LMFDB - Embedded Newform 27.6.e.a.4.11

Newspace parameters

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

Newform invariants

Self dual:	No
Analytic conductor:	$4.33036313495$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$14$ over $\Q(\zeta_{9})$
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			4.11
Character	$\chi$	=	27.4
Dual form			27.6.e.a.7.11

$q$-expansion

$f(q)$	$=$	$q+(5.36004 + 1.95090i) q^{2} +(9.76327 + 12.1523i) q^{3} +(0.410645 + 0.344572i) q^{4} +(-14.4659 + 82.0402i) q^{5} +(28.6236 + 84.1840i) q^{6} +(131.197 - 110.088i) q^{7} +(-89.7358 - 155.427i) q^{8} +(-52.3572 + 237.292i) q^{9} +O(q^{10})$	\(q+(5.36004 + 1.95090i) q^{2} +(9.76327 + 12.1523i) q^{3} +(0.410645 + 0.344572i) q^{4} +(-14.4659 + 82.0402i) q^{5} +(28.6236 + 84.1840i) q^{6} +(131.197 - 110.088i) q^{7} +(-89.7358 - 155.427i) q^{8} +(-52.3572 + 237.292i) q^{9} +(-237.590 + 411.517i) q^{10} +(-10.5058 - 59.5813i) q^{11} +(-0.178108 + 8.35443i) q^{12} +(790.371 - 287.672i) q^{13} +(917.994 - 334.122i) q^{14} +(-1138.21 + 625.186i) q^{15} +(-180.745 - 1025.05i) q^{16} +(-173.221 + 300.027i) q^{17} +(-743.570 + 1169.75i) q^{18} +(-1016.68 - 1760.95i) q^{19} +(-34.2091 + 28.7048i) q^{20} +(2618.74 + 519.536i) q^{21} +(59.9254 - 339.854i) q^{22} +(-1790.96 - 1502.79i) q^{23} +(1012.68 - 2607.97i) q^{24} +(-3584.79 - 1304.76i) q^{25} +4797.64 q^{26} +(-3394.83 + 1680.49i) q^{27} +91.8086 q^{28} +(7235.39 + 2633.47i) q^{29} +(-7320.54 + 1130.49i) q^{30} +(-2053.60 - 1723.18i) q^{31} +(33.6971 - 191.106i) q^{32} +(621.479 - 709.377i) q^{33} +(-1513.79 + 1270.22i) q^{34} +(7133.73 + 12356.0i) q^{35} +(-103.264 + 79.4021i) q^{36} +(-5490.42 + 9509.69i) q^{37} +(-2014.04 - 11422.2i) q^{38} +(11212.5 + 6796.22i) q^{39} +(14049.4 - 5113.55i) q^{40} +(-8626.75 + 3139.88i) q^{41} +(13023.0 + 7893.61i) q^{42} +(1320.52 + 7489.05i) q^{43} +(16.2159 - 28.0867i) q^{44} +(-18710.1 - 7728.04i) q^{45} +(-6667.81 - 11549.0i) q^{46} +(-5301.15 + 4448.19i) q^{47} +(10692.1 - 12204.3i) q^{48} +(2174.96 - 12334.8i) q^{49} +(-16669.2 - 13987.1i) q^{50} +(-5337.23 + 824.214i) q^{51} +(423.685 + 154.209i) q^{52} -1428.94 q^{53} +(-21474.9 + 2384.54i) q^{54} +5040.03 q^{55} +(-28883.7 - 10512.8i) q^{56} +(11473.4 - 29547.6i) q^{57} +(33644.4 + 28231.0i) q^{58} +(6586.05 - 37351.3i) q^{59} +(-682.822 - 135.466i) q^{60} +(5320.79 - 4464.67i) q^{61} +(-7645.65 - 13242.7i) q^{62} +(19253.9 + 36896.0i) q^{63} +(-16100.4 + 27886.7i) q^{64} +(12167.2 + 69003.6i) q^{65} +(4715.08 - 2589.85i) q^{66} +(15558.7 - 5662.90i) q^{67} +(-174.513 + 63.5176i) q^{68} +(776.789 - 36436.4i) q^{69} +(14131.9 + 80145.7i) q^{70} +(2175.24 - 3767.63i) q^{71} +(41580.0 - 13155.9i) q^{72} +(-24178.2 - 41877.8i) q^{73} +(-47981.3 + 40261.1i) q^{74} +(-19143.4 - 56302.1i) q^{75} +(189.277 - 1073.44i) q^{76} +(-7937.50 - 6660.35i) q^{77} +(46840.7 + 58302.4i) q^{78} +(-21195.8 - 7714.64i) q^{79} +86710.2 q^{80} +(-53566.5 - 24847.9i) q^{81} -52365.3 q^{82} +(-34164.4 - 12434.8i) q^{83} +(896.352 + 1115.69i) q^{84} +(-22108.5 - 18551.2i) q^{85} +(-7532.31 + 42717.9i) q^{86} +(38638.4 + 113638. i) q^{87} +(-8317.79 + 6979.45i) q^{88} +(22962.3 + 39771.9i) q^{89} +(-85210.5 - 77924.1i) q^{90} +(72025.6 - 124752. i) q^{91} +(-217.627 - 1234.23i) q^{92} +(890.706 - 41779.8i) q^{93} +(-37092.3 + 13500.5i) q^{94} +(159176. - 57935.2i) q^{95} +(2651.37 - 1456.32i) q^{96} +(27918.1 + 158332. i) q^{97} +(35721.7 - 61871.9i) q^{98} +(14688.2 + 626.563i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84q - 6q^{2} - 6q^{3} - 6q^{4} - 93q^{5} - 126q^{6} - 6q^{7} + 573q^{8} + 324q^{9} + O(q^{10}) $	\( 84q - 6q^{2} - 6q^{3} - 6q^{4} - 93q^{5} - 126q^{6} - 6q^{7} + 573q^{8} + 324q^{9} - 3q^{10} + 111q^{11} - 2769q^{12} - 6q^{13} - 1641q^{14} + 1989q^{15} + 90q^{16} + 3465q^{17} - 99q^{18} - 3q^{19} + 9987q^{20} + 5424q^{21} - 2850q^{22} - 7716q^{23} - 18486q^{24} + 4953q^{25} - 7806q^{26} - 8109q^{27} - 12q^{28} - 20418q^{29} - 6453q^{30} - 6657q^{31} + 51192q^{32} + 50634q^{33} - 11394q^{34} + 35868q^{35} - 3600q^{36} - 3q^{37} - 44076q^{38} - 13971q^{39} + 12441q^{40} - 79077q^{41} - 64422q^{42} - 9465q^{43} + 110757q^{44} + 92493q^{45} - 3q^{46} + 103557q^{47} + 134049q^{48} + 5484q^{49} - 105513q^{50} - 124866q^{51} + 68625q^{52} - 206406q^{53} - 350946q^{54} - 12q^{55} - 147237q^{56} + 67767q^{57} - 9753q^{58} + 116484q^{59} + 241290q^{60} - 70116q^{61} + 246066q^{62} + 135981q^{63} - 86019q^{64} - 19815q^{65} - 32931q^{66} + 48117q^{67} - 48105q^{68} + 25263q^{69} + 270111q^{70} + 279531q^{71} + 441684q^{72} - 27012q^{73} + 233691q^{74} + 18399q^{75} - 125670q^{76} - 345135q^{77} - 520974q^{78} - 216186q^{79} - 924114q^{80} - 428616q^{81} - 12q^{82} - 370401q^{83} - 522390q^{84} - 43731q^{85} + 116682q^{86} + 304173q^{87} + 371418q^{88} + 154827q^{89} + 327366q^{90} - 91002q^{91} + 1279059q^{92} + 890079q^{93} + 11667q^{94} + 1087671q^{95} + 1165698q^{96} - 420621q^{97} + 463410q^{98} - 28323q^{99} + O(q^{100}) \)

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 $

$2$	5.36004	+	1.95090i	0.947531	+	0.344873i	0.769135	−	0.639086i	$-0.220687\pi$
$2$	5.36004	+	1.95090i	0.947531	+	0.344873i	0.178395	+	0.983959i	$0.442909\pi$
$3$	9.76327	+	12.1523i	0.626314	+	0.779571i
$3$	9.76327	+	12.1523i	0.626314	+	0.779571i
$4$	0.410645	+	0.344572i	0.0128326	+	0.0107679i
$5$	−14.4659	+	82.0402i	−0.258774	+	1.46758i	0.527423	+	0.849603i	$0.323158\pi$
$5$	−14.4659	+	82.0402i	−0.258774	+	1.46758i	−0.786197	+	0.617976i	$0.787953\pi$
$6$	28.6236	+	84.1840i	0.324599	+	0.954666i
$7$	131.197	−	110.088i	1.01200	−	0.849168i	0.0233981	−	0.999726i	$-0.492551\pi$
$7$	131.197	−	110.088i	1.01200	−	0.849168i	0.988601	+	0.150558i	$0.0481070\pi$
$8$	−89.7358	−	155.427i	−0.495725	−	0.858621i
$9$	−52.3572	+	237.292i	−0.215462	+	0.976512i
$10$	−237.590	+	411.517i	−0.751324	+	1.30133i
$11$	−10.5058	−	59.5813i	−0.0261786	−	0.148466i	0.968917	−	0.247387i	$-0.0795720\pi$
$11$	−10.5058	−	59.5813i	−0.0261786	−	0.148466i	−0.995095	+	0.0989210i	$0.968461\pi$
$12$	−0.178108	+	8.35443i	−0.000357052	+	0.0167480i
$13$	790.371	−	287.672i	1.29710	−	0.472105i	0.401047	−	0.916057i	$-0.368646\pi$
$13$	790.371	−	287.672i	1.29710	−	0.472105i	0.896050	+	0.443952i	$0.146424\pi$
$14$	917.994	−	334.122i	1.25176	−	0.455602i
$15$	−1138.21	+	625.186i	−1.30616	+	0.717433i
$16$	−180.745	−	1025.05i	−0.176508	−	1.00103i
$17$	−173.221	+	300.027i	−0.145371	+	0.251790i	−0.929511	−	0.368794i	$-0.879771\pi$
$17$	−173.221	+	300.027i	−0.145371	+	0.251790i	0.784140	+	0.620584i	$0.213104\pi$
$18$	−743.570	+	1169.75i	−0.540929	+	0.850969i
$19$	−1016.68	−	1760.95i	−0.646103	−	1.11908i	−0.984046	−	0.177916i	$-0.943064\pi$
$19$	−1016.68	−	1760.95i	−0.646103	−	1.11908i	0.337943	−	0.941167i	$-0.390269\pi$
$20$	−34.2091	+	28.7048i	−0.0191235	+	0.0160465i
$21$	2618.74	+	519.536i	1.29582	+	0.257079i
$22$	59.9254	−	339.854i	0.0263970	−	0.149705i
$23$	−1790.96	−	1502.79i	−0.705936	−	0.592351i	0.217520	−	0.976056i	$-0.430203\pi$
$23$	−1790.96	−	1502.79i	−0.705936	−	0.592351i	−0.923456	+	0.383705i	$0.874648\pi$
$24$	1012.68	−	2607.97i	0.358876	−	0.924219i
$25$	−3584.79	−	1304.76i	−1.14713	−	0.417522i
$26$	4797.64			1.39186
$27$	−3394.83	+	1680.49i	−0.896207	+	0.443636i
$28$	91.8086			0.0221304
$29$	7235.39	+	2633.47i	1.59760	+	0.581478i	0.978934	−	0.204179i	$-0.0654525\pi$
$29$	7235.39	+	2633.47i	1.59760	+	0.581478i	0.618663	+	0.785657i	$0.287675\pi$
$30$	−7320.54	+	1130.49i	−1.48505	+	0.229332i
$31$	−2053.60	−	1723.18i	−0.383806	−	0.322052i	0.430388	−	0.902644i	$-0.358377\pi$
$31$	−2053.60	−	1723.18i	−0.383806	−	0.322052i	−0.814194	+	0.580592i	$0.802821\pi$
$32$	33.6971	−	191.106i	0.00581724	−	0.0329912i
$33$	621.479	−	709.377i	0.0993440	−	0.113395i
$34$	−1513.79	+	1270.22i	−0.224579	+	0.188444i
$35$	7133.73	+	12356.0i	0.984343	+	1.70493i
$36$	−103.264	+	79.4021i	−0.0132799	+	0.0102112i
$37$	−5490.42	+	9509.69i	−0.659328	+	1.14199i	0.321462	+	0.946923i	$0.395826\pi$
$37$	−5490.42	+	9509.69i	−0.659328	+	1.14199i	−0.980790	+	0.195067i	$0.937507\pi$
$38$	−2014.04	−	11422.2i	−0.226261	−	1.28319i
$39$	11212.5	+	6796.22i	1.18043	+	0.715494i
$40$	14049.4	−	5113.55i	1.38837	−	0.505327i
$41$	−8626.75	+	3139.88i	−0.801471	+	0.291712i	−0.710096	−	0.704105i	$-0.751348\pi$
$41$	−8626.75	+	3139.88i	−0.801471	+	0.291712i	−0.0913750	+	0.995817i	$0.529126\pi$
$42$	13023.0	+	7893.61i	1.13917	+	0.690483i
$43$	1320.52	+	7489.05i	0.108912	+	0.617669i	0.989586	+	0.143946i	$0.0459791\pi$
$43$	1320.52	+	7489.05i	0.108912	+	0.617669i	−0.880674	+	0.473723i	$0.842910\pi$
$44$	16.2159	−	28.0867i	0.00126273	−	0.00218710i
$45$	−18710.1	−	7728.04i	−1.37735	−	0.568903i
$46$	−6667.81	−	11549.0i	−0.464610	−	0.804729i
$47$	−5301.15	+	4448.19i	−0.350046	+	0.293724i	−0.800809	−	0.598920i	$-0.795597\pi$
$47$	−5301.15	+	4448.19i	−0.350046	+	0.293724i	0.450762	+	0.892644i	$0.351152\pi$
$48$	10692.1	−	12204.3i	0.669823	−	0.764559i
$49$	2174.96	−	12334.8i	0.129408	−	0.733908i
$50$	−16669.2	−	13987.1i	−0.942951	−	0.791230i
$51$	−5337.23	+	824.214i	−0.287336	+	0.0443726i
$52$	423.685	+	154.209i	0.0217288	+	0.00790862i
$53$	−1428.94			−0.0698753			−0.0349377	−	0.999389i	$-0.511123\pi$
$53$	−1428.94			−0.0698753			−0.0349377	+	0.999389i	$0.511123\pi$
$54$	−21474.9	+	2384.54i	−1.00218	+	0.111281i
$55$	5040.03			0.224660
$56$	−28883.7	−	10512.8i	−1.23079	−	0.447970i
$57$	11473.4	−	29547.6i	0.467741	−	1.20458i
$58$	33644.4	+	28231.0i	1.31324	+	1.10194i
$59$	6586.05	−	37351.3i	0.246317	−	1.39693i	−0.571096	−	0.820883i	$-0.693482\pi$
$59$	6586.05	−	37351.3i	0.246317	−	1.39693i	0.817414	−	0.576051i	$-0.195407\pi$
$60$	−682.822	−	135.466i	−0.0244867	−	0.00485795i
$61$	5320.79	−	4464.67i	0.183084	−	0.153626i	−0.546639	−	0.837368i	$-0.684093\pi$
$61$	5320.79	−	4464.67i	0.183084	−	0.153626i	0.729724	+	0.683742i	$0.239649\pi$
$62$	−7645.65	−	13242.7i	−0.252601	−	0.437518i
$63$	19253.9	+	36896.0i	0.611176	+	1.17119i
$64$	−16100.4	+	27886.7i	−0.491346	+	0.851036i
$65$	12167.2	+	69003.6i	0.357197	+	2.02576i
$66$	4715.08	−	2589.85i	0.133238	−	0.0731838i
$67$	15558.7	−	5662.90i	0.423434	−	0.154118i	−0.121509	−	0.992590i	$-0.538773\pi$
$67$	15558.7	−	5662.90i	0.423434	−	0.154118i	0.544943	+	0.838473i	$0.316551\pi$
$68$	−174.513	+	63.5176i	−0.00457674	+	0.00166580i
$69$	776.789	−	36436.4i	0.0196418	−	0.921325i
$70$	14131.9	+	80145.7i	0.344710	+	1.95495i
$71$	2175.24	−	3767.63i	0.0512108	−	0.0886996i	−0.839284	−	0.543694i	$-0.817025\pi$
$71$	2175.24	−	3767.63i	0.0512108	−	0.0886996i	0.890494	+	0.454994i	$0.150359\pi$
$72$	41580.0	−	13155.9i	0.945263	−	0.299082i
$73$	−24178.2	−	41877.8i	−0.531026	−	0.919765i	−0.999344	−	0.0362047i	$-0.988473\pi$
$73$	−24178.2	−	41877.8i	−0.531026	−	0.919765i	0.468318	−	0.883560i	$-0.344860\pi$
$74$	−47981.3	+	40261.1i	−1.01858	+	0.854686i
$75$	−19143.4	−	56302.1i	−0.392977	−	1.15577i
$76$	189.277	−	1073.44i	0.00375893	−	0.0213179i
$77$	−7937.50	−	6660.35i	−0.152566	−	0.128018i
$78$	46840.7	+	58302.4i	0.871739	+	1.08505i
$79$	−21195.8	−	7714.64i	−0.382105	−	0.139075i	0.143824	−	0.989603i	$-0.454060\pi$
$79$	−21195.8	−	7714.64i	−0.382105	−	0.139075i	−0.525929	+	0.850529i	$0.676282\pi$
$80$	86710.2			1.51476
$81$	−53566.5	−	24847.9i	−0.907153	−	0.420802i
$82$	−52365.3			−0.860022
$83$	−34164.4	−	12434.8i	−0.544350	−	0.198127i	0.0551843	−	0.998476i	$-0.482425\pi$
$83$	−34164.4	−	12434.8i	−0.544350	−	0.198127i	−0.599535	+	0.800349i	$0.704648\pi$
$84$	896.352	+	1115.69i	0.0138606	+	0.0172522i
$85$	−22108.5	−	18551.2i	−0.331904	−	0.278500i
$86$	−7532.31	+	42717.9i	−0.109820	+	0.622821i
$87$	38638.4	+	113638.i	0.547294	+	1.60963i
$88$	−8317.79	+	6979.45i	−0.114499	+	0.0960759i
$89$	22962.3	+	39771.9i	0.307284	+	0.532232i	0.977767	−	0.209693i	$-0.0672464\pi$
$89$	22962.3	+	39771.9i	0.307284	+	0.532232i	−0.670483	+	0.741925i	$0.733913\pi$
$90$	−85210.5	−	77924.1i	−1.10889	−	1.01406i
$91$	72025.6	−	124752.i	0.911766	−	1.57922i
$92$	−217.627	−	1234.23i	−0.00268067	−	0.0152029i
$93$	890.706	−	41779.8i	0.0106789	−	0.500909i
$94$	−37092.3	+	13500.5i	−0.432977	+	0.157591i
$95$	159176.	−	57935.2i	1.80954	−	0.658617i
$96$	2651.37	−	1456.32i	0.0293624	−	0.0161279i
$97$	27918.1	+	158332.i	0.301271	+	1.70859i	0.640559	+	0.767909i	$0.278703\pi$
$97$	27918.1	+	158332.i	0.301271	+	1.70859i	−0.339288	+	0.940683i	$0.610186\pi$
$98$	35721.7	−	61871.9i	0.375723	−	0.650771i
$99$	14688.2	+	626.563i	0.150620	+	0.00642505i
$100$	−1022.49	−	1771.01i	−0.0102249	−	0.0177101i
$101$	33331.9	−	27968.8i	0.325129	−	0.272816i	−0.465582	−	0.885005i	$-0.654155\pi$
$101$	33331.9	−	27968.8i	0.325129	−	0.272816i	0.790712	+	0.612189i	$0.209711\pi$
$102$	−30215.7	−	5994.55i	−0.287563	−	0.0570501i
$103$	24292.0	−	137767.i	0.225617	−	1.27954i	−0.635886	−	0.771783i	$-0.719365\pi$
$103$	24292.0	−	137767.i	0.225617	−	1.27954i	0.861503	−	0.507753i	$-0.169524\pi$
$104$	−115636.	−	97030.5i	−1.04836	−	0.879681i
$105$	−80505.1	+	207326.i	−0.712607	+	1.83519i
$106$	−7659.17	−	2787.71i	−0.0662090	−	0.0240981i
$107$	−56007.5			−0.472919			−0.236459	−	0.971641i	$-0.575987\pi$
$107$	−56007.5			−0.472919			−0.236459	+	0.971641i	$0.575987\pi$
$108$	−1973.12	−	479.678i	−0.0162777	−	0.00395722i
$109$	−151535.			−1.22165			−0.610826	−	0.791765i	$-0.709162\pi$
$109$	−151535.			−1.22165			−0.610826	+	0.791765i	$0.709162\pi$
$110$	27014.8	+	9832.58i	0.212873	+	0.0774793i
$111$	−169169.	+	26124.4i	−1.30321	+	0.201251i
$112$	−136559.	−	114587.i	−1.02867	−	0.863155i
$113$	−9672.57	+	54855.9i	−0.0712600	+	0.404135i	0.928224	+	0.372021i	$0.121335\pi$
$113$	−9672.57	+	54855.9i	−0.0712600	+	0.404135i	−0.999484	+	0.0321142i	$0.989776\pi$
$114$	119142.	−	135993.i	0.858626	−	0.980065i
$115$	149197.	−	125191.i	1.05200	−	0.882732i
$116$	2063.76	+	3574.53i	0.0142401	+	0.0246646i
$117$	26880.7	+	202611.i	0.181542	+	1.36835i
$118$	108170.	−	187356.i	0.715158	−	1.23869i
$119$	10303.2	+	58432.3i	0.0666967	+	0.378256i
$120$	199309.	+	120807.i	1.26350	+	0.765843i
$121$	147899.	−	53830.8i	0.918336	−	0.334247i
$122$	37229.8	−	13550.5i	0.226460	−	0.0824245i
$123$	−122382.	−	74179.5i	−0.729382	−	0.442100i
$124$	−249.543	−	1415.23i	−0.00145744	−	0.00826555i
$125$	28734.3	−	49769.2i	0.164485	−	0.284896i
$126$	31221.2	+	235327.i	0.175195	+	1.32052i
$127$	82065.4	+	142141.i	0.451493	+	0.782008i	0.998479	−	0.0551334i	$-0.0175584\pi$
$127$	82065.4	+	142141.i	0.451493	+	0.782008i	−0.546986	+	0.837141i	$0.684225\pi$
$128$	−145460.	+	122055.i	−0.784727	+	0.658464i
$129$	−78116.7	+	89165.0i	−0.413304	+	0.471759i
$130$	−69402.2	+	393599.i	−0.360176	+	2.04266i
$131$	57894.8	+	48579.5i	0.294755	+	0.247329i	0.778157	−	0.628070i	$-0.216155\pi$
$131$	57894.8	+	48579.5i	0.294755	+	0.247329i	−0.483402	+	0.875398i	$0.660599\pi$
$132$	499.639	−	77.1579i	0.00249586	−	0.000385430i
$133$	−327245.	−	119107.i	−1.60414	−	0.583861i
$134$	94443.0			0.454368
$135$	−88758.4	−	302822.i	−0.419156	−	1.43006i
$136$	62176.4			0.288256
$137$	152174.	+	55386.7i	0.692689	+	0.252118i	0.664286	−	0.747478i	$-0.268736\pi$
$137$	152174.	+	55386.7i	0.692689	+	0.252118i	0.0284028	+	0.999597i	$0.490958\pi$
$138$	75247.2	−	193785.i	0.336351	−	0.866209i
$139$	288496.	+	242077.i	1.26649	+	1.06271i	0.994959	+	0.100286i	$0.0319756\pi$
$139$	288496.	+	242077.i	1.26649	+	1.06271i	0.271535	+	0.962429i	$0.412469\pi$
$140$	−1328.09	+	7532.00i	−0.00572676	+	0.0324781i
$141$	−105812.	−	20992.3i	−0.448217	−	0.0889226i
$142$	19009.6	−	15951.0i	0.0791139	−	0.0663844i
$143$	−25443.3	−	44069.1i	−0.104048	−	0.180216i
$144$	252701.	+	10779.6i	1.01555	+	0.0433207i
$145$	−320717.	+	555497.i	−1.26678	+	2.19413i
$146$	−47896.7	−	271636.i	−0.185962	−	1.05464i
$147$	171131.	−	93997.1i	0.653183	−	0.358774i
$148$	−5531.39	+	2013.26i	−0.0207577	+	0.00755519i
$149$	−49809.4	+	18129.1i	−0.183800	+	0.0668977i	−0.432281	−	0.901739i	$-0.642291\pi$
$149$	−49809.4	+	18129.1i	−0.183800	+	0.0668977i	0.248481	+	0.968637i	$0.420069\pi$
$150$	7229.90	−	339129.i	0.0262364	−	1.23066i
$151$	−38705.3	−	219509.i	−0.138143	−	0.783447i	−0.972619	−	0.232404i	$-0.925341\pi$
$151$	−38705.3	−	219509.i	−0.138143	−	0.783447i	0.834477	−	0.551043i	$-0.185770\pi$
$152$	−182466.	+	316040.i	−0.640578	+	1.10951i
$153$	−62124.9	−	56812.6i	−0.214554	−	0.196208i
$154$	−29551.7	−	51185.0i	−0.100411	−	0.173917i
$155$	171077.	−	143551.i	0.571955	−	0.479927i
$156$	2262.56	+	6654.34i	0.00744370	+	0.0218924i
$157$	72672.4	−	412145.i	0.235299	−	1.33445i	−0.606684	−	0.794943i	$-0.707501\pi$
$157$	72672.4	−	412145.i	0.235299	−	1.33445i	0.841983	−	0.539504i	$-0.181388\pi$
$158$	−98560.0	−	82701.6i	−0.314093	−	0.263555i
$159$	−13951.1	−	17364.9i	−0.0437639	−	0.0544728i
$160$	15190.9	+	5529.02i	0.0469119	+	0.0170745i
$161$	−400408.			−1.21741
$162$	−238643.	−	237689.i	−0.714432	−	0.711575i
$163$	239195.			0.705154			0.352577	−	0.935783i	$-0.385306\pi$
$163$	239195.			0.705154			0.352577	+	0.935783i	$0.385306\pi$
$164$	−4624.44	−	1683.16i	−0.0134261	−	0.00488670i
$165$	49207.2	+	61248.0i	0.140708	+	0.175139i
$166$	−158864.	−	133302.i	−0.447460	−	0.375463i
$167$	−120668.	+	684341.i	−0.334811	+	1.89881i	0.0942756	+	0.995546i	$0.469947\pi$
$167$	−120668.	+	684341.i	−0.334811	+	1.89881i	−0.429087	+	0.903263i	$0.641165\pi$
$168$	−154244.	−	453643.i	−0.421635	−	1.24005i
$169$	257505.	−	216072.i	0.693535	−	0.581945i
$170$	−82311.0	−	142567.i	−0.218442	−	0.378352i
$171$	471090.	−	149053.i	1.23201	−	0.389808i
$172$	−2038.25	+	3530.36i	−0.00525335	+	0.00909908i
$173$	−89777.4	−	509153.i	−0.228061	−	1.29340i	−0.856745	−	0.515739i	$-0.827517\pi$
$173$	−89777.4	−	509153.i	−0.228061	−	1.29340i	0.628684	−	0.777661i	$-0.283594\pi$
$174$	−14592.5	+	684484.i	−0.0365391	+	1.71392i
$175$	−613952.	+	223460.i	−1.51544	+	0.551576i
$176$	−59175.1	+	21538.0i	−0.143998	+	0.0524111i
$177$	518206.	−	284635.i	1.24328	−	0.682898i
$178$	45488.1	+	257976.i	0.107609	+	0.610280i
$179$	−169167.	+	293005.i	−0.394623	+	0.683507i	−0.993053	−	0.117668i	$-0.962458\pi$
$179$	−169167.	+	293005.i	−0.394623	+	0.683507i	0.598430	+	0.801175i	$0.295791\pi$
$180$	−5020.35	−	9620.46i	−0.0115492	−	0.0221317i
$181$	349422.	+	605217.i	0.792783	+	1.37314i	0.924237	+	0.381818i	$0.124702\pi$
$181$	349422.	+	605217.i	0.792783	+	1.37314i	−0.131454	+	0.991322i	$0.541965\pi$
$182$	629438.	−	528161.i	1.40856	−	1.18192i
$183$	106204.	+	21070.1i	0.234431	+	0.0465091i
$184$	−72861.3	+	413217.i	−0.158654	+	0.899774i
$185$	−700753.	−	588002.i	−1.50534	−	1.26313i
$186$	86282.3	−	222204.i	0.182869	−	0.470944i
$187$	19695.8	+	7168.69i	0.0411880	+	0.0149912i
$188$	−3709.61			−0.00765479
$189$	−260392.	+	594205.i	−0.530240	+	1.20999i
$190$	966213.			1.94173
$191$	117622.	+	42810.9i	0.233295	+	0.0849123i	0.456022	−	0.889968i	$-0.349274\pi$
$191$	117622.	+	42810.9i	0.233295	+	0.0849123i	−0.222728	+	0.974881i	$0.571496\pi$
$192$	−496081.	+	76608.5i	−0.971180	+	0.149977i
$193$	57597.5	+	48330.0i	0.111304	+	0.0933950i	0.696741	−	0.717323i	$-0.254633\pi$
$193$	57597.5	+	48330.0i	0.111304	+	0.0933950i	−0.585437	+	0.810718i	$0.699077\pi$
$194$	−159246.	+	903130.i	−0.303784	+	1.72284i
$195$	−719762.	+	821560.i	−1.35551	+	1.54722i
$196$	5143.35	−	4315.79i	0.00956326	−	0.00802453i
$197$	75692.7	+	131104.i	0.138959	+	0.240685i	0.927103	−	0.374807i	$-0.122291\pi$
$197$	75692.7	+	131104.i	0.138959	+	0.240685i	−0.788144	+	0.615491i	$0.788958\pi$
$198$	77507.2	+	32013.6i	0.140501	+	0.0580326i
$199$	120924.	−	209447.i	0.216461	−	0.374922i	−0.737262	−	0.675607i	$-0.763882\pi$
$199$	120924.	−	209447.i	0.216461	−	0.374922i	0.953724	+	0.300684i	$0.0972151\pi$
$200$	118889.	+	674256.i	0.210169	+	1.19193i
$201$	220721.	+	133786.i	0.385348	+	0.233571i
$202$	233224.	−	84886.7i	0.402157	−	0.146373i
$203$	1.23918e6	−	451024.i	2.11054	−	0.768173i
$204$	−2475.70	−	1500.60i	−0.00416508	−	0.00252458i
$205$	−132803.	−	753161.i	−0.220710	−	1.25171i
$206$	398976.	−	691046.i	0.655056	−	1.13459i
$207$	450370.	−	346299.i	0.730540	−	0.561726i
$208$	−437734.	−	758178.i	−0.701539	−	1.21510i
$209$	−94238.4	+	79075.4i	−0.149232	+	0.125221i
$210$	−835982.	+	954219.i	−1.30812	+	1.49314i
$211$	18660.3	−	105828.i	0.0288544	−	0.163642i	−0.966976	−	0.254869i	$-0.917968\pi$
$211$	18660.3	−	105828.i	0.0288544	−	0.163642i	0.995830	+	0.0912270i	$0.0290789\pi$
$212$	−586.786	−	492.372i	−0.000896685	−	0.000752408i
$213$	67022.8	−	10350.2i	0.101222	−	0.0156314i
$214$	−300203.	−	109265.i	−0.448105	−	0.163097i
$215$	−633506.			−0.934662
$216$	565831.	+	376848.i	0.825187	+	0.549581i
$217$	−459128.			−0.661888
$218$	−812235.	−	295629.i	−1.15755	−	0.421315i
$219$	272854.	−	702685.i	0.384433	−	0.990034i
$220$	2069.66	+	1736.65i	0.00288299	+	0.00241911i
$221$	−50599.4	+	286964.i	−0.0696891	+	0.395227i
$222$	−957720.	−	190004.i	−1.30424	−	0.258750i
$223$	−374072.	+	313883.i	−0.503724	+	0.422674i	−0.858914	−	0.512119i	$-0.828860\pi$
$223$	−374072.	+	313883.i	−0.503724	+	0.422674i	0.355190	+	0.934794i	$0.384416\pi$
$224$	−16617.4	−	28782.2i	−0.0221280	−	0.0383269i
$225$	497298.	−	782330.i	0.654878	−	1.03023i
$226$	−158863.	+	275160.i	−0.206896	+	0.358355i
$227$	32422.3	+	183876.i	0.0417618	+	0.236843i	0.998543	−	0.0539667i	$-0.0171865\pi$
$227$	32422.3	+	183876.i	0.0417618	+	0.236843i	−0.956781	+	0.290810i	$0.906075\pi$
$228$	14892.8	−	8180.16i	0.0189731	−	0.0104214i
$229$	−624170.	+	227179.i	−0.786528	+	0.286273i	−0.703892	−	0.710307i	$-0.748556\pi$
$229$	−624170.	+	227179.i	−0.786528	+	0.286273i	−0.0826360	+	0.996580i	$0.526334\pi$
$230$	1.04394e6	−	379962.i	1.30123	−	0.473610i
$231$	3442.72	−	161486.i	0.00424494	−	0.199115i
$232$	−239962.	−	1.36089e6i	−0.292700	−	1.65998i
$233$	81499.7	−	141162.i	0.0983482	−	0.170344i	−0.812653	−	0.582748i	$-0.801977\pi$
$233$	81499.7	−	141162.i	0.0983482	−	0.170344i	0.911001	+	0.412404i	$0.135311\pi$
$234$	−251191.	+	1.13844e6i	−0.299892	+	1.35916i
$235$	−288244.	−	499254.i	−0.340480	−	0.589728i
$236$	15574.7	−	13068.8i	0.0182029	−	0.0152741i
$237$	−113190.	−	332898.i	−0.130899	−	0.384982i
$238$	−58769.8	+	333300.i	−0.0672530	+	0.381411i
$239$	1.06412e6	+	892905.i	1.20503	+	1.01114i	0.999472	+	0.0324922i	$0.0103444\pi$
$239$	1.06412e6	+	892905.i	1.20503	+	1.01114i	0.205555	+	0.978646i	$0.434100\pi$
$240$	846575.	+	1.05373e6i	0.948718	+	1.18087i
$241$	1.39867e6	+	509074.i	1.55122	+	0.564597i	0.968703	−	0.248224i	$-0.0798469\pi$
$241$	1.39867e6	+	509074.i	1.55122	+	0.564597i	0.582514	+	0.812821i	$0.302069\pi$
$242$	897763.			0.985424
$243$	−221024.	−	893553.i	−0.240117	−	0.970744i
$244$	3723.35			0.00400368
$245$	980485.	+	356867.i	1.04358	+	0.379832i
$246$	−511257.	−	636360.i	−0.538644	−	0.670448i
$247$	−1.31013e6	−	1.09933e6i	−1.36638	−	1.14653i
$248$	−83546.4	+	473815.i	−0.0862579	+	0.489193i
$249$	−182444.	−	536581.i	−0.186480	−	0.548449i
$250$	251112.	−	210708.i	0.254107	−	0.213221i
$251$	−925163.	−	1.60243e6i	−0.926902	−	1.60544i	−0.788473	−	0.615069i	$-0.789128\pi$
$251$	−925163.	−	1.60243e6i	−0.926902	−	1.60544i	−0.138429	−	0.990372i	$-0.544205\pi$
$252$	−4806.84	+	21785.5i	−0.00476824	+	0.0216106i
$253$	−70722.8	+	122495.i	−0.0694637	+	0.120315i
$254$	162571.	+	921985.i	0.158110	+	0.896684i
$255$	9589.09	−	449790.i	0.00923478	−	0.433171i
$256$	−49504.9	+	18018.3i	−0.0472115	+	0.0171836i
$257$	379835.	−	138249.i	0.358726	−	0.130566i	−0.156369	−	0.987699i	$-0.549979\pi$
$257$	379835.	−	138249.i	0.358726	−	0.130566i	0.515095	+	0.857133i	$0.327757\pi$
$258$	−592661.	+	325531.i	−0.554315	+	0.304469i
$259$	326571.	+	1.85208e6i	0.302502	+	1.71557i
$260$	−18780.3	+	32528.4i	−0.0172294	+	0.0298421i
$261$	−1.00373e6	+	1.57902e6i	−0.912041	+	1.43479i
$262$	215545.	+	373335.i	0.193992	+	0.336005i
$263$	−229128.	+	192261.i	−0.204263	+	0.171397i	−0.739181	−	0.673507i	$-0.764787\pi$
$263$	−229128.	+	192261.i	−0.204263	+	0.171397i	0.534918	+	0.844904i	$0.320343\pi$
$264$	−166025.	−	32938.0i	−0.146610	−	0.0290863i
$265$	20670.9	−	117230.i	0.0180819	−	0.102548i
$266$	−1.52168e6	−	1.27684e6i	−1.31862	−	1.10645i
$267$	−259133.	+	667348.i	−0.222456	+	0.572894i
$268$	8340.37	+	3035.65i	0.00709330	+	0.00258175i
$269$	−658980.			−0.555254			−0.277627	−	0.960689i	$-0.589548\pi$
$269$	−658980.			−0.555254			−0.277627	+	0.960689i	$0.589548\pi$
$270$	115025.	−	1.79630e6i	0.0960250	−	1.49958i
$271$	−820179.			−0.678399			−0.339199	−	0.940714i	$-0.610156\pi$
$271$	−820179.			−0.678399			−0.339199	+	0.940714i	$0.610156\pi$
$272$	338853.	+	123332.i	0.277708	+	0.101078i
$273$	2.21923e6	−	342710.i	1.80217	−	0.278304i
$274$	707604.	+	593750.i	0.569395	+	0.477779i
$275$	−40078.0	+	227294.i	−0.0319576	+	0.181241i
$276$	12873.9	−	14694.8i	0.0101728	−	0.0116115i
$277$	−1.71884e6	+	1.44228e6i	−1.34597	+	1.12940i	−0.365923	+	0.930645i	$0.619247\pi$
$277$	−1.71884e6	+	1.44228e6i	−1.34597	+	1.12940i	−0.980048	+	0.198759i	$0.936309\pi$
$278$	1.07408e6	+	1.86037e6i	0.833540	+	1.44373i
$279$	516418.	−	397084.i	0.397183	−	0.305402i
$280$	1.28030e6	−	2.21755e6i	0.975926	−	1.69035i
$281$	−395906.	−	2.24529e6i	−0.299106	−	1.69632i	−0.650026	−	0.759912i	$-0.725242\pi$
$281$	−395906.	−	2.24529e6i	−0.299106	−	1.69632i	0.350920	−	0.936406i	$-0.385869\pi$
$282$	−526205.	−	318948.i	−0.394032	−	0.238835i
$283$	1.38550e6	−	504280.i	1.02835	−	0.374287i	0.227895	−	0.973686i	$-0.426816\pi$
$283$	1.38550e6	−	504280.i	1.02835	−	0.374287i	0.800451	+	0.599398i	$0.204593\pi$
$284$	2191.47	−	797.629i	0.00161228	−	0.000586820i
$285$	2.25812e6	+	1.36871e6i	1.64678	+	0.998161i
$286$	−50403.0	−	285850.i	−0.0364369	−	0.206644i
$287$	−786145.	+	1.36164e6i	−0.563376	+	0.975795i
$288$	43583.6	+	18001.8i	0.0309629	+	0.0127889i
$289$	649918.	+	1.12569e6i	0.457735	+	0.792819i
$290$	−2.80277e6	+	2.35181e6i	−1.95701	+	1.64213i
$291$	−1.65152e6	+	1.88510e6i	−1.14328	+	1.30498i
$292$	4501.28	−	25528.0i	0.00308943	−	0.0175210i
$293$	−1.65170e6	−	1.38594e6i	−1.12399	−	0.943138i	−0.125189	−	0.992133i	$-0.539954\pi$
$293$	−1.65170e6	−	1.38594e6i	−1.12399	−	0.943138i	−0.998799	+	0.0489951i	$0.984398\pi$
$294$	1.10065e6	−	169970.i	0.742642	−	0.114684i
$295$	2.96904e6	+	1.08064e6i	1.98637	+	0.722980i
$296$	1.97075e6			1.30738
$297$	135791.	+	184613.i	0.0893264	+	0.121443i
$298$	−302348.			−0.197227
$299$	−1.84783e6	−	672555.i	−1.19532	−	0.435061i
$300$	11539.0	−	29716.5i	0.00740225	−	0.0190631i
$301$	997702.	+	837171.i	0.634724	+	0.532596i
$302$	220777.	−	1.25209e6i	0.139295	−	0.789982i
$303$	665313.	+	131993.i	0.416312	+	0.0825930i
$304$	−1.62130e6	+	1.36044e6i	−1.00619	+	0.844295i
$305$	289312.	+	501104.i	0.178081	+	0.308445i
$306$	−222157.	−	425717.i	−0.135630	−	0.259907i
$307$	510371.	−	883988.i	0.309058	−	0.535304i	−0.669099	−	0.743174i	$-0.733320\pi$
$307$	510371.	−	883988.i	0.309058	−	0.535304i	0.978157	+	0.207870i	$0.0666530\pi$
$308$	−964.522	−	5470.08i	−0.000579342	−	0.00328561i
$309$	1.91136e6	−	1.04985e6i	1.13880	−	0.625507i
$310$	1.19703e6	−	435684.i	0.707459	−	0.257494i
$311$	−1.97227e6	+	717847.i	−1.15629	+	0.420854i	−0.847769	−	0.530365i	$-0.822055\pi$
$311$	−1.97227e6	+	717847.i	−1.15629	+	0.420854i	−0.308517	+	0.951219i	$0.599833\pi$
$312$	50154.8	−	2.35259e6i	0.0291693	−	1.36823i
$313$	−66359.5	−	376343.i	−0.0382862	−	0.217132i	0.959662	−	0.281156i	$-0.0907177\pi$
$313$	−66359.5	−	376343.i	−0.0382862	−	0.217132i	−0.997948	+	0.0640239i	$0.979607\pi$
$314$	1.19358e6	−	2.06734e6i	0.683168	−	1.18328i
$315$	−3.30548e6	+	1.04586e6i	−1.87697	+	0.593875i
$316$	−6045.70	−	10471.5i	−0.00340587	−	0.00589915i
$317$	1.01522e6	−	851871.i	0.567430	−	0.476130i	−0.313362	−	0.949634i	$-0.601455\pi$
$317$	1.01522e6	−	851871.i	0.567430	−	0.476130i	0.880792	+	0.473504i	$0.157011\pi$
$318$	−40901.4	−	120294.i	−0.0226814	−	0.0667076i
$319$	80891.8	−	458760.i	0.0445070	−	0.252412i
$320$	−2.05493e6	−	1.72429e6i	−1.12182	−	0.941315i
$321$	−546816.	−	680620.i	−0.296196	−	0.368674i
$322$	−2.14620e6	−	781154.i	−1.15354	−	0.419853i
$323$	704443.			0.375698
$324$	−13434.9	−	28661.2i	−0.00711003	−	0.0151681i
$325$	−3.20865e6			−1.68506
$326$	1.28210e6	+	466645.i	0.668155	+	0.243188i
$327$	−1.47948e6	−	1.84150e6i	−0.765137	−	0.952364i
$328$	1.26215e6	+	1.05907e6i	0.647778	+	0.543551i
$329$	−205806.	+	1.16718e6i	−0.104826	+	0.594496i
$330$	144264.	+	424290.i	0.0729245	+	0.214476i
$331$	1.67508e6	−	1.40556e6i	0.840363	−	0.705148i	−0.117283	−	0.993099i	$-0.537418\pi$
$331$	1.67508e6	−	1.40556e6i	0.840363	−	0.705148i	0.957645	+	0.287951i	$0.0929739\pi$
$332$	−9744.74	−	16878.4i	−0.00485205	−	0.00840399i
$333$	−1.96912e6	−	1.80074e6i	−0.973107	−	0.889897i
$334$	−1.98186e6	+	3.43269e6i	−0.972092	+	1.68371i
$335$	239515.	+	1.35836e6i	0.116606	+	0.661305i
$336$	59229.5	−	2.77825e6i	0.0286214	−	1.34253i
$337$	352011.	−	128122.i	0.168843	−	0.0614537i	−0.256216	−	0.966620i	$-0.582476\pi$
$337$	352011.	−	128122.i	0.168843	−	0.0614537i	0.425058	+	0.905166i	$0.360254\pi$
$338$	1.80177e6	−	655791.i	0.857843	−	0.312229i
$339$	−761061.	+	418028.i	−0.359683	+	0.197563i
$340$	−2686.50	−	15235.9i	−0.00126035	−	0.00714779i
$341$	−81094.3	+	140459.i	−0.0377663	+	0.0654132i
$342$	2.81585e6	+	120117.i	1.30180	+	0.0555315i
$343$	366675.	+	635099.i	0.168285	+	0.291478i
$344$	1.04550e6	−	877281.i	0.476353	−	0.399708i
$345$	2.97801e6	+	590813.i	1.34703	+	0.267240i
$346$	512094.	−	2.90423e6i	0.229964	−	1.30419i
$347$	359203.	+	301407.i	0.160146	+	0.134378i	0.719339	−	0.694659i	$-0.244445\pi$
$347$	359203.	+	301407.i	0.160146	+	0.134378i	−0.559193	+	0.829037i	$0.688889\pi$
$348$	−23289.8	+	59978.5i	−0.0103090	+	0.0265490i
$349$	−655226.	−	238483.i	−0.287957	−	0.104808i	0.194003	−	0.981001i	$-0.437853\pi$
$349$	−655226.	−	238483.i	−0.287957	−	0.104808i	−0.481960	+	0.876193i	$0.660075\pi$
$350$	−3.72676e6			−1.62615
$351$	−2.19975e6	+	2.30481e6i	−0.953026	+	0.998543i
$352$	−11740.3			−0.00505037
$353$	−746614.	−	271745.i	−0.318903	−	0.116071i	0.177609	−	0.984101i	$-0.443164\pi$
$353$	−746614.	−	271745.i	−0.318903	−	0.116071i	−0.496512	+	0.868030i	$0.665386\pi$
$354$	3.33290e6	−	514691.i	1.41356	−	0.218292i
$355$	277630.	+	232959.i	0.116922	+	0.0981090i
$356$	−4274.92	+	24244.3i	−0.00178773	+	0.0101387i
$357$	−609494.	+	695698.i	−0.253104	+	0.288902i
$358$	−1.47836e6	+	1.24049e6i	−0.609641	+	0.511549i
$359$	1.61932e6	+	2.80475e6i	0.663129	+	1.14857i	0.979789	+	0.200033i	$0.0641051\pi$
$359$	1.61932e6	+	2.80475e6i	0.663129	+	1.14857i	−0.316661	+	0.948539i	$0.602562\pi$
$360$	477822.	+	3.60154e6i	0.194317	+	1.46464i
$361$	−829239.	+	1.43628e6i	−0.334897	+	0.580059i
$362$	692203.	+	3.92568e6i	0.277627	+	1.57450i
$363$	2.09814e6	+	1.27175e6i	0.835736	+	0.506564i
$364$	72562.9	−	26410.7i	0.0287052	−	0.0104479i
$365$	3.78542e6	−	1.37778e6i	1.48724	−	0.541312i
$366$	528154.	+	320130.i	0.206091	+	0.124918i
$367$	−148483.	−	842086.i	−0.0575453	−	0.326356i	0.942422	−	0.334426i	$-0.108542\pi$
$367$	−148483.	−	842086.i	−0.0575453	−	0.326356i	−0.999967	+	0.00806992i	$0.997431\pi$
$368$	−1.21673e6	+	2.10745e6i	−0.468356	+	0.811217i
$369$	−293398.	−	2.21146e6i	−0.112174	−	0.845499i
$370$	−2.60894e6	−	4.51881e6i	−0.990739	−	1.71601i
$371$	−187473.	+	157309.i	−0.0707138	+	0.0593359i
$372$	14761.9	−	16849.8i	0.00553077	−	0.00631301i
$373$	130100.	−	737836.i	0.0484180	−	0.274592i	−0.950981	−	0.309248i	$-0.899923\pi$
$373$	130100.	−	737836.i	0.0484180	−	0.274592i	0.999399	+	0.0346563i	$0.0110337\pi$
$374$	91585.1	+	76849.0i	0.0338568	+	0.0284092i
$375$	885352.	−	136723.i	0.325115	−	0.0502067i
$376$	1.16707e6	+	424779.i	0.425724	+	0.154951i
$377$	6.47622e6			2.34676
$378$	−2.55494e6	+	2.67697e6i	−0.919711	+	0.963637i
$379$	−374614.			−0.133963			−0.0669816	−	0.997754i	$-0.521337\pi$
$379$	−374614.			−0.133963			−0.0669816	+	0.997754i	$0.521337\pi$
$380$	85327.4	+	31056.6i	0.0303130	+	0.0110330i
$381$	−926120.	+	2.38505e6i	−0.326855	+	0.841753i
$382$	546939.	+	458936.i	0.191770	+	0.160914i
$383$	−573.937	+	3254.96i	−0.000199925	+	0.00113383i	−0.984908	−	0.173081i	$-0.944628\pi$
$383$	−573.937	+	3254.96i	−0.000199925	+	0.00113383i	0.984708	+	0.174215i	$0.0557388\pi$
$384$	−2.90342e6	−	576015.i	−1.00481	−	0.199345i
$385$	661239.	−	554846.i	0.227356	−	0.190775i
$386$	214438.	+	371418.i	0.0732544	+	0.126880i
$387$	−1.84624e6	−	78755.7i	−0.626628	−	0.0267303i
$388$	−43092.2	+	74637.8i	−0.0145318	+	0.0251698i
$389$	−649609.	−	3.68412e6i	−0.217660	−	1.23441i	−0.876231	−	0.481891i	$-0.839950\pi$
$389$	−649609.	−	3.68412e6i	−0.217660	−	1.23441i	0.658571	−	0.752519i	$-0.271161\pi$
$390$	−5.46073e6	+	2.99942e6i	−1.81798	+	0.998563i
$391$	761109.	−	277021.i	0.251771	−	0.0916370i
$392$	−2.11233e6	+	768825.i	−0.694299	+	0.252704i
$393$	−25110.6	+	1.17785e6i	−0.00820117	+	0.384688i
$394$	149947.	+	850389.i	0.0486627	+	0.275980i
$395$	939527.	−	1.62731e6i	0.302982	−	0.524780i
$396$	5815.75	+	5318.45i	0.00186367	+	0.00170430i
$397$	−692020.	−	1.19861e6i	−0.220365	−	0.381683i	0.734554	−	0.678550i	$-0.237392\pi$
$397$	−692020.	−	1.19861e6i	−0.220365	−	0.381683i	−0.954919	+	0.296867i	$0.904058\pi$
$398$	1.05677e6	−	886734.i	0.334404	−	0.280599i
$399$	−1.74755e6	−	5.13966e6i	−0.549537	−	1.61622i
$400$	−689514.	+	3.91043e6i	−0.215473	+	1.22201i
$401$	1.47773e6	+	1.23996e6i	0.458916	+	0.385076i	0.842732	−	0.538333i	$-0.180946\pi$
$401$	1.47773e6	+	1.23996e6i	0.458916	+	0.385076i	−0.383816	+	0.923410i	$0.625390\pi$
$402$	922072.	+	1.14770e6i	0.284577	+	0.354212i
$403$	−2.11882e6	−	771186.i	−0.649876	−	0.236536i
$404$	23324.8			0.00710992
$405$	2.81341e6	−	4.03515e6i	0.852307	−	1.22243i
$406$	7.52194e6			2.26472
$407$	624281.	+	227220.i	0.186807	+	0.0679923i
$408$	607045.	+	755587.i	0.180539	+	0.224716i
$409$	−4.46374e6	−	3.74552e6i	−1.31944	−	1.10714i	−0.986423	−	0.164223i	$-0.947488\pi$
$409$	−4.46374e6	−	3.74552e6i	−1.31944	−	1.10714i	−0.333019	−	0.942920i	$-0.608067\pi$
$410$	757512.	−	4.29606e6i	0.222551	−	1.26215i
$411$	812637.	+	2.39002e6i	0.237297	+	0.697905i
$412$	57446.0	−	48202.9i	0.0166731	−	0.0139904i
$413$	−3.24785e6	−	5.62544e6i	−0.936959	−	1.62286i
$414$	3.08960e6	−	977549.i	0.885933	−	0.280310i
$415$	1.51437e6	−	2.62297e6i	0.431631	−	0.747607i
$416$	−28342.4	−	160738.i	−0.00802979	−	0.0455392i
$417$	−125129.	+	5.86936e6i	−0.0352385	+	1.65291i
$418$	−659390.	+	239998.i	−0.184587	+	0.0671842i
$419$	−4.71805e6	+	1.71723e6i	−1.31289	+	0.477852i	−0.901172	−	0.433461i	$-0.857292\pi$
$419$	−4.71805e6	+	1.71723e6i	−1.31289	+	0.477852i	−0.411714	+	0.911313i	$0.635070\pi$
$420$	−104498.	+	57397.5i	−0.0289057	+	0.0158770i
$421$	−186623.	−	1.05839e6i	−0.0513168	−	0.291032i	0.948339	−	0.317258i	$-0.102762\pi$
$421$	−186623.	−	1.05839e6i	−0.0513168	−	0.291032i	−0.999656	+	0.0262260i	$0.991651\pi$
$422$	306479.	−	530837.i	0.0837760	−	0.145104i
$423$	−777969.	−	1.49082e6i	−0.211403	−	0.405110i
$424$	128227.	+	222095.i	0.0346389	+	0.0599964i
$425$	1.01242e6	−	849523.i	0.271888	−	0.228141i
$426$	379437.	+	75277.2i	0.101301	+	0.0200974i
$427$	206568.	−	1.17151e6i	0.0548269	−	0.310939i
$428$	−22999.2	−	19298.6i	−0.00606880	−	0.00509233i
$429$	287131.	−	739453.i	0.0753247	−	0.193985i
$430$	−3.39562e6	−	1.23590e6i	−0.885621	−	0.322340i
$431$	−2.16988e6			−0.562654			−0.281327	−	0.959612i	$-0.590775\pi$
$431$	−2.16988e6			−0.562654			−0.281327	+	0.959612i	$0.590775\pi$
$432$	2.33619e6	+	3.17614e6i	0.602280	+	0.818824i
$433$	2.36558e6			0.606343			0.303171	−	0.952936i	$-0.401955\pi$
$433$	2.36558e6			0.606343			0.303171	+	0.952936i	$0.401955\pi$
$434$	−2.46094e6	−	895711.i	−0.627159	−	0.228267i
$435$	−9.88182e6	+	1.52602e6i	−2.50388	+	0.386668i
$436$	−62227.1	−	52214.8i	−0.0156770	−	0.0131546i
$437$	−825499.	+	4.68164e6i	−0.206782	+	1.17272i
$438$	2.83337e6	−	3.23411e6i	0.705698	−	0.805507i
$439$	5.90020e6	−	4.95085e6i	1.46118	−	1.22608i	0.537310	−	0.843385i	$-0.319440\pi$
$439$	5.90020e6	−	4.95085e6i	1.46118	−	1.22608i	0.923875	−	0.382695i	$-0.125004\pi$
$440$	−452271.	−	783357.i	−0.111370	−	0.192898i
$441$	2.81308e6	+	1.16192e6i	0.688787	+	0.284497i
$442$	−831051.	+	1.43942e6i	−0.202336	+	0.350455i
$443$	349582.	+	1.98258e6i	0.0846331	+	0.479978i	0.997435	+	0.0715760i	$0.0228028\pi$
$443$	349582.	+	1.98258e6i	0.0846331	+	0.479978i	−0.912802	+	0.408402i	$0.866086\pi$
$444$	−78470.2	−	47563.1i	−0.0188907	−	0.0114502i
$445$	−3.59506e6	+	1.30850e6i	−0.860610	+	0.313236i
$446$	−2.61739e6	+	952653.i	−0.623063	+	0.226776i
$447$	−706613.	−	428299.i	−0.167268	−	0.101386i
$448$	957654.	+	5.43113e6i	0.225431	+	1.27848i
$449$	−553618.	+	958895.i	−0.129597	+	0.224468i	−0.923520	−	0.383549i	$-0.874702\pi$
$449$	−553618.	+	958895.i	−0.129597	+	0.224468i	0.793924	+	0.608018i	$0.208035\pi$
$450$	4.19178e6	−	3.22314e6i	0.975815	−	0.750323i
$451$	277709.	+	481006.i	0.0642907	+	0.111355i
$452$	−22873.8	+	19193.4i	−0.00526613	+	0.00441881i
$453$	2.28965e6	−	2.61348e6i	0.524232	−	0.598376i
$454$	−184938.	+	1.04884e6i	−0.0421101	+	0.238818i
$455$	9.19276e6	+	7.71364e6i	2.08170	+	1.74675i
$456$	−5.62207e6	+	868202.i	−1.26615	+	0.195528i
$457$	3.56091e6	+	1.29607e6i	0.797574	+	0.290293i	0.708481	−	0.705730i	$-0.249381\pi$
$457$	3.56091e6	+	1.29607e6i	0.797574	+	0.290293i	0.0890930	+	0.996023i	$0.471603\pi$
$458$	−3.78878e6			−0.843987
$459$	83862.3	−	1.30964e6i	0.0185795	−	0.290148i
$460$	104404.			0.0230051
$461$	1.32800e6	+	483353.i	0.291036	+	0.105928i	0.483412	−	0.875393i	$-0.339397\pi$
$461$	1.32800e6	+	483353.i	0.291036	+	0.105928i	−0.192377	+	0.981321i	$0.561619\pi$
$462$	333495.	−	858854.i	0.0726916	−	0.187204i
$463$	−2.97520e6	−	2.49649e6i	−0.645006	−	0.541224i	0.260545	−	0.965462i	$-0.416098\pi$
$463$	−2.97520e6	−	2.49649e6i	−0.645006	−	0.541224i	−0.905551	+	0.424238i	$0.860542\pi$
$464$	1.39169e6	−	7.89265e6i	0.300087	−	1.70188i
$465$	3.41474e6	+	677456.i	0.732361	+	0.145294i
$466$	712234.	−	597635.i	0.151935	−	0.127489i
$467$	1.92081e6	+	3.32694e6i	0.407560	+	0.705915i	0.994616	−	0.103632i	$-0.0330464\pi$
$467$	1.92081e6	+	3.32694e6i	0.407560	+	0.705915i	−0.587056	+	0.809546i	$0.699713\pi$
$468$	−58775.6	+	92463.4i	−0.0124046	+	0.0195144i
$469$	1.41784e6	−	2.45578e6i	0.297644	−	0.515534i
$470$	−571010.	−	3.23836e6i	−0.119234	−	0.676208i
$471$	5.71804e6	−	3.14075e6i	1.18767	−	0.652351i
$472$	−6.39640e6	+	2.32810e6i	−1.32154	+	0.481002i
$473$	432334.	−	157357.i	0.0888519	−	0.0323395i
$474$	42748.3	−	2.00517e6i	0.00873922	−	0.409926i
$475$	1.34699e6	+	7.63914e6i	0.273923	+	1.55350i
$476$	−15903.2	+	27545.1i	−0.00321711	+	0.00557220i
$477$	74815.2	−	339076.i	0.0150554	−	0.0682341i
$478$	3.96178e6	+	6.86200e6i	0.793086	+	1.37367i
$479$	−1.55050e6	+	1.30102e6i	−0.308768	+	0.259087i	−0.783983	−	0.620783i	$-0.786815\pi$
$479$	−1.55050e6	+	1.30102e6i	−0.308768	+	0.259087i	0.475214	+	0.879870i	$0.342370\pi$
$480$	81122.1	+	238585.i	0.0160708	+	0.0472651i
$481$	−1.60380e6	+	9.09563e6i	−0.316074	+	1.79254i
$482$	6.50378e6	+	5.45732e6i	1.27511	+	1.06995i
$483$	−3.90929e6	−	4.86588e6i	−0.762482	−	0.949059i
$484$	79282.5	+	28856.5i	0.0153838	+	0.00559925i
$485$	−1.33934e7			−2.58545
$486$	558531.	−	5.22068e6i	0.107265	−	1.00262i
$487$	−4.43291e6			−0.846967			−0.423484	−	0.905904i	$-0.639193\pi$
$487$	−4.43291e6			−0.846967			−0.423484	+	0.905904i	$0.639193\pi$
$488$	−1.17139e6	−	426353.i	−0.222666	−	0.0810438i
$489$	2.33533e6	+	2.90678e6i	0.441648	+	0.549717i
$490$	4.55923e6	+	3.82565e6i	0.857830	+	0.719805i
$491$	−251122.	+	1.42419e6i	−0.0470090	+	0.266602i	−0.999249	−	0.0387493i	$-0.987663\pi$
$491$	−251122.	+	1.42419e6i	−0.0470090	+	0.266602i	0.952240	+	0.305351i	$0.0987737\pi$
$492$	−24695.4	−	72630.8i	−0.00459943	−	0.0135272i
$493$	−2.04343e6	+	1.71464e6i	−0.378654	+	0.317729i
$494$	−4.87768e6	−	8.44839e6i	−0.899282	−	1.55760i
$495$	−263882.	+	1.19596e6i	−0.0484057	+	0.219384i
$496$	−1.39517e6	+	2.41651e6i	−0.254638	+	0.441046i
$497$	−129383.	−	733770.i	−0.0234957	−	0.133251i
$498$	68903.7	−	3.23203e6i	0.0124500	−	0.583985i
$499$	4.11362e6	−	1.49723e6i	0.739558	−	0.269177i	0.0553531	−	0.998467i	$-0.482372\pi$
$499$	4.11362e6	−	1.49723e6i	0.739558	−	0.269177i	0.684205	+	0.729290i	$0.260149\pi$
$500$	28948.7	−	10536.4i	0.00517849	−	0.00188482i
$501$	−9.49443e6	+	5.21501e6i	−1.68995	+	0.928242i
$502$	−1.83274e6	−	1.03940e7i	−0.324595	−	1.84087i
$503$	−66422.0	+	115046.i	−0.0117056	+	0.0202746i	−0.871819	−	0.489828i	$-0.837059\pi$
$503$	−66422.0	+	115046.i	−0.0117056	+	0.0202746i	0.860113	+	0.510103i	$0.170393\pi$
$504$	4.00688e6	−	6.30346e6i	0.702635	−	1.10536i
$505$	1.81239e6	+	3.13915e6i	0.316244	+	0.547751i
$506$	−618053.	+	518608.i	−0.107312	+	0.0900457i
$507$	5.13986e6	+	1.01971e6i	0.888038	+	0.176180i
$508$	−15278.2	+	86647.0i	−0.00262672	+	0.0148968i
$509$	−3.15217e6	−	2.64498e6i	−0.539280	−	0.452510i	0.332011	−	0.943275i	$-0.392273\pi$
$509$	−3.15217e6	−	2.64498e6i	−0.539280	−	0.452510i	−0.871292	+	0.490765i	$0.836717\pi$
$510$	928891.	−	2.39219e6i	0.158139	−	0.407258i
$511$	−7.78234e6	−	2.83254e6i	−1.31843	−	0.479870i
$512$	5.77581e6			0.973728
$513$	6.41072e6	+	4.26959e6i	1.07551	+	0.716296i
$514$	2.30564e6			0.384932
$515$	1.09510e7	+	3.98585e6i	1.81944	+	0.662220i
$516$	−62802.0	+	9698.35i	−0.0103836	+	0.00160352i
$517$	320722.	+	269117.i	0.0527718	+	0.0442808i
$518$	−1.86277e6	+	1.05643e7i	−0.305025	+	1.72988i
$519$	5.31086e6	−	6.06200e6i	0.865459	−	0.987865i
$520$	9.63319e6	−	8.08320e6i	1.56229	−	1.31092i
$521$	629944.	+	1.09110e6i	0.101674	+	0.176104i	0.912374	−	0.409357i	$-0.134247\pi$
$521$	629944.	+	1.09110e6i	0.101674	+	0.176104i	−0.810701	+	0.585461i	$0.800914\pi$
$522$	−8.46053e6	+	6.50547e6i	−1.35901	+	1.04497i
$523$	970649.	−	1.68121e6i	0.155170	−	0.268762i	−0.777951	−	0.628325i	$-0.783741\pi$
$523$	970649.	−	1.68121e6i	0.155170	−	0.268762i	0.933121	+	0.359563i	$0.117074\pi$
$524$	7035.06	+	39897.8i	0.00111928	+	0.00634777i
$525$	−8.70974e6	−	5.27924e6i	−1.37914	−	0.835935i
$526$	−1.60322e6	+	583524.i	−0.252655	+	0.0919590i
$527$	872726.	−	317646.i	0.136884	−	0.0498216i
$528$	−839479.	−	508833.i	−0.131046	−	0.0794311i
$529$	−168515.	−	955698.i	−0.0261818	−	0.148485i
$530$	339501.	−	588033.i	0.0524990	−	0.0909310i
$531$	8.51836e6	+	3.51843e6i	1.31105	+	0.541517i
$532$	−93340.3	−	161670.i	−0.0142985	−	0.0247657i
$533$	−5.91508e6	+	4.96334e6i	−0.901868	+	0.756757i
$534$	−2.69089e6	+	3.07147e6i	−0.408360	+	0.466116i
$535$	810199.	−	4.59486e6i	0.122379	−	0.694046i
$536$	−2.27634e6	−	1.91008e6i	−0.342235	−	0.287170i
$537$	−5.21231e6	+	804924.i	−0.780000	+	0.120453i
$538$	−3.53216e6	−	1.28560e6i	−0.526120	−	0.191492i
$539$	−757772.			−0.112348
$540$	67895.8	−	154936.i	0.0100198	−	0.0228648i
$541$	128241.			0.0188379			0.00941897	−	0.999956i	$-0.497002\pi$
$541$	128241.			0.0188379			0.00941897	+	0.999956i	$0.497002\pi$
$542$	−4.39619e6	−	1.60008e6i	−0.642804	−	0.233961i
$543$	−3.94328e6	+	1.01552e7i	−0.573929	+	1.47805i
$544$	51499.8	+	43213.5i	0.00746120	+	0.00626069i
$545$	2.19209e6	−	1.24320e7i	0.316131	−	1.79287i
$546$	1.25638e7	+	2.49255e6i	1.80359	+	0.357817i
$547$	2.17955e6	−	1.82886e6i	0.311457	−	0.261343i	−0.473637	−	0.880720i	$-0.657059\pi$
$547$	2.17955e6	−	1.82886e6i	0.311457	−	0.261343i	0.785094	+	0.619377i	$0.212615\pi$
$548$	43404.6	+	75179.0i	0.00617426	+	0.0106941i
$549$	780851.	+	1.49634e6i	0.110570	+	0.211885i
$550$	−658246.	+	1.14012e6i	−0.0927858	+	0.160710i
$551$	−2.71870e6	−	1.54185e7i	−0.381490	−	2.16354i
$552$	−5.73290e6	+	3.14891e6i	−0.800805	+	0.439859i
$553$	−3.63012e6	+	1.32126e6i	−0.504787	+	0.183728i
$554$	−1.20268e7	+	4.37739e6i	−1.66485	+	0.605956i
$555$	303937.	−	1.42566e7i	0.0418842	−	1.96464i
$556$	35056.5	+	198815.i	0.00480930	+	0.0272749i
$557$	537968.	−	931788.i	0.0734715	−	0.127256i	−0.826949	−	0.562277i	$-0.809926\pi$
$557$	537968.	−	931788.i	0.0734715	−	0.127256i	0.900421	+	0.435021i	$0.143259\pi$
$558$	3.54269e6	−	1.12091e6i	0.481668	−	0.152400i
$559$	3.19809e6	+	5.53926e6i	0.432874	+	0.749760i
$560$	1.13762e7	−	9.54573e6i	1.53294	−	1.28629i
$561$	105179.	+	309340.i	0.0141099	+	0.0414981i
$562$	2.25826e6	−	1.28072e7i	0.301601	−	1.71047i
$563$	−3.37213e6	−	2.82955e6i	−0.448367	−	0.376224i	0.390463	−	0.920619i	$-0.372315\pi$
$563$	−3.37213e6	−	2.82955e6i	−0.448367	−	0.376224i	−0.838829	+	0.544395i	$0.816759\pi$
$564$	−36217.9	−	45080.3i	−0.00479430	−	0.00596745i
$565$	−4.36046e6	−	1.58708e6i	−0.574661	−	0.209159i
$566$	8.41012e6			1.10347
$567$	−9.76323e6	+	2.63702e6i	−1.27537	+	0.344474i
$568$	−780787.			−0.101546
$569$	−2.37185e6	−	863283.i	−0.307119	−	0.111782i	0.183863	−	0.982952i	$-0.441140\pi$
$569$	−2.37185e6	−	863283.i	−0.307119	−	0.111782i	−0.490982	+	0.871170i	$0.663362\pi$
$570$	9.43340e6	+	1.17417e7i	1.21613	+	1.51372i
$571$	6.63834e6	+	5.57023e6i	0.852058	+	0.714961i	0.960242	−	0.279169i	$-0.0900591\pi$
$571$	6.63834e6	+	5.57023e6i	0.852058	+	0.714961i	−0.108184	+	0.994131i	$0.534504\pi$
$572$	4736.81	−	26863.8i	0.000605335	−	0.00343303i
$573$	628123.	+	1.84735e6i	0.0799205	+	0.235051i
$574$	−6.87020e6	+	5.76478e6i	−0.870341	+	0.730303i
$575$	4.45942e6	+	7.72394e6i	0.562482	+	0.974248i
$576$	−5.77434e6	−	5.28058e6i	−0.725181	−	0.663171i
$577$	4.96402e6	−	8.59793e6i	0.620717	−	1.07511i	−0.368636	−	0.929574i	$-0.620175\pi$
$577$	4.96402e6	−	8.59793e6i	0.620717	−	1.07511i	0.989352	−	0.145539i	$-0.0464917\pi$
$578$	1.28748e6	+	7.30167e6i	0.160296	+	0.909081i
$579$	−24981.7	+	1.17180e6i	−0.00309688	+	0.145264i
$580$	−323109.	+	117602.i	−0.0398822	+	0.0145159i
$581$	−5.85120e6	+	2.12966e6i	−0.719125	+	0.261740i
$582$	−1.25299e7	+	6.88229e6i	−1.53334	+	0.842220i
$583$	15012.1	+	85137.9i	0.00182924	+	0.0103741i
$584$	−4.33929e6	+	7.51587e6i	−0.526486	+	0.911900i
$585$	−1.70111e7	−	725649.i	−2.05514	−	0.0876672i
$586$	−6.14935e6	−	1.06510e7i	−0.739750	−	1.28129i
$587$	8.61774e6	−	7.23114e6i	1.03228	−	0.866187i	0.0411608	−	0.999153i	$-0.486894\pi$
$587$	8.61774e6	−	7.23114e6i	1.03228	−	0.866187i	0.991121	+	0.132966i	$0.0424500\pi$
$588$	102663.	+	20367.4i	0.0122453	+	0.00242937i
$589$	−946559.	+	5.36821e6i	−0.112424	+	0.637589i
$590$	1.38059e7	+	1.15846e7i	1.63281	+	1.37009i
$591$	−854203.	+	2.19984e6i	−0.100599	+	0.259073i
$592$	1.07403e7	+	3.90915e6i	1.25954	+	0.458436i
$593$	9.00454e6			1.05154			0.525769	−	0.850628i	$-0.323778\pi$
$593$	9.00454e6			1.05154			0.525769	+	0.850628i	$0.323778\pi$
$594$	367684.	+	1.25445e6i	0.0427572	+	0.145877i
$595$	−4.94284e6			−0.572380
$596$	−26700.7	−	9718.27i	−0.00307899	−	0.00112066i
$597$	3.72588e6	−	575378.i	0.427851	−	0.0660720i
$598$	−8.59236e6	−	7.20985e6i	−0.982561	−	0.824467i
$599$	2.83453e6	−	1.60754e7i	0.322786	−	1.83061i	−0.202011	−	0.979383i	$-0.564748\pi$
$599$	2.83453e6	−	1.60754e7i	0.322786	−	1.83061i	0.524797	−	0.851227i	$-0.324141\pi$
$600$	−7.03301e6	+	8.02772e6i	−0.797560	+	0.910362i
$601$	−4.97312e6	+	4.17294e6i	−0.561620	+	0.471255i	−0.878853	−	0.477092i	$-0.841691\pi$
$601$	−4.97312e6	+	4.17294e6i	−0.561620	+	0.471255i	0.317233	+	0.948348i	$0.397246\pi$
$602$	3.71449e6	+	6.43369e6i	0.417742	+	0.723550i
$603$	529155.	+	3.98845e6i	0.0592638	+	0.446695i
$604$	59742.4	−	103477.i	0.00666332	−	0.0115412i
$605$	2.27680e6	+	1.29124e7i	0.252892	+	1.43422i
$606$	3.30860e6	+	2.00544e6i	0.365985	+	0.221834i
$607$	1.25383e7	−	4.56357e6i	1.38123	−	0.502728i	0.458682	−	0.888601i	$-0.348322\pi$
$607$	1.25383e7	−	4.56357e6i	1.38123	−	0.502728i	0.922552	+	0.385873i	$0.126100\pi$
$608$	−370786.	+	134955.i	−0.0406784	+	0.0148057i
$609$	1.75794e7	+	1.06554e7i	1.92071	+	1.16420i
$610$	573125.	+	3.25036e6i	0.0623627	+	0.353677i
$611$	−2.91026e6	+	5.04071e6i	−0.315376	+	0.546247i
$612$	−5935.23	−	44736.3i	−0.000640559	−	0.00482815i
$613$	9.01424e6	+	1.56131e7i	0.968897	+	1.67818i	0.698758	+	0.715358i	$0.253736\pi$
$613$	9.01424e6	+	1.56131e7i	0.968897	+	1.67818i	0.270139	+	0.962821i	$0.412930\pi$
$614$	4.46018e6	−	3.74253e6i	0.477454	−	0.400631i
$615$	7.85606e6	−	8.96718e6i	0.837562	−	0.956022i
$616$	−322920.	+	1.83137e6i	−0.0342881	+	0.194458i
$617$	1.96709e6	+	1.65058e6i	0.208023	+	0.174552i	0.740846	−	0.671675i	$-0.234425\pi$
$617$	1.96709e6	+	1.65058e6i	0.208023	+	0.174552i	−0.532824	+	0.846226i	$0.678869\pi$
$618$	1.22931e7	−	1.89839e6i	1.29476	−	0.199947i
$619$	−8.86766e6	−	3.22756e6i	−0.930213	−	0.338570i	−0.167919	−	0.985801i	$-0.553705\pi$
$619$	−8.86766e6	−	3.22756e6i	−0.930213	−	0.338570i	−0.762294	+	0.647231i	$0.775927\pi$
$620$	119715.			0.0125075
$621$	8.60541e6	+	2.09203e6i	0.895453	+	0.217691i
$622$	−1.19719e7			−1.24076
$623$	7.39099e6	+	2.69010e6i	0.762926	+	0.277682i
$624$	4.93989e6	−	1.27218e7i	0.507874	−	1.30793i
$625$	−5.46492e6	−	4.58561e6i	−0.559608	−	0.469567i
$626$	378517.	−	2.14668e6i	0.0386056	−	0.218943i
$627$	−1.88102e6	−	373179.i	−0.191084	−	0.0379096i
$628$	171856.	−	144204.i	0.0173887	−	0.0145908i
$629$	−1.90211e6	−	3.29455e6i	−0.191694	−	0.332024i
$630$	−1.97579e7	−	842821.i	−1.98330	−	0.0846027i
$631$	−3.82533e6	+	6.62566e6i	−0.382468	+	0.662454i	−0.991414	−	0.130757i	$-0.958259\pi$
$631$	−3.82533e6	+	6.62566e6i	−0.382468	+	0.662454i	0.608946	+	0.793211i	$0.291592\pi$
$632$	702959.	+	3.98668e6i	0.0700063	+	0.397026i
$633$	1.46824e6	−	806460.i	0.145642	−	0.0799969i
$634$	7.10354e6	−	2.58548e6i	0.701861	−	0.255457i
$635$	−1.28485e7	+	4.67645e6i	−1.26449	+	0.460238i
$636$	254.506	−	11938.0i	2.49491e−5	−	0.00117027i
$637$	−1.82935e6	−	1.03747e7i	−0.178627	−	1.01304i
$638$	1.32858e6	−	2.30116e6i	0.129222	−	0.223818i
$639$	780140.	+	713430.i	0.0755823	+	0.0691193i
$640$	−7.90924e6	−	1.36992e7i	−0.763282	−	1.32204i
$641$	−1.32103e7	+	1.10848e7i	−1.26990	+	1.06557i	−0.275343	+	0.961346i	$0.588792\pi$
$641$	−1.32103e7	+	1.10848e7i	−1.26990	+	1.06557i	−0.994554	+	0.104224i	$0.966764\pi$
$642$	−1.60314e6	−	4.71494e6i	−0.153509	−	0.451480i
$643$	887197.	−	5.03154e6i	0.0846238	−	0.479925i	−0.912813	−	0.408377i	$-0.866095\pi$
$643$	887197.	−	5.03154e6i	0.0846238	−	0.479925i	0.997437	−	0.0715483i	$-0.0227940\pi$
$644$	−164425.	−	137969.i	−0.0156226	−	0.0131089i
$645$	−6.18509e6	−	7.69856e6i	−0.585392	−	0.728635i
$646$	3.77584e6	+	1.37429e6i	0.355986	+	0.129568i
$647$	−7.51130e6			−0.705431			−0.352715	−	0.935731i	$-0.614742\pi$
$647$	−7.51130e6			−0.705431			−0.352715	+	0.935731i	$0.614742\pi$
$648$	944790.	+	1.05554e7i	0.0883889	+	0.987502i
$649$	−2.29463e6			−0.213846
$650$	−1.71985e7	−	6.25975e6i	−1.59664	−	0.581130i
$651$	−4.48259e6	−	5.57946e6i	−0.414549	−	0.515988i
$652$	98224.3	+	82420.0i	0.00904899	+	0.00759300i
$653$	2.18834e6	−	1.24107e7i	0.200832	−	1.13897i	−0.703034	−	0.711156i	$-0.748172\pi$
$653$	2.18834e6	−	1.24107e7i	0.200832	−	1.13897i	0.903866	−	0.427816i	$-0.140717\pi$
$654$	−4.33749e6	−	1.27568e7i	−0.396547	−	1.16627i
$655$	−4.82297e6	+	4.04695e6i	−0.439249	+	0.368574i
$656$	4.77778e6	+	8.27537e6i	0.433478	+	0.750806i
$657$	1.12032e7	−	3.54469e6i	1.01258	−	0.320380i
$658$	−3.38018e6	+	5.85464e6i	−0.304351	+	0.527152i
$659$	92980.5	+	527319.i	0.00834024	+	0.0472998i	0.988694	−	0.149948i	$-0.0479107\pi$
$659$	92980.5	+	527319.i	0.00834024	+	0.0472998i	−0.980354	+	0.197248i	$0.936800\pi$
$660$	−897.672	+	42106.6i	−8.02154e−5	+	0.00376262i
$661$	−3.21197e6	+	1.16906e6i	−0.285935	+	0.104072i	−0.481006	−	0.876717i	$-0.659729\pi$
$661$	−3.21197e6	+	1.16906e6i	−0.285935	+	0.104072i	0.195071	+	0.980789i	$0.437506\pi$
$662$	1.17206e7	−	4.26596e6i	1.03946	−	0.378331i
$663$	−3.98129e6	+	2.18680e6i	−0.351754	+	0.193208i
$664$	1.13306e6	+	6.42591e6i	0.0997318	+	0.565607i
$665$	1.45055e7	−	2.51242e7i	1.27197	−	2.20312i
$666$	−7.04150e6	−	1.34936e7i	−0.615148	−	1.17880i
$667$	−9.00072e6	−	1.55897e7i	−0.783362	−	1.35682i
$668$	−285356.	+	239442.i	−0.0247426	+	0.0207615i
$669$	−7.46657e6	−	1.48131e6i	−0.644994	−	0.127962i
$670$	−1.36620e6	+	7.74812e6i	−0.117579	+	0.666821i
$671$	−321910.	−	270114.i	−0.0276012	−	0.0231601i
$672$	187530.	−	482948.i	0.0160194	−	0.0412551i
$673$	1.94973e7	+	7.09644e6i	1.65935	+	0.603952i	0.990260	−	0.139233i	$-0.0444637\pi$
$673$	1.94973e7	+	7.09644e6i	1.65935	+	0.603952i	0.669086	+	0.743185i	$0.266686\pi$
$674$	2.13675e6			0.181177
$675$	1.43624e7	−	1.59478e6i	1.21330	−	0.134723i
$676$	180195.			0.0151662
$677$	−4.70694e6	−	1.71318e6i	−0.394700	−	0.143659i	0.137043	−	0.990565i	$-0.456240\pi$
$677$	−4.70694e6	−	1.71318e6i	−0.394700	−	0.143659i	−0.531742	+	0.846906i	$0.678462\pi$
$678$	−4.89485e6	+	755899.i	−0.408945	+	0.0631524i
$679$	2.10932e7	+	1.76993e7i	1.75577	+	1.47326i
$680$	−899438.	+	5.10096e6i	−0.0745931	+	0.423039i
$681$	−1.91797e6	+	2.18924e6i	−0.158480	+	0.180894i
$682$	−708691.	+	594662.i	−0.0583440	+	0.0489564i
$683$	−7.69704e6	−	1.33317e7i	−0.631353	−	1.09353i	−0.987275	−	0.159019i	$-0.949167\pi$
$683$	−7.69704e6	−	1.33317e7i	−0.631353	−	1.09353i	0.355923	−	0.934515i	$-0.384167\pi$
$684$	244810.	+	101116.i	0.0200073	+	0.00826384i
$685$	−6.74526e6	+	1.16831e7i	−0.549253	+	0.951334i
$686$	726380.	+	4.11950e6i	0.0589323	+	0.334222i
$687$	−8.85469e6	−	5.36709e6i	−0.715783	−	0.433858i
$688$	7.43800e6	−	2.70721e6i	0.599081	−	0.218048i
$689$	−1.12939e6	+	411065.i	−0.0906351	+	0.0329885i
$690$	1.48097e7	+	8.97657e6i	1.18419	+	0.717774i
$691$	−65140.1	−	369428.i	−0.00518983	−	0.0294330i	0.982103	−	0.188345i	$-0.0603124\pi$
$691$	−65140.1	−	369428.i	−0.00518983	−	0.0294330i	−0.987293	+	0.158912i	$0.949201\pi$
$692$	138573.	−	240016.i	0.0110005	−	0.0190535i
$693$	1.99604e6	−	1.53479e6i	0.157883	−	0.121399i
$694$	1.33733e6	+	2.31632e6i	0.105400	+	0.182558i
$695$	−2.40334e7	+	2.01664e7i	−1.88735	+	1.58368i
$696$	1.41952e7	−	1.62028e7i	1.11075	−	1.26785i
$697$	552283.	−	3.13215e6i	0.0430606	−	0.244209i
$698$	−3.04679e6	−	2.55656e6i	−0.236703	−	0.198617i
$699$	2.51114e6	−	387789.i	0.194392	−	0.0300195i
$700$	−329114.	−	119788.i	−0.0253864	−	0.00923991i
$701$	1.41346e7			1.08639			0.543197	−	0.839605i	$-0.317214\pi$
$701$	1.41346e7			1.08639			0.543197	+	0.839605i	$0.317214\pi$
$702$	−1.62872e7	+	8.06239e6i	−1.24739	+	0.617477i
$703$	2.23281e7			1.70397
$704$	1.83068e6	+	666311.i	0.139213	+	0.0506694i
$705$	3.25288e6	−	8.37719e6i	0.246488	−	0.634783i
$706$	−3.47173e6	−	2.91313e6i	−0.262141	−	0.219962i
$707$	1.29404e6	−	7.33886e6i	0.0973641	−	0.552179i
$708$	310876.	+	61675.2i	0.0233079	+	0.00462410i
$709$	−1.33424e7	+	1.11956e7i	−0.996826	+	0.836436i	−0.986542	−	0.163511i	$-0.947718\pi$
$709$	−1.33424e7	+	1.11956e7i	−0.996826	+	0.836436i	−0.0102846	+	0.999947i	$0.503274\pi$
$710$	1.03363e6	+	1.79030e6i	0.0769518	+	0.133284i
$711$	2.94038e6	−	4.62569e6i	0.218137	−	0.343165i
$712$	4.12108e6	−	7.13792e6i	0.304657	−	0.527681i
$713$	1.08834e6	+	6.17226e6i	0.0801751	+	0.454696i
$714$	−4.62415e6	+	2.53991e6i	−0.339458	+	0.186454i
$715$	3.98350e6	−	1.44987e6i	0.291407	−	0.106063i
$716$	−170429.	+	62031.0i	−0.0124240	+	0.00452196i
$717$	−461540.	+	2.16492e7i	−0.0335283	+	1.57269i
$718$	3.20787e6	+	1.81927e7i	0.232223	+	1.31700i
$719$	−9.46989e6	+	1.64023e7i	−0.683160	+	1.18327i	0.290851	+	0.956768i	$0.406062\pi$
$719$	−9.46989e6	+	1.64023e7i	−0.683160	+	1.18327i	−0.974011	+	0.226500i	$0.927272\pi$
$720$	−4.53990e6	+	2.05757e7i	−0.326374	+	1.47919i
$721$	−1.19794e7	−	2.07489e7i	−0.858217	−	1.48648i
$722$	−7.24679e6	+	6.08078e6i	−0.517372	+	0.434127i
$723$	7.46916e6	+	2.19673e7i	0.531405	+	1.56290i
$724$	−65052.4	+	368930.i	−0.00461229	+	0.0261576i
$725$	−2.25013e7	−	1.88808e7i	−1.58987	−	1.33406i
$726$	8.76510e6	+	1.09099e7i	0.617185	+	0.768208i
$727$	6.37724e6	+	2.32113e6i	0.447504	+	0.162878i	0.555935	−	0.831226i	$-0.312360\pi$
$727$	6.37724e6	+	2.32113e6i	0.447504	+	0.162878i	−0.108431	+	0.994104i	$0.534583\pi$
$728$	−2.58531e7			−1.80794
$729$	8.70082e6	−	1.14099e7i	0.606375	−	0.795179i
$730$	2.29779e7			1.59589
$731$	−2.47566e6	−	901068.i	−0.171356	−	0.0623683i
$732$	36352.1	+	45247.3i	0.00250756	+	0.00312115i
$733$	1.06213e6	+	891233.i	0.0730160	+	0.0612677i	0.678565	−	0.734540i	$-0.262602\pi$
$733$	1.06213e6	+	891233.i	0.0730160	+	0.0612677i	−0.605549	+	0.795808i	$0.707047\pi$
$734$	846950.	−	4.80329e6i	0.0580253	−	0.329078i
$735$	5.23598e6	+	1.53994e7i	0.357503	+	1.05144i
$736$	−347541.	+	291622.i	−0.0236490	+	0.0198438i
$737$	−500859.	−	867513.i	−0.0339662	−	0.0588312i
$738$	2.74170e6	−	1.24259e7i	0.185302	−	0.839822i
$739$	3.67789e6	−	6.37029e6i	0.247735	−	0.429090i	−0.715162	−	0.698959i	$-0.753647\pi$
$739$	3.67789e6	−	6.37029e6i	0.247735	−	0.429090i	0.962897	+	0.269869i	$0.0869804\pi$
$740$	−85151.7	−	482919.i	−0.00571629	−	0.0324187i
$741$	568241.	−	2.66542e7i	0.0380178	−	1.78328i
$742$	−1.31176e6	+	477440.i	−0.0874668	+	0.0318353i
$743$	6.39066e6	−	2.32601e6i	0.424691	−	0.154575i	−0.120828	−	0.992674i	$-0.538555\pi$
$743$	6.39066e6	−	2.32601e6i	0.424691	−	0.154575i	0.545519	+	0.838098i	$0.316333\pi$
$744$	−6.57364e6	+	3.61071e6i	−0.435385	+	0.239144i
$745$	−766780.	−	4.34862e6i	−0.0506151	−	0.287052i
$746$	2.13679e6	−	3.70102e6i	0.140577	−	0.243486i
$747$	4.73944e6	−	7.45590e6i	0.310760	−	0.488876i
$748$	5617.86	+	9730.41i	0.000367127	+	0.000635883i
$749$	−7.34804e6	+	6.16574e6i	−0.478594	+	0.401588i
$750$	5.01225e6	+	994390.i	0.325372	+	0.0645511i
$751$	−2.44936e6	+	1.38910e7i	−0.158472	+	0.898740i	0.797070	+	0.603886i	$0.206382\pi$
$751$	−2.44936e6	+	1.38910e7i	−0.158472	+	0.898740i	−0.955542	+	0.294854i	$0.904729\pi$
$752$	5.51779e6	+	4.62997e6i	0.355812	+	0.298562i
$753$	1.04406e7	−	2.68878e7i	0.671024	−	1.72810i
$754$	3.47128e7	+	1.26344e7i	2.22362	+	0.809333i
$755$	1.85685e7			1.18552
$756$	−311675.	+	154283.i	−0.0198334	+	0.00981782i
$757$	−1.29168e7			−0.819247			−0.409623	−	0.912255i	$-0.634340\pi$
$757$	−1.29168e7			−0.819247			−0.409623	+	0.912255i	$0.634340\pi$
$758$	−2.00795e6	−	730833.i

Introduction	Features
Universe	News

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

\(f(q)\)	\(=\)	\(q+(5.36004 + 1.95090i) q^{2} +(9.76327 + 12.1523i) q^{3} +(0.410645 + 0.344572i) q^{4} +(-14.4659 + 82.0402i) q^{5} +(28.6236 + 84.1840i) q^{6} +(131.197 - 110.088i) q^{7} +(-89.7358 - 155.427i) q^{8} +(-52.3572 + 237.292i) q^{9} +O(q^{10})\)	\(q+(5.36004 + 1.95090i) q^{2} +(9.76327 + 12.1523i) q^{3} +(0.410645 + 0.344572i) q^{4} +(-14.4659 + 82.0402i) q^{5} +(28.6236 + 84.1840i) q^{6} +(131.197 - 110.088i) q^{7} +(-89.7358 - 155.427i) q^{8} +(-52.3572 + 237.292i) q^{9} +(-237.590 + 411.517i) q^{10} +(-10.5058 - 59.5813i) q^{11} +(-0.178108 + 8.35443i) q^{12} +(790.371 - 287.672i) q^{13} +(917.994 - 334.122i) q^{14} +(-1138.21 + 625.186i) q^{15} +(-180.745 - 1025.05i) q^{16} +(-173.221 + 300.027i) q^{17} +(-743.570 + 1169.75i) q^{18} +(-1016.68 - 1760.95i) q^{19} +(-34.2091 + 28.7048i) q^{20} +(2618.74 + 519.536i) q^{21} +(59.9254 - 339.854i) q^{22} +(-1790.96 - 1502.79i) q^{23} +(1012.68 - 2607.97i) q^{24} +(-3584.79 - 1304.76i) q^{25} +4797.64 q^{26} +(-3394.83 + 1680.49i) q^{27} +91.8086 q^{28} +(7235.39 + 2633.47i) q^{29} +(-7320.54 + 1130.49i) q^{30} +(-2053.60 - 1723.18i) q^{31} +(33.6971 - 191.106i) q^{32} +(621.479 - 709.377i) q^{33} +(-1513.79 + 1270.22i) q^{34} +(7133.73 + 12356.0i) q^{35} +(-103.264 + 79.4021i) q^{36} +(-5490.42 + 9509.69i) q^{37} +(-2014.04 - 11422.2i) q^{38} +(11212.5 + 6796.22i) q^{39} +(14049.4 - 5113.55i) q^{40} +(-8626.75 + 3139.88i) q^{41} +(13023.0 + 7893.61i) q^{42} +(1320.52 + 7489.05i) q^{43} +(16.2159 - 28.0867i) q^{44} +(-18710.1 - 7728.04i) q^{45} +(-6667.81 - 11549.0i) q^{46} +(-5301.15 + 4448.19i) q^{47} +(10692.1 - 12204.3i) q^{48} +(2174.96 - 12334.8i) q^{49} +(-16669.2 - 13987.1i) q^{50} +(-5337.23 + 824.214i) q^{51} +(423.685 + 154.209i) q^{52} -1428.94 q^{53} +(-21474.9 + 2384.54i) q^{54} +5040.03 q^{55} +(-28883.7 - 10512.8i) q^{56} +(11473.4 - 29547.6i) q^{57} +(33644.4 + 28231.0i) q^{58} +(6586.05 - 37351.3i) q^{59} +(-682.822 - 135.466i) q^{60} +(5320.79 - 4464.67i) q^{61} +(-7645.65 - 13242.7i) q^{62} +(19253.9 + 36896.0i) q^{63} +(-16100.4 + 27886.7i) q^{64} +(12167.2 + 69003.6i) q^{65} +(4715.08 - 2589.85i) q^{66} +(15558.7 - 5662.90i) q^{67} +(-174.513 + 63.5176i) q^{68} +(776.789 - 36436.4i) q^{69} +(14131.9 + 80145.7i) q^{70} +(2175.24 - 3767.63i) q^{71} +(41580.0 - 13155.9i) q^{72} +(-24178.2 - 41877.8i) q^{73} +(-47981.3 + 40261.1i) q^{74} +(-19143.4 - 56302.1i) q^{75} +(189.277 - 1073.44i) q^{76} +(-7937.50 - 6660.35i) q^{77} +(46840.7 + 58302.4i) q^{78} +(-21195.8 - 7714.64i) q^{79} +86710.2 q^{80} +(-53566.5 - 24847.9i) q^{81} -52365.3 q^{82} +(-34164.4 - 12434.8i) q^{83} +(896.352 + 1115.69i) q^{84} +(-22108.5 - 18551.2i) q^{85} +(-7532.31 + 42717.9i) q^{86} +(38638.4 + 113638. i) q^{87} +(-8317.79 + 6979.45i) q^{88} +(22962.3 + 39771.9i) q^{89} +(-85210.5 - 77924.1i) q^{90} +(72025.6 - 124752. i) q^{91} +(-217.627 - 1234.23i) q^{92} +(890.706 - 41779.8i) q^{93} +(-37092.3 + 13500.5i) q^{94} +(159176. - 57935.2i) q^{95} +(2651.37 - 1456.32i) q^{96} +(27918.1 + 158332. i) q^{97} +(35721.7 - 61871.9i) q^{98} +(14688.2 + 626.563i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84q - 6q^{2} - 6q^{3} - 6q^{4} - 93q^{5} - 126q^{6} - 6q^{7} + 573q^{8} + 324q^{9} + O(q^{10}) \)	\( 84q - 6q^{2} - 6q^{3} - 6q^{4} - 93q^{5} - 126q^{6} - 6q^{7} + 573q^{8} + 324q^{9} - 3q^{10} + 111q^{11} - 2769q^{12} - 6q^{13} - 1641q^{14} + 1989q^{15} + 90q^{16} + 3465q^{17} - 99q^{18} - 3q^{19} + 9987q^{20} + 5424q^{21} - 2850q^{22} - 7716q^{23} - 18486q^{24} + 4953q^{25} - 7806q^{26} - 8109q^{27} - 12q^{28} - 20418q^{29} - 6453q^{30} - 6657q^{31} + 51192q^{32} + 50634q^{33} - 11394q^{34} + 35868q^{35} - 3600q^{36} - 3q^{37} - 44076q^{38} - 13971q^{39} + 12441q^{40} - 79077q^{41} - 64422q^{42} - 9465q^{43} + 110757q^{44} + 92493q^{45} - 3q^{46} + 103557q^{47} + 134049q^{48} + 5484q^{49} - 105513q^{50} - 124866q^{51} + 68625q^{52} - 206406q^{53} - 350946q^{54} - 12q^{55} - 147237q^{56} + 67767q^{57} - 9753q^{58} + 116484q^{59} + 241290q^{60} - 70116q^{61} + 246066q^{62} + 135981q^{63} - 86019q^{64} - 19815q^{65} - 32931q^{66} + 48117q^{67} - 48105q^{68} + 25263q^{69} + 270111q^{70} + 279531q^{71} + 441684q^{72} - 27012q^{73} + 233691q^{74} + 18399q^{75} - 125670q^{76} - 345135q^{77} - 520974q^{78} - 216186q^{79} - 924114q^{80} - 428616q^{81} - 12q^{82} - 370401q^{83} - 522390q^{84} - 43731q^{85} + 116682q^{86} + 304173q^{87} + 371418q^{88} + 154827q^{89} + 327366q^{90} - 91002q^{91} + 1279059q^{92} + 890079q^{93} + 11667q^{94} + 1087671q^{95} + 1165698q^{96} - 420621q^{97} + 463410q^{98} - 28323q^{99} + O(q^{100}) \)

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

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