LMFDB - Embedded newform 147.6.e.p.67.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,6,Mod(67,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("147.67");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	147.e (of order $3$, degree $2$, not 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:	$23.5764215125$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 63 x^{10} - 126 x^{9} + 2784 x^{8} - 5290 x^{7} + 62015 x^{6} - 99530 x^{5} + \cdots + 5466244 $ x^12 - 2x^11 + 63x^10 - 126x^9 + 2784x^8 - 5290x^7 + 62015x^6 - 99530x^5 + 973971x^4 - 1176024x^3 + 5644794x^2 + 4339328*x + 5466244
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8}\cdot 7^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.3
Root			$-2.55045 + 4.41750i$ of defining polynomial
Character	$\chi$	$=$	147.67
Dual form			147.6.e.p.79.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.69017 - 2.92745i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(10.2867 - 17.8171i) q^{4} +(27.2626 + 47.2203i) q^{5} +30.4230 q^{6} -177.715 q^{8} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})$	\(q+(-1.69017 - 2.92745i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(10.2867 - 17.8171i) q^{4} +(27.2626 + 47.2203i) q^{5} +30.4230 q^{6} -177.715 q^{8} +(-40.5000 - 70.1481i) q^{9} +(92.1567 - 159.620i) q^{10} +(-240.956 + 417.347i) q^{11} +(92.5801 + 160.354i) q^{12} +512.622 q^{13} -490.728 q^{15} +(-28.8055 - 49.8926i) q^{16} +(-295.372 + 511.599i) q^{17} +(-136.903 + 237.124i) q^{18} +(-1225.51 - 2122.64i) q^{19} +1121.77 q^{20} +1629.02 q^{22} +(-887.452 - 1537.11i) q^{23} +(799.719 - 1385.15i) q^{24} +(75.9967 - 131.630i) q^{25} +(-866.416 - 1500.68i) q^{26} +729.000 q^{27} -4246.44 q^{29} +(829.411 + 1436.58i) q^{30} +(-4883.69 + 8458.79i) q^{31} +(-2940.82 + 5093.65i) q^{32} +(-2168.60 - 3756.13i) q^{33} +1996.91 q^{34} -1666.44 q^{36} +(4984.83 + 8633.97i) q^{37} +(-4142.62 + 7175.23i) q^{38} +(-2306.80 + 3995.49i) q^{39} +(-4844.99 - 8391.77i) q^{40} -3377.54 q^{41} -18223.4 q^{43} +(4957.27 + 8586.24i) q^{44} +(2208.27 - 3824.84i) q^{45} +(-2999.88 + 5195.95i) q^{46} +(-660.320 - 1143.71i) q^{47} +518.500 q^{48} -513.788 q^{50} +(-2658.35 - 4604.39i) q^{51} +(5273.18 - 9133.42i) q^{52} +(-17418.5 + 30169.7i) q^{53} +(-1232.13 - 2134.11i) q^{54} -26276.3 q^{55} +22059.1 q^{57} +(7177.19 + 12431.3i) q^{58} +(-5796.25 + 10039.4i) q^{59} +(-5047.96 + 8743.32i) q^{60} +(-15703.1 - 27198.5i) q^{61} +33016.9 q^{62} +18038.3 q^{64} +(13975.4 + 24206.2i) q^{65} +(-7330.59 + 12696.9i) q^{66} +(-13778.0 + 23864.1i) q^{67} +(6076.79 + 10525.3i) q^{68} +15974.1 q^{69} -22868.5 q^{71} +(7197.47 + 12466.4i) q^{72} +(-7968.20 + 13801.3i) q^{73} +(16850.4 - 29185.7i) q^{74} +(683.970 + 1184.67i) q^{75} -50425.6 q^{76} +15595.5 q^{78} +(-43582.6 - 75487.3i) q^{79} +(1570.63 - 2720.41i) q^{80} +(-3280.50 + 5681.99i) q^{81} +(5708.60 + 9887.59i) q^{82} +90307.5 q^{83} -32210.5 q^{85} +(30800.6 + 53348.2i) q^{86} +(19109.0 - 33097.7i) q^{87} +(42821.5 - 74169.0i) q^{88} +(63284.8 + 109612. i) q^{89} -14929.4 q^{90} -36515.7 q^{92} +(-43953.2 - 76129.1i) q^{93} +(-2232.10 + 3866.11i) q^{94} +(66821.2 - 115738. i) q^{95} +(-26467.4 - 45842.8i) q^{96} -16573.1 q^{97} +39034.8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} - 54 q^{3} - 150 q^{4} - 100 q^{5} + 36 q^{6} - 228 q^{8} - 486 q^{9}+O(q^{10}) $ 12 * q - 2 * q^2 - 54 * q^3 - 150 * q^4 - 100 * q^5 + 36 * q^6 - 228 * q^8 - 486 * q^9	\( 12 q - 2 q^{2} - 54 q^{3} - 150 q^{4} - 100 q^{5} + 36 q^{6} - 228 q^{8} - 486 q^{9} - 864 q^{10} - 604 q^{11} - 1350 q^{12} + 2704 q^{13} + 1800 q^{15} - 4578 q^{16} - 3028 q^{17} - 162 q^{18} - 1728 q^{19} + 904 q^{20} - 8232 q^{22} + 4484 q^{23} + 1026 q^{24} - 4806 q^{25} - 14172 q^{26} + 8748 q^{27} - 10640 q^{29} - 7776 q^{30} - 3976 q^{31} + 37326 q^{32} - 5436 q^{33} - 32672 q^{34} + 24300 q^{36} - 22680 q^{37} - 52744 q^{38} - 12168 q^{39} - 100600 q^{40} + 57512 q^{41} - 13536 q^{43} + 64940 q^{44} - 8100 q^{45} - 540 q^{46} - 51552 q^{47} + 82404 q^{48} - 81244 q^{50} - 27252 q^{51} - 119296 q^{52} - 80884 q^{53} - 1458 q^{54} + 23312 q^{55} + 31104 q^{57} + 70464 q^{58} - 8872 q^{59} - 4068 q^{60} - 50896 q^{61} + 23648 q^{62} + 399180 q^{64} - 3492 q^{65} + 37044 q^{66} - 6480 q^{67} - 37348 q^{68} - 80712 q^{69} - 221704 q^{71} + 9234 q^{72} - 64232 q^{73} + 27464 q^{74} - 43254 q^{75} - 389728 q^{76} + 255096 q^{78} - 111696 q^{79} + 308940 q^{80} - 39366 q^{81} + 189640 q^{82} + 202256 q^{83} - 46584 q^{85} - 3824 q^{86} + 47880 q^{87} + 97788 q^{88} + 35012 q^{89} + 139968 q^{90} - 898520 q^{92} - 35784 q^{93} + 121016 q^{94} + 119080 q^{95} + 335934 q^{96} + 141904 q^{97} + 97848 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 - 54 * q^3 - 150 * q^4 - 100 * q^5 + 36 * q^6 - 228 * q^8 - 486 * q^9 - 864 * q^10 - 604 * q^11 - 1350 * q^12 + 2704 * q^13 + 1800 * q^15 - 4578 * q^16 - 3028 * q^17 - 162 * q^18 - 1728 * q^19 + 904 * q^20 - 8232 * q^22 + 4484 * q^23 + 1026 * q^24 - 4806 * q^25 - 14172 * q^26 + 8748 * q^27 - 10640 * q^29 - 7776 * q^30 - 3976 * q^31 + 37326 * q^32 - 5436 * q^33 - 32672 * q^34 + 24300 * q^36 - 22680 * q^37 - 52744 * q^38 - 12168 * q^39 - 100600 * q^40 + 57512 * q^41 - 13536 * q^43 + 64940 * q^44 - 8100 * q^45 - 540 * q^46 - 51552 * q^47 + 82404 * q^48 - 81244 * q^50 - 27252 * q^51 - 119296 * q^52 - 80884 * q^53 - 1458 * q^54 + 23312 * q^55 + 31104 * q^57 + 70464 * q^58 - 8872 * q^59 - 4068 * q^60 - 50896 * q^61 + 23648 * q^62 + 399180 * q^64 - 3492 * q^65 + 37044 * q^66 - 6480 * q^67 - 37348 * q^68 - 80712 * q^69 - 221704 * q^71 + 9234 * q^72 - 64232 * q^73 + 27464 * q^74 - 43254 * q^75 - 389728 * q^76 + 255096 * q^78 - 111696 * q^79 + 308940 * q^80 - 39366 * q^81 + 189640 * q^82 + 202256 * q^83 - 46584 * q^85 - 3824 * q^86 + 47880 * q^87 + 97788 * q^88 + 35012 * q^89 + 139968 * q^90 - 898520 * q^92 - 35784 * q^93 + 121016 * q^94 + 119080 * q^95 + 335934 * q^96 + 141904 * q^97 + 97848 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.69017	−	2.92745i	−0.298782	−	0.517505i	0.677076	−	0.735913i	$-0.263247\pi$
$2$	−1.69017	−	2.92745i	−0.298782	−	0.517505i	−0.975858	+	0.218408i	$0.929914\pi$
$3$	−4.50000	+	7.79423i	−0.288675	+	0.500000i
$3$	−4.50000	+	7.79423i	−0.288675	+	0.500000i
$4$	10.2867	−	17.8171i	0.321459	−	0.556783i
$5$	27.2626	+	47.2203i	0.487689	+	0.844702i	0.999900	−	0.0141577i	$-0.00450668\pi$
$5$	27.2626	+	47.2203i	0.487689	+	0.844702i	−0.512211	+	0.858860i	$0.671173\pi$
$6$	30.4230			0.345004
$7$		0			0
$7$		0			0
$8$	−177.715			−0.981748
$9$	−40.5000	−	70.1481i	−0.166667	−	0.288675i
$10$	92.1567	−	159.620i	0.291425	−	0.504763i
$11$	−240.956	+	417.347i	−0.600420	+	1.03996i	0.392337	+	0.919821i	$0.371667\pi$
$11$	−240.956	+	417.347i	−0.600420	+	1.03996i	−0.992757	+	0.120137i	$0.961667\pi$
$12$	92.5801	+	160.354i	0.185594	+	0.321459i
$13$	512.622			0.841277			0.420638	−	0.907228i	$-0.361806\pi$
$13$	512.622			0.841277			0.420638	+	0.907228i	$0.361806\pi$
$14$		0			0
$15$	−490.728			−0.563135
$16$	−28.8055	−	49.8926i	−0.0281304	−	0.0487233i
$17$	−295.372	+	511.599i	−0.247883	+	0.429346i	−0.962938	−	0.269722i	$-0.913068\pi$
$17$	−295.372	+	511.599i	−0.247883	+	0.429346i	0.715055	+	0.699068i	$0.246402\pi$
$18$	−136.903	+	237.124i	−0.0995939	+	0.172502i
$19$	−1225.51	−	2122.64i	−0.778811	−	1.34894i	−0.932627	−	0.360841i	$-0.882490\pi$
$19$	−1225.51	−	2122.64i	−0.778811	−	1.34894i	0.153817	−	0.988099i	$-0.450844\pi$
$20$	1121.77			0.627088
$21$		0			0
$22$	1629.02			0.717579
$23$	−887.452	−	1537.11i	−0.349804	−	0.605879i	0.636410	−	0.771351i	$-0.280419\pi$
$23$	−887.452	−	1537.11i	−0.349804	−	0.605879i	−0.986214	+	0.165472i	$0.947085\pi$
$24$	799.719	−	1385.15i	0.283406	−	0.490874i
$25$	75.9967	−	131.630i	0.0243189	−	0.0421216i
$26$	−866.416	−	1500.68i	−0.251358	−	0.435365i
$27$	729.000			0.192450
$28$		0			0
$29$	−4246.44			−0.937627			−0.468814	−	0.883297i	$-0.655318\pi$
$29$	−4246.44			−0.937627			−0.468814	+	0.883297i	$0.655318\pi$
$30$	829.411	+	1436.58i	0.168254	+	0.291425i
$31$	−4883.69	+	8458.79i	−0.912733	+	1.58090i	−0.102545	+	0.994728i	$0.532699\pi$
$31$	−4883.69	+	8458.79i	−0.912733	+	1.58090i	−0.810187	+	0.586171i	$0.800635\pi$
$32$	−2940.82	+	5093.65i	−0.507684	+	0.879334i
$33$	−2168.60	−	3756.13i	−0.346653	−	0.600420i
$34$	1996.91			0.296252
$35$		0			0
$36$	−1666.44			−0.214306
$37$	4984.83	+	8633.97i	0.598612	+	1.03683i	0.993026	+	0.117894i	$0.0376143\pi$
$37$	4984.83	+	8633.97i	0.598612	+	1.03683i	−0.394414	+	0.918933i	$0.629052\pi$
$38$	−4142.62	+	7175.23i	−0.465389	+	0.806078i
$39$	−2306.80	+	3995.49i	−0.242856	+	0.420638i
$40$	−4844.99	−	8391.77i	−0.478788	−	0.829284i
$41$	−3377.54			−0.313791			−0.156896	−	0.987615i	$-0.550149\pi$
$41$	−3377.54			−0.313791			−0.156896	+	0.987615i	$0.550149\pi$
$42$		0			0
$43$	−18223.4			−1.50300			−0.751500	−	0.659733i	$-0.770669\pi$
$43$	−18223.4			−1.50300			−0.751500	+	0.659733i	$0.770669\pi$
$44$	4957.27	+	8586.24i	0.386021	+	0.668608i
$45$	2208.27	−	3824.84i	0.162563	−	0.281567i
$46$	−2999.88	+	5195.95i	−0.209030	+	0.362051i
$47$	−660.320	−	1143.71i	−0.0436023	−	0.0755214i	0.843401	−	0.537285i	$-0.180550\pi$
$47$	−660.320	−	1143.71i	−0.0436023	−	0.0755214i	−0.887003	+	0.461764i	$0.847217\pi$
$48$	518.500			0.0324822
$49$		0			0
$50$	−513.788			−0.0290642
$51$	−2658.35	−	4604.39i	−0.143115	−	0.247883i
$52$	5273.18	−	9133.42i	0.270436	−	0.468409i
$53$	−17418.5	+	30169.7i	−0.851767	+	1.47530i	0.0278456	+	0.999612i	$0.491135\pi$
$53$	−17418.5	+	30169.7i	−0.851767	+	1.47530i	−0.879612	+	0.475691i	$0.842198\pi$
$54$	−1232.13	−	2134.11i	−0.0575006	−	0.0995939i
$55$	−26276.3			−1.17127
$56$		0			0
$57$	22059.1			0.899293
$58$	7177.19	+	12431.3i	0.280146	+	0.485227i
$59$	−5796.25	+	10039.4i	−0.216779	+	0.375472i	−0.953821	−	0.300374i	$-0.902888\pi$
$59$	−5796.25	+	10039.4i	−0.216779	+	0.375472i	0.737043	+	0.675846i	$0.236222\pi$
$60$	−5047.96	+	8743.32i	−0.181025	+	0.313544i
$61$	−15703.1	−	27198.5i	−0.540331	−	0.935881i	−0.998885	−	0.0472144i	$-0.984966\pi$
$61$	−15703.1	−	27198.5i	−0.540331	−	0.935881i	0.458554	−	0.888667i	$-0.348368\pi$
$62$	33016.9			1.09083
$63$		0			0
$64$	18038.3			0.550486
$65$	13975.4	+	24206.2i	0.410281	+	0.710628i
$66$	−7330.59	+	12696.9i	−0.207147	+	0.358789i
$67$	−13778.0	+	23864.1i	−0.374971	+	0.649469i	−0.990323	−	0.138784i	$-0.955681\pi$
$67$	−13778.0	+	23864.1i	−0.374971	+	0.649469i	0.615352	+	0.788253i	$0.289014\pi$
$68$	6076.79	+	10525.3i	0.159368	+	0.276034i
$69$	15974.1			0.403919
$70$		0			0
$71$	−22868.5			−0.538384			−0.269192	−	0.963086i	$-0.586757\pi$
$71$	−22868.5			−0.538384			−0.269192	+	0.963086i	$0.586757\pi$
$72$	7197.47	+	12466.4i	0.163625	+	0.283406i
$73$	−7968.20	+	13801.3i	−0.175006	+	0.303120i	−0.940163	−	0.340724i	$-0.889328\pi$
$73$	−7968.20	+	13801.3i	−0.175006	+	0.303120i	0.765157	+	0.643843i	$0.222661\pi$
$74$	16850.4	−	29185.7i	0.357709	−	0.619570i
$75$	683.970	+	1184.67i	0.0140405	+	0.0243189i
$76$	−50425.6			−1.00142
$77$		0			0
$78$	15595.5			0.290243
$79$	−43582.6	−	75487.3i	−0.785680	−	1.36084i	−0.928592	−	0.371103i	$-0.878980\pi$
$79$	−43582.6	−	75487.3i	−0.785680	−	1.36084i	0.142912	−	0.989735i	$-0.454354\pi$
$80$	1570.63	−	2720.41i	0.0274378	−	0.0475236i
$81$	−3280.50	+	5681.99i	−0.0555556	+	0.0962250i
$82$	5708.60	+	9887.59i	0.0937551	+	0.162389i
$83$	90307.5			1.43889			0.719447	−	0.694548i	$-0.244395\pi$
$83$	90307.5			1.43889			0.719447	+	0.694548i	$0.244395\pi$
$84$		0			0
$85$	−32210.5			−0.483559
$86$	30800.6	+	53348.2i	0.449069	+	0.777811i
$87$	19109.0	−	33097.7i	0.270670	−	0.468814i
$88$	42821.5	−	74169.0i	0.589461	−	1.02098i
$89$	63284.8	+	109612.i	0.846884	+	1.46685i	0.883975	+	0.467535i	$0.154858\pi$
$89$	63284.8	+	109612.i	0.846884	+	1.46685i	−0.0370902	+	0.999312i	$0.511809\pi$
$90$	−14929.4			−0.194283
$91$		0			0
$92$	−36515.7			−0.449791
$93$	−43953.2	−	76129.1i	−0.526966	−	0.912733i
$94$	−2232.10	+	3866.11i	−0.0260552	+	0.0451289i
$95$	66821.2	−	115738.i	0.759635	−	1.31573i
$96$	−26467.4	−	45842.8i	−0.293111	−	0.507684i
$97$	−16573.1			−0.178844			−0.0894219	−	0.995994i	$-0.528502\pi$
$97$	−16573.1			−0.178844			−0.0894219	+	0.995994i	$0.528502\pi$
$98$		0			0
$99$	39034.8			0.400280
$100$	−1563.51	−	2708.07i	−0.0156351	−	0.0270807i
$101$	38305.0	−	66346.3i	0.373639	−	0.647162i	−0.616483	−	0.787368i	$-0.711443\pi$
$101$	38305.0	−	66346.3i	0.373639	−	0.647162i	0.990122	+	0.140206i	$0.0447765\pi$
$102$	−8986.09	+	15564.4i	−0.0855205	+	0.148126i
$103$	−40217.9	−	69659.5i	−0.373531	−	0.646974i	0.616575	−	0.787296i	$-0.288520\pi$
$103$	−40217.9	−	69659.5i	−0.373531	−	0.646974i	−0.990106	+	0.140322i	$0.955186\pi$
$104$	−91100.8			−0.825922
$105$		0			0
$106$	117760.			1.01797
$107$	−74021.1	−	128208.i	−0.625023	−	1.08257i	−0.988536	−	0.150983i	$-0.951756\pi$
$107$	−74021.1	−	128208.i	−0.625023	−	1.08257i	0.363513	−	0.931589i	$-0.381577\pi$
$108$	7498.99	−	12988.6i	0.0618648	−	0.107153i
$109$	62491.1	−	108238.i	0.503793	−	0.872594i	−0.496198	−	0.868210i	$-0.665271\pi$
$109$	62491.1	−	108238.i	0.503793	−	0.872594i	0.999990	−	0.00438493i	$-0.00139577\pi$
$110$	44411.4	+	76922.7i	0.349955	+	0.606140i
$111$	−89726.9			−0.691218
$112$		0			0
$113$	−194474.			−1.43273			−0.716366	−	0.697724i	$-0.754196\pi$
$113$	−194474.			−1.43273			−0.716366	+	0.697724i	$0.754196\pi$
$114$	−37283.6	−	64577.1i	−0.268693	−	0.465389i
$115$	48388.6	−	83811.4i	0.341191	−	0.590961i
$116$	−43681.8	+	75659.1i	−0.301409	+	0.522055i
$117$	−20761.2	−	35959.4i	−0.140213	−	0.242856i
$118$	39186.5			0.259078
$119$		0			0
$120$	87209.8			0.552856
$121$	−35593.7	−	61650.1i	−0.221009	−	0.382799i
$122$	−53081.6	+	91940.0i	−0.322882	+	0.559249i
$123$	15198.9	−	26325.3i	0.0905838	−	0.156896i
$124$	100474.	+	174026.i	0.586812	+	1.01639i
$125$	178679.			1.02282
$126$		0			0
$127$	239766.			1.31910			0.659551	−	0.751660i	$-0.270746\pi$
$127$	239766.			1.31910			0.659551	+	0.751660i	$0.270746\pi$
$128$	63618.4	+	110190.i	0.343208	+	0.594455i
$129$	82005.5	−	142038.i	0.433879	−	0.751500i
$130$	47241.6	−	81824.8i	0.245169	−	0.424646i
$131$	174788.	+	302741.i	0.889883	+	1.54132i	0.840012	+	0.542567i	$0.182548\pi$
$131$	174788.	+	302741.i	0.889883	+	1.54132i	0.0498711	+	0.998756i	$0.484119\pi$
$132$	−89230.8			−0.445738
$133$		0			0
$134$	93148.1			0.448138
$135$	19874.5	+	34423.6i	0.0938558	+	0.162563i
$136$	52492.1	−	90919.0i	0.243359	−	0.421509i
$137$	140483.	−	243323.i	0.639472	−	1.10760i	−0.346076	−	0.938206i	$-0.612486\pi$
$137$	140483.	−	243323.i	0.639472	−	1.10760i	0.985549	−	0.169392i	$-0.0541804\pi$
$138$	−26998.9	−	46763.5i	−0.120684	−	0.209030i
$139$	50042.9			0.219688			0.109844	−	0.993949i	$-0.464965\pi$
$139$	50042.9			0.219688			0.109844	+	0.993949i	$0.464965\pi$
$140$		0			0
$141$	11885.8			0.0503476
$142$	38651.6	+	66946.5i	0.160859	+	0.278617i
$143$	−123519.	+	213941.i	−0.505120	+	0.874893i
$144$	−2333.25	+	4041.30i	−0.00937680	+	0.0162411i
$145$	−115769.	−	200518.i	−0.457270	−	0.792016i
$146$	53870.3			0.209155
$147$		0			0
$148$	205109.			0.769717
$149$	164406.	+	284760.i	0.606671	+	1.05079i	0.991785	+	0.127916i	$0.0408288\pi$
$149$	164406.	+	284760.i	0.606671	+	1.05079i	−0.385114	+	0.922869i	$0.625838\pi$
$150$	2312.05	−	4004.58i	0.00839012	−	0.0145321i
$151$	−255652.	+	442802.i	−0.912445	+	1.58040i	−0.101844	+	0.994800i	$0.532474\pi$
$151$	−255652.	+	442802.i	−0.912445	+	1.58040i	−0.810600	+	0.585600i	$0.800859\pi$
$152$	217792.	+	377226.i	0.764596	+	1.32432i
$153$	47850.2			0.165255
$154$		0			0
$155$	−532569.			−1.78052
$156$	47458.6	+	82200.8i	0.156136	+	0.270436i
$157$	37721.1	−	65334.8i	0.122134	−	0.211541i	−0.798475	−	0.602028i	$-0.794360\pi$
$157$	37721.1	−	65334.8i	0.122134	−	0.211541i	0.920609	+	0.390486i	$0.127693\pi$
$158$	−147324.	+	255172.i	−0.469494	+	0.813187i
$159$	−156766.	−	271527.i	−0.491768	−	0.851767i
$160$	−320698.			−0.990367
$161$		0			0
$162$	22178.3			0.0663960
$163$	−170376.	−	295101.i	−0.502274	−	0.869963i	−0.999997	−	0.00262731i	$-0.999164\pi$
$163$	−170376.	−	295101.i	−0.502274	−	0.869963i	0.497723	−	0.867336i	$-0.334170\pi$
$164$	−34743.7	+	60177.8i	−0.100871	+	0.174714i
$165$	118244.	−	204804.i	0.338117	−	0.585637i
$166$	−152635.	−	264371.i	−0.429915	−	0.744635i
$167$	−132392.			−0.367342			−0.183671	−	0.982988i	$-0.558798\pi$
$167$	−132392.			−0.367342			−0.183671	+	0.982988i	$0.558798\pi$
$168$		0			0
$169$	−108512.			−0.292253
$170$	54441.0	+	94294.6i	0.144479	+	0.250244i
$171$	−99266.1	+	171934.i	−0.259604	+	0.449647i
$172$	−187459.	+	324688.i	−0.483153	+	0.836845i
$173$	−224661.	−	389124.i	−0.570706	−	0.988492i	−0.996494	−	0.0836688i	$-0.973336\pi$
$173$	−224661.	−	389124.i	−0.570706	−	0.988492i	0.425788	−	0.904823i	$-0.359997\pi$
$174$	−129189.			−0.323485
$175$		0			0
$176$	27763.4			0.0675602
$177$	−52166.2	−	90354.5i	−0.125157	−	0.216779i
$178$	213923.	−	370526.i	0.506067	−	0.876534i
$179$	46833.4	−	81117.8i	0.109250	−	0.189227i	−0.806216	−	0.591621i	$-0.798488\pi$
$179$	46833.4	−	81117.8i	0.109250	−	0.189227i	0.915467	+	0.402393i	$0.131822\pi$
$180$	−45431.6	−	78689.9i	−0.104515	−	0.181025i
$181$	399795.			0.907071			0.453535	−	0.891238i	$-0.350163\pi$
$181$	399795.			0.907071			0.453535	+	0.891238i	$0.350163\pi$
$182$		0			0
$183$	282655.			0.623921
$184$	157714.	+	273168.i	0.343420	+	0.594820i
$185$	−271799.	+	470770.i	−0.583873	+	1.01130i
$186$	−148576.	+	257342.i	−0.314896	+	0.545416i
$187$	−142343.	−	246545.i	−0.297668	−	0.515576i
$188$	−27170.0			−0.0560654
$189$		0			0
$190$	−451755.			−0.907861
$191$	−13911.4	−	24095.2i	−0.0275922	−	0.0477911i	0.851900	−	0.523705i	$-0.175451\pi$
$191$	−13911.4	−	24095.2i	−0.0275922	−	0.0477911i	−0.879492	+	0.475914i	$0.842117\pi$
$192$	−81172.4	+	140595.i	−0.158912	+	0.275243i
$193$	33232.1	−	57559.7i	0.0642192	−	0.111231i	−0.832128	−	0.554583i	$-0.812878\pi$
$193$	33232.1	−	57559.7i	0.0642192	−	0.111231i	0.896347	+	0.443352i	$0.146211\pi$
$194$	28011.3	+	48516.9i	0.0534353	+	0.0925527i
$195$	−251558.			−0.473752
$196$		0			0
$197$	−492506.			−0.904162			−0.452081	−	0.891977i	$-0.649318\pi$
$197$	−492506.			−0.904162			−0.452081	+	0.891977i	$0.649318\pi$
$198$	−65975.3	−	114273.i	−0.119596	−	0.207147i
$199$	−174603.	+	302421.i	−0.312549	+	0.541351i	−0.978914	−	0.204275i	$-0.934516\pi$
$199$	−174603.	+	302421.i	−0.312549	+	0.541351i	0.666364	+	0.745626i	$0.267850\pi$
$200$	−13505.8	+	23392.7i	−0.0238751	+	0.0413528i
$201$	−124002.	−	214777.i	−0.216490	−	0.374971i
$202$	−258967.			−0.446547
$203$		0			0
$204$	−109382.			−0.184023
$205$	−92080.7	−	159488.i	−0.153033	−	0.265060i
$206$	−135950.	+	235472.i	−0.223208	+	0.386608i
$207$	−71883.6	+	124506.i	−0.116601	+	0.201960i
$208$	−14766.4	−	25576.1i	−0.0236655	−	0.0409898i
$209$	1.18117e6			1.87046
$210$		0			0
$211$	−218250.			−0.337480			−0.168740	−	0.985661i	$-0.553970\pi$
$211$	−218250.			−0.337480			−0.168740	+	0.985661i	$0.553970\pi$
$212$	358357.	+	620692.i	0.547616	+	0.948499i
$213$	102908.	−	178243.i	0.155418	−	0.269192i
$214$	−250216.	+	433386.i	−0.373491	+	0.646905i
$215$	−496819.	−	860516.i	−0.732997	−	1.26959i
$216$	−129554.			−0.188937
$217$		0			0
$218$	−422481.			−0.602096
$219$	−71713.8	−	124212.i	−0.101040	−	0.175006i
$220$	−270296.	+	468167.i	−0.376516	+	0.652145i
$221$	−151414.	+	262257.i	−0.208538	+	0.361199i
$222$	151653.	+	262671.i	0.206523	+	0.357709i
$223$	1.24807e6			1.68065			0.840324	−	0.542084i	$-0.182365\pi$
$223$	1.24807e6			1.68065			0.840324	+	0.542084i	$0.182365\pi$
$224$		0			0
$225$	−12311.5			−0.0162126
$226$	328693.	+	569313.i	0.428074	+	0.741447i
$227$	260487.	−	451176.i	0.335522	−	0.581141i	−0.648063	−	0.761587i	$-0.724421\pi$
$227$	260487.	−	451176.i	0.335522	−	0.581141i	0.983585	+	0.180446i	$0.0577541\pi$
$228$	226915.	−	393029.i	0.289086	−	0.500711i
$229$	262826.	+	455227.i	0.331191	+	0.573640i	0.982746	−	0.184962i	$-0.0592161\pi$
$229$	262826.	+	455227.i	0.331191	+	0.573640i	−0.651554	+	0.758602i	$0.725883\pi$
$230$	−327139.			−0.407767
$231$		0			0
$232$	754658.			0.920514
$233$	−105103.	−	182043.i	−0.126831	−	0.219677i	0.795616	−	0.605801i	$-0.207147\pi$
$233$	−105103.	−	182043.i	−0.126831	−	0.219677i	−0.922447	+	0.386124i	$0.873814\pi$
$234$	−70179.7	+	121555.i	−0.0837861	+	0.145122i
$235$	36004.1	−	62360.9i	0.0425287	−	0.0736619i
$236$	119248.	+	206544.i	0.139371	+	0.241398i
$237$	784488.			0.907225
$238$		0			0
$239$	805791.			0.912489			0.456244	−	0.889855i	$-0.349194\pi$
$239$	805791.			0.912489			0.456244	+	0.889855i	$0.349194\pi$
$240$	14135.7	+	24483.7i	0.0158412	+	0.0274378i
$241$	−568975.	+	985493.i	−0.631030	+	1.09298i	0.356311	+	0.934367i	$0.384034\pi$
$241$	−568975.	+	985493.i	−0.631030	+	1.09298i	−0.987341	+	0.158609i	$0.949299\pi$
$242$	−120318.	+	208398.i	−0.132067	+	0.228746i
$243$	−29524.5	−	51137.9i	−0.0320750	−	0.0555556i
$244$	−646130.			−0.694777
$245$		0			0
$246$	−102755.			−0.108259
$247$	−628222.	−	1.08811e6i	−0.655196	−	1.13483i
$248$	867906.	−	1.50326e6i	0.896073	−	1.55204i
$249$	−406384.	+	703877.i	−0.415373	+	0.719447i
$250$	−301997.	−	523074.i	−0.305600	−	0.529314i
$251$	−1.16566e6			−1.16785			−0.583927	−	0.811806i	$-0.698484\pi$
$251$	−1.16566e6			−1.16785			−0.583927	+	0.811806i	$0.698484\pi$
$252$		0			0
$253$	855346.			0.840118
$254$	−405244.	−	701904.i	−0.394124	−	0.682643i
$255$	144947.	−	251056.i	0.139592	−	0.241780i
$256$	503664.	−	872372.i	0.480332	−	0.831959i
$257$	514406.	+	890977.i	0.485817	+	0.841460i	0.999867	−	0.0162999i	$-0.00518866\pi$
$257$	514406.	+	890977.i	0.485817	+	0.841460i	−0.514050	+	0.857760i	$0.671855\pi$
$258$	−554411.			−0.518540
$259$		0			0
$260$	575043.			0.527554
$261$	171981.	+	297880.i	0.156271	+	0.270670i
$262$	590841.	−	1.02337e6i	0.531762	−	0.921039i
$263$	328673.	−	569278.i	0.293004	−	0.507499i	−0.681514	−	0.731805i	$-0.738678\pi$
$263$	328673.	−	569278.i	0.293004	−	0.507499i	0.974519	+	0.224306i	$0.0720116\pi$
$264$	385394.	+	667521.i	0.340326	+	0.589461i
$265$	−1.89950e6			−1.66159
$266$		0			0
$267$	−1.13913e6			−0.977898
$268$	283459.	+	490965.i	0.241076	+	0.417555i
$269$	−2737.93	+	4742.23i	−0.00230697	+	0.00399578i	−0.867177	−	0.498001i	$-0.834068\pi$
$269$	−2737.93	+	4742.23i	−0.00230697	+	0.00399578i	0.864870	+	0.501997i	$0.167401\pi$
$270$	67182.3	−	116363.i	0.0560848	−	0.0971417i
$271$	384573.	+	666101.i	0.318094	+	0.550956i	0.980090	−	0.198552i	$-0.0636237\pi$
$271$	384573.	+	666101.i	0.318094	+	0.550956i	−0.661996	+	0.749507i	$0.730290\pi$
$272$	34033.4			0.0278922
$273$		0			0
$274$	−949757.			−0.764251
$275$	36623.7	+	63434.0i	0.0292032	+	0.0505814i
$276$	164321.	−	284612.i	0.129843	−	0.224895i
$277$	586918.	−	1.01657e6i	0.459598	−	0.796047i	−0.539341	−	0.842087i	$-0.681327\pi$
$277$	586918.	−	1.01657e6i	0.459598	−	0.796047i	0.998940	+	0.0460398i	$0.0146601\pi$
$278$	−84580.8	−	146498.i	−0.0656386	−	0.113689i
$279$	791157.			0.608488
$280$		0			0
$281$	837649.			0.632843			0.316422	−	0.948619i	$-0.397519\pi$
$281$	837649.			0.632843			0.316422	+	0.948619i	$0.397519\pi$
$282$	−20088.9	−	34795.0i	−0.0150430	−	0.0260552i
$283$	298611.	−	517209.i	0.221635	−	0.383884i	−0.733669	−	0.679507i	$-0.762194\pi$
$283$	298611.	−	517209.i	0.221635	−	0.383884i	0.955305	+	0.295623i	$0.0955272\pi$
$284$	−235241.	+	407450.i	−0.173068	+	0.299763i
$285$	601390.	+	1.04164e6i	0.438575	+	0.759635i
$286$	835071.			0.603682
$287$		0			0
$288$	476412.			0.338456
$289$	535440.	+	927408.i	0.377108	+	0.653170i
$290$	−391338.	+	677818.i	−0.273248	+	0.473280i
$291$	74578.9	−	129174.i	0.0516278	−	0.0894219i
$292$	163933.	+	283940.i	0.112515	+	0.194881i
$293$	−851321.			−0.579328			−0.289664	−	0.957128i	$-0.593543\pi$
$293$	−851321.			−0.579328			−0.289664	+	0.957128i	$0.593543\pi$
$294$		0			0
$295$	−632084.			−0.422883
$296$	−885880.	−	1.53439e6i	−0.587686	−	1.01790i
$297$	−175657.	+	304246.i	−0.115551	+	0.200140i
$298$	555748.	−	962584.i	0.362525	−	0.627911i
$299$	−454927.	−	787957.i	−0.294282	−	0.509712i
$300$	28143.1			0.0180538
$301$		0			0
$302$	1.72838e6			1.09049
$303$	344745.	+	597117.i	0.215721	+	0.373639i
$304$	−70602.8	+	122288.i	−0.0438165	+	0.0758925i
$305$	856215.	−	1.48301e6i	0.527027	−	0.912838i
$306$	−80874.8	−	140079.i	−0.0493753	−	0.0855205i
$307$	−600906.			−0.363882			−0.181941	−	0.983309i	$-0.558238\pi$
$307$	−600906.			−0.363882			−0.181941	+	0.983309i	$0.558238\pi$
$308$		0			0
$309$	723923.			0.431316
$310$	900129.	+	1.55907e6i	0.531987	+	0.921428i
$311$	232933.	−	403452.i	0.136562	−	0.236533i	−0.789631	−	0.613582i	$-0.789728\pi$
$311$	232933.	−	403452.i	0.136562	−	0.236533i	0.926193	+	0.377049i	$0.123061\pi$
$312$	409954.	−	710061.i	0.238423	−	0.412961i
$313$	1.48683e6	+	2.57526e6i	0.857827	+	1.48580i	0.873997	+	0.485931i	$0.161519\pi$
$313$	1.48683e6	+	2.57526e6i	0.857827	+	1.48580i	−0.0161698	+	0.999869i	$0.505147\pi$
$314$	−255019.			−0.145965
$315$		0			0
$316$	−1.79328e6			−1.01026
$317$	−1.27760e6	−	2.21288e6i	−0.714082	−	1.23683i	−0.963312	−	0.268383i	$-0.913511\pi$
$317$	−1.27760e6	−	2.21288e6i	−0.714082	−	1.23683i	0.249230	−	0.968444i	$-0.419822\pi$
$318$	−529922.	+	917852.i	−0.293863	+	0.508985i
$319$	1.02320e6	−	1.77224e6i	0.562970	−	0.975093i
$320$	491772.	+	851774.i	0.268466	+	0.464997i
$321$	1.33238e6			0.721714
$322$		0			0
$323$	1.44792e6			0.772216
$324$	67490.9	+	116898.i	0.0357176	+	0.0618648i
$325$	38957.6	−	67476.5i	0.0204590	−	0.0354360i
$326$	−575928.	+	997537.i	−0.300140	+	0.519859i
$327$	562420.	+	974140.i	0.290865	+	0.503793i
$328$	600241.			0.308064
$329$		0			0
$330$	−799405.			−0.404093
$331$	−1.28069e6	−	2.21822e6i	−0.642502	−	1.11285i	−0.984872	−	0.173281i	$-0.944563\pi$
$331$	−1.28069e6	−	2.21822e6i	−0.642502	−	1.11285i	0.342370	−	0.939565i	$-0.388770\pi$
$332$	928965.	−	1.60901e6i	0.462545	−	0.801152i
$333$	403771.	−	699352.i	0.199537	−	0.345609i
$334$	223764.	+	387571.i	0.109755	+	0.190101i
$335$	−1.50249e6			−0.731477
$336$		0			0
$337$	−1.21525e6			−0.582894			−0.291447	−	0.956587i	$-0.594137\pi$
$337$	−1.21525e6			−0.582894			−0.291447	+	0.956587i	$0.594137\pi$
$338$	183403.	+	317662.i	0.0873200	+	0.151243i
$339$	875132.	−	1.51577e6i	0.413594	−	0.716366i
$340$	−331339.	+	573896.i	−0.155444	+	0.269238i
$341$	−2.35350e6	−	4.07639e6i	−1.09605	−	1.89841i
$342$	671105.			0.310259
$343$		0			0
$344$	3.23858e6			1.47557
$345$	435497.	+	754303.i	0.196987	+	0.341191i
$346$	−759429.	+	1.31537e6i	−0.341033	+	0.590687i
$347$	−626590.	+	1.08529e6i	−0.279357	+	0.483861i	−0.971225	−	0.238163i	$-0.923455\pi$
$347$	−626590.	+	1.08529e6i	−0.279357	+	0.483861i	0.691868	+	0.722024i	$0.256788\pi$
$348$	−393136.	−	680932.i	−0.174018	−	0.301409i
$349$	450403.			0.197942			0.0989709	−	0.995090i	$-0.468445\pi$
$349$	450403.			0.197942			0.0989709	+	0.995090i	$0.468445\pi$
$350$		0			0
$351$	373702.			0.161904
$352$	−1.41721e6	−	2.45468e6i	−0.609647	−	1.05594i
$353$	−272640.	+	472227.i	−0.116454	+	0.201704i	−0.918360	−	0.395746i	$-0.870486\pi$
$353$	−272640.	+	472227.i	−0.116454	+	0.201704i	0.801906	+	0.597450i	$0.203819\pi$
$354$	−176339.	+	305428.i	−0.0747895	+	0.129539i
$355$	−623456.	−	1.07986e6i	−0.262564	−	0.454774i
$356$	2.60396e6			1.08895
$357$		0			0
$358$	−316625.			−0.130568
$359$	505793.	+	876060.i	0.207127	+	0.358755i	0.950808	−	0.309780i	$-0.100255\pi$
$359$	505793.	+	876060.i	0.207127	+	0.358755i	−0.743681	+	0.668534i	$0.766922\pi$
$360$	−392444.	+	679733.i	−0.159596	+	0.276428i
$361$	−1.76569e6	+	3.05826e6i	−0.713093	+	1.23511i
$362$	−675720.	−	1.17038e6i	−0.271016	−	0.469414i
$363$	640686.			0.255199
$364$		0			0
$365$	−868937.			−0.341394
$366$	−477734.	−	827460.i	−0.186416	−	0.322882i
$367$	545190.	−	944298.i	0.211292	−	0.365968i	−0.740827	−	0.671696i	$-0.765566\pi$
$367$	545190.	−	944298.i	0.211292	−	0.365968i	0.952119	+	0.305727i	$0.0988996\pi$
$368$	−51127.0	+	88554.6i	−0.0196803	+	0.0340872i
$369$	136790.	+	236928.i	0.0522986	+	0.0905838i
$370$	1.83754e6			0.697803
$371$		0			0
$372$	−1.80853e6			−0.677592
$373$	1.56501e6	+	2.71068e6i	0.582433	+	1.00880i	0.995190	+	0.0979624i	$0.0312325\pi$
$373$	1.56501e6	+	2.71068e6i	0.582433	+	1.00880i	−0.412757	+	0.910841i	$0.635434\pi$
$374$	−481166.	+	833404.i	−0.177876	+	0.308089i
$375$	−804055.	+	1.39266e6i	−0.295262	+	0.511409i
$376$	117349.	+	203254.i	0.0428065	+	0.0741430i
$377$	−2.17682e6			−0.788804
$378$		0			0
$379$	−1.27933e6			−0.457492			−0.228746	−	0.973486i	$-0.573463\pi$
$379$	−1.27933e6			−0.457492			−0.228746	+	0.973486i	$0.573463\pi$
$380$	−1.37474e6	−	2.38111e6i	−0.488383	−	0.845904i
$381$	−1.07895e6	+	1.86879e6i	−0.380792	+	0.659551i
$382$	−47025.0	+	81449.7i	−0.0164881	+	0.0285582i
$383$	−653329.	−	1.13160e6i	−0.227580	−	0.394181i	0.729510	−	0.683970i	$-0.239748\pi$
$383$	−653329.	−	1.13160e6i	−0.227580	−	0.394181i	−0.957090	+	0.289789i	$0.906415\pi$
$384$	−1.14513e6			−0.396303
$385$		0			0
$386$	−224671.			−0.0767501
$387$	738049.	+	1.27834e6i	0.250500	+	0.433879i
$388$	−170482.	+	295284.i	−0.0574909	+	0.0995772i
$389$	18244.1	−	31599.7i	0.00611292	−	0.0105879i	−0.862953	−	0.505285i	$-0.831388\pi$
$389$	18244.1	−	31599.7i	0.00611292	−	0.0105879i	0.869066	+	0.494697i	$0.164721\pi$
$390$	425174.	+	736423.i	0.141549	+	0.245169i
$391$	1.04851e6			0.346842
$392$		0			0
$393$	−3.14618e6			−1.02755
$394$	832417.	+	1.44179e6i	0.270147	+	0.467909i
$395$	2.37636e6	−	4.11597e6i	0.766335	−	1.32733i
$396$	401539.	−	695485.i	0.128674	−	0.222869i
$397$	−320102.	−	554433.i	−0.101932	−	0.176552i	0.810548	−	0.585672i	$-0.199169\pi$
$397$	−320102.	−	554433.i	−0.101932	−	0.176552i	−0.912481	+	0.409120i	$0.865836\pi$
$398$	1.18043e6			0.373536
$399$		0			0
$400$	−8756.50			−0.00273641
$401$	1.34575e6	+	2.33090e6i	0.417929	+	0.723874i	0.995731	−	0.0923027i	$-0.0294227\pi$
$401$	1.34575e6	+	2.33090e6i	0.417929	+	0.723874i	−0.577802	+	0.816177i	$0.696089\pi$
$402$	−419166.	+	726018.i	−0.129366	+	0.224069i
$403$	−2.50349e6	+	4.33616e6i	−0.767861	+	1.32997i
$404$	−788064.	−	1.36497e6i	−0.240219	−	0.416072i
$405$	−357740.			−0.108375
$406$		0			0
$407$	−4.80449e6			−1.43768
$408$	472429.	+	818271.i	0.140503	+	0.243359i
$409$	−1.46286e6	+	2.53375e6i	−0.432409	+	0.748954i	−0.997080	−	0.0763622i	$-0.975669\pi$
$409$	−1.46286e6	+	2.53375e6i	−0.432409	+	0.748954i	0.564672	+	0.825316i	$0.309003\pi$
$410$	−311263.	+	539124.i	−0.0914467	+	0.158390i
$411$	1.26435e6	+	2.18991e6i	0.369199	+	0.639472i
$412$	−1.65484e6			−0.480299
$413$		0			0
$414$	485981.			0.139354
$415$	2.46202e6	+	4.26435e6i	0.701733	+	1.21544i
$416$	−1.50753e6	+	2.61112e6i	−0.427103	+	0.739763i
$417$	−225193.	+	390046.i	−0.0634183	+	0.109844i
$418$	−1.99638e6	−	3.45782e6i	−0.558858	−	0.967971i
$419$	−5.52810e6			−1.53830			−0.769150	−	0.639068i	$-0.779320\pi$
$419$	−5.52810e6			−1.53830			−0.769150	+	0.639068i	$0.779320\pi$
$420$		0			0
$421$	5.77477e6			1.58792			0.793961	−	0.607968i	$-0.208015\pi$
$421$	5.77477e6			1.58792			0.793961	+	0.607968i	$0.208015\pi$
$422$	368878.	+	638916.i	0.100833	+	0.174648i
$423$	−53485.9	+	92640.3i	−0.0145341	+	0.0251738i
$424$	3.09553e6	−	5.36162e6i	0.836220	−	1.44838i
$425$	44894.6	+	77759.6i	0.0120565	+	0.0208825i
$426$	−695729.			−0.185744
$427$		0			0
$428$	−3.04573e6			−0.803677
$429$	−1.11167e6	−	1.92547e6i	−0.291631	−	0.505120i
$430$	−1.67941e6	+	2.90883e6i	−0.438012	+	0.758659i
$431$	−1.10482e6	+	1.91360e6i	−0.286483	+	0.496203i	−0.972968	−	0.230941i	$-0.925819\pi$
$431$	−1.10482e6	+	1.91360e6i	−0.286483	+	0.496203i	0.686485	+	0.727144i	$0.259153\pi$
$432$	−20999.2	−	36371.7i	−0.00541370	−	0.00937680i
$433$	4.97215e6			1.27446			0.637228	−	0.770676i	$-0.280081\pi$
$433$	4.97215e6			1.27446			0.637228	+	0.770676i	$0.280081\pi$
$434$		0			0
$435$	2.08385e6			0.528010
$436$	−1.28565e6	−	2.22681e6i	−0.323897	−	0.561006i
$437$	−2.17516e6	+	3.76748e6i	−0.544863	+	0.943730i
$438$	−242416.	+	419878.i	−0.0603777	+	0.104577i
$439$	1.43202e6	+	2.48034e6i	0.354641	+	0.614257i	0.987056	−	0.160373i	$-0.0512697\pi$
$439$	1.43202e6	+	2.48034e6i	0.354641	+	0.614257i	−0.632415	+	0.774630i	$0.717936\pi$
$440$	4.66971e6			1.14990
$441$		0			0
$442$	1.02366e6			0.249230
$443$	2.83117e6	+	4.90373e6i	0.685419	+	1.18718i	0.973305	+	0.229516i	$0.0737144\pi$
$443$	2.83117e6	+	4.90373e6i	0.685419	+	1.18718i	−0.287886	+	0.957665i	$0.592952\pi$
$444$	−922992.	+	1.59867e6i	−0.222198	+	0.384858i
$445$	−3.45062e6	+	5.97665e6i	−0.826032	+	1.43073i
$446$	−2.10944e6	−	3.65367e6i	−0.502147	−	0.869744i
$447$	−2.95932e6			−0.700523
$448$		0			0
$449$	7.54480e6			1.76617			0.883084	−	0.469215i	$-0.155463\pi$
$449$	7.54480e6			1.76617			0.883084	+	0.469215i	$0.155463\pi$
$450$	20808.4	+	36041.2i	0.00484404	+	0.00839012i
$451$	813837.	−	1.40961e6i	0.188407	−	0.326330i
$452$	−2.00049e6	+	3.46495e6i	−0.460565	+	0.797721i
$453$	−2.30087e6	−	3.98522e6i	−0.526800	−	0.912445i
$454$	−1.76106e6			−0.400991
$455$		0			0
$456$	−3.92025e6			−0.882879
$457$	294507.	+	510101.i	0.0659638	+	0.114253i	0.897121	−	0.441785i	$-0.145654\pi$
$457$	294507.	+	510101.i	0.0659638	+	0.114253i	−0.831157	+	0.556037i	$0.812321\pi$
$458$	888437.	−	1.53882e6i	0.197908	−	0.342787i
$459$	−215326.	+	372956.i	−0.0477051	+	0.0826277i
$460$	−995516.	−	1.72428e6i	−0.219358	−	0.379939i
$461$	−5.94951e6			−1.30385			−0.651927	−	0.758282i	$-0.726039\pi$
$461$	−5.94951e6			−1.30385			−0.651927	+	0.758282i	$0.726039\pi$
$462$		0			0
$463$	−2.16083e6			−0.468456			−0.234228	−	0.972182i	$-0.575256\pi$
$463$	−2.16083e6			−0.468456			−0.234228	+	0.972182i	$0.575256\pi$
$464$	122321.	+	211866.i	0.0263758	+	0.0456843i
$465$	2.39656e6	−	4.15096e6i	0.513991	−	0.890259i
$466$	−355282.	+	615366.i	−0.0757893	+	0.131271i
$467$	−252883.	−	438006.i	−0.0536571	−	0.0929368i	0.837949	−	0.545748i	$-0.183754\pi$
$467$	−252883.	−	438006.i	−0.0536571	−	0.0929368i	−0.891606	+	0.452811i	$0.850421\pi$
$468$	−854255.			−0.180291
$469$		0			0
$470$	−243412.			−0.0508272
$471$	339490.	+	588013.i	0.0705138	+	0.122134i
$472$	1.03008e6	−	1.78415e6i	0.212822	−	0.368619i
$473$	4.39104e6	−	7.60550e6i	0.902432	−	1.56306i
$474$	−1.32591e6	−	2.29655e6i	−0.271062	−	0.469494i
$475$	−372538.			−0.0757594
$476$		0			0
$477$	2.82179e6			0.567845
$478$	−1.36192e6	−	2.35891e6i	−0.272635	−	0.472218i
$479$	273534.	−	473774.i	0.0544718	−	0.0943480i	−0.837504	−	0.546432i	$-0.815986\pi$
$479$	273534.	−	473774.i	0.0544718	−	0.0943480i	0.891976	+	0.452084i	$0.149319\pi$
$480$	1.44314e6	−	2.49959e6i	0.285894	−	0.495183i
$481$	2.55533e6	+	4.42596e6i	0.503599	+	0.872258i
$482$	3.84665e6			0.754162
$483$		0			0
$484$	−1.46456e6			−0.284181
$485$	−451826.	−	782586.i	−0.0872202	−	0.151070i
$486$	−99802.6	+	172863.i	−0.0191669	+	0.0331980i
$487$	−1.18944e6	+	2.06018e6i	−0.227259	+	0.393625i	−0.956995	−	0.290105i	$-0.906310\pi$
$487$	−1.18944e6	+	2.06018e6i	−0.227259	+	0.393625i	0.729736	+	0.683729i	$0.239643\pi$
$488$	2.79068e6	+	4.83359e6i	0.530469	+	0.918799i
$489$	3.06677e6			0.579976
$490$		0			0
$491$	−7.19719e6			−1.34728			−0.673642	−	0.739058i	$-0.735271\pi$
$491$	−7.19719e6			−1.34728			−0.673642	+	0.739058i	$0.735271\pi$
$492$	−312693.	−	541600.i	−0.0582379	−	0.100871i
$493$	1.25428e6	−	2.17248e6i	0.232422	−	0.402566i
$494$	−2.12360e6	+	3.67818e6i	−0.391521	+	0.678134i
$495$	1.06419e6	+	1.84323e6i	0.195212	+	0.338117i
$496$	562709.			0.102702
$497$		0			0
$498$	2.74742e6			0.496423
$499$	−1.11118e6	−	1.92462e6i	−0.199771	−	0.346014i	0.748683	−	0.662928i	$-0.230687\pi$
$499$	−1.11118e6	−	1.92462e6i	−0.199771	−	0.346014i	−0.948454	+	0.316914i	$0.897353\pi$
$500$	1.83801e6	−	3.18353e6i	0.328794	−	0.569488i
$501$	595764.	−	1.03189e6i	0.106042	−	0.183671i
$502$	1.97016e6	+	3.41242e6i	0.348933	+	0.604370i
$503$	−305857.			−0.0539013			−0.0269506	−	0.999637i	$-0.508580\pi$
$503$	−305857.			−0.0539013			−0.0269506	+	0.999637i	$0.508580\pi$
$504$		0			0
$505$	4.17719e6			0.728879
$506$	−1.44568e6	−	2.50398e6i	−0.251012	−	0.434766i
$507$	488302.	−	845764.i	0.0843662	−	0.146127i
$508$	2.46640e6	−	4.27193e6i	0.424037	−	0.734454i
$509$	4.53210e6	+	7.84983e6i	0.775363	+	1.34297i	0.934590	+	0.355726i	$0.115766\pi$
$509$	4.53210e6	+	7.84983e6i	0.775363	+	1.34297i	−0.159228	+	0.987242i	$0.550900\pi$
$510$	−979938.			−0.166830
$511$		0			0
$512$	666475.			0.112359
$513$	−893395.	−	1.54741e6i	−0.149882	−	0.259604i
$514$	1.73886e6	−	3.01180e6i	0.290307	−	0.502826i
$515$	2.19289e6	−	3.79820e6i	0.364334	−	0.631045i
$516$	−1.68713e6	−	2.92219e6i	−0.278948	−	0.483153i
$517$	636431.			0.104719
$518$		0			0
$519$	4.04390e6			0.658995
$520$	−2.48365e6	−	4.30181e6i	−0.402793	−	0.697658i
$521$	−4.22324e6	+	7.31487e6i	−0.681635	+	1.18063i	0.292847	+	0.956159i	$0.405397\pi$
$521$	−4.22324e6	+	7.31487e6i	−0.681635	+	1.18063i	−0.974482	+	0.224467i	$0.927936\pi$
$522$	581352.	−	1.00693e6i	0.0933820	−	0.161742i
$523$	−1.95793e6	−	3.39123e6i	−0.312998	−	0.542129i	0.666012	−	0.745941i	$-0.268000\pi$
$523$	−1.95793e6	−	3.39123e6i	−0.312998	−	0.542129i	−0.979010	+	0.203812i	$0.934667\pi$
$524$	7.19195e6			1.14424
$525$		0			0
$526$	−2.22204e6			−0.350178
$527$	−2.88501e6	−	4.99698e6i	−0.452502	−	0.783756i
$528$	−124935.	+	216394.i	−0.0195030	+	0.0337801i
$529$	1.64303e6	−	2.84581e6i	0.255274	−	0.442147i
$530$	3.21046e6	+	5.56068e6i	0.496453	+	0.859881i
$531$	938992.			0.144519
$532$		0			0
$533$	−1.73140e6			−0.263985
$534$	1.92531e6	+	3.33474e6i	0.292178	+	0.506067i
$535$	4.03602e6	−	6.99059e6i	0.609634	−	1.05592i
$536$	2.44855e6	−	4.24102e6i	0.368127	−	0.637615i
$537$	421501.	+	730061.i	0.0630758	+	0.109250i
$538$	18510.2			0.00275712
$539$		0			0
$540$	817769.			0.120683
$541$	1.47401e6	+	2.55306e6i	0.216524	+	0.375031i	0.953743	−	0.300623i	$-0.0971946\pi$
$541$	1.47401e6	+	2.55306e6i	0.216524	+	0.375031i	−0.737219	+	0.675654i	$0.763861\pi$
$542$	1.29999e6	−	2.25164e6i	0.190082	−	0.329231i
$543$	−1.79908e6	+	3.11610e6i	−0.261849	+	0.453535i
$544$	−1.73727e6	−	3.00904e6i	−0.251692	−	0.435944i
$545$	6.81469e6			0.982776
$546$		0			0
$547$	−5.50670e6			−0.786906			−0.393453	−	0.919345i	$-0.628720\pi$
$547$	−5.50670e6			−0.786906			−0.393453	+	0.919345i	$0.628720\pi$
$548$	−2.89020e6	−	5.00598e6i	−0.411128	−	0.712095i
$549$	−1.27195e6	+	2.20308e6i	−0.180110	+	0.311960i
$550$	123800.	−	214428.i	0.0174508	−	0.0302256i
$551$	5.20405e6	+	9.01368e6i	0.730234	+	1.26480i
$552$	−2.83885e6			−0.396547
$553$		0			0
$554$	−3.96796e6			−0.549278
$555$	−2.44619e6	−	4.23693e6i	−0.337099	−	0.583873i
$556$	514775.	−	891617.i	0.0706205	−	0.122318i
$557$	2.48618e6	−	4.30618e6i	0.339542	−	0.588105i	−0.644804	−	0.764348i	$-0.723061\pi$
$557$	2.48618e6	−	4.30618e6i	0.339542	−	0.588105i	0.984347	+	0.176243i	$0.0563945\pi$
$558$	−1.33719e6	−	2.31607e6i	−0.181805	−	0.314896i
$559$	−9.34174e6			−1.26444
$560$		0			0
$561$	2.56217e6			0.343717
$562$	−1.41577e6	−	2.45218e6i	−0.189082	−	0.327500i
$563$	−6.56986e6	+	1.13793e7i	−0.873544	+	1.51302i	−0.0152390	+	0.999884i	$0.504851\pi$
$563$	−6.56986e6	+	1.13793e7i	−0.873544	+	1.51302i	−0.858305	+	0.513139i	$0.828482\pi$
$564$	122265.	−	211769.i	0.0161847	−	0.0280327i
$565$	−5.30187e6	−	9.18311e6i	−0.698728	−	1.21023i
$566$	−2.01880e6			−0.264882
$567$		0			0
$568$	4.06409e6			0.528558
$569$	6.92946e6	+	1.20022e7i	0.897261	+	1.55410i	0.830981	+	0.556301i	$0.187780\pi$
$569$	6.92946e6	+	1.20022e7i	0.897261	+	1.55410i	0.0662804	+	0.997801i	$0.478887\pi$
$570$	2.03290e6	−	3.52108e6i	0.262077	−	0.453930i
$571$	5.34885e6	−	9.26448e6i	0.686547	−	1.18913i	−0.286401	−	0.958110i	$-0.592459\pi$
$571$	5.34885e6	−	9.26448e6i	0.686547	−	1.18913i	0.972948	−	0.231025i	$-0.0742078\pi$
$572$	2.54120e6	+	4.40150e6i	0.324750	+	0.562484i
$573$	250404.			0.0318607
$574$		0			0
$575$	−269774.			−0.0340275
$576$	−730552.	−	1.26535e6i	−0.0917476	−	0.158912i
$577$	2.80949e6	−	4.86618e6i	0.351308	−	0.608483i	−0.635171	−	0.772372i	$-0.719070\pi$
$577$	2.80949e6	−	4.86618e6i	0.351308	−	0.608483i	0.986479	+	0.163888i	$0.0524037\pi$
$578$	1.80996e6	−	3.13495e6i	0.225346	−	0.390311i
$579$	299089.	+	518038.i	0.0370770	+	0.0642192i
$580$	−4.76353e6			−0.587975
$581$		0			0
$582$	−504203.			−0.0617018
$583$	−8.39416e6	−	1.45391e7i	−1.02284	−	1.77160i
$584$	1.41607e6	−	2.45271e6i	0.171812	−	0.297587i
$585$	1.13201e6	−	1.96070e6i	0.136760	−	0.236876i
$586$	1.43887e6	+	2.49220e6i	0.173093	+	0.299805i
$587$	−6.86832e6			−0.822726			−0.411363	−	0.911471i	$-0.634947\pi$
$587$	−6.86832e6			−0.822726			−0.411363	+	0.911471i	$0.634947\pi$
$588$		0			0
$589$	2.39400e7			2.84338
$590$	1.06833e6	+	1.85040e6i	0.126350	+	0.218844i
$591$	2.21628e6	−	3.83871e6i	0.261009	−	0.452081i
$592$	287181.	−	497412.i	0.0336784	−	0.0583327i
$593$	−2.03868e6	−	3.53110e6i	−0.238075	−	0.412357i	0.722087	−	0.691802i	$-0.243183\pi$
$593$	−2.03868e6	−	3.53110e6i	−0.238075	−	0.412357i	−0.960162	+	0.279445i	$0.909850\pi$
$594$	1.18755e6			0.138098
$595$		0			0
$596$	6.76479e6			0.780079
$597$	−1.57143e6	−	2.72179e6i	−0.180450	−	0.312549i
$598$	−1.53780e6	+	2.66356e6i	−0.175852	+	0.304585i
$599$	−291496.	+	504887.i	−0.0331945	+	0.0574946i	−0.882145	−	0.470977i	$-0.843901\pi$
$599$	−291496.	+	504887.i	−0.0331945	+	0.0574946i	0.848951	+	0.528472i	$0.177235\pi$
$600$	−121552.	−	210534.i	−0.0137843	−	0.0238751i
$601$	−6.87250e6			−0.776119			−0.388060	−	0.921634i	$-0.626855\pi$
$601$	−6.87250e6			−0.776119			−0.388060	+	0.921634i	$0.626855\pi$
$602$		0			0
$603$	2.23203e6			0.249981
$604$	5.25962e6	+	9.10993e6i	0.586627	+	1.01607i
$605$	1.94076e6	−	3.36149e6i	0.215567	−	0.373373i
$606$	1.16535e6	−	2.01845e6i	0.128907	−	0.223273i
$607$	1.20281e6	+	2.08333e6i	0.132503	+	0.229502i	0.924641	−	0.380840i	$-0.124365\pi$
$607$	1.20281e6	+	2.08333e6i	0.132503	+	0.229502i	−0.792138	+	0.610342i	$0.791032\pi$
$608$	1.44160e7			1.58156
$609$		0			0
$610$	−5.78858e6			−0.629865
$611$	−338494.	−	586289.i	−0.0366816	−	0.0635344i
$612$	492220.	−	852550.i	0.0531228	−	0.0920114i
$613$	5.81225e6	−	1.00671e7i	0.624731	−	1.08207i	−0.363861	−	0.931453i	$-0.618542\pi$
$613$	5.81225e6	−	1.00671e7i	0.624731	−	1.08207i	0.988593	−	0.150613i	$-0.0481248\pi$
$614$	1.01563e6	+	1.75912e6i	0.108721	+	0.188311i
$615$	1.65745e6			0.176707
$616$		0			0
$617$	−1.37370e7			−1.45271			−0.726353	−	0.687322i	$-0.758786\pi$
$617$	−1.37370e7			−1.45271			−0.726353	+	0.687322i	$0.758786\pi$
$618$	−1.22355e6	−	2.11925e6i	−0.128869	−	0.223208i
$619$	−8.20042e6	+	1.42035e7i	−0.860220	+	1.48994i	0.0114968	+	0.999934i	$0.496340\pi$
$619$	−8.20042e6	+	1.42035e7i	−0.860220	+	1.48994i	−0.871717	+	0.490010i	$0.836993\pi$
$620$	−5.47837e6	+	9.48881e6i	−0.572363	+	0.991362i
$621$	−646952.	−	1.12055e6i	−0.0673199	−	0.116601i
$622$	−1.57478e6			−0.163209
$623$		0			0
$624$	265794.			0.0273265
$625$	4.63377e6	+	8.02593e6i	0.474498	+	0.821855i
$626$	5.02597e6	−	8.70523e6i	0.512606	−	0.887860i
$627$	−5.31527e6	+	9.20632e6i	−0.539954	+	0.935228i
$628$	−776049.	−	1.34416e6i	−0.0785218	−	0.136004i
$629$	−5.88951e6			−0.593543
$630$		0			0
$631$	−7.28252e6			−0.728129			−0.364065	−	0.931374i	$-0.618611\pi$
$631$	−7.28252e6			−0.728129			−0.364065	+	0.931374i	$0.618611\pi$
$632$	7.74530e6	+	1.34153e7i	0.771340	+	1.33600i
$633$	982124.	−	1.70109e6i	0.0974220	−	0.168740i
$634$	−4.31873e6	+	7.48025e6i	−0.426710	+	0.739083i
$635$	6.53666e6	+	1.13218e7i	0.643312	+	1.11425i
$636$	−6.45042e6			−0.632332
$637$		0			0
$638$	−6.91754e6			−0.672821
$639$	926175.	+	1.60418e6i	0.0897307	+	0.155418i
$640$	−3.46881e6	+	6.00816e6i	−0.334758	+	0.579818i
$641$	53757.1	−	93110.0i	0.00516762	−	0.00895058i	−0.863430	−	0.504469i	$-0.831688\pi$
$641$	53757.1	−	93110.0i	0.00516762	−	0.00895058i	0.868598	+	0.495518i	$0.165022\pi$
$642$	−2.25194e6	−	3.90048e6i	−0.215635	−	0.373491i
$643$	9.75913e6			0.930858			0.465429	−	0.885085i	$-0.345900\pi$
$643$	9.75913e6			0.930858			0.465429	+	0.885085i	$0.345900\pi$
$644$		0			0
$645$	8.94274e6			0.846392
$646$	−2.44723e6	−	4.23872e6i	−0.230724	−	0.399626i
$647$	3.37794e6	−	5.85077e6i	0.317243	−	0.549480i	−0.662669	−	0.748912i	$-0.730576\pi$
$647$	3.37794e6	−	5.85077e6i	0.317243	−	0.549480i	0.979912	+	0.199432i	$0.0639097\pi$
$648$	582995.	−	1.00978e6i	0.0545415	−	0.0944687i
$649$	−2.79328e6	−	4.83810e6i	−0.260317	−	0.450882i
$650$	−263379.			−0.0244511
$651$		0			0
$652$	−7.01043e6			−0.645841
$653$	−1.10173e6	−	1.90825e6i	−0.101110	−	0.175127i	0.811033	−	0.585001i	$-0.198906\pi$
$653$	−1.10173e6	−	1.90825e6i	−0.101110	−	0.175127i	−0.912142	+	0.409874i	$0.865573\pi$
$654$	1.90116e6	−	3.29291e6i	0.173810	−	0.301048i
$655$	−9.53036e6	+	1.65071e7i	−0.867973	+	1.50337i
$656$	97291.8	+	168514.i	0.00882708	+	0.0152889i
$657$	1.29085e6			0.116671
$658$		0			0
$659$	−1.39630e7			−1.25247			−0.626233	−	0.779636i	$-0.715404\pi$
$659$	−1.39630e7			−1.25247			−0.626233	+	0.779636i	$0.715404\pi$
$660$	−2.43267e6	−	4.21350e6i	−0.217382	−	0.376516i
$661$	25526.4	−	44213.1i	0.00227241	−	0.00393593i	−0.864887	−	0.501967i	$-0.832610\pi$
$661$	25526.4	−	44213.1i	0.00227241	−	0.00393593i	0.867159	+	0.498031i	$0.165943\pi$
$662$	−4.32916e6	+	7.49833e6i	−0.383936	+	0.664997i
$663$	−1.36273e6	−	2.36031e6i	−0.120400	−	0.208538i
$664$	−1.60490e7			−1.41263
$665$		0			0
$666$	−2.72976e6			−0.238473
$667$	3.76851e6	+	6.52726e6i	0.327986	+	0.568089i
$668$	−1.36187e6	+	2.35883e6i	−0.118085	+	0.204530i
$669$	−5.61632e6	+	9.72774e6i	−0.485161	+	0.840324i
$670$	2.53946e6	+	4.39848e6i	0.218552	+	0.378543i
$671$	1.51350e7			1.29770
$672$		0			0
$673$	6.71688e6			0.571650			0.285825	−	0.958282i	$-0.407732\pi$
$673$	6.71688e6			0.571650			0.285825	+	0.958282i	$0.407732\pi$
$674$	2.05397e6	+	3.55757e6i	0.174158	+	0.301651i
$675$	55401.6	−	95958.4i	0.00468018	−	0.00810631i
$676$	−1.11622e6	+	1.93336e6i	−0.0939474	+	0.162722i
$677$	−7.28274e6	−	1.26141e7i	−0.610693	−	1.05775i	−0.991124	−	0.132942i	$-0.957558\pi$
$677$	−7.28274e6	−	1.26141e7i	−0.610693	−	1.05775i	0.380430	−	0.924810i	$-0.375776\pi$
$678$	−5.91647e6			−0.494298
$679$		0			0
$680$	5.72429e6			0.474733
$681$	2.34438e6	+	4.06058e6i	0.193714	+	0.335522i
$682$	−7.95562e6	+	1.37795e7i	−0.654957	+	1.13442i
$683$	812824.	−	1.40785e6i	0.0666722	−	0.115480i	−0.830762	−	0.556627i	$-0.812095\pi$
$683$	812824.	−	1.40785e6i	0.0666722	−	0.115480i	0.897435	+	0.441148i	$0.145428\pi$
$684$	2.04224e6	+	3.53726e6i	0.166904	+	0.289086i
$685$	1.53197e7			1.24745
$686$		0			0
$687$	−4.73086e6			−0.382427
$688$	524936.	+	909215.i	0.0422800	+	0.0732311i
$689$	−8.92910e6	+	1.54657e7i	−0.716572	+	1.24114i
$690$	1.47212e6	−	2.54979e6i	0.117712	−	0.203884i
$691$	1.40778e6	+	2.43834e6i	0.112160	+	0.194267i	0.916641	−	0.399711i	$-0.130890\pi$
$691$	1.40778e6	+	2.43834e6i	0.112160	+	0.194267i	−0.804481	+	0.593979i	$0.797556\pi$
$692$	−9.24407e6			−0.733834
$693$		0			0
$694$	4.23616e6			0.333867
$695$	1.36430e6	+	2.36304e6i	0.107139	+	0.185571i
$696$	−3.39596e6	+	5.88198e6i	−0.265729	+	0.460257i
$697$	997630.	−	1.72795e6i	0.0777835	−	0.134725i
$698$	−761255.	−	1.31853e6i	−0.0591414	−	0.102436i
$699$	1.89185e6			0.146451
$700$		0			0
$701$	1.40996e7			1.08371			0.541855	−	0.840472i	$-0.317722\pi$
$701$	1.40996e7			1.08371			0.541855	+	0.840472i	$0.317722\pi$
$702$	−631617.	−	1.09399e6i	−0.0483739	−	0.0837861i
$703$	1.22179e7	−	2.11620e7i	0.932412	−	1.61498i
$704$	−4.34643e6	+	7.52824e6i	−0.330523	+	0.572482i
$705$	324037.	+	561249.i	0.0245540	+	0.0425287i
$706$	1.84323e6			0.139177
$707$		0			0
$708$	−2.14647e6			−0.160932
$709$	4.22472e6	+	7.31742e6i	0.315633	+	0.546692i	0.979572	−	0.201095i	$-0.0644499\pi$
$709$	4.22472e6	+	7.31742e6i	0.315633	+	0.546692i	−0.663939	+	0.747787i	$0.731117\pi$
$710$	−2.10749e6	+	3.65028e6i	−0.156899	+	0.271757i
$711$	−3.53019e6	+	6.11448e6i	−0.261893	+	0.453613i
$712$	−1.12467e7	−	1.94798e7i	−0.831427	−	1.44007i
$713$	1.73361e7			1.27711
$714$		0			0
$715$	−1.34698e7			−0.985365
$716$	−963521.	−	1.66887e6i	−0.0702390	−	0.121658i
$717$	−3.62606e6	+	6.28052e6i	−0.263413	+	0.456244i
$718$	1.70975e6	−	2.96137e6i	0.123772	−	0.214379i
$719$	−9.13284e6	−	1.58185e7i	−0.658846	−	1.14115i	−0.980915	−	0.194438i	$-0.937712\pi$
$719$	−9.13284e6	−	1.58185e7i	−0.658846	−	1.14115i	0.322069	−	0.946716i	$-0.395622\pi$
$720$	−254442.			−0.0182918
$721$		0			0
$722$	1.19372e7			0.852237
$723$	−5.12077e6	−	8.86944e6i	−0.364326	−	0.631030i
$724$	4.11257e6	−	7.12318e6i	0.291586	−	0.505042i
$725$	−322716.	+	558960.i	−0.0228021	+	0.0394944i
$726$	−1.08287e6	−	1.87558e6i	−0.0762488	−	0.132067i
$727$	1.37476e6			0.0964700			0.0482350	−	0.998836i	$-0.484640\pi$
$727$	1.37476e6			0.0964700			0.0482350	+	0.998836i	$0.484640\pi$
$728$		0			0
$729$	531441.			0.0370370
$730$	1.46865e6	+	2.54377e6i	0.102002	+	0.176673i
$731$	5.38269e6	−	9.32309e6i	0.372568	−	0.645307i
$732$	2.90759e6	−	5.03609e6i	0.200565	−	0.347389i
$733$	−8.23126e6	−	1.42570e7i	−0.565857	−	0.980093i	−0.996969	−	0.0777948i	$-0.975212\pi$
$733$	−8.23126e6	−	1.42570e7i	−0.565857	−	0.980093i	0.431112	−	0.902298i	$-0.358121\pi$
$734$	−3.68585e6			−0.252521
$735$		0			0
$736$	1.04393e7			0.710360
$737$	−6.63975e6	−	1.15004e7i	−0.450280	−	0.779909i
$738$	462397.	−	800895.i	0.0312517	−	0.0541296i
$739$	−1.36498e6	+	2.36422e6i	−0.0919425	+	0.159249i	−0.908328	−	0.418258i	$-0.862641\pi$
$739$	−1.36498e6	+	2.36422e6i	−0.0919425	+	0.159249i	0.816386	+	0.577507i	$0.195974\pi$
$740$	5.59182e6	+	9.68532e6i	0.375382	+	0.650181i
$741$	1.13080e7			0.756555
$742$		0			0
$743$	−2.34396e7			−1.55768			−0.778839	−	0.627224i	$-0.784191\pi$
$743$	−2.34396e7			−1.55768			−0.778839	+	0.627224i	$0.784191\pi$
$744$	7.81115e6	+	1.35293e7i	0.517348	+	0.896073i
$745$	−8.96431e6	+	1.55266e7i	−0.591734	+	1.02491i
$746$	5.29026e6	−	9.16300e6i	0.348041	−	0.602824i
$747$	−3.65745e6	−	6.33490e6i	−0.239816	−	0.415373i
$748$	−5.85695e6			−0.382752
$749$		0			0
$750$	5.43595e6			0.352876
$751$	−8.97034e6	−	1.55371e7i	−0.580376	−	1.00524i	−0.995435	−	0.0954455i	$-0.969572\pi$
$751$	−8.97034e6	−	1.55371e7i	−0.580376	−	1.00524i	0.415059	−	0.909794i	$-0.363761\pi$
$752$	−38041.7	+	65890.2i	−0.00245310	+	0.00424890i
$753$	5.24548e6	−	9.08544e6i	0.337130	−	0.583927i
$754$	3.67919e6	+	6.37254e6i	0.235680	+	0.408210i
$755$	−2.78790e7			−1.77996
$756$		0			0
$757$	−2.30823e7			−1.46399			−0.731997	−	0.681308i	$-0.761412\pi$
$757$	−2.30823e7			−1.46399			−0.731997	+	0.681308i	$0.761412\pi$
$758$	2.16228e6	+	3.74517e6i	0.136690	+	0.236755i
$759$	−3.84906e6	+	6.66676e6i	−0.242521	+	0.420059i
$760$	−1.18751e7	+	2.05684e7i	−0.745770	+	1.29171i
$761$	−9.57936e6	−	1.65919e7i	−0.599618	−	1.03857i	−0.992877	−	0.119141i	$-0.961986\pi$
$761$	−9.57936e6	−	1.65919e7i	−0.599618	−	1.03857i	0.393259	−	0.919428i	$-0.371348\pi$
$762$	7.29440e6			0.455095
$763$		0			0
$764$	−572407.			−0.0354790
$765$	1.30452e6	+	2.25950e6i	0.0805932	+	0.139592i
$766$	−2.20847e6	+	3.82518e6i	−0.135994	+	0.235548i
$767$	−2.97128e6	+	5.14641e6i	−0.182371	+	0.315876i
$768$	4.53298e6	+	7.85135e6i	0.277320	+	0.480332i
$769$	1.73017e7			1.05505			0.527526	−	0.849539i	$-0.323120\pi$
$769$	1.73017e7			1.05505			0.527526	+	0.849539i	$0.323120\pi$
$770$		0			0
$771$	−9.25931e6			−0.560974
$772$	−683697.	−	1.18420e6i	−0.0412877	−	0.0715123i
$773$	−1.56143e7	+	2.70448e7i	−0.939885	+	1.62793i	−0.174202	+	0.984710i	$0.555735\pi$
$773$	−1.56143e7	+	2.70448e7i	−0.939885	+	1.62793i	−0.765683	+	0.643218i	$0.777599\pi$
$774$	2.49485e6	−	4.32121e6i	0.149690	−	0.259270i
$775$	742288.	+	1.28568e6i	0.0443934	+	0.0768916i
$776$	2.94529e6			0.175580
$777$		0			0
$778$	−123342.			−0.00730572
$779$	4.13920e6	+	7.16931e6i	0.244384	+	0.423286i
$780$	−2.58770e6	+	4.48202e6i	−0.152292	+	0.263777i
$781$	5.51030e6	−	9.54412e6i	0.323257	−	0.559897i
$782$	−1.77216e6	−	3.06947e6i	−0.103630	−	0.179493i
$783$	−3.09566e6			−0.180446
$784$		0			0
$785$	4.11350e6			0.238253
$786$	5.31757e6	+	9.21030e6i	0.307013	+	0.531762i
$787$	1.24346e7	−	2.15373e7i	0.715638	−	1.23952i	−0.247075	−	0.968996i	$-0.579469\pi$
$787$	1.24346e7	−	2.15373e7i	0.715638	−	1.23952i	0.962713	−	0.270525i	$-0.0871974\pi$
$788$	−5.06626e6	+	8.77501e6i	−0.290651	+	0.503422i
$789$	2.95805e6	+	5.12350e6i	0.169166	+	0.293004i
$790$	−1.60657e7			−0.915868
$791$		0			0
$792$	−6.93708e6			−0.392974
$793$	−8.04974e6	−	1.39426e7i	−0.454568	−	0.787335i
$794$	−1.08205e6	+	1.87417e6i	−0.0609110	+	0.105501i
$795$	8.54773e6	−	1.48051e7i	0.479659	−	0.830795i
$796$	3.59217e6	+	6.22182e6i	0.200943	+	0.348044i
$797$	584574.			0.0325982			0.0162991	−	0.999867i	$-0.494812\pi$
$797$	584574.			0.0325982			0.0162991	+	0.999867i	$0.494812\pi$
$798$		0			0
$799$	780159.			0.0432331
$800$	446985.	+	774200.i	0.0246927	+	0.0427689i
$801$	5.12607e6	−	8.87861e6i	0.282295	−	0.488949i
$802$	4.54907e6	−	7.87922e6i	0.249739	−	0.432561i
$803$	−3.83997e6	−	6.65102e6i	−0.210154	−	0.363998i
$804$	−5.10226e6			−0.278370
$805$		0			0
$806$	1.69252e7			0.917691
$807$	−24641.3	−	42680.1i	−0.00133193	−	0.00230697i
$808$	−6.80739e6	+	1.17908e7i	−0.366820	+	0.635350i
$809$	5.52762e6	−	9.57412e6i	0.296939	−	0.514313i	−0.678495	−	0.734605i	$-0.737368\pi$
$809$	5.52762e6	−	9.57412e6i	0.296939	−	0.514313i	0.975434	+	0.220292i	$0.0707009\pi$
$810$	604640.	+	1.04727e6i	0.0323806	+	0.0560848i
$811$	1.62780e7			0.869060			0.434530	−	0.900657i	$-0.356914\pi$
$811$	1.62780e7			0.869060			0.434530	+	0.900657i	$0.356914\pi$
$812$		0			0
$813$	−6.92232e6			−0.367304
$814$	8.12038e6	+	1.40649e7i	0.429551	+	0.744005i
$815$	9.28982e6	−	1.60904e7i	0.489907	−	0.848543i
$816$	−153150.	+	265264.i	−0.00805178	+	0.0139461i
$817$	2.23330e7	+	3.86818e7i	1.17055	+	2.02746i
$818$	9.88989e6			0.516783
$819$		0			0
$820$	−3.78882e6			−0.196775
$821$	−1.64287e7	−	2.84553e7i	−0.850638	−	1.47335i	−0.880633	−	0.473798i	$-0.842883\pi$
$821$	−1.64287e7	−	2.84553e7i	−0.850638	−	1.47335i	0.0299951	−	0.999550i	$-0.490451\pi$
$822$	4.27390e6	−	7.40262e6i	0.220620	−	0.382125i
$823$	−5.30231e6	+	9.18386e6i	−0.272876	+	0.472635i	−0.969597	−	0.244707i	$-0.921308\pi$
$823$	−5.30231e6	+	9.18386e6i	−0.272876	+	0.472635i	0.696721	+	0.717342i	$0.254642\pi$
$824$	7.14734e6	+	1.23796e7i	0.366713	+	0.635166i
$825$	−659226.			−0.0337209
$826$		0			0
$827$	1.57582e7			0.801203			0.400602	−	0.916252i	$-0.368801\pi$
$827$	1.57582e7			0.801203			0.400602	+	0.916252i	$0.368801\pi$
$828$	1.47889e6	+	2.56151e6i	0.0749651	+	0.129843i
$829$	1.35068e7	−	2.33944e7i	0.682598	−	1.18229i	−0.291588	−	0.956544i	$-0.594184\pi$
$829$	1.35068e7	−	2.33944e7i	0.682598	−	1.18229i	0.974185	−	0.225750i	$-0.0724832\pi$
$830$	8.32245e6	−	1.44149e7i	0.419330	−	0.726301i
$831$	5.28227e6	+	9.14915e6i	0.265349	+	0.459598i
$832$	9.24684e6			0.463111
$833$		0			0
$834$	1.52245e6			0.0757930
$835$	−3.60935e6	−	6.25158e6i	−0.179149	−	0.310294i
$836$	1.21503e7	−	2.10450e7i	0.601274	−	1.04144i
$837$	−3.56021e6	+	6.16646e6i	−0.175655	+	0.304244i
$838$	9.34341e6	+	1.61833e7i	0.459616	+	0.796078i
$839$	−3.50490e7			−1.71898			−0.859489	−	0.511154i	$-0.829218\pi$
$839$	−3.50490e7			−1.71898			−0.859489	+	0.511154i	$0.829218\pi$
$840$		0			0
$841$	−2.47888e6			−0.120855
$842$	−9.76031e6	−	1.69054e7i	−0.474442	−	0.821758i
$843$	−3.76942e6	+	6.52883e6i	−0.182686	+	0.316422i
$844$	−2.24507e6	+	3.88857e6i	−0.108486	+	0.187903i
$845$	−2.95831e6	−	5.12395e6i	−0.142529	−	0.246867i
$846$	361600.			0.0173701
$847$		0			0
$848$	2.00699e6			0.0958422
$849$	2.68749e6	+	4.65488e6i	0.127961	+	0.221635i
$850$	151758.	−	262853.i	0.00720453	−	0.0124786i
$851$	8.84758e6	−	1.53245e7i	0.418794	−	0.725373i
$852$	−2.11717e6	−	3.66705e6i	−0.0999211	−	0.173068i
$853$	−538313.			−0.0253316			−0.0126658	−	0.999920i	$-0.504032\pi$
$853$	−538313.			−0.0253316			−0.0126658	+	0.999920i	$0.504032\pi$
$854$		0			0
$855$	−1.08250e7			−0.506423
$856$	1.31547e7	+	2.27846e7i	0.613615	+	1.06281i
$857$	1.84137e6	−	3.18935e6i	0.0856426	−	0.148337i	−0.820022	−	0.572332i	$-0.806039\pi$
$857$	1.84137e6	−	3.18935e6i	0.0856426	−	0.148337i	0.905665	+	0.423994i	$0.139372\pi$
$858$	−3.75782e6	+	6.50874e6i	−0.174268	+	0.301841i
$859$	9.44416e6	+	1.63578e7i	0.436697	+	0.756382i	0.997432	−	0.0716134i	$-0.0228148\pi$
$859$	9.44416e6	+	1.63578e7i	0.436697	+	0.756382i	−0.560735	+	0.827995i	$0.689481\pi$
$860$	−2.04425e7			−0.942513
$861$		0			0
$862$	7.46931e6			0.342383
$863$	−1.39272e7	−	2.41226e7i	−0.636557	−	1.10255i	−0.986183	−	0.165659i	$-0.947025\pi$
$863$	−1.39272e7	−	2.41226e7i	−0.636557	−	1.10255i	0.349626	−	0.936889i	$-0.386308\pi$
$864$	−2.14386e6	+	3.71327e6i	−0.0977038	+	0.169228i
$865$	1.22497e7	−	2.12171e7i	0.556654	−	0.964153i
$866$	−8.40376e6	−	1.45557e7i	−0.380784	−	0.659537i
$867$	−9.63791e6			−0.435447
$868$		0			0
$869$	4.20059e7			1.88695
$870$	−3.52204e6	−	6.10036e6i	−0.157760	−	0.273248i
$871$	−7.06289e6	+	1.22333e7i	−0.315455	+	0.546383i
$872$	−1.11056e7	+	1.92355e7i	−0.494597	+	0.856668i
$873$	671210.	+	1.16257e6i	0.0298073	+	0.0516278i
$874$	1.47055e7			0.651180
$875$		0			0
$876$	−2.95079e6			−0.129921
$877$	8.75262e6	+	1.51600e7i	0.384272	+	0.665579i	0.991668	−	0.128821i	$-0.0411191\pi$
$877$	8.75262e6	+	1.51600e7i	0.384272	+	0.665579i	−0.607396	+	0.794399i	$0.707786\pi$
$878$	4.84072e6	−	8.38437e6i	0.211921	−	0.367057i
$879$	3.83094e6	−	6.63539e6i	0.167237	−	0.289664i
$880$	756904.	+	1.31100e6i	0.0329484	+	0.0570683i
$881$	−5.66292e6			−0.245811			−0.122905	−	0.992418i	$-0.539221\pi$
$881$	−5.66292e6			−0.245811			−0.122905	+	0.992418i	$0.539221\pi$
$882$		0			0
$883$	1.43933e7			0.621239			0.310620	−	0.950534i	$-0.399463\pi$
$883$	1.43933e7			0.621239			0.310620	+	0.950534i	$0.399463\pi$
$884$	3.11510e6	+	5.39551e6i	0.134073	+	0.232221i
$885$	2.84438e6	−	4.92661e6i	0.122076	−	0.211441i
$886$	9.57028e6	−	1.65762e7i	0.409582	−	0.709416i
$887$	−2.75097e6	−	4.76481e6i	−0.117402	−	0.203347i	0.801335	−	0.598215i	$-0.204123\pi$
$887$	−2.75097e6	−	4.76481e6i	−0.117402	−	0.203347i	−0.918737	+	0.394869i	$0.870790\pi$
$888$	1.59458e7			0.678602
$889$		0			0
$890$	2.33285e7			0.987214
$891$	−1.58091e6	−	2.73822e6i	−0.0667134	−	0.115551i
$892$	1.28385e7	−	2.22369e7i	0.540259	−	0.935756i
$893$	−1.61845e6	+	2.80324e6i	−0.0679159	+	0.117634i
$894$	5.00173e6	+	8.66326e6i	0.209304	+	0.362525i
$895$	5.10721e6			0.213121
$896$		0			0
$897$	8.18869e6			0.339808
$898$	−1.27520e7	−	2.20870e7i	−0.527699	−	0.914001i
$899$	2.07383e7	−	3.59198e7i	0.855803	−	1.48229i
$900$	−126644.	+	219354.i	−0.00521169	+	0.00902692i
$901$	−1.02899e7	−	1.78226e7i	−0.422277	−	0.731405i
$902$	−5.50208e6			−0.225170
$903$		0			0
$904$	3.45610e7			1.40658
$905$	1.08995e7	+	1.88784e7i	0.442368	+	0.766205i
$906$	−7.77769e6	+	1.34714e7i	−0.314797	+	0.545244i
$907$	−3.00778e6	+	5.20962e6i	−0.121402	+	0.210275i	−0.920321	−	0.391164i	$-0.872072\pi$
$907$	−3.00778e6	+	5.20962e6i	−0.121402	+	0.210275i	0.798919	+	0.601439i	$0.205406\pi$
$908$	−5.35909e6	−	9.28221e6i	−0.215713	−	0.373626i
$909$	−6.20542e6			−0.249093
$910$		0			0
$911$	−1.47513e7			−0.588892			−0.294446	−	0.955668i	$-0.595135\pi$
$911$	−1.47513e7			−0.588892			−0.294446	+	0.955668i	$0.595135\pi$
$912$	−635425.	−	1.10059e6i	−0.0252975	−	0.0438165i
$913$	−2.17601e7	+	3.76896e7i	−0.863941	+	1.49639i
$914$	995532.	−	1.72431e6i	0.0394175	−	0.0682732i
$915$	7.70593e6	+	1.33471e7i	0.304279	+	0.527027i
$916$	1.08144e7			0.425858
$917$		0			0
$918$	1.45575e6			0.0570137
$919$	1.77001e7	+	3.06574e7i	0.691331	+	1.19742i	0.971402	+	0.237442i	$0.0763089\pi$
$919$	1.77001e7	+	3.06574e7i	0.691331	+	1.19742i	−0.280070	+	0.959979i	$0.590358\pi$
$920$	−8.59939e6	+	1.48946e7i	−0.334964	+	0.580175i
$921$	2.70408e6	−	4.68360e6i	0.105044	−	0.181941i
$922$	1.00557e7	+	1.74169e7i	0.389568	+	0.674751i
$923$	−1.17229e7			−0.452930
$924$		0			0
$925$	1.51532e6			0.0582305
$926$	3.65217e6	+	6.32574e6i	0.139966	+	0.242429i
$927$	−3.25765e6	+	5.64242e6i	−0.124510	+	0.215658i
$928$	1.24880e7	−	2.16299e7i	0.476018	−	0.824487i
$929$	1.91633e7	+	3.31918e7i	0.728502	+	1.26180i	0.957516	+	0.288379i	$0.0931164\pi$
$929$	1.91633e7	+	3.31918e7i	0.728502	+	1.26180i	−0.229014	+	0.973423i	$0.573550\pi$
$930$	−1.62023e7			−0.614285
$931$		0			0
$932$	−4.32463e6			−0.163083
$933$	2.09640e6	+	3.63107e6i	0.0788442	+	0.136562i
$934$	−854828.	+	1.48061e6i	−0.0320635	+	0.0555357i
$935$	7.76129e6	−	1.34429e7i	0.290339	−	0.502881i
$936$	3.68958e6	+	6.39055e6i	0.137654	+	0.238423i
$937$	1.48693e7			0.553274			0.276637	−	0.960974i	$-0.410780\pi$
$937$	1.48693e7			0.553274			0.276637	+	0.960974i	$0.410780\pi$
$938$		0			0
$939$	−2.67629e7			−0.990534
$940$	−740726.	−	1.28297e6i	−0.0273425	−	0.0473586i
$941$	1.75447e6	−	3.03883e6i	0.0645909	−	0.111875i	−0.831922	−	0.554893i	$-0.812759\pi$
$941$	1.75447e6	−	3.03883e6i	0.0645909	−	0.111875i	0.896512	+	0.443019i	$0.146092\pi$
$942$	1.14759e6	−	1.98768e6i	0.0421365	−	0.0729825i
$943$	2.99740e6	+	5.19166e6i	0.109766	+	0.190120i
$944$	667856.			0.0243923
$945$		0			0
$946$	−2.96863e7			−1.07852
$947$	−1.94887e7	−	3.37554e7i	−0.706168	−	1.22312i	−0.966268	−	0.257537i	$-0.917089\pi$
$947$	−1.94887e7	−	3.37554e7i	−0.706168	−	1.22312i	0.260100	−	0.965582i	$-0.416244\pi$
$948$	8.06977e6	−	1.39773e7i	0.291636	−	0.505128i
$949$	−4.08468e6	+	7.07487e6i	−0.147229	+	0.255007i
$950$	629651.	+	1.09059e6i	0.0226355	+	0.0392059i
$951$	2.29969e7			0.824551
$952$		0			0
$953$	7.11438e6			0.253749			0.126875	−	0.991919i	$-0.459505\pi$
$953$	7.11438e6			0.253749			0.126875	+	0.991919i	$0.459505\pi$
$954$	−4.76930e6	−	8.26067e6i	−0.169662	−	0.293863i
$955$	758521.	−	1.31380e6i	0.0269128	−	0.0466144i
$956$	8.28891e6	−	1.43568e7i	0.293328	−	0.508058i
$957$	9.20884e6	+	1.59502e7i	0.325031	+	0.562970i
$958$	−1.84927e6			−0.0651008
$959$		0			0
$960$	−8.85190e6			−0.309998
$961$	−3.33862e7	−	5.78266e7i	−1.16616	−	2.01985i
$962$	8.63787e6	−	1.49612e7i	0.300932	−	0.521230i
$963$	−5.99571e6	+	1.03849e7i	−0.208341	+	0.360857i
$964$	1.17057e7	+	2.02749e7i	0.405701	+	0.702694i
$965$	3.62398e6			0.125276
$966$		0			0
$967$	−1.99357e7			−0.685592			−0.342796	−	0.939410i	$-0.611374\pi$
$967$	−1.99357e7			−0.685592			−0.342796	+	0.939410i	$0.611374\pi$
$968$	6.32555e6	+	1.09562e7i	0.216975	+	0.375812i
$969$	−6.51565e6	+	1.12854e7i	−0.222920	+	0.386108i
$970$	−1.52732e6	+	2.64540e6i	−0.0521196	+	0.0902738i
$971$	−2.47944e7	−	4.29452e7i	−0.843928	−	1.46173i	−0.886549	−	0.462635i	$-0.846904\pi$
$971$	−2.47944e7	−	4.29452e7i	−0.843928	−	1.46173i	0.0426206	−	0.999091i	$-0.486429\pi$
$972$	−1.21484e6			−0.0412432
$973$		0			0
$974$	8.04143e6			0.271604
$975$	350618.	+	607289.i	0.0118120	+	0.0204590i
$976$	−904671.	+	1.56694e6i	−0.0303995	+	0.0526534i
$977$	177674.	−	307740.i	0.00595508	−	0.0103145i	−0.863033	−	0.505148i	$-0.831438\pi$
$977$	177674.	−	307740.i	0.00595508	−	0.0103145i	0.868988	+	0.494834i	$0.164771\pi$
$978$	−5.18336e6	−	8.97784e6i	−0.173286	−	0.300140i
$979$	−6.09953e7			−2.03395
$980$		0			0
$981$	−1.01236e7			−0.335862
$982$	1.21644e7	+	2.10694e7i	0.402544	+	0.697226i
$983$	495877.	−	858884.i	0.0163678	−	0.0283499i	−0.857725	−	0.514108i	$-0.828123\pi$
$983$	495877.	−	858884.i	0.0163678	−	0.0283499i	0.874093	+	0.485758i	$0.161456\pi$
$984$	−2.70108e6	+	4.67841e6i	−0.0889304	+	0.154032i
$985$	−1.34270e7	−	2.32563e7i	−0.440950	−	0.763748i
$986$	−8.47976e6			−0.277774
$987$		0			0
$988$	−2.58493e7			−0.842474
$989$	1.61724e7	+	2.80115e7i	0.525756	+	0.910636i
$990$	3.59732e6	−	6.23074e6i	0.116652	−	0.202047i
$991$	−5.33372e6	+	9.23828e6i	−0.172523	+	0.298818i	−0.939301	−	0.343094i	$-0.888525\pi$
$991$	−5.33372e6	+	9.23828e6i	−0.172523	+	0.298818i	0.766778	+	0.641912i	$0.221858\pi$
$992$	−2.87241e7	−	4.97515e7i	−0.926759	−	1.60519i
$993$	2.30524e7			0.741898
$994$		0			0
$995$	−1.90405e7			−0.609707
$996$	8.36068e6	+	1.44811e7i	0.267051	+	0.462545i
$997$	−2.79142e7	+	4.83488e7i	−0.889379	+	1.54045i	−0.0487677	+	0.998810i	$0.515529\pi$
$997$	−2.79142e7	+	4.83488e7i	−0.889379	+	1.54045i	−0.840611	+	0.541639i	$0.817804\pi$
$998$	−3.75616e6	+	6.50586e6i	−0.119376	+	0.206766i
$999$	3.63394e6	+	6.29416e6i	0.115203	+	0.199537i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.6.e.p.67.3		12
7.2	even	3	inner	147.6.e.p.79.3		12
7.3	odd	6		147.6.a.n.1.4	✓	6
7.4	even	3		147.6.a.o.1.4	yes	6
7.5	odd	6		147.6.e.q.79.3		12
7.6	odd	2		147.6.e.q.67.3		12
21.11	odd	6		441.6.a.ba.1.3		6
21.17	even	6		441.6.a.bb.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.6.a.n.1.4	✓	6	7.3	odd	6
147.6.a.o.1.4	yes	6	7.4	even	3
147.6.e.p.67.3		12	1.1	even	1	trivial
147.6.e.p.79.3		12	7.2	even	3	inner
147.6.e.q.67.3		12	7.6	odd	2
147.6.e.q.79.3		12	7.5	odd	6
441.6.a.ba.1.3		6	21.11	odd	6
441.6.a.bb.1.3		6	21.17	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:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	147.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.69017 - 2.92745i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(10.2867 - 17.8171i) q^{4} +(27.2626 + 47.2203i) q^{5} +30.4230 q^{6} -177.715 q^{8} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})\)	\(q+(-1.69017 - 2.92745i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(10.2867 - 17.8171i) q^{4} +(27.2626 + 47.2203i) q^{5} +30.4230 q^{6} -177.715 q^{8} +(-40.5000 - 70.1481i) q^{9} +(92.1567 - 159.620i) q^{10} +(-240.956 + 417.347i) q^{11} +(92.5801 + 160.354i) q^{12} +512.622 q^{13} -490.728 q^{15} +(-28.8055 - 49.8926i) q^{16} +(-295.372 + 511.599i) q^{17} +(-136.903 + 237.124i) q^{18} +(-1225.51 - 2122.64i) q^{19} +1121.77 q^{20} +1629.02 q^{22} +(-887.452 - 1537.11i) q^{23} +(799.719 - 1385.15i) q^{24} +(75.9967 - 131.630i) q^{25} +(-866.416 - 1500.68i) q^{26} +729.000 q^{27} -4246.44 q^{29} +(829.411 + 1436.58i) q^{30} +(-4883.69 + 8458.79i) q^{31} +(-2940.82 + 5093.65i) q^{32} +(-2168.60 - 3756.13i) q^{33} +1996.91 q^{34} -1666.44 q^{36} +(4984.83 + 8633.97i) q^{37} +(-4142.62 + 7175.23i) q^{38} +(-2306.80 + 3995.49i) q^{39} +(-4844.99 - 8391.77i) q^{40} -3377.54 q^{41} -18223.4 q^{43} +(4957.27 + 8586.24i) q^{44} +(2208.27 - 3824.84i) q^{45} +(-2999.88 + 5195.95i) q^{46} +(-660.320 - 1143.71i) q^{47} +518.500 q^{48} -513.788 q^{50} +(-2658.35 - 4604.39i) q^{51} +(5273.18 - 9133.42i) q^{52} +(-17418.5 + 30169.7i) q^{53} +(-1232.13 - 2134.11i) q^{54} -26276.3 q^{55} +22059.1 q^{57} +(7177.19 + 12431.3i) q^{58} +(-5796.25 + 10039.4i) q^{59} +(-5047.96 + 8743.32i) q^{60} +(-15703.1 - 27198.5i) q^{61} +33016.9 q^{62} +18038.3 q^{64} +(13975.4 + 24206.2i) q^{65} +(-7330.59 + 12696.9i) q^{66} +(-13778.0 + 23864.1i) q^{67} +(6076.79 + 10525.3i) q^{68} +15974.1 q^{69} -22868.5 q^{71} +(7197.47 + 12466.4i) q^{72} +(-7968.20 + 13801.3i) q^{73} +(16850.4 - 29185.7i) q^{74} +(683.970 + 1184.67i) q^{75} -50425.6 q^{76} +15595.5 q^{78} +(-43582.6 - 75487.3i) q^{79} +(1570.63 - 2720.41i) q^{80} +(-3280.50 + 5681.99i) q^{81} +(5708.60 + 9887.59i) q^{82} +90307.5 q^{83} -32210.5 q^{85} +(30800.6 + 53348.2i) q^{86} +(19109.0 - 33097.7i) q^{87} +(42821.5 - 74169.0i) q^{88} +(63284.8 + 109612. i) q^{89} -14929.4 q^{90} -36515.7 q^{92} +(-43953.2 - 76129.1i) q^{93} +(-2232.10 + 3866.11i) q^{94} +(66821.2 - 115738. i) q^{95} +(-26467.4 - 45842.8i) q^{96} -16573.1 q^{97} +39034.8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} - 54 q^{3} - 150 q^{4} - 100 q^{5} + 36 q^{6} - 228 q^{8} - 486 q^{9}+O(q^{10}) \) 12 * q - 2 * q^2 - 54 * q^3 - 150 * q^4 - 100 * q^5 + 36 * q^6 - 228 * q^8 - 486 * q^9	\( 12 q - 2 q^{2} - 54 q^{3} - 150 q^{4} - 100 q^{5} + 36 q^{6} - 228 q^{8} - 486 q^{9} - 864 q^{10} - 604 q^{11} - 1350 q^{12} + 2704 q^{13} + 1800 q^{15} - 4578 q^{16} - 3028 q^{17} - 162 q^{18} - 1728 q^{19} + 904 q^{20} - 8232 q^{22} + 4484 q^{23} + 1026 q^{24} - 4806 q^{25} - 14172 q^{26} + 8748 q^{27} - 10640 q^{29} - 7776 q^{30} - 3976 q^{31} + 37326 q^{32} - 5436 q^{33} - 32672 q^{34} + 24300 q^{36} - 22680 q^{37} - 52744 q^{38} - 12168 q^{39} - 100600 q^{40} + 57512 q^{41} - 13536 q^{43} + 64940 q^{44} - 8100 q^{45} - 540 q^{46} - 51552 q^{47} + 82404 q^{48} - 81244 q^{50} - 27252 q^{51} - 119296 q^{52} - 80884 q^{53} - 1458 q^{54} + 23312 q^{55} + 31104 q^{57} + 70464 q^{58} - 8872 q^{59} - 4068 q^{60} - 50896 q^{61} + 23648 q^{62} + 399180 q^{64} - 3492 q^{65} + 37044 q^{66} - 6480 q^{67} - 37348 q^{68} - 80712 q^{69} - 221704 q^{71} + 9234 q^{72} - 64232 q^{73} + 27464 q^{74} - 43254 q^{75} - 389728 q^{76} + 255096 q^{78} - 111696 q^{79} + 308940 q^{80} - 39366 q^{81} + 189640 q^{82} + 202256 q^{83} - 46584 q^{85} - 3824 q^{86} + 47880 q^{87} + 97788 q^{88} + 35012 q^{89} + 139968 q^{90} - 898520 q^{92} - 35784 q^{93} + 121016 q^{94} + 119080 q^{95} + 335934 q^{96} + 141904 q^{97} + 97848 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 - 54 * q^3 - 150 * q^4 - 100 * q^5 + 36 * q^6 - 228 * q^8 - 486 * q^9 - 864 * q^10 - 604 * q^11 - 1350 * q^12 + 2704 * q^13 + 1800 * q^15 - 4578 * q^16 - 3028 * q^17 - 162 * q^18 - 1728 * q^19 + 904 * q^20 - 8232 * q^22 + 4484 * q^23 + 1026 * q^24 - 4806 * q^25 - 14172 * q^26 + 8748 * q^27 - 10640 * q^29 - 7776 * q^30 - 3976 * q^31 + 37326 * q^32 - 5436 * q^33 - 32672 * q^34 + 24300 * q^36 - 22680 * q^37 - 52744 * q^38 - 12168 * q^39 - 100600 * q^40 + 57512 * q^41 - 13536 * q^43 + 64940 * q^44 - 8100 * q^45 - 540 * q^46 - 51552 * q^47 + 82404 * q^48 - 81244 * q^50 - 27252 * q^51 - 119296 * q^52 - 80884 * q^53 - 1458 * q^54 + 23312 * q^55 + 31104 * q^57 + 70464 * q^58 - 8872 * q^59 - 4068 * q^60 - 50896 * q^61 + 23648 * q^62 + 399180 * q^64 - 3492 * q^65 + 37044 * q^66 - 6480 * q^67 - 37348 * q^68 - 80712 * q^69 - 221704 * q^71 + 9234 * q^72 - 64232 * q^73 + 27464 * q^74 - 43254 * q^75 - 389728 * q^76 + 255096 * q^78 - 111696 * q^79 + 308940 * q^80 - 39366 * q^81 + 189640 * q^82 + 202256 * q^83 - 46584 * q^85 - 3824 * q^86 + 47880 * q^87 + 97788 * q^88 + 35012 * q^89 + 139968 * q^90 - 898520 * q^92 - 35784 * q^93 + 121016 * q^94 + 119080 * q^95 + 335934 * q^96 + 141904 * q^97 + 97848 * q^99

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