LMFDB - Embedded newform 9.6.c.a.4.4

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			4.4
Root			$2.56934i$ of defining polynomial
Character	$\chi$	$=$	9.4
Dual form			9.6.c.a.7.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.96163 + 8.59380i) q^{2} +(-3.07760 - 15.2816i) q^{3} +(-33.2356 + 57.5657i) q^{4} +(23.6560 - 40.9735i) q^{5} +(116.057 - 102.270i) q^{6} +(1.01546 + 1.75882i) q^{7} -342.066 q^{8} +(-224.057 + 94.0614i) q^{9} +O(q^{10})$	\(q+(4.96163 + 8.59380i) q^{2} +(-3.07760 - 15.2816i) q^{3} +(-33.2356 + 57.5657i) q^{4} +(23.6560 - 40.9735i) q^{5} +(116.057 - 102.270i) q^{6} +(1.01546 + 1.75882i) q^{7} -342.066 q^{8} +(-224.057 + 94.0614i) q^{9} +469.490 q^{10} +(-91.8836 - 159.147i) q^{11} +(981.984 + 330.730i) q^{12} +(-364.672 + 631.630i) q^{13} +(-10.0766 + 17.4532i) q^{14} +(-698.946 - 235.403i) q^{15} +(-633.668 - 1097.55i) q^{16} +1212.88 q^{17} +(-1920.03 - 1458.80i) q^{18} -473.092 q^{19} +(1572.44 + 2723.55i) q^{20} +(23.7525 - 20.9308i) q^{21} +(911.785 - 1579.26i) q^{22} +(1806.42 - 3128.81i) q^{23} +(1052.74 + 5227.33i) q^{24} +(443.283 + 767.788i) q^{25} -7237.47 q^{26} +(2126.97 + 3134.47i) q^{27} -134.997 q^{28} +(663.121 + 1148.56i) q^{29} +(-1444.90 - 7174.58i) q^{30} +(2590.41 - 4486.72i) q^{31} +(814.997 - 1411.62i) q^{32} +(-2149.25 + 1893.92i) q^{33} +(6017.88 + 10423.3i) q^{34} +96.0867 q^{35} +(2031.95 - 16024.2i) q^{36} -14715.2 q^{37} +(-2347.31 - 4065.65i) q^{38} +(10774.7 + 3628.88i) q^{39} +(-8091.94 + 14015.6i) q^{40} +(-3159.83 + 5472.98i) q^{41} +(297.726 + 100.273i) q^{42} +(-3067.89 - 5313.75i) q^{43} +12215.2 q^{44} +(-1446.28 + 11405.5i) q^{45} +35851.1 q^{46} +(-1584.17 - 2743.86i) q^{47} +(-14822.1 + 13061.3i) q^{48} +(8401.44 - 14551.7i) q^{49} +(-4398.81 + 7618.96i) q^{50} +(-3732.76 - 18534.8i) q^{51} +(-24240.2 - 41985.2i) q^{52} -12265.0 q^{53} +(-16383.8 + 33830.8i) q^{54} -8694.41 q^{55} +(-347.353 - 601.633i) q^{56} +(1455.98 + 7229.61i) q^{57} +(-6580.32 + 11397.5i) q^{58} +(14773.5 - 25588.5i) q^{59} +(36781.0 - 32411.5i) q^{60} +(20153.6 + 34907.1i) q^{61} +51410.7 q^{62} +(-392.957 - 298.561i) q^{63} -24379.9 q^{64} +(17253.4 + 29883.8i) q^{65} +(-26939.7 - 9073.25i) q^{66} +(-11748.9 + 20349.7i) q^{67} +(-40310.9 + 69820.5i) q^{68} +(-53372.8 - 17975.8i) q^{69} +(476.747 + 825.750i) q^{70} -123.786 q^{71} +(76642.3 - 32175.2i) q^{72} +35217.6 q^{73} +(-73011.4 - 126459. i) q^{74} +(10368.8 - 9137.03i) q^{75} +(15723.5 - 27233.8i) q^{76} +(186.607 - 323.214i) q^{77} +(22274.0 + 110600. i) q^{78} +(24072.8 + 41695.3i) q^{79} -59960.3 q^{80} +(41353.9 - 42150.2i) q^{81} -62711.6 q^{82} +(-5167.97 - 8951.18i) q^{83} +(415.466 + 2062.98i) q^{84} +(28692.0 - 49696.1i) q^{85} +(30443.5 - 52729.7i) q^{86} +(15511.0 - 13668.4i) q^{87} +(31430.3 + 54438.8i) q^{88} -42585.7 q^{89} +(-105193. + 44160.9i) q^{90} -1481.23 q^{91} +(120075. + 207976. i) q^{92} +(-76536.7 - 25777.4i) q^{93} +(15720.1 - 27228.1i) q^{94} +(-11191.5 + 19384.2i) q^{95} +(-24080.0 - 8110.10i) q^{96} +(-49347.3 - 85472.1i) q^{97} +166739. q^{98} +(35556.7 + 27015.3i) 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 $

$2$	4.96163	+	8.59380i	0.877101	+	1.51918i	0.854508	+	0.519438i	$0.173859\pi$
$2$	4.96163	+	8.59380i	0.877101	+	1.51918i	0.0225929	+	0.999745i	$0.492808\pi$
$3$	−3.07760	−	15.2816i	−0.197428	−	0.980317i
$3$	−3.07760	−	15.2816i	−0.197428	−	0.980317i
$4$	−33.2356	+	57.5657i	−1.03861	+	1.79893i
$5$	23.6560	−	40.9735i	0.423172	−	0.732956i	−0.573076	−	0.819503i	$-0.694250\pi$
$5$	23.6560	−	40.9735i	0.423172	−	0.732956i	0.996248	+	0.0865467i	$0.0275832\pi$
$6$	116.057	−	102.270i	1.31612	−	1.15977i
$7$	1.01546	+	1.75882i	0.00783278	+	0.0135668i	0.869915	−	0.493201i	$-0.164173\pi$
$7$	1.01546	+	1.75882i	0.00783278	+	0.0135668i	−0.862082	+	0.506768i	$0.830840\pi$
$8$	−342.066			−1.88967
$9$	−224.057	+	94.0614i	−0.922044	+	0.387084i
$10$	469.490			1.48466
$11$	−91.8836	−	159.147i	−0.228958	−	0.396567i	0.728541	−	0.685002i	$-0.240199\pi$
$11$	−91.8836	−	159.147i	−0.228958	−	0.396567i	−0.957500	+	0.288435i	$0.906865\pi$
$12$	981.984	+	330.730i	1.96857	+	0.663011i
$13$	−364.672	+	631.630i	−0.598472	+	1.03658i	0.394574	+	0.918864i	$0.370892\pi$
$13$	−364.672	+	631.630i	−0.598472	+	1.03658i	−0.993047	+	0.117720i	$0.962441\pi$
$14$	−10.0766	+	17.4532i	−0.0137403	+	0.0237989i
$15$	−698.946	−	235.403i	−0.802075	−	0.270137i
$16$	−633.668	−	1097.55i	−0.618817	−	1.07182i
$17$	1212.88			1.01788			0.508940	−	0.860802i	$-0.330037\pi$
$17$	1212.88			1.01788			0.508940	+	0.860802i	$0.330037\pi$
$18$	−1920.03	−	1458.80i	−1.39678	−	1.06124i
$19$	−473.092			−0.300650			−0.150325	−	0.988637i	$-0.548032\pi$
$19$	−473.092			−0.300650			−0.150325	+	0.988637i	$0.548032\pi$
$20$	1572.44	+	2723.55i	0.879023	+	1.52251i
$21$	23.7525	−	20.9308i	0.0117533	−	0.0103571i
$22$	911.785	−	1579.26i	0.401639	−	0.695659i
$23$	1806.42	−	3128.81i	0.712031	−	1.23327i	−0.252063	−	0.967711i	$-0.581109\pi$
$23$	1806.42	−	3128.81i	0.712031	−	1.23327i	0.964094	−	0.265563i	$-0.0855578\pi$
$24$	1052.74	+	5227.33i	0.373073	+	1.85247i
$25$	443.283	+	767.788i	0.141850	+	0.245692i
$26$	−7237.47			−2.09968
$27$	2126.97	+	3134.47i	0.561502	+	0.827475i
$28$	−134.997			−0.0325409
$29$	663.121	+	1148.56i	0.146419	+	0.253605i	0.929901	−	0.367809i	$-0.119892\pi$
$29$	663.121	+	1148.56i	0.146419	+	0.253605i	−0.783482	+	0.621414i	$0.786559\pi$
$30$	−1444.90	−	7174.58i	−0.293113	−	1.45544i
$31$	2590.41	−	4486.72i	0.484133	−	0.838542i	−0.515701	−	0.856769i	$-0.672469\pi$
$31$	2590.41	−	4486.72i	0.484133	−	0.838542i	0.999834	+	0.0182261i	$0.00580186\pi$
$32$	814.997	−	1411.62i	0.140696	−	0.243692i
$33$	−2149.25	+	1893.92i	−0.343559	+	0.302745i
$34$	6017.88	+	10423.3i	0.892784	+	1.54635i
$35$	96.0867			0.0132585
$36$	2031.95	−	16024.2i	0.261310	−	2.06072i
$37$	−14715.2			−1.76710			−0.883552	−	0.468334i	$-0.844854\pi$
$37$	−14715.2			−1.76710			−0.883552	+	0.468334i	$0.844854\pi$
$38$	−2347.31	−	4065.65i	−0.263700	−	0.456742i
$39$	10774.7	+	3628.88i	1.13434	+	0.382042i
$40$	−8091.94	+	14015.6i	−0.799655	+	1.38504i
$41$	−3159.83	+	5472.98i	−0.293564	+	0.508469i	−0.974650	−	0.223735i	$-0.928175\pi$
$41$	−3159.83	+	5472.98i	−0.293564	+	0.508469i	0.681085	+	0.732204i	$0.261508\pi$
$42$	297.726	+	100.273i	0.0260431	+	0.00877128i
$43$	−3067.89	−	5313.75i	−0.253028	−	0.438258i	0.711330	−	0.702858i	$-0.248093\pi$
$43$	−3067.89	−	5313.75i	−0.253028	−	0.438258i	−0.964358	+	0.264600i	$0.914760\pi$
$44$	12215.2			0.951195
$45$	−1446.28	+	11405.5i	−0.106468	+	0.839621i
$46$	35851.1			2.49809
$47$	−1584.17	−	2743.86i	−0.104606	−	0.181183i	0.808971	−	0.587848i	$-0.200025\pi$
$47$	−1584.17	−	2743.86i	−0.104606	−	0.181183i	−0.913577	+	0.406665i	$0.866692\pi$
$48$	−14822.1	+	13061.3i	−0.928554	+	0.818244i
$49$	8401.44	−	14551.7i	0.499877	−	0.865813i
$50$	−4398.81	+	7618.96i	−0.248834	+	0.430994i
$51$	−3732.76	−	18534.8i	−0.200958	−	0.997846i
$52$	−24240.2	−	41985.2i	−1.24316	−	2.15322i
$53$	−12265.0			−0.599763			−0.299881	−	0.953977i	$-0.596947\pi$
$53$	−12265.0			−0.599763			−0.299881	+	0.953977i	$0.596947\pi$
$54$	−16383.8	+	33830.8i	−0.764592	+	1.57880i
$55$	−8694.41			−0.387555
$56$	−347.353	−	601.633i	−0.0148013	−	0.0256367i
$57$	1455.98	+	7229.61i	0.0593567	+	0.294732i
$58$	−6580.32	+	11397.5i	−0.256849	+	0.444875i
$59$	14773.5	−	25588.5i	0.552528	−	0.957006i	−0.445563	−	0.895250i	$-0.646997\pi$
$59$	14773.5	−	25588.5i	0.552528	−	0.957006i	0.998091	−	0.0617560i	$-0.0196701\pi$
$60$	36781.0	−	32411.5i	1.31900	−	1.16231i
$61$	20153.6	+	34907.1i	0.693472	+	1.20113i	0.970693	+	0.240323i	$0.0772534\pi$
$61$	20153.6	+	34907.1i	0.693472	+	1.20113i	−0.277221	+	0.960806i	$0.589413\pi$
$62$	51410.7			1.69853
$63$	−392.957	−	298.561i	−0.0124737	−	0.00947723i
$64$	−24379.9			−0.744016
$65$	17253.4	+	29883.8i	0.506514	+	0.877308i
$66$	−26939.7	−	9073.25i	−0.761261	−	0.256391i
$67$	−11748.9	+	20349.7i	−0.319750	+	0.553823i	−0.980436	−	0.196840i	$-0.936932\pi$
$67$	−11748.9	+	20349.7i	−0.319750	+	0.553823i	0.660686	+	0.750662i	$0.270266\pi$
$68$	−40310.9	+	69820.5i	−1.05718	+	1.83109i
$69$	−53372.8	−	17975.8i	−1.34957	−	0.454534i
$70$	476.747	+	825.750i	0.0116290	+	0.0201420i
$71$	−123.786			−0.00291425			−0.00145713	−	0.999999i	$-0.500464\pi$
$71$	−123.786			−0.00291425			−0.00145713	+	0.999999i	$0.500464\pi$
$72$	76642.3	−	32175.2i	1.74236	−	0.731460i
$73$	35217.6			0.773486			0.386743	−	0.922188i	$-0.373600\pi$
$73$	35217.6			0.773486			0.386743	+	0.922188i	$0.373600\pi$
$74$	−73011.4	−	126459.i	−1.54993	−	2.68455i
$75$	10368.8	−	9137.03i	0.212851	−	0.187565i
$76$	15723.5	−	27233.8i	0.312259	−	0.540848i
$77$	186.607	−	323.214i	0.00358676	−	0.00621245i
$78$	22274.0	+	110600.i	0.414536	+	2.05836i
$79$	24072.8	+	41695.3i	0.433969	+	0.751656i	0.997211	−	0.0746359i	$-0.0237794\pi$
$79$	24072.8	+	41695.3i	0.433969	+	0.751656i	−0.563242	+	0.826292i	$0.690446\pi$
$80$	−59960.3			−1.04746
$81$	41353.9	−	42150.2i	0.700332	−	0.713817i
$82$	−62711.6			−1.02994
$83$	−5167.97	−	8951.18i	−0.0823426	−	0.142622i	0.821913	−	0.569613i	$-0.192907\pi$
$83$	−5167.97	−	8951.18i	−0.0823426	−	0.142622i	−0.904256	+	0.426991i	$0.859574\pi$
$84$	415.466	+	2062.98i	0.00642447	+	0.0319004i
$85$	28692.0	−	49696.1i	0.430739	−	0.746062i
$86$	30443.5	−	52729.7i	0.443863	−	0.768793i
$87$	15511.0	−	13668.4i	0.219706	−	0.193606i
$88$	31430.3	+	54438.8i	0.432655	+	0.749380i
$89$	−42585.7			−0.569887			−0.284944	−	0.958544i	$-0.591975\pi$
$89$	−42585.7			−0.569887			−0.284944	+	0.958544i	$0.591975\pi$
$90$	−105193.	+	44160.9i	−1.36892	+	0.574688i
$91$	−1481.23			−0.0187508
$92$	120075.	+	207976.i	1.47905	+	2.56178i
$93$	−76536.7	−	25777.4i	−0.917619	−	0.309052i
$94$	15720.1	−	27228.1i	0.183500	−	0.317832i
$95$	−11191.5	+	19384.2i	−0.127227	+	0.220363i
$96$	−24080.0	−	8110.10i	−0.266673	−	0.0898149i
$97$	−49347.3	−	85472.1i	−0.532518	−	0.922348i	−0.999279	−	0.0379646i	$-0.987913\pi$
$97$	−49347.3	−	85472.1i	−0.532518	−	0.922348i	0.466761	−	0.884383i	$-0.345421\pi$
$98$	166739.			1.75377
$99$	35556.7	+	27015.3i	0.364614	+	0.277027i
$100$	−58931.0			−0.589310
$101$	37818.9	+	65504.3i	0.368898	+	0.638949i	0.989393	−	0.145260i	$-0.0464020\pi$
$101$	37818.9	+	65504.3i	0.368898	+	0.638949i	−0.620496	+	0.784210i	$0.713069\pi$
$102$	140764.	−	124042.i	1.33965	−	1.18050i
$103$	−73869.1	+	127945.i	−0.686072	+	1.18831i	0.287026	+	0.957923i	$0.407333\pi$
$103$	−73869.1	+	127945.i	−0.686072	+	1.18831i	−0.973099	+	0.230389i	$0.926000\pi$
$104$	124742.	−	216059.i	1.13091	−	1.95880i
$105$	−295.716	−	1468.36i	−0.00261759	−	0.0129975i
$106$	−60854.6	−	105403.i	−0.526052	−	0.911149i
$107$	−209139.			−1.76594			−0.882969	−	0.469430i	$-0.844459\pi$
$107$	−209139.			−1.76594			−0.882969	+	0.469430i	$0.844459\pi$
$108$	−251129.	+	18264.4i	−2.07175	+	0.150677i
$109$	115605.			0.931988			0.465994	−	0.884788i	$-0.345697\pi$
$109$	115605.			0.931988			0.465994	+	0.884788i	$0.345697\pi$
$110$	−43138.5	−	74718.0i	−0.339925	−	0.588767i
$111$	45287.4	+	224872.i	0.348875	+	1.73232i
$112$	1286.92	−	2229.02i	0.00969411	−	0.0167907i
$113$	−23415.8	+	40557.3i	−0.172509	+	0.298795i	−0.939296	−	0.343107i	$-0.888521\pi$
$113$	−23415.8	+	40557.3i	−0.172509	+	0.298795i	0.766787	+	0.641901i	$0.221854\pi$
$114$	−54905.8	+	48383.1i	−0.395691	+	0.348684i
$115$	−85465.5	−	148031.i	−0.602623	−	1.04377i
$116$	−88156.8			−0.608290
$117$	22295.2	−	175823.i	0.150573	−	1.18744i
$118$	293203.			1.93849
$119$	1231.63	+	2133.25i	0.00797283	+	0.0138094i
$120$	239086.	+	80523.5i	1.51566	+	0.510469i
$121$	63640.3	−	110228.i	0.395156	−	0.684431i
$122$	−199990.	+	346393.i	−1.21649	+	2.10702i
$123$	93360.7	+	31443.7i	0.556418	+	0.187400i
$124$	172188.	+	298238.i	1.00565	+	1.74184i
$125$	189796.			1.08645
$126$	616.062	−	4858.34i	0.00345699	−	0.0272622i
$127$	−93444.5			−0.514096			−0.257048	−	0.966399i	$-0.582750\pi$
$127$	−93444.5			−0.514096			−0.257048	+	0.966399i	$0.582750\pi$
$128$	−147044.	−	254688.i	−0.793273	−	1.37399i
$129$	−71761.0	+	63236.0i	−0.379677	+	0.334572i
$130$	−171210.	+	296544.i	−0.888527	+	1.53897i
$131$	183869.	−	318470.i	0.936115	−	1.62140i	0.163481	−	0.986546i	$-0.447728\pi$
$131$	183869.	−	318470.i	0.936115	−	1.62140i	0.772634	−	0.634852i	$-0.218939\pi$
$132$	−37593.5	−	186668.i	−0.187792	−	0.932473i
$133$	−480.404	−	832.083i	−0.00235493	−	0.00407885i
$134$	−233175.			−1.12181
$135$	178746.	−	13000.1i	0.844115	−	0.0613919i
$136$	−414887.			−1.92346
$137$	76809.2	+	133037.i	0.349632	+	0.605581i	0.986184	−	0.165653i	$-0.0529731\pi$
$137$	76809.2	+	133037.i	0.349632	+	0.605581i	−0.636552	+	0.771234i	$0.719640\pi$
$138$	−110335.	−	547864.i	−0.493193	−	2.44892i
$139$	−122213.	+	211679.i	−0.536513	+	0.929268i	0.462575	+	0.886580i	$0.346925\pi$
$139$	−122213.	+	211679.i	−0.536513	+	0.929268i	−0.999088	+	0.0426878i	$0.986408\pi$
$140$	−3193.50	+	5531.30i	−0.0137704	+	0.0238510i
$141$	−37055.3	+	32653.2i	−0.156965	+	0.138318i
$142$	−614.183	−	1063.80i	−0.00255609	−	0.00442728i
$143$	134029.			0.548101
$144$	245214.	+	186309.i	0.985461	+	0.748734i
$145$	62747.3			0.247842
$146$	174737.	+	302653.i	0.678425	+	1.17507i
$147$	−248230.	−	83603.4i	−0.947461	−	0.319103i
$148$	489068.	−	847091.i	1.83533	−	3.17889i
$149$	4924.61	−	8529.67i	0.0181721	−	0.0314751i	−0.856796	−	0.515655i	$-0.827549\pi$
$149$	4924.61	−	8529.67i	0.0181721	−	0.0314751i	0.874968	+	0.484180i	$0.160882\pi$
$150$	129968.	+	43772.9i	0.471637	+	0.158846i
$151$	109892.	+	190339.i	0.392216	+	0.679338i	0.992741	−	0.120268i	$-0.0383753\pi$
$151$	109892.	+	190339.i	0.392216	+	0.679338i	−0.600526	+	0.799606i	$0.705042\pi$
$152$	161829.			0.568128
$153$	−271755.	+	114086.i	−0.938531	+	0.394005i
$154$	3703.51			0.0125838
$155$	−122558.	−	212276.i	−0.409743	−	0.709696i
$156$	−567001.	+	499643.i	−1.86540	+	1.64380i
$157$	−15290.5	+	26483.9i	−0.0495077	+	0.0857498i	−0.889717	−	0.456512i	$-0.849099\pi$
$157$	−15290.5	+	26483.9i	−0.0495077	+	0.0857498i	0.840210	+	0.542262i	$0.182432\pi$
$158$	−238881.	+	413753.i	−0.761269	+	1.31856i
$159$	37746.8	+	187430.i	0.118410	+	0.587958i
$160$	−38559.2	−	66786.5i	−0.119077	−	0.206248i
$161$	7337.35			0.0223087
$162$	567413.	+	146253.i	1.69868	+	0.437843i
$163$	−272367.			−0.802945			−0.401472	−	0.915871i	$-0.631501\pi$
$163$	−272367.			−0.802945			−0.401472	+	0.915871i	$0.631501\pi$
$164$	−210037.	−	363795.i	−0.609799	−	1.05620i
$165$	26757.9	+	132865.i	0.0765142	+	0.379927i
$166$	51283.1	−	88824.9i	0.144445	−	0.250187i
$167$	99337.8	−	172058.i	0.275628	−	0.477402i	−0.694665	−	0.719333i	$-0.744448\pi$
$167$	99337.8	−	172058.i	0.275628	−	0.477402i	0.970293	+	0.241931i	$0.0777809\pi$
$168$	−8124.93	+	7159.71i	−0.0222099	+	0.0195714i
$169$	−80324.9	−	139127.i	−0.216338	−	0.374709i
$170$	569437.			1.51121
$171$	105999.	−	44499.6i	0.277213	−	0.116377i
$172$	407853.			1.05119
$173$	−33895.9	−	58709.5i	−0.0861058	−	0.149140i	0.819756	−	0.572713i	$-0.194109\pi$
$173$	−33895.9	−	58709.5i	−0.0861058	−	0.149140i	−0.905862	+	0.423573i	$0.860776\pi$
$174$	194423.	+	65481.3i	0.486828	+	0.163962i
$175$	−900.268	+	1559.31i	−0.00222217	+	0.00384891i
$176$	−116447.	+	201693.i	−0.283366	+	0.490805i
$177$	−436501.	−	147013.i	−1.04725	−	0.352713i
$178$	−211295.	−	365973.i	−0.499848	−	0.865763i
$179$	21849.0			0.0509681			0.0254840	−	0.999675i	$-0.491887\pi$
$179$	21849.0			0.0509681			0.0254840	+	0.999675i	$0.491887\pi$
$180$	−608498.	−	462325.i	−1.39984	−	1.06357i
$181$	188080.			0.426722			0.213361	−	0.976973i	$-0.431559\pi$
$181$	188080.			0.426722			0.213361	+	0.976973i	$0.431559\pi$
$182$	−7349.33	−	12729.4i	−0.0164463	−	0.0284859i
$183$	471414.	−	415411.i	1.04058	−	0.916959i
$184$	−617915.	+	1.07026e6i	−1.34550	+	2.33048i
$185$	−348104.	+	602933.i	−0.747789	+	1.29521i
$186$	−158221.	−	785639.i	−0.335338	−	1.66510i
$187$	−111444.	−	193027.i	−0.233052	−	0.403658i
$188$	210603.			0.434581
$189$	−3353.13	+	6923.87i	−0.00682804	+	0.0140992i
$190$	−222112.			−0.446363
$191$	123200.	+	213389.i	0.244359	+	0.423241i	0.961951	−	0.273222i	$-0.0880893\pi$
$191$	123200.	+	213389.i	0.244359	+	0.423241i	−0.717592	+	0.696463i	$0.754756\pi$
$192$	75031.5	+	372565.i	0.146889	+	0.729372i
$193$	113565.	−	196701.i	0.219459	−	0.380114i	−0.735184	−	0.677868i	$-0.762904\pi$
$193$	113565.	−	196701.i	0.219459	−	0.380114i	0.954643	+	0.297754i	$0.0962375\pi$
$194$	489686.	−	848162.i	0.934144	−	1.61798i
$195$	403574.	−	355630.i	0.760040	−	0.669749i
$196$	558453.	+	967269.i	1.03836	+	1.79849i
$197$	−503086.			−0.923584			−0.461792	−	0.886988i	$-0.652793\pi$
$197$	−503086.			−0.923584			−0.461792	+	0.886988i	$0.652793\pi$
$198$	−55744.4	+	439607.i	−0.101051	+	0.796896i
$199$	4126.65			0.00738694			0.00369347	−	0.999993i	$-0.498824\pi$
$199$	4126.65			0.00738694			0.00369347	+	0.999993i	$0.498824\pi$
$200$	−151632.	−	262634.i	−0.268050	−	0.464276i
$201$	347135.	+	116914.i	0.606050	+	0.204116i
$202$	−375287.	+	650016.i	−0.647121	+	1.12085i
$203$	−1346.74	+	2332.62i	−0.00229374	+	0.00397287i
$204$	1.19103e6	+	401137.i	2.00377	+	0.674866i
$205$	149498.	+	258938.i	0.248457	+	0.430340i
$206$	−1.46605e6			−2.40702
$207$	−110440.	+	870945.i	−0.179144	+	1.41275i
$208$	924324.			1.48138
$209$	43469.3	+	75291.1i	0.0688363	+	0.119228i
$210$	11151.6	−	9826.79i	0.0174497	−	0.0153767i
$211$	494954.	−	857285.i	0.765347	−	1.32562i	−0.174716	−	0.984619i	$-0.555901\pi$
$211$	494954.	−	857285.i	0.765347	−	1.32562i	0.940063	−	0.341001i	$-0.110766\pi$
$212$	407636.	−	706046.i	0.622921	−	1.07893i
$213$	380.965	+	1891.66i	0.000575355	+	0.00285689i
$214$	−1.03767e6	−	1.79730e6i	−1.54891	−	2.68278i
$215$	−290297.			−0.428298
$216$	−727564.	−	1.07220e6i	−1.06105	−	1.56365i
$217$	10521.8			0.0151684
$218$	573589.	+	993485.i	0.817447	+	1.41586i
$219$	−108385.	−	538182.i	−0.152708	−	0.758262i
$220$	288964.	−	500500.i	0.402519	−	0.697184i
$221$	−442305.	+	766094.i	−0.609173	+	1.05512i
$222$	−1.70781e6	+	1.50492e6i	−2.32572	+	2.04943i
$223$	523910.	+	907438.i	0.705496	+	1.22195i	0.966512	+	0.256620i	$0.0826089\pi$
$223$	523910.	+	907438.i	0.705496	+	1.22195i	−0.261017	+	0.965334i	$0.584058\pi$
$224$	3310.37			0.00440816
$225$	−171540.	−	130332.i	−0.225896	−	0.171631i
$226$	−464722.			−0.605232
$227$	−355537.	−	615808.i	−0.457952	−	0.793196i	0.540900	−	0.841087i	$-0.318084\pi$
$227$	−355537.	−	615808.i	−0.457952	−	0.793196i	−0.998853	+	0.0478902i	$0.984750\pi$
$228$	−464568.	−	156466.i	−0.591851	−	0.199334i
$229$	−147071.	+	254734.i	−0.185327	+	0.320995i	−0.943687	−	0.330841i	$-0.892668\pi$
$229$	−147071.	+	254734.i	−0.185327	+	0.320995i	0.758360	+	0.651836i	$0.226001\pi$
$230$	848096.	−	1.46895e6i	1.05712	−	1.83099i
$231$	−5513.53	−	1856.95i	−0.00679830	−	0.00228965i
$232$	−226831.	−	392883.i	−0.276683	−	0.479230i
$233$	1.56670e6			1.89059			0.945294	−	0.326218i	$-0.105774\pi$
$233$	1.56670e6			1.89059			0.945294	+	0.326218i	$0.105774\pi$
$234$	1.62161e6	−	680767.i	1.93600	−	0.812753i
$235$	−149901.			−0.177066
$236$	982013.	+	1.70090e6i	1.14772	+	1.98792i
$237$	563086.	−	496193.i	0.651184	−	0.573825i
$238$	−12221.8	+	21168.8i	−0.0139860	+	0.0242244i
$239$	−260961.	+	451998.i	−0.295516	+	0.511849i	−0.975105	−	0.221744i	$-0.928825\pi$
$239$	−260961.	+	451998.i	−0.295516	+	0.511849i	0.679589	+	0.733593i	$0.262158\pi$
$240$	184534.	+	916292.i	0.206799	+	1.02685i
$241$	213855.	+	370407.i	0.237179	+	0.410806i	0.959904	−	0.280330i	$-0.0904439\pi$
$241$	213855.	+	370407.i	0.237179	+	0.410806i	−0.722725	+	0.691136i	$0.757111\pi$
$242$	1.26304e6			1.38637
$243$	−771394.	−	502234.i	−0.838032	−	0.545620i
$244$	−2.67927e6			−2.88099
$245$	−397490.	−	688472.i	−0.423068	−	0.732776i
$246$	193001.	+	958335.i	0.203339	+	1.00967i
$247$	172523.	−	298819.i	0.179931	−	0.311649i
$248$	−886092.	+	1.53476e6i	−0.914849	+	1.58457i
$249$	−120884.	+	106523.i	−0.123558	+	0.108879i
$250$	941696.	+	1.63106e6i	0.952929	+	1.65052i
$251$	−231914.			−0.232350			−0.116175	−	0.993229i	$-0.537063\pi$
$251$	−231914.			−0.232350			−0.116175	+	0.993229i	$0.537063\pi$
$252$	30247.0	−	12698.0i	0.0300041	−	0.0125960i
$253$	−663921.			−0.652101
$254$	−463637.	−	803043.i	−0.450914	−	0.781006i
$255$	−847740.	−	285517.i	−0.816417	−	0.274967i
$256$	1.06908e6	−	1.85170e6i	1.01955	−	1.76592i
$257$	707127.	−	1.22478e6i	0.667828	−	1.15671i	−0.310682	−	0.950514i	$-0.600557\pi$
$257$	707127.	−	1.22478e6i	0.667828	−	1.15671i	0.978510	−	0.206199i	$-0.0661093\pi$
$258$	−899489.	−	302946.i	−0.841292	−	0.283345i
$259$	−14942.6	−	25881.4i	−0.0138413	−	0.0239739i
$260$	−2.29371e6			−2.10428
$261$	−256612.	−	194968.i	−0.233171	−	0.177159i
$262$	3.64915e6			3.28427
$263$	615838.	+	1.06666e6i	0.549006	+	0.950907i	0.998343	+	0.0575445i	$0.0183271\pi$
$263$	615838.	+	1.06666e6i	0.549006	+	0.950907i	−0.449336	+	0.893363i	$0.648340\pi$
$264$	735185.	−	647847.i	0.649212	−	0.572087i
$265$	−290143.	+	502542.i	−0.253803	+	0.439600i
$266$	4767.17	−	8256.98i	0.00413101	−	0.00715513i
$267$	131062.	+	650779.i	0.112512	+	0.558670i
$268$	−780963.	−	1.35267e6i	−0.664192	−	1.15041i
$269$	119245.			0.100475			0.0502377	−	0.998737i	$-0.484002\pi$
$269$	119245.			0.100475			0.0502377	+	0.998737i	$0.484002\pi$
$270$	998591.	+	1.47160e6i	0.833639	+	1.22852i
$271$	50141.4			0.0414738			0.0207369	−	0.999785i	$-0.493399\pi$
$271$	50141.4			0.0414738			0.0207369	+	0.999785i	$0.493399\pi$
$272$	−768566.	−	1.33120e6i	−0.629881	−	1.09099i
$273$	4558.64	+	22635.7i	0.00370193	+	0.0183817i
$274$	−762198.	+	1.32017e6i	−0.613326	+	1.06231i
$275$	81460.8	−	141094.i	0.0649557	−	0.112506i
$276$	2.80866e6	−	2.47500e6i	2.21936	−	1.95570i
$277$	−235820.	−	408452.i	−0.184663	−	0.319846i	0.758800	−	0.651324i	$-0.225786\pi$
$277$	−235820.	−	408452.i	−0.184663	−	0.319846i	−0.943463	+	0.331478i	$0.892453\pi$
$278$	−2.42550e6			−1.88230
$279$	−158372.	+	1.24894e6i	−0.121806	+	0.960573i
$280$	−32868.0			−0.0250541
$281$	−1.03652e6	−	1.79530e6i	−0.783087	−	1.35635i	−0.930135	−	0.367217i	$-0.880311\pi$
$281$	−1.03652e6	−	1.79530e6i	−0.783087	−	1.35635i	0.147048	−	0.989129i	$-0.453023\pi$
$282$	−464470.	−	156432.i	−0.347804	−	0.117140i
$283$	−758046.	+	1.31297e6i	−0.562639	+	0.974519i	0.434626	+	0.900611i	$0.356880\pi$
$283$	−758046.	+	1.31297e6i	−0.562639	+	0.974519i	−0.997265	+	0.0739079i	$0.976453\pi$
$284$	4114.11	−	7125.86i	0.00302678	−	0.00524253i
$285$	330665.	+	111367.i	0.241144	+	0.0812168i
$286$	665005.	+	1.15182e6i	0.480739	+	0.832665i
$287$	−12834.7			−0.00919770
$288$	−49827.0	+	392942.i	−0.0353984	+	0.279156i
$289$	51229.6			0.0360808
$290$	311329.	+	539237.i	0.217382	+	0.376517i
$291$	−1.15428e6	+	1.01716e6i	−0.799060	+	0.704134i
$292$	−1.17048e6	+	2.02733e6i	−0.803352	+	1.39145i
$293$	−385100.	+	667013.i	−0.262062	+	0.453905i	−0.966790	−	0.255573i	$-0.917736\pi$
$293$	−385100.	+	667013.i	−0.262062	+	0.453905i	0.704727	+	0.709478i	$0.251069\pi$
$294$	−513156.	−	2.54805e6i	−0.346243	−	1.71925i
$295$	−698967.	−	1.21065e6i	−0.467629	−	0.809957i
$296$	5.03357e6			3.33924
$297$	303408.	−	626507.i	0.199589	−	0.412131i
$298$	97736.4			0.0637552
$299$	1.31750e6	+	2.28198e6i	0.852262	+	1.47616i
$300$	181366.	+	900562.i	0.116346	+	0.577711i
$301$	6230.62	−	10791.8i	0.00396383	−	0.00686556i
$302$	−1.09049e6	+	1.88879e6i	−0.688026	+	1.19170i
$303$	884622.	−	779531.i	0.553543	−	0.487783i
$304$	299783.	+	519240.i	0.186047	+	0.322243i
$305$	1.90702e6			1.17383
$306$	−2.32878e6	−	1.76936e6i	−1.42175	−	1.08022i
$307$	2.13559e6			1.29322			0.646610	−	0.762821i	$-0.276186\pi$
$307$	2.13559e6			1.29322			0.646610	+	0.762821i	$0.276186\pi$
$308$	12404.0	+	21484.4i	0.00745050	+	0.0129046i
$309$	2.18255e6	+	735078.i	1.30037	+	0.437963i
$310$	1.21617e6	−	2.10647e6i	0.718772	−	1.24495i
$311$	301713.	−	522582.i	0.176886	−	0.306375i	−0.763927	−	0.645303i	$-0.776731\pi$
$311$	301713.	−	522582.i	0.176886	−	0.306375i	0.940812	+	0.338928i	$0.110064\pi$
$312$	−3.68565e6	−	1.24132e6i	−2.14352	−	0.721932i
$313$	−1.08619e6	−	1.88133e6i	−0.626677	−	1.08544i	−0.988214	−	0.153079i	$-0.951081\pi$
$313$	−1.08619e6	−	1.88133e6i	−0.626677	−	1.08544i	0.361537	−	0.932358i	$-0.382252\pi$
$314$	−303463.			−0.173693
$315$	−21528.9	+	9038.05i	−0.0122249	+	0.00513214i
$316$	−3.20029e6			−1.80290
$317$	−1.60049e6	−	2.77213e6i	−0.894550	−	1.54941i	−0.834361	−	0.551218i	$-0.814163\pi$
$317$	−1.60049e6	−	2.77213e6i	−0.894550	−	1.54941i	−0.0601886	−	0.998187i	$-0.519170\pi$
$318$	−1.42345e6	+	1.25435e6i	−0.789358	+	0.695585i
$319$	121860.	−	211067.i	0.0670477	−	0.116130i
$320$	−576732.	+	998930.i	−0.314847	+	0.545331i
$321$	643645.	+	3.19599e6i	0.348646	+	1.73118i
$322$	36405.2	+	63055.7i	0.0195670	+	0.0338910i
$323$	−573805.			−0.306026
$324$	1.05198e6	+	3.78145e6i	0.556733	+	2.00123i
$325$	−646611.			−0.339574
$326$	−1.35139e6	−	2.34067e6i	−0.704263	−	1.21982i
$327$	−355785.	−	1.76663e6i	−0.184000	−	0.913644i
$328$	1.08087e6	−	1.87212e6i	0.554739	−	0.960836i
$329$	3217.31	−	5572.54i	0.00163871	−	0.00283834i
$330$	−1.00905e6	+	889178.i	−0.510068	+	0.449473i
$331$	−1.30413e6	−	2.25883e6i	−0.654263	−	1.13322i	−0.982078	−	0.188475i	$-0.939645\pi$
$331$	−1.30413e6	−	2.25883e6i	−0.654263	−	1.13322i	0.327815	−	0.944742i	$-0.393688\pi$
$332$	687041.			0.342088
$333$	3.29704e6	−	1.38413e6i	1.62935	−	0.684017i
$334$	1.97151e6			0.967014
$335$	555865.	+	962787.i	0.270618	+	0.468725i
$336$	−38023.7	−	12806.3i	−0.0183741	−	0.00618835i
$337$	414934.	−	718687.i	0.199024	−	0.344719i	−0.749189	−	0.662357i	$-0.769556\pi$
$337$	414934.	−	718687.i	0.199024	−	0.344719i	0.948212	+	0.317638i	$0.102890\pi$
$338$	797085.	−	1.38059e6i	0.379501	−	0.657315i
$339$	691846.	+	233012.i	0.326972	+	0.110123i
$340$	1.90719e6	+	3.30335e6i	0.894741	+	1.54974i
$341$	−952065.			−0.443385
$342$	908351.	+	690146.i	0.419941	+	0.319063i
$343$	68258.7			0.0313273
$344$	1.04942e6	+	1.81765e6i	0.478139	+	0.828161i
$345$	−1.99912e6	+	1.76163e6i	−0.904256	+	0.796832i
$346$	336358.	−	582589.i	0.151047	−	0.261621i
$347$	−1.15930e6	+	2.00796e6i	−0.516858	+	0.895224i	0.482951	+	0.875648i	$0.339565\pi$
$347$	−1.15930e6	+	2.00796e6i	−0.516858	+	0.895224i	−0.999808	+	0.0195761i	$0.993768\pi$
$348$	271311.	+	1.34718e6i	0.120093	+	0.596318i
$349$	1.56680e6	+	2.71377e6i	0.688572	+	1.19264i	0.972300	+	0.233737i	$0.0750955\pi$
$349$	1.56680e6	+	2.71377e6i	0.688572	+	1.19264i	−0.283728	+	0.958905i	$0.591571\pi$
$350$	−17867.2			−0.00779626
$351$	−2.75547e6	+	200404.i	−1.19379	+	0.0868236i
$352$	−299539.			−0.128854
$353$	1.33508e6	+	2.31243e6i	0.570259	+	0.987717i	0.996539	+	0.0831261i	$0.0264904\pi$
$353$	1.33508e6	+	2.31243e6i	0.570259	+	0.987717i	−0.426280	+	0.904591i	$0.640176\pi$
$354$	−902361.	−	4.48062e6i	−0.382712	−	1.90034i
$355$	−2928.30	+	5071.96i	−0.00123323	+	0.00213602i
$356$	1.41536e6	−	2.45148e6i	0.591891	−	1.02519i
$357$	28809.0	−	25386.6i	0.0119635	−	0.0105423i
$358$	108407.	+	187766.i	0.0447041	+	0.0774299i
$359$	−2.05907e6			−0.843210			−0.421605	−	0.906780i	$-0.638533\pi$
$359$	−2.05907e6			−0.843210			−0.421605	+	0.906780i	$0.638533\pi$
$360$	494722.	−	3.90144e6i	0.201190	−	1.58660i
$361$	−2.25228e6			−0.909610
$362$	933182.	+	1.61632e6i	0.374278	+	0.648269i
$363$	−1.88033e6	−	633290.i	−0.748974	−	0.252253i
$364$	49229.6	−	85268.2i	0.0194748	−	0.0337314i
$365$	833109.	−	1.44299e6i	0.327318	−	0.566931i
$366$	5.90894e6	+	1.99012e6i	2.30572	+	0.776562i
$367$	509190.	+	881943.i	0.197340	+	0.341803i	0.947665	−	0.319266i	$-0.103436\pi$
$367$	509190.	+	881943.i	0.197340	+	0.341803i	−0.750325	+	0.661069i	$0.770103\pi$
$368$	−4.57868e6			−1.76247
$369$	193184.	−	1.52348e6i	0.0738595	−	0.582465i
$370$	−6.90865e6			−2.62355
$371$	−12454.6	−	21572.0i	−0.00469781	−	0.00813685i
$372$	4.02764e6	−	3.54916e6i	1.50901	−	1.32975i
$373$	−2.61768e6	+	4.53395e6i	−0.974191	+	1.68735i	−0.291612	+	0.956537i	$0.594192\pi$
$373$	−2.61768e6	+	4.53395e6i	−0.974191	+	1.68735i	−0.682579	+	0.730812i	$0.739142\pi$
$374$	1.10589e6	−	1.91546e6i	0.408820	−	0.708098i
$375$	−584114.	−	2.90039e6i	−0.214496	−	1.06507i
$376$	541891.	+	938583.i	0.197671	+	0.342376i
$377$	−967286.			−0.350511
$378$	−76139.4	+	5537.57i	−0.0274082	+	0.00199338i
$379$	2.73883e6			0.979417			0.489708	−	0.871886i	$-0.337103\pi$
$379$	2.73883e6			0.979417			0.489708	+	0.871886i	$0.337103\pi$
$380$	−743910.	−	1.28849e6i	−0.264278	−	0.457743i
$381$	287584.	+	1.42799e6i	0.101497	+	0.503978i
$382$	−1.22255e6	+	2.11751e6i	−0.428654	+	0.742451i
$383$	2.17454e6	−	3.76641e6i	0.757478	−	1.31199i	−0.186655	−	0.982425i	$-0.559765\pi$
$383$	2.17454e6	−	3.76641e6i	0.757478	−	1.31199i	0.944133	−	0.329564i	$-0.106902\pi$
$384$	−3.43950e6	+	3.03090e6i	−1.19033	+	1.04892i
$385$	−8828.79	−	15291.9i	−0.00303563	−	0.00525787i
$386$	2.25388e6			0.769950
$387$	1.18720e6	+	902011.i	0.402946	+	0.306150i
$388$	6.56035e6			2.21232
$389$	−1.50378e6	−	2.60462e6i	−0.503860	−	0.872712i	−0.999990	−	0.00446327i	$-0.998579\pi$
$389$	−1.50378e6	−	2.60462e6i	−0.503860	−	0.872712i	0.496130	−	0.868248i	$-0.334754\pi$
$390$	5.05860e6	+	1.70373e6i	1.68410	+	0.567202i
$391$	2.19098e6	−	3.79488e6i	0.724762	−	1.25533i
$392$	−2.87385e6	+	4.97765e6i	−0.944602	+	1.63610i
$393$	−5.43261e6	−	1.82969e6i	−1.77430	−	0.597581i
$394$	−2.49613e6	−	4.32342e6i	−0.810077	−	1.40309i
$395$	2.27787e6			0.734574
$396$	−2.73690e6	+	1.14898e6i	−0.877044	+	0.368192i
$397$	2.16602e6			0.689740			0.344870	−	0.938650i	$-0.387923\pi$
$397$	2.16602e6			0.689740			0.344870	+	0.938650i	$0.387923\pi$
$398$	20474.9	+	35463.6i	0.00647910	+	0.0112221i
$399$	−11237.1	+	9902.17i	−0.00353364	+	0.00311385i
$400$	561788.	−	973046.i	0.175559	−	0.304077i
$401$	−1.76996e6	+	3.06566e6i	−0.549670	+	0.952057i	0.448626	+	0.893719i	$0.351913\pi$
$401$	−1.76996e6	+	3.06566e6i	−0.549670	+	0.952057i	−0.998297	+	0.0583377i	$0.981420\pi$
$402$	717618.	+	3.56329e6i	0.221477	+	1.09973i
$403$	1.88930e6	+	3.27236e6i	0.579480	+	1.00369i
$404$	−5.02774e6			−1.53257
$405$	−748770.	−	2.69152e6i	−0.226835	−	0.815380i
$406$	−26728.1			−0.00804735
$407$	1.35209e6	+	2.34188e6i	0.404593	+	0.700775i
$408$	1.27685e6	+	6.34014e6i	0.379744	+	1.88560i
$409$	783644.	−	1.35731e6i	0.231638	−	0.401210i	−0.726652	−	0.687006i	$-0.758925\pi$
$409$	783644.	−	1.35731e6i	0.231638	−	0.401210i	0.958290	+	0.285796i	$0.0922580\pi$
$410$	−1.48351e6	+	2.56951e6i	−0.435843	+	0.754902i
$411$	1.79664e6	−	1.58321e6i	0.524635	−	0.462309i
$412$	−4.91016e6	−	8.50465e6i	−1.42513	−	2.46839i
$413$	60007.5			0.0173113
$414$	−8.03269e6	+	3.37221e6i	−2.30335	+	0.966971i
$415$	−489015.			−0.139380
$416$	594413.	+	1.02955e6i	0.168405	+	0.291686i
$417$	3.61092e6	+	1.21615e6i	1.01690	+	0.342490i
$418$	−431358.	+	747133.i	−0.120753	+	0.209150i
$419$	1.18321e6	−	2.04937e6i	0.329250	−	0.570277i	−0.653114	−	0.757260i	$-0.726538\pi$
$419$	1.18321e6	−	2.04937e6i	0.329250	−	0.570277i	0.982363	+	0.186983i	$0.0598709\pi$
$420$	94355.6	+	31778.8i	0.0261002	+	0.00879050i
$421$	1.84288e6	+	3.19196e6i	0.506747	+	0.877712i	0.999970	+	0.00780885i	$0.00248566\pi$
$421$	1.84288e6	+	3.19196e6i	0.506747	+	0.877712i	−0.493222	+	0.869903i	$0.664181\pi$
$422$	9.82311e6			2.68515
$423$	613036.	+	465772.i	0.166585	+	0.126568i
$424$	4.19546e6			1.13335
$425$	537650.	+	931238.i	0.144387	+	0.250085i
$426$	−14366.3	+	12659.7i	−0.00383550	+	0.00337985i
$427$	−40930.3	+	70893.3i	−0.0108636	+	0.0188164i
$428$	6.95086e6	−	1.20392e7i	1.83412	−	3.17680i
$429$	−412489.	−	2.04819e6i	−0.108210	−	0.537313i
$430$	−1.44035e6	−	2.49475e6i	−0.375661	−	0.650664i
$431$	−6.78152e6			−1.75847			−0.879233	−	0.476391i	$-0.841945\pi$
$431$	−6.78152e6			−1.75847			−0.879233	+	0.476391i	$0.841945\pi$
$432$	2.09243e6	−	4.32066e6i	0.539439	−	1.11389i
$433$	−3.20434e6			−0.821332			−0.410666	−	0.911786i	$-0.634704\pi$
$433$	−3.20434e6			−0.821332			−0.410666	+	0.911786i	$0.634704\pi$
$434$	52205.2	+	90422.1i	0.0133042	+	0.0230436i
$435$	−193111.	−	958881.i	−0.0489309	−	0.242964i
$436$	−3.84220e6	+	6.65488e6i	−0.967973	+	1.67658i
$437$	−854601.	+	1.48021e6i	−0.214072	+	0.370784i
$438$	4.08726e6	−	3.60171e6i	1.01800	−	0.897063i
$439$	−698435.	−	1.20972e6i	−0.172967	−	0.299588i	0.766489	−	0.642258i	$-0.222002\pi$
$439$	−698435.	−	1.20972e6i	−0.172967	−	0.299588i	−0.939456	+	0.342670i	$0.888669\pi$
$440$	2.97406e6			0.732350
$441$	−513645.	+	4.05066e6i	−0.125767	+	0.991812i
$442$	−8.77821e6			−2.13723
$443$	2.48597e6	+	4.30583e6i	0.601847	+	1.04243i	0.992541	+	0.121910i	$0.0389018\pi$
$443$	2.48597e6	+	4.30583e6i	0.601847	+	1.04243i	−0.390694	+	0.920521i	$0.627765\pi$
$444$	−1.44501e7	−	4.86676e6i	−3.47867	−	1.17161i
$445$	−1.00741e6	+	1.74488e6i	−0.241160	+	0.417702i
$446$	−5.19889e6	+	9.00475e6i	−1.23758	+	2.14355i
$447$	−145503.	−	49005.2i	−0.0344432	−	0.0116004i
$448$	−24756.7	−	42879.9i	−0.00582771	−	0.0100939i
$449$	4.85114e6			1.13561			0.567804	−	0.823164i	$-0.307793\pi$
$449$	4.85114e6			1.13561			0.567804	+	0.823164i	$0.307793\pi$
$450$	268933.	−	2.12084e6i	0.0626056	−	0.493715i
$451$	1.16134e6			0.268856
$452$	−1.55647e6	−	2.69589e6i	−0.358340	−	0.620663i
$453$	2.57049e6	−	2.26512e6i	0.588532	−	0.518616i
$454$	3.52809e6	−	6.11083e6i	0.803340	−	1.39143i
$455$	−35040.1	+	60691.3i	−0.00793482	+	0.0137435i
$456$	−498043.	−	2.47301e6i	−0.112164	−	0.556946i
$457$	−2.14244e6	−	3.71081e6i	−0.479864	−	0.831149i	0.519869	−	0.854246i	$-0.325981\pi$
$457$	−2.14244e6	−	3.71081e6i	−0.479864	−	0.831149i	−0.999733	+	0.0230972i	$0.992647\pi$
$458$	−2.91885e6			−0.650201
$459$	2.57976e6	+	3.80175e6i	0.571542	+	0.842271i
$460$	1.13620e7			2.50357
$461$	−11973.0	−	20737.8i	−0.00262392	−	0.00454476i	0.864710	−	0.502271i	$-0.167502\pi$
$461$	−11973.0	−	20737.8i	−0.00262392	−	0.00454476i	−0.867334	+	0.497726i	$0.834169\pi$
$462$	−11397.9	−	56595.7i	−0.00248439	−	0.0123361i
$463$	1.76420e6	−	3.05569e6i	0.382469	−	0.662456i	−0.608945	−	0.793212i	$-0.708407\pi$
$463$	1.76420e6	−	3.05569e6i	0.382469	−	0.662456i	0.991415	+	0.130756i	$0.0417405\pi$
$464$	840397.	−	1.45561e6i	0.181213	−	0.313870i
$465$	−2.86675e6	+	2.52618e6i	−0.614832	+	0.541792i
$466$	7.77341e6	+	1.34639e7i	1.65824	+	2.87215i
$467$	−4.66263e6			−0.989324			−0.494662	−	0.869086i	$-0.664708\pi$
$467$	−4.66263e6			−0.989324			−0.494662	+	0.869086i	$0.664708\pi$
$468$	9.38036e6	+	7.12701e6i	1.97973	+	1.50415i
$469$	−47722.0			−0.0100181
$470$	−743753.	−	1.28822e6i	−0.155304	−	0.268995i
$471$	451776.	+	152157.i	0.0938362	+	0.0316038i
$472$	−5.05353e6	+	8.75296e6i	−1.04409	+	1.80842i
$473$	−563778.	+	976492.i	−0.115866	+	0.200686i
$474$	7.05800e6	+	2.37712e6i	1.44290	+	0.485965i
$475$	−209713.	−	363234.i	−0.0426473	−	0.0738673i
$476$	−163736.			−0.0331227
$477$	2.74807e6	−	1.15367e6i	0.553008	−	0.232158i
$478$	−5.17917e6			−1.03679
$479$	−3.27492e6	−	5.67232e6i	−0.652171	−	1.12959i	−0.982595	−	0.185760i	$-0.940525\pi$
$479$	−3.27492e6	−	5.67232e6i	−0.652171	−	1.12959i	0.330424	−	0.943832i	$-0.392808\pi$
$480$	−901938.	+	794790.i	−0.178679	+	0.157452i
$481$	5.36622e6	−	9.29457e6i	1.05756	−	1.83175i
$482$	−2.12214e6	+	3.67565e6i	−0.416060	+	0.720637i
$483$	−22581.4	−	112127.i	−0.00440436	−	0.0218696i
$484$	4.23024e6	+	7.32700e6i	0.820828	+	1.42172i
$485$	−4.66945e6			−0.901387
$486$	488724.	−	9.12111e6i	0.0938584	−	1.75169i
$487$	−9.23457e6			−1.76439			−0.882194	−	0.470886i	$-0.843934\pi$
$487$	−9.23457e6			−1.76439			−0.882194	+	0.470886i	$0.843934\pi$
$488$	−6.89388e6	−	1.19406e7i	−1.31043	−	2.26973i
$489$	838236.	+	4.16221e6i	0.158524	+	0.787141i
$490$	3.94439e6	−	6.83189e6i	0.742147	−	1.28544i
$491$	2.62130e6	−	4.54023e6i	0.490697	−	0.849912i	−0.509246	−	0.860621i	$-0.670075\pi$
$491$	2.62130e6	−	4.54023e6i	0.490697	−	0.849912i	0.999943	+	0.0107089i	$0.00340882\pi$
$492$	−4.91298e6	+	4.32933e6i	−0.915023	+	0.806320i
$493$	804288.	+	1.39307e6i	0.149037	+	0.258140i
$494$	3.42399e6			0.631269
$495$	1.94804e6	−	817808.i	0.357343	−	0.150016i
$496$	−6.56584e6			−1.19836
$497$	−125.700	−	217.718i	−2.28267e−5	−	3.95370e-5i
$498$	−1.51522e6	−	510322.i	−0.273780	−	0.0922086i
$499$	−3.23974e6	+	5.61140e6i	−0.582451	+	1.00883i	0.412737	+	0.910850i	$0.364573\pi$
$499$	−3.23974e6	+	5.61140e6i	−0.582451	+	1.00883i	−0.995188	+	0.0979844i	$0.968760\pi$
$500$	−6.30796e6	+	1.09257e7i	−1.12840	+	1.95445i
$501$	−2.93505e6	−	988519.i	−0.522422	−	0.175951i
$502$	−1.15067e6	−	1.99302e6i	−0.203794	−	0.352982i
$503$	4.42908e6			0.780538			0.390269	−	0.920701i	$-0.372382\pi$
$503$	4.42908e6			0.780538			0.390269	+	0.920701i	$0.372382\pi$
$504$	134417.	+	102128.i	0.0235710	+	0.0179088i
$505$	3.57859e6			0.624429
$506$	−3.29413e6	−	5.70560e6i	−0.571959	−	0.990661i
$507$	−1.87888e6	+	1.65567e6i	−0.324622	+	0.286058i
$508$	3.10568e6	−	5.37920e6i	0.533946	−	0.924822i
$509$	−2.14026e6	+	3.70704e6i	−0.366162	+	0.634210i	−0.988962	−	0.148170i	$-0.952662\pi$
$509$	−2.14026e6	+	3.70704e6i	−0.366162	+	0.634210i	0.622800	+	0.782381i	$0.285995\pi$
$510$	−1.75250e6	−	8.70193e6i	−0.298354	−	1.48146i
$511$	35761.9	+	61941.4i	0.00605855	+	0.0104937i
$512$	1.18067e7			1.99046
$513$	−1.00625e6	−	1.48289e6i	−0.168816	−	0.248780i
$514$	1.40340e7			2.34301
$515$	3.49490e6	+	6.05335e6i	0.580653	+	1.00572i
$516$	−1.25521e6	−	6.23266e6i	−0.207535	−	1.03050i
$517$	−291118.	+	504232.i	−0.0479009	+	0.0829667i
$518$	148280.	−	256828.i	0.0242805	−	0.0420550i
$519$	−792859.	+	698669.i	−0.129204	+	0.113855i
$520$	−5.90181e6	−	1.02222e7i	−0.957142	−	1.65782i
$521$	8.64335e6			1.39504			0.697522	−	0.716564i	$-0.254286\pi$
$521$	8.64335e6			1.39504			0.697522	+	0.716564i	$0.254286\pi$
$522$	402306.	−	3.17263e6i	0.0646220	−	0.509616i
$523$	−9.11201e6			−1.45667			−0.728333	−	0.685224i	$-0.759704\pi$
$523$	−9.11201e6			−1.45667			−0.728333	+	0.685224i	$0.759704\pi$
$524$	1.22220e7	+	2.11690e7i	1.94452	+	3.36801i
$525$	26599.5	+	8958.64i	0.00421187	+	0.00141855i
$526$	−6.11113e6	+	1.05848e7i	−0.963068	+	1.66808i
$527$	3.14187e6	−	5.44187e6i	0.492789	−	0.853536i
$528$	3.44057e6	+	1.15878e6i	0.537089	+	0.180890i
$529$	−3.30813e6	−	5.72984e6i	−0.513976	−	0.890233i
$530$	−5.75832e6			−0.890443
$531$	−903220.	+	7.12290e6i	−0.139014	+	1.09628i
$532$	63865.9			0.00978341
$533$	−2.30460e6	−	3.99168e6i	−0.351380	−	0.608609i
$534$	−4.94239e6	+	4.35524e6i	−0.750038	+	0.660936i
$535$	−4.94740e6	+	8.56915e6i	−0.747296	+	1.29436i
$536$	4.01890e6	−	6.96094e6i	0.604221	−	1.04654i
$537$	−67242.3	−	333888.i	−0.0100625	−	0.0499649i
$538$	591650.	+	1.02477e6i	0.0881271	+	0.152641i
$539$	−3.08782e6			−0.457804
$540$	−5.19236e6	+	1.07217e7i	−0.766268	+	1.58226i
$541$	5.76360e6			0.846643			0.423322	−	0.905979i	$-0.360864\pi$
$541$	5.76360e6			0.846643			0.423322	+	0.905979i	$0.360864\pi$
$542$	248783.	+	430905.i	0.0363767	+	0.0630062i
$543$	−578833.	−	2.87416e6i	−0.0842468	−	0.418323i
$544$	988496.	−	1.71213e6i	0.143211	−	0.248050i
$545$	2.73476e6	−	4.73674e6i	0.394391	−	0.683106i
$546$	−171908.	+	151486.i	−0.0246783	+	0.0217466i
$547$	2.80744e6	+	4.86263e6i	0.401183	+	0.694869i	0.993869	−	0.110564i	$-0.0352659\pi$
$547$	2.80744e6	+	4.86263e6i	0.401183	+	0.694869i	−0.592686	+	0.805434i	$0.701933\pi$
$548$	−1.02112e7			−1.45253
$549$	−7.79898e6	−	5.92550e6i	−1.10435	−	0.839063i
$550$	1.61671e6			0.227891
$551$	−313717.	−	543374.i	−0.0440209	−	0.0762464i
$552$	1.82570e7	+	6.14892e6i	2.55025	+	0.858917i
$553$	−48889.7	+	84679.4i	−0.00679837	+	0.0117751i
$554$	2.34010e6	−	4.05317e6i	0.323937	−	0.561075i
$555$	1.02851e7	+	3.46401e6i	1.41735	+	0.477360i
$556$	−8.12364e6	−	1.40705e7i	−1.11446	−	1.93030i
$557$	2.18422e6			0.298303			0.149152	−	0.988814i	$-0.452346\pi$
$557$	2.18422e6			0.298303			0.149152	+	0.988814i	$0.452346\pi$
$558$	−1.15189e7	+	4.83576e6i	−1.56612	+	0.657475i
$559$	4.47510e6			0.605722
$560$	−60887.1	−	105460.i	−0.00820456	−	0.0142107i
$561$	−2.60679e6	+	2.29711e6i	−0.349702	+	0.308158i
$562$	1.02856e7	−	1.78152e7i	1.37369	−	2.37931i
$563$	−339673.	+	588330.i	−0.0451637	+	0.0782258i	−0.887724	−	0.460377i	$-0.847714\pi$
$563$	−339673.	+	588330.i	−0.0451637	+	0.0782258i	0.842560	+	0.538603i	$0.181048\pi$
$564$	−648152.	−	3.21836e6i	−0.0857983	−	0.426027i
$565$	1.10785e6	+	1.91885e6i	0.146002	+	0.252883i
$566$	−1.50446e7			−1.97396
$567$	116128.	+	29932.5i	0.0151697	+	0.00391007i
$568$	42343.2			0.00550697
$569$	3.28195e6	+	5.68451e6i	0.424964	+	0.736059i	0.996417	−	0.0845759i	$-0.0269536\pi$
$569$	3.28195e6	+	5.68451e6i	0.424964	+	0.736059i	−0.571453	+	0.820635i	$0.693620\pi$
$570$	683571.	+	3.39423e6i	0.0881244	+	0.437577i
$571$	952119.	−	1.64912e6i	0.122208	−	0.211671i	−0.798430	−	0.602088i	$-0.794336\pi$
$571$	952119.	−	1.64912e6i	0.122208	−	0.211671i	0.920638	+	0.390417i	$0.127669\pi$
$572$	−4.45455e6	+	7.71550e6i	−0.569264	+	0.985994i
$573$	2.88177e6	−	2.53942e6i	0.366668	−	0.323109i
$574$	−63680.8	−	110298.i	−0.00806731	−	0.0139730i
$575$	3.20302e6			0.404008
$576$	5.46249e6	−	2.29321e6i	0.686016	−	0.287997i
$577$	1.13367e7			1.41758			0.708792	−	0.705417i	$-0.249240\pi$
$577$	1.13367e7			1.41758			0.708792	+	0.705417i	$0.249240\pi$
$578$	254182.	+	440257.i	0.0316465	+	0.0548133i
$579$	−3.35542e6	−	1.13010e6i	−0.415959	−	0.140094i
$580$	−2.08544e6	+	3.61209e6i	−0.257412	+	0.445850i
$581$	10495.7	−	18179.1i	0.00128994	−	0.00223425i
$582$	−1.44684e7	−	4.87291e6i	−1.77056	−	0.596322i
$583$	1.12696e6	+	1.95195e6i	0.137321	+	0.237846i
$584$	−1.20467e7			−1.46163
$585$	−6.67665e6	−	5.07278e6i	−0.806620	−	0.612853i
$586$	−7.64290e6			−0.919420
$587$	−6.88666e6	−	1.19280e7i	−0.824923	−	1.42881i	−0.901978	−	0.431781i	$-0.857885\pi$
$587$	−6.88666e6	−	1.19280e7i	−0.824923	−	1.42881i	0.0770557	−	0.997027i	$-0.475448\pi$
$588$	1.30628e7	−	1.15109e7i	1.55809	−	1.37299i
$589$	−1.22550e6	+	2.12263e6i	−0.145554	+	0.252108i
$590$	6.93603e6	−	1.20136e7i	0.820315	−	1.42083i
$591$	1.54830e6	+	7.68798e6i	0.182341	+	0.905406i
$592$	9.32456e6	+	1.61506e7i	1.09351	+	1.89402i
$593$	9.94674e6			1.16157			0.580783	−	0.814058i	$-0.302746\pi$
$593$	9.94674e6			1.16157			0.580783	+	0.814058i	$0.302746\pi$
$594$	6.88948e6	−	501067.i	0.801162	−	0.0582679i
$595$	116542.			0.0134955
$596$	327344.	+	566977.i	0.0377476	+	0.0653807i
$597$	−12700.2	−	63062.0i	−0.00145839	−	0.00724155i
$598$	−1.30739e7	+	2.26447e7i	−1.49504	+	2.58948i
$599$	−2.77125e6	+	4.79995e6i	−0.315579	+	0.546600i	−0.979561	−	0.201150i	$-0.935532\pi$
$599$	−2.77125e6	+	4.79995e6i	−0.315579	+	0.546600i	0.663981	+	0.747749i	$0.268866\pi$
$600$	−3.54682e6	+	3.12547e6i	−0.402218	+	0.354435i
$601$	−6.63325e6	−	1.14891e7i	−0.749101	−	1.29748i	−0.948254	−	0.317513i	$-0.897152\pi$
$601$	−6.63325e6	−	1.14891e7i	−0.749101	−	1.29748i	0.199153	−	0.979968i	$-0.436181\pi$
$602$	123656.			0.0139067
$603$	718301.	−	5.66461e6i	0.0804476	−	0.634419i
$604$	−1.46093e7			−1.62944
$605$	−3.01096e6	−	5.21513e6i	−0.334438	−	0.579264i
$606$	1.10883e7	+	3.73451e6i	1.22654	+	0.413098i
$607$	−3.04326e6	+	5.27108e6i	−0.335249	+	0.580668i	−0.983533	−	0.180731i	$-0.942154\pi$
$607$	−3.04326e6	+	5.27108e6i	−0.335249	+	0.580668i	0.648284	+	0.761399i	$0.275487\pi$
$608$	−385568.	+	667824.i	−0.0423002	+	0.0732660i
$609$	39791.0	+	13401.5i	0.00434752	+	0.00146424i
$610$	9.46194e6	+	1.63886e7i	1.02957	+	1.78327i
$611$	2.31081e6			0.250416
$612$	2.46451e6	−	1.94355e7i	0.265982	−	2.09757i
$613$	−4.59806e6			−0.494223			−0.247112	−	0.968987i	$-0.579481\pi$
$613$	−4.59806e6			−0.494223			−0.247112	+	0.968987i	$0.579481\pi$
$614$	1.05960e7	+	1.83528e7i	1.13428	+	1.96464i
$615$	3.49690e6	−	3.08148e6i	0.372817	−	0.328527i
$616$	−63832.1	+	110560.i	−0.00677778	+	0.0117395i
$617$	−8.01311e6	+	1.38791e7i	−0.847399	+	1.46774i	0.0361221	+	0.999347i	$0.488499\pi$
$617$	−8.01311e6	+	1.38791e7i	−0.847399	+	1.46774i	−0.883521	+	0.468391i	$0.844834\pi$
$618$	4.51189e6	+	2.24036e7i	0.475212	+	2.35964i
$619$	−1.19878e6	−	2.07634e6i	−0.125751	−	0.217807i	0.796275	−	0.604934i	$-0.206801\pi$
$619$	−1.19878e6	−	2.07634e6i	−0.125751	−	0.217807i	−0.922026	+	0.387127i	$0.873467\pi$
$620$	1.62931e7			1.70226
$621$	1.36494e7	−	992709.i	1.42031	−	0.103298i
$622$	5.98795e6			0.620587
$623$	−43243.9	−	74900.6i	−0.00446380	−	0.00773153i
$624$	−2.84470e6	−	1.41252e7i	−0.292465	−	1.45222i
$625$	3.10456e6	−	5.37725e6i	0.317906	−	0.550630i
$626$	1.07785e7	−	1.86689e7i	1.09932	−	1.90407i
$627$	1.01679e6	−	895998.i	0.103291	−	0.0910203i
$628$	−1.01638e6	−	1.76042e6i	−0.102839	−	0.178122i
$629$	−1.78478e7			−1.79870
$630$	−184490.	−	140171.i	−0.0185191	−	0.0140704i
$631$	6.25228e6			0.625122			0.312561	−	0.949898i	$-0.398813\pi$
$631$	6.25228e6			0.625122			0.312561	+	0.949898i	$0.398813\pi$
$632$	−8.23449e6	−	1.42625e7i	−0.820057	−	1.42038i
$633$	−1.46240e7	−	4.92533e6i	−1.45063	−	0.488569i
$634$	1.58821e7	−	2.75086e7i	1.56922	−	2.71797i
$635$	−2.21053e6	+	3.82875e6i	−0.217551	+	0.376810i
$636$	−1.20441e7	−	4.05642e6i	−1.18068	−	0.397649i
$637$	6.12754e6	+	1.06132e7i	0.598325	+	1.03633i
$638$	2.41849e6			0.235230
$639$	27735.2	−	11643.5i	0.00268707	−	0.00112806i
$640$	−1.39139e7			−1.34276
$641$	9.48142e6	+	1.64223e7i	0.911440	+	1.57866i	0.812031	+	0.583614i	$0.198362\pi$
$641$	9.48142e6	+	1.64223e7i	0.911440	+	1.57866i	0.0994090	+	0.995047i	$0.468305\pi$
$642$	−2.42721e7	+	2.13887e7i	−2.32418	+	2.04808i
$643$	1.64962e6	−	2.85722e6i	0.157346	−	0.272532i	−0.776565	−	0.630038i	$-0.783039\pi$
$643$	1.64962e6	−	2.85722e6i	0.157346	−	0.272532i	0.933911	+	0.357506i	$0.116373\pi$
$644$	−243861.	+	422380.i	−0.0231701	+	0.0401318i
$645$	893417.	+	4.43621e6i	0.0845580	+	0.419868i
$646$	−2.84701e6	−	4.93116e6i	−0.268415	−	0.464909i
$647$	−1.56481e7			−1.46961			−0.734805	−	0.678278i	$-0.762726\pi$
$647$	−1.56481e7			−1.46961			−0.734805	+	0.678278i	$0.762726\pi$
$648$	−1.41458e7	+	1.44182e7i	−1.32339	+	1.34888i
$649$	−5.42978e6			−0.506023
$650$	−3.20825e6	−	5.55685e6i	−0.297841	−	0.515876i
$651$	−32381.8	−	160790.i	−0.00299467	−	0.0148699i
$652$	9.05228e6	−	1.56790e7i	0.833948	−	1.44444i
$653$	−7.78514e6	+	1.34843e7i	−0.714469	+	1.23750i	0.248695	+	0.968582i	$0.419998\pi$
$653$	−7.78514e6	+	1.34843e7i	−0.714469	+	1.23750i	−0.963164	+	0.268915i	$0.913335\pi$
$654$	1.34168e7	−	1.18229e7i	1.22661	−	1.08089i
$655$	−8.69921e6	−	1.50675e7i	−0.792276	−	1.37226i
$656$	8.00912e6			0.726650
$657$	−7.89074e6	+	3.31262e6i	−0.713189	+	0.299404i
$658$	63852.4			0.00574927
$659$	−6.40513e6	−	1.10940e7i	−0.574532	−	0.995119i	−0.996092	−	0.0883184i	$-0.971851\pi$
$659$	−6.40513e6	−	1.10940e7i	−0.574532	−	0.995119i	0.421560	−	0.906800i	$-0.361483\pi$
$660$	−8.53777e6	−	2.87550e6i	−0.762930	−	0.256953i
$661$	−230248.	+	398801.i	−0.0204971	+	0.0355020i	−0.876092	−	0.482144i	$-0.839858\pi$
$661$	−230248.	+	398801.i	−0.0204971	+	0.0355020i	0.855595	+	0.517646i	$0.173192\pi$
$662$	1.29413e7	−	2.24149e7i	1.14771	−	1.98789i
$663$	1.30684e7	+	4.40141e6i	1.15462	+	0.388873i
$664$	1.76779e6	+	3.06190e6i	0.155600	+	0.269507i
$665$	−45457.8			−0.00398616
$666$	2.82537e7	+	2.14665e7i	2.46825	+	1.87533i
$667$	4.79150e6			0.417020
$668$	6.60310e6	+	1.14369e7i	0.572541	+	0.991670i
$669$	1.22548e7	−	1.07989e7i	1.05862	−	0.932857i
$670$	−5.51600e6	+	9.55399e6i	−0.474719	+	0.822238i
$671$	3.70358e6	−	6.41479e6i	0.317552	−	0.550017i
$672$	−10188.0	−	50587.9i	−0.000870293	−	0.00432139i
$673$	4.03608e6	+	6.99069e6i	0.343496	+	0.594952i	0.985079	−	0.172101i	$-0.0550555\pi$
$673$	4.03608e6	+	6.99069e6i	0.343496	+	0.594952i	−0.641583	+	0.767053i	$0.721722\pi$
$674$	8.23500e6			0.698255
$675$	−1.46376e6	+	3.02252e6i	−0.123655	+	0.255334i
$676$	1.06786e7			0.898766
$677$	−1.82149e6	−	3.15491e6i	−0.152741	−	0.264554i	0.779493	−	0.626410i	$-0.215477\pi$
$677$	−1.82149e6	−	3.15491e6i	−0.152741	−	0.264554i	−0.932234	+	0.361856i	$0.882143\pi$
$678$	1.43023e6	+	7.10171e6i	0.119490	+	0.593319i
$679$	100220.	−	173586.i	0.00834219	−	0.0144491i
$680$	−9.81458e6	+	1.69993e7i	−0.813953	+	1.40981i
$681$	−8.31636e6	+	7.32839e6i	−0.687172	+	0.605538i
$682$	−4.72380e6	−	8.18185e6i	−0.388893	−	0.673582i
$683$	9.57475e6			0.785373			0.392686	−	0.919672i	$-0.371546\pi$
$683$	9.57475e6			0.785373			0.392686	+	0.919672i	$0.371546\pi$
$684$	−961297.	+	7.58090e6i	−0.0785628	+	0.619556i
$685$	7.26801e6			0.591819
$686$	338674.	+	586601.i	0.0274772	+	0.0475919i
$687$	4.34538e6	+	1.46351e6i	0.351266	+	0.118306i
$688$	−3.88805e6	+	6.73431e6i	−0.313156	+	0.542403i
$689$	4.47272e6	−	7.74698e6i	0.358941	−	0.621705i
$690$	−2.50580e7	−	8.43948e6i	−2.00366	−	0.674828i
$691$	−3.01871e6	−	5.22857e6i	−0.240506	−	0.416569i	0.720352	−	0.693608i	$-0.243980\pi$
$691$	−3.01871e6	−	5.22857e6i	−0.240506	−	0.416569i	−0.960859	+	0.277039i	$0.910647\pi$
$692$	4.50620e6			0.357722
$693$	−11408.8	+	89970.8i	−0.000902412	+	0.00711653i
$694$	−2.30080e7			−1.81334
$695$	5.78215e6	+	1.00150e7i	0.454075	+	0.786481i
$696$	−5.30580e6	+	4.67549e6i	−0.415172	+	0.365851i
$697$	−3.83250e6	+	6.63809e6i	−0.298814	+	0.517560i
$698$	−1.55478e7	+	2.69295e7i	−1.20789	+	2.09213i
$699$	−4.82168e6	−	2.39418e7i	−0.373255	−	1.85338i
$700$	−59841.8	−	103649.i	−0.00461594	−	0.00799504i
$701$	1.37603e7			1.05763			0.528813	−	0.848739i	$-0.322637\pi$
$701$	1.37603e7			1.05763			0.528813	+	0.848739i	$0.322637\pi$
$702$	−1.53939e7	−	2.26857e7i	−1.17898	−	1.73743i
$703$	6.96164e6			0.531279
$704$	2.24011e6	+	3.87999e6i	0.170349	+	0.295052i
$705$	461334.	+	2.29073e6i	0.0349577	+	0.173581i
$706$	−1.32484e7	+	2.29469e7i	−1.00035	+	1.73266i
$707$	−76806.9	+	133033.i	−0.00577899	+	0.0100095i
$708$	2.29702e7	−	2.02414e7i	1.72220	−	1.51760i
$709$	809892.	+	1.40277e6i	0.0605078	+	0.104803i	0.894693	−	0.446683i	$-0.147395\pi$
$709$	809892.	+	1.40277e6i	0.0605078	+	0.104803i	−0.834185	+	0.551485i	$0.814061\pi$
$710$	−58116.6			−0.00432667
$711$	−9.31559e6	−	7.07779e6i	−0.691093	−	0.525078i
$712$	1.45671e7			1.07690
$713$	−9.35873e6	−	1.62098e7i	−0.689435	−	1.19414i
$714$	361107.	+	121620.i	0.0265088	+	0.00892811i
$715$	3.17061e6	−	5.49165e6i	0.231941	−	0.401734i
$716$	−726163.	+	1.25775e6i	−0.0529360	+	0.0916879i
$717$	7.71040e6	+	2.59685e6i	0.560118	+	0.188646i
$718$	−1.02164e7	−	1.76953e7i	−0.739580	−	1.28099i
$719$	1.42931e7			1.03111			0.515555	−	0.856856i	$-0.327586\pi$
$719$	1.42931e7			1.03111			0.515555	+	0.856856i	$0.327586\pi$
$720$	1.34345e7	−	5.63995e6i	0.965809	−	0.405457i
$721$	−300043.			−0.0214954
$722$	−1.11750e7	−	1.93557e7i	−0.797819	−	1.38186i
$723$	5.00227e6	−	4.40802e6i	0.355895	−	0.313615i
$724$	−6.25093e6	+	1.08269e7i	−0.443199	+	0.767643i
$725$	−587900.	+	1.01827e6i	−0.0415392	+	0.0719481i
$726$	−3.88712e6	−	1.93013e7i	−0.273708	−	1.35908i
$727$	1.37208e7	+	2.37652e7i	0.962818	+	1.66765i	0.715367	+	0.698749i	$0.246259\pi$
$727$	1.37208e7	+	2.37652e7i	0.962818	+	1.66765i	0.247450	+	0.968901i	$0.420407\pi$
$728$	506680.			0.0354328
$729$	−5.30092e6	+	1.33338e7i	−0.369430	+	0.929258i
$730$	1.65343e7			1.14836
$731$	−3.72100e6	−	6.44496e6i	−0.257553	−	0.446094i
$732$	8.24572e6	+	4.09437e7i	0.568788	+	2.82429i
$733$	2.55310e6	−	4.42209e6i	0.175512	−	0.303996i	−0.764826	−	0.644237i	$-0.777175\pi$
$733$	2.55310e6	−	4.42209e6i	0.175512	−	0.303996i	0.940338	+	0.340241i	$0.110509\pi$
$734$	−5.05283e6	+	8.75175e6i	−0.346174	+	0.599591i
$735$	−9.29767e6	+	8.19313e6i	−0.634828	+	0.559412i
$736$	−2.94445e6	−	5.09994e6i	−0.200359	−	0.347033i
$737$	4.31812e6			0.292837
$738$	1.40510e7	−	5.89874e6i	0.949653	−	0.398674i
$739$	−1.34356e7			−0.904997			−0.452498	−	0.891765i	$-0.649467\pi$
$739$	−1.34356e7			−0.904997			−0.452498	+	0.891765i	$0.649467\pi$
$740$	−2.31388e7	−	4.00776e7i	−1.55332	−	2.69044i
$741$	−5.09740e6	−	1.71679e6i	−0.341038	−	0.114861i
$742$	123590.	−	214065.i	0.00824091	−	0.0142737i
$743$	343246.	−	594519.i	0.0228104	−	0.0395088i	−0.854395	−	0.519624i	$-0.826072\pi$
$743$	343246.	−	594519.i	0.0228104	−	0.0395088i	0.877205	+	0.480116i	$0.159405\pi$
$744$	2.61806e7	+	8.81758e6i	1.73399	+	0.584005i
$745$	−232994.	−	403557.i	−0.0153799	−	0.0266387i
$746$	−5.19518e7			−3.41786
$747$	1.99988e6	+	1.51947e6i	0.131130	+	0.0996299i
$748$	1.48156e7			0.968203
$749$	−212371.	−	367838.i	−0.0138322	−	0.0239581i
$750$	2.20272e7	−	1.94104e7i	1.42990	−	1.26003i
$751$	−5.46542e6	+	9.46639e6i	−0.353610	+	0.612470i	−0.986879	−	0.161462i	$-0.948379\pi$
$751$	−5.46542e6	+	9.46639e6i	−0.353610	+	0.612470i	0.633269	+	0.773931i	$0.281712\pi$
$752$	−2.00768e6	+	3.47740e6i	−0.129464	+	0.224238i
$753$	713738.	+	3.54403e6i	0.0458724	+	0.227777i
$754$	−4.79932e6	−	8.31266e6i	−0.307434	−	0.532491i
$755$	1.03985e7			0.663900
$756$	−287134.	−	423144.i	−0.0182718	−	0.0269268i
$757$	−2.31128e7			−1.46593			−0.732966	−	0.680265i	$-0.761865\pi$
$757$	−2.31128e7			−1.46593			−0.732966	+	0.680265i	$0.761865\pi$
$758$	1.35891e7	+	2.35370e7i	0.859047	+	1.48791i
$759$	2.04328e6	+	1.01458e7i	0.128743	+	0.639266i
$760$	3.82823e6	−	6.63068e6i	0.240416	−	0.416413i
$761$	5.94528e6	−	1.02975e7i	0.372144	−	0.644572i	−0.617751	−	0.786374i	$-0.711956\pi$
$761$	5.94528e6	−	1.02975e7i	0.372144	−	0.644572i	0.989895	+	0.141801i	$0.0452894\pi$
$762$	−1.08449e7	+	9.55658e6i	−0.676611	+	0.596232i
$763$	117392.	+	203328.i	0.00730005	+	0.0126441i
$764$	−1.63785e7			−1.01517
$765$	−1.75417e6	+	1.38336e7i	−0.108372	+	0.854634i
$766$	4.31570e7			2.65754
$767$	1.07750e7	+	1.86628e7i	0.661345	+	1.14548i
$768$	−3.15872e7	−	1.06385e7i	−1.93245	−	0.650844i
$769$	−1.32545e6	+	2.29575e6i	−0.0808253	+	0.139994i	−0.903605	−	0.428367i	$-0.859089\pi$
$769$	−1.32545e6	+	2.29575e6i	−0.0808253	+	0.139994i	0.822779	+	0.568361i	$0.192422\pi$
$770$	87610.4	−	151746.i	0.00532511	−	0.00922337i
$771$	−2.08929e7	−	7.03668e6i	−1.26579	−	0.426316i
$772$	7.54883e6	+	1.30750e7i	0.455865	+	0.789581i
$773$	−2.12893e7			−1.28148			−0.640742	−	0.767757i	$-0.721373\pi$
$773$	−2.12893e7			−1.28148			−0.640742	+	0.767757i	$0.721373\pi$
$774$	−1.86125e6	+	1.46780e7i	−0.111674	+	0.880673i
$775$	4.59314e6			0.274698
$776$	1.68801e7	+	2.92371e7i	1.00628	+	1.74293i
$777$	−349523.	+	308000.i	−0.0207694	+	0.0183020i
$778$	1.49224e7	−	2.58464e7i	0.883873	−	1.53091i
$779$	1.49489e6	−	2.58922e6i	0.0882601	−	0.152871i
$780$	7.05910e6	+	3.50516e7i	0.415444	+	2.06287i
$781$	11373.9	+	19700.3i	0.000667242	+	0.00115570i
$782$	4.34833e7			2.54276
$783$	−2.18969e6	+	4.52148e6i	−0.127637	+	0.263558i
$784$	−2.12949e7			−1.23733
$785$	723426.	+	1.25301e6i	0.0419006	+	0.0725739i
$786$	−1.12306e7	−	5.57650e7i	−0.648406	−	3.21963i
$787$	1.14439e7	−	1.98214e7i	0.658623	−	1.14077i	−0.322349	−	0.946621i	$-0.604472\pi$
$787$	1.14439e7	−	1.98214e7i	0.658623	−	1.14077i	0.980972	−	0.194148i	$-0.0621942\pi$
$788$	1.67203e7	−	2.89605e7i	0.959246	−	1.66146i
$789$	1.44051e7	−	1.26938e7i	0.823802	−	0.725936i
$790$	1.13019e7	+	1.95755e7i	0.644296	+	1.11595i
$791$	−95110.7			−0.00540491
$792$	−1.21628e7	−	9.24102e6i	−0.689000	−	0.523488i
$793$	−2.93979e7			−1.66010
$794$	1.07470e7	+	1.86143e7i	0.604972	+	1.04784i
$795$	8.57260e6	+	2.88723e6i	0.481055	+	0.162018i
$796$	−137152.	+	237553.i	−0.00767217	+	0.0132886i
$797$	1.28424e7	−	2.22437e7i	0.716146	−	1.24040i	−0.246370	−	0.969176i	$-0.579238\pi$
$797$	1.28424e7	−	2.22437e7i	0.716146	−	1.24040i	0.962516	−	0.271225i	$-0.0874287\pi$
$798$	−140852.	−	47438.5i	−0.00782987	−	0.00263708i
$799$	−1.92141e6	−	3.32799e6i	−0.106477	−	0.184423i
$800$	1.44510e6			0.0798310
$801$	9.54162e6	−	4.00567e6i	0.525461	−	0.220594i
$802$	−3.51275e7			−1.92847
$803$	−3.23592e6	−	5.60478e6i	−0.177096	−	0.306739i
$804$	−1.82675e7	+	1.60974e7i	−0.996641	+	0.878242i
$805$	173573.	−	300637.i	0.00944043	−	0.0163513i
$806$	−1.87480e7	+	3.24725e7i	−1.01652	+	1.76067i
$807$	−366988.	−	1.82226e6i	−0.0198366	−	0.0984978i
$808$	−1.29366e7	−	2.24068e7i	−0.697094	−	1.20740i
$809$	−5.88061e6			−0.315901			−0.157951	−	0.987447i	$-0.550489\pi$
$809$	−5.88061e6			−0.315901			−0.157951	+	0.987447i	$0.550489\pi$
$810$	1.94153e7	−	1.97891e7i	1.03975	−	1.05978i
$811$	−2.04938e7			−1.09414			−0.547068	−	0.837088i	$-0.684256\pi$
$811$	−2.04938e7			−1.09414			−0.547068	+	0.837088i	$0.684256\pi$
$812$	−89519.3	−	155052.i	−0.00476460	−	0.00825254i
$813$	−154315.	−	766243.i	−0.00818808	−	0.0406575i
$814$	−1.34171e7	+	2.32391e7i	−0.709737	+	1.22930i
$815$	−6.44313e6	+	1.11598e7i	−0.339784	+	0.588523i
$816$	−1.79775e7	+	1.58418e7i	−0.945157	+	0.832875i
$817$	1.45139e6	+	2.51389e6i	0.0760730	+	0.131762i
$818$	1.55526e7			0.812681
$819$	331880.	−	139327.i	0.0172891	−	0.00725814i
$820$	−1.98746e7			−1.03220
$821$	1.81711e6	+	3.14732e6i	0.0940855	+	0.162961i	0.909227	−	0.416302i	$-0.136674\pi$
$821$	1.81711e6	+	3.14732e6i	0.0940855	+	0.162961i	−0.815141	+	0.579263i	$0.803341\pi$
$822$	2.25200e7	+	7.58470e6i	1.16249	+	0.391524i
$823$	7.90337e6	−	1.36890e7i	0.406736	−	0.704488i	−0.587786	−	0.809017i	$-0.700000\pi$
$823$	7.90337e6	−	1.36890e7i	0.406736	−	0.704488i	0.994522	+	0.104529i	$0.0333335\pi$
$824$	2.52681e7	−	4.37657e7i	1.29645	−	2.24551i
$825$	−2.40685e6	−	810623.i	−0.123116	−	0.0414652i
$826$	297735.	+	515692.i	0.0151838	+	0.0262991i
$827$	−1.98096e6			−0.100719			−0.0503597	−	0.998731i	$-0.516037\pi$
$827$	−1.98096e6			−0.100719			−0.0503597	+	0.998731i	$0.516037\pi$
$828$	−4.64660e7	−	3.53039e7i	−2.35537	−	1.78956i
$829$	2.56811e7			1.29786			0.648929	−	0.760849i	$-0.275217\pi$
$829$	2.56811e7			1.29786			0.648929	+	0.760849i	$0.275217\pi$
$830$	−2.42631e6	−	4.20249e6i	−0.122251	−	0.211744i
$831$	−5.51605e6	+	4.86076e6i	−0.277093	+	0.244175i
$832$	8.89067e6	−	1.53991e7i	0.445273	−	0.771235i
$833$	1.01900e7	−	1.76495e7i	0.508815	−	0.881294i
$834$	7.46472e6	+	3.70656e7i	0.371619	+	1.84526i
$835$	−4.69988e6	−	8.14043e6i	−0.233276	−	0.404046i
$836$	−5.77891e6			−0.285977
$837$	1.95732e7	−	1.42355e6i	0.965715	−	0.0702358i
$838$	2.34825e7			1.15514
$839$	−2.27342e6	−	3.93767e6i	−0.111500	−	0.193123i	0.804875	−	0.593444i	$-0.202232\pi$
$839$	−2.27342e6	−	3.93767e6i	−0.111500	−	0.193123i	−0.916375	+	0.400321i	$0.868899\pi$
$840$	101154.	+	502277.i	0.00494637	+	0.0245609i
$841$	9.37612e6	−	1.62399e7i	0.457123	−	0.791760i
$842$	−1.82874e7	+	3.16747e7i	−0.888937	+	1.53968i
$843$	−2.42451e7	+	2.13649e7i	−1.17505	+	1.03545i
$844$	3.29001e7	+	5.69847e7i	1.58980	+	2.75361i
$845$	−7.60068e6			−0.366193
$846$	−961093.	+	7.57929e6i	−0.0461678	+	0.364085i
$847$	258496.			0.0123807
$848$	7.77197e6	+	1.34614e7i	0.371143	+	0.642839i
$849$	2.23974e7	+	7.54338e6i	1.06642	+	0.359167i
$850$	−5.33525e6	+	9.24092e6i	−0.253284	+	0.438700i
$851$	−2.65818e7	+	4.60411e7i	−1.25823	+	2.17932i
$852$	−121556.	−	40939.9i	−0.00573692	−	0.00193218i
$853$	−708511.	−	1.22718e6i	−0.0333407	−	0.0577477i	0.848874	−	0.528596i	$-0.177281\pi$
$853$	−708511.	−	1.22718e6i	−0.0333407	−	0.0577477i	−0.882214	+	0.470848i	$0.843948\pi$
$854$	−812324.			−0.0381140
$855$	684221.	−	5.39585e6i	0.0320097	−	0.252432i
$856$	7.15394e7			3.33704
$857$	4.07200e6	+	7.05290e6i	0.189389	+	0.328032i	0.945047	−	0.326935i	$-0.106016\pi$
$857$	4.07200e6	+	7.05290e6i	0.189389	+	0.328032i	−0.755658	+	0.654967i	$0.772683\pi$
$858$	1.55551e7	−	1.37072e7i	0.721365	−	0.635669i
$859$	−5.33500e6	+	9.24050e6i	−0.246690	+	0.427280i	−0.962605	−	0.270907i	$-0.912676\pi$
$859$	−5.33500e6	+	9.24050e6i	−0.246690	+	0.427280i	0.715915	+	0.698187i	$0.246010\pi$
$860$	9.64819e6	−	1.67111e7i	0.444836	−	0.770478i
$861$	39499.9	+	196134.i	0.00181588	+	0.00901667i
$862$	−3.36474e7	−	5.82791e7i	−1.54235	−	2.67143i
$863$	−1.21144e7			−0.553701			−0.276851	−	0.960913i	$-0.589291\pi$
$863$	−1.21144e7			−0.553701			−0.276851	+	0.960913i	$0.589291\pi$
$864$	6.15814e6	−	447878.i	0.280650	−	0.0204115i
$865$	−3.20737e6			−0.145750
$866$	−1.58987e7	−	2.75374e7i	−0.720391	−	1.24775i
$867$	−157664.	−	782872.i	−0.00712335	−	0.0353706i
$868$	−349698.	+	605694.i	−0.0157541	+	0.0272869i
$869$	4.42379e6	−	7.66222e6i	0.198721	−	0.344196i
$870$	7.28229e6	−	6.41717e6i	0.326189	−	0.287439i
$871$	−8.56899e6	−	1.48419e7i	−0.382723	−	0.662895i
$872$	−3.95445e7			−1.76115
$873$	1.90962e7	+	1.45089e7i	0.848031	+	0.644317i
$874$	−1.69609e7			−0.751051
$875$	192729.	+	333816.i	0.00850995	+	0.0147397i
$876$	3.45831e7	+	1.16475e7i	1.52266	+	0.512829i
$877$	−1.65673e7	+	2.86954e7i	−0.727366	+	1.25983i	0.230627	+	0.973042i	$0.425922\pi$
$877$	−1.65673e7	+	2.86954e7i	−0.727366	+	1.25983i	−0.957993	+	0.286792i	$0.907411\pi$
$878$	6.93075e6	−	1.20044e7i	0.303420	−	0.525538i
$879$	1.13782e7	+	3.83216e6i	0.496710	+	0.167291i
$880$	5.50937e6	+	9.54251e6i	0.239826	+	0.415390i
$881$	49573.7			0.00215185			0.00107592	−	0.999999i	$-0.499658\pi$
$881$	49573.7			0.00215185			0.00107592	+	0.999999i	$0.499658\pi$
$882$	−3.73591e7	+	1.56837e7i	−1.61706	+	0.678857i
$883$	4.21109e7			1.81758			0.908788	−	0.417259i	$-0.137009\pi$
$883$	4.21109e7			1.81758			0.908788	+	0.417259i	$0.137009\pi$
$884$	−2.94005e7	−	5.09232e7i	−1.26539	−	2.19172i
$885$	−1.63495e7	+	1.44072e7i	−0.701692	+	0.618333i
$886$	−2.46689e7	+	4.27278e7i	−1.05576	+	1.82863i
$887$	−550680.	+	953806.i	−0.0235012	+	0.0407053i	−0.877537	−	0.479509i	$-0.840815\pi$
$887$	−550680.	+	953806.i	−0.0235012	+	0.0407053i	0.854036	+	0.520215i	$0.174148\pi$
$888$	−1.54913e7	−	7.69212e7i	−0.659258	−	3.27351i
$889$	−94888.8	−	164352.i	−0.00402680	−	0.00697463i
$890$	−1.99936e7			−0.846088
$891$	−1.05078e7	−	2.70844e6i	−0.443423	−	0.114294i
$892$	−6.96498e7			−2.93094
$893$	749458.	+	1.29810e6i	0.0314498	+	0.0544727i
$894$	−300793.	−	1.49357e6i	−0.0125870	−	0.0625003i
$895$	516860.	−	895228.i	0.0215683	−	0.0373574i
$896$	298633.	−	517248.i	0.0124271	−	0.0215243i
$897$	3.08176e7	−	2.71566e7i	1.27885	−	1.12692i
$898$	2.40696e7	+	4.16898e7i	0.996042	+	1.72520i
$899$	6.87102e6			0.283545
$900$	1.32039e7	−	5.54313e6i	0.543370	−	0.228112i
$901$	−1.48761e7			−0.610487
$902$	5.76216e6	+	9.98036e6i	0.235814	+	0.408441i
$903$	−184091.	−	62001.4i	−0.00751299	−	0.00253036i
$904$	8.00974e6	−	1.38733e7i	0.325985	−	0.564622i
$905$	4.44922e6	−	7.70627e6i	0.180577	−	0.312769i
$906$	3.22198e7	+	1.08516e7i	1.30408	+	0.439210i
$907$	3.72157e6	+	6.44595e6i	0.150213	+	0.260177i	0.931306	−	0.364238i	$-0.118671\pi$
$907$	3.72157e6	+	6.44595e6i	0.150213	+	0.260177i	−0.781093	+	0.624415i	$0.785337\pi$
$908$	4.72659e7			1.90254
$909$	−1.46350e7	−	1.11194e7i	−0.587467	−	0.446345i
$910$	−695425.			−0.0278386
$911$	1.61672e7	+	2.80024e7i	0.645414	+	1.11789i	0.984206	+	0.177028i	$0.0566483\pi$
$911$	1.61672e7	+	2.80024e7i	0.645414	+	1.11789i	−0.338792	+	0.940861i	$0.610018\pi$
$912$	7.01222e6	−	6.17918e6i	0.279170	−	0.246005i
$913$	−949703.	+	1.64493e6i	−0.0377060	+	0.0653087i
$914$	2.12600e7	−	3.68234e7i	0.841778	−	1.45800i
$915$	−5.86905e6	−	2.91424e7i	−0.231747	−	1.15073i
$916$	−9.77597e6	−	1.69325e7i	−0.384965	−	0.666779i
$917$	746841.			0.0293295
$918$	−1.98716e7	+	4.10329e7i	−0.778263	+	1.60703i
$919$	3.18905e7			1.24558			0.622792	−	0.782388i	$-0.285998\pi$
$919$	3.18905e7			1.24558			0.622792	+	0.782388i	$0.285998\pi$
$920$	2.92348e7	+	5.06362e7i	1.13876	+	1.97239i
$921$	−6.57249e6	−	3.26353e7i	−0.255318	−	1.26777i
$922$	118811.	−	205787.i	0.00460288	−	0.00797243i
$923$	45141.5	−	78187.3i	0.00174410	−	0.00302087i
$924$	290142.	−	255674.i	0.0111797	−	0.00985159i
$925$	−6.52299e6	−	1.12982e7i	−0.250664	−	0.434163i
$926$	3.50133e7			1.34186
$927$	4.51619e6	−	3.56152e7i	0.172613	−	1.36124i
$928$	2.16177e6			0.0824022
$929$	7.20450e6	+	1.24786e7i	0.273883	+	0.474379i	0.969853	−	0.243692i	$-0.0783586\pi$
$929$	7.20450e6	+	1.24786e7i	0.273883	+	0.474379i	−0.695970	+	0.718071i	$0.745025\pi$
$930$	−3.59332e7	−	1.21022e7i	−1.36235	−	0.458837i
$931$	−3.97465e6	+	6.88429e6i	−0.150288	+	0.260307i
$932$	−5.20703e7	+	9.01884e7i	−1.96359	+	3.40103i
$933$	−8.91446e6	−	3.00237e6i	−0.335267	−	0.112917i
$934$	−2.31342e7	−	4.00697e7i	−0.867737	−	1.50296i
$935$	−1.05453e7			−0.394485
$936$	−7.62644e6	+	6.01430e7i	−0.284533	+	2.24386i
$937$	2.33199e7			0.867718			0.433859	−	0.900981i	$-0.357152\pi$
$937$	2.33199e7			0.867718			0.433859	+	0.900981i	$0.357152\pi$
$938$	−236779.	−	410113.i	−0.00878690	−	0.0152194i
$939$	−2.54070e7	+	2.23887e7i	−0.940349	+	0.828638i
$940$	4.98204e6	−	8.62915e6i	0.183902	−	0.318528i
$941$	2.35788e7	−	4.08396e7i	0.868054	−	1.50351i	0.00407185	−	0.999992i	$-0.498704\pi$
$941$	2.35788e7	−	4.08396e7i	0.868054	−	1.50351i	0.863982	−	0.503522i	$-0.167963\pi$
$942$	933937.	+	4.63742e6i	0.0342918	+	0.170274i
$943$	1.14159e7	+	1.97730e7i	0.418054	+	0.724091i
$944$	−3.74461e7			−1.36765
$945$	204373.	+	301181.i	0.00744466	+	0.0109710i
$946$	−1.11890e7			−0.406504
$947$	−1.21868e7	−	2.11081e7i	−0.441585	−	0.764847i	0.556223	−	0.831033i	$-0.312250\pi$
$947$	−1.21868e7	−	2.11081e7i	−0.441585	−	0.764847i	−0.997807	+	0.0661864i	$0.978917\pi$
$948$	9.84920e6	+	4.89057e7i	0.355943	+	1.76741i
$949$	−1.28429e7	+	2.22445e7i	−0.462910	+	0.801784i
$950$	2.08104e6	−	3.60447e6i	0.0748120	−	0.129578i
$951$	−3.74370e7	+	3.29896e7i	−1.34230	+	1.18284i
$952$	−421299.	−	729711.i	−0.0150660	−	0.0260951i
$953$	−4.33987e7			−1.54790			−0.773952	−	0.633244i	$-0.781723\pi$
$953$	−4.33987e7			−1.54790			−0.773952	+	0.633244i	$0.781723\pi$
$954$	2.35493e7	+	1.78923e7i	0.837735	+	0.636494i
$955$	1.16577e7			0.413623
$956$	−1.73464e7	−	3.00448e7i	−0.613853	−	1.06322i
$957$	−3.60049e6	−	1.21264e6i	−0.127081	−	0.0428007i
$958$	3.24978e7	−	5.62879e7i	1.14404	−	1.98153i
$959$	−155993.	+	270187.i	−0.00547719	+	0.00948677i
$960$	1.70402e7	+	5.73911e6i	0.596757	+	0.200986i
$961$	894119.	+	1.54866e6i	0.0312311	+	0.0540938i
$962$	1.06501e8			3.71035
$963$	4.68590e7	−	1.96719e7i	1.62827	−	0.683567i
$964$	−2.84303e7			−0.985348
$965$	−5.37302e6	−	9.30634e6i	−0.185738	−	0.321707i
$966$	851554.	−	750392.i	0.0293609	−	0.0258729i
$967$	−137300.	+	237810.i	−0.00472176	+	0.00817832i	−0.868377	−	0.495905i	$-0.834836\pi$
$967$	−137300.	+	237810.i	−0.00472176	+	0.00817832i	0.863655	+	0.504084i	$0.168170\pi$
$968$	−2.17692e7	+	3.77054e7i	−0.746714	+	1.29335i
$969$	1.76594e6	+	8.76868e6i	0.0604180	+	0.300002i
$970$	−2.31681e7	−	4.01283e7i	−0.790607	−	1.36937i
$971$	3.36920e7			1.14678			0.573388	−	0.819284i	$-0.305629\pi$
$971$	3.36920e7			1.14678			0.573388	+	0.819284i	$0.305629\pi$
$972$	5.45492e7	−	2.77138e7i	1.85192	−	0.940872i
$973$	−496407.			−0.0168096
$974$	−4.58185e7	−	7.93600e7i	−1.54755	−	2.68043i
$975$	1.99001e6	+	9.88128e6i	0.0670414	+	0.332891i
$976$	2.55415e7	−	4.42391e7i	0.858264	−	1.48656i
$977$	−6.93084e6	+	1.20046e7i	−0.232300	+	0.402356i	−0.958485	−	0.285144i	$-0.907959\pi$
$977$	−6.93084e6	+	1.20046e7i	−0.232300	+	0.402356i	0.726184	+	0.687500i	$0.241292\pi$
$978$	−3.16102e7	+	2.78550e7i	−1.05677	+	0.931228i
$979$	3.91293e6	+	6.77739e6i	0.130480	+	0.225999i
$980$	5.28432e7			1.75762
$981$	−2.59021e7	+	1.08740e7i	−0.859334	+	0.360757i
$982$	5.20238e7			1.72156
$983$	4.34952e6	+	7.53359e6i	0.143568	+	0.248667i	0.928838	−	0.370487i	$-0.120809\pi$
$983$	4.34952e6	+	7.53359e6i	0.143568	+	0.248667i	−0.785270	+	0.619154i	$0.787476\pi$
$984$	−3.19356e7	−	1.07558e7i	−1.05145	−	0.354125i
$985$	−1.19010e7	+	2.06132e7i	−0.390835	+	0.676947i
$986$	−7.98116e6	+	1.38238e7i	−0.261441	+	0.452829i
$987$	−95059.2	−	32015.7i	−0.00310600	−	0.00104609i
$988$	1.14678e7	+	1.98628e7i	0.373756	+	0.647365i
$989$	−2.21676e7			−0.720656
$990$	1.66935e7	+	1.26834e7i	0.541328	+	0.411290i
$991$	−4.44501e7			−1.43777			−0.718884	−	0.695130i	$-0.755347\pi$
$991$	−4.44501e7			−1.43777			−0.718884	+	0.695130i	$0.755347\pi$
$992$	−4.22235e6	−	7.31333e6i	−0.136231	−	0.235959i
$993$	−3.05050e7	+	2.68811e7i	−0.981743	+	0.865114i
$994$	1247.35	−	2160.48i	4.00426e−5	−	6.93559e-5i
$995$	97620.2	−	169083.i	0.00312595	−	0.00541430i
$996$	−2.11444e6	−	1.04991e7i	−0.0675377	−	0.335355i
$997$	8.21072e6	+	1.42214e7i	0.261603	+	0.453110i	0.966668	−	0.256033i	$-0.0824154\pi$
$997$	8.21072e6	+	1.42214e7i	0.261603	+	0.453110i	−0.705065	+	0.709143i	$0.749082\pi$
$998$	−6.42977e7			−2.04347
$999$	−3.12988e7	−	4.61244e7i	−0.992232	−	1.46223i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.6.c.a.4.4	✓	8
3.2	odd	2		27.6.c.a.10.1		8
4.3	odd	2		144.6.i.c.49.3		8
9.2	odd	6		27.6.c.a.19.1		8
9.4	even	3		81.6.a.c.1.1		4
9.5	odd	6		81.6.a.d.1.4		4
9.7	even	3	inner	9.6.c.a.7.4	yes	8
12.11	even	2		432.6.i.c.145.2		8
36.7	odd	6		144.6.i.c.97.3		8
36.11	even	6		432.6.i.c.289.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.6.c.a.4.4	✓	8	1.1	even	1	trivial
9.6.c.a.7.4	yes	8	9.7	even	3	inner
27.6.c.a.10.1		8	3.2	odd	2
27.6.c.a.19.1		8	9.2	odd	6
81.6.a.c.1.1		4	9.4	even	3
81.6.a.d.1.4		4	9.5	odd	6
144.6.i.c.49.3		8	4.3	odd	2
144.6.i.c.97.3		8	36.7	odd	6
432.6.i.c.145.2		8	12.11	even	2
432.6.i.c.289.2		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)

\(f(q)\)	\(=\)	\(q+(4.96163 + 8.59380i) q^{2} +(-3.07760 - 15.2816i) q^{3} +(-33.2356 + 57.5657i) q^{4} +(23.6560 - 40.9735i) q^{5} +(116.057 - 102.270i) q^{6} +(1.01546 + 1.75882i) q^{7} -342.066 q^{8} +(-224.057 + 94.0614i) q^{9} +O(q^{10})\)	\(q+(4.96163 + 8.59380i) q^{2} +(-3.07760 - 15.2816i) q^{3} +(-33.2356 + 57.5657i) q^{4} +(23.6560 - 40.9735i) q^{5} +(116.057 - 102.270i) q^{6} +(1.01546 + 1.75882i) q^{7} -342.066 q^{8} +(-224.057 + 94.0614i) q^{9} +469.490 q^{10} +(-91.8836 - 159.147i) q^{11} +(981.984 + 330.730i) q^{12} +(-364.672 + 631.630i) q^{13} +(-10.0766 + 17.4532i) q^{14} +(-698.946 - 235.403i) q^{15} +(-633.668 - 1097.55i) q^{16} +1212.88 q^{17} +(-1920.03 - 1458.80i) q^{18} -473.092 q^{19} +(1572.44 + 2723.55i) q^{20} +(23.7525 - 20.9308i) q^{21} +(911.785 - 1579.26i) q^{22} +(1806.42 - 3128.81i) q^{23} +(1052.74 + 5227.33i) q^{24} +(443.283 + 767.788i) q^{25} -7237.47 q^{26} +(2126.97 + 3134.47i) q^{27} -134.997 q^{28} +(663.121 + 1148.56i) q^{29} +(-1444.90 - 7174.58i) q^{30} +(2590.41 - 4486.72i) q^{31} +(814.997 - 1411.62i) q^{32} +(-2149.25 + 1893.92i) q^{33} +(6017.88 + 10423.3i) q^{34} +96.0867 q^{35} +(2031.95 - 16024.2i) q^{36} -14715.2 q^{37} +(-2347.31 - 4065.65i) q^{38} +(10774.7 + 3628.88i) q^{39} +(-8091.94 + 14015.6i) q^{40} +(-3159.83 + 5472.98i) q^{41} +(297.726 + 100.273i) q^{42} +(-3067.89 - 5313.75i) q^{43} +12215.2 q^{44} +(-1446.28 + 11405.5i) q^{45} +35851.1 q^{46} +(-1584.17 - 2743.86i) q^{47} +(-14822.1 + 13061.3i) q^{48} +(8401.44 - 14551.7i) q^{49} +(-4398.81 + 7618.96i) q^{50} +(-3732.76 - 18534.8i) q^{51} +(-24240.2 - 41985.2i) q^{52} -12265.0 q^{53} +(-16383.8 + 33830.8i) q^{54} -8694.41 q^{55} +(-347.353 - 601.633i) q^{56} +(1455.98 + 7229.61i) q^{57} +(-6580.32 + 11397.5i) q^{58} +(14773.5 - 25588.5i) q^{59} +(36781.0 - 32411.5i) q^{60} +(20153.6 + 34907.1i) q^{61} +51410.7 q^{62} +(-392.957 - 298.561i) q^{63} -24379.9 q^{64} +(17253.4 + 29883.8i) q^{65} +(-26939.7 - 9073.25i) q^{66} +(-11748.9 + 20349.7i) q^{67} +(-40310.9 + 69820.5i) q^{68} +(-53372.8 - 17975.8i) q^{69} +(476.747 + 825.750i) q^{70} -123.786 q^{71} +(76642.3 - 32175.2i) q^{72} +35217.6 q^{73} +(-73011.4 - 126459. i) q^{74} +(10368.8 - 9137.03i) q^{75} +(15723.5 - 27233.8i) q^{76} +(186.607 - 323.214i) q^{77} +(22274.0 + 110600. i) q^{78} +(24072.8 + 41695.3i) q^{79} -59960.3 q^{80} +(41353.9 - 42150.2i) q^{81} -62711.6 q^{82} +(-5167.97 - 8951.18i) q^{83} +(415.466 + 2062.98i) q^{84} +(28692.0 - 49696.1i) q^{85} +(30443.5 - 52729.7i) q^{86} +(15511.0 - 13668.4i) q^{87} +(31430.3 + 54438.8i) q^{88} -42585.7 q^{89} +(-105193. + 44160.9i) q^{90} -1481.23 q^{91} +(120075. + 207976. i) q^{92} +(-76536.7 - 25777.4i) q^{93} +(15720.1 - 27228.1i) q^{94} +(-11191.5 + 19384.2i) q^{95} +(-24080.0 - 8110.10i) q^{96} +(-49347.3 - 85472.1i) q^{97} +166739. q^{98} +(35556.7 + 27015.3i) 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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