{19} +(-31586.5 + 26504.2i) q^{20} +(40442.5 + 35607.2i) q^{21} +(11340.8 - 64317.0i) q^{22} +(-79672.0 - 66852.8i) q^{23} +(32503.8 - 25982.8i) q^{24} +(23439.9 + 8531.43i) q^{25} +141049. q^{26} +(-44696.9 - 91992.1i) q^{27} +206017. q^{28} +(-132448. - 48207.1i) q^{29} +(175921. + 68808.2i) q^{30} +(-10109.4 - 8482.81i) q^{31} +(-41983.7 + 238101. i) q^{32} +(-165225. + 55726.4i) q^{33} +(288400. - 241996. i) q^{34} +(132856. + 230114. i) q^{35} +(-360684. - 151055. i) q^{36} +(-203213. + 351975. i) q^{37} +(33836.0 + 191894. i) q^{38} +(-180489. - 330518. i) q^{39} +(192825. - 70182.5i) q^{40} +(-121630. + 44269.8i) q^{41} +(-452346. - 828354. i) q^{42} +(6197.05 + 35145.2i) q^{43} +(-333339. + 577359. i) q^{44} +(-63875.0 - 500282. i) q^{45} +(910857. + 1.57765e6i) q^{46} +(814928. - 683806. i) q^{47} +(323517. - 109115. i) q^{48} +(87529.3 - 496403. i) q^{49} +(-334697. - 280844. i) q^{50} +(-936108. - 366140. i) q^{51} +(-1.35300e6 - 492451. i) q^{52} +666315. q^{53} +(184584. + 1.78190e6i) q^{54} -859851. q^{55} +(-963429. - 350659. i) q^{56} +(406364. - 324838. i) q^{57} +(1.89122e6 + 1.58692e6i) q^{58} +(-293561. + 1.66487e6i) q^{59} +(-1.44727e6 - 1.27424e6i) q^{60} +(-1.87164e6 + 1.57049e6i) q^{61} +(115577. + 200185. i) q^{62} +(-1.36224e6 + 2.11995e6i) q^{63} +(1.65018e6 - 2.85819e6i) q^{64} +(-322470. - 1.82882e6i) q^{65} +(3.05334e6 + 72594.8i) q^{66} +(3.89129e6 - 1.41632e6i) q^{67} +(-3.61134e6 + 1.31442e6i) q^{68} +(2.53133e6 - 4.15319e6i) q^{69} +(-808184. - 4.58344e6i) q^{70} +(-2.19506e6 + 3.80195e6i) q^{71} +(1.42961e6 + 1.32031e6i) q^{72} +(1.13112e6 + 1.95915e6i) q^{73} +(5.45336e6 - 4.57591e6i) q^{74} +(-229813. + 1.14366e6i) q^{75} +(345399. - 1.95885e6i) q^{76} +(3.29105e6 + 2.76152e6i) q^{77} +(990694. + 6.52139e6i) q^{78} +(-7.23906e6 - 2.63480e6i) q^{79} +1.68362e6 q^{80} +(3.93931e6 - 2.71269e6i) q^{81} +2.26717e6 q^{82} +(-1.87778e6 - 683455. i) q^{83} +(1.44702e6 + 9.52520e6i) q^{84} +(-3.79703e6 - 3.18609e6i) q^{85} +(108546. - 615594. i) q^{86} +(1.29857e6 - 6.46231e6i) q^{87} +(2.54155e6 - 2.13262e6i) q^{88} +(-3.29415e6 - 5.70564e6i) q^{89} +(-1.94571e6 + 8.61700e6i) q^{90} +(-4.63923e6 + 8.03539e6i) q^{91} +(-3.22918e6 - 1.83136e7i) q^{92} +(321196. - 526989. i) q^{93} +(-1.75097e7 + 6.37302e6i) q^{94} +(2.41070e6 - 877424. i) q^{95} +(-1.13035e7 - 268746. i) q^{96} +(1.19613e6 + 6.78360e6i) q^{97} +(-4.41450e6 + 7.64614e6i) q^{98} +(-3.73700e6 - 7.24775e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120q - 6q^{2} - 6q^{3} - 6q^{4} - 219q^{5} + 1386q^{6} - 6q^{7} - 4611q^{8} - 1728q^{9} + O(q^{10}) \)	\( 120q - 6q^{2} - 6q^{3} - 6q^{4} - 219q^{5} + 1386q^{6} - 6q^{7} - 4611q^{8} - 1728q^{9} - 3q^{10} + 9399q^{11} - 10545q^{12} - 6q^{13} + 16647q^{14} + 11709q^{15} + 378q^{16} - 58959q^{17} - 156051q^{18} - 3q^{19} + 240243q^{20} - 516q^{21} + 105762q^{22} - 144084q^{23} - 150894q^{24} - 107997q^{25} + 443202q^{26} + 114363q^{27} - 12q^{28} + 107886q^{29} - 179901q^{30} + 297975q^{31} - 639576q^{32} - 31338q^{33} - 265806q^{34} - 450672q^{35} + 51264q^{36} - 3q^{37} - 145596q^{38} + 1919661q^{39} + 283521q^{40} + 227085q^{41} + 3792042q^{42} - 1080969q^{43} - 1205115q^{44} - 4430925q^{45} - 3q^{46} - 5184339q^{47} - 2424039q^{48} + 976008q^{49} + 2324559q^{50} + 2918034q^{51} - 3366135q^{52} + 5631750q^{53} + 11971422q^{54} - 12q^{55} + 5254923q^{56} - 284637q^{57} + 3884295q^{58} - 12534492q^{59} - 29390886q^{60} + 3865440q^{61} - 9923646q^{62} + 3292389q^{63} - 10223619q^{64} + 17158395q^{65} + 39100653q^{66} + 5567061q^{67} + 19858455q^{68} - 12682935q^{69} - 1020993q^{70} - 18563877q^{71} - 33138540q^{72} + 3770934q^{73} - 36278085q^{74} - 26317941q^{75} - 1156998q^{76} + 8471751q^{77} + 36593658q^{78} + 16415526q^{79} + 101080590q^{80} + 45736524q^{81} - 12q^{82} + 3147699q^{83} - 27588054q^{84} - 7672131q^{85} - 70854834q^{86} - 55384731q^{87} - 34323078q^{88} - 54647613q^{89} - 25256970q^{90} + 3315066q^{91} + 73858515q^{92} + 69808065q^{93} + 22126539q^{94} + 32541447q^{95} + 33014034q^{96} + 41250117q^{97} - 88493274q^{98} - 111262167q^{99} + O(q^{100}) \)

\(n\)	\(2\)
\(\chi(n)\)	\(e\left(\frac{1}{9}\right)\)

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