LMFDB - Embedded Newform 27.8.e.a.4.14

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			4.14
Character	$\chi$	=	27.4
Dual form			27.8.e.a.7.14

$q$-expansion

$f(q)$	$=$	$q+(7.46251 + 2.71613i) q^{2} +(42.7022 + 19.0664i) q^{3} +(-49.7420 - 41.7385i) q^{4} +(71.4552 - 405.243i) q^{5} +(266.878 + 258.268i) q^{6} +(898.235 - 753.709i) q^{7} +(-766.085 - 1326.90i) q^{8} +(1459.95 + 1628.35i) q^{9} +O(q^{10})$	\(q+(7.46251 + 2.71613i) q^{2} +(42.7022 + 19.0664i) q^{3} +(-49.7420 - 41.7385i) q^{4} +(71.4552 - 405.243i) q^{5} +(266.878 + 258.268i) q^{6} +(898.235 - 753.709i) q^{7} +(-766.085 - 1326.90i) q^{8} +(1459.95 + 1628.35i) q^{9} +(1633.93 - 2830.04i) q^{10} +(1289.55 + 7313.38i) q^{11} +(-1328.29 - 2730.72i) q^{12} +(-3791.99 + 1380.17i) q^{13} +(8750.26 - 3184.83i) q^{14} +(10777.8 - 15942.3i) q^{15} +(-669.609 - 3797.54i) q^{16} +(7380.03 - 12782.6i) q^{17} +(6472.06 + 16117.0i) q^{18} +(-1194.93 - 2069.69i) q^{19} +(-20468.5 + 17175.2i) q^{20} +(52727.1 - 15058.9i) q^{21} +(-10240.9 + 58078.8i) q^{22} +(-782.904 - 656.935i) q^{23} +(-7414.36 - 71267.9i) q^{24} +(-85702.2 - 31193.0i) q^{25} -32046.4 q^{26} +(31296.2 + 97369.9i) q^{27} -76138.7 q^{28} +(-127204. - 46298.5i) q^{29} +(123731. - 89695.9i) q^{30} +(123510. + 103637. i) q^{31} +(-28737.8 + 162980. i) q^{32} +(-84373.2 + 336884. i) q^{33} +(89792.7 - 75345.0i) q^{34} +(-241251. - 417860. i) q^{35} +(-4655.87 - 141933. i) q^{36} +(-120547. + 208793. i) q^{37} +(-3295.66 - 18690.6i) q^{38} +(-188241. - 13363.1i) q^{39} +(-592456. + 215636. i) q^{40} +(154404. - 56198.5i) q^{41} +(434378. + 30836.3i) q^{42} +(177068. + 1.00420e6i) q^{43} +(241105. - 417606. i) q^{44} +(764197. - 475279. i) q^{45} +(-4058.11 - 7028.85i) q^{46} +(797496. - 669179. i) q^{47} +(43811.6 - 174930. i) q^{48} +(95742.7 - 542984. i) q^{49} +(-554829. - 465557. i) q^{50} +(558861. - 405134. i) q^{51} +(246227. + 89619.4i) q^{52} -749747. q^{53} +(-30921.2 + 811628. i) q^{54} +3.05584e6 q^{55} +(-1.68822e6 - 614461. i) q^{56} +(-11564.9 - 111163. i) q^{57} +(-823509. - 691006. i) q^{58} +(50040.2 - 283792. i) q^{59} +(-1.20152e6 + 343155. i) q^{60} +(-1.80233e6 + 1.51233e6i) q^{61} +(640202. + 1.10886e6i) q^{62} +(2.53868e6 + 362265. i) q^{63} +(-903924. + 1.56564e6i) q^{64} +(288346. + 1.63529e6i) q^{65} +(-1.54466e6 + 2.28483e6i) q^{66} +(-2.96301e6 + 1.07845e6i) q^{67} +(-900624. + 327800. i) q^{68} +(-20906.3 - 42979.6i) q^{69} +(-665379. - 3.77355e6i) q^{70} +(968628. - 1.67771e6i) q^{71} +(1.04221e6 - 3.18466e6i) q^{72} +(-1.90937e6 - 3.30713e6i) q^{73} +(-1.46669e6 + 1.23070e6i) q^{74} +(-3.06493e6 - 2.96604e6i) q^{75} +(-26947.2 + 152825. i) q^{76} +(6.67048e6 + 5.59720e6i) q^{77} +(-1.36845e6 - 611009. i) q^{78} +(5.86605e6 + 2.13507e6i) q^{79} -1.58677e6 q^{80} +(-520074. + 4.75461e6i) q^{81} +1.30488e6 q^{82} +(3.52512e6 + 1.28304e6i) q^{83} +(-3.25129e6 - 1.45169e6i) q^{84} +(-4.65271e6 - 3.90408e6i) q^{85} +(-1.40617e6 + 7.97480e6i) q^{86} +(-4.54914e6 - 4.40236e6i) q^{87} +(8.71621e6 - 7.31377e6i) q^{88} +(-4.12096e6 - 7.13772e6i) q^{89} +(6.99375e6 - 1.47111e6i) q^{90} +(-2.36585e6 + 4.09777e6i) q^{91} +(11523.8 + 65354.5i) q^{92} +(3.29816e6 + 6.78042e6i) q^{93} +(7.76890e6 - 2.82765e6i) q^{94} +(-924109. + 336348. i) q^{95} +(-4.33461e6 + 6.41168e6i) q^{96} +(-1.50671e6 - 8.54498e6i) q^{97} +(2.18930e6 - 3.79197e6i) q^{98} +(-1.00261e7 + 1.27770e7i) 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 $

$2$	7.46251	+	2.71613i	0.659599	+	0.240074i	0.650063	−	0.759880i	$-0.274742\pi$
$2$	7.46251	+	2.71613i	0.659599	+	0.240074i	0.00953567	+	0.999955i	$0.496965\pi$
$3$	42.7022	+	19.0664i	0.913115	+	0.407703i
$3$	42.7022	+	19.0664i	0.913115	+	0.407703i
$4$	−49.7420	−	41.7385i	−0.388610	−	0.326082i
$5$	71.4552	−	405.243i	0.255646	−	1.44984i	−0.538763	−	0.842457i	$-0.681108\pi$
$5$	71.4552	−	405.243i	0.255646	−	1.44984i	0.794409	−	0.607383i	$-0.207781\pi$
$6$	266.878	+	258.268i	0.504411	+	0.488136i
$7$	898.235	−	753.709i	0.989799	−	0.830540i	0.00426019	−	0.999991i	$-0.498644\pi$
$7$	898.235	−	753.709i	0.989799	−	0.830540i	0.985539	+	0.169451i	$0.0541995\pi$
$8$	−766.085	−	1326.90i	−0.529008	−	0.916268i
$9$	1459.95	+	1628.35i	0.667557	+	0.744558i
$10$	1633.93	−	2830.04i	0.516693	−	0.894939i
$11$	1289.55	+	7313.38i	0.292121	+	1.65670i	0.678679	+	0.734435i	$0.262553\pi$
$11$	1289.55	+	7313.38i	0.292121	+	1.65670i	−0.386558	+	0.922265i	$0.626336\pi$
$12$	−1328.29	−	2730.72i	−0.221901	−	0.456188i
$13$	−3791.99	+	1380.17i	−0.478702	+	0.174233i	−0.570090	−	0.821582i	$-0.693092\pi$
$13$	−3791.99	+	1380.17i	−0.478702	+	0.174233i	0.0913885	+	0.995815i	$0.470869\pi$
$14$	8750.26	−	3184.83i	0.852261	−	0.310198i
$15$	10777.8	−	15942.3i	0.824537	−	1.21964i
$16$	−669.609	−	3797.54i	−0.0408697	−	0.231784i
$17$	7380.03	−	12782.6i	0.364323	−	0.631026i	−0.624344	−	0.781149i	$-0.714634\pi$
$17$	7380.03	−	12782.6i	0.364323	−	0.631026i	0.988667	+	0.150123i	$0.0479670\pi$
$18$	6472.06	+	16117.0i	0.261571	+	0.651373i
$19$	−1194.93	−	2069.69i	−0.0399674	−	0.0692256i	0.845350	−	0.534213i	$-0.179392\pi$
$19$	−1194.93	−	2069.69i	−0.0399674	−	0.0692256i	−0.885317	+	0.464988i	$0.846059\pi$
$20$	−20468.5	+	17175.2i	−0.572113	+	0.480060i
$21$	52727.1	−	15058.9i	1.24241	−	0.354835i
$22$	−10240.9	+	58078.8i	−0.205049	+	1.16289i
$23$	−782.904	−	656.935i	−0.0134172	−	0.0112583i	0.636054	−	0.771644i	$-0.280565\pi$
$23$	−782.904	−	656.935i	−0.0134172	−	0.0112583i	−0.649472	+	0.760386i	$0.725010\pi$
$24$	−7414.36	−	71267.9i	−0.109480	−	1.05234i
$25$	−85702.2	−	31193.0i	−1.09699	−	0.399271i
$26$	−32046.4			−0.357580
$27$	31296.2	+	97369.9i	0.305998	+	0.952032i
$28$	−76138.7			−0.655469
$29$	−127204.	−	46298.5i	−0.968519	−	0.352512i	−0.191153	−	0.981560i	$-0.561223\pi$
$29$	−127204.	−	46298.5i	−0.968519	−	0.352512i	−0.777366	+	0.629048i	$0.783445\pi$
$30$	123731.	−	89695.9i	0.836669	−	0.606525i
$31$	123510.	+	103637.i	0.744623	+	0.624813i	0.934075	−	0.357077i	$-0.116227\pi$
$31$	123510.	+	103637.i	0.744623	+	0.624813i	−0.189452	+	0.981890i	$0.560671\pi$
$32$	−28737.8	+	162980.i	−0.155035	+	0.879246i
$33$	−84373.2	+	336884.i	−0.408701	+	1.63186i
$34$	89792.7	−	75345.0i	0.391800	−	0.328760i
$35$	−241251.	−	417860.i	−0.951112	−	1.64737i
$36$	−4655.87	−	141933.i	−0.0166319	−	0.507021i
$37$	−120547.	+	208793.i	−0.391246	+	0.677658i	−0.992614	−	0.121314i	$-0.961289\pi$
$37$	−120547.	+	208793.i	−0.391246	+	0.677658i	0.601368	+	0.798972i	$0.294622\pi$
$38$	−3295.66	−	18690.6i	−0.00974317	−	0.0552563i
$39$	−188241.	−	13363.1i	−0.508145	−	0.0360730i
$40$	−592456.	+	215636.i	−1.46368	+	0.532736i
$41$	154404.	−	56198.5i	0.349877	−	0.127345i	−0.161103	−	0.986938i	$-0.551505\pi$
$41$	154404.	−	56198.5i	0.349877	−	0.127345i	0.510980	+	0.859593i	$0.329283\pi$
$42$	434378.	+	30836.3i	0.904681	+	0.0642230i
$43$	177068.	+	1.00420e6i	0.339625	+	1.92611i	0.375655	+	0.926759i	$0.377418\pi$
$43$	177068.	+	1.00420e6i	0.339625	+	1.92611i	−0.0360301	+	0.999351i	$0.511471\pi$
$44$	241105.	−	417606.i	0.426699	−	0.739065i
$45$	764197.	−	475279.i	1.25015	−	0.777508i
$46$	−4058.11	−	7028.85i	−0.00614711	−	0.0106471i
$47$	797496.	−	669179.i	1.12043	−	0.940155i	0.121807	−	0.992554i	$-0.461131\pi$
$47$	797496.	−	669179.i	1.12043	−	0.940155i	0.998626	+	0.0523986i	$0.0166866\pi$
$48$	43811.6	−	174930.i	0.0571801	−	0.228308i
$49$	95742.7	−	542984.i	0.116257	−	0.659327i
$50$	−554829.	−	465557.i	−0.627717	−	0.526717i
$51$	558861.	−	405134.i	0.589940	−	0.427664i
$52$	246227.	+	89619.4i	0.242842	+	0.0883874i
$53$	−749747.			−0.691750			−0.345875	−	0.938281i	$-0.612418\pi$
$53$	−749747.			−0.691750			−0.345875	+	0.938281i	$0.612418\pi$
$54$	−30921.2	+	811628.i	−0.0267225	+	0.701422i
$55$	3.05584e6			2.47663
$56$	−1.68822e6	−	614461.i	−1.28461	−	0.467559i
$57$	−11564.9	−	111163.i	−0.00827139	−	0.0795057i
$58$	−823509.	−	691006.i	−0.554205	−	0.465033i
$59$	50040.2	−	283792.i	0.0317203	−	0.179895i	−0.964831	−	0.262870i	$-0.915331\pi$
$59$	50040.2	−	283792.i	0.0317203	−	0.179895i	0.996552	+	0.0829750i	$0.0264422\pi$
$60$	−1.20152e6	+	343155.i	−0.718127	+	0.205098i
$61$	−1.80233e6	+	1.51233e6i	−1.01667	+	0.853086i	−0.989205	−	0.146537i	$-0.953187\pi$
$61$	−1.80233e6	+	1.51233e6i	−1.01667	+	0.853086i	−0.0274630	+	0.999623i	$0.508743\pi$
$62$	640202.	+	1.10886e6i	0.341151	+	0.590890i
$63$	2.53868e6	+	362265.i	1.27913	+	0.182530i
$64$	−903924.	+	1.56564e6i	−0.431025	+	0.746557i
$65$	288346.	+	1.63529e6i	0.130232	+	0.738583i
$66$	−1.54466e6	+	2.28483e6i	−0.661345	+	0.978252i
$67$	−2.96301e6	+	1.07845e6i	−1.20357	+	0.438063i	−0.864469	−	0.502687i	$-0.832345\pi$
$67$	−2.96301e6	+	1.07845e6i	−1.20357	+	0.438063i	−0.339100	+	0.940750i	$0.610123\pi$
$68$	−900624.	+	327800.i	−0.347346	+	0.126424i
$69$	−20906.3	−	42979.6i	−0.00766136	−	0.0157504i
$70$	−665379.	−	3.77355e6i	−0.231860	−	1.31494i
$71$	968628.	−	1.67771e6i	0.321183	−	0.556306i	−0.659549	−	0.751661i	$-0.729253\pi$
$71$	968628.	−	1.67771e6i	0.321183	−	0.556306i	0.980732	+	0.195356i	$0.0625861\pi$
$72$	1.04221e6	−	3.18466e6i	0.329072	−	1.00554i
$73$	−1.90937e6	−	3.30713e6i	−0.574460	−	0.994995i	−0.996100	−	0.0882312i	$-0.971879\pi$
$73$	−1.90937e6	−	3.30713e6i	−0.574460	−	0.994995i	0.421640	−	0.906764i	$-0.361455\pi$
$74$	−1.46669e6	+	1.23070e6i	−0.420754	+	0.353054i
$75$	−3.06493e6	−	2.96604e6i	−0.838892	−	0.811825i
$76$	−26947.2	+	152825.i	−0.00704151	+	0.0399344i
$77$	6.67048e6	+	5.59720e6i	1.66510	+	1.39718i
$78$	−1.36845e6	−	611009.i	−0.326512	−	0.145786i
$79$	5.86605e6	+	2.13507e6i	1.33860	+	0.487211i	0.909372	−	0.415985i	$-0.136563\pi$
$79$	5.86605e6	+	2.13507e6i	1.33860	+	0.487211i	0.429229	+	0.903196i	$0.358785\pi$
$80$	−1.58677e6			−0.346497
$81$	−520074.	+	4.75461e6i	−0.108735	+	0.994071i
$82$	1.30488e6			0.261351
$83$	3.52512e6	+	1.28304e6i	0.676707	+	0.246301i	0.657433	−	0.753513i	$-0.271642\pi$
$83$	3.52512e6	+	1.28304e6i	0.676707	+	0.246301i	0.0192742	+	0.999814i	$0.493864\pi$
$84$	−3.25129e6	−	1.45169e6i	−0.598519	−	0.267237i
$85$	−4.65271e6	−	3.90408e6i	−0.821749	−	0.689530i
$86$	−1.40617e6	+	7.97480e6i	−0.238393	+	1.35200i
$87$	−4.54914e6	−	4.40236e6i	−0.740649	−	0.716752i
$88$	8.71621e6	−	7.31377e6i	1.36345	−	1.14407i
$89$	−4.12096e6	−	7.13772e6i	−0.619632	−	1.07323i	−0.989553	−	0.144171i	$-0.953949\pi$
$89$	−4.12096e6	−	7.13772e6i	−0.619632	−	1.07323i	0.369921	−	0.929063i	$-0.379385\pi$
$90$	6.99375e6	−	1.47111e6i	1.01126	−	0.212715i
$91$	−2.36585e6	+	4.09777e6i	−0.329111	+	0.570037i
$92$	11523.8	+	65354.5i	0.00154290	+	0.00875020i
$93$	3.29816e6	+	6.78042e6i	0.425188	+	0.874110i
$94$	7.76890e6	−	2.82765e6i	0.964744	−	0.351138i
$95$	−924109.	+	336348.i	−0.110584	+	0.0402491i
$96$	−4.33461e6	+	6.41168e6i	−0.500035	+	0.739644i
$97$	−1.50671e6	−	8.54498e6i	−0.167621	−	0.950627i	−0.946321	−	0.323230i	$-0.895231\pi$
$97$	−1.50671e6	−	8.54498e6i	−0.167621	−	0.950627i	0.778699	−	0.627397i	$-0.215880\pi$
$98$	2.18930e6	−	3.79197e6i	0.234970	−	0.406981i
$99$	−1.00261e7	+	1.27770e7i	−1.03850	+	1.32344i
$100$	2.96105e6	+	5.12869e6i	0.296105	+	0.512869i
$101$	8.19828e6	−	6.87918e6i	0.791768	−	0.664373i	−0.154414	−	0.988006i	$-0.549349\pi$
$101$	8.19828e6	−	6.87918e6i	0.791768	−	0.664373i	0.946182	+	0.323634i	$0.104905\pi$
$102$	5.27090e6	−	1.50537e6i	0.491795	−	0.140457i
$103$	−729870.	+	4.13930e6i	−0.0658135	+	0.373247i	0.934057	+	0.357125i	$0.116243\pi$
$103$	−729870.	+	4.13930e6i	−0.0658135	+	0.373247i	−0.999870	+	0.0161218i	$0.994868\pi$
$104$	4.73633e6	+	3.97425e6i	0.412881	+	0.346448i
$105$	−2.33489e6	−	2.24433e7i	−0.196836	−	1.89201i
$106$	−5.59500e6	−	2.03641e6i	−0.456278	−	0.166072i
$107$	−1.27099e7			−1.00300			−0.501498	−	0.865159i	$-0.667218\pi$
$107$	−1.27099e7			−1.00300			−0.501498	+	0.865159i	$0.667218\pi$
$108$	2.50734e6	−	6.14963e6i	0.191527	−	0.469749i
$109$	2.03485e7			1.50501			0.752506	−	0.658585i	$-0.228845\pi$
$109$	2.03485e7			1.50501			0.752506	+	0.658585i	$0.228845\pi$
$110$	2.28042e7	+	8.30006e6i	1.63358	+	0.594575i
$111$	−9.12854e6	+	6.61753e6i	−0.633535	+	0.459267i
$112$	−3.46371e6	−	2.90640e6i	−0.232958	−	0.195475i
$113$	−404160.	+	2.29211e6i	−0.0263499	+	0.149438i	−0.995144	−	0.0984288i	$-0.968618\pi$
$113$	−404160.	+	2.29211e6i	−0.0263499	+	0.149438i	0.968794	+	0.247867i	$0.0797294\pi$
$114$	215631.	−	860967.i	0.0136315	−	0.0544276i
$115$	−322160.	+	270325.i	−0.0197528	+	0.0165746i
$116$	4.39496e6	+	7.61229e6i	0.261428	+	0.452806i
$117$	−7.78350e6	−	4.15970e6i	−0.449288	−	0.240111i
$118$	1.14424e6	−	1.98189e6i	0.0641108	−	0.111043i
$119$	−3.00535e6	−	1.70442e7i	−0.163486	−	0.927174i
$120$	−2.94106e7	−	2.08784e6i	−1.55371	−	0.110297i
$121$	−3.35107e7	+	1.21969e7i	−1.71963	+	0.625894i
$122$	−1.75576e7	+	6.39044e6i	−0.875397	+	0.318619i
$123$	7.66489e6	+	544128.i	0.371397	+	0.0263653i
$124$	−1.81797e6	−	1.03102e7i	−0.0856272	−	0.485616i
$125$	−2.69063e6	+	4.66031e6i	−0.123217	+	0.213417i
$126$	1.79609e7	+	9.59879e6i	0.799894	+	0.427484i
$127$	1.35005e7	+	2.33836e7i	0.584840	+	1.01297i	0.994895	+	0.100912i	$0.0321761\pi$
$127$	1.35005e7	+	2.33836e7i	0.584840	+	1.01297i	−0.410055	+	0.912061i	$0.634491\pi$
$128$	5.22932e6	−	4.38792e6i	0.220399	−	0.184937i
$129$	−1.15853e7	+	4.62576e7i	−0.475163	+	1.89723i
$130$	−2.28988e6	+	1.29866e7i	−0.0914138	+	0.518434i
$131$	−2.88021e7	−	2.41678e7i	−1.11937	−	0.939264i	−0.120799	−	0.992677i	$-0.538546\pi$
$131$	−2.88021e7	−	2.41678e7i	−1.11937	−	0.939264i	−0.998573	+	0.0534125i	$0.982990\pi$
$132$	1.82579e7	−	1.32357e7i	0.690944	−	0.500885i
$133$	−2.63327e6	−	958432.i	−0.0970543	−	0.0353249i
$134$	−2.50407e7			−0.899040
$135$	4.16947e7	−	5.72497e6i	1.45852	−	0.200265i
$136$	−2.26149e7			−0.770919
$137$	1.80096e7	+	6.55497e6i	0.598388	+	0.217796i	0.623415	−	0.781891i	$-0.285745\pi$
$137$	1.80096e7	+	6.55497e6i	0.598388	+	0.217796i	−0.0250266	+	0.999687i	$0.507967\pi$
$138$	−39275.4	−	377520.i	−0.00127217	−	0.0122282i
$139$	−1.35167e7	−	1.13418e7i	−0.426892	−	0.358205i	0.403885	−	0.914810i	$-0.367659\pi$
$139$	−1.35167e7	−	1.13418e7i	−0.426892	−	0.358205i	−0.830778	+	0.556604i	$0.812104\pi$
$140$	−5.44051e6	+	3.08546e7i	−0.167568	+	0.950326i
$141$	4.68136e7	−	1.33700e7i	1.40639	−	0.401666i
$142$	1.17853e7	−	9.88903e6i	0.345407	−	0.289831i
$143$	−1.49837e7	−	2.59524e7i	−0.428491	−	0.742168i
$144$	5.20613e6	−	6.63457e6i	0.145294	−	0.185159i
$145$	−2.78515e7	+	4.82402e7i	−0.758684	+	1.31408i
$146$	−5.26610e6	−	2.98656e7i	−0.140041	−	0.794210i
$147$	1.44411e7	−	2.13611e7i	0.374965	−	0.554643i
$148$	1.47110e7	−	5.35435e6i	0.373014	−	0.135766i
$149$	−2.54922e7	+	9.27840e6i	−0.631328	+	0.229785i	−0.637809	−	0.770194i	$-0.720159\pi$
$149$	−2.54922e7	+	9.27840e6i	−0.631328	+	0.229785i	0.00648111	+	0.999979i	$0.497937\pi$
$150$	−1.48159e7	−	3.04588e7i	−0.358434	−	0.736875i
$151$	−9.77375e6	−	5.54297e7i	−0.231016	−	1.31016i	−0.850844	−	0.525418i	$-0.823909\pi$
$151$	−9.77375e6	−	5.54297e7i	−0.231016	−	1.31016i	0.619828	−	0.784738i	$-0.287202\pi$
$152$	−1.83084e6	+	3.17111e6i	−0.0422861	+	0.0732418i
$153$	3.15890e7	−	6.64464e6i	0.713043	−	0.149986i
$154$	3.45758e7	+	5.98870e7i	0.762868	+	1.32133i
$155$	5.08236e7	−	4.26461e7i	1.09624	−	0.919853i
$156$	8.80572e6	+	8.52160e6i	0.185707	+	0.179715i
$157$	2.82266e6	−	1.60081e7i	0.0582116	−	0.330134i	−0.941770	−	0.336259i	$-0.890838\pi$
$157$	2.82266e6	−	1.60081e7i	0.0582116	−	0.330134i	0.999981	+	0.00612431i	$0.00194944\pi$
$158$	3.79763e7	+	3.18659e7i	0.765973	+	0.642727i
$159$	−3.20158e7	−	1.42950e7i	−0.631648	−	0.282028i
$160$	6.39931e7	+	2.32916e7i	1.23513	+	0.449551i
$161$	−1.19837e6			−0.0226308
$162$	−1.67952e7	+	3.40687e7i	−0.310372	+	0.629584i
$163$	−6.74542e7			−1.21998			−0.609990	−	0.792409i	$-0.708827\pi$
$163$	−6.74542e7			−1.21998			−0.609990	+	0.792409i	$0.708827\pi$
$164$	−1.00260e7	−	3.64917e6i	−0.177490	−	0.0646012i
$165$	1.30491e8	+	5.82637e7i	2.26145	+	1.00973i
$166$	2.28214e7	+	1.91494e7i	0.387225	+	0.324920i
$167$	7.11829e6	−	4.03698e7i	0.118268	−	0.670733i	−0.866812	−	0.498636i	$-0.833835\pi$
$167$	7.11829e6	−	4.03698e7i	0.118268	−	0.670733i	0.985080	−	0.172097i	$-0.0550543\pi$
$168$	−6.03750e7	−	5.84270e7i	−0.982370	−	0.950673i
$169$	−3.55939e7	+	2.98668e7i	−0.567246	+	0.475976i
$170$	−2.41169e7	−	4.17716e7i	−0.376487	−	0.652094i
$171$	1.62563e6	−	4.96740e6i	0.0248620	−	0.0759701i
$172$	3.31062e7	−	5.73415e7i	0.496089	−	0.859250i
$173$	8.83323e6	+	5.00957e7i	0.129705	+	0.735596i	0.978401	+	0.206715i	$0.0662772\pi$
$173$	8.83323e6	+	5.00957e7i	0.129705	+	0.735596i	−0.848696	+	0.528881i	$0.822612\pi$
$174$	−2.19906e7	−	4.52088e7i	−0.316457	−	0.650579i
$175$	−1.00491e8	+	3.65758e7i	−1.41741	+	0.515894i
$176$	2.69094e7	−	9.79422e6i	0.372057	−	0.135418i
$177$	7.54771e6	−	1.11645e7i	0.102308	−	0.151332i
$178$	−1.13657e7	−	6.44583e7i	−0.151053	−	0.856661i
$179$	9.62002e6	−	1.66624e7i	0.125369	−	0.217146i	−0.796508	−	0.604628i	$-0.793322\pi$
$179$	9.62002e6	−	1.66624e7i	0.125369	−	0.217146i	0.921877	+	0.387482i	$0.126655\pi$
$180$	−5.78502e7	−	8.25512e6i	−0.739351	−	0.105504i
$181$	1.22175e7	+	2.11614e7i	0.153147	+	0.265258i	0.932383	−	0.361473i	$-0.117726\pi$
$181$	1.22175e7	+	2.11614e7i	0.153147	+	0.265258i	−0.779236	+	0.626731i	$0.784393\pi$
$182$	−2.87852e7	+	2.41537e7i	−0.353932	+	0.296984i
$183$	−1.05798e8	+	3.02160e7i	−1.27614	+	0.364467i
$184$	−271914.	+	1.54210e6i	−0.00321788	+	0.0182495i
$185$	7.59982e7	+	6.37701e7i	0.882475	+	0.740484i
$186$	6.19604e6	+	5.95572e7i	0.0706023	+	0.678639i
$187$	1.03001e8	+	3.74892e7i	1.15185	+	0.419238i
$188$	−6.75996e7			−0.741979
$189$	1.01500e8	+	6.38728e7i	1.09358	+	0.688177i
$190$	−7.80974e6			−0.0826036
$191$	−1.06937e8	−	3.89219e7i	−1.11048	−	0.404182i	−0.279311	−	0.960201i	$-0.590106\pi$
$191$	−1.06937e8	−	3.89219e7i	−1.11048	−	0.404182i	−0.831170	+	0.556019i	$0.812328\pi$
$192$	−6.84506e7	+	4.96218e7i	−0.697948	+	0.505962i
$193$	2.99836e7	+	2.51592e7i	0.300215	+	0.251910i	0.780434	−	0.625238i	$-0.214998\pi$
$193$	2.99836e7	+	2.51592e7i	0.300215	+	0.251910i	−0.480219	+	0.877149i	$0.659443\pi$
$194$	1.19655e7	−	6.78594e7i	0.117658	−	0.667274i
$195$	−1.88661e7	+	7.53283e7i	−0.182205	+	0.727507i
$196$	−2.74258e7	+	2.30130e7i	−0.260173	+	0.218311i
$197$	−2.08522e7	−	3.61170e7i	−0.194321	−	0.336573i	0.752357	−	0.658756i	$-0.228917\pi$
$197$	−2.08522e7	−	3.61170e7i	−0.194321	−	0.336573i	−0.946678	+	0.322182i	$0.895584\pi$
$198$	−1.09524e8	+	6.81163e7i	−1.00272	+	0.623624i
$199$	6.83716e7	−	1.18423e8i	0.615021	−	1.06525i	−0.375360	−	0.926879i	$-0.622481\pi$
$199$	6.83716e7	−	1.18423e8i	0.615021	−	1.06525i	0.990381	−	0.138368i	$-0.0441857\pi$
$200$	2.42652e7	+	1.37615e8i	0.214476	+	1.21635i
$201$	−1.47089e8	−	1.04418e7i	−1.27760	−	0.0906961i
$202$	7.98645e7	−	2.90683e7i	0.681748	−	0.248136i
$203$	−1.49155e8	+	5.42879e7i	−1.25141	+	0.455477i
$204$	−4.47085e7	−	3.17384e6i	−0.368710	−	0.0261746i
$205$	−1.17410e7	−	6.65868e7i	−0.0951850	−	0.539821i
$206$	−1.66895e7	+	2.89071e7i	−0.133018	+	0.230393i
$207$	−73280.1	−	2.23393e6i	−0.000574235	−	0.0175055i
$208$	7.78041e6	+	1.34761e7i	0.0599488	+	0.103834i
$209$	1.35955e7	−	1.14080e7i	0.103011	−	0.0864363i
$210$	4.35348e7	−	1.73825e8i	0.324391	−	1.29522i
$211$	3.09369e6	−	1.75452e7i	0.0226719	−	0.128579i	−0.971371	−	0.237567i	$-0.923650\pi$
$211$	3.09369e6	−	1.75452e7i	0.0226719	−	0.128579i	0.994043	+	0.108988i	$0.0347611\pi$
$212$	3.72940e7	+	3.12933e7i	0.268821	+	0.225567i
$213$	7.33504e7	−	5.31738e7i	0.520084	−	0.377024i
$214$	−9.48479e7	−	3.45218e7i	−0.661575	−	0.240794i
$215$	4.19597e8			2.87938
$216$	1.05224e8	−	1.16121e8i	0.710441	−	0.784009i
$217$	1.89053e8			1.25596
$218$	1.51851e8	+	5.52692e7i	0.992704	+	0.361315i
$219$	−1.84794e7	−	1.77626e8i	−0.118886	−	1.14275i
$220$	−1.52004e8	−	1.27546e8i	−0.962442	−	0.807585i
$221$	−1.03428e7	+	5.86571e7i	−0.0644564	+	0.365551i
$222$	−8.60959e7	+	2.45891e7i	−0.528137	+	0.150837i
$223$	−9.93408e7	+	8.33569e7i	−0.599875	+	0.503355i	−0.891405	−	0.453207i	$-0.850280\pi$
$223$	−9.93408e7	+	8.33569e7i	−0.599875	+	0.503355i	0.291530	+	0.956562i	$0.405836\pi$
$224$	9.70264e7	+	1.68055e8i	0.576795	+	0.999039i
$225$	−7.43275e7	−	1.85093e8i	−0.435022	−	1.08331i
$226$	−9.24171e6	+	1.60071e7i	−0.0532565	+	0.0922430i
$227$	−3.02196e7	−	1.71384e8i	−0.171474	−	0.972479i	−0.942135	−	0.335233i	$-0.891185\pi$
$227$	−3.02196e7	−	1.71384e8i	−0.171474	−	0.972479i	0.770661	−	0.637245i	$-0.219926\pi$
$228$	−4.06452e6	+	6.01218e6i	−0.0227111	+	0.0335938i
$229$	9.95192e7	−	3.62220e7i	0.547624	−	0.199319i	−0.0533664	−	0.998575i	$-0.516995\pi$
$229$	9.95192e7	−	3.62220e7i	0.547624	−	0.199319i	0.600991	+	0.799256i	$0.294773\pi$
$230$	−3.13836e6	+	1.14227e6i	−0.0170081	+	0.00619044i
$231$	1.78126e8	+	3.66194e8i	0.950790	+	1.95465i
$232$	3.60157e7	+	2.04255e8i	0.189358	+	1.07390i
$233$	−5.72793e7	+	9.92107e7i	−0.296655	+	0.513822i	−0.975369	−	0.220581i	$-0.929205\pi$
$233$	−5.72793e7	+	9.92107e7i	−0.296655	+	0.513822i	0.678713	+	0.734403i	$0.262538\pi$
$234$	−4.67861e7	−	5.21828e7i	−0.238705	−	0.266239i
$235$	−2.14194e8	−	3.70996e8i	−1.07664	−	1.86480i
$236$	−1.43342e7	+	1.20278e7i	−0.0709873	+	0.0595654i
$237$	2.09785e8	+	2.03016e8i	1.02366	+	0.990630i
$238$	2.38668e7	−	1.35355e8i	0.114756	−	0.650812i
$239$	1.12338e8	+	9.42625e7i	0.532271	+	0.446628i	0.868885	−	0.495014i	$-0.164837\pi$
$239$	1.12338e8	+	9.42625e7i	0.532271	+	0.446628i	−0.336614	+	0.941643i	$0.609282\pi$
$240$	−6.77586e7	−	3.02540e7i	−0.316392	−	0.141268i
$241$	1.05544e7	+	3.84149e6i	0.0485706	+	0.0176783i	0.366191	−	0.930540i	$-0.380662\pi$
$241$	1.05544e7	+	3.84149e6i	0.0485706	+	0.0176783i	−0.317621	+	0.948218i	$0.602884\pi$
$242$	−2.83202e8			−1.28453
$243$	−1.12861e8	+	1.93116e8i	−0.504572	+	0.863369i
$244$	1.52774e8			0.673263
$245$	−2.13199e8	−	7.75981e7i	−0.926198	−	0.337108i
$246$	5.57214e7	+	2.48794e7i	0.238643	+	0.106553i
$247$	7.38769e6	+	6.19901e6i	0.0311939	+	0.0261748i
$248$	4.28968e7	−	2.43280e8i	0.178585	−	1.01280i
$249$	1.26067e8	+	1.22000e8i	0.517494	+	0.500797i
$250$	−3.27369e7	+	2.74695e7i	−0.132509	+	0.111189i
$251$	−2.31229e6	−	4.00501e6i	−0.00922964	−	0.0159862i	0.861374	−	0.507972i	$-0.169605\pi$
$251$	−2.31229e6	−	4.00501e6i	−0.00922964	−	0.0159862i	−0.870603	+	0.491986i	$0.836271\pi$
$252$	−1.11159e8	−	1.23980e8i	−0.437563	−	0.488035i
$253$	3.79482e6	−	6.57283e6i	0.0147323	−	0.0255170i
$254$	3.72348e7	+	2.11169e8i	0.142571	+	0.808561i
$255$	−1.24244e8	−	2.55423e8i	−0.469229	−	0.964649i
$256$	2.68391e8	−	9.76864e7i	0.999835	−	0.363910i
$257$	1.44716e8	−	5.26723e7i	0.531802	−	0.193560i	−0.0621405	−	0.998067i	$-0.519793\pi$
$257$	1.44716e8	−	5.26723e7i	0.531802	−	0.193560i	0.593943	+	0.804507i	$0.297570\pi$
$258$	−2.12097e8	+	3.13730e8i	−0.768892	+	1.13733i
$259$	4.90899e7	+	2.78403e8i	0.175567	+	0.995690i
$260$	5.39118e7	−	9.33780e7i	0.190229	−	0.329487i
$261$	−1.10321e8	−	2.74726e8i	−0.384076	−	0.956441i
$262$	−1.49293e8	−	2.58583e8i	−0.512843	−	0.888270i
$263$	−4.34720e8	+	3.64774e8i	−1.47355	+	1.23646i	−0.560790	+	0.827958i	$0.689503\pi$
$263$	−4.34720e8	+	3.64774e8i	−1.47355	+	1.23646i	−0.912760	+	0.408497i	$0.866053\pi$
$264$	5.11648e8	−	1.46127e8i	1.71142	−	0.488785i
$265$	−5.35734e7	+	3.03830e8i	−0.176843	+	1.00293i
$266$	−1.70476e7	−	1.43046e7i	−0.0555363	−	0.0466005i
$267$	−3.98837e7	−	3.83368e8i	−0.128235	−	1.23261i
$268$	1.92399e8	+	7.00274e7i	0.610563	+	0.222227i
$269$	5.48496e7			0.171807			0.0859034	−	0.996303i	$-0.472622\pi$
$269$	5.48496e7			0.171807			0.0859034	+	0.996303i	$0.472622\pi$
$270$	3.26697e8	+	7.05256e7i	1.01012	+	0.218059i
$271$	−3.42655e8			−1.04584			−0.522919	−	0.852382i	$-0.675157\pi$
$271$	−3.42655e8			−1.04584			−0.522919	+	0.852382i	$0.675157\pi$
$272$	−5.34842e7	−	1.94666e7i	−0.161151	−	0.0586543i
$273$	−1.79156e8	+	1.29875e8i	−0.532921	+	0.386329i
$274$	1.16593e8	+	9.78331e7i	0.342409	+	0.287315i
$275$	1.17610e8	−	6.66998e8i	0.341019	−	1.93402i
$276$	−753983.	+	3.01049e6i	−0.00215864	+	0.00861898i
$277$	−3.21375e8	+	2.69666e8i	−0.908517	+	0.762336i	−0.971836	−	0.235657i	$-0.924276\pi$
$277$	−3.21375e8	+	2.69666e8i	−0.908517	+	0.762336i	0.0633195	+	0.997993i	$0.479831\pi$
$278$	−7.00624e7	−	1.21352e8i	−0.195582	−	0.338758i
$279$	1.15606e7	+	3.52422e8i	0.0318688	+	0.971513i
$280$	−3.69638e8	+	6.40232e8i	−1.00629	+	1.74295i
$281$	−7.23299e7	−	4.10203e8i	−0.194467	−	1.10288i	−0.913176	−	0.407565i	$-0.866378\pi$
$281$	−7.23299e7	−	4.10203e8i	−0.194467	−	1.10288i	0.718709	−	0.695311i	$-0.244733\pi$
$282$	3.85662e8	+	2.73780e7i	1.02408	+	0.0726992i
$283$	−2.06159e8	+	7.50356e7i	−0.540691	+	0.196795i	−0.597906	−	0.801566i	$-0.704000\pi$
$283$	−2.06159e8	+	7.50356e7i	−0.540691	+	0.196795i	0.0572147	+	0.998362i	$0.481778\pi$
$284$	−1.18207e8	+	4.30237e7i	−0.306216	+	0.111454i
$285$	−4.58744e7	−	3.25660e6i	−0.117385	−	0.00833313i
$286$	−4.13254e7	−	2.34368e8i	−0.104457	−	0.592403i
$287$	9.63339e7	−	1.66855e8i	0.240543	−	0.416633i
$288$	−3.07345e8	+	1.91148e8i	−0.758144	+	0.471514i
$289$	9.62397e7	+	1.66692e8i	0.234537	+	0.406230i
$290$	−3.38869e8	+	2.84345e8i	−0.815904	+	0.684624i
$291$	9.85819e7	−	3.93617e8i	0.234516	−	0.936371i
$292$	−4.30586e7	+	2.44197e8i	−0.101209	+	0.573986i
$293$	−2.69906e8	−	2.26478e8i	−0.626868	−	0.526005i	0.273086	−	0.961990i	$-0.411956\pi$
$293$	−2.69906e8	−	2.26478e8i	−0.626868	−	0.526005i	−0.899954	+	0.435985i	$0.856400\pi$
$294$	1.65787e8	−	1.20183e8i	0.380482	−	0.275822i
$295$	−1.11429e8	−	4.05569e7i	−0.252709	−	0.0919787i
$296$	3.69396e8			0.827888
$297$	−6.71746e8	+	3.54444e8i	−1.48784	+	0.785056i
$298$	−2.15437e8			−0.471589
$299$	3.87544e6	+	1.41055e6i	0.00838440	+	0.00305167i
$300$	2.86578e7	+	2.75462e8i	0.0612799	+	0.589031i
$301$	9.15924e8	+	7.68551e8i	1.93587	+	1.62439i
$302$	7.76176e7	−	4.40191e8i	0.162157	−	0.919638i
$303$	4.81245e8	−	1.37444e8i	0.993842	−	0.283842i
$304$	−7.05958e6	+	5.92369e6i	−0.0144119	+	0.0120930i
$305$	4.84076e8	+	8.38444e8i	0.976931	+	1.69209i
$306$	2.53781e8	+	3.62141e7i	0.506330	+	0.0722525i
$307$	1.62919e8	−	2.82183e8i	0.321356	−	0.556605i	−0.659412	−	0.751782i	$-0.729195\pi$
$307$	1.62919e8	−	2.82183e8i	0.321356	−	0.556605i	0.980768	+	0.195177i	$0.0625280\pi$
$308$	−9.81844e7	−	5.56832e8i	−0.191476	−	1.08592i
$309$	−1.10088e8	+	1.62841e8i	−0.212269	+	0.313985i
$310$	4.95104e8	−	1.80203e8i	0.943910	−	0.343555i
$311$	−7.80914e8	+	2.84230e8i	−1.47212	+	0.535806i	−0.948674	−	0.316255i	$-0.897574\pi$
$311$	−7.80914e8	+	2.84230e8i	−1.47212	+	0.535806i	−0.523442	+	0.852061i	$0.675352\pi$
$312$	1.26477e8	+	2.60014e8i	0.235760	+	0.484680i
$313$	−6.41430e7	−	3.63773e8i	−0.118234	−	0.670541i	−0.985098	−	0.171995i	$-0.944979\pi$
$313$	−6.41430e7	−	3.63773e8i	−0.118234	−	0.670541i	0.866863	−	0.498546i	$-0.166132\pi$
$314$	6.45442e7	−	1.11794e8i	0.117653	−	0.203781i
$315$	3.28207e8	−	1.00289e9i	0.591645	−	1.80787i
$316$	−2.02675e8	−	3.51043e8i	−0.361322	−	0.625828i
$317$	2.87148e8	−	2.40946e8i	0.506290	−	0.424827i	−0.353532	−	0.935423i	$-0.615019\pi$
$317$	2.87148e8	−	2.40946e8i	0.506290	−	0.424827i	0.859821	+	0.510595i	$0.170575\pi$
$318$	−2.00091e8	−	1.93635e8i	−0.348926	−	0.337668i
$319$	1.74563e8	−	9.89996e8i	0.301082	−	1.70752i
$320$	5.69875e8	+	4.78182e8i	0.972198	+	0.815771i
$321$	−5.42741e8	−	2.42332e8i	−0.915851	−	0.408924i
$322$	−8.94284e6	−	3.25493e6i	−0.0149273	−	0.00543308i
$323$	−3.52746e7			−0.0582442
$324$	2.24320e8	−	2.14797e8i	0.366404	−	0.350849i
$325$	3.68033e8			0.594696
$326$	−5.03378e8	−	1.83215e8i	−0.804697	−	0.292886i
$327$	8.68925e8	+	3.87972e8i	1.37425	+	0.613597i
$328$	−1.92856e8	−	1.61826e8i	−0.301770	−	0.253215i
$329$	2.11973e8	−	1.20216e9i	0.328167	−	1.86113i
$330$	8.15538e8	+	7.89224e8i	1.24924	+	1.20893i
$331$	−2.26648e8	+	1.90180e8i	−0.343521	+	0.288249i	−0.798182	−	0.602416i	$-0.794205\pi$
$331$	−2.26648e8	+	1.90180e8i	−0.343521	+	0.288249i	0.454661	+	0.890665i	$0.349760\pi$
$332$	−1.21795e8	−	2.10954e8i	−0.182660	−	0.316377i
$333$	−5.15980e8	+	1.08535e8i	−0.765735	+	0.161070i
$334$	1.62770e8	−	2.81926e8i	0.239035	−	0.414021i
$335$	2.25310e8	+	1.27780e9i	0.327434	+	1.85697i
$336$	−9.24934e7	−	1.90150e8i	−0.133022	−	0.273469i
$337$	−5.31072e8	+	1.93295e8i	−0.755873	+	0.275115i	−0.691075	−	0.722783i	$-0.742863\pi$
$337$	−5.31072e8	+	1.93295e8i	−0.755873	+	0.275115i	−0.0647983	+	0.997898i	$0.520640\pi$
$338$	−3.46742e8	+	1.26204e8i	−0.488425	+	0.177772i
$339$	−6.09606e7	+	9.01720e7i	−0.0849866	+	0.125711i
$340$	6.84844e7	+	3.88394e8i	0.0944964	+	0.535916i
$341$	−5.98667e8	+	1.03692e9i	−0.817607	+	1.41614i
$342$	2.56234e7	−	3.26539e7i	0.0346374	−	0.0441411i
$343$	1.59576e8	+	2.76393e8i	0.213519	+	0.369826i
$344$	1.19682e9	−	1.00425e9i	1.58517	−	1.33011i
$345$	−1.89110e7	+	5.40102e6i	−0.0247941	+	0.00708123i
$346$	−7.01485e7	+	3.97832e8i	−0.0910442	+	0.516337i
$347$	5.68368e8	+	4.76918e8i	0.730259	+	0.612760i	0.930202	−	0.367048i	$-0.119631\pi$
$347$	5.68368e8	+	4.76918e8i	0.730259	+	0.612760i	−0.199944	+	0.979807i	$0.564076\pi$
$348$	4.25355e7	+	4.08857e8i	0.0541033	+	0.520049i
$349$	−1.99505e8	−	7.26137e7i	−0.251226	−	0.0914386i	0.213338	−	0.976978i	$-0.431566\pi$
$349$	−1.99505e8	−	7.26137e7i	−0.251226	−	0.0914386i	−0.464563	+	0.885540i	$0.653789\pi$
$350$	−8.49261e8			−1.05877
$351$	−2.53062e8	−	3.26031e8i	−0.312357	−	0.402424i
$352$	−1.22900e9			−1.50194
$353$	1.12513e9	+	4.09516e8i	1.36142	+	0.495517i	0.916494	−	0.400048i	$-0.131007\pi$
$353$	1.12513e9	+	4.09516e8i	1.36142	+	0.495517i	0.444929	+	0.895566i	$0.353229\pi$
$354$	8.66490e7	−	6.28143e7i	0.103813	−	0.0752570i
$355$	−6.10667e8	−	5.12411e8i	−0.724445	−	0.607881i
$356$	−9.29327e7	+	5.27047e8i	−0.109168	+	0.619120i
$357$	1.96635e8	−	7.85123e8i	0.228730	−	0.913270i
$358$	1.17047e8	−	9.82138e7i	0.134824	−	0.113131i
$359$	6.38946e7	+	1.10669e8i	0.0728842	+	0.126239i	0.900164	−	0.435551i	$-0.143446\pi$
$359$	6.38946e7	+	1.10669e8i	0.0728842	+	0.126239i	−0.827280	+	0.561790i	$0.810113\pi$
$360$	−1.21609e9	−	6.49908e8i	−1.37374	−	0.734164i
$361$	4.44080e8	−	7.69169e8i	0.496805	−	0.860492i
$362$	3.36963e7	+	1.91101e8i	0.0373338	+	0.211731i
$363$	−1.66353e9	−	1.18093e8i	−1.82540	−	0.129584i
$364$	2.88717e8	−	1.05084e8i	0.313774	−	0.114205i
$365$	−1.47662e9	+	5.37447e8i	−1.58944	+	0.578509i
$366$	−8.71589e8	−	6.18738e7i	−0.929240	−	0.0659664i
$367$	1.94065e8	+	1.10060e9i	0.204935	+	1.16224i	0.897542	+	0.440929i	$0.145351\pi$
$367$	1.94065e8	+	1.10060e9i	0.204935	+	1.16224i	−0.692607	+	0.721315i	$0.743538\pi$
$368$	−1.97050e6	+	3.41300e6i	−0.00206115	+	0.00357001i
$369$	3.16933e8	+	1.69377e8i	0.328379	+	0.175494i
$370$	3.93929e8	+	6.82306e8i	0.404308	+	0.700282i
$371$	−6.73450e8	+	5.65091e8i	−0.684694	+	0.574526i
$372$	1.18947e8	−	4.74932e8i	0.119799	−	0.478334i
$373$	9.72250e7	−	5.51391e8i	0.0970057	−	0.550147i	−0.897109	−	0.441810i	$-0.854337\pi$
$373$	9.72250e7	−	5.51391e8i	0.0970057	−	0.550147i	0.994114	−	0.108336i	$-0.0345524\pi$
$374$	6.66819e8	+	5.59528e8i	0.659109	+	0.553058i
$375$	−2.03751e8	+	1.47705e8i	−0.199522	+	0.144639i
$376$	−1.49888e9	−	5.45548e8i	−1.45415	−	0.529268i
$377$	5.46256e8			0.525051
$378$	5.83957e8	+	7.52339e8i	0.556109	+	0.716460i
$379$	1.60910e9			1.51826			0.759131	−	0.650938i	$-0.225624\pi$
$379$	1.60910e9			1.51826			0.759131	+	0.650938i	$0.225624\pi$
$380$	6.00057e7	+	2.18403e7i	0.0560983	+	0.0204181i
$381$	1.30661e8	+	1.25593e9i	0.121035	+	1.16340i
$382$	−6.92301e8	−	5.80910e8i	−0.635438	−	0.533196i
$383$	2.96979e6	−	1.68425e7i	0.00270104	−	0.0153183i	−0.983427	−	0.181302i	$-0.941969\pi$
$383$	2.96979e6	−	1.68425e7i	0.00270104	−	0.0153183i	0.986128	+	0.165984i	$0.0530799\pi$
$384$	3.06965e8	−	8.76695e7i	0.276649	−	0.0790113i
$385$	2.74486e9	−	2.30321e9i	2.45137	−	2.05694i
$386$	1.55417e8	+	2.69190e8i	0.137544	+	0.238234i
$387$	−1.37668e9	+	1.75441e9i	−1.20738	+	1.53866i
$388$	−2.81708e8	+	4.87933e8i	−0.244843	+	0.424081i
$389$	2.70902e7	+	1.53636e8i	0.0233340	+	0.132334i	0.994249	−	0.107089i	$-0.0341530\pi$
$389$	2.70902e7	+	1.53636e8i	0.0233340	+	0.132334i	−0.970915	+	0.239423i	$0.923042\pi$
$390$	−3.45390e8	+	5.10895e8i	−0.294838	+	0.436120i
$391$	−1.41752e7	+	5.15934e6i	−0.0119925	+	0.00436491i
$392$	−7.93831e8	+	2.88931e8i	−0.665621	+	0.242266i
$393$	−7.69119e8	−	1.58117e9i	−0.639174	−	1.31403i
$394$	−5.75109e7	−	3.26161e8i	−0.0473711	−	0.268655i
$395$	1.28438e9	−	2.22461e9i	1.04859	−	1.81620i
$396$	1.03201e9	−	2.17080e8i	0.835123	−	0.175666i
$397$	2.55273e8	+	4.42146e8i	0.204757	+	0.354649i	0.950055	−	0.312082i	$-0.101026\pi$
$397$	2.55273e8	+	4.42146e8i	0.204757	+	0.354649i	−0.745299	+	0.666731i	$0.767693\pi$
$398$	8.31876e8	−	6.98027e8i	0.661406	−	0.554985i
$399$	−9.41725e7	−	9.11340e7i	−0.0742197	−	0.0718250i
$400$	−6.10700e7	+	3.46345e8i	−0.0477109	+	0.270582i
$401$	1.34601e9	+	1.12943e9i	1.04242	+	0.874692i	0.992276	−	0.124050i	$-0.0395884\pi$
$401$	1.34601e9	+	1.12943e9i	1.04242	+	0.874692i	0.0501412	+	0.998742i	$0.484033\pi$
$402$	−1.06929e9	−	4.77435e8i	−0.820927	−	0.366541i
$403$	−6.11385e8	−	2.22526e8i	−0.465315	−	0.169361i
$404$	−6.94926e8			−0.524329
$405$	1.88961e9	+	5.50498e8i	1.41345	+	0.411778i
$406$	−1.26052e9			−0.934780
$407$	−1.68244e9	−	6.12357e8i	−1.23697	−	0.450219i
$408$	−9.65706e8	−	4.31184e8i	−0.703938	−	0.314306i
$409$	9.54709e8	+	8.01096e8i	0.689985	+	0.578966i	0.918905	−	0.394479i	$-0.129075\pi$
$409$	9.54709e8	+	8.01096e8i	0.689985	+	0.578966i	−0.228920	+	0.973445i	$0.573519\pi$
$410$	9.32408e7	−	5.28795e8i	0.0668132	−	0.378917i
$411$	6.44071e8	+	6.23290e8i	0.457601	+	0.442837i
$412$	2.09073e8	−	1.75433e8i	0.147285	−	0.123587i
$413$	−1.68949e8	−	2.92628e8i	−0.118013	−	0.204405i
$414$	5.52080e6	−	1.68698e7i	0.00382385	−	0.0116844i
$415$	7.71831e8	−	1.33685e9i	0.530095	−	0.918151i
$416$	−1.15967e8	−	6.57682e8i	−0.0789784	−	0.447909i
$417$	−3.60944e8	−	7.42035e8i	−0.243761	−	0.501128i
$418$	1.32442e8	−	4.82049e7i	0.0886969	−	0.0322830i
$419$	2.14322e9	−	7.80069e8i	1.42337	−	0.518065i	0.488347	−	0.872650i	$-0.337600\pi$
$419$	2.14322e9	−	7.80069e8i	1.42337	−	0.518065i	0.935024	+	0.354585i	$0.115378\pi$
$420$	−8.20607e8	+	1.21383e9i	−0.540459	+	0.799439i
$421$	−2.54639e8	−	1.44413e9i	−0.166318	−	0.943234i	−0.947695	−	0.319176i	$-0.896594\pi$
$421$	−2.54639e8	−	1.44413e9i	−0.166318	−	0.943234i	0.781378	−	0.624058i	$-0.214517\pi$
$422$	7.07417e7	−	1.22528e8i	0.0458228	−	0.0793675i
$423$	2.25396e9	+	3.21636e8i	1.44795	+	0.206621i
$424$	5.74370e8	+	9.94838e8i	0.365941	+	0.633829i
$425$	−1.03121e9	+	8.65290e8i	−0.651609	+	0.546765i
$426$	6.91805e8	−	1.97580e8i	0.433561	−	0.123825i
$427$	−4.79056e8	+	2.71686e9i	−0.297775	+	1.68877i
$428$	6.32217e8	+	5.30493e8i	0.389774	+	0.327059i
$429$	−1.45015e8	−	1.39391e9i	−0.0886776	−	0.852381i
$430$	3.13125e9	+	1.13968e9i	1.89923	+	0.691264i
$431$	−2.14893e8			−0.129286			−0.0646431	−	0.997908i	$-0.520591\pi$
$431$	−2.14893e8			−0.129286			−0.0646431	+	0.997908i	$0.520591\pi$
$432$	3.48810e8	−	1.84049e8i	0.208159	−	0.109835i
$433$	3.25358e7			0.0192599			0.00962993	−	0.999954i	$-0.496935\pi$
$433$	3.25358e7			0.0192599			0.00962993	+	0.999954i	$0.496935\pi$
$434$	1.41081e9	+	5.13494e8i	0.828429	+	0.301523i
$435$	−2.10909e9	+	1.52894e9i	−1.22852	+	0.890588i
$436$	−1.01218e9	−	8.49317e8i	−0.584862	−	0.490758i
$437$	−424130.	+	2.40536e6i	−0.000243116	+	0.00137878i
$438$	3.44554e8	−	1.37573e9i	0.195928	−	0.782300i
$439$	−5.87509e7	+	4.92978e7i	−0.0331427	+	0.0278101i	−0.659209	−	0.751960i	$-0.729109\pi$
$439$	−5.87509e7	+	4.92978e7i	−0.0331427	+	0.0278101i	0.626066	+	0.779770i	$0.284664\pi$
$440$	−2.34103e9	−	4.05479e9i	−1.31016	−	2.26926i
$441$	1.02395e9	−	6.36826e8i	0.568516	−	0.353578i
$442$	−2.36504e8	+	4.09636e8i	−0.130275	+	0.225642i
$443$	1.72570e8	+	9.78692e8i	0.0943087	+	0.534851i	0.994957	+	0.100302i	$0.0319810\pi$
$443$	1.72570e8	+	9.78692e8i	0.0943087	+	0.534851i	−0.900648	+	0.434549i	$0.856908\pi$
$444$	7.30278e8	+	5.18421e7i	0.395957	+	0.0281088i
$445$	−3.18697e9	+	1.15996e9i	−1.71442	+	0.623999i
$446$	−9.67740e8	+	3.52229e8i	−0.516519	+	0.187998i
$447$	−1.26548e9	−	8.98357e7i	−0.670159	−	0.0475743i
$448$	3.68102e8	+	2.08761e9i	0.193417	+	1.09692i
$449$	−9.08229e8	+	1.57310e9i	−0.473514	+	0.820151i	−0.999540	−	0.0303177i	$-0.990348\pi$
$449$	−9.08229e8	+	1.57310e9i	−0.473514	+	0.820151i	0.526026	+	0.850468i	$0.323681\pi$
$450$	−5.19322e7	−	1.58314e9i	−0.0268654	−	0.818986i
$451$	6.10113e8	+	1.05675e9i	0.313179	+	0.542441i
$452$	1.15773e8	−	9.71450e7i	0.0589688	−	0.0494807i
$453$	6.39482e8	−	2.55332e9i	0.323210	−	1.29051i
$454$	2.39987e8	−	1.36104e9i	0.120363	−	0.682612i
$455$	1.49154e9	+	1.25155e9i	0.742326	+	0.622885i
$456$	−1.38642e8	+	1.00506e8i	−0.0684730	+	0.0496380i
$457$	−2.07512e9	−	7.55280e8i	−1.01703	−	0.370170i	−0.220904	−	0.975296i	$-0.570901\pi$
$457$	−2.07512e9	−	7.55280e8i	−1.01703	−	0.370170i	−0.796130	+	0.605125i	$0.793123\pi$
$458$	8.41047e8			0.409064
$459$	1.47561e9	+	3.18546e8i	0.712240	+	0.153755i
$460$	2.73079e7			0.0130808
$461$	−2.68736e8	−	9.78120e7i	−0.127754	−	0.0464985i	0.277352	−	0.960768i	$-0.410543\pi$
$461$	−2.68736e8	−	9.78120e7i	−0.127754	−	0.0464985i	−0.405106	+	0.914270i	$0.632765\pi$
$462$	3.34633e8	+	3.21654e9i	0.157878	+	1.51755i
$463$	−3.05563e9	−	2.56397e9i	−1.43076	−	1.20055i	−0.945262	−	0.326312i	$-0.894194\pi$
$463$	−3.05563e9	−	2.56397e9i	−1.43076	−	1.20055i	−0.485497	−	0.874238i	$-0.661361\pi$
$464$	−9.06435e7	+	5.14065e8i	−0.0421235	+	0.238894i
$465$	2.98338e9	−	8.52058e8i	1.37602	−	0.392992i
$466$	−6.96917e8	+	5.84783e8i	−0.319029	+	0.267697i
$467$	−4.82347e8	−	8.35449e8i	−0.219154	−	0.379587i	0.735395	−	0.677638i	$-0.236997\pi$
$467$	−4.82347e8	−	8.35449e8i	−0.219154	−	0.379587i	−0.954550	+	0.298052i	$0.903663\pi$
$468$	2.13547e8	+	5.31784e8i	0.0963016	+	0.239814i
$469$	−1.84864e9	+	3.20194e9i	−0.827462	+	1.43321i
$470$	−5.90755e8	−	3.35034e9i	−0.262461	−	1.48849i
$471$	4.25750e8	−	6.29762e8i	0.187751	−	0.277718i
$472$	−4.14898e8	+	1.51011e8i	−0.181612	+	0.0661014i
$473$	−7.11577e9	+	2.58993e9i	−3.09178	+	1.12531i
$474$	1.01410e9	+	2.08481e9i	0.437379	+	0.899173i
$475$	3.78486e7	+	2.14650e8i	0.0162040	+	0.0918975i
$476$	−5.61906e8	+	9.73250e8i	−0.238803	+	0.413618i
$477$	−1.09459e9	−	1.22085e9i	−0.461783	−	0.515049i
$478$	5.82291e8	+	1.00856e9i	0.243861	+	0.422380i
$479$	1.59895e9	−	1.34168e9i	0.664755	−	0.557796i	−0.246753	−	0.969078i	$-0.579364\pi$
$479$	1.59895e9	−	1.34168e9i	0.664755	−	0.557796i	0.911508	+	0.411283i	$0.134919\pi$
$480$	2.28856e9	+	2.21472e9i	0.944534	+	0.914058i
$481$	1.68942e8	−	9.58116e8i	0.0692196	−	0.392564i
$482$	6.83283e7	+	5.73343e7i	0.0277930	+	0.0233211i
$483$	−5.11729e7	−	2.28485e7i	−0.0206645	−	0.00922664i
$484$	2.17597e9	+	7.91988e8i	0.872357	+	0.317512i
$485$	−3.57045e9			−1.42111
$486$	−1.36676e9	+	1.13458e9i	−0.540088	+	0.448343i
$487$	3.84291e9			1.50768			0.753839	−	0.657059i	$-0.228200\pi$
$487$	3.84291e9			1.50768			0.753839	+	0.657059i	$0.228200\pi$
$488$	3.38745e9	+	1.23293e9i	1.31948	+	0.480252i
$489$	−2.88044e9	−	1.28611e9i	−1.11398	−	0.497389i
$490$	−1.38023e9	−	1.15815e9i	−0.529988	−	0.444713i
$491$	4.53422e8	−	2.57149e9i	0.172869	−	0.980390i	−0.767705	−	0.640803i	$-0.778602\pi$
$491$	4.53422e8	−	2.57149e9i	0.172869	−	0.980390i	0.940575	−	0.339587i	$-0.110287\pi$
$492$	−3.58556e8	−	3.46987e8i	−0.135731	−	0.131352i
$493$	−1.53058e9	+	1.28431e9i	−0.575298	+	0.482733i
$494$	3.82934e7	+	6.63261e7i	0.0142915	+	0.0247537i
$495$	4.46137e9	+	4.97597e9i	1.65329	+	1.84400i
$496$	3.10863e8	−	5.38431e8i	0.114389	−	0.198127i
$497$	−3.94451e8	−	2.23704e9i	−0.144127	−	0.817386i
$498$	6.09412e8	+	1.25284e9i	0.221110	+	0.454562i
$499$	8.22020e8	−	2.99191e8i	0.296163	−	0.107794i	−0.189665	−	0.981849i	$-0.560740\pi$
$499$	8.22020e8	−	2.99191e8i	0.296163	−	0.107794i	0.485828	+	0.874054i	$0.338518\pi$
$500$	3.28352e8	−	1.19510e8i	0.117475	−	0.0427573i
$501$	1.07367e9	−	1.58816e9i	0.381452	−	0.564238i
$502$	−6.37738e6	−	3.61679e7i	−0.00224998	−	0.0127603i
$503$	7.41112e8	−	1.28364e9i	0.259654	−	0.449735i	−0.706495	−	0.707718i	$-0.749725\pi$
$503$	7.41112e8	−	1.28364e9i	0.259654	−	0.449735i	0.966149	+	0.257984i	$0.0830580\pi$
$504$	−1.46415e9	−	3.64609e9i	−0.509424	−	1.26859i
$505$	−2.20193e9	−	3.81385e9i	−0.760822	−	1.31778i
$506$	4.61716e7	−	3.87425e7i	0.0158434	−	0.0132942i
$507$	−2.08939e9	+	5.96731e8i	−0.712018	+	0.203353i
$508$	3.04453e8	−	1.72664e9i	0.103038	−	0.584357i
$509$	−1.10451e9	−	9.26796e8i	−0.371243	−	0.311510i	0.438010	−	0.898970i	$-0.355683\pi$
$509$	−1.10451e9	−	9.26796e8i	−0.371243	−	0.311510i	−0.809253	+	0.587460i	$0.800128\pi$
$510$	−2.33409e8	−	2.24356e9i	−0.0779151	−	0.748931i
$511$	−4.20767e9	−	1.53147e9i	−1.39498	−	0.507732i
$512$	1.39442e9			0.459145
$513$	1.64128e8	−	1.81124e8i	0.0536751	−	0.0592332i
$514$	1.22301e9			0.397245
$515$	1.62527e9	+	5.91549e8i	0.524323	+	0.190838i
$516$	2.50700e9	−	1.81739e9i	0.803304	−	0.582338i
$517$	5.92237e9	+	4.96946e9i	1.88486	+	1.58158i
$518$	−3.89844e8	+	2.21092e9i	−0.123236	+	0.698905i
$519$	−5.77945e8	+	2.30761e9i	−0.181468	+	0.724565i
$520$	1.94897e9	−	1.63538e9i	0.607846	−	0.510043i
$521$	1.85636e9	+	3.21531e9i	0.575083	+	0.996073i	0.996033	+	0.0889887i	$0.0283635\pi$
$521$	1.85636e9	+	3.21531e9i	0.575083	+	0.996073i	−0.420950	+	0.907084i	$0.638303\pi$
$522$	−7.70807e7	−	2.34979e9i	−0.0237192	−	0.723074i
$523$	−2.61830e9	+	4.53503e9i	−0.800321	+	1.38620i	0.119085	+	0.992884i	$0.462004\pi$
$523$	−2.61830e9	+	4.53503e9i	−0.800321	+	1.38620i	−0.919405	+	0.393312i	$0.871329\pi$
$524$	4.23945e8	+	2.40431e9i	0.128721	+	0.730014i
$525$	−4.98856e9	−	3.54136e8i	−1.50459	−	0.106810i
$526$	−4.23488e9	+	1.54137e9i	−1.26879	+	0.461803i
$527$	2.23626e9	−	8.13932e8i	0.665557	−	0.242243i
$528$	1.33583e9	+	9.48301e7i	0.394941	+	0.0280367i
$529$	−5.91060e8	−	3.35207e9i	−0.173595	−	0.984506i
$530$	−1.22503e9	+	2.12182e9i	−0.357423	+	0.619074i
$531$	5.35169e8	−	3.32839e8i	0.155117	−	0.0964724i
$532$	9.09807e7	+	1.57583e8i	0.0261974	+	0.0453753i
$533$	−5.07935e8	+	4.26208e8i	−0.145299	+	0.121920i
$534$	7.43644e8	−	2.96921e9i	0.211335	−	0.843815i
$535$	−9.08190e8	+	5.15060e9i	−0.256412	+	1.45418i
$536$	3.70090e9	+	3.10543e9i	1.03808	+	0.871053i
$537$	7.28487e8	−	5.28100e8i	0.203007	−	0.147166i
$538$	4.09315e8	+	1.48979e8i	0.113324	+	0.0412464i
$539$	4.09451e9			1.12627
$540$	−2.31293e9	−	1.45550e9i	−0.632098	−	0.397773i
$541$	2.80583e9			0.761851			0.380926	−	0.924606i	$-0.375605\pi$
$541$	2.80583e9			0.761851			0.380926	+	0.924606i	$0.375605\pi$
$542$	−2.55707e9	−	9.30696e8i	−0.689834	−	0.251079i
$543$	1.18244e8	+	1.13658e9i	0.0316942	+	0.304649i
$544$	1.87122e9	+	1.57014e9i	0.498344	+	0.418161i
$545$	1.45401e9	−	8.24608e9i	0.384750	−	2.18203i
$546$	−1.68971e9	+	4.82585e8i	−0.444262	+	0.126882i
$547$	2.54860e9	−	2.13853e9i	0.665802	−	0.558674i	−0.246017	−	0.969265i	$-0.579122\pi$
$547$	2.54860e9	−	2.13853e9i	0.665802	−	0.558674i	0.911820	+	0.410591i	$0.134678\pi$
$548$	−6.22241e8	−	1.07775e9i	−0.161520	−	0.279761i
$549$	−5.09391e9	−	7.26893e8i	−1.31386	−	0.187485i
$550$	2.68932e9	−	4.65803e9i	0.689243	−	1.19380i
$551$	5.61771e7	+	3.18596e8i	0.0143063	+	0.0811353i
$552$	−4.10136e7	+	6.06666e7i	−0.0103787	+	0.0153519i
$553$	6.87831e9	−	2.50350e9i	1.72959	−	0.629520i
$554$	−3.13071e9	+	1.13949e9i	−0.782274	+	0.284724i
$555$	2.02942e9	+	4.17213e9i	0.503903	+	1.03593i
$556$	1.98955e8	+	1.12833e9i	0.0490901	+	0.278404i
$557$	2.47502e9	−	4.28686e9i	0.606856	−	1.05111i	−0.384899	−	0.922959i	$-0.625764\pi$
$557$	2.47502e9	−	4.28686e9i	0.606856	−	1.05111i	0.991755	−	0.128147i	$-0.0409028\pi$
$558$	−8.70954e8	+	2.66135e9i	−0.212215	+	0.648460i
$559$	−2.05741e9	−	3.56353e9i	−0.498171	−	0.862858i
$560$	−1.42530e9	+	1.19597e9i	−0.342963	+	0.287780i
$561$	3.68357e9	+	3.56472e9i	0.880845	+	0.852424i
$562$	5.74403e8	−	3.25760e9i	0.136502	−	0.774142i
$563$	−1.46145e9	−	1.22630e9i	−0.345146	−	0.289612i	0.453691	−	0.891159i	$-0.350107\pi$
$563$	−1.46145e9	−	1.22630e9i	−0.345146	−	0.289612i	−0.798838	+	0.601547i	$0.794551\pi$
$564$	−2.88665e9	−	1.28888e9i	−0.677512	−	0.302507i
$565$	8.99980e8	+	3.27566e8i	0.209925	+	0.0764063i
$566$	−1.74227e9			−0.403885
$567$	3.11644e9	+	4.66274e9i	0.717990	+	1.07424i
$568$	−2.96821e9			−0.679634
$569$	−2.41126e9	−	8.77625e8i	−0.548719	−	0.199717i	0.0527581	−	0.998607i	$-0.483199\pi$
$569$	−2.41126e9	−	8.77625e8i	−0.548719	−	0.199717i	−0.601477	+	0.798890i	$0.705421\pi$
$570$	−3.33493e8	−	1.48903e8i	−0.0754265	−	0.0336777i
$571$	7.48290e8	+	6.27890e8i	0.168207	+	0.141142i	0.723005	−	0.690843i	$-0.242760\pi$
$571$	7.48290e8	+	6.27890e8i	0.168207	+	0.141142i	−0.554799	+	0.831985i	$0.687205\pi$
$572$	−3.37899e8	+	1.91632e9i	−0.0754921	+	0.428137i
$573$	−3.82434e9	−	3.70095e9i	−0.849210	−	0.821810i
$574$	1.17209e9	−	9.83503e8i	0.258685	−	0.217062i
$575$	4.66048e7	+	8.07219e7i	0.0102234	+	0.0177074i
$576$	−3.86910e9	+	8.13852e8i	−0.843589	+	0.177446i
$577$	−9.22146e8	+	1.59720e9i	−0.199841	+	0.346135i	−0.948477	−	0.316847i	$-0.897376\pi$
$577$	−9.22146e8	+	1.59720e9i	−0.199841	+	0.346135i	0.748636	+	0.662982i	$0.230709\pi$
$578$	2.65432e8	+	1.50534e9i	0.0571750	+	0.324255i
$579$	8.00668e8	+	1.64603e9i	0.171426	+	0.352422i
$580$	3.39887e9	−	1.23709e9i	0.723329	−	0.263270i
$581$	4.13343e9	−	1.50444e9i	0.874367	−	0.318244i
$582$	1.80478e9	−	2.66961e9i	0.379485	−	0.561328i
$583$	−9.66834e8	−	5.48319e9i	−0.202075	−	1.14602i
$584$	−2.92548e9	+	5.06708e9i	−0.607788	+	1.05272i
$585$	−2.24186e9	+	2.85697e9i	−0.462981	+	0.590012i
$586$	−1.39903e9	−	2.42319e9i	−0.287201	−	0.497447i
$587$	1.53175e9	−	1.28529e9i	0.312575	−	0.262282i	−0.472980	−	0.881073i	$-0.656822\pi$
$587$	1.53175e9	−	1.28529e9i	0.312575	−	0.262282i	0.785556	+	0.618791i	$0.212377\pi$
$588$	−1.60991e9	+	4.59793e8i	−0.326574	+	0.0932700i
$589$	6.69102e7	−	3.79466e8i	0.0134924	−	0.0765191i
$590$	−7.21383e8	−	6.05312e8i	−0.144605	−	0.121338i
$591$	−2.01812e8	−	1.93985e9i	−0.0402153	−	0.386555i
$592$	8.73621e8	+	3.17972e8i	0.173060	+	0.0629887i
$593$	1.89048e9			0.372290			0.186145	−	0.982522i	$-0.440401\pi$
$593$	1.89048e9			0.372290			0.186145	+	0.982522i	$0.440401\pi$
$594$	−5.97562e9	+	8.20494e8i	−1.16985	+	0.160629i
$595$	−7.12177e9			−1.38605
$596$	1.65530e9	+	6.02480e8i	0.320269	+	0.116568i
$597$	5.17751e9	−	3.75332e9i	0.995889	−	0.721948i
$598$	2.50893e7	+	2.10524e7i	0.00479771	+	0.00402576i
$599$	−9.44111e8	+	5.35432e9i	−0.179485	+	1.01791i	0.753353	+	0.657617i	$0.228435\pi$
$599$	−9.44111e8	+	5.35432e9i	−0.179485	+	1.01791i	−0.932838	+	0.360296i	$0.882676\pi$
$600$	−1.58763e9	+	6.33909e9i	−0.300069	+	1.19811i
$601$	−5.33341e9	+	4.47526e9i	−1.00218	+	0.840925i	−0.987284	−	0.158964i	$-0.949185\pi$
$601$	−5.33341e9	+	4.47526e9i	−1.00218	+	0.840925i	−0.0148915	+	0.999889i	$0.504740\pi$
$602$	4.74760e9	+	8.22309e9i	0.886925	+	1.53620i
$603$	−6.08192e9	−	3.25034e9i	−1.12961	−	0.603695i
$604$	−1.82739e9	+	3.16513e9i	−0.337443	+	0.584469i
$605$	2.54819e9	+	1.44515e10i	0.467830	+	2.65319i
$606$	3.96461e9	+	2.81446e8i	0.723680	+	0.0513738i
$607$	−3.62773e8	+	1.32039e8i	−0.0658377	+	0.0239630i	−0.374729	−	0.927134i	$-0.622264\pi$
$607$	−3.62773e8	+	1.32039e8i	−0.0658377	+	0.0239630i	0.308891	+	0.951097i	$0.400042\pi$
$608$	3.71658e8	−	1.35272e8i	0.0670627	−	0.0244088i
$609$	−7.40430e9	−	5.25629e8i	−1.32838	−	0.0943015i
$610$	1.33510e9	+	7.57171e9i	0.238154	+	1.35064i
$611$	−2.10051e9	+	3.63820e9i	−0.372547	+	0.645270i
$612$	−1.84864e9	−	9.87959e8i	−0.326003	−	0.174224i
$613$	2.53466e9	+	4.39015e9i	0.444434	+	0.769782i	0.998013	−	0.0630146i	$-0.0200715\pi$
$613$	2.53466e9	+	4.39015e9i	0.444434	+	0.769782i	−0.553579	+	0.832797i	$0.686738\pi$
$614$	1.98223e9	−	1.66329e9i	0.345593	−	0.289987i
$615$	7.68200e8	−	3.06726e9i	0.133172	−	0.531725i
$616$	2.31676e9	−	1.31390e10i	0.399344	−	2.26479i
$617$	−3.81077e9	−	3.19762e9i	−0.653153	−	0.548061i	0.254873	−	0.966975i	$-0.417966\pi$
$617$	−3.81077e9	−	3.19762e9i	−0.653153	−	0.548061i	−0.908026	+	0.418914i	$0.862411\pi$
$618$	−1.26383e9	+	9.16188e8i	−0.215392	+	0.156144i
$619$	1.14328e9	+	4.16121e8i	0.193748	+	0.0705184i	0.437072	−	0.899427i	$-0.356016\pi$
$619$	1.14328e9	+	4.16121e8i	0.193748	+	0.0705184i	−0.243324	+	0.969945i	$0.578238\pi$
$620$	−4.30806e9			−0.725956
$621$	3.94637e7	−	9.67909e7i	0.00661268	−	0.0162186i
$622$	−6.59958e9			−1.09964
$623$	−9.08135e9	−	3.30534e9i	−1.50467	−	0.547657i
$624$	7.53007e7	+	7.23801e8i	0.0124066	+	0.119254i
$625$	−3.76191e9	−	3.15662e9i	−0.616352	−	0.517181i
$626$	5.09387e8	−	2.88888e9i	0.0829923	−	0.470673i
$627$	7.98065e8	−	2.27928e8i	0.129301	−	0.0369285i
$628$	−8.08559e8	+	6.78461e8i	−0.130273	+	0.109312i
$629$	1.77928e9	+	3.08180e9i	0.285080	+	0.493773i
$630$	5.17324e9	−	6.59266e9i	0.824272	−	1.05043i
$631$	4.93297e9	−	8.54416e9i	0.781639	−	1.35384i	−0.149348	−	0.988785i	$-0.547718\pi$
$631$	4.93297e9	−	8.54416e9i	0.781639	−	1.35384i	0.930987	−	0.365053i	$-0.118949\pi$
$632$	−1.66088e9	−	9.41929e9i	−0.261714	−	1.48426i
$633$	4.66630e8	−	6.90232e8i	0.0731240	−	0.108164i
$634$	2.79729e9	−	1.01813e9i	0.435938	−	0.158669i
$635$	1.04407e10	−	3.80010e9i	1.61816	−	0.588962i
$636$	9.95882e8	+	2.04735e9i	0.153500	+	0.315568i
$637$	3.86355e8	+	2.19113e9i	0.0592241	+	0.335877i
$638$	3.99164e9	−	6.91372e9i	0.608526	−	1.05400i
$639$	4.14605e9	−	8.72109e8i	0.628610	−	0.132226i
$640$	−1.40451e9	−	2.43268e9i	−0.211785	−	0.366822i
$641$	−5.17518e9	+	4.34249e9i	−0.776108	+	0.651232i	−0.942265	−	0.334867i	$-0.891308\pi$
$641$	−5.17518e9	+	4.34249e9i	−0.776108	+	0.651232i	0.166157	+	0.986099i	$0.446864\pi$
$642$	−3.39200e9	−	3.28256e9i	−0.505922	−	0.489598i
$643$	−2.25179e9	+	1.27705e10i	−0.334033	+	1.89439i	0.102546	+	0.994728i	$0.467301\pi$
$643$	−2.25179e9	+	1.27705e10i	−0.334033	+	1.89439i	−0.436579	+	0.899666i	$0.643810\pi$
$644$	5.96093e7	+	5.00182e7i	0.00879455	+	0.00737950i
$645$	1.79177e10	+	8.00020e9i	2.62920	+	1.17393i
$646$	−2.63237e8	−	9.58104e7i	−0.0384178	−	0.0139829i
$647$	9.52972e9			1.38330			0.691648	−	0.722235i	$-0.256885\pi$
$647$	9.52972e9			1.38330			0.691648	+	0.722235i	$0.256885\pi$
$648$	6.70730e9	−	2.95235e9i	0.968357	−	0.426241i
$649$	2.14001e9			0.307298
$650$	2.74645e9	+	9.99626e8i	0.392261	+	0.142771i
$651$	8.07298e9	+	3.60456e9i	1.14683	+	0.512057i
$652$	3.35531e9	+	2.81544e9i	0.474096	+	0.397814i
$653$	9.82710e8	−	5.57322e9i	0.138111	−	0.783268i	−0.834531	−	0.550961i	$-0.814261\pi$
$653$	9.82710e8	−	5.57322e9i	0.138111	−	0.783268i	0.972642	−	0.232307i	$-0.0746275\pi$
$654$	5.43058e9	+	5.25536e9i	0.759144	+	0.734650i
$655$	−1.18519e10	+	9.94491e9i	−1.64795	+	1.38279i
$656$	−3.16807e8	−	5.48725e8i	−0.0438158	−	0.0758912i
$657$	2.59758e9	−	7.93735e9i	0.357346	−	1.09194i
$658$	4.84707e9	−	8.39538e9i	0.663268	−	1.14881i
$659$	−1.35503e9	−	7.68475e9i	−0.184438	−	1.04600i	−0.926676	−	0.375861i	$-0.877347\pi$
$659$	−1.35503e9	−	7.68475e9i	−0.184438	−	1.04600i	0.742238	−	0.670136i	$-0.233764\pi$
$660$	−4.05904e9	−	8.34465e9i	−0.549566	−	1.12981i
$661$	4.59509e9	−	1.67248e9i	0.618856	−	0.225245i	−0.0135179	−	0.999909i	$-0.504303\pi$
$661$	4.59509e9	−	1.67248e9i	0.618856	−	0.225245i	0.632374	+	0.774664i	$0.282081\pi$
$662$	−2.20792e9	+	8.03616e8i	−0.295787	+	0.107658i
$663$	−1.56004e9	+	2.30758e9i	−0.207892	+	0.307511i
$664$	−9.98080e8	−	5.66040e9i	−0.132305	−	0.750341i
$665$	−5.76559e8	+	9.98629e8i	−0.0760270	+	0.131683i
$666$	−4.14530e9	−	5.91528e8i	−0.543746	−	0.0775917i
$667$	6.91735e7	+	1.19812e8i	0.00902609	+	0.0156336i
$668$	−2.03906e9	+	1.71097e9i	−0.264674	+	0.222088i
$669$	−5.83138e9	+	1.66545e9i	−0.752974	+	0.215050i
$670$	−1.78929e9	+	1.01475e10i	−0.229836	+	1.30346i
$671$	−1.33845e10	−	1.12309e10i	−1.71030	−	1.43511i
$672$	9.39045e8	+	9.02623e9i	0.119370	+	1.14740i
$673$	1.11074e10	+	4.04277e9i	1.40462	+	0.511241i	0.929547	−	0.368703i	$-0.120198\pi$
$673$	1.11074e10	+	4.04277e9i	1.40462	+	0.511241i	0.475077	+	0.879944i	$0.342420\pi$
$674$	−4.48815e9			−0.564621
$675$	3.55110e8	−	9.32104e9i	0.0444426	−	1.16654i
$676$	3.01711e9			0.375645
$677$	−3.14303e9	−	1.14397e9i	−0.389304	−	0.141695i	0.139950	−	0.990159i	$-0.455306\pi$
$677$	−3.14303e9	−	1.14397e9i	−0.389304	−	0.141695i	−0.529254	+	0.848464i	$0.677528\pi$
$678$	−6.99838e8	+	5.07332e8i	−0.0862370	+	0.0625156i
$679$	−7.79381e9	−	6.53978e9i	−0.955445	−	0.801713i
$680$	−1.61595e9	+	9.16453e9i	−0.197082	+	1.11771i
$681$	1.97723e9	−	7.89465e9i	0.239906	−	0.957895i
$682$	−7.28397e9	+	6.11198e9i	−0.879271	+	0.737796i
$683$	2.88772e9	+	5.00168e9i	0.346803	+	0.600680i	0.985680	−	0.168629i	$-0.0539340\pi$
$683$	2.88772e9	+	5.00168e9i	0.346803	+	0.600680i	−0.638877	+	0.769309i	$0.720601\pi$
$684$	−2.88194e8	+	1.79237e8i	−0.0344341	+	0.0214157i
$685$	3.94324e9	−	6.82989e9i	0.468744	−	0.811889i
$686$	4.40115e8	+	2.49601e9i	0.0520513	+	0.295197i
$687$	4.94031e9	+	3.50711e8i	0.581307	+	0.0412667i
$688$	3.69493e9	−	1.34485e9i	0.432561	−	0.157439i
$689$	2.84303e9	−	1.03478e9i	0.331142	−	0.120526i
$690$	−1.55794e8	−	1.10597e7i	−0.0180542	−	0.00128166i
$691$	−1.79484e8	−	1.01790e9i	−0.0206944	−	0.117364i	0.972711	−	0.232021i	$-0.0745340\pi$
$691$	−1.79484e8	−	1.01790e9i	−0.0206944	−	0.117364i	−0.993405	+	0.114658i	$0.963423\pi$
$692$	1.65154e9	−	2.86055e9i	0.189460	−	0.328154i
$693$	6.24359e8	+	1.90335e10i	0.0712637	+	2.17246i
$694$	2.94608e9	+	5.10276e9i	0.334570	+	0.579492i
$695$	−5.56204e9	+	4.66710e9i	−0.628473	+	0.527352i
$696$	−2.35646e9	+	9.40884e9i	−0.264928	+	1.05780i
$697$	4.21145e8	−	2.38843e9i	0.0471104	−	0.267176i
$698$	−1.29158e9	−	1.08376e9i	−0.143756	−	0.120626i
$699$	−4.33754e9	+	3.14440e9i	−0.480367	+	0.348232i
$700$	6.52526e9	+	2.37500e9i	0.719042	+	0.261710i
$701$	2.79968e9			0.306969			0.153485	−	0.988151i	$-0.450950\pi$
$701$	2.79968e9			0.306969			0.153485	+	0.988151i	$0.450950\pi$
$702$	−1.00293e9	−	3.12036e9i	−0.109419	−	0.340428i
$703$	5.76182e8			0.0625484
$704$	−1.26158e10	−	4.59178e9i	−1.36273	−	0.495994i
$705$	−2.07303e9	−	1.99262e10i	−0.222814	−	2.14172i
$706$	7.28403e9	+	6.11203e9i	0.779032	+	0.653685i
$707$	2.17909e9	−	1.23582e10i	0.231904	−	1.31519i
$708$	−8.41426e8	+	2.40312e8i	−0.0891045	+	0.0254484i
$709$	−6.11326e9	+	5.12963e9i	−0.644185	+	0.540536i	−0.905300	−	0.424772i	$-0.860354\pi$
$709$	−6.11326e9	+	5.12963e9i	−0.644185	+	0.540536i	0.261115	+	0.965308i	$0.415910\pi$
$710$	−3.16534e9	−	5.48252e9i	−0.331906	−	0.574879i
$711$	5.08749e9	+	1.26691e10i	0.530836	+	1.32191i
$712$	−6.31401e9	+	1.09362e10i	−0.655580	+	1.13550i
$713$	−2.86136e7	−	1.62276e8i	−0.00295638	−	0.0167664i
$714$	3.59989e9	−	5.32490e9i	0.370123	−	0.547480i
$715$	−1.15877e10	+	4.21758e9i	−1.18557	+	0.431511i
$716$	−1.17398e9	+	4.27295e8i	−0.119527	+	0.0435043i
$717$	2.99982e9	+	6.16708e9i	0.303933	+	0.624831i
$718$	1.76223e8	+	9.99412e8i	0.0177676	+	0.100765i
$719$	3.42217e9	−	5.92737e9i	0.343361	−	0.594718i	−0.641694	−	0.766961i	$-0.721768\pi$
$719$	3.42217e9	−	5.92737e9i	0.343361	−	0.594718i	0.985055	+	0.172243i	$0.0551013\pi$
$720$	−2.31661e9	−	2.58382e9i	−0.231307	−	0.257988i
$721$	2.46423e9	+	4.26817e9i	0.244854	+	0.424100i
$722$	5.40312e9	−	4.53375e9i	0.534274	−	0.448309i
$723$	3.77452e8	+	3.65274e8i	0.0371431	+	0.0359447i
$724$	2.75520e8	−	1.56255e9i	0.0269816	−	0.153020i
$725$	9.45748e9	+	7.93577e9i	0.921706	+	0.773403i
$726$	−1.20933e10	−	5.39964e9i	−1.17292	−	0.523705i
$727$	−1.56029e10	−	5.67899e9i	−1.50603	−	0.548152i	−0.548420	−	0.836203i	$-0.684770\pi$
$727$	−1.56029e10	−	5.67899e9i	−1.50603	−	0.548152i	−0.957615	+	0.288052i	$0.906993\pi$
$728$	7.24976e9			0.696408
$729$	−8.50145e9	+	6.09462e9i	−0.812730	+	0.582640i
$730$	−1.24791e10			−1.18728
$731$	1.41431e10	+	5.14765e9i	1.33916	+	0.487414i
$732$	6.52377e9	+	2.91284e9i	0.614766	+	0.274491i
$733$	4.93762e9	+	4.14316e9i	0.463078	+	0.388568i	0.844262	−	0.535931i	$-0.180039\pi$
$733$	4.93762e9	+	4.14316e9i	0.463078	+	0.388568i	−0.381184	+	0.924499i	$0.624484\pi$
$734$	−1.54116e9	+	8.74033e9i	−0.143850	+	0.815815i
$735$	−7.62454e9	−	7.37853e9i	−0.708285	−	0.685432i
$736$	1.29566e8	−	1.08719e8i	0.0119790	−	0.0100516i
$737$	−1.17080e10	−	2.02789e10i	−1.07733	−	1.86599i
$738$	1.90506e9	+	2.12481e9i	0.174467	+	0.194591i
$739$	−1.30675e9	+	2.26335e9i	−0.119107	+	0.206299i	−0.919414	−	0.393291i	$-0.871336\pi$
$739$	−1.30675e9	+	2.26335e9i	−0.119107	+	0.206299i	0.800307	+	0.599590i	$0.204670\pi$
$740$	−1.11864e9	−	6.34410e9i	−0.101479	−	0.575518i
$741$	1.97278e8	+	4.05567e8i	0.0178121	+	0.0366184i
$742$	−6.56048e9	+	2.38782e9i	−0.589552	+	0.214579i
$743$	2.73895e9	−	9.96895e8i	0.244975	−	0.0891638i	−0.216614	−	0.976257i	$-0.569501\pi$
$743$	2.73895e9	−	9.96895e8i	0.244975	−	0.0891638i	0.461590	+	0.887093i	$0.347279\pi$
$744$	6.47025e9	−	9.57070e9i	0.575991	−	0.851997i
$745$	1.93845e9	+	1.09935e10i	0.171755	+	0.974068i
$746$	2.22319e9	−	3.85068e9i	0.196061	−	0.339587i
$747$	3.05726e9	+	7.61330e9i	0.268355	+	0.668268i
$748$	−3.55873e9	−	6.16389e9i	−0.310913	−	0.538517i
$749$	−1.14165e10	+	9.57958e9i	−0.992765	+	0.833029i
$750$	−1.92168e9	+	5.48833e8i	−0.166328	+	0.0475036i
$751$	2.19413e9	−	1.24435e10i	0.189026	−	1.07202i	−0.731646	−	0.681685i	$-0.761247\pi$
$751$	2.19413e9	−	1.24435e10i	0.189026	−	1.07202i	0.920672	−	0.390337i	$-0.127641\pi$
$752$	−3.07525e9	−	2.58044e9i	−0.263704	−	0.221274i
$753$	−2.23789e7	−	2.15110e8i	−0.00191010	−	0.0183602i
$754$	4.07644e9	+	1.48370e9i	0.346323	+	0.126051i
$755$	−2.31608e10			−1.95857

Introduction	Features
Universe	News

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

\(f(q)\)	\(=\)	\(q+(7.46251 + 2.71613i) q^{2} +(42.7022 + 19.0664i) q^{3} +(-49.7420 - 41.7385i) q^{4} +(71.4552 - 405.243i) q^{5} +(266.878 + 258.268i) q^{6} +(898.235 - 753.709i) q^{7} +(-766.085 - 1326.90i) q^{8} +(1459.95 + 1628.35i) q^{9} +O(q^{10})\)	\(q+(7.46251 + 2.71613i) q^{2} +(42.7022 + 19.0664i) q^{3} +(-49.7420 - 41.7385i) q^{4} +(71.4552 - 405.243i) q^{5} +(266.878 + 258.268i) q^{6} +(898.235 - 753.709i) q^{7} +(-766.085 - 1326.90i) q^{8} +(1459.95 + 1628.35i) q^{9} +(1633.93 - 2830.04i) q^{10} +(1289.55 + 7313.38i) q^{11} +(-1328.29 - 2730.72i) q^{12} +(-3791.99 + 1380.17i) q^{13} +(8750.26 - 3184.83i) q^{14} +(10777.8 - 15942.3i) q^{15} +(-669.609 - 3797.54i) q^{16} +(7380.03 - 12782.6i) q^{17} +(6472.06 + 16117.0i) q^{18} +(-1194.93 - 2069.69i) q^{19} +(-20468.5 + 17175.2i) q^{20} +(52727.1 - 15058.9i) q^{21} +(-10240.9 + 58078.8i) q^{22} +(-782.904 - 656.935i) q^{23} +(-7414.36 - 71267.9i) q^{24} +(-85702.2 - 31193.0i) q^{25} -32046.4 q^{26} +(31296.2 + 97369.9i) q^{27} -76138.7 q^{28} +(-127204. - 46298.5i) q^{29} +(123731. - 89695.9i) q^{30} +(123510. + 103637. i) q^{31} +(-28737.8 + 162980. i) q^{32} +(-84373.2 + 336884. i) q^{33} +(89792.7 - 75345.0i) q^{34} +(-241251. - 417860. i) q^{35} +(-4655.87 - 141933. i) q^{36} +(-120547. + 208793. i) q^{37} +(-3295.66 - 18690.6i) q^{38} +(-188241. - 13363.1i) q^{39} +(-592456. + 215636. i) q^{40} +(154404. - 56198.5i) q^{41} +(434378. + 30836.3i) q^{42} +(177068. + 1.00420e6i) q^{43} +(241105. - 417606. i) q^{44} +(764197. - 475279. i) q^{45} +(-4058.11 - 7028.85i) q^{46} +(797496. - 669179. i) q^{47} +(43811.6 - 174930. i) q^{48} +(95742.7 - 542984. i) q^{49} +(-554829. - 465557. i) q^{50} +(558861. - 405134. i) q^{51} +(246227. + 89619.4i) q^{52} -749747. q^{53} +(-30921.2 + 811628. i) q^{54} +3.05584e6 q^{55} +(-1.68822e6 - 614461. i) q^{56} +(-11564.9 - 111163. i) q^{57} +(-823509. - 691006. i) q^{58} +(50040.2 - 283792. i) q^{59} +(-1.20152e6 + 343155. i) q^{60} +(-1.80233e6 + 1.51233e6i) q^{61} +(640202. + 1.10886e6i) q^{62} +(2.53868e6 + 362265. i) q^{63} +(-903924. + 1.56564e6i) q^{64} +(288346. + 1.63529e6i) q^{65} +(-1.54466e6 + 2.28483e6i) q^{66} +(-2.96301e6 + 1.07845e6i) q^{67} +(-900624. + 327800. i) q^{68} +(-20906.3 - 42979.6i) q^{69} +(-665379. - 3.77355e6i) q^{70} +(968628. - 1.67771e6i) q^{71} +(1.04221e6 - 3.18466e6i) q^{72} +(-1.90937e6 - 3.30713e6i) q^{73} +(-1.46669e6 + 1.23070e6i) q^{74} +(-3.06493e6 - 2.96604e6i) q^{75} +(-26947.2 + 152825. i) q^{76} +(6.67048e6 + 5.59720e6i) q^{77} +(-1.36845e6 - 611009. i) q^{78} +(5.86605e6 + 2.13507e6i) q^{79} -1.58677e6 q^{80} +(-520074. + 4.75461e6i) q^{81} +1.30488e6 q^{82} +(3.52512e6 + 1.28304e6i) q^{83} +(-3.25129e6 - 1.45169e6i) q^{84} +(-4.65271e6 - 3.90408e6i) q^{85} +(-1.40617e6 + 7.97480e6i) q^{86} +(-4.54914e6 - 4.40236e6i) q^{87} +(8.71621e6 - 7.31377e6i) q^{88} +(-4.12096e6 - 7.13772e6i) q^{89} +(6.99375e6 - 1.47111e6i) q^{90} +(-2.36585e6 + 4.09777e6i) q^{91} +(11523.8 + 65354.5i) q^{92} +(3.29816e6 + 6.78042e6i) q^{93} +(7.76890e6 - 2.82765e6i) q^{94} +(-924109. + 336348. i) q^{95} +(-4.33461e6 + 6.41168e6i) q^{96} +(-1.50671e6 - 8.54498e6i) q^{97} +(2.18930e6 - 3.79197e6i) q^{98} +(-1.00261e7 + 1.27770e7i) 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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