LMFDB - Embedded newform 9.6.c.a.4.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,6,Mod(4,9)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("9.4");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	9.c (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.44345437832$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			4.1
Root			$3.62198i$ of defining polynomial
Character	$\chi$	$=$	9.4
Dual form			9.6.c.a.7.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.77467 - 6.53793i) q^{2} +(-15.5883 + 0.0716805i) q^{3} +(-12.4963 + 21.6443i) q^{4} +(43.7155 - 75.7175i) q^{5} +(59.3094 + 101.645i) q^{6} +(20.6033 + 35.6859i) q^{7} -52.9007 q^{8} +(242.990 - 2.23475i) q^{9} +O(q^{10})$	\(q+(-3.77467 - 6.53793i) q^{2} +(-15.5883 + 0.0716805i) q^{3} +(-12.4963 + 21.6443i) q^{4} +(43.7155 - 75.7175i) q^{5} +(59.3094 + 101.645i) q^{6} +(20.6033 + 35.6859i) q^{7} -52.9007 q^{8} +(242.990 - 2.23475i) q^{9} -660.048 q^{10} +(3.84390 + 6.65783i) q^{11} +(193.245 - 338.293i) q^{12} +(302.642 - 524.191i) q^{13} +(155.541 - 269.405i) q^{14} +(-676.023 + 1183.44i) q^{15} +(599.566 + 1038.48i) q^{16} -566.131 q^{17} +(-931.818 - 1580.21i) q^{18} +2060.59 q^{19} +(1092.57 + 1892.38i) q^{20} +(-323.728 - 554.806i) q^{21} +(29.0189 - 50.2623i) q^{22} +(137.210 - 237.655i) q^{23} +(824.632 - 3.79195i) q^{24} +(-2259.59 - 3913.73i) q^{25} -4569.50 q^{26} +(-3787.63 + 52.2536i) q^{27} -1029.86 q^{28} +(2410.58 + 4175.25i) q^{29} +(10289.0 - 47.3125i) q^{30} +(-2230.39 + 3863.15i) q^{31} +(3679.92 - 6373.81i) q^{32} +(-60.3970 - 103.509i) q^{33} +(2136.96 + 3701.32i) q^{34} +3602.73 q^{35} +(-2988.11 + 5287.27i) q^{36} +242.525 q^{37} +(-7778.07 - 13472.0i) q^{38} +(-4680.09 + 8192.93i) q^{39} +(-2312.58 + 4005.51i) q^{40} +(1754.78 - 3039.37i) q^{41} +(-2405.31 + 4210.72i) q^{42} +(-4267.58 - 7391.66i) q^{43} -192.139 q^{44} +(10453.2 - 18496.3i) q^{45} -2071.70 q^{46} +(8995.40 + 15580.5i) q^{47} +(-9420.65 - 16145.1i) q^{48} +(7554.51 - 13084.8i) q^{49} +(-17058.5 + 29546.1i) q^{50} +(8825.02 - 40.5805i) q^{51} +(7563.83 + 13100.9i) q^{52} +2025.98 q^{53} +(14638.7 + 24566.0i) q^{54} +672.152 q^{55} +(-1089.93 - 1887.81i) q^{56} +(-32121.1 + 147.704i) q^{57} +(18198.3 - 31520.5i) q^{58} +(-1009.31 + 1748.18i) q^{59} +(-17166.9 - 29420.7i) q^{60} +(14152.6 + 24513.0i) q^{61} +33676.0 q^{62} +(5086.13 + 8625.27i) q^{63} -17189.8 q^{64} +(-26460.3 - 45830.6i) q^{65} +(-448.753 + 785.583i) q^{66} +(-20947.0 + 36281.3i) q^{67} +(7074.57 - 12253.5i) q^{68} +(-2121.84 + 3714.47i) q^{69} +(-13599.1 - 23554.4i) q^{70} -32656.7 q^{71} +(-12854.3 + 118.220i) q^{72} +32820.4 q^{73} +(-915.453 - 1585.61i) q^{74} +(35503.8 + 60846.4i) q^{75} +(-25749.9 + 44600.1i) q^{76} +(-158.394 + 274.346i) q^{77} +(71230.6 - 327.544i) q^{78} +(-44069.6 - 76330.8i) q^{79} +104841. q^{80} +(59039.0 - 1086.04i) q^{81} -26494.9 q^{82} +(5289.91 + 9162.39i) q^{83} +(16053.8 - 73.8210i) q^{84} +(-24748.7 + 42866.0i) q^{85} +(-32217.4 + 55802.2i) q^{86} +(-37876.2 - 64912.3i) q^{87} +(-203.345 - 352.204i) q^{88} -124555. q^{89} +(-160385. + 1475.04i) q^{90} +24941.6 q^{91} +(3429.25 + 5939.64i) q^{92} +(34491.0 - 60379.7i) q^{93} +(67909.4 - 117623. i) q^{94} +(90080.0 - 156023. i) q^{95} +(-56906.8 + 99620.6i) q^{96} +(81494.3 + 141152. i) q^{97} -114063. q^{98} +(948.906 + 1609.19i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{2} - 12 q^{3} - 49 q^{4} + 78 q^{5} + 171 q^{6} + 28 q^{7} - 750 q^{8} - 414 q^{9}+O(q^{10}) $ 8 * q + 3 * q^2 - 12 * q^3 - 49 * q^4 + 78 * q^5 + 171 * q^6 + 28 * q^7 - 750 * q^8 - 414 * q^9	\( 8 q + 3 q^{2} - 12 q^{3} - 49 q^{4} + 78 q^{5} + 171 q^{6} + 28 q^{7} - 750 q^{8} - 414 q^{9} + 60 q^{10} + 444 q^{11} + 2724 q^{12} - 182 q^{13} + 1392 q^{14} - 2052 q^{15} - 289 q^{16} - 4356 q^{17} - 8100 q^{18} + 952 q^{19} + 6684 q^{20} + 8670 q^{21} + 1011 q^{22} + 8844 q^{23} + 549 q^{24} - 1654 q^{25} - 24888 q^{26} - 10152 q^{27} - 1604 q^{28} + 12018 q^{29} + 22104 q^{30} + 1132 q^{31} + 8703 q^{32} - 8820 q^{33} + 10125 q^{34} - 16224 q^{35} - 14589 q^{36} - 15176 q^{37} - 11145 q^{38} + 8220 q^{39} - 8736 q^{40} + 1248 q^{41} + 10098 q^{42} - 6092 q^{43} + 49530 q^{44} + 43038 q^{45} + 45960 q^{46} - 60 q^{47} - 57405 q^{48} + 9090 q^{49} - 57057 q^{50} - 9396 q^{51} - 32510 q^{52} + 20952 q^{53} + 8181 q^{54} - 36120 q^{55} - 61170 q^{56} - 104298 q^{57} + 8328 q^{58} + 2076 q^{59} + 88308 q^{60} + 48142 q^{61} + 241764 q^{62} + 133524 q^{63} - 20926 q^{64} - 13146 q^{65} - 100998 q^{66} - 7148 q^{67} - 123129 q^{68} - 125982 q^{69} - 654 q^{70} - 71856 q^{71} + 35451 q^{72} + 122452 q^{73} - 160320 q^{74} - 18732 q^{75} - 49571 q^{76} + 39534 q^{77} + 181422 q^{78} - 59516 q^{79} + 124512 q^{80} + 194562 q^{81} - 233598 q^{82} + 117696 q^{83} + 108354 q^{84} + 28836 q^{85} - 15915 q^{86} - 142956 q^{87} + 104523 q^{88} - 451728 q^{89} - 539892 q^{90} + 111392 q^{91} + 134034 q^{92} + 113898 q^{93} + 169464 q^{94} + 294888 q^{95} + 42768 q^{96} + 33976 q^{97} + 57654 q^{98} + 33696 q^{99}+O(q^{100}) \) 8 * q + 3 * q^2 - 12 * q^3 - 49 * q^4 + 78 * q^5 + 171 * q^6 + 28 * q^7 - 750 * q^8 - 414 * q^9 + 60 * q^10 + 444 * q^11 + 2724 * q^12 - 182 * q^13 + 1392 * q^14 - 2052 * q^15 - 289 * q^16 - 4356 * q^17 - 8100 * q^18 + 952 * q^19 + 6684 * q^20 + 8670 * q^21 + 1011 * q^22 + 8844 * q^23 + 549 * q^24 - 1654 * q^25 - 24888 * q^26 - 10152 * q^27 - 1604 * q^28 + 12018 * q^29 + 22104 * q^30 + 1132 * q^31 + 8703 * q^32 - 8820 * q^33 + 10125 * q^34 - 16224 * q^35 - 14589 * q^36 - 15176 * q^37 - 11145 * q^38 + 8220 * q^39 - 8736 * q^40 + 1248 * q^41 + 10098 * q^42 - 6092 * q^43 + 49530 * q^44 + 43038 * q^45 + 45960 * q^46 - 60 * q^47 - 57405 * q^48 + 9090 * q^49 - 57057 * q^50 - 9396 * q^51 - 32510 * q^52 + 20952 * q^53 + 8181 * q^54 - 36120 * q^55 - 61170 * q^56 - 104298 * q^57 + 8328 * q^58 + 2076 * q^59 + 88308 * q^60 + 48142 * q^61 + 241764 * q^62 + 133524 * q^63 - 20926 * q^64 - 13146 * q^65 - 100998 * q^66 - 7148 * q^67 - 123129 * q^68 - 125982 * q^69 - 654 * q^70 - 71856 * q^71 + 35451 * q^72 + 122452 * q^73 - 160320 * q^74 - 18732 * q^75 - 49571 * q^76 + 39534 * q^77 + 181422 * q^78 - 59516 * q^79 + 124512 * q^80 + 194562 * q^81 - 233598 * q^82 + 117696 * q^83 + 108354 * q^84 + 28836 * q^85 - 15915 * q^86 - 142956 * q^87 + 104523 * q^88 - 451728 * q^89 - 539892 * q^90 + 111392 * q^91 + 134034 * q^92 + 113898 * q^93 + 169464 * q^94 + 294888 * q^95 + 42768 * q^96 + 33976 * q^97 + 57654 * q^98 + 33696 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/9\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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	−0.978663	−	0.205471i	$-0.934127\pi$
$2$	−3.77467	−	6.53793i	−0.667275	−	1.15575i	0.311389	−	0.950283i	$-0.399206\pi$
$3$	−15.5883	+	0.0716805i	−0.999989	+	0.00459830i
$3$	−15.5883	+	0.0716805i	−0.999989	+	0.00459830i
$4$	−12.4963	+	21.6443i	−0.390511	+	0.676384i
$5$	43.7155	−	75.7175i	0.782007	−	1.35448i	−0.148764	−	0.988873i	$-0.547529\pi$
$5$	43.7155	−	75.7175i	0.782007	−	1.35448i	0.930771	−	0.365603i	$-0.119137\pi$
$6$	59.3094	+	101.645i	0.672582	+	1.15267i
$7$	20.6033	+	35.6859i	0.158925	+	0.275265i	0.934481	−	0.356013i	$-0.115864\pi$
$7$	20.6033	+	35.6859i	0.158925	+	0.275265i	−0.775557	+	0.631278i	$0.782531\pi$
$8$	−52.9007			−0.292238
$9$	242.990	−	2.23475i	0.999958	−	0.00919651i
$10$	−660.048			−2.08725
$11$	3.84390	+	6.65783i	0.00957834	+	0.0165902i	0.870775	−	0.491682i	$-0.163618\pi$
$11$	3.84390	+	6.65783i	0.00957834	+	0.0165902i	−0.861197	+	0.508272i	$0.830284\pi$
$12$	193.245	−	338.293i	0.387396	−	0.678173i
$13$	302.642	−	524.191i	0.496673	−	0.860263i	−0.503320	−	0.864100i	$-0.667888\pi$
$13$	302.642	−	524.191i	0.496673	−	0.860263i	0.999993	+	0.00383763i	$0.00122156\pi$
$14$	155.541	−	269.405i	0.212093	−	0.367355i
$15$	−676.023	+	1183.44i	−0.775771	+	1.35806i
$16$	599.566	+	1038.48i	0.585514	+	1.01414i
$17$	−566.131			−0.475111			−0.237555	−	0.971374i	$-0.576346\pi$
$17$	−566.131			−0.475111			−0.237555	+	0.971374i	$0.576346\pi$
$18$	−931.818	−	1580.21i	−0.677875	−	1.14957i
$19$	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
$21$	−323.728	−	554.806i	−0.160189	−	0.274532i
$22$	29.0189	−	50.2623i	0.0127828	−	0.0221404i
$23$	137.210	−	237.655i	0.0540838	−	0.0936759i	−0.837716	−	0.546106i	$-0.816110\pi$
$23$	137.210	−	237.655i	0.0540838	−	0.0936759i	0.891800	+	0.452430i	$0.149443\pi$
$24$	824.632	−	3.79195i	0.292235	−	0.00134380i
$25$	−2259.59	−	3913.73i	−0.723070	−	1.25239i
$26$	−4569.50			−1.32567
$27$	−3787.63	+	52.2536i	−0.999905	+	0.0137945i
$28$	−1029.86			−0.248247
$29$	2410.58	+	4175.25i	0.532264	+	0.921909i	0.999290	+	0.0376653i	$0.0119921\pi$
$29$	2410.58	+	4175.25i	0.532264	+	0.921909i	−0.467026	+	0.884244i	$0.654675\pi$
$30$	10289.0	−	47.3125i	2.08723	−	0.00959783i
$31$	−2230.39	+	3863.15i	−0.416847	+	0.722000i	−0.995620	−	0.0934885i	$-0.970198\pi$
$31$	−2230.39	+	3863.15i	−0.416847	+	0.722000i	0.578774	+	0.815488i	$0.303531\pi$
$32$	3679.92	−	6373.81i	0.635278	−	1.10033i
$33$	−60.3970	−	103.509i	−0.00965452	−	0.0165459i
$34$	2136.96	+	3701.32i	0.317029	+	0.549111i
$35$	3602.73			0.497121
$36$	−2988.11	+	5287.27i	−0.384274	+	0.679947i
$37$	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
$39$	−4680.09	+	8192.93i	−0.492712	+	0.862537i
$40$	−2312.58	+	4005.51i	−0.228532	+	0.395829i
$41$	1754.78	−	3039.37i	0.163028	−	0.282373i	−0.772925	−	0.634497i	$-0.781207\pi$
$41$	1754.78	−	3039.37i	0.163028	−	0.282373i	0.935953	+	0.352124i	$0.114541\pi$
$42$	−2405.31	+	4210.72i	−0.210401	+	0.368327i
$43$	−4267.58	−	7391.66i	−0.351974	−	0.609636i	0.634621	−	0.772823i	$-0.281156\pi$
$43$	−4267.58	−	7391.66i	−0.351974	−	0.609636i	−0.986595	+	0.163187i	$0.947823\pi$
$44$	−192.139			−0.0149618
$45$	10453.2	−	18496.3i	0.769518	−	1.36161i
$46$	−2071.70			−0.144355
$47$	8995.40	+	15580.5i	0.593985	+	1.02881i	0.993689	+	0.112168i	$0.0357796\pi$
$47$	8995.40	+	15580.5i	0.593985	+	1.02881i	−0.399704	+	0.916644i	$0.630887\pi$
$48$	−9420.65	−	16145.1i	−0.590171	−	1.01144i
$49$	7554.51	−	13084.8i	0.449486	−	0.778533i
$50$	−17058.5	+	29546.1i	−0.964973	+	1.67138i
$51$	8825.02	−	40.5805i	0.475106	−	0.00218470i
$52$	7563.83	+	13100.9i	0.387912	+	0.671883i
$53$	2025.98			0.0990708			0.0495354	−	0.998772i	$-0.484226\pi$
$53$	2025.98			0.0990708			0.0495354	+	0.998772i	$0.484226\pi$
$54$	14638.7	+	24566.0i	0.683154	+	1.14644i
$55$	672.152			0.0299613
$56$	−1089.93	−	1887.81i	−0.0464438	−	0.0804430i
$57$	−32121.1	+	147.704i	−1.30950	+	0.00602152i
$58$	18198.3	−	31520.5i	0.710333	−	1.23033i
$59$	−1009.31	+	1748.18i	−0.0377481	+	0.0653816i	−0.884282	−	0.466953i	$-0.845352\pi$
$59$	−1009.31	+	1748.18i	−0.0377481	+	0.0653816i	0.846534	+	0.532334i	$0.178685\pi$
$60$	−17166.9	−	29420.7i	−0.615622	−	1.05505i
$61$	14152.6	+	24513.0i	0.486981	+	0.843476i	0.999888	−	0.0149684i	$-0.00476476\pi$
$61$	14152.6	+	24513.0i	0.486981	+	0.843476i	−0.512907	+	0.858444i	$0.671431\pi$
$62$	33676.0			1.11260
$63$	5086.13	+	8625.27i	0.161449	+	0.273792i
$64$	−17189.8			−0.524591
$65$	−26460.3	−	45830.6i	−0.776803	−	1.34546i
$66$	−448.753	+	785.583i	−0.0126808	+	0.0221989i
$67$	−20947.0	+	36281.3i	−0.570079	+	0.987405i	0.426479	+	0.904498i	$0.359754\pi$
$67$	−20947.0	+	36281.3i	−0.570079	+	0.987405i	−0.996557	+	0.0829074i	$0.973579\pi$
$68$	7074.57	−	12253.5i	0.185536	−	0.321357i
$69$	−2121.84	+	3714.47i	−0.0536525	+	0.0939236i
$70$	−13599.1	−	23554.4i	−0.331716	−	0.574549i
$71$	−32656.7			−0.768822			−0.384411	−	0.923162i	$-0.625596\pi$
$71$	−32656.7			−0.768822			−0.384411	+	0.923162i	$0.625596\pi$
$72$	−12854.3	+	118.220i	−0.292226	+	0.00268757i
$73$	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
$75$	35503.8	+	60846.4i	0.728822	+	1.24906i
$76$	−25749.9	+	44600.1i	−0.511377	+	0.885731i
$77$	−158.394	+	274.346i	−0.00304447	+	0.00527317i
$78$	71230.6	−	327.544i	1.32565	−	0.00609583i
$79$	−44069.6	−	76330.8i	−0.794459	−	1.37604i	−0.923182	−	0.384363i	$-0.874421\pi$
$79$	−44069.6	−	76330.8i	−0.794459	−	1.37604i	0.128723	−	0.991681i	$-0.458912\pi$
$80$	104841.			1.83150
$81$	59039.0	−	1086.04i	0.999831	−	0.0183922i
$82$	−26494.9			−0.435138
$83$	5289.91	+	9162.39i	0.0842855	+	0.145987i	0.905087	−	0.425227i	$-0.139806\pi$
$83$	5289.91	+	9162.39i	0.0842855	+	0.145987i	−0.820801	+	0.571214i	$0.806473\pi$
$84$	16053.8	−	73.8210i	0.248244	−	0.00114151i
$85$	−24748.7	+	42866.0i	−0.371540	+	0.643526i
$86$	−32217.4	+	55802.2i	−0.469726	+	0.813590i
$87$	−37876.2	−	64912.3i	−0.536498	−	0.919452i
$88$	−203.345	−	352.204i	−0.00279915	−	0.00484828i
$89$	−124555.			−1.66681			−0.833407	−	0.552660i	$-0.813613\pi$
$89$	−124555.			−1.66681			−0.833407	+	0.552660i	$0.813613\pi$
$90$	−160385.	+	1475.04i	−2.08717	+	0.0191955i
$91$	24941.6			0.315734
$92$	3429.25	+	5939.64i	0.0422406	+	0.0731628i
$93$	34491.0	−	60379.7i	0.413522	−	0.723909i
$94$	67909.4	−	117623.i	0.792702	−	1.37300i
$95$	90080.0	−	156023.i	1.02405	−	1.77370i
$96$	−56906.8	+	99620.6i	−0.630211	+	1.10324i
$97$	81494.3	+	141152.i	0.879423	+	1.52321i	0.851975	+	0.523582i	$0.175405\pi$
$97$	81494.3	+	141152.i	0.879423	+	1.52321i	0.0274474	+	0.999623i	$0.491262\pi$
$98$	−114063.			−1.19972
$99$	948.906	+	1609.19i	0.00973050	+	0.0165014i
$100$	112947.			1.12947
$101$	92925.6	+	160952.i	0.906425	+	1.56997i	0.818992	+	0.573804i	$0.194533\pi$
$101$	92925.6	+	160952.i	0.906425	+	1.56997i	0.0874330	+	0.996170i	$0.472134\pi$
$102$	−33576.9	−	57544.2i	−0.319551	−	0.547647i
$103$	24409.2	−	42277.9i	0.226704	−	0.392663i	−0.730125	−	0.683314i	$-0.760538\pi$
$103$	24409.2	−	42277.9i	0.226704	−	0.392663i	0.956829	+	0.290650i	$0.0938716\pi$
$104$	−16010.0	+	27730.1i	−0.145147	+	0.251401i
$105$	−56160.4	+	258.246i	−0.497115	+	0.00228591i
$106$	−7647.42	−	13245.7i	−0.0661074	−	0.114501i
$107$	131842.			1.11325			0.556626	−	0.830763i	$-0.312095\pi$
$107$	131842.			1.11325			0.556626	+	0.830763i	$0.312095\pi$
$108$	46200.6	−	82633.6i	0.381143	−	0.681707i
$109$	−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
$111$	−3780.55	+	17.3843i	−0.0291238	+	0.000133921i
$112$	−24706.0	+	42792.1i	−0.186105	+	0.322343i
$113$	−81762.9	+	141618.i	−0.602366	+	1.04333i	0.390096	+	0.920774i	$0.372442\pi$
$113$	−81762.9	+	141618.i	−0.602366	+	1.04333i	−0.992462	+	0.122554i	$0.960892\pi$
$114$	122213.	+	209448.i	0.880752	+	1.50944i
$115$	−11996.4	−	20778.4i	−0.0845878	−	0.146510i
$116$	−120494.			−0.831419
$117$	72367.4	−	128049.i	0.488740	−	0.864794i
$118$	15239.3			0.100753
$119$	−11664.2	−	20202.9i	−0.0755068	−	0.130782i
$120$	35762.1	−	62604.9i	0.226710	−	0.396876i
$121$	80495.9	−	139423.i	0.499817	−	0.865708i
$122$	106843.	−	185058.i	0.649900	−	1.12566i
$123$	−27136.1	+	47504.3i	−0.161728	+	0.283120i
$124$	−55743.4	−	96550.4i	−0.325566	−	0.563897i
$125$	−121895.			−0.697770
$126$	37192.9	−	65810.3i	0.208705	−	0.369290i
$127$	−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
$129$	67054.1	+	114917.i	0.354773	+	0.608012i
$130$	−199758.	+	345991.i	−1.03668	+	1.79559i
$131$	86709.6	−	150185.i	0.441457	−	0.764626i	−0.556341	−	0.830954i	$-0.687795\pi$
$131$	86709.6	−	150185.i	0.441457	−	0.764626i	0.997798	+	0.0663279i	$0.0211283\pi$
$132$	2995.11	−	13.7726i	0.0149616	−	6.87988e-5i
$133$	42455.0	+	73534.2i	0.208113	+	0.360463i
$134$	316272.			1.52160
$135$	−161622.	+	289075.i	−0.763248	+	1.36513i
$136$	29948.8			0.138845
$137$	−23981.7	−	41537.5i	−0.109164	−	0.189077i	0.806268	−	0.591550i	$-0.201484\pi$
$137$	−23981.7	−	41537.5i	−0.109164	−	0.189077i	−0.915432	+	0.402473i	$0.868151\pi$
$138$	32294.2	−	148.500i	0.144353	−	0.000663788i
$139$	95222.3	−	164930.i	0.418025	−	0.724040i	−0.577716	−	0.816238i	$-0.696056\pi$
$139$	95222.3	−	164930.i	0.418025	−	0.724040i	0.995741	+	0.0921980i	$0.0293893\pi$
$140$	−45021.0	+	77978.6i	−0.194131	+	0.336245i
$141$	−141340.	−	242228.i	−0.598710	−	1.02607i
$142$	123268.	+	213507.i	0.513016	+	0.888569i
$143$	4653.30			0.0190292
$144$	148009.	+	251000.i	0.594815	+	1.00871i
$145$	421520.			1.66494
$146$	−123886.	−	214577.i	−0.480996	−	0.833109i
$147$	−116824.	+	204511.i	−0.445901	+	0.780591i
$148$	−3030.67	+	5249.28i	−0.0113733	+	0.0196991i
$149$	−24272.2	+	42040.6i	−0.0895660	+	0.155133i	−0.907328	−	0.420424i	$-0.861881\pi$
$149$	−24272.2	+	42040.6i	−0.0895660	+	0.155133i	0.817762	+	0.575557i	$0.195215\pi$
$150$	263795.	−	461797.i	0.957277	−	1.67580i
$151$	−112968.	−	195667.i	−0.403194	−	0.698352i	0.590916	−	0.806733i	$-0.298767\pi$
$151$	−112968.	−	195667.i	−0.403194	−	0.698352i	−0.994109	+	0.108381i	$0.965433\pi$
$152$	−109007.			−0.382688
$153$	−137564.	+	1265.16i	−0.475091	+	0.00436936i
$154$	2391.54			0.00812598
$155$	195005.	+	337759.i	0.651954	+	1.12922i
$156$	−118846.	−	203679.i	−0.390997	−	0.670092i
$157$	−80599.2	+	139602.i	−0.260965	+	0.452004i	−0.966499	−	0.256672i	$-0.917374\pi$
$157$	−80599.2	+	139602.i	−0.260965	+	0.452004i	0.705534	+	0.708676i	$0.250707\pi$
$158$	−332697.	+	576248.i	−1.06024	+	1.83640i
$159$	−31581.6	+	145.223i	−0.0990697	+	0.000455558i
$160$	−321739.	−	557269.i	−0.993583	−	1.72094i
$161$	11307.9			0.0343810
$162$	−229954.	−	381893.i	−0.688419	−	1.14329i
$163$	−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
$165$	−10477.7	+	48.1802i	−0.0299610	+	0.000137771i
$166$	39935.4	−	69170.1i	0.112483	−	0.194827i
$167$	−63474.6	+	109941.i	−0.176120	+	0.305049i	−0.940548	−	0.339660i	$-0.889688\pi$
$167$	−63474.6	+	109941.i	−0.176120	+	0.305049i	0.764428	+	0.644709i	$0.223021\pi$
$168$	17125.4	+	29349.6i	0.0468132	+	0.0802286i
$169$	2462.49	+	4265.15i	0.00663219	+	0.0114873i
$170$	373674.			0.991676
$171$	500703.	−	4604.92i	1.30945	−	0.0120429i
$172$	213316.			0.549798
$173$	−265893.	−	460540.i	−0.675447	−	1.16991i	−0.976338	−	0.216250i	$-0.930617\pi$
$173$	−265893.	−	460540.i	−0.675447	−	1.16991i	0.300891	−	0.953659i	$-0.402716\pi$
$174$	−281422.	+	492655.i	−0.704668	+	1.23359i
$175$	93110.1	−	161271.i	0.229827	−	0.398073i
$176$	−4609.34	+	7983.61i	−0.0112165	+	0.0194275i
$177$	15608.1	−	27323.5i	0.0374471	−	0.0655545i
$178$	470156.	+	814333.i	1.11222	+	1.92643i
$179$	365415.			0.852421			0.426211	−	0.904624i	$-0.359848\pi$
$179$	365415.			0.852421			0.426211	+	0.904624i	$0.359848\pi$
$180$	269712.	+	457388.i	0.620467	+	1.05221i
$181$	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
$183$	−222372.	−	381102.i	−0.490854	−	0.841228i
$184$	−7258.53	+	12572.1i	−0.0158053	+	0.0273757i
$185$	10602.1	−	18363.4i	0.0227752	−	0.0394478i
$186$	−524951.	+	2413.91i	−1.11259	+	0.00511610i
$187$	−2176.15	−	3769.20i	−0.00455077	−	0.00788216i
$188$	−449638.			−0.927830
$189$	−79902.4	−	134089.i	−0.162707	−	0.273047i
$190$	−1.36009e6			−2.73328
$191$	−76457.7	−	132429.i	−0.151648	−	0.262663i	0.780185	−	0.625549i	$-0.215125\pi$
$191$	−76457.7	−	132429.i	−0.151648	−	0.262663i	−0.931834	+	0.362886i	$0.881791\pi$
$192$	267960.	−	1232.17i	0.524585	−	0.00241223i
$193$	−194153.	+	336283.i	−0.375190	+	0.649848i	−0.990355	−	0.138550i	$-0.955756\pi$
$193$	−194153.	+	336283.i	−0.375190	+	0.649848i	0.615166	+	0.788398i	$0.289089\pi$
$194$	615229.	−	1.06561e6i	1.17363	−	2.03279i
$195$	415756.	+	712523.i	0.782982	+	1.34188i
$196$	188807.	+	327024.i	0.351058	+	0.608050i
$197$	116484.			0.213845			0.106923	−	0.994267i	$-0.465900\pi$
$197$	116484.			0.213845			0.106923	+	0.994267i	$0.465900\pi$
$198$	6938.98	−	12278.1i	0.0125786	−	0.0222570i
$199$	−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
$201$	323927.	−	567064.i	0.565532	−	0.990016i
$202$	701528.	−	1.21508e6i	1.20967	−	2.09521i
$203$	−99331.8	+	172048.i	−0.169180	+	0.293028i
$204$	−109402.	+	191518.i	−0.184056	+	0.322207i
$205$	−153422.	−	265735.i	−0.254978	−	0.441636i
$206$	−368547.			−0.605096
$207$	32809.6	−	58054.4i	0.0532200	−	0.0941693i
$208$	725815.			1.16323
$209$	7920.71	+	13719.1i	0.0125429	+	0.0217250i
$210$	213676.	+	366198.i	0.334354	+	0.573017i
$211$	−592009.	+	1.02539e6i	−0.915424	+	1.58556i	−0.109145	+	0.994026i	$0.534811\pi$
$211$	−592009.	+	1.02539e6i	−0.915424	+	1.58556i	−0.806279	+	0.591535i	$0.798522\pi$
$212$	−25317.3	+	43850.9i	−0.0386882	+	0.0670099i
$213$	509062.	−	2340.85i	0.768814	−	0.00353528i
$214$	−497660.	−	861973.i	−0.742845	−	1.28665i
$215$	−746238.			−1.10098
$216$	200369.	−	2764.25i	0.292210	−	0.00403129i
$217$	−183813.			−0.264989
$218$	615212.	+	1.06558e6i	0.876766	+	1.51860i
$219$	−511614.	+	2352.58i	−0.720829	+	0.00331463i
$220$	−8399.44	+	14548.3i	−0.0117002	+	0.0202654i
$221$	−171335.	+	296761.i	−0.235975	+	0.408720i
$222$	14384.0	+	24651.3i	0.0195883	+	0.0335705i
$223$	407368.	+	705583.i	0.548561	+	0.950136i	0.998373	+	0.0570127i	$0.0181576\pi$
$223$	407368.	+	705583.i	0.548561	+	0.950136i	−0.449812	+	0.893123i	$0.648509\pi$
$224$	303274.			0.403845
$225$	−557805.	−	945947.i	−0.734557	−	1.24569i
$226$	1.23451e6			1.60777
$227$	187705.	+	325115.i	0.241775	+	0.418767i	0.961220	−	0.275783i	$-0.0889370\pi$
$227$	187705.	+	325115.i	0.241775	+	0.418767i	−0.719445	+	0.694550i	$0.755604\pi$
$228$	398200.	−	697085.i	0.507299	−	0.888073i
$229$	−62886.2	+	108922.i	−0.0792441	+	0.137255i	−0.902924	−	0.429800i	$-0.858584\pi$
$229$	−62886.2	+	108922.i	−0.0792441	+	0.137255i	0.823680	+	0.567055i	$0.191917\pi$
$230$	−90565.3	+	156864.i	−0.112887	+	0.195525i
$231$	2449.42	−	4287.94i	0.00302019	−	0.00528711i
$232$	−127522.	−	220874.i	−0.155548	−	0.269417i
$233$	423564.			0.511128			0.255564	−	0.966792i	$-0.417739\pi$
$233$	423564.			0.511128			0.255564	+	0.966792i	$0.417739\pi$
$234$	−1.11034e6	+	10211.7i	−1.32561	+	0.0121915i
$235$	1.57295e6			1.85800
$236$	−25225.4	−	43691.7i	−0.0294821	−	0.0510644i
$237$	692441.	+	1.18671e6i	0.800778	+	1.37238i
$238$	−88056.8	+	152519.i	−0.100767	+	0.174534i
$239$	611920.	−	1.05988e6i	0.692947	−	1.20022i	−0.277921	−	0.960604i	$-0.589645\pi$
$239$	611920.	−	1.05988e6i	0.692947	−	1.20022i	0.970868	−	0.239616i	$-0.0770215\pi$
$240$	−1.63430e6	+	7515.08i	−1.83148	+	0.00842181i
$241$	−379300.	−	656966.i	−0.420668	−	0.728619i	0.575337	−	0.817917i	$-0.304871\pi$
$241$	−379300.	−	656966.i	−0.420668	−	0.728619i	−0.996005	+	0.0892979i	$0.971538\pi$
$242$	−1.21538e6			−1.33406
$243$	−920240.	+	21161.5i	−0.999736	+	0.0229896i
$244$	−707423.			−0.760685
$245$	−660499.	−	1.14402e6i	−0.703002	−	1.21764i
$246$	413010.	−	1899.16i	0.435134	−	0.00200090i
$247$	623622.	−	1.08014e6i	0.650398	−	1.12652i
$248$	117989.	−	204363.i	0.121818	−	0.210996i
$249$	−83117.4	−	142447.i	−0.0849559	−	0.145598i
$250$	460116.	+	796944.i	0.465604	+	0.806450i
$251$	−510893.			−0.511854			−0.255927	−	0.966696i	$-0.582381\pi$
$251$	−510893.			−0.511854			−0.255927	+	0.966696i	$0.582381\pi$
$252$	−250246.	+	2301.49i	−0.248236	+	0.00228301i
$253$	2109.69			0.00207213
$254$	880577.	+	1.52520e6i	0.856412	+	1.48335i
$255$	382718.	−	669982.i	0.368577	−	0.645228i
$256$	−674183.	+	1.16772e6i	−0.642951	+	1.11362i
$257$	−919950.	+	1.59340e6i	−0.868823	+	1.50485i	−0.00562328	+	0.999984i	$0.501790\pi$
$257$	−919950.	+	1.59340e6i	−0.868823	+	1.50485i	−0.863200	+	0.504862i	$0.831543\pi$
$258$	498215.	−	872171.i	0.465980	−	0.815741i
$259$	4996.81	+	8654.72i	0.00462853	+	0.00801685i
$260$	1.32263e6			1.21340
$261$	595078.	+	1.00916e6i	0.540720	+	0.916975i
$262$	−1.30920e6			−1.17829
$263$	−408180.	−	706988.i	−0.363883	−	0.630264i	0.624713	−	0.780854i	$-0.285216\pi$
$263$	−408180.	−	706988.i	−0.363883	−	0.630264i	−0.988596	+	0.150590i	$0.951883\pi$
$264$	3195.05	+	5475.68i	0.00282142	+	0.00483536i
$265$	88566.8	−	153402.i	0.0774740	−	0.134189i
$266$	320508.	−	555135.i	0.277737	−	0.481055i
$267$	1.94160e6	−	8928.18i	1.66680	−	0.00766452i
$268$	−523521.	−	906766.i	−0.445243	−	0.771184i
$269$	1.25381e6			1.05646			0.528228	−	0.849103i	$-0.322857\pi$
$269$	1.25381e6			1.05646			0.528228	+	0.849103i	$0.322857\pi$
$270$	2.50002e6	−	34489.9i	2.08706	−	0.0287927i
$271$	−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
$273$	−388798.	+	1787.83i	−0.315731	+	0.00145184i
$274$	−181046.	+	313581.i	−0.145684	+	0.252333i
$275$	17371.3	−	30088.0i	0.0138516	−	0.0239917i
$276$	−53881.9	−	92343.0i	−0.0425766	−	0.0729678i
$277$	141233.	+	244622.i	0.110595	+	0.191556i	0.916010	−	0.401155i	$-0.131391\pi$
$277$	141233.	+	244622.i	0.110595	+	0.191556i	−0.805415	+	0.592711i	$0.798058\pi$
$278$	−1.43773e6			−1.11575
$279$	−533328.	+	943689.i	−0.410189	+	0.725803i
$280$	−190587.			−0.145278
$281$	614335.	+	1.06406e6i	0.464130	+	0.803897i	0.999162	−	0.0409352i	$-0.0130337\pi$
$281$	614335.	+	1.06406e6i	0.464130	+	0.803897i	−0.535032	+	0.844832i	$0.679700\pi$
$282$	−1.05016e6	+	1.83840e6i	−0.786381	+	1.37663i
$283$	223824.	−	387674.i	0.166127	−	0.287741i	−0.770928	−	0.636922i	$-0.780207\pi$
$283$	223824.	−	387674.i	0.166127	−	0.287741i	0.937055	+	0.349182i	$0.113540\pi$
$284$	408089.	−	706830.i	0.300233	−	0.520019i
$285$	−1.39301e6	+	2.43859e6i	−1.01588	+	1.77839i
$286$	−17564.7	−	30422.9i	−0.0126977	−	0.0219931i
$287$	144617.			0.103637
$288$	879939.	−	1.55699e6i	0.625131	−	1.10613i
$289$	−1.09935e6			−0.774270
$290$	−1.59110e6	−	2.75587e6i	−1.11097	−	1.92426i
$291$	−1.28047e6	−	2.19448e6i	−0.886418	−	1.51915i
$292$	−410135.	+	710375.i	−0.281494	+	0.487562i
$293$	699361.	−	1.21133e6i	0.475918	−	0.824314i	−0.523701	−	0.851902i	$-0.675449\pi$
$293$	699361.	−	1.21133e6i	0.475918	−	0.824314i	0.999619	+	0.0275878i	$0.00878258\pi$
$294$	1.77805e6	−	8176.11i	1.19971	−	0.00551669i
$295$	88245.1	+	152845.i	0.0590386	+	0.102258i
$296$	−12829.7			−0.00851116
$297$	−14907.2	−	25016.6i	−0.00980628	−	0.0164565i
$298$	366478.			0.239060
$299$	−83051.1	−	143849.i	−0.0537239	−	0.0930525i
$300$	−1.76065e6	+	8096.07i	−1.12945	+	0.00519363i
$301$	175852.	−	304585.i	0.111875	−	0.193772i
$302$	−852836.	+	1.47716e6i	−0.538082	+	0.931985i
$303$	−1.46009e6	−	2.50230e6i	−0.913635	−	1.56579i
$304$	1.23546e6	+	2.13988e6i	0.766735	+	1.32802i
$305$	2.47476e6			1.52329
$306$	527531.	+	894608.i	0.322066	+	0.546172i
$307$	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
$309$	−377467.	+	660790.i	−0.224896	+	0.393702i
$310$	1.47216e6	−	2.54986e6i	0.870065	−	1.50700i
$311$	−1.48208e6	+	2.56704e6i	−0.868903	+	1.50498i	−0.00578452	+	0.999983i	$0.501841\pi$
$311$	−1.48208e6	+	2.56704e6i	−0.868903	+	1.50498i	−0.863119	+	0.505001i	$0.831492\pi$
$312$	247580.	−	433412.i	0.143989	−	0.252066i
$313$	414425.	+	717806.i	0.239103	+	0.414139i	0.960457	−	0.278428i	$-0.0898132\pi$
$313$	414425.	+	717806.i	0.239103	+	0.414139i	−0.721354	+	0.692567i	$0.756480\pi$
$314$	1.21694e6			0.696540
$315$	875427.	−	8051.21i	0.497100	−	0.00457178i
$316$	2.20283e6			1.24098
$317$	−165751.	−	287090.i	−0.0926423	−	0.160461i	0.815980	−	0.578080i	$-0.196198\pi$
$317$	−165751.	−	287090.i	−0.0926423	−	0.160461i	−0.908622	+	0.417619i	$0.862865\pi$
$318$	120160.	+	205930.i	0.0666332	+	0.114196i
$319$	−18532.1	+	32098.5i	−0.0101964	+	0.0176607i
$320$	−751461.	+	1.30157e6i	−0.410234	+	0.710546i
$321$	−2.05519e6	+	9450.49i	−1.11324	+	0.00511908i
$322$	−42683.7	−	73930.4i	−0.0229415	−	0.0397359i
$323$	−1.16657e6			−0.622162
$324$	−714265.	+	1.29143e6i	−0.378004	+	0.683452i
$325$	−2.73539e6			−1.43652
$326$	98656.8	+	170879.i	0.0514142	+	0.0890520i
$327$	2.54065e6	−	11682.8i	1.31394	−	0.00604195i
$328$	−92829.1	+	160785.i	−0.0476430	+	0.0825202i
$329$	−370669.	+	642018.i	−0.188798	+	0.327007i
$330$	39864.9	+	68320.6i	0.0201514	+	0.0345356i
$331$	−1.29421e6	−	2.24164e6i	−0.649284	−	1.12459i	−0.983294	−	0.182024i	$-0.941735\pi$
$331$	−1.29421e6	−	2.24164e6i	−0.649284	−	1.12459i	0.334010	−	0.942570i	$-0.391598\pi$
$332$	−264418.			−0.131658
$333$	58931.1	−	541.983i	0.0291228	−	0.000267840i
$334$	958384.			0.470082
$335$	1.83142e6	+	3.17211e6i	0.891611	+	1.54432i
$336$	382058.	−	668827.i	0.184621	−	0.323196i
$337$	880045.	−	1.52428e6i	0.422114	−	0.731124i	−0.574032	−	0.818833i	$-0.694621\pi$
$337$	880045.	−	1.52428e6i	0.422114	−	0.731124i	0.996146	+	0.0877095i	$0.0279547\pi$
$338$	18590.2	−	32199.1i	0.00885099	−	0.0153304i
$339$	1.26439e6	−	2.21344e6i	0.597562	−	1.04609i
$340$	−618537.	−	1.07134e6i	−0.290181	−	0.502607i
$341$	−34293.6			−0.0159708
$342$	−1.92010e6	−	3.25618e6i	−0.887684	−	1.50537i
$343$	1.31515e6			0.603587
$344$	225758.	+	391024.i	0.102860	+	0.178159i
$345$	188493.	+	323041.i	0.0852606	+	0.146120i
$346$	−2.00732e6	+	3.47678e6i	−0.901417	+	1.56130i
$347$	782422.	−	1.35520e6i	0.348833	−	0.604197i	−0.637209	−	0.770691i	$-0.719911\pi$
$347$	782422.	−	1.35520e6i	0.348833	−	0.604197i	0.986042	+	0.166494i	$0.0532447\pi$
$348$	1.87829e6	−	8637.06i	0.831410	−	0.00382312i
$349$	−360712.	−	624772.i	−0.158525	−	0.274573i	0.775812	−	0.630964i	$-0.217340\pi$
$349$	−360712.	−	624772.i	−0.158525	−	0.274573i	−0.934337	+	0.356391i	$0.884007\pi$
$350$	−1.40584e6			−0.613432
$351$	−1.11891e6	+	2.00126e6i	−0.484759	+	0.867032i
$352$	56581.0			0.0243396
$353$	−880430.	−	1.52495e6i	−0.376061	−	0.651356i	0.614424	−	0.788976i	$-0.289388\pi$
$353$	−880430.	−	1.52495e6i	−0.376061	−	0.651356i	−0.990485	+	0.137619i	$0.956055\pi$
$354$	−237554.	+	1092.36i	−0.100752	+	0.000463295i
$355$	−1.42760e6	+	2.47268e6i	−0.601225	+	1.04135i
$356$	1.55648e6	−	2.69591e6i	0.650908	−	1.12741i
$357$	183272.	+	314093.i	0.0761073	+	0.130433i
$358$	−1.37932e6	−	2.38906e6i	−0.568799	−	0.985189i
$359$	−2.43938e6			−0.998947			−0.499474	−	0.866329i	$-0.666473\pi$
$359$	−2.43938e6			−0.998947			−0.499474	+	0.866329i	$0.666473\pi$
$360$	−552983.	+	978467.i	−0.224882	+	0.397914i
$361$	1.76995e6			0.714814
$362$	−1.65165e6	−	2.86073e6i	−0.662438	−	1.14738i
$363$	−1.24480e6	+	2.17914e6i	−0.495830	+	0.867997i
$364$	−311679.	+	539844.i	−0.123297	+	0.213558i
$365$	1.43476e6	−	2.48508e6i	0.563699	−	0.976356i
$366$	−1.65224e6	+	2.89239e6i	−0.644717	+	1.12864i
$367$	2.27310e6	+	3.93713e6i	0.880956	+	1.52586i	0.850280	+	0.526331i	$0.176433\pi$
$367$	2.27310e6	+	3.93713e6i	0.880956	+	1.52586i	0.0306760	+	0.999529i	$0.490234\pi$
$368$	329066.			0.126667
$369$	419601.	−	742456.i	0.160424	−	0.283860i
$370$	−160078.			−0.0607893
$371$	41741.8	+	72299.0i	0.0157448	+	0.0272708i
$372$	875865.	+	1.50106e6i	0.328156	+	0.562394i
$373$	166277.	−	288000.i	0.0618814	−	0.107182i	−0.833425	−	0.552633i	$-0.813623\pi$
$373$	166277.	−	288000.i	0.0618814	−	0.107182i	0.895306	+	0.445451i	$0.146957\pi$
$374$	−16428.5	+	28455.0i	−0.00607323	+	0.0105191i
$375$	1.90014e6	−	8737.52i	0.697763	−	0.00320856i
$376$	−475863.	−	824219.i	−0.173585	−	0.300658i
$377$	2.91817e6			1.05744
$378$	−575056.	+	1.02854e6i	−0.207005	+	0.370246i
$379$	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
$381$	3.63652e6	−	16722.0i	1.28343	−	0.00590169i
$382$	−577206.	+	999750.i	−0.202382	+	0.350536i
$383$	1.82779e6	−	3.16582e6i	0.636690	−	1.10278i	−0.349464	−	0.936950i	$-0.613636\pi$
$383$	1.82779e6	−	3.16582e6i	0.636690	−	1.10278i	0.986154	−	0.165830i	$-0.0530303\pi$
$384$	830742.	+	1.42373e6i	0.287500	+	0.492718i
$385$	13848.5	+	23986.4i	0.00476159	+	0.00824731i
$386$	2.93146e6			1.00142
$387$	−1.05350e6	−	1.78656e6i	−0.357565	−	0.606374i
$388$	−4.07352e6			−1.37370
$389$	−1.41448e6	−	2.44995e6i	−0.473939	−	0.820886i	0.525616	−	0.850722i	$-0.323835\pi$
$389$	−1.41448e6	−	2.44995e6i	−0.473939	−	0.820886i	−0.999555	+	0.0298360i	$0.990502\pi$
$390$	3.08908e6	−	5.40773e6i	1.02841	−	1.80033i
$391$	−77679.0	+	134544.i	−0.0256958	+	0.0445064i
$392$	−399639.	+	692195.i	−0.131357	+	0.227517i
$393$	−1.34089e6	+	2.34735e6i	−0.437937	+	0.766648i
$394$	−439688.	−	761563.i	−0.142694	−	0.247153i
$395$	−7.70610e6			−2.48509
$396$	−46687.7	+	429.382i	−0.0149611	+	0.000137596i
$397$	−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
$399$	−667072.	−	1.14323e6i	−0.209769	−	0.359502i
$400$	2.70955e6	−	4.69308e6i	0.846735	−	1.46659i
$401$	−1.81834e6	+	3.14946e6i	−0.564695	+	0.978081i	0.432383	+	0.901690i	$0.357673\pi$
$401$	−1.81834e6	+	3.14946e6i	−0.564695	+	0.978081i	−0.997078	+	0.0763908i	$0.975660\pi$
$402$	−4.93015e6	+	22670.6i	−1.52158	+	0.00699676i
$403$	1.35002e6	+	2.33830e6i	0.414073	+	0.717195i
$404$	−4.64492e6			−1.41587
$405$	2.49869e6	−	4.51776e6i	0.756963	−	1.36863i
$406$	1.49978e6			0.451557
$407$	932.241	+	1614.69i	0.000278960	+	0.000483173i
$408$	−466850.	+	2146.74i	−0.138844	+	0.000638454i
$409$	2.44052e6	−	4.22711e6i	0.721397	−	1.24950i	−0.239043	−	0.971009i	$-0.576834\pi$
$409$	2.44052e6	−	4.22711e6i	0.721397	−	1.24950i	0.960440	−	0.278487i	$-0.0898329\pi$
$410$	−1.15824e6	+	2.00613e6i	−0.340281	+	0.589384i
$411$	376811.	+	645780.i	0.110032	+	0.188573i
$412$	610050.	+	1.05664e6i	0.177061	+	0.306678i
$413$	−83180.4			−0.0239964
$414$	−503401.	+	4629.73i	−0.144349	+	0.00132756i
$415$	925005.			0.263648
$416$	−2.22739e6	−	3.85796e6i	−0.631050	−	1.09301i
$417$	−1.47253e6	+	2.57780e6i	−0.414691	+	0.725954i
$418$	59796.2	−	103570.i	0.0167391	−	0.0289930i
$419$	390244.	−	675923.i	0.108593	−	0.188088i	−0.806608	−	0.591087i	$-0.798699\pi$
$419$	390244.	−	675923.i	0.108593	−	0.188088i	0.915200	+	0.402999i	$0.132032\pi$
$420$	696210.	−	1.21878e6i	0.192583	−	0.337134i
$421$	−1.38356e6	−	2.39639e6i	−0.380446	−	0.658951i	0.610680	−	0.791877i	$-0.290896\pi$
$421$	−1.38356e6	−	2.39639e6i	−0.380446	−	0.658951i	−0.991126	+	0.132926i	$0.957563\pi$
$422$	8.93857e6			2.44336
$423$	2.22061e6	+	3.76579e6i	0.603422	+	1.02331i
$424$	−107176.			−0.0289523
$425$	1.27923e6	+	2.21569e6i	0.343538	+	0.595026i
$426$	−1.93685e6	−	3.31937e6i	−0.517096	−	0.886201i
$427$	−583180.	+	1.01010e6i	−0.154787	+	0.268098i
$428$	−1.64754e6	+	2.85362e6i	−0.434737	+	0.752987i
$429$	−72536.9	+	333.550i	−0.0190290	+	8.75021e-5i
$430$	2.81680e6	+	4.87885e6i	0.734659	+	1.27247i
$431$	893280.			0.231630			0.115815	−	0.993271i	$-0.463052\pi$
$431$	893280.			0.231630			0.115815	+	0.993271i	$0.463052\pi$
$432$	−2.32520e6	−	3.90205e6i	−0.599447	−	1.00597i
$433$	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
$435$	−6.57077e6	+	30214.7i	−1.66492	+	0.00765589i
$436$	2.03671e6	−	3.52768e6i	0.513112	−	0.888736i
$437$	282735.	−	489711.i	0.0708232	−	0.122669i
$438$	1.94656e6	+	3.33602e6i	0.484822	+	0.830889i
$439$	116736.	+	202192.i	0.0289096	+	0.0500729i	0.880118	−	0.474755i	$-0.157463\pi$
$439$	116736.	+	202192.i	0.0289096	+	0.0500729i	−0.851209	+	0.524827i	$0.824130\pi$
$440$	−35557.3			−0.00875584
$441$	1.80643e6	−	3.19635e6i	0.442307	−	0.782633i
$442$	2.58693e6			0.629839
$443$	1.30744e6	+	2.26456e6i	0.316529	+	0.548244i	0.979761	−	0.200170i	$-0.0641493\pi$
$443$	1.30744e6	+	2.26456e6i	0.316529	+	0.548244i	−0.663233	+	0.748413i	$0.730816\pi$
$444$	46866.7	−	82044.5i	0.0112826	−	0.0197511i
$445$	−5.44500e6	+	9.43101e6i	−1.30346	+	2.25766i
$446$	3.07537e6	−	5.32669e6i	0.732082	−	1.26800i
$447$	375348.	−	657082.i	0.0888517	−	0.155543i
$448$	−354166.	−	613433.i	−0.0833704	−	0.144402i
$449$	−8.32454e6			−1.94870			−0.974349	−	0.225044i	$-0.927747\pi$
$449$	−8.32454e6			−1.94870			−0.974349	+	0.225044i	$0.927747\pi$
$450$	−4.07900e6	+	7.21753e6i	−0.949561	+	1.68019i
$451$	26980.8			0.00624616
$452$	−2.04347e6	−	3.53940e6i	−0.470460	−	0.814861i
$453$	1.77501e6	+	3.04201e6i	0.406401	+	0.696491i
$454$	1.41705e6	−	2.45441e6i	0.322661	−	0.558865i
$455$	1.09034e6	−	1.88852e6i	0.246906	−	0.427654i
$456$	1.69923e6	−	7813.67i	0.382684	−	0.00175972i
$457$	−398114.	−	689554.i	−0.0891697	−	0.154446i	0.817991	−	0.575231i	$-0.195088\pi$
$457$	−398114.	−	689554.i	−0.0891697	−	0.154446i	−0.907160	+	0.420785i	$0.861755\pi$
$458$	949500.			0.211510
$459$	2.14430e6	−	29582.4i	0.475065	−	0.00655393i
$460$	599646.			0.132130
$461$	−700324.	−	1.21300e6i	−0.153478	−	0.265832i	0.779026	−	0.626992i	$-0.215714\pi$
$461$	−700324.	−	1.21300e6i	−0.153478	−	0.265832i	−0.932504	+	0.361160i	$0.882381\pi$
$462$	−37280.0	+	171.427i	−0.00812589	+	3.73657e-5i
$463$	−574265.	+	994656.i	−0.124497	+	0.215635i	−0.921536	−	0.388292i	$-0.873065\pi$
$463$	−574265.	+	994656.i	−0.124497	+	0.215635i	0.797039	+	0.603928i	$0.206398\pi$
$464$	−2.89061e6	+	5.00668e6i	−0.623296	+	1.07958i
$465$	−3.06401e6	−	5.25111e6i	−0.657140	−	1.12621i
$466$	−1.59882e6	−	2.76923e6i	−0.341063	−	0.590738i
$467$	5.64483e6			1.19773			0.598865	−	0.800850i	$-0.295619\pi$
$467$	5.64483e6			1.19773			0.598865	+	0.800850i	$0.295619\pi$
$468$	1.86721e6	+	3.16649e6i	0.394075	+	0.668287i
$469$	−1.72631e6			−0.362398
$470$	−5.93739e6	−	1.02839e7i	−1.23980	−	2.14739i
$471$	1.24640e6	−	2.18193e6i	0.258883	−	0.453199i
$472$	53393.3	−	92479.9i	0.0110314	−	0.0191070i
$473$	32808.3	−	56825.6i	0.00674265	−	0.0116786i
$474$	5.14487e6	−	9.00657e6i	1.05179	−	1.84125i
$475$	−4.65611e6	−	8.06462e6i	−0.946867	−	1.64002i
$476$	583037.			0.117945
$477$	492292.	−	4527.56i	0.0990666	−	0.000911106i
$478$	−9.23920e6			−1.84954
$479$	2.85304e6	+	4.94162e6i	0.568159	+	0.984080i	0.996748	+	0.0805805i	$0.0256774\pi$
$479$	2.85304e6	+	4.94162e6i	0.568159	+	0.984080i	−0.428589	+	0.903499i	$0.640989\pi$
$480$	5.05531e6	+	8.66381e6i	1.00149	+	1.71635i
$481$	73398.1	−	127129.i	0.0144651	−	0.0250543i
$482$	−2.86346e6	+	4.95967e6i	−0.561402	+	0.972377i
$483$	−176271.	+	810.557i	−0.0343806	+	0.000158094i
$484$	2.01181e6	+	3.48456e6i	0.390367	+	0.676136i
$485$	1.42503e7			2.75086
$486$	3.61196e6	+	5.93658e6i	0.693668	+	1.14011i
$487$	−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
$489$	407423.	−	1873.48i	0.0770502	−	0.000354304i
$490$	−4.98634e6	+	8.63659e6i	−0.938191	+	1.62499i
$491$	−479847.	+	831119.i	−0.0898253	+	0.155582i	−0.907437	−	0.420188i	$-0.861964\pi$
$491$	−479847.	+	831119.i	−0.0898253	+	0.155582i	0.817612	+	0.575770i	$0.195298\pi$
$492$	−689095.	−	1.18097e6i	−0.128341	−	0.219952i
$493$	−1.36471e6	−	2.36374e6i	−0.252884	−	0.438009i
$494$	−9.41588e6			−1.73597
$495$	163326.	−	1502.09i	0.0299600	−	0.000275540i
$496$	−5.34906e6			−0.976278
$497$	−672834.	−	1.16538e6i	−0.122185	−	0.211630i
$498$	−617566.	+	1.08111e6i	−0.111586	+	0.195342i
$499$	1.13098e6	−	1.95891e6i	0.203331	−	0.352179i	−0.746269	−	0.665645i	$-0.768157\pi$
$499$	1.13098e6	−	1.95891e6i	0.203331	−	0.352179i	0.949600	+	0.313466i	$0.101490\pi$
$500$	1.52325e6	−	2.63834e6i	0.272487	−	0.471961i
$501$	981580.	−	1.71835e6i	0.174715	−	0.305855i
$502$	1.92846e6	+	3.34018e6i	0.341547	+	0.591577i
$503$	−997842.			−0.175850			−0.0879249	−	0.996127i	$-0.528024\pi$
$503$	−997842.			−0.175850			−0.0879249	+	0.996127i	$0.528024\pi$
$504$	−269060.	−	456283.i	−0.0471816	−	0.0800125i
$505$	1.62492e7			2.83532
$506$	−7963.39	−	13793.0i	−0.00138268	−	0.00239487i
$507$	−38691.7	−	66309.9i	−0.00668494	−	0.0114567i
$508$	2.91521e6	−	5.04930e6i	0.501200	−	0.868104i
$509$	−1.03760e6	+	1.79718e6i	−0.177516	+	0.307466i	−0.941029	−	0.338326i	$-0.890139\pi$
$509$	−1.03760e6	+	1.79718e6i	−0.177516	+	0.307466i	0.763513	+	0.645792i	$0.223473\pi$
$510$	−5.82493e6	+	26785.1i	−0.991666	+	0.00456003i
$511$	676208.	+	1.17123e6i	0.114559	+	0.198421i
$512$	6.79550e6			1.14564
$513$	−7.80478e6	+	107673.i	−1.30938	+	0.0180641i
$514$	1.38901e7			2.31897
$515$	−2.13412e6	−	3.69640e6i	−0.354569	−	0.614131i
$516$	−3.32524e6	+	15290.6i	−0.549792	+	0.00252814i
$517$	−69154.8	+	119780.i	−0.0113788	+	0.0197086i
$518$	37722.6	−	65337.5i	0.00617700	−	0.0106989i
$519$	4.17783e6	+	7.15997e6i	0.680819	+	1.16679i
$520$	1.39977e6	+	2.42447e6i	0.227012	+	0.393196i
$521$	−4.77686e6			−0.770989			−0.385494	−	0.922710i	$-0.625969\pi$
$521$	−4.77686e6			−0.770989			−0.385494	+	0.922710i	$0.625969\pi$
$522$	4.35157e6	−	7.69982e6i	0.698988	−	1.23681i
$523$	−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
$525$	−1.43987e6	+	2.52062e6i	−0.227994	+	0.399125i
$526$	−3.08149e6	+	5.33730e6i	−0.485620	+	0.841119i
$527$	1.26269e6	−	2.18705e6i	0.198048	−	0.343030i
$528$	71279.5	−	124781.i	0.0111270	−	0.0194789i
$529$	3.18052e6	+	5.50882e6i	0.494150	+	0.855893i
$530$	−1.33724e6			−0.206786
$531$	−241345.	+	427045.i	−0.0371452	+	0.0657260i
$532$	−2.12213e6			−0.325082
$533$	−1.06214e6	−	1.83968e6i	−0.161943	−	0.280494i
$534$	−7.38729e6	−	1.26604e7i	−1.12107	−	1.92129i
$535$	5.76354e6	−	9.98274e6i	0.870572	−	1.50787i
$536$	1.10811e6	−	1.91931e6i	0.166599	−	0.288557i
$537$	−5.69620e6	+	26193.1i	−0.852412	+	0.00391969i
$538$	−4.73273e6	−	8.19732e6i	−0.704946	−	1.22100i
$539$	116155.			0.0172213
$540$	−4.23713e6	−	7.11057e6i	−0.625299	−	1.04935i
$541$	−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
$543$	−6.82081e6	+	31364.5i	−0.992742	+	0.00456498i
$544$	−2.08332e6	+	3.60841e6i	−0.301827	+	0.522780i
$545$	−7.12494e6	+	1.23408e7i	−1.02752	+	1.77972i
$546$	1.47927e6	+	2.53518e6i	0.212357	+	0.363938i
$547$	−2.49201e6	−	4.31630e6i	−0.356108	−	0.616798i	0.631199	−	0.775621i	$-0.282563\pi$
$547$	−2.49201e6	−	4.31630e6i	−0.356108	−	0.616798i	−0.987307	+	0.158823i	$0.949230\pi$
$548$	1.19873e6			0.170518
$549$	3.49372e6	+	5.92479e6i	0.494717	+	0.838962i
$550$	−262284.			−0.0369713
$551$	4.96724e6	+	8.60351e6i	0.697005	+	1.20725i
$552$	112247.	−	196498.i	0.0156793	−	0.0274480i
$553$	1.81596e6	−	3.14533e6i	0.252518	−	0.437374i
$554$	1.06622e6	−	1.84674e6i	0.147595	−	0.255641i
$555$	−163952.	+	287014.i	−0.0225936	+	0.0395522i
$556$	2.37986e6	+	4.12204e6i	0.326486	+	0.565490i
$557$	−9.32179e6			−1.27310			−0.636548	−	0.771237i	$-0.719638\pi$
$557$	−9.32179e6			−1.27310			−0.636548	+	0.771237i	$0.719638\pi$
$558$	8.18292e6	−	75257.5i	1.11256	−	0.0102321i
$559$	−5.16619e6			−0.699263
$560$	2.16008e6	+	3.74136e6i	0.291071	+	0.504150i
$561$	34192.6	+	58599.4i	0.00458697	+	0.00786116i
$562$	4.63783e6	−	8.03296e6i	0.619404	−	1.07284i
$563$	6.18276e6	−	1.07088e7i	0.822074	−	1.42387i	−0.0820605	−	0.996627i	$-0.526150\pi$
$563$	6.18276e6	−	1.07088e7i	0.822074	−	1.42387i	0.904135	−	0.427247i	$-0.140517\pi$
$564$	7.00909e6	−	32230.3i	0.927820	−	0.00426644i
$565$	7.14862e6	+	1.23818e7i	0.942109	+	1.63178i
$566$	−3.37945e6			−0.443409
$567$	1.25515e6	+	2.08449e6i	0.163960	+	0.272296i
$568$	1.72756e6			0.224679
$569$	1.15181e6	+	1.99499e6i	0.149141	+	0.258321i	0.930910	−	0.365248i	$-0.119016\pi$
$569$	1.15181e6	+	1.99499e6i	0.149141	+	0.258321i	−0.781769	+	0.623568i	$0.785682\pi$
$570$	2.12015e7	−	97491.9i	2.73325	−	0.0125684i
$571$	5.92568e6	−	1.02636e7i	0.760585	−	1.31737i	−0.181964	−	0.983305i	$-0.558245\pi$
$571$	5.92568e6	−	1.02636e7i	0.760585	−	1.31737i	0.942549	−	0.334067i	$-0.108421\pi$
$572$	−58149.1	+	100717.i	−0.00743110	+	0.0128710i
$573$	1.20134e6	+	2.05886e6i	0.152855	+	0.261963i
$574$	−545881.	−	945494.i	−0.0691542	−	0.119779i
$575$	−1.24016e6			−0.156426
$576$	−4.17694e6	+	38414.9i	−0.524569	+	0.00482441i
$577$	−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
$579$	3.00241e6	−	5.25600e6i	0.372198	−	0.651566i
$580$	−5.26745e6	+	9.12350e6i	−0.650176	+	1.12614i
$581$	−217979.	+	377551.i	−0.0267901	+	0.0464018i
$582$	−9.51398e6	+	1.66551e7i	−1.16427	+	2.03817i
$583$	7787.66	+	13488.6i	0.000948933	+	0.00164360i
$584$	−1.73622e6			−0.210656
$585$	−6.53200e6	−	1.10772e7i	−0.789144	−	1.33826i
$586$	−1.05594e7			−1.27027
$587$	−3.72719e6	−	6.45569e6i	−0.446464	−	0.773299i	0.551689	−	0.834050i	$-0.313984\pi$
$587$	−3.72719e6	−	6.45569e6i	−0.446464	−	0.773299i	−0.998153	+	0.0607515i	$0.980650\pi$
$588$	−2.96663e6	−	5.08421e6i	−0.353850	−	0.606430i
$589$	−4.59593e6	+	7.96038e6i	−0.545865	+	0.945465i
$590$	666193.	−	1.15388e6i	0.0787899	−	0.136468i
$591$	−1.81578e6	+	8349.61i	−0.213843	+	0.000983326i
$592$	145410.	+	251857.i	0.0170525	+	0.0295359i
$593$	3.98887e6			0.465815			0.232908	−	0.972499i	$-0.425176\pi$
$593$	3.98887e6			0.465815			0.232908	+	0.972499i	$0.425176\pi$
$594$	−107287.	+	191891.i	−0.0124761	+	0.0223146i
$595$	−2.03962e6			−0.236187
$596$	−606627.	−	1.05071e6i	−0.0699529	−	0.121162i
$597$	1.41064e7	−	64866.2i	1.61987	−	0.00744873i
$598$	−626982.	+	1.08596e6i	−0.0716972	+	0.124183i
$599$	6.35985e6	−	1.10156e7i	0.724236	−	1.25441i	−0.235052	−	0.971983i	$-0.575526\pi$
$599$	6.35985e6	−	1.10156e7i	0.724236	−	1.25441i	0.959288	−	0.282430i	$-0.0911405\pi$
$600$	−1.87818e6	−	3.21882e6i	−0.212989	−	0.365022i
$601$	−1.55315e6	−	2.69013e6i	−0.175399	−	0.303800i	0.764900	−	0.644149i	$-0.222788\pi$
$601$	−1.55315e6	−	2.69013e6i	−0.175399	−	0.303800i	−0.940299	+	0.340349i	$0.889455\pi$
$602$	−2.65514e6			−0.298604
$603$	−5.00882e6	+	8.86278e6i	−0.560974	+	0.992606i
$604$	5.64675e6			0.629806
$605$	−7.03785e6	−	1.21899e7i	−0.781720	−	1.35398i
$606$	−1.08485e7	+	1.89913e7i	−1.20002	+	2.10075i
$607$	−6.20584e6	+	1.07488e7i	−0.683642	+	1.18410i	0.290219	+	0.956960i	$0.406272\pi$
$607$	−6.20584e6	+	1.07488e7i	−0.683642	+	1.18410i	−0.973861	+	0.227143i	$0.927062\pi$
$608$	7.58282e6	−	1.31338e7i	0.831902	−	1.44090i
$609$	1.53608e6	−	2.68905e6i	0.167831	−	0.293803i
$610$	−9.34140e6	−	1.61798e7i	−1.01645	−	1.76055i
$611$	1.08895e7			1.18007
$612$	1.69166e6	−	2.99329e6i	0.182573	−	0.323050i
$613$	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
$615$	2.41064e6	+	4.13136e6i	0.257006	+	0.440458i
$616$	8379.15	−	14513.1i	0.000889709	−	0.00154102i
$617$	−3.60754e6	+	6.24844e6i	−0.381503	+	0.660782i	−0.991277	−	0.131793i	$-0.957927\pi$
$617$	−3.60754e6	+	6.24844e6i	−0.381503	+	0.660782i	0.609774	+	0.792575i	$0.291260\pi$
$618$	5.74501e6	−	26417.6i	0.605090	−	0.00278242i
$619$	6.36680e6	+	1.10276e7i	0.667874	+	1.15679i	0.978497	+	0.206259i	$0.0661290\pi$
$619$	6.36680e6	+	1.10276e7i	0.667874	+	1.15679i	−0.310623	+	0.950533i	$0.600538\pi$
$620$	−9.74741e6			−1.01838
$621$	−507284.	+	907321.i	−0.0527864	+	0.0944130i
$622$	2.23775e7			2.31919
$623$	−2.56625e6	−	4.44487e6i	−0.264898	−	0.458816i
$624$	−1.13142e7	+	52026.7i	−1.16322	+	0.00534891i
$625$	1.73251e6	−	3.00079e6i	0.177409	−	0.307281i
$626$	3.12864e6	−	5.41897e6i	0.319095	−	0.552689i
$627$	−124454.	−	213289.i	−0.0126427	−	0.0216671i
$628$	−2.01439e6	−	3.48903e6i	−0.203819	−	0.353025i
$629$	−137301.			−0.0138372
$630$	−3.35709e6	−	5.69309e6i	−0.336986	−	0.571474i
$631$	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
$633$	9.15491e6	−	1.60265e7i	0.908124	−	1.58975i
$634$	−1.25132e6	+	2.16734e6i	−0.123636	+	0.214143i
$635$	−1.01982e7	+	1.76638e7i	−1.00367	+	1.73840i
$636$	391511.	−	685376.i	0.0383796	−	0.0671871i
$637$	−4.57262e6	−	7.92001e6i	−0.446495	−	0.773352i
$638$	279810.			0.0272152
$639$	−7.93523e6	+	72979.6i	−0.768790	+	0.00707048i
$640$	−9.24524e6			−0.892212
$641$	7.33397e6	+	1.27028e7i	0.705008	+	1.22111i	0.966689	+	0.255956i	$0.0823901\pi$
$641$	7.33397e6	+	1.27028e7i	0.705008	+	1.22111i	−0.261680	+	0.965155i	$0.584277\pi$
$642$	7.81946e6	+	1.34010e7i	0.748754	+	1.28322i
$643$	−6.46256e6	+	1.11935e7i	−0.616420	+	1.06767i	0.373713	+	0.927544i	$0.378084\pi$
$643$	−6.46256e6	+	1.11935e7i	−0.616420	+	1.06767i	−0.990134	+	0.140127i	$0.955249\pi$
$644$	−141308.	+	244752.i	−0.0134261	+	0.0232547i
$645$	1.16326e7	−	53490.7i	1.10097	−	0.00506266i
$646$	4.40341e6	+	7.62693e6i	0.415153	+	0.719065i
$647$	−6.80424e6			−0.639027			−0.319513	−	0.947582i	$-0.603519\pi$
$647$	−6.80424e6			−0.639027			−0.319513	+	0.947582i	$0.603519\pi$
$648$	−3.12321e6	+	57452.5i	−0.292189	+	0.00537491i
$649$	−15518.8			−0.00144626
$650$	1.03252e7	+	1.78838e7i	0.958552	+	1.66026i
$651$	2.86533e6	−	13175.8i	0.264986	−	0.00121850i
$652$	326610.	−	565706.i	0.0300892	−	0.0521161i
$653$	844518.	−	1.46275e6i	0.0775043	−	0.134241i	−0.824668	−	0.565617i	$-0.808638\pi$
$653$	844518.	−	1.46275e6i	0.0775043	−	0.134241i	0.902173	+	0.431375i	$0.141972\pi$
$654$	−9.66649e6	−	1.65665e7i	−0.883740	−	1.51456i
$655$	−7.58111e6	−	1.31309e7i	−0.690446	−	1.19589i
$656$	4.20842e6			0.381821
$657$	7.97502e6	−	73345.5i	0.720806	−	0.00662918i
$658$	5.59662e6			0.503920
$659$	3.67278e6	+	6.36143e6i	0.329443	+	0.570613i	0.982402	−	0.186781i	$-0.0598056\pi$
$659$	3.67278e6	+	6.36143e6i	0.329443	+	0.570613i	−0.652958	+	0.757394i	$0.726472\pi$
$660$	129890.	−	227385.i	0.0116069	−	0.0203189i
$661$	4.43977e6	−	7.68990e6i	0.395236	−	0.684569i	−0.597895	−	0.801574i	$-0.703996\pi$
$661$	4.43977e6	−	7.68990e6i	0.395236	−	0.684569i	0.993131	+	0.117005i	$0.0373294\pi$
$662$	−9.77045e6	+	1.69229e7i	−0.866502	+	1.50082i
$663$	2.64955e6	−	4.63827e6i	0.234093	−	0.409801i
$664$	−279840.	−	484697.i	−0.0246314	−	0.0426629i
$665$	7.42377e6			0.650984
$666$	−225989.	−	383241.i	−0.0197425	−	0.0334801i
$667$	1.32303e6			0.115147
$668$	−1.58640e6	−	2.74773e6i	−0.137553	−	0.238250i
$669$	−6.40075e6	−	1.09696e7i	−0.552924	−	0.947603i
$670$	1.38260e7	−	2.39474e7i	1.18990	−	2.06096i
$671$	−108802.	+	188451.i	−0.00932894	+	0.0161582i
$672$	−4.72752e6	+	21738.8i	−0.403841	+	0.00185700i
$673$	3.81952e6	+	6.61560e6i	0.325065	+	0.563030i	0.981526	−	0.191331i	$-0.0612803\pi$
$673$	3.81952e6	+	6.61560e6i	0.325065	+	0.563030i	−0.656460	+	0.754361i	$0.727947\pi$
$674$	−1.32875e7			−1.12666
$675$	8.76303e6	+	1.47057e7i	0.740278	+	1.24230i
$676$	−123088.			−0.0103598
$677$	−9.78051e6	−	1.69403e7i	−0.820143	−	1.42053i	−0.905575	−	0.424186i	$-0.860560\pi$
$677$	−9.78051e6	−	1.69403e7i	−0.820143	−	1.42053i	0.0854320	−	0.996344i	$-0.472773\pi$
$678$	−1.92440e7	+	88490.5i	−1.60776	+	0.00739303i
$679$	−3.35810e6	+	5.81639e6i	−0.279524	+	0.484149i
$680$	1.30923e6	−	2.26765e6i	0.108578	−	0.188063i
$681$	−2.94931e6	−	5.05453e6i	−0.243698	−	0.417651i
$682$	129447.	+	224209.i	0.0106569	+	0.0184583i
$683$	1.08911e7			0.893349			0.446675	−	0.894696i	$-0.352608\pi$
$683$	1.08911e7			0.893349			0.446675	+	0.894696i	$0.352608\pi$
$684$	−6.15729e6	+	1.08949e7i	−0.503210	+	0.890397i
$685$	−4.19349e6			−0.341467
$686$	−4.96426e6	−	8.59835e6i	−0.402758	−	0.697597i
$687$	972482.	−	1.70242e6i	0.0786121	−	0.137618i
$688$	5.11739e6	−	8.86358e6i	0.412171	−	0.713901i
$689$	613146.	−	1.06200e6i	0.0492058	−	0.0852269i
$690$	1.40051e6	−	2.45173e6i	0.111986	−	0.196042i
$691$	8.95944e6	+	1.55182e7i	0.713815	+	1.23636i	0.963415	+	0.268015i	$0.0863677\pi$
$691$	8.95944e6	+	1.55182e7i	0.713815	+	1.23636i	−0.249599	+	0.968349i	$0.580299\pi$
$692$	1.32907e7			1.05508
$693$	−37875.0	+	67017.2i	−0.00299584	+	0.00530095i
$694$	−1.18136e7			−0.931070
$695$	−8.32539e6	−	1.44200e7i	−0.653796	−	1.13241i
$696$	2.00368e6	+	3.43391e6i	0.156785	+	0.268699i
$697$	−993435.	+	1.72068e6i	−0.0774564	+	0.134158i
$698$	−2.72314e6	+	4.71662e6i	−0.211559	+	0.366431i
$699$	−6.60265e6	+	30361.3i	−0.511123	+	0.00235032i
$700$	2.32707e6	+	4.03060e6i	0.179500	+	0.310903i
$701$	−1.32211e7			−1.01619			−0.508094	−	0.861302i	$-0.669650\pi$
$701$	−1.32211e7			−1.01619			−0.508094	+	0.861302i	$0.669650\pi$
$702$	1.73076e7	−	238773.i	1.32554	−	0.0182870i
$703$	499745.			0.0381382
$704$	−66075.8	−	114447.i	−0.00502471	−	0.00870305i
$705$	−2.45197e7	+	112750.i	−1.85798	+	0.00854366i
$706$	−6.64667e6	+	1.15124e7i	−0.501872	+	0.869267i
$707$	−3.82914e6	+	6.63227e6i	−0.288107	+	0.499015i
$708$	396353.	+	679270.i	0.0297166	+	0.0509283i
$709$	501449.	+	868535.i	0.0374637	+	0.0648891i	0.884149	−	0.467204i	$-0.154739\pi$
$709$	501449.	+	868535.i	0.0374637	+	0.0648891i	−0.846686	+	0.532094i	$0.821405\pi$
$710$	2.15550e7			1.60473
$711$	−1.08790e7	−	1.84491e7i	−0.807080	−	1.36868i
$712$	6.58907e6			0.487106
$713$	612065.	+	1.06013e6i	0.0450893	+	0.0780970i
$714$	1.36172e6	−	2.38382e6i	0.0999638	−	0.174996i
$715$	203421.	−	352336.i	0.0148810	−	0.0257746i
$716$	−4.56635e6	+	7.90916e6i	−0.332879	+	0.576564i
$717$	−9.46282e6	+	1.65655e7i	−0.687421	+	1.20339i
$718$	9.20785e6	+	1.59485e7i	0.666572	+	1.15454i
$719$	1.12752e7			0.813394			0.406697	−	0.913563i	$-0.366681\pi$
$719$	1.12752e7			0.813394			0.406697	+	0.913563i	$0.366681\pi$
$720$	2.54754e7	−	234294.i	1.83143	−	0.0168434i
$721$	2.01163e6			0.144116
$722$	−6.68099e6	−	1.15718e7i	−0.476977	−	0.826149i
$723$	5.95972e6	+	1.02138e7i	0.424014	+	0.726677i
$724$	−5.46789e6	+	9.47067e6i	−0.387680	+	0.671482i
$725$	1.08939e7	−	1.88688e7i	0.769729	−	1.33321i
$726$	1.89458e7	−	87119.3i	1.33405	−	0.00613441i
$727$	−9.98334e6	−	1.72917e7i	−0.700551	−	1.21339i	−0.968273	−	0.249894i	$-0.919604\pi$
$727$	−9.98334e6	−	1.72917e7i	−0.700551	−	1.21339i	0.267722	−	0.963496i	$-0.413729\pi$
$728$	−1.31943e6			−0.0922695
$729$	1.43434e7	−	395835.i	0.999619	−	0.0275864i
$730$	−2.16630e7			−1.50457
$731$	2.41601e6	+	4.18465e6i	0.167226	+	0.289645i
$732$	1.10275e7	−	50708.4i	0.760677	−	0.00349786i
$733$	4.06124e6	−	7.03427e6i	0.279189	−	0.483570i	−0.691994	−	0.721903i	$-0.743268\pi$
$733$	4.06124e6	−	7.03427e6i	0.279189	−	0.483570i	0.971183	+	0.238333i	$0.0766011\pi$
$734$	1.71605e7	−	2.97228e7i	1.17568	−	2.03634i
$735$	1.03781e7	+	1.77859e7i	0.708594	+	1.21439i
$736$	−1.00985e6	−	1.74910e6i	−0.0687164	−	0.119020i
$737$	−322072.			−0.0218416
$738$	−6.43798e6	+	59209.5i	−0.435120	+	0.00400175i
$739$	−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
$741$	−9.64377e6	+	1.68823e7i	−0.645211	+	1.12950i
$742$	315124.	−	545810.i	0.0210122	−	0.0363942i
$743$	−1.23128e7	+	2.13263e7i	−0.818245	+	1.41724i	0.0887298	+	0.996056i	$0.471719\pi$
$743$	−1.23128e7	+	2.13263e7i	−0.818245	+	1.41724i	−0.906974	+	0.421186i	$0.861614\pi$
$744$	−1.82460e6	+	3.19413e6i	−0.120847	+	0.211554i
$745$	2.12214e6	+	3.67566e6i	0.140082	+	0.242630i
$746$	−2.51057e6			−0.165168
$747$	1.30587e6	+	2.21455e6i	0.0856245	+	0.145206i
$748$	108776.			0.00710849
$749$	2.71637e6	+	4.70490e6i	0.176923	+	0.306440i
$750$	−7.22954e6	−	1.23900e7i	−0.469308	−	0.804301i
$751$	1.51225e6	−	2.61930e6i	0.0978418	−	0.169467i	−0.812949	−	0.582334i	$-0.802139\pi$
$751$	1.51225e6	−	2.61930e6i	0.0978418	−	0.169467i	0.910791	+	0.412867i	$0.135473\pi$
$752$	−1.07867e7	+	1.86831e7i	−0.695573	+	1.20477i
$753$	7.96396e6	−	36621.1i	0.511848	−	0.00235366i
$754$	−1.10152e7	−	1.90788e7i	−0.705606	−	1.22215i
$755$	−1.97539e7			−1.26120
$756$	3.90074e6	−	53814.0i	0.248223	−	0.00342445i
$757$	−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
$759$	−32886.5	+	151.224i	−0.00207211	+	9.52829e-6i
$760$	−4.76530e6	+	8.25374e6i	−0.299265	+	0.518342i
$761$	−982452.	+	1.70166e6i	−0.0614964	+	0.106515i	−0.895134	−	0.445796i	$-0.852921\pi$
$761$	−982452.	+	1.70166e6i	−0.0614964	+	0.106515i	0.833638	+	0.552311i	$0.186254\pi$
$762$	−1.38360e7	−	2.37122e7i	−0.863224	−	1.47940i
$763$	−3.35801e6	−	5.81624e6i	−0.208819	−	0.361685i
$764$	3.82177e6			0.236881
$765$	−5.91789e6	+	1.04713e7i	−0.365606	+	0.646916i
$766$	−2.75972e7			−1.69939
$767$	610919.	+	1.05814e6i	0.0374969	+	0.0649465i
$768$	1.04257e7	−	1.82511e7i	0.637823	−	1.11657i
$769$	3.90798e6	−	6.76883e6i	0.238307	−	0.412760i	−0.721922	−	0.691975i	$-0.756741\pi$
$769$	3.90798e6	−	6.76883e6i	0.238307	−	0.412760i	0.960229	+	0.279215i	$0.0900742\pi$
$770$	104547.	−	181081.i	0.00635457	−	0.0110064i
$771$	1.42262e7	−	2.49043e7i	0.861894	−	1.50883i
$772$	−4.85241e6	−	8.40461e6i	−0.293031	−	0.507545i
$773$	8.88127e6			0.534597			0.267298	−	0.963614i	$-0.413869\pi$
$773$	8.88127e6			0.534597			0.267298	+	0.963614i	$0.413869\pi$
$774$	−7.70380e6	+	1.36314e7i	−0.462224	+	0.817875i
$775$	2.01591e7			1.20564
$776$	−4.31111e6	−	7.46706e6i	−0.257001	−	0.445139i
$777$	−78512.0	−	134554.i	−0.00466534	−	0.00799548i
$778$	−1.06784e7	+	1.84955e7i	−0.632494	+	1.09551i
$779$	3.61589e6	−	6.26290e6i	0.213487	−	0.369770i
$780$	−2.06175e7	+	94806.5i	−1.21339	+	0.00557958i
$781$	−125529.	−	217422.i	−0.00736404	−	0.0127549i
$782$	1.17285e6			0.0685846
$783$	−9.34858e6	−	1.56884e7i	−0.544931	−	0.914479i
$784$	1.81177e7			1.05272
$785$	7.04688e6	+	1.22055e7i	0.408153	+	0.706941i
$786$	2.04082e7	−	93844.2i	1.17828	−	0.00541815i
$787$	6.53957e6	−	1.13269e7i	0.376368	−	0.651888i	−0.614163	−	0.789179i	$-0.710506\pi$
$787$	6.53957e6	−	1.13269e7i	0.376368	−	0.651888i	0.990531	+	0.137291i	$0.0438395\pi$
$788$	−1.45562e6	+	2.52121e6i	−0.0835089	+	0.144642i
$789$	6.41350e6	+	1.09915e7i	0.366778	+	0.628584i
$790$	2.90880e7	+	5.03820e7i	1.65824	+	2.87215i
$791$	−6.73834e6			−0.382923
$792$	−50197.8	−	85127.5i	−0.00284362	−	0.00482233i
$793$	1.71327e7			0.967481
$794$	1.91247e7	+	3.31250e7i	1.07657	+	1.86468i
$795$	−1.36961e6	+	2.39763e6i	−0.0768562	+	0.134544i
$796$	1.13084e7	−	1.95867e7i	0.632583	−	1.09567i
$797$	9.76620e6	−	1.69155e7i	0.544603	−	0.943279i	−0.454029	−	0.890987i	$-0.650014\pi$
$797$	9.76620e6	−	1.69155e7i	0.544603	−	0.943279i	0.998632	−	0.0522925i	$-0.0166528\pi$
$798$	−4.95637e6	+	8.67659e6i	−0.275522	+	0.482327i
$799$	−5.09257e6	−	8.82060e6i	−0.282209	−	0.488800i
$800$	−3.32605e7			−1.83740
$801$	−3.02656e7	+	278350.i	−1.66674	+	0.0153289i
$802$	2.74546e7			1.50723
$803$	126158.	+	218513.i	0.00690442	+	0.0119588i
$804$	8.22580e6	+	1.40974e7i	0.448785	+	0.769129i
$805$	494332.	−	856208.i	0.0268862	−	0.0465682i
$806$	1.01918e7	−	1.76526e7i	0.552601	−	0.957132i
$807$	−1.95448e7	+	89873.7i	−1.05644	+	0.00485790i
$808$	−4.91583e6	−	8.51448e6i	−0.264892	−	0.458806i
$809$	1.72600e7			0.927194			0.463597	−	0.886046i	$-0.346559\pi$
$809$	1.72600e7			0.927194			0.463597	+	0.886046i	$0.346559\pi$
$810$	−3.89686e7	+	716841.i	−2.08690	+	0.0383893i
$811$	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
$813$	5.41374e6	−	24894.3i	0.287257	−	0.00132091i
$814$	7037.81	−	12189.8i	0.000372286	−	0.000644818i
$815$	−1.14257e6	+	1.97899e6i	−0.0602544	+	0.104364i
$816$	5.33332e6	+	9.14026e6i	0.280396	+	0.480544i
$817$	−8.79375e6	−	1.52312e7i	−0.460913	−	0.798324i
$818$	−3.68487e7			−1.92548
$819$	6.06056e6	−	55738.4i	0.315721	−	0.00290365i
$820$	7.66886e6			0.398287
$821$	7.48035e6	+	1.29563e7i	0.387315	+	0.670849i	0.992087	−	0.125549i	$-0.0400693\pi$
$821$	7.48035e6	+	1.29563e7i	0.387315	+	0.670849i	−0.604773	+	0.796398i	$0.706736\pi$
$822$	2.79972e6	−	4.90117e6i	0.144522	−	0.253000i
$823$	−1.52885e7	+	2.64805e7i	−0.786802	+	1.36278i	0.141115	+	0.989993i	$0.454931\pi$
$823$	−1.52885e7	+	2.64805e7i	−0.786802	+	1.36278i	−0.927917	+	0.372787i	$0.878402\pi$
$824$	−1.29126e6	+	2.23653e6i	−0.0662516	+	0.114751i
$825$	−268632.	+	470265.i	−0.0137412	+	0.0240552i
$826$	313979.	+	543828.i	0.0160122	+	0.0277339i
$827$	3.03602e7			1.54362			0.771810	−	0.635853i	$-0.219352\pi$
$827$	3.03602e7			1.54362			0.771810	+	0.635853i	$0.219352\pi$
$828$	846547.	+	1.43561e6i	0.0429116	+	0.0727713i
$829$	−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
$831$	−2.21911e6	−	3.80312e6i	−0.111475	−	0.191046i
$832$	−5.20235e6	+	9.01073e6i	−0.260550	+	0.451286i
$833$	−4.27684e6	+	7.40771e6i	−0.213556	+	0.369889i
$834$	2.24118e7	−	103057.i	1.11574	−	0.00513055i
$835$	5.54965e6	+	9.61228e6i	0.275454	+	0.477101i
$836$	−395920.			−0.0195926
$837$	8.24604e6	−	1.47487e7i	0.406847	−	0.727681i
$838$	−5.89218e6			−0.289845
$839$	1.87744e6	+	3.25182e6i	0.0920791	+	0.159486i	0.908386	−	0.418133i	$-0.137315\pi$
$839$	1.87744e6	+	3.25182e6i	0.0920791	+	0.159486i	−0.816307	+	0.577619i	$0.803982\pi$
$840$	2.97093e6	−	13661.4i	0.145276	−	0.000668031i
$841$	−1.36626e6	+	2.36643e6i	−0.0666105	+	0.115373i
$842$	−1.04450e7	+	1.80912e7i	−0.507723	+	0.879402i
$843$	−9.65271e6	−	1.65428e7i	−0.467822	−	0.801754i
$844$	−1.47959e7	−	2.56272e7i	−0.714966	−	1.23836i
$845$	430596.			0.0207457
$846$	1.62384e7	−	2.87328e7i	0.780042	−	1.38023i
$847$	6.63392e6			0.317733
$848$	1.21471e6	+	2.10394e6i	0.0580073	+	0.100472i
$849$	−3.46124e6	+	6.05923e6i	−0.164802	+	0.288501i
$850$	9.65733e6	−	1.67270e7i	0.458469	−	0.794091i
$851$	33276.9	−	57637.3i	0.00157514	−	0.00272822i
$852$	−6.31074e6	+	1.10475e7i	−0.297839	+	0.521394i
$853$	−1.08366e7	−	1.87695e7i	−0.509940	−	0.883242i	−0.999934	−	0.0115163i	$-0.996334\pi$
$853$	−1.08366e7	−	1.87695e7i	−0.509940	−	0.883242i	0.489993	−	0.871726i	$-0.336999\pi$
$854$	8.80526e6			0.413140
$855$	2.15398e7	−	3.81133e7i	1.00769	−	1.78304i
$856$	−6.97453e6			−0.325335
$857$	7.00812e6	+	1.21384e7i	0.325949	+	0.564560i	0.981704	−	0.190414i	$-0.0609830\pi$
$857$	7.00812e6	+	1.21384e7i	0.325949	+	0.564560i	−0.655755	+	0.754974i	$0.727650\pi$
$858$	275984.	+	472982.i	0.0127987	+	0.0219344i
$859$	318841.	−	552249.i	0.0147432	−	0.0255360i	−0.858560	−	0.512714i	$-0.828640\pi$
$859$	318841.	−	552249.i	0.0147432	−	0.0255360i	0.873303	+	0.487178i	$0.161974\pi$
$860$	9.32524e6	−	1.61518e7i	0.429946	−	0.744688i
$861$	−2.25433e6	+	10366.2i	−0.103636	+	0.000476553i
$862$	−3.37184e6	−	5.84020e6i	−0.154561	−	0.267707i
$863$	−3.79097e7			−1.73270			−0.866350	−	0.499437i	$-0.833540\pi$
$863$	−3.79097e7			−1.73270			−0.866350	+	0.499437i	$0.833540\pi$
$864$	−1.36051e7	+	2.43340e7i	−0.620039	+	1.10899i
$865$	−4.64946e7			−2.11282
$866$	−1.83033e7	−	3.17022e7i	−0.829343	−	1.43646i
$867$	1.71370e7	−	78802.1i	0.774262	−	0.00356033i
$868$	2.29699e6	−	3.97851e6i	0.103481	−	0.179234i
$869$	338798.	−	586816.i	0.0152192	−	0.0263604i
$870$	2.50001e7	+	4.28452e7i	1.11981	+	1.91913i
$871$	1.26789e7	+	2.19604e7i	0.566285	+	0.980834i
$872$	8.62199e6			0.383987
$873$	2.01177e7	+	3.41164e7i	0.893394	+	1.51505i
$874$	−4.26893e6			−0.189034
$875$	−2.51145e6	−	4.34995e6i	−0.110893	−	0.192072i
$876$	6.34238e6	−	1.11029e7i	0.279249	−	0.488852i
$877$	−2.01603e7	+	3.49186e7i	−0.885111	+	1.53306i	−0.0395244	+	0.999219i	$0.512584\pi$
$877$	−2.01603e7	+	3.49186e7i	−0.885111	+	1.53306i	−0.845587	+	0.533838i	$0.820749\pi$
$878$	881277.	−	1.52642e6i	0.0385812	−	0.0668247i
$879$	−1.08150e7	+	1.89327e7i	−0.472122	+	0.826494i
$880$	402999.	+	698016.i	0.0175428	+	0.0303849i
$881$	−3.52506e7			−1.53013			−0.765063	−	0.643956i	$-0.777292\pi$
$881$	−3.52506e7			−1.53013			−0.765063	+	0.643956i	$0.777292\pi$
$882$	−2.77162e7	+	254903.i	−1.19967	+	0.0110333i
$883$	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
$885$	−1.38655e6	−	2.37627e6i	−0.0595081	−	0.101985i
$886$	9.87033e6	−	1.70959e7i	0.422423	−	0.731658i
$887$	1.30625e7	−	2.26249e7i	0.557464	−	0.965556i	−0.440243	−	0.897879i	$-0.645108\pi$
$887$	1.30625e7	−	2.26249e7i	0.557464	−	0.965556i	0.997707	−	0.0676777i	$-0.0215590\pi$
$888$	199994.	−	919.642i	0.00851107	−	3.91369e-5i
$889$	−4.80644e6	−	8.32501e6i	−0.203972	−	0.353289i
$890$	8.22124e7			3.47906
$891$	234171.	+	388897.i	0.00988185	+	0.0164112i
$892$	−2.03624e7			−0.856876
$893$	1.85359e7	+	3.21051e7i	0.777829	+	1.34724i
$894$	−5.71277e6	+	26269.3i	−0.239058	+	0.00109927i
$895$	1.59743e7	−	2.76683e7i	0.666600	−	1.15458i
$896$	2.17865e6	−	3.77354e6i	0.0906606	−	0.157029i
$897$	1.30494e6	+	2.23640e6i	0.0541512	+	0.0928045i
$898$	3.14224e7	+	5.44252e7i	1.30032	+	2.25221i
$899$	−2.15062e7			−0.887491
$900$	2.74449e7	−	252408.i	1.12942	−	0.0103872i
$901$	−1.14697e6			−0.0470696
$902$	−101844.	−	176398.i	−0.00416790	−	0.00721901i
$903$	−2.71940e6	+	4.76056e6i	−0.110982	+	0.194285i
$904$	4.32532e6	−	7.49167e6i	0.176034	−	0.304900i
$905$	1.91282e7	−	3.31309e7i	0.776339	−	1.34466i
$906$	1.31884e7	−	2.30875e7i	0.533791	−	0.934450i
$907$	2.18243e7	+	3.78008e7i	0.880892	+	1.52575i	0.850351	+	0.526216i	$0.176390\pi$
$907$	2.18243e7	+	3.78008e7i	0.880892	+	1.52575i	0.0305409	+	0.999534i	$0.490277\pi$
$908$	−9.38251e6			−0.377663
$909$	2.29397e7	+	3.89020e7i	0.920825	+	1.56157i
$910$	−1.64627e7			−0.659017
$911$	−8.65618e6	−	1.49929e7i	−0.345566	−	0.598537i	0.639891	−	0.768466i	$-0.278980\pi$
$911$	−8.65618e6	−	1.49929e7i	−0.345566	−	0.598537i	−0.985456	+	0.169929i	$0.945646\pi$
$912$	−1.94121e7	−	3.32686e7i	−0.772834	−	1.32448i
$913$	−40667.7	+	70438.6i	−0.00161463	+	0.00279662i
$914$	−3.00550e6	+	5.20568e6i	−0.119001	+	0.206116i
$915$	−3.85772e7	+	177392.i	−1.52327	+	0.00700455i
$916$	−1.57170e6	−	2.72226e6i	−0.0618913	−	0.107199i
$917$	7.14600e6			0.280634
$918$	−8.28743e6	−	1.39076e7i	−0.324574	−	0.544685i
$919$	−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
$921$	−9.58260e6	+	44064.2i	−0.372250	+	0.00171174i
$922$	−5.28699e6	+	9.15733e6i	−0.204824	+	0.354766i
$923$	−9.88327e6	+	1.71183e7i	−0.381853	+	0.661389i
$924$	62200.6	+	106600.i	0.00239671	+	0.00410748i
$925$	−548008.	−	949178.i	−0.0210587	−	0.0364748i
$926$	8.67065e6			0.332295
$927$	5.83669e6	−	1.03276e7i	0.223084	−	0.394732i
$928$	3.54830e7			1.35254
$929$	−2.28832e7	−	3.96349e7i	−0.869916	−	1.50674i	−0.862082	−	0.506769i	$-0.830840\pi$
$929$	−2.28832e7	−	3.96349e7i	−0.869916	−	1.50674i	−0.00783438	−	0.999969i	$-0.502494\pi$
$930$	−2.27657e7	+	3.98535e7i	−0.863126	+	1.51098i
$931$	1.55668e7	−	2.69625e7i	0.588606	−	1.01950i
$932$	−5.29300e6	+	9.16775e6i	−0.199601	+	0.345719i
$933$	2.29191e7	−	4.01220e7i	0.861974	−	1.50896i
$934$	−2.13074e7	−	3.69055e7i	−0.799215	−	1.38428i
$935$	−380526.			−0.0142349
$936$	−3.82829e6	+	6.77390e6i	−0.142829	+	0.252726i
$937$	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
$939$	−6.51164e6	−	1.11597e7i	−0.241005	−	0.413035i
$940$	−1.96562e7	+	3.40455e7i	−0.725570	+	1.25672i
$941$	−1.55476e7	+	2.69292e7i	−0.572385	+	0.991400i	0.423936	+	0.905692i	$0.360648\pi$
$941$	−1.55476e7	+	2.69292e7i	−0.572385	+	0.991400i	−0.996320	+	0.0857072i	$0.972685\pi$
$942$	−1.89701e7	+	87231.1i	−0.696533	+	0.00320290i
$943$	−481547.	−	834064.i	−0.0176344	−	0.0305436i
$944$	−2.42059e6			−0.0884081
$945$	−1.36458e7	+	188256.i	−0.497073	+	0.00685754i
$946$	−495362.			−0.0179968
$947$	−2.10665e7	−	3.64883e7i	−0.763339	−	1.32214i	−0.941120	−	0.338072i	$-0.890225\pi$
$947$	−2.10665e7	−	3.64883e7i	−0.763339	−	1.32214i	0.177781	−	0.984070i	$-0.443108\pi$
$948$	−3.43384e7	+	157900.i	−1.24097	+	0.00570640i
$949$	9.93283e6	−	1.72042e7i	0.358020	−	0.620109i
$950$	−3.51506e7	+	6.08826e7i	−1.26364	+	2.18869i
$951$	2.60436e6	+	4.46336e6i	0.0933791	+	0.160033i
$952$	617042.	+	1.06875e6i	0.0220660	+	0.0382193i
$953$	−1.27052e7			−0.453158			−0.226579	−	0.973993i	$-0.572754\pi$
$953$	−1.27052e7			−0.453158			−0.226579	+	0.973993i	$0.572754\pi$
$954$	−1.88784e6	−	3.20148e6i	−0.0671576	−	0.113889i
$955$	−1.33696e7			−0.474361
$956$	1.52935e7	+	2.64892e7i	0.541206	+	0.937397i
$957$	286583.	−	501689.i	0.0101151	−	0.0177074i
$958$	2.15386e7	−	3.73060e7i	0.758236	−	1.31330i
$959$	988202.	−	1.71162e6i	0.0346976	−	0.0600980i
$960$	1.16207e7	−	2.03431e7i	0.406962	−	0.712425i
$961$	4.36530e6	+	7.56093e6i	0.152478	+	0.264099i
$962$	−1.10822e6			−0.0386089
$963$	3.20362e7	−	294634.i	1.11321	−	0.0102380i
$964$	1.89594e7			0.657102
$965$	1.69750e7	+	2.94016e7i	0.586802	+	1.01637i
$966$	670666.	+	1.14939e6i	0.0231240	+	0.0396300i
$967$	−2.11678e7	+	3.66637e7i	−0.727964	+	1.26087i	0.229779	+	0.973243i	$0.426200\pi$
$967$	−2.11678e7	+	3.66637e7i	−0.727964	+	1.26087i	−0.957743	+	0.287627i	$0.907134\pi$
$968$	−4.25830e6	+	7.37558e6i	−0.146065	+	0.252993i
$969$	1.81848e7	−	83620.1i	0.622155	−	0.00286089i
$970$	−5.37901e7	−	9.31672e7i	−1.83558	−	3.17932i
$971$	4.04024e7			1.37518			0.687589	−	0.726100i	$-0.258669\pi$
$971$	4.04024e7			1.37518			0.687589	+	0.726100i	$0.258669\pi$
$972$	1.10416e7	−	2.01824e7i	0.374858	−	0.685183i
$973$	7.84757e6			0.265737
$974$	1.05226e7	+	1.82257e7i	0.355407	+	0.615583i
$975$	4.26401e7	−	196074.i	1.43650	−	0.00660555i
$976$	−1.69708e7	+	2.93944e7i	−0.570268	+	0.987733i
$977$	1.88733e7	−	3.26895e7i	0.632574	−	1.09565i	−0.354449	−	0.935075i	$-0.615332\pi$
$977$	1.88733e7	−	3.26895e7i	0.632574	−	1.09565i	0.987024	−	0.160576i	$-0.0513351\pi$
$978$	−1.55014e6	−	2.65663e6i	−0.0518231	−	0.0888146i
$979$	−478778.	−	829267.i	−0.0159653	−	0.0276527i
$980$	3.30153e7			1.09812
$981$	−3.96035e7	+	364229.i	−1.31390	+	0.0120838i
$982$	7.24506e6			0.239753
$983$	−2.44599e6	−	4.23658e6i	−0.0807367	−	0.139840i	0.822830	−	0.568288i	$-0.192394\pi$
$983$	−2.44599e6	−	4.23658e6i	−0.0807367	−	0.139840i	−0.903567	+	0.428448i	$0.859061\pi$
$984$	1.43552e6	−	2.51301e6i	0.0472631	−	0.0827384i
$985$	5.09215e6	−	8.81986e6i	0.167229	−	0.289649i
$986$	−1.03026e7	+	1.78447e7i	−0.337487	+	0.584544i
$987$	5.73208e6	−	1.00345e7i	0.187292	−	0.327872i
$988$	1.55860e7	+	2.69957e7i	0.507974	+	0.879837i
$989$	−2.34222e6			−0.0761443
$990$	−626323.	−	1.06214e6i	−0.0203100	−	0.0344426i
$991$	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
$993$	2.03352e7	+	3.48505e7i	0.654449	+	1.12160i
$994$	−5.07946e6	+	8.79788e6i	−0.163062	+	0.282431i
$995$	−3.95597e7	+	6.85194e7i	−1.26676	+	2.19410i
$996$	4.12183e6	−	18953.6i	0.131656	−	0.000605402i
$997$	1.25206e7	+	2.16863e7i	0.398921	+	0.690951i	0.993593	−	0.113017i	$-0.0360515\pi$
$997$	1.25206e7	+	2.16863e7i	0.398921	+	0.690951i	−0.594672	+	0.803968i	$0.702718\pi$
$998$	−1.70763e7			−0.542709
$999$	−918596.	+	12672.8i	−0.0291213	+	0.000401753i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.6.c.a.4.1	✓	8	1.1	even	1	trivial
9.6.c.a.7.1	yes	8	9.7	even	3	inner
27.6.c.a.10.4		8	3.2	odd	2
27.6.c.a.19.4		8	9.2	odd	6
81.6.a.c.1.4		4	9.4	even	3
81.6.a.d.1.1		4	9.5	odd	6
144.6.i.c.49.4		8	4.3	odd	2
144.6.i.c.97.4		8	36.7	odd	6
432.6.i.c.145.1		8	12.11	even	2
432.6.i.c.289.1		8	36.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	9.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.77467 - 6.53793i) q^{2} +(-15.5883 + 0.0716805i) q^{3} +(-12.4963 + 21.6443i) q^{4} +(43.7155 - 75.7175i) q^{5} +(59.3094 + 101.645i) q^{6} +(20.6033 + 35.6859i) q^{7} -52.9007 q^{8} +(242.990 - 2.23475i) q^{9} +O(q^{10})\)	\(q+(-3.77467 - 6.53793i) q^{2} +(-15.5883 + 0.0716805i) q^{3} +(-12.4963 + 21.6443i) q^{4} +(43.7155 - 75.7175i) q^{5} +(59.3094 + 101.645i) q^{6} +(20.6033 + 35.6859i) q^{7} -52.9007 q^{8} +(242.990 - 2.23475i) q^{9} -660.048 q^{10} +(3.84390 + 6.65783i) q^{11} +(193.245 - 338.293i) q^{12} +(302.642 - 524.191i) q^{13} +(155.541 - 269.405i) q^{14} +(-676.023 + 1183.44i) q^{15} +(599.566 + 1038.48i) q^{16} -566.131 q^{17} +(-931.818 - 1580.21i) q^{18} +2060.59 q^{19} +(1092.57 + 1892.38i) q^{20} +(-323.728 - 554.806i) q^{21} +(29.0189 - 50.2623i) q^{22} +(137.210 - 237.655i) q^{23} +(824.632 - 3.79195i) q^{24} +(-2259.59 - 3913.73i) q^{25} -4569.50 q^{26} +(-3787.63 + 52.2536i) q^{27} -1029.86 q^{28} +(2410.58 + 4175.25i) q^{29} +(10289.0 - 47.3125i) q^{30} +(-2230.39 + 3863.15i) q^{31} +(3679.92 - 6373.81i) q^{32} +(-60.3970 - 103.509i) q^{33} +(2136.96 + 3701.32i) q^{34} +3602.73 q^{35} +(-2988.11 + 5287.27i) q^{36} +242.525 q^{37} +(-7778.07 - 13472.0i) q^{38} +(-4680.09 + 8192.93i) q^{39} +(-2312.58 + 4005.51i) q^{40} +(1754.78 - 3039.37i) q^{41} +(-2405.31 + 4210.72i) q^{42} +(-4267.58 - 7391.66i) q^{43} -192.139 q^{44} +(10453.2 - 18496.3i) q^{45} -2071.70 q^{46} +(8995.40 + 15580.5i) q^{47} +(-9420.65 - 16145.1i) q^{48} +(7554.51 - 13084.8i) q^{49} +(-17058.5 + 29546.1i) q^{50} +(8825.02 - 40.5805i) q^{51} +(7563.83 + 13100.9i) q^{52} +2025.98 q^{53} +(14638.7 + 24566.0i) q^{54} +672.152 q^{55} +(-1089.93 - 1887.81i) q^{56} +(-32121.1 + 147.704i) q^{57} +(18198.3 - 31520.5i) q^{58} +(-1009.31 + 1748.18i) q^{59} +(-17166.9 - 29420.7i) q^{60} +(14152.6 + 24513.0i) q^{61} +33676.0 q^{62} +(5086.13 + 8625.27i) q^{63} -17189.8 q^{64} +(-26460.3 - 45830.6i) q^{65} +(-448.753 + 785.583i) q^{66} +(-20947.0 + 36281.3i) q^{67} +(7074.57 - 12253.5i) q^{68} +(-2121.84 + 3714.47i) q^{69} +(-13599.1 - 23554.4i) q^{70} -32656.7 q^{71} +(-12854.3 + 118.220i) q^{72} +32820.4 q^{73} +(-915.453 - 1585.61i) q^{74} +(35503.8 + 60846.4i) q^{75} +(-25749.9 + 44600.1i) q^{76} +(-158.394 + 274.346i) q^{77} +(71230.6 - 327.544i) q^{78} +(-44069.6 - 76330.8i) q^{79} +104841. q^{80} +(59039.0 - 1086.04i) q^{81} -26494.9 q^{82} +(5289.91 + 9162.39i) q^{83} +(16053.8 - 73.8210i) q^{84} +(-24748.7 + 42866.0i) q^{85} +(-32217.4 + 55802.2i) q^{86} +(-37876.2 - 64912.3i) q^{87} +(-203.345 - 352.204i) q^{88} -124555. q^{89} +(-160385. + 1475.04i) q^{90} +24941.6 q^{91} +(3429.25 + 5939.64i) q^{92} +(34491.0 - 60379.7i) q^{93} +(67909.4 - 117623. i) q^{94} +(90080.0 - 156023. i) q^{95} +(-56906.8 + 99620.6i) q^{96} +(81494.3 + 141152. i) q^{97} -114063. q^{98} +(948.906 + 1609.19i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{2} - 12 q^{3} - 49 q^{4} + 78 q^{5} + 171 q^{6} + 28 q^{7} - 750 q^{8} - 414 q^{9}+O(q^{10}) \) 8 * q + 3 * q^2 - 12 * q^3 - 49 * q^4 + 78 * q^5 + 171 * q^6 + 28 * q^7 - 750 * q^8 - 414 * q^9	\( 8 q + 3 q^{2} - 12 q^{3} - 49 q^{4} + 78 q^{5} + 171 q^{6} + 28 q^{7} - 750 q^{8} - 414 q^{9} + 60 q^{10} + 444 q^{11} + 2724 q^{12} - 182 q^{13} + 1392 q^{14} - 2052 q^{15} - 289 q^{16} - 4356 q^{17} - 8100 q^{18} + 952 q^{19} + 6684 q^{20} + 8670 q^{21} + 1011 q^{22} + 8844 q^{23} + 549 q^{24} - 1654 q^{25} - 24888 q^{26} - 10152 q^{27} - 1604 q^{28} + 12018 q^{29} + 22104 q^{30} + 1132 q^{31} + 8703 q^{32} - 8820 q^{33} + 10125 q^{34} - 16224 q^{35} - 14589 q^{36} - 15176 q^{37} - 11145 q^{38} + 8220 q^{39} - 8736 q^{40} + 1248 q^{41} + 10098 q^{42} - 6092 q^{43} + 49530 q^{44} + 43038 q^{45} + 45960 q^{46} - 60 q^{47} - 57405 q^{48} + 9090 q^{49} - 57057 q^{50} - 9396 q^{51} - 32510 q^{52} + 20952 q^{53} + 8181 q^{54} - 36120 q^{55} - 61170 q^{56} - 104298 q^{57} + 8328 q^{58} + 2076 q^{59} + 88308 q^{60} + 48142 q^{61} + 241764 q^{62} + 133524 q^{63} - 20926 q^{64} - 13146 q^{65} - 100998 q^{66} - 7148 q^{67} - 123129 q^{68} - 125982 q^{69} - 654 q^{70} - 71856 q^{71} + 35451 q^{72} + 122452 q^{73} - 160320 q^{74} - 18732 q^{75} - 49571 q^{76} + 39534 q^{77} + 181422 q^{78} - 59516 q^{79} + 124512 q^{80} + 194562 q^{81} - 233598 q^{82} + 117696 q^{83} + 108354 q^{84} + 28836 q^{85} - 15915 q^{86} - 142956 q^{87} + 104523 q^{88} - 451728 q^{89} - 539892 q^{90} + 111392 q^{91} + 134034 q^{92} + 113898 q^{93} + 169464 q^{94} + 294888 q^{95} + 42768 q^{96} + 33976 q^{97} + 57654 q^{98} + 33696 q^{99}+O(q^{100}) \) 8 * q + 3 * q^2 - 12 * q^3 - 49 * q^4 + 78 * q^5 + 171 * q^6 + 28 * q^7 - 750 * q^8 - 414 * q^9 + 60 * q^10 + 444 * q^11 + 2724 * q^12 - 182 * q^13 + 1392 * q^14 - 2052 * q^15 - 289 * q^16 - 4356 * q^17 - 8100 * q^18 + 952 * q^19 + 6684 * q^20 + 8670 * q^21 + 1011 * q^22 + 8844 * q^23 + 549 * q^24 - 1654 * q^25 - 24888 * q^26 - 10152 * q^27 - 1604 * q^28 + 12018 * q^29 + 22104 * q^30 + 1132 * q^31 + 8703 * q^32 - 8820 * q^33 + 10125 * q^34 - 16224 * q^35 - 14589 * q^36 - 15176 * q^37 - 11145 * q^38 + 8220 * q^39 - 8736 * q^40 + 1248 * q^41 + 10098 * q^42 - 6092 * q^43 + 49530 * q^44 + 43038 * q^45 + 45960 * q^46 - 60 * q^47 - 57405 * q^48 + 9090 * q^49 - 57057 * q^50 - 9396 * q^51 - 32510 * q^52 + 20952 * q^53 + 8181 * q^54 - 36120 * q^55 - 61170 * q^56 - 104298 * q^57 + 8328 * q^58 + 2076 * q^59 + 88308 * q^60 + 48142 * q^61 + 241764 * q^62 + 133524 * q^63 - 20926 * q^64 - 13146 * q^65 - 100998 * q^66 - 7148 * q^67 - 123129 * q^68 - 125982 * q^69 - 654 * q^70 - 71856 * q^71 + 35451 * q^72 + 122452 * q^73 - 160320 * q^74 - 18732 * q^75 - 49571 * q^76 + 39534 * q^77 + 181422 * q^78 - 59516 * q^79 + 124512 * q^80 + 194562 * q^81 - 233598 * q^82 + 117696 * q^83 + 108354 * q^84 + 28836 * q^85 - 15915 * q^86 - 142956 * q^87 + 104523 * q^88 - 451728 * q^89 - 539892 * q^90 + 111392 * q^91 + 134034 * q^92 + 113898 * q^93 + 169464 * q^94 + 294888 * q^95 + 42768 * q^96 + 33976 * q^97 + 57654 * q^98 + 33696 * q^99

Introduction

L-functions

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