LMFDB - Embedded newform 27.6.c.a.19.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [27,6,Mod(10,27)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("27.10"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(27, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	27.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.33036313495$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 40x^{6} + 568x^{4} + 3363x^{2} + 7056 $ x^8 + 40x^6 + 568x^4 + 3363*x^2 + 7056
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{8} $
Twist minimal:	no (minimal twist has level 9)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			19.4
Root			$-3.62198i$ of defining polynomial
Character	$\chi$	$=$	27.19
Dual form			27.6.c.a.10.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.77467 - 6.53793i) q^{2} +(-12.4963 - 21.6443i) q^{4} +(-43.7155 - 75.7175i) q^{5} +(20.6033 - 35.6859i) q^{7} +52.9007 q^{8} -660.048 q^{10} +(-3.84390 + 6.65783i) q^{11} +(302.642 + 524.191i) q^{13} +(-155.541 - 269.405i) q^{14} +(599.566 - 1038.48i) q^{16} +566.131 q^{17} +2060.59 q^{19} +(-1092.57 + 1892.38i) q^{20} +(29.0189 + 50.2623i) q^{22} +(-137.210 - 237.655i) q^{23} +(-2259.59 + 3913.73i) q^{25} +4569.50 q^{26} -1029.86 q^{28} +(-2410.58 + 4175.25i) q^{29} +(-2230.39 - 3863.15i) q^{31} +(-3679.92 - 6373.81i) q^{32} +(2136.96 - 3701.32i) q^{34} -3602.73 q^{35} +242.525 q^{37} +(7778.07 - 13472.0i) q^{38} +(-2312.58 - 4005.51i) q^{40} +(-1754.78 - 3039.37i) q^{41} +(-4267.58 + 7391.66i) q^{43} +192.139 q^{44} -2071.70 q^{46} +(-8995.40 + 15580.5i) q^{47} +(7554.51 + 13084.8i) q^{49} +(17058.5 + 29546.1i) q^{50} +(7563.83 - 13100.9i) q^{52} -2025.98 q^{53} +672.152 q^{55} +(1089.93 - 1887.81i) q^{56} +(18198.3 + 31520.5i) q^{58} +(1009.31 + 1748.18i) q^{59} +(14152.6 - 24513.0i) q^{61} -33676.0 q^{62} -17189.8 q^{64} +(26460.3 - 45830.6i) q^{65} +(-20947.0 - 36281.3i) q^{67} +(-7074.57 - 12253.5i) q^{68} +(-13599.1 + 23554.4i) q^{70} +32656.7 q^{71} +32820.4 q^{73} +(915.453 - 1585.61i) q^{74} +(-25749.9 - 44600.1i) q^{76} +(158.394 + 274.346i) q^{77} +(-44069.6 + 76330.8i) q^{79} -104841. q^{80} -26494.9 q^{82} +(-5289.91 + 9162.39i) q^{83} +(-24748.7 - 42866.0i) q^{85} +(32217.4 + 55802.2i) q^{86} +(-203.345 + 352.204i) q^{88} +124555. q^{89} +24941.6 q^{91} +(-3429.25 + 5939.64i) q^{92} +(67909.4 + 117623. i) q^{94} +(-90080.0 - 156023. i) q^{95} +(81494.3 - 141152. i) q^{97} +114063. q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 3 q^{2} - 49 q^{4} - 78 q^{5} + 28 q^{7} + 750 q^{8} + 60 q^{10} - 444 q^{11} - 182 q^{13} - 1392 q^{14} - 289 q^{16} + 4356 q^{17} + 952 q^{19} - 6684 q^{20} + 1011 q^{22} - 8844 q^{23} - 1654 q^{25}+ \cdots - 57654 q^{98}+O(q^{100}) $ 8 * q - 3 * q^2 - 49 * q^4 - 78 * q^5 + 28 * q^7 + 750 * q^8 + 60 * q^10 - 444 * q^11 - 182 * q^13 - 1392 * q^14 - 289 * q^16 + 4356 * q^17 + 952 * q^19 - 6684 * q^20 + 1011 * q^22 - 8844 * q^23 - 1654 * q^25 + 24888 * q^26 - 1604 * q^28 - 12018 * q^29 + 1132 * q^31 - 8703 * q^32 + 10125 * q^34 + 16224 * q^35 - 15176 * q^37 + 11145 * q^38 - 8736 * q^40 - 1248 * q^41 - 6092 * q^43 - 49530 * q^44 + 45960 * q^46 + 60 * q^47 + 9090 * q^49 + 57057 * q^50 - 32510 * q^52 - 20952 * q^53 - 36120 * q^55 + 61170 * q^56 + 8328 * q^58 - 2076 * q^59 + 48142 * q^61 - 241764 * q^62 - 20926 * q^64 + 13146 * q^65 - 7148 * q^67 + 123129 * q^68 - 654 * q^70 + 71856 * q^71 + 122452 * q^73 + 160320 * q^74 - 49571 * q^76 - 39534 * q^77 - 59516 * q^79 - 124512 * q^80 - 233598 * q^82 - 117696 * q^83 + 28836 * q^85 + 15915 * q^86 + 104523 * q^88 + 451728 * q^89 + 111392 * q^91 - 134034 * q^92 + 169464 * q^94 - 294888 * q^95 + 33976 * q^97 - 57654 * q^98

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	3.77467	−	6.53793i	0.667275	−	1.15575i	−0.311389	−	0.950283i	$-0.600794\pi$
$2$	3.77467	−	6.53793i	0.667275	−	1.15575i	0.978663	−	0.205471i	$-0.0658725\pi$
$3$		0			0
$3$		0			0
$4$	−12.4963	−	21.6443i	−0.390511	−	0.676384i
$5$	−43.7155	−	75.7175i	−0.782007	−	1.35448i	−0.930771	−	0.365603i	$-0.880863\pi$
$5$	−43.7155	−	75.7175i	−0.782007	−	1.35448i	0.148764	−	0.988873i	$-0.452471\pi$
$6$		0			0
$7$	20.6033	−	35.6859i	0.158925	−	0.275265i	−0.775557	−	0.631278i	$-0.782531\pi$
$7$	20.6033	−	35.6859i	0.158925	−	0.275265i	0.934481	+	0.356013i	$0.115864\pi$
$8$	52.9007			0.292238
$9$		0			0
$10$	−660.048			−2.08725
$11$	−3.84390	+	6.65783i	−0.00957834	+	0.0165902i	−0.870775	−	0.491682i	$-0.836382\pi$
$11$	−3.84390	+	6.65783i	−0.00957834	+	0.0165902i	0.861197	+	0.508272i	$0.169716\pi$
$12$		0			0
$13$	302.642	+	524.191i	0.496673	+	0.860263i	0.999993	−	0.00383763i	$-0.00122156\pi$
$13$	302.642	+	524.191i	0.496673	+	0.860263i	−0.503320	+	0.864100i	$0.667888\pi$
$14$	−155.541	−	269.405i	−0.212093	−	0.367355i
$15$		0			0
$16$	599.566	−	1038.48i	0.585514	−	1.01414i
$17$	566.131			0.475111			0.237555	−	0.971374i	$-0.423654\pi$
$17$	566.131			0.475111			0.237555	+	0.971374i	$0.423654\pi$
$18$		0			0
$19$	2060.59			1.30951			0.654755	−	0.755842i	$-0.272772\pi$
$19$	2060.59			1.30951			0.654755	+	0.755842i	$0.272772\pi$
$20$	−1092.57	+	1892.38i	−0.610764	+	1.05787i
$21$		0			0
$22$	29.0189	+	50.2623i	0.0127828	+	0.0221404i
$23$	−137.210	−	237.655i	−0.0540838	−	0.0936759i	0.837716	−	0.546106i	$-0.183890\pi$
$23$	−137.210	−	237.655i	−0.0540838	−	0.0936759i	−0.891800	+	0.452430i	$0.850557\pi$
$24$		0			0
$25$	−2259.59	+	3913.73i	−0.723070	+	1.25239i
$26$	4569.50			1.32567
$27$		0			0
$28$	−1029.86			−0.248247
$29$	−2410.58	+	4175.25i	−0.532264	+	0.921909i	0.467026	+	0.884244i	$0.345325\pi$
$29$	−2410.58	+	4175.25i	−0.532264	+	0.921909i	−0.999290	+	0.0376653i	$0.988008\pi$
$30$		0			0
$31$	−2230.39	−	3863.15i	−0.416847	−	0.722000i	0.578774	−	0.815488i	$-0.303531\pi$
$31$	−2230.39	−	3863.15i	−0.416847	−	0.722000i	−0.995620	+	0.0934885i	$0.970198\pi$
$32$	−3679.92	−	6373.81i	−0.635278	−	1.10033i
$33$		0			0
$34$	2136.96	−	3701.32i	0.317029	−	0.549111i
$35$	−3602.73			−0.497121
$36$		0			0
$37$	242.525			0.0291241			0.0145620	−	0.999894i	$-0.495365\pi$
$37$	242.525			0.0291241			0.0145620	+	0.999894i	$0.495365\pi$
$38$	7778.07	−	13472.0i	0.873802	−	1.51347i
$39$		0			0
$40$	−2312.58	−	4005.51i	−0.228532	−	0.395829i
$41$	−1754.78	−	3039.37i	−0.163028	−	0.282373i	0.772925	−	0.634497i	$-0.218793\pi$
$41$	−1754.78	−	3039.37i	−0.163028	−	0.282373i	−0.935953	+	0.352124i	$0.885459\pi$
$42$		0			0
$43$	−4267.58	+	7391.66i	−0.351974	+	0.609636i	−0.986595	−	0.163187i	$-0.947823\pi$
$43$	−4267.58	+	7391.66i	−0.351974	+	0.609636i	0.634621	+	0.772823i	$0.281156\pi$
$44$	192.139			0.0149618
$45$		0			0
$46$	−2071.70			−0.144355
$47$	−8995.40	+	15580.5i	−0.593985	+	1.02881i	0.399704	+	0.916644i	$0.369113\pi$
$47$	−8995.40	+	15580.5i	−0.593985	+	1.02881i	−0.993689	+	0.112168i	$0.964220\pi$
$48$		0			0
$49$	7554.51	+	13084.8i	0.449486	+	0.778533i
$50$	17058.5	+	29546.1i	0.964973	+	1.67138i
$51$		0			0
$52$	7563.83	−	13100.9i	0.387912	−	0.671883i
$53$	−2025.98			−0.0990708			−0.0495354	−	0.998772i	$-0.515774\pi$
$53$	−2025.98			−0.0990708			−0.0495354	+	0.998772i	$0.515774\pi$
$54$		0			0
$55$	672.152			0.0299613
$56$	1089.93	−	1887.81i	0.0464438	−	0.0804430i
$57$		0			0
$58$	18198.3	+	31520.5i	0.710333	+	1.23033i
$59$	1009.31	+	1748.18i	0.0377481	+	0.0653816i	0.884282	−	0.466953i	$-0.154648\pi$
$59$	1009.31	+	1748.18i	0.0377481	+	0.0653816i	−0.846534	+	0.532334i	$0.821315\pi$
$60$		0			0
$61$	14152.6	−	24513.0i	0.486981	−	0.843476i	−0.512907	−	0.858444i	$-0.671431\pi$
$61$	14152.6	−	24513.0i	0.486981	−	0.843476i	0.999888	+	0.0149684i	$0.00476476\pi$
$62$	−33676.0			−1.11260
$63$		0			0
$64$	−17189.8			−0.524591
$65$	26460.3	−	45830.6i	0.776803	−	1.34546i
$66$		0			0
$67$	−20947.0	−	36281.3i	−0.570079	−	0.987405i	−0.996557	−	0.0829074i	$-0.973579\pi$
$67$	−20947.0	−	36281.3i	−0.570079	−	0.987405i	0.426479	−	0.904498i	$-0.359754\pi$
$68$	−7074.57	−	12253.5i	−0.185536	−	0.321357i
$69$		0			0
$70$	−13599.1	+	23554.4i	−0.331716	+	0.574549i
$71$	32656.7			0.768822			0.384411	−	0.923162i	$-0.374404\pi$
$71$	32656.7			0.768822			0.384411	+	0.923162i	$0.374404\pi$
$72$		0			0
$73$	32820.4			0.720837			0.360418	−	0.932791i	$-0.382634\pi$
$73$	32820.4			0.720837			0.360418	+	0.932791i	$0.382634\pi$
$74$	915.453	−	1585.61i	0.0194337	−	0.0336602i
$75$		0			0
$76$	−25749.9	−	44600.1i	−0.511377	−	0.885731i
$77$	158.394	+	274.346i	0.00304447	+	0.00527317i
$78$		0			0
$79$	−44069.6	+	76330.8i	−0.794459	+	1.37604i	0.128723	+	0.991681i	$0.458912\pi$
$79$	−44069.6	+	76330.8i	−0.794459	+	1.37604i	−0.923182	+	0.384363i	$0.874421\pi$
$80$	−104841.			−1.83150
$81$		0			0
$82$	−26494.9			−0.435138
$83$	−5289.91	+	9162.39i	−0.0842855	+	0.145987i	−0.905087	−	0.425227i	$-0.860194\pi$
$83$	−5289.91	+	9162.39i	−0.0842855	+	0.145987i	0.820801	+	0.571214i	$0.193527\pi$
$84$		0			0
$85$	−24748.7	−	42866.0i	−0.371540	−	0.643526i
$86$	32217.4	+	55802.2i	0.469726	+	0.813590i
$87$		0			0
$88$	−203.345	+	352.204i	−0.00279915	+	0.00484828i
$89$	124555.			1.66681			0.833407	−	0.552660i	$-0.186387\pi$
$89$	124555.			1.66681			0.833407	+	0.552660i	$0.186387\pi$
$90$		0			0
$91$	24941.6			0.315734
$92$	−3429.25	+	5939.64i	−0.0422406	+	0.0731628i
$93$		0			0
$94$	67909.4	+	117623.i	0.792702	+	1.37300i
$95$	−90080.0	−	156023.i	−1.02405	−	1.77370i
$96$		0			0
$97$	81494.3	−	141152.i	0.879423	−	1.52321i	0.0274474	−	0.999623i	$-0.491262\pi$
$97$	81494.3	−	141152.i	0.879423	−	1.52321i	0.851975	−	0.523582i	$-0.175405\pi$
$98$	114063.			1.19972
$99$		0			0
$100$	112947.			1.12947
$101$	−92925.6	+	160952.i	−0.906425	+	1.56997i	−0.0874330	+	0.996170i	$0.527866\pi$
$101$	−92925.6	+	160952.i	−0.906425	+	1.56997i	−0.818992	+	0.573804i	$0.805467\pi$
$102$		0			0
$103$	24409.2	+	42277.9i	0.226704	+	0.392663i	0.956829	−	0.290650i	$-0.0938716\pi$
$103$	24409.2	+	42277.9i	0.226704	+	0.392663i	−0.730125	+	0.683314i	$0.760538\pi$
$104$	16010.0	+	27730.1i	0.145147	+	0.251401i
$105$		0			0
$106$	−7647.42	+	13245.7i	−0.0661074	+	0.114501i
$107$	−131842.			−1.11325			−0.556626	−	0.830763i	$-0.687905\pi$
$107$	−131842.			−1.11325			−0.556626	+	0.830763i	$0.687905\pi$
$108$		0			0
$109$	−162984.			−1.31395			−0.656976	−	0.753912i	$-0.728165\pi$
$109$	−162984.			−1.31395			−0.656976	+	0.753912i	$0.728165\pi$
$110$	2537.16	−	4394.48i	0.0199924	−	0.0346279i
$111$		0			0
$112$	−24706.0	−	42792.1i	−0.186105	−	0.322343i
$113$	81762.9	+	141618.i	0.602366	+	1.04333i	0.992462	+	0.122554i	$0.0391085\pi$
$113$	81762.9	+	141618.i	0.602366	+	1.04333i	−0.390096	+	0.920774i	$0.627558\pi$
$114$		0			0
$115$	−11996.4	+	20778.4i	−0.0845878	+	0.146510i
$116$	120494.			0.831419
$117$		0			0
$118$	15239.3			0.100753
$119$	11664.2	−	20202.9i	0.0755068	−	0.130782i
$120$		0			0
$121$	80495.9	+	139423.i	0.499817	+	0.865708i
$122$	−106843.	−	185058.i	−0.649900	−	1.12566i
$123$		0			0
$124$	−55743.4	+	96550.4i	−0.325566	+	0.563897i
$125$	121895.			0.697770
$126$		0			0
$127$	−233286.			−1.28345			−0.641724	−	0.766935i	$-0.721781\pi$
$127$	−233286.			−1.28345			−0.641724	+	0.766935i	$0.721781\pi$
$128$	52871.6	−	91576.3i	0.285231	−	0.494035i
$129$		0			0
$130$	−199758.	−	345991.i	−1.03668	−	1.79559i
$131$	−86709.6	−	150185.i	−0.441457	−	0.764626i	0.556341	−	0.830954i	$-0.312205\pi$
$131$	−86709.6	−	150185.i	−0.441457	−	0.764626i	−0.997798	+	0.0663279i	$0.978872\pi$
$132$		0			0
$133$	42455.0	−	73534.2i	0.208113	−	0.360463i
$134$	−316272.			−1.52160
$135$		0			0
$136$	29948.8			0.138845
$137$	23981.7	−	41537.5i	0.109164	−	0.189077i	−0.806268	−	0.591550i	$-0.798516\pi$
$137$	23981.7	−	41537.5i	0.109164	−	0.189077i	0.915432	+	0.402473i	$0.131849\pi$
$138$		0			0
$139$	95222.3	+	164930.i	0.418025	+	0.724040i	0.995741	−	0.0921980i	$-0.0293893\pi$
$139$	95222.3	+	164930.i	0.418025	+	0.724040i	−0.577716	+	0.816238i	$0.696056\pi$
$140$	45021.0	+	77978.6i	0.194131	+	0.336245i
$141$		0			0
$142$	123268.	−	213507.i	0.513016	−	0.888569i
$143$	−4653.30			−0.0190292
$144$		0			0
$145$	421520.			1.66494
$146$	123886.	−	214577.i	0.480996	−	0.833109i
$147$		0			0
$148$	−3030.67	−	5249.28i	−0.0113733	−	0.0196991i
$149$	24272.2	+	42040.6i	0.0895660	+	0.155133i	0.907328	−	0.420424i	$-0.138119\pi$
$149$	24272.2	+	42040.6i	0.0895660	+	0.155133i	−0.817762	+	0.575557i	$0.804785\pi$
$150$		0			0
$151$	−112968.	+	195667.i	−0.403194	+	0.698352i	−0.994109	−	0.108381i	$-0.965433\pi$
$151$	−112968.	+	195667.i	−0.403194	+	0.698352i	0.590916	+	0.806733i	$0.298767\pi$
$152$	109007.			0.382688
$153$		0			0
$154$	2391.54			0.00812598
$155$	−195005.	+	337759.i	−0.651954	+	1.12922i
$156$		0			0
$157$	−80599.2	−	139602.i	−0.260965	−	0.452004i	0.705534	−	0.708676i	$-0.250707\pi$
$157$	−80599.2	−	139602.i	−0.260965	−	0.452004i	−0.966499	+	0.256672i	$0.917374\pi$
$158$	332697.	+	576248.i	1.06024	+	1.83640i
$159$		0			0
$160$	−321739.	+	557269.i	−0.993583	+	1.72094i
$161$	−11307.9			−0.0343810
$162$		0			0
$163$	−26136.5			−0.0770510			−0.0385255	−	0.999258i	$-0.512266\pi$
$163$	−26136.5			−0.0770510			−0.0385255	+	0.999258i	$0.512266\pi$
$164$	−43856.6	+	75961.9i	−0.127328	+	0.220539i
$165$		0			0
$166$	39935.4	+	69170.1i	0.112483	+	0.194827i
$167$	63474.6	+	109941.i	0.176120	+	0.305049i	0.940548	−	0.339660i	$-0.110312\pi$
$167$	63474.6	+	109941.i	0.176120	+	0.305049i	−0.764428	+	0.644709i	$0.776979\pi$
$168$		0			0
$169$	2462.49	−	4265.15i	0.00663219	−	0.0114873i
$170$	−373674.			−0.991676
$171$		0			0
$172$	213316.			0.549798
$173$	265893.	−	460540.i	0.675447	−	1.16991i	−0.300891	−	0.953659i	$-0.597284\pi$
$173$	265893.	−	460540.i	0.675447	−	1.16991i	0.976338	−	0.216250i	$-0.0693826\pi$
$174$		0			0
$175$	93110.1	+	161271.i	0.229827	+	0.398073i
$176$	4609.34	+	7983.61i	0.0112165	+	0.0194275i
$177$		0			0
$178$	470156.	−	814333.i	1.11222	−	1.92643i
$179$	−365415.			−0.852421			−0.426211	−	0.904624i	$-0.640152\pi$
$179$	−365415.			−0.852421			−0.426211	+	0.904624i	$0.640152\pi$
$180$		0			0
$181$	437560.			0.992752			0.496376	−	0.868108i	$-0.334664\pi$
$181$	437560.			0.992752			0.496376	+	0.868108i	$0.334664\pi$
$182$	94146.6	−	163067.i	0.210681	−	0.364911i
$183$		0			0
$184$	−7258.53	−	12572.1i	−0.0158053	−	0.0273757i
$185$	−10602.1	−	18363.4i	−0.0227752	−	0.0394478i
$186$		0			0
$187$	−2176.15	+	3769.20i	−0.00455077	+	0.00788216i
$188$	449638.			0.927830
$189$		0			0
$190$	−1.36009e6			−2.73328
$191$	76457.7	−	132429.i	0.151648	−	0.262663i	−0.780185	−	0.625549i	$-0.784875\pi$
$191$	76457.7	−	132429.i	0.151648	−	0.262663i	0.931834	+	0.362886i	$0.118209\pi$
$192$		0			0
$193$	−194153.	−	336283.i	−0.375190	−	0.649848i	0.615166	−	0.788398i	$-0.289089\pi$
$193$	−194153.	−	336283.i	−0.375190	−	0.649848i	−0.990355	+	0.138550i	$0.955756\pi$
$194$	−615229.	−	1.06561e6i	−1.17363	−	2.03279i
$195$		0			0
$196$	188807.	−	327024.i	0.351058	−	0.608050i
$197$	−116484.			−0.213845			−0.106923	−	0.994267i	$-0.534100\pi$
$197$	−116484.			−0.213845			−0.106923	+	0.994267i	$0.534100\pi$
$198$		0			0
$199$	−904935.			−1.61989			−0.809943	−	0.586508i	$-0.800502\pi$
$199$	−904935.			−1.61989			−0.809943	+	0.586508i	$0.800502\pi$
$200$	−119534.	+	207039.i	−0.211309	+	0.365997i
$201$		0			0
$202$	701528.	+	1.21508e6i	1.20967	+	2.09521i
$203$	99331.8	+	172048.i	0.169180	+	0.293028i
$204$		0			0
$205$	−153422.	+	265735.i	−0.254978	+	0.441636i
$206$	368547.			0.605096
$207$		0			0
$208$	725815.			1.16323
$209$	−7920.71	+	13719.1i	−0.0125429	+	0.0217250i
$210$		0			0
$211$	−592009.	−	1.02539e6i	−0.915424	−	1.58556i	−0.806279	−	0.591535i	$-0.798522\pi$
$211$	−592009.	−	1.02539e6i	−0.915424	−	1.58556i	−0.109145	−	0.994026i	$-0.534811\pi$
$212$	25317.3	+	43850.9i	0.0386882	+	0.0670099i
$213$		0			0
$214$	−497660.	+	861973.i	−0.742845	+	1.28665i
$215$	746238.			1.10098
$216$		0			0
$217$	−183813.			−0.264989
$218$	−615212.	+	1.06558e6i	−0.876766	+	1.51860i
$219$		0			0
$220$	−8399.44	−	14548.3i	−0.0117002	−	0.0202654i
$221$	171335.	+	296761.i	0.235975	+	0.408720i
$222$		0			0
$223$	407368.	−	705583.i	0.548561	−	0.950136i	−0.449812	−	0.893123i	$-0.648509\pi$
$223$	407368.	−	705583.i	0.548561	−	0.950136i	0.998373	−	0.0570127i	$-0.0181576\pi$
$224$	−303274.			−0.403845
$225$		0			0
$226$	1.23451e6			1.60777
$227$	−187705.	+	325115.i	−0.241775	+	0.418767i	−0.961220	−	0.275783i	$-0.911063\pi$
$227$	−187705.	+	325115.i	−0.241775	+	0.418767i	0.719445	+	0.694550i	$0.244396\pi$
$228$		0			0
$229$	−62886.2	−	108922.i	−0.0792441	−	0.137255i	0.823680	−	0.567055i	$-0.191917\pi$
$229$	−62886.2	−	108922.i	−0.0792441	−	0.137255i	−0.902924	+	0.429800i	$0.858584\pi$
$230$	90565.3	+	156864.i	0.112887	+	0.195525i
$231$		0			0
$232$	−127522.	+	220874.i	−0.155548	+	0.269417i
$233$	−423564.			−0.511128			−0.255564	−	0.966792i	$-0.582261\pi$
$233$	−423564.			−0.511128			−0.255564	+	0.966792i	$0.582261\pi$
$234$		0			0
$235$	1.57295e6			1.85800
$236$	25225.4	−	43691.7i	0.0294821	−	0.0510644i
$237$		0			0
$238$	−88056.8	−	152519.i	−0.100767	−	0.174534i
$239$	−611920.	−	1.05988e6i	−0.692947	−	1.20022i	−0.970868	−	0.239616i	$-0.922979\pi$
$239$	−611920.	−	1.05988e6i	−0.692947	−	1.20022i	0.277921	−	0.960604i	$-0.410355\pi$
$240$		0			0
$241$	−379300.	+	656966.i	−0.420668	+	0.728619i	−0.996005	−	0.0892979i	$-0.971538\pi$
$241$	−379300.	+	656966.i	−0.420668	+	0.728619i	0.575337	+	0.817917i	$0.304871\pi$
$242$	1.21538e6			1.33406
$243$		0			0
$244$	−707423.			−0.760685
$245$	660499.	−	1.14402e6i	0.703002	−	1.21764i
$246$		0			0
$247$	623622.	+	1.08014e6i	0.650398	+	1.12652i
$248$	−117989.	−	204363.i	−0.121818	−	0.210996i
$249$		0			0
$250$	460116.	−	796944.i	0.465604	−	0.806450i
$251$	510893.			0.511854			0.255927	−	0.966696i	$-0.417619\pi$
$251$	510893.			0.511854			0.255927	+	0.966696i	$0.417619\pi$
$252$		0			0
$253$	2109.69			0.00207213
$254$	−880577.	+	1.52520e6i	−0.856412	+	1.48335i
$255$		0			0
$256$	−674183.	−	1.16772e6i	−0.642951	−	1.11362i
$257$	919950.	+	1.59340e6i	0.868823	+	1.50485i	0.863200	+	0.504862i	$0.168457\pi$
$257$	919950.	+	1.59340e6i	0.868823	+	1.50485i	0.00562328	+	0.999984i	$0.498210\pi$
$258$		0			0
$259$	4996.81	−	8654.72i	0.00462853	−	0.00801685i
$260$	−1.32263e6			−1.21340
$261$		0			0
$262$	−1.30920e6			−1.17829
$263$	408180.	−	706988.i	0.363883	−	0.630264i	−0.624713	−	0.780854i	$-0.714784\pi$
$263$	408180.	−	706988.i	0.363883	−	0.630264i	0.988596	+	0.150590i	$0.0481174\pi$
$264$		0			0
$265$	88566.8	+	153402.i	0.0774740	+	0.134189i
$266$	−320508.	−	555135.i	−0.277737	−	0.481055i
$267$		0			0
$268$	−523521.	+	906766.i	−0.445243	+	0.771184i
$269$	−1.25381e6			−1.05646			−0.528228	−	0.849103i	$-0.677143\pi$
$269$	−1.25381e6			−1.05646			−0.528228	+	0.849103i	$0.677143\pi$
$270$		0			0
$271$	−347295.			−0.287260			−0.143630	−	0.989631i	$-0.545878\pi$
$271$	−347295.			−0.287260			−0.143630	+	0.989631i	$0.545878\pi$
$272$	339433.	−	587915.i	0.278184	−	0.481828i
$273$		0			0
$274$	−181046.	−	313581.i	−0.145684	−	0.252333i
$275$	−17371.3	−	30088.0i	−0.0138516	−	0.0239917i
$276$		0			0
$277$	141233.	−	244622.i	0.110595	−	0.191556i	−0.805415	−	0.592711i	$-0.798058\pi$
$277$	141233.	−	244622.i	0.110595	−	0.191556i	0.916010	+	0.401155i	$0.131391\pi$
$278$	1.43773e6			1.11575
$279$		0			0
$280$	−190587.			−0.145278
$281$	−614335.	+	1.06406e6i	−0.464130	+	0.803897i	−0.999162	−	0.0409352i	$-0.986966\pi$
$281$	−614335.	+	1.06406e6i	−0.464130	+	0.803897i	0.535032	+	0.844832i	$0.320300\pi$
$282$		0			0
$283$	223824.	+	387674.i	0.166127	+	0.287741i	0.937055	−	0.349182i	$-0.113540\pi$
$283$	223824.	+	387674.i	0.166127	+	0.287741i	−0.770928	+	0.636922i	$0.780207\pi$
$284$	−408089.	−	706830.i	−0.300233	−	0.520019i
$285$		0			0
$286$	−17564.7	+	30422.9i	−0.0126977	+	0.0219931i
$287$	−144617.			−0.103637
$288$		0			0
$289$	−1.09935e6			−0.774270
$290$	1.59110e6	−	2.75587e6i	1.11097	−	1.92426i
$291$		0			0
$292$	−410135.	−	710375.i	−0.281494	−	0.487562i
$293$	−699361.	−	1.21133e6i	−0.475918	−	0.824314i	0.523701	−	0.851902i	$-0.324551\pi$
$293$	−699361.	−	1.21133e6i	−0.475918	−	0.824314i	−0.999619	+	0.0275878i	$0.991217\pi$
$294$		0			0
$295$	88245.1	−	152845.i	0.0590386	−	0.102258i
$296$	12829.7			0.00851116
$297$		0			0
$298$	366478.			0.239060
$299$	83051.1	−	143849.i	0.0537239	−	0.0930525i
$300$		0			0
$301$	175852.	+	304585.i	0.111875	+	0.193772i
$302$	852836.	+	1.47716e6i	0.538082	+	0.931985i
$303$		0			0
$304$	1.23546e6	−	2.13988e6i	0.766735	−	1.32802i
$305$	−2.47476e6			−1.52329
$306$		0			0
$307$	614731.			0.372254			0.186127	−	0.982526i	$-0.440406\pi$
$307$	614731.			0.372254			0.186127	+	0.982526i	$0.440406\pi$
$308$	3958.68	−	6856.64i	0.00237779	−	0.00411846i
$309$		0			0
$310$	1.47216e6	+	2.54986e6i	0.870065	+	1.50700i
$311$	1.48208e6	+	2.56704e6i	0.868903	+	1.50498i	0.863119	+	0.505001i	$0.168508\pi$
$311$	1.48208e6	+	2.56704e6i	0.868903	+	1.50498i	0.00578452	+	0.999983i	$0.498159\pi$
$312$		0			0
$313$	414425.	−	717806.i	0.239103	−	0.414139i	−0.721354	−	0.692567i	$-0.756480\pi$
$313$	414425.	−	717806.i	0.239103	−	0.414139i	0.960457	+	0.278428i	$0.0898132\pi$
$314$	−1.21694e6			−0.696540
$315$		0			0
$316$	2.20283e6			1.24098
$317$	165751.	−	287090.i	0.0926423	−	0.160461i	−0.815980	−	0.578080i	$-0.803802\pi$
$317$	165751.	−	287090.i	0.0926423	−	0.160461i	0.908622	+	0.417619i	$0.137135\pi$
$318$		0			0
$319$	−18532.1	−	32098.5i	−0.0101964	−	0.0176607i
$320$	751461.	+	1.30157e6i	0.410234	+	0.710546i
$321$		0			0
$322$	−42683.7	+	73930.4i	−0.0229415	+	0.0397359i
$323$	1.16657e6			0.622162
$324$		0			0
$325$	−2.73539e6			−1.43652
$326$	−98656.8	+	170879.i	−0.0514142	+	0.0890520i
$327$		0			0
$328$	−92829.1	−	160785.i	−0.0476430	−	0.0825202i
$329$	370669.	+	642018.i	0.188798	+	0.327007i
$330$		0			0
$331$	−1.29421e6	+	2.24164e6i	−0.649284	+	1.12459i	0.334010	+	0.942570i	$0.391598\pi$
$331$	−1.29421e6	+	2.24164e6i	−0.649284	+	1.12459i	−0.983294	+	0.182024i	$0.941735\pi$
$332$	264418.			0.131658
$333$		0			0
$334$	958384.			0.470082
$335$	−1.83142e6	+	3.17211e6i	−0.891611	+	1.54432i
$336$		0			0
$337$	880045.	+	1.52428e6i	0.422114	+	0.731124i	0.996146	−	0.0877095i	$-0.0279547\pi$
$337$	880045.	+	1.52428e6i	0.422114	+	0.731124i	−0.574032	+	0.818833i	$0.694621\pi$
$338$	−18590.2	−	32199.1i	−0.00885099	−	0.0153304i
$339$		0			0
$340$	−618537.	+	1.07134e6i	−0.290181	+	0.502607i
$341$	34293.6			0.0159708
$342$		0			0
$343$	1.31515e6			0.603587
$344$	−225758.	+	391024.i	−0.102860	+	0.178159i
$345$		0			0
$346$	−2.00732e6	−	3.47678e6i	−0.901417	−	1.56130i
$347$	−782422.	−	1.35520e6i	−0.348833	−	0.604197i	0.637209	−	0.770691i	$-0.280089\pi$
$347$	−782422.	−	1.35520e6i	−0.348833	−	0.604197i	−0.986042	+	0.166494i	$0.946755\pi$
$348$		0			0
$349$	−360712.	+	624772.i	−0.158525	+	0.274573i	−0.934337	−	0.356391i	$-0.884007\pi$
$349$	−360712.	+	624772.i	−0.158525	+	0.274573i	0.775812	+	0.630964i	$0.217340\pi$
$350$	1.40584e6			0.613432
$351$		0			0
$352$	56581.0			0.0243396
$353$	880430.	−	1.52495e6i	0.376061	−	0.651356i	−0.614424	−	0.788976i	$-0.710612\pi$
$353$	880430.	−	1.52495e6i	0.376061	−	0.651356i	0.990485	+	0.137619i	$0.0439450\pi$
$354$		0			0
$355$	−1.42760e6	−	2.47268e6i	−0.601225	−	1.04135i
$356$	−1.55648e6	−	2.69591e6i	−0.650908	−	1.12741i
$357$		0			0
$358$	−1.37932e6	+	2.38906e6i	−0.568799	+	0.985189i
$359$	2.43938e6			0.998947			0.499474	−	0.866329i	$-0.333527\pi$
$359$	2.43938e6			0.998947			0.499474	+	0.866329i	$0.333527\pi$
$360$		0			0
$361$	1.76995e6			0.714814
$362$	1.65165e6	−	2.86073e6i	0.662438	−	1.14738i
$363$		0			0
$364$	−311679.	−	539844.i	−0.123297	−	0.213558i
$365$	−1.43476e6	−	2.48508e6i	−0.563699	−	0.976356i
$366$		0			0
$367$	2.27310e6	−	3.93713e6i	0.880956	−	1.52586i	0.0306760	−	0.999529i	$-0.490234\pi$
$367$	2.27310e6	−	3.93713e6i	0.880956	−	1.52586i	0.850280	−	0.526331i	$-0.176433\pi$
$368$	−329066.			−0.126667
$369$		0			0
$370$	−160078.			−0.0607893
$371$	−41741.8	+	72299.0i	−0.0157448	+	0.0272708i
$372$		0			0
$373$	166277.	+	288000.i	0.0618814	+	0.107182i	0.895306	−	0.445451i	$-0.146957\pi$
$373$	166277.	+	288000.i	0.0618814	+	0.107182i	−0.833425	+	0.552633i	$0.813623\pi$
$374$	16428.5	+	28455.0i	0.00607323	+	0.0105191i
$375$		0			0
$376$	−475863.	+	824219.i	−0.173585	+	0.300658i
$377$	−2.91817e6			−1.05744
$378$		0			0
$379$	911738.			0.326041			0.163021	−	0.986623i	$-0.447876\pi$
$379$	911738.			0.326041			0.163021	+	0.986623i	$0.447876\pi$
$380$	−2.25134e6	+	3.89943e6i	−0.799801	+	1.38530i
$381$		0			0
$382$	−577206.	−	999750.i	−0.202382	−	0.350536i
$383$	−1.82779e6	−	3.16582e6i	−0.636690	−	1.10278i	−0.986154	−	0.165830i	$-0.946970\pi$
$383$	−1.82779e6	−	3.16582e6i	−0.636690	−	1.10278i	0.349464	−	0.936950i	$-0.386364\pi$
$384$		0			0
$385$	13848.5	−	23986.4i	0.00476159	−	0.00824731i
$386$	−2.93146e6			−1.00142
$387$		0			0
$388$	−4.07352e6			−1.37370
$389$	1.41448e6	−	2.44995e6i	0.473939	−	0.820886i	−0.525616	−	0.850722i	$-0.676165\pi$
$389$	1.41448e6	−	2.44995e6i	0.473939	−	0.820886i	0.999555	+	0.0298360i	$0.00949849\pi$
$390$		0			0
$391$	−77679.0	−	134544.i	−0.0256958	−	0.0445064i
$392$	399639.	+	692195.i	0.131357	+	0.227517i
$393$		0			0
$394$	−439688.	+	761563.i	−0.142694	+	0.247153i
$395$	7.70610e6			2.48509
$396$		0			0
$397$	−5.06659e6			−1.61339			−0.806695	−	0.590968i	$-0.798746\pi$
$397$	−5.06659e6			−1.61339			−0.806695	+	0.590968i	$0.798746\pi$
$398$	−3.41584e6	+	5.91640e6i	−1.08091	+	1.87219i
$399$		0			0
$400$	2.70955e6	+	4.69308e6i	0.846735	+	1.46659i
$401$	1.81834e6	+	3.14946e6i	0.564695	+	0.978081i	0.997078	+	0.0763908i	$0.0243397\pi$
$401$	1.81834e6	+	3.14946e6i	0.564695	+	0.978081i	−0.432383	+	0.901690i	$0.642327\pi$
$402$		0			0
$403$	1.35002e6	−	2.33830e6i	0.414073	−	0.717195i
$404$	4.64492e6			1.41587
$405$		0			0
$406$	1.49978e6			0.451557
$407$	−932.241	+	1614.69i	−0.000278960	+	0.000483173i
$408$		0			0
$409$	2.44052e6	+	4.22711e6i	0.721397	+	1.24950i	0.960440	+	0.278487i	$0.0898329\pi$
$409$	2.44052e6	+	4.22711e6i	0.721397	+	1.24950i	−0.239043	+	0.971009i	$0.576834\pi$
$410$	1.15824e6	+	2.00613e6i	0.340281	+	0.589384i
$411$		0			0
$412$	610050.	−	1.05664e6i	0.177061	−	0.306678i
$413$	83180.4			0.0239964
$414$		0			0
$415$	925005.			0.263648
$416$	2.22739e6	−	3.85796e6i	0.631050	−	1.09301i
$417$		0			0
$418$	59796.2	+	103570.i	0.0167391	+	0.0289930i
$419$	−390244.	−	675923.i	−0.108593	−	0.188088i	0.806608	−	0.591087i	$-0.201301\pi$
$419$	−390244.	−	675923.i	−0.108593	−	0.188088i	−0.915200	+	0.402999i	$0.867968\pi$
$420$		0			0
$421$	−1.38356e6	+	2.39639e6i	−0.380446	+	0.658951i	−0.991126	−	0.132926i	$-0.957563\pi$
$421$	−1.38356e6	+	2.39639e6i	−0.380446	+	0.658951i	0.610680	+	0.791877i	$0.290896\pi$
$422$	−8.93857e6			−2.44336
$423$		0			0
$424$	−107176.			−0.0289523
$425$	−1.27923e6	+	2.21569e6i	−0.343538	+	0.595026i
$426$		0			0
$427$	−583180.	−	1.01010e6i	−0.154787	−	0.268098i
$428$	1.64754e6	+	2.85362e6i	0.434737	+	0.752987i
$429$		0			0
$430$	2.81680e6	−	4.87885e6i	0.734659	−	1.27247i
$431$	−893280.			−0.231630			−0.115815	−	0.993271i	$-0.536948\pi$
$431$	−893280.			−0.231630			−0.115815	+	0.993271i	$0.536948\pi$
$432$		0			0
$433$	4.84897e6			1.24288			0.621441	−	0.783461i	$-0.286548\pi$
$433$	4.84897e6			1.24288			0.621441	+	0.783461i	$0.286548\pi$
$434$	−693835.	+	1.20176e6i	−0.176820	+	0.306262i
$435$		0			0
$436$	2.03671e6	+	3.52768e6i	0.513112	+	0.888736i
$437$	−282735.	−	489711.i	−0.0708232	−	0.122669i
$438$		0			0
$439$	116736.	−	202192.i	0.0289096	−	0.0500729i	−0.851209	−	0.524827i	$-0.824130\pi$
$439$	116736.	−	202192.i	0.0289096	−	0.0500729i	0.880118	+	0.474755i	$0.157463\pi$
$440$	35557.3			0.00875584
$441$		0			0
$442$	2.58693e6			0.629839
$443$	−1.30744e6	+	2.26456e6i	−0.316529	+	0.548244i	−0.979761	−	0.200170i	$-0.935851\pi$
$443$	−1.30744e6	+	2.26456e6i	−0.316529	+	0.548244i	0.663233	+	0.748413i	$0.269184\pi$
$444$		0			0
$445$	−5.44500e6	−	9.43101e6i	−1.30346	−	2.25766i
$446$	−3.07537e6	−	5.32669e6i	−0.732082	−	1.26800i
$447$		0			0
$448$	−354166.	+	613433.i	−0.0833704	+	0.144402i
$449$	8.32454e6			1.94870			0.974349	−	0.225044i	$-0.0722526\pi$
$449$	8.32454e6			1.94870			0.974349	+	0.225044i	$0.0722526\pi$
$450$		0			0
$451$	26980.8			0.00624616
$452$	2.04347e6	−	3.53940e6i	0.470460	−	0.814861i
$453$		0			0
$454$	1.41705e6	+	2.45441e6i	0.322661	+	0.558865i
$455$	−1.09034e6	−	1.88852e6i	−0.246906	−	0.427654i
$456$		0			0
$457$	−398114.	+	689554.i	−0.0891697	+	0.154446i	−0.907160	−	0.420785i	$-0.861755\pi$
$457$	−398114.	+	689554.i	−0.0891697	+	0.154446i	0.817991	+	0.575231i	$0.195088\pi$
$458$	−949500.			−0.211510
$459$		0			0
$460$	599646.			0.132130
$461$	700324.	−	1.21300e6i	0.153478	−	0.265832i	−0.779026	−	0.626992i	$-0.784286\pi$
$461$	700324.	−	1.21300e6i	0.153478	−	0.265832i	0.932504	+	0.361160i	$0.117619\pi$
$462$		0			0
$463$	−574265.	−	994656.i	−0.124497	−	0.215635i	0.797039	−	0.603928i	$-0.206398\pi$
$463$	−574265.	−	994656.i	−0.124497	−	0.215635i	−0.921536	+	0.388292i	$0.873065\pi$
$464$	2.89061e6	+	5.00668e6i	0.623296	+	1.07958i
$465$		0			0
$466$	−1.59882e6	+	2.76923e6i	−0.341063	+	0.590738i
$467$	−5.64483e6			−1.19773			−0.598865	−	0.800850i	$-0.704381\pi$
$467$	−5.64483e6			−1.19773			−0.598865	+	0.800850i	$0.704381\pi$
$468$		0			0
$469$	−1.72631e6			−0.362398
$470$	5.93739e6	−	1.02839e7i	1.23980	−	2.14739i
$471$		0			0
$472$	53393.3	+	92479.9i	0.0110314	+	0.0191070i
$473$	−32808.3	−	56825.6i	−0.00674265	−	0.0116786i
$474$		0			0
$475$	−4.65611e6	+	8.06462e6i	−0.946867	+	1.64002i
$476$	−583037.			−0.117945
$477$		0			0
$478$	−9.23920e6			−1.84954
$479$	−2.85304e6	+	4.94162e6i	−0.568159	+	0.984080i	0.428589	+	0.903499i	$0.359011\pi$
$479$	−2.85304e6	+	4.94162e6i	−0.568159	+	0.984080i	−0.996748	+	0.0805805i	$0.974323\pi$
$480$		0			0
$481$	73398.1	+	127129.i	0.0144651	+	0.0250543i
$482$	2.86346e6	+	4.95967e6i	0.561402	+	0.972377i
$483$		0			0
$484$	2.01181e6	−	3.48456e6i	0.390367	−	0.676136i
$485$	−1.42503e7			−2.75086
$486$		0			0
$487$	−2.78768e6			−0.532624			−0.266312	−	0.963887i	$-0.585805\pi$
$487$	−2.78768e6			−0.532624			−0.266312	+	0.963887i	$0.585805\pi$
$488$	748684.	−	1.29676e6i	0.142314	−	0.246496i
$489$		0			0
$490$	−4.98634e6	−	8.63659e6i	−0.938191	−	1.62499i
$491$	479847.	+	831119.i	0.0898253	+	0.155582i	0.907437	−	0.420188i	$-0.138036\pi$
$491$	479847.	+	831119.i	0.0898253	+	0.155582i	−0.817612	+	0.575770i	$0.804702\pi$
$492$		0			0
$493$	−1.36471e6	+	2.36374e6i	−0.252884	+	0.438009i
$494$	9.41588e6			1.73597
$495$		0			0
$496$	−5.34906e6			−0.976278
$497$	672834.	−	1.16538e6i	0.122185	−	0.211630i
$498$		0			0
$499$	1.13098e6	+	1.95891e6i	0.203331	+	0.352179i	0.949600	−	0.313466i	$-0.101490\pi$
$499$	1.13098e6	+	1.95891e6i	0.203331	+	0.352179i	−0.746269	+	0.665645i	$0.768157\pi$
$500$	−1.52325e6	−	2.63834e6i	−0.272487	−	0.471961i
$501$		0			0
$502$	1.92846e6	−	3.34018e6i	0.341547	−	0.591577i
$503$	997842.			0.175850			0.0879249	−	0.996127i	$-0.471976\pi$
$503$	997842.			0.175850			0.0879249	+	0.996127i	$0.471976\pi$
$504$		0			0
$505$	1.62492e7			2.83532
$506$	7963.39	−	13793.0i	0.00138268	−	0.00239487i
$507$		0			0
$508$	2.91521e6	+	5.04930e6i	0.501200	+	0.868104i
$509$	1.03760e6	+	1.79718e6i	0.177516	+	0.307466i	0.941029	−	0.338326i	$-0.109861\pi$
$509$	1.03760e6	+	1.79718e6i	0.177516	+	0.307466i	−0.763513	+	0.645792i	$0.776527\pi$
$510$		0			0
$511$	676208.	−	1.17123e6i	0.114559	−	0.198421i
$512$	−6.79550e6			−1.14564
$513$		0			0
$514$	1.38901e7			2.31897
$515$	2.13412e6	−	3.69640e6i	0.354569	−	0.614131i
$516$		0			0
$517$	−69154.8	−	119780.i	−0.0113788	−	0.0197086i
$518$	−37722.6	−	65337.5i	−0.00617700	−	0.0106989i
$519$		0			0
$520$	1.39977e6	−	2.42447e6i	0.227012	−	0.393196i
$521$	4.77686e6			0.770989			0.385494	−	0.922710i	$-0.374031\pi$
$521$	4.77686e6			0.770989			0.385494	+	0.922710i	$0.374031\pi$
$522$		0			0
$523$	−7.14547e6			−1.14229			−0.571146	−	0.820849i	$-0.693501\pi$
$523$	−7.14547e6			−1.14229			−0.571146	+	0.820849i	$0.693501\pi$
$524$	−2.16710e6	+	3.75353e6i	−0.344787	+	0.597189i
$525$		0			0
$526$	−3.08149e6	−	5.33730e6i	−0.485620	−	0.841119i
$527$	−1.26269e6	−	2.18705e6i	−0.198048	−	0.343030i
$528$		0			0
$529$	3.18052e6	−	5.50882e6i	0.494150	−	0.855893i
$530$	1.33724e6			0.206786
$531$		0			0
$532$	−2.12213e6			−0.325082
$533$	1.06214e6	−	1.83968e6i	0.161943	−	0.280494i
$534$		0			0
$535$	5.76354e6	+	9.98274e6i	0.870572	+	1.50787i
$536$	−1.10811e6	−	1.91931e6i	−0.166599	−	0.288557i
$537$		0			0
$538$	−4.73273e6	+	8.19732e6i	−0.704946	+	1.22100i
$539$	−116155.			−0.0172213
$540$		0			0
$541$	−2.23232e6			−0.327917			−0.163958	−	0.986467i	$-0.552426\pi$
$541$	−2.23232e6			−0.327917			−0.163958	+	0.986467i	$0.552426\pi$
$542$	−1.31093e6	+	2.27059e6i	−0.191681	+	0.332002i
$543$		0			0
$544$	−2.08332e6	−	3.60841e6i	−0.301827	−	0.522780i
$545$	7.12494e6	+	1.23408e7i	1.02752	+	1.77972i
$546$		0			0
$547$	−2.49201e6	+	4.31630e6i	−0.356108	+	0.616798i	−0.987307	−	0.158823i	$-0.949230\pi$
$547$	−2.49201e6	+	4.31630e6i	−0.356108	+	0.616798i	0.631199	+	0.775621i	$0.282563\pi$
$548$	−1.19873e6			−0.170518
$549$		0			0
$550$	−262284.			−0.0369713
$551$	−4.96724e6	+	8.60351e6i	−0.697005	+	1.20725i
$552$		0			0
$553$	1.81596e6	+	3.14533e6i	0.252518	+	0.437374i
$554$	−1.06622e6	−	1.84674e6i	−0.147595	−	0.255641i
$555$		0			0
$556$	2.37986e6	−	4.12204e6i	0.326486	−	0.565490i
$557$	9.32179e6			1.27310			0.636548	−	0.771237i	$-0.280362\pi$
$557$	9.32179e6			1.27310			0.636548	+	0.771237i	$0.280362\pi$
$558$		0			0
$559$	−5.16619e6			−0.699263
$560$	−2.16008e6	+	3.74136e6i	−0.291071	+	0.504150i
$561$		0			0
$562$	4.63783e6	+	8.03296e6i	0.619404	+	1.07284i
$563$	−6.18276e6	−	1.07088e7i	−0.822074	−	1.42387i	−0.904135	−	0.427247i	$-0.859483\pi$
$563$	−6.18276e6	−	1.07088e7i	−0.822074	−	1.42387i	0.0820605	−	0.996627i	$-0.473850\pi$
$564$		0			0
$565$	7.14862e6	−	1.23818e7i	0.942109	−	1.63178i
$566$	3.37945e6			0.443409
$567$		0			0
$568$	1.72756e6			0.224679
$569$	−1.15181e6	+	1.99499e6i	−0.149141	+	0.258321i	−0.930910	−	0.365248i	$-0.880984\pi$
$569$	−1.15181e6	+	1.99499e6i	−0.149141	+	0.258321i	0.781769	+	0.623568i	$0.214318\pi$
$570$		0			0
$571$	5.92568e6	+	1.02636e7i	0.760585	+	1.31737i	0.942549	+	0.334067i	$0.108421\pi$
$571$	5.92568e6	+	1.02636e7i	0.760585	+	1.31737i	−0.181964	+	0.983305i	$0.558245\pi$
$572$	58149.1	+	100717.i	0.00743110	+	0.0128710i
$573$		0			0
$574$	−545881.	+	945494.i	−0.0691542	+	0.119779i
$575$	1.24016e6			0.156426
$576$		0			0
$577$	−7.25199e6			−0.906813			−0.453407	−	0.891304i	$-0.649791\pi$
$577$	−7.25199e6			−0.906813			−0.453407	+	0.891304i	$0.649791\pi$
$578$	−4.14970e6	+	7.18749e6i	−0.516651	+	0.894865i
$579$		0			0
$580$	−5.26745e6	−	9.12350e6i	−0.650176	−	1.12614i
$581$	217979.	+	377551.i	0.0267901	+	0.0464018i
$582$		0			0
$583$	7787.66	−	13488.6i	0.000948933	−	0.00164360i
$584$	1.73622e6			0.210656
$585$		0			0
$586$	−1.05594e7			−1.27027
$587$	3.72719e6	−	6.45569e6i	0.446464	−	0.773299i	−0.551689	−	0.834050i	$-0.686016\pi$
$587$	3.72719e6	−	6.45569e6i	0.446464	−	0.773299i	0.998153	+	0.0607515i	$0.0193497\pi$
$588$		0			0
$589$	−4.59593e6	−	7.96038e6i	−0.545865	−	0.945465i
$590$	−666193.	−	1.15388e6i	−0.0787899	−	0.136468i
$591$		0			0
$592$	145410.	−	251857.i	0.0170525	−	0.0295359i
$593$	−3.98887e6			−0.465815			−0.232908	−	0.972499i	$-0.574824\pi$
$593$	−3.98887e6			−0.465815			−0.232908	+	0.972499i	$0.574824\pi$
$594$		0			0
$595$	−2.03962e6			−0.236187
$596$	606627.	−	1.05071e6i	0.0699529	−	0.121162i
$597$		0			0
$598$	−626982.	−	1.08596e6i	−0.0716972	−	0.124183i
$599$	−6.35985e6	−	1.10156e7i	−0.724236	−	1.25441i	−0.959288	−	0.282430i	$-0.908860\pi$
$599$	−6.35985e6	−	1.10156e7i	−0.724236	−	1.25441i	0.235052	−	0.971983i	$-0.424474\pi$
$600$		0			0
$601$	−1.55315e6	+	2.69013e6i	−0.175399	+	0.303800i	−0.940299	−	0.340349i	$-0.889455\pi$
$601$	−1.55315e6	+	2.69013e6i	−0.175399	+	0.303800i	0.764900	+	0.644149i	$0.222788\pi$
$602$	2.65514e6			0.298604
$603$		0			0
$604$	5.64675e6			0.629806
$605$	7.03785e6	−	1.21899e7i	0.781720	−	1.35398i
$606$		0			0
$607$	−6.20584e6	−	1.07488e7i	−0.683642	−	1.18410i	−0.973861	−	0.227143i	$-0.927062\pi$
$607$	−6.20584e6	−	1.07488e7i	−0.683642	−	1.18410i	0.290219	−	0.956960i	$-0.406272\pi$
$608$	−7.58282e6	−	1.31338e7i	−0.831902	−	1.44090i
$609$		0			0
$610$	−9.34140e6	+	1.61798e7i	−1.01645	+	1.76055i
$611$	−1.08895e7			−1.18007
$612$		0			0
$613$	2.25539e6			0.242421			0.121211	−	0.992627i	$-0.461322\pi$
$613$	2.25539e6			0.242421			0.121211	+	0.992627i	$0.461322\pi$
$614$	2.32041e6	−	4.01906e6i	0.248395	−	0.430233i
$615$		0			0
$616$	8379.15	+	14513.1i	0.000889709	+	0.00154102i
$617$	3.60754e6	+	6.24844e6i	0.381503	+	0.660782i	0.991277	−	0.131793i	$-0.0420733\pi$
$617$	3.60754e6	+	6.24844e6i	0.381503	+	0.660782i	−0.609774	+	0.792575i	$0.708740\pi$
$618$		0			0
$619$	6.36680e6	−	1.10276e7i	0.667874	−	1.15679i	−0.310623	−	0.950533i	$-0.600538\pi$
$619$	6.36680e6	−	1.10276e7i	0.667874	−	1.15679i	0.978497	−	0.206259i	$-0.0661290\pi$
$620$	9.74741e6			1.01838
$621$		0			0
$622$	2.23775e7			2.31919
$623$	2.56625e6	−	4.44487e6i	0.264898	−	0.458816i
$624$		0			0
$625$	1.73251e6	+	3.00079e6i	0.177409	+	0.307281i
$626$	−3.12864e6	−	5.41897e6i	−0.319095	−	0.552689i
$627$		0			0
$628$	−2.01439e6	+	3.48903e6i	−0.203819	+	0.353025i
$629$	137301.			0.0138372
$630$		0			0
$631$	4.72216e6			0.472136			0.236068	−	0.971737i	$-0.424141\pi$
$631$	4.72216e6			0.472136			0.236068	+	0.971737i	$0.424141\pi$
$632$	−2.33131e6	+	4.03796e6i	−0.232171	+	0.402132i
$633$		0			0
$634$	−1.25132e6	−	2.16734e6i	−0.123636	−	0.214143i
$635$	1.01982e7	+	1.76638e7i	1.00367	+	1.73840i
$636$		0			0
$637$	−4.57262e6	+	7.92001e6i	−0.446495	+	0.773352i
$638$	−279810.			−0.0272152
$639$		0			0
$640$	−9.24524e6			−0.892212
$641$	−7.33397e6	+	1.27028e7i	−0.705008	+	1.22111i	0.261680	+	0.965155i	$0.415723\pi$
$641$	−7.33397e6	+	1.27028e7i	−0.705008	+	1.22111i	−0.966689	+	0.255956i	$0.917610\pi$
$642$		0			0
$643$	−6.46256e6	−	1.11935e7i	−0.616420	−	1.06767i	−0.990134	−	0.140127i	$-0.955249\pi$
$643$	−6.46256e6	−	1.11935e7i	−0.616420	−	1.06767i	0.373713	−	0.927544i	$-0.378084\pi$
$644$	141308.	+	244752.i	0.0134261	+	0.0232547i
$645$		0			0
$646$	4.40341e6	−	7.62693e6i	0.415153	−	0.719065i
$647$	6.80424e6			0.639027			0.319513	−	0.947582i	$-0.396481\pi$
$647$	6.80424e6			0.639027			0.319513	+	0.947582i	$0.396481\pi$
$648$		0			0
$649$	−15518.8			−0.00144626
$650$	−1.03252e7	+	1.78838e7i	−0.958552	+	1.66026i
$651$		0			0
$652$	326610.	+	565706.i	0.0300892	+	0.0521161i
$653$	−844518.	−	1.46275e6i	−0.0775043	−	0.134241i	0.824668	−	0.565617i	$-0.191362\pi$
$653$	−844518.	−	1.46275e6i	−0.0775043	−	0.134241i	−0.902173	+	0.431375i	$0.858028\pi$
$654$		0			0
$655$	−7.58111e6	+	1.31309e7i	−0.690446	+	1.19589i
$656$	−4.20842e6			−0.381821
$657$		0			0
$658$	5.59662e6			0.503920
$659$	−3.67278e6	+	6.36143e6i	−0.329443	+	0.570613i	−0.982402	−	0.186781i	$-0.940194\pi$
$659$	−3.67278e6	+	6.36143e6i	−0.329443	+	0.570613i	0.652958	+	0.757394i	$0.273528\pi$
$660$		0			0
$661$	4.43977e6	+	7.68990e6i	0.395236	+	0.684569i	0.993131	−	0.117005i	$-0.0373294\pi$
$661$	4.43977e6	+	7.68990e6i	0.395236	+	0.684569i	−0.597895	+	0.801574i	$0.703996\pi$
$662$	9.77045e6	+	1.69229e7i	0.866502	+	1.50082i
$663$		0			0
$664$	−279840.	+	484697.i	−0.0246314	+	0.0426629i
$665$	−7.42377e6			−0.650984
$666$		0			0
$667$	1.32303e6			0.115147
$668$	1.58640e6	−	2.74773e6i	0.137553	−	0.238250i
$669$		0			0
$670$	1.38260e7	+	2.39474e7i	1.18990	+	2.06096i
$671$	108802.	+	188451.i	0.00932894	+	0.0161582i
$672$		0			0
$673$	3.81952e6	−	6.61560e6i	0.325065	−	0.563030i	−0.656460	−	0.754361i	$-0.727947\pi$
$673$	3.81952e6	−	6.61560e6i	0.325065	−	0.563030i	0.981526	+	0.191331i	$0.0612803\pi$
$674$	1.32875e7			1.12666
$675$		0			0
$676$	−123088.			−0.0103598
$677$	9.78051e6	−	1.69403e7i	0.820143	−	1.42053i	−0.0854320	−	0.996344i	$-0.527227\pi$
$677$	9.78051e6	−	1.69403e7i	0.820143	−	1.42053i	0.905575	−	0.424186i	$-0.139440\pi$
$678$		0			0
$679$	−3.35810e6	−	5.81639e6i	−0.279524	−	0.484149i
$680$	−1.30923e6	−	2.26765e6i	−0.108578	−	0.188063i
$681$		0			0
$682$	129447.	−	224209.i	0.0106569	−	0.0184583i
$683$	−1.08911e7			−0.893349			−0.446675	−	0.894696i	$-0.647392\pi$
$683$	−1.08911e7			−0.893349			−0.446675	+	0.894696i	$0.647392\pi$
$684$		0			0
$685$	−4.19349e6			−0.341467
$686$	4.96426e6	−	8.59835e6i	0.402758	−	0.697597i
$687$		0			0
$688$	5.11739e6	+	8.86358e6i	0.412171	+	0.713901i
$689$	−613146.	−	1.06200e6i	−0.0492058	−	0.0852269i
$690$		0			0
$691$	8.95944e6	−	1.55182e7i	0.713815	−	1.23636i	−0.249599	−	0.968349i	$-0.580299\pi$
$691$	8.95944e6	−	1.55182e7i	0.713815	−	1.23636i	0.963415	−	0.268015i	$-0.0863677\pi$
$692$	−1.32907e7			−1.05508
$693$		0			0
$694$	−1.18136e7			−0.931070
$695$	8.32539e6	−	1.44200e7i	0.653796	−	1.13241i
$696$		0			0
$697$	−993435.	−	1.72068e6i	−0.0774564	−	0.134158i
$698$	2.72314e6	+	4.71662e6i	0.211559	+	0.366431i
$699$		0			0
$700$	2.32707e6	−	4.03060e6i	0.179500	−	0.310903i
$701$	1.32211e7			1.01619			0.508094	−	0.861302i	$-0.330350\pi$
$701$	1.32211e7			1.01619			0.508094	+	0.861302i	$0.330350\pi$
$702$		0			0
$703$	499745.			0.0381382
$704$	66075.8	−	114447.i	0.00502471	−	0.00870305i
$705$		0			0
$706$	−6.64667e6	−	1.15124e7i	−0.501872	−	0.869267i
$707$	3.82914e6	+	6.63227e6i	0.288107	+	0.499015i
$708$		0			0
$709$	501449.	−	868535.i	0.0374637	−	0.0648891i	−0.846686	−	0.532094i	$-0.821405\pi$
$709$	501449.	−	868535.i	0.0374637	−	0.0648891i	0.884149	+	0.467204i	$0.154739\pi$
$710$	−2.15550e7			−1.60473
$711$		0			0
$712$	6.58907e6			0.487106
$713$	−612065.	+	1.06013e6i	−0.0450893	+	0.0780970i
$714$		0			0
$715$	203421.	+	352336.i	0.0148810	+	0.0257746i
$716$	4.56635e6	+	7.90916e6i	0.332879	+	0.576564i
$717$		0			0
$718$	9.20785e6	−	1.59485e7i	0.666572	−	1.15454i
$719$	−1.12752e7			−0.813394			−0.406697	−	0.913563i	$-0.633319\pi$
$719$	−1.12752e7			−0.813394			−0.406697	+	0.913563i	$0.633319\pi$
$720$		0			0
$721$	2.01163e6			0.144116
$722$	6.68099e6	−	1.15718e7i	0.476977	−	0.826149i
$723$		0			0
$724$	−5.46789e6	−	9.47067e6i	−0.387680	−	0.671482i
$725$	−1.08939e7	−	1.88688e7i	−0.769729	−	1.33321i
$726$		0			0
$727$	−9.98334e6	+	1.72917e7i	−0.700551	+	1.21339i	0.267722	+	0.963496i	$0.413729\pi$
$727$	−9.98334e6	+	1.72917e7i	−0.700551	+	1.21339i	−0.968273	+	0.249894i	$0.919604\pi$
$728$	1.31943e6			0.0922695
$729$		0			0
$730$	−2.16630e7			−1.50457
$731$	−2.41601e6	+	4.18465e6i	−0.167226	+	0.289645i
$732$		0			0
$733$	4.06124e6	+	7.03427e6i	0.279189	+	0.483570i	0.971183	−	0.238333i	$-0.0766011\pi$
$733$	4.06124e6	+	7.03427e6i	0.279189	+	0.483570i	−0.691994	+	0.721903i	$0.743268\pi$
$734$	−1.71605e7	−	2.97228e7i	−1.17568	−	2.03634i
$735$		0			0
$736$	−1.00985e6	+	1.74910e6i	−0.0687164	+	0.119020i
$737$	322072.			0.0218416
$738$		0			0
$739$	−165272.			−0.0111324			−0.00556619	−	0.999985i	$-0.501772\pi$
$739$	−165272.			−0.0111324			−0.00556619	+	0.999985i	$0.501772\pi$
$740$	−264975.	+	458950.i	−0.0177879	+	0.0308096i
$741$		0			0
$742$	315124.	+	545810.i	0.0210122	+	0.0363942i
$743$	1.23128e7	+	2.13263e7i	0.818245	+	1.41724i	0.906974	+	0.421186i	$0.138386\pi$
$743$	1.23128e7	+	2.13263e7i	0.818245	+	1.41724i	−0.0887298	+	0.996056i	$0.528281\pi$
$744$		0			0
$745$	2.12214e6	−	3.67566e6i	0.140082	−	0.242630i
$746$	2.51057e6			0.165168
$747$		0			0
$748$	108776.			0.00710849
$749$	−2.71637e6	+	4.70490e6i	−0.176923	+	0.306440i
$750$		0			0
$751$	1.51225e6	+	2.61930e6i	0.0978418	+	0.169467i	0.910791	−	0.412867i	$-0.135473\pi$
$751$	1.51225e6	+	2.61930e6i	0.0978418	+	0.169467i	−0.812949	+	0.582334i	$0.802139\pi$
$752$	1.07867e7	+	1.86831e7i	0.695573	+	1.20477i
$753$		0			0
$754$	−1.10152e7	+	1.90788e7i	−0.705606	+	1.22215i
$755$	1.97539e7			1.26120
$756$		0			0
$757$	−8.86322e6			−0.562150			−0.281075	−	0.959686i	$-0.590691\pi$
$757$	−8.86322e6			−0.562150			−0.281075	+	0.959686i	$0.590691\pi$
$758$	3.44152e6	−	5.96088e6i	0.217559	−	0.376823i
$759$		0			0
$760$	−4.76530e6	−	8.25374e6i	−0.299265	−	0.518342i
$761$	982452.	+	1.70166e6i	0.0614964	+	0.106515i	0.895134	−	0.445796i	$-0.147079\pi$
$761$	982452.	+	1.70166e6i	0.0614964	+	0.106515i	−0.833638	+	0.552311i	$0.813746\pi$
$762$		0			0
$763$	−3.35801e6	+	5.81624e6i	−0.208819	+	0.361685i
$764$	−3.82177e6			−0.236881
$765$		0			0
$766$	−2.75972e7			−1.69939
$767$	−610919.	+	1.05814e6i	−0.0374969	+	0.0649465i
$768$		0			0
$769$	3.90798e6	+	6.76883e6i	0.238307	+	0.412760i	0.960229	−	0.279215i	$-0.0900742\pi$
$769$	3.90798e6	+	6.76883e6i	0.238307	+	0.412760i	−0.721922	+	0.691975i	$0.756741\pi$
$770$	−104547.	−	181081.i	−0.00635457	−	0.0110064i
$771$		0			0
$772$	−4.85241e6	+	8.40461e6i	−0.293031	+	0.507545i
$773$	−8.88127e6			−0.534597			−0.267298	−	0.963614i	$-0.586131\pi$
$773$	−8.88127e6			−0.534597			−0.267298	+	0.963614i	$0.586131\pi$
$774$		0			0
$775$	2.01591e7			1.20564
$776$	4.31111e6	−	7.46706e6i	0.257001	−	0.445139i
$777$		0			0
$778$	−1.06784e7	−	1.84955e7i	−0.632494	−	1.09551i
$779$	−3.61589e6	−	6.26290e6i	−0.213487	−	0.369770i
$780$		0			0
$781$	−125529.	+	217422.i	−0.00736404	+	0.0127549i
$782$	−1.17285e6			−0.0685846
$783$		0			0
$784$	1.81177e7			1.05272
$785$	−7.04688e6	+	1.22055e7i	−0.408153	+	0.706941i
$786$		0			0
$787$	6.53957e6	+	1.13269e7i	0.376368	+	0.651888i	0.990531	−	0.137291i	$-0.0438395\pi$
$787$	6.53957e6	+	1.13269e7i	0.376368	+	0.651888i	−0.614163	+	0.789179i	$0.710506\pi$
$788$	1.45562e6	+	2.52121e6i	0.0835089	+	0.144642i
$789$		0			0
$790$	2.90880e7	−	5.03820e7i	1.65824	−	2.87215i
$791$	6.73834e6			0.382923
$792$		0			0
$793$	1.71327e7			0.967481
$794$	−1.91247e7	+	3.31250e7i	−1.07657	+	1.86468i
$795$		0			0
$796$	1.13084e7	+	1.95867e7i	0.632583	+	1.09567i
$797$	−9.76620e6	−	1.69155e7i	−0.544603	−	0.943279i	−0.998632	−	0.0522925i	$-0.983347\pi$
$797$	−9.76620e6	−	1.69155e7i	−0.544603	−	0.943279i	0.454029	−	0.890987i	$-0.349986\pi$
$798$		0			0
$799$	−5.09257e6	+	8.82060e6i	−0.282209	+	0.488800i
$800$	3.32605e7			1.83740
$801$		0			0
$802$	2.74546e7			1.50723
$803$	−126158.	+	218513.i	−0.00690442	+	0.0119588i
$804$		0			0
$805$	494332.	+	856208.i	0.0268862	+	0.0465682i
$806$	−1.01918e7	−	1.76526e7i	−0.552601	−	0.957132i
$807$		0			0
$808$	−4.91583e6	+	8.51448e6i	−0.264892	+	0.458806i
$809$	−1.72600e7			−0.927194			−0.463597	−	0.886046i	$-0.653441\pi$
$809$	−1.72600e7			−0.927194			−0.463597	+	0.886046i	$0.653441\pi$
$810$		0			0
$811$	1.10857e7			0.591849			0.295924	−	0.955211i	$-0.404372\pi$
$811$	1.10857e7			0.591849			0.295924	+	0.955211i	$0.404372\pi$
$812$	2.48257e6	−	4.29993e6i	0.132133	−	0.228861i
$813$		0			0
$814$	7037.81	+	12189.8i	0.000372286	+	0.000644818i
$815$	1.14257e6	+	1.97899e6i	0.0602544	+	0.104364i
$816$		0			0
$817$	−8.79375e6	+	1.52312e7i	−0.460913	+	0.798324i
$818$	3.68487e7			1.92548
$819$		0			0
$820$	7.66886e6			0.398287
$821$	−7.48035e6	+	1.29563e7i	−0.387315	+	0.670849i	−0.992087	−	0.125549i	$-0.959931\pi$
$821$	−7.48035e6	+	1.29563e7i	−0.387315	+	0.670849i	0.604773	+	0.796398i	$0.293264\pi$
$822$		0			0
$823$	−1.52885e7	−	2.64805e7i	−0.786802	−	1.36278i	−0.927917	−	0.372787i	$-0.878402\pi$
$823$	−1.52885e7	−	2.64805e7i	−0.786802	−	1.36278i	0.141115	−	0.989993i	$-0.454931\pi$
$824$	1.29126e6	+	2.23653e6i	0.0662516	+	0.114751i
$825$		0			0
$826$	313979.	−	543828.i	0.0160122	−	0.0277339i
$827$	−3.03602e7			−1.54362			−0.771810	−	0.635853i	$-0.780648\pi$
$827$	−3.03602e7			−1.54362			−0.771810	+	0.635853i	$0.780648\pi$
$828$		0			0
$829$	−1.09888e7			−0.555348			−0.277674	−	0.960675i	$-0.589563\pi$
$829$	−1.09888e7			−0.555348			−0.277674	+	0.960675i	$0.589563\pi$
$830$	3.49159e6	−	6.04762e6i	0.175925	−	0.304712i
$831$		0			0
$832$	−5.20235e6	−	9.01073e6i	−0.260550	−	0.451286i
$833$	4.27684e6	+	7.40771e6i	0.213556	+	0.369889i
$834$		0			0
$835$	5.54965e6	−	9.61228e6i	0.275454	−	0.477101i
$836$	395920.			0.0195926
$837$		0			0
$838$	−5.89218e6			−0.289845
$839$	−1.87744e6	+	3.25182e6i	−0.0920791	+	0.159486i	−0.908386	−	0.418133i	$-0.862685\pi$
$839$	−1.87744e6	+	3.25182e6i	−0.0920791	+	0.159486i	0.816307	+	0.577619i	$0.196018\pi$
$840$		0			0
$841$	−1.36626e6	−	2.36643e6i	−0.0666105	−	0.115373i
$842$	1.04450e7	+	1.80912e7i	0.507723	+	0.879402i
$843$		0			0
$844$	−1.47959e7	+	2.56272e7i	−0.714966	+	1.23836i
$845$	−430596.			−0.0207457
$846$		0			0
$847$	6.63392e6			0.317733
$848$	−1.21471e6	+	2.10394e6i	−0.0580073	+	0.100472i
$849$		0			0
$850$	9.65733e6	+	1.67270e7i	0.458469	+	0.794091i
$851$	−33276.9	−	57637.3i	−0.00157514	−	0.00272822i
$852$		0			0
$853$	−1.08366e7	+	1.87695e7i	−0.509940	+	0.883242i	0.489993	+	0.871726i	$0.336999\pi$
$853$	−1.08366e7	+	1.87695e7i	−0.509940	+	0.883242i	−0.999934	+	0.0115163i	$0.996334\pi$
$854$	−8.80526e6			−0.413140
$855$		0			0
$856$	−6.97453e6			−0.325335
$857$	−7.00812e6	+	1.21384e7i	−0.325949	+	0.564560i	−0.981704	−	0.190414i	$-0.939017\pi$
$857$	−7.00812e6	+	1.21384e7i	−0.325949	+	0.564560i	0.655755	+	0.754974i	$0.272350\pi$
$858$		0			0
$859$	318841.	+	552249.i	0.0147432	+	0.0255360i	0.873303	−	0.487178i	$-0.161974\pi$
$859$	318841.	+	552249.i	0.0147432	+	0.0255360i	−0.858560	+	0.512714i	$0.828640\pi$
$860$	−9.32524e6	−	1.61518e7i	−0.429946	−	0.744688i
$861$		0			0
$862$	−3.37184e6	+	5.84020e6i	−0.154561	+	0.267707i
$863$	3.79097e7			1.73270			0.866350	−	0.499437i	$-0.166460\pi$
$863$	3.79097e7			1.73270			0.866350	+	0.499437i	$0.166460\pi$
$864$		0			0
$865$	−4.64946e7			−2.11282
$866$	1.83033e7	−	3.17022e7i	0.829343	−	1.43646i
$867$		0			0
$868$	2.29699e6	+	3.97851e6i	0.103481	+	0.179234i
$869$	−338798.	−	586816.i	−0.0152192	−	0.0263604i
$870$		0			0
$871$	1.26789e7	−	2.19604e7i	0.566285	−	0.980834i
$872$	−8.62199e6			−0.383987
$873$		0			0
$874$	−4.26893e6			−0.189034
$875$	2.51145e6	−	4.34995e6i	0.110893	−	0.192072i
$876$		0			0
$877$	−2.01603e7	−	3.49186e7i	−0.885111	−	1.53306i	−0.845587	−	0.533838i	$-0.820749\pi$
$877$	−2.01603e7	−	3.49186e7i	−0.885111	−	1.53306i	−0.0395244	−	0.999219i	$-0.512584\pi$
$878$	−881277.	−	1.52642e6i	−0.0385812	−	0.0668247i
$879$		0			0
$880$	402999.	−	698016.i	0.0175428	−	0.0303849i
$881$	3.52506e7			1.53013			0.765063	−	0.643956i	$-0.222708\pi$
$881$	3.52506e7			1.53013			0.765063	+	0.643956i	$0.222708\pi$
$882$		0			0
$883$	2.35541e6			0.101663			0.0508316	−	0.998707i	$-0.483813\pi$
$883$	2.35541e6			0.101663			0.0508316	+	0.998707i	$0.483813\pi$
$884$	4.28212e6	−	7.41685e6i	0.184301	−	0.319219i
$885$		0			0
$886$	9.87033e6	+	1.70959e7i	0.422423	+	0.731658i
$887$	−1.30625e7	−	2.26249e7i	−0.557464	−	0.965556i	−0.997707	−	0.0676777i	$-0.978441\pi$
$887$	−1.30625e7	−	2.26249e7i	−0.557464	−	0.965556i	0.440243	−	0.897879i	$-0.354892\pi$
$888$		0			0
$889$	−4.80644e6	+	8.32501e6i	−0.203972	+	0.353289i
$890$	−8.22124e7			−3.47906
$891$		0			0
$892$	−2.03624e7			−0.856876
$893$	−1.85359e7	+	3.21051e7i	−0.777829	+	1.34724i
$894$		0			0
$895$	1.59743e7	+	2.76683e7i	0.666600	+	1.15458i
$896$	−2.17865e6	−	3.77354e6i	−0.0906606	−	0.157029i
$897$		0			0
$898$	3.14224e7	−	5.44252e7i	1.30032	−	2.25221i
$899$	2.15062e7			0.887491
$900$		0			0
$901$	−1.14697e6			−0.0470696
$902$	101844.	−	176398.i	0.00416790	−	0.00721901i
$903$		0			0
$904$	4.32532e6	+	7.49167e6i	0.176034	+	0.304900i
$905$	−1.91282e7	−	3.31309e7i	−0.776339	−	1.34466i
$906$		0			0
$907$	2.18243e7	−	3.78008e7i	0.880892	−	1.52575i	0.0305409	−	0.999534i	$-0.490277\pi$
$907$	2.18243e7	−	3.78008e7i	0.880892	−	1.52575i	0.850351	−	0.526216i	$-0.176390\pi$
$908$	9.38251e6			0.377663
$909$		0			0
$910$	−1.64627e7			−0.659017
$911$	8.65618e6	−	1.49929e7i	0.345566	−	0.598537i	−0.639891	−	0.768466i	$-0.721020\pi$
$911$	8.65618e6	−	1.49929e7i	0.345566	−	0.598537i	0.985456	+	0.169929i	$0.0543538\pi$
$912$		0			0
$913$	−40667.7	−	70438.6i	−0.00161463	−	0.00279662i
$914$	3.00550e6	+	5.20568e6i	0.119001	+	0.206116i
$915$		0			0
$916$	−1.57170e6	+	2.72226e6i	−0.0618913	+	0.107199i
$917$	−7.14600e6			−0.280634
$918$		0			0
$919$	−2.03151e7			−0.793468			−0.396734	−	0.917934i	$-0.629856\pi$
$919$	−2.03151e7			−0.793468			−0.396734	+	0.917934i	$0.629856\pi$
$920$	−634621.	+	1.09920e6i	−0.0247198	+	0.0428159i
$921$		0			0
$922$	−5.28699e6	−	9.15733e6i	−0.204824	−	0.354766i
$923$	9.88327e6	+	1.71183e7i	0.381853	+	0.661389i
$924$		0			0
$925$	−548008.	+	949178.i	−0.0210587	+	0.0364748i
$926$	−8.67065e6			−0.332295
$927$		0			0
$928$	3.54830e7			1.35254
$929$	2.28832e7	−	3.96349e7i	0.869916	−	1.50674i	0.00783438	−	0.999969i	$-0.497506\pi$
$929$	2.28832e7	−	3.96349e7i	0.869916	−	1.50674i	0.862082	−	0.506769i	$-0.169160\pi$
$930$		0			0
$931$	1.55668e7	+	2.69625e7i	0.588606	+	1.01950i
$932$	5.29300e6	+	9.16775e6i	0.199601	+	0.345719i
$933$		0			0
$934$	−2.13074e7	+	3.69055e7i	−0.799215	+	1.38428i
$935$	380526.			0.0142349
$936$		0			0
$937$	4.11001e7			1.52930			0.764652	−	0.644444i	$-0.222911\pi$
$937$	4.11001e7			1.52930			0.764652	+	0.644444i	$0.222911\pi$
$938$	−6.51625e6	+	1.12865e7i	−0.241819	+	0.418843i
$939$		0			0
$940$	−1.96562e7	−	3.40455e7i	−0.725570	−	1.25672i
$941$	1.55476e7	+	2.69292e7i	0.572385	+	0.991400i	0.996320	+	0.0857072i	$0.0273150\pi$
$941$	1.55476e7	+	2.69292e7i	0.572385	+	0.991400i	−0.423936	+	0.905692i	$0.639352\pi$
$942$		0			0
$943$	−481547.	+	834064.i	−0.0176344	+	0.0305436i
$944$	2.42059e6			0.0884081
$945$		0			0
$946$	−495362.			−0.0179968
$947$	2.10665e7	−	3.64883e7i	0.763339	−	1.32214i	−0.177781	−	0.984070i	$-0.556892\pi$
$947$	2.10665e7	−	3.64883e7i	0.763339	−	1.32214i	0.941120	−	0.338072i	$-0.109775\pi$
$948$		0			0
$949$	9.93283e6	+	1.72042e7i	0.358020	+	0.620109i
$950$	3.51506e7	+	6.08826e7i	1.26364	+	2.18869i
$951$		0			0
$952$	617042.	−	1.06875e6i	0.0220660	−	0.0382193i
$953$	1.27052e7			0.453158			0.226579	−	0.973993i	$-0.427246\pi$
$953$	1.27052e7			0.453158			0.226579	+	0.973993i	$0.427246\pi$
$954$		0			0
$955$	−1.33696e7			−0.474361
$956$	−1.52935e7	+	2.64892e7i	−0.541206	+	0.937397i
$957$		0			0
$958$	2.15386e7	+	3.73060e7i	0.758236	+	1.31330i
$959$	−988202.	−	1.71162e6i	−0.0346976	−	0.0600980i
$960$		0			0
$961$	4.36530e6	−	7.56093e6i	0.152478	−	0.264099i
$962$	1.10822e6			0.0386089
$963$		0			0
$964$	1.89594e7			0.657102
$965$	−1.69750e7	+	2.94016e7i	−0.586802	+	1.01637i
$966$		0			0
$967$	−2.11678e7	−	3.66637e7i	−0.727964	−	1.26087i	−0.957743	−	0.287627i	$-0.907134\pi$
$967$	−2.11678e7	−	3.66637e7i	−0.727964	−	1.26087i	0.229779	−	0.973243i	$-0.426200\pi$
$968$	4.25830e6	+	7.37558e6i	0.146065	+	0.252993i
$969$		0			0
$970$	−5.37901e7	+	9.31672e7i	−1.83558	+	3.17932i
$971$	−4.04024e7			−1.37518			−0.687589	−	0.726100i	$-0.741331\pi$
$971$	−4.04024e7			−1.37518			−0.687589	+	0.726100i	$0.741331\pi$
$972$		0			0
$973$	7.84757e6			0.265737
$974$	−1.05226e7	+	1.82257e7i	−0.355407	+	0.615583i
$975$		0			0
$976$	−1.69708e7	−	2.93944e7i	−0.570268	−	0.987733i
$977$	−1.88733e7	−	3.26895e7i	−0.632574	−	1.09565i	−0.987024	−	0.160576i	$-0.948665\pi$
$977$	−1.88733e7	−	3.26895e7i	−0.632574	−	1.09565i	0.354449	−	0.935075i	$-0.384668\pi$
$978$		0			0
$979$	−478778.	+	829267.i	−0.0159653	+	0.0276527i
$980$	−3.30153e7			−1.09812
$981$		0			0
$982$	7.24506e6			0.239753
$983$	2.44599e6	−	4.23658e6i	0.0807367	−	0.139840i	−0.822830	−	0.568288i	$-0.807606\pi$
$983$	2.44599e6	−	4.23658e6i	0.0807367	−	0.139840i	0.903567	+	0.428448i	$0.140939\pi$
$984$		0			0
$985$	5.09215e6	+	8.81986e6i	0.167229	+	0.289649i
$986$	1.03026e7	+	1.78447e7i	0.337487	+	0.584544i
$987$		0			0
$988$	1.55860e7	−	2.69957e7i	0.507974	−	0.879837i
$989$	2.34222e6			0.0761443
$990$		0			0
$991$	3.66907e7			1.18678			0.593392	−	0.804913i	$-0.297788\pi$
$991$	3.66907e7			1.18678			0.593392	+	0.804913i	$0.297788\pi$
$992$	−1.64153e7	+	2.84321e7i	−0.529627	+	0.917340i
$993$		0			0
$994$	−5.07946e6	−	8.79788e6i	−0.163062	−	0.282431i
$995$	3.95597e7	+	6.85194e7i	1.26676	+	2.19410i
$996$		0			0
$997$	1.25206e7	−	2.16863e7i	0.398921	−	0.690951i	−0.594672	−	0.803968i	$-0.702718\pi$
$997$	1.25206e7	−	2.16863e7i	0.398921	−	0.690951i	0.993593	+	0.113017i	$0.0360515\pi$
$998$	1.70763e7			0.542709
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.6.c.a.19.4		8
3.2	odd	2		9.6.c.a.7.1	yes	8
4.3	odd	2		432.6.i.c.289.1		8
9.2	odd	6		81.6.a.c.1.4		4
9.4	even	3	inner	27.6.c.a.10.4		8
9.5	odd	6		9.6.c.a.4.1	✓	8
9.7	even	3		81.6.a.d.1.1		4
12.11	even	2		144.6.i.c.97.4		8
36.23	even	6		144.6.i.c.49.4		8
36.31	odd	6		432.6.i.c.145.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.6.c.a.4.1	✓	8	9.5	odd	6
9.6.c.a.7.1	yes	8	3.2	odd	2
27.6.c.a.10.4		8	9.4	even	3	inner
27.6.c.a.19.4		8	1.1	even	1	trivial
81.6.a.c.1.4		4	9.2	odd	6
81.6.a.d.1.1		4	9.7	even	3
144.6.i.c.49.4		8	36.23	even	6
144.6.i.c.97.4		8	12.11	even	2
432.6.i.c.145.1		8	36.31	odd	6
432.6.i.c.289.1		8	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	27.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.77467 - 6.53793i) q^{2} +(-12.4963 - 21.6443i) q^{4} +(-43.7155 - 75.7175i) q^{5} +(20.6033 - 35.6859i) q^{7} +52.9007 q^{8} -660.048 q^{10} +(-3.84390 + 6.65783i) q^{11} +(302.642 + 524.191i) q^{13} +(-155.541 - 269.405i) q^{14} +(599.566 - 1038.48i) q^{16} +566.131 q^{17} +2060.59 q^{19} +(-1092.57 + 1892.38i) q^{20} +(29.0189 + 50.2623i) q^{22} +(-137.210 - 237.655i) q^{23} +(-2259.59 + 3913.73i) q^{25} +4569.50 q^{26} -1029.86 q^{28} +(-2410.58 + 4175.25i) q^{29} +(-2230.39 - 3863.15i) q^{31} +(-3679.92 - 6373.81i) q^{32} +(2136.96 - 3701.32i) q^{34} -3602.73 q^{35} +242.525 q^{37} +(7778.07 - 13472.0i) q^{38} +(-2312.58 - 4005.51i) q^{40} +(-1754.78 - 3039.37i) q^{41} +(-4267.58 + 7391.66i) q^{43} +192.139 q^{44} -2071.70 q^{46} +(-8995.40 + 15580.5i) q^{47} +(7554.51 + 13084.8i) q^{49} +(17058.5 + 29546.1i) q^{50} +(7563.83 - 13100.9i) q^{52} -2025.98 q^{53} +672.152 q^{55} +(1089.93 - 1887.81i) q^{56} +(18198.3 + 31520.5i) q^{58} +(1009.31 + 1748.18i) q^{59} +(14152.6 - 24513.0i) q^{61} -33676.0 q^{62} -17189.8 q^{64} +(26460.3 - 45830.6i) q^{65} +(-20947.0 - 36281.3i) q^{67} +(-7074.57 - 12253.5i) q^{68} +(-13599.1 + 23554.4i) q^{70} +32656.7 q^{71} +32820.4 q^{73} +(915.453 - 1585.61i) q^{74} +(-25749.9 - 44600.1i) q^{76} +(158.394 + 274.346i) q^{77} +(-44069.6 + 76330.8i) q^{79} -104841. q^{80} -26494.9 q^{82} +(-5289.91 + 9162.39i) q^{83} +(-24748.7 - 42866.0i) q^{85} +(32217.4 + 55802.2i) q^{86} +(-203.345 + 352.204i) q^{88} +124555. q^{89} +24941.6 q^{91} +(-3429.25 + 5939.64i) q^{92} +(67909.4 + 117623. i) q^{94} +(-90080.0 - 156023. i) q^{95} +(81494.3 - 141152. i) q^{97} +114063. q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 3 q^{2} - 49 q^{4} - 78 q^{5} + 28 q^{7} + 750 q^{8} + 60 q^{10} - 444 q^{11} - 182 q^{13} - 1392 q^{14} - 289 q^{16} + 4356 q^{17} + 952 q^{19} - 6684 q^{20} + 1011 q^{22} - 8844 q^{23} - 1654 q^{25}+ \cdots - 57654 q^{98}+O(q^{100}) \) 8 * q - 3 * q^2 - 49 * q^4 - 78 * q^5 + 28 * q^7 + 750 * q^8 + 60 * q^10 - 444 * q^11 - 182 * q^13 - 1392 * q^14 - 289 * q^16 + 4356 * q^17 + 952 * q^19 - 6684 * q^20 + 1011 * q^22 - 8844 * q^23 - 1654 * q^25 + 24888 * q^26 - 1604 * q^28 - 12018 * q^29 + 1132 * q^31 - 8703 * q^32 + 10125 * q^34 + 16224 * q^35 - 15176 * q^37 + 11145 * q^38 - 8736 * q^40 - 1248 * q^41 - 6092 * q^43 - 49530 * q^44 + 45960 * q^46 + 60 * q^47 + 9090 * q^49 + 57057 * q^50 - 32510 * q^52 - 20952 * q^53 - 36120 * q^55 + 61170 * q^56 + 8328 * q^58 - 2076 * q^59 + 48142 * q^61 - 241764 * q^62 - 20926 * q^64 + 13146 * q^65 - 7148 * q^67 + 123129 * q^68 - 654 * q^70 + 71856 * q^71 + 122452 * q^73 + 160320 * q^74 - 49571 * q^76 - 39534 * q^77 - 59516 * q^79 - 124512 * q^80 - 233598 * q^82 - 117696 * q^83 + 28836 * q^85 + 15915 * q^86 + 104523 * q^88 + 451728 * q^89 + 111392 * q^91 - 134034 * q^92 + 169464 * q^94 - 294888 * q^95 + 33976 * q^97 - 57654 * q^98

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